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lfunc_lfunctions • Show schema
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{'Lhash': '1141836774056521697649745716820', 'a10': [-121.42265014083705, 210.31019923359008], 'a2': [5.111926281448734, 8.854116044015848], 'a3': [0.0, 0.0], 'a4': [-36.26358061393256, 62.810364087700975], 'a5': [11.876408564564192, 20.57054304527134], 'a6': [0.0, 0.0], 'a7': [30.684045850480313, 125.95828408741373], 'a8': [-414.3437211864677, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.104180648217781, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-30.684045850480313, -125.95828408741373]]]], 'bad_primes': [3, 7], 'central_character': '63.46', 'coefficient_field': 'CDF', 'conductor': 63, 'conductor_radical': 21, 'conjugate': '3927218927637592818492636946989', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.111926281448734, -8.854116044015848], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-11.876408564564192, -20.57054304527134], [-1562.5, 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'5.04437905922265098265754137820275', '7.14391194419255722606568844501984', '9.338492493681443476343619835911764', '10.18020752216039981552873494097698', '11.24976790682755540012549660377847', '12.42402010727372423110855778097149', '12.99533326876130253629722119211397'], 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.9441125899566575, 'root_number': '-0.9846261806553511 + 0.17467479602981031*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.472056294978', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.900750391196867634479850628379', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.44655853350267015015861280444', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22625444851309139243255449987', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.104180648217781, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 63, 'conductor_radical': 21, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/e/46/4'], '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': '2-63-7.4-c5-0-4', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-63-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.47205629497832874, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.900750391196867634479850628379', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1141836774056521697649745716820', 'Lhash_array': ['1141836774056521697649745716820'], 'label': '2-63-7.4-c5-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/e/46/4'}