Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,5,Mod(34,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.34");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.g (of order \(4\), degree \(2\), 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: | \(6.71904760045\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 34.10 | ||
Character | \(\chi\) | \(=\) | 65.34 |
Dual form | 65.5.g.a.44.10 |
$q$-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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96266 | + | 1.96266i | −0.490664 | + | 0.490664i | −0.908515 | − | 0.417852i | \(-0.862783\pi\) |
0.417852 | + | 0.908515i | \(0.362783\pi\) | |||||||
\(3\) | 11.7087i | 1.30097i | 0.759520 | + | 0.650484i | \(0.225434\pi\) | ||||
−0.759520 | + | 0.650484i | \(0.774566\pi\) | |||||||
\(4\) | 8.29597i | 0.518498i | ||||||||
\(5\) | −20.0793 | + | 14.8937i | −0.803172 | + | 0.595747i | ||||
\(6\) | −22.9802 | − | 22.9802i | −0.638338 | − | 0.638338i | ||||
\(7\) | 49.2380 | + | 49.2380i | 1.00486 | + | 1.00486i | 0.999988 | + | 0.00486952i | \(0.00155002\pi\) |
0.00486952 | + | 0.999988i | \(0.498450\pi\) | |||||||
\(8\) | −47.6846 | − | 47.6846i | −0.745072 | − | 0.745072i | ||||
\(9\) | −56.0939 | −0.692517 | ||||||||
\(10\) | 10.1776 | − | 68.6399i | 0.101776 | − | 0.686399i | ||||
\(11\) | 36.9838 | − | 36.9838i | 0.305652 | − | 0.305652i | −0.537569 | − | 0.843220i | \(-0.680657\pi\) |
0.843220 | + | 0.537569i | \(0.180657\pi\) | |||||||
\(12\) | −97.1351 | −0.674549 | ||||||||
\(13\) | 167.514 | − | 22.3654i | 0.991204 | − | 0.132339i | ||||
\(14\) | −193.275 | −0.986095 | ||||||||
\(15\) | −174.386 | − | 235.103i | −0.775048 | − | 1.04490i | ||||
\(16\) | 54.4414 | 0.212662 | ||||||||
\(17\) | 2.83570 | 0.00981212 | 0.00490606 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490606 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(18\) | 110.093 | − | 110.093i | 0.339793 | − | 0.339793i | ||||
\(19\) | −74.4440 | − | 74.4440i | −0.206216 | − | 0.206216i | 0.596441 | − | 0.802657i | \(-0.296581\pi\) |
−0.802657 | + | 0.596441i | \(0.796581\pi\) | |||||||
\(20\) | −123.558 | − | 166.577i | −0.308894 | − | 0.416443i | ||||
\(21\) | −576.514 | + | 576.514i | −1.30729 | + | 1.30729i | ||||
\(22\) | 145.173i | 0.299944i | ||||||||
\(23\) | −858.183 | −1.62227 | −0.811137 | − | 0.584856i | \(-0.801151\pi\) | ||||
−0.811137 | + | 0.584856i | \(0.801151\pi\) | |||||||
\(24\) | 558.325 | − | 558.325i | 0.969315 | − | 0.969315i | ||||
\(25\) | 181.357 | − | 598.109i | 0.290171 | − | 0.956975i | ||||
\(26\) | −284.876 | + | 372.667i | −0.421414 | + | 0.551282i | ||||
\(27\) | 291.618i | 0.400025i | ||||||||
\(28\) | −408.477 | + | 408.477i | −0.521017 | + | 0.521017i | ||||
\(29\) | 1280.13 | 1.52215 | 0.761076 | − | 0.648663i | \(-0.224671\pi\) | ||||
0.761076 | + | 0.648663i | \(0.224671\pi\) | |||||||
\(30\) | 803.685 | + | 119.166i | 0.892983 | + | 0.132407i | ||||
\(31\) | 975.637 | + | 975.637i | 1.01523 | + | 1.01523i | 0.999882 | + | 0.0153483i | \(0.00488572\pi\) |
0.0153483 | + | 0.999882i | \(0.495114\pi\) | |||||||
\(32\) | 656.104 | − | 656.104i | 0.640727 | − | 0.640727i | ||||
\(33\) | 433.033 | + | 433.033i | 0.397643 | + | 0.397643i | ||||
\(34\) | −5.56551 | + | 5.56551i | −0.00481445 | + | 0.00481445i | ||||
\(35\) | −1722.00 | − | 255.330i | −1.40571 | − | 0.208432i | ||||
\(36\) | − | 465.353i | − | 0.359069i | ||||||
\(37\) | 573.577 | + | 573.577i | 0.418975 | + | 0.418975i | 0.884850 | − | 0.465875i | \(-0.154260\pi\) |
−0.465875 | + | 0.884850i | \(0.654260\pi\) | |||||||
\(38\) | 292.216 | 0.202366 | ||||||||
\(39\) | 261.869 | + | 1961.37i | 0.172169 | + | 1.28953i | ||||
\(40\) | 1667.67 | + | 247.274i | 1.04230 | + | 0.154546i | ||||
\(41\) | 276.665 | + | 276.665i | 0.164584 | + | 0.164584i | 0.784594 | − | 0.620010i | \(-0.212872\pi\) |
−0.620010 | + | 0.784594i | \(0.712872\pi\) | |||||||
\(42\) | − | 2263.00i | − | 1.28288i | ||||||
\(43\) | −3340.52 | −1.80666 | −0.903332 | − | 0.428942i | \(-0.858887\pi\) | ||||
−0.903332 | + | 0.428942i | \(0.858887\pi\) | |||||||
\(44\) | 306.817 | + | 306.817i | 0.158480 | + | 0.158480i | ||||
\(45\) | 1126.33 | − | 835.445i | 0.556211 | − | 0.412565i | ||||
\(46\) | 1684.32 | − | 1684.32i | 0.795991 | − | 0.795991i | ||||
\(47\) | 345.914 | + | 345.914i | 0.156593 | + | 0.156593i | 0.781055 | − | 0.624462i | \(-0.214682\pi\) |
−0.624462 | + | 0.781055i | \(0.714682\pi\) | |||||||
\(48\) | 637.439i | 0.276666i | ||||||||
\(49\) | 2447.77i | 1.01948i | ||||||||
\(50\) | 817.942 | + | 1529.82i | 0.327177 | + | 0.611929i | ||||
\(51\) | 33.2024i | 0.0127652i | ||||||||
\(52\) | 185.542 | + | 1389.69i | 0.0686177 | + | 0.513938i | ||||
\(53\) | − | 1606.43i | − | 0.571888i | −0.958246 | − | 0.285944i | \(-0.907693\pi\) | ||
0.958246 | − | 0.285944i | \(-0.0923071\pi\) | |||||||
\(54\) | −572.346 | − | 572.346i | −0.196278 | − | 0.196278i | ||||
\(55\) | −191.784 | + | 1293.43i | −0.0633997 | + | 0.427582i | ||||
\(56\) | − | 4695.79i | − | 1.49738i | ||||||
\(57\) | 871.644 | − | 871.644i | 0.268281 | − | 0.268281i | ||||
\(58\) | −2512.45 | + | 2512.45i | −0.746865 | + | 0.746865i | ||||
\(59\) | −641.576 | + | 641.576i | −0.184308 | + | 0.184308i | −0.793230 | − | 0.608922i | \(-0.791602\pi\) |
0.608922 | + | 0.793230i | \(0.291602\pi\) | |||||||
\(60\) | 1950.40 | − | 1446.70i | 0.541779 | − | 0.401861i | ||||
\(61\) | −5200.73 | −1.39767 | −0.698836 | − | 0.715282i | \(-0.746298\pi\) | ||||
−0.698836 | + | 0.715282i | \(0.746298\pi\) | |||||||
\(62\) | −3829.68 | −0.996274 | ||||||||
\(63\) | −2761.95 | − | 2761.95i | −0.695881 | − | 0.695881i | ||||
\(64\) | 3446.47i | 0.841424i | ||||||||
\(65\) | −3030.45 | + | 2943.97i | −0.717267 | + | 0.696799i | ||||
\(66\) | −1699.79 | −0.390218 | ||||||||
\(67\) | 2958.39 | − | 2958.39i | 0.659031 | − | 0.659031i | −0.296119 | − | 0.955151i | \(-0.595693\pi\) |
0.955151 | + | 0.296119i | \(0.0956926\pi\) | |||||||
\(68\) | 23.5249i | 0.00508756i | ||||||||
\(69\) | − | 10048.2i | − | 2.11053i | ||||||
\(70\) | 3880.82 | − | 2878.57i | 0.792004 | − | 0.587463i | ||||
\(71\) | −1343.74 | − | 1343.74i | −0.266562 | − | 0.266562i | 0.561151 | − | 0.827713i | \(-0.310359\pi\) |
−0.827713 | + | 0.561151i | \(0.810359\pi\) | |||||||
\(72\) | 2674.82 | + | 2674.82i | 0.515975 | + | 0.515975i | ||||
\(73\) | 1183.61 | + | 1183.61i | 0.222107 | + | 0.222107i | 0.809385 | − | 0.587278i | \(-0.199800\pi\) |
−0.587278 | + | 0.809385i | \(0.699800\pi\) | |||||||
\(74\) | −2251.47 | −0.411152 | ||||||||
\(75\) | 7003.09 | + | 2123.45i | 1.24499 | + | 0.377503i | ||||
\(76\) | 617.585 | − | 617.585i | 0.106923 | − | 0.106923i | ||||
\(77\) | 3642.02 | 0.614273 | ||||||||
\(78\) | −4363.45 | − | 3335.53i | −0.717201 | − | 0.548246i | ||||
\(79\) | 2812.08 | 0.450581 | 0.225291 | − | 0.974292i | \(-0.427667\pi\) | ||||
0.225291 | + | 0.974292i | \(0.427667\pi\) | |||||||
\(80\) | −1093.15 | + | 810.833i | −0.170804 | + | 0.126693i | ||||
\(81\) | −7958.08 | −1.21294 | ||||||||
\(82\) | −1086.00 | −0.161511 | ||||||||
\(83\) | −7138.41 | + | 7138.41i | −1.03620 | + | 1.03620i | −0.0368852 | + | 0.999320i | \(0.511744\pi\) |
−0.999320 | + | 0.0368852i | \(0.988256\pi\) | |||||||
\(84\) | −4782.74 | − | 4782.74i | −0.677826 | − | 0.677826i | ||||
\(85\) | −56.9389 | + | 42.2340i | −0.00788082 | + | 0.00584554i | ||||
\(86\) | 6556.29 | − | 6556.29i | 0.886465 | − | 0.886465i | ||||
\(87\) | 14988.7i | 1.98027i | ||||||||
\(88\) | −3527.12 | −0.455465 | ||||||||
\(89\) | −1031.96 | + | 1031.96i | −0.130282 | + | 0.130282i | −0.769241 | − | 0.638959i | \(-0.779365\pi\) |
0.638959 | + | 0.769241i | \(0.279365\pi\) | |||||||
\(90\) | −570.901 | + | 3850.28i | −0.0704815 | + | 0.475343i | ||||
\(91\) | 9349.26 | + | 7146.81i | 1.12900 | + | 0.863037i | ||||
\(92\) | − | 7119.46i | − | 0.841146i | ||||||
\(93\) | −11423.4 | + | 11423.4i | −1.32078 | + | 1.32078i | ||||
\(94\) | −1357.82 | −0.153669 | ||||||||
\(95\) | 2603.53 | + | 386.039i | 0.288480 | + | 0.0427744i | ||||
\(96\) | 7682.13 | + | 7682.13i | 0.833565 | + | 0.833565i | ||||
\(97\) | 8066.83 | − | 8066.83i | 0.857353 | − | 0.857353i | −0.133673 | − | 0.991026i | \(-0.542677\pi\) |
0.991026 | + | 0.133673i | \(0.0426770\pi\) | |||||||
\(98\) | −4804.12 | − | 4804.12i | −0.500221 | − | 0.500221i | ||||
\(99\) | −2074.57 | + | 2074.57i | −0.211669 | + | 0.211669i | ||||
\(100\) | 4961.90 | + | 1504.53i | 0.496190 | + | 0.150453i | ||||
\(101\) | − | 3934.27i | − | 0.385675i | −0.981231 | − | 0.192838i | \(-0.938231\pi\) | ||
0.981231 | − | 0.192838i | \(-0.0617691\pi\) | |||||||
\(102\) | −65.1649 | − | 65.1649i | −0.00626345 | − | 0.00626345i | ||||
\(103\) | 15584.3 | 1.46897 | 0.734485 | − | 0.678625i | \(-0.237424\pi\) | ||||
0.734485 | + | 0.678625i | \(0.237424\pi\) | |||||||
\(104\) | −9054.30 | − | 6921.34i | −0.837121 | − | 0.639916i | ||||
\(105\) | 2989.58 | − | 20162.4i | 0.271164 | − | 1.82879i | ||||
\(106\) | 3152.87 | + | 3152.87i | 0.280605 | + | 0.280605i | ||||
\(107\) | − | 4354.40i | − | 0.380330i | −0.981752 | − | 0.190165i | \(-0.939098\pi\) | ||
0.981752 | − | 0.190165i | \(-0.0609024\pi\) | |||||||
\(108\) | −2419.26 | −0.207412 | ||||||||
\(109\) | 14256.5 | + | 14256.5i | 1.19994 | + | 1.19994i | 0.974185 | + | 0.225752i | \(0.0724840\pi\) |
0.225752 | + | 0.974185i | \(0.427516\pi\) | |||||||
\(110\) | −2162.16 | − | 2914.97i | −0.178691 | − | 0.240907i | ||||
