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lfunc_lfunctions • Show schema
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{'Lhash': '2021707153909482402559280747963', 'a10': [17.36992267979343, 0.0], 'a2': [0.6947969071917371, 0.0], 'a3': [-9.0, 0.0], 'a4': [-31.517257257756796, 0.0], 'a5': [25.0, 0.0], 'a6': [-6.253172164725634, 0.0], 'a7': [83.16826313352594, 0.0], 'a8': [-44.131593895991344, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.1', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6947969071917371, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [-83.16826313352594, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [674.6552574851338, 0], [371293.0, 0]], [[1.0, 0], [-1927.6574547275004, 0], [1419857.0, 0]], 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['1.59484573552482972426383062529363', '3.65395604422640982017472634607418', '5.03436452128696154400275564747713', '5.60948020799022816143088308015736', '7.22066646521201092076179309306230', '8.347440477958327608953965417041102', '9.607877424638736412911168724111066', '10.20538566570068564590945717519321', '11.60461963771608919651196250168749'], 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59484573552482972426383062529', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65395604422640982017472634607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03436452128696154400275564748', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/a/c/1/2'], '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': '2-165-1.1-c5-0-20', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-165-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59484573552482972426383062529', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2021707153909482402559280747963', 'Lhash_array': ['2021707153909482402559280747963'], 'label': '2-165-1.1-c5-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/a/c/1/2'}