Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(161,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.j (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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 161.12 | ||
Character | \(\chi\) | \(=\) | 1152.161 |
Dual form | 1152.3.j.b.737.12 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.92848 | + | 1.92848i | 0.385696 | + | 0.385696i | 0.873149 | − | 0.487453i | \(-0.162074\pi\) |
−0.487453 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43162i | 0.347375i | 0.984801 | + | 0.173687i | \(0.0555682\pi\) | ||||
−0.984801 | + | 0.173687i | \(0.944432\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.79147 | − | 2.79147i | −0.253770 | − | 0.253770i | 0.568744 | − | 0.822514i | \(-0.307429\pi\) |
−0.822514 | + | 0.568744i | \(0.807429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.54064 | + | 1.54064i | 0.118511 | + | 0.118511i | 0.763875 | − | 0.645364i | \(-0.223294\pi\) |
−0.645364 | + | 0.763875i | \(0.723294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 20.3746i | − | 1.19850i | −0.800561 | − | 0.599252i | \(-0.795465\pi\) | ||
0.800561 | − | 0.599252i | \(-0.204535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.0179 | − | 25.0179i | −1.31673 | − | 1.31673i | −0.916349 | − | 0.400380i | \(-0.868878\pi\) |
−0.400380 | − | 0.916349i | \(-0.631122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.55894 | 0.154737 | 0.0773683 | − | 0.997003i | \(-0.475348\pi\) | ||||
0.0773683 | + | 0.997003i | \(0.475348\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 17.5619i | − | 0.702477i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −23.4539 | + | 23.4539i | −0.808756 | + | 0.808756i | −0.984446 | − | 0.175690i | \(-0.943784\pi\) |
0.175690 | + | 0.984446i | \(0.443784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.3241 | 0.429808 | 0.214904 | − | 0.976635i | \(-0.431056\pi\) | ||||
0.214904 | + | 0.976635i | \(0.431056\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.68934 | + | 4.68934i | −0.133981 | + | 0.133981i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.4406 | − | 25.4406i | 0.687584 | − | 0.687584i | −0.274113 | − | 0.961697i | \(-0.588384\pi\) |
0.961697 | + | 0.274113i | \(0.0883844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 64.0726 | 1.56275 | 0.781373 | − | 0.624064i | \(-0.214520\pi\) | ||||
0.781373 | + | 0.624064i | \(0.214520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −24.6791 | + | 24.6791i | −0.573932 | + | 0.573932i | −0.933225 | − | 0.359293i | \(-0.883018\pi\) |
0.359293 | + | 0.933225i | \(0.383018\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 79.5718i | − | 1.69302i | −0.532375 | − | 0.846508i | \(-0.678701\pi\) | ||
0.532375 | − | 0.846508i | \(-0.321299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.0872 | 0.879331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39.8061 | + | 39.8061i | 0.751058 | + | 0.751058i | 0.974677 | − | 0.223619i | \(-0.0717871\pi\) |
−0.223619 | + | 0.974677i | \(0.571787\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.7666i | − | 0.195757i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 19.2371 | + | 19.2371i | 0.326053 | + | 0.326053i | 0.851083 | − | 0.525030i | \(-0.175946\pi\) |
−0.525030 | + | 0.851083i | \(0.675946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −63.5441 | − | 63.5441i | −1.04171 | − | 1.04171i | −0.999092 | − | 0.0426158i | \(-0.986431\pi\) |
−0.0426158 | − | 0.999092i | \(-0.513569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.94218i | 0.0914182i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −65.1837 | − | 65.1837i | −0.972891 | − | 0.972891i | 0.0267514 | − | 0.999642i | \(-0.491484\pi\) |
−0.999642 | + | 0.0267514i | \(0.991484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.6981 | 1.19293 | 0.596466 | − | 0.802639i | \(-0.296571\pi\) | ||||
0.596466 | + | 0.802639i | \(0.296571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 39.7473i | − | 0.544483i | −0.962229 | − | 0.272242i | \(-0.912235\pi\) | ||
0.962229 | − | 0.272242i | \(-0.0877650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.78781 | − | 6.78781i | 0.0881533 | − | 0.0881533i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −109.386 | −1.38463 | −0.692317 | − | 0.721593i | \(-0.743410\pi\) | ||||
−0.692317 | + | 0.721593i | \(0.743410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7433 | − | 14.7433i | 0.177630 | − | 0.177630i | −0.612692 | − | 0.790322i | \(-0.709913\pi\) |
0.790322 | + | 0.612692i | \(0.209913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 39.2920 | − | 39.2920i | 0.462258 | − | 0.462258i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 32.3085 | 0.363017 | 0.181508 | − | 0.983389i | \(-0.441902\pi\) | ||||
0.181508 | + | 0.983389i | \(0.441902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.74625 | + | 3.74625i | −0.0411676 | + | 0.0411676i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 96.4929i | − | 1.01572i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 123.467 | 1.27286 | 0.636428 | − | 0.771336i | \(-0.280411\pi\) | ||||
0.636428 | + | 0.771336i | \(0.280411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.5696 | + | 83.5696i | 0.827422 | + | 0.827422i | 0.987160 | − | 0.159737i | \(-0.0510648\pi\) |
−0.159737 | + | 0.987160i | \(0.551065\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 38.0120i | − | 0.369049i | −0.982828 | − | 0.184524i | \(-0.940926\pi\) | ||
0.982828 | − | 0.184524i | \(-0.0590744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −69.3864 | − | 69.3864i | −0.648471 | − | 0.648471i | 0.304153 | − | 0.952623i | \(-0.401627\pi\) |
−0.952623 | + | 0.304153i | \(0.901627\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −46.2338 | − | 46.2338i | −0.424163 | − | 0.424163i | 0.462471 | − | 0.886634i | \(-0.346963\pi\) |
