Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 124.3 | ||
Character | \(\chi\) | \(=\) | 225.124 |
Dual form | 225.4.k.d.49.3 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.69081 | − | 2.13089i | −1.30490 | − | 0.753383i | −0.323658 | − | 0.946174i | \(-0.604913\pi\) |
−0.981240 | + | 0.192791i | \(0.938246\pi\) | |||||||
\(3\) | 2.76977 | + | 4.39640i | 0.533043 | + | 0.846088i | ||||
\(4\) | 5.08138 | + | 8.80120i | 0.635172 | + | 1.10015i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.854448 | − | 22.1284i | −0.0581378 | − | 1.50564i | ||||
\(7\) | 26.6423 | + | 15.3820i | 1.43855 | + | 0.830548i | 0.997749 | − | 0.0670561i | \(-0.0213606\pi\) |
0.440802 | + | 0.897604i | \(0.354694\pi\) | |||||||
\(8\) | − | 9.21718i | − | 0.407346i | ||||||
\(9\) | −11.6567 | + | 24.3541i | −0.431731 | + | 0.902003i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.3573 | + | 35.2599i | −0.557996 | + | 0.966478i | 0.439667 | + | 0.898161i | \(0.355096\pi\) |
−0.997664 | + | 0.0683175i | \(0.978237\pi\) | |||||||
\(12\) | −24.6194 | + | 46.7171i | −0.592250 | + | 1.12384i | ||||
\(13\) | 54.7482 | − | 31.6089i | 1.16803 | − | 0.674364i | 0.214817 | − | 0.976654i | \(-0.431085\pi\) |
0.953216 | + | 0.302290i | \(0.0977512\pi\) | |||||||
\(14\) | −65.5545 | − | 113.544i | −1.25144 | − | 2.16756i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 21.0102 | − | 36.3908i | 0.328285 | − | 0.568606i | ||||
\(17\) | 6.58990i | 0.0940168i | 0.998894 | + | 0.0470084i | \(0.0149687\pi\) | ||||
−0.998894 | + | 0.0470084i | \(0.985031\pi\) | |||||||
\(18\) | 94.9186 | − | 65.0470i | 1.24292 | − | 0.851763i | ||||
\(19\) | −75.3803 | −0.910180 | −0.455090 | − | 0.890445i | \(-0.650393\pi\) | ||||
−0.455090 | + | 0.890445i | \(0.650393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.16789 | + | 159.735i | 0.0640926 | + | 1.65986i | ||||
\(22\) | 150.270 | − | 86.7584i | 1.45626 | − | 0.840770i | ||||
\(23\) | −54.0077 | + | 31.1814i | −0.489626 | + | 0.282686i | −0.724419 | − | 0.689360i | \(-0.757892\pi\) |
0.234793 | + | 0.972045i | \(0.424559\pi\) | |||||||
\(24\) | 40.5225 | − | 25.5295i | 0.344651 | − | 0.217133i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −269.420 | −2.03222 | ||||||||
\(27\) | −139.357 | + | 16.2075i | −0.993305 | + | 0.115524i | ||||
\(28\) | 312.646i | 2.11016i | ||||||||
\(29\) | 24.8042 | − | 42.9621i | 0.158828 | − | 0.275099i | −0.775618 | − | 0.631202i | \(-0.782562\pi\) |
0.934446 | + | 0.356104i | \(0.115895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.5021 | − | 89.2043i | −0.298389 | − | 0.516824i | 0.677379 | − | 0.735634i | \(-0.263116\pi\) |
−0.975767 | + | 0.218810i | \(0.929783\pi\) | |||||||
\(32\) | −218.948 | + | 126.410i | −1.20953 | + | 0.698321i | ||||
\(33\) | −211.402 | + | 8.16291i | −1.11516 | + | 0.0430600i | ||||
\(34\) | 14.0423 | − | 24.3221i | 0.0708306 | − | 0.122682i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −273.577 | + | 21.1590i | −1.26656 | + | 0.0979582i | ||||
\(37\) | 282.029i | 1.25312i | 0.779374 | + | 0.626559i | \(0.215537\pi\) | ||||
−0.779374 | + | 0.626559i | \(0.784463\pi\) | |||||||
\(38\) | 278.214 | + | 160.627i | 1.18769 | + | 0.685714i | ||||
\(39\) | 290.606 | + | 153.146i | 1.19318 | + | 0.628794i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 78.7700 | + | 136.434i | 0.300044 | + | 0.519692i | 0.976146 | − | 0.217117i | \(-0.0696653\pi\) |
−0.676102 | + | 0.736808i | \(0.736332\pi\) | |||||||
\(42\) | 317.613 | − | 602.695i | 1.16688 | − | 2.21423i | ||||
\(43\) | 292.555 | + | 168.907i | 1.03754 | + | 0.599025i | 0.919136 | − | 0.393940i | \(-0.128888\pi\) |
0.118406 | + | 0.992965i | \(0.462222\pi\) | |||||||
\(44\) | −413.773 | −1.41770 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 265.776 | 0.851882 | ||||||||
\(47\) | 38.5518 | + | 22.2579i | 0.119646 | + | 0.0690777i | 0.558629 | − | 0.829418i | \(-0.311328\pi\) |
−0.438983 | + | 0.898496i | \(0.644661\pi\) | |||||||
\(48\) | 218.182 | − | 8.42472i | 0.656081 | − | 0.0253334i | ||||
\(49\) | 301.710 | + | 522.577i | 0.879620 | + | 1.52355i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28.9719 | + | 18.2525i | −0.0795465 | + | 0.0501150i | ||||
\(52\) | 556.393 | + | 321.234i | 1.48380 | + | 0.856675i | ||||
\(53\) | 26.2752i | 0.0680978i | 0.999420 | + | 0.0340489i | \(0.0108402\pi\) | ||||
−0.999420 | + | 0.0340489i | \(0.989160\pi\) | |||||||
\(54\) | 548.876 | + | 237.135i | 1.38319 | + | 0.597592i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 141.778 | − | 245.567i | 0.338320 | − | 0.585988i | ||||
\(57\) | −208.786 | − | 331.402i | −0.485165 | − | 0.770093i | ||||
\(58\) | −183.095 | + | 105.710i | −0.414509 | + | 0.239317i | ||||
\(59\) | −212.963 | − | 368.863i | −0.469923 | − | 0.813930i | 0.529486 | − | 0.848319i | \(-0.322385\pi\) |
−0.999409 | + | 0.0343889i | \(0.989052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −425.297 | + | 736.637i | −0.892684 | + | 1.54617i | −0.0560400 | + | 0.998429i | \(0.517847\pi\) |
−0.836644 | + | 0.547746i | \(0.815486\pi\) | |||||||
\(62\) | 438.981i | 0.899204i | ||||||||
\(63\) | −685.176 | + | 469.546i | −1.37022 | + | 0.939004i | ||||
\(64\) | 741.296 | 1.44784 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 797.638 | + | 420.346i | 1.48761 | + | 0.783955i | ||||
\(67\) | −83.4048 | + | 48.1538i | −0.152082 | + | 0.0878048i | −0.574110 | − | 0.818778i | \(-0.694652\pi\) |
0.422028 | + | 0.906583i | \(0.361319\pi\) | |||||||
\(68\) | −57.9990 | + | 33.4858i | −0.103433 | + | 0.0597168i | ||||
\(69\) | −286.675 | − | 151.075i | −0.500169 | − | 0.263583i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 952.164 | 1.59156 | 0.795782 | − | 0.605583i | \(-0.207060\pi\) | ||||
0.795782 | + | 0.605583i | \(0.207060\pi\) | |||||||
\(72\) | 224.476 | + | 107.442i | 0.367427 | + | 0.175864i | ||||
\(73\) | − | 50.8558i | − | 0.0815373i | −0.999169 | − | 0.0407686i | \(-0.987019\pi\) | ||
0.999169 | − | 0.0407686i | \(-0.0129807\pi\) | |||||||
\(74\) | 600.973 | − | 1040.92i | 0.944077 | − | 1.63519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −383.036 | − | 663.437i | −0.578121 | − | 1.00134i | ||||
\(77\) | −1084.73 | + | 626.271i | −1.60541 | + | 0.926886i | ||||
\(78\) | −746.233 | − | 1184.48i | −1.08326 | − | 1.71944i | ||||
\(79\) | −98.6395 | + | 170.849i | −0.140479 | + | 0.243316i | −0.927677 | − | 0.373384i | \(-0.878197\pi\) |
0.787198 | + | 0.616700i | \(0.211531\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −457.241 | − | 567.778i | −0.627217 | − | 0.778844i | ||||
\(82\) | − | 671.400i | − | 0.904192i | ||||||
\(83\) | 171.247 | + | 98.8693i | 0.226467 | + | 0.130751i | 0.608941 | − | 0.793215i | \(-0.291595\pi\) |
−0.382474 | + | 0.923966i | \(0.624928\pi\) | |||||||
\(84\) | −1374.52 | + | 865.959i | −1.78539 | + | 1.12481i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −719.844 | − | 1246.81i | −0.902590 | − | 1.56333i | ||||
\(87\) | 257.581 | − | 9.94603i | 0.317420 | − | 0.0122566i | ||||
\(88\) | 324.997 | + | 187.637i | 0.393691 | + | 0.227298i | ||||
\(89\) | −1364.54 | −1.62519 | −0.812593 | − | 0.582832i | \(-0.801944\pi\) | ||||
−0.812593 | + | 0.582832i | \(0.801944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1944.83 | 2.24037 | ||||||||
\(92\) | −548.868 | − | 316.889i | −0.621993 | − | 0.359108i | ||||
\(93\) | 249.529 | − | 473.499i | 0.278225 | − | 0.527953i | ||||
\(94\) | −94.8583 | − | 164.299i | −0.104084 | − | 0.180279i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1162.18 | − | 612.458i | −1.23557 | − | 0.651132i | ||||
\(97\) | −1239.42 | − | 715.579i | −1.29736 | − | 0.749031i | −0.317413 | − | 0.948288i | \(-0.602814\pi\) |
−0.979947 | + | 0.199256i | \(0.936147\pi\) | |||||||
\(98\) | − | 2571.64i | − | 2.65076i | ||||||
\(99\) | −621.422 | − | 906.799i | −0.630862 | − | 0.920573i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −553.808 | + | 959.224i | −0.545604 | + | 0.945013i | 0.452965 | + | 0.891528i | \(0.350366\pi\) |
−0.998569 | + | 0.0534851i | \(0.982967\pi\) | |||||||
\(102\) | 145.824 | − | 5.63073i | 0.141556 | − | 0.00546593i | ||||
\(103\) | 458.018 | − | 264.437i | 0.438154 | − | 0.252969i | −0.264660 | − | 0.964342i | \(-0.585260\pi\) |
0.702814 | + | 0.711373i | \(0.251926\pi\) | |||||||
\(104\) | −291.345 | − | 504.624i | −0.274699 | − | 0.475793i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 55.9896 | − | 96.9769i | 0.0513037 | − | 0.0888607i | ||||
\(107\) | − | 490.910i | − | 0.443533i | −0.975100 | − | 0.221766i | \(-0.928818\pi\) | ||
0.975100 | − | 0.221766i | \(-0.0711823\pi\) | |||||||
\(108\) | −850.770 | − | 1144.15i | −0.758013 | − | 1.01941i | ||||
\(109\) | 351.634 | 0.308994 | 0.154497 | − | 0.987993i | \(-0.450624\pi\) | ||||
0.154497 | + | 0.987993i | \(0.450624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1239.91 | + | 781.157i | −1.06025 | + | 0.667965i | ||||
\(112\) | 1119.52 | − | 646.357i | 0.944509 | − | 0.545313i | ||||
\(113\) | 1526.33 | − | 881.226i | 1.27066 | − | 0.733618i | 0.295550 | − | 0.955327i | \(-0.404497\pi\) |
0.975113 | + | 0.221710i | \(0.0711637\pi\) | |||||||
\(114\) | 64.4085 | + | 1668.04i | 0.0529159 | + | 1.37041i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 504.158 | 0.403533 | ||||||||
