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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_231.2', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.10452846326765347, 0.9945218953682733], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [-0.9135454576426009, -0.4067366430758002], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '231.2', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.116', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^17', 0, 0, 'a^24', 0, 'a^25', 0, 0, 'a^3', 0, 0, 'a^2', 'a^22', 0, 'a^29', 'a^3', 0, 0, 'a^5', 0, 'a^4', 'a^11', 0, 0, 'a^6', 0, 'a^28', 'a^10', 0, 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'185.26193269677681385589391637110', '186.20233193960679930987882819765', '186.97047620662606312194506023662', '187.33090846115623670312722162865', '188.18634995466571209579832390642', '188.579735090325398712964520162453', '189.51499661939815448113601667321', '190.12451908246606570117306856607', '190.93609524930887689358586324282', '191.45691730342249302842040138751', '192.13215672104306620498582332833', '193.148000692776319586420760744929', '193.92590937365776993604739922040', '194.93151658986317437176898291995', '195.28562766165938142731718750131', '195.78366424756741748855860379707', '196.67539533937612264247715043167', '197.342660593823815264905432457375', '197.965480526408043939542156408203', '198.7404653993239444290921767973', '199.38204954778944096856503051682', '199.98502199637312692707496451110'], 'prelabel': '1-231-231.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.1399206770320849, 'root_number': '0.637807935062318836044200273560+0.770195454395532562168148336362*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.139920677032', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.794463782489755784686504586405+0.309274628922000435951334138538*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.99006661754', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.38790217936', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.50194930991', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'bad_primes': [3, 7, 11], 'central_character': '231.2', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/2'], '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': '1-231-231.2-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': '1-231-231.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0727594900246897, 'root_angle': 0.1399206770320849, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.99006661754', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_231.2', 'Lhash_array': ['dirichlet_L_231.2'], 'factors': ['1-231-231.2-r0-0-0'], 'label': '1-231-231.2-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/2'}
Lfunction data - 1-231-231.2-r0-0-0