Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,5,Mod(19,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.19");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.g (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: | \(30.3907691467\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.31 |
Dual form | 294.5.g.c.19.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | − | 2.44949i | −0.353553 | − | 0.612372i | ||||
\(3\) | 4.50000 | + | 2.59808i | 0.500000 | + | 0.288675i | ||||
\(4\) | −4.00000 | + | 6.92820i | −0.250000 | + | 0.433013i | ||||
\(5\) | 12.2574 | − | 7.07679i | 0.490294 | − | 0.283072i | −0.234402 | − | 0.972140i | \(-0.575313\pi\) |
0.724697 | + | 0.689068i | \(0.241980\pi\) | |||||||
\(6\) | − | 14.6969i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | 13.5000 | + | 23.3827i | 0.166667 | + | 0.288675i | ||||
\(10\) | −34.6690 | − | 20.0162i | −0.346690 | − | 0.200162i | ||||
\(11\) | −32.0147 | + | 55.4511i | −0.264584 | + | 0.458274i | −0.967455 | − | 0.253044i | \(-0.918568\pi\) |
0.702870 | + | 0.711318i | \(0.251901\pi\) | |||||||
\(12\) | −36.0000 | + | 20.7846i | −0.250000 | + | 0.144338i | ||||
\(13\) | − | 228.919i | − | 1.35455i | −0.735729 | − | 0.677276i | \(-0.763161\pi\) | ||
0.735729 | − | 0.677276i | \(-0.236839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 73.5442 | 0.326863 | ||||||||
\(16\) | −32.0000 | − | 55.4256i | −0.125000 | − | 0.216506i | ||||
\(17\) | 195.250 | + | 112.728i | 0.675605 | + | 0.390061i | 0.798197 | − | 0.602397i | \(-0.205787\pi\) |
−0.122592 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(18\) | 38.1838 | − | 66.1362i | 0.117851 | − | 0.204124i | ||||
\(19\) | 255.250 | − | 147.369i | 0.707063 | − | 0.408223i | −0.102910 | − | 0.994691i | \(-0.532815\pi\) |
0.809973 | + | 0.586468i | \(0.199482\pi\) | |||||||
\(20\) | 113.229i | 0.283072i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 181.103 | 0.374179 | ||||||||
\(23\) | −354.749 | − | 614.444i | −0.670604 | − | 1.16152i | −0.977733 | − | 0.209852i | \(-0.932702\pi\) |
0.307129 | − | 0.951668i | \(-0.400632\pi\) | |||||||
\(24\) | 101.823 | + | 58.7878i | 0.176777 | + | 0.102062i | ||||
\(25\) | −212.338 | + | 367.780i | −0.339741 | + | 0.588449i | ||||
\(26\) | −560.735 | + | 323.741i | −0.829490 | + | 0.478906i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 740.397 | 0.880377 | 0.440188 | − | 0.897905i | \(-0.354912\pi\) | ||||
0.440188 | + | 0.897905i | \(0.354912\pi\) | |||||||
\(30\) | −104.007 | − | 180.146i | −0.115563 | − | 0.200162i | ||||
\(31\) | 577.390 | + | 333.356i | 0.600822 | + | 0.346885i | 0.769365 | − | 0.638809i | \(-0.220573\pi\) |
−0.168543 | + | 0.985694i | \(0.553906\pi\) | |||||||
\(32\) | −90.5097 | + | 156.767i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −288.132 | + | 166.353i | −0.264584 | + | 0.152758i | ||||
\(34\) | − | 637.683i | − | 0.551629i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | 416.882 | + | 722.061i | 0.304516 | + | 0.527437i | 0.977153 | − | 0.212535i | \(-0.0681720\pi\) |
−0.672638 | + | 0.739972i | \(0.734839\pi\) | |||||||
\(38\) | −721.955 | − | 416.821i | −0.499969 | − | 0.288657i | ||||
\(39\) | 594.749 | − | 1030.14i | 0.391025 | − | 0.677276i | ||||
\(40\) | 277.352 | − | 160.129i | 0.173345 | − | 0.100081i | ||||
\(41\) | − | 2817.60i | − | 1.67615i | −0.545558 | − | 0.838073i | \(-0.683682\pi\) | ||
0.545558 | − | 0.838073i | \(-0.316318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3066.41 | 1.65841 | 0.829207 | − | 0.558942i | \(-0.188793\pi\) | ||||
0.829207 | + | 0.558942i | \(0.188793\pi\) | |||||||
\(44\) | −256.118 | − | 443.609i | −0.132292 | − | 0.229137i | ||||
\(45\) | 330.949 | + | 191.073i | 0.163431 | + | 0.0943572i | ||||
\(46\) | −1003.38 | + | 1737.91i | −0.474188 | + | 0.821318i | ||||
\(47\) | 531.502 | − | 306.863i | 0.240608 | − | 0.138915i | −0.374848 | − | 0.927086i | \(-0.622305\pi\) |
0.615456 | + | 0.788171i | \(0.288972\pi\) | |||||||
\(48\) | − | 332.554i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1201.17 | 0.480466 | ||||||||
\(51\) | 585.749 | + | 1014.55i | 0.225202 | + | 0.390061i | ||||
\(52\) | 1586.00 | + | 915.677i | 0.586538 | + | 0.338638i | ||||
\(53\) | 576.300 | − | 998.181i | 0.205162 | − | 0.355351i | −0.745022 | − | 0.667040i | \(-0.767561\pi\) |
0.950184 | + | 0.311688i | \(0.100895\pi\) | |||||||
\(54\) | 343.654 | − | 198.409i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 906.246i | 0.299585i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1531.50 | 0.471375 | ||||||||
\(58\) | −1047.08 | − | 1813.59i | −0.311260 | − | 0.539119i | ||||
\(59\) | 3024.67 | + | 1746.30i | 0.868909 | + | 0.501665i | 0.866986 | − | 0.498333i | \(-0.166054\pi\) |
0.00192348 | + | 0.999998i | \(0.499388\pi\) | |||||||
\(60\) | −294.177 | + | 509.529i | −0.0817157 | + | 0.141536i | ||||
\(61\) | −1967.79 | + | 1136.11i | −0.528834 | + | 0.305323i | −0.740542 | − | 0.672010i | \(-0.765431\pi\) |
0.211707 | + | 0.977333i | \(0.432098\pi\) | |||||||
\(62\) | − | 1885.75i | − | 0.490569i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | −1620.01 | − | 2805.94i | −0.383435 | − | 0.664129i | ||||
\(66\) | 814.962 | + | 470.518i | 0.187089 | + | 0.108016i | ||||
\(67\) | 4337.31 | − | 7512.44i | 0.966208 | − | 1.67352i | 0.259874 | − | 0.965642i | \(-0.416319\pi\) |
0.706334 | − | 0.707879i | \(-0.250348\pi\) | |||||||
\(68\) | −1562.00 | + | 901.820i | −0.337802 | + | 0.195030i | ||||
\(69\) | − | 3686.66i | − | 0.774346i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −353.591 | −0.0701431 | −0.0350715 | − | 0.999385i | \(-0.511166\pi\) | ||||
−0.0350715 | + | 0.999385i | \(0.511166\pi\) | |||||||
\(72\) | 305.470 | + | 529.090i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −3524.68 | − | 2034.97i | −0.661415 | − | 0.381868i | 0.131401 | − | 0.991329i | \(-0.458052\pi\) |
−0.792816 | + | 0.609461i | \(0.791386\pi\) | |||||||
\(74\) | 1179.12 | − | 2042.30i | 0.215325 | − | 0.372954i | ||||
\(75\) | −1911.04 | + | 1103.34i | −0.339741 | + | 0.196150i | ||||
\(76\) | 2357.90i | 0.408223i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3364.41 | −0.552993 | ||||||||
\(79\) | −3236.41 | − | 5605.63i | −0.518573 | − | 0.898194i | −0.999767 | − | 0.0215805i | \(-0.993130\pi\) |
0.481194 | − | 0.876614i | \(-0.340203\pi\) | |||||||
\(80\) | −784.471 | − | 452.915i | −0.122574 | − | 0.0707679i | ||||
\(81\) | −364.500 | + | 631.333i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −6901.69 | + | 3984.69i | −1.02643 | + | 0.592607i | ||||
\(83\) | − | 8225.83i | − | 1.19405i | −0.802222 | − | 0.597026i | \(-0.796349\pi\) | ||
0.802222 | − | 0.597026i | \(-0.203651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3191.00 | 0.441660 | ||||||||
\(86\) | −4336.55 | − | 7511.13i | −0.586338 | − | 1.01557i | ||||
\(87\) | 3331.79 | + | 1923.61i | 0.440188 | + | 0.254143i | ||||
\(88\) | −724.410 | + | 1254.72i | −0.0935447 | + | 0.162024i | ||||
\(89\) | 13456.5 | − | 7769.13i | 1.69884 | − | 0.980828i | 0.751983 | − | 0.659183i | \(-0.229098\pi\) |
0.946860 | − | 0.321645i | \(-0.104236\pi\) | |||||||
\(90\) | − | 1080.87i | − | 0.133441i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5675.99 | 0.670604 | ||||||||
\(93\) | 1732.17 | + | 3000.21i | 0.200274 | + | 0.346885i | ||||
\(94\) | −1503.32 | − | 867.939i | −0.170135 | − | 0.0982276i | ||||
\(95\) | 2085.79 | − | 3612.70i | 0.231113 | − | 0.400299i | ||||
\(96\) | −814.587 | + | 470.302i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | 1558.61i | 0.165651i | 0.996564 | + | 0.0828254i | \(0.0263944\pi\) | ||||
−0.996564 | + | 0.0828254i | \(0.973606\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1728.79 | −0.176390 | ||||||||
\(100\) | −1698.70 | − | 2942.24i | −0.169870 | − | 0.294224i | ||||
\(101\) | −13627.2 | − | 7867.66i | −1.33587 | − | 0.771264i | −0.349676 | − | 0.936871i | \(-0.613708\pi\) |
−0.986192 | + | 0.165607i | \(0.947042\pi\) | |||||||
\(102\) | 1656.75 | − | 2869.57i | 0.159242 | − | 0.275814i | ||||
\(103\) | −29.2099 | + | 16.8644i | −0.00275332 | + | 0.00158963i | −0.501376 | − | 0.865229i | \(-0.667173\pi\) |
0.498623 | + | 0.866819i | \(0.333839\pi\) | |||||||
\(104\) | − | 5179.85i | − | 0.478906i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3260.05 | −0.290143 | ||||||||
\(107\) | 2723.23 | + | 4716.78i | 0.237858 | + | 0.411981i | 0.960099 | − | 0.279659i | \(-0.0902215\pi\) |
−0.722242 | + | 0.691641i | \(0.756888\pi\) | |||||||
\(108\) | −972.000 | − | 561.184i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −8348.89 | + | 14460.7i | −0.702709 | + | 1.21713i | 0.264803 | + | 0.964303i | \(0.414693\pi\) |
−0.967512 | + | 0.252825i | \(0.918640\pi\) | |||||||
\(110\) | 2219.84 | − | 1281.62i | 0.183458 | − | 0.105919i | ||||
\(111\) | 4332.37i | 0.351625i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9455.64 | 0.740515 | 0.370258 | − | 0.928929i | \(-0.379269\pi\) | ||||
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(114\) | −2165.87 | − | 3751.39i | −0.166656 | − | 0.288657i | ||||