−0.886634 | + | 0.462471i | \(0.846963\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 97.1603i | 0.859826i | 0.902870 | + | 0.429913i | \(0.141456\pi\) | ||||
−0.902870 | + | 0.429913i | \(0.858544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.86335 | + | 6.86335i | 0.0596813 | + | 0.0596813i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 49.5432 | 0.416330 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 105.415i | − | 0.871201i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 82.0799 | − | 82.0799i | 0.656639 | − | 0.656639i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −187.433 | −1.47585 | −0.737926 | − | 0.674881i | \(-0.764195\pi\) | ||||
−0.737926 | + | 0.674881i | \(0.764195\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 79.2297 | − | 79.2297i | 0.604807 | − | 0.604807i | −0.336778 | − | 0.941584i | \(-0.609337\pi\) |
0.941584 | + | 0.336778i | \(0.109337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 60.8340 | − | 60.8340i | 0.457398 | − | 0.457398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46186 | 0.0252691 | 0.0126345 | − | 0.999920i | \(-0.495978\pi\) | ||||
0.0126345 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1054 | + | 14.1054i | −0.101478 | + | 0.101478i | −0.756023 | − | 0.654545i | \(-0.772860\pi\) |
0.654545 | + | 0.756023i | \(0.272860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.60130i | − | 0.0601489i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −90.4609 | −0.623868 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −85.7760 | − | 85.7760i | −0.575678 | − | 0.575678i | 0.358032 | − | 0.933709i | \(-0.383448\pi\) |
−0.933709 | + | 0.358032i | \(0.883448\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 221.163i | − | 1.46465i | −0.680953 | − | 0.732327i | \(-0.738434\pi\) | ||
0.680953 | − | 0.732327i | \(-0.261566\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.6952 | + | 25.6952i | 0.165775 | + | 0.165775i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 114.407 | + | 114.407i | 0.728709 | + | 0.728709i | 0.970363 | − | 0.241654i | \(-0.0776898\pi\) |
−0.241654 | + | 0.970363i | \(0.577690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.65400i | 0.0537516i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −124.266 | − | 124.266i | −0.762366 | − | 0.762366i | 0.214383 | − | 0.976750i | \(-0.431226\pi\) |
−0.976750 | + | 0.214383i | \(0.931226\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −230.474 | −1.38008 | −0.690041 | − | 0.723770i | \(-0.742408\pi\) | ||||
−0.690041 | + | 0.723770i | \(0.742408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 164.253i | − | 0.971910i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 43.4882 | − | 43.4882i | 0.251377 | − | 0.251377i | −0.570158 | − | 0.821535i | \(-0.693118\pi\) |
0.821535 | + | 0.570158i | \(0.193118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.7039 | 0.244023 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 145.904 | − | 145.904i | 0.815104 | − | 0.815104i | −0.170290 | − | 0.985394i | \(-0.554470\pi\) |
0.985394 | + | 0.170290i | \(0.0544704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 184.775 | − | 184.775i | 1.02085 | − | 1.02085i | 0.0210758 | − | 0.999778i | \(-0.493291\pi\) |
0.999778 | − | 0.0210758i | \(-0.00670914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 98.1235 | 0.530397 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −56.8750 | + | 56.8750i | −0.304145 | + | 0.304145i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 352.205i | 1.84401i | 0.387182 | + | 0.922003i | \(0.373449\pi\) | ||||
−0.387182 | + | 0.922003i | \(0.626551\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −145.660 | −0.754715 | −0.377357 | − | 0.926068i | \(-0.623167\pi\) | ||||
−0.377357 | + | 0.926068i | \(0.623167\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7746 | + | 18.7746i | 0.0953027 | + | 0.0953027i | 0.753151 | − | 0.657848i | \(-0.228533\pi\) |
−0.657848 | + | 0.753151i | \(0.728533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 260.124i | 1.30716i | 0.756858 | + | 0.653579i | \(0.226733\pi\) | ||||
−0.756858 | + | 0.653579i | \(0.773267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −57.0310 | − | 57.0310i | −0.280941 | − | 0.280941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 123.563 | + | 123.563i | 0.602745 | + | 0.602745i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 139.673i | 0.668293i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 127.020 | + | 127.020i | 0.601991 | + | 0.601991i | 0.940840 | − | 0.338850i | \(-0.110038\pi\) |
−0.338850 | + | 0.940840i | \(0.610038\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −95.1863 | −0.442727 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.3991i | 0.149304i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.3898 | − | 31.3898i | 0.142035 | − | 0.142035i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 70.2119 | 0.314852 | 0.157426 | − | 0.987531i | \(-0.449680\pi\) | ||||
0.157426 | + | 0.987531i | \(0.449680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 57.6438 | − | 57.6438i | 0.253938 | − | 0.253938i | −0.568645 | − | 0.822583i | \(-0.692532\pi\) |
0.822583 | + | 0.568645i | \(0.192532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −136.406 | + | 136.406i | −0.595660 | + | 0.595660i | −0.939155 | − | 0.343495i | \(-0.888389\pi\) |
0.343495 | + | 0.939155i | \(0.388389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −171.152 | −0.734556 | −0.367278 | − | 0.930111i | \(-0.619710\pi\) | ||||
