Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1343,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1343");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.n (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1407.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1407 |
Dual form | 1600.2.n.u.1343.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | 0.472879 | − | 0.881127i | \(-0.343215\pi\) |
−0.881127 | + | 0.472879i | \(0.843215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | − | 2.82843i | 1.06904 | − | 1.06904i | 0.0716124 | − | 0.997433i | \(-0.477186\pi\) |
0.997433 | − | 0.0716124i | \(-0.0228145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.00000i | − | 0.666667i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | − | 2.44949i | 0.679366 | − | 0.679366i | −0.280491 | − | 0.959857i | \(-0.590497\pi\) |
0.959857 | + | 0.280491i | \(0.0904971\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.67423 | + | 3.67423i | 0.891133 | + | 0.891133i | 0.994630 | − | 0.103497i | \(-0.0330032\pi\) |
−0.103497 | + | 0.994630i | \(0.533003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205 | 0.397360 | 0.198680 | − | 0.980064i | \(-0.436335\pi\) | ||||
0.198680 | + | 0.980064i | \(0.436335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | −0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | + | 4.24264i | 0.884652 | + | 0.884652i | 0.994003 | − | 0.109351i | \(-0.0348774\pi\) |
−0.109351 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.53553 | + | 3.53553i | −0.680414 | + | 0.680414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.67423 | − | 3.67423i | 0.639602 | − | 0.639602i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.46410 | −0.554700 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843 | + | 2.82843i | 0.431331 | + | 0.431331i | 0.889081 | − | 0.457750i | \(-0.151344\pi\) |
−0.457750 | + | 0.889081i | \(0.651344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.24264 | + | 4.24264i | −0.618853 | + | 0.618853i | −0.945237 | − | 0.326384i | \(-0.894170\pi\) |
0.326384 | + | 0.945237i | \(0.394170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 9.00000i | − | 1.28571i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 5.19615i | − | 0.727607i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.34847 | − | 7.34847i | 1.00939 | − | 1.00939i | 0.00943438 | − | 0.999955i | \(-0.496997\pi\) |
0.999955 | − | 0.00943438i | \(-0.00300310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.22474 | − | 1.22474i | −0.162221 | − | 0.162221i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3923 | −1.35296 | −0.676481 | − | 0.736460i | \(-0.736496\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.65685 | − | 5.65685i | −0.712697 | − | 0.712697i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.94975 | − | 4.94975i | 0.604708 | − | 0.604708i | −0.336850 | − | 0.941558i | \(-0.609362\pi\) |
0.941558 | + | 0.336850i | \(0.109362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0227 | − | 11.0227i | 1.29011 | − | 1.29011i | 0.355393 | − | 0.934717i | \(-0.384347\pi\) |
0.934717 | − | 0.355393i | \(-0.115653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.6969 | + | 14.6969i | 1.67487 | + | 1.67487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.12132 | − | 2.12132i | −0.232845 | − | 0.232845i | 0.581034 | − | 0.813879i | \(-0.302648\pi\) |
−0.813879 | + | 0.581034i | \(0.802648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.24264 | + | 4.24264i | −0.454859 | + | 0.454859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.00000i | − | 0.317999i | −0.987279 | − | 0.159000i | \(-0.949173\pi\) | ||
0.987279 | − | 0.159000i | \(-0.0508269\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.8564i | − | 1.45255i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.44949 | + | 2.44949i | −0.254000 | + | 0.254000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.89898 | + | 4.89898i | 0.497416 | + | 0.497416i | 0.910633 | − | 0.413217i | \(-0.135595\pi\) |
−0.413217 | + | 0.910633i | \(0.635595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3923 | 1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.89949 | − | 9.89949i | −0.975426 | − | 0.975426i | 0.0242790 | − | 0.999705i | \(-0.492271\pi\) |
−0.999705 | + | 0.0242790i | \(0.992271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6066 | − | 10.6066i | 1.02538 | − | 1.02538i | 0.0257094 | − | 0.999669i | \(-0.491816\pi\) |
0.999669 | − | 0.0257094i | \(-0.00818447\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.00000i | − | 0.766261i | −0.923694 | − | 0.383131i | \(-0.874846\pi\) | ||
0.923694 | − | 0.383131i | \(-0.125154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.67423 | + | 3.67423i | −0.345643 | + | 0.345643i | −0.858484 | − | 0.512841i | \(-0.828593\pi\) |
0.512841 | + | 0.858484i | \(0.328593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.89898 | − | 4.89898i | −0.452911 | − | 0.452911i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.7846 | 1.90532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.12132 | + | 2.12132i | 0.191273 | + | 0.191273i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41421 | − | 1.41421i | 0.125491 | − | 0.125491i | −0.641572 | − | 0.767063i | \(-0.721717\pi\) |
