Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(719,2880)]
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, 1, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.u (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: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 719.9 | ||
Character | \(\chi\) | \(=\) | 2880.719 |
Dual form | 2880.2.u.a.2159.9 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | −1.81012 | + | 1.31281i | −0.809509 | + | 0.587107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40695i | 0.531777i | 0.964004 | + | 0.265889i | \(0.0856653\pi\) | ||||
−0.964004 | + | 0.265889i | \(0.914335\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.176123 | − | 0.176123i | −0.0531031 | − | 0.0531031i | 0.680057 | − | 0.733160i | \(-0.261955\pi\) |
−0.733160 | + | 0.680057i | \(0.761955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.72742 | − | 1.72742i | −0.479100 | − | 0.479100i | 0.425744 | − | 0.904844i | \(-0.360012\pi\) |
−0.904844 | + | 0.425744i | \(0.860012\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15721 | 0.765735 | 0.382867 | − | 0.923803i | \(-0.374937\pi\) | ||||
0.382867 | + | 0.923803i | \(0.374937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.47385 | − | 3.47385i | −0.796956 | − | 0.796956i | 0.185658 | − | 0.982614i | \(-0.440558\pi\) |
−0.982614 | + | 0.185658i | \(0.940558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.97613 | −0.412052 | −0.206026 | − | 0.978546i | \(-0.566053\pi\) | ||||
−0.206026 | + | 0.978546i | \(0.566053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.55305 | − | 4.75269i | 0.310611 | − | 0.950537i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.62046 | + | 2.62046i | 0.486607 | + | 0.486607i | 0.907234 | − | 0.420627i | \(-0.138190\pi\) |
−0.420627 | + | 0.907234i | \(0.638190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.95492i | − | 1.06953i | −0.844999 | − | 0.534767i | \(-0.820399\pi\) | ||
0.844999 | − | 0.534767i | \(-0.179601\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.84706 | − | 2.54675i | −0.312210 | − | 0.430479i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.72522 | + | 5.72522i | −0.941221 | + | 0.941221i | −0.998366 | − | 0.0571453i | \(-0.981800\pi\) |
0.0571453 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.159470 | 0.0249050 | 0.0124525 | − | 0.999922i | \(-0.496036\pi\) | ||||
0.0124525 | + | 0.999922i | \(0.496036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.63058 | − | 6.63058i | −1.01115 | − | 1.01115i | −0.999937 | − | 0.0112162i | \(-0.996430\pi\) |
−0.0112162 | − | 0.999937i | \(-0.503570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.15223i | 0.168069i | 0.996463 | + | 0.0840347i | \(0.0267807\pi\) | ||||
−0.996463 | + | 0.0840347i | \(0.973219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.02049 | 0.717213 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.35087 | + | 5.35087i | 0.734999 | + | 0.734999i | 0.971606 | − | 0.236606i | \(-0.0760352\pi\) |
−0.236606 | + | 0.971606i | \(0.576035\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.550020 | + | 0.0875872i | 0.0741646 | + | 0.0118103i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.48547 | + | 4.48547i | 0.583959 | + | 0.583959i | 0.935989 | − | 0.352030i | \(-0.114508\pi\) |
−0.352030 | + | 0.935989i | \(0.614508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.80718 | − | 6.80718i | 0.871570 | − | 0.871570i | −0.121074 | − | 0.992643i | \(-0.538634\pi\) |
0.992643 | + | 0.121074i | \(0.0386338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.39461 | + | 0.859057i | 0.669118 | + | 0.106553i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.97278 | − | 9.97278i | 1.21837 | − | 1.21837i | 0.250166 | − | 0.968203i | \(-0.419515\pi\) |
0.968203 | − | 0.250166i | \(-0.0804851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0951463i | 0.0112918i | 0.999984 | + | 0.00564589i | \(0.00179715\pi\) | ||||
−0.999984 | + | 0.00564589i | \(0.998203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.99125 | 0.935305 | 0.467653 | − | 0.883912i | \(-0.345100\pi\) | ||||
0.467653 | + | 0.883912i | \(0.345100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.247796 | − | 0.247796i | 0.0282390 | − | 0.0282390i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.66620i | − | 0.637497i | −0.947839 | − | 0.318748i | \(-0.896737\pi\) | ||
0.947839 | − | 0.318748i | \(-0.103263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2672 | − | 12.2672i | −1.34650 | − | 1.34650i | −0.889432 | − | 0.457068i | \(-0.848900\pi\) |
−0.457068 | − | 0.889432i | \(-0.651100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.71492 | + | 4.14481i | −0.619870 | + | 0.449568i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9299 | 1.15857 | 0.579284 | − | 0.815126i | \(-0.303332\pi\) | ||||
0.579284 | + | 0.815126i | \(0.303332\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.43039 | − | 2.43039i | 0.254774 | − | 0.254774i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.8486 | + | 1.72757i | 1.11304 | + | 0.177245i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4415i | 1.06017i | 0.847944 | + | 0.530086i | \(0.177840\pi\) | ||||
−0.847944 | + | 0.530086i | \(0.822160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.54532 | − | 4.54532i | 0.452276 | − | 0.452276i | −0.443833 | − | 0.896109i | \(-0.646382\pi\) |
0.896109 | + | 0.443833i | \(0.146382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.65680i | 0.754447i | 0.926122 | + | 0.377224i | \(0.123121\pi\) | ||||
−0.926122 | + | 0.377224i | \(0.876879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.25185 | + | 4.25185i | −0.411042 | + | 0.411042i | −0.882102 | − | 0.471059i | \(-0.843872\pi\) |
0.471059 | + | 0.882102i | \(0.343872\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.180834 | − | 0.180834i | 0.0173208 | − | 0.0173208i | −0.698393 | − | 0.715714i | \(-0.746101\pi\) |
