Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(200,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.200");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.d (of order \(2\), degree \(1\), 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: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 7 x^{18} + 32 x^{16} + 128 x^{14} + 423 x^{12} + 1186 x^{10} + 3807 x^{8} + 10368 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 200.1 | ||
Root | \(-0.362922 + 1.69360i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.200 |
Dual form | 201.2.d.a.200.2 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50456 | −1.77099 | −0.885497 | − | 0.464646i | \(-0.846182\pi\) | ||||
−0.885497 | + | 0.464646i | \(0.846182\pi\) | |||||||
\(3\) | −0.362922 | − | 1.69360i | −0.209533 | − | 0.977802i | ||||
\(4\) | 4.27284 | 2.13642 | ||||||||
\(5\) | 2.28042 | 1.01983 | 0.509917 | − | 0.860223i | \(-0.329676\pi\) | ||||
0.509917 | + | 0.860223i | \(0.329676\pi\) | |||||||
\(6\) | 0.908961 | + | 4.24173i | 0.371082 | + | 1.73168i | ||||
\(7\) | 3.79080i | 1.43279i | 0.697697 | + | 0.716393i | \(0.254208\pi\) | ||||
−0.697697 | + | 0.716393i | \(0.745792\pi\) | |||||||
\(8\) | −5.69246 | −2.01259 | ||||||||
\(9\) | −2.73658 | + | 1.22929i | −0.912192 | + | 0.409764i | ||||
\(10\) | −5.71146 | −1.80612 | ||||||||
\(11\) | 3.32556 | 1.00269 | 0.501346 | − | 0.865247i | \(-0.332838\pi\) | ||||
0.501346 | + | 0.865247i | \(0.332838\pi\) | |||||||
\(12\) | −1.55071 | − | 7.23648i | −0.447650 | − | 2.08899i | ||||
\(13\) | 0.642388i | 0.178166i | 0.996024 | + | 0.0890831i | \(0.0283937\pi\) | ||||
−0.996024 | + | 0.0890831i | \(0.971606\pi\) | |||||||
\(14\) | − | 9.49429i | − | 2.53746i | ||||||
\(15\) | −0.827614 | − | 3.86212i | −0.213689 | − | 0.997196i | ||||
\(16\) | 5.71146 | 1.42786 | ||||||||
\(17\) | 6.62832i | 1.60760i | 0.594897 | + | 0.803802i | \(0.297193\pi\) | ||||
−0.594897 | + | 0.803802i | \(0.702807\pi\) | |||||||
\(18\) | 6.85393 | − | 3.07884i | 1.61549 | − | 0.725689i | ||||
\(19\) | 7.09076 | 1.62673 | 0.813366 | − | 0.581753i | \(-0.197633\pi\) | ||||
0.813366 | + | 0.581753i | \(0.197633\pi\) | |||||||
\(20\) | 9.74386 | 2.17879 | ||||||||
\(21\) | 6.42010 | − | 1.37576i | 1.40098 | − | 0.300216i | ||||
\(22\) | −8.32906 | −1.77576 | ||||||||
\(23\) | − | 4.00860i | − | 0.835850i | −0.908482 | − | 0.417925i | \(-0.862757\pi\) | ||
0.908482 | − | 0.417925i | \(-0.137243\pi\) | |||||||
\(24\) | 2.06592 | + | 9.64076i | 0.421704 | + | 1.96791i | ||||
\(25\) | 0.200315 | 0.0400629 | ||||||||
\(26\) | − | 1.60890i | − | 0.315531i | ||||||
\(27\) | 3.07509 | + | 4.18853i | 0.591802 | + | 0.806084i | ||||
\(28\) | 16.1975i | 3.06103i | ||||||||
\(29\) | − | 5.77864i | − | 1.07307i | −0.843879 | − | 0.536533i | \(-0.819734\pi\) | ||
0.843879 | − | 0.536533i | \(-0.180266\pi\) | |||||||
\(30\) | 2.07281 | + | 9.67293i | 0.378442 | + | 1.76603i | ||||
\(31\) | − | 6.65258i | − | 1.19484i | −0.801929 | − | 0.597419i | \(-0.796193\pi\) | ||
0.801929 | − | 0.597419i | \(-0.203807\pi\) | |||||||
\(32\) | −2.91978 | −0.516149 | ||||||||
\(33\) | −1.20692 | − | 5.63217i | −0.210097 | − | 0.980434i | ||||
\(34\) | − | 16.6010i | − | 2.84706i | ||||||
\(35\) | 8.64461i | 1.46121i | ||||||||
\(36\) | −11.6929 | + | 5.25256i | −1.94882 | + | 0.875426i | ||||
\(37\) | 2.27593 | 0.374160 | 0.187080 | − | 0.982345i | \(-0.440098\pi\) | ||||
0.187080 | + | 0.982345i | \(0.440098\pi\) | |||||||
\(38\) | −17.7592 | −2.88093 | ||||||||
\(39\) | 1.08795 | − | 0.233137i | 0.174211 | − | 0.0373317i | ||||
\(40\) | −12.9812 | −2.05251 | ||||||||
\(41\) | −3.28305 | −0.512726 | −0.256363 | − | 0.966581i | \(-0.582524\pi\) | ||||
−0.256363 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(42\) | −16.0795 | + | 3.44569i | −2.48113 | + | 0.531681i | ||||
\(43\) | − | 1.72449i | − | 0.262982i | −0.991317 | − | 0.131491i | \(-0.958024\pi\) | ||
0.991317 | − | 0.131491i | \(-0.0419764\pi\) | |||||||
\(44\) | 14.2096 | 2.14217 | ||||||||
\(45\) | −6.24054 | + | 2.80330i | −0.930285 | + | 0.417891i | ||||
\(46\) | 10.0398i | 1.48029i | ||||||||
\(47\) | 3.84745i | 0.561209i | 0.959824 | + | 0.280604i | \(0.0905349\pi\) | ||||
−0.959824 | + | 0.280604i | \(0.909465\pi\) | |||||||
\(48\) | −2.07281 | − | 9.67293i | −0.299185 | − | 1.39617i | ||||
\(49\) | −7.37014 | −1.05288 | ||||||||
\(50\) | −0.501701 | −0.0709512 | ||||||||
\(51\) | 11.2257 | − | 2.40556i | 1.57192 | − | 0.336846i | ||||
\(52\) | 2.74482i | 0.380638i | ||||||||
\(53\) | −1.46035 | −0.200595 | −0.100297 | − | 0.994958i | \(-0.531979\pi\) | ||||
−0.100297 | + | 0.994958i | \(0.531979\pi\) | |||||||
\(54\) | −7.70176 | − | 10.4904i | −1.04808 | − | 1.42757i | ||||
\(55\) | 7.58366 | 1.02258 | ||||||||
\(56\) | − | 21.5790i | − | 2.88361i | ||||||
\(57\) | −2.57339 | − | 12.0089i | −0.340854 | − | 1.59062i | ||||
\(58\) | 14.4730i | 1.90039i | ||||||||
\(59\) | 6.37672i | 0.830178i | 0.909781 | + | 0.415089i | \(0.136249\pi\) | ||||
−0.909781 | + | 0.415089i | \(0.863751\pi\) | |||||||
\(60\) | −3.53626 | − | 16.5022i | −0.456529 | − | 2.13043i | ||||
\(61\) | 8.90249i | 1.13985i | 0.821698 | + | 0.569923i | \(0.193027\pi\) | ||||
−0.821698 | + | 0.569923i | \(0.806973\pi\) | |||||||
\(62\) | 16.6618i | 2.11605i | ||||||||
\(63\) | −4.65999 | − | 10.3738i | −0.587104 | − | 1.30698i | ||||
\(64\) | −4.11014 | −0.513768 | ||||||||
\(65\) | 1.46491i | 0.181700i | ||||||||
\(66\) | 3.02280 | + | 14.1061i | 0.372081 | + | 1.73634i | ||||
\(67\) | 2.41692 | − | 7.82039i | 0.295274 | − | 0.955413i | ||||
\(68\) | 28.3217i | 3.43451i | ||||||||
\(69\) | −6.78897 | + | 1.45481i | −0.817296 | + | 0.175138i | ||||
\(70\) | − | 21.6510i | − | 2.58779i | ||||||
\(71\) | 4.06748i | 0.482721i | 0.970435 | + | 0.241361i | \(0.0775937\pi\) | ||||
−0.970435 | + | 0.241361i | \(0.922406\pi\) | |||||||
\(72\) | 15.5778 | − | 6.99769i | 1.83587 | − | 0.824686i | ||||
\(73\) | −12.2408 | −1.43268 | −0.716341 | − | 0.697751i | \(-0.754184\pi\) | ||||
−0.716341 | + | 0.697751i | \(0.754184\pi\) | |||||||
\(74\) | −5.70020 | −0.662635 | ||||||||
\(75\) | −0.0726986 | − | 0.339253i | −0.00839451 | − | 0.0391736i | ||||
\(76\) | 30.2976 | 3.47538 | ||||||||
\(77\) | 12.6065i | 1.43664i | ||||||||
\(78\) | −2.72484 | + | 0.583905i | −0.308527 | + | 0.0661142i | ||||
\(79\) | − | 0.616736i | − | 0.0693882i | −0.999398 | − | 0.0346941i | \(-0.988954\pi\) | ||
0.999398 | − | 0.0346941i | \(-0.0110457\pi\) | |||||||
\(80\) | 13.0245 | 1.45619 | ||||||||
\(81\) | 5.97769 | − | 6.72809i | 0.664188 | − | 0.747566i | ||||
\(82\) | 8.22260 | 0.908034 | ||||||||
\(83\) | − | 13.9103i | − | 1.52685i | −0.645896 | − | 0.763426i | \(-0.723516\pi\) | ||
0.645896 | − | 0.763426i | \(-0.276484\pi\) | |||||||
\(84\) | 27.4320 | − | 5.87841i | 2.99308 | − | 0.641387i | ||||
\(85\) | 15.1154i | 1.63949i | ||||||||
\(86\) | 4.31909i | 0.465739i | ||||||||
\(87\) | −9.78672 | + | 2.09720i | −1.04925 | + | 0.224843i | ||||
\(88\) | −18.9306 | −2.01801 | ||||||||
\(89\) | 1.85514i | 0.196645i | 0.995155 | + | 0.0983225i | \(0.0313477\pi\) | ||||
−0.995155 | + | 0.0983225i | \(0.968652\pi\) | |||||||
\(90\) | 15.6298 | − | 7.02104i | 1.64753 | − | 0.740082i | ||||
\(91\) | −2.43516 | −0.255274 | ||||||||
\(92\) | − | 17.1281i | − | 1.78573i | ||||||
\(93\) | −11.2668 | + | 2.41437i | −1.16831 | + | 0.250358i | ||||
\(94\) | − | 9.63619i | − | 0.993897i | ||||||
\(95\) | 16.1699 | 1.65900 | ||||||||
\(96\) | 1.05965 | + | 4.94494i | 0.108150 | + | 0.504691i | ||||
\(97\) | − | 3.55200i | − | 0.360651i | −0.983607 | − | 0.180326i | \(-0.942285\pi\) | ||
0.983607 | − | 0.180326i | \(-0.0577151\pi\) | |||||||
\(98\) | 18.4590 | 1.86464 | ||||||||
\(99\) | −9.10063 | + | 4.08807i | −0.914648 | + | 0.410867i | ||||
\(100\) | 0.855912 | 0.0855912 | ||||||||
\(101\) | 9.53612 | 0.948879 | 0.474440 | − | 0.880288i | \(-0.342651\pi\) | ||||
0.474440 | + | 0.880288i | \(0.342651\pi\) | |||||||
\(102\) | −28.1156 | + | 6.02488i | −2.78386 | + | 0.596552i | ||||
\(103\) | 13.4883 | 1.32904 | 0.664521 | − | 0.747270i | \(-0.268636\pi\) | ||||
0.664521 | + | 0.747270i | \(0.268636\pi\) | |||||||
\(104\) | − | 3.65677i | − | 0.358575i | ||||||
\(105\) | 14.6405 | − | 3.13732i | 1.42877 | − | 0.306171i | ||||
\(106\) | 3.65754 | 0.355252 | ||||||||
\(107\) | − | 9.37985i | − | 0.906784i | −0.891311 | − | 0.453392i | \(-0.850214\pi\) | ||
0.891311 | − | 0.453392i | \(-0.149786\pi\) | |||||||
\(108\) | 13.1394 | + | 17.8969i | 1.26434 | + | 1.72213i | ||||
\(109\) | 15.2545i | 1.46112i | 0.682851 | + | 0.730558i | \(0.260740\pi\) | ||||
