Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.6 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.5 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.28857 | −1.51624 | −0.758119 | − | 0.652116i | \(-0.773881\pi\) | ||||
−0.758119 | + | 0.652116i | \(0.773881\pi\) | |||||||
\(3\) | 2.85039i | 0.548557i | 0.961650 | + | 0.274279i | \(0.0884391\pi\) | ||||
−0.961650 | + | 0.274279i | \(0.911561\pi\) | |||||||
\(4\) | 10.3918 | 1.29898 | ||||||||
\(5\) | − 6.36629i | − 0.569418i | −0.958614 | − | 0.284709i | \(-0.908103\pi\) | ||||
0.958614 | − | 0.284709i | \(-0.0918971\pi\) | |||||||
\(6\) | − 12.2241i | − 0.831744i | ||||||||
\(7\) | − 29.4308i | − 1.58911i | −0.607190 | − | 0.794556i | \(-0.707703\pi\) | ||||
0.607190 | − | 0.794556i | \(-0.292297\pi\) | |||||||
\(8\) | −10.2575 | −0.453322 | ||||||||
\(9\) | 18.8753 | 0.699085 | ||||||||
\(10\) | 27.3023i | 0.863374i | ||||||||
\(11\) | − 61.3595i | − 1.68187i | −0.541136 | − | 0.840935i | \(-0.682005\pi\) | ||||
0.541136 | − | 0.840935i | \(-0.317995\pi\) | |||||||
\(12\) | 29.6207i | 0.712564i | ||||||||
\(13\) | 18.5582 | 0.395933 | 0.197967 | − | 0.980209i | \(-0.436566\pi\) | ||||
0.197967 | + | 0.980209i | \(0.436566\pi\) | |||||||
\(14\) | 126.216i | 2.40947i | ||||||||
\(15\) | 18.1464 | 0.312359 | ||||||||
\(16\) | −39.1446 | −0.611634 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −80.9480 | −1.05998 | ||||||||
\(19\) | −115.793 | −1.39815 | −0.699075 | − | 0.715049i | \(-0.746404\pi\) | ||||
−0.699075 | + | 0.715049i | \(0.746404\pi\) | |||||||
\(20\) | − 66.1574i | − 0.739662i | ||||||||
\(21\) | 83.8892 | 0.871720 | ||||||||
\(22\) | 263.144i | 2.55012i | ||||||||
\(23\) | 7.38352i | 0.0669378i | 0.999440 | + | 0.0334689i | \(0.0106555\pi\) | ||||
−0.999440 | + | 0.0334689i | \(0.989345\pi\) | |||||||
\(24\) | − 29.2379i | − 0.248673i | ||||||||
\(25\) | 84.4703 | 0.675763 | ||||||||
\(26\) | −79.5883 | −0.600329 | ||||||||
\(27\) | 130.762i | 0.932046i | ||||||||
\(28\) | − 305.840i | − 2.06422i | ||||||||
\(29\) | 164.974i | 1.05638i | 0.849127 | + | 0.528188i | \(0.177128\pi\) | ||||
−0.849127 | + | 0.528188i | \(0.822872\pi\) | |||||||
\(30\) | −77.8221 | −0.473610 | ||||||||
\(31\) | − 127.132i | − 0.736570i | −0.929713 | − | 0.368285i | \(-0.879945\pi\) | ||||
0.929713 | − | 0.368285i | \(-0.120055\pi\) | |||||||
\(32\) | 249.934 | 1.38070 | ||||||||
\(33\) | 174.898 | 0.922603 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −187.365 | −0.904870 | ||||||||
\(36\) | 196.149 | 0.908096 | ||||||||
\(37\) | − 158.120i | − 0.702559i | −0.936271 | − | 0.351280i | \(-0.885747\pi\) | ||||
0.936271 | − | 0.351280i | \(-0.114253\pi\) | |||||||
\(38\) | 496.588 | 2.11993 | ||||||||
\(39\) | 52.8982i | 0.217192i | ||||||||
\(40\) | 65.3022i | 0.258130i | ||||||||
\(41\) | 31.3736i | 0.119506i | 0.998213 | + | 0.0597528i | \(0.0190313\pi\) | ||||
−0.998213 | + | 0.0597528i | \(0.980969\pi\) | |||||||
\(42\) | −359.764 | −1.32173 | ||||||||
\(43\) | −157.708 | −0.559309 | −0.279654 | − | 0.960101i | \(-0.590220\pi\) | ||||
−0.279654 | + | 0.960101i | \(0.590220\pi\) | |||||||
\(44\) | − 637.637i | − 2.18471i | ||||||||
\(45\) | − 120.166i | − 0.398072i | ||||||||
\(46\) | − 31.6647i | − 0.101494i | ||||||||
\(47\) | −460.704 | −1.42980 | −0.714900 | − | 0.699227i | \(-0.753528\pi\) | ||||
−0.714900 | + | 0.699227i | \(0.753528\pi\) | |||||||
\(48\) | − 111.577i | − 0.335517i | ||||||||
\(49\) | −523.171 | −1.52528 | ||||||||
\(50\) | −362.257 | −1.02462 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 192.854 | 0.514308 | ||||||||
\(53\) | 166.846 | 0.432417 | 0.216208 | − | 0.976347i | \(-0.430631\pi\) | ||||
0.216208 | + | 0.976347i | \(0.430631\pi\) | |||||||
\(54\) | − 560.783i | − 1.41320i | ||||||||
\(55\) | −390.632 | −0.957688 | ||||||||
\(56\) | 301.886i | 0.720379i | ||||||||
\(57\) | − 330.056i | − 0.766965i | ||||||||
\(58\) | − 707.502i | − 1.60172i | ||||||||
\(59\) | 343.136 | 0.757161 | 0.378581 | − | 0.925568i | \(-0.376412\pi\) | ||||
0.378581 | + | 0.925568i | \(0.376412\pi\) | |||||||
\(60\) | 188.574 | 0.405747 | ||||||||
\(61\) | − 112.359i | − 0.235837i | −0.993023 | − | 0.117918i | \(-0.962378\pi\) | ||||
0.993023 | − | 0.117918i | \(-0.0376221\pi\) | |||||||
\(62\) | 545.216i | 1.11682i | ||||||||
\(63\) | − 555.515i | − 1.11092i | ||||||||
\(64\) | −758.704 | −1.48184 | ||||||||
\(65\) | − 118.147i | − 0.225452i | ||||||||
\(66\) | −750.063 | −1.39889 | ||||||||
\(67\) | −984.209 | −1.79463 | −0.897316 | − | 0.441390i | \(-0.854486\pi\) | ||||
−0.897316 | + | 0.441390i | \(0.854486\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.0459 | −0.0367192 | ||||||||
\(70\) | 803.528 | 1.37200 | ||||||||
\(71\) | 524.337i | 0.876442i | 0.898867 | + | 0.438221i | \(0.144391\pi\) | ||||
−0.898867 | + | 0.438221i | \(0.855609\pi\) | |||||||
\(72\) | −193.613 | −0.316910 | ||||||||
\(73\) | − 852.636i | − 1.36703i | −0.729934 | − | 0.683517i | \(-0.760449\pi\) | ||||
0.729934 | − | 0.683517i | \(-0.239551\pi\) | |||||||
\(74\) | 678.106i | 1.06525i | ||||||||
\(75\) | 240.773i | 0.370695i | ||||||||
\(76\) | −1203.30 | −1.81616 | ||||||||
\(77\) | −1805.86 | −2.67268 | ||||||||
\(78\) | − 226.858i | − 0.329315i | ||||||||
\(79\) | − 201.021i | − 0.286286i | −0.989702 | − | 0.143143i | \(-0.954279\pi\) | ||||
0.989702 | − | 0.143143i | \(-0.0457209\pi\) | |||||||
\(80\) | 249.206i | 0.348276i | ||||||||
\(81\) | 136.909 | 0.187804 | ||||||||
\(82\) | − 134.548i | − 0.181199i | ||||||||
\(83\) | 22.5351 | 0.0298017 | 0.0149009 | − | 0.999889i | \(-0.495257\pi\) | ||||
0.0149009 | + | 0.999889i | \(0.495257\pi\) | |||||||
\(84\) | 871.761 | 1.13234 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 676.342 | 0.848045 | ||||||||
\(87\) | −470.240 | −0.579483 | ||||||||
\(88\) | 629.395i | 0.762428i | ||||||||
\(89\) | 502.230 | 0.598161 | 0.299080 | − | 0.954228i | \(-0.403320\pi\) | ||||
0.299080 | + | 0.954228i | \(0.403320\pi\) | |||||||
\(90\) | 515.338i | 0.603572i | ||||||||
\(91\) | − 546.184i | − 0.629182i | ||||||||
\(92\) | 76.7282i | 0.0869507i | ||||||||
\(93\) | 362.377 | 0.404051 | ||||||||
\(94\) | 1975.76 | 2.16792 | ||||||||
\(95\) | 737.175i | 0.796132i | ||||||||
\(96\) | 712.410i | 0.757396i | ||||||||
\(97\) | − 680.691i | − 0.712512i | −0.934388 | − | 0.356256i | \(-0.884053\pi\) | ||||
0.934388 | − | 0.356256i | \(-0.115947\pi\) | |||||||
\(98\) | 2243.65 | 2.31269 | ||||||||
\(99\) | − 1158.18i | − 1.17577i | ||||||||
\(100\) | 877.801 | 0.877801 | ||||||||
\(101\) | 1921.92 | 1.89345 | 0.946724 | − | 0.322045i | \(-0.104370\pi\) | ||||
0.946724 | + | 0.322045i | \(0.104370\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1123.80 | −1.07506 | −0.537529 | − | 0.843245i | \(-0.680642\pi\) | ||||
−0.537529 | + | 0.843245i | \(0.680642\pi\) | |||||||
\(104\) | −190.361 | −0.179485 | ||||||||
\(105\) | − 534.063i | − 0.496373i | ||||||||
\(106\) | −715.532 | −0.655647 | ||||||||
\(107\) | 122.786i | 0.110937i | 0.998460 | + | 0.0554683i | \(0.0176652\pi\) | ||||
−0.998460 | + | 0.0554683i | \(0.982335\pi\) | |||||||
\(108\) | 1358.86i | 1.21071i | ||||||||
\(109\) | 791.497i | 0.695520i | 0.937584 | + | 0.347760i | \(0.113058\pi\) | ||||
−0.937584 | + | 0.347760i | \(0.886942\pi\) | |||||||
