Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(27,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.27");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.d (of order \(6\), 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: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.8 | ||
Root | \(0.500000 - 14.3823i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.27 |
Dual form | 38.5.d.a.31.8 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | + | 1.41421i | 0.612372 | + | 0.353553i | ||||
\(3\) | 10.4807 | + | 6.05105i | 1.16453 | + | 0.672339i | 0.952384 | − | 0.304900i | \(-0.0986230\pi\) |
0.212141 | + | 0.977239i | \(0.431956\pi\) | |||||||
\(4\) | 4.00000 | + | 6.92820i | 0.250000 | + | 0.433013i | ||||
\(5\) | 9.13314 | − | 15.8191i | 0.365326 | − | 0.632763i | −0.623503 | − | 0.781821i | \(-0.714291\pi\) |
0.988828 | + | 0.149059i | \(0.0476243\pi\) | |||||||
\(6\) | 17.1150 | + | 29.6440i | 0.475416 | + | 0.823444i | ||||
\(7\) | −40.6944 | −0.830498 | −0.415249 | − | 0.909708i | \(-0.636306\pi\) | ||||
−0.415249 | + | 0.909708i | \(0.636306\pi\) | |||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 32.7305 | + | 56.6909i | 0.404080 | + | 0.699887i | ||||
\(10\) | 44.7431 | − | 25.8324i | 0.447431 | − | 0.258324i | ||||
\(11\) | −52.4698 | −0.433634 | −0.216817 | − | 0.976212i | \(-0.569568\pi\) | ||||
−0.216817 | + | 0.976212i | \(0.569568\pi\) | |||||||
\(12\) | 96.8168i | 0.672339i | ||||||||
\(13\) | 133.461 | − | 77.0538i | 0.789711 | − | 0.455940i | −0.0501501 | − | 0.998742i | \(-0.515970\pi\) |
0.839861 | + | 0.542802i | \(0.182637\pi\) | |||||||
\(14\) | −99.6805 | − | 57.5506i | −0.508574 | − | 0.293625i | ||||
\(15\) | 191.444 | − | 110.530i | 0.850862 | − | 0.491245i | ||||
\(16\) | −32.0000 | + | 55.4256i | −0.125000 | + | 0.216506i | ||||
\(17\) | −137.797 | + | 238.671i | −0.476805 | + | 0.825850i | −0.999647 | − | 0.0265796i | \(-0.991538\pi\) |
0.522842 | + | 0.852430i | \(0.324872\pi\) | |||||||
\(18\) | 185.152i | 0.571455i | ||||||||
\(19\) | −70.6137 | − | 354.026i | −0.195606 | − | 0.980683i | ||||
\(20\) | 146.130 | 0.365326 | ||||||||
\(21\) | −426.507 | − | 246.244i | −0.967136 | − | 0.558376i | ||||
\(22\) | −128.524 | − | 74.2034i | −0.265546 | − | 0.153313i | ||||
\(23\) | −448.573 | − | 776.951i | −0.847964 | − | 1.46872i | −0.883022 | − | 0.469332i | \(-0.844495\pi\) |
0.0350577 | − | 0.999385i | \(-0.488838\pi\) | |||||||
\(24\) | −136.920 | + | 237.152i | −0.237708 | + | 0.411722i | ||||
\(25\) | 145.671 | + | 252.310i | 0.233074 | + | 0.403697i | ||||
\(26\) | 435.882 | 0.644796 | ||||||||
\(27\) | − | 188.055i | − | 0.257963i | ||||||
\(28\) | −162.778 | − | 281.939i | −0.207625 | − | 0.359616i | ||||
\(29\) | 268.560 | − | 155.053i | 0.319334 | − | 0.184368i | −0.331762 | − | 0.943363i | \(-0.607643\pi\) |
0.651096 | + | 0.758996i | \(0.274310\pi\) | |||||||
\(30\) | 625.253 | 0.694726 | ||||||||
\(31\) | 904.934i | 0.941659i | 0.882224 | + | 0.470829i | \(0.156045\pi\) | ||||
−0.882224 | + | 0.470829i | \(0.843955\pi\) | |||||||
\(32\) | −156.767 | + | 90.5097i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −549.921 | − | 317.497i | −0.504978 | − | 0.291549i | ||||
\(34\) | −675.063 | + | 389.748i | −0.583964 | + | 0.337152i | ||||
\(35\) | −371.668 | + | 643.747i | −0.303402 | + | 0.525508i | ||||
\(36\) | −261.844 | + | 453.527i | −0.202040 | + | 0.349944i | ||||
\(37\) | − | 115.035i | − | 0.0840282i | −0.999117 | − | 0.0420141i | \(-0.986623\pi\) | ||
0.999117 | − | 0.0420141i | \(-0.0133774\pi\) | |||||||
\(38\) | 327.702 | − | 967.047i | 0.226940 | − | 0.669700i | ||||
\(39\) | 1865.03 | 1.22618 | ||||||||
\(40\) | 357.945 | + | 206.659i | 0.223715 | + | 0.129162i | ||||
\(41\) | 1836.56 | + | 1060.34i | 1.09254 | + | 0.630778i | 0.934251 | − | 0.356615i | \(-0.116069\pi\) |
0.158288 | + | 0.987393i | \(0.449402\pi\) | |||||||
\(42\) | −696.483 | − | 1206.34i | −0.394832 | − | 0.683869i | ||||
\(43\) | −1000.64 | + | 1733.16i | −0.541179 | + | 0.937350i | 0.457657 | + | 0.889129i | \(0.348689\pi\) |
−0.998837 | + | 0.0482214i | \(0.984645\pi\) | |||||||
\(44\) | −209.879 | − | 363.521i | −0.108409 | − | 0.187769i | ||||
\(45\) | 1195.73 | 0.590483 | ||||||||
\(46\) | − | 2537.51i | − | 1.19920i | ||||||
\(47\) | 2012.65 | + | 3486.01i | 0.911113 | + | 1.57809i | 0.812495 | + | 0.582968i | \(0.198109\pi\) |
0.0986174 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(48\) | −670.767 | + | 387.267i | −0.291131 | + | 0.168085i | ||||
\(49\) | −744.965 | −0.310273 | ||||||||
\(50\) | 824.042i | 0.329617i | ||||||||
\(51\) | −2888.42 | + | 1667.63i | −1.11050 | + | 0.641149i | ||||
\(52\) | 1067.69 | + | 616.430i | 0.394855 | + | 0.227970i | ||||
\(53\) | 2557.89 | − | 1476.80i | 0.910607 | − | 0.525739i | 0.0299806 | − | 0.999550i | \(-0.490455\pi\) |
0.880626 | + | 0.473811i | \(0.157122\pi\) | |||||||
\(54\) | 265.950 | − | 460.639i | 0.0912037 | − | 0.157970i | ||||
\(55\) | −479.214 | + | 830.022i | −0.158418 | + | 0.274388i | ||||
\(56\) | − | 920.809i | − | 0.293625i | ||||||
\(57\) | 1402.15 | − | 4137.74i | 0.431563 | − | 1.27354i | ||||
\(58\) | 877.113 | 0.260735 | ||||||||
\(59\) | −5202.69 | − | 3003.77i | −1.49460 | − | 0.862905i | −0.494615 | − | 0.869112i | \(-0.664691\pi\) |
−0.999981 | + | 0.00620675i | \(0.998024\pi\) | |||||||
\(60\) | 1531.55 | + | 884.242i | 0.425431 | + | 0.245623i | ||||
\(61\) | 606.668 | + | 1050.78i | 0.163039 | + | 0.282392i | 0.935957 | − | 0.352114i | \(-0.114537\pi\) |
−0.772918 | + | 0.634506i | \(0.781204\pi\) | |||||||
\(62\) | −1279.77 | + | 2216.63i | −0.332927 | + | 0.576646i | ||||
\(63\) | −1331.95 | − | 2307.00i | −0.335588 | − | 0.581255i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 2814.97i | − | 0.666266i | ||||||
\(66\) | −898.018 | − | 1555.41i | −0.206157 | − | 0.357074i | ||||
\(67\) | −5554.61 | + | 3206.96i | −1.23738 | + | 0.714404i | −0.968559 | − | 0.248785i | \(-0.919969\pi\) |
−0.268825 | + | 0.963189i | \(0.586635\pi\) | |||||||
\(68\) | −2204.75 | −0.476805 | ||||||||
\(69\) | − | 10857.4i | − | 2.28048i | ||||||
\(70\) | −1820.79 | + | 1051.24i | −0.371590 | + | 0.214538i | ||||
\(71\) | −2812.41 | − | 1623.75i | −0.557907 | − | 0.322108i | 0.194398 | − | 0.980923i | \(-0.437725\pi\) |
−0.752305 | + | 0.658815i | \(0.771058\pi\) | |||||||
\(72\) | −1282.77 | + | 740.606i | −0.247447 | + | 0.142864i | ||||
\(73\) | −3824.61 | + | 6624.43i | −0.717698 | + | 1.24309i | 0.244211 | + | 0.969722i | \(0.421471\pi\) |
−0.961910 | + | 0.273368i | \(0.911862\pi\) | |||||||
\(74\) | 162.683 | − | 281.776i | 0.0297085 | − | 0.0514565i | ||||
\(75\) | 3525.86i | 0.626820i | ||||||||
\(76\) | 2170.31 | − | 1905.33i | 0.375747 | − | 0.329870i | ||||
\(77\) | 2135.23 | 0.360133 | ||||||||
\(78\) | 4568.36 | + | 2637.55i | 0.750881 | + | 0.433522i | ||||
\(79\) | 5809.97 | + | 3354.39i | 0.930936 | + | 0.537476i | 0.887107 | − | 0.461563i | \(-0.152711\pi\) |
0.0438282 | + | 0.999039i | \(0.486045\pi\) | |||||||
\(80\) | 584.521 | + | 1012.42i | 0.0913314 | + | 0.158191i | ||||
\(81\) | 3789.10 | − | 6562.91i | 0.577519 | − | 1.00029i | ||||
\(82\) | 2999.09 | + | 5194.57i | 0.446027 | + | 0.772542i | ||||
\(83\) | 8748.10 | 1.26986 | 0.634932 | − | 0.772568i | \(-0.281028\pi\) | ||||
0.634932 | + | 0.772568i | \(0.281028\pi\) | |||||||
\(84\) | − | 3939.90i | − | 0.558376i | ||||||
\(85\) | 2517.03 | + | 4359.63i | 0.348378 | + | 0.603408i | ||||
\(86\) | −4902.12 | + | 2830.24i | −0.662807 | + | 0.382672i | ||||
\(87\) | 3752.94 | 0.495830 | ||||||||
\(88\) | − | 1187.26i | − | 0.153313i | ||||||
\(89\) | 6846.92 | − | 3953.07i | 0.864401 | − | 0.499062i | −0.00108292 | − | 0.999999i | \(-0.500345\pi\) |
0.865483 | + | 0.500938i | \(0.167011\pi\) | |||||||
\(90\) | 2928.92 | + | 1691.02i | 0.361596 | + | 0.208767i | ||||
\(91\) | −5431.12 | + | 3135.66i | −0.655853 | + | 0.378657i | ||||
\(92\) | 3588.58 | − | 6215.61i | 0.423982 | − | 0.734359i | ||||
\(93\) | −5475.80 | + | 9484.37i | −0.633114 | + | 1.09659i | ||||
\(94\) | 11385.3i | 1.28851i | ||||||||
\(95\) | −6245.29 | − | 2116.33i | −0.691999 | − | 0.234497i | ||||
\(96\) | −2190.72 | −0.237708 | ||||||||
\(97\) | 6081.56 | + | 3511.19i | 0.646356 | + | 0.373174i | 0.787059 | − | 0.616878i | \(-0.211603\pi\) |
−0.140703 | + | 0.990052i | \(0.544936\pi\) | |||||||
\(98\) | −1824.78 | − | 1053.54i | −0.190003 | − | 0.109698i | ||||
\(99\) | −1717.36 | − | 2974.56i | −0.175223 | − | 0.303495i | ||||
\(100\) | −1165.37 | + | 2018.48i | −0.116537 | + | 0.201848i | ||||
\(101\) | −4727.68 | − | 8188.57i | −0.463452 | − | 0.802723i | 0.535678 | − | 0.844422i | \(-0.320056\pi\) |
−0.999130 | + | 0.0416997i | \(0.986723\pi\) | |||||||
\(102\) | −9433.53 | −0.906722 | ||||||||
\(103\) | − | 1584.35i | − | 0.149340i | −0.997208 | − | 0.0746699i | \(-0.976210\pi\) | ||
0.997208 | − | 0.0746699i | \(-0.0237903\pi\) | |||||||
\(104\) | 1743.53 | + | 3019.88i | 0.161199 | + | 0.279205i | ||||
\(105\) | −7790.70 | + | 4497.96i | −0.706639 | + | 0.407978i | ||||
\(106\) | 8354.05 | 0.743507 | ||||||||
\(107\) | − | 5489.78i | − | 0.479498i | −0.970835 | − | 0.239749i | \(-0.922935\pi\) | ||
0.970835 | − | 0.239749i | \(-0.0770652\pi\) | |||||||
\(108\) | 1302.88 | − | 752.221i | 0.111701 | − | 0.0644908i | ||||
\(109\) | −1219.92 | − | 704.320i | −0.102678 | − | 0.0592812i | 0.447782 | − | 0.894143i | \(-0.352214\pi\) |
−0.550460 | + | 0.834862i | \(0.685548\pi\) | |||||||
\(110\) | −2347.66 | + | 1355.42i | −0.194021 | + | 0.112018i | ||||
\(111\) | 696.080 | − | 1205.65i | 0.0564954 | − | 0.0978530i | ||||
\(112\) | 1302.22 | − | 2255.51i | 0.103812 | − | 0.179808i | ||||
