Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.9 | ||
Root | \(2.70166 - 0.837276i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.d.151.10 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.08838 | − | 2.54203i | 0.772095 | − | 0.635507i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | 3.07620 | − | 15.7015i | 0.192262 | − | 0.981344i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −13.2088 | − | 16.0477i | −0.366910 | − | 0.445769i | ||||
\(7\) | − | 86.5709i | − | 1.76675i | −0.468665 | − | 0.883376i | \(-0.655265\pi\) | ||
0.468665 | − | 0.883376i | \(-0.344735\pi\) | |||||||
\(8\) | −30.4132 | − | 56.3120i | −0.475206 | − | 0.879875i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 97.6947i | − | 0.807394i | −0.914893 | − | 0.403697i | \(-0.867725\pi\) | ||
0.914893 | − | 0.403697i | \(-0.132275\pi\) | |||||||
\(12\) | −81.5874 | − | 15.9844i | −0.566579 | − | 0.111003i | ||||
\(13\) | 297.644 | 1.76121 | 0.880603 | − | 0.473856i | \(-0.157138\pi\) | ||||
0.880603 | + | 0.473856i | \(0.157138\pi\) | |||||||
\(14\) | −220.066 | − | 267.364i | −1.12278 | − | 1.36410i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −237.074 | − | 96.6018i | −0.926070 | − | 0.377351i | ||||
\(17\) | 58.8402 | 0.203599 | 0.101800 | − | 0.994805i | \(-0.467540\pi\) | ||||
0.101800 | + | 0.994805i | \(0.467540\pi\) | |||||||
\(18\) | −83.3863 | + | 68.6347i | −0.257365 | + | 0.211836i | ||||
\(19\) | 497.315i | 1.37760i | 0.724949 | + | 0.688802i | \(0.241863\pi\) | ||||
−0.724949 | + | 0.688802i | \(0.758137\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −449.835 | −1.02004 | ||||||||
\(22\) | −248.343 | − | 301.718i | −0.513104 | − | 0.623385i | ||||
\(23\) | − | 120.919i | − | 0.228581i | −0.993447 | − | 0.114290i | \(-0.963541\pi\) | ||
0.993447 | − | 0.114290i | \(-0.0364594\pi\) | |||||||
\(24\) | −292.606 | + | 158.031i | −0.507996 | + | 0.274360i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 919.237 | − | 756.618i | 1.35982 | − | 1.11926i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | −1359.29 | − | 266.309i | −1.73379 | − | 0.339680i | ||||
\(29\) | −947.079 | −1.12613 | −0.563067 | − | 0.826411i | \(-0.690379\pi\) | ||||
−0.563067 | + | 0.826411i | \(0.690379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 559.454i | 0.582158i | 0.956699 | + | 0.291079i | \(0.0940142\pi\) | ||||
−0.956699 | + | 0.291079i | \(0.905986\pi\) | |||||||
\(32\) | −977.739 | + | 304.306i | −0.954824 | + | 0.297173i | ||||
\(33\) | −507.636 | −0.466149 | ||||||||
\(34\) | 181.721 | − | 149.573i | 0.157198 | − | 0.129389i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −83.0573 | + | 423.940i | −0.0640874 | + | 0.327115i | ||||
\(37\) | −1163.36 | −0.849789 | −0.424894 | − | 0.905243i | \(-0.639689\pi\) | ||||
−0.424894 | + | 0.905243i | \(0.639689\pi\) | |||||||
\(38\) | 1264.19 | + | 1535.90i | 0.875477 | + | 1.06364i | ||||
\(39\) | − | 1546.60i | − | 1.01683i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3178.56 | 1.89088 | 0.945438 | − | 0.325802i | \(-0.105634\pi\) | ||||
0.945438 | + | 0.325802i | \(0.105634\pi\) | |||||||
\(42\) | −1389.26 | + | 1143.49i | −0.787564 | + | 0.648239i | ||||
\(43\) | − | 1166.21i | − | 0.630727i | −0.948971 | − | 0.315364i | \(-0.897874\pi\) | ||
0.948971 | − | 0.315364i | \(-0.102126\pi\) | |||||||
\(44\) | −1533.95 | − | 300.528i | −0.792331 | − | 0.155231i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −307.380 | − | 373.445i | −0.145265 | − | 0.176486i | ||||
\(47\) | − | 1060.01i | − | 0.479859i | −0.970790 | − | 0.239930i | \(-0.922876\pi\) | ||
0.970790 | − | 0.239930i | \(-0.0771244\pi\) | |||||||
\(48\) | −501.958 | + | 1231.87i | −0.217863 | + | 0.534667i | ||||
\(49\) | −5093.52 | −2.12141 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 305.743i | − | 0.117548i | ||||||
\(52\) | 915.610 | − | 4673.45i | 0.338613 | − | 1.72835i | ||||
\(53\) | −1440.77 | −0.512911 | −0.256455 | − | 0.966556i | \(-0.582555\pi\) | ||||
−0.256455 | + | 0.966556i | \(0.582555\pi\) | |||||||
\(54\) | 356.637 | + | 433.288i | 0.122303 | + | 0.148590i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4874.98 | + | 2632.89i | −1.55452 | + | 0.839571i | ||||
\(57\) | 2584.13 | 0.795360 | ||||||||
\(58\) | −2924.94 | + | 2407.50i | −0.869483 | + | 0.715666i | ||||
\(59\) | − | 2004.76i | − | 0.575914i | −0.957643 | − | 0.287957i | \(-0.907024\pi\) | ||
0.957643 | − | 0.287957i | \(-0.0929760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3522.56 | 0.946671 | 0.473335 | − | 0.880882i | \(-0.343050\pi\) | ||||
0.473335 | + | 0.880882i | \(0.343050\pi\) | |||||||
\(62\) | 1422.15 | + | 1727.81i | 0.369965 | + | 0.449481i | ||||
\(63\) | 2337.41i | 0.588917i | ||||||||
\(64\) | −2246.08 | + | 3425.25i | −0.548359 | + | 0.836243i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1567.77 | + | 1290.43i | −0.359912 | + | 0.296241i | ||||
\(67\) | 6169.67i | 1.37440i | 0.726470 | + | 0.687199i | \(0.241160\pi\) | ||||
−0.726470 | + | 0.687199i | \(0.758840\pi\) | |||||||
\(68\) | 181.004 | − | 923.879i | 0.0391445 | − | 0.199801i | ||||
\(69\) | −628.315 | −0.131971 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 882.122i | 0.174990i | 0.996165 | + | 0.0874948i | \(0.0278861\pi\) | ||||
−0.996165 | + | 0.0874948i | \(0.972114\pi\) | |||||||
\(72\) | 821.156 | + | 1520.42i | 0.158402 | + | 0.293292i | ||||
\(73\) | −1659.75 | −0.311457 | −0.155728 | − | 0.987800i | \(-0.549772\pi\) | ||||
−0.155728 | + | 0.987800i | \(0.549772\pi\) | |||||||
\(74\) | −3592.90 | + | 2957.30i | −0.656118 | + | 0.540047i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7808.59 | + | 1529.84i | 1.35190 | + | 0.264861i | ||||
\(77\) | −8457.51 | −1.42647 | ||||||||
\(78\) | −3931.50 | − | 4776.50i | −0.646204 | − | 0.785091i | ||||
\(79\) | 7276.52i | 1.16592i | 0.812500 | + | 0.582961i | \(0.198106\pi\) | ||||
−0.812500 | + | 0.582961i | \(0.801894\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 9816.61 | − | 8079.99i | 1.45994 | − | 1.20166i | ||||
\(83\) | − | 5346.39i | − | 0.776076i | −0.921643 | − | 0.388038i | \(-0.873153\pi\) | ||
0.921643 | − | 0.388038i | \(-0.126847\pi\) | |||||||
\(84\) | −1383.78 | + | 7063.09i | −0.196114 | + | 1.00100i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2964.55 | − | 3601.72i | −0.400831 | − | 0.486982i | ||||
\(87\) | 4921.17i | 0.650174i | ||||||||
\(88\) | −5501.38 | + | 2971.20i | −0.710406 | + | 0.383678i | ||||
\(89\) | 9009.81 | 1.13746 | 0.568730 | − | 0.822525i | \(-0.307435\pi\) | ||||
0.568730 | + | 0.822525i | \(0.307435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 25767.3i | − | 3.11161i | ||||||
\(92\) | −1898.61 | − | 371.971i | −0.224316 | − | 0.0439475i | ||||
\(93\) | 2907.01 | 0.336109 | ||||||||
\(94\) | −2694.57 | − | 3273.71i | −0.304954 | − | 0.370497i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1581.22 | + | 5080.48i | 0.171573 | + | 0.551268i | ||||
\(97\) | 9798.06 | 1.04135 | 0.520675 | − | 0.853755i | \(-0.325680\pi\) | ||||
0.520675 | + | 0.853755i | \(0.325680\pi\) | |||||||
\(98\) | −15730.7 | + | 12947.9i | −1.63793 | + | 1.34817i | ||||
\(99\) | 2637.76i | 0.269131i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5404.90 | 0.529841 | 0.264920 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264920 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(102\) | −777.206 | − | 944.250i | −0.0747026 | − | 0.0907584i | ||||
\(103\) | − | 8294.77i | − | 0.781862i | −0.920420 | − | 0.390931i | \(-0.872153\pi\) | ||
0.920420 | − | 0.390931i | \(-0.127847\pi\) | |||||||
\(104\) | −9052.29 | − | 16760.9i | −0.836935 | − | 1.54964i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4449.64 | + | 3662.47i | −0.396016 | + | 0.325958i | ||||
\(107\) | − | 5744.62i | − | 0.501758i | −0.968018 | − | 0.250879i | \(-0.919280\pi\) | ||
0.968018 | − | 0.250879i | \(-0.0807196\pi\) | |||||||
\(108\) | 2202.86 | + | 431.578i | 0.188860 | + | 0.0370009i | ||||
\(109\) | 4709.84 | 0.396418 | 0.198209 | − | 0.980160i | \(-0.436488\pi\) | ||||
0.198209 | + | 0.980160i | \(0.436488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6045.00i | 0.490626i | ||||||||
\(112\) | −8362.90 | + | 20523.7i | −0.666685 | + | 1.63614i | ||||
\(113\) | −241.555 | −0.0189173 | −0.00945864 | − | 0.999955i | \(-0.503011\pi\) | ||||
−0.00945864 | + | 0.999955i | \(0.503011\pi\) | |||||||
\(114\) | 7980.76 | − | 6568.92i | 0.614094 | − | 0.505457i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2913.40 | + | 14870.6i | −0.216513 | + | 1.10513i | ||||
