Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Character | \(\chi\) | \(=\) | 256.97 |
Dual form | 256.4.g.a.161.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −5.56908 | + | 2.30679i | −1.07177 | + | 0.443942i | −0.847615 | − | 0.530612i | \(-0.821962\pi\) |
−0.224155 | + | 0.974553i | \(0.571962\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.28381 | + | 15.1704i | −0.562041 | + | 1.35689i | 0.346091 | + | 0.938201i | \(0.387509\pi\) |
−0.908131 | + | 0.418685i | \(0.862491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.6573 | + | 16.6573i | 0.899411 | + | 0.899411i | 0.995384 | − | 0.0959733i | \(-0.0305963\pi\) |
−0.0959733 | + | 0.995384i | \(0.530596\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.60151 | − | 6.60151i | 0.244500 | − | 0.244500i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.11257 | + | 1.28927i | 0.0853158 | + | 0.0353390i | 0.424933 | − | 0.905225i | \(-0.360298\pi\) |
−0.339617 | + | 0.940564i | \(0.610298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.8862 | + | 69.7374i | 0.616275 | + | 1.48782i | 0.855998 | + | 0.516979i | \(0.172943\pi\) |
−0.239723 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 98.9809i | − | 1.70378i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.2302i | 0.944893i | 0.881359 | + | 0.472447i | \(0.156629\pi\) | ||||
−0.881359 | + | 0.472447i | \(0.843371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.5299 | − | 30.2498i | −0.151292 | − | 0.365251i | 0.830004 | − | 0.557758i | \(-0.188338\pi\) |
−0.981296 | + | 0.192507i | \(0.938338\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −131.191 | − | 54.3410i | −1.36325 | − | 0.564676i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 63.7309 | − | 63.7309i | 0.577775 | − | 0.577775i | −0.356515 | − | 0.934290i | \(-0.616035\pi\) |
0.934290 | + | 0.356515i | \(0.116035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −102.268 | − | 102.268i | −0.818143 | − | 0.818143i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 40.7473 | − | 98.3726i | 0.290438 | − | 0.701178i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −190.908 | + | 79.0767i | −1.22244 | + | 0.506351i | −0.898184 | − | 0.439619i | \(-0.855113\pi\) |
−0.324255 | + | 0.945970i | \(0.605113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −123.811 | −0.717325 | −0.358662 | − | 0.933467i | \(-0.616767\pi\) | ||||
−0.358662 | + | 0.933467i | \(0.616767\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −20.3082 | −0.107127 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −357.370 | + | 148.028i | −1.72590 | + | 0.714892i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 46.0901 | − | 111.271i | 0.204788 | − | 0.494403i | −0.787799 | − | 0.615932i | \(-0.788780\pi\) |
0.992588 | + | 0.121529i | \(0.0387797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −321.739 | − | 321.739i | −1.32101 | − | 1.32101i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −100.187 | + | 100.187i | −0.381624 | + | 0.381624i | −0.871687 | − | 0.490063i | \(-0.836974\pi\) |
0.490063 | + | 0.871687i | \(0.336974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.5836 | + | 11.4255i | 0.0978246 | + | 0.0405203i | 0.431059 | − | 0.902324i | \(-0.358140\pi\) |
−0.333234 | + | 0.942844i | \(0.608140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 58.6652 | + | 141.630i | 0.194340 | + | 0.469178i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 394.293i | 1.22369i | 0.790976 | + | 0.611847i | \(0.209573\pi\) | ||||
−0.790976 | + | 0.611847i | \(0.790427\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 211.932i | 0.617879i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −152.779 | − | 368.841i | −0.419478 | − | 1.01271i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −135.196 | − | 56.0002i | −0.350390 | − | 0.145136i | 0.200545 | − | 0.979684i | \(-0.435729\pi\) |
−0.550935 | + | 0.834548i | \(0.685729\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.1175 | + | 39.1175i | −0.0959019 | + | 0.0959019i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 139.560 | + | 139.560i | 0.324301 | + | 0.324301i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 297.070 | − | 717.190i | 0.655512 | − | 1.58254i | −0.149152 | − | 0.988814i | \(-0.547654\pi\) |
0.804664 | − | 0.593731i | \(-0.202346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 548.826 | − | 227.331i | 1.15197 | − | 0.477160i | 0.276774 | − | 0.960935i | \(-0.410735\pi\) |
0.875193 | + | 0.483775i | \(0.160735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 219.927 | 0.439812 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1239.46 | −2.36517 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 163.352 | − | 67.6626i | 0.297860 | − | 0.123378i | −0.228749 | − | 0.973486i | \(-0.573463\pi\) |
0.526609 | + | 0.850108i | \(0.323463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −207.909 | + | 501.937i | −0.362743 | + | 0.875740i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −194.022 | − | 194.022i | −0.324312 | − | 0.324312i | 0.526107 | − | 0.850419i | \(-0.323651\pi\) |
−0.850419 | + | 0.526107i | \(0.823651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 547.142 | − | 547.142i | 0.877235 | − | 0.877235i | −0.116013 | − | 0.993248i | \(-0.537011\pi\) |
0.993248 | + | 0.116013i | \(0.0370113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 805.449 | + | 333.628i | 1.24007 | + | 0.513654i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30.3713 | + | 73.3227i | 0.0449497 | + | 0.108518i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 715.813i | 1.01943i | 0.860342 | + | 0.509717i | \(0.170250\pi\) | ||||
−0.860342 | + | 0.509717i | \(0.829750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 893.911i | 1.22621i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 54.6375 | + | 131.907i | 0.0722560 | + | 0.174441i | 0.955881 | − | 0.293754i | \(-0.0949045\pi\) |
−0.883625 | + | 0.468195i | \(0.844904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1004.74 | − | 416.178i | −1.28211 | − | 0.531068i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 880.769 | − | 880.769i | 1.08538 | − | 1.08538i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 220.576 | + | 220.576i | 0.262708 | + | 0.262708i | 0.826153 | − | 0.563445i | \(-0.190524\pi\) |
−0.563445 | + | 0.826153i | \(0.690524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −680.471 | + | 1642.80i | −0.783877 | + | 1.89245i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 689.512 | − | 285.605i | 0.768807 | − | 0.318450i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 537.638 | 0.580637 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1364.39 | 1.42817 | 0.714087 | − | 0.700057i | \(-0.246842\pi\) | ||||
0.714087 | + | 0.700057i | \(0.246842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.0587 | − | 12.0365i | 0.0295001 | − | 0.0122194i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 349.311 | − | 843.310i | 0.344136 | − | 0.830817i | −0.653153 | − | 0.757226i | \(-0.726554\pi\) |
0.997289 | − | 0.0735909i | \(-0.0234459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −273.149 | − | 273.149i | −0.261302 | − | 0.261302i | 0.564281 | − | 0.825583i | \(-0.309154\pi\) |
−0.825583 | + | 0.564281i | \(0.809154\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1648.76 | − | 1648.76i | 1.53240 | − | 1.53240i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −675.362 | − | 279.744i | −0.610185 | − | 0.252747i | 0.0561229 | − | 0.998424i | \(-0.482126\pi\) |
−0.666307 | + | 0.745677i | \(0.732126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 602.506 | + | 1454.58i | 0.529446 | + | 1.27820i | 0.931887 | + | 0.362749i | \(0.118162\pi\) |
−0.402441 | + | 0.915446i | \(0.631838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 726.000i | 0.620801i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 315.691i | − | 0.262812i | −0.991329 | − | 0.131406i | \(-0.958051\pi\) | ||
