Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(107,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.f (of order \(4\), degree \(2\), 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: | \(10.7798042729\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.593 |
Dual form | 1350.2.f.c.107.3 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.19615i | 1.56670i | 0.621582 | + | 0.783349i | \(0.286490\pi\) | ||||
−0.621582 | + | 0.783349i | \(0.713510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.67423 | + | 3.67423i | 1.01905 | + | 1.01905i | 0.999815 | + | 0.0192343i | \(0.00612285\pi\) |
0.0192343 | + | 0.999815i | \(0.493877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.12132 | − | 2.12132i | −0.514496 | − | 0.514496i | 0.401405 | − | 0.915901i | \(-0.368522\pi\) |
−0.915901 | + | 0.401405i | \(0.868522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.67423 | + | 3.67423i | −0.783349 | + | 0.783349i | ||||
\(23\) | 2.12132 | − | 2.12132i | 0.442326 | − | 0.442326i | −0.450467 | − | 0.892793i | \(-0.648743\pi\) |
0.892793 | + | 0.450467i | \(0.148743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.19615i | 1.01905i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.19615 | −0.964901 | −0.482451 | − | 0.875923i | \(-0.660253\pi\) | ||||
−0.482451 | + | 0.875923i | \(0.660253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.00000i | − | 0.514496i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 1.41421 | − | 1.41421i | 0.229416 | − | 0.229416i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 1.62301i | 0.584349 | + | 0.811503i | \(0.301350\pi\) | ||||
−0.584349 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.67423 | + | 3.67423i | 0.560316 | + | 0.560316i | 0.929397 | − | 0.369082i | \(-0.120328\pi\) |
−0.369082 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(44\) | −5.19615 | −0.783349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | 6.36396 | + | 6.36396i | 0.928279 | + | 0.928279i | 0.997595 | − | 0.0693157i | \(-0.0220816\pi\) |
−0.0693157 | + | 0.997595i | \(0.522082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.67423 | + | 3.67423i | −0.509525 | + | 0.509525i | ||||
\(53\) | −8.48528 | + | 8.48528i | −1.16554 | + | 1.16554i | −0.182300 | + | 0.983243i | \(0.558354\pi\) |
−0.983243 | + | 0.182300i | \(0.941646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.67423 | − | 3.67423i | −0.482451 | − | 0.482451i | ||||
\(59\) | −10.3923 | −1.35296 | −0.676481 | − | 0.736460i | \(-0.736496\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | −3.53553 | − | 3.53553i | −0.449013 | − | 0.449013i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.34847 | − | 7.34847i | 0.897758 | − | 0.897758i | −0.0974792 | − | 0.995238i | \(-0.531078\pi\) |
0.995238 | + | 0.0974792i | \(0.0310779\pi\) | |||||||
\(68\) | 2.12132 | − | 2.12132i | 0.257248 | − | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34847 | + | 7.34847i | 0.860073 | + | 0.860073i | 0.991346 | − | 0.131273i | \(-0.0419064\pi\) |
−0.131273 | + | 0.991346i | \(0.541906\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.00000i | − | 0.112509i | −0.998416 | − | 0.0562544i | \(-0.982084\pi\) | ||
0.998416 | − | 0.0562544i | \(-0.0179158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.34847 | + | 7.34847i | −0.811503 | + | 0.811503i | ||||
\(83\) | 8.48528 | − | 8.48528i | 0.931381 | − | 0.931381i | −0.0664117 | − | 0.997792i | \(-0.521155\pi\) |
0.997792 | + | 0.0664117i | \(0.0211551\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.19615i | 0.560316i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.67423 | − | 3.67423i | −0.391675 | − | 0.391675i | ||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.12132 | + | 2.12132i | 0.221163 | + | 0.221163i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.00000i | 0.928279i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.34847 | − | 7.34847i | 0.746124 | − | 0.746124i | −0.227625 | − | 0.973749i | \(-0.573096\pi\) |
0.973749 | + | 0.227625i | \(0.0730960\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19615i | 0.517036i | 0.966006 | + | 0.258518i | \(0.0832342\pi\) | ||||
−0.966006 | + | 0.258518i | \(0.916766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.34847 | − | 7.34847i | −0.724066 | − | 0.724066i | 0.245365 | − | 0.969431i | \(-0.421092\pi\) |
−0.969431 | + | 0.245365i | \(0.921092\pi\) | |||||||
\(104\) | −5.19615 | −0.509525 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | −12.7279 | − | 12.7279i | −1.23045 | − | 1.23045i | −0.963789 | − | 0.266666i | \(-0.914078\pi\) |
−0.266666 | − | 0.963789i | \(-0.585922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.0000i | − | 1.53252i | −0.642529 | − | 0.766261i | \(-0.722115\pi\) | ||
0.642529 | − | 0.766261i | \(-0.277885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.36396 | − | 6.36396i | 0.598671 | − | 0.598671i | −0.341288 | − | 0.939959i | \(-0.610863\pi\) |
0.939959 | + | 0.341288i | \(0.110863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 5.19615i | − | 0.482451i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.34847 | − | 7.34847i | −0.676481 | − | 0.676481i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0000 | −1.45455 | ||||||||
\(122\) | 5.65685 | + | 5.65685i | 0.512148 | + | 0.512148i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.00000i | − | 0.449013i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6969 | − | 14.6969i | 1.30414 | − | 1.30414i | 0.378570 | − | 0.925573i | \(-0.376416\pi\) |
