Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(37,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.e (of order \(3\), 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: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.7 | ||
Character | \(\chi\) | \(=\) | 201.37 |
Dual form | 201.4.e.b.163.7 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.829978 | − | 1.43756i | −0.293442 | − | 0.508256i | 0.681180 | − | 0.732116i | \(-0.261467\pi\) |
−0.974621 | + | 0.223861i | \(0.928134\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 2.62227 | − | 4.54191i | 0.327784 | − | 0.567739i | ||||
\(5\) | −7.05463 | −0.630985 | −0.315492 | − | 0.948928i | \(-0.602170\pi\) | ||||
−0.315492 | + | 0.948928i | \(0.602170\pi\) | |||||||
\(6\) | 2.48993 | + | 4.31269i | 0.169419 | + | 0.293442i | ||||
\(7\) | 18.3944 | − | 31.8600i | 0.993202 | − | 1.72028i | 0.395793 | − | 0.918340i | \(-0.370470\pi\) |
0.597409 | − | 0.801937i | \(-0.296197\pi\) | |||||||
\(8\) | −21.9854 | −0.971625 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 5.85519 | + | 10.1415i | 0.185157 | + | 0.320702i | ||||
\(11\) | 11.1840 | − | 19.3712i | 0.306555 | − | 0.530968i | −0.671052 | − | 0.741411i | \(-0.734157\pi\) |
0.977606 | + | 0.210442i | \(0.0674904\pi\) | |||||||
\(12\) | −7.86682 | + | 13.6257i | −0.189246 | + | 0.327784i | ||||
\(13\) | 31.4911 | + | 54.5442i | 0.671851 | + | 1.16368i | 0.977379 | + | 0.211496i | \(0.0678337\pi\) |
−0.305528 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(14\) | −61.0677 | −1.16579 | ||||||||
\(15\) | 21.1639 | 0.364299 | ||||||||
\(16\) | −2.73081 | − | 4.72990i | −0.0426689 | − | 0.0739047i | ||||
\(17\) | −45.1811 | − | 78.2560i | −0.644590 | − | 1.11646i | −0.984396 | − | 0.175968i | \(-0.943695\pi\) |
0.339806 | − | 0.940496i | \(-0.389639\pi\) | |||||||
\(18\) | −7.46980 | − | 12.9381i | −0.0978139 | − | 0.169419i | ||||
\(19\) | 13.0185 | + | 22.5488i | 0.157192 | + | 0.272265i | 0.933855 | − | 0.357651i | \(-0.116422\pi\) |
−0.776663 | + | 0.629917i | \(0.783089\pi\) | |||||||
\(20\) | −18.4992 | + | 32.0415i | −0.206827 | + | 0.358235i | ||||
\(21\) | −55.1831 | + | 95.5799i | −0.573425 | + | 0.993202i | ||||
\(22\) | −37.1299 | −0.359824 | ||||||||
\(23\) | −67.0215 | − | 116.085i | −0.607607 | − | 1.05241i | −0.991634 | − | 0.129084i | \(-0.958796\pi\) |
0.384027 | − | 0.923322i | \(-0.374537\pi\) | |||||||
\(24\) | 65.9561 | 0.560968 | ||||||||
\(25\) | −75.2323 | −0.601858 | ||||||||
\(26\) | 52.2738 | − | 90.5409i | 0.394298 | − | 0.682944i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −96.4700 | − | 167.091i | −0.651112 | − | 1.12776i | ||||
\(29\) | −124.991 | + | 216.491i | −0.800354 | + | 1.38625i | 0.119030 | + | 0.992891i | \(0.462022\pi\) |
−0.919383 | + | 0.393363i | \(0.871312\pi\) | |||||||
\(30\) | −17.5656 | − | 30.4244i | −0.106901 | − | 0.185157i | ||||
\(31\) | 59.8781 | − | 103.712i | 0.346917 | − | 0.600878i | −0.638783 | − | 0.769387i | \(-0.720562\pi\) |
0.985700 | + | 0.168509i | \(0.0538952\pi\) | |||||||
\(32\) | −92.4745 | + | 160.171i | −0.510854 | + | 0.884825i | ||||
\(33\) | −33.5520 | + | 58.1137i | −0.176989 | + | 0.306555i | ||||
\(34\) | −74.9987 | + | 129.902i | −0.378299 | + | 0.655233i | ||||
\(35\) | −129.765 | + | 224.760i | −0.626696 | + | 1.08547i | ||||
\(36\) | 23.6005 | − | 40.8772i | 0.109261 | − | 0.189246i | ||||
\(37\) | 66.0047 | + | 114.324i | 0.293273 | + | 0.507964i | 0.974582 | − | 0.224032i | \(-0.0719221\pi\) |
−0.681308 | + | 0.731996i | \(0.738589\pi\) | |||||||
\(38\) | 21.6102 | − | 37.4299i | 0.0922536 | − | 0.159788i | ||||
\(39\) | −94.4733 | − | 163.633i | −0.387893 | − | 0.671851i | ||||
\(40\) | 155.099 | 0.613081 | ||||||||
\(41\) | −190.750 | + | 330.389i | −0.726590 | + | 1.25849i | 0.231726 | + | 0.972781i | \(0.425563\pi\) |
−0.958316 | + | 0.285710i | \(0.907770\pi\) | |||||||
\(42\) | 183.203 | 0.673067 | ||||||||
\(43\) | −209.124 | −0.741653 | −0.370827 | − | 0.928702i | \(-0.620926\pi\) | ||||
−0.370827 | + | 0.928702i | \(0.620926\pi\) | |||||||
\(44\) | −58.6550 | − | 101.593i | −0.200967 | − | 0.348086i | ||||
\(45\) | −63.4916 | −0.210328 | ||||||||
\(46\) | −111.253 | + | 192.696i | −0.356594 | + | 0.617639i | ||||
\(47\) | 158.666 | − | 274.818i | 0.492422 | − | 0.852900i | −0.507540 | − | 0.861628i | \(-0.669445\pi\) |
0.999962 | + | 0.00872796i | \(0.00277823\pi\) | |||||||
\(48\) | 8.19243 | + | 14.1897i | 0.0246349 | + | 0.0426689i | ||||
\(49\) | −505.205 | − | 875.041i | −1.47290 | − | 2.55114i | ||||
\(50\) | 62.4411 | + | 108.151i | 0.176610 | + | 0.305898i | ||||
\(51\) | 135.543 | + | 234.768i | 0.372154 | + | 0.644590i | ||||
\(52\) | 330.313 | 0.880888 | ||||||||
\(53\) | 393.851 | 1.02075 | 0.510374 | − | 0.859953i | \(-0.329507\pi\) | ||||
0.510374 | + | 0.859953i | \(0.329507\pi\) | |||||||
\(54\) | 22.4094 | + | 38.8142i | 0.0564729 | + | 0.0978139i | ||||
\(55\) | −78.8989 | + | 136.657i | −0.193431 | + | 0.335033i | ||||
\(56\) | −404.407 | + | 700.453i | −0.965020 | + | 1.67146i | ||||
\(57\) | −39.0556 | − | 67.6463i | −0.0907551 | − | 0.157192i | ||||
\(58\) | 414.959 | 0.939428 | ||||||||
\(59\) | −138.863 | −0.306413 | −0.153206 | − | 0.988194i | \(-0.548960\pi\) | ||||
−0.153206 | + | 0.988194i | \(0.548960\pi\) | |||||||
\(60\) | 55.4975 | − | 96.1244i | 0.119412 | − | 0.206827i | ||||
\(61\) | 64.3634 | + | 111.481i | 0.135097 | + | 0.233994i | 0.925634 | − | 0.378419i | \(-0.123532\pi\) |
−0.790538 | + | 0.612413i | \(0.790199\pi\) | |||||||
\(62\) | −198.790 | −0.407199 | ||||||||
\(63\) | 165.549 | − | 286.740i | 0.331067 | − | 0.573425i | ||||
\(64\) | 263.314 | 0.514286 | ||||||||
\(65\) | −222.158 | − | 384.789i | −0.423928 | − | 0.734264i | ||||
\(66\) | 111.390 | 0.207744 | ||||||||
\(67\) | −381.403 | − | 394.074i | −0.695460 | − | 0.718565i | ||||
\(68\) | −473.909 | −0.845146 | ||||||||
\(69\) | 201.065 | + | 348.254i | 0.350802 | + | 0.607607i | ||||
\(70\) | 430.810 | 0.735594 | ||||||||
\(71\) | 222.721 | − | 385.764i | 0.372284 | − | 0.644814i | −0.617633 | − | 0.786467i | \(-0.711908\pi\) |
0.989916 | + | 0.141652i | \(0.0452415\pi\) | |||||||
\(72\) | −197.868 | −0.323875 | ||||||||
\(73\) | 554.926 | + | 961.159i | 0.889714 | + | 1.54103i | 0.840213 | + | 0.542256i | \(0.182430\pi\) |
0.0495009 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(74\) | 109.565 | − | 189.772i | 0.172117 | − | 0.298116i | ||||
\(75\) | 225.697 | 0.347483 | ||||||||
\(76\) | 136.553 | 0.206101 | ||||||||
\(77\) | −411.445 | − | 712.643i | −0.608941 | − | 1.05472i | ||||
\(78\) | −156.822 | + | 271.623i | −0.227648 | + | 0.394298i | ||||
\(79\) | 476.244 | − | 824.880i | 0.678249 | − | 1.17476i | −0.297259 | − | 0.954797i | \(-0.596072\pi\) |
0.975508 | − | 0.219965i | \(-0.0705943\pi\) | |||||||
\(80\) | 19.2648 | + | 33.3677i | 0.0269234 | + | 0.0466327i | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 633.275 | 0.852847 | ||||||||
\(83\) | 290.083 | + | 502.438i | 0.383623 | + | 0.664455i | 0.991577 | − | 0.129517i | \(-0.0413427\pi\) |
−0.607954 | + | 0.793972i | \(0.708009\pi\) | |||||||
\(84\) | 289.410 | + | 501.273i | 0.375919 | + | 0.651112i | ||||
\(85\) | 318.736 | + | 552.067i | 0.406727 | + | 0.704471i | ||||
\(86\) | 173.568 | + | 300.629i | 0.217632 | + | 0.376949i | ||||
\(87\) | 374.973 | − | 649.473i | 0.462084 | − | 0.800354i | ||||
\(88\) | −245.884 | + | 425.884i | −0.297856 | + | 0.515902i | ||||
\(89\) | 525.436 | 0.625799 | 0.312900 | − | 0.949786i | \(-0.398700\pi\) | ||||
0.312900 | + | 0.949786i | \(0.398700\pi\) | |||||||
\(90\) | 52.6967 | + | 91.2733i | 0.0617191 | + | 0.106901i | ||||
\(91\) | 2317.03 | 2.66913 | ||||||||
\(92\) | −702.995 | −0.796655 | ||||||||
\(93\) | −179.634 | + | 311.136i | −0.200293 | + | 0.346917i | ||||
\(94\) | −526.758 | −0.577989 | ||||||||
\(95\) | −91.8409 | − | 159.073i | −0.0991860 | − | 0.171795i | ||||
\(96\) | 277.423 | − | 480.512i | 0.294942 | − | 0.510854i | ||||
\(97\) | −743.743 | − | 1288.20i | −0.778512 | − | 1.34842i | −0.932799 | − | 0.360396i | \(-0.882642\pi\) |
0.154287 | − | 0.988026i | \(-0.450692\pi\) | |||||||
\(98\) | −838.618 | + | 1452.53i | −0.864421 | + | 1.49722i | ||||
\(99\) | 100.656 | − | 174.341i | 0.102185 | − | 0.176989i | ||||
\(100\) | −197.279 | + | 341.698i | −0.197279 | + | 0.341698i | ||||
\(101\) | 484.923 | − | 839.911i | 0.477739 | − | 0.827468i | −0.521935 | − | 0.852985i | \(-0.674790\pi\) |
0.999674 | + | 0.0255166i | \(0.00812308\pi\) | |||||||
\(102\) | 224.996 | − | 389.705i | 0.218411 | − | 0.378299i | ||||
\(103\) | 817.098 | − | 1415.26i | 0.781661 | − | 1.35388i | −0.149313 | − | 0.988790i | \(-0.547706\pi\) |
0.930974 | − | 0.365086i | \(-0.118961\pi\) | |||||||
\(104\) | −692.343 | − | 1199.17i | −0.652787 | − | 1.13066i | ||||
\(105\) | 389.296 | − | 674.280i | 0.361823 | − | 0.626696i | ||||
\(106\) | −326.888 | − | 566.186i | −0.299530 | − | 0.518801i | ||||
\(107\) | 352.369 | 0.318362 | 0.159181 | − | 0.987249i | \(-0.449115\pi\) | ||||
0.159181 | + | 0.987249i | \(0.449115\pi\) | |||||||
\(108\) | −70.8014 | + | 122.632i | −0.0630821 | + | 0.109261i | ||||
\(109\) | −1786.30 | −1.56969 | −0.784845 | − | 0.619693i | \(-0.787257\pi\) | ||||
−0.784845 | + | 0.619693i | \(0.787257\pi\) | |||||||
\(110\) | 261.937 | 0.227043 | ||||||||
\(111\) | −198.014 | − | 342.971i | −0.169321 | − | 0.293273i | ||||
\(112\) | −200.926 | −0.169515 | ||||||||
