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 | 288.7 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.25752 | −1.15171 | −0.575854 | − | 0.817552i | \(-0.695330\pi\) | ||||
−0.575854 | + | 0.817552i | \(0.695330\pi\) | |||||||
\(3\) | − 6.51757i | − 1.25431i | −0.778896 | − | 0.627153i | \(-0.784220\pi\) | ||||
0.778896 | − | 0.627153i | \(-0.215780\pi\) | |||||||
\(4\) | 2.61146 | 0.326432 | ||||||||
\(5\) | 19.1073i | 1.70901i | 0.519441 | + | 0.854506i | \(0.326140\pi\) | ||||
−0.519441 | + | 0.854506i | \(0.673860\pi\) | |||||||
\(6\) | 21.2311i | 1.44460i | ||||||||
\(7\) | − 22.0995i | − 1.19326i | −0.802515 | − | 0.596631i | \(-0.796505\pi\) | ||||
0.802515 | − | 0.596631i | \(-0.203495\pi\) | |||||||
\(8\) | 17.5533 | 0.775753 | ||||||||
\(9\) | −15.4787 | −0.573284 | ||||||||
\(10\) | − 62.2426i | − 1.96828i | ||||||||
\(11\) | 8.25972i | 0.226400i | 0.993572 | + | 0.113200i | \(0.0361101\pi\) | ||||
−0.993572 | + | 0.113200i | \(0.963890\pi\) | |||||||
\(12\) | − 17.0204i | − 0.409446i | ||||||||
\(13\) | −0.398269 | −0.00849693 | −0.00424846 | − | 0.999991i | \(-0.501352\pi\) | ||||
−0.00424846 | + | 0.999991i | \(0.501352\pi\) | |||||||
\(14\) | 71.9898i | 1.37429i | ||||||||
\(15\) | 124.533 | 2.14362 | ||||||||
\(16\) | −78.0720 | −1.21987 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 50.4221 | 0.660256 | ||||||||
\(19\) | −103.371 | −1.24816 | −0.624078 | − | 0.781362i | \(-0.714525\pi\) | ||||
−0.624078 | + | 0.781362i | \(0.714525\pi\) | |||||||
\(20\) | 49.8980i | 0.557877i | ||||||||
\(21\) | −144.035 | −1.49672 | ||||||||
\(22\) | − 26.9062i | − 0.260747i | ||||||||
\(23\) | − 138.311i | − 1.25391i | −0.779056 | − | 0.626955i | \(-0.784301\pi\) | ||||
0.779056 | − | 0.626955i | \(-0.215699\pi\) | |||||||
\(24\) | − 114.405i | − 0.973032i | ||||||||
\(25\) | −240.090 | −1.92072 | ||||||||
\(26\) | 1.29737 | 0.00978598 | ||||||||
\(27\) | − 75.0910i | − 0.535233i | ||||||||
\(28\) | − 57.7120i | − 0.389520i | ||||||||
\(29\) | 222.296i | 1.42342i | 0.702471 | + | 0.711712i | \(0.252080\pi\) | ||||
−0.702471 | + | 0.711712i | \(0.747920\pi\) | |||||||
\(30\) | −405.670 | −2.46883 | ||||||||
\(31\) | 49.1520i | 0.284773i | 0.989811 | + | 0.142386i | \(0.0454776\pi\) | ||||
−0.989811 | + | 0.142386i | \(0.954522\pi\) | |||||||
\(32\) | 113.895 | 0.629186 | ||||||||
\(33\) | 53.8333 | 0.283975 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 422.263 | 2.03930 | ||||||||
\(36\) | −40.4219 | −0.187138 | ||||||||
\(37\) | 61.3077i | 0.272403i | 0.990681 | + | 0.136202i | \(0.0434895\pi\) | ||||
−0.990681 | + | 0.136202i | \(0.956510\pi\) | |||||||
\(38\) | 336.734 | 1.43751 | ||||||||
\(39\) | 2.59575i | 0.0106577i | ||||||||
\(40\) | 335.397i | 1.32577i | ||||||||
\(41\) | 387.391i | 1.47562i | 0.675011 | + | 0.737808i | \(0.264139\pi\) | ||||
−0.675011 | + | 0.737808i | \(0.735861\pi\) | |||||||
\(42\) | 469.198 | 1.72378 | ||||||||
\(43\) | 20.3847 | 0.0722939 | 0.0361470 | − | 0.999346i | \(-0.488492\pi\) | ||||
0.0361470 | + | 0.999346i | \(0.488492\pi\) | |||||||
\(44\) | 21.5699i | 0.0739043i | ||||||||
\(45\) | − 295.756i | − 0.979749i | ||||||||
\(46\) | 450.553i | 1.44414i | ||||||||
\(47\) | 44.1322 | 0.136965 | 0.0684824 | − | 0.997652i | \(-0.478184\pi\) | ||||
0.0684824 | + | 0.997652i | \(0.478184\pi\) | |||||||
\(48\) | 508.839i | 1.53010i | ||||||||
\(49\) | −145.389 | −0.423876 | ||||||||
\(50\) | 782.100 | 2.21211 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.04006 | −0.00277367 | ||||||||
\(53\) | −59.6456 | −0.154584 | −0.0772920 | − | 0.997009i | \(-0.524627\pi\) | ||||
−0.0772920 | + | 0.997009i | \(0.524627\pi\) | |||||||
\(54\) | 244.611i | 0.616432i | ||||||||
\(55\) | −157.821 | −0.386920 | ||||||||
\(56\) | − 387.920i | − 0.925678i | ||||||||
\(57\) | 673.728i | 1.56557i | ||||||||
\(58\) | − 724.134i | − 1.63937i | ||||||||
\(59\) | −238.069 | −0.525321 | −0.262660 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262660 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(60\) | 325.214 | 0.699749 | ||||||||
\(61\) | 595.816i | 1.25060i | 0.780386 | + | 0.625298i | \(0.215023\pi\) | ||||
−0.780386 | + | 0.625298i | \(0.784977\pi\) | |||||||
\(62\) | − 160.114i | − 0.327975i | ||||||||
\(63\) | 342.071i | 0.684078i | ||||||||
\(64\) | 253.561 | 0.495235 | ||||||||
\(65\) | − 7.60987i | − 0.0145214i | ||||||||
\(66\) | −175.363 | −0.327056 | ||||||||
\(67\) | −408.815 | −0.745442 | −0.372721 | − | 0.927943i | \(-0.621575\pi\) | ||||
−0.372721 | + | 0.927943i | \(0.621575\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −901.454 | −1.57279 | ||||||||
\(70\) | −1375.53 | −2.34868 | ||||||||
\(71\) | 1037.38i | 1.73400i | 0.498309 | + | 0.866999i | \(0.333954\pi\) | ||||
−0.498309 | + | 0.866999i | \(0.666046\pi\) | |||||||
\(72\) | −271.702 | −0.444727 | ||||||||
\(73\) | 22.3789i | 0.0358802i | 0.999839 | + | 0.0179401i | \(0.00571082\pi\) | ||||
−0.999839 | + | 0.0179401i | \(0.994289\pi\) | |||||||
\(74\) | − 199.711i | − 0.313729i | ||||||||
\(75\) | 1564.80i | 2.40917i | ||||||||
\(76\) | −269.949 | −0.407438 | ||||||||
\(77\) | 182.536 | 0.270155 | ||||||||
\(78\) | − 8.45571i | − 0.0122746i | ||||||||
\(79\) | 682.688i | 0.972259i | 0.873887 | + | 0.486129i | \(0.161592\pi\) | ||||
−0.873887 | + | 0.486129i | \(0.838408\pi\) | |||||||
\(80\) | − 1491.75i | − 2.08478i | ||||||||
\(81\) | −907.335 | −1.24463 | ||||||||
\(82\) | − 1261.93i | − 1.69948i | ||||||||
\(83\) | 312.352 | 0.413073 | 0.206536 | − | 0.978439i | \(-0.433781\pi\) | ||||
0.206536 | + | 0.978439i | \(0.433781\pi\) | |||||||
\(84\) | −376.142 | −0.488577 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −66.4037 | −0.0832616 | ||||||||
\(87\) | 1448.83 | 1.78541 | ||||||||
\(88\) | 144.985i | 0.175630i | ||||||||
\(89\) | −904.392 | −1.07714 | −0.538570 | − | 0.842581i | \(-0.681035\pi\) | ||||
−0.538570 | + | 0.842581i | \(0.681035\pi\) | |||||||
\(90\) | 963.433i | 1.12839i | ||||||||
\(91\) | 8.80157i | 0.0101391i | ||||||||
\(92\) | − 361.195i | − 0.409317i | ||||||||
\(93\) | 320.351 | 0.357192 | ||||||||
\(94\) | −143.762 | −0.157744 | ||||||||
\(95\) | − 1975.15i | − 2.13311i | ||||||||
\(96\) | − 742.317i | − 0.789192i | ||||||||
\(97\) | 1006.72i | 1.05378i | 0.849933 | + | 0.526891i | \(0.176642\pi\) | ||||
−0.849933 | + | 0.526891i | \(0.823358\pi\) | |||||||
\(98\) | 473.610 | 0.488182 | ||||||||
\(99\) | − 127.849i | − 0.129791i | ||||||||
\(100\) | −626.986 | −0.626986 | ||||||||
\(101\) | −1124.60 | −1.10794 | −0.553968 | − | 0.832538i | \(-0.686887\pi\) | ||||
−0.553968 | + | 0.832538i | \(0.686887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −396.677 | −0.379473 | −0.189736 | − | 0.981835i | \(-0.560763\pi\) | ||||
−0.189736 | + | 0.981835i | \(0.560763\pi\) | |||||||
\(104\) | −6.99094 | −0.00659152 | ||||||||
\(105\) | − 2752.13i | − 2.55791i | ||||||||
\(106\) | 194.297 | 0.178036 | ||||||||
\(107\) | − 288.906i | − 0.261024i | −0.991447 | − | 0.130512i | \(-0.958338\pi\) | ||||
0.991447 | − | 0.130512i | \(-0.0416621\pi\) | |||||||
\(108\) | − 196.097i | − 0.174717i | ||||||||
\(109\) | − 1379.15i | − 1.21191i | −0.795499 | − | 0.605955i | \(-0.792791\pi\) | ||||
0.795499 | − | 0.605955i | \(-0.207209\pi\) | |||||||
\(110\) | 514.106 | 0.445619 | ||||||||
