Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [164,5,Mod(163,164)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(164, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("164.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 164 = 2^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 164.d (of order \(2\), degree \(1\), 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: | \(16.9526739458\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Character | \(\chi\) | \(=\) | 164.163 |
Dual form | 164.5.d.f.163.3 |
$q$-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 \(\left(\mathbb{Z}/164\mathbb{Z}\right)^\times\).
\(n\) | \(83\) | \(129\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.71258 | − | 1.48887i | −0.928146 | − | 0.372216i | ||||
\(3\) | −10.9113 | −1.21237 | −0.606183 | − | 0.795325i | \(-0.707300\pi\) | ||||
−0.606183 | + | 0.795325i | \(0.707300\pi\) | |||||||
\(4\) | 11.5666 | + | 11.0551i | 0.722910 | + | 0.690942i | ||||
\(5\) | 8.39889 | 0.335955 | 0.167978 | − | 0.985791i | \(-0.446276\pi\) | ||||
0.167978 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(6\) | 40.5091 | + | 16.2454i | 1.12525 | + | 0.451262i | ||||
\(7\) | −64.7429 | −1.32128 | −0.660642 | − | 0.750701i | \(-0.729716\pi\) | ||||
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(8\) | −26.4823 | − | 58.2639i | −0.413786 | − | 0.910374i | ||||
\(9\) | 38.0563 | 0.469830 | ||||||||
\(10\) | −31.1816 | − | 12.5048i | −0.311816 | − | 0.125048i | ||||
\(11\) | −53.4978 | −0.442131 | −0.221065 | − | 0.975259i | \(-0.570953\pi\) | ||||
−0.221065 | + | 0.975259i | \(0.570953\pi\) | |||||||
\(12\) | −126.206 | − | 120.625i | −0.876431 | − | 0.837674i | ||||
\(13\) | 211.963i | 1.25422i | 0.778931 | + | 0.627109i | \(0.215762\pi\) | ||||
−0.778931 | + | 0.627109i | \(0.784238\pi\) | |||||||
\(14\) | 240.363 | + | 96.3934i | 1.22634 | + | 0.491803i | ||||
\(15\) | −91.6427 | −0.407301 | ||||||||
\(16\) | 11.5707 | + | 255.738i | 0.0451981 | + | 0.998978i | ||||
\(17\) | 86.3903i | 0.298928i | 0.988767 | + | 0.149464i | \(0.0477549\pi\) | ||||
−0.988767 | + | 0.149464i | \(0.952245\pi\) | |||||||
\(18\) | −141.287 | − | 56.6606i | −0.436071 | − | 0.174879i | ||||
\(19\) | −370.107 | −1.02523 | −0.512614 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512614 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(20\) | 97.1462 | + | 92.8503i | 0.242866 | + | 0.232126i | ||||
\(21\) | 706.428 | 1.60188 | ||||||||
\(22\) | 198.615 | + | 79.6511i | 0.410362 | + | 0.164568i | ||||
\(23\) | 759.854i | 1.43640i | 0.695839 | + | 0.718198i | \(0.255033\pi\) | ||||
−0.695839 | + | 0.718198i | \(0.744967\pi\) | |||||||
\(24\) | 288.956 | + | 635.735i | 0.501660 | + | 1.10371i | ||||
\(25\) | −554.459 | −0.887134 | ||||||||
\(26\) | 315.584 | − | 786.930i | 0.466840 | − | 1.16410i | ||||
\(27\) | 468.572 | 0.642759 | ||||||||
\(28\) | −748.853 | − | 715.737i | −0.955169 | − | 0.912930i | ||||
\(29\) | − | 1221.22i | − | 1.45211i | −0.687638 | − | 0.726053i | \(-0.741353\pi\) | ||
0.687638 | − | 0.726053i | \(-0.258647\pi\) | |||||||
\(30\) | 340.231 | + | 136.444i | 0.378035 | + | 0.151604i | ||||
\(31\) | − | 1548.55i | − | 1.61139i | −0.592330 | − | 0.805695i | \(-0.701792\pi\) | ||
0.592330 | − | 0.805695i | \(-0.298208\pi\) | |||||||
\(32\) | 337.803 | − | 966.677i | 0.329885 | − | 0.944021i | ||||
\(33\) | 583.730 | 0.536024 | ||||||||
\(34\) | 128.623 | − | 320.731i | 0.111266 | − | 0.277449i | ||||
\(35\) | −543.768 | −0.443892 | ||||||||
\(36\) | 440.180 | + | 420.715i | 0.339645 | + | 0.324626i | ||||
\(37\) | 1773.91 | 1.29577 | 0.647886 | − | 0.761737i | \(-0.275653\pi\) | ||||
0.647886 | + | 0.761737i | \(0.275653\pi\) | |||||||
\(38\) | 1374.05 | + | 551.040i | 0.951561 | + | 0.381606i | ||||
\(39\) | − | 2312.79i | − | 1.52057i | ||||||
\(40\) | −222.422 | − | 489.352i | −0.139014 | − | 0.305845i | ||||
\(41\) | 1638.20 | + | 376.900i | 0.974540 | + | 0.224212i | ||||
\(42\) | −2622.67 | − | 1051.78i | −1.48678 | − | 0.596245i | ||||
\(43\) | − | 966.166i | − | 0.522534i | −0.965267 | − | 0.261267i | \(-0.915860\pi\) | ||
0.965267 | − | 0.261267i | \(-0.0841404\pi\) | |||||||
\(44\) | −618.786 | − | 591.423i | −0.319621 | − | 0.305487i | ||||
\(45\) | 319.630 | 0.157842 | ||||||||
\(46\) | 1131.32 | − | 2821.02i | 0.534650 | − | 1.33319i | ||||
\(47\) | −1379.97 | −0.624701 | −0.312351 | − | 0.949967i | \(-0.601116\pi\) | ||||
−0.312351 | + | 0.949967i | \(0.601116\pi\) | |||||||
\(48\) | −126.251 | − | 2790.44i | −0.0547966 | − | 1.21113i | ||||
\(49\) | 1790.64 | 0.745790 | ||||||||
\(50\) | 2058.47 | + | 825.514i | 0.823390 | + | 0.330206i | ||||
\(51\) | − | 942.630i | − | 0.362410i | ||||||
\(52\) | −2343.27 | + | 2451.68i | −0.866592 | + | 0.906687i | ||||
\(53\) | 49.7786i | 0.0177211i | 0.999961 | + | 0.00886056i | \(0.00282044\pi\) | ||||
−0.999961 | + | 0.00886056i | \(0.997180\pi\) | |||||||
\(54\) | −1739.61 | − | 697.640i | −0.596575 | − | 0.239246i | ||||
\(55\) | −449.322 | −0.148536 | ||||||||
\(56\) | 1714.54 | + | 3772.18i | 0.546729 | + | 1.20286i | ||||
\(57\) | 4038.35 | 1.24295 | ||||||||
\(58\) | −1818.23 | + | 4533.89i | −0.540498 | + | 1.34777i | ||||
\(59\) | − | 2186.63i | − | 0.628163i | −0.949396 | − | 0.314081i | \(-0.898304\pi\) | ||
0.949396 | − | 0.314081i | \(-0.101696\pi\) | |||||||
\(60\) | −1059.99 | − | 1013.12i | −0.294442 | − | 0.281421i | ||||
\(61\) | −1860.90 | −0.500107 | −0.250053 | − | 0.968232i | \(-0.580448\pi\) | ||||
−0.250053 | + | 0.968232i | \(0.580448\pi\) | |||||||
\(62\) | −2305.58 | + | 5749.11i | −0.599786 | + | 1.49561i | ||||
\(63\) | −2463.87 | −0.620779 | ||||||||
\(64\) | −2693.37 | + | 3085.93i | −0.657562 | + | 0.753401i | ||||
\(65\) | 1780.25i | 0.421361i | ||||||||
\(66\) | −2167.15 | − | 869.096i | −0.497509 | − | 0.199517i | ||||
\(67\) | 1144.73 | 0.255008 | 0.127504 | − | 0.991838i | \(-0.459303\pi\) | ||||
0.127504 | + | 0.991838i | \(0.459303\pi\) | |||||||
\(68\) | −955.051 | + | 999.239i | −0.206542 | + | 0.216098i | ||||
\(69\) | − | 8290.98i | − | 1.74144i | ||||||
\(70\) | 2018.78 | + | 809.597i | 0.411997 | + | 0.165224i | ||||
\(71\) | 4669.47 | 0.926298 | 0.463149 | − | 0.886280i | \(-0.346719\pi\) | ||||
0.463149 | + | 0.886280i | \(0.346719\pi\) | |||||||
\(72\) | −1007.82 | − | 2217.31i | −0.194409 | − | 0.427721i | ||||
\(73\) | 8288.70 | 1.55539 | 0.777697 | − | 0.628639i | \(-0.216388\pi\) | ||||
0.777697 | + | 0.628639i | \(0.216388\pi\) | |||||||
\(74\) | −6585.80 | − | 2641.12i | −1.20267 | − | 0.482307i | ||||
\(75\) | 6049.86 | 1.07553 | ||||||||
\(76\) | −4280.87 | − | 4091.56i | −0.741147 | − | 0.708373i | ||||
\(77\) | 3463.60 | 0.584180 | ||||||||
\(78\) | −3443.43 | + | 8586.42i | −0.565981 | + | 1.41131i | ||||
\(79\) | 5692.98 | 0.912191 | 0.456095 | − | 0.889931i | \(-0.349248\pi\) | ||||
0.456095 | + | 0.889931i | \(0.349248\pi\) | |||||||
\(80\) | 97.1810 | + | 2147.92i | 0.0151845 | + | 0.335612i | ||||
\(81\) | −8195.28 | −1.24909 | ||||||||
\(82\) | −5520.81 | − | 3838.34i | −0.821060 | − | 0.570841i | ||||
\(83\) | 3047.28i | 0.442341i | 0.975235 | + | 0.221170i | \(0.0709877\pi\) | ||||
−0.975235 | + | 0.221170i | \(0.929012\pi\) | |||||||
\(84\) | 8170.95 | + | 7809.62i | 1.15801 | + | 1.10681i | ||||
\(85\) | 725.582i | 0.100427i | ||||||||
\(86\) | −1438.49 | + | 3586.97i | −0.194496 | + | 0.484988i | ||||
\(87\) | 13325.1i | 1.76048i | ||||||||
\(88\) | 1416.75 | + | 3116.99i | 0.182948 | + | 0.402505i | ||||
\(89\) | − | 13007.7i | − | 1.64218i | −0.570798 | − | 0.821090i | \(-0.693366\pi\) | ||
0.570798 | − | 0.821090i | \(-0.306634\pi\) | |||||||
\(90\) | −1186.65 | − | 475.886i | −0.146500 | − | 0.0587514i | ||||
\(91\) | − | 13723.1i | − | 1.65718i | ||||||
\(92\) | −8400.24 | + | 8788.89i | −0.992467 | + | 1.03839i | ||||
\(93\) | 16896.6i | 1.95359i | ||||||||
\(94\) | 5123.24 | + | 2054.58i | 0.579814 | + | 0.232524i | ||||
\(95\) | −3108.49 | −0.344431 | ||||||||
\(96\) | −3685.86 | + | 10547.7i | −0.399942 | + | 1.14450i | ||||
\(97\) | 1202.68i | 0.127822i | 0.997956 | + | 0.0639109i | \(0.0203574\pi\) | ||||
−0.997956 | + | 0.0639109i | \(0.979643\pi\) | |||||||
\(98\) | −6647.90 | − | 2666.02i | −0.692202 | − | 0.277595i | ||||
\(99\) | −2035.93 | −0.207727 | ||||||||
\(100\) | −6413.18 | − | 6129.58i | −0.641318 | − | 0.612958i | ||||
\(101\) | 5757.94i | 0.564449i | 0.959348 | + | 0.282225i | \(0.0910723\pi\) | ||||
−0.959348 | + | 0.282225i | \(0.908928\pi\) | |||||||
\(102\) | −1403.45 | + | 3499.59i | −0.134895 | + | 0.336370i | ||||
\(103\) | − | 3187.97i | − | 0.300496i | −0.988648 | − | 0.150248i | \(-0.951993\pi\) | ||
0.988648 | − | 0.150248i | \(-0.0480073\pi\) | |||||||
\(104\) | 12349.8 | − | 5613.27i | 1.14181 | − | 0.518978i | ||||
\(105\) | 5933.21 | 0.538160 | ||||||||
\(106\) | 74.1137 | − | 184.807i | 0.00659609 | − | 0.0164478i | ||||
\(107\) | 17012.0i | 1.48589i | 0.669352 | + | 0.742945i | \(0.266572\pi\) | ||||
−0.669352 | + | 0.742945i | \(0.733428\pi\) | |||||||
\(108\) | 5419.76 | + | 5180.09i | 0.464657 | + | 0.444110i | ||||
\(109\) | − | 17305.0i | − | 1.45653i | −0.685296 | − | 0.728264i | \(-0.740327\pi\) | ||
