Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.13 | ||
Character | \(\chi\) | \(=\) | 169.23 |
Dual form | 169.4.e.h.147.13 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92949 | − | 1.11399i | 0.682179 | − | 0.393856i | −0.118496 | − | 0.992954i | \(-0.537807\pi\) |
0.800676 | + | 0.599098i | \(0.204474\pi\) | |||||||
\(3\) | 4.87434 | + | 8.44260i | 0.938066 | + | 1.62478i | 0.769072 | + | 0.639162i | \(0.220719\pi\) |
0.168994 | + | 0.985617i | \(0.445948\pi\) | |||||||
\(4\) | −1.51803 | + | 2.62931i | −0.189754 | + | 0.328664i | ||||
\(5\) | − | 8.20685i | − | 0.734043i | −0.930212 | − | 0.367022i | \(-0.880377\pi\) | ||
0.930212 | − | 0.367022i | \(-0.119623\pi\) | |||||||
\(6\) | 18.8100 | + | 10.8600i | 1.27986 | + | 0.738927i | ||||
\(7\) | 7.23560 | + | 4.17747i | 0.390686 | + | 0.225562i | 0.682457 | − | 0.730926i | \(-0.260911\pi\) |
−0.291772 | + | 0.956488i | \(0.594245\pi\) | |||||||
\(8\) | 24.5882i | 1.08666i | ||||||||
\(9\) | −34.0183 | + | 58.9214i | −1.25994 | + | 2.18228i | ||||
\(10\) | −9.14239 | − | 15.8351i | −0.289108 | − | 0.500749i | ||||
\(11\) | 8.39957 | − | 4.84949i | 0.230233 | − | 0.132925i | −0.380446 | − | 0.924803i | \(-0.624230\pi\) |
0.610680 | + | 0.791878i | \(0.290896\pi\) | |||||||
\(12\) | −29.5976 | −0.712009 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 18.6147 | 0.355357 | ||||||||
\(15\) | 69.2872 | − | 40.0030i | 1.19266 | − | 0.688581i | ||||
\(16\) | 15.2469 | + | 26.4084i | 0.238232 | + | 0.412630i | ||||
\(17\) | 22.3109 | − | 38.6437i | 0.318306 | − | 0.551322i | −0.661829 | − | 0.749655i | \(-0.730219\pi\) |
0.980135 | + | 0.198333i | \(0.0635528\pi\) | |||||||
\(18\) | 151.585i | 1.98494i | ||||||||
\(19\) | −75.9867 | − | 43.8709i | −0.917502 | − | 0.529720i | −0.0346647 | − | 0.999399i | \(-0.511036\pi\) |
−0.882837 | + | 0.469679i | \(0.844370\pi\) | |||||||
\(20\) | 21.5784 | + | 12.4583i | 0.241254 | + | 0.139288i | ||||
\(21\) | 81.4497i | 0.846370i | ||||||||
\(22\) | 10.8046 | − | 18.7141i | 0.104707 | − | 0.181358i | ||||
\(23\) | 53.5263 | + | 92.7102i | 0.485261 | + | 0.840496i | 0.999857 | − | 0.0169365i | \(-0.00539131\pi\) |
−0.514596 | + | 0.857433i | \(0.672058\pi\) | |||||||
\(24\) | −207.589 | + | 119.851i | −1.76558 | + | 1.01936i | ||||
\(25\) | 57.6475 | 0.461180 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −400.052 | −2.85149 | ||||||||
\(28\) | −21.9678 | + | 12.6831i | −0.148269 | + | 0.0856029i | ||||
\(29\) | 7.02150 | + | 12.1616i | 0.0449607 | + | 0.0778742i | 0.887630 | − | 0.460557i | \(-0.152350\pi\) |
−0.842669 | + | 0.538431i | \(0.819017\pi\) | |||||||
\(30\) | 89.1261 | − | 154.371i | 0.542404 | − | 0.939472i | ||||
\(31\) | 171.090i | 0.991247i | 0.868537 | + | 0.495624i | \(0.165060\pi\) | ||||
−0.868537 | + | 0.495624i | \(0.834940\pi\) | |||||||
\(32\) | −111.515 | − | 64.3831i | −0.616038 | − | 0.355670i | ||||
\(33\) | 81.8846 | + | 47.2761i | 0.431948 | + | 0.249385i | ||||
\(34\) | − | 99.4170i | − | 0.501467i | ||||||
\(35\) | 34.2839 | − | 59.3815i | 0.165573 | − | 0.286780i | ||||
\(36\) | −103.282 | − | 178.890i | −0.478157 | − | 0.828192i | ||||
\(37\) | 358.495 | − | 206.977i | 1.59287 | − | 0.919643i | 0.600057 | − | 0.799957i | \(-0.295144\pi\) |
0.992812 | − | 0.119686i | \(-0.0381889\pi\) | |||||||
\(38\) | −195.488 | −0.834534 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 201.792 | 0.797653 | ||||||||
\(41\) | 223.678 | − | 129.141i | 0.852017 | − | 0.491912i | −0.00931374 | − | 0.999957i | \(-0.502965\pi\) |
0.861331 | + | 0.508044i | \(0.169631\pi\) | |||||||
\(42\) | 90.7344 | + | 157.157i | 0.333348 | + | 0.577376i | ||||
\(43\) | 30.5359 | − | 52.8897i | 0.108295 | − | 0.187572i | −0.806785 | − | 0.590845i | \(-0.798794\pi\) |
0.915080 | + | 0.403273i | \(0.132128\pi\) | |||||||
\(44\) | 29.4468i | 0.100892i | ||||||||
\(45\) | 483.560 | + | 279.183i | 1.60188 | + | 0.924849i | ||||
\(46\) | 206.557 | + | 119.256i | 0.662070 | + | 0.382246i | ||||
\(47\) | 68.7115i | 0.213247i | 0.994299 | + | 0.106623i | \(0.0340039\pi\) | ||||
−0.994299 | + | 0.106623i | \(0.965996\pi\) | |||||||
\(48\) | −148.637 | + | 257.446i | −0.446955 | + | 0.774150i | ||||
\(49\) | −136.597 | − | 236.594i | −0.398243 | − | 0.689777i | ||||
\(50\) | 111.231 | − | 64.2190i | 0.314608 | − | 0.181639i | ||||
\(51\) | 435.004 | 1.19437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 328.701 | 0.851896 | 0.425948 | − | 0.904748i | \(-0.359941\pi\) | ||||
0.425948 | + | 0.904748i | \(0.359941\pi\) | |||||||
\(54\) | −771.899 | + | 445.656i | −1.94522 | + | 1.12308i | ||||
\(55\) | −39.7991 | − | 68.9340i | −0.0975728 | − | 0.169001i | ||||
\(56\) | −102.717 | + | 177.911i | −0.245109 | + | 0.424541i | ||||
\(57\) | − | 855.367i | − | 1.98765i | ||||||
\(58\) | 27.0959 | + | 15.6438i | 0.0613425 | + | 0.0354161i | ||||
\(59\) | 127.431 | + | 73.5721i | 0.281187 | + | 0.162344i | 0.633961 | − | 0.773365i | \(-0.281428\pi\) |
−0.352773 | + | 0.935709i | \(0.614761\pi\) | |||||||
\(60\) | 242.904i | 0.522645i | ||||||||
\(61\) | 48.9041 | − | 84.7045i | 0.102648 | − | 0.177792i | −0.810127 | − | 0.586255i | \(-0.800602\pi\) |
0.912775 | + | 0.408463i | \(0.133935\pi\) | |||||||
\(62\) | 190.593 | + | 330.117i | 0.390409 | + | 0.676208i | ||||
\(63\) | −492.286 | + | 284.221i | −0.984479 | + | 0.568389i | ||||
\(64\) | −530.839 | −1.03680 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 210.661 | 0.392888 | ||||||||
\(67\) | 586.817 | − | 338.799i | 1.07002 | − | 0.617774i | 0.141830 | − | 0.989891i | \(-0.454701\pi\) |
0.928186 | + | 0.372117i | \(0.121368\pi\) | |||||||
\(68\) | 67.7376 | + | 117.325i | 0.120800 | + | 0.209231i | ||||
\(69\) | −521.810 | + | 903.802i | −0.910414 | + | 1.57688i | ||||
\(70\) | − | 152.768i | − | 0.260847i | ||||||
\(71\) | −681.360 | − | 393.383i | −1.13891 | − | 0.657549i | −0.192749 | − | 0.981248i | \(-0.561740\pi\) |
−0.946160 | + | 0.323699i | \(0.895074\pi\) | |||||||
\(72\) | −1448.77 | − | 836.450i | −2.37138 | − | 1.36912i | ||||
\(73\) | − | 997.675i | − | 1.59958i | −0.600282 | − | 0.799788i | \(-0.704945\pi\) | ||
0.600282 | − | 0.799788i | \(-0.295055\pi\) | |||||||
\(74\) | 461.142 | − | 798.722i | 0.724415 | − | 1.25472i | ||||
\(75\) | 280.994 | + | 486.695i | 0.432618 | + | 0.749316i | ||||
\(76\) | 230.701 | − | 133.195i | 0.348200 | − | 0.201033i | ||||
\(77\) | 81.0345 | 0.119932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 383.897 | 0.546731 | 0.273366 | − | 0.961910i | \(-0.411863\pi\) | ||||
0.273366 | + | 0.961910i | \(0.411863\pi\) | |||||||
\(80\) | 216.729 | − | 125.129i | 0.302889 | − | 0.174873i | ||||
\(81\) | −1031.50 | − | 1786.60i | −1.41495 | − | 2.45076i | ||||
\(82\) | 287.724 | − | 498.353i | 0.387486 | − | 0.671145i | ||||
\(83\) | 519.718i | 0.687307i | 0.939096 | + | 0.343654i | \(0.111665\pi\) | ||||
−0.939096 | + | 0.343654i | \(0.888335\pi\) | |||||||
\(84\) | −214.157 | − | 123.643i | −0.278171 | − | 0.160602i | ||||
\(85\) | −317.143 | − | 183.103i | −0.404694 | − | 0.233650i | ||||
\(86\) | − | 136.067i | − | 0.170610i | ||||||
\(87\) | −68.4503 | + | 118.559i | −0.0843522 | + | 0.146102i | ||||
\(88\) | 119.240 | + | 206.530i | 0.144444 | + | 0.250184i | ||||
\(89\) | −591.687 | + | 341.611i | −0.704705 | + | 0.406862i | −0.809097 | − | 0.587675i | \(-0.800044\pi\) |
0.104393 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(90\) | 1244.03 | 1.45703 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −325.019 | −0.368321 | ||||||||
\(93\) | −1444.44 | + | 833.950i | −1.61056 | + | 0.929856i | ||||
\(94\) | 76.5442 | + | 132.578i | 0.0839887 | + | 0.145473i | ||||
\(95\) | −360.042 | + | 623.612i | −0.388837 | + | 0.673486i | ||||
\(96\) | − | 1255.30i | − | 1.33457i | ||||||
\(97\) | 300.765 | + | 173.647i | 0.314826 | + | 0.181765i | 0.649084 | − | 0.760717i | \(-0.275152\pi\) |
−0.334258 | + | 0.942482i | \(0.608486\pi\) | |||||||
\(98\) | −527.128 | − | 304.337i | −0.543346 | − | 0.313701i | ||||
\(99\) | 659.886i | 0.669909i | ||||||||
\(100\) | −87.5110 | + | 151.573i | −0.0875110 | + | 0.151573i | ||||
\(101\) | 277.397 | + | 480.466i | 0.273288 | + | 0.473348i | 0.969702 | − | 0.244292i | \(-0.0785556\pi\) |
−0.696414 | + | 0.717640i | \(0.745222\pi\) | |||||||
\(102\) | 839.338 | − | 484.592i | 0.814773 | − | 0.470409i | ||||
\(103\) | −1137.13 | −1.08781 | −0.543905 | − | 0.839147i | \(-0.683055\pi\) | ||||
−0.543905 | + | 0.839147i | \(0.683055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 668.445 | 0.621272 | ||||||||
\(106\) | 634.226 | − | 366.171i | 0.581146 | − | 0.335525i | ||||
\(107\) | 778.069 | + | 1347.66i | 0.702980 | + | 1.21760i | 0.967416 | + | 0.253193i | \(0.0814808\pi\) |
−0.264436 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(108\) | 607.293 | − | 1051.86i | 0.541082 | − | 0.937181i | ||||
\(109\) | − | 71.6448i | − | 0.0629572i | −0.999504 | − | 0.0314786i | \(-0.989978\pi\) | ||
0.999504 | − | 0.0314786i | \(-0.0100216\pi\) | |||||||
\(110\) | −153.584 | − | 88.6719i | −0.133124 | − | 0.0768594i | ||||
\(111\) | 3494.85 | + | 2017.75i | 2.98843 | + | 1.72537i | ||||
\(112\) | 254.774i | 0.214945i | ||||||||
\(113\) | 490.436 | − | 849.460i | 0.408286 | − | 0.707173i | −0.586411 | − | 0.810013i | \(-0.699460\pi\) |
0.994698 | + | 0.102841i | \(0.0327931\pi\) | |||||||
\(114\) | −952.873 | − | 1650.42i | −0.782849 | − | 1.35593i | ||||