\(111\) | 399.577 | 0.341677 | ||||||||
\(112\) | 1725.35i | 1.45563i | ||||||||
\(113\) | 1364.42i | 1.13587i | 0.823072 | + | 0.567937i | \(0.192258\pi\) | ||||
−0.823072 | + | 0.567937i | \(0.807742\pi\) | |||||||
\(114\) | − 2194.68i | − 1.80308i | ||||||||
\(115\) | 2642.76 | 2.14295 | ||||||||
\(116\) | 580.517i | 0.464652i | ||||||||
\(117\) | 6.16468 | 0.00487115 | ||||||||
\(118\) | 775.515 | 0.605016 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2185.97 | 1.66292 | ||||||||
\(121\) | 1262.78 | 0.948743 | ||||||||
\(122\) | − 1940.88i | − 1.44032i | ||||||||
\(123\) | 2524.84 | 1.85087 | ||||||||
\(124\) | 128.358i | 0.0929591i | ||||||||
\(125\) | − 2199.07i | − 1.57353i | ||||||||
\(126\) | − 1114.31i | − 0.787859i | ||||||||
\(127\) | −1003.33 | −0.701032 | −0.350516 | − | 0.936557i | \(-0.613994\pi\) | ||||
−0.350516 | + | 0.936557i | \(0.613994\pi\) | |||||||
\(128\) | −1737.14 | −1.19955 | ||||||||
\(129\) | − 132.859i | − 0.0906787i | ||||||||
\(130\) | 24.7893i | 0.0167244i | ||||||||
\(131\) | − 218.014i | − 0.145404i | −0.997354 | − | 0.0727022i | \(-0.976838\pi\) | ||||
0.997354 | − | 0.0727022i | \(-0.0231623\pi\) | |||||||
\(132\) | 140.583 | 0.0926986 | ||||||||
\(133\) | 2284.45i | 1.48938i | ||||||||
\(134\) | 1331.72 | 0.858532 | ||||||||
\(135\) | 1434.79 | 0.914719 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1625.34 | −1.01359 | −0.506797 | − | 0.862066i | \(-0.669171\pi\) | ||||
−0.506797 | + | 0.862066i | \(0.669171\pi\) | |||||||
\(138\) | 2936.51 | 1.81139 | ||||||||
\(139\) | 1034.35i | 0.631166i | 0.948898 | + | 0.315583i | \(0.102200\pi\) | ||||
−0.948898 | + | 0.315583i | \(0.897800\pi\) | |||||||
\(140\) | 1102.72 | 0.665694 | ||||||||
\(141\) | − 287.635i | − 0.171796i | ||||||||
\(142\) | − 3379.28i | − 1.99706i | ||||||||
\(143\) | − 3.28959i | − 0.00192370i | ||||||||
\(144\) | 1208.45 | 0.699334 | ||||||||
\(145\) | −4247.48 | −2.43265 | ||||||||
\(146\) | − 72.8999i | − 0.0413236i | ||||||||
\(147\) | 947.585i | 0.531670i | ||||||||
\(148\) | 160.103i | 0.0889213i | ||||||||
\(149\) | −650.200 | −0.357493 | −0.178747 | − | 0.983895i | \(-0.557204\pi\) | ||||
−0.178747 | + | 0.983895i | \(0.557204\pi\) | |||||||
\(150\) | − 5097.39i | − 2.77467i | ||||||||
\(151\) | −1023.67 | −0.551689 | −0.275845 | − | 0.961202i | \(-0.588958\pi\) | ||||
−0.275845 | + | 0.961202i | \(0.588958\pi\) | |||||||
\(152\) | −1814.50 | −0.968261 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −594.615 | −0.311139 | ||||||||
\(155\) | −939.164 | −0.486680 | ||||||||
\(156\) | 6.77869i | 0.00347903i | ||||||||
\(157\) | 671.612 | 0.341404 | 0.170702 | − | 0.985323i | \(-0.445396\pi\) | ||||
0.170702 | + | 0.985323i | \(0.445396\pi\) | |||||||
\(158\) | − 2223.87i | − 1.11976i | ||||||||
\(159\) | 388.744i | 0.193896i | ||||||||
\(160\) | 2176.23i | 1.07529i | ||||||||
\(161\) | −3056.62 | −1.49624 | ||||||||
\(162\) | 2955.66 | 1.43345 | ||||||||
\(163\) | 1893.45i | 0.909857i | 0.890528 | + | 0.454929i | \(0.150335\pi\) | ||||
−0.890528 | + | 0.454929i | \(0.849665\pi\) | |||||||
\(164\) | 1011.65i | 0.481689i | ||||||||
\(165\) | 1028.61i | 0.485316i | ||||||||
\(166\) | −1017.49 | −0.475739 | ||||||||
\(167\) | 290.246i | 0.134491i | 0.997736 | + | 0.0672453i | \(0.0214210\pi\) | ||||
−0.997736 | + | 0.0672453i | \(0.978579\pi\) | |||||||
\(168\) | −2528.29 | −1.16108 | ||||||||
\(169\) | −2196.84 | −0.999928 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1600.05 | 0.715547 | ||||||||
\(172\) | 53.2339 | 0.0235991 | ||||||||
\(173\) | − 3665.86i | − 1.61104i | −0.592567 | − | 0.805521i | \(-0.701886\pi\) | ||||
0.592567 | − | 0.805521i | \(-0.298114\pi\) | |||||||
\(174\) | −4719.59 | −2.05627 | ||||||||
\(175\) | 5305.89i | 2.29193i | ||||||||
\(176\) | − 644.852i | − 0.276179i | ||||||||
\(177\) | 1551.63i | 0.658913i | ||||||||
\(178\) | 2946.08 | 1.24055 | ||||||||
\(179\) | 3628.67 | 1.51519 | 0.757597 | − | 0.652723i | \(-0.226373\pi\) | ||||
0.757597 | + | 0.652723i | \(0.226373\pi\) | |||||||
\(180\) | − 772.355i | − 0.319822i | ||||||||
\(181\) | − 3827.78i | − 1.57191i | −0.618281 | − | 0.785957i | \(-0.712171\pi\) | ||||
0.618281 | − | 0.785957i | \(-0.287829\pi\) | |||||||
\(182\) | − 28.6713i | − 0.0116773i | ||||||||
\(183\) | 3883.27 | 1.56863 | ||||||||
\(184\) | − 2427.82i | − 0.972725i | ||||||||
\(185\) | −1171.43 | −0.465541 | ||||||||
\(186\) | −1043.55 | −0.411382 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 115.249 | 0.0447097 | ||||||||
\(189\) | −1659.48 | −0.638673 | ||||||||
\(190\) | 6434.08i | 2.45672i | ||||||||
\(191\) | −877.247 | −0.332332 | −0.166166 | − | 0.986098i | \(-0.553139\pi\) | ||||
−0.166166 | + | 0.986098i | \(0.553139\pi\) | |||||||
\(192\) | − 1652.60i | − 0.621177i | ||||||||
\(193\) | 4769.70i | 1.77891i | 0.457018 | + | 0.889457i | \(0.348917\pi\) | ||||
−0.457018 | + | 0.889457i | \(0.651083\pi\) | |||||||
\(194\) | − 3279.41i | − 1.21365i | ||||||||
\(195\) | −49.5978 | −0.0182142 | ||||||||
\(196\) | −379.679 | −0.138367 | ||||||||
\(197\) | − 1492.97i | − 0.539949i | −0.962867 | − | 0.269974i | \(-0.912985\pi\) | ||||
0.962867 | − | 0.269974i | \(-0.0870152\pi\) | |||||||
\(198\) | 416.473i | 0.149482i | ||||||||
\(199\) | − 3091.28i | − 1.10118i | −0.834775 | − | 0.550591i | \(-0.814402\pi\) | ||||
0.834775 | − | 0.550591i | \(-0.185598\pi\) | |||||||
\(200\) | −4214.38 | −1.49001 | ||||||||
\(201\) | 2664.48i | 0.935013i | ||||||||
\(202\) | 3663.40 | 1.27602 | ||||||||
\(203\) | 4912.63 | 1.69852 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7402.00 | −2.52185 | ||||||||
\(206\) | 1292.18 | 0.437042 | ||||||||
\(207\) | 2140.88i | 0.718846i | ||||||||
\(208\) | 31.0937 | 0.0103652 | ||||||||
\(209\) | − 853.816i | − 0.282582i | ||||||||
\(210\) | 8965.12i | 2.94596i | ||||||||
\(211\) | 2776.38i | 0.905848i | 0.891549 | + | 0.452924i | \(0.149619\pi\) | ||||
−0.891549 | + | 0.452924i | \(0.850381\pi\) | |||||||
\(212\) | −155.762 | −0.0504612 | ||||||||
\(213\) | 6761.17 | 2.17497 | ||||||||
\(214\) | 941.118i | 0.300624i | ||||||||
\(215\) | 389.498i | 0.123551i | ||||||||
\(216\) | − 1318.10i | − 0.415209i | ||||||||
\(217\) | 1086.24 | 0.339809 | ||||||||
\(218\) | 4492.60i | 1.39577i | ||||||||
\(219\) | 145.856 | 0.0450048 | ||||||||
\(220\) | −412.144 | −0.126303 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1301.63 | −0.393513 | ||||||||
\(223\) | −4641.22 | −1.39372 | −0.696859 | − | 0.717209i | \(-0.745419\pi\) | ||||
−0.696859 | + | 0.717209i | \(0.745419\pi\) | |||||||
\(224\) | − 2517.02i | − 0.750784i | ||||||||
\(225\) | 3716.28 | 1.10112 | ||||||||
\(226\) | − 4444.63i | − 1.30820i | ||||||||
\(227\) | − 1712.30i | − 0.500658i | −0.968161 | − | 0.250329i | \(-0.919461\pi\) | ||||
0.968161 | − | 0.250329i | \(-0.0805388\pi\) | |||||||
\(228\) | 1759.41i | 0.511052i | ||||||||
\(229\) | 6028.18 | 1.73954 | 0.869768 | − | 0.493461i | \(-0.164269\pi\) | ||||
0.869768 | + | 0.493461i | \(0.164269\pi\) | |||||||
\(230\) | −8608.86 | −2.46805 | ||||||||
\(231\) | − 1189.69i | − 0.338857i | ||||||||
\(232\) | 3902.02i | 1.10423i | ||||||||
\(233\) | 2663.60i | 0.748919i | 0.927243 | + | 0.374459i | \(0.122172\pi\) | ||||
−0.927243 | + | 0.374459i | \(0.877828\pi\) | |||||||
\(234\) | −20.0816 | −0.00561015 | ||||||||
