Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(17,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.17");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.k (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 89.2 | ||
Character | \(\chi\) | \(=\) | 324.89 |
Dual form | 324.5.k.a.233.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −23.3523 | − | 27.8302i | −0.934092 | − | 1.11321i | −0.993369 | − | 0.114966i | \(-0.963324\pi\) |
0.0592770 | − | 0.998242i | \(-0.481120\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.9114 | − | 16.3464i | 0.916558 | − | 0.333600i | 0.159690 | − | 0.987167i | \(-0.448951\pi\) |
0.756868 | + | 0.653567i | \(0.226728\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 93.1464 | − | 111.008i | 0.769805 | − | 0.917418i | −0.228620 | − | 0.973516i | \(-0.573421\pi\) |
0.998425 | + | 0.0560975i | \(0.0178658\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.5560 | + | 235.676i | 0.245894 | + | 1.39453i | 0.818408 | + | 0.574637i | \(0.194857\pi\) |
−0.572515 | + | 0.819895i | \(0.694032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 70.2567 | − | 40.5627i | 0.243103 | − | 0.140355i | −0.373499 | − | 0.927631i | \(-0.621842\pi\) |
0.616602 | + | 0.787275i | \(0.288509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 327.274 | − | 566.855i | 0.906576 | − | 1.57024i | 0.0877883 | − | 0.996139i | \(-0.472020\pi\) |
0.818788 | − | 0.574096i | \(-0.194647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −117.142 | + | 321.845i | −0.221440 | + | 0.608403i | −0.999812 | − | 0.0194015i | \(-0.993824\pi\) |
0.778371 | + | 0.627804i | \(0.216046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −120.660 | + | 684.294i | −0.193055 | + | 1.09487i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1287.14 | − | 226.958i | −1.53049 | − | 0.269867i | −0.655944 | − | 0.754809i | \(-0.727729\pi\) |
−0.874546 | + | 0.484942i | \(0.838841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 208.261 | + | 75.8006i | 0.216712 | + | 0.0788768i | 0.448095 | − | 0.893986i | \(-0.352103\pi\) |
−0.231383 | + | 0.972863i | \(0.574325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1503.71 | − | 868.166i | −1.22752 | − | 0.708707i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −577.060 | − | 999.497i | −0.421519 | − | 0.730093i | 0.574569 | − | 0.818456i | \(-0.305170\pi\) |
−0.996088 | + | 0.0883635i | \(0.971836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2496.16 | − | 440.141i | 1.48493 | − | 0.261833i | 0.628382 | − | 0.777905i | \(-0.283718\pi\) |
0.856545 | + | 0.516072i | \(0.172606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2375.48 | − | 1993.27i | −1.28474 | − | 1.07802i | −0.992572 | − | 0.121657i | \(-0.961179\pi\) |
−0.292167 | − | 0.956367i | \(-0.594376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −989.606 | − | 2718.92i | −0.447988 | − | 1.23084i | −0.934122 | − | 0.356954i | \(-0.883815\pi\) |
0.486134 | − | 0.873884i | \(-0.338407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −89.4477 | + | 75.0556i | −0.0372544 | + | 0.0312601i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2001.37i | 0.712485i | 0.934394 | + | 0.356242i | \(0.115942\pi\) | ||||
−0.934394 | + | 0.356242i | \(0.884058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5264.55 | −1.74035 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −352.871 | − | 420.535i | −0.101370 | − | 0.120809i | 0.712974 | − | 0.701190i | \(-0.247348\pi\) |
−0.814344 | + | 0.580382i | \(0.802903\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2801.19 | + | 1019.55i | −0.752805 | + | 0.273998i | −0.689785 | − | 0.724014i | \(-0.742295\pi\) |
−0.0630192 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5588.48 | − | 6660.09i | 1.32272 | − | 1.57635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −206.959 | − | 1173.72i | −0.0461035 | − | 0.261466i | 0.953040 | − | 0.302844i | \(-0.0979363\pi\) |
−0.999144 | + | 0.0413782i | \(0.986825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3982.84 | − | 2299.50i | 0.790090 | − | 0.456159i | −0.0499044 | − | 0.998754i | \(-0.515892\pi\) |
0.839994 | + | 0.542595i | \(0.182558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 750.689 | − | 1300.23i | 0.140869 | − | 0.243992i | −0.786955 | − | 0.617010i | \(-0.788344\pi\) |
0.927824 | + | 0.373018i | \(0.121677\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2368.76 | − | 6508.11i | 0.399521 | − | 1.09767i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 157.278 | − | 891.966i | 0.0252007 | − | 0.142920i | −0.969611 | − | 0.244651i | \(-0.921327\pi\) |
0.994812 | + | 0.101730i | \(0.0324379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2210.32 | − | 389.740i | −0.320848 | − | 0.0565742i | 0.0109047 | − | 0.999941i | \(-0.496529\pi\) |
−0.331753 | + | 0.943366i | \(0.607640\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2769.53 | − | 1008.02i | −0.383325 | − | 0.139519i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3605.84 | + | 2081.83i | 0.455226 | + | 0.262825i | 0.710035 | − | 0.704167i | \(-0.248679\pi\) |
−0.254809 | + | 0.966991i | \(0.582013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5718.79 | + | 9905.23i | 0.690592 | + | 1.19614i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23418.3 | + | 4129.28i | −2.59482 | + | 0.457538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12717.1 | − | 10670.9i | −1.35159 | − | 1.13412i | −0.978483 | − | 0.206327i | \(-0.933849\pi\) |
−0.373104 | − | 0.927789i | \(-0.621707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1625.30 | + | 4465.47i | 0.159327 | + | 0.437748i | 0.993511 | − | 0.113739i | \(-0.0362828\pi\) |
−0.834183 | + | 0.551487i | \(0.814061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3110.55 | − | 2610.06i | 0.293199 | − | 0.246023i | −0.484308 | − | 0.874898i | \(-0.660929\pi\) |
0.777507 | + | 0.628874i | \(0.216484\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13840.5i | − | 1.20888i | −0.796650 | − | 0.604441i | \(-0.793397\pi\) | ||
