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lfunc_lfunctions • Show schema
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{'Lhash': '978003515536466862021299279601', 'a10': [-12.295549444445353, -10.50901723232157], 'a2': [0.31240673726130663, 3.987781592629384], 'a3': [1.6354610945705892, 8.850156326763159], 'a4': [-15.80480406102749, 2.4916196725280857], 'a5': [-2.8593048725281998, 2.8593048725281998], 'a6': [-34.78156142728601, 9.28671011068669], 'a7': [0.0, 27.258012439339105], 'a8': [-14.873562335700601, -62.24770793728897], 'a9': [-75.65053401629194, 28.948172706577804], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.961758228024529, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.31240673726130663, -3.987781592629384]]], [3, [[1.0, 0], [-1.6354610945705892, -8.850156326763159]]]], 'bad_primes': [2, 3], 'central_character': '48.5', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '4573479335830673709354288913065', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.31240673726130663, 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'rational': False, 'root_analytic_conductor': 2.2275004440009725, 'root_angle': 0.9672907010860443, 'root_number': '-0.994724908134065 + 0.10257854131189403*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.483645350543', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77150873857542913194436434777', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62575186229691777188715727888', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.60102930497993366446597427365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.961758228024529, 'bad_primes': [2, 3], 'central_character': '48.5', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/5/i/a/5/16'], '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': '2-48-48.5-c4-0-8', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-48-48.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2275004440009725, 'root_angle': 0.48364535054302216, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77150873857542913194436434777', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '978003515536466862021299279601', 'Lhash_array': ['978003515536466862021299279601'], 'label': '2-48-48.5-c4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/5/i/a/5/16'}