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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 2, 'A4': 1, 'A5': 0, 'A6': -2, 'A7': 0, 'A8': -1, 'A9': -2, 'Lhash': '949255988833603891389294434282', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 163.83992391926287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1, 0, -1]], [11, [1, -2, 8, 11]], [73, [1, 15, 87, 73]]], 'bad_primes': [2, 5, 11, 73], 'central_character': '2569600.1', 'coefficient_field': '1.1.1.1', 'conductor': 2569600, 'conductor_radical': 8030, 'degree': 4, 'euler_factors': [[1, 1], [1, -2, 6, -6, 9], [1, 0, -1], [1, 0, -10, 0, 49], [1, -2, 8, 11], [1, 0, -14, 0, 169], [1, -8, 50, -136, 289], [1, -5, 24, -95, 361], [1, 0, -20, 0, 529], [1, 0, 16, 0, 841], [1, 0, -50, 0, 961], [1, 0, 8, 0, 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'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 271471147549050176, 'z1': {'__RealLiteral__': 0, 'data': '0.74883093863774344006289096179869', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.28013969129174437251913879612662', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.11117772225304628916970063943017', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 163.83992391926287, 'bad_primes': [2, 5, 11, 73], 'central_character': '1.1', 'conductor': 2569600, 'conductor_radical': 8030, 'degree': 4, 'dirichlet_coefficients': [1, -1, 2, 1, 0, -2, 0, -1, -2, 0, 2, 2, 0, 0, 0, 1, 8, 2, 5, 0, 0, -2, 0, -2, 1, 0, -10, 0, 0, 0, 0, -1, 4, -8, 0, -2, 0, -5, 0, 0, 14, 0, 3, 2, 0, 0, 0, 2, 10, -1, 16, 0, 0, 10, 0, 0, 10, 0, 1, 0, 0, 0, 0, 1, 0, -4, 2, 8, 0, 0, 0, 2, -15, 0, 2, 5, 0, 0, 0, 0, -5, -14, 3, 0, 0, -3, 0, -2, 6, 0, 0, 0, 0, 0, 0, -2, -16, -10, -4, 1], 'euler11': [1, -2, 8, 11, 0], 'euler13': [1, 0, -14, 0, 169], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, -5, 24, -95, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, -20, 0, 529], 'euler29': [1, 0, 16, 0, 841], 'euler3': [1, -2, 6, -6, 9], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, 0, 8, 0, 1369], 'euler41': [1, -14, 130, -574, 1681], 'euler43': [1, -3, 58, -129, 1849], 'euler47': [1, 0, -53, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, -86, 0, 2809], 'euler59': [1, -1, 76, -59, 3481], 'euler61': [1, 0, 35, 0, 3721], 'euler67': [1, -2, 131, -134, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, -8, 0, 5041], 'euler73': [1, 15, 87, 73, 0], 'euler79': [1, 0, -14, 0, 6241], 'euler83': [1, -3, 162, -249, 6889], 'euler89': [1, -6, 43, -534, 7921], 'euler97': [1, 16, 222, 1552, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, -2, 6, -6, 9], [1, 0, -1, 0, 0], [1, 0, -10, 0, 49], [1, -2, 8, 11, 0], [1, 0, -14, 0, 169], [1, -8, 50, -136, 289], [1, -5, 24, -95, 361], [1, 0, -20, 0, 529], [1, 0, 16, 0, 841], [1, 0, -50, 0, 961], [1, 0, 8, 0, 1369], [1, -14, 130, -574, 1681], [1, -3, 58, -129, 1849], [1, 0, -53, 0, 2209], [1, 0, -86, 0, 2809], [1, -1, 76, -59, 3481], [1, 0, 35, 0, 3721], [1, -2, 131, -134, 4489], [1, 0, -8, 0, 5041], [1, 15, 87, 73, 0], [1, 0, -14, 0, 6241], [1, -3, 162, -249, 6889], [1, -6, 43, -534, 7921], [1, 16, 222, 1552, 9409]], 'index': 1, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/40150.2/a', 'EllipticCurve/2.0.8.1/40150.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/40150.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/40150.3/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': '4-2569600-1.1-c1e2-0-1', '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': '4-2569600-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.5777083486634096, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 271471147549050176, 'z1': {'__RealLiteral__': 0, 'data': '0.74883093863774344006289096179869', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9864034
{'Lhash': '949255988833603891389294434282', 'Lhash_array': ['949255988833603891389294434282'], 'label': '4-2569600-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/40150.3/a'}
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id: 9863910
{'Lhash': '949255988833603891389294434282', 'Lhash_array': ['949255988833603891389294434282'], 'label': '4-2569600-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/40150.2/a'}
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id: 9863635
{'Lhash': '949255988833603891389294434282', 'Lhash_array': ['949255988833603891389294434282'], 'label': '4-2569600-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/40150.3/a'}
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id: 9863633
{'Lhash': '949255988833603891389294434282', 'Lhash_array': ['949255988833603891389294434282'], 'label': '4-2569600-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/40150.2/a'}