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lfunc_lfunctions • Show schema
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{'Lhash': '1208414592096793429786987144773', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 64, 'a5': -198, 'a6': 0, 'a7': -343, 'a8': 0, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.934921609406445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[7, [1, 343]], [13, [1, -2197]]], 'bad_primes': [7, 13], 'central_character': '91.90', 'coefficient_field': '1.1.1.1', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[1, 0, -64], [1, 0, -729], [1, 198, 15625], [1, 343], [1, 0, -1771561], [1, -2197], [1, 0, -24137569], [1, -11450, 47045881], [1, 19710, 148035889], [1, -47322, 594823321], [1, -7810, 887503681], [1, 0, -2565726409], [1, -124290, 4750104241], [1, -27610, 6321363049], [1, -5346, 10779215329], [1, 123030, 22164361129], [1, 210870, 42180533641], [1, 0, -51520374361], [1, 0, -90458382169], [1, 0, -128100283921], [1, -439234, 151334226289], [1, 953678, 243087455521], [1, -733626, 326940373369], [1, 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'3.09174731571012501073196587746865', '4.11160659142009205949268565211083', '6.19511514927744308186693114276709', '7.25284868518562052705655619608414', '8.077656031098149842566433419296760', '9.786326236716095479402582486778304', '10.87390212793482459572903981220027', '11.94742534616199455018316934348810', '12.49441924924866274103486417845358'], 'prelabel': '2-91-91.90-c6-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.575469550702577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c6-0', 'trace_hash': 593778912074102850, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.953271029003756203305006493149154', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '3.09174731571012501073196587746865', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.11160659142009205949268565211083', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.934921609406445, 'bad_primes': [7, 13], 'central_character': '91.90', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 64, -198, 0, -343, 0, 729, 0, 0, 0, 2197, 0, 0, 4096, 0, 0, 11450, -12672, 0, 0, -19710, 0, 23579, 0, 0, -21952, 47322, 0, 7810, 0, 0, 0, 67914, 46656, 0, 0, 0, 0, 124290, 0, 27610, 0, -144342, 0, 5346, 0, 117649, 0, 0, 140608, -123030, 0, 0, 0, 0, 0, -210870, 0, 0, 0, -250047, 262144, -435006, 0, 0, 0, 0, 0, 0, 0, 439234, 0, 0, 732800, 0, 0, -953678, -811008, 531441, 0, 733626, 0, 0, 0, 0, 0, -571230, 0, -753571, -1261440, 0, 0, -2267100, 0, -1449646, 0, 0, 1509056], 'euler11': [1, 0, -1771561], 'euler13': [1, -2197, 0], 'euler17': [1, 0, -24137569], 'euler19': [1, -11450, 47045881], 'euler2': [1, 0, -64], 'euler23': [1, 19710, 148035889], 'euler29': [1, -47322, 594823321], 'euler3': [1, 0, -729], 'euler31': [1, -7810, 887503681], 'euler37': [1, 0, -2565726409], 'euler41': [1, -124290, 4750104241], 'euler43': [1, -27610, 6321363049], 'euler47': [1, -5346, 10779215329], 'euler5': [1, 198, 15625], 'euler53': [1, 123030, 22164361129], 'euler59': [1, 210870, 42180533641], 'euler61': [1, 0, -51520374361], 'euler67': [1, 0, -90458382169], 'euler7': [1, 343, 0], 'euler71': [1, 0, -128100283921], 'euler73': [1, -439234, 151334226289], 'euler79': [1, 953678, 243087455521], 'euler83': [1, -733626, 326940373369], 'euler89': [1, 571230, 496981290961], 'euler97': [1, 1449646, 832972004929], 'euler_factors': [[1, 0, -64], [1, 0, -729], [1, 198, 15625], [1, 343, 0], [1, 0, -1771561], [1, -2197, 0], [1, 0, -24137569], [1, -11450, 47045881], [1, 19710, 148035889], [1, -47322, 594823321], [1, -7810, 887503681], [1, 0, -2565726409], [1, -124290, 4750104241], [1, -27610, 6321363049], [1, -5346, 10779215329], [1, 123030, 22164361129], [1, 210870, 42180533641], [1, 0, -51520374361], [1, 0, -90458382169], [1, 0, -128100283921], [1, -439234, 151334226289], [1, 953678, 243087455521], [1, -733626, 326940373369], [1, 571230, 496981290961], [1, 1449646, 832972004929]], 'index': 23, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/7/b/a', 'ModularForm/GL2/Q/holomorphic/91/7/b/a/90/1'], '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': '2-91-91.90-c6-0-23', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-91-91.90-c6-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.575469550702577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c6-0', 'trace_hash': 593778912074102850, 'z1': {'__RealLiteral__': 0, 'data': '0.953271029003756203305006493149154', 'prec': 117}}
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lfunc_instances • Show schema
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id: 24558014
{'Lhash': '1208414592096793429786987144773', 'Lhash_array': ['1208414592096793429786987144773'], 'label': '2-91-91.90-c6-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/7/b/a/90/1'}
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id: 23322436
{'Lhash': '1208414592096793429786987144773', 'Lhash_array': ['1208414592096793429786987144773'], 'label': '2-91-91.90-c6-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/7/b/a'}