Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(65,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.65");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.b (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: | \(7.55224448073\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.65 |
Dual form | 128.4.b.a.65.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 8.00000i | 1.53960i | 0.638285 | + | 0.769800i | \(0.279644\pi\) | ||||
−0.638285 | + | 0.769800i | \(0.720356\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 12.0000i | − 1.07331i | −0.843801 | − | 0.536656i | \(-0.819687\pi\) | ||||
0.843801 | − | 0.536656i | \(-0.180313\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 8.00000i | 0.219281i | 0.993971 | + | 0.109640i | \(0.0349700\pi\) | ||||
−0.993971 | + | 0.109640i | \(0.965030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 20.0000i | − 0.426692i | −0.976977 | − | 0.213346i | \(-0.931564\pi\) | ||||
0.976977 | − | 0.213346i | \(-0.0684362\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 88.0000i | − 1.06256i | −0.847197 | − | 0.531279i | \(-0.821712\pi\) | ||||
0.847197 | − | 0.531279i | \(-0.178288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 256.000i | − 2.66018i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 80.0000i | − 0.570222i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 172.000i | 1.10137i | 0.834715 | + | 0.550683i | \(0.185633\pi\) | ||||
−0.834715 | + | 0.550683i | \(0.814367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −256.000 | −1.48319 | −0.741596 | − | 0.670847i | \(-0.765931\pi\) | ||||
−0.741596 | + | 0.670847i | \(0.765931\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −64.0000 | −0.337605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 384.000i | 1.85451i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 92.0000i | − 0.408776i | −0.978890 | − | 0.204388i | \(-0.934480\pi\) | ||||
0.978890 | − | 0.204388i | \(-0.0655204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 160.000 | 0.656936 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −102.000 | −0.388530 | −0.194265 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 296.000i | 1.04976i | 0.851177 | + | 0.524879i | \(0.175889\pi\) | ||||
−0.851177 | + | 0.524879i | \(0.824111\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 444.000i | 1.47084i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −320.000 | −0.993123 | −0.496562 | − | 0.868001i | \(-0.665404\pi\) | ||||
−0.496562 | + | 0.868001i | \(0.665404\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 784.000i | − 2.15259i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 76.0000i | − 0.196970i | −0.995139 | − | 0.0984849i | \(-0.968600\pi\) | ||||
0.995139 | − | 0.0984849i | \(-0.0313996\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 96.0000 | 0.235357 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 704.000 | 1.63591 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 408.000i | − 0.900289i | −0.892956 | − | 0.450145i | \(-0.851372\pi\) | ||||
0.892956 | − | 0.450145i | \(-0.148628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 636.000i | 1.33494i | 0.744636 | + | 0.667471i | \(0.232623\pi\) | ||||
−0.744636 | + | 0.667471i | \(0.767377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1184.00 | 2.36778 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −240.000 | −0.457974 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 552.000i | 1.00653i | 0.864132 | + | 0.503265i | \(0.167868\pi\) | ||||
−0.864132 | + | 0.503265i | \(0.832132\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 256.000i | 0.446649i | ||||||||
\(70\) | 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 | \(-0.535286\pi\) | ||||
−0.110628 | + | 0.993862i | \(0.535286\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 152.000i | − 0.234019i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 256.000i | − 0.378882i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.0000 | −0.0911464 | −0.0455732 | − | 0.998961i | \(-0.514511\pi\) | ||||
−0.0455732 | + | 0.998961i | \(0.514511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −359.000 | −0.492455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 392.000i | 0.518405i | 0.965823 | + | 0.259202i | \(0.0834597\pi\) | ||||
−0.965823 | + | 0.259202i | \(0.916540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1176.00i | 1.50065i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1376.00 | −1.69566 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 582.000 | 0.693167 | 0.346584 | − | 0.938019i | \(-0.387342\pi\) | ||||
0.346584 | + | 0.938019i | \(0.387342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 640.000i | 0.737255i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2048.00i | − 2.28352i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 296.000i | − 0.300496i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1468.00i | − 1.44625i | −0.690716 | − | 0.723126i | \(-0.742705\pi\) | ||||
0.690716 | − | 0.723126i | \(-0.257295\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 584.000i | 0.527639i | 0.964572 | + | 0.263820i | \(0.0849824\pi\) | ||||
−0.964572 | + | 0.263820i | \(0.915018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 740.000i | − 0.650267i | −0.945668 | − | 0.325134i | \(-0.894591\pi\) | ||||
