# Number fields downloaded from the LMFDB on 01 May 2026.
# Search link: https://www.lmfdb.org/NumberField/?degree=32
# Query "{'degree': 32}" returned 7283 fields, sorted by degree.

# Each entry in the following data list has the form:
#    [Label, Polynomial, Discriminant, Galois group, Class group]
# For more details, see the definitions at the bottom of the file.



"32.0.24788700386255228556692600250244140625.1"	[1, -1, 55, -293, 639, -564, -465, 1624, -528, -2784, 3435, 870, -4074, 1255, 2706, -1988, -775, 976, 369, -500, -204, 275, 130, -233, 32, 77, -25, -23, 14, 1, 0, -2, 1]	24788700386255228556692600250244140625	"32T402"	[]
"32.0.47330370277129322496000000000000000000000000.1"	[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]	47330370277129322496000000000000000000000000	"32T34"	[4]
"32.0.352701833122210710593389803720131611763844129.1"	[1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1]	352701833122210710593389803720131611763844129	"32T32"	[5]
"32.0.515207889456069254383620937908064472169867121.1"	[79, 264, 1626, 2074, 1466, -4990, -6940, -13445, -319, -2318, 13232, 5659, 18165, 194, 17256, -3062, 12591, -5501, 12053, -10628, 13240, -10830, 9744, -6238, 4413, -2247, 1255, -519, 220, -73, 22, -5, 1]	515207889456069254383620937908064472169867121	"32T402"	[]
"32.0.4722366482869645213696000000000000000000000000.1"	[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1]	4722366482869645213696000000000000000000000000	"32T36"	[5]
"32.0.5512695749115635425536000000000000000000000000.1"	[1, 0, 1, 0, -14, 0, -103, 0, 62, 0, 736, 0, 1892, 0, 4382, 0, 7111, 0, 4382, 0, 1892, 0, 736, 0, 62, 0, -103, 0, -14, 0, 1, 0, 1]	5512695749115635425536000000000000000000000000	"32T262"	[2, 4]
"32.0.7669926418924454281216000000000000000000000000.1"	[65536, -131072, 163840, -163840, 139264, -65536, -8192, 57344, -78848, 77824, -56320, 30208, -8576, -5376, 11840, -12352, 9744, -6176, 2960, -672, -536, 944, -880, 608, -308, 112, -8, -32, 34, -20, 10, -4, 1]	7669926418924454281216000000000000000000000000	"32T204"	[5]
"32.0.14648040110065267094876580444599852735215435776.1"	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]	14648040110065267094876580444599852735215435776	"32T37"	[3, 3]
"32.0.14680252274932068764306928624388060814210236416.1"	[65536, 0, -65536, 0, 40960, 0, -32768, 0, 21248, 0, -13312, 0, 7328, 0, -3824, 0, 2113, 0, -956, 0, 458, 0, -208, 0, 83, 0, -32, 0, 10, 0, -4, 0, 1]	14680252274932068764306928624388060814210236416	"32T12882"	[4]
"32.0.23790908696561643372461609312578223409406672896.1"	[65536, 0, -131072, 0, 131072, 0, -81920, 0, 32512, 0, -5120, 0, -3584, 0, 3744, 0, -2175, 0, 936, 0, -224, 0, -80, 0, 127, 0, -80, 0, 32, 0, -8, 0, 1]	23790908696561643372461609312578223409406672896	"32T262"	[12]
"32.0.35190667333271321019306672876612934335729762304.1"	[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1]	35190667333271321019306672876612934335729762304	"32T32"	[8]
"32.0.87993561227221187133696000000000000000000000000.1"	[65536, 0, -81920, 0, 77824, 0, -71680, 0, 55040, 0, -37760, 0, 23456, 0, -13360, 0, 7009, 0, -3340, 0, 1466, 0, -590, 0, 215, 0, -70, 0, 19, 0, -5, 0, 1]	87993561227221187133696000000000000000000000000	"32T262"	[4, 4]
"32.0.366225584701948244050176000000000000000000000000.1"	[65536, 0, -49152, 0, 16384, 0, -9216, 0, 6912, 0, -5952, 0, 3008, 0, -1116, 0, 581, 0, -279, 0, 188, 0, -93, 0, 27, 0, -9, 0, 4, 0, -3, 0, 1]	366225584701948244050176000000000000000000000000	"32T34"	NULL
