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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.272', 'a10': [0.9009688679024191, -0.4338837391175581], 'a2': [0.9888308262251285, 0.14904226617617444], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9555728057861407, 0.2947551744109042], 'a5': [0.8262387743159949, -0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.047995390047135, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.272', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.167', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^38', 0, 0, 'a^3', 0, 'a^39', 'a^1', 0, 'a^29', 0, 0, 'a^4', 'a^12', 0, 'a^21', 'a^40', 0, 'a^2', 'a^23', 0, 'a^34', 'a^30', 0, 0, 'a^19', 0, 'a^35', 'a^5', 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'192.18330102658179908201478949458', '192.50253099644268192975114423745', '192.98486802906185746457999766276', '193.93672854584208952750484794639', '194.29731830438117039460242593516', '194.98644945173413968030514433504', '195.95651846147201576935659618410', '196.21771760600755556244138659168', '196.89741652792949285250997536735', '197.450937725724304531206396721998', '198.236345899188535562794932299074', '198.726411469132027139101914874484', '199.84438647574464672229577034999'], 'prelabel': '1-21e2-441.272-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.0022675736961451248, 'root_number': '0.999898504867348548094880918956+0.0142471037071031343854498565613*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00226757369615', 'prec': 57}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.15667921879264096386100103906+0.0301975952665890556195832937765*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.51568788839', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.47371433617', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87797142625', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.272', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/272'], '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': '1-21e2-441.272-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': '1-21e2-441.272-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.0022675736961451248, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51568788839', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.272', 'Lhash_array': ['dirichlet_L_441.272'], 'factors': ['1-21e2-441.272-r0-0-0'], 'label': '1-21e2-441.272-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/272'}
Lfunction data - 1-21e2-441.272-r0-0-0