Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,3,Mod(391,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.391");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.0545988610\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.15 | ||
Root | \(-2.63284 + 4.56021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.391 |
Dual form | 1470.3.f.d.391.9 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | −0.526446 | −0.0478587 | −0.0239293 | − | 0.999714i | \(-0.507618\pi\) | ||||
−0.0239293 | + | 0.999714i | \(0.507618\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − 4.22307i | − 0.324851i | −0.986721 | − | 0.162426i | \(-0.948068\pi\) | ||||
0.986721 | − | 0.162426i | \(-0.0519318\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 33.3506i | 1.96180i | 0.194513 | + | 0.980900i | \(0.437687\pi\) | ||||
−0.194513 | + | 0.980900i | \(0.562313\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 3.17697i | 0.167209i | 0.996499 | + | 0.0836044i | \(0.0266432\pi\) | ||||
−0.996499 | + | 0.0836044i | \(0.973357\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.744507 | −0.0338412 | ||||||||
\(23\) | 11.0591 | 0.480829 | 0.240415 | − | 0.970670i | \(-0.422717\pi\) | ||||
0.240415 | + | 0.970670i | \(0.422717\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − 5.97232i | − 0.229705i | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −56.1302 | −1.93552 | −0.967762 | − | 0.251866i | \(-0.918956\pi\) | ||||
−0.967762 | + | 0.251866i | \(0.918956\pi\) | |||||||
\(30\) | −5.47723 | −0.182574 | ||||||||
\(31\) | 1.89160i | 0.0610194i | 0.999534 | + | 0.0305097i | \(0.00971304\pi\) | ||||
−0.999534 | + | 0.0305097i | \(0.990287\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − 0.911831i | − 0.0276312i | ||||||||
\(34\) | 47.1649i | 1.38720i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −9.75363 | −0.263612 | −0.131806 | − | 0.991276i | \(-0.542078\pi\) | ||||
−0.131806 | + | 0.991276i | \(0.542078\pi\) | |||||||
\(38\) | 4.49291i | 0.118234i | ||||||||
\(39\) | 7.31457 | 0.187553 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 4.07377i | 0.0993603i | 0.998765 | + | 0.0496802i | \(0.0158202\pi\) | ||||
−0.998765 | + | 0.0496802i | \(0.984180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.3519 | 1.07795 | 0.538975 | − | 0.842322i | \(-0.318812\pi\) | ||||
0.538975 | + | 0.842322i | \(0.318812\pi\) | |||||||
\(44\) | −1.05289 | −0.0239293 | ||||||||
\(45\) | − 6.70820i | − 0.149071i | ||||||||
\(46\) | 15.6399 | 0.339998 | ||||||||
\(47\) | 63.2740i | 1.34625i | 0.739527 | + | 0.673127i | \(0.235049\pi\) | ||||
−0.739527 | + | 0.673127i | \(0.764951\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | −57.7649 | −1.13265 | ||||||||
\(52\) | − 8.44614i | − 0.162426i | ||||||||
\(53\) | −46.5211 | −0.877757 | −0.438878 | − | 0.898546i | \(-0.644624\pi\) | ||||
−0.438878 | + | 0.898546i | \(0.644624\pi\) | |||||||
\(54\) | − 7.34847i | − 0.136083i | ||||||||
\(55\) | − 1.17717i | − 0.0214031i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.50267 | −0.0965380 | ||||||||
\(58\) | −79.3801 | −1.36862 | ||||||||
\(59\) | 50.5313i | 0.856463i | 0.903669 | + | 0.428231i | \(0.140863\pi\) | ||||
−0.903669 | + | 0.428231i | \(0.859137\pi\) | |||||||
\(60\) | −7.74597 | −0.129099 | ||||||||
\(61\) | 103.298i | 1.69340i | 0.532068 | + | 0.846702i | \(0.321415\pi\) | ||||
−0.532068 | + | 0.846702i | \(0.678585\pi\) | |||||||
\(62\) | 2.67513i | 0.0431472i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 9.44307 | 0.145278 | ||||||||
\(66\) | − 1.28952i | − 0.0195382i | ||||||||
\(67\) | 8.73896 | 0.130432 | 0.0652161 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652161 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(68\) | 66.7012i | 0.980900i | ||||||||
\(69\) | 19.1549i | 0.277607i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.0608 | 0.409307 | 0.204653 | − | 0.978835i | \(-0.434393\pi\) | ||||
0.204653 | + | 0.978835i | \(0.434393\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | − 16.7329i | − 0.229218i | −0.993411 | − | 0.114609i | \(-0.963438\pi\) | ||||
0.993411 | − | 0.114609i | \(-0.0365616\pi\) | |||||||
\(74\) | −13.7937 | −0.186402 | ||||||||
\(75\) | − 8.66025i | − 0.115470i | ||||||||
\(76\) | 6.35393i | 0.0836044i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.3444 | 0.132620 | ||||||||
\(79\) | −132.295 | −1.67462 | −0.837308 | − | 0.546732i | \(-0.815872\pi\) | ||||
−0.837308 | + | 0.546732i | \(0.815872\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 5.76119i | 0.0702584i | ||||||||
\(83\) | 12.4838i | 0.150407i | 0.997168 | + | 0.0752033i | \(0.0239606\pi\) | ||||
−0.997168 | + | 0.0752033i | \(0.976039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −74.5742 | −0.877344 | ||||||||
\(86\) | 65.5515 | 0.762226 | ||||||||
\(87\) | − 97.2204i | − 1.11748i | ||||||||
\(88\) | −1.48901 | −0.0169206 | ||||||||
\(89\) | − 68.2544i | − 0.766904i | −0.923561 | − | 0.383452i | \(-0.874735\pi\) | ||||
0.923561 | − | 0.383452i | \(-0.125265\pi\) | |||||||
\(90\) | − 9.48683i | − 0.105409i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 22.1182 | 0.240415 | ||||||||
\(93\) | −3.27635 | −0.0352296 | ||||||||
\(94\) | 89.4829i | 0.951946i | ||||||||
\(95\) | −7.10391 | −0.0747780 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | − 149.281i | − 1.53898i | −0.638659 | − | 0.769490i | \(-0.720510\pi\) | ||||
0.638659 | − | 0.769490i | \(-0.279490\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.57934 | 0.0159529 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | − 96.7453i | − 0.957874i | −0.877849 | − | 0.478937i | \(-0.841022\pi\) | ||||
0.877849 | − | 0.478937i | \(-0.158978\pi\) | |||||||
\(102\) | −81.6919 | −0.800901 | ||||||||
\(103\) | 104.762i | 1.01711i | 0.861030 | + | 0.508555i | \(0.169820\pi\) | ||||
−0.861030 | + | 0.508555i | \(0.830180\pi\) | |||||||
\(104\) | − 11.9446i | − 0.114852i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −65.7908 | −0.620668 | ||||||||
\(107\) | −124.604 | −1.16453 | −0.582263 | − | 0.813000i | \(-0.697833\pi\) | ||||
−0.582263 | + | 0.813000i | \(0.697833\pi\) | |||||||
\(108\) | − 10.3923i | − 0.0962250i | ||||||||
\(109\) | 84.6085 | 0.776224 | 0.388112 | − | 0.921612i | \(-0.373127\pi\) | ||||
0.388112 | + | 0.921612i | \(0.373127\pi\) | |||||||
\(110\) | − 1.66477i | − 0.0151342i | ||||||||
\(111\) | − 16.8938i | − 0.152196i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −116.241 | −1.02868 | −0.514340 | − | 0.857586i | \(-0.671963\pi\) | ||||
−0.514340 | + | 0.857586i | \(0.671963\pi\) | |||||||
\(114\) | −7.78195 | −0.0682627 | ||||||||
\(115\) | 24.7288i | 0.215033i | ||||||||
\(116\) | −112.260 | −0.967762 | ||||||||
\(117\) | 12.6692i | 0.108284i | ||||||||
\(118\) | 71.4621i | 0.605611i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.9545 | −0.0912871 | ||||||||
\(121\) | −120.723 | −0.997710 | ||||||||
\(122\) | 146.085i | 1.19742i | ||||||||
\(123\) | −7.05598 | −0.0573657 | ||||||||
\(124\) | 3.78320i | 0.0305097i | ||||||||