\(113\) | 378.916 | − | 656.301i | 0.315446 | − | 0.546369i | −0.664086 | − | 0.747656i | \(-0.731179\pi\) |
0.979532 | + | 0.201287i | \(0.0645125\pi\) | |||||||
\(114\) | −64.8306 | + | 112.290i | −0.0532626 | + | 0.0922536i | ||||
\(115\) | 472.812 | + | 818.934i | 0.383391 | + | 0.664052i | ||||
\(116\) | 655.521 | + | 1135.40i | 0.524686 | + | 0.908784i | ||||
\(117\) | 283.420 | + | 490.898i | 0.223950 | + | 0.387893i | ||||
\(118\) | 115.253 | + | 199.624i | 0.0899143 | + | 0.155736i | ||||
\(119\) | −3324.31 | −2.56083 | ||||||||
\(120\) | −465.296 | −0.353962 | ||||||||
\(121\) | 415.337 | + | 719.384i | 0.312048 | + | 0.540484i | ||||
\(122\) | 106.840 | − | 185.053i | 0.0792859 | − | 0.137327i | ||||
\(123\) | 572.251 | − | 991.168i | 0.419497 | − | 0.726590i | ||||
\(124\) | −314.033 | − | 543.922i | −0.227428 | − | 0.393916i | ||||
\(125\) | 1412.56 | 1.01075 | ||||||||
\(126\) | −549.609 | −0.388596 | ||||||||
\(127\) | −756.462 | + | 1310.23i | −0.528544 | + | 0.915465i | 0.470902 | + | 0.882186i | \(0.343929\pi\) |
−0.999446 | + | 0.0332799i | \(0.989405\pi\) | |||||||
\(128\) | 521.251 | + | 902.833i | 0.359941 | + | 0.623437i | ||||
\(129\) | 627.371 | 0.428194 | ||||||||
\(130\) | −368.772 | + | 638.732i | −0.248796 | + | 0.430927i | ||||
\(131\) | −1940.54 | −1.29424 | −0.647120 | − | 0.762388i | \(-0.724027\pi\) | ||||
−0.647120 | + | 0.762388i | \(0.724027\pi\) | |||||||
\(132\) | 175.965 | + | 304.780i | 0.116029 | + | 0.200967i | ||||
\(133\) | 957.870 | 0.624495 | ||||||||
\(134\) | −249.951 | + | 875.365i | −0.161138 | + | 0.564328i | ||||
\(135\) | 190.475 | 0.121433 | ||||||||
\(136\) | 993.324 | + | 1720.49i | 0.626300 | + | 1.08478i | ||||
\(137\) | 693.301 | 0.432356 | 0.216178 | − | 0.976354i | \(-0.430641\pi\) | ||||
0.216178 | + | 0.976354i | \(0.430641\pi\) | |||||||
\(138\) | 333.758 | − | 578.087i | 0.205880 | − | 0.356594i | ||||
\(139\) | −843.314 | −0.514597 | −0.257298 | − | 0.966332i | \(-0.582832\pi\) | ||||
−0.257298 | + | 0.966332i | \(0.582832\pi\) | |||||||
\(140\) | 680.560 | + | 1178.76i | 0.410842 | + | 0.711599i | ||||
\(141\) | −475.999 | + | 824.454i | −0.284300 | + | 0.492422i | ||||
\(142\) | −739.415 | −0.436974 | ||||||||
\(143\) | 1408.78 | 0.823836 | ||||||||
\(144\) | −24.5773 | − | 42.5691i | −0.0142230 | − | 0.0246349i | ||||
\(145\) | 881.765 | − | 1527.26i | 0.505011 | − | 0.874705i | ||||
\(146\) | 921.152 | − | 1595.48i | 0.522158 | − | 0.904405i | ||||
\(147\) | 1515.61 | + | 2625.12i | 0.850380 | + | 1.47290i | ||||
\(148\) | 692.330 | 0.384521 | ||||||||
\(149\) | 1043.20 | 0.573570 | 0.286785 | − | 0.957995i | \(-0.407413\pi\) | ||||
0.286785 | + | 0.957995i | \(0.407413\pi\) | |||||||
\(150\) | −187.323 | − | 324.454i | −0.101966 | − | 0.176610i | ||||
\(151\) | 866.011 | + | 1499.97i | 0.466722 | + | 0.808385i | 0.999277 | − | 0.0380094i | \(-0.0121017\pi\) |
−0.532556 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(152\) | −286.217 | − | 495.743i | −0.152732 | − | 0.264540i | ||||
\(153\) | −406.630 | − | 704.304i | −0.214863 | − | 0.372154i | ||||
\(154\) | −682.980 | + | 1182.96i | −0.357377 | + | 0.618996i | ||||
\(155\) | −422.418 | + | 731.649i | −0.218899 | + | 0.379145i | ||||
\(156\) | −990.939 | −0.508581 | ||||||||
\(157\) | −415.941 | − | 720.430i | −0.211437 | − | 0.366220i | 0.740727 | − | 0.671806i | \(-0.234481\pi\) |
−0.952165 | + | 0.305586i | \(0.901148\pi\) | |||||||
\(158\) | −1581.09 | −0.796106 | ||||||||
\(159\) | −1181.55 | −0.589329 | ||||||||
\(160\) | 652.373 | − | 1129.94i | 0.322341 | − | 0.558311i | ||||
\(161\) | −4931.27 | −2.41391 | ||||||||
\(162\) | −67.2282 | − | 116.443i | −0.0326046 | − | 0.0564729i | ||||
\(163\) | 520.787 | − | 902.030i | 0.250253 | − | 0.433450i | −0.713343 | − | 0.700815i | \(-0.752820\pi\) |
0.963595 | + | 0.267365i | \(0.0861530\pi\) | |||||||
\(164\) | 1000.40 | + | 1732.74i | 0.476330 | + | 0.825027i | ||||
\(165\) | 236.697 | − | 409.971i | 0.111678 | − | 0.193431i | ||||
\(166\) | 481.525 | − | 834.026i | 0.225142 | − | 0.389958i | ||||
\(167\) | 619.286 | − | 1072.63i | 0.286957 | − | 0.497024i | −0.686125 | − | 0.727484i | \(-0.740690\pi\) |
0.973082 | + | 0.230460i | \(0.0740230\pi\) | |||||||
\(168\) | 1213.22 | − | 2101.36i | 0.557155 | − | 0.965020i | ||||
\(169\) | −884.878 | + | 1532.65i | −0.402766 | + | 0.697612i | ||||
\(170\) | 529.088 | − | 916.407i | 0.238701 | − | 0.413442i | ||||
\(171\) | 117.167 | + | 202.939i | 0.0523975 | + | 0.0907551i | ||||
\(172\) | −548.380 | + | 949.821i | −0.243102 | + | 0.421065i | ||||
\(173\) | −1524.03 | − | 2639.70i | −0.669769 | − | 1.16007i | −0.977968 | − | 0.208753i | \(-0.933060\pi\) |
0.308199 | − | 0.951322i | \(-0.400274\pi\) | |||||||
\(174\) | −1244.88 | −0.542379 | ||||||||
\(175\) | −1383.85 | + | 2396.90i | −0.597767 | + | 1.03536i | ||||
\(176\) | −122.165 | −0.0523214 | ||||||||
\(177\) | 416.588 | 0.176908 | ||||||||
\(178\) | −436.101 | − | 755.348i | −0.183635 | − | 0.318066i | ||||
\(179\) | −3631.31 | −1.51630 | −0.758148 | − | 0.652083i | \(-0.773896\pi\) | ||||
−0.758148 | + | 0.652083i | \(0.773896\pi\) | |||||||
\(180\) | −166.492 | + | 288.373i | −0.0689423 | + | 0.119412i | ||||
\(181\) | 285.281 | − | 494.122i | 0.117154 | − | 0.202916i | −0.801485 | − | 0.598015i | \(-0.795956\pi\) |
0.918639 | + | 0.395099i | \(0.129290\pi\) | |||||||
\(182\) | −1923.09 | − | 3330.89i | −0.783235 | − | 1.35660i | ||||
\(183\) | −193.090 | − | 334.442i | −0.0779980 | − | 0.135097i | ||||
\(184\) | 1473.49 | + | 2552.16i | 0.590366 | + | 1.02254i | ||||
\(185\) | −465.639 | − | 806.510i | −0.185051 | − | 0.320518i | ||||
\(186\) | 596.370 | 0.235097 | ||||||||
\(187\) | −2021.22 | −0.790409 | ||||||||
\(188\) | −832.132 | − | 1441.30i | −0.322816 | − | 0.559134i | ||||
\(189\) | −496.648 | + | 860.219i | −0.191142 | + | 0.331067i | ||||
\(190\) | −152.452 | + | 264.054i | −0.0582106 | + | 0.100824i | ||||
\(191\) | 724.684 | + | 1255.19i | 0.274535 | + | 0.475509i | 0.970018 | − | 0.243034i | \(-0.0781426\pi\) |
−0.695482 | + | 0.718543i | \(0.744809\pi\) | |||||||
\(192\) | −789.943 | −0.296923 | ||||||||
\(193\) | −3563.95 | −1.32922 | −0.664608 | − | 0.747192i | \(-0.731401\pi\) | ||||
−0.664608 | + | 0.747192i | \(0.731401\pi\) | |||||||
\(194\) | −1234.58 | + | 2138.36i | −0.456896 | + | 0.791366i | ||||
\(195\) | 666.474 | + | 1154.37i | 0.244755 | + | 0.423928i | ||||
\(196\) | −5299.14 | −1.93117 | ||||||||
\(197\) | 1153.29 | − | 1997.55i | 0.417097 | − | 0.722434i | −0.578549 | − | 0.815648i | \(-0.696381\pi\) |
0.995646 | + | 0.0932140i | \(0.0297141\pi\) | |||||||
\(198\) | −334.169 | −0.119941 | ||||||||
\(199\) | −1050.89 | − | 1820.20i | −0.374350 | − | 0.648393i | 0.615879 | − | 0.787840i | \(-0.288801\pi\) |
−0.990230 | + | 0.139447i | \(0.955467\pi\) | |||||||
\(200\) | 1654.01 | 0.584780 | ||||||||
\(201\) | 1144.21 | + | 1182.22i | 0.401524 | + | 0.414864i | ||||
\(202\) | −1609.90 | −0.560754 | ||||||||
\(203\) | 4598.26 | + | 7964.42i | 1.58983 | + | 2.75366i | ||||
\(204\) | 1421.73 | 0.487945 | ||||||||
\(205\) | 1345.67 | − | 2330.77i | 0.458468 | − | 0.794089i | ||||
\(206\) | −2712.69 | −0.917487 | ||||||||
\(207\) | −603.194 | − | 1044.76i | −0.202536 | − | 0.350802i | ||||
\(208\) | 171.992 | − | 297.899i | 0.0573342 | − | 0.0993058i | ||||
\(209\) | 582.397 | 0.192752 | ||||||||
\(210\) | −1292.43 | −0.424695 | ||||||||
\(211\) | 647.337 | + | 1121.22i | 0.211206 | + | 0.365820i | 0.952092 | − | 0.305811i | \(-0.0989276\pi\) |
−0.740886 | + | 0.671631i | \(0.765594\pi\) | |||||||
\(212\) | 1032.78 | − | 1788.84i | 0.334585 | − | 0.579518i | ||||
\(213\) | −668.163 | + | 1157.29i | −0.214938 | + | 0.372284i | ||||
\(214\) | −292.458 | − | 506.553i | −0.0934207 | − | 0.161809i | ||||
\(215\) | 1475.29 | 0.467972 | ||||||||
\(216\) | 593.605 | 0.186989 | ||||||||
\(217\) | −2202.84 | − | 3815.43i | −0.689117 | − | 1.19359i | ||||
\(218\) | 1482.59 | + | 2567.92i | 0.460612 | + | 0.797803i | ||||
\(219\) | −1664.78 | − | 2883.48i | −0.513677 | − | 0.889714i | ||||
\(220\) | 413.789 | + | 716.703i | 0.126807 | + | 0.219637i | ||||
\(221\) | 2845.61 | − | 4928.74i | 0.866137 | − | 1.50019i | ||||
\(222\) | −328.695 | + | 569.316i | −0.0993719 | + | 0.172117i | ||||
\(223\) | 4200.35 | 1.26133 | 0.630664 | − | 0.776056i | \(-0.282783\pi\) | ||||
0.630664 | + | 0.776056i | \(0.282783\pi\) | |||||||
\(224\) | 3402.02 | + | 5892.47i | 1.01476 | + | 1.75762i | ||||
\(225\) | −677.090 | −0.200619 | ||||||||
\(226\) | −1257.97 | −0.370260 | ||||||||
\(227\) | 2127.89 | − | 3685.61i | 0.622171 | − | 1.07763i | −0.366910 | − | 0.930257i | \(-0.619584\pi\) |
0.989081 | − | 0.147375i | \(-0.0470825\pi\) | |||||||
\(228\) | −409.658 | −0.118992 | ||||||||
\(229\) | −1877.18 | − | 3251.37i | −0.541692 | − | 0.938239i | −0.998807 | − | 0.0488310i | \(-0.984450\pi\) |
0.457115 | − | 0.889408i | \(-0.348883\pi\) | |||||||
\(230\) | 784.847 | − | 1359.39i | 0.225006 | − | 0.389721i | ||||
\(231\) | 1234.33 | + | 2137.93i | 0.351572 | + | 0.608941i | ||||
\(232\) | 2747.97 | − | 4759.63i | 0.777644 | − | 1.34692i | ||||
\(233\) | 1738.01 | − | 3010.32i | 0.488672 | − | 0.846405i | −0.511243 | − | 0.859436i | \(-0.670815\pi\) |
0.999915 | + | 0.0130314i | \(0.00414813\pi\) | |||||||
\(234\) | 470.465 | − | 814.868i | 0.131433 | − | 0.227648i | ||||
\(235\) | −1119.33 | + | 1938.74i | −0.310711 | + | 0.538167i | ||||
\(236\) | −364.135 | + | 630.701i | −0.100437 | + | 0.173962i | ||||
