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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_175.108', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9945218953682733, 0.10452846326765347], 'a3': [0.20791169081775934, 0.9781476007338057], 'a4': [0.9781476007338057, -0.20791169081775934], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.30901699437494745, -0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, 0.30901699437494745], 'a9': [-0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '175.108', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 175, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_175.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^13', 'a^58', 0, 'a^42', 0, 'a^27', 'a^26', 0, 'a^4', 'a^11', 'a^21', 0, 0, 'a^56', 'a^7', 'a^55', 'a^32', 0, 0, 'a^33', 'a^59', 'a^40', 0, 'a^50', 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'189.19260188354864040553588447926', '190.116112359683781621789279313859', '190.50310763727064067079804707914', '191.62843214275302648640907963483', '191.995982326874584127946515567103', '192.7087779502220711652181108577', '193.43822813710747972241063475262', '193.908211692543737260686266533122', '195.17145016123626189894300052696', '195.87326210589695452757026577112', '196.95292145987481300716031970523', '197.34787299357217228480550386332', '198.33787215342105918658094602243', '198.48253491902643703129610463285', '199.32781997188532544515175375456'], 'prelabel': '1-175-175.108-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': 0.31350628638727945, 'root_number': '-0.388517142524689812691895555894+0.921441495681874456572311544346*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313506286387', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.629452967321125351208856388457+0.358889378461614315487430930065*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.79942757624', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.30092007642', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.70446571955', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8126965833520376, 'bad_primes': [5, 7], 'central_character': '175.108', 'conductor': 175, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/175/108'], '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': '1-175-175.108-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': '1-175-175.108-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8126965833520376, 'root_angle': 0.31350628638727945, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79942757624', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_175.108', 'Lhash_array': ['dirichlet_L_175.108'], 'factors': ['1-175-175.108-r0-0-0'], 'label': '1-175-175.108-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/175/108'}
Lfunction data - 1-175-175.108-r0-0-0