Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3599.2 | ||
Character | \(\chi\) | \(=\) | 4032.3599 |
Dual form | 4032.2.v.e.1583.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.62814 | + | 2.62814i | −1.17534 | + | 1.17534i | −0.194421 | + | 0.980918i | \(0.562283\pi\) |
−0.980918 | + | 0.194421i | \(0.937717\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.583140 | + | 0.583140i | 0.175823 | + | 0.175823i | 0.789532 | − | 0.613709i | \(-0.210323\pi\) |
−0.613709 | + | 0.789532i | \(0.710323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76590 | − | 1.76590i | 0.489774 | − | 0.489774i | −0.418461 | − | 0.908235i | \(-0.637430\pi\) |
0.908235 | + | 0.418461i | \(0.137430\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.63734i | 0.882186i | 0.897462 | + | 0.441093i | \(0.145409\pi\) | ||||
−0.897462 | + | 0.441093i | \(0.854591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.963353 | − | 0.963353i | −0.221008 | − | 0.221008i | 0.587915 | − | 0.808923i | \(-0.299949\pi\) |
−0.808923 | + | 0.587915i | \(0.799949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.77401i | − | 0.786935i | −0.919338 | − | 0.393468i | \(-0.871275\pi\) | ||
0.919338 | − | 0.393468i | \(-0.128725\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 8.81423i | − | 1.76285i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.76058 | − | 4.76058i | −0.884018 | − | 0.884018i | 0.109922 | − | 0.993940i | \(-0.464940\pi\) |
−0.993940 | + | 0.109922i | \(0.964940\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.89207i | − | 0.878641i | −0.898330 | − | 0.439320i | \(-0.855219\pi\) | ||
0.898330 | − | 0.439320i | \(-0.144781\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.62814 | − | 2.62814i | 0.444237 | − | 0.444237i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.66911 | − | 4.66911i | −0.767598 | − | 0.767598i | 0.210085 | − | 0.977683i | \(-0.432626\pi\) |
−0.977683 | + | 0.210085i | \(0.932626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.83668 | −0.599188 | −0.299594 | − | 0.954067i | \(-0.596851\pi\) | ||||
−0.299594 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.45278 | − | 3.45278i | 0.526544 | − | 0.526544i | −0.392996 | − | 0.919540i | \(-0.628561\pi\) |
0.919540 | + | 0.392996i | \(0.128561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6693 | 1.70214 | 0.851070 | − | 0.525052i | \(-0.175954\pi\) | ||||
0.851070 | + | 0.525052i | \(0.175954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.48624 | + | 5.48624i | −0.753593 | + | 0.753593i | −0.975148 | − | 0.221555i | \(-0.928887\pi\) |
0.221555 | + | 0.975148i | \(0.428887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.06515 | −0.413304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.40688 | + | 4.40688i | 0.573727 | + | 0.573727i | 0.933168 | − | 0.359441i | \(-0.117033\pi\) |
−0.359441 | + | 0.933168i | \(0.617033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.99959 | + | 7.99959i | −1.02424 | + | 1.02424i | −0.0245439 | + | 0.999699i | \(0.507813\pi\) |
−0.999699 | + | 0.0245439i | \(0.992187\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.28208i | 1.15130i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3524 | + | 11.3524i | 1.38692 | + | 1.38692i | 0.831708 | + | 0.555213i | \(0.187363\pi\) |
0.555213 | + | 0.831708i | \(0.312637\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.85120i | 0.694409i | 0.937789 | + | 0.347205i | \(0.112869\pi\) | ||||
−0.937789 | + | 0.347205i | \(0.887131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.564936i | − | 0.0661207i | −0.999453 | − | 0.0330604i | \(-0.989475\pi\) | ||
0.999453 | − | 0.0330604i | \(-0.0105254\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.583140 | − | 0.583140i | −0.0664550 | − | 0.0664550i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16.4692i | − | 1.85293i | −0.376382 | − | 0.926465i | \(-0.622832\pi\) | ||
0.376382 | − | 0.926465i | \(-0.377168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.92234 | + | 6.92234i | −0.759826 | + | 0.759826i | −0.976290 | − | 0.216465i | \(-0.930547\pi\) |
0.216465 | + | 0.976290i | \(0.430547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.55945 | − | 9.55945i | −1.03687 | − | 1.03687i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.7726 | 1.14189 | 0.570946 | − | 0.820988i | \(-0.306577\pi\) | ||||
0.570946 | + | 0.820988i | \(0.306577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.76590 | + | 1.76590i | −0.185117 | + | 0.185117i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.06365 | 0.519520 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.64969 | 0.878243 | 0.439122 | − | 0.898428i | \(-0.355290\pi\) | ||||
0.439122 | + | 0.898428i | \(0.355290\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9849 | − | 10.9849i | 1.09303 | − | 1.09303i | 0.0978307 | − | 0.995203i | \(-0.468810\pi\) |
0.995203 | − | 0.0978307i | \(-0.0311904\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.31765 | 0.228365 | 0.114183 | − | 0.993460i | \(-0.463575\pi\) | ||||
0.114183 | + | 0.993460i | \(0.463575\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.38720 | + | 4.38720i | 0.424127 | + | 0.424127i | 0.886622 | − | 0.462495i | \(-0.153046\pi\) |
−0.462495 | + | 0.886622i | \(0.653046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.97102 | − | 1.97102i | 0.188790 | − | 0.188790i | −0.606383 | − | 0.795173i | \(-0.707380\pi\) |
0.795173 | + | 0.606383i | \(0.207380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.79490i | − | 0.733283i | −0.930362 | − | 0.366641i | \(-0.880508\pi\) | ||