\(115\) | 760.859 | − | 439.282i | 0.616961 | − | 0.356203i | ||||
\(116\) | −42.6355 | −0.0341259 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 327.836 | 0.255760 | ||||||||
\(119\) | 322.866 | − | 186.407i | 0.248715 | − | 0.143596i | ||||
\(120\) | 983.602 | + | 1703.65i | 0.748252 | + | 1.29601i | ||||
\(121\) | −618.465 | + | 1071.21i | −0.464662 | + | 0.804818i | ||||
\(122\) | − | 217.916i | − | 0.161714i | ||||||
\(123\) | 2180.57 | + | 1258.95i | 1.59850 | + | 0.922893i | ||||
\(124\) | −449.849 | − | 259.720i | −0.325787 | − | 0.188093i | ||||
\(125\) | − | 1498.96i | − | 1.07257i | ||||||
\(126\) | −633.241 | + | 1096.81i | −0.447727 | + | 0.775486i | ||||
\(127\) | −1088.65 | − | 1885.60i | −0.760649 | − | 1.31748i | −0.942517 | − | 0.334159i | \(-0.891548\pi\) |
0.181868 | − | 0.983323i | \(-0.441786\pi\) | |||||||
\(128\) | −132.133 | + | 76.2873i | −0.0912426 | + | 0.0526790i | ||||
\(129\) | 595.369 | 0.406351 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1919.81 | −1.28041 | −0.640207 | − | 0.768202i | \(-0.721152\pi\) | ||||
−0.640207 | + | 0.768202i | \(0.721152\pi\) | |||||||
\(132\) | −248.607 | + | 143.534i | −0.163928 | + | 0.0946438i | ||||
\(133\) | −366.539 | − | 634.865i | −0.238970 | − | 0.413908i | ||||
\(134\) | 754.839 | − | 1307.42i | 0.486628 | − | 0.842865i | ||||
\(135\) | 3283.17i | 2.09311i | ||||||||
\(136\) | 950.180 | + | 548.587i | 0.599098 | + | 0.345889i | ||||
\(137\) | −644.334 | − | 372.006i | −0.401819 | − | 0.231990i | 0.285450 | − | 0.958394i | \(-0.407857\pi\) |
−0.687268 | + | 0.726404i | \(0.741190\pi\) | |||||||
\(138\) | 2325.17i | 1.43429i | ||||||||
\(139\) | −1410.00 | + | 2442.19i | −0.860392 | + | 1.49024i | 0.0111596 | + | 0.999938i | \(0.496448\pi\) |
−0.871551 | + | 0.490304i | \(0.836886\pi\) | |||||||
\(140\) | 104.088 | + | 180.286i | 0.0628362 | + | 0.108836i | ||||
\(141\) | −580.104 | + | 334.923i | −0.346479 | + | 0.200040i | ||||
\(142\) | −1752.91 | −1.03592 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2074.69 | −1.20063 | ||||||||
\(145\) | 99.8084 | − | 57.6244i | 0.0571630 | − | 0.0330031i | ||||
\(146\) | −1111.40 | − | 1925.01i | −0.630003 | − | 1.09120i | ||||
\(147\) | 1331.64 | − | 2306.47i | 0.747157 | − | 1.29411i | ||||
\(148\) | 1256.79i | 0.698025i | ||||||||
\(149\) | −2506.80 | − | 1447.30i | −1.37829 | − | 0.795755i | −0.386335 | − | 0.922359i | \(-0.626259\pi\) |
−0.991953 | + | 0.126604i | \(0.959592\pi\) | |||||||
\(150\) | 1084.35 | + | 626.050i | 0.590246 | + | 0.340779i | ||||
\(151\) | − | 494.004i | − | 0.266235i | −0.991100 | − | 0.133118i | \(-0.957501\pi\) | ||
0.991100 | − | 0.133118i | \(-0.0424988\pi\) | |||||||
\(152\) | 1078.71 | − | 1868.38i | 0.575624 | − | 0.997010i | ||||
\(153\) | 1517.96 | + | 2629.19i | 0.802091 | + | 1.38926i | ||||
\(154\) | 156.356 | − | 90.2720i | 0.0818149 | − | 0.0472359i | ||||
\(155\) | 1404.11 | 0.727618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 50.7450 | 0.0257955 | 0.0128977 | − | 0.999917i | \(-0.495894\pi\) | ||||
0.0128977 | + | 0.999917i | \(0.495894\pi\) | |||||||
\(158\) | 740.727 | − | 427.659i | 0.372969 | − | 0.215334i | ||||
\(159\) | 1602.20 | + | 2775.09i | 0.799135 | + | 1.38414i | ||||
\(160\) | −528.383 | + | 915.185i | −0.261077 | + | 0.452199i | ||||
\(161\) | 894.419i | 0.437826i | ||||||||
\(162\) | −3980.53 | − | 2298.16i | −1.93049 | − | 1.11457i | ||||
\(163\) | −651.079 | − | 375.900i | −0.312861 | − | 0.180631i | 0.335345 | − | 0.942095i | \(-0.391147\pi\) |
−0.648206 | + | 0.761465i | \(0.724481\pi\) | |||||||
\(164\) | 784.161i | 0.373370i | ||||||||
\(165\) | 387.988 | − | 672.015i | 0.183060 | − | 0.317069i | ||||
\(166\) | 578.963 | + | 1002.79i | 0.270700 | + | 0.468867i | ||||
\(167\) | −2575.84 | + | 1487.16i | −1.19356 | + | 0.689102i | −0.959112 | − | 0.283027i | \(-0.908662\pi\) |
−0.234448 | + | 0.972129i | \(0.575328\pi\) | |||||||
\(168\) | −2002.70 | −0.919714 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −815.901 | −0.368099 | ||||||||
\(171\) | 5169.88 | − | 2984.83i | 2.31199 | − | 1.33483i | ||||
\(172\) | 92.7090 | + | 160.577i | 0.0410988 | + | 0.0711852i | ||||
\(173\) | 816.869 | − | 1414.86i | 0.358991 | − | 0.621790i | −0.628802 | − | 0.777566i | \(-0.716454\pi\) |
0.987792 | + | 0.155775i | \(0.0497876\pi\) | |||||||
\(174\) | 305.013i | 0.132891i | ||||||||
\(175\) | 417.114 | + | 240.821i | 0.180177 | + | 0.104025i | ||||
\(176\) | 256.134 | + | 147.879i | 0.109698 | + | 0.0633341i | ||||
\(177\) | 1434.46i | 0.609156i | ||||||||
\(178\) | −761.105 | + | 1318.27i | −0.320490 | + | 0.555105i | ||||
\(179\) | 1696.32 | + | 2938.12i | 0.708320 | + | 1.22685i | 0.965480 | + | 0.260477i | \(0.0838798\pi\) |
−0.257160 | + | 0.966369i | \(0.582787\pi\) | |||||||
\(180\) | −1468.12 | + | 847.620i | −0.607929 | + | 0.350988i | ||||
\(181\) | 3801.07 | 1.56095 | 0.780473 | − | 0.625190i | \(-0.214979\pi\) | ||||
0.780473 | + | 0.625190i | \(0.214979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 953.501 | 0.385163 | ||||||||
\(184\) | −2279.58 | + | 1316.12i | −0.913331 | + | 0.527312i | ||||
\(185\) | −1698.63 | − | 2942.11i | −0.675058 | − | 1.16924i | ||||
\(186\) | −1858.03 | + | 3218.20i | −0.732459 | + | 1.26866i | ||||
\(187\) | − | 432.787i | − | 0.169243i | ||||||
\(188\) | −180.664 | − | 104.306i | −0.0700866 | − | 0.0404645i | ||||
\(189\) | −2894.62 | − | 1671.21i | −1.11403 | − | 0.643188i | ||||
\(190\) | 1604.34i | 0.612584i | ||||||||
\(191\) | −632.755 | + | 1095.96i | −0.239710 | + | 0.415189i | −0.960631 | − | 0.277828i | \(-0.910386\pi\) |
0.720921 | + | 0.693017i | \(0.243719\pi\) | |||||||
\(192\) | −2587.49 | − | 4481.66i | −0.972583 | − | 1.68456i | ||||
\(193\) | 1915.92 | − | 1106.16i | 0.714565 | − | 0.412555i | −0.0981838 | − | 0.995168i | \(-0.531303\pi\) |
0.812749 | + | 0.582614i | \(0.197970\pi\) | |||||||
\(194\) | 773.767 | 0.286357 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 829.438 | 0.302273 | ||||||||
\(197\) | −3773.49 | + | 2178.63i | −1.36472 | + | 0.787923i | −0.990248 | − | 0.139315i | \(-0.955510\pi\) |
−0.374474 | + | 0.927238i | \(0.622177\pi\) | |||||||
\(198\) | 735.109 | + | 1273.25i | 0.263848 | + | 0.456998i | ||||
\(199\) | 545.316 | − | 944.516i | 0.194254 | − | 0.336457i | −0.752402 | − | 0.658704i | \(-0.771105\pi\) |
0.946656 | + | 0.322247i | \(0.104438\pi\) | |||||||
\(200\) | 1417.45i | 0.501145i | ||||||||
\(201\) | 5720.68 | + | 3302.84i | 2.00749 | + | 1.15903i | ||||
\(202\) | 1070.47 | + | 618.038i | 0.372862 | + | 0.215272i | ||||
\(203\) | 117.329i | 0.0405658i | ||||||||
\(204\) | −660.351 | + | 1143.76i | −0.226636 | + | 0.392546i | ||||
\(205\) | −1059.84 | − | 1835.70i | −0.361085 | − | 0.625418i | ||||
\(206\) | −2194.08 | + | 1266.75i | −0.742081 | + | 0.428441i | ||||
\(207\) | −7283.49 | −2.44559 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −851.007 | −0.281652 | ||||||||
\(210\) | 1289.76 | − | 744.644i | 0.423819 | − | 0.244692i | ||||
\(211\) | 363.724 | + | 629.989i | 0.118672 | + | 0.205546i | 0.919242 | − | 0.393694i | \(-0.128803\pi\) |
−0.800570 | + | 0.599240i | \(0.795470\pi\) | |||||||
\(212\) | −498.979 | + | 864.257i | −0.161651 | + | 0.279988i | ||||
\(213\) | − | 7669.93i | − | 2.46730i | ||||||
\(214\) | 3002.56 | + | 1733.53i | 0.959116 | + | 0.553746i | ||||
\(215\) | −434.058 | − | 250.603i | −0.137686 | − | 0.0794931i | ||||
\(216\) | − | 9836.58i | − | 3.09859i | ||||||
\(217\) | −714.724 | + | 1237.94i | −0.223588 | + | 0.387266i | ||||
\(218\) | −79.8119 | − | 138.238i | −0.0247961 | − | 0.0429481i | ||||
\(219\) | 8422.97 | − | 4863.01i | 2.59896 | − | 1.50051i | ||||
\(220\) | 241.665 | 0.0740595 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8991.05 | 2.71820 | ||||||||
\(223\) | −879.405 | + | 507.725i | −0.264078 | + | 0.152465i | −0.626193 | − | 0.779668i | \(-0.715388\pi\) |
0.362116 | + | 0.932133i | \(0.382055\pi\) | |||||||
\(224\) | −537.917 | − | 931.700i | −0.160451 | − | 0.277910i | ||||
\(225\) | −1961.07 | + | 3396.68i | −0.581058 | + | 1.00642i | ||||
\(226\) | − | 2185.37i | − | 0.643225i | ||||||
\(227\) | −4583.51 | − | 2646.29i | −1.34017 | − | 0.773747i | −0.353338 | − | 0.935496i | \(-0.614953\pi\) |
−0.986832 | + | 0.161748i | \(0.948287\pi\) | |||||||
\(228\) | 2249.03 | + | 1298.48i | 0.653269 | + | 0.377165i | ||||
\(229\) | 3010.03i | 0.868597i | 0.900769 | + | 0.434298i | \(0.143004\pi\) | ||||
−0.900769 | + | 0.434298i | \(0.856996\pi\) | |||||||
\(230\) | 978.716 | − | 1695.19i | 0.280585 | − | 0.485988i | ||||
\(231\) | 394.989 | + | 684.142i | 0.112504 | + | 0.194862i | ||||
\(232\) | −299.032 | + | 172.646i | −0.0846225 | + | 0.0488568i | ||||
\(233\) | 2373.96 | 0.667482 | 0.333741 | − | 0.942665i | \(-0.391689\pi\) | ||||
0.333741 | + | 0.942665i | \(0.391689\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 563.905 | 0.156532 | ||||||||
\(236\) | −386.888 | + | 223.370i | −0.106713 | + | 0.0616108i | ||||
\(237\) | 1871.24 | + | 3241.09i | 0.512870 | + | 0.888318i | ||||
\(238\) | 415.312 | − | 719.342i | 0.113112 | − | 0.195916i | ||||
\(239\) | − | 783.439i | − | 0.212035i | −0.994364 | − | 0.106018i | \(-0.966190\pi\) | ||
0.994364 | − | 0.106018i | \(-0.0338100\pi\) | |||||||
\(240\) | 2112.82 | + | 1219.84i | 0.568259 | + | 0.328085i | ||||
