Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} + 124x^{6} + 4272x^{4} + 28129x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.2 | ||
Root | \(-0.0119250i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.o.599.7 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 2.98808i | 0.575055i | 0.957772 | + | 0.287528i | \(0.0928333\pi\) | ||||
−0.957772 | + | 0.287528i | \(0.907167\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.97615 | 0.406626 | ||||||||
\(7\) | − 2.98517i | − 0.161184i | −0.996747 | − | 0.0805921i | \(-0.974319\pi\) | ||||
0.996747 | − | 0.0805921i | \(-0.0256811\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 18.0714 | 0.669311 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 68.6262 | 1.88105 | 0.940527 | − | 0.339720i | \(-0.110332\pi\) | ||||
0.940527 | + | 0.339720i | \(0.110332\pi\) | |||||||
\(12\) | − 11.9523i | − 0.287528i | ||||||||
\(13\) | − 12.0028i | − 0.256074i | −0.991769 | − | 0.128037i | \(-0.959132\pi\) | ||||
0.991769 | − | 0.128037i | \(-0.0408677\pi\) | |||||||
\(14\) | −5.97035 | −0.113974 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 106.208i | − 1.51525i | −0.652693 | − | 0.757623i | \(-0.726361\pi\) | ||||
0.652693 | − | 0.757623i | \(-0.273639\pi\) | |||||||
\(18\) | − 36.1428i | − 0.473275i | ||||||||
\(19\) | 48.4891 | 0.585482 | 0.292741 | − | 0.956192i | \(-0.405433\pi\) | ||||
0.292741 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.91992 | 0.0926898 | ||||||||
\(22\) | − 137.252i | − 1.33011i | ||||||||
\(23\) | − 23.0000i | − 0.208514i | ||||||||
\(24\) | −23.9046 | −0.203313 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −24.0055 | −0.181072 | ||||||||
\(27\) | 134.677i | 0.959946i | ||||||||
\(28\) | 11.9407i | 0.0805921i | ||||||||
\(29\) | −135.226 | −0.865890 | −0.432945 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432945 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −230.782 | −1.33709 | −0.668544 | − | 0.743673i | \(-0.733082\pi\) | ||||
−0.668544 | + | 0.743673i | \(0.733082\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 205.060i | 1.08171i | ||||||||
\(34\) | −212.416 | −1.07144 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −72.2856 | −0.334656 | ||||||||
\(37\) | 107.956i | 0.479672i | 0.970813 | + | 0.239836i | \(0.0770937\pi\) | ||||
−0.970813 | + | 0.239836i | \(0.922906\pi\) | |||||||
\(38\) | − 96.9782i | − 0.413998i | ||||||||
\(39\) | 35.8651 | 0.147257 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 394.637 | 1.50322 | 0.751610 | − | 0.659608i | \(-0.229278\pi\) | ||||
0.751610 | + | 0.659608i | \(0.229278\pi\) | |||||||
\(42\) | − 17.8398i | − 0.0655416i | ||||||||
\(43\) | 136.063i | 0.482543i | 0.970458 | + | 0.241272i | \(0.0775645\pi\) | ||||
−0.970458 | + | 0.241272i | \(0.922436\pi\) | |||||||
\(44\) | −274.505 | −0.940527 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 50.4512i | 0.156576i | 0.996931 | + | 0.0782880i | \(0.0249454\pi\) | ||||
−0.996931 | + | 0.0782880i | \(0.975055\pi\) | |||||||
\(48\) | 47.8092i | 0.143764i | ||||||||
\(49\) | 334.089 | 0.974020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 317.357 | 0.871350 | ||||||||
\(52\) | 48.0110i | 0.128037i | ||||||||
\(53\) | − 414.707i | − 1.07480i | −0.843327 | − | 0.537400i | \(-0.819406\pi\) | ||||
0.843327 | − | 0.537400i | \(-0.180594\pi\) | |||||||
\(54\) | 269.353 | 0.678785 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 23.8814 | 0.0569872 | ||||||||
\(57\) | 144.889i | 0.336685i | ||||||||
\(58\) | 270.452i | 0.612277i | ||||||||
\(59\) | 183.586 | 0.405100 | 0.202550 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202550 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −98.4751 | −0.206696 | −0.103348 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103348 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(62\) | 461.565i | 0.945464i | ||||||||
\(63\) | − 53.9463i | − 0.107882i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 410.121 | 0.764884 | ||||||||
\(67\) | − 136.925i | − 0.249672i | −0.992177 | − | 0.124836i | \(-0.960160\pi\) | ||||
0.992177 | − | 0.124836i | \(-0.0398404\pi\) | |||||||
\(68\) | 424.831i | 0.757623i | ||||||||
\(69\) | 68.7257 | 0.119907 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −708.800 | −1.18478 | −0.592388 | − | 0.805653i | \(-0.701815\pi\) | ||||
−0.592388 | + | 0.805653i | \(0.701815\pi\) | |||||||
\(72\) | 144.571i | 0.236637i | ||||||||
\(73\) | − 689.605i | − 1.10565i | −0.833299 | − | 0.552823i | \(-0.813551\pi\) | ||||
0.833299 | − | 0.552823i | \(-0.186449\pi\) | |||||||
\(74\) | 215.912 | 0.339179 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −193.956 | −0.292741 | ||||||||
\(77\) | − 204.861i | − 0.303196i | ||||||||
\(78\) | − 71.7303i | − 0.104126i | ||||||||
\(79\) | −546.583 | −0.778423 | −0.389212 | − | 0.921148i | \(-0.627252\pi\) | ||||
−0.389212 | + | 0.921148i | \(0.627252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 85.5038 | 0.117289 | ||||||||
\(82\) | − 789.275i | − 1.06294i | ||||||||
\(83\) | − 20.2622i | − 0.0267959i | −0.999910 | − | 0.0133980i | \(-0.995735\pi\) | ||||
0.999910 | − | 0.0133980i | \(-0.00426483\pi\) | |||||||
\(84\) | −35.6797 | −0.0463449 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 272.125 | 0.341210 | ||||||||
\(87\) | − 404.065i | − 0.497935i | ||||||||
\(88\) | 549.010i | 0.665053i | ||||||||
\(89\) | 1087.31 | 1.29499 | 0.647495 | − | 0.762069i | \(-0.275817\pi\) | ||||
0.647495 | + | 0.762069i | \(0.275817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.8303 | −0.0412751 | ||||||||
\(92\) | 92.0000i | 0.104257i | ||||||||
\(93\) | − 689.595i | − 0.768900i | ||||||||
\(94\) | 100.902 | 0.110716 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 95.6184 | 0.101656 | ||||||||
\(97\) | 1115.90i | 1.16807i | 0.811728 | + | 0.584036i | \(0.198527\pi\) | ||||
−0.811728 | + | 0.584036i | \(0.801473\pi\) | |||||||
\(98\) | − 668.177i | − 0.688736i | ||||||||
\(99\) | 1240.17 | 1.25901 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −134.565 | −0.132572 | −0.0662859 | − | 0.997801i | \(-0.521115\pi\) | ||||
−0.0662859 | + | 0.997801i | \(0.521115\pi\) | |||||||
\(102\) | − 634.714i | − 0.616137i | ||||||||
\(103\) | − 925.953i | − 0.885795i | −0.896572 | − | 0.442898i | \(-0.853951\pi\) | ||||
0.896572 | − | 0.442898i | \(-0.146049\pi\) | |||||||
\(104\) | 96.0221 | 0.0905360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −829.415 | −0.759999 | ||||||||
\(107\) | − 1871.13i | − 1.69055i | −0.534334 | − | 0.845273i | \(-0.679438\pi\) | ||||
0.534334 | − | 0.845273i | \(-0.320562\pi\) | |||||||
\(108\) | − 538.707i | − 0.479973i | ||||||||
\(109\) | 978.242 | 0.859620 | 0.429810 | − | 0.902919i | \(-0.358581\pi\) | ||||
0.429810 | + | 0.902919i | \(0.358581\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −322.581 | −0.275838 | ||||||||
\(112\) | − 47.7628i | − 0.0402961i | ||||||||
\(113\) | − 1760.45i | − 1.46557i | −0.680459 | − | 0.732786i | \(-0.738220\pi\) | ||||