\(237\) | −1428.73 | + | 2474.64i | −0.391587 | + | 0.678249i | ||||
\(238\) | 2759.11 | + | 4778.91i | 0.751455 | + | 1.30156i | ||||
\(239\) | −1167.11 | + | 2021.49i | −0.315874 | + | 0.547110i | −0.979623 | − | 0.200846i | \(-0.935631\pi\) |
0.663749 | + | 0.747955i | \(0.268964\pi\) | |||||||
\(240\) | −57.7945 | − | 100.103i | −0.0155442 | − | 0.0269234i | ||||
\(241\) | 2639.66 | 0.705540 | 0.352770 | − | 0.935710i | \(-0.385240\pi\) | ||||
0.352770 | + | 0.935710i | \(0.385240\pi\) | |||||||
\(242\) | 689.440 | − | 1194.15i | 0.183136 | − | 0.317201i | ||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 675.114 | 0.177130 | ||||||||
\(245\) | 3564.03 | + | 6173.08i | 0.929378 | + | 1.60973i | ||||
\(246\) | −1899.82 | −0.492392 | ||||||||
\(247\) | −819.935 | + | 1420.17i | −0.211220 | + | 0.365843i | ||||
\(248\) | −1316.44 | + | 2280.14i | −0.337073 | + | 0.583828i | ||||
\(249\) | −870.249 | − | 1507.32i | −0.221485 | − | 0.383623i | ||||
\(250\) | −1172.40 | − | 2030.65i | −0.296596 | − | 0.513719i | ||||
\(251\) | −380.358 | − | 658.800i | −0.0956494 | − | 0.165670i | 0.814230 | − | 0.580542i | \(-0.197159\pi\) |
−0.909879 | + | 0.414873i | \(0.863826\pi\) | |||||||
\(252\) | −868.230 | − | 1503.82i | −0.217037 | − | 0.375919i | ||||
\(253\) | −2998.27 | −0.745059 | ||||||||
\(254\) | 2511.39 | 0.620387 | ||||||||
\(255\) | −956.208 | − | 1656.20i | −0.234824 | − | 0.406727i | ||||
\(256\) | 1918.51 | − | 3322.96i | 0.468386 | − | 0.811269i | ||||
\(257\) | 2154.32 | − | 3731.40i | 0.522891 | − | 0.905674i | −0.476754 | − | 0.879037i | \(-0.658187\pi\) |
0.999645 | − | 0.0266375i | \(-0.00847999\pi\) | |||||||
\(258\) | −520.705 | − | 901.887i | −0.125650 | − | 0.217632i | ||||
\(259\) | 4856.46 | 1.16512 | ||||||||
\(260\) | −2330.23 | −0.555827 | ||||||||
\(261\) | −1124.92 | + | 1948.42i | −0.266785 | + | 0.462084i | ||||
\(262\) | 1610.60 | + | 2789.65i | 0.379784 | + | 0.657805i | ||||
\(263\) | 4352.34 | 1.02044 | 0.510222 | − | 0.860043i | \(-0.329563\pi\) | ||||
0.510222 | + | 0.860043i | \(0.329563\pi\) | |||||||
\(264\) | 737.653 | − | 1277.65i | 0.171967 | − | 0.297856i | ||||
\(265\) | −2778.47 | −0.644076 | ||||||||
\(266\) | −795.011 | − | 1377.00i | −0.183253 | − | 0.317403i | ||||
\(267\) | −1576.31 | −0.361305 | ||||||||
\(268\) | −2789.99 | + | 698.929i | −0.635918 | + | 0.159306i | ||||
\(269\) | 1774.24 | 0.402145 | 0.201073 | − | 0.979576i | \(-0.435557\pi\) | ||||
0.201073 | + | 0.979576i | \(0.435557\pi\) | |||||||
\(270\) | −158.090 | − | 273.820i | −0.0356335 | − | 0.0617191i | ||||
\(271\) | −631.572 | −0.141569 | −0.0707846 | − | 0.997492i | \(-0.522550\pi\) | ||||
−0.0707846 | + | 0.997492i | \(0.522550\pi\) | |||||||
\(272\) | −246.762 | + | 427.405i | −0.0550079 | + | 0.0952765i | ||||
\(273\) | −6951.10 | −1.54102 | ||||||||
\(274\) | −575.425 | − | 996.665i | −0.126871 | − | 0.219747i | ||||
\(275\) | −841.397 | + | 1457.34i | −0.184502 | + | 0.319568i | ||||
\(276\) | 2108.98 | 0.459949 | ||||||||
\(277\) | 2997.35 | 0.650156 | 0.325078 | − | 0.945687i | \(-0.394609\pi\) | ||||
0.325078 | + | 0.945687i | \(0.394609\pi\) | |||||||
\(278\) | 699.932 | + | 1212.32i | 0.151004 | + | 0.261547i | ||||
\(279\) | 538.903 | − | 933.407i | 0.115639 | − | 0.200293i | ||||
\(280\) | 2852.94 | − | 4941.43i | 0.608913 | − | 1.05467i | ||||
\(281\) | 755.171 | + | 1308.00i | 0.160319 | + | 0.277681i | 0.934983 | − | 0.354692i | \(-0.115414\pi\) |
−0.774664 | + | 0.632373i | \(0.782081\pi\) | |||||||
\(282\) | 1580.27 | 0.333702 | ||||||||
\(283\) | 7519.83 | 1.57953 | 0.789766 | − | 0.613408i | \(-0.210202\pi\) | ||||
0.789766 | + | 0.613408i | \(0.210202\pi\) | |||||||
\(284\) | −1168.07 | − | 2023.16i | −0.244057 | − | 0.422720i | ||||
\(285\) | 275.523 | + | 477.219i | 0.0572651 | + | 0.0991860i | ||||
\(286\) | −1169.26 | − | 2025.22i | −0.241748 | − | 0.418719i | ||||
\(287\) | 7017.46 | + | 12154.6i | 1.44330 | + | 2.49987i | ||||
\(288\) | −832.270 | + | 1441.53i | −0.170285 | + | 0.294942i | ||||
\(289\) | −1626.17 | + | 2816.61i | −0.330993 | + | 0.573297i | ||||
\(290\) | −2927.38 | −0.592765 | ||||||||
\(291\) | 2231.23 | + | 3864.60i | 0.449474 | + | 0.778512i | ||||
\(292\) | 5820.67 | 1.16654 | ||||||||
\(293\) | 3743.75 | 0.746457 | 0.373229 | − | 0.927739i | \(-0.378251\pi\) | ||||
0.373229 | + | 0.927739i | \(0.378251\pi\) | |||||||
\(294\) | 2515.85 | − | 4357.59i | 0.499073 | − | 0.864421i | ||||
\(295\) | 979.623 | 0.193342 | ||||||||
\(296\) | −1451.14 | − | 2513.45i | −0.284952 | − | 0.493551i | ||||
\(297\) | −301.968 | + | 523.024i | −0.0589965 | + | 0.102185i | ||||
\(298\) | −865.830 | − | 1499.66i | −0.168309 | − | 0.291520i | ||||
\(299\) | 4221.16 | − | 7311.27i | 0.816442 | − | 1.41412i | ||||
\(300\) | 591.838 | − | 1025.09i | 0.113899 | − | 0.197279i | ||||
\(301\) | −3846.70 | + | 6662.68i | −0.736611 | + | 1.27585i | ||||
\(302\) | 1437.54 | − | 2489.89i | 0.273911 | − | 0.474428i | ||||
\(303\) | −1454.77 | + | 2519.73i | −0.275823 | + | 0.477739i | ||||
\(304\) | 71.1022 | − | 123.153i | 0.0134145 | − | 0.0232345i | ||||
\(305\) | −454.060 | − | 786.455i | −0.0852439 | − | 0.147647i | ||||
\(306\) | −674.988 | + | 1169.11i | −0.126100 | + | 0.218411i | ||||
\(307\) | 566.159 | + | 980.616i | 0.105252 | + | 0.182302i | 0.913841 | − | 0.406072i | \(-0.133102\pi\) |
−0.808589 | + | 0.588374i | \(0.799768\pi\) | |||||||
\(308\) | −4315.68 | −0.798405 | ||||||||
\(309\) | −2451.29 | + | 4245.77i | −0.451292 | + | 0.781661i | ||||
\(310\) | 1402.39 | 0.256937 | ||||||||
\(311\) | −4228.64 | −0.771011 | −0.385505 | − | 0.922706i | \(-0.625973\pi\) | ||||
−0.385505 | + | 0.922706i | \(0.625973\pi\) | |||||||
\(312\) | 2077.03 | + | 3597.52i | 0.376887 | + | 0.652787i | ||||
\(313\) | −7527.97 | −1.35944 | −0.679722 | − | 0.733470i | \(-0.737900\pi\) | ||||
−0.679722 | + | 0.733470i | \(0.737900\pi\) | |||||||
\(314\) | −690.443 | + | 1195.88i | −0.124089 | + | 0.214929i | ||||
\(315\) | −1167.89 | + | 2022.84i | −0.208899 | + | 0.361823i | ||||
\(316\) | −2497.69 | − | 4326.12i | −0.444639 | − | 0.770137i | ||||
\(317\) | 683.056 | + | 1183.09i | 0.121023 | + | 0.209618i | 0.920171 | − | 0.391516i | \(-0.128049\pi\) |
−0.799148 | + | 0.601134i | \(0.794716\pi\) | |||||||
\(318\) | 980.663 | + | 1698.56i | 0.172934 | + | 0.299530i | ||||
\(319\) | 2795.80 | + | 4842.47i | 0.490704 | + | 0.849925i | ||||
\(320\) | −1857.58 | −0.324506 | ||||||||
\(321\) | −1057.11 | −0.183807 | ||||||||
\(322\) | 4092.85 | + | 7089.02i | 0.708340 | + | 1.22688i | ||||
\(323\) | 1176.38 | − | 2037.56i | 0.202649 | − | 0.350999i | ||||
\(324\) | 212.404 | − | 367.895i | 0.0364205 | − | 0.0630821i | ||||
\(325\) | −2369.15 | − | 4103.48i | −0.404359 | − | 0.700370i | ||||
\(326\) | −1728.97 | −0.293738 | ||||||||
\(327\) | 5358.89 | 0.906260 | ||||||||
\(328\) | 4193.72 | − | 7263.73i | 0.705973 | − | 1.22278i | ||||
\(329\) | −5837.13 | − | 10110.2i | −0.978150 | − | 1.69420i | ||||
\(330\) | −785.812 | −0.131083 | ||||||||
\(331\) | −165.605 | + | 286.836i | −0.0274999 | + | 0.0476313i | −0.879448 | − | 0.475995i | \(-0.842088\pi\) |
0.851948 | + | 0.523627i | \(0.175421\pi\) | |||||||
\(332\) | 3042.71 | 0.502983 | ||||||||
\(333\) | 594.043 | + | 1028.91i | 0.0977578 | + | 0.169321i | ||||
\(334\) | −2055.98 | −0.336820 | ||||||||
\(335\) | 2690.66 | + | 2780.05i | 0.438825 | + | 0.453403i | ||||
\(336\) | 602.778 | 0.0978697 | ||||||||
\(337\) | 168.929 | + | 292.593i | 0.0273060 | + | 0.0472955i | 0.879356 | − | 0.476166i | \(-0.157974\pi\) |
−0.852049 | + | 0.523461i | \(0.824640\pi\) | |||||||
\(338\) | 2937.72 | 0.472754 | ||||||||
\(339\) | −1136.75 | + | 1968.90i | −0.182123 | + | 0.315446i | ||||
\(340\) | 3343.25 | 0.533274 | ||||||||
\(341\) | −1339.35 | − | 2319.83i | −0.212698 | − | 0.368404i | ||||
\(342\) | 194.492 | − | 336.870i | 0.0307512 | − | 0.0532626i | ||||
\(343\) | −24553.2 | −3.86515 | ||||||||
\(344\) | 4597.66 | 0.720609 | ||||||||
\(345\) | −1418.44 | − | 2456.80i | −0.221351 | − | 0.383391i | ||||
\(346\) | −2529.83 | + | 4381.79i | −0.393076 | + | 0.680828i | ||||
\(347\) | 4207.30 | − | 7287.26i | 0.650893 | − | 1.12738i | −0.332014 | − | 0.943274i | \(-0.607728\pi\) |
0.982907 | − | 0.184105i | \(-0.0589386\pi\) | |||||||
\(348\) | −1966.56 | − | 3406.19i | −0.302928 | − | 0.524686i | ||||
\(349\) | 2075.92 | 0.318400 | 0.159200 | − | 0.987246i | \(-0.449109\pi\) | ||||
0.159200 | + | 0.987246i | \(0.449109\pi\) | |||||||
\(350\) | 4594.26 | 0.701638 | ||||||||
\(351\) | −850.260 | − | 1472.69i | −0.129298 | − | 0.223950i | ||||
\(352\) | 2068.47 | + | 3582.69i | 0.313209 | + | 0.542495i | ||||
\(353\) | −2412.26 | − | 4178.15i | −0.363716 | − | 0.629974i | 0.624854 | − | 0.780742i | \(-0.285159\pi\) |
−0.988569 | + | 0.150768i | \(0.951825\pi\) | |||||||
\(354\) | −345.759 | − | 598.871i | −0.0519120 | − | 0.0899143i | ||||
\(355\) | −1571.21 | + | 2721.42i | −0.234905 | + | 0.406868i | ||||
\(356\) | 1377.84 | − | 2386.48i | 0.205127 | − | 0.355290i | ||||
\(357\) | 9972.94 | 1.47850 | ||||||||
\(358\) | 3013.91 | + | 5220.24i | 0.444944 | + | 0.770666i | ||||
\(359\) | −7650.94 | −1.12479 | −0.562397 | − | 0.826867i | \(-0.690121\pi\) | ||||
−0.562397 | + | 0.826867i | \(0.690121\pi\) | |||||||
\(360\) | 1395.89 | 0.204360 | ||||||||
\(361\) | 3090.54 | − | 5352.96i | 0.450581 | − | 0.780429i | ||||
\(362\) | −947.109 | −0.137511 | ||||||||
\(363\) | −1246.01 | − | 2158.15i | −0.180161 | − | 0.312048i | ||||