\(235\) | 843.249i | 0.234075i | ||||||||
\(236\) | −621.707 | −0.171482 | ||||||||
\(237\) | 4449.47 | 1.21951 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6020.73 | 1.62949 | 0.814747 | − | 0.579817i | \(-0.196876\pi\) | ||||
0.814747 | + | 0.579817i | \(0.196876\pi\) | |||||||
\(240\) | −9722.56 | −2.61495 | ||||||||
\(241\) | 6080.97i | 1.62535i | 0.582716 | + | 0.812676i | \(0.301990\pi\) | ||||
−0.582716 | + | 0.812676i | \(0.698010\pi\) | |||||||
\(242\) | −4113.53 | −1.09268 | ||||||||
\(243\) | 3886.16i | 1.02591i | ||||||||
\(244\) | 1555.95i | 0.408235i | ||||||||
\(245\) | − 2778.01i | − 0.724409i | ||||||||
\(246\) | −8224.74 | −2.13167 | ||||||||
\(247\) | 41.1695 | 0.0106055 | ||||||||
\(248\) | 862.780i | 0.220914i | ||||||||
\(249\) | − 2035.77i | − 0.518120i | ||||||||
\(250\) | 7163.52i | 1.81224i | ||||||||
\(251\) | −3296.82 | −0.829058 | −0.414529 | − | 0.910036i | \(-0.636054\pi\) | ||||
−0.414529 | + | 0.910036i | \(0.636054\pi\) | |||||||
\(252\) | 893.305i | 0.223305i | ||||||||
\(253\) | 1142.41 | 0.283885 | ||||||||
\(254\) | 3268.37 | 0.807384 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3630.28 | 0.886300 | ||||||||
\(257\) | 1243.37 | 0.301786 | 0.150893 | − | 0.988550i | \(-0.451785\pi\) | ||||
0.150893 | + | 0.988550i | \(0.451785\pi\) | |||||||
\(258\) | 432.790i | 0.104435i | ||||||||
\(259\) | 1354.87 | 0.325049 | ||||||||
\(260\) | − 19.8729i | − 0.00474024i | ||||||||
\(261\) | − 3440.84i | − 0.816026i | ||||||||
\(262\) | 710.186i | 0.167463i | ||||||||
\(263\) | −4523.81 | −1.06065 | −0.530324 | − | 0.847795i | \(-0.677930\pi\) | ||||
−0.530324 | + | 0.847795i | \(0.677930\pi\) | |||||||
\(264\) | 944.951 | 0.220294 | ||||||||
\(265\) | − 1139.67i | − 0.264186i | ||||||||
\(266\) | − 7441.66i | − 1.71533i | ||||||||
\(267\) | 5894.44i | 1.35106i | ||||||||
\(268\) | −1067.60 | −0.243337 | ||||||||
\(269\) | − 2155.56i | − 0.488576i | −0.969703 | − | 0.244288i | \(-0.921446\pi\) | ||||
0.969703 | − | 0.244288i | \(-0.0785542\pi\) | |||||||
\(270\) | −4673.86 | −1.05349 | ||||||||
\(271\) | −5433.12 | −1.21785 | −0.608927 | − | 0.793226i | \(-0.708400\pi\) | ||||
−0.608927 | + | 0.793226i | \(0.708400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 57.3648 | 0.0127175 | ||||||||
\(274\) | 5294.59 | 1.16736 | ||||||||
\(275\) | − 1983.08i | − 0.434851i | ||||||||
\(276\) | −2354.11 | −0.513408 | ||||||||
\(277\) | − 3349.75i | − 0.726595i | −0.931673 | − | 0.363297i | \(-0.881651\pi\) | ||||
0.931673 | − | 0.363297i | \(-0.118349\pi\) | |||||||
\(278\) | − 3369.40i | − 0.726919i | ||||||||
\(279\) | − 760.807i | − 0.163256i | ||||||||
\(280\) | 7412.11 | 1.58199 | ||||||||
\(281\) | 2668.18 | 0.566441 | 0.283221 | − | 0.959055i | \(-0.408597\pi\) | ||||
0.283221 | + | 0.959055i | \(0.408597\pi\) | |||||||
\(282\) | 936.977i | 0.197859i | ||||||||
\(283\) | − 5452.65i | − 1.14532i | −0.819792 | − | 0.572662i | \(-0.805911\pi\) | ||||
0.819792 | − | 0.572662i | \(-0.194089\pi\) | |||||||
\(284\) | 2709.07i | 0.566033i | ||||||||
\(285\) | −12873.1 | −2.67558 | ||||||||
\(286\) | 10.7159i | 0.00221555i | ||||||||
\(287\) | 8561.15 | 1.76080 | ||||||||
\(288\) | −1762.94 | −0.360702 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 13836.3 | 2.80170 | ||||||||
\(291\) | 6561.36 | 1.32177 | ||||||||
\(292\) | 58.4417i | 0.0117125i | ||||||||
\(293\) | 6341.24 | 1.26437 | 0.632183 | − | 0.774819i | \(-0.282159\pi\) | ||||
0.632183 | + | 0.774819i | \(0.282159\pi\) | |||||||
\(294\) | − 3086.78i | − 0.612329i | ||||||||
\(295\) | − 4548.86i | − 0.897780i | ||||||||
\(296\) | 1076.15i | 0.211318i | ||||||||
\(297\) | 620.231 | 0.121177 | ||||||||
\(298\) | 2118.04 | 0.411728 | ||||||||
\(299\) | 55.0852i | 0.0106544i | ||||||||
\(300\) | 4086.42i | 0.786433i | ||||||||
\(301\) | − 450.493i | − 0.0862657i | ||||||||
\(302\) | 3334.63 | 0.635385 | ||||||||
\(303\) | 7329.63i | 1.38969i | ||||||||
\(304\) | 8070.38 | 1.52259 | ||||||||
\(305\) | −11384.5 | −2.13729 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 820.602 | 0.152555 | 0.0762773 | − | 0.997087i | \(-0.475697\pi\) | ||||
0.0762773 | + | 0.997087i | \(0.475697\pi\) | |||||||
\(308\) | 476.685 | 0.0881872 | ||||||||
\(309\) | 2585.37i | 0.475975i | ||||||||
\(310\) | 3059.35 | 0.560514 | ||||||||
\(311\) | 7492.46i | 1.36610i | 0.730369 | + | 0.683052i | \(0.239348\pi\) | ||||
−0.730369 | + | 0.683052i | \(0.760652\pi\) | |||||||
\(312\) | 45.5639i | 0.00826779i | ||||||||
\(313\) | − 1217.76i | − 0.219910i | −0.993937 | − | 0.109955i | \(-0.964929\pi\) | ||||
0.993937 | − | 0.109955i | \(-0.0350707\pi\) | |||||||
\(314\) | −2187.79 | −0.393198 | ||||||||
\(315\) | −6536.07 | −1.16910 | ||||||||
\(316\) | 1782.81i | 0.317377i | ||||||||
\(317\) | 5682.18i | 1.00676i | 0.864065 | + | 0.503380i | \(0.167910\pi\) | ||||
−0.864065 | + | 0.503380i | \(0.832090\pi\) | |||||||
\(318\) | − 1266.34i | − 0.223311i | ||||||||
\(319\) | −1836.10 | −0.322263 | ||||||||
\(320\) | 4844.87i | 0.846363i | ||||||||
\(321\) | −1882.96 | −0.327404 | ||||||||
\(322\) | 9957.00 | 1.72324 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2369.47 | −0.406287 | ||||||||
\(325\) | 95.6206 | 0.0163202 | ||||||||
\(326\) | − 6167.97i | − 1.04789i | ||||||||
\(327\) | −8988.68 | −1.52011 | ||||||||
\(328\) | 6799.98i | 1.14471i | ||||||||
\(329\) | − 975.301i | − 0.163435i | ||||||||
\(330\) | − 3350.72i | − 0.558943i | ||||||||
\(331\) | −7387.94 | −1.22682 | −0.613411 | − | 0.789764i | \(-0.710203\pi\) | ||||
−0.613411 | + | 0.789764i | \(0.710203\pi\) | |||||||
\(332\) | 815.693 | 0.134840 | ||||||||
\(333\) | − 948.962i | − 0.156165i | ||||||||
\(334\) | − 945.483i | − 0.154894i | ||||||||
\(335\) | − 7811.36i | − 1.27397i | ||||||||
\(336\) | 11245.1 | 1.82581 | ||||||||
\(337\) | − 5104.29i | − 0.825069i | −0.910942 | − | 0.412534i | \(-0.864644\pi\) | ||||
0.910942 | − | 0.412534i | \(-0.135356\pi\) | |||||||
\(338\) | 7156.26 | 1.15163 | ||||||||
\(339\) | 8892.69 | 1.42473 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −405.982 | −0.0644725 | ||||||||
\(342\) | −5212.19 | −0.824102 | ||||||||
\(343\) | − 4367.10i | − 0.687467i | ||||||||
\(344\) | 357.819 | 0.0560823 | ||||||||
\(345\) | − 17224.4i | − 2.68791i | ||||||||
\(346\) | 11941.6i | 1.85545i | ||||||||
\(347\) | − 8986.15i | − 1.39021i | −0.718910 | − | 0.695103i | \(-0.755359\pi\) | ||||
0.718910 | − | 0.695103i | \(-0.244641\pi\) | |||||||
\(348\) | 3783.55 | 0.582816 | ||||||||
\(349\) | −1924.65 | −0.295198 | −0.147599 | − | 0.989047i | \(-0.547155\pi\) | ||||
−0.147599 | + | 0.989047i | \(0.547155\pi\) | |||||||
\(350\) | − 17284.0i | − 2.63963i | ||||||||
\(351\) | 29.9065i | 0.00454783i | ||||||||
\(352\) | 940.739i | 0.142448i | ||||||||
\(353\) | 4574.33 | 0.689709 | 0.344854 | − | 0.938656i | \(-0.387928\pi\) | ||||
0.344854 | + | 0.938656i | \(0.387928\pi\) | |||||||
\(354\) | − 5054.47i | − 0.758876i | ||||||||
\(355\) | −19821.5 | −2.96343 | ||||||||
\(356\) | −2361.78 | −0.351613 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11820.5 | −1.74506 | ||||||||
\(359\) | −9358.89 | −1.37589 | −0.687943 | − | 0.725765i | \(-0.741486\pi\) | ||||
−0.687943 | + | 0.725765i | \(0.741486\pi\) | |||||||
\(360\) | − 5191.50i | − 0.760044i | ||||||||