0.925573 | − | 0.378570i | \(-0.123584\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.19615i | − | 0.453990i | −0.973896 | − | 0.226995i | \(-0.927110\pi\) | ||
0.973896 | − | 0.226995i | \(-0.0728901\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.3923 | 0.897758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | 4.24264 | + | 4.24264i | 0.362473 | + | 0.362473i | 0.864723 | − | 0.502249i | \(-0.167494\pi\) |
−0.502249 | + | 0.864723i | \(0.667494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.34847 | + | 7.34847i | −0.616670 | + | 0.616670i | ||||
\(143\) | −19.0919 | + | 19.0919i | −1.59654 | + | 1.59654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.3923i | 0.860073i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5885 | 1.27706 | 0.638528 | − | 0.769599i | \(-0.279544\pi\) | ||||
0.638528 | + | 0.769599i | \(0.279544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0000 | 1.54620 | 0.773099 | − | 0.634285i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | 1.41421 | + | 1.41421i | 0.114708 | + | 0.114708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.67423 | + | 3.67423i | −0.293236 | + | 0.293236i | −0.838357 | − | 0.545121i | \(-0.816484\pi\) |
0.545121 | + | 0.838357i | \(0.316484\pi\) | |||||||
\(158\) | 0.707107 | − | 0.707107i | 0.0562544 | − | 0.0562544i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0227 | − | 11.0227i | −0.863365 | − | 0.863365i | 0.128363 | − | 0.991727i | \(-0.459028\pi\) |
−0.991727 | + | 0.128363i | \(0.959028\pi\) | |||||||
\(164\) | −10.3923 | −0.811503 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 8.48528 | + | 8.48528i | 0.656611 | + | 0.656611i | 0.954577 | − | 0.297966i | \(-0.0963081\pi\) |
−0.297966 | + | 0.954577i | \(0.596308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.0000i | 1.07692i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.67423 | + | 3.67423i | −0.280158 | + | 0.280158i | ||||
\(173\) | 16.9706 | − | 16.9706i | 1.29025 | − | 1.29025i | 0.355616 | − | 0.934632i | \(-0.384271\pi\) |
0.934632 | − | 0.355616i | \(-0.115729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.19615i | − | 0.391675i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.34847 | − | 7.34847i | −0.550791 | − | 0.550791i | ||||
\(179\) | 10.3923 | 0.776757 | 0.388379 | − | 0.921500i | \(-0.373035\pi\) | ||||
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000i | 0.221163i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0227 | − | 11.0227i | 0.806060 | − | 0.806060i | ||||
\(188\) | −6.36396 | + | 6.36396i | −0.464140 | + | 0.464140i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6969 | + | 14.6969i | 1.05791 | + | 1.05791i | 0.998217 | + | 0.0596919i | \(0.0190118\pi\) |
0.0596919 | + | 0.998217i | \(0.480988\pi\) | |||||||
\(194\) | 10.3923 | 0.746124 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −4.24264 | − | 4.24264i | −0.302276 | − | 0.302276i | 0.539628 | − | 0.841904i | \(-0.318565\pi\) |
−0.841904 | + | 0.539628i | \(0.818565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000i | 0.779769i | 0.920864 | + | 0.389885i | \(0.127485\pi\) | ||||
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.67423 | + | 3.67423i | −0.258518 | + | 0.258518i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 10.3923i | − | 0.724066i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.67423 | − | 3.67423i | −0.254762 | − | 0.254762i | ||||
\(209\) | 10.3923 | 0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | −8.48528 | − | 8.48528i | −0.582772 | − | 0.582772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 18.0000i | − | 1.23045i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.3137 | − | 11.3137i | 0.766261 | − | 0.766261i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.5885i | − | 1.04859i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.34847 | − | 7.34847i | −0.492090 | − | 0.492090i | 0.416874 | − | 0.908964i | \(-0.363126\pi\) |
−0.908964 | + | 0.416874i | \(0.863126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | 0.598671 | ||||||||
\(227\) | −4.24264 | − | 4.24264i | −0.281594 | − | 0.281594i | 0.552151 | − | 0.833744i | \(-0.313807\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.0000i | − | 0.925146i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) | ||
0.886581 | − | 0.462573i | \(-0.153074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.67423 | − | 3.67423i | 0.241225 | − | 0.241225i | ||||
\(233\) | −12.7279 | + | 12.7279i | −0.833834 | + | 0.833834i | −0.988039 | − | 0.154205i | \(-0.950718\pi\) |
0.154205 | + | 0.988039i | \(0.450718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 10.3923i | − | 0.676481i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | −11.3137 | − | 11.3137i | −0.727273 | − | 0.727273i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.34847 | − | 7.34847i | 0.467572 | − | 0.467572i | ||||
\(248\) | 3.53553 | − | 3.53553i | 0.224507 | − | 0.224507i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.5885i | − | 0.983935i | −0.870614 | − | 0.491967i | \(-0.836278\pi\) | ||
0.870614 | − | 0.491967i | \(-0.163722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0227 | + | 11.0227i | 0.692991 | + | 0.692991i | ||||
\(254\) | 20.7846 | 1.30414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.6066 | + | 10.6066i | 0.661622 | + | 0.661622i | 0.955762 | − | 0.294141i | \(-0.0950334\pi\) |
−0.294141 | + | 0.955762i | \(0.595033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.67423 | − | 3.67423i | 0.226995 | − | 0.226995i | ||||