\(117\) | −8036.38 | −0.587068 | ||||||||
\(118\) | −5096.14 | − | 6191.45i | −0.365997 | − | 0.444660i | ||||
\(119\) | − | 5093.85i | − | 0.359710i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5096.75 | 0.348115 | ||||||||
\(122\) | 10879.0 | − | 8954.45i | 0.730920 | − | 0.601616i | ||||
\(123\) | − | 16516.3i | − | 1.09170i | ||||||
\(124\) | 8784.26 | + | 1720.99i | 0.571297 | + | 0.111927i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5941.77 | + | 7218.82i | 0.374261 | + | 0.454700i | ||||
\(127\) | − | 6882.74i | − | 0.426731i | −0.976972 | − | 0.213365i | \(-0.931558\pi\) | ||
0.976972 | − | 0.213365i | \(-0.0684425\pi\) | |||||||
\(128\) | 1770.34 | + | 16288.1i | 0.108053 | + | 0.994145i | ||||
\(129\) | −6059.83 | −0.364151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1247.82i | − | 0.0727126i | −0.999339 | − | 0.0363563i | \(-0.988425\pi\) | ||
0.999339 | − | 0.0363563i | \(-0.0115751\pi\) | |||||||
\(132\) | −1561.59 | + | 7970.65i | −0.0896229 | + | 0.457452i | ||||
\(133\) | 43053.0 | 2.43389 | ||||||||
\(134\) | 15683.5 | + | 19054.3i | 0.873439 | + | 1.06117i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1789.52 | − | 3313.41i | −0.0967516 | − | 0.179142i | ||||
\(137\) | −1712.53 | −0.0912422 | −0.0456211 | − | 0.998959i | \(-0.514527\pi\) | ||||
−0.0456211 | + | 0.998959i | \(0.514527\pi\) | |||||||
\(138\) | −1940.48 | + | 1597.19i | −0.101894 | + | 0.0838686i | ||||
\(139\) | − | 6748.58i | − | 0.349287i | −0.984632 | − | 0.174644i | \(-0.944123\pi\) | ||
0.984632 | − | 0.174644i | \(-0.0558773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5507.97 | −0.277047 | ||||||||
\(142\) | 2242.38 | + | 2724.33i | 0.111207 | + | 0.135109i | ||||
\(143\) | − | 29078.2i | − | 1.42199i | ||||||
\(144\) | 6401.00 | + | 2608.25i | 0.308690 | + | 0.125784i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5125.95 | + | 4219.14i | −0.240474 | + | 0.197933i | ||||
\(147\) | 26466.7i | 1.22480i | ||||||||
\(148\) | −3578.73 | + | 18266.5i | −0.163382 | + | 0.833935i | ||||
\(149\) | −38109.7 | −1.71657 | −0.858287 | − | 0.513170i | \(-0.828471\pi\) | ||||
−0.858287 | + | 0.513170i | \(0.828471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4383.99i | 0.192272i | 0.995368 | + | 0.0961360i | \(0.0306484\pi\) | ||||
−0.995368 | + | 0.0961360i | \(0.969352\pi\) | |||||||
\(152\) | 28004.8 | − | 15124.9i | 1.21212 | − | 0.654645i | ||||
\(153\) | −1588.69 | −0.0678665 | ||||||||
\(154\) | −26120.0 | + | 21499.2i | −1.10137 | + | 0.906528i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −24284.0 | − | 4757.65i | −0.997862 | − | 0.195498i | ||||
\(157\) | −18910.0 | −0.767173 | −0.383586 | − | 0.923505i | \(-0.625311\pi\) | ||||
−0.383586 | + | 0.923505i | \(0.625311\pi\) | |||||||
\(158\) | 18497.1 | + | 22472.7i | 0.740951 | + | 0.900202i | ||||
\(159\) | 7486.44i | 0.296129i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10468.1 | −0.403846 | ||||||||
\(162\) | 2251.43 | − | 1853.14i | 0.0857884 | − | 0.0706119i | ||||
\(163\) | − | 2243.95i | − | 0.0844575i | −0.999108 | − | 0.0422288i | \(-0.986554\pi\) | ||
0.999108 | − | 0.0422288i | \(-0.0134458\pi\) | |||||||
\(164\) | 9777.88 | − | 49908.2i | 0.363544 | − | 1.85560i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13590.7 | − | 16511.7i | −0.493201 | − | 0.599204i | ||||
\(167\) | − | 24011.7i | − | 0.860972i | −0.902597 | − | 0.430486i | \(-0.858342\pi\) | ||
0.902597 | − | 0.430486i | \(-0.141658\pi\) | |||||||
\(168\) | 13680.9 | + | 25331.1i | 0.484726 | + | 0.897503i | ||||
\(169\) | 60030.7 | 2.10184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 13427.5i | − | 0.459201i | ||||||
\(172\) | −18311.3 | − | 3587.51i | −0.618960 | − | 0.121265i | ||||
\(173\) | 38810.8 | 1.29676 | 0.648381 | − | 0.761316i | \(-0.275446\pi\) | ||||
0.648381 | + | 0.761316i | \(0.275446\pi\) | |||||||
\(174\) | 12509.7 | + | 15198.4i | 0.413190 | + | 0.501996i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9437.48 | + | 23160.9i | −0.304671 | + | 0.747704i | ||||
\(177\) | −10417.0 | −0.332504 | ||||||||
\(178\) | 27825.7 | − | 22903.2i | 0.878227 | − | 0.722863i | ||||
\(179\) | − | 56139.5i | − | 1.75211i | −0.482207 | − | 0.876057i | \(-0.660165\pi\) | ||
0.482207 | − | 0.876057i | \(-0.339835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19958.6 | 0.609217 | 0.304609 | − | 0.952478i | \(-0.401474\pi\) | ||||
0.304609 | + | 0.952478i | \(0.401474\pi\) | |||||||
\(182\) | −65501.1 | − | 79579.2i | −1.97745 | − | 2.40246i | ||||
\(183\) | − | 18303.8i | − | 0.546561i | ||||||
\(184\) | −6809.20 | + | 3677.54i | −0.201122 | + | 0.108623i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8977.95 | − | 7389.69i | 0.259508 | − | 0.213600i | ||||
\(187\) | − | 5748.38i | − | 0.164385i | ||||||
\(188\) | −16643.7 | − | 3260.80i | −0.470907 | − | 0.0922588i | ||||
\(189\) | 12145.6 | 0.340012 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 57207.0i | − | 1.56813i | −0.620677 | − | 0.784066i | \(-0.713142\pi\) | ||
0.620677 | − | 0.784066i | \(-0.286858\pi\) | |||||||
\(192\) | 17798.1 | + | 11671.0i | 0.482805 | + | 0.316595i | ||||
\(193\) | 4603.04 | 0.123575 | 0.0617874 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617874 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(194\) | 30260.1 | − | 24906.9i | 0.804021 | − | 0.661785i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15668.7 | + | 79975.8i | −0.407868 | + | 2.08184i | ||||
\(197\) | −30077.6 | −0.775017 | −0.387509 | − | 0.921866i | \(-0.626664\pi\) | ||||
−0.387509 | + | 0.921866i | \(0.626664\pi\) | |||||||
\(198\) | 6705.25 | + | 8146.40i | 0.171035 | + | 0.207795i | ||||
\(199\) | 42243.9i | 1.06674i | 0.845883 | + | 0.533369i | \(0.179074\pi\) | ||||
−0.845883 | + | 0.533369i | \(0.820926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32058.5 | 0.793509 | ||||||||
\(202\) | 16692.4 | − | 13739.4i | 0.409087 | − | 0.336717i | ||||
\(203\) | 81989.5i | 1.98960i | ||||||||
\(204\) | −4800.62 | − | 940.525i | −0.115355 | − | 0.0226001i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21085.5 | − | 25617.4i | −0.496878 | − | 0.603672i | ||||
\(207\) | 3264.82i | 0.0761936i | ||||||||
\(208\) | −70563.6 | − | 28752.9i | −1.63100 | − | 0.664592i | ||||
\(209\) | 48585.0 | 1.11227 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3093.80i | − | 0.0694908i | −0.999396 | − | 0.0347454i | \(-0.988938\pi\) | ||
0.999396 | − | 0.0347454i | \(-0.0110620\pi\) | |||||||
\(212\) | −4432.08 | + | 22622.2i | −0.0986134 | + | 0.503342i | ||||
\(213\) | 4583.64 | 0.101030 | ||||||||
\(214\) | −14603.0 | − | 17741.6i | −0.318870 | − | 0.387405i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7900.35 | − | 4266.85i | 0.169332 | − | 0.0914534i | ||||
\(217\) | 48432.4 | 1.02853 | ||||||||
\(218\) | 14545.8 | − | 11972.5i | 0.306072 | − | 0.251926i | ||||
\(219\) | 8624.33i | 0.179820i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17513.4 | 0.358580 | ||||||||
\(222\) | 15366.6 | + | 18669.3i | 0.311796 | + | 0.378810i | ||||
\(223\) | − | 43059.5i | − | 0.865884i | −0.901422 | − | 0.432942i | \(-0.857475\pi\) | ||
0.901422 | − | 0.432942i | \(-0.142525\pi\) | |||||||
\(224\) | 26344.0 | + | 84643.7i | 0.525032 | + | 1.68694i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −746.013 | + | 614.039i | −0.0146059 | + | 0.0120221i | ||||
\(227\) | 43385.8i | 0.841968i | 0.907068 | + | 0.420984i | \(0.138315\pi\) | ||||
−0.907068 | + | 0.420984i | \(0.861685\pi\) | |||||||
\(228\) | 7949.28 | − | 40574.6i | 0.152918 | − | 0.780522i | ||||
\(229\) | 56036.8 | 1.06857 | 0.534285 | − | 0.845305i | \(-0.320581\pi\) | ||||
0.534285 | + | 0.845305i | \(0.320581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 43946.5i | 0.823570i | ||||||||
\(232\) | 28803.7 | + | 53331.9i | 0.535146 | + | 0.990857i | ||||
\(233\) | 41638.3 | 0.766974 | 0.383487 | − | 0.923546i | \(-0.374723\pi\) | ||||
0.383487 | + | 0.923546i | \(0.374723\pi\) | |||||||
\(234\) | −24819.4 | + | 20428.7i | −0.453273 | + | 0.373086i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −31477.7 | − | 6167.02i | −0.565169 | − | 0.110726i | ||||
\(237\) | 37809.9 | 0.673145 | ||||||||
\(238\) | −12948.7 | − | 15731.7i | −0.228598 | − | 0.277730i | ||||
\(239\) | − | 71028.3i | − | 1.24347i | −0.783227 | − | 0.621736i | \(-0.786428\pi\) | ||
0.783227 | − | 0.621736i | \(-0.213572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −58695.9 | −1.01059 | −0.505294 | − | 0.862947i | \(-0.668616\pi\) | ||||
