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hmf_forms • Show schema
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{'deg': 2, 'dimension': 2, 'disc': 437, 'field_bad_primes': [19, 23], 'field_label': '2.2.437.1', 'is_CM': 'yes', 'is_base_change': 'no', 'label': '2.2.437.1-1.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [], 'level_ideal': '[1, 1, 1]', 'level_label': '1.1', 'level_norm': 1, 'parallel_weight': 2, 'short_label': '1.1-b', 'weight': '[2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [], 'hecke_eigenvalues': [-2, -3, 0, 4, -9, 0, 0, 'e', '-e + 13', -5, 0, 0, 0, 0, '-3*e + 25', '3*e - 14', 0, 0, 0, 0, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 3, '5*e - 29', '-5*e + 36', '-5*e + 37', '5*e - 28', '-2*e + 25', '2*e - 1', -13, 0, 0, '4*e - 15', '-4*e + 37', 0, 0, '-7*e + 46', '7*e - 45', '7*e - 43', '-7*e + 48', 0, 0, 20, 20, 'e - 23', '-e - 10', 0, 0, 15, 0, 0, 'e + 11', '-e + 24', 0, 0, 37, 37, '3*e - 37', '-3*e + 2', '-8*e + 59', '8*e - 45', 0, 0, 0, 0, 0, 0, '9*e - 62', '-9*e + 55', 0, 0, 0, 0, 0, 0, 0, 0, '-7*e + 60', '7*e - 31', '5*e - 51', '-5*e + 14', 41, 41, '10*e - 61', '-10*e + 69', '5*e - 52', '-5*e + 13', 0, 0, 0, 0, '9*e - 46', '-9*e + 71', 0, 0, 0, 0, '11*e - 73', '-11*e + 70', '-11*e + 68', '11*e - 75', 34, 34, 0, 0, '-11*e + 63', '11*e - 80', '7*e - 66', '-7*e + 25', 0, 0, 0, 0, 0, 0, -35, -35, 49, 49, '-7*e + 23', '7*e - 68', 0, 0, 0, 0, '-e + 34', 'e + 21', 0, 0, 0, 0, 0, 0, 5, 5, -53, -53, '-13*e + 80', '13*e - 89', 0, 0, 0, 0, -29, 26, 26, '13*e - 92', '-13*e + 77', -51, -51, 0, 0, 0, 0, '8*e - 27', '-8*e + 77', 0, 0, '-14*e + 87', '14*e - 95', 0, 0, -31, '14*e - 85', '-14*e + 97', 0, 0, 0, 0, 0, 0, -63, -63], 'hecke_polynomial': 'x^2 - 13*x + 28', 'label': '2.2.437.1-1.1-b'}
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hmf_fields • Show schema
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{'degree': 2, 'discriminant': 437, 'ideals': ['[1, 1, 1]', '[4, 2, 2]', '[9, 3, 3]', '[16, 4, 4]', '[19, 19, -w - 9]', '[23, 23, w + 11]', '[25, 5, 5]', '[36, 6, 6]', '[37, 37, w + 8]', '[37, 37, -w + 9]', '[47, 47, w + 12]', '[47, 47, -w + 13]', '[49, 7, 7]', '[53, 53, -w - 7]', '[53, 53, w - 8]', '[64, 8, 8]', '[67, 67, -w - 6]', '[67, 67, w - 7]', '[73, 73, -w - 13]', '[73, 73, w - 14]', '[76, 38, -2*w - 18]', '[79, 79, -w - 5]', '[79, 79, w - 6]', '[81, 9, 9]', '[89, 89, -w - 4]', '[89, 89, w - 5]', '[92, 46, 2*w + 22]', '[97, 97, -w - 3]', '[97, 97, w - 4]', '[100, 10, 10]', '[101, 101, -w - 14]', '[101, 101, w - 15]', '[103, 103, -w - 2]', '[103, 103, w - 3]', '[107, 107, -w - 1]', '[107, 107, w - 2]', '[109, 109, -w]', '[109, 109, w - 1]', '[113, 113, 2*w - 19]', '[113, 113, -2*w - 17]', '[121, 11, -11]', '[131, 131, -w - 15]', '[131, 131, w - 16]', '[139, 139, 2*w - 25]', '[139, 139, 2*w + 23]', '[144, 12, 12]', '[148, 74, 2*w + 16]', '[148, 74, -2*w + 18]', '[163, 