Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.148347072.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 29x^{4} + 223x^{2} + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.3 | ||
Root | \(1.13993i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.s.271.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92514 | − | 3.33444i | 0.680641 | − | 1.17890i | −0.294145 | − | 0.955761i | \(-0.595035\pi\) |
0.974786 | − | 0.223143i | \(-0.0716318\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.41235 | − | 5.91036i | −0.426543 | − | 0.738795i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.1641 | − | 22.8009i | 0.710795 | − | 1.23113i | −0.253765 | − | 0.967266i | \(-0.581669\pi\) |
0.964559 | − | 0.263866i | \(-0.0849978\pi\) | |||||||
\(8\) | 4.52526 | 0.199990 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 19.2514 | 0.608783 | ||||||||
\(11\) | 2.53997 | − | 4.39937i | 0.0696210 | − | 0.120587i | −0.829113 | − | 0.559080i | \(-0.811154\pi\) |
0.898735 | + | 0.438493i | \(0.144488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.3605 | + | 71.6385i | 0.882411 | + | 1.52838i | 0.848653 | + | 0.528950i | \(0.177414\pi\) |
0.0337582 | + | 0.999430i | \(0.489252\pi\) | |||||||
\(14\) | −50.6855 | − | 87.7899i | −0.967591 | − | 1.67592i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 36.0106 | − | 62.3721i | 0.562665 | − | 0.974564i | ||||
\(17\) | 52.5976 | 0.750399 | 0.375199 | − | 0.926944i | \(-0.377574\pi\) | ||||
0.375199 | + | 0.926944i | \(0.377574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −29.8611 | −0.360559 | −0.180279 | − | 0.983615i | \(-0.557700\pi\) | ||||
−0.180279 | + | 0.983615i | \(0.557700\pi\) | |||||||
\(20\) | 17.0617 | − | 29.5518i | 0.190756 | − | 0.330399i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.77963 | − | 16.9388i | −0.0947738 | − | 0.164153i | ||||
\(23\) | 49.1340 | + | 85.1026i | 0.445441 | + | 0.771527i | 0.998083 | − | 0.0618920i | \(-0.0197134\pi\) |
−0.552641 | + | 0.833419i | \(0.686380\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 318.499 | 2.40242 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −179.682 | −1.21274 | ||||||||
\(29\) | 83.9679 | − | 145.437i | 0.537671 | − | 0.931273i | −0.461358 | − | 0.887214i | \(-0.652638\pi\) |
0.999029 | − | 0.0440590i | \(-0.0140290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −95.3871 | − | 165.215i | −0.552646 | − | 0.957211i | −0.998083 | − | 0.0618974i | \(-0.980285\pi\) |
0.445437 | − | 0.895314i | \(-0.353048\pi\) | |||||||
\(32\) | −120.550 | − | 208.798i | −0.665950 | − | 1.15346i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 101.258 | − | 175.384i | 0.510752 | − | 0.884648i | ||||
\(35\) | 131.641 | 0.635754 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −365.864 | −1.62561 | −0.812807 | − | 0.582533i | \(-0.802062\pi\) | ||||
−0.812807 | + | 0.582533i | \(0.802062\pi\) | |||||||
\(38\) | −57.4869 | + | 99.5703i | −0.245411 | + | 0.425064i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.3132 | + | 19.5950i | 0.0447192 | + | 0.0774559i | ||||
\(41\) | −55.8564 | − | 96.7461i | −0.212763 | − | 0.368517i | 0.739815 | − | 0.672810i | \(-0.234913\pi\) |
−0.952578 | + | 0.304293i | \(0.901580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 201.802 | − | 349.531i | 0.715685 | − | 1.23960i | −0.247010 | − | 0.969013i | \(-0.579448\pi\) |
0.962695 | − | 0.270590i | \(-0.0872187\pi\) | |||||||
\(44\) | −34.6691 | −0.118786 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 378.360 | 1.21274 | ||||||||
\(47\) | 116.088 | − | 201.070i | 0.360280 | − | 0.624023i | −0.627727 | − | 0.778434i | \(-0.716014\pi\) |
0.988007 | + | 0.154411i | \(0.0493478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −175.087 | − | 303.260i | −0.510458 | − | 0.884139i | ||||
\(50\) | 48.1286 | + | 83.3611i | 0.136128 | + | 0.235781i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 282.273 | − | 488.911i | 0.752773 | − | 1.30384i | ||||
\(53\) | 410.528 | 1.06397 | 0.531984 | − | 0.846754i | \(-0.321447\pi\) | ||||
0.531984 | + | 0.846754i | \(0.321447\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25.3997 | 0.0622709 | ||||||||
\(56\) | 59.5710 | − | 103.180i | 0.142152 | − | 0.246214i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −323.300 | − | 559.973i | −0.731921 | − | 1.26772i | ||||
\(59\) | 76.0067 | + | 131.647i | 0.167716 | + | 0.290492i | 0.937616 | − | 0.347672i | \(-0.113028\pi\) |
−0.769901 | + | 0.638164i | \(0.779694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −266.125 | + | 460.942i | −0.558588 | + | 0.967502i | 0.439027 | + | 0.898474i | \(0.355323\pi\) |
−0.997615 | + | 0.0690283i | \(0.978010\pi\) | |||||||
\(62\) | −734.535 | −1.50461 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −352.134 | −0.687761 | ||||||||
\(65\) | −206.803 | + | 358.193i | −0.394626 | + | 0.683513i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −306.702 | − | 531.224i | −0.559248 | − | 0.968647i | −0.997559 | − | 0.0698233i | \(-0.977756\pi\) |
0.438311 | − | 0.898823i | \(-0.355577\pi\) | |||||||
\(68\) | −179.481 | − | 310.870i | −0.320078 | − | 0.554391i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 253.428 | − | 438.950i | 0.432720 | − | 0.749493i | ||||
\(71\) | 413.938 | 0.691908 | 0.345954 | − | 0.938252i | \(-0.387555\pi\) | ||||
0.345954 | + | 0.938252i | \(0.387555\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −114.484 | −0.183552 | −0.0917761 | − | 0.995780i | \(-0.529254\pi\) | ||||
−0.0917761 | + | 0.995780i | \(0.529254\pi\) | |||||||
\(74\) | −704.341 | + | 1219.95i | −1.10646 | + | 1.91644i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 101.897 | + | 176.490i | 0.153794 | + | 0.266379i | ||||
\(77\) | −66.8730 | − | 115.827i | −0.0989725 | − | 0.171425i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39.5526 | + | 68.5072i | −0.0563294 | + | 0.0975653i | −0.892815 | − | 0.450423i | \(-0.851273\pi\) |
0.836486 | + | 0.547989i | \(0.184606\pi\) | |||||||
\(80\) | 360.106 | 0.503263 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −430.126 | −0.579262 | ||||||||
\(83\) | −713.664 | + | 1236.10i | −0.943792 | + | 1.63470i | −0.185641 | + | 0.982618i | \(0.559436\pi\) |
−0.758151 | + | 0.652079i | \(0.773897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 131.494 | + | 227.754i | 0.167794 | + | 0.290628i | ||||
\(86\) | −776.994 | − | 1345.79i | −0.974249 | − | 1.68745i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.4941 | − | 19.9083i | 0.0139235 | − | 0.0241163i | ||||
\(89\) | −450.084 | −0.536054 | −0.268027 | − | 0.963411i | \(-0.586372\pi\) | ||||
−0.268027 | + | 0.963411i | \(0.586372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2177.90 | 2.50885 | ||||||||
\(92\) | 335.325 | − | 580.799i | 0.380000 | − | 0.658180i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −446.971 | − | 774.177i | −0.490442 | − | 0.849471i | ||||
\(95\) | −74.6528 | − | 129.302i | −0.0806233 | − | 0.139644i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −718.438 | + | 1244.37i | −0.752024 | + | 1.30254i | 0.194816 | + | 0.980840i | \(0.437589\pi\) |
−0.946840 | + | 0.321705i | \(0.895744\pi\) | |||||||
\(98\) | −1348.27 | −1.38975 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 170.617 | 0.170617 | ||||||||
\(101\) | −923.517 | + | 1599.58i | −0.909835 | + | 1.57588i | −0.0955437 | + | 0.995425i | \(0.530459\pi\) |
−0.814292 | + | 0.580456i | \(0.802874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −23.8766 | − | 41.3554i | −0.0228410 | − | 0.0395618i | 0.854379 | − | 0.519650i | \(-0.173938\pi\) |
−0.877220 | + | 0.480089i | \(0.840604\pi\) | |||||||
\(104\) | 187.167 | + | 324.183i | 0.176474 | + | 0.305661i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 790.324 | − | 1368.88i | 0.724180 | − | 1.25432i | ||||
\(107\) | 1839.39 | 1.66187 | 0.830936 | − | 0.556368i | \(-0.187806\pi\) | ||||
0.830936 | + | 0.556368i | \(0.187806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 559.158 | 0.491354 | 0.245677 | − | 0.969352i | \(-0.420990\pi\) | ||||
0.245677 | + | 0.969352i | \(0.420990\pi\) | |||||||
\(110\) | 48.8981 | − | 84.6941i | 0.0423841 | − | 0.0734115i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −948.093 | − | 1642.15i | −0.799878 | − | 1.38543i | ||||