0.685296 | − | 0.728264i | \(-0.259673\pi\) | |||||||
\(110\) | 1668.15 | + | 668.980i | 0.137863 | + | 0.0552876i | ||||
\(111\) | −19355.7 | −1.57095 | ||||||||
\(112\) | −749.121 | − | 16557.2i | −0.0597194 | − | 1.31993i | ||||
\(113\) | −7981.54 | −0.625072 | −0.312536 | − | 0.949906i | \(-0.601178\pi\) | ||||
−0.312536 | + | 0.949906i | \(0.601178\pi\) | |||||||
\(114\) | −14992.7 | − | 6012.55i | −1.15364 | − | 0.462646i | ||||
\(115\) | 6381.92i | 0.482565i | ||||||||
\(116\) | 13500.7 | − | 14125.3i | 1.00332 | − | 1.04974i | ||||
\(117\) | 8066.51i | 0.589270i | ||||||||
\(118\) | −3255.60 | + | 8118.06i | −0.233812 | + | 0.583027i | ||||
\(119\) | − | 5593.16i | − | 0.394969i | ||||||
\(120\) | 2426.91 | + | 5339.46i | 0.168535 | + | 0.370796i | ||||
\(121\) | −11779.0 | −0.804520 | ||||||||
\(122\) | 6908.74 | + | 2770.63i | 0.464172 | + | 0.186148i | ||||
\(123\) | −17874.9 | − | 4112.47i | −1.18150 | − | 0.271827i | ||||
\(124\) | 17119.3 | − | 17911.4i | 1.11338 | − | 1.16489i | ||||
\(125\) | −9906.14 | −0.633993 | ||||||||
\(126\) | 9147.33 | + | 3668.37i | 0.576174 | + | 0.231064i | ||||
\(127\) | − | 12068.8i | − | 0.748265i | −0.927375 | − | 0.374132i | \(-0.877941\pi\) | ||
0.927375 | − | 0.374132i | \(-0.122059\pi\) | |||||||
\(128\) | 14593.9 | − | 7446.70i | 0.890741 | − | 0.454511i | ||||
\(129\) | 10542.1i | 0.633503i | ||||||||
\(130\) | 2650.55 | − | 6609.34i | 0.156838 | − | 0.391085i | ||||
\(131\) | 28203.8i | 1.64348i | 0.569859 | + | 0.821742i | \(0.306998\pi\) | ||||
−0.569859 | + | 0.821742i | \(0.693002\pi\) | |||||||
\(132\) | 6751.75 | + | 6453.18i | 0.387497 | + | 0.370362i | ||||
\(133\) | 23961.8 | 1.35462 | ||||||||
\(134\) | −4249.90 | − | 1704.35i | −0.236684 | − | 0.0949180i | ||||
\(135\) | 3935.48 | 0.215939 | ||||||||
\(136\) | 5033.44 | − | 2287.82i | 0.272137 | − | 0.123692i | ||||
\(137\) | 21965.2i | 1.17029i | 0.810928 | + | 0.585145i | \(0.198963\pi\) | ||||
−0.810928 | + | 0.585145i | \(0.801037\pi\) | |||||||
\(138\) | −12344.2 | + | 30781.0i | −0.648191 | + | 1.61631i | ||||
\(139\) | − | 7395.26i | − | 0.382758i | −0.981516 | − | 0.191379i | \(-0.938704\pi\) | ||
0.981516 | − | 0.191379i | \(-0.0612959\pi\) | |||||||
\(140\) | −6289.53 | − | 6011.40i | −0.320894 | − | 0.306704i | ||||
\(141\) | 15057.2 | 0.757366 | ||||||||
\(142\) | −17335.8 | − | 6952.21i | −0.859740 | − | 0.344783i | ||||
\(143\) | − | 11339.6i | − | 0.554529i | ||||||
\(144\) | 440.338 | + | 9732.45i | 0.0212354 | + | 0.469350i | ||||
\(145\) | − | 10256.9i | − | 0.487843i | ||||||
\(146\) | −30772.5 | − | 12340.8i | −1.44363 | − | 0.578943i | ||||
\(147\) | −19538.2 | −0.904170 | ||||||||
\(148\) | 20518.1 | + | 19610.7i | 0.936727 | + | 0.895304i | ||||
\(149\) | 33575.6i | 1.51235i | 0.654371 | + | 0.756173i | \(0.272933\pi\) | ||||
−0.654371 | + | 0.756173i | \(0.727067\pi\) | |||||||
\(150\) | −22460.6 | − | 9007.43i | −0.998250 | − | 0.400330i | ||||
\(151\) | 26884.0 | 1.17907 | 0.589536 | − | 0.807742i | \(-0.299311\pi\) | ||||
0.589536 | + | 0.807742i | \(0.299311\pi\) | |||||||
\(152\) | 9801.30 | + | 21563.9i | 0.424225 | + | 0.933340i | ||||
\(153\) | 3287.69i | 0.140446i | ||||||||
\(154\) | −12858.9 | − | 5156.84i | −0.542205 | − | 0.217441i | ||||
\(155\) | − | 13006.1i | − | 0.541356i | ||||||
\(156\) | 25568.0 | − | 26751.0i | 1.05063 | − | 1.09924i | ||||
\(157\) | − | 31732.0i | − | 1.28735i | −0.765298 | − | 0.643677i | \(-0.777408\pi\) | ||
0.765298 | − | 0.643677i | \(-0.222592\pi\) | |||||||
\(158\) | −21135.7 | − | 8476.08i | −0.846646 | − | 0.339532i | ||||
\(159\) | − | 543.149i | − | 0.0214845i | ||||||
\(160\) | 2837.17 | − | 8119.01i | 0.110827 | − | 0.317149i | ||||
\(161\) | − | 49195.1i | − | 1.89789i | ||||||
\(162\) | 30425.7 | + | 12201.7i | 1.15934 | + | 0.464932i | ||||
\(163\) | − | 26471.0i | − | 0.996313i | −0.867087 | − | 0.498156i | \(-0.834011\pi\) | ||
0.867087 | − | 0.498156i | \(-0.165989\pi\) | |||||||
\(164\) | 14781.7 | + | 22469.9i | 0.549588 | + | 0.835436i | ||||
\(165\) | 4902.69 | 0.180080 | ||||||||
\(166\) | 4536.99 | − | 11313.3i | 0.164646 | − | 0.410557i | ||||
\(167\) | 21454.0 | 0.769264 | 0.384632 | − | 0.923070i | \(-0.374328\pi\) | ||||
0.384632 | + | 0.923070i | \(0.374328\pi\) | |||||||
\(168\) | −18707.9 | − | 41159.3i | −0.662835 | − | 1.45831i | ||||
\(169\) | −16367.3 | −0.573063 | ||||||||
\(170\) | 1080.29 | − | 2693.78i | 0.0373804 | − | 0.0932106i | ||||
\(171\) | −14084.9 | −0.481683 | ||||||||
\(172\) | 10681.0 | − | 11175.2i | 0.361041 | − | 0.377745i | ||||
\(173\) | −40986.3 | −1.36945 | −0.684725 | − | 0.728802i | \(-0.740078\pi\) | ||||
−0.684725 | + | 0.728802i | \(0.740078\pi\) | |||||||
\(174\) | 19839.3 | − | 49470.6i | 0.655281 | − | 1.63399i | ||||
\(175\) | 35897.3 | 1.17216 | ||||||||
\(176\) | −619.008 | − | 13681.5i | −0.0199835 | − | 0.441679i | ||||
\(177\) | 23859.0i | 0.761563i | ||||||||
\(178\) | −19366.7 | + | 48292.2i | −0.611246 | + | 1.52418i | ||||
\(179\) | −418.430 | −0.0130592 | −0.00652960 | − | 0.999979i | \(-0.502078\pi\) | ||||
−0.00652960 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(180\) | 3697.02 | + | 3533.54i | 0.114106 | + | 0.109060i | ||||
\(181\) | − | 31402.8i | − | 0.958542i | −0.877667 | − | 0.479271i | \(-0.840901\pi\) | ||
0.877667 | − | 0.479271i | \(-0.159099\pi\) | |||||||
\(182\) | −20431.8 | + | 50948.1i | −0.616828 | + | 1.53810i | ||||
\(183\) | 20304.8 | 0.606312 | ||||||||
\(184\) | 44272.1 | − | 20122.7i | 1.30766 | − | 0.594361i | ||||
\(185\) | 14898.9 | 0.435322 | ||||||||
\(186\) | 25156.8 | − | 62730.2i | 0.727160 | − | 1.81322i | ||||
\(187\) | − | 4621.69i | − | 0.132165i | ||||||
\(188\) | −15961.5 | − | 15255.6i | −0.451603 | − | 0.431632i | ||||
\(189\) | −30336.7 | −0.849267 | ||||||||
\(190\) | 11540.5 | + | 4628.12i | 0.319682 | + | 0.128203i | ||||
\(191\) | 39525.7 | 1.08346 | 0.541729 | − | 0.840553i | \(-0.317770\pi\) | ||||
0.541729 | + | 0.840553i | \(0.317770\pi\) | |||||||
\(192\) | 29388.2 | − | 33671.5i | 0.797205 | − | 0.913397i | ||||
\(193\) | − | 11715.0i | − | 0.314505i | −0.987558 | − | 0.157253i | \(-0.949736\pi\) | ||
0.987558 | − | 0.157253i | \(-0.0502637\pi\) | |||||||
\(194\) | 1790.62 | − | 4465.03i | 0.0475774 | − | 0.118637i | ||||
\(195\) | − | 19424.8i | − | 0.510844i | ||||||
\(196\) | 20711.6 | + | 19795.7i | 0.539139 | + | 0.515297i | ||||
\(197\) | −16057.4 | −0.413755 | −0.206877 | − | 0.978367i | \(-0.566330\pi\) | ||||
−0.206877 | + | 0.978367i | \(0.566330\pi\) | |||||||
\(198\) | 7558.55 | + | 3031.22i | 0.192801 | + | 0.0773192i | ||||
\(199\) | 7311.67 | 0.184633 | 0.0923167 | − | 0.995730i | \(-0.470573\pi\) | ||||
0.0923167 | + | 0.995730i | \(0.470573\pi\) | |||||||
\(200\) | 14683.4 | + | 32304.9i | 0.367084 | + | 0.807624i | ||||
\(201\) | −12490.5 | −0.309163 | ||||||||
\(202\) | 8572.80 | − | 21376.9i | 0.210097 | − | 0.523891i | ||||
\(203\) | 79065.4i | 1.91864i | ||||||||
\(204\) | 10420.8 | − | 10903.0i | 0.250405 | − | 0.261990i | ||||
\(205\) | 13759.1 | + | 3165.54i | 0.327402 | + | 0.0753252i | ||||
\(206\) | −4746.45 | + | 11835.6i | −0.111850 | + | 0.278905i | ||||
\(207\) | 28917.2i | 0.674863i | ||||||||
\(208\) | −54207.0 | + | 2452.56i | −1.25294 | + | 0.0566882i | ||||
\(209\) | 19799.9 | 0.453285 | ||||||||
\(210\) | −22027.5 | − | 8833.75i | −0.499491 | − | 0.200312i | ||||
\(211\) | −33084.4 | −0.743120 | −0.371560 | − | 0.928409i | \(-0.621177\pi\) | ||||
−0.371560 | + | 0.928409i | \(0.621177\pi\) | |||||||
\(212\) | −550.306 | + | 575.768i | −0.0122443 | + | 0.0128108i | ||||
\(213\) | −50949.9 | −1.12301 | ||||||||
\(214\) | 25328.5 | − | 63158.3i | 0.553073 | − | 1.37912i | ||||
\(215\) | − | 8114.72i | − | 0.175548i | ||||||
\(216\) | −12408.9 | − | 27300.8i | −0.265965 | − | 0.585152i | ||||
\(217\) | 100257.i | 2.12910i | ||||||||
\(218\) | −25764.8 | + | 64246.3i | −0.542144 | + | 1.35187i | ||||
\(219\) | −90440.4 | −1.88571 | ||||||||
\(220\) | −5197.11 | − | 4967.29i | −0.107378 | − | 0.102630i | ||||
\(221\) | −18311.5 | −0.374921 | ||||||||
\(222\) | 71859.6 | + | 28818.0i | 1.45807 | + | 0.584733i | ||||
\(223\) | 67686.9i | 1.36111i | 0.732695 | + | 0.680557i | \(0.238262\pi\) | ||||
−0.732695 | + | 0.680557i | \(0.761738\pi\) | |||||||
\(224\) | −21870.3 | + | 62585.5i | −0.435872 | + | 1.24732i | ||||
\(225\) | −21100.6 | −0.416802 | ||||||||
\(226\) | 29632.1 | + | 11883.4i | 0.580158 | + | 0.232662i | ||||
\(227\) | 25028.0 | 0.485707 | 0.242854 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242854 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(228\) | 46709.8 | + | 44644.2i | 0.898541 | + | 0.858807i | ||||
\(229\) | 94720.5i | 1.80623i | 0.429399 | + | 0.903115i | \(0.358725\pi\) | ||||
−0.429399 | + | 0.903115i | \(0.641275\pi\) | |||||||
\(230\) | 9501.82 | − | 23693.4i | 0.179619 | − | 0.447891i | ||||
\(231\) | −37792.4 | −0.708240 | ||||||||
\(232\) | −71153.2 | + | 32340.8i | −1.32196 | + | 0.600862i | ||||
\(233\) | − | 43248.7i | − | 0.796638i | −0.917247 | − | 0.398319i | \(-0.869594\pi\) | ||