0.767063 | + | 0.641572i | \(0.221717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.00000i | − | 0.352180i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3923i | 0.907980i | 0.891007 | + | 0.453990i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.89898 | − | 4.89898i | 0.424795 | − | 0.424795i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.67423 | − | 3.67423i | −0.313911 | − | 0.313911i | 0.532512 | − | 0.846423i | \(-0.321248\pi\) |
−0.846423 | + | 0.532512i | \(0.821248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.5885 | 1.32220 | 0.661098 | − | 0.750300i | \(-0.270091\pi\) | ||||
0.661098 | + | 0.750300i | \(0.270091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7279 | + | 12.7279i | 1.06436 | + | 1.06436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.36396 | + | 6.36396i | −0.524891 | + | 0.524891i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.92820i | − | 0.563809i | −0.959442 | − | 0.281905i | \(-0.909034\pi\) | ||
0.959442 | − | 0.281905i | \(-0.0909662\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.34847 | − | 7.34847i | 0.594089 | − | 0.594089i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.44949 | − | 2.44949i | −0.195491 | − | 0.195491i | 0.602573 | − | 0.798064i | \(-0.294142\pi\) |
−0.798064 | + | 0.602573i | \(0.794142\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.3923 | −0.824163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.707107 | − | 0.707107i | −0.0553849 | − | 0.0553849i | 0.678872 | − | 0.734257i | \(-0.262469\pi\) |
−0.734257 | + | 0.678872i | \(0.762469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24264 | − | 4.24264i | 0.328305 | − | 0.328305i | −0.523636 | − | 0.851942i | \(-0.675425\pi\) |
0.851942 | + | 0.523636i | \(0.175425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.46410i | − | 0.264906i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.34847 | + | 7.34847i | 0.552345 | + | 0.552345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.5885 | −1.16514 | −0.582568 | − | 0.812782i | \(-0.697952\pi\) | ||||
−0.582568 | + | 0.812782i | \(0.697952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0000 | −1.93256 | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.82843 | − | 2.82843i | −0.209083 | − | 0.209083i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.0919 | + | 19.0919i | −1.39614 | + | 1.39614i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.0000i | 1.45479i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.57321 | + | 8.57321i | −0.617113 | + | 0.617113i | −0.944790 | − | 0.327677i | \(-0.893734\pi\) |
0.327677 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.34847 | − | 7.34847i | −0.523557 | − | 0.523557i | 0.395087 | − | 0.918644i | \(-0.370714\pi\) |
−0.918644 | + | 0.395087i | \(0.870714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8564 | −0.982255 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.00000 | −0.493742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.9706 | − | 16.9706i | −1.19110 | − | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.48528 | − | 8.48528i | 0.589768 | − | 0.589768i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.00000i | 0.622543i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0526i | 1.31163i | 0.754921 | + | 0.655816i | \(0.227675\pi\) | ||||
−0.754921 | + | 0.655816i | \(0.772325\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.34847 | − | 7.34847i | 0.503509 | − | 0.503509i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.79796 | − | 9.79796i | −0.665129 | − | 0.665129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.5885 | −1.05337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.0000 | 1.21081 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82843 | + | 2.82843i | 0.189405 | + | 0.189405i | 0.795439 | − | 0.606034i | \(-0.207240\pi\) |
−0.606034 | + | 0.795439i | \(0.707240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 20.7846i | − | 1.36753i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6969 | + | 14.6969i | −0.962828 | + | 0.962828i | −0.999333 | − | 0.0365050i | \(-0.988378\pi\) |
0.0365050 | + | 0.999333i | \(0.488378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.3923 | −0.672222 | −0.336111 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336111 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | 0.837404 | 0.418702 | − | 0.908124i | \(-0.362485\pi\) | ||||
0.418702 | + | 0.908124i | \(0.362485\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3137 | + | 11.3137i | 0.725775 | + | 0.725775i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.24264 | − | 4.24264i | 0.269953 | − | 0.269953i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000i | 0.190117i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615i | 0.327978i | 0.986462 | + | 0.163989i | \(0.0524362\pi\) | ||||
−0.986462 | + | 0.163989i | \(0.947564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.0454 | + | 22.0454i | −1.38598 | + | 1.38598i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6969 | + | 14.6969i | 0.916770 | + | 0.916770i | 0.996793 | − | 0.0800232i | \(-0.0254994\pi\) |
−0.0800232 | + | 0.996793i | \(0.525499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.0000 | −0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7279 | + | 12.7279i | 0.784837 | + | 0.784837i | 0.980643 | − | 0.195805i | \(-0.0627321\pi\) |
−0.195805 | + | 0.980643i | \(0.562732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.12132 | + | 2.12132i | −0.129823 | + | 0.129823i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.0000i | − | 1.46331i | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||
