Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.a.337.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | 5.19615i | 0.464758i | 0.972625 | + | 0.232379i | \(0.0746510\pi\) | ||||
−0.972625 | + | 0.232379i | \(0.925349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 10.3923i | − 0.561132i | −0.959835 | − | 0.280566i | \(-0.909478\pi\) | ||||
0.959835 | − | 0.280566i | \(-0.0905221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.9615i | 1.42427i | 0.702042 | + | 0.712136i | \(0.252272\pi\) | ||||
−0.702042 | + | 0.712136i | \(0.747728\pi\) | |||||||
\(12\) | −24.0000 | −0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 15.5885i | − 0.268328i | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | −117.000 | −1.66922 | −0.834608 | − | 0.550845i | \(-0.814306\pi\) | ||||
−0.834608 | + | 0.550845i | \(0.814306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.2487i | 0.292791i | 0.989226 | + | 0.146396i | \(0.0467673\pi\) | ||||
−0.989226 | + | 0.146396i | \(0.953233\pi\) | |||||||
\(20\) | 41.5692i | 0.464758i | ||||||||
\(21\) | 31.1769i | 0.323970i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.0000 | 0.163185 | 0.0815926 | − | 0.996666i | \(-0.473999\pi\) | ||||
0.0815926 | + | 0.996666i | \(0.473999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 98.0000 | 0.784000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | − 83.1384i | − 0.561132i | ||||||||
\(29\) | −99.0000 | −0.633925 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.990i | 1.12392i | 0.827164 | + | 0.561961i | \(0.189953\pi\) | ||||
−0.827164 | + | 0.561961i | \(0.810047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 155.885i | − 0.822304i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 54.0000 | 0.260790 | ||||||||
\(36\) | 72.0000 | 0.333333 | ||||||||
\(37\) | 112.583i | 0.500232i | 0.968216 | + | 0.250116i | \(0.0804687\pi\) | ||||
−0.968216 | + | 0.250116i | \(0.919531\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 36.3731i | − 0.138549i | −0.997598 | − | 0.0692746i | \(-0.977932\pi\) | ||||
0.997598 | − | 0.0692746i | \(-0.0220685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −82.0000 | −0.290811 | −0.145406 | − | 0.989372i | \(-0.546449\pi\) | ||||
−0.145406 | + | 0.989372i | \(0.546449\pi\) | |||||||
\(44\) | 415.692i | 1.42427i | ||||||||
\(45\) | 46.7654i | 0.154919i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 72.7461i | − 0.225768i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) | ||||
0.993608 | − | 0.112884i | \(-0.0360089\pi\) | |||||||
\(48\) | −192.000 | −0.577350 | ||||||||
\(49\) | 235.000 | 0.685131 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 351.000 | 0.963722 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −261.000 | −0.676436 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −270.000 | −0.661942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 72.7461i | − 0.169043i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 789.815i | 1.74280i | 0.490574 | + | 0.871400i | \(0.336787\pi\) | ||||
−0.490574 | + | 0.871400i | \(0.663213\pi\) | |||||||
\(60\) | − 124.708i | − 0.268328i | ||||||||
\(61\) | −719.000 | −1.50916 | −0.754578 | − | 0.656210i | \(-0.772158\pi\) | ||||
−0.754578 | + | 0.656210i | \(0.772158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 93.5307i | − 0.187044i | ||||||||
\(64\) | 512.000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 703.213i | − 1.28226i | −0.767434 | − | 0.641128i | \(-0.778467\pi\) | ||||
0.767434 | − | 0.641128i | \(-0.221533\pi\) | |||||||
\(68\) | −936.000 | −1.66922 | ||||||||
\(69\) | −54.0000 | −0.0942150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 467.654i | 0.781694i | 0.920456 | + | 0.390847i | \(0.127818\pi\) | ||||
−0.920456 | + | 0.390847i | \(0.872182\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 684.160i | 1.09692i | 0.836178 | + | 0.548458i | \(0.184785\pi\) | ||||
−0.836178 | + | 0.548458i | \(0.815215\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −294.000 | −0.452643 | ||||||||
\(76\) | 193.990i | 0.292791i | ||||||||
\(77\) | 540.000 | 0.799204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −440.000 | −0.626631 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(80\) | 332.554i | 0.464758i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1195.12i | 1.58049i | 0.612789 | + | 0.790247i | \(0.290048\pi\) | ||||
−0.612789 | + | 0.790247i | \(0.709952\pi\) | |||||||
\(84\) | 249.415i | 0.323970i | ||||||||
\(85\) | − 607.950i | − 0.775781i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 297.000 | 0.365997 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1517.28i | 1.80709i | 0.428493 | + | 0.903545i | \(0.359045\pi\) | ||||
−0.428493 | + | 0.903545i | \(0.640955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 144.000 | 0.163185 | ||||||||
\(93\) | − 581.969i | − 0.648897i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −126.000 | −0.136077 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1157.01i | 1.21110i | 0.795808 | + | 0.605549i | \(0.207047\pi\) | ||||
−0.795808 | + | 0.605549i | \(0.792953\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 467.654i | 0.474757i | ||||||||
\(100\) | 784.000 | 0.784000 | ||||||||
\(101\) | 1575.00 | 1.55167 | 0.775833 | − | 0.630938i | \(-0.217330\pi\) | ||||
0.775833 | + | 0.630938i | \(0.217330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 794.000 | 0.759565 | 0.379782 | − | 0.925076i | \(-0.375999\pi\) | ||||
0.379782 | + | 0.925076i | \(0.375999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −162.000 | −0.150567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 450.000 | 0.406571 | 0.203286 | − | 0.979119i | \(-0.434838\pi\) | ||||
0.203286 | + | 0.979119i | \(0.434838\pi\) | |||||||
\(108\) | −216.000 | −0.192450 | ||||||||
\(109\) | 595.825i | 0.523576i | 0.965125 | + | 0.261788i | \(0.0843120\pi\) | ||||
−0.965125 | + | 0.261788i | \(0.915688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 337.750i | − 0.288809i | ||||||||
\(112\) | − 665.108i | − 0.561132i | ||||||||
\(113\) | −1701.00 | −1.41608 | −0.708038 | − | 0.706174i | \(-0.750420\pi\) | ||||
−0.708038 | + | 0.706174i | \(0.750420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 93.5307i | 0.0758416i | ||||||||
\(116\) | −792.000 | −0.633925 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1215.90i | 0.936650i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1369.00 | −1.02855 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 109.119i | 0.0799914i | ||||||||
