Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), 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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 48x^{6} + 668x^{4} + 2217x^{2} + 2116 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.1 | ||
Root | \(-4.75345i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.n.274.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.75345i | − 1.68060i | −0.542123 | − | 0.840299i | \(-0.682379\pi\) | ||||
0.542123 | − | 0.840299i | \(-0.317621\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −14.5953 | −1.82441 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.2604 | 0.970294 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 31.3504i | 1.38551i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.31799 | 0.200587 | 0.100293 | − | 0.994958i | \(-0.468022\pi\) | ||||
0.100293 | + | 0.994958i | \(0.468022\pi\) | |||||||
\(12\) | − 43.7859i | − 1.05332i | ||||||||
\(13\) | − 4.15422i | − 0.0886288i | −0.999018 | − | 0.0443144i | \(-0.985890\pi\) | ||||
0.999018 | − | 0.0443144i | \(-0.0141103\pi\) | |||||||
\(14\) | −33.2742 | −0.635207 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 32.2604 | 0.504068 | ||||||||
\(17\) | − 53.5216i | − 0.763582i | −0.924249 | − | 0.381791i | \(-0.875307\pi\) | ||||
0.924249 | − | 0.381791i | \(-0.124693\pi\) | |||||||
\(18\) | 42.7811i | 0.560200i | ||||||||
\(19\) | −88.9019 | −1.07345 | −0.536724 | − | 0.843758i | \(-0.680338\pi\) | ||||
−0.536724 | + | 0.843758i | \(0.680338\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | − 34.7857i | − 0.337106i | ||||||||
\(23\) | 156.780i | 1.42134i | 0.703526 | + | 0.710670i | \(0.251608\pi\) | ||||
−0.703526 | + | 0.710670i | \(0.748392\pi\) | |||||||
\(24\) | −94.0513 | −0.799922 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −19.7469 | −0.148949 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 102.167i | 0.689563i | ||||||||
\(29\) | −42.2570 | −0.270584 | −0.135292 | − | 0.990806i | \(-0.543197\pi\) | ||||
−0.135292 | + | 0.990806i | \(0.543197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.0248 | −0.0812557 | −0.0406279 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406279 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(32\) | 97.4554i | 0.538370i | ||||||||
\(33\) | 21.9540i | 0.115809i | ||||||||
\(34\) | −254.412 | −1.28328 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 131.358 | 0.608137 | ||||||||
\(37\) | 293.336i | 1.30335i | 0.758496 | + | 0.651677i | \(0.225934\pi\) | ||||
−0.758496 | + | 0.651677i | \(0.774066\pi\) | |||||||
\(38\) | 422.591i | 1.80403i | ||||||||
\(39\) | 12.4627 | 0.0511699 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −127.214 | −0.484571 | −0.242286 | − | 0.970205i | \(-0.577897\pi\) | ||||
−0.242286 | + | 0.970205i | \(0.577897\pi\) | |||||||
\(42\) | − 99.8225i | − 0.366737i | ||||||||
\(43\) | − 210.189i | − 0.745431i | −0.927946 | − | 0.372715i | \(-0.878427\pi\) | ||||
0.927946 | − | 0.372715i | \(-0.121573\pi\) | |||||||
\(44\) | −106.808 | −0.365953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 745.244 | 2.38870 | ||||||||
\(47\) | 468.688i | 1.45458i | 0.686332 | + | 0.727289i | \(0.259220\pi\) | ||||
−0.686332 | + | 0.727289i | \(0.740780\pi\) | |||||||
\(48\) | 96.7811i | 0.291024i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 160.565 | 0.440854 | ||||||||
\(52\) | 60.6321i | 0.161696i | ||||||||
\(53\) | 115.973i | 0.300569i | 0.988643 | + | 0.150285i | \(0.0480190\pi\) | ||||
−0.988643 | + | 0.150285i | \(0.951981\pi\) | |||||||
\(54\) | −128.343 | −0.323431 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 219.453 | 0.523672 | ||||||||
\(57\) | − 266.706i | − 0.619755i | ||||||||
\(58\) | 200.867i | 0.454743i | ||||||||
\(59\) | 314.090 | 0.693069 | 0.346534 | − | 0.938037i | \(-0.387358\pi\) | ||||
0.346534 | + | 0.938037i | \(0.387358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 768.386 | 1.61281 | 0.806407 | − | 0.591361i | \(-0.201409\pi\) | ||||
0.806407 | + | 0.591361i | \(0.201409\pi\) | |||||||
\(62\) | 66.6662i | 0.136558i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | 721.332 | 1.40885 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 104.357 | 0.194628 | ||||||||
\(67\) | 717.081i | 1.30754i | 0.756692 | + | 0.653772i | \(0.226814\pi\) | ||||
−0.756692 | + | 0.653772i | \(0.773186\pi\) | |||||||
\(68\) | 781.164i | 1.39309i | ||||||||
\(69\) | −470.339 | −0.820610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −737.783 | −1.23322 | −0.616611 | − | 0.787268i | \(-0.711495\pi\) | ||||
−0.616611 | + | 0.787268i | \(0.711495\pi\) | |||||||
\(72\) | − 282.154i | − 0.461835i | ||||||||
\(73\) | 477.618i | 0.765767i | 0.923797 | + | 0.382884i | \(0.125069\pi\) | ||||
−0.923797 | + | 0.382884i | \(0.874931\pi\) | |||||||
\(74\) | 1394.36 | 2.19042 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1297.55 | 1.95841 | ||||||||
\(77\) | − 51.2259i | − 0.0758147i | ||||||||
\(78\) | − 59.2407i | − 0.0859960i | ||||||||
\(79\) | 279.262 | 0.397714 | 0.198857 | − | 0.980029i | \(-0.436277\pi\) | ||||
0.198857 | + | 0.980029i | \(0.436277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 604.703i | 0.814370i | ||||||||
\(83\) | 776.981i | 1.02753i | 0.857932 | + | 0.513764i | \(0.171749\pi\) | ||||
−0.857932 | + | 0.513764i | \(0.828251\pi\) | |||||||
\(84\) | −306.501 | −0.398119 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −999.123 | −1.25277 | ||||||||
\(87\) | − 126.771i | − 0.156222i | ||||||||
\(88\) | 229.422i | 0.277914i | ||||||||
\(89\) | 29.7626 | 0.0354476 | 0.0177238 | − | 0.999843i | \(-0.494358\pi\) | ||||
0.0177238 | + | 0.999843i | \(0.494358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.0796 | −0.0334985 | ||||||||
\(92\) | − 2288.24i | − 2.59311i | ||||||||
\(93\) | − 42.0744i | − 0.0469130i | ||||||||
\(94\) | 2227.88 | 2.44456 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −292.366 | −0.310828 | ||||||||
\(97\) | 231.793i | 0.242629i | 0.992614 | + | 0.121314i | \(0.0387109\pi\) | ||||
−0.992614 | + | 0.121314i | \(0.961289\pi\) | |||||||
\(98\) | 232.919i | 0.240086i | ||||||||
\(99\) | −65.8619 | −0.0668623 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1898.26 | −1.87014 | −0.935069 | − | 0.354467i | \(-0.884662\pi\) | ||||
−0.935069 | + | 0.354467i | \(0.884662\pi\) | |||||||
\(102\) | − 763.237i | − 0.740899i | ||||||||
\(103\) | 1375.67i | 1.31601i | 0.753015 | + | 0.658003i | \(0.228599\pi\) | ||||
−0.753015 | + | 0.658003i | \(0.771401\pi\) | |||||||
\(104\) | 130.237 | 0.122796 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 551.274 | 0.505136 | ||||||||
\(107\) | − 166.359i | − 0.150304i | −0.997172 | − | 0.0751521i | \(-0.976056\pi\) | ||||
0.997172 | − | 0.0751521i | \(-0.0239442\pi\) | |||||||
\(108\) | 394.073i | 0.351108i | ||||||||
\(109\) | 1346.00 | 1.18279 | 0.591393 | − | 0.806383i | \(-0.298578\pi\) | ||||
0.591393 | + | 0.806383i | \(0.298578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −880.008 | −0.752492 | ||||||||
\(112\) | − 225.822i | − 0.190520i | ||||||||