−0.682851 | + | 0.730558i | \(0.739260\pi\) | |||||||
\(110\) | −18.9938 | −1.81098 | ||||||||
\(111\) | −0.825984 | − | 3.85451i | −0.0783989 | − | 0.365854i | ||||
\(112\) | 21.6510i | 2.04582i | ||||||||
\(113\) | −6.65189 | −0.625757 | −0.312878 | − | 0.949793i | \(-0.601293\pi\) | ||||
−0.312878 | + | 0.949793i | \(0.601293\pi\) | |||||||
\(114\) | 6.44522 | + | 30.0771i | 0.603650 | + | 2.81698i | ||||
\(115\) | − | 9.14128i | − | 0.852429i | ||||||
\(116\) | − | 24.6912i | − | 2.29252i | ||||||
\(117\) | −0.789681 | − | 1.75794i | −0.0730060 | − | 0.162522i | ||||
\(118\) | − | 15.9709i | − | 1.47024i | ||||||
\(119\) | −25.1266 | −2.30335 | ||||||||
\(120\) | 4.71116 | + | 21.9850i | 0.430068 | + | 2.00695i | ||||
\(121\) | 0.0593167 | 0.00539243 | ||||||||
\(122\) | − | 22.2968i | − | 2.01866i | ||||||
\(123\) | 1.19149 | + | 5.56017i | 0.107433 | + | 0.501344i | ||||
\(124\) | − | 28.4254i | − | 2.55267i | ||||||
\(125\) | −10.9453 | −0.978977 | ||||||||
\(126\) | 11.6712 | + | 25.9818i | 1.03976 | + | 2.31465i | ||||
\(127\) | −3.67347 | −0.325967 | −0.162984 | − | 0.986629i | \(-0.552112\pi\) | ||||
−0.162984 | + | 0.986629i | \(0.552112\pi\) | |||||||
\(128\) | 16.1337 | 1.42603 | ||||||||
\(129\) | −2.92060 | + | 0.625854i | −0.257144 | + | 0.0551034i | ||||
\(130\) | − | 3.66897i | − | 0.321790i | ||||||
\(131\) | 3.00313i | 0.262385i | 0.991357 | + | 0.131192i | \(0.0418806\pi\) | ||||
−0.991357 | + | 0.131192i | \(0.958119\pi\) | |||||||
\(132\) | −5.15696 | − | 24.0653i | −0.448856 | − | 2.09462i | ||||
\(133\) | 26.8796i | 2.33076i | ||||||||
\(134\) | −6.05334 | + | 19.5867i | −0.522929 | + | 1.69203i | ||||
\(135\) | 7.01250 | + | 9.55161i | 0.603540 | + | 0.822072i | ||||
\(136\) | − | 37.7315i | − | 3.23545i | ||||||
\(137\) | −14.9061 | −1.27352 | −0.636758 | − | 0.771064i | \(-0.719725\pi\) | ||||
−0.636758 | + | 0.771064i | \(0.719725\pi\) | |||||||
\(138\) | 17.0034 | − | 3.64366i | 1.44743 | − | 0.310169i | ||||
\(139\) | − | 7.41193i | − | 0.628672i | −0.949312 | − | 0.314336i | \(-0.898218\pi\) | ||
0.949312 | − | 0.314336i | \(-0.101782\pi\) | |||||||
\(140\) | 36.9370i | 3.12175i | ||||||||
\(141\) | 6.51605 | − | 1.39633i | 0.548751 | − | 0.117592i | ||||
\(142\) | − | 10.1873i | − | 0.854896i | ||||||
\(143\) | 2.13630i | 0.178646i | ||||||||
\(144\) | −15.6298 | + | 7.02104i | −1.30249 | + | 0.585087i | ||||
\(145\) | − | 13.1777i | − | 1.09435i | ||||||
\(146\) | 30.6579 | 2.53727 | ||||||||
\(147\) | 2.67479 | + | 12.4821i | 0.220613 | + | 1.02951i | ||||
\(148\) | 9.72466 | 0.799362 | ||||||||
\(149\) | − | 13.6469i | − | 1.11800i | −0.829169 | − | 0.558998i | \(-0.811186\pi\) | ||
0.829169 | − | 0.558998i | \(-0.188814\pi\) | |||||||
\(150\) | 0.182078 | + | 0.849681i | 0.0148666 | + | 0.0693762i | ||||
\(151\) | −5.76883 | −0.469461 | −0.234730 | − | 0.972061i | \(-0.575421\pi\) | ||||
−0.234730 | + | 0.972061i | \(0.575421\pi\) | |||||||
\(152\) | −40.3639 | −3.27394 | ||||||||
\(153\) | −8.14813 | − | 18.1389i | −0.658738 | − | 1.46644i | ||||
\(154\) | − | 31.5738i | − | 2.54429i | ||||||
\(155\) | − | 15.1707i | − | 1.21854i | ||||||
\(156\) | 4.64863 | − | 0.996154i | 0.372188 | − | 0.0797562i | ||||
\(157\) | −15.6023 | −1.24520 | −0.622598 | − | 0.782542i | \(-0.713923\pi\) | ||||
−0.622598 | + | 0.782542i | \(0.713923\pi\) | |||||||
\(158\) | 1.54465i | 0.122886i | ||||||||
\(159\) | 0.529993 | + | 2.47325i | 0.0420312 | + | 0.196142i | ||||
\(160\) | −6.65832 | −0.526386 | ||||||||
\(161\) | 15.1958 | 1.19759 | ||||||||
\(162\) | −14.9715 | + | 16.8509i | −1.17627 | + | 1.32393i | ||||
\(163\) | 1.04302 | 0.0816958 | 0.0408479 | − | 0.999165i | \(-0.486994\pi\) | ||||
0.0408479 | + | 0.999165i | \(0.486994\pi\) | |||||||
\(164\) | −14.0279 | −1.09540 | ||||||||
\(165\) | −2.75228 | − | 12.8437i | −0.214265 | − | 0.999881i | ||||
\(166\) | 34.8392i | 2.70404i | ||||||||
\(167\) | 17.2185i | 1.33241i | 0.745768 | + | 0.666205i | \(0.232083\pi\) | ||||
−0.745768 | + | 0.666205i | \(0.767917\pi\) | |||||||
\(168\) | −36.5462 | + | 7.83148i | −2.81960 | + | 0.604212i | ||||
\(169\) | 12.5873 | 0.968257 | ||||||||
\(170\) | − | 37.8574i | − | 2.90353i | ||||||
\(171\) | −19.4044 | + | 8.71660i | −1.48389 | + | 0.666575i | ||||
\(172\) | − | 7.36845i | − | 0.561839i | ||||||
\(173\) | − | 7.53153i | − | 0.572611i | −0.958138 | − | 0.286306i | \(-0.907573\pi\) | ||
0.958138 | − | 0.286306i | \(-0.0924273\pi\) | |||||||
\(174\) | 24.5114 | − | 5.25256i | 1.85821 | − | 0.398195i | ||||
\(175\) | 0.759352i | 0.0574016i | ||||||||
\(176\) | 18.9938 | 1.43171 | ||||||||
\(177\) | 10.7996 | − | 2.31425i | 0.811749 | − | 0.173950i | ||||
\(178\) | − | 4.64633i | − | 0.348257i | ||||||
\(179\) | −20.1193 | −1.50379 | −0.751895 | − | 0.659283i | \(-0.770860\pi\) | ||||
−0.751895 | + | 0.659283i | \(0.770860\pi\) | |||||||
\(180\) | −26.6648 | + | 11.9780i | −1.98748 | + | 0.892790i | ||||
\(181\) | 1.69322 | 0.125856 | 0.0629280 | − | 0.998018i | \(-0.479956\pi\) | ||||
0.0629280 | + | 0.998018i | \(0.479956\pi\) | |||||||
\(182\) | 6.09901 | 0.452089 | ||||||||
\(183\) | 15.0773 | − | 3.23091i | 1.11454 | − | 0.238836i | ||||
\(184\) | 22.8188i | 1.68222i | ||||||||
\(185\) | 5.19007 | 0.381581 | ||||||||
\(186\) | 28.2185 | − | 6.04693i | 2.06908 | − | 0.443383i | ||||
\(187\) | 22.0428i | 1.61193i | ||||||||
\(188\) | 16.4395i | 1.19898i | ||||||||
\(189\) | −15.8779 | + | 11.6571i | −1.15495 | + | 0.847926i | ||||
\(190\) | −40.4985 | −2.93807 | ||||||||
\(191\) | 0.993418 | 0.0718812 | 0.0359406 | − | 0.999354i | \(-0.488557\pi\) | ||||
0.0359406 | + | 0.999354i | \(0.488557\pi\) | |||||||
\(192\) | 1.49166 | + | 6.96095i | 0.107651 | + | 0.502363i | ||||
\(193\) | −14.1028 | −1.01514 | −0.507571 | − | 0.861610i | \(-0.669457\pi\) | ||||
−0.507571 | + | 0.861610i | \(0.669457\pi\) | |||||||
\(194\) | 8.89621i | 0.638711i | ||||||||
\(195\) | 2.48098 | − | 0.531649i | 0.177667 | − | 0.0380722i | ||||
\(196\) | −31.4914 | −2.24939 | ||||||||
\(197\) | 10.3052 | 0.734213 | 0.367106 | − | 0.930179i | \(-0.380349\pi\) | ||||
0.367106 | + | 0.930179i | \(0.380349\pi\) | |||||||
\(198\) | 22.7931 | − | 10.2388i | 1.61984 | − | 0.727643i | ||||
\(199\) | 5.03684 | 0.357052 | 0.178526 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178526 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(200\) | −1.14028 | −0.0806302 | ||||||||
\(201\) | −14.1218 | − | 1.25512i | −0.996074 | − | 0.0885291i | ||||
\(202\) | −23.8838 | −1.68046 | ||||||||
\(203\) | 21.9056 | 1.53748 | ||||||||
\(204\) | 47.9657 | − | 10.2786i | 3.35827 | − | 0.719644i | ||||
\(205\) | −7.48672 | −0.522895 | ||||||||
\(206\) | −33.7823 | −2.35372 | ||||||||
\(207\) | 4.92773 | + | 10.9698i | 0.342501 | + | 0.762456i | ||||
\(208\) | 3.66897i | 0.254397i | ||||||||
\(209\) | 23.5807 | 1.63111 | ||||||||
\(210\) | −36.6681 | + | 7.85761i | −2.53034 | + | 0.542227i | ||||
\(211\) | −3.86760 | −0.266257 | −0.133128 | − | 0.991099i | \(-0.542502\pi\) | ||||
−0.133128 | + | 0.991099i | \(0.542502\pi\) | |||||||
\(212\) | −6.23984 | −0.428554 | ||||||||
\(213\) | 6.88869 | − | 1.47618i | 0.472006 | − | 0.101146i | ||||
\(214\) | 23.4924i | 1.60591i | ||||||||
\(215\) | − | 3.93256i | − | 0.268198i | ||||||
\(216\) | −17.5048 | − | 23.8431i | −1.19105 | − | 1.62231i | ||||
\(217\) | 25.2186 | 1.71195 | ||||||||
\(218\) | − | 38.2059i | − | 2.58763i | ||||||
\(219\) | 4.44247 | + | 20.7311i | 0.300194 | + | 1.40088i | ||||
\(220\) | 32.4037 | 2.18466 | ||||||||
\(221\) | −4.25795 | −0.286421 | ||||||||
\(222\) | 2.06873 | + | 9.65387i | 0.138844 | + | 0.647925i | ||||
\(223\) | 0.688187 | 0.0460844 | 0.0230422 | − | 0.999734i | \(-0.492665\pi\) | ||||
0.0230422 | + | 0.999734i | \(0.492665\pi\) | |||||||
\(224\) | − | 11.0683i | − | 0.739531i | ||||||
\(225\) | −0.548176 | + | 0.246245i | −0.0365451 | + | 0.0164163i | ||||
\(226\) | 16.6601 | 1.10821 | ||||||||
\(227\) | − | 27.5016i | − | 1.82534i | −0.408692 | − | 0.912672i | \(-0.634015\pi\) | ||
0.408692 | − | 0.912672i | \(-0.365985\pi\) | |||||||
\(228\) | −10.9957 | − | 51.3122i | −0.728207 | − | 3.39823i | ||||
\(229\) | − | 20.9485i | − | 1.38432i | −0.721745 | − | 0.692159i | \(-0.756660\pi\) | ||
0.721745 | − | 0.692159i | \(-0.243340\pi\) | |||||||
\(230\) | 22.8949i | 1.50965i | ||||||||
\(231\) | 21.3504 | − | 4.57518i | 1.40475 | − | 0.301025i | ||||
\(232\) | 32.8947i | 2.15964i | ||||||||
\(233\) | 27.8137 | 1.82214 | 0.911069 | − | 0.412253i | \(-0.135258\pi\) | ||||
0.911069 | + | 0.412253i | \(0.135258\pi\) | |||||||