\(125\) | − 11.1803i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −81.3744 | −0.640743 | −0.320372 | − | 0.947292i | \(-0.603808\pi\) | ||||
−0.320372 | + | 0.947292i | \(0.603808\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 80.2838i | 0.622355i | ||||||||
\(130\) | 13.3545 | 0.102727 | ||||||||
\(131\) | 240.626i | 1.83684i | 0.395604 | + | 0.918421i | \(0.370535\pi\) | ||||
−0.395604 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(132\) | − 1.82366i | − 0.0138156i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.3588 | 0.0922295 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | 94.3297i | 0.693601i | ||||||||
\(137\) | 233.661 | 1.70556 | 0.852778 | − | 0.522273i | \(-0.174916\pi\) | ||||
0.852778 | + | 0.522273i | \(0.174916\pi\) | |||||||
\(138\) | 27.0891i | 0.196298i | ||||||||
\(139\) | − 211.491i | − 1.52152i | −0.649033 | − | 0.760760i | \(-0.724826\pi\) | ||||
0.649033 | − | 0.760760i | \(-0.275174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −109.594 | −0.777261 | ||||||||
\(142\) | 41.0981 | 0.289424 | ||||||||
\(143\) | 2.22322i | 0.0155470i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | − 125.511i | − 0.865593i | ||||||||
\(146\) | − 23.6640i | − 0.162082i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.5073 | −0.131806 | ||||||||
\(149\) | 144.080 | 0.966982 | 0.483491 | − | 0.875349i | \(-0.339369\pi\) | ||||
0.483491 | + | 0.875349i | \(0.339369\pi\) | |||||||
\(150\) | − 12.2474i | − 0.0816497i | ||||||||
\(151\) | 93.5125 | 0.619288 | 0.309644 | − | 0.950853i | \(-0.399790\pi\) | ||||
0.309644 | + | 0.950853i | \(0.399790\pi\) | |||||||
\(152\) | 8.98582i | 0.0591172i | ||||||||
\(153\) | − 100.052i | − 0.653933i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.22975 | −0.0272887 | ||||||||
\(156\) | 14.6291 | 0.0937765 | ||||||||
\(157\) | 171.225i | 1.09061i | 0.838238 | + | 0.545304i | \(0.183586\pi\) | ||||
−0.838238 | + | 0.545304i | \(0.816414\pi\) | |||||||
\(158\) | −187.093 | −1.18413 | ||||||||
\(159\) | − 80.5769i | − 0.506773i | ||||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 93.0129 | 0.570631 | 0.285316 | − | 0.958434i | \(-0.407902\pi\) | ||||
0.285316 | + | 0.958434i | \(0.407902\pi\) | |||||||
\(164\) | 8.14755i | 0.0496802i | ||||||||
\(165\) | 2.03892 | 0.0123571 | ||||||||
\(166\) | 17.6547i | 0.106354i | ||||||||
\(167\) | 104.991i | 0.628688i | 0.949309 | + | 0.314344i | \(0.101784\pi\) | ||||
−0.949309 | + | 0.314344i | \(0.898216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 151.166 | 0.894472 | ||||||||
\(170\) | −105.464 | −0.620376 | ||||||||
\(171\) | − 9.53090i | − 0.0557362i | ||||||||
\(172\) | 92.7038 | 0.538975 | ||||||||
\(173\) | 204.157i | 1.18010i | 0.807367 | + | 0.590049i | \(0.200892\pi\) | ||||
−0.807367 | + | 0.590049i | \(0.799108\pi\) | |||||||
\(174\) | − 137.490i | − 0.790174i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.10578 | −0.0119647 | ||||||||
\(177\) | −87.5228 | −0.494479 | ||||||||
\(178\) | − 96.5264i | − 0.542283i | ||||||||
\(179\) | −195.899 | −1.09441 | −0.547204 | − | 0.836999i | \(-0.684308\pi\) | ||||
−0.547204 | + | 0.836999i | \(0.684308\pi\) | |||||||
\(180\) | − 13.4164i | − 0.0745356i | ||||||||
\(181\) | 119.031i | 0.657632i | 0.944394 | + | 0.328816i | \(0.106650\pi\) | ||||
−0.944394 | + | 0.328816i | \(0.893350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −178.917 | −0.977687 | ||||||||
\(184\) | 31.2798 | 0.169999 | ||||||||
\(185\) | − 21.8098i | − 0.117891i | ||||||||
\(186\) | −4.63346 | −0.0249111 | ||||||||
\(187\) | − 17.5573i | − 0.0938892i | ||||||||
\(188\) | 126.548i | 0.673127i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0464 | −0.0528760 | ||||||||
\(191\) | −65.7314 | −0.344143 | −0.172072 | − | 0.985084i | \(-0.555046\pi\) | ||||
−0.172072 | + | 0.985084i | \(0.555046\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −96.8700 | −0.501917 | −0.250959 | − | 0.967998i | \(-0.580746\pi\) | ||||
−0.250959 | + | 0.967998i | \(0.580746\pi\) | |||||||
\(194\) | − 211.115i | − 1.08822i | ||||||||
\(195\) | 16.3559i | 0.0838763i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 186.672 | 0.947574 | 0.473787 | − | 0.880640i | \(-0.342887\pi\) | ||||
0.473787 | + | 0.880640i | \(0.342887\pi\) | |||||||
\(198\) | 2.23352 | 0.0112804 | ||||||||
\(199\) | − 115.292i | − 0.579354i | −0.957124 | − | 0.289677i | \(-0.906452\pi\) | ||||
0.957124 | − | 0.289677i | \(-0.0935480\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 15.1363i | 0.0753051i | ||||||||
\(202\) | − 136.818i | − 0.677319i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −115.530 | −0.566323 | ||||||||
\(205\) | −9.10923 | −0.0444353 | ||||||||
\(206\) | 148.156i | 0.719205i | ||||||||
\(207\) | −33.1772 | −0.160276 | ||||||||
\(208\) | − 16.8923i | − 0.0812129i | ||||||||
\(209\) | − 1.67250i | − 0.00800239i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.433 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(212\) | −93.0422 | −0.438878 | ||||||||
\(213\) | 50.3347i | 0.236313i | ||||||||
\(214\) | −176.217 | −0.823445 | ||||||||
\(215\) | 103.646i | 0.482074i | ||||||||
\(216\) | − 14.6969i | − 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 119.654 | 0.548874 | ||||||||
\(219\) | 28.9823 | 0.132339 | ||||||||
\(220\) | − 2.35434i | − 0.0107015i | ||||||||
\(221\) | 140.842 | 0.637294 | ||||||||
\(222\) | − 23.8914i | − 0.107619i | ||||||||
\(223\) | − 258.055i | − 1.15720i | −0.815612 | − | 0.578599i | \(-0.803600\pi\) | ||||
0.815612 | − | 0.578599i | \(-0.196400\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −164.389 | −0.727387 | ||||||||
\(227\) | − 331.032i | − 1.45829i | −0.684358 | − | 0.729146i | \(-0.739918\pi\) | ||||
0.684358 | − | 0.729146i | \(-0.260082\pi\) | |||||||
\(228\) | −11.0053 | −0.0482690 | ||||||||
\(229\) | 244.238i | 1.06654i | 0.845944 | + | 0.533271i | \(0.179037\pi\) | ||||
−0.845944 | + | 0.533271i | \(0.820963\pi\) | |||||||
\(230\) | 34.9719i | 0.152052i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −158.760 | −0.684311 | ||||||||
\(233\) | 211.490 | 0.907680 | 0.453840 | − | 0.891083i | \(-0.350054\pi\) | ||||
0.453840 | + | 0.891083i | \(0.350054\pi\) | |||||||
\(234\) | 17.9170i | 0.0765682i | ||||||||
\(235\) | −141.485 | −0.602063 | ||||||||
\(236\) | 101.063i | 0.428231i | ||||||||
\(237\) | − 229.141i | − 0.966840i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 344.134 | 1.43989 | 0.719946 | − | 0.694030i | \(-0.244167\pi\) | ||||
0.719946 | + | 0.694030i | \(0.244167\pi\) | |||||||
\(240\) | −15.4919 | −0.0645497 | ||||||||
\(241\) | 171.348i | 0.710989i | 0.934678 | + | 0.355495i | \(0.115688\pi\) | ||||
−0.934678 | + | 0.355495i | \(0.884312\pi\) | |||||||
\(242\) | −170.728 | −0.705487 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 206.595i | 0.846702i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.97867 | −0.0405637 | ||||||||
\(247\) | 13.4165 | 0.0543180 | ||||||||
\(248\) | 5.35025i | 0.0215736i | ||||||||
\(249\) | −21.6225 | −0.0868373 | ||||||||
\(250\) | − 15.8114i | − 0.0632456i | ||||||||
\(251\) | 327.538i | 1.30493i | 0.757818 | + | 0.652467i | \(0.226266\pi\) | ||||
