Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(4,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.j (of order \(6\), degree \(2\), 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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.5 | ||
Root | \(5.04537i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.4 |
Dual form | 39.4.j.c.10.5 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.36942 | + | 2.52268i | 1.54482 | + | 0.891903i | 0.998524 | + | 0.0543124i | \(0.0172967\pi\) |
0.546298 | + | 0.837591i | \(0.316037\pi\) | |||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 8.72787 | + | 15.1171i | 1.09098 | + | 1.88964i | ||||
\(5\) | − | 20.1174i | − | 1.79935i | −0.436556 | − | 0.899677i | \(-0.643802\pi\) | ||
0.436556 | − | 0.899677i | \(-0.356198\pi\) | |||||||
\(6\) | −13.1082 | + | 7.56805i | −0.891903 | + | 0.514941i | ||||
\(7\) | −13.3609 | + | 7.71395i | −0.721423 | + | 0.416514i | −0.815276 | − | 0.579072i | \(-0.803415\pi\) |
0.0938530 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(8\) | 47.7076i | 2.10840i | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 50.7498 | − | 87.9013i | 1.60485 | − | 2.77968i | ||||
\(11\) | 23.3283 | + | 13.4686i | 0.639432 | + | 0.369176i | 0.784396 | − | 0.620261i | \(-0.212973\pi\) |
−0.144964 | + | 0.989437i | \(0.546307\pi\) | |||||||
\(12\) | −52.3672 | −1.25976 | ||||||||
\(13\) | −3.96071 | − | 46.7045i | −0.0845002 | − | 0.996423i | ||||
\(14\) | −77.8394 | −1.48596 | ||||||||
\(15\) | 52.2665 | + | 30.1761i | 0.899677 | + | 0.519429i | ||||
\(16\) | −50.5283 | + | 87.5177i | −0.789505 | + | 1.36746i | ||||
\(17\) | 11.6167 | + | 20.1207i | 0.165733 | + | 0.287059i | 0.936915 | − | 0.349556i | \(-0.113668\pi\) |
−0.771182 | + | 0.636615i | \(0.780334\pi\) | |||||||
\(18\) | − | 45.4083i | − | 0.594602i | ||||||
\(19\) | −39.0399 | + | 22.5397i | −0.471388 | + | 0.272156i | −0.716821 | − | 0.697258i | \(-0.754403\pi\) |
0.245433 | + | 0.969414i | \(0.421070\pi\) | |||||||
\(20\) | 304.117 | − | 175.582i | 3.40013 | − | 1.96307i | ||||
\(21\) | − | 46.2837i | − | 0.480949i | ||||||
\(22\) | 67.9540 | + | 117.700i | 0.658539 | + | 1.14062i | ||||
\(23\) | −71.0050 | + | 122.984i | −0.643720 | + | 1.11496i | 0.340875 | + | 0.940109i | \(0.389277\pi\) |
−0.984595 | + | 0.174848i | \(0.944057\pi\) | |||||||
\(24\) | −123.948 | − | 71.5615i | −1.05420 | − | 0.608643i | ||||
\(25\) | −279.710 | −2.23768 | ||||||||
\(26\) | 100.515 | − | 214.063i | 0.758176 | − | 1.61466i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −233.225 | − | 134.653i | −1.57412 | − | 0.908820i | ||||
\(29\) | −1.14534 | + | 1.98379i | −0.00733394 | + | 0.0127028i | −0.869669 | − | 0.493635i | \(-0.835668\pi\) |
0.862335 | + | 0.506338i | \(0.169001\pi\) | |||||||
\(30\) | 152.249 | + | 263.704i | 0.926561 | + | 1.60485i | ||||
\(31\) | − | 37.7740i | − | 0.218852i | −0.993995 | − | 0.109426i | \(-0.965099\pi\) | ||
0.993995 | − | 0.109426i | \(-0.0349012\pi\) | |||||||
\(32\) | −111.031 | + | 64.1035i | −0.613363 | + | 0.354125i | ||||
\(33\) | −69.9849 | + | 40.4058i | −0.369176 | + | 0.213144i | ||||
\(34\) | 117.221i | 0.591273i | ||||||||
\(35\) | 155.185 | + | 268.787i | 0.749456 | + | 1.29810i | ||||
\(36\) | 78.5508 | − | 136.054i | 0.363661 | − | 0.629879i | ||||
\(37\) | 271.793 | + | 156.920i | 1.20764 | + | 0.697228i | 0.962242 | − | 0.272195i | \(-0.0877497\pi\) |
0.245393 | + | 0.969424i | \(0.421083\pi\) | |||||||
\(38\) | −227.442 | −0.970947 | ||||||||
\(39\) | 127.283 | + | 59.7666i | 0.522605 | + | 0.245393i | ||||
\(40\) | 959.753 | 3.79376 | ||||||||
\(41\) | 5.08201 | + | 2.93410i | 0.0193580 | + | 0.0111763i | 0.509648 | − | 0.860383i | \(-0.329776\pi\) |
−0.490290 | + | 0.871559i | \(0.663109\pi\) | |||||||
\(42\) | 116.759 | − | 202.233i | 0.428960 | − | 0.742980i | ||||
\(43\) | −180.449 | − | 312.547i | −0.639958 | − | 1.10844i | −0.985441 | − | 0.170015i | \(-0.945618\pi\) |
0.345483 | − | 0.938425i | \(-0.387715\pi\) | |||||||
\(44\) | 470.209i | 1.61106i | ||||||||
\(45\) | −156.800 | + | 90.5283i | −0.519429 | + | 0.299892i | ||||
\(46\) | −620.501 | + | 358.246i | −1.98887 | + | 1.14827i | ||||
\(47\) | 209.748i | 0.650956i | 0.945550 | + | 0.325478i | \(0.105525\pi\) | ||||
−0.945550 | + | 0.325478i | \(0.894475\pi\) | |||||||
\(48\) | −151.585 | − | 262.553i | −0.455821 | − | 0.789505i | ||||
\(49\) | −52.4900 | + | 90.9154i | −0.153032 | + | 0.265060i | ||||
\(50\) | −1222.17 | − | 705.619i | −3.45681 | − | 1.99579i | ||||
\(51\) | −69.7003 | −0.191372 | ||||||||
\(52\) | 671.469 | − | 467.505i | 1.79069 | − | 1.24676i | ||||
\(53\) | 276.886 | 0.717609 | 0.358804 | − | 0.933413i | \(-0.383185\pi\) | ||||
0.358804 | + | 0.933413i | \(0.383185\pi\) | |||||||
\(54\) | 117.974 | + | 68.1125i | 0.297301 | + | 0.171647i | ||||
\(55\) | 270.953 | − | 469.305i | 0.664278 | − | 1.15056i | ||||
\(56\) | −368.014 | − | 637.419i | −0.878178 | − | 1.52105i | ||||
\(57\) | − | 135.238i | − | 0.314259i | ||||||
\(58\) | −10.0089 | + | 5.77866i | −0.0226593 | + | 0.0130823i | ||||
\(59\) | 470.415 | − | 271.594i | 1.03801 | − | 0.599298i | 0.118744 | − | 0.992925i | \(-0.462113\pi\) |
0.919270 | + | 0.393627i | \(0.128780\pi\) | |||||||
\(60\) | 1053.49i | 2.26675i | ||||||||
\(61\) | −102.894 | − | 178.218i | −0.215971 | − | 0.374073i | 0.737601 | − | 0.675236i | \(-0.235958\pi\) |
−0.953573 | + | 0.301163i | \(0.902625\pi\) | |||||||
\(62\) | 95.2917 | − | 165.050i | 0.195195 | − | 0.338087i | ||||
\(63\) | 120.249 | + | 69.4255i | 0.240474 | + | 0.138838i | ||||
\(64\) | 161.602 | 0.315629 | ||||||||
\(65\) | −939.573 | + | 79.6791i | −1.79292 | + | 0.152046i | ||||
\(66\) | −407.724 | −0.760415 | ||||||||
\(67\) | −426.585 | − | 246.289i | −0.777846 | − | 0.449090i | 0.0578203 | − | 0.998327i | \(-0.481585\pi\) |
−0.835666 | + | 0.549237i | \(0.814918\pi\) | |||||||
\(68\) | −202.778 | + | 351.222i | −0.361625 | + | 0.626352i | ||||
\(69\) | −213.015 | − | 368.953i | −0.371652 | − | 0.643720i | ||||
\(70\) | 1565.93i | 2.67377i | ||||||||
\(71\) | 716.081 | − | 413.430i | 1.19695 | − | 0.691057i | 0.237073 | − | 0.971492i | \(-0.423812\pi\) |
0.959873 | + | 0.280435i | \(0.0904786\pi\) | |||||||
\(72\) | 371.844 | − | 214.684i | 0.608643 | − | 0.351400i | ||||
\(73\) | − | 66.1205i | − | 0.106011i | −0.998594 | − | 0.0530056i | \(-0.983120\pi\) | ||
0.998594 | − | 0.0530056i | \(-0.0168801\pi\) | |||||||
\(74\) | 791.718 | + | 1371.30i | 1.24372 | + | 2.15419i | ||||
\(75\) | 419.564 | − | 726.707i | 0.645962 | − | 1.11884i | ||||
\(76\) | −681.470 | − | 393.447i | −1.02855 | − | 0.593835i | ||||
\(77\) | −415.584 | −0.615068 | ||||||||
\(78\) | 405.380 | + | 582.240i | 0.588465 | + | 0.845201i | ||||
\(79\) | 317.642 | 0.452374 | 0.226187 | − | 0.974084i | \(-0.427374\pi\) | ||||
0.226187 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(80\) | 1760.63 | + | 1016.50i | 2.46055 | + | 1.42060i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 14.8036 | + | 25.6406i | 0.0199364 | + | 0.0345309i | ||||
\(83\) | 141.450i | 0.187063i | 0.995616 | + | 0.0935313i | \(0.0298155\pi\) | ||||
−0.995616 | + | 0.0935313i | \(0.970184\pi\) | |||||||
\(84\) | 699.675 | − | 403.958i | 0.908820 | − | 0.524707i | ||||
\(85\) | 404.777 | − | 233.698i | 0.516520 | − | 0.298213i | ||||
\(86\) | − | 1820.86i | − | 2.28312i | ||||||
\(87\) | −3.43602 | − | 5.95136i | −0.00423425 | − | 0.00733394i | ||||
\(88\) | −642.555 | + | 1112.94i | −0.778371 | + | 1.34818i | ||||
\(89\) | 555.399 | + | 320.660i | 0.661486 | + | 0.381909i | 0.792843 | − | 0.609426i | \(-0.208600\pi\) |
−0.131357 | + | 0.991335i | \(0.541933\pi\) | |||||||
\(90\) | −913.497 | −1.06990 | ||||||||
\(91\) | 413.195 | + | 593.464i | 0.475985 | + | 0.683648i | ||||
\(92\) | −2478.89 | −2.80915 | ||||||||
\(93\) | 98.1396 | + | 56.6609i | 0.109426 | + | 0.0631771i | ||||
\(94\) | −529.129 | + | 916.478i | −0.580590 | + | 1.00561i | ||||
\(95\) | 453.440 | + | 785.381i | 0.489705 | + | 0.848194i | ||||
\(96\) | − | 384.621i | − | 0.408909i | ||||||
\(97\) | −965.551 | + | 557.461i | −1.01069 | + | 0.583522i | −0.911394 | − | 0.411536i | \(-0.864992\pi\) |
−0.0992962 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(98\) | −458.702 | + | 264.832i | −0.472815 | + | 0.272980i | ||||
\(99\) | − | 242.435i | − | 0.246117i | ||||||
\(100\) | −2441.27 | − | 4228.40i | −2.44127 | − | 4.22840i | ||||
\(101\) | 794.953 | − | 1376.90i | 0.783177 | − | 1.35650i | −0.146906 | − | 0.989150i | \(-0.546931\pi\) |
0.930082 | − | 0.367351i | \(-0.119735\pi\) | |||||||
\(102\) | −304.550 | − | 175.832i | −0.295636 | − | 0.170686i | ||||
\(103\) | −527.502 | −0.504625 | −0.252312 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252312 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(104\) | 2228.16 | − | 188.956i | 2.10086 | − | 0.178160i | ||||
\(105\) | −931.107 | −0.865398 | ||||||||
\(106\) | 1209.83 | + | 698.497i | 1.10858 | + | 0.640038i | ||||
\(107\) | −875.982 | + | 1517.25i | −0.791443 | + | 1.37082i | 0.133630 | + | 0.991031i | \(0.457337\pi\) |
−0.925073 | + | 0.379788i | \(0.875997\pi\) | |||||||
\(108\) | 235.652 | + | 408.162i | 0.209960 | + | 0.363661i | ||||
\(109\) | 967.122i | 0.849848i | 0.905229 | + | 0.424924i | \(0.139699\pi\) | ||||
−0.905229 | + | 0.424924i | \(0.860301\pi\) | |||||||
\(110\) | 2367.81 | − | 1367.06i | 2.05238 | − | 1.18494i | ||||
\(111\) | −815.379 | + | 470.759i | −0.697228 | + | 0.402545i | ||||
\(112\) | − | 1559.09i | − | 1.31536i | ||||||
\(113\) | −955.487 | − | 1654.95i | −0.795439 | − | 1.37774i | −0.922560 | − | 0.385854i | \(-0.873907\pi\) |
0.127120 | − | 0.991887i | \(-0.459427\pi\) | |||||||