0.681677 | − | 0.731653i | \(-0.261251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.1769i | 1.89386i | 0.321436 | + | 0.946931i | \(0.395835\pi\) | ||||
−0.321436 | + | 0.946931i | \(0.604165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.79796 | + | 9.79796i | −0.592999 | + | 0.592999i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.1464 | − | 17.1464i | −1.03023 | − | 1.03023i | −0.999529 | − | 0.0307004i | \(-0.990226\pi\) |
−0.0307004 | − | 0.999529i | \(-0.509774\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.92820 | −0.414781 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.94975 | + | 4.94975i | 0.294232 | + | 0.294232i | 0.838749 | − | 0.544518i | \(-0.183287\pi\) |
−0.544518 | + | 0.838749i | \(0.683287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48528 | + | 8.48528i | −0.500870 | + | 0.500870i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0000i | 0.588235i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.92820i | − | 0.406138i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6969 | + | 14.6969i | −0.858604 | + | 0.858604i | −0.991174 | − | 0.132569i | \(-0.957677\pi\) |
0.132569 | + | 0.991174i | \(0.457677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.3712 | − | 18.3712i | −1.06600 | − | 1.06600i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.7846 | 1.20201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | 0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0208 | − | 12.0208i | 0.686064 | − | 0.686064i | −0.275295 | − | 0.961360i | \(-0.588776\pi\) |
0.961360 | + | 0.275295i | \(0.0887757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0000i | 0.796432i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.89898 | − | 4.89898i | 0.276907 | − | 0.276907i | −0.554966 | − | 0.831873i | \(-0.687269\pi\) |
0.831873 | + | 0.554966i | \(0.187269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6969 | + | 14.6969i | 0.825462 | + | 0.825462i | 0.986885 | − | 0.161423i | \(-0.0516083\pi\) |
−0.161423 | + | 0.986885i | \(0.551608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.1769 | 1.74557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0000 | −0.837218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.36396 | + | 6.36396i | 0.354100 | + | 0.354100i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.65685 | + | 5.65685i | −0.312825 | + | 0.312825i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000i | 1.32316i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5885i | 0.856819i | 0.903585 | + | 0.428410i | \(0.140926\pi\) | ||||
−0.903585 | + | 0.428410i | \(0.859074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.57321 | − | 8.57321i | −0.467013 | − | 0.467013i | 0.433933 | − | 0.900945i | \(-0.357126\pi\) |
−0.900945 | + | 0.433933i | \(0.857126\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19615 | 0.282216 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0000 | 0.974755 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.65685 | − | 5.65685i | −0.305441 | − | 0.305441i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0919 | − | 19.0919i | 1.02491 | − | 1.02491i | 0.0252242 | − | 0.999682i | \(-0.491970\pi\) |
0.999682 | − | 0.0252242i | \(-0.00802995\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0000i | 1.49881i | 0.662114 | + | 0.749403i | \(0.269659\pi\) | ||||
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.3205i | 0.924500i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6969 | + | 14.6969i | −0.782239 | + | 0.782239i | −0.980208 | − | 0.197969i | \(-0.936565\pi\) |
0.197969 | + | 0.980208i | \(0.436565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.6969 | − | 14.6969i | −0.777844 | − | 0.777844i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7846 | 1.09697 | 0.548485 | − | 0.836160i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3137 | + | 11.3137i | 0.593816 | + | 0.593816i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.82843 | + | 2.82843i | −0.147643 | + | 0.147643i | −0.777064 | − | 0.629421i | \(-0.783292\pi\) |
0.629421 | + | 0.777064i | \(0.283292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 41.5692i | − | 2.15817i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.44949 | − | 2.44949i | 0.126830 | − | 0.126830i | −0.640843 | − | 0.767672i | \(-0.721415\pi\) |
0.767672 | + | 0.640843i | \(0.221415\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.6969 | − | 14.6969i | −0.756931 | − | 0.756931i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.73205 | −0.0889695 | −0.0444847 | − | 0.999010i | \(-0.514165\pi\) | ||||
−0.0444847 | + | 0.999010i | \(0.514165\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | −0.102463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.4558 | − | 25.4558i | −1.30073 | − | 1.30073i | −0.927898 | − | 0.372835i | \(-0.878386\pi\) |
−0.372835 | − | 0.927898i | \(-0.621614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.65685 | − | 5.65685i | 0.287554 | − | 0.287554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.0000i | 1.52106i | 0.649303 | + | 0.760530i | \(0.275061\pi\) | ||||
−0.649303 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.1769i | 1.57668i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.34847 | − | 7.34847i | 0.370681 | − | 0.370681i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.79796 | + | 9.79796i | 0.491745 | + | 0.491745i | 0.908856 | − | 0.417110i | \(-0.136957\pi\) |
