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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_113.8', 'a10': [-0.9749279121818236, -0.2225209339563144], 'a2': [0.6234898018587335, -0.7818314824680298], 'a3': [-0.4338837391175581, 0.9009688679024191], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [-0.4338837391175581, -0.9009688679024191], 'a6': [0.4338837391175581, 0.9009688679024191], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [-0.6234898018587335, -0.7818314824680298], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.8', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.99', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^9', 'a^20', 'a^19', 'a^5', 'a^16', 'a^16', 'a^18', 'a^15', 'a^22', 'a^1', 'a^2', 'a^12', 'a^0', 'a^12', 'a^17', 'a^14', 'a^23', 'a^11', 'a^25', 'a^18', 'a^5', 'a^25', 'a^10', 'a^26', 'a^27', 'a^8', 'a^17', 'a^24', 'a^2', 'a^8', 'a^3', 'a^13', 'a^7', 'a^10', 'a^15', 'a^19', 'a^11', 'a^7', 'a^6', 'a^21', 'a^3', 'a^14', 'a^9', 'a^1', 'a^27', 'a^21', 'a^4', 'a^6', 'a^26', 'a^22', 'a^20', 'a^23', 'a^13', 'a^4', 'a^4', 'a^13', 'a^23', 'a^20', 'a^22', 'a^26', 'a^6', 'a^4', 'a^21', 'a^27', 'a^1', 'a^9', 'a^14', 'a^3', 'a^21', 'a^6', 'a^7', 'a^11', 'a^19', 'a^15', 'a^10', 'a^7', 'a^13', 'a^3', 'a^8', 'a^2', 'a^24', 'a^17', 'a^8', 'a^27', 'a^26', 'a^10', 'a^25', 'a^5', 'a^18', 'a^25', 'a^11', 'a^23', 'a^14', 'a^17', 'a^12', 'a^0', 'a^12', 'a^2'], 'euler_factors': [[1, 'a^24'], [1, 'a^9'], [1, 'a^19'], [1, 'a^16'], [1, 'a^22'], [1, 'a^2'], [1, 'a^17'], [1, 'a^23'], [1, 'a^5'], [1, 'a^17'], [1, 'a^2'], [1, 'a^15'], [1, 'a^6'], [1, 'a^3'], [1, 'a^27'], [1, 'a^20'], [1, 'a^23'], [1, 'a^22'], [1, 'a^1'], [1, 'a^21'], [1, 'a^7'], [1, 'a^13'], [1, 'a^24'], [1, 'a^25'], [1, 'a^12'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-113-113.8-r0-0-0', 'leading_term': '0.386392366501161994464583912549-0.784733941215494575880063030518*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/113/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8747036180249693, 0.6118927836622694, 0.2234752470672309, -0.4559246214943135, -1.3349773866626067, -2.182504762146279, -2.7273040377881457, -2.7632411422587526, -2.2445496335838286, -1.3308335695760722, -0.3477045093061877, 0.33827066339776846, 0.48670302519392716, 0.11499882350079035, -0.4830993886980459, -0.8658229802309695, -0.6781949018118998, 0.11624765758087408, 1.1390672682798626, 1.7194878668840021, 1.2116277833209985, -0.634493240224125, -3.4471906604507905, -6.304877335800305, -8.113773673081484, -8.127281057289665, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.8', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/8'], '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': '1-113-113.8-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': '1-113-113.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': -0.35436105287837216, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.743223402066', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_113.8', 'Lhash_array': ['dirichlet_L_113.8'], 'label': '1-113-113.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/8'}