"32.0.520402924666472696020370152488960000000000000000.1"	[1, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 0, 0, 2208, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 0, 0, 1]	520402924666472696020370152488960000000000000000	"32T34"	[20]
"32.0.550026747803854214004736000000000000000000000000.1"	[1, 0, 0, 0, 6, 0, 0, 0, 315, 0, 0, 0, -2036, 0, 0, 0, 5109, 0, 0, 0, -2036, 0, 0, 0, 315, 0, 0, 0, 6, 0, 0, 0, 1]	550026747803854214004736000000000000000000000000	"32T262"	[3, 6]
"32.0.845222867573683465013147373404160000000000000000.1"	[1, 0, -6, -64, 18, 120, 884, 1360, 2453, -592, 11300, 12152, -15370, 39248, 6590, -25344, 75876, -25344, 6590, 39248, -15370, 12152, 11300, -592, 2453, 1360, 884, 120, 18, -64, -6, 0, 1]	845222867573683465013147373404160000000000000000	"32T273"	[4, 4]
"32.0.1033818800357475102568684143000990752577071087616.1"	[65536, -131072, 131072, -131072, 102400, -49152, 24576, -10240, 0, -4608, 9728, -8192, 6800, -4672, 1184, 8, 113, 4, 296, -584, 425, -256, 152, -36, 0, -20, 24, -24, 25, -16, 8, -4, 1]	1033818800357475102568684143000990752577071087616	"32T12882"	[3, 6]
"32.0.1156745857256138299057661301456078800598048178176.1"	[1679616, 3359232, 3919104, 0, -3545856, -4385664, -62208, 3872448, 4596912, 1407456, -1681344, -2309040, -662400, 758160, 1107228, 443172, 96553, -135456, 12262, -21776, 37676, -11384, 7684, -5760, 2547, -876, 604, -208, 56, -28, 10, 0, 1]	1156745857256138299057661301456078800598048178176	"32T1016"	[2, 6]
"32.0.1250223652010309685753479160887484565582275390625.1"	[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, -987, 610, -377, 233, -144, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1]	1250223652010309685753479160887484565582275390625	"32T32"	[17]
"32.0.1461501637330902918203684832716283019655932542976.1"	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]	1461501637330902918203684832716283019655932542976	"32T32"	[17]
"32.2.1478570811461626154162295475745342334411977277407.1"	[-1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]	-1478570811461626154162295475745342334411977277407	"32T2801324"	[]
"32.0.2294081869728198830572049522437155246734619140625.1"	[3131, -7709, 25063, -54894, 79930, -97500, 157773, -215882, 132237, -50246, 366311, -946897, 1021466, -315448, -441722, 581095, -229142, -149755, 359728, -419617, 387026, -307078, 211471, -127199, 67152, -30713, 12498, -4335, 1315, -336, 68, -11, 1]	2294081869728198830572049522437155246734619140625	"32T402"	[]
"32.0.5037920877776643425304576000000000000000000000000.1"	[65536, -65536, 49152, -16384, 0, -24576, 17408, -12288, 768, 1024, 6464, -4096, 3328, -272, 156, -1452, 877, -726, 39, -34, 208, -128, 101, 8, 3, -24, 17, -12, 0, -2, 3, -2, 1]	5037920877776643425304576000000000000000000000000	"32T204"	[4, 4]
"32.0.6142666889587199870339155304469168186187744140625.1"	[16531, -166271, 868340, -3036857, 7973462, -17496051, 32429638, -51698016, 74479117, -94103904, 110357640, -113727761, 110710129, -94829103, 77474162, -55684805, 38310126, -23161945, 13440516, -6839883, 3366820, -1445800, 612551, -222738, 83386, -25571, 8745, -2191, 699, -130, 38, -4, 1]	6142666889587199870339155304469168186187744140625	"32T402"	[]
"32.0.6649076259173893054484111016591360000000000000000.1"	[1, -4, 20, -80, 264, -916, 3860, -13676, 42617, -119572, 258862, -535544, 1173576, -2095500, 2866688, -2949980, 2225756, -1090772, 309318, -53384, 4242, 20712, -31738, 23304, -9359, 844, 1264, -712, 178, -40, 22, -8, 1]	6649076259173893054484111016591360000000000000000	"32T273"	[2, 12]