0.680459 | − | 0.732786i | \(-0.261780\pi\) | |||||||
\(114\) | 289.778 | 0.238072 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 540.903 | 0.432945 | ||||||||
\(117\) | − 216.907i | − 0.171393i | ||||||||
\(118\) | − 367.172i | − 0.286449i | ||||||||
\(119\) | −317.049 | −0.244234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3378.56 | 2.53836 | ||||||||
\(122\) | 196.950i | 0.146156i | ||||||||
\(123\) | 1179.21i | 0.864434i | ||||||||
\(124\) | 923.129 | 0.668544 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −107.893 | −0.0762844 | ||||||||
\(127\) | 1260.87i | 0.880980i | 0.897758 | + | 0.440490i | \(0.145195\pi\) | ||||
−0.897758 | + | 0.440490i | \(0.854805\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −406.566 | −0.277489 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 444.283 | 0.296314 | 0.148157 | − | 0.988964i | \(-0.452666\pi\) | ||||
0.148157 | + | 0.988964i | \(0.452666\pi\) | |||||||
\(132\) | − 820.241i | − 0.540855i | ||||||||
\(133\) | − 144.748i | − 0.0943705i | ||||||||
\(134\) | −273.849 | −0.176545 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 849.662 | 0.535720 | ||||||||
\(137\) | − 429.072i | − 0.267577i | −0.991010 | − | 0.133789i | \(-0.957286\pi\) | ||||
0.991010 | − | 0.133789i | \(-0.0427143\pi\) | |||||||
\(138\) | − 137.451i | − 0.0847873i | ||||||||
\(139\) | 249.755 | 0.152402 | 0.0762012 | − | 0.997092i | \(-0.475721\pi\) | ||||
0.0762012 | + | 0.997092i | \(0.475721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −150.752 | −0.0900398 | ||||||||
\(142\) | 1417.60i | 0.837763i | ||||||||
\(143\) | − 823.704i | − 0.481689i | ||||||||
\(144\) | 289.143 | 0.167328 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1379.21 | −0.781809 | ||||||||
\(147\) | 998.282i | 0.560115i | ||||||||
\(148\) | − 431.824i | − 0.239836i | ||||||||
\(149\) | 1564.18 | 0.860020 | 0.430010 | − | 0.902824i | \(-0.358510\pi\) | ||||
0.430010 | + | 0.902824i | \(0.358510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1860.04 | −1.00244 | −0.501219 | − | 0.865321i | \(-0.667115\pi\) | ||||
−0.501219 | + | 0.865321i | \(0.667115\pi\) | |||||||
\(152\) | 387.913i | 0.206999i | ||||||||
\(153\) | − 1919.32i | − 1.01417i | ||||||||
\(154\) | −409.722 | −0.214392 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −143.461 | −0.0736285 | ||||||||
\(157\) | − 2834.52i | − 1.44089i | −0.693512 | − | 0.720445i | \(-0.743938\pi\) | ||||
0.693512 | − | 0.720445i | \(-0.256062\pi\) | |||||||
\(158\) | 1093.17i | 0.550428i | ||||||||
\(159\) | 1239.18 | 0.618070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −68.6590 | −0.0336092 | ||||||||
\(162\) | − 171.008i | − 0.0829359i | ||||||||
\(163\) | 2114.51i | 1.01608i | 0.861333 | + | 0.508041i | \(0.169630\pi\) | ||||
−0.861333 | + | 0.508041i | \(0.830370\pi\) | |||||||
\(164\) | −1578.55 | −0.751610 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −40.5244 | −0.0189476 | ||||||||
\(167\) | − 2487.41i | − 1.15258i | −0.817244 | − | 0.576291i | \(-0.804499\pi\) | ||||
0.817244 | − | 0.576291i | \(-0.195501\pi\) | |||||||
\(168\) | 71.3594i | 0.0327708i | ||||||||
\(169\) | 2052.93 | 0.934426 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 876.266 | 0.391870 | ||||||||
\(172\) | − 544.251i | − 0.241272i | ||||||||
\(173\) | 3672.32i | 1.61388i | 0.590634 | + | 0.806939i | \(0.298878\pi\) | ||||
−0.590634 | + | 0.806939i | \(0.701122\pi\) | |||||||
\(174\) | −808.130 | −0.352093 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1098.02 | 0.470263 | ||||||||
\(177\) | 548.569i | 0.232955i | ||||||||
\(178\) | − 2174.61i | − 0.915697i | ||||||||
\(179\) | 3224.63 | 1.34648 | 0.673240 | − | 0.739424i | \(-0.264902\pi\) | ||||
0.673240 | + | 0.739424i | \(0.264902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2224.23 | −0.913401 | −0.456700 | − | 0.889621i | \(-0.650969\pi\) | ||||
−0.456700 | + | 0.889621i | \(0.650969\pi\) | |||||||
\(182\) | 71.6606i | 0.0291859i | ||||||||
\(183\) | − 294.251i | − 0.118862i | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1379.19 | −0.543694 | ||||||||
\(187\) | − 7288.64i | − 2.85026i | ||||||||
\(188\) | − 201.805i | − 0.0782880i | ||||||||
\(189\) | 402.033 | 0.154728 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3273.53 | 1.24013 | 0.620063 | − | 0.784552i | \(-0.287107\pi\) | ||||
0.620063 | + | 0.784552i | \(0.287107\pi\) | |||||||
\(192\) | − 191.237i | − 0.0718819i | ||||||||
\(193\) | 5126.86i | 1.91212i | 0.293166 | + | 0.956062i | \(0.405291\pi\) | ||||
−0.293166 | + | 0.956062i | \(0.594709\pi\) | |||||||
\(194\) | 2231.81 | 0.825951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1336.35 | −0.487010 | ||||||||
\(197\) | − 3262.57i | − 1.17994i | −0.807425 | − | 0.589971i | \(-0.799139\pi\) | ||||
0.807425 | − | 0.589971i | \(-0.200861\pi\) | |||||||
\(198\) | − 2480.34i | − 0.890255i | ||||||||
\(199\) | 168.282 | 0.0599457 | 0.0299728 | − | 0.999551i | \(-0.490458\pi\) | ||||
0.0299728 | + | 0.999551i | \(0.490458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 409.141 | 0.143575 | ||||||||
\(202\) | 269.131i | 0.0937424i | ||||||||
\(203\) | 403.673i | 0.139568i | ||||||||
\(204\) | −1269.43 | −0.435675 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1851.91 | −0.626352 | ||||||||
\(207\) | − 415.642i | − 0.139561i | ||||||||
\(208\) | − 192.044i | − 0.0640186i | ||||||||
\(209\) | 3327.62 | 1.10132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4197.01 | 1.36936 | 0.684678 | − | 0.728846i | \(-0.259943\pi\) | ||||
0.684678 | + | 0.728846i | \(0.259943\pi\) | |||||||
\(212\) | 1658.83i | 0.537400i | ||||||||
\(213\) | − 2117.95i | − 0.681312i | ||||||||
\(214\) | −3742.25 | −1.19540 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1077.41 | −0.339392 | ||||||||
\(217\) | 688.925i | 0.215518i | ||||||||
\(218\) | − 1956.48i | − 0.607843i | ||||||||
\(219\) | 2060.59 | 0.635807 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1274.79 | −0.388015 | ||||||||
\(222\) | 645.162i | 0.195047i | ||||||||
\(223\) | 5192.66i | 1.55931i | 0.626208 | + | 0.779656i | \(0.284606\pi\) | ||||
−0.626208 | + | 0.779656i | \(0.715394\pi\) | |||||||
\(224\) | −95.5256 | −0.0284936 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3520.91 | −1.03632 | ||||||||
\(227\) | − 4701.24i | − 1.37459i | −0.726378 | − | 0.687295i | \(-0.758798\pi\) | ||||
0.726378 | − | 0.687295i | \(-0.241202\pi\) | |||||||
\(228\) | − 579.556i | − 0.168342i | ||||||||
\(229\) | 2125.17 | 0.613255 | 0.306628 | − | 0.951830i | \(-0.400799\pi\) | ||||
0.306628 | + | 0.951830i | \(0.400799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 612.141 | 0.174355 | ||||||||
\(232\) | − 1081.81i | − 0.306138i | ||||||||
\(233\) | − 1646.67i | − 0.462992i | −0.972836 | − | 0.231496i | \(-0.925638\pi\) | ||||
0.972836 | − | 0.231496i | \(-0.0743620\pi\) | |||||||
\(234\) | −433.814 | −0.121193 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −734.345 | −0.202550 | ||||||||
\(237\) | − 1633.23i | − 0.447636i | ||||||||
\(238\) | 634.097i | 0.172699i | ||||||||
