Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.217 |
Dual form | 648.4.i.o.433.2 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.70820 | + | 9.88690i | 0.510557 | + | 0.884311i | 0.999925 | + | 0.0122337i | \(0.00389421\pi\) |
−0.489368 | + | 0.872077i | \(0.662772\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.9164 | − | 25.8360i | 0.805410 | − | 1.39501i | −0.110603 | − | 0.993865i | \(-0.535278\pi\) |
0.916014 | − | 0.401147i | \(-0.131388\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.1246 | + | 57.3735i | −0.907950 | + | 1.57261i | −0.0910416 | + | 0.995847i | \(0.529020\pi\) |
−0.816908 | + | 0.576768i | \(0.804314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.9164 | − | 34.4962i | −0.424909 | − | 0.735964i | 0.571503 | − | 0.820600i | \(-0.306361\pi\) |
−0.996412 | + | 0.0846360i | \(0.973027\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 107.416 | 1.53249 | 0.766244 | − | 0.642549i | \(-0.222123\pi\) | ||||
0.766244 | + | 0.642549i | \(0.222123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.3313 | 0.849216 | 0.424608 | − | 0.905377i | \(-0.360412\pi\) | ||||
0.424608 | + | 0.905377i | \(0.360412\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.45898 | − | 5.99113i | −0.0313586 | − | 0.0543146i | 0.849920 | − | 0.526911i | \(-0.176650\pi\) |
−0.881279 | + | 0.472597i | \(0.843317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.66718 | + | 4.61970i | −0.0213375 | + | 0.0369576i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −18.3344 | + | 31.7561i | −0.117400 | + | 0.203343i | −0.918737 | − | 0.394871i | \(-0.870789\pi\) |
0.801336 | + | 0.598214i | \(0.204123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 115.666 | + | 200.339i | 0.670134 | + | 1.16071i | 0.977866 | + | 0.209233i | \(0.0670968\pi\) |
−0.307732 | + | 0.951473i | \(0.599570\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 340.584 | 1.64483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.8359 | 0.163670 | 0.0818350 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818350 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −214.663 | − | 371.806i | −0.817674 | − | 1.41625i | −0.907391 | − | 0.420286i | \(-0.861930\pi\) |
0.0897170 | − | 0.995967i | \(-0.471404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37.1672 | − | 64.3755i | 0.131813 | − | 0.228306i | −0.792563 | − | 0.609790i | \(-0.791254\pi\) |
0.924375 | + | 0.381484i | \(0.124587\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26.2918 | + | 45.5387i | −0.0815969 | + | 0.141330i | −0.903936 | − | 0.427668i | \(-0.859335\pi\) |
0.822339 | + | 0.568998i | \(0.192669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −273.498 | − | 473.713i | −0.797372 | − | 1.38109i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 288.170 | 0.746853 | 0.373427 | − | 0.927660i | \(-0.378183\pi\) | ||||
0.373427 | + | 0.927660i | \(0.378183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −756.328 | −1.85424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 391.872 | + | 678.743i | 0.864702 | + | 1.49771i | 0.867343 | + | 0.497712i | \(0.165826\pi\) |
−0.00264051 | + | 0.999997i | \(0.500841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −219.579 | + | 380.322i | −0.460889 | + | 0.798282i | −0.999005 | − | 0.0445878i | \(-0.985803\pi\) |
0.538117 | + | 0.842870i | \(0.319136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 227.374 | − | 393.823i | 0.433881 | − | 0.751504i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.169 | + | 189.086i | 0.199061 | + | 0.344784i | 0.948224 | − | 0.317602i | \(-0.102877\pi\) |
−0.749163 | + | 0.662385i | \(0.769544\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 790.492 | 1.32133 | 0.660663 | − | 0.750682i | \(-0.270275\pi\) | ||||
0.660663 | + | 0.750682i | \(0.270275\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1098.00 | 1.76042 | 0.880211 | − | 0.474582i | \(-0.157401\pi\) | ||||
0.880211 | + | 0.474582i | \(0.157401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 988.200 | + | 1711.61i | 1.46254 | + | 2.53320i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −219.913 | + | 380.901i | −0.313192 | + | 0.542465i | −0.979052 | − | 0.203613i | \(-0.934732\pi\) |
0.665859 | + | 0.746077i | \(0.268065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 25.4226 | − | 44.0333i | 0.0336204 | − | 0.0582323i | −0.848726 | − | 0.528833i | \(-0.822630\pi\) |
0.882346 | + | 0.470601i | \(0.155963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 613.155 | + | 1062.02i | 0.782423 | + | 1.35520i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 719.745 | 0.857222 | 0.428611 | − | 0.903489i | \(-0.359003\pi\) | ||||
0.428611 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1188.33 | −1.36890 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 401.465 | + | 695.358i | 0.433573 | + | 0.750971i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 599.822 | − | 1038.92i | 0.627863 | − | 1.08749i | −0.360117 | − | 0.932907i | \(-0.617263\pi\) |
0.987980 | − | 0.154583i | \(-0.0494034\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −122.991 | + | 213.026i | −0.121169 | + | 0.209870i | −0.920229 | − | 0.391381i | \(-0.871998\pi\) |
0.799060 | + | 0.601251i | \(0.205331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −287.910 | − | 498.675i | −0.275424 | − | 0.477048i | 0.694818 | − | 0.719185i | \(-0.255485\pi\) |
−0.970242 | + | 0.242138i | \(0.922151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1015.89 | −0.917849 | −0.458924 | − | 0.888475i | \(-0.651765\pi\) | ||||
−0.458924 | + | 0.888475i | \(0.651765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1471.64 | 1.29319 | 0.646595 | − | 0.762834i | \(-0.276193\pi\) | ||||
