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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_231.116', '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': '231.116', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 231, 'conductor_radical': 231, 'conjugate': 'dirichlet_L_231.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 0, 'a^14', 'a^13', 0, 0, 'a^6', 0, 'a^5', 0, 0, 'a^27', 0, 0, 'a^28', 'a^8', 0, 'a^1', 'a^27', 0, 0, 'a^25', 0, 'a^26', 'a^19', 0, 0, 'a^24', 0, 'a^2', 'a^20', 0, 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'186.62121880962793703289315190094', '186.94762393262983376933719498482', '187.714106163788546983105087836126', '188.83816847568145311613461414216', '189.48334034081938203057178430087', '190.31762826064304821878655677122', '190.86479146118028375180140695929', '191.420646326215679459099805334647', '192.204340186677184231475801917972', '192.7244253847170148368029491519', '193.61051356085904826625457581340', '194.31189155040027891898494293106', '194.97490119736753773022284153884', '195.23883799375948123872687556750', '196.31250223821917356549120955171', '197.15125858583767681906966588299', '198.061507992373162720342793013193', '198.866353396849723540907682225053', '199.28158930146298290904344721643', '199.83954830396233940623444013924'], 'prelabel': '1-231-231.116-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': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.794463782489755784686504586405-0.309274628922000435951334138538*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.04700992265', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.76974582424', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.6796262727', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0727594900246897, 'bad_primes': [3, 7, 11], 'central_character': '231.116', 'conductor': 231, 'conductor_radical': 231, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/231/116'], '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': '1-231-231.116-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': '1-231-231.116-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': '1.04700992265', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_231.116', 'Lhash_array': ['dirichlet_L_231.116'], 'factors': ['1-231-231.116-r0-0-0'], 'label': '1-231-231.116-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/231/116'}
Lfunction data - 1-231-231.116-r0-0-0