Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(25,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.n (of order \(10\), degree \(4\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 25.12 | ||
Character | \(\chi\) | \(=\) | 143.25 |
Dual form | 143.4.n.a.103.12 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38497 | − | 1.90624i | −0.489660 | − | 0.673959i | 0.490665 | − | 0.871348i | \(-0.336754\pi\) |
−0.980325 | + | 0.197389i | \(0.936754\pi\) | |||||||
\(3\) | −0.928232 | − | 2.85681i | −0.178638 | − | 0.549793i | 0.821143 | − | 0.570723i | \(-0.193337\pi\) |
−0.999781 | + | 0.0209307i | \(0.993337\pi\) | |||||||
\(4\) | 0.756503 | − | 2.32828i | 0.0945629 | − | 0.291035i | ||||
\(5\) | 7.86101 | − | 10.8197i | 0.703110 | − | 0.967747i | −0.296808 | − | 0.954937i | \(-0.595922\pi\) |
0.999918 | − | 0.0128103i | \(-0.00407777\pi\) | |||||||
\(6\) | −4.16020 | + | 5.72602i | −0.283066 | + | 0.389606i | ||||
\(7\) | −12.3082 | − | 3.99917i | −0.664579 | − | 0.215935i | −0.0427473 | − | 0.999086i | \(-0.513611\pi\) |
−0.621831 | + | 0.783151i | \(0.713611\pi\) | |||||||
\(8\) | −23.4134 | + | 7.60747i | −1.03474 | + | 0.336206i | ||||
\(9\) | 14.5437 | − | 10.5666i | 0.538657 | − | 0.391357i | ||||
\(10\) | −31.5123 | −0.996507 | ||||||||
\(11\) | 5.26848 | − | 36.1005i | 0.144410 | − | 0.989518i | ||||
\(12\) | −7.35365 | −0.176901 | ||||||||
\(13\) | 45.2544 | − | 12.2082i | 0.965486 | − | 0.260457i | ||||
\(14\) | 9.42303 | + | 29.0011i | 0.179886 | + | 0.553634i | ||||
\(15\) | −38.2068 | − | 12.4141i | −0.657663 | − | 0.213688i | ||||
\(16\) | 31.0841 | + | 22.5839i | 0.485689 | + | 0.352874i | ||||
\(17\) | 84.5701 | + | 61.4438i | 1.20654 | + | 0.876606i | 0.994912 | − | 0.100743i | \(-0.0321220\pi\) |
0.211632 | + | 0.977349i | \(0.432122\pi\) | |||||||
\(18\) | −40.2852 | − | 13.0895i | −0.527518 | − | 0.171401i | ||||
\(19\) | −126.227 | + | 41.0136i | −1.52413 | + | 0.495219i | −0.946945 | − | 0.321397i | \(-0.895848\pi\) |
−0.577182 | + | 0.816616i | \(0.695848\pi\) | |||||||
\(20\) | −19.2445 | − | 26.4878i | −0.215160 | − | 0.296142i | ||||
\(21\) | 38.8742i | 0.403955i | ||||||||
\(22\) | −76.1130 | + | 39.9550i | −0.737606 | + | 0.387201i | ||||
\(23\) | −96.3465 | −0.873462 | −0.436731 | − | 0.899592i | \(-0.643864\pi\) | ||||
−0.436731 | + | 0.899592i | \(0.643864\pi\) | |||||||
\(24\) | 43.4662 | + | 59.8260i | 0.369687 | + | 0.508831i | ||||
\(25\) | −16.6444 | − | 51.2261i | −0.133155 | − | 0.409809i | ||||
\(26\) | −85.9476 | − | 69.3580i | −0.648297 | − | 0.523163i | ||||
\(27\) | −109.301 | − | 79.4116i | −0.779071 | − | 0.566029i | ||||
\(28\) | −18.6223 | + | 25.6314i | −0.125689 | + | 0.172996i | ||||
\(29\) | −26.8636 | + | 82.6777i | −0.172015 | + | 0.529409i | −0.999485 | − | 0.0321021i | \(-0.989780\pi\) |
0.827469 | + | 0.561511i | \(0.189780\pi\) | |||||||
\(30\) | 29.2508 | + | 90.0246i | 0.178014 | + | 0.547872i | ||||
\(31\) | −19.2997 | − | 26.5637i | −0.111817 | − | 0.153903i | 0.749440 | − | 0.662072i | \(-0.230323\pi\) |
−0.861257 | + | 0.508169i | \(0.830323\pi\) | |||||||
\(32\) | 106.415i | 0.587863i | ||||||||
\(33\) | −108.022 | + | 18.4586i | −0.569827 | + | 0.0973706i | ||||
\(34\) | − | 246.309i | − | 1.24240i | ||||||
\(35\) | −140.025 | + | 101.734i | −0.676242 | + | 0.491318i | ||||
\(36\) | −13.5997 | − | 41.8555i | −0.0629615 | − | 0.193776i | ||||
\(37\) | 165.962 | + | 53.9243i | 0.737405 | + | 0.239597i | 0.653553 | − | 0.756881i | \(-0.273278\pi\) |
0.0838518 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(38\) | 253.002 | + | 183.817i | 1.08006 | + | 0.784710i | ||||
\(39\) | −76.8830 | − | 117.951i | −0.315670 | − | 0.484289i | ||||
\(40\) | −101.742 | + | 313.129i | −0.402170 | + | 1.23775i | ||||
\(41\) | 85.4150 | − | 27.7530i | 0.325355 | − | 0.105714i | −0.141785 | − | 0.989897i | \(-0.545284\pi\) |
0.467141 | + | 0.884183i | \(0.345284\pi\) | |||||||
\(42\) | 74.1037 | − | 53.8395i | 0.272249 | − | 0.197800i | ||||
\(43\) | 243.311 | 0.862897 | 0.431448 | − | 0.902138i | \(-0.358003\pi\) | ||||
0.431448 | + | 0.902138i | \(0.358003\pi\) | |||||||
\(44\) | −80.0662 | − | 39.5766i | −0.274328 | − | 0.135600i | ||||
\(45\) | − | 240.424i | − | 0.796451i | ||||||
\(46\) | 133.437 | + | 183.660i | 0.427700 | + | 0.588678i | ||||
\(47\) | 284.931 | − | 92.5796i | 0.884285 | − | 0.287322i | 0.168550 | − | 0.985693i | \(-0.446092\pi\) |
0.715736 | + | 0.698371i | \(0.246092\pi\) | |||||||
\(48\) | 35.6646 | − | 109.764i | 0.107245 | − | 0.330065i | ||||
\(49\) | −141.995 | − | 103.166i | −0.413980 | − | 0.300774i | ||||
\(50\) | −74.5975 | + | 102.675i | −0.210994 | + | 0.290408i | ||||
\(51\) | 97.0322 | − | 298.634i | 0.266416 | − | 0.819945i | ||||
\(52\) | 5.81110 | − | 114.600i | 0.0154972 | − | 0.305619i | ||||
\(53\) | 15.4371 | − | 11.2157i | 0.0400086 | − | 0.0290679i | −0.567601 | − | 0.823304i | \(-0.692128\pi\) |
0.607610 | + | 0.794236i | \(0.292128\pi\) | |||||||
\(54\) | 318.336i | 0.802224i | ||||||||
\(55\) | −349.182 | − | 340.789i | −0.856068 | − | 0.835492i | ||||
\(56\) | 318.600 | 0.760262 | ||||||||
\(57\) | 234.336 | + | 322.535i | 0.544535 | + | 0.749488i | ||||
\(58\) | 194.809 | − | 63.2973i | 0.441029 | − | 0.143299i | ||||
\(59\) | 237.585 | + | 77.1959i | 0.524252 | + | 0.170340i | 0.559174 | − | 0.829050i | \(-0.311118\pi\) |
−0.0349220 | + | 0.999390i | \(0.511118\pi\) | |||||||
\(60\) | −57.8070 | + | 79.5646i | −0.124381 | + | 0.171196i | ||||
\(61\) | −468.587 | − | 340.448i | −0.983548 | − | 0.714589i | −0.0250492 | − | 0.999686i | \(-0.507974\pi\) |
−0.958499 | + | 0.285097i | \(0.907974\pi\) | |||||||
\(62\) | −23.9075 | + | 73.5799i | −0.0489720 | + | 0.150720i | ||||
\(63\) | −221.264 | + | 71.8932i | −0.442487 | + | 0.143773i | ||||
\(64\) | 451.525 | − | 328.052i | 0.881885 | − | 0.640727i | ||||
\(65\) | 223.656 | − | 585.610i | 0.426786 | − | 1.11748i | ||||
\(66\) | 184.794 | + | 180.353i | 0.344645 | + | 0.336361i | ||||
\(67\) | − | 671.282i | − | 1.22403i | −0.790845 | − | 0.612016i | \(-0.790359\pi\) | ||
0.790845 | − | 0.612016i | \(-0.209641\pi\) | |||||||
\(68\) | 207.036 | − | 150.420i | 0.369217 | − | 0.268252i | ||||
\(69\) | 89.4320 | + | 275.243i | 0.156034 | + | 0.480223i | ||||
\(70\) | 387.859 | + | 126.023i | 0.662257 | + | 0.215180i | ||||
\(71\) | −232.650 | + | 320.215i | −0.388879 | + | 0.535246i | −0.957910 | − | 0.287070i | \(-0.907319\pi\) |
0.569030 | + | 0.822317i | \(0.307319\pi\) | |||||||
\(72\) | −260.133 | + | 358.042i | −0.425791 | + | 0.586051i | ||||
\(73\) | 267.819 | + | 87.0198i | 0.429396 | + | 0.139519i | 0.515738 | − | 0.856746i | \(-0.327518\pi\) |
−0.0863423 | + | 0.996266i | \(0.527518\pi\) | |||||||
\(74\) | −127.059 | − | 391.047i | −0.199599 | − | 0.614302i | ||||
\(75\) | −130.893 | + | 95.0994i | −0.201523 | + | 0.146415i | ||||
\(76\) | 324.918i | 0.490403i | ||||||||
\(77\) | −209.217 | + | 423.261i | −0.309643 | + | 0.626429i | ||||
\(78\) | −118.363 | + | 309.916i | −0.171820 | + | 0.449886i | ||||
\(79\) | 982.682 | − | 713.960i | 1.39950 | − | 1.01680i | 0.404752 | − | 0.914427i | \(-0.367358\pi\) |
0.994747 | − | 0.102369i | \(-0.0326421\pi\) | |||||||
\(80\) | 488.705 | − | 158.790i | 0.682986 | − | 0.221915i | ||||
\(81\) | 24.5836 | − | 75.6607i | 0.0337224 | − | 0.103787i | ||||
\(82\) | −171.201 | − | 124.385i | −0.230561 | − | 0.167512i | ||||
\(83\) | 110.645 | − | 152.289i | 0.146323 | − | 0.201397i | −0.729564 | − | 0.683913i | \(-0.760277\pi\) |
0.875887 | + | 0.482516i | \(0.160277\pi\) | |||||||
\(84\) | 90.5099 | + | 29.4084i | 0.117565 | + | 0.0381991i | ||||
\(85\) | 1329.61 | − | 432.017i | 1.69667 | − | 0.551280i | ||||
\(86\) | −336.978 | − | 463.810i | −0.422526 | − | 0.581557i | ||||
\(87\) | 261.130 | 0.321794 | ||||||||
\(88\) | 151.280 | + | 885.314i | 0.183256 | + | 1.07244i | ||||
\(89\) | 64.9589i | 0.0773666i | 0.999252 | + | 0.0386833i | \(0.0123163\pi\) | ||||
−0.999252 | + | 0.0386833i | \(0.987684\pi\) | |||||||
\(90\) | −458.307 | + | 332.979i | −0.536775 | + | 0.389990i | ||||
\(91\) | −605.821 | − | 30.7197i | −0.697883 | − | 0.0353879i | ||||
\(92\) | −72.8864 | + | 224.321i | −0.0825971 | + | 0.254208i | ||||
\(93\) | −57.9729 | + | 79.7928i | −0.0646398 | + | 0.0889691i | ||||
\(94\) | −571.099 | − | 414.928i | −0.626642 | − | 0.455282i | ||||
\(95\) | −548.513 | + | 1688.15i | −0.592381 | + | 1.82316i | ||||
\(96\) | 304.006 | − | 98.7774i | 0.323202 | − | 0.105015i | ||||
\(97\) | −27.8646 | − | 38.3524i | −0.0291673 | − | 0.0401453i | 0.794184 | − | 0.607677i | \(-0.207898\pi\) |
−0.823352 | + | 0.567532i | \(0.807898\pi\) | |||||||
\(98\) | 413.558i | 0.426283i | ||||||||
\(99\) | −304.837 | − | 580.706i | −0.309468 | − | 0.589526i | ||||
\(100\) | −131.860 | −0.131860 | ||||||||
\(101\) | −1036.54 | + | 753.093i | −1.02119 | + | 0.741937i | −0.966526 | − | 0.256568i | \(-0.917408\pi\) |
−0.0546620 | + | 0.998505i | \(0.517408\pi\) | |||||||
\(102\) | −703.657 | + | 228.632i | −0.683063 | + | 0.221941i | ||||
\(103\) | 237.201 | − | 730.029i | 0.226914 | − | 0.698368i | −0.771178 | − | 0.636619i | \(-0.780332\pi\) |
0.998092 | − | 0.0617487i | \(-0.0196677\pi\) | |||||||
\(104\) | −966.686 | + | 630.106i | −0.911455 | + | 0.594106i | ||||
\(105\) | 420.609 | + | 305.590i | 0.390926 | + | 0.284024i | ||||
\(106\) | −42.7599 | − | 13.8935i | −0.0391812 | − | 0.0127307i | ||||
\(107\) | −379.386 | − | 1167.63i | −0.342772 | − | 1.05494i | −0.962766 | − | 0.270337i | \(-0.912865\pi\) |
0.619993 | − | 0.784607i | \(-0.287135\pi\) | |||||||
\(108\) | −267.579 | + | 194.407i | −0.238405 | + | 0.173211i | ||||
\(109\) | − | 1798.21i | − | 1.58016i | −0.613002 | − | 0.790081i | \(-0.710038\pi\) | ||
0.613002 | − | 0.790081i | \(-0.289962\pi\) | |||||||
\(110\) | −166.022 | + | 1137.61i | −0.143905 | + | 0.986062i | ||||
\(111\) | − | 524.175i | − | 0.448221i | ||||||
\(112\) | −292.272 | − | 402.277i | −0.246581 | − | 0.339390i | ||||
\(113\) | 548.979 | + | 1689.58i | 0.457023 | + | 1.40657i | 0.868744 | + | 0.495262i | \(0.164928\pi\) |
−0.411721 | + | 0.911310i | \(0.635072\pi\) | |||||||