\(113\) | 1182.42 | + | 2048.01i | 0.984359 | + | 1.70496i | 0.644751 | + | 0.764393i | \(0.276961\pi\) |
0.339609 | + | 0.940567i | \(0.389705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −245.670 | + | 425.513i | −0.199207 | + | 0.345037i | ||||
\(116\) | −1146.11 | −0.917360 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 585.295 | 0.456616 | ||||||||
\(119\) | 692.399 | − | 1199.27i | 0.533379 | − | 0.923840i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 652.597 | + | 1130.33i | 0.490306 | + | 0.849235i | ||||
\(122\) | 1024.66 | + | 1774.76i | 0.760395 | + | 1.31704i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −650.988 | + | 1127.54i | −0.471455 | + | 0.816584i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2403.43 | −1.67929 | −0.839646 | − | 0.543134i | \(-0.817238\pi\) | ||||
−0.839646 | + | 0.543134i | \(0.817238\pi\) | |||||||
\(128\) | 286.491 | − | 496.218i | 0.197832 | − | 0.342655i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 796.249 | + | 1379.14i | 0.537197 | + | 0.930453i | ||||
\(131\) | −817.404 | − | 1415.78i | −0.545167 | − | 0.944257i | −0.998596 | − | 0.0529648i | \(-0.983133\pi\) |
0.453429 | − | 0.891292i | \(-0.350200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −393.095 | + | 680.860i | −0.256283 | + | 0.443895i | ||||
\(134\) | −2361.78 | −1.52259 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 238.018 | 0.150072 | ||||||||
\(137\) | 1263.19 | − | 2187.91i | 0.787749 | − | 1.36442i | −0.139594 | − | 0.990209i | \(-0.544580\pi\) |
0.927343 | − | 0.374212i | \(-0.122087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −945.422 | − | 1637.52i | −0.576904 | − | 0.999227i | −0.995832 | − | 0.0912078i | \(-0.970927\pi\) |
0.418928 | − | 0.908020i | \(-0.362406\pi\) | |||||||
\(140\) | −449.205 | − | 778.045i | −0.271177 | − | 0.469692i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 796.890 | − | 1380.25i | 0.470940 | − | 0.815693i | ||||
\(143\) | 420.219 | 0.245737 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 839.679 | 0.480907 | ||||||||
\(146\) | −220.398 | + | 381.740i | −0.124933 | + | 0.216391i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1248.46 | + | 2162.39i | 0.693395 | + | 1.20099i | ||||
\(149\) | −139.451 | − | 241.535i | −0.0766727 | − | 0.132801i | 0.825140 | − | 0.564929i | \(-0.191096\pi\) |
−0.901812 | + | 0.432128i | \(0.857763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 215.976 | − | 374.081i | 0.116396 | − | 0.201604i | −0.801941 | − | 0.597404i | \(-0.796199\pi\) |
0.918337 | + | 0.395799i | \(0.129532\pi\) | |||||||
\(152\) | −135.129 | −0.0721082 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −514.960 | −0.269459 | ||||||||
\(155\) | 476.935 | − | 826.076i | 0.247151 | − | 0.428078i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 222.554 | + | 385.474i | 0.113132 | + | 0.195950i | 0.917031 | − | 0.398815i | \(-0.130578\pi\) |
−0.803900 | + | 0.594765i | \(0.797245\pi\) | |||||||
\(158\) | 152.289 | + | 263.772i | 0.0766801 | + | 0.132814i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 602.749 | − | 1043.99i | 0.297822 | − | 0.515843i | ||||
\(161\) | 2587.22 | 1.26647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2533.56 | −1.21745 | −0.608723 | − | 0.793382i | \(-0.708318\pi\) | ||||
−0.608723 | + | 0.793382i | \(0.708318\pi\) | |||||||
\(164\) | −381.203 | + | 660.263i | −0.181506 | + | 0.314377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2747.81 | + | 4759.34i | 1.28477 | + | 2.22528i | ||||
\(167\) | 1082.74 | + | 1875.37i | 0.501707 | + | 0.868983i | 0.999998 | + | 0.00197267i | \(0.000627922\pi\) |
−0.498291 | + | 0.867010i | \(0.666039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2322.88 | + | 4023.35i | −1.05730 | + | 1.83129i | ||||
\(170\) | 1012.58 | 0.456830 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2754.47 | −1.22108 | ||||||||
\(173\) | 681.847 | − | 1180.99i | 0.299653 | − | 0.519013i | −0.676404 | − | 0.736531i | \(-0.736463\pi\) |
0.976056 | + | 0.217517i | \(0.0697959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 329.102 | + | 570.022i | 0.142159 | + | 0.246226i | ||||
\(176\) | −182.932 | − | 316.847i | −0.0783466 | − | 0.135700i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −866.476 | + | 1500.78i | −0.364860 | + | 0.631957i | ||||
\(179\) | 1198.29 | 0.500358 | 0.250179 | − | 0.968200i | \(-0.419511\pi\) | ||||
0.250179 | + | 0.968200i | \(0.419511\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1098.13 | 0.450959 | 0.225480 | − | 0.974248i | \(-0.427605\pi\) | ||||
0.225480 | + | 0.974248i | \(0.427605\pi\) | |||||||
\(182\) | 4192.76 | − | 7262.07i | 1.70763 | − | 2.95770i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 222.344 | + | 385.112i | 0.0890839 | + | 0.154298i | ||||
\(185\) | −914.661 | − | 1584.24i | −0.363498 | − | 0.629597i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 133.596 | − | 231.396i | 0.0522435 | − | 0.0904885i | ||||
\(188\) | −1584.53 | −0.614700 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −574.869 | −0.219502 | ||||||||
\(191\) | −625.013 | + | 1082.55i | −0.236777 | + | 0.410110i | −0.959788 | − | 0.280727i | \(-0.909424\pi\) |
0.723011 | + | 0.690837i | \(0.242758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1620.76 | − | 2807.23i | −0.604480 | − | 1.04699i | −0.992133 | − | 0.125185i | \(-0.960048\pi\) |
0.387654 | − | 0.921805i | \(-0.373286\pi\) | |||||||
\(194\) | 2766.19 | + | 4791.19i | 1.02372 | + | 1.77313i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1194.92 | + | 2069.65i | −0.435465 | + | 0.754247i | ||||
\(197\) | −714.141 | −0.258276 | −0.129138 | − | 0.991627i | \(-0.541221\pi\) | ||||
−0.129138 | + | 0.991627i | \(0.541221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −666.927 | −0.237574 | −0.118787 | − | 0.992920i | \(-0.537901\pi\) | ||||
−0.118787 | + | 0.992920i | \(0.537901\pi\) | |||||||
\(200\) | −56.5658 | + | 97.9748i | −0.0199990 | + | 0.0346393i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3555.80 | + | 6158.83i | 1.23854 | + | 2.14522i | ||||
\(203\) | −2210.72 | − | 3829.09i | −0.764347 | − | 1.32389i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 279.282 | − | 483.731i | 0.0951507 | − | 0.164806i | ||||
\(206\) | −183.863 | −0.0621862 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5957.66 | 1.98601 | ||||||||
\(209\) | −75.8465 | + | 131.370i | −0.0251025 | + | 0.0434787i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2479.61 | + | 4294.80i | 0.809019 | + | 1.40126i | 0.913544 | + | 0.406740i | \(0.133335\pi\) |
−0.104525 | + | 0.994522i | \(0.533332\pi\) | |||||||
\(212\) | −1400.86 | − | 2426.37i | −0.453829 | − | 0.786054i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3541.08 | − | 6133.33i | 1.13114 | − | 1.95919i | ||||
\(215\) | 2018.02 | 0.640128 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5022.74 | −1.57127 | ||||||||
\(218\) | 1076.46 | − | 1864.48i | 0.334436 | − | 0.579260i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −86.6728 | − | 150.122i | −0.0265613 | − | 0.0460054i | ||||
\(221\) | 2175.46 | + | 3768.01i | 0.662160 | + | 1.14689i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −561.885 | + | 973.213i | −0.168729 | + | 0.292248i | −0.937973 | − | 0.346707i | \(-0.887300\pi\) |
0.769244 | + | 0.638955i | \(0.220633\pi\) | |||||||
\(224\) | −6347.72 | −1.89341 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9105.30 | 2.67998 | ||||||||
\(227\) | −612.555 | + | 1060.98i | −0.179104 | + | 0.310218i | −0.941574 | − | 0.336806i | \(-0.890653\pi\) |
0.762470 | + | 0.647024i | \(0.223987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1789.09 | + | 3098.79i | 0.516272 | + | 0.894209i | 0.999822 | + | 0.0188922i | \(0.00601392\pi\) |
−0.483550 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(230\) | 945.900 | + | 1638.35i | 0.271177 | + | 0.469693i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 379.977 | − | 658.139i | 0.107529 | − | 0.186246i | ||||
\(233\) | −527.061 | −0.148193 | −0.0740963 | − | 0.997251i | \(-0.523607\pi\) | ||||
−0.0740963 | + | 0.997251i | \(0.523607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1160.88 | 0.322244 | ||||||||
\(236\) | 518.722 | − | 898.453i | 0.143076 | − | 0.247815i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2665.93 | − | 4617.53i | −0.726079 | − | 1.25761i | ||||