0.991329 | − | 0.131406i | \(-0.0419491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 566.354 | + | 1367.30i | 0.459242 | + | 1.10871i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 651.064 | + | 269.679i | 0.514452 | + | 0.213093i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1103.22 | + | 1103.22i | −0.849847 | + | 0.849847i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −933.133 | − | 933.133i | −0.701077 | − | 0.701077i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 326.839 | − | 789.060i | 0.239594 | − | 0.578432i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 297.776 | − | 123.343i | 0.213071 | − | 0.0882569i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −356.698 | −0.249227 | −0.124613 | − | 0.992205i | \(-0.539769\pi\) | ||||
−0.124613 | + | 0.992205i | \(0.539769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −179.971 | −0.122834 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2481.91 | + | 1028.04i | −1.65531 | + | 0.685652i | −0.997705 | − | 0.0677095i | \(-0.978431\pi\) |
−0.657606 | + | 0.753362i | \(0.728431\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 295.166 | − | 712.594i | 0.192437 | − | 0.464585i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1236.31 | + | 1236.31i | 0.788181 | + | 0.788181i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −811.069 | + | 811.069i | −0.505798 | + | 0.505798i | −0.913234 | − | 0.407436i | \(-0.866423\pi\) |
0.407436 | + | 0.913234i | \(0.366423\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2505.86 | + | 1037.96i | 1.52910 | + | 0.633373i | 0.979389 | − | 0.201984i | \(-0.0647387\pi\) |
0.549709 | + | 0.835356i | \(0.314739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −909.552 | − | 2195.85i | −0.543249 | − | 1.31152i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 254.304i | 0.148713i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3393.06i | − | 1.94330i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −488.883 | − | 1180.27i | −0.274302 | − | 0.662224i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 610.519 | + | 252.885i | 0.335676 | + | 0.139041i | 0.544154 | − | 0.838986i | \(-0.316851\pi\) |
−0.208478 | + | 0.978027i | \(0.566851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1314.56 | − | 1314.56i | 0.708457 | − | 0.708457i | −0.257753 | − | 0.966211i | \(-0.582982\pi\) |
0.966211 | + | 0.257753i | \(0.0829822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 437.219 | + | 437.219i | 0.231027 | + | 0.231027i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 778.003 | − | 1878.26i | 0.403166 | − | 0.973328i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2290.74 | + | 948.857i | −1.16447 | + | 0.482338i | −0.879360 | − | 0.476158i | \(-0.842029\pi\) |
−0.285107 | + | 0.958496i | \(0.592029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 882.101 | 0.439969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2123.17 | 1.03931 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −26.3934 | + | 10.9325i | −0.0126828 | + | 0.00525338i | −0.389016 | − | 0.921231i | \(-0.627185\pi\) |
0.376333 | + | 0.926484i | \(0.377185\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 127.613 | − | 308.085i | 0.0602100 | − | 0.145360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 111.233 | + | 111.233i | 0.0515415 | + | 0.0515415i | 0.732408 | − | 0.680866i | \(-0.238397\pi\) |
−0.680866 | + | 0.732408i | \(0.738397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2475.38 | + | 2475.38i | −1.12671 | + | 1.12671i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −282.410 | − | 116.978i | −0.126295 | − | 0.0523131i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 835.349 | + | 2016.71i | 0.367112 | + | 0.886287i | 0.994221 | + | 0.107355i | \(0.0342382\pi\) |
−0.627109 | + | 0.778932i | \(0.715762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3407.02i | − | 1.47169i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4679.37i | 1.98713i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 539.124 | + | 1301.56i | 0.225117 | + | 0.543481i | 0.995571 | − | 0.0940151i | \(-0.0299702\pi\) |
−0.770454 | + | 0.637496i | \(0.779970\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 702.054 | + | 290.800i | 0.288305 | + | 0.119420i | 0.522149 | − | 0.852854i | \(-0.325130\pi\) |
−0.233844 | + | 0.972274i | \(0.575130\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2532.05 | + | 2532.05i | −1.02281 | + | 1.02281i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1398.42 | + | 1398.42i | 0.555749 | + | 0.555749i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −85.3885 | + | 206.146i | −0.0333916 | + | 0.0806144i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2317.36 | − | 959.883i | 0.891870 | − | 0.369425i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2407.52 | −0.912052 | −0.456026 | − | 0.889966i | \(-0.650728\pi\) | ||||
−0.456026 | + | 0.889966i | \(0.650728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1721.96 | −0.642224 | −0.321112 | − | 0.947041i | \(-0.604057\pi\) | ||||
−0.321112 | + | 0.947041i | \(0.604057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6902.66 | − | 2859.18i | 2.53492 | − | 1.05000i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −160.639 | + | 387.816i | −0.0580966 | + | 0.140258i | −0.950262 | − | 0.311451i | \(-0.899185\pi\) |
0.892166 | + | 0.451708i | \(0.149185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 854.977 | + | 854.977i | 0.304562 | + | 0.304562i | 0.842795 | − | 0.538234i | \(-0.180908\pi\) |
−0.538234 | + | 0.842795i | \(0.680908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −753.637 | + | 753.637i | −0.264465 | + | 0.264465i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4497.22 | − | 1862.81i | −1.55489 | − | 0.644057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −890.326 | − | 2149.44i | −0.303332 | − | 0.732308i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 841.441i | − | 0.282532i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 110.309i | − | 0.0365082i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −819.136 | − | 1977.57i | −0.267259 | − | 0.645221i | 0.732093 | − | 0.681204i | \(-0.238544\pi\) |
−0.999352 | + | 0.0359838i | \(0.988544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1528.09 | + | 632.956i | 0.491563 | + | 0.203612i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −346.660 | + | 346.660i | −0.109963 | + | 0.109963i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2062.36 | − | 2062.36i | −0.645170 | − | 0.645170i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1784.94 | + | 4309.22i | −0.550753 | + | 1.32964i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4618.72 | + | 1913.14i | −1.40583 | + | 0.582314i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3155.56 | −0.947587 | −0.473793 | − | 0.880636i | \(-0.657116\pi\) | ||||
−0.473793 | + | 0.880636i | \(0.657116\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1350.24 | −0.400073 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 329.052 | − | 136.298i | 0.0962112 | − | 0.0398520i | −0.334059 | − | 0.942552i | \(-0.608418\pi\) |
0.430270 | + | 0.902700i | \(0.358418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1834.29 | + | 4428.38i | −0.529317 | + | 1.27788i | 0.402654 | + | 0.915352i | \(0.368088\pi\) |
−0.931971 | + | 0.362532i | \(0.881912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −338.280 | − | 338.280i | −0.0963515 | − | 0.0963515i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2068.42 | + | 2068.42i | −0.581573 | + | 0.581573i | −0.935335 | − | 0.353762i | \(-0.884902\pi\) |
0.353762 | + | 0.935335i | \(0.384902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5981.61 | − | 2477.66i | −1.66041 | − | 0.687766i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1651.23 | − | 3986.42i | −0.452569 | − | 1.09260i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1635.41i | − | 0.442620i | −0.975204 | − | 0.221310i | \(-0.928967\pi\) | ||
