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lfunc_lfunctions • Show schema
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{'Lhash': '1876671898634013044931742641896', 'a10': [-2.0591083614170724, -0.8718215161042422], 'a2': [-0.5877852522924731, -0.8090169943749475], 'a3': [-0.008203908477451293, 0.011291711305564152], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [1.9156319503031387, -1.1534098278486244], 'a6': [0.013957322755980191, 2.7783878735099756e-61], 'a7': [1.519945565253183, 0.4938602513526173], 'a8': [0.9510565162951535, -0.30901699437494745], 'a9': [0.9269907844949404, 2.8529842765532516], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.4753624626596933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5877852522924731, 0.8090169943749475]]], [5, [[1.0, 0], [-1.9156319503031387, 1.1534098278486244]]], [31, [[1.0, 0], [0.6390446421772461, 5.5309693495177275]]]], 'bad_primes': [2, 5, 31], 'central_character': '310.109', 'coefficient_field': 'CDF', 'conductor': 310, 'conductor_radical': 310, 'conjugate': 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0930775787474', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48043309275926243888921984950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34290712218279679275767237346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98520714262158425002671749149', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4753624626596933, 'bad_primes': [2, 5, 31], 'central_character': '155.109', 'conductor': 310, 'conductor_radical': 310, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/310/2/n/a/109/4'], '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': '2-310-155.109-c1-0-9', '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': '2-310-155.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5733284662331937, 'root_angle': 0.09307757874737838, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48043309275926243888921984950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1876671898634013044931742641896', 'Lhash_array': ['1876671898634013044931742641896'], 'label': '2-310-155.109-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/310/2/n/a/109/4'}