\(114\) | 341.163 | − | 590.912i | 0.280288 | − | 0.485474i | ||||
\(115\) | 2474.12 | + | 1428.44i | 2.00620 | + | 1.15828i | ||||
\(116\) | −39.9855 | −0.0320048 | ||||||||
\(117\) | −346.203 | + | 241.041i | −0.273559 | + | 0.190464i | ||||
\(118\) | 2740.59 | 2.13806 | ||||||||
\(119\) | −310.421 | − | 179.221i | −0.239128 | − | 0.138061i | ||||
\(120\) | −1439.63 | + | 2493.51i | −1.09516 | + | 1.89688i | ||||
\(121\) | −302.694 | − | 524.281i | −0.227418 | − | 0.393900i | ||||
\(122\) | − | 1038.28i | − | 0.770501i | ||||||
\(123\) | −15.2460 | + | 8.80230i | −0.0111763 | + | 0.00645266i | ||||
\(124\) | 571.033 | − | 329.686i | 0.413551 | − | 0.238764i | ||||
\(125\) | 3112.35i | 2.22702i | ||||||||
\(126\) | 350.277 | + | 606.698i | 0.247660 | + | 0.428960i | ||||
\(127\) | 616.557 | − | 1067.91i | 0.430792 | − | 0.746154i | −0.566150 | − | 0.824302i | \(-0.691568\pi\) |
0.996942 | + | 0.0781488i | \(0.0249009\pi\) | |||||||
\(128\) | 1594.35 | + | 920.499i | 1.10095 | + | 0.635636i | ||||
\(129\) | 1082.69 | 0.738960 | ||||||||
\(130\) | −4306.39 | − | 2022.10i | −2.90535 | − | 1.36423i | ||||
\(131\) | −1274.90 | −0.850292 | −0.425146 | − | 0.905125i | \(-0.639777\pi\) | ||||
−0.425146 | + | 0.905125i | \(0.639777\pi\) | |||||||
\(132\) | −1221.64 | − | 705.313i | −0.805530 | − | 0.465073i | ||||
\(133\) | 347.740 | − | 602.304i | 0.226713 | − | 0.392679i | ||||
\(134\) | −1242.62 | − | 2152.28i | −0.801089 | − | 1.38753i | ||||
\(135\) | − | 543.170i | − | 0.346286i | ||||||
\(136\) | −959.913 | + | 554.206i | −0.605234 | + | 0.349432i | ||||
\(137\) | −1759.18 | + | 1015.66i | −1.09706 | + | 0.633385i | −0.935446 | − | 0.353470i | \(-0.885002\pi\) |
−0.161609 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(138\) | − | 2149.48i | − | 1.32591i | ||||||
\(139\) | 722.832 | + | 1251.98i | 0.441078 | + | 0.763969i | 0.997770 | − | 0.0667498i | \(-0.0212629\pi\) |
−0.556692 | + | 0.830719i | \(0.687930\pi\) | |||||||
\(140\) | −2708.86 | + | 4691.88i | −1.63529 | + | 2.83240i | ||||
\(141\) | −544.942 | − | 314.623i | −0.325478 | − | 0.187915i | ||||
\(142\) | 4171.81 | 2.46542 | ||||||||
\(143\) | 536.648 | − | 1142.88i | 0.313824 | − | 0.668340i | ||||
\(144\) | 909.510 | 0.526337 | ||||||||
\(145\) | 39.9086 | + | 23.0413i | 0.0228568 | + | 0.0131964i | ||||
\(146\) | 166.801 | − | 288.908i | 0.0945517 | − | 0.163768i | ||||
\(147\) | −157.470 | − | 272.746i | −0.0883532 | − | 0.153032i | ||||
\(148\) | 5478.30i | 3.04266i | ||||||||
\(149\) | 836.856 | − | 483.159i | 0.460120 | − | 0.265650i | −0.251975 | − | 0.967734i | \(-0.581080\pi\) |
0.712095 | + | 0.702083i | \(0.247747\pi\) | |||||||
\(150\) | 3666.50 | − | 2116.86i | 1.99579 | − | 1.15227i | ||||
\(151\) | − | 1463.09i | − | 0.788505i | −0.919002 | − | 0.394252i | \(-0.871004\pi\) | ||
0.919002 | − | 0.394252i | \(-0.128996\pi\) | |||||||
\(152\) | −1075.32 | − | 1862.50i | −0.573813 | − | 0.993874i | ||||
\(153\) | 104.550 | − | 181.087i | 0.0552445 | − | 0.0956862i | ||||
\(154\) | −1815.86 | − | 1048.39i | −0.950170 | − | 0.548581i | ||||
\(155\) | −759.914 | −0.393792 | ||||||||
\(156\) | 207.411 | + | 2445.78i | 0.106450 | + | 1.25525i | ||||
\(157\) | −66.0424 | −0.0335717 | −0.0167859 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167859 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(158\) | 1387.91 | + | 801.311i | 0.698838 | + | 0.403474i | ||||
\(159\) | −415.330 | + | 719.372i | −0.207156 | + | 0.358804i | ||||
\(160\) | 1289.60 | + | 2233.65i | 0.637197 | + | 1.10366i | ||||
\(161\) | − | 2190.92i | − | 1.07247i | ||||||
\(162\) | −353.923 | + | 204.337i | −0.171647 | + | 0.0991004i | ||||
\(163\) | −3052.95 | + | 1762.62i | −1.46703 | + | 0.846988i | −0.999319 | − | 0.0368953i | \(-0.988253\pi\) |
−0.467707 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(164\) | 102.434i | 0.0487728i | ||||||||
\(165\) | 812.859 | + | 1407.91i | 0.383521 | + | 0.664278i | ||||
\(166\) | −356.834 | + | 618.055i | −0.166842 | + | 0.288978i | ||||
\(167\) | 225.731 | + | 130.326i | 0.104596 | + | 0.0603887i | 0.551386 | − | 0.834250i | \(-0.314099\pi\) |
−0.446789 | + | 0.894639i | \(0.647433\pi\) | |||||||
\(168\) | 2208.08 | 1.01403 | ||||||||
\(169\) | −2165.63 | + | 369.966i | −0.985719 | + | 0.168396i | ||||
\(170\) | 2358.19 | 1.06391 | ||||||||
\(171\) | 351.359 | + | 202.857i | 0.157129 | + | 0.0907186i | ||||
\(172\) | 3149.87 | − | 5455.73i | 1.39637 | − | 2.41858i | ||||
\(173\) | 455.876 | + | 789.601i | 0.200345 | + | 0.347007i | 0.948640 | − | 0.316359i | \(-0.102460\pi\) |
−0.748295 | + | 0.663366i | \(0.769127\pi\) | |||||||
\(174\) | − | 34.6720i | − | 0.0151062i | ||||||
\(175\) | 3737.18 | − | 2157.66i | 1.61431 | − | 0.932023i | ||||
\(176\) | −2357.48 | + | 1361.09i | −1.00967 | + | 0.582933i | ||||
\(177\) | 1629.57i | 0.692009i | ||||||||
\(178\) | 1617.85 | + | 2802.19i | 0.681252 | + | 1.17996i | ||||
\(179\) | 1345.24 | − | 2330.03i | 0.561721 | − | 0.972930i | −0.435625 | − | 0.900128i | \(-0.643473\pi\) |
0.997346 | − | 0.0728016i | \(-0.0231940\pi\) | |||||||
\(180\) | −2737.05 | − | 1580.24i | −1.13338 | − | 0.654355i | ||||
\(181\) | −4773.85 | −1.96043 | −0.980213 | − | 0.197944i | \(-0.936573\pi\) | ||||
−0.980213 | + | 0.197944i | \(0.936573\pi\) | |||||||
\(182\) | 308.299 | + | 3635.45i | 0.125564 | + | 1.48065i | ||||
\(183\) | 617.364 | 0.249382 | ||||||||
\(184\) | −5867.29 | − | 3387.48i | −2.35077 | − | 1.35722i | ||||
\(185\) | 3156.82 | − | 5467.77i | 1.25456 | − | 2.17296i | ||||
\(186\) | 285.875 | + | 495.150i | 0.112696 | + | 0.195195i | ||||
\(187\) | 625.844i | 0.244739i | ||||||||
\(188\) | −3170.79 | + | 1830.66i | −1.23007 | + | 0.710182i | ||||
\(189\) | −360.746 | + | 208.277i | −0.138838 | + | 0.0801582i | ||||
\(190\) | 4575.54i | 1.74708i | ||||||||
\(191\) | 1028.74 | + | 1781.82i | 0.389721 | + | 0.675017i | 0.992412 | − | 0.122958i | \(-0.0392380\pi\) |
−0.602691 | + | 0.797975i | \(0.705905\pi\) | |||||||
\(192\) | −242.403 | + | 419.854i | −0.0911142 | + | 0.157814i | ||||
\(193\) | 632.089 | + | 364.937i | 0.235745 | + | 0.136107i | 0.613219 | − | 0.789913i | \(-0.289874\pi\) |
−0.377475 | + | 0.926020i | \(0.623207\pi\) | |||||||
\(194\) | −5625.20 | −2.08178 | ||||||||
\(195\) | 1202.35 | − | 2560.60i | 0.441548 | − | 0.940351i | ||||
\(196\) | −1832.50 | −0.667822 | ||||||||
\(197\) | 1473.21 | + | 850.557i | 0.532801 | + | 0.307613i | 0.742156 | − | 0.670227i | \(-0.233803\pi\) |
−0.209355 | + | 0.977840i | \(0.567137\pi\) | |||||||
\(198\) | 611.586 | − | 1059.30i | 0.219513 | − | 0.380207i | ||||
\(199\) | −920.440 | − | 1594.25i | −0.327881 | − | 0.567906i | 0.654211 | − | 0.756312i | \(-0.273001\pi\) |
−0.982091 | + | 0.188407i | \(0.939668\pi\) | |||||||
\(200\) | − | 13344.3i | − | 4.71792i | ||||||
\(201\) | 1279.76 | − | 738.867i | 0.449090 | − | 0.259282i | ||||
\(202\) | 6946.97 | − | 4010.83i | 2.41974 | − | 1.39704i | ||||
\(203\) | − | 35.3404i | − | 0.0122188i | ||||||
\(204\) | −608.335 | − | 1053.67i | −0.208784 | − | 0.361625i | ||||
\(205\) | 59.0265 | − | 102.237i | 0.0201102 | − | 0.0348319i | ||||
\(206\) | −2304.88 | − | 1330.72i | −0.779555 | − | 0.450077i | ||||
\(207\) | 1278.09 | 0.429147 | ||||||||
\(208\) | 4287.60 | + | 2013.27i | 1.42929 | + | 0.671131i | ||||
\(209\) | −1214.31 | −0.401894 | ||||||||
\(210\) | −4068.39 | − | 2348.89i | −1.33689 | − | 0.771851i | ||||
\(211\) | −71.4850 | + | 123.816i | −0.0233234 | + | 0.0403972i | −0.877452 | − | 0.479665i | \(-0.840758\pi\) |
0.854128 | + | 0.520063i | \(0.174091\pi\) | |||||||
\(212\) | 2416.63 | + | 4185.72i | 0.782899 | + | 1.35602i | ||||
\(213\) | 2480.58i | 0.797964i | ||||||||
\(214\) | −7655.06 | + | 4419.65i | −2.44528 | + | 1.41178i | ||||
\(215\) | −6287.63 | + | 3630.16i | −1.99448 | + | 1.15151i | ||||
\(216\) | 1288.11i | 0.405762i | ||||||||
\(217\) | 291.386 | + | 504.696i | 0.0911548 | + | 0.157885i | ||||
\(218\) | −2439.74 | + | 4225.76i | −0.757983 | + | 1.31286i | ||||
\(219\) | 171.786 | + | 99.1807i | 0.0530056 | + | 0.0306028i | ||||
\(220\) | 9459.37 | 2.89887 | ||||||||
\(221\) | 893.719 | − | 622.246i | 0.272027 | − | 0.189397i | ||||
\(222\) | −4750.31 | −1.43613 | ||||||||
\(223\) | −2025.39 | − | 1169.36i | −0.608205 | − | 0.351148i | 0.164057 | − | 0.986451i | \(-0.447542\pi\) |
−0.772263 | + | 0.635303i | \(0.780875\pi\) | |||||||
\(224\) | 988.982 | − | 1712.97i | 0.294996 | − | 0.510949i | ||||
\(225\) | 1258.69 | + | 2180.12i | 0.372946 | + | 0.645962i | ||||
\(226\) | − | 9641.57i | − | 2.83782i | ||||||
\(227\) | −2840.01 | + | 1639.68i | −0.830388 | + | 0.479425i | −0.853986 | − | 0.520297i | \(-0.825821\pi\) |
0.0235973 | + | 0.999722i | \(0.492488\pi\) | |||||||
\(228\) | 2044.41 | − | 1180.34i | 0.593835 | − | 0.342851i | ||||
\(229\) | 1143.72i | 0.330041i | 0.986290 | + | 0.165021i | \(0.0527690\pi\) | ||||
−0.986290 | + | 0.165021i | \(0.947231\pi\) | |||||||
\(230\) | 7206.98 | + | 12482.9i | 2.06615 | + | 3.57868i | ||||
\(231\) | 623.376 | − | 1079.72i | 0.177555 | − | 0.307534i | ||||
\(232\) | −94.6418 | − | 54.6415i | −0.0267825 | − | 0.0154629i | ||||
\(233\) | 4238.17 | 1.19164 | 0.595819 | − | 0.803118i | \(-0.296827\pi\) | ||||
0.595819 | + | 0.803118i | \(0.296827\pi\) | |||||||
\(234\) | −2120.77 | + | 179.849i | −0.592476 | + | 0.0502440i | ||||
\(235\) | 4219.59 | 1.17130 | ||||||||
\(236\) | 8211.44 | + | 4740.88i | 2.26491 | + | 1.30765i | ||||
\(237\) | −476.464 | + | 825.259i | −0.130589 | + | 0.226187i | ||||
\(238\) | −904.238 | − | 1566.19i | −0.246273 | − | 0.426558i | ||||
\(239\) | 3310.03i | 0.895849i | 0.894072 | + | 0.447924i | \(0.147837\pi\) | ||||
−0.894072 | + | 0.447924i | \(0.852163\pi\) | |||||||