"32.0.7790452574060543254749837160138952789467349385216.1"	[48016, -506176, 2744800, -9914240, 26721528, -57484000, 103163456, -160135088, 222647745, -285681476, 344722538, -394223580, 426399702, -431986068, 405080242, -348358772, 273242634, -194983784, 126485556, -74587072, 39982438, -19473044, 8605010, -3440780, 1239490, -399684, 114266, -28580, 6134, -1096, 156, -16, 1]	7790452574060543254749837160138952789467349385216	"32T1016"	[2, 12]
"32.0.8779518136340480467664896000000000000000000000000.1"	[65536, 0, 0, 0, 53248, 0, 0, 0, 19968, 0, 0, 0, 5696, 0, 0, 0, 1505, 0, 0, 0, 356, 0, 0, 0, 78, 0, 0, 0, 13, 0, 0, 0, 1]	8779518136340480467664896000000000000000000000000	"32T262"	[2, 2, 8]
"32.0.36539993586348786372837376000000000000000000000000.1"	[65536, 0, 0, 0, -4096, 0, 0, 0, -3840, 0, 0, 0, 496, 0, 0, 0, 209, 0, 0, 0, 31, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1]	36539993586348786372837376000000000000000000000000	"32T34"	NULL
"32.0.42655280577413385127292283461599409580230712890625.1"	[256, -5760, 88384, -823424, 5444944, -7358464, 7858456, -15762104, 15430857, -9966741, 15573178, -12326083, 4092091, -6468687, 4807173, -126545, 909785, -1040496, -200297, 80587, 145847, 7049, -33617, -6234, 5076, 1761, -822, -256, 110, 32, -14, -2, 1]	42655280577413385127292283461599409580230712890625	"32T262"	NULL
"32.0.44580746322432044939368312527587514829553937678336.1"	[65536, 0, 32768, 0, 36864, 0, 4096, 0, 6656, 0, -2880, 0, 160, 0, -1612, 0, -171, 0, -403, 0, 10, 0, -45, 0, 26, 0, 4, 0, 9, 0, 2, 0, 1]	44580746322432044939368312527587514829553937678336	"32T405"	[2, 10]
"32.0.51922968585348276285304963292200960000000000000000.1"	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2207, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]	51922968585348276285304963292200960000000000000000	"32T37"	[17]
"32.0.59647719207059933350876409342295283657151229198336.1"	[65536, 0, -16384, 0, 4096, 0, -8192, 0, 5120, 0, -1024, 0, 512, 0, -512, 0, 64, 0, -128, 0, 32, 0, -16, 0, 20, 0, -8, 0, 1, 0, -1, 0, 1]	59647719207059933350876409342295283657151229198336	"32T34907"	[2, 8]
"32.0.90220386589172305242198553166127486468521067544576.1"	[65536, 0, 0, 0, -16384, 0, 0, 0, 5632, 0, 0, 0, -576, 0, 0, 0, 209, 0, 0, 0, -36, 0, 0, 0, 22, 0, 0, 0, -4, 0, 0, 0, 1]	90220386589172305242198553166127486468521067544576	"32T96908"	[24]
"32.0.97424180758632937220739951448553101324025212174336.1"	[65536, 0, 0, 0, -40960, 0, 0, 0, 6912, 0, 0, 0, 2400, 0, 0, 0, -1215, 0, 0, 0, 150, 0, 0, 0, 27, 0, 0, 0, -10, 0, 0, 0, 1]	97424180758632937220739951448553101324025212174336	"32T96908"	[2, 8]
"32.0.111539154030155436264757885742310633531656776974336.1"	[65536, 0, 114688, 0, 94208, 0, 38912, 0, 2816, 0, -6016, 0, -2976, 0, -96, 0, 385, 0, -24, 0, -186, 0, -94, 0, 11, 0, 38, 0, 23, 0, 7, 0, 1]	111539154030155436264757885742310633531656776974336	"32T96908"	[3, 6]
"32.0.113341328678310292663197722067951895712000278265856.1"	[65536, 0, 0, 0, 0, 0, 0, 0, 7936, 0, 0, 0, 0, 0, 0, 0, 705, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 1]	113341328678310292663197722067951895712000278265856	"32T34"	[4, 4, 4]
"32.0.126945864674316252168838917102904812361796913463296.1"	[65536, 0, 32768, 0, 4096, 0, -6144, 0, -7168, 0, -3712, 0, 144, 0, 920, 0, 593, 0, 230, 0, 9, 0, -58, 0, -28, 0, -6, 0, 1, 0, 2, 0, 1]	126945864674316252168838917102904812361796913463296	"32T96908"	[12]
"32.0.133516116647406931991162570051420160000000000000000.1"	[65536, 65536, -262144, -196608, 577536, 245760, -872448, 35840, 1079296, -637184, -1000960, 1515008, 732752, -2163488, -441520, 1973876, 284105, -986938, -110380, 270436, 45797, -47344, -15640, 4978, 4216, -70, -852, -120, 141, 24, -16, -2, 1]	133516116647406931991162570051420160000000000000000	"32T12882"	[20]
