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lfunc_lfunctions • Show schema
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{'Lhash': '2699622005007703238914672885606', 'a10': [2.589326546179195, 0.0], 'a2': [0.0, 2.7138081941168117], 'a3': [0.26578140604630845, 0.0], 'a4': [-5.364754914455551, 0.0], 'a5': [0.0, -0.95413027044156], 'a6': [0.0, 0.7212797575723594], 'a7': [0.0, -4.284519179867441], 'a8': [0.0, -9.131299458044285], 'a9': [-2.9293602442000473, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-0.7558955313182655, 3.5254250730561667]]], [31, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [13, 31], 'central_character': '403.311', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '525942598703889052612099117360', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.7138081941168117], [-2.0, 0]], [[1.0, 0], [-0.26578140604630845, 0], [3.0, 0]], [[1.0, 0], [0, 0.95413027044156], [-5.0, 0]], [[1.0, 0], [0, 4.284519179867441], [-7.0, 0]], 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['2.12962625862493964227764309698265', '2.66480443416022957560624528637886', '3.94112232960077448631019972840995', '5.16396320088319407315040491360533', '6.23844685099547457350647770252436', '8.258935562039015828478262271708207', '8.980549374664927104454213063918598', '9.424755182912250136311848689395007', '10.69663411392135735976762705022842', '11.42096909230972130329776978512845'], 'prelabel': '2-403-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.06723170753871163, 'root_number': '0.9777769899007992 + 0.20964769977400782*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0336158537694', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12962625862493964227764309698', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66480443416022957560624528638', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94112232960077448631019972841', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '13.12', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/c/b/311/32'], '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': '2-403-13.12-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-403-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.033615853769355816, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12962625862493964227764309698', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2699622005007703238914672885606', 'Lhash_array': ['2699622005007703238914672885606'], 'label': '2-403-13.12-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/c/b/311/32'}