Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,7,Mod(17,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.17");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.d (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: | \(12.4229205155\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{18} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.4 | ||
Root | \(-4.28281i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 54.35 |
Dual form | 54.7.d.a.17.4 |
$q$-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 \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).
\(n\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.89898 | + | 2.82843i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | + | 27.7128i | 0.250000 | + | 0.433013i | ||||
\(5\) | −156.951 | + | 90.6160i | −1.25561 | + | 0.724928i | −0.972218 | − | 0.234076i | \(-0.924794\pi\) |
−0.283394 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 104.306 | − | 180.663i | 0.304099 | − | 0.526715i | −0.672961 | − | 0.739678i | \(-0.734978\pi\) |
0.977060 | + | 0.212963i | \(0.0683113\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1025.20 | −1.02520 | ||||||||
\(11\) | −2301.99 | − | 1329.05i | −1.72952 | − | 0.998538i | −0.891782 | − | 0.452465i | \(-0.850545\pi\) |
−0.837737 | − | 0.546074i | \(-0.816122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −438.599 | − | 759.676i | −0.199636 | − | 0.345779i | 0.748775 | − | 0.662825i | \(-0.230642\pi\) |
−0.948410 | + | 0.317046i | \(0.897309\pi\) | |||||||
\(14\) | 1021.99 | − | 590.043i | 0.372444 | − | 0.215030i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | + | 886.810i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4428.53i | 0.901389i | 0.892678 | + | 0.450695i | \(0.148824\pi\) | ||||
−0.892678 | + | 0.450695i | \(0.851176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4194.21 | −0.611491 | −0.305745 | − | 0.952113i | \(-0.598906\pi\) | ||||
−0.305745 | + | 0.952113i | \(0.598906\pi\) | |||||||
\(20\) | −5022.45 | − | 2899.71i | −0.627806 | − | 0.362464i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7518.27 | − | 13022.0i | −0.706073 | − | 1.22295i | ||||
\(23\) | −10399.9 | + | 6004.40i | −0.854766 | + | 0.493499i | −0.862256 | − | 0.506473i | \(-0.830949\pi\) |
0.00749035 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8610.01 | − | 14913.0i | 0.551041 | − | 0.954431i | ||||
\(26\) | − | 4962.18i | − | 0.282327i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6675.58 | 0.304099 | ||||||||
\(29\) | −2288.79 | − | 1321.43i | −0.0938450 | − | 0.0541815i | 0.452343 | − | 0.891844i | \(-0.350588\pi\) |
−0.546188 | + | 0.837663i | \(0.683922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2902.50 | − | 5027.28i | −0.0974289 | − | 0.168752i | 0.813191 | − | 0.581997i | \(-0.197729\pi\) |
−0.910620 | + | 0.413245i | \(0.864395\pi\) | |||||||
\(32\) | −5016.55 | + | 2896.31i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12525.8 | + | 21695.3i | −0.318689 | + | 0.551986i | ||||
\(35\) | 37807.1i | 0.881799i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41579.5 | 0.820869 | 0.410435 | − | 0.911890i | \(-0.365377\pi\) | ||||
0.410435 | + | 0.911890i | \(0.365377\pi\) | |||||||
\(38\) | −20547.4 | − | 11863.0i | −0.374460 | − | 0.216195i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16403.2 | − | 28411.3i | −0.256301 | − | 0.443926i | ||||
\(41\) | 64721.2 | − | 37366.8i | 0.939063 | − | 0.542168i | 0.0493965 | − | 0.998779i | \(-0.484270\pi\) |
0.889666 | + | 0.456611i | \(0.150937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −73052.9 | + | 126531.i | −0.918824 | + | 1.59145i | −0.117620 | + | 0.993059i | \(0.537526\pi\) |
−0.801204 | + | 0.598391i | \(0.795807\pi\) | |||||||
\(44\) | − | 85059.5i | − | 0.998538i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −67932.1 | −0.697913 | ||||||||
\(47\) | 22319.7 | + | 12886.3i | 0.214978 | + | 0.124118i | 0.603623 | − | 0.797270i | \(-0.293723\pi\) |
−0.388645 | + | 0.921388i | \(0.627057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 37065.1 | + | 64198.6i | 0.315048 | + | 0.545679i | ||||
\(50\) | 84360.6 | − | 48705.6i | 0.674885 | − | 0.389645i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14035.2 | − | 24309.6i | 0.0998178 | − | 0.172889i | ||||
\(53\) | 197505.i | 1.32663i | 0.748340 | + | 0.663316i | \(0.230851\pi\) | ||||
−0.748340 | + | 0.663316i | \(0.769149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 481734. | 2.89547 | ||||||||
\(56\) | 32703.5 | + | 18881.4i | 0.186222 | + | 0.107515i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7475.15 | − | 12947.3i | −0.0383121 | − | 0.0663585i | ||||
\(59\) | 31321.5 | − | 18083.5i | 0.152506 | − | 0.0880493i | −0.421805 | − | 0.906687i | \(-0.638603\pi\) |
0.574311 | + | 0.818637i | \(0.305270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11967.3 | + | 20728.0i | −0.0527239 | + | 0.0913204i | −0.891183 | − | 0.453644i | \(-0.850124\pi\) |
0.838459 | + | 0.544965i | \(0.183457\pi\) | |||||||
\(62\) | − | 32838.1i | − | 0.137785i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 137678. | + | 79488.2i | 0.501330 | + | 0.289443i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −176540. | − | 305776.i | −0.586973 | − | 1.01667i | −0.994626 | − | 0.103530i | \(-0.966986\pi\) |
0.407653 | − | 0.913137i | \(-0.366347\pi\) | |||||||
\(68\) | −122727. | + | 70856.4i | −0.390313 | + | 0.225347i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −106935. | + | 185216.i | −0.311763 | + | 0.539989i | ||||
\(71\) | − | 496781.i | − | 1.38800i | −0.719974 | − | 0.694001i | \(-0.755846\pi\) | ||
0.719974 | − | 0.694001i | \(-0.244154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −382139. | −0.982319 | −0.491160 | − | 0.871070i | \(-0.663427\pi\) | ||||
−0.491160 | + | 0.871070i | \(0.663427\pi\) | |||||||
\(74\) | 203697. | + | 117605.i | 0.502678 | + | 0.290221i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −67107.4 | − | 116233.i | −0.152873 | − | 0.264783i | ||||
\(77\) | −480222. | + | 277257.i | −1.05189 | + | 0.607309i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −193328. | + | 334855.i | −0.392116 | + | 0.679165i | −0.992728 | − | 0.120376i | \(-0.961590\pi\) |
0.600613 | + | 0.799540i | \(0.294923\pi\) | |||||||
\(80\) | − | 185582.i | − | 0.362464i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 422757. | 0.766742 | ||||||||
\(83\) | −359691. | − | 207667.i | −0.629064 | − | 0.363190i | 0.151326 | − | 0.988484i | \(-0.451646\pi\) |
−0.780389 | + | 0.625294i | \(0.784979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −401295. | − | 695064.i | −0.653442 | − | 1.13180i | ||||
\(86\) | −715770. | + | 413250.i | −1.12533 | + | 0.649707i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 240585. | − | 416705.i | 0.353037 | − | 0.611477i | ||||
\(89\) | 405654.i | 0.575421i | 0.957717 | + | 0.287710i | \(0.0928941\pi\) | ||||
−0.957717 | + | 0.287710i | \(0.907106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −182994. | −0.242836 | ||||||||
\(92\) | −332798. | − | 192141.i | −0.427383 | − | 0.246750i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 72895.7 | + | 126259.i | 0.0877644 | + | 0.152012i | ||||
\(95\) | 658288. | − | 380063.i | 0.767795 | − | 0.443287i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −178244. | + | 308727.i | −0.195298 | + | 0.338267i | −0.946998 | − | 0.321239i | \(-0.895901\pi\) |
0.751700 | + | 0.659505i | \(0.229234\pi\) | |||||||
\(98\) | 419343.i | 0.445545i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 551041. | 0.551041 | ||||||||
\(101\) | −1.41963e6 | − | 819621.i | −1.37787 | − | 0.795516i | −0.385971 | − | 0.922511i | \(-0.626133\pi\) |
−0.991903 | + | 0.126995i | \(0.959467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −462737. | − | 801484.i | −0.423470 | − | 0.733472i | 0.572806 | − | 0.819691i | \(-0.305855\pi\) |
−0.996276 | + | 0.0862192i | \(0.972521\pi\) | |||||||
\(104\) | 137516. | − | 79394.9i | 0.122251 | − | 0.0705818i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −558628. | + | 967573.i | −0.469035 | + | 0.812393i | ||||
\(107\) | 266819.i | 0.217804i | 0.994053 | + | 0.108902i | \(0.0347334\pi\) | ||||
−0.994053 | + | 0.108902i | \(0.965267\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 169960. | 0.131240 | 0.0656200 | − | 0.997845i | \(-0.479097\pi\) | ||||
0.0656200 | + | 0.997845i | \(0.479097\pi\) | |||||||
\(110\) | 2.36001e6 | + | 1.36255e6i | 1.77311 | + | 1.02370i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 106809. | + | 184999.i | 0.0760247 | + | 0.131679i | ||||