\(240\) | −5281.88 | + | 3049.50i | −1.42060 | + | 0.820184i | ||||
\(241\) | 4938.82 | − | 2851.43i | 1.32007 | − | 0.762145i | 0.336333 | − | 0.941743i | \(-0.390813\pi\) |
0.983740 | + | 0.179598i | \(0.0574798\pi\) | |||||||
\(242\) | − | 3054.40i | − | 0.811340i | ||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 1796.09 | − | 3110.92i | 0.471242 | − | 0.816214i | ||||
\(245\) | 1828.98 | + | 1055.96i | 0.476936 | + | 0.275359i | ||||
\(246\) | −88.8217 | −0.0230206 | ||||||||
\(247\) | 1207.33 | + | 1734.07i | 0.311015 | + | 0.446705i | ||||
\(248\) | 1802.11 | 0.461427 | ||||||||
\(249\) | −367.499 | − | 212.175i | −0.0935313 | − | 0.0540003i | ||||
\(250\) | −7851.48 | + | 13599.2i | −1.98629 | + | 3.44035i | ||||
\(251\) | −1955.12 | − | 3386.36i | −0.491657 | − | 0.851574i | 0.508297 | − | 0.861182i | \(-0.330275\pi\) |
−0.999954 | + | 0.00960748i | \(0.996942\pi\) | |||||||
\(252\) | 2423.75i | 0.605880i | ||||||||
\(253\) | −3312.85 | + | 1912.68i | −0.823230 | + | 0.475292i | ||||
\(254\) | 5387.99 | − | 3110.76i | 1.33099 | − | 0.768450i | ||||
\(255\) | 1402.19i | 0.344347i | ||||||||
\(256\) | 3997.85 | + | 6924.47i | 0.976037 | + | 1.69055i | ||||
\(257\) | 3486.40 | − | 6038.63i | 0.846209 | − | 1.46568i | −0.0383576 | − | 0.999264i | \(-0.512213\pi\) |
0.884567 | − | 0.466413i | \(-0.154454\pi\) | |||||||
\(258\) | 4730.74 | + | 2731.29i | 1.14156 | + | 0.659081i | ||||
\(259\) | −4841.88 | −1.16162 | ||||||||
\(260\) | −9404.99 | − | 13508.2i | −2.24336 | − | 3.22209i | ||||
\(261\) | 20.6161 | 0.00488930 | ||||||||
\(262\) | −5570.56 | − | 3216.16i | −1.31355 | − | 0.758378i | ||||
\(263\) | −140.845 | + | 243.951i | −0.0330224 | + | 0.0571965i | −0.882064 | − | 0.471129i | \(-0.843847\pi\) |
0.849042 | + | 0.528326i | \(0.177180\pi\) | |||||||
\(264\) | −1927.67 | − | 3338.81i | −0.449392 | − | 0.778371i | ||||
\(265\) | − | 5570.23i | − | 1.29123i | ||||||
\(266\) | 3038.84 | − | 1754.48i | 0.700464 | − | 0.404413i | ||||
\(267\) | −1666.20 | + | 961.980i | −0.381909 | + | 0.220495i | ||||
\(268\) | − | 8598.31i | − | 1.95980i | ||||||
\(269\) | −2166.56 | − | 3752.60i | −0.491070 | − | 0.850558i | 0.508877 | − | 0.860839i | \(-0.330061\pi\) |
−0.999947 | + | 0.0102813i | \(0.996727\pi\) | |||||||
\(270\) | 1370.25 | − | 2373.33i | 0.308854 | − | 0.534950i | ||||
\(271\) | 371.175 | + | 214.298i | 0.0832003 | + | 0.0480357i | 0.541023 | − | 0.841008i | \(-0.318037\pi\) |
−0.457823 | + | 0.889044i | \(0.651371\pi\) | |||||||
\(272\) | −2347.89 | −0.523390 | ||||||||
\(273\) | −2161.66 | + | 183.316i | −0.479229 | + | 0.0406403i | ||||
\(274\) | −10248.8 | −2.25967 | ||||||||
\(275\) | −6525.15 | − | 3767.30i | −1.43084 | − | 0.826096i | ||||
\(276\) | 3718.33 | − | 6440.34i | 0.810933 | − | 1.40458i | ||||
\(277\) | 4469.37 | + | 7741.18i | 0.969454 | + | 1.67914i | 0.697140 | + | 0.716935i | \(0.254455\pi\) |
0.272313 | + | 0.962209i | \(0.412211\pi\) | |||||||
\(278\) | 7293.91i | 1.57360i | ||||||||
\(279\) | −294.419 | + | 169.983i | −0.0631771 | + | 0.0364753i | ||||
\(280\) | −12823.2 | + | 7403.49i | −2.73691 | + | 1.58015i | ||||
\(281\) | − | 775.819i | − | 0.164703i | −0.996603 | − | 0.0823514i | \(-0.973757\pi\) | ||
0.996603 | − | 0.0823514i | \(-0.0262430\pi\) | |||||||
\(282\) | −1587.39 | − | 2749.43i | −0.335204 | − | 0.580590i | ||||
\(283\) | −2007.27 | + | 3476.69i | −0.421624 | + | 0.730274i | −0.996098 | − | 0.0882484i | \(-0.971873\pi\) |
0.574475 | + | 0.818522i | \(0.305206\pi\) | |||||||
\(284\) | 12499.7 | + | 7216.71i | 2.61170 | + | 1.50786i | ||||
\(285\) | −2720.64 | −0.565463 | ||||||||
\(286\) | 5227.97 | − | 3639.94i | 1.08090 | − | 0.752566i | ||||
\(287\) | −90.5340 | −0.0186204 | ||||||||
\(288\) | 999.275 | + | 576.932i | 0.204454 | + | 0.118042i | ||||
\(289\) | 2186.60 | − | 3787.31i | 0.445065 | − | 0.770875i | ||||
\(290\) | 116.252 | + | 201.354i | 0.0235398 | + | 0.0407721i | ||||
\(291\) | − | 3344.77i | − | 0.673793i | ||||||
\(292\) | 999.550 | − | 577.091i | 0.200323 | − | 0.115656i | ||||
\(293\) | 4292.21 | − | 2478.11i | 0.855814 | − | 0.494104i | −0.00679458 | − | 0.999977i | \(-0.502163\pi\) |
0.862608 | + | 0.505873i | \(0.168829\pi\) | |||||||
\(294\) | − | 1588.99i | − | 0.315210i | ||||||
\(295\) | −5463.77 | − | 9463.53i | −1.07835 | − | 1.86776i | ||||
\(296\) | −7486.27 | + | 12966.6i | −1.47004 | + | 2.54618i | ||||
\(297\) | 629.864 | + | 363.652i | 0.123059 | + | 0.0710480i | ||||
\(298\) | 4875.43 | 0.947738 | ||||||||
\(299\) | 6025.15 | + | 2829.15i | 1.16536 | + | 0.547204i | ||||
\(300\) | 14647.6 | 2.81893 | ||||||||
\(301\) | 4821.94 | + | 2783.95i | 0.923362 | + | 0.533103i | ||||
\(302\) | 3690.90 | − | 6392.83i | 0.703270 | − | 1.21810i | ||||
\(303\) | 2384.86 | + | 4130.70i | 0.452167 | + | 0.783177i | ||||
\(304\) | − | 4555.58i | − | 0.859474i | ||||||
\(305\) | −3585.28 | + | 2069.96i | −0.673090 | + | 0.388608i | ||||
\(306\) | 913.649 | − | 527.495i | 0.170686 | − | 0.0985454i | ||||
\(307\) | 3894.90i | 0.724084i | 0.932162 | + | 0.362042i | \(0.117920\pi\) | ||||
−0.932162 | + | 0.362042i | \(0.882080\pi\) | |||||||
\(308\) | −3627.16 | − | 6282.43i | −0.671029 | − | 1.16226i | ||||
\(309\) | 791.254 | − | 1370.49i | 0.145673 | − | 0.252312i | ||||
\(310\) | −3320.38 | − | 1917.02i | −0.608338 | − | 0.351224i | ||||
\(311\) | −3097.44 | −0.564758 | −0.282379 | − | 0.959303i | \(-0.591124\pi\) | ||||
−0.282379 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(312\) | −2851.32 | + | 6072.37i | −0.517386 | + | 1.10186i | ||||
\(313\) | 4487.36 | 0.810353 | 0.405177 | − | 0.914238i | \(-0.367210\pi\) | ||||
0.405177 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(314\) | −288.567 | − | 166.604i | −0.0518623 | − | 0.0299427i | ||||
\(315\) | 1396.66 | − | 2419.09i | 0.249819 | − | 0.432699i | ||||
\(316\) | 2772.34 | + | 4801.83i | 0.493533 | + | 0.854824i | ||||
\(317\) | 6820.62i | 1.20847i | 0.796807 | + | 0.604233i | \(0.206521\pi\) | ||||
−0.796807 | + | 0.604233i | \(0.793479\pi\) | |||||||
\(318\) | −3629.50 | + | 2095.49i | −0.640038 | + | 0.369526i | ||||
\(319\) | −53.4377 | + | 30.8523i | −0.00937911 | + | 0.00541503i | ||||
\(320\) | − | 3251.01i | − | 0.567928i | ||||||
\(321\) | −2627.95 | − | 4551.74i | −0.456940 | − | 0.791443i | ||||
\(322\) | 5526.99 | − | 9573.02i | 0.956543 | − | 1.65678i | ||||
\(323\) | −907.031 | − | 523.675i | −0.156249 | − | 0.0902106i | ||||
\(324\) | −1413.91 | −0.242441 | ||||||||
\(325\) | 1107.85 | + | 13063.7i | 0.189084 | + | 2.22967i | ||||
\(326\) | −17786.1 | −3.02173 | ||||||||
\(327\) | −2512.66 | − | 1450.68i | −0.424924 | − | 0.245330i | ||||
\(328\) | −139.979 | + | 242.451i | −0.0235642 | + | 0.0408143i | ||||
\(329\) | −1617.99 | − | 2802.44i | −0.271132 | − | 0.469615i | ||||
\(330\) | 8202.35i | 1.36826i | ||||||||
\(331\) | 4341.35 | − | 2506.48i | 0.720913 | − | 0.416219i | −0.0941759 | − | 0.995556i | \(-0.530022\pi\) |
0.815088 | + | 0.579337i | \(0.196688\pi\) | |||||||
\(332\) | −2138.32 | + | 1234.56i | −0.353481 | + | 0.204082i | ||||
\(333\) | − | 2824.56i | − | 0.464819i | ||||||
\(334\) | 657.542 | + | 1138.90i | 0.107722 | + | 0.186580i | ||||
\(335\) | −4954.70 | + | 8581.78i | −0.808071 | + | 1.39962i | ||||
\(336\) | 4050.64 | + | 2338.64i | 0.657680 | + | 0.379712i | ||||
\(337\) | −3220.79 | −0.520616 | −0.260308 | − | 0.965526i | \(-0.583824\pi\) | ||||
−0.260308 | + | 0.965526i | \(0.583824\pi\) | |||||||
\(338\) | −10395.8 | − | 3846.65i | −1.67295 | − | 0.619025i | ||||
\(339\) | 5732.92 | 0.918494 | ||||||||
\(340\) | 7065.68 | + | 4079.37i | 1.12703 | + | 0.650691i | ||||
\(341\) | 508.762 | − | 881.202i | 0.0807948 | − | 0.139941i | ||||
\(342\) | 1023.49 | + | 1772.74i | 0.161825 | + | 0.280288i | ||||
\(343\) | − | 6911.39i | − | 1.08799i | ||||||
\(344\) | 14910.9 | − | 8608.79i | 2.33703 | − | 1.34929i | ||||
\(345\) | −7422.37 | + | 4285.31i | −1.15828 | + | 0.668734i | ||||
\(346\) | 4600.13i | 0.714753i | ||||||||
\(347\) | 1680.36 | + | 2910.46i | 0.259960 | + | 0.450265i | 0.966231 | − | 0.257677i | \(-0.0829571\pi\) |
−0.706271 | + | 0.707942i | \(0.749624\pi\) | |||||||
\(348\) | 59.9783 | − | 103.885i | 0.00923900 | − | 0.0160024i | ||||
\(349\) | 3976.20 | + | 2295.66i | 0.609859 | + | 0.352102i | 0.772910 | − | 0.634515i | \(-0.218800\pi\) |
−0.163051 | + | 0.986618i | \(0.552134\pi\) | |||||||
\(350\) | 21772.4 | 3.32510 | ||||||||
\(351\) | −106.939 | − | 1261.02i | −0.0162621 | − | 0.191762i | ||||
\(352\) | −3453.54 | −0.522938 | ||||||||
\(353\) | 1506.96 | + | 870.044i | 0.227216 | + | 0.131183i | 0.609287 | − | 0.792950i | \(-0.291456\pi\) |
−0.382071 | + | 0.924133i | \(0.624789\pi\) | |||||||
\(354\) | −4110.88 | + | 7120.25i | −0.617205 | + | 1.06903i | ||||
\(355\) | −8317.12 | − | 14405.7i | −1.24346 | − | 2.15373i | ||||
\(356\) | 11194.7i | 1.66662i | ||||||||
\(357\) | 931.262 | − | 537.664i | 0.138061 | − | 0.0797093i | ||||
\(358\) | 11755.8 | − | 6787.24i | 1.73552 | − | 1.00200i | ||||
\(359\) | 1425.49i | 0.209567i | 0.994495 | + | 0.104784i | \(0.0334150\pi\) | ||||
−0.994495 | + | 0.104784i | \(0.966585\pi\) | |||||||
\(360\) | −4318.89 | − | 7480.54i | −0.632293 | − | 1.09516i | ||||
\(361\) | −2413.42 | + | 4180.17i | −0.351862 | + | 0.609443i | ||||
\(362\) | −20858.9 | − | 12042.9i | −3.02851 | − | 1.74851i | ||||
\(363\) | 1816.16 | 0.262600 | ||||||||
\(364\) | −5365.15 | + | 11426.0i | −0.772555 | + | 1.64529i | ||||
\(365\) | −1330.17 | −0.190752 | ||||||||
\(366\) | 2697.52 | + | 1557.42i | 0.385251 | + | 0.222425i | ||||
\(367\) | −5424.61 | + | 9395.69i | −0.771559 | + | 1.33638i | 0.165149 | + | 0.986269i | \(0.447189\pi\) |
