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lfunc_lfunctions • Show schema
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{'Lhash': '1070926210579734911147199703160', 'a10': [-94339194709115260, 0.0], 'a2': [262144.0, 0.0], 'a3': [-1158686329.1289358, 0.0], 'a4': [68719476736.0, 0.0], 'a5': [-359875468098.12646, 0.0], 'a6': [-303742669063175.75, 0.0], 'a7': [-6584322597724269.0, 0.0], 'a8': [18014398509481984, 0.0], 'a9': [892270103419291000, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.342807624921097, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '18.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [-262144.0, 0]]]], 'bad_primes': [2], 'central_character': '2.1', 'coefficient_field': 'CDF', 'conductor': 2, 'conductor_radical': 2, 'conjugate': '1070926210579734911147199703160', 'degree': 2, 'euler_factors': [[[1.0, 0], [-262144.0, 0]], [[1.0, 0], [1158686329.1289358, 0], [450283905890997400, 0]], [[1.0, 0], [359875468098.12646, 0], [72759576141834256000000000, 0]], [[1.0, 0], [6584322597724269.0, 0], [18562115921017575000000000000000, 0]], [[1.0, 0], 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['0.844811819902837591930642767390411', '3.72453168370163521021637470904896', '5.69411201142775513597962334610621', '6.61171213408361419346297653220069', '10.24672736015074998865242365012194', '11.83403183625011824699565345154252', '13.08662161694281413678592112086065', '15.84735804575658006118092166087303', '16.87358798325217309157824296803588', '18.92295359697899073731511353686517'], 'prelabel': '2-2-1.1-c37-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1644696691080725, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c37-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844811819902837591930642767390', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.72453168370163521021637470905', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.69411201142775513597962334611', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.342807624921097, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 2, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2/38/a/b/1/1'], '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': '2-2-1.1-c37-0-0', 'motivic_weight': 37, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [37], 'order_of_vanishing': 0, 'prelabel': '2-2-1.1-c37-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1644696691080725, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c37-0', 'z1': {'__RealLiteral__': 0, 'data': '0.844811819902837591930642767390', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1070926210579734911147199703160', 'Lhash_array': ['1070926210579734911147199703160'], 'label': '2-2-1.1-c37-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2/38/a/b/1/1'}