Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,4,Mod(1,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.a (trivial) |
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: | yes |
Analytic conductor: | \(28.3209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{201}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 50 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.58872\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 480.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.3549 | −1.63901 | −0.819505 | − | 0.573072i | \(-0.805752\pi\) | ||||
−0.819505 | + | 0.573072i | \(0.805752\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.3549 | 0.348925 | 0.174463 | − | 0.984664i | \(-0.444181\pi\) | ||||
0.174463 | + | 0.984664i | \(0.444181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −69.0647 | −0.985332 | −0.492666 | − | 0.870218i | \(-0.663978\pi\) | ||||
−0.492666 | + | 0.870218i | \(0.663978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −86.3549 | −1.04269 | −0.521347 | − | 0.853345i | \(-0.674570\pi\) | ||||
−0.521347 | + | 0.853345i | \(0.674570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 91.0647 | 0.946283 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.3549 | 0.311456 | 0.155728 | − | 0.987800i | \(-0.450228\pi\) | ||||
0.155728 | + | 0.987800i | \(0.450228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −39.4196 | −0.252415 | −0.126207 | − | 0.992004i | \(-0.540280\pi\) | ||||
−0.126207 | + | 0.992004i | \(0.540280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 217.194 | 1.25836 | 0.629181 | − | 0.777259i | \(-0.283391\pi\) | ||||
0.629181 | + | 0.777259i | \(0.283391\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 60.0000 | 0.316505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 151.774 | 0.732988 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 281.774 | 1.25198 | 0.625992 | − | 0.779829i | \(-0.284694\pi\) | ||||
0.625992 | + | 0.779829i | \(0.284694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −49.0647 | −0.201452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 342.710 | 1.30542 | 0.652711 | − | 0.757607i | \(-0.273632\pi\) | ||||
0.652711 | + | 0.757607i | \(0.273632\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −373.420 | −1.32432 | −0.662162 | − | 0.749361i | \(-0.730361\pi\) | ||||
−0.662162 | + | 0.749361i | \(0.730361\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −198.614 | −0.616399 | −0.308200 | − | 0.951322i | \(-0.599727\pi\) | ||||
−0.308200 | + | 0.951322i | \(0.599727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 578.420 | 1.68635 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 207.194 | 0.568882 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 91.8706 | 0.238102 | 0.119051 | − | 0.992888i | \(-0.462015\pi\) | ||||
0.119051 | + | 0.992888i | \(0.462015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 100.000 | 0.245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 259.065 | 0.601999 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 49.1608 | 0.108478 | 0.0542390 | − | 0.998528i | \(-0.482727\pi\) | ||||
0.0542390 | + | 0.998528i | \(0.482727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −309.808 | −0.650276 | −0.325138 | − | 0.945667i | \(-0.605411\pi\) | ||||
−0.325138 | + | 0.945667i | \(0.605411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −273.194 | −0.546337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −81.7745 | −0.156044 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −651.098 | −1.18723 | −0.593614 | − | 0.804750i | \(-0.702299\pi\) | ||||
−0.593614 | + | 0.804750i | \(0.702299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −103.065 | −0.179819 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 850.839 | 1.42220 | 0.711099 | − | 0.703092i | \(-0.248198\pi\) | ||||
0.711099 | + | 0.703092i | \(0.248198\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 964.388 | 1.54621 | 0.773103 | − | 0.634280i | \(-0.218703\pi\) | ||||
0.773103 | + | 0.634280i | \(0.218703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 607.098 | 0.898509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 724.484 | 1.03178 | 0.515891 | − | 0.856654i | \(-0.327461\pi\) | ||||
0.515891 | + | 0.856654i | \(0.327461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 433.678 | 0.573523 | 0.286761 | − | 0.958002i | \(-0.407421\pi\) | ||||
0.286761 | + | 0.958002i | \(0.407421\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 345.323 | 0.440654 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 118.259 | 0.145732 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1264.65 | 1.50621 | 0.753103 | − | 0.657903i | \(-0.228556\pi\) | ||||
0.753103 | + | 0.657903i | \(0.228556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −496.451 | −0.571892 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −651.582 | −0.726515 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 431.774 | 0.466307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1745.87 | −1.82749 | −0.913746 | − | 0.406287i | \(-0.866823\pi\) | ||||
−0.913746 | + | 0.406287i | \(0.866823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −180.000 | −0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1739.94 | 1.71416 | 0.857080 | − | 0.515183i | \(-0.172276\pi\) | ||||
0.857080 | + | 0.515183i | \(0.172276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 236.484 | 0.226228 | 0.113114 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113114 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −455.323 | −0.423191 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 514.647 | 0.464979 | 0.232490 | − | 0.972599i | \(-0.425313\pi\) | ||||
0.232490 | + | 0.972599i | \(0.425313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 342.902 | 0.301322 | 0.150661 | − | 0.988586i | \(-0.451860\pi\) | ||||
0.150661 | + | 0.988586i | \(0.451860\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −845.323 | −0.722834 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 534.677 | 0.445116 | 0.222558 | − | 0.974919i | \(-0.428559\pi\) | ||||
0.222558 | + | 0.974919i | \(0.428559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −171.774 | −0.139287 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 147.194 | 0.116308 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2096.45 | 1.61497 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1028.13 | −0.753685 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 627.582 | 0.438495 | 0.219248 | − | 0.975669i | \(-0.429640\pi\) | ||||