0.945668 | − | 0.325134i | \(-0.105409\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 384.000i | − 0.311376i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 740.000i | 0.584727i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3136.00 | 2.41577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1267.00 | 0.951916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 816.000i | − 0.598181i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1272.00i | − 0.910169i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1664.00 | −1.16265 | −0.581323 | − | 0.813673i | \(-0.697465\pi\) | ||||
−0.581323 | + | 0.813673i | \(0.697465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2368.00 | −1.61621 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2328.00i | − 1.55266i | −0.630327 | − | 0.776329i | \(-0.717079\pi\) | ||||
0.630327 | − | 0.776329i | \(-0.282921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2816.00i | 1.83593i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −960.000 | −0.612027 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1734.00 | −1.08135 | −0.540677 | − | 0.841230i | \(-0.681832\pi\) | ||||
−0.540677 | + | 0.841230i | \(0.681832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3032.00i | − 1.85015i | −0.379784 | − | 0.925075i | \(-0.624002\pi\) | ||||
0.379784 | − | 0.925075i | \(-0.375998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2560.00i | − 1.52901i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 160.000 | 0.0935655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2064.00 | 1.18211 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5448.00i | 3.05676i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1788.00i | − 0.983078i | −0.870855 | − | 0.491539i | \(-0.836434\pi\) | ||||
0.870855 | − | 0.491539i | \(-0.163566\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 3072.00i | 1.59193i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2300.00i | 1.16917i | 0.811332 | + | 0.584586i | \(0.198743\pi\) | ||||
−0.811332 | + | 0.584586i | \(0.801257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 608.000 | 0.303255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1024.00 | −0.501258 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1592.00i | − 0.765000i | −0.923955 | − | 0.382500i | \(-0.875063\pi\) | ||||
0.923955 | − | 0.382500i | \(-0.124937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 768.000i | 0.362356i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 3256.00i | 1.45610i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3948.00i | 1.73503i | 0.497408 | + | 0.867517i | \(0.334285\pi\) | ||||
−0.497408 | + | 0.867517i | \(0.665715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 608.000 | 0.262631 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3264.00 | 1.38609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2104.00i | − 0.878549i | −0.898353 | − | 0.439275i | \(-0.855235\pi\) | ||||
0.898353 | − | 0.439275i | \(-0.144765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1412.00i | 0.579852i | 0.957049 | + | 0.289926i | \(0.0936306\pi\) | ||||
−0.957049 | + | 0.289926i | \(0.906369\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5088.00 | −2.05528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1104.00 | −0.438744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 784.000i | − 0.306587i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2560.00i | 0.985252i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3712.00 | 1.40624 | 0.703118 | − | 0.711074i | \(-0.251791\pi\) | ||||
0.703118 | + | 0.711074i | \(0.251791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1614.00 | 0.601960 | 0.300980 | − | 0.953630i | \(-0.402686\pi\) | ||||
0.300980 | + | 0.953630i | \(0.402686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1920.00i | − 0.705098i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 684.000i | − 0.247376i | −0.992321 | − | 0.123688i | \(-0.960528\pi\) | ||||
0.992321 | − | 0.123688i | \(-0.0394721\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − 5504.00i | − 1.90298i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1224.00i | 0.417014i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1184.00 | −0.397554 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 704.000 | 0.232999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2120.00i | 0.691691i | 0.938291 | + | 0.345846i | \(0.112408\pi\) | ||||
−0.938291 | + | 0.345846i | \(0.887592\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3328.00i | − 1.07057i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3552.00 | 1.12672 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8192.00 | 2.56272 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1104.00i | − 0.340646i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1960.00i | 0.596579i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2816.00 | 0.845620 | 0.422810 | − | 0.906218i | \(-0.361044\pi\) | ||||
0.422810 | + | 0.906218i | \(0.361044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 703.000 | 0.208296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3848.00i | 1.12511i | 0.826759 | + | 0.562557i | \(0.190182\pi\) | ||||
−0.826759 | + | 0.562557i | \(0.809818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 652.000i | − 0.188146i | −0.995565 | − | 0.0940729i | \(-0.970011\pi\) | ||||
0.995565 | − | 0.0940729i | \(-0.0299887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2048.00 | 0.583327 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3050.00 | −0.857563 | −0.428781 | − | 0.903408i | \(-0.641057\pi\) | ||||