\(239\) | 48.1693 | + | 83.4317i | 0.0130369 | + | 0.0225805i | 0.872470 | − | 0.488667i | \(-0.162517\pi\) |
−0.859433 | + | 0.511248i | \(0.829183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −461.973 | + | 800.160i | −0.123478 | + | 0.213871i | −0.921137 | − | 0.389238i | \(-0.872738\pi\) |
0.797659 | + | 0.603109i | \(0.206072\pi\) | |||||||
\(242\) | 5025.37 | 1.33489 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3632.45 | 0.953047 | ||||||||
\(245\) | 875.435 | − | 1516.30i | 0.228284 | − | 0.395399i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1235.07 | − | 2139.21i | −0.318161 | − | 0.551071i | ||||
\(248\) | −431.652 | − | 747.643i | −0.110524 | − | 0.191433i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −240.643 | + | 416.806i | −0.0608783 | + | 0.105444i | ||||
\(251\) | 4134.83 | 1.03979 | 0.519897 | − | 0.854229i | \(-0.325970\pi\) | ||||
0.519897 | + | 0.854229i | \(0.325970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 499.197 | 0.124048 | ||||||||
\(254\) | −4626.95 | + | 8014.11i | −1.14299 | + | 1.97972i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2511.61 | − | 4350.23i | −0.613185 | − | 1.06207i | ||||
\(257\) | 893.588 | + | 1547.74i | 0.216889 | + | 0.375663i | 0.953855 | − | 0.300267i | \(-0.0970757\pi\) |
−0.736966 | + | 0.675930i | \(0.763742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4816.27 | + | 8342.03i | −1.15548 | + | 2.00135i | ||||
\(260\) | 2822.73 | 0.673301 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6294.47 | −1.48425 | ||||||||
\(263\) | −2674.07 | + | 4631.63i | −0.626960 | + | 1.08593i | 0.361199 | + | 0.932489i | \(0.382368\pi\) |
−0.988158 | + | 0.153437i | \(0.950966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1026.32 | + | 1777.64i | 0.237911 | + | 0.412073i | ||||
\(266\) | 1513.53 | + | 2621.51i | 0.348873 | + | 0.604266i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2093.15 | + | 3625.44i | −0.477087 | + | 0.826340i | ||||
\(269\) | −8266.59 | −1.87369 | −0.936846 | − | 0.349743i | \(-0.886269\pi\) | ||||
−0.936846 | + | 0.349743i | \(0.886269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7114.58 | −1.59476 | −0.797380 | − | 0.603478i | \(-0.793781\pi\) | ||||
−0.797380 | + | 0.603478i | \(0.793781\pi\) | |||||||
\(272\) | 1894.07 | − | 3280.62i | 0.422223 | − | 0.731312i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4863.64 | − | 8424.07i | −1.07235 | − | 1.85736i | ||||
\(275\) | 63.4994 | + | 109.984i | 0.0139242 | + | 0.0241174i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1948.74 | − | 3375.32i | 0.422702 | − | 0.732141i | −0.573501 | − | 0.819205i | \(-0.694415\pi\) |
0.996203 | + | 0.0870636i | \(0.0277483\pi\) | |||||||
\(278\) | −7280.29 | −1.57066 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 595.710 | 0.127145 | ||||||||
\(281\) | −2647.47 | + | 4585.55i | −0.562045 | + | 0.973490i | 0.435273 | + | 0.900299i | \(0.356652\pi\) |
−0.997318 | + | 0.0731918i | \(0.976681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2321.50 | + | 4020.95i | 0.487628 | + | 0.844596i | 0.999899 | − | 0.0142281i | \(-0.00452909\pi\) |
−0.512271 | + | 0.858824i | \(0.671196\pi\) | |||||||
\(284\) | −1412.50 | − | 2446.52i | −0.295129 | − | 0.511178i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 808.981 | − | 1401.20i | 0.167259 | − | 0.289701i | ||||
\(287\) | −2941.20 | −0.604924 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2146.50 | −0.436902 | ||||||||
\(290\) | 1616.50 | − | 2799.86i | 0.327325 | − | 0.566944i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 390.658 | + | 676.640i | 0.0782930 | + | 0.135607i | ||||
\(293\) | −1957.53 | − | 3390.55i | −0.390309 | − | 0.676034i | 0.602182 | − | 0.798359i | \(-0.294298\pi\) |
−0.992490 | + | 0.122325i | \(0.960965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −380.033 | + | 658.237i | −0.0750047 | + | 0.129912i | ||||
\(296\) | −1655.63 | −0.325107 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1073.85 | −0.208746 | ||||||||
\(299\) | −4064.42 | + | 7039.78i | −0.786125 | + | 1.36161i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5313.07 | − | 9202.51i | −1.01741 | − | 1.76221i | ||||
\(302\) | −831.568 | − | 1440.32i | −0.158448 | − | 0.274440i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1075.32 | + | 1862.50i | −0.202874 | + | 0.351387i | ||||
\(305\) | −2661.25 | −0.499616 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6637.24 | 1.23390 | 0.616950 | − | 0.787002i | \(-0.288368\pi\) | ||||
0.616950 | + | 0.787002i | \(0.288368\pi\) | |||||||
\(308\) | −456.387 | + | 790.486i | −0.0844321 | + | 0.146241i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1836.34 | − | 3180.63i | −0.336442 | − | 0.582734i | ||||
\(311\) | −1118.61 | − | 1937.49i | −0.203957 | − | 0.353263i | 0.745843 | − | 0.666122i | \(-0.232047\pi\) |
−0.949800 | + | 0.312858i | \(0.898713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −657.096 | + | 1138.12i | −0.118662 | + | 0.205529i | −0.919238 | − | 0.393703i | \(-0.871194\pi\) |
0.800576 | + | 0.599232i | \(0.204527\pi\) | |||||||
\(314\) | 1713.79 | 0.308009 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 539.869 | 0.0961077 | ||||||||
\(317\) | 470.230 | − | 814.462i | 0.0833147 | − | 0.144305i | −0.821357 | − | 0.570414i | \(-0.806783\pi\) |
0.904672 | + | 0.426109i | \(0.140116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −426.553 | − | 738.811i | −0.0748664 | − | 0.129672i | ||||
\(320\) | −880.334 | − | 1524.78i | −0.153788 | − | 0.266369i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4980.77 | − | 8626.94i | 0.862010 | − | 1.49305i | ||||
\(323\) | −1570.62 | −0.270563 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2068.03 | −0.352964 | ||||||||
\(326\) | −4877.47 | + | 8448.02i | −0.828644 | + | 1.43525i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −252.765 | − | 437.802i | −0.0425506 | − | 0.0736999i | ||||
\(329\) | −3056.38 | − | 5293.81i | −0.512170 | − | 0.887105i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1121.23 | − | 1942.03i | 0.186188 | − | 0.322487i | −0.757788 | − | 0.652501i | \(-0.773720\pi\) |
0.943976 | + | 0.330013i | \(0.107053\pi\) | |||||||
\(332\) | 9741.07 | 1.61027 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8337.73 | 1.36593 | ||||||||
\(335\) | 1533.51 | − | 2656.12i | 0.250103 | − | 0.433192i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1561.83 | + | 2705.16i | 0.252457 | + | 0.437269i | 0.964202 | − | 0.265170i | \(-0.0854279\pi\) |
−0.711744 | + | 0.702438i | \(0.752095\pi\) | |||||||
\(338\) | 8943.76 | + | 15491.1i | 1.43928 | + | 2.49291i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 897.405 | − | 1554.35i | 0.143143 | − | 0.247931i | ||||
\(341\) | −969.123 | −0.153903 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −188.878 | −0.0297332 | ||||||||
\(344\) | 913.206 | − | 1581.72i | 0.143130 | − | 0.247909i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2625.31 | − | 4547.16i | −0.407911 | − | 0.706523i | ||||
\(347\) | −5361.13 | − | 9285.75i | −0.829397 | − | 1.43656i | −0.898512 | − | 0.438948i | \(-0.855351\pi\) |
0.0691157 | − | 0.997609i | \(-0.477982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3050.82 | − | 5284.18i | 0.467928 | − | 0.810475i | −0.531400 | − | 0.847121i | \(-0.678334\pi\) |
0.999328 | + | 0.0366457i | \(0.0116673\pi\) | |||||||
\(350\) | 2534.28 | 0.387037 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1224.77 | −0.185456 | ||||||||
\(353\) | −5164.28 | + | 8944.79i | −0.778659 | + | 1.34868i | 0.154056 | + | 0.988062i | \(0.450766\pi\) |
−0.932715 | + | 0.360615i | \(0.882567\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1034.85 | + | 1792.41i | 0.154715 | + | 0.267975i | ||||
\(356\) | 1535.84 | + | 2660.16i | 0.228650 | + | 0.396034i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2306.87 | − | 3995.62i | 0.340564 | − | 0.589874i | ||||
\(359\) | −1122.33 | −0.164998 | −0.0824992 | − | 0.996591i | \(-0.526290\pi\) | ||||
−0.0824992 | + | 0.996591i | \(0.526290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5967.31 | −0.869998 | ||||||||
\(362\) | 2114.06 | − | 3661.67i | 0.306941 | − | 0.531638i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7431.73 | − | 12872.1i | −1.07013 | − | 1.85353i | ||||