\(364\) | 6075.89 | − | 10523.8i | 0.874900 | − | 1.51537i | ||||
\(365\) | −3914.79 | − | 6780.62i | −0.561396 | − | 0.972367i | ||||
\(366\) | −320.521 | + | 555.159i | −0.0457757 | + | 0.0792859i | ||||
\(367\) | −1020.62 | + | 1767.77i | −0.145167 | + | 0.251436i | −0.929435 | − | 0.368986i | \(-0.879705\pi\) |
0.784269 | + | 0.620422i | \(0.213038\pi\) | |||||||
\(368\) | −366.046 | + | 634.010i | −0.0518518 | + | 0.0898100i | ||||
\(369\) | −1716.75 | + | 2973.50i | −0.242197 | + | 0.419497i | ||||
\(370\) | −772.940 | + | 1338.77i | −0.108603 | + | 0.188107i | ||||
\(371\) | 7244.64 | − | 12548.1i | 1.01381 | − | 1.75597i | ||||
\(372\) | 942.100 | + | 1631.77i | 0.131305 | + | 0.227428i | ||||
\(373\) | −1118.58 | + | 1937.44i | −0.155276 | + | 0.268945i | −0.933159 | − | 0.359463i | \(-0.882960\pi\) |
0.777884 | + | 0.628408i | \(0.216293\pi\) | |||||||
\(374\) | 1677.57 | + | 2905.64i | 0.231939 | + | 0.401730i | ||||
\(375\) | −4237.69 | −0.583556 | ||||||||
\(376\) | −3488.34 | + | 6041.97i | −0.478450 | + | 0.828699i | ||||
\(377\) | −15744.4 | −2.15087 | ||||||||
\(378\) | 1648.83 | 0.224356 | ||||||||
\(379\) | −961.927 | − | 1666.11i | −0.130372 | − | 0.225810i | 0.793448 | − | 0.608638i | \(-0.208284\pi\) |
−0.923820 | + | 0.382827i | \(0.874950\pi\) | |||||||
\(380\) | −963.327 | −0.130046 | ||||||||
\(381\) | 2269.38 | − | 3930.69i | 0.305155 | − | 0.528544i | ||||
\(382\) | 1202.94 | − | 2083.56i | 0.161120 | − | 0.279068i | ||||
\(383\) | 6090.79 | + | 10549.6i | 0.812597 | + | 1.40746i | 0.911040 | + | 0.412317i | \(0.135280\pi\) |
−0.0984433 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(384\) | −1563.75 | − | 2708.50i | −0.207812 | − | 0.359941i | ||||
\(385\) | 2902.59 | + | 5027.43i | 0.384233 | + | 0.665511i | ||||
\(386\) | 2958.00 | + | 5123.41i | 0.390047 | + | 0.675582i | ||||
\(387\) | −1882.11 | −0.247218 | ||||||||
\(388\) | −7801.19 | −1.02074 | ||||||||
\(389\) | 6383.57 | + | 11056.7i | 0.832031 | + | 1.44112i | 0.896425 | + | 0.443195i | \(0.146155\pi\) |
−0.0643944 | + | 0.997925i | \(0.520512\pi\) | |||||||
\(390\) | 1106.32 | − | 1916.20i | 0.143642 | − | 0.248796i | ||||
\(391\) | −6056.22 | + | 10489.7i | −0.783315 | + | 1.35674i | ||||
\(392\) | 11107.1 | + | 19238.1i | 1.43111 | + | 2.47875i | ||||
\(393\) | 5821.61 | 0.747230 | ||||||||
\(394\) | −3828.81 | −0.489575 | ||||||||
\(395\) | −3359.73 | + | 5819.22i | −0.427965 | + | 0.741257i | ||||
\(396\) | −527.895 | − | 914.340i | −0.0669892 | − | 0.116029i | ||||
\(397\) | 7600.70 | 0.960876 | 0.480438 | − | 0.877029i | \(-0.340478\pi\) | ||||
0.480438 | + | 0.877029i | \(0.340478\pi\) | |||||||
\(398\) | −1744.43 | + | 3021.45i | −0.219700 | + | 0.380531i | ||||
\(399\) | −2873.61 | −0.360552 | ||||||||
\(400\) | 205.445 | + | 355.841i | 0.0256806 | + | 0.0444801i | ||||
\(401\) | 1687.67 | 0.210170 | 0.105085 | − | 0.994463i | \(-0.466488\pi\) | ||||
0.105085 | + | 0.994463i | \(0.466488\pi\) | |||||||
\(402\) | 749.852 | − | 2626.09i | 0.0930329 | − | 0.325815i | ||||
\(403\) | 7542.51 | 0.932305 | ||||||||
\(404\) | −2543.20 | − | 4404.95i | −0.313191 | − | 0.542462i | ||||
\(405\) | −571.425 | −0.0701094 | ||||||||
\(406\) | 7632.91 | − | 13220.6i | 0.933042 | − | 1.61608i | ||||
\(407\) | 2952.79 | 0.359617 | ||||||||
\(408\) | −2979.97 | − | 5161.46i | −0.361595 | − | 0.626300i | ||||
\(409\) | 1292.30 | − | 2238.33i | 0.156235 | − | 0.270607i | −0.777273 | − | 0.629163i | \(-0.783398\pi\) |
0.933508 | + | 0.358557i | \(0.116731\pi\) | |||||||
\(410\) | −4467.52 | −0.538134 | ||||||||
\(411\) | −2079.90 | −0.249621 | ||||||||
\(412\) | −4285.31 | − | 7422.37i | −0.512432 | − | 0.887558i | ||||
\(413\) | −2554.29 | + | 4424.15i | −0.304330 | + | 0.527115i | ||||
\(414\) | −1001.28 | + | 1734.26i | −0.118865 | + | 0.205880i | ||||
\(415\) | −2046.43 | − | 3544.52i | −0.242061 | − | 0.419261i | ||||
\(416\) | −11648.5 | −1.37287 | ||||||||
\(417\) | 2529.94 | 0.297103 | ||||||||
\(418\) | −483.376 | − | 837.233i | −0.0565615 | − | 0.0979674i | ||||
\(419\) | −5793.43 | − | 10034.5i | −0.675483 | − | 1.16997i | −0.976327 | − | 0.216298i | \(-0.930602\pi\) |
0.300845 | − | 0.953673i | \(-0.402731\pi\) | |||||||
\(420\) | −2041.68 | − | 3536.29i | −0.237200 | − | 0.410842i | ||||
\(421\) | 2066.75 | + | 3579.71i | 0.239257 | + | 0.414405i | 0.960501 | − | 0.278276i | \(-0.0897629\pi\) |
−0.721244 | + | 0.692681i | \(0.756430\pi\) | |||||||
\(422\) | 1074.55 | − | 1861.18i | 0.123953 | − | 0.214693i | ||||
\(423\) | 1428.00 | − | 2473.36i | 0.164141 | − | 0.284300i | ||||
\(424\) | −8658.96 | −0.991783 | ||||||||
\(425\) | 3399.08 | + | 5887.38i | 0.387952 | + | 0.671952i | ||||
\(426\) | 2218.24 | 0.252287 | ||||||||
\(427\) | 4735.69 | 0.536713 | ||||||||
\(428\) | 924.007 | − | 1600.43i | 0.104354 | − | 0.180747i | ||||
\(429\) | −4226.35 | −0.475642 | ||||||||
\(430\) | −1224.46 | − | 2120.82i | −0.137322 | − | 0.237849i | ||||
\(431\) | 3637.38 | − | 6300.12i | 0.406511 | − | 0.704098i | −0.587985 | − | 0.808872i | \(-0.700079\pi\) |
0.994496 | + | 0.104774i | \(0.0334119\pi\) | |||||||
\(432\) | 73.7318 | + | 127.707i | 0.00821163 | + | 0.0142230i | ||||
\(433\) | −919.913 | + | 1593.34i | −0.102097 | + | 0.176838i | −0.912549 | − | 0.408968i | \(-0.865889\pi\) |
0.810451 | + | 0.585806i | \(0.199222\pi\) | |||||||
\(434\) | −3656.62 | + | 6333.44i | −0.404431 | + | 0.700495i | ||||
\(435\) | −2645.30 | + | 4581.79i | −0.291568 | + | 0.505011i | ||||
\(436\) | −4684.15 | + | 8113.19i | −0.514519 | + | 0.891173i | ||||
\(437\) | 1745.04 | − | 3022.50i | 0.191022 | − | 0.330860i | ||||
\(438\) | −2763.46 | + | 4786.45i | −0.301468 | + | 0.522158i | ||||
\(439\) | −311.820 | − | 540.088i | −0.0339006 | − | 0.0587175i | 0.848577 | − | 0.529071i | \(-0.177460\pi\) |
−0.882478 | + | 0.470354i | \(0.844126\pi\) | |||||||
\(440\) | 1734.62 | − | 3004.45i | 0.187943 | − | 0.325526i | ||||
\(441\) | −4546.84 | − | 7875.36i | −0.490967 | − | 0.850380i | ||||
\(442\) | −9447.17 | −1.01664 | ||||||||
\(443\) | 5584.06 | − | 9671.87i | 0.598886 | − | 1.03730i | −0.394099 | − | 0.919068i | \(-0.628943\pi\) |
0.992986 | − | 0.118234i | \(-0.0377232\pi\) | |||||||
\(444\) | −2076.99 | −0.222003 | ||||||||
\(445\) | −3706.76 | −0.394870 | ||||||||
\(446\) | −3486.20 | − | 6038.27i | −0.370126 | − | 0.641077i | ||||
\(447\) | −3129.59 | −0.331151 | ||||||||
\(448\) | 4843.50 | − | 8389.18i | 0.510790 | − | 0.884713i | ||||
\(449\) | −5319.52 | + | 9213.69i | −0.559118 | + | 0.968420i | 0.438453 | + | 0.898754i | \(0.355527\pi\) |
−0.997570 | + | 0.0696661i | \(0.977807\pi\) | |||||||
\(450\) | 561.970 | + | 973.361i | 0.0588701 | + | 0.101966i | ||||
\(451\) | 4266.70 | + | 7390.15i | 0.445479 | + | 0.771593i | ||||
\(452\) | −1987.24 | − | 3442.00i | −0.206796 | − | 0.358182i | ||||
\(453\) | −2598.03 | − | 4499.92i | −0.269462 | − | 0.466722i | ||||
\(454\) | −7064.40 | −0.730284 | ||||||||
\(455\) | −16345.8 | −1.68418 | ||||||||
\(456\) | 858.651 | + | 1487.23i | 0.0881799 | + | 0.152732i | ||||
\(457\) | 114.371 | − | 198.096i | 0.0117068 | − | 0.0202769i | −0.860113 | − | 0.510104i | \(-0.829607\pi\) |
0.871819 | + | 0.489827i | \(0.162940\pi\) | |||||||
\(458\) | −3116.04 | + | 5397.13i | −0.317910 | + | 0.550637i | ||||
\(459\) | 1219.89 | + | 2112.91i | 0.124051 | + | 0.214863i | ||||
\(460\) | 4959.37 | 0.502678 | ||||||||
\(461\) | −12161.7 | −1.22869 | −0.614344 | − | 0.789039i | \(-0.710579\pi\) | ||||
−0.614344 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(462\) | 2048.94 | − | 3548.87i | 0.206332 | − | 0.357377i | ||||
\(463\) | −6300.68 | − | 10913.1i | −0.632435 | − | 1.09541i | −0.987052 | − | 0.160398i | \(-0.948722\pi\) |
0.354617 | − | 0.935012i | \(-0.384611\pi\) | |||||||
\(464\) | 1365.31 | 0.136601 | ||||||||
\(465\) | 1267.25 | − | 2194.95i | 0.126382 | − | 0.218899i | ||||
\(466\) | −5770.03 | −0.573587 | ||||||||
\(467\) | 3467.50 | + | 6005.89i | 0.343591 | + | 0.595116i | 0.985097 | − | 0.172002i | \(-0.0550234\pi\) |
−0.641506 | + | 0.767118i | \(0.721690\pi\) | |||||||
\(468\) | 2972.82 | 0.293629 | ||||||||
\(469\) | −19570.9 | + | 4902.75i | −1.92686 | + | 0.482704i | ||||
\(470\) | 3716.08 | 0.364702 | ||||||||
\(471\) | 1247.82 | + | 2161.29i | 0.122073 | + | 0.211437i | ||||
\(472\) | 3052.94 | 0.297718 | ||||||||
\(473\) | −2338.84 | + | 4050.99i | −0.227357 | + | 0.393794i | ||||
\(474\) | 4743.27 | 0.459632 | ||||||||
\(475\) | −979.413 | − | 1696.39i | −0.0946075 | − | 0.163865i | ||||
\(476\) | −8717.25 | + | 15098.7i | −0.839401 | + | 1.45388i | ||||
\(477\) | 3544.66 | 0.340249 | ||||||||
\(478\) | 3874.69 | 0.370762 | ||||||||
\(479\) | −5451.10 | − | 9441.59i | −0.519973 | − | 0.900620i | −0.999730 | − | 0.0232189i | \(-0.992609\pi\) |
0.479757 | − | 0.877401i | \(-0.340725\pi\) | |||||||
\(480\) | −1957.12 | + | 3389.83i | −0.186104 | + | 0.322341i | ||||
\(481\) | −4157.12 | + | 7200.35i | −0.394072 | + | 0.682552i | ||||
\(482\) | −2190.86 | − | 3794.67i | −0.207035 | − | 0.358595i | ||||
\(483\) | 14793.8 | 1.39367 | ||||||||
\(484\) | 4356.50 | 0.409138 | ||||||||
\(485\) | 5246.83 | + | 9087.77i | 0.491229 | + | 0.850834i | ||||
\(486\) | 201.685 | + | 349.328i | 0.0188243 | + | 0.0326046i | ||||
\(487\) | 5919.72 | + | 10253.2i | 0.550817 | + | 0.954043i | 0.998216 | + | 0.0597087i | \(0.0190172\pi\) |
−0.447399 | + | 0.894335i | \(0.647649\pi\) | |||||||
\(488\) | −1415.05 | − | 2450.94i | −0.131263 | − | 0.227355i | ||||