\(114\) | 290.284 | − | 893.402i | 0.238487 | − | 0.733989i | ||||
\(115\) | −757.380 | + | 1042.44i | −0.614140 | + | 0.845291i | ||||
\(116\) | 172.174 | + | 125.092i | 0.137810 | + | 0.100125i | ||||
\(117\) | 529.169 | − | 655.739i | 0.418134 | − | 0.518146i | ||||
\(118\) | −181.893 | − | 559.808i | −0.141903 | − | 0.436733i | ||||
\(119\) | −795.179 | − | 1094.47i | −0.612554 | − | 0.843109i | ||||
\(120\) | 988.990 | 0.752350 | ||||||||
\(121\) | −1275.49 | − | 380.389i | −0.958292 | − | 0.285792i | ||||
\(122\) | 1364.75i | 1.01278i | ||||||||
\(123\) | −158.570 | − | 218.253i | −0.116242 | − | 0.159993i | ||||
\(124\) | −76.4480 | + | 24.8395i | −0.0553648 | + | 0.0179891i | ||||
\(125\) | 904.827 | + | 293.996i | 0.647442 | + | 0.210367i | ||||
\(126\) | 443.490 | + | 322.214i | 0.313565 | + | 0.227819i | ||||
\(127\) | 1205.85 | + | 876.104i | 0.842537 | + | 0.612139i | 0.923078 | − | 0.384612i | \(-0.125665\pi\) |
−0.0805412 | + | 0.996751i | \(0.525665\pi\) | |||||||
\(128\) | −441.045 | − | 143.304i | −0.304557 | − | 0.0989565i | ||||
\(129\) | −225.849 | − | 695.092i | −0.154146 | − | 0.474414i | ||||
\(130\) | −1426.07 | + | 384.708i | −0.962113 | + | 0.259547i | ||||
\(131\) | −893.062 | −0.595628 | −0.297814 | − | 0.954624i | \(-0.596257\pi\) | ||||
−0.297814 | + | 0.954624i | \(0.596257\pi\) | |||||||
\(132\) | −38.7425 | + | 265.470i | −0.0255462 | + | 0.175047i | ||||
\(133\) | 1717.64 | 1.11984 | ||||||||
\(134\) | −1279.63 | + | 929.704i | −0.824948 | + | 0.599360i | ||||
\(135\) | −1718.43 | + | 558.351i | −1.09555 | + | 0.355964i | ||||
\(136\) | −2447.51 | − | 795.243i | −1.54318 | − | 0.501408i | ||||
\(137\) | −18.2290 | + | 25.0901i | −0.0113680 | + | 0.0156466i | −0.814663 | − | 0.579934i | \(-0.803078\pi\) |
0.803295 | + | 0.595581i | \(0.203078\pi\) | |||||||
\(138\) | 400.821 | − | 551.682i | 0.247247 | − | 0.340307i | ||||
\(139\) | −772.027 | + | 2376.05i | −0.471097 | + | 1.44989i | 0.380053 | + | 0.924965i | \(0.375906\pi\) |
−0.851150 | + | 0.524923i | \(0.824094\pi\) | |||||||
\(140\) | 130.935 | + | 402.978i | 0.0790433 | + | 0.243270i | ||||
\(141\) | −528.964 | − | 728.056i | −0.315935 | − | 0.434847i | ||||
\(142\) | 932.620 | 0.551153 | ||||||||
\(143\) | −202.299 | − | 1698.02i | −0.118301 | − | 0.992978i | ||||
\(144\) | 690.715 | 0.399719 | ||||||||
\(145\) | 683.377 | + | 940.587i | 0.391389 | + | 0.538700i | ||||
\(146\) | −205.040 | − | 631.049i | −0.116228 | − | 0.357712i | ||||
\(147\) | −162.919 | + | 501.414i | −0.0914106 | + | 0.281333i | ||||
\(148\) | 251.101 | − | 345.611i | 0.139462 | − | 0.191953i | ||||
\(149\) | −1487.19 | + | 2046.94i | −0.817687 | + | 1.12545i | 0.172404 | + | 0.985026i | \(0.444846\pi\) |
−0.990091 | + | 0.140424i | \(0.955154\pi\) | |||||||
\(150\) | 362.566 | + | 117.805i | 0.197356 | + | 0.0641248i | ||||
\(151\) | 2502.89 | − | 813.238i | 1.34889 | − | 0.438281i | 0.456571 | − | 0.889687i | \(-0.349078\pi\) |
0.892318 | + | 0.451407i | \(0.149078\pi\) | |||||||
\(152\) | 2643.39 | − | 1920.53i | 1.41057 | − | 1.02484i | ||||
\(153\) | 1879.22 | 0.992980 | ||||||||
\(154\) | 1096.60 | − | 187.384i | 0.573808 | − | 0.0980509i | ||||
\(155\) | −439.128 | −0.227559 | ||||||||
\(156\) | −332.785 | + | 89.7745i | −0.170796 | + | 0.0460751i | ||||
\(157\) | −744.911 | − | 2292.60i | −0.378665 | − | 1.16541i | −0.940973 | − | 0.338483i | \(-0.890086\pi\) |
0.562308 | − | 0.826928i | \(-0.309914\pi\) | |||||||
\(158\) | −2721.97 | − | 884.421i | −1.37056 | − | 0.445321i | ||||
\(159\) | −46.3704 | − | 33.6901i | −0.0231284 | − | 0.0168038i | ||||
\(160\) | 1151.38 | + | 836.525i | 0.568903 | + | 0.413332i | ||||
\(161\) | 1185.85 | + | 385.306i | 0.580484 | + | 0.188611i | ||||
\(162\) | −178.275 | + | 57.9252i | −0.0864607 | + | 0.0280928i | ||||
\(163\) | −431.516 | − | 593.930i | −0.207355 | − | 0.285400i | 0.692655 | − | 0.721269i | \(-0.256441\pi\) |
−0.900010 | + | 0.435869i | \(0.856441\pi\) | |||||||
\(164\) | − | 219.865i | − | 0.104686i | ||||||
\(165\) | −649.447 | + | 1313.88i | −0.306420 | + | 0.619911i | ||||
\(166\) | −443.540 | −0.207382 | ||||||||
\(167\) | 1199.03 | + | 1650.32i | 0.555591 | + | 0.764705i | 0.990758 | − | 0.135645i | \(-0.0433106\pi\) |
−0.435167 | + | 0.900350i | \(0.643311\pi\) | |||||||
\(168\) | −295.734 | − | 910.177i | −0.135812 | − | 0.417986i | ||||
\(169\) | 1898.92 | − | 1104.95i | 0.864325 | − | 0.502934i | ||||
\(170\) | −2665.00 | − | 1936.24i | −1.20233 | − | 0.873544i | ||||
\(171\) | −1402.43 | + | 1930.28i | −0.627174 | + | 0.863231i | ||||
\(172\) | 184.065 | − | 566.495i | 0.0815980 | − | 0.251133i | ||||
\(173\) | −487.393 | − | 1500.04i | −0.214195 | − | 0.659226i | −0.999210 | − | 0.0397480i | \(-0.987344\pi\) |
0.785014 | − | 0.619478i | \(-0.212656\pi\) | |||||||
\(174\) | −361.656 | − | 497.777i | −0.157570 | − | 0.216876i | ||||
\(175\) | 697.063i | 0.301103i | ||||||||
\(176\) | 979.056 | − | 1003.17i | 0.419313 | − | 0.429640i | ||||
\(177\) | − | 750.389i | − | 0.318659i | ||||||
\(178\) | 123.827 | − | 89.9659i | 0.0521419 | − | 0.0378833i | ||||
\(179\) | 1020.07 | + | 3139.47i | 0.425944 | + | 1.31092i | 0.902088 | + | 0.431553i | \(0.142034\pi\) |
−0.476144 | + | 0.879368i | \(0.657966\pi\) | |||||||
\(180\) | −559.773 | − | 181.881i | −0.231795 | − | 0.0753147i | ||||
\(181\) | −3858.79 | − | 2803.57i | −1.58465 | − | 1.15131i | −0.911111 | − | 0.412161i | \(-0.864774\pi\) |
−0.673537 | − | 0.739153i | \(-0.735226\pi\) | |||||||
\(182\) | 780.484 | + | 1197.39i | 0.317875 | + | 0.487673i | ||||
\(183\) | −537.637 | + | 1654.68i | −0.217176 | + | 0.668400i | ||||
\(184\) | 2255.80 | − | 732.954i | 0.903803 | − | 0.293663i | ||||
\(185\) | 1888.07 | − | 1371.77i | 0.750346 | − | 0.545158i | ||||
\(186\) | 232.395 | 0.0916131 | ||||||||
\(187\) | 2663.70 | − | 2729.30i | 1.04165 | − | 1.06731i | ||||
\(188\) | − | 733.434i | − | 0.284528i | ||||||
\(189\) | 1027.71 | + | 1414.52i | 0.395529 | + | 0.544399i | ||||
\(190\) | 3977.70 | − | 1292.43i | 1.51880 | − | 0.493489i | ||||
\(191\) | 0.289707 | − | 0.891627i | 0.000109751 | − | 0.000337779i | −0.951002 | − | 0.309186i | \(-0.899943\pi\) |
0.951111 | + | 0.308848i | \(0.0999435\pi\) | |||||||
\(192\) | −1356.30 | − | 985.411i | −0.509805 | − | 0.370395i | ||||
\(193\) | −216.630 | + | 298.166i | −0.0807947 | + | 0.111204i | −0.847501 | − | 0.530793i | \(-0.821894\pi\) |
0.766707 | + | 0.641998i | \(0.221894\pi\) | |||||||
\(194\) | −34.5174 | + | 106.234i | −0.0127743 | + | 0.0393151i | ||||
\(195\) | −1880.58 | − | 95.3595i | −0.690620 | − | 0.0350197i | ||||
\(196\) | −347.618 | + | 252.559i | −0.126683 | + | 0.0920405i | ||||
\(197\) | 1403.57i | 0.507614i | 0.967255 | + | 0.253807i | \(0.0816828\pi\) | ||||
−0.967255 | + | 0.253807i | \(0.918317\pi\) | |||||||
\(198\) | −684.777 | + | 1385.35i | −0.245783 | + | 0.497236i | ||||
\(199\) | 2135.37 | 0.760664 | 0.380332 | − | 0.924850i | \(-0.375810\pi\) | ||||
0.380332 | + | 0.924850i | \(0.375810\pi\) | |||||||
\(200\) | 779.402 | + | 1072.76i | 0.275560 | + | 0.379276i | ||||
\(201\) | −1917.72 | + | 623.106i | −0.672964 | + | 0.218659i | ||||
\(202\) | 2871.16 | + | 932.897i | 1.00007 | + | 0.324942i | ||||
\(203\) | 661.284 | − | 910.179i | 0.228636 | − | 0.314690i | ||||
\(204\) | −621.899 | − | 451.836i | −0.213439 | − | 0.155073i | ||||
\(205\) | 371.167 | − | 1142.33i | 0.126456 | − | 0.389191i | ||||
\(206\) | −1720.13 | + | 558.904i | −0.581782 | + | 0.189032i | ||||
\(207\) | −1401.24 | + | 1018.06i | −0.470497 | + | 0.341836i | ||||
\(208\) | 1682.40 | + | 642.542i | 0.560834 | + | 0.214194i | ||||
\(209\) | 815.586 | + | 4772.92i | 0.269929 | + | 1.57966i | ||||
\(210\) | − | 1225.02i | − | 0.402544i | ||||||
\(211\) | −2679.22 | + | 1946.57i | −0.874148 | + | 0.635106i | −0.931697 | − | 0.363237i | \(-0.881672\pi\) |
0.0575487 | + | 0.998343i | \(0.481672\pi\) | |||||||
\(212\) | −14.4351 | − | 44.4267i | −0.00467645 | − | 0.0143926i | ||||
\(213\) | 1130.74 | + | 367.401i | 0.363743 | + | 0.118187i | ||||
\(214\) | −1700.35 | + | 2340.33i | −0.543148 | + | 0.747579i | ||||
\(215\) | 1912.67 | − | 2632.56i | 0.606711 | − | 0.835066i | ||||
\(216\) | 3163.22 | + | 1027.79i | 0.996435 | + | 0.323761i | ||||
\(217\) | 131.311 | + | 404.134i | 0.0410782 | + | 0.126426i | ||||
\(218\) | −3427.84 | + | 2490.47i | −1.06496 | + | 0.773742i | ||||
\(219\) | − | 845.882i | − | 0.261002i | ||||||
\(220\) | −1057.61 | + | 555.185i | −0.324109 | + | 0.170139i | ||||
\(221\) | 4577.29 | + | 1748.16i | 1.39322 | + | 0.532098i | ||||
\(222\) | −999.206 | + | 725.966i | −0.302083 | + | 0.219476i | ||||
\(223\) | 2166.76 | − | 704.022i | 0.650659 | − | 0.211412i | 0.0349541 | − | 0.999389i | \(-0.488872\pi\) |
0.615705 | + | 0.787977i | \(0.288872\pi\) | |||||||
\(224\) | 425.569 | − | 1309.77i | 0.126940 | − | 0.390681i | ||||
\(225\) | −783.359 | − | 569.144i | −0.232106 | − | 0.168635i | ||||
\(226\) | 2460.44 | − | 3386.51i | 0.724186 | − | 0.996757i | ||||
\(227\) | 1898.37 | + | 616.818i | 0.555063 | + | 0.180351i | 0.573099 | − | 0.819486i | \(-0.305741\pi\) |
−0.0180354 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(228\) | 928.227 | − | 301.599i | 0.269620 | − | 0.0876048i | ||||
\(229\) | 3394.71 | + | 4672.42i | 0.979602 | + | 1.34831i | 0.937043 | + | 0.349213i | \(0.113551\pi\) |
0.0425590 | + | 0.999094i | \(0.486449\pi\) | |||||||
\(230\) | 3036.10 | 0.870412 | ||||||||
\(231\) | 1403.38 | + | 204.808i | 0.399720 | + | 0.0583349i | ||||
\(232\) | − | 2140.13i | − | 0.605631i | ||||||
\(233\) | 4310.92 | − | 3132.07i | 1.21209 | − | 0.880638i | 0.216675 | − | 0.976244i | \(-0.430479\pi\) |
0.995419 | + | 0.0956061i | \(0.0304789\pi\) | |||||||
\(234\) | −1982.88 | − | 100.547i | −0.553953 | − | 0.0280896i | ||||
\(235\) | 1238.15 | − | 3810.65i | 0.343695 | − | 1.05778i | ||||
\(236\) | 359.467 | − | 494.764i | 0.0991496 | − | 0.136468i | ||||
\(237\) | −2951.80 | − | 2144.61i | −0.809031 | − | 0.587795i | ||||
\(238\) | −985.031 | + | 3031.61i | −0.268278 | + | 0.825673i | ||||
