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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1210', 'a10': [0.4702719069927368, -0.8825215767863213], 'a2': [0.5855825596032286, -0.8106127718513515], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.3141861317770625, -0.9493614035755648], 'a5': [0.9907662885836834, -0.13558082978840788], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.03399337025129776, -0.9994220583812218], 'a8': [-0.9535463980789276, -0.30124618953723425], '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': '6003.1210', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.511', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^785', 0, 'a^646', 'a^904', 0, 'a^698', 'a^507', 0, 'a^765', 'a^95', 0, 'a^886', 'a^559', 0, 'a^368', 'a^399', 0, 'a^723', 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'-0.624847286668127254055169531875-0.780746993810081346736204356752*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, '1.41059775590269217206042220916-1.14104965483061527275819708402*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.809192479038', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.29937431099', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.17750769474', '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': '6003.1210', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1210'], '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': '1-6003-6003.1210-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': '1-6003-6003.1210-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.3574193877190996, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.809192479038', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1210', 'Lhash_array': ['dirichlet_L_6003.1210'], 'label': '1-6003-6003.1210-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1210'}