−0.757818 | + | 0.652467i | \(0.773734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.82200 | −0.0230119 | ||||||||
\(254\) | −115.081 | −0.453074 | ||||||||
\(255\) | − 129.166i | − 0.506535i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 220.358i | − 0.857426i | −0.903441 | − | 0.428713i | \(-0.858967\pi\) | ||||
0.903441 | − | 0.428713i | \(-0.141033\pi\) | |||||||
\(258\) | 113.538i | 0.440072i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.8861 | 0.0726390 | ||||||||
\(261\) | 168.391 | 0.645175 | ||||||||
\(262\) | 340.297i | 1.29884i | ||||||||
\(263\) | 133.195 | 0.506445 | 0.253223 | − | 0.967408i | \(-0.418509\pi\) | ||||
0.253223 | + | 0.967408i | \(0.418509\pi\) | |||||||
\(264\) | − 2.57905i | − 0.00976912i | ||||||||
\(265\) | − 104.024i | − 0.392545i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 118.220 | 0.442772 | ||||||||
\(268\) | 17.4779 | 0.0652161 | ||||||||
\(269\) | 26.5157i | 0.0985713i | 0.998785 | + | 0.0492857i | \(0.0156945\pi\) | ||||
−0.998785 | + | 0.0492857i | \(0.984306\pi\) | |||||||
\(270\) | 16.4317 | 0.0608581 | ||||||||
\(271\) | − 107.015i | − 0.394889i | −0.980314 | − | 0.197444i | \(-0.936736\pi\) | ||||
0.980314 | − | 0.197444i | \(-0.0632642\pi\) | |||||||
\(272\) | 133.402i | 0.490450i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 330.447 | 1.20601 | ||||||||
\(275\) | 2.63223 | 0.00957174 | ||||||||
\(276\) | 38.3098i | 0.138803i | ||||||||
\(277\) | 440.381 | 1.58982 | 0.794912 | − | 0.606725i | \(-0.207517\pi\) | ||||
0.794912 | + | 0.606725i | \(0.207517\pi\) | |||||||
\(278\) | − 299.094i | − 1.07588i | ||||||||
\(279\) | − 5.67480i | − 0.0203398i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 322.069 | 1.14615 | 0.573076 | − | 0.819502i | \(-0.305750\pi\) | ||||
0.573076 | + | 0.819502i | \(0.305750\pi\) | |||||||
\(282\) | −154.989 | −0.549606 | ||||||||
\(283\) | 68.5331i | 0.242166i | 0.992642 | + | 0.121083i | \(0.0386368\pi\) | ||||
−0.992642 | + | 0.121083i | \(0.961363\pi\) | |||||||
\(284\) | 58.1216 | 0.204653 | ||||||||
\(285\) | − 12.3043i | − 0.0431731i | ||||||||
\(286\) | 3.14410i | 0.0109934i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −823.262 | −2.84866 | ||||||||
\(290\) | − 177.499i | − 0.612066i | ||||||||
\(291\) | 258.562 | 0.888531 | ||||||||
\(292\) | − 33.4659i | − 0.114609i | ||||||||
\(293\) | − 147.510i | − 0.503448i | −0.967799 | − | 0.251724i | \(-0.919003\pi\) | ||||
0.967799 | − | 0.251724i | \(-0.0809975\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −112.991 | −0.383022 | ||||||||
\(296\) | −27.5874 | −0.0932008 | ||||||||
\(297\) | 2.73549i | 0.00921041i | ||||||||
\(298\) | 203.760 | 0.683760 | ||||||||
\(299\) | − 46.7032i | − 0.156198i | ||||||||
\(300\) | − 17.3205i | − 0.0577350i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 132.247 | 0.437903 | ||||||||
\(303\) | 167.568 | 0.553029 | ||||||||
\(304\) | 12.7079i | 0.0418022i | ||||||||
\(305\) | −230.980 | −0.757313 | ||||||||
\(306\) | − 141.495i | − 0.462401i | ||||||||
\(307\) | − 376.010i | − 1.22479i | −0.790553 | − | 0.612394i | \(-0.790207\pi\) | ||||
0.790553 | − | 0.612394i | \(-0.209793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −181.454 | −0.587228 | ||||||||
\(310\) | −5.98177 | −0.0192960 | ||||||||
\(311\) | 389.826i | 1.25346i | 0.779236 | + | 0.626730i | \(0.215607\pi\) | ||||
−0.779236 | + | 0.626730i | \(0.784393\pi\) | |||||||
\(312\) | 20.6887 | 0.0663100 | ||||||||
\(313\) | − 143.056i | − 0.457049i | −0.973538 | − | 0.228524i | \(-0.926610\pi\) | ||||
0.973538 | − | 0.228524i | \(-0.0733901\pi\) | |||||||
\(314\) | 242.149i | 0.771176i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −264.589 | −0.837308 | ||||||||
\(317\) | 384.444 | 1.21276 | 0.606378 | − | 0.795176i | \(-0.292622\pi\) | ||||
0.606378 | + | 0.795176i | \(0.292622\pi\) | |||||||
\(318\) | − 113.953i | − 0.358343i | ||||||||
\(319\) | 29.5495 | 0.0926317 | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | − 215.821i | − 0.672340i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −105.954 | −0.328030 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 21.1153i | 0.0649703i | ||||||||
\(326\) | 131.540 | 0.403497 | ||||||||
\(327\) | 146.546i | 0.448153i | ||||||||
\(328\) | 11.5224i | 0.0351292i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.88346 | 0.00873776 | ||||||||
\(331\) | 193.908 | 0.585824 | 0.292912 | − | 0.956139i | \(-0.405376\pi\) | ||||
0.292912 | + | 0.956139i | \(0.405376\pi\) | |||||||
\(332\) | 24.9675i | 0.0752033i | ||||||||
\(333\) | 29.2609 | 0.0878706 | ||||||||
\(334\) | 148.479i | 0.444549i | ||||||||
\(335\) | 19.5409i | 0.0583310i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 125.477 | 0.372337 | 0.186168 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186168 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(338\) | 213.781 | 0.632487 | ||||||||
\(339\) | − 201.335i | − 0.593909i | ||||||||
\(340\) | −149.148 | −0.438672 | ||||||||
\(341\) | − 0.995825i | − 0.00292031i | ||||||||
\(342\) | − 13.4787i | − 0.0394115i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 131.103 | 0.381113 | ||||||||
\(345\) | −42.8316 | −0.124150 | ||||||||
\(346\) | 288.722i | 0.834456i | ||||||||
\(347\) | −503.597 | −1.45129 | −0.725644 | − | 0.688071i | \(-0.758458\pi\) | ||||
−0.725644 | + | 0.688071i | \(0.758458\pi\) | |||||||
\(348\) | − 194.441i | − 0.558738i | ||||||||
\(349\) | 47.7682i | 0.136872i | 0.997656 | + | 0.0684358i | \(0.0218008\pi\) | ||||
−0.997656 | + | 0.0684358i | \(0.978199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.9437 | −0.0625177 | ||||||||
\(352\) | −2.97803 | −0.00846030 | ||||||||
\(353\) | − 32.9103i | − 0.0932304i | −0.998913 | − | 0.0466152i | \(-0.985157\pi\) | ||||
0.998913 | − | 0.0466152i | \(-0.0148435\pi\) | |||||||
\(354\) | −123.776 | −0.349650 | ||||||||
\(355\) | 64.9819i | 0.183048i | ||||||||
\(356\) | − 136.509i | − 0.383452i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −277.043 | −0.773863 | ||||||||
\(359\) | 267.797 | 0.745952 | 0.372976 | − | 0.927841i | \(-0.378337\pi\) | ||||
0.372976 | + | 0.927841i | \(0.378337\pi\) | |||||||
\(360\) | − 18.9737i | − 0.0527046i | ||||||||
\(361\) | 350.907 | 0.972041 | ||||||||
\(362\) | 168.336i | 0.465016i | ||||||||
\(363\) | − 209.098i | − 0.576028i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.4160 | 0.102510 | ||||||||
\(366\) | −253.026 | −0.691329 | ||||||||
\(367\) | 158.723i | 0.432487i | 0.976339 | + | 0.216243i | \(0.0693805\pi\) | ||||
−0.976339 | + | 0.216243i | \(0.930620\pi\) | |||||||
\(368\) | 44.2363 | 0.120207 | ||||||||
\(369\) | − 12.2213i | − 0.0331201i | ||||||||
\(370\) | − 30.8437i | − 0.0833614i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.55270 | −0.0176148 | ||||||||
\(373\) | 414.344 | 1.11084 | 0.555421 | − | 0.831570i | \(-0.312557\pi\) | ||||
0.555421 | + | 0.831570i | \(0.312557\pi\) | |||||||
\(374\) | − 24.8297i | − 0.0663897i | ||||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 178.966i | 0.475973i | ||||||||
