Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), 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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1534132224.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 107x^{4} + 210x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.8 | ||
Root | \(-0.0690906i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.4.d.f.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.4288i | 1.55888i | 0.626475 | + | 0.779441i | \(0.284497\pi\) | ||||
−0.626475 | + | 0.779441i | \(0.715503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.99032 | 0.161462 | 0.0807310 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807310 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.6274i | 0.291299i | 0.989336 | + | 0.145649i | \(0.0465271\pi\) | ||||
−0.989336 | + | 0.145649i | \(0.953473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.3156i | 0.924121i | 0.886848 | + | 0.462061i | \(0.152890\pi\) | ||||
−0.886848 | + | 0.462061i | \(0.847110\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −52.2865 | −0.900021 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −37.8823 | −0.540459 | −0.270229 | − | 0.962796i | \(-0.587100\pi\) | ||||
−0.270229 | + | 0.962796i | \(0.587100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.8823i | 0.964539i | 0.876023 | + | 0.482270i | \(0.160187\pi\) | ||||
−0.876023 | + | 0.482270i | \(0.839813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.97095i | 0.0932201i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 191.204 | 1.73343 | 0.866714 | − | 0.498806i | \(-0.166228\pi\) | ||||
0.866714 | + | 0.498806i | \(0.166228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −178.765 | −1.43012 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 138.918i | − 0.889530i | −0.895647 | − | 0.444765i | \(-0.853287\pi\) | ||||
0.895647 | − | 0.444765i | \(-0.146713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.136 | −1.22906 | −0.614529 | − | 0.788894i | \(-0.710654\pi\) | ||||
−0.614529 | + | 0.788894i | \(0.710654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −31.8823 | −0.168181 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.1177i | 0.251700i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 270.404i | − 1.20146i | −0.799451 | − | 0.600731i | \(-0.794876\pi\) | ||||
0.799451 | − | 0.600731i | \(-0.205124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −129.947 | −0.533542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −441.411 | −1.68139 | −0.840693 | − | 0.541511i | \(-0.817852\pi\) | ||||
−0.840693 | + | 0.541511i | \(0.817852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 64.1177i | − 0.227392i | −0.993516 | − | 0.113696i | \(-0.963731\pi\) | ||||
0.993516 | − | 0.113696i | \(-0.0362690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 156.860i | − 0.519628i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 436.234 | 1.35386 | 0.676929 | − | 0.736049i | \(-0.263311\pi\) | ||||
0.676929 | + | 0.736049i | \(0.263311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.058 | −0.973930 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 113.647i | − 0.312034i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 278.348i | 0.721398i | 0.932682 | + | 0.360699i | \(0.117462\pi\) | ||||
−0.932682 | + | 0.360699i | \(0.882538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.224 | −0.454101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −239.647 | −0.556877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 830.039i | − 1.83156i | −0.401684 | − | 0.915778i | \(-0.631575\pi\) | ||||
0.401684 | − | 0.915778i | \(-0.368425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 724.580i | 1.52087i | 0.649416 | + | 0.760434i | \(0.275014\pi\) | ||||
−0.649416 | + | 0.760434i | \(0.724986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26.9128 | −0.0538206 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −754.940 | −1.44060 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 859.529i | 1.56729i | 0.621211 | + | 0.783643i | \(0.286641\pi\) | ||||
−0.621211 | + | 0.783643i | \(0.713359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 573.613i | 1.00079i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −681.264 | −1.13875 | −0.569374 | − | 0.822078i | \(-0.692814\pi\) | ||||
−0.569374 | + | 0.822078i | \(0.692814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −785.058 | −1.25869 | −0.629343 | − | 0.777128i | \(-0.716676\pi\) | ||||
−0.629343 | + | 0.777128i | \(0.716676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 536.294i | − 0.825678i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.7793i | 0.0470337i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1018.82 | 1.45096 | 0.725481 | − | 0.688243i | \(-0.241618\pi\) | ||||
0.725481 | + | 0.688243i | \(0.241618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 467.334i | 0.618031i | 0.951057 | + | 0.309015i | \(0.0999995\pi\) | ||||
−0.951057 | + | 0.309015i | \(0.900001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 660.244i | − 0.842512i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 416.753 | 0.513570 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 510.706 | 0.608256 | 0.304128 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304128 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 129.527i | 0.149210i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 636.409i | − 0.709597i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1392.26 | −1.50360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −234.235 | −0.245186 | −0.122593 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122593 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 95.6468i | − 0.0970996i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 205.555i | − 0.202509i | −0.994861 | − | 0.101255i | \(-0.967714\pi\) | ||||
0.994861 | − | 0.101255i | \(-0.0322857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 391.379 | 0.374405 | 0.187203 | − | 0.982321i | \(-0.440058\pi\) | ||||
0.187203 | + | 0.982321i | \(0.440058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −156.353 | −0.145319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 934.274i | − 0.844109i | −0.906570 | − | 0.422055i | \(-0.861309\pi\) | ||||
0.906570 | − | 0.422055i | \(-0.138691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 584.123i | − 0.513292i | −0.966505 | − | 0.256646i | \(-0.917383\pi\) | ||||
0.966505 | − | 0.256646i | \(-0.0826174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 811.211 | 0.693664 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −582.706 | −0.485101 | −0.242551 | − | 0.970139i | \(-0.577984\pi\) | ||||
