Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
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([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.472963 + 1.66622i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.97 |
Dual form | 432.2.u.d.49.2 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 | ||||||||
\(3\) | 1.43334 | + | 0.972387i | 0.827539 | + | 0.561408i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.94709 | − | 1.43662i | −1.76519 | − | 0.642478i | −0.765195 | − | 0.643799i | \(-0.777357\pi\) |
−0.999999 | + | 0.00132064i | \(0.999580\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.610312 | + | 3.46125i | −0.230676 | + | 1.30823i | 0.620854 | + | 0.783926i | \(0.286786\pi\) |
−0.851531 | + | 0.524305i | \(0.824325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.10893 | + | 2.78752i | 0.369642 | + | 0.929174i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73646 | + | 0.632019i | −0.523562 | + | 0.190561i | −0.590261 | − | 0.807212i | \(-0.700975\pi\) |
0.0666996 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.78502 | + | 1.49781i | −0.495075 | + | 0.415418i | −0.855841 | − | 0.517239i | \(-0.826960\pi\) |
0.360766 | + | 0.932656i | \(0.382515\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.26057 | − | 5.89728i | −1.10007 | − | 1.52267i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.799928 | − | 1.38552i | −0.194011 | − | 0.336037i | 0.752565 | − | 0.658518i | \(-0.228816\pi\) |
−0.946576 | + | 0.322481i | \(0.895483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.31046 | + | 4.00184i | −0.530056 | + | 0.918085i | 0.469329 | + | 0.883024i | \(0.344496\pi\) |
−0.999385 | + | 0.0350612i | \(0.988837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.24046 | + | 4.36769i | −0.925345 | + | 0.953108i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.308317 | + | 1.74855i | 0.0642885 | + | 0.364598i | 0.999932 | + | 0.0116518i | \(0.00370898\pi\) |
−0.935644 | + | 0.352946i | \(0.885180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.68544 | + | 8.12705i | 1.93709 | + | 1.62541i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.12109 | + | 5.07377i | −0.215753 | + | 0.976448i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.882314 | + | 0.740350i | 0.163842 | + | 0.137479i | 0.721022 | − | 0.692912i | \(-0.243672\pi\) |
−0.557181 | + | 0.830391i | \(0.688117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.322800 | − | 1.83069i | −0.0579766 | − | 0.328802i | 0.942000 | − | 0.335612i | \(-0.108943\pi\) |
−0.999977 | + | 0.00681062i | \(0.997832\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.10350 | − | 0.782612i | −0.540250 | − | 0.136235i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.38148 | − | 12.7851i | 1.24770 | − | 2.16108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.38364 | − | 7.59269i | −0.720666 | − | 1.24823i | −0.960733 | − | 0.277474i | \(-0.910503\pi\) |
0.240067 | − | 0.970756i | \(-0.422830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.01499 | + | 0.411139i | −0.642913 | + | 0.0658349i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.98440 | − | 2.50421i | 0.466085 | − | 0.391092i | −0.379279 | − | 0.925282i | \(-0.623828\pi\) |
0.845364 | + | 0.534191i | \(0.179384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41848 | − | 0.880255i | 0.368815 | − | 0.134238i | −0.150962 | − | 0.988540i | \(-0.548237\pi\) |
0.519777 | + | 0.854302i | \(0.326015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.372408 | − | 12.5957i | −0.0555152 | − | 1.87766i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.29725 | + | 7.35705i | −0.189223 | + | 1.07314i | 0.731186 | + | 0.682178i | \(0.238967\pi\) |
−0.920409 | + | 0.390958i | \(0.872144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.02994 | − | 1.83075i | −0.718563 | − | 0.261535i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.200690 | − | 2.76375i | 0.0281022 | − | 0.387003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.02417 | 1.10220 | 0.551102 | − | 0.834438i | \(-0.314207\pi\) | ||||
0.551102 | + | 0.834438i | \(0.314207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.76194 | 1.04662 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.20302 | + | 3.48933i | −0.954063 | + | 0.462173i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.15006 | + | 0.418589i | 0.149726 | + | 0.0544957i | 0.415796 | − | 0.909458i | \(-0.363503\pi\) |
−0.266070 | + | 0.963954i | \(0.585725\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.754920 | + | 4.28136i | −0.0966575 | + | 0.548172i | 0.897569 | + | 0.440873i | \(0.145331\pi\) |
−0.994227 | + | 0.107299i | \(0.965780\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.3251 | + | 2.13701i | −1.30084 | + | 0.269238i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.19743 | − | 3.34759i | 1.14080 | − | 0.415218i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.86356 | − | 4.08101i | 0.594178 | − | 0.498574i | −0.295390 | − | 0.955377i | \(-0.595450\pi\) |
0.889568 | + | 0.456802i | \(0.151005\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.25835 | + | 2.80607i | −0.151487 | + | 0.337811i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.871328 | − | 1.50918i | −0.103408 | − | 0.179107i | 0.809679 | − | 0.586873i | \(-0.199641\pi\) |
−0.913087 | + | 0.407766i | \(0.866308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.37908 | + | 2.38864i | −0.161409 | + | 0.279569i | −0.935374 | − | 0.353659i | \(-0.884937\pi\) |
0.773965 | + | 0.633228i | \(0.218271\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.97988 | + | 21.0668i | 0.690497 | + | 2.43259i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.12780 | − | 6.39605i | −0.128524 | − | 0.728897i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.63735 | + | 6.40849i | 0.859268 | + | 0.721012i | 0.961810 | − | 0.273717i | \(-0.0882531\pi\) |
−0.102542 | + | 0.994729i | \(0.532698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.54057 | + | 6.18231i | −0.726730 | + | 0.686923i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.65194 | − | 7.25984i | −0.949674 | − | 0.796871i | 0.0295686 | − | 0.999563i | \(-0.490587\pi\) |
−0.979243 | + | 0.202692i | \(0.935031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.16692 | + | 6.61795i | 0.126571 | + | 0.717818i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.544749 | + | 1.91912i | 0.0584033 | + | 0.205752i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.71167 | + | 4.69675i | −0.287436 | + | 0.497854i | −0.973197 | − | 0.229973i | \(-0.926136\pi\) |
0.685761 | + | 0.727827i | \(0.259470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.09488 | − | 7.09254i | −0.429260 | − | 0.743500i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.31746 | − | 2.93789i | 0.136614 | − | 0.304645i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.8688 | − | 12.4764i | 1.52550 | − | 1.28005i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3643 | − | 4.13626i | 1.15387 | − | 0.419974i | 0.306966 | − | 0.951721i | \(-0.400686\pi\) |
0.846903 | + | 0.531747i | \(0.178464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.68737 | − | 4.13955i | −0.370595 | − | 0.416041i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.45951 | + | 13.9486i | −0.244731 | + | 1.38794i | 0.576386 | + | 0.817178i | \(0.304462\pi\) |
−0.821117 | + | 0.570760i | \(0.806649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.41828 | + | 0.516213i | 0.139748 | + | 0.0508640i | 0.410947 | − | 0.911659i | \(-0.365198\pi\) |
−0.271199 | + | 0.962523i | \(0.587420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23.0122 | − | 11.1477i | 2.24576 | − | 1.08791i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4114 | −1.87658 | −0.938288 | − | 0.345856i | \(-0.887589\pi\) | ||||
−0.938288 | + | 0.345856i | \(0.887589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2590 | 1.46155 | 0.730775 | − | 0.682619i | \(-0.239159\pi\) | ||||
0.730775 | + | 0.682619i | \(0.239159\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.09979 | − | 15.1455i | 0.104387 | − | 1.43755i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6990 | + | 3.89411i | 1.00647 | + | 0.366327i | 0.792078 | − | 0.610420i | \(-0.208999\pi\) |