\(489\) | −1562.36 | + | 2706.09i | −0.144483 | + | 0.250253i | ||||
\(490\) | 5916.14 | − | 10247.0i | 0.545436 | − | 0.944723i | ||||
\(491\) | −3578.18 | −0.328882 | −0.164441 | − | 0.986387i | \(-0.552582\pi\) | ||||
−0.164441 | + | 0.986387i | \(0.552582\pi\) | |||||||
\(492\) | −3001.20 | − | 5198.23i | −0.275009 | − | 0.476330i | ||||
\(493\) | 22589.0 | 2.06360 | ||||||||
\(494\) | 2722.11 | 0.247922 | ||||||||
\(495\) | −710.090 | + | 1229.91i | −0.0644771 | + | 0.111678i | ||||
\(496\) | −654.063 | −0.0592102 | ||||||||
\(497\) | −8193.63 | − | 14191.8i | −0.739506 | − | 1.28086i | ||||
\(498\) | −1444.58 | + | 2502.08i | −0.129986 | + | 0.225142i | ||||
\(499\) | 9423.01 | + | 16321.1i | 0.845354 | + | 1.46420i | 0.885313 | + | 0.464995i | \(0.153944\pi\) |
−0.0399591 | + | 0.999201i | \(0.512723\pi\) | |||||||
\(500\) | 3704.13 | − | 6415.74i | 0.331307 | − | 0.573841i | ||||
\(501\) | −1857.86 | + | 3217.90i | −0.165675 | + | 0.286957i | ||||
\(502\) | −631.378 | + | 1093.58i | −0.0561350 | + | 0.0972287i | ||||
\(503\) | 6224.16 | − | 10780.6i | 0.551733 | − | 0.955630i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) |
0.998150 | − | 0.0608044i | \(-0.0193666\pi\) | |||||||
\(504\) | −3639.66 | + | 6304.08i | −0.321673 | + | 0.557155i | ||||
\(505\) | −3420.95 | + | 5925.26i | −0.301446 | + | 0.522120i | ||||
\(506\) | 2488.50 | + | 4310.21i | 0.218631 | + | 0.378680i | ||||
\(507\) | 2654.63 | − | 4597.96i | 0.232537 | − | 0.402766i | ||||
\(508\) | 3967.30 | + | 6871.56i | 0.346497 | + | 0.600150i | ||||
\(509\) | 13601.2 | 1.18440 | 0.592201 | − | 0.805790i | \(-0.298259\pi\) | ||||
0.592201 | + | 0.805790i | \(0.298259\pi\) | |||||||
\(510\) | −1587.26 | + | 2749.22i | −0.137814 | + | 0.238701i | ||||
\(511\) | 40830.0 | 3.53466 | ||||||||
\(512\) | 1970.73 | 0.170107 | ||||||||
\(513\) | −351.500 | − | 608.816i | −0.0302517 | − | 0.0523975i | ||||
\(514\) | −7152.17 | −0.613752 | ||||||||
\(515\) | −5764.32 | + | 9984.10i | −0.493216 | + | 0.854276i | ||||
\(516\) | 1645.14 | − | 2849.46i | 0.140355 | − | 0.243102i | ||||
\(517\) | −3549.04 | − | 6147.13i | −0.301909 | − | 0.522921i | ||||
\(518\) | −4030.76 | − | 6981.47i | −0.341894 | − | 0.592178i | ||||
\(519\) | 4572.10 | + | 7919.11i | 0.386692 | + | 0.669769i | ||||
\(520\) | 4884.22 | + | 8459.72i | 0.411899 | + | 0.713429i | ||||
\(521\) | 546.677 | 0.0459700 | 0.0229850 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229850 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(522\) | 3734.63 | 0.313143 | ||||||||
\(523\) | 9586.48 | + | 16604.3i | 0.801505 | + | 1.38825i | 0.918625 | + | 0.395130i | \(0.129301\pi\) |
−0.117120 | + | 0.993118i | \(0.537366\pi\) | |||||||
\(524\) | −5088.62 | + | 8813.74i | −0.424231 | + | 0.734790i | ||||
\(525\) | 4151.55 | − | 7190.69i | 0.345121 | − | 0.597767i | ||||
\(526\) | −3612.34 | − | 6256.76i | −0.299440 | − | 0.518646i | ||||
\(527\) | −10821.4 | −0.894477 | ||||||||
\(528\) | 366.496 | 0.0302078 | ||||||||
\(529\) | −2900.27 | + | 5023.42i | −0.238372 | + | 0.412872i | ||||
\(530\) | 2306.07 | + | 3994.23i | 0.188999 | + | 0.327355i | ||||
\(531\) | −1249.76 | −0.102138 | ||||||||
\(532\) | 2511.80 | − | 4350.56i | 0.204700 | − | 0.354550i | ||||
\(533\) | −24027.8 | −1.95264 | ||||||||
\(534\) | 1308.30 | + | 2266.04i | 0.106022 | + | 0.183635i | ||||
\(535\) | −2485.83 | −0.200882 | ||||||||
\(536\) | 8385.29 | + | 8663.87i | 0.675727 | + | 0.698175i | ||||
\(537\) | 10893.9 | 0.875434 | ||||||||
\(538\) | −1472.58 | − | 2550.58i | −0.118006 | − | 0.204393i | ||||
\(539\) | −22600.8 | −1.80610 | ||||||||
\(540\) | 499.477 | − | 865.120i | 0.0398038 | − | 0.0689423i | ||||
\(541\) | −18396.4 | −1.46197 | −0.730983 | − | 0.682395i | \(-0.760938\pi\) | ||||
−0.730983 | + | 0.682395i | \(0.760938\pi\) | |||||||
\(542\) | 524.191 | + | 907.926i | 0.0415423 | + | 0.0719534i | ||||
\(543\) | −855.844 | + | 1482.37i | −0.0676387 | + | 0.117154i | ||||
\(544\) | 16712.4 | 1.31717 | ||||||||
\(545\) | 12601.6 | 0.990450 | ||||||||
\(546\) | 5769.26 | + | 9992.66i | 0.452201 | + | 0.783235i | ||||
\(547\) | 3183.22 | − | 5513.50i | 0.248820 | − | 0.430969i | −0.714378 | − | 0.699760i | \(-0.753290\pi\) |
0.963199 | + | 0.268790i | \(0.0866238\pi\) | |||||||
\(548\) | 1818.02 | − | 3148.91i | 0.141719 | − | 0.245465i | ||||
\(549\) | 579.271 | + | 1003.33i | 0.0450322 | + | 0.0779980i | ||||
\(550\) | 2793.36 | 0.216563 | ||||||||
\(551\) | −6508.80 | −0.503238 | ||||||||
\(552\) | −4420.48 | − | 7656.49i | −0.340848 | − | 0.590366i | ||||
\(553\) | −17520.4 | − | 30346.3i | −1.34728 | − | 2.33355i | ||||
\(554\) | −2487.73 | − | 4308.88i | −0.190783 | − | 0.330446i | ||||
\(555\) | 1396.92 | + | 2419.53i | 0.106839 | + | 0.185051i | ||||
\(556\) | −2211.40 | + | 3830.25i | −0.168677 | + | 0.292156i | ||||
\(557\) | −4062.03 | + | 7035.64i | −0.309001 | + | 0.535206i | −0.978144 | − | 0.207928i | \(-0.933328\pi\) |
0.669143 | + | 0.743134i | \(0.266661\pi\) | |||||||
\(558\) | −1789.11 | −0.135733 | ||||||||
\(559\) | −6585.54 | − | 11406.5i | −0.498280 | − | 0.863046i | ||||
\(560\) | 1417.46 | 0.106962 | ||||||||
\(561\) | 6063.67 | 0.456343 | ||||||||
\(562\) | 1253.55 | − | 2171.22i | 0.0940888 | − | 0.162967i | ||||
\(563\) | −243.293 | −0.0182124 | −0.00910621 | − | 0.999959i | \(-0.502899\pi\) | ||||
−0.00910621 | + | 0.999959i | \(0.502899\pi\) | |||||||
\(564\) | 2496.40 | + | 4323.89i | 0.186378 | + | 0.322816i | ||||
\(565\) | −2673.11 | + | 4629.96i | −0.199042 | + | 0.344750i | ||||
\(566\) | −6241.29 | − | 10810.2i | −0.463500 | − | 0.802806i | ||||
\(567\) | 1489.94 | − | 2580.66i | 0.110356 | − | 0.191142i | ||||
\(568\) | −4896.61 | + | 8481.17i | −0.361720 | + | 0.626518i | ||||
\(569\) | −1827.11 | + | 3164.65i | −0.134616 | + | 0.233162i | −0.925451 | − | 0.378868i | \(-0.876313\pi\) |
0.790835 | + | 0.612030i | \(0.209647\pi\) | |||||||
\(570\) | 457.355 | − | 792.163i | 0.0336079 | − | 0.0582106i | ||||
\(571\) | −4034.53 | + | 6988.02i | −0.295692 | + | 0.512153i | −0.975146 | − | 0.221565i | \(-0.928883\pi\) |
0.679454 | + | 0.733718i | \(0.262217\pi\) | |||||||
\(572\) | 3694.22 | − | 6398.57i | 0.270040 | − | 0.467723i | ||||
\(573\) | −2174.05 | − | 3765.57i | −0.158503 | − | 0.274535i | ||||
\(574\) | 11648.7 | − | 20176.1i | 0.847050 | − | 1.46713i | ||||
\(575\) | 5042.18 | + | 8733.31i | 0.365693 | + | 0.633399i | ||||
\(576\) | 2369.83 | 0.171429 | ||||||||
\(577\) | 3483.40 | − | 6033.43i | 0.251328 | − | 0.435312i | −0.712564 | − | 0.701607i | \(-0.752466\pi\) |
0.963892 | + | 0.266295i | \(0.0857996\pi\) | |||||||
\(578\) | 5398.74 | 0.388509 | ||||||||
\(579\) | 10691.8 | 0.767423 | ||||||||
\(580\) | −4624.46 | − | 8009.80i | −0.331069 | − | 0.573429i | ||||
\(581\) | 21343.6 | 1.52406 | ||||||||
\(582\) | 3703.74 | − | 6415.07i | 0.263789 | − | 0.456896i | ||||
\(583\) | 4404.83 | − | 7629.39i | 0.312915 | − | 0.541984i | ||||
\(584\) | −12200.2 | − | 21131.4i | −0.864469 | − | 1.49730i | ||||
\(585\) | −1999.42 | − | 3463.10i | −0.141309 | − | 0.244755i | ||||
\(586\) | −3107.23 | − | 5381.88i | −0.219042 | − | 0.379391i | ||||
\(587\) | −10197.5 | − | 17662.6i | −0.717029 | − | 1.24193i | −0.962172 | − | 0.272444i | \(-0.912168\pi\) |
0.245143 | − | 0.969487i | \(-0.421165\pi\) | |||||||
\(588\) | 15897.4 | 1.11496 | ||||||||
\(589\) | 3118.10 | 0.218131 | ||||||||
\(590\) | −813.066 | − | 1408.27i | −0.0567345 | − | 0.0982671i | ||||
\(591\) | −3459.86 | + | 5992.65i | −0.240811 | + | 0.417097i | ||||
\(592\) | 360.493 | − | 624.392i | 0.0250273 | − | 0.0433486i | ||||
\(593\) | 6348.26 | + | 10995.5i | 0.439615 | + | 0.761436i | 0.997660 | − | 0.0683749i | \(-0.0217814\pi\) |
−0.558044 | + | 0.829811i | \(0.688448\pi\) | |||||||
\(594\) | 1002.51 | 0.0692481 | ||||||||
\(595\) | 23451.8 | 1.61585 | ||||||||
\(596\) | 2735.54 | − | 4738.10i | 0.188007 | − | 0.325638i | ||||
\(597\) | 3152.67 | + | 5460.59i | 0.216131 | + | 0.374350i | ||||
\(598\) | −14013.9 | −0.958312 | ||||||||
\(599\) | −3617.42 | + | 6265.56i | −0.246751 | + | 0.427385i | −0.962622 | − | 0.270847i | \(-0.912696\pi\) |
0.715871 | + | 0.698232i | \(0.246030\pi\) | |||||||
\(600\) | −4962.03 | −0.337623 | ||||||||
\(601\) | 6194.70 | + | 10729.5i | 0.420444 | + | 0.728231i | 0.995983 | − | 0.0895440i | \(-0.0285410\pi\) |
−0.575539 | + | 0.817774i | \(0.695208\pi\) | |||||||
\(602\) | 12770.7 | 0.864610 | ||||||||
\(603\) | −3432.63 | − | 3546.67i | −0.231820 | − | 0.239522i | ||||
\(604\) | 9083.67 | 0.611936 | ||||||||
\(605\) | −2930.04 | − | 5074.98i | −0.196898 | − | 0.341037i | ||||
\(606\) | 4829.71 | 0.323752 | ||||||||
\(607\) | 1375.56 | − | 2382.54i | 0.0919808 | − | 0.159315i | −0.816364 | − | 0.577538i | \(-0.804014\pi\) |
0.908345 | + | 0.418223i | \(0.137347\pi\) | |||||||
\(608\) | −4815.53 | −0.321210 | ||||||||
\(609\) | −13794.8 | − | 23893.3i | −0.917887 | − | 1.58983i | ||||
\(610\) | −753.719 | + | 1305.48i | −0.0500282 | + | 0.0866514i | ||||
\(611\) | 19986.3 | 1.32334 | ||||||||
\(612\) | −4265.18 | −0.281715 | ||||||||
\(613\) | 11746.6 | + | 20345.7i | 0.773965 | + | 1.34055i | 0.935374 | + | 0.353660i | \(0.115063\pi\) |
−0.161409 | + | 0.986888i | \(0.551604\pi\) | |||||||
\(614\) | 939.799 | − | 1627.78i | 0.0617707 | − | 0.106990i | ||||
\(615\) | −4037.02 | + | 6992.32i | −0.264696 | + | 0.458468i | ||||
\(616\) | 9045.77 | + | 15667.7i | 0.591663 | + | 1.02479i | ||||
