Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, 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("2880.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bl (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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 431.3 | ||
Character | \(\chi\) | \(=\) | 2880.431 |
Dual form | 2880.2.bl.b.1871.3 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.527405 | 0.199340 | 0.0996702 | − | 0.995021i | \(-0.468221\pi\) | ||||
0.0996702 | + | 0.995021i | \(0.468221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36838 | − | 1.36838i | 0.412582 | − | 0.412582i | −0.470055 | − | 0.882637i | \(-0.655766\pi\) |
0.882637 | + | 0.470055i | \(0.155766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.79215 | − | 2.79215i | −0.774403 | − | 0.774403i | 0.204470 | − | 0.978873i | \(-0.434453\pi\) |
−0.978873 | + | 0.204470i | \(0.934453\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.68546i | 1.62146i | 0.585419 | + | 0.810731i | \(0.300930\pi\) | ||||
−0.585419 | + | 0.810731i | \(0.699070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.79610 | + | 3.79610i | −0.870886 | + | 0.870886i | −0.992569 | − | 0.121683i | \(-0.961171\pi\) |
0.121683 | + | 0.992569i | \(0.461171\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.00971i | − | 1.04460i | −0.852763 | − | 0.522298i | \(-0.825075\pi\) | ||
0.852763 | − | 0.522298i | \(-0.174925\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.94130 | + | 2.94130i | −0.546185 | + | 0.546185i | −0.925335 | − | 0.379150i | \(-0.876216\pi\) |
0.379150 | + | 0.925335i | \(0.376216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.21862i | − | 1.11690i | −0.829539 | − | 0.558448i | \(-0.811397\pi\) | ||
0.829539 | − | 0.558448i | \(-0.188603\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.372932 | − | 0.372932i | −0.0630370 | − | 0.0630370i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.42437 | + | 6.42437i | −1.05616 | + | 1.05616i | −0.0578329 | + | 0.998326i | \(0.518419\pi\) |
−0.998326 | + | 0.0578329i | \(0.981581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.16008 | −0.337347 | −0.168674 | − | 0.985672i | \(-0.553948\pi\) | ||||
−0.168674 | + | 0.985672i | \(0.553948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.71629 | − | 4.71629i | −0.719228 | − | 0.719228i | 0.249219 | − | 0.968447i | \(-0.419826\pi\) |
−0.968447 | + | 0.249219i | \(0.919826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3428 | 1.65451 | 0.827256 | − | 0.561826i | \(-0.189901\pi\) | ||||
0.827256 | + | 0.561826i | \(0.189901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.72184 | −0.960263 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.23408 | + | 4.23408i | 0.581595 | + | 0.581595i | 0.935342 | − | 0.353746i | \(-0.115092\pi\) |
−0.353746 | + | 0.935342i | \(0.615092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.93518 | −0.260940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.322982 | + | 0.322982i | −0.0420487 | + | 0.0420487i | −0.727818 | − | 0.685770i | \(-0.759466\pi\) |
0.685770 | + | 0.727818i | \(0.259466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.887268 | − | 0.887268i | −0.113603 | − | 0.113603i | 0.648020 | − | 0.761623i | \(-0.275597\pi\) |
−0.761623 | + | 0.648020i | \(0.775597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.94870i | 0.489776i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.24370 | + | 1.24370i | −0.151942 | + | 0.151942i | −0.778985 | − | 0.627043i | \(-0.784265\pi\) |
0.627043 | + | 0.778985i | \(0.284265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3113i | 1.69844i | 0.528041 | + | 0.849219i | \(0.322927\pi\) | ||||
−0.528041 | + | 0.849219i | \(0.677073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.97372i | 0.933254i | 0.884454 | + | 0.466627i | \(0.154531\pi\) | ||||
−0.884454 | + | 0.466627i | \(0.845469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.721691 | − | 0.721691i | 0.0822443 | − | 0.0822443i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.37359i | 0.604576i | 0.953217 | + | 0.302288i | \(0.0977505\pi\) | ||||
−0.953217 | + | 0.302288i | \(0.902250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.43723 | − | 2.43723i | −0.267520 | − | 0.267520i | 0.560580 | − | 0.828100i | \(-0.310578\pi\) |
−0.828100 | + | 0.560580i | \(0.810578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.72733 | − | 4.72733i | 0.512751 | − | 0.512751i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1796 | −1.18504 | −0.592518 | − | 0.805557i | \(-0.701866\pi\) | ||||
−0.592518 | + | 0.805557i | \(0.701866\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.47259 | − | 1.47259i | −0.154370 | − | 0.154370i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.36850 | 0.550797 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.81084 | 0.285398 | 0.142699 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142699 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.95132 | − | 2.95132i | −0.293667 | − | 0.293667i | 0.544860 | − | 0.838527i | \(-0.316583\pi\) |
−0.838527 | + | 0.544860i | \(0.816583\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.36823 | −0.331881 | −0.165941 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165941 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.26471 | + | 2.26471i | −0.218938 | + | 0.218938i | −0.808051 | − | 0.589113i | \(-0.799477\pi\) |
0.589113 | + | 0.808051i | \(0.299477\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.05900 | − | 1.05900i | −0.101433 | − | 0.101433i | 0.654569 | − | 0.756002i | \(-0.272850\pi\) |