−0.367278 | + | 0.930111i | \(0.619710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 153.453 | − | 153.453i | 0.652990 | − | 0.652990i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 79.7138i | − | 0.333531i | −0.985997 | − | 0.166765i | \(-0.946668\pi\) | ||
0.985997 | − | 0.166765i | \(-0.0533322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −68.5687 | −0.284517 | −0.142259 | − | 0.989830i | \(-0.545436\pi\) | ||||
−0.142259 | + | 0.989830i | \(0.545436\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 83.0929 | + | 83.0929i | 0.339155 | + | 0.339155i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 77.0869i | − | 0.312093i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6232 | − | 11.6232i | −0.0463074 | − | 0.0463074i | 0.683574 | − | 0.729881i | \(-0.260425\pi\) |
−0.729881 | + | 0.683574i | \(0.760425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.93469 | − | 9.93469i | −0.0392675 | − | 0.0392675i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 44.8750i | − | 0.174611i | −0.996182 | − | 0.0873055i | \(-0.972174\pi\) | ||
0.996182 | − | 0.0873055i | \(-0.0278256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 61.8619 | + | 61.8619i | 0.238849 | + | 0.238849i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 384.441 | 1.46175 | 0.730876 | − | 0.682510i | \(-0.239112\pi\) | ||||
0.730876 | + | 0.682510i | \(0.239112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 153.531i | 0.579360i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.844060 | − | 0.844060i | 0.00313777 | − | 0.00313777i | −0.705536 | − | 0.708674i | \(-0.749294\pi\) |
0.708674 | + | 0.705536i | \(0.249294\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 37.3816 | 0.137939 | 0.0689697 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689697 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −49.0236 | + | 49.0236i | −0.178268 | + | 0.178268i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −342.799 | + | 342.799i | −1.23754 | + | 1.23754i | −0.276541 | + | 0.961002i | \(0.589188\pi\) |
−0.961002 | + | 0.276541i | \(0.910812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −303.846 | −1.08130 | −0.540651 | − | 0.841247i | \(-0.681822\pi\) | ||||
−0.540651 | + | 0.841247i | \(0.681822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3395 | + | 10.3395i | −0.0365354 | + | 0.0365354i | −0.725138 | − | 0.688603i | \(-0.758224\pi\) |
0.688603 | + | 0.725138i | \(0.258224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 155.800i | 0.542858i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −126.123 | −0.436411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −230.634 | − | 230.634i | −0.787148 | − | 0.787148i | 0.193877 | − | 0.981026i | \(-0.437894\pi\) |
−0.981026 | + | 0.193877i | \(0.937894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 74.1969i | 0.251515i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.48304 | + | 5.48304i | 0.0183379 | + | 0.0183379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −60.0102 | − | 60.0102i | −0.199369 | − | 0.199369i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 245.087i | − | 0.803565i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 255.002 | + | 255.002i | 0.830625 | + | 0.830625i | 0.987602 | − | 0.156978i | \(-0.0501750\pi\) |
−0.156978 | + | 0.987602i | \(0.550175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −333.987 | −1.07391 | −0.536957 | − | 0.843610i | \(-0.680426\pi\) | ||||
−0.536957 | + | 0.843610i | \(0.680426\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 159.757i | 0.510405i | 0.966888 | + | 0.255203i | \(0.0821421\pi\) | ||||
−0.966888 | + | 0.255203i | \(0.917858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −265.214 | + | 265.214i | −0.836637 | + | 0.836637i | −0.988415 | − | 0.151778i | \(-0.951500\pi\) |
0.151778 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 130.942 | 0.410476 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −509.728 | + | 509.728i | −1.57810 | + | 1.57810i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.0566 | − | 27.0566i | 0.0832509 | − | 0.0832509i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 193.488 | 0.588111 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −83.6950 | + | 83.6950i | −0.252855 | + | 0.252855i | −0.822140 | − | 0.569285i | \(-0.807220\pi\) |
0.569285 | + | 0.822140i | \(0.307220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 251.411i | − | 0.750481i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 346.530 | 1.02828 | 0.514140 | − | 0.857706i | \(-0.328111\pi\) | ||||
0.514140 | + | 0.857706i | \(0.328111\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.1937 | − | 37.1937i | −0.109073 | − | 0.109073i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 223.921i | 0.652832i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 394.994 | + | 394.994i | 1.13831 | + | 1.13831i | 0.988753 | + | 0.149559i | \(0.0477855\pi\) |
0.149559 | + | 0.988753i | \(0.452214\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −100.763 | − | 100.763i | −0.288719 | − | 0.288719i | 0.547854 | − | 0.836574i | \(-0.315445\pi\) |
−0.836574 | + | 0.547854i | \(0.815445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 211.250i | 0.598442i | 0.954184 | + | 0.299221i | \(0.0967268\pi\) | ||||
−0.954184 | + | 0.299221i | \(0.903273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 163.339 | + | 163.339i | 0.460109 | + | 0.460109i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 180.058 | 0.501555 | 0.250777 | − | 0.968045i | \(-0.419314\pi\) | ||||
0.250777 | + | 0.968045i | \(0.419314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 890.786i | 2.46755i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 76.6519 | − | 76.6519i | 0.210005 | − | 0.210005i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 611.746 | 1.66688 | 0.833442 | − | 0.552608i | \(-0.186367\pi\) | ||||