−0.242551 | + | 0.970139i | \(0.577984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3332.47i | 2.70221i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 389.840i | − 0.308040i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −113.280 | −0.0872635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1218.06 | 0.915145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1324.23i | − 0.970749i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 937.053i | − 0.670501i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1461.03 | −1.02083 | −0.510416 | − | 0.859928i | \(-0.670509\pi\) | ||||
−0.510416 | + | 0.859928i | \(0.670509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 192.353 | 0.131285 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 98.4323i | 0.0656494i | 0.999461 | + | 0.0328247i | \(0.0104503\pi\) | ||||
−0.999461 | + | 0.0328247i | \(0.989550\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 238.873i | 0.155736i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 470.579 | 0.300007 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2171.06 | 1.35391 | 0.676956 | − | 0.736024i | \(-0.263299\pi\) | ||||
0.676956 | + | 0.736024i | \(0.263299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1624.70i | 0.991407i | 0.868492 | + | 0.495703i | \(0.165090\pi\) | ||||
−0.868492 | + | 0.495703i | \(0.834910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1308.70i | 0.781650i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −460.333 | −0.269195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2421.17 | 1.38667 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1002.17i | − 0.562299i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 636.658i | 0.350047i | 0.984564 | + | 0.175024i | \(0.0560002\pi\) | ||||
−0.984564 | + | 0.175024i | \(0.944000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1819.34 | 0.980503 | 0.490252 | − | 0.871581i | \(-0.336905\pi\) | ||||
0.490252 | + | 0.871581i | \(0.336905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 340.940 | 0.180153 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 3697.29i | − 1.91596i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1656.50i | 0.842059i | 0.907047 | + | 0.421029i | \(0.138331\pi\) | ||||
−0.907047 | + | 0.421029i | \(0.861669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −835.045 | −0.416499 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 571.761 | 0.279882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.82i | 1.07101i | 0.844532 | + | 0.535505i | \(0.179879\pi\) | ||||
−0.844532 | + | 0.535505i | \(0.820121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 555.671i | − 0.262175i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1667.01 | 0.772439 | 0.386219 | − | 0.922407i | \(-0.373781\pi\) | ||||
0.386219 | + | 0.922407i | \(0.373781\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 320.761 | 0.146000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 718.940i | − 0.321513i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2500.53i | 1.09891i | 0.835522 | + | 0.549457i | \(0.185165\pi\) | ||||
−0.835522 | + | 0.549457i | \(0.814835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −534.562 | −0.230909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2490.12 | 1.05745 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 378.742i | − 0.158148i | −0.996869 | − | 0.0790740i | \(-0.974804\pi\) | ||||
0.996869 | − | 0.0790740i | \(-0.0251963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3093.88i | 1.27053i | 0.772294 | + | 0.635265i | \(0.219109\pi\) | ||||
−0.772294 | + | 0.635265i | \(0.780891\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2173.74 | −0.878073 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4712.82 | 1.87294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 402.590i | − 0.157435i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 80.7385i | − 0.0310734i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3656.98 | 1.38539 | 0.692695 | − | 0.721230i | \(-0.256423\pi\) | ||||
0.692695 | + | 0.721230i | \(0.256423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2788.12 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 2264.82i | − 0.831729i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1147.74i | − 0.415091i | −0.978225 | − | 0.207546i | \(-0.933452\pi\) | ||||
0.978225 | − | 0.207546i | \(-0.0665475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4842.73 | −1.72508 | −0.862542 | − | 0.505986i | \(-0.831129\pi\) | ||||
−0.862542 | + | 0.505986i | \(0.831129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2578.59 | −0.904873 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 415.408i | − 0.143625i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7693.29i | − 2.62109i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1720.84 | −0.577809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −848.942 | −0.280969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3222.35i | 1.05135i | 0.850684 | + | 0.525677i | \(0.176188\pi\) | ||||
−0.850684 | + | 0.525677i | \(0.823812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2043.79i | − 0.657457i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1117.50 | 0.354478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −634.355 | −0.198446 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2355.17i | − 0.726703i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1640.89i | − 0.499449i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4932.61 | 1.48122 | 0.740610 | − | 0.671935i | \(-0.234537\pi\) | ||||
0.740610 | + | 0.671935i | \(0.234537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1608.88 | 0.476705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3619.49i | − 1.05830i | −0.848529 | − | 0.529150i | \(-0.822511\pi\) | ||||
0.848529 | − | 0.529150i | \(-0.177489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 305.759i | − 0.0882320i | −0.999026 | − | 0.0441160i | \(-0.985953\pi\) | ||||
0.999026 | − | 0.0441160i | \(-0.0140471\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −95.3380 | −0.0271549 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 639.648 | 0.179849 | 0.0899244 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899244 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7603.05i | 2.11050i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3056.45i | 0.837713i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1744.94 | 0.472262 | 0.236131 | − | 0.971721i | \(-0.424121\pi\) | ||||
