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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.277', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [-0.9781476007338057, -0.20791169081775934], 'a3': [0.5, 0.8660254037844386], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [-0.10452846326765347, -0.9945218953682733], 'a6': [-0.30901699437494745, -0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.277', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.86', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^5', 'a^2', 'a^22', 'a^21', 0, 'a^18', 'a^10', 'a^8', 'a^23', 'a^7', 'a^21', 0, 'a^27', 'a^4', 'a^23', 'a^26', 'a^19', 'a^24', 0, 'a^9', 'a^16', 'a^23', 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'195.02735128396807437319556051238', '196.3448871330894657476201354994', '196.63798481275553089333099692780', '197.21762230468707984907338907517', '198.11372494008609645121074152184', '198.689242637632581626214359510649', '199.22323354484942884840169320257', '199.95220800260997583156526748444'], 'prelabel': '1-287-287.277-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.21611715928673814, 'root_number': '0.211287652731426045371318840191-0.977423924304722711031092562944*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.216117159287', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.715145694850722966407305648530-0.141397092851843696876501575791*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.601583718829', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.37513287563', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.44586499696', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.277', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/277'], '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': '1-287-287.277-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': '1-287-287.277-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.21611715928673814, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.601583718829', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.277', 'Lhash_array': ['dirichlet_L_287.277'], 'factors': ['1-287-287.277-r0-0-0'], 'label': '1-287-287.277-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/277'}
Lfunction data - 1-287-287.277-r0-0-0