−0.936708 | + | 0.350111i | \(0.886144\pi\) | |||||||
\(368\) | −7175.53 | − | 12428.4i | −1.01644 | − | 1.76053i | ||||
\(369\) | − | 52.8138i | − | 0.00745089i | ||||||
\(370\) | 27586.9 | − | 15927.3i | 3.87615 | − | 2.23789i | ||||
\(371\) | −3699.46 | + | 2135.89i | −0.517700 | + | 0.298894i | ||||
\(372\) | 1978.12i | 0.275700i | ||||||||
\(373\) | 247.374 | + | 428.465i | 0.0343393 | + | 0.0594774i | 0.882684 | − | 0.469966i | \(-0.155734\pi\) |
−0.848345 | + | 0.529444i | \(0.822401\pi\) | |||||||
\(374\) | −1578.81 | + | 2734.57i | −0.218284 | + | 0.378078i | ||||
\(375\) | −8086.13 | − | 4668.53i | −1.11351 | − | 0.642885i | ||||
\(376\) | −10006.6 | −1.37248 | ||||||||
\(377\) | 97.1882 | + | 45.6354i | 0.0132770 | + | 0.00623433i | ||||
\(378\) | −2101.66 | −0.285973 | ||||||||
\(379\) | 10949.4 | + | 6321.66i | 1.48400 | + | 0.856786i | 0.999835 | − | 0.0181912i | \(-0.00579076\pi\) |
0.484163 | + | 0.874978i | \(0.339124\pi\) | |||||||
\(380\) | −7915.13 | + | 13709.4i | −1.06852 | + | 1.85073i | ||||
\(381\) | 1849.67 | + | 3203.72i | 0.248718 | + | 0.430792i | ||||
\(382\) | 10380.7i | 1.39037i | ||||||||
\(383\) | 2010.48 | − | 1160.75i | 0.268227 | − | 0.154861i | −0.359855 | − | 0.933008i | \(-0.617174\pi\) |
0.628082 | + | 0.778147i | \(0.283840\pi\) | |||||||
\(384\) | −4783.05 | + | 2761.50i | −0.635636 | + | 0.366984i | ||||
\(385\) | 8360.47i | 1.10673i | ||||||||
\(386\) | 1841.24 | + | 3189.12i | 0.242789 | + | 0.420523i | ||||
\(387\) | −1624.04 | + | 2812.92i | −0.213319 | + | 0.369480i | ||||
\(388\) | −16854.4 | − | 9730.90i | −2.20529 | − | 1.27323i | ||||
\(389\) | 10477.6 | 1.36564 | 0.682821 | − | 0.730586i | \(-0.260753\pi\) | ||||
0.682821 | + | 0.730586i | \(0.260753\pi\) | |||||||
\(390\) | 11713.1 | − | 8155.19i | 1.52082 | − | 1.05886i | ||||
\(391\) | −3299.38 | −0.426744 | ||||||||
\(392\) | −4337.36 | − | 2504.18i | −0.558851 | − | 0.322653i | ||||
\(393\) | 1912.35 | − | 3312.28i | 0.245458 | − | 0.425146i | ||||
\(394\) | 4291.37 | + | 7432.88i | 0.548722 | + | 0.950414i | ||||
\(395\) | − | 6390.14i | − | 0.813982i | ||||||
\(396\) | 3664.91 | − | 2115.94i | 0.465073 | − | 0.268510i | ||||
\(397\) | 1530.14 | − | 883.424i | 0.193439 | − | 0.111682i | −0.400152 | − | 0.916449i | \(-0.631043\pi\) |
0.593592 | + | 0.804766i | \(0.297709\pi\) | |||||||
\(398\) | − | 9287.91i | − | 1.16975i | ||||||
\(399\) | 1043.22 | + | 1806.91i | 0.130893 | + | 0.226713i | ||||
\(400\) | 14133.3 | − | 24479.5i | 1.76666 | − | 3.05994i | ||||
\(401\) | −4331.55 | − | 2500.82i | −0.539420 | − | 0.311434i | 0.205424 | − | 0.978673i | \(-0.434143\pi\) |
−0.744844 | + | 0.667239i | \(0.767476\pi\) | |||||||
\(402\) | 7455.71 | 0.925018 | ||||||||
\(403\) | −1764.21 | + | 149.612i | −0.218069 | + | 0.0184930i | ||||
\(404\) | 27753.0 | 3.41773 | ||||||||
\(405\) | 1411.20 | + | 814.754i | 0.173143 | + | 0.0999641i | ||||
\(406\) | 89.1526 | − | 154.417i | 0.0108980 | − | 0.0188758i | ||||
\(407\) | 4226.98 | + | 7321.34i | 0.514800 | + | 0.891660i | ||||
\(408\) | − | 3325.24i | − | 0.403490i | ||||||
\(409\) | −9706.92 | + | 5604.29i | −1.17354 | + | 0.677541i | −0.954510 | − | 0.298178i | \(-0.903621\pi\) |
−0.219025 | + | 0.975719i | \(0.570288\pi\) | |||||||
\(410\) | 515.822 | − | 297.810i | 0.0621333 | − | 0.0358727i | ||||
\(411\) | − | 6093.96i | − | 0.731370i | ||||||
\(412\) | −4603.97 | − | 7974.31i | −0.550537 | − | 0.953558i | ||||
\(413\) | −4190.13 | + | 7257.51i | −0.499232 | + | 0.864695i | ||||
\(414\) | 5584.51 | + | 3224.22i | 0.662956 | + | 0.382758i | ||||
\(415\) | 2845.61 | 0.336592 | ||||||||
\(416\) | 3433.68 | + | 4931.73i | 0.404688 | + | 0.581246i | ||||
\(417\) | −4336.99 | −0.509313 | ||||||||
\(418\) | −5305.84 | − | 3063.33i | −0.620854 | − | 0.358450i | ||||
\(419\) | −1642.59 | + | 2845.06i | −0.191518 | + | 0.331719i | −0.945753 | − | 0.324885i | \(-0.894674\pi\) |
0.754236 | + | 0.656604i | \(0.228008\pi\) | |||||||
\(420\) | −8126.58 | − | 14075.6i | −0.944134 | − | 1.63529i | ||||
\(421\) | − | 13289.9i | − | 1.53850i | −0.638948 | − | 0.769250i | \(-0.720630\pi\) | ||
0.638948 | − | 0.769250i | \(-0.279370\pi\) | |||||||
\(422\) | −624.695 | + | 360.668i | −0.0720609 | + | 0.0416044i | ||||
\(423\) | 1634.83 | − | 943.868i | 0.187915 | − | 0.108493i | ||||
\(424\) | 13209.6i | 1.51301i | ||||||||
\(425\) | −3249.31 | − | 5627.96i | −0.370858 | − | 0.642344i | ||||
\(426\) | −6257.71 | + | 10838.7i | −0.711707 | + | 1.23271i | ||||
\(427\) | 2749.52 | + | 1587.44i | 0.311613 | + | 0.179910i | ||||
\(428\) | −30581.8 | −3.45380 | ||||||||
\(429\) | 2164.32 | + | 3108.58i | 0.243577 | + | 0.349845i | ||||
\(430\) | −36631.0 | −4.10815 | ||||||||
\(431\) | 11857.8 | + | 6846.13i | 1.32523 | + | 0.765119i | 0.984557 | − | 0.175064i | \(-0.0560134\pi\) |
0.340668 | + | 0.940184i | \(0.389347\pi\) | |||||||
\(432\) | −1364.27 | + | 2362.98i | −0.151940 | + | 0.263168i | ||||
\(433\) | −5001.26 | − | 8662.43i | −0.555070 | − | 0.961409i | −0.997898 | − | 0.0648023i | \(-0.979358\pi\) |
0.442829 | − | 0.896606i | \(-0.353975\pi\) | |||||||
\(434\) | 2940.30i | 0.325205i | ||||||||
\(435\) | −119.726 | + | 69.1238i | −0.0131964 | + | 0.00761892i | ||||
\(436\) | −14620.1 | + | 8440.91i | −1.60591 | + | 0.927170i | ||||
\(437\) | − | 6401.73i | − | 0.700769i | ||||||
\(438\) | 500.403 | + | 866.724i | 0.0545895 | + | 0.0945517i | ||||
\(439\) | 2243.60 | − | 3886.04i | 0.243921 | − | 0.422484i | −0.717907 | − | 0.696139i | \(-0.754900\pi\) |
0.961828 | + | 0.273656i | \(0.0882329\pi\) | |||||||
\(440\) | 22389.4 | + | 12926.5i | 2.42585 | + | 1.40056i | ||||
\(441\) | 944.821 | 0.102021 | ||||||||
\(442\) | 5474.76 | − | 464.279i | 0.589158 | − | 0.0499627i | ||||
\(443\) | 2035.35 | 0.218290 | 0.109145 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109145 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(444\) | −14233.0 | − | 8217.45i | −1.52133 | − | 0.878340i | ||||
\(445\) | 6450.84 | − | 11173.2i | 0.687190 | − | 1.19025i | ||||
\(446\) | −5899.83 | − | 10218.8i | −0.626379 | − | 1.08492i | ||||
\(447\) | 2898.95i | 0.306747i | ||||||||
\(448\) | −2159.15 | + | 1246.59i | −0.227702 | + | 0.131464i | ||||
\(449\) | −3096.55 | + | 1787.79i | −0.325468 | + | 0.187909i | −0.653827 | − | 0.756644i | \(-0.726838\pi\) |
0.328359 | + | 0.944553i | \(0.393504\pi\) | |||||||
\(450\) | 12701.1i | 1.33053i | ||||||||
\(451\) | 79.0365 | + | 136.895i | 0.00825207 | + | 0.0142930i | ||||
\(452\) | 16678.7 | − | 28888.4i | 1.73562 | − | 3.00619i | ||||
\(453\) | 3801.21 | + | 2194.63i | 0.394252 | + | 0.227622i | ||||
\(454\) | −16545.6 | −1.71040 | ||||||||
\(455\) | 11939.0 | − | 8312.41i | 1.23012 | − | 0.856465i | ||||
\(456\) | 6451.90 | 0.662583 | ||||||||
\(457\) | −6978.95 | − | 4029.30i | −0.714358 | − | 0.412435i | 0.0983147 | − | 0.995155i | \(-0.468655\pi\) |
−0.812672 | + | 0.582721i | \(0.801988\pi\) | |||||||
\(458\) | −2885.25 | + | 4997.41i | −0.294365 | + | 0.509855i | ||||
\(459\) | 313.651 | + | 543.260i | 0.0318954 | + | 0.0552445i | ||||
\(460\) | 49868.8i | 5.05466i | ||||||||
\(461\) | 10125.7 | − | 5846.07i | 1.02300 | − | 0.590626i | 0.108025 | − | 0.994148i | \(-0.465547\pi\) |
0.914970 | + | 0.403522i | \(0.132214\pi\) | |||||||
\(462\) | 5447.58 | − | 3145.16i | 0.548581 | − | 0.316723i | ||||
\(463\) | − | 1732.40i | − | 0.173891i | −0.996213 | − | 0.0869455i | \(-0.972289\pi\) | ||
0.996213 | − | 0.0869455i | \(-0.0277106\pi\) | |||||||
\(464\) | −115.744 | − | 200.475i | −0.0115804 | − | 0.0200578i | ||||
\(465\) | 1139.87 | − | 1974.31i | 0.113678 | − | 0.196896i | ||||
\(466\) | 18518.3 | + | 10691.6i | 1.84087 | + | 1.06283i | ||||
\(467\) | −10769.9 | −1.06718 | −0.533588 | − | 0.845745i | \(-0.679157\pi\) | ||||
−0.533588 | + | 0.845745i | \(0.679157\pi\) | |||||||
\(468\) | −6665.45 | − | 3129.81i | −0.658356 | − | 0.309135i | ||||
\(469\) | 7599.44 | 0.748208 | ||||||||
\(470\) | 18437.1 | + | 10644.7i | 1.80945 | + | 1.04469i | ||||
\(471\) | 99.0636 | − | 171.583i | 0.00969132 | − | 0.0167859i | ||||
\(472\) | 12957.1 | + | 22442.4i | 1.26356 | + | 2.18855i | ||||
\(473\) | − | 9721.58i | − | 0.945029i | ||||||
\(474\) | −4163.74 | + | 2403.93i | −0.403474 | + | 0.232946i | ||||
\(475\) | 10919.8 | − | 6304.57i | 1.05481 | − | 0.608997i | ||||
\(476\) | − | 6256.88i | − | 0.602487i | ||||||
\(477\) | −1245.99 | − | 2158.12i | −0.119601 | − | 0.207156i | ||||
\(478\) | −8350.15 | + | 14462.9i | −0.799010 | + | 1.38393i | ||||
\(479\) | 6851.68 | + | 3955.82i | 0.653572 | + | 0.377340i | 0.789824 | − | 0.613334i | \(-0.210172\pi\) |
−0.136251 | + | 0.990674i | \(0.543505\pi\) | |||||||
\(480\) | −7737.57 | −0.735772 | ||||||||
\(481\) | 6252.37 | − | 13315.5i | 0.592689 | − | 1.26223i | ||||
\(482\) | 28773.0 | 2.71904 | ||||||||
\(483\) | 5692.17 | + | 3286.37i | 0.536237 | + | 0.309597i | ||||
\(484\) | 5283.74 | − | 9151.70i | 0.496219 | − | 0.859476i | ||||
\(485\) | 11214.7 | + | 19424.4i | 1.04996 | + | 1.81859i | ||||
\(486\) | − | 1226.02i | − | 0.114431i | ||||||
\(487\) | −9495.78 | + | 5482.39i | −0.883562 | + | 0.510125i | −0.871831 | − | 0.489806i | \(-0.837067\pi\) |
−0.0117307 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(488\) | 8502.35 | − | 4908.83i | 0.788695 | − | 0.455353i | ||||
\(489\) | − | 10575.7i | − | 0.978018i | ||||||
\(490\) | 5327.72 | + | 9227.88i | 0.491188 | + | 0.850762i | ||||
\(491\) | −4569.69 | + | 7914.93i | −0.420014 | + | 0.727486i | −0.995940 | − | 0.0900157i | \(-0.971308\pi\) |
0.575926 | + | 0.817502i | \(0.304642\pi\) | |||||||
\(492\) | −266.131 | − | 153.651i | −0.0243864 | − | 0.0140795i | ||||
\(493\) | −53.2204 | −0.00486192 | ||||||||
