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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_555.224', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.984807753012208, 0.17364817766693036], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.766044443118978, 0.6427876096865394], 'a8': [0.8660254037844386, 0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.577409164345034, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [37, [1]]], 'bad_primes': [3, 5, 37], 'central_character': '555.224', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 555, 'conductor_radical': 555, 'conjugate': 'dirichlet_L_555.389', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 0, 0, 'a^14', 'a^3', 0, 0, 'a^12', 0, 'a^29', 'a^15', 0, 'a^4', 'a^7', 0, 'a^35', 0, 0, 'a^13', 'a^15', 0, 0, 'a^30', 0, 'a^16', 'a^3', 0, 'a^9', 'a^5', 0, 'a^8', 0, 0, 0, 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'187.880305679499029482195925636575', '188.35469958679117995265724279135', '189.303823567950098746907008247442', '189.75250840090772996469024270549', '190.51068142154189040841950123370', '191.34138518744859523027914131595', '191.98388815588349841144478506186', '192.7827891635883113700976225178', '193.269173306898773220688662180354', '193.8114579276969320840780515213', '194.43300845985205992300824881896', '195.025007604408592011692191199381', '195.87085051362859902883454022176', '196.35134385736655636500955677863', '196.87422821658640729551490435121', '197.325888935696249366065791126992', '198.27065796550006426948860760952', '198.94828343525295196090808804706', '199.384979509219863729694536670941'], 'prelabel': '1-555-555.224-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': 0.19673531949936895, 'root_number': '0.328459251409171154952454417133+0.944518141786449169450679948824*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196735319499', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.70103003127445578646521975652+0.555906304673830798946919131115*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.68142183205', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.90255091081', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.58017058144', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.577409164345034, 'bad_primes': [3, 5, 37], 'central_character': '555.224', 'conductor': 555, 'conductor_radical': 555, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/555/224'], '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': '1-555-555.224-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': '1-555-555.224-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': 0.19673531949936895, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68142183205', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_555.224', 'Lhash_array': ['dirichlet_L_555.224'], 'factors': ['1-555-555.224-r0-0-0'], 'label': '1-555-555.224-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/555/224'}
Lfunction data - 1-555-555.224-r0-0-0