0.219248 | + | 0.975669i | \(0.429640\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1120.26 | 0.764599 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2188.58 | −1.45968 | −0.729838 | − | 0.683621i | \(-0.760404\pi\) | ||||
−0.729838 | + | 0.683621i | \(0.760404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2621.29 | 1.70898 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1896.35 | −1.18260 | −0.591301 | − | 0.806451i | \(-0.701386\pi\) | ||||
−0.591301 | + | 0.806451i | \(0.701386\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −441.128 | −0.269180 | −0.134590 | − | 0.990901i | \(-0.542972\pi\) | ||||
−0.134590 | + | 0.990901i | \(0.542972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 595.841 | 0.355878 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −327.098 | −0.191282 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 197.098 | 0.112883 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1735.26 | −0.973617 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −571.294 | −0.314109 | −0.157054 | − | 0.987590i | \(-0.550200\pi\) | ||||
−0.157054 | + | 0.987590i | \(0.550200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2883.71 | −1.55413 | −0.777064 | − | 0.629421i | \(-0.783292\pi\) | ||||
−0.777064 | + | 0.629421i | \(0.783292\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −621.582 | −0.328444 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1085.97 | −0.562756 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −167.579 | −0.0851862 | −0.0425931 | − | 0.999093i | \(-0.513562\pi\) | ||||
−0.0425931 | + | 0.999093i | \(0.513562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −275.612 | −0.137468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1042.84 | −0.510480 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2257.16 | −1.08463 | −0.542314 | − | 0.840176i | \(-0.682452\pi\) | ||||
−0.542314 | + | 0.840176i | \(0.682452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −300.000 | −0.141545 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3820.29 | 1.77020 | 0.885099 | − | 0.465403i | \(-0.154091\pi\) | ||||
0.885099 | + | 0.465403i | \(0.154091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1929.52 | −0.878251 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −777.194 | −0.347564 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4185.87 | −1.83957 | −0.919786 | − | 0.392419i | \(-0.871638\pi\) | ||||
−0.919786 | + | 0.392419i | \(0.871638\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −758.872 | −0.327802 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −147.483 | −0.0626298 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1930.26 | 0.806003 | 0.403002 | − | 0.915199i | \(-0.367967\pi\) | ||||
0.403002 | + | 0.915199i | \(0.367967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2310.01 | −0.948627 | −0.474313 | − | 0.880356i | \(-0.657304\pi\) | ||||
−0.474313 | + | 0.880356i | \(0.657304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 929.423 | 0.375437 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1408.87 | −0.559905 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1381.29 | 0.540161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 819.582 | 0.315428 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4642.97 | 1.75892 | 0.879460 | − | 0.475973i | \(-0.157904\pi\) | ||||
0.879460 | + | 0.475973i | \(0.157904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4003.23 | 1.49305 | 0.746526 | − | 0.665356i | \(-0.231720\pi\) | ||||
0.746526 | + | 0.665356i | \(0.231720\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 245.323 | 0.0900922 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4118.97 | −1.48967 | −0.744833 | − | 0.667250i | \(-0.767471\pi\) | ||||
−0.744833 | + | 0.667250i | \(0.767471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2384.68 | 0.849474 | 0.424737 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424737 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1953.29 | 0.685446 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1196.58 | 0.413711 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1713.55 | −0.583802 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 309.194 | 0.103819 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1727.10 | 0.571607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1310.29 | −0.427507 | −0.213754 | − | 0.976888i | \(-0.568569\pi\) | ||||
−0.213754 | + | 0.976888i | \(0.568569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2552.52 | −0.821106 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1867.10 | 0.592256 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6592.90 | −2.06247 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2893.16 | −0.892703 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1129.55 | −0.343807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −883.967 | −0.265448 | −0.132724 | − | 0.991153i | \(-0.542372\pi\) | ||||
−0.132724 | + | 0.991153i | \(0.542372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2407.36 | 0.703885 | 0.351942 | − | 0.936022i | \(-0.385521\pi\) | ||||
0.351942 | + | 0.936022i | \(0.385521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5505.94 | 1.58883 | 0.794417 | − | 0.607373i | \(-0.207777\pi\) | ||||
0.794417 | + | 0.607373i | \(0.207777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1821.29 | −0.518755 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −673.523 | −0.189373 | −0.0946865 | − | 0.995507i | \(-0.530185\pi\) | ||||
−0.0946865 | + | 0.995507i | \(0.530185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 993.068 | 0.275662 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2173.45 | −0.595700 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 914.773 | 0.247580 | 0.123790 | − | 0.992308i | \(-0.460495\pi\) | ||||
0.123790 | + | 0.992308i | \(0.460495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5516.33 | −1.47443 | −0.737216 | − | 0.675657i | \(-0.763860\pi\) | ||||