\(111\) | −6715.85 | + | 6715.85i | −0.545073 | + | 0.545073i | ||||
\(112\) | 2680.59 | + | 2680.59i | 0.213695 | + | 0.213695i | ||||
\(113\) | − | 18625.6i | − | 1.45866i | −0.684162 | − | 0.729330i | \(-0.739832\pi\) | ||
0.684162 | − | 0.729330i | \(-0.260168\pi\) | |||||||
\(114\) | 3421.47i | 0.263271i | ||||||||
\(115\) | 17231.7 | − | 12781.5i | 1.30297 | − | 0.966465i | ||||
\(116\) | 10619.9i | 0.789233i | ||||||||
\(117\) | −9396.49 | + | 1254.56i | −0.686426 | + | 0.0916473i | ||||
\(118\) | − | 2518.38i | − | 0.180866i | ||||||
\(119\) | 139.624 | + | 139.624i | 0.00985978 | + | 0.00985978i | ||||
\(120\) | −2895.26 | + | 19526.3i | −0.201060 | + | 1.35599i | ||||
\(121\) | 11905.4i | 0.813154i | ||||||||
\(122\) | 10207.2 | − | 10207.2i | 0.685787 | − | 0.685787i | ||||
\(123\) | −3239.39 | + | 3239.39i | −0.214118 | + | 0.214118i | ||||
\(124\) | −8093.85 | + | 8093.85i | −0.526395 | + | 0.526395i | ||||
\(125\) | 5266.54 | + | 14710.7i | 0.337058 | + | 0.941484i | ||||
\(126\) | 10841.5 | 0.682888 | ||||||||
\(127\) | −20800.0 | −1.28961 | −0.644803 | − | 0.764349i | \(-0.723060\pi\) | ||||
−0.644803 | + | 0.764349i | \(0.723060\pi\) | |||||||
\(128\) | 3733.42 | + | 3733.42i | 0.227870 | + | 0.227870i | ||||
\(129\) | − | 39113.2i | − | 2.35041i | ||||||
\(130\) | 169.728 | − | 11725.7i | 0.0100431 | − | 0.693831i | ||||
\(131\) | 7041.46 | 0.410317 | 0.205159 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205159 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(132\) | −3592.43 | + | 3592.43i | −0.206177 | + | 0.206177i | ||||
\(133\) | − | 7330.95i | − | 0.414436i | ||||||
\(134\) | 11612.6i | 0.646726i | ||||||||
\(135\) | −4343.27 | − | 5855.49i | −0.238314 | − | 0.321289i | ||||
\(136\) | −135.219 | − | 135.219i | −0.00731073 | − | 0.00731073i | ||||
\(137\) | 15382.9 | + | 15382.9i | 0.819591 | + | 0.819591i | 0.986049 | − | 0.166457i | \(-0.0532328\pi\) |
−0.166457 | + | 0.986049i | \(0.553233\pi\) | |||||||
\(138\) | 19721.2 | + | 19721.2i | 1.03556 | + | 1.03556i | ||||
\(139\) | 14481.8 | 0.749539 | 0.374769 | − | 0.927118i | \(-0.377722\pi\) | ||||
0.374769 | + | 0.927118i | \(0.377722\pi\) | |||||||
\(140\) | 2118.21 | − | 14285.7i | 0.108072 | − | 0.728860i | ||||
\(141\) | −4050.21 | + | 4050.21i | −0.203722 | + | 0.203722i | ||||
\(142\) | 5274.60 | 0.261585 | ||||||||
\(143\) | 5368.14 | − | 7022.45i | 0.262513 | − | 0.343413i | ||||
\(144\) | −3053.83 | −0.147272 | ||||||||
\(145\) | −25704.1 | + | 19065.8i | −1.22255 | + | 0.906818i | ||||
\(146\) | −4646.03 | −0.217960 | ||||||||
\(147\) | −28660.2 | −1.32631 | ||||||||
\(148\) | −4758.38 | + | 4758.38i | −0.217238 | + | 0.217238i | ||||
\(149\) | −12147.7 | − | 12147.7i | −0.547170 | − | 0.547170i | 0.378451 | − | 0.925621i | \(-0.376457\pi\) |
−0.925621 | + | 0.378451i | \(0.876457\pi\) | |||||||
\(150\) | −17912.3 | + | 9577.05i | −0.796100 | + | 0.425646i | ||||
\(151\) | −6761.45 | + | 6761.45i | −0.296542 | + | 0.296542i | −0.839658 | − | 0.543116i | \(-0.817244\pi\) |
0.543116 | + | 0.839658i | \(0.317244\pi\) | |||||||
\(152\) | 7099.67i | 0.307292i | ||||||||
\(153\) | −159.066 | −0.00679506 | ||||||||
\(154\) | −7148.03 | + | 7148.03i | −0.301401 | + | 0.301401i | ||||
\(155\) | −34120.9 | − | 5059.28i | −1.42023 | − | 0.210584i | ||||
\(156\) | −16271.4 | + | 2172.46i | −0.668616 | + | 0.0892694i | ||||
\(157\) | − | 12263.3i | − | 0.497519i | −0.968565 | − | 0.248759i | \(-0.919977\pi\) | ||
0.968565 | − | 0.248759i | \(-0.0800228\pi\) | |||||||
\(158\) | −5519.14 | + | 5519.14i | −0.221084 | + | 0.221084i | ||||
\(159\) | 18809.3 | 0.744008 | ||||||||
\(160\) | −3402.31 | + | 22945.9i | −0.132903 | + | 0.896325i | ||||
\(161\) | −42255.2 | − | 42255.2i | −1.63015 | − | 1.63015i | ||||
\(162\) | 15619.0 | − | 15619.0i | 0.595144 | − | 0.595144i | ||||
\(163\) | 2052.00 | + | 2052.00i | 0.0772329 | + | 0.0772329i | 0.744668 | − | 0.667435i | \(-0.232608\pi\) |
−0.667435 | + | 0.744668i | \(0.732608\pi\) | |||||||
\(164\) | −2295.21 | + | 2295.21i | −0.0853364 | + | 0.0853364i | ||||
\(165\) | −15144.5 | − | 2245.54i | −0.556270 | − | 0.0824810i | ||||
\(166\) | − | 28020.5i | − | 1.01686i | ||||||
\(167\) | 21065.0 | + | 21065.0i | 0.755316 | + | 0.755316i | 0.975466 | − | 0.220150i | \(-0.0706546\pi\) |
−0.220150 | + | 0.975466i | \(0.570655\pi\) | |||||||
\(168\) | 54981.7 | 1.94805 | ||||||||
\(169\) | 27560.6 | − | 7493.00i | 0.964973 | − | 0.262351i | ||||
\(170\) | 28.8606 | − | 194.642i | 0.000998637 | − | 0.00673503i | ||||
\(171\) | 4175.86 | + | 4175.86i | 0.142808 | + | 0.142808i | ||||
\(172\) | − | 27712.9i | − | 0.936752i | ||||||
\(173\) | −6229.06 | −0.208128 | −0.104064 | − | 0.994571i | \(-0.533185\pi\) | ||||
−0.104064 | + | 0.994571i | \(0.533185\pi\) | |||||||
\(174\) | −29417.6 | − | 29417.6i | −0.971647 | − | 0.971647i | ||||
\(175\) | 38379.4 | − | 20520.1i | 1.25320 | − | 0.670043i | ||||
\(176\) | 2013.45 | − | 2013.45i | 0.0650004 | − | 0.0650004i | ||||
\(177\) | −7512.03 | − | 7512.03i | −0.239779 | − | 0.239779i | ||||
\(178\) | − | 4050.78i | − | 0.127849i | ||||||
\(179\) | 38292.2i | 1.19510i | 0.801832 | + | 0.597549i | \(0.203859\pi\) | ||||
−0.801832 | + | 0.597549i | \(0.796141\pi\) | |||||||
\(180\) | 6930.82 | + | 9343.97i | 0.213914 | + | 0.288394i | ||||
\(181\) | − | 38251.7i | − | 1.16760i | −0.811898 | − | 0.583800i | \(-0.801565\pi\) | ||
0.811898 | − | 0.583800i | \(-0.198435\pi\) | |||||||
\(182\) | −32376.1 | + | 4322.65i | −0.977421 | + | 0.130499i | ||||
\(183\) | − | 60893.9i | − | 1.81833i | ||||||
\(184\) | 40922.1 | + | 40922.1i | 1.20871 | + | 1.20871i | ||||
\(185\) | −20059.7 | − | 2974.35i | −0.586113 | − | 0.0869059i | ||||
\(186\) | − | 44840.6i | − | 1.29612i | ||||||
\(187\) | 104.875 | − | 104.875i | 0.00299909 | − | 0.00299909i | ||||
\(188\) | −2869.69 | + | 2869.69i | −0.0811931 | + | 0.0811931i | ||||
\(189\) | −14358.7 | + | 14358.7i | −0.401968 | + | 0.401968i | ||||
\(190\) | −5867.49 | + | 4352.17i | −0.162534 | + | 0.120559i | ||||
\(191\) | 58381.3 | 1.60032 | 0.800160 | − | 0.599786i | \(-0.204748\pi\) | ||||
0.800160 | + | 0.599786i | \(0.204748\pi\) | |||||||
\(192\) | −40353.8 | −1.09467 | ||||||||
\(193\) | 18900.7 | + | 18900.7i | 0.507414 | + | 0.507414i | 0.913732 | − | 0.406318i | \(-0.133187\pi\) |
−0.406318 | + | 0.913732i | \(0.633187\pi\) | |||||||
\(194\) | 31664.8i | 0.841344i | ||||||||
\(195\) | −34470.1 | − | 35482.7i | −0.906513 | − | 0.933141i | ||||
\(196\) | −20306.6 | −0.528597 | ||||||||
\(197\) | −41161.7 | + | 41161.7i | −1.06062 | + | 1.06062i | −0.0625830 | + | 0.998040i | \(0.519934\pi\) |
−0.998040 | + | 0.0625830i | \(0.980066\pi\) | |||||||
\(198\) | − | 8143.32i | − | 0.207717i | ||||||
\(199\) | 7371.87i | 0.186154i | 0.995659 | + | 0.0930768i | \(0.0296702\pi\) | ||||
−0.995659 | + | 0.0930768i | \(0.970330\pi\) | |||||||
\(200\) | −37168.5 | + | 19872.7i | −0.929213 | + | 0.496817i | ||||
\(201\) | 34639.0 | + | 34639.0i | 0.857379 | + | 0.857379i | ||||
\(202\) | 7721.62 | + | 7721.62i | 0.189237 | + | 0.189237i | ||||
\(203\) | 63031.1 | + | 63031.1i | 1.52955 | + | 1.52955i | ||||
\(204\) | −275.446 | −0.00661876 | ||||||||
\(205\) | −9675.81 | − | 1434.68i | −0.230239 | − | 0.0341388i | ||||
\(206\) | −30586.6 | + | 30586.6i | −0.720770 | + | 0.720770i | ||||
\(207\) | 48138.8 | 1.12345 | ||||||||
\(208\) | 9119.67 | − | 1217.60i | 0.210791 | − | 0.0281435i | ||||
\(209\) | −5506.45 | −0.126061 | ||||||||
\(210\) | 33704.3 | + | 45439.4i | 0.764271 | + | 1.03037i | ||||
\(211\) | −20922.5 | −0.469946 | −0.234973 | − | 0.972002i | \(-0.575500\pi\) | ||||
−0.234973 | + | 0.972002i | \(0.575500\pi\) | |||||||
\(212\) | 13326.9 | 0.296523 | ||||||||
\(213\) | 15733.5 | − | 15733.5i | 0.346789 | − | 0.346789i | ||||
\(214\) | 8546.19 | + | 8546.19i | 0.186614 | + | 0.186614i | ||||
\(215\) | 67075.4 | − | 49752.7i | 1.45106 | − | 1.07632i | ||||
\(216\) | 13905.7 | − | 13905.7i | 0.298047 | − | 0.298047i | ||||
\(217\) | 96076.8i | 2.04032i | ||||||||
\(218\) | −55961.0 | −1.17753 | ||||||||
\(219\) | −13858.5 | + | 13858.5i | −0.288954 | + | 0.288954i | ||||
\(220\) | −10730.3 | − | 1591.04i | −0.221700 | − | 0.0328726i | ||||
\(221\) | 475.018 | − | 63.4215i | 0.00972581 | − | 0.00129853i | ||||
\(222\) | − | 26361.8i | − | 0.534896i | ||||||
\(223\) | 34337.0 | − | 34337.0i | 0.690483 | − | 0.690483i | −0.271855 | − | 0.962338i | \(-0.587637\pi\) |
0.962338 | + | 0.271855i | \(0.0876372\pi\) | |||||||
\(224\) | 64610.5 | 1.28768 | ||||||||
\(225\) | −10173.0 | + | 33550.3i | −0.200948 | + | 0.662722i | ||||
\(226\) | 36555.7 | + | 36555.7i | 0.715712 | + | 0.715712i | ||||
\(227\) | 37503.4 | − | 37503.4i | 0.727812 | − | 0.727812i | −0.242371 | − | 0.970184i | \(-0.577925\pi\) |
0.970184 | + | 0.242371i | \(0.0779252\pi\) | |||||||
\(228\) | 7231.13 | + | 7231.13i | 0.139103 | + | 0.139103i | ||||
\(229\) | 5100.19 | − | 5100.19i | 0.0972557 | − | 0.0972557i | −0.656805 | − | 0.754061i | \(-0.728092\pi\) |
0.754061 | + | 0.656805i | \(0.228092\pi\) | |||||||
\(230\) | −8734.23 | + | 58905.6i | −0.165108 | + | 1.11353i | ||||
\(231\) | 42643.4i | 0.799149i | ||||||||
\(232\) | −61042.5 | − | 61042.5i | −1.13411 | − | 1.13411i | ||||
\(233\) | 61062.0 | 1.12476 | 0.562379 | − | 0.826880i | \(-0.309886\pi\) | ||||
0.562379 | + | 0.826880i | \(0.309886\pi\) | |||||||
\(234\) | 15979.8 | − | 20904.3i | 0.291837 | − | 0.381773i | ||||
\(235\) | −12097.6 | − | 1793.78i | −0.219061 | − | 0.0324813i | ||||