0.833442 | + | 0.552608i | \(0.186367\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −96.7933 | + | 96.7933i | −0.260898 | + | 0.260898i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −250.082 | + | 250.082i | −0.670462 | + | 0.670462i | −0.957823 | − | 0.287360i | \(-0.907222\pi\) |
0.287360 | + | 0.957823i | \(0.407222\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −72.2680 | −0.191692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 196.949 | − | 196.949i | 0.519655 | − | 0.519655i | −0.397812 | − | 0.917467i | \(-0.630230\pi\) |
0.917467 | + | 0.397812i | \(0.130230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 27.7580i | − | 0.0724752i | −0.999343 | − | 0.0362376i | \(-0.988463\pi\) | ||
0.999343 | − | 0.0362376i | \(-0.0115373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.1803 | 0.0680008 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −250.685 | − | 250.685i | −0.644434 | − | 0.644434i | 0.307208 | − | 0.951642i | \(-0.400605\pi\) |
−0.951642 | + | 0.307208i | \(0.900605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 72.5119i | − | 0.185452i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −210.949 | − | 210.949i | −0.534048 | − | 0.534048i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −211.973 | − | 211.973i | −0.533936 | − | 0.533936i | 0.387805 | − | 0.921741i | \(-0.373233\pi\) |
−0.921741 | + | 0.387805i | \(0.873233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 603.861i | − | 1.50589i | −0.658085 | − | 0.752944i | \(-0.728633\pi\) | ||
0.658085 | − | 0.752944i | \(-0.271367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.5275 | + | 20.5275i | 0.0509368 | + | 0.0509368i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −142.034 | −0.348977 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 229.079i | 0.560094i | 0.959986 | + | 0.280047i | \(0.0903501\pi\) | ||||
−0.959986 | + | 0.280047i | \(0.909650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −46.7774 | + | 46.7774i | −0.113262 | + | 0.113262i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 56.8642 | 0.137022 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −581.441 | + | 581.441i | −1.38769 | + | 1.38769i | −0.557531 | + | 0.830156i | \(0.688251\pi\) |
−0.830156 | + | 0.557531i | \(0.811749\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −212.037 | + | 212.037i | −0.503650 | + | 0.503650i | −0.912570 | − | 0.408920i | \(-0.865905\pi\) |
0.408920 | + | 0.912570i | \(0.365905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −357.816 | −0.841921 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 154.515 | − | 154.515i | 0.361863 | − | 0.361863i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 71.0623i | − | 0.164878i | −0.996596 | − | 0.0824388i | \(-0.973729\pi\) | ||
0.996596 | − | 0.0824388i | \(-0.0262709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −71.8456 | −0.165925 | −0.0829626 | − | 0.996553i | \(-0.526438\pi\) | ||||
−0.0829626 | + | 0.996553i | \(0.526438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −89.0371 | − | 89.0371i | −0.203746 | − | 0.203746i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 75.0323i | 0.170916i | 0.996342 | + | 0.0854582i | \(0.0272354\pi\) | ||||
−0.996342 | + | 0.0854582i | \(0.972765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 407.393 | + | 407.393i | 0.919623 | + | 0.919623i | 0.997002 | − | 0.0773783i | \(-0.0246549\pi\) |
−0.0773783 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 62.3064 | + | 62.3064i | 0.140014 | + | 0.140014i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 537.780i | − | 1.19773i | −0.800851 | − | 0.598864i | \(-0.795619\pi\) | ||
0.800851 | − | 0.598864i | \(-0.204381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −178.857 | − | 178.857i | −0.396578 | − | 0.396578i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.4491 | −0.0317564 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 670.548i | − | 1.46728i | −0.679537 | − | 0.733641i | \(-0.737820\pi\) | ||
0.679537 | − | 0.733641i | \(-0.262180\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −624.560 | + | 624.560i | −1.35479 | + | 1.35479i | −0.474584 | + | 0.880210i | \(0.657401\pi\) |
−0.880210 | + | 0.474584i | \(0.842599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 556.663 | 1.20230 | 0.601148 | − | 0.799138i | \(-0.294710\pi\) | ||||
0.601148 | + | 0.799138i | \(0.294710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 135.903 | − | 135.903i | 0.291013 | − | 0.291013i | −0.546468 | − | 0.837480i | \(-0.684028\pi\) |
0.837480 | + | 0.546468i | \(0.184028\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 158.502 | − | 158.502i | 0.337957 | − | 0.337957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 137.782 | 0.291294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −439.362 | + | 439.362i | −0.924972 | + | 0.924972i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 754.590i | 1.57534i | 0.616095 | + | 0.787672i | \(0.288714\pi\) | ||||
−0.616095 | + | 0.787672i | \(0.711286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 78.3895 | 0.162972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 238.104 | + | 238.104i | 0.490936 | + | 0.490936i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 752.536i | 1.54525i | 0.634863 | + | 0.772624i | \(0.281056\pi\) | ||||
−0.634863 | + | 0.772624i | \(0.718944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −577.864 | − | 577.864i | −1.17691 | − | 1.17691i | −0.980527 | − | 0.196387i | \(-0.937079\pi\) |
−0.196387 | − | 0.980527i | \(-0.562921\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 477.863 | + | 477.863i | 0.969297 | + | 0.969297i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 205.954i | 0.414394i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 46.1997 | + | 46.1997i | 0.0925846 | + | 0.0925846i | 0.751882 | − | 0.659298i | \(-0.229146\pi\) |
