Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(1,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 128) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 256.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.00000 | −1.53960 | −0.769800 | − | 0.638285i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.0000 | 1.07331 | 0.536656 | − | 0.843801i | \(-0.319687\pi\) | ||||
0.536656 | + | 0.843801i | \(0.319687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.0000 | −1.72784 | −0.863919 | − | 0.503631i | \(-0.831997\pi\) | ||||
−0.863919 | + | 0.503631i | \(0.831997\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 37.0000 | 1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.00000 | 0.219281 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.0000 | −0.426692 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −96.0000 | −1.65247 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −98.0000 | −1.39815 | −0.699073 | − | 0.715050i | \(-0.746404\pi\) | ||||
−0.699073 | + | 0.715050i | \(0.746404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 88.0000 | 1.06256 | 0.531279 | − | 0.847197i | \(-0.321712\pi\) | ||||
0.531279 | + | 0.847197i | \(0.321712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 256.000 | 2.66018 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 32.0000 | 0.290107 | 0.145054 | − | 0.989424i | \(-0.453665\pi\) | ||||
0.145054 | + | 0.989424i | \(0.453665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −80.0000 | −0.570222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 172.000 | 1.10137 | 0.550683 | − | 0.834715i | \(-0.314367\pi\) | ||||
0.550683 | + | 0.834715i | \(0.314367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 256.000 | 1.48319 | 0.741596 | − | 0.670847i | \(-0.234069\pi\) | ||||
0.741596 | + | 0.670847i | \(0.234069\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −64.0000 | −0.337605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −384.000 | −1.85451 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 92.0000 | 0.408776 | 0.204388 | − | 0.978890i | \(-0.434480\pi\) | ||||
0.204388 | + | 0.978890i | \(0.434480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 160.000 | 0.656936 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 102.000 | 0.388530 | 0.194265 | − | 0.980949i | \(-0.437768\pi\) | ||||
0.194265 | + | 0.980949i | \(0.437768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 296.000 | 1.04976 | 0.524879 | − | 0.851177i | \(-0.324111\pi\) | ||||
0.524879 | + | 0.851177i | \(0.324111\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 444.000 | 1.47084 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 320.000 | 0.993123 | 0.496562 | − | 0.868001i | \(-0.334596\pi\) | ||||
0.496562 | + | 0.868001i | \(0.334596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 784.000 | 2.15259 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 76.0000 | 0.196970 | 0.0984849 | − | 0.995139i | \(-0.468600\pi\) | ||||
0.0984849 | + | 0.995139i | \(0.468600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 96.0000 | 0.235357 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −704.000 | −1.63591 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −408.000 | −0.900289 | −0.450145 | − | 0.892956i | \(-0.648628\pi\) | ||||
−0.450145 | + | 0.892956i | \(0.648628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 636.000 | 1.33494 | 0.667471 | − | 0.744636i | \(-0.267377\pi\) | ||||
0.667471 | + | 0.744636i | \(0.267377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1184.00 | −2.36778 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −240.000 | −0.457974 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −552.000 | −1.00653 | −0.503265 | − | 0.864132i | \(-0.667868\pi\) | ||||
−0.503265 | + | 0.864132i | \(0.667868\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −256.000 | −0.446649 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −416.000 | −0.695354 | −0.347677 | − | 0.937614i | \(-0.613029\pi\) | ||||
−0.347677 | + | 0.937614i | \(0.613029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 138.000 | 0.221256 | 0.110628 | − | 0.993862i | \(-0.464714\pi\) | ||||
0.110628 | + | 0.993862i | \(0.464714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −152.000 | −0.234019 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −256.000 | −0.378882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 64.0000 | 0.0911464 | 0.0455732 | − | 0.998961i | \(-0.485489\pi\) | ||||
0.0455732 | + | 0.998961i | \(0.485489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −392.000 | −0.518405 | −0.259202 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259202 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1176.00 | −1.50065 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1376.00 | −1.69566 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −582.000 | −0.693167 | −0.346584 | − | 0.938019i | \(-0.612658\pi\) | ||||
−0.346584 | + | 0.938019i | \(0.612658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 640.000 | 0.737255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2048.00 | −2.28352 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1056.00 | 1.14046 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 238.000 | 0.249126 | 0.124563 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124563 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 296.000 | 0.300496 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1468.00 | 1.44625 | 0.723126 | − | 0.690716i | \(-0.242705\pi\) | ||||
0.723126 | + | 0.690716i | \(0.242705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 992.000 | 0.948977 | 0.474489 | − | 0.880262i | \(-0.342633\pi\) | ||||
0.474489 | + | 0.880262i | \(0.342633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3072.00 | 2.85520 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 584.000 | 0.527639 | 0.263820 | − | 0.964572i | \(-0.415018\pi\) | ||||
0.263820 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −740.000 | −0.650267 | −0.325134 | − | 0.945668i | \(-0.605409\pi\) | ||||
−0.325134 | + | 0.945668i | \(0.605409\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −736.000 | −0.629352 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −302.000 | −0.251414 | −0.125707 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125707 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 384.000 | 0.311376 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −740.000 | −0.584727 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3136.00 | 2.41577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −816.000 | −0.598181 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1272.00 | −0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1664.00 | 1.16265 | 0.581323 | − | 0.813673i | \(-0.302535\pi\) | ||||