\(234\) | 1.97781 | + | 4.40288i | 0.129293 | + | 0.287825i | ||||
\(235\) | 8.77381i | 0.572340i | ||||||||
\(236\) | 27.2467i | 1.77361i | ||||||||
\(237\) | −1.04451 | + | 0.223827i | −0.0678479 | + | 0.0145391i | ||||
\(238\) | 62.9312 | 4.07922 | ||||||||
\(239\) | 0.389883 | 0.0252194 | 0.0126097 | − | 0.999920i | \(-0.495986\pi\) | ||||
0.0126097 | + | 0.999920i | \(0.495986\pi\) | |||||||
\(240\) | −4.72688 | − | 22.0583i | −0.305119 | − | 1.42386i | ||||
\(241\) | −17.0093 | −1.09566 | −0.547832 | − | 0.836588i | \(-0.684547\pi\) | ||||
−0.547832 | + | 0.836588i | \(0.684547\pi\) | |||||||
\(242\) | −0.148563 | −0.00954996 | ||||||||
\(243\) | −13.5641 | − | 7.68205i | −0.870140 | − | 0.492804i | ||||
\(244\) | 38.0389i | 2.43519i | ||||||||
\(245\) | −16.8070 | −1.07376 | ||||||||
\(246\) | −2.98416 | − | 13.9258i | −0.190263 | − | 0.887877i | ||||
\(247\) | 4.55501i | 0.289829i | ||||||||
\(248\) | 37.8695i | 2.40472i | ||||||||
\(249\) | −23.5585 | + | 5.04834i | −1.49296 | + | 0.319926i | ||||
\(250\) | 27.4132 | 1.73376 | ||||||||
\(251\) | 10.9321 | 0.690031 | 0.345016 | − | 0.938597i | \(-0.387874\pi\) | ||||
0.345016 | + | 0.938597i | \(0.387874\pi\) | |||||||
\(252\) | −19.9114 | − | 44.3256i | −1.25430 | − | 2.79225i | ||||
\(253\) | − | 13.3308i | − | 0.838101i | ||||||
\(254\) | 9.20043 | 0.577286 | ||||||||
\(255\) | 25.5994 | − | 5.48569i | 1.60310 | − | 0.343527i | ||||
\(256\) | −32.1875 | −2.01172 | ||||||||
\(257\) | − | 23.8590i | − | 1.48829i | −0.668020 | − | 0.744143i | \(-0.732858\pi\) | ||
0.668020 | − | 0.744143i | \(-0.267142\pi\) | |||||||
\(258\) | 7.31481 | − | 1.56749i | 0.455400 | − | 0.0975878i | ||||
\(259\) | 8.62757i | 0.536091i | ||||||||
\(260\) | 6.25933i | 0.388187i | ||||||||
\(261\) | 7.10363 | + | 15.8137i | 0.439704 | + | 0.978842i | ||||
\(262\) | − | 7.52154i | − | 0.464682i | ||||||
\(263\) | 12.8212i | 0.790587i | 0.918555 | + | 0.395294i | \(0.129357\pi\) | ||||
−0.918555 | + | 0.395294i | \(0.870643\pi\) | |||||||
\(264\) | 6.87033 | + | 32.0609i | 0.422839 | + | 1.97321i | ||||
\(265\) | −3.33021 | −0.204573 | ||||||||
\(266\) | − | 67.3217i | − | 4.12776i | ||||||
\(267\) | 3.14188 | − | 0.673273i | 0.192280 | − | 0.0412036i | ||||
\(268\) | 10.3271 | − | 33.4152i | 0.630829 | − | 2.04116i | ||||
\(269\) | 12.6656i | 0.772235i | 0.922450 | + | 0.386117i | \(0.126184\pi\) | ||||
−0.922450 | + | 0.386117i | \(0.873816\pi\) | |||||||
\(270\) | −17.5633 | − | 23.9226i | −1.06887 | − | 1.45588i | ||||
\(271\) | − | 10.5222i | − | 0.639180i | −0.947556 | − | 0.319590i | \(-0.896455\pi\) | ||
0.947556 | − | 0.319590i | \(-0.103545\pi\) | |||||||
\(272\) | 37.8574i | 2.29544i | ||||||||
\(273\) | 0.883773 | + | 4.12419i | 0.0534884 | + | 0.249608i | ||||
\(274\) | 37.3333 | 2.25539 | ||||||||
\(275\) | 0.666157 | 0.0401708 | ||||||||
\(276\) | −29.0081 | + | 6.21615i | −1.74608 | + | 0.374169i | ||||
\(277\) | 10.5955 | 0.636625 | 0.318312 | − | 0.947986i | \(-0.396884\pi\) | ||||
0.318312 | + | 0.947986i | \(0.396884\pi\) | |||||||
\(278\) | 18.5636i | 1.11337i | ||||||||
\(279\) | 8.17795 | + | 18.2053i | 0.489601 | + | 1.08992i | ||||
\(280\) | − | 49.2091i | − | 2.94081i | ||||||
\(281\) | −20.0851 | −1.19818 | −0.599089 | − | 0.800683i | \(-0.704470\pi\) | ||||
−0.599089 | + | 0.800683i | \(0.704470\pi\) | |||||||
\(282\) | −16.3199 | + | 3.49718i | −0.971834 | + | 0.208254i | ||||
\(283\) | 11.8682 | 0.705490 | 0.352745 | − | 0.935719i | \(-0.385248\pi\) | ||||
0.352745 | + | 0.935719i | \(0.385248\pi\) | |||||||
\(284\) | 17.3797i | 1.03129i | ||||||||
\(285\) | −5.86841 | − | 27.3854i | −0.347615 | − | 1.62217i | ||||
\(286\) | − | 5.35049i | − | 0.316381i | ||||||
\(287\) | − | 12.4454i | − | 0.734626i | ||||||
\(288\) | 7.99019 | − | 3.58926i | 0.470827 | − | 0.211499i | ||||
\(289\) | −26.9346 | −1.58439 | ||||||||
\(290\) | 33.0044i | 1.93809i | ||||||||
\(291\) | −6.01568 | + | 1.28910i | −0.352645 | + | 0.0755684i | ||||
\(292\) | −52.3031 | −3.06081 | ||||||||
\(293\) | − | 0.0262169i | − | 0.00153160i | −1.00000 | 0.000765802i | \(-0.999756\pi\) | |||
1.00000 | 0.000765802i | \(-0.000243763\pi\) | ||||||||
\(294\) | −6.69917 | − | 31.2622i | −0.390704 | − | 1.82325i | ||||
\(295\) | 14.5416i | 0.846644i | ||||||||
\(296\) | −12.9556 | −0.753030 | ||||||||
\(297\) | 10.2264 | + | 13.9292i | 0.593395 | + | 0.808254i | ||||
\(298\) | 34.1795i | 1.97996i | ||||||||
\(299\) | 2.57507 | 0.148920 | ||||||||
\(300\) | −0.310629 | − | 1.44957i | −0.0179342 | − | 0.0836912i | ||||
\(301\) | 6.53718 | 0.376797 | ||||||||
\(302\) | 14.4484 | 0.831412 | ||||||||
\(303\) | −3.46087 | − | 16.1504i | −0.198822 | − | 0.927816i | ||||
\(304\) | 40.4985 | 2.32275 | ||||||||
\(305\) | 20.3014i | 1.16246i | ||||||||
\(306\) | 20.4075 | + | 45.4300i | 1.16662 | + | 2.59706i | ||||
\(307\) | −20.5808 | −1.17461 | −0.587304 | − | 0.809367i | \(-0.699811\pi\) | ||||
−0.587304 | + | 0.809367i | \(0.699811\pi\) | |||||||
\(308\) | 53.8655i | 3.06927i | ||||||||
\(309\) | −4.89520 | − | 22.8438i | −0.278478 | − | 1.29954i | ||||
\(310\) | 37.9959i | 2.15802i | ||||||||
\(311\) | −29.9008 | −1.69552 | −0.847761 | − | 0.530379i | \(-0.822050\pi\) | ||||
−0.847761 | + | 0.530379i | \(0.822050\pi\) | |||||||
\(312\) | −6.19311 | + | 1.32712i | −0.350616 | + | 0.0751334i | ||||
\(313\) | − | 18.2037i | − | 1.02893i | −0.857510 | − | 0.514467i | \(-0.827990\pi\) | ||
0.857510 | − | 0.514467i | \(-0.172010\pi\) | |||||||
\(314\) | 39.0769 | 2.20523 | ||||||||
\(315\) | −10.6267 | − | 23.6566i | −0.598749 | − | 1.33290i | ||||
\(316\) | − | 2.63521i | − | 0.148242i | ||||||
\(317\) | − | 14.4179i | − | 0.809789i | −0.914363 | − | 0.404895i | \(-0.867308\pi\) | ||
0.914363 | − | 0.404895i | \(-0.132692\pi\) | |||||||
\(318\) | −1.32740 | − | 6.19441i | −0.0744370 | − | 0.347366i | ||||
\(319\) | − | 19.2172i | − | 1.07596i | ||||||
\(320\) | −9.37285 | −0.523958 | ||||||||
\(321\) | −15.8857 | + | 3.40415i | −0.886655 | + | 0.190001i | ||||
\(322\) | −38.0588 | −2.12093 | ||||||||
\(323\) | 46.9998i | 2.61514i | ||||||||
\(324\) | 25.5417 | − | 28.7480i | 1.41898 | − | 1.59711i | ||||
\(325\) | 0.128680i | 0.00713786i | ||||||||
\(326\) | −2.61231 | −0.144683 | ||||||||
\(327\) | 25.8351 | − | 5.53619i | 1.42868 | − | 0.306152i | ||||
\(328\) | 18.6886 | 1.03191 | ||||||||
\(329\) | −14.5849 | −0.804092 | ||||||||
\(330\) | 6.89325 | + | 32.1679i | 0.379461 | + | 1.77078i | ||||
\(331\) | − | 28.8976i | − | 1.58836i | −0.607686 | − | 0.794178i | \(-0.707902\pi\) | ||
0.607686 | − | 0.794178i | \(-0.292098\pi\) | |||||||
\(332\) | − | 59.4363i | − | 3.26199i | ||||||
\(333\) | −6.22824 | + | 2.79777i | −0.341306 | + | 0.153317i | ||||
\(334\) | − | 43.1249i | − | 2.35969i | ||||||
\(335\) | 5.51160 | − | 17.8338i | 0.301131 | − | 0.974363i | ||||
\(336\) | 36.6681 | − | 7.85761i | 2.00041 | − | 0.428668i | ||||
\(337\) | 9.68749i | 0.527711i | 0.964562 | + | 0.263856i | \(0.0849943\pi\) | ||||
−0.964562 | + | 0.263856i | \(0.915006\pi\) | |||||||
\(338\) | −31.5258 | −1.71478 | ||||||||
\(339\) | 2.41412 | + | 11.2656i | 0.131117 | + | 0.611866i | ||||
\(340\) | 64.5854i | 3.50264i | ||||||||
\(341\) | − | 22.1235i | − | 1.19806i | ||||||
\(342\) | 48.5995 | − | 21.8313i | 2.62796 | − | 1.18050i | ||||
\(343\) | − | 1.40314i | − | 0.0757622i | ||||||
\(344\) | 9.81658i | 0.529274i | ||||||||
\(345\) | −15.4817 | + | 3.31757i | −0.833506 | + | 0.178612i | ||||
\(346\) | 18.8632i | 1.01409i | ||||||||
\(347\) | −24.1144 | −1.29453 | −0.647265 | − | 0.762265i | \(-0.724087\pi\) | ||||
−0.647265 | + | 0.762265i | \(0.724087\pi\) | |||||||
\(348\) | −41.8170 | + | 8.96097i | −2.24163 | + | 0.480358i | ||||
\(349\) | 3.99596 | 0.213899 | 0.106949 | − | 0.994264i | \(-0.465892\pi\) | ||||
0.106949 | + | 0.994264i | \(0.465892\pi\) | |||||||
\(350\) | − | 1.90185i | − | 0.101658i | ||||||
\(351\) | −2.69066 | + | 1.97540i | −0.143617 | + | 0.105439i | ||||
\(352\) | −9.70988 | −0.517538 | ||||||||
\(353\) | 12.0605 | 0.641917 | 0.320958 | − | 0.947093i | \(-0.395995\pi\) | ||||
0.320958 | + | 0.947093i | \(0.395995\pi\) | |||||||
\(354\) | −27.0483 | + | 5.79618i | −1.43760 | + | 0.308064i | ||||
\(355\) | 9.27557i | 0.492296i | ||||||||
\(356\) | 7.92673i | 0.420116i | ||||||||
\(357\) | 9.11900 | + | 42.5545i | 0.482629 | + | 2.25222i | ||||
\(358\) | 50.3901 | 2.66320 | ||||||||
\(359\) | 20.2456i | 1.06852i | 0.845319 | + | 0.534262i | \(0.179411\pi\) | ||||
−0.845319 | + | 0.534262i | \(0.820589\pi\) | |||||||
