MAGMA 2012



Triadic Quantum Class Groups

over Bicyclic Biquadratic Fields of Eisenstein-Scholz-Reichardt Type

3.0. Real Quadratic Base Objects Q(D1/2)

We start our investigations by using the following table of
all 870 discriminants D in the range 0 < D < 3*104
of real quadratic fields R = Q(D1/2)
having class number h(R) divisible by 3.
It was computed in 1991 at the University of Manitoba, Winnipeg.
Since the smallest discriminant of 3-class rank two is D = 32009,
all 870 fields have a non-trivial cyclic 3-class group Cl3(R).
(Output format is discriminant D, comma separated.)

3.1. Reflection at Eisenstein's Cyclotomic Q((-3)1/2)

3.1.0. Dual Complex Quadratic Base Objects Q((-3*D)1/2)

According to the Scholz-Reichardt reflection theorem, the 3-class group Cl3(C)
of the complex quadratic field C = Q((-3*D)1/2)
with dual discriminant d(C) of d(R) = D has 3-rank 1 or 2.

3.1.1. Bicyclic Biquadratic Composita Q((-3)1/2,D1/2)

Composition of R and C yields a bicyclic biquadratic Eisenstein-Scholz-Reichardt field B = R*C,
which is also constructible by composition B = R*E or B = C*E
with Eisenstein's cyclotomic E = Q((-3)1/2)
having discriminant d(E) = -3 and trivial class group Cl(E) = 1.

According to theories developed by Dirichlet, Hilbert, Herglotz, Kuroda, and Kubota,
the discriminant of B is the product d(B) = d(R)*d(C)*d(E) = gcd(d(R),d(C))2*d(E)2
and the 3-class group of B, Cl3(B) = Cl3(R)*Cl3(C), is a direct product.