\(361\) | 3826.58 | 0.557892 | ||||||||
\(362\) | 12469.1i | 1.81039i | ||||||||
\(363\) | − 8230.23i | − 1.19001i | ||||||||
\(364\) | 22.9849i | 0.00330972i | ||||||||
\(365\) | −427.602 | −0.0613198 | ||||||||
\(366\) | −12649.8 | −1.80661 | ||||||||
\(367\) | 1596.51i | 0.227077i | 0.993534 | + | 0.113539i | \(0.0362186\pi\) | ||||
−0.993534 | + | 0.113539i | \(0.963781\pi\) | |||||||
\(368\) | 10798.2i | 1.52961i | ||||||||
\(369\) | − 5996.29i | − 0.845947i | ||||||||
\(370\) | 3815.95 | 0.536167 | ||||||||
\(371\) | 1318.14i | 0.184459i | ||||||||
\(372\) | 836.585 | 0.116599 | ||||||||
\(373\) | −10884.6 | −1.51094 | −0.755471 | − | 0.655182i | \(-0.772592\pi\) | ||||
−0.755471 | + | 0.655182i | \(0.772592\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14332.6 | −1.97368 | ||||||||
\(376\) | 774.666 | 0.106251 | ||||||||
\(377\) | − 88.5336i | − 0.0120947i | ||||||||
\(378\) | 5405.79 | 0.735565 | ||||||||
\(379\) | − 1561.47i | − 0.211629i | −0.994386 | − | 0.105814i | \(-0.966255\pi\) | ||||
0.994386 | − | 0.105814i | \(-0.0337449\pi\) | |||||||
\(380\) | − 5158.01i | − 0.696317i | ||||||||
\(381\) | 6539.26i | 0.879308i | ||||||||
\(382\) | 2857.65 | 0.382749 | ||||||||
\(383\) | 4409.48 | 0.588287 | 0.294143 | − | 0.955761i | \(-0.404966\pi\) | ||||
0.294143 | + | 0.955761i | \(0.404966\pi\) | |||||||
\(384\) | 11321.9i | 1.50461i | ||||||||
\(385\) | 3487.78i | 0.461697i | ||||||||
\(386\) | − 15537.4i | − 2.04879i | ||||||||
\(387\) | −315.528 | −0.0414450 | ||||||||
\(388\) | 2629.01i | 0.343989i | ||||||||
\(389\) | 8017.21 | 1.04496 | 0.522479 | − | 0.852652i | \(-0.325007\pi\) | ||||
0.522479 | + | 0.852652i | \(0.325007\pi\) | |||||||
\(390\) | 161.566 | 0.0209775 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2552.06 | −0.328823 | ||||||||
\(393\) | −1420.92 | −0.182382 | ||||||||
\(394\) | 4863.39i | 0.621864i | ||||||||
\(395\) | −13044.4 | −1.66160 | ||||||||
\(396\) | − 333.874i | − 0.0423681i | ||||||||
\(397\) | 9437.12i | 1.19304i | 0.802599 | + | 0.596519i | \(0.203450\pi\) | ||||
−0.802599 | + | 0.596519i | \(0.796550\pi\) | |||||||
\(398\) | 10069.9i | 1.26824i | ||||||||
\(399\) | 14889.1 | 1.86814 | ||||||||
\(400\) | 18744.3 | 2.34304 | ||||||||
\(401\) | − 4509.28i | − 0.561553i | −0.959773 | − | 0.280777i | \(-0.909408\pi\) | ||||
0.959773 | − | 0.280777i | \(-0.0905920\pi\) | |||||||
\(402\) | − 8679.59i | − 1.07686i | ||||||||
\(403\) | − 19.5757i | − 0.00241969i | ||||||||
\(404\) | −2936.84 | −0.361666 | ||||||||
\(405\) | − 17336.8i | − 2.12709i | ||||||||
\(406\) | −16003.0 | −1.95620 | ||||||||
\(407\) | −506.384 | −0.0616721 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12446.9 | 1.50480 | 0.752398 | − | 0.658709i | \(-0.228897\pi\) | ||||
0.752398 | + | 0.658709i | \(0.228897\pi\) | |||||||
\(410\) | 24112.2 | 2.90443 | ||||||||
\(411\) | 10593.3i | 1.27136i | ||||||||
\(412\) | −1035.91 | −0.123872 | ||||||||
\(413\) | 5261.21i | 0.626846i | ||||||||
\(414\) | − 6973.95i | − 0.827901i | ||||||||
\(415\) | 5968.21i | 0.705946i | ||||||||
\(416\) | −45.3608 | −0.00534615 | ||||||||
\(417\) | 6741.41 | 0.791675 | ||||||||
\(418\) | 2781.33i | 0.325452i | ||||||||
\(419\) | − 1648.22i | − 0.192173i | −0.995373 | − | 0.0960867i | \(-0.969367\pi\) | ||||
0.995373 | − | 0.0960867i | \(-0.0306326\pi\) | |||||||
\(420\) | − 7187.07i | − 0.834984i | ||||||||
\(421\) | 14395.5 | 1.66649 | 0.833247 | − | 0.552901i | \(-0.186479\pi\) | ||||
0.833247 | + | 0.552901i | \(0.186479\pi\) | |||||||
\(422\) | − 9044.13i | − 1.04327i | ||||||||
\(423\) | −683.108 | −0.0785197 | ||||||||
\(424\) | −1046.98 | −0.119919 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22024.7 | −2.50493 | ||||||||
\(427\) | 13167.3 | 1.49229 | ||||||||
\(428\) | − 754.466i | − 0.0852068i | ||||||||
\(429\) | −21.4401 | −0.00241291 | ||||||||
\(430\) | − 1268.80i | − 0.142295i | ||||||||
\(431\) | 5351.92i | 0.598127i | 0.954233 | + | 0.299064i | \(0.0966743\pi\) | ||||
−0.954233 | + | 0.299064i | \(0.903326\pi\) | |||||||
\(432\) | 5862.50i | 0.652916i | ||||||||
\(433\) | −15578.0 | −1.72894 | −0.864472 | − | 0.502680i | \(-0.832347\pi\) | ||||
−0.864472 | + | 0.502680i | \(0.832347\pi\) | |||||||
\(434\) | −3538.44 | −0.391361 | ||||||||
\(435\) | 27683.2i | 3.05129i | ||||||||
\(436\) | − 3601.58i | − 0.395607i | ||||||||
\(437\) | 14297.4i | 1.56507i | ||||||||
\(438\) | −475.130 | −0.0518324 | ||||||||
\(439\) | − 16584.8i | − 1.80307i | −0.432707 | − | 0.901535i | \(-0.642442\pi\) | ||||
0.432707 | − | 0.901535i | \(-0.357558\pi\) | |||||||
\(440\) | −2770.28 | −0.300155 | ||||||||
\(441\) | 2250.44 | 0.243001 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5163.31 | 0.553761 | 0.276881 | − | 0.960904i | \(-0.410699\pi\) | ||||
0.276881 | + | 0.960904i | \(0.410699\pi\) | |||||||
\(444\) | 1043.48 | 0.111535 | ||||||||
\(445\) | − 17280.5i | − 1.84084i | ||||||||
\(446\) | 15118.9 | 1.60516 | ||||||||
\(447\) | 4237.72i | 0.448406i | ||||||||
\(448\) | − 5603.57i | − 0.590946i | ||||||||
\(449\) | − 10771.9i | − 1.13220i | −0.824337 | − | 0.566099i | \(-0.808452\pi\) | ||||
0.824337 | − | 0.566099i | \(-0.191548\pi\) | |||||||
\(450\) | −12105.9 | −1.26817 | ||||||||
\(451\) | −3199.74 | −0.334079 | ||||||||
\(452\) | 3563.13i | 0.370786i | ||||||||
\(453\) | 6671.84i | 0.691987i | ||||||||
\(454\) | 5577.86i | 0.576612i | ||||||||
\(455\) | −168.175 | −0.0173278 | ||||||||
\(456\) | 11826.1i | 1.21450i | ||||||||
\(457\) | −5024.59 | −0.514312 | −0.257156 | − | 0.966370i | \(-0.582785\pi\) | ||||
−0.257156 | + | 0.966370i | \(0.582785\pi\) | |||||||
\(458\) | −19636.9 | −2.00344 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6901.47 | 0.699527 | ||||||||
\(461\) | 2366.96 | 0.239133 | 0.119567 | − | 0.992826i | \(-0.461849\pi\) | ||||
0.119567 | + | 0.992826i | \(0.461849\pi\) | |||||||
\(462\) | 3875.44i | 0.390264i | ||||||||
\(463\) | −17712.9 | −1.77795 | −0.888974 | − | 0.457958i | \(-0.848581\pi\) | ||||
−0.888974 | + | 0.457958i | \(0.848581\pi\) | |||||||
\(464\) | − 17355.1i | − 1.73640i | ||||||||
\(465\) | 6121.06i | 0.610446i | ||||||||
\(466\) | − 8676.73i | − 0.862536i | ||||||||
\(467\) | 19592.7 | 1.94141 | 0.970707 | − | 0.240267i | \(-0.0772349\pi\) | ||||
0.970707 | + | 0.240267i | \(0.0772349\pi\) | |||||||
\(468\) | 16.0988 | 0.00159010 | ||||||||
\(469\) | 9034.61i | 0.889509i | ||||||||
\(470\) | − 2746.90i | − 0.269586i | ||||||||
\(471\) | − 4377.27i | − 0.428225i | ||||||||
\(472\) | −4178.89 | −0.407519 | ||||||||
\(473\) | 168.372i | 0.0163673i | ||||||||
\(474\) | −14494.2 | −1.40452 | ||||||||
\(475\) | 24818.4 | 2.39736 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 923.234 | 0.0886205 | ||||||||
\(478\) | −19612.7 | −1.87670 | ||||||||
\(479\) | − 4060.41i | − 0.387317i | −0.981069 | − | 0.193659i | \(-0.937965\pi\) | ||||
0.981069 | − | 0.193659i | \(-0.0620354\pi\) | |||||||
\(480\) | 14183.7 | 1.34874 | ||||||||
\(481\) | − 24.4170i | − 0.00231459i | ||||||||
\(482\) | − 19808.9i | − 1.87193i | ||||||||
\(483\) | 19921.7i | 1.87675i | ||||||||
\(484\) | 3297.69 | 0.309701 | ||||||||
\(485\) | −19235.7 | −1.80093 | ||||||||
\(486\) | − 12659.2i | − 1.18155i | ||||||||
\(487\) | 7256.96i | 0.675244i | 0.941282 | + | 0.337622i | \(0.109623\pi\) | ||||