\(241\) | 3046.16 | + | 1758.70i | 0.814192 | + | 0.470074i | 0.848410 | − | 0.529340i | \(-0.177560\pi\) |
−0.0342172 | + | 0.999414i | \(0.510894\pi\) | |||||||
\(242\) | 2755.86i | 0.732040i | ||||||||
\(243\) | 4655.01 | − | 8062.71i | 1.22888 | − | 2.12849i | ||||
\(244\) | 148.476 | + | 257.169i | 0.0389558 | + | 0.0674735i | ||||
\(245\) | −1941.69 | + | 1121.04i | −0.506327 | + | 0.292328i | ||||
\(246\) | 5609.86 | 1.45395 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4206.80 | −1.07715 | ||||||||
\(249\) | −4387.77 | + | 2533.28i | −1.11672 | + | 0.644740i | ||||
\(250\) | −1669.83 | − | 2892.24i | −0.422438 | − | 0.731685i | ||||
\(251\) | 708.480 | − | 1227.12i | 0.178163 | − | 0.308587i | −0.763088 | − | 0.646294i | \(-0.776318\pi\) |
0.941251 | + | 0.337707i | \(0.109651\pi\) | |||||||
\(252\) | − | 1725.83i | − | 0.431417i | ||||||
\(253\) | 899.195 | + | 519.150i | 0.223446 | + | 0.129007i | ||||
\(254\) | −4201.10 | − | 2425.51i | −1.03780 | − | 0.599173i | ||||
\(255\) | − | 3570.02i | − | 0.876718i | ||||||
\(256\) | 1953.39 | − | 3383.37i | 0.476902 | − | 0.826018i | ||||
\(257\) | −741.317 | − | 1284.00i | −0.179930 | − | 0.311648i | 0.761926 | − | 0.647664i | \(-0.224254\pi\) |
−0.941856 | + | 0.336015i | \(0.890921\pi\) | |||||||
\(258\) | 1148.76 | − | 663.237i | 0.277204 | − | 0.160044i | ||||
\(259\) | 3458.56 | 0.829748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −955.438 | −0.226591 | ||||||||
\(262\) | −3704.26 | + | 2138.65i | −0.873473 | + | 0.504300i | ||||
\(263\) | −3614.82 | − | 6261.05i | −0.847526 | − | 1.46796i | −0.883409 | − | 0.468603i | \(-0.844758\pi\) |
0.0358825 | − | 0.999356i | \(-0.488576\pi\) | |||||||
\(264\) | −1162.44 | + | 2013.40i | −0.270996 | + | 0.469379i | ||||
\(265\) | − | 2697.60i | − | 0.625329i | ||||||
\(266\) | −1414.47 | − | 816.645i | −0.326041 | − | 0.188240i | ||||
\(267\) | −5768.17 | − | 3330.25i | −1.32212 | − | 0.763326i | ||||
\(268\) | 2057.23i | 0.468901i | ||||||||
\(269\) | 247.452 | − | 428.599i | 0.0560870 | − | 0.0971456i | −0.836619 | − | 0.547786i | \(-0.815471\pi\) |
0.892706 | + | 0.450640i | \(0.148804\pi\) | |||||||
\(270\) | 3657.43 | + | 6334.86i | 0.824387 | + | 1.42788i | ||||
\(271\) | −3642.14 | + | 2102.79i | −0.816399 | + | 0.471348i | −0.849173 | − | 0.528115i | \(-0.822899\pi\) |
0.0327741 | + | 0.999463i | \(0.489566\pi\) | |||||||
\(272\) | 1360.69 | 0.303323 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1657.65 | −0.365483 | ||||||||
\(275\) | 484.214 | − | 279.561i | 0.106179 | − | 0.0613025i | ||||
\(276\) | −1584.25 | − | 2744.00i | −0.345510 | − | 0.598441i | ||||
\(277\) | 2104.27 | − | 3644.71i | 0.456439 | − | 0.790575i | −0.542331 | − | 0.840165i | \(-0.682458\pi\) |
0.998770 | + | 0.0495898i | \(0.0157914\pi\) | |||||||
\(278\) | 6282.92i | 1.35548i | ||||||||
\(279\) | −10080.9 | − | 5820.19i | −2.16317 | − | 1.24891i | ||||
\(280\) | 1460.09 | + | 842.981i | 0.311632 | + | 0.179921i | ||||
\(281\) | − | 4740.83i | − | 1.00646i | −0.864153 | − | 0.503228i | \(-0.832145\pi\) | ||
0.864153 | − | 0.503228i | \(-0.167855\pi\) | |||||||
\(282\) | −746.205 | + | 1292.46i | −0.157574 | + | 0.272926i | ||||
\(283\) | −1871.41 | − | 3241.38i | −0.393088 | − | 0.680848i | 0.599767 | − | 0.800175i | \(-0.295260\pi\) |
−0.992855 | + | 0.119326i | \(0.961927\pi\) | |||||||
\(284\) | 2068.66 | − | 1194.34i | 0.432226 | − | 0.249546i | ||||
\(285\) | −7019.87 | −1.45902 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2157.93 | 0.443828 | ||||||||
\(288\) | 7587.09 | − | 4380.41i | 1.55234 | − | 0.896243i | ||||
\(289\) | 1460.94 | + | 2530.43i | 0.297363 | + | 0.515047i | ||||
\(290\) | 128.387 | − | 222.372i | 0.0259970 | − | 0.0450280i | ||||
\(291\) | 3385.66i | 0.682030i | ||||||||
\(292\) | 2623.20 | + | 1514.51i | 0.525723 | + | 0.303526i | ||||
\(293\) | −4550.94 | − | 2627.49i | −0.907402 | − | 0.523889i | −0.0278075 | − | 0.999613i | \(-0.508853\pi\) |
−0.879594 | + | 0.475725i | \(0.842186\pi\) | |||||||
\(294\) | − | 5933.77i | − | 1.17709i | ||||||
\(295\) | 603.795 | − | 1045.80i | 0.119167 | − | 0.206404i | ||||
\(296\) | 5089.20 | + | 8814.75i | 0.999337 | + | 1.73090i | ||||
\(297\) | −3360.27 | + | 1940.05i | −0.656507 | + | 0.379034i | ||||
\(298\) | −6449.14 | −1.25365 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1706.23 | −0.328364 | ||||||||
\(301\) | 441.891 | − | 255.126i | 0.0846185 | − | 0.0488545i | ||||
\(302\) | −550.318 | − | 953.179i | −0.104858 | − | 0.181620i | ||||
\(303\) | −2704.25 | + | 4683.91i | −0.512724 | + | 0.888064i | ||||
\(304\) | − | 2675.58i | − | 0.504786i | ||||||
\(305\) | −695.157 | − | 401.349i | −0.130507 | − | 0.0753482i | ||||
\(306\) | 5857.79 | + | 3382.00i | 1.09434 | + | 0.631817i | ||||
\(307\) | − | 252.464i | − | 0.0469344i | −0.999725 | − | 0.0234672i | \(-0.992529\pi\) | ||
0.999725 | − | 0.0234672i | \(-0.00747053\pi\) | |||||||
\(308\) | −123.013 | + | 213.065i | −0.0227576 | + | 0.0394172i | ||||
\(309\) | −5542.74 | − | 9600.30i | −1.02044 | − | 1.76745i | ||||
\(310\) | 2709.22 | − | 1564.17i | 0.496366 | − | 0.286577i | ||||
\(311\) | −2561.20 | −0.466986 | −0.233493 | − | 0.972359i | \(-0.575016\pi\) | ||||
−0.233493 | + | 0.972359i | \(0.575016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −695.893 | −0.125668 | −0.0628342 | − | 0.998024i | \(-0.520014\pi\) | ||||
−0.0628342 | + | 0.998024i | \(0.520014\pi\) | |||||||
\(314\) | 97.9122 | − | 56.5296i | 0.0175971 | − | 0.0101597i | ||||
\(315\) | 2332.56 | + | 4040.12i | 0.417222 | + | 0.722650i | ||||
\(316\) | −582.769 | + | 1009.39i | −0.103745 | + | 0.179691i | ||||
\(317\) | 5747.37i | 1.01831i | 0.860675 | + | 0.509155i | \(0.170042\pi\) | ||||
−0.860675 | + | 0.509155i | \(0.829958\pi\) | |||||||
\(318\) | 6182.86 | + | 3569.68i | 1.09031 | + | 0.629489i | ||||
\(319\) | 117.955 | + | 68.1014i | 0.0207029 | + | 0.0119528i | ||||
\(320\) | 4356.52i | 0.761053i | ||||||||
\(321\) | −7585.14 | + | 13137.9i | −1.31888 | + | 2.28437i | ||||
\(322\) | 996.377 | + | 1725.78i | 0.172441 | + | 0.298676i | ||||
\(323\) | −3390.67 | + | 1957.60i | −0.584092 | + | 0.337226i | ||||
\(324\) | 6263.39 | 1.07397 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1675.00 | −0.284570 | ||||||||
\(327\) | 604.869 | − | 349.221i | 0.102291 | − | 0.0590580i | ||||
\(328\) | 3175.34 | + | 5499.86i | 0.534540 | + | 0.925850i | ||||
\(329\) | −287.041 | + | 497.169i | −0.0481005 | + | 0.0833125i | ||||
\(330\) | − | 1728.87i | − | 0.288397i | ||||||
\(331\) | 3676.07 | + | 2122.38i | 0.610438 | + | 0.352437i | 0.773137 | − | 0.634239i | \(-0.218686\pi\) |
−0.162699 | + | 0.986676i | \(0.552020\pi\) | |||||||
\(332\) | −1366.50 | − | 788.950i | −0.225893 | − | 0.130419i | ||||
\(333\) | 28164.0i | 4.63477i | ||||||||
\(334\) | −3313.38 | + | 5738.94i | −0.542815 | + | 0.940182i | ||||
\(335\) | −2780.47 | − | 4815.92i | −0.453473 | − | 0.785438i | ||||
\(336\) | −2150.95 | + | 1241.85i | −0.349238 | + | 0.201633i | ||||
\(337\) | 7122.49 | 1.15130 | 0.575648 | − | 0.817698i | \(-0.304750\pi\) | ||||
0.575648 | + | 0.817698i | \(0.304750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9562.20 | 1.53200 | ||||||||
\(340\) | 962.868 | − | 555.912i | 0.153585 | − | 0.0886723i | ||||
\(341\) | 829.699 | + | 1437.08i | 0.131762 | + | 0.228218i | ||||
\(342\) | 6650.16 | − | 11518.4i | 1.05146 | − | 1.82118i | ||||
\(343\) | − | 5148.28i | − | 0.810440i | ||||||
\(344\) | 1300.46 | + | 750.823i | 0.203827 | + | 0.117679i | ||||
\(345\) | 7417.37 | + | 4282.42i | 1.15750 | + | 0.668283i | ||||
\(346\) | − | 3639.95i | − | 0.565563i | ||||||
\(347\) | 1683.95 | − | 2916.69i | 0.260517 | − | 0.451228i | −0.705863 | − | 0.708349i | \(-0.749440\pi\) |
0.966379 | + | 0.257121i | \(0.0827738\pi\) | |||||||
\(348\) | −207.820 | − | 359.954i | −0.0320124 | − | 0.0554471i | ||||
\(349\) | −5265.18 | + | 3039.86i | −0.807561 | + | 0.466246i | −0.846108 | − | 0.533011i | \(-0.821060\pi\) |
0.0385471 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(350\) | 1073.09 | 0.163884 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1248.90 | −0.189110 | ||||||||
\(353\) | 2798.12 | − | 1615.50i | 0.421895 | − | 0.243581i | −0.273993 | − | 0.961732i | \(-0.588344\pi\) |
0.695888 | + | 0.718151i | \(0.255011\pi\) | |||||||
\(354\) | 1597.98 | + | 2767.78i | 0.239920 | + | 0.415554i | ||||
\(355\) | −3228.44 | + | 5591.82i | −0.482670 | + | 0.836009i | ||||
\(356\) | − | 2074.31i | − | 0.308815i | ||||||
\(357\) | 3147.52 | + | 1817.22i | 0.466622 | + | 0.269405i | ||||
\(358\) | 6546.10 | + | 3779.39i | 0.966402 | + | 0.557952i | ||||
\(359\) | − | 5345.81i | − | 0.785908i | −0.919558 | − | 0.392954i | \(-0.871453\pi\) | ||
0.919558 | − | 0.392954i | \(-0.128547\pi\) | |||||||
\(360\) | −6864.62 | + | 11889.9i | −1.00499 | + | 1.74070i | ||||
\(361\) | 419.816 | + | 727.143i | 0.0612066 | + | 0.106013i | ||||
\(362\) | 7334.14 | − | 4234.37i | 1.06484 | − | 0.614788i | ||||
\(363\) | −12058.4 | −1.74353 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8187.78 | −1.17416 | ||||||||
\(366\) | 1839.77 | − | 1062.19i | 0.262750 | − | 0.151699i | ||||
\(367\) | 6085.66 | + | 10540.7i | 0.865583 | + | 1.49923i | 0.866467 | + | 0.499234i | \(0.166385\pi\) |
−0.000883749 | 1.00000i | \(0.500281\pi\) | ||||||||
\(368\) | −1632.22 | + | 2827.08i | −0.231210 | + | 0.400467i | ||||