It turns out that the 870 bicyclic biquadratic fields B = Q((-3)1/2,D1/2)
constructed by composing the real quadratic fields R = Q(D1/2)
with Eisenstein's cyclotomic E = Q((-3)1/2)
are partitioned into the following three sets,
according to the structure of their 3-class group Cl3(B):
there are 549 fields of type (3,3),
213 fields of type (9,3),
and 108 fields of one of the more complicated types (27,3), (81,3), (9,9), (3,3,3), (9,3,3), etc.
229, 257, 316, 321, 469, 473, 568, 697,
733, 761, 785, 892, 940, 985, 993,1016,
1101,1129,1229,1257,1304,1345,1373,1384,
1436,1489,1509,1708,1765,1772,1901,1929,
1937,1957,2021,2024,2089,2101,2177,2213,
2233,2296,2429,2505,2557,2589,2636,2677,
2713,2777,2857,2917,2920,2941,2981,2993,
3021,3137,3144,3173,3221,3229,3261,3281,
3305,3356,3368,3496,3569,3576,3580,3592,
3596,3624,3736,3873,3877,3889,3941,3957,
3973,3981,4001,4065,4193,4281,4344,4345,
4360,4364,4409,4481,4493,4597,4641,4649,
4684,4729,4749,4764,4765,4841,4844,4853,
4857,4892,4933,5073,5081,5089,5261,5281,
5297,5333,5353,5356,5368,5369,5468,5477,
5497,5521,5529,5613,5621,5624,5629,5637,
5685,5741,5821,5853,5901,5912,5980,6053,
6088,6092,6108,6133,6153,6184,6185,6209,
6268,6289,6396,6401,6508,6549,6556,6557,
6584,6601,6616,6637,6681,6685,6809,6856,
6901,6940,6997,7032,7053,7057,7084,7117,
7148,7224,7244,7249,7273,7388,7404,7441,
7453,7464,7465,7473,7481,7528,7537,7573,
7601,7628,7665,7673,7709,7721,7745,7753,
7816,7873,7881,7948,8017,8057,8069,8113,
8173,8220,8277,8285,8373,8396,8472,8545,
8556,8572,8581,8597,8637,8680,8713,8745,
8761,8769,8789,8828,8837,8905,8909,8920,
9052,9073,9133,9149,9192,9217,9281,9293,
9301,9413,9517,9565,9676,9745,9749,9805,
9813,9833,9836,9869,9897,9905,9937,9980,
10040,10069,10077,10172,10216,10261,10273,10301,
10333,10353,10457,10540,10552,10561,10636,10641,
10661,10664,10712,10721,10733,10812,10844,10865,
10889,10904,10929,10941,10949,10997,11013,11020,
11032,11057,11085,11137,11197,11289,11293,11321,
11324,11401,11505,11545,11576,11608,11641,11656,
11665,11672,11688,11697,11705,11757,11777,11789,
11821,11829,11848,11884,11885,11965,12001,12065,
12081,12092,12140,12188,12197,12216,12248,12269,
12284,12309,12317,12333,12401,12409,12441,12552,
12577,12632,12652,12657,12664,12685,12765,12821,
12849,13069,13089,13117,13148,13153,13245,13269,
13273,13333,13433,13537,13549,13564,13576,13577,
13589,13676,13688,13693,13765,13768,13785,13801,
13861,13877,13897,13928,14056,14089,14129,14141,
14165,14189,14197,14296,14316,14360,14376,14385,
14389,14397,14408,14424,14457,14505,14597,14609,
14653,14668,14680,14824,14876,14956,14969,14977,
14993,15009,15033,15061,15089,15193,15212,15265,
15349,15357,15384,15436,15465,15501,15517,15521,
15529,15592,15593,15629,15641,15657,15661,15689,
15709,15733,15737,15757,15773,15820,15832,15848,
15873,15881,15897,15961,16013,16044,16045,16141,
16201,16321,16357,16369,16376,16385,16392,16409,
16424,16477,16481,16553,16585,16604,16609,16629,
16636,16645,16649,16661,16673,16684,16689,16721,
16737,16773,16777,16860,16908,16913,16952,16997,
17053,17081,17113,17116,17132,17144,17165,17176,
17273,17417,17420,17448,17465,17468,17477,17581,
17609,17717,17736,17737,17884,17889,17893,17905,
17929,17989,18044,18065,18097,18109,18136,18201,
18257,18269,18329,18409,18492,18521,18541,18604,
18633,18661,18680,18697,18701,18796,18824,18853,
18977,18989,19020,19045,19084,19112,19113,19213,
19261,19265,19288,19409,19429,19441,19461,19469,
19544,19605,19628,19633,19640,19653,19708,19736,
19741,19749,19756,19757,19816,19821,19864,19869,
19877,19880,19885,19928,19949,19976,19985,20033,
20044,20073,20077,20093,20137,20141,20153,20168,
20189,20249,20252,20281,20289,20297,20329,20341,
20353,20380,20381,20392,20396,20408,20453,20501,
20521,20524,20545,20549,20613,20621,20649,20693,
20712,20733,20749,20829,20865,20913,20949,21020,
21052,21064,21101,21109,21208,21212,21281,21289,
21293,21308,21324,21337,21361,21385,21433,21469,
21532,21557,21589,21597,21637,21641,21713,21724,
21737,21781,21809,21865,21877,21913,22012,22044,
22053,22061,22168,22229,22312,22341,22377,22380,
22397,22476,22485,22492,22497,22633,22661,22709,
22717,22721,22732,22769,22873,22888,22909,22952,
23005,23033,23105,23109,23192,23196,23249,23297,
23321,23377,23417,23497,23512,23592,23612,23613,
23617,23665,23672,23689,23720,23721,23752,23816,
23909,23917,23953,23957,23964,23993,24001,24005,
24029,24104,24145,24149,24169,24177,24197,24232,
24281,24328,24393,24413,24433,24437,24461,24513,
24533,24577,24617,24621,24645,24648,24665,24697,
24749,24781,24917,24952,24965,24972,25129,25177,
25185,25228,25244,25249,25277,25301,25336,25361,
25377,25409,25464,25465,25469,25513,25537,25645,
25656,25692,25705,25708,25717,25729,25741,25761,
25793,25945,25949,25961,25981,25996,26029,26060,
26093,26113,26121,26232,26236,26284,26376,26421,
26489,26492,26524,26537,26556,26573,26601,26677,
26680,26744,26761,26821,26845,26853,26873,26893,
26933,26997,27004,27013,27049,27064,27065,27080,
27093,27128,27129,27164,27165,27192,27193,27213,
27221,27224,27228,27245,27276,27289,27329,27336,
27340,27349,27409,27437,27445,27548,27557,27617,
27633,27661,27673,27708,27713,27833,27980,28024,
28041,28056,28061,28076,28097,28137,28145,28165,
28220,28232,28309,28349,28361,28381,28389,28428,
28441,28473,28504,28529,28613,28657,28669,28733,
28837,28901,28904,28936,28940,28968,28985,29013,
29036,29048,29113,29116,29165,29221,29240,29244,
29245,29273,29276,29281,29317,29397,29469,29485,
29496,29548,29553,29569,29629,29660,29692,29813,
29836,29884,29901,29905,29933,29989.
The 549 bicyclic biquadratic fields B of type (3,3) are given in the following table.
(Output format is Counter: d(R) Cl(R), d(C) Cl(C), d(B) Cl(B).)
1: dr=229 gr=[3], dc=-687 gc=[12], db=471969 gb=[6, 3]
2: dr=257 gr=[3], dc=-771 gc=[6], db=594441 gb=[3, 3]
3: dr=316 gr=[3], dc=-948 gc=[6, 2], db=898704 gb=[6, 3]
4: dr=321 gr=[3], dc=-107 gc=[3], db=103041 gb=[3, 3]
5: dr=469 gr=[3], dc=-1407 gc=[12, 2], db=1979649 gb=[6, 6]
6: dr=473 gr=[3], dc=-1419 gc=[6, 2], db=2013561 gb=[6, 3]
7: dr=568 gr=[3], dc=-1704 gc=[12, 2], db=2903616 gb=[12, 3]
8: dr=697 gr=[6], dc=-2091 gc=[6, 2], db=4372281 gb=[12, 3]
9: dr=761 gr=[3], dc=-2283 gc=[6], db=5212089 gb=[3, 3]
10: dr=785 gr=[6], dc=-2355 gc=[6, 2], db=5546025 gb=[6, 6]
11: dr=892 gr=[3], dc=-2676 gc=[6, 2], db=7160976 gb=[6, 3]
12: dr=940 gr=[6], dc=-2820 gc=[6, 2, 2], db=7952400 gb=[12, 6]
13: dr=985 gr=[6], dc=-2955 gc=[6, 2], db=8732025 gb=[12, 3]
14: dr=993 gr=[3], dc=-331 gc=[3], db=986049 gb=[3, 3]
15: dr=1016 gr=[3], dc=-3048 gc=[6, 2], db=9290304 gb=[6, 3]
16: dr=1229 gr=[3], dc=-3687 gc=[42], db=13593969 gb=[21, 3]
17: dr=1304 gr=[3], dc=-3912 gc=[12, 2], db=15303744 gb=[12, 3]
18: dr=1345 gr=[6], dc=-4035 gc=[6, 2], db=16281225 gb=[12, 3]
19: dr=1384 gr=[6], dc=-4152 gc=[6, 2], db=17239104 gb=[12, 3]
20: dr=1436 gr=[3], dc=-4308 gc=[12, 2], db=18558864 gb=[12, 3]
21: dr=1489 gr=[3], dc=-4467 gc=[12], db=19954089 gb=[6, 3]
22: dr=1509 gr=[3], dc=-503 gc=[21], db=2277081 gb=[21, 3]
23: dr=1708 gr=[6], dc=-5124 gc=[6, 2, 2], db=26255376 gb=[6, 6, 2]
24: dr=1765 gr=[6], dc=-5295 gc=[30, 2], db=28037025 gb=[60, 3]
25: dr=1929 gr=[3], dc=-643 gc=[3], db=3721041 gb=[3, 3]
26: dr=1937 gr=[6], dc=-5811 gc=[6, 2], db=33767721 gb=[6, 6]
27: dr=2024 gr=[6], dc=-6072 gc=[6, 2, 2], db=36869184 gb=[12, 6]
28: dr=2089 gr=[3], dc=-6267 gc=[12], db=39275289 gb=[6, 3]
29: dr=2101 gr=[3], dc=-6303 gc=[24, 2], db=39727809 gb=[24, 3]
30: dr=2177 gr=[3], dc=-6531 gc=[12, 2], db=42653961 gb=[12, 3]
31: dr=2233 gr=[6], dc=-6699 gc=[6, 2, 2], db=44876601 gb=[12, 6]
32: dr=2296 gr=[6], dc=-6888 gc=[6, 2, 2], db=47444544 gb=[12, 6]
33: dr=2505 gr=[6], dc=-835 gc=[6], db=6275025 gb=[6, 3]
34: dr=2557 gr=[3], dc=-7671 gc=[84], db=58844241 gb=[42, 3]
35: dr=2589 gr=[3], dc=-863 gc=[21], db=6702921 gb=[21, 3]
36: dr=2677 gr=[3], dc=-8031 gc=[60], db=64496961 gb=[30, 3]
37: dr=2920 gr=[6, 2], dc=-8760 gc=[6, 2, 2], db=76737600 gb=[12, 6, 2]
38: dr=2941 gr=[6], dc=-8823 gc=[30, 2], db=77845329 gb=[60, 3]
39: dr=2981 gr=[3], dc=-8943 gc=[30, 2], db=79977249 gb=[30, 3]
40: dr=2993 gr=[6], dc=-8979 gc=[12, 2], db=80622441 gb=[12, 6]
41: dr=3021 gr=[6], dc=-1007 gc=[30], db=9126441 gb=[30, 3]
42: dr=3144 gr=[6], dc=-1048 gc=[6], db=9884736 gb=[6, 3]
43: dr=3173 gr=[3], dc=-9519 gc=[48, 2], db=90611361 gb=[48, 3]
44: dr=3229 gr=[3], dc=-9687 gc=[60], db=93837969 gb=[30, 3]
45: dr=3281 gr=[6], dc=-9843 gc=[6, 2], db=96884649 gb=[6, 6]
46: dr=3305 gr=[6], dc=-9915 gc=[12, 2], db=98307225 gb=[12, 6]
47: dr=3356 gr=[3], dc=-10068 gc=[12, 2], db=101364624 gb=[12, 3]
48: dr=3368 gr=[6], dc=-10104 gc=[30, 2], db=102090816 gb=[30, 6]
49: dr=3496 gr=[6], dc=-10488 gc=[6, 2, 2], db=109998144 gb=[12, 6]
50: dr=3569 gr=[3], dc=-10707 gc=[6, 2], db=114639849 gb=[6, 3]
51: dr=3576 gr=[6], dc=-1192 gc=[6], db=12787776 gb=[6, 3]
52: dr=3580 gr=[6], dc=-10740 gc=[6, 2, 2], db=115347600 gb=[12, 6]
53: dr=3592 gr=[6], dc=-10776 gc=[30, 2], db=116122176 gb=[60, 3]
54: dr=3596 gr=[6], dc=-10788 gc=[6, 2, 2], db=116380944 gb=[12, 6]
55: dr=3624 gr=[6], dc=-1208 gc=[12], db=13133376 gb=[12, 3]
56: dr=3736 gr=[3], dc=-11208 gc=[12, 2], db=125619264 gb=[12, 3]
57: dr=3889 gr=[3], dc=-11667 gc=[24], db=136118889 gb=[12, 3]
58: dr=3941 gr=[3], dc=-11823 gc=[24, 2], db=139783329 gb=[24, 3]
59: dr=3981 gr=[3], dc=-1327 gc=[15], db=15848361 gb=[15, 3]
60: dr=4001 gr=[3], dc=-12003 gc=[30], db=144072009 gb=[15, 3]
61: dr=4065 gr=[6], dc=-1355 gc=[12], db=16524225 gb=[12, 3]
62: dr=4281 gr=[3], dc=-1427 gc=[15], db=18326961 gb=[15, 3]
63: dr=4345 gr=[12], dc=-13035 gc=[6, 2, 2], db=169911225 gb=[24, 6]
64: dr=4360 gr=[6, 2], dc=-13080 gc=[6, 2, 2], db=171086400 gb=[12, 6, 2]
65: dr=4481 gr=[3], dc=-13443 gc=[30], db=180714249 gb=[15, 3]
66: dr=4493 gr=[3], dc=-13479 gc=[78], db=181683441 gb=[39, 3]
67: dr=4597 gr=[3], dc=-13791 gc=[96], db=190191681 gb=[48, 3]
68: dr=4641 gr=[6, 2], dc=-1547 gc=[6, 2], db=21538881 gb=[6, 6, 2]
69: dr=4749 gr=[3], dc=-1583 gc=[33], db=22553001 gb=[33, 3]
70: dr=4764 gr=[6], dc=-1588 gc=[6], db=22695696 gb=[6, 6]
71: dr=4765 gr=[6], dc=-14295 gc=[30, 2], db=204347025 gb=[60, 3]
72: dr=4841 gr=[3], dc=-14523 gc=[12, 2], db=210917529 gb=[12, 3]
73: dr=4844 gr=[6], dc=-14532 gc=[6, 2, 2], db=211179024 gb=[12, 6]
74: dr=4853 gr=[3], dc=-14559 gc=[60, 2], db=211964481 gb=[60, 3]
75: dr=4857 gr=[3], dc=-1619 gc=[15], db=23590449 gb=[15, 3]
76: dr=4892 gr=[3], dc=-14676 gc=[24, 2], db=215384976 gb=[24, 3]
77: dr=4933 gr=[3], dc=-14799 gc=[84], db=219010401 gb=[42, 3]
78: dr=5089 gr=[3], dc=-15267 gc=[12, 2], db=233081289 gb=[6, 6]
79: dr=5281 gr=[3], dc=-15843 gc=[24], db=251000649 gb=[12, 3]
80: dr=5297 gr=[3], dc=-15891 gc=[30], db=252523881 gb=[15, 3]
81: dr=5333 gr=[3], dc=-15999 gc=[102], db=255968001 gb=[51, 3]
82: dr=5356 gr=[6], dc=-16068 gc=[12, 2, 2], db=258180624 gb=[12, 6, 2]
83: dr=5368 gr=[6], dc=-16104 gc=[12, 2, 2], db=259338816 gb=[12, 6, 2]
84: dr=5369 gr=[6], dc=-16107 gc=[6, 2, 2], db=259435449 gb=[6, 6, 2]
85: dr=5468 gr=[3], dc=-16404 gc=[24, 2], db=269091216 gb=[24, 3]
86: dr=5477 gr=[3], dc=-16431 gc=[114], db=269977761 gb=[57, 3]
87: dr=5497 gr=[3], dc=-16491 gc=[24, 2], db=271953081 gb=[24, 3]
88: dr=5529 gr=[6], dc=-1843 gc=[6], db=30569841 gb=[6, 6]
89: dr=5624 gr=[6], dc=-16872 gc=[6, 2, 2], db=284664384 gb=[6, 6, 2]
90: dr=5629 gr=[12], dc=-16887 gc=[24, 4], db=285170769 gb=[48, 6, 2]
91: dr=5685 gr=[6], dc=-1895 gc=[48], db=32319225 gb=[48, 3]
92: dr=5741 gr=[3], dc=-17223 gc=[78], db=296631729 gb=[39, 3]
