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{'Lhash': '1989832928402813693062528666518,2166170139292235013926859178989,2373136125257294346902590481691,2593812353034066649788678549395,2763880772559155782417109590457,3556677351030296860969424123185,3773859297557801226916327527098', 'a10': 2, 'a2': -1, 'a3': -7, 'a4': -5, 'a5': -2, 'a6': 7, 'a7': -2, 'a8': 6, 'a9': 15, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12329.778755296511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [1, -7, 21, -35, 35, -21, 7, -1]], [37, [1, -7, 21, -35, 35, -21, 7, -1]]], 'bad_primes': [13, 37], 'central_character': '481.1', 'coefficient_field': '1.1.1.1', 'conductor': 5956834506121961761, 'conductor_radical': 481, 'degree': 14, 'euler_factors': [[1, 1, 6, 5, 21, 16, 53, 34, 106, 64, 168, 80, 192, 64, 128], [1, 7, 34, 121, 355, 875, 1864, 3451, 5592, 7875, 9585, 9801, 8262, 5103, 2187], [1, 2, 16, 22, 123, 185, 825, 1262, 4125, 4625, 15375, 13750, 50000, 31250, 78125], [1, 2, 34, 73, 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'7.29775392301994043172357571267411', '7.46684824293698616918403347983655', '7.47676878690145197437089978320831', '7.57334319588023570858520566416847', '7.80562051889622724065444808957225', '7.946968709403993303246986146978664', '8.052537593820012687649433094151675', '8.069286989841168785409957931674568', '8.196063691877125680524910621932307', '8.347228855022433806226624135401400', '8.354286797164363918461512198918677', '8.596419977108111480304995616079768', '8.792772587245437085764126526597183', '8.841045645309113032836488883150351', '9.073820902701203679968197054709259', '9.243545209601653983581162946895537', '9.394394045921235435410609677772389', '9.472443476251961303444211171242627', '9.489919679157236225742916978637499', '9.545436619500605792541830121483512', '9.879638486051324454524000289440601', '10.04536553088536880291415599566589', '10.07175621909680568518083124587622', '10.32569214427146780084717711852575', '10.32804048454174885953165044485340', '10.42982207616081320096669114336083', '10.55504319827059958880482049660614', '10.78069358667435013378073405744873', '10.81931024141484861516400646237796', '11.25539470527019072337343000687884'], 'prelabel': '14-481e7-1.1-c1e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9597970142909158, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e7-0', 'trace_hash': 192968607478820758, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56970140513842038242971126360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70880693694479774587298214227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.87207431198315367587987011933', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12329.778755296511, 'bad_primes': [13, 37], 'central_character': '1.1', 'conductor': 5956834506121961761, 'conductor_radical': 481, 'degree': 14, 'dirichlet_coefficients': [1, -1, -7, -5, -2, 7, -2, 6, 15, 2, -13, 35, 7, 2, 14, 8, -10, -15, -2, 10, 14, 13, -24, -42, -12, -7, 12, 10, -17, -14, -11, -14, 91, 10, 4, -75, 7, 2, -49, -12, -17, -14, -3, 65, -30, 24, -21, -56, -30, 12, 70, -35, -16, -12, 26, -12, 14, 17, -18, -70, -20, 11, -30, 4, -14, -91, 7, 50, 168, -4, -35, 90, 8, -7, 84, 10, 26, 49, -18, -16, -102, 17, 19, -70, 20, 3, 119, -78, -1, 30, -14, 120, 77, 21, 4, 98, 22, 30, -195, 60], 'euler11': [1, 13, 117, 771, 4280, 19827, 80807, 284641, 888877, 2399067, 5696680, 11288211, 18842967, 23030293, 19487171], 'euler13': [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, 10, 100, 704, 4339, 22855, 110667, 468484, 1881339, 6605095, 21317507, 58798784, 141985700, 241375690, 