0.236131 | + | 0.971721i | \(0.424121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3357.29 | 0.897354 | 0.448677 | − | 0.893694i | \(-0.351895\pi\) | ||||
0.448677 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 5822.24i | − 1.51824i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3460.15 | −0.891351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1402.00 | −0.356820 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1317.45i | 0.331301i | 0.986185 | + | 0.165650i | \(0.0529723\pi\) | ||||
−0.986185 | + | 0.165650i | \(0.947028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2032.01i | 0.504945i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1980.73 | 0.486424 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3036.12 | −0.736917 | −0.368459 | − | 0.929644i | \(-0.620114\pi\) | ||||
−0.368459 | + | 0.929644i | \(0.620114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 808.592i | − 0.193990i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1250.26i | 0.296510i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1655.76 | −0.388206 | −0.194103 | − | 0.980981i | \(-0.562180\pi\) | ||||
−0.194103 | + | 0.980981i | \(0.562180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4851.29 | −1.12458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1532.12i | 0.351177i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5292.72i | 1.19964i | 0.800135 | + | 0.599820i | \(0.204761\pi\) | ||||
−0.800135 | + | 0.599820i | \(0.795239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8010.52 | −1.79559 | −0.897795 | − | 0.440414i | \(-0.854832\pi\) | ||||
−0.897795 | + | 0.440414i | \(0.854832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −388.582 | −0.0861467 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1899.80i | − 0.416591i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5692.81i | 1.23483i | 0.786638 | + | 0.617415i | \(0.211820\pi\) | ||||
−0.786638 | + | 0.617415i | \(0.788180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1909.23 | 0.409686 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2024.83 | 0.429861 | 0.214931 | − | 0.976629i | \(-0.431047\pi\) | ||||
0.214931 | + | 0.976629i | \(0.431047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 247.761i | 0.0520419i | 0.999661 | + | 0.0260210i | \(0.00828366\pi\) | ||||
−0.999661 | + | 0.0260210i | \(0.991716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 4176.77i | − 0.868106i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1319.96 | −0.271480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3477.94 | −0.707905 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 702.706i | − 0.141558i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8133.61i | 1.62174i | 0.585225 | + | 0.810871i | \(0.301006\pi\) | ||||
−0.585225 | + | 0.810871i | \(0.698994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14466.6 | 2.85518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 286.940 | 0.0560605 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8282.12i | 1.60190i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 191.732i | − 0.0367152i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 616.664 | 0.116919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12628.6 | −2.37085 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2974.82i | − 0.553035i | −0.961009 | − | 0.276518i | \(-0.910820\pi\) | ||||
0.961009 | − | 0.276518i | \(-0.0891805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1174.14i | 0.216163i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4451.52 | −0.811648 | −0.405824 | − | 0.913951i | \(-0.633015\pi\) | ||||
−0.405824 | + | 0.913951i | \(0.633015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8273.75 | −1.49412 | −0.747061 | − | 0.664755i | \(-0.768536\pi\) | ||||
−0.747061 | + | 0.664755i | \(0.768536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 469.060i | − 0.0839001i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 429.036i | − 0.0760160i | −0.999277 | − | 0.0380080i | \(-0.987899\pi\) | ||||
0.999277 | − | 0.0380080i | \(-0.0121012\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1476.34 | 0.259119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2802.82 | 0.487347 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3026.12i | − 0.521293i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7743.29i | − 1.32160i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1752.37 | 0.296349 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1304.48 | 0.218596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8196.71i | 1.36112i | 0.732691 | + | 0.680562i | \(0.238264\pi\) | ||||
−0.732691 | + | 0.680562i | \(0.761736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2433.63i | 0.400487i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14980.6 | −2.44322 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2000.35 | −0.323341 | −0.161670 | − | 0.986845i | \(-0.551688\pi\) | ||||
−0.161670 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1748.12i | − 0.280073i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2254.46i | − 0.358023i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2024.62 | −0.318715 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9997.40 | −1.56012 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 7707.48i | − 1.19239i | −0.802840 | − | 0.596195i | \(-0.796679\pi\) | ||||
0.802840 | − | 0.596195i | \(-0.203321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9681.98i | 1.48500i | 0.669847 | + | 0.742499i | \(0.266360\pi\) | ||||
−0.669847 | + | 0.742499i | \(0.733640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1169.52 | 0.177847 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10540.3 | −1.58925 | −0.794626 | − | 0.607099i | \(-0.792333\pi\) | ||||
−0.794626 | + | 0.607099i | \(0.792333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 11873.6i | − 1.77518i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 339.840i | − 0.0503816i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 514.158 | 0.0755884 | 0.0377942 | − | 0.999286i | \(-0.487967\pi\) | ||||
0.0377942 | + | 0.999286i | \(0.487967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 477.826 | 0.0696641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3654.17i | 0.528359i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 13682.7i | − 1.96214i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11272.4 | 1.60331 | 0.801657 | − | 0.597785i | \(-0.203952\pi\) | ||||