\(365\) | −286.209 | − | 495.729i | −0.0410435 | − | 0.0710895i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1821.44 | − | 3154.82i | 0.259069 | − | 0.448720i | −0.706924 | − | 0.707290i | \(-0.749918\pi\) |
0.965993 | + | 0.258569i | \(0.0832510\pi\) | |||||||
\(368\) | 7077.37 | 1.00254 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7043.41 | −0.989647 | ||||||||
\(371\) | 5404.23 | − | 9360.40i | 0.756263 | − | 1.30989i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4767.16 | − | 8256.97i | −0.661755 | − | 1.14619i | −0.980154 | − | 0.198236i | \(-0.936479\pi\) |
0.318400 | − | 0.947957i | \(-0.396855\pi\) | |||||||
\(374\) | −514.384 | − | 890.940i | −0.0711181 | − | 0.123180i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 525.328 | − | 909.895i | 0.0720525 | − | 0.124799i | ||||
\(377\) | 13891.8 | 1.89779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10826.9 | 1.46738 | 0.733691 | − | 0.679483i | \(-0.237796\pi\) | ||||
0.733691 | + | 0.679483i | \(0.237796\pi\) | |||||||
\(380\) | −509.483 | + | 882.450i | −0.0687787 | + | 0.119128i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2406.48 | + | 4168.14i | 0.322320 | + | 0.558274i | ||||
\(383\) | −3336.87 | − | 5779.63i | −0.445185 | − | 0.771084i | 0.552880 | − | 0.833261i | \(-0.313529\pi\) |
−0.998065 | + | 0.0621773i | \(0.980196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 334.365 | − | 579.137i | 0.0442618 | − | 0.0766638i | ||||
\(386\) | −12480.7 | −1.64573 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9806.24 | 1.28308 | ||||||||
\(389\) | −631.501 | + | 1093.79i | −0.0823094 | + | 0.142564i | −0.904242 | − | 0.427021i | \(-0.859563\pi\) |
0.821932 | + | 0.569585i | \(0.192896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2584.33 | + | 4476.19i | 0.334259 | + | 0.578953i | ||||
\(392\) | −792.315 | − | 1372.33i | −0.102087 | − | 0.176819i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1374.82 | + | 2381.26i | −0.175793 | + | 0.304483i | ||||
\(395\) | −395.526 | −0.0503825 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −888.172 | −0.112282 | −0.0561411 | − | 0.998423i | \(-0.517880\pi\) | ||||
−0.0561411 | + | 0.998423i | \(0.517880\pi\) | |||||||
\(398\) | −1283.93 | + | 2223.83i | −0.161703 | + | 0.280077i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 900.264 | + | 1559.30i | 0.112533 | + | 0.194913i | ||||
\(401\) | −6186.20 | − | 10714.8i | −0.770385 | − | 1.33435i | −0.937352 | − | 0.348383i | \(-0.886731\pi\) |
0.166968 | − | 0.985962i | \(-0.446602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7890.52 | − | 13666.8i | 0.975322 | − | 1.68931i | ||||
\(404\) | 12605.4 | 1.55234 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17023.8 | −2.08098 | ||||||||
\(407\) | −929.286 | + | 1609.57i | −0.113177 | + | 0.196028i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6323.64 | + | 10952.9i | 0.764508 | + | 1.32417i | 0.940506 | + | 0.339776i | \(0.110351\pi\) |
−0.175999 | + | 0.984390i | \(0.556315\pi\) | |||||||
\(410\) | −1075.32 | − | 1862.50i | −0.129527 | − | 0.224347i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −162.950 | + | 282.238i | −0.0194854 | + | 0.0337497i | ||||
\(413\) | 4002.24 | 0.476846 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7136.64 | −0.844154 | ||||||||
\(416\) | 9972.01 | − | 17272.0i | 1.17528 | − | 2.03565i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 292.031 | + | 505.812i | 0.0341715 | + | 0.0591868i | ||||
\(419\) | 7126.00 | + | 12342.6i | 0.830855 | + | 1.43908i | 0.897361 | + | 0.441296i | \(0.145481\pi\) |
−0.0665067 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1272.84 | + | 2204.63i | −0.147351 | + | 0.255219i | −0.930247 | − | 0.366933i | \(-0.880408\pi\) |
0.782897 | + | 0.622151i | \(0.213741\pi\) | |||||||
\(422\) | 19094.4 | 2.20261 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1857.75 | 0.212783 | ||||||||
\(425\) | −657.469 | + | 1138.77i | −0.0750399 | + | 0.129973i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7006.60 | + | 12135.8i | 0.794082 | + | 1.37539i | ||||
\(428\) | −6276.63 | − | 10871.4i | −0.708860 | − | 1.22778i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3884.97 | − | 6728.96i | 0.435697 | − | 0.754650i | ||||
\(431\) | −3068.41 | −0.342923 | −0.171462 | − | 0.985191i | \(-0.554849\pi\) | ||||
−0.171462 | + | 0.985191i | \(0.554849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13982.0 | −1.55180 | −0.775900 | − | 0.630856i | \(-0.782704\pi\) | ||||
−0.775900 | + | 0.630856i | \(0.782704\pi\) | |||||||
\(434\) | −9669.49 | + | 16748.0i | −1.06947 | + | 1.85238i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1908.04 | − | 3304.82i | −0.209584 | − | 0.363010i | ||||
\(437\) | −1467.20 | − | 2541.26i | −0.160608 | − | 0.278181i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3846.22 | + | 6661.85i | −0.418155 | + | 0.724266i | −0.995754 | − | 0.0920549i | \(-0.970656\pi\) |
0.577599 | + | 0.816321i | \(0.303990\pi\) | |||||||
\(440\) | 114.941 | 0.0124536 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16752.3 | 1.80277 | ||||||||
\(443\) | 17.9124 | − | 31.0252i | 0.00192109 | − | 0.00332743i | −0.865063 | − | 0.501663i | \(-0.832722\pi\) |
0.866984 | + | 0.498335i | \(0.166055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1125.21 | − | 1948.92i | −0.119865 | − | 0.207613i | ||||
\(446\) | 2163.42 | + | 3747.15i | 0.229688 | + | 0.397831i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4635.52 | + | 8028.96i | −0.488857 | + | 0.846725i | ||||
\(449\) | −2602.16 | −0.273505 | −0.136752 | − | 0.990605i | \(-0.543666\pi\) | ||||
−0.136752 | + | 0.990605i | \(0.543666\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −567.495 | −0.0592512 | ||||||||
\(452\) | 8069.64 | − | 13977.0i | 0.839744 | − | 1.45448i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2358.51 | + | 4085.06i | 0.243811 | + | 0.422294i | ||||
\(455\) | 5444.74 | + | 9430.56i | 0.560996 | + | 0.971674i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4075.83 | + | 7059.55i | −0.417198 | + | 0.722608i | −0.995656 | − | 0.0931041i | \(-0.970321\pi\) |
0.578459 | + | 0.815712i | \(0.303654\pi\) | |||||||
\(458\) | 13777.0 | 1.40558 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3353.25 | 0.339882 | ||||||||
\(461\) | 3373.66 | − | 5843.34i | 0.340839 | − | 0.590351i | −0.643750 | − | 0.765236i | \(-0.722622\pi\) |
0.984589 | + | 0.174886i | \(0.0559555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −419.278 | − | 726.210i | −0.0420853 | − | 0.0728939i | 0.844215 | − | 0.536004i | \(-0.180067\pi\) |
−0.886301 | + | 0.463110i | \(0.846733\pi\) | |||||||
\(464\) | −6047.46 | − | 10474.5i | −0.605057 | − | 1.04799i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1014.67 | + | 1757.45i | −0.100866 | + | 0.174705i | ||||
\(467\) | 7253.46 | 0.718737 | 0.359369 | − | 0.933196i | \(-0.382992\pi\) | ||||
0.359369 | + | 0.933196i | \(0.382992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16149.8 | −1.59004 | ||||||||
\(470\) | 2234.86 | − | 3870.89i | 0.219332 | − | 0.379895i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 343.950 | + | 595.739i | 0.0335415 | + | 0.0580956i | ||||
\(473\) | −1025.14 | − | 1775.60i | −0.0996535 | − | 0.172605i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 373.264 | − | 646.512i | 0.0360559 | − | 0.0624506i | ||||
\(476\) | −9450.83 | −0.910038 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 370.931 | 0.0354937 | ||||||||
\(479\) | 5175.92 | − | 8964.95i | 0.493724 | − | 0.855154i | −0.506250 | − | 0.862387i | \(-0.668969\pi\) |
0.999974 | + | 0.00723223i | \(0.00230211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15132.3 | − | 26210.0i | −1.43446 | − | 2.48456i | ||||
\(482\) | 1778.73 | + | 3080.85i | 0.168089 | + | 0.291138i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4453.78 | − | 7714.16i | 0.418273 | − | 0.724471i | ||||
\(485\) | −7184.38 | −0.672631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5202.70 | 0.484100 | 0.242050 | − | 0.970264i | \(-0.422180\pi\) | ||||
0.242050 | + | 0.970264i | \(0.422180\pi\) | |||||||
\(488\) | −1204.29 | + | 2085.89i | −0.111712 | + | 0.193491i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3370.67 | − | 5838.18i | −0.310758 | − | 0.538249i | ||||