0.715714 | + | 0.698393i | \(0.246101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.88868 | 0.648032 | 0.324016 | − | 0.946052i | \(-0.394967\pi\) | ||||
0.324016 | + | 0.946052i | \(0.394967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.57703 | − | 2.59429i | 0.333560 | − | 0.241919i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.44203i | 0.407200i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.9380i | − | 0.994360i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.42817 | + | 10.6418i | 0.306625 | + | 0.951831i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.18115 | −0.282281 | −0.141141 | − | 0.989990i | \(-0.545077\pi\) | ||||
−0.141141 | + | 0.989990i | \(0.545077\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.49459 | − | 8.49459i | 0.742175 | − | 0.742175i | −0.230821 | − | 0.972996i | \(-0.574141\pi\) |
0.972996 | + | 0.230821i | \(0.0741411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.88754 | − | 4.88754i | 0.423803 | − | 0.423803i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.1013i | − | 1.29019i | −0.764102 | − | 0.645096i | \(-0.776818\pi\) | ||
0.764102 | − | 0.645096i | \(-0.223182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6635 | − | 11.6635i | 0.989286 | − | 0.989286i | −0.0106573 | − | 0.999943i | \(-0.503392\pi\) |
0.999943 | + | 0.0106573i | \(0.00339237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.608476i | 0.0508833i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.18351 | − | 1.30317i | −0.679604 | − | 0.108223i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1281 | − | 11.1281i | 0.911646 | − | 0.911646i | −0.0847561 | − | 0.996402i | \(-0.527011\pi\) |
0.996402 | + | 0.0847561i | \(0.0270111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8766 | 1.78030 | 0.890148 | − | 0.455672i | \(-0.150601\pi\) | ||||
0.890148 | + | 0.455672i | \(0.150601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.81768 | + | 10.7791i | 0.627931 | + | 0.865798i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3928 | − | 15.3928i | −1.22848 | − | 1.22848i | −0.964541 | − | 0.263935i | \(-0.914980\pi\) |
−0.263935 | − | 0.964541i | \(-0.585020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.78032i | − | 0.219120i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.90113 | + | 4.90113i | −0.383886 | + | 0.383886i | −0.872500 | − | 0.488614i | \(-0.837503\pi\) |
0.488614 | + | 0.872500i | \(0.337503\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4380 | 1.34939 | 0.674695 | − | 0.738097i | \(-0.264275\pi\) | ||||
0.674695 | + | 0.738097i | \(0.264275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.03205i | − | 0.540927i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.4288 | + | 17.4288i | −1.32509 | + | 1.32509i | −0.415490 | + | 0.909598i | \(0.636390\pi\) |
−0.909598 | + | 0.415490i | \(0.863610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.68679 | + | 2.18507i | 0.505474 | + | 0.165176i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4635 | + | 12.4635i | −0.931565 | + | 0.931565i | −0.997804 | − | 0.0662383i | \(-0.978900\pi\) |
0.0662383 | + | 0.997804i | \(0.478900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07994 | − | 7.07994i | −0.526248 | − | 0.526248i | 0.393203 | − | 0.919451i | \(-0.371367\pi\) |
−0.919451 | + | 0.393203i | \(0.871367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.84719 | − | 17.8795i | 0.209330 | − | 1.31452i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.556057 | − | 0.556057i | −0.0406629 | − | 0.0406629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6011 | 0.911781 | 0.455891 | − | 0.890036i | \(-0.349321\pi\) | ||||
0.455891 | + | 0.890036i | \(0.349321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.15723i | − | 0.371226i | −0.982623 | − | 0.185613i | \(-0.940573\pi\) | ||
0.982623 | − | 0.185613i | \(-0.0594270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.59790 | + | 3.59790i | 0.256340 | + | 0.256340i | 0.823564 | − | 0.567224i | \(-0.191983\pi\) |
−0.567224 | + | 0.823564i | \(0.691983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.58554 | −0.537725 | −0.268862 | − | 0.963179i | \(-0.586648\pi\) | ||||
−0.268862 | + | 0.963179i | \(0.586648\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.68686 | + | 3.68686i | −0.258767 | + | 0.258767i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.288659 | + | 0.209353i | −0.0201608 | + | 0.0146219i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.22365i | 0.0846417i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.605008 | − | 0.605008i | −0.0416505 | − | 0.0416505i | 0.685975 | − | 0.727625i | \(-0.259376\pi\) |
−0.727625 | + | 0.685975i | \(0.759376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.7068 | + | 3.29743i | 1.41219 | + | 0.224883i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.37827 | 0.568754 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.45382 | − | 5.45382i | −0.366863 | − | 0.366863i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.2652 | −1.69188 | −0.845940 | − | 0.533278i | \(-0.820960\pi\) | ||||
−0.845940 | + | 0.533278i | \(0.820960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.61823 | − | 6.61823i | −0.439267 | − | 0.439267i | 0.452498 | − | 0.891765i | \(-0.350533\pi\) |
−0.891765 | + | 0.452498i | \(0.850533\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0446899 | − | 0.0446899i | −0.00295319 | − | 0.00295319i | 0.705629 | − | 0.708582i | \(-0.250665\pi\) |
−0.708582 | + | 0.705629i | \(0.750665\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.5011i | − | 0.884488i | −0.896895 | − | 0.442244i | \(-0.854183\pi\) | ||
