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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1175', 'a10': [-0.9535463980789276, 0.30124618953723425], 'a2': [0.991665322644042, -0.12884055209943887], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9668002242694236, -0.25553341533465307], 'a5': [-0.9844116218848333, 0.17587995536180925], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6751723096548833, -0.7376600519719706], 'a8': [0.9258191900208981, -0.37796670142890654], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1175', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.1829', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^905', 0, 'a^886', 'a^436', 0, 'a^584', 'a^867', 0, 'a^417', 'a^701', 0, 'a^274', 'a^565', 0, 'a^848', 'a^357', 0, 'a^39', 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-0.11798905627284004, 'root_number': '0.932083567199938594671143238367-0.362243321202527561460428392605*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(924)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.56262077416573103070449995303-0.214673876332223175622079677067*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.696348297786', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.60413918834', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.78253882046', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1175', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1175'], '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': '1-6003-6003.1175-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': '1-6003-6003.1175-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.05899452813642002, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.696348297786', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1175', 'Lhash_array': ['dirichlet_L_6003.1175'], 'label': '1-6003-6003.1175-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1175'}