\(491\) | 1230.26 | + | 2130.87i | 0.113077 | + | 0.195855i | 0.917009 | − | 0.398866i | \(-0.130596\pi\) |
−0.803932 | + | 0.594721i | \(0.797263\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4416.51 | − | 7649.61i | 0.403467 | − | 0.698826i | ||||
\(494\) | −9510.75 | −0.866213 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13739.8 | −1.24382 | ||||||||
\(497\) | 5449.12 | − | 9438.16i | 0.491804 | − | 0.851830i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6428.16 | + | 11133.9i | 0.576681 | + | 0.998842i | 0.995857 | + | 0.0909363i | \(0.0289860\pi\) |
−0.419175 | + | 0.907905i | \(0.637681\pi\) | |||||||
\(500\) | 426.543 | + | 738.795i | 0.0381512 | + | 0.0660798i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7960.14 | − | 13787.4i | 0.707726 | − | 1.22582i | ||||
\(503\) | −21744.3 | −1.92750 | −0.963749 | − | 0.266810i | \(-0.914030\pi\) | ||||
−0.963749 | + | 0.266810i | \(0.914030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9235.17 | −0.813782 | ||||||||
\(506\) | 961.025 | − | 1664.54i | 0.0844323 | − | 0.146241i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8201.34 | + | 14205.1i | 0.716291 | + | 1.24065i | ||||
\(509\) | 4871.91 | + | 8438.40i | 0.424251 | + | 0.734824i | 0.996350 | − | 0.0853605i | \(-0.0272042\pi\) |
−0.572099 | + | 0.820184i | \(0.693871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1507.08 | + | 2610.33i | −0.130468 | + | 0.225977i | ||||
\(512\) | −14756.9 | −1.27377 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6881.13 | 0.590494 | ||||||||
\(515\) | 119.383 | − | 206.777i | 0.0102148 | − | 0.0176926i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −589.721 | − | 1021.43i | −0.0501661 | − | 0.0868903i | ||||
\(518\) | 18544.0 | + | 32119.2i | 1.57293 | + | 2.72439i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −935.836 | + | 1620.92i | −0.0789214 | + | 0.136696i | ||||
\(521\) | −17889.5 | −1.50432 | −0.752161 | − | 0.658980i | \(-0.770988\pi\) | ||||
−0.752161 | + | 0.658980i | \(0.770988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5012.48 | 0.419083 | 0.209542 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209542 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(524\) | −5578.53 | + | 9662.30i | −0.465075 | + | 0.805533i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10295.9 | + | 17833.1i | 0.853468 | + | 1.47825i | ||||
\(527\) | −5017.13 | − | 8689.92i | −0.414705 | − | 0.718290i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1255.20 | − | 2174.06i | 0.103164 | − | 0.178685i | ||||
\(530\) | 7903.24 | 0.647726 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5365.50 | 0.437263 | ||||||||
\(533\) | 4620.50 | − | 8002.94i | 0.375490 | − | 0.650367i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4598.47 | + | 7964.78i | 0.371606 | + | 0.643640i | ||||
\(536\) | −1387.91 | − | 2403.93i | −0.111844 | − | 0.193720i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15914.4 | + | 27564.5i | −1.27531 | + | 2.20890i | ||||
\(539\) | −1778.87 | −0.142154 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12629.5 | 1.00367 | 0.501834 | − | 0.864964i | \(-0.332659\pi\) | ||||
0.501834 | + | 0.864964i | \(0.332659\pi\) | |||||||
\(542\) | −13696.6 | + | 23723.2i | −1.08546 | + | 1.88007i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6340.63 | − | 10982.3i | −0.499728 | − | 0.865554i | ||||
\(545\) | 1397.89 | + | 2421.22i | 0.109870 | + | 0.190301i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3665.93 | + | 6349.57i | −0.286552 | + | 0.496322i | −0.972984 | − | 0.230871i | \(-0.925842\pi\) |
0.686433 | + | 0.727193i | \(0.259176\pi\) | |||||||
\(548\) | −17241.8 | −1.34404 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 488.981 | 0.0379095 | ||||||||
\(551\) | −2507.38 | + | 4342.90i | −0.193862 | + | 0.335778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1041.35 | + | 1803.67i | 0.0800772 | + | 0.138698i | ||||
\(554\) | −7503.21 | − | 12995.9i | −0.575416 | − | 0.996650i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6452.22 | + | 11175.6i | −0.492149 | + | 0.852428i | ||||
\(557\) | 11389.0 | 0.866371 | 0.433185 | − | 0.901305i | \(-0.357390\pi\) | ||||
0.433185 | + | 0.901305i | \(0.357390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33386.5 | 2.52611 | ||||||||
\(560\) | 4740.46 | − | 8210.73i | 0.357716 | − | 0.619583i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10193.5 | + | 17655.7i | 0.765101 | + | 1.32519i | ||||
\(563\) | −6610.55 | − | 11449.8i | −0.494852 | − | 0.857109i | 0.505130 | − | 0.863043i | \(-0.331444\pi\) |
−0.999982 | + | 0.00593423i | \(0.998111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5912.09 | + | 10240.0i | −0.440219 | + | 0.762481i | ||||
\(566\) | 17876.8 | 1.32760 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1873.18 | 0.138375 | ||||||||
\(569\) | 4170.89 | − | 7224.20i | 0.307299 | − | 0.532257i | −0.670472 | − | 0.741935i | \(-0.733908\pi\) |
0.977770 | + | 0.209678i | \(0.0672416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10801.2 | − | 18708.3i | −0.791625 | − | 1.37114i | −0.924960 | − | 0.380064i | \(-0.875902\pi\) |
0.133335 | − | 0.991071i | \(-0.457431\pi\) | |||||||
\(572\) | −1433.93 | − | 2483.64i | −0.104818 | − | 0.181549i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5662.22 | + | 9807.26i | −0.411736 | + | 0.713148i | ||||
\(575\) | −2456.70 | −0.178177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −696.389 | −0.0502444 | −0.0251222 | − | 0.999684i | \(-0.507997\pi\) | ||||
−0.0251222 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(578\) | −4132.31 | + | 7157.38i | −0.297373 | + | 0.515065i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2865.28 | − | 4962.80i | −0.205128 | − | 0.355292i | ||||
\(581\) | 18789.5 | + | 32544.3i | 1.34169 | + | 2.32387i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1042.73 | − | 1806.06i | 0.0740746 | − | 0.128301i | ||||
\(584\) | −518.069 | −0.0367087 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15074.1 | −1.06264 | ||||||||
\(587\) | −11962.1 | + | 20719.0i | −0.841105 | + | 1.45684i | 0.0478566 | + | 0.998854i | \(0.484761\pi\) |
−0.888961 | + | 0.457982i | \(0.848572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2848.37 | + | 4933.51i | 0.199261 | + | 0.345131i | ||||
\(590\) | 1463.24 | + | 2534.40i | 0.102103 | + | 0.176847i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13175.0 | + | 22819.7i | −0.914676 | + | 1.58426i | ||||
\(593\) | 11887.8 | 0.823226 | 0.411613 | − | 0.911359i | \(-0.364966\pi\) | ||||
0.411613 | + | 0.911359i | \(0.364966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6923.99 | 0.477069 | ||||||||
\(596\) | −951.707 | + | 1648.41i | −0.0654085 | + | 0.113291i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15649.2 | + | 27105.1i | 1.07014 | + | 1.85353i | ||||
\(599\) | 2453.71 | + | 4249.95i | 0.167372 | + | 0.289897i | 0.937495 | − | 0.347998i | \(-0.113139\pi\) |
−0.770123 | + | 0.637895i | \(0.779805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5632.34 | + | 9755.49i | −0.382276 | + | 0.662121i | −0.991387 | − | 0.130964i | \(-0.958193\pi\) |
0.609111 | + | 0.793085i | \(0.291526\pi\) | |||||||
\(602\) | −40913.7 | −2.76996 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2947.94 | −0.198592 | ||||||||
\(605\) | −3262.99 | + | 5651.66i | −0.219271 | + | 0.379789i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2511.33 | − | 4349.75i | −0.167927 | − | 0.290858i | 0.769764 | − | 0.638329i | \(-0.220374\pi\) |
−0.937691 | + | 0.347471i | \(0.887041\pi\) | |||||||
\(608\) | 3599.75 | + | 6234.96i | 0.240114 | + | 0.415890i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5123.29 | + | 8873.80i | −0.340059 | + | 0.588999i | ||||
\(611\) | 19205.8 | 1.27166 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19450.0 | 1.28153 | 0.640766 | − | 0.767736i | \(-0.278617\pi\) | ||||
0.640766 | + | 0.767736i | \(0.278617\pi\) | |||||||
\(614\) | 12777.6 | − | 22131.5i | 0.839843 | − | 1.45465i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −302.618 | − | 524.149i | −0.0197935 | − | 0.0342834i | ||||
\(617\) | −1009.02 | − | 1747.68i | −0.0658375 | − | 0.114034i | 0.831228 | − | 0.555932i | \(-0.187639\pi\) |
−0.897065 | + | 0.441898i | \(0.854305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4548.76 | + | 7878.69i | −0.295364 | + | 0.511585i | −0.975069 | − | 0.221900i | \(-0.928774\pi\) |