−0.659298 | + | 0.751882i | \(0.729146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −442.969 | −0.880655 | −0.440327 | − | 0.897837i | \(-0.645138\pi\) | ||||
−0.440327 | + | 0.897837i | \(0.645138\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 322.325i | 0.638267i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 166.024 | − | 166.024i | 0.326178 | − | 0.326178i | −0.524953 | − | 0.851131i | \(-0.675917\pi\) |
0.851131 | + | 0.524953i | \(0.175917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 96.6504 | 0.189140 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 73.3054 | − | 73.3054i | 0.142341 | − | 0.142341i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −222.122 | + | 222.122i | −0.429637 | + | 0.429637i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.42117 | 0.0142441 | 0.00712204 | − | 0.999975i | \(-0.497733\pi\) | ||||
0.00712204 | + | 0.999975i | \(0.497733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 653.700 | − | 653.700i | 1.24990 | − | 1.24990i | 0.294143 | − | 0.955761i | \(-0.404966\pi\) |
0.955761 | − | 0.294143i | \(-0.0950343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 271.472i | − | 0.515127i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −516.334 | −0.976057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 98.7126 | + | 98.7126i | 0.185202 | + | 0.185202i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 267.621i | − | 0.500226i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −120.277 | − | 120.277i | −0.223148 | − | 0.223148i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 192.630 | + | 192.630i | 0.356063 | + | 0.356063i | 0.862360 | − | 0.506296i | \(-0.168986\pi\) |
−0.506296 | + | 0.862360i | \(0.668986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 178.322i | − | 0.327196i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −131.598 | − | 131.598i | −0.240582 | − | 0.240582i | 0.576509 | − | 0.817091i | \(-0.304415\pi\) |
−0.817091 | + | 0.576509i | \(0.804415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1173.53 | 2.12982 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 265.986i | − | 0.480987i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 109.222 | − | 109.222i | 0.196090 | − | 0.196090i | −0.602231 | − | 0.798322i | \(-0.705722\pi\) |
0.798322 | + | 0.602231i | \(0.205722\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −76.0430 | −0.136034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 640.646 | − | 640.646i | 1.13791 | − | 1.13791i | 0.149090 | − | 0.988824i | \(-0.452365\pi\) |
0.988824 | − | 0.149090i | \(-0.0476346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −187.372 | + | 187.372i | −0.331632 | + | 0.331632i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 273.069 | 0.479911 | 0.239955 | − | 0.970784i | \(-0.422867\pi\) | ||||
0.239955 | + | 0.970784i | \(0.422867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −663.916 | + | 663.916i | −1.16273 | + | 1.16273i | −0.178849 | + | 0.983877i | \(0.557237\pi\) |
−0.983877 | + | 0.178849i | \(0.942763\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 62.5018i | − | 0.108699i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −403.711 | −0.699672 | −0.349836 | − | 0.936811i | \(-0.613763\pi\) | ||||
−0.349836 | + | 0.936811i | \(0.613763\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.8501 | + | 35.8501i | 0.0617041 | + | 0.0617041i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 222.235i | − | 0.381192i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 703.189 | + | 703.189i | 1.19794 | + | 1.19794i | 0.974783 | + | 0.223154i | \(0.0716353\pi\) |
0.223154 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −333.339 | − | 333.339i | −0.565941 | − | 0.565941i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 668.046i | 1.12655i | 0.826268 | + | 0.563277i | \(0.190460\pi\) | ||||
−0.826268 | + | 0.563277i | \(0.809540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 95.5432 | + | 95.5432i | 0.160577 | + | 0.160577i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −677.684 | −1.13136 | −0.565679 | − | 0.824625i | \(-0.691386\pi\) | ||||
−0.565679 | + | 0.824625i | \(0.691386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 170.941i | 0.284427i | 0.989836 | + | 0.142214i | \(0.0454220\pi\) | ||||
−0.989836 | + | 0.142214i | \(0.954578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 203.292 | − | 203.292i | 0.336019 | − | 0.336019i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1112.69 | −1.83310 | −0.916548 | − | 0.399925i | \(-0.869036\pi\) | ||||
−0.916548 | + | 0.399925i | \(0.869036\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 122.591 | − | 122.591i | 0.200640 | − | 0.200640i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 455.272 | − | 455.272i | 0.742696 | − | 0.742696i | −0.230400 | − | 0.973096i | \(-0.574004\pi\) |
0.973096 | + | 0.230400i | \(0.0740036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −229.336 | −0.371695 | −0.185847 | − | 0.982579i | \(-0.559503\pi\) | ||||
−0.185847 | + | 0.982579i | \(0.559503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 163.423 | − | 163.423i | 0.264011 | − | 0.264011i | −0.562670 | − | 0.826681i | \(-0.690226\pi\) |
0.826681 | + | 0.562670i | \(0.190226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 78.5621i | 0.126103i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −122.469 | −0.195950 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −518.341 | − | 518.341i | −0.824072 | − | 0.824072i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 555.849i | − | 0.880902i | −0.897777 | − | 0.440451i | \(-0.854819\pi\) | ||