0.917247 | − | 0.398319i | \(-0.130406\pi\) | |||||||
\(234\) | 12010.0 | − | 29947.6i | 0.219336 | − | 0.546928i | ||||
\(235\) | −11590.2 | −0.209872 | ||||||||
\(236\) | 24173.4 | − | 25291.8i | 0.434024 | − | 0.454105i | ||||
\(237\) | −62117.8 | −1.10591 | ||||||||
\(238\) | −8327.46 | + | 20765.1i | −0.147014 | + | 0.366589i | ||||
\(239\) | 45302.7 | 0.793101 | 0.396550 | − | 0.918013i | \(-0.370207\pi\) | ||||
0.396550 | + | 0.918013i | \(0.370207\pi\) | |||||||
\(240\) | −1060.37 | − | 23436.6i | −0.0184092 | − | 0.406885i | ||||
\(241\) | 41114.1 | 0.707875 | 0.353937 | − | 0.935269i | \(-0.384843\pi\) | ||||
0.353937 | + | 0.935269i | \(0.384843\pi\) | |||||||
\(242\) | 43730.5 | + | 17537.3i | 0.746712 | + | 0.299456i | ||||
\(243\) | 51466.8 | 0.871594 | ||||||||
\(244\) | −21524.2 | − | 20572.4i | −0.361532 | − | 0.345545i | ||||
\(245\) | 15039.4 | 0.250552 | ||||||||
\(246\) | 60239.2 | + | 41881.2i | 0.995425 | + | 0.692068i | ||||
\(247\) | − | 78449.0i | − | 1.28586i | ||||||
\(248\) | −90224.4 | + | 41009.1i | −1.46697 | + | 0.666771i | ||||
\(249\) | − | 33249.8i | − | 0.536278i | ||||||
\(250\) | 36777.4 | + | 14748.9i | 0.588438 | + | 0.235982i | ||||
\(251\) | − | 31230.5i | − | 0.495714i | −0.968797 | − | 0.247857i | \(-0.920274\pi\) | ||
0.968797 | − | 0.247857i | \(-0.0797262\pi\) | |||||||
\(252\) | −28498.5 | − | 27238.3i | −0.448767 | − | 0.428922i | ||||
\(253\) | − | 40650.5i | − | 0.635075i | ||||||
\(254\) | −17968.8 | + | 44806.3i | −0.278516 | + | 0.694499i | ||||
\(255\) | − | 7917.04i | − | 0.121754i | ||||||
\(256\) | −65268.2 | + | 5918.15i | −0.995914 | + | 0.0903038i | ||||
\(257\) | − | 108313.i | − | 1.63989i | −0.572441 | − | 0.819946i | \(-0.694003\pi\) | ||
0.572441 | − | 0.819946i | \(-0.305997\pi\) | |||||||
\(258\) | 15695.8 | − | 39138.5i | 0.235800 | − | 0.587983i | ||||
\(259\) | −114848. | −1.71208 | ||||||||
\(260\) | −19680.8 | + | 20591.4i | −0.291136 | + | 0.304606i | ||||
\(261\) | − | 46475.1i | − | 0.682244i | ||||||
\(262\) | 41991.7 | − | 104709.i | 0.611732 | − | 1.52539i | ||||
\(263\) | 79971.4 | 1.15617 | 0.578087 | − | 0.815975i | \(-0.303799\pi\) | ||||
0.578087 | + | 0.815975i | \(0.303799\pi\) | |||||||
\(264\) | −15458.5 | − | 34010.4i | −0.221800 | − | 0.487983i | ||||
\(265\) | 418.085i | 0.00595351i | ||||||||
\(266\) | −88960.2 | − | 35675.9i | −1.25728 | − | 0.504210i | ||||
\(267\) | 141931.i | 1.99092i | ||||||||
\(268\) | 13240.6 | + | 12655.1i | 0.184348 | + | 0.176196i | ||||
\(269\) | −31997.5 | −0.442192 | −0.221096 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221096 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(270\) | −14610.8 | − | 5859.40i | −0.200422 | − | 0.0803758i | ||||
\(271\) | 697.687i | 0.00949997i | 0.999989 | + | 0.00474999i | \(0.00151197\pi\) | ||||
−0.999989 | + | 0.00474999i | \(0.998488\pi\) | |||||||
\(272\) | −22093.3 | + | 999.597i | −0.298623 | + | 0.0135110i | ||||
\(273\) | 149737.i | 2.00911i | ||||||||
\(274\) | 32703.2 | − | 81547.6i | 0.435601 | − | 1.08620i | ||||
\(275\) | 29662.3 | 0.392229 | ||||||||
\(276\) | 91657.4 | − | 95898.2i | 1.20323 | − | 1.25890i | ||||
\(277\) | −24514.1 | −0.319489 | −0.159744 | − | 0.987158i | \(-0.551067\pi\) | ||||
−0.159744 | + | 0.987158i | \(0.551067\pi\) | |||||||
\(278\) | −11010.5 | + | 27455.5i | −0.142469 | + | 0.355255i | ||||
\(279\) | − | 58931.9i | − | 0.757080i | ||||||
\(280\) | 14400.2 | + | 31682.1i | 0.183677 | + | 0.404108i | ||||
\(281\) | 98113.6i | 1.24256i | 0.783589 | + | 0.621279i | \(0.213387\pi\) | ||||
−0.783589 | + | 0.621279i | \(0.786613\pi\) | |||||||
\(282\) | −55901.1 | − | 22418.1i | −0.702947 | − | 0.281904i | ||||
\(283\) | 18480.4i | 0.230748i | 0.993322 | + | 0.115374i | \(0.0368067\pi\) | ||||
−0.993322 | + | 0.115374i | \(0.963193\pi\) | |||||||
\(284\) | 54009.7 | + | 51621.3i | 0.669630 | + | 0.640018i | ||||
\(285\) | 33917.6 | 0.417576 | ||||||||
\(286\) | −16883.1 | + | 42099.1i | −0.206405 | + | 0.514684i | ||||
\(287\) | −106062. | − | 24401.6i | −1.28764 | − | 0.296247i | ||||
\(288\) | 12855.5 | − | 36788.1i | 0.154990 | − | 0.443530i | ||||
\(289\) | 76057.7 | 0.910642 | ||||||||
\(290\) | −15271.1 | + | 38079.6i | −0.181583 | + | 0.452790i | ||||
\(291\) | − | 13122.7i | − | 0.154967i | ||||||
\(292\) | 95871.8 | + | 91632.2i | 1.12441 | + | 1.07469i | ||||
\(293\) | − | 13202.8i | − | 0.153791i | −0.997039 | − | 0.0768953i | \(-0.975499\pi\) | ||
0.997039 | − | 0.0768953i | \(-0.0245007\pi\) | |||||||
\(294\) | 72537.2 | + | 29089.7i | 0.839201 | + | 0.336547i | ||||
\(295\) | − | 18365.3i | − | 0.211035i | ||||||
\(296\) | −46977.3 | − | 103355.i | −0.536173 | − | 1.17964i | ||||
\(297\) | −25067.6 | −0.284184 | ||||||||
\(298\) | 49989.6 | − | 124652.i | 0.562920 | − | 1.40368i | ||||
\(299\) | −161061. | −1.80155 | ||||||||
\(300\) | 69976.1 | + | 66881.6i | 0.777512 | + | 0.743129i | ||||
\(301\) | 62552.4i | 0.690416i | ||||||||
\(302\) | −99809.1 | − | 40026.7i | −1.09435 | − | 0.438870i | ||||
\(303\) | − | 62826.6i | − | 0.684319i | ||||||
\(304\) | −4282.40 | − | 94650.6i | −0.0463383 | − | 1.02418i | ||||
\(305\) | −15629.5 | −0.168014 | ||||||||
\(306\) | 4894.93 | − | 12205.8i | 0.0522761 | − | 0.130354i | ||||
\(307\) | − | 22851.6i | − | 0.242460i | −0.992624 | − | 0.121230i | \(-0.961316\pi\) | ||
0.992624 | − | 0.121230i | \(-0.0386839\pi\) | |||||||
\(308\) | 40062.0 | + | 38290.4i | 0.422310 | + | 0.403635i | ||||
\(309\) | 34784.8i | 0.364311i | ||||||||
\(310\) | −19364.3 | + | 48286.1i | −0.201501 | + | 0.502457i | ||||
\(311\) | 158073. | 1.63432 | 0.817159 | − | 0.576412i | \(-0.195548\pi\) | ||||
0.817159 | + | 0.576412i | \(0.195548\pi\) | |||||||
\(312\) | −134752. | + | 61248.0i | −1.38429 | + | 0.629191i | ||||
\(313\) | − | 62359.7i | − | 0.636525i | −0.948003 | − | 0.318263i | \(-0.896901\pi\) | ||
0.948003 | − | 0.318263i | \(-0.103099\pi\) | |||||||
\(314\) | −47244.6 | + | 117808.i | −0.479174 | + | 1.19485i | ||||
\(315\) | −20693.8 | −0.208554 | ||||||||
\(316\) | 65848.2 | + | 62936.3i | 0.659432 | + | 0.630271i | ||||
\(317\) | 12742.6i | 0.126806i | 0.997988 | + | 0.0634030i | \(0.0201953\pi\) | ||||
−0.997988 | + | 0.0634030i | \(0.979805\pi\) | |||||||
\(318\) | −808.676 | + | 2016.49i | −0.00799687 | + | 0.0199407i | ||||
\(319\) | 65332.7i | 0.642021i | ||||||||
\(320\) | −22621.3 | + | 25918.4i | −0.220911 | + | 0.253109i | ||||
\(321\) | − | 185622.i | − | 1.80144i | ||||||
\(322\) | −73244.9 | + | 182641.i | −0.706424 | + | 1.76152i | ||||
\(323\) | − | 31973.7i | − | 0.306470i | ||||||
\(324\) | −94791.2 | − | 90599.4i | −0.902980 | − | 0.863049i | ||||
\(325\) | − | 117525.i | − | 1.11266i | ||||||
\(326\) | −39411.8 | + | 98276.0i | −0.370844 | + | 0.924724i | ||||
\(327\) | 188820.i | 1.76585i | ||||||||
\(328\) | −21423.7 | − | 105429.i | −0.199135 | − | 0.979972i | ||||
\(329\) | 89342.9 | 0.825407 | ||||||||
\(330\) | −18201.6 | − | 7299.44i | −0.167141 | − | 0.0670288i | ||||
\(331\) | 4782.50 | 0.0436514 | 0.0218257 | − | 0.999762i | \(-0.493052\pi\) | ||||
0.0218257 | + | 0.999762i | \(0.493052\pi\) | |||||||
\(332\) | −33687.9 | + | 35246.6i | −0.305632 | + | 0.319772i | ||||
\(333\) | 67508.5 | 0.608793 | ||||||||
\(334\) | −79649.8 | − | 31942.1i | −0.713989 | − | 0.286333i | ||||
\(335\) | 9614.45 | 0.0856712 | ||||||||
\(336\) | 8173.87 | + | 180661.i | 0.0724018 | + | 1.60024i | ||||
\(337\) | 179723. | 1.58250 | 0.791251 | − | 0.611492i | \(-0.209430\pi\) | ||||
0.791251 | + | 0.611492i | \(0.209430\pi\) | |||||||
\(338\) | 60764.8 | + | 24368.6i | 0.531886 | + | 0.213303i | ||||
\(339\) | 87088.9 | 0.757816 | ||||||||
\(340\) | −8021.36 | + | 8392.49i | −0.0693890 | + | 0.0725994i | ||||
\(341\) | 82843.9i | 0.712446i | ||||||||
\(342\) | 52291.3 | + | 20970.5i | 0.447072 | + | 0.179290i | ||||
\(343\) | 39516.4 | 0.335884 | ||||||||
\(344\) | −56292.6 | + | 25586.3i | −0.475702 | + | 0.216218i | ||||
\(345\) | − | 69635.0i | − | 0.585045i | ||||||
\(346\) | 152165. | + | 61023.0i | 1.27105 | + | 0.509732i | ||||
\(347\) | 30157.9 | 0.250462 | 0.125231 | − | 0.992128i | \(-0.460033\pi\) | ||||
0.125231 | + | 0.992128i | \(0.460033\pi\) | |||||||
\(348\) | −147310. | + | 154126.i | −1.21639 | + | 1.27267i | ||||
\(349\) | −205819. | −1.68979 | −0.844897 | − | 0.534929i | \(-0.820338\pi\) | ||||
−0.844897 | + | 0.534929i | \(0.820338\pi\) | |||||||
\(350\) | −133272. | − | 53446.2i | −1.08793 | − | 0.436295i | ||||
\(351\) | 99319.8i | 0.806161i | ||||||||
\(352\) | −18071.7 | + | 51715.2i | −0.145853 | + | 0.417381i | ||||
\(353\) | 37308.9 | 0.299408 | 0.149704 | − | 0.988731i | \(-0.452168\pi\) | ||||
0.149704 | + | 0.988731i | \(0.452168\pi\) | |||||||
\(354\) | 35522.8 | − | 88578.6i | 0.283466 | − | 0.706842i | ||||
\(355\) | 39218.3 | 0.311195 | ||||||||
\(356\) | 143801. | − | 150455.i | 1.13465 | − | 1.18715i | ||||
\(357\) | 61028.6i | 0.478847i | ||||||||
\(358\) | 1553.46 | + | 622.986i | 0.0121208 | + | 0.00486085i | ||||
\(359\) | − | 157948.i | − | 1.22553i | −0.790265 | − | 0.612766i | \(-0.790057\pi\) | ||
0.790265 | − | 0.612766i | \(-0.209943\pi\) | |||||||
