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lfunc_lfunctions • Show schema
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{'Lhash': '3502643008173109741434382741495', 'a10': -2, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': -2, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8144741006170603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '102.1', 'coefficient_field': '1.1.1.1', 'conductor': 102, 'conductor_radical': 102, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 2, 5], [1, 0, 7], [1, 4, 11], [1, 2, 13], [1, -1], [1, -4, 19], [1, 0, 23], [1, 10, 29], [1, -8, 31], [1, 2, 37], [1, -10, 41], [1, -12, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, 12, 67], [1, 0, 71], [1, -10, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, 14, 97], [1, 10, 101], [1, 8, 103], [1, 4, 107], [1, 10, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [[[1, 2, 5], 1]], [[[1, 0, 7], 1]], [[[1, 4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -1], 1]], [[[1, -4, 19], 1]], [[[1, 0, 23], 1]], [[[1, 10, 29], 1]], [[[1, -8, 31], 1]], [[[1, 2, 37], 1]], [[[1, -10, 41], 1]], [[[1, -12, 43], 1]], [[[1, 0, 47], 1]], [[[1, -6, 53], 1]], [[[1, -12, 59], 1]], [[[1, 10, 61], 1]], [[[1, 12, 67], 1]], [[[1, 0, 71], 1]], [[[1, -10, 73], 1]], [[[1, 8, 79], 1]], [[[1, -4, 83], 1]], [[[1, 6, 89], 1]], [[[1, 14, 97], 1]], [[[1, 10, 101], 1]], [[[1, 8, 103], 1]], [[[1, 4, 107], 1]], [[[1, 10, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-102-1.1-c1-0-1', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/102/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4796779277944783, 1.4896980342820154, 1.518968235835808, 1.565224322104513, 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-0.4499966362826537, -0.4285572827169774, -0.21876593165027475, 0.0666646691496939, 0.2913022517516683, 0.3354203282169249, 0.13237919608492268, -0.3087930042080716], 'positive_zeros': ['2.76309813409348720224135008444252', '4.13875090005906653574798019220750', '5.51457882926074302977186886249634', '7.36440720073199929079936076773581', '7.958882066985845549410362974675453', '9.570394810938145814587700544155604', '10.84353554600873070196710460126995', '11.93324918288479588422006823319200', '12.87130622556280185790540229129103', '13.82453782976520878118936880007635'], 'prelabel': '2-102-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9024821885317518, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2057986112349787613, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.76309813409348720224135008444', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13875090005906653574798019221', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.51457882926074302977186886250', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8144741006170603, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 102, 'conductor_radical': 102, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -2, 1, 0, 1, 1, -2, -4, 1, -2, 0, -2, 1, 1, 1, 4, -2, 0, -4, 0, 1, -1, -2, 1, 0, -10, -2, 8, 1, -4, 1, 0, 1, -2, 4, -2, -2, 10, 0, 12, -4, -2, 0, 0, 1, -7, -1, 1, -2, 6, 1, 8, 0, 4, -10, 12, -2, -10, 8, 0, 1, 4, -4, -12, 1, 0, 0, 0, 1, 10, -2, -1, 4, 0, -2, -8, -2, 1, 10, 4, 0, -2, 12, -10, -4, -6, -2, 0, 0, 8, 0, -8, 1, -14, -7, -4, -1], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, -12, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 2, 5], [1, 0, 7], [1, 4, 11], [1, 2, 13], [1, -1, 0], [1, -4, 19], [1, 0, 23], [1, 10, 29], [1, -8, 31], [1, 2, 37], [1, -10, 41], [1, -12, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, 10, 61], [1, 12, 67], [1, 0, 71], [1, -10, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, 14, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/102/c', 'ModularForm/GL2/Q/holomorphic/102/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/102/2/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': '2-102-1.1-c1-0-1', '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': '2-102-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9024821885317518, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2057986112349787613, 'z1': {'__RealLiteral__': 0, 'data': '2.76309813409348720224135008444', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9965205
{'Lhash': '3502643008173109741434382741495', 'Lhash_array': ['3502643008173109741434382741495'], 'label': '2-102-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/102/2/a/c'}
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id: 24546712
{'Lhash': '3502643008173109741434382741495', 'Lhash_array': ['3502643008173109741434382741495'], 'label': '2-102-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/102/2/a/c/1/1'}
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id: 22100
{'Lhash': '2057986112349787613', 'Lhash_array': ['2057986112349787613'], 'label': '2-102-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/102/c'}