−0.941282 | + | 0.337622i | \(0.890377\pi\) | |||||||
\(488\) | 10458.5i | 0.970155i | ||||||||
\(489\) | 12340.7 | 1.14124 | ||||||||
\(490\) | 9049.42i | 0.834308i | ||||||||
\(491\) | 769.855 | 0.0707598 | 0.0353799 | − | 0.999374i | \(-0.488736\pi\) | ||||
0.0353799 | + | 0.999374i | \(0.488736\pi\) | |||||||
\(492\) | 6593.53 | 0.604185 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −134.111 | −0.0122144 | ||||||||
\(495\) | 2442.86 | 0.221815 | ||||||||
\(496\) | − 3837.39i | − 0.347387i | ||||||||
\(497\) | 22925.5 | 2.06912 | ||||||||
\(498\) | 6631.58i | 0.596723i | ||||||||
\(499\) | − 1432.66i | − 0.128526i | −0.997933 | − | 0.0642630i | \(-0.979530\pi\) | ||||
0.997933 | − | 0.0642630i | \(-0.0204697\pi\) | |||||||
\(500\) | − 5742.78i | − 0.513650i | ||||||||
\(501\) | 1891.70 | 0.168692 | ||||||||
\(502\) | 10739.5 | 0.954833 | ||||||||
\(503\) | − 16206.3i | − 1.43659i | −0.695739 | − | 0.718295i | \(-0.744923\pi\) | ||||
0.695739 | − | 0.718295i | \(-0.255077\pi\) | |||||||
\(504\) | 6004.48i | 0.530676i | ||||||||
\(505\) | − 21488.0i | − 1.89348i | ||||||||
\(506\) | −3721.44 | −0.326953 | ||||||||
\(507\) | 14318.1i | 1.25422i | ||||||||
\(508\) | −2620.15 | −0.228839 | ||||||||
\(509\) | 15009.4 | 1.30703 | 0.653517 | − | 0.756912i | \(-0.273293\pi\) | ||||
0.653517 | + | 0.756912i | \(0.273293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 494.564 | 0.0428145 | ||||||||
\(512\) | 2071.37 | 0.178794 | ||||||||
\(513\) | 7762.24i | 0.668053i | ||||||||
\(514\) | −4050.29 | −0.347570 | ||||||||
\(515\) | − 7579.44i | − 0.648524i | ||||||||
\(516\) | − 346.955i | − 0.0296005i | ||||||||
\(517\) | 364.520i | 0.0310088i | ||||||||
\(518\) | −4413.53 | −0.374361 | ||||||||
\(519\) | −23892.5 | −2.02074 | ||||||||
\(520\) | − 133.578i | − 0.0112650i | ||||||||
\(521\) | − 19626.5i | − 1.65039i | −0.564846 | − | 0.825196i | \(-0.691064\pi\) | ||||
0.564846 | − | 0.825196i | \(-0.308936\pi\) | |||||||
\(522\) | 11208.6i | 0.939824i | ||||||||
\(523\) | −9267.41 | −0.774829 | −0.387414 | − | 0.921906i | \(-0.626632\pi\) | ||||
−0.387414 | + | 0.921906i | \(0.626632\pi\) | |||||||
\(524\) | − 569.335i | − 0.0474647i | ||||||||
\(525\) | 34581.5 | 2.87478 | ||||||||
\(526\) | 14736.4 | 1.22156 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −4202.87 | −0.346414 | ||||||||
\(529\) | −6963.04 | −0.572289 | ||||||||
\(530\) | 3712.50i | 0.304265i | ||||||||
\(531\) | 3684.99 | 0.301158 | ||||||||
\(532\) | 5965.76i | 0.486181i | ||||||||
\(533\) | − 154.286i | − 0.0125382i | ||||||||
\(534\) | − 19201.3i | − 1.55603i | ||||||||
\(535\) | 5520.22 | 0.446094 | ||||||||
\(536\) | −7176.04 | −0.578280 | ||||||||
\(537\) | − 23650.1i | − 1.90052i | ||||||||
\(538\) | 7021.79i | 0.562697i | ||||||||
\(539\) | − 1200.88i | − 0.0959655i | ||||||||
\(540\) | 3746.90 | 0.298594 | ||||||||
\(541\) | − 907.733i | − 0.0721377i | −0.999349 | − | 0.0360689i | \(-0.988516\pi\) | ||||
0.999349 | − | 0.0360689i | \(-0.0114836\pi\) | |||||||
\(542\) | 17698.5 | 1.40261 | ||||||||
\(543\) | −24947.8 | −1.97166 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26351.8 | 2.07117 | ||||||||
\(546\) | −186.867 | −0.0146468 | ||||||||
\(547\) | − 11197.7i | − 0.875281i | −0.899150 | − | 0.437640i | \(-0.855814\pi\) | ||||
0.899150 | − | 0.437640i | \(-0.144186\pi\) | |||||||
\(548\) | −4244.51 | −0.330870 | ||||||||
\(549\) | − 9222.44i | − 0.716947i | ||||||||
\(550\) | 6459.92i | 0.500822i | ||||||||
\(551\) | − 22979.0i | − 1.77665i | ||||||||
\(552\) | −15823.5 | −1.22009 | ||||||||
\(553\) | 15087.1 | 1.16016 | ||||||||
\(554\) | 10911.9i | 0.836825i | ||||||||
\(555\) | 7634.85i | 0.583931i | ||||||||
\(556\) | 2701.15i | 0.206033i | ||||||||
\(557\) | −3207.25 | −0.243978 | −0.121989 | − | 0.992531i | \(-0.538927\pi\) | ||||
−0.121989 | + | 0.992531i | \(0.538927\pi\) | |||||||
\(558\) | 2478.35i | 0.188023i | ||||||||
\(559\) | −8.11861 | −0.000614276 0 | ||||||||
\(560\) | −32966.9 | −2.48769 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8691.64 | −0.652375 | ||||||||
\(563\) | 6522.79 | 0.488282 | 0.244141 | − | 0.969740i | \(-0.421494\pi\) | ||||
0.244141 | + | 0.969740i | \(0.421494\pi\) | |||||||
\(564\) | − 751.146i | − 0.0560797i | ||||||||
\(565\) | −26070.4 | −1.94122 | ||||||||
\(566\) | 17762.2i | 1.31908i | ||||||||
\(567\) | 20051.7i | 1.48517i | ||||||||
\(568\) | 18209.4i | 1.34516i | ||||||||
\(569\) | 3040.50 | 0.224015 | 0.112007 | − | 0.993707i | \(-0.464272\pi\) | ||||
0.112007 | + | 0.993707i | \(0.464272\pi\) | |||||||
\(570\) | 41934.6 | 3.08148 | ||||||||
\(571\) | − 17273.2i | − 1.26596i | −0.774169 | − | 0.632979i | \(-0.781832\pi\) | ||||
0.774169 | − | 0.632979i | \(-0.218168\pi\) | |||||||
\(572\) | − 8.59064i | 0 0.000627959i | ||||||||
\(573\) | 5717.51i | 0.416846i | ||||||||
\(574\) | −27888.2 | −2.02793 | ||||||||
\(575\) | 33207.2i | 2.40841i | ||||||||
\(576\) | −3924.78 | −0.283910 | ||||||||
\(577\) | −5804.29 | −0.418779 | −0.209390 | − | 0.977832i | \(-0.567148\pi\) | ||||
−0.209390 | + | 0.977832i | \(0.567148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31086.8 | 2.23130 | ||||||||
\(580\) | −11092.1 | −0.794096 | ||||||||
\(581\) | − 6902.83i | − 0.492904i | ||||||||
\(582\) | −21373.8 | −1.52229 | ||||||||
\(583\) | − 492.656i | − 0.0349978i | ||||||||
\(584\) | 392.824i | 0.0278342i | ||||||||
\(585\) | 117.791i | 0.00832486i | ||||||||
\(586\) | −20656.8 | −1.45618 | ||||||||
\(587\) | −12862.4 | −0.904407 | −0.452204 | − | 0.891915i | \(-0.649362\pi\) | ||||
−0.452204 | + | 0.891915i | \(0.649362\pi\) | |||||||
\(588\) | 2474.58i | 0.173554i | ||||||||
\(589\) | − 5080.89i | − 0.355441i | ||||||||
\(590\) | 14818.0i | 1.03398i | ||||||||
\(591\) | −9730.55 | −0.677261 | ||||||||
\(592\) | − 4786.41i | − 0.332298i | ||||||||
\(593\) | −1319.33 | −0.0913631 | −0.0456816 | − | 0.998956i | \(-0.514546\pi\) | ||||
−0.0456816 | + | 0.998956i | \(0.514546\pi\) | |||||||
\(594\) | −2020.42 | −0.139560 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1697.97 | −0.116697 | ||||||||
\(597\) | −20147.6 | −1.38122 | ||||||||
\(598\) | − 179.441i | − 0.0122707i | ||||||||
\(599\) | −16269.3 | −1.10976 | −0.554881 | − | 0.831930i | \(-0.687236\pi\) | ||||
−0.554881 | + | 0.831930i | \(0.687236\pi\) | |||||||
\(600\) | 27467.5i | 1.86893i | ||||||||
\(601\) | 7427.38i | 0.504108i | 0.967713 | + | 0.252054i | \(0.0811061\pi\) | ||||
−0.967713 | + | 0.252054i | \(0.918894\pi\) | |||||||
\(602\) | 1467.49i | 0.0993529i | ||||||||
\(603\) | 6327.90 | 0.427350 | ||||||||
\(604\) | −2673.27 | −0.180089 | ||||||||
\(605\) | 24128.3i | 1.62141i | ||||||||
\(606\) | − 23876.4i | − 1.60052i | ||||||||
\(607\) | − 7212.10i | − 0.482257i | −0.970493 | − | 0.241129i | \(-0.922482\pi\) | ||||
0.970493 | − | 0.241129i | \(-0.0775176\pi\) | |||||||
\(608\) | −11773.4 | −0.785322 | ||||||||
\(609\) | − 32018.4i | − 2.13046i | ||||||||
\(610\) | 37085.1 | 2.46153 | ||||||||
\(611\) | −17.5765 | −0.00116378 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15446.5 | −1.01775 | −0.508873 | − | 0.860842i | \(-0.669938\pi\) | ||||
−0.508873 | + | 0.860842i | \(0.669938\pi\) | |||||||
\(614\) | −2673.13 | −0.175698 | ||||||||
\(615\) | 48243.1i | 3.16317i | ||||||||
\(616\) | 3204.11 | 0.209573 | ||||||||