\(239\) | −2877.88 | −0.778888 | −0.389444 | − | 0.921050i | \(-0.627333\pi\) | ||||
−0.389444 | + | 0.921050i | \(0.627333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4244.54 | −1.13450 | −0.567251 | − | 0.823545i | \(-0.691993\pi\) | ||||
−0.567251 | + | 0.823545i | \(0.691993\pi\) | |||||||
\(242\) | − 6757.12i | − 1.79489i | ||||||||
\(243\) | 3891.76i | 1.02739i | ||||||||
\(244\) | 393.900 | 0.103348 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2358.41 | 0.611247 | ||||||||
\(247\) | − 582.003i | − 0.149927i | ||||||||
\(248\) | − 1846.26i | − 0.472732i | ||||||||
\(249\) | 60.5449 | 0.0154092 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4401.99 | 1.10698 | 0.553488 | − | 0.832857i | \(-0.313296\pi\) | ||||
0.553488 | + | 0.832857i | \(0.313296\pi\) | |||||||
\(252\) | 215.785i | 0.0539412i | ||||||||
\(253\) | − 1578.40i | − 0.392227i | ||||||||
\(254\) | 2521.75 | 0.622947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 1694.78i | − 0.411352i | −0.978620 | − | 0.205676i | \(-0.934061\pi\) | ||||
0.978620 | − | 0.205676i | \(-0.0659393\pi\) | |||||||
\(258\) | 813.131i | 0.196214i | ||||||||
\(259\) | 322.268 | 0.0773156 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2443.72 | −0.579550 | ||||||||
\(262\) | − 888.566i | − 0.209526i | ||||||||
\(263\) | − 727.462i | − 0.170560i | −0.996357 | − | 0.0852799i | \(-0.972822\pi\) | ||||
0.996357 | − | 0.0852799i | \(-0.0271784\pi\) | |||||||
\(264\) | −1640.48 | −0.382442 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −289.497 | −0.0667300 | ||||||||
\(267\) | 3248.95i | 0.744691i | ||||||||
\(268\) | 547.698i | 0.124836i | ||||||||
\(269\) | −94.9937 | −0.0215311 | −0.0107656 | − | 0.999942i | \(-0.503427\pi\) | ||||
−0.0107656 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5321.54 | 1.19284 | 0.596422 | − | 0.802671i | \(-0.296589\pi\) | ||||
0.596422 | + | 0.802671i | \(0.296589\pi\) | |||||||
\(272\) | − 1699.32i | − 0.378811i | ||||||||
\(273\) | − 107.064i | − 0.0237355i | ||||||||
\(274\) | −858.143 | −0.189206 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −274.903 | −0.0599537 | ||||||||
\(277\) | − 2561.25i | − 0.555562i | −0.960644 | − | 0.277781i | \(-0.910401\pi\) | ||||
0.960644 | − | 0.277781i | \(-0.0895989\pi\) | |||||||
\(278\) | − 499.510i | − 0.107765i | ||||||||
\(279\) | −4170.56 | −0.894928 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8753.73 | −1.85838 | −0.929188 | − | 0.369606i | \(-0.879493\pi\) | ||||
−0.929188 | + | 0.369606i | \(0.879493\pi\) | |||||||
\(282\) | 301.504i | 0.0636678i | ||||||||
\(283\) | − 2400.14i | − 0.504147i | −0.967708 | − | 0.252073i | \(-0.918888\pi\) | ||||
0.967708 | − | 0.252073i | \(-0.0811125\pi\) | |||||||
\(284\) | 2835.20 | 0.592388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1647.41 | −0.340606 | ||||||||
\(287\) | − 1178.06i | − 0.242295i | ||||||||
\(288\) | − 578.285i | − 0.118319i | ||||||||
\(289\) | −6367.09 | −1.29597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3334.41 | −0.671706 | ||||||||
\(292\) | 2758.42i | 0.552823i | ||||||||
\(293\) | 1045.56i | 0.208472i | 0.994553 | + | 0.104236i | \(0.0332397\pi\) | ||||
−0.994553 | + | 0.104236i | \(0.966760\pi\) | |||||||
\(294\) | 1996.56 | 0.396061 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −863.649 | −0.169590 | ||||||||
\(297\) | 9242.36i | 1.80571i | ||||||||
\(298\) | − 3128.37i | − 0.608126i | ||||||||
\(299\) | −276.063 | −0.0533952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 406.171 | 0.0777784 | ||||||||
\(302\) | 3720.08i | 0.708830i | ||||||||
\(303\) | − 402.091i | − 0.0762361i | ||||||||
\(304\) | 775.826 | 0.146371 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3838.65 | −0.717127 | ||||||||
\(307\) | 7905.84i | 1.46974i | 0.678208 | + | 0.734870i | \(0.262757\pi\) | ||||
−0.678208 | + | 0.734870i | \(0.737243\pi\) | |||||||
\(308\) | 819.445i | 0.151598i | ||||||||
\(309\) | 2766.82 | 0.509381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9227.63 | −1.68248 | −0.841240 | − | 0.540662i | \(-0.818174\pi\) | ||||
−0.841240 | + | 0.540662i | \(0.818174\pi\) | |||||||
\(312\) | 286.921i | 0.0520632i | ||||||||
\(313\) | 2712.57i | 0.489852i | 0.969542 | + | 0.244926i | \(0.0787637\pi\) | ||||
−0.969542 | + | 0.244926i | \(0.921236\pi\) | |||||||
\(314\) | −5669.05 | −1.01886 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2186.33 | 0.389212 | ||||||||
\(317\) | 3440.29i | 0.609546i | 0.952425 | + | 0.304773i | \(0.0985805\pi\) | ||||
−0.952425 | + | 0.304773i | \(0.901419\pi\) | |||||||
\(318\) | − 2478.35i | − 0.437041i | ||||||||
\(319\) | −9280.04 | −1.62879 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5591.06 | 0.972158 | ||||||||
\(322\) | 137.318i | 0.0237653i | ||||||||
\(323\) | − 5149.92i | − 0.887149i | ||||||||
\(324\) | −342.015 | −0.0586446 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4229.03 | 0.718479 | ||||||||
\(327\) | 2923.06i | 0.494329i | ||||||||
\(328\) | 3157.10i | 0.531468i | ||||||||
\(329\) | 150.606 | 0.0252376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3259.75 | 0.541305 | 0.270652 | − | 0.962677i | \(-0.412761\pi\) | ||||
0.270652 | + | 0.962677i | \(0.412761\pi\) | |||||||
\(332\) | 81.0487i | 0.0133980i | ||||||||
\(333\) | 1950.92i | 0.321050i | ||||||||
\(334\) | −4974.81 | −0.814999 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 142.719 | 0.0231725 | ||||||||
\(337\) | − 7163.38i | − 1.15790i | −0.815361 | − | 0.578952i | \(-0.803462\pi\) | ||||
0.815361 | − | 0.578952i | \(-0.196538\pi\) | |||||||
\(338\) | − 4105.87i | − 0.660739i | ||||||||
\(339\) | 5260.37 | 0.842785 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15837.7 | −2.51513 | ||||||||
\(342\) | − 1752.53i | − 0.277094i | ||||||||
\(343\) | − 2021.23i | − 0.318181i | ||||||||
\(344\) | −1088.50 | −0.170605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7344.63 | 1.14118 | ||||||||
\(347\) | 1833.45i | 0.283645i | 0.989892 | + | 0.141822i | \(0.0452962\pi\) | ||||
−0.989892 | + | 0.141822i | \(0.954704\pi\) | |||||||
\(348\) | 1616.26i | 0.248967i | ||||||||
\(349\) | 10400.3 | 1.59517 | 0.797583 | − | 0.603209i | \(-0.206112\pi\) | ||||
0.797583 | + | 0.603209i | \(0.206112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1616.49 | 0.245818 | ||||||||
\(352\) | − 2196.04i | − 0.332526i | ||||||||
\(353\) | − 3156.48i | − 0.475928i | −0.971274 | − | 0.237964i | \(-0.923520\pi\) | ||||
0.971274 | − | 0.237964i | \(-0.0764800\pi\) | |||||||
\(354\) | 1097.14 | 0.164724 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4349.22 | −0.647495 | ||||||||
\(357\) | − 947.365i | − 0.140448i | ||||||||
\(358\) | − 6449.25i | − 0.952105i | ||||||||
\(359\) | 9324.16 | 1.37078 | 0.685390 | − | 0.728176i | \(-0.259632\pi\) | ||||
0.685390 | + | 0.728176i | \(0.259632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4507.81 | −0.657211 | ||||||||
\(362\) | 4448.45i | 0.645872i | ||||||||
\(363\) | 10095.4i | 1.45970i | ||||||||