\(263\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.34847 | + | 7.34847i | 0.448879 | + | 0.448879i | ||||
\(269\) | 5.19615 | 0.316815 | 0.158408 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158408 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 2.12132 | + | 2.12132i | 0.128624 | + | 0.128624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000i | 0.362473i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6969 | + | 14.6969i | −0.883053 | + | 0.883053i | −0.993844 | − | 0.110790i | \(-0.964662\pi\) |
0.110790 | + | 0.993844i | \(0.464662\pi\) | |||||||
\(278\) | −2.82843 | + | 2.82843i | −0.169638 | + | 0.169638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 31.1769i | − | 1.85986i | −0.367738 | − | 0.929929i | \(-0.619868\pi\) | ||
0.367738 | − | 0.929929i | \(-0.380132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.34847 | − | 7.34847i | −0.436821 | − | 0.436821i | 0.454120 | − | 0.890941i | \(-0.349954\pi\) |
−0.890941 | + | 0.454120i | \(0.849954\pi\) | |||||||
\(284\) | −10.3923 | −0.616670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.0000 | −1.59654 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 8.00000i | − | 0.470588i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.34847 | + | 7.34847i | −0.430037 | + | 0.430037i | ||||
\(293\) | 4.24264 | − | 4.24264i | 0.247858 | − | 0.247858i | −0.572233 | − | 0.820091i | \(-0.693923\pi\) |
0.820091 | + | 0.572233i | \(0.193923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.0227 | + | 11.0227i | 0.638528 | + | 0.638528i | ||||
\(299\) | 15.5885 | 0.901504 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.4350 | + | 13.4350i | 0.773099 | + | 0.773099i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000i | 0.114708i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0227 | + | 11.0227i | −0.629099 | + | 0.629099i | −0.947841 | − | 0.318742i | \(-0.896740\pi\) |
0.318742 | + | 0.947841i | \(0.396740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.3923i | − | 0.589294i | −0.955606 | − | 0.294647i | \(-0.904798\pi\) | ||
0.955606 | − | 0.294647i | \(-0.0952020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0454 | + | 22.0454i | 1.24608 | + | 1.24608i | 0.957437 | + | 0.288643i | \(0.0932042\pi\) |
0.288643 | + | 0.957437i | \(0.406796\pi\) | |||||||
\(314\) | −5.19615 | −0.293236 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.00000 | 0.0562544 | ||||||||
\(317\) | 8.48528 | + | 8.48528i | 0.476581 | + | 0.476581i | 0.904036 | − | 0.427456i | \(-0.140590\pi\) |
−0.427456 | + | 0.904036i | \(0.640590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.0000i | − | 1.51171i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.24264 | + | 4.24264i | −0.236067 | + | 0.236067i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 15.5885i | − | 0.863365i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.34847 | − | 7.34847i | −0.405751 | − | 0.405751i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0000 | 1.42909 | 0.714545 | − | 0.699590i | \(-0.246634\pi\) | ||||
0.714545 | + | 0.699590i | \(0.246634\pi\) | |||||||
\(332\) | 8.48528 | + | 8.48528i | 0.465690 | + | 0.465690i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000i | 0.656611i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | −9.89949 | + | 9.89949i | −0.538462 | + | 0.538462i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 25.9808i | − | 1.40694i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.19615 | −0.280158 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0000 | 1.29025 | ||||||||
\(347\) | −12.7279 | − | 12.7279i | −0.683271 | − | 0.683271i | 0.277465 | − | 0.960736i | \(-0.410506\pi\) |
−0.960736 | + | 0.277465i | \(0.910506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0000i | 1.49881i | 0.662114 | + | 0.749403i | \(0.269659\pi\) | ||||
−0.662114 | + | 0.749403i | \(0.730341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.67423 | − | 3.67423i | 0.195837 | − | 0.195837i | ||||
\(353\) | 6.36396 | − | 6.36396i | 0.338719 | − | 0.338719i | −0.517166 | − | 0.855885i | \(-0.673013\pi\) |
0.855885 | + | 0.517166i | \(0.173013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 10.3923i | − | 0.550791i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.34847 | + | 7.34847i | 0.388379 | + | 0.388379i | ||||
\(359\) | 10.3923 | 0.548485 | 0.274242 | − | 0.961661i | \(-0.411573\pi\) | ||||
0.274242 | + | 0.961661i | \(0.411573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −1.41421 | − | 1.41421i | −0.0743294 | − | 0.0743294i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.34847 | + | 7.34847i | −0.383587 | + | 0.383587i | −0.872393 | − | 0.488806i | \(-0.837433\pi\) |
0.488806 | + | 0.872393i | \(0.337433\pi\) | |||||||
\(368\) | −2.12132 | + | 2.12132i | −0.110581 | + | 0.110581i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.67423 | + | 3.67423i | 0.190245 | + | 0.190245i | 0.795802 | − | 0.605557i | \(-0.207050\pi\) |
−0.605557 | + | 0.795802i | \(0.707050\pi\) | |||||||
\(374\) | 15.5885 | 0.806060 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | −19.0919 | − | 19.0919i | −0.983282 | − | 0.983282i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.34847 | − | 7.34847i | 0.375980 | − | 0.375980i | ||||
\(383\) | 10.6066 | − | 10.6066i | 0.541972 | − | 0.541972i | −0.382135 | − | 0.924107i | \(-0.624811\pi\) |
0.924107 | + | 0.382135i | \(0.124811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.7846i | 1.05791i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.34847 | + | 7.34847i | 0.373062 | + | 0.373062i | ||||