\(239\) | −6661.51 | + | 2164.46i | −1.80292 | + | 0.585803i | −0.999948 | − | 0.0102174i | \(-0.996748\pi\) |
−0.802969 | + | 0.596021i | \(0.796748\pi\) | |||||||
\(240\) | −907.263 | − | 1248.74i | −0.244015 | − | 0.335858i | ||||
\(241\) | − | 3315.33i | − | 0.886139i | −0.896487 | − | 0.443069i | \(-0.853889\pi\) | ||
0.896487 | − | 0.443069i | \(-0.146111\pi\) | |||||||
\(242\) | 1041.39 | + | 2958.22i | 0.276625 | + | 0.785790i | ||||
\(243\) | −3886.75 | −1.02607 | ||||||||
\(244\) | −1147.15 | + | 833.450i | −0.300977 | + | 0.218673i | ||||
\(245\) | −2232.45 | + | 725.367i | −0.582147 | + | 0.189151i | ||||
\(246\) | −196.429 | + | 604.546i | −0.0509100 | + | 0.156685i | ||||
\(247\) | −5211.62 | + | 3397.04i | −1.34254 | + | 0.875095i | ||||
\(248\) | 653.954 | + | 475.126i | 0.167444 | + | 0.121655i | ||||
\(249\) | −537.765 | − | 174.730i | −0.136865 | − | 0.0444703i | ||||
\(250\) | −692.728 | − | 2132.00i | −0.175248 | − | 0.539357i | ||||
\(251\) | 9.88428 | − | 7.18135i | 0.00248562 | − | 0.00180591i | −0.586542 | − | 0.809919i | \(-0.699511\pi\) |
0.589027 | + | 0.808113i | \(0.299511\pi\) | |||||||
\(252\) | 569.552i | 0.142375i | ||||||||
\(253\) | −507.599 | + | 3478.15i | −0.126136 | + | 0.864307i | ||||
\(254\) | − | 3512.03i | − | 0.867576i | ||||||
\(255\) | −2468.38 | − | 3397.43i | −0.606180 | − | 0.834335i | ||||
\(256\) | −1042.08 | − | 3207.18i | −0.254413 | − | 0.783004i | ||||
\(257\) | 1406.42 | − | 4328.51i | 0.341362 | − | 1.05060i | −0.622141 | − | 0.782905i | \(-0.713737\pi\) |
0.963503 | − | 0.267699i | \(-0.0862631\pi\) | |||||||
\(258\) | −1012.22 | + | 1393.20i | −0.244256 | + | 0.336190i | ||||
\(259\) | −1827.03 | − | 1327.42i | −0.438326 | − | 0.318462i | ||||
\(260\) | −1194.26 | − | 963.748i | −0.284866 | − | 0.229881i | ||||
\(261\) | 482.928 | + | 1486.30i | 0.114531 | + | 0.352489i | ||||
\(262\) | 1236.86 | + | 1702.40i | 0.291655 | + | 0.401429i | ||||
\(263\) | 4555.18 | 1.06800 | 0.534001 | − | 0.845484i | \(-0.320688\pi\) | ||||
0.534001 | + | 0.845484i | \(0.320688\pi\) | |||||||
\(264\) | 2388.75 | − | 1253.96i | 0.556883 | − | 0.292332i | ||||
\(265\) | − | 255.193i | − | 0.0591561i | ||||||
\(266\) | −2378.88 | − | 3274.24i | −0.548339 | − | 0.754724i | ||||
\(267\) | 185.575 | − | 60.2969i | 0.0425356 | − | 0.0138206i | ||||
\(268\) | −1562.93 | − | 507.827i | −0.356236 | − | 0.115748i | ||||
\(269\) | −2516.48 | − | 1828.33i | −0.570380 | − | 0.414405i | 0.264863 | − | 0.964286i | \(-0.414673\pi\) |
−0.835243 | + | 0.549881i | \(0.814673\pi\) | |||||||
\(270\) | 3444.32 | + | 2502.44i | 0.776350 | + | 0.564052i | ||||
\(271\) | −5437.70 | − | 1766.82i | −1.21888 | − | 0.396038i | −0.372207 | − | 0.928150i | \(-0.621399\pi\) |
−0.846674 | + | 0.532111i | \(0.821399\pi\) | |||||||
\(272\) | 1241.14 | + | 3819.85i | 0.276674 | + | 0.851516i | ||||
\(273\) | 474.583 | + | 1759.23i | 0.105213 | + | 0.390012i | ||||
\(274\) | 73.0744 | 0.0161116 | ||||||||
\(275\) | −1936.98 | + | 330.986i | −0.424742 | + | 0.0725789i | ||||
\(276\) | 708.498 | 0.154517 | ||||||||
\(277\) | −1828.18 | + | 1328.25i | −0.396552 | + | 0.288112i | −0.768135 | − | 0.640288i | \(-0.778815\pi\) |
0.371583 | + | 0.928400i | \(0.378815\pi\) | |||||||
\(278\) | 5598.57 | − | 1819.09i | 1.20784 | − | 0.392452i | ||||
\(279\) | −561.379 | − | 182.403i | −0.120462 | − | 0.0391405i | ||||
\(280\) | 2504.51 | − | 3447.17i | 0.534547 | − | 0.735741i | ||||
\(281\) | 2927.36 | − | 4029.17i | 0.621466 | − | 0.855375i | −0.375993 | − | 0.926623i | \(-0.622698\pi\) |
0.997459 | + | 0.0712481i | \(0.0226982\pi\) | |||||||
\(282\) | −655.256 | + | 2016.67i | −0.138368 | + | 0.425854i | ||||
\(283\) | 179.582 | + | 552.696i | 0.0377210 | + | 0.116093i | 0.968144 | − | 0.250394i | \(-0.0805603\pi\) |
−0.930423 | + | 0.366487i | \(0.880560\pi\) | |||||||
\(284\) | 569.548 | + | 783.916i | 0.119002 | + | 0.163792i | ||||
\(285\) | 5331.86 | 1.10818 | ||||||||
\(286\) | −2956.67 | + | 2737.34i | −0.611299 | + | 0.565952i | ||||
\(287\) | −1162.29 | −0.239052 | ||||||||
\(288\) | 1124.44 | + | 1547.66i | 0.230064 | + | 0.316656i | ||||
\(289\) | 1858.56 | + | 5720.07i | 0.378295 | + | 1.16427i | ||||
\(290\) | 846.535 | − | 2605.37i | 0.171415 | − | 0.527560i | ||||
\(291\) | −83.7004 | + | 115.204i | −0.0168612 | + | 0.0232074i | ||||
\(292\) | 405.212 | − | 557.727i | 0.0812098 | − | 0.111776i | ||||
\(293\) | 2681.07 | + | 871.131i | 0.534572 | + | 0.173693i | 0.563848 | − | 0.825878i | \(-0.309320\pi\) |
−0.0292764 | + | 0.999571i | \(0.509320\pi\) | |||||||
\(294\) | 1181.46 | − | 383.878i | 0.234367 | − | 0.0761505i | ||||
\(295\) | 2702.89 | − | 1963.77i | 0.533453 | − | 0.387576i | ||||
\(296\) | −4295.96 | −0.843573 | ||||||||
\(297\) | −3442.64 | + | 3527.43i | −0.672601 | + | 0.689165i | ||||
\(298\) | 5961.68 | 1.15890 | ||||||||
\(299\) | −4360.10 | + | 1176.21i | −0.843315 | + | 0.227499i | ||||
\(300\) | 122.397 | + | 376.698i | 0.0235553 | + | 0.0724956i | ||||
\(301\) | −2994.71 | − | 973.040i | −0.573463 | − | 0.186329i | ||||
\(302\) | −5016.65 | − | 3644.81i | −0.955880 | − | 0.694488i | ||||
\(303\) | 3113.60 | + | 2262.16i | 0.590335 | + | 0.428903i | ||||
\(304\) | −4849.89 | − | 1575.83i | −0.915001 | − | 0.297302i | ||||
\(305\) | −7367.13 | + | 2393.73i | −1.38308 | + | 0.449391i | ||||
\(306\) | −2602.66 | − | 3582.25i | −0.486223 | − | 0.669228i | ||||
\(307\) | − | 4140.36i | − | 0.769716i | −0.922976 | − | 0.384858i | \(-0.874250\pi\) | ||
0.922976 | − | 0.384858i | \(-0.125750\pi\) | |||||||
\(308\) | 827.195 | + | 807.313i | 0.153032 | + | 0.149354i | ||||
\(309\) | −2305.73 | −0.424493 | ||||||||
\(310\) | 608.178 | + | 837.085i | 0.111426 | + | 0.153365i | ||||
\(311\) | −571.430 | − | 1758.68i | −0.104189 | − | 0.320661i | 0.885350 | − | 0.464925i | \(-0.153919\pi\) |
−0.989539 | + | 0.144264i | \(0.953919\pi\) | |||||||
\(312\) | 2697.40 | + | 2176.75i | 0.489456 | + | 0.394981i | ||||
\(313\) | 4944.36 | + | 3592.29i | 0.892881 | + | 0.648716i | 0.936628 | − | 0.350326i | \(-0.113929\pi\) |
−0.0437463 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(314\) | −3338.58 | + | 4595.16i | −0.600022 | + | 0.825860i | ||||
\(315\) | −961.495 | + | 2959.18i | −0.171981 | + | 0.529304i | ||||
\(316\) | −918.895 | − | 2828.07i | −0.163582 | − | 0.503454i | ||||
\(317\) | 2226.27 | + | 3064.20i | 0.394447 | + | 0.542910i | 0.959339 | − | 0.282255i | \(-0.0910824\pi\) |
−0.564892 | + | 0.825165i | \(0.691082\pi\) | |||||||
\(318\) | 135.053i | 0.0238157i | ||||||||
\(319\) | 2843.17 | + | 1405.37i | 0.499019 | + | 0.246664i | ||||
\(320\) | − | 7464.20i | − | 1.30394i | ||||||
\(321\) | −2983.53 | + | 2167.66i | −0.518768 | + | 0.376907i | ||||
\(322\) | −907.876 | − | 2794.15i | −0.157124 | − | 0.483578i | ||||
\(323\) | −13195.0 | − | 4287.33i | −2.27304 | − | 0.738555i | ||||
\(324\) | −157.561 | − | 114.475i | −0.0270167 | − | 0.0196288i | ||||
\(325\) | −1378.61 | − | 2115.01i | −0.235296 | − | 0.360983i | ||||
\(326\) | −534.541 | + | 1645.15i | −0.0908144 | + | 0.279498i | ||||
\(327\) | −5137.15 | + | 1669.16i | −0.868761 | + | 0.282278i | ||||
\(328\) | −1788.72 | + | 1299.58i | −0.301115 | + | 0.218773i | ||||
\(329\) | −3877.22 | −0.649720 | ||||||||
\(330\) | 3404.04 | − | 581.674i | 0.567836 | − | 0.0970305i | ||||
\(331\) | 1299.67i | 0.215820i | 0.994161 | + | 0.107910i | \(0.0344158\pi\) | ||||
−0.994161 | + | 0.107910i | \(0.965584\pi\) | |||||||
\(332\) | −270.869 | − | 372.819i | −0.0447767 | − | 0.0616298i | ||||
\(333\) | 2983.50 | − | 969.399i | 0.490976 | − | 0.159528i | ||||
\(334\) | 1485.30 | − | 4571.29i | 0.243329 | − | 0.748891i | ||||
\(335\) | −7263.10 | − | 5276.95i | −1.18455 | − | 0.860629i | ||||
\(336\) | −877.932 | + | 1208.37i | −0.142545 | + | 0.196196i | ||||
\(337\) | −3247.72 | + | 9995.44i | −0.524969 | + | 1.61569i | 0.239410 | + | 0.970919i | \(0.423046\pi\) |
−0.764378 | + | 0.644768i | \(0.776954\pi\) | |||||||
\(338\) | −4736.24 | − | 2089.49i | −0.762182 | − | 0.336253i | ||||
\(339\) | 4317.23 | − | 3136.65i | 0.691681 | − | 0.502535i | ||||
\(340\) | − | 3422.53i | − | 0.545919i | ||||||
\(341\) | −1060.64 | + | 556.777i | −0.168437 | + | 0.0884199i | ||||
\(342\) | 5621.92 | 0.888884 | ||||||||
\(343\) | 3944.28 | + | 5428.83i | 0.620907 | + | 0.854605i | ||||
\(344\) | −5696.73 | + | 1850.98i | −0.892870 | + | 0.290111i | ||||
\(345\) | 3681.09 | + | 1196.06i | 0.574444 | + | 0.186648i | ||||
\(346\) | −2184.42 | + | 3006.60i | −0.339408 | + | 0.467155i | ||||
\(347\) | −1069.79 | − | 777.244i | −0.165502 | − | 0.120244i | 0.501952 | − | 0.864896i | \(-0.332616\pi\) |
−0.667453 | + | 0.744652i | \(0.732616\pi\) | |||||||
\(348\) | 197.545 | − | 607.982i | 0.0304297 | − | 0.0936531i | ||||
\(349\) | 7163.78 | − | 2327.65i | 1.09876 | − | 0.357010i | 0.297137 | − | 0.954835i | \(-0.403968\pi\) |
0.801627 | + | 0.597825i | \(0.203968\pi\) | |||||||
\(350\) | 1328.77 | − | 965.410i | 0.202931 | − | 0.147438i | ||||
\(351\) | −5915.81 | − | 2259.36i | −0.899608 | − | 0.343578i | ||||
\(352\) | 3841.61 | + | 560.642i | 0.581701 | + | 0.0848930i | ||||
\(353\) | 10836.3i | 1.63387i | 0.576728 | + | 0.816936i | \(0.304329\pi\) | ||||
−0.576728 | + | 0.816936i | \(0.695671\pi\) | |||||||
\(354\) | −1430.42 | + | 1039.26i | −0.214763 | + | 0.156035i | ||||
\(355\) | 1635.78 | + | 5034.42i | 0.244559 | + | 0.752674i | ||||
\(356\) | 151.242 | + | 49.1416i | 0.0225163 | + | 0.00731601i | ||||
\(357\) | −2388.58 | + | 3287.60i | −0.354109 | + | 0.487389i | ||||
\(358\) | 4571.82 | − | 6292.57i | 0.674939 | − | 0.928974i | ||||
\(359\) | 11578.5 | + | 3762.08i | 1.70220 | + | 0.553078i | 0.989004 | − | 0.147887i | \(-0.0472472\pi\) |
0.713195 | + | 0.700965i | \(0.247247\pi\) | |||||||
\(360\) | 1829.02 | + | 5629.14i | 0.267772 | + | 0.824116i | ||||
\(361\) | 8702.03 | − | 6322.40i | 1.26870 | − | 0.921767i | ||||
\(362\) | 11238.6i | 1.63174i | ||||||||
\(363\) | 97.2510 | + | 3996.91i | 0.0140616 | + | 0.577915i | ||||
\(364\) | −529.830 | + | 1387.28i | −0.0762929 | + | 0.199762i | ||||
