-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_65.12', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-1.0, -1.4081532572346456e-30], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 6.9852201116506265, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [13, [1]]], 'bad_primes': [5, 13], 'central_character': '65.12', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 65, 'conductor_radical': 65, 'conjugate': 'dirichlet_L_65.38', 'degree': 1, 'dirichlet_coefficients': [1, '-I', '-I', -1, 0, -1, '-I', 'I', -1, 0, -1, 'I', 0, -1, 0, 1, 'I', 'I', 1, 0, -1, 'I', '-I', 1, 0, 0, 'I', 'I', -1, 0, -1, '-I', 'I', 1, 0, 1, '-I', '-I', 0, 0, -1, 'I', '-I', 1, 0, -1, '-I', '-I', -1, 0, 1, 0, '-I', 1, 0, 1, '-I', 'I', 1, 0, 1, 'I', 'I', -1, 0, 1, '-I', '-I', -1, 0, -1, '-I', 'I', -1, 0, -1, 'I', 0, -1, 0, 1, 'I', 'I', 1, 0, -1, 'I', '-I', 1, 0, 0, 'I', 'I', -1, 0, -1, '-I', 'I', 1, 0], 'euler_factors': [[1, 0], [1, 1], [0], [1, '-I'], [1, -1], [0], [1, -1], [1, '-I'], [1, 'I'], [1, -1], [1, 0], [1, -1], [1, 'I'], [1, 0], [1, -1], [1, 0], [1, 1], [1, 'I'], [1, 'I'], [1, 1], [1, 0], [1, -1], [1, 'I'], [1, '-I'], [1, 1], [1, 0]], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-65-65.12-r1-0-0', 'leading_term': '-0.369557029606514600334123768333-0.662839148845721493953203231433*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/65/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.7588992919841939, -0.13767693189101274, 0.35103156750683295, 0.6684012992585756, 0.7584417444082081, 0.5831843517734044, 0.16331409854592585, -0.3978166070281314, -0.9214711564743074, -1.1967932542222175, -1.0517560526376402, -0.42990775409640336, 0.5577143442770471, 1.6342518792353993, 2.425841670338177, 2.58556911920916, 1.933450767819652, 0.5569551850273037, -1.17861395379044, -2.7315270841515082, -3.5732414360140474, -3.398980129382087, -2.2711078315956508, -0.6234690350475092, 0.8923927353555421, 1.6681620758503495, 1.3998132503541882, 0.22954695175995726, -1.3065748783994795, -2.5143344807689427, -2.859334911954183, -2.217666980192861, -0.9326431015011372, 0.35878916873814315, 1.049590187570332, 0.8724309863874675, 0.030575267223226624, -0.9265633649943973, -1.4218335078654956, -1.1880395587831099, -0.428415560313794, 0.30584321317837987, 0.465935464936946, -0.1137591842098177, -1.039164399099885, -1.5180485158763586, -0.8009863505151896, 1.333901055549159, 4.340867820873445, 7.0836324322065245, 8.37117734776127, 7.576751796044854, 4.993740222511594, 1.7119527618453572, -0.935301638337669, -2.0517556562689485, -1.6023616846182749, -0.34217516264399556, 0.695900406683547, 0.8351525935846132, 0.12069556695750214, -0.7999893608846791, -1.1853888743353356, -0.7480009851498755, 0.1324781854327306, 0.6800790098245859, 0.29478411562609175, -0.9731516295116804, -2.3930614865728526, -3.0161645745275685, -2.331006159770166, -0.6568273521707488, 1.023451794561107, 1.710622936262088, 1.090586743487189, -0.20373695711675208, -0.9855586656048754, -0.32929809258007164, 1.7384909549712817, 4.165904602257158, 5.51084058112607, 4.886065494529172, 2.5803231291618745, -0.08211564296212207, -1.5721511204183334, -1.1295930915354768, 0.7745660416178421, 2.795423055855693, 3.634373265435164, 2.8796867149433347, 1.1939595375912564, -0.24893162546889092, -0.6360773993932713, -0.04812341747290781, 0.7210832992612546, 0.8800325293011252, 0.3040000434387432, -0.3888950561138571, -0.41315018632159306, 0.4287482022776347, 1.4538659715655673, 1.5666828226718346, 0.17322422197619222, -2.1738589527863397, -3.9688284425616023, -3.7389615924526236, -1.1461068526634408, 2.6244306687277854, 5.537330380369515, 6.017512779422623, 3.9798413778249078, 0.8397527918557401, -1.4982361003540647, -1.9303654210502053, -0.7866030272052927, 0.6156334198776409, 1.0955248101135466, 0.511066087118423, -0.2488258571301426, -0.12424339991749124, 1.1447153127826573, 2.7492781708916727, 3.466278565552222, 2.684396970980624, 