0.646595 | + | 0.762834i | \(0.276193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 951.787 | + | 1648.54i | 0.792359 | + | 1.37241i | 0.924503 | + | 0.381176i | \(0.124481\pi\) |
−0.132143 | + | 0.991231i | \(0.542186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39.4891 | − | 68.3972i | 0.0320207 | − | 0.0554615i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1602.27 | − | 2775.21i | 1.23428 | − | 2.13784i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1528.98 | − | 2648.27i | −1.14875 | − | 1.98968i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1366.15 | 0.977539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 230.310 | 0.160919 | 0.0804593 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804593 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −397.155 | − | 687.892i | −0.264882 | − | 0.458789i | 0.702651 | − | 0.711535i | \(-0.252000\pi\) |
−0.967533 | + | 0.252746i | \(0.918666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1049.09 | − | 1817.08i | 0.683967 | − | 1.18467i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 341.538 | − | 591.561i | 0.212989 | − | 0.368909i | −0.739659 | − | 0.672982i | \(-0.765013\pi\) |
0.952649 | + | 0.304073i | \(0.0983467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 756.320 | + | 1309.99i | 0.461513 | + | 0.799363i | 0.999037 | − | 0.0438851i | \(-0.0139736\pi\) |
−0.537524 | + | 0.843248i | \(0.680640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2638.89 | 1.54318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −418.625 | −0.239758 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1153.57 | − | 1998.04i | −0.634255 | − | 1.09856i | −0.986672 | − | 0.162719i | \(-0.947974\pi\) |
0.352418 | − | 0.935843i | \(-0.385360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1261.59 | + | 2185.13i | −0.679910 | + | 1.17764i | 0.295098 | + | 0.955467i | \(0.404648\pi\) |
−0.975008 | + | 0.222171i | \(0.928686\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1320.49 | + | 2287.15i | −0.684284 | + | 1.18521i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1459.49 | + | 2527.91i | 0.741912 | + | 1.28503i | 0.951624 | + | 0.307266i | \(0.0994141\pi\) |
−0.209712 | + | 0.977763i | \(0.567253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −206.382 | −0.101026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1096.99 | 0.527133 | 0.263567 | − | 0.964641i | \(-0.415101\pi\) | ||||
0.263567 | + | 0.964641i | \(0.415101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 366.365 | + | 634.562i | 0.169761 | + | 0.294035i | 0.938336 | − | 0.345725i | \(-0.112367\pi\) |
−0.768575 | + | 0.639760i | \(0.779034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 305.173 | − | 528.576i | 0.138905 | − | 0.240590i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −361.337 | + | 625.855i | −0.158798 | + | 0.275045i | −0.934435 | − | 0.356133i | \(-0.884095\pi\) |
0.775638 | + | 0.631178i | \(0.217428\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 79.5696 | + | 137.819i | 0.0343708 | + | 0.0595320i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1010.16 | 0.421806 | 0.210903 | − | 0.977507i | \(-0.432360\pi\) | ||||
0.210903 | + | 0.977507i | \(0.432360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4256.79 | −1.74809 | −0.874045 | − | 0.485844i | \(-0.838512\pi\) | ||||
−0.874045 | + | 0.485844i | \(0.838512\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 210.267 | + | 364.193i | 0.0835629 | + | 0.144735i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3558.13 | + | 6162.86i | −1.39142 | + | 2.41001i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1714.69 | + | 2969.93i | −0.649585 | + | 1.12511i | 0.333637 | + | 0.942702i | \(0.391724\pi\) |
−0.983222 | + | 0.182413i | \(0.941609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −483.670 | − | 837.742i | −0.180390 | − | 0.312445i | 0.761623 | − | 0.648020i | \(-0.224403\pi\) |
−0.942014 | + | 0.335575i | \(0.891069\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −468.413 | −0.169406 | −0.0847032 | − | 0.996406i | \(-0.526994\pi\) | ||||
−0.0847032 | + | 0.996406i | \(0.526994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2673.47 | −0.952347 | −0.476174 | − | 0.879351i | \(-0.657977\pi\) | ||||
−0.476174 | + | 0.879351i | \(0.657977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 546.966 | + | 947.373i | 0.189111 | + | 0.327549i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2450.67 | − | 4244.69i | 0.834939 | − | 1.44616i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2329.70 | + | 4035.15i | −0.771045 | + | 1.33549i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1435.31 | − | 2486.03i | −0.468297 | − | 0.811114i | 0.531046 | − | 0.847343i | \(-0.321799\pi\) |
−0.999344 | + | 0.0362284i | \(0.988466\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 848.631 | 0.269192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6901.26 | 2.15893 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2139.35 | − | 3705.46i | −0.651168 | − | 1.12786i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 623.300 | − | 1079.59i | 0.187172 | − | 0.324191i | −0.757135 | − | 0.653259i | \(-0.773401\pi\) |
0.944306 | + | 0.329068i | \(0.106735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −280.231 | + | 485.374i | −0.0819364 | + | 0.141918i | −0.904082 | − | 0.427360i | \(-0.859444\pi\) |
0.822145 | + | 0.569278i | \(0.192777\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 572.690 | + | 991.929i | 0.165260 | + | 0.286238i | 0.936747 | − | 0.350006i | \(-0.113820\pi\) |
−0.771488 | + | 0.636244i | \(0.780487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −623.709 | −0.175367 | −0.0876836 | − | 0.996148i | \(-0.527946\pi\) | ||||