0.896895 | − | 0.442244i | \(-0.145817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.51265 | − | 2.08566i | −0.0986747 | − | 0.136054i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.58106 | −0.361009 | −0.180504 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180504 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7677 | 1.01569 | 0.507845 | − | 0.861449i | \(-0.330442\pi\) | ||||
0.507845 | + | 0.861449i | \(0.330442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.08768 | + | 6.59096i | −0.580591 | + | 0.421081i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0016i | 0.763643i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5401 | − | 10.5401i | −0.665287 | − | 0.665287i | 0.291334 | − | 0.956621i | \(-0.405901\pi\) |
−0.956621 | + | 0.291334i | \(0.905901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.348043 | + | 0.348043i | 0.0218812 | + | 0.0218812i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.0698 | −1.25192 | −0.625959 | − | 0.779856i | \(-0.715292\pi\) | ||||
−0.625959 | + | 0.779856i | \(0.715292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.05510 | − | 8.05510i | −0.500520 | − | 0.500520i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.6944 | 1.76937 | 0.884687 | − | 0.466185i | \(-0.154372\pi\) | ||||
0.884687 | + | 0.466185i | \(0.154372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.7104 | − | 2.66103i | −1.02651 | − | 0.163466i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.7007 | + | 13.7007i | 0.835349 | + | 0.835349i | 0.988243 | − | 0.152894i | \(-0.0488592\pi\) |
−0.152894 | + | 0.988243i | \(0.548859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.47842i | − | 0.393536i | −0.980450 | − | 0.196768i | \(-0.936955\pi\) | ||
0.980450 | − | 0.196768i | \(-0.0630445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.11059 | + | 0.563529i | −0.0669708 | + | 0.0339821i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7023 | − | 10.7023i | 0.643041 | − | 0.643041i | −0.308261 | − | 0.951302i | \(-0.599747\pi\) |
0.951302 | + | 0.308261i | \(0.0997469\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.3237 | −1.39138 | −0.695688 | − | 0.718344i | \(-0.744900\pi\) | ||||
−0.695688 | + | 0.718344i | \(0.744900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.39967 | + | 7.39967i | 0.439865 | + | 0.439865i | 0.891966 | − | 0.452102i | \(-0.149326\pi\) |
−0.452102 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.224366i | 0.0132439i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.03205 | −0.413650 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.94867 | + | 5.94867i | 0.347525 | + | 0.347525i | 0.859187 | − | 0.511662i | \(-0.170970\pi\) |
−0.511662 | + | 0.859187i | \(0.670970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0078 | − | 2.23066i | −0.815567 | − | 0.129874i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.41361 | + | 3.41361i | 0.197414 | + | 0.197414i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.32889 | − | 9.32889i | 0.537708 | − | 0.537708i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.38526 | + | 21.2583i | −0.193839 | + | 1.21725i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0570 | − | 12.0570i | 0.688130 | − | 0.688130i | −0.273689 | − | 0.961818i | \(-0.588244\pi\) |
0.961818 | + | 0.273689i | \(0.0882437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.3243i | − | 1.77624i | −0.459615 | − | 0.888118i | \(-0.652012\pi\) | ||
0.459615 | − | 0.888118i | \(-0.347988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0690 | 1.36046 | 0.680230 | − | 0.732999i | \(-0.261880\pi\) | ||||
0.680230 | + | 0.732999i | \(0.261880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2657 | + | 10.2657i | −0.576579 | + | 0.576579i | −0.933959 | − | 0.357380i | \(-0.883670\pi\) |
0.357380 | + | 0.933959i | \(0.383670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.923046i | − | 0.0516807i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9677 | − | 10.9677i | −0.610257 | − | 0.610257i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8927 | + | 5.52710i | −0.604216 | + | 0.306589i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.62112 | −0.0893755 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7608 | − | 12.7608i | 0.701395 | − | 0.701395i | −0.263315 | − | 0.964710i | \(-0.584816\pi\) |
0.964710 | + | 0.263315i | \(0.0848157\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.95953 | + | 31.1443i | −0.270968 | + | 1.70159i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.3967i | 0.947660i | 0.880616 | + | 0.473830i | \(0.157129\pi\) | ||||
−0.880616 | + | 0.473830i | \(0.842871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.04880 | + | 1.04880i | −0.0567956 | + | 0.0567956i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9122i | 0.913175i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.64234 | + | 9.64234i | −0.517628 | + | 0.517628i | −0.916853 | − | 0.399225i | \(-0.869279\pi\) |
0.399225 | + | 0.916853i | \(0.369279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.66120 | + | 3.66120i | −0.195980 | + | 0.195980i | −0.798274 | − | 0.602294i | \(-0.794253\pi\) |
0.602294 | + | 0.798274i | \(0.294253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.9960 | 1.01106 | 0.505528 | − | 0.862810i | \(-0.331298\pi\) | ||||
0.505528 | + | 0.862810i | \(0.331298\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.124909 | − | 0.172226i | −0.00662949 | − | 0.00914081i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.71770i | 0.460103i | 0.973178 | + | 0.230051i | \(0.0738894\pi\) | ||||
−0.973178 | + | 0.230051i | \(0.926111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.13530i | 0.270279i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4651 | + | 10.4910i | −0.757138 | + | 0.549124i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.0501 | −1.46420 | −0.732101 | − | 0.681196i | \(-0.761460\pi\) | ||||