\(113\) | 1.65439e6 | − | 955161.i | 1.14657 | − | 0.661974i | 0.198523 | − | 0.980096i | \(-0.436385\pi\) |
0.948050 | + | 0.318122i | \(0.103052\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.08819e6 | − | 1.88480e6i | 0.715503 | − | 1.23929i | ||||
\(116\) | − | 84571.6i | − | 0.0541815i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 204591. | 0.124520 | ||||||||
\(119\) | 800071. | + | 461921.i | 0.474775 | + | 0.274111i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.64699e6 | + | 4.58473e6i | 1.49416 | + | 2.58796i | ||||
\(122\) | −117255. | + | 67697.4i | −0.0645733 | + | 0.0372814i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 92880.1 | − | 160873.i | 0.0487144 | − | 0.0843759i | ||||
\(125\) | 289070.i | 0.148004i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.75663e6 | −0.857571 | −0.428786 | − | 0.903406i | \(-0.641058\pi\) | ||||
−0.428786 | + | 0.903406i | \(0.641058\pi\) | |||||||
\(128\) | −160530. | − | 92681.9i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 449653. | + | 778822.i | 0.204667 | + | 0.354493i | ||||
\(131\) | 2.07548e6 | − | 1.19828e6i | 0.923221 | − | 0.533022i | 0.0385598 | − | 0.999256i | \(-0.487723\pi\) |
0.884661 | + | 0.466234i | \(0.154390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −437481. | + | 757740.i | −0.185954 | + | 0.322081i | ||||
\(134\) | − | 1.99732e6i | − | 0.830105i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −801649. | −0.318689 | ||||||||
\(137\) | −1.15495e6 | − | 666808.i | −0.449159 | − | 0.259322i | 0.258316 | − | 0.966060i | \(-0.416832\pi\) |
−0.707475 | + | 0.706739i | \(0.750166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.08878e6 | − | 1.88583e6i | −0.405412 | − | 0.702194i | 0.588957 | − | 0.808164i | \(-0.299539\pi\) |
−0.994369 | + | 0.105970i | \(0.966205\pi\) | |||||||
\(140\) | −1.04774e6 | + | 604914.i | −0.381830 | + | 0.220450i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.40511e6 | − | 2.43372e6i | 0.490733 | − | 0.849974i | ||||
\(143\) | 2.33169e6i | 0.797375i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 478971. | 0.157111 | ||||||||
\(146\) | −1.87209e6 | − | 1.08085e6i | −0.601545 | − | 0.347302i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 665272. | + | 1.15228e6i | 0.205217 | + | 0.355447i | ||||
\(149\) | −3.35022e6 | + | 1.93425e6i | −1.01278 | + | 0.584727i | −0.912004 | − | 0.410182i | \(-0.865465\pi\) |
−0.100774 | + | 0.994909i | \(0.532132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −480879. | + | 832907.i | −0.139671 | + | 0.241917i | −0.927372 | − | 0.374141i | \(-0.877938\pi\) |
0.787701 | + | 0.616057i | \(0.211271\pi\) | |||||||
\(152\) | − | 759234.i | − | 0.216195i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.13680e6 | −0.858864 | ||||||||
\(155\) | 911105. | + | 526027.i | 0.244666 | + | 0.141258i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 796173. | + | 1.37901e6i | 0.205735 | + | 0.356344i | 0.950367 | − | 0.311132i | \(-0.100708\pi\) |
−0.744632 | + | 0.667476i | \(0.767375\pi\) | |||||||
\(158\) | −1.89422e6 | + | 1.09363e6i | −0.480242 | + | 0.277268i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 524904. | − | 909160.i | 0.128150 | − | 0.221963i | ||||
\(161\) | 2.50518e6i | 0.600290i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 702280. | 0.162161 | 0.0810807 | − | 0.996708i | \(-0.474163\pi\) | ||||
0.0810807 | + | 0.996708i | \(0.474163\pi\) | |||||||
\(164\) | 2.07108e6 | + | 1.19574e6i | 0.469531 | + | 0.271084i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.17474e6 | − | 2.03472e6i | −0.256814 | − | 0.444815i | ||||
\(167\) | 3.27789e6 | − | 1.89249e6i | 0.703794 | − | 0.406335i | −0.104965 | − | 0.994476i | \(-0.533473\pi\) |
0.808759 | + | 0.588140i | \(0.200140\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.02867e6 | − | 3.51375e6i | 0.420291 | − | 0.727966i | ||||
\(170\) | − | 4.54014e6i | − | 0.924107i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.67539e6 | −0.918824 | ||||||||
\(173\) | −3.78706e6 | − | 2.18646e6i | −0.731416 | − | 0.422283i | 0.0875242 | − | 0.996162i | \(-0.472104\pi\) |
−0.818940 | + | 0.573879i | \(0.805438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.79615e6 | − | 3.11102e6i | −0.335142 | − | 0.580483i | ||||
\(176\) | 2.35724e6 | − | 1.36095e6i | 0.432380 | − | 0.249635i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.14736e6 | + | 1.98729e6i | −0.203442 | + | 0.352372i | ||||
\(179\) | − | 49288.2i | − | 0.00859377i | −0.999991 | − | 0.00429688i | \(-0.998632\pi\) | ||
0.999991 | − | 0.00429688i | \(-0.00136775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.52205e6 | −0.762605 | −0.381303 | − | 0.924450i | \(-0.624524\pi\) | ||||
−0.381303 | + | 0.924450i | \(0.624524\pi\) | |||||||
\(182\) | −896484. | − | 517585.i | −0.148706 | − | 0.0858554i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.08691e6 | − | 1.88259e6i | −0.174478 | − | 0.302205i | ||||
\(185\) | −6.52596e6 | + | 3.76777e6i | −1.03069 | + | 0.595071i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.88575e6 | − | 1.01944e7i | 0.900072 | − | 1.55897i | ||||
\(188\) | 824721.i | 0.124118i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.29992e6 | 0.626902 | ||||||||
\(191\) | −1.07831e6 | − | 622561.i | −0.154754 | − | 0.0893473i | 0.420623 | − | 0.907235i | \(-0.361811\pi\) |
−0.575377 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.47671e6 | + | 9.48595e6i | 0.761812 | + | 1.31950i | 0.941915 | + | 0.335850i | \(0.109024\pi\) |
−0.180103 | + | 0.983648i | \(0.557643\pi\) | |||||||
\(194\) | −1.74642e6 | + | 1.00830e6i | −0.239191 | + | 0.138097i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.18608e6 | + | 2.05435e6i | −0.157524 | + | 0.272839i | ||||
\(197\) | 1.07910e7i | 1.41144i | 0.708492 | + | 0.705719i | \(0.249376\pi\) | ||||
−0.708492 | + | 0.705719i | \(0.750624\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.05948e6 | 0.642017 | 0.321008 | − | 0.947076i | \(-0.395978\pi\) | ||||
0.321008 | + | 0.947076i | \(0.395978\pi\) | |||||||
\(200\) | 2.69954e6 | + | 1.55858e6i | 0.337442 | + | 0.194822i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.63648e6 | − | 8.03061e6i | −0.562515 | − | 0.974304i | ||||
\(203\) | −477468. | + | 275666.i | −0.0570763 | + | 0.0329530i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.77205e6 | + | 1.17295e7i | −0.786066 | + | 1.36151i | ||||
\(206\) | − | 5.23527e6i | − | 0.598877i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 898251. | 0.0998178 | ||||||||
\(209\) | 9.65504e6 | + | 5.57434e6i | 1.05758 | + | 0.610597i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.72915e6 | + | 2.99498e6i | 0.184071 | + | 0.318821i | 0.943263 | − | 0.332046i | \(-0.107739\pi\) |
−0.759192 | + | 0.650867i | \(0.774406\pi\) | |||||||
\(212\) | −5.47342e6 | + | 3.16008e6i | −0.574448 | + | 0.331658i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −754677. | + | 1.30714e6i | −0.0770052 | + | 0.133377i | ||||
\(215\) | − | 2.64791e7i | − | 2.66432i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.21099e6 | −0.118512 | ||||||||
\(218\) | 832629. | + | 480718.i | 0.0803678 | + | 0.0464003i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.70775e6 | + | 1.33502e7i | 0.723868 | + | 1.25378i | ||||
\(221\) | 3.36425e6 | − | 1.94235e6i | 0.311681 | − | 0.179949i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.78005e6 | + | 6.54724e6i | −0.340865 | + | 0.590396i | −0.984594 | − | 0.174858i | \(-0.944053\pi\) |
0.643728 | + | 0.765254i | \(0.277387\pi\) | |||||||
\(224\) | 1.20841e6i | 0.107515i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.08064e7 | 0.936173 | ||||||||
\(227\) | 4.44652e6 | + | 2.56720e6i | 0.380139 | + | 0.219473i | 0.677879 | − | 0.735174i | \(-0.262899\pi\) |
−0.297740 | + | 0.954647i | \(0.596233\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.32792e6 | − | 1.61564e7i | −0.776744 | − | 1.34536i | −0.933809 | − | 0.357772i | \(-0.883536\pi\) |
0.157064 | − | 0.987588i | \(-0.449797\pi\) | |||||||
\(230\) | 1.06620e7 | − | 6.15573e6i | 0.876308 | − | 0.505937i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 239205. | − | 414315.i | 0.0191560 | − | 0.0331792i | ||||
\(233\) | 421669.i | 0.0333352i | 0.999861 | + | 0.0166676i | \(0.00530571\pi\) | ||||
−0.999861 | + | 0.0166676i | \(0.994694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.67081e6 | −0.359905 | ||||||||
\(236\) | 1.00229e6 | + | 578671.i | 0.0762529 | + | 0.0440246i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.61302e6 | + | 4.52589e6i | 0.193826 | + | 0.335717i | ||||
\(239\) | 1.93062e7 | − | 1.11465e7i | 1.41418 | − | 0.816475i | 0.418398 | − | 0.908264i | \(-0.362592\pi\) |