\(377\) | 237.042i | 0.628758i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −72.8000 | −0.192084 | −0.0960422 | − | 0.995377i | \(-0.530618\pi\) | ||||
−0.0960422 | + | 0.995377i | \(0.530618\pi\) | |||||||
\(380\) | −14.2078 | −0.0373890 | ||||||||
\(381\) | − 140.945i | − 0.369933i | ||||||||
\(382\) | −92.9582 | −0.243346 | ||||||||
\(383\) | − 285.014i | − 0.744163i | −0.928200 | − | 0.372082i | \(-0.878644\pi\) | ||||
0.928200 | − | 0.372082i | \(-0.121356\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −136.995 | −0.354909 | ||||||||
\(387\) | −139.056 | −0.359317 | ||||||||
\(388\) | − 298.562i | − 0.769490i | ||||||||
\(389\) | −97.1383 | −0.249713 | −0.124856 | − | 0.992175i | \(-0.539847\pi\) | ||||
−0.124856 | + | 0.992175i | \(0.539847\pi\) | |||||||
\(390\) | 23.1307i | 0.0593095i | ||||||||
\(391\) | 368.827i | 0.943291i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −416.777 | −1.06050 | ||||||||
\(394\) | 263.994 | 0.670036 | ||||||||
\(395\) | − 295.820i | − 0.748911i | ||||||||
\(396\) | 3.15867 | 0.00797645 | ||||||||
\(397\) | − 791.704i | − 1.99422i | −0.0759985 | − | 0.997108i | \(-0.524214\pi\) | ||||
0.0759985 | − | 0.997108i | \(-0.475786\pi\) | |||||||
\(398\) | − 163.047i | − 0.409665i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 503.226 | 1.25493 | 0.627464 | − | 0.778645i | \(-0.284093\pi\) | ||||
0.627464 | + | 0.778645i | \(0.284093\pi\) | |||||||
\(402\) | 21.4060i | 0.0532487i | ||||||||
\(403\) | 7.98836 | 0.0198222 | ||||||||
\(404\) | − 193.491i | − 0.478937i | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.13476 | 0.0126161 | ||||||||
\(408\) | −163.384 | −0.400451 | ||||||||
\(409\) | − 749.857i | − 1.83339i | −0.399586 | − | 0.916696i | \(-0.630846\pi\) | ||||
0.399586 | − | 0.916696i | \(-0.369154\pi\) | |||||||
\(410\) | −12.8824 | −0.0314205 | ||||||||
\(411\) | 404.713i | 0.984704i | ||||||||
\(412\) | 209.525i | 0.508555i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −46.9197 | −0.113333 | ||||||||
\(415\) | −27.9145 | −0.0672639 | ||||||||
\(416\) | − 23.8893i | − 0.0574262i | ||||||||
\(417\) | 366.314 | 0.878450 | ||||||||
\(418\) | − 2.36527i | − 0.00565855i | ||||||||
\(419\) | − 465.759i | − 1.11160i | −0.831317 | − | 0.555799i | \(-0.812413\pi\) | ||||
0.831317 | − | 0.555799i | \(-0.187587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 345.980 | 0.821805 | 0.410902 | − | 0.911679i | \(-0.365214\pi\) | ||||
0.410902 | + | 0.911679i | \(0.365214\pi\) | |||||||
\(422\) | 197.188 | 0.467269 | ||||||||
\(423\) | − 189.822i | − 0.448752i | ||||||||
\(424\) | −131.582 | −0.310334 | ||||||||
\(425\) | − 166.753i | − 0.392360i | ||||||||
\(426\) | 71.1841i | 0.167099i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −249.209 | −0.582263 | ||||||||
\(429\) | −3.85072 | −0.00897605 | ||||||||
\(430\) | 146.578i | 0.340878i | ||||||||
\(431\) | 494.600 | 1.14756 | 0.573782 | − | 0.819008i | \(-0.305476\pi\) | ||||
0.573782 | + | 0.819008i | \(0.305476\pi\) | |||||||
\(432\) | − 20.7846i | − 0.0481125i | ||||||||
\(433\) | 730.022i | 1.68596i | 0.537943 | + | 0.842981i | \(0.319201\pi\) | ||||
−0.537943 | + | 0.842981i | \(0.680799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 217.391 | 0.499750 | ||||||||
\(436\) | 169.217 | 0.388112 | ||||||||
\(437\) | 35.1343i | 0.0803989i | ||||||||
\(438\) | 40.9872 | 0.0935780 | ||||||||
\(439\) | − 371.388i | − 0.845986i | −0.906133 | − | 0.422993i | \(-0.860979\pi\) | ||||
0.906133 | − | 0.422993i | \(-0.139021\pi\) | |||||||
\(440\) | − 3.32953i | − 0.00756712i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 199.180 | 0.450635 | ||||||||
\(443\) | 408.708 | 0.922591 | 0.461295 | − | 0.887247i | \(-0.347385\pi\) | ||||
0.461295 | + | 0.887247i | \(0.347385\pi\) | |||||||
\(444\) | − 33.7876i | − 0.0760982i | ||||||||
\(445\) | 152.622 | 0.342970 | ||||||||
\(446\) | − 364.945i | − 0.818263i | ||||||||
\(447\) | 249.555i | 0.558288i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 725.469 | 1.61574 | 0.807872 | − | 0.589358i | \(-0.200619\pi\) | ||||
0.807872 | + | 0.589358i | \(0.200619\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | − 2.14462i | − 0.00475526i | ||||||||
\(452\) | −232.482 | −0.514340 | ||||||||
\(453\) | 161.968i | 0.357546i | ||||||||
\(454\) | − 468.150i | − 1.03117i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.5639 | −0.0341313 | ||||||||
\(457\) | 401.530 | 0.878622 | 0.439311 | − | 0.898335i | \(-0.355223\pi\) | ||||
0.439311 | + | 0.898335i | \(0.355223\pi\) | |||||||
\(458\) | 345.405i | 0.754159i | ||||||||
\(459\) | 173.295 | 0.377549 | ||||||||
\(460\) | 49.4577i | 0.107517i | ||||||||
\(461\) | 653.050i | 1.41659i | 0.705915 | + | 0.708297i | \(0.250536\pi\) | ||||
−0.705915 | + | 0.708297i | \(0.749464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −869.580 | −1.87814 | −0.939072 | − | 0.343722i | \(-0.888312\pi\) | ||||
−0.939072 | + | 0.343722i | \(0.888312\pi\) | |||||||
\(464\) | −224.521 | −0.483881 | ||||||||
\(465\) | − 7.32614i | − 0.0157551i | ||||||||
\(466\) | 299.091 | 0.641827 | ||||||||
\(467\) | 739.202i | 1.58287i | 0.611251 | + | 0.791437i | \(0.290667\pi\) | ||||
−0.611251 | + | 0.791437i | \(0.709333\pi\) | |||||||
\(468\) | 25.3384i | 0.0541419i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −200.090 | −0.425723 | ||||||||
\(471\) | −296.571 | −0.629663 | ||||||||
\(472\) | 142.924i | 0.302805i | ||||||||
\(473\) | −24.4017 | −0.0515893 | ||||||||
\(474\) | − 324.054i | − 0.683659i | ||||||||
\(475\) | − 15.8848i | − 0.0334417i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 139.563 | 0.292586 | ||||||||
\(478\) | 486.679 | 1.01816 | ||||||||
\(479\) | 606.225i | 1.26560i | 0.774313 | + | 0.632802i | \(0.218095\pi\) | ||||
−0.774313 | + | 0.632802i | \(0.781905\pi\) | |||||||
\(480\) | −21.9089 | −0.0456435 | ||||||||
\(481\) | 41.1903i | 0.0856347i | ||||||||
\(482\) | 242.323i | 0.502745i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −241.446 | −0.498855 | ||||||||
\(485\) | 333.803 | 0.688253 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 649.576 | 1.33383 | 0.666916 | − | 0.745133i | \(-0.267614\pi\) | ||||
0.666916 | + | 0.745133i | \(0.267614\pi\) | |||||||
\(488\) | 292.170i | 0.598708i | ||||||||
\(489\) | 161.103i | 0.329454i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 266.629 | 0.543033 | 0.271516 | − | 0.962434i | \(-0.412475\pi\) | ||||
0.271516 | + | 0.962434i | \(0.412475\pi\) | |||||||
\(492\) | −14.1120 | −0.0286829 | ||||||||
\(493\) | − 1871.98i | − 3.79711i | ||||||||
\(494\) | 18.9739 | 0.0384086 | ||||||||
\(495\) | 3.53150i | 0.00713435i | ||||||||
\(496\) | 7.56640i | 0.0152548i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −30.5788 | −0.0614033 | ||||||||
\(499\) | −681.106 | −1.36494 | −0.682471 | − | 0.730913i | \(-0.739095\pi\) | ||||
−0.682471 | + | 0.730913i | \(0.739095\pi\) | |||||||
\(500\) | − 22.3607i | − 0.0447214i | ||||||||
\(501\) | −181.849 | −0.362973 | ||||||||
\(502\) | 463.209i | 0.922727i | ||||||||
\(503\) | 453.326i | 0.901245i | 0.892715 | + | 0.450622i | \(0.148798\pi\) | ||||