\(124\) | 1551.92i | 1.12392i | ||||||||
\(125\) | 1158.74i | 0.829128i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1664.00 | −1.16265 | −0.581323 | − | 0.813673i | \(-0.697465\pi\) | ||||
−0.581323 | + | 0.813673i | \(0.697465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 246.000 | 0.167900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1476.00 | −0.984418 | −0.492209 | − | 0.870477i | \(-0.663810\pi\) | ||||
−0.492209 | + | 0.870477i | \(0.663810\pi\) | |||||||
\(132\) | − 1247.08i | − 0.822304i | ||||||||
\(133\) | 252.000 | 0.164295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 140.296i | − 0.0894427i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1013.25i | − 0.631882i | −0.948779 | − | 0.315941i | \(-0.897680\pi\) | ||||
0.948779 | − | 0.315941i | \(-0.102320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1124.00 | 0.685874 | 0.342937 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342937 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(140\) | 432.000 | 0.260790 | ||||||||
\(141\) | 218.238i | 0.130347i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 576.000 | 0.333333 | ||||||||
\(145\) | − 514.419i | − 0.294622i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −705.000 | −0.395561 | ||||||||
\(148\) | 900.666i | 0.500232i | ||||||||
\(149\) | − 3268.38i | − 1.79702i | −0.438952 | − | 0.898510i | \(-0.644650\pi\) | ||||
0.438952 | − | 0.898510i | \(-0.355350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1638.52i | − 0.883052i | −0.897248 | − | 0.441526i | \(-0.854437\pi\) | ||||
0.897248 | − | 0.441526i | \(-0.145563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1053.00 | −0.556405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1259.00 | 0.639995 | 0.319997 | − | 0.947418i | \(-0.396318\pi\) | ||||
0.319997 | + | 0.947418i | \(0.396318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 783.000 | 0.390540 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 187.061i | − 0.0915684i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2951.41i | − 1.41824i | −0.705089 | − | 0.709118i | \(-0.749093\pi\) | ||||
0.705089 | − | 0.709118i | \(-0.250907\pi\) | |||||||
\(164\) | − 290.985i | − 0.138549i | ||||||||
\(165\) | 810.000 | 0.382172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3138.48i | − 1.45427i | −0.686496 | − | 0.727133i | \(-0.740852\pi\) | ||||
0.686496 | − | 0.727133i | \(-0.259148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 218.238i | 0.0975971i | ||||||||
\(172\) | −656.000 | −0.290811 | ||||||||
\(173\) | 4266.00 | 1.87479 | 0.937393 | − | 0.348273i | \(-0.113232\pi\) | ||||
0.937393 | + | 0.348273i | \(0.113232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1018.45i | − 0.439927i | ||||||||
\(176\) | 3325.54i | 1.42427i | ||||||||
\(177\) | − 2369.45i | − 1.00621i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3006.00 | 1.25519 | 0.627595 | − | 0.778540i | \(-0.284039\pi\) | ||||
0.627595 | + | 0.778540i | \(0.284039\pi\) | |||||||
\(180\) | 374.123i | 0.154919i | ||||||||
\(181\) | −1873.00 | −0.769166 | −0.384583 | − | 0.923090i | \(-0.625655\pi\) | ||||
−0.384583 | + | 0.923090i | \(0.625655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2157.00 | 0.871312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −585.000 | −0.232487 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6079.50i | − 2.37742i | ||||||||
\(188\) | − 581.969i | − 0.225768i | ||||||||
\(189\) | 280.592i | 0.107990i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2736.00 | −1.03649 | −0.518246 | − | 0.855232i | \(-0.673415\pi\) | ||||
−0.518246 | + | 0.855232i | \(0.673415\pi\) | |||||||
\(192\) | −1536.00 | −0.577350 | ||||||||
\(193\) | − 2603.27i | − 0.970920i | −0.874259 | − | 0.485460i | \(-0.838652\pi\) | ||||
0.874259 | − | 0.485460i | \(-0.161348\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1880.00 | 0.685131 | ||||||||
\(197\) | 3720.45i | 1.34554i | 0.739853 | + | 0.672768i | \(0.234895\pi\) | ||||
−0.739853 | + | 0.672768i | \(0.765105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1198.00 | 0.426754 | 0.213377 | − | 0.976970i | \(-0.431554\pi\) | ||||
0.213377 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2109.64i | 0.740310i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1028.84i | 0.355716i | ||||||||
\(204\) | 2808.00 | 0.963722 | ||||||||
\(205\) | 189.000 | 0.0643919 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 162.000 | 0.0543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1260.00 | −0.417014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2392.00 | 0.780436 | 0.390218 | − | 0.920722i | \(-0.372400\pi\) | ||||
0.390218 | + | 0.920722i | \(0.372400\pi\) | |||||||
\(212\) | −2088.00 | −0.676436 | ||||||||
\(213\) | − 1402.96i | − 0.451311i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 426.084i | − 0.135157i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2016.00 | 0.630668 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2052.48i | − 0.633305i | ||||||||
\(220\) | −2160.00 | −0.661942 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2036.89i | − 0.611661i | −0.952086 | − | 0.305830i | \(-0.901066\pi\) | ||||
0.952086 | − | 0.305830i | \(-0.0989341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 882.000 | 0.261333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2151.21i | − 0.628990i | −0.949259 | − | 0.314495i | \(-0.898165\pi\) | ||||
0.949259 | − | 0.314495i | \(-0.101835\pi\) | |||||||
\(228\) | − 581.969i | − 0.169043i | ||||||||
\(229\) | 3471.03i | 1.00162i | 0.865556 | + | 0.500812i | \(0.166965\pi\) | ||||
−0.865556 | + | 0.500812i | \(0.833035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1620.00 | −0.461421 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1854.00 | −0.521286 | −0.260643 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260643 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 378.000 | 0.104928 | ||||||||
\(236\) | 6318.52i | 1.74280i | ||||||||
\(237\) | 1320.00 | 0.361786 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4458.30i | − 1.20662i | −0.797505 | − | 0.603312i | \(-0.793847\pi\) | ||||
0.797505 | − | 0.603312i | \(-0.206153\pi\) | |||||||
\(240\) | − 997.661i | − 0.268328i | ||||||||
\(241\) | 417.424i | 0.111571i | 0.998443 | + | 0.0557856i | \(0.0177663\pi\) | ||||
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −5752.00 | −1.50916 | ||||||||
