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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2624.413', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3826834323650898, -0.9238795325112867], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9238795325112867, -0.3826834323650898], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-1.0, -5.8021815821459605e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7071067811865476, 0.7071067811865476], 'algebraic': True, 'analytic_conductor': 281.98796266109605, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [41, [1]]], 'bad_primes': [2, 41], 'central_character': '2624.413', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 2624, 'conductor_radical': 82, 'conjugate': 'dirichlet_L_2624.629', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^11', 0, 'a^15', 0, 'a^24', 0, 'a^6', 0, 'a^9', 0, 'a^15', 0, 'a^26', 0, 'a^10', 0, 'a^19', 0, 'a^19', 0, 'a^18', 0, 'a^14', 0, 'a^17', 0, 'a^19', 0, 'a^0', 0, 'a^20', 0, 'a^23', 0, 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'190.34634793384256806787980357241', '191.172588770084572849055818095034', '191.28387929416350512696766649468', '191.99684054824853718707244919651', '192.84840795812549941181664396780', '193.427999807362814820953204331154', '193.71957477033397561056072379524', '194.394591138025321194772233396958', '194.744115657408225704571427093332', '195.72821739426688099887744884125', '195.94706641064967251711954474557', '196.62264186975434541084859057703', '197.06413295465506647265733170968', '197.52631200003946738647453330472', '197.81480298713680280834464699203', '199.183027327571782955003086876985', '199.54107575725706038688438975897', '199.87355040294376818053182592706'], 'prelabel': '1-2624-2624.413-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 281.98796266109605, 'root_angle': 0.6948376427706742, 'root_number': '-0.574587871591205919505654520569+0.818442898326015079748109025468*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.347418821385', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(16)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.792058548338165098213109881209-0.347701193148106965426585332272*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0693626456089', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '0.944222219861', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.75756847732', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 281.98796266109605, 'bad_primes': [2, 41], 'central_character': '2624.413', 'conductor': 2624, 'conductor_radical': 82, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2624/413'], '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': '1-2624-2624.413-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2624-2624.413-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 281.98796266109605, 'root_angle': 0.3474188213853371, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0693626456089', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2624.413', 'Lhash_array': ['dirichlet_L_2624.413'], 'label': '1-2624-2624.413-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2624/413'}
Lfunction data - 1-2624-2624.413-r1-0-0