−0.505294 | + | 0.862947i | \(0.668616\pi\) | |||||||
\(242\) | 15740.7 | − | 12956.1i | 0.268778 | − | 0.221229i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | 10836.1 | − | 55309.5i | 0.182009 | − | 0.929009i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −41984.9 | − | 51008.6i | −0.693781 | − | 0.842895i | ||||
\(247\) | 148023.i | 2.42624i | ||||||||
\(248\) | 31504.0 | − | 17014.8i | 0.512226 | − | 0.276645i | ||||
\(249\) | −27780.6 | −0.448068 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 40236.7i | 0.638668i | 0.947642 | + | 0.319334i | \(0.103459\pi\) | ||||
−0.947642 | + | 0.319334i | \(0.896541\pi\) | |||||||
\(252\) | 36700.9 | + | 7190.34i | 0.577930 | + | 0.113227i | ||||
\(253\) | −11813.2 | −0.184555 | ||||||||
\(254\) | −17496.1 | − | 21256.5i | −0.271190 | − | 0.329477i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 46872.2 | + | 45803.5i | 0.715213 | + | 0.698907i | ||||
\(257\) | 85304.1 | 1.29153 | 0.645763 | − | 0.763538i | \(-0.276539\pi\) | ||||
0.645763 | + | 0.763538i | \(0.276539\pi\) | |||||||
\(258\) | −18715.1 | + | 15404.3i | −0.281159 | + | 0.231420i | ||||
\(259\) | 100713.i | 1.50137i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25571.1 | 0.375378 | ||||||||
\(262\) | −3172.00 | − | 3853.75i | −0.0462094 | − | 0.0561411i | ||||
\(263\) | − | 87162.9i | − | 1.26014i | −0.776537 | − | 0.630072i | \(-0.783025\pi\) | ||
0.776537 | − | 0.630072i | \(-0.216975\pi\) | |||||||
\(264\) | 15438.8 | + | 28586.0i | 0.221517 | + | 0.410153i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 132964. | − | 109442.i | 1.87919 | − | 1.54675i | ||||
\(267\) | − | 46816.4i | − | 0.656712i | ||||||
\(268\) | 96873.0 | + | 18979.1i | 1.34876 | + | 0.264245i | ||||
\(269\) | −125878. | −1.73958 | −0.869789 | − | 0.493424i | \(-0.835745\pi\) | ||||
−0.869789 | + | 0.493424i | \(0.835745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 94283.5i | 1.28380i | 0.766789 | + | 0.641899i | \(0.221853\pi\) | ||||
−0.766789 | + | 0.641899i | \(0.778147\pi\) | |||||||
\(272\) | −13949.5 | − | 5684.07i | −0.188547 | − | 0.0768283i | ||||
\(273\) | −133891. | −1.79649 | ||||||||
\(274\) | −5288.93 | + | 4353.29i | −0.0704477 | + | 0.0579850i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1932.82 | + | 9865.48i | −0.0253731 | + | 0.129509i | ||||
\(277\) | −65798.3 | −0.857541 | −0.428771 | − | 0.903413i | \(-0.641053\pi\) | ||||
−0.428771 | + | 0.903413i | \(0.641053\pi\) | |||||||
\(278\) | −17155.1 | − | 20842.2i | −0.221974 | − | 0.269683i | ||||
\(279\) | − | 15105.3i | − | 0.194053i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16122.0 | 0.204177 | 0.102088 | − | 0.994775i | \(-0.467448\pi\) | ||||
0.102088 | + | 0.994775i | \(0.467448\pi\) | |||||||
\(282\) | −17010.7 | + | 14001.4i | −0.213907 | + | 0.176065i | ||||
\(283\) | 128462.i | 1.60399i | 0.597329 | + | 0.801997i | \(0.296229\pi\) | ||||
−0.597329 | + | 0.801997i | \(0.703771\pi\) | |||||||
\(284\) | 13850.6 | + | 2713.58i | 0.171725 | + | 0.0336439i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −73917.6 | − | 89804.6i | −0.903682 | − | 1.09791i | ||||
\(287\) | − | 275171.i | − | 3.34071i | ||||||
\(288\) | 26399.0 | − | 8216.25i | 0.318275 | − | 0.0990578i | ||||
\(289\) | −80058.8 | −0.958547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 50912.2i | − | 0.601224i | ||||||
\(292\) | −5105.73 | + | 26060.6i | −0.0598814 | + | 0.305646i | ||||
\(293\) | −161599. | −1.88236 | −0.941180 | − | 0.337906i | \(-0.890282\pi\) | ||||
−0.941180 | + | 0.337906i | \(0.890282\pi\) | |||||||
\(294\) | 67279.0 | + | 81739.2i | 0.778368 | + | 0.945662i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 35381.5 | + | 65511.2i | 0.403825 | + | 0.747708i | ||||
\(297\) | 13706.2 | 0.155383 | ||||||||
\(298\) | −117697. | + | 96875.8i | −1.32536 | + | 1.09089i | ||||
\(299\) | − | 35990.8i | − | 0.402578i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −100960. | −1.11434 | ||||||||
\(302\) | 11144.2 | + | 13539.4i | 0.122190 | + | 0.148452i | ||||
\(303\) | − | 28084.7i | − | 0.305904i | ||||||
\(304\) | 48041.5 | − | 117901.i | 0.519840 | − | 1.27576i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4906.47 | + | 4038.48i | −0.0523994 | + | 0.0431296i | ||||
\(307\) | 39700.0i | 0.421224i | 0.977570 | + | 0.210612i | \(0.0675457\pi\) | ||||
−0.977570 | + | 0.210612i | \(0.932454\pi\) | |||||||
\(308\) | −26017.0 | + | 132796.i | −0.274255 | + | 1.39985i | ||||
\(309\) | −43100.9 | −0.451408 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16610.8i | 0.171739i | 0.996306 | + | 0.0858696i | \(0.0273669\pi\) | ||||
−0.996306 | + | 0.0858696i | \(0.972633\pi\) | |||||||
\(312\) | −87092.2 | + | 47037.1i | −0.894685 | + | 0.483205i | ||||
\(313\) | 34354.3 | 0.350665 | 0.175332 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175332 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(314\) | −58401.4 | + | 48069.8i | −0.592331 | + | 0.487544i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 114252. | + | 22384.0i | 1.14417 | + | 0.224163i | ||||
\(317\) | 51349.0 | 0.510991 | 0.255495 | − | 0.966810i | \(-0.417761\pi\) | ||||
0.255495 | + | 0.966810i | \(0.417761\pi\) | |||||||
\(318\) | 19030.7 | + | 23121.0i | 0.188192 | + | 0.228640i | ||||
\(319\) | 92524.6i | 0.909234i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29849.9 | −0.289690 | ||||||||
\(322\) | −32329.4 | + | 26610.2i | −0.311807 | + | 0.256647i | ||||
\(323\) | 29262.1i | 0.280479i | ||||||||
\(324\) | 2242.55 | − | 11446.4i | 0.0213625 | − | 0.109038i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5704.19 | − | 6930.18i | −0.0536733 | − | 0.0652092i | ||||
\(327\) | − | 24473.0i | − | 0.228872i | ||||||
\(328\) | −96670.1 | − | 178991.i | −0.898555 | − | 1.66373i | ||||
\(329\) | −91765.9 | −0.847792 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 28680.3i | − | 0.261775i | −0.991397 | − | 0.130887i | \(-0.958217\pi\) | ||
0.991397 | − | 0.130887i | \(-0.0417826\pi\) | |||||||
\(332\) | −83946.3 | − | 16446.5i | −0.761597 | − | 0.149210i | ||||
\(333\) | 31410.7 | 0.283263 | ||||||||
\(334\) | −61038.3 | − | 74157.2i | −0.547154 | − | 0.664753i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 106644. | + | 43454.9i | 0.944624 | + | 0.384911i | ||||
\(337\) | −99523.5 | −0.876326 | −0.438163 | − | 0.898895i | \(-0.644371\pi\) | ||||
−0.438163 | + | 0.898895i | \(0.644371\pi\) | |||||||
\(338\) | 185398. | − | 152600.i | 1.62282 | − | 1.33574i | ||||
\(339\) | 1255.16i | 0.0109219i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 54655.7 | 0.470031 | ||||||||
\(342\) | −34133.1 | − | 41469.3i | −0.291826 | − | 0.354547i | ||||
\(343\) | 233093.i | 1.98126i | ||||||||
\(344\) | −65671.9 | + | 35468.3i | −0.554961 | + | 0.299725i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 119863. | − | 98658.1i | 1.00122 | − | 0.824102i | ||||
\(347\) | 47129.6i | 0.391413i | 0.980663 | + | 0.195706i | \(0.0626999\pi\) | ||||
−0.980663 | + | 0.195706i | \(0.937300\pi\) | |||||||
\(348\) | 77269.7 | + | 15138.5i | 0.638044 | + | 0.125004i | ||||
\(349\) | 171932. | 1.41158 | 0.705792 | − | 0.708419i | \(-0.250591\pi\) | ||||
0.705792 | + | 0.708419i | \(0.250591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 41758.2i | 0.338944i | ||||||||
\(352\) | 29729.0 | + | 95519.9i | 0.239936 | + | 0.770919i | ||||
\(353\) | −210420. | −1.68864 | −0.844321 | − | 0.535837i | \(-0.819996\pi\) | ||||
−0.844321 | + | 0.535837i | \(0.819996\pi\) | |||||||
\(354\) | −32171.7 | + | 26480.3i | −0.256725 | + | 0.211308i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 27716.0 | − | 141468.i | 0.218690 | − | 1.11624i | ||||
\(357\) | −26468.4 | −0.207678 | ||||||||
\(358\) | −142708. | − | 173380.i | −1.11348 | − | 1.35280i | ||||
\(359\) | 123067.i | 0.954888i | 0.878662 | + | 0.477444i | \(0.158437\pi\) | ||||
−0.878662 | + | 0.477444i | \(0.841563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −117001. | −0.897794 | ||||||||
\(362\) | 61639.6 | − | 50735.2i | 0.470374 | − | 0.387162i | ||||
\(363\) | − | 26483.5i | − | 0.200984i | ||||||
\(364\) | −404585. | − | 79265.2i | −3.05356 | − | 0.598246i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −46528.7 | − | 56529.0i | −0.347343 | − | 0.421997i | ||||
\(367\) | − | 113887.i | − | 0.845553i | −0.906234 | − | 0.422777i | \(-0.861056\pi\) | ||
0.906234 | − | 0.422777i | \(-0.138944\pi\) | |||||||
\(368\) | −11681.0 | + | 28666.8i | −0.0862551 | + | 0.211682i | ||||