0.796650 | − | 0.604441i | \(-0.206603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20651.8 | −1.73822 | −0.869112 | − | 0.494616i | \(-0.835309\pi\) | ||||
−0.869112 | + | 0.494616i | \(0.835309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6495.37 | − | 7740.88i | −0.508682 | − | 0.606224i | 0.449184 | − | 0.893439i | \(-0.351715\pi\) |
−0.957866 | + | 0.287215i | \(0.907270\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11692.5 | − | 4255.74i | 0.884125 | − | 0.321795i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2492.27 | − | 2970.17i | 0.175995 | − | 0.209743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1104.05 | − | 6261.36i | −0.0754078 | − | 0.427659i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2197.67 | − | 1268.82i | 0.140651 | − | 0.0812047i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2913.07 | + | 5045.59i | −0.180611 | + | 0.312827i | −0.942089 | − | 0.335364i | \(-0.891141\pi\) |
0.761478 | + | 0.648191i | \(0.224474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7585.77 | + | 20841.7i | −0.442035 | + | 1.21448i | 0.496116 | + | 0.868256i | \(0.334759\pi\) |
−0.938151 | + | 0.346226i | \(0.887463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5432.28 | − | 30808.0i | 0.307099 | − | 1.74165i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23386.2 | − | 4123.61i | −1.24600 | − | 0.219703i | −0.488515 | − | 0.872556i | \(-0.662461\pi\) |
−0.757485 | + | 0.652852i | \(0.773572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19862.6 | + | 7229.41i | 1.02803 | + | 0.374174i | 0.800332 | − | 0.599557i | \(-0.204657\pi\) |
0.227702 | + | 0.973731i | \(0.426879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30032.6 | + | 17339.3i | 1.46866 | + | 0.847931i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23741.5 | + | 41121.4i | 1.12920 | + | 1.95583i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10205.6 | − | 1799.53i | 0.459692 | − | 0.0810561i | 0.0609936 | − | 0.998138i | \(-0.480573\pi\) |
0.398699 | + | 0.917082i | \(0.369462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 33851.0 | + | 28404.4i | 1.48463 | + | 1.24575i | 0.901065 | + | 0.433684i | \(0.142787\pi\) |
0.583564 | + | 0.812067i | \(0.301658\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2753.82 | − | 7566.05i | −0.114623 | − | 0.314924i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8441.79 | − | 7083.50i | 0.342480 | − | 0.287375i | −0.455282 | − | 0.890347i | \(-0.650462\pi\) |
0.797762 | + | 0.602972i | \(0.206017\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16369.3i | 0.631509i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −29240.4 | −1.10055 | −0.550273 | − | 0.834985i | \(-0.685476\pi\) | ||||
−0.550273 | + | 0.834985i | \(0.685476\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21160.9 | + | 25218.5i | 0.758753 | + | 0.904247i | 0.997768 | − | 0.0667690i | \(-0.0212691\pi\) |
−0.239015 | + | 0.971016i | \(0.576825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26977.7 | + | 9819.07i | −0.944563 | + | 0.343793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13402.4 | − | 15972.4i | 0.447807 | − | 0.533675i | −0.494165 | − | 0.869368i | \(-0.664526\pi\) |
0.941971 | + | 0.335693i | \(0.108971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5766.76 | + | 32704.9i | 0.188302 | + | 1.06792i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10186.4 | − | 5881.11i | 0.317917 | − | 0.183550i | −0.332547 | − | 0.943087i | \(-0.607908\pi\) |
0.650464 | + | 0.759537i | \(0.274575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12812.8 | − | 22192.4i | 0.391099 | − | 0.677403i | −0.601496 | − | 0.798876i | \(-0.705428\pi\) |
0.992595 | + | 0.121473i | \(0.0387618\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14340.5 | + | 39400.2i | −0.419007 | + | 1.15121i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2041.39 | − | 11577.3i | 0.0583772 | − | 0.331073i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 43133.9 | + | 7605.67i | 1.18237 | + | 0.208483i | 0.730062 | − | 0.683381i | \(-0.239491\pi\) |
0.452304 | + | 0.891864i | \(0.350602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42585.5 | + | 15499.8i | 1.14326 | + | 0.416114i | 0.843091 | − | 0.537770i | \(-0.180733\pi\) |
0.300173 | + | 0.953885i | \(0.402955\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 41059.8 | + | 23705.9i | 1.05800 | + | 0.610835i | 0.924878 | − | 0.380265i | \(-0.124167\pi\) |
0.133120 | + | 0.991100i | \(0.457500\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8841.99 | − | 15314.8i | −0.223277 | − | 0.386727i | 0.732524 | − | 0.680741i | \(-0.238342\pi\) |
−0.955801 | + | 0.294014i | \(0.905009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −61517.3 | + | 10847.2i | −1.49281 | + | 0.263223i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −70540.3 | − | 59190.4i | −1.67853 | − | 1.40846i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32440.8 | − | 89130.4i | −0.742676 | − | 2.04049i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 46294.0 | − | 38845.3i | 1.03982 | − | 0.872515i | 0.0478364 | − | 0.998855i | \(-0.484767\pi\) |
0.991987 | + | 0.126340i | \(0.0403229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 112658.i | 2.43716i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10592.3 | 0.224943 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12479.2 | + | 14872.2i | 0.255508 | + | 0.304502i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14524.0 | + | 5286.30i | −0.292063 | + | 0.106302i | −0.483896 | − | 0.875125i | \(-0.660779\pi\) |
0.191834 | + | 0.981427i | \(0.438557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21204.1 | + | 25270.1i | −0.411499 | + | 0.490405i | −0.931490 | − | 0.363766i | \(-0.881491\pi\) |
0.519991 | + | 0.854172i | \(0.325935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11374.1 | + | 64505.7i | 0.216893 | + | 1.23006i | 0.877591 | + | 0.479410i | \(0.159149\pi\) |
−0.660698 | + | 0.750652i | \(0.729740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10438.5 | + | 6026.66i | −0.192276 | + | 0.111011i | −0.593048 | − | 0.805167i | \(-0.702075\pi\) |