\(494\) | 900.832 | + | 10622.6i | 0.0820452 | + | 0.967474i | ||||
\(495\) | −4877.16 | −0.442852 | ||||||||
\(496\) | 3305.89 | + | 1908.66i | 0.299272 | + | 0.172785i | ||||
\(497\) | −6378.35 | + | 11047.6i | −0.575670 | + | 0.997090i | ||||
\(498\) | −1070.50 | − | 1854.17i | −0.0963261 | − | 0.166842i | ||||
\(499\) | − | 12577.5i | − | 1.12835i | −0.825655 | − | 0.564175i | \(-0.809194\pi\) | ||
0.825655 | − | 0.564175i | \(-0.190806\pi\) | |||||||
\(500\) | −47049.8 | + | 27164.2i | −4.20826 | + | 2.42964i | ||||
\(501\) | −677.193 | + | 390.978i | −0.0603887 | + | 0.0348655i | ||||
\(502\) | − | 19728.6i | − | 1.75404i | ||||||
\(503\) | −6607.30 | − | 11444.2i | −0.585696 | − | 1.01446i | −0.994788 | − | 0.101962i | \(-0.967488\pi\) |
0.409092 | − | 0.912493i | \(-0.365845\pi\) | |||||||
\(504\) | −3312.13 | + | 5736.77i | −0.292726 | + | 0.507016i | ||||
\(505\) | −27699.6 | − | 15992.4i | −2.44083 | − | 1.40921i | ||||
\(506\) | −19300.3 | −1.69566 | ||||||||
\(507\) | 2287.24 | − | 6181.41i | 0.200355 | − | 0.541471i | ||||
\(508\) | 21524.9 | 1.87995 | ||||||||
\(509\) | −18809.9 | − | 10859.9i | −1.63798 | − | 0.945689i | −0.981527 | − | 0.191323i | \(-0.938722\pi\) |
−0.656454 | − | 0.754366i | \(-0.727945\pi\) | |||||||
\(510\) | −3537.28 | + | 6126.74i | −0.307124 | + | 0.531955i | ||||
\(511\) | 510.050 | + | 883.432i | 0.0441551 | + | 0.0764789i | ||||
\(512\) | 25613.2i | 2.21085i | ||||||||
\(513\) | −1054.08 | + | 608.572i | −0.0907186 | + | 0.0523764i | ||||
\(514\) | 30467.1 | − | 17590.2i | 2.61449 | − | 1.50947i | ||||
\(515\) | 10612.0i | 0.907999i | ||||||||
\(516\) | 9449.60 | + | 16367.2i | 0.806193 | + | 1.39637i | ||||
\(517\) | −2825.02 | + | 4893.07i | −0.240317 | + | 0.416242i | ||||
\(518\) | −21156.2 | − | 12214.5i | −1.79450 | − | 1.03605i | ||||
\(519\) | −2735.26 | −0.231338 | ||||||||
\(520\) | −3801.30 | − | 44824.8i | −0.320573 | − | 3.78019i | ||||
\(521\) | −4627.05 | −0.389088 | −0.194544 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194544 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(522\) | 90.0804 | + | 52.0080i | 0.00755309 | + | 0.00436078i | ||||
\(523\) | −6891.98 | + | 11937.3i | −0.576224 | + | 0.998049i | 0.419683 | + | 0.907671i | \(0.362141\pi\) |
−0.995907 | + | 0.0903788i | \(0.971192\pi\) | |||||||
\(524\) | −11127.1 | − | 19272.8i | −0.927654 | − | 1.60674i | ||||
\(525\) | 12946.0i | 1.07621i | ||||||||
\(526\) | −1230.82 | + | 710.617i | −0.102028 | + | 0.0589056i | ||||
\(527\) | 760.040 | − | 438.809i | 0.0628233 | − | 0.0362710i | ||||
\(528\) | − | 8166.55i | − | 0.673113i | ||||||
\(529\) | −3999.93 | − | 6928.07i | −0.328752 | − | 0.569415i | ||||
\(530\) | 14051.9 | − | 24338.7i | 1.15165 | − | 1.99472i | ||||
\(531\) | −4233.74 | − | 2444.35i | −0.346005 | − | 0.199766i | ||||
\(532\) | 12140.1 | 0.989362 | ||||||||
\(533\) | 116.907 | − | 248.974i | 0.00950061 | − | 0.0202331i | ||||
\(534\) | −9707.09 | −0.786642 | ||||||||
\(535\) | 30523.0 | + | 17622.5i | 2.46659 | + | 1.42409i | ||||
\(536\) | 11749.9 | − | 20351.4i | 0.946860 | − | 1.64001i | ||||
\(537\) | 4035.73 | + | 6990.08i | 0.324310 | + | 0.561721i | ||||
\(538\) | − | 21862.2i | − | 1.75195i | ||||||
\(539\) | −2449.01 | + | 1413.93i | −0.195707 | + | 0.112992i | ||||
\(540\) | 8211.15 | − | 4740.71i | 0.654355 | − | 0.377792i | ||||
\(541\) | − | 454.638i | − | 0.0361302i | −0.999837 | − | 0.0180651i | \(-0.994249\pi\) | ||
0.999837 | − | 0.0180651i | \(-0.00575061\pi\) | |||||||
\(542\) | 1081.21 | + | 1872.72i | 0.0856865 | + | 0.148413i | ||||
\(543\) | 7160.77 | − | 12402.8i | 0.565926 | − | 0.980213i | ||||
\(544\) | −2579.62 | − | 1489.34i | −0.203309 | − | 0.117381i | ||||
\(545\) | 19456.0 | 1.52918 | ||||||||
\(546\) | −9907.63 | − | 4652.19i | −0.776570 | − | 0.364644i | ||||
\(547\) | 11611.4 | 0.907621 | 0.453810 | − | 0.891098i | \(-0.350064\pi\) | ||||
0.453810 | + | 0.891098i | \(0.350064\pi\) | |||||||
\(548\) | −30707.7 | − | 17729.1i | −2.39374 | − | 1.38202i | ||||
\(549\) | −926.047 | + | 1603.96i | −0.0719904 | + | 0.124691i | ||||
\(550\) | −19007.4 | − | 32921.8i | −1.47360 | − | 2.55234i | ||||
\(551\) | − | 103.263i | − | 0.00798390i | ||||||
\(552\) | 17601.9 | − | 10162.4i | 1.35722 | − | 0.783591i | ||||
\(553\) | −4244.00 | + | 2450.28i | −0.326353 | + | 0.188420i | ||||
\(554\) | 45099.3i | 3.45864i | ||||||||
\(555\) | 9470.45 | + | 16403.3i | 0.724321 | + | 1.25456i | ||||
\(556\) | −12617.6 | + | 21854.3i | −0.962417 | + | 1.66696i | ||||
\(557\) | 4229.61 | + | 2441.97i | 0.321749 | + | 0.185762i | 0.652172 | − | 0.758071i | \(-0.273858\pi\) |
−0.330423 | + | 0.943833i | \(0.607191\pi\) | |||||||
\(558\) | −1715.25 | −0.130130 | ||||||||
\(559\) | −13882.6 | + | 9665.69i | −1.05040 | + | 0.731333i | ||||
\(560\) | −31364.9 | −2.36680 | ||||||||
\(561\) | −1625.99 | − | 938.766i | −0.122370 | − | 0.0706501i | ||||
\(562\) | 1957.14 | − | 3389.87i | 0.146899 | − | 0.254436i | ||||
\(563\) | 9808.67 | + | 16989.1i | 0.734256 | + | 1.27177i | 0.955049 | + | 0.296448i | \(0.0958022\pi\) |
−0.220793 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(564\) | − | 10983.9i | − | 0.820048i | ||||||
\(565\) | −33293.3 | + | 19221.9i | −2.47905 | + | 1.43128i | ||||
\(566\) | −17541.2 | + | 10127.4i | −1.30267 | + | 0.752095i | ||||
\(567\) | − | 1249.66i | − | 0.0925587i | ||||||
\(568\) | 19723.7 | + | 34162.5i | 1.45702 | + | 2.52364i | ||||
\(569\) | 3737.59 | − | 6473.70i | 0.275374 | − | 0.476963i | −0.694855 | − | 0.719150i | \(-0.744531\pi\) |
0.970230 | + | 0.242187i | \(0.0778648\pi\) | |||||||
\(570\) | −11887.6 | − | 6863.31i | −0.873539 | − | 0.504338i | ||||
\(571\) | 7799.56 | 0.571631 | 0.285816 | − | 0.958285i | \(-0.407735\pi\) | ||||
0.285816 | + | 0.958285i | \(0.407735\pi\) | |||||||
\(572\) | 21960.9 | − | 1862.36i | 1.60530 | − | 0.136135i | ||||
\(573\) | −6172.42 | −0.450011 | ||||||||
\(574\) | −395.581 | − | 228.389i | −0.0287652 | − | 0.0166076i | ||||
\(575\) | 19860.8 | − | 34399.9i | 1.44044 | − | 2.49491i | ||||
\(576\) | −727.209 | − | 1259.56i | −0.0526048 | − | 0.0911142i | ||||
\(577\) | 13136.1i | 0.947771i | 0.880587 | + | 0.473885i | \(0.157149\pi\) | ||||
−0.880587 | + | 0.473885i | \(0.842851\pi\) | |||||||
\(578\) | 19108.4 | − | 11032.2i | 1.37509 | − | 0.793910i | ||||
\(579\) | −1896.27 | + | 1094.81i | −0.136107 | + | 0.0785816i | ||||
\(580\) | 804.404i | 0.0575880i | ||||||||
\(581\) | −1091.14 | − | 1889.91i | −0.0779142 | − | 0.134951i | ||||
\(582\) | 8437.79 | − | 14614.7i | 0.600958 | − | 1.04089i | ||||
\(583\) | 6459.29 | + | 3729.27i | 0.458862 | + | 0.264924i | ||||
\(584\) | 3154.45 | 0.223514 | ||||||||
\(585\) | 4849.12 | + | 6964.69i | 0.342712 | + | 0.492230i | ||||
\(586\) | 25005.9 | 1.76277 | ||||||||
\(587\) | −19183.1 | − | 11075.3i | −1.34884 | − | 0.778754i | −0.360756 | − | 0.932660i | \(-0.617481\pi\) |
−0.988085 | + | 0.153907i | \(0.950814\pi\) | |||||||
\(588\) | 2748.76 | − | 4760.99i | 0.192784 | − | 0.333911i | ||||
\(589\) | 851.414 | + | 1474.69i | 0.0595618 | + | 0.103164i | ||||
\(590\) | − | 55133.4i | − | 3.84713i | ||||||
\(591\) | −4419.63 | + | 2551.67i | −0.307613 | + | 0.177600i | ||||
\(592\) | −27466.5 | + | 15857.8i | −1.90687 | + | 1.10093i | ||||
\(593\) | 22770.3i | 1.57684i | 0.615138 | + | 0.788419i | \(0.289100\pi\) | ||||
−0.615138 | + | 0.788419i | \(0.710900\pi\) | |||||||
\(594\) | 1834.76 | + | 3177.90i | 0.126736 | + | 0.219513i | ||||
\(595\) | −3605.47 | + | 6244.86i | −0.248420 | + | 0.430276i | ||||
\(596\) | 14607.9 | + | 8433.89i | 1.00397 | + | 0.579640i | ||||
\(597\) | 5522.64 | 0.378604 | ||||||||
\(598\) | 19189.4 | + | 27561.3i | 1.31223 | + | 1.88472i | ||||
\(599\) | −7214.11 | −0.492088 | −0.246044 | − | 0.969259i | \(-0.579131\pi\) | ||||
−0.246044 | + | 0.969259i | \(0.579131\pi\) | |||||||
\(600\) | 34669.5 | + | 20016.4i | 2.35896 | + | 1.36194i | ||||
\(601\) | −13638.4 | + | 23622.4i | −0.925658 | + | 1.60329i | −0.135160 | + | 0.990824i | \(0.543155\pi\) |
−0.790499 | + | 0.612464i | \(0.790179\pi\) | |||||||
\(602\) | 14046.0 | + | 24328.4i | 0.950953 | + | 1.64710i | ||||
\(603\) | 4433.20i | 0.299393i | ||||||||
\(604\) | 22117.6 | − | 12769.6i | 1.48999 | − | 0.860245i | ||||
\(605\) | −10547.2 | + | 6089.41i | −0.708765 | + | 0.409206i | ||||
\(606\) | 24065.0i | 1.61316i | ||||||||
\(607\) | −5783.08 | − | 10016.6i | −0.386701 | − | 0.669787i | 0.605302 | − | 0.795996i | \(-0.293052\pi\) |
−0.992004 | + | 0.126209i | \(0.959719\pi\) | |||||||
\(608\) | 2889.75 | − | 5005.19i | 0.192755 | − | 0.333861i | ||||
\(609\) | 91.8170 | + | 53.0106i | 0.00610938 | + | 0.00352725i | ||||
\(610\) | −20887.4 | −1.38640 | ||||||||
\(611\) | 9796.20 | − | 830.752i | 0.648628 | − | 0.0550059i | ||||
\(612\) | 3650.01 | 0.241083 | ||||||||
\(613\) | −21197.3 | − | 12238.3i | −1.39666 | − | 0.806362i | −0.402619 | − | 0.915368i | \(-0.631900\pi\) |
−0.994041 | + | 0.109006i | \(0.965233\pi\) | |||||||
\(614\) | −9825.61 | + | 17018.5i | −0.645813 | + | 1.11858i | ||||
\(615\) | 177.079 | + | 306.711i | 0.0116106 | + | 0.0201102i | ||||
\(616\) | − | 19826.5i | − | 1.29681i | ||||||
\(617\) | 2098.62 | − | 1211.64i | 0.136933 | − | 0.0790581i | −0.429969 | − | 0.902844i | \(-0.641475\pi\) |
0.566901 | + | 0.823786i | \(0.308142\pi\) | |||||||
\(618\) | 6914.63 | − | 3992.17i | 0.450077 | − | 0.259852i | ||||
\(619\) | − | 17223.4i | − | 1.11836i | −0.829045 | − | 0.559182i | \(-0.811115\pi\) | ||
0.829045 | − | 0.559182i | \(-0.188885\pi\) | |||||||
\(620\) | −6632.42 | − | 11487.7i | −0.429620 | − | 0.744124i | ||||
\(621\) | −1917.14 | + | 3320.58i | −0.123884 | + | 0.214573i | ||||