\(117\) | 131.620 | + | 1701.80i | 0.104002 | + | 1.34471i | ||||
\(118\) | 1815.20i | 1.41613i | ||||||||
\(119\) | −101.366 | + | 175.570i | −0.0780854 | + | 0.135248i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −163.340 | − | 282.914i | −0.122720 | − | 0.212557i | ||||
\(122\) | 3139.38 | − | 1812.52i | 2.32972 | − | 1.34507i | ||||
\(123\) | −381.642 | + | 724.195i | −0.279769 | + | 0.530882i | ||||
\(124\) | 523.403 | − | 906.561i | 0.379056 | − | 0.656545i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3529.40 | − | 272.971i | 2.49543 | − | 0.193001i | ||||
\(127\) | 1506.12i | 1.05234i | 0.850380 | + | 0.526169i | \(0.176372\pi\) | ||||
−0.850380 | + | 0.526169i | \(0.823628\pi\) | |||||||
\(128\) | −984.399 | − | 568.343i | −0.679761 | − | 0.392460i | ||||
\(129\) | 67.7286 | + | 1754.03i | 0.0462262 | + | 1.19716i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −637.562 | − | 1104.29i | −0.425222 | − | 0.736506i | 0.571219 | − | 0.820798i | \(-0.306471\pi\) |
−0.996441 | + | 0.0842915i | \(0.973137\pi\) | |||||||
\(132\) | −1146.06 | − | 1819.11i | −0.755692 | − | 1.19950i | ||||
\(133\) | −2008.31 | − | 1159.50i | −1.30934 | − | 0.755948i | ||||
\(134\) | 410.441 | 0.264603 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 60.7403 | 0.0382973 | ||||||||
\(137\) | 1246.58 | + | 719.712i | 0.777389 | + | 0.448826i | 0.835504 | − | 0.549484i | \(-0.185176\pi\) |
−0.0581150 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(138\) | 736.140 | + | 1168.46i | 0.454090 | + | 0.720768i | ||||
\(139\) | −1269.75 | − | 2199.27i | −0.774811 | − | 1.34201i | −0.934901 | − | 0.354909i | \(-0.884512\pi\) |
0.160090 | − | 0.987102i | \(-0.448822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.92502 | + | 231.139i | 0.00533065 | + | 0.138052i | ||||
\(142\) | −3514.25 | − | 2028.96i | −2.07683 | − | 1.19906i | ||||
\(143\) | 2573.89i | 1.50517i | ||||||||
\(144\) | 641.353 | + | 935.882i | 0.371153 | + | 0.541598i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −108.368 | + | 187.699i | −0.0614288 | + | 0.106398i | ||||
\(147\) | −1461.79 | + | 2773.86i | −0.820180 | + | 1.55635i | ||||
\(148\) | −2482.20 | + | 1433.10i | −1.37862 | + | 0.795945i | ||||
\(149\) | 46.8796 | + | 81.1979i | 0.0257754 | + | 0.0446442i | 0.878625 | − | 0.477512i | \(-0.158461\pi\) |
−0.852850 | + | 0.522156i | \(0.825128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534.065 | − | 925.027i | 0.287825 | − | 0.498527i | −0.685465 | − | 0.728105i | \(-0.740401\pi\) |
0.973290 | + | 0.229578i | \(0.0737345\pi\) | |||||||
\(152\) | 694.794i | 0.370758i | ||||||||
\(153\) | −160.491 | − | 76.8166i | −0.0848034 | − | 0.0405899i | ||||
\(154\) | 5338.06 | 2.79320 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 128.809 | + | 3335.87i | 0.0661087 | + | 1.71207i | ||||
\(157\) | −157.370 | + | 90.8574i | −0.0799966 | + | 0.0461861i | −0.539465 | − | 0.842008i | \(-0.681373\pi\) |
0.459468 | + | 0.888194i | \(0.348040\pi\) | |||||||
\(158\) | 728.119 | − | 420.380i | 0.366621 | − | 0.211668i | ||||
\(159\) | −115.517 | + | 72.7764i | −0.0576167 | + | 0.0362990i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1918.52 | −0.939136 | ||||||||
\(162\) | 477.719 | + | 3069.89i | 0.231686 | + | 1.48885i | ||||
\(163\) | − | 1103.07i | − | 0.530056i | −0.964241 | − | 0.265028i | \(-0.914619\pi\) | ||
0.964241 | − | 0.265028i | \(-0.0853813\pi\) | |||||||
\(164\) | −800.520 | + | 1386.54i | −0.381159 | + | 0.660187i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −421.359 | − | 729.816i | −0.197011 | − | 0.341233i | ||||
\(167\) | 3500.22 | − | 2020.85i | 1.62189 | − | 0.936396i | 0.635470 | − | 0.772126i | \(-0.280806\pi\) |
0.986415 | − | 0.164270i | \(-0.0525269\pi\) | |||||||
\(168\) | 1472.31 | − | 56.8506i | 0.676137 | − | 0.0261078i | ||||
\(169\) | 899.745 | − | 1558.40i | 0.409534 | − | 0.709333i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 878.687 | − | 1835.82i | 0.392953 | − | 0.820985i | ||||
\(172\) | 3433.12i | 1.52194i | ||||||||
\(173\) | 2379.63 | + | 1373.88i | 1.04578 | + | 0.603780i | 0.921465 | − | 0.388463i | \(-0.126994\pi\) |
0.124314 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(174\) | −971.875 | − | 512.167i | −0.423435 | − | 0.223145i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 855.423 | + | 1481.64i | 0.366363 | + | 0.634560i | ||||
\(177\) | 1031.81 | − | 1957.94i | 0.438168 | − | 0.831456i | ||||
\(178\) | 5036.27 | + | 2907.69i | 2.12070 | + | 1.22439i | ||||
\(179\) | 2838.32 | 1.18517 | 0.592587 | − | 0.805506i | \(-0.298107\pi\) | ||||
0.592587 | + | 0.805506i | \(0.298107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3442.25 | 1.41359 | 0.706796 | − | 0.707417i | \(-0.250140\pi\) | ||||
0.706796 | + | 0.707417i | \(0.250140\pi\) | |||||||
\(182\) | −7177.99 | − | 4144.21i | −2.92345 | − | 1.68785i | ||||
\(183\) | −4416.53 | + | 170.537i | −1.78404 | + | 0.0688876i | ||||
\(184\) | 287.405 | + | 497.799i | 0.115151 | + | 0.199447i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1929.94 | + | 1215.88i | −0.760806 | + | 0.479314i | ||||
\(187\) | −232.359 | − | 134.153i | −0.0908652 | − | 0.0524610i | ||||
\(188\) | 452.403i | 0.175505i | ||||||||
\(189\) | −3962.10 | − | 1711.77i | −1.52487 | − | 0.658801i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 373.148 | − | 646.311i | 0.141361 | − | 0.244845i | −0.786648 | − | 0.617402i | \(-0.788185\pi\) |
0.928010 | + | 0.372557i | \(0.121519\pi\) | |||||||
\(192\) | 2053.22 | + | 3259.04i | 0.771763 | + | 1.22500i | ||||
\(193\) | 93.4506 | − | 53.9538i | 0.0348535 | − | 0.0201227i | −0.482472 | − | 0.875911i | \(-0.660261\pi\) |
0.517326 | + | 0.855789i | \(0.326928\pi\) | |||||||
\(194\) | 3049.64 | + | 5282.13i | 1.12861 | + | 1.95482i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3066.20 | + | 5310.82i | −1.11742 | + | 1.93543i | ||||
\(197\) | 3361.02i | 1.21555i | 0.794110 | + | 0.607774i | \(0.207937\pi\) | ||||
−0.794110 | + | 0.607774i | \(0.792063\pi\) | |||||||
\(198\) | 361.264 | + | 4671.00i | 0.129666 | + | 1.67653i | ||||
\(199\) | −1368.99 | −0.487663 | −0.243831 | − | 0.969818i | \(-0.578404\pi\) | ||||
−0.243831 | + | 0.969818i | \(0.578404\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −442.716 | − | 233.306i | −0.155357 | − | 0.0818714i | ||||
\(202\) | 4088.00 | − | 2360.21i | 1.42391 | − | 0.822097i | ||||
\(203\) | 1321.68 | − | 763.074i | 0.456965 | − | 0.263829i | ||||
\(204\) | −307.861 | − | 162.239i | −0.105660 | − | 0.0556815i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2253.94 | −0.762329 | ||||||||
\(207\) | −129.840 | − | 1678.78i | −0.0435966 | − | 0.563688i | ||||
\(208\) | − | 2656.44i | − | 0.885534i | ||||||
\(209\) | 1534.54 | − | 2657.90i | 0.507877 | − | 0.879669i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1251.27 | − | 2167.27i | −0.408252 | − | 0.707114i | 0.586442 | − | 0.809991i | \(-0.300528\pi\) |
−0.994694 | + | 0.102878i | \(0.967195\pi\) | |||||||
\(212\) | −231.254 | + | 133.514i | −0.0749178 | + | 0.0432538i | ||||
\(213\) | 2637.28 | + | 4186.10i | 0.848372 | + | 1.34660i | ||||
\(214\) | −1046.07 | + | 1811.85i | −0.334150 | + | 0.578765i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 149.388 | + | 1284.48i | 0.0470581 | + | 0.404619i | ||||
\(217\) | − | 3168.81i | − | 0.991305i | ||||||
\(218\) | −1297.81 | − | 749.292i | −0.403206 | − | 0.232791i | ||||
\(219\) | 223.583 | − | 140.859i | 0.0689877 | − | 0.0434629i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 208.299 | + | 360.785i | 0.0634015 | + | 0.109815i | ||||
\(222\) | 6240.85 | − | 240.979i | 1.88675 | − | 0.0728535i | ||||
\(223\) | −1623.39 | − | 937.263i | −0.487489 | − | 0.281452i | 0.236043 | − | 0.971743i | \(-0.424149\pi\) |
−0.723532 | + | 0.690291i | \(0.757483\pi\) | |||||||
\(224\) | −7777.72 | −2.31996 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7511.18 | −2.21078 | ||||||||
\(227\) | 4398.32 | + | 2539.37i | 1.28602 | + | 0.742484i | 0.977942 | − | 0.208877i | \(-0.0669808\pi\) |
0.308078 | + | 0.951361i | \(0.400314\pi\) | |||||||
\(228\) | 1855.82 | − | 3521.55i | 0.539055 | − | 1.02290i | ||||
\(229\) | 432.933 | + | 749.861i | 0.124930 | + | 0.216385i | 0.921706 | − | 0.387890i | \(-0.126796\pi\) |
−0.796776 | + | 0.604275i | \(0.793463\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5757.80 | − | 3034.30i | −1.63998 | − | 0.864252i | ||||
\(232\) | −395.990 | − | 228.625i | −0.112060 | − | 0.0646981i | ||||
\(233\) | 1142.10i | 0.321122i | 0.987026 | + | 0.160561i | \(0.0513304\pi\) | ||||
−0.987026 | + | 0.160561i | \(0.948670\pi\) | |||||||
\(234\) | 3140.56 | − | 6561.48i | 0.877371 | − | 1.83307i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2164.29 | − | 3748.66i | 0.596964 | − | 1.03397i | ||||
\(237\) | −1024.33 | + | 39.5527i | −0.280748 | + | 0.0108406i | ||||
\(238\) | 748.242 | − | 431.998i | 0.203787 | − | 0.117657i | ||||
\(239\) | −1574.68 | − | 2727.43i | −0.426183 | − | 0.738171i | 0.570347 | − | 0.821404i | \(-0.306809\pi\) |
−0.996530 | + | 0.0832330i | \(0.973475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2252.18 | + | 3900.90i | −0.601975 | + | 1.04265i | 0.390547 | + | 0.920583i | \(0.372286\pi\) |