\(245\) | 1221.10i | 0.318420i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 3585.35i | − 0.912498i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4104.00 | 1.03204 | 0.516020 | − | 0.856576i | \(-0.327413\pi\) | ||||
0.516020 | + | 0.856576i | \(0.327413\pi\) | |||||||
\(252\) | − 748.246i | − 0.187044i | ||||||||
\(253\) | 935.307i | 0.232420i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1823.85i | 0.447898i | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 1989.00 | 0.482764 | 0.241382 | − | 0.970430i | \(-0.422399\pi\) | ||||
0.241382 | + | 0.970430i | \(0.422399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1170.00 | 0.280696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −891.000 | −0.211308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 738.000 | 0.173031 | 0.0865153 | − | 0.996251i | \(-0.472427\pi\) | ||||
0.0865153 | + | 0.996251i | \(0.472427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 1356.20i | − 0.314379i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 4551.83i | − 1.04332i | ||||||||
\(268\) | − 5625.70i | − 1.28226i | ||||||||
\(269\) | −2106.00 | −0.477342 | −0.238671 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238671 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 685.892i | 0.153745i | 0.997041 | + | 0.0768727i | \(0.0244935\pi\) | ||||
−0.997041 | + | 0.0768727i | \(0.975507\pi\) | |||||||
\(272\) | −7488.00 | −1.66922 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5092.23i | 1.11663i | ||||||||
\(276\) | −432.000 | −0.0942150 | ||||||||
\(277\) | 3665.00 | 0.794977 | 0.397488 | − | 0.917607i | \(-0.369882\pi\) | ||||
0.397488 | + | 0.917607i | \(0.369882\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1745.91i | 0.374641i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 1719.93i | − 0.365132i | −0.983194 | − | 0.182566i | \(-0.941560\pi\) | ||||
0.983194 | − | 0.182566i | \(-0.0584404\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1826.00 | −0.383549 | −0.191775 | − | 0.981439i | \(-0.561424\pi\) | ||||
−0.191775 | + | 0.981439i | \(0.561424\pi\) | |||||||
\(284\) | 3741.23i | 0.781694i | ||||||||
\(285\) | 378.000 | 0.0785642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −378.000 | −0.0777444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8776.00 | 1.78628 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 3471.03i | − 0.699228i | ||||||||
\(292\) | 5473.28i | 1.09692i | ||||||||
\(293\) | 504.027i | 0.100497i | 0.998737 | + | 0.0502484i | \(0.0160013\pi\) | ||||
−0.998737 | + | 0.0502484i | \(0.983999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4104.00 | −0.809980 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1402.96i | − 0.274101i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2352.00 | −0.452643 | ||||||||
\(301\) | 852.169i | 0.163183i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4725.00 | −0.895855 | ||||||||
\(304\) | 1551.92i | 0.292791i | ||||||||
\(305\) | − 3736.03i | − 0.701392i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1950.29i | 0.362570i | 0.983431 | + | 0.181285i | \(0.0580256\pi\) | ||||
−0.983431 | + | 0.181285i | \(0.941974\pi\) | |||||||
\(308\) | 4320.00 | 0.799204 | ||||||||
\(309\) | −2382.00 | −0.438535 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3798.00 | −0.692491 | −0.346246 | − | 0.938144i | \(-0.612544\pi\) | ||||
−0.346246 | + | 0.938144i | \(0.612544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1378.00 | 0.248847 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 486.000 | 0.0869302 | ||||||||
\(316\) | −3520.00 | −0.626631 | ||||||||
\(317\) | 7103.14i | 1.25852i | 0.777193 | + | 0.629262i | \(0.216643\pi\) | ||||
−0.777193 | + | 0.629262i | \(0.783357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 5144.19i | − 0.902882i | ||||||||
\(320\) | 2660.43i | 0.464758i | ||||||||
\(321\) | −1350.00 | −0.234734 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2837.10i | − 0.488732i | ||||||||
\(324\) | 648.000 | 0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1787.48i | − 0.302286i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −756.000 | −0.126686 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 10073.6i | − 1.67280i | −0.548122 | − | 0.836398i | \(-0.684657\pi\) | ||||
0.548122 | − | 0.836398i | \(-0.315343\pi\) | |||||||
\(332\) | 9560.92i | 1.58049i | ||||||||
\(333\) | 1013.25i | 0.166744i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3654.00 | 0.595938 | ||||||||
\(336\) | 1995.32i | 0.323970i | ||||||||
\(337\) | 9001.00 | 1.45494 | 0.727471 | − | 0.686138i | \(-0.240695\pi\) | ||||
0.727471 | + | 0.686138i | \(0.240695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5103.00 | 0.817572 | ||||||||
\(340\) | − 4863.60i | − 0.775781i | ||||||||
\(341\) | −10080.0 | −1.60077 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6006.75i | − 0.945581i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 280.592i | − 0.0437872i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3294.00 | 0.509600 | 0.254800 | − | 0.966994i | \(-0.417990\pi\) | ||||
0.254800 | + | 0.966994i | \(0.417990\pi\) | |||||||
\(348\) | 2376.00 | 0.365997 | ||||||||
\(349\) | − 10544.7i | − 1.61732i | −0.588273 | − | 0.808662i | \(-0.700192\pi\) | ||||
0.588273 | − | 0.808662i | \(-0.299808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2478.56i | − 0.373713i | −0.982387 | − | 0.186856i | \(-0.940170\pi\) | ||||
0.982387 | − | 0.186856i | \(-0.0598299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2430.00 | −0.363299 | ||||||||
\(356\) | 12138.2i | 1.80709i | ||||||||
\(357\) | − 3647.70i | − 0.540775i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 5414.39i | − 0.795991i | −0.917387 | − | 0.397995i | \(-0.869706\pi\) | ||||
0.917387 | − | 0.397995i | \(-0.130294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6271.00 | 0.914273 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4107.00 | 0.593834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3555.00 | −0.509801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9946.00 | −1.41465 | −0.707326 | − | 0.706888i | \(-0.750099\pi\) | ||||
−0.707326 | + | 0.706888i | \(0.750099\pi\) | |||||||
\(368\) | 1152.00 | 0.163185 | ||||||||
\(369\) | − 327.358i | − 0.0461831i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2712.39i | 0.379570i | ||||||||
\(372\) | − 4655.75i | − 0.648897i | ||||||||
\(373\) | −7301.00 | −1.01349 | −0.506745 | − | 0.862096i | \(-0.669151\pi\) | ||||
