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lfunc_lfunctions • Show schema
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{'Lhash': '1248341221626102234115227040558', 'a10': 0, 'a2': 0, 'a3': 158, 'a4': 0, 'a5': -625, 'a6': 0, 'a7': 1922, 'a8': 0, 'a9': 18403, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 130.36115521956074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 625]]], 'bad_primes': [2, 5], 'central_character': '320.319', 'coefficient_field': '1.1.1.1', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[1], [1, -158, 6561], [1, 625], [1, -1922, 5764801], [1, 0, -214358881], [1, 0, -815730721], [1, 0, -6975757441], [1, 0, -16983563041], [1, -211202, 78310985281], [1, 20642, 500246412961], [1, 0, -852891037441], [1, 0, -3512479453921], [1, 5419198, 7984925229121], [1, -2519518, 11688200277601], [1, -9618242, 23811286661761], [1, 0, -62259690411361], [1, 0, -146830437604321], [1, -11061598, 191707312997281], [1, -20249758, 406067677556641], [1, 0, -645753531245761], [1, 0, -806460091894081], [1, 0, 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'0.984767586116670727188127507535', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.11417562067079059331440748298', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16179533194050274124056986071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 130.36115521956074, 'bad_primes': [2, 5], 'central_character': '20.19', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'dirichlet_coefficients': [1, 0, 158, 0, -625, 0, 1922, 0, 18403, 0, 0, 0, 0, 0, -98750, 0, 0, 0, 0, 0, 303676, 0, 211202, 0, 390625, 0, 1871036, 0, -20642, 0, 0, 0, 0, 0, -1201250, 0, 0, 0, 0, 0, -5419198, 0, 2519518, 0, -11501875, 0, 9618242, 0, -2070717, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11061598, 0, 35370566, 0, 0, 0, 20249758, 0, 33369916, 0, 0, 0, 0, 0, 61718750, 0, 0, 0, 0, 0, 174881605, 0, 30884638, 0, 0, 0, -3261436, 0, -106804798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -214358881], 'euler13': [1, 0, -815730721], 'euler17': [1, 0, -6975757441], 'euler19': [1, 0, -16983563041], 'euler2': [1, 0, 0], 'euler23': [1, -211202, 78310985281], 'euler29': [1, 20642, 500246412961], 'euler3': [1, -158, 6561], 'euler31': [1, 0, -852891037441], 'euler37': [1, 0, -3512479453921], 'euler41': [1, 5419198, 7984925229121], 'euler43': [1, -2519518, 11688200277601], 'euler47': [1, -9618242, 23811286661761], 'euler5': [1, 625, 0], 'euler53': [1, 0, -62259690411361], 'euler59': [1, 0, -146830437604321], 'euler61': [1, -11061598, 191707312997281], 'euler67': [1, -20249758, 406067677556641], 'euler7': [1, -1922, 5764801], 'euler71': [1, 0, -645753531245761], 'euler73': [1, 0, -806460091894081], 'euler79': [1, 0, -1517108809906561], 'euler83': [1, -30884638, 2252292232139041], 'euler89': [1, 106804798, 3936588805702081], 'euler97': [1, 0, -7837433594376961], 'euler_factors': [[1, 0, 0], [1, -158, 6561], [1, 625, 0], [1, -1922, 5764801], [1, 0, -214358881], [1, 0, -815730721], [1, 0, -6975757441], [1, 0, -16983563041], [1, -211202, 78310985281], [1, 20642, 500246412961], [1, 0, -852891037441], [1, 0, -3512479453921], [1, 5419198, 7984925229121], [1, -2519518, 11688200277601], [1, -9618242, 23811286661761], [1, 0, -62259690411361], [1, 0, -146830437604321], [1, -11061598, 191707312997281], [1, -20249758, 406067677556641], [1, 0, -645753531245761], [1, 0, -806460091894081], [1, 0, -1517108809906561], [1, -30884638, 2252292232139041], [1, 106804798, 3936588805702081], [1, 0, -7837433594376961]], 'index': 67, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/9/h/b', 'ModularForm/GL2/Q/holomorphic/320/9/h/b/319/1'], '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': '2-320-20.19-c8-0-67', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-320-20.19-c8-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.417580970571688, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c8-0', 'trace_hash': 1378202193156035774, 'z1': {'__RealLiteral__': 0, 'data': '0.984767586116670727188127507535', 'prec': 107}}
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lfunc_instances • Show schema
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id: 24593133
{'Lhash': '1248341221626102234115227040558', 'Lhash_array': ['1248341221626102234115227040558'], 'label': '2-320-20.19-c8-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/9/h/b/319/1'}
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id: 24019936
{'Lhash': '1248341221626102234115227040558', 'Lhash_array': ['1248341221626102234115227040558'], 'label': '2-320-20.19-c8-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/9/h/b'}