−0.756002 | + | 0.654569i | \(0.772850\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6370i | 1.65915i | 0.558395 | + | 0.829575i | \(0.311417\pi\) | ||||
−0.558395 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.54240 | + | 3.54240i | −0.330330 | + | 0.330330i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.52595i | 0.323223i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.25507i | 0.659552i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.3319i | − | 1.27175i | −0.771791 | − | 0.635876i | \(-0.780639\pi\) | ||
0.771791 | − | 0.635876i | \(-0.219361\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.42254 | + | 4.42254i | 0.386399 | + | 0.386399i | 0.873401 | − | 0.487002i | \(-0.161909\pi\) |
−0.487002 | + | 0.873401i | \(0.661909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00209 | + | 2.00209i | −0.173603 | + | 0.173603i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.20075 | −0.102587 | −0.0512937 | − | 0.998684i | \(-0.516334\pi\) | ||||
−0.0512937 | + | 0.998684i | \(0.516334\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.61065 | − | 7.61065i | −0.645527 | − | 0.645527i | 0.306382 | − | 0.951909i | \(-0.400882\pi\) |
−0.951909 | + | 0.306382i | \(0.900882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.64145 | −0.639010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.15962 | 0.345438 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.41054 | − | 5.41054i | −0.443249 | − | 0.443249i | 0.449853 | − | 0.893102i | \(-0.351476\pi\) |
−0.893102 | + | 0.449853i | \(0.851476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3534 | −1.73772 | −0.868858 | − | 0.495062i | \(-0.835146\pi\) | ||||
−0.868858 | + | 0.495062i | \(0.835146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.39723 | + | 4.39723i | −0.353194 | + | 0.353194i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.1462 | − | 16.1462i | −1.28861 | − | 1.28861i | −0.935633 | − | 0.352975i | \(-0.885170\pi\) |
−0.352975 | − | 0.935633i | \(-0.614830\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.64215i | − | 0.208230i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6070 | + | 14.6070i | −1.14411 | + | 1.14411i | −0.156419 | + | 0.987691i | \(0.549995\pi\) |
−0.987691 | + | 0.156419i | \(0.950005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8807i | 0.996741i | 0.866964 | + | 0.498370i | \(0.166068\pi\) | ||||
−0.866964 | + | 0.498370i | \(0.833932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.59221i | 0.199401i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.98756 | − | 1.98756i | 0.151112 | − | 0.151112i | −0.627503 | − | 0.778614i | \(-0.715923\pi\) |
0.778614 | + | 0.627503i | \(0.215923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.527405i | 0.0398681i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6119 | − | 15.6119i | −1.16689 | − | 1.16689i | −0.982935 | − | 0.183954i | \(-0.941110\pi\) |
−0.183954 | − | 0.982935i | \(-0.558890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8656 | + | 11.8656i | −0.881966 | + | 0.881966i | −0.993734 | − | 0.111769i | \(-0.964348\pi\) |
0.111769 | + | 0.993734i | \(0.464348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.08542 | 0.667974 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.14825 | + | 9.14825i | 0.668986 | + | 0.668986i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.83695 | 0.567062 | 0.283531 | − | 0.958963i | \(-0.408494\pi\) | ||||
0.283531 | + | 0.958963i | \(0.408494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.61910 | 0.476453 | 0.238226 | − | 0.971210i | \(-0.423434\pi\) | ||||
0.238226 | + | 0.971210i | \(0.423434\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.0068 | + | 11.0068i | 0.784200 | + | 0.784200i | 0.980537 | − | 0.196336i | \(-0.0629045\pi\) |
−0.196336 | + | 0.980537i | \(0.562904\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.50842 | 0.177817 | 0.0889085 | − | 0.996040i | \(-0.471662\pi\) | ||||
0.0889085 | + | 0.996040i | \(0.471662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.55125 | + | 1.55125i | −0.108877 | + | 0.108877i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52741 | + | 1.52741i | 0.106679 | + | 0.106679i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3890i | 0.718624i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.6265 | + | 15.6265i | −1.07577 | + | 1.07577i | −0.0788863 | + | 0.996884i | \(0.525136\pi\) |
−0.996884 | + | 0.0788863i | \(0.974864\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.66985i | 0.454880i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.27973i | − | 0.222643i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6668 | − | 18.6668i | 1.25567 | − | 1.25567i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.13280i | − | 0.477647i | −0.971063 | − | 0.238824i | \(-0.923238\pi\) | ||
0.971063 | − | 0.238824i | \(-0.0767618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.288353 | − | 0.288353i | −0.0191386 | − | 0.0191386i | 0.697473 | − | 0.716611i | \(-0.254308\pi\) |
−0.716611 | + | 0.697473i | \(0.754308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.34086 | + | 7.34086i | −0.485098 | + | 0.485098i | −0.906755 | − | 0.421658i | \(-0.861448\pi\) |
0.421658 | + | 0.906755i | \(0.361448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.34352 | −0.481090 | −0.240545 | − | 0.970638i | \(-0.577326\pi\) | ||||