−0.506745 | + | 0.862096i | \(0.669151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 3476.23i | − 0.478697i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3422.53i | − 0.463862i | −0.972732 | − | 0.231931i | \(-0.925496\pi\) | ||||
0.972732 | − | 0.231931i | \(-0.0745044\pi\) | |||||||
\(380\) | −1008.00 | −0.136077 | ||||||||
\(381\) | 4992.00 | 0.671254 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5778.12i | 0.770883i | 0.922732 | + | 0.385442i | \(0.125951\pi\) | ||||
−0.922732 | + | 0.385442i | \(0.874049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2805.92i | 0.371436i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −738.000 | −0.0969371 | ||||||||
\(388\) | 9256.08i | 1.21110i | ||||||||
\(389\) | 9153.00 | 1.19300 | 0.596498 | − | 0.802614i | \(-0.296558\pi\) | ||||
0.596498 | + | 0.802614i | \(0.296558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2106.00 | −0.272391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4428.00 | 0.568354 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2286.31i | − 0.291232i | ||||||||
\(396\) | 3741.23i | 0.474757i | ||||||||
\(397\) | − 2023.04i | − 0.255751i | −0.991790 | − | 0.127876i | \(-0.959184\pi\) | ||||
0.991790 | − | 0.127876i | \(-0.0408158\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −756.000 | −0.0948555 | ||||||||
\(400\) | 6272.00 | 0.784000 | ||||||||
\(401\) | 8308.65i | 1.03470i | 0.855774 | + | 0.517349i | \(0.173081\pi\) | ||||
−0.855774 | + | 0.517349i | \(0.826919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12600.0 | 1.55167 | ||||||||
\(405\) | 420.888i | 0.0516398i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5850.00 | −0.712466 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10418.3i | 1.25954i | 0.776782 | + | 0.629769i | \(0.216850\pi\) | ||||
−0.776782 | + | 0.629769i | \(0.783150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3039.75i | 0.364817i | ||||||||
\(412\) | 6352.00 | 0.759565 | ||||||||
\(413\) | 8208.00 | 0.977940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6210.00 | −0.734547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3372.00 | −0.395989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4176.00 | 0.486900 | 0.243450 | − | 0.969913i | \(-0.421721\pi\) | ||||
0.243450 | + | 0.969913i | \(0.421721\pi\) | |||||||
\(420\) | −1296.00 | −0.150567 | ||||||||
\(421\) | 14471.3i | 1.67527i | 0.546233 | + | 0.837633i | \(0.316061\pi\) | ||||
−0.546233 | + | 0.837633i | \(0.683939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 654.715i | − 0.0752561i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11466.0 | −1.30867 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7472.07i | 0.846835i | ||||||||
\(428\) | 3600.00 | 0.406571 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 6578.33i | − 0.735190i | −0.929986 | − | 0.367595i | \(-0.880181\pi\) | ||||
0.929986 | − | 0.367595i | \(-0.119819\pi\) | |||||||
\(432\) | −1728.00 | −0.192450 | ||||||||
\(433\) | −6605.00 | −0.733062 | −0.366531 | − | 0.930406i | \(-0.619455\pi\) | ||||
−0.366531 | + | 0.930406i | \(0.619455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1543.26i | 0.170100i | ||||||||
\(436\) | 4766.60i | 0.523576i | ||||||||
\(437\) | 436.477i | 0.0477792i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8542.00 | −0.928673 | −0.464336 | − | 0.885659i | \(-0.653707\pi\) | ||||
−0.464336 | + | 0.885659i | \(0.653707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2115.00 | 0.228377 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14328.0 | −1.53667 | −0.768334 | − | 0.640049i | \(-0.778914\pi\) | ||||
−0.768334 | + | 0.640049i | \(0.778914\pi\) | |||||||
\(444\) | − 2702.00i | − 0.288809i | ||||||||
\(445\) | −7884.00 | −0.839859 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9805.14i | 1.03751i | ||||||||
\(448\) | − 5320.86i | − 0.561132i | ||||||||
\(449\) | − 3013.77i | − 0.316767i | −0.987378 | − | 0.158384i | \(-0.949372\pi\) | ||||
0.987378 | − | 0.158384i | \(-0.0506283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1890.00 | 0.197332 | ||||||||
\(452\) | −13608.0 | −1.41608 | ||||||||
\(453\) | 4915.56i | 0.509830i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2887.33i | − 0.295544i | −0.989021 | − | 0.147772i | \(-0.952790\pi\) | ||||
0.989021 | − | 0.147772i | \(-0.0472102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3159.00 | 0.321241 | ||||||||
\(460\) | 748.246i | 0.0758416i | ||||||||
\(461\) | − 3600.93i | − 0.363801i | −0.983317 | − | 0.181900i | \(-0.941775\pi\) | ||||
0.983317 | − | 0.181900i | \(-0.0582249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2677.75i | 0.268781i | 0.990928 | + | 0.134391i | \(0.0429077\pi\) | ||||
−0.990928 | + | 0.134391i | \(0.957092\pi\) | |||||||
\(464\) | −6336.00 | −0.633925 | ||||||||
\(465\) | 3024.00 | 0.301580 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13878.0 | 1.37515 | 0.687577 | − | 0.726111i | \(-0.258674\pi\) | ||||
0.687577 | + | 0.726111i | \(0.258674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7308.00 | −0.719514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3777.00 | −0.369501 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4260.84i | − 0.414194i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2376.37i | 0.229548i | ||||||||
\(476\) | 9727.20i | 0.936650i | ||||||||
\(477\) | −2349.00 | −0.225479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1101.58i | 0.105079i | 0.998619 | + | 0.0525393i | \(0.0167315\pi\) | ||||
−0.998619 | + | 0.0525393i | \(0.983269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 561.184i | 0.0528670i | ||||||||
\(484\) | −10952.0 | −1.02855 | ||||||||
\(485\) | −6012.00 | −0.562868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17123.1i | 1.59326i | 0.604464 | + | 0.796632i | \(0.293387\pi\) | ||||
−0.604464 | + | 0.796632i | \(0.706613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8854.24i | 0.818820i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 450.000 | 0.0413609 | 0.0206805 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206805 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(492\) | 872.954i | 0.0799914i | ||||||||
\(493\) | 11583.0 | 1.05816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2430.00 | −0.220647 | ||||||||
\(496\) | 12415.3i | 1.12392i | ||||||||
\(497\) | 4860.00 | 0.438633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13219.0i | 1.18590i | 0.805239 | + | 0.592950i | \(0.202037\pi\) | ||||
−0.805239 | + | 0.592950i | \(0.797963\pi\) | |||||||