−0.992522 | + | 0.122068i | \(0.961047\pi\) | |||||||
\(242\) | 1392.24i | 0.369821i | ||||||||
\(243\) | 1229.72 | − | 3582.83i | 0.324637 | − | 0.945839i | ||||
\(244\) | −8644.39 | −2.26803 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2951.75 | − | 1859.63i | 0.765027 | − | 0.481973i | ||||
\(247\) | −4126.94 | + | 2382.69i | −1.06312 | + | 0.613793i | ||||
\(248\) | −822.212 | + | 474.704i | −0.210526 | + | 0.121547i | ||||
\(249\) | 39.6448 | + | 1026.72i | 0.0100899 | + | 0.261307i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 886.861 | 0.223021 | 0.111510 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111510 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(252\) | −7614.21 | − | 3644.43i | −1.90337 | − | 0.911023i | ||||
\(253\) | − | 2539.08i | − | 0.630950i | ||||||
\(254\) | 3209.38 | − | 5558.81i | 0.792813 | − | 1.37319i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −543.033 | − | 940.561i | −0.132576 | − | 0.229629i | ||||
\(257\) | −1958.98 | + | 1131.02i | −0.475478 | + | 0.274517i | −0.718530 | − | 0.695496i | \(-0.755185\pi\) |
0.243052 | + | 0.970013i | \(0.421851\pi\) | |||||||
\(258\) | 3487.66 | − | 6618.09i | 0.841598 | − | 1.59699i | ||||
\(259\) | −4338.17 | + | 7513.92i | −1.04077 | + | 1.80267i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 757.166 | + | 1104.88i | 0.179569 | + | 0.262032i | ||||
\(262\) | 5434.30i | 1.28142i | ||||||||
\(263\) | −6305.20 | − | 3640.31i | −1.47831 | − | 0.853503i | −0.478611 | − | 0.878027i | \(-0.658859\pi\) |
−0.999699 | + | 0.0245245i | \(0.992193\pi\) | |||||||
\(264\) | 75.2391 | + | 1948.53i | 0.0175403 | + | 0.454257i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4941.52 | + | 8558.96i | 1.13904 | + | 1.97287i | ||||
\(267\) | −3779.48 | − | 5999.09i | −0.866293 | − | 1.37505i | ||||
\(268\) | −847.622 | − | 489.375i | −0.193197 | − | 0.111542i | ||||
\(269\) | 106.781 | 0.0242028 | 0.0121014 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121014 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5908.85 | 1.32449 | 0.662246 | − | 0.749287i | \(-0.269603\pi\) | ||||
0.662246 | + | 0.749287i | \(0.269603\pi\) | |||||||
\(272\) | 239.811 | + | 138.455i | 0.0534585 | + | 0.0308643i | ||||
\(273\) | 5386.73 | + | 8550.25i | 1.19421 | + | 1.89555i | ||||
\(274\) | −3067.25 | − | 5312.64i | −0.676276 | − | 1.17134i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −127.067 | − | 3290.75i | −0.0277120 | − | 0.717681i | ||||
\(277\) | 2849.30 | + | 1645.04i | 0.618042 | + | 0.356827i | 0.776106 | − | 0.630602i | \(-0.217192\pi\) |
−0.158064 | + | 0.987429i | \(0.550525\pi\) | |||||||
\(278\) | 10822.8i | 2.33492i | ||||||||
\(279\) | 2772.83 | − | 214.456i | 0.595000 | − | 0.0460184i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −169.861 | + | 294.209i | −0.0360608 | + | 0.0624591i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(282\) | 459.590 | − | 872.107i | 0.0970504 | − | 0.184160i | ||||
\(283\) | 2251.37 | − | 1299.83i | 0.472898 | − | 0.273028i | −0.244554 | − | 0.969636i | \(-0.578642\pi\) |
0.717452 | + | 0.696608i | \(0.245308\pi\) | |||||||
\(284\) | 4838.30 | + | 8380.19i | 1.01092 | + | 1.75096i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5484.67 | − | 9499.73i | 1.13397 | − | 1.96409i | ||||
\(287\) | 4846.55i | 0.996804i | ||||||||
\(288\) | −526.373 | − | 6805.80i | −0.107697 | − | 1.39248i | ||||
\(289\) | 4869.57 | 0.991161 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −286.934 | − | 7430.98i | −0.0578020 | − | 1.49695i | ||||
\(292\) | 447.592 | − | 258.418i | 0.0897033 | − | 0.0517902i | ||||
\(293\) | 154.227 | − | 89.0427i | 0.0307509 | − | 0.0177540i | −0.484546 | − | 0.874766i | \(-0.661015\pi\) |
0.515297 | + | 0.857012i | \(0.327682\pi\) | |||||||
\(294\) | 11306.0 | − | 7122.86i | 2.24278 | − | 1.41297i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2599.52 | 0.510452 | ||||||||
\(297\) | 2265.45 | − | 5243.65i | 0.442609 | − | 1.02447i | ||||
\(298\) | − | 399.581i | − | 0.0776749i | ||||||
\(299\) | −1971.22 | + | 3414.25i | −0.381266 | + | 0.660372i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5196.24 | + | 9000.16i | 0.995038 | + | 1.72346i | ||||
\(302\) | −3942.26 | + | 2276.07i | −0.751164 | + | 0.433685i | ||||
\(303\) | −5751.06 | + | 222.067i | −1.09039 | + | 0.0421037i | ||||
\(304\) | −1583.76 | + | 2743.15i | −0.298798 | + | 0.517534i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 428.653 | + | 625.504i | 0.0800800 | + | 0.116855i | ||||
\(307\) | − | 1537.60i | − | 0.285848i | −0.989734 | − | 0.142924i | \(-0.954349\pi\) | ||
0.989734 | − | 0.142924i | \(-0.0456505\pi\) | |||||||
\(308\) | −11023.9 | − | 6364.64i | −2.03943 | − | 1.17746i | ||||
\(309\) | 2431.18 | + | 1281.20i | 0.447589 | + | 0.235874i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −472.662 | − | 818.674i | −0.0861807 | − | 0.149269i | 0.819713 | − | 0.572774i | \(-0.194133\pi\) |
−0.905894 | + | 0.423505i | \(0.860800\pi\) | |||||||
\(312\) | 1411.57 | − | 2678.57i | 0.256137 | − | 0.486038i | ||||
\(313\) | −1719.52 | − | 992.767i | −0.310521 | − | 0.179280i | 0.336638 | − | 0.941634i | \(-0.390710\pi\) |
−0.647160 | + | 0.762354i | \(0.724043\pi\) | |||||||
\(314\) | 774.428 | 0.139183 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2004.90 | −0.356913 | ||||||||
\(317\) | −4488.81 | − | 2591.62i | −0.795321 | − | 0.459179i | 0.0465112 | − | 0.998918i | \(-0.485190\pi\) |
−0.841833 | + | 0.539739i | \(0.818523\pi\) | |||||||
\(318\) | 581.428 | − | 22.4508i | 0.102531 | − | 0.00395906i | ||||
\(319\) | 1009.89 | + | 1749.19i | 0.177251 | + | 0.307008i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2158.24 | − | 1359.71i | 0.375268 | − | 0.236422i | ||||
\(322\) | 7080.91 | + | 4088.16i | 1.22548 | + | 0.707529i | ||||
\(323\) | − | 496.748i | − | 0.0855722i | ||||||
\(324\) | 2673.71 | − | 6909.37i | 0.458455 | − | 1.18473i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2350.52 | + | 4071.22i | −0.399336 | + | 0.691670i | ||||
\(327\) | 973.945 | + | 1545.92i | 0.164707 | + | 0.261437i | ||||
\(328\) | 1257.53 | − | 726.037i | 0.211694 | − | 0.122222i | ||||
\(329\) | 684.741 | + | 1186.01i | 0.114745 | + | 0.198744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1086.68 | − | 1882.19i | 0.180451 | − | 0.312551i | −0.761583 | − | 0.648067i | \(-0.775578\pi\) |
0.942034 | + | 0.335517i | \(0.108911\pi\) | |||||||
\(332\) | 2009.57i | 0.332197i | ||||||||
\(333\) | −6868.56 | − | 3287.54i | −1.13032 | − | 0.541009i | ||||
\(334\) | −17224.8 | −2.82186 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5942.47 | + | 3131.61i | 0.964846 | + | 0.508463i | ||||
\(337\) | 6798.57 | − | 3925.16i | 1.09894 | − | 0.634472i | 0.162995 | − | 0.986627i | \(-0.447884\pi\) |
0.935942 | + | 0.352155i | \(0.114551\pi\) | |||||||
\(338\) | −6641.58 | + | 3834.52i | −1.06880 | + | 0.617071i | ||||
\(339\) | 8101.81 | + | 4269.56i | 1.29802 | + | 0.684043i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4193.78 | 0.665999 | ||||||||
\(342\) | −7154.99 | + | 4903.26i | −1.13128 | + | 0.775257i | ||||
\(343\) | 8011.53i | 1.26117i | ||||||||
\(344\) | 1556.85 | − | 2696.54i | 0.244010 | − | 0.422638i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5855.16 | − | 10141.4i | −0.909756 | − | 1.57574i | ||||
\(347\) | 8116.60 | − | 4686.12i | 1.25568 | − | 0.724969i | 0.283451 | − | 0.958987i | \(-0.408521\pi\) |
0.972232 | + | 0.234018i | \(0.0751875\pi\) | |||||||
\(348\) | 1396.40 | + | 2216.48i | 0.215101 | + | 0.341425i | ||||
\(349\) | −588.952 | + | 1020.10i | −0.0903321 | + | 0.156460i | −0.907651 | − | 0.419726i | \(-0.862126\pi\) |
0.817319 | + | 0.576186i | \(0.195460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7117.23 | + | 5292.25i | −1.08231 | + | 0.804784i | ||||
\(352\) | − | 10293.4i | − | 1.55864i | ||||||
\(353\) | 6289.19 | + | 3631.06i | 0.948271 | + | 0.547484i | 0.892543 | − | 0.450962i | \(-0.148919\pi\) |
0.0557274 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(354\) | −7980.37 | + | 5027.70i | −1.19817 | + | 0.754856i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6933.77 | − | 12009.6i | −1.03227 | − | 1.78795i | ||||
\(357\) | −1052.64 | + | 40.6458i | −0.156055 | + | 0.00602578i | ||||
\(358\) | −10475.7 | − | 6048.15i | −1.54653 | − | 0.892890i | ||||
\(359\) | 1939.95 | 0.285199 | 0.142600 | − | 0.989780i | \(-0.454454\pi\) | ||||
0.142600 | + | 0.989780i | \(0.454454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1176.81 | −0.171572 | ||||||||
\(362\) | −12704.7 | − | 7335.05i | −1.84459 | − | 1.06498i | ||||
\(363\) | 791.388 | − | 1501.72i | 0.114427 | − | 0.217134i | ||||
\(364\) | 9882.41 | + | 17116.8i | 1.42302 | + | 2.46474i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16664.0 | + | 8781.72i | 2.37989 | + | 1.25417i | ||||
\(367\) | 5630.85 | + | 3250.97i | 0.800893 | + | 0.462396i | 0.843783 | − | 0.536684i | \(-0.180323\pi\) |
−0.0428901 | + | 0.999080i | \(0.513657\pi\) | |||||||
\(368\) | 2620.51i | 0.371205i | ||||||||