−0.428781 | + | 0.903408i | \(0.641057\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3840.00i | 1.06593i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 512.000i | − 0.140329i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6336.00 | −1.71482 | −0.857410 | − | 0.514635i | \(-0.827928\pi\) | ||||
−0.857410 | + | 0.514635i | \(0.827928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4610.00 | −1.23218 | −0.616092 | − | 0.787674i | \(-0.711285\pi\) | ||||
−0.616092 | + | 0.787674i | \(0.711285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5032.00i | − 1.32841i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 8172.00i | − 2.13098i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1760.00 | −0.453385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3136.00 | −0.798136 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 792.000i | − 0.199166i | −0.995029 | − | 0.0995829i | \(-0.968249\pi\) | ||||
0.995029 | − | 0.0995829i | \(-0.0317508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 256.000i | 0.0636149i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 2944.00i | 0.706298i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 6364.00i | − 1.50928i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 4656.00i | 1.06720i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4764.00i | 1.07980i | 0.841729 | + | 0.539900i | \(0.181538\pi\) | ||||
−0.841729 | + | 0.539900i | \(0.818462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1344.00 | 0.301263 | 0.150631 | − | 0.988590i | \(-0.451869\pi\) | ||||
0.150631 | + | 0.988590i | \(0.451869\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5120.00 | −1.13508 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 152.000i | − 0.0333307i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8596.00i | 1.86456i | 0.361735 | + | 0.932281i | \(0.382184\pi\) | ||||
−0.361735 | + | 0.932281i | \(0.617816\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9472.00 | 2.03252 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2874.00 | −0.610137 | −0.305068 | − | 0.952330i | \(-0.598679\pi\) | ||||
−0.305068 | + | 0.952330i | \(0.598679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2888.00i | 0.606621i | 0.952892 | + | 0.303311i | \(0.0980920\pi\) | ||||
−0.952892 | + | 0.303311i | \(0.901908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 8448.00i | − 1.75585i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3264.00 | 0.671316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4691.00 | 0.954814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1904.00i | 0.383555i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6540.00i | − 1.30400i | −0.758221 | − | 0.651998i | \(-0.773931\pi\) | ||||
0.758221 | − | 0.651998i | \(-0.226069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4896.00 | −0.966292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 640.000 | 0.125039 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 640.000i | − 0.123786i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 9472.00i | − 1.81381i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11744.0 | 2.22665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7632.00 | 1.43281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 10584.0i | − 1.96762i | −0.179202 | − | 0.983812i | \(-0.557351\pi\) | ||||
0.179202 | − | 0.983812i | \(-0.442649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7936.00i | 1.46105i | ||||||||
\(310\) | 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 | \(-0.790327\pi\) | ||||
−0.790785 | + | 0.612094i | \(0.790327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 14208.0i | − 2.54137i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 716.000i | 0.126860i | 0.997986 | + | 0.0634299i | \(0.0202039\pi\) | ||||
−0.997986 | + | 0.0634299i | \(0.979796\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1376.00 | −0.241508 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4672.00 | −0.812354 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8624.00i | 1.48561i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 380.000i | 0.0648573i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5920.00 | 1.00115 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10240.0 | 1.71596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4408.00i | − 0.731981i | −0.930619 | − | 0.365990i | \(-0.880730\pi\) | ||||
0.930619 | − | 0.365990i | \(-0.119270\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3404.00i | 0.560174i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 2416.00i | − 0.387077i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2048.00i | − 0.325236i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10816.0 | −1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3072.00 | 0.479394 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5160.00i | 0.798280i | 0.916890 | + | 0.399140i | \(0.130691\pi\) | ||||
−0.916890 | + | 0.399140i | \(0.869309\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4876.00i | 0.747869i | 0.927455 | + | 0.373935i | \(0.121992\pi\) | ||||
−0.927455 | + | 0.373935i | \(0.878008\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 4992.00i | 0.746332i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25088.0i | 3.71932i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 10136.0i | 1.46557i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1656.00i | 0.237477i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4416.00 | −0.628102 | −0.314051 | − | 0.949406i | \(-0.601686\pi\) | ||||