0.897777 | − | 0.440451i | \(-0.145181\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −361.462 | − | 361.462i | −0.569231 | − | 0.569231i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 66.3818 | + | 66.3818i | 0.104210 | + | 0.104210i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 982.994i | 1.53353i | 0.641927 | + | 0.766766i | \(0.278135\pi\) | ||||
−0.641927 | + | 0.766766i | \(0.721865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −163.762 | − | 163.762i | −0.254684 | − | 0.254684i | 0.568204 | − | 0.822888i | \(-0.307639\pi\) |
−0.822888 | + | 0.568204i | \(0.807639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −655.404 | −1.01299 | −0.506495 | − | 0.862243i | \(-0.669059\pi\) | ||||
−0.506495 | + | 0.862243i | \(0.669059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 107.400i | − | 0.165485i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 469.752 | − | 469.752i | 0.719376 | − | 0.719376i | −0.249102 | − | 0.968477i | \(-0.580135\pi\) |
0.968477 | + | 0.249102i | \(0.0801353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 305.586 | 0.466543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 576.834 | − | 576.834i | 0.875317 | − | 0.875317i | −0.117728 | − | 0.993046i | \(-0.537561\pi\) |
0.993046 | + | 0.117728i | \(0.0375612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 679.417 | − | 679.417i | 1.02786 | − | 1.02786i | 0.0282616 | − | 0.999601i | \(-0.491003\pi\) |
0.999601 | − | 0.0282616i | \(-0.00899714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 234.634 | 0.352834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −83.4711 | + | 83.4711i | −0.125144 | + | 0.125144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 354.764i | 0.528709i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 929.909 | 1.38174 | 0.690868 | − | 0.722981i | \(-0.257228\pi\) | ||||
0.690868 | + | 0.722981i | \(0.257228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 597.623 | + | 597.623i | 0.882751 | + | 0.882751i | 0.993813 | − | 0.111062i | \(-0.0354253\pi\) |
−0.111062 | + | 0.993813i | \(0.535425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 300.225i | 0.442158i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −286.314 | − | 286.314i | −0.419200 | − | 0.419200i | 0.465728 | − | 0.884928i | \(-0.345793\pi\) |
−0.884928 | + | 0.465728i | \(0.845793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.67614 | + | 6.67614i | 0.00974619 | + | 0.00974619i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 122.653i | 0.178017i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 483.066 | + | 483.066i | 0.699083 | + | 0.699083i | 0.964213 | − | 0.265130i | \(-0.0854149\pi\) |
−0.265130 | + | 0.964213i | \(0.585415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −54.4039 | −0.0782790 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1305.45i | − | 1.87296i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 349.679 | − | 349.679i | 0.498829 | − | 0.498829i | −0.412244 | − | 0.911073i | \(-0.635255\pi\) |
0.911073 | + | 0.412244i | \(0.135255\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1272.94 | −1.81072 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −203.210 | + | 203.210i | −0.287425 | + | 0.287425i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 374.404 | − | 374.404i | 0.528074 | − | 0.528074i | −0.391924 | − | 0.919998i | \(-0.628190\pi\) |
0.919998 | + | 0.391924i | \(0.128190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 47.4195 | 0.0665071 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.5874 | − | 16.5874i | 0.0231992 | − | 0.0231992i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 819.536i | − | 1.13983i | −0.821704 | − | 0.569914i | \(-0.806976\pi\) | ||
0.821704 | − | 0.569914i | \(-0.193024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 92.4308 | 0.128198 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 411.896 | + | 411.896i | 0.568132 | + | 0.568132i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1089.99i | − | 1.49930i | −0.661836 | − | 0.749649i | \(-0.730222\pi\) | ||
0.661836 | − | 0.749649i | \(-0.269778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 502.825 | + | 502.825i | 0.687860 | + | 0.687860i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −165.917 | − | 165.917i | −0.226354 | − | 0.226354i | 0.584814 | − | 0.811168i | \(-0.301168\pi\) |
−0.811168 | + | 0.584814i | \(0.801168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 363.917i | 0.493781i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −316.451 | − | 316.451i | −0.428215 | − | 0.428215i | 0.459805 | − | 0.888020i | \(-0.347919\pi\) |
−0.888020 | + | 0.459805i | \(0.847919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1074.58 | 1.44627 | 0.723134 | − | 0.690708i | \(-0.242701\pi\) | ||||
0.723134 | + | 0.690708i | \(0.242701\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 330.835i | − | 0.444073i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 168.721 | − | 168.721i | 0.225262 | − | 0.225262i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −425.307 | −0.566320 | −0.283160 | − | 0.959073i | \(-0.591383\pi\) | ||||
−0.283160 | + | 0.959073i | \(0.591383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 426.508 | − | 426.508i | 0.564912 | − | 0.564912i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −93.5146 | + | 93.5146i | −0.123533 | + | 0.123533i | −0.766170 | − | 0.642637i | \(-0.777840\pi\) |
0.642637 | + | 0.766170i | \(0.277840\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −430.074 | −0.565144 | −0.282572 | − | 0.959246i | \(-0.591188\pi\) | ||||