0.581323 | + | 0.813673i | \(0.302535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2368.00 | −1.61621 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2328.00 | 1.55266 | 0.776329 | − | 0.630327i | \(-0.217079\pi\) | ||||
0.776329 | + | 0.630327i | \(0.217079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2816.00 | −1.83593 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −960.000 | −0.612027 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1734.00 | 1.08135 | 0.540677 | − | 0.841230i | \(-0.318168\pi\) | ||||
0.540677 | + | 0.841230i | \(0.318168\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3032.00 | −1.85015 | −0.925075 | − | 0.379784i | \(-0.875998\pi\) | ||||
−0.925075 | + | 0.379784i | \(0.875998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2560.00 | −1.52901 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160.000 | −0.0935655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2064.00 | 1.18211 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5448.00 | −3.05676 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1788.00 | 0.983078 | 0.491539 | − | 0.870855i | \(-0.336434\pi\) | ||||
0.491539 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −480.000 | −0.258688 | −0.129344 | − | 0.991600i | \(-0.541287\pi\) | ||||
−0.129344 | + | 0.991600i | \(0.541287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3626.00 | −1.91598 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3072.00 | 1.59193 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2300.00 | 1.16917 | 0.584586 | − | 0.811332i | \(-0.301257\pi\) | ||||
0.584586 | + | 0.811332i | \(0.301257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −608.000 | −0.303255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1024.00 | −0.501258 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1592.00 | 0.765000 | 0.382500 | − | 0.923955i | \(-0.375063\pi\) | ||||
0.382500 | + | 0.923955i | \(0.375063\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −768.000 | −0.362356 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2208.00 | −1.02311 | −0.511557 | − | 0.859249i | \(-0.670931\pi\) | ||||
−0.511557 | + | 0.859249i | \(0.670931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1797.00 | −0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3256.00 | 1.45610 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3948.00 | 1.73503 | 0.867517 | − | 0.497408i | \(-0.165715\pi\) | ||||
0.867517 | + | 0.497408i | \(0.165715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −608.000 | −0.262631 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3264.00 | 1.38609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2104.00 | 0.878549 | 0.439275 | − | 0.898353i | \(-0.355235\pi\) | ||||
0.439275 | + | 0.898353i | \(0.355235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1412.00 | −0.579852 | −0.289926 | − | 0.957049i | \(-0.593631\pi\) | ||||
−0.289926 | + | 0.957049i | \(0.593631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5088.00 | −2.05528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1104.00 | 0.438744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −784.000 | −0.306587 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2560.00 | 0.985252 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3712.00 | −1.40624 | −0.703118 | − | 0.711074i | \(-0.748209\pi\) | ||||
−0.703118 | + | 0.711074i | \(0.748209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1614.00 | 0.601960 | 0.300980 | − | 0.953630i | \(-0.402686\pi\) | ||||
0.300980 | + | 0.953630i | \(0.402686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1920.00 | 0.705098 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 684.000 | 0.247376 | 0.123688 | − | 0.992321i | \(-0.460528\pi\) | ||||
0.123688 | + | 0.992321i | \(0.460528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4064.00 | 1.44769 | 0.723843 | − | 0.689965i | \(-0.242374\pi\) | ||||
0.723843 | + | 0.689965i | \(0.242374\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4416.00 | 1.54965 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5504.00 | −1.90298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1224.00 | 0.417014 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1184.00 | 0.397554 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 704.000 | 0.232999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2120.00 | −0.691691 | −0.345846 | − | 0.938291i | \(-0.612408\pi\) | ||||
−0.345846 | + | 0.938291i | \(0.612408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3328.00 | 1.07057 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3552.00 | 1.12672 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8192.00 | −2.56272 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1104.00 | −0.340646 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1960.00 | 0.596579 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2816.00 | −0.845620 | −0.422810 | − | 0.906218i | \(-0.638956\pi\) | ||||
−0.422810 | + | 0.906218i | \(0.638956\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 703.000 | 0.208296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3848.00 | −1.12511 | −0.562557 | − | 0.826759i | \(-0.690182\pi\) | ||||
−0.562557 | + | 0.826759i | \(0.690182\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 652.000 | 0.188146 | 0.0940729 | − | 0.995565i | \(-0.470011\pi\) | ||||
0.0940729 | + | 0.995565i | \(0.470011\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2048.00 | 0.583327 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3050.00 | 0.857563 | 0.428781 | − | 0.903408i | \(-0.358943\pi\) | ||||
0.428781 | + | 0.903408i | \(0.358943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3840.00 | 1.06593 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −512.000 | −0.140329 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6336.00 | 1.71482 | 0.857410 | − | 0.514635i | \(-0.172072\pi\) | ||||
0.857410 | + | 0.514635i | \(0.172072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4610.00 | −1.23218 | −0.616092 | − | 0.787674i | \(-0.711285\pi\) | ||||