163, -w - 16]', '[163, 163, w - 17]', '[169, 13, -13]', '[171, 57, -3*w - 27]', '[181, 181, 2*w - 17]', '[181, 181, -2*w - 15]', '[188, 94, 2*w + 24]', '[188, 94, -2*w + 26]', '[196, 14, 14]', '[197, 197, -w - 17]', '[197, 197, w - 18]', '[207, 69, 3*w + 33]', '[212, 106, -2*w - 14]', '[212, 106, 2*w - 16]', '[225, 15, 15]', '[227, 227, 3*w - 29]', '[227, 227, -3*w - 26]', '[233, 233, -w - 18]', '[233, 233, w - 19]', '[239, 239, 2*w - 27]', '[239, 239, -2*w - 25]', '[241, 241, 2*w - 15]', '[241, 241, -2*w - 13]', '[256, 16, 16]', '[268, 134, -2*w - 12]', '[268, 134, 2*w - 14]', '[271, 271, -w - 19]', '[271, 271, w - 20]', '[277, 277, -4*w - 43]', '[277, 277, 4*w - 47]', '[281, 281, -3*w - 25]', '[281, 281, 3*w - 28]', '[289, 17, -17]', '[292, 146, -2*w - 26]', '[292, 146, 2*w - 28]', '[293, 293, 2*w - 13]', '[293, 293, -2*w - 11]', '[304, 76, -4*w - 36]', '[311, 311, -w - 20]', '[311, 311, w - 21]', '[316, 158, -2*w - 10]', '[316, 158, 2*w - 12]', '[324, 18, 18]', '[333, 111, 3*w + 24]', '[333, 111, -3*w + 27]', '[337, 337, 2*w - 11]', '[337, 337, -2*w - 9]', '[347, 347, 2*w - 29]', '[347, 347, -2*w - 27]', '[349, 349, -3*w - 35]', '[349, 349, 3*w - 38]', '[353, 353, -w - 21]', '[353, 353, w - 22]', '[356, 178, -2*w - 8]', '[356, 178, 2*w - 10]', '[361, 19, 19]', '[368, 92, 4*w + 44]', '[373, 373, 2*w - 9]', '[373, 373, -2*w - 7]', '[379, 379, -5*w - 46]', '[379, 379, 5*w - 51]', '[383, 383, 3*w - 26]', '[383, 383, -3*w - 23]', '[388, 194, -2*w - 6]', '[388, 194, 2*w - 8]', '[397, 397, -w - 22]', '[397, 397, w - 23]', '[400, 20, 20]', '[401, 401, 2*w - 7]', '[401, 401, -2*w - 5]', '[404, 202, -2*w - 28]', '[404, 202, 2*w - 30]', '[412, 206, -2*w - 4]', '[412, 206, 2*w - 6]', '[421, 421, 2*w - 5]', '[421, 421, -2*w - 3]', '[423, 141, 3*w + 36]', '[423, 141, -3*w + 39]', '[428, 214, -2*w - 2]', '[428, 214, 2*w - 4]', '[431, 431, -3*w - 22]', '[431, 431, 3*w - 25]', '[433, 433, 2*w - 3]', '[433, 433, -2*w - 1]', '[436, 218, -2*w]', '[436, 218, 2*w - 2]', '[437, 437, -2*w + 1]', '[441, 21, 21]', '[443, 443, -w - 23]', '[443, 443, w - 24]', '[452, 226, 4*w - 38]', '[452, 226, -4*w - 34]', '[461, 461, -5*w - 54]', '[461, 461, 5*w - 59]', '[463, 463, 2*w - 31]', '[463, 463, -2*w - 29]', '[475, 95, -5*w - 45]', '[477, 159, -3*w - 21]', '[477, 159, 3*w - 24]', '[484, 22, -22]', '[491, 491, -w - 24]', '[491, 491, w - 25]', '[499, 499, 3*w - 40]', '[499, 499, -3*w - 37]', '[521, 521, 3*w - 23]', '[521, 521, -3*w - 20]', '[523, 523, -4*w - 33]', '[523, 523, 4*w - 37]', '[524, 262, -2*w - 30]', '[524, 262, 2*w - 32]', '[529, 23, 23]', '[541, 541, -w - 25]', '[541, 541, w - 26]', '[556, 278, 4*w - 50]', '[556, 278, 4*w + 46]', '[563, 563, -3*w - 19]', '[563, 563, 3*w - 22]', '[569, 569, -6*w - 55]', '[569, 569, 6*w - 61]', '[575, 115, 5*w + 55]', '[576, 24, 24]', '[577, 577, -3*w - 38]', '[577, 577, 3*w - 41]', '[587, 587, 2*w - 33]', '[587, 587, -2*w - 