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lfunc_lfunctions • Show schema
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{'Lhash': '335954793808340688709114174763', 'a10': [-472237.24173750915, 304492.46164011664], 'a2': [0.0, -80.41157128172745], 'a3': [0.0, 243.0], 'a4': [-4418.0207959963345, 0.0], 'a5': [-3786.674688563247, -5872.752319227709], 'a6': [19540.01182145977, 0.0], 'a7': [0.0, 53961.21354695914], 'a8': [0.0, 190577.0961764357], 'a9': [-59049.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.525147708393837, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -243.0]]], [5, [[1.0, 0], [3786.674688563247, 5872.752319227709]]]], 'bad_primes': [3, 5], 'central_character': '15.4', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '2198242258446111606497411841472', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 80.41157128172745], [-2048.0, 0]], [[1.0, 0], [0, -243.0]], [[1.0, 0], [3786.674688563247, 5872.752319227709]], [[1.0, 0], [0, -53961.21354695914], [-1977326743.0, 0]], [[1.0, 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0.541904768787537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0911483307857', 'prec': 54}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26502160275698600775970147457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.03880979881105779259581420904', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.27151207365398964383747297970', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.525147708393837, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/12/b/a/4/2'], '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': '2-15-5.4-c11-0-1', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-15-5.4-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3948707940647513, 'root_angle': -0.09114833078573019, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26502160275698600775970147457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '335954793808340688709114174763', 'Lhash_array': ['335954793808340688709114174763'], 'label': '2-15-5.4-c11-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/12/b/a/4/2'}