"32.0.170408552095468407540899423358812160000000000000000.1"	[1, 0, -24, 0, 407, 0, -3048, 0, 15745, 0, -51120, 0, 120578, 0, -196608, 0, 236974, 0, -196608, 0, 120578, 0, -51120, 0, 15745, 0, -3048, 0, 407, 0, -24, 0, 1]	170408552095468407540899423358812160000000000000000	"32T273"	[2, 4, 8]
"32.0.184085596562491198850839682056048266622946116632576.1"	[16, 0, -1184, 0, 81152, 0, -452512, 0, 1644300, 0, -3494768, 0, 5324752, 0, -5310988, 0, 3886261, 0, -2005384, 0, 769870, 0, -205348, 0, 40319, 0, -5304, 0, 502, 0, -28, 0, 1]	184085596562491198850839682056048266622946116632576	"32T273"	NULL
"32.0.272292877590407567597186433188495333554574218609249.1"	[65536, -32768, -16384, 24576, -4096, -10240, 7168, 1536, -4352, 1408, 1472, -1440, -16, 728, -356, -186, 271, -93, -89, 91, -1, -45, 23, 11, -17, 3, 7, -5, -1, 3, -1, -1, 1]	272292877590407567597186433188495333554574218609249	"32T32"	[3, 15]
"32.0.301756981416745756154944013144439800625000000000000.1"	[1, 0, 49, 0, 959, 0, 10001, 0, 63092, 0, 257219, 0, 701262, 0, 1296861, 0, 1627006, 0, 1370784, 0, 763587, 0, 277346, 0, 65207, 0, 9779, 0, 899, 0, 46, 0, 1]	301756981416745756154944013144439800625000000000000	"32T96908"	[18]
"32.0.334285232879825411498534254159851729760457815228416.1"	[65536, 0, -16384, 0, -12288, 0, 20480, 0, -3072, 0, -4096, 0, 2560, 0, 256, 0, -704, 0, 64, 0, 160, 0, -64, 0, -12, 0, 20, 0, -3, 0, -1, 0, 1]	334285232879825411498534254159851729760457815228416	"32T34907"	[4, 4]
"32.0.351509915919708142388734226325389286150171856470016.1"	[65536, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 1024, 0, 0, 0, 16, 0, 0, 0, 64, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1]	351509915919708142388734226325389286150171856470016	"32T96908"	[2, 24]
"32.0.361280028614042283247927296000000000000000000000000.1"	[65536, 0, 32768, 0, -229376, 0, -843776, 0, 253952, 0, 1507328, 0, 1937408, 0, 2243584, 0, 1820416, 0, 560896, 0, 121088, 0, 23552, 0, 992, 0, -824, 0, -56, 0, 2, 0, 1]	361280028614042283247927296000000000000000000000000	"32T262"	NULL
"32.0.361280028614042283247927296000000000000000000000000.2"	[65536, 0, -32768, 0, -229376, 0, 843776, 0, 253952, 0, -1507328, 0, 1937408, 0, -2243584, 0, 1820416, 0, -560896, 0, 121088, 0, -23552, 0, 992, 0, 824, 0, -56, 0, -2, 0, 1]	361280028614042283247927296000000000000000000000000	"32T262"	NULL
"32.0.368622913612148362854567389427658855145582683488256.1"	[65536, 0, 0, 0, -24576, 0, 0, 0, 12544, 0, 0, 0, -3968, 0, 0, 0, 1072, 0, 0, 0, -248, 0, 0, 0, 49, 0, 0, 0, -6, 0, 0, 0, 1]	368622913612148362854567389427658855145582683488256	"32T96908"	[4, 8]
"32.0.385049567410499609358247677435067162906957579288576.1"	[65536, 0, 0, 0, 0, 0, 0, 0, 10240, 0, 0, 0, 256, 0, 0, 0, 784, 0, 0, 0, 16, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 1]	385049567410499609358247677435067162906957579288576	"32T96908"	[2, 20]
"32.0.480960519379403029833827263813614000556122650443776.1"	[4096, 0, -25856, 0, 145744, 0, -228564, 0, 364625, 0, 1345276, 0, 788932, 0, 772588, 0, 1013620, 0, 567784, 0, 212422, 0, 58148, 0, 12276, 0, 1948, 0, 236, 0, 20, 0, 1]	480960519379403029833827263813614000556122650443776	"32T1369"	[2, 2, 4]
"32.0.480960519379403029833827263813614000556122650443776.2"	[65536, 0, 0, 0, 12288, 0, 0, 0, 3328, 0, 0, 0, -1728, 0, 0, 0, -384, 0, 0, 0, -108, 0, 0, 0, 13, 0, 0, 0, 3, 0, 0, 0, 1]	480960519379403029833827263813614000556122650443776	"32T1369"	[2, 4, 8]