0.214397 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.29506 | − | 7.34463i | 0.120765 | − | 0.684890i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.15463 | − | 3.31483i | −0.568996 | − | 0.306456i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.28382 | − | 1.92315i | 0.484367 | − | 0.176295i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.81065 | + | 4.87572i | −0.528241 | + | 0.443247i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.71272 | − | 0.687389i | 0.605265 | − | 0.0619797i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16.0528 | − | 27.8042i | −1.43581 | − | 2.48689i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.804999 | + | 1.39430i | −0.0714321 | + | 0.123724i | −0.899529 | − | 0.436861i | \(-0.856090\pi\) |
0.828097 | + | 0.560585i | \(0.189424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.32246 | + | 1.09000i | 0.380571 | + | 0.0959688i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.914583 | + | 5.18686i | 0.0799075 | + | 0.453178i | 0.998340 | + | 0.0575995i | \(0.0183446\pi\) |
−0.918432 | + | 0.395578i | \(0.870544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.4413 | − | 10.4395i | −1.07879 | − | 0.905216i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.7141 | − | 18.4161i | 1.00819 | − | 1.58500i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9771 | − | 10.0500i | −1.02328 | − | 0.858630i | −0.0332397 | − | 0.999447i | \(-0.510582\pi\) |
−0.990036 | + | 0.140818i | \(0.955027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.12790 | + | 12.0679i | 0.180486 | + | 1.02359i | 0.931619 | + | 0.363436i | \(0.118397\pi\) |
−0.751133 | + | 0.660151i | \(0.770492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.01330 | + | 9.28373i | −0.759057 | + | 0.781831i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.15297 | − | 3.72905i | 0.180040 | − | 0.311839i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.41897 | − | 4.18978i | −0.200885 | − | 0.347943i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.42942 | − | 7.51513i | −0.447811 | − | 0.619838i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0411 | − | 13.4601i | 1.31414 | − | 1.10269i | 0.326626 | − | 0.945154i | \(-0.394088\pi\) |
0.987513 | − | 0.157540i | \(-0.0503562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.06208 | + | 3.29833i | −0.737462 | + | 0.268414i | −0.683320 | − | 0.730119i | \(-0.739465\pi\) |
−0.0541419 | + | 0.998533i | \(0.517242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.97510 | − | 3.76625i | 0.240522 | − | 0.304483i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.35589 | + | 7.68965i | −0.108908 | + | 0.617647i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0515 | + | 4.02243i | 0.882008 | + | 0.321025i | 0.743020 | − | 0.669269i | \(-0.233393\pi\) |
0.138988 | + | 0.990294i | \(0.455615\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5014 | + | 7.80260i | 0.912117 | + | 0.618787i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.24034 | −0.491808 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3539 | 1.12429 | 0.562143 | − | 0.827040i | \(-0.309977\pi\) | ||||
0.562143 | + | 0.827040i | \(0.309977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1255 | + | 7.54761i | 0.866118 | + | 0.587581i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.95006 | + | 2.89359i | 0.615194 | + | 0.223912i | 0.630774 | − | 0.775966i | \(-0.282737\pi\) |
−0.0155803 | + | 0.999879i | \(0.504960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.31456 | + | 7.45526i | −0.101120 | + | 0.573482i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.7173 | − | 2.00273i | −1.04899 | − | 0.153152i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.5461 | + | 8.57008i | −1.79018 | + | 0.651571i | −0.790965 | + | 0.611861i | \(0.790421\pi\) |
−0.999211 | + | 0.0397102i | \(0.987357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34.0409 | + | 28.5637i | −2.57325 | + | 2.15921i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.24140 | + | 1.71829i | 0.0933095 | + | 0.129154i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.84160 | + | 8.38590i | 0.361878 | + | 0.626792i | 0.988270 | − | 0.152717i | \(-0.0488023\pi\) |
−0.626392 | + | 0.779508i | \(0.715469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.302082 | − | 0.523221i | 0.0224535 | − | 0.0388907i | −0.854580 | − | 0.519319i | \(-0.826186\pi\) |
0.877034 | + | 0.480429i | \(0.159519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.24520 | + | 5.40257i | −0.387736 | + | 0.399370i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.39479 | + | 36.2667i | 0.470155 | + | 2.66638i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.26471 | + | 1.90032i | 0.165612 | + | 0.138965i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.8774 | − | 6.97695i | −1.22765 | − | 0.507498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8632 | + | 13.3108i | 1.14782 | + | 0.963138i | 0.999666 | − | 0.0258260i | \(-0.00822160\pi\) |
0.148157 | + | 0.988964i | \(0.452666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.93360 | − | 10.9660i | −0.139184 | − | 0.789350i | −0.971855 | − | 0.235582i | \(-0.924300\pi\) |
0.832671 | − | 0.553768i | \(-0.186811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.4382 | + | 4.14523i | 1.17716 | + | 0.296846i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.31196 | + | 10.9326i | −0.449709 | + | 0.778918i | −0.998367 | − | 0.0571286i | \(-0.981806\pi\) |
0.548658 | + | 0.836047i | \(0.315139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.5243 | − | 18.2286i | −0.746049 | − | 1.29219i | −0.949703 | − | 0.313152i | \(-0.898615\pi\) |
0.203654 | − | 0.979043i | \(-0.434718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9394 | − | 1.12021i | 0.771609 | − | 0.0790135i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.10102 | + | 2.60207i | −0.217649 | + | 0.182629i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3773 | + | 5.59688i | −1.07400 | + | 0.390903i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.53222 | + | 2.79845i | −0.315011 | + | 0.194506i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.48278 | − | 8.40928i | 0.102566 | − | 0.581682i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.8317 | − | 7.58212i | −1.43411 | − | 0.521975i | −0.496006 | − | 0.868319i | \(-0.665201\pi\) |
−0.938108 | + | 0.346344i | \(0.887423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.218603 | − | 3.01044i | 0.0149784 | − | 0.206272i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8106 | −0.737275 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.53349 | 0.443522 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.29938 | + | 2.08273i | −0.290525 | + | 0.140738i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.50312 | + | 1.27503i | 0.235646 | + | 0.0857680i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.39430 | + | 13.5787i | −0.160334 | + | 0.909299i | 0.793412 | + | 0.608685i | \(0.208303\pi\) |
−0.953746 | + | 0.300614i | \(0.902808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.9139 | + | 36.0107i | −0.794260 | + | 2.40071i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.73632 | + | 3.17976i | −0.579850 | + | 0.211048i | −0.615259 | − | 0.788325i | \(-0.710949\pi\) |
0.0354095 | + | 0.999373i | \(0.488726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.113444 | + | 0.0951912i | −0.00749662 | + | 0.00629041i | −0.646528 | − | 0.762890i | \(-0.723780\pi\) |
0.639032 | + | 0.769180i | \(0.279335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.60292 | − | 10.2644i | 0.302850 | − | 0.675346i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.824403 | + | 1.42791i | 0.0540084 | + | 0.0935454i | 0.891766 | − | 0.452498i | \(-0.149467\pi\) |
−0.837757 | + | 0.546043i | \(0.816134\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6897 | − | 27.1753i | 1.02348 | − | 1.77272i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.71537 | + | 16.6120i | 0.306296 | + | 1.07907i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.11203 | + | 11.9779i | 0.136616 | + | 0.774787i | 0.973721 | + | 0.227745i | \(0.0731351\pi\) |
−0.837105 | + | 0.547042i | \(0.815754\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.743637 | + | 0.623986i | 0.0479019 | + | 0.0401945i | 0.666424 | − | 0.745573i | \(-0.267824\pi\) |