0.975204 | − | 0.221310i | \(-0.0710332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3798.84i | − | 1.01537i | −0.861542 | − | 0.507686i | \(-0.830501\pi\) | ||
0.861542 | − | 0.507686i | \(-0.169499\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −961.887 | − | 2322.20i | −0.253930 | − | 0.613042i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3215.11 | − | 1331.74i | −0.838391 | − | 0.347273i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1747.60 | − | 1747.60i | 0.450191 | − | 0.450191i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −608.562 | − | 608.562i | −0.154884 | − | 0.154884i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −641.114 | + | 1547.79i | −0.161222 | + | 0.389224i | −0.983761 | − | 0.179485i | \(-0.942557\pi\) |
0.822539 | + | 0.568709i | \(0.192557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 280.533 | − | 116.201i | 0.0697113 | − | 0.0288754i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6555.52 | 1.60989 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −576.329 | −0.139885 | −0.0699424 | − | 0.997551i | \(-0.522282\pi\) | ||||
−0.0699424 | + | 0.997551i | \(0.522282\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2621.22 | − | 1085.75i | 0.628860 | − | 0.260482i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −738.255 | + | 1782.31i | −0.175084 | + | 0.422690i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5045.11 | − | 5045.11i | −1.18287 | − | 1.18287i | −0.978997 | − | 0.203873i | \(-0.934647\pi\) |
−0.203873 | − | 0.978997i | \(-0.565353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1699.10 | − | 1699.10i | 0.393867 | − | 0.393867i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1737.23 | − | 719.583i | −0.398190 | − | 0.164936i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −555.865 | − | 1341.98i | −0.125991 | − | 0.304170i | 0.848280 | − | 0.529548i | \(-0.177638\pi\) |
−0.974271 | + | 0.225378i | \(0.927638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6517.54i | − | 1.46093i | −0.682950 | − | 0.730465i | \(-0.739303\pi\) | ||
0.682950 | − | 0.730465i | \(-0.260697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10718.6i | − | 2.37626i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −186.465 | − | 450.166i | −0.0408882 | − | 0.0987129i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5983.48 | + | 2478.44i | 1.29788 | + | 0.537599i | 0.921324 | − | 0.388795i | \(-0.127109\pi\) |
0.376555 | + | 0.926394i | \(0.377109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −817.338 | + | 817.338i | −0.175386 | + | 0.175386i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3663.87 | + | 3663.87i | 0.777822 | + | 0.777822i | 0.979460 | − | 0.201638i | \(-0.0646264\pi\) |
−0.201638 | + | 0.979460i | \(0.564626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1065.93 | − | 2573.38i | 0.223897 | − | 0.540535i | −0.771516 | − | 0.636210i | \(-0.780501\pi\) |
0.995413 | + | 0.0956751i | \(0.0305010\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2994.15 | + | 1240.22i | −0.622309 | + | 0.257769i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3337.69 | −0.686473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 526.558 | 0.107177 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7598.40 | + | 3147.36i | −1.53067 | + | 0.634026i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1873.89 | + | 4523.96i | −0.373630 | + | 0.902023i | 0.619499 | + | 0.784997i | \(0.287336\pi\) |
−0.993129 | + | 0.117025i | \(0.962664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9013.36 | + | 9013.36i | 1.77891 | + | 1.77891i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 253.657 | − | 253.657i | 0.0495578 | − | 0.0495578i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6285.37 | + | 2603.49i | 1.21569 | + | 0.503557i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 269.151 | + | 649.787i | 0.0515401 | + | 0.124429i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5502.25i | 1.04322i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9754.44i | 1.83127i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3251.76 | + | 7850.45i | 0.604521 | + | 1.45944i | 0.868882 | + | 0.495019i | \(0.164839\pi\) |
−0.264361 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2151.28 | + | 891.091i | 0.396059 | + | 0.164053i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1620.08 | + | 1620.08i | −0.295389 | + | 0.295389i | −0.839205 | − | 0.543815i | \(-0.816979\pi\) |
0.543815 | + | 0.839205i | \(0.316979\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4904.15 | + | 4904.15i | 0.885620 | + | 0.885620i | 0.994099 | − | 0.108479i | \(-0.0345979\pi\) |
−0.108479 | + | 0.994099i | \(0.534598\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1381.98 | + | 3336.39i | −0.247192 | + | 0.596775i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1326.36 | − | 549.398i | 0.235003 | − | 0.0973415i | −0.262074 | − | 0.965048i | \(-0.584407\pi\) |
0.497077 | + | 0.867706i | \(0.334407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −696.165 | −0.122187 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4406.46 | 0.766182 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2003.45 | − | 829.856i | 0.345124 | − | 0.142955i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4177.77 | − | 10086.0i | 0.713049 | − | 1.72145i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6710.81 | − | 6710.81i | −1.13489 | − | 1.13489i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6567.87 | + | 6567.87i | −1.10060 | + | 1.10060i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3808.89 | + | 1577.69i | 0.632494 | + | 0.261988i | 0.675812 | − | 0.737074i | \(-0.263793\pi\) |
−0.0433183 | + | 0.999061i | \(0.513793\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −430.295 | − | 1038.82i | −0.0708109 | − | 0.170953i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2903.30i | 0.473505i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 528.946i | − | 0.0855000i | −0.999086 | − | 0.0427500i | \(-0.986388\pi\) | ||
0.999086 | − | 0.0427500i | \(-0.0136119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 728.232 | + | 1758.11i | 0.116673 | + | 0.281674i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −385.369 | − | 159.625i | −0.0611992 | − | 0.0253495i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2183.23 | − | 2183.23i | 0.343684 | − | 0.343684i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6308.14 | − | 6308.14i | −0.984403 | − | 0.984403i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2777.92 | − | 6706.49i | 0.429759 | − | 1.03753i | −0.549605 | − | 0.835425i | \(-0.685222\pi\) |
0.979364 | − | 0.202105i | \(-0.0647784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2949.74 | − | 1221.82i | 0.452424 | − | 0.187400i | −0.144823 | − | 0.989458i | \(-0.546261\pi\) |
0.597247 | + | 0.802058i | \(0.296261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8037.28 | 1.22222 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9005.55 | 1.35784 | 0.678919 | − | 0.734213i | \(-0.262449\pi\) | ||||
0.678919 | + | 0.734213i | \(0.262449\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4162.59 | − | 1724.20i | 0.622331 | − | 0.257778i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3599.02 | − | 8688.80i | 0.533558 | − | 1.28812i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7280.93 | + | 7280.93i | 1.07040 | + | 1.07040i | 0.997327 | + | 0.0730705i | \(0.0232798\pi\) |