\(369\) | −85821.2 | −0.630292 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 124728.i | 0.906187i | ||||||||
\(372\) | 8942.52 | − | 45644.4i | 0.0646211 | − | 0.329838i | ||||
\(373\) | 69712.3 | 0.501062 | 0.250531 | − | 0.968109i | \(-0.419395\pi\) | ||||
0.250531 | + | 0.968109i | \(0.419395\pi\) | |||||||
\(374\) | −14612.5 | − | 17753.2i | −0.104468 | − | 0.126921i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −59691.2 | + | 32238.2i | −0.422216 | + | 0.228032i | ||||
\(377\) | −281892. | −1.98335 | ||||||||
\(378\) | 37510.1 | − | 30874.3i | 0.262521 | − | 0.216080i | ||||
\(379\) | − | 35367.5i | − | 0.246222i | −0.992393 | − | 0.123111i | \(-0.960713\pi\) | ||
0.992393 | − | 0.123111i | \(-0.0392871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35763.8 | −0.246373 | ||||||||
\(382\) | −145422. | − | 176677.i | −0.996559 | − | 1.21075i | ||||
\(383\) | 256391.i | 1.74785i | 0.486058 | + | 0.873926i | \(0.338434\pi\) | ||||
−0.486058 | + | 0.873926i | \(0.661566\pi\) | |||||||
\(384\) | 84635.3 | − | 9198.93i | 0.573970 | − | 0.0623843i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14215.9 | − | 11701.1i | 0.0954116 | − | 0.0785327i | ||||
\(387\) | 31487.8i | 0.210242i | ||||||||
\(388\) | 30140.8 | − | 153844.i | 0.200212 | − | 1.02192i | ||||
\(389\) | 55802.7 | 0.368770 | 0.184385 | − | 0.982854i | \(-0.440971\pi\) | ||||
0.184385 | + | 0.982854i | \(0.440971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7114.91i | − | 0.0465389i | ||||||
\(392\) | 154910. | + | 286826.i | 1.00811 | + | 1.86658i | ||||
\(393\) | −6483.87 | −0.0419806 | ||||||||
\(394\) | −92891.2 | + | 76458.2i | −0.598387 | + | 0.492529i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 41416.7 | + | 8114.25i | 0.264110 | + | 0.0517438i | ||||
\(397\) | 264607. | 1.67888 | 0.839442 | − | 0.543449i | \(-0.182882\pi\) | ||||
0.839442 | + | 0.543449i | \(0.182882\pi\) | |||||||
\(398\) | 107385. | + | 130465.i | 0.677919 | + | 0.823623i | ||||
\(399\) | − | 223710.i | − | 1.40520i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −232397. | −1.44525 | −0.722623 | − | 0.691243i | \(-0.757063\pi\) | ||||
−0.722623 | + | 0.691243i | \(0.757063\pi\) | |||||||
\(402\) | 99009.0 | − | 81493.7i | 0.612664 | − | 0.504280i | ||||
\(403\) | 166518.i | 1.02530i | ||||||||
\(404\) | 16626.5 | − | 84865.1i | 0.101868 | − | 0.519956i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 208419. | + | 253215.i | 1.26441 | + | 1.53616i | ||||
\(407\) | 113654.i | 0.686114i | ||||||||
\(408\) | −17217.0 | + | 9298.60i | −0.103428 | + | 0.0558596i | ||||
\(409\) | −72108.2 | −0.431060 | −0.215530 | − | 0.976497i | \(-0.569148\pi\) | ||||
−0.215530 | + | 0.976497i | \(0.569148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8898.54i | 0.0526787i | ||||||||
\(412\) | −130240. | − | 25516.3i | −0.767275 | − | 0.150322i | ||||
\(413\) | −173553. | −1.01750 | ||||||||
\(414\) | 8299.26 | + | 10083.0i | 0.0484216 | + | 0.0588287i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −291018. | + | 90574.6i | −1.68164 | + | 0.523383i | ||||
\(417\) | −35066.6 | −0.201661 | ||||||||
\(418\) | 150049. | − | 123504.i | 0.858778 | − | 0.706855i | ||||
\(419\) | 36120.5i | 0.205743i | 0.994695 | + | 0.102872i | \(0.0328031\pi\) | ||||
−0.994695 | + | 0.102872i | \(0.967197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 218504. | 1.23281 | 0.616405 | − | 0.787429i | \(-0.288589\pi\) | ||||
0.616405 | + | 0.787429i | \(0.288589\pi\) | |||||||
\(422\) | −7864.53 | − | 9554.84i | −0.0441619 | − | 0.0536535i | ||||
\(423\) | 28620.2i | 0.159953i | ||||||||
\(424\) | 43818.3 | + | 81132.4i | 0.243738 | + | 0.451297i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14156.0 | − | 11651.7i | 0.0780050 | − | 0.0642054i | ||||
\(427\) | − | 304951.i | − | 1.67253i | ||||||
\(428\) | −90199.2 | − | 17671.6i | −0.492397 | − | 0.0964691i | ||||
\(429\) | −151095. | −0.820984 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 84359.7i | 0.454130i | 0.973880 | + | 0.227065i | \(0.0729130\pi\) | ||||
−0.973880 | + | 0.227065i | \(0.927087\pi\) | |||||||
\(432\) | 13552.9 | − | 33260.6i | 0.0726212 | − | 0.178222i | ||||
\(433\) | 80951.5 | 0.431767 | 0.215883 | − | 0.976419i | \(-0.430737\pi\) | ||||
0.215883 | + | 0.976419i | \(0.430737\pi\) | |||||||
\(434\) | 149578. | − | 123116.i | 0.794122 | − | 0.653637i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14488.4 | − | 73951.5i | 0.0762161 | − | 0.389022i | ||||
\(437\) | 60135.0 | 0.314894 | ||||||||
\(438\) | 21923.3 | + | 26635.2i | 0.114277 | + | 0.138838i | ||||
\(439\) | − | 31983.1i | − | 0.165955i | −0.996551 | − | 0.0829777i | \(-0.973557\pi\) | ||
0.996551 | − | 0.0829777i | \(-0.0264430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 137525. | 0.707138 | ||||||||
\(442\) | 54088.1 | − | 44519.6i | 0.276858 | − | 0.227880i | ||||
\(443\) | − | 376981.i | − | 1.92093i | −0.278394 | − | 0.960467i | \(-0.589802\pi\) | ||
0.278394 | − | 0.960467i | \(-0.410198\pi\) | |||||||
\(444\) | 94915.6 | + | 18595.6i | 0.481473 | + | 0.0943288i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −109459. | − | 132984.i | −0.550275 | − | 0.668545i | ||||
\(447\) | 198024.i | 0.991064i | ||||||||
\(448\) | 296527. | + | 194445.i | 1.47743 | + | 0.968815i | ||||
\(449\) | −105390. | −0.522767 | −0.261384 | − | 0.965235i | \(-0.584179\pi\) | ||||
−0.261384 | + | 0.965235i | \(0.584179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 310529.i | − | 1.52668i | ||||||
\(452\) | −743.070 | + | 3792.77i | −0.00363708 | + | 0.0185644i | ||||
\(453\) | 22779.9 | 0.111008 | ||||||||
\(454\) | 110288. | + | 133992.i | 0.535076 | + | 0.650080i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −78591.4 | − | 145517.i | −0.377960 | − | 0.699817i | ||||
\(457\) | 260309. | 1.24640 | 0.623200 | − | 0.782063i | \(-0.285832\pi\) | ||||
0.623200 | + | 0.782063i | \(0.285832\pi\) | |||||||
\(458\) | 173063. | − | 142447.i | 0.825037 | − | 0.679083i | ||||
\(459\) | 8255.05i | 0.0391827i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 112820. | 0.530865 | 0.265433 | − | 0.964129i | \(-0.414485\pi\) | ||||
0.265433 | + | 0.964129i | \(0.414485\pi\) | |||||||
\(462\) | 111713. | + | 135724.i | 0.523384 | + | 0.635875i | ||||
\(463\) | − | 188351.i | − | 0.878628i | −0.898334 | − | 0.439314i | \(-0.855222\pi\) | ||
0.898334 | − | 0.439314i | \(-0.144778\pi\) | |||||||
\(464\) | 224528. | + | 91489.5i | 1.04288 | + | 0.424948i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 128595. | − | 105846.i | 0.592177 | − | 0.487417i | ||||
\(467\) | 373875.i | 1.71432i | 0.515048 | + | 0.857161i | \(0.327774\pi\) | ||||
−0.515048 | + | 0.857161i | \(0.672226\pi\) | |||||||
\(468\) | −24721.5 | + | 126183.i | −0.112871 | + | 0.576116i | ||||
\(469\) | 534114. | 2.42822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 98259.5i | 0.442927i | ||||||||
\(472\) | −112892. | + | 60971.0i | −0.506732 | + | 0.273677i | ||||
\(473\) | −113933. | −0.509245 | ||||||||
\(474\) | 116771. | − | 96113.7i | 0.519732 | − | 0.427788i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −79981.0 | − | 15669.7i | −0.352999 | − | 0.0691586i | ||||
\(477\) | 38900.7 | 0.170970 | ||||||||
\(478\) | −180556. | − | 219363.i | −0.790235 | − | 0.960079i | ||||
\(479\) | − | 169326.i | − | 0.737993i | −0.929431 | − | 0.368997i | \(-0.879701\pi\) | ||
0.929431 | − | 0.368997i | \(-0.120299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −346267. | −1.49665 | ||||||||
\(482\) | −181275. | + | 149207.i | −0.780270 | + | 0.642235i | ||||
\(483\) | 54393.8i | 0.233160i | ||||||||
\(484\) | 15678.6 | − | 80026.6i | 0.0669294 | − | 0.341620i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9629.19 | − | 11698.8i | −0.0407678 | − | 0.0495299i | ||||
\(487\) | − | 27221.0i | − | 0.114774i | −0.998352 | − | 0.0573872i | \(-0.981723\pi\) | ||
0.998352 | − | 0.0573872i | \(-0.0182770\pi\) | |||||||
\(488\) | −107132. | − | 198362.i | −0.449863 | − | 0.832952i | ||||
\(489\) | −11659.9 | −0.0487616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 437686.i | 1.81552i | 0.419495 | + | 0.907758i | \(0.362207\pi\) | ||||
−0.419495 | + | 0.907758i | \(0.637793\pi\) | |||||||
\(492\) | −259331. | − | 50807.4i | −1.07133 | − | 0.209892i | ||||
\(493\) | −55726.3 | −0.229280 | ||||||||
\(494\) | 376278. | + | 457151.i | 1.54189 | + | 1.87329i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 54044.2 | − | 132632.i | 0.219678 | − | 0.539119i | ||||
