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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_116.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9749279121818236, -0.2225209339563144], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.6234898018587335, -0.7818314824680298], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.2225209339563144, 0.9749279121818236], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.5387017352504936, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [29, [1]]], 'bad_primes': [2, 29], 'central_character': '116.11', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 116, 'conductor_radical': 58, 'conjugate': 'dirichlet_L_116.95', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^27', 0, 'a^18', 0, 'a^34', 0, 'a^26', 0, 'a^23', 0, 'a^2', 0, 'a^17', 0, 'a^21', 0, 'a^15', 0, 'a^5', 0, 'a^38', 0, 'a^8', 0, 'a^25', 0, 0, 0, 'a^39', 0, 'a^22', 0, 'a^24', 0, 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-0.15289351589858216, 'root_number': '0.886842881814501821110797121852-0.462071101644486695234735967153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0764467579493', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(28)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.29224892687226872099690473367-0.194398345798427801035611164860*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.55004184082', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.16707739678', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.41303074967', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5387017352504936, 'bad_primes': [2, 29], 'central_character': '116.11', 'conductor': 116, 'conductor_radical': 58, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/116/11'], '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': '1-116-116.11-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': '1-116-116.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5387017352504936, 'root_angle': -0.07644675794929108, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55004184082', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_116.11', 'Lhash_array': ['dirichlet_L_116.11'], 'label': '1-116-116.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/116/11'}