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lfunc_lfunctions • Show schema
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{'Lhash': '2240494401203103251436175531059', 'a10': 1, 'a2': -1, 'a3': 2, 'a4': -1, 'a5': -1, 'a6': -2, 'a7': 4, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2376812313298466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 1]], [31, [1, -1]]], 'bad_primes': [5, 31], 'central_character': '155.1', 'coefficient_field': '1.1.1.1', 'conductor': 155, 'conductor_radical': 155, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -2, 3], [1, 1], [1, -4, 7], [1, -4, 11], [1, 0, 13], [1, 8, 17], [1, -4, 19], [1, -2, 23], [1, 6, 29], [1, -1], [1, 4, 37], [1, 6, 41], [1, 6, 43], [1, -8, 47], [1, 12, 53], [1, 4, 59], [1, -10, 61], [1, -8, 67], [1, 0, 71], [1, 4, 73], [1, 0, 79], [1, -2, 83], [1, -14, 89], [1, 18, 97], [1, -10, 101], [1, -8, 103], [1, 4, 107], [1, -10, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, -2, 3], 1]], [[[1, 1], 1]], [[[1, -4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 0, 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{'__RealLiteral__': 0, 'data': '3.83108286299930817257651347819', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89232440280039987399206936754', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2376812313298466, 'bad_primes': [5, 31], 'central_character': '1.1', 'conductor': 155, 'conductor_radical': 155, 'degree': 2, 'dirichlet_coefficients': [1, -1, 2, -1, -1, -2, 4, 3, 1, 1, 4, -2, 0, -4, -2, -1, -8, -1, 4, 1, 8, -4, 2, 6, 1, 0, -4, -4, -6, 2, 1, -5, 8, 8, -4, -1, -4, -4, 0, -3, -6, -8, -6, -4, -1, -2, 8, -2, 9, -1, -16, 0, -12, 4, -4, 12, 8, 6, -4, 2, 10, -1, 4, 7, 0, -8, 8, 8, 4, 4, 0, 3, -4, 4, 2, -4, 16, 0, 0, 1, -11, 6, 2, -8, 8, 6, -12, 12, 14, 1, 0, -2, 2, -8, -4, -10, -18, -9, 4, -1], 'euler11': [1, -4, 11], 'euler13': [1, 0, 13], 'euler17': [1, 8, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, -2, 23], 'euler29': [1, 6, 29], 'euler3': [1, -2, 3], 'euler31': [1, -1, 0], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, 6, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 12, 53], 'euler59': [1, 4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 4, 73], 'euler79': [1, 0, 79], 'euler83': [1, -2, 83], 'euler89': [1, -14, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 1, 2], [1, -2, 3], [1, 1, 0], [1, -4, 7], [1, -4, 11], [1, 0, 13], [1, 8, 17], [1, -4, 19], [1, -2, 23], [1, 6, 29], [1, -1, 0], [1, 4, 37], [1, 6, 41], [1, 6, 43], [1, -8, 47], [1, 12, 53], [1, 4, 59], [1, -10, 61], [1, -8, 67], [1, 0, 71], [1, 4, 73], [1, 0, 79], [1, -2, 83], [1, -14, 89], [1, 18, 97]], 'index': 4, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/155/b', 'ModularForm/GL2/Q/holomorphic/155/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/155/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-155-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-155-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1125112275073212, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1147127673115350820, 'z1': {'__RealLiteral__': 0, 'data': '1.76743844147568883236115154570', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9990386
{'Lhash': '2240494401203103251436175531059', 'Lhash_array': ['2240494401203103251436175531059'], 'label': '2-155-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/155/2/a/b'}
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id: 24547415
{'Lhash': '2240494401203103251436175531059', 'Lhash_array': ['2240494401203103251436175531059'], 'label': '2-155-1.1-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/155/2/a/b/1/1'}
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id: 22015
{'Lhash': '1147127673115350820', 'Lhash_array': ['1147127673115350820'], 'label': '2-155-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/155/b'}