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lfunc_lfunctions • Show schema
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{'Lhash': '2283656372000476671507155292938', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.2224351559460502, -2.2224351559460502], 'a4': [0, 0], 'a5': [-1.6663341953031217, 1.6663341953031217], 'a6': [0, 0], 'a7': [4.68880789116204, 5.197603347676368], 'a8': [0, 0], 'a9': [0, 0.8784360447698876], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.207115843341303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-4.68880789116204, -5.197603347676368]]]], 'bad_primes': [2, 7], 'central_character': '448.433', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '108160634574895839982921523803', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.2224351559460502, 2.2224351559460502], [0, 9.0]], [[1.0, 0], [1.6663341953031217, -1.6663341953031217], [0, -25.0]], [[1.0, 0], [-4.68880789116204, -5.197603347676368]], [[1.0, 0], [-1.3606630930660715, 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0.148080208654431258479161352156320156943931964891388059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47634531057166096', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80148723283002770523234561004', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.99429964839032998033774945974', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.40832155548338568201761757604', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.207115843341303, 'bad_primes': [2, 7], 'central_character': '112.69', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/3/l/b/433/8'], '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': '2-448-112.69-c2-0-22', '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': '2-448-112.69-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.49386832083599, 'root_angle': -0.47634531057166096, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80148723283002770523234561004', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2283656372000476671507155292938', 'Lhash_array': ['2283656372000476671507155292938'], 'label': '2-448-112.69-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/3/l/b/433/8'}