93: dr=5853 gr=[3], dc=-1951 gc=[33], db=34257609 gb=[33, 3]
94: dr=5912 gr=[3], dc=-17736 gc=[24, 2], db=314565696 gb=[24, 3]
95: dr=5980 gr=[6, 2], dc=-17940 gc=[6, 2, 2, 2], db=321843600 gb=[12, 6, 2, 2]
96: dr=6053 gr=[3], dc=-18159 gc=[78], db=329749281 gb=[39, 3]
97: dr=6092 gr=[3], dc=-18276 gc=[30, 2], db=334012176 gb=[30, 3]
98: dr=6108 gr=[6], dc=-2036 gc=[30], db=37307664 gb=[30, 3]
99: dr=6209 gr=[3], dc=-18627 gc=[12, 2], db=346965129 gb=[12, 3]
100: dr=6289 gr=[3], dc=-18867 gc=[12, 2], db=355963689 gb=[6, 6]
101: dr=6396 gr=[6, 2], dc=-2132 gc=[6, 2], db=40908816 gb=[6, 6, 2]
102: dr=6401 gr=[12], dc=-19203 gc=[12, 2], db=368755209 gb=[12, 12]
103: dr=6508 gr=[3], dc=-19524 gc=[30, 2], db=381186576 gb=[30, 3]
104: dr=6549 gr=[6], dc=-2183 gc=[42], db=42889401 gb=[42, 6]
105: dr=6556 gr=[6], dc=-19668 gc=[12, 2, 2], db=386830224 gb=[12, 12]
106: dr=6557 gr=[3], dc=-19671 gc=[42, 2], db=386948241 gb=[42, 3]
107: dr=6601 gr=[6], dc=-19803 gc=[6, 2, 2], db=392158809 gb=[12, 6]
108: dr=6637 gr=[3], dc=-19911 gc=[120], db=396447921 gb=[60, 3]
109: dr=6681 gr=[6], dc=-2227 gc=[6], db=44635761 gb=[6, 3]
110: dr=6685 gr=[6], dc=-20055 gc=[30, 2, 2], db=402203025 gb=[60, 6]
111: dr=6901 gr=[3], dc=-20703 gc=[24, 2], db=428614209 gb=[12, 6]
112: dr=6940 gr=[6], dc=-20820 gc=[12, 2, 2], db=433472400 gb=[12, 12]
113: dr=6997 gr=[3], dc=-20991 gc=[156], db=440622081 gb=[78, 3]
114: dr=7057 gr=[21], dc=-21171 gc=[48], db=448211241 gb=[168, 3]
115: dr=7084 gr=[6, 2], dc=-21252 gc=[6, 2, 2, 2], db=451647504 gb=[12, 12, 2]
116: dr=7117 gr=[3], dc=-21351 gc=[60, 2], db=455865201 gb=[60, 3]
117: dr=7148 gr=[3], dc=-21444 gc=[30, 2], db=459845136 gb=[30, 3]
118: dr=7224 gr=[6, 2], dc=-2408 gc=[12, 2], db=52186176 gb=[12, 6, 2]
119: dr=7249 gr=[3], dc=-21747 gc=[12, 2], db=472932009 gb=[12, 3]
120: dr=7273 gr=[3], dc=-21819 gc=[24, 2], db=476068761 gb=[12, 6]
121: dr=7404 gr=[6], dc=-2468 gc=[12], db=54819216 gb=[12, 3]
122: dr=7441 gr=[3], dc=-22323 gc=[12, 2], db=498316329 gb=[6, 6]
123: dr=7453 gr=[6], dc=-22359 gc=[66, 2], db=499924881 gb=[132, 3]
124: dr=7464 gr=[6], dc=-2488 gc=[12], db=55711296 gb=[12, 3]
125: dr=7473 gr=[6], dc=-2491 gc=[12], db=55845729 gb=[12, 3]
126: dr=7528 gr=[6], dc=-22584 gc=[30, 2], db=510037056 gb=[60, 3]
127: dr=7537 gr=[3], dc=-22611 gc=[48], db=511257321 gb=[24, 3]
128: dr=7601 gr=[3], dc=-22803 gc=[12, 2], db=519976809 gb=[12, 3]
129: dr=7628 gr=[3], dc=-22884 gc=[30, 2], db=523677456 gb=[30, 3]
130: dr=7665 gr=[6, 2], dc=-2555 gc=[6, 2], db=58752225 gb=[6, 6, 2]
131: dr=7673 gr=[3], dc=-23019 gc=[66], db=529874361 gb=[33, 3]
132: dr=7709 gr=[6], dc=-23127 gc=[30, 2], db=534858129 gb=[30, 6]
133: dr=7745 gr=[12], dc=-23235 gc=[12, 2], db=539865225 gb=[12, 12]
134: dr=7816 gr=[6], dc=-23448 gc=[30, 2], db=549808704 gb=[60, 3]
135: dr=7881 gr=[12], dc=-2627 gc=[12], db=62110161 gb=[12, 6]
136: dr=7948 gr=[3], dc=-23844 gc=[30, 2], db=568536336 gb=[30, 3]
137: dr=8017 gr=[3], dc=-24051 gc=[48], db=578450601 gb=[24, 3]
138: dr=8057 gr=[3], dc=-24171 gc=[24, 2], db=584237241 gb=[24, 3]
139: dr=8113 gr=[6], dc=-24339 gc=[12, 2, 2], db=592386921 gb=[6, 6, 2, 2]
140: dr=8220 gr=[6, 2], dc=-2740 gc=[6, 2], db=67568400 gb=[12, 6]
141: dr=8285 gr=[6], dc=-24855 gc=[78, 2], db=617771025 gb=[78, 6]
142: dr=8373 gr=[3], dc=-2791 gc=[39], db=70107129 gb=[39, 3]
143: dr=8472 gr=[6], dc=-2824 gc=[24], db=71774784 gb=[24, 3]
144: dr=8556 gr=[6, 2], dc=-2852 gc=[12, 2], db=73205136 gb=[24, 6]
145: dr=8572 gr=[3], dc=-25716 gc=[30, 2], db=661312656 gb=[30, 3]
146: dr=8597 gr=[3], dc=-25791 gc=[186], db=665175681 gb=[93, 3]
147: dr=8637 gr=[3], dc=-2879 gc=[57], db=74597769 gb=[57, 3]
148: dr=8680 gr=[6, 2], dc=-26040 gc=[6, 2, 2, 2], db=678081600 gb=[12, 6, 2, 2]
149: dr=8745 gr=[6, 2], dc=-2915 gc=[12, 2], db=76475025 gb=[12, 12]
150: dr=8769 gr=[6], dc=-2923 gc=[6], db=76895361 gb=[6, 6]
151: dr=8789 gr=[6], dc=-26367 gc=[30, 2, 2], db=695218689 gb=[60, 6]
152: dr=8828 gr=[3], dc=-26484 gc=[48, 2], db=701402256 gb=[48, 3]
153: dr=8905 gr=[6, 2], dc=-26715 gc=[12, 2, 2], db=713691225 gb=[24, 6, 2]
154: dr=8909 gr=[3], dc=-26727 gc=[42, 2], db=714332529 gb=[42, 3]
155: dr=9073 gr=[3], dc=-27219 gc=[24, 2], db=740873961 gb=[12, 6]
156: dr=9133 gr=[3], dc=-27399 gc=[84], db=750705201 gb=[42, 3]
157: dr=9149 gr=[3], dc=-27447 gc=[60, 2], db=753337809 gb=[60, 3]
158: dr=9192 gr=[6], dc=-3064 gc=[24], db=84492864 gb=[24, 3]
159: dr=9281 gr=[3], dc=-27843 gc=[30], db=775232649 gb=[15, 3]
160: dr=9413 gr=[3], dc=-28239 gc=[150], db=797441121 gb=[75, 3]
161: dr=9517 gr=[3], dc=-28551 gc=[96, 2], db=815159601 gb=[48, 6]
162: dr=9749 gr=[3], dc=-29247 gc=[66], db=855387009 gb=[33, 3]
163: dr=9805 gr=[6, 2], dc=-29415 gc=[30, 2, 2], db=865242225 gb=[60, 6, 2]
164: dr=9833 gr=[3], dc=-29499 gc=[42], db=870191001 gb=[21, 3]
165: dr=9836 gr=[3], dc=-29508 gc=[30, 2], db=870722064 gb=[30, 3]
166: dr=9869 gr=[3], dc=-29607 gc=[30, 2], db=876574449 gb=[30, 3]
167: dr=9905 gr=[6], dc=-29715 gc=[12, 2, 2], db=882981225 gb=[12, 6, 2]
168: dr=9937 gr=[3], dc=-29811 gc=[24, 2], db=888695721 gb=[12, 6]
169: dr=9980 gr=[6], dc=-29940 gc=[12, 2, 2], db=896403600 gb=[24, 6]
170: dr=10069 gr=[3], dc=-30207 gc=[60], db=912462849 gb=[30, 3]
171: dr=10077 gr=[3], dc=-3359 gc=[69], db=101545929 gb=[69, 3]
172: dr=10172 gr=[3], dc=-30516 gc=[48, 2], db=931226256 gb=[48, 3]
173: dr=10261 gr=[3], dc=-30783 gc=[48, 2], db=947593089 gb=[24, 6]
174: dr=10301 gr=[3], dc=-30903 gc=[78], db=954995409 gb=[39, 3]
175: dr=10333 gr=[3], dc=-30999 gc=[156], db=960938001 gb=[78, 3]
176: dr=10353 gr=[6, 2], dc=-3451 gc=[6, 2], db=107184609 gb=[12, 6]
177: dr=10457 gr=[3], dc=-31371 gc=[42], db=984139641 gb=[21, 3]
178: dr=10540 gr=[6, 2], dc=-31620 gc=[6, 2, 2, 2], db=999824400 gb=[12, 12, 2]
179: dr=10561 gr=[3], dc=-31683 gc=[12, 2], db=1003812489 gb=[12, 3]
180: dr=10664 gr=[6], dc=-31992 gc=[12, 2, 2], db=1023488064 gb=[12, 6, 2]
181: dr=10812 gr=[6, 2], dc=-3604 gc=[12, 2], db=116899344 gb=[24, 6]
182: dr=10844 gr=[3], dc=-32532 gc=[24, 2], db=1058331024 gb=[24, 3]
183: dr=10865 gr=[6, 2], dc=-32595 gc=[12, 2, 2], db=1062434025 gb=[24, 12]
184: dr=10889 gr=[3], dc=-32667 gc=[42], db=1067132889 gb=[21, 3]
185: dr=10904 gr=[6], dc=-32712 gc=[12, 2, 2], db=1070074944 gb=[24, 6]
186: dr=10949 gr=[3], dc=-32847 gc=[102], db=1078925409 gb=[51, 3]
187: dr=11020 gr=[6, 2], dc=-33060 gc=[6, 2, 2, 2], db=1092963600 gb=[12, 12, 2]
188: dr=11057 gr=[3], dc=-33171 gc=[66], db=1100315241 gb=[33, 3]
189: dr=11137 gr=[6], dc=-33411 gc=[12, 2, 2], db=1116294921 gb=[6, 6, 2, 2]
190: dr=11321 gr=[15], dc=-33963 gc=[42], db=1153485369 gb=[105, 3]
191: dr=11324 gr=[6], dc=-33972 gc=[12, 2, 2], db=1154096784 gb=[24, 6]
192: dr=11401 gr=[6], dc=-34203 gc=[12, 2], db=1169845209 gb=[6, 6, 2]
193: dr=11505 gr=[6, 2], dc=-3835 gc=[6, 2], db=132365025 gb=[6, 6, 2]
194: dr=11545 gr=[6], dc=-34635 gc=[30, 2], db=1199583225 gb=[60, 3]
195: dr=11608 gr=[3], dc=-34824 gc=[48, 2], db=1212710976 gb=[48, 3]
196: dr=11697 gr=[6], dc=-3899 gc=[24], db=136819809 gb=[24, 3]
197: dr=11705 gr=[6], dc=-35115 gc=[24, 2], db=1233063225 gb=[24, 6]
198: dr=11757 gr=[3], dc=-3919 gc=[39], db=138227049 gb=[39, 3]
199: dr=11821 gr=[3], dc=-35463 gc=[120], db=1257624369 gb=[60, 3]
200: dr=11848 gr=[6], dc=-35544 gc=[30, 2], db=1263375936 gb=[60, 3]
201: dr=11885 gr=[6], dc=-35655 gc=[42, 2], db=1271279025 gb=[42, 6]
202: dr=11965 gr=[6], dc=-35895 gc=[78, 2], db=1288451025 gb=[156, 3]
203: dr=12001 gr=[3], dc=-36003 gc=[12, 2], db=1296216009 gb=[12, 3]
204: dr=12065 gr=[6], dc=-36195 gc=[12, 2, 2], db=1310078025 gb=[12, 6, 2]
205: dr=12188 gr=[6], dc=-36564 gc=[24, 2, 2], db=1336926096 gb=[24, 6, 2]
206: dr=12248 gr=[3], dc=-36744 gc=[24, 2], db=1350121536 gb=[24, 3]
207: dr=12284 gr=[6], dc=-36852 gc=[12, 2, 2], db=1358069904 gb=[12, 6, 2]
208: dr=12309 gr=[6], dc=-4103 gc=[42], db=151511481 gb=[42, 6]
209: dr=12317 gr=[6], dc=-36951 gc=[96, 2], db=1365376401 gb=[96, 6]
210: dr=12333 gr=[3], dc=-4111 gc=[39], db=152102889 gb=[39, 3]
211: dr=12401 gr=[3], dc=-37203 gc=[42], db=1384063209 gb=[21, 3]
212: dr=12441 gr=[6, 2], dc=-4147 gc=[6, 2], db=154778481 gb=[6, 6, 2]
213: dr=12552 gr=[6], dc=-4184 gc=[42], db=157552704 gb=[42, 3]
214: dr=12632 gr=[3], dc=-37896 gc=[48, 2], db=1436106816 gb=[48, 3]
215: dr=12652 gr=[3], dc=-37956 gc=[42, 2], db=1440657936 gb=[42, 3]
216: dr=12664 gr=[3], dc=-37992 gc=[24, 2], db=1443392064 gb=[24, 3]
217: dr=12685 gr=[6], dc=-38055 gc=[42, 2, 2], db=1448183025 gb=[84, 6]
218: dr=12849 gr=[3], dc=-4283 gc=[21], db=165096801 gb=[21, 3]
219: dr=13148 gr=[6], dc=-39444 gc=[24, 2, 2], db=1555829136 gb=[48, 6]
220: dr=13245 gr=[6], dc=-4415 gc=[66], db=175430025 gb=[66, 3]
221: dr=13269 gr=[3], dc=-4423 gc=[33], db=176066361 gb=[33, 3]
222: dr=13333 gr=[3], dc=-39999 gc=[48, 2], db=1599920001 gb=[24, 6]
223: dr=13537 gr=[3], dc=-40611 gc=[60], db=1649253321 gb=[30, 3]
224: dr=13549 gr=[12], dc=-40647 gc=[78, 2], db=1652178609 gb=[312, 3]
225: dr=13576 gr=[6], dc=-40728 gc=[30, 2], db=1658769984 gb=[60, 3]
226: dr=13589 gr=[3], dc=-40767 gc=[78, 2], db=1661948289 gb=[78, 3]
227: dr=13676 gr=[6], dc=-41028 gc=[12, 2, 2], db=1683296784 gb=[12, 6, 2]
228: dr=13693 gr=[15], dc=-41079 gc=[156], db=1687484241 gb=[390, 3]
229: dr=13765 gr=[6], dc=-41295 gc=[66, 2], db=1705277025 gb=[132, 3]
230: dr=13768 gr=[6], dc=-41304 gc=[42, 2], db=1706020416 gb=[84, 3]
231: dr=13785 gr=[6], dc=-4595 gc=[24], db=190026225 gb=[24, 3]
232: dr=13801 gr=[12], dc=-41403 gc=[12, 4], db=1714208409 gb=[24, 6, 2]
233: dr=13897 gr=[6], dc=-41691 gc=[12, 4], db=1738139481 gb=[12, 6, 2]
234: dr=13928 gr=[6], dc=-41784 gc=[42, 2], db=1745902656 gb=[42, 6]
235: dr=14056 gr=[6], dc=-42168 gc=[12, 2, 2], db=1778140224 gb=[12, 12]
236: dr=14089 gr=[6], dc=-42267 gc=[12, 2], db=1786499289 gb=[6, 6, 2]
237: dr=14129 gr=[3], dc=-42387 gc=[12, 2], db=1796657769 gb=[12, 3]
238: dr=14165 gr=[6], dc=-42495 gc=[66, 2], db=1805825025 gb=[66, 6]
239: dr=14360 gr=[6], dc=-43080 gc=[12, 2, 2], db=1855886400 gb=[24, 6]
240: dr=14376 gr=[6], dc=-4792 gc=[12], db=206669376 gb=[12, 3]
241: dr=14385 gr=[6, 2], dc=-4795 gc=[6, 2], db=206928225 gb=[12, 6]
242: dr=14389 gr=[3], dc=-43167 gc=[132], db=1863389889 gb=[66, 3]
243: dr=14408 gr=[6], dc=-43224 gc=[48, 2], db=1868314176 gb=[48, 6]
244: dr=14424 gr=[12], dc=-4808 gc=[24], db=208051776 gb=[24, 6]
245: dr=14505 gr=[6], dc=-4835 gc=[30], db=210395025 gb=[30, 3]
246: dr=14597 gr=[3], dc=-43791 gc=[102, 2], db=1917651681 gb=[102, 3]
247: dr=14653 gr=[3], dc=-43959 gc=[156], db=1932393681 gb=[78, 3]
248: dr=14824 gr=[6, 2], dc=-44472 gc=[12, 2, 2], db=1977758784 gb=[24, 6, 2]
249: dr=14956 gr=[3], dc=-44868 gc=[30, 2], db=2013137424 gb=[30, 3]
250: dr=14969 gr=[3], dc=-44907 gc=[30], db=2016638649 gb=[15, 3]
251: dr=14977 gr=[6], dc=-44931 gc=[42, 2], db=2018794761 gb=[84, 3]
252: dr=14993 gr=[6], dc=-44979 gc=[12, 2, 2], db=2023110441 gb=[24, 6]
253: dr=15009 gr=[3], dc=-5003 gc=[15], db=225270081 gb=[15, 3]
254: dr=15033 gr=[3], dc=-5011 gc=[21], db=225991089 gb=[21, 3]
255: dr=15061 gr=[3], dc=-45183 gc=[120], db=2041503489 gb=[60, 3]
256: dr=15089 gr=[3], dc=-45267 gc=[24, 2], db=2049101289 gb=[24, 3]
257: dr=15193 gr=[3], dc=-45579 gc=[60], db=2077445241 gb=[30, 3]
258: dr=15212 gr=[3], dc=-45636 gc=[42, 2], db=2082644496 gb=[42, 3]
259: dr=15265 gr=[6], dc=-45795 gc=[12, 2, 2], db=2097182025 gb=[24, 6]
260: dr=15357 gr=[3], dc=-5119 gc=[39], db=235837449 gb=[39, 3]
261: dr=15384 gr=[6], dc=-5128 gc=[12], db=236667456 gb=[12, 3]