\(617\) | − 8746.54i | − 0.570701i | −0.958423 | − | 0.285350i | \(-0.907890\pi\) | ||||
0.958423 | − | 0.285350i | \(-0.0921100\pi\) | |||||||
\(618\) | − 8421.89i | − 0.548185i | ||||||||
\(619\) | − 4740.09i | − 0.307787i | −0.988087 | − | 0.153894i | \(-0.950819\pi\) | ||||
0.988087 | − | 0.153894i | \(-0.0491813\pi\) | |||||||
\(620\) | −2452.59 | −0.158868 | ||||||||
\(621\) | −10385.9 | −0.671133 | ||||||||
\(622\) | − 24406.9i | − 1.57335i | ||||||||
\(623\) | 19986.7i | 1.28531i | ||||||||
\(624\) | − 202.655i | − 0.0130011i | ||||||||
\(625\) | 12007.1 | 0.768453 | ||||||||
\(626\) | 3966.89i | 0.253273i | ||||||||
\(627\) | −5564.80 | −0.354445 | ||||||||
\(628\) | 1753.89 | 0.111445 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 21291.4 | 1.34646 | ||||||||
\(631\) | 17055.1 | 1.07600 | 0.537998 | − | 0.842946i | \(-0.319181\pi\) | ||||
0.537998 | + | 0.842946i | \(0.319181\pi\) | |||||||
\(632\) | 11983.4i | 0.754233i | ||||||||
\(633\) | 18095.2 | 1.13621 | ||||||||
\(634\) | − 18509.8i | − 1.15949i | ||||||||
\(635\) | − 19170.9i | − 1.19807i | ||||||||
\(636\) | 1015.19i | 0.0632938i | ||||||||
\(637\) | 57.9042 | 0.00360164 | ||||||||
\(638\) | 5981.14 | 0.371153 | ||||||||
\(639\) | − 16057.2i | − 0.994074i | ||||||||
\(640\) | − 33192.1i | − 2.05005i | ||||||||
\(641\) | 16050.5i | 0.989012i | 0.869174 | + | 0.494506i | \(0.164651\pi\) | ||||
−0.869174 | + | 0.494506i | \(0.835349\pi\) | |||||||
\(642\) | 6133.80 | 0.377074 | ||||||||
\(643\) | 14821.5i | 0.909027i | 0.890740 | + | 0.454514i | \(0.150187\pi\) | ||||
−0.890740 | + | 0.454514i | \(0.849813\pi\) | |||||||
\(644\) | −7982.23 | −0.488422 | ||||||||
\(645\) | 2538.58 | 0.154971 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30527.0 | −1.85493 | −0.927465 | − | 0.373910i | \(-0.878017\pi\) | ||||
−0.927465 | + | 0.373910i | \(0.878017\pi\) | |||||||
\(648\) | −15926.7 | −0.965526 | ||||||||
\(649\) | − 1966.38i | − 0.118933i | ||||||||
\(650\) | −311.486 | −0.0187962 | ||||||||
\(651\) | − 7079.62i | − 0.426224i | ||||||||
\(652\) | 4944.68i | 0.297007i | ||||||||
\(653\) | 20173.6i | 1.20897i | 0.796618 | + | 0.604483i | \(0.206620\pi\) | ||||
−0.796618 | + | 0.604483i | \(0.793380\pi\) | |||||||
\(654\) | 29280.8 | 1.75072 | ||||||||
\(655\) | 4165.67 | 0.248498 | ||||||||
\(656\) | − 30244.3i | − 1.80007i | ||||||||
\(657\) | − 346.396i | − 0.0205696i | ||||||||
\(658\) | 3177.07i | 0.188229i | ||||||||
\(659\) | −21503.0 | −1.27107 | −0.635537 | − | 0.772071i | \(-0.719221\pi\) | ||||
−0.635537 | + | 0.772071i | \(0.719221\pi\) | |||||||
\(660\) | 2686.17i | 0.158423i | ||||||||
\(661\) | 1772.12 | 0.104278 | 0.0521389 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521389 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(662\) | 24066.4 | 1.41294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5482.80 | 0.320443 | ||||||||
\(665\) | −43649.8 | −2.54536 | ||||||||
\(666\) | 3091.26i | 0.179856i | ||||||||
\(667\) | 30746.0 | 1.78485 | ||||||||
\(668\) | 757.966i | 0.0439021i | ||||||||
\(669\) | 30249.4i | 1.74815i | ||||||||
\(670\) | 25445.7i | 1.46724i | ||||||||
\(671\) | −4921.27 | −0.283135 | ||||||||
\(672\) | −16404.9 | −0.941713 | ||||||||
\(673\) | 33449.4i | 1.91587i | 0.286983 | + | 0.957936i | \(0.407348\pi\) | ||||
−0.286983 | + | 0.957936i | \(0.592652\pi\) | |||||||
\(674\) | 16627.3i | 0.950239i | ||||||||
\(675\) | 18028.6i | 1.02803i | ||||||||
\(676\) | −5736.96 | −0.326409 | ||||||||
\(677\) | 805.765i | 0.0457431i | 0.999738 | + | 0.0228716i | \(0.00728088\pi\) | ||||
−0.999738 | + | 0.0228716i | \(0.992719\pi\) | |||||||
\(678\) | −28968.2 | −1.64088 | ||||||||
\(679\) | 22248.0 | 1.25744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11160.0 | −0.627978 | ||||||||
\(682\) | 1322.49 | 0.0742536 | ||||||||
\(683\) | − 993.802i | − 0.0556761i | −0.999612 | − | 0.0278380i | \(-0.991138\pi\) | ||||
0.999612 | − | 0.0278380i | \(-0.00886227\pi\) | |||||||
\(684\) | 4178.46 | 0.233578 | ||||||||
\(685\) | − 31056.0i | − 1.73224i | ||||||||
\(686\) | 14225.9i | 0.791762i | ||||||||
\(687\) | − 39289.1i | − 2.18191i | ||||||||
\(688\) | −1591.47 | −0.0881895 | ||||||||
\(689\) | 23.7550 | 0.00131349 | ||||||||
\(690\) | 56108.8i | 3.09569i | ||||||||
\(691\) | 33450.1i | 1.84154i | 0.390111 | + | 0.920768i | \(0.372437\pi\) | ||||
−0.390111 | + | 0.920768i | \(0.627563\pi\) | |||||||
\(692\) | − 9573.25i | − 0.525896i | ||||||||
\(693\) | −2825.41 | −0.154875 | ||||||||
\(694\) | 29272.6i | 1.60111i | ||||||||
\(695\) | −19763.6 | −1.07867 | ||||||||
\(696\) | 25431.7 | 1.38504 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6269.59 | 0.339982 | ||||||||
\(699\) | 17360.2 | 0.939373 | ||||||||
\(700\) | 13856.1i | 0.748159i | ||||||||
\(701\) | −18290.5 | −0.985481 | −0.492740 | − | 0.870176i | \(-0.664005\pi\) | ||||
−0.492740 | + | 0.870176i | \(0.664005\pi\) | |||||||
\(702\) | − 97.4210i | − 0.00523778i | ||||||||
\(703\) | − 6337.44i | − 0.340002i | ||||||||
\(704\) | 2094.34i | 0.112121i | ||||||||
\(705\) | 5495.93 | 0.293601 | ||||||||
\(706\) | −14901.0 | −0.794343 | ||||||||
\(707\) | 24853.1i | 1.32206i | ||||||||
\(708\) | 4052.02i | 0.215091i | ||||||||
\(709\) | − 6780.00i | − 0.359137i | −0.983745 | − | 0.179569i | \(-0.942530\pi\) | ||||
0.983745 | − | 0.179569i | \(-0.0574702\pi\) | |||||||
\(710\) | 64569.0 | 3.41300 | ||||||||
\(711\) | − 10567.1i | − 0.557380i | ||||||||
\(712\) | −15875.1 | −0.835595 | ||||||||
\(713\) | 6798.28 | 0.357079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.8554 | 0.00328763 | ||||||||
\(716\) | 9476.13 | 0.494608 | ||||||||
\(717\) | − 39240.5i | − 2.04388i | ||||||||
\(718\) | 30486.8 | 1.58462 | ||||||||
\(719\) | 24591.0i | 1.27551i | 0.770240 | + | 0.637754i | \(0.220136\pi\) | ||||
−0.770240 | + | 0.637754i | \(0.779864\pi\) | |||||||
\(720\) | 23090.3i | 1.19517i | ||||||||
\(721\) | 8766.37i | 0.452811i | ||||||||
\(722\) | −12465.2 | −0.642528 | ||||||||
\(723\) | 39633.1 | 2.03869 | ||||||||
\(724\) | − 9996.08i | − 0.513124i | ||||||||
\(725\) | − 53371.1i | − 2.73400i | ||||||||
\(726\) | 26810.2i | 1.37055i | ||||||||
\(727\) | −9819.79 | −0.500957 | −0.250479 | − | 0.968122i | \(-0.580588\pi\) | ||||
−0.250479 | + | 0.968122i | \(0.580588\pi\) | |||||||
\(728\) | 154.497i | 0.00786542i | ||||||||
\(729\) | 830.242 | 0.0421806 | ||||||||
\(730\) | 1392.92 | 0.0706225 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 10141.0 | 0.512052 | ||||||||
\(733\) | 10751.8 | 0.541783 | 0.270892 | − | 0.962610i | \(-0.412682\pi\) | ||||
0.270892 | + | 0.962610i | \(0.412682\pi\) | |||||||
\(734\) | − 5200.68i | − 0.261527i | ||||||||
\(735\) | −18105.8 | −0.908631 | ||||||||
\(736\) | − 15753.0i | − 0.788942i | ||||||||
\(737\) | − 3376.69i | − 0.168768i | ||||||||
\(738\) | 19533.1i | 0.974284i | ||||||||
\(739\) | 1809.70 | 0.0900823 | 0.0450412 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450412 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(740\) | −3059.13 | −0.151968 | ||||||||
\(741\) | − 268.325i | − 0.0133025i | ||||||||
\(742\) | − 4293.87i | − 0.212443i | ||||||||
\(743\) | 895.790i | 0.0442306i | 0.999755 | + | 0.0221153i | \(0.00704010\pi\) | ||||
−0.999755 | + | 0.0221153i | \(0.992960\pi\) | |||||||
\(744\) | 5623.22 | 0.277093 | ||||||||