−0.618522 | + | 0.785767i | \(0.712268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3865 | + | 2.50138i | −0.987042 | + | 0.160464i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2235 | + | 14.4523i | 1.10037 | + | 0.923322i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86977 | − | 10.6040i | −0.118971 | − | 0.674716i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.34179 | − | 18.8189i | −0.338522 | − | 1.19260i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1814 | + | 21.0988i | −0.768884 | + | 1.33175i | 0.169284 | + | 0.985567i | \(0.445855\pi\) |
−0.938168 | + | 0.346180i | \(0.887479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.64050 | − | 2.84142i | −0.103137 | − | 0.178639i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.76262 | + | 10.6205i | −0.298247 | + | 0.665080i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.702943 | + | 0.589839i | −0.0438484 | + | 0.0367931i | −0.664448 | − | 0.747334i | \(-0.731333\pi\) |
0.620600 | + | 0.784127i | \(0.286889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.9556 | − | 10.5390i | 1.79921 | − | 0.654860i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.08532 | + | 3.28046i | −0.0671797 | + | 0.203056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.07212 | − | 23.0941i | 0.251097 | − | 1.42404i | −0.554797 | − | 0.831986i | \(-0.687204\pi\) |
0.805895 | − | 0.592059i | \(-0.201685\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.6722 | − | 11.5277i | −1.94561 | − | 0.708142i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.45380 | + | 4.09524i | −0.517364 | + | 0.250625i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5865 | 1.01130 | 0.505649 | − | 0.862739i | \(-0.331253\pi\) | ||||
0.505649 | + | 0.862739i | \(0.331253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5443 | −1.06574 | −0.532869 | − | 0.846198i | \(-0.678886\pi\) | ||||
−0.532869 | + | 0.846198i | \(0.678886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.02734 | − | 14.1478i | 0.0621776 | − | 0.856265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.9548 | − | 7.99089i | −1.32392 | − | 0.481869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.20802 | − | 23.8648i | 0.252835 | − | 1.43390i | −0.548734 | − | 0.835997i | \(-0.684890\pi\) |
0.801569 | − | 0.597902i | \(-0.203999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.74513 | − | 2.92991i | 0.284084 | − | 0.175409i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8477 | + | 7.22397i | −1.18401 | + | 0.430946i | −0.857618 | − | 0.514287i | \(-0.828057\pi\) |
−0.326397 | + | 0.945233i | \(0.605835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.7119 | − | 16.5402i | 1.17175 | − | 0.983214i | 0.171751 | − | 0.985140i | \(-0.445058\pi\) |
0.999998 | + | 0.00192598i | \(0.000613059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.4438 | − | 3.42468i | 1.98104 | − | 0.202861i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.84628 | + | 11.8581i | 0.404123 | + | 0.699962i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.22023 | − | 12.5058i | 0.424720 | − | 0.735636i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.3109 | + | 5.12182i | 1.19065 | + | 0.300247i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.17783 | + | 18.0224i | 0.185651 | + | 1.05288i | 0.925116 | + | 0.379684i | \(0.123967\pi\) |
−0.739465 | + | 0.673195i | \(0.764922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.93806 | − | 3.30442i | −0.229282 | − | 0.192391i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.26000 | − | 9.51894i | −0.0731127 | − | 0.552345i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.16935 | − | 2.65940i | −0.183288 | − | 0.153797i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.57076 | + | 8.90821i | 0.0905369 | + | 0.513460i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.0888 | + | 17.6015i | −0.981724 | + | 1.01118i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.13045 | − | 15.8144i | 0.522808 | − | 0.905530i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.26334 | − | 10.8484i | −0.357468 | − | 0.619152i | 0.630069 | − | 0.776539i | \(-0.283026\pi\) |
−0.987537 | + | 0.157387i | \(0.949693\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.53092 | + | 2.11903i | 0.0870912 | + | 0.120547i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00776 | − | 5.04111i | 0.340669 | − | 0.285855i | −0.456361 | − | 0.889795i | \(-0.650848\pi\) |
0.797030 | + | 0.603939i | \(0.206403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.04147 | + | 2.19892i | −0.341484 | + | 0.124290i | −0.507069 | − | 0.861905i | \(-0.669271\pi\) |
0.165585 | + | 0.986196i | \(0.447049\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 43.8243 | + | 6.39833i | 2.46922 | + | 0.360505i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.31089 | + | 18.7770i | −0.185958 | + | 1.05462i | 0.738760 | + | 0.673969i | \(0.235412\pi\) |
−0.924718 | + | 0.380653i | \(0.875699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00002 | − | 0.727946i | −0.111979 | − | 0.0407572i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.8232 | − | 18.8754i | −1.55294 | − | 1.05352i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.39281 | 0.411347 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.4615 | −1.63423 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.8714 | + | 14.8377i | 1.20949 | + | 0.820526i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.6729 | − | 8.98020i | −1.36026 | − | 0.495094i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.61923 | + | 14.8544i | −0.143966 | + | 0.816472i | 0.824225 | + | 0.566262i | \(0.191611\pi\) |
−0.968191 | + | 0.250210i | \(0.919500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.3037 | − | 20.6392i | 0.893435 | − | 1.13102i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.0598 | + | 9.12102i | −1.36916 | + | 0.498334i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.78707 | + | 2.33863i | −0.151821 | + | 0.127393i | −0.715534 | − | 0.698577i | \(-0.753817\pi\) |
0.563713 | + | 0.825971i | \(0.309372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5487 | + | 15.9851i | 0.627238 | + | 0.868193i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.71756 | + | 2.97490i | 0.0930111 | + | 0.161100i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.89475 | + | 5.01386i | −0.156302 | + | 0.270723i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.99808 | − | 9.26805i | 0.484440 | − | 0.498975i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.96153 | + | 11.1244i | 0.105300 | + | 0.597187i | 0.991100 | + | 0.133120i | \(0.0424994\pi\) |
−0.885800 | + | 0.464068i | \(0.846389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4174 | + | 17.1322i | 1.09292 | + | 0.917065i | 0.996928 | − | 0.0783174i | \(-0.0249548\pi\) |
0.0959872 | + | 0.995383i | \(0.469399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.59838 | − | 10.7360i | −0.298820 | − | 0.573043i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.46470 | + | 1.22903i | 0.0779579 | + | 0.0654144i | 0.680934 | − | 0.732345i | \(-0.261574\pi\) |
−0.602976 | + | 0.797759i | \(0.706019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.27108 | + | 7.20866i | 0.0674620 | + | 0.382596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.44357 | + | 2.38139i | 0.499806 | + | 0.126037i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.2372 | − | 22.9275i | 0.698631 | − | 1.21006i | −0.270310 | − | 0.962773i | \(-0.587126\pi\) |
0.968941 | − | 0.247291i | \(-0.0795405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.17647 | − | 2.03771i | −0.0619197 | − | 0.107248i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.0697 | + | 1.33835i | −0.685982 | + | 0.0702452i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.87495 | − | 7.44697i | 0.464536 | − | 0.389792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7457 | − | 4.27510i | 0.613123 | − | 0.223159i | −0.0167461 | − | 0.999860i | \(-0.505331\pi\) |