\(497\) | 76366.1 | 0.309163 | ||||||||
\(498\) | −85797.2 | + | 70619.1i | −0.345951 | + | 0.284750i | ||||
\(499\) | 347647.i | 1.39617i | 0.716016 | + | 0.698084i | \(0.245964\pi\) | ||||
−0.716016 | + | 0.698084i | \(0.754036\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −124768. | −0.497083 | ||||||||
\(502\) | 102283. | + | 124266.i | 0.405878 | + | 0.493112i | ||||
\(503\) | − | 262758.i | − | 1.03853i | −0.854612 | − | 0.519267i | \(-0.826205\pi\) | ||
0.854612 | − | 0.519267i | \(-0.173795\pi\) | |||||||
\(504\) | 131624. | − | 71088.1i | 0.518174 | − | 0.279857i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −36483.6 | + | 30029.4i | −0.142494 | + | 0.117286i | ||||
\(507\) | − | 311929.i | − | 1.21350i | ||||||
\(508\) | −108069. | − | 21172.7i | −0.418769 | − | 0.0820442i | ||||
\(509\) | 192747. | 0.743963 | 0.371981 | − | 0.928240i | \(-0.378679\pi\) | ||||
0.371981 | + | 0.928240i | \(0.378679\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 143686.i | 0.550267i | ||||||||
\(512\) | 261193. | + | 22308.4i | 0.996372 | + | 0.0850998i | ||||
\(513\) | −69771.4 | −0.265120 | ||||||||
\(514\) | 263451. | − | 216845.i | 0.997182 | − | 0.820774i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −18641.2 | + | 95148.4i | −0.0700124 | + | 0.357357i | ||||
\(517\) | −103557. | −0.387435 | ||||||||
\(518\) | 256016. | + | 311041.i | 0.954129 | + | 1.15920i | ||||
\(519\) | − | 201667.i | − | 0.748686i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 377715. | 1.39152 | 0.695760 | − | 0.718275i | \(-0.255068\pi\) | ||||
0.695760 | + | 0.718275i | \(0.255068\pi\) | |||||||
\(522\) | 78973.4 | − | 65002.5i | 0.289828 | − | 0.238555i | ||||
\(523\) | 234085.i | 0.855798i | 0.903827 | + | 0.427899i | \(0.140746\pi\) | ||||
−0.903827 | + | 0.427899i | \(0.859254\pi\) | |||||||
\(524\) | −19592.7 | − | 3838.54i | −0.0713561 | − | 0.0139799i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −221570. | − | 269192.i | −0.800830 | − | 0.972951i | ||||
\(527\) | 32918.4i | 0.118527i | ||||||||
\(528\) | 120347. | + | 49038.6i | 0.431687 | + | 0.175902i | ||||
\(529\) | 265220. | 0.947751 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54128.4i | 0.191971i | ||||||||
\(532\) | 132439. | − | 675997.i | 0.467944 | − | 2.38848i | ||||
\(533\) | 946079. | 3.33022 | ||||||||
\(534\) | −119008. | − | 144587.i | −0.417345 | − | 0.507044i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 347426. | − | 187639.i | 1.20930 | − | 0.653121i | ||||
\(537\) | −291709. | −1.01158 | ||||||||
\(538\) | −388758. | + | 319984.i | −1.34312 | + | 1.10551i | ||||
\(539\) | 497609.i | 1.71282i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27230.3 | −0.0930374 | −0.0465187 | − | 0.998917i | \(-0.514813\pi\) | ||||
−0.0465187 | + | 0.998917i | \(0.514813\pi\) | |||||||
\(542\) | 239671. | + | 291183.i | 0.815863 | + | 0.991215i | ||||
\(543\) | − | 103708.i | − | 0.351732i | ||||||
\(544\) | −57530.4 | + | 17905.4i | −0.194401 | + | 0.0605043i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −413505. | + | 340354.i | −1.38706 | + | 1.14168i | ||||
\(547\) | − | 219088.i | − | 0.732225i | −0.930571 | − | 0.366112i | \(-0.880689\pi\) | ||
0.930571 | − | 0.366112i | \(-0.119311\pi\) | |||||||
\(548\) | −5268.06 | + | 26889.2i | −0.0175424 | + | 0.0895400i | ||||
\(549\) | −95109.2 | −0.315557 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 470997.i | − | 1.55137i | ||||||
\(552\) | 19109.0 | + | 35381.7i | 0.0627135 | + | 0.116118i | ||||
\(553\) | 629934. | 2.05989 | ||||||||
\(554\) | −203210. | + | 167261.i | −0.662104 | + | 0.544973i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −105963. | − | 20759.9i | −0.342771 | − | 0.0671547i | ||||
\(557\) | 507368. | 1.63536 | 0.817678 | − | 0.575675i | \(-0.195261\pi\) | ||||
0.817678 | + | 0.575675i | \(0.195261\pi\) | |||||||
\(558\) | −38398.0 | − | 46650.8i | −0.123322 | − | 0.149827i | ||||
\(559\) | − | 347116.i | − | 1.11084i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29869.4 | −0.0949077 | ||||||||
\(562\) | 49790.9 | − | 40982.6i | 0.157644 | − | 0.129756i | ||||
\(563\) | 165410.i | 0.521850i | 0.965359 | + | 0.260925i | \(0.0840276\pi\) | ||||
−0.965359 | + | 0.260925i | \(0.915972\pi\) | |||||||
\(564\) | −16943.6 | + | 86483.3i | −0.0532656 | + | 0.271878i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 326554. | + | 396740.i | 1.01935 | + | 1.23844i | ||||
\(567\) | − | 63110.2i | − | 0.196306i | ||||||
\(568\) | 49674.1 | − | 26828.1i | 0.153969 | − | 0.0831561i | ||||
\(569\) | 59830.4 | 0.184798 | 0.0923990 | − | 0.995722i | \(-0.470546\pi\) | ||||
0.0923990 | + | 0.995722i | \(0.470546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 149969.i | − | 0.459969i | −0.973194 | − | 0.229984i | \(-0.926132\pi\) | ||
0.973194 | − | 0.229984i | \(-0.0738675\pi\) | |||||||
\(572\) | −456571. | − | 89450.2i | −1.39546 | − | 0.273394i | ||||
\(573\) | −297256. | −0.905361 | ||||||||
\(574\) | −699492. | − | 849833.i | −2.12304 | − | 2.57935i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 60644.1 | − | 92481.8i | 0.182786 | − | 0.278748i | ||||
\(577\) | 195679. | 0.587750 | 0.293875 | − | 0.955844i | \(-0.405055\pi\) | ||||
0.293875 | + | 0.955844i | \(0.405055\pi\) | |||||||
\(578\) | −247252. | + | 203512.i | −0.740090 | + | 0.609163i | ||||
\(579\) | − | 23918.1i | − | 0.0713460i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −462841. | −1.37113 | ||||||||
\(582\) | −129420. | − | 157236.i | −0.382082 | − | 0.464202i | ||||
\(583\) | 140755.i | 0.414121i | ||||||||
\(584\) | 50478.4 | + | 93464.0i | 0.148006 | + | 0.274043i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −499078. | + | 410788.i | −1.45336 | + | 1.19625i | ||||
\(587\) | 273284.i | 0.793119i | 0.918009 | + | 0.396559i | \(0.129796\pi\) | ||||
−0.918009 | + | 0.396559i | \(0.870204\pi\) | |||||||
\(588\) | 415567. | + | 81416.7i | 1.20195 | + | 0.235483i | ||||
\(589\) | −278225. | −0.801983 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 156288.i | 0.447456i | ||||||||
\(592\) | 275803. | + | 112383.i | 0.786964 | + | 0.320668i | ||||
\(593\) | −151488. | −0.430794 | −0.215397 | − | 0.976527i | \(-0.569105\pi\) | ||||
−0.215397 | + | 0.976527i | \(0.569105\pi\) | |||||||
\(594\) | 42329.9 | − | 34841.5i | 0.119971 | − | 0.0987470i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −117233. | + | 598379.i | −0.330032 | + | 1.68455i | ||||
\(597\) | 219506. | 0.615881 | ||||||||
\(598\) | −91489.7 | − | 111153.i | −0.255841 | − | 0.310828i | ||||
\(599\) | − | 371626.i | − | 1.03575i | −0.855458 | − | 0.517873i | \(-0.826724\pi\) | ||
0.855458 | − | 0.517873i | \(-0.173276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 368841. | 1.02115 | 0.510575 | − | 0.859833i | \(-0.329433\pi\) | ||||
0.510575 | + | 0.859833i | \(0.329433\pi\) | |||||||
\(602\) | −311804. | + | 256644.i | −0.860376 | + | 0.708170i | ||||
\(603\) | − | 166581.i | − | 0.458132i | ||||||
\(604\) | 68835.2 | + | 13486.0i | 0.188685 | + | 0.0369666i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −71392.1 | − | 86736.3i | −0.194404 | − | 0.236187i | ||||
\(607\) | 511656.i | 1.38868i | 0.719649 | + | 0.694338i | \(0.244303\pi\) | ||||
−0.719649 | + | 0.694338i | \(0.755697\pi\) | |||||||
\(608\) | −151336. | − | 486245.i | −0.409387 | − | 1.31537i | ||||
\(609\) | 426030. | 1.14870 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 315505.i | − | 0.845130i | ||||||
\(612\) | −4887.11 | + | 24944.7i | −0.0130482 | + | 0.0666003i | ||||
\(613\) | 384682. | 1.02372 | 0.511859 | − | 0.859069i | \(-0.328957\pi\) | ||||
0.511859 | + | 0.859069i | \(0.328957\pi\) | |||||||
\(614\) | 100918. | + | 122609.i | 0.267691 | + | 0.325225i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 257220. | + | 476259.i | 0.677864 | + | 1.25511i | ||||
\(617\) | −326231. | −0.856949 | −0.428475 | − | 0.903554i | \(-0.640949\pi\) | ||||
−0.428475 | + | 0.903554i | \(0.640949\pi\) | |||||||
\(618\) | −133112. | + | 109564.i | −0.348530 | + | 0.286873i | ||||
\(619\) | 752595.i | 1.96417i | 0.188428 | + | 0.982087i | \(0.439661\pi\) | ||||
−0.188428 | + | 0.982087i | \(0.560339\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16964.5 | 0.0439904 | ||||||||
\(622\) | 42225.1 | + | 51300.5i | 0.109141 | + | 0.132599i | ||||
\(623\) | − | 779987.i | − | 2.00961i | ||||||
\(624\) | −149404. | + | 366659.i | −0.383702 | + | 0.941658i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 106099. | − | 87329.5i | 0.270746 | − | 0.222850i | ||||
