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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3724.1251', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.2708404681430051, -0.962624246950012], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.2708404681430051, 0.962624246950012], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8532908816321556, -0.5214352033794981], 'algebraic': True, 'analytic_conductor': 17.29418329373136, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [19, [1]]], 'bad_primes': [2, 7, 19], 'central_character': '3724.1251', 'coeff_info': ['x^126 - 1', '0.998756921218922 + 0.0498458856606972*I', '\\\\zeta_{126}'], 'conductor': 3724, 'conductor_radical': 266, 'conjugate': 'dirichlet_L_3724.899', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^100', 0, 'a^37', 0, 0, 0, 'a^74', 0, 'a^171', 0, 'a^59', 0, 'a^137', 0, 'a^43', 0, 0, 0, 0, 0, 'a^167', 0, 'a^74', 0, 'a^174', 0, 'a^8', 0, 'a^84', 0, 'a^19', 0, 0, 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'prelabel': '1-3724-3724.1251-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.29418329373136, 'root_angle': -0.6901880133673445, 'root_number': '-0.562571804354832093738198526018-0.826748429055023074430466047822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(126)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.809409541302591387746162810433-0.0682543560934914583556928722547*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.144492573628', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.65942672247', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.28246841198', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.29418329373136, 'bad_primes': [2, 7, 19], 'central_character': '3724.1251', 'conductor': 3724, 'conductor_radical': 266, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3724/1251'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-3724-3724.1251-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3724-3724.1251-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.29418329373136, 'root_angle': -0.34509400668367224, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.144492573628', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3724.1251', 'Lhash_array': ['dirichlet_L_3724.1251'], 'label': '1-3724-3724.1251-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3724/1251'}