0.629869 | + | 0.776701i | \(0.283108\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.2900 | + | 5.54210i | 0.535677 | + | 0.288510i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89725 | + | 27.7737i | −0.254253 | + | 1.44194i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.01015 | + | 1.09561i | 0.155860 | + | 0.0567284i | 0.418772 | − | 0.908091i | \(-0.362461\pi\) |
−0.262912 | + | 0.964820i | \(0.584683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.02740 | − | 55.4625i | 0.207974 | − | 2.86407i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.68385 | −0.138225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7650 | −0.552963 | −0.276481 | − | 0.961019i | \(-0.589168\pi\) | ||||
−0.276481 | + | 0.961019i | \(0.589168\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.50964 | + | 1.21573i | −0.128573 | + | 0.0622839i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3359 | − | 10.3134i | −1.44789 | − | 0.526990i | −0.505892 | − | 0.862597i | \(-0.668837\pi\) |
−0.942002 | + | 0.335606i | \(0.891059\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.73720 | + | 26.8660i | −0.241430 | + | 1.36922i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.13565 | + | 5.76544i | 0.261060 | + | 0.293074i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.1771 | − | 6.25195i | 0.870913 | − | 0.316986i | 0.132376 | − | 0.991200i | \(-0.457739\pi\) |
0.738537 | + | 0.674213i | \(0.235517\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17601 | − | 1.82589i | 0.110046 | − | 0.0923393i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.73273 | + | 8.32385i | −0.188291 | + | 0.419883i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.9387 | − | 36.2669i | −1.05354 | − | 1.82479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.90869 | + | 8.50210i | −0.246360 | + | 0.426708i | −0.962513 | − | 0.271235i | \(-0.912568\pi\) |
0.716153 | + | 0.697943i | \(0.245901\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.68136 | − | 27.0610i | −0.384549 | − | 1.35475i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.00593 | − | 22.7188i | −0.200047 | − | 1.13452i | −0.905046 | − | 0.425313i | \(-0.860164\pi\) |
0.705000 | − | 0.709208i | \(-0.250947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.31823 | + | 2.78433i | 0.165293 | + | 0.138697i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 34.6979 | − | 15.0058i | 1.72415 | − | 0.745645i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.4107 | + | 10.4138i | 0.615177 | + | 0.516195i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.26154 | − | 18.4971i | −0.161273 | − | 0.914623i | −0.952825 | − | 0.303521i | \(-0.901838\pi\) |
0.791552 | − | 0.611102i | \(-0.209273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.39480 | − | 26.0515i | −0.364758 | − | 1.28502i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.15074 | + | 3.72519i | −0.105831 | + | 0.183305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.7204 | + | 41.0849i | 1.16439 | + | 2.01678i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.68469 | + | 19.3666i | −0.425291 | + | 0.948385i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0404 | − | 20.1723i | 1.17445 | − | 0.985483i | 0.174453 | − | 0.984665i | \(-0.444184\pi\) |
1.00000 | 0.000817323i | \(-0.000260162\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5621 | − | 7.12002i | 0.953398 | − | 0.347008i | 0.181955 | − | 0.983307i | \(-0.441758\pi\) |
0.771443 | + | 0.636299i | \(0.219535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.9465 | + | 4.54231i | −1.06708 | + | 0.220855i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.51250 | − | 19.9204i | 0.170381 | − | 0.966280i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3581 | − | 5.22593i | −0.694839 | − | 0.252901i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.71201 | − | 3.25148i | 0.324059 | − | 0.156983i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.8928 | 1.48806 | 0.744028 | − | 0.668149i | \(-0.232913\pi\) | ||||
0.744028 | + | 0.668149i | \(0.232913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5840 | −0.748917 | −0.374459 | − | 0.927244i | \(-0.622171\pi\) | ||||
−0.374459 | + | 0.927244i | \(0.622171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.606884 | − | 8.35756i | 0.0290978 | − | 0.400714i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.70977 | − | 2.80613i | −0.368808 | − | 0.134235i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.93807 | − | 10.9914i | 0.0924992 | − | 0.524589i | −0.902986 | − | 0.429670i | \(-0.858630\pi\) |
0.995485 | − | 0.0949187i | \(-0.0302591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.474574 | − | 16.0512i | −0.0225988 | − | 0.764345i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6033 | − | 4.95121i | 0.646315 | − | 0.235239i | 0.00199787 | − | 0.999998i | \(-0.499364\pi\) |
0.644317 | + | 0.764759i | \(0.277142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4507 | − | 14.6428i | 0.827241 | − | 0.694138i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.0808 | − | 3.69471i | 1.70656 | − | 0.174754i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6936 | + | 32.3783i | 0.882207 | + | 1.52803i | 0.848882 | + | 0.528583i | \(0.177276\pi\) |
0.0333252 | + | 0.999445i | \(0.489390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.59958 | + | 6.23465i | −0.169497 | + | 0.293578i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1963 | − | 4.08423i | −0.760968 | − | 0.191894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.97355 | + | 33.8777i | 0.280044 | + | 1.58821i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5050 | + | 8.81472i | 0.491402 | + | 0.412335i | 0.854528 | − | 0.519405i | \(-0.173846\pi\) |
−0.363126 | + | 0.931740i | \(0.618291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.92658 | − | 2.50537i | 0.369981 | − | 0.116941i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.09478 | + | 3.43593i | 0.190713 | + | 0.160027i | 0.733145 | − | 0.680073i | \(-0.238052\pi\) |
−0.542432 | + | 0.840100i | \(0.682496\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.31705 | − | 35.8258i | −0.293578 | − | 1.66496i | −0.672926 | − | 0.739710i | \(-0.734963\pi\) |
0.379348 | − | 0.925254i | \(-0.376148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.42077 | + | 9.70343i | −0.436878 | + | 0.449986i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.61809 | − | 4.53466i | 0.121151 | − | 0.209839i | −0.799071 | − | 0.601237i | \(-0.794675\pi\) |
0.920222 | + | 0.391397i | \(0.128008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1571 | + | 19.3247i | 0.515188 | + | 0.892331i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.9292 | + | 16.5119i | 0.549670 | + | 0.760827i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.64325 | + | 3.05705i | −0.167517 | + | 0.140563i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54.9010 | + | 19.9823i | −2.51903 | + | 0.916852i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.89821 | + | 22.3676i | 0.407421 | + | 1.02414i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.03109 | + | 11.5189i | −0.0928027 | + | 0.526310i | 0.902596 | + | 0.430489i | \(0.141659\pi\) |
−0.995399 | + | 0.0958213i | \(0.969452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1973 | + | 6.98724i | 0.875320 | + | 0.318591i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.94453 | − | 6.06803i | −0.406990 | − | 0.276105i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −50.7982 | −2.30663 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7362 | −0.939645 | −0.469823 | − | 0.882761i | \(-0.655682\pi\) | ||||
−0.469823 | + | 0.882761i | \(0.655682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.5741 | + | 13.9576i | 0.930391 | + | 0.631184i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.28722 | + | 3.38027i | 0.419126 | + | 0.152550i | 0.542970 | − | 0.839752i | \(-0.317300\pi\) |
−0.123843 | + | 0.992302i | \(0.539522\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.319978 | − | 1.81469i | 0.0144111 | − | 0.0817293i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.60741 | + | 21.6366i | 0.386874 | + | 0.972492i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.75545 | − | 2.09481i | 0.258167 | − | 0.0939652i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5261 | − | 13.0279i | 0.695042 | − | 0.583210i | −0.225316 | − | 0.974286i | \(-0.572341\pi\) |