\(369\) | 17572.6i | 2.47911i | ||||||||
\(370\) | −6554.99 | − | 3784.53i | −0.921021 | − | 0.531752i | ||||
\(371\) | 2378.35 | + | 1373.14i | 0.332824 | + | 0.192156i | ||||
\(372\) | − | 5063.86i | − | 0.705776i | ||||||
\(373\) | 2231.98 | − | 3865.90i | 0.309832 | − | 0.536645i | −0.668493 | − | 0.743718i | \(-0.733061\pi\) |
0.978325 | + | 0.207073i | \(0.0663938\pi\) | |||||||
\(374\) | −482.122 | − | 835.060i | −0.0666576 | − | 0.115454i | ||||
\(375\) | 12655.1 | − | 7306.44i | 1.74269 | − | 1.00614i | ||||
\(376\) | −1689.49 | −0.231726 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7446.87 | −1.01330 | ||||||||
\(379\) | 4649.74 | − | 2684.53i | 0.630188 | − | 0.363839i | −0.150637 | − | 0.988589i | \(-0.548132\pi\) |
0.780825 | + | 0.624750i | \(0.214799\pi\) | |||||||
\(380\) | −1093.11 | − | 1893.33i | −0.147567 | − | 0.255594i | ||||
\(381\) | 10612.9 | − | 18382.1i | 1.42708 | − | 2.47177i | ||||
\(382\) | 2819.54i | 0.377645i | ||||||||
\(383\) | −168.948 | − | 97.5419i | −0.0225400 | − | 0.0130135i | 0.488688 | − | 0.872459i | \(-0.337476\pi\) |
−0.511228 | + | 0.859445i | \(0.670809\pi\) | |||||||
\(384\) | −1288.13 | − | 743.700i | −0.171183 | − | 0.0988327i | ||||
\(385\) | − | 665.038i | − | 0.0880351i | ||||||
\(386\) | 2464.51 | − | 4268.65i | 0.324974 | − | 0.562872i | ||||
\(387\) | 2077.56 | + | 3598.44i | 0.272889 | + | 0.472658i | ||||
\(388\) | −913.145 | + | 527.204i | −0.119479 | + | 0.0689813i | ||||
\(389\) | −9120.52 | −1.18876 | −0.594381 | − | 0.804183i | \(-0.702603\pi\) | ||||
−0.594381 | + | 0.804183i | \(0.702603\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4776.89 | 0.617845 | ||||||||
\(392\) | 5817.42 | − | 3358.69i | 0.749551 | − | 0.432754i | ||||
\(393\) | −9357.79 | − | 16208.2i | −1.20111 | − | 2.08039i | ||||
\(394\) | −4853.95 | + | 8407.30i | −0.620657 | + | 1.07501i | ||||
\(395\) | − | 3150.59i | − | 0.401325i | ||||||
\(396\) | −1735.05 | − | 1001.73i | −0.220175 | − | 0.127118i | ||||
\(397\) | −5727.43 | − | 3306.73i | −0.724059 | − | 0.418036i | 0.0921859 | − | 0.995742i | \(-0.470615\pi\) |
−0.816245 | + | 0.577706i | \(0.803948\pi\) | |||||||
\(398\) | − | 2429.92i | − | 0.306032i | ||||||
\(399\) | 3573.27 | − | 6189.09i | 0.448339 | − | 0.776546i | ||||
\(400\) | 878.945 | + | 1522.38i | 0.109868 | + | 0.190297i | ||||
\(401\) | −7438.51 | + | 4294.63i | −0.926338 | + | 0.534822i | −0.885652 | − | 0.464350i | \(-0.846288\pi\) |
−0.0406868 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(402\) | 14717.4 | 1.82596 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1684.39 | −0.207430 | ||||||||
\(405\) | −14662.4 | + | 8465.34i | −1.79896 | + | 1.03863i | ||||
\(406\) | 130.703 | + | 226.385i | 0.0159771 | + | 0.0276731i | ||||
\(407\) | 2007.47 | − | 3477.03i | 0.244487 | − | 0.423465i | ||||
\(408\) | 10696.0i | 1.29787i | ||||||||
\(409\) | −6508.70 | − | 3757.80i | −0.786881 | − | 0.454306i | 0.0519824 | − | 0.998648i | \(-0.483446\pi\) |
−0.838863 | + | 0.544342i | \(0.816779\pi\) | |||||||
\(410\) | −4089.91 | − | 2361.31i | −0.492649 | − | 0.284431i | ||||
\(411\) | − | 7253.14i | − | 0.870489i | ||||||
\(412\) | 1726.20 | − | 2989.86i | 0.206417 | − | 0.357524i | ||||
\(413\) | 614.691 | + | 1064.68i | 0.0732372 | + | 0.126851i | ||||
\(414\) | −14053.5 | + | 8113.77i | −1.66833 | + | 0.963212i | ||||
\(415\) | 4265.25 | 0.504513 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27491.2 | −3.22842 | ||||||||
\(418\) | −1642.01 | + | 948.016i | −0.192137 | + | 0.110931i | ||||
\(419\) | 2278.67 | + | 3946.76i | 0.265680 | + | 0.460172i | 0.967742 | − | 0.251945i | \(-0.0810701\pi\) |
−0.702061 | + | 0.712117i | \(0.747737\pi\) | |||||||
\(420\) | −1014.72 | + | 1757.55i | −0.117889 | + | 0.204190i | ||||
\(421\) | 2225.19i | 0.257599i | 0.991671 | + | 0.128800i | \(0.0411124\pi\) | ||||
−0.991671 | + | 0.128800i | \(0.958888\pi\) | |||||||
\(422\) | 1403.61 | + | 810.373i | 0.161911 | + | 0.0934795i | ||||
\(423\) | −4048.58 | − | 2337.45i | −0.465363 | − | 0.268678i | ||||
\(424\) | 8082.17i | 0.925719i | ||||||||
\(425\) | 1286.17 | − | 2227.71i | 0.146796 | − | 0.254259i | ||||
\(426\) | −8544.26 | − | 14799.1i | −0.971762 | − | 1.68314i | ||||
\(427\) | 707.701 | − | 408.592i | 0.0802063 | − | 0.0463071i | ||||
\(428\) | −4724.54 | −0.533574 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1116.68 | −0.125235 | ||||||||
\(431\) | 342.970 | − | 198.014i | 0.0383302 | − | 0.0221299i | −0.480712 | − | 0.876878i | \(-0.659622\pi\) |
0.519043 | + | 0.854748i | \(0.326289\pi\) | |||||||
\(432\) | −6099.55 | − | 10564.7i | −0.679316 | − | 1.17661i | ||||
\(433\) | 2594.03 | − | 4492.99i | 0.287901 | − | 0.498659i | −0.685408 | − | 0.728159i | \(-0.740376\pi\) |
0.973308 | + | 0.229501i | \(0.0737093\pi\) | |||||||
\(434\) | 3184.79i | 0.352246i | ||||||||
\(435\) | 973.000 | + | 561.762i | 0.107245 | + | 0.0619182i | ||||
\(436\) | 188.377 | + | 108.759i | 0.0206918 | + | 0.0119464i | ||||
\(437\) | − | 9392.99i | − | 1.02821i | ||||||
\(438\) | 10834.7 | − | 18766.3i | 1.18197 | − | 2.04723i | ||||
\(439\) | 5664.93 | + | 9811.94i | 0.615882 | + | 1.06674i | 0.990229 | + | 0.139450i | \(0.0445336\pi\) |
−0.374347 | + | 0.927289i | \(0.622133\pi\) | |||||||
\(440\) | 1694.97 | − | 978.589i | 0.183646 | − | 0.106028i | ||||
\(441\) | 18587.2 | 2.00705 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15625.2 | 1.67579 | 0.837897 | − | 0.545828i | \(-0.183785\pi\) | ||||
0.837897 | + | 0.545828i | \(0.183785\pi\) | |||||||
\(444\) | −10610.6 | + | 6126.03i | −1.13414 | + | 0.654794i | ||||
\(445\) | 2803.55 | + | 4855.89i | 0.298654 | + | 0.517284i | ||||
\(446\) | −1131.20 | + | 1959.30i | −0.120099 | + | 0.208017i | ||||
\(447\) | − | 28218.5i | − | 2.98588i | ||||||
\(448\) | −3840.94 | − | 2217.57i | −0.405061 | − | 0.233862i | ||||
\(449\) | 11852.9 | + | 6843.29i | 1.24582 | + | 0.719276i | 0.970273 | − | 0.242011i | \(-0.0778071\pi\) |
0.275549 | + | 0.961287i | \(0.411140\pi\) | |||||||
\(450\) | 8738.49i | 0.915414i | ||||||||
\(451\) | 1252.53 | − | 2169.45i | 0.130775 | − | 0.226509i | ||||
\(452\) | 1489.00 | + | 2579.02i | 0.154948 | + | 0.268378i | ||||
\(453\) | 4170.68 | − | 2407.94i | 0.432573 | − | 0.249746i | ||||
\(454\) | −11791.8 | −1.21898 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21031.9 | 2.15989 | ||||||||
\(457\) | 10975.2 | − | 6336.55i | 1.12341 | − | 0.648602i | 0.181142 | − | 0.983457i | \(-0.442020\pi\) |
0.942270 | + | 0.334854i | \(0.108687\pi\) | |||||||
\(458\) | 3353.16 | + | 5807.84i | 0.342102 | + | 0.592539i | ||||
\(459\) | −8925.55 | + | 15459.5i | −0.907645 | + | 1.57209i | ||||
\(460\) | 2667.38i | 0.270364i | ||||||||
\(461\) | −7928.34 | − | 4577.43i | −0.800996 | − | 0.462456i | 0.0428230 | − | 0.999083i | \(-0.486365\pi\) |
−0.843819 | + | 0.536627i | \(0.819698\pi\) | |||||||
\(462\) | 1524.26 | + | 880.032i | 0.153496 | + | 0.0886207i | ||||
\(463\) | − | 6910.59i | − | 0.693655i | −0.937929 | − | 0.346827i | \(-0.887259\pi\) | ||
0.937929 | − | 0.346827i | \(-0.112741\pi\) | |||||||
\(464\) | −214.112 | + | 370.852i | −0.0214222 | + | 0.0371043i | ||||
\(465\) | 6844.11 | + | 11854.3i | 0.682554 | + | 1.18222i | ||||
\(466\) | 4580.55 | − | 2644.58i | 0.455343 | − | 0.262892i | ||||
\(467\) | −2920.19 | −0.289359 | −0.144679 | − | 0.989479i | \(-0.546215\pi\) | ||||
−0.144679 | + | 0.989479i | \(0.546215\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5661.29 | 0.557386 | ||||||||
\(470\) | 1088.05 | − | 628.187i | 0.106783 | − | 0.0616513i | ||||
\(471\) | 247.348 | + | 428.420i | 0.0241979 | + | 0.0419120i | ||||
\(472\) | −1809.01 | + | 3133.29i | −0.176412 | + | 0.305554i | ||||
\(473\) | − | 592.334i | − | 0.0575804i | ||||||
\(474\) | 7221.10 | + | 4169.11i | 0.699739 | + | 0.403995i | ||||
\(475\) | −4380.45 | − | 2529.05i | −0.423134 | − | 0.244296i | ||||
\(476\) | 1131.89i | 0.108992i | ||||||||
\(477\) | −11181.8 | + | 19367.5i | −1.07334 | + | 1.85907i | ||||
\(478\) | −872.746 | − | 1511.64i | −0.0835115 | − | 0.144646i | ||||
\(479\) | 14799.2 | − | 8544.31i | 1.41167 | − | 0.815030i | 0.416128 | − | 0.909306i | \(-0.363387\pi\) |
0.995546 | + | 0.0942761i | \(0.0300536\pi\) | |||||||
\(480\) | −10302.1 | −0.979630 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7836.73 | 0.740567 | ||||||||
\(483\) | −7551.22 | + | 4359.70i | −0.711371 | + | 0.410710i | ||||
\(484\) | −1877.70 | − | 3252.28i | −0.176343 | − | 0.305435i | ||||
\(485\) | 1425.10 | − | 2468.34i | 0.133423 | − | 0.231096i | ||||
\(486\) | − | 20742.6i | − | 1.93602i | ||||||
\(487\) | 11962.4 | + | 6906.48i | 1.11307 | + | 0.642634i | 0.939624 | − | 0.342209i | \(-0.111175\pi\) |
0.173450 | + | 0.984843i | \(0.444508\pi\) | |||||||
\(488\) | 2082.73 | + | 1202.47i | 0.193199 | + | 0.111543i | ||||
\(489\) | − | 7329.06i | − | 0.677774i | ||||||
\(490\) | −2497.65 | + | 4326.06i | −0.230270 | + | 0.398840i | ||||
\(491\) | −5924.21 | − | 10261.0i | −0.544513 | − | 0.943125i | −0.998637 | − | 0.0521862i | \(-0.983381\pi\) |
0.454124 | − | 0.890938i | \(-0.349952\pi\) | |||||||
\(492\) | −6620.35 | + | 3822.26i | −0.606644 | + | 0.350246i | ||||
\(493\) | 626.625 | 0.0572450 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5415.59 | 0.491743 | ||||||||
\(496\) | −4518.20 | + | 2608.59i | −0.409019 | + | 0.236147i | ||||