\(365\) | 3046.86 | − | 2213.67i | 0.436931 | − | 0.317449i | ||||
\(366\) | 3898.83 | − | 1266.81i | 0.556817 | − | 0.180921i | ||||
\(367\) | −2889.59 | + | 8893.25i | −0.410996 | + | 1.26492i | 0.504788 | + | 0.863244i | \(0.331571\pi\) |
−0.915784 | + | 0.401672i | \(0.868429\pi\) | |||||||
\(368\) | −2994.85 | − | 2175.88i | −0.424231 | − | 0.308222i | ||||
\(369\) | 948.996 | − | 1306.18i | 0.133883 | − | 0.184274i | ||||
\(370\) | −5229.84 | − | 1699.28i | −0.734829 | − | 0.238760i | ||||
\(371\) | −234.856 | + | 76.3095i | −0.0328656 | + | 0.0106787i | ||||
\(372\) | 141.923 | + | 195.340i | 0.0197806 | + | 0.0272256i | ||||
\(373\) | −86.3592 | −0.0119880 | −0.00599398 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599398 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(374\) | −8891.87 | − | 1297.67i | −1.22938 | − | 0.179415i | ||||
\(375\) | − | 2857.81i | − | 0.393538i | ||||||
\(376\) | −5966.90 | + | 4335.21i | −0.818402 | + | 0.594604i | ||||
\(377\) | −206.354 | + | 4069.49i | −0.0281903 | + | 0.555939i | ||||
\(378\) | 1273.08 | − | 3918.14i | 0.173228 | − | 0.533141i | ||||
\(379\) | 4887.30 | − | 6726.79i | 0.662384 | − | 0.911694i | −0.337173 | − | 0.941443i | \(-0.609471\pi\) |
0.999557 | + | 0.0297490i | \(0.00947081\pi\) | |||||||
\(380\) | 3515.53 | + | 2554.18i | 0.474586 | + | 0.344807i | ||||
\(381\) | 1383.55 | − | 4258.12i | 0.186040 | − | 0.572572i | ||||
\(382\) | −2.10089 | + | 0.682622i | −0.000281390 | + | 9.14292e-5i | ||||
\(383\) | −1362.30 | − | 1875.05i | −0.181751 | − | 0.250158i | 0.708414 | − | 0.705797i | \(-0.249411\pi\) |
−0.890165 | + | 0.455639i | \(0.849411\pi\) | |||||||
\(384\) | 1393.00i | 0.185121i | ||||||||
\(385\) | 2934.92 | + | 5590.93i | 0.388513 | + | 0.740105i | ||||
\(386\) | 868.402 | 0.114509 | ||||||||
\(387\) | 3538.65 | − | 2570.98i | 0.464805 | − | 0.337701i | ||||
\(388\) | −110.375 | + | 35.8629i | −0.0144418 | + | 0.00469243i | ||||
\(389\) | −167.108 | + | 514.306i | −0.0217808 | + | 0.0670343i | −0.961356 | − | 0.275308i | \(-0.911220\pi\) |
0.939575 | + | 0.342342i | \(0.111220\pi\) | |||||||
\(390\) | 2422.76 | + | 3716.91i | 0.314567 | + | 0.482598i | ||||
\(391\) | −8148.03 | − | 5919.89i | −1.05387 | − | 0.765683i | ||||
\(392\) | 4109.42 | + | 1335.23i | 0.529482 | + | 0.172039i | ||||
\(393\) | 828.970 | + | 2551.31i | 0.106402 | + | 0.327472i | ||||
\(394\) | 2675.54 | − | 1943.89i | 0.342111 | − | 0.248558i | ||||
\(395\) | − | 16244.8i | − | 2.06928i | ||||||
\(396\) | −1582.65 | + | 270.440i | −0.200837 | + | 0.0343185i | ||||
\(397\) | 7613.80i | 0.962533i | 0.876574 | + | 0.481266i | \(0.159823\pi\) | ||||
−0.876574 | + | 0.481266i | \(0.840177\pi\) | |||||||
\(398\) | −2957.41 | − | 4070.53i | −0.372467 | − | 0.512656i | ||||
\(399\) | −1594.37 | − | 4906.96i | −0.200046 | − | 0.615678i | ||||
\(400\) | 639.511 | − | 1968.21i | 0.0799389 | − | 0.246027i | ||||
\(401\) | 9030.35 | − | 12429.2i | 1.12457 | − | 1.54784i | 0.326588 | − | 0.945167i | \(-0.394101\pi\) |
0.797986 | − | 0.602676i | \(-0.205899\pi\) | |||||||
\(402\) | 3843.78 | + | 2792.67i | 0.476891 | + | 0.346482i | ||||
\(403\) | −1197.69 | − | 966.513i | −0.148043 | − | 0.119468i | ||||
\(404\) | 969.261 | + | 2983.08i | 0.119363 | + | 0.367361i | ||||
\(405\) | −625.377 | − | 860.758i | −0.0767290 | − | 0.105608i | ||||
\(406\) | −2650.88 | −0.324042 | ||||||||
\(407\) | 2821.06 | − | 5707.20i | 0.343574 | − | 0.695075i | ||||
\(408\) | 7730.22i | 0.937997i | ||||||||
\(409\) | 1778.27 | + | 2447.58i | 0.214987 | + | 0.295905i | 0.902867 | − | 0.429920i | \(-0.141458\pi\) |
−0.687880 | + | 0.725825i | \(0.741458\pi\) | |||||||
\(410\) | −2691.62 | + | 874.562i | −0.324219 | + | 0.105345i | ||||
\(411\) | 88.5982 | + | 28.7873i | 0.0106332 | + | 0.00345492i | ||||
\(412\) | −1520.27 | − | 1104.54i | −0.181792 | − | 0.132079i | ||||
\(413\) | −2615.51 | − | 1900.28i | −0.311625 | − | 0.226408i | ||||
\(414\) | 3881.34 | + | 1261.12i | 0.460767 | + | 0.149712i | ||||
\(415\) | −777.953 | − | 2394.29i | −0.0920198 | − | 0.283208i | ||||
\(416\) | 1299.13 | + | 4815.72i | 0.153113 | + | 0.567573i | ||||
\(417\) | 7504.55 | 0.881293 | ||||||||
\(418\) | 7968.80 | − | 8165.05i | 0.932456 | − | 0.955420i | ||||
\(419\) | 13631.4 | 1.58935 | 0.794677 | − | 0.607033i | \(-0.207640\pi\) | ||||
0.794677 | + | 0.607033i | \(0.207640\pi\) | |||||||
\(420\) | 1029.69 | − | 748.114i | 0.119628 | − | 0.0869148i | ||||
\(421\) | 20.9177 | − | 6.79658i | 0.00242154 | − | 0.000786805i | −0.307806 | − | 0.951449i | \(-0.599595\pi\) |
0.310228 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(422\) | 7421.27 | + | 2411.32i | 0.856071 | + | 0.278154i | ||||
\(423\) | 3165.70 | − | 4357.21i | 0.363881 | − | 0.500839i | ||||
\(424\) | −276.112 | + | 380.036i | −0.0316255 | + | 0.0435287i | ||||
\(425\) | 1739.91 | − | 5354.89i | 0.198583 | − | 0.611177i | ||||
\(426\) | −865.688 | − | 2664.31i | −0.0984571 | − | 0.303020i | ||||
\(427\) | 4405.94 | + | 6064.25i | 0.499340 | + | 0.687283i | ||||
\(428\) | −3005.57 | −0.339439 | ||||||||
\(429\) | −4663.14 | + | 2154.09i | −0.524799 | + | 0.242425i | ||||
\(430\) | −7667.29 | −0.859883 | ||||||||
\(431\) | −33.0621 | − | 45.5061i | −0.00369500 | − | 0.00508574i | 0.807165 | − | 0.590325i | \(-0.201000\pi\) |
−0.810860 | + | 0.585239i | \(0.801000\pi\) | |||||||
\(432\) | −1604.09 | − | 4936.88i | −0.178650 | − | 0.549828i | ||||
\(433\) | 885.094 | − | 2724.04i | 0.0982330 | − | 0.302330i | −0.889850 | − | 0.456254i | \(-0.849191\pi\) |
0.988083 | + | 0.153924i | \(0.0491910\pi\) | |||||||
\(434\) | 588.516 | − | 810.023i | 0.0650914 | − | 0.0895907i | ||||
\(435\) | 2052.74 | − | 2825.36i | 0.226256 | − | 0.311415i | ||||
\(436\) | −4186.74 | − | 1360.35i | −0.459882 | − | 0.149425i | ||||
\(437\) | 12161.5 | − | 3951.51i | 1.33127 | − | 0.432555i | ||||
\(438\) | −1612.46 | + | 1171.52i | −0.175905 | + | 0.127802i | ||||
\(439\) | 12323.2 | 1.33975 | 0.669877 | − | 0.742472i | \(-0.266347\pi\) | ||||
0.669877 | + | 0.742472i | \(0.266347\pi\) | |||||||
\(440\) | 10768.1 | + | 5322.64i | 1.16670 | + | 0.576698i | ||||
\(441\) | −3155.25 | −0.340703 | ||||||||
\(442\) | −3006.98 | − | 11146.6i | −0.323592 | − | 1.19952i | ||||
\(443\) | 472.218 | + | 1453.34i | 0.0506451 | + | 0.155869i | 0.973180 | − | 0.230043i | \(-0.0738867\pi\) |
−0.922535 | + | 0.385912i | \(0.873887\pi\) | |||||||
\(444\) | −1220.42 | − | 396.540i | −0.130448 | − | 0.0423850i | ||||
\(445\) | 702.838 | + | 510.642i | 0.0748713 | + | 0.0543972i | ||||
\(446\) | −4342.93 | − | 3155.32i | −0.461084 | − | 0.334997i | ||||
\(447\) | 7228.18 | + | 2348.58i | 0.764834 | + | 0.248510i | ||||
\(448\) | −6869.38 | + | 2232.00i | −0.724437 | + | 0.235384i | ||||
\(449\) | −799.912 | − | 1100.98i | −0.0840762 | − | 0.115721i | 0.764907 | − | 0.644141i | \(-0.222785\pi\) |
−0.848983 | + | 0.528420i | \(0.822785\pi\) | |||||||
\(450\) | 2281.52i | 0.239004i | ||||||||
\(451\) | −551.890 | − | 3229.74i | −0.0576219 | − | 0.337211i | ||||
\(452\) | 4349.12 | 0.452578 | ||||||||
\(453\) | −4646.53 | − | 6395.39i | −0.481927 | − | 0.663315i | ||||
\(454\) | −1453.38 | − | 4473.04i | −0.150243 | − | 0.462401i | ||||
\(455\) | −5094.74 | + | 6313.34i | −0.524935 | + | 0.650493i | ||||
\(456\) | −7940.27 | − | 5768.94i | −0.815432 | − | 0.592446i | ||||
\(457\) | −9677.95 | + | 13320.6i | −0.990625 | + | 1.36348i | −0.0597207 | + | 0.998215i | \(0.519021\pi\) |
−0.930904 | + | 0.365263i | \(0.880979\pi\) | |||||||
\(458\) | 4205.21 | − | 12942.3i | 0.429032 | − | 1.32042i | ||||
\(459\) | −4364.22 | − | 13431.7i | −0.443801 | − | 1.36588i | ||||
\(460\) | 1854.14 | + | 2552.00i | 0.187934 | + | 0.258669i | ||||
\(461\) | − | 6218.34i | − | 0.628237i | −0.949384 | − | 0.314118i | \(-0.898291\pi\) | ||
0.949384 | − | 0.314118i | \(-0.101709\pi\) | |||||||
\(462\) | −1553.22 | − | 2958.83i | −0.156412 | − | 0.297960i | ||||
\(463\) | − | 5055.65i | − | 0.507464i | −0.967275 | − | 0.253732i | \(-0.918342\pi\) | ||
0.967275 | − | 0.253732i | \(-0.0816581\pi\) | |||||||
\(464\) | −2702.22 | + | 1963.28i | −0.270361 | + | 0.196429i | ||||
\(465\) | 407.613 | + | 1254.50i | 0.0406507 | + | 0.125110i | ||||
\(466\) | −11941.0 | − | 3879.86i | −1.18703 | − | 0.385689i | ||||
\(467\) | 11288.1 | + | 8201.28i | 1.11852 | + | 0.812655i | 0.983985 | − | 0.178253i | \(-0.0570446\pi\) |
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(468\) | −1126.42 | − | 1728.12i | −0.111259 | − | 0.170689i | ||||
\(469\) | −2684.57 | + | 8262.25i | −0.264311 | + | 0.813466i | ||||
\(470\) | −8978.83 | + | 2917.40i | −0.881197 | + | 0.286318i | ||||
\(471\) | −5858.07 | + | 4256.13i | −0.573090 | + | 0.416374i | ||||
\(472\) | −6149.93 | −0.599732 | ||||||||
\(473\) | 1281.88 | − | 8783.63i | 0.124611 | − | 0.853852i | ||||
\(474\) | 8597.08i | 0.833074i | ||||||||
\(475\) | 4201.93 | + | 5783.46i | 0.405890 | + | 0.558659i | ||||
\(476\) | −3149.79 | + | 1023.43i | −0.303299 | + | 0.0985477i | ||||
\(477\) | 106.001 | − | 326.237i | 0.0101749 | − | 0.0313153i | ||||
\(478\) | 13352.0 | + | 9700.76i | 1.27762 | + | 0.928248i | ||||
\(479\) | −3143.26 | + | 4326.33i | −0.299832 | + | 0.412683i | −0.932176 | − | 0.362004i | \(-0.882093\pi\) |
0.632345 | + | 0.774687i | \(0.282093\pi\) | |||||||
\(480\) | 1321.04 | − | 4065.75i | 0.125619 | − | 0.386615i | ||||
\(481\) | 8168.82 | + | 414.221i | 0.774358 | + | 0.0392658i | ||||
\(482\) | −6319.84 | + | 4591.63i | −0.597222 | + | 0.433907i | ||||
\(483\) | − | 3745.39i | − | 0.352839i | ||||||
\(484\) | −1850.56 | + | 2681.92i | −0.173794 | + | 0.251871i | ||||
\(485\) | −634.007 | −0.0593583 | ||||||||
\(486\) | 5383.03 | + | 7409.10i | 0.502426 | + | 0.691530i | ||||
\(487\) | −12108.8 | + | 3934.40i | −1.12670 | + | 0.366088i | −0.812322 | − | 0.583209i | \(-0.801797\pi\) |
−0.314381 | + | 0.949297i | \(0.601797\pi\) | |||||||
\(488\) | 13561.2 | + | 4406.29i | 1.25796 | + | 0.408736i | ||||
\(489\) | −1296.20 | + | 1784.06i | −0.119869 | + | 0.164986i | ||||
\(490\) | 4474.60 | + | 3250.99i | 0.412534 | + | 0.299724i | ||||