0.920358 | + | 0.391076i | \(0.127897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.58145 | + | 11.8780i | 0.383391 | + | 0.530671i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.34704 | + | 2.33314i | 0.0600614 | + | 0.104029i | 0.894493 | − | 0.447083i | \(-0.147537\pi\) |
−0.834431 | + | 0.551112i | \(0.814204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.7468 | − | 51.5230i | 1.32372 | − | 2.29274i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.13362 | + | 9.40766i | −0.405638 | + | 0.417809i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.409562 | − | 2.32274i | −0.0181535 | − | 0.102954i | 0.974385 | − | 0.224888i | \(-0.0722015\pi\) |
−0.992538 | + | 0.121934i | \(0.961090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.42602 | − | 6.23117i | −0.328508 | − | 0.275651i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.7142 | − | 16.2092i | −0.782101 | − | 0.715652i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.85650 | − | 4.07508i | −0.214003 | − | 0.179570i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.39718 | − | 13.5951i | −0.105428 | − | 0.597912i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.0830 | − | 10.6121i | −1.84724 | − | 0.465819i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5589 | − | 30.4129i | 0.769270 | − | 1.33241i | −0.168690 | − | 0.985669i | \(-0.553954\pi\) |
0.937959 | − | 0.346745i | \(-0.112713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.8599 | + | 25.7381i | 0.649777 | + | 1.12545i | 0.983176 | + | 0.182661i | \(0.0584711\pi\) |
−0.333399 | + | 0.942786i | \(0.608196\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −76.5672 | + | 7.84055i | −3.34166 | + | 0.342190i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.27823 | + | 1.91166i | −0.0992414 | + | 0.0832734i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6506 | − | 6.78825i | 0.810894 | − | 0.295141i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.108508 | + | 3.67001i | 0.00470886 | + | 0.159265i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.57638 | + | 8.94012i | −0.0682808 | + | 0.387240i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 76.6188 | + | 27.8870i | 3.31252 | + | 1.20566i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.21468 | + | 16.7278i | −0.0524175 | + | 0.721856i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.89135 | 0.426050 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.06242 | −0.174657 | −0.0873286 | − | 0.996180i | \(-0.527833\pi\) | ||||
−0.0873286 | + | 0.996180i | \(0.527833\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.941759 | − | 0.456213i | 0.0404147 | − | 0.0195780i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −60.2288 | − | 21.9215i | −2.57992 | − | 0.939013i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.47203 | − | 36.7047i | 0.276724 | − | 1.56938i | −0.456708 | − | 0.889617i | \(-0.650972\pi\) |
0.733432 | − | 0.679763i | \(-0.237917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.7715 | + | 2.64335i | −0.545076 | + | 0.112816i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.00131 | + | 1.82033i | −0.213063 | + | 0.0775486i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8426 | + | 22.5236i | −1.14146 | + | 0.957801i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.0994 | + | 58.2007i | −1.10786 | + | 2.47048i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.81761 | − | 8.34434i | −0.204128 | − | 0.353561i | 0.745726 | − | 0.666253i | \(-0.232103\pi\) |
−0.949855 | + | 0.312692i | \(0.898769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.99858 | + | 5.19370i | −0.126827 | + | 0.219670i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.39826 | + | 4.92598i | 0.0590344 | + | 0.207975i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.77978 | − | 15.7649i | −0.117154 | − | 0.664413i | −0.985661 | − | 0.168737i | \(-0.946031\pi\) |
0.868507 | − | 0.495677i | \(-0.165080\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.6355 | − | 30.7408i | −1.54127 | − | 1.29328i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.4067 | − | 26.4117i | −0.731015 | − | 1.10919i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7944 | + | 12.4139i | 0.620212 | + | 0.520419i | 0.897870 | − | 0.440260i | \(-0.145114\pi\) |
−0.277658 | + | 0.960680i | \(0.589558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61529 | + | 9.16077i | 0.0675978 | + | 0.383366i | 0.999772 | + | 0.0213560i | \(0.00679835\pi\) |
−0.932174 | + | 0.362010i | \(0.882091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.79411 | + | 34.5041i | 0.409155 | + | 1.44143i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.2244 | + | 19.4412i | −0.468089 | + | 0.810753i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.05082 | − | 5.28418i | −0.127007 | − | 0.219983i | 0.795508 | − | 0.605943i | \(-0.207204\pi\) |
−0.922516 | + | 0.385959i | \(0.873871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.89169 | − | 17.5982i | 0.327968 | − | 0.731357i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.4085 | − | 25.5158i | 1.26156 | − | 1.05857i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9336 | + | 5.07143i | −0.577072 | + | 0.210037i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.5307 | + | 21.9258i | 0.807497 | + | 0.906521i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.95166 | − | 22.4110i | 0.163102 | − | 0.925000i | −0.787897 | − | 0.615807i | \(-0.788830\pi\) |
0.950999 | − | 0.309193i | \(-0.100059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.07194 | + | 2.93795i | 0.332599 | + | 0.121056i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6779 | + | 9.53251i | −0.809442 | + | 0.392115i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4186 | 0.674233 | 0.337117 | − | 0.941463i | \(-0.390548\pi\) | ||||
0.337117 | + | 0.941463i | \(0.390548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.6186 | −0.968268 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.64039 | − | 36.3616i | 0.108064 | − | 1.48818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.1090 | + | 11.3227i | 1.27108 | + | 0.462635i | 0.887472 | − | 0.460861i | \(-0.152459\pi\) |
0.383607 | + | 0.923496i | \(0.374682\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.94541 | − | 22.3755i | 0.160937 | − | 0.912716i | −0.792219 | − | 0.610237i | \(-0.791074\pi\) |
0.953156 | − | 0.302480i | \(-0.0978145\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.7692 | + | 9.03174i | 0.682896 | + | 0.367801i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.9398 | − | 10.8972i | 1.21722 | − | 0.443033i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1172 | − | 11.0066i | 0.532410 | − | 0.446745i | −0.336523 | − | 0.941675i | \(-0.609251\pi\) |
0.868933 | + | 0.494930i | \(0.164806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.97504 | + | 0.714251i | −0.282643 | + | 0.0289429i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.70385 | − | 15.0755i | −0.352120 | − | 0.609890i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8362 | + | 36.0893i | −0.841564 | + | 1.45763i | 0.0470074 | + | 0.998895i | \(0.485032\pi\) |
−0.888572 | + | 0.458738i | \(0.848302\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.4832 | − | 6.93047i | −1.10823 | − | 0.279463i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.15015 | + | 17.8654i | 0.126820 | + | 0.719233i | 0.980210 | + | 0.197960i | \(0.0634317\pi\) |
−0.853390 | + | 0.521273i | \(0.825457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.11217 | + | 5.12872i | 0.245669 | + | 0.206141i | 0.757305 | − | 0.653062i | \(-0.226516\pi\) |
−0.511636 | + | 0.859202i | \(0.670960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.21740 | − | 0.395947i | −0.369881 | − | 0.0158888i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6017 | − | 12.2522i | −0.585003 | − | 0.490876i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4400 | + | 70.5510i | 0.497602 | + | 2.82204i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3024 | − | 10.6115i | 0.411439 | − | 0.423783i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.01319 | + | 12.1472i | −0.279634 | + | 0.484340i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.118628 | − | 0.205470i | −0.00472251 | − | 0.00817962i | 0.863654 | − | 0.504084i | \(-0.168170\pi\) |