0.400772 | + | 0.916178i | \(0.368742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −52558.5 | + | 91034.0i | −0.951716 | + | 1.64842i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2021.25 | − | 5553.34i | 0.0353854 | − | 0.0972207i | −0.920742 | − | 0.390173i | \(-0.872415\pi\) |
0.956127 | + | 0.292952i | \(0.0946376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2803.01 | − | 15896.7i | 0.0482604 | − | 0.273698i | −0.951123 | − | 0.308813i | \(-0.900068\pi\) |
0.999383 | + | 0.0351143i | \(0.0111795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4177.62 | + | 736.628i | 0.0695980 | + | 0.0122720i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 147194. | + | 53574.3i | 2.41266 | + | 0.878138i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −39754.0 | − | 22952.0i | −0.631006 | − | 0.364311i | 0.150136 | − | 0.988665i | \(-0.452029\pi\) |
−0.781141 | + | 0.624354i | \(0.785362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24815.9 | + | 42982.4i | 0.387694 | + | 0.671505i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −86522.3 | + | 15256.2i | −1.30997 | + | 0.230983i | −0.784660 | − | 0.619926i | \(-0.787163\pi\) |
−0.525312 | + | 0.850910i | \(0.676051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −42254.7 | − | 35455.9i | −0.629906 | − | 0.528554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5894.23 | − | 16194.3i | −0.0852149 | − | 0.234126i | 0.889765 | − | 0.456419i | \(-0.150868\pi\) |
−0.974980 | + | 0.222293i | \(0.928646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 55698.5 | − | 46736.6i | 0.793144 | − | 0.665526i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 21865.7i | − | 0.302176i | −0.988520 | − | 0.151088i | \(-0.951722\pi\) | ||
0.988520 | − | 0.151088i | \(-0.0482776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 57620.5 | 0.784582 | 0.392291 | − | 0.919841i | \(-0.371683\pi\) | ||||
0.392291 | + | 0.919841i | \(0.371683\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 64722.8 | + | 77133.7i | 0.855839 | + | 1.01995i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 89309.9 | − | 32506.1i | 1.16396 | − | 0.423649i | 0.313453 | − | 0.949604i | \(-0.398514\pi\) |
0.850512 | + | 0.525955i | \(0.176292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 58640.0 | − | 69884.4i | 0.742645 | − | 0.885049i | −0.253974 | − | 0.967211i | \(-0.581738\pi\) |
0.996619 | + | 0.0821616i | \(0.0261824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22694.5 | − | 128707.i | −0.283366 | − | 1.60705i | −0.711065 | − | 0.703127i | \(-0.751787\pi\) |
0.427699 | − | 0.903921i | \(-0.359324\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 104911. | − | 60570.6i | 1.27367 | − | 0.735356i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38469.8 | + | 66631.7i | −0.460601 | + | 0.797784i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 40038.7 | − | 110006.i | 0.466386 | − | 1.28138i | −0.454220 | − | 0.890890i | \(-0.650082\pi\) |
0.920605 | − | 0.390494i | \(-0.127696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3463.22 | + | 19640.9i | −0.0397957 | + | 0.225693i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −80719.1 | − | 14232.9i | −0.902888 | − | 0.159203i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −139269. | − | 50689.7i | −1.53717 | − | 0.559483i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 93788.4 | + | 54148.8i | 1.00821 | + | 0.582088i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26734.0 | − | 46304.7i | −0.283653 | − | 0.491302i | 0.688628 | − | 0.725114i | \(-0.258213\pi\) |
−0.972282 | + | 0.233812i | \(0.924880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −140065. | + | 24697.2i | −1.44813 | + | 0.255345i | −0.841768 | − | 0.539840i | \(-0.818485\pi\) |
−0.606367 | + | 0.795185i | \(0.707374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1973.39 | + | 1655.87i | 0.0201430 | + | 0.0169019i | 0.652804 | − | 0.757527i | \(-0.273593\pi\) |
−0.632661 | + | 0.774429i | \(0.718037\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31672.4 | − | 87019.3i | −0.315183 | − | 0.865959i | −0.991589 | − | 0.129429i | \(-0.958686\pi\) |
0.676406 | − | 0.736529i | \(-0.263537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −145087. | + | 121742.i | −1.42576 | + | 1.19636i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 53100.5i | − | 0.508972i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −166286. | −1.57430 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −88889.1 | − | 105934.i | −0.821215 | − | 0.978686i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 40376.6 | − | 14695.9i | 0.368531 | − | 0.134134i | −0.151115 | − | 0.988516i | \(-0.548286\pi\) |
0.519645 | + | 0.854382i | \(0.326064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27831.9 | + | 33168.8i | −0.248001 | + | 0.295556i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5958.86 | + | 33794.4i | 0.0524691 | + | 0.297567i | 0.999738 | − | 0.0228716i | \(-0.00728088\pi\) |
−0.947269 | + | 0.320438i | \(0.896170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27813.2 | − | 16057.9i | 0.239189 | − | 0.138096i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60166.6 | + | 104212.i | −0.511408 | + | 0.885784i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15708.7 | + | 43159.3i | −0.130461 | + | 0.358439i | −0.987674 | − | 0.156523i | \(-0.949972\pi\) |
0.857213 | + | 0.514962i | \(0.172194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25659.0 | − | 145519.i | 0.210663 | − | 1.19473i | −0.677612 | − | 0.735420i | \(-0.736985\pi\) |
0.888275 | − | 0.459312i | \(-0.151904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 150996. | + | 26624.7i | 1.21176 | + | 0.213666i | 0.742775 | − | 0.669541i | \(-0.233509\pi\) |
0.468984 | + | 0.883207i | \(0.344620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −157004. | − | 57144.8i | −1.24582 | − | 0.453440i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1793.35 | + | 1035.39i | 0.0139147 | + | 0.00803368i | 0.506941 | − | 0.861981i | \(-0.330776\pi\) |