−0.240545 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.02054 | − | 8.02054i | −0.523202 | − | 0.523202i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.4178 | 1.70882 | 0.854411 | − | 0.519597i | \(-0.173918\pi\) | ||||
0.854411 | + | 0.519597i | \(0.173918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7860 | 1.14570 | 0.572849 | − | 0.819661i | \(-0.305838\pi\) | ||||
0.572849 | + | 0.819661i | \(0.305838\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.75306 | + | 4.75306i | 0.303662 | + | 0.303662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.1986 | 1.34883 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.9075 | + | 16.9075i | −1.06719 | + | 1.06719i | −0.0696174 | + | 0.997574i | \(0.522178\pi\) |
−0.997574 | + | 0.0696174i | \(0.977822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.85518 | − | 6.85518i | −0.430982 | − | 0.430982i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4607i | 1.46344i | 0.681605 | + | 0.731720i | \(0.261282\pi\) | ||||
−0.681605 | + | 0.731720i | \(0.738718\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.38824 | + | 3.38824i | −0.210535 | + | 0.210535i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.85113i | 0.545784i | 0.962045 | + | 0.272892i | \(0.0879801\pi\) | ||||
−0.962045 | + | 0.272892i | \(0.912020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.98789i | − | 0.367833i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.2562 | − | 19.2562i | 1.17407 | − | 1.17407i | 0.192842 | − | 0.981230i | \(-0.438230\pi\) |
0.981230 | − | 0.192842i | \(-0.0617705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.60120i | − | 0.461740i | −0.972985 | − | 0.230870i | \(-0.925843\pi\) | ||
0.972985 | − | 0.230870i | \(-0.0741573\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.36838 | + | 1.36838i | 0.0825164 | + | 0.0825164i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6425 | − | 10.6425i | 0.639447 | − | 0.639447i | −0.310972 | − | 0.950419i | \(-0.600655\pi\) |
0.950419 | + | 0.310972i | \(0.100655\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.6112 | −1.16991 | −0.584954 | − | 0.811066i | \(-0.698887\pi\) | ||||
−0.584954 | + | 0.811066i | \(0.698887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3190 | + | 17.3190i | 1.02951 | + | 1.02951i | 0.999551 | + | 0.0299545i | \(0.00953625\pi\) |
0.0299545 | + | 0.999551i | \(0.490464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.13924 | −0.0672470 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.6953 | −1.62914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.26943 | − | 4.26943i | −0.249423 | − | 0.249423i | 0.571311 | − | 0.820734i | \(-0.306435\pi\) |
−0.820734 | + | 0.571311i | \(0.806435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.456765 | 0.0265939 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.9879 | + | 13.9879i | −0.808938 | + | 0.808938i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.48740 | − | 2.48740i | −0.143371 | − | 0.143371i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.25479i | 0.0718489i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.1738 | − | 22.1738i | 1.26552 | − | 1.26552i | 0.317147 | − | 0.948376i | \(-0.397275\pi\) |
0.948376 | − | 0.317147i | \(-0.102725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5304i | 0.710536i | 0.934765 | + | 0.355268i | \(0.115610\pi\) | ||||
−0.934765 | + | 0.355268i | \(0.884390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.9129i | − | 0.955974i | −0.878367 | − | 0.477987i | \(-0.841367\pi\) | ||
0.878367 | − | 0.477987i | \(-0.158633\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.49210 | − | 6.49210i | 0.364633 | − | 0.364633i | −0.500882 | − | 0.865515i | \(-0.666991\pi\) |
0.865515 | + | 0.500882i | \(0.166991\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.04962i | 0.450692i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.3787 | − | 25.3787i | −1.41211 | − | 1.41211i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.79215 | − | 2.79215i | 0.154881 | − | 0.154881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.98223 | 0.329811 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.294551 | − | 0.294551i | −0.0161900 | − | 0.0161900i | 0.698965 | − | 0.715155i | \(-0.253644\pi\) |
−0.715155 | + | 0.698965i | \(0.753644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.75886 | 0.0960966 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2233 | −1.21058 | −0.605291 | − | 0.796004i | \(-0.706943\pi\) | ||||
−0.605291 | + | 0.796004i | \(0.706943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.50943 | − | 8.50943i | −0.460812 | − | 0.460812i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.23697 | −0.390760 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.5776 | − | 16.5776i | 0.889930 | − | 0.889930i | −0.104586 | − | 0.994516i | \(-0.533352\pi\) |
0.994516 | + | 0.104586i | \(0.0333518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.60364 | − | 8.60364i | −0.460543 | − | 0.460543i | 0.438291 | − | 0.898833i | \(-0.355584\pi\) |
−0.898833 | + | 0.438291i | \(0.855584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 25.0941i | − | 1.33563i | −0.744329 | − | 0.667813i | \(-0.767231\pi\) | ||
0.744329 | − | 0.667813i | \(-0.232769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1196 | − | 10.1196i | 0.537093 | − | 0.537093i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.8516i | − | 1.15328i | −0.816998 | − | 0.576641i | \(-0.804363\pi\) | ||
