Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.6 | ||
Character | \(\chi\) | \(=\) | 432.47 |
Dual form | 432.2.be.a.239.6 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) |
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 | ||||||||
\(3\) | 1.72868 | − | 0.107984i | 0.998055 | − | 0.0623444i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.902279 | − | 0.159096i | 0.403511 | − | 0.0711499i | 0.0317906 | − | 0.999495i | \(-0.489879\pi\) |
0.371721 | + | 0.928345i | \(0.378768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30964 | − | 2.75253i | 0.872963 | − | 1.04036i | −0.125869 | − | 0.992047i | \(-0.540172\pi\) |
0.998832 | − | 0.0483102i | \(-0.0153836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.97668 | − | 0.373339i | 0.992226 | − | 0.124446i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.316002 | + | 1.79214i | −0.0952783 | + | 0.540350i | 0.899383 | + | 0.437161i | \(0.144016\pi\) |
−0.994662 | + | 0.103189i | \(0.967095\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.18526 | − | 1.52331i | −1.16078 | − | 0.422491i | −0.311406 | − | 0.950277i | \(-0.600800\pi\) |
−0.849377 | + | 0.527786i | \(0.823022\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54257 | − | 0.372458i | 0.398290 | − | 0.0961682i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.92200 | + | 2.26437i | −0.951226 | + | 0.549190i | −0.893461 | − | 0.449140i | \(-0.851731\pi\) |
−0.0577643 | + | 0.998330i | \(0.518397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.794277 | − | 0.458576i | −0.182220 | − | 0.105205i | 0.406115 | − | 0.913822i | \(-0.366883\pi\) |
−0.588335 | + | 0.808617i | \(0.700216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.69541 | − | 5.00764i | 0.806405 | − | 1.09276i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.68258 | − | 4.76825i | 1.18490 | − | 0.994248i | 0.184965 | − | 0.982745i | \(-0.440783\pi\) |
0.999934 | − | 0.0115034i | \(-0.00366171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.90967 | + | 1.42300i | −0.781934 | + | 0.284601i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10542 | − | 0.966817i | 0.982538 | − | 0.186064i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.02791 | + | 8.31913i | 0.562270 | + | 1.54482i | 0.816301 | + | 0.577627i | \(0.196021\pi\) |
−0.254031 | + | 0.967196i | \(0.581757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84549 | + | 4.58288i | 0.690671 | + | 0.823110i | 0.991437 | − | 0.130588i | \(-0.0416866\pi\) |
−0.300766 | + | 0.953698i | \(0.597242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.352746 | + | 3.13216i | −0.0614052 | + | 0.545239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.64603 | − | 2.85100i | 0.278229 | − | 0.481907i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.15380 | − | 5.46255i | −0.518482 | − | 0.898037i | −0.999769 | − | 0.0214743i | \(-0.993164\pi\) |
0.481287 | − | 0.876563i | \(-0.340169\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.39948 | − | 2.18138i | −1.18487 | − | 0.349300i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.16283 | + | 3.19486i | −0.181604 | + | 0.498953i | −0.996773 | − | 0.0802698i | \(-0.974422\pi\) |
0.815169 | + | 0.579223i | \(0.196644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.919062 | − | 0.162055i | −0.140156 | − | 0.0247132i | 0.103130 | − | 0.994668i | \(-0.467114\pi\) |
−0.243286 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.62640 | − | 0.810434i | 0.391520 | − | 0.120812i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.999632 | − | 0.838791i | −0.145811 | − | 0.122350i | 0.566964 | − | 0.823742i | \(-0.308118\pi\) |
−0.712776 | + | 0.701392i | \(0.752562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.02641 | − | 5.82105i | −0.146630 | − | 0.831579i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.53538 | + | 4.33789i | −0.915136 | + | 0.607426i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.53299i | 0.347934i | 0.984752 | + | 0.173967i | \(0.0556585\pi\) | ||||
−0.984752 | + | 0.173967i | \(0.944341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66728i | 0.224816i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.42257 | − | 0.706963i | −0.188424 | − | 0.0936395i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.13801 | + | 12.1253i | 0.278346 | + | 1.57858i | 0.728130 | + | 0.685439i | \(0.240390\pi\) |
−0.449785 | + | 0.893137i | \(0.648499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.66045 | − | 2.23238i | −0.340636 | − | 0.285827i | 0.456381 | − | 0.889784i | \(-0.349145\pi\) |
−0.797017 | + | 0.603957i | \(0.793590\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.84744 | − | 9.05567i | 0.736709 | − | 1.14091i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.01863 | − | 0.708592i | −0.498449 | − | 0.0878901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.986708 | + | 2.71096i | −0.120546 | + | 0.331196i | −0.985259 | − | 0.171069i | \(-0.945278\pi\) |
0.864713 | + | 0.502266i | \(0.167500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.30847 | − | 8.85641i | 1.12061 | − | 1.06619i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.44194 | − | 7.69367i | −0.527161 | − | 0.913070i | −0.999499 | − | 0.0316527i | \(-0.989923\pi\) |
0.472337 | − | 0.881418i | \(-0.343410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.528554 | + | 0.915482i | −0.0618625 | + | 0.107149i | −0.895298 | − | 0.445468i | \(-0.853037\pi\) |
0.833435 | + | 0.552617i | \(0.186371\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.60491 | + | 2.88210i | −0.762669 | + | 0.332796i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.20306 | + | 5.00901i | 0.478983 | + | 0.570829i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.99634 | − | 10.9798i | −0.449623 | − | 1.23533i | −0.932987 | − | 0.359910i | \(-0.882807\pi\) |
0.483364 | − | 0.875420i | \(-0.339415\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.72124 | − | 2.22262i | 0.969026 | − | 0.246958i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7994 | + | 5.75052i | −1.73421 | + | 0.631201i | −0.998916 | − | 0.0465461i | \(-0.985179\pi\) |
−0.735295 | + | 0.677747i | \(0.762956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.17849 | + | 2.66707i | −0.344755 | + | 0.289284i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.13263 | + | 14.0542i | 0.657487 | + | 1.50676i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1352 | + | 7.58359i | 1.39232 | + | 0.803859i | 0.993572 | − | 0.113200i | \(-0.0361102\pi\) |
0.398752 | + | 0.917059i | \(0.369444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.8594 | + | 8.00174i | −1.45286 | + | 0.838811i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.14251 | + | 7.50709i | 0.740644 | + | 0.778449i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.789617 | − | 0.287397i | −0.0810130 | − | 0.0294863i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.86037 | − | 10.5507i | 0.188892 | − | 1.07126i | −0.731960 | − | 0.681347i | \(-0.761394\pi\) |
0.920852 | − | 0.389912i | \(-0.127495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.271563 | + | 5.45260i | −0.0272931 | + | 0.548007i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.54770 | + | 3.03623i | −0.253506 | + | 0.302116i | −0.877756 | − | 0.479108i | \(-0.840960\pi\) |
0.624250 | + | 0.781225i | \(0.285405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.32334 | − | 0.409667i | 0.228925 | − | 0.0403657i | −0.0580087 | − | 0.998316i | \(-0.518475\pi\) |
0.286934 | + | 0.957950i | \(0.407364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.53759 | − | 5.10622i | 0.247644 | − | 0.498316i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.73225 | −0.747504 | −0.373752 | − | 0.927529i | \(-0.621929\pi\) | ||||
−0.373752 | + | 0.927529i | \(0.621929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.5672 | −1.49107 | −0.745533 | − | 0.666469i | \(-0.767805\pi\) | ||||
−0.745533 | + | 0.666469i | \(0.767805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.04179 | − | 9.10244i | −0.573461 | − | 0.863966i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.66087 | + | 1.70347i | −0.908818 | + | 0.160249i | −0.608467 | − | 0.793579i | \(-0.708215\pi\) |