−0.732101 | + | 0.681196i | \(0.761460\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.52841 | + | 7.52841i | −0.390856 | + | 0.390856i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.90740 | − | 4.90740i | 0.254096 | − | 0.254096i | −0.568552 | − | 0.822647i | \(-0.692496\pi\) |
0.822647 | + | 0.568552i | \(0.192496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9.05326i | − | 0.466267i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0620 | + | 26.0620i | −1.33872 | + | 1.33872i | −0.441412 | + | 0.897305i | \(0.645522\pi\) |
−0.897305 | + | 0.441412i | \(0.854478\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.91314i | − | 0.353245i | −0.984279 | − | 0.176623i | \(-0.943483\pi\) | ||
0.984279 | − | 0.176623i | \(-0.0565172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.123231 | + | 0.773850i | −0.00628042 | + | 0.0394391i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.5222 | + | 14.5222i | −0.736302 | + | 0.736302i | −0.971860 | − | 0.235558i | \(-0.924308\pi\) |
0.235558 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.23906 | −0.315523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.43864 | + | 10.2565i | 0.374279 | + | 0.516060i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3367 | − | 18.3367i | −0.920291 | − | 0.920291i | 0.0767588 | − | 0.997050i | \(-0.475543\pi\) |
−0.997050 | + | 0.0767588i | \(0.975543\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.5380i | − | 1.67481i | −0.546585 | − | 0.837404i | \(-0.684073\pi\) | ||
0.546585 | − | 0.837404i | \(-0.315927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2866 | + | 10.2866i | −0.512414 | + | 0.512414i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.01669 | 0.0999634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0044i | 0.890260i | 0.895466 | + | 0.445130i | \(0.146842\pi\) | ||||
−0.895466 | + | 0.445130i | \(0.853158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.31084 | + | 6.31084i | −0.310536 | + | 0.310536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.3096 | + | 6.10056i | 1.88054 | + | 0.299465i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7671 | − | 16.7671i | 0.819126 | − | 0.819126i | −0.166856 | − | 0.985981i | \(-0.553361\pi\) |
0.985981 | + | 0.166856i | \(0.0533614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.17528 | + | 9.17528i | 0.447176 | + | 0.447176i | 0.894415 | − | 0.447239i | \(-0.147593\pi\) |
−0.447239 | + | 0.894415i | \(0.647593\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.90331 | − | 15.0052i | 0.237846 | − | 0.727859i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.57736 | + | 9.57736i | 0.463481 | + | 0.463481i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.6726 | −1.76646 | −0.883228 | − | 0.468943i | \(-0.844635\pi\) | ||||
−0.883228 | + | 0.468943i | \(0.844635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.1455i | − | 1.35259i | −0.736633 | − | 0.676293i | \(-0.763586\pi\) | ||
0.736633 | − | 0.676293i | \(-0.236414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.86480 | + | 6.86480i | 0.328388 | + | 0.328388i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.32665 | 0.158772 | 0.0793862 | − | 0.996844i | \(-0.474704\pi\) | ||||
0.0793862 | + | 0.996844i | \(0.474704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.03644 | − | 6.03644i | 0.286800 | − | 0.286800i | −0.549013 | − | 0.835814i | \(-0.684996\pi\) |
0.835814 | + | 0.549013i | \(0.184996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.7844 | + | 14.3489i | −0.937871 | + | 0.680203i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2691i | 0.673402i | 0.941612 | + | 0.336701i | \(0.109311\pi\) | ||||
−0.941612 | + | 0.336701i | \(0.890689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0280862 | − | 0.0280862i | −0.00132253 | − | 0.00132253i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.20865 | + | 7.58994i | −0.0566624 | + | 0.355822i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0611 | 1.17231 | 0.586154 | − | 0.810200i | \(-0.300641\pi\) | ||||
0.586154 | + | 0.810200i | \(0.300641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6030 | − | 11.6030i | −0.540407 | − | 0.540407i | 0.383241 | − | 0.923648i | \(-0.374808\pi\) |
−0.923648 | + | 0.383241i | \(0.874808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.74913 | 0.406607 | 0.203303 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203303 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3047 | + | 19.3047i | 0.893316 | + | 0.893316i | 0.994834 | − | 0.101518i | \(-0.0323698\pi\) |
−0.101518 | + | 0.994834i | \(0.532370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0312 | + | 14.0312i | 0.647901 | + | 0.647901i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.33559i | 0.107391i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.9052 | + | 11.1150i | −1.00508 | + | 0.509993i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.9695 | 0.912431 | 0.456215 | − | 0.889869i | \(-0.349205\pi\) | ||||
0.456215 | + | 0.889869i | \(0.349205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.7797 | 0.901877 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.7077 | − | 18.9003i | −0.622434 | − | 0.858219i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8592i | 1.57962i | 0.613351 | + | 0.789811i | \(0.289821\pi\) | ||||
−0.613351 | + | 0.789811i | \(0.710179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.4659 | − | 21.4659i | −0.968743 | − | 0.968743i | 0.0307829 | − | 0.999526i | \(-0.490200\pi\) |
−0.999526 | + | 0.0307829i | \(0.990200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.27333 | + | 8.27333i | 0.372612 | + | 0.372612i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.133866 | −0.00600471 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0781 | + | 18.0781i | 0.809287 | + | 0.809287i | 0.984526 | − | 0.175239i | \(-0.0560697\pi\) |