0.816998 | − | 0.576641i | \(-0.195637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 9.82081i | − | 0.516885i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.63827 | − | 5.63827i | 0.295121 | − | 0.295121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.06483i | 0.264382i | 0.991224 | + | 0.132191i | \(0.0422012\pi\) | ||||
−0.991224 | + | 0.132191i | \(0.957799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.23308 | + | 2.23308i | 0.115935 | + | 0.115935i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.6071 | + | 21.6071i | −1.11878 | + | 1.11878i | −0.126854 | + | 0.991921i | \(0.540488\pi\) |
−0.991921 | + | 0.126854i | \(0.959512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.4251 | 0.845935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4241 | + | 14.4241i | 0.740918 | + | 0.740918i | 0.972755 | − | 0.231837i | \(-0.0744735\pi\) |
−0.231837 | + | 0.972755i | \(0.574474\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.246311 | −0.0125859 | −0.00629296 | − | 0.999980i | \(-0.502003\pi\) | ||||
−0.00629296 | + | 0.999980i | \(0.502003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.02063 | −0.0520159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.0404 | − | 20.0404i | −1.01609 | − | 1.01609i | −0.999868 | − | 0.0162190i | \(-0.994837\pi\) |
−0.0162190 | − | 0.999868i | \(-0.505163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.4922 | 1.69377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.79970 | − | 3.79970i | 0.191184 | − | 0.191184i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.46763 | − | 5.46763i | −0.274413 | − | 0.274413i | 0.556461 | − | 0.830874i | \(-0.312159\pi\) |
−0.830874 | + | 0.556461i | \(0.812159\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 21.4643i | − | 1.07187i | −0.844258 | − | 0.535937i | \(-0.819959\pi\) | ||
0.844258 | − | 0.535937i | \(-0.180041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.3633 | + | 17.3633i | −0.864928 | + | 0.864928i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5819i | 0.871505i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.9009i | 1.77518i | 0.460631 | + | 0.887592i | \(0.347623\pi\) | ||||
−0.460631 | + | 0.887592i | \(0.652377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.170342 | + | 0.170342i | −0.00838200 | + | 0.00838200i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.44676i | 0.169195i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.1538 | − | 25.1538i | −1.22884 | − | 1.22884i | −0.964402 | − | 0.264440i | \(-0.914813\pi\) |
−0.264440 | − | 0.964402i | \(-0.585187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4663 | − | 19.4663i | 0.948729 | − | 0.948729i | −0.0500192 | − | 0.998748i | \(-0.515928\pi\) |
0.998748 | + | 0.0500192i | \(0.0159283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.68546 | −0.324292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.467950 | − | 0.467950i | −0.0226457 | − | 0.0226457i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.07105 | −0.340600 | −0.170300 | − | 0.985392i | \(-0.554474\pi\) | ||||
−0.170300 | + | 0.985392i | \(0.554474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.9959 | 1.63374 | 0.816868 | − | 0.576824i | \(-0.195708\pi\) | ||||
0.816868 | + | 0.576824i | \(0.195708\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.0174 | + | 19.0174i | 0.909724 | + | 0.909724i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9140 | 0.711804 | 0.355902 | − | 0.934523i | \(-0.384174\pi\) | ||||
0.355902 | + | 0.934523i | \(0.384174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.3933 | − | 19.3933i | 0.921401 | − | 0.921401i | −0.0757274 | − | 0.997129i | \(-0.524128\pi\) |
0.997129 | + | 0.0757274i | \(0.0241279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.90518 | + | 7.90518i | 0.374742 | + | 0.374742i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.7444i | 1.63969i | 0.572586 | + | 0.819844i | \(0.305940\pi\) | ||||
−0.572586 | + | 0.819844i | \(0.694060\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.95581 | + | 2.95581i | −0.139184 | + | 0.139184i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.08256i | 0.0976321i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.46940i | − | 0.209070i | −0.994521 | − | 0.104535i | \(-0.966665\pi\) | ||
0.994521 | − | 0.104535i | \(-0.0333354\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.21550 | + | 4.21550i | −0.196335 | + | 0.196335i | −0.798427 | − | 0.602092i | \(-0.794334\pi\) |
0.602092 | + | 0.798427i | \(0.294334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.8356i | − | 0.735943i | −0.929837 | − | 0.367972i | \(-0.880052\pi\) | ||
0.929837 | − | 0.367972i | \(-0.119948\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1414 | + | 19.1414i | 0.885760 | + | 0.885760i | 0.994113 | − | 0.108352i | \(-0.0345575\pi\) |
−0.108352 | + | 0.994113i | \(0.534558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.655933 | + | 0.655933i | −0.0302882 | + | 0.0302882i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.9074 | −0.593481 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.79610 | − | 3.79610i | −0.174177 | − | 0.174177i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.8319 | −1.81997 | −0.909983 | − | 0.414645i | \(-0.863906\pi\) | ||||
−0.909983 | + | 0.414645i | \(0.863906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.8756 | 1.63579 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.98756 | − | 1.98756i | −0.0902506 | − | 0.0902506i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6470 | 0.844978 | 0.422489 | − | 0.906368i | \(-0.361156\pi\) | ||||
0.422489 | + | 0.906368i | \(0.361156\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.48009 | − | 2.48009i | 0.111925 | − | 0.111925i | −0.648926 | − | 0.760851i | \(-0.724782\pi\) |
