Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,5,Mod(751,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.751");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.e (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: | \(124.043955701\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-43})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} - 11x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 751.3 | ||
Root | \(-2.58945 - 2.07237i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.751 |
Dual form | 1200.5.e.f.751.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 61.8613i | − 1.26248i | −0.775589 | − | 0.631238i | \(-0.782547\pi\) | ||||
0.775589 | − | 0.631238i | \(-0.217453\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 83.3929i | 0.689197i | 0.938750 | + | 0.344599i | \(0.111985\pi\) | ||||
−0.938750 | + | 0.344599i | \(0.888015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.0000 | 0.218935 | 0.109467 | − | 0.993990i | \(-0.465085\pi\) | ||||
0.109467 | + | 0.993990i | \(0.465085\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −164.147 | −0.567982 | −0.283991 | − | 0.958827i | \(-0.591659\pi\) | ||||
−0.283991 | + | 0.958827i | \(0.591659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 596.351i | 1.65194i | 0.563713 | + | 0.825970i | \(0.309372\pi\) | ||||
−0.563713 | + | 0.825970i | \(0.690628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 321.441 | 0.728890 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 326.389i | − 0.616992i | −0.951226 | − | 0.308496i | \(-0.900174\pi\) | ||||
0.951226 | − | 0.308496i | \(-0.0998257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 140.296i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1089.91 | 1.29597 | 0.647984 | − | 0.761654i | \(-0.275612\pi\) | ||||
0.647984 | + | 0.761654i | \(0.275612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1606.41i | − 1.67160i | −0.549034 | − | 0.835800i | \(-0.685004\pi\) | ||||
0.549034 | − | 0.835800i | \(-0.314996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −433.322 | −0.397908 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −389.706 | −0.284665 | −0.142332 | − | 0.989819i | \(-0.545460\pi\) | ||||
−0.142332 | + | 0.989819i | \(0.545460\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 192.258i | 0.126402i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2642.26 | −1.57184 | −0.785919 | − | 0.618329i | \(-0.787810\pi\) | ||||
−0.785919 | + | 0.618329i | \(0.787810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.9026i | − 0.00643732i | −0.999995 | − | 0.00321866i | \(-0.998975\pi\) | ||||
0.999995 | − | 0.00321866i | \(-0.00102453\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1620.79i | − 0.733721i | −0.930276 | − | 0.366860i | \(-0.880433\pi\) | ||||
0.930276 | − | 0.366860i | \(-0.119567\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1425.82 | −0.593844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 852.932i | − 0.327925i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1647.03 | 0.586340 | 0.293170 | − | 0.956060i | \(-0.405290\pi\) | ||||
0.293170 | + | 0.956060i | \(0.405290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3098.73 | −0.953749 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2974.65i | 0.854538i | 0.904125 | + | 0.427269i | \(0.140524\pi\) | ||||
−0.904125 | + | 0.427269i | \(0.859476\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1237.76 | 0.332641 | 0.166321 | − | 0.986072i | \(-0.446811\pi\) | ||||
0.166321 | + | 0.986072i | \(0.446811\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1670.25i | 0.420825i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 492.264i | 0.109660i | 0.998496 | + | 0.0548301i | \(0.0174617\pi\) | ||||
−0.998496 | + | 0.0548301i | \(0.982538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1695.97 | 0.356221 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2870.16i | 0.569362i | 0.958622 | + | 0.284681i | \(0.0918877\pi\) | ||||
−0.958622 | + | 0.284681i | \(0.908112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4209.23 | 0.789873 | 0.394936 | − | 0.918708i | \(-0.370767\pi\) | ||||
0.394936 | + | 0.918708i | \(0.370767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5158.79 | 0.870095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 746.145i | 0.119555i | 0.998212 | + | 0.0597777i | \(0.0190392\pi\) | ||||
−0.998212 | + | 0.0597777i | \(0.980961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9512.21i | 1.38078i | 0.723436 | + | 0.690391i | \(0.242562\pi\) | ||||
−0.723436 | + | 0.690391i | \(0.757438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5663.34i | 0.748228i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11355.8 | −1.43363 | −0.716813 | − | 0.697265i | \(-0.754400\pi\) | ||||
−0.716813 | + | 0.697265i | \(0.754400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2288.87i | − 0.276400i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8347.14 | 0.965098 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2710.04 | 0.288026 | 0.144013 | − | 0.989576i | \(-0.453999\pi\) | ||||
0.144013 | + | 0.989576i | \(0.453999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2251.61i | − 0.229732i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13821.3 | −1.35490 | −0.677449 | − | 0.735570i | \(-0.736914\pi\) | ||||
−0.677449 | + | 0.735570i | \(0.736914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1375.02i | 0.129609i | 0.997898 | + | 0.0648044i | \(0.0206423\pi\) | ||||
−0.997898 | + | 0.0648044i | \(0.979358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19402.8i | 1.69471i | 0.531025 | + | 0.847356i | \(0.321807\pi\) | ||||
