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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '1109212453153758397481816280819', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.120761435790342, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 1, 17, -19]]], 'bad_primes': [2, 3, 19], 'central_character': '393984.1', 'coefficient_field': '1.1.1.1', 'conductor': 393984, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, 4, 0, 25], [1, -2, 14, -14, 49], [1, 0, -14, 0, 121], [1, -6, 26, -78, 169], [1, 0, 4, 0, 289], [1, 1, 17, -19], [1, 0, 30, 0, 529], [1, 0, -10, 0, 841], [1, -10, 62, -310, 961], [1, 8, 86, 296, 1369], [1, 0, -14, 0, 1681], [1, 4, 54, 172, 1849], [1, 0, -26, 0, 2209], [1, 0, -34, 0, 2809], [1, 0, -10, 0, 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1102501269802425359, 'z1': {'__RealLiteral__': 0, 'data': '0.875014339877293000445539850222771', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.73335948261466440694058262987872', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.28749937847289049955988250593087', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.120761435790342, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 393984, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 0, 0, 0], 'euler11': [1, 0, -14, 0, 121], 'euler13': [1, -6, 26, -78, 169], 'euler17': [1, 0, 4, 0, 289], 'euler19': [1, 1, 17, -19, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, -10, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -10, 62, -310, 961], 'euler37': [1, 8, 86, 296, 1369], 'euler41': [1, 0, -14, 0, 1681], 'euler43': [1, 4, 54, 172, 1849], 'euler47': [1, 0, -26, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, 0, -34, 0, 2809], 'euler59': [1, 0, -10, 0, 3481], 'euler61': [1, 8, 102, 488, 3721], 'euler67': [1, -18, 190, -1206, 4489], 'euler7': [1, -2, 14, -14, 49], 'euler71': [1, 0, -82, 0, 5041], 'euler73': [1, -20, 230, -1460, 5329], 'euler79': [1, -24, 302, -1896, 6241], 'euler83': [1, 0, -86, 0, 6889], 'euler89': [1, 0, 50, 0, 7921], 'euler97': [1, -6, 178, -582, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 4, 0, 25], [1, -2, 14, -14, 49], [1, 0, -14, 0, 121], [1, -6, 26, -78, 169], [1, 0, 4, 0, 289], [1, 1, 17, -19, 0], [1, 0, 30, 0, 529], [1, 0, -10, 0, 841], [1, -10, 62, -310, 961], [1, 8, 86, 296, 1369], [1, 0, -14, 0, 1681], [1, 4, 54, 172, 1849], [1, 0, -26, 0, 2209], [1, 0, -34, 0, 2809], [1, 0, -10, 0, 3481], [1, 8, 102, 488, 3721], [1, -18, 190, -1206, 4489], [1, 0, -82, 0, 5041], [1, -20, 230, -1460, 5329], [1, -24, 302, -1896, 6241], [1, 0, -86, 0, 6889], [1, 0, 50, 0, 7921], [1, -6, 178, -582, 9409]], 'index': 7, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/43776.2/p', 'EllipticCurve/2.0.3.1/43776.1/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43776.1/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43776.2/p'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-393984-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-393984-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2387634076361764, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1102501269802425359, 'z1': {'__RealLiteral__': 0, 'data': '0.875014339877293000445539850222771', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9768133
{'Lhash': '1109212453153758397481816280819', 'Lhash_array': ['1109212453153758397481816280819'], 'label': '4-393984-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43776.2/p'}
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id: 9767692
{'Lhash': '1109212453153758397481816280819', 'Lhash_array': ['1109212453153758397481816280819'], 'label': '4-393984-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/43776.1/k'}
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id: 9767567
{'Lhash': '1109212453153758397481816280819', 'Lhash_array': ['1109212453153758397481816280819'], 'label': '4-393984-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/43776.1/k'}
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id: 9767243
{'Lhash': '1109212453153758397481816280819', 'Lhash_array': ['1109212453153758397481816280819'], 'label': '4-393984-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/43776.2/p'}