−0.493026 | + | 0.870014i | \(0.664109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −149056. | − | 258172.i | −1.14376 | − | 1.98105i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −53716.0 | + | 9471.58i | −0.403198 | + | 0.0710946i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −61804.0 | − | 51859.7i | −0.458864 | − | 0.385033i | 0.383849 | − | 0.923396i | \(-0.374598\pi\) |
−0.842713 | + | 0.538363i | \(0.819043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32715.2 | + | 89884.2i | 0.237685 | + | 0.653034i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 94740.5 | − | 79496.7i | 0.680954 | − | 0.571388i | −0.235331 | − | 0.971915i | \(-0.575617\pi\) |
0.916285 | + | 0.400527i | \(0.131173\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 312780.i | − | 2.20068i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 253183. | 1.76261 | 0.881306 | − | 0.472546i | \(-0.156665\pi\) | ||||
0.881306 | + | 0.472546i | \(0.156665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 62618.3 | + | 74625.6i | 0.426878 | + | 0.508733i | 0.936019 | − | 0.351950i | \(-0.114481\pi\) |
−0.509141 | + | 0.860683i | \(0.670037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −236438. | + | 86056.4i | −1.59513 | + | 0.580579i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27505.9 | + | 32780.3i | −0.181772 | + | 0.216627i | −0.849234 | − | 0.528016i | \(-0.822936\pi\) |
0.667462 | + | 0.744644i | \(0.267381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4824.90 | + | 27363.4i | 0.0315598 | + | 0.178985i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28496.4 | + | 16452.4i | −0.182640 | + | 0.105447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −88498.8 | + | 153284.i | −0.561509 | + | 0.972562i | 0.435856 | + | 0.900016i | \(0.356446\pi\) |
−0.997365 | + | 0.0725454i | \(0.976888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 66578.7 | − | 182923.i | 0.414044 | − | 1.13758i | −0.540977 | − | 0.841037i | \(-0.681945\pi\) |
0.955021 | − | 0.296539i | \(-0.0958324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9209.90 | + | 52232.0i | −0.0567081 | + | 0.321608i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −164703. | − | 29041.5i | −0.994288 | − | 0.175320i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12003.2 | + | 4368.82i | 0.0717548 | + | 0.0261166i | 0.377648 | − | 0.925949i | \(-0.376733\pi\) |
−0.305893 | + | 0.952066i | \(0.598955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22722.1 | − | 13118.6i | −0.133214 | − | 0.0769110i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40769.6 | + | 70615.0i | 0.236723 | + | 0.410016i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 193351. | − | 34093.0i | 1.10133 | − | 0.194195i | 0.406702 | − | 0.913561i | \(-0.366679\pi\) |
0.694631 | + | 0.719366i | \(0.255568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14748.7 | − | 12375.7i | −0.0832129 | − | 0.0698239i | 0.600232 | − | 0.799826i | \(-0.295075\pi\) |
−0.683445 | + | 0.730002i | \(0.739519\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19279.7 | + | 52970.5i | 0.106739 | + | 0.293262i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −109139. | + | 91578.6i | −0.598583 | + | 0.502271i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37209.8i | 0.200310i | 0.994972 | + | 0.100155i | \(0.0319339\pi\) | ||||
−0.994972 | + | 0.100155i | \(0.968066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 120422. | 0.642289 | 0.321145 | − | 0.947030i | \(-0.395932\pi\) | ||||
0.321145 | + | 0.947030i | \(0.395932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 144102. | + | 171734.i | 0.754583 | + | 0.899277i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 72962.8 | − | 26556.3i | 0.378593 | − | 0.137797i | −0.145712 | − | 0.989327i | \(-0.546547\pi\) |
0.524305 | + | 0.851530i | \(0.324325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 144700. | − | 172446.i | 0.737327 | − | 0.878712i | −0.258864 | − | 0.965914i | \(-0.583348\pi\) |
0.996191 | + | 0.0872021i | \(0.0277926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26266.9 | − | 148967.i | −0.132644 | − | 0.752264i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −236745. | + | 136685.i | −1.17432 | + | 0.677995i | −0.954694 | − | 0.297588i | \(-0.903818\pi\) |
−0.219628 | + | 0.975584i | \(0.570484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 183650. | − | 318090.i | 0.902894 | − | 1.56386i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 142118. | − | 390465.i | 0.686476 | − | 1.88608i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35070.4 | + | 198894.i | −0.167922 | + | 0.952334i | 0.778078 | + | 0.628168i | \(0.216195\pi\) |
−0.946000 | + | 0.324166i | \(0.894916\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −96757.1 | − | 17060.9i | −0.455282 | − | 0.0802786i | −0.0586958 | − | 0.998276i | \(-0.518694\pi\) |
−0.396586 | + | 0.917997i | \(0.629805\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 368771. | + | 134222.i | 1.72026 | + | 0.626124i | 0.997862 | − | 0.0653505i | \(-0.0208165\pi\) |
0.722400 | + | 0.691475i | \(0.243039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −158722. | − | 91638.0i | −0.727784 | − | 0.420186i | 0.0898270 | − | 0.995957i | \(-0.471369\pi\) |
−0.817611 | + | 0.575771i | \(0.804702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28480.9 | − | 49330.4i | −0.129482 | − | 0.224269i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −442536. | + | 78031.0i | −1.97800 | + | 0.348774i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 348407. | + | 292348.i | 1.54419 | + | 1.29573i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15394.6 | + | 42296.4i | 0.0670962 | + | 0.184345i | 0.968709 | − | 0.248198i | \(-0.0798384\pi\) |
−0.901613 | + | 0.432544i | \(0.857616\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 211577. | − | 177534.i | 0.914488 | − | 0.767347i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 603109.i | 2.56397i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −89812.6 | −0.378686 | −0.189343 | − | 0.981911i | \(-0.560636\pi\) | ||||