−0.0876836 | + | 0.996148i | \(0.527946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −600.316 | −0.166639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3132.90 | − | 5426.34i | −0.847910 | − | 1.46862i | −0.883070 | − | 0.469241i | \(-0.844528\pi\) |
0.0351605 | − | 0.999382i | \(-0.488806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 320.327 | − | 554.822i | 0.0856185 | − | 0.148296i | −0.820036 | − | 0.572312i | \(-0.806047\pi\) |
0.905655 | + | 0.424016i | \(0.139380\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3122.37 | − | 5408.10i | 0.814208 | − | 1.41025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1400.75 | − | 2426.16i | −0.360839 | − | 0.624992i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7748.91 | −1.94863 | −0.974316 | − | 0.225183i | \(-0.927702\pi\) | ||||
−0.974316 | + | 0.225183i | \(0.927702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 458.310 | 0.113888 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1595.88 | − | 2764.14i | −0.387347 | − | 0.670904i | 0.604745 | − | 0.796419i | \(-0.293275\pi\) |
−0.992092 | + | 0.125515i | \(0.959942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 549.460 | − | 951.692i | 0.131821 | − | 0.228321i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1888.21 | − | 3270.47i | 0.442706 | − | 0.766790i | −0.555183 | − | 0.831728i | \(-0.687352\pi\) |
0.997889 | + | 0.0649384i | \(0.0206851\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1644.93 | + | 2849.11i | 0.381311 | + | 0.660451i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4065.91 | −0.921572 | −0.460786 | − | 0.887511i | \(-0.652432\pi\) | ||||
−0.460786 | + | 0.887511i | \(0.652432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5508.17 | −1.23468 | −0.617339 | − | 0.786697i | \(-0.711789\pi\) | ||||
−0.617339 | + | 0.786697i | \(0.711789\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −176.699 | − | 306.051i | −0.0387467 | − | 0.0671113i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4153.45 | − | 7194.00i | 0.900928 | − | 1.56045i | 0.0746351 | − | 0.997211i | \(-0.476221\pi\) |
0.826292 | − | 0.563241i | \(-0.190446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1481.34 | − | 2565.75i | 0.314481 | − | 0.544697i | −0.664846 | − | 0.746980i | \(-0.731503\pi\) |
0.979327 | + | 0.202283i | \(0.0648362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2254.83 | + | 3905.48i | 0.473625 | + | 0.820343i | 0.999544 | − | 0.0301919i | \(-0.00961185\pi\) |
−0.525919 | + | 0.850535i | \(0.676279\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12808.0 | −2.63425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6625.28 | 1.34852 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −907.228 | − | 1571.37i | −0.180890 | − | 0.313311i | 0.761294 | − | 0.648407i | \(-0.224565\pi\) |
−0.942184 | + | 0.335096i | \(0.891231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4473.77 | + | 7748.80i | −0.882960 | + | 1.52933i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −137.781 | + | 238.644i | −0.0266491 | + | 0.0461576i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1108.80 | − | 1920.50i | −0.212326 | − | 0.367760i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5013.61 | −0.941240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4395.62 | 0.817171 | 0.408585 | − | 0.912720i | \(-0.366022\pi\) | ||||
0.408585 | + | 0.912720i | \(0.366022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 688.614 | + | 1192.71i | 0.125555 | + | 0.217468i | 0.921950 | − | 0.387309i | \(-0.126595\pi\) |
−0.796395 | + | 0.604777i | \(0.793262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3673.97 | + | 6363.51i | −0.663467 | + | 1.14916i | 0.316231 | + | 0.948682i | \(0.397582\pi\) |
−0.979698 | + | 0.200477i | \(0.935751\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1303.89 | + | 2258.40i | −0.231021 | + | 0.400141i | −0.958109 | − | 0.286404i | \(-0.907540\pi\) |
0.727088 | + | 0.686545i | \(0.240873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1214.64 | − | 2103.81i | −0.213187 | − | 0.369251i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7554.73 | 1.30141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 212.483 | 0.0362659 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 784.358 | + | 1358.55i | 0.131438 | + | 0.227657i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3270.67 | − | 5664.96i | 0.543118 | − | 0.940708i | −0.455605 | − | 0.890182i | \(-0.650577\pi\) |
0.998723 | − | 0.0505260i | \(-0.0160898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1246.31 | + | 2158.68i | −0.203264 | + | 0.352064i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2157.83 | − | 3737.47i | −0.348797 | − | 0.604134i | 0.637239 | − | 0.770666i | \(-0.280076\pi\) |
−0.986036 | + | 0.166532i | \(0.946743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15325.5 | −2.43379 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6085.80 | −0.958025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1947.88 | − | 3373.82i | −0.301347 | − | 0.521949i | 0.675094 | − | 0.737732i | \(-0.264103\pi\) |
−0.976441 | + | 0.215783i | \(0.930770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2438.71 | − | 4223.97i | 0.374044 | − | 0.647863i | −0.616140 | − | 0.787637i | \(-0.711304\pi\) |
0.990183 | + | 0.139774i | \(0.0446377\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −869.896 | + | 1506.70i | −0.131161 | + | 0.227178i | −0.924124 | − | 0.382092i | \(-0.875204\pi\) |
0.792963 | + | 0.609269i | \(0.208537\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4512.29 | + | 7815.52i | 0.674613 | + | 1.16846i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 188.828 | 0.0277604 | 0.0138802 | − | 0.999904i | \(-0.495582\pi\) | ||||