\(497\) | −3286.70 | − | 5692.73i | −0.296637 | − | 0.513790i | ||||
\(498\) | −5644.12 | + | 9775.90i | −0.507870 | + | 0.879656i | ||||
\(499\) | − | 5224.46i | − | 0.468696i | −0.972153 | − | 0.234348i | \(-0.924705\pi\) | ||
0.972153 | − | 0.234348i | \(-0.0752955\pi\) | |||||||
\(500\) | 3941.24 | + | 2275.48i | 0.352515 | + | 0.203525i | ||||
\(501\) | −25111.0 | − | 14497.9i | −2.23928 | − | 1.29285i | ||||
\(502\) | − | 3156.97i | − | 0.280682i | ||||||
\(503\) | −3942.20 | + | 6828.08i | −0.349451 | + | 0.605267i | −0.986152 | − | 0.165844i | \(-0.946965\pi\) |
0.636701 | + | 0.771111i | \(0.280299\pi\) | |||||||
\(504\) | −6988.50 | − | 12104.4i | −0.617644 | − | 1.06979i | ||||
\(505\) | 3943.11 | − | 2276.56i | 0.347458 | − | 0.200605i | ||||
\(506\) | 2313.32 | 0.203241 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6610.45 | 0.577345 | ||||||||
\(509\) | −3487.10 | + | 2013.28i | −0.303660 | + | 0.175318i | −0.644086 | − | 0.764953i | \(-0.722762\pi\) |
0.340426 | + | 0.940271i | \(0.389429\pi\) | |||||||
\(510\) | −3976.98 | − | 6888.33i | −0.345301 | − | 0.598079i | ||||
\(511\) | 4167.76 | − | 7218.78i | 0.360804 | − | 0.624931i | ||||
\(512\) | − | 9924.86i | − | 0.856681i | ||||||
\(513\) | 30398.7 | + | 17550.7i | 2.61624 | + | 1.51049i | ||||
\(514\) | −2860.73 | − | 1651.65i | −0.245489 | − | 0.141733i | ||||
\(515\) | 9332.23i | 0.798499i | ||||||||
\(516\) | −903.790 | + | 1565.41i | −0.0771068 | + | 0.133553i | ||||
\(517\) | 333.216 | + | 577.147i | 0.0283459 | + | 0.0490965i | ||||
\(518\) | 6673.28 | − | 3852.82i | 0.566037 | − | 0.326802i | ||||
\(519\) | 15926.8 | 1.34703 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6196.12 | 0.521030 | 0.260515 | − | 0.965470i | \(-0.416108\pi\) | ||||
0.260515 | + | 0.965470i | \(0.416108\pi\) | |||||||
\(522\) | −1843.51 | + | 1064.35i | −0.154575 | + | 0.0892441i | ||||
\(523\) | −3949.69 | − | 6841.07i | −0.330226 | − | 0.571968i | 0.652330 | − | 0.757935i | \(-0.273792\pi\) |
−0.982556 | + | 0.185967i | \(0.940458\pi\) | |||||||
\(524\) | 2914.33 | − | 5047.77i | 0.242964 | − | 0.420826i | ||||
\(525\) | 4695.37i | 0.390329i | ||||||||
\(526\) | −13949.6 | − | 8053.78i | −1.15633 | − | 0.667607i | ||||
\(527\) | 6611.55 | + | 3817.18i | 0.546496 | + | 0.315520i | ||||
\(528\) | 2883.25i | 0.237646i | ||||||||
\(529\) | 353.376 | − | 612.065i | 0.0290438 | − | 0.0503053i | ||||
\(530\) | −3005.11 | − | 5205.00i | −0.246290 | − | 0.426586i | ||||
\(531\) | −8669.95 | + | 5005.60i | −0.708557 | + | 0.409085i | ||||
\(532\) | 2225.68 | 0.181382 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −14839.5 | −1.20256 | ||||||||
\(535\) | 11060.0 | − | 6385.50i | 0.893768 | − | 0.516017i | ||||
\(536\) | 8330.46 | + | 14428.8i | 0.671308 | + | 1.16274i | ||||
\(537\) | −16536.9 | + | 28642.8i | −1.32890 | + | 2.30173i | ||||
\(538\) | − | 1102.64i | − | 0.0883609i | ||||||
\(539\) | −2294.72 | − | 1324.86i | −0.183378 | − | 0.105873i | ||||
\(540\) | −8632.49 | − | 4983.97i | −0.687932 | − | 0.397178i | ||||
\(541\) | 6146.22i | 0.488441i | 0.969720 | + | 0.244220i | \(0.0785320\pi\) | ||||
−0.969720 | + | 0.244220i | \(0.921468\pi\) | |||||||
\(542\) | −4684.99 | + | 8114.64i | −0.371287 | + | 0.643088i | ||||
\(543\) | 18527.7 | + | 32090.9i | 1.46427 | + | 2.53619i | ||||
\(544\) | −4976.00 | + | 2872.89i | −0.392177 | + | 0.226423i | ||||
\(545\) | −587.979 | −0.0462133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5555.49 | 0.434252 | 0.217126 | − | 0.976144i | \(-0.430332\pi\) | ||||
0.217126 | + | 0.976144i | \(0.430332\pi\) | |||||||
\(548\) | 1956.24 | − | 1129.44i | 0.152494 | − | 0.0880422i | ||||
\(549\) | 3327.27 | + | 5763.00i | 0.258660 | + | 0.448013i | ||||
\(550\) | 622.859 | − | 1078.82i | 0.0482887 | − | 0.0836385i | ||||
\(551\) | − | 1232.16i | − | 0.0952663i | ||||||
\(552\) | −22222.9 | − | 12830.4i | −1.71353 | − | 0.989307i | ||||
\(553\) | 2777.72 | + | 1603.72i | 0.213600 | + | 0.123322i | ||||
\(554\) | − | 9376.59i | − | 0.719085i | ||||||
\(555\) | 16559.4 | − | 28681.7i | 1.26650 | − | 2.19364i | ||||
\(556\) | −4280.85 | − | 7414.65i | −0.326526 | − | 0.565560i | ||||
\(557\) | −6565.08 | + | 3790.35i | −0.499410 | + | 0.288335i | −0.728470 | − | 0.685078i | \(-0.759768\pi\) |
0.229060 | + | 0.973412i | \(0.426435\pi\) | |||||||
\(558\) | −25934.6 | −1.96756 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2090.89 | 0.157779 | ||||||||
\(561\) | 3653.85 | − | 2109.55i | 0.274983 | − | 0.158762i | ||||
\(562\) | −5281.26 | − | 9147.41i | −0.396399 | − | 0.686584i | ||||
\(563\) | −6797.30 | + | 11773.3i | −0.508831 | + | 0.881322i | 0.491116 | + | 0.871094i | \(0.336589\pi\) |
−0.999948 | + | 0.0102278i | \(0.996744\pi\) | |||||||
\(564\) | − | 2033.70i | − | 0.151834i | ||||||
\(565\) | −6971.40 | − | 4024.94i | −0.519095 | − | 0.299700i | ||||
\(566\) | −7221.76 | − | 4169.48i | −0.536313 | − | 0.309640i | ||||
\(567\) | − | 17236.2i | − | 1.27664i | ||||||
\(568\) | 9672.60 | − | 16753.4i | 0.714530 | − | 1.23760i | ||||
\(569\) | 2825.07 | + | 4893.16i | 0.208143 | + | 0.360513i | 0.951129 | − | 0.308793i | \(-0.0999249\pi\) |
−0.742987 | + | 0.669306i | \(0.766592\pi\) | |||||||
\(570\) | −13544.8 | + | 7820.09i | −0.995314 | + | 0.574645i | ||||
\(571\) | −6297.53 | −0.461547 | −0.230773 | − | 0.973008i | \(-0.574126\pi\) | ||||
−0.230773 | + | 0.973008i | \(0.574126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12337.0 | −0.899454 | ||||||||
\(574\) | 4163.71 | − | 2403.92i | 0.302770 | − | 0.174804i | ||||
\(575\) | 3085.66 | + | 5344.52i | 0.223793 | + | 0.387620i | ||||
\(576\) | 18058.3 | − | 31277.8i | 1.30630 | − | 2.26257i | ||||
\(577\) | 17838.9i | 1.28707i | 0.765415 | + | 0.643537i | \(0.222534\pi\) | ||||
−0.765415 | + | 0.643537i | \(0.777466\pi\) | |||||||
\(578\) | 5637.76 | + | 3254.96i | 0.405709 | + | 0.234236i | ||||
\(579\) | 18677.7 | + | 10783.6i | 1.34062 | + | 0.774007i | ||||
\(580\) | 349.903i | 0.0250499i | ||||||||
\(581\) | −2171.11 | + | 3760.47i | −0.155031 | + | 0.268521i | ||||
\(582\) | 3771.60 | + | 6532.60i | 0.268622 | + | 0.465266i | ||||
\(583\) | 2760.94 | − | 1594.03i | 0.196135 | − | 0.113238i | ||||
\(584\) | 24531.1 | 1.73819 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11708.0 | −0.825348 | ||||||||
\(587\) | −394.120 | + | 227.545i | −0.0277122 | + | 0.0159997i | −0.513792 | − | 0.857915i | \(-0.671760\pi\) |
0.486080 | + | 0.873914i | \(0.338426\pi\) | |||||||
\(588\) | 4042.96 | + | 7002.61i | 0.283553 | + | 0.491127i | ||||
\(589\) | 7505.87 | − | 13000.6i | 0.525083 | − | 0.909471i | ||||
\(590\) | − | 2690.50i | − | 0.187739i | ||||||
\(591\) | −36786.5 | − | 21238.7i | −2.56040 | − | 1.47825i | ||||
\(592\) | 10931.8 | + | 6311.50i | 0.758946 | + | 0.438178i | ||||
\(593\) | 16240.6i | 1.12466i | 0.826913 | + | 0.562330i | \(0.190095\pi\) | ||||
−0.826913 | + | 0.562330i | \(0.809905\pi\) | |||||||
\(594\) | −4322.41 | + | 7486.63i | −0.298570 | + | 0.517139i | ||||
\(595\) | −1529.81 | − | 2649.71i | −0.105405 | − | 0.182568i | ||||
\(596\) | 7610.81 | − | 4394.10i | 0.523072 | − | 0.301996i | ||||
\(597\) | 10632.2 | 0.728891 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6704.05 | −0.457296 | −0.228648 | − | 0.973509i | \(-0.573430\pi\) | ||||
−0.228648 | + | 0.973509i | \(0.573430\pi\) | |||||||
\(600\) | −11967.0 | + | 6909.13i | −0.814249 | + | 0.470107i | ||||
\(601\) | −13206.6 | − | 22874.5i | −0.896354 | − | 1.55253i | −0.832120 | − | 0.554596i | \(-0.812873\pi\) |
−0.0642341 | − | 0.997935i | \(-0.520460\pi\) | |||||||
\(602\) | 568.417 | − | 984.527i | 0.0384833 | − | 0.0666550i | ||||
\(603\) | 46101.4i | 3.11343i | ||||||||
\(604\) | 1298.89 | + | 749.916i | 0.0875019 | + | 0.0505193i | ||||
\(605\) | 8791.29 | + | 5075.65i | 0.590771 | + | 0.341082i | ||||
\(606\) | 12050.1i | 0.807758i | ||||||||
\(607\) | 1663.19 | − | 2880.72i | 0.111214 | − | 0.192628i | −0.805046 | − | 0.593212i | \(-0.797860\pi\) |
0.916260 | + | 0.400584i | \(0.131193\pi\) | |||||||
\(608\) | 5649.09 | + | 9784.51i | 0.376811 | + | 0.652655i | ||||
\(609\) | −990.558 | + | 571.899i | −0.0659104 | + | 0.0380534i | ||||
\(610\) | −1788.40 | −0.118705 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −9217.27 | −0.608801 | ||||||||
\(613\) | −22740.7 | + | 13129.3i | −1.49835 | + | 0.865072i | −0.999998 | − | 0.00190303i | \(-0.999394\pi\) |
−0.498351 | + | 0.866975i | \(0.666061\pi\) | |||||||
\(614\) | −281.243 | − | 487.127i | −0.0184854 | − | 0.0320177i | ||||
\(615\) | 10332.0 | − | 17895.6i | 0.677443 | − | 1.17337i | ||||
\(616\) | 1992.50i | 0.130325i | ||||||||
\(617\) | 23688.3 | + | 13676.4i | 1.54563 | + | 0.892370i | 0.998467 | + | 0.0553441i | \(0.0176256\pi\) |
0.547163 | + | 0.837026i | \(0.315708\pi\) | |||||||
\(618\) | −21389.4 | − | 12349.1i | −1.39224 | − | 0.803812i | ||||
\(619\) | − | 13056.5i | − | 0.847795i | −0.905710 | − | 0.423897i | \(-0.860662\pi\) | ||
0.905710 | − | 0.423897i | \(-0.139338\pi\) | |||||||
\(620\) | −2131.49 | + | 3691.85i | −0.138069 | + | 0.239142i | ||||
\(621\) | −21413.3 | − | 37089.0i | −1.38371 | − | 2.39666i | ||||
\(622\) | −4941.83 | + | 2853.17i | −0.318568 | + | 0.183925i | ||||
\(623\) | −5708.28 | −0.367091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5095.82 | −0.326132 | ||||||||
\(626\) | −1342.72 | + | 775.220i | −0.0857283 | + | 0.0494953i | ||||
