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lfunc_lfunctions • Show schema
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{'Lhash': '1044866094330784628905264947901,1892155714848333954088027337737', 'a10': -2, 'a2': -2, 'a3': 1, 'a4': 3, 'a5': 1, 'a6': -2, 'a7': 3, 'a8': -4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, -1, 1]], [5, [1, -1, 1]], [31, [1, 7, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -1, 1], [1, -1, 1], [1, -3, 2, -21, 49], [1, -3, -2, -33, 121], [1, 4, 3, 52, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, -4, 50, -92, 529], [1, -2, 59, -58, 841], [1, 7, 31], [1, -6, -1, -222, 1369], [1, -2, -37, -82, 1681], [1, 4, -27, 172, 1849], [1, -8, 110, -376, 2209], [1, -3, -44, -159, 2809], [1, -9, 22, -531, 3481], [1, 4, 126, 244, 3721], [1, 2, -63, 134, 4489], [1, 4, -55, 284, 5041], [1, 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2.725084840510306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1895110565608034460, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.824254013008525873639844661898', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.49264767003436741142285984151', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.09682530844649868937651155686', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, -2, 1, 3, 1, -2, 3, -4, 0, -2, 3, 3, -4, -6, 1, 5, 4, 0, 0, 3, 3, -6, 4, -4, 0, 8, -1, 9, 2, -2, -7, -6, 3, -8, 3, 0, 6, 0, -4, -4, 2, -6, -4, 9, 0, -8, 8, 5, 7, 0, 4, -12, 3, 2, 3, -12, 0, -4, 9, 3, -4, 14, 0, 7, -4, -6, -2, 12, 4, -6, -4, 0, -2, -12, 0, 0, 9, 8, 4, 5, -1, -4, -9, 9, 4, 8, 2, -12, 20, 0, -12, 12, -7, -16, 0, -6, 22, -14, 0, 0], 'euler11': [1, -3, -2, -33, 121], 'euler13': [1, 4, 3, 52, 169], 'euler17': [1, -4, -1, -68, 289], 'euler19': [1, 0, -19, 0, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, -4, 50, -92, 529], 'euler29': [1, -2, 59, -58, 841], 'euler3': [1, -1, 1, 0, 0], 'euler31': [1, 7, 31, 0, 0], 'euler37': [1, -6, -1, -222, 1369], 'euler41': [1, -2, -37, -82, 1681], 'euler43': [1, 4, -27, 172, 1849], 'euler47': [1, -8, 110, -376, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -3, -44, -159, 2809], 'euler59': [1, -9, 22, -531, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, -3, 2, -21, 49], 'euler71': [1, 4, -55, 284, 5041], 'euler73': [1, 2, -69, 146, 5329], 'euler79': [1, -4, -63, -316, 6241], 'euler83': [1, 9, -2, 747, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, -22, 315, -2134, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -1, 1, 0, 0], [1, -1, 1, 0, 0], [1, -3, 2, -21, 49], [1, -3, -2, -33, 121], [1, 4, 3, 52, 169], [1, -4, -1, -68, 289], [1, 0, -19, 0, 361], [1, -4, 50, -92, 529], [1, -2, 59, -58, 841], [1, 7, 31, 0, 0], [1, -6, -1, -222, 1369], [1, -2, -37, -82, 1681], [1, 4, -27, 172, 1849], [1, -8, 110, -376, 2209], [1, -3, -44, -159, 2809], [1, -9, 22, -531, 3481], [1, 4, 126, 244, 3721], [1, 2, -63, 134, 4489], [1, 4, -55, 284, 5041], [1, 2, -69, 146, 5329], [1, -4, -63, -316, 6241], [1, 9, -2, 747, 6889], [1, -20, 278, -1780, 7921], [1, -22, 315, -2134, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/i/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '4-930e2-1.1-c1e2-0-10', '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': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1895110565608034460, 'z1': {'__RealLiteral__': 0, 'data': '0.824254013008525873639844661898', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1044866094330784628905264947901,1892155714848333954088027337737', 'Lhash_array': ['1044866094330784628905264947901', '1892155714848333954088027337737'], 'label': '4-930e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/i/c'}