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lfunc_lfunctions • Show schema
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{'Lhash': '406111012663853765102946973518', 'a10': [-9.033182842865072, -7.579740391805016], 'a2': [0.32614009210243955, 1.37609325277156], 'a3': [1.7397370509872427, -2.4440366186745672], 'a4': [-1.7872652806468246, 0.8975983604009243], 'a5': [-6.688256347636567, 4.979222365811288], 'a6': [3.9306203025276956, 1.5969420895439776], 'a7': [-10.245759371952234, 6.738741948275035], 'a8': [-1.8180779106881748, -2.1667008816788074], 'a9': [-2.9466299868444246, -8.503962118955448], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.41418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.32614009210243955, -1.37609325277156]]], [3, [[1.0, 0], [-1.7397370509872427, 2.4440366186745672]]]], 'bad_primes': [2, 3], 'central_character': '162.5', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3754739938431260929126862043097', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': -0.9407422158450766, 'root_number': '-0.9827215044584859 - 0.18509036894136313*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.470371107923', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.32036510107022947003319185117', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.13033285640920146237851100459', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05787328235848446197845890175', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.41418028263681, 'bad_primes': [2, 3], 'central_character': '81.5', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/3/h/a/5/15'], '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': '2-162-81.5-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-162-81.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.100995069636483, 'root_angle': -0.4703711079225383, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.32036510107022947003319185117', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '406111012663853765102946973518', 'Lhash_array': ['406111012663853765102946973518'], 'label': '2-162-81.5-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/3/h/a/5/15'}