\(627\) | −4148.09 | − | 7184.71i | −0.264209 | − | 0.457623i | ||||
\(628\) | −77.0326 | + | 133.424i | −0.00489480 | + | 0.00847805i | ||||
\(629\) | − | 18471.4i | − | 1.17091i | ||||||
\(630\) | 9001.33 | + | 5196.92i | 0.569241 | + | 0.328651i | ||||
\(631\) | −5674.99 | − | 3276.46i | −0.358031 | − | 0.206709i | 0.310186 | − | 0.950676i | \(-0.399609\pi\) |
−0.668217 | + | 0.743967i | \(0.732942\pi\) | |||||||
\(632\) | 9439.35i | 0.594109i | ||||||||
\(633\) | −3545.83 | + | 6141.55i | −0.222645 | + | 0.385632i | ||||
\(634\) | 6402.54 | + | 11089.5i | 0.401068 | + | 0.694671i | ||||
\(635\) | −15474.9 | + | 8934.42i | −0.967089 | + | 0.558349i | ||||
\(636\) | −9728.76 | −0.606557 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 303.458 | 0.0188308 | ||||||||
\(639\) | 46357.4 | − | 26764.5i | 2.86991 | − | 1.65694i | ||||
\(640\) | 626.079 | + | 1084.40i | 0.0386686 | + | 0.0669760i | ||||
\(641\) | −2882.38 | + | 4992.44i | −0.177609 | + | 0.307628i | −0.941061 | − | 0.338237i | \(-0.890170\pi\) |
0.763452 | + | 0.645864i | \(0.223503\pi\) | |||||||
\(642\) | 33799.2i | 2.07780i | ||||||||
\(643\) | 10634.4 | + | 6139.75i | 0.652221 | + | 0.376560i | 0.789307 | − | 0.613999i | \(-0.210440\pi\) |
−0.137086 | + | 0.990559i | \(0.543774\pi\) | |||||||
\(644\) | −2351.71 | − | 1357.76i | −0.143898 | − | 0.0830795i | ||||
\(645\) | − | 4886.10i | − | 0.298279i | ||||||
\(646\) | −4361.52 | + | 7554.37i | −0.265637 | + | 0.460097i | ||||
\(647\) | −14512.1 | − | 25135.8i | −0.881810 | − | 1.52734i | −0.849327 | − | 0.527867i | \(-0.822992\pi\) |
−0.0324826 | − | 0.999472i | \(-0.510341\pi\) | |||||||
\(648\) | 43929.4 | − | 25362.7i | 2.66313 | − | 1.53756i | ||||
\(649\) | 1427.15 | 0.0863182 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13935.2 | −0.838962 | ||||||||
\(652\) | 1976.72 | − | 1141.26i | 0.118734 | − | 0.0685509i | ||||
\(653\) | 8583.57 | + | 14867.2i | 0.514396 | + | 0.890961i | 0.999860 | + | 0.0167042i | \(0.00531736\pi\) |
−0.485464 | + | 0.874257i | \(0.661349\pi\) | |||||||
\(654\) | 778.060 | − | 1347.64i | 0.0465207 | − | 0.0805763i | ||||
\(655\) | 15755.6i | 0.939880i | ||||||||
\(656\) | 6820.79 | + | 3937.99i | 0.405956 | + | 0.234379i | ||||
\(657\) | 58784.5 | + | 33939.2i | 3.49072 | + | 2.01537i | ||||
\(658\) | 1279.05i | 0.0757787i | ||||||||
\(659\) | −9156.49 | + | 15859.5i | −0.541254 | + | 0.937479i | 0.457579 | + | 0.889169i | \(0.348717\pi\) |
−0.998832 | + | 0.0483096i | \(0.984617\pi\) | |||||||
\(660\) | 1177.96 | + | 2040.28i | 0.0694727 | + | 0.120330i | ||||
\(661\) | 5962.85 | − | 3442.65i | 0.350874 | − | 0.202577i | −0.314196 | − | 0.949358i | \(-0.601735\pi\) |
0.665070 | + | 0.746781i | \(0.268402\pi\) | |||||||
\(662\) | 9457.28 | 0.555238 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12779.0 | −0.746867 | ||||||||
\(665\) | −5210.24 | + | 3008.13i | −0.303826 | + | 0.175414i | ||||
\(666\) | 31374.6 | + | 54342.3i | 1.82543 | + | 3.16175i | ||||
\(667\) | −751.669 | + | 1301.93i | −0.0436353 | + | 0.0755786i | ||||
\(668\) | − | 9030.25i | − | 0.523040i | ||||||
\(669\) | −8573.03 | − | 4949.64i | −0.495445 | − | 0.286045i | ||||
\(670\) | −10729.8 | − | 6194.86i | −0.618699 | − | 0.357206i | ||||
\(671\) | − | 948.641i | − | 0.0545781i | ||||||
\(672\) | 5243.98 | − | 9082.84i | 0.301028 | − | 0.521396i | ||||
\(673\) | 3119.13 | + | 5402.50i | 0.178653 | + | 0.309437i | 0.941420 | − | 0.337238i | \(-0.109493\pi\) |
−0.762766 | + | 0.646674i | \(0.776159\pi\) | |||||||
\(674\) | 13742.8 | − | 7934.41i | 0.785390 | − | 0.453445i | ||||
\(675\) | −23062.0 | −1.31505 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25482.4 | 1.44663 | 0.723316 | − | 0.690517i | \(-0.242617\pi\) | ||||
0.723316 | + | 0.690517i | \(0.242617\pi\) | |||||||
\(678\) | 18450.2 | − | 10652.2i | 1.04510 | − | 0.603388i | ||||
\(679\) | 1450.81 | + | 2512.88i | 0.0819986 | + | 0.142026i | ||||
\(680\) | 4502.17 | − | 7797.99i | 0.253898 | − | 0.439764i | ||||
\(681\) | − | 51595.7i | − | 2.90331i | ||||||
\(682\) | 3201.80 | + | 1848.56i | 0.179770 | + | 0.103790i | ||||
\(683\) | 23752.0 | + | 13713.2i | 1.33067 | + | 0.768261i | 0.985402 | − | 0.170243i | \(-0.0544554\pi\) |
0.345266 | + | 0.938505i | \(0.387789\pi\) | |||||||
\(684\) | 18124.3i | 1.01316i | ||||||||
\(685\) | −3053.00 | + | 5287.95i | −0.170291 | + | 0.294952i | ||||
\(686\) | −5735.15 | − | 9933.57i | −0.319197 | − | 0.552865i | ||||
\(687\) | −25412.5 | + | 14671.9i | −1.41128 | + | 0.814802i | ||||
\(688\) | 1862.31 | 0.103197 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19082.4 | 1.05283 | ||||||||
\(691\) | −12025.9 | + | 6943.15i | −0.662064 | + | 0.382243i | −0.793063 | − | 0.609140i | \(-0.791515\pi\) |
0.130999 | + | 0.991383i | \(0.458182\pi\) | |||||||
\(692\) | 2480.07 | + | 4295.61i | 0.136240 | + | 0.235975i | ||||
\(693\) | −2756.66 | + | 4774.67i | −0.151106 | + | 0.261724i | ||||
\(694\) | − | 7503.65i | − | 0.410425i | ||||||
\(695\) | 20042.7 | + | 11571.6i | 1.09390 | + | 0.631565i | ||||
\(696\) | −2915.17 | − | 1683.07i | −0.158763 | − | 0.0916619i | ||||
\(697\) | − | 11525.0i | − | 0.626314i | ||||||
\(698\) | −6772.76 | + | 11730.8i | −0.367268 | + | 0.636126i | ||||
\(699\) | 11571.5 | + | 20042.4i | 0.626143 | + | 1.08451i | ||||
\(700\) | −1266.39 | + | 731.150i | −0.0683785 | + | 0.0394784i | ||||
\(701\) | −15744.4 | −0.848301 | −0.424151 | − | 0.905592i | \(-0.639427\pi\) | ||||
−0.424151 | + | 0.905592i | \(0.639427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36321.1 | −1.94861 | ||||||||
\(704\) | −4458.82 | + | 2574.30i | −0.238705 | + | 0.137816i | ||||
\(705\) | 2748.66 | + | 4760.83i | 0.146838 | + | 0.254331i | ||||
\(706\) | 3599.30 | − | 6234.18i | 0.191872 | − | 0.332332i | ||||
\(707\) | 4635.28i | 0.246574i | ||||||||
\(708\) | −3771.65 | − | 2177.56i | −0.200208 | − | 0.115590i | ||||
\(709\) | −24845.5 | − | 14344.6i | −1.31607 | − | 0.759833i | −0.332976 | − | 0.942935i | \(-0.608053\pi\) |
−0.983094 | + | 0.183102i | \(0.941386\pi\) | |||||||
\(710\) | 14385.9i | 0.760410i | ||||||||
\(711\) | −13059.5 | + | 22619.8i | −0.688847 | + | 1.19312i | ||||
\(712\) | −8399.61 | − | 14548.5i | −0.442119 | − | 0.765772i | ||||
\(713\) | −15861.8 | + | 9157.81i | −0.833140 | + | 0.481013i | ||||
\(714\) | 8097.48 | 0.424427 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10300.3 | −0.537627 | ||||||||
\(717\) | 6614.26 | − | 3818.75i | 0.344511 | − | 0.198903i | ||||
\(718\) | −5955.20 | − | 10314.7i | −0.309535 | − | 0.536130i | ||||
\(719\) | −6309.54 | + | 10928.4i | −0.327269 | + | 0.566846i | −0.981969 | − | 0.189043i | \(-0.939462\pi\) |
0.654700 | + | 0.755889i | \(0.272795\pi\) | |||||||
\(720\) | 17026.7i | 0.881315i | ||||||||
\(721\) | −8227.79 | − | 4750.32i | −0.424991 | − | 0.245369i | ||||
\(722\) | 1620.07 | + | 935.345i | 0.0835078 | + | 0.0482132i | ||||
\(723\) | 34290.0i | 1.76384i | ||||||||
\(724\) | −5770.15 | + | 9994.19i | −0.296196 | + | 0.513027i | ||||
\(725\) | 404.772 | + | 701.086i | 0.0207350 | + | 0.0359140i | ||||
\(726\) | −23266.7 | + | 13433.0i | −1.18940 | + | 0.686702i | ||||
\(727\) | 12644.5 | 0.645061 | 0.322531 | − | 0.946559i | \(-0.395466\pi\) | ||||
0.322531 | + | 0.946559i | \(0.395466\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35059.5 | 1.78121 | ||||||||
\(730\) | −15798.3 | + | 9121.13i | −0.800986 | + | 0.462450i | ||||
\(731\) | −1362.57 | − | 2360.04i | −0.0689418 | − | 0.119411i | ||||
\(732\) | −1447.45 | + | 2507.05i | −0.0730863 | + | 0.126589i | ||||
\(733\) | 19109.0i | 0.962903i | 0.876473 | + | 0.481451i | \(0.159890\pi\) | ||||
−0.876473 | + | 0.481451i | \(0.840110\pi\) | |||||||
\(734\) | 23484.5 | + | 13558.8i | 1.18097 | + | 0.681831i | ||||
\(735\) | −18928.9 | − | 10928.6i | −0.949936 | − | 0.548446i | ||||
\(736\) | − | 13784.7i | − | 0.690370i | ||||||
\(737\) | 3286.00 | − | 5691.52i | 0.164235 | − | 0.284464i | ||||
\(738\) | 19575.8 | + | 33906.2i | 0.976415 | + | 1.69120i | ||||
\(739\) | 12205.4 | − | 7046.78i | 0.607554 | − | 0.350771i | −0.164454 | − | 0.986385i | \(-0.552586\pi\) |
0.772007 | + | 0.635614i | \(0.219253\pi\) | |||||||
\(740\) | 10314.3 | 0.512381 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6118.67 | 0.302727 | ||||||||
\(743\) | −15231.1 | + | 8793.70i | −0.752054 | + | 0.434198i | −0.826436 | − | 0.563031i | \(-0.809635\pi\) |
0.0743817 | + | 0.997230i | \(0.476302\pi\) | |||||||
\(744\) | −20505.4 | − | 35516.3i | −1.01043 | − | 1.75012i | ||||
\(745\) | −11877.8 | + | 20572.9i | −0.584119 | + | 1.01172i | ||||
\(746\) | − | 9945.63i | − | 0.488117i | ||||||
\(747\) | −30622.5 | − | 17679.9i | −1.49989 | − | 0.865964i | ||||
\(748\) | 1137.93 | + | 656.985i | 0.0556242 | + | 0.0321147i | ||||
\(749\) | 13001.5i | 0.634263i | ||||||||
\(750\) | 16278.7 | − | 28195.5i | 0.792551 | − | 1.37274i | ||||
\(751\) | −8293.48 | − | 14364.7i | −0.402974 | − | 0.697971i | 0.591109 | − | 0.806591i | \(-0.298690\pi\) |
−0.994083 | + | 0.108620i | \(0.965357\pi\) | |||||||
\(752\) | −1814.56 | + | 1047.64i | −0.0879922 | + | 0.0508023i | ||||
\(753\) | 13813.5 | 0.668514 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4054.22 | −0.195428 | ||||||||
\(756\) | 8788.26 | − | 5073.91i | 0.422786 | − | 0.244095i | ||||