\(110\) | 1675.25 | 1.45208 | ||||||||
\(111\) | 450.702 | 0.385394 | ||||||||
\(112\) | 1152.06i | 0.971956i | ||||||||
\(113\) | − 73.7910i | − 0.0614307i | −0.999528 | − | 0.0307154i | \(-0.990221\pi\) | ||||
0.999528 | − | 0.0307154i | \(-0.00977854\pi\) | |||||||
\(114\) | 1415.47i | 1.16290i | ||||||||
\(115\) | 47.0056 | 0.0381156 | ||||||||
\(116\) | 1714.38i | 1.37221i | ||||||||
\(117\) | 350.292 | 0.276791 | ||||||||
\(118\) | −1471.56 | −1.14804 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −186.137 | −0.141599 | ||||||||
\(121\) | −2433.98 | −1.82869 | ||||||||
\(122\) | 481.857i | 0.357585i | ||||||||
\(123\) | −89.4269 | −0.0655557 | ||||||||
\(124\) | − 1321.14i | − 0.956788i | ||||||||
\(125\) | − 1333.55i | − 0.954210i | ||||||||
\(126\) | 2382.36i | 1.68443i | ||||||||
\(127\) | 1475.81 | 1.03115 | 0.515577 | − | 0.856843i | \(-0.327577\pi\) | ||||
0.515577 | + | 0.856843i | \(0.327577\pi\) | |||||||
\(128\) | 1254.28 | 0.866122 | ||||||||
\(129\) | − 449.529i | − 0.306813i | ||||||||
\(130\) | 506.682i | 0.341838i | ||||||||
\(131\) | 1029.79i | 0.686821i | 0.939185 | + | 0.343410i | \(0.111582\pi\) | ||||
−0.939185 | + | 0.343410i | \(0.888418\pi\) | |||||||
\(132\) | 1817.51 | 1.19844 | ||||||||
\(133\) | 3407.89i | 2.22182i | ||||||||
\(134\) | 4220.85 | 2.72109 | ||||||||
\(135\) | 832.471 | 0.530724 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1018.26 | −0.635008 | −0.317504 | − | 0.948257i | \(-0.602845\pi\) | ||||
−0.317504 | + | 0.948257i | \(0.602845\pi\) | |||||||
\(138\) | 90.2567 | 0.0556751 | ||||||||
\(139\) | 1506.59i | 0.919332i | 0.888092 | + | 0.459666i | \(0.152031\pi\) | ||||
−0.888092 | + | 0.459666i | \(0.847969\pi\) | |||||||
\(140\) | −1947.06 | −1.17541 | ||||||||
\(141\) | − 1313.18i | − 0.784327i | ||||||||
\(142\) | − 2248.66i | − 1.32890i | ||||||||
\(143\) | − 1138.72i | − 0.665908i | ||||||||
\(144\) | −738.865 | −0.427584 | ||||||||
\(145\) | 1050.27 | 0.601520 | ||||||||
\(146\) | 3656.59i | 2.07275i | ||||||||
\(147\) | − 1491.24i | − 0.836704i | ||||||||
\(148\) | − 1643.15i | − 0.912609i | ||||||||
\(149\) | −424.614 | −0.233462 | −0.116731 | − | 0.993164i | \(-0.537241\pi\) | ||||
−0.116731 | + | 0.993164i | \(0.537241\pi\) | |||||||
\(150\) | − 1032.57i | − 0.562061i | ||||||||
\(151\) | −1566.83 | −0.844418 | −0.422209 | − | 0.906499i | \(-0.638745\pi\) | ||||
−0.422209 | + | 0.906499i | \(0.638745\pi\) | |||||||
\(152\) | 1187.75 | 0.633811 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7744.54 | 4.05242 | ||||||||
\(155\) | −809.362 | −0.419416 | ||||||||
\(156\) | 549.709i | 0.282128i | ||||||||
\(157\) | −762.291 | −0.387500 | −0.193750 | − | 0.981051i | \(-0.562065\pi\) | ||||
−0.193750 | + | 0.981051i | \(0.562065\pi\) | |||||||
\(158\) | 862.092i | 0.434078i | ||||||||
\(159\) | 475.577i | 0.237206i | ||||||||
\(160\) | − 1591.15i | − 0.786199i | ||||||||
\(161\) | 217.303 | 0.106372 | ||||||||
\(162\) | −587.145 | −0.284756 | ||||||||
\(163\) | − 2253.74i | − 1.08299i | −0.840705 | − | 0.541493i | \(-0.817859\pi\) | ||||
0.840705 | − | 0.541493i | \(-0.182141\pi\) | |||||||
\(164\) | 326.029i | 0.155235i | ||||||||
\(165\) | − 1113.45i | − 0.525347i | ||||||||
\(166\) | −96.6432 | −0.0451865 | ||||||||
\(167\) | − 1995.81i | − 0.924792i | −0.886673 | − | 0.462396i | \(-0.846990\pi\) | ||||
0.886673 | − | 0.462396i | \(-0.153010\pi\) | |||||||
\(168\) | −860.493 | −0.395169 | ||||||||
\(169\) | −1852.59 | −0.843237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2185.63 | −0.977425 | ||||||||
\(172\) | −1638.88 | −0.726529 | ||||||||
\(173\) | 1853.93i | 0.814749i | 0.913261 | + | 0.407375i | \(0.133556\pi\) | ||||
−0.913261 | + | 0.407375i | \(0.866444\pi\) | |||||||
\(174\) | 2016.66 | 0.878634 | ||||||||
\(175\) | − 2486.03i | − 1.07386i | ||||||||
\(176\) | 2401.89i | 1.02869i | ||||||||
\(177\) | 978.071i | 0.415346i | ||||||||
\(178\) | −2153.85 | −0.906954 | ||||||||
\(179\) | 1623.39 | 0.677865 | 0.338933 | − | 0.940811i | \(-0.389934\pi\) | ||||
0.338933 | + | 0.940811i | \(0.389934\pi\) | |||||||
\(180\) | − 1248.74i | − 0.517086i | ||||||||
\(181\) | 759.107i | 0.311735i | 0.987778 | + | 0.155867i | \(0.0498173\pi\) | ||||
−0.987778 | + | 0.155867i | \(0.950183\pi\) | |||||||
\(182\) | 2342.35i | 0.953990i | ||||||||
\(183\) | 320.266 | 0.129370 | ||||||||
\(184\) | − 75.7364i | − 0.0303444i | ||||||||
\(185\) | −1006.64 | −0.400050 | ||||||||
\(186\) | −1554.08 | −0.612637 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4787.55 | −1.85728 | ||||||||
\(189\) | 3848.44 | 1.48113 | ||||||||
\(190\) | − 3161.42i | − 1.20713i | ||||||||
\(191\) | −1878.32 | −0.711572 | −0.355786 | − | 0.934567i | \(-0.615787\pi\) | ||||
−0.355786 | + | 0.934567i | \(0.615787\pi\) | |||||||
\(192\) | − 2162.60i | − 0.812876i | ||||||||
\(193\) | 497.364i | 0.185498i | 0.995690 | + | 0.0927489i | \(0.0295654\pi\) | ||||
−0.995690 | + | 0.0927489i | \(0.970435\pi\) | |||||||
\(194\) | 2919.19i | 1.08034i | ||||||||
\(195\) | 336.765 | 0.123673 | ||||||||
\(196\) | −5436.70 | −1.98130 | ||||||||
\(197\) | − 1052.05i | − 0.380486i | −0.981737 | − | 0.190243i | \(-0.939072\pi\) | ||||
0.981737 | − | 0.190243i | \(-0.0609276\pi\) | |||||||
\(198\) | 4966.92i | 1.78275i | ||||||||
\(199\) | − 1783.55i | − 0.635338i | −0.948202 | − | 0.317669i | \(-0.897100\pi\) | ||||
0.948202 | − | 0.317669i | \(-0.102900\pi\) | |||||||
\(200\) | −866.454 | −0.306338 | ||||||||
\(201\) | − 2805.38i | − 0.984458i | ||||||||
\(202\) | −8242.29 | −2.87092 | ||||||||
\(203\) | 4855.31 | 1.67870 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 199.733 | 0.0680487 | ||||||||
\(206\) | 4819.48 | 1.63004 | ||||||||
\(207\) | 139.366i | 0.0467952i | ||||||||
\(208\) | −726.455 | −0.242166 | ||||||||
\(209\) | 7105.02i | 2.35151i | ||||||||
\(210\) | 2290.37i | 0.752620i | ||||||||
\(211\) | − 3756.09i | − 1.22550i | −0.790278 | − | 0.612748i | \(-0.790064\pi\) | ||||
0.790278 | − | 0.612748i | \(-0.209936\pi\) | |||||||
\(212\) | 1733.84 | 0.561700 | ||||||||
\(213\) | −1494.57 | −0.480779 | ||||||||
\(214\) | − 526.578i | − 0.168206i | ||||||||
\(215\) | 1004.02i | 0.318481i | ||||||||
\(216\) | − 1341.30i | − 0.422517i | ||||||||
\(217\) | −3741.61 | −1.17049 | ||||||||
\(218\) | − 3394.39i | − 1.05457i | ||||||||
\(219\) | 2430.34 | 0.749897 | ||||||||
\(220\) | −4059.38 | −1.24402 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1932.87 | −0.584349 | ||||||||
\(223\) | 3356.40 | 1.00790 | 0.503949 | − | 0.863733i | \(-0.331880\pi\) | ||||
0.503949 | + | 0.863733i | \(0.331880\pi\) | |||||||
\(224\) | − 7355.76i | − 2.19410i | ||||||||
\(225\) | 1594.40 | 0.472415 | ||||||||
\(226\) | 316.458i | 0.0931436i | ||||||||
\(227\) | − 1988.64i | − 0.581457i | −0.956806 | − | 0.290728i | \(-0.906102\pi\) | ||||
0.956806 | − | 0.290728i | \(-0.0938976\pi\) | |||||||
\(228\) | − 3429.89i | − 0.996271i | ||||||||
\(229\) | −5203.50 | −1.50156 | −0.750779 | − | 0.660554i | \(-0.770322\pi\) | ||||
−0.750779 | + | 0.660554i | \(0.770322\pi\) | |||||||
\(230\) | −201.587 | −0.0577924 | ||||||||
\(231\) | − 5147.39i | − 1.46612i | ||||||||
\(232\) | − 1692.22i | − 0.478878i | ||||||||
\(233\) | − 5702.70i | − 1.60342i | −0.597714 | − | 0.801709i | \(-0.703924\pi\) | ||||