"32.0.506364211574415072751124736000000000000000000000000.1"	[43046721, 0, -23914845, 0, 4782969, 0, -590490, 0, 328050, 0, -411885, 0, 141426, 0, -10170, 0, -911, 0, -1130, 0, 1746, 0, -565, 0, 50, 0, -10, 0, 9, 0, -5, 0, 1]	506364211574415072751124736000000000000000000000000	"32T34"	NULL
"32.0.521143114025817015981290920201678636397399841439744.1"	[65536, 0, 0, 0, -28672, 0, 0, 0, 6144, 0, 0, 0, -256, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 24, 0, 0, 0, -7, 0, 0, 0, 1]	521143114025817015981290920201678636397399841439744	"32T34907"	[2, 20]
"32.0.626252666869320322751622400249765248287881461497856.1"	[65536, 0, 81920, 0, 65536, 0, 52224, 0, 33536, 0, 19904, 0, 10752, 0, 5444, 0, 2837, 0, 1361, 0, 672, 0, 311, 0, 131, 0, 51, 0, 16, 0, 5, 0, 1]	626252666869320322751622400249765248287881461497856	"32T96908"	[3, 18]
"32.0.680862905186642025391905387356033384799957275390625.1"	[3748096, -8688768, 21055936, 383680, -11479280, 66031424, 14753584, -4659656, 64804449, 9083451, -8901272, 28791815, 1283719, -5748567, 7359921, -77015, -1565509, 1133286, -41579, -218141, 93791, -2629, -13895, 2352, 516, 147, -138, -10, 44, 8, -8, -2, 1]	680862905186642025391905387356033384799957275390625	"32T262"	NULL
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"32.32.831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584.1"	[240995744399752167424, 0, -49745288366826373251072, 0, 48051441417099604000768, 0, -18739384249084437397504, 0, 3998386793367549003776, 0, -528064707395448537088, 0, 46047616638423365632, 0, -2752494320298371072, 0, 115298322894561920, 0, -3423975146786304, 0, 72306877326272, 0, -1079916548608, 0, 11227573554, 0, -78801680, 0, 353012, 0, -904, 0, 1]	831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584	"32T32"	NULL
"32.0.831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584.2"	[1209030011632139370496, 0, 4590478625271774707712, 0, 6280858905711056912384, 0, 3962743364006231474176, 0, 1314265101161494005760, 0, 246961996020229144576, 0, 28004045738135779328, 0, 2020101664070936576, 0, 96323589064542848, 0, 3114152216866304, 0, 69250740465600, 0, 1063425274368, 0, 11190491474, 0, 78801680, 0, 353012, 0, 904, 0, 1]	831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584	"32T32"	NULL
"32.32.831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584.2"	[1209030011632139370496, 0, -4590478625271774707712, 0, 6280858905711056912384, 0, -3962743364006231474176, 0, 1314265101161494005760, 0, -246961996020229144576, 0, 28004045738135779328, 0, -2020101664070936576, 0, 96323589064542848, 0, -3114152216866304, 0, 69250740465600, 0, -1063425274368, 0, 11190491474, 0, -78801680, 0, 353012, 0, -904, 0, 1]	831903146322634124221214929623812218283060654712060701163984567311040840781063324015250161568579584	"32T32"	NULL
"32.0.5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064.1"	[3005547753963360420864, 0, 581099826970367262867456, 0, 27788949410010109232449536, 0, 8084956200454215674984448, 0, 1036279984343418281996928, 0, 77318651468496620524032, 0, 3750965595972381826368, 0, 125383124563415370432, 0, 2987601946947833858, 0, 51750095490682048, 0, 657415158681936, 0, 6118148162400, 0, 41199330324, 0, 195254560, 0, 617288, 0, 1168, 0, 1]	5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064	"32T32"	NULL
"32.32.5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064.1"	[3005547753963360420864, 0, -581099826970367262867456, 0, 27788949410010109232449536, 0, -8084956200454215674984448, 0, 1036279984343418281996928, 0, -77318651468496620524032, 0, 3750965595972381826368, 0, -125383124563415370432, 0, 2987601946947833858, 0, -51750095490682048, 0, 657415158681936, 0, -6118148162400, 0, 41199330324, 0, -195254560, 0, 617288, 0, -1168, 0, 1]	5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064	"32T32"	NULL