0.0138802 | + | 0.999904i | \(0.495582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1912.51 | −0.278833 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6267.59 | + | 10855.8i | 0.898796 | + | 1.55676i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3169.07 | − | 5489.00i | 0.450747 | − | 0.780718i | −0.547685 | − | 0.836685i | \(-0.684491\pi\) |
0.998433 | + | 0.0559670i | \(0.0178242\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4298.47 | − | 7445.16i | 0.601523 | − | 1.04187i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4320.70 | − | 7483.68i | −0.599779 | − | 1.03885i | −0.992853 | − | 0.119341i | \(-0.961922\pi\) |
0.393075 | − | 0.919507i | \(-0.371411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1460.62 | 0.199538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4143.88 | −0.561627 | −0.280814 | − | 0.959762i | \(-0.590604\pi\) | ||||
−0.280814 | + | 0.959762i | \(0.590604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2096.97 | + | 3632.06i | 0.279766 | + | 0.484568i | 0.971326 | − | 0.237750i | \(-0.0764099\pi\) |
−0.691561 | + | 0.722318i | \(0.743077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11281.7 | + | 19540.5i | −1.49343 | + | 2.58669i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5435.21 | + | 9414.07i | −0.708422 | + | 1.22702i | 0.257020 | + | 0.966406i | \(0.417259\pi\) |
−0.965442 | + | 0.260617i | \(0.916074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −371.551 | − | 643.546i | −0.0480567 | − | 0.0832366i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5021.24 | −0.639610 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8890.87 | −1.12398 | −0.561990 | − | 0.827144i | \(-0.689964\pi\) | ||||
−0.561990 | + | 0.827144i | \(0.689964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7547.71 | − | 13073.0i | −0.939936 | − | 1.62802i | −0.765586 | − | 0.643334i | \(-0.777551\pi\) |
−0.174351 | − | 0.984684i | \(-0.555783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4607.29 | − | 7980.06i | 0.569492 | − | 0.986389i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1220.18 | + | 2113.41i | −0.148604 | + | 0.257390i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −809.169 | − | 1401.52i | −0.0978260 | − | 0.169440i | 0.812959 | − | 0.582322i | \(-0.197856\pi\) |
−0.910785 | + | 0.412882i | \(0.864522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23381.3 | 2.78576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 580.470 | 0.0686606 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5005.94 | − | 8670.54i | −0.583666 | − | 1.01094i | −0.995040 | − | 0.0994728i | \(-0.968284\pi\) |
0.411374 | − | 0.911467i | \(-0.365049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3617.22 | + | 6265.20i | −0.418747 | + | 0.725291i | −0.995814 | − | 0.0914063i | \(-0.970864\pi\) |
0.577067 | + | 0.816697i | \(0.304197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −286.499 | + | 496.231i | −0.0326994 | + | 0.0566371i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6550.66 | + | 11346.1i | 0.742409 | + | 1.28589i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5379.03 | 0.601157 | 0.300579 | − | 0.953757i | \(-0.402820\pi\) | ||||
0.300579 | + | 0.953757i | \(0.402820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1602.96 | −0.177906 | −0.0889530 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889530 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −243.274 | − | 421.364i | −0.0266302 | − | 0.0461249i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3362.93 | + | 5824.77i | −0.365613 | + | 0.633260i | −0.988874 | − | 0.148753i | \(-0.952474\pi\) |
0.623261 | + | 0.782014i | \(0.285807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −584.961 | + | 1013.18i | −0.0627367 | + | 0.108663i | −0.895688 | − | 0.444683i | \(-0.853316\pi\) |
0.832951 | + | 0.553347i | \(0.186650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4108.45 | + | 7116.04i | 0.437661 | + | 0.758051i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2996.56 | −0.314958 | −0.157479 | − | 0.987522i | \(-0.550337\pi\) | ||||
−0.157479 | + | 0.987522i | \(0.550337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28442.5 | 2.96963 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6783.20 | − | 11748.9i | −0.698904 | − | 1.21054i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5576.04 | − | 9657.98i | 0.570757 | − | 0.988580i | −0.425731 | − | 0.904850i | \(-0.639983\pi\) |
0.996488 | − | 0.0837307i | \(-0.0266835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1473.59 | − | 2552.33i | 0.148876 | − | 0.257860i | −0.781936 | − | 0.623358i | \(-0.785768\pi\) |
0.930812 | + | 0.365498i | \(0.119101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3281.69 | − | 5684.05i | −0.329402 | − | 0.570541i | 0.652991 | − | 0.757365i | \(-0.273514\pi\) |
−0.982393 | + | 0.186824i | \(0.940180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2727.33 | −0.270248 | −0.135124 | − | 0.990829i | \(-0.543143\pi\) | ||||
−0.135124 | + | 0.990829i | \(0.543143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6513.62 | 0.641303 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2462.30 | + | 4264.82i | 0.239358 | + | 0.414581i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −187.586 | + | 324.909i | −0.0181201 | + | 0.0313850i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7256.06 | + | 12567.9i | −0.692146 | + | 1.19883i | 0.278988 | + | 0.960295i | \(0.410001\pi\) |
−0.971133 | + | 0.238537i | \(0.923332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −733.639 | − | 1270.70i | −0.0695448 | − | 0.120455i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13695.6 | 1.28224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14189.9 | −1.32034 | −0.660170 | − | 0.751116i | \(-0.729516\pi\) | ||||
−0.660170 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3607.96 | + | 6249.17i | 0.331619 | + | 0.574381i | 0.982829 | − | 0.184516i | \(-0.0590719\pi\) |