\(113\) | − | 2362.53i | − | 0.185021i | −0.995712 | − | 0.0925105i | \(-0.970511\pi\) | ||
0.995712 | − | 0.0925105i | \(-0.0294892\pi\) | |||||||
\(114\) | 9286.20 | − | 8152.42i | 0.714543 | − | 0.627302i | ||||
\(115\) | −16387.5 | −1.23913 | ||||||||
\(116\) | 2148.48 | + | 1240.43i | 0.159667 | + | 0.0921838i | ||||
\(117\) | 8736.49 | + | 5044.02i | 0.638212 | + | 0.368472i | ||||
\(118\) | −8495.95 | − | 14715.4i | −0.610166 | − | 1.05684i | ||||
\(119\) | 5607.55 | − | 9712.56i | 0.395985 | − | 0.685867i | ||||
\(120\) | 2501.01 | + | 4331.88i | 0.173682 | + | 0.300825i | ||||
\(121\) | −11887.9 | −0.811961 | ||||||||
\(122\) | 3431.83i | 0.230572i | ||||||||
\(123\) | 12832.3 | + | 22226.2i | 0.848194 | + | 1.46911i | ||||
\(124\) | −6269.57 | + | 3619.74i | −0.407750 | + | 0.235415i | ||||
\(125\) | 16738.2 | 1.07124 | ||||||||
\(126\) | − | 7534.63i | − | 0.474593i | ||||||
\(127\) | 20297.0 | − | 11718.5i | 1.25842 | − | 0.726547i | 0.285650 | − | 0.958334i | \(-0.407790\pi\) |
0.972767 | + | 0.231786i | \(0.0744570\pi\) | |||||||
\(128\) | −1254.14 | − | 724.077i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −20974.9 | + | 12109.9i | −1.26043 | + | 0.727712i | ||||
\(130\) | 3980.97 | − | 6895.25i | 0.235560 | − | 0.408003i | ||||
\(131\) | 1960.23 | − | 3395.22i | 0.114226 | − | 0.197845i | −0.803244 | − | 0.595650i | \(-0.796895\pi\) |
0.917470 | + | 0.397805i | \(0.130228\pi\) | |||||||
\(132\) | − | 5079.96i | − | 0.291549i | ||||||
\(133\) | 2873.58 | + | 14406.9i | 0.162450 | + | 0.814455i | ||||
\(134\) | −18141.3 | −1.01032 | ||||||||
\(135\) | −2974.86 | − | 1717.53i | −0.163229 | − | 0.0942405i | ||||
\(136\) | −5400.50 | − | 3117.98i | −0.291982 | − | 0.168576i | ||||
\(137\) | −13070.8 | − | 22639.4i | −0.696406 | − | 1.20621i | −0.969704 | − | 0.244281i | \(-0.921448\pi\) |
0.273298 | − | 0.961929i | \(-0.411885\pi\) | |||||||
\(138\) | 15354.6 | − | 26595.0i | 0.806271 | − | 1.39650i | ||||
\(139\) | −9845.46 | − | 17052.8i | −0.509573 | − | 0.882606i | −0.999939 | − | 0.0110893i | \(-0.996470\pi\) |
0.490366 | − | 0.871517i | \(-0.336863\pi\) | |||||||
\(140\) | −5946.68 | −0.303402 | ||||||||
\(141\) | 48714.5i | 2.45031i | ||||||||
\(142\) | −4592.64 | − | 7954.69i | −0.227765 | − | 0.394500i | ||||
\(143\) | −7002.67 | + | 4042.99i | −0.342446 | + | 0.197711i | ||||
\(144\) | −4189.50 | −0.202040 | ||||||||
\(145\) | − | 5664.49i | − | 0.269417i | ||||||
\(146\) | −18736.7 | + | 10817.6i | −0.878997 | + | 0.507489i | ||||
\(147\) | −7807.78 | − | 4507.82i | −0.361321 | − | 0.208609i | ||||
\(148\) | 796.983 | − | 460.138i | 0.0363853 | − | 0.0210070i | ||||
\(149\) | 10988.5 | − | 19032.6i | 0.494953 | − | 0.857284i | −0.505030 | − | 0.863102i | \(-0.668518\pi\) |
0.999983 | + | 0.00581763i | \(0.00185182\pi\) | |||||||
\(150\) | −4986.32 | + | 8636.57i | −0.221614 | + | 0.383847i | ||||
\(151\) | 22987.8i | 1.00819i | 0.863647 | + | 0.504096i | \(0.168174\pi\) | ||||
−0.863647 | + | 0.504096i | \(0.831826\pi\) | |||||||
\(152\) | 8010.70 | − | 1597.80i | 0.346724 | − | 0.0691571i | ||||
\(153\) | −18040.6 | −0.770669 | ||||||||
\(154\) | 5230.21 | + | 3019.67i | 0.220535 | + | 0.127326i | ||||
\(155\) | 14315.2 | + | 8264.89i | 0.595846 | + | 0.344012i | ||||
\(156\) | 7460.11 | + | 12921.3i | 0.306546 | + | 0.530953i | ||||
\(157\) | 20607.3 | − | 35692.9i | 0.836029 | − | 1.44804i | −0.0571609 | − | 0.998365i | \(-0.518205\pi\) |
0.893190 | − | 0.449680i | \(-0.148462\pi\) | |||||||
\(158\) | 9487.64 | + | 16433.1i | 0.380053 | + | 0.658271i | ||||
\(159\) | 35744.8 | 1.41390 | ||||||||
\(160\) | 3306.55i | 0.129162i | ||||||||
\(161\) | 18254.4 | + | 31617.6i | 0.704233 | + | 1.21977i | ||||
\(162\) | 18562.7 | − | 10717.2i | 0.707313 | − | 0.408367i | ||||
\(163\) | −3003.65 | −0.113051 | −0.0565254 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565254 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(164\) | 16965.4i | 0.630778i | ||||||||
\(165\) | −10045.0 | + | 5799.49i | −0.368963 | + | 0.213021i | ||||
\(166\) | 21428.4 | + | 12371.7i | 0.777630 | + | 0.448965i | ||||
\(167\) | −28990.2 | + | 16737.5i | −1.03949 | + | 0.600147i | −0.919688 | − | 0.392651i | \(-0.871558\pi\) |
−0.119798 | + | 0.992798i | \(0.538225\pi\) | |||||||
\(168\) | 5571.87 | − | 9650.75i | 0.197416 | − | 0.341934i | ||||
\(169\) | −2405.93 | + | 4167.19i | −0.0842381 | + | 0.145905i | ||||
\(170\) | 14238.5i | 0.492681i | ||||||||
\(171\) | 17758.8 | − | 15590.6i | 0.607327 | − | 0.533176i | ||||
\(172\) | −16010.2 | −0.541179 | ||||||||
\(173\) | 24129.7 | + | 13931.3i | 0.806231 | + | 0.465478i | 0.845645 | − | 0.533745i | \(-0.179216\pi\) |
−0.0394143 | + | 0.999223i | \(0.512549\pi\) | |||||||
\(174\) | 9192.79 | + | 5307.46i | 0.303633 | + | 0.175303i | ||||
\(175\) | −5928.01 | − | 10267.6i | −0.193568 | − | 0.335269i | ||||
\(176\) | 1679.03 | − | 2908.17i | 0.0542043 | − | 0.0938846i | ||||
\(177\) | −36352.0 | − | 62963.5i | −1.16033 | − | 2.00975i | ||||
\(178\) | 22361.9 | 0.705780 | ||||||||
\(179\) | − | 9775.14i | − | 0.305082i | −0.988297 | − | 0.152541i | \(-0.951254\pi\) | ||
0.988297 | − | 0.152541i | \(-0.0487457\pi\) | |||||||
\(180\) | 4782.91 | + | 8284.25i | 0.147621 | + | 0.255687i | ||||
\(181\) | −20831.3 | + | 12027.0i | −0.635858 | + | 0.367113i | −0.783017 | − | 0.622000i | \(-0.786320\pi\) |
0.147159 | + | 0.989113i | \(0.452987\pi\) | |||||||
\(182\) | −17738.0 | −0.535502 | ||||||||
\(183\) | 14683.9i | 0.438470i | ||||||||
\(184\) | 17580.4 | − | 10150.0i | 0.519270 | − | 0.299801i | ||||
\(185\) | −1819.74 | − | 1050.63i | −0.0531699 | − | 0.0306977i | ||||
\(186\) | −26825.8 | + | 15487.9i | −0.775403 | + | 0.447679i | ||||
\(187\) | 7230.15 | − | 12523.0i | 0.206759 | − | 0.358117i | ||||
\(188\) | −16101.2 | + | 27888.1i | −0.455556 | + | 0.789047i | ||||
\(189\) | 7652.79i | 0.214238i | ||||||||
\(190\) | −12304.8 | − | 14016.1i | −0.340854 | − | 0.388258i | ||||
\(191\) | 6591.39 | 0.180680 | 0.0903400 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903400 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(192\) | −5366.13 | − | 3098.14i | −0.145566 | − | 0.0840424i | ||||
\(193\) | 11519.8 | + | 6650.95i | 0.309264 | + | 0.178554i | 0.646597 | − | 0.762832i | \(-0.276192\pi\) |
−0.337333 | + | 0.941385i | \(0.609525\pi\) | |||||||
\(194\) | 9931.15 | + | 17201.3i | 0.263874 | + | 0.457043i | ||||
\(195\) | 17033.5 | − | 29503.0i | 0.447957 | − | 0.775883i | ||||
\(196\) | −2979.86 | − | 5161.27i | −0.0775682 | − | 0.134352i | ||||
\(197\) | −8607.77 | −0.221798 | −0.110899 | − | 0.993832i | \(-0.535373\pi\) | ||||
−0.110899 | + | 0.993832i | \(0.535373\pi\) | |||||||
\(198\) | − | 9714.86i | − | 0.247803i | ||||||
\(199\) | −18628.0 | − | 32264.6i | −0.470391 | − | 0.814742i | 0.529035 | − | 0.848600i | \(-0.322554\pi\) |
−0.999427 | + | 0.0338581i | \(0.989221\pi\) | |||||||
\(200\) | −5709.13 | + | 3296.17i | −0.142728 | + | 0.0824042i | ||||
\(201\) | −77621.9 | −1.92129 | ||||||||
\(202\) | − | 26743.8i | − | 0.655420i | ||||||
\(203\) | −10928.9 | + | 6309.80i | −0.265206 | + | 0.153117i | ||||
\(204\) | −23107.3 | − | 13341.0i | −0.555251 | − | 0.320575i | ||||
\(205\) | 33547.1 | − | 19368.4i | 0.798266 | − | 0.460879i | ||||
\(206\) | 2240.60 | − | 3880.84i | 0.0527996 | − | 0.0914515i | ||||
\(207\) | 29364.0 | − | 50860.0i | 0.685291 | − | 1.18696i | ||||
\(208\) | 9862.89i | 0.227970i | ||||||||
\(209\) | 3705.08 | + | 18575.7i | 0.0848214 | + | 0.425258i | ||||
\(210\) | −25444.3 | −0.576969 | ||||||||
\(211\) | 64223.3 | + | 37079.3i | 1.44254 | + | 0.832850i | 0.998019 | − | 0.0629190i | \(-0.0200410\pi\) |
0.444520 | + | 0.895769i | \(0.353374\pi\) | |||||||
\(212\) | 20463.2 | + | 11814.4i | 0.455303 | + | 0.262870i | ||||
\(213\) | −19650.7 | − | 34036.1i | −0.433131 | − | 0.750205i | ||||
\(214\) | 7763.71 | − | 13447.1i | 0.169528 | − | 0.293631i | ||||
\(215\) | 18278.0 | + | 31658.4i | 0.395413 | + | 0.684876i | ||||
\(216\) | 4255.20 | 0.0912037 | ||||||||
\(217\) | − | 36825.8i | − | 0.782046i | ||||||
\(218\) | −1992.12 | − | 3450.45i | −0.0419181 | − | 0.0726043i | ||||
\(219\) | −80169.5 | + | 46285.9i | −1.67156 | + | 0.965073i | ||||
\(220\) | −7667.42 | −0.158418 | ||||||||
\(221\) | 42471.0i | 0.869577i | ||||||||
\(222\) | 3410.08 | − | 1968.81i | 0.0691925 | − | 0.0399483i | ||||
\(223\) | −73682.3 | − | 42540.5i | −1.48168 | − | 0.855447i | −0.481894 | − | 0.876230i | \(-0.660051\pi\) |
−0.999784 | + | 0.0207829i | \(0.993384\pi\) | |||||||
\(224\) | 6379.55 | − | 3683.24i | 0.127144 | − | 0.0734064i | ||||
\(225\) | −9535.79 | + | 16516.5i | −0.188361 | + | 0.326251i | ||||
\(226\) | 3341.13 | − | 5787.00i | 0.0654148 | − | 0.113302i | ||||
\(227\) | − | 34377.0i | − | 0.667140i | −0.942725 | − | 0.333570i | \(-0.891747\pi\) | ||
0.942725 | − | 0.333570i | \(-0.108253\pi\) | |||||||
\(228\) | 34275.7 | − | 6836.59i | 0.659351 | − | 0.131513i | ||||
\(229\) | −16889.2 | −0.322062 | −0.161031 | − | 0.986949i | \(-0.551482\pi\) | ||||
−0.161031 | + | 0.986949i | \(0.551482\pi\) | |||||||
\(230\) | −40141.1 | − | 23175.5i | −0.758810 | − | 0.438099i | ||||
\(231\) | 22378.7 | + | 12920.4i | 0.419384 | + | 0.242131i | ||||
\(232\) | 3508.45 | + | 6076.82i | 0.0651838 | + | 0.112902i | ||||
\(233\) | −7596.98 | + | 13158.4i | −0.139936 | + | 0.242376i | −0.927472 | − | 0.373892i | \(-0.878023\pi\) |
0.787536 | + | 0.616268i | \(0.211356\pi\) | |||||||
\(234\) | 14266.6 | + | 24710.5i | 0.260549 | + | 0.451284i | ||||
\(235\) | 73527.2 | 1.33141 | ||||||||
\(236\) | − | 48060.4i | − | 0.862905i | ||||||
