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{'Lhash': '1498827887243423624131684345641,1831847715378242794406432927824,2042334873369113553339928292531', 'a10': -9, 'a2': 3, 'a3': 3, 'a4': 6, 'a5': -3, 'a6': 9, 'a7': 3, 'a8': 10, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 530.817443505252, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -3, 3, -1]], [3, [1, -3, 3, -1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.1', 'coefficient_field': '1.1.1.1', 'conductor': 1042590744, 'conductor_radical': 78, 'degree': 6, 'euler_factors': [[1, -3, 3, -1], [1, -3, 3, -1], [1, 3, 11, 31, 55, 75, 125], [1, -3, 17, -43, 119, -147, 343], [1, -1, 17, -35, 187, -121, 1331], [1], [1, -12, 71, -304, 1207, -3468, 4913], [1, -4, 25, -88, 475, -1444, 6859], [1, -16, 145, -840, 3335, -8464, 12167], [1, -13, 99, -531, 2871, -10933, 24389], [1, 9, 71, 529, 2201, 8649, 29791], [1, 12, 131, 896, 4847, 16428, 50653], [1, 14, 179, 1204, 7339, 23534, 68921], [1, 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'3.78826683053152034517761369151658', '4.36982047888807898836709379630862', '4.74552887541911428073683140399480', '4.83993880642181214309290634498731', '5.34167414345820092380154285060437', '5.46765643659823242065605418548678', '5.49796056869188660020166585706892', '6.48446213074067317772895634041271', '6.62800985141558394163668824548911', '6.86070391608869888729693546100631', '7.32414158715904383617297145133205', '7.41243678578284885324547662894960', '7.58572510315508435458140344308053', '8.005866956444706997993098420887143', '8.175257530052979246896455844341331', '8.359873835161890311639533985352857', '8.845218238706019495384329167900505', '8.979556125130113988977573990487683', '9.258956647684940162198927378292538', '9.956414029867099092408017800636476', '10.03087626637773667181130769081315', '10.12823724369186474243603408764329'], 'prelabel': '6-1014e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1599055550887976443, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18236672390134377279201613725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44507304698032299892028334665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.61111813697039943435414343039', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 530.817443505252, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 1042590744, 'conductor_radical': 78, 'degree': 6, 'dirichlet_coefficients': [1, 3, 3, 6, -3, 9, 3, 10, 6, -9, 1, 18, 0, 9, -9, 15, 12, 18, 4, -18, 9, 3, 16, 30, -2, 0, 10, 18, 13, -27, -9, 21, 3, 36, -9, 36, -12, 12, 0, -30, -14, 27, -8, 6, -18, 48, 4, 45, -8, -6, 36, 0, 15, 30, -3, 30, 12, 39, -9, -54, -10, -27, 18, 28, 0, 9, -6, 72, 48, -27, 6, 60, 5, -36, -6, 24, 3, 0, -5, -45, 15, -42, -7, 54, -36, -24, 39, 10, -10, -54, 0, 96, -27, 12, -12, 63, 7, -24, 6, -12], 'euler11': [1, -1, 17, -35, 187, -121, 1331], 'euler13': [1, 0, 0, 0, 0, 0, 0], 'euler17': [1, -12, 71, -304, 1207, -3468, 4913], 'euler19': [1, -4, 25, -88, 475, -1444, 6859], 'euler2': [1, -3, 3, -1, 0, 0, 0], 'euler23': [1, -16, 145, -840, 3335, -8464, 12167], 'euler29': [1, -13, 99, -531, 2871, -10933, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, 9, 71, 529, 2201, 8649, 29791], 'euler37': [1, 12, 131, 896, 4847, 16428, 50653], 'euler41': [1, 14, 179, 1204, 7339, 23534, 68921], 'euler43': [1, 8, 85, 344, 3655, 14792, 79507], 'euler47': [1, -4, 109, -312, 5123, -8836, 103823], 'euler5': [1, 3, 11, 31, 55, 75, 125], 'euler53': [1, -15, 87, -343, 4611, -42135, 148877], 'euler59': [1, 9, 197, 1075, 11623, 31329, 205379], 'euler61': [1, 10, 207, 1228, 12627, 37210, 226981], 'euler67': [1, 6, 17, -308, 1139, 26934, 300763], 'euler7': [1, -3, 17, -43, 119, -147, 343], 'euler71': [1, -6, 141, -748, 10011, -30246, 357911], 'euler73': [1, -5, 197, -717, 14381, -26645, 389017], 'euler79': [1, 5, 33, -679, 2607, 31205, 493039], 'euler83': [1, 7, 25, -315, 2075, 48223, 571787], 'euler89': [1, 10, 291, 1788, 25899, 79210, 704969], 'euler97': [1, -7, 277, -1351, 26869, -65863, 912673], 'euler_factors': [[1, -3, 3, -1, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 3, 11, 31, 55, 75, 125], [1, -3, 17, -43, 119, -147, 343], [1, -1, 17, -35, 187, -121, 1331], [1, 0, 0, 0, 0, 0, 0], [1, -12, 71, -304, 1207, -3468, 4913], [1, -4, 25, -88, 475, -1444, 6859], [1, -16, 145, -840, 3335, -8464, 12167], [1, -13, 99, -531, 2871, -10933, 24389], [1, 9, 71, 529, 2201, 8649, 29791], [1, 12, 131, 896, 4847, 16428, 50653], [1, 14, 179, 1204, 7339, 23534, 68921], [1, 8, 85, 344, 3655, 14792, 79507], [1, -4, 109, -312, 5123, -8836, 103823], [1, -15, 87, -343, 4611, -42135, 148877], [1, 9, 197, 1075, 11623, 31329, 205379], [1, 10, 207, 1228, 12627, 37210, 226981], [1, 6, 17, -308, 1139, 26934, 300763], [1, -6, 141, -748, 10011, -30246, 357911], [1, -5, 197, -717, 14381, -26645, 389017], [1, 5, 33, -679, 2607, 31205, 493039], [1, 7, 25, -315, 2075, 48223, 571787], [1, 10, 291, 1788, 25899, 79210, 704969], [1, -7, 277, -1351, 26869, -65863, 912673]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/2/a/o'], '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': '6-1014e3-1.1-c1e3-0-3', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-1014e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.845493061836179, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1599055550887976443, 'z1': {'__RealLiteral__': 0, 'data': '1.18236672390134377279201613725', 'prec': 103}}
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{'Lhash': '1498827887243423624131684345641,1831847715378242794406432927824,2042334873369113553339928292531', 'Lhash_array': ['1498827887243423624131684345641', '1831847715378242794406432927824', '2042334873369113553339928292531'], 'label': '6-1014e3-1.1-c1e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/2/a/o'}