\(364\) | 143.321 | 0.0206376 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −588.502 | −0.0840478 | ||||||||
\(367\) | − 3802.68i | − 0.540867i | −0.962739 | − | 0.270434i | \(-0.912833\pi\) | ||||
0.962739 | − | 0.270434i | \(-0.0871671\pi\) | |||||||
\(368\) | − 368.000i | − 0.0521286i | ||||||||
\(369\) | 7131.65 | 1.00612 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1237.97 | −0.173241 | ||||||||
\(372\) | 2758.38i | 0.384450i | ||||||||
\(373\) | − 8928.03i | − 1.23935i | −0.784860 | − | 0.619673i | \(-0.787265\pi\) | ||||
0.784860 | − | 0.619673i | \(-0.212735\pi\) | |||||||
\(374\) | −14577.3 | −2.01544 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −403.610 | −0.0553580 | ||||||||
\(377\) | 1623.08i | 0.221732i | ||||||||
\(378\) | − 804.067i | − 0.109409i | ||||||||
\(379\) | −3798.13 | −0.514768 | −0.257384 | − | 0.966309i | \(-0.582860\pi\) | ||||
−0.257384 | + | 0.966309i | \(0.582860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3767.58 | −0.506612 | ||||||||
\(382\) | − 6547.05i | − 0.876901i | ||||||||
\(383\) | 1456.41i | 0.194306i | 0.995269 | + | 0.0971530i | \(0.0309736\pi\) | ||||
−0.995269 | + | 0.0971530i | \(0.969026\pi\) | |||||||
\(384\) | −382.474 | −0.0508282 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10253.7 | 1.35208 | ||||||||
\(387\) | 2458.84i | 0.322972i | ||||||||
\(388\) | − 4463.62i | − 0.584036i | ||||||||
\(389\) | 8211.34 | 1.07026 | 0.535130 | − | 0.844769i | \(-0.320262\pi\) | ||||
0.535130 | + | 0.844769i | \(0.320262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2442.78 | −0.315950 | ||||||||
\(392\) | 2672.71i | 0.344368i | ||||||||
\(393\) | 1327.55i | 0.170397i | ||||||||
\(394\) | −6525.14 | −0.834345 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4960.69 | −0.629505 | ||||||||
\(397\) | − 914.365i | − 0.115594i | −0.998328 | − | 0.0577968i | \(-0.981592\pi\) | ||||
0.998328 | − | 0.0577968i | \(-0.0184076\pi\) | |||||||
\(398\) | − 336.564i | − 0.0423880i | ||||||||
\(399\) | 432.519 | 0.0542683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9414.97 | 1.17247 | 0.586236 | − | 0.810140i | \(-0.300609\pi\) | ||||
0.586236 | + | 0.810140i | \(0.300609\pi\) | |||||||
\(402\) | − 818.282i | − 0.101523i | ||||||||
\(403\) | 2770.02i | 0.342394i | ||||||||
\(404\) | 538.261 | 0.0662859 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 807.345 | 0.0986894 | ||||||||
\(407\) | 7408.62i | 0.902289i | ||||||||
\(408\) | 2538.85i | 0.308069i | ||||||||
\(409\) | −3299.41 | −0.398889 | −0.199444 | − | 0.979909i | \(-0.563914\pi\) | ||||
−0.199444 | + | 0.979909i | \(0.563914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1282.10 | 0.153872 | ||||||||
\(412\) | 3703.81i | 0.442898i | ||||||||
\(413\) | − 548.037i | − 0.0652957i | ||||||||
\(414\) | −831.285 | −0.0986846 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −384.088 | −0.0452680 | ||||||||
\(417\) | 746.286i | 0.0876398i | ||||||||
\(418\) | − 6655.25i | − 0.778753i | ||||||||
\(419\) | 3554.64 | 0.414452 | 0.207226 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207226 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11655.5 | 1.34930 | 0.674649 | − | 0.738139i | \(-0.264295\pi\) | ||||
0.674649 | + | 0.738139i | \(0.264295\pi\) | |||||||
\(422\) | − 8394.02i | − 0.968281i | ||||||||
\(423\) | 911.725i | 0.104798i | ||||||||
\(424\) | 3317.66 | 0.380000 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4235.90 | −0.481760 | ||||||||
\(427\) | 293.965i | 0.0333161i | ||||||||
\(428\) | 7484.50i | 0.845273i | ||||||||
\(429\) | 2461.29 | 0.276998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4727.38 | 0.528330 | 0.264165 | − | 0.964478i | \(-0.414904\pi\) | ||||
0.264165 | + | 0.964478i | \(0.414904\pi\) | |||||||
\(432\) | 2154.83i | 0.239987i | ||||||||
\(433\) | 3936.24i | 0.436868i | 0.975852 | + | 0.218434i | \(0.0700948\pi\) | ||||
−0.975852 | + | 0.218434i | \(0.929905\pi\) | |||||||
\(434\) | 1377.85 | 0.152394 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3912.97 | −0.429810 | ||||||||
\(437\) | − 1115.25i | − 0.122081i | ||||||||
\(438\) | − 4121.18i | − 0.449584i | ||||||||
\(439\) | −6859.77 | −0.745784 | −0.372892 | − | 0.927875i | \(-0.621634\pi\) | ||||
−0.372892 | + | 0.927875i | \(0.621634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6037.45 | 0.651922 | ||||||||
\(442\) | 2549.57i | 0.274368i | ||||||||
\(443\) | 16814.4i | 1.80334i | 0.432430 | + | 0.901668i | \(0.357656\pi\) | ||||
−0.432430 | + | 0.901668i | \(0.642344\pi\) | |||||||
\(444\) | 1290.32 | 0.137919 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10385.3 | 1.10260 | ||||||||
\(447\) | 4673.90i | 0.494559i | ||||||||
\(448\) | 191.051i | 0.0201480i | ||||||||
\(449\) | −10673.8 | −1.12189 | −0.560943 | − | 0.827855i | \(-0.689561\pi\) | ||||
−0.560943 | + | 0.827855i | \(0.689561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27082.5 | 2.82764 | ||||||||
\(452\) | 7041.82i | 0.732786i | ||||||||
\(453\) | − 5557.94i | − 0.576457i | ||||||||
\(454\) | −9402.47 | −0.971982 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1159.11 | −0.119036 | ||||||||
\(457\) | − 15493.0i | − 1.58585i | −0.609318 | − | 0.792926i | \(-0.708557\pi\) | ||||
0.609318 | − | 0.792926i | \(-0.291443\pi\) | |||||||
\(458\) | − 4250.35i | − 0.433637i | ||||||||
\(459\) | 14303.7 | 1.45455 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10793.0 | −1.09041 | −0.545207 | − | 0.838302i | \(-0.683549\pi\) | ||||
−0.545207 | + | 0.838302i | \(0.683549\pi\) | |||||||
\(462\) | − 1224.28i | − 0.123287i | ||||||||
\(463\) | − 6165.87i | − 0.618904i | −0.950915 | − | 0.309452i | \(-0.899854\pi\) | ||||
0.950915 | − | 0.309452i | \(-0.100146\pi\) | |||||||
\(464\) | −2163.61 | −0.216473 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3293.34 | −0.327385 | ||||||||
\(467\) | 10736.4i | 1.06386i | 0.846789 | + | 0.531929i | \(0.178533\pi\) | ||||
−0.846789 | + | 0.531929i | \(0.821467\pi\) | |||||||
\(468\) | 867.627i | 0.0856967i | ||||||||
\(469\) | −408.744 | −0.0402431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8469.77 | 0.828591 | ||||||||
\(472\) | 1468.69i | 0.143224i | ||||||||
\(473\) | 9337.47i | 0.907690i | ||||||||
\(474\) | −3266.46 | −0.316527 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1268.19 | 0.122117 | ||||||||
\(477\) | − 7494.35i | − 0.719377i | ||||||||
\(478\) | 5755.75i | 0.550757i | ||||||||
\(479\) | −6333.30 | −0.604125 | −0.302062 | − | 0.953288i | \(-0.597675\pi\) | ||||
−0.302062 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1295.77 | 0.122832 | ||||||||
\(482\) | 8489.08i | 0.802213i | ||||||||
\(483\) | − 205.158i | − 0.0193272i | ||||||||
\(484\) | −13514.2 | −1.26918 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7783.53 | 0.726477 | ||||||||
\(487\) | 16833.3i | 1.56630i | 0.621834 | + | 0.783149i | \(0.286388\pi\) | ||||
−0.621834 | + | 0.783149i | \(0.713612\pi\) | |||||||
\(488\) | − 787.801i | − 0.0730780i | ||||||||