\(113\) | − 1322.25i | − 1.10077i | −0.834911 | − | 0.550386i | \(-0.814481\pi\) | ||||
0.834911 | − | 0.550386i | \(-0.185519\pi\) | |||||||
\(114\) | −1267.77 | −1.04156 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 616.754 | 0.493657 | ||||||||
\(117\) | 37.3880i | 0.0295429i | ||||||||
\(118\) | − 1493.01i | − 1.16477i | ||||||||
\(119\) | −374.651 | −0.288607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1277.45 | −0.959765 | ||||||||
\(122\) | − 3652.48i | − 2.71049i | ||||||||
\(123\) | − 381.641i | − 0.279767i | ||||||||
\(124\) | 204.696 | 0.148244 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 299.467 | 0.211736 | ||||||||
\(127\) | − 2111.85i | − 1.47556i | −0.675040 | − | 0.737781i | \(-0.735874\pi\) | ||||
0.675040 | − | 0.737781i | \(-0.264126\pi\) | |||||||
\(128\) | − 2649.18i | − 1.82935i | ||||||||
\(129\) | 630.567 | 0.430375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −209.773 | −0.139908 | −0.0699541 | − | 0.997550i | \(-0.522285\pi\) | ||||
−0.0699541 | + | 0.997550i | \(0.522285\pi\) | |||||||
\(132\) | − 320.425i | − 0.211283i | ||||||||
\(133\) | 622.313i | 0.405725i | ||||||||
\(134\) | 3408.61 | 2.19746 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1677.93 | 1.05795 | ||||||||
\(137\) | − 2386.27i | − 1.48812i | −0.668111 | − | 0.744062i | \(-0.732897\pi\) | ||||
0.668111 | − | 0.744062i | \(-0.267103\pi\) | |||||||
\(138\) | 2235.73i | 1.37912i | ||||||||
\(139\) | −1215.45 | −0.741675 | −0.370838 | − | 0.928698i | \(-0.620929\pi\) | ||||
−0.370838 | + | 0.928698i | \(0.620929\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1406.06 | −0.839801 | ||||||||
\(142\) | 3507.01i | 2.07255i | ||||||||
\(143\) | − 30.4006i | − 0.0177778i | ||||||||
\(144\) | −290.343 | −0.168023 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2270.34 | 1.28695 | ||||||||
\(147\) | − 147.000i | − 0.0824786i | ||||||||
\(148\) | − 4281.33i | − 2.37786i | ||||||||
\(149\) | −2849.51 | −1.56672 | −0.783359 | − | 0.621570i | \(-0.786495\pi\) | ||||
−0.783359 | + | 0.621570i | \(0.786495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2643.84 | −1.42485 | −0.712426 | − | 0.701747i | \(-0.752403\pi\) | ||||
−0.712426 | + | 0.701747i | \(0.752403\pi\) | |||||||
\(152\) | − 2787.11i | − 1.48727i | ||||||||
\(153\) | 481.695i | 0.254527i | ||||||||
\(154\) | −243.500 | −0.127414 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −181.896 | −0.0933549 | ||||||||
\(157\) | 2563.09i | 1.30291i | 0.758688 | + | 0.651454i | \(0.225841\pi\) | ||||
−0.758688 | + | 0.651454i | \(0.774159\pi\) | |||||||
\(158\) | − 1327.46i | − 0.668398i | ||||||||
\(159\) | −347.920 | −0.173534 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1097.46 | 0.537216 | ||||||||
\(162\) | − 385.030i | − 0.186733i | ||||||||
\(163\) | − 1403.46i | − 0.674400i | −0.941433 | − | 0.337200i | \(-0.890520\pi\) | ||||
0.941433 | − | 0.337200i | \(-0.109480\pi\) | |||||||
\(164\) | 1856.72 | 0.884057 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3693.34 | 1.72686 | ||||||||
\(167\) | 2658.97i | 1.23208i | 0.787715 | + | 0.616040i | \(0.211264\pi\) | ||||
−0.787715 | + | 0.616040i | \(0.788736\pi\) | |||||||
\(168\) | 658.359i | 0.302342i | ||||||||
\(169\) | 2179.74 | 0.992145 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 800.117 | 0.357816 | ||||||||
\(172\) | 3067.77i | 1.35997i | ||||||||
\(173\) | 3763.19i | 1.65382i | 0.562336 | + | 0.826909i | \(0.309903\pi\) | ||||
−0.562336 | + | 0.826909i | \(0.690097\pi\) | |||||||
\(174\) | −602.600 | −0.262546 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 236.081 | 0.101109 | ||||||||
\(177\) | 942.270i | 0.400143i | ||||||||
\(178\) | − 141.475i | − 0.0595731i | ||||||||
\(179\) | 1056.94 | 0.441336 | 0.220668 | − | 0.975349i | \(-0.429176\pi\) | ||||
0.220668 | + | 0.975349i | \(0.429176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 537.439 | 0.220705 | 0.110352 | − | 0.993893i | \(-0.464802\pi\) | ||||
0.110352 | + | 0.993893i | \(0.464802\pi\) | |||||||
\(182\) | 138.228i | 0.0562976i | ||||||||
\(183\) | 2305.16i | 0.931159i | ||||||||
\(184\) | −4915.11 | −1.96927 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −199.999 | −0.0788420 | ||||||||
\(187\) | − 391.670i | − 0.153165i | ||||||||
\(188\) | − 6840.64i | − 2.65375i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3236.34 | −1.22604 | −0.613020 | − | 0.790068i | \(-0.710045\pi\) | ||||
−0.613020 | + | 0.790068i | \(0.710045\pi\) | |||||||
\(192\) | 2164.00i | 0.813401i | ||||||||
\(193\) | 4620.71i | 1.72335i | 0.507464 | + | 0.861673i | \(0.330583\pi\) | ||||
−0.507464 | + | 0.861673i | \(0.669417\pi\) | |||||||
\(194\) | 1101.82 | 0.407762 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 715.170 | 0.260630 | ||||||||
\(197\) | 2519.57i | 0.911230i | 0.890177 | + | 0.455615i | \(0.150581\pi\) | ||||
−0.890177 | + | 0.455615i | \(0.849419\pi\) | |||||||
\(198\) | 313.071i | 0.112369i | ||||||||
\(199\) | 2121.77 | 0.755819 | 0.377910 | − | 0.925842i | \(-0.376643\pi\) | ||||
0.377910 | + | 0.925842i | \(0.376643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2151.24 | −0.754911 | ||||||||
\(202\) | 9023.28i | 3.14295i | ||||||||
\(203\) | 295.799i | 0.102271i | ||||||||
\(204\) | −2343.49 | −0.804300 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6539.17 | 2.21168 | ||||||||
\(207\) | − 1411.02i | − 0.473780i | ||||||||
\(208\) | − 134.017i | − 0.0446750i | ||||||||
\(209\) | −650.583 | −0.215319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1557.91 | −0.508297 | −0.254149 | − | 0.967165i | \(-0.581795\pi\) | ||||
−0.254149 | + | 0.967165i | \(0.581795\pi\) | |||||||
\(212\) | − 1692.67i | − 0.548362i | ||||||||
\(213\) | − 2213.35i | − 0.712001i | ||||||||
\(214\) | −790.780 | −0.252601 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 846.462 | 0.266641 | ||||||||
\(217\) | 98.1736i | 0.0307118i | ||||||||
\(218\) | − 6398.16i | − 1.98779i | ||||||||
\(219\) | −1432.85 | −0.442116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −222.341 | −0.0676754 | ||||||||
\(222\) | 4183.07i | 1.26464i | ||||||||
\(223\) | 1319.83i | 0.396333i | 0.980168 | + | 0.198167i | \(0.0634987\pi\) | ||||
−0.980168 | + | 0.198167i | \(0.936501\pi\) | |||||||
\(224\) | 682.188 | 0.203485 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6285.27 | −1.84995 | ||||||||
\(227\) | − 6442.42i | − 1.88369i | −0.336043 | − | 0.941847i | \(-0.609089\pi\) | ||||
0.336043 | − | 0.941847i | \(-0.390911\pi\) | |||||||
\(228\) | 3892.65i | 1.13069i | ||||||||
\(229\) | −4654.11 | −1.34302 | −0.671511 | − | 0.740995i | \(-0.734354\pi\) | ||||
−0.671511 | + | 0.740995i | \(0.734354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 153.678 | 0.0437716 | ||||||||
\(232\) | − 1324.78i | − 0.374896i | ||||||||
\(233\) | − 2628.61i | − 0.739080i | −0.929215 | − | 0.369540i | \(-0.879515\pi\) | ||||
0.929215 | − | 0.369540i | \(-0.120485\pi\) | |||||||
\(234\) | 177.722 | 0.0496498 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4584.24 | −1.26444 | ||||||||