\(745\) | − 12423.6i | − 0.610960i | ||||||||
\(746\) | 35456.7 | 1.74016 | ||||||||
\(747\) | −4834.79 | −0.236808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6384.69 | −0.311470 | ||||||||
\(750\) | 46688.7 | 2.27311 | ||||||||
\(751\) | 11683.1i | 0.567672i | 0.958873 | + | 0.283836i | \(0.0916071\pi\) | ||||
−0.958873 | + | 0.283836i | \(0.908393\pi\) | |||||||
\(752\) | −3445.49 | −0.167080 | ||||||||
\(753\) | 21487.2i | 1.03989i | ||||||||
\(754\) | 288.400i | 0.0139296i | ||||||||
\(755\) | − 19559.6i | − 0.942844i | ||||||||
\(756\) | −4333.66 | −0.208484 | ||||||||
\(757\) | 12621.2 | 0.605976 | 0.302988 | − | 0.952994i | \(-0.402016\pi\) | ||||
0.302988 | + | 0.952994i | \(0.402016\pi\) | |||||||
\(758\) | 5086.53i | 0.243735i | ||||||||
\(759\) | − 7445.75i | − 0.356079i | ||||||||
\(760\) | − 34670.3i | − 1.65477i | ||||||||
\(761\) | −5759.46 | −0.274350 | −0.137175 | − | 0.990547i | \(-0.543802\pi\) | ||||
−0.137175 | + | 0.990547i | \(0.543802\pi\) | |||||||
\(762\) | − 21301.8i | − 1.01271i | ||||||||
\(763\) | −30478.5 | −1.44613 | ||||||||
\(764\) | −2290.89 | −0.108484 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14364.0 | −0.677535 | ||||||||
\(767\) | 94.8156 | 0.00446361 | ||||||||
\(768\) | − 23660.6i | − 1.11169i | ||||||||
\(769\) | 3245.56 | 0.152195 | 0.0760975 | − | 0.997100i | \(-0.475754\pi\) | ||||
0.0760975 | + | 0.997100i | \(0.475754\pi\) | |||||||
\(770\) | − 11361.5i | − 0.531741i | ||||||||
\(771\) | − 8103.72i | − 0.378532i | ||||||||
\(772\) | 12455.9i | 0.580695i | ||||||||
\(773\) | 2500.27 | 0.116337 | 0.0581684 | − | 0.998307i | \(-0.481474\pi\) | ||||
0.0581684 | + | 0.998307i | \(0.481474\pi\) | |||||||
\(774\) | 1027.84 | 0.0477325 | ||||||||
\(775\) | − 11800.9i | − 0.546970i | ||||||||
\(776\) | 17671.2i | 0.817475i | ||||||||
\(777\) | − 8830.47i | − 0.407711i | ||||||||
\(778\) | −26116.2 | −1.20349 | ||||||||
\(779\) | − 40045.0i | − 1.84180i | ||||||||
\(780\) | −129.523 | −0.00594571 | ||||||||
\(781\) | −8568.44 | −0.392577 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16692.4 | 0.761863 | ||||||||
\(784\) | 11350.8 | 0.517075 | ||||||||
\(785\) | 12832.7i | 0.583464i | ||||||||
\(786\) | 4628.68 | 0.210050 | ||||||||
\(787\) | − 15270.8i | − 0.691671i | −0.938295 | − | 0.345835i | \(-0.887596\pi\) | ||||
0.938295 | − | 0.345835i | \(-0.112404\pi\) | |||||||
\(788\) | − 3898.84i | − 0.176257i | ||||||||
\(789\) | 29484.2i | 1.33038i | ||||||||
\(790\) | 42492.3 | 1.91368 | ||||||||
\(791\) | 30153.0 | 1.35540 | ||||||||
\(792\) | − 2244.18i | − 0.100686i | ||||||||
\(793\) | − 237.295i | − 0.0106262i | ||||||||
\(794\) | − 30741.7i | − 1.37403i | ||||||||
\(795\) | −7427.86 | −0.331370 | ||||||||
\(796\) | − 8072.76i | − 0.359462i | ||||||||
\(797\) | −6885.20 | −0.306006 | −0.153003 | − | 0.988226i | \(-0.548894\pi\) | ||||
−0.153003 | + | 0.988226i | \(0.548894\pi\) | |||||||
\(798\) | −48501.5 | −2.15155 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −27345.1 | −1.20849 | ||||||||
\(801\) | 13998.8 | 0.617507 | ||||||||
\(802\) | 14689.1i | 0.646746i | ||||||||
\(803\) | −184.844 | −0.00812328 | ||||||||
\(804\) | 6958.17i | 0.305219i | ||||||||
\(805\) | − 58403.8i | − 2.55710i | ||||||||
\(806\) | 63.7684i | 0.00278678i | ||||||||
\(807\) | −14049.0 | −0.612824 | ||||||||
\(808\) | −19740.4 | −0.859485 | ||||||||
\(809\) | − 13606.4i | − 0.591318i | −0.955294 | − | 0.295659i | \(-0.904461\pi\) | ||||
0.955294 | − | 0.295659i | \(-0.0955392\pi\) | |||||||
\(810\) | 56474.9i | 2.44978i | ||||||||
\(811\) | 12718.7i | 0.550694i | 0.961345 | + | 0.275347i | \(0.0887927\pi\) | ||||
−0.961345 | + | 0.275347i | \(0.911207\pi\) | |||||||
\(812\) | 12829.1 | 0.554452 | ||||||||
\(813\) | 35410.7i | 1.52756i | ||||||||
\(814\) | 1649.56 | 0.0710283 | ||||||||
\(815\) | −36178.9 | −1.55496 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2107.19 | −0.0902341 | ||||||||
\(818\) | −40546.2 | −1.73309 | ||||||||
\(819\) | − 136.237i | − 0.00581257i | ||||||||
\(820\) | −19330.0 | −0.823212 | ||||||||
\(821\) | 29119.6i | 1.23786i | 0.785447 | + | 0.618929i | \(0.212433\pi\) | ||||
−0.785447 | + | 0.618929i | \(0.787567\pi\) | |||||||
\(822\) | − 34507.8i | − 1.46423i | ||||||||
\(823\) | 6284.88i | 0.266193i | 0.991103 | + | 0.133097i | \(0.0424921\pi\) | ||||
−0.991103 | + | 0.133097i | \(0.957508\pi\) | |||||||
\(824\) | −6962.98 | −0.294377 | ||||||||
\(825\) | −12924.8 | −0.545437 | ||||||||
\(826\) | − 17138.5i | − 0.721944i | ||||||||
\(827\) | − 5383.60i | − 0.226368i | −0.993574 | − | 0.113184i | \(-0.963895\pi\) | ||||
0.993574 | − | 0.113184i | \(-0.0361049\pi\) | |||||||
\(828\) | 5590.81i | 0.234655i | ||||||||
\(829\) | 25382.6 | 1.06342 | 0.531709 | − | 0.846927i | \(-0.321550\pi\) | ||||
0.531709 | + | 0.846927i | \(0.321550\pi\) | |||||||
\(830\) | − 19441.6i | − 0.813045i | ||||||||
\(831\) | −21832.2 | −0.911372 | ||||||||
\(832\) | −100.985 | −0.00420798 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21960.3 | −0.911779 | ||||||||
\(835\) | −5545.83 | −0.229846 | ||||||||
\(836\) | − 2229.71i | − 0.0922440i | ||||||||
\(837\) | 3690.88 | 0.152420 | ||||||||
\(838\) | 5369.10i | 0.221328i | ||||||||
\(839\) | − 2499.44i | − 0.102849i | −0.998677 | − | 0.0514246i | \(-0.983624\pi\) | ||||
0.998677 | − | 0.0514246i | \(-0.0163762\pi\) | |||||||
\(840\) | − 48308.9i | − 1.98431i | ||||||||
\(841\) | −25026.4 | −1.02614 | ||||||||
\(842\) | −46893.7 | −1.91932 | ||||||||
\(843\) | − 17390.0i | − 0.710491i | ||||||||
\(844\) | 7250.41i | 0.295698i | ||||||||
\(845\) | − 41975.8i | − 1.70889i | ||||||||
\(846\) | 2225.24 | 0.0904318 | ||||||||
\(847\) | − 27906.8i | − 1.13210i | ||||||||
\(848\) | 4656.65 | 0.188573 | ||||||||
\(849\) | −35538.0 | −1.43659 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8479.55 | 0.341569 | ||||||||
\(852\) | 17656.5 | 0.709979 | ||||||||
\(853\) | − 38293.9i | − 1.53711i | −0.639781 | − | 0.768557i | \(-0.720975\pi\) | ||||
0.639781 | − | 0.768557i | \(-0.279025\pi\) | |||||||
\(854\) | −42892.6 | −1.71868 | ||||||||
\(855\) | 30572.6i | 1.22288i | ||||||||
\(856\) | − 5071.25i | − 0.202490i | ||||||||
\(857\) | − 426.303i | − 0.0169921i | −0.999964 | − | 0.00849606i | \(-0.997296\pi\) | ||||
0.999964 | − | 0.00849606i | \(-0.00270441\pi\) | |||||||
\(858\) | 69.8418 | 0.00277897 | ||||||||
\(859\) | −30976.1 | −1.23037 | −0.615186 | − | 0.788382i | \(-0.710919\pi\) | ||||
−0.615186 | + | 0.788382i | \(0.710919\pi\) | |||||||
\(860\) | 1017.16i | 0.0403311i | ||||||||
\(861\) | − 55797.9i | − 2.20858i | ||||||||
\(862\) | − 17434.0i | − 0.688868i | ||||||||
\(863\) | 38201.4 | 1.50682 | 0.753412 | − | 0.657549i | \(-0.228407\pi\) | ||||
0.753412 | + | 0.657549i | \(0.228407\pi\) | |||||||
\(864\) | − 8552.48i | − 0.336761i | ||||||||
\(865\) | 70044.8 | 2.75329 | ||||||||
\(866\) | 50745.8 | 1.99124 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2836.66 | 0.110925 | ||||||||
\(869\) | −5638.81 | −0.220119 | ||||||||
\(870\) | − 90178.8i | − 3.51419i | ||||||||
\(871\) | 162.818 | 0.00633397 | ||||||||
\(872\) | − 24208.6i | − 0.940144i | ||||||||
\(873\) | − 15582.7i | − 0.604116i | ||||||||
\(874\) | − 46574.1i | − 1.80251i | ||||||||
\(875\) | −48598.4 | −1.87763 | ||||||||
\(876\) | 380.898 | 0.0146910 | ||||||||