0.0730705 | + | 0.997327i | \(0.476720\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4091.99 | − | 4091.99i | 0.596588 | − | 0.596588i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7349.24 | + | 3044.15i | 1.06263 | + | 0.440156i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4862.26 | + | 11738.5i | 0.697266 | + | 1.68335i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2730.08i | 0.388308i | 0.980971 | + | 0.194154i | \(0.0621961\pi\) | ||||
−0.980971 | + | 0.194154i | \(0.937804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1322.77i | 0.186614i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1319.20 | − | 3184.82i | −0.184607 | − | 0.445681i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −807.251 | − | 334.374i | −0.112059 | − | 0.0464162i | 0.325950 | − | 0.945387i | \(-0.394316\pi\) |
−0.438008 | + | 0.898971i | \(0.644316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1373.81 | + | 1373.81i | −0.189182 | + | 0.189182i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11029.2 | − | 11029.2i | −1.50672 | − | 1.50672i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −511.994 | + | 1236.06i | −0.0693914 | + | 0.167526i | −0.954770 | − | 0.297344i | \(-0.903899\pi\) |
0.885379 | + | 0.464870i | \(0.153899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1986.48 | − | 822.826i | 0.267114 | − | 0.110642i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7830.32 | −1.04468 | −0.522338 | − | 0.852739i | \(-0.674940\pi\) | ||||
−0.522338 | + | 0.852739i | \(0.674940\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1303.19 | −0.172510 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 257.519 | − | 106.668i | 0.0338254 | − | 0.0140109i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1347.70 | + | 3253.64i | −0.175659 | + | 0.424077i | −0.987047 | − | 0.160430i | \(-0.948712\pi\) |
0.811389 | + | 0.584507i | \(0.198712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4220.91 | + | 4220.91i | 0.545936 | + | 0.545936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11450.5 | − | 11450.5i | 1.46972 | − | 1.46972i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10859.2 | − | 4498.03i | −1.38326 | − | 0.572963i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4283 | + | 56.5609i | 0.00296180 | + | 0.00715041i | 0.925354 | − | 0.379105i | \(-0.123768\pi\) |
−0.922392 | + | 0.386256i | \(0.873768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4649.38i | 0.583359i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12034.3i | 1.49866i | 0.662195 | + | 0.749332i | \(0.269625\pi\) | ||||
−0.662195 | + | 0.749332i | \(0.730375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3576.42 | − | 8634.24i | −0.442070 | − | 1.06725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13561.0 | − | 5617.16i | −1.66383 | − | 0.689183i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 286.917 | − | 286.917i | 0.0349434 | − | 0.0349434i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8440.37 | + | 8440.37i | 1.02041 | + | 1.02041i | 0.999787 | + | 0.0206265i | \(0.00656608\pi\) |
0.0206265 | + | 0.999787i | \(0.493434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2645.94 | − | 6387.87i | 0.317554 | − | 0.766644i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16894.8 | − | 6998.07i | 2.01293 | − | 0.833784i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2344.41 | −0.277308 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16349.7 | −1.92002 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14617.4 | + | 6054.71i | −1.70431 | + | 0.705947i | −0.999992 | − | 0.00393979i | \(-0.998746\pi\) |
−0.704315 | + | 0.709887i | \(0.748746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5214.86 | − | 12589.8i | 0.603697 | − | 1.45745i | −0.266051 | − | 0.963959i | \(-0.585719\pi\) |
0.869749 | − | 0.493495i | \(-0.164281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2602.93 | + | 2602.93i | 0.299194 | + | 0.299194i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6773.23 | − | 6773.23i | 0.773058 | − | 0.773058i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12928.7 | + | 5355.24i | 1.46525 | + | 0.606928i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −586.626 | − | 1416.24i | −0.0660200 | − | 0.159386i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3490.31i | − | 0.390075i | −0.980796 | − | 0.195037i | \(-0.937517\pi\) | ||
0.980796 | − | 0.195037i | \(-0.0624828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11691.1i | − | 1.29755i | −0.760980 | − | 0.648775i | \(-0.775282\pi\) | ||
0.760980 | − | 0.648775i | \(-0.224718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7827.08 | + | 18896.2i | 0.862712 | + | 2.08277i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2726.39 | − | 1129.31i | −0.298446 | − | 0.123620i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6721.98 | + | 6721.98i | −0.730804 | + | 0.730804i | −0.970779 | − | 0.239975i | \(-0.922861\pi\) |
0.239975 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1399.07 | + | 1399.07i | 0.151072 | + | 0.151072i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3951.12 | + | 9538.86i | −0.423755 | + | 1.02304i | 0.557475 | + | 0.830194i | \(0.311770\pi\) |
−0.981230 | + | 0.192842i | \(0.938230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4732.29 | + | 1960.18i | −0.504117 | + | 0.208812i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3983.39 | −0.421494 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3683.45 | −0.387155 | −0.193578 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193578 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −441.006 | + | 182.671i | −0.0460448 | + | 0.0190724i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4288.47 | + | 10353.3i | −0.444790 | + | 1.07382i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20646.1 | − | 20646.1i | −2.12726 | − | 2.12726i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6693.56 | + | 6693.56i | −0.685146 | + | 0.685146i | −0.961155 | − | 0.276009i | \(-0.910988\pi\) |
0.276009 | + | 0.961155i | \(0.410988\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6515.24 | + | 2698.70i | 0.662539 | + | 0.274432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2097.99 | + | 5065.00i | 0.211959 | + | 0.511715i | 0.993724 | − | 0.111858i | \(-0.0356803\pi\) |
−0.781765 | + | 0.623573i | \(0.785680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17006.8i | 1.70707i | 0.521038 | + | 0.853534i | \(0.325545\pi\) | ||||
−0.521038 | + | 0.853534i | \(0.674455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12254.9i | 1.22217i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7003.63 | − | 16908.3i | −0.693981 | − | 1.67542i | −0.736601 | − | 0.676328i | \(-0.763570\pi\) |
0.0426191 | − | 0.999091i | \(-0.486430\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3848.08 | + | 1593.93i | 0.378866 | + | 0.156931i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10568.5 | − | 10568.5i | 1.03391 | − | 1.03391i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 71.1253 | + | 71.1253i | 0.00691404 | + | 0.00691404i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1812.18 | + | 4374.99i | −0.175049 | + | 0.422607i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1262.19 | + | 522.815i | −0.121156 | + | 0.0501846i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12250.2 | 1.16853 | 0.584263 | − | 0.811564i | \(-0.301384\pi\) | ||||
0.584263 | + | 0.811564i | \(0.301384\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9091.14 | 0.861789 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11824.1 | + | 4897.71i | −1.11391 | + | 0.461395i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8573.56 | + | 20698.4i | −0.802691 | + | 1.93787i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6781.49 | − | 6781.49i | −0.631003 | − | 0.631003i | 0.317317 | − | 0.948320i | \(-0.397218\pi\) |
−0.948320 | + | 0.317317i | \(0.897218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 121.768 | − | 121.768i | 0.0112608 | − | 0.0112608i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2990.34 | − | 1238.64i | −0.274851 | − | 0.113847i | 0.241000 | − | 0.970525i | \(-0.422524\pi\) |