\(389\) | −15.5885 | −0.790366 | −0.395183 | − | 0.918602i | \(-0.629319\pi\) | ||||
−0.395183 | + | 0.918602i | \(0.629319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | −0.455150 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 6.00000i | − | 0.302276i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.7196 | + | 25.7196i | −1.29083 | + | 1.29083i | −0.356559 | + | 0.934273i | \(0.616050\pi\) |
−0.934273 | + | 0.356559i | \(0.883950\pi\) | |||||||
\(398\) | −7.77817 | + | 7.77817i | −0.389885 | + | 0.389885i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.3712 | − | 18.3712i | −0.915133 | − | 0.915133i | ||||
\(404\) | −5.19615 | −0.258518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.00000i | − | 0.247234i | −0.992330 | − | 0.123617i | \(-0.960551\pi\) | ||
0.992330 | − | 0.123617i | \(-0.0394494\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.34847 | − | 7.34847i | 0.362033 | − | 0.362033i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 5.19615i | − | 0.254762i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.34847 | + | 7.34847i | 0.359425 | + | 0.359425i | ||||
\(419\) | 15.5885 | 0.761546 | 0.380773 | − | 0.924669i | \(-0.375658\pi\) | ||||
0.380773 | + | 0.924669i | \(0.375658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −2.82843 | − | 2.82843i | −0.137686 | − | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.0000i | − | 0.582772i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.7279 | − | 12.7279i | 0.615227 | − | 0.615227i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.7846i | − | 1.00116i | −0.865690 | − | 0.500580i | \(-0.833120\pi\) | ||
0.865690 | − | 0.500580i | \(-0.166880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.34847 | + | 7.34847i | 0.353145 | + | 0.353145i | 0.861278 | − | 0.508133i | \(-0.169664\pi\) |
−0.508133 | + | 0.861278i | \(0.669664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | 0.766261 | ||||||||
\(437\) | −4.24264 | − | 4.24264i | −0.202953 | − | 0.202953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000i | 0.381819i | 0.981608 | + | 0.190910i | \(0.0611437\pi\) | ||||
−0.981608 | + | 0.190910i | \(0.938856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.0227 | − | 11.0227i | 0.524297 | − | 0.524297i | ||||
\(443\) | 4.24264 | − | 4.24264i | 0.201574 | − | 0.201574i | −0.599100 | − | 0.800674i | \(-0.704475\pi\) |
0.800674 | + | 0.599100i | \(0.204475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 10.3923i | − | 0.492090i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7846 | 0.980886 | 0.490443 | − | 0.871473i | \(-0.336835\pi\) | ||||
0.490443 | + | 0.871473i | \(0.336835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −54.0000 | −2.54276 | ||||||||
\(452\) | 6.36396 | + | 6.36396i | 0.299336 | + | 0.299336i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6969 | + | 14.6969i | −0.687494 | + | 0.687494i | −0.961677 | − | 0.274184i | \(-0.911592\pi\) |
0.274184 | + | 0.961677i | \(0.411592\pi\) | |||||||
\(458\) | 9.89949 | − | 9.89949i | 0.462573 | − | 0.462573i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.5692i | 1.93607i | 0.250812 | + | 0.968036i | \(0.419302\pi\) | ||||
−0.250812 | + | 0.968036i | \(0.580698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.34847 | − | 7.34847i | −0.341512 | − | 0.341512i | 0.515423 | − | 0.856936i | \(-0.327635\pi\) |
−0.856936 | + | 0.515423i | \(0.827635\pi\) | |||||||
\(464\) | 5.19615 | 0.241225 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.0000 | −0.833834 | ||||||||
\(467\) | 21.2132 | + | 21.2132i | 0.981630 | + | 0.981630i | 0.999834 | − | 0.0182043i | \(-0.00579493\pi\) |
−0.0182043 | + | 0.999834i | \(0.505795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.34847 | − | 7.34847i | 0.338241 | − | 0.338241i | ||||
\(473\) | −19.0919 | + | 19.0919i | −0.877846 | + | 0.877846i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.3923 | −0.474837 | −0.237418 | − | 0.971408i | \(-0.576301\pi\) | ||||
−0.237418 | + | 0.971408i | \(0.576301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.707107 | − | 0.707107i | −0.0322078 | − | 0.0322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 16.0000i | − | 0.727273i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6969 | − | 14.6969i | 0.665982 | − | 0.665982i | −0.290802 | − | 0.956783i | \(-0.593922\pi\) |
0.956783 | + | 0.290802i | \(0.0939219\pi\) | |||||||
\(488\) | −5.65685 | + | 5.65685i | −0.256074 | + | 0.256074i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3923i | 0.468998i | 0.972116 | + | 0.234499i | \(0.0753450\pi\) | ||||
−0.972116 | + | 0.234499i | \(0.924655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0227 | + | 11.0227i | 0.496438 | + | 0.496438i | ||||
\(494\) | 10.3923 | 0.467572 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 40.0000i | − | 1.79065i | −0.445418 | − | 0.895323i | \(-0.646945\pi\) | ||
0.445418 | − | 0.895323i | \(-0.353055\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.0227 | − | 11.0227i | 0.491967 | − | 0.491967i | ||||
\(503\) | 14.8492 | − | 14.8492i | 0.662095 | − | 0.662095i | −0.293779 | − | 0.955874i | \(-0.594913\pi\) |
0.955874 | + | 0.293779i | \(0.0949128\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.5885i | 0.692991i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.6969 | + | 14.6969i | 0.652071 | + | 0.652071i | ||||
