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lfunc_lfunctions • Show schema
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{'Lhash': '2925330979190825621265856530837', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-4.0, -6.928203230275509], 'a5': [0.0, 5.196152422706632], 'a6': [0.0, 0.0], 'a7': [9.0, -5.196152422706632], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.903223470671655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [32.5, 33.77499074759311]]]], 'bad_primes': [3, 13], 'central_character': '117.82', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '538752358035410002701343076442', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.196152422706632], [-125.0, 0]], [[1.0, 0], [-9.0, 5.196152422706632], [171.5, -297.04671349806245]], [[1.0, 0], [45.0, 25.98076211353316], [665.5, 1152.6798124370878]], [[1.0, 0], [32.5, 33.77499074759311]], [[1.0, 0], 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{'__RealLiteral__': 0, 'data': '2.30767924431554354842679496555', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.22199163034342550816395719015', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16005717873446258472430934273', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.903223470671655, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/4/q/b/82/1'], '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': '2-117-13.4-c3-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-117-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': 0.37602047569628333, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30767924431554354842679496555', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2925330979190825621265856530837', 'Lhash_array': ['2925330979190825621265856530837'], 'label': '2-117-13.4-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/4/q/b/82/1'}