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lfunc_lfunctions • Show schema
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{'Lhash': '1626436822196716327675349012664', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, -1.79128784747792], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.79128784747792, 0], 'a7': [0, 2.79128784747792], 'a8': [0, 1.0], 'a9': [-0.20871215252208, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.182796232447249, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1150.599', 'coefficient_field': 'CDF', 'conductor': 1150, 'conductor_radical': 230, 'conjugate': '1112554595442021787897139030713', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 1.79128784747792], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.79128784747792], [-7.0, 0]], [[1.0, 0], [-3.79128784747792, 0], [11.0, 0]], [[1.0, 0], [0, 1.20871215252208], [-13.0, 0]], [[1.0, 0], [0, 3.79128784747792], [-17.0, 0]], [[1.0, 0], 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'6.69246874172419418028203814060945', '7.51835413098945120501715516639116', '8.532002671330897523529697683309409', '9.229867233457764723539480574500788', '10.09922298474026099650807761648741'], 'prelabel': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28303242384288746874006320830', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36338250020110385661381208095', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30519325339976193162150469409', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.182796232447249, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1150, 'conductor_radical': 230, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1150/2/b/g/599/1'], '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': '2-1150-5.4-c1-0-20', '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': '2-1150-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.03031289348926, 'root_angle': 0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28303242384288746874006320830', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1626436822196716327675349012664', 'Lhash_array': ['1626436822196716327675349012664'], 'label': '2-1150-5.4-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1150/2/b/g/599/1'}