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lfunc_lfunctions • Show schema
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{'Lhash': '1094854574833789918782373734145', 'a10': [6390548645.248502, 6.369508326347018e-67], 'a2': [-627.0693741524935, -362.03867196751236], 'a3': [27305.712743294578, 52356.3028925905], 'a4': [262144.0, 454046.72689933574], 'a5': [-7643351.248678291, 4412890.900935274], 'a6': [1832430.1676367894, -42716758.06650386], 'a7': [-72044539.46987742, 124784802.76972905], 'a8': [1.1017237140622124e-67, -379625062.49700624], 'a9': [-1995580504.1613603, 2859252334.171998], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.63247771847912, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.0', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [627.0693741524935, 362.03867196751236]]], [3, [[1.0, 0], [-27305.712743294578, -52356.3028925905]]]], 'bad_primes': [2, 3], 'central_character': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '366419214187976814495195283355', 'degree': 2, 'euler_factors': [[[1.0, 0], [627.0693741524935, 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{'__RealLiteral__': 0, 'data': '0.12475735394864222', 'prec': 64}, 'spectral_label': 'c20-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.863687970988749526157846230196', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.30816960699843634008116373386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20561908650047523078850100198', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.63247771847912, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/21/d/a/11/6'], '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': '2-18-9.2-c20-0-13', 'motivic_weight': 20, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [20], 'order_of_vanishing': 0, 'prelabel': '2-18-9.2-c20-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.755181545930436, 'root_angle': 0.12475735394864222, 'self_dual': False, 'spectral_label': 'c20-0', 'z1': {'__RealLiteral__': 0, 'data': '0.863687970988749526157846230196', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1094854574833789918782373734145', 'Lhash_array': ['1094854574833789918782373734145'], 'factors': ['2-18-9.2-c20-0-13'], 'label': '2-18-9.2-c20-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/21/d/a/11/6'}