\(115\) | −8696.58 | − | 5020.97i | −0.657586 | − | 0.379658i | ||||
\(116\) | −2961.59 | + | 5129.62i | −0.220094 | + | 0.381214i | ||||
\(117\) | 5352.74 | − | 3090.41i | 0.391025 | − | 0.225759i | ||||
\(118\) | − | 9878.54i | − | 0.709461i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1664.11 | 0.115563 | ||||||||
\(121\) | 5270.62 | + | 9128.97i | 0.359990 | + | 0.623521i | ||||
\(122\) | 5565.76 | + | 3213.39i | 0.373942 | + | 0.215896i | ||||
\(123\) | 7320.35 | − | 12679.2i | 0.483862 | − | 0.838073i | ||||
\(124\) | −4619.12 | + | 2666.85i | −0.300411 | + | 0.173442i | ||||
\(125\) | 14856.7i | 0.950827i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2380.07 | −0.147564 | −0.0737822 | − | 0.997274i | \(-0.523507\pi\) | ||||
−0.0737822 | + | 0.997274i | \(0.523507\pi\) | |||||||
\(128\) | −724.077 | − | 1254.14i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 13798.8 | + | 7966.76i | 0.829207 | + | 0.478743i | ||||
\(130\) | −4582.09 | + | 7936.41i | −0.271129 | + | 0.469610i | ||||
\(131\) | 3758.37 | − | 2169.90i | 0.219006 | − | 0.126443i | −0.386484 | − | 0.922296i | \(-0.626310\pi\) |
0.605490 | + | 0.795853i | \(0.292977\pi\) | |||||||
\(132\) | − | 2661.65i | − | 0.152758i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −24535.5 | −1.36642 | ||||||||
\(135\) | 992.846 | + | 1719.66i | 0.0544772 | + | 0.0943572i | ||||
\(136\) | 4418.00 | + | 2550.73i | 0.238862 | + | 0.137907i | ||||
\(137\) | 15379.6 | − | 26638.2i | 0.819414 | − | 1.41927i | −0.0867001 | − | 0.996234i | \(-0.527632\pi\) |
0.906114 | − | 0.423033i | \(-0.139034\pi\) | |||||||
\(138\) | −9030.44 | + | 5213.73i | −0.474188 | + | 0.273773i | ||||
\(139\) | 27186.6i | 1.40710i | 0.710644 | + | 0.703551i | \(0.248404\pi\) | ||||
−0.710644 | + | 0.703551i | \(0.751596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3189.01 | 0.160405 | ||||||||
\(142\) | 500.054 | + | 866.118i | 0.0247993 | + | 0.0429537i | ||||
\(143\) | 12693.8 | + | 7328.78i | 0.620755 | + | 0.358393i | ||||
\(144\) | 864.000 | − | 1496.49i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 9075.31 | − | 5239.63i | 0.431644 | − | 0.249210i | ||||
\(146\) | 11511.6i | 0.540043i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6670.12 | −0.304516 | ||||||||
\(149\) | 2913.46 | + | 5046.26i | 0.131231 | + | 0.227299i | 0.924151 | − | 0.382027i | \(-0.124774\pi\) |
−0.792920 | + | 0.609325i | \(0.791440\pi\) | |||||||
\(150\) | 5405.25 | + | 3120.72i | 0.240233 | + | 0.138699i | ||||
\(151\) | −12593.4 | + | 21812.4i | −0.552317 | + | 0.956642i | 0.445789 | + | 0.895138i | \(0.352923\pi\) |
−0.998107 | + | 0.0615039i | \(0.980410\pi\) | |||||||
\(152\) | 5775.64 | − | 3334.57i | 0.249985 | − | 0.144329i | ||||
\(153\) | 6087.29i | 0.260040i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9436.37 | 0.392773 | ||||||||
\(156\) | 4757.99 | + | 8241.09i | 0.195513 | + | 0.338638i | ||||
\(157\) | −20694.6 | − | 11948.0i | −0.839571 | − | 0.484726i | 0.0175475 | − | 0.999846i | \(-0.494414\pi\) |
−0.857118 | + | 0.515120i | \(0.827747\pi\) | |||||||
\(158\) | −9153.96 | + | 15855.1i | −0.366686 | + | 0.635119i | ||||
\(159\) | 5186.70 | − | 2994.54i | 0.205162 | − | 0.118450i | ||||
\(160\) | 2562.07i | 0.100081i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2061.92 | 0.0785674 | ||||||||
\(163\) | 21293.0 | + | 36880.5i | 0.801422 | + | 1.38810i | 0.918680 | + | 0.395001i | \(0.129256\pi\) |
−0.117259 | + | 0.993101i | \(0.537411\pi\) | |||||||
\(164\) | 19520.9 | + | 11270.4i | 0.725793 | + | 0.419037i | ||||
\(165\) | −2354.50 | + | 4078.11i | −0.0864828 | + | 0.149793i | ||||
\(166\) | −20149.1 | + | 11633.1i | −0.731205 | + | 0.422161i | ||||
\(167\) | − | 26356.3i | − | 0.945043i | −0.881319 | − | 0.472521i | \(-0.843344\pi\) | ||
0.881319 | − | 0.472521i | \(-0.156656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23843.0 | −0.834809 | ||||||||
\(170\) | −4512.75 | − | 7816.31i | −0.156150 | − | 0.270461i | ||||
\(171\) | 6891.74 | + | 3978.95i | 0.235688 | + | 0.136074i | ||||
\(172\) | −12265.6 | + | 21244.7i | −0.414603 | + | 0.718114i | ||||
\(173\) | −24265.3 | + | 14009.6i | −0.810763 | + | 0.468094i | −0.847221 | − | 0.531241i | \(-0.821726\pi\) |
0.0364578 | + | 0.999335i | \(0.488393\pi\) | |||||||
\(174\) | − | 10881.6i | − | 0.359412i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4097.88 | 0.132292 | ||||||||
\(177\) | 9074.02 | + | 15716.7i | 0.289636 | + | 0.501665i | ||||
\(178\) | −38060.8 | − | 21974.4i | −1.20126 | − | 0.693550i | ||||
\(179\) | −12699.2 | + | 21995.7i | −0.396343 | + | 0.686487i | −0.993272 | − | 0.115808i | \(-0.963054\pi\) |
0.596928 | + | 0.802295i | \(0.296388\pi\) | |||||||
\(180\) | −2647.59 | + | 1528.59i | −0.0817157 | + | 0.0471786i | ||||
\(181\) | 44097.2i | 1.34603i | 0.739630 | + | 0.673014i | \(0.235001\pi\) | ||||
−0.739630 | + | 0.673014i | \(0.764999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11806.8 | −0.352556 | ||||||||
\(184\) | −8027.06 | − | 13903.3i | −0.237094 | − | 0.410659i | ||||
\(185\) | 10219.8 | + | 5900.38i | 0.298605 | + | 0.172400i | ||||
\(186\) | 4899.32 | − | 8485.87i | 0.141615 | − | 0.245285i | ||||
\(187\) | −12501.7 | + | 7217.88i | −0.357509 | + | 0.206408i | ||||
\(188\) | 4909.81i | 0.138915i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11799.0 | −0.326843 | ||||||||
\(191\) | 32279.6 | + | 55909.8i | 0.884832 | + | 1.53257i | 0.845906 | + | 0.533332i | \(0.179060\pi\) |
0.0389256 | + | 0.999242i | \(0.487606\pi\) | |||||||
\(192\) | 2304.00 | + | 1330.22i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −18337.3 | + | 31761.1i | −0.492290 | + | 0.852670i | −0.999961 | − | 0.00888055i | \(-0.997173\pi\) |
0.507671 | + | 0.861551i | \(0.330507\pi\) | |||||||
\(194\) | 3817.80 | − | 2204.20i | 0.101440 | − | 0.0585664i | ||||
\(195\) | − | 16835.7i | − | 0.442753i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −73147.0 | −1.88480 | −0.942398 | − | 0.334494i | \(-0.891434\pi\) | ||||
−0.942398 | + | 0.334494i | \(0.891434\pi\) | |||||||
\(198\) | 2444.89 | + | 4234.67i | 0.0623632 | + | 0.108016i | ||||
\(199\) | 1213.33 | + | 700.514i | 0.0306387 | + | 0.0176893i | 0.515241 | − | 0.857045i | \(-0.327702\pi\) |
−0.484602 | + | 0.874735i | \(0.661036\pi\) | |||||||
\(200\) | −4804.66 | + | 8321.92i | −0.120117 | + | 0.208048i | ||||
\(201\) | 39035.8 | − | 22537.3i | 0.966208 | − | 0.557840i | ||||
\(202\) | 44506.2i | 1.09073i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9371.99 | −0.225202 | ||||||||
\(205\) | −19939.6 | − | 34536.4i | −0.474469 | − | 0.821805i | ||||
\(206\) | 82.6182 | + | 47.6996i | 0.00194689 | + | 0.00112404i | ||||
\(207\) | 9578.23 | − | 16590.0i | 0.223535 | − | 0.387173i | ||||
\(208\) | −12688.0 | + | 7325.41i | −0.293269 | + | 0.169319i | ||||
\(209\) | 18871.8i | 0.432038i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 58231.7 | 1.30796 | 0.653980 | − | 0.756512i | \(-0.273098\pi\) | ||||
0.653980 | + | 0.756512i | \(0.273098\pi\) | |||||||
\(212\) | 4610.40 | + | 7985.45i | 0.102581 | + | 0.177676i | ||||
\(213\) | −1591.16 | − | 918.657i | −0.0350715 | − | 0.0202486i | ||||
\(214\) | 7702.46 | − | 13341.1i | 0.168191 | − | 0.291315i | ||||
\(215\) | 37586.1 | − | 21700.3i | 0.813111 | − | 0.469450i | ||||
\(216\) | 3174.54i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 47228.4 | 0.993781 | ||||||||
\(219\) | −10574.0 | − | 18314.8i | −0.220472 | − | 0.381868i | ||||
\(220\) | −6278.65 | − | 3624.98i | −0.129724 | − | 0.0748963i | ||||
\(221\) | 25805.5 | − | 44696.4i | 0.528357 | − | 0.915141i | ||||
\(222\) | 10612.1 | − | 6126.89i | 0.215325 | − | 0.124318i | ||||
\(223\) | 61050.9i | 1.22767i | 0.789434 | + | 0.613836i | \(0.210374\pi\) | ||||
−0.789434 | + | 0.613836i | \(0.789626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11466.3 | −0.226494 | ||||||||
\(226\) | −13372.3 | − | 23161.5i | −0.261812 | − | 0.453471i | ||||
\(227\) | −21645.2 | − | 12496.8i | −0.420058 | − | 0.242520i | 0.275044 | − | 0.961432i | \(-0.411307\pi\) |
−0.695102 | + | 0.718911i | \(0.744641\pi\) | |||||||
\(228\) | −6125.99 | + | 10610.5i | −0.117844 | + | 0.204112i | ||||
\(229\) | 16392.9 | − | 9464.44i | 0.312597 | − | 0.180478i | −0.335491 | − | 0.942043i | \(-0.608902\pi\) |
0.648088 | + | 0.761565i | \(0.275569\pi\) | |||||||
\(230\) | 28402.9i | 0.536917i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16753.3 | 0.311260 | ||||||||
\(233\) | −3342.37 | − | 5789.15i | −0.0615662 | − | 0.106636i | 0.833599 | − | 0.552369i | \(-0.186276\pi\) |
−0.895166 | + | 0.445734i | \(0.852943\pi\) | |||||||
\(234\) | −15139.8 | − | 8740.99i | −0.276497 | − | 0.159635i | ||||
\(235\) | 4343.21 | − | 7522.66i | 0.0786457 | − | 0.136218i | ||||
\(236\) | −24197.4 | + | 13970.4i | −0.434455 | + | 0.250832i | ||||
\(237\) | − | 33633.8i | − | 0.598796i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −96461.0 | −1.68871 | −0.844356 | − | 0.535782i | \(-0.820017\pi\) | ||||
−0.844356 | + | 0.535782i | \(0.820017\pi\) | |||||||
\(240\) | −2353.41 | − | 4076.23i | −0.0408579 | − | 0.0707679i | ||||