\(491\) | −3227.63 | + | 9933.62i | −0.296662 | + | 0.913031i | 0.685997 | + | 0.727605i | \(0.259367\pi\) |
−0.982658 | + | 0.185426i | \(0.940633\pi\) | |||||||
\(492\) | −628.111 | + | 204.086i | −0.0575558 | + | 0.0187010i | ||||
\(493\) | −7351.89 | + | 5341.46i | −0.671628 | + | 0.487966i | ||||
\(494\) | 13693.5 | + | 5229.82i | 1.24717 | + | 0.476317i | ||||
\(495\) | −8679.41 | − | 1266.67i | −0.788102 | − | 0.115015i | ||||
\(496\) | − | 1261.57i | − | 0.114206i | ||||||
\(497\) | 4144.08 | − | 3010.85i | 0.374019 | − | 0.271741i | ||||
\(498\) | 411.708 | + | 1267.11i | 0.0370464 | + | 0.114017i | ||||
\(499\) | −16165.0 | − | 5252.34i | −1.45019 | − | 0.471196i | −0.525134 | − | 0.851020i | \(-0.675985\pi\) |
−0.925059 | + | 0.379824i | \(0.875985\pi\) | |||||||
\(500\) | 1369.01 | − | 1884.28i | 0.122448 | − | 0.168535i | ||||
\(501\) | 3601.67 | − | 4957.28i | 0.321179 | − | 0.442065i | ||||
\(502\) | −27.3788 | − | 8.89592i | −0.00243422 | − | 0.000790925i | ||||
\(503\) | 267.168 | + | 822.260i | 0.0236828 | + | 0.0728882i | 0.962199 | − | 0.272346i | \(-0.0877995\pi\) |
−0.938517 | + | 0.345234i | \(0.887800\pi\) | |||||||
\(504\) | 4633.63 | − | 3366.53i | 0.409520 | − | 0.297534i | ||||
\(505\) | 17135.2i | 1.50991i | ||||||||
\(506\) | 7333.22 | − | 3849.52i | 0.644272 | − | 0.338206i | ||||
\(507\) | −4919.26 | − | 4399.20i | −0.430911 | − | 0.385356i | ||||
\(508\) | 2952.04 | − | 2144.79i | 0.257826 | − | 0.187322i | ||||
\(509\) | 20399.3 | − | 6628.14i | 1.77639 | − | 0.577185i | 0.777716 | − | 0.628616i | \(-0.216378\pi\) |
0.998677 | + | 0.0514313i | \(0.0163783\pi\) | |||||||
\(510\) | −3057.71 | + | 9410.67i | −0.265486 | + | 0.817081i | ||||
\(511\) | −2948.36 | − | 2142.11i | −0.255240 | − | 0.185443i | ||||
\(512\) | −6851.08 | + | 9429.70i | −0.591363 | + | 0.813941i | ||||
\(513\) | 17053.6 | + | 5541.06i | 1.46771 | + | 0.476888i | ||||
\(514\) | −10199.1 | + | 3313.87i | −0.875216 | + | 0.284375i | ||||
\(515\) | −6034.09 | − | 8305.22i | −0.516299 | − | 0.710624i | ||||
\(516\) | −1789.22 | −0.152647 | ||||||||
\(517\) | −1841.02 | − | 10773.9i | −0.156611 | − | 0.916508i | ||||
\(518\) | 5321.21i | 0.451352i | ||||||||
\(519\) | −3832.91 | + | 2784.77i | −0.324174 | + | 0.235526i | ||||
\(520\) | −781.534 | + | 15412.6i | −0.0659087 | + | 1.29978i | ||||
\(521\) | −4999.79 | + | 15387.8i | −0.420431 | + | 1.29395i | 0.486870 | + | 0.873474i | \(0.338138\pi\) |
−0.907302 | + | 0.420480i | \(0.861862\pi\) | |||||||
\(522\) | 2164.41 | − | 2979.06i | 0.181482 | − | 0.249789i | ||||
\(523\) | 3798.03 | + | 2759.43i | 0.317545 | + | 0.230710i | 0.735127 | − | 0.677929i | \(-0.237122\pi\) |
−0.417582 | + | 0.908639i | \(0.637122\pi\) | |||||||
\(524\) | −675.604 | + | 2079.30i | −0.0563243 | + | 0.173348i | ||||
\(525\) | 1991.37 | − | 647.036i | 0.165544 | − | 0.0537885i | ||||
\(526\) | −6308.78 | − | 8683.29i | −0.522958 | − | 0.719790i | ||||
\(527\) | − | 3432.34i | − | 0.283710i | ||||||
\(528\) | −3774.65 | − | 1865.80i | −0.311118 | − | 0.153785i | ||||
\(529\) | −2884.35 | −0.237063 | ||||||||
\(530\) | −486.460 | + | 353.434i | −0.0398688 | + | 0.0289664i | ||||
\(531\) | 4271.07 | − | 1387.75i | 0.349056 | − | 0.113415i | ||||
\(532\) | 1299.40 | − | 3999.14i | 0.105895 | − | 0.325911i | ||||
\(533\) | 3526.59 | − | 2298.71i | 0.286592 | − | 0.186807i | ||||
\(534\) | −371.956 | − | 270.242i | −0.0301425 | − | 0.0218998i | ||||
\(535\) | −15615.8 | − | 5073.89i | −1.26193 | − | 0.410025i | ||||
\(536\) | 5106.76 | + | 15717.0i | 0.411527 | + | 1.26655i | ||||
\(537\) | 8021.98 | − | 5828.31i | 0.644644 | − | 0.468362i | ||||
\(538\) | 7329.19i | 0.587331i | ||||||||
\(539\) | −4472.42 | + | 4582.57i | −0.357404 | + | 0.366206i | ||||
\(540\) | 4423.37i | 0.352503i | ||||||||
\(541\) | −13865.2 | − | 19083.7i | −1.10187 | − | 1.51659i | −0.832888 | − | 0.553442i | \(-0.813314\pi\) |
−0.268978 | − | 0.963146i | \(-0.586686\pi\) | |||||||
\(542\) | 4163.06 | + | 12812.6i | 0.329924 | + | 1.01540i | ||||
\(543\) | −4427.41 | + | 13626.2i | −0.349905 | + | 1.07690i | ||||
\(544\) | −6538.51 | + | 8999.49i | −0.515324 | + | 0.709283i | ||||
\(545\) | −19456.2 | − | 14135.8i | −1.52920 | − | 1.11103i | ||||
\(546\) | 2696.24 | − | 3341.15i | 0.211334 | − | 0.261882i | ||||
\(547\) | −2832.00 | − | 8715.99i | −0.221366 | − | 0.681296i | −0.998640 | − | 0.0521331i | \(-0.983398\pi\) |
0.777274 | − | 0.629163i | \(-0.216602\pi\) | |||||||
\(548\) | 44.6263 | + | 61.4229i | 0.00347873 | + | 0.00478806i | ||||
\(549\) | −10412.4 | −0.809454 | ||||||||
\(550\) | 3313.59 | + | 3233.94i | 0.256894 | + | 0.250720i | ||||
\(551\) | − | 11537.9i | − | 0.892072i | ||||||
\(552\) | −4187.81 | − | 5764.03i | −0.322908 | − | 0.444445i | ||||
\(553\) | −14950.3 | + | 4857.63i | −1.14964 | + | 0.373540i | ||||
\(554\) | 5063.95 | + | 1645.38i | 0.388351 | + | 0.126183i | ||||
\(555\) | −5671.44 | − | 4120.54i | −0.433765 | − | 0.315148i | ||||
\(556\) | 4948.07 | + | 3594.99i | 0.377419 | + | 0.274211i | ||||
\(557\) | −12996.7 | − | 4222.89i | −0.988668 | − | 0.321238i | −0.230340 | − | 0.973110i | \(-0.573984\pi\) |
−0.758329 | + | 0.651873i | \(0.773984\pi\) | |||||||
\(558\) | 429.787 | + | 1322.75i | 0.0326063 | + | 0.100352i | ||||
\(559\) | 11010.9 | − | 2970.38i | 0.833114 | − | 0.224747i | ||||
\(560\) | −6650.09 | −0.501817 | ||||||||
\(561\) | −10269.6 | − | 5076.26i | −0.772877 | − | 0.382032i | ||||
\(562\) | −11734.9 | −0.880795 | ||||||||
\(563\) | −7461.67 | + | 5421.22i | −0.558564 | + | 0.405821i | −0.830933 | − | 0.556372i | \(-0.812193\pi\) |
0.272369 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(564\) | −2095.28 | + | 680.798i | −0.156431 | + | 0.0508276i | ||||
\(565\) | 22596.4 | + | 7342.01i | 1.68254 | + | 0.546691i | ||||
\(566\) | 804.859 | − | 1107.79i | 0.0597716 | − | 0.0822686i | ||||
\(567\) | −605.159 | + | 832.930i | −0.0448224 | + | 0.0616927i | ||||
\(568\) | 3011.09 | − | 9267.19i | 0.222434 | − | 0.684582i | ||||
\(569\) | −2526.23 | − | 7774.95i | −0.186125 | − | 0.572834i | 0.813841 | − | 0.581088i | \(-0.197373\pi\) |
−0.999966 | + | 0.00825362i | \(0.997373\pi\) | |||||||
\(570\) | −7384.46 | − | 10163.8i | −0.542633 | − | 0.746870i | ||||
\(571\) | −13990.3 | −1.02535 | −0.512675 | − | 0.858582i | \(-0.671346\pi\) | ||||
−0.512675 | + | 0.858582i | \(0.671346\pi\) | |||||||
\(572\) | −4106.51 | − | 813.552i | −0.300178 | − | 0.0594691i | ||||
\(573\) | −2.81612 | −0.000205314 | ||||||||
\(574\) | 1609.73 | + | 2215.61i | 0.117054 | + | 0.161111i | ||||
\(575\) | 1603.63 | + | 4935.45i | 0.116306 | + | 0.357952i | ||||
\(576\) | 3100.45 | − | 9542.20i | 0.224280 | − | 0.690264i | ||||
\(577\) | −6829.32 | + | 9399.75i | −0.492735 | + | 0.678192i | −0.980890 | − | 0.194565i | \(-0.937670\pi\) |
0.488154 | + | 0.872757i | \(0.337670\pi\) | |||||||
\(578\) | 8329.81 | − | 11465.0i | 0.599437 | − | 0.825054i | ||||
\(579\) | 1052.88 | + | 342.103i | 0.0755723 | + | 0.0245549i | ||||
\(580\) | 2706.92 | − | 879.533i | 0.193791 | − | 0.0629666i | ||||
\(581\) | −1970.86 | + | 1431.92i | −0.140732 | + | 0.102248i | ||||
\(582\) | 335.529 | 0.0238971 | ||||||||
\(583\) | −323.563 | − | 616.378i | −0.0229856 | − | 0.0437869i | ||||
\(584\) | −6932.56 | −0.491218 | ||||||||
\(585\) | −2935.13 | − | 10880.2i | −0.207441 | − | 0.768962i | ||||
\(586\) | −2052.60 | − | 6317.26i | −0.144697 | − | 0.445330i | ||||
\(587\) | 3676.54 | + | 1194.58i | 0.258513 | + | 0.0839958i | 0.435406 | − | 0.900234i | \(-0.356605\pi\) |
−0.176893 | + | 0.984230i | \(0.556605\pi\) | |||||||
\(588\) | 1044.18 | + | 758.643i | 0.0732336 | + | 0.0532073i | ||||
\(589\) | 3525.61 | + | 2561.51i | 0.246639 | + | 0.179194i | ||||
\(590\) | −7486.84 | − | 2432.62i | −0.522421 | − | 0.169745i | ||||
\(591\) | 4009.71 | − | 1302.84i | 0.279082 | − | 0.0906793i | ||||
\(592\) | 3940.96 | + | 5424.26i | 0.273602 | + | 0.376581i | ||||
\(593\) | 20857.4i | 1.44437i | 0.691700 | + | 0.722185i | \(0.256862\pi\) | ||||
−0.691700 | + | 0.722185i | \(0.743138\pi\) | |||||||
\(594\) | 11492.1 | + | 1677.15i | 0.793815 | + | 0.115849i | ||||
\(595\) | −18092.8 | −1.24661 | ||||||||
\(596\) | 3640.78 | + | 5011.11i | 0.250222 | + | 0.344401i | ||||
\(597\) | −1982.12 | − | 6100.33i | −0.135884 | − | 0.418207i | ||||
\(598\) | 8280.75 | + | 6682.41i | 0.566263 | + | 0.456963i | ||||
\(599\) | 21270.2 | + | 15453.7i | 1.45088 | + | 1.05412i | 0.985625 | + | 0.168945i | \(0.0540361\pi\) |
0.465252 | + | 0.885178i | \(0.345964\pi\) | |||||||
\(600\) | 2341.19 | − | 3222.37i | 0.159298 | − | 0.219254i | ||||
\(601\) | −777.825 | + | 2393.90i | −0.0527923 | + | 0.162478i | −0.973977 | − | 0.226649i | \(-0.927223\pi\) |
0.921184 | + | 0.389127i | \(0.127223\pi\) | |||||||
\(602\) | 2292.72 | + | 7056.28i | 0.155223 | + | 0.477728i | ||||
\(603\) | −7093.20 | − | 9762.95i | −0.479034 | − | 0.659333i | ||||
\(604\) | − | 6442.64i | − | 0.434018i | ||||||
\(605\) | −14142.3 | + | 10810.2i | −0.950358 | + | 0.726441i | ||||
\(606\) | − | 9068.29i | − | 0.607878i | ||||||
\(607\) | 22265.6 | − | 16176.9i | 1.48885 | − | 1.08171i | 0.514281 | − | 0.857622i | \(-0.328059\pi\) |
0.974568 | − | 0.224091i | \(-0.0719413\pi\) | |||||||
\(608\) | −4364.44 | − | 13432.4i | −0.291121 | − | 0.895977i | ||||
\(609\) | −3214.03 | − | 1044.30i | −0.213857 | − | 0.0694864i | ||||
\(610\) | 14766.3 | + | 10728.3i | 0.980112 | + | 0.712093i | ||||
\(611\) | 11764.1 | − | 7668.12i | 0.778930 | − | 0.507723i | ||||
\(612\) | 1421.64 | − | 4375.34i | 0.0938990 | − | 0.288991i | ||||
\(613\) | 2341.34 | − | 760.747i | 0.154267 | − | 0.0501244i | −0.230865 | − | 0.972986i | \(-0.574156\pi\) |
0.385133 | + | 0.922861i | \(0.374156\pi\) | |||||||
\(614\) | −7892.54 | + | 5734.26i | −0.518757 | + | 0.376899i | ||||
\(615\) | −3607.96 | −0.236564 | ||||||||
\(616\) | 1678.53 | − | 11501.6i | 0.109789 | − | 0.752293i | ||||
\(617\) | − | 13863.2i | − | 0.904556i | −0.891877 | − | 0.452278i | \(-0.850612\pi\) | ||
0.891877 | − | 0.452278i | \(-0.149388\pi\) | |||||||
\(618\) | 3193.36 | + | 4395.28i | 0.207857 | + | 0.286091i | ||||
