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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_196.131', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9888308262251285, 0.14904226617617444], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.36534102436639504, 0.9308737486442042], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9555728057861407, -0.2947551744109042], 'algebraic': True, 'analytic_conductor': 0.9102201733542822, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.131', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^62', 0, 'a^13', 0, 0, 0, 'a^40', 0, 'a^23', 0, 'a^9', 0, 'a^33', 0, 'a^17', 0, 'a^28', 0, 0, 0, 'a^25', 0, 'a^26', 0, 'a^60', 0, 'a^24', 0, 'a^56', 0, 'a^1', 0, 0, 0, 'a^10', 0, 'a^29', 0, 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'0.509821279254853155309846559196+0.161389777833515824426387213940*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.13141587857', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.74293093105', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.86773357917', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102201733542822, 'bad_primes': [2, 7], 'central_character': '196.131', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/131'], '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': '1-14e2-196.131-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': '1-14e2-196.131-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9102201733542822, 'root_angle': 0.4914965986394558, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13141587857', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_196.131', 'Lhash_array': ['dirichlet_L_196.131'], 'label': '1-14e2-196.131-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/131'}