\(489\) | −6318.33 | −0.584304 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.80428 | −0.000441577 0 | −0.000220788 | − | 1.00000i | \(-0.500070\pi\) | ||||
−0.000220788 | 1.00000i | \(0.500070\pi\) | ||||||||
\(492\) | − 4716.82i | − 0.432217i | ||||||||
\(493\) | 14362.0i | 1.31204i | ||||||||
\(494\) | −1164.01 | −0.106014 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3692.52 | −0.334272 | ||||||||
\(497\) | 2115.89i | 0.190967i | ||||||||
\(498\) | − 121.090i | − 0.0108959i | ||||||||
\(499\) | −21206.9 | −1.90251 | −0.951253 | − | 0.308412i | \(-0.900203\pi\) | ||||
−0.951253 | + | 0.308412i | \(0.900203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7432.56 | 0.662799 | ||||||||
\(502\) | − 8803.98i | − 0.782750i | ||||||||
\(503\) | 14513.7i | 1.28655i | 0.765635 | + | 0.643275i | \(0.222425\pi\) | ||||
−0.765635 | + | 0.643275i | \(0.777575\pi\) | |||||||
\(504\) | 431.570 | 0.0381422 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3156.81 | −0.277346 | ||||||||
\(507\) | 6134.32i | 0.537347i | ||||||||
\(508\) | − 5043.49i | − 0.440490i | ||||||||
\(509\) | 2545.77 | 0.221689 | 0.110844 | − | 0.993838i | \(-0.464645\pi\) | ||||
0.110844 | + | 0.993838i | \(0.464645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2058.59 | −0.178213 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 6530.35i | 0.562032i | ||||||||
\(514\) | −3389.56 | −0.290870 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1626.26 | 0.138745 | ||||||||
\(517\) | 3462.28i | 0.294528i | ||||||||
\(518\) | − 644.535i | − 0.0546704i | ||||||||
\(519\) | −10973.2 | −0.928070 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21343.1 | −1.79473 | −0.897367 | − | 0.441285i | \(-0.854523\pi\) | ||||
−0.897367 | + | 0.441285i | \(0.854523\pi\) | |||||||
\(522\) | 4887.44i | 0.409804i | ||||||||
\(523\) | − 789.191i | − 0.0659827i | −0.999456 | − | 0.0329913i | \(-0.989497\pi\) | ||||
0.999456 | − | 0.0329913i | \(-0.0105034\pi\) | |||||||
\(524\) | −1777.13 | −0.148157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1454.92 | −0.120604 | ||||||||
\(527\) | 24510.9i | 2.02602i | ||||||||
\(528\) | 3280.96i | 0.270427i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3317.66 | 0.271138 | ||||||||
\(532\) | 578.994i | 0.0471852i | ||||||||
\(533\) | − 4736.74i | − 0.384936i | ||||||||
\(534\) | 6497.90 | 0.526576 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1095.40 | 0.0882723 | ||||||||
\(537\) | 9635.42i | 0.774300i | ||||||||
\(538\) | 189.987i | 0.0152248i | ||||||||
\(539\) | 22927.2 | 1.83218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13405.1 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(542\) | − 10643.1i | − 0.843468i | ||||||||
\(543\) | − 6646.16i | − 0.525256i | ||||||||
\(544\) | −3398.65 | −0.267860 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −214.127 | −0.0167835 | ||||||||
\(547\) | − 10088.8i | − 0.788605i | −0.918981 | − | 0.394303i | \(-0.870986\pi\) | ||||
0.918981 | − | 0.394303i | \(-0.129014\pi\) | |||||||
\(548\) | 1716.29i | 0.133789i | ||||||||
\(549\) | −1779.58 | −0.138344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6556.98 | −0.506963 | ||||||||
\(552\) | 549.806i | 0.0423936i | ||||||||
\(553\) | 1631.65i | 0.125470i | ||||||||
\(554\) | −5122.50 | −0.392842 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −999.019 | −0.0762012 | ||||||||
\(557\) | 11657.7i | 0.886809i | 0.896322 | + | 0.443405i | \(0.146230\pi\) | ||||
−0.896322 | + | 0.443405i | \(0.853770\pi\) | |||||||
\(558\) | 8341.12i | 0.632810i | ||||||||
\(559\) | 1633.13 | 0.123567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21779.0 | 1.63906 | ||||||||
\(562\) | 17507.5i | 1.31407i | ||||||||
\(563\) | 4839.43i | 0.362270i | 0.983458 | + | 0.181135i | \(0.0579770\pi\) | ||||
−0.983458 | + | 0.181135i | \(0.942023\pi\) | |||||||
\(564\) | 603.008 | 0.0450199 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4800.28 | −0.356486 | ||||||||
\(567\) | − 255.244i | − 0.0189052i | ||||||||
\(568\) | − 5670.40i | − 0.418882i | ||||||||
\(569\) | 646.680 | 0.0476454 | 0.0238227 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238227 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3263.66 | 0.239194 | 0.119597 | − | 0.992822i | \(-0.461840\pi\) | ||||
0.119597 | + | 0.992822i | \(0.461840\pi\) | |||||||
\(572\) | 3294.82i | 0.240845i | ||||||||
\(573\) | 9781.54i | 0.713141i | ||||||||
\(574\) | −2356.12 | −0.171329 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1156.57 | −0.0836639 | ||||||||
\(577\) | 8980.46i | 0.647940i | 0.946067 | + | 0.323970i | \(0.105018\pi\) | ||||
−0.946067 | + | 0.323970i | \(0.894982\pi\) | |||||||
\(578\) | 12734.2i | 0.916388i | ||||||||
\(579\) | −15319.5 | −1.09958 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60.4861 | −0.00431908 | ||||||||
\(582\) | 6668.81i | 0.474968i | ||||||||
\(583\) | − 28459.8i | − 2.02176i | ||||||||
\(584\) | 5516.84 | 0.390905 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2091.12 | 0.147412 | ||||||||
\(587\) | 6538.05i | 0.459718i | 0.973224 | + | 0.229859i | \(0.0738265\pi\) | ||||
−0.973224 | + | 0.229859i | \(0.926174\pi\) | |||||||
\(588\) | − 3993.13i | − 0.280058i | ||||||||
\(589\) | −11190.4 | −0.782841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9748.80 | 0.678532 | ||||||||
\(592\) | 1727.30i | 0.119918i | ||||||||
\(593\) | 7803.41i | 0.540384i | 0.962806 | + | 0.270192i | \(0.0870872\pi\) | ||||
−0.962806 | + | 0.270192i | \(0.912913\pi\) | |||||||
\(594\) | 18484.7 | 1.27683 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6256.73 | −0.430010 | ||||||||
\(597\) | 502.839i | 0.0344721i | ||||||||
\(598\) | 552.127i | 0.0377561i | ||||||||
\(599\) | 27812.0 | 1.89711 | 0.948555 | − | 0.316613i | \(-0.102546\pi\) | ||||
0.948555 | + | 0.316613i | \(0.102546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 483.216 | 0.0327966 | 0.0163983 | − | 0.999866i | \(-0.494780\pi\) | ||||
0.0163983 | + | 0.999866i | \(0.494780\pi\) | |||||||
\(602\) | − 812.342i | − 0.0549976i | ||||||||
\(603\) | − 2474.42i | − 0.167108i | ||||||||
\(604\) | 7440.17 | 0.501219 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −804.183 | −0.0539071 | ||||||||
\(607\) | 18104.0i | 1.21058i | 0.796006 | + | 0.605289i | \(0.206942\pi\) | ||||
−0.796006 | + | 0.605289i | \(0.793058\pi\) | |||||||
\(608\) | − 1551.65i | − 0.103500i | ||||||||
\(609\) | −1206.20 | −0.0802592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 605.554 | 0.0400951 | ||||||||
\(612\) | 7677.30i | 0.507085i | ||||||||
\(613\) | 2191.19i | 0.144374i | 0.997391 | + | 0.0721870i | \(0.0229978\pi\) | ||||
−0.997391 | + | 0.0721870i | \(0.977002\pi\) | |||||||
\(614\) | 15811.7 | 1.03926 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1638.89 | 0.107196 | ||||||||
\(617\) | 8243.06i | 0.537849i | 0.963161 | + | 0.268925i | \(0.0866683\pi\) | ||||
−0.963161 | + | 0.268925i | \(0.913332\pi\) | |||||||
\(618\) | − 5533.64i | − 0.360187i | ||||||||
\(619\) | −18298.0 | −1.18814 | −0.594069 | − | 0.804414i | \(-0.702479\pi\) | ||||