0.597714 | − | 0.801709i | \(-0.296076\pi\) | |||||||
\(234\) | −1502.25 | −0.419681 | ||||||||
\(235\) | 2932.98i | 0.814154i | ||||||||
\(236\) | 3565.81 | 0.983536 | ||||||||
\(237\) | 572.988 | 0.157045 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1418.04 | 0.383787 | 0.191894 | − | 0.981416i | \(-0.438537\pi\) | ||||
0.191894 | + | 0.981416i | \(0.438537\pi\) | |||||||
\(240\) | −710.334 | −0.191049 | ||||||||
\(241\) | 6215.71i | 1.66137i | 0.556746 | + | 0.830683i | \(0.312050\pi\) | ||||
−0.556746 | + | 0.830683i | \(0.687950\pi\) | |||||||
\(242\) | 10438.3 | 2.77273 | ||||||||
\(243\) | 3920.83i | 1.03507i | ||||||||
\(244\) | − 1167.61i | − 0.306347i | ||||||||
\(245\) | 3330.66i | 0.868523i | ||||||||
\(246\) | 383.514 | 0.0993981 | ||||||||
\(247\) | −2148.92 | −0.553573 | ||||||||
\(248\) | 1304.06i | 0.333903i | ||||||||
\(249\) | 64.2337i | 0.0163480i | ||||||||
\(250\) | 5719.02i | 1.44681i | ||||||||
\(251\) | 1547.45 | 0.389139 | 0.194570 | − | 0.980889i | \(-0.437669\pi\) | ||||
0.194570 | + | 0.980889i | \(0.437669\pi\) | |||||||
\(252\) | − 5772.81i | − 1.44307i | ||||||||
\(253\) | 453.049 | 0.112581 | ||||||||
\(254\) | −6329.10 | −1.56348 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 690.569 | 0.168596 | ||||||||
\(257\) | −7251.45 | −1.76005 | −0.880025 | − | 0.474928i | \(-0.842474\pi\) | ||||
−0.880025 | + | 0.474928i | \(0.842474\pi\) | |||||||
\(258\) | 1927.84i | 0.465201i | ||||||||
\(259\) | −4653.58 | −1.11645 | ||||||||
\(260\) | − 1227.76i | − 0.292857i | ||||||||
\(261\) | 3113.93i | 0.738496i | ||||||||
\(262\) | − 4416.34i | − 1.04138i | ||||||||
\(263\) | −4635.13 | −1.08675 | −0.543373 | − | 0.839491i | \(-0.682853\pi\) | ||||
−0.543373 | + | 0.839491i | \(0.682853\pi\) | |||||||
\(264\) | −1794.02 | −0.418236 | ||||||||
\(265\) | − 1062.19i | − 0.246226i | ||||||||
\(266\) | − 14615.0i | − 3.36880i | ||||||||
\(267\) | 1431.55i | 0.328126i | ||||||||
\(268\) | −10227.7 | −2.33119 | ||||||||
\(269\) | 7116.95i | 1.61311i | 0.591156 | + | 0.806557i | \(0.298672\pi\) | ||||
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(270\) | −3570.11 | −0.804704 | ||||||||
\(271\) | 163.713 | 0.0366970 | 0.0183485 | − | 0.999832i | \(-0.494159\pi\) | ||||
0.0183485 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1556.83 | 0.345143 | ||||||||
\(274\) | 4366.89 | 0.962823 | ||||||||
\(275\) | − 5183.05i | − 1.13655i | ||||||||
\(276\) | −218.705 | −0.0476975 | ||||||||
\(277\) | − 4174.84i | − 0.905567i | −0.891620 | − | 0.452784i | \(-0.850431\pi\) | ||||
0.891620 | − | 0.452784i | \(-0.149569\pi\) | |||||||
\(278\) | − 6461.11i | − 1.39393i | ||||||||
\(279\) | − 2399.66i | − 0.514925i | ||||||||
\(280\) | 1921.90 | 0.410197 | ||||||||
\(281\) | 6920.09 | 1.46910 | 0.734551 | − | 0.678553i | \(-0.237393\pi\) | ||||
0.734551 | + | 0.678553i | \(0.237393\pi\) | |||||||
\(282\) | 5631.68i | 1.18923i | ||||||||
\(283\) | − 6292.91i | − 1.32182i | −0.750466 | − | 0.660909i | \(-0.770171\pi\) | ||||
0.750466 | − | 0.660909i | \(-0.229829\pi\) | |||||||
\(284\) | 5448.82i | 1.13848i | ||||||||
\(285\) | −2101.23 | −0.436724 | ||||||||
\(286\) | 4883.50i | 1.00968i | ||||||||
\(287\) | 923.350 | 0.189908 | ||||||||
\(288\) | 4717.58 | 0.965230 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −4504.17 | −0.912048 | ||||||||
\(291\) | 1940.23 | 0.390854 | ||||||||
\(292\) | − 8860.45i | − 1.77575i | ||||||||
\(293\) | 2292.96 | 0.457189 | 0.228595 | − | 0.973522i | \(-0.426587\pi\) | ||||
0.228595 | + | 0.973522i | \(0.426587\pi\) | |||||||
\(294\) | 6395.29i | 1.26864i | ||||||||
\(295\) | − 2184.50i | − 0.431142i | ||||||||
\(296\) | 1621.91i | 0.318485i | ||||||||
\(297\) | 8023.51 | 1.56758 | ||||||||
\(298\) | 1820.99 | 0.353983 | ||||||||
\(299\) | 137.025i | 0.0265029i | ||||||||
\(300\) | 2502.07i | 0.481524i | ||||||||
\(301\) | 4641.47i | 0.888804i | ||||||||
\(302\) | 6719.47 | 1.28034 | ||||||||
\(303\) | 5478.22i | 1.03867i | ||||||||
\(304\) | 4532.69 | 0.855156 | ||||||||
\(305\) | −715.308 | −0.134290 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2300.11 | 0.427604 | 0.213802 | − | 0.976877i | \(-0.431415\pi\) | ||||
0.213802 | + | 0.976877i | \(0.431415\pi\) | |||||||
\(308\) | −18766.1 | −3.47176 | ||||||||
\(309\) | − 3203.26i | − 0.589731i | ||||||||
\(310\) | 3471.01 | 0.635935 | ||||||||
\(311\) | 5775.22i | 1.05300i | 0.850175 | + | 0.526499i | \(0.176496\pi\) | ||||
−0.850175 | + | 0.526499i | \(0.823504\pi\) | |||||||
\(312\) | − 542.603i | − 0.0984579i | ||||||||
\(313\) | − 2799.69i | − 0.505585i | −0.967521 | − | 0.252792i | \(-0.918651\pi\) | ||||
0.967521 | − | 0.252792i | \(-0.0813490\pi\) | |||||||
\(314\) | 3269.14 | 0.587542 | ||||||||
\(315\) | −3536.57 | −0.632581 | ||||||||
\(316\) | − 2088.97i | − 0.371880i | ||||||||
\(317\) | − 5140.47i | − 0.910781i | −0.890292 | − | 0.455390i | \(-0.849500\pi\) | ||||
0.890292 | − | 0.455390i | \(-0.150500\pi\) | |||||||
\(318\) | − 2039.54i | − 0.359660i | ||||||||
\(319\) | 10122.7 | 1.77669 | ||||||||
\(320\) | 4830.13i | 0.843789i | ||||||||
\(321\) | −349.989 | −0.0608550 | ||||||||
\(322\) | −931.917 | −0.161285 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1422.74 | 0.243954 | ||||||||
\(325\) | 1567.62 | 0.267557 | ||||||||
\(326\) | 9665.33i | 1.64206i | ||||||||
\(327\) | −2256.07 | −0.381533 | ||||||||
\(328\) | − 321.815i | − 0.0541745i | ||||||||
\(329\) | 13558.9i | 2.27211i | ||||||||
\(330\) | 4775.12i | 0.796551i | ||||||||
\(331\) | −459.510 | −0.0763050 | −0.0381525 | − | 0.999272i | \(-0.512147\pi\) | ||||
−0.0381525 | + | 0.999272i | \(0.512147\pi\) | |||||||
\(332\) | 234.180 | 0.0387118 | ||||||||
\(333\) | − 2984.55i | − 0.491148i | ||||||||
\(334\) | 8559.16i | 1.40221i | ||||||||
\(335\) | 6265.76i | 1.02190i | ||||||||
\(336\) | −3283.81 | −0.533174 | ||||||||
\(337\) | − 6233.46i | − 1.00759i | −0.863823 | − | 0.503796i | \(-0.831937\pi\) | ||||
0.863823 | − | 0.503796i | \(-0.168063\pi\) | |||||||
\(338\) | 7944.97 | 1.27855 | ||||||||
\(339\) | 210.333 | 0.0336983 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7800.78 | −1.23882 | ||||||||
\(342\) | 9373.24 | 1.48201 | ||||||||
\(343\) | 5302.57i | 0.834729i | ||||||||
\(344\) | 1617.69 | 0.253547 | ||||||||
\(345\) | 133.984i | 0.0209086i | ||||||||
\(346\) | − 7950.70i | − 1.23535i | ||||||||
\(347\) | 6370.01i | 0.985476i | 0.870178 | + | 0.492738i | \(0.164004\pi\) | ||||
−0.870178 | + | 0.492738i | \(0.835996\pi\) | |||||||
\(348\) | −4886.65 | −0.752735 | ||||||||
\(349\) | 6494.79 | 0.996155 | 0.498078 | − | 0.867132i | \(-0.334039\pi\) | ||||
0.498078 | + | 0.867132i | \(0.334039\pi\) | |||||||
\(350\) | 10661.5i | 1.62823i | ||||||||
\(351\) | 2426.72i | 0.369028i | ||||||||
\(352\) | − 15335.8i | − 2.32217i | ||||||||
\(353\) | 502.630 | 0.0757856 | 0.0378928 | − | 0.999282i | \(-0.487935\pi\) | ||||
0.0378928 | + | 0.999282i | \(0.487935\pi\) | |||||||
\(354\) | − 4194.53i | − 0.629764i | ||||||||
\(355\) | 3338.09 | 0.499062 | ||||||||
\(356\) | 5219.09 | 0.776998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6962.02 | −1.02781 | ||||||||
\(359\) | 974.431 | 0.143255 | 0.0716275 | − | 0.997431i | \(-0.477181\pi\) | ||||
0.0716275 | + | 0.997431i | \(0.477181\pi\) | |||||||
\(360\) | 1232.60i | 0.180455i | ||||||||