0.760851 | + | 0.648926i | \(0.224782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6639 | − | 19.6639i | −0.885618 | − | 0.885618i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.54785i | 0.338567i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.41367 | − | 3.41367i | 0.152817 | − | 0.152817i | −0.626558 | − | 0.779375i | \(-0.715537\pi\) |
0.779375 | + | 0.626558i | \(0.215537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.65191i | − | 0.0736549i | −0.999322 | − | 0.0368274i | \(-0.988275\pi\) | ||
0.999322 | − | 0.0368274i | \(-0.0117252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.17379i | 0.185731i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.87832 | − | 4.87832i | 0.216228 | − | 0.216228i | −0.590679 | − | 0.806907i | \(-0.701140\pi\) |
0.806907 | + | 0.590679i | \(0.201140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.20538i | 0.186035i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.38170 | + | 2.38170i | 0.104950 | + | 0.104950i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.5212 | − | 15.5212i | 0.682622 | − | 0.682622i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9371 | 0.698218 | 0.349109 | − | 0.937082i | \(-0.386484\pi\) | ||||
0.349109 | + | 0.937082i | \(0.386484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8688 | + | 26.8688i | 1.17489 | + | 1.17489i | 0.981029 | + | 0.193861i | \(0.0621009\pi\) |
0.193861 | + | 0.981029i | \(0.437899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.5743 | 1.81100 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.09716 | −0.0911807 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.03126 | + | 6.03126i | 0.261243 | + | 0.261243i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.20279 | 0.138469 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.19804 | + | 9.19804i | −0.396188 | + | 0.396188i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.22798 | + | 4.22798i | 0.181775 | + | 0.181775i | 0.792129 | − | 0.610354i | \(-0.208973\pi\) |
−0.610354 | + | 0.792129i | \(0.708973\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.49765i | 0.0641521i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.243066 | + | 0.243066i | −0.0103928 | + | 0.0103928i | −0.712284 | − | 0.701891i | \(-0.752339\pi\) |
0.701891 | + | 0.712284i | \(0.252339\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 22.3309i | − | 0.951329i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.83406i | 0.120517i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.5236 | + | 19.5236i | −0.827242 | + | 0.827242i | −0.987134 | − | 0.159893i | \(-0.948885\pi\) |
0.159893 | + | 0.987134i | \(0.448885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.3372i | 1.11395i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.1772 | + | 24.1772i | 1.01895 | + | 1.01895i | 0.999817 | + | 0.0191314i | \(0.00609008\pi\) |
0.0191314 | + | 0.999817i | \(0.493910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4713 | − | 12.4713i | 0.524670 | − | 0.524670i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6423 | −0.571916 | −0.285958 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285958 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4689 | − | 17.4689i | −0.731052 | − | 0.731052i | 0.239777 | − | 0.970828i | \(-0.422926\pi\) |
−0.970828 | + | 0.239777i | \(0.922926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.00971 | 0.208919 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.6591 | 1.94244 | 0.971222 | − | 0.238176i | \(-0.0765495\pi\) | ||||
0.971222 | + | 0.238176i | \(0.0765495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.28541 | − | 1.28541i | −0.0533276 | − | 0.0533276i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.5877 | 0.479912 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.11982 | + | 2.11982i | −0.0874944 | + | 0.0874944i | −0.749499 | − | 0.662005i | \(-0.769706\pi\) |
0.662005 | + | 0.749499i | \(0.269706\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.6065 | + | 23.6065i | 0.972689 | + | 0.972689i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 29.5952i | − | 1.21533i | −0.794193 | − | 0.607665i | \(-0.792106\pi\) | ||
0.794193 | − | 0.607665i | \(-0.207894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.49322 | − | 2.49322i | 0.102212 | − | 0.102212i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 23.8940i | − | 0.976283i | −0.872765 | − | 0.488141i | \(-0.837675\pi\) | ||
0.872765 | − | 0.488141i | \(-0.162325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1676i | 0.577909i | 0.957343 | + | 0.288955i | \(0.0933076\pi\) | ||||
−0.957343 | + | 0.288955i | \(0.906692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.13011 | − | 5.13011i | 0.208569 | − | 0.208569i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 34.3109i | − | 1.39263i | −0.717734 | − | 0.696317i | \(-0.754821\pi\) | ||
0.717734 | − | 0.696317i | \(-0.245179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.6707 | − | 31.6707i | −1.28126 | − | 1.28126i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9012 | + | 14.9012i | −0.601855 | + | 0.601855i | −0.940805 | − | 0.338950i | \(-0.889928\pi\) |
0.338950 | + | 0.940805i | \(0.389928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0403 | 0.686015 | 0.343008 | − | 0.939333i | \(-0.388554\pi\) | ||||
0.343008 | + | 0.939333i | \(0.388554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9842 | − | 30.9842i | −1.24536 | − | 1.24536i | −0.957747 | − | 0.287611i | \(-0.907139\pi\) |
