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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_225.142', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.4067366430758002, 0.9135454576426009], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6691306063588582, -0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, -0.5], 'a8': [0.9510565162951535, -0.30901699437494745], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 24.17960807879063, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.142', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 225, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_225.103', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 0, 'a^38', 0, 0, 'a^55', 'a^57', 0, 0, 'a^4', 0, 'a^41', 'a^14', 0, 'a^16', 'a^27', 0, 'a^42', 0, 0, 'a^23', 'a^29', 0, 0, 'a^0', 0, 'a^33', 'a^58', 0, 'a^32', 'a^35', 0, 'a^46', 0, 0, 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'185.563103090808225652486645167093', '186.36538264484490695961874152139', '186.82362460139786036517730000166', '187.81218679888649189237819171692', '188.41104958194289838019033949684', '188.785200593340625088033046404462', '189.70178060757867984482317167558', '190.38646496870738560754729505351', '190.89933563608134480630613130741', '191.94924617812537692054105126096', '192.18965524480824285933810828814', '193.22016687021137494977795919865', '194.31977379407405962576979753566', '194.89248896537322636707955432526', '195.43181105939312366330952432808', '196.20027263529750305418025744398', '196.8800476770177681924119459692', '197.626980278780854149766439088079', '198.26271680158354810465306361450', '198.85594137382063574162397311566', '199.34706206933443256289045703213'], 'prelabel': '1-15e2-225.142-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.17960807879063, 'root_angle': -0.2688888888888889, 'root_number': '0.663926212652241594900990021760-0.747798090498531878105720508059*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134444444444', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.850483709888397434380781341317+0.114542334964626052733152045373*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.452032027339', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.91065666982', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.08470190265', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.17960807879063, 'bad_primes': [3, 5], 'central_character': '225.142', 'conductor': 225, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/225/142'], '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': '1-15e2-225.142-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-15e2-225.142-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.17960807879063, 'root_angle': -0.13444444444444445, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.452032027339', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_225.142', 'Lhash_array': ['dirichlet_L_225.142'], 'label': '1-15e2-225.142-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/225/142'}
Lfunction data - 1-15e2-225.142-r1-0-0