\(241\) | −47371.8 | − | 27350.1i | −0.815616 | − | 0.470896i | 0.0332863 | − | 0.999446i | \(-0.489403\pi\) |
−0.848902 | + | 0.528550i | \(0.822736\pi\) | |||||||
\(242\) | 14907.6 | − | 25820.6i | 0.254551 | − | 0.440896i | ||||
\(243\) | −3280.50 | + | 1894.00i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | − | 18177.7i | − | 0.305323i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −41410.1 | −0.684284 | ||||||||
\(247\) | −33735.5 | − | 58431.6i | −0.552959 | − | 0.957753i | ||||
\(248\) | 13064.9 | + | 7542.99i | 0.212423 | + | 0.122642i | ||||
\(249\) | 21371.3 | − | 37016.2i | 0.344693 | − | 0.597026i | ||||
\(250\) | 36391.3 | − | 21010.5i | 0.582260 | − | 0.336168i | ||||
\(251\) | − | 108137.i | − | 1.71643i | −0.513286 | − | 0.858217i | \(-0.671572\pi\) | ||
0.513286 | − | 0.858217i | \(-0.328428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45428.8 | 0.709725 | ||||||||
\(254\) | 3365.92 | + | 5829.95i | 0.0521719 | + | 0.0903643i | ||||
\(255\) | 14359.5 | + | 8290.45i | 0.220830 | + | 0.127496i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −31078.3 | + | 17943.0i | −0.470533 | + | 0.271663i | −0.716463 | − | 0.697625i | \(-0.754240\pi\) |
0.245930 | + | 0.969288i | \(0.420907\pi\) | |||||||
\(258\) | − | 45066.8i | − | 0.677045i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 25920.2 | 0.383435 | ||||||||
\(261\) | 9995.36 | + | 17312.5i | 0.146729 | + | 0.254143i | ||||
\(262\) | −10630.3 | − | 6137.39i | −0.154861 | − | 0.0894090i | ||||
\(263\) | 32715.8 | − | 56665.4i | 0.472984 | − | 0.819232i | −0.526538 | − | 0.850151i | \(-0.676510\pi\) |
0.999522 | + | 0.0309199i | \(0.00984367\pi\) | |||||||
\(264\) | −6519.69 | + | 3764.15i | −0.0935447 | + | 0.0540081i | ||||
\(265\) | − | 16313.4i | − | 0.232302i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 80739.2 | 1.13256 | ||||||||
\(268\) | 34698.5 | + | 60099.5i | 0.483104 | + | 0.836761i | ||||
\(269\) | 59938.7 | + | 34605.6i | 0.828329 | + | 0.478236i | 0.853280 | − | 0.521453i | \(-0.174610\pi\) |
−0.0249511 | + | 0.999689i | \(0.507943\pi\) | |||||||
\(270\) | 2808.19 | − | 4863.93i | 0.0385212 | − | 0.0667206i | ||||
\(271\) | −5672.94 | + | 3275.27i | −0.0772449 | + | 0.0445973i | −0.538125 | − | 0.842865i | \(-0.680867\pi\) |
0.460880 | + | 0.887462i | \(0.347534\pi\) | |||||||
\(272\) | − | 14429.1i | − | 0.195030i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −87000.1 | −1.15883 | ||||||||
\(275\) | −13595.9 | − | 23548.8i | −0.179780 | − | 0.311389i | ||||
\(276\) | 25542.0 | + | 14746.7i | 0.335302 | + | 0.193587i | ||||
\(277\) | −39551.6 | + | 68505.4i | −0.515471 | + | 0.892823i | 0.484367 | + | 0.874865i | \(0.339050\pi\) |
−0.999839 | + | 0.0179578i | \(0.994284\pi\) | |||||||
\(278\) | 66593.4 | − | 38447.7i | 0.861671 | − | 0.497486i | ||||
\(279\) | 18001.2i | 0.231257i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 34363.1 | 0.435191 | 0.217596 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217596 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(282\) | −4509.95 | − | 7811.45i | −0.0567118 | − | 0.0982276i | ||||
\(283\) | −79598.4 | − | 45956.1i | −0.993874 | − | 0.573813i | −0.0874439 | − | 0.996169i | \(-0.527870\pi\) |
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(284\) | 1414.37 | − | 2449.75i | 0.0175358 | − | 0.0303729i | ||||
\(285\) | 18772.1 | − | 10838.1i | 0.231113 | − | 0.133433i | ||||
\(286\) | − | 41457.8i | − | 0.506844i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4887.52 | −0.0589256 | ||||||||
\(289\) | −16345.5 | − | 28311.3i | −0.195705 | − | 0.338972i | ||||
\(290\) | −25668.9 | − | 14819.9i | −0.305218 | − | 0.176218i | ||||
\(291\) | −4049.38 | + | 7013.74i | −0.0478193 | + | 0.0828254i | ||||
\(292\) | 28197.4 | − | 16279.8i | 0.330707 | − | 0.190934i | ||||
\(293\) | 23218.2i | 0.270453i | 0.990815 | + | 0.135227i | \(0.0431763\pi\) | ||||
−0.990815 | + | 0.135227i | \(0.956824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 49432.7 | 0.568028 | ||||||||
\(296\) | 9432.97 | + | 16338.4i | 0.107663 | + | 0.186477i | ||||
\(297\) | −7779.58 | − | 4491.54i | −0.0881948 | − | 0.0509193i | ||||
\(298\) | 8240.51 | − | 14273.0i | 0.0927943 | − | 0.160724i | ||||
\(299\) | −140658. | + | 81208.9i | −1.57334 | + | 0.908367i | ||||
\(300\) | − | 17653.5i | − | 0.196150i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 71239.0 | 0.781095 | ||||||||
\(303\) | −40881.6 | − | 70808.9i | −0.445289 | − | 0.771264i | ||||
\(304\) | −16336.0 | − | 9431.59i | −0.176766 | − | 0.102056i | ||||
\(305\) | −16080.0 | + | 27851.3i | −0.172856 | + | 0.299396i | ||||
\(306\) | 14910.7 | − | 8608.72i | 0.159242 | − | 0.0919382i | ||||
\(307\) | − | 66385.9i | − | 0.704367i | −0.935931 | − | 0.352183i | \(-0.885439\pi\) | ||
0.935931 | − | 0.352183i | \(-0.114561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −175.260 | −0.00183555 | ||||||||
\(310\) | −13345.0 | − | 23114.3i | −0.138866 | − | 0.240523i | ||||
\(311\) | 82879.0 | + | 47850.2i | 0.856888 | + | 0.494724i | 0.862969 | − | 0.505257i | \(-0.168602\pi\) |
−0.00608108 | + | 0.999982i | \(0.501936\pi\) | |||||||
\(312\) | 13457.6 | − | 23309.3i | 0.138248 | − | 0.239453i | ||||
\(313\) | −41486.1 | + | 23952.0i | −0.423461 | + | 0.244486i | −0.696557 | − | 0.717501i | \(-0.745286\pi\) |
0.273096 | + | 0.961987i | \(0.411952\pi\) | |||||||
\(314\) | 67588.2i | 0.685507i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 51782.6 | 0.518573 | ||||||||
\(317\) | 17064.1 | + | 29555.9i | 0.169811 | + | 0.294121i | 0.938353 | − | 0.345678i | \(-0.112351\pi\) |
−0.768543 | + | 0.639799i | \(0.779018\pi\) | |||||||
\(318\) | −14670.2 | − | 8469.85i | −0.145071 | − | 0.0837571i | ||||
\(319\) | −23703.6 | + | 41055.8i | −0.232934 | + | 0.403454i | ||||
\(320\) | 6275.77 | − | 3623.32i | 0.0612868 | − | 0.0353839i | ||||
\(321\) | 28300.7i | 0.274654i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 66450.0 | 0.636927 | ||||||||
\(324\) | −2916.00 | − | 5050.66i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 84192.0 | + | 48608.3i | 0.797084 | + | 0.460196i | ||||
\(326\) | 60225.6 | − | 104314.i | 0.566691 | − | 0.981537i | ||||
\(327\) | −75140.0 | + | 43382.1i | −0.702709 | + | 0.405709i | ||||
\(328\) | − | 63755.1i | − | 0.592607i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13319.0 | 0.122305 | ||||||||
\(331\) | −66642.6 | − | 115428.i | −0.608270 | − | 1.05355i | −0.991526 | − | 0.129912i | \(-0.958531\pi\) |
0.383256 | − | 0.923642i | \(-0.374803\pi\) | |||||||
\(332\) | 56990.2 | + | 32903.3i | 0.517040 | + | 0.298513i | ||||
\(333\) | −11255.8 | + | 19495.7i | −0.101505 | + | 0.175812i | ||||
\(334\) | −64559.5 | + | 37273.4i | −0.578718 | + | 0.334123i | ||||
\(335\) | − | 122777.i | − | 1.09402i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −49734.4 | −0.437922 | −0.218961 | − | 0.975734i | \(-0.570267\pi\) | ||||
−0.218961 | + | 0.975734i | \(0.570267\pi\) | |||||||
\(338\) | 33719.0 | + | 58403.1i | 0.295149 | + | 0.511214i | ||||
\(339\) | 42550.4 | + | 24566.5i | 0.370258 | + | 0.213768i | ||||
\(340\) | −12764.0 | + | 22107.9i | −0.110415 | + | 0.191245i | ||||
\(341\) | −36970.0 | + | 21344.6i | −0.317936 | + | 0.183561i | ||||
\(342\) | − | 22508.3i | − | 0.192438i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 69384.9 | 0.586338 | ||||||||
\(345\) | −26089.7 | − | 45188.8i | −0.219195 | − | 0.379658i | ||||
\(346\) | 68632.7 | + | 39625.1i | 0.573296 | + | 0.330993i | ||||
\(347\) | −9384.77 | + | 16254.9i | −0.0779408 | + | 0.134997i | −0.902361 | − | 0.430980i | \(-0.858168\pi\) |
0.824421 | + | 0.565978i | \(0.191501\pi\) | |||||||
\(348\) | −26654.3 | + | 15388.9i | −0.220094 | + | 0.127071i | ||||
\(349\) | − | 4574.17i | − | 0.0375545i | −0.999824 | − | 0.0187772i | \(-0.994023\pi\) | ||
0.999824 | − | 0.0187772i | \(-0.00597733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32116.5 | 0.260683 | ||||||||
\(352\) | −5795.28 | − | 10037.7i | −0.0467724 | − | 0.0810121i | ||||
\(353\) | −52734.9 | − | 30446.5i | −0.423203 | − | 0.244336i | 0.273244 | − | 0.961945i | \(-0.411903\pi\) |
−0.696447 | + | 0.717608i | \(0.745237\pi\) | |||||||
\(354\) | 25665.2 | − | 44453.4i | 0.204804 | − | 0.354731i | ||||
\(355\) | −4334.10 | + | 2502.29i | −0.0343908 | + | 0.0198555i | ||||
\(356\) | 124306.i | 0.980828i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 71837.7 | 0.560514 | ||||||||
\(359\) | −116059. | − | 201020.i | −0.900513 | − | 1.55973i | −0.826830 | − | 0.562452i | \(-0.809858\pi\) |
−0.0736826 | − | 0.997282i | \(-0.523475\pi\) | |||||||
\(360\) | 7488.51 | + | 4323.50i | 0.0577817 | + | 0.0333603i | ||||
\(361\) | −21725.5 | + | 37629.7i | −0.166708 | + | 0.288746i | ||||
\(362\) | 108016. | − | 62362.9i | 0.824271 | − | 0.475893i | ||||
\(363\) | 54773.8i | 0.415681i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −57604.4 | −0.432384 | ||||||||
\(366\) | 16697.3 | + | 28920.5i | 0.124647 | + | 0.215896i | ||||
\(367\) | 125329. | + | 72358.9i | 0.930509 | + | 0.537229i | 0.886972 | − | 0.461822i | \(-0.152804\pi\) |
0.0435362 | + | 0.999052i | \(0.486138\pi\) | |||||||