0.930362 | − | 0.366641i | \(-0.119492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.91862 | + | 9.91862i | 0.924916 | + | 0.924916i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.63734i | − | 0.333435i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.3199i | − | 0.938172i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0243 | + | 10.0243i | 0.896603 | + | 0.896603i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.11789i | − | 0.454139i | −0.973879 | − | 0.227070i | \(-0.927086\pi\) | ||
0.973879 | − | 0.227070i | \(-0.0729145\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.29337 | − | 6.29337i | 0.549854 | − | 0.549854i | −0.376544 | − | 0.926399i | \(-0.622888\pi\) |
0.926399 | + | 0.376544i | \(0.122888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.963353 | + | 0.963353i | 0.0835333 | + | 0.0835333i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2421 | 1.21678 | 0.608392 | − | 0.793636i | \(-0.291815\pi\) | ||||
0.608392 | + | 0.793636i | \(0.291815\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.23142 | + | 1.23142i | −0.104448 | + | 0.104448i | −0.757400 | − | 0.652952i | \(-0.773530\pi\) |
0.652952 | + | 0.757400i | \(0.273530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.05954 | 0.172227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.0229 | 2.07804 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.2649 | + | 14.2649i | −1.16863 | + | 1.16863i | −0.186098 | + | 0.982531i | \(0.559584\pi\) |
−0.982531 | + | 0.186098i | \(0.940416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2951 | 1.24470 | 0.622349 | − | 0.782740i | \(-0.286178\pi\) | ||||
0.622349 | + | 0.782740i | \(0.286178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.8570 | + | 12.8570i | 1.03270 | + | 1.03270i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.79120 | + | 4.79120i | −0.382379 | + | 0.382379i | −0.871959 | − | 0.489580i | \(-0.837150\pi\) |
0.489580 | + | 0.871959i | \(0.337150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.77401i | 0.297434i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.28056 | − | 3.28056i | −0.256953 | − | 0.256953i | 0.566861 | − | 0.823814i | \(-0.308158\pi\) |
−0.823814 | + | 0.566861i | \(0.808158\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.8772i | − | 1.69291i | −0.532461 | − | 0.846455i | \(-0.678733\pi\) | ||
0.532461 | − | 0.846455i | \(-0.321267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.76317i | 0.520244i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4598 | + | 12.4598i | 0.947304 | + | 0.947304i | 0.998679 | − | 0.0513757i | \(-0.0163606\pi\) |
−0.0513757 | + | 0.998679i | \(0.516361\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.81423i | 0.666293i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.24841 | − | 9.24841i | 0.691259 | − | 0.691259i | −0.271250 | − | 0.962509i | \(-0.587437\pi\) |
0.962509 | + | 0.271250i | \(0.0874371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.6449 | − | 16.6449i | −1.23721 | − | 1.23721i | −0.961137 | − | 0.276072i | \(-0.910967\pi\) |
−0.276072 | − | 0.961137i | \(-0.589033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5422 | 1.80438 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.12108 | + | 2.12108i | −0.155109 | + | 0.155109i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.93740 | 0.140185 | 0.0700927 | − | 0.997540i | \(-0.477670\pi\) | ||||
0.0700927 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0684 | −0.724742 | −0.362371 | − | 0.932034i | \(-0.618033\pi\) | ||||
−0.362371 | + | 0.932034i | \(0.618033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.45632 | − | 1.45632i | 0.103758 | − | 0.103758i | −0.653322 | − | 0.757080i | \(-0.726625\pi\) |
0.757080 | + | 0.653322i | \(0.226625\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3258 | 1.15730 | 0.578652 | − | 0.815574i | \(-0.303579\pi\) | ||||
0.578652 | + | 0.815574i | \(0.303579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.76058 | + | 4.76058i | 0.334127 | + | 0.334127i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0833 | − | 10.0833i | 0.704250 | − | 0.704250i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.12354i | − | 0.0777168i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.81896 | + | 6.81896i | 0.469437 | + | 0.469437i | 0.901732 | − | 0.432295i | \(-0.142296\pi\) |
−0.432295 | + | 0.901732i | \(0.642296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.1488i | 1.23774i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.89207i | 0.332095i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.42320 | + | 6.42320i | 0.432071 | + | 0.432071i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.90066i | 0.194243i | 0.995273 | + | 0.0971213i | \(0.0309635\pi\) | ||||
−0.995273 | + | 0.0971213i | \(0.969037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.48182 | − | 9.48182i | 0.629331 | − | 0.629331i | −0.318569 | − | 0.947900i | \(-0.603202\pi\) |
0.947900 | + | 0.318569i | \(0.103202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9933 | + | 14.9933i | 0.990786 | + | 0.990786i | 0.999958 | − | 0.00917178i | \(-0.00291951\pi\) |
−0.00917178 | + | 0.999958i | \(0.502920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.9359 | −0.781945 | −0.390973 | − | 0.920402i | \(-0.627861\pi\) | ||||
−0.390973 | + | 0.920402i | \(0.627861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.6685 | + | 30.6685i | −2.00059 | + | 2.00059i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.4892 | −0.937227 | −0.468614 | − | 0.883403i | \(-0.655246\pi\) | ||||