−0.300352 | + | 0.953829i | \(0.597104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.36866 | − | 5.20636i | 0.407379 | − | 0.485496i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.0269 | − | 2.97189i | −1.20434 | − | 0.274751i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82569 | + | 16.0253i | −0.259031 | + | 1.46904i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.22471 | + | 2.62958i | 0.656792 | + | 0.239053i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.66518 | + | 5.64846i | −0.150144 | + | 0.509305i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.26847 | + | 4.19645i | −0.650112 | + | 0.375342i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7402 | − | 9.66498i | −1.48546 | − | 0.857628i | −0.485593 | − | 0.874185i | \(-0.661396\pi\) |
−0.999863 | + | 0.0165567i | \(0.994730\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.60627 | − | 0.180899i | −0.141424 | − | 0.0159272i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4142 | − | 11.2558i | 1.17200 | − | 0.983427i | 0.172004 | − | 0.985096i | \(-0.444976\pi\) |
0.999999 | + | 0.00166932i | \(0.000531362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09674 | + | 1.12712i | −0.268521 | + | 0.0977338i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.45269 | − | 1.68459i | 0.383227 | − | 0.144986i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.50764 | − | 15.1321i | −0.470549 | − | 1.29282i | −0.917312 | − | 0.398170i | \(-0.869645\pi\) |
0.446762 | − | 0.894653i | \(-0.352577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6052 | + | 12.6388i | 0.899525 | + | 1.07201i | 0.997048 | + | 0.0767785i | \(0.0244634\pi\) |
−0.0975235 | + | 0.995233i | \(0.531092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.81862 | − | 1.34206i | −0.153156 | − | 0.113022i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.05254 | − | 7.01921i | 0.338890 | − | 0.586975i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.05556 | + | 7.02444i | 0.336796 | + | 0.583348i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.40291 | − | 9.95191i | −0.198189 | − | 0.820820i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.32731 | + | 6.39423i | −0.190661 | + | 0.523836i | −0.997783 | − | 0.0665481i | \(-0.978801\pi\) |
0.807123 | + | 0.590384i | \(0.201024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6770 | + | 2.58795i | 1.19440 | + | 0.210604i | 0.735275 | − | 0.677769i | \(-0.237053\pi\) |
0.459121 | + | 0.888374i | \(0.348164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.8292 | + | 8.20454i | −0.875487 | + | 0.663298i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.19882 | + | 3.52323i | 0.337258 | + | 0.282993i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.99263 | + | 11.3007i | 0.159029 | + | 0.901897i | 0.955009 | + | 0.296575i | \(0.0958446\pi\) |
−0.795981 | + | 0.605322i | \(0.793044\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.273522 | + | 4.37874i | 0.0216917 | + | 0.347257i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 26.6544i | − | 2.10066i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.48604i | 0.273047i | 0.990637 | + | 0.136524i | \(0.0435930\pi\) | ||||
−0.990637 | + | 0.136524i | \(0.956407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.180039 | + | 2.88220i | 0.0140160 | + | 0.224379i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.759638 | + | 4.30812i | 0.0587826 | + | 0.333372i | 0.999990 | − | 0.00445650i | \(-0.00141855\pi\) |
−0.941208 | + | 0.337829i | \(0.890307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.23738 | + | 4.39469i | 0.402876 | + | 0.338053i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.53551 | − | 1.06850i | −0.193895 | − | 0.0817102i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3347 | + | 1.82229i | 0.785732 | + | 0.138546i | 0.552098 | − | 0.833779i | \(-0.313827\pi\) |
0.233634 | + | 0.972325i | \(0.424938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.11309 | + | 14.0481i | −0.386513 | + | 1.06194i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00527 | + | 20.7299i | 0.376219 | + | 1.55815i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6163 | − | 21.8521i | −0.942988 | − | 1.63330i | −0.759731 | − | 0.650238i | \(-0.774669\pi\) |
−0.183257 | − | 0.983065i | \(-0.558664\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.92076 | − | 3.32686i | 0.142769 | − | 0.247283i | −0.785769 | − | 0.618520i | \(-0.787733\pi\) |
0.928538 | + | 0.371236i | \(0.121066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.84013 | − | 3.57179i | −0.357793 | − | 0.264034i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.71468 | − | 4.42698i | −0.273109 | − | 0.325478i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.81870 | − | 7.74432i | −0.206124 | − | 0.566321i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.13050 | − | 16.2858i | 0.664146 | − | 1.18462i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.28905 | − | 3.38094i | 0.672132 | − | 0.244636i | 0.0166663 | − | 0.999861i | \(-0.494695\pi\) |
0.655465 | + | 0.755225i | \(0.272472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.95376 | − | 6.67400i | 0.572524 | − | 0.480405i | −0.309958 | − | 0.950750i | \(-0.600315\pi\) |
0.882482 | + | 0.470345i | \(0.155871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.02344 | − | 0.790984i | −0.502959 | − | 0.0566436i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0769 | + | 6.39528i | 0.789200 | + | 0.455645i | 0.839681 | − | 0.543080i | \(-0.182742\pi\) |
−0.0504809 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.79765 | + | 3.92463i | −0.481873 | + | 0.278209i | −0.721197 | − | 0.692730i | \(-0.756408\pi\) |
0.239324 | + | 0.970940i | \(0.423074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.41296 | + | 4.79293i | −0.0996628 | + | 0.338067i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.8920 | + | 10.8798i | 2.09801 | + | 0.763613i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.540911 | + | 3.06766i | −0.0377788 | + | 0.214254i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.1350 | − | 16.3151i | 1.05196 | − | 1.13398i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.07283 | − | 1.27854i | 0.0742089 | − | 0.0884387i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.3624 | − | 5.00106i | 1.95255 | − | 0.344287i | 0.953467 | − | 0.301497i | \(-0.0974862\pi\) |
0.999084 | − | 0.0427907i | \(-0.0136249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.50949 | − | 12.8202i | −0.583061 | − | 0.878429i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.855033 | −0.0583127 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.4962 | 1.45926 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.814844 | + | 1.63965i | −0.0550620 | + | 0.110797i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8640 | − | 3.50255i | 1.33620 | − | 0.235607i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0617 | − | 17.9499i | 1.00861 | − | 1.20201i | 0.0293149 | − | 0.999570i | \(-0.490667\pi\) |
0.979294 | − | 0.202443i | \(-0.0648881\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.1066 | + | 5.69545i | −0.740438 | + | 0.379697i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.871006 | + | 4.93972i | −0.0578107 | + | 0.327861i | −0.999973 | − | 0.00729519i | \(-0.997678\pi\) |
0.942163 | + | 0.335156i | \(0.108789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.01670 | − | 3.28181i | −0.595840 | − | 0.216868i | 0.0264559 | − | 0.999650i | \(-0.491578\pi\) |
−0.622296 | + | 0.782782i | \(0.713800\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.80664 | + | 8.20512i | 0.513639 | + | 0.539857i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7009 | + | 10.7969i | −1.22513 | + | 0.707332i | −0.966008 | − | 0.258512i | \(-0.916768\pi\) |