0.801657 | + | 0.597785i | \(0.203952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3972.70 | 0.560462 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 832.350i | 0.116478i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6956.92i | − 0.965726i | −0.875696 | − | 0.482863i | \(-0.839597\pi\) | ||||
0.875696 | − | 0.482863i | \(-0.160403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2811.16 | 0.387114 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6017.30 | 0.822034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10201.3i | − 1.38260i | −0.722569 | − | 0.691299i | \(-0.757039\pi\) | ||||
0.722569 | − | 0.691299i | \(-0.242961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 4383.10i | − 0.589378i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2461.56 | 0.328406 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −553.877 | −0.0733200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 577.060i | 0.0757974i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 546.451i | − 0.0712240i | −0.999366 | − | 0.0356120i | \(-0.988662\pi\) | ||||
0.999366 | − | 0.0356120i | \(-0.0113381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7243.25 | −0.936846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −295.297 | −0.0379027 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17756.8i | 2.26188i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2084.56i | − 0.263529i | −0.991281 | − | 0.131764i | \(-0.957936\pi\) | ||||
0.991281 | − | 0.131764i | \(-0.0420642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −716.620 | −0.0899144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9710.59 | −1.20929 | −0.604643 | − | 0.796497i | \(-0.706684\pi\) | ||||
−0.604643 | + | 0.796497i | \(0.706684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9188.81i | − 1.13580i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1411.74i | 0.173209i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2873.69 | 0.349984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6659.89 | −0.805160 | −0.402580 | − | 0.915385i | \(-0.631886\pi\) | ||||
−0.402580 | + | 0.915385i | \(0.631886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6513.17i | 0.781681i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2482.08i | − 0.295727i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8145.09 | −0.963438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4874.11 | −0.572389 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10576.7i | − 1.23318i | −0.787283 | − | 0.616592i | \(-0.788513\pi\) | ||||
0.787283 | − | 0.616592i | \(-0.211487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4871.09i | − 0.563901i | −0.959429 | − | 0.281951i | \(-0.909019\pi\) | ||||
0.959429 | − | 0.281951i | \(-0.0909814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3926.11 | −0.451286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6772.00 | 0.772918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2166.72i | 0.245562i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1381.00i | − 0.155420i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16916.7 | 1.89060 | 0.945302 | − | 0.326196i | \(-0.105767\pi\) | ||||
0.945302 | + | 0.326196i | \(0.105767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1163.88 | −0.129174 | −0.0645870 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645870 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7263.52i | 0.800596i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15273.8i | 1.67196i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1856.28 | −0.201812 | −0.100906 | − | 0.994896i | \(-0.532174\pi\) | ||||
−0.100906 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3006.52 | 0.324643 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1472.21i | − 0.157893i | −0.996879 | − | 0.0789465i | \(-0.974844\pi\) | ||||
0.996879 | − | 0.0789465i | \(-0.0251556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8901.02i | 0.948200i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1909.97 | −0.202100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9620.94 | 1.01123 | 0.505613 | − | 0.862761i | \(-0.331267\pi\) | ||||
0.505613 | + | 0.862761i | \(0.331267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4691.06i | − 0.489786i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5458.03i | 0.566094i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2257.51 | −0.232602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3613.53 | 0.369877 | 0.184938 | − | 0.982750i | \(-0.440791\pi\) | ||||
0.184938 | + | 0.982750i | \(0.440791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1022.82i | 0.104011i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17710.7i | 1.78931i | 0.446759 | + | 0.894654i | \(0.352578\pi\) | ||||
−0.446759 | + | 0.894654i | \(0.647422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1674.57 | −0.168087 | −0.0840433 | − | 0.996462i | \(-0.526783\pi\) | ||||
−0.0840433 | + | 0.996462i | \(0.526783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11091.9 | 1.10618 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15208.3i | 1.50697i | 0.657466 | + | 0.753484i | \(0.271628\pi\) | ||||
−0.657466 | + | 0.753484i | \(0.728372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2570.26i | 0.253057i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4969.51 | −0.486163 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 681.406 | 0.0662391 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 14280.1i | − 1.37940i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2505.14i | − 0.240466i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6458.37 | 0.616056 | 0.308028 | − | 0.951377i | \(-0.400331\pi\) | ||||
0.308028 | + | 0.951377i | \(0.400331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11712.7 | 1.11030 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1715.28i | 0.161590i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4082.45i | − 0.382216i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11337.7 | −1.05495 | −0.527474 | − | 0.849571i | \(-0.676861\pi\) | ||||
−0.527474 | + | 0.849571i | \(0.676861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6686.46 | −0.618348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14946.7i | 1.37380i | 0.726754 | + | 0.686898i | \(0.241028\pi\) | ||||
−0.726754 | + | 0.686898i | \(0.758972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5262.51i | 0.480754i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1667.01 | 0.151367 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2037.19 | −0.183865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2631.77i | 0.236101i | 0.993008 | + | 0.118051i | \(0.0376645\pi\) | ||||