\(237\) | 40595.1 | + | 70312.9i | 0.722732 | + | 1.25181i | ||||
\(238\) | 27471.3 | − | 15860.5i | 0.484981 | − | 0.280004i | ||||
\(239\) | 35768.6 | 0.626190 | 0.313095 | − | 0.949722i | \(-0.398634\pi\) | ||||
0.313095 | + | 0.949722i | \(0.398634\pi\) | |||||||
\(240\) | 14147.9i | 0.245623i | ||||||||
\(241\) | −91819.3 | + | 53011.9i | −1.58088 | + | 0.912723i | −0.586153 | + | 0.810201i | \(0.699358\pi\) |
−0.994731 | + | 0.102523i | \(0.967309\pi\) | |||||||
\(242\) | −29119.3 | − | 16812.1i | −0.497223 | − | 0.287072i | ||||
\(243\) | 66233.4 | − | 38239.9i | 1.12167 | − | 0.647595i | ||||
\(244\) | −4853.34 | + | 8406.24i | −0.0815195 | + | 0.141196i | ||||
\(245\) | −6803.87 | + | 11784.7i | −0.113351 | + | 0.196329i | ||||
\(246\) | 72590.6i | 1.19953i | ||||||||
\(247\) | −36703.3 | − | 41807.7i | −0.601604 | − | 0.685271i | ||||
\(248\) | −20476.3 | −0.332927 | ||||||||
\(249\) | 91686.4 | + | 52935.2i | 1.47879 | + | 0.853780i | ||||
\(250\) | 41000.0 | + | 23671.4i | 0.656000 | + | 0.378742i | ||||
\(251\) | −27632.2 | − | 47860.4i | −0.438600 | − | 0.759678i | 0.558982 | − | 0.829180i | \(-0.311192\pi\) |
−0.997582 | + | 0.0695024i | \(0.977859\pi\) | |||||||
\(252\) | 10655.6 | − | 18456.0i | 0.167794 | − | 0.290627i | ||||
\(253\) | 23536.5 | + | 40766.4i | 0.367706 | + | 0.636886i | ||||
\(254\) | 66289.8 | 1.02749 | ||||||||
\(255\) | 60922.7i | 0.936913i | ||||||||
\(256\) | −2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 38690.0 | − | 22337.7i | 0.585778 | − | 0.338199i | −0.177649 | − | 0.984094i | \(-0.556849\pi\) |
0.763426 | + | 0.645895i | \(0.223516\pi\) | |||||||
\(258\) | −68503.7 | −1.02914 | ||||||||
\(259\) | 4681.26i | 0.0697853i | ||||||||
\(260\) | 19502.7 | − | 11259.9i | 0.288502 | − | 0.166566i | ||||
\(261\) | 17580.2 | + | 10149.9i | 0.258073 | + | 0.148999i | ||||
\(262\) | 9603.13 | − | 5544.37i | 0.139898 | − | 0.0807699i | ||||
\(263\) | −29030.4 | + | 50282.2i | −0.419703 | + | 0.726947i | −0.995909 | − | 0.0903572i | \(-0.971199\pi\) |
0.576206 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(264\) | 7184.14 | − | 12443.3i | 0.103078 | − | 0.178537i | ||||
\(265\) | − | 53951.3i | − | 0.768264i | ||||||
\(266\) | −13335.6 | + | 39353.4i | −0.188473 | + | 0.556185i | ||||
\(267\) | 95680.9 | 1.34216 | ||||||||
\(268\) | −44436.9 | − | 25655.7i | −0.618692 | − | 0.357202i | ||||
\(269\) | 62637.7 | + | 36163.9i | 0.865627 | + | 0.499770i | 0.865893 | − | 0.500230i | \(-0.166751\pi\) |
−0.000265353 | 1.00000i | \(0.500084\pi\) | ||||||||
\(270\) | −4857.92 | − | 8414.16i | −0.0666381 | − | 0.115421i | ||||
\(271\) | −43116.8 | + | 74680.5i | −0.587094 | + | 1.01688i | 0.407516 | + | 0.913198i | \(0.366395\pi\) |
−0.994611 | + | 0.103680i | \(0.966938\pi\) | |||||||
\(272\) | −8818.98 | − | 15274.9i | −0.119201 | − | 0.206463i | ||||
\(273\) | −75896.1 | −1.01834 | ||||||||
\(274\) | − | 73939.9i | − | 0.984867i | ||||||
\(275\) | −7643.35 | − | 13238.7i | −0.101069 | − | 0.175057i | ||||
\(276\) | 75222.0 | − | 43429.4i | 0.987476 | − | 0.570120i | ||||
\(277\) | 133588. | 1.74103 | 0.870516 | − | 0.492139i | \(-0.163785\pi\) | ||||
0.870516 | + | 0.492139i | \(0.163785\pi\) | |||||||
\(278\) | − | 55694.3i | − | 0.720645i | ||||||
\(279\) | −51301.5 | + | 29618.9i | −0.659055 | + | 0.380505i | ||||
\(280\) | −14566.3 | − | 8409.88i | −0.185795 | − | 0.107269i | ||||
\(281\) | −67741.3 | + | 39110.5i | −0.857908 | + | 0.495314i | −0.863311 | − | 0.504672i | \(-0.831614\pi\) |
0.00540286 | + | 0.999985i | \(0.498280\pi\) | |||||||
\(282\) | −68892.8 | + | 119326.i | −0.866314 | + | 1.50050i | ||||
\(283\) | 1941.73 | − | 3363.17i | 0.0242446 | − | 0.0419929i | −0.853649 | − | 0.520849i | \(-0.825615\pi\) |
0.877893 | + | 0.478857i | \(0.158949\pi\) | |||||||
\(284\) | − | 25979.9i | − | 0.322108i | ||||||
\(285\) | −52649.2 | − | 59971.3i | −0.648189 | − | 0.738335i | ||||
\(286\) | −22870.6 | −0.279606 | ||||||||
\(287\) | −74737.7 | − | 43149.8i | −0.907352 | − | 0.523860i | ||||
\(288\) | −10262.1 | − | 5924.85i | −0.123724 | − | 0.0714319i | ||||
\(289\) | 3784.71 | + | 6555.31i | 0.0453145 | + | 0.0784870i | ||||
\(290\) | 8010.80 | − | 13875.1i | 0.0952533 | − | 0.164984i | ||||
\(291\) | 42492.8 | + | 73599.7i | 0.501799 | + | 0.869141i | ||||
\(292\) | −61193.8 | −0.717698 | ||||||||
\(293\) | − | 115090.i | − | 1.34061i | −0.742087 | − | 0.670304i | \(-0.766164\pi\) | ||
0.742087 | − | 0.670304i | \(-0.233836\pi\) | |||||||
\(294\) | −12750.1 | − | 22083.7i | −0.147509 | − | 0.255492i | ||||
\(295\) | −95033.8 | + | 54867.8i | −1.09203 | + | 0.630483i | ||||
\(296\) | 2602.94 | 0.0297085 | ||||||||
\(297\) | 9867.21i | 0.111862i | ||||||||
\(298\) | 53832.2 | − | 31080.1i | 0.606192 | − | 0.349985i | ||||
\(299\) | −119734. | − | 69128.5i | −1.33929 | − | 0.773241i | ||||
\(300\) | −24427.9 | + | 14103.5i | −0.271421 | + | 0.156705i | ||||
\(301\) | 40720.5 | − | 70529.9i | 0.449448 | − | 0.778467i | ||||
\(302\) | −32509.7 | + | 56308.4i | −0.356450 | + | 0.617389i | ||||
\(303\) | − | 114430.i | − | 1.24639i | ||||||
\(304\) | 21881.8 | + | 7415.04i | 0.236775 | + | 0.0802354i | ||||
\(305\) | 22163.1 | 0.238249 | ||||||||
\(306\) | −44190.2 | − | 25513.2i | −0.471936 | − | 0.272473i | ||||
\(307\) | 24719.2 | + | 14271.7i | 0.262276 | + | 0.151425i | 0.625372 | − | 0.780327i | \(-0.284947\pi\) |
−0.363096 | + | 0.931752i | \(0.618280\pi\) | |||||||
\(308\) | 8540.90 | + | 14793.3i | 0.0900331 | + | 0.155942i | ||||
\(309\) | 9586.96 | − | 16605.1i | 0.100407 | − | 0.173910i | ||||
\(310\) | 23376.6 | + | 40489.5i | 0.243253 | + | 0.421327i | ||||
\(311\) | −13146.5 | −0.135921 | −0.0679607 | − | 0.997688i | \(-0.521649\pi\) | ||||
−0.0679607 | + | 0.997688i | \(0.521649\pi\) | |||||||
\(312\) | 42200.7i | 0.433522i | ||||||||
\(313\) | −87731.9 | − | 151956.i | −0.895507 | − | 1.55106i | −0.833176 | − | 0.553008i | \(-0.813480\pi\) |
−0.0623313 | − | 0.998056i | \(-0.519854\pi\) | |||||||
\(314\) | 100955. | − | 58286.2i | 1.02392 | − | 0.591162i | ||||
\(315\) | −48659.5 | −0.490395 | ||||||||
\(316\) | 53670.2i | 0.537476i | ||||||||
\(317\) | 75547.7 | − | 43617.5i | 0.751801 | − | 0.434052i | −0.0745435 | − | 0.997218i | \(-0.523750\pi\) |
0.826344 | + | 0.563165i | \(0.190417\pi\) | |||||||
\(318\) | 87556.5 | + | 50550.8i | 0.865834 | + | 0.499889i | ||||
\(319\) | −14091.3 | + | 8135.60i | −0.138474 | + | 0.0799482i | ||||
\(320\) | −4676.17 | + | 8099.36i | −0.0456657 | + | 0.0790953i | ||||
\(321\) | 33218.9 | − | 57536.9i | 0.322385 | − | 0.558388i | ||||
\(322\) | 103263.i | 0.995935i | ||||||||
\(323\) | 94226.0 | + | 31930.2i | 0.903162 | + | 0.306053i | ||||
\(324\) | 60625.6 | 0.577519 | ||||||||
\(325\) | 38882.9 | + | 22449.1i | 0.368123 | + | 0.212536i | ||||
\(326\) | −7357.40 | − | 4247.80i | −0.0692292 | − | 0.0399695i | ||||
\(327\) | −8523.75 | − | 14763.6i | −0.0797141 | − | 0.138069i | ||||
\(328\) | −23992.7 | + | 41556.6i | −0.223014 | + | 0.386271i | ||||
\(329\) | −81903.5 | − | 141861.i | −0.756677 | − | 1.31060i | ||||
\(330\) | −32806.9 | −0.301257 | ||||||||
\(331\) | 161860.i | 1.47735i | 0.674060 | + | 0.738677i | \(0.264549\pi\) | ||||
−0.674060 | + | 0.738677i | \(0.735451\pi\) | |||||||
\(332\) | 34992.4 | + | 60608.6i | 0.317466 | + | 0.549867i | ||||
\(333\) | 6521.41 | − | 3765.14i | 0.0588102 | − | 0.0339541i | ||||
\(334\) | −94681.7 | −0.848737 | ||||||||
\(335\) | 117158.i | 1.04396i | ||||||||
\(336\) | 27296.5 | − | 15759.6i | 0.241784 | − | 0.139594i | ||||
\(337\) | 110393. | + | 63735.2i | 0.972031 | + | 0.561203i | 0.899855 | − | 0.436189i | \(-0.143672\pi\) |
0.0721764 | + | 0.997392i | \(0.477006\pi\) | |||||||
\(338\) | −11786.6 | + | 6804.99i | −0.103170 | + | 0.0595654i | ||||
\(339\) | 14295.8 | − | 24761.1i | 0.124397 | − | 0.215462i | ||||
\(340\) | −20136.2 | + | 34877.0i | −0.174189 | + | 0.301704i | ||||
\(341\) | − | 47481.7i | − | 0.408336i | ||||||
\(342\) | 65548.5 | − | 13074.2i | 0.560416 | − | 0.111780i | ||||
\(343\) | 128023. | 1.08818 | ||||||||
\(344\) | −39216.9 | − | 22641.9i | −0.331403 | − | 0.191336i | ||||
\(345\) | −171753. | − | 99161.8i | −1.44300 | − | 0.833117i | ||||
\(346\) | 39403.6 | + | 68249.1i | 0.329142 | + | 0.570091i | ||||
\(347\) | −71952.7 | + | 124626.i | −0.597569 | + | 1.03502i | 0.395609 | + | 0.918419i | \(0.370533\pi\) |
−0.993179 | + | 0.116602i | \(0.962800\pi\) | |||||||
\(348\) | 15011.8 | + | 26001.1i | 0.123958 | + | 0.214701i | ||||
\(349\) | −66908.7 | −0.549328 | −0.274664 | − | 0.961540i | \(-0.588567\pi\) | ||||
−0.274664 | + | 0.961540i | \(0.588567\pi\) | |||||||
\(350\) | − | 33533.9i | − | 0.273746i | ||||||
\(351\) | −14490.4 | − | 25098.0i | −0.117616 | − | 0.203716i | ||||
\(352\) | 8225.54 | − | 4749.02i | 0.0663864 | − | 0.0383282i | ||||
\(353\) | 116126. | 0.931921 | 0.465961 | − | 0.884806i | \(-0.345709\pi\) | ||||
0.465961 | + | 0.884806i | \(0.345709\pi\) | |||||||
\(354\) | − | 205638.i | − | 1.64095i | ||||||
\(355\) | −51372.3 | + | 29659.8i | −0.407635 | + | 0.235348i | ||||
\(356\) | 54775.3 | + | 31624.6i | 0.432200 | + | 0.249531i | ||||
\(357\) | 117542. | − | 67863.2i | 0.922270 | − | 0.532473i | ||||
\(358\) | 13824.1 | − | 23944.1i | 0.107863 | − | 0.186824i | ||||
\(359\) | 46490.7 | − | 80524.3i | 0.360726 | − | 0.624795i | −0.627355 | − | 0.778734i | \(-0.715862\pi\) |
0.988080 | + | 0.153938i | \(0.0491957\pi\) | |||||||
\(360\) | 27056.2i | 0.208767i | ||||||||
\(361\) | −120348. | + | 49998.2i | −0.923477 | + | 0.383654i | ||||
\(362\) | −68034.9 | −0.519176 | ||||||||
\(363\) | −124594. | − | 71934.5i | −0.945550 | − | 0.545913i | ||||