\(236\) | −5322.49 | − | 5322.49i | −0.0955633 | − | 0.0955633i | ||||
\(237\) | 32925.8i | 0.586192i | ||||||||
\(238\) | −548.069 | −0.00967568 | ||||||||
\(239\) | −14053.0 | − | 14053.0i | −0.246021 | − | 0.246021i | 0.573315 | − | 0.819335i | \(-0.305657\pi\) |
−0.819335 | + | 0.573315i | \(0.805657\pi\) | |||||||
\(240\) | −9493.81 | − | 12799.3i | −0.164823 | − | 0.222210i | ||||
\(241\) | 18222.3 | − | 18222.3i | 0.313739 | − | 0.313739i | −0.532617 | − | 0.846356i | \(-0.678792\pi\) |
0.846356 | + | 0.532617i | \(0.178792\pi\) | |||||||
\(242\) | −23366.2 | − | 23366.2i | −0.398985 | − | 0.398985i | ||||
\(243\) | − | 69557.8i | − | 1.17797i | ||||||
\(244\) | − | 43145.1i | − | 0.724690i | ||||||
\(245\) | −36456.2 | − | 49149.4i | −0.607351 | − | 0.818816i | ||||
\(246\) | − | 12715.6i | − | 0.210120i | ||||||
\(247\) | −14135.4 | − | 10805.4i | −0.231693 | − | 0.177112i | ||||
\(248\) | − | 93045.7i | − | 1.51284i | ||||||
\(249\) | −83581.6 | − | 83581.6i | −1.34807 | − | 1.34807i | ||||
\(250\) | −39208.4 | − | 18535.6i | −0.627334 | − | 0.296570i | ||||
\(251\) | 117416.i | 1.86372i | 0.362821 | + | 0.931859i | \(0.381814\pi\) | ||||
−0.362821 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(252\) | 22913.1 | − | 22913.1i | 0.360813 | − | 0.360813i | ||||
\(253\) | −31738.9 | + | 31738.9i | −0.495851 | + | 0.495851i | ||||
\(254\) | 40823.3 | − | 40823.3i | 0.632763 | − | 0.632763i | ||||
\(255\) | −494.506 | − | 666.681i | −0.00760486 | − | 0.0102527i | ||||
\(256\) | −69798.4 | −1.06504 | ||||||||
\(257\) | 66273.8 | 1.00340 | 0.501701 | − | 0.865041i | \(-0.332708\pi\) | ||||
0.501701 | + | 0.865041i | \(0.332708\pi\) | |||||||
\(258\) | 76765.8 | + | 76765.8i | 1.15326 | + | 1.15326i | ||||
\(259\) | 56483.6i | 0.842021i | ||||||||
\(260\) | −24423.1 | − | 25140.5i | −0.361289 | − | 0.371901i | ||||
\(261\) | −71807.5 | −1.05412 | ||||||||
\(262\) | −13819.9 | + | 13819.9i | −0.201328 | + | 0.201328i | ||||
\(263\) | − | 20370.0i | − | 0.294496i | −0.989100 | − | 0.147248i | \(-0.952958\pi\) | ||
0.989100 | − | 0.147248i | \(-0.0470415\pi\) | |||||||
\(264\) | − | 41298.0i | − | 0.592545i | ||||||
\(265\) | 23925.7 | + | 32256.1i | 0.340701 | + | 0.459324i | ||||
\(266\) | 14388.1 | + | 14388.1i | 0.203349 | + | 0.203349i | ||||
\(267\) | −12083.0 | − | 12083.0i | −0.169493 | − | 0.169493i | ||||
\(268\) | 24542.7 | + | 24542.7i | 0.341707 | + | 0.341707i | ||||
\(269\) | −24183.0 | −0.334199 | −0.167099 | − | 0.985940i | \(-0.553440\pi\) | ||||
−0.167099 | + | 0.985940i | \(0.553440\pi\) | |||||||
\(270\) | 20016.6 | + | 2967.97i | 0.274577 | + | 0.0407129i | ||||
\(271\) | 45864.2 | − | 45864.2i | 0.624504 | − | 0.624504i | −0.322176 | − | 0.946680i | \(-0.604414\pi\) |
0.946680 | + | 0.322176i | \(0.104414\pi\) | |||||||
\(272\) | 154.380 | 0.00208666 | ||||||||
\(273\) | −83679.9 | + | 109468.i | −1.12278 | + | 1.46879i | ||||
\(274\) | −60382.7 | −0.804287 | ||||||||
\(275\) | −15413.1 | − | 28827.6i | −0.203810 | − | 0.381192i | ||||
\(276\) | 83359.7 | 1.09430 | ||||||||
\(277\) | −91774.5 | −1.19609 | −0.598043 | − | 0.801464i | \(-0.704055\pi\) | ||||
−0.598043 | + | 0.801464i | \(0.704055\pi\) | |||||||
\(278\) | −28422.9 | + | 28422.9i | −0.367772 | + | 0.367772i | ||||
\(279\) | −54727.3 | − | 54727.3i | −0.703065 | − | 0.703065i | ||||
\(280\) | 69937.6 | + | 94288.2i | 0.892062 | + | 1.20266i | ||||
\(281\) | 4584.41 | − | 4584.41i | 0.0580591 | − | 0.0580591i | −0.677481 | − | 0.735540i | \(-0.736928\pi\) |
0.735540 | + | 0.677481i | \(0.236928\pi\) | |||||||
\(282\) | − | 15898.3i | − | 0.199918i | ||||||
\(283\) | −104879. | −1.30953 | −0.654766 | − | 0.755832i | \(-0.727233\pi\) | ||||
−0.654766 | + | 0.755832i | \(0.727233\pi\) | |||||||
\(284\) | 11147.6 | − | 11147.6i | 0.138212 | − | 0.138212i | ||||
\(285\) | −4520.01 | + | 30484.0i | −0.0556481 | + | 0.375303i | ||||
\(286\) | 3246.85 | + | 24318.4i | 0.0396944 | + | 0.297306i | ||||
\(287\) | 27244.9i | 0.330767i | ||||||||
\(288\) | −36803.4 | + | 36803.4i | −0.443714 | + | 0.443714i | ||||
\(289\) | −83513.0 | −0.999904 | ||||||||
\(290\) | 13028.6 | − | 87868.0i | 0.154918 | − | 1.04480i | ||||
\(291\) | 94452.2 | + | 94452.2i | 1.11539 | + | 1.11539i | ||||
\(292\) | −9819.19 | + | 9819.19i | −0.115162 | + | 0.115162i | ||||
\(293\) | −110200. | − | 110200.i | −1.28365 | − | 1.28365i | −0.938574 | − | 0.345078i | \(-0.887852\pi\) |
−0.345078 | − | 0.938574i | \(-0.612148\pi\) | |||||||
\(294\) | 56250.1 | − | 56250.1i | 0.650771 | − | 0.650771i | ||||
\(295\) | 3326.97 | − | 22437.8i | 0.0382300 | − | 0.257832i | ||||
\(296\) | − | 54701.6i | − | 0.624334i | ||||||
\(297\) | 10785.2 | + | 10785.2i | 0.122268 | + | 0.122268i | ||||
\(298\) | 47683.6 | 0.536954 | ||||||||
\(299\) | −143757. | + | 19193.6i | −1.60801 | + | 0.214691i | ||||
\(300\) | −17616.1 | + | 58097.4i | −0.195734 | + | 0.645527i | ||||
\(301\) | −164481. | − | 164481.i | −1.81544 | − | 1.81544i | ||||
\(302\) | − | 26540.8i | − | 0.291005i | ||||||
\(303\) | 46065.3 | 0.501751 | ||||||||
\(304\) | −4052.84 | − | 4052.84i | −0.0438543 | − | 0.0438543i | ||||
\(305\) | 104427. | − | 77458.1i | 1.12257 | − | 0.832659i | ||||
\(306\) | 312.191 | − | 312.191i | 0.00333409 | − | 0.00333409i | ||||
\(307\) | 86941.0 | + | 86941.0i | 0.922461 | + | 0.922461i | 0.997203 | − | 0.0747419i | \(-0.0238133\pi\) |
−0.0747419 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(308\) | 30214.1i | 0.318499i | ||||||||
\(309\) | 182472.i | 1.91108i | ||||||||
\(310\) | 76897.2 | − | 57038.0i | 0.800179 | − | 0.593527i | ||||
\(311\) | 97359.6i | 1.00660i | 0.864111 | + | 0.503301i | \(0.167881\pi\) | ||||
−0.864111 | + | 0.503301i | \(0.832119\pi\) | |||||||
\(312\) | 81039.9 | − | 106014.i | 0.832511 | − | 1.08907i | ||||
\(313\) | 43692.2i | 0.445979i | 0.974821 | + | 0.222990i | \(0.0715816\pi\) | ||||
−0.974821 | + | 0.222990i | \(0.928418\pi\) | |||||||
\(314\) | 24068.7 | + | 24068.7i | 0.244114 | + | 0.244114i | ||||
\(315\) | 96593.7 | + | 14322.4i | 0.973482 | + | 0.144343i | ||||
\(316\) | 23328.9i | 0.233626i | ||||||||
\(317\) | 72240.4 | − | 72240.4i | 0.718889 | − | 0.718889i | −0.249489 | − | 0.968378i | \(-0.580263\pi\) |
0.968378 | + | 0.249489i | \(0.0802626\pi\) | |||||||
\(318\) | −36916.1 | + | 36916.1i | −0.365058 | + | 0.365058i | ||||
\(319\) | 47344.1 | − | 47344.1i | 0.465248 | − | 0.465248i | ||||
\(320\) | −51330.7 | − | 69202.8i | −0.501276 | − | 0.675809i | ||||
\(321\) | 50984.4 | 0.494798 | ||||||||
\(322\) | 165865. | 1.59972 | ||||||||
\(323\) | −211.101 | − | 211.101i | −0.00202342 | − | 0.00202342i | ||||
\(324\) | − | 66020.0i | − | 0.628906i | ||||||
\(325\) | 17002.8 | − | 104248.i | 0.160973 | − | 0.986959i | ||||
\(326\) | −8054.74 | −0.0757908 | ||||||||
\(327\) | −166925. | + | 166925.i | −1.56108 | + | 1.56108i | ||||
\(328\) | − | 26385.4i | − | 0.245254i | ||||||
\(329\) | 34064.2i | 0.314707i | ||||||||
\(330\) | 34130.6 | − | 25316.1i | 0.313412 | − | 0.232471i | ||||
\(331\) | −86768.0 | − | 86768.0i | −0.791961 | − | 0.791961i | 0.189852 | − | 0.981813i | \(-0.439199\pi\) |
−0.981813 | + | 0.189852i | \(0.939199\pi\) | |||||||
\(332\) | −59220.1 | − | 59220.1i | −0.537270 | − | 0.537270i | ||||
\(333\) | −32174.2 | − | 32174.2i | −0.290148 | − | 0.290148i | ||||
\(334\) | −82686.7 | −0.741213 | ||||||||
\(335\) | −15341.1 | + | 103464.i | −0.136699 | + | 0.921932i | ||||
\(336\) | −31386.2 | + | 31386.2i | −0.278010 | + | 0.278010i | ||||
\(337\) | −3730.58 | −0.0328486 | −0.0164243 | − | 0.999865i | \(-0.505228\pi\) | ||||
−0.0164243 | + | 0.999865i | \(0.505228\pi\) | |||||||
\(338\) | −39385.7 | + | 68798.1i | −0.344751 | + | 0.602203i | ||||
\(339\) | 218082. | 1.89767 | ||||||||
\(340\) | −350.372 | − | 472.363i | −0.00303090 | − | 0.00408619i | ||||
\(341\) | 72165.6 | 0.620614 | ||||||||
\(342\) | −16391.5 | −0.140142 | ||||||||
\(343\) | −2302.68 | + | 2302.68i | −0.0195725 | + | 0.0195725i | ||||
\(344\) | 159292. | + | 159292.i | 1.34610 | + | 1.34610i | ||||
\(345\) | 149655. | + | 201761.i | 1.25734 | + | 1.69512i | ||||
\(346\) | 12225.5 | − | 12225.5i | 0.102121 | − | 0.102121i | ||||
\(347\) | 34660.7i | 0.287858i | 0.989588 | + | 0.143929i | \(0.0459737\pi\) | ||||
−0.989588 | + | 0.143929i | \(0.954026\pi\) | |||||||
\(348\) | −124346. | −1.02677 | ||||||||
\(349\) | −7412.49 | + | 7412.49i | −0.0608574 | + | 0.0608574i | −0.736880 | − | 0.676023i | \(-0.763702\pi\) |
0.676023 | + | 0.736880i | \(0.263702\pi\) | |||||||
\(350\) | −35051.6 | + | 115599.i | −0.286136 | + | 0.943668i | ||||
\(351\) | 6522.14 | + | 48850.0i | 0.0529391 | + | 0.396507i | ||||
\(352\) | − | 48530.5i | − | 0.391678i | ||||||
\(353\) | 95189.5 | − | 95189.5i | 0.763906 | − | 0.763906i | −0.213120 | − | 0.977026i | \(-0.568363\pi\) |
0.977026 | + | 0.213120i | \(0.0683626\pi\) | |||||||
\(354\) | 29487.0 | 0.235301 | ||||||||
\(355\) | 46994.6 | + | 6968.12i | 0.372899 | + | 0.0552916i | ||||
\(356\) | −8561.14 | − | 8561.14i | −0.0675509 | − | 0.0675509i | ||||
\(357\) | −1634.82 | + | 1634.82i | −0.0128273 | + | 0.0128273i | ||||
\(358\) | −75154.3 | − | 75154.3i | −0.586392 | − | 0.586392i | ||||
\(359\) | 74820.5 | − | 74820.5i | 0.580539 | − | 0.580539i | −0.354512 | − | 0.935051i | \(-0.615353\pi\) |
0.935051 | + | 0.354512i | \(0.115353\pi\) | |||||||
\(360\) | −93546.3 | − | 13870.6i | −0.721808 | − | 0.107026i | ||||
\(361\) | − | 119237.i | − | 0.914950i | ||||||