31]', '[592, 148, 4*w + 32]', '[592, 148, -4*w + 36]', '[593, 593, -w - 26]', '[593, 593, w - 27]', '[603, 201, -3*w - 18]', '[603, 201, 3*w - 21]', '[625, 25, 25]', '[641, 641, 3*w - 20]', '[641, 641, -3*w - 17]', '[647, 647, -w - 27]', '[647, 647, w - 28]', '[652, 326, -2*w - 32]', '[652, 326, 2*w - 34]', '[653, 653, -4*w - 47]', '[653, 653, 4*w - 51]', '[657, 219, -3*w - 39]', '[657, 219, 3*w - 42]', '[659, 659, 4*w - 35]', '[659, 659, -4*w - 31]', '[661, 661, -5*w - 43]', '[661, 661, 5*w - 48]', '[676, 26, -26]', '[677, 677, -3*w - 16]', '[677, 677, 3*w - 19]', '[684, 114, -6*w - 54]', '[691, 691, -6*w - 65]', '[691, 691, 6*w - 71]', '[703, 703, w + 28]', '[703, 703, w - 29]', '[711, 237, -3*w - 15]', '[711, 237, 3*w - 18]', '[719, 719, 2*w - 35]', '[719, 719, -2*w - 33]', '[724, 362, 4*w - 34]', '[724, 362, -4*w - 30]', '[729, 27, 27]', '[739, 739, 3*w - 43]', '[739, 739, -3*w - 40]', '[743, 743, 3*w - 17]', '[743, 743, -3*w - 14]', '[751, 751, 5*w - 47]', '[751, 751, -5*w - 42]', '[752, 188, 4*w + 48]', '[752, 188, -4*w + 52]', '[761, 761, -w - 29]', '[761, 761, w - 30]', '[773, 773, -3*w - 13]', '[773, 773, 3*w - 16]', '[784, 28, 28]', '[787, 787, -4*w - 29]', '[787, 787, 4*w - 33]', '[788, 394, -2*w - 34]', '[788, 394, 2*w - 36]', '[797, 797, -7*w - 64]', '[797, 797, 7*w - 71]', '[801, 267, -3*w - 12]', '[801, 267, 3*w - 15]', '[809, 809, -5*w - 57]', '[809, 809, 5*w - 62]', '[821, 821, -w - 30]', '[821, 821, w - 31]', '[823, 823, -3*w - 41]', '[823, 823, 3*w - 44]', '[827, 827, 3*w - 14]', '[827, 827, -3*w - 11]', '[828, 138, 6*w + 66]', '[839, 839, -5*w - 41]', '[839, 839, 5*w - 46]', '[841, 29, -29]', '[848, 212, -4*w - 28]', '[848, 212, 4*w - 32]', '[851, 851, -3*w - 10]', '[851, 851, 3*w - 13]', '[853, 853, 4*w - 53]', '[853, 853, -4*w - 49]', '[859, 859, 2*w - 37]', '[859, 859, -2*w - 35]', '[873, 291, -3*w - 9]', '[873, 291, 3*w - 12]', '[883, 883, -w - 31]', '[883, 883, w - 32]', '[893, 893, -3*w + 11]', '[893, 893, -3*w - 8]', '[900, 30, 30]', '[907, 907, 4*w - 31]', '[907, 907, -4*w - 27]', '[908, 454, 6*w - 58]', '[908, 454, -6*w - 52]', '[909, 303, -3*w - 42]', '[909, 303, 3*w - 45]', '[911, 911, -3*w - 7]', '[911, 911, 3*w - 10]', '[925, 185, 5*w + 40]', '[925, 185, -5*w + 45]', '[927, 309, -3*w - 6]', '[927, 309, 3*w - 9]', '[929, 929, 5*w - 63]', '[929, 929, -5*w - 58]', '[931, 133, -7*w - 63]', '[932, 466, -2*w - 36]', '[932, 466, 2*w - 38]', '[941, 941, 3*w - 8]', '[941, 941, -3*w - 5]', '[947, 947, -w - 32]', '[947, 947, w - 33]', '[953, 953, -3*w - 4]', '[953, 953, 3*w - 7]', '[956, 478, 4*w - 54]', '[956, 478, -4*w - 50]', '[961, 31, -31]', '[963, 321, -3*w - 3]', '[963, 321, 3*w - 6]', '[964, 482, 4*w - 30]', '[964, 482, -4*w - 26]', '[967, 967, -7*w - 76]', '[967, 967, 7*w - 83]', '[971, 971, 3*w - 5]', '[971, 971, -3*w - 2]', '[977, 977, -3*w - 1]', '[977, 977, 3*w - 4]', '[981, 327, -3*w]', '[981, 327, 3*w - 