−0.468614 | + | 0.883403i | \(0.655246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5295 | 0.807094 | 0.403547 | − | 0.914959i | \(-0.367777\pi\) | ||||
0.403547 | + | 0.914959i | \(0.367777\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.62814 | + | 2.62814i | −0.167906 | + | 0.167906i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.40238 | −0.216488 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.1384 | + | 12.1384i | 0.766166 | + | 0.766166i | 0.977429 | − | 0.211263i | \(-0.0677576\pi\) |
−0.211263 | + | 0.977429i | \(0.567758\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.20078 | − | 2.20078i | 0.138362 | − | 0.138362i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 12.8533i | − | 0.801764i | −0.916130 | − | 0.400882i | \(-0.868704\pi\) | ||
0.916130 | − | 0.400882i | \(-0.131296\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.66911 | + | 4.66911i | 0.290125 | + | 0.290125i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.0594i | 1.54523i | 0.634877 | + | 0.772613i | \(0.281051\pi\) | ||||
−0.634877 | + | 0.772613i | \(0.718949\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.8372i | − | 1.77145i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.1085 | + | 21.1085i | 1.28701 | + | 1.28701i | 0.936597 | + | 0.350409i | \(0.113957\pi\) |
0.350409 | + | 0.936597i | \(0.386043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.0517i | − | 1.64327i | −0.570013 | − | 0.821636i | \(-0.693062\pi\) | ||
0.570013 | − | 0.821636i | \(-0.306938\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.13993 | − | 5.13993i | 0.309949 | − | 0.309949i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.25373 | + | 9.25373i | 0.556003 | + | 0.556003i | 0.928167 | − | 0.372164i | \(-0.121384\pi\) |
−0.372164 | + | 0.928167i | \(0.621384\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.2367 | −0.968600 | −0.484300 | − | 0.874902i | \(-0.660926\pi\) | ||||
−0.484300 | + | 0.874902i | \(0.660926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.02844 | − | 9.02844i | 0.536685 | − | 0.536685i | −0.385869 | − | 0.922554i | \(-0.626098\pi\) |
0.922554 | + | 0.385869i | \(0.126098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.83668 | 0.226472 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.76973 | 0.221749 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6256 | − | 20.6256i | 1.20496 | − | 1.20496i | 0.232324 | − | 0.972639i | \(-0.425367\pi\) |
0.972639 | − | 0.232324i | \(-0.0746328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.1638 | −1.34865 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.66454 | − | 6.66454i | −0.385420 | − | 0.385420i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.45278 | + | 3.45278i | −0.199015 | + | 0.199015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 42.0481i | − | 2.40767i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.53094 | − | 9.53094i | −0.543959 | − | 0.543959i | 0.380728 | − | 0.924687i | \(-0.375673\pi\) |
−0.924687 | + | 0.380728i | \(0.875673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.39638i | − | 0.249296i | −0.992201 | − | 0.124648i | \(-0.960220\pi\) | ||
0.992201 | − | 0.124648i | \(-0.0397802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8579i | 1.57462i | 0.616558 | + | 0.787310i | \(0.288527\pi\) | ||||
−0.616558 | + | 0.787310i | \(0.711473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5283 | + | 11.5283i | 0.647491 | + | 0.647491i | 0.952386 | − | 0.304895i | \(-0.0986214\pi\) |
−0.304895 | + | 0.952386i | \(0.598621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.55217i | − | 0.310862i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.50405 | − | 3.50405i | 0.194970 | − | 0.194970i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5651 | − | 15.5651i | −0.863395 | − | 0.863395i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.6693 | −0.643349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.4888 | − | 21.4888i | 1.18113 | − | 1.18113i | 0.201682 | − | 0.979451i | \(-0.435359\pi\) |
0.979451 | − | 0.201682i | \(-0.0646408\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −59.6716 | −3.26021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.64762 | 0.362119 | 0.181059 | − | 0.983472i | \(-0.442047\pi\) | ||||
0.181059 | + | 0.983472i | \(0.442047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.85276 | − | 2.85276i | 0.154486 | − | 0.154486i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.4459 | − | 19.4459i | −1.04391 | − | 1.04391i | −0.998991 | − | 0.0449218i | \(-0.985696\pi\) |
−0.0449218 | − | 0.998991i | \(-0.514304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.38328 | + | 6.38328i | −0.341689 | + | 0.341689i | −0.857002 | − | 0.515313i | \(-0.827676\pi\) |
0.515313 | + | 0.857002i | \(0.327676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.05143i | 0.375310i | 0.982235 | + | 0.187655i | \(0.0600886\pi\) | ||||
−0.982235 | + | 0.187655i | \(0.939911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.3778 | − | 15.3778i | −0.816167 | − | 0.816167i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7598i | 1.51788i | 0.651159 | + | 0.758941i | \(0.274283\pi\) | ||||
−0.651159 | + | 0.758941i | \(0.725717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 17.1439i | − | 0.902311i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.48473 | + | 1.48473i | 0.0777143 | + | 0.0777143i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.89445i | 0.516486i | 0.966080 | + | 0.258243i | \(0.0831435\pi\) | ||||