−0.616092 | + | 0.787674i | \(0.711285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5032.00 | 1.32841 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8172.00 | 2.13098 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1760.00 | −0.453385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3136.00 | 0.798136 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −792.000 | −0.199166 | −0.0995829 | − | 0.995029i | \(-0.531751\pi\) | ||||
−0.0995829 | + | 0.995029i | \(0.531751\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 256.000 | 0.0636149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9408.00 | 2.31040 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5374.00 | −1.30436 | −0.652181 | − | 0.758063i | \(-0.726146\pi\) | ||||
−0.652181 | + | 0.758063i | \(0.726146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2944.00 | −0.706298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6364.00 | 1.50928 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3488.00 | −0.817792 | −0.408896 | − | 0.912581i | \(-0.634086\pi\) | ||||
−0.408896 | + | 0.912581i | \(0.634086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 912.000 | 0.211410 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4656.00 | 1.06720 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4764.00 | 1.07980 | 0.539900 | − | 0.841729i | \(-0.318462\pi\) | ||||
0.539900 | + | 0.841729i | \(0.318462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1344.00 | −0.301263 | −0.150631 | − | 0.988590i | \(-0.548131\pi\) | ||||
−0.150631 | + | 0.988590i | \(0.548131\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5120.00 | −1.13508 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 152.000 | 0.0333307 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8596.00 | −1.86456 | −0.932281 | − | 0.361735i | \(-0.882184\pi\) | ||||
−0.932281 | + | 0.361735i | \(0.882184\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9472.00 | 2.03252 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2874.00 | 0.610137 | 0.305068 | − | 0.952330i | \(-0.401321\pi\) | ||||
0.305068 | + | 0.952330i | \(0.401321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2888.00 | 0.606621 | 0.303311 | − | 0.952892i | \(-0.401908\pi\) | ||||
0.303311 | + | 0.952892i | \(0.401908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8448.00 | −1.75585 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3264.00 | −0.671316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4691.00 | 0.954814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1904.00 | −0.383555 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6540.00 | 1.30400 | 0.651998 | − | 0.758221i | \(-0.273931\pi\) | ||||
0.651998 | + | 0.758221i | \(0.273931\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4896.00 | −0.966292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −640.000 | −0.125039 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −640.000 | −0.123786 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9472.00 | −1.81381 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11744.0 | −2.22665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7632.00 | 1.43281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10584.0 | 1.96762 | 0.983812 | − | 0.179202i | \(-0.0573515\pi\) | ||||
0.983812 | + | 0.179202i | \(0.0573515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7936.00 | −1.46105 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6368.00 | −1.16108 | −0.580540 | − | 0.814231i | \(-0.697159\pi\) | ||||
−0.580540 | + | 0.814231i | \(0.697159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8758.00 | 1.58157 | 0.790785 | − | 0.612094i | \(-0.209673\pi\) | ||||
0.790785 | + | 0.612094i | \(0.209673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14208.0 | −2.54137 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 716.000 | 0.126860 | 0.0634299 | − | 0.997986i | \(-0.479796\pi\) | ||||
0.0634299 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1376.00 | 0.241508 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4672.00 | −0.812354 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8624.00 | −1.48561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −380.000 | −0.0648573 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5920.00 | 1.00115 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10240.0 | −1.71596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4408.00 | −0.731981 | −0.365990 | − | 0.930619i | \(-0.619270\pi\) | ||||
−0.365990 | + | 0.930619i | \(0.619270\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3404.00 | 0.560174 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6624.00 | −1.08032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1202.00 | 0.194294 | 0.0971471 | − | 0.995270i | \(-0.469028\pi\) | ||||
0.0971471 | + | 0.995270i | \(0.469028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2416.00 | 0.387077 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2048.00 | 0.325236 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3072.00 | −0.479394 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5160.00 | 0.798280 | 0.399140 | − | 0.916890i | \(-0.369309\pi\) | ||||
0.399140 | + | 0.916890i | \(0.369309\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4876.00 | 0.747869 | 0.373935 | − | 0.927455i | \(-0.378008\pi\) | ||||
0.373935 | + | 0.927455i | \(0.378008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1600.00 | 0.243310 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4834.00 | 0.728861 | 0.364430 | − | 0.931231i | \(-0.381264\pi\) | ||||
0.364430 | + | 0.931231i | \(0.381264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4992.00 | −0.746332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25088.0 | −3.71932 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4128.00 | −0.606873 | −0.303437 | − | 0.952852i | \(-0.598134\pi\) | ||||
−0.303437 | + | 0.952852i | \(0.598134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 885.000 | 0.129028 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10136.0 | 1.46557 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1656.00 | 0.237477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4416.00 | 0.628102 | 0.314051 | − | 0.949406i | \(-0.398314\pi\) | ||||
0.314051 | + | 0.949406i | \(0.398314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3774.00 | 0.532430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2432.00 | −0.340332 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4180.00 | −0.580247 | −0.290124 | − | 0.956989i | \(-0.593696\pi\) | ||||
