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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 5, 'A8': -1, 'A9': -2, 'Lhash': '1152085422704773720526677458737', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.8898223650461363, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.722767091609805, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [7, [1, -5, 7]], [389, [1, 16, 404, 389]]], 'bad_primes': [2, 7, 389], 'central_character': '152488.1', 'coefficient_field': '1.1.1.1', 'conductor': 152488, 'conductor_radical': 5446, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, 2, 0, 9], [1, 0, 4, 0, 25], [1, -5, 7], [1, 3, 4, 33, 121], [1, 0, -20, 0, 169], [1, 0, -23, 0, 289], [1, 0, 28, 0, 361], [1, -9, 64, -207, 529], [1, -6, 58, -174, 841], [1, 0, -26, 0, 961], [1, 2, 39, 74, 1369], [1, 0, 58, 0, 1681], [1, 8, 102, 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'symplectic', 'trace_hash': 1685124307671157167, 'z1': {'__RealLiteral__': 0, 'data': '0.908835149446819824255408357005985', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.89169188862927323439729918994495', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.53889129361503103527314251265640', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.722767091609805, 'bad_primes': [2, 7, 389], 'central_character': '1.1', 'conductor': 152488, 'conductor_radical': 5446, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 5, -1, -2, 0, -3, 0, 0, -5, 0, 1, 0, 2, 0, 0, 0, 3, 9, 0, -4, 0, 0, 5, 6, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, -8, -3, 0, -9, 0, 0, 18, 4, 0, 0, 6, 0, 0, -5, 0, -6, 0, 0, 0, 0, -10, 1, 0, 0, 19, 0, 0, 0, 3, 2, 0, 2, 0, 0, -15, 0, 7, 0, -5, 0, 0, 0, 0, 8, 0, 3, 0, 0, 0, 9, 0, 0, 0, 0, 0, -18, 6, -4], 'euler11': [1, 3, 4, 33, 121], 'euler13': [1, 0, -20, 0, 169], 'euler17': [1, 0, -23, 0, 289], 'euler19': [1, 0, 28, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, -9, 64, -207, 529], 'euler29': [1, -6, 58, -174, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, 2, 39, 74, 1369], 'euler41': [1, 0, 58, 0, 1681], 'euler43': [1, 8, 102, 344, 1849], 'euler47': [1, 0, -68, 0, 2209], 'euler5': [1, 0, 4, 0, 25], 'euler53': [1, -6, 79, -318, 2809], 'euler59': [1, 0, -20, 0, 3481], 'euler61': [1, 0, 91, 0, 3721], 'euler67': [1, -19, 222, -1273, 4489], 'euler7': [1, -5, 7, 0, 0], 'euler71': [1, -3, -38, -213, 5041], 'euler73': [1, 0, -5, 0, 5329], 'euler79': [1, -7, 150, -553, 6241], 'euler83': [1, 0, -23, 0, 6889], 'euler89': [1, 0, 106, 0, 7921], 'euler97': [1, 0, 19, 0, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, 4, 0, 25], [1, -5, 7, 0, 0], [1, 3, 4, 33, 121], [1, 0, -20, 0, 169], [1, 0, -23, 0, 289], [1, 0, 28, 0, 361], [1, -9, 64, -207, 529], [1, -6, 58, -174, 841], [1, 0, -26, 0, 961], [1, 2, 39, 74, 1369], [1, 0, 58, 0, 1681], [1, 8, 102, 344, 1849], [1, 0, -68, 0, 2209], [1, -6, 79, -318, 2809], [1, 0, -20, 0, 3481], [1, 0, 91, 0, 3721], [1, -19, 222, -1273, 4489], [1, -3, -38, -213, 5041], [1, 0, -5, 0, 5329], [1, -7, 150, -553, 6241], [1, 0, -23, 0, 6889], [1, 0, 106, 0, 7921], [1, 0, 19, 0, 9409]], 'index': 0, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/3112.3/b', 'EllipticCurve/2.0.7.1/3112.6/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3112.3/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3112.6/b'], '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': '4-152488-1.1-c1e2-0-0', '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': '4-152488-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7658242252752656, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1685124307671157167, 'z1': {'__RealLiteral__': 0, 'data': '0.908835149446819824255408357005985', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9625345
{'Lhash': '1152085422704773720526677458737', 'Lhash_array': ['1152085422704773720526677458737'], 'factors': ['4-152488-1.1-c1e2-0-0'], 'label': '4-152488-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3112.6/b'}
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id: 9624756
{'Lhash': '1152085422704773720526677458737', 'Lhash_array': ['1152085422704773720526677458737'], 'factors': ['4-152488-1.1-c1e2-0-0'], 'label': '4-152488-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/3112.3/b'}
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id: 9624585
{'Lhash': '1152085422704773720526677458737', 'Lhash_array': ['1152085422704773720526677458737'], 'factors': ['4-152488-1.1-c1e2-0-0'], 'label': '4-152488-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/3112.6/b'}
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id: 9624558
{'Lhash': '1152085422704773720526677458737', 'Lhash_array': ['1152085422704773720526677458737'], 'factors': ['4-152488-1.1-c1e2-0-0'], 'label': '4-152488-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/3112.3/b'}