−0.417110 | + | 0.908856i | \(0.636957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | −0.346844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0000 | 1.34832 | 0.674158 | − | 0.738587i | \(-0.264507\pi\) | ||||
0.674158 | + | 0.738587i | \(0.264507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.48528 | − | 8.48528i | −0.422682 | − | 0.422682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0000i | 1.23617i | 0.786111 | + | 0.618085i | \(0.212091\pi\) | ||||
−0.786111 | + | 0.618085i | \(0.787909\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.19615i | 0.256307i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29.3939 | + | 29.3939i | −1.44638 | + | 1.44638i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0227 | − | 11.0227i | −0.539784 | − | 0.539784i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5885 | −0.761546 | −0.380773 | − | 0.924669i | \(-0.624342\pi\) | ||||
−0.380773 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.48528 | + | 8.48528i | 0.412568 | + | 0.412568i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3137 | − | 11.3137i | 0.547509 | − | 0.547509i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 18.0000i | − | 0.869048i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.7846i | − | 1.00116i | −0.865690 | − | 0.500580i | \(-0.833120\pi\) | ||
0.865690 | − | 0.500580i | \(-0.166880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.22474 | + | 1.22474i | −0.0588575 | + | 0.0588575i | −0.735923 | − | 0.677065i | \(-0.763251\pi\) |
0.677065 | + | 0.735923i | \(0.263251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.34847 | + | 7.34847i | 0.351525 | + | 0.351525i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1051 | −1.81866 | −0.909329 | − | 0.416078i | \(-0.863404\pi\) | ||||
−0.909329 | + | 0.416078i | \(0.863404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.0000 | −0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.12132 | − | 2.12132i | −0.100787 | − | 0.100787i | 0.654915 | − | 0.755702i | \(-0.272704\pi\) |
−0.755702 | + | 0.654915i | \(0.772704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.24264 | + | 4.24264i | −0.200670 | + | 0.200670i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.0000i | − | 1.27421i | −0.770778 | − | 0.637104i | \(-0.780132\pi\) | ||
0.770778 | − | 0.637104i | \(-0.219868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.5885i | − | 0.734032i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.89898 | + | 4.89898i | −0.230174 | + | 0.230174i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0227 | − | 11.0227i | −0.515620 | − | 0.515620i | 0.400623 | − | 0.916243i | \(-0.368794\pi\) |
−0.916243 | + | 0.400623i | \(0.868794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.9808 | −1.21268 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.82843 | − | 2.82843i | −0.131448 | − | 0.131448i | 0.638322 | − | 0.769770i | \(-0.279629\pi\) |
−0.769770 | + | 0.638322i | \(0.779629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4558 | + | 25.4558i | −1.17796 | + | 1.17796i | −0.197692 | + | 0.980264i | \(0.563345\pi\) |
−0.980264 | + | 0.197692i | \(0.936655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 28.0000i | − | 1.29292i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.46410i | 0.159617i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.6969 | + | 14.6969i | −0.675766 | + | 0.675766i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.6969 | − | 14.6969i | −0.672927 | − | 0.672927i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.9706 | − | 16.9706i | −0.772187 | − | 0.772187i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.3848 | + | 18.3848i | −0.833094 | + | 0.833094i | −0.987939 | − | 0.154845i | \(-0.950512\pi\) |
0.154845 | + | 0.987939i | \(0.450512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.00000i | 0.0452216i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.3923i | − | 0.468998i | −0.972116 | − | 0.234499i | \(-0.924655\pi\) | ||
0.972116 | − | 0.234499i | \(-0.0753450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0454 | − | 22.0454i | 0.992875 | − | 0.992875i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.3939 | + | 29.3939i | 1.31850 | + | 1.31850i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46410 | 0.155074 | 0.0775372 | − | 0.996989i | \(-0.475294\pi\) | ||||
0.0775372 | + | 0.996989i | \(0.475294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9706 | − | 16.9706i | −0.756680 | − | 0.756680i | 0.219037 | − | 0.975717i | \(-0.429709\pi\) |
−0.975717 | + | 0.219037i | \(0.929709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.707107 | − | 0.707107i | 0.0314037 | − | 0.0314037i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.0000i | 1.32973i | 0.746965 | + | 0.664863i | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 62.3538i | − | 2.75837i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.12372 | + | 6.12372i | −0.270369 | + | 0.270369i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.0454 | − | 22.0454i | −0.969556 | − | 0.969556i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0208 | + | 12.0208i | 0.525634 | + | 0.525634i | 0.919267 | − | 0.393634i | \(-0.128782\pi\) |