\(619\) | −3488.44 | + | 1133.46i | −0.226514 | + | 0.0735990i | −0.420075 | − | 0.907489i | \(-0.637996\pi\) |
0.193561 | + | 0.981088i | \(0.437996\pi\) | |||||||
\(620\) | −332.202 | + | 1022.41i | −0.0215186 | + | 0.0662275i | ||||
\(621\) | 10530.7 | + | 7651.03i | 0.680490 | + | 0.494405i | ||||
\(622\) | −2561.06 | + | 3525.00i | −0.165095 | + | 0.227234i | ||||
\(623\) | 259.781 | − | 799.525i | 0.0167061 | − | 0.0514162i | ||||
\(624\) | 273.959 | − | 5402.72i | 0.0175755 | − | 0.346606i | ||||
\(625\) | 15740.8 | − | 11436.3i | 1.00741 | − | 0.731925i | ||||
\(626\) | − | 14400.4i | − | 0.919416i | ||||||
\(627\) | 12878.3 | − | 6760.35i | 0.820268 | − | 0.430594i | ||||
\(628\) | −5901.34 | −0.374983 | ||||||||
\(629\) | 10722.1 | + | 14757.7i | 0.679679 | + | 0.935498i | ||||
\(630\) | 6972.56 | − | 2265.52i | 0.440942 | − | 0.143271i | ||||
\(631\) | 1685.34 | + | 547.600i | 0.106327 | + | 0.0345477i | 0.361697 | − | 0.932296i | \(-0.382197\pi\) |
−0.255370 | + | 0.966843i | \(0.582197\pi\) | |||||||
\(632\) | −17576.5 | + | 24192.0i | −1.10626 | + | 1.52263i | ||||
\(633\) | 8047.91 | + | 5847.15i | 0.505333 | + | 0.367146i | ||||
\(634\) | 2757.80 | − | 8487.63i | 0.172754 | − | 0.531682i | ||||
\(635\) | 18958.4 | − | 6159.97i | 1.18479 | − | 0.384962i | ||||
\(636\) | −113.519 | + | 82.4765i | −0.00707756 | + | 0.00514215i | ||||
\(637\) | −7685.37 | − | 2935.19i | −0.478030 | − | 0.182569i | ||||
\(638\) | −1258.72 | − | 7366.18i | −0.0781082 | − | 0.457100i | ||||
\(639\) | 7115.44i | 0.440505i | ||||||||
\(640\) | −5017.58 | + | 3645.48i | −0.309902 | + | 0.225157i | ||||
\(641\) | −3954.62 | − | 12171.1i | −0.243679 | − | 0.749966i | −0.995851 | − | 0.0909993i | \(-0.970994\pi\) |
0.752172 | − | 0.658966i | \(-0.229006\pi\) | |||||||
\(642\) | 8264.20 | + | 2685.20i | 0.508040 | + | 0.165072i | ||||
\(643\) | −12942.2 | + | 17813.4i | −0.793764 | + | 1.09252i | 0.199865 | + | 0.979824i | \(0.435950\pi\) |
−0.993629 | + | 0.112700i | \(0.964050\pi\) | |||||||
\(644\) | 1794.20 | − | 2469.50i | 0.109785 | − | 0.151105i | ||||
\(645\) | −9296.12 | − | 3020.49i | −0.567495 | − | 0.184390i | ||||
\(646\) | 10102.0 | + | 31090.8i | 0.615260 | + | 1.89358i | ||||
\(647\) | −11489.9 | + | 8347.90i | −0.698167 | + | 0.507248i | −0.879335 | − | 0.476204i | \(-0.842012\pi\) |
0.181167 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(648\) | 1958.49i | 0.118730i | ||||||||
\(649\) | 4038.52 | − | 8170.21i | 0.244261 | − | 0.494158i | ||||
\(650\) | −2122.40 | + | 5557.18i | −0.128073 | + | 0.335339i | ||||
\(651\) | 1032.64 | − | 750.260i | 0.0621698 | − | 0.0451690i | ||||
\(652\) | −1709.28 | + | 555.378i | −0.102669 | + | 0.0333593i | ||||
\(653\) | 8350.10 | − | 25699.0i | 0.500405 | − | 1.54009i | −0.307955 | − | 0.951401i | \(-0.599645\pi\) |
0.808361 | − | 0.588688i | \(-0.200355\pi\) | |||||||
\(654\) | 10296.6 | + | 7480.93i | 0.615641 | + | 0.447290i | ||||
\(655\) | −7020.37 | + | 9662.71i | −0.418792 | + | 0.576417i | ||||
\(656\) | 3281.82 | + | 1066.33i | 0.195325 | + | 0.0634651i | ||||
\(657\) | 4814.60 | − | 1564.36i | 0.285899 | − | 0.0928941i | ||||
\(658\) | 5369.82 | + | 7390.92i | 0.318142 | + | 0.437885i | ||||
\(659\) | 1957.86 | 0.115732 | 0.0578661 | − | 0.998324i | \(-0.481570\pi\) | ||||
0.0578661 | + | 0.998324i | \(0.481570\pi\) | |||||||
\(660\) | 2567.76 | + | 2506.04i | 0.151439 | + | 0.147799i | ||||
\(661\) | − | 12936.0i | − | 0.761198i | −0.924740 | − | 0.380599i | \(-0.875718\pi\) | ||
0.924740 | − | 0.380599i | \(-0.124282\pi\) | |||||||
\(662\) | 2477.49 | − | 1800.00i | 0.145454 | − | 0.105678i | ||||
\(663\) | 745.356 | − | 14699.1i | 0.0436610 | − | 0.861035i | ||||
\(664\) | −1432.03 | + | 4407.34i | −0.0836951 | + | 0.257587i | ||||
\(665\) | 13502.4 | − | 18584.4i | 0.787368 | − | 1.08372i | ||||
\(666\) | −5979.97 | − | 4344.70i | −0.347927 | − | 0.252784i | ||||
\(667\) | 2588.22 | − | 7965.71i | 0.150249 | − | 0.462419i | ||||
\(668\) | 4749.48 | − | 1543.20i | 0.275094 | − | 0.0893834i | ||||
\(669\) | −4022.51 | − | 5536.51i | −0.232465 | − | 0.319961i | ||||
\(670\) | 21153.7i | 1.21976i | ||||||||
\(671\) | −14759.1 | + | 15122.6i | −0.849133 | + | 0.870045i | ||||
\(672\) | −4136.78 | −0.237470 | ||||||||
\(673\) | −4827.35 | + | 3507.27i | −0.276494 | + | 0.200885i | −0.717387 | − | 0.696675i | \(-0.754662\pi\) |
0.440893 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(674\) | 23551.7 | − | 7652.43i | 1.34596 | − | 0.437330i | ||||
\(675\) | −2248.71 | + | 6920.80i | −0.128226 | + | 0.394640i | ||||
\(676\) | −1136.08 | − | 5257.11i | −0.0646382 | − | 0.299107i | ||||
\(677\) | 19306.9 | + | 14027.3i | 1.09605 | + | 0.796326i | 0.980411 | − | 0.196965i | \(-0.0631086\pi\) |
0.115639 | + | 0.993291i | \(0.463109\pi\) | |||||||
\(678\) | −11958.4 | − | 3885.54i | −0.677377 | − | 0.220093i | ||||
\(679\) | 189.585 | + | 583.483i | 0.0107152 | + | 0.0329779i | ||||
\(680\) | −27844.2 | + | 20230.0i | −1.57026 | + | 1.14086i | ||||
\(681\) | − | 5995.83i | − | 0.337387i | ||||||
\(682\) | 2530.31 | + | 1250.73i | 0.142068 | + | 0.0702241i | ||||
\(683\) | 3289.66i | 0.184298i | 0.995745 | + | 0.0921490i | \(0.0293736\pi\) | ||||
−0.995745 | + | 0.0921490i | \(0.970626\pi\) | |||||||
\(684\) | 3433.29 | + | 4725.52i | 0.191923 | + | 0.264159i | ||||
\(685\) | 128.170 | + | 394.466i | 0.00714908 | + | 0.0220026i | ||||
\(686\) | 4885.99 | − | 15037.5i | 0.271936 | − | 0.836932i | ||||
\(687\) | 10197.1 | − | 14035.1i | 0.566294 | − | 0.779437i | ||||
\(688\) | 7563.10 | + | 5494.91i | 0.419100 | + | 0.304494i | ||||
\(689\) | 561.675 | − | 696.020i | 0.0310568 | − | 0.0384852i | ||||
\(690\) | −2818.21 | − | 8673.55i | −0.155489 | − | 0.478546i | ||||
\(691\) | 6387.32 | + | 8791.40i | 0.351643 | + | 0.483995i | 0.947797 | − | 0.318875i | \(-0.103305\pi\) |
−0.596154 | + | 0.802870i | \(0.703305\pi\) | |||||||
\(692\) | −3861.23 | −0.212112 | ||||||||
\(693\) | 1429.65 | + | 8366.52i | 0.0783664 | + | 0.458611i | ||||
\(694\) | 3115.73i | 0.170420i | ||||||||
\(695\) | 19639.4 | + | 27031.3i | 1.07189 | + | 1.47533i | ||||
\(696\) | −6113.94 | + | 1986.54i | −0.332971 | + | 0.108189i | ||||
\(697\) | 8928.80 | + | 2901.14i | 0.485226 | + | 0.157659i | ||||
\(698\) | −14358.7 | − | 10432.2i | −0.778631 | − | 0.565709i | ||||
\(699\) | −12949.2 | − | 9408.18i | −0.700695 | − | 0.509084i | ||||
\(700\) | 1622.96 | + | 527.330i | 0.0876313 | + | 0.0284731i | ||||
\(701\) | −6461.11 | − | 19885.2i | −0.348121 | − | 1.07141i | −0.959892 | − | 0.280371i | \(-0.909543\pi\) |
0.611771 | − | 0.791035i | \(-0.290457\pi\) | |||||||
\(702\) | 3886.30 | + | 14406.1i | 0.208945 | + | 0.774536i | ||||
\(703\) | −23160.5 | −1.24255 | ||||||||
\(704\) | −9463.98 | − | 18028.6i | −0.506658 | − | 0.965168i | ||||
\(705\) | −12035.6 | −0.642959 | ||||||||
\(706\) | 20656.6 | − | 15007.9i | 1.10116 | − | 0.800042i | ||||
\(707\) | 15769.7 | − | 5123.89i | 0.838870 | − | 0.272565i | ||||
\(708\) | −1747.11 | − | 567.671i | −0.0927409 | − | 0.0301333i | ||||
\(709\) | 8762.34 | − | 12060.3i | 0.464142 | − | 0.638836i | −0.511220 | − | 0.859450i | \(-0.670806\pi\) |
0.975361 | + | 0.220614i | \(0.0708061\pi\) | |||||||
\(710\) | 7331.33 | − | 10090.7i | 0.387521 | − | 0.533377i | ||||
\(711\) | 6747.71 | − | 20767.3i | 0.355919 | − | 1.09541i | ||||
\(712\) | −494.173 | − | 1520.91i | −0.0260111 | − | 0.0800540i | ||||
\(713\) | 1859.46 | + | 2559.32i | 0.0976679 | + | 0.134428i | ||||
\(714\) | 9575.06 | 0.501874 | ||||||||
\(715\) | −19962.4 | − | 11159.3i | −1.04413 | − | 0.583687i | ||||
\(716\) | 8081.24 | 0.421802 | ||||||||
\(717\) | 12366.9 | + | 17021.5i | 0.644140 | + | 0.886583i | ||||
\(718\) | −8864.40 | − | 27281.8i | −0.460747 | − | 1.41803i | ||||
\(719\) | −10114.9 | + | 31130.3i | −0.524646 | + | 1.61469i | 0.240369 | + | 0.970682i | \(0.422732\pi\) |
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(720\) | 5429.72 | − | 7473.36i | 0.281047 | − | 0.386828i | ||||
\(721\) | −5839.02 | + | 8036.72i | −0.301604 | + | 0.415122i | ||||
\(722\) | −24104.1 | − | 7831.89i | −1.24247 | − | 0.403702i | ||||
\(723\) | −9471.27 | + | 3077.40i | −0.487193 | + | 0.158298i | ||||
\(724\) | −9446.68 | + | 6863.41i | −0.484921 | + | 0.352316i | ||||
\(725\) | 4682.38 | 0.239861 | ||||||||
\(726\) | 7484.39 | − | 5720.97i | 0.382606 | − | 0.292459i | ||||
\(727\) | 26471.9 | 1.35047 | 0.675234 | − | 0.737604i | \(-0.264043\pi\) | ||||
0.675234 | + | 0.737604i | \(0.264043\pi\) | |||||||
\(728\) | 14418.0 | − | 3889.52i | 0.734022 | − | 0.198015i | ||||
\(729\) | 2944.05 | + | 9060.85i | 0.149573 | + | 0.460339i | ||||
\(730\) | −8439.61 | − | 2742.19i | −0.427896 | − | 0.139032i | ||||
\(731\) | 20576.8 | + | 14949.9i | 1.04112 | + | 0.756420i | ||||
\(732\) | 3445.82 | + | 2503.54i | 0.173991 | + | 0.126412i | ||||
\(733\) | −12469.7 | − | 4051.66i | −0.628349 | − | 0.204163i | −0.0225052 | − | 0.999747i | \(-0.507164\pi\) |
−0.605843 | + | 0.795584i | \(0.707164\pi\) | |||||||
\(734\) | 20954.7 | − | 6808.60i | 1.05375 | − | 0.342384i | ||||
\(735\) | 4144.46 | + | 5704.37i | 0.207988 | + | 0.286270i | ||||
\(736\) | − | 10252.7i | − | 0.513476i | ||||||
\(737\) | −24233.6 | − | 3536.63i | −1.21120 | − | 0.176762i | ||||
\(738\) | −3804.23 | −0.189750 | ||||||||
\(739\) | 12922.7 | + | 17786.5i | 0.643259 | + | 0.885370i | 0.998784 | − | 0.0492969i | \(-0.0156981\pi\) |
−0.355525 | + | 0.934667i | \(0.615698\pi\) | |||||||
\(740\) | −1765.52 | − | 5433.71i | −0.0877050 | − | 0.269928i | ||||
\(741\) | 14542.3 | + | 11735.3i | 0.720950 | + | 0.581792i | ||||
\(742\) | 470.733 | + | 342.008i | 0.0232900 | + | 0.0169212i | ||||
\(743\) | −16104.7 | + | 22166.2i | −0.795185 | + | 1.09448i | 0.198258 | + | 0.980150i | \(0.436472\pi\) |
−0.993443 | + | 0.114328i | \(0.963528\pi\) | |||||||
\(744\) | 750.320 | − | 2309.25i | 0.0369732 | − | 0.113792i | ||||
\(745\) | 10456.6 | + | 32182.0i | 0.514228 | + | 1.58263i | ||||
\(746\) | 119.605 | + | 164.622i | 0.00587003 | + | 0.00807940i | ||||