\(627\) | − | 252455.i | − | 0.642169i | ||||||
\(628\) | −58171.0 | + | 296916.i | −0.147498 | + | 0.752860i | ||||
\(629\) | −68452.4 | −0.173016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 514641.i | − | 1.29255i | −0.763106 | − | 0.646273i | \(-0.776327\pi\) | ||
0.763106 | − | 0.646273i | \(-0.223673\pi\) | |||||||
\(632\) | 409755. | − | 221302.i | 1.02586 | − | 0.554053i | ||||
\(633\) | −16075.9 | −0.0401206 | ||||||||
\(634\) | 158585. | − | 130530.i | 0.394534 | − | 0.324738i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 117548. | + | 23029.8i | 0.290605 | + | 0.0569345i | ||||
\(637\) | −1.51605e6 | −3.73625 | ||||||||
\(638\) | 235200. | + | 285751.i | 0.577825 | + | 0.702016i | ||||
\(639\) | − | 23817.3i | − | 0.0583299i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 417472. | 1.01604 | 0.508021 | − | 0.861345i | \(-0.330377\pi\) | ||||
0.508021 | + | 0.861345i | \(0.330377\pi\) | |||||||
\(642\) | −92188.0 | + | 75879.4i | −0.223668 | + | 0.184100i | ||||
\(643\) | − | 347739.i | − | 0.841070i | −0.907276 | − | 0.420535i | \(-0.861842\pi\) | ||
0.907276 | − | 0.420535i | \(-0.138158\pi\) | |||||||
\(644\) | −32201.9 | + | 164365.i | −0.0776443 | + | 0.396311i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 74385.1 | + | 90372.6i | 0.178247 | + | 0.216557i | ||||
\(647\) | 451372.i | 1.07827i | 0.842221 | + | 0.539133i | \(0.181248\pi\) | ||||
−0.842221 | + | 0.539133i | \(0.818752\pi\) | |||||||
\(648\) | −22171.2 | − | 41051.4i | −0.0528006 | − | 0.0977639i | ||||
\(649\) | −195854. | −0.464989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 251662.i | − | 0.593821i | ||||||
\(652\) | −35233.4 | − | 6902.83i | −0.0828818 | − | 0.0162380i | ||||
\(653\) | −378215. | −0.886977 | −0.443489 | − | 0.896280i | \(-0.646259\pi\) | ||||
−0.443489 | + | 0.896280i | \(0.646259\pi\) | |||||||
\(654\) | −62211.1 | − | 75582.1i | −0.145450 | − | 0.176711i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −753555. | − | 307055.i | −1.75108 | − | 0.713523i | ||||
\(657\) | 44813.4 | 0.103819 | ||||||||
\(658\) | −283408. | + | 233271.i | −0.654576 | + | 0.538778i | ||||
\(659\) | − | 625044.i | − | 1.43926i | −0.694357 | − | 0.719631i | \(-0.744311\pi\) | ||
0.694357 | − | 0.719631i | \(-0.255689\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 576980. | 1.32056 | 0.660280 | − | 0.751020i | \(-0.270438\pi\) | ||||
0.660280 | + | 0.751020i | \(0.270438\pi\) | |||||||
\(662\) | −72906.1 | − | 88575.7i | −0.166360 | − | 0.202115i | ||||
\(663\) | − | 91002.4i | − | 0.207026i | ||||||
\(664\) | −301066. | + | 162601.i | −0.682849 | + | 0.368796i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 97008.4 | − | 79847.0i | 0.218706 | − | 0.180016i | ||||
\(667\) | 114520.i | 0.257413i | ||||||||
\(668\) | −377019. | − | 73864.6i | −0.844910 | − | 0.165532i | ||||
\(669\) | −223744. | −0.499918 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 344136.i | − | 0.764336i | ||||||
\(672\) | 439822. | − | 136887.i | 0.973953 | − | 0.303127i | ||||
\(673\) | −411758. | −0.909101 | −0.454550 | − | 0.890721i | \(-0.650200\pi\) | ||||
−0.454550 | + | 0.890721i | \(0.650200\pi\) | |||||||
\(674\) | −307367. | + | 252991.i | −0.676607 | + | 0.556911i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 184666. | − | 942573.i | 0.404105 | − | 2.06263i | ||||
\(677\) | −628737. | −1.37180 | −0.685902 | − | 0.727694i | \(-0.740592\pi\) | ||||
−0.685902 | + | 0.727694i | \(0.740592\pi\) | |||||||
\(678\) | 3190.64 | + | 3876.40i | 0.00694094 | + | 0.00843275i | ||||
\(679\) | − | 848227.i | − | 1.83981i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 225439. | 0.486110 | ||||||||
\(682\) | 168797. | − | 138936.i | 0.362909 | − | 0.298708i | ||||
\(683\) | 531547.i | 1.13946i | 0.821831 | + | 0.569731i | \(0.192953\pi\) | ||||
−0.821831 | + | 0.569731i | \(0.807047\pi\) | |||||||
\(684\) | −210832. | − | 41305.7i | −0.450634 | − | 0.0882871i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 592530. | + | 719881.i | 1.25911 | + | 1.52972i | ||||
\(687\) | − | 291176.i | − | 0.616939i | ||||||
\(688\) | −112658. | + | 276479.i | −0.238005 | + | 0.584098i | ||||
\(689\) | −428835. | −0.903341 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 157186.i | 0.329198i | 0.986361 | + | 0.164599i | \(0.0526330\pi\) | ||||
−0.986361 | + | 0.164599i | \(0.947367\pi\) | |||||||
\(692\) | 119390. | − | 609388.i | 0.249319 | − | 1.27257i | ||||
\(693\) | 228353. | 0.475488 | ||||||||
\(694\) | 119805. | + | 145554.i | 0.248745 | + | 0.302208i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 277121. | − | 149668.i | 0.572072 | − | 0.308967i | ||||
\(697\) | 187027. | 0.384981 | ||||||||
\(698\) | 530993. | − | 437057.i | 1.08988 | − | 0.897071i | ||||
\(699\) | − | 216359.i | − | 0.442813i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −194246. | −0.395290 | −0.197645 | − | 0.980274i | \(-0.563329\pi\) | ||||
−0.197645 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(702\) | 106151. | + | 128965.i | 0.215401 | + | 0.261697i | ||||
\(703\) | − | 578557.i | − | 1.17067i | ||||||
\(704\) | 334629. | + | 219430.i | 0.675178 | + | 0.442742i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −649857. | + | 534893.i | −1.30379 | + | 1.07314i | ||||
\(707\) | − | 467907.i | − | 0.936097i | ||||||
\(708\) | −32044.8 | + | 163563.i | −0.0639279 | + | 0.326301i | ||||
\(709\) | −455572. | −0.906285 | −0.453142 | − | 0.891438i | \(-0.649697\pi\) | ||||
−0.453142 | + | 0.891438i | \(0.649697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 196466.i | − | 0.388640i | ||||||
\(712\) | −274017. | − | 507360.i | −0.540527 | − | 1.00082i | ||||
\(713\) | 67648.7 | 0.133070 | ||||||||
\(714\) | −81744.5 | + | 67283.4i | −0.160348 | + | 0.131981i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −881474. | − | 172696.i | −1.71943 | − | 0.336865i | ||||
\(717\) | −369074. | −0.717919 | ||||||||
\(718\) | 312839. | + | 380077.i | 0.606838 | + | 0.737264i | ||||
\(719\) | 561316.i | 1.08580i | 0.839797 | + | 0.542900i | \(0.182674\pi\) | ||||
−0.839797 | + | 0.542900i | \(0.817326\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −718086. | −1.38136 | ||||||||
\(722\) | −361345. | + | 297421.i | −0.693182 | + | 0.570554i | ||||
\(723\) | 304993.i | 0.583463i | ||||||||
\(724\) | 61396.4 | − | 313379.i | 0.117129 | − | 0.597851i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −67321.8 | − | 81791.1i | −0.127727 | − | 0.155179i | ||||
\(727\) | − | 155857.i | − | 0.294889i | −0.989070 | − | 0.147444i | \(-0.952895\pi\) | ||
0.989070 | − | 0.147444i | \(-0.0471047\pi\) | |||||||
\(728\) | −1.45101e6 | + | 783664.i | −2.73783 | + | 1.47866i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 68620.3i | − | 0.128416i | ||||||
\(732\) | −287397. | − | 56306.0i | −0.536364 | − | 0.105083i | ||||
\(733\) | −744418. | −1.38551 | −0.692754 | − | 0.721174i | \(-0.743603\pi\) | ||||
−0.692754 | + | 0.721174i | \(0.743603\pi\) | |||||||
\(734\) | −289503. | − | 351726.i | −0.537355 | − | 0.652848i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36796.4 | + | 118227.i | 0.0679281 | + | 0.218254i | ||||
\(737\) | 602744. | 1.10968 | ||||||||
\(738\) | −265049. | + | 218160.i | −0.486645 | + | 0.400555i | ||||
\(739\) | 200689.i | 0.367480i | 0.982975 | + | 0.183740i | \(0.0588205\pi\) | ||||
−0.982975 | + | 0.183740i | \(0.941180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 769149. | 1.40079 | ||||||||
\(742\) | 317063. | + | 385209.i | 0.575888 | + | 0.699662i | ||||
\(743\) | − | 20434.2i | − | 0.0370152i | −0.999829 | − | 0.0185076i | \(-0.994109\pi\) | ||
0.999829 | − | 0.0185076i | \(-0.00589149\pi\) | |||||||
\(744\) | −88411.3 | − | 163699.i | −0.159721 | − | 0.295734i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 215298. | − | 177210.i | 0.386868 | − | 0.318428i | ||||
\(747\) | 144352.i | 0.258692i | ||||||||
\(748\) | −90258.1 | − | 17683.1i | −0.161318 | − | 0.0316050i | ||||
\(749\) | −497317. | −0.886482 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 60228.7i | 0.106788i | 0.998574 | + | 0.0533941i | \(0.0170040\pi\) | ||||
−0.998574 | + | 0.0533941i | \(0.982996\pi\) | |||||||
\(752\) | −102399. | + | 251301.i | −0.181075 | + | 0.444383i | ||||
\(753\) | 209076. | 0.368735 | ||||||||
\(754\) | −870590. | + | 716578.i | −1.53134 | + | 1.26044i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 37362.1 | − | 190703.i | 0.0653714 | − | 0.333668i | ||||