−0.531025 | + | 0.847356i | \(0.678193\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −959.542 | −0.0807627 | −0.0403814 | − | 0.999184i | \(-0.512857\pi\) | ||||
−0.0403814 | + | 0.999184i | \(0.512857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 2024.97i | − 0.164351i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15052.5 | −1.17884 | −0.589418 | − | 0.807829i | \(-0.700643\pi\) | ||||
−0.589418 | + | 0.807829i | \(0.700643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −999.000 | −0.0729783 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10154.3i | 0.717064i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7686.63 | 0.525007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 13729.6i | − 0.907501i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16107.1i | 0.998644i | 0.866416 | + | 0.499322i | \(0.166418\pi\) | ||||
−0.866416 | + | 0.499322i | \(0.833582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 61.8477 | 0.00371659 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14129.9i | 0.823372i | 0.911326 | + | 0.411686i | \(0.135060\pi\) | ||||
−0.911326 | + | 0.411686i | \(0.864940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36891.0 | 2.08553 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11319.2 | −0.603082 | −0.301541 | − | 0.953453i | \(-0.597501\pi\) | ||||
−0.301541 | + | 0.953453i | \(0.597501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19054.3i | 0.986199i | 0.869973 | + | 0.493099i | \(0.164136\pi\) | ||||
−0.869973 | + | 0.493099i | \(0.835864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8421.87 | 0.423614 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3085.54i | 0.150889i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 7408.77i | − 0.342856i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −28887.6 | −1.30118 | −0.650592 | − | 0.759428i | \(-0.725479\pi\) | ||||
−0.650592 | + | 0.759428i | \(0.725479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5543.28i | 0.243116i | 0.992584 | + | 0.121558i | \(0.0387890\pi\) | ||||
−0.992584 | + | 0.121558i | \(0.961211\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4431.97 | 0.189327 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −39894.8 | −1.61851 | −0.809257 | − | 0.587454i | \(-0.800130\pi\) | ||||
−0.809257 | + | 0.587454i | \(0.800130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8558.21i | 0.338523i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20190.8 | −0.778937 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 12898.6i | − 0.485474i | −0.970092 | − | 0.242737i | \(-0.921955\pi\) | ||||
0.970092 | − | 0.242737i | \(-0.0780452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 38130.4i | − 1.36722i | −0.729847 | − | 0.683611i | \(-0.760409\pi\) | ||||
0.729847 | − | 0.683611i | \(-0.239591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27192.0 | −0.952068 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 16101.5i | − 0.550647i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 41518.0 | 1.38722 | 0.693609 | − | 0.720352i | \(-0.256020\pi\) | ||||
0.693609 | + | 0.720352i | \(0.256020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15456.7 | −0.493368 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11770.7i | 0.367364i | 0.982986 | + | 0.183682i | \(0.0588017\pi\) | ||||
−0.982986 | + | 0.183682i | \(0.941198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −35937.2 | −1.09695 | −0.548475 | − | 0.836167i | \(-0.684791\pi\) | ||||
−0.548475 | + | 0.836167i | \(0.684791\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6431.58i | 0.192050i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 13688.7i | − 0.391452i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8678.90 | −0.242963 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 3982.68i | − 0.109171i | −0.998509 | − | 0.0545857i | \(-0.982616\pi\) | ||||
0.998509 | − | 0.0545857i | \(-0.0173838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −44119.7 | −1.18445 | −0.592226 | − | 0.805772i | \(-0.701751\pi\) | ||||
−0.592226 | + | 0.805772i | \(0.701751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16021.6 | 0.412833 | 0.206417 | − | 0.978464i | \(-0.433820\pi\) | ||||
0.206417 | + | 0.978464i | \(0.433820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17872.7i | 0.451320i | 0.974206 | + | 0.225660i | \(0.0724538\pi\) | ||||
−0.974206 | + | 0.225660i | \(0.927546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2557.88 | −0.0633123 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 67423.2i | − 1.63613i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8812.50i | 0.205664i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −49731.4 | −1.13851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 10915.5i | − 0.245176i | −0.992458 | − | 0.122588i | \(-0.960881\pi\) | ||||
0.992458 | − | 0.122588i | \(-0.0391194\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14913.8 | −0.328721 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −99374.4 | −2.11035 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21871.8i | 0.456033i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6073.44 | −0.124351 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 80006.4i | − 1.60885i | −0.594056 | − | 0.804424i | \(-0.702474\pi\) | ||||
0.594056 | − | 0.804424i | \(-0.297526\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 62721.8i | 1.21721i | 0.793472 | + | 0.608607i | \(0.208271\pi\) | ||||
−0.793472 | + | 0.608607i | \(0.791729\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −83116.5 | −1.58495 | −0.792476 | − | 0.609903i | \(-0.791208\pi\) | ||||