\(509\) | −15.5885 | −0.690946 | −0.345473 | − | 0.938429i | \(-0.612282\pi\) | ||||
−0.345473 | + | 0.938429i | \(0.612282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0000i | 0.661622i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.0681 | + | 33.0681i | −1.45433 | + | 1.45433i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.1769i | 1.36589i | 0.730472 | + | 0.682943i | \(0.239300\pi\) | ||||
−0.730472 | + | 0.682943i | \(0.760700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7196 | − | 25.7196i | −1.12464 | − | 1.12464i | −0.991034 | − | 0.133607i | \(-0.957344\pi\) |
−0.133607 | − | 0.991034i | \(-0.542656\pi\) | |||||||
\(524\) | 5.19615 | 0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.6066 | + | 10.6066i | 0.462031 | + | 0.462031i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0000i | 0.608696i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.1838 | + | 38.1838i | −1.65392 | + | 1.65392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.3923i | 0.448879i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.67423 | + | 3.67423i | 0.158408 | + | 0.158408i | ||||
\(539\) | −36.3731 | −1.56670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | −11.3137 | − | 11.3137i | −0.485965 | − | 0.485965i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000i | 0.128624i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7196 | − | 25.7196i | 1.09969 | − | 1.09969i | 0.105246 | − | 0.994446i | \(-0.466437\pi\) |
0.994446 | − | 0.105246i | \(-0.0335631\pi\) | |||||||
\(548\) | −4.24264 | + | 4.24264i | −0.181237 | + | 0.181237i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3923i | 0.442727i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.7846 | −0.883053 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 12.7279 | + | 12.7279i | 0.539299 | + | 0.539299i | 0.923323 | − | 0.384024i | \(-0.125462\pi\) |
−0.384024 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.0000i | 1.14198i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.0454 | − | 22.0454i | 0.929929 | − | 0.929929i | ||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 10.3923i | − | 0.436821i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.34847 | − | 7.34847i | −0.308335 | − | 0.308335i | ||||
\(569\) | 20.7846 | 0.871336 | 0.435668 | − | 0.900107i | \(-0.356512\pi\) | ||||
0.435668 | + | 0.900107i | \(0.356512\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | −19.0919 | − | 19.0919i | −0.798272 | − | 0.798272i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6969 | − | 14.6969i | 0.611842 | − | 0.611842i | −0.331584 | − | 0.943426i | \(-0.607583\pi\) |
0.943426 | + | 0.331584i | \(0.107583\pi\) | |||||||
\(578\) | 5.65685 | − | 5.65685i | 0.235294 | − | 0.235294i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.0908 | − | 44.0908i | −1.82605 | − | 1.82605i | ||||
\(584\) | −10.3923 | −0.430037 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 16.9706 | + | 16.9706i | 0.700450 | + | 0.700450i | 0.964507 | − | 0.264057i | \(-0.0850607\pi\) |
−0.264057 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000i | 0.412043i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.5772 | − | 27.5772i | 1.13246 | − | 1.13246i | 0.142691 | − | 0.989767i | \(-0.454424\pi\) |
0.989767 | − | 0.142691i | \(-0.0455756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.5885i | 0.638528i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.0227 | + | 11.0227i | 0.450752 | + | 0.450752i | ||||
\(599\) | 10.3923 | 0.424618 | 0.212309 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212309 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.0000i | 0.773099i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0454 | + | 22.0454i | −0.894795 | + | 0.894795i | −0.994970 | − | 0.100174i | \(-0.968060\pi\) |
0.100174 | + | 0.994970i | \(0.468060\pi\) | |||||||
\(608\) | −1.41421 | + | 1.41421i | −0.0573539 | + | 0.0573539i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.7654i | 1.89192i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.3712 | − | 18.3712i | −0.742005 | − | 0.742005i | 0.230959 | − | 0.972964i | \(-0.425814\pi\) |
−0.972964 | + | 0.230959i | \(0.925814\pi\) | |||||||
\(614\) | −15.5885 | −0.629099 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5772 | − | 27.5772i | −1.11021 | − | 1.11021i | −0.993121 | − | 0.117094i | \(-0.962642\pi\) |
−0.117094 | − | 0.993121i | \(-0.537358\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.0000i | − | 0.401934i | −0.979598 | − | 0.200967i | \(-0.935592\pi\) | ||
0.979598 | − | 0.200967i | \(-0.0644084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.34847 | − | 7.34847i | 0.294647 | − | 0.294647i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.1769i | 1.24608i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.67423 | − | 3.67423i | −0.146618 | − | 0.146618i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 0.707107 | + | 0.707107i | 0.0281272 | + | 0.0281272i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000i | 0.476581i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.7196 | + | 25.7196i | −1.01905 | + | 1.01905i | ||||
\(638\) | 19.0919 | − | 19.0919i | 0.755855 | − | 0.755855i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.7846i | − | 0.820943i | −0.911873 | − | 0.410471i | \(-0.865364\pi\) | ||
0.911873 | − | 0.410471i | \(-0.134636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.0227 | − | 11.0227i | −0.434693 | − | 0.434693i | 0.455528 | − | 0.890221i | \(-0.349450\pi\) |