\(361\) | 6549.11 | 0.954821 | ||||||||
\(362\) | − 3255.48i | − 0.472664i | ||||||||
\(363\) | − 6937.80i | − 1.00314i | ||||||||
\(364\) | − 5675.84i | − 0.817294i | ||||||||
\(365\) | −5428.13 | −0.778415 | ||||||||
\(366\) | −1373.48 | −0.196156 | ||||||||
\(367\) | 4693.11i | 0.667515i | 0.942659 | + | 0.333758i | \(0.108317\pi\) | ||||
−0.942659 | + | 0.333758i | \(0.891683\pi\) | |||||||
\(368\) | − 289.025i | − 0.0409415i | ||||||||
\(369\) | 592.186i | 0.0835446i | ||||||||
\(370\) | 4317.02 | 0.606571 | ||||||||
\(371\) | − 4910.42i | − 0.687159i | ||||||||
\(372\) | 3765.76 | 0.524853 | ||||||||
\(373\) | 8651.16 | 1.20091 | 0.600456 | − | 0.799658i | \(-0.294986\pi\) | ||||
0.600456 | + | 0.799658i | \(0.294986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3801.13 | 0.523439 | ||||||||
\(376\) | 4725.67 | 0.648159 | ||||||||
\(377\) | 3061.63i | 0.418254i | ||||||||
\(378\) | −16504.3 | −2.24574 | ||||||||
\(379\) | − 3490.01i | − 0.473007i | −0.971631 | − | 0.236503i | \(-0.923999\pi\) | ||||
0.971631 | − | 0.236503i | \(-0.0760014\pi\) | |||||||
\(380\) | 7660.59i | 1.03416i | ||||||||
\(381\) | 4206.62i | 0.565648i | ||||||||
\(382\) | 8055.29 | 1.07891 | ||||||||
\(383\) | −3928.41 | −0.524105 | −0.262052 | − | 0.965054i | \(-0.584399\pi\) | ||||
−0.262052 | + | 0.965054i | \(0.584399\pi\) | |||||||
\(384\) | 3575.18i | 0.475118i | ||||||||
\(385\) | 11496.6i | 1.52187i | ||||||||
\(386\) | − 2132.98i | − 0.281259i | ||||||||
\(387\) | −2976.79 | −0.391004 | ||||||||
\(388\) | − 7073.62i | − 0.925537i | ||||||||
\(389\) | −6961.15 | −0.907312 | −0.453656 | − | 0.891177i | \(-0.649880\pi\) | ||||
−0.453656 | + | 0.891177i | \(0.649880\pi\) | |||||||
\(390\) | −1444.24 | −0.187518 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5366.43 | 0.691443 | ||||||||
\(393\) | −2935.31 | −0.376761 | ||||||||
\(394\) | 4511.81i | 0.576908i | ||||||||
\(395\) | −1279.76 | −0.163017 | ||||||||
\(396\) | − 12035.6i | − 1.52730i | ||||||||
\(397\) | 5331.94i | 0.674062i | 0.941494 | + | 0.337031i | \(0.109423\pi\) | ||||
−0.941494 | + | 0.337031i | \(0.890577\pi\) | |||||||
\(398\) | 7648.86i | 0.963323i | ||||||||
\(399\) | −9713.81 | −1.21879 | ||||||||
\(400\) | −3306.56 | −0.413320 | ||||||||
\(401\) | 546.021i | 0.0679975i | 0.999422 | + | 0.0339988i | \(0.0108242\pi\) | ||||
−0.999422 | + | 0.0339988i | \(0.989176\pi\) | |||||||
\(402\) | 12031.1i | 1.49267i | ||||||||
\(403\) | − 2359.35i | − 0.291632i | ||||||||
\(404\) | 19972.3 | 2.45955 | ||||||||
\(405\) | − 871.604i | − 0.106939i | ||||||||
\(406\) | −20822.3 | −2.54531 | ||||||||
\(407\) | −9702.13 | −1.18161 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15964.6 | 1.93007 | 0.965037 | − | 0.262114i | \(-0.0844196\pi\) | ||||
0.965037 | + | 0.262114i | \(0.0844196\pi\) | |||||||
\(410\) | −856.571 | −0.103178 | ||||||||
\(411\) | − 2902.44i | − 0.348338i | ||||||||
\(412\) | −11678.3 | −1.39648 | ||||||||
\(413\) | − 10098.8i | − 1.20321i | ||||||||
\(414\) | − 597.681i | − 0.0709527i | ||||||||
\(415\) | − 143.465i | − 0.0169697i | ||||||||
\(416\) | 4638.34 | 0.546667 | ||||||||
\(417\) | −4294.36 | −0.504306 | ||||||||
\(418\) | − 30470.4i | − 3.56544i | ||||||||
\(419\) | 7643.91i | 0.891240i | 0.895222 | + | 0.445620i | \(0.147017\pi\) | ||||
−0.895222 | + | 0.445620i | \(0.852983\pi\) | |||||||
\(420\) | − 5549.89i | − 0.644778i | ||||||||
\(421\) | −7524.14 | −0.871031 | −0.435516 | − | 0.900181i | \(-0.643434\pi\) | ||||
−0.435516 | + | 0.900181i | \(0.643434\pi\) | |||||||
\(422\) | 16108.2i | 1.85814i | ||||||||
\(423\) | −8695.92 | −0.999551 | ||||||||
\(424\) | −1711.43 | −0.196024 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6409.55 | 0.728975 | ||||||||
\(427\) | −3306.80 | −0.374771 | ||||||||
\(428\) | 1275.97i | 0.144104i | ||||||||
\(429\) | 3245.80 | 0.365289 | ||||||||
\(430\) | − 4305.79i | − 0.482892i | ||||||||
\(431\) | − 12222.4i | − 1.36597i | −0.730431 | − | 0.682986i | \(-0.760681\pi\) | ||||
0.730431 | − | 0.682986i | \(-0.239319\pi\) | |||||||
\(432\) | − 5118.64i | − 0.570071i | ||||||||
\(433\) | 15420.3 | 1.71144 | 0.855719 | − | 0.517440i | \(-0.173115\pi\) | ||||
0.855719 | + | 0.517440i | \(0.173115\pi\) | |||||||
\(434\) | 16046.1 | 1.77475 | ||||||||
\(435\) | 2993.68i | 0.329968i | ||||||||
\(436\) | 8225.10i | 0.903465i | ||||||||
\(437\) | − 854.963i | − 0.0935890i | ||||||||
\(438\) | −10422.7 | −1.13702 | ||||||||
\(439\) | − 17832.7i | − 1.93874i | −0.245607 | − | 0.969369i | \(-0.578987\pi\) | ||||
0.245607 | − | 0.969369i | \(-0.421013\pi\) | |||||||
\(440\) | 4006.91 | 0.434141 | ||||||||
\(441\) | −9875.00 | −1.06630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 241.629 | 0.0259145 | 0.0129573 | − | 0.999916i | \(-0.495875\pi\) | ||||
0.0129573 | + | 0.999916i | \(0.495875\pi\) | |||||||
\(444\) | 4683.62 | 0.500618 | ||||||||
\(445\) | − 3197.35i | − 0.340604i | ||||||||
\(446\) | −14394.2 | −1.52821 | ||||||||
\(447\) | − 1210.32i | − 0.128067i | ||||||||
\(448\) | 22329.2i | 2.35482i | ||||||||
\(449\) | − 14481.4i | − 1.52209i | −0.648698 | − | 0.761046i | \(-0.724686\pi\) | ||||
0.648698 | − | 0.761046i | \(-0.275314\pi\) | |||||||
\(450\) | −6837.70 | −0.716294 | ||||||||
\(451\) | 1925.07 | 0.200993 | ||||||||
\(452\) | − 766.823i | − 0.0797971i | ||||||||
\(453\) | − 4466.08i | − 0.463211i | ||||||||
\(454\) | 8528.42i | 0.881627i | ||||||||
\(455\) | −3477.16 | −0.358268 | ||||||||
\(456\) | 3385.55i | 0.347682i | ||||||||
\(457\) | 1814.51 | 0.185731 | 0.0928654 | − | 0.995679i | \(-0.470397\pi\) | ||||
0.0928654 | + | 0.995679i | \(0.470397\pi\) | |||||||
\(458\) | 22315.6 | 2.27672 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 488.474 | 0.0495114 | ||||||||
\(461\) | 13434.1 | 1.35724 | 0.678621 | − | 0.734489i | \(-0.262578\pi\) | ||||
0.678621 | + | 0.734489i | \(0.262578\pi\) | |||||||
\(462\) | 22075.0i | 2.22299i | ||||||||
\(463\) | −16593.9 | −1.66562 | −0.832810 | − | 0.553559i | \(-0.813269\pi\) | ||||
−0.832810 | + | 0.553559i | \(0.813269\pi\) | |||||||
\(464\) | − 6457.84i | − 0.646116i | ||||||||
\(465\) | − 2307.00i | − 0.230074i | ||||||||
\(466\) | 24456.4i | 2.43116i | ||||||||
\(467\) | 3944.12 | 0.390818 | 0.195409 | − | 0.980722i | \(-0.437397\pi\) | ||||
0.195409 | + | 0.980722i | \(0.437397\pi\) | |||||||
\(468\) | 3640.17 | 0.359545 | ||||||||
\(469\) | 28966.0i | 2.85187i | ||||||||
\(470\) | − 12578.3i | − 1.23445i | ||||||||
\(471\) | − 2172.83i | − 0.212566i | ||||||||
\(472\) | −3519.72 | −0.343238 | ||||||||
\(473\) | 9676.89i | 0.940685i | ||||||||
\(474\) | −2457.30 | −0.238117 | ||||||||
\(475\) | −9781.11 | −0.944817 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3149.27 | 0.302296 | ||||||||
\(478\) | −6081.35 | −0.581913 | ||||||||
\(479\) | − 11162.8i | − 1.06480i | −0.846492 | − | 0.532401i | \(-0.821290\pi\) | ||||
0.846492 | − | 0.532401i | \(-0.178710\pi\) | |||||||
\(480\) | 4535.41 | 0.431275 | ||||||||
\(481\) | − 2934.42i | − 0.278166i | ||||||||
\(482\) | − 26656.5i | − 2.51903i | ||||||||
\(483\) | 619.397i | 0.0583510i | ||||||||
\(484\) | −25293.5 | −2.37543 | ||||||||
\(485\) | −4333.48 | −0.405717 | ||||||||
\(486\) | − 16814.7i | − 1.56941i | ||||||||
\(487\) | 9984.01i | 0.928991i | 0.885575 | + | 0.464496i | \(0.153764\pi\) | ||||