\(368\) | −22704.0 | + | 39324.4i | −0.167651 | + | 0.290380i | ||||
\(369\) | 65883.1 | − | 38037.6i | 0.483862 | − | 0.279358i | ||||
\(370\) | − | 33377.6i | − | 0.243810i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −27714.7 | −0.200274 | ||||||||
\(373\) | 74441.6 | + | 128937.i | 0.535054 | + | 0.926741i | 0.999161 | + | 0.0409616i | \(0.0130421\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(374\) | 35360.2 | + | 20415.2i | 0.252797 | + | 0.145952i | ||||
\(375\) | −38598.8 | + | 66855.0i | −0.274480 | + | 0.475414i | ||||
\(376\) | 12026.5 | − | 6943.52i | 0.0850676 | − | 0.0491138i | ||||
\(377\) | − | 169491.i | − | 1.19252i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 140667. | 0.979299 | 0.489649 | − | 0.871919i | \(-0.337125\pi\) | ||||
0.489649 | + | 0.871919i | \(0.337125\pi\) | |||||||
\(380\) | 16686.3 | + | 28901.6i | 0.115556 | + | 0.200149i | ||||
\(381\) | −10710.3 | − | 6183.59i | −0.0737822 | − | 0.0425982i | ||||
\(382\) | 91300.4 | − | 158137.i | 0.625671 | − | 1.08369i | ||||
\(383\) | −25393.9 | + | 14661.2i | −0.173114 | + | 0.0999473i | −0.584053 | − | 0.811715i | \(-0.698534\pi\) |
0.410939 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(384\) | − | 7524.83i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 103731. | 0.696202 | ||||||||
\(387\) | 41396.5 | + | 71700.8i | 0.276402 | + | 0.478743i | ||||
\(388\) | −10798.4 | − | 6234.43i | −0.0717289 | − | 0.0414127i | ||||
\(389\) | −66209.9 | + | 114679.i | −0.437546 | + | 0.757852i | −0.997500 | − | 0.0706723i | \(-0.977486\pi\) |
0.559954 | + | 0.828524i | \(0.310819\pi\) | |||||||
\(390\) | −41238.8 | + | 23809.2i | −0.271129 | + | 0.156537i | ||||
\(391\) | − | 159960.i | − | 1.04630i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22550.2 | 0.146004 | ||||||||
\(394\) | 103446. | + | 179173.i | 0.666376 | + | 1.15420i | ||||
\(395\) | −79339.7 | − | 45806.8i | −0.508507 | − | 0.293586i | ||||
\(396\) | 6915.18 | − | 11977.4i | 0.0440974 | − | 0.0763790i | ||||
\(397\) | −29642.0 | + | 17113.8i | −0.188073 | + | 0.108584i | −0.591080 | − | 0.806613i | \(-0.701298\pi\) |
0.403007 | + | 0.915197i | \(0.367965\pi\) | |||||||
\(398\) | − | 3962.70i | − | 0.0250164i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27179.3 | 0.169870 | ||||||||
\(401\) | 89540.6 | + | 155089.i | 0.556841 | + | 0.964477i | 0.997758 | + | 0.0669288i | \(0.0213200\pi\) |
−0.440917 | + | 0.897548i | \(0.645347\pi\) | |||||||
\(402\) | −110410. | − | 63745.1i | −0.683212 | − | 0.394453i | ||||
\(403\) | 76311.7 | − | 132176.i | 0.469873 | − | 0.813845i | ||||
\(404\) | 109018. | − | 62941.3i | 0.667934 | − | 0.385632i | ||||
\(405\) | 10318.0i | 0.0629048i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −53385.5 | −0.322281 | ||||||||
\(408\) | 13254.0 | + | 22956.6i | 0.0796208 | + | 0.137907i | ||||
\(409\) | −43099.3 | − | 24883.4i | −0.257646 | − | 0.148752i | 0.365614 | − | 0.930767i | \(-0.380859\pi\) |
−0.623260 | + | 0.782014i | \(0.714192\pi\) | |||||||
\(410\) | −56397.6 | + | 97683.6i | −0.335501 | + | 0.581104i | ||||
\(411\) | 138416. | − | 79914.7i | 0.819414 | − | 0.473089i | ||||
\(412\) | − | 269.830i | − | 0.00158963i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −54182.7 | −0.316126 | ||||||||
\(415\) | −58212.4 | − | 100827.i | −0.338002 | − | 0.585437i | ||||
\(416\) | 35887.0 | + | 20719.4i | 0.207372 | + | 0.119727i | ||||
\(417\) | −70633.0 | + | 122340.i | −0.406196 | + | 0.703551i | ||||
\(418\) | 46226.4 | − | 26688.8i | 0.264568 | − | 0.152748i | ||||
\(419\) | − | 43951.2i | − | 0.250347i | −0.992135 | − | 0.125174i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125174i | \(-0.0399488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −218257. | −1.23141 | −0.615707 | − | 0.787975i | \(-0.711129\pi\) | ||||
−0.615707 | + | 0.787975i | \(0.711129\pi\) | |||||||
\(422\) | −82352.0 | − | 142638.i | −0.462433 | − | 0.800958i | ||||
\(423\) | 14350.6 | + | 8285.30i | 0.0802025 | + | 0.0463050i | ||||
\(424\) | 13040.2 | − | 22586.3i | 0.0725357 | − | 0.125636i | ||||
\(425\) | −82917.9 | + | 47872.7i | −0.459061 | + | 0.265039i | ||||
\(426\) | 5196.71i | 0.0286358i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −43571.7 | −0.237858 | ||||||||
\(429\) | 38081.5 | + | 65959.0i | 0.206918 | + | 0.358393i | ||||
\(430\) | −106309. | − | 61377.8i | −0.574956 | − | 0.331951i | ||||
\(431\) | 38369.8 | − | 66458.5i | 0.206555 | − | 0.357763i | −0.744072 | − | 0.668099i | \(-0.767108\pi\) |
0.950627 | + | 0.310336i | \(0.100442\pi\) | |||||||
\(432\) | 7776.00 | − | 4489.48i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 216713.i | 1.15587i | 0.816083 | + | 0.577935i | \(0.196141\pi\) | ||||
−0.816083 | + | 0.577935i | \(0.803859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 54451.9 | 0.287763 | ||||||||
\(436\) | −66791.1 | − | 115686.i | −0.351354 | − | 0.608564i | ||||
\(437\) | −181099. | − | 104558.i | −0.948318 | − | 0.547512i | ||||
\(438\) | −29907.9 | + | 51802.0i | −0.155897 | + | 0.270021i | ||||
\(439\) | −20578.6 | + | 11881.0i | −0.106779 | + | 0.0616489i | −0.552438 | − | 0.833554i | \(-0.686303\pi\) |
0.445659 | + | 0.895203i | \(0.352969\pi\) | |||||||
\(440\) | 20506.0i | 0.105919i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −145978. | −0.747210 | ||||||||
\(443\) | −87432.4 | − | 151437.i | −0.445517 | − | 0.771659i | 0.552571 | − | 0.833466i | \(-0.313647\pi\) |
−0.998088 | + | 0.0618072i | \(0.980314\pi\) | |||||||
\(444\) | −30015.5 | − | 17329.5i | −0.152258 | − | 0.0879062i | ||||
\(445\) | 109961. | − | 190458.i | 0.555289 | − | 0.961788i | ||||
\(446\) | 149544. | − | 86339.0i | 0.751793 | − | 0.434048i | ||||
\(447\) | 30277.6i | 0.151532i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −195154. | −0.968023 | −0.484011 | − | 0.875062i | \(-0.660821\pi\) | ||||
−0.484011 | + | 0.875062i | \(0.660821\pi\) | |||||||
\(450\) | 16215.7 | + | 28086.5i | 0.0800777 | + | 0.138699i | ||||
\(451\) | 156239. | + | 90204.7i | 0.768134 | + | 0.443482i | ||||
\(452\) | −37822.6 | + | 65510.6i | −0.185129 | + | 0.320653i | ||||
\(453\) | −113340. | + | 65437.2i | −0.552317 | + | 0.318881i | ||||
\(454\) | 70692.8i | 0.342976i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 34653.9 | 0.166656 | ||||||||
\(457\) | −29236.1 | − | 50638.5i | −0.139987 | − | 0.242464i | 0.787505 | − | 0.616309i | \(-0.211373\pi\) |
−0.927491 | + | 0.373844i | \(0.878039\pi\) | |||||||
\(458\) | −46366.1 | − | 26769.5i | −0.221039 | − | 0.127617i | ||||
\(459\) | −15815.2 | + | 27392.8i | −0.0750672 | + | 0.130020i | ||||
\(460\) | 69572.6 | − | 40167.8i | 0.328793 | − | 0.189829i | ||||
\(461\) | 307243.i | 1.44571i | 0.691002 | + | 0.722853i | \(0.257169\pi\) | ||||
−0.691002 | + | 0.722853i | \(0.742831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17772.2 | −0.0829049 | −0.0414524 | − | 0.999140i | \(-0.513199\pi\) | ||||
−0.0414524 | + | 0.999140i | \(0.513199\pi\) | |||||||
\(464\) | −23692.7 | − | 41037.0i | −0.110047 | − | 0.190607i | ||||
\(465\) | 42463.7 | + | 24516.4i | 0.196387 | + | 0.113384i | ||||
\(466\) | −9453.65 | + | 16374.2i | −0.0435339 | + | 0.0754029i | ||||
\(467\) | −56261.4 | + | 32482.5i | −0.257974 | + | 0.148942i | −0.623410 | − | 0.781895i | \(-0.714253\pi\) |
0.365436 | + | 0.930837i | \(0.380920\pi\) | |||||||
\(468\) | 49446.5i | 0.225759i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24568.9 | −0.111222 | ||||||||
\(471\) | −62083.7 | − | 107532.i | −0.279857 | − | 0.484726i | ||||
\(472\) | 68440.5 | + | 39514.2i | 0.307206 | + | 0.177365i | ||||
\(473\) | −98170.2 | + | 170036.i | −0.438790 | + | 0.760007i | ||||
\(474\) | −82385.6 | + | 47565.4i | −0.366686 | + | 0.211706i | ||||
\(475\) | 125168.i | 0.554760i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31120.2 | 0.136775 | ||||||||
\(478\) | 136416. | + | 236280.i | 0.597050 | + | 1.03412i | ||||
\(479\) | −182677. | − | 105468.i | −0.796181 | − | 0.459675i | 0.0459530 | − | 0.998944i | \(-0.485368\pi\) |
−0.842134 | + | 0.539268i | \(0.818701\pi\) | |||||||
\(480\) | −6656.46 | + | 11529.3i | −0.0288909 | + | 0.0500405i | ||||
\(481\) | 165294. | − | 95432.3i | 0.714440 | − | 0.412482i | ||||
\(482\) | 154716.i | 0.665948i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −84329.8 | −0.359990 | ||||||||
\(485\) | 11029.9 | + | 19104.4i | 0.0468910 | + | 0.0812177i | ||||
\(486\) | 9278.66 | + | 5357.03i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | 114444. | − | 198223.i | 0.482542 | − | 0.835787i | −0.517257 | − | 0.855830i | \(-0.673047\pi\) |
0.999799 | + | 0.0200431i | \(0.00638033\pi\) | |||||||
\(488\) | −44526.1 | + | 25707.1i | −0.186971 | + | 0.107948i | ||||
\(489\) | 221283.i | 0.925402i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 140350. | 0.582169 | 0.291085 | − | 0.956697i | \(-0.405984\pi\) | ||||
0.291085 | + | 0.956697i | \(0.405984\pi\) | |||||||
\(492\) | 58562.8 | + | 101434.i | 0.241931 | + | 0.419037i | ||||
\(493\) | 144562. | + | 83463.1i | 0.594787 | + | 0.343400i | ||||