\(617\) | 25962.2 | 1.69400 | 0.847001 | − | 0.531591i | \(-0.178406\pi\) | ||||
0.847001 | + | 0.531591i | \(0.178406\pi\) | |||||||
\(618\) | 8138.08 | 0.529711 | ||||||||
\(619\) | −603.378 | − | 1045.08i | −0.0391790 | − | 0.0678601i | 0.845771 | − | 0.533546i | \(-0.179141\pi\) |
−0.884950 | + | 0.465686i | \(0.845808\pi\) | |||||||
\(620\) | 2215.39 | + | 3837.17i | 0.143503 | + | 0.248555i | ||||
\(621\) | 1809.58 | + | 3134.29i | 0.116934 | + | 0.202536i | ||||
\(622\) | 3509.68 | + | 6078.94i | 0.226247 | + | 0.391871i | ||||
\(623\) | 9665.06 | − | 16740.4i | 0.621545 | − | 1.07655i | ||||
\(624\) | −515.977 | + | 893.698i | −0.0331019 | + | 0.0573342i | ||||
\(625\) | −561.076 | −0.0359089 | ||||||||
\(626\) | 6248.05 | + | 10821.9i | 0.398917 | + | 0.690945i | ||||
\(627\) | −1747.19 | −0.111286 | ||||||||
\(628\) | −4362.84 | −0.277223 | ||||||||
\(629\) | 5964.34 | − | 10330.5i | 0.378082 | − | 0.654858i | ||||
\(630\) | 3877.29 | 0.245198 | ||||||||
\(631\) | 348.175 | + | 603.057i | 0.0219661 | + | 0.0380464i | 0.876800 | − | 0.480856i | \(-0.159674\pi\) |
−0.854833 | + | 0.518903i | \(0.826341\pi\) | |||||||
\(632\) | −10470.4 | + | 18135.3i | −0.659004 | + | 1.14143i | ||||
\(633\) | −1942.01 | − | 3363.66i | −0.121940 | − | 0.211206i | ||||
\(634\) | 1133.84 | − | 1963.87i | 0.0710262 | − | 0.123021i | ||||
\(635\) | 5336.55 | − | 9243.18i | 0.333503 | − | 0.577645i | ||||
\(636\) | −3098.35 | + | 5366.51i | −0.193173 | + | 0.334585i | ||||
\(637\) | 31818.9 | − | 55112.0i | 1.97914 | − | 3.42797i | ||||
\(638\) | 4640.90 | − | 8038.28i | 0.287986 | − | 0.498807i | ||||
\(639\) | 2004.49 | − | 3471.88i | 0.124095 | − | 0.214938i | ||||
\(640\) | −3677.23 | − | 6369.15i | −0.227118 | − | 0.393379i | ||||
\(641\) | −6208.42 | + | 10753.3i | −0.382555 | + | 0.662605i | −0.991427 | − | 0.130664i | \(-0.958289\pi\) |
0.608871 | + | 0.793269i | \(0.291623\pi\) | |||||||
\(642\) | 877.375 | + | 1519.66i | 0.0539365 | + | 0.0934207i | ||||
\(643\) | −23562.2 | −1.44510 | −0.722552 | − | 0.691316i | \(-0.757031\pi\) | ||||
−0.722552 | + | 0.691316i | \(0.757031\pi\) | |||||||
\(644\) | −12931.1 | + | 22397.4i | −0.791240 | + | 1.37047i | ||||
\(645\) | −4425.87 | −0.270184 | ||||||||
\(646\) | −3905.49 | −0.237863 | ||||||||
\(647\) | 10869.4 | + | 18826.4i | 0.660467 | + | 1.14396i | 0.980493 | + | 0.196554i | \(0.0629750\pi\) |
−0.320026 | + | 0.947409i | \(0.603692\pi\) | |||||||
\(648\) | −1780.81 | −0.107958 | ||||||||
\(649\) | −1553.04 | + | 2689.94i | −0.0939323 | + | 0.162695i | ||||
\(650\) | −3932.68 | + | 6811.60i | −0.237311 | + | 0.411035i | ||||
\(651\) | 6608.52 | + | 11446.3i | 0.397862 | + | 0.689117i | ||||
\(652\) | −2731.29 | − | 4730.74i | −0.164058 | − | 0.284156i | ||||
\(653\) | −9139.01 | − | 15829.2i | −0.547683 | − | 0.948615i | −0.998433 | − | 0.0559644i | \(-0.982177\pi\) |
0.450750 | − | 0.892650i | \(-0.351157\pi\) | |||||||
\(654\) | −4447.76 | − | 7703.75i | −0.265934 | − | 0.460612i | ||||
\(655\) | 13689.8 | 0.816646 | ||||||||
\(656\) | 2083.61 | 0.124011 | ||||||||
\(657\) | 4994.33 | + | 8650.43i | 0.296571 | + | 0.513677i | ||||
\(658\) | −9689.38 | + | 16782.5i | −0.574060 | + | 0.994300i | ||||
\(659\) | −10944.7 | + | 18956.8i | −0.646957 | + | 1.12056i | 0.336889 | + | 0.941544i | \(0.390625\pi\) |
−0.983846 | + | 0.179018i | \(0.942708\pi\) | |||||||
\(660\) | −1241.37 | − | 2150.11i | −0.0732123 | − | 0.126807i | ||||
\(661\) | −3905.06 | −0.229787 | −0.114893 | − | 0.993378i | \(-0.536653\pi\) | ||||
−0.114893 | + | 0.993378i | \(0.536653\pi\) | |||||||
\(662\) | 549.794 | 0.0322785 | ||||||||
\(663\) | −8536.82 | + | 14786.2i | −0.500064 | + | 0.866137i | ||||
\(664\) | −6377.58 | − | 11046.3i | −0.372738 | − | 0.645601i | ||||
\(665\) | −6757.41 | −0.394047 | ||||||||
\(666\) | 986.085 | − | 1707.95i | 0.0573724 | − | 0.0993719i | ||||
\(667\) | 33508.4 | 1.94520 | ||||||||
\(668\) | −3247.87 | − | 5625.48i | −0.188120 | − | 0.325833i | ||||
\(669\) | −12601.0 | −0.728228 | ||||||||
\(670\) | 1763.31 | − | 6175.37i | 0.101675 | − | 0.356083i | ||||
\(671\) | 2879.36 | 0.165658 | ||||||||
\(672\) | −10206.1 | − | 17677.4i | −0.585874 | − | 1.01476i | ||||
\(673\) | −2390.82 | −0.136938 | −0.0684691 | − | 0.997653i | \(-0.521811\pi\) | ||||
−0.0684691 | + | 0.997653i | \(0.521811\pi\) | |||||||
\(674\) | 280.414 | − | 485.692i | 0.0160255 | − | 0.0277569i | ||||
\(675\) | 2031.27 | 0.115828 | ||||||||
\(676\) | 4640.78 | + | 8038.07i | 0.264041 | + | 0.457332i | ||||
\(677\) | −2864.24 | + | 4961.01i | −0.162602 | + | 0.281635i | −0.935801 | − | 0.352528i | \(-0.885322\pi\) |
0.773199 | + | 0.634164i | \(0.218655\pi\) | |||||||
\(678\) | 3773.90 | 0.213770 | ||||||||
\(679\) | −54722.7 | −3.09288 | ||||||||
\(680\) | −7007.53 | − | 12137.4i | −0.395186 | − | 0.684482i | ||||
\(681\) | −6383.66 | + | 11056.8i | −0.359211 | + | 0.622171i | ||||
\(682\) | −2223.27 | + | 3850.81i | −0.124829 | + | 0.216210i | ||||
\(683\) | −13011.4 | − | 22536.5i | −0.728944 | − | 1.26257i | −0.957330 | − | 0.288997i | \(-0.906678\pi\) |
0.228386 | − | 0.973571i | \(-0.426655\pi\) | |||||||
\(684\) | 1228.97 | 0.0687002 | ||||||||
\(685\) | −4890.98 | −0.272810 | ||||||||
\(686\) | 20378.6 | + | 35296.7i | 1.13419 | + | 1.96448i | ||||
\(687\) | 5631.54 | + | 9754.11i | 0.312746 | + | 0.541692i | ||||
\(688\) | 571.077 | + | 989.135i | 0.0316455 | + | 0.0548116i | ||||
\(689\) | 12402.8 | + | 21482.3i | 0.685790 | + | 1.18782i | ||||
\(690\) | −2354.54 | + | 4078.18i | −0.129907 | + | 0.225006i | ||||
\(691\) | 15047.0 | − | 26062.2i | 0.828388 | − | 1.43481i | −0.0709141 | − | 0.997482i | \(-0.522592\pi\) |
0.899302 | − | 0.437328i | \(-0.144075\pi\) | |||||||
\(692\) | −15985.7 | −0.878159 | ||||||||
\(693\) | −3703.00 | − | 6413.79i | −0.202980 | − | 0.351572i | ||||
\(694\) | −13967.9 | −0.763996 | ||||||||
\(695\) | 5949.26 | 0.324703 | ||||||||
\(696\) | −8243.92 | + | 14278.9i | −0.448973 | + | 0.777644i | ||||
\(697\) | 34473.3 | 1.87341 | ||||||||
\(698\) | −1722.97 | − | 2984.27i | −0.0934317 | − | 0.161829i | ||||
\(699\) | −5214.02 | + | 9030.95i | −0.282135 | + | 0.488672i | ||||
\(700\) | 7257.66 | + | 12570.6i | 0.391877 | + | 0.678750i | ||||
\(701\) | −357.484 | + | 619.181i | −0.0192610 | + | 0.0333611i | −0.875495 | − | 0.483227i | \(-0.839465\pi\) |
0.856234 | + | 0.516588i | \(0.172798\pi\) | |||||||
\(702\) | −1411.39 | + | 2444.61i | −0.0758826 | + | 0.131433i | ||||
\(703\) | −1718.57 | + | 2976.65i | −0.0922007 | + | 0.159696i | ||||
\(704\) | 2944.91 | − | 5100.73i | 0.157657 | − | 0.273069i | ||||
\(705\) | 3357.99 | − | 5816.21i | 0.179389 | − | 0.310711i | ||||
\(706\) | −4004.24 | + | 6935.55i | −0.213459 | + | 0.369721i | ||||
\(707\) | −17839.7 | − | 30899.3i | −0.948983 | − | 1.64369i | ||||
\(708\) | 1092.41 | − | 1892.10i | 0.0579875 | − | 0.100437i | ||||
\(709\) | 2025.74 | + | 3508.69i | 0.107304 | + | 0.185856i | 0.914677 | − | 0.404185i | \(-0.132445\pi\) |
−0.807373 | + | 0.590041i | \(0.799112\pi\) | |||||||
\(710\) | 5216.29 | 0.275724 | ||||||||
\(711\) | 4286.20 | − | 7423.92i | 0.226083 | − | 0.391587i | ||||
\(712\) | −11551.9 | −0.608042 | ||||||||
\(713\) | −16052.5 | −0.843156 | ||||||||
\(714\) | −8277.32 | − | 14336.7i | −0.433853 | − | 0.751455i | ||||
\(715\) | −9938.45 | −0.519828 | ||||||||
\(716\) | −9522.29 | + | 16493.1i | −0.497018 | + | 0.860860i | ||||
\(717\) | 3501.32 | − | 6064.46i | 0.182370 | − | 0.315874i | ||||
\(718\) | 6350.12 | + | 10998.7i | 0.330062 | + | 0.571683i | ||||
\(719\) | 16197.3 | + | 28054.6i | 0.840136 | + | 1.45516i | 0.889779 | + | 0.456391i | \(0.150858\pi\) |
−0.0496436 | + | 0.998767i | \(0.515809\pi\) | |||||||
\(720\) | 173.384 | + | 300.309i | 0.00897448 | + | 0.0155442i | ||||
\(721\) | −30060.0 | − | 52065.4i | −1.55269 | − | 2.68935i | ||||
\(722\) | −10260.3 | −0.528877 | ||||||||
\(723\) | −7918.97 | −0.407344 | ||||||||
\(724\) | −1496.17 | − | 2591.44i | −0.0768022 | − | 0.133025i | ||||
\(725\) | 9403.36 | − | 16287.1i | 0.481699 | − | 0.834328i | ||||
\(726\) | −2068.32 | + | 3582.44i | −0.105734 | + | 0.183136i | ||||
\(727\) | 5688.01 | + | 9851.92i | 0.290174 | + | 0.502596i | 0.973851 | − | 0.227189i | \(-0.0729534\pi\) |
−0.683677 | + | 0.729785i | \(0.739620\pi\) | |||||||
\(728\) | −50940.8 | −2.59340 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −6498.38 | + | 11255.5i | −0.329474 | + | 0.570666i | ||||
\(731\) | 9448.45 | + | 16365.2i | 0.478062 | + | 0.828028i | ||||
\(732\) | −2025.34 | −0.102266 | ||||||||
\(733\) | 3226.28 | − | 5588.08i | 0.162572 | − | 0.281583i | −0.773218 | − | 0.634140i | \(-0.781354\pi\) |
0.935790 | + | 0.352557i | \(0.114688\pi\) | |||||||
\(734\) | 3388.38 | 0.170392 | ||||||||
\(735\) | −10692.1 | − | 18519.3i | −0.536577 | − | 0.929378i | ||||
\(736\) | 24791.1 | 1.24159 | ||||||||
\(737\) | −11899.3 | + | 2980.93i | −0.594732 | + | 0.148988i | ||||
\(738\) | 5699.47 | 0.284282 | ||||||||
\(739\) | 9385.89 | + | 16256.8i | 0.467206 | + | 0.809225i | 0.999298 | − | 0.0374617i | \(-0.0119272\pi\) |
−0.532092 | + | 0.846687i | \(0.678594\pi\) | |||||||
\(740\) | −4884.13 | −0.242627 | ||||||||
\(741\) | 2459.81 | − | 4260.51i | 0.121948 | − | 0.211220i | ||||
\(742\) | −24051.6 | −1.18997 | ||||||||
\(743\) | 7100.58 | + | 12298.6i | 0.350599 | + | 0.607255i | 0.986355 | − | 0.164635i | \(-0.0526447\pi\) |
−0.635756 | + | 0.771890i | \(0.719311\pi\) | |||||||
\(744\) | 3949.33 | − | 6840.43i | 0.194609 | − | 0.337073i | ||||
