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{'Lhash': 'dirichlet_L_644.395', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.8888354486549235, -0.4582265217274104], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9954719225730846, 0.09505604330418266], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5800569095711982, 0.8145759520503357], 'algebraic': True, 'analytic_conductor': 2.9907234267354985, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]], [23, [1]]], 'bad_primes': [2, 7, 23], 'central_character': '644.395', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 644, 'conductor_radical': 322, 'conjugate': 'dirichlet_L_644.75', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^38', 0, 'a^1', 0, 0, 0, 'a^10', 0, 'a^53', 0, 'a^3', 0, 'a^39', 0, 'a^29', 0, 'a^70', 0, 0, 0, 0, 0, 'a^2', 0, 'a^48', 0, 'a^18', 0, 'a^50', 0, 'a^25', 0, 0, 0, 'a^10', 0, 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'0.961301541450056422676285537851-0.275498360078141760045362553809*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0444214315641', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04423169757379207545724829647-0.112462288696212764562942843797*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05869447913', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.91670948392', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.29519481882', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.9907234267354985, 'bad_primes': [2, 7, 23], 'central_character': '644.395', 'conductor': 644, 'conductor_radical': 322, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/644/395'], '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': '1-644-644.395-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': '1-644-644.395-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9907234267354985, 'root_angle': -0.04442143156409896, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05869447913', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_644.395', 'Lhash_array': ['dirichlet_L_644.395'], 'factors': ['1-644-644.395-r0-0-0'], 'label': '1-644-644.395-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/644/395'}