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lfunc_lfunctions • Show schema
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{'Lhash': '3368230842789249560305353908063', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': -1, 'a5': 0, 'a6': -1, 'a7': -1, 'a8': -3, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.9624499149895036, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1, 1]], [53, [1, 1]]], 'bad_primes': [7, 53], 'central_character': '371.1', 'coefficient_field': '1.1.1.1', 'conductor': 371, 'conductor_radical': 371, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 1, 3], [1, 0, 5], [1, 1], [1, 0, 11], [1, -1, 13], [1, 7, 17], [1, 7, 19], [1, -1, 23], [1, -9, 29], [1, -4, 31], [1, 3, 37], [1, 10, 41], [1, -6, 43], [1, -6, 47], [1, 1], [1, 14, 59], [1, -4, 61], [1, -4, 67], [1, -7, 71], [1, 8, 73], [1, -1, 79], [1, 11, 83], [1, 6, 89], [1, 11, 97], [1, -10, 101], [1, -5, 103], [1, -10, 107], [1, 20, 109], [1, -15, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, 1, 3], 1]], [[[1, 0, 5], 1]], [[[1, 1], 1]], [[[1, 0, 11], 1]], [[[1, 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'4.07348635622139479294973747045', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.90399558150416474100355981272', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9624499149895036, 'bad_primes': [7, 53], 'central_character': '1.1', 'conductor': 371, 'conductor_radical': 371, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, -1, 0, -1, -1, -3, -2, 0, 0, 1, 1, -1, 0, -1, -7, -2, -7, 0, 1, 0, 1, 3, -5, 1, 5, 1, 9, 0, 4, 5, 0, -7, 0, 2, -3, -7, -1, 0, -10, 1, 6, 0, 0, 1, 6, 1, 1, -5, 7, -1, -1, 5, 0, 3, 7, 9, -14, 0, 4, 4, 2, 7, 0, 0, 4, 7, -1, 0, 7, 6, -8, -3, 5, 7, 0, -1, 1, 0, 1, -10, -11, -1, 0, 6, -9, 0, -6, 0, -1, -1, -4, 6, 0, -5, -11, 1, 0, 5], 'euler11': [1, 0, 11], 'euler13': [1, -1, 13], 'euler17': [1, 7, 17], 'euler19': [1, 7, 19], 'euler2': [1, -1, 2], 'euler23': [1, -1, 23], 'euler29': [1, -9, 29], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, 3, 37], 'euler41': [1, 10, 41], 'euler43': [1, -6, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 1, 0], 'euler59': [1, 14, 59], 'euler61': [1, -4, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -7, 71], 'euler73': [1, 8, 73], 'euler79': [1, -1, 79], 'euler83': [1, 11, 83], 'euler89': [1, 6, 89], 'euler97': [1, 11, 97], 'euler_factors': [[1, -1, 2], [1, 1, 3], [1, 0, 5], [1, 1, 0], [1, 0, 11], [1, -1, 13], [1, 7, 17], [1, 7, 19], [1, -1, 23], [1, -9, 29], [1, -4, 31], [1, 3, 37], [1, 10, 41], [1, -6, 43], [1, -6, 47], [1, 1, 0], [1, 14, 59], [1, -4, 61], [1, -4, 67], [1, -7, 71], [1, 8, 73], [1, -1, 79], [1, 11, 83], [1, 6, 89], [1, 11, 97]], 'index': 24, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/371/a', 'ModularForm/GL2/Q/holomorphic/371/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/371/2/a/a'], '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': '2-371-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-371-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.721176898226764, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2066949333843874328, 'z1': {'__RealLiteral__': 0, 'data': '2.65706563163605891202165369262', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10445075
{'Lhash': '3368230842789249560305353908063', 'Lhash_array': ['3368230842789249560305353908063'], 'factors': ['2-371-1.1-c1-0-24'], 'label': '2-371-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/371/2/a/a'}
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id: 24549149
{'Lhash': '3368230842789249560305353908063', 'Lhash_array': ['3368230842789249560305353908063'], 'factors': ['2-371-1.1-c1-0-24'], 'label': '2-371-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/371/2/a/a/1/1'}
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id: 94677
{'Lhash': '2066949333843874328', 'Lhash_array': ['2066949333843874328'], 'factors': ['2-371-1.1-c1-0-24'], 'label': '2-371-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/371/a'}