−0.189343 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 193660. | + | 230794.i | 0.803296 | + | 0.957331i | 0.999731 | − | 0.0231855i | \(-0.00738084\pi\) |
−0.196435 | + | 0.980517i | \(0.562936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −99636.4 | + | 36264.7i | −0.409944 | + | 0.149207i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 141286. | − | 168379.i | 0.571989 | − | 0.681670i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 46801.6 | + | 265425.i | 0.187958 | + | 1.06596i | 0.922096 | + | 0.386961i | \(0.126475\pi\) |
−0.734138 | + | 0.679000i | \(0.762414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −330182. | + | 190631.i | −1.30502 | + | 0.753454i | −0.981261 | − | 0.192685i | \(-0.938280\pi\) |
−0.323760 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 86320.4 | − | 149511.i | 0.338478 | − | 0.586261i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 83468.2 | − | 229327.i | 0.322170 | − | 0.885156i | −0.667858 | − | 0.744289i | \(-0.732789\pi\) |
0.990028 | − | 0.140867i | \(-0.0449891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12460.4 | − | 70666.2i | 0.0477187 | − | 0.270626i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −145277. | − | 25616.3i | −0.547750 | − | 0.0965831i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −393999. | − | 143404.i | −1.47406 | − | 0.536513i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −210341. | − | 121440.i | −0.774904 | − | 0.447391i | 0.0597174 | − | 0.998215i | \(-0.480980\pi\) |
−0.834621 | + | 0.550824i | \(0.814313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25165.4 | − | 43587.7i | −0.0920027 | − | 0.159353i | 0.816351 | − | 0.577556i | \(-0.195993\pi\) |
−0.908354 | + | 0.418203i | \(0.862660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17706.4 | − | 3122.11i | 0.0637542 | − | 0.0112416i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 124509. | + | 104475.i | 0.444927 | + | 0.373338i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 207461. | + | 569995.i | 0.730268 | + | 2.00639i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −385184. | + | 323207.i | −1.34574 | + | 1.12921i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16920.5i | 0.0582420i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 223428. | 0.763383 | 0.381692 | − | 0.924290i | \(-0.375342\pi\) | ||||
0.381692 | + | 0.924290i | \(0.375342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 482268. | + | 574745.i | 1.62366 | + | 1.93500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32840.0 | + | 11952.8i | −0.109756 | + | 0.0399480i | −0.396314 | − | 0.918115i | \(-0.629711\pi\) |
0.286558 | + | 0.958063i | \(0.407489\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −549900. | + | 655346.i | −1.81126 | + | 2.15858i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7516.87 | − | 42630.3i | −0.0245803 | − | 0.139402i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 342072. | − | 197495.i | 1.10257 | − | 0.636571i | 0.165677 | − | 0.986180i | \(-0.447019\pi\) |
0.936896 | + | 0.349609i | \(0.113686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 371049. | − | 642676.i | 1.18743 | − | 2.05669i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 88564.9 | − | 243330.i | 0.279412 | − | 0.767678i | −0.718018 | − | 0.696025i | \(-0.754950\pi\) |
0.997430 | − | 0.0716530i | \(-0.0228274\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −63748.3 | + | 361535.i | −0.199697 | + | 1.13254i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 433798. | + | 76490.4i | 1.33987 | + | 0.236256i | 0.797213 | − | 0.603698i | \(-0.206307\pi\) |
0.542659 | + | 0.839953i | \(0.317418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −320339. | − | 116594.i | −0.982511 | − | 0.357605i | −0.199695 | − | 0.979858i | \(-0.563995\pi\) |
−0.782816 | + | 0.622253i | \(0.786217\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −206102. | − | 118993.i | −0.623372 | − | 0.359904i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 315660. | + | 546740.i | 0.948132 | + | 1.64221i | 0.749356 | + | 0.662167i | \(0.230363\pi\) |
0.198775 | + | 0.980045i | \(0.436304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −105639. | + | 18627.1i | −0.312949 | + | 0.0551814i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 222167. | + | 186420.i | 0.653646 | + | 0.548474i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22503.9 | + | 61828.9i | 0.0653102 | + | 0.179438i | 0.968055 | − | 0.250738i | \(-0.0806734\pi\) |
−0.902745 | + | 0.430177i | \(0.858451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 111126. | − | 93246.0i | 0.320321 | − | 0.268782i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 660484.i | − | 1.87825i | −0.343579 | − | 0.939124i | \(-0.611639\pi\) | ||
0.343579 | − | 0.939124i | \(-0.388361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −140861. | −0.397883 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 249715. | + | 297598.i | 0.695969 | + | 0.829424i | 0.992064 | − | 0.125735i | \(-0.0401288\pi\) |
−0.296094 | + | 0.955159i | \(0.595684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 308372. | − | 112238.i | 0.853740 | − | 0.310736i | 0.122176 | − | 0.992508i | \(-0.461013\pi\) |
0.731564 | + | 0.681772i | \(0.238791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −148473. | + | 176943.i | −0.405636 | + | 0.483418i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42611.4 | − | 241662.i | −0.115651 | − | 0.655889i | −0.986426 | − | 0.164207i | \(-0.947493\pi\) |
0.870775 | − | 0.491682i | \(-0.163618\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 599660. | − | 346214.i | 1.60629 | − | 0.927389i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −60158.0 | + | 104197.i | −0.160093 | + | 0.277289i | −0.934902 | − | 0.354906i | \(-0.884513\pi\) |