−0.890221 | + | 0.455528i | \(0.849450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | −0.236067 | ||||||||
\(647\) | −16.9706 | − | 16.9706i | −0.667182 | − | 0.667182i | 0.289881 | − | 0.957063i | \(-0.406384\pi\) |
−0.957063 | + | 0.289881i | \(0.906384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 54.0000i | − | 2.11969i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.0227 | − | 11.0227i | 0.431682 | − | 0.431682i | ||||
\(653\) | 4.24264 | − | 4.24264i | 0.166027 | − | 0.166027i | −0.619203 | − | 0.785231i | \(-0.712544\pi\) |
0.785231 | + | 0.619203i | \(0.212544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 10.3923i | − | 0.405751i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1769 | −1.21448 | −0.607240 | − | 0.794518i | \(-0.707723\pi\) | ||||
−0.607240 | + | 0.794518i | \(0.707723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.0000 | −1.24466 | −0.622328 | − | 0.782757i | \(-0.713813\pi\) | ||||
−0.622328 | + | 0.782757i | \(0.713813\pi\) | |||||||
\(662\) | 18.3848 | + | 18.3848i | 0.714545 | + | 0.714545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000i | 0.465690i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0227 | + | 11.0227i | −0.426801 | + | 0.426801i | ||||
\(668\) | −8.48528 | + | 8.48528i | −0.328305 | + | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.5692i | 1.60476i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6969 | + | 14.6969i | 0.566525 | + | 0.566525i | 0.931153 | − | 0.364628i | \(-0.118804\pi\) |
−0.364628 | + | 0.931153i | \(0.618804\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.0000 | −0.538462 | ||||||||
\(677\) | −25.4558 | − | 25.4558i | −0.978348 | − | 0.978348i | 0.0214229 | − | 0.999771i | \(-0.493180\pi\) |
−0.999771 | + | 0.0214229i | \(0.993180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 18.3712 | − | 18.3712i | 0.703469 | − | 0.703469i | ||||
\(683\) | 16.9706 | − | 16.9706i | 0.649361 | − | 0.649361i | −0.303478 | − | 0.952838i | \(-0.598148\pi\) |
0.952838 | + | 0.303478i | \(0.0981479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.67423 | − | 3.67423i | −0.140079 | − | 0.140079i | ||||
\(689\) | −62.3538 | −2.37549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 16.9706 | + | 16.9706i | 0.645124 | + | 0.645124i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 18.0000i | − | 0.683271i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0454 | − | 22.0454i | 0.835029 | − | 0.835029i | ||||
\(698\) | −19.7990 | + | 19.7990i | −0.749403 | + | 0.749403i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.3731i | 1.37379i | 0.726756 | + | 0.686896i | \(0.241027\pi\) | ||||
−0.726756 | + | 0.686896i | \(0.758973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.19615 | 0.195837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | 0.338719 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0000i | 1.05156i | 0.850620 | + | 0.525781i | \(0.176227\pi\) | ||||
−0.850620 | + | 0.525781i | \(0.823773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.34847 | − | 7.34847i | 0.275396 | − | 0.275396i | ||||
\(713\) | −10.6066 | + | 10.6066i | −0.397220 | + | 0.397220i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.3923i | 0.388379i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.34847 | + | 7.34847i | 0.274242 | + | 0.274242i | ||||
\(719\) | −41.5692 | −1.55027 | −0.775135 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775135 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.6066 | + | 10.6066i | 0.394737 | + | 0.394737i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2.00000i | − | 0.0743294i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.5885i | − | 0.576560i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.3939 | − | 29.3939i | −1.08569 | − | 1.08569i | −0.995967 | − | 0.0897206i | \(-0.971403\pi\) |
−0.0897206 | − | 0.995967i | \(-0.528597\pi\) | |||||||
\(734\) | −10.3923 | −0.383587 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 38.1838 | + | 38.1838i | 1.40652 | + | 1.40652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0000i | 1.25071i | 0.780340 | + | 0.625355i | \(0.215046\pi\) | ||||
−0.780340 | + | 0.625355i | \(0.784954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.0919 | + | 19.0919i | −0.700413 | + | 0.700413i | −0.964499 | − | 0.264086i | \(-0.914930\pi\) |
0.264086 | + | 0.964499i | \(0.414930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.19615i | 0.190245i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.0227 | + | 11.0227i | 0.403030 | + | 0.403030i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0000 | −0.839282 | −0.419641 | − | 0.907690i | \(-0.637844\pi\) | ||||
−0.419641 | + | 0.907690i | \(0.637844\pi\) | |||||||
\(752\) | −6.36396 | − | 6.36396i | −0.232070 | − | 0.232070i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 27.0000i | − | 0.983282i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.7196 | + | 25.7196i | −0.934796 | + | 0.934796i | −0.998001 | − | 0.0632043i | \(-0.979868\pi\) |
0.0632043 | + | 0.998001i | \(0.479868\pi\) | |||||||
\(758\) | −11.3137 | + | 11.3137i | −0.410932 | + | 0.410932i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7846i | 0.753442i | 0.926327 | + | 0.376721i | \(0.122948\pi\) | ||||
−0.926327 | + | 0.376721i | \(0.877052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.3923 | 0.375980 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0000 | 0.541972 | ||||||||
\(767\) | −38.1838 | − | 38.1838i | −1.37874 | − | 1.37874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.0000i | − | 0.468792i | −0.972141 | − | 0.234396i | \(-0.924689\pi\) | ||