−0.868377 | + | 0.495905i | \(0.834837\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.4862 | − | 31.1242i | −0.893744 | − | 1.23708i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.18049 | − | 4.34695i | 0.205582 | − | 0.172503i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.7207 | − | 4.26597i | 0.464389 | − | 0.169024i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.24065 | − | 4.10242i | 0.128198 | − | 0.162289i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.15329 | − | 23.5545i | 0.164045 | − | 0.930345i | −0.785999 | − | 0.618228i | \(-0.787851\pi\) |
0.950044 | − | 0.312117i | \(-0.101038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2499 | − | 8.82623i | −0.956321 | − | 0.348073i | −0.183730 | − | 0.982977i | \(-0.558817\pi\) |
−0.772591 | + | 0.634904i | \(0.781040\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.4952 | − | 10.5121i | −0.610124 | − | 0.413912i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.60899 | −0.259826 | −0.129913 | − | 0.991525i | \(-0.541470\pi\) | ||||
−0.129913 | + | 0.991525i | \(0.541470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.26159 | −0.0887753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.36471 | + | 6.35308i | 0.367032 | + | 0.248997i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.4279 | + | 8.52708i | 0.916807 | + | 0.333690i | 0.756967 | − | 0.653453i | \(-0.226680\pi\) |
0.159839 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.84162 | − | 21.7869i | 0.150105 | − | 0.851285i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18769 | − | 1.19540i | −0.319432 | − | 0.0466370i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.25426 | − | 2.64034i | 0.282586 | − | 0.102853i | −0.196839 | − | 0.980436i | \(-0.563068\pi\) |
0.479425 | + | 0.877583i | \(0.340845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6830 | − | 11.4814i | 0.532208 | − | 0.446575i | −0.336655 | − | 0.941628i | \(-0.609296\pi\) |
0.868863 | + | 0.495053i | \(0.164851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.78134 | + | 5.23395i | 0.146855 | + | 0.203270i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34.1093 | + | 59.0790i | 1.32270 | + | 2.29098i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.02251 | + | 1.77103i | −0.0395916 | + | 0.0685747i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.6356 | + | 17.1348i | −0.643171 | + | 0.662468i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.39502 | − | 7.91153i | −0.0538540 | − | 0.305421i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.74755 | + | 3.14457i | 0.144458 | + | 0.121214i | 0.712153 | − | 0.702025i | \(-0.247720\pi\) |
−0.567695 | + | 0.823239i | \(0.692165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −52.0930 | + | 40.0306i | −2.00506 | + | 1.54078i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9410 | − | 10.8588i | −0.497363 | − | 0.417337i | 0.359294 | − | 0.933225i | \(-0.383018\pi\) |
−0.856656 | + | 0.515888i | \(0.827462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.38089 | + | 41.8591i | 0.283252 | + | 1.60640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.6141 | − | 3.93741i | −0.598332 | − | 0.150882i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.8279 | + | 29.1467i | −0.643900 | + | 1.11527i | 0.340654 | + | 0.940189i | \(0.389352\pi\) |
−0.984554 | + | 0.175080i | \(0.943982\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.8368 | + | 56.8750i | 1.25463 | + | 2.17308i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.255167 | + | 0.0261294i | −0.00973524 | + | 0.000996897i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.3233 | + | 12.0187i | −0.545674 | + | 0.457875i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4088 | − | 5.60833i | 0.586177 | − | 0.213351i | −0.0318704 | − | 0.999492i | \(-0.510146\pi\) |
0.618047 | + | 0.786141i | \(0.287924\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.5785 | − | 10.2365i | 0.629765 | − | 0.388852i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.93805 | − | 50.6902i | 0.339040 | − | 1.92279i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.85692 | − | 2.13174i | −0.221847 | − | 0.0807456i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.206830 | + | 2.84832i | −0.00782304 | + | 0.107733i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.9743 | −1.32096 | −0.660481 | − | 0.750843i | \(-0.729648\pi\) | ||||
−0.660481 | + | 0.750843i | \(0.729648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.5129 | 1.52797 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 48.9136 | − | 23.6950i | 1.84219 | − | 0.892406i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.7786 | − | 17.0260i | −1.75929 | − | 0.640329i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.64168 | + | 26.3243i | −0.174322 | + | 0.988629i | 0.764602 | + | 0.644503i | \(0.222936\pi\) |
−0.938924 | + | 0.344126i | \(0.888175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.39458 | + | 28.3958i | −0.352324 | + | 1.06493i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.10153 | − | 1.12886i | 0.116153 | − | 0.0422763i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.8552 | + | 11.6259i | −0.518155 | + | 0.434784i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.61991 | + | 19.2221i | −0.321917 | + | 0.717863i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.0563 | − | 22.6141i | −0.486916 | − | 0.843364i | 0.512970 | − | 0.858406i | \(-0.328545\pi\) |
−0.999887 | + | 0.0150424i | \(0.995212\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.65234 | + | 4.59399i | −0.0987783 | + | 0.171089i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.459129 | + | 1.61749i | 0.0170752 | + | 0.0601550i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.52874 | + | 14.3412i | 0.0939152 | + | 0.532619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4715 | − | 8.78667i | −0.388368 | − | 0.325880i | 0.427609 | − | 0.903964i | \(-0.359356\pi\) |
−0.815977 | + | 0.578084i | \(0.803801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.4863 | − | 11.3763i | −0.906901 | − | 0.421343i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.15422 | − | 2.64670i | −0.116663 | − | 0.0978918i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.00652 | − | 11.3795i | −0.0741125 | − | 0.420313i | −0.999179 | − | 0.0405082i | \(-0.987102\pi\) |
0.925067 | − | 0.379805i | \(-0.124009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.6340 | + | 37.4630i | 0.392240 | + | 1.38184i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.86609 | + | 10.1604i | −0.216080 | + | 0.374262i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.2426 | + | 43.7215i | 0.928566 | + | 1.60832i | 0.785724 | + | 0.618577i | \(0.212291\pi\) |
0.142841 | + | 0.989746i | \(0.454376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.63117 | − | 17.0173i | 0.280338 | − | 0.625145i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0885 | + | 13.4998i | −0.590228 | + | 0.495260i | −0.888288 | − | 0.459287i | \(-0.848105\pi\) |
0.298060 | + | 0.954547i | \(0.403661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −82.6529 | + | 30.0832i | −3.02817 | + | 1.10216i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.6426 | − | 32.1681i | 0.389393 | − | 1.17697i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.8470 | − | 67.1879i | 0.432882 | − | 2.45499i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5146 | − | 3.82701i | −0.383684 | − | 0.139649i | 0.142975 | − | 0.989726i | \(-0.454333\pi\) |
−0.526659 | + | 0.850077i | \(0.676555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.9764 | + | 18.3967i | −1.38394 | + | 0.670415i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.5073 | 1.47421 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2619 | −0.809123 | −0.404561 | − | 0.914511i | \(-0.632576\pi\) | ||||
−0.404561 | + | 0.914511i | \(0.632576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.411575 | − | 5.66792i | 0.0149392 | − | 0.205732i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.56792 | + | 2.02656i | 0.201837 | + | 0.0734626i | 0.440960 | − | 0.897527i | \(-0.354638\pi\) |