\(360\) | −8464.55 | − | 18622.9i | −0.0653129 | − | 0.143695i | ||||
\(361\) | 6658.27 | 0.0510913 | ||||||||
\(362\) | −46754.5 | + | 116586.i | −0.356785 | + | 0.889667i | ||||
\(363\) | 128524. | 0.975373 | ||||||||
\(364\) | 151710. | − | 158729.i | 1.14501 | − | 1.19799i | ||||
\(365\) | 69615.8 | 0.522543 | ||||||||
\(366\) | −75383.3 | − | 30231.1i | −0.562746 | − | 0.225679i | ||||
\(367\) | − | 123736.i | − | 0.918678i | −0.888261 | − | 0.459339i | \(-0.848086\pi\) | ||
0.888261 | − | 0.459339i | \(-0.151914\pi\) | |||||||
\(368\) | −194324. | + | 8792.04i | −1.43493 | + | 0.0649223i | ||||
\(369\) | 62343.9 | + | 14343.4i | 0.457869 | + | 0.105342i | ||||
\(370\) | −55313.4 | − | 22182.4i | −0.404042 | − | 0.162034i | ||||
\(371\) | − | 3222.81i | − | 0.0234146i | ||||||
\(372\) | −186794. | + | 195436.i | −1.34982 | + | 1.41227i | ||||
\(373\) | −167782. | −1.20595 | −0.602974 | − | 0.797761i | \(-0.706018\pi\) | ||||
−0.602974 | + | 0.797761i | \(0.706018\pi\) | |||||||
\(374\) | −6881.08 | + | 17158.4i | −0.0491941 | + | 0.122669i | ||||
\(375\) | 108089. | 0.768631 | ||||||||
\(376\) | 36544.7 | + | 80402.2i | 0.258493 | + | 0.568712i | ||||
\(377\) | 258854. | 1.82126 | ||||||||
\(378\) | 112627. | + | 45167.2i | 0.788244 | + | 0.316111i | ||||
\(379\) | − | 238729.i | − | 1.66198i | −0.556285 | − | 0.830992i | \(-0.687774\pi\) | ||
0.556285 | − | 0.830992i | \(-0.312226\pi\) | |||||||
\(380\) | −35954.5 | − | 34364.6i | −0.248992 | − | 0.237982i | ||||
\(381\) | 131686.i | 0.907170i | ||||||||
\(382\) | −146742. | − | 58848.4i | −1.00561 | − | 0.403281i | ||||
\(383\) | −237079. | −1.61620 | −0.808100 | − | 0.589045i | \(-0.799504\pi\) | ||||
−0.808100 | + | 0.589045i | \(0.799504\pi\) | |||||||
\(384\) | −159238. | + | 81253.1i | −1.07990 | + | 0.551033i | ||||
\(385\) | 29090.4 | 0.196258 | ||||||||
\(386\) | −17442.1 | + | 43492.9i | −0.117064 | + | 0.291907i | ||||
\(387\) | − | 36768.7i | − | 0.245503i | ||||||
\(388\) | −13295.7 | + | 13910.8i | −0.0883175 | + | 0.0924037i | ||||
\(389\) | 219696. | 1.45185 | 0.725927 | − | 0.687772i | \(-0.241411\pi\) | ||||
0.725927 | + | 0.687772i | \(0.241411\pi\) | |||||||
\(390\) | −28921.0 | + | 72116.4i | −0.190144 | + | 0.474138i | ||||
\(391\) | −65644.0 | −0.429380 | ||||||||
\(392\) | −47420.3 | − | 104330.i | −0.308597 | − | 0.678947i | ||||
\(393\) | − | 307740.i | − | 1.99250i | ||||||
\(394\) | 59614.5 | + | 23907.3i | 0.384025 | + | 0.154006i | ||||
\(395\) | 47814.7 | 0.306455 | ||||||||
\(396\) | −23548.7 | − | 22507.3i | −0.150168 | − | 0.143527i | ||||
\(397\) | − | 11360.1i | − | 0.0720778i | −0.999350 | − | 0.0360389i | \(-0.988526\pi\) | ||
0.999350 | − | 0.0360389i | \(-0.0114740\pi\) | |||||||
\(398\) | −27145.2 | − | 10886.1i | −0.171367 | − | 0.0687236i | ||||
\(399\) | −261454. | −1.64229 | ||||||||
\(400\) | −6415.48 | − | 141796.i | −0.0400967 | − | 0.886227i | ||||
\(401\) | −5772.18 | −0.0358964 | −0.0179482 | − | 0.999839i | \(-0.505713\pi\) | ||||
−0.0179482 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(402\) | 46371.9 | + | 18596.6i | 0.286948 | + | 0.115075i | ||||
\(403\) | 328234. | 2.02104 | ||||||||
\(404\) | −63654.5 | + | 66599.6i | −0.390002 | + | 0.408046i | ||||
\(405\) | −68831.2 | −0.419638 | ||||||||
\(406\) | 117718. | − | 293537.i | 0.714150 | − | 1.78078i | ||||
\(407\) | −94900.5 | −0.572901 | ||||||||
\(408\) | −54921.3 | + | 24963.0i | −0.329929 | + | 0.149960i | ||||
\(409\) | 242850. | 1.45175 | 0.725874 | − | 0.687828i | \(-0.241436\pi\) | ||||
0.725874 | + | 0.687828i | \(0.241436\pi\) | |||||||
\(410\) | −46368.7 | − | 32237.7i | −0.275840 | − | 0.191777i | ||||
\(411\) | − | 239669.i | − | 1.41882i | ||||||
\(412\) | 35243.2 | − | 36873.8i | 0.207626 | − | 0.217232i | ||||
\(413\) | 141569.i | 0.829981i | ||||||||
\(414\) | 43053.8 | − | 107357.i | 0.251195 | − | 0.626371i | ||||
\(415\) | 25593.8i | 0.148607i | ||||||||
\(416\) | 204900. | + | 71601.6i | 1.18401 | + | 0.413748i | ||||
\(417\) | 80691.8i | 0.464042i | ||||||||
\(418\) | −73508.9 | − | 29479.4i | −0.420714 | − | 0.168720i | ||||
\(419\) | − | 112368.i | − | 0.640050i | −0.947409 | − | 0.320025i | \(-0.896309\pi\) | ||
0.947409 | − | 0.320025i | \(-0.103691\pi\) | |||||||
\(420\) | 68626.9 | + | 65592.1i | 0.389041 | + | 0.371837i | ||||
\(421\) | − | 115877.i | − | 0.653780i | −0.945062 | − | 0.326890i | \(-0.893999\pi\) | ||
0.945062 | − | 0.326890i | \(-0.106001\pi\) | |||||||
\(422\) | 122829. | + | 49258.3i | 0.689724 | + | 0.276601i | ||||
\(423\) | −52516.3 | −0.293504 | ||||||||
\(424\) | 2900.30 | − | 1318.25i | 0.0161328 | − | 0.00733276i | ||||
\(425\) | − | 47899.9i | − | 0.265190i | ||||||
\(426\) | 189156. | + | 75857.6i | 1.04232 | + | 0.418003i | ||||
\(427\) | 120480. | 0.660783 | ||||||||
\(428\) | −188068. | + | 196770.i | −1.02666 | + | 1.07417i | ||||
\(429\) | 123729.i | 0.672291i | ||||||||
\(430\) | −12081.7 | + | 30126.6i | −0.0653419 | + | 0.162934i | ||||
\(431\) | 241005.i | 1.29739i | 0.761048 | + | 0.648695i | \(0.224685\pi\) | ||||
−0.761048 | + | 0.648695i | \(0.775315\pi\) | |||||||
\(432\) | 5421.70 | + | 119832.i | 0.0290515 | + | 0.642103i | ||||
\(433\) | 49875.4 | 0.266018 | 0.133009 | − | 0.991115i | \(-0.457536\pi\) | ||||
0.133009 | + | 0.991115i | \(0.457536\pi\) | |||||||
\(434\) | 149270. | − | 372214.i | 0.792487 | − | 1.97612i | ||||
\(435\) | 111916.i | 0.591444i | ||||||||
\(436\) | 191308. | − | 200160.i | 1.00638 | − | 1.05294i | ||||
\(437\) | − | 281227.i | − | 1.47263i | ||||||
\(438\) | 335768. | + | 134654.i | 1.75021 | + | 0.701891i | ||||
\(439\) | −130984. | −0.679658 | −0.339829 | − | 0.940487i | \(-0.610369\pi\) | ||||
−0.339829 | + | 0.940487i | \(0.610369\pi\) | |||||||
\(440\) | 11899.1 | + | 26179.3i | 0.0614623 | + | 0.135224i | ||||
\(441\) | 68145.1 | 0.350395 | ||||||||
\(442\) | 67983.1 | + | 27263.4i | 0.347982 | + | 0.139552i | ||||
\(443\) | − | 20713.2i | − | 0.105546i | −0.998607 | − | 0.0527729i | \(-0.983194\pi\) | ||
0.998607 | − | 0.0527729i | \(-0.0168059\pi\) | |||||||
\(444\) | −223879. | − | 213978.i | −1.13566 | − | 1.08544i | ||||
\(445\) | − | 109250.i | − | 0.551700i | ||||||
\(446\) | 100777. | − | 251293.i | 0.506629 | − | 1.26331i | ||||
\(447\) | − | 366353.i | − | 1.83352i | ||||||
\(448\) | 174377. | − | 199792.i | 0.868825 | − | 0.995456i | ||||
\(449\) | 131041. | 0.650003 | 0.325002 | − | 0.945713i | \(-0.394635\pi\) | ||||
0.325002 | + | 0.945713i | \(0.394635\pi\) | |||||||
\(450\) | 78337.8 | + | 31416.0i | 0.386854 | + | 0.155141i | ||||
\(451\) | −87640.3 | − | 20163.4i | −0.430874 | − | 0.0991310i | ||||
\(452\) | −92319.0 | − | 88236.5i | −0.451871 | − | 0.431888i | ||||
\(453\) | −293339. | −1.42947 | ||||||||
\(454\) | −92918.6 | − | 37263.3i | −0.450807 | − | 0.180788i | ||||
\(455\) | − | 115259.i | − | 0.556738i | ||||||
\(456\) | −106945. | − | 235290.i | −0.514316 | − | 1.13155i | ||||
\(457\) | − | 95912.4i | − | 0.459243i | −0.973280 | − | 0.229621i | \(-0.926251\pi\) | ||
0.973280 | − | 0.229621i | \(-0.0737488\pi\) | |||||||
\(458\) | 141026. | − | 351658.i | 0.672308 | − | 1.67644i | ||||
\(459\) | 40480.0i | 0.192139i | ||||||||
\(460\) | −70552.6 | + | 73816.9i | −0.333425 | + | 0.348851i | ||||
\(461\) | 101343. | 0.476860 | 0.238430 | − | 0.971160i | \(-0.423367\pi\) | ||||
0.238430 | + | 0.971160i | \(0.423367\pi\) | |||||||
\(462\) | 140307. | + | 56267.8i | 0.657350 | + | 0.263618i | ||||
\(463\) | −307663. | −1.43520 | −0.717601 | − | 0.696454i | \(-0.754760\pi\) | ||||
−0.717601 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(464\) | 312313. | − | 14130.4i | 1.45062 | − | 0.0656324i | ||||
\(465\) | 141913.i | 0.656321i | ||||||||
\(466\) | −64391.5 | + | 160564.i | −0.296522 | + | 0.739397i | ||||
\(467\) | − | 15893.5i | − | 0.0728761i | −0.999336 | − | 0.0364380i | \(-0.988399\pi\) | ||
0.999336 | − | 0.0364380i | \(-0.0116012\pi\) | |||||||
\(468\) | −89175.9 | + | 93301.8i | −0.407151 | + | 0.425989i | ||||
\(469\) | −74113.1 | −0.336937 | ||||||||
\(470\) | 43029.5 | + | 17256.2i | 0.194792 | + | 0.0781177i | ||||
\(471\) | 346237.i | 1.56074i | ||||||||
\(472\) | −127402. | + | 57907.2i | −0.571863 | + | 0.259925i | ||||
\(473\) | 51687.8i | 0.231029i | ||||||||
\(474\) | 230617. | + | 92485.0i | 1.02644 | + | 0.411637i | ||||
\(475\) | 205209. | 0.909514 | ||||||||
\(476\) | 61832.8 | − | 64693.6i | 0.272901 | − | 0.285527i | ||||
\(477\) | 1894.39i | 0.00832592i | ||||||||
\(478\) | −168190. | − | 67449.6i | −0.736113 | − | 0.295205i | ||||
\(479\) | −326388. | −1.42254 | −0.711268 | − | 0.702921i | \(-0.751879\pi\) | ||||
−0.711268 | + | 0.702921i | \(0.751879\pi\) | |||||||
\(480\) | −30957.1 | + | 88588.9i | −0.134363 | + | 0.384500i | ||||
\(481\) | 376004.i | 1.62518i | ||||||||
\(482\) | −152639. | − | 61213.3i | −0.657011 | − | 0.263483i | ||||
\(483\) | 536782.i | 2.30093i | ||||||||
\(484\) | −136242. | − | 130218.i | −0.581596 | − | 0.555877i | ||||
\(485\) | 10101.1i | 0.0429424i | ||||||||
\(486\) | −191075. | − | 76627.1i | −0.808967 | − | 0.324421i | ||||
\(487\) | − | 95282.0i | − | 0.401747i | −0.979617 | − | 0.200874i | \(-0.935622\pi\) | ||