\(237\) | 837.786i | 0.229620i | ||||||||
\(238\) | 1780.89i | 0.485033i | ||||||||
\(239\) | −586.369 | −0.158699 | −0.0793495 | − | 0.996847i | \(-0.525284\pi\) | ||||
−0.0793495 | + | 0.996847i | \(0.525284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3141.71 | 0.839731 | 0.419865 | − | 0.907586i | \(-0.362077\pi\) | ||||
0.419865 | + | 0.907586i | \(0.362077\pi\) | |||||||
\(242\) | 6072.28i | 1.61298i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −11214.8 | −2.94244 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1814.11 | −0.470176 | ||||||||
\(247\) | 369.318i | 0.0951383i | ||||||||
\(248\) | − 439.683i | − 0.112580i | ||||||||
\(249\) | −2330.94 | −0.593243 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2929.38 | −0.736656 | −0.368328 | − | 0.929696i | \(-0.620070\pi\) | ||||
−0.368328 | + | 0.929696i | \(0.620070\pi\) | |||||||
\(252\) | − 919.504i | − 0.229854i | ||||||||
\(253\) | 1147.31i | 0.285102i | ||||||||
\(254\) | −10038.6 | −2.47983 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6822.07 | −1.66554 | ||||||||
\(257\) | 388.552i | 0.0943081i | 0.998888 | + | 0.0471541i | \(0.0150152\pi\) | ||||
−0.998888 | + | 0.0471541i | \(0.984985\pi\) | |||||||
\(258\) | − 2997.37i | − 0.723287i | ||||||||
\(259\) | 2053.35 | 0.492622 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 380.313 | 0.0901946 | ||||||||
\(262\) | 997.147i | 0.235130i | ||||||||
\(263\) | 766.349i | 0.179677i | 0.995956 | + | 0.0898387i | \(0.0286351\pi\) | ||||
−0.995956 | + | 0.0898387i | \(0.971365\pi\) | |||||||
\(264\) | −688.266 | −0.160454 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2958.14 | 0.681861 | ||||||||
\(267\) | 89.2879i | 0.0204657i | ||||||||
\(268\) | − 10466.0i | − 2.38550i | ||||||||
\(269\) | −2842.03 | −0.644170 | −0.322085 | − | 0.946711i | \(-0.604384\pi\) | ||||
−0.322085 | + | 0.946711i | \(0.604384\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3512.72 | 0.787390 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(272\) | − 1726.63i | − 0.384897i | ||||||||
\(273\) | − 87.2387i | − 0.0193404i | ||||||||
\(274\) | −11343.0 | −2.50094 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6864.73 | 1.49713 | ||||||||
\(277\) | − 6388.71i | − 1.38578i | −0.721044 | − | 0.692889i | \(-0.756337\pi\) | ||||
0.721044 | − | 0.692889i | \(-0.243663\pi\) | |||||||
\(278\) | 5777.57i | 1.24646i | ||||||||
\(279\) | 126.223 | 0.0270852 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2126.77 | −0.451503 | −0.225752 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225752 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(282\) | 6683.65i | 1.41137i | ||||||||
\(283\) | 8332.13i | 1.75015i | 0.483983 | + | 0.875077i | \(0.339190\pi\) | ||||
−0.483983 | + | 0.875077i | \(0.660810\pi\) | |||||||
\(284\) | 10768.2 | 2.24990 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −144.508 | −0.0298773 | ||||||||
\(287\) | 890.495i | 0.183151i | ||||||||
\(288\) | − 877.099i | − 0.179457i | ||||||||
\(289\) | 2048.44 | 0.416942 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −695.379 | −0.140082 | ||||||||
\(292\) | − 6970.98i | − 1.39707i | ||||||||
\(293\) | − 8654.11i | − 1.72552i | −0.505610 | − | 0.862762i | \(-0.668733\pi\) | ||||
0.505610 | − | 0.862762i | \(-0.331267\pi\) | |||||||
\(294\) | −698.757 | −0.138613 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9196.21 | −1.80581 | ||||||||
\(297\) | − 197.586i | − 0.0386030i | ||||||||
\(298\) | 13545.0i | 2.63302i | ||||||||
\(299\) | 651.297 | 0.125972 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1471.32 | −0.281746 | ||||||||
\(302\) | 12567.4i | 2.39460i | ||||||||
\(303\) | − 5694.78i | − 1.07972i | ||||||||
\(304\) | −2868.01 | −0.541090 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2289.71 | 0.427758 | ||||||||
\(307\) | − 5318.56i | − 0.988749i | −0.869249 | − | 0.494375i | \(-0.835397\pi\) | ||||
0.869249 | − | 0.494375i | \(-0.164603\pi\) | |||||||
\(308\) | 747.657i | 0.138317i | ||||||||
\(309\) | −4127.00 | −0.759796 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7097.87 | −1.29416 | −0.647079 | − | 0.762423i | \(-0.724010\pi\) | ||||
−0.647079 | + | 0.762423i | \(0.724010\pi\) | |||||||
\(312\) | 390.710i | 0.0708962i | ||||||||
\(313\) | − 2080.78i | − 0.375759i | −0.982192 | − | 0.187879i | \(-0.939839\pi\) | ||||
0.982192 | − | 0.187879i | \(-0.0601614\pi\) | |||||||
\(314\) | 12183.5 | 2.18967 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4075.91 | −0.725595 | ||||||||
\(317\) | − 2644.61i | − 0.468568i | −0.972168 | − | 0.234284i | \(-0.924725\pi\) | ||||
0.972168 | − | 0.234284i | \(-0.0752745\pi\) | |||||||
\(318\) | 1653.82i | 0.291641i | ||||||||
\(319\) | −309.236 | −0.0542756 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 499.078 | 0.0867782 | ||||||||
\(322\) | − 5216.71i | − 0.902844i | ||||||||
\(323\) | 4758.17i | 0.819665i | ||||||||
\(324\) | −1182.22 | −0.202712 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6671.26 | −1.13340 | ||||||||
\(327\) | 4038.01i | 0.682882i | ||||||||
\(328\) | − 3988.20i | − 0.671376i | ||||||||
\(329\) | 3280.81 | 0.549779 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1831.16 | −0.304077 | −0.152039 | − | 0.988375i | \(-0.548584\pi\) | ||||
−0.152039 | + | 0.988375i | \(0.548584\pi\) | |||||||
\(332\) | − 11340.3i | − 1.87463i | ||||||||
\(333\) | − 2640.02i | − 0.434452i | ||||||||
\(334\) | 12639.3 | 2.07063 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 677.467 | 0.109997 | ||||||||
\(337\) | − 9307.67i | − 1.50451i | −0.658870 | − | 0.752257i | \(-0.728965\pi\) | ||||
0.658870 | − | 0.752257i | \(-0.271035\pi\) | |||||||
\(338\) | − 10361.3i | − 1.66740i | ||||||||
\(339\) | 3966.76 | 0.635531 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −102.633 | −0.0162988 | ||||||||
\(342\) | − 3803.32i | − 0.601345i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 6589.52 | 1.03280 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17888.2 | 2.77940 | ||||||||
\(347\) | 10802.7i | 1.67124i | 0.549310 | + | 0.835619i | \(0.314891\pi\) | ||||
−0.549310 | + | 0.835619i | \(0.685109\pi\) | |||||||
\(348\) | 1850.26i | 0.285013i | ||||||||
\(349\) | −2242.94 | −0.344017 | −0.172009 | − | 0.985095i | \(-0.555026\pi\) | ||||
−0.172009 | + | 0.985095i | \(0.555026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −112.164 | −0.0170566 | ||||||||
\(352\) | 713.177i | 0.107990i | ||||||||
\(353\) | 3295.68i | 0.496916i | 0.968643 | + | 0.248458i | \(0.0799238\pi\) | ||||
−0.968643 | + | 0.248458i | \(0.920076\pi\) | |||||||
\(354\) | 4479.04 | 0.672480 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −434.395 | −0.0646710 | ||||||||
\(357\) | − 1123.95i | − 0.166627i | ||||||||
\(358\) | − 5024.09i | − 0.741709i | ||||||||
\(359\) | 4634.55 | 0.681344 | 0.340672 | − | 0.940182i | \(-0.389345\pi\) | ||||
0.340672 | + | 0.940182i | \(0.389345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1044.55 | 0.152289 | ||||||||
\(362\) | − 2554.69i | − 0.370916i | ||||||||
\(363\) | − 3832.34i | − 0.554121i | ||||||||