−0.737216 | + | 0.675657i | \(0.763860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2892.10 | −0.754161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1412.33 | −0.363822 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1301.03 | −0.331123 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4923.93 | 1.23823 | 0.619115 | − | 0.785300i | \(-0.287491\pi\) | ||||
0.619115 | + | 0.785300i | \(0.287491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −687.098 | −0.170741 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1035.97 | −0.254412 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −767.771 | −0.186351 | −0.0931756 | − | 0.995650i | \(-0.529702\pi\) | ||||
−0.0931756 | + | 0.995650i | \(0.529702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8553.23 | −2.05202 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −354.776 | −0.0841383 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2623.97 | 0.615212 | 0.307606 | − | 0.951514i | \(-0.400472\pi\) | ||||
0.307606 | + | 0.951514i | \(0.400472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −459.353 | −0.106482 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3793.94 | −0.869608 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4539.69 | 1.02896 | 0.514479 | − | 0.857503i | \(-0.327985\pi\) | ||||
0.514479 | + | 0.857503i | \(0.327985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3841.51 | −0.861090 | −0.430545 | − | 0.902569i | \(-0.641679\pi\) | ||||
−0.430545 | + | 0.902569i | \(0.641679\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1489.35 | 0.330182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −500.000 | −0.109640 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8471.07 | −1.83746 | −0.918732 | − | 0.394881i | \(-0.870786\pi\) | ||||
−0.918732 | + | 0.394881i | \(0.870786\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1954.75 | 0.419454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3931.10 | 0.834555 | 0.417277 | − | 0.908779i | \(-0.362984\pi\) | ||||
0.417277 | + | 0.908779i | \(0.362984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5678.84 | 1.19283 | 0.596417 | − | 0.802675i | \(-0.296591\pi\) | ||||
0.596417 | + | 0.802675i | \(0.296591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1295.32 | −0.269222 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10402.9 | −2.13960 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −143.070 | −0.0291207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5237.62 | 1.05510 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6180.79 | 1.23237 | 0.616187 | − | 0.787600i | \(-0.288677\pi\) | ||||
0.616187 | + | 0.787600i | \(0.288677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −245.804 | −0.0485128 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 540.000 | 0.105502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 561.871 | 0.108675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11335.1 | 2.17058 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5219.81 | −0.989671 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1549.04 | 0.290812 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5058.91 | −0.940480 | −0.470240 | − | 0.882539i | \(-0.655833\pi\) | ||||
−0.470240 | + | 0.882539i | \(0.655833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −709.453 | −0.130613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7795.82 | 1.42142 | 0.710708 | − | 0.703487i | \(-0.248375\pi\) | ||||
0.710708 | + | 0.703487i | \(0.248375\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8138.34 | −1.46967 | −0.734834 | − | 0.678247i | \(-0.762740\pi\) | ||||
−0.734834 | + | 0.678247i | \(0.762740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1365.97 | 0.244329 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6911.10 | −1.22450 | −0.612249 | − | 0.790665i | \(-0.709735\pi\) | ||||
−0.612249 | + | 0.790665i | \(0.709735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 788.392 | 0.138374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1543.94 | −0.268456 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5964.07 | 1.02740 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 408.872 | 0.0697851 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1028.71 | −0.173968 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6028.90 | 1.01028 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6510.62 | 1.08114 | 0.540568 | − | 0.841300i | \(-0.318209\pi\) | ||||
0.540568 | + | 0.841300i | \(0.318209\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2535.97 | 0.417328 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3255.49 | 0.530944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −247.990 | −0.0400856 | −0.0200428 | − | 0.999799i | \(-0.506380\pi\) | ||||
−0.0200428 | + | 0.999799i | \(0.506380\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1604.03 | −0.256988 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4343.88 | −0.689837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7146.14 | −1.12494 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 515.323 | 0.0804176 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6105.88 | 0.944613 | 0.472306 | − | 0.881434i | \(-0.343422\pi\) | ||||
0.472306 | + | 0.881434i | \(0.343422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7452.90 | 1.14311 | 0.571554 | − | 0.820565i | \(-0.306341\pi\) | ||||
0.571554 | + | 0.820565i | \(0.306341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −441.582 | −0.0671507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12974.6 | 1.95629 | 0.978144 | − | 0.207929i | \(-0.0666724\pi\) | ||||
0.978144 | + | 0.207929i | \(0.0666724\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4254.20 | −0.636026 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6289.35 | −0.932403 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5776.40 | −0.849211 | −0.424605 | − | 0.905379i | \(-0.639587\pi\) | ||||
−0.424605 | + | 0.905379i | \(0.639587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 598.168 | 0.0872092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2793.00 | 0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4821.94 | −0.691485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7191.40 | 1.02286 | 0.511428 | − | 0.859326i | \(-0.329117\pi\) | ||||