\(364\) | −43449.0 | − | 25085.3i | −0.327927 | − | 0.189328i | ||||
\(365\) | 69861.5 | + | 121004.i | 0.524387 | + | 0.908265i | ||||
\(366\) | −20766.2 | + | 35968.1i | −0.155023 | + | 0.268507i | ||||
\(367\) | 5846.49 | + | 10126.4i | 0.0434073 | + | 0.0751837i | 0.886913 | − | 0.461937i | \(-0.152845\pi\) |
−0.843505 | + | 0.537121i | \(0.819512\pi\) | |||||||
\(368\) | 57417.4 | 0.423982 | ||||||||
\(369\) | 138821.i | 1.01954i | ||||||||
\(370\) | −2971.62 | − | 5147.00i | −0.0217065 | − | 0.0375968i | ||||
\(371\) | −104092. | + | 60097.6i | −0.756257 | + | 0.436625i | ||||
\(372\) | −87612.9 | −0.633114 | ||||||||
\(373\) | 56159.4i | 0.403650i | 0.979422 | + | 0.201825i | \(0.0646872\pi\) | ||||
−0.979422 | + | 0.201825i | \(0.935313\pi\) | |||||||
\(374\) | 35420.4 | − | 20450.0i | 0.253227 | − | 0.146201i | ||||
\(375\) | 175428. | + | 101284.i | 1.24749 | + | 0.720239i | ||||
\(376\) | −78879.4 | + | 45541.0i | −0.557940 | + | 0.322127i | ||||
\(377\) | 23894.9 | − | 41387.1i | 0.168121 | − | 0.291194i | ||||
\(378\) | −10822.7 | + | 18745.4i | −0.0757445 | + | 0.131193i | ||||
\(379\) | 77613.7i | 0.540331i | 0.962814 | + | 0.270165i | \(0.0870784\pi\) | ||||
−0.962814 | + | 0.270165i | \(0.912922\pi\) | |||||||
\(380\) | −10318.8 | − | 51734.0i | −0.0714598 | − | 0.358268i | ||||
\(381\) | 283637. | 1.95395 | ||||||||
\(382\) | 16145.5 | + | 9321.63i | 0.110643 | + | 0.0638800i | ||||
\(383\) | −203087. | − | 117252.i | −1.38447 | − | 0.799327i | −0.391789 | − | 0.920055i | \(-0.628144\pi\) |
−0.992686 | + | 0.120728i | \(0.961477\pi\) | |||||||
\(384\) | −8762.86 | − | 15177.7i | −0.0594270 | − | 0.102930i | ||||
\(385\) | 19501.3 | − | 33777.3i | 0.131566 | − | 0.227878i | ||||
\(386\) | 18811.7 | + | 32582.8i | 0.126257 | + | 0.218683i | ||||
\(387\) | −131006. | −0.874719 | ||||||||
\(388\) | 56179.1i | 0.373174i | ||||||||
\(389\) | 60585.7 | + | 104938.i | 0.400379 | + | 0.693476i | 0.993772 | − | 0.111437i | \(-0.0355453\pi\) |
−0.593393 | + | 0.804913i | \(0.702212\pi\) | |||||||
\(390\) | 83447.0 | − | 48178.1i | 0.548632 | − | 0.316753i | ||||
\(391\) | 247247. | 1.61725 | ||||||||
\(392\) | − | 16856.6i | − | 0.109698i | ||||||
\(393\) | 41089.3 | − | 23722.9i | 0.266038 | − | 0.153597i | ||||
\(394\) | −21084.6 | − | 12173.2i | −0.135823 | − | 0.0784175i | ||||
\(395\) | 106127. | − | 61272.2i | 0.680189 | − | 0.392707i | ||||
\(396\) | 13738.9 | − | 23796.4i | 0.0876115 | − | 0.151748i | ||||
\(397\) | −84743.0 | + | 146779.i | −0.537679 | + | 0.931287i | 0.461350 | + | 0.887218i | \(0.347365\pi\) |
−0.999029 | + | 0.0440685i | \(0.985968\pi\) | |||||||
\(398\) | − | 105376.i | − | 0.665234i | ||||||
\(399\) | −57059.7 | + | 168383.i | −0.358413 | + | 1.05768i | ||||
\(400\) | −18646.0 | −0.116537 | ||||||||
\(401\) | 53887.1 | + | 31111.8i | 0.335117 | + | 0.193480i | 0.658111 | − | 0.752921i | \(-0.271356\pi\) |
−0.322994 | + | 0.946401i | \(0.604689\pi\) | |||||||
\(402\) | −190134. | − | 109774.i | −1.17654 | − | 0.679277i | ||||
\(403\) | 69728.6 | + | 120773.i | 0.429339 | + | 0.743638i | ||||
\(404\) | 37821.4 | − | 65508.6i | 0.231726 | − | 0.401361i | ||||
\(405\) | −69212.8 | − | 119880.i | −0.421965 | − | 0.730864i | ||||
\(406\) | −35693.6 | −0.216540 | ||||||||
\(407\) | 6035.84i | 0.0364375i | ||||||||
\(408\) | −37734.1 | − | 65357.4i | −0.226680 | − | 0.392622i | ||||
\(409\) | −19314.6 | + | 11151.3i | −0.115462 | + | 0.0666621i | −0.556619 | − | 0.830768i | \(-0.687902\pi\) |
0.441157 | + | 0.897430i | \(0.354568\pi\) | |||||||
\(410\) | 109564. | 0.651781 | ||||||||
\(411\) | − | 316369.i | − | 1.87288i | ||||||
\(412\) | 10976.7 | − | 6337.38i | 0.0646660 | − | 0.0373349i | ||||
\(413\) | 211720. | + | 122237.i | 1.24126 | + | 0.716641i | ||||
\(414\) | 143854. | − | 83054.0i | 0.839306 | − | 0.484574i | ||||
\(415\) | 79897.6 | − | 138387.i | 0.463914 | − | 0.803523i | ||||
\(416\) | −13948.2 | + | 24159.0i | −0.0805995 | + | 0.139602i | ||||
\(417\) | − | 238302.i | − | 1.37042i | ||||||
\(418\) | −17194.4 | + | 50740.7i | −0.0984090 | + | 0.290405i | ||||
\(419\) | −276136. | −1.57288 | −0.786438 | − | 0.617669i | \(-0.788077\pi\) | ||||
−0.786438 | + | 0.617669i | \(0.788077\pi\) | |||||||
\(420\) | −62325.6 | − | 35983.7i | −0.353320 | − | 0.203989i | ||||
\(421\) | −245912. | − | 141977.i | −1.38744 | − | 0.801041i | −0.394417 | − | 0.918931i | \(-0.629054\pi\) |
−0.993027 | + | 0.117890i | \(0.962387\pi\) | |||||||
\(422\) | 104876. | + | 181651.i | 0.588914 | + | 1.02003i | ||||
\(423\) | −131750. | + | 228197.i | −0.736325 | + | 1.27535i | ||||
\(424\) | 33416.2 | + | 57878.6i | 0.185877 | + | 0.321948i | ||||
\(425\) | −80292.1 | −0.444524 | ||||||||
\(426\) | − | 111161.i | − | 0.612540i | ||||||
\(427\) | −24688.0 | − | 42760.9i | −0.135404 | − | 0.234526i | ||||
\(428\) | 38034.3 | − | 21959.1i | 0.207629 | − | 0.119875i | ||||
\(429\) | −97857.5 | −0.531716 | ||||||||
\(430\) | 103396.i | 0.559199i | ||||||||
\(431\) | 91869.3 | − | 53040.8i | 0.494557 | − | 0.285532i | −0.231906 | − | 0.972738i | \(-0.574496\pi\) |
0.726463 | + | 0.687206i | \(0.241163\pi\) | |||||||
\(432\) | 10423.1 | + | 6017.76i | 0.0558507 | + | 0.0322454i | ||||
\(433\) | −154599. | + | 89257.9i | −0.824577 | + | 0.476070i | −0.851992 | − | 0.523554i | \(-0.824606\pi\) |
0.0274149 | + | 0.999624i | \(0.491272\pi\) | |||||||
\(434\) | 52079.5 | − | 90204.3i | 0.276495 | − | 0.478903i | ||||
\(435\) | 34276.1 | − | 59368.0i | 0.181140 | − | 0.313743i | ||||
\(436\) | − | 11269.1i | − | 0.0592812i | ||||||
\(437\) | −243386. | + | 213670.i | −1.27448 | + | 1.11887i | ||||
\(438\) | −261833. | −1.36482 | ||||||||
\(439\) | −156345. | − | 90265.9i | −0.811252 | − | 0.468376i | 0.0361388 | − | 0.999347i | \(-0.488494\pi\) |
−0.847390 | + | 0.530970i | \(0.821827\pi\) | |||||||
\(440\) | −18781.3 | − | 10843.4i | −0.0970107 | − | 0.0560091i | ||||
\(441\) | −24383.1 | − | 42232.7i | −0.125375 | − | 0.217156i | ||||
\(442\) | −60063.1 | + | 104032.i | −0.307442 | + | 0.532505i | ||||
\(443\) | −116330. | − | 201489.i | −0.592766 | − | 1.02670i | −0.993858 | − | 0.110663i | \(-0.964702\pi\) |
0.401092 | − | 0.916038i | \(-0.368631\pi\) | |||||||
\(444\) | 11137.3 | 0.0564954 | ||||||||
\(445\) | − | 144416.i | − | 0.729280i | ||||||
\(446\) | −120323. | − | 208405.i | −0.604892 | − | 1.04770i | ||||
\(447\) | 230334. | − | 132983.i | 1.15277 | − | 0.665553i | ||||
\(448\) | 20835.5 | 0.103812 | ||||||||
\(449\) | 182552.i | 0.905510i | 0.891635 | + | 0.452755i | \(0.149559\pi\) | ||||
−0.891635 | + | 0.452755i | \(0.850441\pi\) | |||||||
\(450\) | −46715.7 | + | 26971.3i | −0.230695 | + | 0.133192i | ||||
\(451\) | −96363.8 | − | 55635.7i | −0.473763 | − | 0.273527i | ||||
\(452\) | 16368.1 | − | 9450.13i | 0.0801164 | − | 0.0462553i | ||||
\(453\) | −139100. | + | 240929.i | −0.677848 | + | 1.17407i | ||||
\(454\) | 48616.5 | − | 84206.2i | 0.235869 | − | 0.408538i | ||||
\(455\) | 114554.i | 0.553332i | ||||||||
\(456\) | 93626.4 | + | 31727.0i | 0.450266 | + | 0.152581i | ||||
\(457\) | 78140.6 | 0.374149 | 0.187074 | − | 0.982346i | \(-0.440099\pi\) | ||||
0.187074 | + | 0.982346i | \(0.440099\pi\) | |||||||
\(458\) | −41370.0 | − | 23885.0i | −0.197222 | − | 0.113866i | ||||
\(459\) | 44883.2 | + | 25913.4i | 0.213039 | + | 0.122998i | ||||
\(460\) | −65550.1 | − | 113536.i | −0.309783 | − | 0.536560i | ||||
\(461\) | −110657. | + | 191663.i | −0.520687 | + | 0.901856i | 0.479024 | + | 0.877802i | \(0.340991\pi\) |
−0.999711 | + | 0.0240539i | \(0.992343\pi\) | |||||||
\(462\) | 36544.3 | + | 63296.6i | 0.171213 | + | 0.296549i | ||||
\(463\) | 330182. | 1.54025 | 0.770126 | − | 0.637891i | \(-0.220193\pi\) | ||||
0.770126 | + | 0.637891i | \(0.220193\pi\) | |||||||
\(464\) | 19846.8i | 0.0921838i | ||||||||
\(465\) | 100023. | + | 173244.i | 0.462586 | + | 0.801222i | ||||
\(466\) | −37217.5 | + | 21487.5i | −0.171386 | + | 0.0989496i | ||||
\(467\) | 123478. | 0.566183 | 0.283092 | − | 0.959093i | \(-0.408640\pi\) | ||||
0.283092 | + | 0.959093i | \(0.408640\pi\) | |||||||
\(468\) | 80704.2i | 0.368472i | ||||||||
\(469\) | 226042. | − | 130505.i | 1.02764 | − | 0.593311i | ||||
\(470\) | 180104. | + | 103983.i | 0.815319 | + | 0.470725i | ||||
\(471\) | 431959. | − | 249391.i | 1.94715 | − | 1.12419i | ||||
\(472\) | 67967.6 | − | 117723.i | 0.305083 | − | 0.528419i | ||||
\(473\) | 52503.4 | − | 90938.5i | 0.234674 | − | 0.406467i | ||||
\(474\) | 229641.i | 1.02210i | ||||||||
\(475\) | 79038.2 | − | 69388.1i | 0.350308 | − | 0.307537i | ||||
\(476\) | 89720.8 | 0.395985 | ||||||||
\(477\) | 167442. | + | 96672.8i | 0.735916 | + | 0.424881i | ||||
\(478\) | 87614.8 | + | 50584.4i | 0.383461 | + | 0.221391i | ||||
\(479\) | 70014.4 | + | 121269.i | 0.305152 | + | 0.528539i | 0.977295 | − | 0.211882i | \(-0.0679593\pi\) |
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(480\) | −20008.1 | + | 34655.1i | −0.0868408 | + | 0.150413i | ||||
\(481\) | −8863.85 | − | 15352.6i | −0.0383118 | − | 0.0663579i | ||||
\(482\) | −299881. | −1.29079 | ||||||||
\(483\) | 441834.i | 1.89393i | ||||||||
\(484\) | −47551.7 | − | 82362.0i | −0.202990 | − | 0.351590i | ||||
\(485\) | 111088. | − | 64136.4i | 0.472261 | − | 0.272660i | ||||
\(486\) | 216317. | 0.915838 | ||||||||
\(487\) | − | 141943.i | − | 0.598489i | −0.954176 | − | 0.299245i | \(-0.903265\pi\) | ||
0.954176 | − | 0.299245i | \(-0.0967347\pi\) | |||||||
\(488\) | −23776.4 | + | 13727.3i | −0.0998406 | + | 0.0576430i | ||||
\(489\) | −31480.4 | − | 18175.2i | −0.131650 | − | 0.0760084i | ||||
\(490\) | −33332.0 | + | 19244.3i | −0.138826 | + | 0.0801510i | ||||
