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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_225.214', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9781476007338057, -0.20791169081775934], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9135454576426009, -0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.214', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 225, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_225.184', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 0, 'a^28', 0, 0, 'a^5', 'a^27', 0, 0, 'a^14', 0, 'a^1', 'a^4', 0, 'a^26', 'a^27', 0, 'a^12', 0, 0, 'a^13', 'a^19', 0, 0, 'a^0', 0, 'a^3', 'a^8', 0, 'a^22', 'a^25', 0, 'a^26', 0, 0, 'a^21', 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'186.45812793985944788614222288410', '186.83585946331406998183104108567', '187.82123224837191593541741179326', '188.30611270851894356357950790828', '189.3030420037679552160372421373', '189.72232033103775226436434351962', '190.87677573813455478265443364168', '191.67475851764726119726673585659', '192.224989220686401243372953238527', '192.89641185441589908012423243174', '193.61819293972224930865601615158', '194.20502300676562675329783938297', '194.95204660974568536739191340601', '195.68462312149622156811050796634', '196.35775133357674337776602635787', '196.67847894214075251285080043291', '197.703167686917375121629051203281', '198.43189677571767508070886029517', '199.1894672927160475885891167457'], 'prelabel': '1-15e2-225.214-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': -0.024444444444444442, 'root_number': '0.988228381446552819709705622322-0.152985836284038068120562483966*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0244444444444', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.87409115743109229092414335012-0.135861897350691399188598051657*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.7438871597', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.82228141355', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.15298540876', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'bad_primes': [3, 5], 'central_character': '225.214', 'conductor': 225, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/225/214'], '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': '1-15e2-225.214-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': '1-15e2-225.214-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': -0.024444444444444442, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.7438871597', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_225.214', 'Lhash_array': ['dirichlet_L_225.214'], 'factors': ['1-15e2-225.214-r0-0-0'], 'label': '1-15e2-225.214-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/225/214'}
Lfunction data - 1-15e2-225.214-r0-0-0