\(369\) | −4240.91 | + | 328.000i | −0.598301 | + | 0.0462737i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −404.165 | + | 700.034i | −0.0565585 | + | 0.0979622i | ||||
\(372\) | 5435.32 | − | 209.875i | 0.757548 | − | 0.0292514i | ||||
\(373\) | 11533.8 | − | 6659.02i | 1.60106 | − | 0.924372i | 0.609784 | − | 0.792568i | \(-0.291256\pi\) |
0.991276 | − | 0.131805i | \(-0.0420772\pi\) | |||||||
\(374\) | 571.729 | + | 990.263i | 0.0790465 | + | 0.136913i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 205.155 | − | 355.339i | 0.0281385 | − | 0.0487373i | ||||
\(377\) | − | 3136.13i | − | 0.428432i | ||||||
\(378\) | 10975.7 | + | 14760.6i | 1.49347 | + | 2.00848i | ||||
\(379\) | 3198.42 | 0.433488 | 0.216744 | − | 0.976228i | \(-0.430456\pi\) | ||||
0.216744 | + | 0.976228i | \(0.430456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6621.53 | + | 4171.62i | −0.890370 | + | 0.560941i | ||||
\(382\) | −2754.43 | + | 1590.27i | −0.368924 | + | 0.212999i | ||||
\(383\) | −2026.93 | + | 1170.25i | −0.270422 | + | 0.156128i | −0.629079 | − | 0.777341i | \(-0.716568\pi\) |
0.358658 | + | 0.933469i | \(0.383235\pi\) | |||||||
\(384\) | −227.895 | − | 5902.00i | −0.0302858 | − | 0.784336i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −459.878 | −0.0606403 | ||||||||
\(387\) | −7523.81 | + | 5156.01i | −0.988261 | + | 0.677248i | ||||
\(388\) | − | 14544.5i | − | 1.90305i | ||||||
\(389\) | 1995.97 | − | 3457.12i | 0.260153 | − | 0.450599i | −0.706129 | − | 0.708083i | \(-0.749560\pi\) |
0.966282 | + | 0.257484i | \(0.0828936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −205.482 | − | 355.906i | −0.0265772 | − | 0.0460330i | ||||
\(392\) | 4816.69 | − | 2780.91i | 0.620611 | − | 0.358310i | ||||
\(393\) | 3089.00 | − | 5861.61i | 0.396488 | − | 0.752365i | ||||
\(394\) | 7161.96 | − | 12404.9i | 0.915773 | − | 1.58616i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4823.24 | − | 10077.1i | 0.612063 | − | 1.27876i | ||||
\(397\) | 4960.90i | 0.627155i | 0.949563 | + | 0.313577i | \(0.101528\pi\) | ||||
−0.949563 | + | 0.313577i | \(0.898472\pi\) | |||||||
\(398\) | 5052.66 | + | 2917.16i | 0.636350 | + | 0.367397i | ||||
\(399\) | −464.937 | − | 12040.9i | −0.0583358 | − | 1.51077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −413.811 | − | 716.742i | −0.0515330 | − | 0.0892578i | 0.839108 | − | 0.543965i | \(-0.183077\pi\) |
−0.890641 | + | 0.454707i | \(0.849744\pi\) | |||||||
\(402\) | 1136.83 | + | 1804.47i | 0.141044 | + | 0.223877i | ||||
\(403\) | −5639.30 | − | 3255.85i | −0.697056 | − | 0.402445i | ||||
\(404\) | −11256.4 | −1.38621 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6504.11 | −0.795058 | ||||||||
\(407\) | −9944.33 | − | 5741.36i | −1.21111 | − | 0.699235i | ||||
\(408\) | 168.237 | + | 267.039i | 0.0204141 | + | 0.0324029i | ||||
\(409\) | −4183.82 | − | 7246.59i | −0.505811 | − | 0.876090i | −0.999977 | − | 0.00672263i | \(-0.997860\pi\) |
0.494167 | − | 0.869367i | \(-0.335473\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 288.592 | + | 7473.90i | 0.0346354 | + | 0.896983i | ||||
\(412\) | 4654.73 | + | 2687.41i | 0.556607 | + | 0.321357i | ||||
\(413\) | − | 13103.2i | − | 1.56117i | ||||||
\(414\) | −3098.08 | + | 6472.74i | −0.367784 | + | 0.768400i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7991.34 | + | 13841.4i | −0.941845 | + | 1.63132i | ||||
\(417\) | 6151.96 | − | 11673.8i | 0.722453 | − | 1.37091i | ||||
\(418\) | −11327.4 | + | 6539.87i | −1.32546 | + | 0.765252i | ||||
\(419\) | 2100.36 | + | 3637.93i | 0.244891 | + | 0.424163i | 0.962101 | − | 0.272694i | \(-0.0879145\pi\) |
−0.717210 | + | 0.696857i | \(0.754581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3469.38 | + | 6009.14i | −0.401632 | + | 0.695648i | −0.993923 | − | 0.110077i | \(-0.964890\pi\) |
0.592291 | + | 0.805724i | \(0.298224\pi\) | |||||||
\(422\) | 10665.3i | 1.23028i | ||||||||
\(423\) | −991.459 | + | 679.440i | −0.113963 | + | 0.0780981i | ||||
\(424\) | 242.184 | 0.0277394 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −813.575 | − | 21069.8i | −0.0925301 | − | 2.39633i | ||||
\(427\) | −22661.8 | + | 13083.8i | −2.56835 | + | 1.48283i | ||||
\(428\) | 4320.60 | − | 2494.50i | 0.487953 | − | 0.281720i | ||||
\(429\) | −11315.9 | + | 7129.09i | −1.27351 | + | 0.802321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6827.09 | 0.762991 | 0.381496 | − | 0.924371i | \(-0.375409\pi\) | ||||
0.381496 | + | 0.924371i | \(0.375409\pi\) | |||||||
\(432\) | −2338.11 | + | 5411.83i | −0.260399 | + | 0.602724i | ||||
\(433\) | − | 2199.59i | − | 0.244124i | −0.992522 | − | 0.122062i | \(-0.961049\pi\) | ||
0.992522 | − | 0.122062i | \(-0.0389507\pi\) | |||||||
\(434\) | −6752.39 | + | 11695.5i | −0.746832 | + | 1.29355i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1786.78 | + | 3094.80i | 0.196265 | + | 0.339940i | ||||
\(437\) | 4071.12 | − | 2350.46i | 0.445648 | − | 0.257295i | ||||
\(438\) | −1125.36 | + | 43.4536i | −0.122766 | + | 0.00474040i | ||||
\(439\) | 4162.16 | − | 7209.07i | 0.452504 | − | 0.783759i | −0.546037 | − | 0.837761i | \(-0.683864\pi\) |
0.998541 | + | 0.0540018i | \(0.0171977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16243.8 | + | 1256.33i | −1.75400 | + | 0.135658i | ||||
\(442\) | − | 1775.45i | − | 0.191063i | ||||||
\(443\) | 9410.93 | + | 5433.41i | 1.00932 | + | 0.582729i | 0.910991 | − | 0.412426i | \(-0.135318\pi\) |
0.0983247 | + | 0.995154i | \(0.468652\pi\) | |||||||
\(444\) | −13175.6 | − | 6943.39i | −1.40830 | − | 0.742159i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3994.41 | + | 6918.51i | 0.424082 | + | 0.734532i | ||||
\(447\) | −227.133 | + | 431.001i | −0.0240336 | + | 0.0456055i | ||||
\(448\) | 19749.9 | + | 11402.6i | 2.08280 | + | 1.20250i | ||||
\(449\) | 4947.73 | 0.520040 | 0.260020 | − | 0.965603i | \(-0.416271\pi\) | ||||
0.260020 | + | 0.965603i | \(0.416271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6414.18 | −0.669694 | ||||||||
\(452\) | 15511.7 | + | 8955.69i | 1.61418 | + | 0.931947i | ||||
\(453\) | 5546.03 | − | 214.150i | 0.575221 | − | 0.0222112i | ||||
\(454\) | −10822.2 | − | 18744.7i | −1.11875 | − | 1.93773i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3054.59 | + | 1924.42i | −0.313694 | + | 0.197630i | ||||
\(457\) | −12295.6 | − | 7098.85i | −1.25856 | − | 0.726630i | −0.285766 | − | 0.958299i | \(-0.592248\pi\) |
−0.972795 | + | 0.231669i | \(0.925581\pi\) | |||||||
\(458\) | − | 3690.13i | − | 0.376481i | ||||||
\(459\) | −106.806 | − | 918.347i | −0.0108612 | − | 0.0933873i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9114.02 | − | 15785.9i | 0.920786 | − | 1.59485i | 0.122584 | − | 0.992458i | \(-0.460882\pi\) |
0.798202 | − | 0.602390i | \(-0.205785\pi\) | |||||||
\(462\) | 14785.2 | + | 23468.3i | 1.48890 | + | 2.36329i | ||||
\(463\) | 3759.58 | − | 2170.59i | 0.377370 | − | 0.217875i | −0.299303 | − | 0.954158i | \(-0.596754\pi\) |
0.676674 | + | 0.736283i | \(0.263421\pi\) | |||||||
\(464\) | −1042.28 | − | 1805.29i | −0.104282 | − | 0.180621i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2433.69 | − | 4215.28i | 0.241928 | − | 0.419032i | ||||
\(467\) | − | 4919.63i | − | 0.487481i | −0.969841 | − | 0.243740i | \(-0.921626\pi\) | ||
0.969841 | − | 0.243740i | \(-0.0783744\pi\) | |||||||
\(468\) | −14309.1 | + | 9805.90i | −1.41333 | + | 0.968542i | ||||
\(469\) | −2962.80 | −0.291704 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −835.324 | − | 440.206i | −0.0817191 | − | 0.0430650i | ||||
\(472\) | −3399.88 | + | 1962.92i | −0.331551 | + | 0.191421i | ||||
\(473\) | −11911.3 | + | 6876.98i | −1.15789 | + | 0.668508i | ||||
\(474\) | 3864.88 | + | 2036.75i | 0.374515 | + | 0.197365i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2060.31 | −0.198391 | ||||||||
\(477\) | −639.909 | − | 306.283i | −0.0614244 | − | 0.0293999i | ||||
\(478\) | 13421.9i | 1.28432i | ||||||||
\(479\) | 2286.41 | − | 3960.19i | 0.218098 | − | 0.377757i | −0.736128 | − | 0.676842i | \(-0.763348\pi\) |
0.954226 | + | 0.299085i | \(0.0966814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8914.64 | + | 15440.6i | 0.845057 | + | 1.46368i | ||||
\(482\) | 16624.8 | − | 9598.31i | 1.57103 | − | 0.907035i | ||||
\(483\) | −5313.87 | − | 8434.61i | −0.500600 | − | 0.794592i | ||||
\(484\) | 1659.99 | − | 2875.19i | 0.155897 | − | 0.270021i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −12173.3 | + | 10603.1i | −1.13620 | + | 0.989646i | ||||
\(487\) | − | 15751.5i | − | 1.46564i | −0.680421 | − | 0.732822i | \(-0.738203\pi\) | ||
0.680421 | − | 0.732822i | \(-0.261797\pi\) | |||||||
\(488\) | 6789.72 | + | 3920.04i | 0.629828 | + | 0.363631i | ||||
\(489\) | 4849.55 | − | 3055.26i | 0.448475 | − | 0.282543i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7654.18 | − | 13257.4i | −0.703520 | − | 1.21853i | −0.967223 | − | 0.253928i | \(-0.918277\pi\) |
0.263703 | − | 0.964604i | \(-0.415056\pi\) | |||||||
\(492\) | −8313.05 | + | 320.994i | −0.761751 | + | 0.0294137i | ||||
\(493\) | 283.116 | + | 163.457i | 0.0258639 | + | 0.0149325i | ||||
\(494\) | 20309.0 | 1.84968 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4328.28 | −0.391826 | ||||||||
\(497\) | 25367.9 | + | 14646.2i | 2.28955 | + | 1.32187i | ||||