0.979617 | − | 0.200874i | \(-0.0643781\pi\) | |||||||
\(488\) | 49280.9 | + | 108423.i | 0.206937 | + | 0.455284i | ||||
\(489\) | 288833.i | 1.20790i | ||||||||
\(490\) | −55835.0 | − | 22391.6i | −0.232549 | − | 0.0932595i | ||||
\(491\) | − | 166293.i | − | 0.689782i | −0.938643 | − | 0.344891i | \(-0.887916\pi\) | ||
0.938643 | − | 0.344891i | \(-0.112084\pi\) | |||||||
\(492\) | −161288. | − | 245175.i | −0.666301 | − | 1.01285i | ||||
\(493\) | 105502. | 0.434076 | ||||||||
\(494\) | −116800. | + | 291248.i | −0.478618 | + | 1.19346i | ||||
\(495\) | −17099.5 | −0.0697869 | ||||||||
\(496\) | 396023. | − | 17917.8i | 1.60974 | − | 0.0728318i | ||||
\(497\) | −302315. | −1.22390 | ||||||||
\(498\) | −49504.5 | + | 123443.i | −0.199612 | + | 0.497745i | ||||
\(499\) | −18690.1 | −0.0750605 | −0.0375302 | − | 0.999295i | \(-0.511949\pi\) | ||||
−0.0375302 | + | 0.999295i | \(0.511949\pi\) | |||||||
\(500\) | −114580. | − | 109513.i | −0.458320 | − | 0.438052i | ||||
\(501\) | −234091. | −0.932629 | ||||||||
\(502\) | −46497.9 | + | 115946.i | −0.184513 | + | 0.460095i | ||||
\(503\) | 155261. | 0.613660 | 0.306830 | − | 0.951764i | \(-0.400732\pi\) | ||||
0.306830 | + | 0.951764i | \(0.400732\pi\) | |||||||
\(504\) | 65249.0 | + | 143555.i | 0.256870 | + | 0.565141i | ||||
\(505\) | 48360.3i | 0.189630i | ||||||||
\(506\) | −60523.2 | + | 150919.i | −0.236385 | + | 0.589443i | ||||
\(507\) | 178588. | 0.694762 | ||||||||
\(508\) | 133421. | − | 139594.i | 0.517007 | − | 0.540928i | ||||
\(509\) | 22301.9i | 0.0860810i | 0.999073 | + | 0.0430405i | \(0.0137044\pi\) | ||||
−0.999073 | + | 0.0430405i | \(0.986296\pi\) | |||||||
\(510\) | −11787.4 | + | 29392.7i | −0.0453187 | + | 0.113005i | ||||
\(511\) | −536634. | −2.05512 | ||||||||
\(512\) | 251125. | + | 75204.0i | 0.957966 | + | 0.286880i | ||||
\(513\) | −173422. | −0.658975 | ||||||||
\(514\) | −161264. | + | 402122.i | −0.610395 | + | 1.52206i | ||||
\(515\) | − | 26775.4i | − | 0.100953i | ||||||
\(516\) | −116544. | + | 121936.i | −0.437714 | + | 0.457966i | ||||
\(517\) | 73825.2 | 0.276200 | ||||||||
\(518\) | 426384. | + | 170993.i | 1.58906 | + | 0.637265i | ||||
\(519\) | 447213. | 1.66027 | ||||||||
\(520\) | 103724. | − | 47145.2i | 0.383596 | − | 0.174354i | ||||
\(521\) | − | 160459.i | − | 0.591136i | −0.955322 | − | 0.295568i | \(-0.904491\pi\) | ||
0.955322 | − | 0.295568i | \(-0.0955089\pi\) | |||||||
\(522\) | −69195.2 | + | 172543.i | −0.253942 | + | 0.633222i | ||||
\(523\) | 439631.i | 1.60725i | 0.595133 | + | 0.803627i | \(0.297100\pi\) | ||||
−0.595133 | + | 0.803627i | \(0.702900\pi\) | |||||||
\(524\) | −311795. | + | 326221.i | −1.13555 | + | 1.18809i | ||||
\(525\) | −391685. | −1.42108 | ||||||||
\(526\) | −296900. | − | 119067.i | −1.07310 | − | 0.430347i | ||||
\(527\) | 133779. | 0.481690 | ||||||||
\(528\) | 6754.17 | + | 149282.i | 0.0242273 | + | 0.535477i | ||||
\(529\) | −297537. | −1.06323 | ||||||||
\(530\) | 622.472 | − | 1552.18i | 0.00221599 | − | 0.00552572i | ||||
\(531\) | − | 83215.1i | − | 0.295130i | ||||||
\(532\) | 277156. | + | 264899.i | 0.979266 | + | 0.935961i | ||||
\(533\) | −79888.9 | + | 347238.i | −0.281211 | + | 1.22229i | ||||
\(534\) | 211316. | − | 526931.i | 0.741054 | − | 1.84787i | ||||
\(535\) | 142882.i | 0.499193i | ||||||||
\(536\) | −30315.1 | − | 66696.4i | −0.105519 | − | 0.232152i | ||||
\(537\) | 4565.61 | 0.0158325 | ||||||||
\(538\) | 118793. | + | 47639.9i | 0.410419 | + | 0.164591i | ||||
\(539\) | −95795.4 | −0.329737 | ||||||||
\(540\) | 45520.0 | + | 43507.0i | 0.156104 | + | 0.149201i | ||||
\(541\) | −456987. | −1.56138 | −0.780691 | − | 0.624917i | \(-0.785133\pi\) | ||||
−0.780691 | + | 0.624917i | \(0.785133\pi\) | |||||||
\(542\) | 1038.76 | − | 2590.22i | 0.00353604 | − | 0.00881736i | ||||
\(543\) | 342645.i | 1.16210i | ||||||||
\(544\) | 83511.6 | + | 29182.9i | 0.282195 | + | 0.0986121i | ||||
\(545\) | − | 145343.i | − | 0.489329i | ||||||
\(546\) | 222938. | − | 555910.i | 0.747822 | − | 1.86474i | ||||
\(547\) | 223278. | 0.746226 | 0.373113 | − | 0.927786i | \(-0.378290\pi\) | ||||
0.373113 | + | 0.927786i | \(0.378290\pi\) | |||||||
\(548\) | −242827. | + | 254062.i | −0.808603 | + | 0.846015i | ||||
\(549\) | −70818.8 | −0.234965 | ||||||||
\(550\) | −110124. | − | 44163.2i | −0.364046 | − | 0.145994i | ||||
\(551\) | 451983.i | 1.48874i | ||||||||
\(552\) | −483065. | + | 219565.i | −1.58536 | + | 0.720583i | ||||
\(553\) | −368580. | −1.20526 | ||||||||
\(554\) | 91010.5 | + | 36498.1i | 0.296532 | + | 0.118919i | ||||
\(555\) | −162566. | −0.527769 | ||||||||
\(556\) | 81755.1 | − | 85537.7i | 0.264463 | − | 0.276699i | ||||
\(557\) | − | 501110.i | − | 1.61519i | −0.589740 | − | 0.807593i | \(-0.700770\pi\) | ||
0.589740 | − | 0.807593i | \(-0.299230\pi\) | |||||||
\(558\) | −87741.6 | + | 218790.i | −0.281798 | + | 0.702681i | ||||
\(559\) | 204791. | 0.655372 | ||||||||
\(560\) | −6291.78 | − | 139062.i | −0.0200631 | − | 0.443439i | ||||
\(561\) | 50428.6i | 0.160233i | ||||||||
\(562\) | 146078. | − | 364255.i | 0.462500 | − | 1.15328i | ||||
\(563\) | −364685. | −1.15054 | −0.575269 | − | 0.817965i | \(-0.695102\pi\) | ||||
−0.575269 | + | 0.817965i | \(0.695102\pi\) | |||||||
\(564\) | 174160. | + | 166458.i | 0.547508 | + | 0.523296i | ||||
\(565\) | −67036.1 | −0.209996 | ||||||||
\(566\) | 27514.8 | − | 68610.0i | 0.0858883 | − | 0.214168i | ||||
\(567\) | 530586. | 1.65040 | ||||||||
\(568\) | −123658. | − | 272062.i | −0.383289 | − | 0.843278i | ||||
\(569\) | 593925. | 1.83445 | 0.917227 | − | 0.398365i | \(-0.130422\pi\) | ||||
0.917227 | + | 0.398365i | \(0.130422\pi\) | |||||||
\(570\) | −125922. | − | 50498.7i | −0.387571 | − | 0.155429i | ||||
\(571\) | 323291. | 0.991565 | 0.495783 | − | 0.868447i | \(-0.334881\pi\) | ||||
0.495783 | + | 0.868447i | \(0.334881\pi\) | |||||||
\(572\) | 125360. | − | 131160.i | 0.383147 | − | 0.400874i | ||||
\(573\) | −431276. | −1.31355 | ||||||||
\(574\) | 357433. | + | 248505.i | 1.08485 | + | 0.754243i | ||||
\(575\) | − | 421307.i | − | 1.27428i | ||||||
\(576\) | −102500. | + | 117439.i | −0.308943 | + | 0.353970i | ||||
\(577\) | 60102.3i | 0.180526i | 0.995918 | + | 0.0902630i | \(0.0287707\pi\) | ||||
−0.995918 | + | 0.0902630i | \(0.971229\pi\) | |||||||
\(578\) | −282371. | − | 113240.i | −0.845209 | − | 0.338956i | ||||
\(579\) | 127826.i | 0.381295i | ||||||||
\(580\) | 113391. | − | 118637.i | 0.337071 | − | 0.352667i | ||||
\(581\) | − | 197290.i | − | 0.584457i | ||||||
\(582\) | −19538.0 | + | 48719.3i | −0.0576812 | + | 0.143832i | ||||
\(583\) | − | 2663.05i | − | 0.00783505i | ||||||
\(584\) | −219504. | − | 482932.i | −0.643601 | − | 1.41599i | ||||
\(585\) | 67749.7i | 0.197968i | ||||||||
\(586\) | −19657.2 | + | 49016.4i | −0.0572434 | + | 0.142740i | ||||
\(587\) | 350288. | 1.01660 | 0.508298 | − | 0.861181i | \(-0.330275\pi\) | ||||
0.508298 | + | 0.861181i | \(0.330275\pi\) | |||||||
\(588\) | −225990. | − | 215996.i | −0.653633 | − | 0.624729i | ||||
\(589\) | 573128.i | 1.65204i | ||||||||
\(590\) | −27343.4 | + | 68182.7i | −0.0785505 | + | 0.195871i | ||||
\(591\) | 175207. | 0.501622 | ||||||||
\(592\) | 20525.4 | + | 453657.i | 0.0585664 | + | 1.29445i | ||||
\(593\) | 519422.i | 1.47710i | 0.674197 | + | 0.738552i | \(0.264490\pi\) | ||||
−0.674197 | + | 0.738552i | \(0.735510\pi\) | |||||||
\(594\) | 93065.5 | + | 37322.2i | 0.263764 | + | 0.105778i | ||||
\(595\) | − | 46976.3i | − | 0.132692i | ||||||
\(596\) | −371181. | + | 388354.i | −1.04494 | + | 1.09329i | ||||
\(597\) | −79779.8 | −0.223843 | ||||||||
\(598\) | 597952. | + | 239798.i | 1.67211 | + | 0.670568i | ||||
\(599\) | − | 306566.i | − | 0.854419i | −0.904153 | − | 0.427210i | \(-0.859497\pi\) | ||
0.904153 | − | 0.427210i | \(-0.140503\pi\) | |||||||
\(600\) | −160214. | − | 352489.i | −0.445040 | − | 0.979135i | ||||
\(601\) | − | 539204.i | − | 1.49281i | −0.665492 | − | 0.746405i | \(-0.731778\pi\) | ||
0.665492 | − | 0.746405i | \(-0.268222\pi\) | |||||||
\(602\) | 93132.0 | − | 232231.i | 0.256984 | − | 0.640807i | ||||
\(603\) | 43564.1 | 0.119810 | ||||||||
\(604\) | 310956. | + | 297205.i | 0.852363 | + | 0.814670i | ||||
\(605\) | −98930.3 | −0.270283 | ||||||||
\(606\) | −93540.3 | + | 233249.i | −0.254715 | + | 0.635148i | ||||
\(607\) | 565998.i | 1.53616i | 0.640352 | + | 0.768081i | \(0.278788\pi\) | ||||
−0.640352 | + | 0.768081i | \(0.721212\pi\) | |||||||
\(608\) | −125023. | + | 357774.i | −0.338208 | + | 0.967836i | ||||
\(609\) | − | 862706.i | − | 2.32610i | ||||||
\(610\) | 58025.7 | + | 23270.2i | 0.155941 | + | 0.0625374i | ||||
\(611\) | − | 292501.i | − | 0.783512i | ||||||
\(612\) | −36345.7 | + | 38027.3i | −0.0970398 | + | 0.101530i | ||||
\(613\) | −434334. | −1.15585 | −0.577927 | − | 0.816089i | \(-0.696138\pi\) | ||||
−0.577927 | + | 0.816089i | \(0.696138\pi\) | |||||||
\(614\) | −34023.0 | + | 84838.6i | −0.0902476 | + | 0.225038i | ||||
\(615\) | −150129. | − | 34540.1i | −0.396931 | − | 0.0913217i | ||||
\(616\) | −91724.3 | − | 201803.i | −0.241726 | − | 0.531822i | ||||