\(494\) | −95418.3 | + | 165269.i | −0.391001 | + | 0.677234i | ||||
\(495\) | −21190.5 | + | 12234.3i | −0.0864828 | + | 0.0499309i | ||||
\(496\) | − | 42669.6i | − | 0.173442i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −120894. | −0.487470 | ||||||||
\(499\) | 172663. | + | 299062.i | 0.693424 | + | 1.20105i | 0.970709 | + | 0.240258i | \(0.0772322\pi\) |
−0.277285 | + | 0.960788i | \(0.589434\pi\) | |||||||
\(500\) | −102930. | − | 59426.7i | −0.411720 | − | 0.237707i | ||||
\(501\) | 68475.7 | − | 118603.i | 0.272810 | − | 0.472521i | ||||
\(502\) | −264881. | + | 152929.i | −1.05110 | + | 0.606851i | ||||
\(503\) | − | 58979.0i | − | 0.233110i | −0.993184 | − | 0.116555i | \(-0.962815\pi\) | ||
0.993184 | − | 0.116555i | \(-0.0371851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −222711. | −0.873291 | ||||||||
\(506\) | −64246.0 | − | 111277.i | −0.250926 | − | 0.434616i | ||||
\(507\) | −107293. | − | 61945.9i | −0.417404 | − | 0.240988i | ||||
\(508\) | 9520.26 | − | 16489.6i | 0.0368911 | − | 0.0638972i | ||||
\(509\) | −20653.6 | + | 11924.3i | −0.0797186 | + | 0.0460255i | −0.539329 | − | 0.842095i | \(-0.681322\pi\) |
0.459611 | + | 0.888120i | \(0.347989\pi\) | |||||||
\(510\) | − | 46897.9i | − | 0.180307i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | 20675.2 | + | 35810.6i | 0.0785626 | + | 0.136074i | ||||
\(514\) | 87902.6 | + | 50750.6i | 0.332717 | + | 0.192094i | ||||
\(515\) | −238.691 | + | 413.425i | −0.000899957 | + | 0.00155877i | ||||
\(516\) | −110391. | + | 63734.1i | −0.414603 | + | 0.239371i | ||||
\(517\) | 39296.5i | 0.147019i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −145592. | −0.540509 | ||||||||
\(520\) | −36656.7 | − | 63491.3i | −0.135565 | − | 0.234805i | ||||
\(521\) | −417171. | − | 240854.i | −1.53688 | − | 0.887315i | −0.999019 | − | 0.0442788i | \(-0.985901\pi\) |
−0.537856 | − | 0.843037i | \(-0.680766\pi\) | |||||||
\(522\) | 28271.1 | − | 48967.1i | 0.103753 | − | 0.179706i | ||||
\(523\) | 399593. | − | 230705.i | 1.46088 | − | 0.843438i | 0.461826 | − | 0.886970i | \(-0.347194\pi\) |
0.999052 | + | 0.0435320i | \(0.0138610\pi\) | |||||||
\(524\) | 34718.3i | 0.126443i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −185068. | −0.668900 | ||||||||
\(527\) | 75156.9 | + | 130176.i | 0.270612 | + | 0.468714i | ||||
\(528\) | 18440.5 | + | 10646.6i | 0.0661461 | + | 0.0381895i | ||||
\(529\) | −111774. | + | 193598.i | −0.399419 | + | 0.691813i | ||||
\(530\) | −39959.6 | + | 23070.7i | −0.142255 | + | 0.0821312i | ||||
\(531\) | 94299.9i | 0.334443i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −645003. | −2.27043 | ||||||||
\(534\) | −114182. | − | 197770.i | −0.400421 | − | 0.693550i | ||||
\(535\) | 66759.3 | + | 38543.5i | 0.233240 | + | 0.134661i | ||||
\(536\) | 98142.1 | − | 169987.i | 0.341606 | − | 0.591679i | ||||
\(537\) | −114293. | + | 65987.2i | −0.396343 | + | 0.228829i | ||||
\(538\) | − | 195759.i | − | 0.676328i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −15885.5 | −0.0544772 | ||||||||
\(541\) | 254098. | + | 440111.i | 0.868174 | + | 1.50372i | 0.863861 | + | 0.503731i | \(0.168040\pi\) |
0.00431302 | + | 0.999991i | \(0.498627\pi\) | |||||||
\(542\) | 16045.5 | + | 9263.87i | 0.0546204 | + | 0.0315351i | ||||
\(543\) | −114568. | + | 198438.i | −0.388565 | + | 0.673014i | ||||
\(544\) | −35344.0 | + | 20405.9i | −0.119431 | + | 0.0689536i | ||||
\(545\) | 236333.i | 0.795668i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40170.8 | 0.134257 | 0.0671283 | − | 0.997744i | \(-0.478616\pi\) | ||||
0.0671283 | + | 0.997744i | \(0.478616\pi\) | |||||||
\(548\) | 123037. | + | 213106.i | 0.409707 | + | 0.709634i | ||||
\(549\) | −53130.4 | − | 30674.9i | −0.176278 | − | 0.101774i | ||||
\(550\) | −38455.0 | + | 66606.0i | −0.127124 | + | 0.220185i | ||||
\(551\) | 188986. | − | 109111.i | 0.622482 | − | 0.359390i | ||||
\(552\) | − | 83419.7i | − | 0.273773i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 223738. | 0.728987 | ||||||||
\(555\) | 30659.3 | + | 53103.4i | 0.0995350 | + | 0.172400i | ||||
\(556\) | −188355. | − | 108747.i | −0.609293 | − | 0.351776i | ||||
\(557\) | 39230.2 | − | 67948.7i | 0.126447 | − | 0.219013i | −0.795850 | − | 0.605493i | \(-0.792976\pi\) |
0.922298 | + | 0.386480i | \(0.126309\pi\) | |||||||
\(558\) | 44093.9 | − | 25457.6i | 0.141615 | − | 0.0817616i | ||||
\(559\) | − | 701959.i | − | 2.24641i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −75010.4 | −0.238339 | ||||||||
\(562\) | −48596.8 | − | 84172.2i | −0.153863 | − | 0.266499i | ||||
\(563\) | 355612. | + | 205312.i | 1.12191 | + | 0.647737i | 0.941889 | − | 0.335926i | \(-0.109049\pi\) |
0.180024 | + | 0.983662i | \(0.442382\pi\) | |||||||
\(564\) | −12756.1 | + | 22094.1i | −0.0401013 | + | 0.0694574i | ||||
\(565\) | 115901. | − | 66915.6i | 0.363071 | − | 0.209619i | ||||
\(566\) | 259967.i | 0.811495i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8000.86 | −0.0247993 | ||||||||
\(569\) | 74404.3 | + | 128872.i | 0.229812 | + | 0.398047i | 0.957752 | − | 0.287594i | \(-0.0928554\pi\) |
−0.727940 | + | 0.685641i | \(0.759522\pi\) | |||||||
\(570\) | −53095.6 | − | 30654.8i | −0.163421 | − | 0.0943514i | ||||
\(571\) | −36146.3 | + | 62607.3i | −0.110864 | + | 0.192023i | −0.916119 | − | 0.400906i | \(-0.868695\pi\) |
0.805255 | + | 0.592929i | \(0.202029\pi\) | |||||||
\(572\) | −101551. | + | 58630.3i | −0.310378 | + | 0.179197i | ||||
\(573\) | 335459.i | 1.02172i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 301307. | 0.911326 | ||||||||
\(576\) | 6912.00 | + | 11971.9i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 482666. | + | 278667.i | 1.44976 | + | 0.837018i | 0.998466 | − | 0.0553596i | \(-0.0176305\pi\) |
0.451290 | + | 0.892377i | \(0.350964\pi\) | |||||||
\(578\) | −46232.1 | + | 80076.3i | −0.138385 | + | 0.239689i | ||||
\(579\) | −165036. | + | 95283.4i | −0.492290 | + | 0.284223i | ||||
\(580\) | 83834.1i | 0.249210i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 22906.8 | 0.0676267 | ||||||||
\(583\) | 36900.2 | + | 63913.0i | 0.108565 | + | 0.188041i | ||||
\(584\) | −79754.4 | − | 46046.2i | −0.233845 | − | 0.135011i | ||||
\(585\) | 43740.3 | − | 75760.5i | 0.127812 | − | 0.221376i | ||||
\(586\) | 56872.6 | − | 32835.4i | 0.165618 | − | 0.0956197i | ||||
\(587\) | − | 308119.i | − | 0.894217i | −0.894480 | − | 0.447109i | \(-0.852454\pi\) | ||
0.894480 | − | 0.447109i | \(-0.147546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 196505. | 0.566426 | ||||||||
\(590\) | −69908.3 | − | 121085.i | −0.200828 | − | 0.347845i | ||||
\(591\) | −329162. | − | 190042.i | −0.942398 | − | 0.544094i | ||||
\(592\) | 26680.5 | − | 46211.9i | 0.0761290 | − | 0.131859i | ||||
\(593\) | 200805. | − | 115935.i | 0.571038 | − | 0.329689i | −0.186526 | − | 0.982450i | \(-0.559723\pi\) |
0.757564 | + | 0.652761i | \(0.226389\pi\) | |||||||
\(594\) | 25408.0i | 0.0720108i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −46615.3 | −0.131231 | ||||||||
\(597\) | 3639.98 | + | 6304.62i | 0.0102129 | + | 0.0176893i | ||||
\(598\) | 397841. | + | 229693.i | 1.11252 | + | 0.642312i | ||||
\(599\) | 167042. | − | 289325.i | 0.465555 | − | 0.806365i | −0.533671 | − | 0.845692i | \(-0.679188\pi\) |
0.999226 | + | 0.0393269i | \(0.0125214\pi\) | |||||||
\(600\) | −43242.0 | + | 24965.8i | −0.120117 | + | 0.0693493i | ||||
\(601\) | 645072.i | 1.78591i | 0.450147 | + | 0.892955i | \(0.351372\pi\) | ||||
−0.450147 | + | 0.892955i | \(0.648628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 234215. | 0.644139 | ||||||||
\(604\) | −100747. | − | 174499.i | −0.276159 | − | 0.478321i | ||||
\(605\) | 129208. | + | 74598.1i | 0.353002 | + | 0.203806i | ||||
\(606\) | −115631. | + | 200278.i | −0.314867 | + | 0.545366i | ||||
\(607\) | −120643. | + | 69653.0i | −0.327433 | + | 0.189044i | −0.654701 | − | 0.755888i | \(-0.727205\pi\) |
0.327268 | + | 0.944932i | \(0.393872\pi\) | |||||||
\(608\) | 53353.1i | 0.144329i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 90962.0 | 0.244456 | ||||||||
\(611\) | −70246.8 | − | 121671.i | −0.188167 | − | 0.325915i | ||||
\(612\) | −42174.0 | − | 24349.1i | −0.112601 | − | 0.0650101i | ||||
\(613\) | 203665. | − | 352759.i | 0.541997 | − | 0.938765i | −0.456793 | − | 0.889573i | \(-0.651002\pi\) |
0.998789 | − | 0.0491924i | \(-0.0156647\pi\) | |||||||
\(614\) | −162611. | + | 93883.8i | −0.431335 | + | 0.249031i | ||||
\(615\) | − | 207218.i | − | 0.547870i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 276504. | 0.726325 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(618\) | 247.855 | + | 429.297i | 0.000648963 | + | 0.00112404i | ||||
\(619\) | −193904. | − | 111950.i | −0.506064 | − | 0.292176i | 0.225150 | − | 0.974324i | \(-0.427713\pi\) |
−0.731214 | + | 0.682148i | \(0.761046\pi\) | |||||||
\(620\) | −37745.5 | + | 65377.1i | −0.0981933 | + | 0.170076i | ||||
\(621\) | 86204.1 | − | 49770.0i | 0.223535 | − | 0.129058i | ||||
\(622\) | − | 270682.i | − | 0.699646i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −76127.9 | −0.195513 | ||||||||