\(747\) | − | 3384.00i | − | 0.165748i | ||||||
\(748\) | −4339.48 | − | 8266.57i | −0.212122 | − | 0.404085i | ||||
\(749\) | 15888.6i | 0.775110i | ||||||||
\(750\) | −5447.69 | + | 3957.98i | −0.265229 | + | 0.192700i | ||||
\(751\) | 10619.2 | + | 32682.4i | 0.515977 | + | 1.58801i | 0.781498 | + | 0.623908i | \(0.214456\pi\) |
−0.265521 | + | 0.964105i | \(0.585544\pi\) | |||||||
\(752\) | 10947.6 | + | 3557.10i | 0.530876 | + | 0.172492i | ||||
\(753\) | −29.6906 | − | 21.5715i | −0.00143690 | − | 0.00104397i | ||||
\(754\) | 8043.23 | − | 5242.75i | 0.388484 | − | 0.253222i | ||||
\(755\) | 10876.2 | − | 33473.5i | 0.524272 | − | 1.61354i | ||||
\(756\) | 4070.87 | − | 1322.71i | 0.195841 | − | 0.0636327i | ||||
\(757\) | 12226.3 | − | 8882.95i | 0.587019 | − | 0.426494i | −0.254229 | − | 0.967144i | \(-0.581822\pi\) |
0.841248 | + | 0.540650i | \(0.181822\pi\) | |||||||
\(758\) | −19591.7 | −0.938787 | ||||||||
\(759\) | 10407.6 | − | 1778.42i | 0.497722 | − | 0.0850496i | ||||
\(760\) | − | 43698.1i | − | 2.08565i | ||||||
\(761\) | −16035.5 | − | 22071.0i | −0.763847 | − | 1.05135i | −0.996884 | − | 0.0788778i | \(-0.974866\pi\) |
0.233037 | − | 0.972468i | \(-0.425134\pi\) | |||||||
\(762\) | −10033.2 | + | 3259.98i | −0.476987 | + | 0.154982i | ||||
\(763\) | −7191.36 | + | 22132.7i | −0.341212 | + | 1.05014i | ||||
\(764\) | −1.85679 | − | 1.34904i | −8.79271e−5 | − | 6.38827e-5i | ||||
\(765\) | 14772.6 | − | 20332.7i | 0.698174 | − | 0.960954i | ||||
\(766\) | −1687.56 | + | 5193.77i | −0.0796005 | + | 0.244985i | ||||
\(767\) | 11694.2 | + | 592.983i | 0.550524 | + | 0.0279157i | ||||
\(768\) | −8195.01 | + | 5954.02i | −0.385042 | + | 0.279749i | ||||
\(769\) | 27744.9i | 1.30105i | 0.759486 | + | 0.650524i | \(0.225451\pi\) | ||||
−0.759486 | + | 0.650524i | \(0.774549\pi\) | |||||||
\(770\) | 6592.91 | − | 13337.9i | 0.308561 | − | 0.624241i | ||||
\(771\) | −13671.2 | −0.638595 | ||||||||
\(772\) | 530.331 | + | 729.938i | 0.0247241 | + | 0.0340298i | ||||
\(773\) | 13819.4 | − | 4490.21i | 0.643015 | − | 0.208928i | 0.0306833 | − | 0.999529i | \(-0.490232\pi\) |
0.612332 | + | 0.790601i | \(0.290232\pi\) | |||||||
\(774\) | −9801.83 | − | 3184.81i | −0.455193 | − | 0.147901i | ||||
\(775\) | −1039.53 | + | 1430.78i | −0.0481818 | + | 0.0663165i | ||||
\(776\) | 944.171 | + | 685.980i | 0.0436775 | + | 0.0317336i | ||||
\(777\) | −2096.26 | + | 6451.64i | −0.0967864 | + | 0.297878i | ||||
\(778\) | 1211.83 | − | 393.748i | 0.0558436 | − | 0.0181447i | ||||
\(779\) | −9643.40 | + | 7006.34i | −0.443531 | + | 0.322244i | ||||
\(780\) | −1644.69 | + | 4306.36i | −0.0754990 | + | 0.197683i | ||||
\(781\) | 10334.2 | + | 10085.8i | 0.473478 | + | 0.462098i | ||||
\(782\) | 23731.0i | 1.08519i | ||||||||
\(783\) | 9501.78 | − | 6903.45i | 0.433673 | − | 0.315082i | ||||
\(784\) | −2083.91 | − | 6413.62i | −0.0949303 | − | 0.292165i | ||||
\(785\) | −30661.1 | − | 9962.40i | −1.39407 | − | 0.452960i | ||||
\(786\) | 3715.32 | − | 5113.70i | 0.168602 | − | 0.232060i | ||||
\(787\) | −22139.3 | + | 30472.2i | −1.00277 | + | 1.38020i | −0.0791629 | + | 0.996862i | \(0.525225\pi\) |
−0.923609 | + | 0.383336i | \(0.874775\pi\) | |||||||
\(788\) | 3267.89 | + | 1061.80i | 0.147733 | + | 0.0480014i | ||||
\(789\) | −4228.27 | − | 13013.3i | −0.190786 | − | 0.587180i | ||||
\(790\) | −30966.6 | + | 22498.5i | −1.39461 | + | 1.01324i | ||||
\(791\) | − | 22991.1i | − | 1.03346i | ||||||
\(792\) | 11555.0 | + | 11277.2i | 0.518420 | + | 0.505959i | ||||
\(793\) | −25361.9 | − | 9686.20i | −1.13572 | − | 0.433754i | ||||
\(794\) | 14513.8 | − | 10544.9i | 0.648708 | − | 0.471314i | ||||
\(795\) | −729.036 | + | 236.878i | −0.0325236 | + | 0.0105676i | ||||
\(796\) | 1615.41 | − | 4971.72i | 0.0719305 | − | 0.221379i | ||||
\(797\) | 29869.4 | + | 21701.4i | 1.32751 | + | 0.964496i | 0.999806 | + | 0.0197168i | \(0.00627646\pi\) |
0.327709 | + | 0.944779i | \(0.393724\pi\) | |||||||
\(798\) | −7145.72 | + | 9835.25i | −0.316987 | + | 0.436296i | ||||
\(799\) | 29785.1 | + | 9677.75i | 1.31880 | + | 0.428503i | ||||
\(800\) | 5451.20 | − | 1771.20i | 0.240911 | − | 0.0782768i | ||||
\(801\) | 686.397 | + | 944.744i | 0.0302780 | + | 0.0416740i | ||||
\(802\) | −36199.9 | −1.59384 | ||||||||
\(803\) | 4552.45 | − | 9209.94i | 0.200065 | − | 0.404747i | ||||
\(804\) | 4936.37i | 0.216533i | ||||||||
\(805\) | 13490.9 | − | 9801.69i | 0.590672 | − | 0.429148i | ||||
\(806\) | −183.647 | + | 3621.68i | −0.00802565 | + | 0.158273i | ||||
\(807\) | −2887.30 | + | 8886.20i | −0.125945 | + | 0.387619i | ||||
\(808\) | 18539.9 | − | 25518.0i | 0.807216 | − | 1.11104i | ||||
\(809\) | −21393.3 | − | 15543.1i | −0.929724 | − | 0.675484i | 0.0162012 | − | 0.999869i | \(-0.494843\pi\) |
−0.945925 | + | 0.324385i | \(0.894843\pi\) | |||||||
\(810\) | −774.688 | + | 2384.24i | −0.0336046 | + | 0.103424i | ||||
\(811\) | −20335.6 | + | 6607.44i | −0.880493 | + | 0.286090i | −0.714162 | − | 0.699980i | \(-0.753192\pi\) |
−0.166331 | + | 0.986070i | \(0.553192\pi\) | |||||||
\(812\) | −1618.89 | − | 2228.20i | −0.0699652 | − | 0.0962988i | ||||
\(813\) | 17174.5i | 0.740879i | ||||||||
\(814\) | −14786.4 | + | 2526.66i | −0.636687 | + | 0.108796i | ||||
\(815\) | −9818.32 | −0.421989 | ||||||||
\(816\) | 9760.50 | − | 7091.42i | 0.418733 | − | 0.304227i | ||||
\(817\) | −30712.3 | + | 9979.04i | −1.31516 | + | 0.427323i | ||||
\(818\) | 2202.84 | − | 6779.64i | 0.0941570 | − | 0.289785i | ||||
\(819\) | −9135.51 | + | 5954.72i | −0.389769 | + | 0.254059i | ||||
\(820\) | −2378.88 | − | 1728.36i | −0.101310 | − | 0.0736060i | ||||
\(821\) | 4860.87 | + | 1579.39i | 0.206633 | + | 0.0671390i | 0.410505 | − | 0.911859i | \(-0.365353\pi\) |
−0.203872 | + | 0.978998i | \(0.565353\pi\) | |||||||
\(822\) | −67.8301 | − | 208.759i | −0.00287816 | − | 0.00885806i | ||||
\(823\) | 18117.7 | − | 13163.3i | 0.767367 | − | 0.557524i | −0.133794 | − | 0.991009i | \(-0.542716\pi\) |
0.901161 | + | 0.433485i | \(0.142716\pi\) | |||||||
\(824\) | 18897.0i | 0.798916i | ||||||||
\(825\) | 2743.53 | + | 5226.33i | 0.115779 | + | 0.220555i | ||||
\(826\) | 7617.63i | 0.320885i | ||||||||
\(827\) | −7497.15 | − | 10318.9i | −0.315238 | − | 0.433887i | 0.621768 | − | 0.783201i | \(-0.286415\pi\) |
−0.937006 | + | 0.349314i | \(0.886415\pi\) | |||||||
\(828\) | 1310.28 | + | 4032.63i | 0.0549945 | + | 0.169256i | ||||
\(829\) | −2829.22 | + | 8707.44i | −0.118532 | + | 0.364803i | −0.992667 | − | 0.120879i | \(-0.961429\pi\) |
0.874135 | + | 0.485682i | \(0.161429\pi\) | |||||||
\(830\) | −3486.67 | + | 4798.99i | −0.145812 | + | 0.200693i | ||||
\(831\) | 5491.54 | + | 3989.83i | 0.229241 | + | 0.166553i | ||||
\(832\) | 16428.6 | − | 20358.1i | 0.684565 | − | 0.848305i | ||||
\(833\) | −5669.67 | − | 17449.4i | −0.235825 | − | 0.725795i | ||||
\(834\) | −10393.6 | − | 14305.5i | −0.431534 | − | 0.593956i | ||||
\(835\) | 27281.6 | 1.13068 | ||||||||
\(836\) | 11729.7 | + | 1711.82i | 0.485262 | + | 0.0708189i | ||||
\(837\) | 4436.06i | 0.183193i | ||||||||
\(838\) | −18879.1 | − | 25984.9i | −0.778243 | − | 1.07116i | ||||
\(839\) | −10725.5 | + | 3484.94i | −0.441343 | + | 0.143401i | −0.521255 | − | 0.853401i | \(-0.674536\pi\) |
0.0799121 | + | 0.996802i | \(0.474536\pi\) | |||||||
\(840\) | −12172.7 | − | 3955.14i | −0.499996 | − | 0.162458i | ||||
\(841\) | 13617.2 | + | 9893.45i | 0.558332 | + | 0.405652i | ||||
\(842\) | −41.9263 | − | 30.4612i | −0.00171600 | − | 0.00124675i | ||||
\(843\) | −14227.8 | − | 4622.90i | −0.581296 | − | 0.188875i | ||||
\(844\) | 2505.31 | + | 7710.56i | 0.102176 | + | 0.314465i | ||||
\(845\) | 2972.19 | − | 29231.8i | 0.121002 | − | 1.19007i | ||||
\(846\) | −12690.3 | −0.515723 | ||||||||
\(847\) | 14177.7 | + | 9782.77i | 0.575148 | + | 0.396859i | ||||
\(848\) | 733.145 | 0.0296890 | ||||||||
\(849\) | 1412.25 | − | 1026.06i | 0.0570888 | − | 0.0414774i | ||||
\(850\) | −12617.4 | + | 4099.66i | −0.509147 | + | 0.165432i | ||||
\(851\) | −15989.8 | − | 5195.42i | −0.644095 | − | 0.209279i | ||||
\(852\) | 1710.82 | − | 2354.75i | 0.0687932 | − | 0.0946858i | ||||
\(853\) | −15020.3 | + | 20673.6i | −0.602912 | + | 0.829837i | −0.995971 | − | 0.0896764i | \(-0.971417\pi\) |
0.393059 | + | 0.919513i | \(0.371417\pi\) | |||||||
\(854\) | 5457.87 | − | 16797.6i | 0.218694 | − | 0.673070i | ||||
\(855\) | 9860.64 | + | 30347.9i | 0.394417 | + | 1.21389i | ||||
\(856\) | 17765.4 | + | 24452.0i | 0.709357 | + | 0.976347i | ||||
\(857\) | −11712.6 | −0.466856 | −0.233428 | − | 0.972374i | \(-0.574994\pi\) | ||||
−0.233428 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(858\) | 10564.5 | + | 5905.75i | 0.420358 | + | 0.234987i | ||||
\(859\) | 13886.5 | 0.551573 | 0.275786 | − | 0.961219i | \(-0.411062\pi\) | ||||
0.275786 | + | 0.961219i | \(0.411062\pi\) | |||||||
\(860\) | −4682.39 | − | 6444.76i | −0.185661 | − | 0.255540i | ||||
\(861\) | 1078.88 | + | 3320.44i | 0.0427038 | + | 0.131429i | ||||
\(862\) | −40.9558 | + | 126.049i | −0.00161828 | + | 0.00498056i | ||||
\(863\) | −19461.4 | + | 26786.4i | −0.767642 | + | 1.05657i | 0.228898 | + | 0.973451i | \(0.426488\pi\) |
−0.996540 | + | 0.0831182i | \(0.973512\pi\) | |||||||
\(864\) | 8450.55 | − | 11631.2i | 0.332747 | − | 0.457987i | ||||
\(865\) | −20061.5 | − | 6518.36i | −0.788567 | − | 0.256221i | ||||
\(866\) | −6418.51 | + | 2085.50i | −0.251859 | + | 0.0818339i | ||||
\(867\) | 14616.0 | − | 10619.1i | 0.572531 | − | 0.415968i | ||||
\(868\) | 1040.27 | 0.0406787 | ||||||||
\(869\) | −20597.1 | − | 39236.8i | −0.804036 | − | 1.53166i | ||||
\(870\) | −8228.81 | −0.320670 | ||||||||
\(871\) | −8195.12 | − | 30378.5i | −0.318807 | − | 1.18179i | ||||
\(872\) | 13679.9 | + | 42102.3i | 0.531260 | + | 1.63505i | ||||
\(873\) | −810.512 | − | 263.351i | −0.0314223 | − | 0.0102097i | ||||
\(874\) | −24375.8 | − | 17710.1i | −0.943393 | − | 0.685415i | ||||
\(875\) | −9961.02 | − | 7237.11i | −0.384850 | − | 0.279610i | ||||
\(876\) | −1969.45 | − | 639.912i | −0.0759606 | − | 0.0246811i | ||||