\(757\) | −16909.7 | − | 29288.5i | −0.811882 | − | 1.40622i | −0.911545 | − | 0.411199i | \(-0.865110\pi\) |
0.0996637 | − | 0.995021i | \(-0.468223\pi\) | |||||||
\(758\) | 5981.10 | − | 10359.6i | 0.286601 | − | 0.496407i | ||||
\(759\) | 10122.1i | 0.484068i | ||||||||
\(760\) | −15333.5 | − | 8852.80i | −0.731848 | − | 0.422533i | ||||
\(761\) | −24362.4 | − | 14065.6i | −1.16049 | − | 0.670011i | −0.209071 | − | 0.977901i | \(-0.567044\pi\) |
−0.951422 | + | 0.307890i | \(0.900377\pi\) | |||||||
\(762\) | − | 47290.9i | − | 2.24825i | ||||||
\(763\) | 299.295 | − | 518.393i | 0.0142008 | − | 0.0245965i | ||||
\(764\) | −1921.09 | − | 3327.42i | −0.0909719 | − | 0.157568i | ||||
\(765\) | 21577.3 | − | 12457.7i | 1.01978 | − | 0.588769i | ||||
\(766\) | −434.645 | −0.0205018 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38085.9 | 1.78946 | ||||||||
\(769\) | 20555.1 | − | 11867.5i | 0.963897 | − | 0.556506i | 0.0665267 | − | 0.997785i | \(-0.478808\pi\) |
0.897370 | + | 0.441279i | \(0.145475\pi\) | |||||||
\(770\) | −740.849 | − | 1283.19i | −0.0346732 | − | 0.0600557i | ||||
\(771\) | 7226.86 | − | 12517.3i | 0.337573 | − | 0.584694i | ||||
\(772\) | 6716.75i | 0.313136i | ||||||||
\(773\) | −8258.64 | − | 4768.13i | −0.384272 | − | 0.221860i | 0.295403 | − | 0.955373i | \(-0.404546\pi\) |
−0.679675 | + | 0.733513i | \(0.737879\pi\) | |||||||
\(774\) | 8017.27 | + | 4628.77i | 0.372319 | + | 0.214958i | ||||
\(775\) | 9862.92i | 0.457144i | ||||||||
\(776\) | −4269.67 | + | 7395.29i | −0.197516 | + | 0.342108i | ||||
\(777\) | 16858.2 | + | 29199.3i | 0.778359 | + | 1.34816i | ||||
\(778\) | −17598.0 | + | 10160.2i | −0.810949 | + | 0.468202i | ||||
\(779\) | −22662.1 | −1.04230 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7630.84 | −0.349619 | ||||||||
\(782\) | 9216.98 | − | 5321.42i | 0.421481 | − | 0.243342i | ||||
\(783\) | −2808.97 | − | 4865.28i | −0.128205 | − | 0.222057i | ||||
\(784\) | 4165.37 | − | 7214.62i | 0.189749 | − | 0.328655i | ||||
\(785\) | − | 416.457i | − | 0.0189350i | ||||||
\(786\) | −36111.6 | − | 20849.0i | −1.63875 | − | 0.946133i | ||||
\(787\) | −15325.4 | − | 8848.10i | −0.694143 | − | 0.400763i | 0.111019 | − | 0.993818i | \(-0.464588\pi\) |
−0.805162 | + | 0.593055i | \(0.797922\pi\) | |||||||
\(788\) | − | 13228.9i | − | 0.598047i | ||||||
\(789\) | 35239.7 | − | 61037.0i | 1.59007 | − | 2.75409i | ||||
\(790\) | −3509.73 | − | 6079.04i | −0.158064 | − | 0.273775i | ||||
\(791\) | 7097.20 | − | 4097.57i | 0.319023 | − | 0.184188i | ||||
\(792\) | −16225.4 | −0.727961 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14734.7 | −0.658584 | ||||||||
\(795\) | 22774.7 | − | 13149.0i | 1.01602 | − | 0.586600i | ||||
\(796\) | 1655.62 | + | 2867.61i | 0.0737209 | + | 0.127688i | ||||
\(797\) | −16283.4 | + | 28203.6i | −0.723696 | + | 1.25348i | 0.235812 | + | 0.971799i | \(0.424225\pi\) |
−0.959508 | + | 0.281680i | \(0.909108\pi\) | |||||||
\(798\) | − | 15922.4i | − | 0.706325i | ||||||
\(799\) | 2655.27 | + | 1533.02i | 0.117568 | + | 0.0678777i | ||||
\(800\) | −6428.55 | − | 3711.53i | −0.284105 | − | 0.164028i | ||||
\(801\) | − | 46484.1i | − | 2.05048i | ||||||
\(802\) | −9568.38 | + | 16572.9i | −0.421286 | + | 0.729689i | ||||
\(803\) | −4838.22 | − | 8380.04i | −0.212624 | − | 0.368275i | ||||
\(804\) | −17368.4 | + | 10027.6i | −0.761860 | + | 0.439860i | ||||
\(805\) | 7340.36 | 0.321384 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4824.66 | 0.210453 | ||||||||
\(808\) | −11813.8 | + | 6820.71i | −0.514367 | + | 0.296970i | ||||
\(809\) | −5811.13 | − | 10065.2i | −0.252544 | − | 0.437420i | 0.711681 | − | 0.702502i | \(-0.247934\pi\) |
−0.964226 | + | 0.265083i | \(0.914601\pi\) | |||||||
\(810\) | −18860.7 | + | 32667.6i | −0.818144 | + | 1.41707i | ||||
\(811\) | − | 6494.39i | − | 0.281195i | −0.990067 | − | 0.140597i | \(-0.955098\pi\) | ||
0.990067 | − | 0.140597i | \(-0.0449023\pi\) | |||||||
\(812\) | −308.493 | − | 178.109i | −0.0133325 | − | 0.00769753i | ||||
\(813\) | −35506.0 | − | 20499.4i | −1.53167 | − | 0.884312i | ||||
\(814\) | − | 8945.22i | − | 0.385172i | ||||||
\(815\) | −3084.96 | + | 5343.31i | −0.132591 | + | 0.229654i | ||||
\(816\) | 6632.45 | + | 11487.7i | 0.284537 | + | 0.492833i | ||||
\(817\) | −4640.64 | + | 2679.27i | −0.198721 | + | 0.114732i | ||||
\(818\) | −16744.7 | −0.715725 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6435.49 | 0.274070 | ||||||||
\(821\) | −30222.4 | + | 17448.9i | −1.28474 | + | 0.741743i | −0.977710 | − | 0.209959i | \(-0.932667\pi\) |
−0.307026 | + | 0.951701i | \(0.599334\pi\) | |||||||
\(822\) | −8079.95 | − | 13994.9i | −0.342847 | − | 0.593829i | ||||
\(823\) | 751.307 | − | 1301.30i | 0.0318213 | − | 0.0551161i | −0.849676 | − | 0.527305i | \(-0.823203\pi\) |
0.881497 | + | 0.472189i | \(0.156536\pi\) | |||||||
\(824\) | − | 27959.9i | − | 1.18208i | ||||||
\(825\) | 4720.45 | + | 2725.35i | 0.199206 | + | 0.115012i | ||||
\(826\) | 2372.09 | + | 1369.52i | 0.0999218 | + | 0.0576899i | ||||
\(827\) | 27887.8i | 1.17262i | 0.810088 | + | 0.586308i | \(0.199419\pi\) | ||||
−0.810088 | + | 0.586308i | \(0.800581\pi\) | |||||||
\(828\) | 11056.6 | − | 19150.6i | 0.464062 | − | 0.803779i | ||||
\(829\) | 15421.8 | + | 26711.4i | 0.646107 | + | 1.11909i | 0.984045 | + | 0.177922i | \(0.0569373\pi\) |
−0.337938 | + | 0.941168i | \(0.609729\pi\) | |||||||
\(830\) | 8229.78 | − | 4751.47i | 0.344168 | − | 0.198706i | ||||
\(831\) | 41027.8 | 1.71268 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12190.5 | −0.507053 | ||||||||
\(834\) | −53044.1 | + | 30625.0i | −2.20236 | + | 1.27153i | ||||
\(835\) | 12204.9 | + | 21139.5i | 0.505831 | + | 0.876125i | ||||
\(836\) | 1291.86 | − | 2237.56i | 0.0534448 | − | 0.0925690i | ||||
\(837\) | − | 68445.0i | − | 2.82653i | ||||||
\(838\) | 8793.35 | + | 5076.84i | 0.362483 | + | 0.209280i | ||||
\(839\) | 31695.5 | + | 18299.4i | 1.30423 | + | 0.752997i | 0.981127 | − | 0.193366i | \(-0.0619405\pi\) |
0.323103 | + | 0.946364i | \(0.395274\pi\) | |||||||
\(840\) | 16435.9i | 0.675110i | ||||||||
\(841\) | 12095.9 | − | 20950.7i | 0.495957 | − | 0.859023i | ||||
\(842\) | 2478.85 | + | 4293.50i | 0.101457 | + | 0.175729i | ||||
\(843\) | 40024.9 | − | 23108.4i | 1.63527 | − | 0.944123i | ||||
\(844\) | −2208.58 | −0.0900741 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10415.6 | −0.423282 | ||||||||
\(847\) | −8949.93 | + | 5167.24i | −0.363073 | + | 0.209620i | ||||
\(848\) | 5011.66 | + | 8680.44i | 0.202949 | + | 0.351518i | ||||
\(849\) | 18243.8 | − | 31599.2i | 0.737485 | − | 1.27736i | ||||
\(850\) | − | 5731.15i | − | 0.231267i | ||||||
\(851\) | 38377.8 | + | 22157.4i | 1.54591 | + | 0.892534i | ||||
\(852\) | 20166.6 | + | 11643.2i | 0.810913 | + | 0.468181i | ||||
\(853\) | 21578.4i | 0.866155i | 0.901357 | + | 0.433077i | \(0.142572\pi\) | ||||
−0.901357 | + | 0.433077i | \(0.857428\pi\) | |||||||
\(854\) | 910.337 | − | 1576.75i | 0.0364767 | − | 0.0631795i | ||||
\(855\) | −24496.1 | − | 42428.4i | −0.979822 | − | 1.69710i | ||||
\(856\) | −33136.5 | + | 19131.4i | −1.32311 | + | 0.763897i | ||||
\(857\) | 31199.6 | 1.24359 | 0.621795 | − | 0.783180i | \(-0.286404\pi\) | ||||
0.621795 | + | 0.783180i | \(0.286404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8035.71 | 0.319179 | 0.159590 | − | 0.987183i | \(-0.448983\pi\) | ||||
0.159590 | + | 0.987183i | \(0.448983\pi\) | |||||||
\(860\) | 1317.83 | − | 760.849i | 0.0522531 | − | 0.0301683i | ||||
\(861\) | 10518.5 | + | 18218.5i | 0.416340 | + | 0.721122i | ||||
\(862\) | 441.173 | − | 764.134i | 0.0174320 | − | 0.0301932i | ||||
\(863\) | 8741.47i | 0.344801i | 0.985027 | + | 0.172400i | \(0.0551523\pi\) | ||||
−0.985027 | + | 0.172400i | \(0.944848\pi\) | |||||||
\(864\) | 44611.8 | + | 25756.6i | 1.75662 | + | 1.01419i | ||||
\(865\) | −11611.5 | − | 6703.93i | −0.456421 | − | 0.263515i | ||||
\(866\) | − | 11558.9i | − | 0.453566i | ||||||
\(867\) | −14242.3 | + | 24668.3i | −0.557892 | + | 0.966297i | ||||
\(868\) | −2169.95 | − | 3758.47i | −0.0848536 | − | 0.146971i | ||||
\(869\) | 3224.57 | − | 1861.71i | 0.125876 | − | 0.0726744i | ||||
\(870\) | 2503.20 | 0.0975475 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1761.62 | 0.0684128 | ||||||||
\(873\) | −20463.1 | + | 11814.4i | −0.793321 | + | 0.458024i | ||||
\(874\) | −10463.7 | − | 18123.7i | −0.404967 | − | 0.701423i | ||||
\(875\) | 6261.87 | − | 10845.9i | 0.241931 | − | 0.419038i | ||||
\(876\) | 29528.8i | 1.13891i | ||||||||
\(877\) | −1510.46 | − | 872.066i | −0.0581582 | − | 0.0335776i | 0.470639 | − | 0.882326i | \(-0.344023\pi\) |
−0.528797 | + | 0.848748i | \(0.677357\pi\) | |||||||
\(878\) | 21860.9 | + | 12621.4i | 0.840284 | + | 0.485138i | ||||
\(879\) | − | 51229.0i | − | 1.96577i | ||||||
\(880\) | 1213.62 | − | 2102.06i | 0.0464900 | − | 0.0805230i | ||||
\(881\) | −2844.40 | − | 4926.65i | −0.108775 | − | 0.188403i | 0.806500 | − | 0.591235i | \(-0.201359\pi\) |
−0.915274 | + | 0.402832i | \(0.868026\pi\) | |||||||
\(882\) | 35864.0 | − | 20706.1i | 1.36916 | − | 0.790488i | ||||
\(883\) | 3940.14 | 0.150165 | 0.0750827 | − | 0.997177i | \(-0.476078\pi\) | ||||
0.0750827 | + | 0.997177i | \(0.476078\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11772.4 | 0.447147 | ||||||||
\(886\) | 30148.8 | − | 17406.4i | 1.14319 | − | 0.660022i | ||||