−0.892715 | + | 0.450622i | \(0.851202\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 216.329 | 0.428374 | ||||||||
\(506\) | −8.23356 | −0.0162718 | ||||||||
\(507\) | 261.827i | 0.516423i | ||||||||
\(508\) | −162.749 | −0.320372 | ||||||||
\(509\) | − 50.2641i | − 0.0987507i | −0.998780 | − | 0.0493754i | \(-0.984277\pi\) | ||||
0.998780 | − | 0.0493754i | \(-0.0157231\pi\) | |||||||
\(510\) | − 182.669i | − 0.358174i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 16.5080 | 0.0321793 | ||||||||
\(514\) | − 311.634i | − 0.606291i | ||||||||
\(515\) | −234.256 | −0.454865 | ||||||||
\(516\) | 160.568i | 0.311178i | ||||||||
\(517\) | − 33.3103i | − 0.0644300i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −353.610 | −0.681330 | ||||||||
\(520\) | 26.7090 | 0.0513635 | ||||||||
\(521\) | 103.111i | 0.197911i | 0.995092 | + | 0.0989553i | \(0.0315501\pi\) | ||||
−0.995092 | + | 0.0989553i | \(0.968450\pi\) | |||||||
\(522\) | 238.140 | 0.456207 | ||||||||
\(523\) | − 366.867i | − 0.701467i | −0.936475 | − | 0.350733i | \(-0.885932\pi\) | ||||
0.936475 | − | 0.350733i | \(-0.114068\pi\) | |||||||
\(524\) | 481.253i | 0.918421i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 188.366 | 0.358111 | ||||||||
\(527\) | −63.0860 | −0.119708 | ||||||||
\(528\) | − 3.64732i | − 0.00690781i | ||||||||
\(529\) | −406.697 | −0.768803 | ||||||||
\(530\) | − 147.113i | − 0.277571i | ||||||||
\(531\) | − 151.594i | − 0.285488i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2038 | 0.0322773 | ||||||||
\(534\) | 167.189 | 0.313087 | ||||||||
\(535\) | − 278.624i | − 0.520792i | ||||||||
\(536\) | 24.7175 | 0.0461147 | ||||||||
\(537\) | − 339.307i | − 0.631856i | ||||||||
\(538\) | 37.4988i | 0.0697005i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 23.2379 | 0.0430331 | ||||||||
\(541\) | −533.117 | −0.985429 | −0.492714 | − | 0.870191i | \(-0.663995\pi\) | ||||
−0.492714 | + | 0.870191i | \(0.663995\pi\) | |||||||
\(542\) | − 151.342i | − 0.279228i | ||||||||
\(543\) | −206.168 | −0.379684 | ||||||||
\(544\) | 188.659i | 0.346800i | ||||||||
\(545\) | 189.190i | 0.347138i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 69.6218 | 0.127279 | 0.0636396 | − | 0.997973i | \(-0.479729\pi\) | ||||
0.0636396 | + | 0.997973i | \(0.479729\pi\) | |||||||
\(548\) | 467.323 | 0.852778 | ||||||||
\(549\) | − 309.893i | − 0.564468i | ||||||||
\(550\) | 3.72253 | 0.00676824 | ||||||||
\(551\) | − 178.324i | − 0.323637i | ||||||||
\(552\) | 54.1782i | 0.0981489i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 622.793 | 1.12418 | ||||||||
\(555\) | 37.7757 | 0.0680643 | ||||||||
\(556\) | − 422.983i | − 0.760760i | ||||||||
\(557\) | 16.8624 | 0.0302737 | 0.0151368 | − | 0.999885i | \(-0.495182\pi\) | ||||
0.0151368 | + | 0.999885i | \(0.495182\pi\) | |||||||
\(558\) | − 8.02538i | − 0.0143824i | ||||||||
\(559\) | − 195.747i | − 0.350174i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.4101 | 0.0542069 | ||||||||
\(562\) | 455.474 | 0.810452 | ||||||||
\(563\) | − 915.784i | − 1.62662i | −0.581834 | − | 0.813308i | \(-0.697665\pi\) | ||||
0.581834 | − | 0.813308i | \(-0.302335\pi\) | |||||||
\(564\) | −219.187 | −0.388630 | ||||||||
\(565\) | − 259.922i | − 0.460040i | ||||||||
\(566\) | 96.9204i | 0.171237i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 82.1963 | 0.144712 | ||||||||
\(569\) | 407.655 | 0.716441 | 0.358221 | − | 0.933637i | \(-0.383384\pi\) | ||||
0.358221 | + | 0.933637i | \(0.383384\pi\) | |||||||
\(570\) | − 17.4010i | − 0.0305280i | ||||||||
\(571\) | −895.820 | −1.56886 | −0.784431 | − | 0.620216i | \(-0.787045\pi\) | ||||
−0.784431 | + | 0.620216i | \(0.787045\pi\) | |||||||
\(572\) | 4.44643i | 0.00777348i | ||||||||
\(573\) | − 113.850i | − 0.198691i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −55.2954 | −0.0961659 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − 681.406i | − 1.18095i | −0.807057 | − | 0.590473i | \(-0.798941\pi\) | ||||
0.807057 | − | 0.590473i | \(-0.201059\pi\) | |||||||
\(578\) | −1164.27 | −2.01431 | ||||||||
\(579\) | − 167.784i | − 0.289782i | ||||||||
\(580\) | − 251.022i | − 0.432796i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 365.662 | 0.628286 | ||||||||
\(583\) | 24.4908 | 0.0420083 | ||||||||
\(584\) | − 47.3279i | − 0.0810410i | ||||||||
\(585\) | −28.3292 | −0.0484260 | ||||||||
\(586\) | − 208.611i | − 0.355991i | ||||||||
\(587\) | 833.001i | 1.41908i | 0.704665 | + | 0.709541i | \(0.251097\pi\) | ||||
−0.704665 | + | 0.709541i | \(0.748903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00955 | −0.0102030 | ||||||||
\(590\) | −159.794 | −0.270837 | ||||||||
\(591\) | 323.325i | 0.547082i | ||||||||
\(592\) | −39.0145 | −0.0659029 | ||||||||
\(593\) | 312.741i | 0.527388i | 0.964606 | + | 0.263694i | \(0.0849409\pi\) | ||||
−0.964606 | + | 0.263694i | \(0.915059\pi\) | |||||||
\(594\) | 3.86857i | 0.00651274i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 288.161 | 0.483491 | ||||||||
\(597\) | 199.691 | 0.334490 | ||||||||
\(598\) | − 66.0484i | − 0.110449i | ||||||||
\(599\) | 214.243 | 0.357667 | 0.178834 | − | 0.983879i | \(-0.442768\pi\) | ||||
0.178834 | + | 0.983879i | \(0.442768\pi\) | |||||||
\(600\) | − 24.4949i | − 0.0408248i | ||||||||
\(601\) | − 176.849i | − 0.294257i | −0.989117 | − | 0.147129i | \(-0.952997\pi\) | ||||
0.989117 | − | 0.147129i | \(-0.0470031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.2169 | −0.0434774 | ||||||||
\(604\) | 187.025 | 0.309644 | ||||||||
\(605\) | − 269.945i | − 0.446189i | ||||||||
\(606\) | 236.977 | 0.391050 | ||||||||
\(607\) | 37.1010i | 0.0611218i | 0.999533 | + | 0.0305609i | \(0.00972936\pi\) | ||||
−0.999533 | + | 0.0305609i | \(0.990271\pi\) | |||||||
\(608\) | 17.9716i | 0.0295586i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −326.656 | −0.535501 | ||||||||
\(611\) | 267.210 | 0.437333 | ||||||||
\(612\) | − 200.104i | − 0.326967i | ||||||||
\(613\) | −899.719 | −1.46773 | −0.733866 | − | 0.679295i | \(-0.762286\pi\) | ||||
−0.733866 | + | 0.679295i | \(0.762286\pi\) | |||||||
\(614\) | − 531.758i | − 0.866056i | ||||||||
\(615\) | − 15.7777i | − 0.0256547i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −626.244 | −1.01498 | −0.507491 | − | 0.861657i | \(-0.669427\pi\) | ||||
−0.507491 | + | 0.861657i | \(0.669427\pi\) | |||||||
\(618\) | −256.614 | −0.415233 | ||||||||
\(619\) | 896.480i | 1.44827i | 0.689657 | + | 0.724136i | \(0.257761\pi\) | ||||
−0.689657 | + | 0.724136i | \(0.742239\pi\) | |||||||
\(620\) | −8.45950 | −0.0136443 | ||||||||
\(621\) | − 57.4646i | − 0.0925357i | ||||||||
\(622\) | 551.298i | 0.886331i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 29.2583 | 0.0468883 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 202.312i | − 0.323182i | ||||||||
\(627\) | 2.89685 | 0.00462018 | ||||||||
\(628\) | 342.451i | 0.545304i | ||||||||
\(629\) | − 325.290i | − 0.517153i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −500.730 | −0.793550 | −0.396775 | − | 0.917916i | \(-0.629871\pi\) | ||||
−0.396775 | + | 0.917916i | \(0.629871\pi\) | |||||||