\(877\) | 36502.7 | − | 11860.4i | 1.40548 | − | 0.456669i | 0.494524 | − | 0.869164i | \(-0.335343\pi\) |
0.910960 | + | 0.412495i | \(0.135343\pi\) | |||||||
\(878\) | −17067.2 | − | 23490.9i | −0.656024 | − | 0.902940i | ||||
\(879\) | − | 8467.90i | − | 0.324932i | ||||||
\(880\) | −3157.66 | − | 18479.0i | −0.120960 | − | 0.707873i | ||||
\(881\) | −6570.59 | −0.251270 | −0.125635 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(882\) | 4369.92 | + | 6014.68i | 0.166829 | + | 0.229620i | ||||
\(883\) | 702.044 | + | 2160.67i | 0.0267561 | + | 0.0823469i | 0.963543 | − | 0.267554i | \(-0.0862153\pi\) |
−0.936787 | + | 0.349901i | \(0.886215\pi\) | |||||||
\(884\) | 7532.92 | − | 9334.70i | 0.286606 | − | 0.355158i | ||||
\(885\) | −8119.02 | − | 5898.81i | −0.308382 | − | 0.224052i | ||||
\(886\) | 2116.41 | − | 2912.99i | 0.0802508 | − | 0.110456i | ||||
\(887\) | 191.647 | − | 589.829i | 0.00725465 | − | 0.0223275i | −0.947364 | − | 0.320159i | \(-0.896264\pi\) |
0.954618 | + | 0.297832i | \(0.0962635\pi\) | |||||||
\(888\) | 3987.65 | + | 12272.7i | 0.150695 | + | 0.463790i | ||||
\(889\) | −11338.2 | − | 15605.6i | −0.427750 | − | 0.588747i | ||||
\(890\) | − | 2047.00i | − | 0.0770963i | ||||||
\(891\) | −2601.87 | − | 1286.10i | −0.0978292 | − | 0.0483568i | ||||
\(892\) | − | 5577.41i | − | 0.209356i | ||||||
\(893\) | −32168.9 | + | 23372.0i | −1.20548 | + | 0.875829i | ||||
\(894\) | −5533.83 | − | 17031.4i | −0.207023 | − | 0.637153i | ||||
\(895\) | 41987.0 | + | 13642.4i | 1.56813 | + | 0.509515i | ||||
\(896\) | 4855.36 | + | 3527.63i | 0.181034 | + | 0.131529i | ||||
\(897\) | 7407.40 | + | 11364.2i | 0.275726 | + | 0.423008i | ||||
\(898\) | −990.894 | + | 3049.66i | −0.0368224 | + | 0.113328i | ||||
\(899\) | 2714.69 | − | 882.056i | 0.100712 | − | 0.0327233i | ||||
\(900\) | −1917.74 | + | 1393.32i | −0.0710273 | + | 0.0516044i | ||||
\(901\) | 1994.66 | 0.0737532 | ||||||||
\(902\) | −5392.32 | + | 5525.12i | −0.199052 | + | 0.203954i | ||||
\(903\) | 9458.51i | 0.348571i | ||||||||
\(904\) | −25706.9 | − | 35382.5i | −0.945796 | − | 1.30178i | ||||
\(905\) | −60667.9 | + | 19712.2i | −2.22836 | + | 0.724039i | ||||
\(906\) | −5755.90 | + | 17714.8i | −0.211067 | + | 0.649598i | ||||
\(907\) | 23721.0 | + | 17234.3i | 0.868405 | + | 0.630933i | 0.930158 | − | 0.367158i | \(-0.119669\pi\) |
−0.0617536 | + | 0.998091i | \(0.519669\pi\) | |||||||
\(908\) | 2872.25 | − | 3953.31i | 0.104977 | − | 0.144488i | ||||
\(909\) | −7117.55 | + | 21905.6i | −0.259708 | + | 0.799298i | ||||
\(910\) | 19090.8 | + | 968.050i | 0.695445 | + | 0.0352643i | ||||
\(911\) | −18124.1 | + | 13168.0i | −0.659143 | + | 0.478896i | −0.866374 | − | 0.499396i | \(-0.833555\pi\) |
0.207230 | + | 0.978292i | \(0.433555\pi\) | |||||||
\(912\) | 15317.9i | 0.556171i | ||||||||
\(913\) | −4914.79 | − | 4796.66i | −0.178155 | − | 0.173873i | ||||
\(914\) | 38795.9 | 1.40400 | ||||||||
\(915\) | 13676.8 | + | 18824.5i | 0.494144 | + | 0.680131i | ||||
\(916\) | 13446.8 | − | 4369.13i | 0.485038 | − | 0.157598i | ||||
\(917\) | 10992.0 | + | 3571.50i | 0.395841 | + | 0.128617i | ||||
\(918\) | −19559.8 | + | 26921.7i | −0.703235 | + | 0.967919i | ||||
\(919\) | −9307.98 | − | 6762.64i | −0.334104 | − | 0.242741i | 0.408066 | − | 0.912953i | \(-0.366203\pi\) |
−0.742170 | + | 0.670211i | \(0.766203\pi\) | |||||||
\(920\) | 9802.48 | − | 30168.9i | 0.351281 | − | 1.08113i | ||||
\(921\) | −11828.2 | + | 3843.22i | −0.423184 | + | 0.137501i | ||||
\(922\) | −11853.7 | + | 8612.20i | −0.423406 | + | 0.307622i | ||||
\(923\) | −6619.19 | + | 17331.4i | −0.236049 | + | 0.618059i | ||||
\(924\) | 1538.51 | − | 3112.51i | 0.0547762 | − | 0.110816i | ||||
\(925\) | − | 9399.11i | − | 0.334098i | ||||||
\(926\) | −9637.30 | + | 7001.91i | −0.342010 | + | 0.248485i | ||||
\(927\) | −4264.17 | − | 13123.8i | −0.151083 | − | 0.464985i | ||||
\(928\) | −8798.11 | − | 2858.68i | −0.311220 | − | 0.101121i | ||||
\(929\) | −6761.78 | + | 9306.79i | −0.238802 | + | 0.328682i | −0.911550 | − | 0.411189i | \(-0.865114\pi\) |
0.672748 | + | 0.739871i | \(0.265114\pi\) | |||||||
\(930\) | 1826.86 | − | 2514.46i | 0.0644141 | − | 0.0886584i | ||||
\(931\) | 22154.8 | + | 7198.52i | 0.779907 | + | 0.253407i | ||||
\(932\) | −4031.10 | − | 12406.4i | −0.141677 | − | 0.436037i | ||||
\(933\) | −4493.79 | + | 3264.93i | −0.157685 | + | 0.114565i | ||||
\(934\) | − | 32876.4i | − | 1.15176i | ||||||
\(935\) | −8590.99 | − | 50275.7i | −0.300487 | − | 1.75849i | ||||
\(936\) | −7401.12 | + | 19378.7i | −0.258454 | + | 0.676724i | ||||
\(937\) | −27882.3 | + | 20257.7i | −0.972120 | + | 0.706286i | −0.955934 | − | 0.293583i | \(-0.905152\pi\) |
−0.0161860 | + | 0.999869i | \(0.505152\pi\) | |||||||
\(938\) | 19467.9 | − | 6325.51i | 0.677665 | − | 0.220187i | ||||
\(939\) | 5672.96 | − | 17459.6i | 0.197156 | − | 0.606785i | ||||
\(940\) | −7935.57 | − | 5765.53i | −0.275351 | − | 0.200054i | ||||
\(941\) | 14100.3 | − | 19407.3i | 0.488475 | − | 0.672329i | −0.491631 | − | 0.870804i | \(-0.663599\pi\) |
0.980106 | + | 0.198475i | \(0.0635989\pi\) | |||||||
\(942\) | 16226.5 | + | 5272.30i | 0.561239 | + | 0.182358i | ||||
\(943\) | −8229.43 | + | 2673.90i | −0.284186 | + | 0.0923376i | ||||
\(944\) | 5641.72 | + | 7765.16i | 0.194515 | + | 0.267727i | ||||
\(945\) | 23383.6 | 0.804941 | ||||||||
\(946\) | −18519.1 | + | 9721.48i | −0.636478 | + | 0.334115i | ||||
\(947\) | 270.862i | 0.00929443i | 0.999989 | + | 0.00464722i | \(0.00147926\pi\) | ||||
−0.999989 | + | 0.00464722i | \(0.998521\pi\) | |||||||
\(948\) | −7226.30 | + | 5250.21i | −0.247573 | + | 0.179872i | ||||
\(949\) | 13182.4 | + | 668.445i | 0.450914 | + | 0.0228648i | ||||
\(950\) | 5205.15 | − | 16019.8i | 0.177766 | − | 0.547106i | ||||
\(951\) | 6687.32 | − | 9204.30i | 0.228024 | − | 0.313849i | ||||
\(952\) | 26944.0 | + | 19576.0i | 0.917290 | + | 0.666450i | ||||
\(953\) | −14775.2 | + | 45473.4i | −0.502220 | + | 1.54567i | 0.303175 | + | 0.952935i | \(0.401953\pi\) |
−0.805395 | + | 0.592739i | \(0.798047\pi\) | |||||||
\(954\) | −768.696 | + | 249.765i | −0.0260875 | + | 0.00847634i | ||||
\(955\) | −7.36978 | − | 10.1436i | −0.000249718 | − | 0.000343707i | ||||
\(956\) | 17147.3i | 0.580106i | ||||||||
\(957\) | 1375.76 | − | 9426.91i | 0.0464701 | − | 0.318421i | ||||
\(958\) | 12600.4 | 0.424947 | ||||||||
\(959\) | 324.705 | − | 235.912i | 0.0109336 | − | 0.00794369i | ||||
\(960\) | −21323.8 | + | 6928.52i | −0.716898 | + | 0.232934i | ||||
\(961\) | 8872.77 | − | 27307.6i | 0.297834 | − | 0.916639i | ||||
\(962\) | −10524.0 | − | 16145.5i | −0.352709 | − | 0.541113i | ||||
\(963\) | −17855.6 | − | 12972.9i | −0.597497 | − | 0.434107i | ||||
\(964\) | −7719.02 | − | 2508.06i | −0.257897 | − | 0.0837958i | ||||
\(965\) | 1523.15 | + | 4687.76i | 0.0508102 | + | 0.156378i | ||||
\(966\) | −7139.64 | + | 5187.25i | −0.237799 | + | 0.172771i | ||||
\(967\) | − | 41044.1i | − | 1.36493i | −0.730917 | − | 0.682466i | \(-0.760907\pi\) | ||
0.730917 | − | 0.682466i | \(-0.239093\pi\) | |||||||
\(968\) | 32757.3 | − | 797.036i | 1.08766 | − | 0.0264646i | ||||
\(969\) | 41675.3i | 1.38163i | ||||||||
\(970\) | 878.079 | + | 1208.57i | 0.0290654 | + | 0.0400051i | ||||
\(971\) | 13393.2 | + | 41220.0i | 0.442644 | + | 1.36232i | 0.885047 | + | 0.465502i | \(0.154126\pi\) |
−0.442402 | + | 0.896817i | \(0.645874\pi\) | |||||||
\(972\) | −2940.34 | + | 9049.43i | −0.0970282 | + | 0.298622i | ||||
\(973\) | 19004.5 | − | 26157.4i | 0.626162 | − | 0.861838i | ||||
\(974\) | 24270.3 | + | 17633.4i | 0.798430 | + | 0.580093i | ||||
\(975\) | −4762.50 | + | 5901.63i | −0.156433 | + | 0.193850i | ||||
\(976\) | −6876.95 | − | 21165.1i | −0.225539 | − | 0.694137i | ||||
\(977\) | 5644.27 | + | 7768.67i | 0.184827 | + | 0.254393i | 0.891369 | − | 0.453279i | \(-0.149746\pi\) |
−0.706542 | + | 0.707671i | \(0.749746\pi\) | |||||||
\(978\) | 5196.05 | 0.169889 | ||||||||
\(979\) | 2345.04 | + | 342.234i | 0.0765556 | + | 0.0111725i | ||||
\(980\) | 5746.50i | 0.187312i | ||||||||
\(981\) | −19001.1 | − | 26152.7i | −0.618408 | − | 0.851165i | ||||
\(982\) | 23406.1 | − | 7605.10i | 0.760609 | − | 0.247137i | ||||
\(983\) | 9713.33 | + | 3156.05i | 0.315165 | + | 0.102403i | 0.462328 | − | 0.886709i | \(-0.347014\pi\) |
−0.147163 | + | 0.989112i | \(0.547014\pi\) | |||||||
\(984\) | 5373.01 | + | 3903.72i | 0.174070 | + | 0.126470i | ||||
\(985\) | 15186.2 | + | 11033.4i | 0.491242 | + | 0.356908i | ||||
\(986\) | 20364.3 | + | 6616.75i | 0.657738 | + | 0.213712i | ||||
\(987\) | 3598.96 | + | 11076.5i | 0.116065 | + | 0.357211i | ||||
\(988\) | 3966.65 | + | 14704.0i | 0.127729 | + | 0.473477i | ||||
\(989\) | −23442.1 | −0.753708 | ||||||||
\(990\) | 9606.13 | + | 18299.4i | 0.308387 | + | 0.587467i | ||||
\(991\) | −19662.3 | −0.630267 | −0.315133 | − | 0.949047i | \(-0.602049\pi\) | ||||
−0.315133 | + | 0.949047i | \(0.602049\pi\) | |||||||
\(992\) | 2826.77 | − | 2053.77i | 0.0904738 | − | 0.0657330i | ||||
\(993\) | 3712.91 | − | 1206.40i | 0.118656 | − | 0.0385537i | ||||
\(994\) | −11478.8 | − | 3729.70i | −0.366285 | − | 0.119013i | ||||
\(995\) | 16786.1 | − | 23104.1i | 0.534830 | − | 0.736130i | ||||
\(996\) | −813.642 | + | 1119.88i | −0.0258848 | + | 0.0356273i | ||||
\(997\) | 1677.16 | − | 5161.77i | 0.0532760 | − | 0.163967i | −0.920878 | − | 0.389850i | \(-0.872527\pi\) |
0.974154 | + | 0.225883i | \(0.0725268\pi\) | |||||||
\(998\) | 12375.8 | + | 38088.8i | 0.392534 | + | 1.20810i | ||||
\(999\) | −13857.5 | − | 19073.3i | −0.438872 | − | 0.604055i |
(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 | 143.4.n.a.25.12 | ✓ | 160 | |
11.4 | even | 5 | inner | 143.4.n.a.103.29 | yes | 160 | |
13.12 | even | 2 | inner | 143.4.n.a.25.29 | yes | 160 | |
143.103 | even | 10 | inner | 143.4.n.a.103.12 | yes | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.n.a.25.12 | ✓ | 160 | 1.1 | even | 1 | trivial | |
143.4.n.a.25.29 | yes | 160 | 13.12 | even | 2 | inner | |
143.4.n.a.103.12 | yes | 160 | 143.103 | even | 10 | inner | |
143.4.n.a.103.29 | yes | 160 | 11.4 | even | 5 | inner |