\(498\) | 2041.49 | − | 3873.89i | 0.183698 | − | 0.348580i | ||||
\(499\) | 8866.05 | + | 15356.5i | 0.795389 | + | 1.37765i | 0.922592 | + | 0.385777i | \(0.126067\pi\) |
−0.127203 | + | 0.991877i | \(0.540600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18579.3 | + | 9791.07i | 1.65681 | + | 0.873119i | ||||
\(502\) | −3273.23 | − | 1889.80i | −0.291019 | − | 0.168020i | ||||
\(503\) | − | 10511.5i | − | 0.931775i | −0.884844 | − | 0.465887i | \(-0.845735\pi\) | ||
0.884844 | − | 0.465887i | \(-0.154265\pi\) | |||||||
\(504\) | 4327.89 | + | 6315.39i | 0.382499 | + | 0.558155i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5410.49 | + | 9371.25i | −0.475347 | + | 0.823326i | ||||
\(507\) | 9343.47 | − | 360.782i | 0.818457 | − | 0.0316033i | ||||
\(508\) | −13255.7 | + | 7653.18i | −1.15773 | + | 0.668416i | ||||
\(509\) | 9815.42 | + | 17000.8i | 0.854737 | + | 1.48045i | 0.876889 | + | 0.480693i | \(0.159615\pi\) |
−0.0221524 | + | 0.999755i | \(0.507052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 782.262 | − | 1354.92i | 0.0677206 | − | 0.117296i | ||||
\(512\) | 13722.1i | 1.18444i | ||||||||
\(513\) | 10504.8 | − | 1221.73i | 0.904086 | − | 0.105147i | ||||
\(514\) | 9640.30 | 0.827267 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15093.4 | + | 9508.96i | −1.28769 | + | 0.811257i | ||||
\(517\) | −1569.62 | + | 906.223i | −0.133524 | + | 0.0770902i | ||||
\(518\) | 32022.7 | − | 18488.3i | 2.71621 | − | 1.56820i | ||||
\(519\) | 550.900 | + | 14267.1i | 0.0465931 | + | 1.20666i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 88.4336 | 0.00743636 | 0.00371818 | − | 0.999993i | \(-0.498816\pi\) | ||||
0.00371818 | + | 0.999993i | \(0.498816\pi\) | |||||||
\(522\) | −440.179 | − | 5691.34i | −0.0369082 | − | 0.477209i | ||||
\(523\) | 21346.4i | 1.78473i | 0.451317 | + | 0.892363i | \(0.350954\pi\) | ||||
−0.451317 | + | 0.892363i | \(0.649046\pi\) | |||||||
\(524\) | 6479.39 | − | 11222.6i | 0.540178 | − | 0.935616i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15514.2 | + | 26871.4i | 1.28603 | + | 2.22747i | ||||
\(527\) | 587.847 | − | 339.394i | 0.0485902 | − | 0.0280535i | ||||
\(528\) | −4144.55 | + | 7864.58i | −0.341606 | + | 0.648224i | ||||
\(529\) | −4138.94 | + | 7168.86i | −0.340178 | + | 0.589205i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11465.8 | − | 886.783i | 0.937047 | − | 0.0724729i | ||||
\(532\) | − | 23567.4i | − | 1.92063i | ||||||
\(533\) | 8625.03 | + | 4979.67i | 0.700923 | + | 0.404678i | ||||
\(534\) | 1165.93 | + | 30195.1i | 0.0944847 | + | 2.44695i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 443.842 | + | 768.757i | 0.0357669 | + | 0.0619501i | ||||
\(537\) | 7861.51 | + | 12478.4i | 0.631749 | + | 1.00276i | ||||
\(538\) | −394.108 | − | 227.538i | −0.0315821 | − | 0.0182340i | ||||
\(539\) | −24568.0 | −1.96330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14432.6 | −1.14696 | −0.573480 | − | 0.819220i | \(-0.694407\pi\) | ||||
−0.573480 | + | 0.819220i | \(0.694407\pi\) | |||||||
\(542\) | −21808.4 | − | 12591.1i | −1.72833 | − | 0.997850i | ||||
\(543\) | 9534.24 | + | 15133.5i | 0.753505 | + | 1.19602i | ||||
\(544\) | −833.027 | − | 1442.84i | −0.0656539 | − | 0.113716i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1661.75 | − | 43035.9i | −0.130250 | − | 3.37320i | ||||
\(547\) | −14349.7 | − | 8284.80i | −1.12166 | − | 0.647592i | −0.179837 | − | 0.983696i | \(-0.557557\pi\) |
−0.941825 | + | 0.336105i | \(0.890890\pi\) | |||||||
\(548\) | 14628.5i | 1.14033i | ||||||||
\(549\) | −12982.5 | − | 18944.5i | −1.00925 | − | 1.47273i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1869.75 | + | 3238.50i | −0.144562 | + | 0.250389i | ||||
\(552\) | −1392.48 | + | 2642.34i | −0.107369 | + | 0.203742i | ||||
\(553\) | −5255.98 | + | 3034.54i | −0.404172 | + | 0.233349i | ||||
\(554\) | −7010.80 | − | 12143.1i | −0.537654 | − | 0.931245i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12904.1 | − | 22350.6i | 0.984277 | − | 1.70482i | ||||
\(557\) | − | 11597.0i | − | 0.882191i | −0.897460 | − | 0.441096i | \(-0.854590\pi\) | ||
0.897460 | − | 0.441096i | \(-0.145410\pi\) | |||||||
\(558\) | −10691.0 | − | 5117.08i | −0.811084 | − | 0.388214i | ||||
\(559\) | 21355.9 | 1.61584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53.7928 | − | 1393.12i | −0.00404836 | − | 0.104844i | ||||
\(562\) | 1253.85 | − | 723.912i | 0.0941113 | − | 0.0543352i | ||||
\(563\) | −19961.3 | + | 11524.6i | −1.49426 | + | 0.862709i | −0.999978 | − | 0.00659429i | \(-0.997901\pi\) |
−0.494278 | + | 0.869304i | \(0.664568\pi\) | |||||||
\(564\) | −1988.95 | + | 1253.05i | −0.148493 | + | 0.0935516i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11079.2 | −0.822778 | ||||||||
\(567\) | −3448.45 | − | 22160.2i | −0.255417 | − | 1.64134i | ||||
\(568\) | − | 8776.27i | − | 0.648317i | ||||||
\(569\) | 7366.96 | − | 12759.9i | 0.542775 | − | 0.940114i | −0.455968 | − | 0.889996i | \(-0.650707\pi\) |
0.998743 | − | 0.0501179i | \(-0.0159597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7555.94 | − | 13087.3i | −0.553776 | − | 0.959169i | −0.997998 | − | 0.0632515i | \(-0.979853\pi\) |
0.444221 | − | 0.895917i | \(-0.353480\pi\) | |||||||
\(572\) | −22653.3 | + | 13078.9i | −1.65591 | + | 0.956043i | ||||
\(573\) | 3874.98 | − | 149.625i | 0.282512 | − | 0.0109087i | ||||
\(574\) | 10327.5 | − | 17887.7i | 0.750975 | − | 1.30073i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8641.09 | + | 18053.6i | −0.625079 | + | 1.30596i | ||||
\(577\) | 26150.5i | 1.88676i | 0.331715 | + | 0.943380i | \(0.392373\pi\) | ||||
−0.331715 | + | 0.943380i | \(0.607627\pi\) | |||||||
\(578\) | −17972.7 | − | 10376.5i | −1.29336 | − | 0.746724i | ||||
\(579\) | 496.039 | + | 261.407i | 0.0356040 | + | 0.0187629i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3041.61 | + | 5268.22i | 0.217190 | + | 0.376184i | ||||
\(582\) | −14775.6 | + | 28037.7i | −1.05235 | + | 1.99691i | ||||
\(583\) | −926.463 | − | 534.894i | −0.0658150 | − | 0.0379983i | ||||
\(584\) | −468.747 | −0.0332139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −758.961 | −0.0535023 | ||||||||
\(587\) | 1811.33 | + | 1045.77i | 0.127362 | + | 0.0735326i | 0.562327 | − | 0.826915i | \(-0.309906\pi\) |
−0.434965 | + | 0.900447i | \(0.643239\pi\) | |||||||
\(588\) | −31841.2 | + | 1229.49i | −2.23318 | + | 0.0862303i | ||||
\(589\) | 3882.24 | + | 6724.24i | 0.271587 | + | 0.470403i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14776.4 | + | 9309.26i | −1.02846 | + | 0.647939i | ||||
\(592\) | 10263.3 | + | 5925.50i | 0.712530 | + | 0.411379i | ||||
\(593\) | 3260.34i | 0.225778i | 0.993608 | + | 0.112889i | \(0.0360104\pi\) | ||||
−0.993608 | + | 0.112889i | \(0.963990\pi\) | |||||||
\(594\) | −19535.0 | + | 14525.9i | −1.34938 | + | 1.00337i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −476.426 | + | 825.194i | −0.0327436 | + | 0.0567135i | ||||
\(597\) | −3791.78 | − | 6018.61i | −0.259945 | − | 0.412606i | ||||
\(598\) | 14550.8 | − | 8400.90i | 0.995026 | − | 0.574479i | ||||
\(599\) | −11499.6 | − | 19917.9i | −0.784410 | − | 1.35864i | −0.929351 | − | 0.369197i | \(-0.879633\pi\) |
0.144941 | − | 0.989440i | \(-0.453701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7146.93 | − | 12378.9i | 0.485074 | − | 0.840173i | −0.514779 | − | 0.857323i | \(-0.672126\pi\) |
0.999853 | + | 0.0171500i | \(0.00545928\pi\) | |||||||
\(602\) | − | 44290.5i | − | 2.99858i | ||||||
\(603\) | −200.513 | − | 2592.56i | −0.0135415 | − | 0.175087i | ||||
\(604\) | 10855.1 | 0.731274 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 21699.3 | + | 11435.3i | 1.45457 | + | 0.766544i | ||||
\(607\) | 14232.3 | − | 8217.04i | 0.951685 | − | 0.549455i | 0.0580809 | − | 0.998312i | \(-0.481502\pi\) |
0.893604 | + | 0.448856i | \(0.148169\pi\) | |||||||
\(608\) | 16504.4 | − | 9528.80i | 1.10089 | − | 0.635598i | ||||
\(609\) | 7015.54 | + | 3697.11i | 0.466805 | + | 0.246001i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2814.19 | 0.186334 | ||||||||
\(612\) | −139.435 | − | 1802.85i | −0.00920971 | − | 0.119078i | ||||
\(613\) | 3674.45i | 0.242104i | 0.992646 | + | 0.121052i | \(0.0386267\pi\) | ||||
−0.992646 | + | 0.121052i | \(0.961373\pi\) | |||||||
\(614\) | −3276.45 | + | 5674.99i | −0.215353 | + | 0.373003i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5772.46 | + | 9998.19i | 0.377563 | + | 0.653958i | ||||
\(617\) | −7471.69 | + | 4313.78i | −0.487519 | + | 0.281469i | −0.723544 | − | 0.690278i | \(-0.757488\pi\) |
0.236026 | + | 0.971747i | \(0.424155\pi\) | |||||||
\(618\) | −6242.91 | − | 9909.25i | −0.406354 | − | 0.644998i | ||||
\(619\) | −654.905 | + | 1134.33i | −0.0425248 | + | 0.0736551i | −0.886504 | − | 0.462720i | \(-0.846873\pi\) |
0.843980 | + | 0.536375i | \(0.180207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7020.97 | − | 5220.67i | 0.453691 | − | 0.337356i | ||||
\(622\) | 4028.76i | 0.259708i | ||||||||
\(623\) | −36354.7 | − | 20989.4i | −2.33791 | − | 1.34979i | ||||
\(624\) | 11678.8 | − | 7357.73i | 0.749240 | − | 0.472027i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4230.95 | + | 7328.23i | 0.270132 | + | 0.467883i | ||||