−0.993008 | + | 0.118051i | \(0.962336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5001.04i | 0.445968i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6907.45 | 0.612302 | 0.306151 | − | 0.951983i | \(-0.400959\pi\) | ||||
0.306151 | + | 0.951983i | \(0.400959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3582.58 | 0.315689 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 962.283i | 0.0842929i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 12020.3i | − 1.04674i | −0.852107 | − | 0.523368i | \(-0.824675\pi\) | ||||
0.852107 | − | 0.523368i | \(-0.175325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2347.57 | −0.203230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2156.82 | 0.185626 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6821.29i | 0.583654i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4636.04i | 0.394377i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7501.60 | −0.634458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15846.1 | 1.33249 | 0.666247 | − | 0.745731i | \(-0.267899\pi\) | ||||
0.666247 | + | 0.745731i | \(0.267899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8891.64i | − 0.743411i | −0.928351 | − | 0.371706i | \(-0.878773\pi\) | ||||
0.928351 | − | 0.371706i | \(-0.121227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1603.69i | − 0.133316i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8036.20 | 0.664255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24392.0 | 2.00477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7470.35i | 0.610519i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 19120.0i | − 1.55381i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16283.3 | 1.31587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1136.23 | 0.0913068 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3550.17i | − 0.283705i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 12833.5i | − 1.01988i | −0.860210 | − | 0.509940i | \(-0.829667\pi\) | ||||
0.860210 | − | 0.509940i | \(-0.170333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9281.63 | −0.733541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10180.6 | 0.800162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16257.0i | − 1.27075i | −0.772204 | − | 0.635375i | \(-0.780845\pi\) | ||||
0.772204 | − | 0.635375i | \(-0.219155\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6521.22i | − 0.506956i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11097.1 | 0.857986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3046.59 | 0.234275 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14138.5i | 1.08134i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1558.32i | − 0.118542i | −0.998242 | − | 0.0592712i | \(-0.981122\pi\) | ||||
0.998242 | − | 0.0592712i | \(-0.0188777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2777.30 | 0.210138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1207.77 | 0.0908951 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9782.16i | 0.732272i | 0.930561 | + | 0.366136i | \(0.119319\pi\) | ||||
−0.930561 | + | 0.366136i | \(0.880681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10155.9i | − 0.756216i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 242.216 | 0.0179402 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7887.05 | 0.581094 | 0.290547 | − | 0.956861i | \(-0.406163\pi\) | ||||
0.290547 | + | 0.956861i | \(0.406163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 21819.3i | − 1.59914i | −0.600573 | − | 0.799570i | \(-0.705061\pi\) | ||||
0.600573 | − | 0.799570i | \(-0.294939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10970.9i | 0.799856i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34180.5 | −2.47900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7190.22 | 0.518774 | 0.259387 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259387 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8364.35i | 0.600363i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1397.48i | 0.0997884i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2958.12 | −0.210142 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6794.46 | 0.480199 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 13305.6i | − 0.935569i | −0.883843 | − | 0.467785i | \(-0.845052\pi\) | ||||
0.883843 | − | 0.467785i | \(-0.154948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 16945.9i | − 1.18548i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3443.21 | 0.239653 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8062.23 | −0.558307 | −0.279153 | − | 0.960246i | \(-0.590054\pi\) | ||||
−0.279153 | + | 0.960246i | \(0.590054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1974.34i | − 0.136034i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 14528.2i | − 0.995978i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2185.21 | 0.149058 | 0.0745288 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745288 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3542.25 | −0.240418 | −0.120209 | − | 0.992749i | \(-0.538357\pi\) | ||||
−0.120209 | + | 0.992749i | \(0.538357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7735.76i | − 0.522429i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21229.3i | 1.42660i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6050.64 | −0.404593 | −0.202296 | − | 0.979324i | \(-0.564840\pi\) | ||||
−0.202296 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1246.22 | 0.0829220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18895.7i | 1.25113i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22514.2i | 1.48343i | 0.670717 | + | 0.741713i | \(0.265986\pi\) | ||||
−0.670717 | + | 0.741713i | \(0.734014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23079.9 | 1.51328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4255.88 | 0.277691 | 0.138845 | − | 0.990314i | \(-0.455661\pi\) | ||||
0.138845 | + | 0.990314i | \(0.455661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 228.949i | 0.0148663i | 0.999972 | + | 0.00743315i | \(0.00236607\pi\) | ||||
−0.999972 | + | 0.00743315i | \(0.997634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5162.51i | − 0.333598i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1527.17 | 0.0982102 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6013.82 | −0.384884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2546.83i | − 0.162218i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10243.5i | 0.649340i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11429.2 | 0.721058 | 0.360529 | − | 0.932748i | \(-0.382596\pi\) | ||||