0.995779 | + | 0.0917886i | \(0.0292584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.91596e6 | + | 8.51470e6i | −0.351202 | + | 0.608300i | −0.986460 | − | 0.164000i | \(-0.947560\pi\) |
0.635258 | + | 0.772300i | \(0.280894\pi\) | |||||||
\(242\) | 2.99473e7i | 2.11306i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −765908. | −0.0527239 | ||||||||
\(245\) | −1.16348e7 | − | 6.71737e6i | −0.791155 | − | 0.456774i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.83958e6 | + | 3.18624e6i | 0.122075 | + | 0.211441i | ||||
\(248\) | 910036. | − | 525409.i | 0.0596628 | − | 0.0344463i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −817614. | + | 1.41615e6i | −0.0523273 | + | 0.0906336i | ||||
\(251\) | 1.55511e7i | 0.983422i | 0.870759 | + | 0.491711i | \(0.163628\pi\) | ||||
−0.870759 | + | 0.491711i | \(0.836372\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.19207e7 | 1.97111 | ||||||||
\(254\) | −8.60572e6 | − | 4.96851e6i | −0.525153 | − | 0.303197i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | − | 908093.i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.84675e6 | − | 1.06622e6i | 0.108795 | − | 0.0628128i | −0.444615 | − | 0.895722i | \(-0.646660\pi\) |
0.553410 | + | 0.832909i | \(0.313326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.33699e6 | − | 7.51188e6i | 0.249625 | − | 0.432364i | ||||
\(260\) | 5.08725e6i | 0.289443i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.35570e7 | 0.753807 | ||||||||
\(263\) | 911256. | + | 526114.i | 0.0500925 | + | 0.0289209i | 0.524837 | − | 0.851203i | \(-0.324126\pi\) |
−0.474745 | + | 0.880124i | \(0.657460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.78971e7 | − | 3.09987e7i | −0.961712 | − | 1.66573i | ||||
\(266\) | −4.28642e6 | + | 2.47477e6i | −0.227746 | + | 0.131489i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.64927e6 | − | 9.78483e6i | 0.293486 | − | 0.508333i | ||||
\(269\) | − | 9.68762e6i | − | 0.497692i | −0.968543 | − | 0.248846i | \(-0.919949\pi\) | ||
0.968543 | − | 0.248846i | \(-0.0800512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.05637e7 | −1.03322 | −0.516610 | − | 0.856221i | \(-0.672806\pi\) | ||||
−0.516610 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(272\) | −3.92726e6 | − | 2.26741e6i | −0.195157 | − | 0.112674i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.77204e6 | − | 6.53336e6i | −0.183368 | − | 0.317603i | ||||
\(275\) | −3.96403e7 | + | 2.28864e7i | −1.90607 | + | 1.10047i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00696e7 | + | 1.74411e7i | −0.473776 | + | 0.820604i | −0.999549 | − | 0.0300208i | \(-0.990443\pi\) |
0.525773 | + | 0.850625i | \(0.323776\pi\) | |||||||
\(278\) | − | 1.23182e7i | − | 0.573339i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.84382e6 | −0.311763 | ||||||||
\(281\) | −1.75923e7 | − | 1.01569e7i | −0.792873 | − | 0.457766i | 0.0480998 | − | 0.998843i | \(-0.484683\pi\) |
−0.840973 | + | 0.541077i | \(0.818017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.13075e7 | − | 1.95852e7i | −0.498894 | − | 0.864110i | 0.501105 | − | 0.865387i | \(-0.332927\pi\) |
−0.999999 | + | 0.00127619i | \(0.999594\pi\) | |||||||
\(284\) | 1.37672e7 | − | 7.94850e6i | 0.601022 | − | 0.347000i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.59501e6 | + | 1.14229e7i | −0.281915 | + | 0.488290i | ||||
\(287\) | − | 1.55903e7i | − | 0.659491i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.52573e6 | 0.187497 | ||||||||
\(290\) | 2.34647e6 | + | 1.35474e6i | 0.0962102 | + | 0.0555470i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.11422e6 | − | 1.05901e7i | −0.245580 | − | 0.425357i | ||||
\(293\) | 3.34647e6 | − | 1.93209e6i | 0.133041 | − | 0.0768111i | −0.432002 | − | 0.901872i | \(-0.642193\pi\) |
0.565043 | + | 0.825061i | \(0.308859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.27730e6 | + | 5.67646e6i | −0.127659 | + | 0.221111i | ||||
\(296\) | 7.52669e6i | 0.290221i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.18835e7 | −0.826930 | ||||||||
\(299\) | 9.12281e6 | + | 5.26705e6i | 0.341283 | + | 0.197040i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.52397e7 | + | 2.63959e7i | 0.558827 | + | 0.967916i | ||||
\(302\) | −4.71164e6 | + | 2.72026e6i | −0.171061 | + | 0.0987621i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.14744e6 | − | 3.71947e6i | 0.0764363 | − | 0.132392i | ||||
\(305\) | − | 4.33772e6i | − | 0.152884i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.02526e6 | −0.104556 | −0.0522779 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522779 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(308\) | −1.53671e7 | − | 8.87221e6i | −0.525945 | − | 0.303654i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.97566e6 | + | 5.15399e6i | 0.0998844 | + | 0.173005i | ||||
\(311\) | −3.30190e7 | + | 1.90635e7i | −1.09770 | + | 0.633755i | −0.935615 | − | 0.353022i | \(-0.885154\pi\) |
−0.162081 | + | 0.986777i | \(0.551821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.13148e7 | − | 1.95979e7i | 0.368990 | − | 0.639110i | −0.620417 | − | 0.784272i | \(-0.713037\pi\) |
0.989408 | + | 0.145161i | \(0.0463702\pi\) | |||||||
\(314\) | 9.00767e6i | 0.290954i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.23730e7 | −0.392116 | ||||||||
\(317\) | 2.07004e7 | + | 1.19514e7i | 0.649831 | + | 0.375180i | 0.788392 | − | 0.615174i | \(-0.210914\pi\) |
−0.138560 | + | 0.990354i | \(0.544247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.51251e6 | + | 6.08385e6i | 0.108205 | + | 0.187416i | ||||
\(320\) | 5.14299e6 | − | 2.96930e6i | 0.156951 | − | 0.0906160i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.08572e6 | + | 1.22728e7i | −0.212235 | + | 0.367601i | ||||
\(323\) | − | 1.85742e7i | − | 0.551191i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.51054e7 | −0.440029 | ||||||||
\(326\) | 3.44045e6 | + | 1.98635e6i | 0.0993031 | + | 0.0573327i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.76411e6 | + | 1.17158e7i | 0.191685 | + | 0.332009i | ||||
\(329\) | 4.65615e6 | − | 2.68823e6i | 0.130749 | − | 0.0754881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41912e7 | − | 2.45799e7i | 0.391324 | − | 0.677792i | −0.601301 | − | 0.799023i | \(-0.705351\pi\) |
0.992624 | + | 0.121230i | \(0.0386840\pi\) | |||||||
\(332\) | − | 1.32907e7i | − | 0.363190i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.14111e7 | 0.574645 | ||||||||
\(335\) | 5.54164e7 | + | 3.19946e7i | 1.47402 | + | 0.851026i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.56151e7 | + | 2.70461e7i | 0.407994 | + | 0.706666i | 0.994665 | − | 0.103159i | \(-0.0328951\pi\) |
−0.586671 | + | 0.809825i | \(0.699562\pi\) | |||||||
\(338\) | 1.98768e7 | − | 1.14759e7i | 0.514750 | − | 0.297191i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.28414e7 | − | 2.22420e7i | 0.326721 | − | 0.565898i | ||||
\(341\) | 1.54303e7i | 0.389146i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.00074e7 | 0.991420 | ||||||||
\(344\) | −2.29046e7 | − | 1.32240e7i | −0.562663 | − | 0.324853i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.23685e7 | − | 2.14229e7i | −0.298599 | − | 0.517189i | ||||
\(347\) | 1.73955e7 | − | 1.00433e7i | 0.416340 | − | 0.240374i | −0.277170 | − | 0.960821i | \(-0.589397\pi\) |
0.693510 | + | 0.720447i | \(0.256063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.84002e7 | − | 3.18701e7i | 0.432859 | − | 0.749733i | −0.564260 | − | 0.825597i | \(-0.690838\pi\) |
0.997118 | + | 0.0758644i | \(0.0241716\pi\) | |||||||
\(350\) | − | 2.03211e7i | − | 0.473962i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.53974e7 | 0.353037 | ||||||||
\(353\) | 2.05019e7 | + | 1.18368e7i | 0.466089 | + | 0.269097i | 0.714601 | − | 0.699532i | \(-0.246608\pi\) |
−0.248512 | + | 0.968629i | \(0.579942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50163e7 | + | 7.79705e7i | 1.00620 | + | 1.74279i | ||||
\(356\) | −1.12418e7 | + | 6.49046e6i | −0.249165 | + | 0.143855i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 139408. | − | 241462.i | 0.00303836 | − | 0.00526259i | ||||
\(359\) | 3.67159e7i | 0.793544i | 0.917917 | + | 0.396772i | \(0.129870\pi\) | ||||
−0.917917 | + | 0.396772i | \(0.870130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.94545e7 | −0.626079 | ||||||||
\(362\) | −2.21534e7 | − | 1.27903e7i | −0.466999 | − | 0.269622i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.92790e6 | − | 5.07128e6i | −0.0607089 | − | 0.105151i | ||||
\(365\) | 5.99773e7 | − | 3.46279e7i | 1.23341 | − | 0.712111i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.15020e7 | + | 7.18836e7i | −0.839597 | + | 1.45422i | 0.0506351 | + | 0.998717i | \(0.483875\pi\) |