262: dr=15436 gr=[6], dc=-46308 gc=[12, 2, 2], db=2144430864 gb=[24, 6]
263: dr=15465 gr=[6], dc=-5155 gc=[12], db=239166225 gb=[12, 3]
264: dr=15501 gr=[3], dc=-5167 gc=[33], db=240281001 gb=[33, 3]
265: dr=15592 gr=[6], dc=-46776 gc=[30, 2], db=2187994176 gb=[60, 3]
266: dr=15593 gr=[3], dc=-46779 gc=[30, 2], db=2188274841 gb=[30, 3]
267: dr=15641 gr=[3], dc=-46923 gc=[30], db=2201767929 gb=[15, 3]
268: dr=15657 gr=[6], dc=-5219 gc=[24], db=245141649 gb=[24, 3]
269: dr=15661 gr=[3], dc=-46983 gc=[168], db=2207402289 gb=[84, 3]
270: dr=15709 gr=[3], dc=-47127 gc=[48, 2], db=2220954129 gb=[48, 3]
271: dr=15757 gr=[3], dc=-47271 gc=[84, 2], db=2234547441 gb=[42, 6]
272: dr=15773 gr=[3], dc=-47319 gc=[246], db=2239087761 gb=[123, 3]
273: dr=15820 gr=[6, 2], dc=-47460 gc=[12, 2, 2, 2], db=2252451600 gb=[24, 12, 2]
274: dr=15848 gr=[6], dc=-47544 gc=[24, 2, 2], db=2260431936 gb=[24, 6, 2]
275: dr=15881 gr=[3], dc=-47643 gc=[42], db=2269855449 gb=[21, 3]
276: dr=15897 gr=[12], dc=-5299 gc=[12], db=252714609 gb=[12, 6]
277: dr=15961 gr=[3], dc=-47883 gc=[24, 2], db=2292781689 gb=[24, 3]
278: dr=16044 gr=[6, 2], dc=-5348 gc=[12, 2], db=257409936 gb=[24, 6]
279: dr=16045 gr=[6], dc=-48135 gc=[114, 2], db=2316978225 gb=[228, 3]
280: dr=16357 gr=[3], dc=-49071 gc=[96, 2], db=2407963041 gb=[96, 3]
281: dr=16369 gr=[3], dc=-49107 gc=[24], db=2411497449 gb=[12, 3]
282: dr=16385 gr=[6, 2], dc=-49155 gc=[12, 2, 2], db=2416214025 gb=[24, 12]
283: dr=16409 gr=[12], dc=-49227 gc=[24, 2], db=2423297529 gb=[24, 12]
284: dr=16424 gr=[6], dc=-49272 gc=[30, 2], db=2427729984 gb=[30, 6]
285: dr=16481 gr=[3], dc=-49443 gc=[30], db=2444610249 gb=[15, 3]
286: dr=16629 gr=[6], dc=-5543 gc=[78], db=276523641 gb=[78, 6]
287: dr=16636 gr=[3], dc=-49908 gc=[42, 2], db=2490808464 gb=[42, 3]
288: dr=16661 gr=[3], dc=-49983 gc=[150], db=2498300289 gb=[75, 3]
289: dr=16684 gr=[12], dc=-50052 gc=[12, 2, 2], db=2505202704 gb=[24, 6, 2]
290: dr=16689 gr=[3], dc=-5563 gc=[15], db=278522721 gb=[15, 3]
291: dr=16737 gr=[6], dc=-5579 gc=[30], db=280127169 gb=[30, 3]
292: dr=16777 gr=[3], dc=-50331 gc=[24, 2], db=2533209561 gb=[12, 6]
293: dr=16860 gr=[6, 2], dc=-5620 gc=[12, 2], db=284259600 gb=[24, 6]
294: dr=16997 gr=[3], dc=-50991 gc=[120, 2], db=2600082081 gb=[120, 3]
295: dr=17053 gr=[3], dc=-51159 gc=[204], db=2617243281 gb=[102, 3]
296: dr=17081 gr=[6], dc=-51243 gc=[12, 2, 2], db=2625845049 gb=[12, 6, 2]
297: dr=17113 gr=[12], dc=-51339 gc=[12, 4], db=2635692921 gb=[24, 6, 2]
298: dr=17132 gr=[3], dc=-51396 gc=[30, 2], db=2641548816 gb=[30, 3]
299: dr=17144 gr=[3], dc=-51432 gc=[42, 2], db=2645250624 gb=[42, 3]
300: dr=17165 gr=[6], dc=-51495 gc=[78, 2], db=2651735025 gb=[78, 6]
301: dr=17176 gr=[6], dc=-51528 gc=[12, 2, 2], db=2655134784 gb=[24, 6]
302: dr=17420 gr=[6, 2], dc=-52260 gc=[12, 2, 2, 2], db=2731107600 gb=[24, 6, 2, 2]
303: dr=17448 gr=[6], dc=-5816 gc=[60], db=304432704 gb=[60, 3]
304: dr=17465 gr=[6], dc=-52395 gc=[12, 2, 2], db=2745236025 gb=[12, 6, 2]
305: dr=17468 gr=[6], dc=-52404 gc=[24, 2, 2], db=2746179216 gb=[24, 6, 2]
306: dr=17477 gr=[3], dc=-52431 gc=[138], db=2749009761 gb=[69, 3]
307: dr=17581 gr=[3], dc=-52743 gc=[120], db=2781824049 gb=[60, 3]
308: dr=17609 gr=[3], dc=-52827 gc=[42], db=2790691929 gb=[21, 3]
309: dr=17717 gr=[3], dc=-53151 gc=[114, 2], db=2825028801 gb=[114, 3]
310: dr=17736 gr=[6], dc=-5912 gc=[30], db=314565696 gb=[30, 3]
311: dr=17737 gr=[15], dc=-53211 gc=[48], db=2831410521 gb=[120, 3]
312: dr=17884 gr=[12], dc=-53652 gc=[12, 2, 2], db=2878537104 gb=[24, 12]
313: dr=17889 gr=[30], dc=-5963 gc=[24], db=320016321 gb=[120, 3]
314: dr=17893 gr=[6], dc=-53679 gc=[102, 2], db=2881435041 gb=[204, 3]
315: dr=17905 gr=[12], dc=-53715 gc=[30, 2], db=2885301225 gb=[120, 3]
316: dr=17929 gr=[3], dc=-53787 gc=[48], db=2893041369 gb=[24, 3]
317: dr=18044 gr=[6], dc=-54132 gc=[12, 2, 2], db=2930273424 gb=[12, 6, 2]
318: dr=18097 gr=[3], dc=-54291 gc=[84], db=2947512681 gb=[42, 3]
319: dr=18109 gr=[6], dc=-54327 gc=[24, 2, 2], db=2951422929 gb=[12, 6, 2, 2]
320: dr=18201 gr=[3], dc=-6067 gc=[15], db=331276401 gb=[15, 3]
321: dr=18257 gr=[3], dc=-54771 gc=[66], db=2999862441 gb=[33, 3]
322: dr=18329 gr=[15], dc=-54987 gc=[42], db=3023570169 gb=[105, 3]
323: dr=18521 gr=[3], dc=-55563 gc=[42], db=3087246969 gb=[21, 3]
324: dr=18604 gr=[3], dc=-55812 gc=[30, 2], db=3114979344 gb=[30, 3]
325: dr=18661 gr=[3], dc=-55983 gc=[84], db=3134096289 gb=[42, 3]
326: dr=18680 gr=[6], dc=-56040 gc=[24, 2, 2], db=3140481600 gb=[48, 6]
327: dr=18697 gr=[3], dc=-56091 gc=[48, 2], db=3146200281 gb=[24, 6]
328: dr=18701 gr=[3], dc=-56103 gc=[102], db=3147546609 gb=[51, 3]
329: dr=18796 gr=[6], dc=-56388 gc=[24, 2, 2], db=3179606544 gb=[24, 6, 2]
330: dr=18853 gr=[6], dc=-56559 gc=[138, 2], db=3198920481 gb=[276, 3]
331: dr=18977 gr=[3], dc=-56931 gc=[42, 2], db=3241138761 gb=[42, 3]
332: dr=18989 gr=[6], dc=-56967 gc=[42, 2], db=3245239089 gb=[42, 6]
333: dr=19020 gr=[6, 2], dc=-6340 gc=[12, 2], db=361760400 gb=[24, 6]
334: dr=19084 gr=[6], dc=-57252 gc=[24, 2, 2], db=3277791504 gb=[24, 6, 2]
335: dr=19265 gr=[6], dc=-57795 gc=[30, 2], db=3340262025 gb=[30, 6]
336: dr=19288 gr=[3], dc=-57864 gc=[48, 2], db=3348242496 gb=[48, 3]
337: dr=19429 gr=[3], dc=-58287 gc=[120], db=3397374369 gb=[60, 3]
338: dr=19461 gr=[6], dc=-6487 gc=[42], db=378730521 gb=[42, 6]
339: dr=19605 gr=[6], dc=-6535 gc=[30], db=384356025 gb=[30, 3]
340: dr=19628 gr=[6], dc=-58884 gc=[24, 2, 2], db=3467325456 gb=[48, 6]
341: dr=19633 gr=[6], dc=-58899 gc=[30, 2], db=3469092201 gb=[60, 3]
342: dr=19708 gr=[6], dc=-59124 gc=[30, 2, 2], db=3495647376 gb=[30, 6, 2]
343: dr=19736 gr=[3], dc=-59208 gc=[24, 2], db=3505587264 gb=[24, 3]
344: dr=19757 gr=[3], dc=-59271 gc=[96, 2], db=3513051441 gb=[96, 3]
345: dr=19864 gr=[6], dc=-59592 gc=[12, 2, 2], db=3551206464 gb=[12, 6, 2]
346: dr=19869 gr=[6], dc=-6623 gc=[42], db=394777161 gb=[42, 6]
347: dr=19880 gr=[6, 2], dc=-59640 gc=[12, 2, 2, 2], db=3556929600 gb=[24, 12, 2]
348: dr=19928 gr=[6], dc=-59784 gc=[24, 2, 2], db=3574126656 gb=[48, 6]
349: dr=19976 gr=[6], dc=-59928 gc=[12, 2, 2], db=3591365184 gb=[24, 6]
350: dr=19985 gr=[6], dc=-59955 gc=[12, 2, 2], db=3594602025 gb=[12, 6, 2]
351: dr=20044 gr=[3], dc=-60132 gc=[30, 2], db=3615857424 gb=[30, 3]
352: dr=20073 gr=[3], dc=-6691 gc=[21], db=402925329 gb=[21, 3]
353: dr=20077 gr=[6], dc=-60231 gc=[114, 2], db=3627773361 gb=[228, 3]
354: dr=20093 gr=[3], dc=-60279 gc=[78, 2], db=3633557841 gb=[78, 3]
355: dr=20153 gr=[3], dc=-60459 gc=[30, 2], db=3655290681 gb=[30, 3]
356: dr=20168 gr=[12], dc=-60504 gc=[60, 2], db=3660734016 gb=[60, 12]
357: dr=20189 gr=[6], dc=-60567 gc=[78, 2], db=3668361489 gb=[78, 6]
358: dr=20249 gr=[3], dc=-60747 gc=[30], db=3690198009 gb=[15, 3]
359: dr=20252 gr=[6], dc=-60756 gc=[24, 2, 2], db=3691291536 gb=[24, 6, 2]
360: dr=20281 gr=[6], dc=-60843 gc=[30, 2], db=3701870649 gb=[60, 3]
361: dr=20297 gr=[3], dc=-60891 gc=[102], db=3707713881 gb=[51, 3]
362: dr=20329 gr=[6], dc=-60987 gc=[30, 2], db=3719414169 gb=[60, 3]
363: dr=20341 gr=[3], dc=-61023 gc=[132], db=3723806529 gb=[66, 3]
364: dr=20353 gr=[3], dc=-61059 gc=[60], db=3728201481 gb=[30, 3]
365: dr=20396 gr=[3], dc=-61188 gc=[30, 2], db=3743971344 gb=[30, 3]
366: dr=20408 gr=[3], dc=-61224 gc=[42, 2], db=3748378176 gb=[42, 3]
367: dr=20453 gr=[6], dc=-61359 gc=[78, 2], db=3764926881 gb=[78, 6]
368: dr=20501 gr=[6], dc=-61503 gc=[30, 2, 2], db=3782619009 gb=[30, 6, 2]
369: dr=20521 gr=[3], dc=-61563 gc=[60], db=3790002969 gb=[30, 3]
370: dr=20549 gr=[3], dc=-61647 gc=[138], db=3800352609 gb=[69, 3]
371: dr=20621 gr=[6], dc=-61863 gc=[78, 2], db=3827030769 gb=[78, 6]
372: dr=20693 gr=[3], dc=-62079 gc=[258], db=3853802241 gb=[129, 3]
373: dr=20712 gr=[6], dc=-6904 gc=[24], db=428986944 gb=[24, 3]
374: dr=20733 gr=[3], dc=-6911 gc=[87], db=429857289 gb=[87, 3]
375: dr=20829 gr=[6], dc=-6943 gc=[48], db=433847241 gb=[48, 3]
376: dr=20865 gr=[6, 2], dc=-6955 gc=[6, 2], db=435348225 gb=[6, 6, 2]
377: dr=20949 gr=[3], dc=-6983 gc=[57], db=438860601 gb=[57, 3]
378: dr=21020 gr=[6], dc=-63060 gc=[24, 2, 2], db=3976563600 gb=[48, 6]
379: dr=21052 gr=[6], dc=-63156 gc=[24, 2, 2], db=3988680336 gb=[24, 6, 2]
380: dr=21064 gr=[12], dc=-63192 gc=[42, 2], db=3993228864 gb=[168, 3]
381: dr=21109 gr=[6], dc=-63327 gc=[42, 2, 2], db=4010308929 gb=[84, 6]
382: dr=21208 gr=[6], dc=-63624 gc=[24, 2, 2], db=4048013376 gb=[24, 6, 2]
383: dr=21212 gr=[3], dc=-63636 gc=[60, 2], db=4049540496 gb=[60, 3]
384: dr=21281 gr=[6], dc=-63843 gc=[24, 2], db=4075928649 gb=[24, 6]
385: dr=21293 gr=[3], dc=-63879 gc=[84, 2], db=4080526641 gb=[84, 3]
386: dr=21308 gr=[6], dc=-63924 gc=[30, 2, 2], db=4086277776 gb=[60, 6]
387: dr=21324 gr=[12], dc=-7108 gc=[24], db=454712976 gb=[24, 6]
388: dr=21337 gr=[3], dc=-64011 gc=[48, 2], db=4097408121 gb=[24, 6]
389: dr=21361 gr=[6], dc=-64083 gc=[30, 2], db=4106630889 gb=[60, 3]
390: dr=21385 gr=[12, 2], dc=-64155 gc=[6, 2, 2, 2], db=4115864025 gb=[24, 6, 2, 2]
391: dr=21469 gr=[3], dc=-64407 gc=[60, 2], db=4148261649 gb=[30, 6]
392: dr=21532 gr=[6], dc=-64596 gc=[30, 2, 2], db=4172643216 gb=[30, 6, 2]
393: dr=21597 gr=[6], dc=-7199 gc=[114], db=466430409 gb=[114, 6]
394: dr=21637 gr=[6], dc=-64911 gc=[42, 2, 2], db=4213437921 gb=[84, 6]
395: dr=21641 gr=[12], dc=-64923 gc=[12, 2, 2], db=4214995929 gb=[12, 12, 2]
396: dr=21713 gr=[3], dc=-65139 gc=[66], db=4243089321 gb=[33, 3]
397: dr=21724 gr=[3], dc=-65172 gc=[30, 2], db=4247389584 gb=[30, 3]
398: dr=21737 gr=[3], dc=-65211 gc=[78], db=4252474521 gb=[39, 3]
399: dr=21809 gr=[6], dc=-65427 gc=[30, 2], db=4280692329 gb=[30, 6]
400: dr=21877 gr=[3], dc=-65631 gc=[96, 2], db=4307428161 gb=[96, 3]
401: dr=21913 gr=[6], dc=-65739 gc=[30, 2], db=4321616121 gb=[60, 3]
402: dr=22044 gr=[6, 2], dc=-7348 gc=[12, 2], db=485937936 gb=[24, 6]
403: dr=22053 gr=[3], dc=-7351 gc=[33], db=486334809 gb=[33, 3]
404: dr=22168 gr=[6], dc=-66504 gc=[24, 2, 2], db=4422782016 gb=[48, 6]
405: dr=22229 gr=[3], dc=-66687 gc=[186], db=4447155969 gb=[93, 3]
406: dr=22312 gr=[6], dc=-66936 gc=[42, 2], db=4480428096 gb=[84, 3]
407: dr=22341 gr=[6], dc=-7447 gc=[42], db=499120281 gb=[42, 3]
408: dr=22377 gr=[3], dc=-7459 gc=[15], db=500730129 gb=[15, 3]
409: dr=22380 gr=[6, 2], dc=-7460 gc=[24, 2], db=500864400 gb=[24, 6, 2]
410: dr=22476 gr=[12], dc=-7492 gc=[12], db=505170576 gb=[12, 6]
411: dr=22485 gr=[6], dc=-7495 gc=[48], db=505575225 gb=[48, 3]
412: dr=22633 gr=[12], dc=-67899 gc=[24, 4], db=4610274201 gb=[48, 6, 2]
413: dr=22661 gr=[6], dc=-67983 gc=[30, 2, 2], db=4621688289 gb=[30, 6, 2]
414: dr=22709 gr=[3], dc=-68127 gc=[138], db=4641288129 gb=[69, 3]
415: dr=22717 gr=[3], dc=-68151 gc=[276], db=4644558801 gb=[138, 3]
416: dr=22732 gr=[3], dc=-68196 gc=[42, 2], db=4650694416 gb=[42, 3]
417: dr=22769 gr=[3], dc=-68307 gc=[42], db=4665846249 gb=[21, 3]
418: dr=22873 gr=[12], dc=-68619 gc=[42, 2], db=4708567161 gb=[168, 3]
419: dr=22888 gr=[6], dc=-68664 gc=[42, 2], db=4714744896 gb=[84, 3]
420: dr=22909 gr=[3], dc=-68727 gc=[60, 2], db=4723400529 gb=[30, 6]
421: dr=23005 gr=[6], dc=-69015 gc=[30, 2, 2], db=4763070225 gb=[60, 6]
422: dr=23105 gr=[24], dc=-69315 gc=[24, 2], db=4804569225 gb=[24, 24]
423: dr=23192 gr=[6], dc=-69576 gc=[30, 2, 2], db=4840819776 gb=[30, 6, 2]
424: dr=23249 gr=[3], dc=-69747 gc=[24, 2], db=4864644009 gb=[24, 3]
425: dr=23297 gr=[3], dc=-69891 gc=[102], db=4884751881 gb=[51, 3]
426: dr=23377 gr=[12], dc=-70131 gc=[24, 4], db=4918357161 gb=[24, 12, 2]
427: dr=23417 gr=[3], dc=-70251 gc=[78], db=4935203001 gb=[39, 3]