0.9369402316094375, -0.5168907621510884, -0.7227872073012425, 0.1893433564583536, 1.1435667295278662, 1.0701133055464456, -0.13519139816081477, -1.4848136252519426, -1.7568206615677315, -0.6325950624270001, 0.8782150898952006, 1.1669708824854448, -0.6166303527590142, -3.687002339719148, -6.012975955982766, -5.763145552190554, -2.71404011792857, 1.4942510150353703, 4.487866511429661, 4.817737694518058, 2.878166415944899, 0.42056691540464164, -0.8782644839601119, -0.613124207610393, 0.30358632451009704, 0.6611017673437347, 0.0711272056475434, -0.7881233585564615, -0.9503217199806478, -0.1785381191051229, 0.7596327362141797, 0.8353543489281062, -0.17349537272527937, -1.3285626781928752, -1.3101075763932672, 0.30536442317181745, 2.4359558548799116, 3.209238209332361, 1.5016808119259488, -1.9877742834382466, -5.11214049140269, -5.883712428006719, -4.024665641028, -1.1673739483427532, 0.480180777325905, -0.10228755666674477, -2.021605417402105, -3.3572185499719693, -2.855520149599542, -0.9596224487357843, 0.6823175568742924, 0.7385354060221793, -0.6335277937668347, -1.9902869591485335, -1.9519992445438121, -0.44846835960631576, 1.2625228774634487, 1.7824704350421696, 0.8412580922513765, -0.5235866889257912, -1.0087758504003184, -0.2884329639059253, 0.7397354809005663, 0.9348263396843404, 0.14555490322242615, -0.5609920943999143, 0.013962595406081184, 1.7958783633713082, 3.128587058510349, 2.041915505171598, -1.9084664827258493, -6.888646845911103, -9.936655621331967, -9.176947698507135, -5.271294093389806, -0.8747365552480322, 1.444217059941315, 1.0651419465046217, -0.5482897797582204, -1.397840433387237, -0.704718264163709, 0.666174413771405, 1.324240385253832, 0.8003277354756582, -0.09512650023903868, -0.2675220461781049, 0.4055103038666417, 0.8849862601784104, 0.07451967752210513, -1.8984245142110212, -3.5765440892185767, -3.458569817783408, -1.4794854972135125, 0.7951538546047079, 1.5545032984795408, 0.4520159832465597, -1.0124170826823824, -0.885455780374427, 1.3267988294058684, 4.047179986055506, 4.970588733232396, 3.173236135500301, 0.0280487717291103, -1.965202276527172, -1.3905940585396444, 0.8602161958958873, 2.4685503077555393, 1.834874344999962, -0.5061478959796109, -2.4741297876971453, -2.409482020980162, -0.5362418784114114, 1.4015379639991008, 1.865186536267533, 0.8816293525849228, -0.22641343342471684, -0.3334182891345903, 0.36852783857508054, 0.7504293728905912, 0.1462854956439538, -0.7919418089786625, -0.7725824738368472, 0.5933073700646094, 2.0713359412314793, 1.8508181672398218, -0.5215413273914725, -3.270607504719621, -3.6678399307711613, -0.47209531740410576, 4.704265052043975, 8.490225130184603, 8.452839682871602, 5.0205155060659985, 0.9439958010336591, -1.1338021763010353, -0.7410231139272293, 0.5137595613352318, 0.8563530301736326, 0.08003213651892391, -0.5501212555910907, 0.07455183286415791, 1.5693745593494128, 2.430108712210458, 1.6807611474923583, 0.0029954408231552413, -0.8957839247936961, -0.048675498412835694, 1.723907728481234, 2.6218761164883886, 1.724213959045895, -0.040311668331878936, -0.8625154040801437, 0.014777248275458753, 1.4388877286394814, 1.5374037357017456, -0.21666910060975744, -2.243582994179649, -2.3291448110016284, 0.04270075581236189, 2.874218089057826, 3.3312639731932516, 0.4134362189853261, -3.9557123497452475, -6.5319179632738935, -5.57123965572577, -2.2290616785218615, 0.6963214482212065, 1.34808715644286, 0.22164574283650568, -0.7856691588057434, -0.4861501044725956, 0.5487294484544349, 0.9307267639771849, 0.16827766090023769, -0.7928091758513406, -0.7400148725547363, 0.33032478052271586, 1.1806597913025232, 0.8484469541486765, -0.00498586014244963, 0.4220778360745635, 3.0611120649108514, 6.544886329074846, 8.082934518839211, 6.034892982938178, 1.685008514160993, -1.676819381282296, -1.6449363196126363, 1.1766421310633035, 3.8641231345990015, 3.979086305545998, 1.7337616232018405, -0.5253646633818438, -0.8298128022584473, 