410338673], 'euler19': [1, 2, 48, 65, 998, 817, 19292, 11680, 366548, 294937, 6845282, 8470865, 118852752, 94091762, 893871739], 'euler2': [1, 1, 6, 5, 21, 16, 53, 34, 106, 64, 168, 80, 192, 64, 128], 'euler23': [1, 24, 363, 3854, 32657, 226567, 1347956, 6905418, 31002988, 119853943, 397337719, 1078507214, 2336392509, 3552861336, 3404825447], 'euler29': [1, 17, 253, 2656, 24177, 181967, 1209330, 6915074, 35070570, 153034247, 589652853, 1878538336, 5189320697, 10111996457, 17249876309], 'euler3': [1, 7, 34, 121, 355, 875, 1864, 3451, 5592, 7875, 9585, 9801, 8262, 5103, 2187], 'euler31': [1, 11, 142, 958, 7453, 35035, 226517, 956874, 7022027, 33668635, 222032323, 884733118, 4065339442, 9762540491, 27512614111], 'euler37': [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], 'euler41': [1, 17, 257, 2268, 19451, 122334, 863557, 5008487, 35405837, 205643454, 1340582371, 6408825948, 29775043657, 80751772097, 194754273881], 'euler43': [1, 3, 67, -84, 3983, 1809, 241186, 1010, 10370998, 3344841, 316676381, -287179284, 9849565681, 18964089147, 271818611107], 'euler47': [1, 21, 394, 4137, 40498, 260301, 1861770, 10356195, 87503190, 575004909, 4204623854, 20187240297, 90361932758, 226363521909, 506623120463], 'euler5': [1, 2, 16, 22, 123, 185, 825, 1262, 4125, 4625, 15375, 13750, 50000, 31250, 78125], 'euler53': [1, 16, 252, 2751, 30878, 264423, 2331890, 16858495, 123590170, 742764207, 4597024006, 21706713231, 105385264236, 354629778064, 1174711139837], 'euler59': [1, 18, 330, 3588, 43899, 382467, 3673733, 26502258, 216750247, 1331367627, 9015932721, 43477091268, 235925018670, 759249605538, 2488651484819], 'euler61': [1, 20, 335, 3204, 26819, 110665, 380210, -1267472, 23192810, 411784465, 6087403439, 44362074564, 282939760835, 1030407487220, 3142742836021], 'euler67': [1, -7, 310, -1658, 46408, -209174, 4535576, -17300046, 303883592, -938982086, 13957809304, -33410558618, 418538783170, -633208675183, 6060711605323], 'euler7': [1, 2, 34, 73, 568, 1135, 5978, 10119, 41846, 55615, 194824, 175273, 571438, 235298, 823543], 'euler71': [1, 35, 789, 12065, 151898, 1586239, 15235229, 131541155, 1081701259, 7996230799, 54365965078, 306591931265, 1423536957939, 4483509937235, 9095120158391], 'euler73': [1, -8, 400, -2997, 75506, -490305, 8580796, -45886359, 626398108, -2612835345, 29373117602, -85109528277, 829228637200, -1210673810312, 11047398519097], 'euler79': [1, 18, 400, 4755, 69218, 670773, 7626730, 62053274, 602511670, 4186294293, 34127173502, 185207635155, 1230822559600, 4375574199378, 19203908986159], 'euler83': [1, -19, 413, -5540, 83434, -896074, 10322407, -90798361, 856759781, -6173053786, 47706476558, -262919098340, 1626823785559, -6211867094011, 27136050989627], 'euler89': [1, 1, 108, -8, 17873, 44447, 1792625, 1317142, 159543625, 352064687, 12599910937, -501937928, 603078420492, 496981290961, 44231334895529], 'euler97': [1, -22, 681, -11326, 195623, -2537231, 31274594, -319248170, 3033635618, -23872806479, 178539830279, -1002682636606, 5847978715017, -18325384108438, 80798284478113], 'euler_factors': [[1, 1, 6, 5, 21, 16, 53, 34, 106, 64, 168, 80, 192, 64, 128], [1, 7, 34, 121, 355, 875, 1864, 3451, 5592, 7875, 9585, 9801, 8262, 5103, 2187], [1, 2, 16, 22, 123, 185, 825, 1262, 4125, 4625, 15375, 13750, 50000, 31250, 78125], [1, 2, 34, 73, 568, 1135, 5978, 10119, 41846, 55615, 194824, 175273, 571438, 235298, 823543], [1, 13, 117, 771, 4280, 19827, 80807, 284641, 888877, 2399067, 5696680, 11288211, 18842967, 23030293, 19487171], [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], [1, 10, 100, 704, 4339, 22855, 110667, 468484, 1881339, 6605095, 