\(627\) | 15935.5 | − | 615.323i | 1.01500 | − | 0.0391924i | ||||
\(628\) | −1599.31 | − | 923.362i | −0.101623 | − | 0.0586722i | ||||
\(629\) | −1858.54 | −0.117814 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14447.2 | 0.911463 | 0.455731 | − | 0.890117i | \(-0.349378\pi\) | ||||
0.455731 | + | 0.890117i | \(0.349378\pi\) | |||||||
\(632\) | 1574.74 | + | 909.179i | 0.0991138 | + | 0.0572234i | ||||
\(633\) | 6062.45 | − | 11503.9i | 0.380665 | − | 0.722339i | ||||
\(634\) | 11044.9 | + | 19130.3i | 0.691875 | + | 1.19836i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1227.50 | − | 646.881i | −0.0765310 | − | 0.0403309i | ||||
\(637\) | 33036.2 | + | 19073.4i | 2.05485 | + | 1.18637i | ||||
\(638\) | − | 8607.88i | − | 0.534152i | ||||||
\(639\) | −11099.1 | + | 23189.1i | −0.687127 | + | 1.43560i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10036.6 | − | 17383.8i | 0.618440 | − | 1.07117i | −0.371330 | − | 0.928501i | \(-0.621098\pi\) |
0.989770 | − | 0.142669i | \(-0.0455685\pi\) | |||||||
\(642\) | −10863.0 | + | 419.457i | −0.667803 | + | 0.0257860i | ||||
\(643\) | −15359.8 | + | 8867.96i | −0.942037 | + | 0.543885i | −0.890598 | − | 0.454791i | \(-0.849714\pi\) |
−0.0514386 | + | 0.998676i | \(0.516381\pi\) | |||||||
\(644\) | −9748.75 | − | 16885.3i | −0.596513 | − | 1.03319i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1058.52 | + | 1833.40i | −0.0644686 | + | 0.111663i | ||||
\(647\) | 11456.8i | 0.696158i | 0.937465 | + | 0.348079i | \(0.113166\pi\) | ||||
−0.937465 | + | 0.348079i | \(0.886834\pi\) | |||||||
\(648\) | −5233.31 | + | 4214.48i | −0.317259 | + | 0.255494i | ||||
\(649\) | 17341.4 | 1.04886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13931.4 | − | 8776.89i | 0.838731 | − | 0.528408i | ||||
\(652\) | 9708.36 | − | 5605.12i | 0.583142 | − | 0.336677i | ||||
\(653\) | 25177.0 | − | 14536.0i | 1.50881 | − | 0.871113i | 0.508864 | − | 0.860847i | \(-0.330065\pi\) |
0.999947 | − | 0.0102660i | \(-0.00326784\pi\) | |||||||
\(654\) | −300.453 | − | 7781.08i | −0.0179643 | − | 0.465236i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6619.90 | 0.393999 | ||||||||
\(657\) | 1238.55 | + | 592.812i | 0.0735468 | + | 0.0352021i | ||||
\(658\) | − | 5836.43i | − | 0.345787i | ||||||
\(659\) | −2177.54 | + | 3771.62i | −0.128718 | + | 0.222946i | −0.923180 | − | 0.384368i | \(-0.874419\pi\) |
0.794462 | + | 0.607314i | \(0.207753\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13647.7 | − | 23638.5i | −0.803075 | − | 1.39097i | −0.917583 | − | 0.397545i | \(-0.869862\pi\) |
0.114508 | − | 0.993422i | \(-0.463471\pi\) | |||||||
\(662\) | −8021.46 | + | 4631.19i | −0.470941 | + | 0.271898i | ||||
\(663\) | −1009.22 | + | 1915.06i | −0.0591172 | + | 0.112179i | ||||
\(664\) | 911.297 | − | 1578.41i | 0.0532608 | − | 0.0922504i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18345.2 | + | 26769.8i | 1.06736 | + | 1.55752i | ||||
\(667\) | 3093.72i | 0.179594i | ||||||||
\(668\) | 35571.8 | + | 20537.4i | 2.06035 | + | 1.18955i | ||||
\(669\) | −375.825 | − | 9733.06i | −0.0217194 | − | 0.562484i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17315.8 | − | 29991.9i | −0.996230 | − | 1.72552i | ||||
\(672\) | −21542.5 | − | 34194.0i | −1.23664 | − | 1.96289i | ||||
\(673\) | 15380.6 | + | 8880.01i | 0.880951 | + | 0.508617i | 0.870972 | − | 0.491333i | \(-0.163490\pi\) |
0.00997909 | + | 0.999950i | \(0.496824\pi\) | |||||||
\(674\) | −33456.3 | −1.91200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18287.8 | 1.04050 | ||||||||
\(677\) | 1677.78 | + | 968.667i | 0.0952472 | + | 0.0549910i | 0.546867 | − | 0.837219i | \(-0.315820\pi\) |
−0.451620 | + | 0.892210i | \(0.649154\pi\) | |||||||
\(678\) | −20804.3 | − | 33022.2i | −1.17844 | − | 1.87052i | ||||
\(679\) | −22014.0 | − | 38129.4i | −1.24421 | − | 2.15504i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1018.24 | + | 26370.3i | 0.0572968 | + | 1.48386i | ||||
\(682\) | −15478.4 | − | 8936.48i | −0.869061 | − | 0.501753i | ||||
\(683\) | − | 2125.71i | − | 0.119090i | −0.998226 | − | 0.0595448i | \(-0.981035\pi\) | ||
0.998226 | − | 0.0595448i | \(-0.0189649\pi\) | |||||||
\(684\) | 20622.3 | − | 1594.97i | 1.15280 | − | 0.0891596i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17071.7 | − | 29569.0i | 0.950146 | − | 1.64570i | ||||
\(687\) | −2097.57 | + | 3980.29i | −0.116488 | + | 0.221045i | ||||
\(688\) | 12293.3 | − | 7097.55i | 0.681218 | − | 0.393301i | ||||
\(689\) | 830.532 | + | 1438.52i | 0.0459227 | + | 0.0795405i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6913.13 | + | 11973.9i | −0.380590 | + | 0.659201i | −0.991147 | − | 0.132771i | \(-0.957612\pi\) |
0.610557 | + | 0.791973i | \(0.290946\pi\) | |||||||
\(692\) | 27924.8i | 1.53402i | ||||||||
\(693\) | −2607.81 | − | 33717.9i | −0.142947 | − | 1.84825i | ||||
\(694\) | −39942.4 | −2.18472 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −91.6744 | − | 2374.17i | −0.00499268 | − | 0.129300i | ||||
\(697\) | −899.084 | + | 519.086i | −0.0488597 | + | 0.0282092i | ||||
\(698\) | 4347.42 | − | 2509.98i | 0.235748 | − | 0.136109i | ||||
\(699\) | −5021.14 | + | 3163.36i | −0.271698 | + | 0.171172i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24464.0 | −1.31810 | −0.659052 | − | 0.752097i | \(-0.729042\pi\) | ||||
−0.659052 | + | 0.752097i | \(0.729042\pi\) | |||||||
\(702\) | 37545.5 | − | 4366.64i | 2.01861 | − | 0.234769i | ||||
\(703\) | − | 21259.5i | − | 1.14056i | ||||||
\(704\) | −15090.8 | + | 26138.0i | −0.807892 | + | 1.39931i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15474.8 | − | 26803.1i | −0.824931 | − | 1.42882i | ||||
\(707\) | −29509.5 | + | 17037.3i | −1.56976 | + | 0.906300i | ||||
\(708\) | 22475.2 | − | 867.842i | 1.19304 | − | 0.0460671i | ||||
\(709\) | −14749.1 | + | 25546.2i | −0.781263 | + | 1.35319i | 0.149944 | + | 0.988695i | \(0.452091\pi\) |
−0.931206 | + | 0.364492i | \(0.881243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3011.05 | − | 4393.81i | −0.158823 | − | 0.231759i | ||||
\(712\) | 12577.3i | 0.662012i | ||||||||
\(713\) | 5563.02 | + | 3211.81i | 0.292198 | + | 0.168700i | ||||
\(714\) | 3971.70 | + | 2093.04i | 0.208175 | + | 0.109706i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14422.6 | + | 24980.7i | 0.752790 | + | 1.30387i | ||||
\(717\) | 7629.38 | − | 14477.3i | 0.397384 | − | 0.754065i | ||||
\(718\) | −7159.98 | − | 4133.81i | −0.372156 | − | 0.214864i | ||||
\(719\) | 3857.66 | 0.200093 | 0.100046 | − | 0.994983i | \(-0.468101\pi\) | ||||
0.100046 | + | 0.994983i | \(0.468101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16270.2 | 0.840410 | ||||||||
\(722\) | 4343.39 | + | 2507.66i | 0.223884 | + | 0.129260i | ||||
\(723\) | −23387.9 | + | 903.085i | −1.20305 | + | 0.0464538i | ||||
\(724\) | 17491.4 | + | 30295.9i | 0.897874 | + | 1.55516i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6120.86 | + | 3856.19i | −0.312901 | + | 0.197130i | ||||
\(727\) | 7573.48 | + | 4372.55i | 0.386361 | + | 0.223066i | 0.680582 | − | 0.732672i | \(-0.261727\pi\) |
−0.294221 | + | 0.955737i | \(0.595060\pi\) | |||||||
\(728\) | − | 17925.8i | − | 0.912604i | ||||||
\(729\) | 19157.6 | − | 4517.26i | 0.973309 | − | 0.229501i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1113.08 | + | 1927.91i | −0.0563184 | + | 0.0975463i | ||||
\(732\) | −23943.0 | − | 38004.2i | −1.20896 | − | 1.91896i | ||||
\(733\) | −8156.58 | + | 4709.20i | −0.411010 | + | 0.237296i | −0.691223 | − | 0.722641i | \(-0.742928\pi\) |
0.280214 | + | 0.959938i | \(0.409595\pi\) | |||||||
\(734\) | −13854.9 | − | 23997.4i | −0.696723 | − | 1.20676i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7883.26 | − | 13654.2i | 0.394811 | − | 0.683832i | ||||
\(737\) | − | 3921.13i | − | 0.195979i | ||||||
\(738\) | 16351.3 | + | 7826.33i | 0.815584 | + | 0.390368i | ||||
\(739\) | −6219.42 | −0.309587 | −0.154794 | − | 0.987947i | \(-0.549471\pi\) | ||||
−0.154794 | + | 0.987947i | \(0.549471\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21905.9 | − | 11544.2i | −1.08601 | − | 0.572316i | ||||
\(742\) | 2983.39 | − | 1722.46i | 0.147606 | − | 0.0852204i | ||||
\(743\) | −25450.3 | + | 14693.7i | −1.25663 | + | 0.725518i | −0.972419 | − | 0.233242i | \(-0.925067\pi\) |
−0.284216 | + | 0.958760i | \(0.591733\pi\) | |||||||
\(744\) | −4364.33 | − | 2299.95i | −0.215059 | − | 0.113334i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −56758.5 | −2.78563 | ||||||||
\(747\) | −4404.05 | + | 3018.06i | −0.215710 | + | 0.147825i | ||||
\(748\) | − | 2726.72i | − | 0.133287i | ||||||
\(749\) | 7551.15 | − | 13079.0i | 0.368375 | − | 0.638045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10823.6 | + | 18747.0i | 0.525909 | + | 0.910901i | 0.999544 | + | 0.0301801i | \(0.00960808\pi\) |
−0.473636 | + | 0.880721i | \(0.657059\pi\) | |||||||
\(752\) | 1619.97 | − | 935.287i | 0.0785559 | − | 0.0453543i | ||||
\(753\) | 2456.40 | + | 3899.00i | 0.118880 | + | 0.188695i | ||||
\(754\) | −6682.75 | + | 11574.9i | −0.322774 | + | 0.559061i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5067.23 | − | 43569.4i | −0.243774 | − | 2.09604i | ||||