\(757\) | 554160. | 0.967037 | 0.483519 | − | 0.875334i | \(-0.339359\pi\) | ||||
0.483519 | + | 0.875334i | \(0.339359\pi\) | |||||||
\(758\) | −89905.2 | − | 109228.i | −0.156475 | − | 0.190107i | ||||
\(759\) | 61383.0i | 0.106553i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 62269.4 | 0.107524 | 0.0537620 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537620 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(762\) | −110452. | + | 90912.5i | −0.190224 | + | 0.156572i | ||||
\(763\) | − | 407735.i | − | 0.700372i | ||||||
\(764\) | −898236. | − | 175980.i | −1.53888 | − | 0.301493i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 651752. | + | 791833.i | 1.11077 | + | 1.34951i | ||||
\(767\) | − | 596703.i | − | 1.01430i | ||||||
\(768\) | 238002. | − | 243555.i | 0.403514 | − | 0.412928i | ||||
\(769\) | 547774. | 0.926295 | 0.463147 | − | 0.886281i | \(-0.346720\pi\) | ||||
0.463147 | + | 0.886281i | \(0.346720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 443253.i | − | 0.745663i | ||||||
\(772\) | 14159.9 | − | 72274.6i | 0.0237588 | − | 0.121269i | ||||
\(773\) | 23192.7 | 0.0388144 | 0.0194072 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194072 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(774\) | 80042.8 | + | 97246.3i | 0.133610 | + | 0.162327i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −297990. | − | 551748.i | −0.494855 | − | 0.916257i | ||||
\(777\) | 523321. | 0.866814 | ||||||||
\(778\) | 172340. | − | 141852.i | 0.284726 | − | 0.234356i | ||||
\(779\) | 1.58075e6i | 2.60488i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 86178.7 | 0.141286 | ||||||||
\(782\) | −18086.3 | − | 21973.6i | −0.0295758 | − | 0.0359325i | ||||
\(783\) | − | 132872.i | − | 0.216725i | ||||||
\(784\) | 1.20754e6 | + | 492043.i | 1.96458 | + | 0.800517i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −20024.7 | + | 16482.2i | −0.0324131 | + | 0.0266790i | ||||
\(787\) | 642178.i | 1.03683i | 0.855130 | + | 0.518413i | \(0.173477\pi\) | ||||
−0.855130 | + | 0.518413i | \(0.826523\pi\) | |||||||
\(788\) | −92524.7 | + | 472264.i | −0.149007 | + | 0.760558i | ||||
\(789\) | −452912. | −0.727544 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20911.6i | 0.0334222i | ||||||||
\(792\) | 148537. | − | 80222.5i | 0.236802 | − | 0.127893i | ||||
\(793\) | 1.04847e6 | 1.66728 | ||||||||
\(794\) | 817208. | − | 672639.i | 1.29626 | − | 1.06694i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 663292. | + | 129950.i | 1.04684 | + | 0.205093i | ||||
\(797\) | 385649. | 0.607122 | 0.303561 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303561 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(798\) | −568677. | − | 690902.i | −0.893017 | − | 1.08495i | ||||
\(799\) | − | 62371.1i | − | 0.0976990i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −243265. | −0.379153 | ||||||||
\(802\) | −717730. | + | 590759.i | −1.11587 | + | 0.918463i | ||||
\(803\) | 162149.i | 0.251468i | ||||||||
\(804\) | 98618.4 | − | 503367.i | 0.152562 | − | 0.778705i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 423293. | + | 514271.i | 0.651585 | + | 0.791629i | ||||
\(807\) | 654079.i | 1.00435i | ||||||||
\(808\) | −164380. | − | 304361.i | −0.251783 | − | 0.466193i | ||||
\(809\) | 404473. | 0.618006 | 0.309003 | − | 0.951061i | \(-0.400005\pi\) | ||||
0.309003 | + | 0.951061i | \(0.400005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 740872.i | 1.12642i | 0.826313 | + | 0.563212i | \(0.190434\pi\) | ||||
−0.826313 | + | 0.563212i | \(0.809566\pi\) | |||||||
\(812\) | 1.28736e6 | + | 252216.i | 1.95248 | + | 0.382525i | ||||
\(813\) | 489911. | 0.741202 | ||||||||
\(814\) | 288912. | + | 351007.i | 0.436030 | + | 0.529746i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29535.3 | + | 72483.7i | −0.0443569 | + | 0.108858i | ||||
\(817\) | 579976. | 0.868893 | ||||||||
\(818\) | −222698. | + | 183301.i | −0.332820 | + | 0.273942i | ||||
\(819\) | 695716.i | 1.03720i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 326364. | 0.484190 | 0.242095 | − | 0.970253i | \(-0.422165\pi\) | ||||
0.242095 | + | 0.970253i | \(0.422165\pi\) | |||||||
\(822\) | 22620.3 | + | 27482.1i | 0.0334777 | + | 0.0406730i | ||||
\(823\) | 6015.58i | 0.00888132i | 0.999990 | + | 0.00444066i | \(0.00141351\pi\) | ||||
−0.999990 | + | 0.00444066i | \(0.998586\pi\) | |||||||
\(824\) | −467095. | + | 252270.i | −0.687940 | + | 0.371545i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −535999. | + | 441177.i | −0.785604 | + | 0.646626i | ||||
\(827\) | 489341.i | 0.715485i | 0.933820 | + | 0.357742i | \(0.116453\pi\) | ||||
−0.933820 | + | 0.357742i | \(0.883547\pi\) | |||||||
\(828\) | 51262.6 | + | 10043.2i | 0.0747721 | + | 0.0146492i | ||||
\(829\) | −92567.3 | −0.134694 | −0.0673470 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673470 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 341898.i | 0.495102i | ||||||||
\(832\) | −668531. | + | 1.01950e6i | −0.965773 | + | 1.47280i | ||||
\(833\) | −299704. | −0.431919 | ||||||||
\(834\) | −108299. | + | 89140.4i | −0.155702 | + | 0.128157i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 149457. | − | 762858.i | 0.213847 | − | 1.09152i | ||||
\(837\) | −78489.2 | −0.112036 | ||||||||
\(838\) | 91819.2 | + | 111554.i | 0.130751 | + | 0.158853i | ||||
\(839\) | − | 1.34655e6i | − | 1.91293i | −0.291847 | − | 0.956465i | \(-0.594270\pi\) | ||
0.291847 | − | 0.956465i | \(-0.405730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 189678. | 0.268179 | ||||||||
\(842\) | 674825. | − | 555444.i | 0.951846 | − | 0.783459i | ||||
\(843\) | − | 83772.5i | − | 0.117882i | ||||||
\(844\) | −48577.3 | − | 9517.14i | −0.0681944 | − | 0.0133605i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 72753.4 | + | 88390.2i | 0.101651 | + | 0.123499i | ||||
\(847\) | − | 441230.i | − | 0.615033i | ||||||
\(848\) | 341568. | + | 139181.i | 0.474992 | + | 0.193547i | ||||
\(849\) | 667509. | 0.926066 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 140673.i | 0.194245i | ||||||||
\(852\) | 14100.2 | − | 71970.1i | 0.0194243 | − | 0.0991454i | ||||
\(853\) | −1.23563e6 | −1.69820 | −0.849101 | − | 0.528230i | \(-0.822856\pi\) | ||||
−0.849101 | + | 0.528230i | \(0.822856\pi\) | |||||||
\(854\) | −775194. | − | 941806.i | −1.06291 | − | 1.29135i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −323491. | + | 174712.i | −0.441484 | + | 0.238438i | ||||
\(857\) | −496036. | −0.675385 | −0.337693 | − | 0.941256i | \(-0.609646\pi\) | ||||
−0.337693 | + | 0.941256i | \(0.609646\pi\) | |||||||
\(858\) | −466638. | + | 384087.i | −0.633878 | + | 0.521741i | ||||
\(859\) | − | 74255.5i | − | 0.100633i | −0.998733 | − | 0.0503167i | \(-0.983977\pi\) | ||
0.998733 | − | 0.0503167i | \(-0.0160231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.42983e6 | −1.92876 | ||||||||
\(862\) | 214445. | + | 260535.i | 0.288603 | + | 0.350632i | ||||
\(863\) | − | 28282.1i | − | 0.0379743i | −0.999820 | − | 0.0189872i | \(-0.993956\pi\) | ||
0.999820 | − | 0.0189872i | \(-0.00604417\pi\) | |||||||
\(864\) | −42692.9 | − | 137173.i | −0.0571910 | − | 0.183756i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 250009. | − | 205781.i | 0.333365 | − | 0.274391i | ||||
\(867\) | 415998.i | 0.553418i | ||||||||
\(868\) | 148988. | − | 760461.i | 0.197747 | − | 1.00934i | ||||
\(869\) | 710877. | 0.941358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.83636e6i | 2.42060i | ||||||||
\(872\) | −143241. | − | 265220.i | −0.188380 | − | 0.348798i | ||||
\(873\) | −264548. | −0.347117 | ||||||||
\(874\) | 185720. | − | 152865.i | 0.243128 | − | 0.200117i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 135415. | + | 26530.1i | 0.176465 | + | 0.0345725i | ||||
\(877\) | 345796. | 0.449594 | 0.224797 | − | 0.974406i | \(-0.427828\pi\) | ||||
0.224797 | + | 0.974406i | \(0.427828\pi\) | |||||||
\(878\) | −81301.9 | − | 98776.0i | −0.105466 | − | 0.128133i | ||||
\(879\) | 839692.i | 1.08678i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 756432. | 0.974581 | 0.487290 | − | 0.873240i | \(-0.337985\pi\) | ||||
0.487290 | + | 0.873240i | \(0.337985\pi\) | |||||||
\(882\) | 424729. | − | 349592.i | 0.545978 | − | 0.449391i | ||||
\(883\) | 1.37291e6i | 1.76084i | 0.474195 | + | 0.880420i | \(0.342739\pi\) | ||||
−0.474195 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(884\) | 53874.7 | − | 274987.i | 0.0689414 | − | 0.351890i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −958297. | − | 1.16426e6i | −1.22077 | − | 1.48314i | ||||