−0.259126 | + | 0.965843i | \(0.583435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.03540 | − | 0.597786i | −0.0675417 | − | 0.0389952i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.09404 | − | 18.5491i | −0.525764 | − | 1.20490i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.27842 | + | 6.94642i | −0.535486 | + | 0.449326i | −0.869991 | − | 0.493068i | \(-0.835875\pi\) |
0.334505 | + | 0.942394i | \(0.391431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1965 | − | 4.43917i | 0.785646 | − | 0.285952i | 0.0821214 | − | 0.996622i | \(-0.473830\pi\) |
0.703525 | + | 0.710670i | \(0.251608\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8362 | − | 4.78395i | 0.951745 | − | 0.306891i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.85221 | − | 5.08891i | −0.118334 | − | 0.325119i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.62571 | + | 3.12919i | 0.167070 | + | 0.199106i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.6912 | + | 11.6469i | −1.69149 | + | 0.738092i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.36454 | − | 16.2199i | 0.591085 | − | 1.02379i | −0.403002 | − | 0.915199i | \(-0.632033\pi\) |
0.994087 | − | 0.108590i | \(-0.0346335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.74965 | + | 11.6907i | 0.424347 | + | 0.734991i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.20659 | + | 4.95374i | −0.326050 | + | 0.310215i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.97322 | − | 27.4012i | 0.622113 | − | 1.70924i | −0.0796439 | − | 0.996823i | \(-0.525378\pi\) |
0.701756 | − | 0.712417i | \(-0.252399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3200 | − | 3.93561i | −1.38689 | − | 0.244547i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.1190 | + | 23.6329i | 0.750146 | + | 1.46284i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.74060 | − | 5.65604i | −0.415643 | − | 0.348766i | 0.410859 | − | 0.911699i | \(-0.365229\pi\) |
−0.826503 | + | 0.562932i | \(0.809673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.402989 | + | 2.28547i | 0.0247554 | + | 0.140395i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.5254 | + | 11.6912i | 1.43973 | + | 0.715491i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 20.0940i | − | 1.22515i | −0.790412 | − | 0.612575i | \(-0.790134\pi\) | ||
0.790412 | − | 0.612575i | \(-0.209866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.14240i | − | 0.555361i | −0.960673 | − | 0.277681i | \(-0.910434\pi\) | ||
0.960673 | − | 0.277681i | \(-0.0895657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −23.0945 | + | 15.3291i | −1.39774 | + | 0.927757i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.31475 | − | 7.45634i | −0.0792826 | − | 0.449634i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2006 | + | 9.39839i | 0.672977 | + | 0.564694i | 0.913945 | − | 0.405839i | \(-0.133021\pi\) |
−0.240968 | + | 0.970533i | \(0.577465\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1578 | + | 12.2061i | 0.787735 | + | 0.730760i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.33423 | + | 0.764241i | 0.258558 | + | 0.0455908i | 0.301425 | − | 0.953490i | \(-0.402538\pi\) |
−0.0428663 | + | 0.999081i | \(0.513649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.34262 | − | 11.9313i | 0.258142 | − | 0.709239i | −0.741140 | − | 0.671351i | \(-0.765715\pi\) |
0.999282 | − | 0.0378888i | \(-0.0120633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.39603 | − | 0.411552i | −0.0826937 | − | 0.0243782i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.10820 | + | 10.5797i | 0.360556 | + | 0.624501i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.75474 | − | 3.03931i | 0.103220 | − | 0.178783i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.07669 | − | 18.4397i | 0.121737 | − | 1.08095i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6489 | − | 16.2661i | −0.797376 | − | 0.950276i | 0.202201 | − | 0.979344i | \(-0.435190\pi\) |
−0.999577 | + | 0.0290682i | \(0.990746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.85817 | + | 10.6002i | 0.224631 | + | 0.617169i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.119346 | + | 9.45513i | 0.00692517 | + | 0.548642i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.0466 | + | 11.3000i | −1.79547 | + | 0.653498i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.56877 | + | 2.15545i | −0.148061 | + | 0.124238i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.07630 | + | 5.52379i | −0.234177 | + | 0.317333i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.75563 | − | 1.59096i | −0.157787 | − | 0.0910983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.24710 | + | 0.720015i | −0.0711759 | + | 0.0410934i | −0.535166 | − | 0.844747i | \(-0.679751\pi\) |
0.463990 | + | 0.885841i | \(0.346417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.97207 | − | 0.959066i | 0.225963 | − | 0.0545594i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.32511 | + | 3.03009i | 0.472073 | + | 0.171821i | 0.567091 | − | 0.823655i | \(-0.308069\pi\) |
−0.0950180 | + | 0.995476i | \(0.530291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.38779 | + | 30.5557i | −0.304536 | + | 1.72711i | 0.321145 | + | 0.947030i | \(0.395932\pi\) |
−0.625681 | + | 0.780079i | \(0.715179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.83530 | − | 9.10104i | 0.216095 | − | 0.512785i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.05369 | − | 1.25574i | 0.0591813 | − | 0.0705295i | −0.735642 | − | 0.677371i | \(-0.763119\pi\) |
0.794823 | + | 0.606841i | \(0.207564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.8659 | + | 2.79758i | −0.888318 | + | 0.156634i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3666 | + | 0.834957i | −0.746050 | + | 0.0466027i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.15354 | 0.231109 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5307 | 1.02790 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.9107 | + | 1.68100i | −1.48817 | + | 0.0929597i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.61759 | + | 0.814205i | −0.254576 | + | 0.0448886i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.17455 | − | 4.97503i | 0.229454 | − | 0.273452i | −0.639017 | − | 0.769193i | \(-0.720659\pi\) |
0.868471 | + | 0.495740i | \(0.165103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.4272 | − | 15.0828i | −0.626209 | − | 0.826533i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.458983 | + | 2.60302i | −0.0250769 | + | 0.142218i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.8793 | + | 7.23548i | 1.08290 | + | 0.394142i | 0.820985 | − | 0.570950i | \(-0.193425\pi\) |
0.261911 | + | 0.965092i | \(0.415647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5166 | + | 3.98798i | −0.897060 | + | 0.216597i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.42834 | + | 5.44346i | −0.510573 | + | 0.294780i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.38918 | + | 1.95675i | 0.182999 | + | 0.105654i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.98981 | − | 9.47189i | 0.376319 | − | 0.509949i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.60026 | + | 6.37737i | −0.408003 | + | 0.342355i | −0.823577 | − | 0.567204i | \(-0.808025\pi\) |
0.415574 | + | 0.909559i | \(0.363581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6407 | + | 3.87290i | −0.569583 | + | 0.207311i | −0.610726 | − | 0.791842i | \(-0.709122\pi\) |
0.0411427 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.8403 | − | 3.73075i | −1.21912 | − | 0.199133i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.15842 | + | 8.67769i | 0.168106 | + | 0.461867i | 0.994927 | − | 0.100598i | \(-0.0320755\pi\) |
−0.826821 | + | 0.562464i | \(0.809853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.23190 | − | 6.23514i | −0.277680 | − | 0.330927i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.15425 | + | 28.0078i | −0.166941 | + | 1.48233i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.31565 | + | 14.4031i | −0.438883 | + | 0.760168i | −0.997604 | − | 0.0691878i | \(-0.977959\pi\) |