0.511428 | + | 0.859326i | \(0.329117\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3084.39 | 0.435140 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2788.72 | −0.390252 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6487.77 | 0.900601 | 0.450300 | − | 0.892877i | \(-0.351317\pi\) | ||||
0.450300 | + | 0.892877i | \(0.351317\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −644.703 | −0.0880740 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1464.68 | −0.198510 | −0.0992551 | − | 0.995062i | \(-0.531646\pi\) | ||||
−0.0992551 | + | 0.995062i | \(0.531646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1882.75 | −0.253165 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3568.29 | −0.476060 | −0.238030 | − | 0.971258i | \(-0.576502\pi\) | ||||
−0.238030 | + | 0.971258i | \(0.576502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3035.49 | −0.401826 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3360.78 | −0.441441 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5562.52 | 0.725015 | 0.362507 | − | 0.931981i | \(-0.381921\pi\) | ||||
0.362507 | + | 0.931981i | \(0.381921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2372.71 | −0.306888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6565.75 | 0.842744 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3622.42 | −0.461427 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1601.77 | 0.202496 | 0.101248 | − | 0.994861i | \(-0.467717\pi\) | ||||
0.101248 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7863.88 | −0.986683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5435.04 | −0.676840 | −0.338420 | − | 0.940995i | \(-0.609893\pi\) | ||||
−0.338420 | + | 0.940995i | \(0.609893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3552.19 | 0.439074 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5635.49 | −0.686341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11535.2 | 1.39457 | 0.697283 | − | 0.716796i | \(-0.254392\pi\) | ||||
0.697283 | + | 0.716796i | \(0.254392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5689.06 | 0.682776 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1492.27 | −0.177796 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2168.39 | −0.256487 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1323.38 | 0.155411 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8858.90 | −1.03290 | −0.516451 | − | 0.856317i | \(-0.672747\pi\) | ||||
−0.516451 | + | 0.856317i | \(0.672747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13361.9 | 1.54684 | 0.773422 | − | 0.633892i | \(-0.218544\pi\) | ||||
0.773422 | + | 0.633892i | \(0.218544\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1787.52 | −0.205466 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1726.62 | −0.197066 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9404.18 | 1.06581 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 981.294 | 0.110437 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12223.1 | −1.36605 | −0.683024 | − | 0.730396i | \(-0.739336\pi\) | ||||
−0.683024 | + | 0.730396i | \(0.739336\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 110.192 | 0.0122298 | 0.00611490 | − | 0.999981i | \(-0.498054\pi\) | ||||
0.00611490 | + | 0.999981i | \(0.498054\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −591.294 | −0.0651732 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2966.71 | −0.324753 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10838.5 | 1.17834 | 0.589172 | − | 0.808008i | \(-0.299454\pi\) | ||||
0.589172 | + | 0.808008i | \(0.299454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5205.78 | 0.562118 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14291.2 | 1.53272 | 0.766362 | − | 0.642409i | \(-0.222065\pi\) | ||||
0.766362 | + | 0.642409i | \(0.222065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6323.23 | −0.673596 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1713.88 | 0.181351 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2451.92 | 0.257714 | 0.128857 | − | 0.991663i | \(-0.458869\pi\) | ||||
0.128857 | + | 0.991663i | \(0.458869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6854.20 | −0.715635 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8651.14 | 0.897276 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2482.26 | 0.255758 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1352.31 | −0.138421 | −0.0692104 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692104 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1864.75 | 0.189627 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5331.29 | 0.538618 | 0.269309 | − | 0.963054i | \(-0.413205\pi\) | ||||
0.269309 | + | 0.963054i | \(0.413205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.69784 | −0.000170422 0 | −8.52110e−5 | − | 1.00000i | \(-0.500027\pi\) | ||||
−8.52110e−5 | 1.00000i | \(0.500027\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3257.91 | 0.324908 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9081.89 | 0.899914 | 0.449957 | − | 0.893050i | \(-0.351439\pi\) | ||||
0.449957 | + | 0.893050i | \(0.351439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19764.0 | 1.94588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 502.736 | 0.0491823 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7468.39 | 0.725998 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2158.87 | −0.208539 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 826.836 | 0.0793673 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6270.21 | 0.598107 | 0.299053 | − | 0.954236i | \(-0.403329\pi\) | ||||
0.299053 | + | 0.954236i | \(0.403329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4608.39 | 0.436849 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3128.52 | 0.294726 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8729.37 | 0.817279 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13938.7 | 1.29697 | 0.648486 | − | 0.761227i | \(-0.275403\pi\) | ||||
0.648486 | + | 0.761227i | \(0.275403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6771.48 | 0.626211 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5301.54 | 0.487281 | 0.243641 | − | 0.969866i | \(-0.421658\pi\) | ||||
0.243641 | + | 0.969866i | \(0.421658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2722.50 | 0.248712 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 900.000 | 0.0817212 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25827.1 | −2.33100 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12167.0 | 1.09152 | 0.545762 | − | 0.837940i | \(-0.316240\pi\) | ||||