21317507, 58798784, 141985700, 241375690, 410338673], [1, 2, 48, 65, 998, 817, 19292, 11680, 366548, 294937, 6845282, 8470865, 118852752, 94091762, 893871739], [1, 24, 363, 3854, 32657, 226567, 1347956, 6905418, 31002988, 119853943, 397337719, 1078507214, 2336392509, 3552861336, 3404825447], [1, 17, 253, 2656, 24177, 181967, 1209330, 6915074, 35070570, 153034247, 589652853, 1878538336, 5189320697, 10111996457, 17249876309], [1, 11, 142, 958, 7453, 35035, 226517, 956874, 7022027, 33668635, 222032323, 884733118, 4065339442, 9762540491, 27512614111], [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], [1, 17, 257, 2268, 19451, 122334, 863557, 5008487, 35405837, 205643454, 1340582371, 6408825948, 29775043657, 80751772097, 194754273881], [1, 3, 67, -84, 3983, 1809, 241186, 1010, 10370998, 3344841, 316676381, -287179284, 9849565681, 18964089147, 271818611107], [1, 21, 394, 4137, 40498, 260301, 1861770, 10356195, 87503190, 575004909, 4204623854, 20187240297, 90361932758, 226363521909, 506623120463], [1, 16, 252, 2751, 30878, 264423, 2331890, 16858495, 123590170, 742764207, 4597024006, 21706713231, 105385264236, 354629778064, 1174711139837], [1, 18, 330, 3588, 43899, 382467, 3673733, 26502258, 216750247, 1331367627, 9015932721, 43477091268, 235925018670, 759249605538, 2488651484819], [1, 20, 335, 3204, 26819, 110665, 380210, -1267472, 23192810, 411784465, 6087403439, 44362074564, 282939760835, 1030407487220, 3142742836021], [1, -7, 310, -1658, 46408, -209174, 4535576, -17300046, 303883592, -938982086, 13957809304, -33410558618, 418538783170, -633208675183, 6060711605323], [1, 35, 789, 12065, 151898, 1586239, 15235229, 131541155, 1081701259, 7996230799, 54365965078, 306591931265, 1423536957939, 4483509937235, 9095120158391], [1, -8, 400, -2997, 75506, -490305, 8580796, -45886359, 626398108, -2612835345, 29373117602, -85109528277, 829228637200, -1210673810312, 11047398519097], [1, 18, 400, 4755, 69218, 670773, 7626730, 62053274, 602511670, 4186294293, 34127173502, 185207635155, 1230822559600, 4375574199378, 19203908986159], [1, -19, 413, -5540, 83434, -896074, 10322407, -90798361, 856759781, -6173053786, 47706476558, -262919098340, 1626823785559, -6211867094011, 27136050989627], [1, 1, 108, -8, 17873, 44447, 1792625, 1317142, 159543625, 352064687, 12599910937, -501937928, 603078420492, 496981290961, 44231334895529], [1, -22, 681, -11326, 195623, -2537231, 31274594, -319248170, 3033635618, -23872806479, 178539830279, -1002682636606, 5847978715017, -18325384108438, 80798284478113]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/481/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '14-481e7-1.1-c1e7-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 7, 'prelabel': '14-481e7-1.1-c1e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9597970142909158, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e7-0', 'trace_hash': 192968607478820758, 'z1': {'__RealLiteral__': 0, 'data': '1.56970140513842038242971126360', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1989832928402813693062528666518,2166170139292235013926859178989,2373136125257294346902590481691,2593812353034066649788678549395,2763880772559155782417109590457,3556677351030296860969424123185,3773859297557801226916327527098', 'Lhash_array': ['1989832928402813693062528666518', '2166170139292235013926859178989', '2373136125257294346902590481691', '2593812353034066649788678549395', '2763880772559155782417109590457', '3556677351030296860969424123185', '3773859297557801226916327527098'], 'label': '14-481e7-1.1-c1e7-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/481/2/a/c'}