\(491\) | −1364.05 | + | 2362.60i | −0.00565804 | + | 0.00980001i | −0.868841 | − | 0.495092i | \(-0.835134\pi\) |
0.863183 | + | 0.504892i | \(0.168468\pi\) | |||||||
\(492\) | −102659. | + | 177810.i | −0.424097 | + | 0.734557i | ||||
\(493\) | 85463.2i | 0.351630i | ||||||||
\(494\) | −30779.2 | − | 154314.i | −0.126126 | − | 0.632340i | ||||
\(495\) | −62739.6 | −0.256054 | ||||||||
\(496\) | −50156.5 | − | 28957.9i | −0.203875 | − | 0.117707i | ||||
\(497\) | 114449. | + | 66077.3i | 0.463341 | + | 0.267510i | ||||
\(498\) | 149723. | + | 259328.i | 0.603713 | + | 1.04566i | ||||
\(499\) | −105201. | + | 182214.i | −0.422494 | + | 0.731780i | −0.996183 | − | 0.0872927i | \(-0.972178\pi\) |
0.573689 | + | 0.819073i | \(0.305512\pi\) | |||||||
\(500\) | 66952.7 | + | 115966.i | 0.267811 | + | 0.463862i | ||||
\(501\) | −405118. | −1.61401 | ||||||||
\(502\) | − | 156312.i | − | 0.620274i | ||||||
\(503\) | −159932. | − | 277011.i | −0.632121 | − | 1.09486i | −0.987117 | − | 0.159997i | \(-0.948851\pi\) |
0.354997 | − | 0.934867i | \(-0.384482\pi\) | |||||||
\(504\) | 52201.5 | − | 30138.5i | 0.205505 | − | 0.118648i | ||||
\(505\) | −172714. | −0.677244 | ||||||||
\(506\) | 133143.i | 0.520015i | ||||||||
\(507\) | −50431.7 | + | 29116.8i | −0.196195 | + | 0.113273i | ||||
\(508\) | 162376. | + | 93747.9i | 0.629209 | + | 0.363274i | ||||
\(509\) | −116894. | + | 67488.9i | −0.451188 | + | 0.260493i | −0.708332 | − | 0.705880i | \(-0.750552\pi\) |
0.257144 | + | 0.966373i | \(0.417219\pi\) | |||||||
\(510\) | −86157.8 | + | 149230.i | −0.331249 | + | 0.573739i | ||||
\(511\) | 155640. | − | 269577.i | 0.596047 | − | 1.03238i | ||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | −66576.5 | + | 13279.3i | −0.252980 | + | 0.0504591i | ||||
\(514\) | 126361. | 0.478285 | ||||||||
\(515\) | −25062.9 | − | 14470.0i | −0.0944966 | − | 0.0545576i | ||||
\(516\) | −167799. | − | 96878.9i | −0.630217 | − | 0.363856i | ||||
\(517\) | −105603. | − | 182910.i | −0.395090 | − | 0.684315i | ||||
\(518\) | −6620.31 | + | 11466.7i | −0.0246728 | + | 0.0427346i | ||||
\(519\) | 168598. | + | 292020.i | 0.625918 | + | 1.08412i | ||||
\(520\) | 63695.6 | 0.235560 | ||||||||
\(521\) | − | 253689.i | − | 0.934601i | −0.884099 | − | 0.467300i | \(-0.845227\pi\) | ||
0.884099 | − | 0.467300i | \(-0.154773\pi\) | |||||||
\(522\) | 28708.3 | + | 49724.3i | 0.105358 | + | 0.182485i | ||||
\(523\) | 287975. | − | 166262.i | 1.05281 | − | 0.607841i | 0.129377 | − | 0.991596i | \(-0.458702\pi\) |
0.923435 | + | 0.383754i | \(0.125369\pi\) | |||||||
\(524\) | 31363.7 | 0.114226 | ||||||||
\(525\) | − | 143483.i | − | 0.520573i | ||||||
\(526\) | −142220. | + | 82110.5i | −0.514029 | + | 0.296775i | ||||
\(527\) | −215981. | − | 124697.i | −0.777669 | − | 0.448987i | ||||
\(528\) | 35195.0 | − | 20319.8i | 0.126245 | − | 0.0728873i | ||||
\(529\) | −262515. | + | 454689.i | −0.938087 | + | 1.62481i | ||||
\(530\) | 76298.7 | − | 132153.i | 0.271622 | − | 0.470464i | ||||
\(531\) | − | 393260.i | − | 1.39473i | ||||||
\(532\) | −88319.6 | + | 77536.3i | −0.312057 | + | 0.273957i | ||||
\(533\) | 326812. | 1.15039 | ||||||||
\(534\) | 234369. | + | 135313.i | 0.821899 | + | 0.474524i | ||||
\(535\) | −86843.1 | − | 50138.9i | −0.303409 | − | 0.175173i | ||||
\(536\) | −72565.2 | − | 125687.i | −0.252580 | − | 0.437481i | ||||
\(537\) | 59149.9 | − | 102451.i | 0.205119 | − | 0.355276i | ||||
\(538\) | 102287. | + | 177166.i | 0.353391 | + | 0.612091i | ||||
\(539\) | 39088.1 | 0.134545 | ||||||||
\(540\) | − | 27480.5i | − | 0.0942405i | ||||||
\(541\) | −156555. | − | 271161.i | −0.534899 | − | 0.926473i | −0.999168 | − | 0.0407784i | \(-0.987016\pi\) |
0.464269 | − | 0.885694i | \(-0.346317\pi\) | |||||||
\(542\) | −211228. | + | 121953.i | −0.719041 | + | 0.415138i | ||||
\(543\) | −291104. | −0.987297 | ||||||||
\(544\) | − | 49887.7i | − | 0.168576i | ||||||
\(545\) | −22283.4 | + | 12865.3i | −0.0750218 | + | 0.0433139i | ||||
\(546\) | −185907. | − | 107333.i | −0.623606 | − | 0.360039i | ||||
\(547\) | −54608.4 | + | 31528.2i | −0.182509 | + | 0.105372i | −0.588471 | − | 0.808518i | \(-0.700270\pi\) |
0.405962 | + | 0.913890i | \(0.366937\pi\) | |||||||
\(548\) | 104567. | − | 181115.i | 0.348203 | − | 0.603105i | ||||
\(549\) | −39713.1 | + | 68785.0i | −0.131762 | + | 0.228218i | ||||
\(550\) | − | 43237.3i | − | 0.142933i | ||||||
\(551\) | −73856.9 | − | 84128.5i | −0.243270 | − | 0.277102i | ||||
\(552\) | 245674. | 0.806271 | ||||||||
\(553\) | −236433. | − | 136505.i | −0.773140 | − | 0.446373i | ||||
\(554\) | 327222. | + | 188922.i | 1.06616 | + | 0.615548i | ||||
\(555\) | −12714.8 | − | 22022.7i | −0.0412785 | − | 0.0714964i | ||||
\(556\) | 78763.7 | − | 136423.i | 0.254786 | − | 0.441303i | ||||
\(557\) | −98461.3 | − | 170540.i | −0.317362 | − | 0.549688i | 0.662575 | − | 0.748996i | \(-0.269464\pi\) |
−0.979937 | + | 0.199308i | \(0.936130\pi\) | |||||||
\(558\) | −167550. | −0.538116 | ||||||||
\(559\) | 308413.i | 0.986980i | ||||||||
\(560\) | −23786.7 | − | 41199.8i | −0.0758506 | − | 0.131377i | ||||
\(561\) | 151555. | − | 87500.1i | 0.481552 | − | 0.278024i | ||||
\(562\) | −221242. | −0.700479 | ||||||||
\(563\) | 307676.i | 0.970681i | 0.874325 | + | 0.485341i | \(0.161304\pi\) | ||||
−0.874325 | + | 0.485341i | \(0.838696\pi\) | |||||||
\(564\) | −337504. | + | 194858.i | −1.06101 | + | 0.612577i | ||||
\(565\) | −37373.1 | − | 21577.3i | −0.117074 | − | 0.0675929i | ||||
\(566\) | 9512.48 | − | 5492.03i | 0.0296935 | − | 0.0171435i | ||||
\(567\) | −154195. | + | 267074.i | −0.479628 | + | 0.830740i | ||||
\(568\) | 36741.2 | − | 63637.6i | 0.113882 | − | 0.197250i | ||||
\(569\) | − | 249874.i | − | 0.771785i | −0.922544 | − | 0.385892i | \(-0.873894\pi\) | ||
0.922544 | − | 0.385892i | \(-0.126106\pi\) | |||||||
\(570\) | −44151.4 | − | 221356.i | −0.135892 | − | 0.681306i | ||||
\(571\) | 333305. | 1.02228 | 0.511140 | − | 0.859498i | \(-0.329223\pi\) | ||||
0.511140 | + | 0.859498i | \(0.329223\pi\) | |||||||
\(572\) | −56021.4 | − | 32344.0i | −0.171223 | − | 0.0988555i | ||||
\(573\) | 69082.6 | + | 39884.8i | 0.210407 | + | 0.121478i | ||||
\(574\) | −122046. | − | 211390.i | −0.370425 | − | 0.641595i | ||||
\(575\) | 130689. | − | 226359.i | 0.395277 | − | 0.684641i | ||||
\(576\) | −16758.0 | − | 29025.7i | −0.0505100 | − | 0.0874859i | ||||
\(577\) | 452372. | 1.35876 | 0.679382 | − | 0.733785i | \(-0.262248\pi\) | ||||
0.679382 | + | 0.733785i | \(0.262248\pi\) | |||||||
\(578\) | 21409.6i | 0.0640844i | ||||||||
\(579\) | 80490.4 | + | 139414.i | 0.240097 | + | 0.415861i | ||||
\(580\) | 39244.7 | − | 22658.0i | 0.116661 | − | 0.0673542i | ||||
\(581\) | −355999. | −1.05462 | ||||||||
\(582\) | 240376.i | 0.709651i | ||||||||
\(583\) | −134212. | + | 77487.4i | −0.394870 | + | 0.227979i | ||||
\(584\) | −149894. | − | 86541.1i | −0.439499 | − | 0.253745i | ||||
\(585\) | 159583. | − | 92135.4i | 0.466311 | − | 0.269225i | ||||
\(586\) | 162762. | − | 281911.i | 0.473976 | − | 0.820951i | ||||
\(587\) | −112606. | + | 195040.i | −0.326803 | + | 0.566040i | −0.981876 | − | 0.189526i | \(-0.939305\pi\) |
0.655072 | + | 0.755566i | \(0.272638\pi\) | |||||||
\(588\) | − | 72125.2i | − | 0.208609i | ||||||
\(589\) | 320371. | − | 63900.7i | 0.923468 | − | 0.184194i | ||||
\(590\) | −310379. | −0.891637 | ||||||||
\(591\) | −90215.7 | − | 52086.1i | −0.258290 | − | 0.149124i | ||||
\(592\) | 6375.86 | + | 3681.11i | 0.0181926 | + | 0.0105035i | ||||
\(593\) | 225542. | + | 390650.i | 0.641384 | + | 1.11091i | 0.985124 | + | 0.171844i | \(0.0549726\pi\) |
−0.343740 | + | 0.939065i | \(0.611694\pi\) | |||||||
\(594\) | −13954.3 | + | 24169.6i | −0.0395491 | + | 0.0685010i | ||||
\(595\) | −102429. | − | 177412.i | −0.289327 | − | 0.501129i | ||||
\(596\) | 175815. | 0.494953 | ||||||||
\(597\) | − | 450875.i | − | 1.26505i | ||||||
\(598\) | −195525. | − | 338659.i | −0.546764 | − | 0.947023i | ||||
\(599\) | −376004. | + | 217086.i | −1.04795 | + | 0.605032i | −0.922074 | − | 0.387014i | \(-0.873506\pi\) |
−0.125873 | + | 0.992046i | \(0.540173\pi\) | |||||||
\(600\) | −79781.2 | −0.221614 | ||||||||
\(601\) | 545183.i | 1.50936i | 0.656091 | + | 0.754681i | \(0.272209\pi\) | ||||
−0.656091 | + | 0.754681i | \(0.727791\pi\) | |||||||
\(602\) | 199489. | − | 115175.i | 0.550460 | − | 0.317808i | ||||
\(603\) | −363610. | − | 209931.i | −1.00000 | − | 0.577352i | ||||
\(604\) | −159264. | + | 91951.2i | −0.436560 | + | 0.252048i | ||||
\(605\) | −108574. | + | 188056.i | −0.296630 | + | 0.513779i | ||||
\(606\) | 161828. | − | 280294.i | 0.440665 | − | 0.763254i | ||||
\(607\) | 2996.79i | 0.00813352i | 0.999992 | + | 0.00406676i | \(0.00129449\pi\) | ||||
−0.999992 | + | 0.00406676i | \(0.998706\pi\) | |||||||
\(608\) | 43112.7 | + | 49108.6i | 0.116627 | + | 0.132846i | ||||
\(609\) | −152724. | −0.411786 | ||||||||
\(610\) | 54288.4 | + | 31343.4i | 0.145897 | + | 0.0842338i | ||||
\(611\) | 537220. | + | 310164.i | 1.43903 | + | 0.830825i | ||||
\(612\) | −72162.4 | − | 124989.i | −0.192667 | − | 0.333709i | ||||
\(613\) | −42295.9 | + | 73258.7i | −0.112558 | + | 0.194957i | −0.916801 | − | 0.399344i | \(-0.869238\pi\) |
0.804243 | + | 0.594301i | \(0.202571\pi\) | |||||||
\(614\) | 40366.3 | + | 69916.6i | 0.107074 | + | 0.185457i | ||||
\(615\) | 468798. | 1.23947 | ||||||||
\(616\) | 48314.6i | 0.127326i | ||||||||
\(617\) | 276736. | + | 479321.i | 0.726935 | + | 1.25909i | 0.958173 | + | 0.286191i | \(0.0923891\pi\) |
−0.231238 | + | 0.972897i | \(0.574278\pi\) | |||||||
\(618\) | 46966.3 | − | 27116.0i | 0.122973 | − | 0.0709984i | ||||