0.972141 | − | 0.234396i | \(-0.0753112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.6969 | + | 14.6969i | −0.528954 | + | 0.528954i | ||||
\(773\) | 21.2132 | − | 21.2132i | 0.762986 | − | 0.762986i | −0.213875 | − | 0.976861i | \(-0.568609\pi\) |
0.976861 | + | 0.213875i | \(0.0686086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.3923i | 0.373062i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.0227 | − | 11.0227i | −0.395183 | − | 0.395183i | ||||
\(779\) | 20.7846 | 0.744686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | −6.36396 | − | 6.36396i | −0.227575 | − | 0.227575i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3712 | − | 18.3712i | 0.654862 | − | 0.654862i | −0.299298 | − | 0.954160i | \(-0.596752\pi\) |
0.954160 | + | 0.299298i | \(0.0967525\pi\) | |||||||
\(788\) | 4.24264 | − | 4.24264i | 0.151138 | − | 0.151138i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3939 | + | 29.3939i | 1.04381 | + | 1.04381i | ||||
\(794\) | −36.3731 | −1.29083 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0000 | −0.389885 | ||||||||
\(797\) | 21.2132 | + | 21.2132i | 0.751410 | + | 0.751410i | 0.974742 | − | 0.223332i | \(-0.0716935\pi\) |
−0.223332 | + | 0.974742i | \(0.571693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 27.0000i | − | 0.955191i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.1838 | + | 38.1838i | −1.34748 | + | 1.34748i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 25.9808i | − | 0.915133i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.67423 | − | 3.67423i | −0.129259 | − | 0.129259i | ||||
\(809\) | −20.7846 | −0.730748 | −0.365374 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365374 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.34847 | − | 7.34847i | 0.257090 | − | 0.257090i | ||||
\(818\) | 3.53553 | − | 3.53553i | 0.123617 | − | 0.123617i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.5692i | 1.45078i | 0.688340 | + | 0.725388i | \(0.258340\pi\) | ||||
−0.688340 | + | 0.725388i | \(0.741660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.6969 | − | 14.6969i | −0.512303 | − | 0.512303i | 0.402928 | − | 0.915231i | \(-0.367992\pi\) |
−0.915231 | + | 0.402928i | \(0.867992\pi\) | |||||||
\(824\) | 10.3923 | 0.362033 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6985 | + | 29.6985i | 1.03272 | + | 1.03272i | 0.999446 | + | 0.0332711i | \(0.0105925\pi\) |
0.0332711 | + | 0.999446i | \(0.489408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.0000i | − | 0.694629i | −0.937749 | − | 0.347314i | \(-0.887094\pi\) | ||
0.937749 | − | 0.347314i | \(-0.112906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.67423 | − | 3.67423i | 0.127381 | − | 0.127381i | ||||
\(833\) | 14.8492 | − | 14.8492i | 0.514496 | − | 0.514496i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.3923i | 0.359425i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.0227 | + | 11.0227i | 0.380773 | + | 0.380773i | ||||
\(839\) | −10.3923 | −0.358782 | −0.179391 | − | 0.983778i | \(-0.557413\pi\) | ||||
−0.179391 | + | 0.983778i | \(0.557413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | 7.07107 | + | 7.07107i | 0.243685 | + | 0.243685i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.00000i | − | 0.137686i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.48528 | − | 8.48528i | 0.291386 | − | 0.291386i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.67423 | − | 3.67423i | −0.125803 | − | 0.125803i | 0.641402 | − | 0.767205i | \(-0.278353\pi\) |
−0.767205 | + | 0.641402i | \(0.778353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 4.24264 | + | 4.24264i | 0.144926 | + | 0.144926i | 0.775847 | − | 0.630921i | \(-0.217323\pi\) |
−0.630921 | + | 0.775847i | \(0.717323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.0000i | 1.70598i | 0.521929 | + | 0.852989i | \(0.325213\pi\) | ||||
−0.521929 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6969 | − | 14.6969i | 0.500580 | − | 0.500580i | ||||
\(863\) | 36.0624 | − | 36.0624i | 1.22758 | − | 1.22758i | 0.262703 | − | 0.964877i | \(-0.415386\pi\) |
0.964877 | − | 0.262703i | \(-0.0846140\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.3923i | 0.353145i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19615 | 0.176267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.0000 | 1.82972 | ||||||||
\(872\) | 11.3137 | + | 11.3137i | 0.383131 | + | 0.383131i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6.00000i | − | 0.202953i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0227 | + | 11.0227i | −0.372210 | + | 0.372210i | −0.868282 | − | 0.496071i | \(-0.834775\pi\) |
0.496071 | + | 0.868282i | \(0.334775\pi\) | |||||||
\(878\) | −5.65685 | + | 5.65685i | −0.190910 | + | 0.190910i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.3923i | − | 0.350126i | −0.984557 | − | 0.175063i | \(-0.943987\pi\) | ||
0.984557 | − | 0.175063i | \(-0.0560129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.34847 | − | 7.34847i | −0.247296 | − | 0.247296i | 0.572564 | − | 0.819860i | \(-0.305949\pi\) |
−0.819860 | + | 0.572564i | \(0.805949\pi\) | |||||||
\(884\) | 15.5885 | 0.524297 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | 0.201574 | ||||||||
\(887\) | −40.3051 | − | 40.3051i | −1.35331 | − | 1.35331i | −0.881928 | − | 0.471385i | \(-0.843754\pi\) |
−0.471385 | − | 0.881928i | \(-0.656246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.34847 | − | 7.34847i | 0.246045 | − | 0.246045i | ||||