0.679706 | + | 0.733485i | \(0.262108\pi\) | |||||||
\(620\) | −6509.88 | −0.421682 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8613.93 | −0.555285 | ||||||||
\(623\) | −5924.95 | + | 10262.3i | −0.381025 | + | 0.659954i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 2530.01 | + | 4382.10i | 0.161533 | + | 0.279783i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1518.86 | − | 2630.74i | 0.0965113 | − | 0.167163i | ||||
\(629\) | −19243.6 | −1.21986 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3118.35 | 0.196735 | 0.0983674 | − | 0.995150i | \(-0.468638\pi\) | ||||
0.0983674 | + | 0.995150i | \(0.468638\pi\) | |||||||
\(632\) | −178.986 | + | 310.013i | −0.0112653 | + | 0.0195121i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1810.52 | − | 3135.91i | −0.113415 | − | 0.196440i | ||||
\(635\) | −6008.58 | − | 10407.2i | −0.375501 | − | 0.650387i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14483.4 | − | 25085.9i | 0.900867 | − | 1.56035i | ||||
\(638\) | −3284.70 | −0.203828 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2864.91 | 0.176946 | ||||||||
\(641\) | −5227.12 | + | 9053.64i | −0.322089 | + | 0.557874i | −0.980919 | − | 0.194418i | \(-0.937718\pi\) |
0.658830 | + | 0.752292i | \(0.271052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8062.80 | − | 13965.2i | −0.494504 | − | 0.856506i | 0.505476 | − | 0.862841i | \(-0.331317\pi\) |
−0.999980 | + | 0.00633487i | \(0.997984\pi\) | |||||||
\(644\) | −8828.49 | − | 15291.4i | −0.540204 | − | 0.935661i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3023.67 | + | 5237.15i | −0.184156 | + | 0.318967i | ||||
\(647\) | −13627.3 | −0.828045 | −0.414022 | − | 0.910267i | \(-0.635877\pi\) | ||||
−0.414022 | + | 0.910267i | \(0.635877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 772.220 | 0.0467061 | ||||||||
\(650\) | −3981.24 | + | 6895.72i | −0.240242 | + | 0.416111i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8645.39 | + | 14974.3i | 0.519294 | + | 0.899443i | ||||
\(653\) | −1327.33 | − | 2299.01i | −0.0795446 | − | 0.137775i | 0.823509 | − | 0.567303i | \(-0.192013\pi\) |
−0.903054 | + | 0.429528i | \(0.858680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4087.02 | − | 7078.92i | 0.243806 | − | 0.422285i | ||||
\(656\) | −8045.68 | −0.478858 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23535.9 | −1.39441 | ||||||||
\(659\) | −9128.39 | + | 15810.8i | −0.539593 | + | 0.934602i | 0.459333 | + | 0.888264i | \(0.348088\pi\) |
−0.998926 | + | 0.0463379i | \(0.985245\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3519.17 | + | 6095.38i | 0.207080 | + | 0.358673i | 0.950793 | − | 0.309825i | \(-0.100271\pi\) |
−0.743713 | + | 0.668499i | \(0.766937\pi\) | |||||||
\(662\) | −4317.05 | − | 7477.35i | −0.253455 | − | 0.438996i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3229.52 | + | 5593.69i | −0.188749 | + | 0.326923i | ||||
\(665\) | −3930.95 | −0.229226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16502.7 | 0.958003 | ||||||||
\(668\) | 7389.39 | − | 12798.8i | 0.428000 | − | 0.741318i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5904.46 | − | 10226.8i | −0.340461 | − | 0.589696i | ||||
\(671\) | 1351.90 | + | 2341.56i | 0.0777789 | + | 0.134717i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5021.54 | − | 8697.56i | 0.287617 | − | 0.498167i | −0.685624 | − | 0.727956i | \(-0.740470\pi\) |
0.973240 | + | 0.229789i | \(0.0738038\pi\) | |||||||
\(674\) | 12027.0 | 0.687331 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31705.9 | 1.80393 | ||||||||
\(677\) | 12999.6 | − | 22516.0i | 0.737984 | − | 1.27823i | −0.215417 | − | 0.976522i | \(-0.569111\pi\) |
0.953402 | − | 0.301704i | \(-0.0975555\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18915.2 | + | 32762.1i | 1.06907 | + | 1.85168i | ||||
\(680\) | 595.044 | + | 1030.65i | 0.0335572 | + | 0.0581228i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1865.70 | + | 3231.49i | −0.104753 | + | 0.181437i | ||||
\(683\) | 13619.4 | 0.763004 | 0.381502 | − | 0.924368i | \(-0.375407\pi\) | ||||
0.381502 | + | 0.924368i | \(0.375407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12631.9 | 0.704584 | ||||||||
\(686\) | −363.618 | + | 629.805i | −0.0202376 | + | 0.0350525i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14534.0 | − | 25173.6i | −0.805382 | − | 1.39496i | ||||
\(689\) | 16979.6 | + | 29409.6i | 0.938857 | + | 1.62615i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6861.47 | − | 11884.4i | 0.377746 | − | 0.654275i | −0.612988 | − | 0.790092i | \(-0.710033\pi\) |
0.990734 | + | 0.135817i | \(0.0433659\pi\) | |||||||
\(692\) | −9306.80 | −0.511259 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −41283.8 | −2.25808 | ||||||||
\(695\) | 4727.11 | − | 8187.60i | 0.257999 | − | 0.446868i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2937.91 | − | 5088.61i | −0.159657 | − | 0.276535i | ||||
\(698\) | −11746.5 | − | 20345.6i | −0.636982 | − | 1.10328i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2246.02 | − | 3890.23i | 0.121274 | − | 0.210053i | ||||
\(701\) | 11103.4 | 0.598244 | 0.299122 | − | 0.954215i | \(-0.403306\pi\) | ||||
0.299122 | + | 0.954215i | \(0.403306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10925.1 | 0.586129 | ||||||||
\(704\) | −894.410 | + | 1549.16i | −0.0478826 | + | 0.0829351i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19883.9 | + | 34440.0i | 1.05997 | + | 1.83593i | ||||
\(707\) | 24314.5 | + | 42114.0i | 1.29341 | + | 2.24026i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1531.80 | − | 2653.15i | 0.0811395 | − | 0.140538i | −0.822600 | − | 0.568620i | \(-0.807477\pi\) |
0.903740 | + | 0.428082i | \(0.140811\pi\) | |||||||
\(710\) | 7968.90 | 0.421222 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2036.75 | −0.107206 | ||||||||
\(713\) | 9373.50 | − | 16235.4i | 0.492343 | − | 0.852763i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1050.55 | + | 1819.60i | 0.0549486 | + | 0.0951737i | ||||
\(716\) | −4088.96 | − | 7082.29i | −0.213424 | − | 0.369662i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2160.65 | + | 3742.35i | −0.112305 | + | 0.194517i | ||||
\(719\) | 31506.0 | 1.63418 | 0.817089 | − | 0.576511i | \(-0.195586\pi\) | ||||
0.817089 | + | 0.576511i | \(0.195586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1257.25 | −0.0649411 | ||||||||
\(722\) | −11487.9 | + | 19897.7i | −0.592156 | + | 1.02564i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3747.21 | − | 6490.36i | −0.192354 | − | 0.333166i | ||||
\(725\) | 2099.20 | + | 3635.92i | 0.107534 | + | 0.186255i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7528.24 | + | 13039.3i | −0.384054 | + | 0.665200i | −0.991637 | − | 0.129055i | \(-0.958806\pi\) |
0.607584 | + | 0.794256i | \(0.292139\pi\) | |||||||
\(728\) | 9855.55 | 0.501746 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2203.98 | −0.111744 | ||||||||
\(731\) | 10614.3 | − | 18384.5i | 0.537049 | − | 0.930197i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10133.7 | − | 17552.1i | −0.510637 | − | 0.884449i | −0.999924 | − | 0.0123261i | \(-0.996076\pi\) |
0.489287 | − | 0.872123i | \(-0.337257\pi\) | |||||||
\(734\) | −7013.05 | − | 12147.0i | −0.352666 | − | 0.610835i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11846.2 | − | 20518.2i | 0.593283 | − | 1.02760i | ||||
\(737\) | −3116.06 | −0.155742 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22434.4 | −1.11673 | −0.558365 | − | 0.829595i | \(-0.688571\pi\) | ||||
−0.558365 | + | 0.829595i | \(0.688571\pi\) | |||||||
\(740\) | −6242.28 | + | 10811.9i | −0.310096 | + | 0.537101i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20807.8 | − | 36040.2i | −1.02949 | − | 1.78312i | ||||
\(743\) | −18623.1 | − | 32256.2i | −0.919538 | − | 1.59269i | −0.800118 | − | 0.599843i | \(-0.795230\pi\) |
−0.119420 | − | 0.992844i | \(-0.538103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 697.253 | − | 1207.68i | 0.0342891 | − | 0.0593904i | ||||
\(746\) | −36709.9 | −1.80167 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1823.51 | −0.0891365 | ||||||||
\(749\) | 24213.9 | − | 41939.7i | 1.18125 | − | 2.04598i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11115.5 | + | 19252.6i | 0.540093 | + | 0.935468i | 0.998898 | + | 0.0469310i | \(0.0149441\pi\) |
