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lfunc_lfunctions • Show schema
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{'Lhash': '1368779308191018454063861902133', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 2.0], 'a4': [0, 0], 'a5': [2.0, 1.0], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.0, -1.0]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.369', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '1487040458613912614861404322504', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-3.0, 0]], [[1.0, 0], [-2.0, -1.0]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, 5.0], [-17.0, 0]], [[1.0, 0], [-8.0, 0], [19.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-5.0, 0], [29.0, 0]], [[1.0, 0], [-5.0, 0], [31.0, 0]], [[1.0, 0], 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0.394498231346636, 0.6341368717090798, 0.8796720823434041, 1.1127423837015504, 1.3165588272115176, 1.476772818343251, 1.5821992333137502, 1.6253574902670076, 1.6028028380771122, 1.5152312432047055, 1.367353319011579, 1.167545126885955, 0.9272957331510089, 0.6604824869552137, 0.3825144913767137, 0.10939214674707506, -0.14326447048152388, -0.36116356224401375, -0.5322119625938294], 'positive_zeros': ['1.07977648410735711665803284198288', '1.83492881296117993969960863090866', '2.81783495171724879901785858667183', '4.18722899653004125931631119656327', '5.33328016647002968014205843757266', '5.95137489070646669466531836892196', '6.74325802401862703672458195400883', '7.43975023962131211940246693186669', '8.375765579340527809822076059587757', '8.951532487729763002332319976483236'], 'prelabel': '2-1840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07977648410735711665803284198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83492881296117993969960863091', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81783495171724879901785858667', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/e/b/369/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-1840-5.4-c1-0-36', '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': '2-1840-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07977648410735711665803284198', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1368779308191018454063861902133', 'Lhash_array': ['1368779308191018454063861902133'], 'label': '2-1840-5.4-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/e/b/369/2'}