−0.966080 | + | 0.258243i | \(0.916856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.48624 | − | 5.48624i | 0.284831 | − | 0.284831i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6444 | − | 24.6444i | −1.27604 | − | 1.27604i | −0.942865 | − | 0.333175i | \(-0.891880\pi\) |
−0.333175 | − | 0.942865i | \(-0.608120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.8135 | −0.865937 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.92064 | + | 3.92064i | −0.201390 | + | 0.201390i | −0.800595 | − | 0.599206i | \(-0.795483\pi\) |
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.5474 | −0.947730 | −0.473865 | − | 0.880598i | \(-0.657142\pi\) | ||||
−0.473865 | + | 0.880598i | \(0.657142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.06515 | 0.156214 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.7437 | + | 19.7437i | −1.00104 | + | 1.00104i | −0.00104509 | + | 0.999999i | \(0.500333\pi\) |
−0.999999 | + | 0.00104509i | \(0.999667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7274 | 0.694223 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.2833 | + | 43.2833i | 2.17782 | + | 2.17782i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4592 | − | 13.4592i | 0.675497 | − | 0.675497i | −0.283481 | − | 0.958978i | \(-0.591489\pi\) |
0.958978 | + | 0.283481i | \(0.0914893\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.4638i | − | 1.47135i | −0.677334 | − | 0.735676i | \(-0.736865\pi\) | ||
0.677334 | − | 0.735676i | \(-0.263135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.63891 | − | 8.63891i | −0.430335 | − | 0.430335i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.44550i | − | 0.269923i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.9026i | 0.786333i | 0.919467 | + | 0.393167i | \(0.128620\pi\) | ||||
−0.919467 | + | 0.393167i | \(0.871380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.40688 | − | 4.40688i | −0.216848 | − | 0.216848i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 36.3858i | − | 1.78611i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.45606 | + | 6.45606i | −0.315399 | + | 0.315399i | −0.846997 | − | 0.531598i | \(-0.821592\pi\) |
0.531598 | + | 0.846997i | \(0.321592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8827 | + | 11.8827i | 0.579126 | + | 0.579126i | 0.934663 | − | 0.355536i | \(-0.115702\pi\) |
−0.355536 | + | 0.934663i | \(0.615702\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.0604 | 1.55516 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.99959 | − | 7.99959i | 0.387127 | − | 0.387127i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.49791 | 0.264825 | 0.132412 | − | 0.991195i | \(-0.457728\pi\) | ||||
0.132412 | + | 0.991195i | \(0.457728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0080 | 0.961522 | 0.480761 | − | 0.876852i | \(-0.340360\pi\) | ||||
0.480761 | + | 0.876852i | \(0.340360\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.63570 | + | 3.63570i | −0.173919 | + | 0.173919i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.00616772 | 0.000294369 | 0.000147185 | − | 1.00000i | \(-0.499953\pi\) | ||||
0.000147185 | 1.00000i | \(0.499953\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.02537 | − | 4.02537i | −0.191251 | − | 0.191251i | 0.604985 | − | 0.796237i | \(-0.293179\pi\) |
−0.796237 | + | 0.604985i | \(0.793179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.3118 | + | 28.3118i | −1.34211 | + | 1.34211i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6378i | 0.926765i | 0.886158 | + | 0.463382i | \(0.153364\pi\) | ||||
−0.886158 | + | 0.463382i | \(0.846636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.23732 | − | 2.23732i | −0.105351 | − | 0.105351i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.28208i | − | 0.435151i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.0292i | − | 0.843372i | −0.906742 | − | 0.421686i | \(-0.861438\pi\) | ||
0.906742 | − | 0.421686i | \(-0.138562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.06055 | + | 2.06055i | 0.0959694 | + | 0.0959694i | 0.753461 | − | 0.657492i | \(-0.228383\pi\) |
−0.657492 | + | 0.753461i | \(0.728383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 38.8765i | − | 1.80674i | −0.428857 | − | 0.903372i | \(-0.641084\pi\) | ||
0.428857 | − | 0.903372i | \(-0.358916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.88850 | + | 6.88850i | −0.318762 | + | 0.318762i | −0.848291 | − | 0.529530i | \(-0.822368\pi\) |
0.529530 | + | 0.848291i | \(0.322368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.3524 | − | 11.3524i | −0.524207 | − | 0.524207i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.02691 | 0.185157 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.49121 | + | 8.49121i | −0.389604 | + | 0.389604i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.25769 | 0.148848 | 0.0744239 | − | 0.997227i | \(-0.476288\pi\) | ||||
0.0744239 | + | 0.997227i | \(0.476288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4904 | −0.751898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.7326 | + | 22.7326i | −1.03223 | + | 1.03223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.6993 | 1.25517 | 0.627587 | − | 0.778547i | \(-0.284043\pi\) | ||||
0.627587 | + | 0.778547i | \(0.284043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9676 | − | 20.9676i | −0.946256 | − | 0.946256i | 0.0523720 | − | 0.998628i | \(-0.483322\pi\) |