−0.290124 | + | 0.956989i | \(0.593696\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10176.0 | 1.40130 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3440.00 | −0.469944 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13736.0 | 1.86166 | 0.930832 | − | 0.365446i | \(-0.119084\pi\) | ||||
0.930832 | + | 0.365446i | \(0.119084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13312.0 | −1.79001 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −512.000 | −0.0683080 | −0.0341540 | − | 0.999417i | \(-0.510874\pi\) | ||||
−0.0341540 | + | 0.999417i | \(0.510874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3072.00 | −0.406659 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10952.0 | 1.43856 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1732.00 | −0.225748 | −0.112874 | − | 0.993609i | \(-0.536006\pi\) | ||||
−0.112874 | + | 0.993609i | \(0.536006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3136.00 | −0.405612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18624.0 | −2.39047 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 768.000 | 0.0978285 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10436.0 | −1.31931 | −0.659657 | − | 0.751567i | \(-0.729299\pi\) | ||||
−0.659657 | + | 0.751567i | \(0.729299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22528.0 | 2.82659 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12130.0 | −1.51058 | −0.755291 | − | 0.655390i | \(-0.772504\pi\) | ||||
−0.755291 | + | 0.655390i | \(0.772504\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5120.00 | −0.632867 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4308.00 | −0.528559 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 736.000 | 0.0896368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5014.00 | 0.606177 | 0.303088 | − | 0.952962i | \(-0.401982\pi\) | ||||
0.303088 | + | 0.952962i | \(0.401982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13872.0 | −1.66485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13056.0 | 1.55555 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4704.00 | −0.556410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24256.0 | 2.84849 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8024.00 | 0.935556 | 0.467778 | − | 0.883846i | \(-0.345055\pi\) | ||||
0.467778 | + | 0.883846i | \(0.345055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2348.00 | 0.271816 | 0.135908 | − | 0.990721i | \(-0.456605\pi\) | ||||
0.135908 | + | 0.990721i | \(0.456605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11840.0 | 1.36095 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1862.00 | −0.212518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20352.0 | −2.30656 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1280.00 | 0.144054 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1728.00 | 0.193120 | 0.0965601 | − | 0.995327i | \(-0.469216\pi\) | ||||
0.0965601 | + | 0.995327i | \(0.469216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 62.0000 | 0.00688113 | 0.00344057 | − | 0.999994i | \(-0.498905\pi\) | ||||
0.00344057 | + | 0.999994i | \(0.498905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16512.0 | −1.81998 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2816.00 | 0.308255 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14112.0 | 1.53423 | 0.767117 | − | 0.641507i | \(-0.221690\pi\) | ||||
0.767117 | + | 0.641507i | \(0.221690\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25197.0 | 2.72076 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4488.00 | 0.481335 | 0.240667 | − | 0.970608i | \(-0.422634\pi\) | ||||
0.240667 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6984.00 | −0.743985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14304.0 | −1.51355 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2482.00 | −0.260875 | −0.130437 | − | 0.991457i | \(-0.541638\pi\) | ||||
−0.130437 | + | 0.991457i | \(0.541638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 816.000 | 0.0851972 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3840.00 | 0.398276 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7680.00 | 0.791305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5894.00 | 0.603303 | 0.301652 | − | 0.953418i | \(-0.402462\pi\) | ||||
0.301652 | + | 0.953418i | \(0.402462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7840.00 | 0.797255 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7068.00 | 0.714077 | 0.357039 | − | 0.934090i | \(-0.383786\pi\) | ||||
0.357039 | + | 0.934090i | \(0.383786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7616.00 | −0.764461 | −0.382231 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382231 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24576.0 | −2.45093 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13080.0 | 1.29608 | 0.648041 | − | 0.761606i | \(-0.275589\pi\) | ||||
0.648041 | + | 0.761606i | \(0.275589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17664.0 | 1.73912 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18400.0 | −1.80006 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2368.00 | 0.230192 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1672.00 | 0.161509 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2812.00 | 0.269922 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13568.0 | 1.29423 | 0.647117 | − | 0.762391i | \(-0.275975\pi\) | ||||
0.647117 | + | 0.762391i | \(0.275975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1840.00 | −0.174422 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8192.00 | 0.771737 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2856.00 | 0.267390 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1696.00 | −0.157809 | −0.0789046 | − | 0.996882i | \(-0.525142\pi\) | ||||
−0.0789046 | + | 0.996882i | \(0.525142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12736.0 | −1.17780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3096.00 | −0.284563 | −0.142282 | − | 0.989826i | \(-0.545444\pi\) | ||||
−0.142282 | + | 0.989826i | \(0.545444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16856.0 | −1.53987 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3552.00 | 0.322526 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13312.0 | 1.20146 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19208.0 | −1.72318 | −0.861591 | − | 0.507603i | \(-0.830532\pi\) | ||||