−0.314051 | + | 0.949406i | \(0.601686\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3774.00 | 0.532430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2432.00i | 0.340332i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4180.00i | 0.580247i | 0.956989 | + | 0.290124i | \(0.0936964\pi\) | ||||
−0.956989 | + | 0.290124i | \(0.906304\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10176.0 | 1.40130 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3440.00 | 0.469944 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13736.0i | 1.86166i | 0.365446 | + | 0.930832i | \(0.380916\pi\) | ||||
−0.365446 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 13312.0i | − 1.79001i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 512.000 | 0.0683080 | 0.0341540 | − | 0.999417i | \(-0.489126\pi\) | ||||
0.0341540 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3072.00 | −0.406659 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 10952.0i | − 1.43856i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1732.00i | 0.225748i | 0.993609 | + | 0.112874i | \(0.0360056\pi\) | ||||
−0.993609 | + | 0.112874i | \(0.963994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3136.00 | −0.405612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18624.0 | 2.39047 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 768.000i | 0.0978285i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 10436.0i | − 1.31931i | −0.751567 | − | 0.659657i | \(-0.770701\pi\) | ||||
0.751567 | − | 0.659657i | \(-0.229299\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 5120.00i | 0.632867i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4308.00i | 0.528559i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 736.000 | 0.0896368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5014.00 | −0.606177 | −0.303088 | − | 0.952962i | \(-0.598018\pi\) | ||||
−0.303088 | + | 0.952962i | \(0.598018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 13872.0i | − 1.66485i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13056.0i | 1.55555i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4704.00 | 0.556410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24256.0 | 2.84849 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8024.00i | − 0.935556i | −0.883846 | − | 0.467778i | \(-0.845055\pi\) | ||||
0.883846 | − | 0.467778i | \(-0.154945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 2348.00i | − 0.271816i | −0.990721 | − | 0.135908i | \(-0.956605\pi\) | ||||
0.990721 | − | 0.135908i | \(-0.0433952\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11840.0 | 1.36095 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1862.00 | 0.212518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 20352.0i | − 2.30656i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1280.00i | 0.144054i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1728.00 | −0.193120 | −0.0965601 | − | 0.995327i | \(-0.530784\pi\) | ||||
−0.0965601 | + | 0.995327i | \(0.530784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 62.0000 | 0.00688113 | 0.00344057 | − | 0.999994i | \(-0.498905\pi\) | ||||
0.00344057 | + | 0.999994i | \(0.498905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16512.0i | 1.81998i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2816.00i | − 0.308255i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 4488.00i | 0.481335i | 0.970608 | + | 0.240667i | \(0.0773663\pi\) | ||||
−0.970608 | + | 0.240667i | \(0.922634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6984.00i | − 0.743985i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 816.000i | − 0.0851972i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3840.00i | − 0.398276i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7680.00 | 0.791305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5894.00 | −0.603303 | −0.301652 | − | 0.953418i | \(-0.597538\pi\) | ||||
−0.301652 | + | 0.953418i | \(0.597538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7840.00i | 0.797255i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7068.00i | 0.714077i | 0.934090 | + | 0.357039i | \(0.116214\pi\) | ||||
−0.934090 | + | 0.357039i | \(0.883786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7616.00 | 0.764461 | 0.382231 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382231 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24576.0 | −2.45093 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 13080.0i | − 1.29608i | −0.761606 | − | 0.648041i | \(-0.775589\pi\) | ||||
0.761606 | − | 0.648041i | \(-0.224411\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 17664.0i | − 1.73912i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18400.0 | −1.80006 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2368.00 | −0.230192 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1672.00i | 0.161509i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2812.00i | 0.269922i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13568.0 | −1.29423 | −0.647117 | − | 0.762391i | \(-0.724025\pi\) | ||||
−0.647117 | + | 0.762391i | \(0.724025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1840.00 | −0.174422 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8192.00i | − 0.771737i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2856.00i | − 0.267390i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | − 3096.00i | − 0.284563i | −0.989826 | − | 0.142282i | \(-0.954556\pi\) | ||||
