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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_87.44', 'a10': [0.4338837391175581, 0.9009688679024191], 'a2': [-0.9749279121818236, 0.2225209339563144], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9009688679024191, -0.4338837391175581], 'a5': [-0.2225209339563144, -0.9749279121818236], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [-0.7818314824680298, 0.6234898018587335], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.40402630143787016, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '87.44', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 87, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_87.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^26', 'a^20', 0, 'a^16', 'a^11', 0, 'a^5', 'a^17', 0, 'a^10', 'a^1', 0, 'a^24', 'a^21', 0, 'a^19', 'a^18', 0, 'a^2', 'a^22', 0, 'a^12', 'a^23', 0, 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'186.7010305926720814841889349818', '187.31364255180890827492963395447', '188.21821936771679992754022784284', '188.652935387986262375690656146950', '189.41268635218723346708521380947', '190.58856998988419341690438657057', '191.03089825486655401178929200918', '191.70691476488068870833727982076', '192.60351504618022920827745586840', '193.27553746766215216779644198225', '194.18874904938919296796690098132', '195.3709924403704345578247900069', '196.12142393055630780215396732603', '196.95482404613982763912599524826', '197.314074706958784713545827860350', '198.44955730049894442951366895499', '199.14724859195623903308358231742', '199.95574292636259839259176974038'], 'prelabel': '1-87-87.44-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40402630143787016, 'root_angle': -0.6128380657472269, 'root_number': '-0.347113281740588158680209351315-0.937823208093763836128197696966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.306419032874', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(28)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.498378584893169152103191741073-0.166846925076655251454286306544*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.546070267927', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.67569610232', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.77155546566', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.40402630143787016, 'bad_primes': [3, 29], 'central_character': '87.44', 'conductor': 87, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/87/44'], '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': '1-87-87.44-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': '1-87-87.44-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.40402630143787016, 'root_angle': -0.30641903287361344, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.546070267927', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_87.44', 'Lhash_array': ['dirichlet_L_87.44'], 'label': '1-87-87.44-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/87/44'}