−0.792476 | + | 0.609903i | \(0.791208\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26805.9i | 0.502349i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 79756.4 | 1.46911 | 0.734554 | − | 0.678550i | \(-0.237391\pi\) | ||||
0.734554 | + | 0.678550i | \(0.237391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3877.08 | −0.0690253 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9240.62i | 0.161773i | 0.996723 | + | 0.0808864i | \(0.0257751\pi\) | ||||
−0.996723 | + | 0.0808864i | \(0.974225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −40469.4 | −0.696775 | −0.348387 | − | 0.937351i | \(-0.613271\pi\) | ||||
−0.348387 | + | 0.937351i | \(0.613271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22065.0i | 0.361668i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −49426.9 | −0.797195 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 88508.8i | 1.40488i | 0.711743 | + | 0.702440i | \(0.247906\pi\) | ||||
−0.711743 | + | 0.702440i | \(0.752094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27218.5 | 0.425229 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −105642. | −1.59945 | −0.799725 | − | 0.600366i | \(-0.795022\pi\) | ||||
−0.799725 | + | 0.600366i | \(0.795022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24107.7i | 0.359382i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29427.6 | −0.431990 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3704.44i | 0.0535563i | 0.999641 | + | 0.0267782i | \(0.00852478\pi\) | ||||
−0.999641 | + | 0.0267782i | \(0.991475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 59006.2i | − 0.827704i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −83661.4 | −1.15617 | −0.578084 | − | 0.815977i | \(-0.696199\pi\) | ||||
−0.578084 | + | 0.815977i | \(0.696199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 114123.i | 1.55394i | 0.629538 | + | 0.776970i | \(0.283244\pi\) | ||||
−0.629538 | + | 0.776970i | \(0.716756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11893.3 | 0.159580 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113995. | 1.48568 | 0.742842 | − | 0.669467i | \(-0.233477\pi\) | ||||
0.742842 | + | 0.669467i | \(0.233477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 43373.0i | 0.557200i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 94716.2 | 1.19953 | 0.599766 | − | 0.800175i | \(-0.295260\pi\) | ||||
0.599766 | + | 0.800175i | \(0.295260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 41774.6i | 0.521602i | 0.965393 | + | 0.260801i | \(0.0839867\pi\) | ||||
−0.965393 | + | 0.260801i | \(0.916013\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 163454.i | 1.98441i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −56576.8 | −0.677396 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14081.8i | 0.166292i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10439.9 | 0.121608 | 0.0608041 | − | 0.998150i | \(-0.480634\pi\) | ||||
0.0608041 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11699.7 | 0.132636 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 12076.4i | − 0.135081i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −736.310 | −0.00812695 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 71817.6i | − 0.782251i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 55507.0i | 0.588940i | 0.955661 | + | 0.294470i | \(0.0951432\pi\) | ||||
−0.955661 | + | 0.294470i | \(0.904857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7144.81 | −0.0748297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 611.666i | − 0.00632402i | −0.999995 | − | 0.00316201i | \(-0.998993\pi\) | ||||
0.999995 | − | 0.00316201i | \(-0.00100650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 147215. | 1.50267 | 0.751333 | − | 0.659924i | \(-0.229411\pi\) | ||||
0.751333 | + | 0.659924i | \(0.229411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −93749.3 | −0.932931 | −0.466466 | − | 0.884539i | \(-0.654473\pi\) | ||||
−0.466466 | + | 0.884539i | \(0.654473\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 90890.7i | 0.893178i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −100820. | −0.978443 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 97889.1i | − 0.938273i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 4985.93i | − 0.0466284i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −100264. | −0.926304 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 90113.4i | − 0.822495i | −0.911524 | − | 0.411248i | \(-0.865093\pi\) | ||||
0.911524 | − | 0.411248i | \(-0.134907\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10522.1 | 0.0948883 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −67180.6 | −0.591540 | −0.295770 | − | 0.955259i | \(-0.595576\pi\) | ||||
−0.295770 | + | 0.955259i | \(0.595576\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 78215.3i | − 0.680601i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 133963. | 1.15206 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 60325.9i | − 0.512762i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 187996.i | 1.56131i | 0.624960 | + | 0.780657i | \(0.285115\pi\) | ||||
−0.624960 | + | 0.780657i | \(0.714885\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −180728. | −1.48380 | −0.741900 | − | 0.670510i | \(-0.766075\pi\) | ||||
−0.741900 | + | 0.670510i | \(0.766075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 5190.96i | − 0.0421340i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 95669.5 | 0.767758 | 0.383879 | − | 0.923383i | \(-0.374588\pi\) | ||||
0.383879 | + | 0.923383i | \(0.374588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −52763.5 | −0.413997 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 79558.5i | − 0.617302i | −0.951175 | − | 0.308651i | \(-0.900123\pi\) | ||||