−0.515852 | + | 0.856678i | \(0.672524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5237.27 | − | 12643.9i | −0.478447 | − | 1.15507i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 516.469i | 0.0468961i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6463.76i | − | 0.583379i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 672.528 | + | 1623.63i | 0.0603336 | + | 0.145658i | 0.951171 | − | 0.308663i | \(-0.0998817\pi\) |
−0.890838 | + | 0.454322i | \(0.849882\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −876.053 | − | 362.873i | −0.0781221 | − | 0.0323592i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14586.7 | − | 14586.7i | 1.29302 | − | 1.29302i | 0.360107 | − | 0.932911i | \(-0.382740\pi\) |
0.932911 | − | 0.360107i | \(-0.117260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10598.4 | + | 10598.4i | 0.933906 | + | 0.933906i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8075.40 | − | 19495.7i | 0.707379 | − | 1.70776i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10300.8 | + | 4266.74i | −0.897005 | + | 0.371552i | −0.783068 | − | 0.621936i | \(-0.786346\pi\) |
−0.113937 | + | 0.993488i | \(0.536346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18227.8 | 1.57799 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3486.31 | −0.300047 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5860.20 | − | 2427.38i | 0.501420 | − | 0.207695i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −508.350 | + | 1227.26i | −0.0432441 | + | 0.104400i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9304.25 | − | 9304.25i | −0.786919 | − | 0.786919i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10841.1 | − | 10841.1i | 0.911623 | − | 0.911623i | −0.0847773 | − | 0.996400i | \(-0.527018\pi\) |
0.996400 | + | 0.0847773i | \(0.0270179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7489.02 | − | 3102.05i | −0.626142 | − | 0.259356i | 0.0469711 | − | 0.998896i | \(-0.485043\pi\) |
−0.673113 | + | 0.739540i | \(0.735043\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7859.27 | + | 18974.0i | 0.653346 | + | 1.57732i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8200.01i | − | 0.677795i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4043.73i | 0.332352i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2773.43 | − | 6695.64i | −0.226660 | − | 0.547205i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9880.79 | − | 4092.76i | −0.802973 | − | 0.332602i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8487.69 | − | 8487.69i | 0.685897 | − | 0.685897i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6004.85 | − | 6004.85i | −0.482548 | − | 0.482548i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −273.238 | + | 659.654i | −0.0218352 | + | 0.0527149i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20246.0 | + | 8386.17i | −1.60895 | + | 0.666451i | −0.992646 | − | 0.121054i | \(-0.961372\pi\) |
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4580.61 | −0.362013 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25852.6 | −2.03194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10328.3 | − | 4278.13i | 0.807325 | − | 0.334405i | 0.0594388 | − | 0.998232i | \(-0.481069\pi\) |
0.747886 | + | 0.663827i | \(0.231069\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2122.35 | − | 5123.81i | 0.164990 | − | 0.398322i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4784.11 | + | 4784.11i | 0.369891 | + | 0.369891i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11923.5 | + | 11923.5i | −0.916890 | + | 0.916890i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11013.7 | − | 4562.04i | −0.842356 | − | 0.348915i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1262.85 | − | 3048.78i | −0.0960657 | − | 0.231923i | 0.868540 | − | 0.495619i | \(-0.165059\pi\) |
−0.964606 | + | 0.263696i | \(0.915059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2253.65i | 0.170517i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1345.02i | − | 0.101224i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3354.10 | + | 8097.52i | 0.251081 | + | 0.606163i | 0.998292 | − | 0.0584237i | \(-0.0186075\pi\) |
−0.747211 | + | 0.664587i | \(0.768607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4789.17 | + | 1983.74i | 0.356605 | + | 0.147711i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14890.2 | + | 14890.2i | −1.10287 | + | 1.10287i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8264.07 | − | 8264.07i | −0.608872 | − | 0.608872i | 0.333780 | − | 0.942651i | \(-0.391676\pi\) |
−0.942651 | + | 0.333780i | \(0.891676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2298.13 | + | 5548.17i | −0.168430 | + | 0.406626i | −0.985446 | − | 0.169989i | \(-0.945627\pi\) |
0.817016 | + | 0.576615i | \(0.195627\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13407.7 | − | 5553.64i | 0.977510 | − | 0.404898i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13035.3 | −0.945405 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7818.78 | −0.564125 | −0.282062 | − | 0.959396i | \(-0.591019\pi\) | ||||
−0.282062 | + | 0.959396i | \(0.591019\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9589.72 | − | 3972.19i | 0.688317 | − | 0.285110i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1287.10 | + | 3107.33i | −0.0919067 | + | 0.221882i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −348.609 | − | 348.609i | −0.0247648 | − | 0.0247648i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8182.32 | + | 8182.32i | −0.578286 | + | 0.578286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12603.6 | + | 5220.58i | 0.886211 | + | 0.367081i | 0.778902 | − | 0.627145i | \(-0.215777\pi\) |
0.107309 | + | 0.994226i | \(0.465777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1551.33 | + | 3745.25i | 0.108526 | + | 0.262004i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2530.34i | − | 0.176116i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22972.2i | 1.59081i | 0.606075 | + | 0.795407i | \(0.292743\pi\) | ||||
−0.606075 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9803.90 | − | 23668.7i | −0.675497 | − | 1.63079i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6733.69 | − | 2789.19i | −0.461628 | − | 0.191212i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7947.99 | + | 7947.99i | −0.542147 | + | 0.542147i | −0.924158 | − | 0.382011i | \(-0.875232\pi\) |
0.382011 | + | 0.924158i | \(0.375232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10055.8 | − | 10055.8i | −0.682506 | − | 0.682506i | 0.278058 | − | 0.960564i | \(-0.410309\pi\) |
−0.960564 | + | 0.278058i | \(0.910309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 631.694 | − | 1525.04i | 0.0426610 | − | 0.102993i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20019.7 | − | 8292.42i | 1.34532 | − | 0.557248i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24716.9 | −1.65277 | −0.826383 | − | 0.563109i | \(-0.809605\pi\) | ||||
−0.826383 | + | 0.563109i | \(0.809605\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29342.5 | 1.95241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27497.0 | + | 11389.6i | −1.82064 | + | 0.754132i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5388.03 | − | 13007.9i | 0.355009 | − | 0.857067i | −0.640977 | − | 0.767560i | \(-0.721471\pi\) |
0.995986 | − | 0.0895074i | \(-0.0285293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9916.59 | + | 9916.59i | 0.650204 | + | 0.650204i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1763.96 | + | 1763.96i | −0.115096 | + | 0.115096i | −0.762309 | − | 0.647213i | \(-0.775934\pi\) |
0.647213 | + | 0.762309i | \(0.275934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21023.8 | − | 8708.35i | −1.36513 | − | 0.565457i | −0.424670 | − | 0.905348i | \(-0.639610\pi\) |