−0.890232 | + | 0.455507i | \(0.849458\pi\) | |||||||
\(368\) | − | 1.22970e7i | − | 0.246750i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.26274e7 | −0.841558 | ||||||||
\(371\) | 3.56819e7 | + | 2.06009e7i | 0.698756 | + | 0.403427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.06825e7 | + | 5.31436e7i | 0.591241 | + | 1.02406i | 0.994066 | + | 0.108782i | \(0.0346950\pi\) |
−0.402825 | + | 0.915277i | \(0.631972\pi\) | |||||||
\(374\) | 5.76684e7 | − | 3.32948e7i | 1.10236 | − | 0.636447i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.33266e6 | + | 4.04029e6i | −0.0438822 | + | 0.0760062i | ||||
\(377\) | 2.31832e6i | 0.0432662i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.94442e6 | 0.164299 | 0.0821495 | − | 0.996620i | \(-0.473822\pi\) | ||||
0.0821495 | + | 0.996620i | \(0.473822\pi\) | |||||||
\(380\) | 2.10652e7 | + | 1.21620e7i | 0.383897 | + | 0.221643i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.52173e6 | − | 6.09982e6i | −0.0631781 | − | 0.109428i | ||||
\(383\) | −7.60170e7 | + | 4.38884e7i | −1.35305 | + | 0.781184i | −0.988676 | − | 0.150068i | \(-0.952051\pi\) |
−0.364375 | + | 0.931252i | \(0.618717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.02477e7 | − | 8.70317e7i | 0.880510 | − | 1.52509i | ||||
\(386\) | 6.19619e7i | 1.07737i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.14076e7 | −0.195298 | ||||||||
\(389\) | −8.09387e7 | − | 4.67300e7i | −1.37501 | − | 0.793865i | −0.383460 | − | 0.923558i | \(-0.625268\pi\) |
−0.991554 | + | 0.129693i | \(0.958601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.65907e7 | − | 4.60564e7i | −0.444835 | − | 0.770477i | ||||
\(392\) | −1.16212e7 | + | 6.70949e6i | −0.192927 | + | 0.111386i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.05215e7 | + | 5.28648e7i | −0.499019 | + | 0.864326i | ||||
\(395\) | − | 7.00746e7i | − | 1.13702i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.21583e8 | −1.94313 | −0.971566 | − | 0.236767i | \(-0.923912\pi\) | ||||
−0.971566 | + | 0.236767i | \(0.923912\pi\) | |||||||
\(398\) | 2.47863e7 | + | 1.43104e7i | 0.393153 | + | 0.226987i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.81665e6 | + | 1.52709e7i | 0.137760 | + | 0.238608i | ||||
\(401\) | −1.85999e7 | + | 1.07387e7i | −0.288455 | + | 0.166540i | −0.637245 | − | 0.770661i | \(-0.719926\pi\) |
0.348790 | + | 0.937201i | \(0.386593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.54607e6 | + | 4.40993e6i | −0.0389005 | + | 0.0673777i | ||||
\(404\) | − | 5.24557e7i | − | 0.795516i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.11881e6 | −0.0466026 | ||||||||
\(407\) | −9.57156e7 | − | 5.52614e7i | −1.41971 | − | 0.819670i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.80930e7 | − | 1.00620e8i | −0.849090 | − | 1.47067i | −0.882022 | − | 0.471209i | \(-0.843818\pi\) |
0.0329322 | − | 0.999458i | \(-0.489515\pi\) | |||||||
\(410\) | −6.63523e7 | + | 3.83085e7i | −0.962730 | + | 0.555832i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.48076e7 | − | 2.56475e7i | 0.211735 | − | 0.366736i | ||||
\(413\) | − | 7.54485e6i | − | 0.107103i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.52720e7 | 1.05315 | ||||||||
\(416\) | 4.40051e6 | + | 2.54064e6i | 0.0611256 | + | 0.0352909i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.15332e7 | + | 5.46172e7i | 0.431757 | + | 0.747825i | ||||
\(419\) | −2.73269e7 | + | 1.57772e7i | −0.371492 | + | 0.214481i | −0.674110 | − | 0.738631i | \(-0.735473\pi\) |
0.302618 | + | 0.953112i | \(0.402139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.50313e6 | − | 1.29958e7i | 0.100553 | − | 0.174163i | −0.811359 | − | 0.584548i | \(-0.801272\pi\) |
0.911913 | + | 0.410384i | \(0.134605\pi\) | |||||||
\(422\) | 1.95631e7i | 0.260316i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.57522e7 | −0.469035 | ||||||||
\(425\) | 6.60425e7 | + | 3.81297e7i | 0.860314 | + | 0.496702i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.49652e6 | + | 4.32411e6i | 0.0320665 | + | 0.0555409i | ||||
\(428\) | −7.39430e6 | + | 4.26910e6i | −0.0943117 | + | 0.0544509i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.48941e7 | − | 1.29720e8i | 0.941981 | − | 1.63156i | ||||
\(431\) | 6.49322e7i | 0.811014i | 0.914092 | + | 0.405507i | \(0.132905\pi\) | ||||
−0.914092 | + | 0.405507i | \(0.867095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.31669e7 | 1.02444 | 0.512220 | − | 0.858854i | \(-0.328823\pi\) | ||||
0.512220 | + | 0.858854i | \(0.328823\pi\) | |||||||
\(434\) | −5.93263e6 | − | 3.42521e6i | −0.0725735 | − | 0.0419003i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.71935e6 | + | 4.71006e6i | 0.0328100 | + | 0.0568286i | ||||
\(437\) | 4.36195e7 | − | 2.51838e7i | 0.522681 | − | 0.301770i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.63576e7 | + | 2.83321e7i | −0.193341 | + | 0.334877i | −0.946356 | − | 0.323127i | \(-0.895266\pi\) |
0.753014 | + | 0.658004i | \(0.228599\pi\) | |||||||
\(440\) | 8.72032e7i | 1.02370i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.19752e7 | 0.254487 | ||||||||
\(443\) | −9.29959e7 | − | 5.36912e7i | −1.06968 | − | 0.617578i | −0.141584 | − | 0.989926i | \(-0.545219\pi\) |
−0.928093 | + | 0.372348i | \(0.878553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.67587e7 | − | 6.36680e7i | −0.417139 | − | 0.722505i | ||||
\(446\) | −3.70368e7 | + | 2.13832e7i | −0.417473 | + | 0.241028i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.41790e6 | + | 5.91997e6i | −0.0380124 | + | 0.0658393i | ||||
\(449\) | 3.79594e7i | 0.419354i | 0.977771 | + | 0.209677i | \(0.0672413\pi\) | ||||
−0.977771 | + | 0.209677i | \(0.932759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.98650e8 | −2.16550 | ||||||||
\(452\) | 5.29404e7 | + | 3.05651e7i | 0.573286 | + | 0.330987i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.45223e7 | + | 2.51533e7i | 0.155191 | + | 0.268799i | ||||
\(455\) | 2.87212e7 | − | 1.65822e7i | 0.304907 | − | 0.176038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.27236e7 | + | 2.20379e7i | −0.133309 | + | 0.230898i | −0.924950 | − | 0.380088i | \(-0.875894\pi\) |
0.791641 | + | 0.610986i | \(0.209227\pi\) | |||||||
\(458\) | − | 1.05533e8i | − | 1.09848i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.96442e7 | 0.715503 | ||||||||
\(461\) | −5.64160e7 | − | 3.25718e7i | −0.575837 | − | 0.332460i | 0.183640 | − | 0.982994i | \(-0.441212\pi\) |
−0.759477 | + | 0.650534i | \(0.774545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44914e7 | − | 2.50999e7i | −0.146005 | − | 0.252888i | 0.783742 | − | 0.621086i | \(-0.213308\pi\) |
−0.929747 | + | 0.368198i | \(0.879975\pi\) | |||||||
\(464\) | 2.34372e6 | − | 1.35315e6i | 0.0234613 | − | 0.0135454i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.19266e6 | + | 2.06575e6i | −0.0117858 | + | 0.0204136i | ||||
\(467\) | 6.09985e7i | 0.598919i | 0.954109 | + | 0.299460i | \(0.0968064\pi\) | ||||
−0.954109 | + | 0.299460i | \(0.903194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.36566e7 | −0.713991 | ||||||||
\(470\) | −2.28822e7 | − | 1.32110e7i | −0.220396 | − | 0.127246i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.27346e6 | + | 5.66980e6i | 0.0311301 | + | 0.0539190i | ||||
\(473\) | 3.36334e8 | − | 1.94183e8i | 3.17825 | − | 1.83496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.61122e7 | + | 6.25482e7i | −0.336956 | + | 0.583626i | ||||
\(476\) | 2.95630e7i | 0.274111i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.26108e8 | 1.15467 | ||||||||
\(479\) | 8.59855e7 | + | 4.96437e7i | 0.782381 | + | 0.451708i | 0.837274 | − | 0.546784i | \(-0.184148\pi\) |
−0.0548922 | + | 0.998492i | \(0.517482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.82367e7 | − | 3.15870e7i | −0.163875 | − | 0.283839i | ||||
\(482\) | −4.81664e7 | + | 2.78089e7i | −0.430133 | + | 0.248338i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.47038e7 | + | 1.46711e8i | −0.747079 | + | 1.29398i | ||||
\(485\) | − | 6.46069e7i | − | 0.566309i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.05049e8 | 0.909504 | 0.454752 | − | 0.890618i | \(-0.349728\pi\) | ||||
0.454752 | + | 0.890618i | \(0.349728\pi\) | |||||||
\(488\) | −3.75217e6 | − | 2.16632e6i | −0.0322866 | − | 0.0186407i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.79992e7 | − | 6.58165e7i | −0.322988 | − | 0.559431i | ||||
\(491\) | −1.64341e8 | + | 9.48823e7i | −1.38836 | + | 0.801569i | −0.993130 | − | 0.117014i | \(-0.962668\pi\) |