\(745\) | −7359.36 | −0.361914 | ||||||||
\(746\) | 3713.58 | 0.182257 | ||||||||
\(747\) | 2610.75 | + | 4521.95i | 0.127874 | + | 0.221485i | ||||
\(748\) | −5300.20 | + | 9180.21i | −0.259083 | + | 0.448746i | ||||
\(749\) | 6481.60 | − | 11226.5i | 0.316198 | − | 0.547671i | ||||
\(750\) | 3517.19 | + | 6091.95i | 0.171240 | + | 0.296596i | ||||
\(751\) | −19594.9 | −0.952100 | −0.476050 | − | 0.879418i | \(-0.657932\pi\) | ||||
−0.476050 | + | 0.879418i | \(0.657932\pi\) | |||||||
\(752\) | −1733.15 | −0.0840445 | ||||||||
\(753\) | 1141.07 | + | 1976.40i | 0.0552232 | + | 0.0956494i | ||||
\(754\) | 13067.5 | + | 22633.6i | 0.631156 | + | 1.09319i | ||||
\(755\) | −6109.38 | − | 10581.8i | −0.294494 | − | 0.510079i | ||||
\(756\) | 2604.69 | + | 4511.46i | 0.125306 | + | 0.217037i | ||||
\(757\) | −8658.56 | + | 14997.1i | −0.415721 | + | 0.720050i | −0.995504 | − | 0.0947212i | \(-0.969804\pi\) |
0.579783 | + | 0.814771i | \(0.303137\pi\) | |||||||
\(758\) | −1596.76 | + | 2765.67i | −0.0765130 | + | 0.132524i | ||||
\(759\) | 8994.82 | 0.430160 | ||||||||
\(760\) | 2019.15 | + | 3497.28i | 0.0963716 | + | 0.166921i | ||||
\(761\) | −2486.17 | −0.118428 | −0.0592139 | − | 0.998245i | \(-0.518859\pi\) | ||||
−0.0592139 | + | 0.998245i | \(0.518859\pi\) | |||||||
\(762\) | −7534.16 | −0.358181 | ||||||||
\(763\) | −32857.8 | + | 56911.3i | −1.55902 | + | 2.70030i | ||||
\(764\) | 7601.27 | 0.359953 | ||||||||
\(765\) | 2868.62 | + | 4968.60i | 0.135576 | + | 0.234824i | ||||
\(766\) | 10110.4 | − | 17511.8i | 0.476900 | − | 0.826014i | ||||
\(767\) | −4372.93 | − | 7574.14i | −0.205864 | − | 0.356566i | ||||
\(768\) | −5755.53 | + | 9968.87i | −0.270423 | + | 0.468386i | ||||
\(769\) | 19368.5 | − | 33547.2i | 0.908251 | − | 1.57314i | 0.0917586 | − | 0.995781i | \(-0.470751\pi\) |
0.816493 | − | 0.577356i | \(-0.195915\pi\) | |||||||
\(770\) | 4818.17 | − | 8345.32i | 0.225500 | − | 0.390577i | ||||
\(771\) | −6462.97 | + | 11194.2i | −0.301891 | + | 0.522891i | ||||
\(772\) | −9345.65 | + | 16187.1i | −0.435696 | + | 0.754647i | ||||
\(773\) | 16451.2 | − | 28494.4i | 0.765472 | − | 1.32584i | −0.174525 | − | 0.984653i | \(-0.555839\pi\) |
0.939997 | − | 0.341184i | \(-0.110828\pi\) | |||||||
\(774\) | 1562.11 | + | 2705.66i | 0.0725440 | + | 0.125650i | ||||
\(775\) | −4504.76 | + | 7802.48i | −0.208795 | + | 0.361643i | ||||
\(776\) | 16351.5 | + | 28321.6i | 0.756422 | + | 1.31016i | ||||
\(777\) | −14569.4 | −0.672682 | ||||||||
\(778\) | 10596.5 | − | 18353.6i | 0.488305 | − | 0.845769i | ||||
\(779\) | −9933.16 | −0.456858 | ||||||||
\(780\) | 6990.70 | 0.320907 | ||||||||
\(781\) | −4981.82 | − | 8628.77i | −0.228251 | − | 0.395342i | ||||
\(782\) | 20106.1 | 0.919429 | ||||||||
\(783\) | 3374.76 | − | 5845.25i | 0.154028 | − | 0.266785i | ||||
\(784\) | −2759.24 | + | 4779.14i | −0.125694 | + | 0.217709i | ||||
\(785\) | 2934.31 | + | 5082.37i | 0.133414 | + | 0.231080i | ||||
\(786\) | −4831.81 | − | 8368.94i | −0.219268 | − | 0.379784i | ||||
\(787\) | −3535.78 | − | 6124.16i | −0.160149 | − | 0.277386i | 0.774773 | − | 0.632239i | \(-0.217864\pi\) |
−0.934922 | + | 0.354854i | \(0.884531\pi\) | |||||||
\(788\) | −6048.46 | − | 10476.2i | −0.273436 | − | 0.473605i | ||||
\(789\) | −13057.0 | −0.589153 | ||||||||
\(790\) | 11154.0 | 0.502331 | ||||||||
\(791\) | −13939.8 | − | 24144.5i | −0.626603 | − | 1.08531i | ||||
\(792\) | −2212.96 | + | 3832.96i | −0.0992854 | + | 0.171967i | ||||
\(793\) | −4053.75 | + | 7021.30i | −0.181529 | + | 0.314418i | ||||
\(794\) | −6308.41 | − | 10926.5i | −0.281961 | − | 0.488371i | ||||
\(795\) | 8335.41 | 0.371857 | ||||||||
\(796\) | −11022.9 | −0.490824 | ||||||||
\(797\) | 7673.36 | − | 13290.6i | 0.341034 | − | 0.590689i | −0.643591 | − | 0.765370i | \(-0.722556\pi\) |
0.984625 | + | 0.174681i | \(0.0558895\pi\) | |||||||
\(798\) | 2385.03 | + | 4131.00i | 0.105801 | + | 0.183253i | ||||
\(799\) | −28674.9 | −1.26964 | ||||||||
\(800\) | 6957.06 | − | 12050.0i | 0.307462 | − | 0.532539i | ||||
\(801\) | 4728.93 | 0.208600 | ||||||||
\(802\) | −1400.73 | − | 2426.14i | −0.0616727 | − | 0.106820i | ||||
\(803\) | 24825.1 | 1.09098 | ||||||||
\(804\) | 8369.98 | − | 2096.79i | 0.367147 | − | 0.0919751i | ||||
\(805\) | 34788.3 | 1.52314 | ||||||||
\(806\) | −6260.12 | − | 10842.8i | −0.273577 | − | 0.473850i | ||||
\(807\) | −5322.71 | −0.232179 | ||||||||
\(808\) | −10661.2 | + | 18465.8i | −0.464183 | + | 0.803989i | ||||
\(809\) | 33307.2 | 1.44749 | 0.723744 | − | 0.690069i | \(-0.242420\pi\) | ||||
0.723744 | + | 0.690069i | \(0.242420\pi\) | |||||||
\(810\) | 474.270 | + | 821.460i | 0.0205730 | + | 0.0356335i | ||||
\(811\) | −19883.6 | + | 34439.4i | −0.860922 | + | 1.49116i | 0.0101183 | + | 0.999949i | \(0.496779\pi\) |
−0.871040 | + | 0.491212i | \(0.836554\pi\) | |||||||
\(812\) | 48231.6 | 2.08448 | ||||||||
\(813\) | 1894.72 | 0.0817351 | ||||||||
\(814\) | −2450.75 | − | 4244.82i | −0.105527 | − | 0.182778i | ||||
\(815\) | −3673.96 | + | 6363.48i | −0.157906 | + | 0.273501i | ||||
\(816\) | 740.286 | − | 1282.21i | 0.0317588 | − | 0.0550079i | ||||
\(817\) | −2722.48 | − | 4715.48i | −0.116582 | − | 0.201926i | ||||
\(818\) | −4290.32 | −0.183383 | ||||||||
\(819\) | 20853.3 | 0.889711 | ||||||||
\(820\) | −7057.44 | − | 12223.8i | −0.300557 | − | 0.520580i | ||||
\(821\) | −8239.24 | − | 14270.8i | −0.350245 | − | 0.606643i | 0.636047 | − | 0.771650i | \(-0.280568\pi\) |
−0.986292 | + | 0.165008i | \(0.947235\pi\) | |||||||
\(822\) | 1726.27 | + | 2989.99i | 0.0732491 | + | 0.126871i | ||||
\(823\) | −6870.52 | − | 11900.1i | −0.290998 | − | 0.504023i | 0.683048 | − | 0.730374i | \(-0.260654\pi\) |
−0.974046 | + | 0.226350i | \(0.927321\pi\) | |||||||
\(824\) | −17964.2 | + | 31114.9i | −0.759481 | + | 1.31546i | ||||
\(825\) | 2524.19 | − | 4372.03i | 0.106523 | − | 0.184502i | ||||
\(826\) | 8480.01 | 0.357212 | ||||||||
\(827\) | −524.614 | − | 908.658i | −0.0220588 | − | 0.0382069i | 0.854785 | − | 0.518982i | \(-0.173689\pi\) |
−0.876844 | + | 0.480775i | \(0.840355\pi\) | |||||||
\(828\) | −6326.95 | −0.265552 | ||||||||
\(829\) | −37990.4 | −1.59163 | −0.795815 | − | 0.605540i | \(-0.792957\pi\) | ||||
−0.795815 | + | 0.605540i | \(0.792957\pi\) | |||||||
\(830\) | −3396.98 | + | 5883.74i | −0.142061 | + | 0.246057i | ||||
\(831\) | −8992.05 | −0.375368 | ||||||||
\(832\) | 8292.05 | + | 14362.3i | 0.345523 | + | 0.598464i | ||||
\(833\) | −45651.5 | + | 79070.7i | −1.89883 | + | 3.28888i | ||||
\(834\) | −2099.80 | − | 3636.95i | −0.0871822 | − | 0.151004i | ||||
\(835\) | −4368.83 | + | 7567.04i | −0.181065 | + | 0.313615i | ||||
\(836\) | 1527.20 | − | 2645.19i | 0.0631811 | − | 0.109433i | ||||
\(837\) | −1616.71 | + | 2800.22i | −0.0667642 | + | 0.115639i | ||||
\(838\) | −9616.83 | + | 16656.8i | −0.396430 | + | 0.686636i | ||||
\(839\) | 19681.0 | − | 34088.6i | 0.809851 | − | 1.40270i | −0.103116 | − | 0.994669i | \(-0.532881\pi\) |
0.912967 | − | 0.408034i | \(-0.133785\pi\) | |||||||
\(840\) | −8558.81 | + | 14824.3i | −0.351556 | + | 0.608913i | ||||
\(841\) | −19051.0 | − | 32997.4i | −0.781132 | − | 1.35296i | ||||
\(842\) | 3430.71 | − | 5942.16i | 0.140416 | − | 0.243207i | ||||
\(843\) | −2265.51 | − | 3923.99i | −0.0925605 | − | 0.160319i | ||||
\(844\) | 6789.97 | 0.276920 | ||||||||
\(845\) | 6242.48 | − | 10812.3i | 0.254140 | − | 0.440183i | ||||
\(846\) | −4740.82 | −0.192663 | ||||||||
\(847\) | 30559.4 | 1.23971 | ||||||||
\(848\) | −1075.53 | − | 1862.88i | −0.0435541 | − | 0.0754380i | ||||
\(849\) | −22559.5 | −0.911943 | ||||||||
\(850\) | 5642.32 | − | 9772.79i | 0.227682 | − | 0.394358i | ||||
\(851\) | 8847.48 | − | 15324.3i | 0.356390 | − | 0.617285i | ||||
\(852\) | 3504.21 | + | 6069.48i | 0.140907 | + | 0.244057i | ||||
\(853\) | −9008.62 | − | 15603.4i | −0.361605 | − | 0.626319i | 0.626620 | − | 0.779325i | \(-0.284438\pi\) |
−0.988225 | + | 0.153006i | \(0.951105\pi\) | |||||||
\(854\) | −3930.52 | − | 6807.87i | −0.157494 | − | 0.272787i | ||||
\(855\) | −826.568 | − | 1431.66i | −0.0330620 | − | 0.0572651i | ||||
\(856\) | −7746.95 | −0.309329 | ||||||||
\(857\) | 14541.1 | 0.579597 | 0.289798 | − | 0.957088i | \(-0.406412\pi\) | ||||
0.289798 | + | 0.957088i | \(0.406412\pi\) | |||||||
\(858\) | 3507.78 | + | 6075.66i | 0.139573 | + | 0.241748i | ||||
\(859\) | 3116.05 | − | 5397.16i | 0.123770 | − | 0.214376i | −0.797482 | − | 0.603343i | \(-0.793835\pi\) |
0.921251 | + | 0.388968i | \(0.127168\pi\) | |||||||
\(860\) | 3868.61 | − | 6700.64i | 0.153394 | − | 0.265686i | ||||
\(861\) | −21052.4 | − | 36463.8i | −0.833291 | − | 1.44330i | ||||
\(862\) | −12075.8 | −0.477149 | ||||||||
\(863\) | −34289.5 | −1.35252 | −0.676262 | − | 0.736661i | \(-0.736401\pi\) | ||||
−0.676262 | + | 0.736661i | \(0.736401\pi\) | |||||||
\(864\) | 2496.81 | − | 4324.60i | 0.0983139 | − | 0.170285i | ||||
\(865\) | 10751.5 | + | 18622.1i | 0.422614 | + | 0.731990i | ||||
\(866\) | 3054.03 | 0.119839 | ||||||||
\(867\) | 4878.51 | − | 8449.83i | 0.191099 | − | 0.330993i | ||||
\(868\) | −23105.8 | −0.903527 | ||||||||
\(869\) | −10652.6 | − | 18450.9i | −0.415841 | − | 0.720258i | ||||
\(870\) | 8782.15 | 0.342233 | ||||||||
\(871\) | 9483.65 | − | 33213.2i | 0.368934 | − | 1.29206i | ||||
\(872\) | 39272.4 | 1.52515 | ||||||||
\(873\) | −6693.69 | − | 11593.8i | −0.259504 | − | 0.449474i | ||||
\(874\) | −5793.39 | −0.224216 | ||||||||