\(617\) | −94005.0 | −0.246934 | −0.123467 | − | 0.992349i | \(-0.539401\pi\) | ||||
−0.123467 | + | 0.992349i | \(0.539401\pi\) | |||||||
\(618\) | 51789.9 | − | 129142.i | 0.135603 | − | 0.338134i | ||||
\(619\) | 503623.i | 1.31439i | 0.753721 | + | 0.657194i | \(0.228257\pi\) | ||||
−0.753721 | + | 0.657194i | \(0.771743\pi\) | |||||||
\(620\) | 143783. | − | 150435.i | 0.374045 | − | 0.391351i | ||||
\(621\) | 356046.i | 0.923257i | ||||||||
\(622\) | −586859. | − | 235349.i | −1.51689 | − | 0.608320i | ||||
\(623\) | 842157.i | 2.16979i | ||||||||
\(624\) | 591469. | − | 26760.6i | 1.51902 | − | 0.0687269i | ||||
\(625\) | 263336. | 0.674141 | ||||||||
\(626\) | −92845.2 | + | 231516.i | −0.236925 | + | 0.590788i | ||||
\(627\) | −216043. | −0.549547 | ||||||||
\(628\) | 350799. | − | 367030.i | 0.889487 | − | 0.930641i | ||||
\(629\) | 153249.i | 0.387343i | ||||||||
\(630\) | 76827.4 | + | 30810.2i | 0.193569 | + | 0.0776272i | ||||
\(631\) | − | 547080.i | − | 1.37402i | −0.726649 | − | 0.687009i | \(-0.758923\pi\) | ||
0.726649 | − | 0.687009i | \(-0.241077\pi\) | |||||||
\(632\) | −150763. | − | 331696.i | −0.377452 | − | 0.830435i | ||||
\(633\) | 360994. | 0.900933 | ||||||||
\(634\) | 18972.0 | − | 47308.0i | 0.0471992 | − | 0.117694i | ||||
\(635\) | − | 101364.i | − | 0.251384i | ||||||
\(636\) | 6004.55 | − | 6282.37i | 0.0148445 | − | 0.0155313i | ||||
\(637\) | 379549.i | 0.935383i | ||||||||
\(638\) | 97271.6 | − | 242553.i | 0.238971 | − | 0.595889i | ||||
\(639\) | 177703. | 0.435203 | ||||||||
\(640\) | 122573. | − | 62544.0i | 0.299249 | − | 0.152695i | ||||
\(641\) | − | 396706.i | − | 0.965500i | −0.875758 | − | 0.482750i | \(-0.839638\pi\) | ||
0.875758 | − | 0.482750i | \(-0.160362\pi\) | |||||||
\(642\) | −276367. | + | 689139.i | −0.670526 | + | 1.67200i | ||||
\(643\) | −638459. | −1.54423 | −0.772113 | − | 0.635485i | \(-0.780800\pi\) | ||||
−0.772113 | + | 0.635485i | \(0.780800\pi\) | |||||||
\(644\) | 543856. | − | 569018.i | 1.31133 | − | 1.37200i | ||||
\(645\) | 88542.1i | 0.212829i | ||||||||
\(646\) | −47604.5 | + | 118705.i | −0.114073 | + | 0.284449i | ||||
\(647\) | − | 573811.i | − | 1.37076i | −0.728187 | − | 0.685378i | \(-0.759637\pi\) | ||
0.728187 | − | 0.685378i | \(-0.240363\pi\) | |||||||
\(648\) | 217030. | + | 477489.i | 0.516856 | + | 1.13714i | ||||
\(649\) | 116980.i | 0.277730i | ||||||||
\(650\) | −174978. | + | 436320.i | −0.414150 | + | 1.03271i | ||||
\(651\) | − | 1.09394e6i | − | 2.58125i | ||||||
\(652\) | 292639. | − | 306179.i | 0.688395 | − | 0.720245i | ||||
\(653\) | 61153.9i | 0.143416i | 0.997426 | + | 0.0717080i | \(0.0228450\pi\) | ||||
−0.997426 | + | 0.0717080i | \(0.977155\pi\) | |||||||
\(654\) | 281128. | − | 701011.i | 0.657276 | − | 1.63896i | ||||
\(655\) | 236881.i | 0.552137i | ||||||||
\(656\) | −77432.7 | + | 423312.i | −0.179935 | + | 0.983678i | ||||
\(657\) | 315437. | 0.730772 | ||||||||
\(658\) | −331693. | − | 133020.i | −0.766099 | − | 0.307230i | ||||
\(659\) | −749776. | −1.72648 | −0.863238 | − | 0.504797i | \(-0.831567\pi\) | ||||
−0.863238 | + | 0.504797i | \(0.831567\pi\) | |||||||
\(660\) | 56707.2 | + | 54199.5i | 0.130182 | + | 0.124425i | ||||
\(661\) | 343879. | 0.787051 | 0.393525 | − | 0.919314i | \(-0.371255\pi\) | ||||
0.393525 | + | 0.919314i | \(0.371255\pi\) | |||||||
\(662\) | −17755.4 | − | 7120.49i | −0.0405149 | − | 0.0162478i | ||||
\(663\) | 199802. | 0.454542 | ||||||||
\(664\) | 177547. | − | 80699.2i | 0.402695 | − | 0.183034i | ||||
\(665\) | 201252. | 0.455091 | ||||||||
\(666\) | −250631. | − | 100511.i | −0.565049 | − | 0.226603i | ||||
\(667\) | 927950. | 2.08580 | ||||||||
\(668\) | 248149. | + | 237176.i | 0.556109 | + | 0.531517i | ||||
\(669\) | − | 738551.i | − | 1.65017i | ||||||
\(670\) | −35694.5 | − | 14314.6i | −0.0795154 | − | 0.0318882i | ||||
\(671\) | 99554.0 | 0.221113 | ||||||||
\(672\) | 238633. | − | 682888.i | 0.528436 | − | 1.51221i | ||||
\(673\) | − | 154257.i | − | 0.340576i | −0.985394 | − | 0.170288i | \(-0.945530\pi\) | ||
0.985394 | − | 0.170288i | \(-0.0544698\pi\) | |||||||
\(674\) | −667237. | − | 267584.i | −1.46879 | − | 0.589033i | ||||
\(675\) | −259804. | −0.570214 | ||||||||
\(676\) | −189313. | − | 180941.i | −0.414273 | − | 0.395954i | ||||
\(677\) | 108868. | 0.237531 | 0.118766 | − | 0.992922i | \(-0.462106\pi\) | ||||
0.118766 | + | 0.992922i | \(0.462106\pi\) | |||||||
\(678\) | −323325. | − | 129664.i | −0.703363 | − | 0.282071i | ||||
\(679\) | − | 77864.7i | − | 0.168889i | ||||||
\(680\) | 42275.3 | − | 19215.1i | 0.0914258 | − | 0.0415552i | ||||
\(681\) | −273088. | −0.588855 | ||||||||
\(682\) | 123343. | − | 307565.i | 0.265184 | − | 0.661254i | ||||
\(683\) | 193799. | 0.415443 | 0.207721 | − | 0.978188i | \(-0.433395\pi\) | ||||
0.207721 | + | 0.978188i | \(0.433395\pi\) | |||||||
\(684\) | −162914. | − | 155710.i | −0.348214 | − | 0.332815i | ||||
\(685\) | 184483.i | 0.393166i | ||||||||
\(686\) | −146708. | − | 58834.6i | −0.311749 | − | 0.125022i | ||||
\(687\) | − | 1.03352e6i | − | 2.18981i | ||||||
\(688\) | 247086. | − | 11179.2i | 0.522000 | − | 0.0236175i | ||||
\(689\) | −10551.2 | −0.0222262 | ||||||||
\(690\) | −103677. | + | 258526.i | −0.217763 | + | 0.543008i | ||||
\(691\) | 105395. | 0.220732 | 0.110366 | − | 0.993891i | \(-0.464798\pi\) | ||||
0.110366 | + | 0.993891i | \(0.464798\pi\) | |||||||
\(692\) | −474070. | − | 453106.i | −0.989989 | − | 0.946211i | ||||
\(693\) | 131812. | 0.274466 | ||||||||
\(694\) | −111964. | − | 44901.1i | −0.232466 | − | 0.0932262i | ||||
\(695\) | − | 62111.9i | − | 0.128589i | ||||||
\(696\) | 776373. | − | 352880.i | 1.60270 | − | 0.728464i | ||||
\(697\) | −32560.5 | + | 141525.i | −0.0670233 | + | 0.291318i | ||||
\(698\) | 764119. | + | 306436.i | 1.56838 | + | 0.628969i | ||||
\(699\) | 471899.i | 0.965817i | ||||||||
\(700\) | 415208. | + | 396847.i | 0.847363 | + | 0.809891i | ||||
\(701\) | 534922. | 1.08857 | 0.544283 | − | 0.838902i | \(-0.316802\pi\) | ||||
0.544283 | + | 0.838902i | \(0.316802\pi\) | |||||||
\(702\) | 147874. | − | 368733.i | 0.300066 | − | 0.748235i | ||||
\(703\) | −656537. | −1.32846 | ||||||||
\(704\) | 144090. | − | 165091.i | 0.290728 | − | 0.333102i | ||||
\(705\) | 126464. | 0.254441 | ||||||||
\(706\) | −138512. | − | 55547.9i | −0.277894 | − | 0.111444i | ||||
\(707\) | − | 372786.i | − | 0.745797i | ||||||
\(708\) | −263763. | + | 275967.i | −0.526196 | + | 0.550542i | ||||
\(709\) | − | 154782.i | − | 0.307913i | −0.988078 | − | 0.153957i | \(-0.950798\pi\) | ||
0.988078 | − | 0.153957i | \(-0.0492016\pi\) | |||||||
\(710\) | −145601. | − | 58390.8i | −0.288834 | − | 0.115832i | ||||
\(711\) | 216654. | 0.428575 | ||||||||
\(712\) | −757881. | + | 344474.i | −1.49500 | + | 0.679512i | ||||
\(713\) | 1.17667e6 | 2.31460 | ||||||||
\(714\) | 90863.3 | − | 226574.i | 0.178235 | − | 0.444440i | ||||
\(715\) | − | 95239.6i | − | 0.186297i | ||||||
\(716\) | −4839.79 | − | 4625.77i | −0.00944063 | − | 0.00902315i | ||||
\(717\) | −494311. | −0.961528 | ||||||||
\(718\) | −235163. | + | 586394.i | −0.456163 | + | 1.13747i | ||||
\(719\) | −158146. | −0.305915 | −0.152957 | − | 0.988233i | \(-0.548880\pi\) | ||||
−0.152957 | + | 0.988233i | \(0.548880\pi\) | |||||||
\(720\) | 3698.35 | + | 81741.7i | 0.00713416 | + | 0.157681i | ||||
\(721\) | 206398.i | 0.397041i | ||||||||
\(722\) | −24719.4 | − | 9913.27i | −0.0474202 | − | 0.0190170i | ||||
\(723\) | −448608. | −0.858203 | ||||||||
\(724\) | 347160. | − | 363222.i | 0.662297 | − | 0.692940i | ||||
\(725\) | 677117.i | 1.28821i | ||||||||
\(726\) | −477156. | − | 191355.i | −0.905288 | − | 0.363050i | ||||
\(727\) | −903429. | −1.70933 | −0.854664 | − | 0.519182i | \(-0.826237\pi\) | ||||
−0.854664 | + | 0.519182i | \(0.826237\pi\) | |||||||
\(728\) | −799561. | + | 363419.i | −1.50865 | + | 0.685717i | ||||
\(729\) | 102249. | 0.192399 | ||||||||
\(730\) | −258455. | − | 103649.i | −0.484997 | − | 0.194499i | ||||
\(731\) | 83467.4 | 0.156200 | ||||||||
\(732\) | 234857. | + | 224471.i | 0.438309 | + | 0.418927i | ||||
\(733\) | −454267. | −0.845479 | −0.422740 | − | 0.906251i | \(-0.638931\pi\) | ||||
−0.422740 | + | 0.906251i | \(0.638931\pi\) | |||||||
\(734\) | −184226. | + | 459380.i | −0.341947 | + | 0.852667i | ||||
\(735\) | −164099. | −0.303761 | ||||||||
\(736\) | 734533. | + | 256681.i | 1.35599 | + | 0.473846i | ||||
\(737\) | −61240.5 | −0.112747 | ||||||||
\(738\) | −210101. | − | 146073.i | −0.385759 | − | 0.268199i | ||||
\(739\) | − | 23069.1i | − | 0.0422417i | −0.999777 | − | 0.0211208i | \(-0.993277\pi\) | ||
0.999777 | − | 0.0211208i | \(-0.00672347\pi\) | |||||||
\(740\) | 172329. | + | 164708.i | 0.314698 | + | 0.300782i | ||||
\(741\) | 855979.i | 1.55893i | ||||||||
\(742\) | −4798.33 | + | 11965.0i | −0.00871530 | + | 0.0217322i | ||||
\(743\) | − | 418800.i | − | 0.758629i | −0.925268 | − | 0.379314i | \(-0.876160\pi\) | ||
0.925268 | − | 0.379314i | \(-0.123840\pi\) | |||||||
\(744\) | 984465. | − | 447462.i | 1.77850 | − | 0.808371i | ||||
\(745\) | 281998.i | 0.508081i | ||||||||
