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lfunc_lfunctions • Show schema
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{'Lhash': '1176741085938539789566001748590,3736509563145137792210602058760', 'a10': 0, 'a2': 0, 'a3': -10, 'a4': 26, 'a5': -10, 'a6': 0, 'a7': -70, 'a8': 0, 'a9': -87, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.089552853245298, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[5, [1, 10, 625]], [7, [1, 70, 2401]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': '1.1.1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 0, -26, 0, 256], [1, 10, 187, 810, 6561], [1, 10, 625], [1, 70, 2401], [1, -178, 37203, -2606098, 214358881], [1, -10, 57147, -285610, 815730721], [1, -970, 402267, -81015370, 6975757441], [1, 0, -212042, 0, 16983563041], [1, 0, -68906, 0, 78310985281], [1, -382, 1451043, -270181342, 500246412961], [1, 0, -737642, 0, 852891037441], [1, 0, -1086986, 0, 3512479453921], [1, 0, 2845078, 0, 7984925229121], [1, 0, -6695306, 0, 11688200277601], [1, -4390, 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'0.0', 'prec': 10}, 'spectral_label': 'c4e2-0', 'trace_hash': 2248129801582957210, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.928285038264232944680980413603', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.94758631634964076960185359270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57956700653466011907015963814', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 13.089552853245298, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, 0, -10, 26, -10, 0, -70, 0, -87, 0, 178, -260, 10, 0, 100, 420, 970, 0, 0, -260, 700, 0, 0, 0, -525, 0, 1930, -1820, 382, 0, 0, 0, -1780, 0, 700, -2262, 0, 0, -100, 0, 0, 0, 0, 4628, 870, 0, 4390, -4200, 2499, 0, -9700, 260, 0, 0, -1780, 0, 0, 0, 0, 2600, 0, 0, 6090, 4264, -100, 0, 0, 25220, 0, 0, 8908, 0, -17300, 0, 5250, 0, -12460, 0, 11122, -4200, -1492, 0, -3980, 18200, -9700, 0, -3820, 0, 0, 0, -700, 0, 0, 0, 0, 0, -18470, 0, -15486, -13650], 'euler11': [1, -178, 37203, -2606098, 214358881], 'euler13': [1, -10, 57147, -285610, 815730721], 'euler17': [1, -970, 402267, -81015370, 6975757441], 'euler19': [1, 0, -212042, 0, 16983563041], 'euler2': [1, 0, -26, 0, 256], 'euler23': [1, 0, -68906, 0, 78310985281], 'euler29': [1, -382, 1451043, -270181342, 500246412961], 'euler3': [1, 10, 187, 810, 6561], 'euler31': [1, 0, -737642, 0, 852891037441], 'euler37': [1, 0, -1086986, 0, 3512479453921], 'euler41': [1, 0, 2845078, 0, 7984925229121], 'euler43': [1, 0, -6695306, 0, 11688200277601], 'euler47': [1, -4390, 14577387, -21421799590, 23811286661761], 'euler5': [1, 10, 625, 0, 0], 'euler53': [1, 0, -13261538, 0, 62259690411361], 'euler59': [1, 0, -11092322, 0, 146830437604321], 'euler61': [1, 0, -23947082, 0, 191707312997281], 'euler67': [1, 0, -36108866, 0, 406067677556641], 'euler7': [1, 70, 2401, 0, 0], 'euler71': [1, -8908, 70661478, -226367254348, 645753531245761], 'euler73': [1, 17300, 131618982, 491289569300, 806460091894081], 'euler79': [1, -11122, 108824883, -433202800882, 1517108809906561], 'euler83': [1, 3980, 98876742, 188884117580, 2252292232139041], 'euler89': [1, 0, -124831082, 0, 3936588805702081], 'euler97': [1, 18470, 262343787, 1635135820070, 7837433594376961], 'euler_factors': [[1, 0, -26, 0, 256], [1, 10, 187, 810, 6561], [1, 10, 625, 0, 0], [1, 70, 2401, 0, 0], [1, -178, 37203, -2606098, 214358881], [1, -10, 57147, -285610, 815730721], [1, -970, 402267, -81015370, 6975757441], [1, 0, -212042, 0, 16983563041], [1, 0, -68906, 0, 78310985281], [1, -382, 1451043, -270181342, 500246412961], [1, 0, -737642, 0, 852891037441], [1, 0, -1086986, 0, 3512479453921], [1, 0, 2845078, 0, 7984925229121], [1, 0, -6695306, 0, 11688200277601], [1, -4390, 14577387, -21421799590, 23811286661761], [1, 0, -13261538, 0, 62259690411361], [1, 0, -11092322, 0, 146830437604321], [1, 0, -23947082, 0, 191707312997281], [1, 0, -36108866, 0, 406067677556641], [1, -8908, 70661478, -226367254348, 645753531245761], [1, 17300, 131618982, 491289569300, 806460091894081], [1, -11122, 108824883, -433202800882, 1517108809906561], [1, 3980, 98876742, 188884117580, 2252292232139041], [1, 0, -124831082, 0, 3936588805702081], [1, 18470, 262343787, 1635135820070, 7837433594376961]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/5/c/c'], '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': '4-35e2-1.1-c4e2-0-0', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4, 4], 'order_of_vanishing': 0, 'prelabel': '4-35e2-1.1-c4e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9020906150692591, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c4e2-0', 'trace_hash': 2248129801582957210, 'z1': {'__RealLiteral__': 0, 'data': '0.928285038264232944680980413603', 'prec': 107}}
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{'Lhash': '1176741085938539789566001748590,3736509563145137792210602058760', 'Lhash_array': ['1176741085938539789566001748590', '3736509563145137792210602058760'], 'label': '4-35e2-1.1-c4e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/5/c/c'}