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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_804.479', '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': [0.6548607339452851, 0.7557495743542583], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8888354486549235, 0.4582265217274104], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.733760302943076, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [67, [1]]], 'bad_primes': [2, 3, 67], 'central_character': '804.479', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 804, 'conductor_radical': 402, 'conjugate': 'dirichlet_L_804.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^9', 0, 'a^71', 0, 0, 0, 'a^86', 0, 'a^40', 0, 0, 0, 'a^1', 0, 'a^61', 0, 0, 0, 'a^52', 0, 'a^18', 0, 0, 0, 'a^11', 0, 'a^59', 0, 0, 0, 'a^80', 0, 'a^22', 0, 0, 0, 'a^23', 0, 'a^45', 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'196.55687502769321931615393914641', '197.20222034467784217174965900848', '197.99718156830292504339932268741', '198.541252004656449275036221558533', '198.91556358859228245122855682658', '199.46502899890878407911935608558'], 'prelabel': '1-804-804.479-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.733760302943076, 'root_angle': 0.31543982025035366, 'root_number': '0.547867429093393180181590740154+0.836565167897035858870610039349*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.157719910125', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.27442026266842483991481975029+0.314848519784848152226583428982*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.36890528282', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.44215787699', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.12151659543', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.733760302943076, 'bad_primes': [2, 3, 67], 'central_character': '804.479', 'conductor': 804, 'conductor_radical': 402, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/804/479'], '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': '1-804-804.479-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': '1-804-804.479-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.733760302943076, 'root_angle': 0.15771991012517683, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36890528282', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_804.479', 'Lhash_array': ['dirichlet_L_804.479'], 'label': '1-804-804.479-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/804/479'}