\(746\) | 622906. | + | 249805.i | 1.11930 | + | 0.448874i | ||||
\(747\) | 115968.i | 0.207825i | ||||||||
\(748\) | 51093.2 | − | 53457.1i | 0.0913187 | − | 0.0955438i | ||||
\(749\) | − | 1.10140e6i | − | 1.96328i | ||||||
\(750\) | −401289. | − | 160930.i | −0.713402 | − | 0.286097i | ||||
\(751\) | −530569. | −0.940723 | −0.470362 | − | 0.882474i | \(-0.655877\pi\) | ||||
−0.470362 | + | 0.882474i | \(0.655877\pi\) | |||||||
\(752\) | −15967.2 | − | 352910.i | −0.0282353 | − | 0.624063i | ||||
\(753\) | 340765.i | 0.600986i | ||||||||
\(754\) | −961016. | − | 385398.i | −1.69039 | − | 0.677902i | ||||
\(755\) | 225796. | 0.396115 | ||||||||
\(756\) | −350891. | − | 335374.i | −0.613944 | − | 0.586795i | ||||
\(757\) | − | 861681.i | − | 1.50368i | −0.659347 | − | 0.751839i | \(-0.729167\pi\) | ||
0.659347 | − | 0.751839i | \(-0.270833\pi\) | |||||||
\(758\) | −355435. | + | 886301.i | −0.618617 | + | 1.54256i | ||||
\(759\) | 443550.i | 0.769943i | ||||||||
\(760\) | 82320.0 | + | 181113.i | 0.142521 | + | 0.313561i | ||||
\(761\) | 541732. | 0.935438 | 0.467719 | − | 0.883877i | \(-0.345076\pi\) | ||||
0.467719 | + | 0.883877i | \(0.345076\pi\) | |||||||
\(762\) | 196062. | − | 488894.i | 0.337663 | − | 0.841986i | ||||
\(763\) | 1.12038e6i | 1.92449i | ||||||||
\(764\) | 457176. | + | 436959.i | 0.783243 | + | 0.748607i | ||||
\(765\) | 27612.9i | 0.0471835i | ||||||||
\(766\) | 880175. | + | 352978.i | 1.50007 | + | 0.601576i | ||||
\(767\) | 463485. | 0.787853 | ||||||||
\(768\) | 712161. | − | 64574.6i | 1.20741 | − | 0.109481i | ||||
\(769\) | 616831. | 1.04307 | 0.521535 | − | 0.853230i | \(-0.325359\pi\) | ||||
0.521535 | + | 0.853230i | \(0.325359\pi\) | |||||||
\(770\) | −108001. | − | 43311.7i | −0.182157 | − | 0.0730506i | ||||
\(771\) | 1.18184e6i | 1.98815i | ||||||||
\(772\) | 129510. | − | 135502.i | 0.217305 | − | 0.227359i | ||||
\(773\) | 977948.i | 1.63665i | 0.574753 | + | 0.818327i | \(0.305098\pi\) | ||||
−0.574753 | + | 0.818327i | \(0.694902\pi\) | |||||||
\(774\) | −54743.6 | + | 136507.i | −0.0913800 | + | 0.227862i | ||||
\(775\) | 858605.i | 1.42952i | ||||||||
\(776\) | 70072.6 | − | 31849.6i | 0.116366 | − | 0.0528909i | ||||
\(777\) | 1.25314e6 | 2.07567 | ||||||||
\(778\) | −815640. | − | 327098.i | −1.34753 | − | 0.540404i | ||||
\(779\) | −606310. | − | 139493.i | −0.999126 | − | 0.229868i | ||||
\(780\) | 214743. | − | 224679.i | 0.352964 | − | 0.369294i | ||||
\(781\) | −249806. | −0.409545 | ||||||||
\(782\) | 243709. | + | 97735.0i | 0.398527 | + | 0.159822i | ||||
\(783\) | − | 572230.i | − | 0.933355i | ||||||
\(784\) | 20719.0 | + | 457936.i | 0.0337082 | + | 0.745027i | ||||
\(785\) | − | 266513.i | − | 0.432493i | ||||||
\(786\) | −458184. | + | 1.14251e6i | −0.741642 | + | 1.84933i | ||||
\(787\) | − | 872525.i | − | 1.40873i | −0.709837 | − | 0.704366i | \(-0.751232\pi\) | ||
0.709837 | − | 0.704366i | \(-0.248768\pi\) | |||||||
\(788\) | −185729. | − | 177516.i | −0.299108 | − | 0.285881i | ||||
\(789\) | −872591. | −1.40171 | ||||||||
\(790\) | −177516. | − | 71189.6i | −0.284435 | − | 0.114068i | ||||
\(791\) | 516748. | 0.825897 | ||||||||
\(792\) | 53916.1 | + | 118621.i | 0.0859544 | + | 0.189109i | ||||
\(793\) | − | 394441.i | − | 0.627243i | ||||||
\(794\) | −16913.7 | + | 42175.4i | −0.0268285 | + | 0.0668987i | ||||
\(795\) | − | 4561.85i | − | 0.00721783i | ||||||
\(796\) | 84570.9 | + | 80831.0i | 0.133473 | + | 0.127571i | ||||
\(797\) | 670191. | 1.05507 | 0.527536 | − | 0.849533i | \(-0.323116\pi\) | ||||
0.527536 | + | 0.849533i | \(0.323116\pi\) | |||||||
\(798\) | 970671. | + | 389270.i | 1.52428 | + | 0.611287i | ||||
\(799\) | − | 119216.i | − | 0.186741i | ||||||
\(800\) | −187298. | + | 535983.i | −0.292653 | + | 0.837473i | ||||
\(801\) | − | 495025.i | − | 0.771546i | ||||||
\(802\) | 21429.7 | + | 8594.00i | 0.0333171 | + | 0.0133612i | ||||
\(803\) | −443428. | −0.687688 | ||||||||
\(804\) | −144472. | − | 138083.i | −0.223497 | − | 0.213613i | ||||
\(805\) | − | 413184.i | − | 0.637605i | ||||||
\(806\) | −1.21860e6 | − | 488697.i | −1.87582 | − | 0.752262i | ||||
\(807\) | 349134. | 0.536098 | ||||||||
\(808\) | 335481. | − | 152484.i | 0.513860 | − | 0.233561i | ||||
\(809\) | − | 527423.i | − | 0.805864i | −0.915230 | − | 0.402932i | \(-0.867991\pi\) | ||
0.915230 | − | 0.402932i | \(-0.132009\pi\) | |||||||
\(810\) | 255542. | + | 102480.i | 0.389486 | + | 0.156196i | ||||
\(811\) | − | 403394.i | − | 0.613321i | −0.951819 | − | 0.306661i | \(-0.900788\pi\) | ||
0.951819 | − | 0.306661i | \(-0.0992117\pi\) | |||||||
\(812\) | −874074. | + | 914515.i | −1.32567 | + | 1.38701i | ||||
\(813\) | − | 7612.67i | − | 0.0115174i | ||||||
\(814\) | 352326. | + | 141294.i | 0.531736 | + | 0.213243i | ||||
\(815\) | − | 222327.i | − | 0.334717i | ||||||
\(816\) | 241067. | − | 10906.9i | 0.362040 | − | 0.0163803i | ||||
\(817\) | 357585.i | 0.535717i | ||||||||
\(818\) | −901600. | − | 361571.i | −1.34743 | − | 0.540364i | ||||
\(819\) | − | 522249.i | − | 0.778592i | ||||||
\(820\) | 124150. | + | 188722.i | 0.184637 | + | 0.280669i | ||||
\(821\) | 302174. | 0.448303 | 0.224151 | − | 0.974554i | \(-0.428039\pi\) | ||||
0.224151 | + | 0.974554i | \(0.428039\pi\) | |||||||
\(822\) | −356834. | + | 889790.i | −0.528108 | + | 1.31687i | ||||
\(823\) | −396407. | −0.585251 | −0.292625 | − | 0.956227i | \(-0.594529\pi\) | ||||
−0.292625 | + | 0.956227i | \(0.594529\pi\) | |||||||
\(824\) | −185743. | + | 84424.7i | −0.273564 | + | 0.124341i | ||||
\(825\) | −323654. | −0.475525 | ||||||||
\(826\) | 210777. | − | 525587.i | 0.308932 | − | 0.770343i | ||||
\(827\) | 1.19767e6 | 1.75115 | 0.875577 | − | 0.483078i | \(-0.160481\pi\) | ||||
0.875577 | + | 0.483078i | \(0.160481\pi\) | |||||||
\(828\) | −319682. | + | 334472.i | −0.466291 | + | 0.487865i | ||||
\(829\) | 464722. | 0.676215 | 0.338107 | − | 0.941108i | \(-0.390213\pi\) | ||||
0.338107 | + | 0.941108i | \(0.390213\pi\) | |||||||
\(830\) | 38105.7 | − | 95019.1i | 0.0553138 | − | 0.137929i | ||||
\(831\) | 267480. | 0.387337 | ||||||||
\(832\) | −654102. | − | 570895.i | −0.944929 | − | 0.824726i | ||||
\(833\) | 154694.i | 0.222938i | ||||||||
\(834\) | 120139. | − | 299575.i | 0.172724 | − | 0.430699i | ||||
\(835\) | 180190. | 0.258438 | ||||||||
\(836\) | 229017. | + | 218890.i | 0.327684 | + | 0.313194i | ||||
\(837\) | − | 725605.i | − | 1.03574i | ||||||
\(838\) | −167301. | + | 417175.i | −0.238237 | + | 0.594060i | ||||
\(839\) | 311715. | 0.442827 | 0.221413 | − | 0.975180i | \(-0.428933\pi\) | ||||
0.221413 | + | 0.975180i | \(0.428933\pi\) | |||||||
\(840\) | −157125. | − | 345692.i | −0.222683 | − | 0.489927i | ||||
\(841\) | −784101. | −1.10861 | ||||||||
\(842\) | −172525. | + | 430202.i | −0.243348 | + | 0.606803i | ||||
\(843\) | − | 1.07055e6i | − | 1.50643i | ||||||
\(844\) | −382673. | − | 365751.i | −0.537209 | − | 0.513453i | ||||
\(845\) | −137467. | −0.192524 | ||||||||
\(846\) | 194971. | + | 78189.7i | 0.272414 | + | 0.109247i | ||||
\(847\) | 762605. | 1.06300 | ||||||||
\(848\) | −12730.3 | + | 575.974i | −0.0177030 | + | 0.000800960i | ||||
\(849\) | − | 201645.i | − | 0.279751i | ||||||
\(850\) | −71316.4 | + | 177832.i | −0.0987078 | + | 0.246135i | ||||
\(851\) | 1.34791e6i | 1.86124i | ||||||||
\(852\) | −589316. | − | 563255.i | −0.811837 | − | 0.775936i | ||||
\(853\) | −1.31916e6 | −1.81301 | −0.906506 | − | 0.422193i | \(-0.861260\pi\) | ||||
−0.906506 | + | 0.422193i | \(0.861260\pi\) | |||||||
\(854\) | −447292. | − | 179378.i | −0.613303 | − | 0.245954i | ||||
\(855\) | −118297. | −0.161824 | ||||||||
\(856\) | 991184. | − | 450516.i | 1.35272 | − | 0.614841i | ||||
\(857\) | −281386. | −0.383125 | −0.191563 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191563 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(858\) | 184216. | − | 459355.i | 0.250238 | − | 0.623985i | ||||
\(859\) | − | 1.39446e6i | − | 1.88982i | −0.327328 | − | 0.944911i | \(-0.606148\pi\) | ||
0.327328 | − | 0.944911i | \(-0.393852\pi\) | |||||||
\(860\) | 89708.8 | − | 93859.4i | 0.121294 | − | 0.126906i | ||||
\(861\) | 1.15727e6 | + | 266253.i | 1.56110 | + | 0.359160i | ||||
\(862\) | 358823. | − | 894750.i | 0.482910 | − | 1.20417i | ||||
\(863\) | 1.15180e6i | 1.54652i | 0.634089 | + | 0.773260i | \(0.281375\pi\) | ||||
−0.634089 | + | 0.773260i | \(0.718625\pi\) | |||||||
\(864\) | 158285. | − | 452958.i | 0.212037 | − | 0.606778i | ||||
\(865\) | −344239. | −0.460074 | ||||||||
\(866\) | −185167. | − | 74257.8i | −0.246903 | − | 0.0990162i | ||||
\(867\) | −829888. | −1.10403 | ||||||||
\(868\) | −1.10835e6 | + | 1.15963e6i | −1.47109 | + | 1.53915i | ||||
\(869\) | −304562. | −0.403308 | ||||||||
\(870\) | 166628. | − | 415498.i | 0.220145 | − | 0.548947i | ||||
\(871\) | 242640.i | 0.319835i | ||||||||
\(872\) | −1.00826e6 | + | 458277.i | −1.32599 | + | 0.602692i | ||||
\(873\) | 45769.3i | 0.0600546i | ||||||||
\(874\) | −418709. | + | 1.04408e6i | −0.548138 | + | 1.36682i | ||||
\(875\) | 641352. | 0.837684 | ||||||||
\(876\) | −1.04608e6 | − | 999825.i | −1.36320 | − | 1.30291i | ||||