−0.940465 | + | 0.339891i | \(0.889610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3672.52 | − | 8866.24i | −0.237316 | − | 0.572931i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7348.41i | 0.472565i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 12786.1i | − | 0.818312i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 254.459 | + | 614.319i | 0.0162075 | + | 0.0391284i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7369.53 | + | 3052.56i | 0.467158 | + | 0.193503i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20760.0 | + | 20760.0i | −1.30973 | + | 1.30973i | −0.388129 | + | 0.921605i | \(0.626878\pi\) |
−0.921605 | + | 0.388129i | \(0.873122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9123.67 | + | 9123.67i | 0.572881 | + | 0.572881i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2241.42 | − | 5411.26i | 0.140076 | − | 0.338172i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14779.6 | + | 6121.92i | −0.919293 | + | 0.380784i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2561.67 | −0.158589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16062.4 | 0.989745 | 0.494872 | − | 0.868966i | \(-0.335215\pi\) | ||||
0.494872 | + | 0.868966i | \(0.335215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24877.7 | − | 10304.7i | 1.52579 | − | 0.632001i | 0.547046 | − | 0.837103i | \(-0.315752\pi\) |
0.978741 | + | 0.205101i | \(0.0657524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1130.91 | − | 2730.25i | 0.0690378 | − | 0.166672i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11101.6 | + | 11101.6i | 0.674572 | + | 0.674572i | 0.958767 | − | 0.284195i | \(-0.0917262\pi\) |
−0.284195 | + | 0.958767i | \(0.591726\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1849.30 | − | 1849.30i | 0.111851 | − | 0.111851i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16242.8 | + | 6728.01i | 0.977891 | + | 0.405056i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1485.55 | − | 3586.44i | −0.0890262 | − | 0.214928i | 0.873095 | − | 0.487550i | \(-0.162109\pi\) |
−0.962121 | + | 0.272622i | \(0.912109\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 44111.8i | − | 2.63143i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7223.93i | − | 0.428968i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10740.4 | + | 25929.6i | 0.634881 | + | 1.53274i | 0.833417 | + | 0.552644i | \(0.186381\pi\) |
−0.198537 | + | 0.980093i | \(0.563619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1477.94 | + | 612.182i | 0.0869670 | + | 0.0360229i | 0.425743 | − | 0.904844i | \(-0.360013\pi\) |
−0.338776 | + | 0.940867i | \(0.610013\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21308.8 | − | 21308.8i | 1.24821 | − | 1.24821i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8955.61 | + | 8955.61i | 0.522231 | + | 0.522231i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7127.12 | + | 17206.4i | −0.413738 | + | 0.998851i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17573.6 | − | 7279.21i | 1.01560 | − | 0.420673i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2001.35 | 0.115143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25713.9 | −1.47281 | −0.736404 | − | 0.676543i | \(-0.763478\pi\) | ||||
−0.736404 | + | 0.676543i | \(0.763478\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14227.5 | + | 5893.22i | −0.811284 | + | 0.336045i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4314.50 | − | 10416.1i | 0.244933 | − | 0.591321i | −0.752827 | − | 0.658219i | \(-0.771310\pi\) |
0.997760 | + | 0.0668981i | \(0.0213102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22727.1 | + | 22727.1i | 1.28451 | + | 1.28451i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1518.11 | + | 1518.11i | −0.0854244 | + | 0.0854244i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1854.70 | − | 768.242i | −0.103907 | − | 0.0430395i | 0.330125 | − | 0.943937i | \(-0.392909\pi\) |
−0.434031 | + | 0.900898i | \(0.642909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7207.68 | − | 17400.9i | −0.402031 | − | 0.970589i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 28893.3i | − | 1.60458i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 11045.9i | − | 0.610761i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2881.88 | − | 6957.49i | −0.158657 | − | 0.383032i | 0.824483 | − | 0.565887i | \(-0.191466\pi\) |
−0.983140 | + | 0.182855i | \(0.941466\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 684.537 | + | 283.544i | 0.0375230 | + | 0.0155425i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31492.7 | + | 31492.7i | −1.71883 | + | 1.71883i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6635.41 | − | 6635.41i | −0.360594 | − | 0.360594i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6747.78 | − | 16290.6i | 0.365128 | − | 0.881497i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26418.3 | + | 10942.8i | −1.42340 | + | 0.589592i | −0.955713 | − | 0.294302i | \(-0.904913\pi\) |
−0.467688 | + | 0.883893i | \(0.654913\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3943.44 | −0.211564 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39027.5 | 2.08491 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19865.9 | − | 8228.71i | 1.05676 | − | 0.437726i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1886.73 | − | 4554.97i | 0.0999404 | − | 0.241277i | −0.865999 | − | 0.500046i | \(-0.833317\pi\) |
0.965939 | + | 0.258768i | \(0.0833166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4725.45 | + | 4725.45i | 0.249252 | + | 0.249252i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7890.58 | + | 7890.58i | −0.414452 | + | 0.414452i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3857.91 | − | 1598.00i | −0.201787 | − | 0.0835828i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3772.55 | + | 9107.75i | 0.196497 | + | 0.474387i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29695.2i | 1.54026i | 0.637889 | + | 0.770129i | \(0.279808\pi\) | ||||
−0.637889 | + | 0.770129i | \(0.720192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9099.85i | − | 0.470036i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8763.12 | + | 21156.0i | 0.450766 | + | 1.08825i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27610.8 | + | 11436.8i | 1.41440 | + | 0.585863i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26485.0 | − | 26485.0i | 1.35113 | − | 1.35113i | 0.466739 | − | 0.884395i | \(-0.345429\pi\) |
0.884395 | − | 0.466739i | \(-0.154571\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6352.78 | − | 6352.78i | −0.322755 | − | 0.322755i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −756.713 | + | 1826.87i | −0.0382873 | + | 0.0924338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3763.54 | + | 1558.91i | −0.189645 | + | 0.0785534i | −0.475485 | − | 0.879724i | \(-0.657727\pi\) |
0.285840 | + | 0.958277i | \(0.407727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20977.3 | 1.05273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 595.679 | 0.0297722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14266.3 | − | 5909.30i | 0.710142 | − | 0.294150i | 0.00177857 | − | 0.999998i | \(-0.499434\pi\) |
0.708363 | + | 0.705848i | \(0.249434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5701.18 | + | 13763.9i | −0.282643 | + | 0.682360i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17888.3 | − | 17888.3i | −0.883253 | − | 0.883253i | 0.110611 | − | 0.993864i | \(-0.464719\pi\) |
−0.993864 | + | 0.110611i | \(0.964719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7672.77 | + | 7672.77i | −0.377327 | + | 0.377327i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1231.47 | + | 510.093i | 0.0603176 | + | 0.0249844i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6589.94 | − | 15909.5i | −0.321483 | − | 0.776130i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20239.7i | 0.983432i | 0.870756 | + | 0.491716i | \(0.163630\pi\) | ||||
