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lfunc_lfunctions • Show schema
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{'Lhash': '100158086587206254795588818358', 'a10': [-2.033610216599172, -5.779833829151957], 'a2': [-2.6060354130425187, 0.8467522347779717], 'a3': [-1.8627457165267778, -2.5638495266625787], 'a4': [4.4563972381803065, -3.2377621152236284], 'a5': [0.05401583471904495, 2.2354154624140015], 'a6': [7.025326619098028, 5.104198561902836], 'a7': [0.0, -2.4781029382748017], 'a8': [-5.6507097882454, 7.777534790370462], 'a9': [-2.1764518078042276, 6.69842989833439], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.393642085904418, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.05401583471904495, -2.2354154624140015]]], [17, [[1.0, 0], [-0.5877852522924731, 0.8090169943749475]]]], 'bad_primes': [5, 17], 'central_character': '425.69', 'coefficient_field': 'CDF', 'conductor': 425, 'conductor_radical': 85, 'conjugate': '1508264793149359436367050478873', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6060354130425187, 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'-0.317690037615', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.079010798850388007122931474829', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.07903033387617666073997051285', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82656474514832448678283922770', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.393642085904418, 'bad_primes': [5, 17], 'central_character': '25.19', 'conductor': 425, 'conductor_radical': 85, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/425/2/r/a/69/1'], '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': '2-425-25.19-c1-0-0', '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': '2-425-25.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8421840532108669, 'root_angle': -0.3176900376146711, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.079010798850388007122931474829', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '100158086587206254795588818358', 'Lhash_array': ['100158086587206254795588818358'], 'factors': ['2-425-25.19-c1-0-0'], 'label': '2-425-25.19-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/425/2/r/a/69/1'}