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lfunc_lfunctions • Show schema
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{'Lhash': '2300735951465784310957893669932', 'a10': [0.3845215900030498, -0.6660109304924512], 'a2': [-1.224744871391589, 0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [1.0, -1.7320508075688772], 'a5': [-0.47094084529557456, 0.27189782380378985], 'a6': [0.0, 0.0], 'a7': [-4.459441598166074, -5.395681665234339], 'a8': [0.0, 2.8284271247461903], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.299753992819223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.224744871391589, -0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [4.459441598166074, 5.395681665234339]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.53', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '157217800419336121833545698819', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.47094084529557456, 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'8.216693905674164318263792326640542', '8.684727740193167374706911179429164', '9.752547617273011954850763093678175', '10.38529542282286576535948063406887', '11.78753885869807982564637745942853'], 'prelabel': '2-378-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2093229804460663, 'root_angle': 0.8003220188384802, 'root_number': '-0.8096112144196701 + 0.586966507976313*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.400161009419', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81496064534782449448616951605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18614194714434117050239715031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36163257038061256524946303555', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.299753992819223, 'bad_primes': [2, 3, 7], 'central_character': '21.11', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/3/s/e/53/3'], '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': '2-378-21.11-c2-0-15', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-378-21.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2093229804460663, 'root_angle': 0.4001610094192401, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81496064534782449448616951605', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2300735951465784310957893669932', 'Lhash_array': ['2300735951465784310957893669932'], 'label': '2-378-21.11-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/3/s/e/53/3'}