−0.287611 | − | 0.957747i | \(-0.592861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.89619 | −0.236226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.9498 | − | 42.9498i | −1.71252 | − | 1.71252i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −47.0036 | −1.87118 | −0.935591 | − | 0.353085i | \(-0.885133\pi\) | ||||
−0.935591 | + | 0.353085i | \(0.885133\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1342 | + | 10.1342i | −0.402164 | + | 0.402164i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.7684 | + | 18.7684i | 0.743631 | + | 0.743631i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.42235i | − | 0.135175i | −0.997713 | − | 0.0675873i | \(-0.978470\pi\) | ||
0.997713 | − | 0.0675873i | \(-0.0215301\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5347 | − | 20.5347i | 0.809809 | − | 0.809809i | −0.174796 | − | 0.984605i | \(-0.555927\pi\) |
0.984605 | + | 0.174796i | \(0.0559266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.6843i | − | 1.20633i | −0.797618 | − | 0.603163i | \(-0.793907\pi\) | ||
0.797618 | − | 0.603163i | \(-0.206093\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.883924i | 0.0346971i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.93695 | − | 5.93695i | 0.232331 | − | 0.232331i | −0.581334 | − | 0.813665i | \(-0.697469\pi\) |
0.813665 | + | 0.581334i | \(0.197469\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.25442i | − | 0.244380i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5713 | − | 21.5713i | −0.840297 | − | 0.840297i | 0.148601 | − | 0.988897i | \(-0.452523\pi\) |
−0.988897 | + | 0.148601i | \(0.952523\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1017 | − | 10.1017i | 0.392911 | − | 0.392911i | −0.482813 | − | 0.875723i | \(-0.660385\pi\) |
0.875723 | + | 0.482813i | \(0.160385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.83138 | 0.109796 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.7350 | + | 14.7350i | 0.570543 | + | 0.570543i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.42824 | −0.0937412 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.35617 | 0.206465 | 0.103233 | − | 0.994657i | \(-0.467081\pi\) | ||||
0.103233 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.3710 | + | 11.3710i | 0.437022 | + | 0.437022i | 0.891009 | − | 0.453986i | \(-0.149998\pi\) |
−0.453986 | + | 0.891009i | \(0.649998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.48245 | 0.0568913 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.71058 | + | 6.71058i | −0.256773 | + | 0.256773i | −0.823740 | − | 0.566967i | \(-0.808117\pi\) |
0.566967 | + | 0.823740i | \(0.308117\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.849062 | + | 0.849062i | 0.0324410 | + | 0.0324410i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 23.6444i | − | 0.900779i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.4167 | + | 23.4167i | −0.890811 | + | 0.890811i | −0.994599 | − | 0.103788i | \(-0.966904\pi\) |
0.103788 | + | 0.994599i | \(0.466904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.7631i | 0.408267i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 14.4411i | − | 0.546996i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.68197 | + | 9.68197i | −0.365683 | + | 0.365683i | −0.865900 | − | 0.500217i | \(-0.833254\pi\) |
0.500217 | + | 0.865900i | \(0.333254\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 48.7751i | − | 1.83959i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.55654 | − | 1.55654i | −0.0585397 | − | 0.0585397i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.3482 | − | 30.3482i | 1.13975 | − | 1.13975i | 0.151254 | − | 0.988495i | \(-0.451669\pi\) |
0.988495 | − | 0.151254i | \(-0.0483313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.1534 | −1.16671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.40332 | + | 5.40332i | 0.202073 | + | 0.202073i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.0246 | 1.26890 | 0.634451 | − | 0.772963i | \(-0.281226\pi\) | ||||
0.634451 | + | 0.772963i | \(0.281226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.77642 | −0.0661574 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.94130 | − | 2.94130i | −0.109237 | − | 0.109237i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.9373 | 1.14740 | 0.573700 | − | 0.819065i | \(-0.305507\pi\) | ||||
0.573700 | + | 0.819065i | \(0.305507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5306 | − | 31.5306i | 1.16620 | − | 1.16620i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.7826 | + | 27.7826i | 1.02617 | + | 1.02617i | 0.999648 | + | 0.0265245i | \(0.00844400\pi\) |
0.0265245 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.40371i | 0.125377i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.9617 | − | 27.9617i | 1.02859 | − | 1.02859i | 0.0290067 | − | 0.999579i | \(-0.490766\pi\) |
0.999579 | − | 0.0290067i | \(-0.00923442\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.366131i | 0.0134321i | 0.999977 | + | 0.00671603i | \(0.00213779\pi\) | ||||
−0.999977 | + | 0.00671603i | \(0.997862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.65166i | 0.280335i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.19442 | + | 1.19442i | −0.0436432 | + | 0.0436432i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18.5853i | − | 0.678186i | −0.940753 | − | 0.339093i | \(-0.889880\pi\) | ||