−0.998628 | + | 0.0523720i | \(0.983322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3159 | − | 17.3159i | 0.779868 | − | 0.779868i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.85120i | − | 0.262462i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46939 | − | 2.46939i | −0.110545 | − | 0.110545i | 0.649671 | − | 0.760216i | \(-0.274907\pi\) |
−0.760216 | + | 0.649671i | \(0.774907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.9403i | 0.889093i | 0.895756 | + | 0.444547i | \(0.146635\pi\) | ||||
−0.895756 | + | 0.444547i | \(0.853365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.7394i | 2.56937i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.45882 | − | 7.45882i | −0.330606 | − | 0.330606i | 0.522210 | − | 0.852817i | \(-0.325108\pi\) |
−0.852817 | + | 0.522210i | \(0.825108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.564936i | 0.0249913i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.09112 | + | 6.09112i | −0.268407 | + | 0.268407i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.80483 | + | 6.80483i | 0.299276 | + | 0.299276i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2354 | −1.01796 | −0.508981 | − | 0.860778i | \(-0.669978\pi\) | ||||
−0.508981 | + | 0.860778i | \(0.669978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1847 | + | 19.1847i | −0.838888 | + | 0.838888i | −0.988713 | − | 0.149824i | \(-0.952129\pi\) |
0.149824 | + | 0.988713i | \(0.452129\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.7941 | 0.775124 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.75685 | 0.380733 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.77520 | + | 6.77520i | −0.293467 | + | 0.293467i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.0604 | −0.996986 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.583140 | + | 0.583140i | 0.0251176 | + | 0.0251176i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.33342 | + | 9.33342i | −0.401275 | + | 0.401275i | −0.878682 | − | 0.477407i | \(-0.841577\pi\) |
0.477407 | + | 0.878682i | \(0.341577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.3602i | 0.443784i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2760 | − | 12.2760i | −0.524883 | − | 0.524883i | 0.394159 | − | 0.919042i | \(-0.371036\pi\) |
−0.919042 | + | 0.394159i | \(0.871036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.17224i | 0.390751i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.4692i | 0.700342i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.3475 | − | 14.3475i | −0.607923 | − | 0.607923i | 0.334480 | − | 0.942403i | \(-0.391439\pi\) |
−0.942403 | + | 0.334480i | \(0.891439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.1946i | − | 0.515775i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8013 | − | 14.8013i | 0.623802 | − | 0.623802i | −0.322700 | − | 0.946501i | \(-0.604590\pi\) |
0.946501 | + | 0.322700i | \(0.104590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.4861 | + | 20.4861i | 0.861856 | + | 0.861856i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.30895 | 0.348329 | 0.174165 | − | 0.984717i | \(-0.444277\pi\) | ||||
0.174165 | + | 0.984717i | \(0.444277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.56981 | + | 9.56981i | −0.400484 | + | 0.400484i | −0.878404 | − | 0.477920i | \(-0.841391\pi\) |
0.477920 | + | 0.878404i | \(0.341391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.2650 | −1.38725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.5616 | 1.52208 | 0.761039 | − | 0.648706i | \(-0.224690\pi\) | ||||
0.761039 | + | 0.648706i | \(0.224690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92234 | − | 6.92234i | 0.287187 | − | 0.287187i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.39849 | −0.264998 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.86143 | + | 2.86143i | 0.118104 | + | 0.118104i | 0.763689 | − | 0.645585i | \(-0.223386\pi\) |
−0.645585 | + | 0.763689i | \(0.723386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.71279 | + | 4.71279i | −0.194187 | + | 0.194187i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 40.5600i | − | 1.66560i | −0.553575 | − | 0.832799i | \(-0.686737\pi\) | ||
0.553575 | − | 0.832799i | \(-0.313263\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.55945 | + | 9.55945i | 0.391899 | + | 0.391899i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 41.0811i | − | 1.67853i | −0.543725 | − | 0.839263i | \(-0.682987\pi\) | ||
0.543725 | − | 0.839263i | \(-0.317013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.2778i | 1.07190i | 0.844251 | + | 0.535948i | \(0.180046\pi\) | ||||
−0.844251 | + | 0.535948i | \(0.819954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.1221 | + | 27.1221i | 1.10267 | + | 1.10267i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 47.8974i | − | 1.94410i | −0.234784 | − | 0.972048i | \(-0.575438\pi\) | ||
0.234784 | − | 0.972048i | \(-0.424562\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.6068 | − | 20.6068i | 0.833663 | − | 0.833663i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.694342 | + | 0.694342i | 0.0280442 | + | 0.0280442i | 0.720990 | − | 0.692946i | \(-0.243687\pi\) |
−0.692946 | + | 0.720990i | \(0.743687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.60105 | −0.185231 | −0.0926156 | − | 0.995702i | \(-0.529523\pi\) | ||||
−0.0926156 | + | 0.995702i | \(0.529523\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.50800 | − | 6.50800i | 0.261579 | − | 0.261579i | −0.564117 | − | 0.825695i | \(-0.690783\pi\) |