−0.861591 | + | 0.507603i | \(0.830532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17664.0 | 1.57519 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16224.0 | −1.43816 | −0.719078 | − | 0.694929i | \(-0.755436\pi\) | ||||
−0.719078 | + | 0.694929i | \(0.755436\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17616.0 | 1.55228 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14376.0 | 1.25929 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11292.0 | 0.983318 | 0.491659 | − | 0.870788i | \(-0.336391\pi\) | ||||
0.491659 | + | 0.870788i | \(0.336391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4416.00 | −0.382294 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7040.00 | −0.605894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11904.0 | 1.01855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2560.00 | 0.217773 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31584.0 | −2.67126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5178.00 | −0.435417 | −0.217709 | − | 0.976014i | \(-0.569858\pi\) | ||||
−0.217709 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6856.00 | 0.573216 | 0.286608 | − | 0.958048i | \(-0.407472\pi\) | ||||
0.286608 | + | 0.958048i | \(0.407472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4864.00 | 0.404347 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25088.0 | −2.07372 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11143.0 | −0.915838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15096.0 | −1.23373 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2040.00 | −0.165783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7008.00 | 0.566322 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16832.0 | −1.35262 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5448.00 | 0.435365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13732.0 | −1.09128 | −0.545642 | − | 0.838018i | \(-0.683714\pi\) | ||||
−0.545642 | + | 0.838018i | \(0.683714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11296.0 | 0.892740 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8880.00 | −0.697940 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10968.0 | 0.857327 | 0.428663 | − | 0.903464i | \(-0.358985\pi\) | ||||
0.428663 | + | 0.903464i | \(0.358985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23532.0 | 1.82936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15136.0 | 1.17026 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2048.00 | −0.157486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8832.00 | −0.675491 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25612.0 | 1.94832 | 0.974161 | − | 0.225855i | \(-0.0725176\pi\) | ||||
0.974161 | + | 0.225855i | \(0.0725176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5920.00 | −0.447924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6272.00 | 0.472021 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9768.00 | −0.731212 | −0.365606 | − | 0.930770i | \(-0.619138\pi\) | ||||
−0.365606 | + | 0.930770i | \(0.619138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3624.00 | −0.269846 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11488.0 | 0.850883 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22838.0 | 1.68263 | 0.841317 | − | 0.540542i | \(-0.181781\pi\) | ||||
0.841317 | + | 0.540542i | \(0.181781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9208.00 | −0.674856 | −0.337428 | − | 0.941351i | \(-0.609557\pi\) | ||||
−0.337428 | + | 0.941351i | \(0.609557\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29696.0 | 2.16504 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 608.000 | 0.0440963 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10878.0 | −0.784848 | −0.392424 | − | 0.919785i | \(-0.628363\pi\) | ||||
−0.392424 | + | 0.919785i | \(0.628363\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12912.0 | −0.926778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12544.0 | 0.895719 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 608.000 | 0.0431917 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8880.00 | −0.627595 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18040.0 | −1.26847 | −0.634234 | − | 0.773141i | \(-0.718684\pi\) | ||||
−0.634234 | + | 0.773141i | \(0.718684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22528.0 | 1.57598 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5472.00 | −0.380860 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26994.0 | 1.86933 | 0.934663 | − | 0.355534i | \(-0.115701\pi\) | ||||
0.934663 | + | 0.355534i | \(0.115701\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37632.0 | 2.59288 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32512.0 | −2.22886 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18336.0 | 1.25073 | 0.625366 | − | 0.780331i | \(-0.284950\pi\) | ||||
0.625366 | + | 0.780331i | \(0.284950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9286.00 | −0.630256 | −0.315128 | − | 0.949049i | \(-0.602047\pi\) | ||||
−0.315128 | + | 0.949049i | \(0.602047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20424.0 | −1.37932 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15204.0 | −1.02170 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17536.0 | 1.17259 | 0.586297 | − | 0.810096i | \(-0.300585\pi\) | ||||
0.586297 | + | 0.810096i | \(0.300585\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44032.0 | 2.92983 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6400.00 | −0.423758 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5868.00 | 0.386633 | 0.193317 | − | 0.981136i | \(-0.438076\pi\) | ||||
0.193317 | + | 0.981136i | \(0.438076\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9792.00 | −0.642035 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19286.0 | −1.25839 | −0.629194 | − | 0.777248i | \(-0.716615\pi\) | ||||
−0.629194 | + | 0.777248i | \(0.716615\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5240.00 | −0.340248 | −0.170124 | − | 0.985423i | \(-0.554417\pi\) | ||||
−0.170124 | + | 0.985423i | \(0.554417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2560.00 | −0.165426 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18624.0 | 1.19768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5632.00 | −0.358725 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9016.00 | −0.571529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15520.0 | 0.979147 | 0.489573 | − | 0.871962i | \(-0.337153\pi\) | ||||