\(362\) | 75075.0 | + | 75075.0i | 0.572899 | + | 0.572899i | ||||
\(363\) | −139397. | −1.05789 | ||||||||
\(364\) | −59289.7 | + | 77561.2i | −0.447483 | + | 0.585385i | ||||
\(365\) | −41394.3 | − | 6137.75i | −0.310710 | − | 0.0460705i | ||||
\(366\) | 119514. | + | 119514.i | 0.892186 | + | 0.892186i | ||||
\(367\) | 77746.8i | 0.577232i | 0.957445 | + | 0.288616i | \(0.0931951\pi\) | ||||
−0.957445 | + | 0.288616i | \(0.906805\pi\) | |||||||
\(368\) | −46720.7 | −0.344996 | ||||||||
\(369\) | −15519.2 | − | 15519.2i | −0.113977 | − | 0.113977i | ||||
\(370\) | 45207.9 | − | 33532.7i | 0.330226 | − | 0.244943i | ||||
\(371\) | 79097.6 | − | 79097.6i | 0.574666 | − | 0.574666i | ||||
\(372\) | −94768.6 | − | 94768.6i | −0.684823 | − | 0.684823i | ||||
\(373\) | − | 228528.i | − | 1.64257i | −0.570522 | − | 0.821283i | \(-0.693259\pi\) | ||
0.570522 | − | 0.821283i | \(-0.306741\pi\) | |||||||
\(374\) | 411.667i | 0.00294309i | ||||||||
\(375\) | −172243. | + | 61664.3i | −1.22484 | + | 0.438502i | ||||
\(376\) | − | 32989.5i | − | 0.233346i | ||||||
\(377\) | 214439. | − | 28630.6i | 1.50876 | − | 0.201441i | ||||
\(378\) | − | 56362.4i | − | 0.394462i | ||||||
\(379\) | 104576. | + | 104576.i | 0.728039 | + | 0.728039i | 0.970229 | − | 0.242190i | \(-0.0778656\pi\) |
−0.242190 | + | 0.970229i | \(0.577866\pi\) | |||||||
\(380\) | −3202.56 | + | 21598.8i | −0.0221784 | + | 0.149576i | ||||
\(381\) | − | 243542.i | − | 1.67773i | ||||||
\(382\) | −114582. | + | 114582.i | −0.785219 | + | 0.785219i | ||||
\(383\) | −188674. | + | 188674.i | −1.28622 | + | 1.28622i | −0.349152 | + | 0.937066i | \(0.613530\pi\) |
−0.937066 | + | 0.349152i | \(0.886470\pi\) | |||||||
\(384\) | −43713.6 | + | 43713.6i | −0.296452 | + | 0.296452i | ||||
\(385\) | −73129.3 | + | 54243.1i | −0.493367 | + | 0.365951i | ||||
\(386\) | −74191.0 | −0.497939 | ||||||||
\(387\) | 187383. | 1.25115 | ||||||||
\(388\) | 66922.2 | + | 66922.2i | 0.444536 | + | 0.444536i | ||||
\(389\) | − | 19213.2i | − | 0.126970i | −0.997983 | − | 0.0634849i | \(-0.979779\pi\) | ||
0.997983 | − | 0.0634849i | \(-0.0202215\pi\) | |||||||
\(390\) | 137293. | + | 1987.29i | 0.902651 | + | 0.0130657i | ||||
\(391\) | −2433.55 | −0.0159179 | ||||||||
\(392\) | 116721. | − | 116721.i | 0.759584 | − | 0.759584i | ||||
\(393\) | 82446.4i | 0.533810i | ||||||||
\(394\) | − | 161572.i | − | 1.04082i | ||||||
\(395\) | −56464.6 | + | 41882.2i | −0.361894 | + | 0.268433i | ||||
\(396\) | −17210.5 | − | 17210.5i | −0.109750 | − | 0.109750i | ||||
\(397\) | −124954. | − | 124954.i | −0.792808 | − | 0.792808i | 0.189142 | − | 0.981950i | \(-0.439430\pi\) |
−0.981950 | + | 0.189142i | \(0.939430\pi\) | |||||||
\(398\) | −14468.4 | − | 14468.4i | −0.0913388 | − | 0.0913388i | ||||
\(399\) | 85836.0 | 0.539168 | ||||||||
\(400\) | 9873.31 | − | 32561.9i | 0.0617082 | − | 0.203512i | ||||
\(401\) | 59134.8 | − | 59134.8i | 0.367752 | − | 0.367752i | −0.498905 | − | 0.866657i | \(-0.666264\pi\) |
0.866657 | + | 0.498905i | \(0.166264\pi\) | |||||||
\(402\) | −135969. | −0.841369 | ||||||||
\(403\) | 185253. | + | 141612.i | 1.14066 | + | 0.871946i | ||||
\(404\) | 32638.6 | 0.199972 | ||||||||
\(405\) | 159793. | − | 118525.i | 0.974197 | − | 0.722604i | ||||
\(406\) | −247417. | −1.50099 | ||||||||
\(407\) | 42426.2 | 0.256121 | ||||||||
\(408\) | 1583.24 | − | 1583.24i | 0.00951103 | − | 0.00951103i | ||||
\(409\) | 75924.7 | + | 75924.7i | 0.453875 | + | 0.453875i | 0.896639 | − | 0.442763i | \(-0.146002\pi\) |
−0.442763 | + | 0.896639i | \(0.646002\pi\) | |||||||
\(410\) | 21806.1 | − | 16174.5i | 0.129721 | − | 0.0962195i | ||||
\(411\) | −180114. | + | 180114.i | −1.06626 | + | 1.06626i | ||||
\(412\) | 129287.i | 0.761658i | ||||||||
\(413\) | −63179.9 | −0.370407 | ||||||||
\(414\) | −94479.9 | + | 94479.9i | −0.551238 | + | 0.551238i | ||||
\(415\) | 37017.1 | − | 249652.i | 0.214935 | − | 1.44957i | ||||
\(416\) | 95232.3 | − | 124580.i | 0.550298 | − | 0.719884i | ||||
\(417\) | 169564.i | 0.975126i | ||||||||
\(418\) | 10807.3 | − | 10807.3i | 0.0618534 | − | 0.0618534i | ||||
\(419\) | −115602. | −0.658473 | −0.329236 | − | 0.944248i | \(-0.606791\pi\) | ||||
−0.329236 | + | 0.944248i | \(0.606791\pi\) | |||||||
\(420\) | 167267. | + | 24801.5i | 0.948224 | + | 0.140598i | ||||
\(421\) | −54540.6 | − | 54540.6i | −0.307720 | − | 0.307720i | 0.536305 | − | 0.844024i | \(-0.319820\pi\) |
−0.844024 | + | 0.536305i | \(0.819820\pi\) | |||||||
\(422\) | 41063.6 | − | 41063.6i | 0.230586 | − | 0.230586i | ||||
\(423\) | −19403.7 | − | 19403.7i | −0.108443 | − | 0.108443i | ||||
\(424\) | −76602.1 | + | 76602.1i | −0.426098 | + | 0.426098i | ||||
\(425\) | 514.273 | − | 1696.06i | 0.00284719 | − | 0.00938995i | ||||
\(426\) | 61758.7i | 0.340313i | ||||||||
\(427\) | −256074. | − | 256074.i | −1.40446 | − | 1.40446i | ||||
\(428\) | 36124.0 | 0.197201 | ||||||||
\(429\) | 82223.8 | + | 62854.0i | 0.446769 | + | 0.341522i | ||||
\(430\) | −33998.5 | + | 229293.i | −0.183875 | + | 1.24009i | ||||
\(431\) | 134785. | + | 134785.i | 0.725583 | + | 0.725583i | 0.969736 | − | 0.244154i | \(-0.0785102\pi\) |
−0.244154 | + | 0.969736i | \(0.578510\pi\) | |||||||
\(432\) | 15876.1i | 0.0850700i | ||||||||
\(433\) | −42349.4 | −0.225877 | −0.112938 | − | 0.993602i | \(-0.536026\pi\) | ||||
−0.112938 | + | 0.993602i | \(0.536026\pi\) | |||||||
\(434\) | −188566. | − | 188566.i | −1.00111 | − | 1.00111i | ||||
\(435\) | −223237. | − | 300962.i | −1.17974 | − | 1.59050i | ||||
\(436\) | −118271. | + | 118271.i | −0.622165 | + | 0.622165i | ||||
\(437\) | 63886.6 | + | 63886.6i | 0.334539 | + | 0.334539i | ||||
\(438\) | − | 54399.1i | − | 0.283559i | ||||||
\(439\) | − | 293456.i | − | 1.52270i | −0.648342 | − | 0.761350i | \(-0.724537\pi\) | ||
0.648342 | − | 0.761350i | \(-0.275463\pi\) | |||||||
\(440\) | 70822.1 | − | 52531.8i | 0.365817 | − | 0.271342i | ||||
\(441\) | − | 137305.i | − | 0.706006i | ||||||
\(442\) | −807.823 | + | 1056.77i | −0.00413496 | + | 0.00540925i | ||||
\(443\) | 239583.i | 1.22081i | 0.792088 | + | 0.610406i | \(0.208994\pi\) | ||||
−0.792088 | + | 0.610406i | \(0.791006\pi\) | |||||||
\(444\) | −55714.5 | − | 55714.5i | −0.282619 | − | 0.282619i | ||||
\(445\) | 5351.37 | − | 36090.8i | 0.0270237 | − | 0.182254i | ||||
\(446\) | 134783.i | 0.677590i | ||||||||
\(447\) | 142234. | − | 142234.i | 0.711851 | − | 0.711851i | ||||
\(448\) | −169698. | + | 169698.i | −0.845512 | + | 0.845512i | ||||
\(449\) | −195773. | + | 195773.i | −0.971091 | + | 0.971091i | −0.999594 | − | 0.0285030i | \(-0.990926\pi\) |
0.0285030 | + | 0.999594i | \(0.490926\pi\) | |||||||
\(450\) | −45881.6 | − | 85813.7i | −0.226576 | − | 0.423772i | ||||
\(451\) | 20464.3 | 0.100611 | ||||||||
\(452\) | 154518. | 0.756312 | ||||||||
\(453\) | −79167.9 | − | 79167.9i | −0.385791 | − | 0.385791i | ||||
\(454\) | 147213.i | 0.714222i | ||||||||
\(455\) | −294169. | − | 4258.04i | −1.42093 | − | 0.0205677i | ||||
\(456\) | −83128.0 | −0.399777 | ||||||||
\(457\) | −87988.1 | + | 87988.1i | −0.421300 | + | 0.421300i | −0.885651 | − | 0.464351i | \(-0.846288\pi\) |
0.464351 | + | 0.885651i | \(0.346288\pi\) | |||||||
\(458\) | 20019.8i | 0.0954397i | ||||||||
\(459\) | 826.942i | 0.00392509i | ||||||||
\(460\) | 106035. | + | 142954.i | 0.501110 | + | 0.675585i | ||||
\(461\) | 56098.7 | + | 56098.7i | 0.263968 | + | 0.263968i | 0.826664 | − | 0.562696i | \(-0.190236\pi\) |
−0.562696 | + | 0.826664i | \(0.690236\pi\) | |||||||
\(462\) | −83694.3 | − | 83694.3i | −0.392113 | − | 0.392113i | ||||
\(463\) | −21715.3 | − | 21715.3i | −0.101299 | − | 0.101299i | 0.654641 | − | 0.755940i | \(-0.272820\pi\) |
−0.755940 | + | 0.654641i | \(0.772820\pi\) | |||||||
\(464\) | 69692.1 | 0.323704 | ||||||||
\(465\) | 59237.7 | − | 399512.i | 0.273963 | − | 1.84767i | ||||
\(466\) | −119844. | + | 119844.i | −0.551878 | + | 0.551878i | ||||
\(467\) | −114586. | −0.525409 | −0.262705 | − | 0.964876i | \(-0.584614\pi\) | ||||
−0.262705 | + | 0.964876i | \(0.584614\pi\) | |||||||
\(468\) | −10407.8 | − | 77953.0i | −0.0475190 | − | 0.355911i | ||||
\(469\) | 291331. | 1.32447 | ||||||||
\(470\) | 27264.1 | − | 20222.9i | 0.123423 | − | 0.0915479i | ||||
\(471\) | 143588. | 0.647256 | ||||||||
\(472\) | 61186.6 | 0.274645 | ||||||||
\(473\) | −123545. | + | 123545.i | −0.552210 | + | 0.552210i | ||||
\(474\) | −64622.0 | − | 64622.0i | −0.287623 | − | 0.287623i | ||||
\(475\) | −58026.6 | + | 31024.8i | −0.257182 | + | 0.137506i | ||||
\(476\) | −1158.32 | + | 1158.32i | −0.00511228 | + | 0.00511228i | ||||
\(477\) | 90111.1i | 0.396042i | ||||||||
\(478\) | 55162.2 | 0.241427 | ||||||||
\(479\) | 258343. | − | 258343.i | 1.12597 | − | 1.12597i | 0.135142 | − | 0.990826i | \(-0.456851\pi\) |
0.990826 | − | 0.135142i | \(-0.0431492\pi\) | |||||||
\(480\) | −268667. | − | 39836.6i | −1.16609 | − | 0.172902i | ||||
\(481\) | 108910. | + | 83253.7i | 0.470737 | + | 0.359843i | ||||
\(482\) | 71528.0i | 0.307880i | ||||||||
\(483\) | 494754. | − | 494754.i | 2.12078 | − | 2.12078i | ||||
\(484\) | −98766.8 | −0.421619 | ||||||||
\(485\) | −41831.5 | + | 282121.i | −0.177836 | + | 1.19937i | ||||
\(486\) | 136518. | + | 136518.i | 0.577986 | + | 0.577986i | ||||
\(487\) | −7983.76 | + | 7983.76i | −0.0336628 | + | 0.0336628i | −0.723738 | − | 0.690075i | \(-0.757577\pi\) |
0.690075 | + | 0.723738i | \(0.257577\pi\) | |||||||
\(488\) | 247995. | + | 247995.i | 1.04137 | + | 1.04137i | ||||