0.558720 | + | 0.829356i | \(0.311293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.07942 | − | 15.7260i | −0.477864 | − | 0.827685i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.7732 | + | 3.76556i | 0.670418 | + | 0.197640i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.331253 | + | 0.910110i | −0.0173386 | + | 0.0476374i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0549 | + | 2.65459i | 0.785860 | + | 0.138568i | 0.552158 | − | 0.833740i | \(-0.313805\pi\) |
0.233703 | + | 0.972308i | \(0.424916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.26862 | + | 9.94420i | −0.118100 | + | 0.517675i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.97213 | + | 5.85032i | 0.361975 | + | 0.303733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.27227 | − | 18.5580i | −0.169432 | − | 0.960896i | −0.944376 | − | 0.328866i | \(-0.893333\pi\) |
0.774945 | − | 0.632029i | \(-0.217778\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1117 | + | 8.03920i | −0.625446 | + | 0.415143i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 39.4302i | − | 2.03076i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.7620i | 1.42604i | 0.701144 | + | 0.713019i | \(0.252673\pi\) | ||||
−0.701144 | + | 0.713019i | \(0.747327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.9822 | − | 14.9000i | −1.53603 | − | 0.763350i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.46348 | − | 30.9849i | −0.279171 | − | 1.58325i | −0.725394 | − | 0.688333i | \(-0.758343\pi\) |
0.446224 | − | 0.894921i | \(-0.352769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.58924 | + | 3.85083i | 0.233889 | + | 0.196256i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.79626 | − | 0.139265i | −0.142142 | − | 0.00707926i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.58341 | − | 1.68981i | −0.485898 | − | 0.0856769i | −0.0746678 | − | 0.997208i | \(-0.523790\pi\) |
−0.411230 | + | 0.911532i | \(0.634901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4900 | + | 31.5685i | −0.581075 | + | 1.59649i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.9734 | − | 20.9063i | 1.10841 | − | 1.05458i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.35266 | − | 9.27108i | −0.269322 | − | 0.466479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.72266 | + | 15.1081i | −0.437778 | + | 0.758253i | −0.997518 | − | 0.0704151i | \(-0.977568\pi\) |
0.559740 | + | 0.828668i | \(0.310901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.23156 | + | 2.28283i | −0.261906 | + | 0.114284i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.59597 | + | 7.86077i | 0.329387 | + | 0.392548i | 0.905167 | − | 0.425057i | \(-0.139746\pi\) |
−0.575780 | + | 0.817605i | \(0.695301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.11325 | − | 25.0385i | −0.453963 | − | 1.24725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.51537 | − | 3.39294i | 0.373442 | − | 0.168596i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7863 | − | 3.92587i | 0.534655 | − | 0.194598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.65802 | + | 4.74764i | −0.279771 | + | 0.234756i | −0.771865 | − | 0.635786i | \(-0.780676\pi\) |
0.492094 | + | 0.870542i | \(0.336232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.1550 | − | 25.5639i | −0.550234 | − | 1.26097i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.3132 | + | 22.1201i | 1.88527 | + | 1.08846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3406 | + | 7.70219i | −0.654864 | + | 0.378086i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.6979 | + | 20.7033i | 0.964609 | + | 1.01385i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7103 | + | 5.71807i | 0.767496 | + | 0.279346i | 0.695949 | − | 0.718091i | \(-0.254984\pi\) |
0.0715474 | + | 0.997437i | \(0.477206\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.99066 | − | 11.2896i | 0.0970187 | − | 0.550221i | −0.897091 | − | 0.441845i | \(-0.854324\pi\) |
0.994110 | − | 0.108375i | \(-0.0345648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.28874 | − | 2.12361i | −0.159904 | − | 0.103253i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1115 | − | 14.4340i | 0.587495 | − | 0.700150i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2894 | + | 2.16695i | −0.594725 | + | 0.104866i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.24759 | − | 12.5716i | 0.301637 | − | 0.606961i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.5555 | −0.797449 | −0.398724 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398724 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.88427 | −0.234723 | −0.117361 | − | 0.993089i | \(-0.537444\pi\) | ||||
−0.117361 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.76930 | + | 11.7051i | 0.372509 | + | 0.561216i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.70014 | + | 1.18142i | −0.320511 | + | 0.0565148i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5417 | + | 23.2889i | −0.932677 | + | 1.11152i | 0.0608757 | + | 0.998145i | \(0.480611\pi\) |
−0.993552 | + | 0.113375i | \(0.963834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.22851 | − | 16.9442i | −0.248977 | − | 0.806867i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.340783 | − | 1.93268i | 0.0161911 | − | 0.0918243i | −0.975641 | − | 0.219372i | \(-0.929599\pi\) |
0.991832 | + | 0.127547i | \(0.0407104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0581 | + | 4.75276i | 0.619013 | + | 0.225302i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.33270 | + | 11.3049i | −0.157631 | + | 0.534703i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2445 | + | 14.5749i | −1.19136 | + | 0.687834i | −0.958616 | − | 0.284704i | \(-0.908105\pi\) |
−0.232747 | + | 0.972537i | \(0.574771\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.35817 | − | 3.09354i | −0.252307 | − | 0.145669i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.6513 | + | 2.88886i | 1.20520 | + | 0.135731i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.2320 | + | 9.42478i | −0.526565 | + | 0.441841i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2232 | − | 10.2724i | 1.32023 | − | 0.480523i | 0.416695 | − | 0.909046i | \(-0.363188\pi\) |
0.903531 | + | 0.428523i | \(0.140966\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.8342 | + | 15.3524i | −0.832431 | + | 0.716589i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.669179 | − | 1.83856i | −0.0311668 | − | 0.0856301i | 0.923133 | − | 0.384480i | \(-0.125619\pi\) |
−0.954300 | + | 0.298850i | \(0.903397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0605 | + | 15.5649i | 0.606974 | + | 0.723363i | 0.978772 | − | 0.204950i | \(-0.0657033\pi\) |
−0.371799 | + | 0.928313i | \(0.621259\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.63888 | + | 5.63714i | 0.354245 | + | 0.261416i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.632284 | + | 1.09515i | −0.0292586 | + | 0.0506774i | −0.880284 | − | 0.474447i | \(-0.842648\pi\) |
0.851025 | + | 0.525125i | \(0.175981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.18304 | + | 8.97729i | 0.239330 | + | 0.414533i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.66491 | + | 19.3202i | 0.214948 | + | 0.890228i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.580852 | − | 1.59588i | 0.0267076 | − | 0.0733785i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.75791 | + | 0.662622i | 0.172425 | + | 0.0304032i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.945665 | + | 7.53991i | 0.0432990 | + | 0.345229i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.46294 | − | 4.58395i | −0.249608 | − | 0.209446i | 0.509395 | − | 0.860533i | \(-0.329869\pi\) |
−0.759004 | + | 0.651086i | \(0.774314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.87834 | + | 27.6664i | 0.222433 | + | 1.26148i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.87824 | − | 46.0770i | −0.130964 | − | 2.09657i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 9.81563i | − | 0.445705i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.3831i | − | 1.60336i | −0.597752 | − | 0.801681i | \(-0.703939\pi\) | ||
