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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1001.212', 'a10': [1.0, 0.0], 'a2': [-0.6691306063588582, -0.7431448254773942], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [-0.6691306063588582, 0.7431448254773942], 'a6': [0.9781476007338057, 0.20791169081775934], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.8090169943749475, -0.5877852522924731], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.212', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.543', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^12', 'a^8', 'a^11', 'a^1', 0, 'a^27', 'a^24', 'a^0', 0, 'a^20', 0, 0, 'a^23', 'a^16', 'a^26', 'a^13', 'a^27', 'a^19', 0, 0, 'a^10', 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'190.24010151254937401362322240516', '191.038706198978936789581350944093', '191.43206433185814729649091076155', '192.22382262894219757745894210680', '192.65128732400511398004274093099', '193.555666443063809696531152016870', '193.75936934295209439156982981764', '194.40676324404056989476108302750', '194.93180235361844051492404193942', '195.47204955952041864348869864175', '196.259371393978061008973074391416', '197.413759179676584290427826059', '197.90567129157090873367361187375', '198.35330196952344332545580723850', '198.93741322231386764993712810091', '199.474192219146381216576541821338', '199.91837562678497216885461063897'], 'prelabel': '1-1001-1001.212-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.7166459516985973, 'root_number': '-0.629269814618962876271277520248-0.777186914718342446932016568485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.358322975849', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.455829598479903086027683891937+0.0287574659994497764107079881998*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.144879053979', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.48731938639', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.03064735085', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.212', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/212'], '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': '1-1001-1001.212-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': '1-1001-1001.212-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': -0.3583229758492987, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.144879053979', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1001.212', 'Lhash_array': ['dirichlet_L_1001.212'], 'label': '1-1001-1001.212-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/212'}
Lfunction data - 1-1001-1001.212-r0-0-0