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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6003.1141', 'a10': [0.04078858606158557, -0.9991677993445829], 'a2': [-0.7984990784462388, 0.6019960313162434], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.27520155655898504, -0.9613865524686268], 'a5': [-0.6340646982057246, 0.7732800000577302], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5349078513860724, -0.8449104038450086], 'a8': [0.3590026998475987, 0.9333365210373668], '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': '6003.1141', 'coeff_info': ['x^924 - 1', '0.999976880197217 + 0.00679993169383467*I', '\\\\zeta_{924}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.2236', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^367', 0, 'a^734', 'a^332', 0, 'a^610', 'a^177', 0, 'a^699', 'a^733', 0, 'a^446', 'a^53', 0, 'a^544', 'a^861', 0, 'a^657', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.7790397396988654, 'root_number': '-0.768586792844435578911500189510-0.639745528991883357886161255270*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, '0.558699328714565419643279694243+0.00925792480108617800923680104971*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.222123048817', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.765664176654', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '2.05174971799', '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': '6003.1141', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1141'], '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': '1-6003-6003.1141-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': '1-6003-6003.1141-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.3895198698494327, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.222123048817', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6003.1141', 'Lhash_array': ['dirichlet_L_6003.1141'], 'label': '1-6003-6003.1141-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1141'}