−0.885575 | + | 0.464496i | \(0.846236\pi\) | |||||||
\(488\) | 1152.52i | 0.106910i | ||||||||
\(489\) | 6424.04 | 0.594080 | ||||||||
\(490\) | − 14283.8i | − 1.31689i | ||||||||
\(491\) | 19639.7 | 1.80514 | 0.902572 | − | 0.430540i | \(-0.141677\pi\) | ||||
0.902572 | + | 0.430540i | \(0.141677\pi\) | |||||||
\(492\) | −929.309 | −0.0851554 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 9215.80 | 0.839349 | ||||||||
\(495\) | −7373.30 | −0.669505 | ||||||||
\(496\) | 4976.55i | 0.450511i | ||||||||
\(497\) | 15431.7 | 1.39277 | ||||||||
\(498\) | − 275.470i | − 0.0247874i | ||||||||
\(499\) | 5764.32i | 0.517127i | 0.965994 | + | 0.258564i | \(0.0832491\pi\) | ||||
−0.965994 | + | 0.258564i | \(0.916751\pi\) | |||||||
\(500\) | − 13858.0i | − 1.23950i | ||||||||
\(501\) | 5688.83 | 0.507302 | ||||||||
\(502\) | −6636.33 | −0.590027 | ||||||||
\(503\) | − 1747.34i | − 0.154890i | −0.996997 | − | 0.0774452i | \(-0.975324\pi\) | ||||
0.996997 | − | 0.0774452i | \(-0.0246763\pi\) | |||||||
\(504\) | 5698.19i | 0.503606i | ||||||||
\(505\) | − 12235.5i | − 1.07816i | ||||||||
\(506\) | −1942.93 | −0.170699 | ||||||||
\(507\) | − 5280.61i | − 0.462564i | ||||||||
\(508\) | 15336.3 | 1.33945 | ||||||||
\(509\) | −9110.89 | −0.793385 | −0.396693 | − | 0.917952i | \(-0.629842\pi\) | ||||
−0.396693 | + | 0.917952i | \(0.629842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25093.8 | −2.17237 | ||||||||
\(512\) | −12995.8 | −1.12175 | ||||||||
\(513\) | − 15141.4i | − 1.30314i | ||||||||
\(514\) | 31098.3 | 2.66865 | ||||||||
\(515\) | 7154.42i | 0.612158i | ||||||||
\(516\) | − 4671.43i | − 0.398543i | ||||||||
\(517\) | 28268.5i | 2.40474i | ||||||||
\(518\) | 19957.2 | 1.69280 | ||||||||
\(519\) | −5284.42 | −0.446937 | ||||||||
\(520\) | 1211.89i | 0.102202i | ||||||||
\(521\) | − 9231.61i | − 0.776285i | −0.921599 | − | 0.388142i | \(-0.873117\pi\) | ||||
0.921599 | − | 0.388142i | \(-0.126883\pi\) | |||||||
\(522\) | − 13354.3i | − 1.11974i | ||||||||
\(523\) | 14927.5 | 1.24806 | 0.624028 | − | 0.781402i | \(-0.285495\pi\) | ||||
0.624028 | + | 0.781402i | \(0.285495\pi\) | |||||||
\(524\) | 10701.4i | 0.892165i | ||||||||
\(525\) | 7086.14 | 0.589076 | ||||||||
\(526\) | 19878.1 | 1.64777 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −6846.32 | −0.564295 | ||||||||
\(529\) | 12112.5 | 0.995519 | ||||||||
\(530\) | 4555.28i | 0.373338i | ||||||||
\(531\) | 6476.79 | 0.529320 | ||||||||
\(532\) | 35414.2i | 2.88609i | ||||||||
\(533\) | 582.239i | 0.0473162i | ||||||||
\(534\) | − 6139.31i | − 0.497516i | ||||||||
\(535\) | 781.694 | 0.0631693 | ||||||||
\(536\) | 10095.5 | 0.813545 | ||||||||
\(537\) | 4627.29i | 0.371848i | ||||||||
\(538\) | − 30521.5i | − 2.44587i | ||||||||
\(539\) | 32101.5i | 2.56532i | ||||||||
\(540\) | 8650.90 | 0.689399 | ||||||||
\(541\) | 9005.10i | 0.715637i | 0.933791 | + | 0.357818i | \(0.116479\pi\) | ||||
−0.933791 | + | 0.357818i | \(0.883521\pi\) | |||||||
\(542\) | −702.096 | −0.0556413 | ||||||||
\(543\) | −2163.75 | −0.171004 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5038.90 | 0.396042 | ||||||||
\(546\) | −6676.59 | −0.523318 | ||||||||
\(547\) | − 6774.33i | − 0.529524i | −0.964314 | − | 0.264762i | \(-0.914707\pi\) | ||||
0.964314 | − | 0.264762i | \(-0.0852933\pi\) | |||||||
\(548\) | −10581.6 | −0.824861 | ||||||||
\(549\) | − 2120.80i | − 0.164870i | ||||||||
\(550\) | 22227.9i | 1.72327i | ||||||||
\(551\) | − 19102.9i | − 1.47697i | ||||||||
\(552\) | 215.878 | 0.0166456 | ||||||||
\(553\) | −5916.20 | −0.454941 | ||||||||
\(554\) | 17904.1i | 1.37306i | ||||||||
\(555\) | − 2869.30i | − 0.219450i | ||||||||
\(556\) | 15656.2i | 1.19419i | ||||||||
\(557\) | −8558.56 | −0.651055 | −0.325528 | − | 0.945533i | \(-0.605542\pi\) | ||||
−0.325528 | + | 0.945533i | \(0.605542\pi\) | |||||||
\(558\) | 10291.1i | 0.780748i | ||||||||
\(559\) | −2926.79 | −0.221449 | ||||||||
\(560\) | 7334.32 | 0.553450 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29677.3 | −2.22751 | ||||||||
\(563\) | −13915.1 | −1.04165 | −0.520827 | − | 0.853662i | \(-0.674376\pi\) | ||||
−0.520827 | + | 0.853662i | \(0.674376\pi\) | |||||||
\(564\) | − 13646.4i | − 1.01882i | ||||||||
\(565\) | −469.775 | −0.0349798 | ||||||||
\(566\) | 26987.6i | 2.00419i | ||||||||
\(567\) | − 4029.35i | − 0.298442i | ||||||||
\(568\) | − 5378.39i | − 0.397310i | ||||||||
\(569\) | 12378.8 | 0.912031 | 0.456015 | − | 0.889972i | \(-0.349276\pi\) | ||||
0.456015 | + | 0.889972i | \(0.349276\pi\) | |||||||
\(570\) | 9011.29 | 0.662178 | ||||||||
\(571\) | 785.845i | 0.0575947i | 0.999585 | + | 0.0287974i | \(0.00916775\pi\) | ||||
−0.999585 | + | 0.0287974i | \(0.990832\pi\) | |||||||
\(572\) | − 11833.4i | − 0.865000i | ||||||||
\(573\) | − 5353.93i | − 0.390338i | ||||||||
\(574\) | −3959.85 | −0.287946 | ||||||||
\(575\) | 623.688i | 0.0452341i | ||||||||
\(576\) | −14320.8 | −1.03593 | ||||||||
\(577\) | 19662.8 | 1.41867 | 0.709334 | − | 0.704873i | \(-0.248996\pi\) | ||||
0.709334 | + | 0.704873i | \(0.248996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1417.68 | −0.101756 | ||||||||
\(580\) | 10914.2 | 0.781361 | ||||||||
\(581\) | − 663.224i | − 0.0473583i | ||||||||
\(582\) | −8320.82 | −0.592627 | ||||||||
\(583\) | − 10237.6i | − 0.727269i | ||||||||
\(584\) | 8745.92i | 0.619707i | ||||||||
\(585\) | − 2230.06i | − 0.157610i | ||||||||
\(586\) | −9833.54 | −0.693208 | ||||||||
\(587\) | 10024.7 | 0.704875 | 0.352438 | − | 0.935835i | \(-0.385353\pi\) | ||||
0.352438 | + | 0.935835i | \(0.385353\pi\) | |||||||
\(588\) | − 15496.7i | − 1.08686i | ||||||||
\(589\) | 14721.1i | 1.02983i | ||||||||
\(590\) | 9368.40i | 0.653713i | ||||||||
\(591\) | 2998.76 | 0.208719 | ||||||||
\(592\) | 6189.52i | 0.429709i | ||||||||
\(593\) | −770.054 | −0.0533260 | −0.0266630 | − | 0.999644i | \(-0.508488\pi\) | ||||
−0.0266630 | + | 0.999644i | \(0.508488\pi\) | |||||||
\(594\) | −34409.4 | −2.37682 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4412.52 | −0.303261 | ||||||||
\(597\) | 5083.80 | 0.348519 | ||||||||
\(598\) | − 587.641i | − 0.0401847i | ||||||||
\(599\) | 20011.7 | 1.36503 | 0.682517 | − | 0.730870i | \(-0.260885\pi\) | ||||
0.682517 | + | 0.730870i | \(0.260885\pi\) | |||||||
\(600\) | − 2469.73i | − 0.168044i | ||||||||
\(601\) | − 16303.2i | − 1.10652i | −0.833008 | − | 0.553261i | \(-0.813383\pi\) | ||||
0.833008 | − | 0.553261i | \(-0.186617\pi\) | |||||||
\(602\) | − 19905.3i | − 1.34764i | ||||||||
\(603\) | −18577.2 | −1.25460 | ||||||||
\(604\) | −16282.2 | −1.09688 | ||||||||
\(605\) | 15495.5i | 1.04129i | ||||||||
\(606\) | − 23493.7i | − 1.57486i | ||||||||
\(607\) | 26777.6i | 1.79056i | 0.445506 | + | 0.895279i | \(0.353024\pi\) | ||||
−0.445506 | + | 0.895279i | \(0.646976\pi\) | |||||||
\(608\) | −28940.7 | −1.93043 | ||||||||
\(609\) | 13839.5i | 0.920864i | ||||||||
\(610\) | 3067.65 | 0.203615 | ||||||||
\(611\) | −8549.85 | −0.566105 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1385.13 | 0.0912639 | 0.0456320 | − | 0.998958i | \(-0.485470\pi\) | ||||
0.0456320 | + | 0.998958i | \(0.485470\pi\) | |||||||
\(614\) | −9864.19 | −0.648349 | ||||||||
\(615\) | 569.318i | 0.0373286i | ||||||||
\(616\) | 18523.6 | 1.21158 | ||||||||