0.989826 | − | 0.142282i | \(-0.0454439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 16856.0i | − 1.53987i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3552.00 | −0.322526 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13312.0 | 1.20146 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19208.0i | 1.72318i | 0.507603 | + | 0.861591i | \(0.330532\pi\) | ||||
−0.507603 | + | 0.861591i | \(0.669468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 17664.0i | − 1.57519i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 14376.0i | 1.25929i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11292.0i | 0.983318i | 0.870788 | + | 0.491659i | \(0.163609\pi\) | ||||
−0.870788 | + | 0.491659i | \(0.836391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4416.00 | 0.382294 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7040.00 | −0.605894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 11904.0i | − 1.01855i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2560.00i | − 0.217773i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −31584.0 | −2.67126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5178.00 | 0.435417 | 0.217709 | − | 0.976014i | \(-0.430142\pi\) | ||||
0.217709 | + | 0.976014i | \(0.430142\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6856.00i | 0.573216i | 0.958048 | + | 0.286608i | \(0.0925277\pi\) | ||||
−0.958048 | + | 0.286608i | \(0.907472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4864.00i | 0.404347i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25088.0 | 2.07372 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11143.0 | −0.915838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15096.0i | 1.23373i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2040.00i | 0.165783i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7008.00 | 0.566322 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16832.0 | 1.35262 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5448.00i | 0.435365i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13732.0i | − 1.09128i | −0.838018 | − | 0.545642i | \(-0.816286\pi\) | ||||
0.838018 | − | 0.545642i | \(-0.183714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11296.0 | −0.892740 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8880.00 | −0.697940 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10968.0i | − 0.857327i | −0.903464 | − | 0.428663i | \(-0.858985\pi\) | ||||
0.903464 | − | 0.428663i | \(-0.141015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 23532.0i | − 1.82936i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15136.0 | 1.17026 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2048.00 | 0.157486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 8832.00i | − 0.675491i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25612.0i | 1.94832i | 0.225855 | + | 0.974161i | \(0.427482\pi\) | ||||
−0.225855 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5920.00 | 0.447924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6272.00 | 0.472021 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9768.00i | 0.731212i | 0.930770 | + | 0.365606i | \(0.119138\pi\) | ||||
−0.930770 | + | 0.365606i | \(0.880862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3624.00i | 0.269846i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11488.0 | 0.850883 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22838.0 | −1.68263 | −0.841317 | − | 0.540542i | \(-0.818219\pi\) | ||||
−0.841317 | + | 0.540542i | \(0.818219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 9208.00i | − 0.674856i | −0.941351 | − | 0.337428i | \(-0.890443\pi\) | ||||
0.941351 | − | 0.337428i | \(-0.109557\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29696.0i | 2.16504i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 12912.0i | 0.926778i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12544.0i | − 0.895719i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 608.000 | 0.0431917 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8880.00 | 0.627595 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 18040.0i | − 1.26847i | −0.773141 | − | 0.634234i | \(-0.781316\pi\) | ||||
0.773141 | − | 0.634234i | \(-0.218684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22528.0i | 1.57598i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 37632.0i | − 2.59288i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32512.0i | 2.22886i | ||||||||
\(598\) | 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 | \(-0.397953\pi\) | ||||
0.315128 | + | 0.949049i | \(0.397953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 20424.0i | − 1.37932i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 15204.0i | − 1.02170i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17536.0 | −1.17259 | −0.586297 | − | 0.810096i | \(-0.699415\pi\) | ||||
−0.586297 | + | 0.810096i | \(0.699415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44032.0 | 2.92983 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6400.00i | 0.423758i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5868.00i | − 0.386633i | −0.981136 | − | 0.193317i | \(-0.938076\pi\) | ||||
0.981136 | − | 0.193317i | \(-0.0619245\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9792.00 | −0.642035 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19286.0 | 1.25839 | 0.629194 | − | 0.777248i | \(-0.283385\pi\) | ||||
0.629194 | + | 0.777248i | \(0.283385\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5240.00i | − 0.340248i | −0.985423 | − | 0.170124i | \(-0.945583\pi\) | ||||