0.951175 | − | 0.308651i | \(-0.0998775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −225313. | −1.72891 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 39940.9i | 0.303113i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 228720.i | − 1.69814i | −0.528283 | − | 0.849068i | \(-0.677164\pi\) | ||||
0.528283 | − | 0.849068i | \(-0.322836\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 71341.0 | 0.523946 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 101887.i | − 0.740239i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19451.7 | −0.139811 | −0.0699054 | − | 0.997554i | \(-0.522270\pi\) | ||||
−0.0699054 | + | 0.997554i | \(0.522270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40326.7 | 0.283733 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 82749.6i | 0.576086i | 0.957617 | + | 0.288043i | \(0.0930046\pi\) | ||||
−0.957617 | + | 0.288043i | \(0.906995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −83695.1 | −0.576568 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 240321.i | 1.63830i | 0.573578 | + | 0.819151i | \(0.305555\pi\) | ||||
−0.573578 | + | 0.819151i | \(0.694445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 321.370i | 0.00214577i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −132179. | −0.873499 | −0.436749 | − | 0.899583i | \(-0.643870\pi\) | ||||
−0.436749 | + | 0.899583i | \(0.643870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 53575.7i | 0.350441i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −73421.1 | −0.475374 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −268305. | −1.70234 | −0.851172 | − | 0.524887i | \(-0.824108\pi\) | ||||
−0.851172 | + | 0.524887i | \(0.824108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 191691.i | 1.20408i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −141049. | −0.877164 | −0.438582 | − | 0.898691i | \(-0.644519\pi\) | ||||
−0.438582 | + | 0.898691i | \(0.644519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 59437.1i | − 0.365971i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 32498.7i | − 0.196190i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 136033. | 0.813203 | 0.406602 | − | 0.913606i | \(-0.366714\pi\) | ||||
0.406602 | + | 0.913606i | \(0.366714\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 58816.5i | − 0.348189i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 184015. | 1.07883 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −99009.3 | −0.569382 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 236816.i | 1.34891i | 0.738315 | + | 0.674456i | \(0.235622\pi\) | ||||
−0.738315 | + | 0.674456i | \(0.764378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 150917. | 0.851481 | 0.425740 | − | 0.904845i | \(-0.360014\pi\) | ||||
0.425740 | + | 0.904845i | \(0.360014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 43761.3i | 0.244574i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 76569.3i | − 0.419951i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16032.9 | −0.0871160 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 182164.i | 0.980638i | 0.871543 | + | 0.490319i | \(0.163120\pi\) | ||||
−0.871543 | + | 0.490319i | \(0.836880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6063.92 | −0.0323428 | −0.0161714 | − | 0.999869i | \(-0.505148\pi\) | ||||
−0.0161714 | + | 0.999869i | \(0.505148\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 194642. | 1.01923 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 352332.i | 1.82820i | 0.405491 | + | 0.914099i | \(0.367100\pi\) | ||||
−0.405491 | + | 0.914099i | \(0.632900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38497.1 | 0.197948 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 85412.4i | − 0.435225i | −0.976035 | − | 0.217612i | \(-0.930173\pi\) | ||||
0.976035 | − | 0.217612i | \(-0.0698268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 150104.i | − 0.751239i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 253197. | 1.25593 | 0.627965 | − | 0.778242i | \(-0.283888\pi\) | ||||
0.627965 | + | 0.778242i | \(0.283888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 220346.i | − 1.08331i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28803.7 | −0.140363 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 131482. | 0.629554 | 0.314777 | − | 0.949166i | \(-0.398070\pi\) | ||||
0.314777 | + | 0.949166i | \(0.398070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23029.2i | 0.109308i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −118423. | −0.557232 | −0.278616 | − | 0.960403i | \(-0.589876\pi\) | ||||
−0.278616 | + | 0.960403i | \(0.589876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 77570.0i | 0.361853i | 0.983497 | + | 0.180926i | \(0.0579096\pi\) | ||||
−0.983497 | + | 0.180926i | \(0.942090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 151100.i | 0.692838i | 0.938080 | + | 0.346419i | \(0.112602\pi\) | ||||
−0.938080 | + | 0.346419i | \(0.887398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30452.1 | 0.138443 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 207299.i | − 0.934450i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 992.592 | 0.00443658 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −44469.8 | −0.195447 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 453553.i | − 1.97677i | −0.151961 | − | 0.988387i | \(-0.548559\pi\) | ||||
0.151961 | − | 0.988387i | \(-0.451441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14419.1 | −0.0623231 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 104915.i | − 0.449720i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 143695.i | 0.605875i | 0.953010 | + | 0.302938i | \(0.0979674\pi\) | ||||