\(617\) | − 818.646i | − 0.0534156i | −0.999643 | − | 0.0267078i | \(-0.991498\pi\) | ||||
0.999643 | − | 0.0267078i | \(-0.00850237\pi\) | |||||||
\(618\) | 13737.4i | 0.894173i | ||||||||
\(619\) | 9468.86i | 0.614839i | 0.951574 | + | 0.307420i | \(0.0994655\pi\) | ||||
−0.951574 | + | 0.307420i | \(0.900534\pi\) | |||||||
\(620\) | −8410.75 | −0.544813 | ||||||||
\(621\) | −965.486 | −0.0623891 | ||||||||
\(622\) | − 24767.4i | − 1.59660i | ||||||||
\(623\) | − 14781.0i | − 0.950545i | ||||||||
\(624\) | − 2070.68i | − 0.132842i | ||||||||
\(625\) | 2069.03 | 0.132418 | ||||||||
\(626\) | 12006.7i | 0.766587i | ||||||||
\(627\) | −20252.1 | −1.28994 | ||||||||
\(628\) | −7921.60 | −0.503354 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 15166.8 | 0.959143 | ||||||||
\(631\) | −11291.5 | −0.712374 | −0.356187 | − | 0.934415i | \(-0.615923\pi\) | ||||
−0.356187 | + | 0.934415i | \(0.615923\pi\) | |||||||
\(632\) | 2061.97i | 0.129780i | ||||||||
\(633\) | 10706.3 | 0.672255 | ||||||||
\(634\) | 22045.3i | 1.38096i | ||||||||
\(635\) | − 9395.41i | − 0.587158i | ||||||||
\(636\) | 4942.11i | 0.308125i | ||||||||
\(637\) | −9709.13 | −0.603909 | ||||||||
\(638\) | −43412.0 | −2.69388 | ||||||||
\(639\) | 9897.02i | 0.612707i | ||||||||
\(640\) | − 7985.10i | − 0.493186i | ||||||||
\(641\) | − 27604.9i | − 1.70098i | −0.525993 | − | 0.850489i | \(-0.676306\pi\) | ||||
0.525993 | − | 0.850489i | \(-0.323694\pi\) | |||||||
\(642\) | 1500.95 | 0.0922707 | ||||||||
\(643\) | − 30899.1i | − 1.89509i | −0.319625 | − | 0.947544i | \(-0.603557\pi\) | ||||
0.319625 | − | 0.947544i | \(-0.396443\pi\) | |||||||
\(644\) | 2258.17 | 0.138175 | ||||||||
\(645\) | −2861.84 | −0.174705 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26023.7 | 1.58129 | 0.790647 | − | 0.612272i | \(-0.209744\pi\) | ||||
0.790647 | + | 0.612272i | \(0.209744\pi\) | |||||||
\(648\) | −1404.35 | −0.0851357 | ||||||||
\(649\) | − 21054.7i | − 1.27345i | ||||||||
\(650\) | −6722.85 | −0.405680 | ||||||||
\(651\) | − 10665.0i | − 0.642082i | ||||||||
\(652\) | − 23420.5i | − 1.40677i | ||||||||
\(653\) | − 18446.4i | − 1.10546i | −0.833362 | − | 0.552728i | \(-0.813587\pi\) | ||||
0.833362 | − | 0.552728i | \(-0.186413\pi\) | |||||||
\(654\) | 9675.33 | 0.578494 | ||||||||
\(655\) | 6555.97 | 0.391088 | ||||||||
\(656\) | − 1228.11i | − 0.0730938i | ||||||||
\(657\) | − 16093.8i | − 0.955673i | ||||||||
\(658\) | − 58148.2i | − 3.44506i | ||||||||
\(659\) | −987.581 | −0.0583774 | −0.0291887 | − | 0.999574i | \(-0.509292\pi\) | ||||
−0.0291887 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(660\) | − 11570.8i | − 0.682414i | ||||||||
\(661\) | −4126.78 | −0.242834 | −0.121417 | − | 0.992602i | \(-0.538744\pi\) | ||||
−0.121417 | + | 0.992602i | \(0.538744\pi\) | |||||||
\(662\) | 1970.64 | 0.115697 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −231.153 | −0.0135098 | ||||||||
\(665\) | 21695.6 | 1.26514 | ||||||||
\(666\) | 12799.5i | 0.744698i | ||||||||
\(667\) | −1218.09 | −0.0707115 | ||||||||
\(668\) | − 20740.1i | − 1.20128i | ||||||||
\(669\) | 9567.05i | 0.552890i | ||||||||
\(670\) | − 26871.2i | − 1.54944i | ||||||||
\(671\) | −6894.26 | −0.396647 | ||||||||
\(672\) | 20966.8 | 1.20359 | ||||||||
\(673\) | − 7788.28i | − 0.446086i | −0.974809 | − | 0.223043i | \(-0.928401\pi\) | ||||
0.974809 | − | 0.223043i | \(-0.0715991\pi\) | |||||||
\(674\) | 26732.6i | 1.52775i | ||||||||
\(675\) | 11045.5i | 0.629842i | ||||||||
\(676\) | −19251.8 | −1.09535 | ||||||||
\(677\) | 849.049i | 0.0482003i | 0.999710 | + | 0.0241001i | \(0.00767206\pi\) | ||||
−0.999710 | + | 0.0241001i | \(0.992328\pi\) | |||||||
\(678\) | −902.027 | −0.0510946 | ||||||||
\(679\) | −20033.3 | −1.13226 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5668.39 | 0.318962 | ||||||||
\(682\) | 33454.2 | 1.87834 | ||||||||
\(683\) | 18449.2i | 1.03359i | 0.856110 | + | 0.516793i | \(0.172874\pi\) | ||||
−0.856110 | + | 0.516793i | \(0.827126\pi\) | |||||||
\(684\) | −22712.7 | −1.26965 | ||||||||
\(685\) | 6482.56i | 0.361585i | ||||||||
\(686\) | − 22740.4i | − 1.26565i | ||||||||
\(687\) | − 14832.0i | − 0.823691i | ||||||||
\(688\) | 6173.42 | 0.342092 | ||||||||
\(689\) | 3096.37 | 0.171208 | ||||||||
\(690\) | − 574.601i | − 0.0317024i | ||||||||
\(691\) | 33194.1i | 1.82744i | 0.406339 | + | 0.913722i | \(0.366805\pi\) | ||||
−0.406339 | + | 0.913722i | \(0.633195\pi\) | |||||||
\(692\) | 19265.7i | 1.05834i | ||||||||
\(693\) | −34086.1 | −1.86843 | ||||||||
\(694\) | − 27318.2i | − 1.49422i | ||||||||
\(695\) | 9591.38 | 0.523484 | ||||||||
\(696\) | 4823.49 | 0.262692 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −27853.4 | −1.51041 | ||||||||
\(699\) | 16254.9 | 0.879567 | ||||||||
\(700\) | − 25834.4i | − 1.39492i | ||||||||
\(701\) | −1102.73 | −0.0594146 | −0.0297073 | − | 0.999559i | \(-0.509458\pi\) | ||||
−0.0297073 | + | 0.999559i | \(0.509458\pi\) | |||||||
\(702\) | − 10407.2i | − 0.559534i | ||||||||
\(703\) | 18309.2i | 0.982282i | ||||||||
\(704\) | 46553.7i | 2.49227i | ||||||||
\(705\) | −8360.12 | −0.446610 | ||||||||
\(706\) | −2155.57 | −0.114909 | ||||||||
\(707\) | − 56563.7i | − 3.00890i | ||||||||
\(708\) | 10163.9i | 0.539526i | ||||||||
\(709\) | − 5881.49i | − 0.311543i | −0.987793 | − | 0.155771i | \(-0.950214\pi\) | ||||
0.987793 | − | 0.155771i | \(-0.0497863\pi\) | |||||||
\(710\) | −14315.6 | −0.756697 | ||||||||
\(711\) | − 3794.33i | − 0.200138i | ||||||||
\(712\) | −5151.63 | −0.271159 | ||||||||
\(713\) | 938.685 | 0.0493044 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7249.45 | −0.379180 | ||||||||
\(716\) | 16870.0 | 0.880532 | ||||||||
\(717\) | 4041.95i | 0.210529i | ||||||||
\(718\) | −4178.92 | −0.217209 | ||||||||
\(719\) | 13392.6i | 0.694661i | 0.937743 | + | 0.347330i | \(0.112912\pi\) | ||||
−0.937743 | + | 0.347330i | \(0.887088\pi\) | |||||||
\(720\) | 4703.83i | 0.243474i | ||||||||
\(721\) | 33074.2i | 1.70839i | ||||||||
\(722\) | −28086.3 | −1.44774 | ||||||||
\(723\) | −17717.2 | −0.911355 | ||||||||
\(724\) | 7888.51i | 0.404937i | ||||||||
\(725\) | 13935.4i | 0.713859i | ||||||||
\(726\) | 29753.2i | 1.52100i | ||||||||
\(727\) | 30483.7 | 1.55513 | 0.777564 | − | 0.628804i | \(-0.216455\pi\) | ||||
0.777564 | + | 0.628804i | \(0.216455\pi\) | |||||||
\(728\) | 5602.48i | 0.285222i | ||||||||
\(729\) | −7479.33 | −0.379989 | ||||||||
\(730\) | 23278.9 | 1.18026 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3328.14 | 0.168049 | ||||||||
\(733\) | −23656.0 | −1.19203 | −0.596013 | − | 0.802975i | \(-0.703249\pi\) | ||||
−0.596013 | + | 0.802975i | \(0.703249\pi\) | |||||||
\(734\) | − 20126.7i | − 1.01211i | ||||||||
\(735\) | −9493.67 | −0.476434 | ||||||||
\(736\) | 1845.39i | 0.0924214i | ||||||||
\(737\) | 60390.5i | 3.01834i | ||||||||
\(738\) | − 2539.63i | − 0.126674i | ||||||||
\(739\) | 27884.4 | 1.38801 | 0.694007 | − | 0.719968i | \(-0.255843\pi\) | ||||
0.694007 | + | 0.719968i | \(0.255843\pi\) | |||||||
\(740\) | −10460.8 | −0.519656 | ||||||||
\(741\) | − 6125.26i | − 0.303667i | ||||||||
\(742\) | 21058.7i | 1.04190i | ||||||||
\(743\) | − 3391.10i | − 0.167439i | −0.996489 | − | 0.0837196i | \(-0.973320\pi\) | ||||
0.996489 | − | 0.0837196i | \(-0.0266800\pi\) | |||||||