\(500\) | 9269.94i | 0.829128i | ||||||||
\(501\) | 9415.43i | 0.839621i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5346.00 | 0.473889 | 0.236945 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236945 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8183.94i | 0.721150i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13312.0 | −1.16265 | ||||||||
\(509\) | − 5866.46i | − 0.510857i | −0.966828 | − | 0.255428i | \(-0.917783\pi\) | ||||
0.966828 | − | 0.255428i | \(-0.0822165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7110.00 | 0.615514 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 654.715i | − 0.0563477i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4125.75i | 0.353014i | ||||||||
\(516\) | 1968.00 | 0.167900 | ||||||||
\(517\) | 3780.00 | 0.321556 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12798.0 | −1.08241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9657.00 | −0.812055 | −0.406028 | − | 0.913861i | \(-0.633086\pi\) | ||||
−0.406028 | + | 0.913861i | \(0.633086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21626.0 | 1.80811 | 0.904053 | − | 0.427421i | \(-0.140578\pi\) | ||||
0.904053 | + | 0.427421i | \(0.140578\pi\) | |||||||
\(524\) | −11808.0 | −0.984418 | ||||||||
\(525\) | 3055.34i | 0.253992i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 22696.8i | − 1.87607i | ||||||||
\(528\) | − 9976.61i | − 0.822304i | ||||||||
\(529\) | −11843.0 | −0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7108.34i | 0.580933i | ||||||||
\(532\) | 2016.00 | 0.164295 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2338.27i | 0.188957i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9018.00 | −0.724684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12211.0i | 0.975813i | ||||||||
\(540\) | − 1122.37i | − 0.0894427i | ||||||||
\(541\) | − 5371.09i | − 0.426841i | −0.976960 | − | 0.213421i | \(-0.931540\pi\) | ||||
0.976960 | − | 0.213421i | \(-0.0684605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5619.00 | 0.444078 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3096.00 | −0.243336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16946.0 | 1.32460 | 0.662302 | − | 0.749237i | \(-0.269579\pi\) | ||||
0.662302 | + | 0.749237i | \(0.269579\pi\) | |||||||
\(548\) | − 8106.00i | − 0.631882i | ||||||||
\(549\) | −6471.00 | −0.503052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 2400.62i | − 0.185608i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4572.61i | 0.351623i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1755.00 | 0.134226 | ||||||||
\(556\) | 8992.00 | 0.685874 | ||||||||
\(557\) | 3860.74i | 0.293689i | 0.989160 | + | 0.146845i | \(0.0469117\pi\) | ||||
−0.989160 | + | 0.146845i | \(0.953088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3456.00 | 0.260790 | ||||||||
\(561\) | 18238.5i | 1.37260i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21672.0 | 1.62232 | 0.811160 | − | 0.584825i | \(-0.198837\pi\) | ||||
0.811160 | + | 0.584825i | \(0.198837\pi\) | |||||||
\(564\) | 1745.91i | 0.130347i | ||||||||
\(565\) | − 8838.66i | − 0.658133i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 841.777i | − 0.0623480i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1386.00 | −0.102116 | −0.0510581 | − | 0.998696i | \(-0.516259\pi\) | ||||
−0.0510581 | + | 0.998696i | \(0.516259\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1162.00 | 0.0851632 | 0.0425816 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425816 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8208.00 | 0.598419 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1764.00 | 0.127937 | ||||||||
\(576\) | 4608.00 | 0.333333 | ||||||||
\(577\) | − 8045.38i | − 0.580474i | −0.956955 | − | 0.290237i | \(-0.906266\pi\) | ||||
0.956955 | − | 0.290237i | \(-0.0937341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7809.82i | 0.560561i | ||||||||
\(580\) | − 4115.35i | − 0.294622i | ||||||||
\(581\) | 12420.0 | 0.886865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 13562.0i | − 0.963429i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 27622.7i | − 1.94227i | −0.238530 | − | 0.971135i | \(-0.576665\pi\) | ||||
0.238530 | − | 0.971135i | \(-0.423335\pi\) | |||||||
\(588\) | −5640.00 | −0.395561 | ||||||||
\(589\) | −4704.00 | −0.329075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 11161.3i | − 0.776846i | ||||||||
\(592\) | 7205.33i | 0.500232i | ||||||||
\(593\) | − 275.396i | − 0.0190711i | −0.999955 | − | 0.00953555i | \(-0.996965\pi\) | ||||
0.999955 | − | 0.00953555i | \(-0.00303531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6318.00 | −0.435316 | ||||||||
\(596\) | − 26147.0i | − 1.79702i | ||||||||
\(597\) | −3594.00 | −0.246386 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22356.0 | 1.52494 | 0.762472 | − | 0.647021i | \(-0.223986\pi\) | ||||
0.762472 | + | 0.647021i | \(0.223986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18083.0 | −1.22732 | −0.613661 | − | 0.789569i | \(-0.710304\pi\) | ||||
−0.613661 | + | 0.789569i | \(0.710304\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6328.91i | − 0.427418i | ||||||||
\(604\) | − 13108.2i | − 0.883052i | ||||||||
\(605\) | − 7113.53i | − 0.478027i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5480.00 | 0.366435 | 0.183218 | − | 0.983072i | \(-0.441349\pi\) | ||||
0.183218 | + | 0.983072i | \(0.441349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − 3086.51i | − 0.205373i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8424.00 | −0.556405 | ||||||||
\(613\) | 17737.9i | 1.16872i | 0.811493 | + | 0.584362i | \(0.198655\pi\) | ||||
−0.811493 | + | 0.584362i | \(0.801345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −567.000 | −0.0371767 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 9867.49i | − 0.643842i | −0.946767 | − | 0.321921i | \(-0.895672\pi\) | ||||
0.946767 | − | 0.321921i | \(-0.104328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4115.35i | 0.267221i | 0.991034 | + | 0.133611i | \(0.0426572\pi\) | ||||
−0.991034 | + | 0.133611i | \(0.957343\pi\) | |||||||
\(620\) | −8064.00 | −0.522352 | ||||||||
\(621\) | −486.000 | −0.0314050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15768.0 | 1.01402 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6229.00 | 0.398656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3780.00 | 0.240763 | ||||||||
\(628\) | 10072.0 | 0.639995 | ||||||||