0.825695 | + | 0.564117i | \(0.190783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7726 | −0.431594 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.61949 | −0.344779 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9832 | − | 16.9832i | 0.677164 | − | 0.677164i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.8637 | −1.22867 | −0.614333 | − | 0.789047i | \(-0.710575\pi\) | ||||
−0.614333 | + | 0.789047i | \(0.710575\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.4505 | + | 13.4505i | 0.533768 | + | 0.533768i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.76590 | − | 1.76590i | 0.0699676 | − | 0.0699676i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.57360i | 0.0621536i | 0.999517 | + | 0.0310768i | \(0.00989365\pi\) | ||||
−0.999517 | + | 0.0310768i | \(0.990106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.203779 | − | 0.203779i | −0.00803626 | − | 0.00803626i | 0.703077 | − | 0.711113i | \(-0.251809\pi\) |
−0.711113 | + | 0.703077i | \(0.751809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.73020i | − | 0.303906i | −0.988388 | − | 0.151953i | \(-0.951444\pi\) | ||
0.988388 | − | 0.151953i | \(-0.0485562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.13966i | 0.201749i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.7507 | − | 25.7507i | −1.00770 | − | 1.00770i | −0.999970 | − | 0.00773247i | \(-0.997539\pi\) |
−0.00773247 | − | 0.999970i | \(-0.502461\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.0797i | 1.29253i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1443 | − | 14.1443i | 0.550984 | − | 0.550984i | −0.375741 | − | 0.926725i | \(-0.622612\pi\) |
0.926725 | + | 0.375741i | \(0.122612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.31619 | − | 8.31619i | −0.323462 | − | 0.323462i | 0.526632 | − | 0.850094i | \(-0.323455\pi\) |
−0.850094 | + | 0.526632i | \(0.823455\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.06365 | −0.196360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.9665 | + | 17.9665i | −0.695665 | + | 0.695665i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.32976 | −0.360172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.9355 | 1.34667 | 0.673333 | − | 0.739339i | \(-0.264862\pi\) | ||||
0.673333 | + | 0.739339i | \(0.264862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.44273 | − | 5.44273i | 0.209181 | − | 0.209181i | −0.594738 | − | 0.803919i | \(-0.702744\pi\) |
0.803919 | + | 0.594738i | \(0.202744\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.64969 | −0.331945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.7753 | − | 33.7753i | −1.29238 | − | 1.29238i | −0.933313 | − | 0.359063i | \(-0.883096\pi\) |
−0.359063 | − | 0.933313i | \(-0.616904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4302 | + | 37.4302i | −1.43014 | + | 1.43014i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3763i | 0.738179i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8468 | + | 31.8468i | 1.21151 | + | 1.21151i | 0.970530 | + | 0.240979i | \(0.0774686\pi\) |
0.240979 | + | 0.970530i | \(0.422531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.47269i | − | 0.245523i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 13.9553i | − | 0.528595i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.0196 | − | 17.0196i | −0.642822 | − | 0.642822i | 0.308426 | − | 0.951248i | \(-0.400198\pi\) |
−0.951248 | + | 0.308426i | \(0.900198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.99601i | 0.339291i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.9849 | + | 10.9849i | −0.413128 | + | 0.413128i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.45471 | + | 4.45471i | 0.167300 | + | 0.167300i | 0.785792 | − | 0.618491i | \(-0.212256\pi\) |
−0.618491 | + | 0.785792i | \(0.712256\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.4627 | −0.691434 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.41275 | + | 5.41275i | −0.202425 | + | 0.202425i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.3426 | 0.646771 | 0.323385 | − | 0.946267i | \(-0.395179\pi\) | ||||
0.323385 | + | 0.946267i | \(0.395179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.31765 | −0.0863139 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.9609 | + | 41.9609i | −1.55839 | + | 1.55839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.938724 | −0.0348153 | −0.0174077 | − | 0.999848i | \(-0.505541\pi\) | ||||
−0.0174077 | + | 0.999848i | \(0.505541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.5590 | + | 12.5590i | 0.464510 | + | 0.464510i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3212 | + | 17.3212i | −0.639775 | + | 0.639775i | −0.950500 | − | 0.310725i | \(-0.899428\pi\) |
0.310725 | + | 0.950500i | \(0.399428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2401i | 0.487706i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.7806 | + | 30.7806i | 1.13228 | + | 1.13228i | 0.989797 | + | 0.142486i | \(0.0455096\pi\) |
0.142486 | + | 0.989797i | \(0.454490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 41.3295i | − | 1.51623i | −0.652120 | − | 0.758116i | \(-0.726120\pi\) | ||
0.652120 | − | 0.758116i | \(-0.273880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 74.9805i | − | 2.74707i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.38720 | − | 4.38720i | −0.160305 | − | 0.160305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.1560i | 1.83022i | 0.403204 | + | 0.915110i | \(0.367896\pi\) | ||||
−0.403204 | + | 0.915110i | \(0.632104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.1977 | + | 40.1977i | −1.46294 | + | 1.46294i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.81463 | − | 2.81463i | −0.102299 | − | 0.102299i | 0.654105 | − | 0.756404i | \(-0.273046\pi\) |