\(877\) | − 13461.8i | − 0.518327i | −0.965833 | − | 0.259163i | \(-0.916553\pi\) | ||||
0.965833 | − | 0.259163i | \(-0.0834468\pi\) | |||||||
\(878\) | 54025.2i | 2.07661i | ||||||||
\(879\) | − 41329.5i | − 1.58590i | ||||||||
\(880\) | 12321.4 | 0.471994 | ||||||||
\(881\) | − 13867.4i | − 0.530310i | −0.964206 | − | 0.265155i | \(-0.914577\pi\) | ||||
0.964206 | − | 0.265155i | \(-0.0854231\pi\) | |||||||
\(882\) | −7330.85 | −0.279867 | ||||||||
\(883\) | −330.794 | −0.0126072 | −0.00630358 | − | 0.999980i | \(-0.502007\pi\) | ||||
−0.00630358 | + | 0.999980i | \(0.502007\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29647.5 | −1.12609 | ||||||||
\(886\) | −16819.6 | −0.637772 | ||||||||
\(887\) | 42906.5i | 1.62419i | 0.583523 | + | 0.812097i | \(0.301674\pi\) | ||||
−0.583523 | + | 0.812097i | \(0.698326\pi\) | |||||||
\(888\) | 7013.90 | 0.265057 | ||||||||
\(889\) | 22173.1i | 0.836515i | ||||||||
\(890\) | 56291.7i | 2.12012i | ||||||||
\(891\) | − 7494.33i | − 0.281784i | ||||||||
\(892\) | −12120.4 | −0.454954 | ||||||||
\(893\) | −4561.99 | −0.170953 | ||||||||
\(894\) | − 13804.5i | − 0.516433i | ||||||||
\(895\) | 69334.3i | 2.58948i | ||||||||
\(896\) | 38389.9i | 1.43138i | ||||||||
\(897\) | 359.021 | 0.0133639 | ||||||||
\(898\) | 35089.7i | 1.30396i | ||||||||
\(899\) | −10926.3 | −0.405353 | ||||||||
\(900\) | 9704.91 | 0.359441 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 10423.2 | 0.384762 | ||||||||
\(903\) | −2936.12 | −0.108204 | ||||||||
\(904\) | 23950.1i | 0.881158i | ||||||||
\(905\) | 73138.6 | 2.68642 | ||||||||
\(906\) | − 21733.7i | − 0.796968i | ||||||||
\(907\) | − 6908.93i | − 0.252930i | −0.991971 | − | 0.126465i | \(-0.959637\pi\) | ||||
0.991971 | − | 0.126465i | \(-0.0403631\pi\) | |||||||
\(908\) | − 4471.60i | − 0.163431i | ||||||||
\(909\) | 17407.2 | 0.635162 | ||||||||
\(910\) | 547.833 | 0.0199566 | ||||||||
\(911\) | 33032.6i | 1.20134i | 0.799497 | + | 0.600669i | \(0.205099\pi\) | ||||
−0.799497 | + | 0.600669i | \(0.794901\pi\) | |||||||
\(912\) | − 52599.2i | − 1.90980i | ||||||||
\(913\) | 2579.94i | 0.0935196i | ||||||||
\(914\) | 16367.7 | 0.592337 | ||||||||
\(915\) | 74198.9i | 2.68081i | ||||||||
\(916\) | 15742.4 | 0.567841 | ||||||||
\(917\) | −4818.01 | −0.173506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8167.05 | 0.293151 | 0.146576 | − | 0.989199i | \(-0.453175\pi\) | ||||
0.146576 | + | 0.989199i | \(0.453175\pi\) | |||||||
\(920\) | 46389.2 | 1.66240 | ||||||||
\(921\) | − 5348.33i | − 0.191350i | ||||||||
\(922\) | −7710.44 | −0.275412 | ||||||||
\(923\) | − 413.155i | − 0.0147337i | ||||||||
\(924\) | − 3106.83i | − 0.110614i | ||||||||
\(925\) | − 14719.4i | − 0.523211i | ||||||||
\(926\) | 57700.3 | 2.04768 | ||||||||
\(927\) | 6140.03 | 0.217546 | ||||||||
\(928\) | 25318.3i | 0.895599i | ||||||||
\(929\) | 1864.03i | 0.0658308i | 0.999458 | + | 0.0329154i | \(0.0104792\pi\) | ||||
−0.999458 | + | 0.0329154i | \(0.989521\pi\) | |||||||
\(930\) | − 19939.5i | − 0.703056i | ||||||||
\(931\) | 15029.1 | 0.529063 | ||||||||
\(932\) | 6955.87i | 0.244471i | ||||||||
\(933\) | 48832.6 | 1.71351 | ||||||||
\(934\) | −63823.6 | −2.23594 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 108.210 | 0.00377881 | ||||||||
\(937\) | 44071.0 | 1.53654 | 0.768270 | − | 0.640126i | \(-0.221118\pi\) | ||||
0.768270 | + | 0.640126i | \(0.221118\pi\) | |||||||
\(938\) | − 29430.5i | − 1.02445i | ||||||||
\(939\) | −7936.84 | −0.275835 | ||||||||
\(940\) | 2202.11i | 0.0764095i | ||||||||
\(941\) | − 33030.1i | − 1.14426i | −0.820162 | − | 0.572131i | \(-0.806117\pi\) | ||||
0.820162 | − | 0.572131i | \(-0.193883\pi\) | |||||||
\(942\) | 14259.1i | 0.493191i | ||||||||
\(943\) | 53580.5 | 1.85029 | ||||||||
\(944\) | 18586.5 | 0.640825 | ||||||||
\(945\) | − 31708.2i | − 1.09150i | ||||||||
\(946\) | − 548.476i | − 0.0188504i | ||||||||
\(947\) | − 9340.37i | − 0.320508i | −0.987076 | − | 0.160254i | \(-0.948769\pi\) | ||||
0.987076 | − | 0.160254i | \(-0.0512314\pi\) | |||||||
\(948\) | 11619.6 | 0.398088 | ||||||||
\(949\) | − 8.91285i | 0 0.000304872i | ||||||||
\(950\) | −80846.5 | −2.76106 | ||||||||
\(951\) | 37034.0 | 1.26278 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21211.2 | 0.720984 | 0.360492 | − | 0.932762i | \(-0.382609\pi\) | ||||
0.360492 | + | 0.932762i | \(0.382609\pi\) | |||||||
\(954\) | −3007.46 | −0.102065 | ||||||||
\(955\) | − 16761.9i | − 0.567959i | ||||||||
\(956\) | 15722.9 | 0.531919 | ||||||||
\(957\) | 11966.9i | 0.404217i | ||||||||
\(958\) | 13226.9i | 0.446077i | ||||||||
\(959\) | 35919.3i | 1.20948i | ||||||||
\(960\) | 31576.7 | 1.06160 | ||||||||
\(961\) | 27375.1 | 0.918904 | ||||||||
\(962\) | 79.5389i | 0.00266574i | ||||||||
\(963\) | 4471.88i | 0.149641i | ||||||||
\(964\) | 15880.2i | 0.530567i | ||||||||
\(965\) | −91136.3 | −3.04019 | ||||||||
\(966\) | − 64895.4i | − 2.16147i | ||||||||
\(967\) | −21688.1 | −0.721242 | −0.360621 | − | 0.932712i | \(-0.617435\pi\) | ||||
−0.360621 | + | 0.932712i | \(0.617435\pi\) | |||||||
\(968\) | 22165.9 | 0.735991 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 62660.8 | 2.07414 | ||||||||
\(971\) | 22478.6 | 0.742918 | 0.371459 | − | 0.928449i | \(-0.378858\pi\) | ||||
0.371459 | + | 0.928449i | \(0.378858\pi\) | |||||||
\(972\) | 10148.5i | 0.334892i | ||||||||
\(973\) | 22858.5 | 0.753146 | ||||||||
\(974\) | − 23639.7i | − 0.777685i | ||||||||
\(975\) | − 623.214i | − 0.0204706i | ||||||||
\(976\) | − 46516.5i | − 1.52557i | ||||||||
\(977\) | −21731.7 | −0.711626 | −0.355813 | − | 0.934557i | \(-0.615796\pi\) | ||||
−0.355813 | + | 0.934557i | \(0.615796\pi\) | |||||||
\(978\) | −40200.2 | −1.31438 | ||||||||
\(979\) | − 7470.03i | − 0.243864i | ||||||||
\(980\) | − 7254.65i | − 0.236471i | ||||||||
\(981\) | 21347.3i | 0.694769i | ||||||||
\(982\) | −2507.82 | −0.0814947 | ||||||||
\(983\) | 34128.8i | 1.10737i | 0.832728 | + | 0.553683i | \(0.186778\pi\) | ||||
−0.832728 | + | 0.553683i | \(0.813222\pi\) | |||||||
\(984\) | 44319.3 | 1.43582 | ||||||||
\(985\) | 28526.7 | 0.922779 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6356.59 | −0.204998 | ||||||||
\(988\) | 107.513 | 0.00346197 | ||||||||
\(989\) | − 2819.44i | − 0.0906501i | ||||||||
\(990\) | −7957.68 | −0.255466 | ||||||||
\(991\) | 39750.8i | 1.27419i | 0.770784 | + | 0.637097i | \(0.219865\pi\) | ||||
−0.770784 | + | 0.637097i | \(0.780135\pi\) | |||||||
\(992\) | 5598.16i | 0.179175i | ||||||||
\(993\) | 48151.4i | 1.53881i | ||||||||
\(994\) | −74680.5 | −2.38302 | ||||||||
\(995\) | 59066.2 | 1.88193 | ||||||||
\(996\) | − 5316.34i | − 0.169131i | ||||||||
\(997\) | − 54112.0i | − 1.71890i | −0.511219 | − | 0.859450i | \(-0.670806\pi\) | ||||
0.511219 | − | 0.859450i | \(-0.329194\pi\) | |||||||
\(998\) | 4666.91i | 0.148024i | ||||||||
\(999\) | 4603.66 | 0.145799 |
(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.288.7 | 24 | ||
17.4 | even | 4 | 289.4.a.i.1.9 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.h.1.9 | ✓ | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.9 | ✓ | 12 | 17.13 | even | 4 | ||
289.4.a.i.1.9 | yes | 12 | 17.4 | even | 4 | ||
289.4.b.f.288.7 | 24 | 1.1 | even | 1 | trivial | ||
289.4.b.f.288.8 | 24 | 17.16 | even | 2 | inner |