\(625\) | −27573.7 | − | 47759.1i | −0.0705888 | − | 0.122263i | ||||
\(626\) | 117340. | + | 67746.5i | 0.299432 | + | 0.172877i | ||||
\(627\) | −49030.5 | + | 84923.3i | −0.124719 | + | 0.216019i | ||||
\(628\) | 165557. | − | 95584.2i | 0.419785 | − | 0.242363i | ||||
\(629\) | 187976.i | 0.475119i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 299528. | 0.752278 | 0.376139 | − | 0.926563i | \(-0.377251\pi\) | ||||
0.376139 | + | 0.926563i | \(0.377251\pi\) | |||||||
\(632\) | −73231.7 | − | 126841.i | −0.183343 | − | 0.317560i | ||||
\(633\) | 262042. | + | 151290.i | 0.653980 | + | 0.377575i | ||||
\(634\) | 48264.6 | − | 83596.7i | 0.120074 | − | 0.207975i | ||||
\(635\) | −29173.3 | + | 16843.2i | −0.0723500 | + | 0.0417713i | ||||
\(636\) | 47912.7i | 0.118450i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 134088. | 0.329418 | ||||||||
\(639\) | −4773.48 | − | 8267.92i | −0.0116905 | − | 0.0202486i | ||||
\(640\) | −17750.6 | − | 10248.3i | −0.0433363 | − | 0.0250202i | ||||
\(641\) | −288942. | + | 500462.i | −0.703226 | + | 1.21802i | 0.264102 | + | 0.964495i | \(0.414924\pi\) |
−0.967328 | + | 0.253528i | \(0.918409\pi\) | |||||||
\(642\) | 69322.2 | − | 40023.2i | 0.168191 | − | 0.0971050i | ||||
\(643\) | − | 135320.i | − | 0.327295i | −0.986519 | − | 0.163647i | \(-0.947674\pi\) | ||
0.986519 | − | 0.163647i | \(-0.0523259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 225516. | 0.542074 | ||||||||
\(646\) | −93974.4 | − | 162768.i | −0.225188 | − | 0.390037i | ||||
\(647\) | −188880. | − | 109050.i | −0.451209 | − | 0.260506i | 0.257132 | − | 0.966376i | \(-0.417223\pi\) |
−0.708341 | + | 0.705871i | \(0.750556\pi\) | |||||||
\(648\) | −8247.69 | + | 14285.4i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −193668. | + | 111814.i | −0.459800 | + | 0.265465i | ||||
\(650\) | − | 274970.i | − | 0.650816i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −340688. | −0.801422 | ||||||||
\(653\) | −72127.2 | − | 124928.i | −0.169150 | − | 0.292977i | 0.768971 | − | 0.639284i | \(-0.220769\pi\) |
−0.938121 | + | 0.346307i | \(0.887436\pi\) | |||||||
\(654\) | 212528. | + | 122703.i | 0.496890 | + | 0.286880i | ||||
\(655\) | 30711.8 | − | 53194.4i | 0.0715851 | − | 0.123989i | ||||
\(656\) | −156167. | + | 90163.3i | −0.362896 | + | 0.209518i | ||||
\(657\) | − | 109889.i | − | 0.254579i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −159392. | −0.367024 | −0.183512 | − | 0.983017i | \(-0.558747\pi\) | ||||
−0.183512 | + | 0.983017i | \(0.558747\pi\) | |||||||
\(660\) | −18836.0 | − | 32624.8i | −0.0432414 | − | 0.0748963i | ||||
\(661\) | −305674. | − | 176481.i | −0.699609 | − | 0.403919i | 0.107593 | − | 0.994195i | \(-0.465686\pi\) |
−0.807202 | + | 0.590276i | \(0.799019\pi\) | |||||||
\(662\) | −188494. | + | 326481.i | −0.430112 | + | 0.744975i | ||||
\(663\) | 232249. | − | 134089.i | 0.528357 | − | 0.305047i | ||||
\(664\) | − | 186129.i | − | 0.422161i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 63672.5 | 0.143550 | ||||||||
\(667\) | −262655. | − | 454932.i | −0.590384 | − | 1.02258i | ||||
\(668\) | 182602. | + | 105425.i | 0.409216 | + | 0.236261i | ||||
\(669\) | −158615. | + | 274729.i | −0.354398 | + | 0.613836i | ||||
\(670\) | −300741. | + | 173633.i | −0.669950 | + | 0.386796i | ||||
\(671\) | − | 145488.i | − | 0.323135i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 504858. | 1.11465 | 0.557326 | − | 0.830294i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830294i | \(0.311827\pi\) | |||||||
\(674\) | 70335.1 | + | 121824.i | 0.154829 | + | 0.268172i | ||||
\(675\) | −51598.2 | − | 29790.2i | −0.113247 | − | 0.0653832i | ||||
\(676\) | 95371.9 | − | 165189.i | 0.208702 | − | 0.361483i | ||||
\(677\) | 169486. | − | 97853.0i | 0.369792 | − | 0.213500i | −0.303576 | − | 0.952807i | \(-0.598180\pi\) |
0.673368 | + | 0.739308i | \(0.264847\pi\) | |||||||
\(678\) | − | 138969.i | − | 0.302314i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 72204.0 | 0.156150 | ||||||||
\(681\) | −64935.5 | − | 112472.i | −0.140019 | − | 0.242520i | ||||
\(682\) | 104567. | + | 60371.7i | 0.224815 | + | 0.129797i | ||||
\(683\) | 117221. | − | 203032.i | 0.251283 | − | 0.435235i | −0.712596 | − | 0.701574i | \(-0.752481\pi\) |
0.963879 | + | 0.266340i | \(0.0858142\pi\) | |||||||
\(684\) | −55134.0 | + | 31831.6i | −0.117844 | + | 0.0680372i | ||||
\(685\) | − | 435352.i | − | 0.927812i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 98357.4 | 0.208398 | ||||||||
\(688\) | −98125.0 | − | 169958.i | −0.207302 | − | 0.359057i | ||||
\(689\) | −228503. | − | 131926.i | −0.481341 | − | 0.277902i | ||||
\(690\) | −73792.9 | + | 127813.i | −0.154995 | + | 0.268459i | ||||
\(691\) | 77344.0 | − | 44654.6i | 0.161983 | − | 0.0935212i | −0.416817 | − | 0.908990i | \(-0.636854\pi\) |
0.578800 | + | 0.815469i | \(0.303521\pi\) | |||||||
\(692\) | − | 224153.i | − | 0.468094i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53088.3 | 0.110225 | ||||||||
\(695\) | 192394. | + | 333236.i | 0.398311 | + | 0.689895i | ||||
\(696\) | 75389.7 | + | 43526.3i | 0.155630 | + | 0.0898531i | ||||
\(697\) | 317621. | − | 550136.i | 0.653799 | − | 1.13241i | ||||
\(698\) | −11204.4 | + | 6468.85i | −0.0229973 | + | 0.0132775i | ||||
\(699\) | − | 34734.9i | − | 0.0710905i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 122213. | 0.248704 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(702\) | −45419.5 | − | 78669.0i | −0.0921655 | − | 0.159635i | ||||
\(703\) | 212818. | + | 122871.i | 0.430624 | + | 0.248621i | ||||
\(704\) | −16391.5 | + | 28391.0i | −0.0330731 | + | 0.0572842i | ||||
\(705\) | 39088.9 | − | 22568.0i | 0.0786457 | − | 0.0454061i | ||||
\(706\) | 172231.i | 0.345544i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −145184. | −0.289636 | ||||||||
\(709\) | −42009.9 | − | 72763.3i | −0.0835717 | − | 0.144750i | 0.821210 | − | 0.570626i | \(-0.193299\pi\) |
−0.904782 | + | 0.425876i | \(0.859966\pi\) | |||||||
\(710\) | 12258.7 | + | 7077.55i | 0.0243179 | + | 0.0140400i | ||||
\(711\) | 87383.1 | − | 151352.i | 0.172858 | − | 0.299398i | ||||
\(712\) | 304487. | − | 175795.i | 0.600632 | − | 0.346775i | ||||
\(713\) | − | 473032.i | − | 0.930489i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 207457. | 0.405804 | ||||||||
\(716\) | −101594. | − | 175966.i | −0.198172 | − | 0.343243i | ||||
\(717\) | −434074. | − | 250613.i | −0.844356 | − | 0.487489i | ||||
\(718\) | −328264. | + | 568570.i | −0.636759 | + | 1.10290i | ||||
\(719\) | −657416. | + | 379560.i | −1.27169 | + | 0.734213i | −0.975307 | − | 0.220855i | \(-0.929115\pi\) |
−0.296388 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(720\) | − | 24457.4i | − | 0.0471786i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 122898. | 0.235760 | ||||||||
\(723\) | −142115. | − | 246151.i | −0.271872 | − | 0.470896i | ||||
\(724\) | −305515. | − | 176389.i | −0.582847 | − | 0.336507i | ||||
\(725\) | −157214. | + | 272303.i | −0.299100 | + | 0.518057i | ||||
\(726\) | 134168. | − | 77461.9i | 0.254551 | − | 0.146965i | ||||
\(727\) | 92384.1i | 0.174795i | 0.996174 | + | 0.0873974i | \(0.0278550\pi\) | ||||
−0.996174 | + | 0.0873974i | \(0.972145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 81464.9 | + | 141101.i | 0.152871 | + | 0.264780i | ||||
\(731\) | 598715. | + | 345668.i | 1.12043 | + | 0.646882i | ||||
\(732\) | 47227.0 | − | 81799.6i | 0.0881391 | − | 0.152661i | ||||
\(733\) | −2903.50 | + | 1676.34i | −0.00540399 | + | 0.00312000i | −0.502700 | − | 0.864461i | \(-0.667660\pi\) |
0.497296 | + | 0.867581i | \(0.334326\pi\) | |||||||
\(734\) | − | 409324.i | − | 0.759757i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 128433. | 0.237094 | ||||||||
\(737\) | 277715. | + | 481017.i | 0.511287 | + | 0.885575i | ||||
\(738\) | −186346. | − | 107587.i | −0.342142 | − | 0.197536i | ||||
\(739\) | 13592.8 | − | 23543.4i | 0.0248897 | − | 0.0431103i | −0.853312 | − | 0.521400i | \(-0.825410\pi\) |
0.878202 | + | 0.478290i | \(0.158743\pi\) | |||||||
\(740\) | −81758.0 | + | 47203.0i | −0.149302 | + | 0.0861998i | ||||
\(741\) | − | 350589.i | − | 0.638502i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 773801. | 1.40169 | 0.700845 | − | 0.713314i | \(-0.252807\pi\) | ||||
0.700845 | + | 0.713314i | \(0.252807\pi\) | |||||||
\(744\) | 39194.6 | + | 67887.0i | 0.0708076 | + | 0.122642i | ||||
\(745\) | 71422.6 | + | 41235.9i | 0.128684 | + | 0.0742955i | ||||
\(746\) | 210553. | − | 364688.i | 0.378340 | − | 0.655305i | ||||
\(747\) | 192342. | − | 111049.i | 0.344693 | − | 0.199009i | ||||
\(748\) | − | 115486.i | − | 0.206408i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 218348. | 0.388174 | ||||||||
\(751\) | −98922.2 | − | 171338.i | −0.175394 | − | 0.303791i | 0.764904 | − | 0.644145i | \(-0.222786\pi\) |
−0.940297 | + | 0.340354i | \(0.889453\pi\) | |||||||
\(752\) | −34016.1 | − | 19639.2i | −0.0601519 | − | 0.0347287i | ||||
\(753\) | 280948. | − | 486617.i | 0.495492 | − | 0.858217i | ||||
\(754\) | −415167. | + | 239697.i | −0.730264 | + | 0.421618i | ||||