\(757\) | 13907.2i | 0.667722i | 0.942622 | + | 0.333861i | \(0.108352\pi\) | ||||
−0.942622 | + | 0.333861i | \(0.891648\pi\) | |||||||
\(758\) | −11804.8 | − | 6815.48i | −0.565657 | − | 0.326582i | ||||
\(759\) | 11162.8 | − | 7032.66i | 0.533840 | − | 0.336324i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11953.0 | + | 20703.3i | 0.569379 | + | 0.986193i | 0.996628 | + | 0.0820585i | \(0.0261494\pi\) |
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(762\) | 33328.0 | − | 1286.90i | 1.58445 | − | 0.0611806i | ||||
\(763\) | 9368.35 | + | 5408.82i | 0.444504 | + | 0.256635i | ||||
\(764\) | 7584.42 | 0.359155 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9974.70 | 0.470497 | ||||||||
\(767\) | −23318.7 | − | 13463.1i | −1.09777 | − | 0.633798i | ||||
\(768\) | 2631.01 | − | 4992.53i | 0.123618 | − | 0.234573i | ||||
\(769\) | −12555.8 | − | 21747.3i | −0.588783 | − | 1.01980i | −0.994392 | − | 0.105755i | \(-0.966274\pi\) |
0.405609 | − | 0.914047i | \(-0.367059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10398.3 | − | 5479.81i | −0.485716 | − | 0.255967i | ||||
\(772\) | 949.716 | + | 548.319i | 0.0442759 | + | 0.0255627i | ||||
\(773\) | 14909.4i | 0.693729i | 0.937915 | + | 0.346865i | \(0.112754\pi\) | ||||
−0.937915 | + | 0.346865i | \(0.887246\pi\) | |||||||
\(774\) | 38755.8 | − | 2997.45i | 1.79981 | − | 0.139200i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6595.62 | + | 11424.0i | −0.305115 | + | 0.528474i | ||||
\(777\) | −45050.0 | + | 1739.53i | −2.08000 | + | 0.0803155i | ||||
\(778\) | −14733.5 | + | 8506.37i | −0.678947 | + | 0.391990i | ||||
\(779\) | −5937.70 | − | 10284.4i | −0.273094 | − | 0.473013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19383.5 | + | 33573.2i | −0.888087 | + | 1.53821i | ||||
\(782\) | 1751.44i | 0.0800912i | ||||||||
\(783\) | −2760.32 | + | 6389.08i | −0.125984 | + | 0.291605i | ||||
\(784\) | 25356.0 | 1.15506 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23891.4 | + | 15051.8i | −1.08419 | + | 0.683052i | ||||
\(787\) | 2302.56 | − | 1329.38i | 0.104292 | − | 0.0602128i | −0.446947 | − | 0.894560i | \(-0.647489\pi\) |
0.551239 | + | 0.834348i | \(0.314155\pi\) | |||||||
\(788\) | −29581.0 | + | 17078.6i | −1.33728 | + | 0.772082i | ||||
\(789\) | −1459.70 | − | 37803.1i | −0.0658640 | − | 1.70573i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54220.0 | 2.43722 | ||||||||
\(792\) | −8358.13 | + | 5727.76i | −0.374991 | + | 0.256979i | ||||
\(793\) | 53772.7i | 2.40798i | ||||||||
\(794\) | 10571.1 | − | 18309.7i | 0.472488 | − | 0.818373i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6956.33 | − | 12048.7i | −0.309750 | − | 0.536502i | ||||
\(797\) | 12273.5 | − | 7086.11i | 0.545483 | − | 0.314935i | −0.201815 | − | 0.979424i | \(-0.564684\pi\) |
0.747298 | + | 0.664489i | \(0.231351\pi\) | |||||||
\(798\) | −23941.8 | + | 45431.3i | −1.06207 | + | 2.01535i | ||||
\(799\) | −146.677 | + | 254.053i | −0.00649446 | + | 0.0112487i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15906.1 | − | 33232.2i | 0.701642 | − | 1.46592i | ||||
\(802\) | 3527.14i | 0.155296i | ||||||||
\(803\) | 1793.17 | + | 1035.29i | 0.0788040 | + | 0.0454975i | ||||
\(804\) | −196.231 | − | 5081.95i | −0.00860761 | − | 0.222918i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13875.7 | + | 24033.4i | 0.606391 | + | 1.05030i | ||||
\(807\) | 295.759 | + | 469.452i | 0.0129011 | + | 0.0204777i | ||||
\(808\) | 8841.34 | + | 5104.55i | 0.384947 | + | 0.222249i | ||||
\(809\) | 21077.7 | 0.916012 | 0.458006 | − | 0.888949i | \(-0.348564\pi\) | ||||
0.458006 | + | 0.888949i | \(0.348564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11937.4 | −0.516868 | −0.258434 | − | 0.966029i | \(-0.583206\pi\) | ||||
−0.258434 | + | 0.966029i | \(0.583206\pi\) | |||||||
\(812\) | 13431.9 | + | 7754.94i | 0.580503 | + | 0.335154i | ||||
\(813\) | 16366.2 | + | 25977.7i | 0.706011 | + | 1.12064i | ||||
\(814\) | 24468.4 | + | 42380.5i | 1.05358 | + | 1.82486i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 55.5180 | + | 1437.80i | 0.00238176 | + | 0.0616826i | ||||
\(817\) | −22052.9 | − | 12732.3i | −0.944350 | − | 0.545221i | ||||
\(818\) | 35661.0i | 1.52428i | ||||||||
\(819\) | −22670.3 | + | 47364.5i | −0.967235 | + | 2.02082i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7400.25 | + | 12817.6i | −0.314580 | + | 0.544869i | −0.979348 | − | 0.202181i | \(-0.935197\pi\) |
0.664768 | + | 0.747050i | \(0.268530\pi\) | |||||||
\(822\) | 14860.9 | − | 28199.7i | 0.630576 | − | 1.19657i | ||||
\(823\) | 28731.8 | − | 16588.3i | 1.21692 | − | 0.702591i | 0.252665 | − | 0.967554i | \(-0.418693\pi\) |
0.964259 | + | 0.264963i | \(0.0853596\pi\) | |||||||
\(824\) | −2437.37 | − | 4221.64i | −0.103046 | − | 0.178480i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27921.4 | + | 48361.3i | −1.17616 | + | 2.03717i | ||||
\(827\) | 29001.3i | 1.21944i | 0.792619 | + | 0.609718i | \(0.208717\pi\) | ||||
−0.792619 | + | 0.609718i | \(0.791283\pi\) | |||||||
\(828\) | 14115.5 | − | 9673.27i | 0.592450 | − | 0.406002i | ||||
\(829\) | −13221.1 | −0.553904 | −0.276952 | − | 0.960884i | \(-0.589324\pi\) | ||||
−0.276952 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 659.632 | + | 17083.0i | 0.0275360 | + | 0.713122i | ||||
\(832\) | 40584.7 | − | 23431.6i | 1.69113 | − | 0.976374i | ||||
\(833\) | −3443.73 | + | 1988.24i | −0.143239 | + | 0.0826991i | ||||
\(834\) | −47581.3 | + | 29976.6i | −1.97555 | + | 1.24461i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 31190.3 | 1.29036 | ||||||||
\(837\) | 8622.95 | + | 11596.5i | 0.356096 | + | 0.478893i | ||||
\(838\) | − | 17902.5i | − | 0.737987i | ||||||
\(839\) | −21062.0 | + | 36480.4i | −0.866675 | + | 1.50112i | −0.00129985 | + | 0.999999i | \(0.500414\pi\) |
−0.865375 | + | 0.501125i | \(0.832920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10964.0 | + | 18990.2i | 0.449547 | + | 0.778638i | ||||
\(842\) | 25609.6 | − | 14785.7i | 1.04818 | − | 0.605166i | ||||
\(843\) | −1763.94 | + | 68.1114i | −0.0720679 | + | 0.00278278i | ||||
\(844\) | 12716.4 | − | 22025.4i | 0.518621 | − | 0.898278i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5107.10 | − | 394.992i | 0.207548 | − | 0.0160521i | ||||
\(847\) | − | 10050.0i | − | 0.407700i | ||||||
\(848\) | 956.177 | + | 552.049i | 0.0387208 | + | 0.0223555i | ||||
\(849\) | 11950.4 | + | 6297.71i | 0.483081 | + | 0.254578i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8794.07 | − | 15231.8i | −0.354238 | − | 0.613559i | ||||
\(852\) | −23441.7 | + | 44482.4i | −0.942605 | + | 1.78866i | ||||
\(853\) | −12498.2 | − | 7215.84i | −0.501677 | − | 0.289643i | 0.227729 | − | 0.973725i | \(-0.426870\pi\) |
−0.729406 | + | 0.684081i | \(0.760203\pi\) | |||||||
\(854\) | 111521. | 4.46857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4524.80 | −0.180671 | ||||||||
\(857\) | 13954.6 | + | 8056.71i | 0.556220 | + | 0.321134i | 0.751627 | − | 0.659588i | \(-0.229269\pi\) |
−0.195407 | + | 0.980722i | \(0.562603\pi\) | |||||||
\(858\) | 56956.0 | − | 2199.25i | 2.26625 | − | 0.0875074i | ||||
\(859\) | −11250.2 | − | 19485.9i | −0.446858 | − | 0.773982i | 0.551321 | − | 0.834293i | \(-0.314124\pi\) |
−0.998180 | + | 0.0603115i | \(0.980791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21307.4 | + | 13423.8i | −0.843384 | + | 0.531339i | ||||
\(862\) | −25197.5 | − | 14547.8i | −0.995626 | − | 0.574825i | ||||
\(863\) | − | 43396.8i | − | 1.71175i | −0.517180 | − | 0.855877i | \(-0.673018\pi\) | ||
0.517180 | − | 0.855877i | \(-0.326982\pi\) | |||||||
\(864\) | 28463.1 | − | 21164.6i | 1.12076 | − | 0.833375i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4687.09 | + | 8118.28i | −0.183919 | + | 0.318557i | ||||
\(867\) | 13487.6 | + | 21408.6i | 0.528331 | + | 0.838610i | ||||
\(868\) | 27889.4 | − | 16101.9i | 1.09058 | − | 0.629649i | ||||
\(869\) | −4016.07 | − | 6956.04i | −0.156773 | − | 0.271539i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3044.18 | + | 5272.67i | −0.118425 | + | 0.205118i | ||||
\(872\) | − | 3241.07i | − | 0.125868i | ||||||
\(873\) | 31874.8 | − | 21843.6i | 1.23574 | − | 0.846842i | ||||
\(874\) | −20034.3 | −0.775366 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2375.84 | + | 1252.04i | 0.0916348 | + | 0.0482905i | ||||
\(877\) | 2135.21 | − | 1232.77i | 0.0822133 | − | 0.0474659i | −0.458330 | − | 0.888782i | \(-0.651552\pi\) |
0.540543 | + | 0.841316i | \(0.318219\pi\) | |||||||
\(878\) | −30723.5 | + | 17738.2i | −1.18094 | + | 0.681817i | ||||
\(879\) | 818.640 | + | 431.414i | 0.0314130 | + | 0.0165543i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24512.9 | 0.937412 | 0.468706 | − | 0.883354i | \(-0.344720\pi\) | ||||
0.468706 | + | 0.883354i | \(0.344720\pi\) | |||||||
\(882\) | 62629.9 | + | 29976.9i | 2.39100 | + | 1.14442i | ||||
\(883\) | 24236.1i | 0.923679i | 0.886963 | + | 0.461840i | \(0.152810\pi\) | ||||
−0.886963 | + | 0.461840i | \(0.847190\pi\) | |||||||
\(884\) | −2116.90 | + | 3666.57i | −0.0805418 | + | 0.139502i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23156.0 | − | 40107.3i | −0.878036 | − | 1.52080i | ||||