\(619\) | 434064. | 1.13285 | 0.566426 | − | 0.824113i | \(-0.308326\pi\) | ||||
0.566426 | + | 0.824113i | \(0.308326\pi\) | |||||||
\(620\) | 132238.i | 0.344012i | ||||||||
\(621\) | −146110. | + | 84356.5i | −0.378875 | + | 0.218744i | ||||
\(622\) | −32202.1 | − | 18591.9i | −0.0832345 | − | 0.0480555i | ||||
\(623\) | −278631. | + | 160868.i | −0.717883 | + | 0.414470i | ||||
\(624\) | −59680.8 | + | 103370.i | −0.153273 | + | 0.265477i | ||||
\(625\) | 61827.5 | − | 107088.i | 0.158278 | − | 0.274146i | ||||
\(626\) | − | 496287.i | − | 1.26644i | ||||||
\(627\) | −73570.5 | + | 217106.i | −0.187141 | + | 0.552252i | ||||
\(628\) | 329716. | 0.836029 | ||||||||
\(629\) | 27455.4 | + | 15851.4i | 0.0693947 | + | 0.0400650i | ||||
\(630\) | −119191. | − | 68814.9i | −0.300304 | − | 0.173381i | ||||
\(631\) | 94963.7 | + | 164482.i | 0.238506 | + | 0.413104i | 0.960286 | − | 0.279018i | \(-0.0900091\pi\) |
−0.721780 | + | 0.692123i | \(0.756676\pi\) | |||||||
\(632\) | −75901.1 | + | 131465.i | −0.190026 | + | 0.329135i | ||||
\(633\) | 448738. | + | 777237.i | 1.11992 | + | 1.93975i | ||||
\(634\) | 246738. | 0.613843 | ||||||||
\(635\) | − | 428106.i | − | 1.06171i | ||||||
\(636\) | 142979. | + | 247647.i | 0.353475 | + | 0.612237i | ||||
\(637\) | −99423.9 | + | 57402.4i | −0.245026 | + | 0.141466i | ||||
\(638\) | −46021.9 | −0.113064 | ||||||||
\(639\) | − | 212584.i | − | 0.520629i | ||||||
\(640\) | −22908.5 | + | 13226.2i | −0.0559288 | + | 0.0322905i | ||||
\(641\) | −176029. | − | 101631.i | −0.428419 | − | 0.247348i | 0.270254 | − | 0.962789i | \(-0.412892\pi\) |
−0.698673 | + | 0.715441i | \(0.746226\pi\) | |||||||
\(642\) | 162739. | − | 93957.3i | 0.394840 | − | 0.227961i | ||||
\(643\) | 262304. | − | 454324.i | 0.634430 | − | 1.09886i | −0.352206 | − | 0.935923i | \(-0.614568\pi\) |
0.986636 | − | 0.162942i | \(-0.0520984\pi\) | |||||||
\(644\) | −146035. | + | 252941.i | −0.352116 | + | 0.609883i | ||||
\(645\) | 442404.i | 1.06341i | ||||||||
\(646\) | 185650. | + | 211468.i | 0.444866 | + | 0.506735i | ||||
\(647\) | 223408. | 0.533690 | 0.266845 | − | 0.963739i | \(-0.414019\pi\) | ||||
0.266845 | + | 0.963739i | \(0.414019\pi\) | |||||||
\(648\) | 148502. | + | 85737.6i | 0.353657 | + | 0.204184i | ||||
\(649\) | 272984. | + | 157607.i | 0.648108 | + | 0.374185i | ||||
\(650\) | 63495.6 | + | 109978.i | 0.150285 | + | 0.260302i | ||||
\(651\) | 222835. | − | 385961.i | 0.525800 | − | 0.910712i | ||||
\(652\) | −12014.6 | − | 20809.9i | −0.0282627 | − | 0.0489524i | ||||
\(653\) | −333259. | −0.781548 | −0.390774 | − | 0.920487i | \(-0.627793\pi\) | ||||
−0.390774 | + | 0.920487i | \(0.627793\pi\) | |||||||
\(654\) | − | 48217.6i | − | 0.112733i | ||||||
\(655\) | −35806.1 | − | 62018.0i | −0.0834593 | − | 0.144556i | ||||
\(656\) | −117540. | + | 67861.6i | −0.273135 | + | 0.157695i | ||||
\(657\) | −500726. | −1.16003 | ||||||||
\(658\) | − | 463316.i | − | 1.07010i | ||||||
\(659\) | 143860. | − | 83057.9i | 0.331261 | − | 0.191254i | −0.325140 | − | 0.945666i | \(-0.605411\pi\) |
0.656401 | + | 0.754412i | \(0.272078\pi\) | |||||||
\(660\) | −80360.2 | − | 46396.0i | −0.184482 | − | 0.106510i | ||||
\(661\) | −177769. | + | 102635.i | −0.406867 | + | 0.234905i | −0.689443 | − | 0.724340i | \(-0.742144\pi\) |
0.282576 | + | 0.959245i | \(0.408811\pi\) | |||||||
\(662\) | −228905. | + | 396475.i | −0.522323 | + | 0.904690i | ||||
\(663\) | −256994. | + | 445127.i | −0.584650 | + | 1.01264i | ||||
\(664\) | 197947.i | 0.448965i | ||||||||
\(665\) | 254148. | + | 86122.8i | 0.574704 | + | 0.194749i | ||||
\(666\) | 21298.8 | 0.0480184 | ||||||||
\(667\) | −240938. | − | 139105.i | −0.541568 | − | 0.312674i | ||||
\(668\) | −231922. | − | 133900.i | −0.519743 | − | 0.300074i | ||||
\(669\) | −514830. | − | 891711.i | −1.15030 | − | 1.99238i | ||||
\(670\) | −165687. | + | 286978.i | −0.369096 | + | 0.639292i | ||||
\(671\) | −31831.7 | − | 55134.2i | −0.0706993 | − | 0.122455i | ||||
\(672\) | 89149.9 | 0.197416 | ||||||||
\(673\) | − | 589468.i | − | 1.30146i | −0.759310 | − | 0.650729i | \(-0.774463\pi\) | ||
0.759310 | − | 0.650729i | \(-0.225537\pi\) | |||||||
\(674\) | 180270. | + | 312238.i | 0.396830 | + | 0.687330i | ||||
\(675\) | 47448.3 | − | 27394.3i | 0.104139 | − | 0.0601246i | ||||
\(676\) | −38494.8 | −0.0842381 | ||||||||
\(677\) | − | 197706.i | − | 0.431362i | −0.976464 | − | 0.215681i | \(-0.930803\pi\) | ||
0.976464 | − | 0.215681i | \(-0.0691971\pi\) | |||||||
\(678\) | 70034.9 | − | 40434.7i | 0.152354 | − | 0.0879619i | ||||
\(679\) | −247486. | − | 142886.i | −0.536797 | − | 0.309920i | ||||
\(680\) | −98647.1 | + | 56953.9i | −0.213337 | + | 0.123170i | ||||
\(681\) | 208017. | − | 360296.i | 0.448544 | − | 0.776901i | ||||
\(682\) | 67149.2 | − | 116306.i | 0.144368 | − | 0.250053i | ||||
\(683\) | 450800.i | 0.966368i | 0.875519 | + | 0.483184i | \(0.160520\pi\) | ||||
−0.875519 | + | 0.483184i | \(0.839480\pi\) | |||||||
\(684\) | 179050. | + | 60674.4i | 0.382704 | + | 0.129686i | ||||
\(685\) | −477511. | −1.01766 | ||||||||
\(686\) | 313591. | + | 181052.i | 0.666371 | + | 0.384729i | ||||
\(687\) | −177012. | − | 102198.i | −0.375049 | − | 0.216535i | ||||
\(688\) | −64041.0 | − | 110922.i | −0.135295 | − | 0.234338i | ||||
\(689\) | 227586. | − | 394191.i | 0.479411 | − | 0.830364i | ||||
\(690\) | −280472. | − | 485791.i | −0.589103 | − | 1.02036i | ||||
\(691\) | 90174.6 | 0.188855 | 0.0944274 | − | 0.995532i | \(-0.469898\pi\) | ||||
0.0944274 | + | 0.995532i | \(0.469898\pi\) | |||||||
\(692\) | 222901.i | 0.465478i | ||||||||
\(693\) | 69887.0 | + | 121048.i | 0.145522 | + | 0.252052i | ||||
\(694\) | −352495. | + | 203513.i | −0.731870 | + | 0.422545i | ||||
\(695\) | −359680. | −0.744640 | ||||||||
\(696\) | 84919.4i | 0.175303i | ||||||||
\(697\) | −506143. | + | 292222.i | −1.04186 | + | 0.601516i | ||||
\(698\) | −163892. | − | 94623.3i | −0.336394 | − | 0.194217i | ||||
\(699\) | −159244. | + | 91939.5i | −0.325918 | + | 0.188169i | ||||
\(700\) | 47424.1 | − | 82141.0i | 0.0967839 | − | 0.167635i | ||||
\(701\) | 52451.2 | − | 90848.2i | 0.106738 | − | 0.184876i | −0.807709 | − | 0.589582i | \(-0.799293\pi\) |
0.914447 | + | 0.404706i | \(0.132626\pi\) | |||||||
\(702\) | − | 81969.9i | − | 0.166334i | ||||||
\(703\) | −40725.3 | + | 8123.01i | −0.0824050 | + | 0.0164364i | ||||
\(704\) | 26864.5 | 0.0542043 | ||||||||
\(705\) | 770619. | + | 444917.i | 1.55046 | + | 0.895160i | ||||
\(706\) | 284449. | + | 164227.i | 0.570683 | + | 0.329484i | ||||
\(707\) | 192390. | + | 333229.i | 0.384896 | + | 0.666660i | ||||
\(708\) | 290816. | − | 503708.i | 0.580165 | − | 1.00488i | ||||
\(709\) | −163355. | − | 282939.i | −0.324968 | − | 0.562860i | 0.656538 | − | 0.754293i | \(-0.272020\pi\) |
−0.981506 | + | 0.191432i | \(0.938687\pi\) | |||||||
\(710\) | −167781. | −0.332833 | ||||||||
\(711\) | 439163.i | 0.868733i | ||||||||
\(712\) | 89447.7 | + | 154928.i | 0.176445 | + | 0.305612i | ||||
\(713\) | 703090. | − | 405929.i | 1.38303 | − | 0.798493i | ||||
\(714\) | 383892. | 0.753031 | ||||||||
\(715\) | 147701.i | 0.288916i | ||||||||
\(716\) | 67724.2 | − | 39100.6i | 0.132105 | − | 0.0762706i | ||||
\(717\) | 374881. | + | 216438.i | 0.729214 | + | 0.421012i | ||||
\(718\) | 227757. | − | 131496.i | 0.441797 | − | 0.255072i | ||||
\(719\) | 395433. | − | 684910.i | 0.764919 | − | 1.32488i | −0.175371 | − | 0.984502i | \(-0.556112\pi\) |
0.940289 | − | 0.340376i | \(-0.110554\pi\) | |||||||
\(720\) | −38263.3 | + | 66274.0i | −0.0738104 | + | 0.127843i | ||||
\(721\) | 64474.0i | 0.124026i | ||||||||
\(722\) | −365500. | − | 47728.3i | −0.701154 | − | 0.0915591i | ||||
\(723\) | −1.28311e6 | −2.45464 | ||||||||
\(724\) | −166651. | − | 96215.8i | −0.317929 | − | 0.183556i | ||||
\(725\) | 78243.1 | + | 45173.7i | 0.148857 | + | 0.0859428i | ||||
\(726\) | −203461. | − | 352405.i | −0.386019 | − | 0.668605i | ||||
\(727\) | 466495. | − | 807992.i | 0.882628 | − | 1.52876i | 0.0342199 | − | 0.999414i | \(-0.489105\pi\) |
0.848408 | − | 0.529342i | \(-0.177561\pi\) | |||||||
\(728\) | −70951.8 | − | 122892.i | −0.133875 | − | 0.231879i | ||||
\(729\) | 311731. | 0.586578 | ||||||||
\(730\) | 395196.i | 0.741595i | ||||||||
\(731\) | −275770. | − | 477647.i | −0.516074 | − | 0.893866i | ||||
\(732\) | −101733. | + | 58735.7i | −0.189863 | + | 0.109617i | ||||
\(733\) | 27589.8 | 0.0513500 | 0.0256750 | − | 0.999670i | \(-0.491826\pi\) | ||||
0.0256750 | + | 0.999670i | \(0.491826\pi\) | |||||||
\(734\) | 33072.7i | 0.0613872i | ||||||||
\(735\) | −142619. | + | 82341.2i | −0.263999 | + | 0.152420i | ||||
\(736\) | 140643. | + | 81200.4i | 0.259635 | + | 0.149900i | ||||
\(737\) | 291449. | − | 168268.i | 0.536572 | − | 0.309790i | ||||
\(738\) | −196323. | + | 340042.i | −0.360462 | + | 0.624338i | ||||
\(739\) | −86704.5 | + | 150177.i | −0.158764 | + | 0.274988i | −0.934423 | − | 0.356164i | \(-0.884084\pi\) |
0.775659 | + | 0.631152i | \(0.217418\pi\) | |||||||
\(740\) | − | 16810.0i | − | 0.0306977i | ||||||
\(741\) | −131696. | − | 660269.i | −0.239849 | − | 1.20250i | ||||
\(742\) | −339963. | −0.617482 | ||||||||
\(743\) | −84623.8 | − | 48857.6i | −0.153290 | − | 0.0885022i | 0.421393 | − | 0.906878i | \(-0.361541\pi\) |
−0.574683 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(744\) | −214607. | − | 123903.i | −0.387702 | − | 0.223840i | ||||
\(745\) | −200718. | − | 347654.i | −0.361638 | − | 0.626376i | ||||
\(746\) | −79421.4 | + | 137562.i | −0.142712 | + | 0.247184i | ||||
\(747\) | 286329. | + | 495937.i | 0.513127 | + | 0.888762i | ||||