−0.953010 | + | 0.302938i | \(0.902033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 67022.9 | 0.280289 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 179466.i | 0.744420i | 0.928149 | + | 0.372210i | \(0.121400\pi\) | ||||
−0.928149 | + | 0.372210i | \(0.878600\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −178905. | −0.736087 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 177552. | 0.718806 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 307441.i | − 1.23470i | −0.786690 | − | 0.617348i | \(-0.788207\pi\) | ||||
0.786690 | − | 0.617348i | \(-0.211793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 198132. | 0.789366 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 191607.i | 0.757313i | 0.925537 | + | 0.378657i | \(0.123614\pi\) | ||||
−0.925537 | + | 0.378657i | \(0.876386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 141294.i | − 0.549676i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −162446. | −0.627010 | −0.313505 | − | 0.949587i | \(-0.601503\pi\) | ||||
−0.313505 | + | 0.949587i | \(0.601503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 260389.i | − 0.997195i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 83665.7 | 0.317916 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 135162. | 0.505678 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 215734.i | 0.800911i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −170445. | −0.627927 | −0.313964 | − | 0.949435i | \(-0.601657\pi\) | ||||
−0.313964 | + | 0.949435i | \(0.601657\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12730.8i | 0.0465429i | 0.999729 | + | 0.0232714i | \(0.00740820\pi\) | ||||
−0.999729 | + | 0.0232714i | \(0.992592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 263687.i | 0.949439i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 173311. | 0.619321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 80315.4i | − 0.284846i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −97763.6 | −0.344130 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −61162.5 | −0.212098 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 118903.i | − 0.409276i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −91472.6 | −0.312534 | −0.156267 | − | 0.987715i | \(-0.549946\pi\) | ||||
−0.156267 | + | 0.987715i | \(0.549946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 186735.i | − 0.633324i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40143.9i | 0.134167i | 0.997747 | + | 0.0670834i | \(0.0213694\pi\) | ||||
−0.997747 | + | 0.0670834i | \(0.978631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33419.4 | −0.110880 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 649968.i | 2.14086i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46157.5 | 0.150936 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 548703. | 1.76859 | 0.884295 | − | 0.466928i | \(-0.154639\pi\) | ||||
0.884295 | + | 0.466928i | \(0.154639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 440.396i | − 0.00140935i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 71128.5 | 0.226005 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 390357.i | 1.23153i | 0.787930 | + | 0.615765i | \(0.211153\pi\) | ||||
−0.787930 | + | 0.615765i | \(0.788847\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 45096.9i | − 0.140275i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −345635. | −1.06756 | −0.533781 | − | 0.845623i | \(-0.679229\pi\) | ||||
−0.533781 | + | 0.845623i | \(0.679229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 179039.i | − 0.549130i | −0.961569 | − | 0.274565i | \(-0.911466\pi\) | ||||
0.961569 | − | 0.274565i | \(-0.0885339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20694.6 | 0.0630302 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −483243. | −1.45149 | −0.725745 | − | 0.687964i | \(-0.758505\pi\) | ||||
−0.725745 | + | 0.687964i | \(0.758505\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 229253.i | − 0.683844i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 588437. | 1.74320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 137350.i | 0.404104i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 503384.i | 1.46091i | 0.682961 | + | 0.730455i | \(0.260692\pi\) | ||||
−0.682961 | + | 0.730455i | \(0.739308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 957982. | 2.76138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 83250.9i | 0.238349i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −364949. | −1.03782 | −0.518910 | − | 0.854829i | \(-0.673662\pi\) | ||||
−0.518910 | + | 0.854829i | \(0.673662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −92869.4 | −0.260570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 535191.i | − 1.49161i | −0.666165 | − | 0.745805i | \(-0.732065\pi\) | ||||
0.666165 | − | 0.745805i | \(-0.267935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 350102. | 0.969273 | 0.484637 | − | 0.874716i | \(-0.338952\pi\) | ||||
0.484637 | + | 0.874716i | \(0.338952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13291.1i | − 0.0365534i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 547130.i | − 1.48495i | −0.669872 | − | 0.742477i | \(-0.733651\pi\) | ||||
0.669872 | − | 0.742477i | \(-0.266349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 350341. | 0.944619 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 59969.2i | − 0.160637i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 56676.1 | 0.150827 | 0.0754135 | − | 0.997152i | \(-0.475972\pi\) | ||||
0.0754135 | + | 0.997152i | \(0.475972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 702781. | 1.84608 | 0.923039 | − | 0.384707i | \(-0.125697\pi\) | ||||
