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lfunc_lfunctions • Show schema
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{'Lhash': '525561783218028876567731147592,1906389228279408018327700247814', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 382.72460434518035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '2450.1', 'coefficient_field': '1.1.1.1', 'conductor': 6002500, 'conductor_radical': 70, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 0, -2, 0, 9], [1], [1], [1, -6, 31, -66, 121], [1, 0, -25, 0, 169], [1, 0, 2, 0, 289], [1, 2, 39, 38, 361], [1, 0, 35, 0, 529], [1, 12, 94, 348, 841], [1, 16, 126, 496, 961], [1, 0, -25, 0, 1369], [1, 6, 91, 246, 1681], [1, 0, -82, 0, 1849], [1, 0, -13, 0, 2209], [1, 0, -25, 0, 2809], [1, 0, 118, 0, 3481], [1, 16, 186, 976, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, -20, 258, -1580, 6241], [1, 0, -166, 0, 6889], 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'4.71777690970606651764939440082373', '5.34788663796958346446342040386605', '5.45300789867343047372748065698331', '6.21532830151476193457497773794514', '6.30277971200210119303747218268615', '6.92683881924668456693936582754250', '7.19545151913731595438329629101208', '7.66663578946429618992588832323777', '7.79983141873359545484443776176742', '8.550850246433368041702615164307149', '8.921303883531473803900210860192251', '9.434853445333141616286163736916993'], 'prelabel': '4-2450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.423047421768582, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1207921718806691721, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41459514405894343044977775641', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50387593232407992736175011635', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.66938604235428700514382012354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 382.72460434518035, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 6002500, 'conductor_radical': 70, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, -16, 0, 0, 0, 0, -2, 0, 0, 0, 0, -6, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 20, 0, -5, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, 0, -25, 0, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 35, 0, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, -25, 0, 1369], 'euler41': [1, 6, 91, 246, 1681], 'euler43': [1, 0, -82, 0, 1849], 'euler47': [1, 0, -13, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -25, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -70, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, -20, 258, -1580, 6241], 'euler83': [1, 0, -166, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, -94, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, -2, 0, 9], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -6, 31, -66, 121], [1, 0, -25, 0, 169], [1, 0, 2, 0, 289], [1, 2, 39, 38, 361], [1, 0, 35, 0, 529], [1, 12, 94, 348, 841], [1, 16, 126, 496, 961], [1, 0, -25, 0, 1369], [1, 6, 91, 246, 1681], [1, 0, -82, 0, 1849], [1, 0, -13, 0, 2209], [1, 0, -25, 0, 2809], [1, 0, 118, 0, 3481], [1, 16, 186, 976, 3721], [1, 0, -70, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -130, 0, 5329], [1, -20, 258, -1580, 6241], [1, 0, -166, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -94, 0, 9409]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2450/2/c/e'], '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': '4-2450e2-1.1-c1e2-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2450e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.423047421768582, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1207921718806691721, 'z1': {'__RealLiteral__': 0, 'data': '0.41459514405894343044977775641', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '525561783218028876567731147592,1906389228279408018327700247814', 'Lhash_array': ['525561783218028876567731147592', '1906389228279408018327700247814'], 'label': '4-2450e2-1.1-c1e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2450/2/c/e'}