\(622\) | −13534.0 | − | 7813.86i | −0.872450 | − | 0.503709i | ||||
\(623\) | −9894.22 | −0.636282 | ||||||||
\(624\) | −11662.0 | + | 8119.60i | −0.748165 | + | 0.520904i | ||||
\(625\) | 27648.7 | 1.76952 | ||||||||
\(626\) | 19607.1 | + | 11320.2i | 1.25185 | + | 0.722757i | ||||
\(627\) | 1821.47 | − | 3154.88i | 0.116017 | − | 0.200947i | ||||
\(628\) | −576.409 | − | 998.370i | −0.0366262 | − | 0.0634384i | ||||
\(629\) | 7291.57i | 0.462216i | ||||||||
\(630\) | 12205.2 | − | 7046.67i | 0.771851 | − | 0.445628i | ||||
\(631\) | −8004.31 | + | 4621.29i | −0.504987 | + | 0.291554i | −0.730771 | − | 0.682623i | \(-0.760839\pi\) |
0.225784 | + | 0.974177i | \(0.427506\pi\) | |||||||
\(632\) | 15154.0i | 0.953786i | ||||||||
\(633\) | −214.455 | − | 371.447i | −0.0134657 | − | 0.0233234i | ||||
\(634\) | −17206.3 | + | 29802.1i | −1.07784 | + | 1.86687i | ||||
\(635\) | −21483.5 | − | 12403.5i | −1.34259 | − | 0.775147i | ||||
\(636\) | −14499.8 | −0.904014 | ||||||||
\(637\) | 4454.06 | + | 2091.43i | 0.277043 | + | 0.130087i | ||||
\(638\) | −311.322 | −0.0193187 | ||||||||
\(639\) | −6444.73 | − | 3720.87i | −0.398982 | − | 0.230352i | ||||
\(640\) | 18518.0 | − | 32074.2i | 1.14373 | − | 1.98100i | ||||
\(641\) | −5799.42 | − | 10044.9i | −0.357353 | − | 0.618953i | 0.630165 | − | 0.776461i | \(-0.282987\pi\) |
−0.987518 | + | 0.157508i | \(0.949654\pi\) | |||||||
\(642\) | − | 26517.9i | − | 1.63018i | ||||||
\(643\) | 21965.8 | − | 12682.0i | 1.34720 | − | 0.777804i | 0.359345 | − | 0.933205i | \(-0.383000\pi\) |
0.987852 | + | 0.155401i | \(0.0496669\pi\) | |||||||
\(644\) | 33120.3 | − | 19122.0i | 2.02659 | − | 1.17005i | ||||
\(645\) | − | 21781.0i | − | 1.32965i | ||||||
\(646\) | −2642.13 | − | 4576.31i | −0.160918 | − | 0.278719i | ||||
\(647\) | −3295.05 | + | 5707.19i | −0.200219 | + | 0.346789i | −0.948599 | − | 0.316481i | \(-0.897499\pi\) |
0.748380 | + | 0.663270i | \(0.230832\pi\) | |||||||
\(648\) | −3346.60 | − | 1932.16i | −0.202881 | − | 0.117133i | ||||
\(649\) | 14632.0 | 0.884985 | ||||||||
\(650\) | −28114.9 | + | 59875.5i | −1.69655 | + | 3.61309i | ||||
\(651\) | −1748.32 | −0.105257 | ||||||||
\(652\) | −53291.4 | − | 30767.8i | −3.20100 | − | 1.84810i | ||||
\(653\) | −7849.12 | + | 13595.1i | −0.470382 | + | 0.814726i | −0.999426 | − | 0.0338683i | \(-0.989217\pi\) |
0.529044 | + | 0.848594i | \(0.322551\pi\) | |||||||
\(654\) | −7319.23 | − | 12677.3i | −0.437621 | − | 0.757983i | ||||
\(655\) | 25647.6i | 1.52998i | ||||||||
\(656\) | −513.571 | + | 296.511i | −0.0305664 | + | 0.0176475i | ||||
\(657\) | −515.358 | + | 297.542i | −0.0306028 | + | 0.0176685i | ||||
\(658\) | − | 16326.7i | − | 0.967295i | ||||||
\(659\) | −1420.41 | − | 2460.22i | −0.0839624 | − | 0.145427i | 0.820986 | − | 0.570948i | \(-0.193424\pi\) |
−0.904949 | + | 0.425521i | \(0.860091\pi\) | |||||||
\(660\) | −14189.1 | + | 24576.2i | −0.836831 | + | 1.44943i | ||||
\(661\) | 18029.9 | + | 10409.5i | 1.06094 | + | 0.612533i | 0.925692 | − | 0.378279i | \(-0.123484\pi\) |
0.135247 | + | 0.990812i | \(0.456817\pi\) | |||||||
\(662\) | 25292.2 | 1.48491 | ||||||||
\(663\) | 276.063 | + | 3255.32i | 0.0161710 | + | 0.190688i | ||||
\(664\) | −6748.26 | −0.394403 | ||||||||
\(665\) | −12116.8 | − | 6995.63i | −0.706569 | − | 0.407938i | ||||
\(666\) | 7125.46 | − | 12341.7i | 0.414574 | − | 0.718063i | ||||
\(667\) | −162.650 | − | 281.718i | −0.00944202 | − | 0.0163541i | ||||
\(668\) | 4549.87i | 0.263532i | ||||||||
\(669\) | 6076.16 | − | 3508.07i | 0.351148 | − | 0.202735i | ||||
\(670\) | −43298.3 | + | 24998.3i | −2.49665 | + | 1.44144i | ||||
\(671\) | − | 5543.36i | − | 0.318925i | ||||||
\(672\) | 2966.95 | + | 5138.90i | 0.170316 | + | 0.294996i | ||||
\(673\) | 15632.3 | − | 27075.9i | 0.895364 | − | 1.55082i | 0.0620102 | − | 0.998076i | \(-0.480249\pi\) |
0.833354 | − | 0.552740i | \(-0.186418\pi\) | |||||||
\(674\) | −14073.0 | − | 8125.04i | −0.804260 | − | 0.464340i | ||||
\(675\) | −7552.16 | −0.430641 | ||||||||
\(676\) | −24494.1 | − | 29509.0i | −1.39361 | − | 1.67894i | ||||
\(677\) | −27953.2 | −1.58689 | −0.793447 | − | 0.608639i | \(-0.791716\pi\) | ||||
−0.793447 | + | 0.608639i | \(0.791716\pi\) | |||||||
\(678\) | 25049.5 | + | 14462.3i | 1.41891 | + | 0.819208i | ||||
\(679\) | 8600.46 | − | 14896.4i | 0.486090 | − | 0.841933i | ||||
\(680\) | 11149.2 | + | 19310.9i | 0.628752 | + | 1.08903i | ||||
\(681\) | − | 9838.09i | − | 0.553592i | ||||||
\(682\) | 4445.99 | − | 2566.89i | 0.249627 | − | 0.144122i | ||||
\(683\) | 30059.7 | − | 17354.9i | 1.68404 | − | 0.972282i | 0.725116 | − | 0.688627i | \(-0.241786\pi\) |
0.958926 | − | 0.283655i | \(-0.0915470\pi\) | |||||||
\(684\) | 7082.05i | 0.395890i | ||||||||
\(685\) | 20432.4 | + | 35390.0i | 1.13968 | + | 1.97399i | ||||
\(686\) | 17435.2 | − | 30198.7i | 0.970380 | − | 1.68075i | ||||
\(687\) | −2971.48 | − | 1715.59i | −0.165021 | − | 0.0952747i | ||||
\(688\) | 36471.1 | 2.02100 | ||||||||
\(689\) | −1096.67 | − | 12931.8i | −0.0606381 | − | 0.715042i | ||||
\(690\) | −43241.9 | −2.38578 | ||||||||
\(691\) | 10271.7 | + | 5930.39i | 0.565492 | + | 0.326487i | 0.755347 | − | 0.655325i | \(-0.227468\pi\) |
−0.189855 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(692\) | −7957.66 | + | 13783.1i | −0.437146 | + | 0.757158i | ||||
\(693\) | 1870.13 | + | 3239.16i | 0.102511 | + | 0.177555i | ||||
\(694\) | 16956.0i | 0.927438i | ||||||||
\(695\) | 25186.6 | − | 14541.5i | 1.37465 | − | 0.793655i | ||||
\(696\) | 283.925 | − | 163.924i | 0.0154629 | − | 0.00892750i | ||||
\(697\) | 136.338i | 0.00740916i | ||||||||
\(698\) | 11582.4 | + | 20061.4i | 0.628083 | + | 1.08787i | ||||
\(699\) | −6357.26 | + | 11011.1i | −0.343996 | + | 0.595819i | ||||
\(700\) | 65235.3 | + | 37663.6i | 3.52237 | + | 2.03364i | ||||
\(701\) | −16100.5 | −0.867486 | −0.433743 | − | 0.901037i | \(-0.642807\pi\) | ||||
−0.433743 | + | 0.901037i | \(0.642807\pi\) | |||||||
\(702\) | 2713.90 | − | 5779.70i | 0.145911 | − | 0.310742i | ||||
\(703\) | −14147.7 | −0.759019 | ||||||||
\(704\) | 3769.90 | + | 2176.55i | 0.201823 | + | 0.116523i | ||||
\(705\) | −6329.39 | + | 10962.8i | −0.338125 | + | 0.585650i | ||||
\(706\) | 4389.69 | + | 7603.17i | 0.234006 | + | 0.405310i | ||||
\(707\) | 24528.9i | 1.30482i | ||||||||
\(708\) | −24634.3 | + | 14222.6i | −1.30765 | + | 0.754971i | ||||
\(709\) | 24651.8 | − | 14232.7i | 1.30581 | − | 0.753910i | 0.324416 | − | 0.945915i | \(-0.394832\pi\) |
0.981394 | + | 0.192005i | \(0.0614990\pi\) | |||||||
\(710\) | − | 83925.9i | − | 4.43617i | ||||||
\(711\) | −1429.39 | − | 2475.78i | −0.0753957 | − | 0.130589i | ||||
\(712\) | −15297.9 | + | 26496.8i | −0.805217 | + | 1.39468i | ||||
\(713\) | 4645.60 | + | 2682.14i | 0.244010 | + | 0.140879i | ||||
\(714\) | 5425.43 | 0.284372 | ||||||||
\(715\) | −22991.8 | − | 10796.0i | −1.20258 | − | 0.564680i | ||||
\(716\) | 46964.4 | 2.45131 | ||||||||
\(717\) | −8599.70 | − | 4965.04i | −0.447924 | − | 0.258609i | ||||
\(718\) | −3596.07 | + | 6228.57i | −0.186914 | + | 0.323744i | ||||
\(719\) | −13911.0 | − | 24094.6i | −0.721550 | − | 1.24976i | −0.960378 | − | 0.278699i | \(-0.910097\pi\) |
0.238829 | − | 0.971062i | \(-0.423237\pi\) | |||||||
\(720\) | − | 18297.0i | − | 0.947067i | ||||||
\(721\) | 7047.93 | − | 4069.13i | 0.364048 | − | 0.210183i | ||||
\(722\) | −21090.5 | + | 12176.6i | −1.08713 | + | 0.627654i | ||||
\(723\) | 17108.6i | 0.880049i | ||||||||
\(724\) | −41665.5 | − | 72166.7i | −2.13879 | − | 3.70450i | ||||
\(725\) | 320.363 | − | 554.884i | 0.0164110 | − | 0.0284247i | ||||
\(726\) | 7935.57 | + | 4581.60i | 0.405670 | + | 0.234214i | ||||
\(727\) | −866.153 | −0.0441869 | −0.0220934 | − | 0.999756i | \(-0.507033\pi\) | ||||
−0.0220934 | + | 0.999756i | \(0.507033\pi\) | |||||||
\(728\) | −28312.8 | + | 19712.6i | −1.44140 | + | 1.00357i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −5812.07 | − | 3355.60i | −0.294677 | − | 0.170132i | ||||
\(731\) | 4192.45 | − | 7261.53i | 0.212125 | − | 0.367411i | ||||
\(732\) | 5388.27 | + | 9332.76i | 0.272071 | + | 0.471242i | ||||
\(733\) | − | 23120.1i | − | 1.16502i | −0.812823 | − | 0.582511i | \(-0.802070\pi\) | ||
0.812823 | − | 0.582511i | \(-0.197930\pi\) | |||||||
\(734\) | −47404.7 | + | 27369.1i | −2.38384 | + | 1.37631i | ||||
\(735\) | −5486.94 | + | 3167.89i | −0.275359 | + | 0.158979i | ||||
\(736\) | − | 18206.7i | − | 0.911831i | ||||||
\(737\) | −6634.34 | − | 11491.0i | −0.331586 | − | 0.574324i | ||||
\(738\) | 133.233 | − | 230.766i | 0.00664547 | − | 0.0115103i | ||||
\(739\) | 17983.1 | + | 10382.6i | 0.895156 | + | 0.516819i | 0.875626 | − | 0.482990i | \(-0.160449\pi\) |
0.0195308 | + | 0.999809i | \(0.493783\pi\) | |||||||
\(740\) | 110209. | 5.47482 | ||||||||
\(741\) | −6316.24 | + | 535.639i | −0.313135 | + | 0.0265549i | ||||
\(742\) | −21552.7 | −1.06634 | ||||||||
\(743\) | 32039.3 | + | 18497.9i | 1.58198 | + | 0.913354i | 0.994571 | + | 0.104061i | \(0.0331838\pi\) |
0.587405 | + | 0.809293i | \(0.300150\pi\) | |||||||
\(744\) | −2703.16 | + | 4682.01i | −0.133202 | + | 0.230713i | ||||
\(745\) | −9719.90 | − | 16835.4i | −0.477999 | − | 0.827919i | ||||
\(746\) | 2496.19i | 0.122509i | ||||||||
\(747\) | 1102.50 | − | 636.526i | 0.0540003 | − | 0.0311771i | ||||
\(748\) | −9460.95 | + | 5462.28i | −0.462468 | + | 0.267006i | ||||
\(749\) | − | 27029.1i | − | 1.31859i | ||||||
\(750\) | −23554.4 | − | 40797.5i | −1.14678 | − | 1.98629i | ||||
\(751\) | −17214.6 | + | 29816.5i | −0.836443 | + | 1.44876i | 0.0564080 | + | 0.998408i | \(0.482035\pi\) |
−0.892851 | + | 0.450353i | \(0.851298\pi\) | |||||||
\(752\) | −18356.7 | − | 10598.2i | −0.890159 | − | 0.513933i | ||||