−0.870756 | + | 0.491716i | \(0.836370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 10098.7i | − | 0.488732i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11682.0 | + | 28202.8i | 0.563114 | + | 1.35948i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15064.3 | + | 6239.82i | 0.723275 | + | 0.299591i | 0.713785 | − | 0.700364i | \(-0.246979\pi\) |
0.00949004 | + | 0.999955i | \(0.496979\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1294.26 | + | 1294.26i | −0.0618955 | + | 0.0618955i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3008.89 | − | 3008.89i | −0.143328 | − | 0.143328i | 0.631802 | − | 0.775130i | \(-0.282316\pi\) |
−0.775130 | + | 0.631802i | \(0.782316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14193.2 | + | 34265.5i | −0.673433 | + | 1.62581i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9380.21 | + | 3885.41i | −0.443323 | + | 0.183631i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58596.1 | 2.75852 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33250.5 | 1.55923 | 0.779613 | − | 0.626261i | \(-0.215416\pi\) | ||||
0.779613 | + | 0.626261i | \(0.215416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3209.62 | − | 1329.47i | 0.149924 | − | 0.0621007i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6032.84 | − | 14564.6i | 0.280707 | − | 0.677686i | −0.719146 | − | 0.694859i | \(-0.755467\pi\) |
0.999853 | + | 0.0171732i | \(0.00546666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12661.9 | + | 12661.9i | 0.586875 | + | 0.586875i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12093.2 | + | 12093.2i | −0.558355 | + | 0.558355i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4285.96 | + | 1775.30i | 0.197125 | + | 0.0816520i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −353.760 | − | 854.052i | −0.0162081 | − | 0.0391298i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22002.3i | 1.00421i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 40714.0i | − | 1.85114i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15236.1 | − | 36783.2i | −0.690100 | − | 1.66605i | −0.744579 | − | 0.667534i | \(-0.767350\pi\) |
0.0544793 | − | 0.998515i | \(-0.482650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39734.6 | + | 16458.6i | 1.79289 | + | 0.742640i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5258.57 | − | 5258.57i | 0.236376 | − | 0.236376i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31706.9 | + | 31706.9i | 1.41986 | + | 1.41986i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5542.95 | + | 13381.9i | −0.247281 | + | 0.596988i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4162.41 | + | 1724.12i | −0.184994 | + | 0.0766269i | −0.473258 | − | 0.880924i | \(-0.656922\pi\) |
0.288264 | + | 0.957551i | \(0.406922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26114.1 | −1.15626 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2912.27 | 0.128464 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2408.43 | − | 997.604i | 0.105843 | − | 0.0438414i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13341.6 | + | 32209.5i | −0.584136 | + | 1.41023i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6191.31 | + | 6191.31i | 0.270068 | + | 0.270068i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24296.9 | − | 24296.9i | 1.05591 | − | 1.05591i | 0.0575706 | − | 0.998341i | \(-0.481665\pi\) |
0.998341 | − | 0.0575706i | \(-0.0183354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11241.7 | − | 4656.46i | −0.486744 | − | 0.201616i | 0.125795 | − | 0.992056i | \(-0.459852\pi\) |
−0.612539 | + | 0.790440i | \(0.709852\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15034.6 | + | 36296.7i | 0.648568 | + | 1.56578i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 469.098i | − | 0.0201617i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 977.558i | − | 0.0418610i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6352.84 | + | 15337.1i | 0.271045 | + | 0.654362i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3924.75 | − | 1625.68i | −0.166839 | − | 0.0691069i | 0.297701 | − | 0.954659i | \(-0.403780\pi\) |
−0.464540 | + | 0.885552i | \(0.653780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14112.0 | + | 14112.0i | −0.597708 | + | 0.597708i | −0.939702 | − | 0.341994i | \(-0.888898\pi\) |
0.341994 | + | 0.939702i | \(0.388898\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2076.88 | + | 2076.88i | 0.0876456 | + | 0.0876456i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8156.23 | − | 19690.9i | 0.342950 | − | 0.827956i | −0.654464 | − | 0.756093i | \(-0.727106\pi\) |
0.997415 | − | 0.0718625i | \(-0.0228943\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19708.8 | − | 8163.65i | 0.825711 | − | 0.342021i | 0.0705076 | − | 0.997511i | \(-0.477538\pi\) |
0.755203 | + | 0.655491i | \(0.227538\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39039.7 | −1.62969 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14036.3 | −0.583830 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2386.41 | + | 988.484i | −0.0989044 | + | 0.0409675i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5044.95 | + | 12179.6i | −0.208338 | + | 0.502973i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18262.0 | − | 18262.0i | −0.751458 | − | 0.751458i | 0.223293 | − | 0.974751i | \(-0.428319\pi\) |
−0.974751 | + | 0.223293i | \(0.928319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12947.1 | − | 12947.1i | 0.530859 | − | 0.530859i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28856.2 | − | 11952.6i | −1.17895 | − | 0.488339i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21997.8 | − | 53107.3i | −0.895558 | − | 2.16207i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31087.0i | − | 1.26111i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16790.2i | 0.678727i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4154.07 | − | 10028.8i | −0.167332 | − | 0.403975i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2913.29 | + | 1206.73i | 0.116939 | + | 0.0484379i | 0.440386 | − | 0.897809i | \(-0.354842\pi\) |
−0.323447 | + | 0.946246i | \(0.604842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3549.22 | − | 3549.22i | 0.141966 | − | 0.141966i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7266.15 | + | 7266.15i | 0.289623 | + | 0.289623i | 0.836931 | − | 0.547308i | \(-0.184347\pi\) |
−0.547308 | + | 0.836931i | \(0.684347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16409.5 | + | 39616.1i | −0.651787 | + | 1.57355i | 0.158396 | + | 0.987376i | \(0.449368\pi\) |
−0.810183 | + | 0.586177i | \(0.800632\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18587.9 | − | 7699.35i | 0.735741 | − | 0.304754i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29533.5 | 1.16493 | 0.582464 | − | 0.812856i | \(-0.302089\pi\) | ||||
0.582464 | + | 0.812856i | \(0.302089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35843.6 | −1.40892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2932.45 | + | 1214.66i | −0.114869 | + | 0.0475802i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −922.875 | + | 2228.02i | −0.0360258 | + | 0.0869739i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9437.22 | + | 9437.22i | 0.367128 | + | 0.367128i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9007.03 | − | 9007.03i | 0.349189 | − | 0.349189i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7014.71 | + | 2905.59i | 0.271018 | + | 0.112259i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12488.6 | − | 30150.2i | −0.480856 | − | 1.16089i | −0.959203 | − | 0.282719i | \(-0.908764\pi\) |
0.478347 | − | 0.878171i | \(-0.341236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 29517.0i | − | 1.13263i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14625.2i | 0.559292i | 0.960103 | + | 0.279646i | \(0.0902171\pi\) | ||||