0.940753 | − | 0.339093i | \(-0.110120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0991 | + | 15.0991i | 0.549514 | + | 0.549514i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.11784 | + | 7.11784i | −0.258702 | + | 0.258702i | −0.824526 | − | 0.565824i | \(-0.808558\pi\) |
0.565824 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2170 | 0.769114 | 0.384557 | − | 0.923101i | \(-0.374354\pi\) | ||||
0.384557 | + | 0.923101i | \(0.374354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.558520 | − | 0.558520i | −0.0202198 | − | 0.0202198i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.80363 | 0.0651252 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.3964 | −1.34855 | −0.674273 | − | 0.738482i | \(-0.735543\pi\) | ||||
−0.674273 | + | 0.738482i | \(0.735543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.67007 | − | 9.67007i | −0.347808 | − | 0.347808i | 0.511484 | − | 0.859293i | \(-0.329096\pi\) |
−0.859293 | + | 0.511484i | \(0.829096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.21862 | 0.223379 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.19988 | − | 8.19988i | 0.293791 | − | 0.293791i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5833 | + | 19.5833i | 0.700745 | + | 0.700745i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.8342i | 0.814987i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.50159 | − | 2.50159i | 0.0891721 | − | 0.0891721i | −0.661114 | − | 0.750286i | \(-0.729916\pi\) |
0.750286 | + | 0.661114i | \(0.229916\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.30185i | 0.330736i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.95477i | 0.175949i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0921 | − | 21.0921i | 0.747121 | − | 0.747121i | −0.226817 | − | 0.973937i | \(-0.572832\pi\) |
0.973937 | + | 0.226817i | \(0.0728319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.8315i | 2.68273i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.9111 | + | 10.9111i | 0.385044 | + | 0.385044i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.86828 | + | 1.86828i | −0.0658482 | + | 0.0658482i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.9517 | −1.89684 | −0.948420 | − | 0.317016i | \(-0.897319\pi\) | ||||
−0.948420 | + | 0.317016i | \(0.897319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7497 | + | 32.7497i | 1.15000 | + | 1.15000i | 0.986552 | + | 0.163445i | \(0.0522605\pi\) |
0.163445 | + | 0.986552i | \(0.447739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.6574 | 0.723598 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.8071 | 1.25273 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.97077 | + | 7.97077i | 0.278182 | + | 0.278182i | 0.832383 | − | 0.554201i | \(-0.186976\pi\) |
−0.554201 | + | 0.832383i | \(0.686976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.9488 | −0.730230 | −0.365115 | − | 0.930962i | \(-0.618970\pi\) | ||||
−0.365115 | + | 0.930962i | \(0.618970\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.12577 | + | 3.12577i | −0.108694 | + | 0.108694i | −0.759362 | − | 0.650668i | \(-0.774489\pi\) |
0.650668 | + | 0.759362i | \(0.274489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.2577 | + | 16.2577i | 0.564655 | + | 0.564655i | 0.930626 | − | 0.365971i | \(-0.119263\pi\) |
−0.365971 | + | 0.930626i | \(0.619263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 44.9386i | − | 1.55703i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.10805 | − | 9.10805i | 0.315197 | − | 0.315197i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 30.7937i | − | 1.06312i | −0.847021 | − | 0.531559i | \(-0.821606\pi\) | ||
0.847021 | − | 0.531559i | \(-0.178394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6976i | 0.403364i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.83297 | − | 1.83297i | 0.0630560 | − | 0.0630560i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.82636i | 0.131475i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.1842 | + | 32.1842i | 1.10326 | + | 1.10326i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.973848 | + | 0.973848i | −0.0333439 | + | 0.0333439i | −0.723582 | − | 0.690238i | \(-0.757506\pi\) |
0.690238 | + | 0.723582i | \(0.257506\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.1170 | 0.618866 | 0.309433 | − | 0.950921i | \(-0.399861\pi\) | ||||
0.309433 | + | 0.950921i | \(0.399861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.9398 | − | 31.9398i | −1.08977 | − | 1.08977i | −0.995551 | − | 0.0942195i | \(-0.969964\pi\) |
−0.0942195 | − | 0.995551i | \(-0.530036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.5050 | −1.68517 | −0.842585 | − | 0.538563i | \(-0.818967\pi\) | ||||
−0.842585 | + | 0.538563i | \(0.818967\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.81084 | −0.0955714 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.35312 | + | 7.35312i | 0.249437 | + | 0.249437i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.94519 | 0.235329 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.372932 | − | 0.372932i | 0.0126074 | − | 0.0126074i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.5440 | − | 14.5440i | −0.491114 | − | 0.491114i | 0.417543 | − | 0.908657i | \(-0.362891\pi\) |
−0.908657 | + | 0.417543i | \(0.862891\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.39383i | 0.148032i | 0.997257 | + | 0.0740159i | \(0.0235816\pi\) | ||||
−0.997257 | + | 0.0740159i | \(0.976418\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.14779 | − | 2.14779i | 0.0722788 | − | 0.0722788i | −0.670043 | − | 0.742322i | \(-0.733724\pi\) |