\(360\) | 35.5240 | − | 15.9577i | 1.87228 | − | 0.841043i | ||||
\(361\) | 31.2788 | 1.64626 | ||||||||
\(362\) | −4.24077 | −0.222890 | ||||||||
\(363\) | −0.0215273 | − | 0.100459i | −0.00112989 | − | 0.00527273i | ||||
\(364\) | −10.4050 | −0.545372 | ||||||||
\(365\) | −27.9142 | −1.46110 | ||||||||
\(366\) | −37.7620 | + | 8.09201i | −1.97385 | + | 0.422976i | ||||
\(367\) | − | 5.72356i | − | 0.298768i | −0.988779 | − | 0.149384i | \(-0.952271\pi\) | ||
0.988779 | − | 0.149384i | \(-0.0477290\pi\) | |||||||
\(368\) | − | 22.8949i | − | 1.19348i | ||||||
\(369\) | 8.98430 | − | 4.03582i | 0.467704 | − | 0.210096i | ||||
\(370\) | −12.9989 | −0.675778 | ||||||||
\(371\) | − | 5.53589i | − | 0.287409i | ||||||
\(372\) | −48.1413 | + | 10.3162i | −2.49601 | + | 0.534870i | ||||
\(373\) | 23.0024i | 1.19102i | 0.803349 | + | 0.595509i | \(0.203050\pi\) | ||||
−0.803349 | + | 0.595509i | \(0.796950\pi\) | |||||||
\(374\) | − | 55.2077i | − | 2.85472i | ||||||
\(375\) | 3.97229 | + | 18.5370i | 0.205128 | + | 0.957245i | ||||
\(376\) | − | 21.9015i | − | 1.12948i | ||||||
\(377\) | 3.71213 | 0.191184 | ||||||||
\(378\) | 39.7671 | − | 29.1958i | 2.04540 | − | 1.50167i | ||||
\(379\) | − | 6.92189i | − | 0.355554i | −0.984071 | − | 0.177777i | \(-0.943109\pi\) | ||
0.984071 | − | 0.177777i | \(-0.0568905\pi\) | |||||||
\(380\) | 69.0914 | 3.54431 | ||||||||
\(381\) | 1.33318 | + | 6.22139i | 0.0683009 | + | 0.318731i | ||||
\(382\) | −2.48808 | −0.127301 | ||||||||
\(383\) | 24.2988 | 1.24161 | 0.620806 | − | 0.783965i | \(-0.286806\pi\) | ||||
0.620806 | + | 0.783965i | \(0.286806\pi\) | |||||||
\(384\) | −5.85526 | − | 27.3240i | −0.298800 | − | 1.39437i | ||||
\(385\) | 28.7481i | 1.46514i | ||||||||
\(386\) | 35.3214 | 1.79781 | ||||||||
\(387\) | 2.11990 | + | 4.71919i | 0.107760 | + | 0.239890i | ||||
\(388\) | − | 15.1771i | − | 0.770502i | ||||||
\(389\) | 19.0497i | 0.965858i | 0.875659 | + | 0.482929i | \(0.160427\pi\) | ||||
−0.875659 | + | 0.482929i | \(0.839573\pi\) | |||||||
\(390\) | −6.21377 | + | 1.33155i | −0.314647 | + | 0.0674256i | ||||
\(391\) | 26.5703 | 1.34372 | ||||||||
\(392\) | 41.9542 | 2.11901 | ||||||||
\(393\) | 5.08611 | − | 1.08990i | 0.256560 | − | 0.0549783i | ||||
\(394\) | −25.8099 | −1.30029 | ||||||||
\(395\) | − | 1.40642i | − | 0.0707645i | ||||||
\(396\) | −38.8855 | + | 17.4677i | −1.95407 | + | 0.877783i | ||||
\(397\) | 2.97569 | 0.149346 | 0.0746729 | − | 0.997208i | \(-0.476209\pi\) | ||||
0.0746729 | + | 0.997208i | \(0.476209\pi\) | |||||||
\(398\) | −12.6151 | −0.632337 | ||||||||
\(399\) | 45.5234 | − | 9.75521i | 2.27902 | − | 0.488371i | ||||
\(400\) | 1.14409 | 0.0572044 | ||||||||
\(401\) | −13.5663 | −0.677470 | −0.338735 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338735 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(402\) | 35.3689 | + | 3.14352i | 1.76404 | + | 0.156785i | ||||
\(403\) | 4.27353 | 0.212880 | ||||||||
\(404\) | 40.7463 | 2.02720 | ||||||||
\(405\) | 13.6316 | − | 15.3429i | 0.677362 | − | 0.762394i | ||||
\(406\) | −54.8641 | −2.72286 | ||||||||
\(407\) | 7.56872 | 0.375167 | ||||||||
\(408\) | −63.9021 | + | 13.6936i | −3.16362 | + | 0.677933i | ||||
\(409\) | 0.807186i | 0.0399128i | 0.999801 | + | 0.0199564i | \(0.00635274\pi\) | ||||
−0.999801 | + | 0.0199564i | \(0.993647\pi\) | |||||||
\(410\) | 18.7510 | 0.926044 | ||||||||
\(411\) | 5.40976 | + | 25.2450i | 0.266844 | + | 1.24525i | ||||
\(412\) | 57.6333 | 2.83939 | ||||||||
\(413\) | −24.1728 | −1.18947 | ||||||||
\(414\) | −12.3418 | − | 27.4746i | −0.606567 | − | 1.35030i | ||||
\(415\) | − | 31.7213i | − | 1.55714i | ||||||
\(416\) | − | 1.87563i | − | 0.0919603i | ||||||
\(417\) | −12.5529 | + | 2.68995i | −0.614716 | + | 0.131728i | ||||
\(418\) | −59.0594 | −2.88869 | ||||||||
\(419\) | 0.0609183i | 0.00297606i | 0.999999 | + | 0.00148803i | \(0.000473654\pi\) | ||||
−0.999999 | + | 0.00148803i | \(0.999526\pi\) | |||||||
\(420\) | 62.5566 | − | 13.4052i | 3.05245 | − | 0.654109i | ||||
\(421\) | 9.58973 | 0.467375 | 0.233687 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233687 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(422\) | 9.68665 | 0.471539 | ||||||||
\(423\) | −4.72964 | − | 10.5288i | −0.229963 | − | 0.511930i | ||||
\(424\) | 8.31299 | 0.403714 | ||||||||
\(425\) | 1.32775i | 0.0644053i | ||||||||
\(426\) | −17.2532 | + | 3.69718i | −0.835919 | + | 0.179129i | ||||
\(427\) | −33.7475 | −1.63316 | ||||||||
\(428\) | − | 40.0786i | − | 1.93727i | ||||||
\(429\) | 3.61803 | − | 0.775308i | 0.174680 | − | 0.0374322i | ||||
\(430\) | 9.84933i | 0.474977i | ||||||||
\(431\) | 0.500789i | 0.0241222i | 0.999927 | + | 0.0120611i | \(0.00383926\pi\) | ||||
−0.999927 | + | 0.0120611i | \(0.996161\pi\) | |||||||
\(432\) | 17.5633 | + | 23.9226i | 0.845012 | + | 1.15098i | ||||
\(433\) | 3.88698i | 0.186796i | 0.995629 | + | 0.0933981i | \(0.0297729\pi\) | ||||
−0.995629 | + | 0.0933981i | \(0.970227\pi\) | |||||||
\(434\) | −63.1615 | −3.03185 | ||||||||
\(435\) | −22.3178 | + | 4.78249i | −1.07006 | + | 0.229303i | ||||
\(436\) | 65.1800i | 3.12156i | ||||||||
\(437\) | − | 28.4240i | − | 1.35970i | ||||||
\(438\) | −11.1264 | − | 51.9223i | −0.531642 | − | 2.48095i | ||||
\(439\) | −25.8449 | −1.23351 | −0.616755 | − | 0.787155i | \(-0.711553\pi\) | ||||
−0.616755 | + | 0.787155i | \(0.711553\pi\) | |||||||
\(440\) | −43.1697 | −2.05803 | ||||||||
\(441\) | 20.1690 | − | 9.06005i | 0.960426 | − | 0.431431i | ||||
\(442\) | 10.6643 | 0.507249 | ||||||||
\(443\) | −0.892276 | −0.0423933 | −0.0211967 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211967 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(444\) | −3.52929 | − | 16.4697i | −0.167493 | − | 0.781618i | ||||
\(445\) | 4.23051i | 0.200545i | ||||||||
\(446\) | −1.72361 | −0.0816152 | ||||||||
\(447\) | −23.1124 | + | 4.95275i | −1.09318 | + | 0.234257i | ||||
\(448\) | − | 15.5807i | − | 0.736120i | ||||||
\(449\) | − | 14.0303i | − | 0.662130i | −0.943608 | − | 0.331065i | \(-0.892592\pi\) | ||
0.943608 | − | 0.331065i | \(-0.107408\pi\) | |||||||
\(450\) | 1.37294 | − | 0.616736i | 0.0647211 | − | 0.0290732i | ||||
\(451\) | −10.9180 | −0.514106 | ||||||||
\(452\) | −28.4224 | −1.33688 | ||||||||
\(453\) | 2.09364 | + | 9.77010i | 0.0983676 | + | 0.459039i | ||||
\(454\) | 68.8795i | 3.23267i | ||||||||
\(455\) | −5.55319 | −0.260338 | ||||||||
\(456\) | 14.6489 | + | 68.3603i | 0.685999 | + | 3.20127i | ||||
\(457\) | 6.57517 | 0.307574 | 0.153787 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153787 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(458\) | 52.4669i | 2.45162i | ||||||||
\(459\) | −27.7629 | + | 20.3827i | −1.29586 | + | 0.951383i | ||||
\(460\) | − | 39.0592i | − | 1.82114i | ||||||
\(461\) | 22.9451i | 1.06866i | 0.845276 | + | 0.534330i | \(0.179436\pi\) | ||||
−0.845276 | + | 0.534330i | \(0.820564\pi\) | |||||||
\(462\) | −53.4734 | + | 11.4588i | −2.48781 | + | 0.533113i | ||||
\(463\) | 11.9996i | 0.557668i | 0.960339 | + | 0.278834i | \(0.0899480\pi\) | ||||
−0.960339 | + | 0.278834i | \(0.910052\pi\) | |||||||
\(464\) | − | 33.0044i | − | 1.53219i | ||||||
\(465\) | −25.6931 | + | 5.50577i | −1.19149 | + | 0.255324i | ||||
\(466\) | −69.6613 | −3.22700 | ||||||||
\(467\) | − | 13.9254i | − | 0.644391i | −0.946673 | − | 0.322195i | \(-0.895579\pi\) | ||
0.946673 | − | 0.322195i | \(-0.104421\pi\) | |||||||
\(468\) | −3.37418 | − | 7.51140i | −0.155971 | − | 0.347214i | ||||
\(469\) | 29.6455 | + | 9.16207i | 1.36890 | + | 0.423065i | ||||
\(470\) | − | 21.9746i | − | 1.01361i | ||||||
\(471\) | 5.66241 | + | 26.4240i | 0.260910 | + | 1.21756i | ||||
\(472\) | − | 36.2992i | − | 1.67081i | ||||||
\(473\) | − | 5.73488i | − | 0.263690i | ||||||
\(474\) | 2.61603 | − | 0.560589i | 0.120158 | − | 0.0257487i | ||||
\(475\) | 1.42038 | 0.0651716 | ||||||||
\(476\) | −107.362 | −4.92093 | ||||||||
\(477\) | 3.99636 | − | 1.79519i | 0.182981 | − | 0.0821963i | ||||
\(478\) | −0.976487 | −0.0446635 | ||||||||
\(479\) | 28.2608i | 1.29127i | 0.763646 | + | 0.645635i | \(0.223407\pi\) | ||||
−0.763646 | + | 0.645635i | \(0.776593\pi\) | |||||||
\(480\) | 2.41645 | + | 11.2765i | 0.110295 | + | 0.514701i | ||||
\(481\) | 1.46203i | 0.0666627i | ||||||||
\(482\) | 42.6009 | 1.94042 | ||||||||
\(483\) | −5.51488 | − | 25.7356i | −0.250936 | − | 1.17101i | ||||
\(484\) | 0.253451 | 0.0115205 | ||||||||
\(485\) | − | 8.10006i | − | 0.367805i | ||||||
\(486\) | 33.9723 | + | 19.2402i | 1.54101 | + | 0.872753i | ||||