\(489\) | −24026.3 | + | 24026.3i | −0.100478 | + | 0.100478i | ||||
\(490\) | 168014. | + | 24912.4i | 0.699769 | + | 0.103758i | ||||
\(491\) | 16818.2i | 0.0697618i | 0.999391 | + | 0.0348809i | \(0.0111052\pi\) | ||||
−0.999391 | + | 0.0348809i | \(0.988895\pi\) | |||||||
\(492\) | −26873.9 | − | 26873.9i | −0.111020 | − | 0.111020i | ||||
\(493\) | 3630.07 | 0.0149355 | ||||||||
\(494\) | 48950.1 | − | 6535.51i | 0.200586 | − | 0.0267809i | ||||
\(495\) | 10757.9 | − | 72553.8i | 0.0439054 | − | 0.296108i | ||||
\(496\) | 53115.0 | + | 53115.0i | 0.215901 | + | 0.215901i | ||||
\(497\) | − | 132326.i | − | 0.535714i | ||||||
\(498\) | 328084. | 1.32290 | ||||||||
\(499\) | −280657. | − | 280657.i | −1.12713 | − | 1.12713i | −0.990641 | − | 0.136492i | \(-0.956417\pi\) |
−0.136492 | − | 0.990641i | \(-0.543583\pi\) | |||||||
\(500\) | −122039. | + | 43691.0i | −0.488158 | + | 0.174764i | ||||
\(501\) | −246644. | + | 246644.i | −0.982642 | + | 0.982642i | ||||
\(502\) | −230447. | − | 230447.i | −0.914459 | − | 0.914459i | ||||
\(503\) | − | 314884.i | − | 1.24456i | −0.782797 | − | 0.622278i | \(-0.786207\pi\) | ||
0.782797 | − | 0.622278i | \(-0.213793\pi\) | |||||||
\(504\) | 263405.i | 1.03696i | ||||||||
\(505\) | 58595.8 | + | 78997.5i | 0.229765 | + | 0.309764i | ||||
\(506\) | − | 124585.i | − | 0.486592i | ||||||
\(507\) | 87733.4 | + | 322699.i | 0.341310 | + | 1.25540i | ||||
\(508\) | − | 172556.i | − | 0.668658i | ||||||
\(509\) | −177611. | − | 177611.i | −0.685544 | − | 0.685544i | 0.275700 | − | 0.961244i | \(-0.411090\pi\) |
−0.961244 | + | 0.275700i | \(0.911090\pi\) | |||||||
\(510\) | 2279.01 | + | 337.920i | 0.00876205 | + | 0.00129919i | ||||
\(511\) | 116557.i | 0.446372i | ||||||||
\(512\) | 77255.5 | − | 77255.5i | 0.294706 | − | 0.294706i | ||||
\(513\) | 21709.2 | − | 21709.2i | 0.0824916 | − | 0.0824916i | ||||
\(514\) | −130073. | + | 130073.i | −0.492334 | + | 0.492334i | ||||
\(515\) | −312922. | + | 232107.i | −1.17983 | + | 0.875134i | ||||
\(516\) | 324482. | 1.21868 | ||||||||
\(517\) | 25586.4 | 0.0957258 | ||||||||
\(518\) | −110858. | − | 110858.i | −0.413149 | − | 0.413149i | ||||
\(519\) | − | 72934.3i | − | 0.270768i | ||||||
\(520\) | 284888. | + | 4123.70i | 1.05358 | + | 0.0152504i | ||||
\(521\) | 336979. | 1.24144 | 0.620722 | − | 0.784031i | \(-0.286840\pi\) | ||||
0.620722 | + | 0.784031i | \(0.286840\pi\) | |||||||
\(522\) | 140933. | − | 140933.i | 0.517217 | − | 0.517217i | ||||
\(523\) | − | 82275.6i | − | 0.300793i | −0.988626 | − | 0.150396i | \(-0.951945\pi\) | ||
0.988626 | − | 0.150396i | \(-0.0480550\pi\) | |||||||
\(524\) | 58415.7i | 0.212749i | ||||||||
\(525\) | 240264. | + | 449373.i | 0.871705 | + | 1.63038i | ||||
\(526\) | 39979.2 | + | 39979.2i | 0.144498 | + | 0.144498i | ||||
\(527\) | 2766.61 | + | 2766.61i | 0.00996156 | + | 0.00996156i | ||||
\(528\) | 23574.9 | + | 23574.9i | 0.0845634 | + | 0.0845634i | ||||
\(529\) | 456637. | 1.63177 | ||||||||
\(530\) | −110265. | − | 16349.6i | −0.392543 | − | 0.0582044i | ||||
\(531\) | 35988.5 | − | 35988.5i | 0.127636 | − | 0.127636i | ||||
\(532\) | 60817.4 | 0.214884 | ||||||||
\(533\) | 52532.9 | + | 40157.5i | 0.184917 | + | 0.141355i | ||||
\(534\) | 47429.4 | 0.166328 | ||||||||
\(535\) | 64853.1 | + | 87433.4i | 0.226581 | + | 0.305471i | ||||
\(536\) | −282140. | −0.982052 | ||||||||
\(537\) | −448352. | −1.55479 | ||||||||
\(538\) | 47462.8 | − | 47462.8i | 0.163979 | − | 0.163979i | ||||
\(539\) | 90527.8 | + | 90527.8i | 0.311605 | + | 0.311605i | ||||
\(540\) | 48577.0 | − | 36031.6i | 0.166588 | − | 0.123565i | ||||
\(541\) | 185136. | − | 185136.i | 0.632551 | − | 0.632551i | −0.316156 | − | 0.948707i | \(-0.602392\pi\) |
0.948707 | + | 0.316156i | \(0.102392\pi\) | |||||||
\(542\) | 180031.i | 0.612843i | ||||||||
\(543\) | 447878. | 1.51901 | ||||||||
\(544\) | 1860.52 | − | 1860.52i | 0.00628688 | − | 0.00628688i | ||||
\(545\) | −498591. | − | 73928.6i | −1.67861 | − | 0.248897i | ||||
\(546\) | −50612.7 | − | 379082.i | −0.169775 | − | 1.27159i | ||||
\(547\) | 463547.i | 1.54924i | 0.632426 | + | 0.774621i | \(0.282059\pi\) | ||||
−0.632426 | + | 0.774621i | \(0.717941\pi\) | |||||||
\(548\) | −127616. | + | 127616.i | −0.424956 | + | 0.424956i | ||||
\(549\) | 291730. | 0.967912 | ||||||||
\(550\) | 86829.3 | + | 26328.1i | 0.287039 | + | 0.0870350i | ||||
\(551\) | −95298.1 | − | 95298.1i | −0.313892 | − | 0.313892i | ||||
\(552\) | −479145. | + | 479145.i | −1.57249 | + | 1.57249i | ||||
\(553\) | 138461. | + | 138461.i | 0.452770 | + | 0.452770i | ||||
\(554\) | 180122. | − | 180122.i | 0.586876 | − | 0.586876i | ||||
\(555\) | 34825.8 | − | 234873.i | 0.113062 | − | 0.762514i | ||||
\(556\) | 120141.i | 0.388634i | ||||||||
\(557\) | 196769. | + | 196769.i | 0.634228 | + | 0.634228i | 0.949126 | − | 0.314897i | \(-0.101970\pi\) |
−0.314897 | + | 0.949126i | \(0.601970\pi\) | |||||||
\(558\) | 214822. | 0.689937 | ||||||||
\(559\) | −559583. | + | 74712.0i | −1.79077 | + | 0.239093i | ||||
\(560\) | −93748.1 | − | 13900.5i | −0.298942 | − | 0.0443256i | ||||
\(561\) | 1227.95 | + | 1227.95i | 0.00390172 | + | 0.00390172i | ||||
\(562\) | 17995.2i | 0.0569750i | ||||||||
\(563\) | 167590. | 0.528725 | 0.264363 | − | 0.964423i | \(-0.414838\pi\) | ||||
0.264363 | + | 0.964423i | \(0.414838\pi\) | |||||||
\(564\) | −33600.4 | − | 33600.4i | −0.105630 | − | 0.105630i | ||||
\(565\) | 277404. | + | 373990.i | 0.868993 | + | 1.17155i | ||||
\(566\) | 205841. | − | 205841.i | 0.642540 | − | 0.642540i | ||||
\(567\) | −391840. | − | 391840.i | −1.21883 | − | 1.21883i | ||||
\(568\) | 128151.i | 0.397216i | ||||||||
\(569\) | 212375.i | 0.655962i | 0.944684 | + | 0.327981i | \(0.106368\pi\) | ||||
−0.944684 | + | 0.327981i | \(0.893632\pi\) | |||||||
\(570\) | −50958.3 | − | 68700.8i | −0.156843 | − | 0.211452i | ||||
\(571\) | 352407.i | 1.08087i | 0.841387 | + | 0.540433i | \(0.181739\pi\) | ||||
−0.841387 | + | 0.540433i | \(0.818261\pi\) | |||||||
\(572\) | 58258.0 | + | 44533.9i | 0.178059 | + | 0.136113i | ||||
\(573\) | 683570.i | 2.08197i | ||||||||
\(574\) | −53472.4 | − | 53472.4i | −0.162295 | − | 0.162295i | ||||
\(575\) | −155637. | + | 513287.i | −0.470736 | + | 1.55248i | ||||
\(576\) | − | 193326.i | − | 0.582701i | ||||||
\(577\) | 339319. | − | 339319.i | 1.01919 | − | 1.01919i | 0.0193799 | − | 0.999812i | \(-0.493831\pi\) |
0.999812 | − | 0.0193799i | \(-0.00616920\pi\) | |||||||
\(578\) | 163907. | − | 163907.i | 0.490617 | − | 0.490617i | ||||
\(579\) | −221302. | + | 221302.i | −0.660129 | + | 0.660129i | ||||
\(580\) | −158170. | − | 213241.i | −0.470183 | − | 0.633890i | ||||
\(581\) | −702963. | −2.08248 | ||||||||
\(582\) | −370754. | −1.09456 | ||||||||
\(583\) | −59412.1 | − | 59412.1i | −0.174798 | − | 0.174798i | ||||
\(584\) | − | 112880.i | − | 0.330972i | ||||||
\(585\) | 169990. | − | 165139.i | 0.496720 | − | 0.482545i | ||||
\(586\) | 432570. | 1.25968 | ||||||||
\(587\) | 151834. | − | 151834.i | 0.440649 | − | 0.440649i | −0.451581 | − | 0.892230i | \(-0.649140\pi\) |
0.892230 | + | 0.451581i | \(0.149140\pi\) | |||||||
\(588\) | − | 237764.i | − | 0.687688i | ||||||
\(589\) | − | 145261.i | − | 0.418714i | ||||||
\(590\) | 37508.0 | + | 50567.4i | 0.107751 | + | 0.145267i | ||||
\(591\) | −481951. | − | 481951.i | −1.37984 | − | 1.37984i | ||||
\(592\) | 31226.3 | + | 31226.3i | 0.0891000 | + | 0.0891000i | ||||
\(593\) | −91914.9 | − | 91914.9i | −0.261383 | − | 0.261383i | 0.564233 | − | 0.825616i | \(-0.309172\pi\) |
−0.825616 | + | 0.564233i | \(0.809172\pi\) | |||||||
\(594\) | −42335.1 | −0.119985 | ||||||||
\(595\) | −4883.08 | − | 724.039i | −0.0137930 | − | 0.00204516i | ||||
\(596\) | 100777. | − | 100777.i | 0.283707 | − | 0.283707i | ||||
\(597\) | −86315.1 | −0.242180 | ||||||||
\(598\) | 244476. | − | 319816.i | 0.683649 | − | 0.894331i | ||||
\(599\) | −90700.3 | −0.252787 | −0.126394 | − | 0.991980i | \(-0.540340\pi\) | ||||
−0.126394 | + | 0.991980i | \(0.540340\pi\) | |||||||
\(600\) | −232684. | − | 435196.i | −0.646343 | − | 1.20888i | ||||
\(601\) | 125558. | 0.347613 | 0.173806 | − | 0.984780i | \(-0.444393\pi\) | ||||
0.173806 | + | 0.984780i | \(0.444393\pi\) | |||||||
\(602\) | 645638. | 1.78154 | ||||||||
\(603\) | −165948. | + | 165948.i | −0.456391 | + | 0.456391i | ||||
\(604\) | −56092.8 | − | 56092.8i | −0.153756 | − | 0.153756i | ||||
\(605\) | −177315. | − | 239052.i | −0.484434 | − | 0.653103i | ||||
\(606\) | −90410.3 | + | 90410.3i | −0.246191 | + | 0.246191i | ||||
\(607\) | − | 247009.i | − | 0.670403i | −0.942147 | − | 0.335201i | \(-0.891196\pi\) | ||
0.942147 | − | 0.335201i | \(-0.108804\pi\) | |||||||
\(608\) | −97686.1 | −0.264256 | ||||||||
\(609\) | −738013. | + | 738013.i | −1.98989 | + | 1.98989i | ||||
\(610\) | −52930.9 | + | 356978.i | −0.142249 | + | 0.959360i | ||||
\(611\) | 65681.7 | + | 50208.8i | 0.175939 | + | 0.134492i | ||||
\(612\) | − | 1319.60i | − | 0.00352323i | ||||||
\(613\) | −134125. | + | 134125.i | −0.356933 | + | 0.356933i | −0.862681 | − | 0.505748i | \(-0.831217\pi\) |
0.505748 | + | 0.862681i | \(0.331217\pi\) | |||||||
\(614\) | −341271. | −0.905237 | ||||||||
\(615\) | 16798.3 | − | 113291.i | 0.0444134 | − | 0.299534i | ||||
\(616\) | −173668. | − | 173668.i | −0.457677 | − | 0.457677i | ||||
\(617\) | 346776. | − | 346776.i | 0.910916 | − | 0.910916i | −0.0854281 | − | 0.996344i | \(-0.527226\pi\) |