0.742322 | + | 0.670043i | \(0.233724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.76736i | − | 0.126496i | −0.997998 | − | 0.0632478i | \(-0.979854\pi\) | ||
0.997998 | − | 0.0632478i | \(-0.0201458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.55873i | − | 0.253512i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.0583 | + | 43.0583i | −1.44089 | + | 1.44089i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0786i | 0.738006i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.2908 | + | 18.2908i | 0.610032 | + | 0.610032i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.3068 | + | 28.3068i | −0.943035 | + | 0.943035i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.7805 | 0.557804 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8859 | − | 34.8859i | −1.15837 | − | 1.15837i | −0.984827 | − | 0.173540i | \(-0.944479\pi\) |
−0.173540 | − | 0.984827i | \(-0.555521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5990 | −1.21258 | −0.606290 | − | 0.795244i | \(-0.707343\pi\) | ||||
−0.606290 | + | 0.795244i | \(0.707343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.67010 | −0.220748 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.33247 | + | 2.33247i | 0.0770250 | + | 0.0770250i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.0080 | −0.989874 | −0.494937 | − | 0.868929i | \(-0.664809\pi\) | ||||
−0.494937 | + | 0.868929i | \(0.664809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.9593 | − | 39.9593i | 1.31528 | − | 1.31528i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.42437 | − | 6.42437i | −0.211232 | − | 0.211232i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 28.4741i | − | 0.934206i | −0.884203 | − | 0.467103i | \(-0.845298\pi\) | ||
0.884203 | − | 0.467103i | \(-0.154702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.5168 | − | 25.5168i | 0.836280 | − | 0.836280i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.9376i | − | 0.423104i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47.7787i | − | 1.56086i | −0.625242 | − | 0.780431i | \(-0.715000\pi\) | ||
0.625242 | − | 0.780431i | \(-0.285000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.4584 | + | 21.4584i | −0.699525 | + | 0.699525i | −0.964308 | − | 0.264783i | \(-0.914700\pi\) |
0.264783 | + | 0.964308i | \(0.414700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8214i | 0.352392i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5052 | + | 13.5052i | 0.438859 | + | 0.438859i | 0.891628 | − | 0.452769i | \(-0.149564\pi\) |
−0.452769 | + | 0.891628i | \(0.649564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.2638 | − | 22.2638i | 0.722714 | − | 0.722714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.79285 | 0.252435 | 0.126218 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126218 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.54156 | − | 5.54156i | −0.179321 | − | 0.179321i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.633284 | −0.0204498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.67119 | −0.247458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.68041 | − | 4.68041i | −0.150668 | − | 0.150668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.87264 | −0.221009 | −0.110505 | − | 0.993876i | \(-0.535247\pi\) | ||||
−0.110505 | + | 0.993876i | \(0.535247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6009 | − | 10.6009i | 0.340200 | − | 0.340200i | −0.516243 | − | 0.856442i | \(-0.672670\pi\) |
0.856442 | + | 0.516243i | \(0.172670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.01390 | − | 4.01390i | −0.128680 | − | 0.128680i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.1936i | 0.518080i | 0.965867 | + | 0.259040i | \(0.0834062\pi\) | ||||
−0.965867 | + | 0.259040i | \(0.916594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.2980 | + | 15.2980i | −0.488925 | + | 0.488925i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 12.7286i | − | 0.405978i | −0.979181 | − | 0.202989i | \(-0.934934\pi\) | ||
0.979181 | − | 0.202989i | \(-0.0650655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 15.5659i | − | 0.495972i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.6272 | + | 23.6272i | −0.751303 | + | 0.751303i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 21.4506i | − | 0.681402i | −0.940172 | − | 0.340701i | \(-0.889336\pi\) | ||
0.940172 | − | 0.340701i | \(-0.110664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.77372 | − | 1.77372i | −0.0562306 | − | 0.0562306i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48964 | − | 8.48964i | 0.268870 | − | 0.268870i | −0.559775 | − | 0.828645i | \(-0.689112\pi\) |
0.828645 | + | 0.559775i | \(0.189112\pi\) | |||||||
\(998\) | 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 | 2880.2.bl.b.431.3 | 24 | ||
3.2 | odd | 2 | inner | 2880.2.bl.b.431.9 | 24 | ||
4.3 | odd | 2 | 720.2.bl.b.611.4 | yes | 24 | ||
12.11 | even | 2 | 720.2.bl.b.611.9 | yes | 24 | ||
16.5 | even | 4 | 720.2.bl.b.251.9 | yes | 24 | ||
16.11 | odd | 4 | inner | 2880.2.bl.b.1871.9 | 24 | ||
48.5 | odd | 4 | 720.2.bl.b.251.4 | ✓ | 24 | ||
48.11 | even | 4 | inner | 2880.2.bl.b.1871.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bl.b.251.4 | ✓ | 24 | 48.5 | odd | 4 | ||
720.2.bl.b.251.9 | yes | 24 | 16.5 | even | 4 | ||
720.2.bl.b.611.4 | yes | 24 | 4.3 | odd | 2 | ||
720.2.bl.b.611.9 | yes | 24 | 12.11 | even | 2 | ||
2880.2.bl.b.431.3 | 24 | 1.1 | even | 1 | trivial | ||
2880.2.bl.b.431.9 | 24 | 3.2 | odd | 2 | inner | ||
2880.2.bl.b.1871.3 | 24 | 48.11 | even | 4 | inner | ||
2880.2.bl.b.1871.9 | 24 | 16.11 | odd | 4 | inner |