−0.282572 | + | 0.959246i | \(0.591188\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 112.423 | − | 112.423i | 0.147343 | − | 0.147343i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 59.2749i | 0.0772814i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −307.931 | −0.400430 | −0.200215 | − | 0.979752i | \(-0.564164\pi\) | ||||
−0.200215 | + | 0.979752i | \(0.564164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −531.375 | − | 531.375i | −0.687419 | − | 0.687419i | 0.274241 | − | 0.961661i | \(-0.411573\pi\) |
−0.961661 | + | 0.274241i | \(0.911573\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 233.996i | − | 0.301930i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1602.96 | − | 1602.96i | −2.05771 | − | 2.05771i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −236.432 | − | 236.432i | −0.302730 | − | 0.302730i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 441.265i | 0.562121i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −114.817 | − | 114.817i | −0.145892 | − | 0.145892i | 0.630388 | − | 0.776280i | \(-0.282896\pi\) |
−0.776280 | + | 0.630388i | \(0.782896\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −236.257 | −0.298682 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 195.797i | − | 0.246907i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 699.220 | − | 699.220i | 0.877315 | − | 0.877315i | −0.115941 | − | 0.993256i | \(-0.536988\pi\) |
0.993256 | + | 0.115941i | \(0.0369883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1621.24 | −2.02909 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −110.953 | + | 110.953i | −0.138174 | + | 0.138174i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.6891 | + | 16.6891i | −0.0207318 | + | 0.0207318i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1160.71 | 1.43475 | 0.717376 | − | 0.696686i | \(-0.245343\pi\) | ||||
0.717376 | + | 0.696686i | \(0.245343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 297.004 | − | 297.004i | 0.366220 | − | 0.366220i | −0.499877 | − | 0.866097i | \(-0.666621\pi\) |
0.866097 | + | 0.499877i | \(0.166621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 479.288i | − | 0.588084i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1234.84 | 1.51143 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 606.627 | + | 606.627i | 0.738888 | + | 0.738888i | 0.972363 | − | 0.233475i | \(-0.0750096\pi\) |
−0.233475 | + | 0.972363i | \(0.575010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 320.341i | − | 0.389236i | −0.980879 | − | 0.194618i | \(-0.937653\pi\) | ||
0.980879 | − | 0.194618i | \(-0.0623467\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 686.333 | + | 686.333i | 0.829907 | + | 0.829907i | 0.987504 | − | 0.157597i | \(-0.0503746\pi\) |
−0.157597 | + | 0.987504i | \(0.550375\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −317.721 | − | 317.721i | −0.383258 | − | 0.383258i | 0.489017 | − | 0.872275i | \(-0.337356\pi\) |
−0.872275 | + | 0.489017i | \(0.837356\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 877.883i | − | 1.05388i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −444.465 | − | 444.465i | −0.532293 | − | 0.532293i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 999.424 | 1.19121 | 0.595605 | − | 0.803278i | \(-0.296913\pi\) | ||||
0.595605 | + | 0.803278i | \(0.296913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 259.172i | − | 0.308171i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 316.759 | − | 316.759i | 0.374862 | − | 0.374862i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 256.330 | 0.302633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 90.5416 | − | 90.5416i | 0.106394 | − | 0.106394i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 437.602 | − | 437.602i | 0.513015 | − | 0.513015i | −0.402434 | − | 0.915449i | \(-0.631836\pi\) |
0.915449 | + | 0.402434i | \(0.131836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −734.356 | −0.856891 | −0.428445 | − | 0.903568i | \(-0.640939\pi\) | ||||
−0.428445 | + | 0.903568i | \(0.640939\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −473.257 | + | 473.257i | −0.550939 | + | 0.550939i | −0.926712 | − | 0.375773i | \(-0.877377\pi\) |
0.375773 | + | 0.926712i | \(0.377377\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 415.374i | 0.481315i | 0.970610 | + | 0.240657i | \(0.0773630\pi\) | ||||
−0.970610 | + | 0.240657i | \(0.922637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 167.732 | 0.193910 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 305.348 | + | 305.348i | 0.351379 | + | 0.351379i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 200.849i | − | 0.230596i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 199.587 | + | 199.587i | 0.228100 | + | 0.228100i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 639.234 | + | 639.234i | 0.728887 | + | 0.728887i | 0.970398 | − | 0.241511i | \(-0.0776429\pi\) |
−0.241511 | + | 0.970398i | \(0.577643\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 434.503i | − | 0.493193i | −0.969118 | − | 0.246596i | \(-0.920688\pi\) | ||
0.969118 | − | 0.246596i | \(-0.0793122\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −597.662 | − | 597.662i | −0.676854 | − | 0.676854i | 0.282433 | − | 0.959287i | \(-0.408858\pi\) |
−0.959287 | + | 0.282433i | \(0.908858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1100.10 | −1.24025 | −0.620125 | − | 0.784503i | \(-0.712918\pi\) | ||||
−0.620125 | + | 0.784503i | \(0.712918\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 455.767i | − | 0.512674i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1990.72 | + | 1990.72i | −2.22924 | + | 2.22924i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 562.745 | 0.628765 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −312.501 | + | 312.501i | −0.347610 | + | 0.347610i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 811.031 | − | 811.031i | 0.900146 | − | 0.900146i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 712.669 | 0.787479 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −344.291 | + | 344.291i | −0.379593 | + | 0.379593i | −0.870955 | − | 0.491362i | \(-0.836499\pi\) |