0.774809 | + | 0.632196i | \(0.217846\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 213630. | − | 586942.i | 0.561166 | − | 1.54179i | −0.256765 | − | 0.966474i | \(-0.582657\pi\) |
0.817931 | − | 0.575316i | \(-0.195121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45927.9 | + | 260470.i | −0.119866 | + | 0.679793i | 0.864360 | + | 0.502874i | \(0.167724\pi\) |
−0.984225 | + | 0.176919i | \(0.943387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 195974. | + | 34555.5i | 0.504919 | + | 0.0890309i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 321459. | + | 117001.i | 0.822935 | + | 0.299524i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −81084.6 | − | 46814.2i | −0.204945 | − | 0.118325i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −129586. | − | 224449.i | −0.325461 | − | 0.563715i | 0.656145 | − | 0.754635i | \(-0.272186\pi\) |
−0.981606 | + | 0.190921i | \(0.938853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 208447. | − | 36754.8i | 0.516949 | − | 0.0911520i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21405.9 | − | 17961.7i | −0.0527539 | − | 0.0442657i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 247047. | + | 678755.i | 0.601261 | + | 1.65195i | 0.748723 | + | 0.662882i | \(0.230667\pi\) |
−0.147463 | + | 0.989068i | \(0.547111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −514473. | + | 431694.i | −1.24435 | + | 1.04413i | −0.247174 | + | 0.968971i | \(0.579502\pi\) |
−0.997172 | + | 0.0751588i | \(0.976054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 161609.i | − | 0.386062i | −0.981193 | − | 0.193031i | \(-0.938168\pi\) | ||
0.981193 | − | 0.193031i | \(-0.0618318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −79551.2 | −0.188868 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −474226. | − | 565160.i | −1.11214 | − | 1.32540i | −0.940330 | − | 0.340265i | \(-0.889483\pi\) |
−0.171809 | − | 0.985130i | \(-0.554961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 757175. | − | 275589.i | 1.76487 | − | 0.642361i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −202725. | + | 241599.i | −0.466807 | + | 0.556319i | −0.947162 | − | 0.320755i | \(-0.896063\pi\) |
0.480355 | + | 0.877074i | \(0.340508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50722.9 | + | 287664.i | 0.116092 | + | 0.658388i | 0.986204 | + | 0.165535i | \(0.0529351\pi\) |
−0.870112 | + | 0.492854i | \(0.835954\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −984248. | + | 568256.i | −2.22567 | + | 1.28499i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 223824. | − | 387674.i | 0.503100 | − | 0.871395i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −147743. | + | 405920.i | −0.328142 | + | 0.901562i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9336.70 | + | 52951.1i | −0.0206141 | + | 0.116908i | −0.993378 | − | 0.114888i | \(-0.963349\pi\) |
0.972764 | + | 0.231796i | \(0.0744602\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 336350. | + | 59307.5i | 0.733860 | + | 0.129399i | 0.528075 | − | 0.849198i | \(-0.322914\pi\) |
0.205785 | + | 0.978597i | \(0.434025\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −745572. | − | 271366.i | −1.61715 | − | 0.588594i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 195201. | + | 112699.i | 0.418446 | + | 0.241590i | 0.694412 | − | 0.719577i | \(-0.255664\pi\) |
−0.275966 | + | 0.961167i | \(0.588998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 431360. | + | 747138.i | 0.919304 | + | 1.59228i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −471674. | + | 83168.9i | −0.993583 | + | 0.175195i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35786.7 | + | 30028.6i | 0.0749489 | + | 0.0628896i | 0.679492 | − | 0.733682i | \(-0.262200\pi\) |
−0.604544 | + | 0.796572i | \(0.706644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −262642. | − | 721604.i | −0.543745 | − | 1.49393i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 157519. | − | 132174.i | 0.324240 | − | 0.272070i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 660244.i | 1.34360i | 0.740735 | + | 0.671798i | \(0.234478\pi\) | ||||
−0.740735 | + | 0.671798i | \(0.765522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −755426. | −1.52856 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 145989. | + | 173982.i | 0.292065 | + | 0.348070i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 277434. | − | 100978.i | 0.551910 | − | 0.200879i | −0.0509851 | − | 0.998699i | \(-0.516236\pi\) |
0.602895 | + | 0.797821i | \(0.294014\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48792.1 | + | 58148.2i | −0.0959777 | + | 0.114382i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −218774. | − | 1.24073e6i | −0.427940 | − | 2.42697i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 152320. | − | 87942.1i | 0.294646 | − | 0.170114i | −0.345389 | − | 0.938459i | \(-0.612253\pi\) |
0.640035 | + | 0.768346i | \(0.278920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 97033.9 | − | 168068.i | 0.186661 | − | 0.323306i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 310612. | − | 853399.i | 0.590938 | − | 1.62359i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −104736. | + | 593990.i | −0.198166 | + | 1.12385i | 0.709672 | + | 0.704532i | \(0.248843\pi\) |
−0.907838 | + | 0.419322i | \(0.862268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −247746. | − | 43684.3i | −0.463630 | − | 0.0817505i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −559477. | − | 203633.i | −1.04130 | − | 0.379001i | −0.235925 | − | 0.971771i | \(-0.575812\pi\) |
−0.805372 | + | 0.592770i | \(0.798034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −149570. | − | 86354.0i | −0.275365 | − | 0.158982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −224309. | − | 388515.i | −0.410731 | − | 0.711408i | 0.584238 | − | 0.811582i | \(-0.301393\pi\) |
−0.994970 | + | 0.100174i | \(0.968060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −847422. | + | 149423.i | −1.53505 | + | 0.270670i | −0.876327 | − | 0.481717i | \(-0.840013\pi\) |