3]', '[983, 983, 3*w - 2]', '[983, 983, 3*w - 1]', '[997, 997, 3*w - 46]', '[997, 997, -3*w - 43]', '[1007, 1007, 17*w + 172]', '[1007, 1007, -2*w - 37]', '[1009, 1009, 5*w - 44]', '[1009, 1009, -5*w - 39]', '[1013, 1013, -w - 33]', '[1013, 1013, w - 34]', '[1017, 339, 6*w - 57]', '[1017, 339, -6*w - 51]', '[1019, 1019, -4*w - 25]', '[1019, 1019, 4*w - 29]', '[1024, 32, 32]', '[1051, 1051, -5*w - 59]', '[1051, 1051, 5*w - 64]', '[1061, 1061, -4*w - 51]', '[1061, 1061, 4*w - 55]', '[1063, 1063, -8*w - 73]', '[1063, 1063, 8*w - 81]', '[1072, 268, -4*w - 24]', '[1072, 268, 4*w - 28]', '[1081, 1081, w + 34]', '[1081, 1081, -w + 35]', '[1084, 542, -2*w - 38]', '[1084, 542, 2*w - 40]', '[1087, 1087, -3*w - 44]', '[1087, 1087, 3*w - 47]', '[1089, 33, -33]', '[1091, 1091, -5*w - 38]', '[1091, 1091, 5*w - 43]', '[1108, 554, -8*w - 86]', '[1108, 554, 8*w - 94]', '[1123, 1123, 4*w - 27]', '[1123, 1123, -4*w - 23]', '[1124, 562, -6*w - 50]', '[1124, 562, 6*w - 56]', '[1127, 161, 7*w + 77]', '[1151, 1151, -w - 35]', '[1151, 1151, w - 36]', '[1156, 34, -34]', '[1163, 1163, 2*w - 41]', '[1163, 1163, -2*w - 39]', '[1168, 292, -4*w - 52]', '[1168, 292, 4*w - 56]', '[1171, 1171, 5*w - 42]', '[1171, 1171, -5*w - 37]', '[1172, 586, 4*w - 26]', '[1172, 586, -4*w - 22]', '[1175, 235, 5*w + 60]', '[1175, 235, -5*w + 65]', '[1179, 393, -3*w - 45]', '[1179, 393, 3*w - 48]', '[1193, 1193, 9*w - 92]', '[1193, 1193, -9*w - 83]', '[1216, 152, -8*w - 72]', '[1219, 1219, 4*w + 21]', '[1219, 1219, -19*w - 186]', '[1223, 1223, -w - 36]', '[1223, 1223, w - 37]', '[1225, 35, 35]', '[1229, 1229, -6*w - 49]', '[1229, 1229, 6*w - 55]', '[1244, 622, -2*w - 40]', '[1244, 622, 2*w - 42]', '[1249, 1249, -5*w - 36]', '[1249, 1249, 5*w - 41]', '[1251, 417, 6*w - 75]', '[1251, 417, 6*w + 69]', '[1264, 316, -4*w - 20]', '[1264, 316, 4*w - 24]', '[1273, 1273, 16*w + 163]', '[1273, 1273, -3*w - 46]', '[1277, 1277, 4*w - 57]', '[1277, 1277, -4*w - 53]', '[1289, 1289, -8*w - 87]', '[1289, 1289, 8*w - 95]', '[1296, 36, 36]', '[1297, 1297, -w - 37]', '[1297, 1297, w - 38]', '[1301, 1301, 5*w - 66]', '[1301, 1301, -5*w - 61]', '[1307, 1307, 4*w - 23]', '[1307, 1307, -4*w - 19]', '[1321, 1321, -7*w - 60]', '[1321, 1321, 7*w - 67]', '[1325, 265, -5*w - 35]', '[1325, 265, 5*w - 40]', '[1327, 1327, 2*w - 43]', '[1327, 1327, -2*w - 41]', '[1332, 222, 6*w + 48]', '[1332, 222, -6*w + 54]', '[1348, 674, 4*w - 22]', '[1348, 674, -4*w - 18]', '[1367, 1367, -9*w - 82]', '[1367, 1367, 9*w - 91]', '[1369, 37, 37]', '[1369, 1369, 3*w + 47]', '[1369, 1369, -3*w + 50]', '[1373, 1373, -w - 38]', '[1373, 1373, w - 39]', '[1387, 1387, 4*w + 17]', '[1387, 1387, 23*w + 226]', '[1388, 694, 4*w - 58]', '[1388, 694, -4*w - 54]', '[1396, 698, -6*w - 70]', '[1396, 698, 6*w - 76]', '[1399, 1399, 5*w - 39]', '[1399, 1399, -5*w - 34]', '[1412, 706, -2*w - 42]', '[1412, 706, 2*w - 44]', '[1424, 356, -4*w - 16]', '[1424, 356, 