0.923039 | + | 0.384707i | \(0.125697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 439023.i | − 1.14579i | −0.819628 | − | 0.572896i | \(-0.805820\pi\) | ||||
0.819628 | − | 0.572896i | \(-0.194180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −45791.1 | −0.118740 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 702481.i | 1.80992i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 258412.i | − 0.657321i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 63969.1 | 0.161685 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 362287.i | 0.909902i | 0.890516 | + | 0.454951i | \(0.150343\pi\) | ||||
−0.890516 | + | 0.454951i | \(0.849657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 56718.6 | 0.141553 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −52755.3 | −0.130013 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 77494.2i | − 0.189787i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 537150. | 1.30731 | 0.653656 | − | 0.756791i | \(-0.273234\pi\) | ||||
0.653656 | + | 0.756791i | \(0.273234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 504622.i | − 1.22052i | −0.792202 | − | 0.610259i | \(-0.791065\pi\) | ||||
0.792202 | − | 0.610259i | \(-0.208935\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 404053.i | − 0.965227i | −0.875834 | − | 0.482613i | \(-0.839688\pi\) | ||||
0.875834 | − | 0.482613i | \(-0.160312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −248064. | −0.588945 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 516365.i | − 1.21841i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −461059. | −1.08126 | −0.540630 | − | 0.841260i | \(-0.681814\pi\) | ||||
−0.540630 | + | 0.841260i | \(0.681814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −113649. | −0.263291 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 329198.i | − 0.758030i | −0.925391 | − | 0.379015i | \(-0.876263\pi\) | ||||
0.925391 | − | 0.379015i | \(-0.123737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12874.2 | −0.0294657 | −0.0147329 | − | 0.999891i | \(-0.504690\pi\) | ||||
−0.0147329 | + | 0.999891i | \(0.504690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 31558.5i | − 0.0717942i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 355734.i | − 0.799603i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 415725. | 0.928869 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 103220.i | 0.229255i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −740449. | −1.63480 | −0.817400 | − | 0.576070i | \(-0.804586\pi\) | ||||
−0.817400 | + | 0.576070i | \(0.804586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 516307. | 1.12650 | 0.563250 | − | 0.826287i | \(-0.309551\pi\) | ||||
0.563250 | + | 0.826287i | \(0.309551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 167647.i | − 0.363626i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −325912. | −0.702759 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 569453.i | − 1.22072i | −0.792124 | − | 0.610361i | \(-0.791025\pi\) | ||||
0.792124 | − | 0.610361i | \(-0.208975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 431886.i | − 0.915073i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 60940.0 | 0.128370 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 383630.i | − 0.803446i | −0.915761 | − | 0.401723i | \(-0.868412\pi\) | ||||
0.915761 | − | 0.401723i | \(-0.131588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −139287. | −0.290032 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 433719. | 0.892776 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 414427.i | 0.848190i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −452921. | −0.921693 | −0.460847 | − | 0.887480i | \(-0.652454\pi\) | ||||
−0.460847 | + | 0.887480i | \(0.652454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 232402.i | − 0.470250i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 855004.i | 1.71052i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 302501. | 0.601774 | 0.300887 | − | 0.953660i | \(-0.402717\pi\) | ||||
0.300887 | + | 0.953660i | \(0.402717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 20145.9i | − 0.0398518i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −524313. | −1.03136 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −48015.7 | −0.0933995 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 108427.i | − 0.209739i | −0.994486 | − | 0.104870i | \(-0.966557\pi\) | ||||
0.994486 | − | 0.104870i | \(-0.0334425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 85060.5 | 0.163628 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 210285.i | − 0.402283i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 659371.i | − 1.24756i | −0.781600 | − | 0.623780i | \(-0.785596\pi\) | ||||
0.781600 | − | 0.623780i | \(-0.214404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1953.77i | 0.00365628i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −448465. | −0.834682 | −0.417341 | − | 0.908750i | \(-0.637038\pi\) | ||||
−0.417341 | + | 0.908750i | \(0.637038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41051.3 | −0.0755775 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 658790.i | 1.20631i | 0.797625 | + | 0.603154i | \(0.206089\pi\) | ||||
−0.797625 | + | 0.603154i | \(0.793911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −114653. | −0.208809 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 117235.i | 0.212364i | 0.994347 | + | 0.106182i | \(0.0338626\pi\) | ||||
−0.994347 | + | 0.106182i | \(0.966137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 256830.i | − 0.460261i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.20028e6 | 2.13953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 19810.5i | − 0.0351249i | −0.999846 | − | 0.0175624i | \(-0.994409\pi\) | ||||