−0.651211 | + | 0.758897i | \(0.725739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1969.41 | + | 3411.12i | −0.179915 | + | 0.311621i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11791.3 | − | 20423.1i | 1.06421 | − | 1.84327i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6516.28 | − | 11286.5i | −0.584587 | − | 1.01253i | −0.994927 | − | 0.100601i | \(-0.967923\pi\) |
0.410340 | − | 0.911932i | \(-0.365410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9502.84 | 0.842367 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2808.22 | −0.247454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1897.15 | − | 3285.96i | −0.165206 | − | 0.286145i | 0.771523 | − | 0.636202i | \(-0.219495\pi\) |
−0.936728 | + | 0.350057i | \(0.886162\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16378.2 | − | 28367.8i | 1.41786 | − | 2.45581i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3286.90 | − | 5693.08i | 0.281239 | − | 0.487120i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1741.81 | − | 3016.91i | −0.148172 | − | 0.256641i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14811.2 | 1.24547 | 0.622735 | − | 0.782432i | \(-0.286021\pi\) | ||||
0.622735 | + | 0.782432i | \(0.286021\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −345.532 | −0.0288892 | −0.0144446 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144446 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12424.4 | + | 21519.7i | 1.02697 | + | 1.77877i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6059.57 | − | 10495.5i | 0.498033 | − | 0.862619i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8550.61 | + | 14810.1i | −0.694875 | + | 1.20356i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5798.91 | − | 10044.0i | −0.468614 | − | 0.811664i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36238.1 | 2.89589 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5474.45 | −0.435056 | −0.217528 | − | 0.976054i | \(-0.569799\pi\) | ||||
−0.217528 | + | 0.976054i | \(0.569799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8400.43 | + | 14550.0i | 0.660247 | + | 1.14358i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −488.639 | + | 846.348i | −0.0381951 | + | 0.0661558i | −0.884491 | − | 0.466557i | \(-0.845494\pi\) |
0.846296 | + | 0.532713i | \(0.178827\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1289.48 | + | 2233.44i | −0.0996981 | + | 0.172682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6560.63 | + | 11363.3i | 0.504496 | + | 0.873813i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18833.3 | −1.43266 | −0.716330 | − | 0.697762i | \(-0.754179\pi\) | ||||
−0.716330 | + | 0.697762i | \(0.754179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2960.95 | −0.224033 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10483.5 | + | 18158.0i | 0.784772 | + | 1.35927i | 0.929135 | + | 0.369741i | \(0.120553\pi\) |
−0.144363 | + | 0.989525i | \(0.546113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10866.0 | + | 18820.4i | −0.809090 | + | 1.40138i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6744.33 | + | 11681.5i | −0.496902 | + | 0.860659i | −0.999994 | − | 0.00357372i | \(-0.998862\pi\) |
0.503092 | + | 0.864233i | \(0.332196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1124.45 | + | 1947.60i | 0.0824110 | + | 0.142740i | 0.904285 | − | 0.426929i | \(-0.140405\pi\) |
−0.821874 | + | 0.569669i | \(0.807071\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.9030 | 0.00267645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1968.87 | −0.142054 | −0.0710270 | − | 0.997474i | \(-0.522628\pi\) | ||||
−0.0710270 | + | 0.997474i | \(0.522628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −758.428 | − | 1313.64i | −0.0541565 | − | 0.0938018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9545.53 | + | 16533.3i | −0.678105 | + | 1.17451i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2053.83 | + | 3557.34i | −0.144413 | + | 0.250131i | −0.929154 | − | 0.369693i | \(-0.879463\pi\) |
0.784741 | + | 0.619824i | \(0.212796\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8134.91 | + | 14090.1i | 0.569088 | + | 0.985690i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7497.21 | −0.519180 | −0.259590 | − | 0.965719i | \(-0.583587\pi\) | ||||
−0.259590 | + | 0.965719i | \(0.583587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36584.3 | 2.52069 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13553.6 | + | 23475.4i | 0.924513 | + | 1.60130i | 0.792343 | + | 0.610076i | \(0.208861\pi\) |
0.132170 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3401.08 | + | 5890.85i | −0.230837 | + | 0.399822i | −0.958055 | − | 0.286585i | \(-0.907480\pi\) |
0.727218 | + | 0.686407i | \(0.240813\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17455.5 | − | 30233.7i | 1.17300 | − | 2.03170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8496.22 | − | 14715.9i | −0.568123 | − | 0.984019i | −0.996752 | − | 0.0805376i | \(-0.974336\pi\) |
0.428628 | − | 0.903481i | \(-0.358997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2094.55 | 0.138685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13766.6 | −0.907062 | −0.453531 | − | 0.891241i | \(-0.649836\pi\) | ||||
−0.453531 | + | 0.891241i | \(0.649836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8678.00 | + | 15030.7i | 0.566229 | + | 0.980737i | 0.996934 | + | 0.0782443i | \(0.0249314\pi\) |
−0.430706 | + | 0.902493i | \(0.641735\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1462.45 | + | 2533.03i | −0.0949608 | + | 0.164477i | −0.909592 | − | 0.415502i | \(-0.863606\pi\) |
