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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_147.2', 'a10': [0.9555728057861407, 0.2947551744109042], 'a2': [-0.8262387743159949, -0.5633200580636221], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.36534102436639504, 0.9308737486442042], 'a5': [-0.9555728057861407, 0.2947551744109042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.2', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.74', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^25', 0, 'a^8', 'a^19', 0, 0, 'a^33', 0, 'a^2', 'a^11', 0, 'a^18', 0, 0, 'a^16', 'a^41', 0, 'a^28', 'a^27', 0, 'a^36', 'a^1', 0, 'a^38', 'a^1', 0, 0, 'a^27', 0, 'a^14', 'a^41', 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'198.04817450846175146139174993359', '198.61236916636145759307917863168', '199.01005318852258629266140845406', '199.90243665893818444022642151872'], 'prelabel': '1-147-147.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.6530612244897959, 'root_number': '-0.462538290240835277697105646430-0.886599306373000060056149286517*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.326530612245', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.539461104554170273332833223856-0.117861334877359839755663460680*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.284180612706', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.13073033907', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.45060838188', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.2', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/2'], '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': '1-147-147.2-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-147-147.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.32653061224489793, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.284180612706', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_147.2', 'Lhash_array': ['dirichlet_L_147.2'], 'label': '1-147-147.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/2'}