\(877\) | 602111. | 0.782848 | 0.391424 | − | 0.920210i | \(-0.371983\pi\) | ||||
0.391424 | + | 0.920210i | \(0.371983\pi\) | |||||||
\(878\) | 486291. | + | 195018.i | 0.630822 | + | 0.252980i | ||||
\(879\) | 144059.i | 0.186451i | ||||||||
\(880\) | −5198.97 | − | 114909.i | −0.00671355 | − | 0.148384i | ||||
\(881\) | 167820. | 0.216218 | 0.108109 | − | 0.994139i | \(-0.465520\pi\) | ||||
0.108109 | + | 0.994139i | \(0.465520\pi\) | |||||||
\(882\) | −252994. | − | 101459.i | −0.325217 | − | 0.130423i | ||||
\(883\) | 1.43605e6 | 1.84182 | 0.920910 | − | 0.389776i | \(-0.127448\pi\) | ||||
0.920910 | + | 0.389776i | \(0.127448\pi\) | |||||||
\(884\) | −211802. | − | 202435.i | −0.271034 | − | 0.259049i | ||||
\(885\) | 200389.i | 0.255851i | ||||||||
\(886\) | −30839.2 | + | 76899.7i | −0.0392858 | + | 0.0979619i | ||||
\(887\) | 497062. | 0.631776 | 0.315888 | − | 0.948796i | \(-0.397698\pi\) | ||||
0.315888 | + | 0.948796i | \(0.397698\pi\) | |||||||
\(888\) | 512583. | + | 1.12774e6i | 0.650037 | + | 1.43015i | ||||
\(889\) | 781366.i | 0.988669i | ||||||||
\(890\) | −162659. | + | 405601.i | −0.205352 | + | 0.512058i | ||||
\(891\) | 438430. | 0.552261 | ||||||||
\(892\) | −748283. | + | 782904.i | −0.940451 | + | 0.983963i | ||||
\(893\) | 510735. | 0.640461 | ||||||||
\(894\) | −545451. | + | 1.36012e6i | −0.682465 | + | 1.70177i | ||||
\(895\) | −3514.34 | −0.00438731 | ||||||||
\(896\) | −944852. | + | 482121.i | −1.17692 | + | 0.600537i | ||||
\(897\) | 1.75738e6 | 2.18414 | ||||||||
\(898\) | −486502. | − | 195103.i | −0.603298 | − | 0.241942i | ||||
\(899\) | −1.89112e6 | −2.33991 | ||||||||
\(900\) | −244062. | − | 233269.i | −0.301311 | − | 0.287986i | ||||
\(901\) | −4300.39 | −0.00529735 | ||||||||
\(902\) | 295351. | + | 205343.i | 0.363016 | + | 0.252387i | ||||
\(903\) | − | 682527.i | − | 0.837037i | ||||||
\(904\) | 211370. | + | 465036.i | 0.258646 | + | 0.569049i | ||||
\(905\) | − | 263749.i | − | 0.322027i | ||||||
\(906\) | 1.08905e6 | + | 436742.i | 1.32675 | + | 0.532070i | ||||
\(907\) | − | 744074.i | − | 0.904485i | −0.891895 | − | 0.452242i | \(-0.850624\pi\) | ||
0.891895 | − | 0.452242i | \(-0.149376\pi\) | |||||||
\(908\) | 289488. | + | 276686.i | 0.351123 | + | 0.335596i | ||||
\(909\) | 219126.i | 0.265195i | ||||||||
\(910\) | −171605. | + | 427907.i | −0.207227 | + | 0.516734i | ||||
\(911\) | − | 1.05100e6i | − | 1.26639i | −0.773992 | − | 0.633196i | \(-0.781743\pi\) | ||
0.773992 | − | 0.633196i | \(-0.218257\pi\) | |||||||
\(912\) | 46726.5 | + | 1.03276e6i | 0.0561790 | + | 1.24168i | ||||
\(913\) | − | 163023.i | − | 0.195572i | ||||||
\(914\) | −142801. | + | 356083.i | −0.170938 | + | 0.426244i | ||||
\(915\) | 170538. | 0.203694 | ||||||||
\(916\) | −1.04714e6 | + | 1.09559e6i | −1.24800 | + | 1.30574i | ||||
\(917\) | − | 1.82600e6i | − | 2.17151i | ||||||
\(918\) | 60269.3 | − | 150286.i | 0.0715173 | − | 0.178333i | ||||
\(919\) | 528431. | 0.625688 | 0.312844 | − | 0.949805i | \(-0.398718\pi\) | ||||
0.312844 | + | 0.949805i | \(0.398718\pi\) | |||||||
\(920\) | 371836. | − | 169008.i | 0.439315 | − | 0.199679i | ||||
\(921\) | 249341.i | 0.293950i | ||||||||
\(922\) | −376244. | − | 150886.i | −0.442596 | − | 0.177495i | ||||
\(923\) | 989754.i | 1.16178i | ||||||||
\(924\) | −437128. | − | 417798.i | −0.511994 | − | 0.489353i | ||||
\(925\) | −983561. | −1.14952 | ||||||||
\(926\) | 1.14222e6 | + | 458069.i | 1.33208 | + | 0.534206i | ||||
\(927\) | − | 121322.i | − | 0.141182i | ||||||
\(928\) | −1.18053e6 | − | 412532.i | −1.37082 | − | 0.479029i | ||||
\(929\) | 1.54286e6i | 1.78770i | 0.448366 | + | 0.893850i | \(0.352006\pi\) | ||||
−0.448366 | + | 0.893850i | \(0.647994\pi\) | |||||||
\(930\) | 211289. | − | 526864.i | 0.244293 | − | 0.609162i | ||||
\(931\) | −662729. | −0.764604 | ||||||||
\(932\) | 478118. | − | 500239.i | 0.550431 | − | 0.575898i | ||||
\(933\) | −1.72478e6 | −1.98139 | ||||||||
\(934\) | −23663.2 | + | 59005.8i | −0.0271257 | + | 0.0676396i | ||||
\(935\) | − | 38817.1i | − | 0.0444017i | ||||||
\(936\) | 469987. | − | 213620.i | 0.536456 | − | 0.243832i | ||||
\(937\) | − | 554710.i | − | 0.631811i | −0.948791 | − | 0.315905i | \(-0.897692\pi\) | ||
0.948791 | − | 0.315905i | \(-0.102308\pi\) | |||||||
\(938\) | 275151. | + | 110344.i | 0.312727 | + | 0.125414i | ||||
\(939\) | 680425.i | 0.771701i | ||||||||
\(940\) | −134058. | − | 128130.i | −0.151718 | − | 0.145009i | ||||
\(941\) | 379562. | 0.428651 | 0.214326 | − | 0.976762i | \(-0.431245\pi\) | ||||
0.214326 | + | 0.976762i | \(0.431245\pi\) | |||||||
\(942\) | 515500. | − | 1.28543e6i | 0.580934 | − | 1.44860i | ||||
\(943\) | −286389. | + | 1.24479e6i | −0.322057 | + | 1.39983i | ||||
\(944\) | 559206. | − | 25300.9i | 0.627521 | − | 0.0283917i | ||||
\(945\) | −254794. | −0.285316 | ||||||||
\(946\) | 76956.2 | − | 191895.i | 0.0859926 | − | 0.214428i | ||||
\(947\) | 223175.i | 0.248855i | 0.992229 | + | 0.124427i | \(0.0397094\pi\) | ||||
−0.992229 | + | 0.124427i | \(0.960291\pi\) | |||||||
\(948\) | −718489. | − | 686717.i | −0.799472 | − | 0.764119i | ||||
\(949\) | 1.75690e6i | 1.95080i | ||||||||
\(950\) | −761856. | − | 305529.i | −0.844162 | − | 0.338536i | ||||
\(951\) | − | 139038.i | − | 0.153735i | ||||||
\(952\) | −325879. | + | 148120.i | −0.359570 | + | 0.163433i | ||||
\(953\) | −262226. | −0.288729 | −0.144364 | − | 0.989525i | \(-0.546114\pi\) | ||||
−0.144364 | + | 0.989525i | \(0.546114\pi\) | |||||||
\(954\) | 2820.49 | − | 7033.08i | 0.00309904 | − | 0.00772767i | ||||
\(955\) | 331972. | 0.363994 | ||||||||
\(956\) | 523997. | + | 500825.i | 0.573341 | + | 0.547987i | ||||
\(957\) | − | 712864.i | − | 0.778364i | ||||||
\(958\) | 1.21174e6 | + | 485947.i | 1.32032 | + | 0.529491i | ||||
\(959\) | − | 1.42209e6i | − | 1.54629i | ||||||
\(960\) | 246828. | − | 282803.i | 0.267825 | − | 0.306861i | ||||
\(961\) | −1.47448e6 | −1.59658 | ||||||||
\(962\) | 559818. | − | 1.39594e6i | 0.604919 | − | 1.50841i | ||||
\(963\) | 647412.i | 0.698117i | ||||||||
\(964\) | 475549. | + | 454519.i | 0.511730 | + | 0.489101i | ||||
\(965\) | − | 98393.0i | − | 0.105660i | ||||||
\(966\) | 799196. | − | 1.99285e6i | 0.856444 | − | 2.13560i | ||||
\(967\) | −1.33860e6 | −1.43152 | −0.715759 | − | 0.698348i | \(-0.753919\pi\) | ||||
−0.715759 | + | 0.698348i | \(0.753919\pi\) | |||||||
\(968\) | 311935. | + | 686290.i | 0.332899 | + | 0.732414i | ||||
\(969\) | 348874.i | 0.371553i | ||||||||
\(970\) | 15039.2 | − | 37501.3i | 0.0159839 | − | 0.0398569i | ||||
\(971\) | −1.12869e6 | −1.19712 | −0.598558 | − | 0.801079i | \(-0.704260\pi\) | ||||
−0.598558 | + | 0.801079i | \(0.704260\pi\) | |||||||
\(972\) | 595293. | + | 568969.i | 0.630084 | + | 0.602221i | ||||
\(973\) | 478790.i | 0.505731i | ||||||||
\(974\) | −141862. | + | 353743.i | −0.149537 | + | 0.372880i | ||||
\(975\) | 1.28235e6i | 1.34895i | ||||||||
\(976\) | −21531.9 | − | 475903.i | −0.0226039 | − | 0.499596i | ||||
\(977\) | − | 1.67211e6i | − | 1.75177i | −0.482520 | − | 0.875885i | \(-0.660279\pi\) | ||
0.482520 | − | 0.875885i | \(-0.339721\pi\) | |||||||
\(978\) | 430034. | − | 1.07232e6i | 0.449598 | − | 1.12110i | ||||
\(979\) | 695885.i | 0.726059i | ||||||||
\(980\) | 173954. | + | 166262.i | 0.181127 | + | 0.173117i | ||||
\(981\) | − | 658564.i | − | 0.684322i | ||||||
\(982\) | −247588. | + | 617378.i | −0.256748 | + | 0.640219i | ||||
\(983\) | 39813.3i | 0.0412022i | 0.999788 | + | 0.0206011i | \(0.00655801\pi\) | ||||
−0.999788 | + | 0.0206011i | \(0.993442\pi\) | |||||||
\(984\) | 233760. | + | 1.15037e6i | 0.241424 | + | 1.18808i | ||||
\(985\) | −134864. | −0.139003 | ||||||||
\(986\) | −391684. | − | 157078.i | −0.402886 | − | 0.161570i | ||||
\(987\) | −974847. | −1.00070 | ||||||||
\(988\) | 867259. | − | 907385.i | 0.888454 | − | 0.929560i | ||||
\(989\) | 734145. | 0.750566 | ||||||||
\(990\) | 63483.4 | + | 25458.9i | 0.0647724 | + | 0.0259758i | ||||
\(991\) | 1.86660e6 | 1.90065 | 0.950327 | − | 0.311253i | \(-0.100749\pi\) | ||||
0.950327 | + | 0.311253i | \(0.100749\pi\) | |||||||
\(992\) | −1.49695e6 | − | 523103.i | −1.52119 | − | 0.531574i | ||||
\(993\) | −52183.2 | −0.0529215 | ||||||||
\(994\) | 1.12237e6 | + | 450106.i | 1.13596 | + | 0.455556i | ||||
\(995\) | 61409.9 | 0.0620286 | ||||||||
\(996\) | 367579. | − | 384586.i | 0.370537 | − | 0.387681i | ||||
\(997\) | 1.59801e6i | 1.60764i | 0.594874 | + | 0.803819i | \(0.297202\pi\) | ||||
−0.594874 | + | 0.803819i | \(0.702798\pi\) | |||||||
\(998\) | 69388.7 | + | 27827.1i | 0.0696671 | + | 0.0279387i | ||||
\(999\) | 831205. | 0.832870 |
(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 | 164.5.d.f.163.1 | ✓ | 72 | |
4.3 | odd | 2 | inner | 164.5.d.f.163.4 | yes | 72 | |
41.40 | even | 2 | inner | 164.5.d.f.163.2 | yes | 72 | |
164.163 | odd | 2 | inner | 164.5.d.f.163.3 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.5.d.f.163.1 | ✓ | 72 | 1.1 | even | 1 | trivial | |
164.5.d.f.163.2 | yes | 72 | 41.40 | even | 2 | inner | |
164.5.d.f.163.3 | yes | 72 | 164.163 | odd | 2 | inner | |
164.5.d.f.163.4 | yes | 72 | 4.3 | odd | 2 | inner |