−0.239124 | + | 0.970989i | \(0.576860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.31277 | + | 52.8153i | −0.337145 | + | 1.91204i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.1537 | + | 10.5916i | −0.620192 | + | 0.382942i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.67985 | + | 0.975387i | −0.0967639 | + | 0.0352192i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.73719 | − | 1.45768i | 0.0626447 | − | 0.0525651i | −0.610928 | − | 0.791686i | \(-0.709203\pi\) |
0.673572 | + | 0.739121i | \(0.264759\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.58111 | + | 0.161907i | −0.0569422 | + | 0.00583093i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.63951 | + | 8.03586i | 0.166872 | + | 0.289030i | 0.937318 | − | 0.348474i | \(-0.113300\pi\) |
−0.770447 | + | 0.637504i | \(0.779967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7516 | − | 20.3544i | 0.422132 | − | 0.731153i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.7512 | + | 13.0501i | 1.85656 | + | 0.468171i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.12609 | + | 17.7290i | 0.112004 | + | 0.635206i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.46686 | + | 2.06994i | 0.0882711 | + | 0.0740683i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.74552 | + | 3.64667i | −0.169591 | + | 0.130321i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.8427 | − | 31.7538i | −1.35066 | − | 1.13334i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00609 | + | 22.7197i | 0.142802 | + | 0.809868i | 0.969106 | + | 0.246644i | \(0.0793280\pi\) |
−0.826304 | + | 0.563224i | \(0.809561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.2932 | − | 29.1420i | 1.00726 | − | 1.03748i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.0082 | + | 34.6552i | −0.711410 | + | 1.23220i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.06512 | − | 8.77304i | −0.179868 | − | 0.311540i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.1875 | − | 47.3208i | −1.21251 | − | 1.67829i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5527 | − | 13.0503i | 0.550906 | − | 0.462265i | −0.324341 | − | 0.945940i | \(-0.605143\pi\) |
0.875248 | + | 0.483675i | \(0.160698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2310 | − | 4.08775i | 0.397325 | − | 0.144614i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0993 | − | 2.35050i | −0.568842 | − | 0.0830507i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.885052 | − | 5.01938i | 0.0312328 | − | 0.177130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.6312 | + | 8.96503i | 0.868136 | + | 0.315976i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.7741 | + | 16.1285i | 0.836888 | + | 0.567751i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.2976 | 1.24100 | 0.620499 | − | 0.784207i | \(-0.286930\pi\) | ||||
0.620499 | + | 0.784207i | \(0.286930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.1846 | 1.41107 | 0.705536 | − | 0.708675i | \(-0.250707\pi\) | ||||
0.705536 | + | 0.708675i | \(0.250707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.1469 | − | 17.0598i | −0.881940 | − | 0.598314i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −56.6563 | − | 20.6212i | −1.98458 | − | 0.722330i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.06517 | + | 11.7122i | −0.0722512 | + | 0.409757i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2297 | − | 19.2797i | 0.532169 | − | 0.673686i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.7450 | + | 4.63881i | −0.444804 | + | 0.161895i | −0.554705 | − | 0.832047i | \(-0.687169\pi\) |
0.109901 | + | 0.993943i | \(0.464947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3197 | + | 13.6939i | −0.568869 | + | 0.477338i | −0.881271 | − | 0.472612i | \(-0.843311\pi\) |
0.312401 | + | 0.949950i | \(0.398867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.6984 | − | 32.8022i | −0.825074 | − | 1.14203i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2719 | + | 45.5043i | 0.913564 | + | 1.58234i | 0.808990 | + | 0.587822i | \(0.200014\pi\) |
0.104573 | + | 0.994517i | \(0.466652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.89163 | + | 11.9366i | −0.239356 | + | 0.414577i | −0.960530 | − | 0.278177i | \(-0.910270\pi\) |
0.721174 | + | 0.692754i | \(0.243603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.2374 | − | 30.1146i | 1.01423 | − | 1.04466i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.48706 | + | 8.43352i | 0.0515235 | + | 0.292204i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.2226 | − | 22.8425i | −0.942078 | − | 0.790497i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.65039 | + | 0.414547i | 0.333566 | + | 0.0143288i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.0984 | − | 16.0254i | −0.659349 | − | 0.553260i | 0.250543 | − | 0.968106i | \(-0.419391\pi\) |
−0.909892 | + | 0.414846i | \(0.863835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.80544 | − | 27.2530i | −0.165705 | − | 0.939758i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.4730 | − | 8.94525i | −1.22176 | − | 0.308091i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.8991 | − | 27.5381i | 0.546946 | − | 0.947339i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.3298 | − | 23.0878i | −0.458016 | − | 0.793308i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.3373 | − | 4.54018i | 1.52165 | − | 0.155819i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.9246 | − | 10.0060i | 0.408771 | − | 0.343000i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.36081 | − | 1.58720i | 0.149311 | − | 0.0543448i | −0.266283 | − | 0.963895i | \(-0.585796\pi\) |
0.415595 | + | 0.909550i | \(0.363574\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 51.2665 | + | 27.6116i | 1.75328 | + | 0.944298i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.29397 | + | 35.6949i | −0.214998 | + | 1.21931i | 0.665912 | + | 0.746031i | \(0.268043\pi\) |
−0.880910 | + | 0.473284i | \(0.843068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.7284 | + | 9.36438i | 0.877842 | + | 0.319508i | 0.741339 | − | 0.671131i | \(-0.234191\pi\) |
0.136503 | + | 0.990640i | \(0.456414\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.71763 | + | 23.6539i | −0.0585366 | + | 0.806124i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.9476 | 0.713065 | 0.356532 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356532 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 105.251 | 3.57863 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5095 | − | 10.9042i | 0.764464 | − | 0.370326i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.3122 | − | 6.30113i | −0.587277 | − | 0.213751i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.56897 | + | 14.5694i | −0.0870463 | + | 0.493664i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.1321 | + | 27.0914i | 0.816747 | + | 0.916906i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 106.035 | − | 38.5935i | 3.58463 | − | 1.30470i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.9493 | − | 11.7049i | 0.471035 | − | 0.395246i | −0.376137 | − | 0.926564i | \(-0.622748\pi\) |
0.847172 | + | 0.531319i | \(0.178303\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9698 | + | 28.9223i | −0.437461 | + | 0.975524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0582 | − | 39.9380i | −0.776851 | − | 1.34555i | −0.933748 | − | 0.357931i | \(-0.883482\pi\) |
0.156897 | − | 0.987615i | \(-0.449851\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.03494 | + | 15.6490i | −0.304050 | + | 0.526630i | −0.977049 | − | 0.213013i | \(-0.931672\pi\) |
0.672999 | + | 0.739643i | \(0.265006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.43139 | − | 8.56567i | −0.0817304 | − | 0.287932i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58846 | − | 26.0224i | −0.154065 | − | 0.873748i | −0.959635 | − | 0.281247i | \(-0.909252\pi\) |