−0.658721 | + | 0.752387i | \(0.728902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −288406. | − | 242001.i | −0.519627 | − | 0.436019i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −226242. | − | 621595.i | −0.403283 | − | 1.10801i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 121600. | − | 102035.i | 0.215603 | − | 0.180912i | −0.528590 | − | 0.848878i | \(-0.677279\pi\) |
0.744193 | + | 0.667965i | \(0.232835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.60539e6i | − | 2.81635i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 782504. | 1.36551 | 0.682755 | − | 0.730648i | \(-0.260782\pi\) | ||||
0.682755 | + | 0.730648i | \(0.260782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 388634. | + | 463156.i | 0.671075 | + | 0.799756i | 0.988930 | − | 0.148383i | \(-0.0474068\pi\) |
−0.317855 | + | 0.948139i | \(0.602962\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −927502. | + | 337583.i | −1.59318 | + | 0.579871i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 84446.0 | − | 100639.i | 0.143545 | − | 0.171070i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 138375. | + | 784764.i | 0.233994 | + | 1.32705i | 0.844722 | + | 0.535206i | \(0.179766\pi\) |
−0.610727 | + | 0.791841i | \(0.709123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −816640. | + | 471487.i | −1.36670 | + | 0.789062i | −0.990505 | − | 0.137480i | \(-0.956100\pi\) |
−0.376191 | + | 0.926542i | \(0.622766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −76998.5 | + | 133365.i | −0.128197 | + | 0.222044i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 567433. | − | 1.55901e6i | 0.935060 | − | 2.56906i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 115726. | − | 656316.i | 0.189727 | − | 1.07600i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −394271. | − | 69520.6i | −0.639816 | − | 0.112817i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 563750. | + | 205188.i | 0.910201 | + | 0.331286i | 0.754333 | − | 0.656492i | \(-0.227960\pi\) |
0.155868 | + | 0.987778i | \(0.450183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −418251. | − | 241477.i | −0.668473 | − | 0.385943i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −356689. | − | 617804.i | −0.567209 | − | 0.982436i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −217709. | + | 38387.9i | −0.342736 | + | 0.0604335i | −0.342367 | − | 0.939566i | \(-0.611229\pi\) |
−0.000368865 | 1.00000i | \(0.500117\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −179813. | − | 150881.i | −0.281662 | − | 0.236343i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −74411.6 | − | 204444.i | −0.115401 | − | 0.317061i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 455562. | − | 382262.i | 0.703001 | − | 0.589888i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 990055.i | 1.51273i | 0.654148 | + | 0.756367i | \(0.273027\pi\) | ||||
−0.654148 | + | 0.756367i | \(0.726973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −453692. | −0.689794 | −0.344897 | − | 0.938640i | \(-0.612086\pi\) | ||||
−0.344897 | + | 0.938640i | \(0.612086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 682831. | + | 813766.i | 1.02801 | + | 1.22514i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.90733e6 | + | 694210.i | −2.85747 | + | 1.04003i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 672797. | − | 801809.i | 0.998155 | − | 1.18955i | 0.0163106 | − | 0.999867i | \(-0.494808\pi\) |
0.981844 | − | 0.189688i | \(-0.0607476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 98469.1 | + | 558446.i | 0.145379 | + | 0.824483i | 0.967062 | + | 0.254539i | \(0.0819238\pi\) |
−0.821684 | + | 0.569944i | \(0.806965\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 624640. | − | 360636.i | 0.913312 | − | 0.527301i | 0.0318165 | − | 0.999494i | \(-0.489871\pi\) |
0.881495 | + | 0.472193i | \(0.156537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −149992. | + | 259793.i | −0.218252 | + | 0.378023i | −0.954274 | − | 0.298935i | \(-0.903369\pi\) |
0.736022 | + | 0.676958i | \(0.236702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3239.85 | + | 8901.40i | −0.00466911 | + | 0.0128283i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 207682. | − | 1.17782e6i | 0.297869 | − | 1.68930i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.35688e6 | + | 239255.i | 1.92761 | + | 0.339889i | 0.999476 | − | 0.0323674i | \(-0.0103047\pi\) |
0.928130 | + | 0.372256i | \(0.121416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 940599. | + | 342350.i | 1.32988 | + | 0.484037i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 903257. | + | 521496.i | 1.26502 | + | 0.730361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −151935. | − | 263159.i | −0.211783 | − | 0.366818i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 389281. | − | 68640.7i | 0.537532 | − | 0.0947813i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15257.8 | − | 12802.8i | −0.0209697 | − | 0.0175957i | 0.632243 | − | 0.774771i | \(-0.282135\pi\) |
−0.653212 | + | 0.757175i | \(0.726579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17076.8 | + | 46918.1i | 0.0232512 | + | 0.0638820i | 0.950775 | − | 0.309881i | \(-0.100289\pi\) |
−0.927524 | + | 0.373764i | \(0.878067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −435201. | + | 365177.i | −0.589798 | + | 0.494899i | −0.888148 | − | 0.459557i | \(-0.848008\pi\) |
0.298350 | + | 0.954456i | \(0.403564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 652821.i | − | 0.876542i | −0.898843 | − | 0.438271i | \(-0.855591\pi\) | ||
0.898843 | − | 0.438271i | \(-0.144409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −757491. | −1.01238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84365.1 | − | 100542.i | −0.111718 | − | 0.133140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 268018. | − | 97550.4i | 0.353286 | − | 0.128586i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 77959.5 | − | 92908.5i | 0.101825 | − | 0.121350i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7936.40 | + | 45009.5i | 0.0103187 | + | 0.0585202i | 0.989532 | − | 0.144311i | \(-0.0460967\pi\) |