\(893\) | 12.7279 | − | 12.7279i | 0.425924 | − | 0.425924i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.6969 | + | 14.6969i | 0.490443 | + | 0.490443i | ||||
\(899\) | 25.9808 | 0.866507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | −38.1838 | − | 38.1838i | −1.27138 | − | 1.27138i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000i | 0.299336i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.3712 | + | 18.3712i | −0.610005 | + | 0.610005i | −0.942947 | − | 0.332942i | \(-0.891959\pi\) |
0.332942 | + | 0.942947i | \(0.391959\pi\) | |||||||
\(908\) | 4.24264 | − | 4.24264i | 0.140797 | − | 0.140797i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5692i | 1.37725i | 0.725118 | + | 0.688625i | \(0.241785\pi\) | ||||
−0.725118 | + | 0.688625i | \(0.758215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.0908 | + | 44.0908i | 1.45919 | + | 1.45919i | ||||
\(914\) | −20.7846 | −0.687494 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0000i | 0.824674i | 0.911031 | + | 0.412337i | \(0.135287\pi\) | ||||
−0.911031 | + | 0.412337i | \(0.864713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.3939 | + | 29.3939i | −0.968036 | + | 0.968036i | ||||
\(923\) | −38.1838 | + | 38.1838i | −1.25683 | + | 1.25683i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 10.3923i | − | 0.341512i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.67423 | + | 3.67423i | 0.120613 | + | 0.120613i | ||||
\(929\) | 10.3923 | 0.340960 | 0.170480 | − | 0.985361i | \(-0.445468\pi\) | ||||
0.170480 | + | 0.985361i | \(0.445468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0000 | 0.458831 | ||||||||
\(932\) | −12.7279 | − | 12.7279i | −0.416917 | − | 0.416917i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0000i | 0.981630i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 46.7654i | − | 1.52451i | −0.647278 | − | 0.762254i | \(-0.724093\pi\) | ||
0.647278 | − | 0.762254i | \(-0.275907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.0454 | + | 22.0454i | 0.717897 | + | 0.717897i | ||||
\(944\) | 10.3923 | 0.338241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.0000 | −0.877846 | ||||||||
\(947\) | −8.48528 | − | 8.48528i | −0.275735 | − | 0.275735i | 0.555669 | − | 0.831404i | \(-0.312462\pi\) |
−0.831404 | + | 0.555669i | \(0.812462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.0000i | 1.75291i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.36396 | − | 6.36396i | 0.206149 | − | 0.206149i | −0.596479 | − | 0.802628i | \(-0.703434\pi\) |
0.802628 | + | 0.596479i | \(0.203434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.34847 | − | 7.34847i | −0.237418 | − | 0.237418i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00000i | − | 0.0322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.34847 | − | 7.34847i | 0.236311 | − | 0.236311i | −0.579010 | − | 0.815321i | \(-0.696561\pi\) |
0.815321 | + | 0.579010i | \(0.196561\pi\) | |||||||
\(968\) | 11.3137 | − | 11.3137i | 0.363636 | − | 0.363636i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 25.9808i | − | 0.833762i | −0.908961 | − | 0.416881i | \(-0.863123\pi\) | ||
0.908961 | − | 0.416881i | \(-0.136877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.7846 | 0.665982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 19.0919 | + | 19.0919i | 0.610803 | + | 0.610803i | 0.943155 | − | 0.332352i | \(-0.107842\pi\) |
−0.332352 | + | 0.943155i | \(0.607842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 54.0000i | − | 1.72585i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.34847 | + | 7.34847i | −0.234499 | + | 0.234499i | ||||
\(983\) | −10.6066 | + | 10.6066i | −0.338298 | + | 0.338298i | −0.855726 | − | 0.517428i | \(-0.826889\pi\) |
0.517428 | + | 0.855726i | \(0.326889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.5885i | 0.496438i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.34847 | + | 7.34847i | 0.233786 | + | 0.233786i | ||||
\(989\) | 15.5885 | 0.495684 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0000 | −0.794151 | −0.397076 | − | 0.917786i | \(-0.629975\pi\) | ||||
−0.397076 | + | 0.917786i | \(0.629975\pi\) | |||||||
\(992\) | 3.53553 | + | 3.53553i | 0.112253 | + | 0.112253i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0227 | + | 11.0227i | −0.349093 | + | 0.349093i | −0.859771 | − | 0.510679i | \(-0.829394\pi\) |
0.510679 | + | 0.859771i | \(0.329394\pi\) | |||||||
\(998\) | 28.2843 | − | 28.2843i | 0.895323 | − | 0.895323i | ||||
\(999\) | 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 | 1350.2.f.c.593.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1350.2.f.c.593.1 | yes | 8 | |
5.2 | odd | 4 | inner | 1350.2.f.c.107.2 | yes | 8 | |
5.3 | odd | 4 | inner | 1350.2.f.c.107.4 | yes | 8 | |
5.4 | even | 2 | inner | 1350.2.f.c.593.2 | yes | 8 | |
15.2 | even | 4 | inner | 1350.2.f.c.107.3 | yes | 8 | |
15.8 | even | 4 | inner | 1350.2.f.c.107.1 | ✓ | 8 | |
15.14 | odd | 2 | inner | 1350.2.f.c.593.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.2.f.c.107.1 | ✓ | 8 | 15.8 | even | 4 | inner | |
1350.2.f.c.107.2 | yes | 8 | 5.2 | odd | 4 | inner | |
1350.2.f.c.107.3 | yes | 8 | 15.2 | even | 4 | inner | |
1350.2.f.c.107.4 | yes | 8 | 5.3 | odd | 4 | inner | |
1350.2.f.c.593.1 | yes | 8 | 3.2 | odd | 2 | inner | |
1350.2.f.c.593.2 | yes | 8 | 5.4 | even | 2 | inner | |
1350.2.f.c.593.3 | yes | 8 | 15.14 | odd | 2 | inner | |
1350.2.f.c.593.4 | yes | 8 | 1.1 | even | 1 | trivial |