0.489573 | + | 0.871962i | \(0.337153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16960.0 | 1.06493 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19968.0 | 1.24788 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13620.0 | −0.847165 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15392.0 | −0.952892 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 654.000 | 0.0402987 | 0.0201493 | − | 0.999797i | \(-0.493586\pi\) | ||||
0.0201493 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8232.00 | −0.504881 | −0.252440 | − | 0.967612i | \(-0.581233\pi\) | ||||
−0.252440 | + | 0.967612i | \(0.581233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28416.0 | −1.73470 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24672.0 | 1.49916 | 0.749580 | − | 0.661914i | \(-0.230256\pi\) | ||||
0.749580 | + | 0.661914i | \(0.230256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3264.00 | −0.197416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 65536.0 | 3.94556 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22052.0 | −1.32153 | −0.660767 | − | 0.750591i | \(-0.729769\pi\) | ||||
−0.660767 | + | 0.750591i | \(0.729769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27936.0 | 1.66649 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5106.00 | 0.303202 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12024.0 | 0.710757 | 0.355378 | − | 0.934723i | \(-0.384352\pi\) | ||||
0.355378 | + | 0.934723i | \(0.384352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19100.0 | 1.12391 | 0.561955 | − | 0.827168i | \(-0.310050\pi\) | ||||
0.561955 | + | 0.827168i | \(0.310050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15680.0 | −0.918493 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33792.0 | −1.97052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5504.00 | 0.319514 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22528.0 | 1.30192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5088.00 | 0.292727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9902.00 | 0.567153 | 0.283577 | − | 0.958950i | \(-0.408479\pi\) | ||||
0.283577 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1520.00 | −0.0866738 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19684.0 | −1.11746 | −0.558728 | − | 0.829351i | \(-0.688710\pi\) | ||||
−0.558728 | + | 0.829351i | \(0.688710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7616.00 | −0.430450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30784.0 | 1.73223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19864.0 | −1.11285 | −0.556424 | − | 0.830899i | \(-0.687827\pi\) | ||||
−0.556424 | + | 0.830899i | \(0.687827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20808.0 | 1.16063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5216.00 | −0.289669 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1520.00 | −0.0840456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3256.00 | 0.179253 | 0.0896267 | − | 0.995975i | \(-0.471433\pi\) | ||||
0.0896267 | + | 0.995975i | \(0.471433\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9472.00 | −0.519209 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36384.0 | −1.98579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9996.00 | −0.543222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24400.0 | −1.32030 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2876.00 | 0.154957 | 0.0774786 | − | 0.996994i | \(-0.475313\pi\) | ||||
0.0774786 | + | 0.996994i | \(0.475313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8096.00 | 0.434348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30720.0 | −1.64111 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46976.0 | −2.49889 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7300.00 | −0.386682 | −0.193341 | − | 0.981132i | \(-0.561932\pi\) | ||||
−0.193341 | + | 0.981132i | \(0.561932\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2368.00 | 0.124904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8192.00 | 0.430284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1920.00 | −0.100425 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −50688.0 | −2.64014 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2880.00 | 0.149382 | 0.0746912 | − | 0.997207i | \(-0.476203\pi\) | ||||
0.0746912 | + | 0.997207i | \(0.476203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31744.0 | −1.63968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36880.0 | 1.89707 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3268.00 | 0.167408 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8800.00 | −0.448933 | −0.224466 | − | 0.974482i | \(-0.572064\pi\) | ||||
−0.224466 | + | 0.974482i | \(0.572064\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30563.0 | −1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29008.0 | −1.46771 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21076.0 | −1.06202 | −0.531009 | − | 0.847366i | \(-0.678187\pi\) | ||||
−0.531009 | + | 0.847366i | \(0.678187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65376.0 | −3.28086 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4416.00 | −0.220713 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19336.0 | −0.962498 | −0.481249 | − | 0.876584i | \(-0.659817\pi\) | ||||
−0.481249 | + | 0.876584i | \(0.659817\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14080.0 | 0.698032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13664.0 | 0.674675 | 0.337338 | − | 0.941384i | \(-0.390474\pi\) | ||||
0.337338 | + | 0.941384i | \(0.390474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21456.0 | 1.05515 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14504.0 | −0.710406 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18688.0 | −0.911675 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19520.0 | −0.948462 | −0.474231 | − | 0.880400i | \(-0.657274\pi\) | ||||
−0.474231 | + | 0.880400i | \(0.657274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6336.00 | 0.306636 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5760.00 | −0.277653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20004.0 | −0.960446 | −0.480223 | − | 0.877146i | \(-0.659444\pi\) | ||||
−0.480223 | + | 0.877146i | \(0.659444\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2048.00 | −0.0979416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31478.0 | 1.49944 | 0.749722 | − | 0.661753i | \(-0.230187\pi\) | ||||