0.597752 | − | 0.801681i | \(-0.296061\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.376435 | + | 6.02625i | 0.0170230 | + | 0.272516i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.202915 | + | 1.15079i | 0.00915741 | + | 0.0519343i | 0.989044 | − | 0.147621i | \(-0.0471615\pi\) |
−0.979887 | + | 0.199555i | \(0.936050\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.7131 | − | 25.7713i | −1.38325 | − | 1.16068i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.622462 | + | 4.96297i | 0.0279776 | + | 0.223069i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.4363 | − | 5.54307i | −1.41011 | − | 0.248641i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.12958 | − | 25.0833i | 0.408696 | − | 1.12288i | −0.549180 | − | 0.835704i | \(-0.685060\pi\) |
0.957877 | − | 0.287180i | \(-0.0927178\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.77838 | + | 7.36534i | 0.0794521 | + | 0.329059i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.9257 | + | 20.6560i | 0.531742 | + | 0.921005i | 0.999313 | + | 0.0370494i | \(0.0117959\pi\) |
−0.467571 | + | 0.883956i | \(0.654871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.81568 | + | 3.14486i | −0.0807969 | + | 0.139944i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.52832 | + | 7.03146i | 0.423168 | + | 0.312278i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0480 | + | 15.5500i | 0.578343 | + | 0.689242i | 0.973321 | − | 0.229449i | \(-0.0736923\pi\) |
−0.394978 | + | 0.918691i | \(0.629248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.29912 | + | 3.56929i | 0.0574695 | + | 0.157896i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.49847 | − | 1.57330i | −0.198612 | − | 0.0694629i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.03112 | − | 0.739267i | 0.0895018 | − | 0.0325760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.81912 | − | 1.52642i | 0.0800046 | − | 0.0671319i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0622 | + | 2.03417i | 0.792841 | + | 0.0892902i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4047 | + | 16.3995i | 1.24443 | + | 0.718474i | 0.969993 | − | 0.243131i | \(-0.0781745\pi\) |
0.274439 | + | 0.961604i | \(0.411508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.4619 | − | 17.5872i | 1.33201 | − | 0.769034i | 0.346399 | − | 0.938087i | \(-0.387404\pi\) |
0.985607 | + | 0.169053i | \(0.0540711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.32193 | + | 24.8368i | −0.319555 | + | 1.08397i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4594 | − | 9.26646i | −1.10903 | − | 0.403653i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.56158 | − | 31.5413i | 0.241808 | − | 1.37136i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8910 | + | 35.2948i | 0.472630 | + | 1.53167i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.73354 | − | 11.6000i | 0.421606 | − | 0.502451i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.97664 | + | 1.23017i | −0.301626 | + | 0.0531849i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.1693 | − | 36.4130i | −1.04298 | − | 1.57134i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.7565 | 0.463315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.1137 | −1.50965 | −0.754827 | − | 0.655924i | \(-0.772279\pi\) | ||||
−0.754827 | + | 0.655924i | \(0.772279\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.96114 | − | 5.95849i | 0.127075 | − | 0.255703i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.0459 | + | 2.47668i | −0.601662 | + | 0.106089i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.15157 | + | 10.9064i | −0.391293 | + | 0.466324i | −0.925345 | − | 0.379127i | \(-0.876224\pi\) |
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.75274 | − | 5.65184i | −0.373558 | − | 0.241214i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.40995 | − | 7.99622i | 0.0600659 | − | 0.340650i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.4524 | − | 14.3595i | −1.67769 | − | 0.610629i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.89954 | − | 7.25172i | −0.292869 | − | 0.307818i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0603 | + | 12.1592i | −0.892352 | + | 0.515200i | −0.874711 | − | 0.484645i | \(-0.838949\pi\) |
−0.0176411 | + | 0.999844i | \(0.505616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.59966 | + | 2.07826i | 0.152249 | + | 0.0879012i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.70890 | − | 13.0831i | −0.241030 | − | 0.552369i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.33375 | + | 4.47555i | −0.224791 | + | 0.188622i | −0.748227 | − | 0.663443i | \(-0.769094\pi\) |
0.523436 | + | 0.852065i | \(0.324650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.44578 | + | 3.07401i | −0.355317 | + | 0.129325i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.0251 | − | 29.1389i | 0.589000 | − | 1.22372i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.42509 | + | 17.6528i | 0.269354 | + | 0.740043i | 0.998451 | + | 0.0556334i | \(0.0177178\pi\) |
−0.729098 | + | 0.684410i | \(0.760060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2113 | − | 20.5116i | −0.720269 | − | 0.858383i | 0.274388 | − | 0.961619i | \(-0.411525\pi\) |
−0.994657 | + | 0.103236i | \(0.967080\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6927 | − | 6.84763i | 0.655573 | − | 0.286064i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.4318 | + | 26.7286i | −0.643549 | + | 1.11466i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.84104 | − | 8.38493i | −0.201535 | − | 0.349069i | 0.747488 | − | 0.664275i | \(-0.231260\pi\) |
−0.949023 | + | 0.315206i | \(0.897926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.0288 | − | 12.3961i | 0.541460 | − | 0.515164i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.6626 | + | 56.7699i | −0.857228 | + | 2.35521i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.53948 | − | 0.800433i | −0.188006 | − | 0.0331505i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.2267 | − | 0.608942i | −0.505512 | − | 0.0251767i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.78871 | − | 5.69641i | −0.280200 | − | 0.235116i | 0.491846 | − | 0.870682i | \(-0.336322\pi\) |
−0.772046 | + | 0.635566i | \(0.780767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.952788 | − | 5.40353i | −0.0392589 | − | 0.222648i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.8391 | + | 9.85927i | 0.816072 | + | 0.405556i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.46963i | 0.265676i | 0.991138 | + | 0.132838i | \(0.0424090\pi\) | ||||
−0.991138 | + | 0.132838i | \(0.957591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9088i | 0.611203i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.3272 | + | 7.51846i | −0.463590 | + | 0.307710i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.995333 | + | 5.64481i | 0.0406682 | + | 0.230641i | 0.998367 | − | 0.0571331i | \(-0.0181959\pi\) |
−0.957698 | + | 0.287774i | \(0.907085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9437 | − | 11.7002i | −0.568777 | − | 0.477260i | 0.312463 | − | 0.949930i | \(-0.398846\pi\) |
−0.881240 | + | 0.472670i | \(0.843290\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.92501 | + | 8.43803i | −0.0783923 | + | 0.343623i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.93706 | + | 1.22319i | 0.282032 | + | 0.0497298i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4668 | − | 34.2523i | 0.506012 | − | 1.39026i | −0.379307 | − | 0.925271i | \(-0.623837\pi\) |
0.885318 | − | 0.464985i | \(-0.153940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 52.8486 | + | 15.5799i | 2.14153 | + | 0.631328i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.90599 | + | 5.03331i | 0.117564 | + | 0.203626i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.95224 | − | 17.2378i | 0.401967 | − | 0.696228i | −0.591996 | − | 0.805941i | \(-0.701660\pi\) |
0.993963 | + | 0.109713i | \(0.0349932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.603805 | + | 5.36141i | −0.0243478 | + | 0.216193i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3239 | + | 12.3036i | 0.415625 | + | 0.495323i | 0.932718 | − | 0.360607i | \(-0.117430\pi\) |