\(744\) | −3717.08 | −0.183165 | ||||||||
\(745\) | 2703.22i | 0.132937i | ||||||||
\(746\) | −37101.1 | −1.82087 | ||||||||
\(747\) | 425.356 | 0.0208339 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3613.70 | 0.176291 | ||||||||
\(750\) | −16301.4 | −0.793658 | ||||||||
\(751\) | 19843.5i | 0.964181i | 0.876121 | + | 0.482091i | \(0.160122\pi\) | ||||
−0.876121 | + | 0.482091i | \(0.839878\pi\) | |||||||
\(752\) | 18034.1 | 0.874514 | ||||||||
\(753\) | 4410.82i | 0.213465i | ||||||||
\(754\) | − 13130.0i | − 0.634173i | ||||||||
\(755\) | 9974.92i | 0.480827i | ||||||||
\(756\) | 39992.3 | 1.92395 | ||||||||
\(757\) | 23915.1 | 1.14823 | 0.574114 | − | 0.818775i | \(-0.305347\pi\) | ||||
0.574114 | + | 0.818775i | \(0.305347\pi\) | |||||||
\(758\) | 14967.1i | 0.717191i | ||||||||
\(759\) | 1291.36i | 0.0617570i | ||||||||
\(760\) | − 7561.57i | − 0.360904i | ||||||||
\(761\) | 17162.3 | 0.817520 | 0.408760 | − | 0.912642i | \(-0.365961\pi\) | ||||
0.408760 | + | 0.912642i | \(0.365961\pi\) | |||||||
\(762\) | − 18040.4i | − 0.857656i | ||||||||
\(763\) | 23294.4 | 1.10526 | ||||||||
\(764\) | −19519.1 | −0.924317 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16847.2 | 0.794668 | ||||||||
\(767\) | 6368.00 | 0.299785 | ||||||||
\(768\) | 1968.39i | 0.0924845i | ||||||||
\(769\) | −18387.3 | −0.862240 | −0.431120 | − | 0.902295i | \(-0.641881\pi\) | ||||
−0.431120 | + | 0.902295i | \(0.641881\pi\) | |||||||
\(770\) | − 49304.0i | − 2.30752i | ||||||||
\(771\) | − 20669.4i | − 0.965488i | ||||||||
\(772\) | 5168.52i | 0.240957i | ||||||||
\(773\) | −4428.78 | −0.206070 | −0.103035 | − | 0.994678i | \(-0.532855\pi\) | ||||
−0.103035 | + | 0.994678i | \(0.532855\pi\) | |||||||
\(774\) | 12766.2 | 0.592855 | ||||||||
\(775\) | − 10738.9i | − 0.497746i | ||||||||
\(776\) | 6982.18i | 0.322997i | ||||||||
\(777\) | − 13264.5i | − 0.612435i | ||||||||
\(778\) | 29853.4 | 1.37570 | ||||||||
\(779\) | − 3632.86i | − 0.167087i | ||||||||
\(780\) | 3499.61 | 0.160649 | ||||||||
\(781\) | 32173.1 | 1.47406 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21572.4 | −0.984591 | ||||||||
\(784\) | 20479.3 | 0.932913 | ||||||||
\(785\) | 4852.97i | 0.220650i | ||||||||
\(786\) | 12588.3 | 0.571259 | ||||||||
\(787\) | 17665.8i | 0.800151i | 0.916482 | + | 0.400075i | \(0.131016\pi\) | ||||
−0.916482 | + | 0.400075i | \(0.868984\pi\) | |||||||
\(788\) | − 10932.8i | − 0.494243i | ||||||||
\(789\) | − 13211.9i | − 0.596143i | ||||||||
\(790\) | 5488.33 | 0.247172 | ||||||||
\(791\) | −2171.73 | −0.0976203 | ||||||||
\(792\) | 11880.0i | 0.533002i | ||||||||
\(793\) | − 2085.18i | − 0.0933756i | ||||||||
\(794\) | − 22866.4i | − 1.02204i | ||||||||
\(795\) | 3027.66 | 0.135069 | ||||||||
\(796\) | − 18534.3i | − 0.825290i | ||||||||
\(797\) | −12688.4 | −0.563921 | −0.281960 | − | 0.959426i | \(-0.590985\pi\) | ||||
−0.281960 | + | 0.959426i | \(0.590985\pi\) | |||||||
\(798\) | 41658.3 | 1.84798 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 21112.0 | 0.933029 | ||||||||
\(801\) | 9479.74 | 0.418165 | ||||||||
\(802\) | − 2341.65i | − 0.103100i | ||||||||
\(803\) | −52317.3 | −2.29918 | ||||||||
\(804\) | − 29153.0i | − 1.27879i | ||||||||
\(805\) | − 1383.41i | − 0.0605700i | ||||||||
\(806\) | 10118.3i | 0.442184i | ||||||||
\(807\) | −20286.1 | −0.884886 | ||||||||
\(808\) | −19714.1 | −0.858342 | ||||||||
\(809\) | 28633.8i | 1.24439i | 0.782863 | + | 0.622194i | \(0.213758\pi\) | ||||
−0.782863 | + | 0.622194i | \(0.786242\pi\) | |||||||
\(810\) | 3737.94i | 0.162145i | ||||||||
\(811\) | − 2305.93i | − 0.0998425i | −0.998753 | − | 0.0499213i | \(-0.984103\pi\) | ||||
0.998753 | − | 0.0499213i | \(-0.0158970\pi\) | |||||||
\(812\) | 50455.6 | 2.18060 | ||||||||
\(813\) | 466.646i | 0.0201304i | ||||||||
\(814\) | 41608.3 | 1.79161 | ||||||||
\(815\) | −14348.0 | −0.616672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18261.6 | 0.781997 | ||||||||
\(818\) | −68465.4 | −2.92645 | ||||||||
\(819\) | − 10309.4i | − 0.439852i | ||||||||
\(820\) | 2075.60 | 0.0883938 | ||||||||
\(821\) | 28803.5i | 1.22442i | 0.790695 | + | 0.612210i | \(0.209719\pi\) | ||||
−0.790695 | + | 0.612210i | \(0.790281\pi\) | |||||||
\(822\) | 12447.3i | 0.528164i | ||||||||
\(823\) | − 14597.0i | − 0.618248i | −0.951022 | − | 0.309124i | \(-0.899964\pi\) | ||||
0.951022 | − | 0.309124i | \(-0.100036\pi\) | |||||||
\(824\) | 11527.3 | 0.487347 | ||||||||
\(825\) | 14773.7 | 0.623460 | ||||||||
\(826\) | 43309.3i | 1.82436i | ||||||||
\(827\) | − 32943.4i | − 1.38519i | −0.721326 | − | 0.692596i | \(-0.756467\pi\) | ||||
0.721326 | − | 0.692596i | \(-0.243533\pi\) | |||||||
\(828\) | 1448.27i | 0.0607859i | ||||||||
\(829\) | −35091.9 | −1.47020 | −0.735098 | − | 0.677961i | \(-0.762864\pi\) | ||||
−0.735098 | + | 0.677961i | \(0.762864\pi\) | |||||||
\(830\) | 615.259i | 0.0257300i | ||||||||
\(831\) | 11899.9 | 0.496756 | ||||||||
\(832\) | −14080.2 | −0.586711 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18416.7 | 0.764648 | ||||||||
\(835\) | −12705.9 | −0.526594 | ||||||||
\(836\) | 73834.1i | 3.05455i | ||||||||
\(837\) | 16624.1 | 0.686517 | ||||||||
\(838\) | − 32781.5i | − 1.35133i | ||||||||
\(839\) | − 19365.1i | − 0.796848i | −0.917201 | − | 0.398424i | \(-0.869557\pi\) | ||||
0.917201 | − | 0.398424i | \(-0.130443\pi\) | |||||||
\(840\) | 5478.15i | 0.225017i | ||||||||
\(841\) | −2827.42 | −0.115930 | ||||||||
\(842\) | 32267.8 | 1.32069 | ||||||||
\(843\) | 19724.9i | 0.805887i | ||||||||
\(844\) | − 39032.6i | − 1.59189i | ||||||||
\(845\) | 11794.1i | 0.480155i | ||||||||
\(846\) | 37293.0 | 1.51556 | ||||||||
\(847\) | 71634.1i | 2.90599i | ||||||||
\(848\) | −6531.13 | −0.264481 | ||||||||
\(849\) | 17937.2 | 0.725094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1167.48 | 0.0470278 | ||||||||
\(852\) | −15531.3 | −0.624521 | ||||||||
\(853\) | 37350.6i | 1.49925i | 0.661863 | + | 0.749625i | \(0.269766\pi\) | ||||
−0.661863 | + | 0.749625i | \(0.730234\pi\) | |||||||
\(854\) | 14181.4 | 0.568242 | ||||||||
\(855\) | 13914.4i | 0.556564i | ||||||||
\(856\) | − 1259.48i | − 0.0502899i | ||||||||
\(857\) | 14189.2i | 0.565569i | 0.959183 | + | 0.282785i | \(0.0912582\pi\) | ||||
−0.959183 | + | 0.282785i | \(0.908742\pi\) | |||||||
\(858\) | −13919.9 | −0.553865 | ||||||||
\(859\) | −24014.5 | −0.953859 | −0.476930 | − | 0.878942i | \(-0.658250\pi\) | ||||
−0.476930 | + | 0.878942i | \(0.658250\pi\) | |||||||
\(860\) | 10433.6i | 0.413699i | ||||||||
\(861\) | 2631.90i | 0.104175i | ||||||||
\(862\) | 52416.8i | 2.07114i | ||||||||
\(863\) | −8498.07 | −0.335200 | −0.167600 | − | 0.985855i | \(-0.553602\pi\) | ||||
−0.167600 | + | 0.985855i | \(0.553602\pi\) | |||||||
\(864\) | 32682.0i | 1.28688i | ||||||||
\(865\) | 11802.7 | 0.463933 | ||||||||
\(866\) | −66131.1 | −2.59495 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −38882.1 | −1.52044 | ||||||||
\(869\) | −12334.5 | −0.481497 | ||||||||
\(870\) | − 12838.6i | − 0.500310i | ||||||||
\(871\) | −18265.2 | −0.710554 | ||||||||
\(872\) | − 8118.78i | − 0.315294i | ||||||||
\(873\) | − 12848.2i | − 0.498106i | ||||||||
\(874\) | 3666.57i | 0.141903i | ||||||||
\(875\) | −39247.4 | −1.51635 | ||||||||
\(876\) | 25255.7 | 0.974100 | ||||||||