428: dr=23497 gr=[3], dc=-70491 gc=[48], db=4968981081 gb=[24, 3]
429: dr=23612 gr=[3], dc=-70836 gc=[60, 2], db=5017738896 gb=[60, 3]
430: dr=23613 gr=[6], dc=-7871 gc=[120], db=557573769 gb=[120, 3]
431: dr=23672 gr=[6], dc=-71016 gc=[30, 2, 2], db=5043272256 gb=[60, 6]
432: dr=23689 gr=[3], dc=-71067 gc=[60], db=5050518489 gb=[30, 3]
433: dr=23720 gr=[6, 2], dc=-71160 gc=[24, 2, 2], db=5063745600 gb=[48, 12]
434: dr=23721 gr=[3], dc=-7907 gc=[21], db=562685841 gb=[21, 3]
435: dr=23909 gr=[3], dc=-71727 gc=[210], db=5144762529 gb=[105, 3]
436: dr=23917 gr=[3], dc=-71751 gc=[204], db=5148206001 gb=[102, 3]
437: dr=23953 gr=[12], dc=-71859 gc=[30, 2], db=5163715881 gb=[120, 3]
438: dr=23957 gr=[3], dc=-71871 gc=[210], db=5165440641 gb=[105, 3]
439: dr=23964 gr=[6], dc=-7988 gc=[42], db=574273296 gb=[42, 3]
440: dr=23993 gr=[3], dc=-71979 gc=[78], db=5180976441 gb=[39, 3]
441: dr=24001 gr=[3], dc=-72003 gc=[60], db=5184432009 gb=[30, 3]
442: dr=24005 gr=[6], dc=-72015 gc=[60, 2], db=5186160225 gb=[60, 6]
443: dr=24104 gr=[6], dc=-72312 gc=[12, 2, 2], db=5229025344 gb=[24, 6]
444: dr=24149 gr=[6], dc=-72447 gc=[30, 2, 2], db=5248567809 gb=[30, 6, 2]
445: dr=24177 gr=[3], dc=-8059 gc=[21], db=584527329 gb=[21, 3]
446: dr=24232 gr=[6, 2], dc=-72696 gc=[30, 2, 2], db=5284708416 gb=[60, 6, 2]
447: dr=24281 gr=[3], dc=-72843 gc=[42], db=5306102649 gb=[21, 3]
448: dr=24328 gr=[6], dc=-72984 gc=[42, 2], db=5326664256 gb=[84, 3]
449: dr=24393 gr=[6], dc=-8131 gc=[12], db=595018449 gb=[12, 3]
450: dr=24433 gr=[12], dc=-73299 gc=[30, 2], db=5372743401 gb=[120, 3]
451: dr=24437 gr=[3], dc=-73311 gc=[132, 2], db=5374502721 gb=[132, 3]
452: dr=24513 gr=[3], dc=-8171 gc=[21], db=600887169 gb=[21, 3]
453: dr=24533 gr=[3], dc=-73599 gc=[150], db=5416812801 gb=[75, 3]
454: dr=24617 gr=[3], dc=-73851 gc=[30, 2], db=5453970201 gb=[30, 3]
455: dr=24621 gr=[6], dc=-8207 gc=[96], db=606193641 gb=[96, 3]
456: dr=24665 gr=[6], dc=-73995 gc=[30, 2], db=5475260025 gb=[30, 6]
457: dr=24917 gr=[3], dc=-74751 gc=[282], db=5587712001 gb=[141, 3]
458: dr=24952 gr=[3], dc=-74856 gc=[60, 2], db=5603420736 gb=[60, 3]
459: dr=24965 gr=[6], dc=-74895 gc=[78, 2], db=5609261025 gb=[78, 6]
460: dr=24972 gr=[6], dc=-8324 gc=[60], db=623600784 gb=[60, 3]
461: dr=25129 gr=[6], dc=-75387 gc=[12, 4], db=5683199769 gb=[12, 6, 2]
462: dr=25185 gr=[6, 2], dc=-8395 gc=[6, 2], db=634284225 gb=[6, 6, 2]
463: dr=25228 gr=[6, 2], dc=-75684 gc=[12, 2, 2, 2], db=5728067856 gb=[24, 12, 2]
464: dr=25249 gr=[3], dc=-75747 gc=[24, 2], db=5737608009 gb=[12, 6]
465: dr=25377 gr=[6], dc=-8459 gc=[42], db=643992129 gb=[42, 6]
466: dr=25465 gr=[6], dc=-76395 gc=[12, 2, 2], db=5836196025 gb=[24, 6]
467: dr=25469 gr=[3], dc=-76407 gc=[114], db=5838029649 gb=[57, 3]
468: dr=25513 gr=[3], dc=-76539 gc=[24, 2], db=5858218521 gb=[12, 6]
469: dr=25645 gr=[6], dc=-76935 gc=[48, 2, 2], db=5918994225 gb=[96, 6]
470: dr=25656 gr=[6], dc=-8552 gc=[42], db=658230336 gb=[42, 6]
471: dr=25692 gr=[6], dc=-8564 gc=[78], db=660078864 gb=[78, 3]
472: dr=25708 gr=[3], dc=-77124 gc=[66, 2], db=5948111376 gb=[66, 3]
473: dr=25717 gr=[3], dc=-77151 gc=[192], db=5952276801 gb=[96, 3]
474: dr=25729 gr=[3], dc=-77187 gc=[24, 2], db=5957832969 gb=[24, 3]
475: dr=25741 gr=[15], dc=-77223 gc=[156], db=5963391729 gb=[390, 3]
476: dr=25793 gr=[3], dc=-77379 gc=[66], db=5987509641 gb=[33, 3]
477: dr=25945 gr=[6], dc=-77835 gc=[30, 2], db=6058287225 gb=[60, 3]
478: dr=25949 gr=[6], dc=-77847 gc=[42, 2, 2], db=6060155409 gb=[42, 6, 2]
479: dr=25981 gr=[3], dc=-77943 gc=[192], db=6075111249 gb=[96, 3]
480: dr=26029 gr=[3], dc=-78087 gc=[120], db=6097579569 gb=[60, 3]
481: dr=26113 gr=[3], dc=-78339 gc=[60], db=6136998921 gb=[30, 3]
482: dr=26121 gr=[3], dc=-8707 gc=[15], db=682306641 gb=[15, 3]
483: dr=26232 gr=[6], dc=-8744 gc=[42], db=688117824 gb=[42, 6]
484: dr=26284 gr=[3], dc=-78852 gc=[30, 2], db=6217637904 gb=[30, 3]
485: dr=26556 gr=[6], dc=-8852 gc=[42], db=705221136 gb=[42, 3]
486: dr=26680 gr=[6, 2], dc=-80040 gc=[12, 2, 2, 2], db=6406401600 gb=[24, 12, 2]
487: dr=26744 gr=[3], dc=-80232 gc=[42, 2], db=6437173824 gb=[42, 3]
488: dr=26761 gr=[3], dc=-80283 gc=[24, 2], db=6445360089 gb=[12, 6]
489: dr=26893 gr=[3], dc=-80679 gc=[168], db=6509101041 gb=[84, 3]
490: dr=26933 gr=[3], dc=-80799 gc=[138, 2], db=6528478401 gb=[138, 3]
491: dr=27049 gr=[3], dc=-81147 gc=[24, 2], db=6584835609 gb=[24, 3]
492: dr=27065 gr=[6], dc=-81195 gc=[30, 2], db=6592628025 gb=[30, 6]
493: dr=27080 gr=[6, 2], dc=-81240 gc=[12, 4, 2], db=6599937600 gb=[24, 24]
494: dr=27129 gr=[3], dc=-9043 gc=[15], db=735982641 gb=[15, 3]
495: dr=27213 gr=[6], dc=-9071 gc=[138], db=740547369 gb=[138, 6]
496: dr=27224 gr=[12], dc=-81672 gc=[24, 2, 2], db=6670315584 gb=[48, 12]
497: dr=27228 gr=[6], dc=-9076 gc=[30], db=741363984 gb=[30, 6]
498: dr=27245 gr=[6], dc=-81735 gc=[96, 2], db=6680610225 gb=[96, 6]
499: dr=27276 gr=[6], dc=-9092 gc=[48], db=743980176 gb=[48, 3]
500: dr=27329 gr=[3], dc=-81987 gc=[78], db=6721868169 gb=[39, 3]
501: dr=27336 gr=[6, 2], dc=-9112 gc=[12, 2], db=747256896 gb=[24, 6]
502: dr=27409 gr=[3], dc=-82227 gc=[60], db=6761279529 gb=[30, 3]
503: dr=27445 gr=[12], dc=-82335 gc=[48, 2, 2], db=6779052225 gb=[48, 24]
504: dr=27548 gr=[6], dc=-82644 gc=[24, 2, 2], db=6830030736 gb=[24, 6, 2]
505: dr=27557 gr=[6], dc=-82671 gc=[114, 2], db=6834494241 gb=[114, 6]
506: dr=27617 gr=[3], dc=-82851 gc=[78], db=6864288201 gb=[39, 3]
507: dr=27708 gr=[6], dc=-9236 gc=[66], db=767733264 gb=[66, 3]
508: dr=27713 gr=[12], dc=-83139 gc=[24, 2, 2], db=6912093321 gb=[24, 12, 2]
509: dr=27980 gr=[6], dc=-83940 gc=[24, 2, 2], db=7045923600 gb=[48, 6]
510: dr=28041 gr=[12], dc=-9347 gc=[24], db=786297681 gb=[48, 6]
511: dr=28056 gr=[6, 2], dc=-9352 gc=[12, 2], db=787139136 gb=[24, 6]
512: dr=28061 gr=[3], dc=-84183 gc=[66, 2], db=7086777489 gb=[66, 3]
513: dr=28076 gr=[3], dc=-84228 gc=[30, 2], db=7094355984 gb=[30, 3]
514: dr=28097 gr=[3], dc=-84291 gc=[66], db=7104972681 gb=[33, 3]
515: dr=28137 gr=[6], dc=-9379 gc=[24], db=791690769 gb=[24, 3]
516: dr=28220 gr=[6, 2], dc=-84660 gc=[12, 2, 2, 2], db=7167315600 gb=[12, 12, 4]
517: dr=28232 gr=[6], dc=-84696 gc=[96, 2], db=7173412416 gb=[96, 6]
518: dr=28349 gr=[3], dc=-85047 gc=[150], db=7232992209 gb=[75, 3]
519: dr=28361 gr=[3], dc=-85083 gc=[24, 2], db=7239116889 gb=[24, 3]
520: dr=28381 gr=[12], dc=-85143 gc=[66, 2], db=7249330449 gb=[264, 3]
521: dr=28529 gr=[3], dc=-85587 gc=[30, 2], db=7325134569 gb=[30, 3]
522: dr=28613 gr=[6], dc=-85839 gc=[66, 2, 2], db=7368333921 gb=[66, 6, 2]
523: dr=28669 gr=[3], dc=-86007 gc=[228], db=7397204049 gb=[114, 3]
524: dr=28733 gr=[3], dc=-86199 gc=[96, 2], db=7430267601 gb=[96, 3]
525: dr=28837 gr=[3], dc=-86511 gc=[336], db=7484153121 gb=[168, 3]
526: dr=28936 gr=[6], dc=-86808 gc=[30, 2], db=7535628864 gb=[60, 3]
527: dr=28940 gr=[6], dc=-86820 gc=[30, 2, 2], db=7537712400 gb=[60, 6]
528: dr=28985 gr=[6, 2], dc=-86955 gc=[6, 2, 2, 2], db=7561172025 gb=[12, 12, 2]
529: dr=29036 gr=[6, 2], dc=-87108 gc=[12, 2, 2, 2], db=7587803664 gb=[24, 6, 2, 2]
530: dr=29048 gr=[3], dc=-87144 gc=[66, 2], db=7594076736 gb=[66, 3]
531: dr=29116 gr=[6], dc=-87348 gc=[24, 2, 2], db=7629673104 gb=[24, 12]
532: dr=29221 gr=[3], dc=-87663 gc=[156], db=7684801569 gb=[78, 3]
533: dr=29245 gr=[12], dc=-87735 gc=[78, 2], db=7697430225 gb=[312, 3]
534: dr=29276 gr=[6], dc=-87828 gc=[24, 2, 2], db=7713757584 gb=[24, 6, 2]
535: dr=29281 gr=[6], dc=-87843 gc=[12, 2, 2], db=7716392649 gb=[24, 6]
536: dr=29397 gr=[6], dc=-9799 gc=[66], db=864183609 gb=[66, 3]
537: dr=29469 gr=[6, 2], dc=-9823 gc=[12, 2], db=868421961 gb=[24, 6]
538: dr=29485 gr=[6], dc=-88455 gc=[138, 2], db=7824287025 gb=[276, 3]
539: dr=29569 gr=[3], dc=-88707 gc=[60], db=7868931849 gb=[30, 3]
540: dr=29629 gr=[3], dc=-88887 gc=[132], db=7900898769 gb=[66, 3]
541: dr=29660 gr=[6], dc=-88980 gc=[24, 2, 2], db=7917440400 gb=[48, 6]
542: dr=29692 gr=[6], dc=-89076 gc=[24, 2, 2], db=7934533776 gb=[24, 6, 2]
543: dr=29813 gr=[3], dc=-89439 gc=[132, 2], db=7999334721 gb=[132, 3]
544: dr=29836 gr=[3], dc=-89508 gc=[42, 2], db=8011682064 gb=[42, 3]
545: dr=29884 gr=[6], dc=-89652 gc=[30, 2, 2], db=8037481104 gb=[30, 6, 2]
546: dr=29901 gr=[3], dc=-9967 gc=[39], db=894069801 gb=[39, 3]
547: dr=29905 gr=[12], dc=-89715 gc=[30, 2], db=8048781225 gb=[120, 3]
548: dr=29933 gr=[6], dc=-89799 gc=[138, 2], db=8063860401 gb=[138, 6]
549: dr=29989 gr=[3], dc=-89967 gc=[132], db=8094061089 gb=[66, 3]
The 213 bicyclic biquadratic fields B of type (9,3) are given in the following table.
(Output format is Counter: d(R) Cl(R), d(C) Cl(C), d(B) Cl(B).)
1: dr=733 gr=[3], dc=-2199 gc=[36], db=4835601 gb=[18, 3]
2: dr=1101 gr=[3], dc=-367 gc=[9], db=1212201 gb=[9, 3]
3: dr=1129 gr=[9], dc=-3387 gc=[12], db=11471769 gb=[18, 3]
4: dr=1257 gr=[3], dc=-419 gc=[9], db=1580049 gb=[9, 3]
5: dr=1772 gr=[3], dc=-5316 gc=[18, 2], db=28259856 gb=[18, 3]
6: dr=1957 gr=[3], dc=-5871 gc=[36, 2], db=34468641 gb=[18, 6]
7: dr=2021 gr=[3], dc=-6063 gc=[18, 2], db=36759969 gb=[18, 3]
8: dr=2213 gr=[3], dc=-6639 gc=[90], db=44076321 gb=[45, 3]
9: dr=2429 gr=[3], dc=-7287 gc=[18, 2], db=53100369 gb=[18, 3]
10: dr=2636 gr=[3], dc=-7908 gc=[18, 2], db=62536464 gb=[18, 3]
11: dr=2713 gr=[3], dc=-8139 gc=[36], db=66243321 gb=[18, 3]
12: dr=2777 gr=[3], dc=-8331 gc=[18], db=69405561 gb=[9, 3]
13: dr=2857 gr=[3], dc=-8571 gc=[36], db=73462041 gb=[18, 3]
14: dr=3137 gr=[9], dc=-9411 gc=[30], db=88566921 gb=[45, 3]
15: dr=3261 gr=[3], dc=-1087 gc=[9], db=10634121 gb=[9, 3]
16: dr=3873 gr=[3], dc=-1291 gc=[9], db=15000129 gb=[9, 3]
17: dr=3877 gr=[3], dc=-11631 gc=[72], db=135280161 gb=[36, 3]
18: dr=3957 gr=[3], dc=-1319 gc=[45], db=15657849 gb=[45, 3]
19: dr=4193 gr=[3], dc=-12579 gc=[18, 2], db=158231241 gb=[18, 3]
20: dr=4344 gr=[6], dc=-1448 gc=[18], db=18870336 gb=[18, 6]
21: dr=4364 gr=[3], dc=-13092 gc=[18, 2], db=171400464 gb=[18, 3]
22: dr=4649 gr=[3], dc=-13947 gc=[18], db=194518809 gb=[9, 3]
23: dr=4684 gr=[3], dc=-14052 gc=[18, 2], db=197458704 gb=[18, 3]
24: dr=4729 gr=[3], dc=-14187 gc=[36], db=201270969 gb=[18, 3]
25: dr=5073 gr=[6], dc=-1691 gc=[18], db=25735329 gb=[18, 3]
26: dr=5081 gr=[3], dc=-15243 gc=[18], db=232349049 gb=[9, 3]
27: dr=5261 gr=[3], dc=-15783 gc=[90], db=249103089 gb=[45, 3]
28: dr=5353 gr=[6], dc=-16059 gc=[18, 2], db=257891481 gb=[36, 3]
29: dr=5521 gr=[9], dc=-16563 gc=[24], db=274332969 gb=[36, 3]
30: dr=5613 gr=[3], dc=-1871 gc=[45], db=31505769 gb=[45, 3]
31: dr=5621 gr=[6], dc=-16863 gc=[18, 2, 2], db=284360769 gb=[18, 6, 2]
32: dr=5901 gr=[6], dc=-1967 gc=[36], db=34821801 gb=[36, 3]
33: dr=6088 gr=[12], dc=-18264 gc=[18, 2], db=333573696 gb=[72, 3]
34: dr=6133 gr=[3], dc=-18399 gc=[144], db=338523201 gb=[72, 3]
35: dr=6153 gr=[6], dc=-2051 gc=[18], db=37859409 gb=[18, 3]
36: dr=6184 gr=[6], dc=-18552 gc=[18, 2], db=344176704 gb=[36, 3]
37: dr=6268 gr=[3], dc=-18804 gc=[18, 2], db=353590416 gb=[18, 3]
38: dr=6584 gr=[3], dc=-19752 gc=[18, 2], db=390141504 gb=[18, 3]
39: dr=6616 gr=[9], dc=-19848 gc=[24, 2], db=393943104 gb=[72, 3]
40: dr=6809 gr=[9], dc=-20427 gc=[12, 2], db=417262329 gb=[36, 3]
41: dr=7032 gr=[6], dc=-2344 gc=[18], db=49449024 gb=[18, 3]
42: dr=7053 gr=[3], dc=-2351 gc=[63], db=49744809 gb=[63, 3]
43: dr=7244 gr=[3], dc=-21732 gc=[18, 2], db=472279824 gb=[18, 3]
44: dr=7388 gr=[3], dc=-22164 gc=[36, 2], db=491242896 gb=[36, 3]
45: dr=7573 gr=[9], dc=-22719 gc=[84], db=516152961 gb=[126, 3]
46: dr=7721 gr=[3], dc=-23163 gc=[18, 2], db=536524569 gb=[18, 3]