0.5299153967966987, 1.588981776236439, 0.9686736212248477, -0.6630567376054513, -1.4365250376523802, -0.41879583511338775, 1.320526623807373, 1.8614568151659092, 0.5193895666264979, -1.4168776429950507, -2.0811686825745666, -1.0121538929312799, 0.4442855471124471, 0.7117019236742532, -0.2619010574898562, -1.0624715292671016, -0.6178576088790096, 0.34359323870196984, -0.011813189466160253, -2.3691375208334287, -4.947511878299669, -4.831608689714093, -0.8752875435998575, 4.756647668309992, 8.17960128457949, 7.164996050159126, 3.0762270465588166, -0.5001323267463467, -1.0450255459105218, 0.8844168090281168, 2.704997816414719, 2.5744075715153305, 0.9732518869221317, -0.2957074094200168, -0.2813847248252544, 0.2505322048461281, 0.05419834683762504, -0.9009752374515313, -1.355286900095522, -0.3960705558301769, 1.1839865101731977, 1.5512108666268567, -0.08211794185451553, -2.3200305366810317, -2.86192369290842, -0.9773161035799595, 1.5308335712727483, 2.0909055089399824, 0.10849692179637567, -2.254053362262062, -2.225128853884847, 0.6709531554739362, 4.015151204815665, 4.885676354185681, 2.76702464266516, -0.049969486694594036, -0.9408492620456885, 0.36950077451530156, 1.7288611783761545, 1.055082417078649, -1.3590963127359188, -3.1956915435986843, -2.636880271968827, -0.2665983746704879, 1.6566537198355384, 1.6247791427362364, 0.28576712191156806, -0.6027110707572275, -0.2975747520883444, 0.22635997926158521, -0.2850043969226315, -1.6249519236128938, -2.269035807171245, -1.297627086837119, 0.24717568530982723, 0.4065688811768712, -1.2224250221261943, -2.465358156987064, -0.5263618070863887, 4.861140243557071, 10.479843970595148, 12.200108666153305, 8.721717886955998, 2.7701182930005026, -1.4513823844529203, -1.9709657820803943, -0.2813204717256503, 0.8234116971173291, 0.23010465542943007, -0.8208709985205387, -0.7121750198037564, 0.482850954696255, 1.225332788460482, 0.5643973337883575, -0.5828857036389992, -0.5150870243332591, 1.1069686823095615, 2.677709522332213, 2.433337811687637, 0.56810531324775, -0.8551913615816783, -0.2200102010096226, 1.7313445111363992, 2.664863869269515, 1.3263673617897218, -0.9334473232663225, -1.6291490052070432, -0.033772418298235726, 1.8239570947114636, 1.3485308568469063, -1.5788344465400963, -4.149783732702933, -3.4555683094354586, 0.37105689011191106, 4.1148031552602475, 4.644920882009762, 1.9476745095981605, -1.119964105949873, -1.9187804976229308, -0.5468428965387993, 0.7713907789959354, 0.42474652494561227, -0.926250434266412, -1.470271367317384, -0.5474378753959714, 0.6791916374178804, 0.8433172225149383, 0.12803582208849856, -0.08903175299396031, 0.7680721970678012, 1.4564867778150292, 0.38584474606343205, -2.051212968549323, -3.2725505219570943, -1.129688687910383, 3.365674991846507, 6.456329616201899, 5.161680238193679, 0.33761601866930374, -4.035772311543886, -4.6977908966012025, -2.0939489651155414, 0.5176541506868817, 0.6603560786250988, -1.0272091300116737, -2.036668285401453, -1.069124398732565, 0.6565534312462122, 1.163696454016319, 0.21644003493822545, -0.48483883011484974, 0.4461615913008903, 2.2093387453565576, 2.6544090879339777, 0.8518645065126297, -1.6975333056079216, -2.7002805947413173, -1.6303881092383061, -0.17940747869946155, -0.10470343875279546, -1.1288891628021833, -1.4773674620780606, -0.3897422399988738, 0.5814809365388764, -0.6809858074487954, -3.977508740493549, -6.344210105136577, -4.990108751579982, -0.550789030669363, 3.1057616987555243, 2.624557110023056, -1.4290047595343667, -5.154039129803201, -5.253763437368525, -2.1193485854437712, 1.0550233924461585, 1.823144293233863, 0.6894112863129328, -0.1612109888658599, 0.3252807841002086, 1.1238527736246142, 0.8641981012947002, -0.23732700354606256, -0.7537456146836583, -0.1334146254049511, 0.3535632517611018, -0.7910291650514365, -3.100850310172272, -4.2837279700133335, -2.8513868334981227, -0.16657902145434592, 