0.805570 | − | 0.592501i | \(-0.201859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.33472 | − | 3.63726i | −0.145382 | − | 0.121990i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.45009 | − | 14.8691i | 0.249587 | − | 0.498133i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.4445 | − | 22.1896i | −0.884931 | − | 0.742545i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.06286 | − | 40.0555i | −0.236086 | − | 1.33891i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.95679 | − | 6.89365i | −0.0653352 | − | 0.230172i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.07054 | − | 1.85423i | 0.0357045 | − | 0.0618420i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.41876 | − | 11.1176i | −0.213840 | − | 0.370381i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.41080 | + | 14.2959i | −0.213338 | + | 0.475737i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.94402 | + | 1.63122i | −0.0646213 | + | 0.0542237i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2748 | − | 12.8390i | 1.17128 | − | 0.426312i | 0.318167 | − | 0.948035i | \(-0.396933\pi\) |
0.853115 | + | 0.521723i | \(0.174711\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.6095 | + | 8.61200i | −1.38010 | + | 0.285642i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.77993 | − | 15.7658i | 0.0921031 | − | 0.522343i | −0.903494 | − | 0.428602i | \(-0.859006\pi\) |
0.995597 | − | 0.0937409i | \(-0.0298825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6121 | + | 7.13822i | 0.649065 | + | 0.236240i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.4648 | − | 13.7891i | 0.941016 | − | 0.455853i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5112 | −0.611294 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8859 | −1.21675 | −0.608377 | − | 0.793648i | \(-0.708179\pi\) | ||||
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.57138 | − | 21.6399i | 0.0517786 | − | 0.713058i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.81581 | + | 1.38884i | 0.125599 | + | 0.0457143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2486 | − | 109.165i | 0.632892 | − | 3.58931i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.133815 | + | 4.52594i | 0.00439506 | + | 0.148651i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9483 | − | 11.6282i | 1.04819 | − | 0.381510i | 0.240211 | − | 0.970721i | \(-0.422783\pi\) |
0.807979 | + | 0.589211i | \(0.200561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9478 | − | 15.8991i | 0.620991 | − | 0.521073i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.5131 | − | 1.38375i | 0.442398 | − | 0.0453020i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.20899 | − | 10.7543i | −0.203056 | − | 0.351703i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.09208 | + | 10.5518i | −0.199020 | + | 0.344712i | −0.948211 | − | 0.317642i | \(-0.897109\pi\) |
0.749191 | + | 0.662354i | \(0.230442\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7977 | − | 2.72286i | −0.352369 | − | 0.0888571i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.86766 | + | 10.5920i | 0.0608839 | + | 0.345290i | 0.999999 | + | 0.00168585i | \(0.000536621\pi\) |
−0.939115 | + | 0.343604i | \(0.888352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.29887 | + | 4.44628i | 0.172555 | + | 0.144791i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 56.5934 | + | 51.7851i | 1.84098 | + | 1.68457i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.3920 | − | 24.6628i | −0.955110 | − | 0.801433i | 0.0250403 | − | 0.999686i | \(-0.492029\pi\) |
−0.980151 | + | 0.198254i | \(0.936473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11604 | − | 6.32937i | −0.0362282 | − | 0.205460i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0041 | + | 23.6943i | −0.745961 | + | 0.768342i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2733 | − | 19.5259i | 0.365177 | − | 0.632506i | −0.623627 | − | 0.781722i | \(-0.714342\pi\) |
0.988805 | + | 0.149216i | \(0.0476750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.4910 | − | 75.3286i | −1.40734 | − | 2.43758i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.15886 | − | 2.98819i | −0.0697859 | − | 0.0965943i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.0954 | − | 35.3222i | 1.35933 | − | 1.14061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.8832 | − | 9.42073i | 0.834943 | − | 0.303895i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.5258 | − | 54.1099i | −0.693661 | − | 1.74367i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.12192 | + | 46.0617i | −0.261454 | + | 1.48278i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5163 | − | 10.0151i | −0.884865 | − | 0.322065i | −0.140694 | − | 0.990053i | \(-0.544933\pi\) |
−0.744172 | + | 0.667988i | \(0.767156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5964 | + | 7.18868i | 0.340406 | + | 0.230934i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.2319 | −1.06646 | −0.533232 | − | 0.845969i | \(-0.679023\pi\) | ||||
−0.533232 | + | 0.845969i | \(0.679023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.0688 | −1.38072 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.2283 | − | 28.6480i | −1.35239 | − | 0.917469i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.90284 | − | 2.14846i | −0.188849 | − | 0.0687352i | 0.245865 | − | 0.969304i | \(-0.420928\pi\) |
−0.434713 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.74026 | − | 9.86953i | 0.0556191 | − | 0.315431i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9211 | + | 42.5349i | 0.540250 | + | 1.35803i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.34031 | − | 0.487834i | 0.0427493 | − | 0.0155595i | −0.320557 | − | 0.947229i | \(-0.603870\pi\) |
0.363306 | + | 0.931670i | \(0.381648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.6200 | − | 34.0842i | 1.29426 | − | 1.08601i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.6324 | − | 36.8633i | −0.847719 | − | 1.17337i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.28483 | + | 3.95744i | 0.0726533 | + | 0.125839i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.58886 | + | 9.68018i | −0.177536 | + | 0.307501i | −0.941036 | − | 0.338307i | \(-0.890146\pi\) |
0.763500 | + | 0.645808i | \(0.223479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.1985 | + | 18.7445i | −0.577512 | + | 0.594839i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.3527 | + | 87.0697i | 0.486714 | + | 2.76029i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.8832 | − | 25.9141i | −0.978082 | − | 0.820708i | 0.00571696 | − | 0.999984i | \(-0.498180\pi\) |
−0.983799 | + | 0.179275i | \(0.942625\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.4380 | − | 13.7295i | 1.37432 | − | 0.434383i |
(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.u.d.97.2 | 18 | ||
4.3 | odd | 2 | 108.2.i.a.97.2 | yes | 18 | ||
12.11 | even | 2 | 324.2.i.a.289.3 | 18 | |||
27.22 | even | 9 | inner | 432.2.u.d.49.2 | 18 | ||
36.7 | odd | 6 | 972.2.i.c.217.3 | 18 | |||
36.11 | even | 6 | 972.2.i.b.217.1 | 18 | |||
36.23 | even | 6 | 972.2.i.d.541.1 | 18 | |||
36.31 | odd | 6 | 972.2.i.a.541.3 | 18 | |||
108.7 | odd | 18 | 2916.2.a.d.1.9 | 9 | |||
108.11 | even | 18 | 2916.2.e.d.1945.9 | 18 | |||
108.23 | even | 18 | 972.2.i.b.757.1 | 18 | |||
108.31 | odd | 18 | 972.2.i.c.757.3 | 18 | |||
108.43 | odd | 18 | 2916.2.e.c.1945.1 | 18 | |||
108.47 | even | 18 | 2916.2.a.c.1.1 | 9 | |||
108.59 | even | 18 | 324.2.i.a.37.3 | 18 | |||
108.67 | odd | 18 | 972.2.i.a.433.3 | 18 | |||
108.79 | odd | 18 | 2916.2.e.c.973.1 | 18 | |||
108.83 | even | 18 | 2916.2.e.d.973.9 | 18 | |||
108.95 | even | 18 | 972.2.i.d.433.1 | 18 | |||
108.103 | odd | 18 | 108.2.i.a.49.2 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.49.2 | ✓ | 18 | 108.103 | odd | 18 | ||
108.2.i.a.97.2 | yes | 18 | 4.3 | odd | 2 | ||
324.2.i.a.37.3 | 18 | 108.59 | even | 18 | |||
324.2.i.a.289.3 | 18 | 12.11 | even | 2 | |||
432.2.u.d.49.2 | 18 | 27.22 | even | 9 | inner | ||
432.2.u.d.97.2 | 18 | 1.1 | even | 1 | trivial | ||
972.2.i.a.433.3 | 18 | 108.67 | odd | 18 | |||
972.2.i.a.541.3 | 18 | 36.31 | odd | 6 | |||
972.2.i.b.217.1 | 18 | 36.11 | even | 6 | |||
972.2.i.b.757.1 | 18 | 108.23 | even | 18 | |||
972.2.i.c.217.3 | 18 | 36.7 | odd | 6 | |||
972.2.i.c.757.3 | 18 | 108.31 | odd | 18 | |||
972.2.i.d.433.1 | 18 | 108.95 | even | 18 | |||
972.2.i.d.541.1 | 18 | 36.23 | even | 6 | |||
2916.2.a.c.1.1 | 9 | 108.47 | even | 18 | |||
2916.2.a.d.1.9 | 9 | 108.7 | odd | 18 | |||
2916.2.e.c.973.1 | 18 | 108.79 | odd | 18 | |||
2916.2.e.c.1945.1 | 18 | 108.43 | odd | 18 | |||
2916.2.e.d.973.9 | 18 | 108.83 | even | 18 | |||
2916.2.e.d.1945.9 | 18 | 108.11 | even | 18 |