−0.594069 | + | 0.804414i | \(0.702479\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3097.57 | 0.200163 | ||||||||
\(622\) | 18455.3i | 1.18969i | ||||||||
\(623\) | − 3245.80i | − 0.208732i | ||||||||
\(624\) | 573.842 | 0.0368142 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5425.15 | 0.346378 | ||||||||
\(627\) | 9943.19i | 0.633322i | ||||||||
\(628\) | 11338.1i | 0.720445i | ||||||||
\(629\) | 11465.8 | 0.726821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26472.0 | −1.67010 | −0.835051 | − | 0.550172i | \(-0.814562\pi\) | ||||
−0.835051 | + | 0.550172i | \(0.814562\pi\) | |||||||
\(632\) | − 4372.67i | − 0.275214i | ||||||||
\(633\) | 12541.0i | 0.787455i | ||||||||
\(634\) | 6880.58 | 0.431014 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4956.71 | −0.309035 | ||||||||
\(637\) | − 4009.99i | − 0.249421i | ||||||||
\(638\) | 18560.1i | 1.15173i | ||||||||
\(639\) | −12809.0 | −0.792984 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7411.93 | 0.456714 | 0.228357 | − | 0.973577i | \(-0.426665\pi\) | ||||
0.228357 | + | 0.973577i | \(0.426665\pi\) | |||||||
\(642\) | − 11182.1i | − 0.687419i | ||||||||
\(643\) | 8405.96i | 0.515550i | 0.966205 | + | 0.257775i | \(0.0829894\pi\) | ||||
−0.966205 | + | 0.257775i | \(0.917011\pi\) | |||||||
\(644\) | 274.636 | 0.0168046 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10299.8 | −0.627309 | ||||||||
\(647\) | − 27878.3i | − 1.69398i | −0.531605 | − | 0.846992i | \(-0.678411\pi\) | ||||
0.531605 | − | 0.846992i | \(-0.321589\pi\) | |||||||
\(648\) | 684.030i | 0.0414680i | ||||||||
\(649\) | 12598.8 | 0.762014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2058.56 | −0.123934 | ||||||||
\(652\) | − 8458.06i | − 0.508041i | ||||||||
\(653\) | − 18871.1i | − 1.13091i | −0.824779 | − | 0.565455i | \(-0.808701\pi\) | ||||
0.824779 | − | 0.565455i | \(-0.191299\pi\) | |||||||
\(654\) | 5846.12 | 0.349543 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6314.20 | 0.375805 | ||||||||
\(657\) | − 12462.1i | − 0.740021i | ||||||||
\(658\) | − 301.211i | − 0.0178457i | ||||||||
\(659\) | 12144.4 | 0.717872 | 0.358936 | − | 0.933362i | \(-0.383140\pi\) | ||||
0.358936 | + | 0.933362i | \(0.383140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32504.2 | −1.91266 | −0.956328 | − | 0.292295i | \(-0.905581\pi\) | ||||
−0.956328 | + | 0.292295i | \(0.905581\pi\) | |||||||
\(662\) | − 6519.49i | − 0.382760i | ||||||||
\(663\) | − 3809.16i | − 0.223130i | ||||||||
\(664\) | 162.097 | 0.00947380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3901.84 | 0.227017 | ||||||||
\(667\) | 3110.19i | 0.180551i | ||||||||
\(668\) | 9949.62i | 0.576291i | ||||||||
\(669\) | −15516.1 | −0.896690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6757.98 | −0.388806 | ||||||||
\(672\) | − 285.438i | − 0.0163854i | ||||||||
\(673\) | − 21387.8i | − 1.22502i | −0.790462 | − | 0.612511i | \(-0.790160\pi\) | ||||
0.790462 | − | 0.612511i | \(-0.209840\pi\) | |||||||
\(674\) | −14326.8 | −0.818762 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8211.74 | −0.467213 | ||||||||
\(677\) | − 10494.6i | − 0.595776i | −0.954601 | − | 0.297888i | \(-0.903718\pi\) | ||||
0.954601 | − | 0.297888i | \(-0.0962821\pi\) | |||||||
\(678\) | − 10520.7i | − 0.595939i | ||||||||
\(679\) | 3331.17 | 0.188275 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14047.6 | 0.790466 | ||||||||
\(682\) | 31675.4i | 1.77847i | ||||||||
\(683\) | 24014.2i | 1.34535i | 0.739937 | + | 0.672677i | \(0.234855\pi\) | ||||
−0.739937 | + | 0.672677i | \(0.765145\pi\) | |||||||
\(684\) | −3505.07 | −0.195935 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4042.45 | −0.224988 | ||||||||
\(687\) | 6350.18i | 0.352656i | ||||||||
\(688\) | 2177.00i | 0.120636i | ||||||||
\(689\) | −4977.63 | −0.275229 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10825.8 | −0.595995 | −0.297997 | − | 0.954567i | \(-0.596319\pi\) | ||||
−0.297997 | + | 0.954567i | \(0.596319\pi\) | |||||||
\(692\) | − 14689.3i | − 0.806939i | ||||||||
\(693\) | − 3702.13i | − 0.202933i | ||||||||
\(694\) | 3666.90 | 0.200567 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3232.52 | 0.176046 | ||||||||
\(697\) | − 41913.6i | − 2.27775i | ||||||||
\(698\) | − 20800.5i | − 1.12795i | ||||||||
\(699\) | 4920.38 | 0.266246 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −171.021 | −0.00921451 | −0.00460726 | − | 0.999989i | \(-0.501467\pi\) | ||||
−0.00460726 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(702\) | − 3232.99i | − 0.173819i | ||||||||
\(703\) | 5234.69i | 0.280840i | ||||||||
\(704\) | −4392.08 | −0.235132 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6312.96 | −0.336532 | ||||||||
\(707\) | 401.701i | 0.0213685i | ||||||||
\(708\) | − 2194.28i | − 0.116477i | ||||||||
\(709\) | −28732.7 | −1.52197 | −0.760987 | − | 0.648767i | \(-0.775285\pi\) | ||||
−0.760987 | + | 0.648767i | \(0.775285\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9877.53 | −0.521007 | ||||||||
\(712\) | 8698.45i | 0.457848i | ||||||||
\(713\) | 5307.99i | 0.278802i | ||||||||
\(714\) | −1894.73 | −0.0993116 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12898.5 | −0.673240 | ||||||||
\(717\) | − 8599.31i | − 0.447904i | ||||||||
\(718\) | − 18648.3i | − 0.969288i | ||||||||
\(719\) | −6976.22 | −0.361849 | −0.180924 | − | 0.983497i | \(-0.557909\pi\) | ||||
−0.180924 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2764.13 | −0.142776 | ||||||||
\(722\) | 9015.61i | 0.464718i | ||||||||
\(723\) | − 12683.0i | − 0.652401i | ||||||||
\(724\) | 8896.91 | 0.456700 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20190.8 | 1.03216 | ||||||||
\(727\) | − 13114.6i | − 0.669042i | −0.942388 | − | 0.334521i | \(-0.891426\pi\) | ||||
0.942388 | − | 0.334521i | \(-0.108574\pi\) | |||||||
\(728\) | − 286.643i | − 0.0145930i | ||||||||
\(729\) | −9320.28 | −0.473519 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14450.9 | 0.731172 | ||||||||
\(732\) | 1177.00i | 0.0594308i | ||||||||
\(733\) | − 22681.7i | − 1.14293i | −0.820626 | − | 0.571466i | \(-0.806375\pi\) | ||||
0.820626 | − | 0.571466i | \(-0.193625\pi\) | |||||||
\(734\) | −7605.36 | −0.382451 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | − 9396.62i | − 0.469646i | ||||||||
\(738\) | − 14263.3i | − 0.711436i | ||||||||
\(739\) | −24237.8 | −1.20650 | −0.603249 | − | 0.797553i | \(-0.706127\pi\) | ||||
−0.603249 | + | 0.797553i | \(0.706127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1739.07 | 0.0862163 | ||||||||
\(742\) | 2475.95i | 0.122500i | ||||||||
\(743\) | 27356.7i | 1.35077i | 0.737466 | + | 0.675384i | \(0.236022\pi\) | ||||
−0.737466 | + | 0.675384i | \(0.763978\pi\) | |||||||
\(744\) | 5516.76 | 0.271847 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17856.1 | −0.876350 | ||||||||
\(747\) | − 366.166i | − 0.0179348i | ||||||||
\(748\) | 29154.6i | 1.42513i | ||||||||
\(749\) | −5585.63 | −0.272489 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22297.8 | 1.08343 | 0.541716 | − | 0.840561i | \(-0.317775\pi\) | ||||