−0.517093 | + | 0.855929i | \(0.672986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8156 | + | 32.4631i | 0.474909 | + | 1.30480i | 0.913764 | + | 0.406245i | \(0.133162\pi\) |
−0.438855 | + | 0.898558i | \(0.644616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.4019 | − | 29.8379i | 0.979214 | − | 1.19735i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.2115 | − | 18.6395i | 2.05175 | − | 0.746775i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0454 | − | 8.42910i | 0.401816 | − | 0.337164i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.71651 | − | 2.32604i | 0.0685509 | − | 0.0928932i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.7385 | + | 14.2828i | 0.986387 | + | 0.569491i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9199 | − | 15.5422i | 1.07166 | − | 0.618725i | 0.143028 | − | 0.989719i | \(-0.454316\pi\) |
0.928635 | + | 0.370994i | \(0.120983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.4896 | − | 11.7079i | 1.92729 | − | 0.465348i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.6420 | − | 6.05720i | −0.660418 | − | 0.240373i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.57149 | + | 25.9262i | −0.181129 | + | 1.02723i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.0946 | − | 21.2432i | −0.636692 | − | 0.840369i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.7440 | + | 28.2970i | −0.937831 | + | 1.11766i | 0.0550422 | + | 0.998484i | \(0.482471\pi\) |
−0.992873 | + | 0.119179i | \(0.961974\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.700721 | − | 0.123556i | 0.0276337 | − | 0.00487257i | −0.159814 | − | 0.987147i | \(-0.551090\pi\) |
0.187448 | + | 0.982275i | \(0.439978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.47808 | + | 0.0923296i | −0.0581993 | + | 0.00363547i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.2439 | 1.30695 | 0.653476 | − | 0.756947i | \(-0.273310\pi\) | ||||
0.653476 | + | 0.756947i | \(0.273310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.4058 | −0.879504 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.1601 | − | 2.32124i | 1.45642 | − | 0.0909766i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.33170 | − | 0.940122i | 0.208645 | − | 0.0367898i | −0.0683484 | − | 0.997662i | \(-0.521773\pi\) |
0.276994 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3126 | − | 12.2900i | 0.402945 | − | 0.480212i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.23155 | + | 2.92242i | −0.0480473 | + | 0.114015i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.94718 | − | 22.3856i | 0.153760 | − | 0.872017i | −0.806150 | − | 0.591711i | \(-0.798453\pi\) |
0.959911 | − | 0.280307i | \(-0.0904361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00411 | + | 0.365468i | 0.0390555 | + | 0.0142150i | 0.361474 | − | 0.932382i | \(-0.382274\pi\) |
−0.322419 | + | 0.946597i | \(0.604496\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.9603 | − | 8.19978i | 1.31891 | − | 0.318453i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.61480 | + | 1.50966i | −0.101398 | + | 0.0585419i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56.8740 | + | 32.8362i | 2.20217 | + | 1.27142i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0987 | − | 32.6561i | 0.931708 | − | 1.26256i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.84145 | − | 4.06246i | 0.186902 | − | 0.156829i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4390 | + | 5.98331i | −0.633677 | + | 0.230640i | −0.638831 | − | 0.769347i | \(-0.720582\pi\) |
0.00515388 | + | 0.999987i | \(0.498359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.5847 | + | 11.0450i | −0.715325 | + | 0.425120i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.164509 | − | 0.451985i | −0.00632259 | − | 0.0173712i | 0.936491 | − | 0.350691i | \(-0.114053\pi\) |
−0.942814 | + | 0.333320i | \(0.891831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.7442 | − | 29.4890i | −0.949597 | − | 1.13169i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.972282 | + | 8.63325i | −0.0372579 | + | 0.330827i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.5853 | − | 35.6548i | 0.787675 | − | 1.36429i | −0.139713 | − | 0.990192i | \(-0.544618\pi\) |
0.927388 | − | 0.374101i | \(-0.122049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.37688 | − | 12.7771i | −0.281856 | − | 0.488189i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9414 | − | 4.69955i | −0.608202 | − | 0.179299i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.85854 | − | 10.6013i | 0.146999 | − | 0.403876i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.6791 | − | 1.88301i | −0.406251 | − | 0.0716330i | −0.0332112 | − | 0.999448i | \(-0.510573\pi\) |
−0.373040 | + | 0.927815i | \(0.621685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.3812 | + | 13.3410i | 0.546297 | + | 0.506784i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.5797 | + | 9.71650i | 0.439242 | + | 0.368568i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.67371 | − | 15.1633i | −0.101274 | − | 0.574353i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.1619 | + | 20.6839i | −1.17865 | + | 0.782336i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.1415i | − | 0.987349i | −0.869647 | − | 0.493675i | \(-0.835653\pi\) | ||
0.869647 | − | 0.493675i | \(-0.164347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.78503i | 0.218187i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.85442 | − | 0.921575i | −0.0698415 | − | 0.0347085i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.47303 | + | 14.0252i | 0.0930077 | + | 0.527473i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19849 | + | 1.00565i | 0.0450101 | + | 0.0377680i | 0.665015 | − | 0.746830i | \(-0.268425\pi\) |
−0.620005 | + | 0.784598i | \(0.712869\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.9950 | − | 31.1915i | −0.599860 | − | 1.16977i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.7046 | + | 7.70630i | 1.63675 | + | 0.288603i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.53979 | − | 6.97802i | 0.0949828 | − | 0.260963i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.5606 | + | 12.9021i | −0.506432 | + | 0.481837i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.4301 | + | 24.9937i | 0.538153 | + | 0.932109i | 0.999004 | + | 0.0446310i | \(0.0142112\pi\) |
−0.460850 | + | 0.887478i | \(0.652455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.23846 | − | 7.34123i | 0.157848 | − | 0.273402i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.6045 | − | 8.99093i | 0.766291 | − | 0.334376i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.6763 | − | 28.2163i | −0.879315 | − | 1.04793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.9968 | + | 38.4560i | 0.519114 | + | 1.42625i | 0.871499 | + | 0.490398i | \(0.163149\pi\) |
−0.352385 | + | 0.935855i | \(0.614629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.1305 | − | 9.87200i | 0.930760 | − | 0.365630i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.97152 | − | 1.44552i | 0.146892 | − | 0.0534643i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.89373 | − | 1.58903i | 0.0699466 | − | 0.0586922i | −0.607144 | − | 0.794592i | \(-0.707685\pi\) |
0.677091 | + | 0.735900i | \(0.263240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.75141 | − | 8.59710i | −0.138373 | − | 0.317109i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.54661 | − | 2.62499i | −0.167477 | − | 0.0966926i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.69724 | + | 5.59870i | −0.356719 | + | 0.205952i | −0.667640 | − | 0.744484i | \(-0.732696\pi\) |
0.310922 | + | 0.950436i | \(0.399362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.87691 | + | 5.12585i | 0.179158 | + | 0.188303i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.9122 | − | 15.2548i | −1.53761 | − | 0.559645i | −0.572140 | − | 0.820156i | \(-0.693887\pi\) |