0.996344 | + | 0.0854281i | \(0.0272258\pi\) | |||||||
\(618\) | −358130. | − | 358130.i | −0.937699 | − | 0.937699i | ||||
\(619\) | 524188. | − | 524188.i | 1.36806 | − | 1.36806i | 0.504860 | − | 0.863201i | \(-0.331544\pi\) |
0.863201 | − | 0.504860i | \(-0.168456\pi\) | |||||||
\(620\) | 41971.6 | − | 283066.i | 0.109187 | − | 0.736384i | ||||
\(621\) | − | 250262.i | − | 0.648950i | ||||||
\(622\) | −191083. | − | 191083.i | −0.493903 | − | 0.493903i | ||||
\(623\) | −101624. | −0.261830 | ||||||||
\(624\) | 14256.5 | + | 106780.i | 0.0366138 | + | 0.274233i | ||||
\(625\) | −324845. | − | 216942.i | −0.831602 | − | 0.555372i | ||||
\(626\) | −85752.6 | − | 85752.6i | −0.218826 | − | 0.218826i | ||||
\(627\) | − | 64473.5i | − | 0.164001i | ||||||
\(628\) | 101736. | 0.257963 | ||||||||
\(629\) | 1626.49 | + | 1626.49i | 0.00411103 | + | 0.00411103i | ||||
\(630\) | −217690. | + | 161470.i | −0.548476 | + | 0.406828i | ||||
\(631\) | 222687. | − | 222687.i | 0.559288 | − | 0.559288i | −0.369817 | − | 0.929105i | \(-0.620580\pi\) |
0.929105 | + | 0.369817i | \(0.120580\pi\) | |||||||
\(632\) | −134093. | − | 134093.i | −0.335716 | − | 0.335716i | ||||
\(633\) | − | 244975.i | − | 0.611385i | ||||||
\(634\) | 283566.i | 0.705465i | ||||||||
\(635\) | 417650. | − | 309789.i | 1.03577 | − | 0.768279i | ||||
\(636\) | 156041.i | 0.385767i | ||||||||
\(637\) | 54745.2 | + | 410034.i | 0.134917 | + | 1.01051i | ||||
\(638\) | 185840.i | 0.456561i | ||||||||
\(639\) | 75375.6 | + | 75375.6i | 0.184599 | + | 0.184599i | ||||
\(640\) | −130569. | − | 19360.1i | −0.318772 | − | 0.0472659i | ||||
\(641\) | 59224.2i | 0.144140i | 0.997400 | + | 0.0720698i | \(0.0229604\pi\) | ||||
−0.997400 | + | 0.0720698i | \(0.977040\pi\) | |||||||
\(642\) | −100065. | + | 100065.i | −0.242779 | + | 0.242779i | ||||
\(643\) | 314696. | − | 314696.i | 0.761147 | − | 0.761147i | −0.215383 | − | 0.976530i | \(-0.569100\pi\) |
0.976530 | + | 0.215383i | \(0.0690999\pi\) | |||||||
\(644\) | 350548. | − | 350548.i | 0.845232 | − | 0.845232i | ||||
\(645\) | 582540. | + | 785366.i | 1.40025 | + | 1.88779i | ||||
\(646\) | 828.637 | 0.00198564 | ||||||||
\(647\) | −88056.1 | −0.210354 | −0.105177 | − | 0.994454i | \(-0.533541\pi\) | ||||
−0.105177 | + | 0.994454i | \(0.533541\pi\) | |||||||
\(648\) | 379478. | + | 379478.i | 0.903725 | + | 0.903725i | ||||
\(649\) | 47455.9i | 0.112668i | ||||||||
\(650\) | 171231. | + | 237973.i | 0.405281 | + | 0.563249i | ||||
\(651\) | −1.12494e6 | −2.65440 | ||||||||
\(652\) | −17023.3 | + | 17023.3i | −0.0400451 | + | 0.0400451i | ||||
\(653\) | 261310.i | 0.612815i | 0.951900 | + | 0.306407i | \(0.0991270\pi\) | ||||
−0.951900 | + | 0.306407i | \(0.900873\pi\) | |||||||
\(654\) | − | 655231.i | − | 1.53193i | ||||||
\(655\) | −141387. | + | 104873.i | −0.329555 | + | 0.244445i | ||||
\(656\) | 15062.0 | + | 15062.0i | 0.0350007 | + | 0.0350007i | ||||
\(657\) | −66393.3 | − | 66393.3i | −0.153813 | − | 0.153813i | ||||
\(658\) | −66856.3 | − | 66856.3i | −0.154415 | − | 0.154415i | ||||
\(659\) | −805533. | −1.85487 | −0.927433 | − | 0.373990i | \(-0.877989\pi\) | ||||
−0.927433 | + | 0.373990i | \(0.877989\pi\) | |||||||
\(660\) | 18629.0 | − | 125638.i | 0.0427662 | − | 0.288425i | ||||
\(661\) | 209700. | − | 209700.i | 0.479949 | − | 0.479949i | −0.425167 | − | 0.905115i | \(-0.639784\pi\) |
0.905115 | + | 0.425167i | \(0.139784\pi\) | |||||||
\(662\) | 340591. | 0.777173 | ||||||||
\(663\) | 742.584 | + | 5561.85i | 0.00168935 | + | 0.0126530i | ||||
\(664\) | 680785. | 1.54409 | ||||||||
\(665\) | 109185. | + | 147200.i | 0.246899 | + | 0.332863i | ||||
\(666\) | 126294. | 0.284730 | ||||||||
\(667\) | −1.09859e6 | −2.46935 | ||||||||
\(668\) | −174755. | + | 174755.i | −0.391630 | + | 0.391630i | ||||
\(669\) | 402042. | + | 402042.i | 0.898296 | + | 0.898296i | ||||
\(670\) | −172954. | − | 233173.i | −0.385285 | − | 0.519432i | ||||
\(671\) | −192343. | + | 192343.i | −0.427200 | + | 0.427200i | ||||
\(672\) | 756506.i | 1.67523i | ||||||||
\(673\) | 583650. | 1.28861 | 0.644306 | − | 0.764768i | \(-0.277146\pi\) | ||||
0.644306 | + | 0.764768i | \(0.277146\pi\) | |||||||
\(674\) | 7321.85 | − | 7321.85i | 0.0161176 | − | 0.0161176i | ||||
\(675\) | 174420. | + | 52886.9i | 0.382814 | + | 0.116075i | ||||
\(676\) | 62161.7 | + | 228642.i | 0.136028 | + | 0.500336i | ||||
\(677\) | − | 313672.i | − | 0.684382i | −0.939630 | − | 0.342191i | \(-0.888831\pi\) | ||
0.939630 | − | 0.342191i | \(-0.111169\pi\) | |||||||
\(678\) | −428020. | + | 428020.i | −0.931118 | + | 0.931118i | ||||
\(679\) | 794390. | 1.72304 | ||||||||
\(680\) | 4729.02 | + | 701.196i | 0.0102271 | + | 0.00151643i | ||||
\(681\) | 439117. | + | 439117.i | 0.946861 | + | 0.946861i | ||||
\(682\) | −141636. | + | 141636.i | −0.304513 | + | 0.304513i | ||||
\(683\) | 224062. | + | 224062.i | 0.480317 | + | 0.480317i | 0.905233 | − | 0.424916i | \(-0.139696\pi\) |
−0.424916 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(684\) | −34642.8 | + | 34642.8i | −0.0740458 | + | 0.0740458i | ||||
\(685\) | −537986. | − | 79769.9i | −1.14654 | − | 0.170004i | ||||
\(686\) | − | 9038.74i | − | 0.0192070i | ||||||
\(687\) | 59716.6 | + | 59716.6i | 0.126527 | + | 0.126527i | ||||
\(688\) | −181863. | −0.384208 | ||||||||
\(689\) | −35928.4 | − | 269099.i | −0.0756833 | − | 0.566858i | ||||
\(690\) | −689709. | − | 102267.i | −1.44866 | − | 0.214801i | ||||
\(691\) | 162862. | + | 162862.i | 0.341086 | + | 0.341086i | 0.856775 | − | 0.515690i | \(-0.172464\pi\) |
−0.515690 | + | 0.856775i | \(0.672464\pi\) | |||||||
\(692\) | − | 51676.1i | − | 0.107914i | ||||||
\(693\) | −204295. | −0.425394 | ||||||||
\(694\) | −68027.0 | − | 68027.0i | −0.141242 | − | 0.141242i | ||||
\(695\) | −290785. | + | 215688.i | −0.602009 | + | 0.446536i | ||||
\(696\) | 714729. | − | 714729.i | 1.47544 | − | 1.47544i | ||||
\(697\) | 784.540 | + | 784.540i | 0.00161492 | + | 0.00161492i | ||||
\(698\) | − | 29096.3i | − | 0.0597210i | ||||||
\(699\) | 714957.i | 1.46327i | ||||||||
\(700\) | 170234. | + | 318394.i | 0.347416 | + | 0.649784i | ||||
\(701\) | 692713.i | 1.40967i | 0.709371 | + | 0.704835i | \(0.248979\pi\) | ||||
−0.709371 | + | 0.704835i | \(0.751021\pi\) | |||||||
\(702\) | −108676. | − | 83075.0i | −0.220527 | − | 0.168576i | ||||
\(703\) | − | 85398.8i | − | 0.172799i | ||||||
\(704\) | 127464. | + | 127464.i | 0.257183 | + | 0.257183i | ||||
\(705\) | 21002.8 | − | 141648.i | 0.0422571 | − | 0.284991i | ||||
\(706\) | 373648.i | 0.749642i | ||||||||
\(707\) | 193716. | − | 193716.i | 0.387549 | − | 0.387549i | ||||
\(708\) | 62319.5 | − | 62319.5i | 0.124325 | − | 0.124325i | ||||
\(709\) | 383095. | − | 383095.i | 0.762103 | − | 0.762103i | −0.214599 | − | 0.976702i | \(-0.568845\pi\) |
0.976702 | + | 0.214599i | \(0.0688445\pi\) | |||||||
\(710\) | −105910. | + | 78558.1i | −0.210098 | + | 0.155838i | ||||
\(711\) | −157741. | −0.312036 | ||||||||
\(712\) | 98417.5 | 0.194139 | ||||||||
\(713\) | −837275. | − | 837275.i | −1.64698 | − | 1.64698i | ||||
\(714\) | − | 6417.18i | − | 0.0125877i | ||||||
\(715\) | −3198.31 | + | 220957.i | −0.00625617 | + | 0.432211i | ||||
\(716\) | −317671. | −0.619657 | ||||||||
\(717\) | 164542. | − | 164542.i | 0.320065 | − | 0.320065i | ||||
\(718\) | 293694.i | 0.569699i | ||||||||
\(719\) | − | 166519.i | − | 0.322112i | −0.986945 | − | 0.161056i | \(-0.948510\pi\) | ||
0.986945 | − | 0.161056i | \(-0.0514900\pi\) | |||||||
\(720\) | 61318.8 | − | 45482.8i | 0.118285 | − | 0.0877368i | ||||
\(721\) | 767340. | + | 767340.i | 1.47610 | + | 1.47610i | ||||
\(722\) | 234021. | + | 234021.i | 0.448933 | + | 0.448933i | ||||
\(723\) | 213359. | + | 213359.i | 0.408164 | + | 0.408164i | ||||
\(724\) | 317335. | 0.605398 | ||||||||
\(725\) | 232160. | − | 765658.i | 0.441684 | − | 1.45666i | ||||
\(726\) | 273588. | − | 273588.i | 0.519067 | − | 0.519067i | ||||
\(727\) | 552802. | 1.04593 | 0.522963 | − | 0.852355i | \(-0.324827\pi\) | ||||
0.522963 | + | 0.852355i | \(0.324827\pi\) | |||||||
\(728\) | −105023. | − | 786609.i | −0.198163 | − | 1.48421i | ||||
\(729\) | 169827. | 0.319560 | ||||||||
\(730\) | 93289.1 | − | 69196.5i | 0.175059 | − | 0.129849i | ||||
\(731\) | −9472.73 | −0.0177272 | ||||||||
\(732\) | 505174. | 0.942798 | ||||||||
\(733\) | 340941. | − | 340941.i | 0.634558 | − | 0.634558i | −0.314650 | − | 0.949208i | \(-0.601887\pi\) |
0.949208 | + | 0.314650i | \(0.101887\pi\) | |||||||
\(734\) | −152590. | − | 152590.i | −0.283227 | − | 0.283227i | ||||
\(735\) | 575477. | − | 426856.i | 1.06525 | − | 0.790144i | ||||
\(736\) | −563057. | + | 563057.i | −1.03943 | + | 1.03943i | ||||
\(737\) | − | 218825.i | − | 0.402868i | ||||||
\(738\) | 60917.8 | 0.111849 | ||||||||
\(739\) | −684691. | + | 684691.i | −1.25373 | + | 1.25373i | −0.299701 | + | 0.954033i | \(0.596887\pi\) |
−0.954033 | + | 0.299701i | \(0.903113\pi\) | |||||||
\(740\) | 24675.1 | − | 166415.i | 0.0450605 | − | 0.303898i | ||||
\(741\) | 126518. | − | 165507.i | 0.230417 | − | 0.301425i | ||||
\(742\) | 310483.i | 0.563936i | ||||||||
\(743\) | 86076.8 | − | 86076.8i | 0.155922 | − | 0.155922i | −0.624835 | − | 0.780757i | \(-0.714834\pi\) |
0.780757 | + | 0.624835i | \(0.214834\pi\) | |||||||
\(744\) | 1.08945e6 | 1.96816 | ||||||||
\(745\) | 424842. | + | 62993.5i | 0.765447 | + | 0.113497i | ||||
\(746\) | 448523. | + | 448523.i | 0.805947 | + | 0.805947i | ||||