0.749722 | + | 0.661753i | \(0.230187\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23680.0 | 1.12356 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −43512.0 | −2.05644 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8160.00 | 0.384147 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7054.00 | 0.330785 | 0.165393 | − | 0.986228i | \(-0.447111\pi\) | ||||
0.165393 | + | 0.986228i | \(0.447111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42992.0 | 2.00820 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9604.00 | −0.446872 | −0.223436 | − | 0.974719i | \(-0.571727\pi\) | ||||
−0.223436 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4864.00 | 0.225445 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23552.0 | 1.08742 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8976.00 | 0.412835 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3328.00 | −0.152478 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13760.0 | −0.628023 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27600.0 | 1.25489 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3144.00 | −0.142403 | −0.0712017 | − | 0.997462i | \(-0.522683\pi\) | ||||
−0.0712017 | + | 0.997462i | \(0.522683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27904.0 | 1.25907 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9664.00 | 0.434402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12720.0 | −0.569610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7296.00 | −0.325487 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22084.0 | −0.981500 | −0.490750 | − | 0.871300i | \(-0.663277\pi\) | ||||
−0.490750 | + | 0.871300i | \(0.663277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31360.0 | −1.38853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21534.0 | −0.949896 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1104.00 | 0.0485172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12288.0 | −0.538006 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38112.0 | −1.66246 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14950.0 | 0.649708 | 0.324854 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324854 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23432.0 | 1.01456 | 0.507280 | − | 0.861781i | \(-0.330651\pi\) | ||||
0.507280 | + | 0.861781i | \(0.330651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10752.0 | 0.463824 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19104.0 | 0.821085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26048.0 | 1.11543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23680.0 | 1.01031 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1044.00 | −0.0443798 | −0.0221899 | − | 0.999754i | \(-0.507064\pi\) | ||||
−0.0221899 | + | 0.999754i | \(0.507064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18208.0 | 0.771192 | 0.385596 | − | 0.922668i | \(-0.373996\pi\) | ||||
0.385596 | + | 0.922668i | \(0.373996\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1216.00 | −0.0513160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12488.0 | 0.525091 | 0.262546 | − | 0.964920i | \(-0.415438\pi\) | ||||
0.262546 | + | 0.964920i | \(0.415438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30172.0 | 1.26407 | 0.632037 | − | 0.774938i | \(-0.282219\pi\) | ||||
0.632037 | + | 0.774938i | \(0.282219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 68768.0 | 2.87068 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −66738.0 | −2.77591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26496.0 | −1.09812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20480.0 | −0.845750 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32544.0 | −1.33915 | −0.669573 | − | 0.742746i | \(-0.733523\pi\) | ||||
−0.669573 | + | 0.742746i | \(0.733523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5195.00 | 0.213006 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22992.0 | −0.939367 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21564.0 | −0.877898 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40544.0 | 1.64476 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23104.0 | −0.933954 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2944.00 | 0.118589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26156.0 | 1.04990 | 0.524950 | − | 0.851133i | \(-0.324084\pi\) | ||||
0.524950 | + | 0.851133i | \(0.324084\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39072.0 | 1.56285 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18646.0 | 0.743215 | 0.371607 | − | 0.928390i | \(-0.378807\pi\) | ||||
0.371607 | + | 0.928390i | \(0.378807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5800.00 | 0.230377 | 0.115188 | − | 0.993344i | \(-0.463253\pi\) | ||||
0.115188 | + | 0.993344i | \(0.463253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26112.0 | 1.03356 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25088.0 | 0.989578 | 0.494789 | − | 0.869013i | \(-0.335245\pi\) | ||||
0.494789 | + | 0.869013i | \(0.335245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47376.0 | 1.86223 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37528.0 | −1.47003 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 512.000 | 0.0199867 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11040.0 | 0.429479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8806.00 | 0.341395 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40704.0 | 1.57262 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3004.00 | 0.115665 | 0.0578323 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578323 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52320.0 | −2.00763 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43282.0 | 1.65517 | 0.827587 | − | 0.561338i | \(-0.189713\pi\) | ||||
0.827587 | + | 0.561338i | \(0.189713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27880.0 | −1.06256 | −0.531278 | − | 0.847198i | \(-0.678288\pi\) | ||||
−0.531278 | + | 0.847198i | \(0.678288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 39168.0 | 1.48770 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7392.00 | −0.279819 | −0.139909 | − | 0.990164i | \(-0.544681\pi\) | ||||
−0.139909 | + | 0.990164i | \(0.544681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53248.0 | −2.00886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2872.00 | −0.107986 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28160.0 | 1.05525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25248.0 | 0.942958 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5120.00 | 0.190582 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44032.0 | 1.63354 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7448.00 | −0.275393 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 75776.0 | 2.79254 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16944.0 | −0.622362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29080.0 | −1.06459 | −0.532296 | − | 0.846558i | \(-0.678671\pi\) | ||||