\(364\) | 424.425 | 0.0611152 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10957.4 | 1.56490 | ||||||||
\(367\) | − 6316.17i | − 0.898369i | −0.893439 | − | 0.449185i | \(-0.851715\pi\) | ||||
0.893439 | − | 0.449185i | \(-0.148285\pi\) | |||||||
\(368\) | 5057.76i | 0.716452i | ||||||||
\(369\) | 1144.92 | 0.161524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 811.814 | 0.113604 | ||||||||
\(372\) | 614.088i | 0.0855887i | ||||||||
\(373\) | − 7880.83i | − 1.09398i | −0.837140 | − | 0.546989i | \(-0.815774\pi\) | ||||
0.837140 | − | 0.546989i | \(-0.184226\pi\) | |||||||
\(374\) | −1861.79 | −0.257408 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14693.6 | −2.01533 | ||||||||
\(377\) | 175.545i | 0.0239815i | ||||||||
\(378\) | 898.402i | 0.122246i | ||||||||
\(379\) | −9853.13 | −1.33541 | −0.667706 | − | 0.744425i | \(-0.732724\pi\) | ||||
−0.667706 | + | 0.744425i | \(0.732724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6335.55 | 0.851916 | ||||||||
\(382\) | 15383.8i | 2.06048i | ||||||||
\(383\) | 1193.49i | 0.159228i | 0.996826 | + | 0.0796141i | \(0.0253688\pi\) | ||||
−0.996826 | + | 0.0796141i | \(0.974631\pi\) | |||||||
\(384\) | 7947.53 | 1.05617 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21964.3 | 2.89625 | ||||||||
\(387\) | 1891.70i | 0.248477i | ||||||||
\(388\) | − 3383.09i | − 0.442655i | ||||||||
\(389\) | 10425.7 | 1.35888 | 0.679442 | − | 0.733729i | \(-0.262222\pi\) | ||||
0.679442 | + | 0.733729i | \(0.262222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8391.09 | 1.08531 | ||||||||
\(392\) | − 1536.17i | − 0.197929i | ||||||||
\(393\) | − 629.320i | − 0.0807761i | ||||||||
\(394\) | 11976.7 | 1.53141 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 961.274 | 0.121984 | ||||||||
\(397\) | − 3650.05i | − 0.461437i | −0.973021 | − | 0.230719i | \(-0.925892\pi\) | ||||
0.973021 | − | 0.230719i | \(-0.0741077\pi\) | |||||||
\(398\) | − 10085.7i | − 1.27023i | ||||||||
\(399\) | −1866.94 | −0.234245 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8202.17 | −1.02144 | −0.510719 | − | 0.859747i | \(-0.670621\pi\) | ||||
−0.510719 | + | 0.859747i | \(0.670621\pi\) | |||||||
\(402\) | 10225.8i | 1.26870i | ||||||||
\(403\) | 58.2622i | 0.00720160i | ||||||||
\(404\) | 27705.7 | 3.41190 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1406.07 | 0.171877 | ||||||||
\(407\) | 2146.63i | 0.261436i | ||||||||
\(408\) | 5033.78i | 0.610807i | ||||||||
\(409\) | −9097.72 | −1.09989 | −0.549943 | − | 0.835202i | \(-0.685351\pi\) | ||||
−0.549943 | + | 0.835202i | \(0.685351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7158.81 | 0.859169 | ||||||||
\(412\) | − 20078.3i | − 2.40094i | ||||||||
\(413\) | − 2198.63i | − 0.261955i | ||||||||
\(414\) | −6707.20 | −0.796234 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 404.852 | 0.0477151 | ||||||||
\(417\) | − 3646.34i | − 0.428206i | ||||||||
\(418\) | 3092.51i | 0.361866i | ||||||||
\(419\) | 4704.01 | 0.548462 | 0.274231 | − | 0.961664i | \(-0.411577\pi\) | ||||
0.274231 | + | 0.961664i | \(0.411577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1596.95 | 0.184871 | 0.0924355 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924355 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(422\) | 7405.44i | 0.854244i | ||||||||
\(423\) | − 4218.19i | − 0.484859i | ||||||||
\(424\) | −3635.82 | −0.416441 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10521.0 | −1.19659 | ||||||||
\(427\) | − 5378.70i | − 0.609587i | ||||||||
\(428\) | 2428.06i | 0.274217i | ||||||||
\(429\) | 91.2017 | 0.0102640 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6235.23 | 0.696845 | 0.348423 | − | 0.937338i | \(-0.386717\pi\) | ||||
0.348423 | + | 0.937338i | \(0.386717\pi\) | |||||||
\(432\) | − 871.030i | − 0.0970079i | ||||||||
\(433\) | 2363.94i | 0.262364i | 0.991358 | + | 0.131182i | \(0.0418772\pi\) | ||||
−0.991358 | + | 0.131182i | \(0.958123\pi\) | |||||||
\(434\) | 466.663 | 0.0516142 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19645.3 | −2.15789 | ||||||||
\(437\) | − 13938.0i | − 1.52573i | ||||||||
\(438\) | 6811.01i | 0.743019i | ||||||||
\(439\) | 17537.7 | 1.90667 | 0.953335 | − | 0.301916i | \(-0.0976261\pi\) | ||||
0.953335 | + | 0.301916i | \(0.0976261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 1056.89i | 0.113735i | ||||||||
\(443\) | − 4488.83i | − 0.481424i | −0.970597 | − | 0.240712i | \(-0.922619\pi\) | ||||
0.970597 | − | 0.240712i | \(-0.0773809\pi\) | |||||||
\(444\) | 12844.0 | 1.37286 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6273.74 | 0.666077 | ||||||||
\(447\) | − 8548.53i | − 0.904544i | ||||||||
\(448\) | − 5049.33i | − 0.532496i | ||||||||
\(449\) | −13188.3 | −1.38618 | −0.693090 | − | 0.720851i | \(-0.743751\pi\) | ||||
−0.693090 | + | 0.720851i | \(0.743751\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −930.947 | −0.0971986 | ||||||||
\(452\) | 19298.7i | 2.00826i | ||||||||
\(453\) | − 7931.52i | − 0.822638i | ||||||||
\(454\) | −30623.7 | −3.16573 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8361.34 | 0.858674 | ||||||||
\(457\) | − 8085.04i | − 0.827576i | −0.910373 | − | 0.413788i | \(-0.864206\pi\) | ||||
0.910373 | − | 0.413788i | \(-0.135794\pi\) | |||||||
\(458\) | 22123.1i | 2.25708i | ||||||||
\(459\) | −1445.08 | −0.146951 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −825.258 | −0.0833754 | −0.0416877 | − | 0.999131i | \(-0.513273\pi\) | ||||
−0.0416877 | + | 0.999131i | \(0.513273\pi\) | |||||||
\(462\) | − 730.499i | − 0.0735626i | ||||||||
\(463\) | 16607.8i | 1.66702i | 0.552505 | + | 0.833509i | \(0.313672\pi\) | ||||
−0.552505 | + | 0.833509i | \(0.686328\pi\) | |||||||
\(464\) | −1363.23 | −0.136393 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12495.0 | −1.24210 | ||||||||
\(467\) | − 6003.84i | − 0.594914i | −0.954735 | − | 0.297457i | \(-0.903862\pi\) | ||||
0.954735 | − | 0.297457i | \(-0.0961385\pi\) | |||||||
\(468\) | − 545.689i | − 0.0538985i | ||||||||
\(469\) | 5019.57 | 0.494205 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7689.26 | −0.752235 | ||||||||
\(472\) | 9846.86i | 0.960251i | ||||||||
\(473\) | − 1538.16i | − 0.149524i | ||||||||
\(474\) | 3982.37 | 0.385900 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5468.15 | 0.526538 | ||||||||
\(477\) | − 1043.76i | − 0.100190i | ||||||||
\(478\) | 2787.28i | 0.266709i | ||||||||
\(479\) | −20386.0 | −1.94459 | −0.972295 | − | 0.233759i | \(-0.924897\pi\) | ||||
−0.972295 | + | 0.233759i | \(0.924897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1218.58 | 0.115515 | ||||||||
\(482\) | − 14933.9i | − 1.41125i | ||||||||
\(483\) | 3292.37i | 0.310162i | ||||||||
\(484\) | 18644.7 | 1.75101 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1155.09 | 0.107810 | ||||||||
\(487\) | − 9422.61i | − 0.876754i | −0.898791 | − | 0.438377i | \(-0.855553\pi\) | ||||
0.898791 | − | 0.438377i | \(-0.144447\pi\) | |||||||
\(488\) | 24089.2i | 2.23456i | ||||||||