\(747\) | 400422. | − | 400422.i | 0.717590 | − | 0.717590i | ||||
\(748\) | 870.041 | + | 870.041i | 0.00155502 | + | 0.00155502i | ||||
\(749\) | 214402. | − | 214402.i | 0.382178 | − | 0.382178i | ||||
\(750\) | 217028. | − | 459080.i | 0.385828 | − | 0.816142i | ||||
\(751\) | − | 142453.i | − | 0.252575i | −0.991994 | − | 0.126288i | \(-0.959694\pi\) | ||
0.991994 | − | 0.126288i | \(-0.0403062\pi\) | |||||||
\(752\) | 18832.0 | + | 18832.0i | 0.0333013 | + | 0.0333013i | ||||
\(753\) | −1.37479e6 | −2.42464 | ||||||||
\(754\) | −364678. | + | 477062.i | −0.641456 | + | 0.839136i | ||||
\(755\) | 35062.3 | − | 236468.i | 0.0615101 | − | 0.414838i | ||||
\(756\) | −119119. | − | 119119.i | −0.208420 | − | 0.208420i | ||||
\(757\) | − | 564032.i | − | 0.984266i | −0.870520 | − | 0.492133i | \(-0.836217\pi\) | ||
0.870520 | − | 0.492133i | \(-0.163783\pi\) | |||||||
\(758\) | −410494. | −0.714445 | ||||||||
\(759\) | −371622. | − | 371622.i | −0.645086 | − | 0.645086i | ||||
\(760\) | −105740. | − | 142556.i | −0.183068 | − | 0.246808i | ||||
\(761\) | −472994. | + | 472994.i | −0.816744 | + | 0.816744i | −0.985635 | − | 0.168891i | \(-0.945981\pi\) |
0.168891 | + | 0.985635i | \(0.445981\pi\) | |||||||
\(762\) | 477988. | + | 477988.i | 0.823204 | + | 0.823204i | ||||
\(763\) | 1.40392e6i | 2.41153i | ||||||||
\(764\) | 484329.i | 0.829763i | ||||||||
\(765\) | 3193.93 | − | 2369.07i | 0.00545760 | − | 0.00404814i | ||||
\(766\) | − | 740604.i | − | 1.26220i | ||||||
\(767\) | −93123.6 | + | 121822.i | −0.158296 | + | 0.207078i | ||||
\(768\) | − | 817250.i | − | 1.38558i | ||||||
\(769\) | −682483. | − | 682483.i | −1.15409 | − | 1.15409i | −0.985725 | − | 0.168363i | \(-0.946152\pi\) |
−0.168363 | − | 0.985725i | \(-0.553848\pi\) | |||||||
\(770\) | 37067.0 | − | 249988.i | 0.0625181 | − | 0.421636i | ||||
\(771\) | 775980.i | 1.30539i | ||||||||
\(772\) | −156799. | + | 156799.i | −0.263093 | + | 0.263093i | ||||
\(773\) | −235511. | + | 235511.i | −0.394141 | + | 0.394141i | −0.876161 | − | 0.482019i | \(-0.839903\pi\) |
0.482019 | + | 0.876161i | \(0.339903\pi\) | |||||||
\(774\) | −367768. | + | 367768.i | −0.613892 | + | 0.613892i | ||||
\(775\) | 760475. | − | 406599.i | 1.26614 | − | 0.676960i | ||||
\(776\) | −769328. | −1.27758 | ||||||||
\(777\) | −661350. | −1.09544 | ||||||||
\(778\) | 37708.9 | + | 37708.9i | 0.0622995 | + | 0.0622995i | ||||
\(779\) | − | 41192.2i | − | 0.0678797i | ||||||
\(780\) | 294363. | − | 285963.i | 0.483832 | − | 0.470025i | ||||
\(781\) | −99393.3 | −0.162950 | ||||||||
\(782\) | 4776.22 | − | 4776.22i | 0.00781036 | − | 0.00781036i | ||||
\(783\) | 373309.i | 0.608899i | ||||||||
\(784\) | 133260.i | 0.216804i | ||||||||
\(785\) | 182646. | + | 246239.i | 0.296395 | + | 0.399593i | ||||
\(786\) | −161814. | − | 161814.i | −0.261921 | − | 0.261921i | ||||
\(787\) | −499795. | − | 499795.i | −0.806942 | − | 0.806942i | 0.177227 | − | 0.984170i | \(-0.443287\pi\) |
−0.984170 | + | 0.177227i | \(0.943287\pi\) | |||||||
\(788\) | −341476. | − | 341476.i | −0.549931 | − | 0.549931i | ||||
\(789\) | 238506. | 0.383130 | ||||||||
\(790\) | 28620.2 | − | 193021.i | 0.0458583 | − | 0.309279i | ||||
\(791\) | 917089. | − | 917089.i | 1.46575 | − | 1.46575i | ||||
\(792\) | 197850. | 0.315417 | ||||||||
\(793\) | −871194. | + | 116316.i | −1.38538 | + | 0.184967i | ||||
\(794\) | 490482. | 0.778005 | ||||||||
\(795\) | −377677. | + | 280139.i | −0.597566 | + | 0.443241i | ||||
\(796\) | −61156.8 | −0.0965203 | ||||||||
\(797\) | 446000. | 0.702131 | 0.351065 | − | 0.936351i | \(-0.385820\pi\) | ||||
0.351065 | + | 0.936351i | \(0.385820\pi\) | |||||||
\(798\) | −168467. | + | 168467.i | −0.264550 | + | 0.264550i | ||||
\(799\) | 980.909 | + | 980.909i | 0.00153651 | + | 0.00153651i | ||||
\(800\) | −273433. | − | 511411.i | −0.427239 | − | 0.799079i | ||||
\(801\) | 57886.9 | − | 57886.9i | 0.0902225 | − | 0.0902225i | ||||
\(802\) | 232122.i | 0.360885i | ||||||||
\(803\) | 87548.8 | 0.135775 | ||||||||
\(804\) | −287364. | + | 287364.i | −0.444549 | + | 0.444549i | ||||
\(805\) | 1.47779e6 | + | 219120.i | 2.28045 | + | 0.338135i | ||||
\(806\) | −641523. | + | 85652.1i | −0.987511 | + | 0.131846i | ||||
\(807\) | − | 283151.i | − | 0.434782i | ||||||
\(808\) | −187604. | + | 187604.i | −0.287356 | + | 0.287356i | ||||
\(809\) | 235436. | 0.359729 | 0.179865 | − | 0.983691i | \(-0.442434\pi\) | ||||
0.179865 | + | 0.983691i | \(0.442434\pi\) | |||||||
\(810\) | −80994.0 | + | 546242.i | −0.123448 | + | 0.832559i | ||||
\(811\) | −75024.6 | − | 75024.6i | −0.114068 | − | 0.114068i | 0.647769 | − | 0.761837i | \(-0.275702\pi\) |
−0.761837 | + | 0.647769i | \(0.775702\pi\) | |||||||
\(812\) | −522904. | + | 522904.i | −0.793067 | + | 0.793067i | ||||
\(813\) | 537011. | + | 537011.i | 0.812460 | + | 0.812460i | ||||
\(814\) | −83267.9 | + | 83267.9i | −0.125669 | + | 0.125669i | ||||
\(815\) | −71764.6 | − | 10640.9i | −0.108043 | − | 0.0160200i | ||||
\(816\) | 1807.59i | 0.00271468i | ||||||||
\(817\) | 248682. | + | 248682.i | 0.372563 | + | 0.372563i | ||||
\(818\) | −298028. | −0.445400 | ||||||||
\(819\) | −524437. | − | 400893.i | −0.781853 | − | 0.597668i | ||||
\(820\) | 11902.1 | − | 80270.2i | 0.0177009 | − | 0.119379i | ||||
\(821\) | −167606. | − | 167606.i | −0.248659 | − | 0.248659i | 0.571761 | − | 0.820420i | \(-0.306260\pi\) |
−0.820420 | + | 0.571761i | \(0.806260\pi\) | |||||||
\(822\) | − | 707003.i | − | 1.04635i | ||||||
\(823\) | −258606. | −0.381803 | −0.190901 | − | 0.981609i | \(-0.561141\pi\) | ||||
−0.190901 | + | 0.981609i | \(0.561141\pi\) | |||||||
\(824\) | −743131. | − | 743131.i | −1.09449 | − | 1.09449i | ||||
\(825\) | 337534. | − | 180468.i | 0.495918 | − | 0.265150i | ||||
\(826\) | 124000. | − | 124000.i | 0.181745 | − | 0.181745i | ||||
\(827\) | 622523. | + | 622523.i | 0.910216 | + | 0.910216i | 0.996289 | − | 0.0860730i | \(-0.0274318\pi\) |
−0.0860730 | + | 0.996289i | \(0.527432\pi\) | |||||||
\(828\) | 399358.i | 0.582508i | ||||||||
\(829\) | 599629.i | 0.872517i | 0.899821 | + | 0.436258i | \(0.143697\pi\) | ||||
−0.899821 | + | 0.436258i | \(0.856303\pi\) | |||||||
\(830\) | 417328. | + | 562632.i | 0.605789 | + | 0.816710i | ||||
\(831\) | − | 1.07456e6i | − | 1.55607i | ||||||
\(832\) | 77081.6 | + | 577331.i | 0.111354 | + | 0.834024i | ||||
\(833\) | 6941.14i | 0.0100032i | ||||||||
\(834\) | −332795. | − | 332795.i | −0.478459 | − | 0.478459i | ||||
\(835\) | −736706. | − | 109235.i | −1.05663 | − | 0.156671i | ||||
\(836\) | − | 45681.4i | − | 0.0653622i | ||||||
\(837\) | −284513. | + | 284513.i | −0.406118 | + | 0.406118i | ||||
\(838\) | 226887. | − | 226887.i | 0.323089 | − | 0.323089i | ||||
\(839\) | −706041. | + | 706041.i | −1.00301 | + | 1.00301i | −0.00301619 | + | 0.999995i | \(0.500960\pi\) |
−0.999995 | + | 0.00301619i | \(0.999040\pi\) | |||||||
\(840\) | −1.10399e6 | + | 818879.i | −1.56462 | + | 1.16054i | ||||
\(841\) | 931452. | 1.31695 | ||||||||
\(842\) | 214089. | 0.301974 | ||||||||
\(843\) | 53677.5 | + | 53677.5i | 0.0755331 | + | 0.0755331i | ||||
\(844\) | − | 173572.i | − | 0.243666i | ||||||
\(845\) | −441799. | + | 560933.i | −0.618744 | + | 0.785592i | ||||
\(846\) | 76165.4 | 0.106418 | ||||||||
\(847\) | −586198. | + | 586198.i | −0.817104 | + | 0.817104i | ||||
\(848\) | − | 87456.5i | − | 0.121619i | ||||||
\(849\) | − | 1.22800e6i | − | 1.70366i | ||||||
\(850\) | 2319.44 | + | 4338.12i | 0.00321030 | + | 0.00600432i | ||||
\(851\) | −492234. | − | 492234.i | −0.679693 | − | 0.679693i | ||||
\(852\) | 130524. | + | 130524.i | 0.179809 | + | 0.179809i | ||||
\(853\) | −423516. | − | 423516.i | −0.582065 | − | 0.582065i | 0.353405 | − | 0.935470i | \(-0.385024\pi\) |
−0.935470 | + | 0.353405i | \(0.885024\pi\) | |||||||
\(854\) | 1.00517e6 | 1.37824 | ||||||||
\(855\) | −146042. | − | 21654.4i | −0.199777 | − | 0.0296220i | ||||
\(856\) | −207638. | + | 207638.i | −0.283374 | + | 0.283374i | ||||
\(857\) | 881968. | 1.20086 | 0.600428 | − | 0.799679i | \(-0.294997\pi\) | ||||
0.600428 | + | 0.799679i | \(0.294997\pi\) | |||||||
\(858\) | −284738. | + | 38016.4i | −0.386786 | + | 0.0516412i | ||||
\(859\) | −793616. | −1.07553 | −0.537767 | − | 0.843093i | \(-0.680732\pi\) | ||||
−0.537767 | + | 0.843093i | \(0.680732\pi\) | |||||||
\(860\) | 412747. | + | 556455.i | 0.558067 | + | 0.752373i | ||||
\(861\) | −319003. | −0.430317 | ||||||||
\(862\) | −529073. | −0.712034 | ||||||||
\(863\) | −137937. | + | 137937.i | −0.185208 | + | 0.185208i | −0.793621 | − | 0.608413i | \(-0.791807\pi\) |
0.608413 | + | 0.793621i | \(0.291807\pi\) | |||||||
\(864\) | 191332. | + | 191332.i | 0.256307 | + | 0.256307i | ||||
\(865\) | 125075. | − | 92773.7i | 0.167163 | − | 0.123992i | ||||
\(866\) | 83117.3 | − | 83117.3i | 0.110830 | − | 0.110830i | ||||
\(867\) | − | 977829.i | − | 1.30084i | ||||||
\(868\) | −797050. | −1.05790 | ||||||||
\(869\) | 104001. | − | 104001.i | 0.137721 | − | 0.137721i | ||||
\(870\) | 1.02882e6 | + | 152549.i | 1.35926 | + | 0.201544i | ||||
\(871\) | 429405. | − | 561736.i | 0.566019 | − | 0.740451i | ||||
\(872\) | − | 1.35963e6i | − | 1.78808i | ||||||
\(873\) | −452500. | + | 452500.i | −0.593732 | + | 0.593732i | ||||
\(874\) | −250775. | −0.328293 | ||||||||
\(875\) | −465011. | + | 983639.i | −0.607362 | + | 1.28475i | ||||
\(876\) | −114970. | − | 114970.i | −0.149822 | − | 0.149822i | ||||
\(877\) | 498804. | − | 498804.i | 0.648531 | − | 0.648531i | −0.304107 | − | 0.952638i | \(-0.598358\pi\) |