0.814631 | + | 0.579979i | \(0.196939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10736.0 | − | 18595.3i | 0.690416 | − | 1.19583i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8131.67 | + | 14084.5i | 0.520427 | + | 0.901406i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3956.78 | 0.250822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6158.40 | 0.388530 | 0.194265 | − | 0.980949i | \(-0.437768\pi\) | ||||
0.194265 | + | 0.980949i | \(0.437768\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1314.65 | + | 2277.05i | 0.0821582 | + | 0.142302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10894.2 | + | 18869.3i | −0.677621 | + | 1.17367i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5907.12 | + | 10231.4i | −0.363990 | + | 0.630448i | −0.988613 | − | 0.150477i | \(-0.951919\pi\) |
0.624624 | + | 0.780926i | \(0.285252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8457.37 | + | 14648.6i | 0.518703 | + | 0.898420i | 0.999764 | + | 0.0217330i | \(0.00691836\pi\) |
−0.481061 | + | 0.876687i | \(0.659748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28652.4 | −1.74103 | −0.870513 | − | 0.492145i | \(-0.836213\pi\) | ||||
−0.870513 | + | 0.492145i | \(0.836213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51922.5 | −3.14042 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2749.24 | + | 4761.82i | 0.164757 | + | 0.285367i | 0.936569 | − | 0.350484i | \(-0.113983\pi\) |
−0.771812 | + | 0.635851i | \(0.780649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4534.08 | − | 7853.26i | 0.270475 | − | 0.468477i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9392.57 | − | 16268.4i | 0.555209 | − | 0.961650i | −0.442679 | − | 0.896680i | \(-0.645972\pi\) |
0.997887 | − | 0.0649692i | \(-0.0206949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8652.23 | + | 14986.1i | 0.509127 | + | 0.881834i | 0.999944 | + | 0.0105712i | \(0.00336497\pi\) |
−0.490817 | + | 0.871263i | \(0.663302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23953.7 | 1.39682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 253.673 | 0.0147260 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14546.9 | − | 25196.0i | −0.836927 | − | 1.44960i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6855.73 | − | 11874.5i | 0.392673 | − | 0.680129i | −0.600128 | − | 0.799904i | \(-0.704884\pi\) |
0.992801 | + | 0.119774i | \(0.0382172\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15283.4 | − | 26471.7i | 0.867637 | − | 1.50279i | 0.00323298 | − | 0.999995i | \(-0.498971\pi\) |
0.864404 | − | 0.502797i | \(-0.167696\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17894.4 | − | 30994.0i | −1.01137 | − | 1.75175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4445.72 | 0.249064 | 0.124532 | − | 0.992216i | \(-0.460257\pi\) | ||||
0.124532 | + | 0.992216i | \(0.460257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7798.27 | 0.434973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5739.32 | − | 9940.79i | −0.317345 | − | 0.549657i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6099.36 | − | 10564.4i | 0.335790 | − | 0.581605i | −0.647846 | − | 0.761771i | \(-0.724330\pi\) |
0.983636 | + | 0.180166i | \(0.0576635\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8634.46 | + | 14955.3i | −0.471257 | + | 0.816242i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23058.3 | − | 39938.1i | −1.25308 | − | 2.17039i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21613.4 | 1.16452 | 0.582258 | − | 0.813004i | \(-0.302169\pi\) | ||||
0.582258 | + | 0.813004i | \(0.302169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2590.72 | 0.138991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3669.16 | + | 6355.17i | 0.195181 | + | 0.338063i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2462.43 | − | 4265.05i | 0.130435 | − | 0.225920i | −0.793409 | − | 0.608688i | \(-0.791696\pi\) |
0.923844 | + | 0.382768i | \(0.125029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 800.170 | − | 1385.94i | 0.0420289 | − | 0.0727962i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15063.3 | + | 26090.5i | 0.787884 | + | 1.36465i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −205.354 | −0.0106515 | −0.00532573 | − | 0.999986i | \(-0.501695\pi\) | ||||
−0.00532573 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17178.3 | −0.887316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −97.8023 | − | 169.399i | −0.00501005 | − | 0.00867766i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7898.02 | + | 13679.8i | −0.402918 | + | 0.697875i | −0.994077 | − | 0.108681i | \(-0.965337\pi\) |
0.591159 | + | 0.806555i | \(0.298671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3992.37 | − | 6914.98i | 0.202001 | − | 0.349877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16062.7 | − | 27821.4i | −0.809398 | − | 1.40192i | −0.913282 | − | 0.407328i | \(-0.866460\pi\) |
0.103884 | − | 0.994589i | \(-0.466873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14464.7 | −0.722949 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28938.9 | 1.44051 | 0.720255 | − | 0.693710i | \(-0.244025\pi\) | ||||
0.720255 | + | 0.693710i | \(0.244025\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18054.2 | − | 31270.8i | −0.891447 | − | 1.54403i | −0.838141 | − | 0.545454i | \(-0.816357\pi\) |
−0.0533063 | − | 0.998578i | \(-0.516976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13169.6 | − | 22810.4i | 0.647647 | − | 1.12176i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15153.4 | + | 26246.5i | −0.739245 | + | 1.28041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11615.8 | + | 20119.2i | 0.564405 | + | 0.977578i | 0.997105 | + | 0.0760399i | \(0.0242277\pi\) |
−0.432700 | + | 0.901538i | \(0.642439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28805.5 | −1.38853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22762.6 | 1.09289 | 0.546447 | − | 0.837494i | \(-0.315980\pi\) | ||||