\(887\) | 18440.2 | + | 31939.3i | 0.698039 | + | 1.20904i | 0.969145 | + | 0.246490i | \(0.0792772\pi\) |
−0.271106 | + | 0.962549i | \(0.587389\pi\) | |||||||
\(888\) | −49612.9 | + | 85932.1i | −1.87489 | + | 3.24740i | ||||
\(889\) | − | 18191.3i | − | 0.686295i | ||||||
\(890\) | 10818.9 | + | 6246.28i | 0.407471 | + | 0.235254i | ||||
\(891\) | −17328.2 | − | 10004.5i | −0.651535 | − | 0.376164i | ||||
\(892\) | − | 3082.97i | − | 0.115724i | ||||||
\(893\) | 3014.44 | − | 5221.16i | 0.112961 | − | 0.195654i | ||||
\(894\) | −31435.3 | − | 54447.5i | −1.17601 | − | 2.03691i | ||||
\(895\) | 24112.7 | − | 13921.5i | 0.900558 | − | 0.519937i | ||||
\(896\) | −1274.75 | −0.0475296 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30493.5 | 1.13317 | ||||||||
\(899\) | −2080.73 | + | 1201.31i | −0.0771926 | + | 0.0445671i | ||||
\(900\) | −5953.95 | − | 10312.5i | −0.220517 | − | 0.381946i | ||||
\(901\) | 7333.62 | − | 12702.2i | 0.271164 | − | 0.469669i | ||||
\(902\) | − | 5581.26i | − | 0.206026i | ||||||
\(903\) | 4307.85 | + | 2487.14i | 0.158755 | + | 0.0916575i | ||||
\(904\) | 20886.7 | + | 12059.0i | 0.768454 | + | 0.443667i | ||||
\(905\) | − | 31194.8i | − | 1.14580i | ||||||
\(906\) | 5364.87 | − | 9292.23i | 0.196728 | − | 0.340743i | ||||
\(907\) | 8955.99 | + | 15512.2i | 0.327871 | + | 0.567889i | 0.982089 | − | 0.188417i | \(-0.0603357\pi\) |
−0.654219 | + | 0.756306i | \(0.727002\pi\) | |||||||
\(908\) | 13915.9 | − | 8034.33i | 0.508606 | − | 0.293644i | ||||
\(909\) | −37746.3 | −1.37730 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51246.0 | 1.86373 | 0.931864 | − | 0.362807i | \(-0.118181\pi\) | ||||
0.931864 | + | 0.362807i | \(0.118181\pi\) | |||||||
\(912\) | 22588.8 | − | 13041.7i | 0.820165 | − | 0.473523i | ||||
\(913\) | 2520.37 | + | 4365.41i | 0.0913604 | + | 0.158241i | ||||
\(914\) | 14117.8 | − | 24452.7i | 0.510912 | − | 0.884926i | ||||
\(915\) | − | 7825.24i | − | 0.282726i | ||||||
\(916\) | −7914.32 | − | 4569.34i | −0.285477 | − | 0.164820i | ||||
\(917\) | −13891.0 | − | 8019.95i | −0.500240 | − | 0.288814i | ||||
\(918\) | 39772.0i | 1.42993i | ||||||||
\(919\) | −12748.3 | + | 22080.6i | −0.457591 | + | 0.792571i | −0.998833 | − | 0.0482959i | \(-0.984621\pi\) |
0.541242 | + | 0.840867i | \(0.317954\pi\) | |||||||
\(920\) | 10801.2 | + | 18708.2i | 0.387070 | + | 0.670425i | ||||
\(921\) | 2131.45 | − | 1230.59i | 0.0762580 | − | 0.0440276i | ||||
\(922\) | −20396.9 | −0.728564 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2398.43 | −0.0853924 | ||||||||
\(925\) | 20666.3 | − | 11931.7i | 0.734600 | − | 0.424121i | ||||
\(926\) | −7698.35 | − | 13333.9i | −0.273200 | − | 0.473197i | ||||
\(927\) | 38683.1 | − | 67001.1i | 1.37057 | − | 2.37390i | ||||
\(928\) | − | 1808.26i | − | 0.0639646i | ||||||
\(929\) | −39013.2 | − | 22524.3i | −1.37781 | − | 0.795477i | −0.385912 | − | 0.922536i | \(-0.626113\pi\) |
−0.991895 | + | 0.127058i | \(0.959447\pi\) | |||||||
\(930\) | 26411.3 | + | 15248.6i | 0.931249 | + | 0.537657i | ||||
\(931\) | 23970.6i | 0.843830i | ||||||||
\(932\) | −3603.76 | + | 6241.89i | −0.126658 | + | 0.219378i | ||||
\(933\) | −12484.2 | − | 21623.2i | −0.438064 | − | 0.758748i | ||||
\(934\) | −5634.50 | + | 3253.08i | −0.197394 | + | 0.113966i | ||||
\(935\) | −3551.82 | −0.124232 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2280.50 | −0.0795099 | −0.0397550 | − | 0.999209i | \(-0.512658\pi\) | ||||
−0.0397550 | + | 0.999209i | \(0.512658\pi\) | |||||||
\(938\) | 10923.4 | − | 6306.65i | 0.380237 | − | 0.219530i | ||||
\(939\) | −3392.02 | − | 5875.14i | −0.117885 | − | 0.204183i | ||||
\(940\) | −856.028 | + | 1482.68i | −0.0297027 | + | 0.0514466i | ||||
\(941\) | 31174.8i | 1.07999i | 0.841669 | + | 0.539994i | \(0.181573\pi\) | ||||
−0.841669 | + | 0.539994i | \(0.818427\pi\) | |||||||
\(942\) | 954.514 | + | 551.089i | 0.0330146 | + | 0.0190610i | ||||
\(943\) | 23945.3 | + | 13824.9i | 0.826901 | + | 0.477412i | ||||
\(944\) | 4486.98i | 0.154702i | ||||||||
\(945\) | −13715.4 | + | 23755.7i | −0.472128 | + | 0.817750i | ||||
\(946\) | −659.856 | − | 1142.90i | −0.0226784 | − | 0.0392802i | ||||
\(947\) | 24589.9 | − | 14197.0i | 0.843784 | − | 0.487159i | −0.0147644 | − | 0.999891i | \(-0.504700\pi\) |
0.858549 | + | 0.512732i | \(0.171366\pi\) | |||||||
\(948\) | −11362.4 | −0.389277 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11269.4 | −0.384871 | ||||||||
\(951\) | −48522.8 | + | 28014.6i | −1.65453 | + | 0.955243i | ||||
\(952\) | 4583.41 | + | 7938.71i | 0.156039 | + | 0.270268i | ||||
\(953\) | −16958.4 | + | 29372.8i | −0.576429 | + | 0.998404i | 0.419456 | + | 0.907776i | \(0.362221\pi\) |
−0.995885 | + | 0.0906283i | \(0.971112\pi\) | |||||||
\(954\) | 49826.0i | 1.69096i | ||||||||
\(955\) | 8994.42 | + | 5192.93i | 0.304767 | + | 0.175957i | ||||
\(956\) | 2059.91 | + | 1189.29i | 0.0696884 | + | 0.0402346i | ||||
\(957\) | 1327.80i | 0.0448501i | ||||||||
\(958\) | 19036.6 | − | 32972.4i | 0.642010 | − | 1.11199i | ||||
\(959\) | −3108.09 | − | 5383.38i | −0.104657 | − | 0.181270i | ||||
\(960\) | −36780.4 | + | 21235.1i | −1.23654 | + | 0.713918i | ||||
\(961\) | 519.228 | 0.0174290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −105874. | −3.54284 | ||||||||
\(964\) | −9248.35 | + | 5339.54i | −0.308993 | + | 0.178397i | ||||
\(965\) | −9078.08 | − | 15723.7i | −0.302833 | − | 0.524522i | ||||
\(966\) | −9713.35 | + | 16824.0i | −0.323522 | + | 0.560356i | ||||
\(967\) | − | 10792.9i | − | 0.358920i | −0.983765 | − | 0.179460i | \(-0.942565\pi\) | ||
0.983765 | − | 0.179460i | \(-0.0574350\pi\) | |||||||
\(968\) | −26339.2 | − | 15207.0i | −0.874561 | − | 0.504928i | ||||
\(969\) | −33054.5 | − | 19084.0i | −1.09584 | − | 0.632681i | ||||
\(970\) | − | 6350.19i | − | 0.210198i | ||||||
\(971\) | −3715.56 | + | 6435.55i | −0.122799 | + | 0.212695i | −0.920871 | − | 0.389868i | \(-0.872520\pi\) |
0.798071 | + | 0.602563i | \(0.205854\pi\) | |||||||
\(972\) | 14132.9 | + | 24478.9i | 0.466372 | + | 0.807780i | ||||
\(973\) | −20404.4 | + | 11780.5i | −0.672285 | + | 0.388144i | ||||
\(974\) | 30775.1 | 1.01242 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2982.54 | 0.0978164 | ||||||||
\(977\) | 10758.3 | − | 6211.30i | 0.352291 | − | 0.203395i | −0.313403 | − | 0.949620i | \(-0.601469\pi\) |
0.665694 | + | 0.746225i | \(0.268136\pi\) | |||||||
\(978\) | −8164.53 | − | 14141.4i | −0.266946 | − | 0.462364i | ||||
\(979\) | −3313.28 | + | 5738.77i | −0.108164 | + | 0.187346i | ||||
\(980\) | − | 6807.08i | − | 0.221882i | ||||||
\(981\) | 4221.42 | + | 2437.24i | 0.137390 | + | 0.0793221i | ||||
\(982\) | −22861.5 | − | 13199.1i | −0.742911 | − | 0.428920i | ||||
\(983\) | 38791.6i | 1.25866i | 0.777140 | + | 0.629328i | \(0.216670\pi\) | ||||
−0.777140 | + | 0.629328i | \(0.783330\pi\) | |||||||
\(984\) | −30955.4 | + | 53616.3i | −1.00287 | + | 1.73702i | ||||
\(985\) | 17879.7 | + | 30968.5i | 0.578369 | + | 1.00177i | ||||
\(986\) | 1209.07 | − | 698.057i | 0.0390513 | − | 0.0225463i | ||||
\(987\) | −5596.53 | −0.180486 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6537.89 | 0.210205 | ||||||||
\(990\) | 10449.3 | − | 6032.93i | 0.335457 | − | 0.193676i | ||||
\(991\) | 533.253 | + | 923.621i | 0.0170932 | + | 0.0296062i | 0.874445 | − | 0.485124i | \(-0.161225\pi\) |
−0.857352 | + | 0.514730i | \(0.827892\pi\) | |||||||
\(992\) | 11015.3 | − | 19079.1i | 0.352557 | − | 0.610646i | ||||
\(993\) | 41380.8i | 1.32244i | ||||||||
\(994\) | −12683.3 | − | 7322.72i | −0.404719 | − | 0.233665i | ||||
\(995\) | −7751.50 | − | 4475.33i | −0.246974 | − | 0.142590i | ||||
\(996\) | − | 15382.4i | − | 0.489369i | ||||||
\(997\) | 15325.8 | − | 26545.0i | 0.486833 | − | 0.843219i | −0.513053 | − | 0.858357i | \(-0.671485\pi\) |
0.999885 | + | 0.0151382i | \(0.00481881\pi\) | |||||||
\(998\) | −5820.02 | − | 10080.6i | −0.184599 | − | 0.319734i | ||||
\(999\) | −143417. | + | 82801.7i | −4.54204 | + | 2.62235i |
(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 | 169.4.e.h.23.13 | 36 | ||
13.2 | odd | 12 | 169.4.a.l.1.6 | yes | 9 | ||
13.3 | even | 3 | 169.4.b.g.168.13 | 18 | |||
13.4 | even | 6 | inner | 169.4.e.h.147.13 | 36 | ||
13.5 | odd | 4 | 169.4.c.k.146.4 | 18 | |||
13.6 | odd | 12 | 169.4.c.k.22.4 | 18 | |||
13.7 | odd | 12 | 169.4.c.l.22.6 | 18 | |||
13.8 | odd | 4 | 169.4.c.l.146.6 | 18 | |||
13.9 | even | 3 | inner | 169.4.e.h.147.6 | 36 | ||
13.10 | even | 6 | 169.4.b.g.168.6 | 18 | |||
13.11 | odd | 12 | 169.4.a.k.1.4 | ✓ | 9 | ||
13.12 | even | 2 | inner | 169.4.e.h.23.6 | 36 | ||
39.2 | even | 12 | 1521.4.a.bg.1.4 | 9 | |||
39.11 | even | 12 | 1521.4.a.bh.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.4 | ✓ | 9 | 13.11 | odd | 12 | ||
169.4.a.l.1.6 | yes | 9 | 13.2 | odd | 12 | ||
169.4.b.g.168.6 | 18 | 13.10 | even | 6 | |||
169.4.b.g.168.13 | 18 | 13.3 | even | 3 | |||
169.4.c.k.22.4 | 18 | 13.6 | odd | 12 | |||
169.4.c.k.146.4 | 18 | 13.5 | odd | 4 | |||
169.4.c.l.22.6 | 18 | 13.7 | odd | 12 | |||
169.4.c.l.146.6 | 18 | 13.8 | odd | 4 | |||
169.4.e.h.23.6 | 36 | 13.12 | even | 2 | inner | ||
169.4.e.h.23.13 | 36 | 1.1 | even | 1 | trivial | ||
169.4.e.h.147.6 | 36 | 13.9 | even | 3 | inner | ||
169.4.e.h.147.13 | 36 | 13.4 | even | 6 | inner | ||
1521.4.a.bg.1.4 | 9 | 39.2 | even | 12 | |||
1521.4.a.bh.1.6 | 9 | 39.11 | even | 12 |