0.545762 | + | 0.837940i | \(0.316240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11460.9 | −1.02202 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12761.8 | −1.13126 | −0.565628 | − | 0.824660i | \(-0.691366\pi\) | ||||
−0.565628 | + | 0.824660i | \(0.691366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8699.69 | −0.766596 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5788.55 | 0.507058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1875.68 | −0.163336 | −0.0816680 | − | 0.996660i | \(-0.526025\pi\) | ||||
−0.0816680 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29273.9 | −2.53425 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2331.58 | 0.200666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1182.42 | −0.101172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3972.27 | 0.337912 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12557.6 | 1.06208 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12565.0 | 1.05659 | 0.528293 | − | 0.849062i | \(-0.322832\pi\) | ||||
0.528293 | + | 0.849062i | \(0.322832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20006.3 | 1.67268 | 0.836341 | − | 0.548209i | \(-0.184690\pi\) | ||||
0.836341 | + | 0.548209i | \(0.184690\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2276.62 | 0.189257 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15000.4 | −1.23990 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10986.7 | −0.902995 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 442.448 | 0.0361593 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5604.98 | 0.455495 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2573.23 | −0.207945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5790.79 | −0.465346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11568.4 | −0.924464 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3930.27 | 0.312339 | 0.156170 | − | 0.987730i | \(-0.450085\pi\) | ||||
0.156170 | + | 0.987730i | \(0.450085\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6930.02 | 0.547690 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1714.51 | −0.134755 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19908.5 | 1.55618 | 0.778088 | − | 0.628156i | \(-0.216190\pi\) | ||||
0.778088 | + | 0.628156i | \(0.216190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2788.27 | −0.216759 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3404.07 | 0.263191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21991.6 | −1.69110 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4226.62 | 0.323261 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11820.0 | 0.899153 | 0.449576 | − | 0.893242i | \(-0.351575\pi\) | ||||
0.449576 | + | 0.893242i | \(0.351575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6107.24 | −0.462091 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4143.88 | −0.311862 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21578.2 | −1.61530 | −0.807648 | − | 0.589665i | \(-0.799260\pi\) | ||||
−0.807648 | + | 0.589665i | \(0.799260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2673.38 | −0.199062 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2458.75 | −0.182112 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22874.5 | 1.68533 | 0.842663 | − | 0.538441i | \(-0.180986\pi\) | ||||
0.842663 | + | 0.538441i | \(0.180986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2857.53 | −0.209429 | −0.104714 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104714 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13928.9 | −1.01551 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 858.872 | 0.0622912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10000.7 | −0.721553 | −0.360776 | − | 0.932652i | \(-0.617488\pi\) | ||||
−0.360776 | + | 0.932652i | \(0.617488\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12009.7 | −0.862014 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13164.3 | −0.940009 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1837.41 | −0.130528 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −735.970 | −0.0520147 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10215.0 | −0.718262 | −0.359131 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359131 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18755.8 | −1.31208 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12356.9 | 0.860060 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3995.50 | −0.276687 | −0.138344 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138344 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10482.3 | −0.722236 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7154.03 | −0.490444 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7844.51 | 0.535089 | 0.267544 | − | 0.963546i | \(-0.413788\pi\) | ||||
0.267544 | + | 0.963546i | \(0.413788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5265.24 | 0.357361 | 0.178680 | − | 0.983907i | \(-0.442817\pi\) | ||||
0.178680 | + | 0.983907i | \(0.442817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5859.88 | −0.395743 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4655.00 | 0.312814 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16213.6 | −1.08416 | −0.542082 | − | 0.840325i | \(-0.682364\pi\) | ||||
−0.542082 | + | 0.840325i | \(0.682364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3589.73 | −0.238856 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3248.30 | −0.215077 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4538.37 | −0.299026 | −0.149513 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149513 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5140.65 | 0.337058 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1715.15 | 0.111911 | 0.0559556 | − | 0.998433i | \(-0.482179\pi\) | ||||
0.0559556 | + | 0.998433i | \(0.482179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 695.376 | 0.0451527 | 0.0225764 | − | 0.999745i | \(-0.492813\pi\) | ||||
0.0225764 | + | 0.999745i | \(0.492813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −927.582 | −0.0599398 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38388.2 | −2.46869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5181.29 | −0.330017 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19460.7 | −1.23362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9877.82 | −0.623185 | −0.311593 | − | 0.950216i | \(-0.600862\pi\) | ||||