0.783706267127428, -1.2243562999938387, -3.987626827492734, -4.087570912040312, -0.692870390208549, 3.3256503712472387, 4.3354583869266206, 1.7300778700453459, -1.6142743983411352, -2.609442010275397, -1.1733936800088047, 0.1609572431024128, -0.4646229891898306, -2.0337532111553625, -2.057242279017161, 0.25715867748603544, 2.9230042687916247, 3.429211366699407, 1.575668442834893, -0.46089492878422067, -0.7708249449207647, 0.20318352568865694, 0.565291442086403, -0.46256257547680696, -1.5937751327665415, -1.2791344164671608, 0.15883508531073942, 0.9055722235819162, 0.13196953273612144, -0.6924441607758949, 0.37618395675299654, 2.8382602078871284, 3.539303979979559, -0.003928346794084493, -6.289993851258871, -10.554875899715938, -9.215364147352718, -3.4239962849433176, 2.094874408434075, 3.656903921946494, 1.7494344830293214, -0.36726152795630074, -0.5359925545973486, 0.4256410507092319, 0.5423318937816637, -0.5355930434336992, -1.2725243009886935, -0.5270017105717213, 0.8105207218470915, 0.9925309359692799, -0.1871268144426833, -1.0021514751537632, -0.05348096923434812, 1.69257051732738, 1.8562879334226763, -0.38275070703603, -2.977846380465051, -3.20583676194201, -0.879811259884299, 1.3376886751106951, 1.0587252616187368, -0.9522002859027071, -1.6869608858728413, 0.3781499650062571, 3.1963772379792355, 3.338314691261879, 0.0006512617502126692, -3.8825051641376853, -4.807946831750272, -2.517167989730859, -0.08393556525209762, -0.2951258159391161, -2.610964931633538, -4.118631974931041, -3.084687511375232, -0.7984763055029281, 0.2711337438190538, -0.5264340693245319, -1.5569063083331778, -1.257789663614475, -0.10209065006177184, 0.29898386294368473, -0.43888271468590173, -0.9372809774564166, -0.1250963441630199, 0.9406953476954582, 0.24901447234609453, -2.181266192389329, -3.4402324346157847, -0.6817286870981989, 5.210429934392646, 9.748949958225058, 9.15791584719666, 4.29856469508837, -0.2125481307271031, -0.7778897753556467, 1.7795088934842953, 3.749302667682382, 2.884932176587984, 0.500397619001306, -0.7109441245961406, -0.037257779414946034, 0.8283719412246443, 0.42203226300930896, -0.4817847591202345, -0.0905392088365197, 1.7020515862349979, 2.8275296512828856, 1.555267468568121, -1.1841641409212746, -2.7289440274923966, -1.8126772672763714, 0.01869009737861083, 0.4835519273220802, -0.5306110691876, -0.9821609476491229, 0.39702360031438577, 2.113969870734115, 1.6500837076790267, -1.0975144100911047, -3.143671668298939, -1.764700358442775, 1.9809392784480229, 3.9928634507234495, 1.6167224534552191, -3.2331713626303262, -6.020807023587873, -4.440915886452317, -0.6688897539259732, 1.3645544017301967, 0.2763545862064251, -1.8083451595434612], 'positive_zeros': ['0.39184480300428952573422920640', '1.9703836689085405062464187484', '3.58367883989269684515199529165', '5.41552356075866429895562411336', '7.305271029617953847303244347751', '8.485565418463994628191552516707', '10.215960135529180046592771840994', '11.25948354792155985136902641183', '12.66404959536644353718705689311', '13.3949005881401251119789296790', '14.51577844851933707436307334913', '16.74675217499687804785617360013', '17.8970685259853354734479554077', '18.78907940802136336618600239613', '19.95255066224156165858986553104', '20.71456924587264684913341939995', '22.29874431025155860588918315258', '23.38778903570555983678039375267', '24.12635177655701527792065644199', '25.92642370030320721848675810338', '26.76311938321296310671869219267', '28.36721855947621313906891060043', '29.080336009712332549022597510405', '30.121622106617950563338806991614', '30.807790262876180284086190038120', '31.900703952801397019284985701125', '33.22303019536704163928413747288', '34.77877601805315889795680991503', '35.787025758883023970147230640448', '36.7496312271355870333031055962', '37.23366712796283122197497133900', '38.926258785628599121460417799095', '39.63565802029998279584808108612', '40.596698348757212879413650612724', '41.68441573063