−0.532296 | + | 0.846558i | \(0.678671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 54316.0 | 1.98190 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26688.0 | −0.970596 | −0.485298 | − | 0.874349i | \(-0.661289\pi\) | ||||
−0.485298 | + | 0.874349i | \(0.661289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3136.00 | −0.113676 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −61056.0 | −2.20596 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −74496.0 | −2.68274 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19680.0 | −0.706402 | −0.353201 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353201 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −84672.0 | −3.02936 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8320.00 | 0.296702 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1748.00 | 0.0621339 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36704.0 | 1.30045 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48466.0 | −1.71164 | −0.855822 | − | 0.517270i | \(-0.826948\pi\) | ||||
−0.855822 | + | 0.517270i | \(0.826948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 59928.0 | 2.10962 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50944.0 | 1.78760 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9408.00 | −0.329064 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13610.0 | 0.474514 | 0.237257 | − | 0.971447i | \(-0.423752\pi\) | ||||
0.237257 | + | 0.971447i | \(0.423752\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −70064.0 | −2.43499 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30692.0 | −1.06326 | −0.531632 | − | 0.846976i | \(-0.678421\pi\) | ||||
−0.531632 | + | 0.846976i | \(0.678421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3264.00 | 0.112715 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30720.0 | 1.05748 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4824.00 | 0.165532 | 0.0827661 | − | 0.996569i | \(-0.473625\pi\) | ||||
0.0827661 | + | 0.996569i | \(0.473625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2760.00 | −0.0944082 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5728.00 | −0.195313 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22986.0 | −0.781311 | −0.390656 | − | 0.920537i | \(-0.627752\pi\) | ||||
−0.390656 | + | 0.920537i | \(0.627752\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44544.0 | −1.50933 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11008.0 | −0.371827 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55488.0 | −1.86841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35745.0 | 1.19986 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21608.0 | 0.723061 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19368.0 | 0.646091 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17184.0 | −0.571458 | −0.285729 | − | 0.958310i | \(-0.592236\pi\) | ||||
−0.285729 | + | 0.958310i | \(0.592236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 68992.0 | 2.28725 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2920.00 | 0.0965059 | 0.0482530 | − | 0.998835i | \(-0.484635\pi\) | ||||
0.0482530 | + | 0.998835i | \(0.484635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 97024.0 | 3.19676 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3040.00 | 0.0998543 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27042.0 | −0.885517 | −0.442759 | − | 0.896641i | \(-0.646000\pi\) | ||||
−0.442759 | + | 0.896641i | \(0.646000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4656.00 | −0.151998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27380.0 | −0.891107 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44192.0 | 1.43388 | 0.716941 | − | 0.697134i | \(-0.245542\pi\) | ||||
0.716941 | + | 0.697134i | \(0.245542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8208.00 | 0.265511 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 81920.0 | 2.64189 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9472.00 | 0.304542 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29824.0 | −0.955995 | −0.477997 | − | 0.878361i | \(-0.658637\pi\) | ||||
−0.477997 | + | 0.878361i | \(0.658637\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35264.0 | 1.12696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48768.0 | 1.55382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11612.0 | 0.368862 | 0.184431 | − | 0.982845i | \(-0.440956\pi\) | ||||
0.184431 | + | 0.982845i | \(0.440956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7360.00 | −0.233093 |
(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 | 256.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 2304.4.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 256.4.a.g.1.1 | 1 | |||
8.3 | odd | 2 | 256.4.a.b.1.1 | 1 | |||
8.5 | even | 2 | 256.4.a.f.1.1 | 1 | |||
12.11 | even | 2 | 2304.4.a.d.1.1 | 1 | |||
16.3 | odd | 4 | 128.4.b.a.65.2 | yes | 2 | ||
16.5 | even | 4 | 128.4.b.d.65.2 | yes | 2 | ||
16.11 | odd | 4 | 128.4.b.a.65.1 | ✓ | 2 | ||
16.13 | even | 4 | 128.4.b.d.65.1 | yes | 2 | ||
24.5 | odd | 2 | 2304.4.a.m.1.1 | 1 | |||
24.11 | even | 2 | 2304.4.a.n.1.1 | 1 | |||
48.5 | odd | 4 | 1152.4.d.h.577.1 | 2 | |||
48.11 | even | 4 | 1152.4.d.a.577.1 | 2 | |||
48.29 | odd | 4 | 1152.4.d.h.577.2 | 2 | |||
48.35 | even | 4 | 1152.4.d.a.577.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.b.a.65.1 | ✓ | 2 | 16.11 | odd | 4 | ||
128.4.b.a.65.2 | yes | 2 | 16.3 | odd | 4 | ||
128.4.b.d.65.1 | yes | 2 | 16.13 | even | 4 | ||
128.4.b.d.65.2 | yes | 2 | 16.5 | even | 4 | ||
256.4.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
256.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
256.4.a.f.1.1 | 1 | 8.5 | even | 2 | |||
256.4.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
1152.4.d.a.577.1 | 2 | 48.11 | even | 4 | |||
1152.4.d.a.577.2 | 2 | 48.35 | even | 4 | |||
1152.4.d.h.577.1 | 2 | 48.5 | odd | 4 | |||
1152.4.d.h.577.2 | 2 | 48.29 | odd | 4 | |||
2304.4.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
2304.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
2304.4.a.m.1.1 | 1 | 24.5 | odd | 2 | |||
2304.4.a.n.1.1 | 1 | 24.11 | even | 2 |