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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '1117514041066556151929699718853', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.389944956870345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 3]], [7, [1, -3, 7]], [13, [1, 3, 9, -13]], [157, [1, -17, 173, -157]]], 'bad_primes': [3, 7, 13, 157], 'central_character': '900081.1', 'coefficient_field': '1.1.1.1', 'conductor': 900081, 'conductor_radical': 42861, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 3], [1, 0, -4, 0, 25], [1, -3, 7], [1, 0, 6, 0, 121], [1, 3, 9, -13], [1, 0, -4, 0, 289], [1, 1, 36, 19, 361], [1, 0, 14, 0, 529], [1, 0, 20, 0, 841], [1, -4, 62, -124, 961], [1, -15, 124, -555, 1369], [1, 0, 16, 0, 1681], 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'symmetry_type': 'symplectic', 'trace_hash': 805754074423152339, 'z1': {'__RealLiteral__': 0, 'data': '0.881563138032954447033656569676162', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.83131597359277800294877006934657', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.39610015411637638726645668952162', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.389944956870345, 'bad_primes': [3, 7, 13, 157], 'central_character': '1.1', 'conductor': 900081, 'conductor_radical': 42861, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 1, 0, 0, 3, 0, 1, 0, 0, 2, -3, 0, 0, -3, 0, 0, -1, 0, 6, 0, 0, 0, 4, 0, -4, 3, 0, 0, 4, 0, 0, 0, 0, 1, 15, 0, -6, 0, 0, 0, 15, 0, 0, 0, 0, -6, 2, 0, 0, -3, 0, 0, 0, 0, -2, 0, 0, 0, -10, 0, 3, -7, 0, 0, 2, 0, 0, 0, 0, 0, -15, 0, 8, -1, 0, 0, 24, 0, -11, 0, 0, 6, 0, 0, 0, 0, 0, 0, -9, 0, 8, 0, 0, 0, 11, 0, 0, 4], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 3, 9, -13, 0], 'euler17': [1, 0, -4, 0, 289], 'euler19': [1, 1, 36, 19, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, 0, 14, 0, 529], 'euler29': [1, 0, 20, 0, 841], 'euler3': [1, -2, 3, 0, 0], 'euler31': [1, -4, 62, -124, 961], 'euler37': [1, -15, 124, -555, 1369], 'euler41': [1, 0, 16, 0, 1681], 'euler43': [1, -15, 142, -645, 1849], 'euler47': [1, 0, 40, 0, 2209], 'euler5': [1, 0, -4, 0, 25], 'euler53': [1, 0, -16, 0, 2809], 'euler59': [1, 0, -73, 0, 3481], 'euler61': [1, 10, 147, 610, 3721], 'euler67': [1, -2, -9, -134, 4489], 'euler7': [1, -3, 7, 0, 0], 'euler71': [1, 0, 63, 0, 5041], 'euler73': [1, 15, 172, 1095, 5329], 'euler79': [1, -24, 301, -1896, 6241], 'euler83': [1, 0, -101, 0, 6889], 'euler89': [1, 0, 30, 0, 7921], 'euler97': [1, -11, 222, -1067, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, -2, 3, 0, 0], [1, 0, -4, 0, 25], [1, -3, 7, 0, 0], [1, 0, 6, 0, 121], [1, 3, 9, -13, 0], [1, 0, -4, 0, 289], [1, 1, 36, 19, 361], [1, 0, 14, 0, 529], [1, 0, 20, 0, 841], [1, -4, 62, -124, 961], [1, -15, 124, -555, 1369], [1, 0, 16, 0, 1681], [1, -15, 142, -645, 1849], [1, 0, 40, 0, 2209], [1, 0, -16, 0, 2809], [1, 0, -73, 0, 3481], [1, 10, 147, 610, 3721], [1, -2, -9, -134, 4489], [1, 0, 63, 0, 5041], [1, 15, 172, 1095, 5329], [1, -24, 301, -1896, 6241], [1, 0, -101, 0, 6889], [1, 0, 30, 0, 7921], [1, -11, 222, -1067, 9409]], 'index': 3, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/100009.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100009.10/a', 'EllipticCurve/2.0.3.1/100009.10/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100009.3/a'], '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': '4-900081-1.1-c1e2-0-3', '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': '4-900081-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.752383540441536, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 805754074423152339, 'z1': {'__RealLiteral__': 0, 'data': '0.881563138032954447033656569676162', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9671055
{'Lhash': '1117514041066556151929699718853', 'Lhash_array': ['1117514041066556151929699718853'], 'label': '4-900081-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100009.3/a'}
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id: 9671053
{'Lhash': '1117514041066556151929699718853', 'Lhash_array': ['1117514041066556151929699718853'], 'label': '4-900081-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100009.10/a'}
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id: 9670868
{'Lhash': '1117514041066556151929699718853', 'Lhash_array': ['1117514041066556151929699718853'], 'label': '4-900081-1.1-c1e2-0-3', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/100009.10/a'}
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id: 9670430
{'Lhash': '1117514041066556151929699718853', 'Lhash_array': ['1117514041066556151929699718853'], 'label': '4-900081-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/100009.3/a'}