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lfunc_lfunctions • Show schema
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{'Lhash': '4354501520859378283208449050002', 'a10': [-17.5, 30.31088913245535], 'a2': [2.5, -4.330127018922194], 'a3': [3.5, -6.06217782649107], 'a4': [-8.5, -14.722431864335457], 'a5': [-7.0, 0.0], 'a6': [-17.5, -30.31088913245535], 'a7': [6.5, 11.258330249197702], 'a8': [-45.0, 0.0], 'a9': [-11.0, -19.05255888325765], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.971322790970168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.22', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '1260193533372572969018453283717', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5, 4.330127018922194], [-4.0, -6.928203230275509]], [[1.0, 0], [-3.5, 6.06217782649107], [-13.5, -23.382685902179844]], [[1.0, 0], [7.0, 0], [125.0, 0]], [[1.0, 0], [-6.5, -11.258330249197702], [-171.5, 297.04671349806245]], [[1.0, 0], [-13.0, 22.516660498395403], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.43509601153140177302241243049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.29682433143681495420698626070', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99765533443047055472738959638', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.971322790970168, 'bad_primes': [13], 'central_character': '13.9', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/4/c/e/22/1'], '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': '2-13e2-13.9-c3-0-32', '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': '2-13e2-13.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': -0.41870761805923334, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.43509601153140177302241243049', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4354501520859378283208449050002', 'Lhash_array': ['4354501520859378283208449050002'], 'label': '2-13e2-13.9-c3-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/4/c/e/22/1'}