\(487\) | − | 19.6516i | − | 0.890498i | −0.895407 | − | 0.445249i | \(-0.853115\pi\) | ||
0.895407 | − | 0.445249i | \(-0.146885\pi\) | |||||||
\(488\) | − | 50.6771i | − | 2.29404i | ||||||
\(489\) | −0.378536 | − | 1.76646i | −0.0171180 | − | 0.0798823i | ||||
\(490\) | 42.0942 | 1.90162 | ||||||||
\(491\) | 6.08065i | 0.274416i | 0.990542 | + | 0.137208i | \(0.0438128\pi\) | ||||
−0.990542 | + | 0.137208i | \(0.956187\pi\) | |||||||
\(492\) | 5.09104 | + | 23.7577i | 0.229522 | + | 1.07108i | ||||
\(493\) | 38.3027 | 1.72507 | ||||||||
\(494\) | − | 11.4083i | − | 0.513285i | ||||||
\(495\) | −20.7533 | + | 9.32252i | −0.932790 | + | 0.419016i | ||||
\(496\) | − | 37.9959i | − | 1.70607i | ||||||
\(497\) | −15.4190 | −0.691637 | ||||||||
\(498\) | 59.0037 | − | 12.6439i | 2.64402 | − | 0.566587i | ||||
\(499\) | − | 33.0747i | − | 1.48063i | −0.672263 | − | 0.740313i | \(-0.734677\pi\) | ||
0.672263 | − | 0.740313i | \(-0.265323\pi\) | |||||||
\(500\) | −46.7675 | −2.09150 | ||||||||
\(501\) | 29.1613 | − | 6.24899i | 1.30283 | − | 0.279184i | ||||
\(502\) | −27.3803 | −1.22204 | ||||||||
\(503\) | 27.5056 | 1.22641 | 0.613206 | − | 0.789923i | \(-0.289879\pi\) | ||||
0.613206 | + | 0.789923i | \(0.289879\pi\) | |||||||
\(504\) | 26.5268 | + | 59.0525i | 1.18160 | + | 2.63041i | ||||
\(505\) | 21.7464 | 0.967700 | ||||||||
\(506\) | 33.3878i | 1.48427i | ||||||||
\(507\) | −4.56822 | − | 21.3179i | −0.202882 | − | 0.946763i | ||||
\(508\) | −15.6961 | −0.696402 | ||||||||
\(509\) | − | 26.5494i | − | 1.17678i | −0.808576 | − | 0.588392i | \(-0.799761\pi\) | ||
0.808576 | − | 0.588392i | \(-0.200239\pi\) | |||||||
\(510\) | −64.1153 | + | 13.7393i | −2.83907 | + | 0.608385i | ||||
\(511\) | − | 46.4025i | − | 2.05273i | ||||||
\(512\) | 48.3483 | 2.13671 | ||||||||
\(513\) | 21.8047 | + | 29.6999i | 0.962703 | + | 1.31128i | ||||
\(514\) | 59.7565i | 2.63575i | ||||||||
\(515\) | 30.7590 | 1.35540 | ||||||||
\(516\) | −12.4792 | + | 2.67417i | −0.549367 | + | 0.117724i | ||||
\(517\) | 12.7949i | 0.562720i | ||||||||
\(518\) | − | 21.6083i | − | 0.949414i | ||||||
\(519\) | −12.7554 | + | 2.73336i | −0.559900 | + | 0.119981i | ||||
\(520\) | − | 8.33896i | − | 0.365688i | ||||||
\(521\) | 19.0527 | 0.834715 | 0.417358 | − | 0.908742i | \(-0.362956\pi\) | ||||
0.417358 | + | 0.908742i | \(0.362956\pi\) | |||||||
\(522\) | −17.7915 | − | 39.6064i | −0.778712 | − | 1.73352i | ||||
\(523\) | −30.2265 | −1.32171 | −0.660856 | − | 0.750513i | \(-0.729807\pi\) | ||||
−0.660856 | + | 0.750513i | \(0.729807\pi\) | |||||||
\(524\) | 12.8319i | 0.560564i | ||||||||
\(525\) | 1.28604 | − | 0.275586i | 0.0561274 | − | 0.0120275i | ||||
\(526\) | − | 32.1114i | − | 1.40013i | ||||||
\(527\) | 44.0954 | 1.92083 | ||||||||
\(528\) | −6.89325 | − | 32.1679i | −0.299990 | − | 1.39993i | ||||
\(529\) | 6.93116 | 0.301355 | ||||||||
\(530\) | 8.34072 | 0.362298 | ||||||||
\(531\) | −7.83884 | − | 17.4504i | −0.340177 | − | 0.757281i | ||||
\(532\) | 114.852i | 4.97948i | ||||||||
\(533\) | − | 2.10899i | − | 0.0913504i | ||||||
\(534\) | −7.86903 | + | 1.68625i | −0.340526 | + | 0.0729714i | ||||
\(535\) | − | 21.3900i | − | 0.924770i | ||||||
\(536\) | −13.7582 | + | 44.5173i | −0.594266 | + | 1.92285i | ||||
\(537\) | 7.30175 | + | 34.0742i | 0.315094 | + | 1.47041i | ||||
\(538\) | − | 31.7218i | − | 1.36762i | ||||||
\(539\) | −24.5098 | −1.05571 | ||||||||
\(540\) | 29.9633 | + | 40.8125i | 1.28941 | + | 1.75629i | ||||
\(541\) | 5.76630i | 0.247913i | 0.992288 | + | 0.123956i | \(0.0395583\pi\) | ||||
−0.992288 | + | 0.123956i | \(0.960442\pi\) | |||||||
\(542\) | 26.3536i | 1.13198i | ||||||||
\(543\) | −0.614506 | − | 2.86764i | −0.0263710 | − | 0.123062i | ||||
\(544\) | − | 19.3532i | − | 0.829763i | ||||||
\(545\) | 34.7867i | 1.49010i | ||||||||
\(546\) | −2.21347 | − | 10.3293i | −0.0947276 | − | 0.442053i | ||||
\(547\) | 20.0366i | 0.856703i | 0.903612 | + | 0.428351i | \(0.140905\pi\) | ||||
−0.903612 | + | 0.428351i | \(0.859095\pi\) | |||||||
\(548\) | −63.6914 | −2.72076 | ||||||||
\(549\) | −10.9437 | − | 24.3623i | −0.467068 | − | 1.03976i | ||||
\(550\) | −1.66843 | −0.0711422 | ||||||||
\(551\) | − | 40.9749i | − | 1.74559i | ||||||
\(552\) | 38.6459 | − | 8.28144i | 1.64488 | − | 0.352481i | ||||
\(553\) | 2.33792 | 0.0994185 | ||||||||
\(554\) | −26.5372 | −1.12746 | ||||||||
\(555\) | −1.88359 | − | 8.78991i | −0.0799539 | − | 0.373111i | ||||
\(556\) | − | 31.6700i | − | 1.34311i | ||||||
\(557\) | 6.58474i | 0.279005i | 0.990222 | + | 0.139502i | \(0.0445503\pi\) | ||||
−0.990222 | + | 0.139502i | \(0.955450\pi\) | |||||||
\(558\) | −20.4822 | − | 45.5963i | −0.867081 | − | 1.93024i | ||||
\(559\) | 1.10779 | 0.0468545 | ||||||||
\(560\) | 49.3733i | 2.08640i | ||||||||
\(561\) | 37.3318 | − | 7.99983i | 1.57615 | − | 0.337753i | ||||
\(562\) | 50.3044 | 2.12196 | ||||||||
\(563\) | −22.9566 | −0.967504 | −0.483752 | − | 0.875205i | \(-0.660726\pi\) | ||||
−0.483752 | + | 0.875205i | \(0.660726\pi\) | |||||||
\(564\) | 27.8420 | − | 5.96627i | 1.17236 | − | 0.251225i | ||||
\(565\) | −15.1691 | −0.638168 | ||||||||
\(566\) | −29.7246 | −1.24942 | ||||||||
\(567\) | 25.5048 | + | 22.6602i | 1.07110 | + | 0.951639i | ||||
\(568\) | − | 23.1540i | − | 0.971519i | ||||||
\(569\) | 11.3646i | 0.476427i | 0.971213 | + | 0.238214i | \(0.0765618\pi\) | ||||
−0.971213 | + | 0.238214i | \(0.923438\pi\) | |||||||
\(570\) | 14.6978 | + | 68.5884i | 0.615624 | + | 2.87285i | ||||
\(571\) | 17.8939 | 0.748837 | 0.374419 | − | 0.927260i | \(-0.377842\pi\) | ||||
0.374419 | + | 0.927260i | \(0.377842\pi\) | |||||||
\(572\) | 9.12804i | 0.381662i | ||||||||
\(573\) | −0.360533 | − | 1.68246i | −0.0150615 | − | 0.0702856i | ||||
\(574\) | 31.1702i | 1.30102i | ||||||||
\(575\) | − | 0.802981i | − | 0.0334866i | ||||||
\(576\) | 11.2477 | − | 5.05256i | 0.468655 | − | 0.210523i | ||||
\(577\) | − | 18.2091i | − | 0.758054i | −0.925386 | − | 0.379027i | \(-0.876259\pi\) | ||
0.925386 | − | 0.379027i | \(-0.123741\pi\) | |||||||
\(578\) | 67.4595 | 2.80595 | ||||||||
\(579\) | 5.11822 | + | 23.8846i | 0.212706 | + | 0.992608i | ||||
\(580\) | − | 56.3063i | − | 2.33799i | ||||||
\(581\) | 52.7310 | 2.18765 | ||||||||
\(582\) | 15.0666 | − | 3.22863i | 0.624533 | − | 0.133831i | ||||
\(583\) | −4.85647 | −0.201135 | ||||||||
\(584\) | 69.6805 | 2.88340 | ||||||||
\(585\) | −1.80080 | − | 4.00885i | −0.0744541 | − | 0.165745i | ||||
\(586\) | 0.0656618i | 0.00271246i | ||||||||
\(587\) | −9.60136 | −0.396291 | −0.198145 | − | 0.980173i | \(-0.563492\pi\) | ||||
−0.198145 | + | 0.980173i | \(0.563492\pi\) | |||||||
\(588\) | 11.4289 | + | 53.3339i | 0.471321 | + | 2.19945i | ||||
\(589\) | − | 47.1718i | − | 1.94368i | ||||||
\(590\) | − | 36.4203i | − | 1.49940i | ||||||
\(591\) | −3.73997 | − | 17.4528i | −0.153842 | − | 0.717914i | ||||
\(592\) | 12.9989 | 0.534249 | ||||||||
\(593\) | 11.2316 | 0.461226 | 0.230613 | − | 0.973046i | \(-0.425927\pi\) | ||||
0.230613 | + | 0.973046i | \(0.425927\pi\) | |||||||
\(594\) | −25.6126 | − | 34.8866i | −1.05090 | − | 1.43141i | ||||
\(595\) | −57.2992 | −2.34904 | ||||||||
\(596\) | − | 58.3109i | − | 2.38851i | ||||||
\(597\) | −1.82798 | − | 8.53040i | −0.0748142 | − | 0.349126i | ||||
\(598\) | −6.44943 | −0.263737 | ||||||||
\(599\) | −10.8447 | −0.443100 | −0.221550 | − | 0.975149i | \(-0.571112\pi\) | ||||
−0.221550 | + | 0.975149i | \(0.571112\pi\) | |||||||
\(600\) | 0.413834 | + | 1.93119i | 0.0168947 | + | 0.0788403i | ||||
\(601\) | 17.5002 | 0.713850 | 0.356925 | − | 0.934133i | \(-0.383825\pi\) | ||||
0.356925 | + | 0.934133i | \(0.383825\pi\) | |||||||
\(602\) | −16.3728 | −0.667305 | ||||||||
\(603\) | 2.99944 | + | 24.3722i | 0.122146 | + | 0.992512i | ||||
\(604\) | −24.6493 | −1.00296 | ||||||||
\(605\) | 0.135267 | 0.00549939 | ||||||||
\(606\) | 8.66796 | + | 40.4497i | 0.352112 | + | 1.64316i | ||||
\(607\) | 39.8577 | 1.61777 | 0.808887 | − | 0.587965i | \(-0.200071\pi\) | ||||
0.808887 | + | 0.587965i | \(0.200071\pi\) | |||||||
\(608\) | −20.7034 | −0.839635 | ||||||||
\(609\) | −7.95004 | − | 37.0995i | −0.322152 | − | 1.50335i | ||||
\(610\) | − | 50.8462i | − | 2.05870i | ||||||
\(611\) | −2.47156 | −0.0999884 | ||||||||
\(612\) | −34.8156 | − | 77.5045i | −1.40734 | − | 3.13294i | ||||
\(613\) | −26.9806 | −1.08973 | −0.544867 | − | 0.838522i | \(-0.683420\pi\) | ||||
−0.544867 | + | 0.838522i | \(0.683420\pi\) | |||||||
\(614\) | 51.5459 | 2.08022 | ||||||||
\(615\) | 2.71710 | + | 12.6795i | 0.109564 | + | 0.511288i | ||||
\(616\) | − | 71.7620i | − | 2.89137i | ||||||