47: dr=7753 gr=[3], dc=-23259 gc=[36], db=540981081 gb=[18, 3]
48: dr=8069 gr=[3], dc=-24207 gc=[90], db=585978849 gb=[45, 3]
49: dr=8173 gr=[3], dc=-24519 gc=[72, 2], db=601181361 gb=[72, 3]
50: dr=8396 gr=[3], dc=-25188 gc=[18, 2], db=634435344 gb=[18, 3]
51: dr=8545 gr=[12], dc=-25635 gc=[18, 2], db=657153225 gb=[72, 3]
52: dr=8581 gr=[3], dc=-25743 gc=[72], db=662702049 gb=[36, 3]
53: dr=8837 gr=[3], dc=-26511 gc=[126], db=702833121 gb=[63, 3]
54: dr=9217 gr=[18], dc=-27651 gc=[24, 2], db=764577801 gb=[36, 6, 2]
55: dr=9293 gr=[3], dc=-27879 gc=[126], db=777238641 gb=[63, 3]
56: dr=9301 gr=[3], dc=-27903 gc=[36, 2], db=778577409 gb=[36, 3]
57: dr=9676 gr=[12], dc=-29028 gc=[18, 2, 2], db=842624784 gb=[72, 6]
58: dr=9745 gr=[6], dc=-29235 gc=[18, 2], db=854685225 gb=[36, 3]
59: dr=10040 gr=[6], dc=-30120 gc=[18, 2, 2], db=907214400 gb=[36, 6]
60: dr=10216 gr=[6], dc=-30648 gc=[18, 2], db=939299904 gb=[36, 3]
61: dr=10273 gr=[9], dc=-30819 gc=[60], db=949810761 gb=[90, 3]
62: dr=10552 gr=[3], dc=-31656 gc=[36, 2], db=1002102336 gb=[36, 3]
63: dr=10641 gr=[3], dc=-3547 gc=[9], db=113230881 gb=[9, 3]
64: dr=10712 gr=[6], dc=-32136 gc=[18, 2, 2], db=1032722496 gb=[18, 6, 2]
65: dr=10721 gr=[9], dc=-32163 gc=[24, 2], db=1034458569 gb=[72, 3]
66: dr=10733 gr=[3], dc=-32199 gc=[198], db=1036775601 gb=[99, 3]
67: dr=10929 gr=[3], dc=-3643 gc=[9], db=119443041 gb=[9, 3]
68: dr=10997 gr=[3], dc=-32991 gc=[72, 2], db=1088406081 gb=[72, 3]
69: dr=11032 gr=[6], dc=-33096 gc=[18, 2, 2], db=1095345216 gb=[36, 6]
70: dr=11085 gr=[6], dc=-3695 gc=[72], db=122877225 gb=[72, 3]
71: dr=11289 gr=[18], dc=-3763 gc=[6], db=127441521 gb=[18, 3]
72: dr=11576 gr=[3], dc=-34728 gc=[18, 2], db=1206033984 gb=[18, 3]
73: dr=11641 gr=[9], dc=-34923 gc=[12, 2], db=1219615929 gb=[18, 6]
74: dr=11656 gr=[12], dc=-34968 gc=[18, 2, 2], db=1222761024 gb=[72, 6]
75: dr=11665 gr=[30], dc=-34995 gc=[18, 2], db=1224650025 gb=[180, 3]
76: dr=11672 gr=[3], dc=-35016 gc=[36, 2], db=1226120256 gb=[36, 3]
77: dr=11884 gr=[3], dc=-35652 gc=[18, 2], db=1271065104 gb=[18, 3]
78: dr=12140 gr=[6], dc=-36420 gc=[18, 2, 2], db=1326416400 gb=[36, 6]
79: dr=12197 gr=[3], dc=-36591 gc=[126], db=1338901281 gb=[63, 3]
80: dr=12216 gr=[6], dc=-4072 gc=[18], db=149230656 gb=[18, 3]
81: dr=12409 gr=[9], dc=-37227 gc=[24], db=1385849529 gb=[36, 3]
82: dr=12577 gr=[3], dc=-37731 gc=[36], db=1423628361 gb=[18, 3]
83: dr=12657 gr=[9], dc=-4219 gc=[15], db=160199649 gb=[45, 3]
84: dr=12765 gr=[6, 2], dc=-4255 gc=[18, 2], db=162945225 gb=[18, 6, 2]
85: dr=13069 gr=[9], dc=-39207 gc=[60, 2], db=1537188849 gb=[90, 6]
86: dr=13089 gr=[3], dc=-4363 gc=[9], db=171321921 gb=[9, 3]
87: dr=13117 gr=[6], dc=-39351 gc=[72, 2], db=1548501201 gb=[36, 6, 2]
88: dr=13153 gr=[3], dc=-39459 gc=[36, 2], db=1557012681 gb=[18, 6]
89: dr=13688 gr=[6], dc=-41064 gc=[18, 2, 2], db=1686252096 gb=[36, 6]
90: dr=14296 gr=[3], dc=-42888 gc=[36, 2], db=1839380544 gb=[36, 3]
91: dr=14316 gr=[6], dc=-4772 gc=[36], db=204947856 gb=[36, 3]
92: dr=14397 gr=[3], dc=-4799 gc=[63], db=207273609 gb=[63, 3]
93: dr=14457 gr=[6], dc=-4819 gc=[18], db=209004849 gb=[18, 6]
94: dr=14680 gr=[6], dc=-44040 gc=[18, 2, 2], db=1939521600 gb=[36, 6]
95: dr=14876 gr=[9], dc=-44628 gc=[24, 2], db=1991658384 gb=[72, 3]
96: dr=15521 gr=[18], dc=-46563 gc=[12, 2, 2], db=2168112969 gb=[72, 6]
97: dr=15629 gr=[9], dc=-46887 gc=[102], db=2198390769 gb=[153, 3]
98: dr=15689 gr=[6], dc=-47067 gc=[18, 2], db=2215302489 gb=[18, 6]
99: dr=15737 gr=[3], dc=-47211 gc=[90], db=2228878521 gb=[45, 3]
100: dr=15832 gr=[3], dc=-47496 gc=[36, 2], db=2255870016 gb=[36, 3]
101: dr=15873 gr=[6, 2], dc=-5291 gc=[18, 2], db=251952129 gb=[18, 6, 2, 2]
102: dr=16141 gr=[3], dc=-48423 gc=[72], db=2344786929 gb=[36, 3]
103: dr=16201 gr=[6], dc=-48603 gc=[18, 2], db=2362251609 gb=[36, 3]
104: dr=16321 gr=[9], dc=-48963 gc=[24, 2], db=2397375369 gb=[36, 6]
105: dr=16392 gr=[6], dc=-5464 gc=[18], db=268697664 gb=[18, 3]
106: dr=16477 gr=[3], dc=-49431 gc=[144], db=2443423761 gb=[72, 3]
107: dr=16585 gr=[6], dc=-49755 gc=[18, 2, 2], db=2475560025 gb=[36, 6]
108: dr=16609 gr=[12], dc=-49827 gc=[18, 2], db=2482729929 gb=[72, 3]
109: dr=16721 gr=[3], dc=-50163 gc=[18, 2], db=2516326569 gb=[18, 3]
110: dr=16773 gr=[3], dc=-5591 gc=[99], db=281333529 gb=[99, 3]
111: dr=16908 gr=[6], dc=-5636 gc=[36], db=285880464 gb=[36, 3]
112: dr=16952 gr=[6], dc=-50856 gc=[18, 2, 2], db=2586332736 gb=[18, 6, 2]
113: dr=17273 gr=[9], dc=-51819 gc=[30, 2], db=2685208761 gb=[90, 3]
114: dr=18269 gr=[3], dc=-54807 gc=[126], db=3003807249 gb=[63, 3]
115: dr=18409 gr=[12], dc=-55227 gc=[18, 2], db=3050021529 gb=[72, 3]
116: dr=18492 gr=[6, 2], dc=-6164 gc=[18, 2], db=341954064 gb=[36, 6]
117: dr=18633 gr=[9], dc=-6211 gc=[15], db=347188689 gb=[45, 3]
118: dr=18824 gr=[6, 2], dc=-56472 gc=[18, 2, 2], db=3189086784 gb=[18, 6, 2, 2]
119: dr=19045 gr=[6, 2], dc=-57135 gc=[36, 2, 2], db=3264408225 gb=[72, 6, 2]
120: dr=19113 gr=[12], dc=-6371 gc=[36], db=365306769 gb=[36, 6]
121: dr=19261 gr=[6], dc=-57783 gc=[36, 2, 2], db=3338875089 gb=[36, 12]
122: dr=19409 gr=[6], dc=-58227 gc=[18, 2], db=3390383529 gb=[18, 6]
123: dr=19441 gr=[9], dc=-58323 gc=[48], db=3401572329 gb=[72, 3]
124: dr=19544 gr=[6], dc=-58632 gc=[18, 2, 2], db=3437711424 gb=[18, 6, 2]
125: dr=19653 gr=[3], dc=-6551 gc=[117], db=386240409 gb=[117, 3]
126: dr=19741 gr=[3], dc=-59223 gc=[72, 2], db=3507363729 gb=[36, 6]
127: dr=19756 gr=[12], dc=-59268 gc=[18, 2, 2], db=3512695824 gb=[72, 6]
128: dr=19816 gr=[18], dc=-59448 gc=[30, 2], db=3534064704 gb=[180, 3]
129: dr=19821 gr=[3], dc=-6607 gc=[45], db=392872041 gb=[45, 3]
130: dr=19885 gr=[6, 2], dc=-59655 gc=[36, 2, 2], db=3558719025 gb=[72, 6, 2]
131: dr=19949 gr=[3], dc=-59847 gc=[90], db=3581663409 gb=[45, 3]
132: dr=20137 gr=[6], dc=-60411 gc=[36, 2], db=3649488921 gb=[18, 6, 2]
133: dr=20141 gr=[3], dc=-60423 gc=[72, 2], db=3650938929 gb=[72, 3]
134: dr=20289 gr=[3], dc=-6763 gc=[9], db=411643521 gb=[9, 3]
135: dr=20380 gr=[6], dc=-61140 gc=[18, 2, 2], db=3738099600 gb=[36, 6]
136: dr=20524 gr=[6], dc=-61572 gc=[18, 2, 2], db=3791111184 gb=[18, 6, 2]
137: dr=20545 gr=[18], dc=-61635 gc=[12, 2, 2], db=3798873225 gb=[72, 6]
138: dr=20613 gr=[3], dc=-6871 gc=[45], db=424895769 gb=[45, 3]
139: dr=20649 gr=[3], dc=-6883 gc=[9], db=426381201 gb=[9, 3]
140: dr=20749 gr=[3], dc=-62247 gc=[180], db=3874689009 gb=[90, 3]
141: dr=20913 gr=[3], dc=-6971 gc=[45], db=437353569 gb=[45, 3]
142: dr=21289 gr=[18], dc=-63867 gc=[24, 2], db=4078993689 gb=[36, 6, 2]
143: dr=21589 gr=[3], dc=-64767 gc=[180], db=4194764289 gb=[90, 3]
144: dr=21781 gr=[9], dc=-65343 gc=[84, 2], db=4269707649 gb=[252, 3]
145: dr=21865 gr=[18], dc=-65595 gc=[42, 2], db=4302704025 gb=[252, 3]
146: dr=22061 gr=[6], dc=-66183 gc=[90, 2], db=4380189489 gb=[90, 6]
147: dr=22492 gr=[9], dc=-67476 gc=[66, 2], db=4553010576 gb=[198, 3]
148: dr=22497 gr=[9], dc=-7499 gc=[33], db=506115009 gb=[99, 3]
149: dr=22952 gr=[6], dc=-68856 gc=[18, 2, 2], db=4741148736 gb=[18, 6, 2]
150: dr=23033 gr=[3], dc=-69099 gc=[36, 2], db=4774671801 gb=[36, 3]
151: dr=23196 gr=[6], dc=-7732 gc=[18], db=538054416 gb=[18, 6]
152: dr=23592 gr=[6], dc=-7864 gc=[36], db=556582464 gb=[36, 3]
153: dr=23617 gr=[6], dc=-70851 gc=[18, 2, 2], db=5019864201 gb=[36, 6]
154: dr=23665 gr=[6], dc=-70995 gc=[18, 2], db=5040290025 gb=[36, 3]
155: dr=23816 gr=[6, 2], dc=-71448 gc=[18, 2, 2], db=5104816704 gb=[18, 6, 2, 2]
156: dr=24169 gr=[9], dc=-72507 gc=[48], db=5257265049 gb=[72, 3]
157: dr=24645 gr=[6, 2], dc=-8215 gc=[18, 2], db=607376025 gb=[36, 6]
158: dr=24648 gr=[6, 2], dc=-8216 gc=[36, 2], db=607523904 gb=[36, 6, 2]
159: dr=24697 gr=[9], dc=-74091 gc=[96], db=5489476281 gb=[144, 3]
160: dr=24749 gr=[3], dc=-74247 gc=[234], db=5512617009 gb=[117, 3]
161: dr=24781 gr=[9], dc=-74343 gc=[204], db=5526881649 gb=[306, 3]
162: dr=25177 gr=[18], dc=-75531 gc=[30, 2], db=5704931961 gb=[180, 3]
163: dr=25244 gr=[3], dc=-75732 gc=[36, 2], db=5735335824 gb=[36, 3]
164: dr=25301 gr=[3], dc=-75903 gc=[126], db=5761265409 gb=[63, 3]
165: dr=25336 gr=[3], dc=-76008 gc=[36, 2], db=5777216064 gb=[36, 3]
166: dr=25361 gr=[9], dc=-76083 gc=[30, 2], db=5788622889 gb=[90, 3]
167: dr=25464 gr=[6], dc=-8488 gc=[18], db=648415296 gb=[18, 3]
168: dr=25705 gr=[6, 2], dc=-77115 gc=[18, 2, 2], db=5946723225 gb=[36, 6, 2]
169: dr=25961 gr=[6], dc=-77883 gc=[18, 2], db=6065761689 gb=[18, 6]
170: dr=25996 gr=[6], dc=-77988 gc=[18, 2, 2], db=6082128144 gb=[18, 6, 2]
171: dr=26376 gr=[6, 2], dc=-8792 gc=[18, 2], db=695693376 gb=[18, 6, 2]
172: dr=26492 gr=[6], dc=-79476 gc=[36, 2, 2], db=6316434576 gb=[36, 6, 2]
173: dr=26524 gr=[18], dc=-79572 gc=[24, 2, 2], db=6331703184 gb=[72, 6, 2]
174: dr=26537 gr=[6], dc=-79611 gc=[18, 2, 2], db=6337911321 gb=[18, 6, 2]
175: dr=26573 gr=[9], dc=-79719 gc=[282], db=6355118961 gb=[423, 3]
176: dr=26677 gr=[6], dc=-80031 gc=[72, 2, 2], db=6404960961 gb=[36, 6, 2, 2]
177: dr=26821 gr=[3], dc=-80463 gc=[144], db=6474294369 gb=[72, 3]
178: dr=26845 gr=[6, 2], dc=-80535 gc=[18, 2, 2, 2], db=6485886225 gb=[36, 6, 2, 2]
179: dr=26873 gr=[6], dc=-80619 gc=[18, 2, 2], db=6499423161 gb=[18, 6, 2]
180: dr=26997 gr=[3], dc=-8999 gc=[99], db=728838009 gb=[99, 3]
181: dr=27004 gr=[6], dc=-81012 gc=[18, 2, 2], db=6562944144 gb=[18, 6, 2]
182: dr=27013 gr=[6], dc=-81039 gc=[72, 2, 2], db=6567319521 gb=[144, 6]
183: dr=27064 gr=[6], dc=-81192 gc=[18, 2, 2], db=6592140864 gb=[36, 6]
184: dr=27164 gr=[3], dc=-81492 gc=[36, 2], db=6640946064 gb=[36, 3]
185: dr=27165 gr=[6], dc=-9055 gc=[36], db=737937225 gb=[36, 3]
186: dr=27192 gr=[6, 2], dc=-9064 gc=[18, 2], db=739404864 gb=[36, 6]
187: dr=27193 gr=[15], dc=-81579 gc=[36, 2], db=6655133241 gb=[180, 3]
188: dr=27221 gr=[9], dc=-81663 gc=[78, 2], db=6668845569 gb=[234, 3]
189: dr=27340 gr=[6], dc=-82020 gc=[18, 2, 2], db=6727280400 gb=[36, 6]
190: dr=27349 gr=[9], dc=-82047 gc=[60, 2], db=6731710209 gb=[90, 6]
191: dr=27437 gr=[3], dc=-82311 gc=[234], db=6775100721 gb=[117, 3]
192: dr=27633 gr=[6], dc=-9211 gc=[18], db=763582689 gb=[18, 6]
193: dr=27833 gr=[12], dc=-83499 gc=[36, 2], db=6972083001 gb=[72, 6]
194: dr=28145 gr=[6, 2], dc=-84435 gc=[18, 2, 2], db=7129269225 gb=[18, 6, 2, 2]
195: dr=28165 gr=[6], dc=-84495 gc=[36, 2, 2], db=7139405025 gb=[72, 6]
196: dr=28309 gr=[3], dc=-84927 gc=[180], db=7212595329 gb=[90, 3]
197: dr=28389 gr=[3], dc=-9463 gc=[45], db=805935321 gb=[45, 3]
198: dr=28428 gr=[6, 2], dc=-9476 gc=[36, 2], db=808151184 gb=[72, 6]
199: dr=28441 gr=[6], dc=-85323 gc=[18, 2, 2], db=7280014329 gb=[36, 6]
200: dr=28473 gr=[3], dc=-9491 gc=[45], db=810711729 gb=[45, 3]
201: dr=28504 gr=[6], dc=-85512 gc=[18, 2, 2], db=7312302144 gb=[36, 6]
202: dr=28657 gr=[3], dc=-85971 gc=[72], db=7391012841 gb=[36, 3]
203: dr=28901 gr=[9], dc=-86703 gc=[102], db=7517410209 gb=[153, 3]
204: dr=28904 gr=[18], dc=-86712 gc=[42, 2], db=7518970944 gb=[126, 6]
205: dr=28968 gr=[6, 2], dc=-9656 gc=[36, 2], db=839145024 gb=[72, 6]
206: dr=29013 gr=[6], dc=-9671 gc=[126], db=841754169 gb=[126, 3]
207: dr=29113 gr=[15], dc=-87339 gc=[36, 2], db=7628100921 gb=[90, 6]
208: dr=29165 gr=[6], dc=-87495 gc=[36, 2, 2], db=7655375025 gb=[36, 6, 2]
209: dr=29273 gr=[6], dc=-87819 gc=[36, 2], db=7712176761 gb=[36, 6]
210: dr=29317 gr=[9], dc=-87951 gc=[132, 2], db=7735378401 gb=[198, 6]
211: dr=29496 gr=[6], dc=-9832 gc=[18], db=870014016 gb=[18, 3]
212: dr=29548 gr=[6], dc=-88644 gc=[36, 2, 2], db=7857758736 gb=[72, 6]
213: dr=29553 gr=[3], dc=-9851 gc=[45], db=873379809 gb=[45, 3]