"32.0.5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064.2"	[140890065637712393622979584, 0, 125814042129155638607364096, 0, 46302266793723571149244416, 0, 9141271606732160949516288, 0, 1066240865023966627648128, 0, 77785294455209635287552, 0, 3755032211125145464128, 0, 125401739610204142272, 0, 2987636824483752578, 0, 51750095490682048, 0, 657415158681936, 0, 6118148162400, 0, 41199330324, 0, 195254560, 0, 617288, 0, 1168, 0, 1]	5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064	"32T32"	NULL
"32.32.5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064.2"	[140890065637712393622979584, 0, -125814042129155638607364096, 0, 46302266793723571149244416, 0, -9141271606732160949516288, 0, 1066240865023966627648128, 0, -77785294455209635287552, 0, 3755032211125145464128, 0, -125401739610204142272, 0, 2987636824483752578, 0, -51750095490682048, 0, 657415158681936, 0, -6118148162400, 0, 41199330324, 0, -195254560, 0, 617288, 0, -1168, 0, 1]	5442261406515589291321596591218789141599788813151150062710195322968759992351928851104472008767832064	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.1"	[105194573767543703834051584, 0, -8645985970118701314224128, 0, 5348961089930445726109696, 0, 137768670165066521585664, 0, -7875190204005596861760, 0, -159762604238239890048, 0, 5616497958943019648, 0, 56569304351346688, 0, -1241694829126527, 0, 20467120067776, 0, 397479199520, 0, -3182195712, 0, 67646320, 0, 668960, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.2"	[105194573767543703834051584, 0, 8645985970118701314224128, 0, 5348961089930445726109696, 0, -137768670165066521585664, 0, -7875190204005596861760, 0, 159762604238239890048, 0, 5616497958943019648, 0, -56569304351346688, 0, -1241694829126527, 0, -20467120067776, 0, 397479199520, 0, 3182195712, 0, 67646320, 0, -668960, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.3"	[172106046928129856823215104, 0, -43304195669219607210045440, 0, 1713273184572230074339328, 0, 142716645484273807321088, 0, 11779462339012145662656, 0, 348180471848062060928, 0, 8238122216285532800, 0, 41708390284288000, 0, -1231632350452607, 0, -27983144302176, 0, 244924491488, 0, 5427297792, 0, 30564240, 0, -253120, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.4"	[172106046928129856823215104, 0, 43304195669219607210045440, 0, 1713273184572230074339328, 0, -142716645484273807321088, 0, 11779462339012145662656, 0, -348180471848062060928, 0, 8238122216285532800, 0, -41708390284288000, 0, -1231632350452607, 0, 27983144302176, 0, 244924491488, 0, -5427297792, 0, 30564240, 0, 253120, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.5"	[192612372193733665992871936, 0, 0, 0, -2751009896936244696428544, 0, 0, 0, 12170092609392305546240, 0, 0, 0, -3172285331085406272, 0, 0, 0, 1413951363692353, 0, 0, 0, 315639721536, 0, 0, 0, 114690480, 0, 0, 0, 10848, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.6"	[192612372193733665992871936, 0, 0, 0, -1074969943538558594150400, 0, 0, 0, 10475430451239695592448, 0, 0, 0, 9446209485753265344, 0, 0, 0, 3007181686554433, 0, 0, 0, 53983889568, 0, 0, 0, -55850928, 0, 0, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.7"	[192612372193733665992871936, 0, 0, 0, 1074969943538558594150400, 0, 0, 0, 10475430451239695592448, 0, 0, 0, -9446209485753265344, 0, 0, 0, 3007181686554433, 0, 0, 0, -53983889568, 0, 0, 0, -55850928, 0, 0, 0, 0, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344.8"	[192612372193733665992871936, 0, 0, 0, 2751009896936244696428544, 0, 0, 0, 12170092609392305546240, 0, 0, 0, 3172285331085406272, 0, 0, 0, 1413951363692353, 0, 0, 0, -315639721536, 0, 0, 0, 114690480, 0, 0, 0, -10848, 0, 0, 0, 1]	13310450341162145987539438873980995492528970475392971218623753076976653452497013184244002585097273344	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.1"	[8368626754430176210966081, 0, -9273644871689610293503104, 0, 31967164650479276500623360, 0, -135511562408327475865824, 0, 132027200946976063168512, 0, -36073149285512263680, 0, 208844512772613825024, 0, 22877441200857600, 0, 90477857262529536, 0, 3830317400448, 0, 16915778705664, 0, 132500256, 0, 1505591712, 0, 0, 0, 63072, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.2"	[8368626754430176210966081, 0, 9273644871689610293503104, 0, 31967164650479276500623360, 0, 135511562408327475865824, 0, 132027200946976063168512, 0, 36073149285512263680, 0, 208844512772613825024, 0, -22877441200857600, 0, 90477857262529536, 0, -3830317400448, 0, 16915778705664, 0, -132500256, 0, 1505591712, 0, 0, 0, 63072, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.3"	[216317825448498953815533121, 0, -75919451031925326781232256, 0, 18445431090394568952668160, 0, -2016990705778227171669216, 0, 161828803688086576392192, 0, -530790625201109022720, 0, 205970071044422490624, 0, 336625206241190400, 0, 90512734798448256, 0, 56360384606592, 0, 16915778705664, 0, 1949646624, 0, 1505591712, 0, 0, 0, 63072, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.4"	[216317825448498953815533121, 0, 75919451031925326781232256, 0, 18445431090394568952668160, 0, 2016990705778227171669216, 0, 161828803688086576392192, 0, 530790625201109022720, 0, 205970071044422490624, 0, -336625206241190400, 0, 90512734798448256, 0, -56360384606592, 0, 16915778705664, 0, -1949646624, 0, 1505591712, 0, 0, 0, 63072, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.5"	[650377879817809571042122834561, 0, 0, 0, 0, 0, 0, 0, -41330679705366071785824, 0, 0, 0, 0, 0, 0, 0, 2257750125127488, 0, 0, 0, 0, 0, 0, 0, -51249504, 0, 0, 0, 0, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.6"	[650377879817809571042122834561, 0, 0, 0, 0, 0, 0, 0, -2808881145024878665056, 0, 0, 0, 0, 0, 0, 0, -938428734096192, 0, 0, 0, 0, 0, 0, 0, -3482976, 0, 0, 0, 0, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.7"	[650377879817809571042122834561, 0, 0, 0, 0, 0, 0, 0, 2808881145024878665056, 0, 0, 0, 0, 0, 0, 0, -938428734096192, 0, 0, 0, 0, 0, 0, 0, 3482976, 0, 0, 0, 0, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL
"32.0.21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256.8"	[650377879817809571042122834561, 0, 0, 0, 0, 0, 0, 0, 41330679705366071785824, 0, 0, 0, 0, 0, 0, 0, 2257750125127488, 0, 0, 0, 0, 0, 0, 0, 51249504, 0, 0, 0, 0, 0, 0, 0, 1]	21769045626062357165286386364875156566399155252604600250840781291875039969407715404417888035071328256	"32T32"	NULL


# Label --
#    Each (global) number field has a unique label of the form d.r.D.i where
#    <ul>
#    <li>\(d\) is the degree;
#    <li>\(r\) is the real signature;  the full signature is therefore \([r,(d-r)/2]\);
#    <li>\(D\) is the absolute value of the discriminant;
#    <li>\(i\) is the index, counting from 1.  This is in case there is more than one
#      field with the same signature and absolute value of the
#      discriminant: for example <a href="/NumberField/4.0.1008.1">4.0.1008.1</a> and <a href="/NumberField/4.0.1008.2">4.0.1008.2</a>.