0.952638 | + | 0.304107i | \(0.0983580\pi\) | |||||||
\(878\) | 575953. | + | 575953.i | 0.747133 | + | 0.747133i | ||||
\(879\) | 1.29030e6 | − | 1.29030e6i | 1.66999 | − | 1.66999i | ||||
\(880\) | −10441.0 | + | 70416.4i | −0.0134827 | + | 0.0909303i | ||||
\(881\) | − | 702325.i | − | 0.904870i | −0.891797 | − | 0.452435i | \(-0.850556\pi\) | ||
0.891797 | − | 0.452435i | \(-0.149444\pi\) | |||||||
\(882\) | 269482. | + | 269482.i | 0.346412 | + | 0.346412i | ||||
\(883\) | 42952.3 | 0.0550890 | 0.0275445 | − | 0.999621i | \(-0.491231\pi\) | ||||
0.0275445 | + | 0.999621i | \(0.491231\pi\) | |||||||
\(884\) | 526.143 | + | 3940.74i | 0.000673285 | + | 0.00504282i | ||||
\(885\) | 262718. | + | 38954.5i | 0.335431 | + | 0.0497361i | ||||
\(886\) | −470219. | − | 470219.i | −0.599009 | − | 0.599009i | ||||
\(887\) | 653556.i | 0.830683i | 0.909666 | + | 0.415342i | \(0.136338\pi\) | ||||
−0.909666 | + | 0.415342i | \(0.863662\pi\) | |||||||
\(888\) | 640485. | 0.812238 | ||||||||
\(889\) | −1.02415e6 | − | 1.02415e6i | −1.29587 | − | 1.29587i | ||||
\(890\) | 60331.0 | + | 81336.8i | 0.0761659 | + | 0.102685i | ||||
\(891\) | −294320. | + | 294320.i | −0.370736 | + | 0.370736i | ||||
\(892\) | 284859. | + | 284859.i | 0.358014 | + | 0.358014i | ||||
\(893\) | − | 51502.4i | − | 0.0645840i | ||||||
\(894\) | 558314.i | 0.698559i | ||||||||
\(895\) | −570311. | − | 768880.i | −0.711977 | − | 0.959870i | ||||
\(896\) | 367653.i | 0.457954i | ||||||||
\(897\) | −224732. | − | 1.68321e6i | −0.279306 | − | 2.09196i | ||||
\(898\) | − | 768469.i | − | 0.952958i | ||||||
\(899\) | 1.24894e6 | + | 1.24894e6i | 1.54534 | + | 1.54534i | ||||
\(900\) | −278332. | − | 84394.9i | −0.343620 | − | 0.104191i | ||||
\(901\) | − | 4555.37i | − | 0.00561143i | ||||||
\(902\) | −40164.3 | + | 40164.3i | −0.0493660 | + | 0.0493660i | ||||
\(903\) | 1.92586e6 | − | 1.92586e6i | 2.36183 | − | 2.36183i | ||||
\(904\) | −888156. | + | 888156.i | −1.08681 | + | 1.08681i | ||||
\(905\) | 569709. | + | 768068.i | 0.695594 | + | 0.937783i | ||||
\(906\) | 310758. | 0.378588 | ||||||||
\(907\) | −906967. | −1.10250 | −0.551248 | − | 0.834341i | \(-0.685848\pi\) | ||||
−0.551248 | + | 0.834341i | \(0.685848\pi\) | |||||||
\(908\) | 311127. | + | 311127.i | 0.377369 | + | 0.377369i | ||||
\(909\) | 220689.i | 0.267087i | ||||||||
\(910\) | 585709. | − | 568995.i | 0.707293 | − | 0.687109i | ||||
\(911\) | 722252. | 0.870266 | 0.435133 | − | 0.900366i | \(-0.356701\pi\) | ||||
0.435133 | + | 0.900366i | \(0.356701\pi\) | |||||||
\(912\) | 47453.5 | − | 47453.5i | 0.0570530 | − | 0.0570530i | ||||
\(913\) | 528012.i | 0.633435i | ||||||||
\(914\) | − | 345381.i | − | 0.413433i | ||||||
\(915\) | 906934. | + | 1.22271e6i | 1.08326 | + | 1.46043i | ||||
\(916\) | 42311.0 | + | 42311.0i | 0.0504269 | + | 0.0504269i | ||||
\(917\) | 346707. | + | 346707.i | 0.412310 | + | 0.412310i | ||||
\(918\) | −1623.00 | − | 1623.00i | −0.00192590 | − | 0.00192590i | ||||
\(919\) | 494776. | 0.585838 | 0.292919 | − | 0.956137i | \(-0.405373\pi\) | ||||
0.292919 | + | 0.956137i | \(0.405373\pi\) | |||||||
\(920\) | −1.43117e6 | − | 212207.i | −1.69089 | − | 0.250717i | ||||
\(921\) | −1.01797e6 | + | 1.01797e6i | −1.20009 | + | 1.20009i | ||||
\(922\) | −220205. | −0.259039 | ||||||||
\(923\) | −255148. | − | 195041.i | −0.299494 | − | 0.228941i | ||||
\(924\) | −353768. | −0.414357 | ||||||||
\(925\) | 447084. | − | 239040.i | 0.522523 | − | 0.279375i | ||||
\(926\) | 85239.4 | 0.0994074 | ||||||||
\(927\) | −874184. | −1.01729 | ||||||||
\(928\) | 839899. | − | 839899.i | 0.975284 | − | 0.975284i | ||||
\(929\) | −462963. | − | 462963.i | −0.536432 | − | 0.536432i | 0.386047 | − | 0.922479i | \(-0.373840\pi\) |
−0.922479 | + | 0.386047i | \(0.873840\pi\) | |||||||
\(930\) | 667841. | + | 900367.i | 0.772160 | + | 1.04101i | ||||
\(931\) | 182222. | − | 182222.i | 0.210233 | − | 0.210233i | ||||
\(932\) | 506568.i | 0.583185i | ||||||||
\(933\) | −1.13996e6 | −1.30956 | ||||||||
\(934\) | 224893. | − | 224893.i | 0.257799 | − | 0.257799i | ||||
\(935\) | −543.843 | + | 3667.80i | −0.000622085 | + | 0.00419548i | ||||
\(936\) | 507891. | + | 388245.i | 0.579721 | + | 0.443153i | ||||
\(937\) | 337190.i | 0.384057i | 0.981389 | + | 0.192029i | \(0.0615066\pi\) | ||||
−0.981389 | + | 0.192029i | \(0.938493\pi\) | |||||||
\(938\) | −571782. | + | 571782.i | −0.649867 | + | 0.649867i | ||||
\(939\) | −511579. | −0.580205 | ||||||||
\(940\) | 14881.1 | − | 100362.i | 0.0168415 | − | 0.113583i | ||||
\(941\) | −192025. | − | 192025.i | −0.216859 | − | 0.216859i | 0.590314 | − | 0.807174i | \(-0.299004\pi\) |
−0.807174 | + | 0.590314i | \(0.799004\pi\) | |||||||
\(942\) | −281814. | + | 281814.i | −0.317585 | + | 0.317585i | ||||
\(943\) | −237429. | − | 237429.i | −0.267000 | − | 0.267000i | ||||
\(944\) | −34928.3 | + | 34928.3i | −0.0391952 | + | 0.0391952i | ||||
\(945\) | 74458.8 | − | 502167.i | 0.0833782 | − | 0.562321i | ||||
\(946\) | − | 484954.i | − | 0.541899i | ||||||
\(947\) | 23050.0 | + | 23050.0i | 0.0257023 | + | 0.0257023i | 0.719841 | − | 0.694139i | \(-0.244215\pi\) |
−0.694139 | + | 0.719841i | \(0.744215\pi\) | |||||||
\(948\) | −273152. | −0.303939 | ||||||||
\(949\) | 224742. | + | 171799.i | 0.249547 | + | 0.190760i | ||||
\(950\) | 52995.3 | − | 174777.i | 0.0587205 | − | 0.193659i | ||||
\(951\) | 845842. | + | 845842.i | 0.935251 | + | 0.935251i | ||||
\(952\) | − | 13315.9i | − | 0.0146925i | ||||||
\(953\) | −1.32264e6 | −1.45632 | −0.728159 | − | 0.685409i | \(-0.759624\pi\) | ||||
−0.728159 | + | 0.685409i | \(0.759624\pi\) | |||||||
\(954\) | −176857. | − | 176857.i | −0.194324 | − | 0.194324i | ||||
\(955\) | −1.17226e6 | + | 869512.i | −1.28533 | + | 0.953387i | ||||
\(956\) | 116583. | − | 116583.i | 0.127561 | − | 0.127561i | ||||
\(957\) | 554339. | + | 554339.i | 0.605273 | + | 0.605273i | ||||
\(958\) | 1.01408e6i | 1.10494i | ||||||||
\(959\) | 1.51485e6i | 1.64714i | ||||||||
\(960\) | 810276. | − | 601016.i | 0.879205 | − | 0.652144i | ||||
\(961\) | 980212.i | 1.06139i | ||||||||
\(962\) | −377151. | + | 50354.9i | −0.407536 | + | 0.0544116i | ||||
\(963\) | 244255.i | 0.263385i | ||||||||
\(964\) | 151171. | + | 151171.i | 0.162673 | + | 0.162673i | ||||
\(965\) | −661013. | − | 98011.7i | −0.709831 | − | 0.105250i | ||||
\(966\) | 1.94206e6i | 2.08118i | ||||||||
\(967\) | 367434. | − | 367434.i | 0.392940 | − | 0.392940i | −0.482794 | − | 0.875734i | \(-0.660378\pi\) |
0.875734 | + | 0.482794i | \(0.160378\pi\) | |||||||
\(968\) | 567704. | − | 567704.i | 0.605859 | − | 0.605859i | ||||
\(969\) | 2471.72 | − | 2471.72i | 0.00263240 | − | 0.00263240i | ||||
\(970\) | −471606. | − | 635808.i | −0.501228 | − | 0.675744i | ||||
\(971\) | 976368. | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326759\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326759\pi\) | |||||||
\(972\) | 577049. | 0.610774 | ||||||||
\(973\) | 713057. | + | 713057.i | 0.753180 | + | 0.753180i | ||||
\(974\) | − | 31338.8i | − | 0.0330342i | ||||||
\(975\) | 1.22060e6 | + | 199080.i | 1.28400 | + | 0.209421i | ||||
\(976\) | −283135. | −0.297231 | ||||||||
\(977\) | −326605. | + | 326605.i | −0.342164 | + | 0.342164i | −0.857180 | − | 0.515016i | \(-0.827786\pi\) |
0.515016 | + | 0.857180i | \(0.327786\pi\) | |||||||
\(978\) | − | 94310.6i | − | 0.0986014i | ||||||
\(979\) | 76331.9i | 0.0796418i | ||||||||
\(980\) | 407742. | − | 302440.i | 0.424555 | − | 0.314910i | ||||
\(981\) | −799700. | − | 799700.i | −0.830977 | − | 0.830977i | ||||
\(982\) | −33008.4 | − | 33008.4i | −0.0342296 | − | 0.0342296i | ||||
\(983\) | 517424. | + | 517424.i | 0.535476 | + | 0.535476i | 0.922197 | − | 0.386721i | \(-0.126392\pi\) |
−0.386721 | + | 0.922197i | \(0.626392\pi\) | |||||||
\(984\) | 308939. | 0.319067 | ||||||||
\(985\) | 213449. | − | 1.43955e6i | 0.219999 | − | 1.48373i | ||||
\(986\) | −7124.57 | + | 7124.57i | −0.00732833 | + | 0.00732833i | ||||
\(987\) | −398848. | −0.409424 | ||||||||
\(988\) | 89641.4 | − | 117266.i | 0.0918322 | − | 0.120132i | ||||
\(989\) | 2.86678e6 | 2.93091 | ||||||||
\(990\) | 121284. | + | 163512.i | 0.123747 | + | 0.166832i | ||||
\(991\) | −1.03885e6 | −1.05781 | −0.528904 | − | 0.848681i | \(-0.677397\pi\) | ||||
−0.528904 | + | 0.848681i | \(0.677397\pi\) | |||||||
\(992\) | 1.28024e6 | 1.30097 | ||||||||
\(993\) | 1.01594e6 | − | 1.01594e6i | 1.03032 | − | 1.03032i | ||||
\(994\) | 259711. | + | 259711.i | 0.262855 | + | 0.262855i | ||||
\(995\) | −109794. | − | 148022.i | −0.110901 | − | 0.149513i | ||||
\(996\) | 693391. | − | 693391.i | 0.698971 | − | 0.698971i | ||||
\(997\) | − | 1.68107e6i | − | 1.69121i | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||
0.533812 | − | 0.845603i | \(-0.320759\pi\) | |||||||
\(998\) | 1.10167e6 | 1.10609 | ||||||||
\(999\) | −167266. | + | 167266.i | −0.167601 | + | 0.167601i |
(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 | 65.5.g.a.34.10 | ✓ | 52 | |
5.4 | even | 2 | inner | 65.5.g.a.34.17 | yes | 52 | |
13.5 | odd | 4 | inner | 65.5.g.a.44.17 | yes | 52 | |
65.44 | odd | 4 | inner | 65.5.g.a.44.10 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.5.g.a.34.10 | ✓ | 52 | 1.1 | even | 1 | trivial | |
65.5.g.a.34.17 | yes | 52 | 5.4 | even | 2 | inner | |
65.5.g.a.44.10 | yes | 52 | 65.44 | odd | 4 | inner | |
65.5.g.a.44.17 | yes | 52 | 13.5 | odd | 4 | inner |