\(629\) | − 13172.2i | − 0.834995i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12664.8i | 0.799011i | 0.916731 | + | 0.399506i | \(0.130818\pi\) | ||||
−0.916731 | + | 0.399506i | \(0.869182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7176.00 | −0.450585 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8646.40i | − 0.540349i | ||||||||
\(636\) | 6264.00 | 0.390540 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4208.88i | 0.260565i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3789.00 | −0.233473 | −0.116737 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116737 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 16911.7i | − 1.03722i | −0.855010 | − | 0.518611i | \(-0.826449\pi\) | ||||
0.855010 | − | 0.518611i | \(-0.173551\pi\) | |||||||
\(644\) | − 1496.49i | − 0.0915684i | ||||||||
\(645\) | 1278.25i | 0.0780328i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27792.0 | −1.68874 | −0.844371 | − | 0.535759i | \(-0.820026\pi\) | ||||
−0.844371 | + | 0.535759i | \(0.820026\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41040.0 | −2.48222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6048.00 | −0.364116 | ||||||||
\(652\) | − 23611.3i | − 1.41824i | ||||||||
\(653\) | −594.000 | −0.0355973 | −0.0177986 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177986 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7669.52i | − 0.457516i | ||||||||
\(656\) | − 2327.88i | − 0.138549i | ||||||||
\(657\) | 6157.44i | 0.365639i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17748.0 | 1.04911 | 0.524555 | − | 0.851376i | \(-0.324232\pi\) | ||||
0.524555 | + | 0.851376i | \(0.324232\pi\) | |||||||
\(660\) | 6480.00 | 0.382172 | ||||||||
\(661\) | 15791.1i | 0.929203i | 0.885520 | + | 0.464601i | \(0.153802\pi\) | ||||
−0.885520 | + | 0.464601i | \(0.846198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1309.43i | 0.0763572i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1782.00 | −0.103447 | ||||||||
\(668\) | − 25107.8i | − 1.45427i | ||||||||
\(669\) | 6110.68i | 0.353143i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 37360.3i | − 2.14945i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20933.0 | 1.19897 | 0.599486 | − | 0.800385i | \(-0.295372\pi\) | ||||
0.599486 | + | 0.800385i | \(0.295372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2646.00 | −0.150881 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3402.00 | 0.193131 | 0.0965653 | − | 0.995327i | \(-0.469214\pi\) | ||||
0.0965653 | + | 0.995327i | \(0.469214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12024.0 | 0.679586 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6453.62i | 0.363147i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 24983.1i | − 1.39964i | −0.714321 | − | 0.699818i | \(-0.753264\pi\) | ||||
0.714321 | − | 0.699818i | \(-0.246736\pi\) | |||||||
\(684\) | 1745.91i | 0.0975971i | ||||||||
\(685\) | 5265.00 | 0.293672 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 10413.1i | − 0.578288i | ||||||||
\(688\) | −5248.00 | −0.290811 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13866.8i | 0.763412i | 0.924284 | + | 0.381706i | \(0.124663\pi\) | ||||
−0.924284 | + | 0.381706i | \(0.875337\pi\) | |||||||
\(692\) | 34128.0 | 1.87479 | ||||||||
\(693\) | 4860.00 | 0.266401 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5840.48i | 0.318765i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4255.65i | 0.231269i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5562.00 | 0.300964 | ||||||||
\(700\) | − 8147.57i | − 0.439927i | ||||||||
\(701\) | −21906.0 | −1.18028 | −0.590141 | − | 0.807300i | \(-0.700928\pi\) | ||||
−0.590141 | + | 0.807300i | \(0.700928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2730.00 | −0.146464 | ||||||||
\(704\) | 26604.3i | 1.42427i | ||||||||
\(705\) | −1134.00 | −0.0605800 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 16367.9i | − 0.870690i | ||||||||
\(708\) | − 18955.6i | − 1.00621i | ||||||||
\(709\) | 13057.9i | 0.691680i | 0.938294 | + | 0.345840i | \(0.112406\pi\) | ||||
−0.938294 | + | 0.345840i | \(0.887594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3960.00 | −0.208877 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3491.81i | 0.183407i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24048.0 | 1.25519 | ||||||||
\(717\) | 13374.9i | 0.696645i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14220.0 | −0.737575 | −0.368788 | − | 0.929514i | \(-0.620227\pi\) | ||||
−0.368788 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(720\) | 2992.98i | 0.154919i | ||||||||
\(721\) | − 8251.49i | − 0.426216i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1252.27i | − 0.0644157i | ||||||||
\(724\) | −14984.0 | −0.769166 | ||||||||
\(725\) | −9702.00 | −0.496998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5282.00 | −0.269462 | −0.134731 | − | 0.990882i | \(-0.543017\pi\) | ||||
−0.134731 | + | 0.990882i | \(0.543017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9594.00 | 0.485427 | ||||||||
\(732\) | 17256.0 | 0.871312 | ||||||||
\(733\) | 11419.4i | 0.575424i | 0.957717 | + | 0.287712i | \(0.0928945\pi\) | ||||
−0.957717 | + | 0.287712i | \(0.907105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 3663.29i | − 0.183840i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36540.0 | 1.82628 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20535.2i | − 1.02219i | −0.859524 | − | 0.511096i | \(-0.829240\pi\) | ||||
0.859524 | − | 0.511096i | \(-0.170760\pi\) | |||||||
\(740\) | −4680.00 | −0.232487 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20826.2i | − 1.02832i | −0.857696 | − | 0.514158i | \(-0.828105\pi\) | ||||
0.857696 | − | 0.514158i | \(-0.171895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16983.0 | 0.835180 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10756.0i | 0.526831i | ||||||||
\(748\) | − 48636.0i | − 2.37742i | ||||||||
\(749\) | − 4676.54i | − 0.228140i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4834.00 | −0.234880 | −0.117440 | − | 0.993080i | \(-0.537469\pi\) | ||||
−0.117440 | + | 0.993080i | \(0.537469\pi\) | |||||||
\(752\) | − 4655.75i | − 0.225768i | ||||||||
\(753\) | −12312.0 | −0.595849 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8514.00 | 0.410406 | ||||||||
\(756\) | 2244.74i | 0.107990i | ||||||||
\(757\) | 9046.00 | 0.434323 | 0.217161 | − | 0.976136i | \(-0.430320\pi\) | ||||