480930705802778759', '42.42320925367970866594962476249', '43.95007456646788595551117341192', '45.3806919005752481459199886411', '46.1429494937237727238102359970', '46.89942647987078910608993901197', '47.86547465487852380381350614985', '48.70815727551861404151035954381', '49.64239619136759003454503803291', '50.76936406055131860620230416146', '52.35982184385169950299585511784', '52.79101562192987239162317481640', '54.21824062937582516440676917291', '54.87711469894641263939607278324', '56.01165743858084528637456002904', '57.057730711899925847835420465830', '57.89308837112723631623121443587', '58.796488030142402857791445269107', '59.37172825699711015741580536158', '60.49588917100487728432788282699', '62.26915187845148521981676439960', '63.01931022677217762150526360421', '63.908408739817242847876795736647', '64.958608892721439815617848665059', '65.46471512197027822734669593608', '66.26475827830361667259327911571', '67.6898250028841611214603476542', '68.52221696838546248714159607974', '69.216370122059353115758159820445', '70.62796023401802292031226658670', '71.45060529646499153099204511475', '72.438286105790009441288556440937', '73.512684483591393580255107326730', '74.603668990254096381818370873280', '75.16449495487768176149190407486', '75.982974883145236894562937791695', '76.763778386646340026619946288377', '77.75737085814013679069118199570', '78.78086377738518429555901588563', '80.41077893481336955965443537045', '81.114332940719315322941880593536', '81.901140153525511023056764973053', '82.48107212010982112217105578581', '83.75059577843030308672924991187', '84.38450312095035059587933710584', '85.61703179522994713484880205547', '86.24685723559968137362069213223', '87.157637312176934565472813352091', '88.12068369592715673568328684385', '89.092983359623838206302452985935', '90.52943303240529384974415509574', '91.300679558297766481728512536755', '92.023150758479195189336225623197', '92.85979347195158561767011871093', '93.66546186933601213435535073145', '94.68451939536912109497936639907', '94.878457586793399370094968465879', '96.69034926435959334936197399375', '97.38731627396580297032804053246', '98.65645324846429115190462642154', '99.27054637946434763581237112566', '100.18636543817304501984515409706', '101.01126987748646735861538667400', '101.95474798916027510199569221829', '103.0136851849462963130931899321', '103.68035911729093188106870213046', '104.55821383084986158034672340114', '104.99742781529729414687277563144', '106.29944869107345478535107384862', '107.75142009341618710806720991777', '108.31724857902432173092009986583', '109.58182956774249722393691521916', '110.15082829308902783164333775187', '110.64773513454524251137745789213', '111.63895248561449438196943471535', '112.48889947091440824212024483464', '113.549803155876543649334770202298', '114.38755609174034098400184399441', '115.25446699167558867311256030911', '116.55533407876026230662313092890', '117.1221504260100551089710864683', '117.96171803133415269441290220484', '119.095669310283876409115497771222', '120.06810973713113450366942269144', '120.76332362598771537241260735112', '121.15688134955551166385583491892', '122.43900072967357887631821711691', '122.916948632962095395278741011433', '123.78940548547825493201066267111', '125.4861384364040601877922664768', '126.30089854532985293073515224916', '126.93565328234879550969307524954', '127.69679285430505752337832585445', '128.57784892844540819448975268703', '129.18671221357614611387408995165', '130.404104122937642283735613956454', '130.97761669217607502280350649835', '132.05075813332039531434308290481', '132.817235095500028804613102970115', '133.60015371057919234125179930948', '134.66142475738215652000268929665', '135.80601061571847802732498851298', '136.663169857308708924758468372772', '137.290969497486105144238263244235', '138.24910963348667396552860937575', '139.12590670286182760989022139019', '139.431308011437316082339833558529', '140.36778172969468356627822