−0.393634 | + | 0.919267i | \(0.628782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.7279 | − | 12.7279i | 0.554437 | − | 0.554437i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.7846i | 0.901975i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.34847 | + | 7.34847i | −0.318298 | + | 0.318298i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.0227 | + | 11.0227i | 0.475665 | + | 0.475665i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 46.7654 | 2.01433 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.3848 | + | 18.3848i | 0.788966 | + | 0.788966i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.7487 | + | 24.7487i | −1.05818 | + | 1.05818i | −0.0599800 | + | 0.998200i | \(0.519104\pi\) |
−0.998200 | + | 0.0599800i | \(0.980896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 8.00000i | − | 0.341432i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.3923i | − | 0.442727i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.0454 | + | 22.0454i | 0.934094 | + | 0.934094i | 0.997959 | − | 0.0638647i | \(-0.0203426\pi\) |
−0.0638647 | + | 0.997959i | \(0.520343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8564 | 0.586064 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.0000 | 1.13994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.48528 | − | 8.48528i | −0.357612 | − | 0.357612i | 0.505320 | − | 0.862932i | \(-0.331374\pi\) |
−0.862932 | + | 0.505320i | \(0.831374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.82843 | + | 2.82843i | −0.118783 | + | 0.118783i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.00000i | − | 0.377300i | −0.982044 | − | 0.188650i | \(-0.939589\pi\) | ||
0.982044 | − | 0.188650i | \(-0.0604111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.46410i | 0.144968i | 0.997370 | + | 0.0724841i | \(0.0230926\pi\) | ||||
−0.997370 | + | 0.0724841i | \(0.976907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.34847 | + | 7.34847i | −0.306987 | + | 0.306987i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.22474 | − | 1.22474i | −0.0509868 | − | 0.0509868i | 0.681154 | − | 0.732140i | \(-0.261479\pi\) |
−0.732140 | + | 0.681154i | \(0.761479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1244 | 0.503871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.1838 | + | 38.1838i | 1.58141 | + | 1.58141i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.3345 | + | 23.3345i | −0.963119 | + | 0.963119i | −0.999344 | − | 0.0362248i | \(-0.988467\pi\) |
0.0362248 | + | 0.999344i | \(0.488467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.00000i | − | 0.247226i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.3923i | 0.427482i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0227 | − | 11.0227i | 0.452648 | − | 0.452648i | −0.443584 | − | 0.896233i | \(-0.646293\pi\) |
0.896233 | + | 0.443584i | \(0.146293\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.79796 | + | 9.79796i | 0.401004 | + | 0.401004i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.7846 | −0.849236 | −0.424618 | − | 0.905373i | \(-0.639592\pi\) | ||||
−0.424618 | + | 0.905373i | \(0.639592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | 0.530281 | 0.265141 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265141 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.89949 | − | 9.89949i | −0.403139 | − | 0.403139i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2843 | − | 28.2843i | 1.14802 | − | 1.14802i | 0.161082 | − | 0.986941i | \(-0.448502\pi\) |
0.986941 | − | 0.161082i | \(-0.0514984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0000i | 0.972529i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846i | 0.840855i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0454 | − | 22.0454i | 0.890406 | − | 0.890406i | −0.104155 | − | 0.994561i | \(-0.533214\pi\) |
0.994561 | + | 0.104155i | \(0.0332139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.3939 | + | 29.3939i | 1.18335 | + | 1.18335i | 0.978870 | + | 0.204483i | \(0.0655512\pi\) |
0.204483 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.1051 | −1.53157 | −0.765787 | − | 0.643094i | \(-0.777650\pi\) | ||||
−0.765787 | + | 0.643094i | \(0.777650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.0000 | −1.20386 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.48528 | − | 8.48528i | −0.339956 | − | 0.339956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.36396 | − | 6.36396i | 0.254152 | − | 0.254152i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.3205i | − | 0.689519i | −0.938691 | − | 0.344759i | \(-0.887961\pi\) | ||
0.938691 | − | 0.344759i | \(-0.112039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.4722 | − | 13.4722i | 0.535472 | − | 0.535472i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0454 | − | 22.0454i | −0.873471 | − | 0.873471i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.7846 | 0.822226 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00000 | 0.236986 | 0.118493 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118493 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.82843 | − | 2.82843i | −0.111542 | − | 0.111542i | 0.649133 | − | 0.760675i | \(-0.275132\pi\) |
−0.760675 | + | 0.649133i | \(0.775132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9706 | − | 16.9706i | 0.667182 | − | 0.667182i | −0.289881 | − | 0.957063i | \(-0.593616\pi\) |