−0.965471 | + | 0.260511i | \(0.916109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.08258 | + | 6.13964i | −0.0396628 | + | 0.224939i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.8829 | + | 23.0160i | −1.64218 | + | 0.842111i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8587 | + | 21.2832i | −0.652544 | + | 0.777671i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5655 | + | 2.03931i | −0.422032 | + | 0.0744156i | −0.380631 | − | 0.924727i | \(-0.624293\pi\) |
−0.0414009 | + | 0.999143i | \(0.513182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.4368 | − | 29.0502i | 0.526107 | − | 1.05865i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6545 | 0.496937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.35502 | 0.194632 | 0.0973158 | − | 0.995254i | \(-0.468974\pi\) | ||||
0.0973158 | + | 0.995254i | \(0.468974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.9304 | + | 19.4807i | 0.469344 | + | 0.707105i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3535 | − | 2.35458i | 0.484064 | − | 0.0853536i | 0.0737099 | − | 0.997280i | \(-0.476516\pi\) |
0.410354 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.9547 | + | 42.8491i | −1.30165 | + | 1.55124i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.46562 | + | 9.12566i | −0.306075 | + | 0.329939i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.52242 | − | 54.0043i | 0.343835 | − | 1.94998i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2757 | − | 5.92388i | −0.586917 | − | 0.213620i | 0.0314556 | − | 0.999505i | \(-0.489986\pi\) |
−0.618373 | + | 0.785885i | \(0.712208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2816 | − | 48.4449i | 0.514341 | − | 1.74470i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.8577 | + | 25.3213i | −1.57745 | + | 0.910743i | −0.582239 | + | 0.813018i | \(0.697823\pi\) |
−0.995213 | + | 0.0977249i | \(0.968843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.5561 | − | 12.4454i | −0.774316 | − | 0.447052i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.0091 | − | 4.39323i | −1.39944 | − | 0.157606i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.38870 | − | 2.00436i | 0.0855840 | − | 0.0718135i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1918 | − | 5.52936i | 0.543605 | − | 0.197856i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.5018 | + | 39.5452i | 0.839887 | + | 1.41323i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.59581 | + | 9.87940i | 0.128340 | + | 0.352611i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.42817 | + | 4.08553i | 0.122201 | + | 0.145634i | 0.823676 | − | 0.567060i | \(-0.191919\pi\) |
−0.701475 | + | 0.712694i | \(0.747475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.2631 | − | 9.04961i | −0.436579 | − | 0.322175i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6243 | + | 30.5262i | −0.626649 | + | 1.08539i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.73407 | + | 13.3958i | 0.274645 | + | 0.475699i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.943434 | + | 3.90733i | 0.0334601 | + | 0.138579i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.46871 | − | 20.5201i | 0.264555 | − | 0.726860i | −0.734291 | − | 0.678835i | \(-0.762485\pi\) |
0.998846 | − | 0.0480248i | \(-0.0152927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.81990 | + | 1.02620i | 0.205893 | + | 0.0363045i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.9304 | + | 17.6700i | 1.48154 | + | 0.624340i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.47365 | − | 1.23654i | −0.0520038 | − | 0.0436364i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.24061 | − | 24.0497i | −0.149462 | − | 0.847640i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.16982 | − | 34.7361i | −0.0763813 | − | 1.22277i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.0378i | 1.23186i | 0.787799 | + | 0.615932i | \(0.211221\pi\) | ||||
−0.787799 | + | 0.615932i | \(0.788779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.1844i | − | 0.954573i | −0.878748 | − | 0.477287i | \(-0.841620\pi\) | ||
0.878748 | − | 0.477287i | \(-0.158380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.987230 | − | 15.8043i | −0.0346237 | − | 0.554281i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.554615 | + | 3.14538i | 0.0194273 | + | 0.110178i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.655675 | + | 0.550177i | 0.0229392 | + | 0.0192483i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.2677 | + | 28.9929i | −1.33718 | + | 1.01309i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.62706 | − | 1.16853i | −0.231286 | − | 0.0407820i | 0.0568037 | − | 0.998385i | \(-0.481909\pi\) |
−0.288090 | + | 0.957603i | \(0.593020\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0376566 | + | 0.103461i | −0.00131263 | + | 0.00360641i | −0.940347 | − | 0.340216i | \(-0.889500\pi\) |
0.939035 | + | 0.343823i | \(0.111722\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.07795 | − | 12.7477i | −0.107161 | − | 0.443817i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.7113 | + | 18.5526i | 0.372470 | + | 0.645137i | 0.989945 | − | 0.141454i | \(-0.0451777\pi\) |
−0.617475 | + | 0.786590i | \(0.711844\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.92370 | − | 13.7242i | 0.275201 | − | 0.476663i | −0.694985 | − | 0.719025i | \(-0.744589\pi\) |
0.970186 | + | 0.242362i | \(0.0779221\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.3771 | + | 15.0373i | 0.706873 | + | 0.521640i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.2066 | + | 20.5060i | 0.596173 | + | 0.710492i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37081 | + | 3.76627i | 0.0474389 | + | 0.130337i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.0636 | + | 19.6796i | 0.831761 | + | 0.680227i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.96451 | − | 1.80693i | 0.171394 | − | 0.0623822i | −0.254898 | − | 0.966968i | \(-0.582042\pi\) |
0.426292 | + | 0.904586i | \(0.359820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.8243 | + | 31.7384i | −1.30429 | + | 1.09443i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.57502 | + | 0.853104i | 0.260898 | + | 0.0293825i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.42476 | + | 3.13198i | 0.186617 | + | 0.107744i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.9245 | − | 13.8128i | 0.822056 | − | 0.474614i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.21863 | − | 21.0943i | 0.213423 | − | 0.723953i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.9685 | − | 16.0032i | −1.50722 | − | 0.548584i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.220692 | − | 1.25161i | 0.00755634 | − | 0.0428541i | −0.980796 | − | 0.195034i | \(-0.937518\pi\) |
0.988353 | + | 0.152180i | \(0.0486293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.45773 | − | 0.560694i | −0.0840527 | − | 0.0191753i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6352 | + | 18.6333i | −0.534087 | + | 0.636500i | −0.963851 | − | 0.266441i | \(-0.914152\pi\) |
0.429764 | + | 0.902941i | \(0.358597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.06237 | − | 1.24529i | 0.240965 | − | 0.0424887i | −0.0518612 | − | 0.998654i | \(-0.516515\pi\) |
0.292826 | + | 0.956166i | \(0.405404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.7016 | + | 17.6294i | 0.398789 | + | 0.600808i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.1184 | −1.29757 | −0.648783 | − | 0.760973i | \(-0.724722\pi\) | ||||
−0.648783 | + | 0.760973i | \(0.724722\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.61469 | 0.326909 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.70520 | − | 5.44348i | 0.0918734 | − | 0.184870i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.9403 | − | 3.69233i | 0.710350 | − | 0.125254i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.25927 | − | 9.84301i | 0.279855 | − | 0.333518i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.59874 | − | 32.1005i | 0.0541093 | − | 1.08644i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.23673 | + | 29.6990i | −0.177034 | + | 1.00401i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.23247 | − | 1.54049i | −0.142921 | − | 0.0520188i | 0.269569 | − | 0.962981i | \(-0.413119\pi\) |