\(617\) | 14.7709i | 0.594653i | 0.954776 | + | 0.297327i | \(0.0960950\pi\) | ||||
−0.954776 | + | 0.297327i | \(0.903905\pi\) | |||||||
\(618\) | 12.2603 | + | 57.2138i | 0.493183 | + | 2.30147i | ||||
\(619\) | 14.8997 | 0.598871 | 0.299436 | − | 0.954117i | \(-0.403202\pi\) | ||||
0.299436 | + | 0.954117i | \(0.403202\pi\) | |||||||
\(620\) | − | 64.8218i | − | 2.60331i | ||||||
\(621\) | 16.7901 | − | 12.3268i | 0.673765 | − | 0.494658i | ||||
\(622\) | 74.8885 | 3.00276 | ||||||||
\(623\) | −7.03248 | −0.281750 | ||||||||
\(624\) | 6.21377 | − | 1.33155i | 0.248750 | − | 0.0533046i | ||||
\(625\) | −25.9614 | −1.03846 | ||||||||
\(626\) | 45.5923i | 1.82224i | ||||||||
\(627\) | −8.55796 | − | 39.9363i | −0.341772 | − | 1.59490i | ||||
\(628\) | −66.6659 | −2.66026 | ||||||||
\(629\) | 15.0856i | 0.601501i | ||||||||
\(630\) | 26.6153 | + | 59.2495i | 1.06038 | + | 2.36056i | ||||
\(631\) | 14.8748i | 0.592157i | 0.955164 | + | 0.296078i | \(0.0956789\pi\) | ||||
−0.955164 | + | 0.296078i | \(0.904321\pi\) | |||||||
\(632\) | 3.51075i | 0.139650i | ||||||||
\(633\) | 1.40364 | + | 6.55017i | 0.0557895 | + | 0.260346i | ||||
\(634\) | 36.1105i | 1.43413i | ||||||||
\(635\) | −8.37704 | −0.332433 | ||||||||
\(636\) | 2.26457 | + | 10.5678i | 0.0897962 | + | 0.419040i | ||||
\(637\) | − | 4.73449i | − | 0.187587i | ||||||
\(638\) | 48.1306i | 1.90551i | ||||||||
\(639\) | −5.00012 | − | 11.1310i | −0.197802 | − | 0.440334i | ||||
\(640\) | 36.7915 | 1.45431 | ||||||||
\(641\) | 18.8228 | 0.743456 | 0.371728 | − | 0.928342i | \(-0.378765\pi\) | ||||
0.371728 | + | 0.928342i | \(0.378765\pi\) | |||||||
\(642\) | 39.7868 | − | 8.52591i | 1.57026 | − | 0.336491i | ||||
\(643\) | −41.1209 | −1.62165 | −0.810824 | − | 0.585290i | \(-0.800981\pi\) | ||||
−0.810824 | + | 0.585290i | \(0.800981\pi\) | |||||||
\(644\) | 64.9291 | 2.55856 | ||||||||
\(645\) | −6.66018 | + | 1.42721i | −0.262244 | + | 0.0561964i | ||||
\(646\) | − | 117.714i | − | 4.63140i | ||||||
\(647\) | −9.74294 | −0.383034 | −0.191517 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191517 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(648\) | −34.0278 | + | 38.2994i | −1.33674 | + | 1.50454i | ||||
\(649\) | 21.2061i | 0.832413i | ||||||||
\(650\) | − | 0.322286i | − | 0.0126411i | ||||||
\(651\) | −9.15237 | − | 42.7102i | −0.358710 | − | 1.67395i | ||||
\(652\) | 4.45666 | 0.174536 | ||||||||
\(653\) | 9.21343 | 0.360549 | 0.180275 | − | 0.983616i | \(-0.442301\pi\) | ||||
0.180275 | + | 0.983616i | \(0.442301\pi\) | |||||||
\(654\) | −64.7055 | + | 13.8657i | −2.53019 | + | 0.542194i | ||||
\(655\) | 6.84840i | 0.267589i | ||||||||
\(656\) | −18.7510 | −0.732102 | ||||||||
\(657\) | 33.4980 | − | 15.0475i | 1.30688 | − | 0.587060i | ||||
\(658\) | 36.5288 | 1.42404 | ||||||||
\(659\) | 25.3068i | 0.985813i | 0.870082 | + | 0.492906i | \(0.164066\pi\) | ||||
−0.870082 | + | 0.492906i | \(0.835934\pi\) | |||||||
\(660\) | −11.7600 | − | 54.8790i | −0.457759 | − | 2.13616i | ||||
\(661\) | 5.99797i | 0.233294i | 0.993173 | + | 0.116647i | \(0.0372146\pi\) | ||||
−0.993173 | + | 0.116647i | \(0.962785\pi\) | |||||||
\(662\) | 72.3758i | 2.81297i | ||||||||
\(663\) | 1.54530 | + | 7.21127i | 0.0600146 | + | 0.280063i | ||||
\(664\) | 79.1837i | 3.07292i | ||||||||
\(665\) | 61.2968i | 2.37699i | ||||||||
\(666\) | 15.5990 | − | 7.00720i | 0.604450 | − | 0.271524i | ||||
\(667\) | −23.1642 | −0.896923 | ||||||||
\(668\) | 73.5720i | 2.84659i | ||||||||
\(669\) | −0.249758 | − | 1.16551i | −0.00965621 | − | 0.0450614i | ||||
\(670\) | −13.8042 | + | 44.6658i | −0.533301 | + | 1.72559i | ||||
\(671\) | 29.6057i | 1.14292i | ||||||||
\(672\) | −18.7453 | + | 4.01692i | −0.723114 | + | 0.154956i | ||||
\(673\) | 9.52121i | 0.367016i | 0.983018 | + | 0.183508i | \(0.0587453\pi\) | ||||
−0.983018 | + | 0.183508i | \(0.941255\pi\) | |||||||
\(674\) | − | 24.2629i | − | 0.934573i | ||||||
\(675\) | 0.615986 | + | 0.839025i | 0.0237093 | + | 0.0322941i | ||||
\(676\) | 53.7836 | 2.06860 | ||||||||
\(677\) | 24.7739 | 0.952137 | 0.476068 | − | 0.879408i | \(-0.342061\pi\) | ||||
0.476068 | + | 0.879408i | \(0.342061\pi\) | |||||||
\(678\) | −6.04630 | − | 28.2155i | −0.232207 | − | 1.08361i | ||||
\(679\) | 13.4649 | 0.516736 | ||||||||
\(680\) | − | 86.0436i | − | 3.29962i | ||||||
\(681\) | −46.5767 | + | 9.98093i | −1.78482 | + | 0.382470i | ||||
\(682\) | 55.4097i | 2.12175i | ||||||||
\(683\) | 50.2944 | 1.92446 | 0.962231 | − | 0.272233i | \(-0.0877621\pi\) | ||||
0.962231 | + | 0.272233i | \(0.0877621\pi\) | |||||||
\(684\) | −82.9118 | + | 37.2446i | −3.17021 | + | 1.42408i | ||||
\(685\) | −33.9922 | −1.29878 | ||||||||
\(686\) | 3.51424i | 0.134174i | ||||||||
\(687\) | −35.4785 | + | 7.60268i | −1.35359 | + | 0.290060i | ||||
\(688\) | − | 9.84933i | − | 0.375502i | ||||||
\(689\) | − | 0.938111i | − | 0.0357392i | ||||||
\(690\) | 38.7749 | − | 8.30907i | 1.47613 | − | 0.316321i | ||||
\(691\) | 37.5188 | 1.42728 | 0.713642 | − | 0.700511i | \(-0.247044\pi\) | ||||
0.713642 | + | 0.700511i | \(0.247044\pi\) | |||||||
\(692\) | − | 32.1810i | − | 1.22334i | ||||||
\(693\) | −15.4971 | − | 34.4986i | −0.588685 | − | 1.31050i | ||||
\(694\) | 60.3961 | 2.29261 | ||||||||
\(695\) | − | 16.9023i | − | 0.641141i | ||||||
\(696\) | 55.7105 | − | 11.9382i | 2.11170 | − | 0.452516i | ||||
\(697\) | − | 21.7611i | − | 0.824260i | ||||||
\(698\) | −10.0081 | −0.378813 | ||||||||
\(699\) | −10.0942 | − | 47.1054i | −0.381798 | − | 1.78169i | ||||
\(700\) | 3.24459i | 0.122634i | ||||||||
\(701\) | −35.1034 | −1.32584 | −0.662919 | − | 0.748691i | \(-0.730683\pi\) | ||||
−0.662919 | + | 0.748691i | \(0.730683\pi\) | |||||||
\(702\) | 6.73893 | − | 4.94752i | 0.254345 | − | 0.186732i | ||||
\(703\) | 16.1380 | 0.608658 | ||||||||
\(704\) | −13.6685 | −0.515151 | ||||||||
\(705\) | 14.8593 | − | 3.18421i | 0.559635 | − | 0.119924i | ||||
\(706\) | −30.2063 | −1.13683 | ||||||||
\(707\) | 36.1495i | 1.35954i | ||||||||
\(708\) | 46.1450 | − | 9.88841i | 1.73424 | − | 0.371629i | ||||
\(709\) | −17.9249 | −0.673183 | −0.336592 | − | 0.941651i | \(-0.609274\pi\) | ||||
−0.336592 | + | 0.941651i | \(0.609274\pi\) | |||||||
\(710\) | − | 23.2312i | − | 0.871853i | ||||||
\(711\) | 0.758148 | + | 1.68774i | 0.0284328 | + | 0.0632954i | ||||
\(712\) | − | 10.5603i | − | 0.395765i | ||||||
\(713\) | −26.6675 | −0.998706 | ||||||||
\(714\) | −22.8391 | − | 106.580i | −0.854732 | − | 3.98867i | ||||
\(715\) | 4.87165i | 0.182189i | ||||||||
\(716\) | −85.9666 | −3.21272 | ||||||||
\(717\) | −0.141497 | − | 0.660307i | −0.00528431 | − | 0.0246596i | ||||
\(718\) | − | 50.7065i | − | 1.89235i | ||||||
\(719\) | 36.3629i | 1.35611i | 0.735012 | + | 0.678054i | \(0.237176\pi\) | ||||
−0.735012 | + | 0.678054i | \(0.762824\pi\) | |||||||
\(720\) | −35.6426 | + | 16.0109i | −1.32832 | + | 0.596692i | ||||
\(721\) | 51.1314i | 1.90423i | ||||||||
\(722\) | −78.3398 | −2.91551 | ||||||||
\(723\) | 6.17305 | + | 28.8070i | 0.229578 | + | 1.07134i | ||||
\(724\) | 7.23485 | 0.268881 | ||||||||
\(725\) | − | 1.15755i | − | 0.0429902i | ||||||
\(726\) | 0.0539166 | + | 0.251606i | 0.00200103 | + | 0.00933797i | ||||
\(727\) | 40.3875i | 1.49789i | 0.662633 | + | 0.748944i | \(0.269439\pi\) | ||||
−0.662633 | + | 0.748944i | \(0.730561\pi\) | |||||||
\(728\) | 13.8621 | 0.513762 | ||||||||
\(729\) | −8.08761 | + | 25.7603i | −0.299541 | + | 0.954083i | ||||
\(730\) | 69.9130 | 2.58759 | ||||||||
\(731\) | 11.4305 | 0.422771 | ||||||||
\(732\) | 64.4227 | − | 13.8051i | 2.38113 | − | 0.510253i | ||||
\(733\) | 47.3781i | 1.74995i | 0.484168 | + | 0.874975i | \(0.339123\pi\) | ||||
−0.484168 | + | 0.874975i | \(0.660877\pi\) | |||||||
\(734\) | 14.3350i | 0.529115i | ||||||||
\(735\) | 6.09964 | + | 28.4644i | 0.224988 | + | 1.04993i | ||||
\(736\) | 11.7042i | 0.431423i | ||||||||
\(737\) | 8.03761 | − | 26.0071i | 0.296069 | − | 0.957985i | ||||
\(738\) | −22.5018 | + | 10.1080i | −0.828301 | + | 0.372079i | ||||
\(739\) | 13.6714i | 0.502910i | 0.967869 | + | 0.251455i | \(0.0809090\pi\) | ||||
−0.967869 | + | 0.251455i | \(0.919091\pi\) | |||||||
\(740\) | 22.1763 | 0.815217 | ||||||||
\(741\) | 7.71438 | − | 1.65311i | 0.283395 | − | 0.0607287i | ||||
\(742\) | 13.8650i | 0.509000i | ||||||||
\(743\) | − | 29.5301i | − | 1.08335i | −0.840587 | − | 0.541676i | \(-0.817790\pi\) | ||
0.840587 | − | 0.541676i | \(-0.182210\pi\) | |||||||
\(744\) | 64.1359 | − | 13.7437i | 2.35134 | − | 0.503868i | ||||
\(745\) | − | 31.1206i | − | 1.14017i | ||||||