−0.175239 | + | 0.984526i | \(0.556070\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.90394 | 0.174068 | 0.0870341 | − | 0.996205i | \(-0.472261\pi\) | ||||
0.0870341 | + | 0.996205i | \(0.472261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.26042 | + | 14.1947i | −0.100587 | + | 0.631656i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.0778 | − | 11.0778i | −0.491014 | − | 0.491014i | 0.417612 | − | 0.908626i | \(-0.362867\pi\) |
−0.908626 | + | 0.417612i | \(0.862867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2433i | 0.497374i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0519 | − | 13.8597i | −0.442941 | − | 0.610732i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.202933 | − | 0.202933i | 0.00892500 | − | 0.00892500i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.61052 | −0.114369 | −0.0571844 | − | 0.998364i | \(-0.518212\pi\) | ||||
−0.0571844 | + | 0.998364i | \(0.518212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.2735 | − | 21.2735i | −0.930226 | − | 0.930226i | 0.0674935 | − | 0.997720i | \(-0.478500\pi\) |
−0.997720 | + | 0.0674935i | \(0.978500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.8009i | − | 0.818980i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0949 | −0.830213 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.275471 | − | 0.275471i | −0.0119320 | − | 0.0119320i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.11448 | − | 13.2782i | 0.0914168 | − | 0.574068i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.884224 | − | 0.884224i | −0.0380862 | − | 0.0380862i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.92150 | + | 8.92150i | −0.383565 | + | 0.383565i | −0.872385 | − | 0.488820i | \(-0.837428\pi\) |
0.488820 | + | 0.872385i | \(0.337428\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0899300 | + | 0.564732i | −0.00385218 | + | 0.0241905i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.0470 | − | 24.0470i | 1.02818 | − | 1.02818i | 0.0285840 | − | 0.999591i | \(-0.490900\pi\) |
0.999591 | − | 0.0285840i | \(-0.00909983\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.2062i | − | 0.775609i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.97205 | 0.339006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5090 | − | 17.5090i | 0.741879 | − | 0.741879i | −0.231060 | − | 0.972939i | \(-0.574220\pi\) |
0.972939 | + | 0.231060i | \(0.0742195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9076i | 0.968886i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2032 | − | 11.2032i | −0.472157 | − | 0.472157i | 0.430455 | − | 0.902612i | \(-0.358353\pi\) |
−0.902612 | + | 0.430455i | \(0.858353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4693 | + | 9.04353i | −0.524588 | + | 0.380464i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.83805 | −0.202821 | −0.101411 | − | 0.994845i | \(-0.532336\pi\) | ||||
−0.101411 | + | 0.994845i | \(0.532336\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.64695 | + | 9.64695i | −0.403712 | + | 0.403712i | −0.879539 | − | 0.475827i | \(-0.842149\pi\) |
0.475827 | + | 0.879539i | \(0.342149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.06904 | + | 9.39194i | −0.127988 | + | 0.391671i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0261i | 0.750438i | 0.926936 | + | 0.375219i | \(0.122432\pi\) | ||||
−0.926936 | + | 0.375219i | \(0.877568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2593 | − | 17.2593i | 0.716038 | − | 0.716038i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.88482i | − | 0.0780614i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.25140 | − | 5.25140i | 0.216749 | − | 0.216749i | −0.590378 | − | 0.807127i | \(-0.701021\pi\) |
0.807127 | + | 0.590378i | \(0.201021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.6865 | + | 20.6865i | −0.852373 | + | 0.852373i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.0811054 | −0.00333060 | −0.00166530 | − | 0.999999i | \(-0.500530\pi\) | ||||
−0.00166530 | + | 0.999999i | \(0.500530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.83155 | − | 8.04060i | −0.239070 | − | 0.329632i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.29253i | − | 0.338824i | −0.985545 | − | 0.169412i | \(-0.945813\pi\) | ||
0.985545 | − | 0.169412i | \(-0.0541868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.82196i | 0.237483i | 0.992925 | + | 0.118741i | \(0.0378859\pi\) | ||||
−0.992925 | + | 0.118741i | \(0.962114\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.3595 | + | 19.7990i | 0.583796 | + | 0.804944i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0548 | −0.895178 | −0.447589 | − | 0.894239i | \(-0.647717\pi\) | ||||
−0.447589 | + | 0.894239i | \(0.647717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.99038 | − | 1.99038i | 0.0805220 | − | 0.0805220i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.9250 | + | 14.9250i | −0.602816 | + | 0.602816i | −0.941059 | − | 0.338243i | \(-0.890168\pi\) |
0.338243 | + | 0.941059i | \(0.390168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.5403i | 1.26976i | 0.772609 | + | 0.634882i | \(0.218951\pi\) | ||||
−0.772609 | + | 0.634882i | \(0.781049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.89013 | + | 6.89013i | −0.276938 | + | 0.276938i | −0.831885 | − | 0.554947i | \(-0.812738\pi\) |
0.554947 | + | 0.831885i | \(0.312738\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3778i | 0.616100i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1760 | − | 14.7624i | −0.807042 | − | 0.590494i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0757 | + | 18.0757i | −0.720725 | + | 0.720725i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9043 | 1.30990 | 0.654950 | − | 0.755672i | \(-0.272690\pi\) | ||||