\(753\) | 11730.7 | 0.567716 | ||||||||
\(754\) | 309.532 | + | 444.575i | 0.0149503 | + | 0.0214728i | ||||
\(755\) | −29433.5 | −1.41880 | ||||||||
\(756\) | −6297.08 | − | 3635.62i | −0.302940 | − | 0.174902i | ||||
\(757\) | −2134.44 | + | 3696.96i | −0.102480 | + | 0.177501i | −0.912706 | − | 0.408617i | \(-0.866011\pi\) |
0.810226 | + | 0.586118i | \(0.199345\pi\) | |||||||
\(758\) | 31895.1 | + | 55244.0i | 1.52834 | + | 2.64717i | ||||
\(759\) | − | 11476.1i | − | 0.548820i | ||||||
\(760\) | −37468.7 | + | 21632.6i | −1.78833 | + | 1.03249i | ||||
\(761\) | 6358.45 | − | 3671.05i | 0.302883 | − | 0.174869i | −0.340854 | − | 0.940116i | \(-0.610716\pi\) |
0.643737 | + | 0.765247i | \(0.277383\pi\) | |||||||
\(762\) | 18664.5i | 0.887329i | ||||||||
\(763\) | −7460.33 | − | 12921.7i | −0.353974 | − | 0.613100i | ||||
\(764\) | −17957.3 | + | 31103.0i | −0.850359 | + | 1.47286i | ||||
\(765\) | −3642.99 | − | 2103.28i | −0.172173 | − | 0.0994044i | ||||
\(766\) | 11712.9 | 0.552484 | ||||||||
\(767\) | −14547.9 | − | 20894.8i | −0.684867 | − | 0.983661i | ||||
\(768\) | −23987.1 | −1.12703 | ||||||||
\(769\) | 12755.2 | + | 7364.23i | 0.598134 | + | 0.345333i | 0.768307 | − | 0.640081i | \(-0.221099\pi\) |
−0.170173 | + | 0.985414i | \(0.554433\pi\) | |||||||
\(770\) | −21090.8 | + | 36530.4i | −0.987092 | + | 1.70969i | ||||
\(771\) | 10459.2 | + | 18115.9i | 0.488559 | + | 0.846209i | ||||
\(772\) | 12740.5i | 0.593963i | ||||||||
\(773\) | 8606.05 | − | 4968.71i | 0.400437 | − | 0.231193i | −0.286235 | − | 0.958159i | \(-0.592404\pi\) |
0.686673 | + | 0.726967i | \(0.259071\pi\) | |||||||
\(774\) | −14192.2 | + | 8193.88i | −0.659081 | + | 0.380521i | ||||
\(775\) | 10565.7i | 0.489719i | ||||||||
\(776\) | −26595.2 | − | 46064.2i | −1.23030 | − | 2.13094i | ||||
\(777\) | 7262.83 | − | 12579.6i | 0.335331 | − | 0.580811i | ||||
\(778\) | 45780.9 | + | 26431.6i | 2.10967 | + | 1.21802i | ||||
\(779\) | −264.535 | −0.0121668 | ||||||||
\(780\) | 49202.8 | − | 4172.57i | 2.25865 | − | 0.191541i | ||||
\(781\) | 22273.3 | 1.02049 | ||||||||
\(782\) | −14416.4 | − | 8323.29i | −0.659243 | − | 0.380614i | ||||
\(783\) | −30.9242 | + | 53.5623i | −0.00141142 | + | 0.00244465i | ||||
\(784\) | −5304.47 | − | 9187.61i | −0.241639 | − | 0.418532i | ||||
\(785\) | 1328.60i | 0.0604074i | ||||||||
\(786\) | 16711.7 | − | 9648.49i | 0.758378 | − | 0.437850i | ||||
\(787\) | −31441.1 | + | 18152.5i | −1.42408 | + | 0.822194i | −0.996645 | − | 0.0818508i | \(-0.973917\pi\) |
−0.427437 | + | 0.904045i | \(0.640584\pi\) | |||||||
\(788\) | 29694.2i | 1.34240i | ||||||||
\(789\) | −422.536 | − | 731.854i | −0.0190655 | − | 0.0330224i | ||||
\(790\) | 16120.3 | − | 27921.2i | 0.725993 | − | 1.25746i | ||||
\(791\) | 25532.4 | + | 14741.2i | 1.14770 | + | 0.662623i | ||||
\(792\) | 11566.0 | 0.518914 | ||||||||
\(793\) | −7916.04 | + | 5511.49i | −0.354485 | + | 0.246808i | ||||
\(794\) | 8914.40 | 0.398439 | ||||||||
\(795\) | 14471.9 | + | 8355.35i | 0.645616 | + | 0.372747i | ||||
\(796\) | 16066.9 | − | 27828.8i | 0.715424 | − | 1.23915i | ||||
\(797\) | −4575.37 | − | 7924.77i | −0.203347 | − | 0.352208i | 0.746258 | − | 0.665657i | \(-0.231849\pi\) |
−0.949605 | + | 0.313449i | \(0.898515\pi\) | |||||||
\(798\) | 10526.9i | 0.466976i | ||||||||
\(799\) | −4220.29 | + | 2436.59i | −0.186863 | + | 0.107885i | ||||
\(800\) | 31056.3 | − | 17930.4i | 1.37251 | − | 0.792418i | ||||
\(801\) | − | 5771.88i | − | 0.254606i | ||||||
\(802\) | −12617.6 | − | 21854.3i | −0.555539 | − | 0.962221i | ||||
\(803\) | 890.550 | − | 1542.48i | 0.0391368 | − | 0.0677869i | ||||
\(804\) | 22339.1 | + | 12897.5i | 0.979898 | + | 0.565745i | ||||
\(805\) | −44075.5 | −1.92976 | ||||||||
\(806\) | −8086.01 | − | 3796.84i | −0.353372 | − | 0.165928i | ||||
\(807\) | 12999.4 | 0.567038 | ||||||||
\(808\) | 65688.6 | + | 37925.4i | 2.86005 | + | 1.65125i | ||||
\(809\) | −15174.9 | + | 26283.8i | −0.659484 | + | 1.14226i | 0.321265 | + | 0.946989i | \(0.395892\pi\) |
−0.980749 | + | 0.195271i | \(0.937441\pi\) | |||||||
\(810\) | 4110.74 | + | 7120.00i | 0.178317 | + | 0.308854i | ||||
\(811\) | − | 4238.72i | − | 0.183529i | −0.995781 | − | 0.0917643i | \(-0.970749\pi\) | ||
0.995781 | − | 0.0917643i | \(-0.0292506\pi\) | |||||||
\(812\) | 534.244 | − | 308.446i | 0.0230890 | − | 0.0133305i | ||||
\(813\) | −1113.53 | + | 642.894i | −0.0480357 | + | 0.0277334i | ||||
\(814\) | 42653.3i | 1.83661i | ||||||||
\(815\) | 35459.3 | + | 61417.3i | 1.52403 | + | 2.63970i | ||||
\(816\) | 3521.84 | − | 6100.01i | 0.151090 | − | 0.261695i | ||||
\(817\) | 14089.4 | + | 8134.53i | 0.603337 | + | 0.348337i | ||||
\(818\) | −56551.4 | −2.41721 | ||||||||
\(819\) | 2766.22 | − | 5891.13i | 0.118021 | − | 0.251346i | ||||
\(820\) | 2060.70 | 0.0877595 | ||||||||
\(821\) | −5139.41 | − | 2967.24i | −0.218473 | − | 0.126136i | 0.386770 | − | 0.922176i | \(-0.373591\pi\) |
−0.605243 | + | 0.796041i | \(0.706924\pi\) | |||||||
\(822\) | 15373.1 | − | 26627.1i | 0.652311 | − | 1.12984i | ||||
\(823\) | −11229.8 | − | 19450.6i | −0.475633 | − | 0.823820i | 0.523978 | − | 0.851732i | \(-0.324448\pi\) |
−0.999610 | + | 0.0279120i | \(0.991114\pi\) | |||||||
\(824\) | − | 25165.9i | − | 1.06395i | ||||||
\(825\) | 19575.4 | − | 11301.9i | 0.826096 | − | 0.476947i | ||||
\(826\) | −36616.8 | + | 21140.7i | −1.54245 | + | 0.890533i | ||||
\(827\) | − | 20138.4i | − | 0.846772i | −0.905949 | − | 0.423386i | \(-0.860841\pi\) | ||
0.905949 | − | 0.423386i | \(-0.139159\pi\) | |||||||
\(828\) | 11155.0 | + | 19321.0i | 0.468192 | + | 0.810933i | ||||
\(829\) | 2922.85 | − | 5062.53i | 0.122455 | − | 0.212098i | −0.798281 | − | 0.602286i | \(-0.794257\pi\) |
0.920735 | + | 0.390188i | \(0.127590\pi\) | |||||||
\(830\) | 12433.7 | + | 7178.58i | 0.519974 | + | 0.300207i | ||||
\(831\) | −26816.2 | −1.11943 | ||||||||
\(832\) | −640.058 | − | 7547.54i | −0.0266707 | − | 0.314500i | ||||
\(833\) | −2439.05 | −0.101450 | ||||||||
\(834\) | −18950.1 | − | 10940.9i | −0.786798 | − | 0.454258i | ||||
\(835\) | 2621.82 | − | 4541.12i | 0.108661 | − | 0.188206i | ||||
\(836\) | −10598.4 | − | 18356.9i | −0.438459 | − | 0.759434i | ||||
\(837\) | − | 1019.90i | − | 0.0421180i | ||||||
\(838\) | −14354.4 | + | 8287.49i | −0.591722 | + | 0.341631i | ||||
\(839\) | 24058.1 | − | 13889.9i | 0.989961 | − | 0.571554i | 0.0846986 | − | 0.996407i | \(-0.473007\pi\) |
0.905263 | + | 0.424852i | \(0.139674\pi\) | |||||||
\(840\) | − | 44420.9i | − | 1.82460i | ||||||
\(841\) | 12191.9 | + | 21116.9i | 0.499892 | + | 0.865839i | ||||
\(842\) | 33526.1 | − | 58069.0i | 1.37219 | − | 2.37671i | ||||
\(843\) | 2015.64 | + | 1163.73i | 0.0823514 | + | 0.0475456i | ||||
\(844\) | −2495.65 | −0.101782 | ||||||||
\(845\) | 7442.75 | + | 43566.7i | 0.303004 | + | 1.77366i | ||||
\(846\) | 9524.32 | 0.387060 | ||||||||
\(847\) | 8088.55 | + | 4669.92i | 0.328130 | + | 0.189446i | ||||
\(848\) | −13990.6 | + | 24232.4i | −0.566556 | + | 0.981304i | ||||
\(849\) | −6021.80 | − | 10430.1i | −0.243425 | − | 0.421624i | ||||
\(850\) | − | 32787.9i | − | 1.32308i | ||||||
\(851\) | −38597.3 | + | 22284.2i | −1.55476 | + | 0.897640i | ||||
\(852\) | −37499.1 | + | 21650.1i | −1.50786 | + | 0.870565i | ||||
\(853\) | − | 16480.5i | − | 0.661526i | −0.943714 | − | 0.330763i | \(-0.892694\pi\) | ||
0.943714 | − | 0.330763i | \(-0.107306\pi\) | |||||||
\(854\) | 8009.21 | + | 13872.4i | 0.320925 | + | 0.555858i | ||||
\(855\) | 4080.96 | − | 7068.43i | 0.163235 | − | 0.282731i | ||||
\(856\) | −72384.2 | − | 41791.0i | −2.89024 | − | 1.66868i | ||||
\(857\) | 45445.2 | 1.81141 | 0.905704 | − | 0.423910i | \(-0.139343\pi\) | ||||
0.905704 | + | 0.423910i | \(0.139343\pi\) | |||||||
\(858\) | 1614.88 | + | 19042.6i | 0.0642552 | + | 0.757695i | ||||
\(859\) | −28243.1 | −1.12182 | −0.560909 | − | 0.827877i | \(-0.689548\pi\) | ||||
−0.560909 | + | 0.827877i | \(0.689548\pi\) | |||||||
\(860\) | −109755. | − | 63367.1i | −4.35188 | − | 2.51256i | ||||
\(861\) | 135.801 | − | 235.214i | 0.00537524 | − | 0.00931020i | ||||
\(862\) | 34541.2 | + | 59827.2i | 1.36482 | + | 2.36395i | ||||
\(863\) | − | 328.319i | − | 0.0129503i | −0.999979 | − | 0.00647514i | \(-0.997939\pi\) | ||
0.999979 | − | 0.00647514i | \(-0.00206112\pi\) | |||||||
\(864\) | −2997.83 | + | 1730.80i | −0.118042 | + | 0.0681514i | ||||
\(865\) | 15884.7 | − | 9171.05i | 0.624389 | − | 0.360491i | ||||
\(866\) | − | 50466.4i | − | 1.98027i | ||||||
\(867\) | 6559.81 | + | 11361.9i | 0.256958 | + | 0.445065i | ||||
\(868\) | −5086.36 | + | 8809.84i | −0.198897 | + | 0.344499i | ||||
\(869\) | 7410.06 | + | 4278.20i | 0.289262 | + | 0.167006i | ||||
\(870\) | −697.510 | −0.0271814 | ||||||||
\(871\) | −9813.24 | + | 20898.9i | −0.381755 | + | 0.813012i | ||||
\(872\) | −46139.1 | −1.79182 | ||||||||
\(873\) | 8689.96 | + | 5017.15i | 0.336897 | + | 0.194507i | ||||
\(874\) | 16149.5 | − | 27971.8i | 0.625018 | − | 1.08256i | ||||
\(875\) | −24008.5 | − | 41584.0i | −0.927584 | − | 1.60662i | ||||
\(876\) | 3462.54i | 0.133549i | ||||||||
\(877\) | 36788.7 | − | 21240.0i | 1.41650 | − | 0.817815i | 0.420507 | − | 0.907289i | \(-0.361852\pi\) |
0.995989 | + | 0.0894746i | \(0.0285188\pi\) | |||||||
\(878\) | 19606.5 | − | 11319.8i | 0.753629 | − | 0.435108i | ||||
\(879\) | 14868.6i | 0.570542i | ||||||||
\(880\) | 27381.6 | + | 47426.4i | 1.04890 | + | 1.81675i | ||||
\(881\) | −2610.47 | + | 4521.47i | −0.0998287 | + | 0.172908i | −0.911614 | − | 0.411048i | \(-0.865163\pi\) |
0.811785 | + | 0.583956i | \(0.198496\pi\) | |||||||
\(882\) | 4128.32 | + | 2383.48i | 0.157605 | + | 0.0909933i | ||||