0.360529 | + | 0.932748i | \(0.382596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9667.04 | −0.606999 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 25464.1i | − 1.59136i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 14469.9i | − 0.900030i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6131.38 | 0.379583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29381.4 | 1.81045 | 0.905223 | − | 0.424938i | \(-0.139704\pi\) | ||||
0.905223 | + | 0.424938i | \(0.139704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 249.316i | 0.0152909i | 0.999971 | + | 0.00764546i | \(0.00243365\pi\) | ||||
−0.999971 | + | 0.00764546i | \(0.997566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3352.49i | 0.204658i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16025.8 | −0.973785 | −0.486893 | − | 0.873462i | \(-0.661870\pi\) | ||||
−0.486893 | + | 0.873462i | \(0.661870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8821.17 | 0.533530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1903.06i | − 0.114573i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14008.6i | − 0.839511i | −0.907637 | − | 0.419755i | \(-0.862116\pi\) | ||||
0.907637 | − | 0.419755i | \(-0.137884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1715.56 | −0.102340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7065.52 | 0.419562 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1011.91i | − 0.0598152i | −0.999553 | − | 0.0299076i | \(-0.990479\pi\) | ||||
0.999553 | − | 0.0299076i | \(-0.00952131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23619.4i | 1.38985i | 0.719084 | + | 0.694923i | \(0.244561\pi\) | ||||
−0.719084 | + | 0.694923i | \(0.755439\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4922.67 | 0.288357 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4163.28 | −0.242775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 26561.6i | − 1.54194i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14797.8i | 0.855183i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7700.41 | −0.443027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25811.9 | −1.47842 | −0.739208 | − | 0.673477i | \(-0.764800\pi\) | ||||
−0.739208 | + | 0.673477i | \(0.764800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4826.64i | 0.275226i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18255.2i | − 1.03634i | −0.855277 | − | 0.518172i | \(-0.826613\pi\) | ||||
0.855277 | − | 0.518172i | \(-0.173387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −700.438 | −0.0395881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10858.5 | 0.611009 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20090.4i | 1.12553i | 0.826617 | + | 0.562765i | \(0.190262\pi\) | ||||
−0.826617 | + | 0.562765i | \(0.809738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37839.0i | 2.11059i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 917.278 | 0.0509408 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12056.8 | −0.666659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16521.5i | 0.909563i | 0.890603 | + | 0.454782i | \(0.150283\pi\) | ||||
−0.890603 | + | 0.454782i | \(0.849717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 286.014i | − 0.0156779i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28316.7 | −1.54549 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16721.7 | 0.908720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1918.95i | 0.103836i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12431.4i | 0.669795i | 0.942255 | + | 0.334897i | \(0.108702\pi\) | ||||
−0.942255 | + | 0.334897i | \(0.891298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21600.4 | 1.15886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22809.2 | −1.21850 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 614.674i | − 0.0326976i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 980.957i | 0.0519614i | 0.999662 | + | 0.0259807i | \(0.00827084\pi\) | ||||
−0.999662 | + | 0.0259807i | \(0.991729\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9169.36 | −0.483654 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40561.4 | −2.13048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8023.06i | − 0.419644i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5234.81i | 0.272660i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4115.73 | 0.213478 | 0.106739 | − | 0.994287i | \(-0.465959\pi\) | ||||
0.106739 | + | 0.994287i | \(0.465959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1170.35 | 0.0604522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10071.9i | 0.518088i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24833.5i | 1.27213i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20850.1 | −1.06367 | −0.531833 | − | 0.846849i | \(-0.678497\pi\) | ||||
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2428.92i | 0.122896i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31517.2i | − 1.58815i | −0.607821 | − | 0.794074i | \(-0.707956\pi\) | ||||
0.607821 | − | 0.794074i | \(-0.292044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17466.7 | 0.876558 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9134.57 | −0.456549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11415.0i | 0.568213i | 0.958793 | + | 0.284106i | \(0.0916969\pi\) | ||||
−0.958793 | + | 0.284106i | \(0.908303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 10380.4i | − 0.514622i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5732.08 | −0.283028 | −0.141514 | − | 0.989936i | \(-0.545197\pi\) | ||||
−0.141514 | + | 0.989936i | \(0.545197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11096.2 | −0.545683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4206.01i | − 0.206010i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2793.78i | − 0.136291i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7843.07 | 0.381089 | 0.190544 | − | 0.981679i | \(-0.438975\pi\) | ||||
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3952.34 | −0.191277 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31709.0i | 1.52849i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29125.9i | − 1.39841i | −0.714920 | − | 0.699206i | \(-0.753537\pi\) | ||||
0.714920 | − | 0.699206i | \(-0.246463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6096.02 | −0.291530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14228.5 | 0.677768 | 0.338884 | − | 0.940828i | \(-0.389951\pi\) | ||||