0.654950 | + | 0.755672i | \(0.272690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.75825 | − | 4.17625i | 0.228509 | − | 0.165729i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.67249 | − | 8.67249i | −0.343617 | − | 0.343617i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.3921i | − | 1.12142i | −0.828013 | − | 0.560710i | \(-0.810528\pi\) | ||
0.828013 | − | 0.560710i | \(-0.189472\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.71547 | + | 2.71547i | −0.107088 | + | 0.107088i | −0.758621 | − | 0.651533i | \(-0.774126\pi\) |
0.651533 | + | 0.758621i | \(0.274126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.2882 | −1.30869 | −0.654346 | − | 0.756195i | \(-0.727056\pi\) | ||||
−0.654346 | + | 0.756195i | \(0.727056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.57999i | − | 0.0620200i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.82719 | − | 4.82719i | 0.188902 | − | 0.188902i | −0.606319 | − | 0.795221i | \(-0.707355\pi\) |
0.795221 | + | 0.606319i | \(0.207355\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.22442 | + | 26.5280i | −0.165062 | + | 1.03653i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.5484 | + | 22.5484i | −0.878359 | + | 0.878359i | −0.993365 | − | 0.115005i | \(-0.963311\pi\) |
0.115005 | + | 0.993365i | \(0.463311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3551 | + | 17.3551i | 0.675035 | + | 0.675035i | 0.958872 | − | 0.283838i | \(-0.0916077\pi\) |
−0.283838 | + | 0.958872i | \(0.591608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.43061 | + | 15.2634i | −0.0942548 | + | 0.591890i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.17838 | − | 5.17838i | −0.200508 | − | 0.200508i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.39780 | −0.0925661 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2889i | 0.782080i | 0.920374 | + | 0.391040i | \(0.127885\pi\) | ||||
−0.920374 | + | 0.391040i | \(0.872115\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.349388 | − | 0.349388i | −0.0134281 | − | 0.0134281i | 0.700361 | − | 0.713789i | \(-0.253022\pi\) |
−0.713789 | + | 0.700361i | \(0.753022\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.6906 | −0.563775 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.40464 | − | 4.40464i | 0.168539 | − | 0.168539i | −0.617798 | − | 0.786337i | \(-0.711975\pi\) |
0.786337 | + | 0.617798i | \(0.211975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.8252 | + | 27.3351i | 0.757480 | + | 1.04442i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18.4864i | − | 0.704276i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7615 | + | 22.7615i | 0.865890 | + | 0.865890i | 0.992014 | − | 0.126125i | \(-0.0402539\pi\) |
−0.126125 | + | 0.992014i | \(0.540254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.80034 | + | 36.4243i | −0.220020 | + | 1.38165i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.503478 | 0.0190706 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.9589 | − | 34.9589i | −1.32038 | − | 1.32038i | −0.913467 | − | 0.406913i | \(-0.866605\pi\) |
−0.406913 | − | 0.913467i | \(-0.633395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.7771 | 1.50022 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.39503 | + | 6.39503i | 0.240510 | + | 0.240510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.7652 | − | 20.7652i | −0.779854 | − | 0.779854i | 0.199952 | − | 0.979806i | \(-0.435922\pi\) |
−0.979806 | + | 0.199952i | \(0.935922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.7677i | 0.440704i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.798814 | − | 1.10141i | −0.0298740 | − | 0.0411905i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.48453 | −0.353713 | −0.176857 | − | 0.984237i | \(-0.556593\pi\) | ||||
−0.176857 | + | 0.984237i | \(0.556593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7727 | −0.401198 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.5239 | − | 8.38451i | 0.613684 | − | 0.311393i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.4631i | − | 1.09272i | −0.837549 | − | 0.546362i | \(-0.816012\pi\) | ||
0.837549 | − | 0.546362i | \(-0.183988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.9341 | − | 20.9341i | −0.774275 | − | 0.774275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.5703 | + | 13.5703i | 0.501231 | + | 0.501231i | 0.911820 | − | 0.410590i | \(-0.134677\pi\) |
−0.410590 | + | 0.911820i | \(0.634677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.51287 | −0.129398 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.19592 | + | 1.19592i | 0.0439927 | + | 0.0439927i | 0.728761 | − | 0.684768i | \(-0.240097\pi\) |
−0.684768 | + | 0.728761i | \(0.740097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.8695 | −1.79285 | −0.896424 | − | 0.443197i | \(-0.853844\pi\) | ||||
−0.896424 | + | 0.443197i | \(0.853844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.53406 | + | 34.7521i | −0.202752 | + | 1.27322i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.98214 | − | 5.98214i | −0.218583 | − | 0.218583i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.8326i | 0.650721i | 0.945590 | + | 0.325360i | \(0.105486\pi\) | ||||
−0.945590 | + | 0.325360i | \(0.894514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.5993 | + | 28.7199i | −1.44117 | + | 1.04522i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.7676 | + | 19.7676i | −0.718467 | + | 0.718467i | −0.968291 | − | 0.249824i | \(-0.919627\pi\) |
0.249824 | + | 0.968291i | \(0.419627\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.72357 | −0.134979 | −0.0674896 | − | 0.997720i | \(-0.521499\pi\) | ||||
−0.0674896 | + | 0.997720i | \(0.521499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.254425 | + | 0.254425i | 0.00921079 | + | 0.00921079i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.4966i | − | 0.559549i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.9937 | −0.648868 | −0.324434 | − | 0.945908i | \(-0.605174\pi\) | ||||