0.546447 | + | 0.837494i | \(0.315980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20259.3 | + | 35090.1i | 0.965044 | + | 1.67150i | 0.709497 | + | 0.704708i | \(0.248922\pi\) |
0.255547 | + | 0.966797i | \(0.417745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21951.6 | − | 38021.3i | 1.04155 | − | 1.80401i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15609.4 | − | 27036.2i | 0.734840 | − | 1.27278i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13700.6 | + | 23730.1i | 0.642464 | + | 1.11278i | 0.984881 | + | 0.173232i | \(0.0554212\pi\) |
−0.342417 | + | 0.939548i | \(0.611246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35698.4 | −1.66104 | −0.830520 | − | 0.556989i | \(-0.811957\pi\) | ||||
−0.830520 | + | 0.556989i | \(0.811957\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1234.01 | −0.0571959 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15097.5 | − | 26149.6i | −0.694382 | − | 1.20270i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26184.7 | + | 45353.3i | −1.19970 | + | 2.07794i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16662.2 | + | 28859.7i | −0.757577 | + | 1.31216i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4783.18 | + | 8284.71i | 0.216648 | + | 0.375245i | 0.953781 | − | 0.300502i | \(-0.0971543\pi\) |
−0.737133 | + | 0.675748i | \(0.763821\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56789.0 | 2.55270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17492.9 | 0.783343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2653.01 | + | 4595.14i | 0.117910 | + | 0.204226i | 0.918939 | − | 0.394399i | \(-0.129047\pi\) |
−0.801029 | + | 0.598625i | \(0.795714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2824.17 | + | 4891.61i | −0.125046 | + | 0.216586i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36370.7 | + | 62995.9i | −1.59837 | + | 2.76847i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1178.07 | − | 2040.48i | −0.0515796 | − | 0.0893385i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9362.75 | 0.406893 | 0.203447 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203447 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32610.2 | 1.41196 | 0.705981 | − | 0.708231i | \(-0.250507\pi\) | ||||
0.705981 | + | 0.708231i | \(0.250507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6261.83 | + | 10845.8i | 0.269132 | + | 0.466150i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2614.02 | − | 4527.61i | 0.111937 | − | 0.193881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9465.34 | + | 16394.5i | −0.402366 | + | 0.696919i | −0.994011 | − | 0.109280i | \(-0.965145\pi\) |
0.591645 | + | 0.806199i | \(0.298479\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20336.6 | − | 35224.0i | −0.861346 | − | 1.49190i | −0.870630 | − | 0.491938i | \(-0.836288\pi\) |
0.00928379 | − | 0.999957i | \(-0.497045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30770.2 | −1.29382 | −0.646908 | − | 0.762568i | \(-0.723938\pi\) | ||||
−0.646908 | + | 0.762568i | \(0.723938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10464.9 | 0.438434 | 0.219217 | − | 0.975676i | \(-0.429650\pi\) | ||||
0.219217 | + | 0.975676i | \(0.429650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29378.2 | − | 50884.6i | −1.22196 | − | 2.11650i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4182.57 | + | 7244.42i | −0.173346 | + | 0.300244i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11358.2 | + | 19673.0i | −0.467376 | + | 0.809519i | −0.999305 | − | 0.0372701i | \(-0.988134\pi\) |
0.531929 | + | 0.846789i | \(0.321467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11522.2 | + | 19957.0i | 0.472434 | + | 0.818280i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6967.97 | 0.283675 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −91227.5 | −3.70084 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −127.415 | − | 220.689i | −0.00513246 | − | 0.00888968i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5090.58 | − | 8817.14i | 0.204335 | − | 0.353919i | −0.745585 | − | 0.666410i | \(-0.767830\pi\) |
0.949921 | + | 0.312491i | \(0.101163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1942.80 | + | 3365.02i | −0.0774384 | + | 0.134127i | −0.902144 | − | 0.431435i | \(-0.858007\pi\) |
0.824706 | + | 0.565562i | \(0.191341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8867.47 | + | 15358.9i | 0.352217 | + | 0.610057i | 0.986638 | − | 0.162931i | \(-0.0520947\pi\) |
−0.634421 | + | 0.772988i | \(0.718761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19658.7 | 0.775421 | 0.387711 | − | 0.921781i | \(-0.373266\pi\) | ||||
0.387711 | + | 0.921781i | \(0.373266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8250.35 | −0.324301 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14569.1 | − | 25234.4i | −0.568725 | − | 0.985061i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4348.50 | − | 7531.82i | 0.169166 | − | 0.293003i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20378.1 | − | 35295.9i | 0.787320 | − | 1.36368i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2793.41 | − | 4838.33i | −0.107556 | − | 0.186293i | 0.807224 | − | 0.590246i | \(-0.200969\pi\) |
−0.914780 | + | 0.403953i | \(0.867636\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8050.03 | −0.307846 | −0.153923 | − | 0.988083i | \(-0.549191\pi\) | ||||
−0.153923 | + | 0.988083i | \(0.549191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2326.88 | −0.0886815 | −0.0443408 | − | 0.999016i | \(-0.514119\pi\) | ||||
−0.0443408 | + | 0.999016i | \(0.514119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9671.74 | + | 16751.9i | 0.366116 | + | 0.634132i | 0.988955 | − | 0.148218i | \(-0.0473539\pi\) |