−0.311593 | + | 0.950216i | \(0.600862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3930.87 | 0.246821 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3137.91 | −0.196101 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9459.99 | 0.588412 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7657.55 | 0.474066 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2441.03 | 0.150413 | 0.0752067 | − | 0.997168i | \(-0.476038\pi\) | ||||
0.0752067 | + | 0.997168i | \(0.476038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8080.27 | 0.495575 | 0.247788 | − | 0.968814i | \(-0.420296\pi\) | ||||
0.247788 | + | 0.968814i | \(0.420296\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5601.29 | −0.341939 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1852.94 | 0.112591 | 0.0562957 | − | 0.998414i | \(-0.482071\pi\) | ||||
0.0562957 | + | 0.998414i | \(0.482071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −983.217 | −0.0594679 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19778.7 | 1.19077 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8211.29 | −0.492087 | −0.246043 | − | 0.969259i | \(-0.579131\pi\) | ||||
−0.246043 | + | 0.969259i | \(0.579131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10942.9 | 0.652787 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8679.49 | 0.515402 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22558.3 | −1.33346 | −0.666728 | − | 0.745301i | \(-0.732306\pi\) | ||||
−0.666728 | + | 0.745301i | \(0.732306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20058.9 | −1.18033 | −0.590166 | − | 0.807282i | \(-0.700938\pi\) | ||||
−0.590166 | + | 0.807282i | \(0.700938\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3388.64 | 0.198497 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13106.5 | −0.764281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1354.26 | −0.0786162 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2651.90 | 0.153256 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6196.15 | 0.356483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12172.8 | 0.697218 | 0.348609 | − | 0.937268i | \(-0.386654\pi\) | ||||
0.348609 | + | 0.937268i | \(0.386654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29440.0 | −1.67130 | −0.835650 | − | 0.549263i | \(-0.814909\pi\) | ||||
−0.835650 | + | 0.549263i | \(0.814909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52995.8 | 2.99528 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7222.07 | −0.406388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21223.7 | 1.18902 | 0.594512 | − | 0.804087i | \(-0.297345\pi\) | ||||
0.594512 | + | 0.804087i | \(0.297345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9481.77 | 0.528876 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16517.8 | −0.917313 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1502.53 | 0.0830798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2278.77 | 0.125454 | 0.0627268 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627268 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5463.88 | 0.299503 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2205.64 | 0.120381 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23669.1 | −1.28627 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2020.57 | 0.109335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8985.49 | −0.484133 | −0.242067 | − | 0.970260i | \(-0.577825\pi\) | ||||
−0.242067 | + | 0.970260i | \(0.577825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24332.6 | −1.30544 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2979.20 | −0.159154 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52815.6 | −2.80953 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −530.836 | −0.0281184 | −0.0140592 | − | 0.999901i | \(-0.504475\pi\) | ||||
−0.0140592 | + | 0.999901i | \(0.504475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6520.36 | 0.343928 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7461.68 | 0.391924 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1635.49 | 0.0855438 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2744.32 | −0.142941 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12797.7 | 0.663804 | 0.331902 | − | 0.943314i | \(-0.392310\pi\) | ||||
0.331902 | + | 0.943314i | \(0.392310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7178.45 | −0.370790 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16549.0 | 0.851263 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −985.489 | −0.0504830 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30477.7 | 1.55482 | 0.777411 | − | 0.628993i | \(-0.216533\pi\) | ||||
0.777411 | + | 0.628993i | \(0.216533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25790.1 | 1.30490 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4322.79 | −0.217825 | −0.108913 | − | 0.994051i | \(-0.534737\pi\) | ||||
−0.108913 | + | 0.994051i | \(0.534737\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8676.29 | 0.435415 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13022.0 | 0.650841 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24280.6 | −1.20863 | −0.604315 | − | 0.796745i | \(-0.706553\pi\) | ||||
−0.604315 | + | 0.796745i | \(0.706553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4236.98 | 0.210053 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11638.4 | 0.574658 | 0.287329 | − | 0.957832i | \(-0.407233\pi\) | ||||
0.287329 | + | 0.957832i | \(0.407233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2856.47 | 0.140474 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3903.10 | 0.191174 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15622.0 | −0.762106 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11817.8 | 0.574216 | 0.287108 | − | 0.957898i | \(-0.407306\pi\) | ||||
0.287108 | + | 0.957898i | \(0.407306\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14771.8 | −0.714893 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14418.6 | 0.695027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −311.180 | −0.0149406 | −0.00747031 | − | 0.999972i | \(-0.502378\pi\) | ||||
