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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_117.4', 'a10': [-0.5, -0.8660254037844386], 'a2': [-1.0, -1.4081532572346456e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.5433457157267909, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '117.4', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 117, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_117.88', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 0, 'a^0', 'a^1', 0, 'a^1', 'a^3', 0, 'a^4', 'a^3', 0, 0, 'a^4', 0, 'a^0', 'a^2', 0, 'a^5', 'a^1', 0, 'a^0', 'a^2', 0, 'a^2', 0, 0, 'a^1', 'a^0', 0, 'a^1', 'a^3', 0, 'a^5', 'a^2', 0, 'a^1', 'a^2', 0, 'a^4', 'a^5', 0, 'a^4', 'a^3', 0, 'a^5', 'a^5', 0, 'a^2', 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'182.96514964448057210390492625226', '183.54848786014437698940554828211', '184.23982279165978605828588699058', '185.64047099802284209313102401079', '186.075830606940186706905762150915', '186.833244166357858126540539007014', '187.91701380429533978542580702946', '188.65643216493095081712607060377', '189.344133403122132494819621916373', '189.96608951659348501756636447669', '190.61849606544115597281627431749', '191.34581117051924552701509043580', '192.30069430267965487244301087877', '192.930519778526784802542812984363', '193.58041355693415166466968787243', '194.41780889194323098859761661036', '195.41574224905712496213317216965', '196.52604884486689485626658869258', '196.89381632828509726274797172461', '197.74245027327892844402258443103', '198.67335863294847082842427902437', '199.014840874019055452669350098397', '199.7412313668478421943953755835'], 'prelabel': '1-117-117.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5433457157267909, 'root_angle': 0.19648539583701116, 'root_number': '0.329942038422432892253919338143+0.944001192415374980200252203462*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196485395837', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.709269901023664692836294733678+0.226751984329882667229796506993*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.94648473112', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.95767116294', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.3929307898', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5433457157267909, 'bad_primes': [3, 13], 'central_character': '117.4', 'conductor': 117, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/117/4'], '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': '1-117-117.4-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': '1-117-117.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5433457157267909, 'root_angle': 0.19648539583701116, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94648473112', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_117.4', 'Lhash_array': ['dirichlet_L_117.4'], 'factors': ['1-117-117.4-r0-0-0'], 'label': '1-117-117.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/117/4'}
Lfunction data - 1-117-117.4-r0-0-0