−0.458806 | + | 0.888537i | \(0.651723\pi\) | |||||||
\(752\) | −8360.78 | − | 14481.3i | −0.405434 | − | 0.702232i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26743.7 | − | 46321.5i | 1.29171 | − | 2.23731i | ||||
\(755\) | 2159.76 | 0.104108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11212.1 | −0.538324 | −0.269162 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269162 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(758\) | 20843.2 | − | 36101.5i | 0.998760 | − | 1.72990i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −337.824 | − | 585.128i | −0.0161239 | − | 0.0279274i | ||||
\(761\) | 6841.43 | + | 11849.7i | 0.325889 | + | 0.564456i | 0.981692 | − | 0.190476i | \(-0.0610031\pi\) |
−0.655803 | + | 0.754932i | \(0.727670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7360.81 | − | 12749.3i | 0.349252 | − | 0.604922i | ||||
\(764\) | 8531.05 | 0.403982 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25695.8 | −1.21205 | ||||||||
\(767\) | −6287.35 | + | 10890.0i | −0.295988 | + | 0.512667i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6837.13 | − | 11842.3i | −0.320616 | − | 0.555322i | 0.660000 | − | 0.751266i | \(-0.270556\pi\) |
−0.980615 | + | 0.195944i | \(0.937223\pi\) | |||||||
\(770\) | −1287.40 | − | 2229.84i | −0.0602528 | − | 0.104361i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11061.2 | + | 19158.5i | −0.515674 | + | 0.893173i | ||||
\(773\) | −28378.8 | −1.32046 | −0.660230 | − | 0.751064i | \(-0.729541\pi\) | ||||
−0.660230 | + | 0.751064i | \(0.729541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4769.35 | 0.221058 | ||||||||
\(776\) | −3251.12 | + | 5631.11i | −0.150398 | + | 0.260496i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2431.46 | + | 4211.41i | 0.112046 | + | 0.194070i | ||||
\(779\) | 1667.93 | + | 2888.95i | 0.0767137 | + | 0.132872i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1051.39 | − | 1821.07i | 0.0481713 | − | 0.0834352i | ||||
\(782\) | 19900.8 | 0.910040 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25219.9 | −1.14887 | ||||||||
\(785\) | −1112.77 | + | 1927.37i | −0.0505941 | + | 0.0876316i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14221.5 | − | 24632.4i | −0.644144 | − | 1.11569i | −0.984498 | − | 0.175393i | \(-0.943880\pi\) |
0.340354 | − | 0.940297i | \(-0.389453\pi\) | |||||||
\(788\) | 2436.90 | + | 4220.83i | 0.110166 | + | 0.190813i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −761.445 | + | 1318.86i | −0.0342924 | + | 0.0593962i | ||||
\(791\) | 62261.9 | 2.79871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44028.3 | −1.97162 | ||||||||
\(794\) | −1709.86 | + | 2961.56i | −0.0764239 | + | 0.132370i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2275.79 | + | 3941.78i | 0.101336 | + | 0.175518i | ||||
\(797\) | 14207.2 | + | 24607.6i | 0.631425 | + | 1.09366i | 0.987261 | + | 0.159112i | \(0.0508630\pi\) |
−0.355836 | + | 0.934549i | \(0.615804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6105.94 | − | 10575.8i | 0.270354 | − | 0.468266i | ||||
\(800\) | 6027.49 | 0.266380 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −47637.3 | −2.09742 | ||||||||
\(803\) | −290.786 | + | 503.656i | −0.0127791 | + | 0.0221340i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6468.05 | + | 11203.0i | 0.283191 | + | 0.490501i | ||||
\(806\) | −30380.7 | − | 52621.0i | −1.32769 | − | 2.29962i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4179.16 | + | 7238.51i | −0.181958 | + | 0.315161i | ||||
\(809\) | 7610.15 | 0.330728 | 0.165364 | − | 0.986233i | \(-0.447120\pi\) | ||||
0.165364 | + | 0.986233i | \(0.447120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25751.6 | 1.11499 | 0.557497 | − | 0.830179i | \(-0.311762\pi\) | ||||
0.557497 | + | 0.830179i | \(0.311762\pi\) | |||||||
\(812\) | −15087.5 | + | 26132.3i | −0.652054 | + | 1.12939i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3578.02 | + | 6197.30i | 0.154066 | + | 0.266849i | ||||
\(815\) | −6333.90 | − | 10970.6i | −0.272229 | − | 0.471515i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6026.02 | + | 10437.4i | −0.258046 | + | 0.446949i | ||||
\(818\) | 48695.6 | 2.08142 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3812.03 | −0.162344 | ||||||||
\(821\) | −10566.5 | + | 18301.8i | −0.449178 | + | 0.777998i | −0.998333 | − | 0.0577220i | \(-0.981616\pi\) |
0.549155 | + | 0.835720i | \(0.314950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1563.62 | + | 2708.28i | 0.0662266 | + | 0.114708i | 0.897237 | − | 0.441548i | \(-0.145571\pi\) |
−0.831011 | + | 0.556256i | \(0.812237\pi\) | |||||||
\(824\) | −108.048 | − | 187.144i | −0.00456799 | − | 0.00791198i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7704.88 | − | 13345.2i | 0.324560 | − | 0.562155i | ||||
\(827\) | −493.085 | −0.0207331 | −0.0103665 | − | 0.999946i | \(-0.503300\pi\) | ||||
−0.0103665 | + | 0.999946i | \(0.503300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2832.98 | 0.118689 | 0.0593447 | − | 0.998238i | \(-0.481099\pi\) | ||||
0.0593447 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(830\) | −13739.0 | + | 23796.7i | −0.574565 | + | 0.995176i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14564.4 | − | 25226.3i | −0.606888 | − | 1.05116i | ||||
\(833\) | −9209.15 | − | 15950.7i | −0.383047 | − | 0.663457i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5413.71 | + | 9376.83i | −0.224370 | + | 0.388621i | ||||
\(836\) | 1035.26 | 0.0428291 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54874.3 | 2.26205 | ||||||||
\(839\) | 5123.05 | − | 8873.38i | 0.210807 | − | 0.365129i | −0.741160 | − | 0.671328i | \(-0.765724\pi\) |
0.951967 | + | 0.306199i | \(0.0990574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1906.72 | − | 3302.54i | −0.0781796 | − | 0.135411i | ||||
\(842\) | 4900.81 | + | 8488.45i | 0.200586 | + | 0.347424i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16922.5 | − | 29310.7i | 0.690164 | − | 1.19540i | ||||
\(845\) | −23228.8 | −0.945676 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34363.4 | 1.39403 | ||||||||
\(848\) | 14783.3 | − | 25605.5i | 0.598658 | − | 1.03691i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2531.44 | + | 4384.59i | 0.102150 | + | 0.176930i | ||||
\(851\) | −17976.4 | − | 31136.0i | −0.724116 | − | 1.25420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12166.2 | − | 21072.5i | 0.488350 | − | 0.845846i | −0.511561 | − | 0.859247i | \(-0.670932\pi\) |
0.999910 | + | 0.0134008i | \(0.00426574\pi\) | |||||||
\(854\) | 53954.8 | 2.16194 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8323.71 | 0.332358 | ||||||||
\(857\) | 12796.7 | − | 22164.5i | 0.510065 | − | 0.883459i | −0.489867 | − | 0.871797i | \(-0.662955\pi\) |
0.999932 | − | 0.0116615i | \(-0.00371205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15525.0 | − | 26890.1i | −0.616654 | − | 1.06808i | −0.990092 | − | 0.140421i | \(-0.955154\pi\) |
0.373438 | − | 0.927655i | \(-0.378179\pi\) | |||||||
\(860\) | −6886.17 | − | 11927.2i | −0.273042 | − | 0.472923i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5907.12 | + | 10231.4i | −0.233408 | + | 0.404274i | ||||
\(863\) | 13274.3 | 0.523596 | 0.261798 | − | 0.965123i | \(-0.415685\pi\) | ||||
0.261798 | + | 0.965123i | \(0.415685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6818.47 | 0.268017 | ||||||||
\(866\) | −26917.2 | + | 46622.0i | −1.05622 | + | 1.82942i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17139.3 | + | 29686.2i | 0.670215 | + | 1.16085i | ||||
\(869\) | 200.925 | + | 348.013i | 0.00784342 | + | 0.0135852i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25370.7 | − | 43943.4i | 0.986974 | − | 1.70949i | ||||
\(872\) | 2530.34 | 0.0982661 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11298.3 | −0.437264 | ||||||||
\(875\) | −1645.51 | + | 2850.11i | −0.0635754 | + | 0.110116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25547.1 | − | 44248.9i | −0.983653 | − | 1.70374i | −0.647775 | − | 0.761832i | \(-0.724300\pi\) |
−0.335878 | − | 0.941905i | \(-0.609033\pi\) | |||||||
\(878\) | 14809.0 | + | 25650.0i | 0.569227 | + | 0.985929i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 914.659 | − | 1584.24i | 0.0350377 | − | 0.0606870i | ||||