3.2. Triadic Quantum Class Group G32(B) of B = Q(D1/2,(-3)1/2),
the bicyclic biquadratic field of Eisenstein-Scholz-Reichardt type

With the aid of MAGMA V2.18-7 , we have computed the
triadic quantum class group G = G32(B)
with abelianization of diamond type (3,3), resp. of double layered type (9,3),
for the 930, resp. 389, bicyclic biquadratic fields B = Q(D1/2,(-3)1/2)
within the extended range 0 < D < 5*104,
having 3-class group Cl3(B) of type (3,3), resp. (9,3)
in March and May 2012.
The discriminants d(B) of these fields B are contained between the bounds
103041 ≤ d(B) ≤ 22482903249.

Our algorithm is based upon the triadic TTT (transfer target type) τ = (str(Cl3(N1)),…,str(Cl3(N4)))
which is well known by our theory of nearly homocyclic and exotic 3-class groups.

The following table shows the minimal representatives of all ground states (GS) and excited states (ES)
of TKTs (transfer kernel types) which occur for the quantum class groups G32(B),
represented by vertices on the coclass graphs G(3,r), 1 ≤ r ≤ 3.

The invariants ε1 and ε denote the cardinalities
ε1 = #{ 1 ≤ i ≤ 4 | Cl3(Ni) ≅ (3,3,3) },
ε = #{ 1 ≤ i ≤ 4 | rank3(Cl3(Ni)) ≥ 3 }.
No. Discriminant 3-Class Group of Cohomology Transfer Kernel Quantum 3-Class
D = d(R) B L1 L2 L3 L4 N1 N2 N3 N4 F31(B) ε1 Type Type (TKT) Group, G32(B)
Coclass 1 (GS)
1 229 (3,3) 1 1 1 1 (3) (3) (3) (3) 1 0 (αααα) a.1 (0000) < 9,2 >
5 469 (3,3) 3 3 3 3 (9,3) (3,3) (3,3) (3,3) (3,3) 0 (αααα) a*.1 (0000) < 81,9 >
Coclass 1 (ES 1)
123 7453 (3,3) 9 3 3 3 (27,9) (3,3) (3,3) (3,3) (9,9) 0 (αααα) a*.1 ↑ (0000) < 729,95 >
Coclass 2 (GS)
30 2177 (3,3) 3 3 3 3 (9,3) (9,3) (3,3,3) (3,3,3) (9,3,3) 2 (ααδδ) b.10 (0043) < 729,37 > = A
35 2589 (3,3) 3 3 3 3 (9,3) (9,3) (3,3,3) (3,3,3) (3,3,3,3) 2 (ααδδ) b.10 (0043) < 729,34 > = H
308 17609 (3,3) 3 9 3 3 (9,3) (9,9) (3,3,3) (3,3,3) (9,3,3) 2 (ααδδ) b*.10 ↑ (0043) < 729,40 > = B
Coclass 2 (ES 1)
235 14056 (3,3) 9 3 3 3 (27,9) (9,3) (3,3,3) (3,3,3) (27,9,3) 2 (ααδδ) b.10 ↑ (0043) < 6561,# >
369 20521 (3,3) 3 9 3 3 (9,3) (27,9) (3,3,3) (3,3,3) (27,9,3) 2 (ααδδ) b.10 ↑ (0043) < 6561,# >
Coclass 2 (ES 2)
826 44581 (3,3) 27 3 3 3 (81,27) (9,3) (3,3,3) (3,3,3) (81,27,3) 2 (ααδδ) b.10 ↑2 (0043) < 59049,# >
Coclass 3 (2*ES 1)
77 4933 (3,3) 9 9 3 3 (27,9) (9,9) (3,3,3) (3,3,3) (9,9,3,3) 2 (ααδδ) b*.10 ↑↑ (0043) < 6561,# >
Coclass 4 (ES 1, ES 2)
884 47597 (3,3) 9 9 3 3 (27,9) (27,9) (3,3,3) (3,3,3) (27,9,9,3) 2 (ααδδ) b.10 ↑↑2 (0043) < 59049,# >
Statistical evaluation of 930 bicyclic biquadratic fields of type (3,3):