−0.395228 | + | 0.918583i | \(0.629334\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.85199e6 | − | 1.01360e7i | 0.0488386 | − | 0.0845909i | ||||
\(494\) | 2.08125e7i | 0.172640i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.94433e6 | 0.0487144 | ||||||||
\(497\) | −8.97500e7 | − | 5.18172e7i | −0.731081 | − | 0.422090i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.01002e8 | + | 1.74941e8i | 0.812887 | + | 1.40796i | 0.910835 | + | 0.412771i | \(0.135439\pi\) |
−0.0979477 | + | 0.995192i | \(0.531228\pi\) | |||||||
\(500\) | −8.01095e6 | + | 4.62512e6i | −0.0640876 | + | 0.0370010i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.39851e7 | + | 7.61845e7i | −0.347692 | + | 0.602220i | ||||
\(503\) | − | 1.88347e8i | − | 1.47998i | −0.672619 | − | 0.739989i | \(-0.734831\pi\) | ||
0.672619 | − | 0.739989i | \(-0.265169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.97083e8 | 2.30677 | ||||||||
\(506\) | 1.56379e8 | + | 9.02854e7i | 1.20705 | + | 0.696893i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.81062e7 | − | 4.86813e7i | −0.214393 | − | 0.371339i | ||||
\(509\) | −1.43572e8 | + | 8.28912e7i | −1.08872 | + | 0.628572i | −0.933235 | − | 0.359266i | \(-0.883027\pi\) |
−0.155484 | + | 0.987838i | \(0.549694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.98593e7 | + | 6.90384e7i | −0.298722 | + | 0.517402i | ||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.20629e7 | 0.0888307 | ||||||||
\(515\) | 1.45255e8 | + | 8.38628e7i | 1.06343 | + | 0.613971i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.42531e7 | − | 5.93281e7i | −0.247873 | − | 0.429328i | ||||
\(518\) | 4.24936e7 | − | 2.45337e7i | 0.305728 | − | 0.176512i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.43889e7 | + | 2.49223e7i | −0.102333 | + | 0.177247i | ||||
\(521\) | 2.76446e8i | 1.95478i | 0.211451 | + | 0.977389i | \(0.432181\pi\) | ||||
−0.211451 | + | 0.977389i | \(0.567819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.78008e7 | 0.613753 | 0.306876 | − | 0.951749i | \(-0.400716\pi\) | ||||
0.306876 | + | 0.951749i | \(0.400716\pi\) | |||||||
\(524\) | 6.64155e7 | + | 3.83450e7i | 0.461611 | + | 0.266511i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.97615e6 | + | 5.15484e6i | 0.0204502 | + | 0.0354208i | ||||
\(527\) | 2.22635e7 | − | 1.28538e7i | 0.152111 | − | 0.0878214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.91221e6 | + | 3.31204e6i | −0.0129172 | + | 0.0223732i | ||||
\(530\) | − | 2.02483e8i | − | 1.36007i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.79988e7 | −0.185954 | ||||||||
\(533\) | −5.67733e7 | − | 3.27781e7i | −0.374941 | − | 0.216472i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.41780e7 | − | 4.18776e7i | −0.157892 | − | 0.273477i | ||||
\(536\) | 5.53513e7 | − | 3.19571e7i | 0.359446 | − | 0.207526i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.74007e7 | − | 4.74595e7i | 0.175961 | − | 0.304773i | ||||
\(539\) | − | 1.97046e8i | − | 1.25835i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.60020e8 | −1.01061 | −0.505305 | − | 0.862941i | \(-0.668620\pi\) | ||||
−0.505305 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(542\) | −1.00741e8 | − | 5.81629e7i | −0.632716 | − | 0.365299i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.28264e7 | − | 2.22159e7i | −0.0796723 | − | 0.137996i | ||||
\(545\) | −2.66754e7 | + | 1.54011e7i | −0.164787 | + | 0.0951395i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10308e7 | − | 1.91059e7i | 0.0673977 | − | 0.116736i | −0.830357 | − | 0.557231i | \(-0.811864\pi\) |
0.897755 | + | 0.440495i | \(0.145197\pi\) | |||||||
\(548\) | − | 4.26757e7i | − | 0.259322i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.58930e8 | −1.55630 | ||||||||
\(551\) | 9.59966e6 | + | 5.54237e6i | 0.0573854 | + | 0.0331315i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.03306e7 | + | 6.98546e7i | 0.238484 | + | 0.413066i | ||||
\(554\) | −9.86615e7 | + | 5.69623e7i | −0.580255 | + | 0.335010i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.48410e7 | − | 6.03464e7i | 0.202706 | − | 0.351097i | ||||
\(557\) | 1.71224e8i | 0.990830i | 0.868657 | + | 0.495415i | \(0.164984\pi\) | ||||
−0.868657 | + | 0.495415i | \(0.835016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.28164e8 | 0.733720 | ||||||||
\(560\) | −3.35277e7 | − | 1.93573e7i | −0.190915 | − | 0.110225i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.74562e7 | − | 9.95171e7i | −0.323689 | − | 0.560646i | ||||
\(563\) | 1.92436e8 | − | 1.11103e8i | 1.07835 | − | 0.622586i | 0.147900 | − | 0.989002i | \(-0.452749\pi\) |
0.930451 | + | 0.366416i | \(0.119415\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.73106e8 | + | 2.99828e8i | −0.959767 | + | 1.66237i | ||||
\(566\) | − | 1.27930e8i | − | 0.705543i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.99270e7 | 0.490733 | ||||||||
\(569\) | 2.25736e8 | + | 1.30329e8i | 1.22536 | + | 0.707461i | 0.966056 | − | 0.258335i | \(-0.0831737\pi\) |
0.259303 | + | 0.965796i | \(0.416507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.09463e7 | − | 1.05562e8i | −0.327370 | − | 0.567022i | 0.654619 | − | 0.755959i | \(-0.272829\pi\) |
−0.981989 | + | 0.188937i | \(0.939496\pi\) | |||||||
\(572\) | −6.46177e7 | + | 3.73070e7i | −0.345274 | + | 0.199344i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.40960e7 | − | 7.63766e7i | 0.233165 | − | 0.403854i | ||||
\(575\) | 2.06792e8i | 1.08775i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.22005e8 | 0.635111 | 0.317555 | − | 0.948240i | \(-0.397138\pi\) | ||||
0.317555 | + | 0.948240i | \(0.397138\pi\) | |||||||
\(578\) | 2.21715e7 | + | 1.28007e7i | 0.114818 | + | 0.0662903i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.66354e6 | + | 1.32736e7i | 0.0392777 | + | 0.0680309i | ||||
\(581\) | −7.50357e7 | + | 4.33219e7i | −0.382595 | + | 0.220891i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.62495e8 | − | 4.54654e8i | 1.32469 | − | 2.29444i | ||||
\(584\) | − | 6.91745e7i | − | 0.347302i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.18591e7 | 0.108627 | ||||||||
\(587\) | 1.15748e8 | + | 6.68273e7i | 0.572269 | + | 0.330400i | 0.758055 | − | 0.652191i | \(-0.226150\pi\) |
−0.185786 | + | 0.982590i | \(0.559483\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.21737e7 | + | 2.10855e7i | 0.0595768 | + | 0.103190i | ||||
\(590\) | −3.21109e7 | + | 1.85392e7i | −0.156349 | + | 0.0902684i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.12887e7 | + | 3.68731e7i | −0.102609 | + | 0.177723i | ||||
\(593\) | 1.98748e7i | 0.0953100i | 0.998864 | + | 0.0476550i | \(0.0151748\pi\) | ||||
−0.998864 | + | 0.0476550i | \(0.984825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.67430e8 | −0.794844 | ||||||||
\(596\) | −1.07207e8 | − | 6.18960e7i | −0.506389 | − | 0.292364i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.97950e7 | + | 5.16064e7i | 0.139328 | + | 0.241324i | ||||
\(599\) | −3.37964e8 | + | 1.95123e8i | −1.57250 | + | 0.907881i | −0.576634 | + | 0.817002i | \(0.695634\pi\) |
−0.995862 | + | 0.0908789i | \(0.971032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.89071e7 | + | 1.36671e8i | −0.363490 | + | 0.629583i | −0.988533 | − | 0.151007i | \(-0.951748\pi\) |
0.625043 | + | 0.780591i | \(0.285082\pi\) | |||||||
\(602\) | 1.72418e8i | 0.790300i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.07763e7 | −0.139671 | ||||||||
\(605\) | −8.30899e8 | − | 4.79720e8i | −3.75217 | − | 2.16631i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.74295e8 | − | 3.01887e8i | −0.779325 | − | 1.34983i | −0.932332 | − | 0.361605i | \(-0.882229\pi\) |
0.153007 | − | 0.988225i | \(-0.451104\pi\) | |||||||
\(608\) | 2.10405e7 | − | 1.21477e7i | 0.0936150 | − | 0.0540486i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.22689e7 | − | 2.12504e7i | 0.0540527 | − | 0.0936219i | ||||
\(611\) | − | 2.26076e7i | − | 0.0991132i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.41726e7 | 0.0615273 | 0.0307636 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307636 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(614\) | −1.48207e7 | − | 8.55674e6i | −0.0640271 | − | 0.0369661i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.01888e7 | − | 8.69295e7i | −0.214716 | − | 0.371899i | ||||
\(617\) | 1.81599e8 | − | 1.04846e8i | 0.773140 | − | 0.446373i | −0.0608535 | − | 0.998147i | \(-0.519382\pi\) |
0.833994 | + | 0.551774i | \(0.186049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.36020e7 | − | 1.44803e8i | 0.352488 | − | 0.610528i | −0.634196 | − | 0.773172i | \(-0.718669\pi\) |
0.986685 | + | 0.162644i | \(0.0520023\pi\) | |||||||