−0.979214 | + | 0.202832i | \(0.934986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 840898. | − | 485493.i | 1.08341 | − | 0.625505i | 0.151593 | − | 0.988443i | \(-0.451560\pi\) |
0.931813 | + | 0.362938i | \(0.118226\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3610.50 | + | 6253.58i | −0.00463070 | + | 0.00802061i | −0.868331 | − | 0.495984i | \(-0.834807\pi\) |
0.863701 | + | 0.504005i | \(0.168141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10779.2 | + | 29615.6i | −0.0137006 | + | 0.0376420i | −0.946354 | − | 0.323131i | \(-0.895265\pi\) |
0.932654 | + | 0.360773i | \(0.117487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48352.8 | + | 274222.i | −0.0611812 | + | 0.346976i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.86511e6 | − | 328869.i | −2.33884 | − | 0.412401i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −401548. | − | 146152.i | −0.501293 | − | 0.182456i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −250857. | − | 144833.i | −0.310390 | − | 0.179204i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 81181.0 | + | 140610.i | 0.100001 | + | 0.173207i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −916827. | + | 161661.i | −1.11941 | + | 0.197383i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −205539. | − | 172468.i | −0.249850 | − | 0.209649i | 0.509258 | − | 0.860614i | \(-0.329920\pi\) |
−0.759108 | + | 0.650965i | \(0.774365\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −71258.5 | − | 195781.i | −0.0858618 | − | 0.235903i | 0.889330 | − | 0.457267i | \(-0.151172\pi\) |
−0.975191 | + | 0.221363i | \(0.928949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −249148. | + | 209060.i | −0.298893 | + | 0.250801i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.06003e6i | 1.26061i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 700477. | 0.829398 | 0.414699 | − | 0.909959i | \(-0.363887\pi\) | ||||
0.414699 | + | 0.909959i | \(0.363887\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 707447. | + | 843102.i | 0.830406 | + | 0.989639i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 753577. | − | 274280.i | 0.880733 | − | 0.320561i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 260643. | − | 310623.i | 0.302006 | − | 0.359916i | −0.593604 | − | 0.804757i | \(-0.702295\pi\) |
0.895610 | + | 0.444841i | \(0.146740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13271.7 | + | 75267.6i | 0.0153118 | + | 0.0868378i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −369870. | + | 213544.i | −0.423083 | + | 0.244267i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −234491. | + | 406149.i | −0.267083 | + | 0.462601i | −0.968107 | − | 0.250536i | \(-0.919393\pi\) |
0.701024 | + | 0.713137i | \(0.252726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −336340. | + | 924087.i | −0.379839 | + | 1.04360i | 0.591584 | + | 0.806243i | \(0.298503\pi\) |
−0.971423 | + | 0.237355i | \(0.923719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −150748. | + | 854936.i | −0.169523 | + | 0.961414i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −720558. | − | 127054.i | −0.803469 | − | 0.141673i | −0.243192 | − | 0.969978i | \(-0.578194\pi\) |
−0.560277 | + | 0.828305i | \(0.689305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 337629. | + | 122887.i | 0.374893 | + | 0.136450i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −408433. | − | 235809.i | −0.449713 | − | 0.259642i | 0.257996 | − | 0.966146i | \(-0.416938\pi\) |
−0.707709 | + | 0.706504i | \(0.750271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −795609. | − | 1.37804e6i | −0.872354 | − | 1.51096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.11771e6 | + | 197083.i | −1.21532 | + | 0.214295i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −669831. | − | 562055.i | −0.725302 | − | 0.608600i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −563105. | − | 1.54712e6i | −0.604693 | − | 1.66138i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 239642. | − | 201084.i | 0.256278 | − | 0.215042i | −0.505592 | − | 0.862773i | \(-0.668726\pi\) |
0.761870 | + | 0.647730i | \(0.224282\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 299653.i | 0.317819i | 0.987293 | + | 0.158909i | \(0.0507978\pi\) | ||||
−0.987293 | + | 0.158909i | \(0.949202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.01023e6 | 1.06708 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −246865. | − | 294202.i | −0.258625 | − | 0.308217i | 0.621070 | − | 0.783755i | \(-0.286698\pi\) |
−0.879695 | + | 0.475537i | \(0.842254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 566971. | − | 206361.i | 0.591555 | − | 0.215309i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −291778. | + | 347728.i | −0.301957 | + | 0.359859i | −0.895592 | − | 0.444876i | \(-0.853248\pi\) |
0.593635 | + | 0.804734i | \(0.297692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −299102. | − | 1.69629e6i | −0.308281 | − | 1.74835i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 919792. | − | 531042.i | 0.940366 | − | 0.542921i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −931055. | + | 1.61263e6i | −0.948043 | + | 1.64206i | −0.198502 | + | 0.980100i | \(0.563608\pi\) |
−0.749541 | + | 0.661958i | \(0.769726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −219732. | + | 603710.i | −0.221946 | + | 0.609792i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 206276. | − | 1.16985e6i | 0.207519 | − | 1.17690i | −0.685907 | − | 0.727689i | \(-0.740594\pi\) |
0.893426 | − | 0.449210i | \(-0.148295\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.5.k.a.89.2 | 72 | ||
3.2 | odd | 2 | 108.5.k.a.29.10 | ✓ | 72 | ||
27.13 | even | 9 | 108.5.k.a.41.10 | yes | 72 | ||
27.14 | odd | 18 | inner | 324.5.k.a.233.2 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.29.10 | ✓ | 72 | 3.2 | odd | 2 | ||
108.5.k.a.41.10 | yes | 72 | 27.13 | even | 9 | ||
324.5.k.a.89.2 | 72 | 1.1 | even | 1 | trivial | ||
324.5.k.a.233.2 | 72 | 27.14 | odd | 18 | inner |