−0.622838 | + | 0.782351i | \(0.714021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3435.39 | − | 5950.27i | 0.129606 | − | 0.224483i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1849.14 | + | 3202.80i | −0.0692933 | + | 0.120020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5766.22 | + | 9987.39i | 0.215356 | + | 0.373007i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8482.63 | −0.314696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30954.2 | 1.14454 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24298.6 | − | 42086.4i | −0.892500 | − | 1.54586i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 149.658 | − | 259.216i | 0.00547886 | − | 0.00948966i | −0.863273 | − | 0.504737i | \(-0.831589\pi\) |
0.868752 | + | 0.495248i | \(0.164923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10511.2 | − | 18206.0i | 0.382275 | − | 0.662121i | −0.609112 | − | 0.793084i | \(-0.708474\pi\) |
0.991387 | + | 0.130964i | \(0.0418072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1684.23 | + | 2917.17i | 0.0610513 | + | 0.105744i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23696.5 | −0.853356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18375.8 | −0.659587 | −0.329794 | − | 0.944053i | \(-0.606979\pi\) | ||||
−0.329794 | + | 0.944053i | \(0.606979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15743.8 | − | 27269.0i | −0.561444 | − | 0.972449i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −98.2482 | + | 170.171i | −0.00349230 | + | 0.00604885i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14774.0 | − | 25589.3i | 0.521764 | − | 0.903722i | −0.477915 | − | 0.878406i | \(-0.658607\pi\) |
0.999679 | − | 0.0253160i | \(-0.00805921\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19235.5 | − | 33316.8i | −0.677140 | − | 1.17284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −81242.1 | −2.84160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36751.2 | 1.28133 | 0.640667 | − | 0.767819i | \(-0.278658\pi\) | ||||
0.640667 | + | 0.767819i | \(0.278658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13012.4 | − | 22538.1i | −0.450788 | − | 0.780787i | 0.547648 | − | 0.836709i | \(-0.315523\pi\) |
−0.998435 | + | 0.0559222i | \(0.982190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1485.03 | + | 2572.14i | −0.0512822 | + | 0.0888234i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20119.3 | + | 34847.6i | −0.690379 | + | 1.19577i | 0.281335 | + | 0.959610i | \(0.409223\pi\) |
−0.971714 | + | 0.236162i | \(0.924110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21868.2 | − | 37876.8i | −0.748019 | − | 1.29561i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52396.4 | −1.78099 | −0.890496 | − | 0.454991i | \(-0.849643\pi\) | ||||
−0.890496 | + | 0.454991i | \(0.849643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39151.3 | −1.32660 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10189.0 | − | 17647.9i | −0.343088 | − | 0.594245i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11861.6 | + | 20544.9i | −0.398160 | + | 0.689633i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5521.78 | − | 9564.00i | 0.184199 | − | 0.319043i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4503.51 | + | 7800.31i | 0.149765 | + | 0.259401i | 0.931141 | − | 0.364660i | \(-0.118815\pi\) |
−0.781375 | + | 0.624061i | \(0.785481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1110.63 | −0.0367062 | −0.0183531 | − | 0.999832i | \(-0.505842\pi\) | ||||
−0.0183531 | + | 0.999832i | \(0.505842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45126.3 | 1.48683 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13772.2 | + | 23854.1i | 0.450984 | + | 0.781128i | 0.998447 | − | 0.0557021i | \(-0.0177397\pi\) |
−0.547463 | + | 0.836830i | \(0.684406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23841.3 | + | 41294.3i | −0.778315 | + | 1.34808i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4328.74 | − | 7497.59i | 0.140453 | − | 0.243272i | −0.787214 | − | 0.616680i | \(-0.788477\pi\) |
0.927667 | + | 0.373408i | \(0.121811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2673.80 | − | 4631.16i | −0.0864917 | − | 0.149808i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −514.242 | −0.0165338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54045.9 | −1.73242 | −0.866208 | − | 0.499683i | \(-0.833450\pi\) | ||||
−0.866208 | + | 0.499683i | \(0.833450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15260.7 | − | 26432.3i | −0.486228 | − | 0.842171i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16295.5 | − | 28224.7i | 0.517638 | − | 0.896575i | −0.482152 | − | 0.876087i | \(-0.660145\pi\) |
0.999790 | − | 0.0204877i | \(-0.00652189\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.4.i.o.217.2 | 4 | ||
3.2 | odd | 2 | 648.4.i.r.217.1 | 4 | |||
9.2 | odd | 6 | 216.4.a.f.1.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 648.4.i.o.433.2 | 4 | ||
9.5 | odd | 6 | 648.4.i.r.433.1 | 4 | |||
9.7 | even | 3 | 216.4.a.g.1.1 | yes | 2 | ||
36.7 | odd | 6 | 432.4.a.r.1.1 | 2 | |||
36.11 | even | 6 | 432.4.a.p.1.2 | 2 | |||
72.11 | even | 6 | 1728.4.a.br.1.1 | 2 | |||
72.29 | odd | 6 | 1728.4.a.bq.1.1 | 2 | |||
72.43 | odd | 6 | 1728.4.a.bj.1.2 | 2 | |||
72.61 | even | 6 | 1728.4.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.f.1.2 | ✓ | 2 | 9.2 | odd | 6 | ||
216.4.a.g.1.1 | yes | 2 | 9.7 | even | 3 | ||
432.4.a.p.1.2 | 2 | 36.11 | even | 6 | |||
432.4.a.r.1.1 | 2 | 36.7 | odd | 6 | |||
648.4.i.o.217.2 | 4 | 1.1 | even | 1 | trivial | ||
648.4.i.o.433.2 | 4 | 9.4 | even | 3 | inner | ||
648.4.i.r.217.1 | 4 | 3.2 | odd | 2 | |||
648.4.i.r.433.1 | 4 | 9.5 | odd | 6 | |||
1728.4.a.bi.1.2 | 2 | 72.61 | even | 6 | |||
1728.4.a.bj.1.2 | 2 | 72.43 | odd | 6 | |||
1728.4.a.bq.1.1 | 2 | 72.29 | odd | 6 | |||
1728.4.a.br.1.1 | 2 | 72.11 | even | 6 |