\(489\) | 4210.37 | 0.389365 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5908.30 | 0.543051 | 0.271525 | − | 0.962431i | \(-0.412472\pi\) | ||||
0.271525 | + | 0.962431i | \(0.412472\pi\) | |||||||
\(492\) | 5570.16i | 0.510411i | ||||||||
\(493\) | 2261.66i | 0.206613i | ||||||||
\(494\) | 1755.54 | 0.159889 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −452.445 | −0.0409584 | ||||||||
\(497\) | 5164.48i | 0.466114i | ||||||||
\(498\) | 11080.0i | 0.997003i | ||||||||
\(499\) | 3237.65 | 0.290455 | 0.145227 | − | 0.989398i | \(-0.453609\pi\) | ||||
0.145227 | + | 0.989398i | \(0.453609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7976.92 | −0.711342 | ||||||||
\(502\) | 13924.7i | 1.23802i | ||||||||
\(503\) | 1112.05i | 0.0985760i | 0.998785 | + | 0.0492880i | \(0.0156952\pi\) | ||||
−0.998785 | + | 0.0492880i | \(0.984305\pi\) | |||||||
\(504\) | −1975.08 | −0.174557 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5453.68 | 0.479142 | ||||||||
\(507\) | 6539.23i | 0.572815i | ||||||||
\(508\) | 30823.1i | 2.69203i | ||||||||
\(509\) | −15737.5 | −1.37044 | −0.685220 | − | 0.728336i | \(-0.740294\pi\) | ||||
−0.685220 | + | 0.728336i | \(0.740294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3343.33 | 0.289433 | ||||||||
\(512\) | 11235.0i | 0.969765i | ||||||||
\(513\) | 2400.35i | 0.206585i | ||||||||
\(514\) | 1846.96 | 0.158494 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9203.32 | −0.785181 | ||||||||
\(517\) | 3429.85i | 0.291769i | ||||||||
\(518\) | − 9760.51i | − 0.827900i | ||||||||
\(519\) | −11289.6 | −0.954832 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5009.73 | −0.421267 | −0.210633 | − | 0.977565i | \(-0.567553\pi\) | ||||
−0.210633 | + | 0.977565i | \(0.567553\pi\) | |||||||
\(522\) | − 1807.80i | − 0.151581i | ||||||||
\(523\) | 14162.2i | 1.18407i | 0.805912 | + | 0.592035i | \(0.201675\pi\) | ||||
−0.805912 | + | 0.592035i | \(0.798325\pi\) | |||||||
\(524\) | 3061.70 | 0.255250 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3642.80 | 0.301965 | ||||||||
\(527\) | 750.630i | 0.0620454i | ||||||||
\(528\) | 708.242i | 0.0583756i | ||||||||
\(529\) | −12412.8 | −1.02020 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2826.81 | −0.231023 | ||||||||
\(532\) | − 9082.85i | − 0.740209i | ||||||||
\(533\) | 528.474i | 0.0429470i | ||||||||
\(534\) | 424.426 | 0.0343946 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −22480.8 | −1.81161 | ||||||||
\(537\) | 3170.81i | 0.254805i | ||||||||
\(538\) | 13509.5i | 1.08259i | ||||||||
\(539\) | −358.581 | −0.0286553 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14815.3 | 1.17738 | 0.588689 | − | 0.808360i | \(-0.299644\pi\) | ||||
0.588689 | + | 0.808360i | \(0.299644\pi\) | |||||||
\(542\) | − 16697.5i | − 1.32329i | ||||||||
\(543\) | 1612.32i | 0.127424i | ||||||||
\(544\) | 5215.97 | 0.411090 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −414.685 | −0.0325034 | ||||||||
\(547\) | − 14248.3i | − 1.11373i | −0.830601 | − | 0.556867i | \(-0.812003\pi\) | ||||
0.830601 | − | 0.556867i | \(-0.187997\pi\) | |||||||
\(548\) | 34828.3i | 2.71495i | ||||||||
\(549\) | −6915.47 | −0.537605 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3756.73 | 0.290458 | ||||||||
\(552\) | − 14745.3i | − 1.13696i | ||||||||
\(553\) | − 1954.83i | − 0.150322i | ||||||||
\(554\) | −30368.4 | −2.32894 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17739.8 | 1.35312 | ||||||||
\(557\) | − 9394.37i | − 0.714636i | −0.933983 | − | 0.357318i | \(-0.883691\pi\) | ||||
0.933983 | − | 0.357318i | \(-0.116309\pi\) | |||||||
\(558\) | − 599.996i | − 0.0455194i | ||||||||
\(559\) | −873.173 | −0.0660667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1175.01 | 0.0884296 | ||||||||
\(562\) | 10109.5i | 0.758796i | ||||||||
\(563\) | − 8572.89i | − 0.641748i | −0.947122 | − | 0.320874i | \(-0.896023\pi\) | ||||
0.947122 | − | 0.320874i | \(-0.103977\pi\) | |||||||
\(564\) | 20521.9 | 1.53214 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 39606.4 | 2.94131 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | − 23129.8i | − 1.70864i | ||||||||
\(569\) | −8954.65 | −0.659751 | −0.329876 | − | 0.944024i | \(-0.607007\pi\) | ||||
−0.329876 | + | 0.944024i | \(0.607007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21592.5 | 1.58252 | 0.791260 | − | 0.611479i | \(-0.209425\pi\) | ||||
0.791260 | + | 0.611479i | \(0.209425\pi\) | |||||||
\(572\) | 443.705i | 0.0324340i | ||||||||
\(573\) | − 9709.03i | − 0.707854i | ||||||||
\(574\) | 4232.92 | 0.307803 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6491.99 | −0.469617 | ||||||||
\(577\) | 17587.5i | 1.26894i | 0.772947 | + | 0.634470i | \(0.218782\pi\) | ||||
−0.772947 | + | 0.634470i | \(0.781218\pi\) | |||||||
\(578\) | − 9737.14i | − 0.700712i | ||||||||
\(579\) | −13862.1 | −0.994974 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5438.87 | 0.388369 | ||||||||
\(582\) | 3305.45i | 0.235421i | ||||||||
\(583\) | 848.692i | 0.0602903i | ||||||||
\(584\) | −14973.5 | −1.06098 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41136.9 | −2.89991 | ||||||||
\(587\) | 4613.88i | 0.324421i | 0.986756 | + | 0.162210i | \(0.0518623\pi\) | ||||
−0.986756 | + | 0.162210i | \(0.948138\pi\) | |||||||
\(588\) | 2145.51i | 0.150475i | ||||||||
\(589\) | 1246.83 | 0.0872237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7558.72 | −0.526099 | ||||||||
\(592\) | 9463.12i | 0.656980i | ||||||||
\(593\) | − 8688.07i | − 0.601647i | −0.953680 | − | 0.300823i | \(-0.902739\pi\) | ||||
0.953680 | − | 0.300823i | \(-0.0972614\pi\) | |||||||
\(594\) | −939.214 | −0.0648761 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 41589.4 | 2.85834 | ||||||||
\(597\) | 6365.30i | 0.436372i | ||||||||
\(598\) | − 3095.91i | − 0.211708i | ||||||||
\(599\) | −7361.43 | −0.502137 | −0.251068 | − | 0.967969i | \(-0.580782\pi\) | ||||
−0.251068 | + | 0.967969i | \(0.580782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16441.9 | 1.11594 | 0.557971 | − | 0.829861i | \(-0.311580\pi\) | ||||
0.557971 | + | 0.829861i | \(0.311580\pi\) | |||||||
\(602\) | 6993.86i | 0.473503i | ||||||||
\(603\) | − 6453.73i | − 0.435848i | ||||||||
\(604\) | 38587.6 | 2.59952 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −27069.9 | −1.81458 | ||||||||
\(607\) | 21024.5i | 1.40586i | 0.711258 | + | 0.702931i | \(0.248126\pi\) | ||||
−0.711258 | + | 0.702931i | \(0.751874\pi\) | |||||||
\(608\) | − 8663.97i | − 0.577912i | ||||||||
\(609\) | −887.398 | −0.0590463 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1947.03 | 0.128917 | ||||||||
\(612\) | − 7030.48i | − 0.464363i | ||||||||
\(613\) | 3278.79i | 0.216034i | 0.994149 | + | 0.108017i | \(0.0344501\pi\) | ||||
−0.994149 | + | 0.108017i | \(0.965550\pi\) | |||||||
\(614\) | −25281.5 | −1.66169 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1605.95 | 0.105042 | ||||||||
\(617\) | − 136.641i | − 0.00891567i | −0.999990 | − | 0.00445783i | \(-0.998581\pi\) | ||||
0.999990 | − | 0.00445783i | \(-0.00141898\pi\) | |||||||
\(618\) | 19617.5i | 1.27691i | ||||||||
