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lfunc_lfunctions • Show schema
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{'Lhash': '2013939697521235299942710340895,2549101271095327339515798189179', 'a10': -3000, 'a2': -12, 'a3': 54, 'a4': -20, 'a5': 250, 'a6': -648, 'a7': 686, 'a8': 672, 'a9': 2187, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1075.868055717538, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -54, 729]], [5, [1, -250, 15625]], [7, [1, -686, 117649]]], 'bad_primes': [3, 5, 7], 'central_character': '105.1', 'coefficient_field': '1.1.1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 12, 164, 1536, 16384], [1, -54, 729], [1, -250, 15625], [1, -686, 117649], [1, 10976, 68803686, 213891188896, 379749833583241], [1, 2796, 126859566, 175444853532, 3937376385699289], [1, 8284, 809618438, 3399245567132, 168377826559400929], [1, 8096, 1803475414, 7236785598944, 799006685782884121], [1, 90976, 7977553070, 309757399866272, 11592836324538749809], [1, 12532, 31965988526, 216175449904388, 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'primitive': False, 'rational': True, 'root_analytic_conductor': 5.727165762908631, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c7e2-0', 'trace_hash': 375545524116104348, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58871829284713238397027166937', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01088633621629174042378525279', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70658491673205986314339038043', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 1075.868055717538, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 11025, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, -12, 54, -20, 250, -648, 686, 672, 2187, -3000, -10976, -1080, -2796, -8232, 13500, -2736, -8284, -26244, -8096, -5000, 37044, 131712, -90976, 36288, 46875, 33552, 78732, -13720, -12532, -162000, -117960, 149952, -592704, 99408, 171500, -43740, -174212, 97152, -150984, 168000, -492700, -444528, -661176, 219520, 546750, 1091712, -1675408, -147744, 352947, -562500, -447336, 55920, -555436, -944784, -2744000, 460992, -437184, 150384, -3121176, -270000, -511588, 1415520, 1500282, -2055232, -699000, 7112448, -252728, 165680, -4912704, -2058000, -1099336, 1469664, 5012588, 2090544, 2531250, 161920, -7529536, 1811808, 83648, -684000, 2657205, 5912400, -4404184, -740880, -2071000, 7934112, -676728, -7375872, -4381564, -6561000, -1918056, 1819520, -6369840, 20104896, -2024000, 8097408, -8539828, -4235364, -24004512, -937500], 'euler11': [1, 10976, 68803686, 213891188896, 379749833583241], 'euler13': [1, 2796, 126859566, 175444853532, 3937376385699289], 'euler17': [1, 8284, 809618438, 3399245567132, 168377826559400929], 'euler19': [1, 8096, 1803475414, 7236785598944, 799006685782884121], 'euler2': [1, 12, 164, 1536, 16384], 'euler23': [1, 90976, 7977553070, 309757399866272, 11592836324538749809], 'euler29': [1, 12532, 31965988526, 216175449904388, 297558232675799463481], 'euler3': [1, -54, 729, 0, 0], 'euler31': [1, 117960, 9090248910, 3245387960533560, 756943935220796320321], 'euler37': [1, 174212, 106259379454, 16538272179094196, 9012061295995008299689], 'euler41': [1, 492700, 358124883062, 95955430741168700, 37929227194915558802161], 'euler43': [1, 661176, 502549980726, 179719942017281832, 73885357344138503765449], 'euler47': [1, 1675408, 1714888352190, 848800429008673904, 256666986187667409334369], 'euler5': [1, -250, 15625, 0, 0], 'euler53': [1, 555436, -793299419970, 652476856666503932, 1379946262057143768386569], 'euler59': [1, 3121176, 6648375612854, 7767519286781427144, 6193386212891813387462761], 'euler61': [1, 511588, 1747585779726, 1607789521994311348, 9876832533361318095112441], 'euler67': [1, 252728, 12123587827590, 1531711522590071144, 36732225162896895721934329], 'euler7': [1, -686, 117649, 0, 0], 'euler71': [1, 1099336, 18156240823806, 9998593014444928376, 82721210695570328927708881], 'euler73': [1, -5012588, 28363475914198, -55376057248043393036, 122045014039746588673695409], 'euler79': [1, -83648, 38379183136222, -1606368578874228032, 368790120348678391253573281], 'euler83': [1, 4404184, 30645544257030, 119512161591699399368, 736365263311636486061599129], 'euler89': [1, 4381564, 93146164629590, 193802424650193627356, 1956410986640441413344189841], 'euler97': [1, 8539828, 4428577747174, 690003452138154784564, 6528362774606076144776040769], 'euler_factors': [[1, 12, 164, 1536, 16384], [1, -54, 729, 0, 0], [1, -250, 15625, 0, 0], [1, -686, 117649, 0, 0], [1, 10976, 68803686, 213891188896, 379749833583241], [1, 2796, 126859566, 175444853532, 3937376385699289], [1, 8284, 809618438, 3399245567132, 168377826559400929], [1, 8096, 1803475414, 7236785598944, 799006685782884121], [1, 90976, 7977553070, 309757399866272, 11592836324538749809], [1, 12532, 31965988526, 216175449904388, 297558232675799463481], [1, 117960, 9090248910, 3245387960533560, 756943935220796320321], [1, 174212, 106259379454, 16538272179094196, 9012061295995008299689], [1, 492700, 358124883062, 95955430741168700, 37929227194915558802161], [1, 661176, 502549980726, 179719942017281832, 73885357344138503765449], [1, 1675408, 1714888352190, 848800429008673904, 256666986187667409334369], [1, 555436, -793299419970, 652476856666503932, 1379946262057143768386569], [1, 3121176, 6648375612854, 7767519286781427144, 6193386212891813387462761], [1, 511588, 1747585779726, 1607789521994311348, 9876832533361318095112441], [1, 252728, 12123587827590, 1531711522590071144, 36732225162896895721934329], [1, 1099336, 18156240823806, 9998593014444928376, 82721210695570328927708881], [1, -5012588, 28363475914198, -55376057248043393036, 122045014039746588673695409], [1, -83648, 38379183136222, -1606368578874228032, 368790120348678391253573281], [1, 4404184, 30645544257030, 119512161591699399368, 736365263311636486061599129], [1, 4381564, 93146164629590, 193802424650193627356, 1956410986640441413344189841], [1, 8539828, 4428577747174, 690003452138154784564, 6528362774606076144776040769]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/8/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': '4-105e2-1.1-c7e2-0-0', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 2, 'prelabel': '4-105e2-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.727165762908631, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 375545524116104348, 'z1': {'__RealLiteral__': 0, 'data': '1.58871829284713238397027166937', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2013939697521235299942710340895,2549101271095327339515798189179', 'Lhash_array': ['2013939697521235299942710340895', '2549101271095327339515798189179'], 'label': '4-105e2-1.1-c7e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/8/a/c'}