\(883\) | −11790.3 | −0.449349 | −0.224674 | − | 0.974434i | \(-0.572132\pi\) | ||||
−0.224674 | + | 0.974434i | \(0.572132\pi\) | |||||||
\(884\) | 17206.8 | + | 8079.57i | 0.654670 | + | 0.307404i | ||||
\(885\) | 32782.6 | 1.24517 | ||||||||
\(886\) | 8893.30 | + | 5134.55i | 0.337219 | + | 0.194694i | ||||
\(887\) | 24676.2 | − | 42740.4i | 0.934097 | − | 1.61790i | 0.157861 | − | 0.987461i | \(-0.449540\pi\) |
0.776236 | − | 0.630443i | \(-0.217127\pi\) | |||||||
\(888\) | −22458.8 | − | 38899.8i | −0.848726 | − | 1.47004i | ||||
\(889\) | 19024.4i | 0.717724i | ||||||||
\(890\) | 56372.8 | − | 32546.9i | 2.12317 | − | 1.22581i | ||||
\(891\) | −1889.59 | + | 1090.96i | −0.0710480 | + | 0.0410196i | ||||
\(892\) | − | 40823.9i | − | 1.53238i | ||||||
\(893\) | −4727.67 | − | 8188.56i | −0.177162 | − | 0.306853i | ||||
\(894\) | −7313.14 | + | 12666.7i | −0.273588 | + | 0.473869i | ||||
\(895\) | −46874.1 | − | 27062.8i | −1.75065 | − | 1.01074i | ||||
\(896\) | −28402.7 | −1.05900 | ||||||||
\(897\) | −16388.1 | + | 11410.1i | −0.610013 | + | 0.424717i | ||||
\(898\) | −18040.1 | −0.670386 | ||||||||
\(899\) | 74.9355 | + | 43.2640i | 0.00278002 | + | 0.00160505i | ||||
\(900\) | −21971.4 | + | 38055.6i | −0.813756 | + | 1.40947i | ||||
\(901\) | 3216.51 | + | 5571.16i | 0.118932 | + | 0.205996i | ||||
\(902\) | 797.536i | 0.0294402i | ||||||||
\(903\) | −14465.8 | + | 8351.84i | −0.533103 | + | 0.307787i | ||||
\(904\) | 78953.9 | − | 45584.0i | 2.90483 | − | 1.67710i | ||||
\(905\) | 96037.3i | 3.52750i | ||||||||
\(906\) | 11072.7 | + | 19178.5i | 0.406033 | + | 0.703270i | ||||
\(907\) | 3044.47 | − | 5273.17i | 0.111455 | − | 0.193046i | −0.804902 | − | 0.593408i | \(-0.797782\pi\) |
0.916357 | + | 0.400362i | \(0.131116\pi\) | |||||||
\(908\) | −49574.5 | − | 28621.8i | −1.81188 | − | 1.04609i | ||||
\(909\) | −14309.2 | −0.522118 | ||||||||
\(910\) | 73135.8 | − | 6202.17i | 2.66421 | − | 0.225934i | ||||
\(911\) | −30301.7 | −1.10202 | −0.551010 | − | 0.834499i | \(-0.685757\pi\) | ||||
−0.551010 | + | 0.834499i | \(0.685757\pi\) | |||||||
\(912\) | 11835.7 | + | 6833.36i | 0.429737 | + | 0.248109i | ||||
\(913\) | −1905.14 | + | 3299.80i | −0.0690590 | + | 0.119614i | ||||
\(914\) | −20329.3 | − | 35211.4i | −0.735704 | − | 1.27428i | ||||
\(915\) | − | 12419.8i | − | 0.448726i | ||||||
\(916\) | −17289.8 | + | 9982.27i | −0.623658 | + | 0.360069i | ||||
\(917\) | 17033.8 | − | 9834.49i | 0.613421 | − | 0.354159i | ||||
\(918\) | 3164.97i | 0.113790i | ||||||||
\(919\) | −17347.9 | − | 30047.4i | −0.622692 | − | 1.07853i | −0.988982 | − | 0.148034i | \(-0.952705\pi\) |
0.366290 | − | 0.930501i | \(-0.380628\pi\) | |||||||
\(920\) | −68147.3 | + | 118035.i | −2.44212 | + | 4.22988i | ||||
\(921\) | −10119.3 | − | 5842.36i | −0.362042 | − | 0.209025i | ||||
\(922\) | 58991.2 | 2.10713 | ||||||||
\(923\) | −22145.2 | − | 31806.7i | −0.789728 | − | 1.13427i | ||||
\(924\) | 21763.0 | 0.774837 | ||||||||
\(925\) | −76023.1 | − | 43892.0i | −2.70230 | − | 1.56017i | ||||
\(926\) | 4370.30 | − | 7569.59i | 0.155094 | − | 0.268631i | ||||
\(927\) | 2373.76 | + | 4111.47i | 0.0841041 | + | 0.145673i | ||||
\(928\) | − | 293.681i | − | 0.0103885i | ||||||
\(929\) | −14714.5 | + | 8495.40i | −0.519662 | + | 0.300027i | −0.736796 | − | 0.676115i | \(-0.763662\pi\) |
0.217134 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(930\) | 9961.14 | − | 5751.06i | 0.351224 | − | 0.202779i | ||||
\(931\) | − | 4732.44i | − | 0.166594i | ||||||
\(932\) | 36990.2 | + | 64068.9i | 1.30006 | + | 2.25177i | ||||
\(933\) | 4646.16 | − | 8047.38i | 0.163032 | − | 0.282379i | ||||
\(934\) | −47058.1 | − | 27169.0i | −1.64860 | − | 0.951817i | ||||
\(935\) | 12590.3 | 0.440372 | ||||||||
\(936\) | −11499.5 | − | 16516.5i | −0.401574 | − | 0.576772i | ||||
\(937\) | 9307.86 | 0.324519 | 0.162260 | − | 0.986748i | \(-0.448122\pi\) | ||||
0.162260 | + | 0.986748i | \(0.448122\pi\) | |||||||
\(938\) | 33205.1 | + | 19171.0i | 1.15585 | + | 0.667330i | ||||
\(939\) | −6731.04 | + | 11658.5i | −0.233929 | + | 0.405177i | ||||
\(940\) | 36828.0 | + | 63788.0i | 1.27787 | + | 2.21334i | ||||
\(941\) | 52285.3i | 1.81132i | 0.424006 | + | 0.905659i | \(0.360623\pi\) | ||||
−0.424006 | + | 0.905659i | \(0.639377\pi\) | |||||||
\(942\) | 865.700 | − | 499.812i | 0.0299427 | − | 0.0172874i | ||||
\(943\) | −721.697 | + | 416.672i | −0.0249222 | + | 0.0143889i | ||||
\(944\) | 54892.8i | 1.89260i | ||||||||
\(945\) | 4189.98 | + | 7257.26i | 0.144233 | + | 0.249819i | ||||
\(946\) | 24524.5 | − | 42477.6i | 0.842874 | − | 1.45990i | ||||
\(947\) | 10694.1 | + | 6174.26i | 0.366962 | + | 0.211865i | 0.672130 | − | 0.740433i | \(-0.265379\pi\) |
−0.305169 | + | 0.952298i | \(0.598713\pi\) | |||||||
\(948\) | −16634.0 | −0.569882 | ||||||||
\(949\) | −3088.13 | + | 261.884i | −0.105632 | + | 0.00895797i | ||||
\(950\) | 63617.7 | 2.17267 | ||||||||
\(951\) | −17720.5 | − | 10230.9i | −0.604233 | − | 0.348854i | ||||
\(952\) | 8550.23 | − | 14809.4i | 0.291087 | − | 0.504177i | ||||
\(953\) | −12815.5 | − | 22197.1i | −0.435609 | − | 0.754497i | 0.561736 | − | 0.827317i | \(-0.310134\pi\) |
−0.997345 | + | 0.0728193i | \(0.976800\pi\) | |||||||
\(954\) | − | 12572.9i | − | 0.426692i | ||||||
\(955\) | 35845.7 | − | 20695.5i | 1.21459 | − | 0.701247i | ||||
\(956\) | −50038.0 | + | 28889.5i | −1.69283 | + | 0.977356i | ||||
\(957\) | − | 185.114i | − | 0.00625274i | ||||||
\(958\) | 19958.6 | + | 34569.2i | 0.673102 | + | 1.16585i | ||||
\(959\) | 15669.5 | − | 27140.4i | 0.527627 | − | 0.913878i | ||||
\(960\) | 8446.37 | + | 4876.51i | 0.283964 | + | 0.163947i | ||||
\(961\) | 28364.1 | 0.952104 | ||||||||
\(962\) | 60909.9 | − | 42408.1i | 2.04139 | − | 1.42130i | ||||
\(963\) | 15767.7 | 0.527629 | ||||||||
\(964\) | 86210.8 | + | 49773.8i | 2.88036 | + | 1.66297i | ||||
\(965\) | 7341.57 | − | 12716.0i | 0.244905 | − | 0.424188i | ||||
\(966\) | 16581.0 | + | 28719.1i | 0.552261 | + | 0.956543i | ||||
\(967\) | − | 11185.6i | − | 0.371981i | −0.982552 | − | 0.185991i | \(-0.940451\pi\) | ||
0.982552 | − | 0.185991i | \(-0.0595494\pi\) | |||||||
\(968\) | 25012.2 | − | 14440.8i | 0.830498 | − | 0.479488i | ||||
\(969\) | 2721.09 | − | 1571.02i | 0.0902106 | − | 0.0520831i | ||||
\(970\) | 113164.i | 3.74586i | ||||||||
\(971\) | 11770.6 | + | 20387.3i | 0.389019 | + | 0.673801i | 0.992318 | − | 0.123714i | \(-0.0394806\pi\) |
−0.603299 | + | 0.797515i | \(0.706147\pi\) | |||||||
\(972\) | 2120.87 | − | 3673.46i | 0.0699866 | − | 0.121220i | ||||
\(973\) | −19315.4 | − | 11151.8i | −0.636408 | − | 0.367430i | ||||
\(974\) | −55321.3 | −1.81993 | ||||||||
\(975\) | −35602.3 | − | 16717.3i | −1.16942 | − | 0.549109i | ||||
\(976\) | 20796.3 | 0.682041 | ||||||||
\(977\) | −20956.8 | − | 12099.4i | −0.686251 | − | 0.396207i | 0.115955 | − | 0.993254i | \(-0.463007\pi\) |
−0.802206 | + | 0.597047i | \(0.796341\pi\) | |||||||
\(978\) | 26679.2 | − | 46209.7i | 0.872297 | − | 1.51086i | ||||
\(979\) | 8637.68 | + | 14960.9i | 0.281983 | + | 0.488409i | ||||
\(980\) | 36865.2i | 1.20165i | ||||||||
\(981\) | 7537.97 | − | 4352.05i | 0.245330 | − | 0.141641i | ||||
\(982\) | −39933.7 | + | 23055.7i | −1.29769 | + | 0.749224i | ||||
\(983\) | 33757.4i | 1.09532i | 0.836702 | + | 0.547658i | \(0.184480\pi\) | ||||
−0.836702 | + | 0.547658i | \(0.815520\pi\) | |||||||
\(984\) | −419.937 | − | 727.352i | −0.0136048 | − | 0.0235642i | ||||
\(985\) | 17111.0 | − | 29637.1i | 0.553504 | − | 0.958697i | ||||
\(986\) | −232.542 | − | 134.258i | −0.00751080 | − | 0.00433636i | ||||
\(987\) | 9707.93 | 0.313077 | ||||||||
\(988\) | −15676.6 | + | 33386.1i | −0.504798 | + | 1.07505i | ||||
\(989\) | 51251.1 | 1.64782 | ||||||||
\(990\) | −21310.3 | − | 12303.5i | −0.684128 | − | 0.394981i | ||||
\(991\) | −12649.3 | + | 21909.2i | −0.405466 | + | 0.702288i | −0.994376 | − | 0.105911i | \(-0.966224\pi\) |
0.588909 | + | 0.808199i | \(0.299558\pi\) | |||||||
\(992\) | 2421.44 | + | 4194.06i | 0.0775009 | + | 0.134236i | ||||
\(993\) | 15038.9i | 0.480608i | ||||||||
\(994\) | −55739.3 | + | 32181.1i | −1.77862 | + | 1.02688i | ||||
\(995\) | −32072.1 | + | 18516.8i | −1.02186 | + | 0.589973i | ||||
\(996\) | − | 7407.36i | − | 0.235654i | ||||||
\(997\) | 14383.0 | + | 24912.2i | 0.456886 | + | 0.791350i | 0.998794 | − | 0.0490874i | \(-0.0156313\pi\) |
−0.541908 | + | 0.840438i | \(0.682298\pi\) | |||||||
\(998\) | 31729.1 | − | 54956.4i | 1.00638 | − | 1.74310i | ||||
\(999\) | 7338.41 | + | 4236.83i | 0.232409 | + | 0.134182i |
(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 | 39.4.j.c.4.5 | ✓ | 10 | |
3.2 | odd | 2 | 117.4.q.e.82.1 | 10 | |||
4.3 | odd | 2 | 624.4.bv.h.433.1 | 10 | |||
13.4 | even | 6 | 507.4.b.i.337.9 | 10 | |||
13.6 | odd | 12 | 507.4.a.r.1.2 | 10 | |||
13.7 | odd | 12 | 507.4.a.r.1.9 | 10 | |||
13.9 | even | 3 | 507.4.b.i.337.2 | 10 | |||
13.10 | even | 6 | inner | 39.4.j.c.10.5 | yes | 10 | |
39.20 | even | 12 | 1521.4.a.bk.1.2 | 10 | |||
39.23 | odd | 6 | 117.4.q.e.10.1 | 10 | |||
39.32 | even | 12 | 1521.4.a.bk.1.9 | 10 | |||
52.23 | odd | 6 | 624.4.bv.h.49.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
39.4.j.c.10.5 | yes | 10 | 13.10 | even | 6 | inner | |
117.4.q.e.10.1 | 10 | 39.23 | odd | 6 | |||
117.4.q.e.82.1 | 10 | 3.2 | odd | 2 | |||
507.4.a.r.1.2 | 10 | 13.6 | odd | 12 | |||
507.4.a.r.1.9 | 10 | 13.7 | odd | 12 | |||
507.4.b.i.337.2 | 10 | 13.9 | even | 3 | |||
507.4.b.i.337.9 | 10 | 13.4 | even | 6 | |||
624.4.bv.h.49.5 | 10 | 52.23 | odd | 6 | |||
624.4.bv.h.433.1 | 10 | 4.3 | odd | 2 | |||
1521.4.a.bk.1.2 | 10 | 39.20 | even | 12 | |||
1521.4.a.bk.1.9 | 10 | 39.32 | even | 12 |