0.541716 | + | 0.840561i | \(0.317775\pi\) | |||||||
\(752\) | 807.220i | 0.0391440i | ||||||||
\(753\) | 13153.5i | 0.636573i | ||||||||
\(754\) | 3246.17 | 0.156788 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1608.13 | −0.0773641 | ||||||||
\(757\) | 16088.4i | 0.772447i | 0.922405 | + | 0.386224i | \(0.126221\pi\) | ||||
−0.922405 | + | 0.386224i | \(0.873779\pi\) | |||||||
\(758\) | 7596.26i | 0.363996i | ||||||||
\(759\) | 4716.39 | 0.225552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22500.2 | 1.07179 | 0.535894 | − | 0.844285i | \(-0.319975\pi\) | ||||
0.535894 | + | 0.844285i | \(0.319975\pi\) | |||||||
\(762\) | 7535.17i | 0.358229i | ||||||||
\(763\) | − 2920.22i | − 0.138557i | ||||||||
\(764\) | −13094.1 | −0.620063 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2912.82 | 0.137395 | ||||||||
\(767\) | − 2203.54i | − 0.103736i | ||||||||
\(768\) | 764.947i | 0.0359410i | ||||||||
\(769\) | 22677.7 | 1.06343 | 0.531716 | − | 0.846923i | \(-0.321547\pi\) | ||||
0.531716 | + | 0.846923i | \(0.321547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5064.13 | 0.236550 | ||||||||
\(772\) | − 20507.5i | − 0.956062i | ||||||||
\(773\) | 20465.1i | 0.952235i | 0.879382 | + | 0.476118i | \(0.157956\pi\) | ||||
−0.879382 | + | 0.476118i | \(0.842044\pi\) | |||||||
\(774\) | 4917.69 | 0.228376 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8927.24 | −0.412976 | ||||||||
\(777\) | 962.960i | 0.0444607i | ||||||||
\(778\) | − 16422.7i | − 0.756789i | ||||||||
\(779\) | 19135.6 | 0.880108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48642.3 | −2.22863 | ||||||||
\(782\) | 4885.56i | 0.223411i | ||||||||
\(783\) | − 18211.8i | − 0.831208i | ||||||||
\(784\) | 5345.42 | 0.243505 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2655.10 | 0.120489 | ||||||||
\(787\) | 28850.8i | 1.30676i | 0.757031 | + | 0.653379i | \(0.226649\pi\) | ||||
−0.757031 | + | 0.653379i | \(0.773351\pi\) | |||||||
\(788\) | 13050.3i | 0.589971i | ||||||||
\(789\) | 2173.71 | 0.0980813 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5255.26 | −0.236227 | ||||||||
\(792\) | 9921.38i | 0.445127i | ||||||||
\(793\) | 1181.97i | 0.0529295i | ||||||||
\(794\) | −1828.73 | −0.0817370 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −673.128 | −0.0299728 | ||||||||
\(797\) | 39332.9i | 1.74811i | 0.485828 | + | 0.874054i | \(0.338518\pi\) | ||||
−0.485828 | + | 0.874054i | \(0.661482\pi\) | |||||||
\(798\) | − 865.038i | − 0.0383735i | ||||||||
\(799\) | 5358.31 | 0.237251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19649.1 | 0.866752 | ||||||||
\(802\) | − 18829.9i | − 0.829063i | ||||||||
\(803\) | − 47325.0i | − 2.07978i | ||||||||
\(804\) | −1636.56 | −0.0717875 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5540.05 | 0.242109 | ||||||||
\(807\) | − 283.848i | − 0.0123816i | ||||||||
\(808\) | − 1076.52i | − 0.0468712i | ||||||||
\(809\) | −33946.5 | −1.47527 | −0.737637 | − | 0.675198i | \(-0.764058\pi\) | ||||
−0.737637 | + | 0.675198i | \(0.764058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20772.2 | −0.899398 | −0.449699 | − | 0.893180i | \(-0.648469\pi\) | ||||
−0.449699 | + | 0.893180i | \(0.648469\pi\) | |||||||
\(812\) | − 1614.69i | − 0.0697839i | ||||||||
\(813\) | 15901.2i | 0.685951i | ||||||||
\(814\) | 14817.2 | 0.638015 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5077.71 | 0.217837 | ||||||||
\(817\) | 6597.56i | 0.282521i | ||||||||
\(818\) | 6598.83i | 0.282057i | ||||||||
\(819\) | −647.504 | −0.0276259 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6466.37 | 0.274882 | 0.137441 | − | 0.990510i | \(-0.456112\pi\) | ||||
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(822\) | − 2564.20i | − 0.108804i | ||||||||
\(823\) | − 16503.7i | − 0.699008i | −0.936935 | − | 0.349504i | \(-0.886350\pi\) | ||||
0.936935 | − | 0.349504i | \(-0.113650\pi\) | |||||||
\(824\) | 7407.63 | 0.313176 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1096.07 | −0.0461710 | ||||||||
\(827\) | − 36540.8i | − 1.53645i | −0.640177 | − | 0.768227i | \(-0.721139\pi\) | ||||
0.640177 | − | 0.768227i | \(-0.278861\pi\) | |||||||
\(828\) | 1662.57i | 0.0697805i | ||||||||
\(829\) | 24874.5 | 1.04213 | 0.521066 | − | 0.853516i | \(-0.325535\pi\) | ||||
0.521066 | + | 0.853516i | \(0.325535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7653.21 | 0.319479 | ||||||||
\(832\) | 768.177i | 0.0320093i | ||||||||
\(833\) | − 35482.8i | − 1.47588i | ||||||||
\(834\) | 1492.57 | 0.0619707 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13310.5 | −0.550662 | ||||||||
\(837\) | − 31081.0i | − 1.28353i | ||||||||
\(838\) | − 7109.28i | − 0.293062i | ||||||||
\(839\) | −15814.3 | −0.650741 | −0.325370 | − | 0.945587i | \(-0.605489\pi\) | ||||
−0.325370 | + | 0.945587i | \(0.605489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6102.97 | −0.250234 | ||||||||
\(842\) | − 23311.0i | − 0.954097i | ||||||||
\(843\) | − 26156.8i | − 1.06867i | ||||||||
\(844\) | −16788.0 | −0.684678 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1823.45 | 0.0741034 | ||||||||
\(847\) | − 10085.6i | − 0.409144i | ||||||||
\(848\) | − 6635.32i | − 0.268700i | ||||||||
\(849\) | 7171.80 | 0.289912 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2482.99 | 0.100019 | ||||||||
\(852\) | 8471.79i | 0.340656i | ||||||||
\(853\) | − 31093.2i | − 1.24808i | −0.781394 | − | 0.624039i | \(-0.785491\pi\) | ||||
0.781394 | − | 0.624039i | \(-0.214509\pi\) | |||||||
\(854\) | 587.931 | 0.0235580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14969.0 | 0.597699 | ||||||||
\(857\) | − 34212.4i | − 1.36368i | −0.731501 | − | 0.681840i | \(-0.761180\pi\) | ||||
0.731501 | − | 0.681840i | \(-0.238820\pi\) | |||||||
\(858\) | − 4922.58i | − 0.195867i | ||||||||
\(859\) | −4821.57 | −0.191513 | −0.0957567 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957567 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3520.13 | 0.139333 | ||||||||
\(862\) | − 9454.77i | − 0.373585i | ||||||||
\(863\) | 19145.6i | 0.755185i | 0.925972 | + | 0.377593i | \(0.123248\pi\) | ||||
−0.925972 | + | 0.377593i | \(0.876752\pi\) | |||||||
\(864\) | 4309.66 | 0.169696 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7872.49 | 0.308912 | ||||||||
\(867\) | − 19025.4i | − 0.745254i | ||||||||
\(868\) | − 2755.70i | − 0.107759i | ||||||||
\(869\) | −37509.9 | −1.46426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1643.47 | −0.0639345 | ||||||||
\(872\) | 7825.93i | 0.303921i | ||||||||
\(873\) | 20166.0i | 0.781804i | ||||||||
\(874\) | −2230.50 | −0.0863246 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8242.36 | −0.317904 | ||||||||
\(877\) | − 16890.8i | − 0.650354i | −0.945653 | − | 0.325177i | \(-0.894576\pi\) | ||||
0.945653 | − | 0.325177i | \(-0.105424\pi\) | |||||||
\(878\) | 13719.5i | 0.527349i | ||||||||
\(879\) | −3124.21 | −0.119883 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27802.3 | −1.06321 | −0.531603 | − | 0.846994i | \(-0.678410\pi\) | ||||