\(746\) | − | 57.6109i | − | 2.10929i | ||||||
\(747\) | 17.0998 | + | 38.0665i | 0.625648 | + | 1.39278i | ||||
\(748\) | 94.1855i | 3.44376i | ||||||||
\(749\) | 35.5571 | 1.29923 | ||||||||
\(750\) | −9.94885 | − | 46.4270i | −0.363281 | − | 1.69528i | ||||
\(751\) | 12.0295 | 0.438963 | 0.219481 | − | 0.975617i | \(-0.429563\pi\) | ||||
0.219481 | + | 0.975617i | \(0.429563\pi\) | |||||||
\(752\) | 21.9746i | 0.801330i | ||||||||
\(753\) | −3.96752 | − | 18.5147i | −0.144584 | − | 0.674714i | ||||
\(754\) | −9.29725 | −0.338586 | ||||||||
\(755\) | −13.1554 | −0.478772 | ||||||||
\(756\) | −67.8436 | + | 49.8087i | −2.46745 | + | 1.81152i | ||||
\(757\) | 17.0764i | 0.620653i | 0.950630 | + | 0.310326i | \(0.100438\pi\) | ||||
−0.950630 | + | 0.310326i | \(0.899562\pi\) | |||||||
\(758\) | 17.3363i | 0.629683i | ||||||||
\(759\) | −22.5771 | + | 4.83804i | −0.819496 | + | 0.175610i | ||||
\(760\) | −92.0466 | −3.33888 | ||||||||
\(761\) | − | 42.8974i | − | 1.55503i | −0.628864 | − | 0.777515i | \(-0.716480\pi\) | ||
0.628864 | − | 0.777515i | \(-0.283520\pi\) | |||||||
\(762\) | −3.33904 | − | 15.5819i | −0.120961 | − | 0.564471i | ||||
\(763\) | −57.8267 | −2.09347 | ||||||||
\(764\) | 4.24471 | 0.153568 | ||||||||
\(765\) | −18.5812 | − | 41.3643i | −0.671803 | − | 1.49553i | ||||
\(766\) | −60.8579 | −2.19889 | ||||||||
\(767\) | −4.09632 | −0.147910 | ||||||||
\(768\) | 11.6816 | + | 54.5128i | 0.421522 | + | 1.96706i | ||||
\(769\) | − | 37.4031i | − | 1.34879i | −0.738371 | − | 0.674395i | \(-0.764404\pi\) | ||
0.738371 | − | 0.674395i | \(-0.235596\pi\) | |||||||
\(770\) | − | 72.0015i | − | 2.59475i | ||||||
\(771\) | −40.4077 | + | 8.65897i | −1.45525 | + | 0.311845i | ||||
\(772\) | −60.2590 | −2.16877 | ||||||||
\(773\) | 25.2597i | 0.908529i | 0.890867 | + | 0.454264i | \(0.150098\pi\) | ||||
−0.890867 | + | 0.454264i | \(0.849902\pi\) | |||||||
\(774\) | −5.30941 | − | 11.8195i | −0.190843 | − | 0.424843i | ||||
\(775\) | − | 1.33261i | − | 0.0478687i | ||||||
\(776\) | 20.2196i | 0.725843i | ||||||||
\(777\) | 14.6117 | − | 3.13114i | 0.524191 | − | 0.112329i | ||||
\(778\) | − | 47.7112i | − | 1.71053i | ||||||
\(779\) | −23.2793 | −0.834067 | ||||||||
\(780\) | 10.6008 | − | 2.27165i | 0.379570 | − | 0.0813381i | ||||
\(781\) | 13.5266i | 0.484021i | ||||||||
\(782\) | −66.5469 | −2.37971 | ||||||||
\(783\) | 24.2040 | − | 17.7699i | 0.864981 | − | 0.635043i | ||||
\(784\) | −42.0942 | −1.50337 | ||||||||
\(785\) | −35.5797 | −1.26989 | ||||||||
\(786\) | −12.7385 | + | 2.72973i | −0.454367 | + | 0.0973663i | ||||
\(787\) | − | 44.1882i | − | 1.57514i | −0.616225 | − | 0.787570i | \(-0.711339\pi\) | ||
0.616225 | − | 0.787570i | \(-0.288661\pi\) | |||||||
\(788\) | 44.0323 | 1.56858 | ||||||||
\(789\) | 21.7140 | − | 4.65308i | 0.773038 | − | 0.165654i | ||||
\(790\) | 3.52246i | 0.125324i | ||||||||
\(791\) | − | 25.2159i | − | 0.896576i | ||||||
\(792\) | 51.8050 | − | 23.2712i | 1.84081 | − | 0.826906i | ||||
\(793\) | −5.71885 | −0.203082 | ||||||||
\(794\) | −7.45281 | −0.264490 | ||||||||
\(795\) | 1.20861 | + | 5.64005i | 0.0428649 | + | 0.200032i | ||||
\(796\) | 21.5216 | 0.762813 | ||||||||
\(797\) | − | 35.1721i | − | 1.24586i | −0.782278 | − | 0.622930i | \(-0.785942\pi\) | ||
0.782278 | − | 0.622930i | \(-0.214058\pi\) | |||||||
\(798\) | −114.016 | + | 24.4325i | −4.03613 | + | 0.864902i | ||||
\(799\) | −25.5022 | −0.902201 | ||||||||
\(800\) | −0.584874 | −0.0206784 | ||||||||
\(801\) | −2.28051 | − | 5.07674i | −0.0805779 | − | 0.179378i | ||||
\(802\) | 33.9777 | 1.19980 | ||||||||
\(803\) | −40.7076 | −1.43654 | ||||||||
\(804\) | −60.3401 | − | 5.36291i | −2.12803 | − | 0.189135i | ||||
\(805\) | 34.6527 | 1.22135 | ||||||||
\(806\) | −10.7033 | −0.377009 | ||||||||
\(807\) | 21.4505 | − | 4.59662i | 0.755092 | − | 0.161809i | ||||
\(808\) | −54.2840 | −1.90970 | ||||||||
\(809\) | −29.0877 | −1.02267 | −0.511335 | − | 0.859381i | \(-0.670849\pi\) | ||||
−0.511335 | + | 0.859381i | \(0.670849\pi\) | |||||||
\(810\) | −34.1413 | + | 38.4272i | −1.19960 | + | 1.35019i | ||||
\(811\) | 15.3903i | 0.540425i | 0.962801 | + | 0.270213i | \(0.0870940\pi\) | ||||
−0.962801 | + | 0.270213i | \(0.912906\pi\) | |||||||
\(812\) | 93.5992 | 3.28469 | ||||||||
\(813\) | −17.8205 | + | 3.81875i | −0.624991 | + | 0.133929i | ||||
\(814\) | −18.9563 | −0.664419 | ||||||||
\(815\) | 2.37853 | 0.0833162 | ||||||||
\(816\) | 64.1153 | − | 13.7393i | 2.24448 | − | 0.480971i | ||||
\(817\) | − | 12.2279i | − | 0.427801i | ||||||
\(818\) | − | 2.02165i | − | 0.0706853i | ||||||
\(819\) | 6.66400 | − | 2.99352i | 0.232859 | − | 0.104602i | ||||
\(820\) | −31.9895 | −1.11712 | ||||||||
\(821\) | 53.7596i | 1.87622i | 0.346336 | + | 0.938111i | \(0.387426\pi\) | ||||
−0.346336 | + | 0.938111i | \(0.612574\pi\) | |||||||
\(822\) | −13.5491 | − | 63.2278i | −0.472579 | − | 2.20532i | ||||
\(823\) | −14.3455 | −0.500051 | −0.250026 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250026 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(824\) | −76.7816 | −2.67481 | ||||||||
\(825\) | −0.241763 | − | 1.12821i | −0.00841711 | − | 0.0392791i | ||||
\(826\) | 60.5424 | 2.10654 | ||||||||
\(827\) | − | 16.2924i | − | 0.566544i | −0.959040 | − | 0.283272i | \(-0.908580\pi\) | ||
0.959040 | − | 0.283272i | \(-0.0914199\pi\) | |||||||
\(828\) | 21.0554 | + | 46.8723i | 0.731725 | + | 1.62892i | ||||
\(829\) | 34.7314 | 1.20627 | 0.603137 | − | 0.797638i | \(-0.293917\pi\) | ||||
0.603137 | + | 0.797638i | \(0.293917\pi\) | |||||||
\(830\) | 79.4479i | 2.75768i | ||||||||
\(831\) | −3.84536 | − | 17.9446i | −0.133394 | − | 0.622492i | ||||
\(832\) | − | 2.64030i | − | 0.0915361i | ||||||
\(833\) | − | 48.8517i | − | 1.69261i | ||||||
\(834\) | 31.4394 | − | 6.73716i | 1.08866 | − | 0.233289i | ||||
\(835\) | 39.2655i | 1.35884i | ||||||||
\(836\) | 100.756 | 3.48474 | ||||||||
\(837\) | 27.8645 | − | 20.4573i | 0.963139 | − | 0.707107i | ||||
\(838\) | − | 0.152574i | − | 0.00527058i | ||||||
\(839\) | − | 8.31696i | − | 0.287133i | −0.989641 | − | 0.143567i | \(-0.954143\pi\) | ||
0.989641 | − | 0.143567i | \(-0.0458572\pi\) | |||||||
\(840\) | −83.3406 | + | 17.8591i | −2.87552 | + | 0.616196i | ||||
\(841\) | −4.39267 | −0.151472 | ||||||||
\(842\) | −24.0181 | −0.827718 | ||||||||
\(843\) | 7.28933 | + | 34.0162i | 0.251058 | + | 1.17158i | ||||
\(844\) | −16.5256 | −0.568835 | ||||||||
\(845\) | 28.7044 | 0.987462 | ||||||||
\(846\) | 11.8457 | + | 26.3702i | 0.407263 | + | 0.906625i | ||||
\(847\) | 0.224858i | 0.00772620i | ||||||||
\(848\) | −8.34072 | −0.286422 | ||||||||
\(849\) | −4.30722 | − | 20.1000i | −0.147824 | − | 0.689830i | ||||
\(850\) | − | 3.32543i | − | 0.114061i | ||||||
\(851\) | − | 9.12327i | − | 0.312742i | ||||||
\(852\) | 29.4343 | − | 6.30747i | 1.00840 | − | 0.216090i | ||||
\(853\) | 3.26257 | 0.111708 | 0.0558542 | − | 0.998439i | \(-0.482212\pi\) | ||||
0.0558542 | + | 0.998439i | \(0.482212\pi\) | |||||||
\(854\) | 84.5228 | 2.89231 | ||||||||
\(855\) | −44.2502 | + | 19.8775i | −1.51332 | + | 0.679797i | ||||
\(856\) | 53.3944i | 1.82498i | ||||||||
\(857\) | −3.88776 | −0.132803 | −0.0664016 | − | 0.997793i | \(-0.521152\pi\) | ||||
−0.0664016 | + | 0.997793i | \(0.521152\pi\) | |||||||
\(858\) | −9.06159 | + | 1.94181i | −0.309358 | + | 0.0662923i | ||||
\(859\) | 36.2780 | 1.23779 | 0.618895 | − | 0.785474i | \(-0.287581\pi\) | ||||
0.618895 | + | 0.785474i | \(0.287581\pi\) | |||||||
\(860\) | − | 16.8032i | − | 0.572983i | ||||||
\(861\) | −21.0775 | + | 4.51669i | −0.718319 | + | 0.153929i | ||||
\(862\) | − | 1.25426i | − | 0.0427202i | ||||||
\(863\) | 18.0830i | 0.615551i | 0.951459 | + | 0.307775i | \(0.0995846\pi\) | ||||
−0.951459 | + | 0.307775i | \(0.900415\pi\) | |||||||
\(864\) | −8.97859 | − | 12.2296i | −0.305458 | − | 0.416059i | ||||
\(865\) | − | 17.1750i | − | 0.583969i | ||||||
\(866\) | − | 9.73517i | − | 0.330815i | ||||||
\(867\) | 9.77517 | + | 45.6166i | 0.331982 | + | 1.54922i | ||||
\(868\) | 107.755 | 3.65744 | ||||||||
\(869\) | − | 2.05099i | − | 0.0695751i | ||||||
\(870\) | 55.8964 | − | 11.9780i | 1.89506 | − | 0.406093i | ||||
\(871\) | 5.02372 | + | 1.55260i | 0.170222 | + | 0.0526079i | ||||
\(872\) | − | 86.8357i | − | 2.94063i | ||||||
\(873\) | 4.36644 | + | 9.72032i | 0.147782 | + | 0.328983i | ||||
\(874\) | 71.1897i | 2.40803i | ||||||||
\(875\) | − | 41.4914i | − | 1.40267i | ||||||
\(876\) | 18.9819 | + | 88.5806i | 0.641340 | + | 2.99286i | ||||
\(877\) | −31.1390 | −1.05149 | −0.525745 | − | 0.850642i | \(-0.676213\pi\) | ||||
