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lfunc_lfunctions • Show schema
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{'Lhash': '1789279212584281574107264466860', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.356242591224525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '2925.1', 'coefficient_field': '1.1.1.1', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1], [1, -1, 7], [1, -3, 11], [1, 1], [1, 3, 17], [1, 4, 19], [1, 9, 23], [1, -6, 29], [1, -2, 31], [1, -1, 37], [1, -3, 41], [1, 2, 43], [1, 6, 47], [1, -9, 53], [1, -12, 59], [1, -5, 61], [1, -4, 67], [1, 9, 71], [1, 14, 73], [1, 7, 79], [1, 0, 83], [1, 15, 89], [1, 5, 97], [1, -12, 101], [1, 14, 103], [1, -3, 107], [1, 10, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [1], [1], [[[1, -1, 7], 1]], [[[1, -3, 11], 1]], [[[1, 1], 1]], [[[1, 3, 17], 1]], 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0.011936429889040867, -0.45675959938637084, -0.8807892090806879, -1.2375974877716474, -1.5085470039304434, -1.6799581275771052, -1.743863158861178, -1.6984305239946809], 'positive_zeros': ['1.41149241933237558048400936281085', '2.56854601966758836508468679404837', '3.97212069424474633277892264236313', '4.25960261379844898363305917119882', '5.17476573972367257507257169597869', '6.11005687269025714279511542678952', '6.76645673034580029340057189177506', '7.86809744691158498969719830425285', '8.492412477320767612496192676444465'], 'prelabel': '2-2925-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.832829667102341, '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': 723172447418352740, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41149241933237558048400936281', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56854601966758836508468679405', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97212069424474633277892264236', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.356242591224525, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 3, 0, -1, 0, 0, 4, -3, 0, -4, 0, 0, 0, -9, 0, 0, 0, 0, -2, 6, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, -2, -6, 0, 0, -6, 0, -6, 0, 0, 2, 9, 0, 0, 0, 0, 0, 12, 0, 5, 0, 0, -8, 0, 0, 4, 6, 0, 0, -9, 0, -14, 0, 0, 8, 3, 0, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, -1, 18, 0, 0, 0, 0, -5, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 2], 'euler23': [1, 9, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -1, 37], 'euler41': [1, -3, 41], 'euler43': [1, 2, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -12, 59], 'euler61': [1, -5, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 7], 'euler71': [1, 9, 71], 'euler73': [1, 14, 73], 'euler79': [1, 7, 79], 'euler83': [1, 0, 83], 'euler89': [1, 15, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 0, 0], [1, -1, 7], [1, -3, 11], [1, 1, 0], [1, 3, 17], [1, 4, 19], [1, 9, 23], [1, -6, 29], [1, -2, 31], [1, -1, 37], [1, -3, 41], [1, 2, 43], [1, 6, 47], [1, -9, 53], [1, -12, 59], [1, -5, 61], [1, -4, 67], [1, 9, 71], [1, 14, 73], [1, 7, 79], [1, 0, 83], [1, 15, 89], [1, 5, 97]], 'index': 71, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2925/k', 'ModularForm/GL2/Q/holomorphic/2925/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/2925/2/a/k'], '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': '2-2925-1.1-c1-0-71', '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': '2-2925-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.832829667102341, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 723172447418352740, 'z1': {'__RealLiteral__': 0, 'data': '1.41149241933237558048400936281', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20154022
{'Lhash': '1789279212584281574107264466860', 'Lhash_array': ['1789279212584281574107264466860'], 'label': '2-2925-1.1-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/2/a/k'}
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id: 24559371
{'Lhash': '1789279212584281574107264466860', 'Lhash_array': ['1789279212584281574107264466860'], 'label': '2-2925-1.1-c1-0-71', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/2/a/k/1/1'}
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id: 26939
{'Lhash': '723172447418352740', 'Lhash_array': ['723172447418352740'], 'label': '2-2925-1.1-c1-0-71', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2925/k'}