−0.756404 | + | 0.654105i | \(0.773046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.6910 | 0.786297 | 0.393149 | − | 0.919475i | \(-0.371386\pi\) | ||||
0.393149 | + | 0.919475i | \(0.371386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.97102 | + | 1.97102i | −0.0713558 | + | 0.0713558i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5642 | 0.561992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.53040 | −0.163371 | −0.0816853 | − | 0.996658i | \(-0.526030\pi\) | ||||
−0.0816853 | + | 0.996658i | \(0.526030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.6600 | − | 23.6600i | 0.850990 | − | 0.850990i | −0.139265 | − | 0.990255i | \(-0.544474\pi\) |
0.990255 | + | 0.139265i | \(0.0444739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.1198 | −1.54891 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.69607 | + | 3.69607i | 0.132426 | + | 0.132426i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.41207 | + | 3.41207i | −0.122093 | + | 0.122093i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 25.1839i | − | 0.898850i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.29221 | + | 1.29221i | 0.0460623 | + | 0.0460623i | 0.729763 | − | 0.683700i | \(-0.239631\pi\) |
−0.683700 | + | 0.729763i | \(0.739631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.79490i | 0.277155i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.2530i | 1.00329i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.95058 | − | 6.95058i | −0.246202 | − | 0.246202i | 0.573208 | − | 0.819410i | \(-0.305699\pi\) |
−0.819410 | + | 0.573208i | \(0.805699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.4452i | 1.50160i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.329437 | − | 0.329437i | 0.0116256 | − | 0.0116256i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.91862 | − | 9.91862i | −0.349586 | − | 0.349586i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.9481 | −0.736495 | −0.368248 | − | 0.929728i | \(-0.620042\pi\) | ||||
−0.368248 | + | 0.929728i | \(0.620042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6400 | + | 15.6400i | −0.549194 | + | 0.549194i | −0.926208 | − | 0.377014i | \(-0.876951\pi\) |
0.377014 | + | 0.926208i | \(0.376951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.2435 | 0.604015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.65249 | −0.232741 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.17232 | + | 7.17232i | −0.250316 | + | 0.250316i | −0.821100 | − | 0.570784i | \(-0.806639\pi\) |
0.570784 | + | 0.821100i | \(0.306639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.57692 | 0.124684 | 0.0623418 | − | 0.998055i | \(-0.480143\pi\) | ||||
0.0623418 | + | 0.998055i | \(0.480143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0753 | − | 13.0753i | −0.454672 | − | 0.454672i | 0.442230 | − | 0.896902i | \(-0.354188\pi\) |
−0.896902 | + | 0.442230i | \(0.854188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.86517 | − | 2.86517i | 0.0995115 | − | 0.0995115i | −0.655598 | − | 0.755110i | \(-0.727584\pi\) |
0.755110 | + | 0.655598i | \(0.227584\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.63734i | 0.126027i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 57.4963 | + | 57.4963i | 1.98974 | + | 1.98974i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 53.9862i | − | 1.86381i | −0.362703 | − | 0.931905i | \(-0.618146\pi\) | ||
0.362703 | − | 0.931905i | \(-0.381854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3263i | 0.562975i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.7746 | − | 17.7746i | −0.611463 | − | 0.611463i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3199i | 0.354596i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.6213 | + | 17.6213i | −0.604050 | + | 0.604050i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.3458 | + | 25.3458i | 0.867823 | + | 0.867823i | 0.992231 | − | 0.124408i | \(-0.0397033\pi\) |
−0.124408 | + | 0.992231i | \(0.539703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.6403 | −0.773379 | −0.386689 | − | 0.922210i | \(-0.626381\pi\) | ||||
−0.386689 | + | 0.922210i | \(0.626381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6166 | − | 26.6166i | 0.908146 | − | 0.908146i | −0.0879765 | − | 0.996123i | \(-0.528040\pi\) |
0.996123 | + | 0.0879765i | \(0.0280400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.5204 | 0.834683 | 0.417342 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417342 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.4924 | −2.22681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.60385 | − | 9.60385i | 0.325788 | − | 0.325788i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.0946 | 1.35855 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.0243 | − | 10.0243i | −0.338884 | − | 0.338884i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.9688 | − | 28.9688i | 0.978206 | − | 0.978206i | −0.0215611 | − | 0.999768i | \(-0.506864\pi\) |
0.999768 | + | 0.0215611i | \(0.00686364\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30.1989i | − | 1.01743i | −0.860936 | − | 0.508713i | \(-0.830122\pi\) | ||
0.860936 | − | 0.508713i | \(-0.169878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.28384 | + | 3.28384i | 0.110510 | + | 0.110510i | 0.760200 | − | 0.649690i | \(-0.225101\pi\) |
−0.649690 | + | 0.760200i | \(0.725101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.4792i | 1.62777i | 0.581024 | + | 0.813886i | \(0.302652\pi\) | ||||