0.217161 | + | 0.976136i | \(0.430320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 2805.92i | − 0.134188i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12034.3i | 0.573249i | 0.958043 | + | 0.286625i | \(0.0925332\pi\) | ||||
−0.958043 | + | 0.286625i | \(0.907467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6192.00 | 0.293795 | ||||||||
\(764\) | −21888.0 | −1.03649 | ||||||||
\(765\) | − 5471.55i | − 0.258594i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12288.0 | −0.577350 | ||||||||
\(769\) | 37543.9i | 1.76056i | 0.474457 | + | 0.880279i | \(0.342645\pi\) | ||||
−0.474457 | + | 0.880279i | \(0.657355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5967.00 | −0.278724 | ||||||||
\(772\) | − 20826.2i | − 0.970920i | ||||||||
\(773\) | 15713.2i | 0.731130i | 0.930786 | + | 0.365565i | \(0.119124\pi\) | ||||
−0.930786 | + | 0.365565i | \(0.880876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19011.0i | 0.881155i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3510.00 | −0.162060 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 882.000 | 0.0405660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24300.0 | −1.11334 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2673.00 | 0.121999 | ||||||||
\(784\) | 15040.0 | 0.685131 | ||||||||
\(785\) | 6541.96i | 0.297443i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3755.09i | 0.170082i | 0.996377 | + | 0.0850409i | \(0.0271021\pi\) | ||||
−0.996377 | + | 0.0850409i | \(0.972898\pi\) | |||||||
\(788\) | 29763.6i | 1.34554i | ||||||||
\(789\) | −2214.00 | −0.0998992 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17677.3i | 0.794605i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4068.59i | 0.181507i | ||||||||
\(796\) | 9584.00 | 0.426754 | ||||||||
\(797\) | −7830.00 | −0.347996 | −0.173998 | − | 0.984746i | \(-0.555669\pi\) | ||||
−0.173998 | + | 0.984746i | \(0.555669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8511.30i | 0.376856i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13655.5i | 0.602363i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35550.0 | −1.56231 | ||||||||
\(804\) | 16877.1i | 0.740310i | ||||||||
\(805\) | 972.000 | 0.0425571 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6318.00 | 0.275594 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6165.00 | −0.267923 | −0.133962 | − | 0.990987i | \(-0.542770\pi\) | ||||
−0.133962 | + | 0.990987i | \(0.542770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 29839.8i | − 1.29201i | −0.763335 | − | 0.646003i | \(-0.776440\pi\) | ||||
0.763335 | − | 0.646003i | \(-0.223560\pi\) | |||||||
\(812\) | 8230.71i | 0.355716i | ||||||||
\(813\) | − 2057.68i | − 0.0887649i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15336.0 | 0.659137 | ||||||||
\(816\) | 22464.0 | 0.963722 | ||||||||
\(817\) | − 1988.39i | − 0.0851470i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1512.00 | 0.0643919 | ||||||||
\(821\) | − 29763.6i | − 1.26523i | −0.774466 | − | 0.632616i | \(-0.781981\pi\) | ||||
0.774466 | − | 0.632616i | \(-0.218019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8920.00 | −0.377803 | −0.188901 | − | 0.981996i | \(-0.560493\pi\) | ||||
−0.188901 | + | 0.981996i | \(0.560493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 15276.7i | − 0.644686i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 18041.0i | − 0.758583i | −0.925277 | − | 0.379292i | \(-0.876168\pi\) | ||||
0.925277 | − | 0.379292i | \(-0.123832\pi\) | |||||||
\(828\) | 1296.00 | 0.0543951 | ||||||||
\(829\) | −21023.0 | −0.880771 | −0.440385 | − | 0.897809i | \(-0.645158\pi\) | ||||
−0.440385 | + | 0.897809i | \(0.645158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10995.0 | −0.458980 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27495.0 | −1.14363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16308.0 | 0.675882 | ||||||||
\(836\) | −10080.0 | −0.417014 | ||||||||
\(837\) | − 5237.72i | − 0.216299i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22073.3i | 0.908288i | 0.890928 | + | 0.454144i | \(0.150055\pi\) | ||||
−0.890928 | + | 0.454144i | \(0.849945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14588.0 | −0.598139 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5159.78i | 0.210809i | ||||||||
\(844\) | 19136.0 | 0.780436 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14227.1i | 0.577152i | ||||||||
\(848\) | −16704.0 | −0.676436 | ||||||||
\(849\) | 5478.00 | 0.221442 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2026.50i | 0.0816304i | ||||||||
\(852\) | − 11223.7i | − 0.451311i | ||||||||
\(853\) | − 26609.5i | − 1.06810i | −0.845452 | − | 0.534051i | \(-0.820669\pi\) | ||||
0.845452 | − | 0.534051i | \(-0.179331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1134.00 | −0.0453590 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12771.0 | −0.509042 | −0.254521 | − | 0.967067i | \(-0.581918\pi\) | ||||
−0.254521 | + | 0.967067i | \(0.581918\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17134.0 | 0.680564 | 0.340282 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340282 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(860\) | − 3408.68i | − 0.135157i | ||||||||
\(861\) | 1134.00 | 0.0448857 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 7929.33i | − 0.312766i | −0.987696 | − | 0.156383i | \(-0.950017\pi\) | ||||
0.987696 | − | 0.156383i | \(-0.0499835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22166.8i | 0.871322i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26328.0 | −1.03131 | ||||||||
\(868\) | 16128.0 | 0.630668 | ||||||||
\(869\) | − 22863.1i | − 0.892493i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10413.1i | 0.403700i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12042.0 | 0.465250 | ||||||||
\(876\) | − 16419.8i | − 0.633305i | ||||||||
\(877\) | − 9864.03i | − 0.379800i | −0.981803 | − | 0.189900i | \(-0.939184\pi\) | ||||
0.981803 | − | 0.189900i | \(-0.0608164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1512.08i | − 0.0580218i | ||||||||
\(880\) | −17280.0 | −0.661942 | ||||||||
\(881\) | 29169.0 | 1.11547 | 0.557735 | − | 0.830019i | \(-0.311671\pi\) | ||||
0.557735 | + | 0.830019i | \(0.311671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 928.000 | 0.0353677 | 0.0176839 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176839 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12312.0 | 0.467642 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14400.0 | −0.545101 | −0.272551 | − | 0.962141i | \(-0.587867\pi\) | ||||