\(887\) | −21822.7 | + | 12599.3i | −0.826082 | + | 0.476939i | −0.852509 | − | 0.522712i | \(-0.824920\pi\) |
0.0264274 | + | 0.999651i | \(0.491587\pi\) | |||||||
\(888\) | 7200.07 | + | 11428.5i | 0.272093 | + | 0.431888i | ||||
\(889\) | −23167.1 | + | 40126.7i | −0.874017 | + | 1.51384i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29328.0 | − | 4563.86i | 1.10272 | − | 0.171599i | ||||
\(892\) | − | 19050.3i | − | 0.715081i | ||||||
\(893\) | −2906.05 | − | 1677.81i | −0.108899 | − | 0.0628731i | ||||
\(894\) | 1756.72 | − | 1106.75i | 0.0657198 | − | 0.0414040i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17484.5 | − | 30284.0i | −0.651914 | − | 1.12915i | ||||
\(897\) | −20470.3 | + | 790.423i | −0.761964 | + | 0.0294219i | ||||
\(898\) | −18261.1 | − | 10543.1i | −0.678599 | − | 0.391789i | ||||
\(899\) | −5109.87 | −0.189570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −173.151 | −0.00640233 | ||||||||
\(902\) | 23673.5 | + | 13667.9i | 0.873882 | + | 0.504536i | ||||
\(903\) | −25175.9 | + | 47773.2i | −0.927798 | + | 1.76057i | ||||
\(904\) | −8122.42 | − | 14068.5i | −0.298836 | − | 0.517599i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20925.7 | − | 11027.6i | −0.767338 | − | 0.404379i | ||||
\(907\) | 23043.3 | + | 13304.0i | 0.843594 | + | 0.487049i | 0.858484 | − | 0.512840i | \(-0.171407\pi\) |
−0.0148906 | + | 0.999889i | \(0.504740\pi\) | |||||||
\(908\) | 51614.0i | 1.88642i | ||||||||
\(909\) | −16905.4 | − | 24668.9i | −0.616851 | − | 0.900127i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12416.1 | + | 21505.2i | −0.451550 | + | 0.782108i | −0.998483 | − | 0.0550686i | \(-0.982462\pi\) |
0.546932 | + | 0.837177i | \(0.315796\pi\) | |||||||
\(912\) | −16446.6 | + | 635.058i | −0.597151 | + | 0.0230580i | ||||
\(913\) | −6972.25 | + | 4025.43i | −0.252736 | + | 0.145917i | ||||
\(914\) | 30253.7 | + | 52401.0i | 1.09486 | + | 1.89636i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4399.79 | + | 7620.66i | −0.158704 | + | 0.274884i | ||||
\(917\) | − | 39227.8i | − | 1.41267i | ||||||
\(918\) | −1562.70 | + | 3617.03i | −0.0561837 | + | 0.130043i | ||||
\(919\) | 26107.2 | 0.937102 | 0.468551 | − | 0.883436i | \(-0.344776\pi\) | ||||
0.468551 | + | 0.883436i | \(0.344776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6759.91 | − | 4258.80i | 0.241853 | − | 0.152369i | ||||
\(922\) | −67276.2 | + | 38841.9i | −2.40306 | + | 1.38741i | ||||
\(923\) | 52129.3 | − | 30096.9i | 1.85900 | − | 1.07329i | ||||
\(924\) | −2552.11 | − | 66094.0i | −0.0908637 | − | 2.35317i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18501.2 | −0.656573 | ||||||||
\(927\) | 1101.12 | + | 14237.1i | 0.0390136 | + | 0.504431i | ||||
\(928\) | 12542.0i | 0.443653i | ||||||||
\(929\) | −11680.8 | + | 20231.7i | −0.412523 | + | 0.714511i | −0.995165 | − | 0.0982184i | \(-0.968686\pi\) |
0.582642 | + | 0.812729i | \(0.302019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22743.0 | − | 39392.0i | −0.800613 | − | 1.38670i | ||||
\(932\) | −10051.9 | + | 5803.45i | −0.353283 | + | 0.203968i | ||||
\(933\) | 2290.06 | − | 4345.55i | 0.0803570 | − | 0.152483i | ||||
\(934\) | −10483.2 | + | 18157.4i | −0.367260 | + | 0.636112i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15685.8 | − | 1213.17i | 0.547763 | − | 0.0423650i | ||||
\(937\) | − | 10548.5i | − | 0.367775i | −0.982947 | − | 0.183888i | \(-0.941132\pi\) | ||
0.982947 | − | 0.183888i | \(-0.0588682\pi\) | |||||||
\(938\) | 10935.1 | + | 6313.40i | 0.380644 | + | 0.219765i | ||||
\(939\) | −398.082 | − | 10309.5i | −0.0138348 | − | 0.358292i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3245.07 | + | 5620.62i | 0.112419 | + | 0.194715i | 0.916745 | − | 0.399473i | \(-0.130807\pi\) |
−0.804326 | + | 0.594188i | \(0.797473\pi\) | |||||||
\(942\) | 2144.99 | + | 3404.70i | 0.0741906 | + | 0.117761i | ||||
\(943\) | −8508.38 | − | 4912.32i | −0.293819 | − | 0.169636i | ||||
\(944\) | −17897.6 | −0.617074 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58616.4 | 2.01457 | ||||||||
\(947\) | 20356.8 | + | 11753.0i | 0.698528 | + | 0.403295i | 0.806799 | − | 0.590826i | \(-0.201198\pi\) |
−0.108271 | + | 0.994121i | \(0.534531\pi\) | |||||||
\(948\) | −5553.11 | − | 8814.34i | −0.190250 | − | 0.301979i | ||||
\(949\) | −1607.50 | − | 2784.26i | −0.0549858 | − | 0.0952382i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1039.19 | − | 26912.8i | −0.0354344 | − | 0.917674i | ||||
\(952\) | 1618.26 | + | 934.305i | 0.0550927 | + | 0.0318078i | ||||
\(953\) | 6740.26i | 0.229106i | 0.993417 | + | 0.114553i | \(0.0365437\pi\) | ||||
−0.993417 | + | 0.114553i | \(0.963456\pi\) | |||||||
\(954\) | 1709.13 | + | 2494.01i | 0.0580032 | + | 0.0846400i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16003.1 | − | 27718.2i | 0.541399 | − | 0.937731i | ||||
\(957\) | −4892.95 | + | 9284.74i | −0.165274 | + | 0.313619i | ||||
\(958\) | −16877.4 | + | 9744.19i | −0.569191 | + | 0.328623i | ||||
\(959\) | 22141.2 | + | 38349.6i | 0.745543 | + | 1.29132i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9590.57 | − | 16611.4i | 0.321928 | − | 0.557596i | ||||
\(962\) | − | 75984.4i | − | 2.54661i | ||||||
\(963\) | 11955.6 | + | 5722.40i | 0.400068 | + | 0.191487i | ||||
\(964\) | −45776.8 | −1.52943 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1639.28 | + | 42453.8i | 0.0545993 | + | 1.41400i | ||||
\(967\) | −14534.1 | + | 8391.27i | −0.483336 | + | 0.279054i | −0.721806 | − | 0.692096i | \(-0.756688\pi\) |
0.238470 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(968\) | −2607.67 | + | 1505.54i | −0.0865844 | + | 0.0499895i | ||||
\(969\) | 2183.91 | − | 1375.88i | 0.0724016 | − | 0.0456136i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46282.7 | −1.52964 | −0.764822 | − | 0.644242i | \(-0.777173\pi\) | ||||
−0.764822 | + | 0.644242i | \(0.777173\pi\) | |||||||
\(972\) | 37781.9 | − | 7382.66i | 1.24677 | − | 0.243620i | ||||
\(973\) | − | 78124.9i | − | 2.57407i | ||||||
\(974\) | −33564.7 | + | 58135.8i | −1.10419 | + | 1.91252i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17871.2 | + | 30953.8i | 0.586109 | + | 1.01517i | ||||
\(977\) | −5861.22 | + | 3383.98i | −0.191931 | + | 0.110812i | −0.592886 | − | 0.805286i | \(-0.702012\pi\) |
0.400955 | + | 0.916098i | \(0.368678\pi\) | |||||||
\(978\) | −24409.2 | + | 942.517i | −0.798076 | + | 0.0308163i | ||||
\(979\) | 27778.5 | − | 48113.7i | 0.906848 | − | 1.57071i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4098.90 | + | 8563.71i | −0.133402 | + | 0.278714i | ||||
\(982\) | 65240.8i | 2.12008i | ||||||||
\(983\) | 43366.1 | + | 25037.4i | 1.40708 | + | 0.812381i | 0.995106 | − | 0.0988128i | \(-0.0315045\pi\) |
0.411979 | + | 0.911194i | \(0.364838\pi\) | |||||||
\(984\) | 6675.04 | + | 3517.67i | 0.216252 | + | 0.113963i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −696.618 | − | 1206.58i | −0.0224998 | − | 0.0389708i | ||||
\(987\) | −3317.58 | + | 6295.36i | −0.106991 | + | 0.203023i | ||||
\(988\) | −41941.0 | − | 24214.7i | −1.35053 | − | 0.779728i | ||||
\(989\) | −21067.0 | −0.677343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2658.60 | −0.0852200 | −0.0426100 | − | 0.999092i | \(-0.513567\pi\) | ||||
−0.0426100 | + | 0.999092i | \(0.513567\pi\) | |||||||
\(992\) | 22552.6 | + | 13020.7i | 0.721819 | + | 0.416742i | ||||
\(993\) | 11284.7 | − | 435.739i | 0.360634 | − | 0.0139252i | ||||
\(994\) | −62418.7 | − | 108112.i | −1.99175 | − | 3.44981i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8834.88 | + | 5566.05i | −0.281068 | + | 0.177075i | ||||
\(997\) | −52498.5 | − | 30310.0i | −1.66765 | − | 0.962817i | −0.968901 | − | 0.247449i | \(-0.920408\pi\) |
−0.698748 | − | 0.715368i | \(-0.746259\pi\) | |||||||
\(998\) | − | 75570.3i | − | 2.39693i | ||||||
\(999\) | −4571.00 | − | 39302.7i | −0.144765 | − | 1.24473i |
(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 | 225.4.k.d.124.3 | 28 | ||
5.2 | odd | 4 | 45.4.e.c.16.6 | ✓ | 14 | ||
5.3 | odd | 4 | 225.4.e.d.151.2 | 14 | |||
5.4 | even | 2 | inner | 225.4.k.d.124.12 | 28 | ||
9.4 | even | 3 | inner | 225.4.k.d.49.12 | 28 | ||
15.2 | even | 4 | 135.4.e.c.46.2 | 14 | |||
45.2 | even | 12 | 405.4.a.n.1.6 | 7 | |||
45.4 | even | 6 | inner | 225.4.k.d.49.3 | 28 | ||
45.7 | odd | 12 | 405.4.a.m.1.2 | 7 | |||
45.13 | odd | 12 | 225.4.e.d.76.2 | 14 | |||
45.22 | odd | 12 | 45.4.e.c.31.6 | yes | 14 | ||
45.32 | even | 12 | 135.4.e.c.91.2 | 14 | |||
45.38 | even | 12 | 2025.4.a.ba.1.2 | 7 | |||
45.43 | odd | 12 | 2025.4.a.bb.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.6 | ✓ | 14 | 5.2 | odd | 4 | ||
45.4.e.c.31.6 | yes | 14 | 45.22 | odd | 12 | ||
135.4.e.c.46.2 | 14 | 15.2 | even | 4 | |||
135.4.e.c.91.2 | 14 | 45.32 | even | 12 | |||
225.4.e.d.76.2 | 14 | 45.13 | odd | 12 | |||
225.4.e.d.151.2 | 14 | 5.3 | odd | 4 | |||
225.4.k.d.49.3 | 28 | 45.4 | even | 6 | inner | ||
225.4.k.d.49.12 | 28 | 9.4 | even | 3 | inner | ||
225.4.k.d.124.3 | 28 | 1.1 | even | 1 | trivial | ||
225.4.k.d.124.12 | 28 | 5.4 | even | 2 | inner | ||
405.4.a.m.1.2 | 7 | 45.7 | odd | 12 | |||
405.4.a.n.1.6 | 7 | 45.2 | even | 12 | |||
2025.4.a.ba.1.2 | 7 | 45.38 | even | 12 | |||
2025.4.a.bb.1.6 | 7 | 45.43 | odd | 12 |