−0.960103 | + | 0.279646i | \(0.909783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18156.7 | + | 43834.1i | 0.691983 | + | 1.67059i | 0.740748 | + | 0.671783i | \(0.234471\pi\) |
−0.0487652 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −70988.1 | − | 29404.2i | −2.69631 | − | 1.11685i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3906.55 | − | 3906.55i | 0.147879 | − | 0.147879i | −0.629291 | − | 0.777170i | \(-0.716654\pi\) |
0.777170 | + | 0.629291i | \(0.216654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5941.62 | − | 5941.62i | −0.224157 | − | 0.224157i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1152.49 | + | 2782.36i | −0.0433332 | + | 0.104616i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11927.3 | − | 4940.45i | 0.446956 | − | 0.185135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23133.0 | −0.863967 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41009.4 | −1.52649 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23636.5 | − | 9790.55i | 0.876886 | − | 0.363218i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3708.91 | − | 8954.09i | 0.137138 | − | 0.331081i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2997.84 | − | 2997.84i | −0.110478 | − | 0.110478i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8823.14 | + | 8823.14i | −0.324079 | + | 0.324079i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15093.4 | + | 6251.90i | 0.552556 | + | 0.228876i | 0.641450 | − | 0.767165i | \(-0.278333\pi\) |
−0.0888937 | + | 0.996041i | \(0.528333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3261.14 | − | 7873.10i | −0.118994 | − | 0.287276i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12262.7i | − | 0.445971i | −0.974822 | − | 0.222986i | \(-0.928420\pi\) | ||
0.974822 | − | 0.222986i | \(-0.0715803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 481.011i | 0.0174361i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22501.4 | − | 54323.3i | −0.812978 | − | 1.96270i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −58466.4 | − | 24217.6i | −2.10549 | − | 0.872121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26825.0 | + | 26825.0i | −0.962866 | + | 0.962866i | −0.999335 | − | 0.0364685i | \(-0.988389\pi\) |
0.0364685 | + | 0.999335i | \(0.488389\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36218.7 | − | 36218.7i | −1.29582 | − | 1.29582i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7926.02 | − | 19135.1i | 0.282652 | − | 0.682383i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16093.0 | + | 6665.96i | −0.572039 | + | 0.236946i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3606.39 | −0.127777 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27282.3 | 0.963512 | 0.481756 | − | 0.876305i | \(-0.339999\pi\) | ||||
0.481756 | + | 0.876305i | \(0.339999\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6410.91 | − | 2655.49i | 0.225681 | − | 0.0934802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5285.16 | − | 12759.5i | 0.185454 | − | 0.447725i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2590.76 | − | 2590.76i | −0.0906171 | − | 0.0906171i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24857.5 | + | 24857.5i | −0.866658 | + | 0.866658i | −0.992101 | − | 0.125443i | \(-0.959965\pi\) |
0.125443 | + | 0.992101i | \(0.459965\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38624.5 | − | 15998.8i | −1.34235 | − | 0.556018i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16878.2 | + | 40747.6i | 0.584712 | + | 1.41162i | 0.888498 | + | 0.458880i | \(0.151749\pi\) |
−0.303786 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12770.0i | 0.440985i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41187.2i | 1.41780i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17615.8 | − | 42528.2i | −0.604472 | − | 1.45933i | −0.868934 | − | 0.494929i | \(-0.835194\pi\) |
0.264461 | − | 0.964396i | \(-0.414806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53961.1 | + | 22351.4i | 1.84579 | + | 0.764550i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6119.28 | + | 6119.28i | −0.208655 | + | 0.208655i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9439.64 | + | 9439.64i | 0.320860 | + | 0.320860i | 0.849097 | − | 0.528237i | \(-0.177147\pi\) |
−0.528237 | + | 0.849097i | \(0.677147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15128.4 | − | 36523.1i | 0.512610 | − | 1.23755i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3877.00 | − | 1605.91i | 0.130957 | − | 0.0542440i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27020.5 | −0.909840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14461.9 | −0.485445 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6305.14 | + | 2611.68i | −0.210987 | + | 0.0873936i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10820.4 | − | 26122.9i | 0.360956 | − | 0.871425i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25745.5 | − | 25745.5i | −0.856173 | − | 0.856173i | 0.134711 | − | 0.990885i | \(-0.456989\pi\) |
−0.990885 | + | 0.134711i | \(0.956989\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9243.07 | + | 9243.07i | −0.306430 | + | 0.306430i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18385.2 | + | 7615.42i | 0.607632 | + | 0.251689i | 0.665216 | − | 0.746651i | \(-0.268340\pi\) |
−0.0575837 | + | 0.998341i | \(0.518340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24451.3 | + | 59030.6i | 0.805624 | + | 1.94495i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 65807.1i | 2.16155i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1781.76i | 0.0583455i | 0.999574 | + | 0.0291727i | \(0.00928729\pi\) | ||||
−0.999574 | + | 0.0291727i | \(0.990713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 402.176 | + | 970.939i | 0.0131293 | + | 0.0316970i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13579.9 | + | 5624.96i | 0.441969 | + | 0.183069i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19228.0 | − | 19228.0i | 0.623883 | − | 0.623883i | −0.322639 | − | 0.946522i | \(-0.604570\pi\) |
0.946522 | + | 0.322639i | \(0.104570\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4873.92 | − | 4873.92i | −0.157661 | − | 0.157661i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21426.3 | − | 51727.7i | 0.690990 | − | 1.66820i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2486.09 | − | 1029.77i | 0.0799322 | − | 0.0331090i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2811.67 | −0.0901269 | −0.0450634 | − | 0.998984i | \(-0.514349\pi\) | ||||
−0.0450634 | + | 0.998984i | \(0.514349\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24851.4 | −0.794196 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18342.9 | + | 7597.88i | −0.584431 | + | 0.242079i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11942.0 | + | 28830.7i | −0.379347 | + | 0.915824i | 0.612742 | + | 0.790283i | \(0.290067\pi\) |
−0.992088 | + | 0.125541i | \(0.959933\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9068.01 | − | 9068.01i | −0.287186 | − | 0.287186i |
(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 | 256.4.g.a.97.3 | 44 | ||
4.3 | odd | 2 | 256.4.g.b.97.9 | 44 | |||
8.3 | odd | 2 | 32.4.g.a.21.2 | ✓ | 44 | ||
8.5 | even | 2 | 128.4.g.a.49.9 | 44 | |||
32.3 | odd | 8 | 256.4.g.b.161.9 | 44 | |||
32.13 | even | 8 | 128.4.g.a.81.9 | 44 | |||
32.19 | odd | 8 | 32.4.g.a.29.2 | yes | 44 | ||
32.29 | even | 8 | inner | 256.4.g.a.161.3 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.2 | ✓ | 44 | 8.3 | odd | 2 | ||
32.4.g.a.29.2 | yes | 44 | 32.19 | odd | 8 | ||
128.4.g.a.49.9 | 44 | 8.5 | even | 2 | |||
128.4.g.a.81.9 | 44 | 32.13 | even | 8 | |||
256.4.g.a.97.3 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.161.3 | 44 | 32.29 | even | 8 | inner | ||
256.4.g.b.97.9 | 44 | 4.3 | odd | 2 | |||
256.4.g.b.161.9 | 44 | 32.3 | odd | 8 |