−0.581024 | + | 0.813886i | \(0.697348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.11789i | 0.171648i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.2416 | − | 11.2416i | −0.376187 | − | 0.376187i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.6122i | 1.62493i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.2891 | + | 23.2891i | −0.776734 | + | 0.776734i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.9553 | − | 19.9553i | −0.664808 | − | 0.664808i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 87.4904 | 2.90828 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.8236 | + | 33.8236i | −1.12310 | + | 1.12310i | −0.131822 | + | 0.991273i | \(0.542083\pi\) |
−0.991273 | + | 0.131822i | \(0.957917\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4793 | −0.512852 | −0.256426 | − | 0.966564i | \(-0.582545\pi\) | ||||
−0.256426 | + | 0.966564i | \(0.582545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.07339 | −0.267190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.29337 | + | 6.29337i | −0.207825 | + | 0.207825i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.5898 | 1.63582 | 0.817908 | − | 0.575349i | \(-0.195134\pi\) | ||||
0.817908 | + | 0.575349i | \(0.195134\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3326 | + | 10.3326i | 0.340103 | + | 0.340103i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.1546 | + | 41.1546i | −1.35316 | + | 1.35316i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.2852i | 0.862391i | 0.902259 | + | 0.431195i | \(0.141908\pi\) | ||||
−0.902259 | + | 0.431195i | \(0.858092\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.963353 | − | 0.963353i | −0.0315726 | − | 0.0315726i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 11.1490i | − | 0.364611i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.51468i | − | 0.0821510i | −0.999156 | − | 0.0410755i | \(-0.986922\pi\) | ||
0.999156 | − | 0.0410755i | \(-0.0130784\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.4678 | − | 15.4678i | −0.504237 | − | 0.504237i | 0.408514 | − | 0.912752i | \(-0.366047\pi\) |
−0.912752 | + | 0.408514i | \(0.866047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4797i | 0.471523i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.9424 | − | 17.9424i | 0.583049 | − | 0.583049i | −0.352691 | − | 0.935740i | \(-0.614733\pi\) |
0.935740 | + | 0.352691i | \(0.114733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.997622 | − | 0.997622i | −0.0323842 | − | 0.0323842i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.59267 | 0.181164 | 0.0905821 | − | 0.995889i | \(-0.471127\pi\) | ||||
0.0905821 | + | 0.995889i | \(0.471127\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.09176 | + | 5.09176i | −0.164766 | + | 0.164766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.2421 | −0.459901 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.06770 | 0.227990 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.4612 | − | 26.4612i | 0.851818 | − | 0.851818i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.6701 | −1.01844 | −0.509220 | − | 0.860636i | \(-0.670066\pi\) | ||||
−0.509220 | + | 0.860636i | \(0.670066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.7252 | − | 19.7252i | −0.633012 | − | 0.633012i | 0.315810 | − | 0.948822i | \(-0.397724\pi\) |
−0.948822 | + | 0.315810i | \(0.897724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.23142 | − | 1.23142i | 0.0394775 | − | 0.0394775i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2206i | 0.486951i | 0.969907 | + | 0.243475i | \(0.0782875\pi\) | ||||
−0.969907 | + | 0.243475i | \(0.921713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.28192 | + | 6.28192i | 0.200771 | + | 0.200771i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 39.8828i | − | 1.27207i | −0.771662 | − | 0.636033i | \(-0.780574\pi\) | ||
0.771662 | − | 0.636033i | \(-0.219426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.65482i | 0.243903i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.0308 | − | 13.0308i | −0.414356 | − | 0.414356i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.0864i | − | 1.52752i | −0.645503 | − | 0.763758i | \(-0.723352\pi\) | ||
0.645503 | − | 0.763758i | \(-0.276648\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.9065 | + | 42.9065i | −1.36023 | + | 1.36023i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.3703 | − | 16.3703i | −0.518452 | − | 0.518452i | 0.398651 | − | 0.917103i | \(-0.369479\pi\) |
−0.917103 | + | 0.398651i | \(0.869479\pi\) | |||||||
\(998\) | 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 | 4032.2.v.e.3599.2 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.3599.19 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.827.7 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.827.14 | yes | 40 | ||
16.3 | odd | 4 | inner | 4032.2.v.e.1583.19 | 40 | ||
16.13 | even | 4 | 1008.2.v.e.323.14 | yes | 40 | ||
48.29 | odd | 4 | 1008.2.v.e.323.7 | ✓ | 40 | ||
48.35 | even | 4 | inner | 4032.2.v.e.1583.2 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.7 | ✓ | 40 | 48.29 | odd | 4 | ||
1008.2.v.e.323.14 | yes | 40 | 16.13 | even | 4 | ||
1008.2.v.e.827.7 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.14 | yes | 40 | 12.11 | even | 2 | ||
4032.2.v.e.1583.2 | 40 | 48.35 | even | 4 | inner | ||
4032.2.v.e.1583.19 | 40 | 16.3 | odd | 4 | inner | ||
4032.2.v.e.3599.2 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.3599.19 | 40 | 3.2 | odd | 2 | inner |