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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.1130', 'a10': [0.6324453755953773, -0.7746049618276546], 'a2': [-0.7994427634035012, -0.6007422642379789], 'a3': [-0.9485364419471455, -0.3166679938014725], 'a4': [0.27821746391645263, 0.9605181116313724], 'a5': [-0.040265940109415144, 0.9991889981715696], 'a6': [0.5680647467311558, 0.8229838658936564], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.3546048870425356, -0.9350162426854148], 'a9': [0.7994427634035012, 0.6007422642379789], 'algebraic': True, 'analytic_conductor': 127.1310060320414, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.1130', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.558', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 'a^43', 'a^16', 'a^20', 'a^12', 0, 'a^63', 'a^8', 'a^67', 'a^31', 'a^59', 0, 0, 'a^63', 'a^32', 'a^37', 'a^55', 'a^26', 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'185.89050051776551683807399199373', '186.761123856757225271809912286513', '187.61803382587591427649186276629', '188.0249323428806483762178231141', '188.76764705678408475584249815681', '189.25325178100938089926116126641', '189.74053257670681743921487420596', '190.40447055201032324818797699313', '190.91846715532590696328273680017', '191.11302075125492798172901995538', '192.14281791532946720499050580260', '192.87125947869703573304334718955', '193.32471129654184228889009249009', '193.98825789948574248860818519265', '194.34328950406457736704005770496', '194.74437016109706315012061142740', '195.748855068920660744901858890655', '196.15250304026546085621910500715', '197.04769119938066324348154091613', '197.749737218470989218421081567172', '198.31775063133014127382559951819', '198.75594008437810250744512277387', '199.43743310523379067657638164061', '199.85353432705438223530590477369'], 'prelabel': '1-1183-1183.1130-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 127.1310060320414, 'root_angle': -0.01138523235039313, 'root_number': '0.997442425300674953342957011506-0.0714745284021340410220056929179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0113852323504', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.460208691024190261810827885379+0.0287641171748095963099463771848*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.370487772', 'prec': 37}, 'z2': {'__RealLiteral__': 0, 'data': '1.88240679731', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36042409684', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 127.1310060320414, 'bad_primes': [7, 13], 'central_character': '1183.1130', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/1130'], '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': '1-1183-1183.1130-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': '1-1183-1183.1130-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 127.1310060320414, 'root_angle': -0.01138523235039313, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.370487772', 'prec': 37}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.1130', 'Lhash_array': ['dirichlet_L_1183.1130'], 'factors': ['1-1183-1183.1130-r1-0-0'], 'label': '1-1183-1183.1130-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/1130'}
Lfunction data - 1-1183-1183.1130-r1-0-0