−0.00747031 | + | 0.999972i | \(0.502378\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2061.29 | 0.0985774 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7381.11 | −0.351597 | −0.175798 | − | 0.984426i | \(-0.556251\pi\) | ||||
−0.175798 | + | 0.984426i | \(0.556251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10408.8 | −0.493869 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3107.91 | 0.146885 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 804.020 | 0.0378507 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6695.05 | −0.313953 | −0.156976 | − | 0.987602i | \(-0.550175\pi\) | ||||
−0.156976 | + | 0.987602i | \(0.550175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2303.31 | 0.107590 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25149.8 | −1.17022 | −0.585108 | − | 0.810955i | \(-0.698948\pi\) | ||||
−0.585108 | + | 0.810955i | \(0.698948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5429.85 | 0.251672 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25659.7 | 1.18473 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29594.7 | −1.36115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17016.8 | −0.779652 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1064.33 | 0.0485773 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 837.894 | 0.0380964 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25047.8 | 1.13451 | 0.567254 | − | 0.823543i | \(-0.308006\pi\) | ||||
0.567254 | + | 0.823543i | \(0.308006\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7871.90 | −0.355193 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16230.1 | −0.729550 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5066.87 | −0.226898 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1378.06 | 0.0614777 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34617.1 | 1.53852 | 0.769260 | − | 0.638936i | \(-0.220625\pi\) | ||||
0.769260 | + | 0.638936i | \(0.220625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13717.2 | 0.607358 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11381.8 | 0.502069 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19287.8 | −0.847634 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5214.20 | 0.228293 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13619.1 | −0.594069 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39309.0 | −1.70832 | −0.854160 | − | 0.520011i | \(-0.825928\pi\) | ||||
−0.854160 | + | 0.520011i | \(0.825928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36235.7 | −1.56894 | −0.784469 | − | 0.620168i | \(-0.787065\pi\) | ||||
−0.784469 | + | 0.620168i | \(0.787065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11524.5 | 0.497150 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11285.8 | 0.485061 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32246.6 | 1.38086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4468.06 | −0.190631 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4570.56 | 0.194292 | 0.0971459 | − | 0.995270i | \(-0.469029\pi\) | ||||
0.0971459 | + | 0.995270i | \(0.469029\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18993.8 | 0.804473 | 0.402237 | − | 0.915536i | \(-0.368233\pi\) | ||||
0.402237 | + | 0.915536i | \(0.368233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1500.00 | 0.0633010 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32809.1 | −1.37954 | −0.689772 | − | 0.724027i | \(-0.742289\pi\) | ||||
−0.689772 | + | 0.724027i | \(0.742289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5188.36 | 0.217369 | 0.108685 | − | 0.994076i | \(-0.465336\pi\) | ||||
0.108685 | + | 0.994076i | \(0.465336\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25413.2 | 1.06086 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39948.4 | −1.66162 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19101.5 | −0.791657 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5864.24 | −0.242172 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4074.61 | −0.167665 | −0.0838327 | − | 0.996480i | \(-0.526716\pi\) | ||||
−0.0838327 | + | 0.996480i | \(0.526716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22835.1 | −0.936287 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11793.3 | −0.481830 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9647.59 | 0.392766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28260.4 | 1.14645 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17036.5 | −0.688683 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9680.33 | 0.389938 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45902.6 | 1.84253 | 0.921263 | − | 0.388941i | \(-0.127159\pi\) | ||||
0.921263 | + | 0.388941i | \(0.127159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3885.97 | 0.155436 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17316.3 | −0.690216 | −0.345108 | − | 0.938563i | \(-0.612158\pi\) | ||||
−0.345108 | + | 0.938563i | \(0.612158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14329.6 | 0.569171 | 0.284586 | − | 0.958651i | \(-0.408144\pi\) | ||||
0.284586 | + | 0.958651i | \(0.408144\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31208.8 | 1.23530 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28679.6 | −1.13125 | −0.565623 | − | 0.824664i | \(-0.691364\pi\) | ||||
−0.565623 | + | 0.824664i | \(0.691364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20929.4 | 0.822682 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 429.209 | 0.0168128 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14489.7 | −0.565626 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10648.6 | −0.414254 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15712.9 | −0.609164 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3794.36 | 0.146598 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30048.4 | −1.15697 | −0.578485 | − | 0.815693i | \(-0.696356\pi\) | ||||
−0.578485 | + | 0.815693i | \(0.696356\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18542.4 | −0.711511 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12576.6 | 0.480948 | 0.240474 | − | 0.970656i | \(-0.422697\pi\) | ||||
0.240474 | + | 0.970656i | \(0.422697\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18031.5 | 0.687213 | 0.343607 | − | 0.939114i | \(-0.388351\pi\) | ||||