573065', '141.335727918195104737288748881835', '142.51979702246707438569126778184', '143.66533275220242364776228952222', '144.20060038159812190394445899567', '145.184084000125950632092393814349', '145.997070323308986096641833989267', '146.46934636930464838647310999990', '147.599610823002216332258550187860', '148.82851004037510485395678642541', '149.00780834188437476736846645072', '150.0871983170902607821533446718', '150.52877158694753540672922822918', '151.91126672071463602423784387756', '152.715943153980090911738831084613', '153.93800241779862903534153434257', '154.8861494417099424976355994886', '155.187178731097173846863755080114', '156.18293431961185959924453230586', '156.92376349227409494420098332662', '157.34817816515550731396169679818', '158.77358231393859103267653723985', '159.230931523439518562889378087204', '160.36134620865996099895793250799', '161.398431906672312506002100405478', '162.42759061643812519098437043158', '162.69466329235820408543368633520', '163.72283462856720405711298500155', '164.90937790454294137550011914774', '165.56336071223996825490620463942', '166.142480924736758171718910824388', '167.15306697683129662495847583720', '167.84710754638665700945781045417', '168.37756020114555011222880385109', '169.37477860168193690934129088376', '170.79905233424893176174108068645', '171.799164834145676268916705181317', '172.36191497628994275198386929993', '172.990117411474579889206585605020', '173.86561844785096329046529937305', '174.64504075124370478029284008233', '175.32216844045411429670505346083', '176.20872890426071633720356186108', '177.28761192134199239862737288486', '177.98243860757535346437251502321', '178.71019881047412919278254551609', '179.68754730660937392864741513667', '180.95864229569880667452309944279', '181.183570885743571647391427805158', '182.65756372084868489292614229204', '182.98166431732576032848935599850', '184.09558347082227318423355079390', '184.53579337123265622038097333193', '185.34250779206046008904431748688', '185.977017250085283053031956726344', '186.91685764558532862180826672582', '188.415080674818312133931311362684', '188.867813517224697536941038695021', '190.07953666446823739369967262346', '190.63517820388932225279680426447', '191.37847053516222169854406757065', '191.895889064878192433680902400071', '192.99140893712808103386505680921', '194.05840157692507359171171149278', '194.54695318823134777467249545165', '195.24837483814301941512600621780', '196.13830120979330727937395682797', '197.02794654374946342087631587810', '197.92043349062035046604250987566', '199.12723808089475575984544212357', '199.72720408406036195028974618397'], 'prelabel': '1-65-65.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9852201116506265, 'root_angle': 0.6762081911747834, 'root_number': '-0.525731112119133606025669084848+0.850650808352039932181540497063*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.338104095587', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.409719721487599657520652901529-0.662940435228076874756945346482*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.391844803004', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.97038366891', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.58367883989', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.9852201116506265, 'bad_primes': [5, 13], 'central_character': '65.12', 'conductor': 65, 'conductor_radical': 65, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/65/12'], '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': '1-65-65.12-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': '1-65-65.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9852201116506265, 'root_angle': 0.3381040955873917, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.391844803004', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_65.12', 'Lhash_array': ['dirichlet_L_65.12'], 'label': '1-65-65.12-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/65/12'}