\(619\) | 13109.0 | 0.851205 | 0.425603 | − | 0.904910i | \(-0.360062\pi\) | ||||
0.425603 | + | 0.904910i | \(0.360062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4233.05 | 0.273537 | ||||||||
\(622\) | 33739.4i | 2.17496i | ||||||||
\(623\) | − 208.338i | − 0.0133979i | ||||||||
\(624\) | 402.050 | 0.0257931 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9890.87 | −0.631500 | ||||||||
\(627\) | − 1951.75i | − 0.124315i | ||||||||
\(628\) | − 37409.0i | − 2.37704i | ||||||||
\(629\) | 15699.8 | 0.995219 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −351.608 | −0.0221827 | −0.0110913 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110913 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(632\) | 8754.98i | 0.551035i | ||||||||
\(633\) | − 4673.72i | − 0.293466i | ||||||||
\(634\) | −12571.0 | −0.787474 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5078.00 | 0.316597 | ||||||||
\(637\) | 203.557i | 0.0126613i | ||||||||
\(638\) | 1469.94i | 0.0912155i | ||||||||
\(639\) | 6640.04 | 0.411074 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17551.0 | −1.08147 | −0.540736 | − | 0.841192i | \(-0.681854\pi\) | ||||
−0.540736 | + | 0.841192i | \(0.681854\pi\) | |||||||
\(642\) | − 2372.34i | − 0.145839i | ||||||||
\(643\) | 20683.7i | 1.26856i | 0.773103 | + | 0.634281i | \(0.218704\pi\) | ||||
−0.773103 | + | 0.634281i | \(0.781296\pi\) | |||||||
\(644\) | −16017.7 | −0.980103 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22617.7 | 1.37753 | ||||||||
\(647\) | − 1782.40i | − 0.108305i | −0.998533 | − | 0.0541526i | \(-0.982754\pi\) | ||||
0.998533 | − | 0.0541526i | \(-0.0172457\pi\) | |||||||
\(648\) | 2539.38i | 0.153945i | ||||||||
\(649\) | 2298.51 | 0.139020 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −294.521 | −0.0177315 | ||||||||
\(652\) | 20483.9i | 1.23038i | ||||||||
\(653\) | − 3642.28i | − 0.218275i | −0.994027 | − | 0.109137i | \(-0.965191\pi\) | ||||
0.994027 | − | 0.109137i | \(-0.0348088\pi\) | |||||||
\(654\) | 19194.5 | 1.14765 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4103.95 | −0.244257 | ||||||||
\(657\) | − 4298.56i | − 0.255256i | ||||||||
\(658\) | − 15595.2i | − 0.923957i | ||||||||
\(659\) | 14883.2 | 0.879768 | 0.439884 | − | 0.898055i | \(-0.355020\pi\) | ||||
0.439884 | + | 0.898055i | \(0.355020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1871.82 | −0.110145 | −0.0550723 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550723 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(662\) | 8704.33i | 0.511032i | ||||||||
\(663\) | − 667.022i | − 0.0390724i | ||||||||
\(664\) | −24358.7 | −1.42365 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12549.2 | −0.730139 | ||||||||
\(667\) | − 6625.04i | − 0.384592i | ||||||||
\(668\) | − 38808.5i | − 2.24782i | ||||||||
\(669\) | −3959.49 | −0.228823 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5623.03 | 0.323509 | ||||||||
\(672\) | 2046.56i | 0.117482i | ||||||||
\(673\) | − 22208.8i | − 1.27205i | −0.771670 | − | 0.636023i | \(-0.780578\pi\) | ||||
0.771670 | − | 0.636023i | \(-0.219422\pi\) | |||||||
\(674\) | −44243.6 | −2.52848 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31814.0 | −1.81008 | ||||||||
\(677\) | 31340.2i | 1.77918i | 0.456762 | + | 0.889589i | \(0.349009\pi\) | ||||
−0.456762 | + | 0.889589i | \(0.650991\pi\) | |||||||
\(678\) | − 18855.8i | − 1.06807i | ||||||||
\(679\) | 1622.55 | 0.0917051 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19327.3 | 1.08755 | ||||||||
\(682\) | 487.862i | 0.0273918i | ||||||||
\(683\) | 27666.5i | 1.54997i | 0.631979 | + | 0.774985i | \(0.282243\pi\) | ||||
−0.631979 | + | 0.774985i | \(0.717757\pi\) | |||||||
\(684\) | −11677.9 | −0.652803 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1630.43 | 0.0907438 | ||||||||
\(687\) | − 13962.3i | − 0.775394i | ||||||||
\(688\) | − 6780.77i | − 0.375748i | ||||||||
\(689\) | 481.780 | 0.0266391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7978.64 | −0.439250 | −0.219625 | − | 0.975584i | \(-0.570483\pi\) | ||||
−0.219625 | + | 0.975584i | \(0.570483\pi\) | |||||||
\(692\) | − 54925.0i | − 3.01724i | ||||||||
\(693\) | 461.033i | 0.0252716i | ||||||||
\(694\) | 51350.1 | 2.80868 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3974.33 | 0.216446 | ||||||||
\(697\) | 6808.67i | 0.370010i | ||||||||
\(698\) | 10661.7i | 0.578155i | ||||||||
\(699\) | 7885.82 | 0.426708 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16299.3 | −0.878197 | −0.439099 | − | 0.898439i | \(-0.644702\pi\) | ||||
−0.439099 | + | 0.898439i | \(0.644702\pi\) | |||||||
\(702\) | 533.166i | 0.0286653i | ||||||||
\(703\) | − 26078.1i | − 1.39908i | ||||||||
\(704\) | 5278.70 | 0.282597 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15665.8 | 0.835116 | ||||||||
\(707\) | 13287.8i | 0.706845i | ||||||||
\(708\) | − 13752.7i | − 0.730026i | ||||||||
\(709\) | 36223.4 | 1.91876 | 0.959379 | − | 0.282122i | \(-0.0910382\pi\) | ||||
0.959379 | + | 0.282122i | \(0.0910382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2513.36 | −0.132571 | ||||||||
\(712\) | 933.071i | 0.0491128i | ||||||||
\(713\) | − 2198.80i | − 0.115492i | ||||||||
\(714\) | −5342.66 | −0.280034 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15426.3 | −0.805179 | ||||||||
\(717\) | − 1759.11i | − 0.0916249i | ||||||||
\(718\) | − 22030.1i | − 1.14507i | ||||||||
\(719\) | 636.264 | 0.0330023 | 0.0165011 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165011 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9629.67 | 0.497403 | ||||||||
\(722\) | − 4965.21i | − 0.255936i | ||||||||
\(723\) | 9425.12i | 0.484819i | ||||||||
\(724\) | −7844.08 | −0.402656 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18216.8 | −0.931254 | ||||||||
\(727\) | 33098.8i | 1.68854i | 0.535918 | + | 0.844270i | \(0.319965\pi\) | ||||
−0.535918 | + | 0.844270i | \(0.680035\pi\) | |||||||
\(728\) | − 911.657i | − 0.0464124i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11249.7 | −0.569198 | ||||||||
\(732\) | − 33644.4i | − 1.69882i | ||||||||
\(733\) | − 12019.8i | − 0.605678i | −0.953042 | − | 0.302839i | \(-0.902066\pi\) | ||||
0.953042 | − | 0.302839i | \(-0.0979345\pi\) | |||||||
\(734\) | −30023.6 | −1.50980 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15279.0 | −0.765207 | ||||||||
\(737\) | 5247.59i | 0.262276i | ||||||||
\(738\) | − 5442.33i | − 0.271457i | ||||||||
\(739\) | −5332.38 | −0.265433 | −0.132716 | − | 0.991154i | \(-0.542370\pi\) | ||||
−0.132716 | + | 0.991154i | \(0.542370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1107.96 | −0.0549281 | ||||||||
\(742\) | − 3858.92i | − 0.190924i | ||||||||
\(743\) | 6547.51i | 0.323290i | 0.986849 | + | 0.161645i | \(0.0516800\pi\) | ||||
−0.986849 | + | 0.161645i | \(0.948320\pi\) | |||||||
\(744\) | 1319.05 | 0.0649983 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −37461.1 | −1.83854 | ||||||||
\(747\) | − 6992.83i | − 0.342509i | ||||||||
\(748\) | 5716.55i | 0.279435i | ||||||||