\(620\) | 3.36657e7i | 0.141258i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.15679e8 | −0.896265 | ||||||||
\(623\) | 7.32867e7 | + | 4.23121e7i | 0.303083 | + | 0.174985i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.08337e8 | + | 1.87645e8i | 0.443749 | + | 0.768595i | ||||
\(626\) | 1.10862e8 | − | 6.40064e7i | 0.451919 | − | 0.260916i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.54775e7 | + | 4.41284e7i | −0.102868 | + | 0.178172i | ||||
\(629\) | 1.84136e8i | 0.739923i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.36933e8 | −1.34108 | −0.670541 | − | 0.741872i | \(-0.733938\pi\) | ||||
−0.670541 | + | 0.741872i | \(0.733938\pi\) | |||||||
\(632\) | −6.06152e7 | − | 3.49962e7i | −0.240121 | − | 0.138634i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.76072e7 | + | 1.17099e8i | 0.265293 | + | 0.459500i | ||||
\(635\) | 2.75706e8 | − | 1.59179e8i | 1.07678 | − | 0.621677i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.25134e7 | − | 5.63149e7i | 0.125789 | − | 0.217874i | ||||
\(638\) | 3.97395e7i | 0.153024i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.35938e7 | 0.128150 | ||||||||
\(641\) | 8.63536e7 | + | 4.98563e7i | 0.327873 | + | 0.189298i | 0.654897 | − | 0.755719i | \(-0.272712\pi\) |
−0.327023 | + | 0.945016i | \(0.606046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.34692e8 | + | 2.33294e8i | 0.506652 | + | 0.877547i | 0.999970 | + | 0.00769844i | \(0.00245051\pi\) |
−0.493318 | + | 0.869849i | \(0.664216\pi\) | |||||||
\(644\) | −6.94256e7 | + | 4.00829e7i | −0.259933 | + | 0.150073i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.25357e7 | − | 9.09945e7i | 0.194875 | − | 0.337534i | ||||
\(647\) | − | 7.78039e7i | − | 0.287269i | −0.989631 | − | 0.143634i | \(-0.954121\pi\) | ||
0.989631 | − | 0.143634i | \(-0.0458790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.61357e7 | −0.351682 | ||||||||
\(650\) | −7.40010e7 | − | 4.27245e7i | −0.269462 | − | 0.155574i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.12365e7 | + | 1.94621e7i | 0.0405403 | + | 0.0702179i | ||||
\(653\) | −1.95063e8 | + | 1.12620e8i | −0.700543 | + | 0.404459i | −0.807550 | − | 0.589800i | \(-0.799207\pi\) |
0.107007 | + | 0.994258i | \(0.465873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.17167e8 | + | 3.76144e8i | −0.772805 | + | 1.33854i | ||||
\(656\) | 7.65272e7i | 0.271084i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.04138e7 | 0.106756 | ||||||||
\(659\) | 1.98537e8 | + | 1.14625e8i | 0.693722 | + | 0.400521i | 0.805005 | − | 0.593268i | \(-0.202163\pi\) |
−0.111283 | + | 0.993789i | \(0.535496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.05495e8 | + | 1.82722e8i | 0.365280 | + | 0.632684i | 0.988821 | − | 0.149107i | \(-0.0476398\pi\) |
−0.623541 | + | 0.781791i | \(0.714306\pi\) | |||||||
\(662\) | 1.39045e8 | − | 8.02777e7i | 0.479272 | − | 0.276708i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.75918e7 | − | 6.51109e7i | 0.128407 | − | 0.222408i | ||||
\(665\) | − | 1.58571e8i | − | 0.539212i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.17376e7 | 0.106954 | ||||||||
\(668\) | 1.04893e8 | + | 6.05597e7i | 0.351897 | + | 0.203168i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.80989e8 | + | 3.13482e8i | 0.601766 | + | 1.04229i | ||||
\(671\) | 5.50973e7 | − | 3.18104e7i | 0.182374 | − | 0.105294i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.87715e8 | − | 4.98336e8i | 0.943880 | − | 1.63485i | 0.185901 | − | 0.982568i | \(-0.440479\pi\) |
0.757978 | − | 0.652280i | \(-0.226187\pi\) | |||||||
\(674\) | 1.76664e8i | 0.576991i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.29835e8 | 0.420291 | ||||||||
\(677\) | 3.05834e8 | + | 1.76573e8i | 0.985644 | + | 0.569062i | 0.903969 | − | 0.427597i | \(-0.140640\pi\) |
0.0816747 | + | 0.996659i | \(0.473973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.71837e7 | + | 6.44041e7i | 0.118780 | + | 0.205733i | ||||
\(680\) | 1.25820e8 | − | 7.26422e7i | 0.400150 | − | 0.231027i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.36436e7 | + | 7.55930e7i | −0.137584 | + | 0.238302i | ||||
\(683\) | − | 4.65139e8i | − | 1.45989i | −0.683506 | − | 0.729945i | \(-0.739546\pi\) | ||
0.683506 | − | 0.729945i | \(-0.260454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.41694e8 | 0.751959 | ||||||||
\(686\) | 1.95995e8 | + | 1.13158e8i | 0.607119 | + | 0.350520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.48062e7 | − | 1.29568e8i | −0.229706 | − | 0.397862i | ||||
\(689\) | 1.50040e8 | − | 8.66255e7i | 0.458721 | − | 0.264843i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.96318e7 | − | 1.03285e8i | 0.180736 | − | 0.313043i | −0.761396 | − | 0.648288i | \(-0.775485\pi\) |
0.942131 | + | 0.335244i | \(0.108819\pi\) | |||||||
\(692\) | − | 1.39934e8i | − | 0.422283i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.13627e8 | 0.339941 | ||||||||
\(695\) | 3.41772e8 | + | 1.97322e8i | 1.01808 | + | 0.587789i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.65480e8 | + | 2.86619e8i | 0.488705 | + | 0.846461i | ||||
\(698\) | 1.80284e8 | − | 1.04087e8i | 0.530141 | − | 0.306077i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.74768e7 | − | 9.95528e7i | 0.167571 | − | 0.290241i | ||||
\(701\) | − | 3.55114e8i | − | 1.03089i | −0.856921 | − | 0.515447i | \(-0.827626\pi\) | ||
0.856921 | − | 0.515447i | \(-0.172374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.74393e8 | −0.501954 | ||||||||
\(704\) | 7.54316e7 | + | 4.35505e7i | 0.216190 | + | 0.124817i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.69588e7 | + | 1.15976e8i | 0.190280 | + | 0.329575i | ||||
\(707\) | −2.96151e8 | + | 1.70983e8i | −0.838020 | + | 0.483831i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.01326e8 | + | 5.21912e8i | −0.845470 | + | 1.46440i | 0.0397425 | + | 0.999210i | \(0.487346\pi\) |
−0.885212 | + | 0.465187i | \(0.845987\pi\) | |||||||
\(710\) | 5.09301e8i | 1.42298i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.34312e7 | −0.203442 | ||||||||
\(713\) | 6.03717e7 | + | 3.48556e7i | 0.166558 | + | 0.0961621i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11288e8 | − | 3.65962e8i | −0.578039 | − | 1.00119i | ||||
\(716\) | 1.36591e6 | − | 788611.i | 0.00372121 | − | 0.00214844i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.03848e8 | + | 1.79871e8i | −0.280560 | + | 0.485944i | ||||
\(719\) | − | 3.36046e8i | − | 0.904092i | −0.891995 | − | 0.452046i | \(-0.850694\pi\) | ||
0.891995 | − | 0.452046i | \(-0.149306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.93065e8 | −0.515107 | ||||||||
\(722\) | −1.44297e8 | − | 8.33098e7i | −0.383394 | − | 0.221352i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.23528e7 | − | 1.25319e8i | −0.190651 | − | 0.330218i | ||||
\(725\) | −3.94130e7 | + | 2.27551e7i | −0.103425 | + | 0.0597124i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.56241e8 | − | 4.43823e8i | 0.666877 | − | 1.15507i | −0.311895 | − | 0.950116i | \(-0.600964\pi\) |
0.978773 | − | 0.204949i | \(-0.0657028\pi\) | |||||||
\(728\) | − | 3.31254e7i | − | 0.0858554i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.91770e8 | 1.00708 | ||||||||
\(731\) | −5.60348e8 | − | 3.23517e8i | −1.43452 | − | 0.828218i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.79393e7 | + | 3.10717e7i | 0.0455505 | + | 0.0788957i | 0.887902 | − | 0.460033i | \(-0.152162\pi\) |
−0.842351 | + | 0.538929i | \(0.818829\pi\) | |||||||
\(734\) | −4.06635e8 | + | 2.34771e8i | −1.02829 | + | 0.593685i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.47812e7 | − | 6.02428e7i | 0.0872391 | − | 0.151103i | ||||
\(737\) | 9.38524e8i | 2.34446i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.58948e7 | −0.0889403 | −0.0444701 | − | 0.999011i | \(-0.514160\pi\) | ||||
−0.0444701 | + | 0.999011i | \(0.514160\pi\) | |||||||
\(740\) | −2.08831e8 | − | 1.20569e8i | −0.515347 | − | 0.297536i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.16536e8 | + | 2.01847e8i | 0.285266 | + | 0.494095i | ||||
\(743\) | 3.77466e8 | − | 2.17930e8i | 0.920261 | − | 0.531313i | 0.0365427 | − | 0.999332i | \(-0.488366\pi\) |
0.883718 | + | 0.468019i | \(0.155032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.50548e8 | − | 6.07166e8i | 0.847771 | − | 1.46838i | ||||
\(746\) | 3.47133e8i | 0.836140i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.76688e8 | 0.900072 | ||||||||
\(749\) | 4.82043e7 | + | 2.78308e7i | 0.114720 | + | 0.0662338i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.14559e8 | + | 3.71627e8i | 0.506556 | + | 0.877380i | 0.999971 | + | 0.00758650i | \(0.00241488\pi\) |
−0.493416 | + | 0.869794i | \(0.664252\pi\) | |||||||