−0.272551 | + | 0.962141i | \(0.587867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17292.8i | 0.652398i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4208.88i | 0.158252i | ||||||||
\(892\) | − 16295.1i | − 0.611661i | ||||||||
\(893\) | 1764.00 | 0.0661030 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15619.6i | 0.583360i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 19205.0i | − 0.712483i | ||||||||
\(900\) | 7056.00 | 0.261333 | ||||||||
\(901\) | 30537.0 | 1.12912 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2556.51i | − 0.0942140i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 9732.39i | − 0.357476i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19684.0 | 0.720614 | 0.360307 | − | 0.932834i | \(-0.382672\pi\) | ||||
0.360307 | + | 0.932834i | \(0.382672\pi\) | |||||||
\(908\) | − 17209.7i | − 0.628990i | ||||||||
\(909\) | 14175.0 | 0.517222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24480.0 | 0.890295 | 0.445147 | − | 0.895457i | \(-0.353151\pi\) | ||||
0.445147 | + | 0.895457i | \(0.353151\pi\) | |||||||
\(912\) | − 4655.75i | − 0.169043i | ||||||||
\(913\) | −62100.0 | −2.25105 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11208.1i | 0.404949i | ||||||||
\(916\) | 27768.2i | 1.00162i | ||||||||
\(917\) | 15339.0i | 0.552388i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38608.0 | 1.38581 | 0.692906 | − | 0.721028i | \(-0.256330\pi\) | ||||
0.692906 | + | 0.721028i | \(0.256330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − 5850.87i | − 0.209330i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12960.0 | −0.461421 | ||||||||
\(925\) | 11033.2i | 0.392182i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7146.00 | 0.253188 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 10210.4i | − 0.360596i | −0.983612 | − | 0.180298i | \(-0.942294\pi\) | ||||
0.983612 | − | 0.180298i | \(-0.0577062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5698.45i | 0.200600i | ||||||||
\(932\) | −14832.0 | −0.521286 | ||||||||
\(933\) | 11394.0 | 0.399810 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31590.0 | 1.10492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28495.0 | 0.993480 | 0.496740 | − | 0.867899i | \(-0.334530\pi\) | ||||
0.496740 | + | 0.867899i | \(0.334530\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4134.00 | −0.143672 | ||||||||
\(940\) | 3024.00 | 0.104928 | ||||||||
\(941\) | 10724.9i | 0.371541i | 0.982593 | + | 0.185771i | \(0.0594782\pi\) | ||||
−0.982593 | + | 0.185771i | \(0.940522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 654.715i | − 0.0226092i | ||||||||
\(944\) | 50548.2i | 1.74280i | ||||||||
\(945\) | −1458.00 | −0.0501891 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33962.1i | 1.16538i | 0.812693 | + | 0.582692i | \(0.198001\pi\) | ||||
−0.812693 | + | 0.582692i | \(0.801999\pi\) | |||||||
\(948\) | 10560.0 | 0.361786 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 21309.4i | − 0.726609i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23814.0 | 0.809456 | 0.404728 | − | 0.914437i | \(-0.367366\pi\) | ||||
0.404728 | + | 0.914437i | \(0.367366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14216.7i | − 0.481718i | ||||||||
\(956\) | − 35666.4i | − 1.20662i | ||||||||
\(957\) | 15432.6i | 0.521279i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10530.0 | −0.354569 | ||||||||
\(960\) | − 7981.29i | − 0.268328i | ||||||||
\(961\) | −7841.00 | −0.263200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4050.00 | 0.135524 | ||||||||
\(964\) | 3339.39i | 0.111571i | ||||||||
\(965\) | 13527.0 | 0.451243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51549.3i | 1.71429i | 0.515079 | + | 0.857143i | \(0.327762\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8511.30i | 0.282170i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12312.0 | −0.406911 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(972\) | −1944.00 | −0.0641500 | ||||||||
\(973\) | − 11681.0i | − 0.384865i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46016.0 | −1.50916 | ||||||||
\(977\) | 21538.1i | 0.705285i | 0.935758 | + | 0.352642i | \(0.114717\pi\) | ||||
−0.935758 | + | 0.352642i | \(0.885283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78840.0 | −2.57379 | ||||||||
\(980\) | 9768.77i | 0.318420i | ||||||||
\(981\) | 5362.43i | 0.174525i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 32611.1i | − 1.05812i | −0.848585 | − | 0.529060i | \(-0.822545\pi\) | ||||
0.848585 | − | 0.529060i | \(-0.177455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19332.0 | −0.625349 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2268.00 | 0.0731421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1476.00 | −0.0474561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22330.0 | −0.715778 | −0.357889 | − | 0.933764i | \(-0.616503\pi\) | ||||
−0.357889 | + | 0.933764i | \(0.616503\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30220.8i | 0.965789i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6224.99i | 0.198337i | ||||||||
\(996\) | − 28682.8i | − 0.912498i | ||||||||
\(997\) | −24931.0 | −0.791949 | −0.395974 | − | 0.918262i | \(-0.629593\pi\) | ||||
−0.395974 | + | 0.918262i | \(0.629593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 3039.75i | − 0.0962697i |
(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 | 507.4.b.a.337.2 | 2 | ||
13.5 | odd | 4 | 507.4.a.g.1.2 | 2 | |||
13.8 | odd | 4 | 507.4.a.g.1.1 | 2 | |||
13.9 | even | 3 | 39.4.j.a.10.1 | yes | 2 | ||
13.10 | even | 6 | 39.4.j.a.4.1 | ✓ | 2 | ||
13.12 | even | 2 | inner | 507.4.b.a.337.1 | 2 | ||
39.5 | even | 4 | 1521.4.a.m.1.1 | 2 | |||
39.8 | even | 4 | 1521.4.a.m.1.2 | 2 | |||
39.23 | odd | 6 | 117.4.q.b.82.1 | 2 | |||
39.35 | odd | 6 | 117.4.q.b.10.1 | 2 | |||
52.23 | odd | 6 | 624.4.bv.a.433.1 | 2 | |||
52.35 | odd | 6 | 624.4.bv.a.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.a.4.1 | ✓ | 2 | 13.10 | even | 6 | ||
39.4.j.a.10.1 | yes | 2 | 13.9 | even | 3 | ||
117.4.q.b.10.1 | 2 | 39.35 | odd | 6 | |||
117.4.q.b.82.1 | 2 | 39.23 | odd | 6 | |||
507.4.a.g.1.1 | 2 | 13.8 | odd | 4 | |||
507.4.a.g.1.2 | 2 | 13.5 | odd | 4 | |||
507.4.b.a.337.1 | 2 | 13.12 | even | 2 | inner | ||
507.4.b.a.337.2 | 2 | 1.1 | even | 1 | trivial | ||
624.4.bv.a.49.1 | 2 | 52.35 | odd | 6 | |||
624.4.bv.a.433.1 | 2 | 52.23 | odd | 6 | |||
1521.4.a.m.1.1 | 2 | 39.5 | even | 4 | |||
1521.4.a.m.1.2 | 2 | 39.8 | even | 4 |