−0.412490 | + | 0.910962i | \(0.635341\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.3510 | − | 26.6450i | −0.855069 | − | 0.898715i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.5813 | + | 11.8826i | −0.693401 | + | 0.400335i | −0.804885 | − | 0.593431i | \(-0.797773\pi\) |
0.111484 | + | 0.993766i | \(0.464440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.93969 | + | 2.85193i | 0.166234 | + | 0.0959751i | 0.580809 | − | 0.814040i | \(-0.302736\pi\) |
−0.414575 | + | 0.910015i | \(0.636070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.81419 | + | 17.9078i | 0.262671 | + | 0.601964i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.84014 | − | 1.54406i | 0.0617857 | − | 0.0518444i | −0.611372 | − | 0.791343i | \(-0.709382\pi\) |
0.673158 | + | 0.739499i | \(0.264938\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.2671 | + | 23.7553i | −2.18899 | + | 0.796726i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.22731 | + | 16.3320i | 0.0411165 | + | 0.547143i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.409335 | + | 1.12464i | 0.0136979 | + | 0.0376346i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8600 | − | 17.7095i | −0.496716 | − | 0.591963i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −52.4495 | + | 22.8867i | −1.75124 | + | 0.764165i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.4817 | + | 45.8677i | −0.883216 | + | 1.52977i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.73564 | − | 9.93442i | −0.191082 | − | 0.330963i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.20783 | + | 4.00348i | −0.140028 | + | 0.133227i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.20377 | − | 3.30734i | 0.0400147 | − | 0.109940i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.9266 | − | 8.09809i | −1.52497 | − | 0.268893i | −0.652584 | − | 0.757717i | \(-0.726315\pi\) |
−0.872382 | + | 0.488824i | \(0.837426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.45015 | + | 9.98905i | −0.213938 | + | 0.331316i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.6584 | + | 23.2082i | 0.916365 | + | 0.768922i | 0.973319 | − | 0.229455i | \(-0.0736944\pi\) |
−0.0569539 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.31307 | − | 30.1319i | −0.175837 | − | 0.997221i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.93540 | − | 2.45271i | −0.163159 | − | 0.0810840i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 62.9199i | − | 2.07780i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.9024i | − | 0.788468i | −0.919010 | − | 0.394234i | \(-0.871010\pi\) | ||
0.919010 | − | 0.394234i | \(-0.128990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.07809 | + | 1.37934i | −0.0684755 | + | 0.0454509i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.87085 | + | 38.9665i | 0.226157 | + | 1.28260i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.1035 | + | 16.8689i | 0.661000 | + | 0.554645i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.76288 | − | 2.08684i | 0.222122 | − | 0.0685408i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3439 | + | 2.00024i | 0.372181 | + | 0.0656256i | 0.356611 | − | 0.934253i | \(-0.383932\pi\) |
0.0155709 | + | 0.999879i | \(0.495043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.85414 | + | 5.09421i | −0.0607671 | + | 0.166956i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.7187 | + | 4.33909i | 0.481867 | + | 0.142055i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.77535 | − | 6.53909i | −0.123467 | − | 0.213851i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.1278 | + | 29.6661i | −0.559539 | + | 0.969150i | 0.437996 | + | 0.898977i | \(0.355689\pi\) |
−0.997535 | + | 0.0701733i | \(0.977645\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.01426 | + | 53.4028i | −0.196268 | + | 1.74274i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8452 | − | 20.0754i | −0.549139 | − | 0.654439i | 0.418071 | − | 0.908414i | \(-0.362706\pi\) |
−0.967211 | + | 0.253975i | \(0.918262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.62599 | + | 23.6997i | 0.280901 | + | 0.771769i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.64725 | − | 16.1469i | 0.183705 | − | 0.525260i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.77710 | − | 2.83063i | 0.252722 | − | 0.0919832i | −0.212553 | − | 0.977150i | \(-0.568178\pi\) |
0.465275 | + | 0.885166i | \(0.345956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.60670 | − | 3.02638i | 0.117078 | − | 0.0982405i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.68590 | − | 2.28456i | 0.0546690 | − | 0.0740819i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.1053 | + | 14.4946i | 0.813241 | + | 0.469525i | 0.848080 | − | 0.529868i | \(-0.177759\pi\) |
−0.0348391 | + | 0.999393i | \(0.511092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.84341 | − | 4.52840i | 0.253807 | − | 0.146535i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.1249 | + | 6.54938i | −0.876824 | + | 0.211711i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −54.3722 | − | 19.7899i | −1.75577 | − | 0.639048i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.831882 | + | 4.71784i | −0.0268349 | + | 0.152188i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.0164 | + | 2.88675i | −0.741694 | + | 0.0930241i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.11470 | − | 7.28721i | 0.196839 | − | 0.234584i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.9337 | + | 6.68873i | −1.21986 | + | 0.215095i | −0.746267 | − | 0.665646i | \(-0.768156\pi\) |
−0.473597 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.18015 | − | 0.448515i | 0.230660 | − | 0.0144084i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.9077 | −1.18442 | −0.592212 | − | 0.805783i | \(-0.701745\pi\) | ||||
−0.592212 | + | 0.805783i | \(0.701745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 59.2830 | 1.90053 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.0336 | − | 2.00101i | 1.02590 | − | 0.0640836i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.6838 | + | 7.70263i | −1.39757 | + | 0.246429i | −0.821144 | − | 0.570722i | \(-0.806663\pi\) |
−0.576424 | + | 0.817151i | \(0.695552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.7416 | + | 21.1436i | −0.567023 | + | 0.675752i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.3385 | + | 5.81184i | −1.47948 | + | 0.185558i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.09294 | − | 34.5548i | 0.194335 | − | 1.10213i | −0.719028 | − | 0.694981i | \(-0.755413\pi\) |
0.913363 | − | 0.407146i | \(-0.133476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0120 | + | 4.00802i | 0.350870 | + | 0.127706i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.89442 | + | 1.90613i | −0.251282 | + | 0.0606727i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.99536 | + | 3.46142i | −0.190641 | + | 0.110067i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.19698 | − | 3.00048i | −0.165088 | − | 0.0953134i | 0.415180 | − | 0.909739i | \(-0.363719\pi\) |
−0.580267 | + | 0.814426i | \(0.697052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.67924 | − | 9.05103i | 0.211959 | − | 0.287226i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.50898 | + | 4.62258i | −0.174646 | + | 0.146546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.5630 | − | 18.7674i | 1.63302 | − | 0.594369i | 0.647218 | − | 0.762305i | \(-0.275933\pi\) |
0.985798 | + | 0.167936i | \(0.0537103\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.3828 | − | 24.8394i | −0.676520 | − | 0.785885i |
(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 | 432.2.be.a.47.6 | yes | 36 | |
4.3 | odd | 2 | inner | 432.2.be.a.47.1 | ✓ | 36 | |
27.23 | odd | 18 | inner | 432.2.be.a.239.1 | yes | 36 | |
108.23 | even | 18 | inner | 432.2.be.a.239.6 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.a.47.1 | ✓ | 36 | 4.3 | odd | 2 | inner | |
432.2.be.a.47.6 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.a.239.1 | yes | 36 | 27.23 | odd | 18 | inner | |
432.2.be.a.239.6 | yes | 36 | 108.23 | even | 18 | inner |