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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1001.129', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.6691306063588582, 0.7431448254773942], 'a3': [-0.9135454576426009, -0.4067366430758002], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [-0.9781476007338057, -0.20791169081775934], 'a6': [-0.30901699437494745, -0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [0.6691306063588582, 0.7431448254773942], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.129', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.194', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^17', 'a^8', 'a^16', 'a^21', 0, 'a^12', 'a^4', 'a^20', 0, 'a^25', 0, 0, 'a^3', 'a^16', 'a^26', 'a^8', 'a^7', 'a^24', 0, 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'189.59333540438910139235006205172', '190.00315955779901364002877320702', '190.75821928698125902975162269992', '191.43202023351027892076615971681', '192.08688872103190115603057316240', '192.98666026542827459216831304087', '193.7874233440659529417477890503', '193.9005006723856759355829702866', '194.758170071377805501418872570794', '195.21344612316473864793965506612', '195.75317163477039161164184696869', '196.09327115443274407376320744215', '196.711508610117527101018521437870', '197.564266845696336399584810401618', '198.313704723662353612249106645114', '198.649846359946884250102840896992', '199.43483056372294634530001529908', '199.88909201928568678985960708282'], 'prelabel': '1-1001-1001.129-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.7708542131603112, 'root_number': '-0.751883056250862514235509503210-0.659296496064450744672573932867*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38542710658', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.680102514689608180662872590650+0.315853826685490415213776822567*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.51451634888', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.14205204893', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.98409824854', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.129', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/129'], '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': '1-1001-1001.129-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': '1-1001-1001.129-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.3854271065801556, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51451634888', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1001.129', 'Lhash_array': ['dirichlet_L_1001.129'], 'label': '1-1001-1001.129-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/129'}
Lfunction data - 1-1001-1001.129-r0-0-0