0.999846 | − | 0.0175624i | \(-0.00559058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −459905. | −0.811108 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 156311. | 0.272770 | 0.136385 | − | 0.990656i | \(-0.456452\pi\) | ||||
0.136385 | + | 0.990656i | \(0.456452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 141432.i | 0.245506i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 890693. | 1.53801 | 0.769004 | − | 0.639244i | \(-0.220753\pi\) | ||||
0.769004 | + | 0.639244i | \(0.220753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 59358.5i | 0.101961i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 110062.i | 0.187088i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.10673e6 | 1.87150 | 0.935750 | − | 0.352664i | \(-0.114724\pi\) | ||||
0.935750 | + | 0.352664i | \(0.114724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 548932.i | − 0.923443i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 866276. | 1.44976 | 0.724882 | − | 0.688873i | \(-0.241894\pi\) | ||||
0.724882 | + | 0.688873i | \(0.241894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −125267. | −0.207490 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.57571e6i | − 2.59658i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −239351. | −0.392403 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 152910.i | − 0.249409i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.22977e6i | − 1.98552i | −0.120095 | − | 0.992762i | \(-0.538320\pi\) | ||||
0.120095 | − | 0.992762i | \(-0.461680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19248.8 | −0.0309208 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 931170.i | 1.48825i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45797.0 | 0.0728267 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −272215. | −0.428543 | −0.214272 | − | 0.976774i | \(-0.568738\pi\) | ||||
−0.214272 | + | 0.976774i | \(0.568738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 266047.i | 0.416740i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 306605. | 0.477875 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 351020.i | 0.544378i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 434718.i | − 0.667514i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 388984. | 0.594340 | 0.297170 | − | 0.954825i | \(-0.403957\pi\) | ||||
0.297170 | + | 0.954825i | \(0.403957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.06377e6i | − 1.61736i | −0.588248 | − | 0.808681i | \(-0.700182\pi\) | ||||
0.588248 | − | 0.808681i | \(-0.299818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −593000. | −0.897167 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7098.12 | 0.0106341 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 61799.4i | 0.0921333i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 73807.8 | 0.109500 | 0.0547502 | − | 0.998500i | \(-0.482564\pi\) | ||||
0.0547502 | + | 0.998500i | \(0.482564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15603e6i | 1.70675i | 0.521293 | + | 0.853377i | \(0.325450\pi\) | ||||
−0.521293 | + | 0.853377i | \(0.674550\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.06525e6i | 1.55755i | 0.627304 | + | 0.778775i | \(0.284158\pi\) | ||||
−0.627304 | + | 0.778775i | \(0.715842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −742002. | −1.07968 | −0.539841 | − | 0.841767i | \(-0.681516\pi\) | ||||
−0.539841 | + | 0.841767i | \(0.681516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 592336.i | 0.857760i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 234044. | 0.337293 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −225373. | −0.321699 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 167829.i | − 0.238420i | −0.992869 | − | 0.119210i | \(-0.961964\pi\) | ||||
0.992869 | − | 0.119210i | \(-0.0380361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 480622. | 0.679535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 492160.i | 0.692550i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 475505.i | − 0.662808i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −217067. | −0.301147 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 127196.i | 0.175636i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −629066. | −0.864566 | −0.432283 | − | 0.901738i | \(-0.642292\pi\) | ||||
−0.432283 | + | 0.901738i | \(0.642292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 941559. | 1.28199 | 0.640997 | − | 0.767544i | \(-0.278521\pi\) | ||||
0.640997 | + | 0.767544i | \(0.278521\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 452274.i | − 0.612936i | −0.951881 | − | 0.306468i | \(-0.900853\pi\) | ||||
0.951881 | − | 0.306468i | \(-0.0991473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −849330. | −1.14570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 484361.i | 0.650350i | 0.945654 | + | 0.325175i | \(0.105423\pi\) | ||||
−0.945654 | + | 0.325175i | \(0.894577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 293982.i | − 0.391095i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62223.2 | −0.0823972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18213.8i | 0.0240084i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −73171.1 | −0.0960088 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 588731. | 0.765451 | 0.382726 | − | 0.923862i | \(-0.374985\pi\) | ||||
0.382726 | + | 0.923862i | \(0.374985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54247.5i | 0.0702105i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.25076e6 | 1.61147 | 0.805733 | − | 0.592279i | \(-0.201772\pi\) | ||||
0.805733 | + | 0.592279i | \(0.201772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 837604.i | − 1.07428i | −0.843493 | − | 0.537140i | \(-0.819505\pi\) | ||||
