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lfunc_lfunctions • Show schema
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{'Lhash': '1442355138192969244653595660948', 'a10': 0, 'a2': -2, 'a3': -1, 'a4': 2, 'a5': 0, 'a6': 2, 'a7': 3, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': '1.1.1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 1], [1], [1, -3, 7], [1], [1, 1, 13], [1, 2, 17], [1, -5, 19], [1, -6, 23], [1, 10, 29], [1, 3, 31], [1, -2, 37], [1, -8, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, 10, 59], [1, 7, 61], [1, 3, 67], [1, 8, 71], [1, -14, 73], [1, 0, 79], [1, 6, 83], [1, 0, 89], [1, -17, 97], [1, 12, 101], [1, 4, 103], [1, 12, 107], [1, 5, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [[[1, 1], 1]], [1], [[[1, -3, 7], 1]], [1], [[[1, 1, 13], 1]], [[[1, 2, 17], 1]], [[[1, -5, 19], 1]], [[[1, -6, 23], 1]], [[[1, 10, 29], 1]], [[[1, 3, 31], 1]], [[[1, -2, 37], 1]], [[[1, -8, 41], 1]], [[[1, 1, 43], 1]], [[[1, -2, 47], 1]], [[[1, 4, 53], 1]], [[[1, 10, 59], 1]], [[[1, 7, 61], 1]], [[[1, 3, 67], 1]], [[[1, 8, 71], 1]], [[[1, -14, 73], 1]], [[[1, 0, 79], 1]], [[[1, 6, 83], 1]], [[[1, 0, 89], 1]], [[[1, -17, 97], 1]], [[[1, 12, 101], 1]], [[[1, 4, 103], 1]], [[[1, 12, 107], 1]], [[[1, 5, 109], 1]], [[[1, 4, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 235, 'label': '2-9075-1.1-c1-0-235', '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/9075/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.5037913032019437e-61, 0.09867830894059067, 0.19621555594156534, 0.29145655122133124, 0.3832201508985335, 0.4702918498960047, 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3.0985320704720962, 3.3227760810800344, 3.4307919700469838, 3.402534770359482, 3.2239825055273506, 2.8883858447580972], 'positive_zeros': ['1.13781757996508329611151326734634', '1.71419845103506630043143205824898', '2.70866001385341573464253183059336', '3.93276270400122129280671872838832', '4.80645524398487230267862763672545', '5.26550699194046601552455316284425', '6.16165631359848537381830780833421', '7.06328550761489343142245284992683', '7.63445690246110755414862928104615'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1975460723967484430, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13781757996508329611151326735', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71419845103506630043143205825', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70866001385341573464253183059', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, -2, -1, 2, 0, 2, 3, 0, 1, 0, 0, -2, -1, -6, 0, -4, -2, -2, 5, 0, -3, 0, 6, 0, 0, 2, -1, 6, -10, 0, -3, 8, 0, 4, 0, 2, 2, -10, 1, 0, 8, 6, -1, 0, 0, -12, 2, 4, 2, 0, 2, -2, -4, 2, 0, 0, -5, 20, -10, 0, -7, 6, 3, -8, 0, 0, -3, -4, -6, 0, -8, 0, 14, -4, 0, 10, 0, -2, 0, 0, 1, -16, -6, -6, 0, 2, 10, 0, 0, 0, -3, 12, 3, -4, 0, -8, 17, -4, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 13], 'euler17': [1, 2, 17], 'euler19': [1, -5, 19], 'euler2': [1, 2, 2], 'euler23': [1, -6, 23], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 3, 31], 'euler37': [1, -2, 37], 'euler41': [1, -8, 41], 'euler43': [1, 1, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, 10, 59], 'euler61': [1, 7, 61], 'euler67': [1, 3, 67], 'euler7': [1, -3, 7], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 2, 2], [1, 1, 0], [1, 0, 0], [1, -3, 7], [1, 0, 0], [1, 1, 13], [1, 2, 17], [1, -5, 19], [1, -6, 23], [1, 10, 29], [1, 3, 31], [1, -2, 37], [1, -8, 41], [1, 1, 43], [1, -2, 47], [1, 4, 53], [1, 10, 59], [1, 7, 61], [1, 3, 67], [1, 8, 71], [1, -14, 73], [1, 0, 79], [1, 6, 83], [1, 0, 89], [1, -17, 97]], 'index': 235, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9075/a', 'ModularForm/GL2/Q/holomorphic/9075/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/9075/2/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': '2-9075-1.1-c1-0-235', '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': '2-9075-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1975460723967484430, 'z1': {'__RealLiteral__': 0, 'data': '1.13781757996508329611151326735', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22951378
{'Lhash': '1442355138192969244653595660948', 'Lhash_array': ['1442355138192969244653595660948'], 'factors': ['2-9075-1.1-c1-0-235'], 'label': '2-9075-1.1-c1-0-235', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/a'}
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id: 24586943
{'Lhash': '1442355138192969244653595660948', 'Lhash_array': ['1442355138192969244653595660948'], 'factors': ['2-9075-1.1-c1-0-235'], 'label': '2-9075-1.1-c1-0-235', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/a/1/1'}
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id: 91318
{'Lhash': '1975460723967484430', 'Lhash_array': ['1975460723967484430'], 'factors': ['2-9075-1.1-c1-0-235'], 'label': '2-9075-1.1-c1-0-235', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9075/a'}