\(881\) | 13020.2 | 0.497913 | 0.248956 | − | 0.968515i | \(-0.419912\pi\) | ||||
0.248956 | + | 0.968515i | \(0.419912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4577.13 | −0.174443 | −0.0872213 | − | 0.996189i | \(-0.527799\pi\) | ||||
−0.0872213 | + | 0.996189i | \(0.527799\pi\) | |||||||
\(884\) | 14846.9 | − | 25715.5i | 0.564880 | − | 0.978401i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −68.9678 | − | 119.456i | −0.00261515 | − | 0.00452957i | ||||
\(887\) | 7499.90 | + | 12990.2i | 0.283903 | + | 0.491734i | 0.972343 | − | 0.233559i | \(-0.0750373\pi\) |
−0.688440 | + | 0.725294i | \(0.741704\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31639.0 | + | 54800.4i | −1.19363 | + | 2.06743i | ||||
\(890\) | −8664.76 | −0.326341 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7669.39 | 0.287881 | ||||||||
\(893\) | −3466.51 | + | 6004.18i | −0.129902 | + | 0.224997i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2995.71 | + | 5188.73i | 0.111883 | + | 0.193788i | ||||
\(896\) | −7542.80 | − | 13064.5i | −0.281236 | − | 0.487115i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5009.53 | + | 8676.76i | −0.186158 | + | 0.322436i | ||||
\(899\) | −32037.8 | −1.18857 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21592.8 | 0.798400 | ||||||||
\(902\) | −1092.51 | + | 1892.28i | −0.0403288 | + | 0.0698515i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5350.76 | + | 9267.78i | 0.196862 | + | 0.340975i | ||||
\(905\) | 2745.33 | + | 4755.06i | 0.100838 | + | 0.174656i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18805.5 | − | 32572.1i | 0.688453 | − | 1.19244i | −0.283885 | − | 0.958858i | \(-0.591623\pi\) |
0.972338 | − | 0.233578i | \(-0.0750434\pi\) | |||||||
\(908\) | 8361.00 | 0.305583 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41927.6 | 1.52735 | ||||||||
\(911\) | −10459.7 | + | 18116.7i | −0.380400 | + | 0.658872i | −0.991119 | − | 0.132975i | \(-0.957547\pi\) |
0.610720 | + | 0.791847i | \(0.290880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3625.38 | + | 6279.34i | 0.131416 | + | 0.227618i | ||||
\(914\) | 15693.1 | + | 27181.3i | 0.567923 | + | 0.983672i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12210.0 | − | 21148.3i | 0.440425 | − | 0.762838i | ||||
\(917\) | −43041.5 | −1.55001 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18211.5 | 0.653689 | 0.326845 | − | 0.945078i | \(-0.394015\pi\) | ||||
0.326845 | + | 0.945078i | \(0.394015\pi\) | |||||||
\(920\) | −1111.72 | + | 1925.56i | −0.0398396 | + | 0.0690041i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12989.5 | − | 22498.5i | −0.463978 | − | 0.803633i | ||||
\(923\) | 17120.7 | + | 29653.9i | 0.610547 | + | 1.05750i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4573.30 | − | 7921.19i | 0.162561 | − | 0.281565i | ||||
\(926\) | −3228.68 | −0.114580 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40489.3 | −1.43225 | ||||||||
\(929\) | 5169.25 | − | 8953.40i | 0.182559 | − | 0.316202i | −0.760192 | − | 0.649698i | \(-0.774895\pi\) |
0.942751 | + | 0.333496i | \(0.108229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5228.29 | + | 9055.67i | 0.184050 | + | 0.318784i | ||||
\(932\) | 1798.51 | + | 3115.12i | 0.0632106 | + | 0.109484i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13963.9 | − | 24186.3i | 0.489202 | − | 0.847322i | ||||
\(935\) | 1335.96 | 0.0467280 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4046.02 | −0.141065 | −0.0705324 | − | 0.997509i | \(-0.522470\pi\) | ||||
−0.0705324 | + | 0.997509i | \(0.522470\pi\) | |||||||
\(938\) | −31090.7 | + | 53850.7i | −1.08225 | + | 1.87451i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3961.32 | − | 6861.21i | −0.137451 | − | 0.238072i | ||||
\(941\) | −3613.06 | − | 6258.00i | −0.125167 | − | 0.216796i | 0.796631 | − | 0.604466i | \(-0.206613\pi\) |
−0.921798 | + | 0.387670i | \(0.873280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5488.90 | − | 9507.05i | 0.189547 | − | 0.328306i | ||||
\(944\) | 10948.2 | 0.377471 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7894.18 | −0.271313 | ||||||||
\(947\) | −23835.6 | + | 41284.5i | −0.817903 | + | 1.41665i | 0.0893215 | + | 0.996003i | \(0.471530\pi\) |
−0.907225 | + | 0.420647i | \(0.861803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4735.11 | − | 8201.45i | −0.161969 | − | 0.280538i | ||||
\(950\) | −1437.17 | − | 2489.26i | −0.0490822 | − | 0.0850128i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3133.29 | − | 5427.02i | 0.106671 | − | 0.184759i | ||||
\(953\) | −50498.6 | −1.71649 | −0.858243 | − | 0.513243i | \(-0.828444\pi\) | ||||
−0.858243 | + | 0.513243i | \(0.828444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6250.13 | −0.211780 | ||||||||
\(956\) | 328.741 | − | 569.396i | 0.0111216 | − | 0.0192632i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19928.7 | − | 34517.6i | −0.672097 | − | 1.16411i | ||||
\(959\) | −33257.5 | − | 57603.7i | −1.11986 | − | 1.93965i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3301.89 | + | 5719.04i | −0.110835 | + | 0.191972i | ||||
\(962\) | −116528. | −3.90540 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6305.65 | 0.210676 | ||||||||
\(965\) | 8103.78 | − | 14036.2i | 0.270332 | − | 0.468228i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11832.7 | − | 20494.8i | −0.393498 | − | 0.681559i | 0.599410 | − | 0.800442i | \(-0.295402\pi\) |
−0.992908 | + | 0.118883i | \(0.962069\pi\) | |||||||
\(968\) | 2953.17 | + | 5115.05i | 0.0980564 | + | 0.169839i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13831.0 | + | 23955.9i | −0.457820 | + | 0.792968i | ||||
\(971\) | 29787.4 | 0.984472 | 0.492236 | − | 0.870462i | \(-0.336180\pi\) | ||||
0.492236 | + | 0.870462i | \(0.336180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49782.5 | −1.64024 | ||||||||
\(974\) | 10015.9 | − | 17348.1i | 0.329498 | − | 0.570708i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19166.6 | + | 33197.6i | 0.628595 | + | 1.08876i | ||||
\(977\) | −5978.62 | − | 10355.3i | −0.195776 | − | 0.339093i | 0.751379 | − | 0.659871i | \(-0.229389\pi\) |
−0.947155 | + | 0.320778i | \(0.896056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1143.20 | + | 1980.09i | −0.0373207 | + | 0.0646413i | ||||
\(980\) | −11949.2 | −0.389491 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9473.69 | 0.307859 | ||||||||
\(983\) | −7968.50 | + | 13801.8i | −0.258551 | + | 0.447823i | −0.965854 | − | 0.259087i | \(-0.916578\pi\) |
0.707303 | + | 0.706911i | \(0.249912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1785.35 | − | 3092.32i | −0.0577523 | − | 0.100030i | ||||
\(986\) | −17004.8 | − | 29453.2i | −0.549233 | − | 0.951299i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8428.98 | + | 14599.4i | −0.271419 | + | 0.470111i | ||||
\(989\) | 39661.3 | 1.27518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42686.5 | 1.36830 | 0.684148 | − | 0.729343i | \(-0.260174\pi\) | ||||
0.684148 | + | 0.729343i | \(0.260174\pi\) | |||||||
\(992\) | −22997.8 | + | 39833.3i | −0.736069 | + | 1.27491i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20980.7 | − | 36339.6i | −0.669484 | − | 1.15958i | ||||
\(995\) | −1667.32 | − | 2887.88i | −0.0531232 | − | 0.0920120i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20684.7 | + | 35827.0i | −0.657063 | + | 1.13807i | 0.324309 | + | 0.945951i | \(0.394868\pi\) |
−0.981372 | + | 0.192116i | \(0.938465\pi\) | |||||||
\(998\) | 49500.5 | 1.57005 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.e.s.136.3 | 6 | ||
3.2 | odd | 2 | 405.4.e.u.136.1 | 6 | |||
9.2 | odd | 6 | 405.4.a.g.1.3 | ✓ | 3 | ||
9.4 | even | 3 | inner | 405.4.e.s.271.3 | 6 | ||
9.5 | odd | 6 | 405.4.e.u.271.1 | 6 | |||
9.7 | even | 3 | 405.4.a.i.1.1 | yes | 3 | ||
45.29 | odd | 6 | 2025.4.a.r.1.1 | 3 | |||
45.34 | even | 6 | 2025.4.a.p.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.g.1.3 | ✓ | 3 | 9.2 | odd | 6 | ||
405.4.a.i.1.1 | yes | 3 | 9.7 | even | 3 | ||
405.4.e.s.136.3 | 6 | 1.1 | even | 1 | trivial | ||
405.4.e.s.271.3 | 6 | 9.4 | even | 3 | inner | ||
405.4.e.u.136.1 | 6 | 3.2 | odd | 2 | |||
405.4.e.u.271.1 | 6 | 9.5 | odd | 6 | |||
2025.4.a.p.1.3 | 3 | 45.34 | even | 6 | |||
2025.4.a.r.1.1 | 3 | 45.29 | odd | 6 |