\(752\) | −2.28553e7 | + | 1.31955e7i | −0.0537445 | + | 0.0310294i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.55719e6 | + | 1.13574e7i | −0.0152969 | + | 0.0264950i | ||||
\(755\) | − | 1.74301e8i | − | 0.405005i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.26773e8 | −1.90589 | −0.952947 | − | 0.303136i | \(-0.901966\pi\) | ||||
−0.952947 | + | 0.303136i | \(0.901966\pi\) | |||||||
\(758\) | 4.38185e7 | + | 2.52987e7i | 0.100612 | + | 0.0580884i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.87987e7 | + | 1.19163e8i | 0.156725 | + | 0.271456i | ||||
\(761\) | −3.22643e8 | + | 1.86278e8i | −0.732097 | + | 0.422677i | −0.819189 | − | 0.573524i | \(-0.805576\pi\) |
0.0870916 | + | 0.996200i | \(0.472243\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.77278e7 | − | 3.07054e7i | 0.0399099 | − | 0.0691260i | ||||
\(764\) | − | 3.98439e7i | − | 0.0893473i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.96541e8 | −1.10476 | ||||||||
\(767\) | −2.74752e7 | − | 1.58628e7i | −0.0608912 | − | 0.0351555i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.05010e8 | − | 3.55087e8i | −0.450812 | − | 0.780829i | 0.547625 | − | 0.836724i | \(-0.315532\pi\) |
−0.998437 | + | 0.0558948i | \(0.982199\pi\) | |||||||
\(770\) | 4.92325e8 | − | 2.84244e8i | 1.07840 | − | 0.622615i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.75255e8 | + | 3.03550e8i | −0.380906 | + | 0.659749i | ||||
\(773\) | − | 6.77485e8i | − | 1.46677i | −0.679815 | − | 0.733384i | \(-0.737940\pi\) | ||
0.679815 | − | 0.733384i | \(-0.262060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.99624e7 | −0.214749 | ||||||||
\(776\) | −5.58856e7 | − | 3.22655e7i | −0.119595 | − | 0.0690484i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.64345e8 | − | 4.57858e8i | −0.561347 | − | 0.972282i | ||||
\(779\) | −2.71454e8 | + | 1.56724e8i | −0.574228 | + | 0.331531i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.60249e8 | + | 1.14359e9i | −1.38597 | + | 2.40058i | ||||
\(782\) | − | 3.00839e8i | − | 0.629091i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.59092e7 | −0.157524 | ||||||||
\(785\) | −2.49921e8 | − | 1.44292e8i | −0.516647 | − | 0.298286i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.70650e8 | − | 4.68779e8i | −0.555244 | − | 0.961710i | −0.997885 | − | 0.0650114i | \(-0.979292\pi\) |
0.442641 | − | 0.896699i | \(-0.354042\pi\) | |||||||
\(788\) | −2.99048e8 | + | 1.72656e8i | −0.611171 | + | 0.352860i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.98201e8 | − | 3.43294e8i | 0.401998 | − | 0.696282i | ||||
\(791\) | − | 3.98516e8i | − | 0.805222i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.09954e7 | 0.0421022 | ||||||||
\(794\) | −5.95634e8 | − | 3.43890e8i | −1.18992 | − | 0.687001i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.09516e7 | + | 1.40212e8i | 0.160504 | + | 0.278001i | ||||
\(797\) | −5.31873e8 | + | 3.07077e8i | −1.05059 | + | 0.606557i | −0.922814 | − | 0.385246i | \(-0.874117\pi\) |
−0.127774 | + | 0.991803i | \(0.540783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.70672e7 | + | 9.88432e7i | −0.111878 | + | 0.193779i | ||||
\(800\) | 9.97491e7i | 0.194822i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.21494e8 | −0.235523 | ||||||||
\(803\) | 8.79680e8 | + | 5.07883e8i | 1.69894 | + | 0.980883i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.27009e8 | − | 3.93192e8i | −0.435167 | − | 0.753731i | ||||
\(806\) | −2.49463e7 | + | 1.44028e7i | −0.0476432 | + | 0.0275068i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.48367e8 | − | 2.56980e8i | 0.281257 | − | 0.487152i | ||||
\(809\) | 1.54965e8i | 0.292677i | 0.989235 | + | 0.146338i | \(0.0467489\pi\) | ||||
−0.989235 | + | 0.146338i | \(0.953251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.47410e8 | 1.58866 | 0.794330 | − | 0.607487i | \(-0.207822\pi\) | ||||
0.794330 | + | 0.607487i | \(0.207822\pi\) | |||||||
\(812\) | −1.52790e7 | − | 8.82132e6i | −0.0285382 | − | 0.0164765i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.12606e8 | − | 5.41449e8i | −0.579594 | − | 1.00389i | ||||
\(815\) | −1.10224e8 | + | 6.36378e7i | −0.203612 | + | 0.117555i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.06400e8 | − | 5.30700e8i | 0.561852 | − | 0.973157i | ||||
\(818\) | − | 6.57247e8i | − | 1.20079i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.33412e8 | −0.786066 | ||||||||
\(821\) | 2.24729e8 | + | 1.29747e8i | 0.406096 | + | 0.234460i | 0.689111 | − | 0.724656i | \(-0.258001\pi\) |
−0.283015 | + | 0.959116i | \(0.591335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.94060e8 | + | 3.36121e8i | 0.348126 | + | 0.602971i | 0.985916 | − | 0.167238i | \(-0.0534850\pi\) |
−0.637791 | + | 0.770210i | \(0.720152\pi\) | |||||||
\(824\) | 1.45084e8 | − | 8.37644e7i | 0.259321 | − | 0.149719i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.13401e7 | − | 3.69621e7i | 0.0378665 | − | 0.0655868i | ||||
\(827\) | 7.11216e8i | 1.25743i | 0.777635 | + | 0.628716i | \(0.216419\pi\) | ||||
−0.777635 | + | 0.628716i | \(0.783581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.26204e8 | 1.62571 | 0.812855 | − | 0.582466i | \(-0.197912\pi\) | ||||
0.812855 | + | 0.582466i | \(0.197912\pi\) | |||||||
\(830\) | 3.68756e8 | + | 2.12901e8i | 0.644918 | + | 0.372344i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.43720e7 | + | 2.48931e7i | 0.0249544 | + | 0.0432224i | ||||
\(833\) | −2.84305e8 | + | 1.64144e8i | −0.491869 | + | 0.283981i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.42980e8 | + | 5.94059e8i | −0.589128 | + | 1.02040i | ||||
\(836\) | 3.56758e8i | 0.610597i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.78499e8 | −0.303322 | ||||||||
\(839\) | −5.79914e8 | − | 3.34814e8i | −0.981924 | − | 0.566914i | −0.0790734 | − | 0.996869i | \(-0.525196\pi\) |
−0.902850 | + | 0.429955i | \(0.858529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.93919e8 | − | 5.09083e8i | −0.494129 | − | 0.855856i | ||||
\(842\) | 7.35154e7 | − | 4.24441e7i | 0.123152 | − | 0.0711019i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.53329e7 | + | 9.58395e7i | −0.0920357 | + | 0.159411i | ||||
\(845\) | 7.35318e8i | 1.21872i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.10439e9 | 1.81749 | ||||||||
\(848\) | −1.75149e8 | − | 1.01123e8i | −0.287224 | − | 0.165829i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.15694e8 | + | 3.73593e8i | 0.351222 | + | 0.608334i | ||||
\(851\) | −4.32424e8 | + | 2.49660e8i | −0.701651 | + | 0.405098i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.01924e8 | − | 1.76538e8i | 0.164221 | − | 0.284440i | −0.772157 | − | 0.635432i | \(-0.780822\pi\) |
0.936379 | + | 0.350992i | \(0.114156\pi\) | |||||||
\(854\) | 2.82449e7i | 0.0453489i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.82994e7 | −0.0770052 | ||||||||
\(857\) | 3.04635e8 | + | 1.75881e8i | 0.483992 | + | 0.279433i | 0.722079 | − | 0.691811i | \(-0.243187\pi\) |
−0.238087 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.89638e8 | − | 3.28462e8i | −0.299189 | − | 0.518210i | 0.676762 | − | 0.736202i | \(-0.263383\pi\) |
−0.975951 | + | 0.217992i | \(0.930049\pi\) | |||||||
\(860\) | 7.33809e8 | − | 4.23665e8i | 1.15369 | − | 0.666081i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.83656e8 | + | 3.18101e8i | −0.286737 | + | 0.496643i | ||||
\(863\) | − | 5.09276e7i | − | 0.0792358i | −0.999215 | − | 0.0396179i | \(-0.987386\pi\) | ||
0.999215 | − | 0.0396179i | \(-0.0126141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.92514e8 | 1.22450 | ||||||||
\(866\) | 4.07433e8 | + | 2.35231e8i | 0.627339 | + | 0.362194i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.93759e7 | − | 3.35600e7i | −0.0296280 | − | 0.0513172i | ||||
\(869\) | 8.90080e8 | − | 5.13888e8i | 1.35634 | − | 0.783086i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.54860e8 | + | 2.68226e8i | −0.234361 | + | 0.405926i | ||||
\(872\) | 3.07660e7i | 0.0464003i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.84922e8 | 0.426767 | ||||||||
\(875\) | 5.22243e7 | + | 3.01517e7i | 0.0779559 | + | 0.0450078i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.47593e8 | + | 7.75254e8i | 0.663567 | + | 1.14933i | 0.979672 | + | 0.200608i | \(0.0642916\pi\) |
−0.316105 | + | 0.948724i | \(0.602375\pi\) | |||||||
\(878\) | −1.60271e8 | + | 9.25323e7i | −0.236794 | + | 0.136713i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.46648e8 | + | 4.27207e8i | −0.361934 | + | 0.626888i | ||||
\(881\) | − | 5.82577e8i | − | 0.851973i | −0.904730 | − | 0.425986i | \(-0.859927\pi\) | ||