0.338884 | + | 0.940828i | \(0.389951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1746.71i | − 0.0828771i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5942.19i | 0.280837i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35953.6 | 1.69258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28133.7 | −1.31928 | −0.659641 | − | 0.751581i | \(-0.729292\pi\) | ||||
−0.659641 | + | 0.751581i | \(0.729292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 9108.35i | − 0.425459i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 14686.9i | − 0.683377i | −0.939813 | − | 0.341689i | \(-0.889001\pi\) | ||||
0.939813 | − | 0.341689i | \(-0.110999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37922.5 | 1.75770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2425.78 | 0.112000 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 35260.9i | − 1.62176i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 7240.08i | − 0.331716i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3750.78 | −0.171190 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28870.9 | −1.31267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21001.0i | 0.951214i | 0.879658 | + | 0.475607i | \(0.157772\pi\) | ||||
−0.879658 | + | 0.475607i | \(0.842228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4967.27i | − 0.224131i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1742.48 | −0.0783253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31385.6 | −1.40547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 14553.9i | − 0.649274i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 13362.7i | − 0.593892i | −0.954894 | − | 0.296946i | \(-0.904032\pi\) | ||||
0.954894 | − | 0.296946i | \(-0.0959682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16525.5 | −0.731704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4596.36 | −0.202752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 8343.14i | − 0.366654i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9965.13i | 0.436304i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15878.2 | −0.692612 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39481.6 | −1.71582 | −0.857911 | − | 0.513798i | \(-0.828238\pi\) | ||||
−0.857911 | + | 0.513798i | \(0.828238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31157.5i | 1.34906i | 0.738247 | + | 0.674531i | \(0.235654\pi\) | ||||
−0.738247 | + | 0.674531i | \(0.764346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 24031.6i | − 1.03668i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38845.8 | −1.66958 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5121.87 | 0.219329 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1165.75i | − 0.0497368i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 21229.9i | − 0.902470i | −0.892405 | − | 0.451235i | \(-0.850984\pi\) | ||||
0.892405 | − | 0.451235i | \(-0.149016\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24603.8 | −1.04208 | −0.521041 | − | 0.853532i | \(-0.674456\pi\) | ||||
−0.521041 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5699.41 | 0.240519 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13668.1i | 0.574710i | 0.957824 | + | 0.287355i | \(0.0927759\pi\) | ||||
−0.957824 | + | 0.287355i | \(0.907224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 27518.8i | − 1.15291i | −0.817127 | − | 0.576457i | \(-0.804435\pi\) | ||||
0.817127 | − | 0.576457i | \(-0.195565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17078.4 | −0.712929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12654.9 | 0.526369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29054.1i | 1.20414i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5727.68i | 0.236532i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29951.5 | 1.23247 | 0.616234 | − | 0.787563i | \(-0.288657\pi\) | ||||
0.616234 | + | 0.787563i | \(0.288657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5090.88 | 0.208737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6074.48i | 0.248180i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5590.49i | 0.227596i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3642.38 | 0.147761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −743.283 | −0.0300464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 51702.3i | − 2.08265i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5174.61i | 0.207708i | 0.994593 | + | 0.103854i | \(0.0331175\pi\) | ||||
−0.994593 | + | 0.103854i | \(0.966882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12530.3 | 0.501201 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9258.34 | 0.369030 | 0.184515 | − | 0.982830i | \(-0.440929\pi\) | ||||
0.184515 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24353.0i | 0.967304i | 0.875260 | + | 0.483652i | \(0.160690\pi\) | ||||
−0.875260 | + | 0.483652i | \(0.839310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 3959.88i | − 0.156739i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42283.4 | 1.66784 | 0.833919 | − | 0.551887i | \(-0.186092\pi\) | ||||
0.833919 | + | 0.551887i | \(0.186092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43581.4 | −1.71308 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 10433.8i | − 0.408709i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10827.4i | 0.422663i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37231.0 | −1.44836 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2108.12 | 0.0817286 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2802.08i | − 0.108260i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49843.1i | 1.91914i | 0.281476 | + | 0.959568i | \(0.409176\pi\) | ||||
−0.281476 | + | 0.959568i | \(0.590824\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24400.8 | −0.936314 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8986.94 | 0.343675 | 0.171837 | − | 0.985125i | \(-0.445030\pi\) | ||||
0.171837 | + | 0.985125i | \(0.445030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3693.99i | − 0.140784i | −0.997519 | − | 0.0703922i | \(-0.977575\pi\) | ||||
0.997519 | − | 0.0703922i | \(-0.0224251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43399.8i | 1.64844i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51613.0 | 1.95377 | 0.976886 | − | 0.213763i | \(-0.0685720\pi\) | ||||
