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lfunc_lfunctions • Show schema
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{'Lhash': '1432547653622859355051828698903', 'a10': [10.0, 0.0], 'a2': [2.0, 0.0], 'a3': [3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [5.0, 0.0], 'a6': [6.0, 0.0], 'a7': [2.4453783326420178, 0.0], 'a8': [8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.8717763053388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [31, [[1.0, 0], [-31.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-2.4453783326420178, 0], [343.0, 0]], [[1.0, 0], [-25.58485665035234, 0], [1331.0, 0]], [[1.0, 0], [73.98159947813014, 0], [2197.0, 0]], [[1.0, 0], [-53.69277332994631, 0], [4913.0, 0]], [[1.0, 0], [33.034764902642415, 0], [6859.0, 0]], [[1.0, 0], 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'3.16557386660950350071284963386399', '4.45742426749114393988551300859758', '5.08986512783435957623730035788560', '6.26228442545647969774739879241726', '7.07639720825996051063315695440766', '7.84713290693159650056050242343432', '8.959390092455241343347346398237736', '9.662964155003185899629133757919984'], 'prelabel': '2-930-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.40754860296838, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13008083880916530277942563477', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41395145554959314049646512796', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16557386660950350071284963386', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.8717763053388, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/4/a/r/1/3'], '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': '2-930-1.1-c3-0-31', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-930-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.40754860296838, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13008083880916530277942563477', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1432547653622859355051828698903', 'Lhash_array': ['1432547653622859355051828698903'], 'label': '2-930-1.1-c3-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/4/a/r/1/3'}