0.904730 | − | 0.425986i | \(-0.140073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.10539e7 | −0.0305810 | −0.0152905 | − | 0.999883i | \(-0.504867\pi\) | ||||
−0.0152905 | + | 0.999883i | \(0.504867\pi\) | |||||||
\(884\) | 1.07656e8 | + | 6.21551e7i | 0.155841 | + | 0.0899747i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.03723e8 | − | 5.26064e8i | −0.436694 | − | 0.756376i | ||||
\(887\) | 9.71754e8 | − | 5.61043e8i | 1.39247 | − | 0.803942i | 0.398881 | − | 0.917003i | \(-0.369399\pi\) |
0.993588 | + | 0.113060i | \(0.0360653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.83227e8 | + | 3.17359e8i | −0.260787 | + | 0.451695i | ||||
\(890\) | − | 4.15878e8i | − | 0.589923i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.41923e8 | −0.340865 | ||||||||
\(893\) | −9.36135e7 | − | 5.40478e7i | −0.131457 | − | 0.0758968i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.46630e6 | + | 7.73585e6i | 0.00622986 | + | 0.0107904i | ||||
\(896\) | −3.34884e7 | + | 1.93345e7i | −0.0465554 | + | 0.0268788i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.07366e8 | + | 1.85963e8i | −0.148264 | + | 0.256801i | ||||
\(899\) | 1.53418e7i | 0.0211154i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.74656e8 | −1.19581 | ||||||||
\(902\) | −9.73182e8 | − | 5.61867e8i | −1.32609 | − | 0.765621i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.72903e8 | + | 2.99476e8i | 0.234043 | + | 0.405375i | ||||
\(905\) | 7.09743e8 | − | 4.09770e8i | 0.957536 | − | 0.552834i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.15685e8 | + | 5.46783e8i | −0.423089 | + | 0.732812i | −0.996240 | − | 0.0866378i | \(-0.972388\pi\) |
0.573150 | + | 0.819450i | \(0.305721\pi\) | |||||||
\(908\) | 1.64301e8i | 0.219473i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.87606e8 | 0.248956 | ||||||||
\(911\) | −1.13526e8 | − | 6.55445e7i | −0.150156 | − | 0.0866924i | 0.423040 | − | 0.906111i | \(-0.360963\pi\) |
−0.573195 | + | 0.819419i | \(0.694296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.52003e8 | + | 9.56097e8i | 0.725319 | + | 1.25629i | ||||
\(914\) | −1.24665e8 | + | 7.19754e7i | −0.163270 | + | 0.0942639i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.98493e8 | − | 5.17006e8i | 0.388372 | − | 0.672680i | ||||
\(917\) | − | 4.99951e8i | − | 0.648365i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.88351e8 | −1.01572 | −0.507859 | − | 0.861440i | \(-0.669563\pi\) | ||||
−0.507859 | + | 0.861440i | \(0.669563\pi\) | |||||||
\(920\) | 3.41185e8 | + | 1.96983e8i | 0.438154 | + | 0.252968i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.84254e8 | − | 3.19137e8i | −0.235084 | − | 0.407178i | ||||
\(923\) | −3.77393e8 | + | 2.17888e8i | −0.479942 | + | 0.277094i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.58000e8 | − | 6.20074e8i | 0.452333 | − | 0.783463i | ||||
\(926\) | − | 1.63952e8i | − | 0.206482i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.53091e7 | 0.0191560 | ||||||||
\(929\) | 8.26532e8 | + | 4.77199e8i | 1.03089 | + | 0.595185i | 0.917240 | − | 0.398336i | \(-0.130412\pi\) |
0.113651 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.55459e8 | − | 2.69262e8i | −0.192649 | − | 0.333677i | ||||
\(932\) | −1.16856e7 | + | 6.74670e6i | −0.0144346 | + | 0.00833381i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.72530e8 | + | 2.98830e8i | −0.211750 | + | 0.366762i | ||||
\(935\) | 2.13337e9i | 2.60995i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.59379e8 | −0.558409 | −0.279205 | − | 0.960232i | \(-0.590071\pi\) | ||||
−0.279205 | + | 0.960232i | \(0.590071\pi\) | |||||||
\(938\) | −3.60842e8 | − | 2.08332e8i | −0.437229 | − | 0.252434i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.47329e7 | − | 1.29441e8i | −0.0899764 | − | 0.155844i | ||||
\(941\) | 1.27228e8 | − | 7.34552e7i | 0.152691 | − | 0.0881563i | −0.421708 | − | 0.906732i | \(-0.638569\pi\) |
0.574399 | + | 0.818575i | \(0.305236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.48730e8 | + | 7.77224e8i | −0.535119 | + | 0.926853i | ||||
\(944\) | 3.70350e7i | 0.0440246i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.19693e9 | 2.59503 | ||||||||
\(947\) | −3.87438e8 | − | 2.23687e8i | −0.456197 | − | 0.263385i | 0.254247 | − | 0.967139i | \(-0.418172\pi\) |
−0.710444 | + | 0.703754i | \(0.751506\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.67606e8 | + | 2.90302e8i | 0.196106 | + | 0.339665i | ||||
\(950\) | −3.53826e8 | + | 2.04282e8i | −0.412686 | + | 0.238264i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.36167e7 | + | 1.44828e8i | −0.0969130 | + | 0.167858i | ||||
\(953\) | 1.69556e8i | 0.195900i | 0.995191 | + | 0.0979500i | \(0.0312285\pi\) | ||||
−0.995191 | + | 0.0979500i | \(0.968771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.25656e8 | 0.259081 | ||||||||
\(956\) | 6.17799e8 | + | 3.56687e8i | 0.707088 | + | 0.408238i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.80827e8 | + | 4.86407e8i | 0.319406 | + | 0.553227i | ||||
\(959\) | −2.40935e8 | + | 1.39104e8i | −0.273177 | + | 0.157719i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.26903e8 | − | 7.39417e8i | 0.481015 | − | 0.833143i | ||||
\(962\) | − | 2.06325e8i | − | 0.231754i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.14622e8 | −0.351202 | ||||||||
\(965\) | −1.71916e9 | − | 9.92556e8i | −1.91308 | − | 1.10452i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.92132e8 | + | 3.32782e8i | 0.212481 | + | 0.368027i | 0.952490 | − | 0.304569i | \(-0.0985124\pi\) |
−0.740010 | + | 0.672596i | \(0.765179\pi\) | |||||||
\(968\) | −8.29924e8 | + | 4.79157e8i | −0.914981 | + | 0.528265i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.82736e8 | − | 3.16508e8i | 0.200221 | − | 0.346792i | ||||
\(971\) | 3.23298e8i | 0.353139i | 0.984288 | + | 0.176569i | \(0.0565000\pi\) | ||||
−0.984288 | + | 0.176569i | \(0.943500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.54265e8 | −0.493141 | ||||||||
\(974\) | 5.14633e8 | + | 2.97123e8i | 0.556955 | + | 0.321558i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.22545e7 | − | 2.12255e7i | −0.0131810 | − | 0.0228301i | ||||
\(977\) | 1.07518e9 | − | 6.20753e8i | 1.15291 | − | 0.665634i | 0.203317 | − | 0.979113i | \(-0.434828\pi\) |
0.949595 | + | 0.313479i | \(0.101495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.39136e8 | − | 9.33811e8i | 0.574580 | − | 0.995202i | ||||
\(980\) | − | 4.29912e8i | − | 0.456774i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.07347e9 | −1.13359 | ||||||||
\(983\) | −5.98285e8 | − | 3.45420e8i | −0.629866 | − | 0.363653i | 0.150834 | − | 0.988559i | \(-0.451804\pi\) |
−0.780700 | + | 0.624906i | \(0.785137\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.77835e8 | − | 1.69366e9i | −1.02319 | − | 1.77222i | ||||
\(986\) | 5.73376e7 | − | 3.31039e7i | 0.0598148 | − | 0.0345341i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.88665e7 | + | 1.01960e8i | −0.0610376 | + | 0.105720i | ||||
\(989\) | − | 1.75456e9i | − | 1.81376i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.68628e9 | −1.73264 | −0.866321 | − | 0.499487i | \(-0.833522\pi\) | ||||
−0.866321 | + | 0.499487i | \(0.833522\pi\) | |||||||
\(992\) | 2.91211e7 | + | 1.68131e7i | 0.0298314 | + | 0.0172232i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.93122e8 | − | 5.07703e8i | −0.298463 | − | 0.516952i | ||||
\(995\) | −7.94092e8 | + | 4.58469e8i | −0.806124 | + | 0.465416i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.84012e8 | − | 1.35795e9i | 0.791110 | − | 1.37024i | −0.134170 | − | 0.990958i | \(-0.542837\pi\) |
0.925280 | − | 0.379285i | \(-0.123830\pi\) | |||||||
\(998\) | 1.14271e9i | 1.14960i | ||||||||
\(999\) | 0 | 0 |
(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 | 54.7.d.a.35.4 | 12 | ||
3.2 | odd | 2 | 18.7.d.a.11.1 | yes | 12 | ||
4.3 | odd | 2 | 432.7.q.b.305.2 | 12 | |||
9.2 | odd | 6 | 162.7.b.c.161.12 | 12 | |||
9.4 | even | 3 | 18.7.d.a.5.1 | ✓ | 12 | ||
9.5 | odd | 6 | inner | 54.7.d.a.17.4 | 12 | ||
9.7 | even | 3 | 162.7.b.c.161.1 | 12 | |||
12.11 | even | 2 | 144.7.q.c.65.5 | 12 | |||
36.23 | even | 6 | 432.7.q.b.17.2 | 12 | |||
36.31 | odd | 6 | 144.7.q.c.113.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.7.d.a.5.1 | ✓ | 12 | 9.4 | even | 3 | ||
18.7.d.a.11.1 | yes | 12 | 3.2 | odd | 2 | ||
54.7.d.a.17.4 | 12 | 9.5 | odd | 6 | inner | ||
54.7.d.a.35.4 | 12 | 1.1 | even | 1 | trivial | ||
144.7.q.c.65.5 | 12 | 12.11 | even | 2 | |||
144.7.q.c.113.5 | 12 | 36.31 | odd | 6 | |||
162.7.b.c.161.1 | 12 | 9.7 | even | 3 | |||
162.7.b.c.161.12 | 12 | 9.2 | odd | 6 | |||
432.7.q.b.17.2 | 12 | 36.23 | even | 6 | |||
432.7.q.b.305.2 | 12 | 4.3 | odd | 2 |