−0.324434 | + | 0.945908i | \(0.605174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5506 | + | 14.5506i | 0.523350 | + | 0.523350i | 0.918582 | − | 0.395232i | \(-0.129336\pi\) |
−0.395232 | + | 0.918582i | \(0.629336\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.3019 | − | 9.24831i | −1.01663 | − | 0.332209i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.553973 | − | 0.553973i | −0.0198482 | − | 0.0198482i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0167574 | − | 0.0167574i | 0.000599629 | − | 0.000599629i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.0705 | + | 7.65492i | 1.71571 | + | 0.273216i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.4478 | − | 27.4478i | 0.978410 | − | 0.978410i | −0.0213618 | − | 0.999772i | \(-0.506800\pi\) |
0.999772 | + | 0.0213618i | \(0.00680019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.69203i | 0.344609i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.5177 | −0.835137 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.5148 | − | 33.5148i | 1.18715 | − | 1.18715i | 0.209303 | − | 0.977851i | \(-0.432880\pi\) |
0.977851 | − | 0.209303i | \(-0.0671197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.63781i | 0.128697i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.40744 | − | 1.40744i | −0.0496676 | − | 0.0496676i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.65004 | + | 5.03271i | 0.128647 | + | 0.177380i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.1238 | −1.55131 | −0.775654 | − | 0.631158i | \(-0.782580\pi\) | ||||
−0.775654 | + | 0.631158i | \(0.782580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.5547 | − | 27.5547i | 0.967578 | − | 0.967578i | −0.0319126 | − | 0.999491i | \(-0.510160\pi\) |
0.999491 | + | 0.0319126i | \(0.0101598\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.43737 | − | 15.3059i | 0.0853772 | − | 0.536142i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.0673i | 1.61169i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.29165 | + | 8.29165i | −0.289381 | + | 0.289381i | −0.836835 | − | 0.547455i | \(-0.815597\pi\) |
0.547455 | + | 0.836835i | \(0.315597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 16.2616i | − | 0.566845i | −0.958995 | − | 0.283422i | \(-0.908530\pi\) | ||
0.958995 | − | 0.283422i | \(-0.0914698\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.8727 | + | 18.8727i | −0.656266 | + | 0.656266i | −0.954495 | − | 0.298228i | \(-0.903604\pi\) |
0.298228 | + | 0.954495i | \(0.403604\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.56155 | − | 7.56155i | 0.262624 | − | 0.262624i | −0.563495 | − | 0.826119i | \(-0.690544\pi\) |
0.826119 | + | 0.563495i | \(0.190544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.8507 | 0.549195 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.5648 | + | 22.8927i | −1.09234 | + | 0.792236i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.30357i | − | 0.0450042i | −0.999747 | − | 0.0225021i | \(-0.992837\pi\) | ||
0.999747 | − | 0.0225021i | \(-0.00716324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 15.2664i | − | 0.526427i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.23175 | + | 12.7288i | 0.317582 | + | 0.437885i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3892 | 0.528778 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3138 | − | 11.3138i | 0.387832 | − | 0.387832i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.3937 | − | 20.3937i | 0.698268 | − | 0.698268i | −0.265769 | − | 0.964037i | \(-0.585626\pi\) |
0.964037 | + | 0.265769i | \(0.0856258\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.9066i | 0.611678i | 0.952083 | + | 0.305839i | \(0.0989369\pi\) | ||||
−0.952083 | + | 0.305839i | \(0.901063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0524 | + | 17.0524i | −0.581821 | + | 0.581821i | −0.935403 | − | 0.353582i | \(-0.884963\pi\) |
0.353582 | + | 0.935403i | \(0.384963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.33105i | − | 0.0453095i | −0.999743 | − | 0.0226548i | \(-0.992788\pi\) | ||
0.999743 | − | 0.0226548i | \(-0.00721185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.66746 | − | 54.4289i | 0.294703 | − | 1.85064i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.997947 | + | 0.997947i | −0.0338530 | + | 0.0338530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.4543 | −1.16744 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.9725 | + | 4.82326i | −0.506162 | + | 0.163056i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.7763 | − | 19.7763i | −0.667799 | − | 0.667799i | 0.289407 | − | 0.957206i | \(-0.406542\pi\) |
−0.957206 | + | 0.289407i | \(0.906542\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.6926i | 0.562389i | 0.959651 | + | 0.281194i | \(0.0907305\pi\) | ||||
−0.959651 | + | 0.281194i | \(0.909269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.2285 | + | 17.2285i | −0.579785 | + | 0.579785i | −0.934844 | − | 0.355059i | \(-0.884461\pi\) |
0.355059 | + | 0.934844i | \(0.384461\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0017 | −0.604436 | −0.302218 | − | 0.953239i | \(-0.597727\pi\) | ||||
−0.302218 | + | 0.953239i | \(0.597727\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.47572i | − | 0.150111i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.00266 | − | 4.00266i | 0.133944 | − | 0.133944i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.19818 | − | 38.9226i | 0.207182 | − | 1.30104i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.6046 | − | 15.6046i | 0.520443 | − | 0.520443i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8938 | + | 16.8938i | 0.562814 | + | 0.562814i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.1102 | + | 3.52090i | 0.734967 | + | 0.117039i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.3515 | + | 25.3515i | 0.841784 | + | 0.841784i | 0.989091 | − | 0.147307i | \(-0.0470604\pi\) |
