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{'Lhash': 'dirichlet_L_4056.2651', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8854560256532099, 0.46472317204376856], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3546048870425356, 0.9350162426854148], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.835984811862083, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '4056.2651', 'coeff_info': ['x^26 - 1', '0.970941817426052 + 0.239315664287558*I', '\\\\zeta_{26}'], 'conductor': 4056, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_4056.1403', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^37', 0, 'a^34', 0, 0, 0, 'a^6', 0, 0, 0, 0, 0, 'a^21', 0, 'a^13', 0, 0, 0, 'a^0', 0, 'a^22', 0, 0, 0, 'a^20', 0, 'a^30', 0, 0, 0, 'a^19', 0, 'a^30', 0, 0, 0, 'a^10', 0, 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'1-4056-4056.2651-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.835984811862083, 'root_angle': 0.1863905325443787, 'root_number': '0.389114436676645688789143509456+0.921189424152175496746125816802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(26)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.886200742560302314417645053045+0.226072408122526221208202791304*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.735143447532', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.08033938006', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73984548122', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.835984811862083, 'bad_primes': [2, 3, 13], 'central_character': '4056.2651', 'conductor': 4056, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4056/2651'], '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': '1-4056-4056.2651-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': '1-4056-4056.2651-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.835984811862083, 'root_angle': 0.1863905325443787, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.735143447532', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4056.2651', 'Lhash_array': ['dirichlet_L_4056.2651'], 'factors': ['1-4056-4056.2651-r0-0-0'], 'label': '1-4056-4056.2651-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4056/2651'}