0.985423 | − | 0.170124i | \(-0.0544168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2560.00i | − 0.165426i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18624.0 | −1.19768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5632.00i | 0.358725i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9016.00i | 0.571529i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 19968.0i | 1.24788i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 13620.0i | − 0.847165i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 8232.00i | 0.504881i | 0.967612 | + | 0.252440i | \(0.0812332\pi\) | ||||
−0.967612 | + | 0.252440i | \(0.918767\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28416.0i | 1.73470i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 65536.0i | 3.94556i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 22052.0i | − 1.32153i | −0.750591 | − | 0.660767i | \(-0.770231\pi\) | ||||
0.750591 | − | 0.660767i | \(-0.229769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27936.0 | −1.66649 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5106.00 | 0.303202 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 12024.0i | − 0.710757i | −0.934723 | − | 0.355378i | \(-0.884352\pi\) | ||||
0.934723 | − | 0.355378i | \(-0.115648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19100.0i | − 1.12391i | −0.827168 | − | 0.561955i | \(-0.810050\pi\) | ||||
0.827168 | − | 0.561955i | \(-0.189950\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15680.0 | −0.918493 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33792.0 | 1.97052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5504.00i | 0.319514i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22528.0i | 1.30192i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 1520.00i | 0.0866738i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19684.0i | 1.11746i | 0.829351 | + | 0.558728i | \(0.188710\pi\) | ||||
−0.829351 | + | 0.558728i | \(0.811290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7616.00 | −0.430450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30784.0 | −1.73223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 19864.0i | − 1.11285i | −0.830899 | − | 0.556424i | \(-0.812173\pi\) | ||||
0.830899 | − | 0.556424i | \(-0.187827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20808.0i | 1.16063i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5216.00 | 0.289669 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1520.00 | −0.0840456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 3256.00i | − 0.179253i | −0.995975 | − | 0.0896267i | \(-0.971433\pi\) | ||||
0.995975 | − | 0.0896267i | \(-0.0285674\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9472.00i | 0.519209i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36384.0 | −1.98579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9996.00 | 0.543222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 24400.0i | − 1.32030i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2876.00i | 0.154957i | 0.996994 | + | 0.0774786i | \(0.0246870\pi\) | ||||
−0.996994 | + | 0.0774786i | \(0.975313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8096.00 | −0.434348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30720.0 | −1.64111 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46976.0i | 2.49889i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7300.00i | 0.386682i | 0.981132 | + | 0.193341i | \(0.0619323\pi\) | ||||
−0.981132 | + | 0.193341i | \(0.938068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2368.00 | 0.124904 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8192.00 | −0.430284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1920.00i | − 0.100425i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 50688.0i | − 2.64014i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2880.00 | −0.149382 | −0.0746912 | − | 0.997207i | \(-0.523797\pi\) | ||||
−0.0746912 | + | 0.997207i | \(0.523797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31744.0 | −1.63968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 36880.0i | − 1.89707i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3268.00i | − 0.167408i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | − 29008.0i | − 1.46771i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21076.0i | − 1.06202i | −0.847366 | − | 0.531009i | \(-0.821813\pi\) | ||||
0.847366 | − | 0.531009i | \(-0.178187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 65376.0 | 3.28086 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4416.00 | −0.220713 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19336.0i | 0.962498i | 0.876584 | + | 0.481249i | \(0.159817\pi\) | ||||
−0.876584 | + | 0.481249i | \(0.840183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 14080.0i | − 0.698032i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 14504.0i | − 0.710406i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 18688.0i | − 0.911675i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19520.0 | 0.948462 | 0.474231 | − | 0.880400i | \(-0.342726\pi\) | ||||
0.474231 | + | 0.880400i | \(0.342726\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6336.00 | 0.306636 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5760.00i | 0.277653i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20004.0i | 0.960446i | 0.877146 | + | 0.480223i | \(0.159444\pi\) | ||||