\(755\) | 356483.i | 0.625381i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −770706. | −1.34492 | −0.672461 | − | 0.740132i | \(-0.734763\pi\) | ||||
−0.672461 | + | 0.740132i | \(0.734763\pi\) | |||||||
\(758\) | −198934. | − | 344564.i | −0.346234 | − | 0.599696i | ||||
\(759\) | 204430. | + | 118027.i | 0.354863 | + | 0.204880i | ||||
\(760\) | 47196.1 | − | 81746.0i | 0.0817107 | − | 0.141527i | ||||
\(761\) | 131757. | − | 76069.9i | 0.227512 | − | 0.131354i | −0.381912 | − | 0.924199i | \(-0.624734\pi\) |
0.609424 | + | 0.792845i | \(0.291401\pi\) | |||||||
\(762\) | 34979.7i | 0.0602429i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −516473. | −0.884832 | ||||||||
\(765\) | 43078.4 | + | 74614.0i | 0.0736100 | + | 0.127496i | ||||
\(766\) | 71824.8 | + | 41468.0i | 0.122410 | + | 0.0706734i | ||||
\(767\) | 399760. | − | 692405.i | 0.679531 | − | 1.17698i | ||||
\(768\) | −18432.0 | + | 10641.7i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 961897.i | − | 1.62658i | −0.581857 | − | 0.813291i | \(-0.697674\pi\) | ||
0.581857 | − | 0.813291i | \(-0.302326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −186470. | −0.313689 | ||||||||
\(772\) | −146698. | − | 254089.i | −0.246145 | − | 0.426335i | ||||
\(773\) | 130829. | + | 75534.4i | 0.218951 | + | 0.126411i | 0.605464 | − | 0.795872i | \(-0.292987\pi\) |
−0.386514 | + | 0.922284i | \(0.626321\pi\) | |||||||
\(774\) | 117087. | − | 202801.i | 0.195446 | − | 0.338522i | ||||
\(775\) | −245204. | + | 141569.i | −0.408248 | + | 0.235702i | ||||
\(776\) | 35267.3i | 0.0585664i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 374540. | 0.618783 | ||||||||
\(779\) | −415226. | − | 719192.i | −0.684242 | − | 1.18514i | ||||
\(780\) | 116641. | + | 67342.7i | 0.191717 | + | 0.110688i | ||||
\(781\) | 11320.1 | − | 19607.0i | 0.0185588 | − | 0.0321447i | ||||
\(782\) | −391821. | + | 226218.i | −0.640728 | + | 0.369924i | ||||
\(783\) | 103875.i | 0.169429i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −338215. | −0.548849 | ||||||||
\(786\) | −31890.8 | − | 55236.5i | −0.0516203 | − | 0.0894090i | ||||
\(787\) | 172244. | + | 99445.4i | 0.278097 | + | 0.160559i | 0.632561 | − | 0.774510i | \(-0.282004\pi\) |
−0.354465 | + | 0.935069i | \(0.615337\pi\) | |||||||
\(788\) | 292588. | − | 506777.i | 0.471199 | − | 0.816140i | ||||
\(789\) | 294442. | − | 169996.i | 0.472984 | − | 0.273077i | ||||
\(790\) | 259123.i | 0.415194i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −39118.2 | −0.0623632 | ||||||||
\(793\) | 260076. | + | 450465.i | 0.413575 | + | 0.716333i | ||||
\(794\) | 83840.2 | + | 48405.1i | 0.132988 | + | 0.0767804i | ||||
\(795\) | 42383.5 | − | 73410.4i | 0.0670599 | − | 0.116151i | ||||
\(796\) | −9706.60 | + | 5604.11i | −0.0153194 | + | 0.00884465i | ||||
\(797\) | 990756.i | 1.55973i | 0.625947 | + | 0.779866i | \(0.284713\pi\) | ||||
−0.625947 | + | 0.779866i | \(0.715287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 138368. | 0.216741 | ||||||||
\(800\) | −38437.3 | − | 66575.4i | −0.0600583 | − | 0.104024i | ||||
\(801\) | 363326. | + | 209767.i | 0.566281 | + | 0.326943i | ||||
\(802\) | 253259. | − | 438657.i | 0.393746 | − | 0.681988i | ||||
\(803\) | 225683. | − | 130298.i | 0.350000 | − | 0.202073i | ||||
\(804\) | 360597.i | 0.557840i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −431684. | −0.664501 | ||||||||
\(807\) | 179816. | + | 311451.i | 0.276110 | + | 0.478236i | ||||
\(808\) | −308348. | − | 178025.i | −0.472301 | − | 0.272683i | ||||
\(809\) | 46144.3 | − | 79924.3i | 0.0705052 | − | 0.122119i | −0.828618 | − | 0.559815i | \(-0.810872\pi\) |
0.899123 | + | 0.437696i | \(0.144206\pi\) | |||||||
\(810\) | 25273.7 | − | 14591.8i | 0.0385212 | − | 0.0222402i | ||||
\(811\) | 617125.i | 0.938277i | 0.883125 | + | 0.469139i | \(0.155436\pi\) | ||||
−0.883125 | + | 0.469139i | \(0.844564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34037.6 | −0.0514966 | ||||||||
\(814\) | 75498.5 | + | 130767.i | 0.113943 | + | 0.197356i | ||||
\(815\) | 521991. | + | 301372.i | 0.785865 | + | 0.453719i | ||||
\(816\) | 37488.0 | − | 64931.0i | 0.0563004 | − | 0.0975152i | ||||
\(817\) | 782700. | − | 451892.i | 1.17260 | − | 0.677003i | ||||
\(818\) | 140762.i | 0.210367i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 319033. | 0.474469 | ||||||||
\(821\) | −153533. | − | 265927.i | −0.227780 | − | 0.394526i | 0.729370 | − | 0.684119i | \(-0.239813\pi\) |
−0.957150 | + | 0.289593i | \(0.906480\pi\) | |||||||
\(822\) | −391500. | − | 226033.i | −0.579413 | − | 0.334524i | ||||
\(823\) | −423429. | + | 733401.i | −0.625146 | + | 1.08278i | 0.363367 | + | 0.931646i | \(0.381627\pi\) |
−0.988513 | + | 0.151138i | \(0.951706\pi\) | |||||||
\(824\) | −660.946 | + | 381.597i | −0.000973445 | + | 0.000562019i | ||||
\(825\) | − | 141293.i | − | 0.207592i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 294059. | 0.429956 | 0.214978 | − | 0.976619i | \(-0.431032\pi\) | ||||
0.214978 | + | 0.976619i | \(0.431032\pi\) | |||||||
\(828\) | 76625.9 | + | 132720.i | 0.111767 | + | 0.193587i | ||||
\(829\) | −895803. | − | 517192.i | −1.30348 | − | 0.752563i | −0.322479 | − | 0.946577i | \(-0.604516\pi\) |
−0.980999 | + | 0.194013i | \(0.937849\pi\) | |||||||
\(830\) | −164650. | + | 285182.i | −0.239004 | + | 0.413967i | ||||
\(831\) | −355964. | + | 205516.i | −0.515471 | + | 0.297608i | ||||
\(832\) | − | 117207.i | − | 0.169319i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 399560. | 0.574447 | ||||||||
\(835\) | −186518. | − | 323059.i | −0.267515 | − | 0.463349i | ||||
\(836\) | −130748. | − | 75487.4i | −0.187078 | − | 0.108009i | ||||
\(837\) | −46768.6 | + | 81005.6i | −0.0667580 | + | 0.115628i | ||||
\(838\) | −107658. | + | 62156.4i | −0.153306 | + | 0.0885111i | ||||
\(839\) | − | 307258.i | − | 0.436495i | −0.975893 | − | 0.218248i | \(-0.929966\pi\) | ||
0.975893 | − | 0.218248i | \(-0.0700340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −159093. | −0.224937 | ||||||||
\(842\) | 308662. | + | 534618.i | 0.435370 | + | 0.754084i | ||||
\(843\) | 154634. | + | 89278.1i | 0.217596 | + | 0.125629i | ||||
\(844\) | −232927. | + | 403441.i | −0.326990 | + | 0.566363i | ||||
\(845\) | −292252. | + | 168732.i | −0.409302 | + | 0.236311i | ||||
\(846\) | − | 46868.7i | − | 0.0654851i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −73766.4 | −0.102581 | ||||||||
\(849\) | −238795. | − | 413605.i | −0.331291 | − | 0.573813i | ||||
\(850\) | 234527. | + | 135404.i | 0.324605 | + | 0.187411i | ||||
\(851\) | 295777. | − | 512302.i | 0.408419 | − | 0.707402i | ||||
\(852\) | 12729.3 | − | 7349.26i | 0.0175358 | − | 0.0101243i | ||||
\(853\) | − | 70737.4i | − | 0.0972190i | −0.998818 | − | 0.0486095i | \(-0.984521\pi\) | ||
0.998818 | − | 0.0486095i | \(-0.0154790\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 112633. | 0.154075 | ||||||||
\(856\) | 61619.7 | + | 106728.i | 0.0840954 | + | 0.145657i | ||||
\(857\) | −285670. | − | 164932.i | −0.388958 | − | 0.224565i | 0.292751 | − | 0.956189i | \(-0.405429\pi\) |
−0.681709 | + | 0.731624i | \(0.738763\pi\) | |||||||
\(858\) | 107711. | − | 186560.i | 0.146313 | − | 0.253422i | ||||
\(859\) | 60589.3 | − | 34981.2i | 0.0821125 | − | 0.0474077i | −0.458382 | − | 0.888756i | \(-0.651571\pi\) |
0.540494 | + | 0.841348i | \(0.318237\pi\) | |||||||
\(860\) | 347205.i | 0.469450i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −217052. | −0.292113 | ||||||||
\(863\) | 386112. | + | 668765.i | 0.518431 | + | 0.897949i | 0.999771 | + | 0.0214151i | \(0.00681715\pi\) |
−0.481339 | + | 0.876534i | \(0.659850\pi\) | |||||||
\(864\) | −21993.8 | − | 12698.2i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | −198286. | + | 343441.i | −0.265008 | + | 0.459008i | ||||
\(866\) | 530836. | − | 306478.i | 0.707823 | − | 0.408662i | ||||
\(867\) | − | 169868.i | − | 0.225981i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 414451. | 0.548825 | ||||||||
\(870\) | −77006.6 | − | 133379.i | −0.101739 | − | 0.176218i | ||||
\(871\) | −1.71974e6 | − | 992893.i | −2.26687 | − | 1.30878i | ||||
\(872\) | −188914. | + | 327208.i | −0.248445 | + | 0.430320i | ||||
\(873\) | −36444.4 | + | 21041.2i | −0.0478193 | + | 0.0276085i | ||||
\(874\) | 591468.i | 0.774299i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 169185. | 0.220472 | ||||||||
\(877\) | −121260. | − | 210028.i | −0.157659 | − | 0.273073i | 0.776365 | − | 0.630283i | \(-0.217061\pi\) |
−0.934024 | + | 0.357211i | \(0.883728\pi\) | |||||||
\(878\) | 58204.9 | + | 33604.6i | 0.0755042 | + | 0.0435923i | ||||
\(879\) | −60322.5 | + | 104482.i | −0.0780732 | + | 0.135227i | ||||
\(880\) | 50229.2 | − | 28999.9i | 0.0648621 | − | 0.0374482i | ||||
\(881\) | − | 646528.i | − | 0.832982i | −0.909140 | − | 0.416491i | \(-0.863260\pi\) | ||
0.909140 | − | 0.416491i | \(-0.136740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −461877. | −0.592387 | −0.296193 | − | 0.955128i | \(-0.595717\pi\) | ||||
−0.296193 | + | 0.955128i | \(0.595717\pi\) | |||||||
