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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_207.83', 'a10': [0.6548607339452851, -0.7557495743542583], 'a2': [0.8888354486549235, 0.4582265217274104], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5800569095711982, 0.8145759520503357], 'a5': [0.23575893550942723, -0.9718115683235417], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.32706796331742166, -0.9450008187146685], 'a8': [0.14231483827328514, 0.9898214418809327], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '207.83', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 207, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_207.5', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 0, 'a^10', 'a^52', 0, 'a^53', 'a^15', 0, 'a^57', 'a^50', 0, 'a^46', 'a^58', 0, 'a^20', 'a^12', 0, 'a^21', 'a^62', 0, 'a^55', 0, 0, 'a^38', 'a^51', 0, 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'187.00951881510575465810578222040', '187.36087044835849252835695954021', '188.2260363786892568215898037754', '188.7877443366430114901957109697', '189.29824253722677185858960871159', '190.080559872926672524025349783', '191.479214918516162964704167329648', '191.922617443365822668384933080548', '192.41455336074182102834529214568', '193.47613092463446357729172907807', '194.08992900701235257114861240140', '194.664974894009972267408722556014', '195.452595429064911275093524171865', '196.071606229658136329350059342381', '196.85764158348894225417224514427', '197.23753349373532509345841095460', '198.078005852548106091685030694536', '198.84572401894345286537322776381', '199.57321109452222614534350361984'], 'prelabel': '1-207-207.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': -0.01564388725403494, 'root_number': '0.998792542964515178558242623403-0.0491269388266468429889053694398*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00782194362702', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.75193245984672456520427369715+0.0799741894840974189383025133057*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.39851732226', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.25183511767', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.32709137624', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9613039585935531, 'bad_primes': [3, 23], 'central_character': '207.83', 'conductor': 207, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/207/83'], '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': '1-207-207.83-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': '1-207-207.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9613039585935531, 'root_angle': -0.00782194362701747, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39851732226', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_207.83', 'Lhash_array': ['dirichlet_L_207.83'], 'label': '1-207-207.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/207/83'}