\(749\) | −1164.51 | −0.0568097 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19316.3 | 0.938565 | 0.469282 | − | 0.883048i | \(-0.344513\pi\) | ||||
0.469282 | + | 0.883048i | \(0.344513\pi\) | |||||||
\(752\) | 15120.0i | 0.733206i | ||||||||
\(753\) | − 8788.14i | − 0.425309i | ||||||||
\(754\) | 834.446 | 0.0403033 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2758.51 | 0.132706 | ||||||||
\(757\) | − 40483.3i | − 1.94371i | −0.235573 | − | 0.971857i | \(-0.575697\pi\) | ||||
0.235573 | − | 0.971857i | \(-0.424303\pi\) | |||||||
\(758\) | 46836.3i | 2.24429i | ||||||||
\(759\) | −3441.93 | −0.164604 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5470.00 | −0.260561 | −0.130281 | − | 0.991477i | \(-0.541588\pi\) | ||||
−0.130281 | + | 0.991477i | \(0.541588\pi\) | |||||||
\(762\) | − 30115.7i | − 1.43173i | ||||||||
\(763\) | − 9422.02i | − 0.447051i | ||||||||
\(764\) | 47235.4 | 2.23680 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5673.19 | 0.267599 | ||||||||
\(767\) | − 1304.80i | − 0.0614258i | ||||||||
\(768\) | − 20466.2i | − 0.961602i | ||||||||
\(769\) | −17692.4 | −0.829653 | −0.414826 | − | 0.909901i | \(-0.636158\pi\) | ||||
−0.414826 | + | 0.909901i | \(0.636158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1165.65 | −0.0544488 | ||||||||
\(772\) | − 67440.6i | − 3.14409i | ||||||||
\(773\) | − 3338.50i | − 0.155340i | −0.996979 | − | 0.0776699i | \(-0.975252\pi\) | ||||
0.996979 | − | 0.0776699i | \(-0.0247480\pi\) | |||||||
\(774\) | 8992.11 | 0.417590 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7266.81 | −0.336164 | ||||||||
\(777\) | 6160.05i | 0.284415i | ||||||||
\(778\) | − 49558.2i | − 2.28374i | ||||||||
\(779\) | 11309.5 | 0.520161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5399.08 | −0.247368 | ||||||||
\(782\) | − 39886.7i | − 1.82397i | ||||||||
\(783\) | 1140.94i | 0.0520739i | ||||||||
\(784\) | −1580.76 | −0.0720097 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2991.44 | −0.135752 | ||||||||
\(787\) | − 11738.0i | − 0.531657i | −0.964020 | − | 0.265829i | \(-0.914354\pi\) | ||||
0.964020 | − | 0.265829i | \(-0.0856456\pi\) | |||||||
\(788\) | − 36773.9i | − 1.66246i | ||||||||
\(789\) | −2299.05 | −0.103737 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9255.77 | −0.416052 | ||||||||
\(792\) | − 2064.80i | − 0.0926381i | ||||||||
\(793\) | − 3192.05i | − 0.142942i | ||||||||
\(794\) | −17350.3 | −0.775491 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30967.8 | −1.37893 | ||||||||
\(797\) | 20150.5i | 0.895568i | 0.894142 | + | 0.447784i | \(0.147787\pi\) | ||||
−0.894142 | + | 0.447784i | \(0.852213\pi\) | |||||||
\(798\) | 8874.41i | 0.393672i | ||||||||
\(799\) | 25084.9 | 1.11069 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −267.864 | −0.0118159 | ||||||||
\(802\) | 38988.6i | 1.71663i | ||||||||
\(803\) | 3495.20i | 0.153603i | ||||||||
\(804\) | 31398.0 | 1.37727 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 276.946 | 0.0121030 | ||||||||
\(807\) | − 8526.09i | − 0.371912i | ||||||||
\(808\) | − 59511.3i | − 2.59109i | ||||||||
\(809\) | 3381.53 | 0.146957 | 0.0734785 | − | 0.997297i | \(-0.476590\pi\) | ||||
0.0734785 | + | 0.997297i | \(0.476590\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11375.3 | 0.492528 | 0.246264 | − | 0.969203i | \(-0.420797\pi\) | ||||
0.246264 | + | 0.969203i | \(0.420797\pi\) | |||||||
\(812\) | − 4317.28i | − 0.186585i | ||||||||
\(813\) | 10538.2i | 0.454600i | ||||||||
\(814\) | 10203.9 | 0.439369 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5179.88 | 0.222221 | ||||||||
\(817\) | 18686.2i | 0.800181i | ||||||||
\(818\) | 43245.6i | 1.84847i | ||||||||
\(819\) | 261.716 | 0.0111662 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9610.94 | −0.408556 | −0.204278 | − | 0.978913i | \(-0.565485\pi\) | ||||
−0.204278 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(822\) | − 34029.1i | − 1.44392i | ||||||||
\(823\) | 13767.3i | 0.583109i | 0.956554 | + | 0.291555i | \(0.0941725\pi\) | ||||
−0.956554 | + | 0.291555i | \(0.905827\pi\) | |||||||
\(824\) | −43127.8 | −1.82333 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10451.1 | −0.440242 | ||||||||
\(827\) | − 31978.6i | − 1.34462i | −0.740268 | − | 0.672312i | \(-0.765301\pi\) | ||||
0.740268 | − | 0.672312i | \(-0.234699\pi\) | |||||||
\(828\) | 20594.2i | 0.864369i | ||||||||
\(829\) | −18477.2 | −0.774111 | −0.387055 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387055 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19166.1 | 0.800080 | ||||||||
\(832\) | − 2996.58i | − 0.124865i | ||||||||
\(833\) | 2622.56i | 0.109083i | ||||||||
\(834\) | −17332.7 | −0.719643 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9495.45 | 0.392831 | ||||||||
\(837\) | 378.669i | 0.0156377i | ||||||||
\(838\) | − 22360.3i | − 0.921745i | ||||||||
\(839\) | 38552.6 | 1.58639 | 0.793196 | − | 0.608967i | \(-0.208416\pi\) | ||||
0.793196 | + | 0.608967i | \(0.208416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22603.3 | −0.926784 | ||||||||
\(842\) | − 7591.04i | − 0.310694i | ||||||||
\(843\) | − 6380.31i | − 0.260676i | ||||||||
\(844\) | 22738.1 | 0.927344 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −20051.0 | −0.814854 | ||||||||
\(847\) | 8942.13i | 0.362757i | ||||||||
\(848\) | 3741.34i | 0.151507i | ||||||||
\(849\) | −24996.4 | −1.01045 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45989.1 | −1.85251 | ||||||||
\(852\) | 32304.5i | 1.29898i | ||||||||
\(853\) | 3080.15i | 0.123637i | 0.998087 | + | 0.0618185i | \(0.0196900\pi\) | ||||
−0.998087 | + | 0.0618185i | \(0.980310\pi\) | |||||||
\(854\) | −25567.4 | −1.02447 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5215.43 | 0.208247 | ||||||||
\(857\) | 28362.3i | 1.13050i | 0.824920 | + | 0.565249i | \(0.191220\pi\) | ||||
−0.824920 | + | 0.565249i | \(0.808780\pi\) | |||||||
\(858\) | − 433.523i | − 0.0172497i | ||||||||
\(859\) | 4928.50 | 0.195761 | 0.0978803 | − | 0.995198i | \(-0.468794\pi\) | ||||
0.0978803 | + | 0.995198i | \(0.468794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2671.48 | −0.105742 | ||||||||
\(862\) | − 29638.9i | − 1.17112i | ||||||||
\(863\) | 39910.8i | 1.57425i | 0.616792 | + | 0.787126i | \(0.288432\pi\) | ||||
−0.616792 | + | 0.787126i | \(0.711568\pi\) | |||||||
\(864\) | 2631.30 | 0.103609 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11236.9 | 0.440928 | ||||||||
\(867\) | 6145.31i | 0.240722i | ||||||||
\(868\) | − 1432.87i | − 0.0560309i | ||||||||
\(869\) | 2043.63 | 0.0797762 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2978.92 | 0.115886 | ||||||||
\(872\) | 42197.8i | 1.63876i | ||||||||
\(873\) | − 2086.14i | − 0.0808763i | ||||||||
\(874\) | −66253.6 | −2.56414 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20912.9 | 0.806602 | ||||||||
\(877\) | 29231.5i | 1.12552i | 0.826621 | + | 0.562759i | \(0.190260\pi\) | ||||
−0.826621 | + | 0.562759i | \(0.809740\pi\) | |||||||
\(878\) | − 83364.5i | − 3.20435i | ||||||||