−0.525745 | + | 0.850642i | \(0.676213\pi\) | |||||||
\(878\) | 64.7302 | 2.18454 | ||||||||
\(879\) | −0.0444009 | + | 0.00951467i | −0.00149761 | + | 0.000320922i | ||||
\(880\) | 43.3137 | 1.46011 | ||||||||
\(881\) | 34.3904i | 1.15864i | 0.815100 | + | 0.579321i | \(0.196682\pi\) | ||||
−0.815100 | + | 0.579321i | \(0.803318\pi\) | |||||||
\(882\) | −50.5144 | + | 22.6915i | −1.70091 | + | 0.764061i | ||||
\(883\) | − | 23.5451i | − | 0.792356i | −0.918174 | − | 0.396178i | \(-0.870336\pi\) | ||
0.918174 | − | 0.396178i | \(-0.129664\pi\) | |||||||
\(884\) | −18.1935 | −0.611914 | ||||||||
\(885\) | 24.6277 | − | 5.27746i | 0.827850 | − | 0.177400i | ||||
\(886\) | 2.23476 | 0.0750783 | ||||||||
\(887\) | 2.37660i | 0.0797985i | 0.999204 | + | 0.0398993i | \(0.0127037\pi\) | ||||
−0.999204 | + | 0.0398993i | \(0.987296\pi\) | |||||||
\(888\) | 4.70188 | + | 21.9417i | 0.157785 | + | 0.736314i | ||||
\(889\) | − | 13.9254i | − | 0.467042i | ||||||
\(890\) | − | 10.5956i | − | 0.355165i | ||||||
\(891\) | 19.8791 | − | 22.3746i | 0.665976 | − | 0.749579i | ||||
\(892\) | 2.94051 | 0.0984555 | ||||||||
\(893\) | 27.2814i | 0.912936i | ||||||||
\(894\) | 57.8864 | − | 12.4045i | 1.93601 | − | 0.414868i | ||||
\(895\) | −45.8805 | −1.53362 | ||||||||
\(896\) | 61.1595i | 2.04319i | ||||||||
\(897\) | −0.934550 | − | 4.36115i | −0.0312037 | − | 0.145614i | ||||
\(898\) | 35.1397i | 1.17263i | ||||||||
\(899\) | −38.4429 | −1.28214 | ||||||||
\(900\) | −2.34227 | + | 1.05216i | −0.0780756 | + | 0.0350721i | ||||
\(901\) | − | 9.67967i | − | 0.322477i | ||||||
\(902\) | 27.3447 | 0.910479 | ||||||||
\(903\) | −2.37249 | − | 11.0714i | −0.0789514 | − | 0.368433i | ||||
\(904\) | 37.8656 | 1.25939 | ||||||||
\(905\) | 3.86125 | 0.128352 | ||||||||
\(906\) | −5.24364 | − | 24.4698i | −0.174208 | − | 0.812956i | ||||
\(907\) | 28.9175 | 0.960189 | 0.480094 | − | 0.877217i | \(-0.340602\pi\) | ||||
0.480094 | + | 0.877217i | \(0.340602\pi\) | |||||||
\(908\) | − | 117.510i | − | 3.89970i | ||||||
\(909\) | −26.0963 | + | 11.7227i | −0.865560 | + | 0.388816i | ||||
\(910\) | 13.9083 | 0.461056 | ||||||||
\(911\) | − | 42.8181i | − | 1.41863i | −0.704893 | − | 0.709313i | \(-0.749005\pi\) | ||
0.704893 | − | 0.709313i | \(-0.250995\pi\) | |||||||
\(912\) | −14.6978 | − | 68.5884i | −0.486693 | − | 2.27119i | ||||
\(913\) | − | 46.2594i | − | 1.53096i | ||||||
\(914\) | −16.4679 | −0.544711 | ||||||||
\(915\) | 34.3825 | − | 7.36783i | 1.13665 | − | 0.243573i | ||||
\(916\) | − | 89.5096i | − | 2.95748i | ||||||
\(917\) | −11.3843 | −0.375942 | ||||||||
\(918\) | 69.5340 | − | 51.0498i | 2.29497 | − | 1.68489i | ||||
\(919\) | − | 2.19036i | − | 0.0722533i | −0.999347 | − | 0.0361267i | \(-0.988498\pi\) | ||
0.999347 | − | 0.0361267i | \(-0.0115020\pi\) | |||||||
\(920\) | 52.0364i | 1.71559i | ||||||||
\(921\) | 7.46922 | + | 34.8557i | 0.246119 | + | 1.14853i | ||||
\(922\) | − | 57.4675i | − | 1.89259i | ||||||
\(923\) | −2.61290 | −0.0860046 | ||||||||
\(924\) | 91.2268 | − | 19.5490i | 3.00114 | − | 0.643114i | ||||
\(925\) | 0.455901 | 0.0149899 | ||||||||
\(926\) | − | 30.0537i | − | 0.987627i | ||||||
\(927\) | −36.9117 | + | 16.5810i | −1.21234 | + | 0.544593i | ||||
\(928\) | 16.8723i | 0.553862i | ||||||||
\(929\) | 47.2048 | 1.54874 | 0.774370 | − | 0.632733i | \(-0.218067\pi\) | ||||
0.774370 | + | 0.632733i | \(0.218067\pi\) | |||||||
\(930\) | 64.3499 | − | 13.7895i | 2.11012 | − | 0.452177i | ||||
\(931\) | −52.2599 | −1.71275 | ||||||||
\(932\) | 118.844 | 3.89285 | ||||||||
\(933\) | 10.8517 | + | 50.6401i | 0.355268 | + | 1.65788i | ||||
\(934\) | 34.8770i | 1.14121i | ||||||||
\(935\) | 50.2669i | 1.64390i | ||||||||
\(936\) | 4.49523 | + | 10.0070i | 0.146931 | + | 0.327090i | ||||
\(937\) | 11.9835i | 0.391485i | 0.980655 | + | 0.195742i | \(0.0627116\pi\) | ||||
−0.980655 | + | 0.195742i | \(0.937288\pi\) | |||||||
\(938\) | −74.2490 | − | 22.9470i | −2.42432 | − | 0.749245i | ||||
\(939\) | −30.8298 | + | 6.60652i | −1.00609 | + | 0.215596i | ||||
\(940\) | 37.4890i | 1.22276i | ||||||||
\(941\) | 4.33529 | 0.141326 | 0.0706632 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706632 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(942\) | −14.1819 | − | 66.1806i | −0.462070 | − | 2.15628i | ||||
\(943\) | 13.1604i | 0.428562i | ||||||||
\(944\) | 36.4203i | 1.18538i | ||||||||
\(945\) | −36.2082 | + | 26.5830i | −1.17785 | + | 0.864744i | ||||
\(946\) | 14.3634i | 0.466993i | ||||||||
\(947\) | − | 1.87045i | − | 0.0607816i | −0.999538 | − | 0.0303908i | \(-0.990325\pi\) | ||
0.999538 | − | 0.0303908i | \(-0.00967518\pi\) | |||||||
\(948\) | −4.46300 | + | 0.956376i | −0.144951 | + | 0.0310617i | ||||
\(949\) | − | 7.86336i | − | 0.255255i | ||||||
\(950\) | −3.55744 | −0.115419 | ||||||||
\(951\) | −24.4182 | + | 5.23257i | −0.791813 | + | 0.169678i | ||||
\(952\) | 143.032 | 4.63570 | ||||||||
\(953\) | 23.5124i | 0.761641i | 0.924649 | + | 0.380820i | \(0.124358\pi\) | ||||
−0.924649 | + | 0.380820i | \(0.875642\pi\) | |||||||
\(954\) | −10.0091 | + | 4.49618i | −0.324058 | + | 0.145569i | ||||
\(955\) | 2.26541 | 0.0733070 | ||||||||
\(956\) | 1.66591 | 0.0538793 | ||||||||
\(957\) | −32.5463 | + | 6.97434i | −1.05207 | + | 0.225448i | ||||
\(958\) | − | 70.7810i | − | 2.28683i | ||||||
\(959\) | − | 56.5061i | − | 1.82468i | ||||||
\(960\) | 3.40161 | + | 15.8739i | 0.109787 | + | 0.512327i | ||||
\(961\) | −13.2568 | −0.427639 | ||||||||
\(962\) | − | 3.66174i | − | 0.118059i | ||||||
\(963\) | 11.5306 | + | 25.6687i | 0.371567 | + | 0.827161i | ||||
\(964\) | −72.6779 | −2.34080 | ||||||||
\(965\) | −32.1603 | −1.03528 | ||||||||
\(966\) | 13.8124 | + | 64.4564i | 0.444406 | + | 2.07385i | ||||
\(967\) | 16.5695 | 0.532838 | 0.266419 | − | 0.963857i | \(-0.414159\pi\) | ||||
0.266419 | + | 0.963857i | \(0.414159\pi\) | |||||||
\(968\) | −0.337658 | −0.0108527 | ||||||||
\(969\) | 79.5990 | − | 17.0573i | 2.55709 | − | 0.547958i | ||||
\(970\) | 20.2871i | 0.651380i | ||||||||
\(971\) | 29.7699i | 0.955361i | 0.878534 | + | 0.477680i | \(0.158522\pi\) | ||||
−0.878534 | + | 0.477680i | \(0.841478\pi\) | |||||||
\(972\) | −57.9574 | − | 32.8242i | −1.85898 | − | 1.05284i | ||||
\(973\) | 28.0971 | 0.900752 | ||||||||
\(974\) | 49.2186i | 1.57707i | ||||||||
\(975\) | 0.217932 | − | 0.0467007i | 0.00697941 | − | 0.00149562i | ||||
\(976\) | 50.8462i | 1.62755i | ||||||||
\(977\) | 1.53083i | 0.0489754i | 0.999700 | + | 0.0244877i | \(0.00779546\pi\) | ||||
−0.999700 | + | 0.0244877i | \(0.992205\pi\) | |||||||
\(978\) | 0.948066 | + | 4.42422i | 0.0303158 | + | 0.141471i | ||||
\(979\) | 6.16939i | 0.197174i | ||||||||
\(980\) | −71.8136 | −2.29400 | ||||||||
\(981\) | −18.7522 | − | 41.7451i | −0.598712 | − | 1.33282i | ||||
\(982\) | − | 15.2294i | − | 0.485988i | ||||||
\(983\) | −3.58107 | −0.114218 | −0.0571091 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571091 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(984\) | −6.78251 | − | 31.6511i | −0.216218 | − | 1.00900i | ||||
\(985\) | 23.5001 | 0.748776 | ||||||||
\(986\) | −95.9315 | −3.05508 | ||||||||
\(987\) | 5.29319 | + | 24.7010i | 0.168484 | + | 0.786243i | ||||
\(988\) | 19.4628i | 0.619195i | ||||||||
\(989\) | −6.91277 | −0.219813 | ||||||||
\(990\) | 51.9779 | − | 23.3489i | 1.65196 | − | 0.742075i | ||||
\(991\) | − | 9.01459i | − | 0.286358i | −0.989697 | − | 0.143179i | \(-0.954268\pi\) | ||
0.989697 | − | 0.143179i | \(-0.0457324\pi\) | |||||||
\(992\) | 19.4241i | 0.616714i | ||||||||
\(993\) | −48.9410 | + | 10.4876i | −1.55310 | + | 0.332813i | ||||
\(994\) | 38.6178 | 1.22488 | ||||||||
\(995\) | 11.4861 | 0.364134 | ||||||||
\(996\) | −100.661 | + | 21.5707i | −3.18958 | + | 0.683495i | ||||
\(997\) | 16.7935 | 0.531856 | 0.265928 | − | 0.963993i | \(-0.414322\pi\) | ||||
0.265928 | + | 0.963993i | \(0.414322\pi\) | |||||||
\(998\) | 82.8376i | 2.62218i | ||||||||
\(999\) | 6.99868 | + | 9.53279i | 0.221429 | + | 0.301604i |
(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 | 201.2.d.a.200.1 | ✓ | 20 | |
3.2 | odd | 2 | inner | 201.2.d.a.200.19 | yes | 20 | |
67.66 | odd | 2 | inner | 201.2.d.a.200.20 | yes | 20 | |
201.200 | even | 2 | inner | 201.2.d.a.200.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.d.a.200.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.2.d.a.200.2 | yes | 20 | 201.200 | even | 2 | inner | |
201.2.d.a.200.19 | yes | 20 | 3.2 | odd | 2 | inner | |
201.2.d.a.200.20 | yes | 20 | 67.66 | odd | 2 | inner |