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{'Lhash': 'dirichlet_L_847.19', 'a10': [-0.8888354486549235, 0.4582265217274104], 'a2': [-0.8799502578106532, 0.4750658309949949], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [0.5486249124420699, -0.8360686009221558], 'a5': [0.9998187455235258, 0.019038805103346677], 'a6': [-0.5644432188667692, -0.825471896962774], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.08557500847883974, 0.9963317308626913], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.19', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.535', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^139', 'a^77', 'a^278', 'a^1', 'a^216', 0, 'a^87', 'a^154', 'a^140', 0, 'a^25', 'a^234', 0, 'a^78', 'a^226', 'a^266', 'a^293', 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'0.813751682167947583740403623790+0.230998737834475652857886087420*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.644263590672', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.24956276691', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.95579381876', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.19', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/19'], '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': '1-847-847.19-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': '1-847-847.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.01990969157415305, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.644263590672', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_847.19', 'Lhash_array': ['dirichlet_L_847.19'], 'label': '1-847-847.19-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/19'}