0.491362 | + | 0.870955i | \(0.336499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 803.034i | − | 0.881486i | −0.897633 | − | 0.440743i | \(-0.854715\pi\) | ||
0.897633 | − | 0.440743i | \(-0.145285\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −82.3109 | −0.0901543 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 192.657 | + | 192.657i | 0.210094 | + | 0.210094i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1119.49i | 1.21816i | 0.793107 | + | 0.609082i | \(0.208462\pi\) | ||||
−0.793107 | + | 0.609082i | \(0.791538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 130.489 | + | 130.489i | 0.141375 | + | 0.141375i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −446.786 | − | 446.786i | −0.483012 | − | 0.483012i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1069.69i | 1.15144i | 0.817647 | + | 0.575721i | \(0.195278\pi\) | ||||
−0.817647 | + | 0.575721i | \(0.804722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1077.95 | − | 1077.95i | −1.15784 | − | 1.15784i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −219.365 | −0.234615 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 61.7823i | 0.0659363i | 0.999456 | + | 0.0329682i | \(0.0104960\pi\) | ||||
−0.999456 | + | 0.0329682i | \(0.989504\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 455.261 | − | 455.261i | 0.483806 | − | 0.483806i | −0.422539 | − | 0.906345i | \(-0.638861\pi\) |
0.906345 | + | 0.422539i | \(0.138861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 228.031 | 0.241814 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1145.09 | − | 1145.09i | 1.20918 | − | 1.20918i | 0.237883 | − | 0.971294i | \(-0.423547\pi\) |
0.971294 | − | 0.237883i | \(-0.0764534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.2362 | − | 61.2362i | 0.0645271 | − | 0.0645271i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1187.58 | 1.24615 | 0.623076 | − | 0.782161i | \(-0.285883\pi\) | ||||
0.623076 | + | 0.782161i | \(0.285883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −679.221 | + | 679.221i | −0.711227 | + | 0.711227i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.41794i | 0.00877783i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −783.470 | −0.815265 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −280.903 | − | 280.903i | −0.291091 | − | 0.291091i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 464.902i | 0.480767i | 0.970678 | + | 0.240384i | \(0.0772732\pi\) | ||||
−0.970678 | + | 0.240384i | \(0.922727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −102.522 | − | 102.522i | −0.105584 | − | 0.105584i | 0.652341 | − | 0.757925i | \(-0.273787\pi\) |
−0.757925 | + | 0.652341i | \(0.773787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.2990 | − | 34.2990i | −0.0352507 | − | 0.0352507i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1273.15i | − | 1.30312i | −0.758597 | − | 0.651560i | \(-0.774115\pi\) | ||
0.758597 | − | 0.651560i | \(-0.225885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −90.1883 | − | 90.1883i | −0.0921229 | − | 0.0921229i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 523.931 | 0.532992 | 0.266496 | − | 0.963836i | \(-0.414134\pi\) | ||||
0.266496 | + | 0.963836i | \(0.414134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.4130i | 0.0735158i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −87.8314 | + | 87.8314i | −0.0888083 | + | 0.0888083i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1675.46 | 1.69067 | 0.845336 | − | 0.534235i | \(-0.179400\pi\) | ||||
0.845336 | + | 0.534235i | \(0.179400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −501.645 | + | 501.645i | −0.504166 | + | 0.504166i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −911.770 | + | 911.770i | −0.914513 | + | 0.914513i | −0.996623 | − | 0.0821099i | \(-0.973834\pi\) |
0.0821099 | + | 0.996623i | \(0.473834\pi\) | |||||||
\(998\) | 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 | 1152.3.j.b.161.12 | 32 | ||
3.2 | odd | 2 | inner | 1152.3.j.b.161.5 | 32 | ||
4.3 | odd | 2 | 1152.3.j.a.161.12 | 32 | |||
8.3 | odd | 2 | 144.3.j.a.125.1 | yes | 32 | ||
8.5 | even | 2 | 576.3.j.a.17.5 | 32 | |||
12.11 | even | 2 | 1152.3.j.a.161.5 | 32 | |||
16.3 | odd | 4 | 144.3.j.a.53.16 | yes | 32 | ||
16.5 | even | 4 | inner | 1152.3.j.b.737.5 | 32 | ||
16.11 | odd | 4 | 1152.3.j.a.737.5 | 32 | |||
16.13 | even | 4 | 576.3.j.a.305.12 | 32 | |||
24.5 | odd | 2 | 576.3.j.a.17.12 | 32 | |||
24.11 | even | 2 | 144.3.j.a.125.16 | yes | 32 | ||
48.5 | odd | 4 | inner | 1152.3.j.b.737.12 | 32 | ||
48.11 | even | 4 | 1152.3.j.a.737.12 | 32 | |||
48.29 | odd | 4 | 576.3.j.a.305.5 | 32 | |||
48.35 | even | 4 | 144.3.j.a.53.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.j.a.53.1 | ✓ | 32 | 48.35 | even | 4 | ||
144.3.j.a.53.16 | yes | 32 | 16.3 | odd | 4 | ||
144.3.j.a.125.1 | yes | 32 | 8.3 | odd | 2 | ||
144.3.j.a.125.16 | yes | 32 | 24.11 | even | 2 | ||
576.3.j.a.17.5 | 32 | 8.5 | even | 2 | |||
576.3.j.a.17.12 | 32 | 24.5 | odd | 2 | |||
576.3.j.a.305.5 | 32 | 48.29 | odd | 4 | |||
576.3.j.a.305.12 | 32 | 16.13 | even | 4 | |||
1152.3.j.a.161.5 | 32 | 12.11 | even | 2 | |||
1152.3.j.a.161.12 | 32 | 4.3 | odd | 2 | |||
1152.3.j.a.737.5 | 32 | 16.11 | odd | 4 | |||
1152.3.j.a.737.12 | 32 | 48.11 | even | 4 | |||
1152.3.j.b.161.5 | 32 | 3.2 | odd | 2 | inner | ||
1152.3.j.b.161.12 | 32 | 1.1 | even | 1 | trivial | ||
1152.3.j.b.737.5 | 32 | 16.5 | even | 4 | inner | ||
1152.3.j.b.737.12 | 32 | 48.5 | odd | 4 | inner |