0.343607 | + | 0.939114i | \(0.388351\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 737.413 | 0.0280089 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7089.07 | 0.268351 | 0.134176 | − | 0.990958i | \(-0.457161\pi\) | ||||
0.134176 | + | 0.990958i | \(0.457161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19050.2 | −0.718698 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1620.00 | −0.0609114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17151.3 | 0.642716 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9651.31 | −0.360456 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1685.61 | −0.0627435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8561.70 | −0.317629 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6345.02 | −0.234609 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34005.3 | −1.25319 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11550.0 | 0.424239 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18949.2 | 0.693714 | 0.346857 | − | 0.937918i | \(-0.387249\pi\) | ||||
0.346857 | + | 0.937918i | \(0.387249\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15659.4 | 0.571387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13418.4 | −0.488005 | −0.244003 | − | 0.969775i | \(-0.578461\pi\) | ||||
−0.244003 | + | 0.969775i | \(0.578461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8673.57 | −0.314407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4647.11 | −0.167900 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 66434.2 | 2.39242 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17684.3 | 0.634768 | 0.317384 | − | 0.948297i | \(-0.397196\pi\) | ||||
0.317384 | + | 0.948297i | \(0.397196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15176.7 | 0.542986 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13915.4 | 0.496241 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7044.36 | 0.250397 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2128.36 | 0.0754093 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34376.8 | 1.21406 | 0.607032 | − | 0.794677i | \(-0.292360\pi\) | ||||
0.607032 | + | 0.794677i | \(0.292360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49949.4 | −1.75835 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23387.5 | −0.820655 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6906.47 | −0.241568 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41657.0 | 1.45237 | 0.726187 | − | 0.687497i | \(-0.241291\pi\) | ||||
0.726187 | + | 0.687497i | \(0.241291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24415.0 | 0.848513 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13683.4 | 0.474035 | 0.237017 | − | 0.971505i | \(-0.423830\pi\) | ||||
0.237017 | + | 0.971505i | \(0.423830\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11773.8 | 0.406581 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4097.91 | −0.141064 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13500.9 | 0.463273 | 0.231637 | − | 0.972802i | \(-0.425592\pi\) | ||||
0.231637 | + | 0.972802i | \(0.425592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15772.5 | 0.539511 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20733.3 | 0.706965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5242.25 | 0.178188 | 0.0890939 | − | 0.996023i | \(-0.471603\pi\) | ||||
0.0890939 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23214.9 | −0.786613 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2365.17 | −0.0798905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57563.7 | 1.93830 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17382.3 | 0.583473 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4631.82 | 0.154993 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20016.2 | −0.667713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45761.1 | 1.52180 | 0.760898 | − | 0.648871i | \(-0.224759\pi\) | ||||
0.760898 | + | 0.648871i | \(0.224759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17892.2 | −0.593169 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47771.8 | 1.57886 | 0.789428 | − | 0.613843i | \(-0.210377\pi\) | ||||
0.789428 | + | 0.613843i | \(0.210377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13390.4 | 0.441188 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1226.62 | −0.0402904 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49812.5 | 1.63116 | 0.815581 | − | 0.578644i | \(-0.196418\pi\) | ||||
0.815581 | + | 0.578644i | \(0.196418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25292.9 | −0.825706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3086.12 | 0.100441 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49131.6 | 1.59416 | 0.797078 | − | 0.603877i | \(-0.206378\pi\) | ||||
0.797078 | + | 0.603877i | \(0.206378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20594.8 | 0.666199 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18086.7 | −0.583288 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12828.8 | −0.412469 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46553.2 | −1.49224 | −0.746121 | − | 0.665811i | \(-0.768086\pi\) | ||||
−0.746121 | + | 0.665811i | \(0.768086\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19531.9 | −0.624194 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11923.4 | −0.379896 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17111.5 | 0.543557 | 0.271778 | − | 0.962360i | \(-0.412388\pi\) | ||||
0.271778 | + | 0.962360i | \(0.412388\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7607.91 | −0.240945 |
(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 | 480.4.a.n.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1440.4.a.ba.1.1 | 2 | |||
4.3 | odd | 2 | 480.4.a.p.1.2 | yes | 2 | ||
5.4 | even | 2 | 2400.4.a.ba.1.2 | 2 | |||
8.3 | odd | 2 | 960.4.a.bl.1.2 | 2 | |||
8.5 | even | 2 | 960.4.a.bp.1.1 | 2 | |||
12.11 | even | 2 | 1440.4.a.bf.1.2 | 2 | |||
20.19 | odd | 2 | 2400.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.n.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
480.4.a.p.1.2 | yes | 2 | 4.3 | odd | 2 | ||
960.4.a.bl.1.2 | 2 | 8.3 | odd | 2 | |||
960.4.a.bp.1.1 | 2 | 8.5 | even | 2 | |||
1440.4.a.ba.1.1 | 2 | 3.2 | odd | 2 | |||
1440.4.a.bf.1.2 | 2 | 12.11 | even | 2 | |||
2400.4.a.z.1.1 | 2 | 20.19 | odd | 2 | |||
2400.4.a.ba.1.2 | 2 | 5.4 | even | 2 |