0.843493 | − | 0.537140i | \(-0.180495\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 506950.i | 0.644344i | 0.946681 | + | 0.322172i | \(0.104413\pi\) | ||||
−0.946681 | + | 0.322172i | \(0.895587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 996408. | 1.26076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 60793.4i | 0.0765775i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 966558. | 1.21206 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 62750.8 | 0.0779891 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.75084e6i | − 2.16634i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −270355. | −0.333031 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3825.98i | − 0.00469210i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.18958e6i | 1.44604i | 0.690829 | + | 0.723018i | \(0.257246\pi\) | ||||
−0.690829 | + | 0.723018i | \(0.742754\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 373175. | 0.451633 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 175647.i | − 0.211644i | −0.994385 | − | 0.105822i | \(-0.966253\pi\) | ||||
0.994385 | − | 0.105822i | \(-0.0337473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −793250. | −0.951631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 874094. | 1.03949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 684071.i | 0.809973i | 0.914323 | + | 0.404986i | \(0.132724\pi\) | ||||
−0.914323 | + | 0.404986i | \(0.867276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −288423. | −0.340025 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 106196.i | 0.124653i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 37125.5i | − 0.0432029i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.28454e6 | −1.48839 | −0.744195 | − | 0.667963i | \(-0.767167\pi\) | ||||
−0.744195 | + | 0.667963i | \(0.767167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 850288.i | − 0.980995i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3178.31 | 0.00365118 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 542198. | 0.617559 | 0.308780 | − | 0.951134i | \(-0.400079\pi\) | ||||
0.308780 | + | 0.951134i | \(0.400079\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 764950.i | 0.867564i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.14252e6 | 1.29029 | 0.645144 | − | 0.764061i | \(-0.276798\pi\) | ||||
0.645144 | + | 0.764061i | \(0.276798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 862404.i | 0.969812i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.54481e6i | 1.72256i | 0.508129 | + | 0.861281i | \(0.330337\pi\) | ||||
−0.508129 | + | 0.861281i | \(0.669663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 155742. | 0.172931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 487136.i | − 0.538628i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 772945. | 0.851065 | 0.425532 | − | 0.904943i | \(-0.360087\pi\) | ||||
0.425532 | + | 0.904943i | \(0.360087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −472282. | −0.515677 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 700223.i | 0.761376i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.65702e6 | −1.79424 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 523875.i | − 0.564904i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44995.2i | 0.0481186i | 0.999711 | + | 0.0240593i | \(0.00765906\pi\) | ||||
−0.999711 | + | 0.0240593i | \(0.992341\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 508647. | 0.541712 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.02778e6i | − 1.09008i | −0.838408 | − | 0.545042i | \(-0.816514\pi\) | ||||
0.838408 | − | 0.545042i | \(-0.183486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.17873e6 | 1.24505 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48136.8 | 0.0504299 | 0.0252149 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252149 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 946989.i | − 0.988051i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25907.6 | 0.0269209 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 707744.i | 0.732435i | 0.930529 | + | 0.366218i | \(0.119347\pi\) | ||||
−0.930529 | + | 0.366218i | \(0.880653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 520987.i | − 0.534802i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3884.87 | −0.00397177 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.67192e6i | 1.70242i | 0.524822 | + | 0.851212i | \(0.324132\pi\) | ||||
−0.524822 | + | 0.851212i | \(0.675868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 468243. | 0.474868 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.62054e6 | −1.63031 | −0.815153 | − | 0.579246i | \(-0.803347\pi\) | ||||
−0.815153 | + | 0.579246i | \(0.803347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 54674.3i | 0.0547838i |
(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 | 1200.5.e.f.751.3 | yes | 4 | |
4.3 | odd | 2 | inner | 1200.5.e.f.751.2 | yes | 4 | |
5.2 | odd | 4 | 1200.5.j.d.799.8 | 8 | |||
5.3 | odd | 4 | 1200.5.j.d.799.2 | 8 | |||
5.4 | even | 2 | 1200.5.e.e.751.2 | ✓ | 4 | ||
20.3 | even | 4 | 1200.5.j.d.799.7 | 8 | |||
20.7 | even | 4 | 1200.5.j.d.799.1 | 8 | |||
20.19 | odd | 2 | 1200.5.e.e.751.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1200.5.e.e.751.2 | ✓ | 4 | 5.4 | even | 2 | ||
1200.5.e.e.751.3 | yes | 4 | 20.19 | odd | 2 | ||
1200.5.e.f.751.2 | yes | 4 | 4.3 | odd | 2 | inner | |
1200.5.e.f.751.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1200.5.j.d.799.1 | 8 | 20.7 | even | 4 | |||
1200.5.j.d.799.2 | 8 | 5.3 | odd | 4 | |||
1200.5.j.d.799.7 | 8 | 20.3 | even | 4 | |||
1200.5.j.d.799.8 | 8 | 5.2 | odd | 4 |