\(887\) | − | 240951.i | − | 0.306254i | −0.988207 | − | 0.153127i | \(-0.951066\pi\) | ||
0.988207 | − | 0.153127i | \(-0.0489344\pi\) | |||||||
\(888\) | 340406. | − | 183848.i | 0.431689 | − | 0.233148i | ||||
\(889\) | −595845. | −0.753928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 71219.4i | − | 0.0897104i | ||||||
\(892\) | −676099. | − | 132460.i | −0.849730 | − | 0.166477i | ||||
\(893\) | 527158. | 0.661056 | ||||||||
\(894\) | 503381. | + | 611572.i | 0.629828 | + | 0.765196i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.41007e6 | − | 153259.i | 1.75641 | − | 0.190902i | ||||
\(897\) | −187014. | −0.232428 | ||||||||
\(898\) | −325486. | + | 267905.i | −0.403626 | + | 0.332222i | ||||
\(899\) | − | 529847.i | − | 0.655588i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84775.0 | −0.104428 | ||||||||
\(902\) | −789372. | − | 959031.i | −0.970217 | − | 1.17874i | ||||
\(903\) | 524605.i | 0.643364i | ||||||||
\(904\) | 7346.45 | + | 13602.4i | 0.00898960 | + | 0.0166448i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 70353.0 | − | 57907.1i | 0.0857089 | − | 0.0705465i | ||||
\(907\) | 125297.i | 0.152310i | 0.997096 | + | 0.0761549i | \(0.0242643\pi\) | ||||
−0.997096 | + | 0.0761549i | \(0.975736\pi\) | |||||||
\(908\) | 681222. | + | 133463.i | 0.826260 | + | 0.161879i | ||||
\(909\) | −145932. | −0.176614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.15679e6i | 1.39386i | 0.717140 | + | 0.696929i | \(0.245451\pi\) | ||||
−0.717140 | + | 0.696929i | \(0.754549\pi\) | |||||||
\(912\) | −612629. | − | 249631.i | −0.736560 | − | 0.300130i | ||||
\(913\) | −522313. | −0.626599 | ||||||||
\(914\) | 803934. | − | 661713.i | 0.962339 | − | 0.792095i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 172380. | − | 879862.i | 0.205445 | − | 1.04863i | ||||
\(917\) | −108025. | −0.128465 | ||||||||
\(918\) | 20984.6 | + | 25494.8i | 0.0249009 | + | 0.0302528i | ||||
\(919\) | − | 1.27592e6i | − | 1.51076i | −0.655290 | − | 0.755378i | \(-0.727453\pi\) | ||
0.655290 | − | 0.755378i | \(-0.272547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 206287. | 0.243194 | ||||||||
\(922\) | 348431. | − | 286792.i | 0.409879 | − | 0.337369i | ||||
\(923\) | 262558.i | 0.308193i | ||||||||
\(924\) | 690026. | + | 135188.i | 0.808205 | + | 0.158341i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −478792. | − | 581698.i | −0.558374 | − | 0.678384i | ||||
\(927\) | 223959.i | 0.260621i | ||||||||
\(928\) | 925997. | − | 288202.i | 1.07526 | − | 0.334657i | ||||
\(929\) | 829467. | 0.961098 | 0.480549 | − | 0.876968i | \(-0.340437\pi\) | ||||
0.480549 | + | 0.876968i | \(0.340437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.53308e6i | − | 2.92247i | ||||||
\(932\) | 128087. | − | 653783.i | 0.147460 | − | 0.752665i | ||||
\(933\) | 86312.2 | 0.0991537 | ||||||||
\(934\) | 950400. | + | 1.15467e6i | 1.08946 | + | 1.32362i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 244412. | + | 452544.i | 0.278978 | + | 0.516547i | ||||
\(937\) | −448946. | −0.511346 | −0.255673 | − | 0.966763i | \(-0.582297\pi\) | ||||
−0.255673 | + | 0.966763i | \(0.582297\pi\) | |||||||
\(938\) | 1.64955e6 | − | 1.35773e6i | 1.87482 | − | 1.54315i | ||||
\(939\) | − | 178510.i | − | 0.202456i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37415.5 | 0.0422544 | 0.0211272 | − | 0.999777i | \(-0.493275\pi\) | ||||
0.0211272 | + | 0.999777i | \(0.493275\pi\) | |||||||
\(942\) | 249778. | + | 303463.i | 0.281483 | + | 0.341982i | ||||
\(943\) | − | 384349.i | − | 0.432218i | ||||||
\(944\) | −193663. | + | 475275.i | −0.217321 | + | 0.533337i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −351868. | + | 289621.i | −0.393186 | + | 0.323629i | ||||
\(947\) | − | 1.58481e6i | − | 1.76717i | −0.468275 | − | 0.883583i | \(-0.655124\pi\) | ||
0.468275 | − | 0.883583i | \(-0.344876\pi\) | |||||||
\(948\) | 116311. | − | 593672.i | 0.129420 | − | 0.660587i | ||||
\(949\) | −494015. | −0.548539 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 266817.i | − | 0.295021i | ||||||
\(952\) | −286845. | + | 154920.i | −0.316499 | + | 0.170936i | ||||
\(953\) | 166901. | 0.183769 | 0.0918846 | − | 0.995770i | \(-0.470711\pi\) | ||||
0.0918846 | + | 0.995770i | \(0.470711\pi\) | |||||||
\(954\) | 120140. | − | 98886.6i | 0.132005 | − | 0.108653i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.11525e6 | − | 218497.i | −1.22027 | − | 0.239073i | ||||
\(957\) | 480772. | 0.524947 | ||||||||
\(958\) | −430431. | − | 522943.i | −0.469000 | − | 0.569801i | ||||
\(959\) | 148255.i | 0.161202i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 610532. | 0.661092 | ||||||||
\(962\) | −1.06940e6 | + | 880220.i | −1.15556 | + | 0.951133i | ||||
\(963\) | 155105.i | 0.167253i | ||||||||
\(964\) | −180560. | + | 921614.i | −0.194298 | + | 0.991734i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 138270. | + | 167989.i | 0.148175 | + | 0.180022i | ||||
\(967\) | − | 873454.i | − | 0.934087i | −0.884234 | − | 0.467043i | \(-0.845319\pi\) | ||
0.884234 | − | 0.467043i | \(-0.154681\pi\) | |||||||
\(968\) | −155008. | − | 287008.i | −0.165426 | − | 0.306298i | ||||
\(969\) | 152050. | 0.161935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.16584e6i | − | 1.23651i | −0.785976 | − | 0.618257i | \(-0.787839\pi\) | ||
0.785976 | − | 0.618257i | \(-0.212161\pi\) | |||||||
\(972\) | −59477.2 | − | 11652.6i | −0.0629532 | − | 0.0123336i | ||||
\(973\) | −584230. | −0.617104 | ||||||||
\(974\) | −69196.4 | − | 84068.7i | −0.0729400 | − | 0.0886168i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −835108. | − | 340286.i | −0.876684 | − | 0.357227i | ||||
\(977\) | −885391. | −0.927569 | −0.463784 | − | 0.885948i | \(-0.653509\pi\) | ||||
−0.463784 | + | 0.885948i | \(0.653509\pi\) | |||||||
\(978\) | −36010.3 | + | 29639.8i | −0.0376486 | + | 0.0309883i | ||||
\(979\) | − | 880211.i | − | 0.918378i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −127166. | −0.132139 | ||||||||
\(982\) | 1.11261e6 | + | 1.35174e6i | 1.15377 | + | 1.40175i | ||||
\(983\) | − | 671668.i | − | 0.695101i | −0.937661 | − | 0.347550i | \(-0.887014\pi\) | ||
0.937661 | − | 0.347550i | \(-0.112986\pi\) | |||||||
\(984\) | −930065. | + | 502313.i | −0.960557 | + | 0.518781i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −172104. | + | 141658.i | −0.177026 | + | 0.145709i | ||||
\(987\) | 476830.i | 0.489473i | ||||||||
\(988\) | 2.32418e6 | + | 455347.i | 2.38098 | + | 0.466475i | ||||
\(989\) | −141018. | −0.144172 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 417477.i | 0.425094i | 0.977151 | + | 0.212547i | \(0.0681759\pi\) | ||||
−0.977151 | + | 0.212547i | \(0.931824\pi\) | |||||||
\(992\) | −170245. | − | 547000.i | −0.173002 | − | 0.555858i | ||||
\(993\) | −149027. | −0.151136 | ||||||||
\(994\) | 235848. | − | 194125.i | 0.238703 | − | 0.196475i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −85458.7 | + | 436198.i | −0.0861465 | + | 0.439708i | ||||
\(997\) | 129166. | 0.129945 | 0.0649724 | − | 0.997887i | \(-0.479304\pi\) | ||||
0.0649724 | + | 0.997887i | \(0.479304\pi\) | |||||||
\(998\) | 883729. | + | 1.07367e6i | 0.887274 | + | 1.07798i | ||||
\(999\) | − | 163215.i | − | 0.163542i |
(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 | 300.5.c.d.151.9 | 16 | ||
4.3 | odd | 2 | inner | 300.5.c.d.151.10 | 16 | ||
5.2 | odd | 4 | 300.5.f.b.199.26 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.7 | 32 | |||
5.4 | even | 2 | 60.5.c.a.31.8 | yes | 16 | ||
15.14 | odd | 2 | 180.5.c.c.91.9 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.25 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.8 | 32 | |||
20.19 | odd | 2 | 60.5.c.a.31.7 | ✓ | 16 | ||
40.19 | odd | 2 | 960.5.e.f.511.9 | 16 | |||
40.29 | even | 2 | 960.5.e.f.511.4 | 16 | |||
60.59 | even | 2 | 180.5.c.c.91.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.7 | ✓ | 16 | 20.19 | odd | 2 | ||
60.5.c.a.31.8 | yes | 16 | 5.4 | even | 2 | ||
180.5.c.c.91.9 | 16 | 15.14 | odd | 2 | |||
180.5.c.c.91.10 | 16 | 60.59 | even | 2 | |||
300.5.c.d.151.9 | 16 | 1.1 | even | 1 | trivial | ||
300.5.c.d.151.10 | 16 | 4.3 | odd | 2 | inner | ||
300.5.f.b.199.7 | 32 | 5.3 | odd | 4 | |||
300.5.f.b.199.8 | 32 | 20.7 | even | 4 | |||
300.5.f.b.199.25 | 32 | 20.3 | even | 4 | |||
300.5.f.b.199.26 | 32 | 5.2 | odd | 4 | |||
960.5.e.f.511.4 | 16 | 40.29 | even | 2 | |||
960.5.e.f.511.9 | 16 | 40.19 | odd | 2 |