\(632\) | −374.186 | −0.592066 | ||||||||
\(633\) | 241.505i | 0.381524i | ||||||||
\(634\) | 543.686 | 0.857549 | ||||||||
\(635\) | − 181.959i | − 0.286549i | ||||||||
\(636\) | − 161.154i | − 0.253387i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 41.7893 | 0.0655005 | ||||||||
\(639\) | −87.1823 | −0.136436 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | 620.578 | 0.968140 | 0.484070 | − | 0.875029i | \(-0.339158\pi\) | ||||
0.484070 | + | 0.875029i | \(0.339158\pi\) | |||||||
\(642\) | − 305.217i | − 0.475416i | ||||||||
\(643\) | − 1127.93i | − 1.75417i | −0.480334 | − | 0.877086i | \(-0.659484\pi\) | ||||
0.480334 | − | 0.877086i | \(-0.340516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −179.520 | −0.278326 | ||||||||
\(646\) | −149.841 | −0.231952 | ||||||||
\(647\) | 135.250i | 0.209041i | 0.994523 | + | 0.104521i | \(0.0333308\pi\) | ||||
−0.994523 | + | 0.104521i | \(0.966669\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | − 26.6020i | − 0.0409892i | ||||||||
\(650\) | 29.8616i | 0.0459409i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 186.026 | 0.285316 | ||||||||
\(653\) | −390.290 | −0.597687 | −0.298843 | − | 0.954302i | \(-0.596601\pi\) | ||||
−0.298843 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(654\) | 207.248i | 0.316892i | ||||||||
\(655\) | −538.057 | −0.821461 | ||||||||
\(656\) | 16.2951i | 0.0248401i | ||||||||
\(657\) | 50.1988i | 0.0764061i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −864.853 | −1.31237 | −0.656186 | − | 0.754599i | \(-0.727831\pi\) | ||||
−0.656186 | + | 0.754599i | \(0.727831\pi\) | |||||||
\(660\) | 4.07783 | 0.00617853 | ||||||||
\(661\) | 1008.21i | 1.52528i | 0.646825 | + | 0.762638i | \(0.276096\pi\) | ||||
−0.646825 | + | 0.762638i | \(0.723904\pi\) | |||||||
\(662\) | 274.227 | 0.414240 | ||||||||
\(663\) | 243.945i | 0.367942i | ||||||||
\(664\) | 35.3094i | 0.0531768i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.3812 | 0.0621339 | ||||||||
\(667\) | −620.748 | −0.930657 | ||||||||
\(668\) | 209.982i | 0.314344i | ||||||||
\(669\) | 446.965 | 0.668109 | ||||||||
\(670\) | 27.6350i | 0.0412463i | ||||||||
\(671\) | − 54.3806i | − 0.0810441i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −109.959 | −0.163386 | −0.0816928 | − | 0.996658i | \(-0.526033\pi\) | ||||
−0.0816928 | + | 0.996658i | \(0.526033\pi\) | |||||||
\(674\) | 177.452 | 0.263282 | ||||||||
\(675\) | 25.9808i | 0.0384900i | ||||||||
\(676\) | 302.331 | 0.447236 | ||||||||
\(677\) | 168.833i | 0.249383i | 0.992196 | + | 0.124692i | \(0.0397942\pi\) | ||||
−0.992196 | + | 0.124692i | \(0.960206\pi\) | |||||||
\(678\) | − 284.731i | − 0.419957i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −210.928 | −0.310188 | ||||||||
\(681\) | 573.365 | 0.841945 | ||||||||
\(682\) | − 1.40831i | − 0.00206497i | ||||||||
\(683\) | −436.130 | −0.638551 | −0.319276 | − | 0.947662i | \(-0.603440\pi\) | ||||
−0.319276 | + | 0.947662i | \(0.603440\pi\) | |||||||
\(684\) | − 19.0618i | − 0.0278681i | ||||||||
\(685\) | 522.482i | 0.762748i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −423.033 | −0.615768 | ||||||||
\(688\) | 185.408 | 0.269488 | ||||||||
\(689\) | 196.462i | 0.285141i | ||||||||
\(690\) | −60.5731 | −0.0877870 | ||||||||
\(691\) | − 68.4471i | − 0.0990552i | −0.998773 | − | 0.0495276i | \(-0.984228\pi\) | ||||
0.998773 | − | 0.0495276i | \(-0.0157716\pi\) | |||||||
\(692\) | 408.314i | 0.590049i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −712.193 | −1.02622 | ||||||||
\(695\) | 472.909 | 0.680444 | ||||||||
\(696\) | − 274.981i | − 0.395087i | ||||||||
\(697\) | −135.863 | −0.194925 | ||||||||
\(698\) | 67.5544i | 0.0967829i | ||||||||
\(699\) | 366.311i | 0.524050i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1283.41 | 1.83083 | 0.915414 | − | 0.402514i | \(-0.131864\pi\) | ||||
0.915414 | + | 0.402514i | \(0.131864\pi\) | |||||||
\(702\) | −31.0331 | −0.0442067 | ||||||||
\(703\) | − 30.9870i | − 0.0440782i | ||||||||
\(704\) | −4.21157 | −0.00598234 | ||||||||
\(705\) | − 245.059i | − 0.347602i | ||||||||
\(706\) | − 46.5422i | − 0.0659238i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −175.046 | −0.247240 | ||||||||
\(709\) | 172.400 | 0.243159 | 0.121580 | − | 0.992582i | \(-0.461204\pi\) | ||||
0.121580 | + | 0.992582i | \(0.461204\pi\) | |||||||
\(710\) | 91.8983i | 0.129434i | ||||||||
\(711\) | 396.884 | 0.558205 | ||||||||
\(712\) | − 193.053i | − 0.271141i | ||||||||
\(713\) | 20.9194i | 0.0293399i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.97126 | −0.00695282 | ||||||||
\(716\) | −391.798 | −0.547204 | ||||||||
\(717\) | 596.058i | 0.831322i | ||||||||
\(718\) | 378.722 | 0.527468 | ||||||||
\(719\) | − 502.312i | − 0.698626i | −0.937006 | − | 0.349313i | \(-0.886415\pi\) | ||||
0.937006 | − | 0.349313i | \(-0.113585\pi\) | |||||||
\(720\) | − 26.8328i | − 0.0372678i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 496.257 | 0.687337 | ||||||||
\(723\) | −296.784 | −0.410490 | ||||||||
\(724\) | 238.063i | 0.328816i | ||||||||
\(725\) | 280.651 | 0.387105 | ||||||||
\(726\) | − 295.709i | − 0.407313i | ||||||||
\(727\) | − 748.693i | − 1.02984i | −0.857238 | − | 0.514920i | \(-0.827822\pi\) | ||||
0.857238 | − | 0.514920i | \(-0.172178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 52.9142 | 0.0724852 | ||||||||
\(731\) | 1545.86i | 2.11472i | ||||||||
\(732\) | −357.833 | −0.488843 | ||||||||
\(733\) | − 938.496i | − 1.28035i | −0.768229 | − | 0.640175i | \(-0.778862\pi\) | ||||
0.768229 | − | 0.640175i | \(-0.221138\pi\) | |||||||
\(734\) | 224.468i | 0.305814i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.5596 | 0.0849994 | ||||||||
\(737\) | −4.60059 | −0.00624231 | ||||||||
\(738\) | − 17.2836i | − 0.0234195i | ||||||||
\(739\) | 213.641 | 0.289095 | 0.144547 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144547 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(740\) | − 43.6196i | − 0.0589454i | ||||||||
\(741\) | 23.2381i | 0.0313605i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 544.013 | 0.732184 | 0.366092 | − | 0.930579i | \(-0.380696\pi\) | ||||
0.366092 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(744\) | −9.26691 | −0.0124555 | ||||||||
\(745\) | 322.173i | 0.432448i | ||||||||
\(746\) | 585.971 | 0.785483 | ||||||||
\(747\) | − 37.4513i | − 0.0501356i | ||||||||
\(748\) | − 35.1146i | − 0.0469446i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 27.3861 | 0.0365148 | ||||||||
\(751\) | 589.409 | 0.784832 | 0.392416 | − | 0.919788i | \(-0.371639\pi\) | ||||
0.392416 | + | 0.919788i | \(0.371639\pi\) | |||||||
\(752\) | 253.096i | 0.336564i | ||||||||
\(753\) | −567.313 | −0.753403 | ||||||||
\(754\) | 335.228i | 0.444599i | ||||||||
\(755\) | 209.100i | 0.276954i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −448.997 | −0.593127 | −0.296564 | − | 0.955013i | \(-0.595841\pi\) | ||||
−0.296564 | + | 0.955013i | \(0.595841\pi\) | |||||||
\(758\) | −102.955 | −0.135824 | ||||||||
\(759\) | − 10.0840i | − 0.0132859i | ||||||||