0.976886 | + | 0.213763i | \(0.0685720\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4368.95 | −0.164825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 860.821i | 0.0323665i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34847.4i | 1.30585i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6601.03 | 0.246534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24846.4 | −0.924856 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29469.5i | 1.09328i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 10544.5i | − 0.389886i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 575.197 | 0.0211975 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −53922.7 | −1.98061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17016.8i | − 0.622971i | −0.950251 | − | 0.311486i | \(-0.899173\pi\) | ||||
0.950251 | − | 0.311486i | \(-0.100827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1849.99i | 0.0675032i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2991.72 | −0.108804 | −0.0544019 | − | 0.998519i | \(-0.517325\pi\) | ||||
−0.0544019 | + | 0.998519i | \(0.517325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4966.55 | −0.180032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 37885.7i | − 1.36881i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 294.344i | 0.0105999i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5174.82 | 0.185747 | 0.0928736 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928736 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8924.46 | 0.319295 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 29509.3i | − 1.05234i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48338.6i | 1.71823i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3522.41 | −0.124802 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49256.5 | 1.73956 | 0.869780 | − | 0.493439i | \(-0.164260\pi\) | ||||
0.869780 | + | 0.493439i | \(0.164260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 26685.3i | − 0.939394i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 13354.6i | − 0.468605i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7016.69 | 0.245423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31566.5 | 1.10057 | 0.550283 | − | 0.834978i | \(-0.314520\pi\) | ||||
0.550283 | + | 0.834978i | \(0.314520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 24821.3i | − 0.862632i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 37575.6i | − 1.30173i | −0.759193 | − | 0.650866i | \(-0.774406\pi\) | ||||
0.759193 | − | 0.650866i | \(-0.225594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84399.7 | −2.91456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1407.18 | 0.0484397 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 10289.3i | − 0.353070i | −0.984294 | − | 0.176535i | \(-0.943511\pi\) | ||||
0.984294 | − | 0.176535i | \(-0.0564889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 34005.2i | − 1.16318i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1287.11 | 0.0438879 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36779.7 | −1.25017 | −0.625085 | − | 0.780557i | \(-0.714936\pi\) | ||||
−0.625085 | + | 0.780557i | \(0.714936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63736.9i | 2.15966i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4429.01i | 0.149602i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6492.15 | 0.218605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15210.9 | 0.510586 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8408.47i | 0.281370i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48593.6i | 1.62102i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35228.9 | 1.17155 | 0.585773 | − | 0.810475i | \(-0.300791\pi\) | ||||
0.585773 | + | 0.810475i | \(0.300791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9078.36 | 0.300969 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15314.8i | 0.506155i | 0.967446 | + | 0.253077i | \(0.0814428\pi\) | ||||
−0.967446 | + | 0.253077i | \(0.918557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4858.38i | 0.160074i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23229.9 | 0.763027 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24074.3 | 0.788337 | 0.394168 | − | 0.919038i | \(-0.371033\pi\) | ||||
0.394168 | + | 0.919038i | \(0.371033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5427.49i | 0.177184i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5257.10i | 0.171097i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15244.1 | −0.494620 | −0.247310 | − | 0.968936i | \(-0.579547\pi\) | ||||
−0.247310 | + | 0.968936i | \(0.579547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20003.7 | 0.647079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3913.43i | 0.126207i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 12259.6i | − 0.394168i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37518.6 | 1.20264 | 0.601321 | − | 0.799008i | \(-0.294641\pi\) | ||||
0.601321 | + | 0.799008i | \(0.294641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24590.1 | −0.785845 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 84403.1i | − 2.68920i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1717.01i | − 0.0545420i | −0.999628 | − | 0.0272710i | \(-0.991318\pi\) | ||||
0.999628 | − | 0.0272710i | \(-0.00868170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7300.90 | −0.231221 |
(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 | 384.4.d.f.193.8 | yes | 8 | |
3.2 | odd | 2 | 1152.4.d.p.577.2 | 8 | |||
4.3 | odd | 2 | inner | 384.4.d.f.193.4 | yes | 8 | |
8.3 | odd | 2 | inner | 384.4.d.f.193.5 | yes | 8 | |
8.5 | even | 2 | inner | 384.4.d.f.193.1 | ✓ | 8 | |
12.11 | even | 2 | 1152.4.d.p.577.1 | 8 | |||
16.3 | odd | 4 | 768.4.a.v.1.4 | 4 | |||
16.5 | even | 4 | 768.4.a.v.1.1 | 4 | |||
16.11 | odd | 4 | 768.4.a.u.1.1 | 4 | |||
16.13 | even | 4 | 768.4.a.u.1.4 | 4 | |||
24.5 | odd | 2 | 1152.4.d.p.577.8 | 8 | |||
24.11 | even | 2 | 1152.4.d.p.577.7 | 8 | |||
48.5 | odd | 4 | 2304.4.a.by.1.4 | 4 | |||
48.11 | even | 4 | 2304.4.a.cb.1.4 | 4 | |||
48.29 | odd | 4 | 2304.4.a.cb.1.1 | 4 | |||
48.35 | even | 4 | 2304.4.a.by.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.f.193.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.4.d.f.193.4 | yes | 8 | 4.3 | odd | 2 | inner | |
384.4.d.f.193.5 | yes | 8 | 8.3 | odd | 2 | inner | |
384.4.d.f.193.8 | yes | 8 | 1.1 | even | 1 | trivial | |
768.4.a.u.1.1 | 4 | 16.11 | odd | 4 | |||
768.4.a.u.1.4 | 4 | 16.13 | even | 4 | |||
768.4.a.v.1.1 | 4 | 16.5 | even | 4 | |||
768.4.a.v.1.4 | 4 | 16.3 | odd | 4 | |||
1152.4.d.p.577.1 | 8 | 12.11 | even | 2 | |||
1152.4.d.p.577.2 | 8 | 3.2 | odd | 2 | |||
1152.4.d.p.577.7 | 8 | 24.11 | even | 2 | |||
1152.4.d.p.577.8 | 8 | 24.5 | odd | 2 | |||
2304.4.a.by.1.1 | 4 | 48.35 | even | 4 | |||
2304.4.a.by.1.4 | 4 | 48.5 | odd | 4 | |||
2304.4.a.cb.1.1 | 4 | 48.29 | odd | 4 | |||
2304.4.a.cb.1.4 | 4 | 48.11 | even | 4 |