4*w - 20]', '[1429, 1429, -5*w - 62]', '[1429, 1429, 5*w - 67]', '[1433, 1433, 6*w - 53]', '[1433, 1433, -6*w - 47]', '[1444, 38, 38]', '[1447, 1447, 7*w - 66]', '[1447, 1447, -7*w - 59]', '[1451, 1451, -w - 39]', '[1451, 1451, w - 40]', '[1453, 1453, 9*w - 106]', '[1453, 1453, -9*w - 97]', '[1459, 1459, 4*w - 19]', '[1459, 1459, -4*w - 15]', '[1467, 489, -3*w - 48]', '[1467, 489, 3*w - 51]', '[1471, 1471, -5*w - 33]', '[1471, 1471, 5*w - 38]', '[1472, 184, 8*w + 88]', '[1492, 746, 4*w - 18]', '[1492, 746, -4*w - 14]', '[1499, 1499, 2*w - 45]', '[1499, 1499, -2*w - 43]', '[1501, 1501, -4*w - 55]', '[1501, 1501, 15*w + 154]', '[1516, 758, -10*w - 92]', '[1516, 758, 10*w - 102]', '[1521, 39, -39]', '[1523, 1523, -4*w - 13]', '[1523, 1523, 4*w - 17]', '[1531, 1531, -w - 40]', '[1531, 1531, w - 41]', '[1532, 766, 6*w - 52]', '[1532, 766, -6*w - 46]', '[1539, 171, -9*w - 81]', '[1541, 1541, -18*w - 175]', '[1541, 1541, 5*w + 32]', '[1543, 1543, -6*w - 71]', '[1543, 1543, -6*w + 77]', '[1552, 388, -4*w - 12]', '[1552, 388, 4*w - 16]', '[1559, 1559, 5*w - 68]', '[1559, 1559, -5*w - 63]', '[1567, 1567, 3*w - 52]', '[1567, 1567, -3*w - 49]', '[1571, 1571, 7*w - 65]', '[1571, 1571, -7*w - 58]', '[1579, 1579, 4*w - 15]', '[1579, 1579, -4*w - 11]', '[1588, 794, -2*w - 44]', '[1588, 794, 2*w - 46]', '[1600, 40, 40]', '[1604, 802, 4*w - 14]', '[1604, 802, -4*w - 10]', '[1609, 1609, -5*w - 31]', '[1609, 1609, 5*w - 36]', '[1613, 1613, -w - 41]', '[1613, 1613, w - 42]', '[1616, 404, -4*w - 56]', '[1616, 404, 4*w - 60]', '[1619, 1619, -7*w - 80]', '[1619, 1619, 7*w - 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5]', '[947, 947, -w - 32]', '[947, 947, w - 33]', '[953, 953, -3*w - 4]', '[953, 953, 3*w - 7]', '[961, 31, -31]', '[967, 967, -7*w - 76]', '[967, 967, 7*w - 83]', '[971, 971, 3*w - 5]', '[971, 971, -3*w - 2]', '[977, 977, -3*w - 1]', '[977, 977, 3*w - 4]', '[983, 983, 3*w - 2]', '[983, 983, 3*w - 1]', '[997, 997, 3*w - 46]', '[997, 997, -3*w - 43]']}
-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-109, -1, 1], 'conductor': 437, 'degree': 2, 'dirichlet_group': [1, 436], 'disc_abs': 437, 'disc_rad': 437, 'disc_sign': 1, 'frobs': [[2, [[2, 1]]], [3, [[2, 1]]], [5, [[2, 1]]], [7, [[2, 1]]], [11, [[2, 1]]], [13, [[2, 1]]], [17, [[2, 1]]], [19, [0]], [23, [0]], [29, [[2, 1]]], [31, [[2, 1]]], [37, [[1, 2]]], [41, [[2, 1]]], [43, [[2, 1]]], [47, [[1, 2]]], [53, [[1, 2]]], [59, [[2, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [1, 1], 'galois_label': '2T1', 'galt': 1, 'grd': 20.904544960366874, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '2.2.437.1', 'local_algs': ['19.2.1.1', '23.2.1.2'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [19, 23], 'rd': 20.9045449604, 'regulator': {'__RealLiteral__': 0, 'data': '3.04224711209', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 10 \\)'], 'used_grh': False, 'zk': ['1', 'a']}