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lfunc_lfunctions • Show schema
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{'Lhash': '2238736249347983997986321642489', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.498457891064382, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '1440.1', 'coefficient_field': '1.1.1.1', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -10, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, 8, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, 14, 73], [1, 12, 79], [1, -4, 83], [1, -14, 89], [1, -2, 97], [1, -10, 101], [1, -8, 103], [1, 12, 107], [1, 10, 109], [1, -10, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, -2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 19], 1]], [[[1, 8, 23], 1]], [[[1, -2, 29], 1]], [[[1, -4, 31], 1]], [[[1, -10, 37], 1]], [[[1, 2, 41], 1]], [[[1, 4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -2, 53], 1]], [[[1, 8, 59], 1]], [[[1, 2, 61], 1]], [[[1, 12, 67], 1]], [[[1, 8, 71], 1]], [[[1, 14, 73], 1]], [[[1, 12, 79], 1]], [[[1, -4, 83], 1]], [[[1, -14, 89], 1]], [[[1, -2, 97], 1]], [[[1, -10, 101], 1]], [[[1, -8, 103], 1]], [[[1, 12, 107], 1]], [[[1, 10, 109], 1]], [[[1, -10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1440-1.1-c1-0-15', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1440/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4980207675710659e-60, 0.13383729072678271, 0.26770421481790113, 0.40159547284838865, 0.5354375946627374, 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-3.2591691273622, -2.991083590847404, -2.653538425663389, -2.2631831262458313, -1.8392839191575687, -1.4028101031422315, -0.9754274221981813, -0.5784466249979691], 'positive_zeros': ['1.76605150421174345688608754901164', '2.93766436334545072959727415675066', '4.15454134720129683204983863493620', '4.64100971652370162406799470499580', '6.10573259978170433716528435757878', '6.48409824978736290432741019569938', '7.65568771791547490159498422449779', '8.339915197949374679379905597749952', '8.986263642102072087677183018302291'], 'prelabel': '2-1440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.390937612381623, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1762578329781223926, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76605150421174345688608754901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93766436334545072959727415675', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15454134720129683204983863494', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.498457891064382, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1440, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, -4, 0, 0, 0, -8, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, -2, 0, -4, 0, 0, 0, -8, 0, -7, 0, 0, 0, 2, 0, 0, 0, 0, 0, -8, 0, -2, 0, 0, 0, -2, 0, -12, 0, 0, 0, -8, 0, -14, 0, 0, 0, 0, 0, -12, 0, 0, 0, 4, 0, 6, 0, 0, 0, 14, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, 14, 73], 'euler79': [1, 12, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -10, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, 8, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, 14, 73], [1, 12, 79], [1, -4, 83], [1, -14, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1440/c', 'ModularForm/GL2/Q/holomorphic/1440/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1440/2/a/c'], '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': '2-1440-1.1-c1-0-15', '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': '2-1440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.390937612381623, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1762578329781223926, 'z1': {'__RealLiteral__': 0, 'data': '1.76605150421174345688608754901', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20600811
{'Lhash': '2238736249347983997986321642489', 'Lhash_array': ['2238736249347983997986321642489'], 'label': '2-1440-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/2/a/c'}
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id: 24553122
{'Lhash': '2238736249347983997986321642489', 'Lhash_array': ['2238736249347983997986321642489'], 'label': '2-1440-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1440/2/a/c/1/1'}
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id: 23920
{'Lhash': '1762578329781223926', 'Lhash_array': ['1762578329781223926'], 'label': '2-1440-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1440/c'}