\(884\) | 206444. | + | 357571.i | 0.264179 | + | 0.457571i | ||||
\(885\) | 222447. | + | 128430.i | 0.284014 | + | 0.163976i | ||||
\(886\) | −247296. | + | 428329.i | −0.315028 | + | 0.545645i | ||||
\(887\) | 186391. | − | 107613.i | 0.236907 | − | 0.136778i | −0.376847 | − | 0.926275i | \(-0.622992\pi\) |
0.613754 | + | 0.789497i | \(0.289658\pi\) | |||||||
\(888\) | 98030.3i | 0.124318i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −622034. | −0.785297 | ||||||||
\(891\) | −23338.7 | − | 40423.9i | −0.0293983 | − | 0.0509193i | ||||
\(892\) | −422973. | − | 244204.i | −0.531598 | − | 0.306918i | ||||
\(893\) | 90443.9 | − | 156653.i | 0.113417 | − | 0.196443i | ||||
\(894\) | 74164.6 | − | 42818.9i | 0.0927943 | − | 0.0535748i | ||||
\(895\) | 359479.i | 0.448774i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −843948. | −1.04889 | ||||||||
\(898\) | 275990. | + | 478029.i | 0.342248 | + | 0.592791i | ||||
\(899\) | 427498. | + | 246816.i | 0.528950 | + | 0.305389i | ||||
\(900\) | 45865.0 | − | 79440.6i | 0.0566235 | − | 0.0980748i | ||||
\(901\) | 225045. | − | 129930.i | 0.277217 | − | 0.160051i | ||||
\(902\) | − | 510275.i | − | 0.627179i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 213957. | 0.261812 | ||||||||
\(905\) | 312067. | + | 540516.i | 0.381022 | + | 0.659950i | ||||
\(906\) | 320575. | + | 185084.i | 0.390547 | + | 0.225483i | ||||
\(907\) | −549134. | + | 951128.i | −0.667519 | + | 1.15618i | 0.311076 | + | 0.950385i | \(0.399311\pi\) |
−0.978596 | + | 0.205793i | \(0.934023\pi\) | |||||||
\(908\) | 173161. | − | 99974.7i | 0.210029 | − | 0.121260i | ||||
\(909\) | − | 424854.i | − | 0.514176i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32312e6 | −1.59427 | −0.797133 | − | 0.603803i | \(-0.793651\pi\) | ||||
−0.797133 | + | 0.603803i | \(0.793651\pi\) | |||||||
\(912\) | −49008.0 | − | 84884.3i | −0.0589219 | − | 0.102056i | ||||
\(913\) | 456131. | + | 263348.i | 0.547203 | + | 0.315928i | ||||
\(914\) | −82692.2 | + | 143227.i | −0.0989857 | + | 0.171448i | ||||
\(915\) | −144720. | + | 83553.9i | −0.172856 | + | 0.0997987i | ||||
\(916\) | 151431.i | 0.180478i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 89464.5 | 0.106161 | ||||||||
\(919\) | −258264. | − | 447326.i | −0.305797 | − | 0.529656i | 0.671642 | − | 0.740876i | \(-0.265589\pi\) |
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(920\) | −196781. | − | 113612.i | −0.232492 | − | 0.134229i | ||||
\(921\) | 172476. | − | 298736.i | 0.203333 | − | 0.352183i | ||||
\(922\) | 752588. | − | 434507.i | 0.885310 | − | 0.511134i | ||||
\(923\) | 80943.8i | 0.0950124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −354080. | −0.413826 | ||||||||
\(926\) | 25133.7 | + | 43532.9i | 0.0293113 | + | 0.0507687i | ||||
\(927\) | −788.669 | − | 455.338i | −0.000917773 | − | 0.000529876i | ||||
\(928\) | −67013.1 | + | 116070.i | −0.0778151 | + | 0.134780i | ||||
\(929\) | −1.07335e6 | + | 619697.i | −1.24368 | + | 0.718039i | −0.969841 | − | 0.243737i | \(-0.921627\pi\) |
−0.273838 | + | 0.961776i | \(0.588293\pi\) | |||||||
\(930\) | − | 138686.i | − | 0.160349i | ||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 53477.9 | 0.0615662 | ||||||||
\(933\) | 248637. | + | 430652.i | 0.285629 | + | 0.494724i | ||||
\(934\) | 159131. | + | 91874.5i | 0.182415 | + | 0.105318i | ||||
\(935\) | −102159. | + | 176944.i | −0.116856 | + | 0.202401i | ||||
\(936\) | 121119. | − | 69928.0i | 0.138248 | − | 0.0798177i | ||||
\(937\) | 1.15260e6i | 1.31281i | 0.754411 | + | 0.656403i | \(0.227923\pi\) | ||||
−0.754411 | + | 0.656403i | \(0.772077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −248917. | −0.282308 | ||||||||
\(940\) | 34745.7 | + | 60181.3i | 0.0393228 | + | 0.0681092i | ||||
\(941\) | −93104.2 | − | 53753.7i | −0.105145 | − | 0.0607057i | 0.446505 | − | 0.894781i | \(-0.352668\pi\) |
−0.551650 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(942\) | −175599. | + | 304147.i | −0.197889 | + | 0.342753i | ||||
\(943\) | −1.73126e6 | + | 999543.i | −1.94688 | + | 1.12403i | ||||
\(944\) | − | 223526.i | − | 0.250832i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 555334. | 0.620543 | ||||||||
\(947\) | 206307. | + | 357335.i | 0.230046 | + | 0.398451i | 0.957821 | − | 0.287364i | \(-0.0927790\pi\) |
−0.727775 | + | 0.685815i | \(0.759446\pi\) | |||||||
\(948\) | 233022. | + | 134535.i | 0.259286 | + | 0.149699i | ||||
\(949\) | −465845. | + | 806867.i | −0.517260 | + | 0.895920i | ||||
\(950\) | 306597. | − | 177014.i | 0.339720 | − | 0.196137i | ||||
\(951\) | 177335.i | 0.196080i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.43052e6 | 1.57510 | 0.787550 | − | 0.616251i | \(-0.211349\pi\) | ||||
0.787550 | + | 0.616251i | \(0.211349\pi\) | |||||||
\(954\) | −44010.6 | − | 76228.6i | −0.0483572 | − | 0.0837571i | ||||
\(955\) | 791324. | + | 456871.i | 0.867656 | + | 0.500942i | ||||
\(956\) | 385844. | − | 668301.i | 0.422178 | − | 0.731234i | ||||
\(957\) | −213332. | + | 123168.i | −0.232934 | + | 0.134485i | ||||
\(958\) | 596619.i | 0.650079i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 37654.6 | 0.0408579 | ||||||||
\(961\) | −239507. | − | 414839.i | −0.259342 | − | 0.449193i | ||||
\(962\) | −467521. | − | 269923.i | −0.505186 | − | 0.291669i | ||||
\(963\) | −73527.3 | + | 127353.i | −0.0792859 | + | 0.137327i | ||||
\(964\) | 378974. | − | 218801.i | 0.407808 | − | 0.235448i | ||||
\(965\) | 519077.i | 0.557413i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −344533. | −0.368449 | −0.184225 | − | 0.982884i | \(-0.558977\pi\) | ||||
−0.184225 | + | 0.982884i | \(0.558977\pi\) | |||||||
\(968\) | 119260. | + | 206565.i | 0.127276 | + | 0.220448i | ||||
\(969\) | 299025. | + | 172642.i | 0.318463 | + | 0.183865i | ||||
\(970\) | 31197.4 | − | 54035.5i | 0.0331570 | − | 0.0574296i | ||||
\(971\) | 1.25848e6 | − | 726581.i | 1.33477 | − | 0.770630i | 0.348744 | − | 0.937218i | \(-0.386608\pi\) |
0.986027 | + | 0.166588i | \(0.0532751\pi\) | |||||||
\(972\) | − | 30304.0i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −647393. | −0.682417 | ||||||||
\(975\) | 252576. | + | 437474.i | 0.265695 | + | 0.460196i | ||||
\(976\) | 125939. | + | 72710.8i | 0.132209 | + | 0.0763307i | ||||
\(977\) | −772853. | + | 1.33862e6i | −0.809669 | + | 1.40239i | 0.103424 | + | 0.994637i | \(0.467020\pi\) |
−0.913093 | + | 0.407751i | \(0.866313\pi\) | |||||||
\(978\) | 542031. | − | 312941.i | 0.566691 | − | 0.327179i | ||||
\(979\) | 994907.i | 1.03805i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −450840. | −0.468473 | ||||||||
\(982\) | −198485. | − | 343786.i | −0.205828 | − | 0.356504i | ||||
\(983\) | −116280. | − | 67134.0i | −0.120336 | − | 0.0694761i | 0.438624 | − | 0.898671i | \(-0.355466\pi\) |
−0.558960 | + | 0.829195i | \(0.688799\pi\) | |||||||
\(984\) | 165641. | − | 286898.i | 0.171071 | − | 0.296304i | ||||
\(985\) | −896589. | + | 517646.i | −0.924105 | + | 0.533532i | ||||
\(986\) | − | 472139.i | − | 0.485641i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 539768. | 0.552959 | ||||||||
\(989\) | −1.08781e6 | − | 1.88414e6i | −1.11214 | − | 1.92628i | ||||
\(990\) | 59935.7 | + | 34603.9i | 0.0611526 | + | 0.0353065i | ||||
\(991\) | 395596. | − | 685192.i | 0.402814 | − | 0.697694i | −0.591251 | − | 0.806488i | \(-0.701366\pi\) |
0.994064 | + | 0.108794i | \(0.0346990\pi\) | |||||||
\(992\) | −104519. | + | 60344.0i | −0.106211 | + | 0.0613212i | ||||
\(993\) | − | 692571.i | − | 0.702369i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19829.5 | 0.0200293 | ||||||||
\(996\) | 170971. | + | 296130.i | 0.172347 | + | 0.298513i | ||||
\(997\) | −582624. | − | 336378.i | −0.586136 | − | 0.338406i | 0.177432 | − | 0.984133i | \(-0.443221\pi\) |
−0.763568 | + | 0.645727i | \(0.776554\pi\) | |||||||
\(998\) | 488366. | − | 845874.i | 0.490325 | − | 0.849268i | ||||
\(999\) | −101302. | + | 58487.0i | −0.101505 | + | 0.0586041i |
(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 | 294.5.g.c.31.1 | 4 | ||
7.2 | even | 3 | 42.5.g.a.19.1 | ✓ | 4 | ||
7.3 | odd | 6 | 294.5.c.a.97.4 | 4 | |||
7.4 | even | 3 | 294.5.c.a.97.3 | 4 | |||
7.5 | odd | 6 | inner | 294.5.g.c.19.1 | 4 | ||
7.6 | odd | 2 | 42.5.g.a.31.1 | yes | 4 | ||
21.2 | odd | 6 | 126.5.n.b.19.2 | 4 | |||
21.11 | odd | 6 | 882.5.c.a.685.1 | 4 | |||
21.17 | even | 6 | 882.5.c.a.685.2 | 4 | |||
21.20 | even | 2 | 126.5.n.b.73.2 | 4 | |||
28.23 | odd | 6 | 336.5.bh.d.145.2 | 4 | |||
28.27 | even | 2 | 336.5.bh.d.241.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.5.g.a.19.1 | ✓ | 4 | 7.2 | even | 3 | ||
42.5.g.a.31.1 | yes | 4 | 7.6 | odd | 2 | ||
126.5.n.b.19.2 | 4 | 21.2 | odd | 6 | |||
126.5.n.b.73.2 | 4 | 21.20 | even | 2 | |||
294.5.c.a.97.3 | 4 | 7.4 | even | 3 | |||
294.5.c.a.97.4 | 4 | 7.3 | odd | 6 | |||
294.5.g.c.19.1 | 4 | 7.5 | odd | 6 | inner | ||
294.5.g.c.31.1 | 4 | 1.1 | even | 1 | trivial | ||
336.5.bh.d.145.2 | 4 | 28.23 | odd | 6 | |||
336.5.bh.d.241.2 | 4 | 28.27 | even | 2 | |||
882.5.c.a.685.1 | 4 | 21.11 | odd | 6 | |||
882.5.c.a.685.2 | 4 | 21.17 | even | 6 |