−0.877146 | + | 0.480223i | \(0.840556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2048.00 | −0.0979416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31478.0 | −1.49944 | −0.749722 | − | 0.661753i | \(-0.769813\pi\) | ||||
−0.749722 | + | 0.661753i | \(0.769813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23680.0i | 1.12356i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 43512.0i | − 2.05644i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 42992.0i | − 2.00820i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9604.00i | 0.446872i | 0.974719 | + | 0.223436i | \(0.0717273\pi\) | ||||
−0.974719 | + | 0.223436i | \(0.928273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4864.00 | 0.225445 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23552.0 | −1.08742 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8976.00i | 0.412835i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3328.00i | − 0.152478i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13760.0 | 0.628023 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27600.0 | 1.25489 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3144.00i | 0.142403i | 0.997462 | + | 0.0712017i | \(0.0226834\pi\) | ||||
−0.997462 | + | 0.0712017i | \(0.977317\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 27904.0i | − 1.25907i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9664.00 | 0.434402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12720.0 | 0.569610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 7296.00i | − 0.325487i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 22084.0i | − 0.981500i | −0.871300 | − | 0.490750i | \(-0.836723\pi\) | ||||
0.871300 | − | 0.490750i | \(-0.163277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31360.0 | 1.38853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21534.0 | −0.949896 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1104.00i | − 0.0485172i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12288.0i | 0.538006i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38112.0 | −1.66246 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14950.0 | −0.649708 | −0.324854 | − | 0.945764i | \(-0.605315\pi\) | ||||
−0.324854 | + | 0.945764i | \(0.605315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23432.0i | 1.01456i | 0.861781 | + | 0.507280i | \(0.169349\pi\) | ||||
−0.861781 | + | 0.507280i | \(0.830651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10752.0i | 0.463824i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19104.0 | −0.821085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26048.0 | 1.11543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 23680.0i | − 1.01031i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1044.00i | 0.0443798i | 0.999754 | + | 0.0221899i | \(0.00706385\pi\) | ||||
−0.999754 | + | 0.0221899i | \(0.992936\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 12488.0i | 0.525091i | 0.964920 | + | 0.262546i | \(0.0845620\pi\) | ||||
−0.964920 | + | 0.262546i | \(0.915438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30172.0i | 1.26407i | 0.774938 | + | 0.632037i | \(0.217781\pi\) | ||||
−0.774938 | + | 0.632037i | \(0.782219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68768.0 | −2.87068 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −66738.0 | −2.77591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26496.0i | 1.09812i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20480.0i | 0.845750i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − 22992.0i | − 0.939367i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 21564.0i | − 0.877898i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40544.0 | −1.64476 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23104.0 | −0.933954 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2944.00i | − 0.118589i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 26156.0i | − 1.04990i | −0.851133 | − | 0.524950i | \(-0.824084\pi\) | ||||
0.851133 | − | 0.524950i | \(-0.175916\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39072.0 | 1.56285 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18646.0 | −0.743215 | −0.371607 | − | 0.928390i | \(-0.621193\pi\) | ||||
−0.371607 | + | 0.928390i | \(0.621193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5800.00i | 0.230377i | 0.993344 | + | 0.115188i | \(0.0367471\pi\) | ||||
−0.993344 | + | 0.115188i | \(0.963253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26112.0i | 1.03356i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25088.0 | −0.989578 | −0.494789 | − | 0.869013i | \(-0.664755\pi\) | ||||
−0.494789 | + | 0.869013i | \(0.664755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47376.0 | 1.86223 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37528.0i | 1.47003i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 512.000i | − 0.0199867i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11040.0 | 0.429479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8806.00 | −0.341395 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40704.0i | 1.57262i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3004.00i | 0.115665i | 0.998326 | + | 0.0578323i | \(0.0184189\pi\) | ||||
−0.998326 | + | 0.0578323i | \(0.981581\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 27880.0i | 1.06256i | 0.847198 | + | 0.531278i | \(0.178288\pi\) | ||||