−0.147307 | + | 0.989091i | \(0.547060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.8371 | −1.81683 | −0.908417 | − | 0.418066i | \(-0.862708\pi\) | ||||
−0.908417 | + | 0.418066i | \(0.862708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.32107i | 0.143007i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9515 | + | 11.9515i | 0.394672 | + | 0.394672i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4141 | 0.871321 | 0.435661 | − | 0.900111i | \(-0.356515\pi\) | ||||
0.435661 | + | 0.900111i | \(0.356515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.164357 | − | 0.164357i | 0.00540989 | − | 0.00540989i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.3186 | + | 36.1018i | 0.602312 | + | 1.18702i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.1302i | 1.41506i | 0.706685 | + | 0.707528i | \(0.250190\pi\) | ||||
−0.706685 | + | 0.707528i | \(0.749810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.4404 | − | 17.4404i | −0.571588 | − | 0.571588i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.73653 | + | 0.276531i | 0.0567904 | + | 0.00904352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.0711 | −0.557689 | −0.278845 | − | 0.960336i | \(-0.589951\pi\) | ||||
−0.278845 | + | 0.960336i | \(0.589951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.6649 | − | 27.6649i | −0.901850 | − | 0.901850i | 0.0937464 | − | 0.995596i | \(-0.470116\pi\) |
−0.995596 | + | 0.0937464i | \(0.970116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.315133 | −0.0102621 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.6985 | + | 38.6985i | 1.25753 | + | 1.25753i | 0.952267 | + | 0.305265i | \(0.0987452\pi\) |
0.305265 | + | 0.952267i | \(0.401255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.8042 | − | 13.8042i | −0.448104 | − | 0.448104i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7149i | 0.703413i | 0.936110 | + | 0.351707i | \(0.114399\pi\) | ||||
−0.936110 | + | 0.351707i | \(0.885601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.8094 | + | 16.5428i | −0.738095 | + | 0.535313i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.2468 | 0.686094 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.46104 | −0.143905 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77047 | + | 9.33520i | 0.217949 | + | 0.300511i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.39782i | − | 0.237898i | −0.992900 | − | 0.118949i | \(-0.962048\pi\) | ||
0.992900 | − | 0.118949i | \(-0.0379525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0731 | + | 14.0731i | 0.451626 | + | 0.451626i | 0.895894 | − | 0.444268i | \(-0.146536\pi\) |
−0.444268 | + | 0.895894i | \(0.646536\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.4100 | + | 16.4100i | 0.526080 | + | 0.526080i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −60.5514 | −1.93721 | −0.968605 | − | 0.248603i | \(-0.920029\pi\) | ||||
−0.968605 | + | 0.248603i | \(0.920029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.92501 | − | 1.92501i | −0.0615235 | − | 0.0615235i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.63756 | −0.211705 | −0.105853 | − | 0.994382i | \(-0.533757\pi\) | ||||
−0.105853 | + | 0.994382i | \(0.533757\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2360 | − | 1.78926i | −0.358008 | − | 0.0570106i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1029 | + | 13.1029i | 0.416648 | + | 0.416648i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.7239i | − | 1.54777i | −0.633328 | − | 0.773883i | \(-0.718312\pi\) | ||
0.633328 | − | 0.773883i | \(-0.281688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.7307 | − | 9.95839i | 0.435293 | − | 0.315702i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.6755 | − | 40.6755i | 1.28821 | − | 1.28821i | 0.352330 | − | 0.935876i | \(-0.385389\pi\) |
0.935876 | − | 0.352330i | \(-0.114611\pi\) | |||||||
\(998\) | 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.u.a.719.9 | 96 | ||
3.2 | odd | 2 | inner | 2880.2.u.a.719.40 | 96 | ||
4.3 | odd | 2 | 720.2.u.a.539.1 | yes | 96 | ||
5.4 | even | 2 | inner | 2880.2.u.a.719.16 | 96 | ||
12.11 | even | 2 | 720.2.u.a.539.48 | yes | 96 | ||
15.14 | odd | 2 | inner | 2880.2.u.a.719.33 | 96 | ||
16.3 | odd | 4 | inner | 2880.2.u.a.2159.33 | 96 | ||
16.13 | even | 4 | 720.2.u.a.179.2 | yes | 96 | ||
20.19 | odd | 2 | 720.2.u.a.539.47 | yes | 96 | ||
48.29 | odd | 4 | 720.2.u.a.179.47 | yes | 96 | ||
48.35 | even | 4 | inner | 2880.2.u.a.2159.16 | 96 | ||
60.59 | even | 2 | 720.2.u.a.539.2 | yes | 96 | ||
80.19 | odd | 4 | inner | 2880.2.u.a.2159.40 | 96 | ||
80.29 | even | 4 | 720.2.u.a.179.48 | yes | 96 | ||
240.29 | odd | 4 | 720.2.u.a.179.1 | ✓ | 96 | ||
240.179 | even | 4 | inner | 2880.2.u.a.2159.9 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.u.a.179.1 | ✓ | 96 | 240.29 | odd | 4 | ||
720.2.u.a.179.2 | yes | 96 | 16.13 | even | 4 | ||
720.2.u.a.179.47 | yes | 96 | 48.29 | odd | 4 | ||
720.2.u.a.179.48 | yes | 96 | 80.29 | even | 4 | ||
720.2.u.a.539.1 | yes | 96 | 4.3 | odd | 2 | ||
720.2.u.a.539.2 | yes | 96 | 60.59 | even | 2 | ||
720.2.u.a.539.47 | yes | 96 | 20.19 | odd | 2 | ||
720.2.u.a.539.48 | yes | 96 | 12.11 | even | 2 | ||
2880.2.u.a.719.9 | 96 | 1.1 | even | 1 | trivial | ||
2880.2.u.a.719.16 | 96 | 5.4 | even | 2 | inner | ||
2880.2.u.a.719.33 | 96 | 15.14 | odd | 2 | inner | ||
2880.2.u.a.719.40 | 96 | 3.2 | odd | 2 | inner | ||
2880.2.u.a.2159.9 | 96 | 240.179 | even | 4 | inner | ||
2880.2.u.a.2159.16 | 96 | 48.35 | even | 4 | inner | ||
2880.2.u.a.2159.33 | 96 | 16.3 | odd | 4 | inner | ||
2880.2.u.a.2159.40 | 96 | 80.19 | odd | 4 | inner |