\(875\) | 25983.2 | − | 45004.2i | 1.00388 | − | 1.73877i | ||||
\(876\) | −17462.0 | −0.673500 | ||||||||
\(877\) | −5351.27 | − | 9268.66i | −0.206043 | − | 0.356876i | 0.744422 | − | 0.667710i | \(-0.232725\pi\) |
−0.950464 | + | 0.310833i | \(0.899392\pi\) | |||||||
\(878\) | −517.607 | + | 896.522i | −0.0198957 | + | 0.0344603i | ||||
\(879\) | −11231.2 | −0.430967 | ||||||||
\(880\) | 861.831 | 0.0330140 | ||||||||
\(881\) | 8039.73 | + | 13925.2i | 0.307452 | + | 0.532523i | 0.977804 | − | 0.209520i | \(-0.0671902\pi\) |
−0.670352 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(882\) | −7547.56 | + | 13072.8i | −0.288140 | + | 0.499073i | ||||
\(883\) | −19446.1 | + | 33681.6i | −0.741124 | + | 1.28366i | 0.210861 | + | 0.977516i | \(0.432373\pi\) |
−0.951984 | + | 0.306147i | \(0.900960\pi\) | |||||||
\(884\) | −14923.9 | − | 25849.0i | −0.567812 | − | 0.983479i | ||||
\(885\) | −2938.87 | −0.111626 | ||||||||
\(886\) | −18538.6 | −0.702953 | ||||||||
\(887\) | 20304.4 | + | 35168.2i | 0.768608 | + | 1.33127i | 0.938318 | + | 0.345773i | \(0.112383\pi\) |
−0.169710 | + | 0.985494i | \(0.554283\pi\) | |||||||
\(888\) | 4353.42 | + | 7540.34i | 0.164517 | + | 0.284952i | ||||
\(889\) | 27829.3 | + | 48201.7i | 1.04990 | + | 1.81848i | ||||
\(890\) | 3076.53 | + | 5328.70i | 0.115871 | + | 0.200695i | ||||
\(891\) | 905.904 | − | 1569.07i | 0.0340616 | − | 0.0589965i | ||||
\(892\) | 11014.5 | − | 19077.6i | 0.413443 | − | 0.716104i | ||||
\(893\) | 8262.40 | 0.309620 | ||||||||
\(894\) | 2597.49 | + | 4498.98i | 0.0971734 | + | 0.168309i | ||||
\(895\) | 25617.5 | 0.956760 | ||||||||
\(896\) | 38352.3 | 1.42998 | ||||||||
\(897\) | −12663.5 | + | 21933.8i | −0.471373 | + | 0.816442i | ||||
\(898\) | 17660.4 | 0.656274 | ||||||||
\(899\) | 14968.5 | + | 25926.1i | 0.555313 | + | 0.961830i | ||||
\(900\) | −1775.52 | + | 3075.28i | −0.0657598 | + | 0.113899i | ||||
\(901\) | −17794.6 | − | 30821.2i | −0.657964 | − | 1.13963i | ||||
\(902\) | 7082.54 | − | 12267.3i | 0.261444 | − | 0.452835i | ||||
\(903\) | 11540.1 | − | 19988.0i | 0.425283 | − | 0.736611i | ||||
\(904\) | −8330.60 | + | 14429.0i | −0.306495 | + | 0.530865i | ||||
\(905\) | −2012.55 | + | 3485.84i | −0.0739221 | + | 0.128037i | ||||
\(906\) | −4312.62 | + | 7469.68i | −0.158143 | + | 0.273911i | ||||
\(907\) | 17036.7 | − | 29508.4i | 0.623697 | − | 1.08028i | −0.365094 | − | 0.930971i | \(-0.618963\pi\) |
0.988791 | − | 0.149305i | \(-0.0477035\pi\) | |||||||
\(908\) | −11159.8 | − | 19329.3i | −0.407876 | − | 0.706461i | ||||
\(909\) | 4364.31 | − | 7559.20i | 0.159246 | − | 0.275823i | ||||
\(910\) | 13566.7 | + | 23498.1i | 0.494209 | + | 0.855996i | ||||
\(911\) | 48525.8 | 1.76480 | 0.882400 | − | 0.470501i | \(-0.155927\pi\) | ||||
0.882400 | + | 0.470501i | \(0.155927\pi\) | |||||||
\(912\) | −213.307 | + | 369.458i | −0.00774484 | + | 0.0134145i | ||||
\(913\) | 12977.1 | 0.470406 | ||||||||
\(914\) | −379.700 | −0.0137411 | ||||||||
\(915\) | 1362.18 | + | 2359.36i | 0.0492156 | + | 0.0852439i | ||||
\(916\) | −19689.9 | −0.710233 | ||||||||
\(917\) | −35694.9 | + | 61825.4i | −1.28544 | + | 2.22645i | ||||
\(918\) | 2024.97 | − | 3507.34i | 0.0728037 | − | 0.126100i | ||||
\(919\) | −6336.79 | − | 10975.6i | −0.227455 | − | 0.393964i | 0.729598 | − | 0.683876i | \(-0.239707\pi\) |
−0.957053 | + | 0.289912i | \(0.906374\pi\) | |||||||
\(920\) | −10394.9 | − | 18004.6i | −0.372512 | − | 0.645210i | ||||
\(921\) | −1698.48 | − | 2941.85i | −0.0607673 | − | 0.105252i | ||||
\(922\) | 10093.9 | + | 17483.2i | 0.360548 | + | 0.624487i | ||||
\(923\) | 28054.9 | 1.00048 | ||||||||
\(924\) | 12947.0 | 0.460959 | ||||||||
\(925\) | −4965.69 | − | 8600.82i | −0.176509 | − | 0.305722i | ||||
\(926\) | −10458.9 | + | 18115.3i | −0.371166 | + | 0.642878i | ||||
\(927\) | 7353.88 | − | 12737.3i | 0.260554 | − | 0.451292i | ||||
\(928\) | −23117.0 | − | 40039.8i | −0.817728 | − | 1.41635i | ||||
\(929\) | 14183.8 | 0.500920 | 0.250460 | − | 0.968127i | \(-0.419418\pi\) | ||||
0.250460 | + | 0.968127i | \(0.419418\pi\) | |||||||
\(930\) | −4207.17 | −0.148342 | ||||||||
\(931\) | 13154.0 | − | 22783.5i | 0.463058 | − | 0.802039i | ||||
\(932\) | −9115.05 | − | 15787.7i | −0.320358 | − | 0.554876i | ||||
\(933\) | 12685.9 | 0.445143 | ||||||||
\(934\) | 5755.90 | − | 9969.51i | 0.201648 | − | 0.349264i | ||||
\(935\) | 14259.0 | 0.498736 | ||||||||
\(936\) | −6231.09 | − | 10792.6i | −0.217596 | − | 0.376887i | ||||
\(937\) | −34760.5 | −1.21193 | −0.605963 | − | 0.795493i | \(-0.707212\pi\) | ||||
−0.605963 | + | 0.795493i | \(0.707212\pi\) | |||||||
\(938\) | 23291.4 | + | 24065.2i | 0.810758 | + | 0.837693i | ||||
\(939\) | 22583.9 | 0.784875 | ||||||||
\(940\) | 5870.38 | + | 10167.8i | 0.203692 | + | 0.352805i | ||||
\(941\) | −50154.2 | −1.73749 | −0.868747 | − | 0.495257i | \(-0.835074\pi\) | ||||
−0.868747 | + | 0.495257i | \(0.835074\pi\) | |||||||
\(942\) | 2071.33 | − | 3587.65i | 0.0716429 | − | 0.124089i | ||||
\(943\) | 51137.5 | 1.76593 | ||||||||
\(944\) | 379.207 | + | 656.806i | 0.0130743 | + | 0.0226453i | ||||
\(945\) | 3503.66 | − | 6068.52i | 0.120608 | − | 0.208899i | ||||
\(946\) | 7764.74 | 0.266864 | ||||||||
\(947\) | −30040.0 | −1.03080 | −0.515400 | − | 0.856950i | \(-0.672357\pi\) | ||||
−0.515400 | + | 0.856950i | \(0.672357\pi\) | |||||||
\(948\) | 7493.06 | + | 12978.4i | 0.256712 | + | 0.444639i | ||||
\(949\) | −34950.4 | + | 60535.9i | −1.19551 | + | 2.07068i | ||||
\(950\) | −1625.78 | + | 2815.94i | −0.0555236 | + | 0.0961696i | ||||
\(951\) | −2049.17 | − | 3549.26i | −0.0698725 | − | 0.121023i | ||||
\(952\) | 73086.2 | 2.48817 | ||||||||
\(953\) | −18412.1 | −0.625842 | −0.312921 | − | 0.949779i | \(-0.601307\pi\) | ||||
−0.312921 | + | 0.949779i | \(0.601307\pi\) | |||||||
\(954\) | −2941.99 | − | 5095.68i | −0.0998432 | − | 0.172934i | ||||
\(955\) | −5112.37 | − | 8854.89i | −0.173228 | − | 0.300039i | ||||
\(956\) | 6120.94 | + | 10601.8i | 0.207077 | + | 0.358668i | ||||
\(957\) | −8387.40 | − | 14527.4i | −0.283308 | − | 0.490704i | ||||
\(958\) | −9048.59 | + | 15672.6i | −0.305164 | + | 0.528559i | ||||
\(959\) | 12752.8 | − | 22088.5i | 0.429416 | − | 0.743771i | ||||
\(960\) | 5572.75 | 0.187354 | ||||||||
\(961\) | 7724.73 | + | 13379.6i | 0.259297 | + | 0.449116i | ||||
\(962\) | 13801.3 | 0.462548 | ||||||||
\(963\) | 3171.32 | 0.106121 | ||||||||
\(964\) | 6921.90 | − | 11989.1i | 0.231265 | − | 0.400562i | ||||
\(965\) | 25142.3 | 0.838715 | ||||||||
\(966\) | −12278.5 | − | 21267.1i | −0.408960 | − | 0.708340i | ||||
\(967\) | −20195.3 | + | 34979.2i | −0.671598 | + | 1.16324i | 0.305852 | + | 0.952079i | \(0.401059\pi\) |
−0.977451 | + | 0.211164i | \(0.932275\pi\) | |||||||
\(968\) | −9131.33 | − | 15815.9i | −0.303194 | − | 0.525148i | ||||
\(969\) | −3529.15 | + | 6112.67i | −0.117000 | + | 0.202649i | ||||
\(970\) | 8709.51 | − | 15085.3i | 0.288294 | − | 0.499340i | ||||
\(971\) | −716.267 | + | 1240.61i | −0.0236726 | + | 0.0410022i | −0.877619 | − | 0.479359i | \(-0.840869\pi\) |
0.853946 | + | 0.520361i | \(0.174203\pi\) | |||||||
\(972\) | −637.212 | + | 1103.68i | −0.0210274 | + | 0.0364205i | ||||
\(973\) | −15512.2 | + | 26867.9i | −0.511098 | + | 0.885248i | ||||
\(974\) | 9826.47 | − | 17019.9i | 0.323265 | − | 0.559912i | ||||
\(975\) | 7107.44 | + | 12310.4i | 0.233457 | + | 0.404359i | ||||
\(976\) | 351.528 | − | 608.865i | 0.0115288 | − | 0.0199685i | ||||
\(977\) | 12803.7 | + | 22176.7i | 0.419270 | + | 0.726198i | 0.995866 | − | 0.0908319i | \(-0.0289526\pi\) |
−0.576596 | + | 0.817029i | \(0.695619\pi\) | |||||||
\(978\) | 5186.90 | 0.169590 | ||||||||
\(979\) | 5876.48 | − | 10178.4i | 0.191842 | − | 0.332279i | ||||
\(980\) | 37383.4 | 1.21854 | ||||||||
\(981\) | −16076.7 | −0.523230 | ||||||||
\(982\) | 2969.81 | + | 5143.86i | 0.0965076 | + | 0.167156i | ||||
\(983\) | −28147.9 | −0.913304 | −0.456652 | − | 0.889645i | \(-0.650952\pi\) | ||||
−0.456652 | + | 0.889645i | \(0.650952\pi\) | |||||||
\(984\) | −12581.2 | + | 21791.2i | −0.407594 | + | 0.705973i | ||||
\(985\) | −8136.00 | + | 14092.0i | −0.263182 | + | 0.455845i | ||||
\(986\) | −18748.3 | − | 32473.1i | −0.605546 | − | 1.04884i | ||||
\(987\) | 17511.4 | + | 30330.6i | 0.564735 | + | 0.978150i | ||||
\(988\) | 4300.19 | + | 7448.15i | 0.138469 | + | 0.239835i | ||||
\(989\) | 14015.8 | + | 24276.1i | 0.450633 | + | 0.780520i | ||||
\(990\) | 2357.44 | 0.0756811 | ||||||||
\(991\) | −31949.4 | −1.02412 | −0.512062 | − | 0.858948i | \(-0.671118\pi\) | ||||
−0.512062 | + | 0.858948i | \(0.671118\pi\) | |||||||
\(992\) | 11074.4 | + | 19181.4i | 0.354448 | + | 0.613922i | ||||
\(993\) | 496.815 | − | 860.509i | 0.0158771 | − | 0.0274999i | ||||
\(994\) | −13601.1 | + | 23557.7i | −0.434003 | + | 0.751716i | ||||
\(995\) | 7413.64 | + | 12840.8i | 0.236209 | + | 0.409126i | ||||
\(996\) | −9128.12 | −0.290397 | ||||||||
\(997\) | 4309.33 | 0.136889 | 0.0684443 | − | 0.997655i | \(-0.478196\pi\) | ||||
0.0684443 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(998\) | 15641.8 | − | 27092.4i | 0.496124 | − | 0.859312i | ||||
\(999\) | −1782.13 | − | 3086.74i | −0.0564405 | − | 0.0977578i |
(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 | 201.4.e.b.37.7 | ✓ | 36 | |
67.29 | even | 3 | inner | 201.4.e.b.163.7 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.e.b.37.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
201.4.e.b.163.7 | yes | 36 | 67.29 | even | 3 | inner |