−0.531603 | + | 0.846994i | \(0.678410\pi\) | |||||||
\(882\) | − 12074.9i | − 0.460979i | ||||||||
\(883\) | 9794.15i | 0.373272i | 0.982429 | + | 0.186636i | \(0.0597585\pi\) | ||||
−0.982429 | + | 0.186636i | \(0.940241\pi\) | |||||||
\(884\) | 5099.15 | 0.194008 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33628.9 | 1.27515 | ||||||||
\(887\) | 41652.4i | 1.57672i | 0.615214 | + | 0.788360i | \(0.289070\pi\) | ||||
−0.615214 | + | 0.788360i | \(0.710930\pi\) | |||||||
\(888\) | − 2580.65i | − 0.0975235i | ||||||||
\(889\) | 3763.93 | 0.142000 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5867.80 | 0.220627 | ||||||||
\(892\) | − 20770.7i | − 0.779656i | ||||||||
\(893\) | 2446.34i | 0.0916724i | ||||||||
\(894\) | 9347.80 | 0.349706 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 382.102 | 0.0142468 | ||||||||
\(897\) | − 824.898i | − 0.0307052i | ||||||||
\(898\) | 21347.5i | 0.793293i | ||||||||
\(899\) | 31207.7 | 1.15777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44045.2 | −1.62859 | ||||||||
\(902\) | − 54164.9i | − 1.99944i | ||||||||
\(903\) | 1213.67i | 0.0447269i | ||||||||
\(904\) | 14083.6 | 0.518158 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11115.9 | −0.407617 | ||||||||
\(907\) | − 5467.21i | − 0.200150i | −0.994980 | − | 0.100075i | \(-0.968092\pi\) | ||||
0.994980 | − | 0.100075i | \(-0.0319082\pi\) | |||||||
\(908\) | 18804.9i | 0.687295i | ||||||||
\(909\) | −2431.79 | −0.0887318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33520.9 | 1.21910 | 0.609549 | − | 0.792749i | \(-0.291351\pi\) | ||||
0.609549 | + | 0.792749i | \(0.291351\pi\) | |||||||
\(912\) | 2318.23i | 0.0841712i | ||||||||
\(913\) | − 1390.52i | − 0.0504046i | ||||||||
\(914\) | −30986.1 | −1.12137 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8500.70 | −0.306628 | ||||||||
\(917\) | − 1326.26i | − 0.0477612i | ||||||||
\(918\) | − 28607.4i | − 1.02853i | ||||||||
\(919\) | −21423.9 | −0.768996 | −0.384498 | − | 0.923126i | \(-0.625625\pi\) | ||||
−0.384498 | + | 0.923126i | \(0.625625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23623.2 | −0.845182 | ||||||||
\(922\) | 21586.0i | 0.771039i | ||||||||
\(923\) | 8507.56i | 0.303391i | ||||||||
\(924\) | −2448.56 | −0.0871773 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12331.7 | −0.437631 | ||||||||
\(927\) | − 16733.3i | − 0.592873i | ||||||||
\(928\) | 4327.23i | 0.153069i | ||||||||
\(929\) | −25838.9 | −0.912538 | −0.456269 | − | 0.889842i | \(-0.650814\pi\) | ||||
−0.456269 | + | 0.889842i | \(0.650814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16199.7 | 0.570271 | ||||||||
\(932\) | 6586.69i | 0.231496i | ||||||||
\(933\) | − 27572.9i | − 0.967519i | ||||||||
\(934\) | 21472.8 | 0.752261 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1735.25 | 0.0605967 | ||||||||
\(937\) | − 48095.9i | − 1.67687i | −0.545003 | − | 0.838434i | \(-0.683472\pi\) | ||||
0.545003 | − | 0.838434i | \(-0.316528\pi\) | |||||||
\(938\) | 817.487i | 0.0284562i | ||||||||
\(939\) | −8105.38 | −0.281692 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32450.4 | −1.12418 | −0.562089 | − | 0.827077i | \(-0.690002\pi\) | ||||
−0.562089 | + | 0.827077i | \(0.690002\pi\) | |||||||
\(942\) | − 16939.5i | − 0.585903i | ||||||||
\(943\) | − 9076.66i | − 0.313443i | ||||||||
\(944\) | 2937.38 | 0.101275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18674.9 | 0.641834 | ||||||||
\(947\) | − 39067.9i | − 1.34059i | −0.742096 | − | 0.670294i | \(-0.766168\pi\) | ||||
0.742096 | − | 0.670294i | \(-0.233832\pi\) | |||||||
\(948\) | 6532.93i | 0.223818i | ||||||||
\(949\) | −8277.16 | −0.283127 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10279.8 | −0.350522 | ||||||||
\(952\) | − 2536.39i | − 0.0863496i | ||||||||
\(953\) | 17756.2i | 0.603546i | 0.953380 | + | 0.301773i | \(0.0975784\pi\) | ||||
−0.953380 | + | 0.301773i | \(0.902422\pi\) | |||||||
\(954\) | −14988.7 | −0.508676 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11511.5 | 0.389444 | ||||||||
\(957\) | − 27729.5i | − 0.936642i | ||||||||
\(958\) | 12666.6i | 0.427181i | ||||||||
\(959\) | −1280.85 | −0.0431292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23469.5 | 0.787805 | ||||||||
\(962\) | − 2591.54i | − 0.0868552i | ||||||||
\(963\) | − 33813.9i | − 1.13150i | ||||||||
\(964\) | 16978.2 | 0.567251 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −410.316 | −0.0136664 | ||||||||
\(967\) | 10696.2i | 0.355705i | 0.984057 | + | 0.177853i | \(0.0569151\pi\) | ||||
−0.984057 | + | 0.177853i | \(0.943085\pi\) | |||||||
\(968\) | 27028.5i | 0.897446i | ||||||||
\(969\) | 15388.3 | 0.510160 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53635.1 | −1.77264 | −0.886320 | − | 0.463074i | \(-0.846746\pi\) | ||||
−0.886320 | + | 0.463074i | \(0.846746\pi\) | |||||||
\(972\) | − 15567.1i | − 0.513697i | ||||||||
\(973\) | − 745.561i | − 0.0245649i | ||||||||
\(974\) | 33666.5 | 1.10754 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1575.60 | −0.0516740 | ||||||||
\(977\) | 21627.7i | 0.708220i | 0.935204 | + | 0.354110i | \(0.115216\pi\) | ||||
−0.935204 | + | 0.354110i | \(0.884784\pi\) | |||||||
\(978\) | 12636.7i | 0.413165i | ||||||||
\(979\) | 74617.7 | 2.43595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17678.2 | 0.575353 | ||||||||
\(982\) | 9.60856i | 0 0.000312242i | ||||||||
\(983\) | 12031.4i | 0.390378i | 0.980766 | + | 0.195189i | \(0.0625321\pi\) | ||||
−0.980766 | + | 0.195189i | \(0.937468\pi\) | |||||||
\(984\) | −9433.65 | −0.305624 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28724.1 | 0.927749 | ||||||||
\(987\) | 450.021i | 0.0145130i | ||||||||
\(988\) | 2328.01i | 0.0749635i | ||||||||
\(989\) | 3129.44 | 0.100617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24573.0 | −0.787675 | −0.393838 | − | 0.919180i | \(-0.628853\pi\) | ||||
−0.393838 | + | 0.919180i | \(0.628853\pi\) | |||||||
\(992\) | 7385.03i | 0.236366i | ||||||||
\(993\) | 9740.36i | 0.311280i | ||||||||
\(994\) | 4231.78 | 0.135034 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −242.180 | −0.00770458 | ||||||||
\(997\) | 14209.7i | 0.451379i | 0.974199 | + | 0.225690i | \(0.0724635\pi\) | ||||
−0.974199 | + | 0.225690i | \(0.927536\pi\) | |||||||
\(998\) | 42413.8i | 1.34527i | ||||||||
\(999\) | −14539.2 | −0.460460 |
(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 | 1150.4.b.o.599.2 | 8 | ||
5.2 | odd | 4 | 230.4.a.j.1.2 | ✓ | 4 | ||
5.3 | odd | 4 | 1150.4.a.n.1.3 | 4 | |||
5.4 | even | 2 | inner | 1150.4.b.o.599.7 | 8 | ||
15.2 | even | 4 | 2070.4.a.bg.1.2 | 4 | |||
20.7 | even | 4 | 1840.4.a.k.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.2 | ✓ | 4 | 5.2 | odd | 4 | ||
1150.4.a.n.1.3 | 4 | 5.3 | odd | 4 | |||
1150.4.b.o.599.2 | 8 | 1.1 | even | 1 | trivial | ||
1150.4.b.o.599.7 | 8 | 5.4 | even | 2 | inner | ||
1840.4.a.k.1.3 | 4 | 20.7 | even | 4 | |||
2070.4.a.bg.1.2 | 4 | 15.2 | even | 4 |