\(748\) | 115682. | 0.206759 | ||||||||
\(749\) | 223403.i | 0.398222i | ||||||||
\(750\) | 286473. | + | 496186.i | 0.509286 | + | 0.882109i | ||||
\(751\) | −878645. | + | 507286.i | −1.55788 | + | 0.899442i | −0.560419 | + | 0.828209i | \(0.689360\pi\) |
−0.997460 | + | 0.0712325i | \(0.977307\pi\) | |||||||
\(752\) | −257619. | −0.455556 | ||||||||
\(753\) | − | 668817.i | − | 1.17955i | ||||||
\(754\) | 117061. | − | 67584.9i | 0.205905 | − | 0.118880i | ||||
\(755\) | 363646. | + | 209951.i | 0.637947 | + | 0.368319i | ||||
\(756\) | −53020.1 | + | 30611.2i | −0.0927677 | + | 0.0535595i | ||||
\(757\) | −35978.1 | + | 62315.9i | −0.0627836 | + | 0.108744i | −0.895709 | − | 0.444641i | \(-0.853331\pi\) |
0.832925 | + | 0.553386i | \(0.186664\pi\) | |||||||
\(758\) | −109762. | + | 190114.i | −0.191036 | + | 0.330884i | ||||
\(759\) | 569683.i | 0.988894i | ||||||||
\(760\) | 47887.1 | − | 141315.i | 0.0829070 | − | 0.244659i | ||||
\(761\) | −376652. | −0.650386 | −0.325193 | − | 0.945648i | \(-0.605429\pi\) | ||||
−0.325193 | + | 0.945648i | \(0.605429\pi\) | |||||||
\(762\) | 694765. | + | 401123.i | 1.19654 | + | 0.690824i | ||||
\(763\) | 49643.8 | + | 28661.9i | 0.0852739 | + | 0.0492329i | ||||
\(764\) | 26365.6 | + | 45666.5i | 0.0451700 | + | 0.0782368i | ||||
\(765\) | −164767. | + | 285385.i | −0.281545 | + | 0.487650i | ||||
\(766\) | −331640. | − | 574417.i | −0.565209 | − | 0.978972i | ||||
\(767\) | −925809. | −1.57373 | ||||||||
\(768\) | − | 49570.2i | − | 0.0840424i | ||||||
\(769\) | −148128. | − | 256565.i | −0.250486 | − | 0.433855i | 0.713173 | − | 0.700988i | \(-0.247257\pi\) |
−0.963660 | + | 0.267132i | \(0.913924\pi\) | |||||||
\(770\) | 95536.5 | − | 55158.1i | 0.161134 | − | 0.0930310i | ||||
\(771\) | 540666. | 0.909537 | ||||||||
\(772\) | 106415.i | 0.178554i | ||||||||
\(773\) | 876530. | − | 506065.i | 1.46693 | − | 0.846930i | 0.467610 | − | 0.883935i | \(-0.345115\pi\) |
0.999315 | + | 0.0370049i | \(0.0117817\pi\) | |||||||
\(774\) | −320897. | − | 185270.i | −0.535654 | − | 0.309260i | ||||
\(775\) | −228324. | + | 131823.i | −0.380144 | + | 0.219477i | ||||
\(776\) | −79449.2 | + | 137610.i | −0.131937 | + | 0.228521i | ||||
\(777\) | −28326.6 | + | 49063.1i | −0.0469194 | + | 0.0812667i | ||||
\(778\) | 342724.i | 0.566221i | ||||||||
\(779\) | 245701. | − | 725065.i | 0.404886 | − | 1.19482i | ||||
\(780\) | 272537. | 0.447957 | ||||||||
\(781\) | 147566. | + | 85197.5i | 0.241928 | + | 0.139677i | ||||
\(782\) | 605630. | + | 349661.i | 0.990361 | + | 0.571785i | ||||
\(783\) | −29158.6 | − | 50504.1i | −0.0475601 | − | 0.0823764i | ||||
\(784\) | 23838.9 | − | 41290.2i | 0.0387841 | − | 0.0671761i | ||||
\(785\) | −376418. | − | 651976.i | −0.610846 | − | 1.05802i | ||||
\(786\) | 134197. | 0.217219 | ||||||||
\(787\) | 1.06296e6i | 1.71620i | 0.513486 | + | 0.858098i | \(0.328354\pi\) | ||||
−0.513486 | + | 0.858098i | \(0.671646\pi\) | |||||||
\(788\) | −34431.1 | − | 59636.4i | −0.0554496 | − | 0.0960415i | ||||
\(789\) | −608521. | + | 351329.i | −0.977510 | + | 0.564366i | ||||
\(790\) | 346608. | 0.555372 | ||||||||
\(791\) | 96141.9i | 0.153660i | ||||||||
\(792\) | 67306.5 | − | 38859.4i | 0.107302 | − | 0.0619507i | ||||
\(793\) | 161933. | + | 93492.1i | 0.257507 | + | 0.148672i | ||||
\(794\) | −415154. | + | 239689.i | −0.658519 | + | 0.380196i | ||||
\(795\) | 326462. | − | 565449.i | 0.516534 | − | 0.894663i | ||||
\(796\) | 149024. | − | 258117.i | 0.235196 | − | 0.407371i | ||||
\(797\) | 492593.i | 0.775482i | 0.921768 | + | 0.387741i | \(0.126745\pi\) | ||||
−0.921768 | + | 0.387741i | \(0.873255\pi\) | |||||||
\(798\) | −377897. | + | 331758.i | −0.593427 | + | 0.520973i | ||||
\(799\) | −1.10934e6 | −1.73769 | ||||||||
\(800\) | −45673.1 | − | 26369.4i | −0.0713642 | − | 0.0412021i | ||||
\(801\) | 448206. | + | 258772.i | 0.698574 | + | 0.403322i | ||||
\(802\) | 87997.3 | + | 152416.i | 0.136811 | + | 0.236964i | ||||
\(803\) | 200677. | − | 347582.i | 0.311219 | − | 0.539046i | ||||
\(804\) | −310488. | − | 537780.i | −0.480322 | − | 0.831941i | ||||
\(805\) | 666881. | 1.02910 | ||||||||
\(806\) | 394445.i | 0.607178i | ||||||||
\(807\) | 437659. | + | 758048.i | 0.672030 | + | 1.16399i | ||||
\(808\) | 185286. | − | 106975.i | 0.283805 | − | 0.163855i | ||||
\(809\) | 955780. | 1.46036 | 0.730181 | − | 0.683253i | \(-0.239436\pi\) | ||||
0.730181 | + | 0.683253i | \(0.239436\pi\) | |||||||
\(810\) | − | 391527.i | − | 0.596748i | ||||||
\(811\) | 159358. | − | 92005.2i | 0.242288 | − | 0.139885i | −0.373940 | − | 0.927453i | \(-0.621993\pi\) |
0.616228 | + | 0.787568i | \(0.288660\pi\) | |||||||
\(812\) | −87431.1 | − | 50478.4i | −0.132603 | − | 0.0765585i | ||||
\(813\) | −903791. | + | 521804.i | −1.36737 | + | 0.789453i | ||||
\(814\) | −8535.96 | + | 14784.7i | −0.0128826 | + | 0.0223133i | ||||
\(815\) | −27432.7 | + | 47514.9i | −0.0413003 | + | 0.0715343i | ||||
\(816\) | − | 213456.i | − | 0.320575i | ||||||
\(817\) | 684243. | + | 231868.i | 1.02510 | + | 0.347374i | ||||
\(818\) | −63081.3 | −0.0942744 | ||||||||
\(819\) | −355526. | − | 205263.i | −0.530034 | − | 0.306015i | ||||
\(820\) | 268377. | + | 154947.i | 0.399133 | + | 0.230439i | ||||
\(821\) | 241392. | + | 418103.i | 0.358126 | + | 0.620293i | 0.987648 | − | 0.156690i | \(-0.0500824\pi\) |
−0.629522 | + | 0.776983i | \(0.716749\pi\) | |||||||
\(822\) | 447414. | − | 774944.i | 0.662165 | − | 1.14690i | ||||
\(823\) | 525182. | + | 909641.i | 0.775372 | + | 1.34298i | 0.934585 | + | 0.355739i | \(0.115771\pi\) |
−0.159214 | + | 0.987244i | \(0.550896\pi\) | |||||||
\(824\) | 35849.6 | 0.0527996 | ||||||||
\(825\) | − | 185001.i | − | 0.271811i | ||||||
\(826\) | 345738. | + | 598835.i | 0.506742 | + | 0.877703i | ||||
\(827\) | −297865. | + | 171973.i | −0.435521 | + | 0.251448i | −0.701696 | − | 0.712477i | \(-0.747573\pi\) |
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(828\) | 469824. | 0.685291 | ||||||||
\(829\) | − | 655153.i | − | 0.953309i | −0.879091 | − | 0.476654i | \(-0.841849\pi\) | ||
0.879091 | − | 0.476654i | \(-0.158151\pi\) | |||||||
\(830\) | 391417. | − | 225985.i | 0.568176 | − | 0.328037i | ||||
\(831\) | 1.40010e6 | + | 808346.i | 2.02748 | + | 1.17056i | ||||
\(832\) | −68332.1 | + | 39451.5i | −0.0987138 | + | 0.0569925i | ||||
\(833\) | 102654. | − | 177801.i | 0.147940 | − | 0.256239i | ||||
\(834\) | 337009. | − | 583717.i | 0.484518 | − | 0.839209i | ||||
\(835\) | 611464.i | 0.876997i | ||||||||
\(836\) | −113876. | + | 99972.3i | −0.162937 | + | 0.143043i | ||||
\(837\) | 170177. | 0.242913 | ||||||||
\(838\) | −676391. | − | 390515.i | −0.963186 | − | 0.556096i | ||||
\(839\) | 4544.02 | + | 2623.49i | 0.00645529 | + | 0.00372697i | 0.503224 | − | 0.864156i | \(-0.332147\pi\) |
−0.496769 | + | 0.867883i | \(0.665480\pi\) | |||||||
\(840\) | −101777. | − | 176283.i | −0.144242 | − | 0.249835i | ||||
\(841\) | −305558. | + | 529241.i | −0.432017 | + | 0.748276i | ||||
\(842\) | −401573. | − | 695544.i | −0.566422 | − | 0.981071i | ||||
\(843\) | −946638. | −1.33208 | ||||||||
\(844\) | 593269.i | 0.832850i | ||||||||
\(845\) | 43947.3 | + | 76119.0i | 0.0615487 | + | 0.106605i | ||||
\(846\) | −645440. | + | 372645.i | −0.901810 | + | 0.520660i | ||||
\(847\) | 483772. | 0.674332 | ||||||||
\(848\) | 189031.i | 0.262870i | ||||||||
\(849\) | 40701.4 | − | 23499.0i | 0.0564669 | − | 0.0326012i | ||||
\(850\) | −196675. | − | 113550.i | −0.272214 | − | 0.157163i | ||||
\(851\) | −89376.3 | + | 51601.4i | −0.123414 | + | 0.0712529i | ||||
\(852\) | 157206. | − | 272289.i | 0.216566 | − | 0.375103i | ||||
\(853\) | 263.952 | − | 457.177i | 0.000362766 | − | 0.000628328i | −0.865844 | − | 0.500314i | \(-0.833218\pi\) |
0.866207 | + | 0.499686i | \(0.166551\pi\) | |||||||
\(854\) | − | 139656.i | − | 0.191490i | ||||||
\(855\) | −84434.7 | − | 423319.i | −0.115502 | − | 0.579077i | ||||
\(856\) | 124219. | 0.169528 | ||||||||
\(857\) | 891345. | + | 514618.i | 1.21362 | + | 0.700686i | 0.963547 | − | 0.267539i | \(-0.0862105\pi\) |
0.250078 | + | 0.968226i | \(0.419544\pi\) | |||||||
\(858\) | −239701. | − | 138391.i | −0.325608 | − | 0.187990i | ||||
\(859\) | 145913. | + | 252730.i | 0.197747 | + | 0.342507i | 0.947797 | − | 0.318873i | \(-0.103304\pi\) |
−0.750051 | + | 0.661380i | \(0.769971\pi\) | |||||||
\(860\) | −146224. | + | 253267.i | −0.197707 | + | 0.342438i | ||||
\(861\) | −522204. | − | 904483.i | −0.704423 | − | 1.22010i | ||||
\(862\) | 300044. | 0.403804 | ||||||||
\(863\) | − | 1.24371e6i | − | 1.66993i | −0.550307 | − | 0.834963i | \(-0.685489\pi\) | ||
0.550307 | − | 0.834963i | \(-0.314511\pi\) | |||||||
\(864\) | 17020.8 | + | 29480.9i | 0.0228009 | + | 0.0394924i | ||||
\(865\) | 440760. | − | 254473.i | 0.589074 | − | 0.340102i | ||||
\(866\) | −504919. | −0.673265 | ||||||||
\(867\) | 91606.0i | 0.121867i | ||||||||
\(868\) | 255136. | − | 147303.i | 0.338636 | − | 0.195511i | ||||
\(869\) | −304848. | − | 176004.i | −0.403686 | − | 0.233068i | ||||
\(870\) | 167918. | − | 96947.5i | 0.221850 | − | 0.128085i | ||||
\(871\) | −494217. | + | 856008.i | −0.651450 | + | 1.12834i | ||||
\(872\) | 15936.9 | − | 27603.6i | 0.0209591 | − | 0.0363022i | ||||
\(873\) | 459692.i | 0.603168i | ||||||||
\(874\) | −898346. | + | 179183.i | −1.17604 | + | 0.234571i | ||||
\(875\) | −681150. | −0.889666 | ||||||||
\(876\) | −641356. | − | 370287.i | −0.835778 | − | 0.482537i | ||||
\(877\) | −806389. | − | 465569.i | −1.04844 | − | 0.605320i | −0.126231 | − | 0.992001i | \(-0.540288\pi\) |
−0.922214 | + | 0.386681i | \(0.873621\pi\) | |||||||
