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lfunc_lfunctions • Show schema
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{'Lhash': '1458324122480330187730820566428', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': -1, 'a5': 0, 'a6': -1, 'a7': 2, 'a8': -3, '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, -1, 2], [1, 1], [1], [1, -2, 7], [1], [1, 4, 13], [1, -6, 17], [1, 6, 19], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -6, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, -4, 61], [1, 12, 67], [1, -8, 71], [1, 16, 73], [1, -2, 79], [1, 0, 83], [1, -10, 89], [1, -6, 97], [1, -14, 101], [1, -8, 103], [1, 8, 107], [1, 0, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, 1], 1]], [1], [[[1, -2, 7], 1]], [1], [[[1, 4, 13], 1]], [[[1, -6, 17], 1]], 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-0.4927961356857159, -0.42289608124497097, -0.2853994692613516, -0.09963051206484806, 0.11310197097921024, 0.33093385698428746, 0.5328834388681155], 'positive_zeros': ['1.15041488736547096377700755887749', '2.32161313475227573311788760929880', '3.17569966876548118518813908856149', '4.13411067705958410301366694386720', '4.79078422918902924777600712566430', '4.99783150819232222291640223924677', '6.08598386330031551698826788433255', '6.28430969819310006189510844616933', '7.41475321437809035491184492201557'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.512593014723068, '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': 280341613909568465, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15041488736547096377700755888', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32161313475227573311788760930', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17569966876548118518813908856', '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, 1, -1, -1, 0, -1, 2, -3, 1, 0, 0, 1, -4, 2, 0, -1, 6, 1, -6, 0, -2, 0, -4, 3, 0, -4, -1, -2, 6, 0, 8, 5, 0, 6, 0, -1, 6, -6, 4, 0, -6, -2, 6, 0, 0, -4, -8, 1, -3, 0, -6, 4, -6, -1, 0, -6, 6, 6, 0, 0, 4, 8, 2, 7, 0, 0, -12, -6, 4, 0, 8, -3, -16, 6, 0, 6, 0, 4, 2, 0, 1, -6, 0, 2, 0, 6, -6, 0, 10, 0, -8, 4, -8, -8, 0, -5, 6, -3, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -6, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, 12, 67], 'euler7': [1, -2, 7], 'euler71': [1, -8, 71], 'euler73': [1, 16, 73], 'euler79': [1, -2, 79], 'euler83': [1, 0, 83], 'euler89': [1, -10, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, -1, 2], [1, 1, 0], [1, 0, 0], [1, -2, 7], [1, 0, 0], [1, 4, 13], [1, -6, 17], [1, 6, 19], [1, 4, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -6, 43], [1, 8, 47], [1, 6, 53], [1, 0, 59], [1, -4, 61], [1, 12, 67], [1, -8, 71], [1, 16, 73], [1, -2, 79], [1, 0, 83], [1, -10, 89], [1, -6, 97]], 'index': 238, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9075/n', 'ModularForm/GL2/Q/holomorphic/9075/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/9075/2/a/n'], '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-c1-0-238', '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': 280341613909568465, 'z1': {'__RealLiteral__': 0, 'data': '1.15041488736547096377700755888', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22934865
{'Lhash': '1458324122480330187730820566428', 'Lhash_array': ['1458324122480330187730820566428'], 'label': '2-9075-1.1-c1-0-238', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/n'}
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id: 24586956
{'Lhash': '1458324122480330187730820566428', 'Lhash_array': ['1458324122480330187730820566428'], 'label': '2-9075-1.1-c1-0-238', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/n/1/1'}
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id: 40353
{'Lhash': '280341613909568465', 'Lhash_array': ['280341613909568465'], 'label': '2-9075-1.1-c1-0-238', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9075/n'}