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lfunc_lfunctions • Show schema
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{'Lhash': '2348989892340176799179565583630', 'a10': [0, 0], 'a2': [0, 1.5391888728108891], 'a3': [0, -3.1700864866260337], 'a4': [-0.3691023861848554, 0], 'a5': [0, 0], 'a6': [4.879361846062957, 0], 'a7': [0, -1.0], 'a8': [0, 2.510259459878101], 'a9': [-7.04944833268899, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.371202389096482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 7, 11], 'central_character': '1925.1849', 'coefficient_field': 'CDF', 'conductor': 1925, 'conductor_radical': 385, 'conjugate': '244058480053192364311034306312', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.5391888728108891], [-2.0, 0]], [[1.0, 0], [0, 3.1700864866260337], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0.8299135133739662], [-13.0, 0]], [[1.0, 0], [0, -2.8299135133739663], [-17.0, 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'3.66497166952055987945809473358949', '4.32887745929204389019752236555659', '5.22049830652046170881452361493548', '6.07936959861035328572401630491372', '7.16931685935627982035411253029165', '8.461120411389414444314688349205127', '9.274566003019491949472238238296555', '9.525056250572880843374298808487966'], 'prelabel': '2-1925-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.920612501777813, 'root_angle': 0.8524163823495667, 'root_number': '-0.8944271909999158785636694674925104941762473438446102897 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85302629282647893466079975045', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95106828439861111106815685527', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66497166952055987945809473359', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.371202389096482, 'bad_primes': [5, 7, 11], 'central_character': '5.4', 'conductor': 1925, 'conductor_radical': 385, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1925/2/b/m/1849/5'], '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': '2-1925-5.4-c1-0-80', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1925-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.920612501777813, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85302629282647893466079975045', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2348989892340176799179565583630', 'Lhash_array': ['2348989892340176799179565583630'], 'label': '2-1925-5.4-c1-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1925/2/b/m/1849/5'}