\(879\) | 25962.3 | 0.996232 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23473.3 | −0.897657 | −0.448829 | − | 0.893618i | \(-0.648159\pi\) | ||||
−0.448829 | + | 0.893618i | \(0.648159\pi\) | |||||||
\(882\) | − 2096.27i | − 0.0800285i | ||||||||
\(883\) | 21250.7i | 0.809902i | 0.914338 | + | 0.404951i | \(0.132711\pi\) | ||||
−0.914338 | + | 0.404951i | \(0.867289\pi\) | |||||||
\(884\) | 3245.13 | 0.123468 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21337.4 | −0.809080 | ||||||||
\(887\) | 48748.6i | 1.84534i | 0.385588 | + | 0.922671i | \(0.373999\pi\) | ||||
−0.385588 | + | 0.922671i | \(0.626001\pi\) | |||||||
\(888\) | − 27588.6i | − 1.04258i | ||||||||
\(889\) | −14783.0 | −0.557710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 592.757 | 0.0222874 | ||||||||
\(892\) | − 19263.3i | − 0.723075i | ||||||||
\(893\) | − 41667.2i | − 1.56141i | ||||||||
\(894\) | −40635.0 | −1.52018 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18544.2 | −0.691428 | ||||||||
\(897\) | 1953.89i | 0.0727297i | ||||||||
\(898\) | 62690.0i | 2.32961i | ||||||||
\(899\) | 592.646 | 0.0219865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6207.08 | 0.229509 | ||||||||
\(902\) | 4425.21i | 0.163352i | ||||||||
\(903\) | − 4413.97i | − 0.162666i | ||||||||
\(904\) | 41453.2 | 1.52513 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −37702.1 | −1.38253 | ||||||||
\(907\) | 13144.5i | 0.481209i | 0.970623 | + | 0.240604i | \(0.0773456\pi\) | ||||
−0.970623 | + | 0.240604i | \(0.922654\pi\) | |||||||
\(908\) | 94029.0i | 3.43663i | ||||||||
\(909\) | 17084.3 | 0.623379 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29731.7 | −1.08129 | −0.540644 | − | 0.841251i | \(-0.681819\pi\) | ||||
−0.540644 | + | 0.841251i | \(0.681819\pi\) | |||||||
\(912\) | − 8604.02i | − 0.312399i | ||||||||
\(913\) | 5685.94i | 0.206108i | ||||||||
\(914\) | −38431.8 | −1.39082 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 67928.1 | 2.45022 | ||||||||
\(917\) | 1468.41i | 0.0528803i | ||||||||
\(918\) | 6869.13i | 0.246966i | ||||||||
\(919\) | 47715.4 | 1.71272 | 0.856358 | − | 0.516383i | \(-0.172722\pi\) | ||||
0.856358 | + | 0.516383i | \(0.172722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15955.7 | 0.570855 | ||||||||
\(922\) | 3922.82i | 0.140121i | ||||||||
\(923\) | 3064.92i | 0.109299i | ||||||||
\(924\) | −2242.97 | −0.0798575 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 78944.4 | 2.80159 | ||||||||
\(927\) | − 12381.0i | − 0.438669i | ||||||||
\(928\) | − 4118.18i | − 0.145674i | ||||||||
\(929\) | 19795.2 | 0.699094 | 0.349547 | − | 0.936919i | \(-0.386335\pi\) | ||||
0.349547 | + | 0.936919i | \(0.386335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4356.19 | 0.153350 | ||||||||
\(932\) | 38365.3i | 1.34839i | ||||||||
\(933\) | − 21293.6i | − 0.747183i | ||||||||
\(934\) | −28539.0 | −0.999811 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1172.13 | −0.0409319 | ||||||||
\(937\) | 17993.9i | 0.627359i | 0.949529 | + | 0.313680i | \(0.101562\pi\) | ||||
−0.949529 | + | 0.313680i | \(0.898438\pi\) | |||||||
\(938\) | − 23860.3i | − 0.830560i | ||||||||
\(939\) | 6242.33 | 0.216944 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34667.7 | −1.20099 | −0.600497 | − | 0.799627i | \(-0.705030\pi\) | ||||
−0.600497 | + | 0.799627i | \(0.705030\pi\) | |||||||
\(942\) | 36550.5i | 1.26420i | ||||||||
\(943\) | − 19944.5i | − 0.688740i | ||||||||
\(944\) | 10132.7 | 0.349354 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7311.57 | −0.251289 | ||||||||
\(947\) | 56727.3i | 1.94656i | 0.229627 | + | 0.973279i | \(0.426249\pi\) | ||||
−0.229627 | + | 0.973279i | \(0.573751\pi\) | |||||||
\(948\) | − 12227.7i | − 0.418922i | ||||||||
\(949\) | 1984.13 | 0.0678690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7933.82 | 0.270528 | ||||||||
\(952\) | − 11745.5i | − 0.399867i | ||||||||
\(953\) | 46267.5i | 1.57267i | 0.617802 | + | 0.786333i | \(0.288023\pi\) | ||||
−0.617802 | + | 0.786333i | \(0.711977\pi\) | |||||||
\(954\) | −4961.46 | −0.168379 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8558.23 | 0.289532 | ||||||||
\(957\) | − 927.709i | − 0.0313360i | ||||||||
\(958\) | 96903.7i | 3.26807i | ||||||||
\(959\) | −16703.9 | −0.562458 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29594.3 | −0.993398 | ||||||||
\(962\) | − 5792.48i | − 0.194134i | ||||||||
\(963\) | 1497.23i | 0.0501014i | ||||||||
\(964\) | −45854.1 | −1.53201 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15650.1 | 0.521257 | ||||||||
\(967\) | − 26514.2i | − 0.881738i | −0.897571 | − | 0.440869i | \(-0.854670\pi\) | ||||
0.897571 | − | 0.440869i | \(-0.145330\pi\) | |||||||
\(968\) | − 40048.5i | − 1.32976i | ||||||||
\(969\) | −14274.5 | −0.473234 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38864.6 | 1.28447 | 0.642237 | − | 0.766506i | \(-0.278006\pi\) | ||||
0.642237 | + | 0.766506i | \(0.278006\pi\) | |||||||
\(972\) | − 3546.66i | − 0.117036i | ||||||||
\(973\) | 8508.13i | 0.280327i | ||||||||
\(974\) | −44789.9 | −1.47347 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24788.4 | 0.812968 | ||||||||
\(977\) | 33774.5i | 1.10598i | 0.833188 | + | 0.552990i | \(0.186513\pi\) | ||||
−0.833188 | + | 0.552990i | \(0.813487\pi\) | |||||||
\(978\) | − 20013.8i | − 0.654367i | ||||||||
\(979\) | 217.803 | 0.00711032 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12114.0 | −0.394262 | ||||||||
\(982\) | − 28084.8i | − 0.912651i | ||||||||
\(983\) | 23536.8i | 0.763691i | 0.924226 | + | 0.381846i | \(0.124711\pi\) | ||||
−0.924226 | + | 0.381846i | \(0.875289\pi\) | |||||||
\(984\) | 11964.6 | 0.387619 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10750.7 | 0.347234 | ||||||||
\(987\) | 9842.44i | 0.317415i | ||||||||
\(988\) | − 5390.31i | − 0.173572i | ||||||||
\(989\) | 32953.3 | 1.05951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29012.6 | 0.929984 | 0.464992 | − | 0.885315i | \(-0.346057\pi\) | ||||
0.464992 | + | 0.885315i | \(0.346057\pi\) | |||||||
\(992\) | − 1366.79i | − 0.0437457i | ||||||||
\(993\) | − 5493.48i | − 0.175559i | ||||||||
\(994\) | 24549.1 | 0.783350 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 34020.8 | 1.08232 | ||||||||
\(997\) | − 14027.1i | − 0.445579i | −0.974867 | − | 0.222790i | \(-0.928484\pi\) | ||||
0.974867 | − | 0.222790i | \(-0.0715163\pi\) | |||||||
\(998\) | − 15390.0i | − 0.488138i | ||||||||
\(999\) | 7920.07 | 0.250831 |
(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 | 525.4.d.n.274.1 | 8 | ||
5.2 | odd | 4 | 525.4.a.u.1.4 | yes | 4 | ||
5.3 | odd | 4 | 525.4.a.t.1.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 525.4.d.n.274.8 | 8 | ||
15.2 | even | 4 | 1575.4.a.bk.1.1 | 4 | |||
15.8 | even | 4 | 1575.4.a.bj.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.t.1.1 | ✓ | 4 | 5.3 | odd | 4 | ||
525.4.a.u.1.4 | yes | 4 | 5.2 | odd | 4 | ||
525.4.d.n.274.1 | 8 | 1.1 | even | 1 | trivial | ||
525.4.d.n.274.8 | 8 | 5.4 | even | 2 | inner | ||
1575.4.a.bj.1.4 | 4 | 15.8 | even | 4 | |||
1575.4.a.bk.1.1 | 4 | 15.2 | even | 4 |