\(878\) | −255311. | − | 442211.i | −0.331192 | − | 0.573641i | ||||
\(879\) | 696415. | − | 1.20623e6i | 0.901343 | − | 1.56117i | ||||
\(880\) | −30669.7 | − | 53121.4i | −0.0396044 | − | 0.0685969i | ||||
\(881\) | −465283. | −0.599467 | −0.299734 | − | 0.954023i | \(-0.596898\pi\) | ||||
−0.299734 | + | 0.954023i | \(0.596898\pi\) | |||||||
\(882\) | − | 137931.i | − | 0.177307i | ||||||
\(883\) | 208028. | + | 360315.i | 0.266809 | + | 0.462126i | 0.968036 | − | 0.250812i | \(-0.0806975\pi\) |
−0.701227 | + | 0.712938i | \(0.747364\pi\) | |||||||
\(884\) | −294248. | + | 169884.i | −0.376538 | + | 0.217394i | ||||
\(885\) | −1.32803e6 | −1.69559 | ||||||||
\(886\) | − | 658061.i | − | 0.838298i | ||||||
\(887\) | −833217. | + | 481058.i | −1.05904 | + | 0.611435i | −0.925166 | − | 0.379564i | \(-0.876074\pi\) |
−0.133871 | + | 0.990999i | \(0.542741\pi\) | |||||||
\(888\) | 27280.7 | + | 15750.5i | 0.0345963 | + | 0.0199742i | ||||
\(889\) | −825975. | + | 476877.i | −1.04511 | + | 0.603396i | ||||
\(890\) | 204235. | − | 353745.i | 0.257840 | − | 0.446591i | ||||
\(891\) | −198813. | + | 344355.i | −0.250432 | + | 0.433761i | ||||
\(892\) | − | 680648.i | − | 0.855447i | ||||||
\(893\) | 1.09202e6 | − | 958690.i | 1.36939 | − | 1.20220i | ||||
\(894\) | 752268. | 0.941234 | ||||||||
\(895\) | −154634. | − | 89277.7i | −0.193045 | − | 0.111454i | ||||
\(896\) | 51036.4 | + | 29465.9i | 0.0635718 | + | 0.0367032i | ||||
\(897\) | −836601. | − | 1.44903e6i | −1.03976 | − | 1.80092i | ||||
\(898\) | −258167. | + | 447159.i | −0.320146 | + | 0.554509i | ||||
\(899\) | 140313. | + | 243029.i | 0.173611 | + | 0.300704i | ||||
\(900\) | −152573. | −0.188361 | ||||||||
\(901\) | 813993.i | 1.00270i | ||||||||
\(902\) | −157361. | − | 272558.i | −0.193413 | − | 0.335001i | ||||
\(903\) | 853561. | − | 492803.i | 1.04679 | − | 0.604364i | ||||
\(904\) | 53458.0 | 0.0654148 | ||||||||
\(905\) | 439376.i | 0.536463i | ||||||||
\(906\) | −681450. | + | 393435.i | −0.830190 | + | 0.479311i | ||||
\(907\) | −214782. | − | 124005.i | −0.261086 | − | 0.150738i | 0.363744 | − | 0.931499i | \(-0.381498\pi\) |
−0.624830 | + | 0.780761i | \(0.714832\pi\) | |||||||
\(908\) | 238171. | − | 137508.i | 0.288880 | − | 0.166785i | ||||
\(909\) | 309478. | − | 536032.i | 0.374543 | − | 0.648728i | ||||
\(910\) | −162003. | + | 280598.i | −0.195633 | + | 0.338845i | ||||
\(911\) | − | 598290.i | − | 0.720900i | −0.932779 | − | 0.360450i | \(-0.882623\pi\) | ||
0.932779 | − | 0.360450i | \(-0.117377\pi\) | |||||||
\(912\) | 184468. | + | 210123.i | 0.221785 | + | 0.252629i | ||||
\(913\) | −459010. | −0.550657 | ||||||||
\(914\) | 191405. | + | 110507.i | 0.229118 | + | 0.132282i | ||||
\(915\) | 232286. | + | 134110.i | 0.277447 | + | 0.160184i | ||||
\(916\) | −67556.9 | − | 117012.i | −0.0805154 | − | 0.139457i | ||||
\(917\) | −79770.4 | + | 138166.i | −0.0948644 | + | 0.164310i | ||||
\(918\) | 73294.0 | + | 126949.i | 0.0869728 | + | 0.150641i | ||||
\(919\) | 1.03278e6 | 1.22286 | 0.611432 | − | 0.791297i | \(-0.290594\pi\) | ||||
0.611432 | + | 0.791297i | \(0.290594\pi\) | |||||||
\(920\) | − | 370807.i | − | 0.438099i | ||||||
\(921\) | 172717. | + | 299155.i | 0.203618 | + | 0.352677i | ||||
\(922\) | −542106. | + | 312985.i | −0.637708 | + | 0.368181i | ||||
\(923\) | −500463. | −0.587447 | ||||||||
\(924\) | 206726.i | 0.242131i | ||||||||
\(925\) | 29024.4 | − | 16757.3i | 0.0339219 | − | 0.0195848i | ||||
\(926\) | 808779. | + | 466949.i | 0.943208 | + | 0.544562i | ||||
\(927\) | 89817.9 | − | 51856.4i | 0.104521 | − | 0.0603452i | ||||
\(928\) | −28067.6 | + | 48614.6i | −0.0325919 | + | 0.0564508i | ||||
\(929\) | −388831. | + | 673475.i | −0.450536 | + | 0.780351i | −0.998419 | − | 0.0562037i | \(-0.982100\pi\) |
0.547883 | + | 0.836555i | \(0.315434\pi\) | |||||||
\(930\) | 565813.i | 0.654195i | ||||||||
\(931\) | 52604.7 | + | 263737.i | 0.0606912 | + | 0.304279i | ||||
\(932\) | −121552. | −0.139936 | ||||||||
\(933\) | −137784. | − | 79549.9i | −0.158284 | − | 0.0913853i | ||||
\(934\) | 302459. | + | 174625.i | 0.346715 | + | 0.200176i | ||||
\(935\) | −132068. | − | 228748.i | −0.151069 | − | 0.261659i | ||||
\(936\) | −114133. | + | 197684.i | −0.130275 | + | 0.225642i | ||||
\(937\) | 587086. | + | 1.01686e6i | 0.668686 | + | 1.15820i | 0.978272 | + | 0.207327i | \(0.0664764\pi\) |
−0.309585 | + | 0.950872i | \(0.600190\pi\) | |||||||
\(938\) | 738249. | 0.839068 | ||||||||
\(939\) | − | 2.12348e6i | − | 2.40834i | ||||||
\(940\) | 294109. | + | 509411.i | 0.332853 | + | 0.576518i | ||||
\(941\) | −698093. | + | 403044.i | −0.788378 | + | 0.455170i | −0.839391 | − | 0.543528i | \(-0.817088\pi\) |
0.0510135 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(942\) | 1.41077e6 | 1.58984 | ||||||||
\(943\) | − | 1.90256e6i | − | 2.13951i | ||||||
\(944\) | 332972. | − | 192242.i | 0.373649 | − | 0.215726i | ||||
\(945\) | 121060. | + | 69894.0i | 0.135562 | + | 0.0782666i | ||||
\(946\) | 257213. | − | 148502.i | 0.287416 | − | 0.165940i | ||||
\(947\) | 91047.7 | − | 157699.i | 0.101524 | − | 0.175845i | −0.810789 | − | 0.585339i | \(-0.800961\pi\) |
0.912313 | + | 0.409494i | \(0.134295\pi\) | |||||||
\(948\) | −324761. | + | 562503.i | −0.361366 | + | 0.625904i | ||||
\(949\) | 1.17880e6i | 1.30891i | ||||||||
\(950\) | 291733. | − | 58188.6i | 0.323250 | − | 0.0644750i | ||||
\(951\) | 1.05573e6 | 1.16732 | ||||||||
\(952\) | 219770. | + | 126884.i | 0.242491 | + | 0.140002i | ||||
\(953\) | −665244. | − | 384079.i | −0.732479 | − | 0.422897i | 0.0868497 | − | 0.996221i | \(-0.472320\pi\) |
−0.819328 | + | 0.573325i | \(0.805653\pi\) | |||||||
\(954\) | 273432. | + | 473598.i | 0.300436 | + | 0.520371i | ||||
\(955\) | 60200.1 | − | 104270.i | 0.0660071 | − | 0.114328i | ||||
\(956\) | 143074. | + | 247812.i | 0.156547 | + | 0.271148i | ||||
\(957\) | −196916. | −0.215009 | ||||||||
\(958\) | 396061.i | 0.431550i | ||||||||
\(959\) | 531910. | + | 921296.i | 0.578364 | + | 1.00176i | ||||
\(960\) | −98019.3 | + | 56591.5i | −0.106358 | + | 0.0614057i | ||||
\(961\) | 104615. | 0.113279 | ||||||||
\(962\) | − | 50141.5i | − | 0.0541810i | ||||||
\(963\) | 311220. | − | 179683.i | 0.335595 | − | 0.193756i | ||||
\(964\) | −734554. | − | 424095.i | −0.790442 | − | 0.456362i | ||||
\(965\) | 210423. | − | 121488.i | 0.225964 | − | 0.130460i | ||||
\(966\) | −624847. | + | 1.08227e6i | −0.669606 | + | 1.15979i | ||||
\(967\) | 42211.1 | − | 73111.7i | 0.0451412 | − | 0.0781869i | −0.842572 | − | 0.538584i | \(-0.818960\pi\) |
0.887713 | + | 0.460397i | \(0.152293\pi\) | |||||||
\(968\) | − | 268993.i | − | 0.287072i | ||||||
\(969\) | 794346. | + | 904819.i | 0.845984 | + | 0.963638i | ||||
\(970\) | 362810. | 0.385599 | ||||||||
\(971\) | −36053.5 | − | 20815.5i | −0.0382392 | − | 0.0220774i | 0.480759 | − | 0.876853i | \(-0.340361\pi\) |
−0.518998 | + | 0.854776i | \(0.673695\pi\) | |||||||
\(972\) | 529867. | + | 305919.i | 0.560834 | + | 0.323798i | ||||
\(973\) | 400655. | + | 693955.i | 0.423199 | + | 0.733003i | ||||
\(974\) | 200738. | − | 347688.i | 0.211598 | − | 0.366498i | ||||
\(975\) | 271681. | + | 470566.i | 0.285792 | + | 0.495006i | ||||
\(976\) | −77653.5 | −0.0815195 | ||||||||
\(977\) | − | 586443.i | − | 0.614380i | −0.951648 | − | 0.307190i | \(-0.900611\pi\) | ||
0.951648 | − | 0.307190i | \(-0.0993887\pi\) | |||||||
\(978\) | −51407.3 | − | 89040.0i | −0.0537461 | − | 0.0930910i | ||||
\(979\) | −359256. | + | 207417.i | −0.374834 | + | 0.216410i | ||||
\(980\) | −108862. | −0.113351 | ||||||||
\(981\) | − | 92210.9i | − | 0.0958173i | ||||||
\(982\) | −6682.43 | + | 3858.10i | −0.00692965 | + | 0.00400084i | ||||
\(983\) | −516678. | − | 298304.i | −0.534703 | − | 0.308711i | 0.208226 | − | 0.978081i | \(-0.433231\pi\) |
−0.742930 | + | 0.669370i | \(0.766564\pi\) | |||||||
\(984\) | −502922. | + | 290362.i | −0.519410 | + | 0.299882i | ||||
\(985\) | −78616.0 | + | 136167.i | −0.0810286 | + | 0.140346i | ||||
\(986\) | −120863. | + | 209341.i | −0.124320 | + | 0.215328i | ||||
\(987\) | − | 1.98241e6i | − | 2.03498i | ||||||
\(988\) | 142839. | − | 421518.i | 0.146330 | − | 0.431820i | ||||
\(989\) | 1.79544e6 | 1.83560 | ||||||||
\(990\) | −153680. | − | 88727.2i | −0.156800 | − | 0.0905287i | ||||
\(991\) | 125022. | + | 72181.2i | 0.127303 | + | 0.0734982i | 0.562299 | − | 0.826934i | \(-0.309917\pi\) |
−0.434996 | + | 0.900432i | \(0.643250\pi\) | |||||||
\(992\) | −81905.3 | − | 141864.i | −0.0832317 | − | 0.144161i | ||||
\(993\) | −979425. | + | 1.69641e6i | −0.993282 | + | 1.72042i | ||||
\(994\) | 186895. | + | 323712.i | 0.189158 | + | 0.327631i | ||||
\(995\) | −680527. | −0.687384 | ||||||||
\(996\) | 846963.i | 0.853780i | ||||||||
\(997\) | −975015. | − | 1.68878e6i | −0.980892 | − | 1.69895i | −0.658934 | − | 0.752201i | \(-0.728992\pi\) |
−0.321958 | − | 0.946754i | \(-0.604341\pi\) | |||||||
\(998\) | −515379. | + | 297554.i | −0.517447 | + | 0.298748i | ||||
\(999\) | −21632.8 | −0.0216762 |
(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 | 38.5.d.a.27.8 | ✓ | 16 | |
3.2 | odd | 2 | 342.5.m.c.217.2 | 16 | |||
4.3 | odd | 2 | 304.5.r.c.65.2 | 16 | |||
19.12 | odd | 6 | inner | 38.5.d.a.31.8 | yes | 16 | |
57.50 | even | 6 | 342.5.m.c.145.2 | 16 | |||
76.31 | even | 6 | 304.5.r.c.145.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.d.a.27.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
38.5.d.a.31.8 | yes | 16 | 19.12 | odd | 6 | inner | |
304.5.r.c.65.2 | 16 | 4.3 | odd | 2 | |||
304.5.r.c.145.2 | 16 | 76.31 | even | 6 | |||
342.5.m.c.145.2 | 16 | 57.50 | even | 6 | |||
342.5.m.c.217.2 | 16 | 3.2 | odd | 2 |