0.957063 | + | 0.289881i | \(0.0936157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 54.0000i | − | 2.11969i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.8564i | 0.543075i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3939 | − | 29.3939i | 1.15027 | − | 1.15027i | 0.163773 | − | 0.986498i | \(-0.447633\pi\) |
0.986498 | − | 0.163773i | \(-0.0523666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0454 | − | 22.0454i | −0.860073 | − | 0.860073i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.9808 | 1.01207 | 0.506033 | − | 0.862514i | \(-0.331111\pi\) | ||||
0.506033 | + | 0.862514i | \(0.331111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | −0.855701 | −0.427850 | − | 0.903850i | \(-0.640729\pi\) | ||||
−0.427850 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.7279 | − | 12.7279i | −0.494312 | − | 0.494312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.4558 | − | 25.4558i | 0.985654 | − | 0.985654i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 4.00000i | − | 0.154649i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7846i | 0.802381i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7128 | 1.06352 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.36396 | + | 6.36396i | 0.243510 | + | 0.243510i | 0.818301 | − | 0.574790i | \(-0.194916\pi\) |
−0.574790 | + | 0.818301i | \(0.694916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1421 | − | 14.1421i | 0.539556 | − | 0.539556i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 36.0000i | − | 1.37149i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5885i | 0.593013i | 0.955031 | + | 0.296506i | \(0.0958216\pi\) | ||||
−0.955031 | + | 0.296506i | \(0.904178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.3939 | − | 29.3939i | 1.11658 | − | 1.11658i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0227 | − | 11.0227i | −0.417515 | − | 0.417515i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.7846 | 0.786146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.00000i | − | 0.150223i | −0.997175 | − | 0.0751116i | \(-0.976069\pi\) | ||
0.997175 | − | 0.0751116i | \(-0.0239313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6969 | − | 14.6969i | 0.550405 | − | 0.550405i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.34847 | + | 7.34847i | 0.274434 | + | 0.274434i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.5692 | −1.55027 | −0.775135 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775135 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.0000 | −2.08555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.19239 | − | 9.19239i | −0.341869 | − | 0.341869i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.89949 | − | 9.89949i | 0.367152 | − | 0.367152i | −0.499286 | − | 0.866437i | \(-0.666404\pi\) |
0.866437 | + | 0.499286i | \(0.166404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 13.0000i | − | 0.481481i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.7846i | 0.768747i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0454 | + | 22.0454i | −0.814266 | + | 0.814266i | −0.985270 | − | 0.171005i | \(-0.945299\pi\) |
0.171005 | + | 0.985270i | \(0.445299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7196 | + | 25.7196i | 0.947395 | + | 0.947395i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.1769 | −1.14686 | −0.573431 | − | 0.819254i | \(-0.694388\pi\) | ||||
−0.573431 | + | 0.819254i | \(0.694388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.6985 | − | 29.6985i | −1.08953 | − | 1.08953i | −0.995576 | − | 0.0939553i | \(-0.970049\pi\) |
−0.0939553 | − | 0.995576i | \(-0.529951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.24264 | + | 4.24264i | −0.155230 | + | 0.155230i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 60.0000i | − | 2.19235i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1769i | 1.13766i | 0.822455 | + | 0.568831i | \(0.192604\pi\) | ||||
−0.822455 | + | 0.568831i | \(0.807396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.67423 | − | 3.67423i | 0.133897 | − | 0.133897i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2929 | + | 34.2929i | 1.24640 | + | 1.24640i | 0.957301 | + | 0.289095i | \(0.0933542\pi\) |
0.289095 | + | 0.957301i | \(0.406646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.1769 | 1.13165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | 0.543750 | 0.271875 | − | 0.962333i | \(-0.412356\pi\) | ||||
0.271875 | + | 0.962333i | \(0.412356\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.6274 | − | 22.6274i | −0.819167 | − | 0.819167i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.4558 | + | 25.4558i | −0.919157 | + | 0.919157i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.00000i | 0.252426i | 0.992003 | + | 0.126213i | \(0.0402824\pi\) | ||||
−0.992003 | + | 0.126213i | \(0.959718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 20.7846i | − | 0.748539i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.0454 | + | 22.0454i | −0.792918 | + | 0.792918i | −0.981968 | − | 0.189049i | \(-0.939459\pi\) |
0.189049 | + | 0.981968i | \(0.439459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.19615 | −0.186171 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.2132 | + | 21.2132i | 0.758098 | + | 0.758098i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.7696 | − | 36.7696i | 1.31069 | − | 1.31069i | 0.389789 | − | 0.920904i | \(-0.372548\pi\) |
