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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_511.130', 'a10': [0.5, 0.8660254037844386], 'a2': [0.766044443118978, -0.6427876096865394], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [-0.17364817766693036, 0.984807753012208], 'a6': [0.17364817766693036, 0.984807753012208], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5, -0.8660254037844386], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 2.37307402338795, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [73, [1]]], 'bad_primes': [7, 73], 'central_character': '511.130', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 511, 'conductor_radical': 511, 'conjugate': 'dirichlet_L_511.114', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^6', 'a^14', 'a^5', 'a^4', 0, 'a^12', 'a^12', 'a^3', 'a^11', 'a^2', 'a^13', 0, 'a^11', 'a^10', 'a^9', 'a^10', 'a^16', 'a^1', 0, 'a^9', 'a^14', 'a^0', 'a^10', 'a^11', 'a^0', 0, 'a^1', 'a^9', 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-0.28269868181888125, 'root_number': '-0.204009554411737591430564750667-0.978968897212125058963904775444*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.282698681819', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04899462830851238874432253073-0.317795010571325717527757593750*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.494429156198', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.65311892895', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.11735088086', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.37307402338795, 'bad_primes': [7, 73], 'central_character': '511.130', 'conductor': 511, 'conductor_radical': 511, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/511/130'], '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': '1-511-511.130-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': '1-511-511.130-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.37307402338795, 'root_angle': -0.28269868181888125, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.494429156198', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_511.130', 'Lhash_array': ['dirichlet_L_511.130'], 'factors': ['1-511-511.130-r0-0-0'], 'label': '1-511-511.130-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/511/130'}