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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -2, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 8, 'A9': 1, 'Lhash': '304833455394853496,2120978339176098767', 'a10': [0.0, 0], 'a2': [-1.4142135623730951, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [2.8284271247461903, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 118.80084147122842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, -1]], [5, [1, 0, -1]], [7, [1, 0, 7]], [13, [1, 0, -1]]], 'bad_primes': [3, 5, 7, 13], 'central_character': '1863225.1', 'coefficient_field': '1.1.1.1', 'conductor': 1863225, 'conductor_radical': 1365, 'degree': 4, 'euler_factors': [[1, 2, 5, 4, 4], [1, 0, -1], [1, 0, -1], [1, 0, 7], [1, -8, 38, -88, 121], [1, 0, -1], [1, 0, 30, 0, 289], [1, 0, 22, 0, 361], [1, -16, 110, -368, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 0, 46, 0, 1681], [1, 8, 102, 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'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 119968785357258312, 'z1': {'__RealLiteral__': 0, 'data': '0.73264725064818620387577910362138', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.16776210284876177743507098510244', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '1.53827946418072491307494025034382', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 118.80084147122842, 'bad_primes': [3, 5, 7, 13], 'central_character': '1.1', 'conductor': 1863225, 'conductor_radical': 1365, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, -1, 0, 0, 0, 8, 1, 0, 8, 0, 0, 0, 0, -7, 0, -2, 0, 0, 0, -16, 16, 0, 1, 0, 0, 0, -4, 0, 0, -14, 0, 0, 0, -1, 12, 0, 0, 0, 0, 0, -8, -8, 0, -32, 0, 0, -7, -2, 0, 0, 12, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 35, 0, 0, -8, 0, 0, 0, 0, 8, 0, -24, 0, 0, 0, 0, 32, 0, 1, 0, 0, 0, 0, 16, 0, 64, 0, 0, 0, -16, 0, 0, 0, 0, 0, 14, 8, -1], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, 0, -1, 0, 0], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 2, 5, 4, 4], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, 0, 7, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, -32, 414, -2528, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 0, 78, 0, 7921], 'euler97': [1, 0, -130, 0, 9409], 'euler_factors': [[1, 2, 5, 4, 4], [1, 0, -1, 0, 0], [1, 0, -1, 0, 0], [1, 0, 7, 0, 0], [1, -8, 38, -88, 121], [1, 0, -1, 0, 0], [1, 0, 30, 0, 289], [1, 0, 22, 0, 361], [1, -16, 110, -368, 529], [1, 4, 62, 116, 841], [1, 0, -2, 0, 961], [1, -12, 110, -444, 1369], [1, 0, 46, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, 30, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -26, 0, 3481], [1, 0, 118, 0, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 0, 110, 0, 5329], [1, -32, 414, -2528, 6241], [1, 0, 150, 0, 6889], [1, 0, 78, 0, 7921], [1, 0, -130, 0, 9409]], 'index': 6, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/38025.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/38025.1/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': '4-1365e2-1.1-c1e2-0-6', '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': '4-1365e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.301451177271107, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 119968785357258312, 'z1': {'__RealLiteral__': 0, 'data': '0.73264725064818620387577910362138', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9637112
{'Lhash': '304833455394853496,2120978339176098767', 'Lhash_array': ['304833455394853496', '2120978339176098767'], 'label': '4-1365e2-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/38025.1/a'}
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id: 9636634
{'Lhash': '304833455394853496,2120978339176098767', 'Lhash_array': ['304833455394853496', '2120978339176098767'], 'label': '4-1365e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/38025.1/a'}