\(760\) | −20.0929 | −0.0264380 | ||||||||
\(761\) | 429.449i | 0.564322i | 0.959367 | + | 0.282161i | \(0.0910513\pi\) | ||||
−0.959367 | + | 0.282161i | \(0.908949\pi\) | |||||||
\(762\) | − 199.326i | − 0.261582i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −131.463 | −0.172072 | ||||||||
\(765\) | 223.723 | 0.292448 | ||||||||
\(766\) | − 403.071i | − 0.526203i | ||||||||
\(767\) | 213.397 | 0.278223 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 32.5790i | 0.0423655i | 0.999776 | + | 0.0211827i | \(0.00674318\pi\) | ||||
−0.999776 | + | 0.0211827i | \(0.993257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 381.672 | 0.495035 | ||||||||
\(772\) | −193.740 | −0.250959 | ||||||||
\(773\) | − 1243.54i | − 1.60871i | −0.594146 | − | 0.804357i | \(-0.702510\pi\) | ||||
0.594146 | − | 0.804357i | \(-0.297490\pi\) | |||||||
\(774\) | −196.654 | −0.254075 | ||||||||
\(775\) | − 9.45800i | − 0.0122039i | ||||||||
\(776\) | − 422.231i | − 0.544112i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −137.374 | −0.176574 | ||||||||
\(779\) | −12.9422 | −0.0166139 | ||||||||
\(780\) | 32.7118i | 0.0419381i | ||||||||
\(781\) | −15.2989 | −0.0195889 | ||||||||
\(782\) | 521.600i | 0.667008i | ||||||||
\(783\) | 291.661i | 0.372492i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −382.872 | −0.487735 | ||||||||
\(786\) | −589.412 | −0.749888 | ||||||||
\(787\) | − 190.628i | − 0.242220i | −0.992639 | − | 0.121110i | \(-0.961355\pi\) | ||||
0.992639 | − | 0.121110i | \(-0.0386455\pi\) | |||||||
\(788\) | 373.344 | 0.473787 | ||||||||
\(789\) | 230.701i | 0.292396i | ||||||||
\(790\) | − 418.352i | − 0.529560i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.46704 | 0.00564020 | ||||||||
\(793\) | 436.233 | 0.550105 | ||||||||
\(794\) | − 1119.64i | − 1.41012i | ||||||||
\(795\) | 180.175 | 0.226636 | ||||||||
\(796\) | − 230.583i | − 0.289677i | ||||||||
\(797\) | 387.796i | 0.486570i | 0.969955 | + | 0.243285i | \(0.0782250\pi\) | ||||
−0.969955 | + | 0.243285i | \(0.921775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2110.23 | −2.64108 | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | 204.763i | 0.255635i | ||||||||
\(802\) | 711.670 | 0.887369 | ||||||||
\(803\) | 8.80899i | 0.0109701i | ||||||||
\(804\) | 30.2726i | 0.0376525i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.2972 | 0.0140164 | ||||||||
\(807\) | −45.9265 | −0.0569102 | ||||||||
\(808\) | − 273.637i | − 0.338660i | ||||||||
\(809\) | 365.226 | 0.451453 | 0.225727 | − | 0.974191i | \(-0.427524\pi\) | ||||
0.225727 | + | 0.974191i | \(0.427524\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | − 944.189i | − 1.16423i | −0.813107 | − | 0.582114i | \(-0.802226\pi\) | ||||
0.813107 | − | 0.582114i | \(-0.197774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 185.355 | 0.227989 | ||||||||
\(814\) | 7.26164 | 0.00892094 | ||||||||
\(815\) | 207.983i | 0.255194i | ||||||||
\(816\) | −231.060 | −0.283161 | ||||||||
\(817\) | 147.258i | 0.180243i | ||||||||
\(818\) | − 1060.46i | − 1.29640i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.2185 | −0.0222176 | ||||||||
\(821\) | −684.675 | −0.833952 | −0.416976 | − | 0.908917i | \(-0.636910\pi\) | ||||
−0.416976 | + | 0.908917i | \(0.636910\pi\) | |||||||
\(822\) | 572.351i | 0.696291i | ||||||||
\(823\) | −1045.67 | −1.27056 | −0.635280 | − | 0.772282i | \(-0.719115\pi\) | ||||
−0.635280 | + | 0.772282i | \(0.719115\pi\) | |||||||
\(824\) | 296.312i | 0.359602i | ||||||||
\(825\) | 4.55915i | 0.00552625i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 830.505 | 1.00424 | 0.502119 | − | 0.864798i | \(-0.332554\pi\) | ||||
0.502119 | + | 0.864798i | \(0.332554\pi\) | |||||||
\(828\) | −66.3545 | −0.0801382 | ||||||||
\(829\) | 718.204i | 0.866349i | 0.901310 | + | 0.433175i | \(0.142607\pi\) | ||||
−0.901310 | + | 0.433175i | \(0.857393\pi\) | |||||||
\(830\) | −39.4771 | −0.0475628 | ||||||||
\(831\) | 762.763i | 0.917885i | ||||||||
\(832\) | − 33.7846i | − 0.0406064i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 518.046 | 0.621158 | ||||||||
\(835\) | −234.767 | −0.281158 | ||||||||
\(836\) | − 3.34500i | − 0.00400120i | ||||||||
\(837\) | 9.82905 | 0.0117432 | ||||||||
\(838\) | − 658.683i | − 0.786018i | ||||||||
\(839\) | 55.2900i | 0.0658999i | 0.999457 | + | 0.0329499i | \(0.0104902\pi\) | ||||
−0.999457 | + | 0.0329499i | \(0.989510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2309.60 | 2.74625 | ||||||||
\(842\) | 489.289 | 0.581104 | ||||||||
\(843\) | 557.839i | 0.661731i | ||||||||
\(844\) | 278.866 | 0.330409 | ||||||||
\(845\) | 338.017i | 0.400020i | ||||||||
\(846\) | − 268.449i | − 0.317315i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −186.084 | −0.219439 | ||||||||
\(849\) | −118.703 | −0.139815 | ||||||||
\(850\) | − 235.824i | − 0.277440i | ||||||||
\(851\) | −107.866 | −0.126752 | ||||||||
\(852\) | 100.669i | 0.118157i | ||||||||
\(853\) | 21.9601i | 0.0257445i | 0.999917 | + | 0.0128723i | \(0.00409748\pi\) | ||||
−0.999917 | + | 0.0128723i | \(0.995903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.3117 | 0.0249260 | ||||||||
\(856\) | −352.434 | −0.411722 | ||||||||
\(857\) | 1615.81i | 1.88542i | 0.333610 | + | 0.942711i | \(0.391733\pi\) | ||||
−0.333610 | + | 0.942711i | \(0.608267\pi\) | |||||||
\(858\) | −5.44575 | −0.00634702 | ||||||||
\(859\) | 891.601i | 1.03795i | 0.854789 | + | 0.518976i | \(0.173687\pi\) | ||||
−0.854789 | + | 0.518976i | \(0.826313\pi\) | |||||||
\(860\) | 207.292i | 0.241037i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 699.470 | 0.811450 | ||||||||
\(863\) | −896.346 | −1.03864 | −0.519320 | − | 0.854580i | \(-0.673815\pi\) | ||||
−0.519320 | + | 0.854580i | \(0.673815\pi\) | |||||||
\(864\) | − 29.3939i | − 0.0340207i | ||||||||
\(865\) | −456.509 | −0.527756 | ||||||||
\(866\) | 1032.41i | 1.19216i | ||||||||
\(867\) | − 1425.93i | − 1.64467i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.6459 | 0.0801449 | ||||||||
\(870\) | 307.438 | 0.353377 | ||||||||
\(871\) | − 36.9052i | − 0.0423711i | ||||||||
\(872\) | 239.309 | 0.274437 | ||||||||
\(873\) | 447.843i | 0.512993i | ||||||||
\(874\) | 49.6874i | 0.0568506i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 57.9646 | 0.0661697 | ||||||||
\(877\) | −337.770 | −0.385143 | −0.192571 | − | 0.981283i | \(-0.561683\pi\) | ||||
−0.192571 | + | 0.981283i | \(0.561683\pi\) | |||||||
\(878\) | − 525.222i | − 0.598203i | ||||||||
\(879\) | 255.495 | 0.290666 | ||||||||
\(880\) | − 4.70867i | − 0.00535076i | ||||||||
\(881\) | − 301.377i | − 0.342085i | −0.985264 | − | 0.171042i | \(-0.945287\pi\) | ||||
0.985264 | − | 0.171042i | \(-0.0547135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.3679 | 0.0434518 | 0.0217259 | − | 0.999764i | \(-0.493084\pi\) | ||||
0.0217259 | + | 0.999764i | \(0.493084\pi\) | |||||||
\(884\) | 281.684 | 0.318647 | ||||||||
\(885\) | − 195.707i | − 0.221138i | ||||||||
\(886\) | 578.000 | 0.652370 | ||||||||
\(887\) | 661.452i | 0.745718i | 0.927888 | + | 0.372859i | \(0.121623\pi\) | ||||
−0.927888 | + | 0.372859i | \(0.878377\pi\) | |||||||