#    </ul>
#    The discriminant portion of the label can take the form \(a_1\) e \(\epsilon_1\) _ \(a_2\) e \(\epsilon_2\) _ \(\cdots\) _ \(a_k\) e \(\epsilon_k\) to mean the absolute value of the
#    discriminant equals \(a_1^{\epsilon_1}a_2^{\epsilon_2}\cdots a_k^{\epsilon_k}\).  The separators are the letter e and the underscore symbol.


#Polynomial (coeffs) --
#    A **defining polynomial** of a number field $K$ is an irreducible polynomial $f\in\Q[x]$ such that $K\cong \mathbb{Q}(a)$, where $a$ is a root of $f(x)$. Equivalently, it is a polynomial $f\in \Q[x]$ such that $K \cong \Q[x]/(f)$.

#    A root \(a \in K\) of the defining polynomial is a generator of \(K\).




#Discriminant (disc) --
#    The **discriminant** of a number field $K$ is the square of the determinant of the matrix
#    \[
#    \left( \begin{array}{ccc}
#     \sigma_1(\beta_1) & \cdots & \sigma_1(\beta_n) \\
#    \vdots & & \vdots \\
#    \sigma_n(\beta_1) & \cdots & \sigma_n(\beta_n) \\
#    \end{array} \right)
#    \]
#    where $\sigma_1,..., \sigma_n$ are the embeddings of $K$ into the complex numbers $\mathbb{C}$, and $\{\beta_1, \ldots, \beta_n\}$ is an integral basis for the ring of integers of $K$.

#    The discriminant of $K$ is a non-zero integer divisible exactly by the primes which ramify in $K$.



#Galois group (galois_label) --
#    Let $K$ be a finite degree $n$ separable extension of a field $F$, and $K^{gal}$ be its
#    Galois (or normal) closure.
#    The **Galois group** for $K/F$ is the automorphism group $\Aut(K^{gal}/F)$.

#    This automorphism group acts on the $n$ embeddings $K\hookrightarrow K^{gal}$ via composition.  As a result, we get an injection $\Aut(K^{gal}/F)\hookrightarrow S_n$, which is well-defined up to the labelling of the $n$ embeddings, which corresponds to being well-defined up to conjugation in $S_n$.

#    We use the notation $\Gal(K/F)$ for $\Aut(K/F)$ when $K=K^{gal}$.

#    There is a naming convention for Galois groups up to degree $47$.





#Class group (class_group) --
#    The **ideal class group** of a number field $K$ with ring of integers $O_K$ is the group of equivalence classes of ideals, given by the quotient of the multiplicative group of all fractional ideals of $O_K$ by the subgroup of principal fractional ideals.

#    Since $K$ is a number field, the ideal class group of $K$ is a finite abelian group, and so has the structure of a product of cyclic groups encoded by a finite list $[a_1,\dots,a_n]$, where the $a_i$ are positive integers with $a_i\mid a_{i+1}$ for $1\leq i < n$.