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lfunc_lfunctions • Show schema
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{'Lhash': '2155665577142036933137225326291', 'a10': [0.0, 0.0], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [0.0, 0.0], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [-0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.247662531582506, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9510565162951535, 0.30901699437494745]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '2500.1999', 'coefficient_field': 'CDF', 'conductor': 2500, 'conductor_radical': 10, 'conjugate': '394143839695213745307366672409', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], 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'2-50e2-100.79-c0-0-5', 'leading_term': '0.37214938581661192960947761300627', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2500/1/h/e/1999/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.37214938581661194, 0.441053361384501, 0.5148508163634634, 0.5949120397261116, 0.681891918718943, 0.7757076945933222, 0.8755898209505931, 0.9801700934961083, 1.0875795322468802, 1.1955418683995445, 1.3014590735384437, 1.4024910934717214, 1.49563386805215, 1.577799502874607, 1.645901336735925, 1.696945287695719, 1.7281275514152414, 1.7369375664591125, 1.7212641716502994, 1.6795020562729441, 1.6106549400274084, 1.5144314171677775, 1.391329065267292, 1.2427022645875874, 1.0708092114085301, 0.8788338489964691, 0.6708788907143285, 0.45192677319102353, 0.2277662484609963, 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'7.935967718288424748632669553072959', '8.678654596774608049580928189358536', '9.202563327004416318755911528160830'], 'prelabel': '2-50e2-100.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 0.8200000000000001, 'root_number': '-0.84432792550201507854855806396698 + 0.53582679497899661827130876786751*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.41', 'prec': 14}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70052029853804210968613347936', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42315183133040485919879929671', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69611484380375774875207772922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.247662531582506, 'bad_primes': [2, 5], 'central_character': '100.79', 'conductor': 2500, 'conductor_radical': 10, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2500/1/h/e/1999/1'], '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': '2-50e2-100.79-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-50e2-100.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1169881519436569, 'root_angle': 0.41000000000000003, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70052029853804210968613347936', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2155665577142036933137225326291', 'Lhash_array': ['2155665577142036933137225326291'], 'label': '2-50e2-100.79-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2500/1/h/e/1999/1'}