0.920904 | − | 0.389789i | \(-0.127452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 18.0000i | − | 0.640817i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7846i | 0.739016i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.79796 | − | 9.79796i | 0.347936 | − | 0.347936i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.34847 | − | 7.34847i | −0.260296 | − | 0.260296i | 0.564878 | − | 0.825174i | \(-0.308923\pi\) |
−0.825174 | + | 0.564878i | \(0.808923\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.1769 | −1.10296 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 57.2756 | + | 57.2756i | 2.02121 | + | 2.02121i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.9706 | + | 16.9706i | −0.597392 | + | 0.597392i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000i | 0.632846i | 0.948618 | + | 0.316423i | \(0.102482\pi\) | ||||
−0.948618 | + | 0.316423i | \(0.897518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 45.0333i | − | 1.58133i | −0.612247 | − | 0.790667i | \(-0.709734\pi\) | ||
0.612247 | − | 0.790667i | \(-0.290266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0454 | − | 22.0454i | 0.773166 | − | 0.773166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.89898 | + | 4.89898i | 0.171394 | + | 0.171394i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.7128 | −0.968364 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.0000 | 1.46581 | 0.732905 | − | 0.680331i | \(-0.238164\pi\) | ||||
0.732905 | + | 0.680331i | \(0.238164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1421 | + | 14.1421i | 0.492964 | + | 0.492964i | 0.909239 | − | 0.416275i | \(-0.136665\pi\) |
−0.416275 | + | 0.909239i | \(0.636665\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.12132 | + | 2.12132i | −0.0737655 | + | 0.0737655i | −0.743027 | − | 0.669261i | \(-0.766611\pi\) |
0.669261 | + | 0.743027i | \(0.266611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.00000i | 0.0694629i | 0.999397 | + | 0.0347314i | \(0.0110576\pi\) | ||||
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.2487i | 0.841178i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.0681 | − | 33.0681i | 1.14574 | − | 1.14574i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2474 | + | 12.2474i | 0.423334 | + | 0.423334i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.5692 | −1.43513 | −0.717564 | − | 0.696492i | \(-0.754743\pi\) | ||||
−0.717564 | + | 0.696492i | \(0.754743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.24264 | − | 4.24264i | −0.146124 | − | 0.146124i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.2548 | + | 45.2548i | −1.55497 | + | 1.55497i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 7.00000i | − | 0.240239i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.9444 | − | 26.9444i | 0.922558 | − | 0.922558i | −0.0746514 | − | 0.997210i | \(-0.523784\pi\) |
0.997210 | + | 0.0746514i | \(0.0237844\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.3712 | + | 18.3712i | 0.627547 | + | 0.627547i | 0.947450 | − | 0.319903i | \(-0.103650\pi\) |
−0.319903 | + | 0.947450i | \(0.603650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5885 | 0.531871 | 0.265936 | − | 0.963991i | \(-0.414319\pi\) | ||||
0.265936 | + | 0.963991i | \(0.414319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | 0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.24264 | + | 4.24264i | 0.144421 | + | 0.144421i | 0.775621 | − | 0.631199i | \(-0.217437\pi\) |
−0.631199 | + | 0.775621i | \(0.717437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.07107 | − | 7.07107i | 0.240146 | − | 0.240146i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.2487i | − | 0.821636i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.79796 | − | 9.79796i | 0.331611 | − | 0.331611i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.4949 | + | 24.4949i | 0.827134 | + | 0.827134i | 0.987119 | − | 0.159985i | \(-0.0511447\pi\) |
−0.159985 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7846 | 0.701047 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.8909 | + | 38.8909i | 1.30878 | + | 1.30878i | 0.922295 | + | 0.386487i | \(0.126312\pi\) |
0.386487 | + | 0.922295i | \(0.373688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.00000i | − | 0.268311i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.19615i | − | 0.174078i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.34847 | + | 7.34847i | −0.245907 | + | 0.245907i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.6969 | − | 14.6969i | −0.490716 | − | 0.490716i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.7846 | −0.693206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.0000 | 1.79900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.3137 | − | 11.3137i | −0.376497 | − | 0.376497i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1127 | + | 31.1127i | −1.03308 | + | 1.03308i | −0.0336464 | + | 0.999434i | \(0.510712\pi\) |
−0.999434 | + | 0.0336464i | \(0.989288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7846i | 0.688625i | 0.938855 | + | 0.344312i | \(0.111888\pi\) | ||||
−0.938855 | + | 0.344312i | \(0.888112\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.0227 | − | 11.0227i | 0.364798 | − | 0.364798i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.3939 | + | 29.3939i | 0.970671 | + | 0.970671i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.0333 | 1.48551 | 0.742756 | − | 0.669562i | \(-0.233518\pi\) | ||||