−0.847198 | + | 0.531278i | \(0.821712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 39168.0i | − 1.48770i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | − 2872.00i | − 0.107986i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28160.0i | 1.05525i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25248.0 | −0.942958 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5120.00 | 0.190582 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 44032.0i | − 1.63354i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7448.00i | 0.275393i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 75776.0 | 2.79254 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16944.0 | 0.622362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 29080.0i | − 1.06459i | −0.846558 | − | 0.532296i | \(-0.821329\pi\) | ||||
0.846558 | − | 0.532296i | \(-0.178671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 54316.0i | 1.98190i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26688.0 | 0.970596 | 0.485298 | − | 0.874349i | \(-0.338711\pi\) | ||||
0.485298 | + | 0.874349i | \(0.338711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3136.00 | −0.113676 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 61056.0i | 2.20596i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 74496.0i | 2.68274i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 8320.00i | 0.296702i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1748.00i | 0.0621339i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 59928.0i | − 2.10962i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 50944.0i | − 1.78760i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9408.00 | −0.329064 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13610.0 | −0.474514 | −0.237257 | − | 0.971447i | \(-0.576248\pi\) | ||||
−0.237257 | + | 0.971447i | \(0.576248\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 70064.0i | − 2.43499i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 30692.0i | − 1.06326i | −0.846976 | − | 0.531632i | \(-0.821579\pi\) | ||||
0.846976 | − | 0.531632i | \(-0.178421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3264.00 | −0.112715 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30720.0 | 1.05748 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4824.00i | − 0.165532i | −0.996569 | − | 0.0827661i | \(-0.973625\pi\) | ||||
0.996569 | − | 0.0827661i | \(-0.0263754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2760.00i | 0.0944082i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5728.00 | −0.195313 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22986.0 | 0.781311 | 0.390656 | − | 0.920537i | \(-0.372248\pi\) | ||||
0.390656 | + | 0.920537i | \(0.372248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 44544.0i | − 1.50933i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 11008.0i | − 0.371827i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 55488.0 | 1.86841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35745.0 | 1.19986 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 21608.0i | − 0.723061i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 19368.0i | − 0.646091i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 2920.00i | 0.0965059i | 0.998835 | + | 0.0482530i | \(0.0153654\pi\) | ||||
−0.998835 | + | 0.0482530i | \(0.984635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 97024.0i | 3.19676i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 4656.00i | 0.151998i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27380.0i | 0.891107i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 81920.0i | 2.64189i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9472.00i | 0.304542i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29824.0 | 0.955995 | 0.477997 | − | 0.878361i | \(-0.341363\pi\) | ||||
0.477997 | + | 0.878361i | \(0.341363\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35264.0 | 1.12696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 48768.0i | − 1.55382i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 11612.0i | − 0.368862i | −0.982845 | − | 0.184431i | \(-0.940956\pi\) | ||||
0.982845 | − | 0.184431i | \(-0.0590443\pi\) | |||||||
\(998\) | 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 | 128.4.b.a.65.2 | yes | 2 | |
3.2 | odd | 2 | 1152.4.d.a.577.2 | 2 | |||
4.3 | odd | 2 | 128.4.b.d.65.1 | yes | 2 | ||
8.3 | odd | 2 | 128.4.b.d.65.2 | yes | 2 | ||
8.5 | even | 2 | inner | 128.4.b.a.65.1 | ✓ | 2 | |
12.11 | even | 2 | 1152.4.d.h.577.2 | 2 | |||
16.3 | odd | 4 | 256.4.a.f.1.1 | 1 | |||
16.5 | even | 4 | 256.4.a.g.1.1 | 1 | |||
16.11 | odd | 4 | 256.4.a.c.1.1 | 1 | |||
16.13 | even | 4 | 256.4.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 1152.4.d.a.577.1 | 2 | |||
24.11 | even | 2 | 1152.4.d.h.577.1 | 2 | |||
48.5 | odd | 4 | 2304.4.a.d.1.1 | 1 | |||
48.11 | even | 4 | 2304.4.a.c.1.1 | 1 | |||
48.29 | odd | 4 | 2304.4.a.n.1.1 | 1 | |||
48.35 | even | 4 | 2304.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.b.a.65.1 | ✓ | 2 | 8.5 | even | 2 | inner | |
128.4.b.a.65.2 | yes | 2 | 1.1 | even | 1 | trivial | |
128.4.b.d.65.1 | yes | 2 | 4.3 | odd | 2 | ||
128.4.b.d.65.2 | yes | 2 | 8.3 | odd | 2 | ||
256.4.a.b.1.1 | 1 | 16.13 | even | 4 | |||
256.4.a.c.1.1 | 1 | 16.11 | odd | 4 | |||
256.4.a.f.1.1 | 1 | 16.3 | odd | 4 | |||
256.4.a.g.1.1 | 1 | 16.5 | even | 4 | |||
1152.4.d.a.577.1 | 2 | 24.5 | odd | 2 | |||
1152.4.d.a.577.2 | 2 | 3.2 | odd | 2 | |||
1152.4.d.h.577.1 | 2 | 24.11 | even | 2 | |||
1152.4.d.h.577.2 | 2 | 12.11 | even | 2 | |||
2304.4.a.c.1.1 | 1 | 48.11 | even | 4 | |||
2304.4.a.d.1.1 | 1 | 48.5 | odd | 4 | |||
2304.4.a.m.1.1 | 1 | 48.35 | even | 4 | |||
2304.4.a.n.1.1 | 1 | 48.29 | odd | 4 |