\(888\) | − 47.7829i | − 0.0538095i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 215.840 | 0.242516 | ||||||||
\(891\) | −4.73801 | −0.00531763 | ||||||||
\(892\) | − 516.110i | − 0.578599i | ||||||||
\(893\) | −201.019 | −0.225106 | ||||||||
\(894\) | 352.923i | 0.394769i | ||||||||
\(895\) | − 438.043i | − 0.489434i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 80.8924 | 0.0901810 | ||||||||
\(898\) | 1025.97 | 1.14250 | ||||||||
\(899\) | − 106.176i | − 0.118104i | ||||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | − 1551.51i | − 1.72198i | ||||||||
\(902\) | − 3.03295i | − 0.00336247i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −328.779 | −0.363693 | ||||||||
\(905\) | −266.162 | −0.294102 | ||||||||
\(906\) | 229.058i | 0.252823i | ||||||||
\(907\) | −968.304 | −1.06759 | −0.533795 | − | 0.845614i | \(-0.679235\pi\) | ||||
−0.533795 | + | 0.845614i | \(0.679235\pi\) | |||||||
\(908\) | − 662.065i | − 0.729146i | ||||||||
\(909\) | 290.236i | 0.319291i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 220.674 | 0.242233 | 0.121116 | − | 0.992638i | \(-0.461353\pi\) | ||||
0.121116 | + | 0.992638i | \(0.461353\pi\) | |||||||
\(912\) | −22.0107 | −0.0241345 | ||||||||
\(913\) | − 6.57202i | − 0.00719827i | ||||||||
\(914\) | 567.850 | 0.621280 | ||||||||
\(915\) | − 400.070i | − 0.437235i | ||||||||
\(916\) | 488.476i | 0.533271i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 245.076 | 0.266967 | ||||||||
\(919\) | −1148.04 | −1.24923 | −0.624613 | − | 0.780934i | \(-0.714743\pi\) | ||||
−0.624613 | + | 0.780934i | \(0.714743\pi\) | |||||||
\(920\) | 69.9437i | 0.0760258i | ||||||||
\(921\) | 651.268 | 0.707132 | ||||||||
\(922\) | 923.552i | 1.00168i | ||||||||
\(923\) | − 122.726i | − 0.132964i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.7682 | 0.0527223 | ||||||||
\(926\) | −1229.77 | −1.32805 | ||||||||
\(927\) | − 314.287i | − 0.339036i | ||||||||
\(928\) | −317.520 | −0.342156 | ||||||||
\(929\) | − 305.300i | − 0.328633i | −0.986408 | − | 0.164317i | \(-0.947458\pi\) | ||||
0.986408 | − | 0.164317i | \(-0.0525419\pi\) | |||||||
\(930\) | − 10.3607i | − 0.0111406i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 422.979 | 0.453840 | ||||||||
\(933\) | −675.199 | −0.723686 | ||||||||
\(934\) | 1045.39i | 1.11926i | ||||||||
\(935\) | 39.2593 | 0.0419885 | ||||||||
\(936\) | 35.8339i | 0.0382841i | ||||||||
\(937\) | 12.4049i | 0.0132390i | 0.999978 | + | 0.00661948i | \(0.00210706\pi\) | ||||
−0.999978 | + | 0.00661948i | \(0.997893\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 247.781 | 0.263877 | ||||||||
\(940\) | −282.970 | −0.301032 | ||||||||
\(941\) | 289.147i | 0.307276i | 0.988127 | + | 0.153638i | \(0.0490990\pi\) | ||||
−0.988127 | + | 0.153638i | \(0.950901\pi\) | |||||||
\(942\) | −419.415 | −0.445239 | ||||||||
\(943\) | 45.0522i | 0.0477754i | ||||||||
\(944\) | 202.125i | 0.214116i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.5093 | −0.0364792 | ||||||||
\(947\) | −1426.96 | −1.50682 | −0.753409 | − | 0.657552i | \(-0.771592\pi\) | ||||
−0.753409 | + | 0.657552i | \(0.771592\pi\) | |||||||
\(948\) | − 458.282i | − 0.483420i | ||||||||
\(949\) | −70.6644 | −0.0744619 | ||||||||
\(950\) | − 22.4645i | − 0.0236469i | ||||||||
\(951\) | 665.876i | 0.700186i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −668.525 | −0.701495 | −0.350747 | − | 0.936470i | \(-0.614072\pi\) | ||||
−0.350747 | + | 0.936470i | \(0.614072\pi\) | |||||||
\(954\) | 197.372 | 0.206889 | ||||||||
\(955\) | − 146.980i | − 0.153906i | ||||||||
\(956\) | 688.268 | 0.719946 | ||||||||
\(957\) | 51.1812i | 0.0534809i | ||||||||
\(958\) | 857.331i | 0.894918i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.9839 | −0.0322749 | ||||||||
\(961\) | 957.422 | 0.996277 | ||||||||
\(962\) | 58.2518i | 0.0605528i | ||||||||
\(963\) | 373.813 | 0.388176 | ||||||||
\(964\) | 342.697i | 0.355495i | ||||||||
\(965\) | − 216.608i | − 0.224464i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1647.14 | 1.70335 | 0.851676 | − | 0.524069i | \(-0.175586\pi\) | ||||
0.851676 | + | 0.524069i | \(0.175586\pi\) | |||||||
\(968\) | −341.456 | −0.352744 | ||||||||
\(969\) | − 183.517i | − 0.189388i | ||||||||
\(970\) | 472.068 | 0.486668 | ||||||||
\(971\) | 1314.93i | 1.35420i | 0.735889 | + | 0.677102i | \(0.236764\pi\) | ||||
−0.735889 | + | 0.677102i | \(0.763236\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 918.639 | 0.943161 | ||||||||
\(975\) | −36.5729 | −0.0375106 | ||||||||
\(976\) | 413.190i | 0.423351i | ||||||||
\(977\) | 1556.04 | 1.59267 | 0.796337 | − | 0.604854i | \(-0.206768\pi\) | ||||
0.796337 | + | 0.604854i | \(0.206768\pi\) | |||||||
\(978\) | 227.834i | 0.232959i | ||||||||
\(979\) | 35.9323i | 0.0367030i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −253.825 | −0.258741 | ||||||||
\(982\) | 377.070 | 0.383982 | ||||||||
\(983\) | 1372.79i | 1.39654i | 0.715837 | + | 0.698268i | \(0.246045\pi\) | ||||
−0.715837 | + | 0.698268i | \(0.753955\pi\) | |||||||
\(984\) | −19.9573 | −0.0202818 | ||||||||
\(985\) | 417.411i | 0.423768i | ||||||||
\(986\) | − 2647.37i | − 2.68496i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.8331 | 0.0271590 | ||||||||
\(989\) | 512.609 | 0.518310 | ||||||||
\(990\) | 4.99430i | 0.00504475i | ||||||||
\(991\) | 643.624 | 0.649470 | 0.324735 | − | 0.945805i | \(-0.394725\pi\) | ||||
0.324735 | + | 0.945805i | \(0.394725\pi\) | |||||||
\(992\) | 10.7005i | 0.0107868i | ||||||||
\(993\) | 335.858i | 0.338226i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 257.800 | 0.259095 | ||||||||
\(996\) | −43.2450 | −0.0434187 | ||||||||
\(997\) | − 704.865i | − 0.706986i | −0.935437 | − | 0.353493i | \(-0.884994\pi\) | ||||
0.935437 | − | 0.353493i | \(-0.115006\pi\) | |||||||
\(998\) | −963.229 | −0.965159 | ||||||||
\(999\) | 50.6814i | 0.0507321i |
(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 | 1470.3.f.d.391.15 | 16 | ||
7.2 | even | 3 | 210.3.o.b.31.4 | ✓ | 16 | ||
7.3 | odd | 6 | 210.3.o.b.61.4 | yes | 16 | ||
7.6 | odd | 2 | inner | 1470.3.f.d.391.9 | 16 | ||
21.2 | odd | 6 | 630.3.v.c.451.6 | 16 | |||
21.17 | even | 6 | 630.3.v.c.271.6 | 16 | |||
35.2 | odd | 12 | 1050.3.q.e.199.12 | 32 | |||
35.3 | even | 12 | 1050.3.q.e.649.12 | 32 | |||
35.9 | even | 6 | 1050.3.p.i.451.6 | 16 | |||
35.17 | even | 12 | 1050.3.q.e.649.4 | 32 | |||
35.23 | odd | 12 | 1050.3.q.e.199.4 | 32 | |||
35.24 | odd | 6 | 1050.3.p.i.901.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.4 | ✓ | 16 | 7.2 | even | 3 | ||
210.3.o.b.61.4 | yes | 16 | 7.3 | odd | 6 | ||
630.3.v.c.271.6 | 16 | 21.17 | even | 6 | |||
630.3.v.c.451.6 | 16 | 21.2 | odd | 6 | |||
1050.3.p.i.451.6 | 16 | 35.9 | even | 6 | |||
1050.3.p.i.901.6 | 16 | 35.24 | odd | 6 | |||
1050.3.q.e.199.4 | 32 | 35.23 | odd | 12 | |||
1050.3.q.e.199.12 | 32 | 35.2 | odd | 12 | |||
1050.3.q.e.649.4 | 32 | 35.17 | even | 12 | |||
1050.3.q.e.649.12 | 32 | 35.3 | even | 12 | |||
1470.3.f.d.391.9 | 16 | 7.6 | odd | 2 | inner | ||
1470.3.f.d.391.15 | 16 | 1.1 | even | 1 | trivial |