0.742756 | + | 0.669562i | \(0.233518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.0000 | −0.560169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.4558 | + | 25.4558i | 0.837889 | + | 0.837889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.7990 | + | 19.7990i | −0.650284 | + | 0.650284i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 54.0000i | − | 1.77168i | −0.463988 | − | 0.885841i | \(-0.653582\pi\) | ||
0.463988 | − | 0.885841i | \(-0.346418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 15.5885i | − | 0.510891i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.22474 | + | 1.22474i | 0.0400107 | + | 0.0400107i | 0.726829 | − | 0.686818i | \(-0.240993\pi\) |
−0.686818 | + | 0.726829i | \(0.740993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.92820 | −0.226093 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7279 | − | 12.7279i | −0.414478 | − | 0.414478i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.48528 | − | 8.48528i | 0.275735 | − | 0.275735i | −0.555669 | − | 0.831404i | \(-0.687538\pi\) |
0.831404 | + | 0.555669i | \(0.187538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 54.0000i | − | 1.75291i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.7846i | − | 0.673987i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.67423 | + | 3.67423i | −0.119020 | + | 0.119020i | −0.764108 | − | 0.645088i | \(-0.776821\pi\) |
0.645088 | + | 0.764108i | \(0.276821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.0454 | − | 22.0454i | −0.712627 | − | 0.712627i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.7846 | −0.671170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.2132 | − | 21.2132i | −0.683586 | − | 0.683586i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.82843 | + | 2.82843i | −0.0909561 | + | 0.0909561i | −0.751121 | − | 0.660165i | \(-0.770486\pi\) |
0.660165 | + | 0.751121i | \(0.270486\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 9.00000i | − | 0.289122i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 46.7654i | − | 1.50077i | −0.661000 | − | 0.750386i | \(-0.729868\pi\) | ||
0.661000 | − | 0.750386i | \(-0.270132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.0908 | − | 44.0908i | 1.41349 | − | 1.41349i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0227 | − | 11.0227i | −0.352648 | − | 0.352648i | 0.508446 | − | 0.861094i | \(-0.330220\pi\) |
−0.861094 | + | 0.508446i | \(0.830220\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5885 | 0.498209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9706 | + | 16.9706i | 0.541277 | + | 0.541277i | 0.923903 | − | 0.382626i | \(-0.124980\pi\) |
−0.382626 | + | 0.923903i | \(0.624980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.9706 | − | 16.9706i | 0.540179 | − | 0.540179i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000i | 0.763156i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8564i | 0.440163i | 0.975481 | + | 0.220082i | \(0.0706324\pi\) | ||||
−0.975481 | + | 0.220082i | \(0.929368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.0227 | − | 11.0227i | 0.349795 | − | 0.349795i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1600.2.n.u.1407.2 | 8 | ||
4.3 | odd | 2 | inner | 1600.2.n.u.1407.3 | 8 | ||
5.2 | odd | 4 | inner | 1600.2.n.u.1343.2 | 8 | ||
5.3 | odd | 4 | inner | 1600.2.n.u.1343.4 | 8 | ||
5.4 | even | 2 | inner | 1600.2.n.u.1407.4 | 8 | ||
8.3 | odd | 2 | 400.2.n.d.207.2 | yes | 8 | ||
8.5 | even | 2 | 400.2.n.d.207.3 | yes | 8 | ||
20.3 | even | 4 | inner | 1600.2.n.u.1343.1 | 8 | ||
20.7 | even | 4 | inner | 1600.2.n.u.1343.3 | 8 | ||
20.19 | odd | 2 | inner | 1600.2.n.u.1407.1 | 8 | ||
24.5 | odd | 2 | 3600.2.x.m.3007.4 | 8 | |||
24.11 | even | 2 | 3600.2.x.m.3007.1 | 8 | |||
40.3 | even | 4 | 400.2.n.d.143.4 | yes | 8 | ||
40.13 | odd | 4 | 400.2.n.d.143.1 | ✓ | 8 | ||
40.19 | odd | 2 | 400.2.n.d.207.4 | yes | 8 | ||
40.27 | even | 4 | 400.2.n.d.143.2 | yes | 8 | ||
40.29 | even | 2 | 400.2.n.d.207.1 | yes | 8 | ||
40.37 | odd | 4 | 400.2.n.d.143.3 | yes | 8 | ||
120.29 | odd | 2 | 3600.2.x.m.3007.2 | 8 | |||
120.53 | even | 4 | 3600.2.x.m.2143.2 | 8 | |||
120.59 | even | 2 | 3600.2.x.m.3007.3 | 8 | |||
120.77 | even | 4 | 3600.2.x.m.2143.4 | 8 | |||
120.83 | odd | 4 | 3600.2.x.m.2143.3 | 8 | |||
120.107 | odd | 4 | 3600.2.x.m.2143.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.n.d.143.1 | ✓ | 8 | 40.13 | odd | 4 | ||
400.2.n.d.143.2 | yes | 8 | 40.27 | even | 4 | ||
400.2.n.d.143.3 | yes | 8 | 40.37 | odd | 4 | ||
400.2.n.d.143.4 | yes | 8 | 40.3 | even | 4 | ||
400.2.n.d.207.1 | yes | 8 | 40.29 | even | 2 | ||
400.2.n.d.207.2 | yes | 8 | 8.3 | odd | 2 | ||
400.2.n.d.207.3 | yes | 8 | 8.5 | even | 2 | ||
400.2.n.d.207.4 | yes | 8 | 40.19 | odd | 2 | ||
1600.2.n.u.1343.1 | 8 | 20.3 | even | 4 | inner | ||
1600.2.n.u.1343.2 | 8 | 5.2 | odd | 4 | inner | ||
1600.2.n.u.1343.3 | 8 | 20.7 | even | 4 | inner | ||
1600.2.n.u.1343.4 | 8 | 5.3 | odd | 4 | inner | ||
1600.2.n.u.1407.1 | 8 | 20.19 | odd | 2 | inner | ||
1600.2.n.u.1407.2 | 8 | 1.1 | even | 1 | trivial | ||
1600.2.n.u.1407.3 | 8 | 4.3 | odd | 2 | inner | ||
1600.2.n.u.1407.4 | 8 | 5.4 | even | 2 | inner | ||
3600.2.x.m.2143.1 | 8 | 120.107 | odd | 4 | |||
3600.2.x.m.2143.2 | 8 | 120.53 | even | 4 | |||
3600.2.x.m.2143.3 | 8 | 120.83 | odd | 4 | |||
3600.2.x.m.2143.4 | 8 | 120.77 | even | 4 | |||
3600.2.x.m.3007.1 | 8 | 24.11 | even | 2 | |||
3600.2.x.m.3007.2 | 8 | 120.29 | odd | 2 | |||
3600.2.x.m.3007.3 | 8 | 120.59 | even | 2 | |||
3600.2.x.m.3007.4 | 8 | 24.5 | odd | 2 |