1. Triadic Quantum Class Groups of Coclass 1:

1.0. Ground States (GS).
There occur 197 cases (21.2%) of the GS of TKT a*.1 (0000), starting with no. 5: d(B) = 1979649, d(R) = 469.
The remaining 605 cases (65.1%) of TKT a.1 (0000) with abelian G, starting with no. 4: d(B) = 103041, d(R) = 321, are clearly dominating.

1.1. First Excited State (ES 1).
There occur 42 cases (4.5%) of ES 1 of TKT a*.1↑ (0000), starting with no. 123: d(B) = 499924881, d(R) = 7453.

2. Triadic Quantum Class Groups of Coclass 2:

2.0. Ground States (GS).
There occur 59 cases (6.3%) of the GS of TKT b.10 (0043), starting with
no. 30: d(B) = 42653961, d(R) = 2177, having Cl3(F31(B)) = (9,3,3),
no. 35: d(B) = 6702921, d(R) = 2589, having Cl3(F31(B)) = (3,3,3,3).
There occur 3 cases of the GS of TKT b*.10 (0043) starting with no. 308: d(B) = 2790691929, d(R) = 17609.

2.1. First Excited State (ES 1).
There occur 17 cases (1.8%) of ES 1 of TKT b.10↑ (0043), starting with no. 235: d(B) = 1778140224, d(R) = 14056.

2.2. Second Excited State (ES 2).
There occurs a single case of ES 2 of TKT b.10↑2 (0043), for no. 826: d(B) = 17887190049, d(R) = 44581.

3. Triadic Quantum Class Groups of Coclass 3:

3.1. Double Excited State (2*ES 1).
There occur 5 cases of (ES 1, ES 1) of TKT b*.10↑↑ (0043), starting with no. 77: d(B) = 219010401, d(R) = 4933.

4. Triadic Quantum Class Groups of Coclass 4:

4.1. Double Excited State (ES 1, ES 2).
There occurs a single case of (ES 1, ES 2) of TKT b.10↑↑2 (0043), for no. 884: d(B) = 20389269681, d(R) = 47597.
No. Discriminant 3-Class Group of Cohomology Transfer Kernel Quantum 3-Class
d(B) B L1 L2 L3 L4 N1 N2 N3 N4 N*4 ε Type Type (pTKT) Group, G32(B)
Coclass 2 (GS)
2 1212201 (9,3) 1 1 1 1 (3,3) (9) (9) (9) (3) 0 (ααα;α) a.1 (000;0) < 27,2 >
Coclass 3 (GS)
1 4835601 (9,3) 3 3 3 3 (9,3,3) (9,3,3) (9,3,3) (9,3,3) (3,3,3,3) 4 (αδδ;δ) b.31 (044;4) < 729,11 >
72 1206033984 (9,3) 3 3 3 3 (3,3,3,3) (9,3,3) (9,3,3) (9,3,3) (3,3,3,3) 4 (ααα;δ) b.15 (000;4) < 729,12 >
Coclass 3 (2*ES 1)
107 2475560025 (9,3) 9 9 3 3 (27,9,3) (27,9,3) (9,3,3) (9,3,3) (9,9,3,3) 4 (αδδ;δ) b.31 ↑↑ (044;4)
48 585978849 (9,3) 3 3 9 9 (3,3,3,3) (9,3,3) (9,9,3) (9,9,3) (9,9,3,3) 4 (ααα;δ) b.15 ↑↑ (000;4)
Statistical evaluation of 213 bicyclic biquadratic fields of type (9,3):

Triadic Quantum Class Groups of Coclass 2:

2.0. Ground State (GS).
The 168 cases (78.9%) of pTKT a.1 (000;0) with abelian G, starting with no. 2: d(B) = 1212201, d(R) = 1101, are clearly dominating.

Triadic Quantum Class Groups of Coclass 3:

3.0. Ground States (GS).
There occur 23 cases (11%) of the GS of pTKT b.31 (044;4), starting with no. 1: d(B) = 4835601, d(R) = 733,
and 6 cases of the GS of pTKT b.15 (000;4), starting with no. 72: d(B) = 1206033984, d(R) = 11576.

3.1. Double Excited States (2*ES 1).
There occur 4 cases of 2*ES 1 of pTKT b.15 ↑↑ (000;4), starting with no. 48: d(B) = 585978849, d(R) = 8069,
and a single case of 2*ES 1 of pTKT b.31 ↑↑ (044;4) for no. 107: d(B) = 2475560025, d(R) = 16585.

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