\(877\) | 16013.2i | 0.616566i | 0.951295 | + | 0.308283i | \(0.0997544\pi\) | ||||
−0.951295 | + | 0.308283i | \(0.900246\pi\) | |||||||
\(878\) | 76476.6i | 2.93959i | ||||||||
\(879\) | 6535.84i | 0.250794i | ||||||||
\(880\) | 15291.1 | 0.585755 | ||||||||
\(881\) | 16824.6i | 0.643399i | 0.946842 | + | 0.321699i | \(0.104254\pi\) | ||||
−0.946842 | + | 0.321699i | \(0.895746\pi\) | |||||||
\(882\) | 42349.6 | 1.61676 | ||||||||
\(883\) | 11327.3 | 0.431703 | 0.215851 | − | 0.976426i | \(-0.430747\pi\) | ||||
0.215851 | + | 0.976426i | \(0.430747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6226.69 | 0.236506 | ||||||||
\(886\) | −1036.24 | −0.0392926 | ||||||||
\(887\) | 11077.4i | 0.419327i | 0.977774 | + | 0.209663i | \(0.0672368\pi\) | ||||
−0.977774 | + | 0.209663i | \(0.932763\pi\) | |||||||
\(888\) | −4623.08 | −0.174708 | ||||||||
\(889\) | − 43434.1i | − 1.63862i | ||||||||
\(890\) | 13712.0i | 0.516436i | ||||||||
\(891\) | − 8400.68i | − 0.315862i | ||||||||
\(892\) | 34879.2 | 1.30924 | ||||||||
\(893\) | 53346.5 | 1.99907 | ||||||||
\(894\) | 5190.52i | 0.194180i | ||||||||
\(895\) | − 10335.0i | − 0.385989i | ||||||||
\(896\) | − 36914.4i | − 1.37637i | ||||||||
\(897\) | −390.575 | −0.0145384 | ||||||||
\(898\) | 62104.5i | 2.30785i | ||||||||
\(899\) | 20973.5 | 0.778095 | ||||||||
\(900\) | 16568.7 | 0.613657 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −8255.78 | −0.304753 | ||||||||
\(903\) | −13230.0 | −0.487560 | ||||||||
\(904\) | 756.911i | 0.0278479i | ||||||||
\(905\) | 4832.70 | 0.177508 | ||||||||
\(906\) | 19153.1i | 0.702339i | ||||||||
\(907\) | 1761.65i | 0.0644924i | 0.999480 | + | 0.0322462i | \(0.0102661\pi\) | ||||
−0.999480 | + | 0.0322462i | \(0.989734\pi\) | |||||||
\(908\) | − 20665.6i | − 0.755299i | ||||||||
\(909\) | 36276.8 | 1.32368 | ||||||||
\(910\) | 14912.1 | 0.543220 | ||||||||
\(911\) | − 44996.2i | − 1.63643i | −0.574909 | − | 0.818217i | \(-0.694963\pi\) | ||||
0.574909 | − | 0.818217i | \(-0.305037\pi\) | |||||||
\(912\) | 12919.9i | 0.469102i | ||||||||
\(913\) | − 1382.74i | − 0.0501227i | ||||||||
\(914\) | −7781.63 | −0.281612 | ||||||||
\(915\) | − 2038.90i | − 0.0736657i | ||||||||
\(916\) | −54073.8 | −1.95049 | ||||||||
\(917\) | 30307.6 | 1.09144 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34461.8 | 1.23699 | 0.618493 | − | 0.785790i | \(-0.287743\pi\) | ||||
0.618493 | + | 0.785790i | \(0.287743\pi\) | |||||||
\(920\) | −482.160 | −0.0172786 | ||||||||
\(921\) | 6556.21i | 0.234565i | ||||||||
\(922\) | −57613.1 | −2.05790 | ||||||||
\(923\) | 9730.78i | 0.347012i | ||||||||
\(924\) | − 53490.8i | − 1.90446i | ||||||||
\(925\) | − 13356.4i | − 0.474763i | ||||||||
\(926\) | 71163.9 | 2.52548 | ||||||||
\(927\) | −21212.0 | −0.751557 | ||||||||
\(928\) | 41232.7i | 1.45854i | ||||||||
\(929\) | − 37878.7i | − 1.33774i | −0.743379 | − | 0.668870i | \(-0.766778\pi\) | ||||
0.743379 | − | 0.668870i | \(-0.233222\pi\) | |||||||
\(930\) | 9893.71i | 0.348847i | ||||||||
\(931\) | 60579.8 | 2.13257 | ||||||||
\(932\) | − 59261.5i | − 2.08281i | ||||||||
\(933\) | −16461.6 | −0.577630 | ||||||||
\(934\) | −16914.6 | −0.592573 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3593.12 | −0.125475 | ||||||||
\(937\) | 599.505 | 0.0209018 | 0.0104509 | − | 0.999945i | \(-0.496673\pi\) | ||||
0.0104509 | + | 0.999945i | \(0.496673\pi\) | |||||||
\(938\) | − 124223.i | − 4.32412i | ||||||||
\(939\) | 7980.22 | 0.277342 | ||||||||
\(940\) | 30479.0i | 1.05757i | ||||||||
\(941\) | 10118.0i | 0.350519i | 0.984522 | + | 0.175260i | \(0.0560765\pi\) | ||||
−0.984522 | + | 0.175260i | \(0.943924\pi\) | |||||||
\(942\) | 9318.32i | 0.322301i | ||||||||
\(943\) | −231.647 | −0.00799945 | ||||||||
\(944\) | −13431.9 | −0.463106 | ||||||||
\(945\) | − 24500.3i | − 0.843380i | ||||||||
\(946\) | − 41500.0i | − 1.42630i | ||||||||
\(947\) | − 39320.2i | − 1.34924i | −0.738163 | − | 0.674622i | \(-0.764307\pi\) | ||||
0.738163 | − | 0.674622i | \(-0.235693\pi\) | |||||||
\(948\) | 5954.39 | 0.203997 | ||||||||
\(949\) | − 15823.4i | − 0.541254i | ||||||||
\(950\) | 41947.0 | 1.43257 | ||||||||
\(951\) | 14652.3 | 0.499616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41203.8 | −1.40055 | −0.700274 | − | 0.713874i | \(-0.746939\pi\) | ||||
−0.700274 | + | 0.713874i | \(0.746939\pi\) | |||||||
\(954\) | −13505.9 | −0.458353 | ||||||||
\(955\) | 11957.9i | 0.405182i | ||||||||
\(956\) | 14736.0 | 0.498531 | ||||||||
\(957\) | 28853.7i | 0.974615i | ||||||||
\(958\) | 47872.3i | 1.61449i | ||||||||
\(959\) | 29968.3i | 1.00910i | ||||||||
\(960\) | −13767.7 | −0.462867 | ||||||||
\(961\) | 13628.3 | 0.457465 | ||||||||
\(962\) | 12584.5i | 0.421766i | ||||||||
\(963\) | 2317.63i | 0.0775540i | ||||||||
\(964\) | 64592.6i | 2.15808i | ||||||||
\(965\) | 3166.37 | 0.105626 | ||||||||
\(966\) | − 2656.33i | − 0.0884740i | ||||||||
\(967\) | −9403.83 | −0.312727 | −0.156363 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156363 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(968\) | 24966.6 | 0.828984 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18584.4 | 0.615164 | ||||||||
\(971\) | 44819.8 | 1.48129 | 0.740646 | − | 0.671895i | \(-0.234519\pi\) | ||||
0.740646 | + | 0.671895i | \(0.234519\pi\) | |||||||
\(972\) | 40744.6i | 1.34453i | ||||||||
\(973\) | 44340.1 | 1.46092 | ||||||||
\(974\) | − 42817.1i | − 1.40857i | ||||||||
\(975\) | 4468.33i | 0.146770i | ||||||||
\(976\) | 4398.23i | 0.144246i | ||||||||
\(977\) | −13700.4 | −0.448632 | −0.224316 | − | 0.974516i | \(-0.572015\pi\) | ||||
−0.224316 | + | 0.974516i | \(0.572015\pi\) | |||||||
\(978\) | −27549.9 | −0.900766 | ||||||||
\(979\) | − 30816.6i | − 1.00603i | ||||||||
\(980\) | 34611.6i | 1.12819i | ||||||||
\(981\) | 14939.7i | 0.486227i | ||||||||
\(982\) | −84226.0 | −2.73703 | ||||||||
\(983\) | − 34126.9i | − 1.10730i | −0.832748 | − | 0.553652i | \(-0.813234\pi\) | ||||
0.832748 | − | 0.553652i | \(-0.186766\pi\) | |||||||
\(984\) | 917.297 | 0.0297178 | ||||||||
\(985\) | −6697.69 | −0.216656 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38648.1 | −1.24638 | ||||||||
\(988\) | −22331.2 | −0.719080 | ||||||||
\(989\) | − 1164.44i | − 0.0374389i | ||||||||
\(990\) | 31620.9 | 1.01513 | ||||||||
\(991\) | − 38645.7i | − 1.23877i | −0.785087 | − | 0.619386i | \(-0.787382\pi\) | ||||
0.785087 | − | 0.619386i | \(-0.212618\pi\) | |||||||
\(992\) | − 31774.8i | − 1.01699i | ||||||||
\(993\) | − 1309.78i | − 0.0418577i | ||||||||
\(994\) | −66179.7 | −2.11176 | ||||||||
\(995\) | −11354.6 | −0.361773 | ||||||||
\(996\) | 667.505i | 0.0212356i | ||||||||
\(997\) | 13993.3i | 0.444505i | 0.974989 | + | 0.222252i | \(0.0713409\pi\) | ||||
−0.974989 | + | 0.222252i | \(0.928659\pi\) | |||||||
\(998\) | − 24720.7i | − 0.784088i | ||||||||
\(999\) | 20676.1 | 0.654817 |
(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 | 289.4.b.f.288.6 | 24 | ||
17.4 | even | 4 | 289.4.a.i.1.10 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.h.1.10 | ✓ | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.10 | ✓ | 12 | 17.13 | even | 4 | ||
289.4.a.i.1.10 | yes | 12 | 17.4 | even | 4 | ||
289.4.b.f.288.5 | 24 | 17.16 | even | 2 | inner | ||
289.4.b.f.288.6 | 24 | 1.1 | even | 1 | trivial |