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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1728.715', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9762960071199334, -0.21643961393810288], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.08715574274765818, -0.9961946980917455], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 185.69939004511204, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1728.715', 'coeff_info': ['x^144 - 1', '0.999048221581858 + 0.0436193873653360*I', '\\\\zeta_{144}'], 'conductor': 1728, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_1728.1699', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^77', 0, 'a^106', 0, 0, 0, 'a^121', 0, 'a^179', 0, 0, 0, 'a^204', 0, 'a^147', 0, 0, 0, 'a^254', 0, 'a^154', 0, 0, 0, 'a^127', 0, 'a^128', 0, 0, 0, 'a^183', 0, 'a^213', 0, 0, 0, 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'197.98741645481692897533038763775', '198.617731835622674470230041445258', '199.24449420161372085158710763515', '199.89148394153055802560391179111'], 'prelabel': '1-12e3-1728.715-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': -0.26967592592592593, 'root_number': '0.662075217080573819247501666379-0.749437393601167363893790108288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134837962963', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(144)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.936387564158331829612389191237-0.167252867717535476554665886209*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.538360401726', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.24530710191', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.64530919455', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 185.69939004511204, 'bad_primes': [2, 3], 'central_character': '1728.715', 'conductor': 1728, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1728/715'], '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': '1-12e3-1728.715-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': '1-12e3-1728.715-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 185.69939004511204, 'root_angle': -0.13483796296296297, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.538360401726', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1728.715', 'Lhash_array': ['dirichlet_L_1728.715'], 'label': '1-12e3-1728.715-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1728/715'}