Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), 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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 28x^{8} + 260x^{6} + 897x^{4} + 1056x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.2 | ||
Root | \(-3.30649i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.u.4049.9 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 3.30649i | − 1.90900i | −0.298206 | − | 0.954501i | \(-0.596388\pi\) | ||||
0.298206 | − | 0.954501i | \(-0.403612\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.55040i | − 0.963960i | −0.876182 | − | 0.481980i | \(-0.839918\pi\) | ||||
0.876182 | − | 0.481980i | \(-0.160082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.93288 | −2.64429 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72314 | −0.821056 | −0.410528 | − | 0.911848i | \(-0.634656\pi\) | ||||
−0.410528 | + | 0.911848i | \(0.634656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.12637i | − 1.97650i | −0.152845 | − | 0.988250i | \(-0.548844\pi\) | ||||
0.152845 | − | 0.988250i | \(-0.451156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.924010i | 0.224105i | 0.993702 | + | 0.112053i | \(0.0357426\pi\) | ||||
−0.993702 | + | 0.112053i | \(0.964257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.51623 | −1.72434 | −0.862171 | − | 0.506617i | \(-0.830896\pi\) | ||||
−0.862171 | + | 0.506617i | \(0.830896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.43286 | −1.84020 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.3105i | 3.13896i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38248 | 0.442415 | 0.221208 | − | 0.975227i | \(-0.429000\pi\) | ||||
0.221208 | + | 0.975227i | \(0.429000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.866248 | 0.155583 | 0.0777913 | − | 0.996970i | \(-0.475213\pi\) | ||||
0.0777913 | + | 0.996970i | \(0.475213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.00402i | 1.56740i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.352855i | 0.0580089i | 0.999579 | + | 0.0290045i | \(0.00923370\pi\) | ||||
−0.999579 | + | 0.0290045i | \(0.990766\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −23.5633 | −3.77315 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.34066 | 0.677896 | 0.338948 | − | 0.940805i | \(-0.389929\pi\) | ||||
0.338948 | + | 0.940805i | \(0.389929\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 13.3239i | − 1.94349i | −0.236027 | − | 0.971746i | \(-0.575845\pi\) | ||||
0.236027 | − | 0.971746i | \(-0.424155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.495474 | 0.0707819 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05523 | 0.427818 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.99262i | − 0.548429i | −0.961669 | − | 0.274214i | \(-0.911582\pi\) | ||||
0.961669 | − | 0.274214i | \(-0.0884178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24.8523i | 3.29177i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.84064 | 0.500009 | 0.250004 | − | 0.968245i | \(-0.419568\pi\) | ||||
0.250004 | + | 0.968245i | \(0.419568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.14262 | −1.17059 | −0.585296 | − | 0.810820i | \(-0.699022\pi\) | ||||
−0.585296 | + | 0.810820i | \(0.699022\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.2320i | 2.54899i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.15933i | − 0.385974i | −0.981201 | − | 0.192987i | \(-0.938183\pi\) | ||||
0.981201 | − | 0.192987i | \(-0.0618175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.30649 | 0.398055 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.07883 | −0.721424 | −0.360712 | − | 0.932677i | \(-0.617466\pi\) | ||||
−0.360712 | + | 0.932677i | \(0.617466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3239i | 1.32536i | 0.748901 | + | 0.662682i | \(0.230582\pi\) | ||||
−0.748901 | + | 0.662682i | \(0.769418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.94508i | 0.791465i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0593 | 1.35677 | 0.678386 | − | 0.734706i | \(-0.262680\pi\) | ||||
0.678386 | + | 0.734706i | \(0.262680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.1319 | 3.34799 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.35285i | 0.697316i | 0.937250 | + | 0.348658i | \(0.113363\pi\) | ||||
−0.937250 | + | 0.348658i | \(0.886637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 7.87765i | − 0.844572i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.71377 | 1.02966 | 0.514829 | − | 0.857293i | \(-0.327855\pi\) | ||||
0.514829 | + | 0.857293i | \(0.327855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.1751 | −1.90527 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.86424i | − 0.297008i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.76465i | 0.889916i | 0.895552 | + | 0.444958i | \(0.146781\pi\) | ||||
−0.895552 | + | 0.444958i | \(0.853219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21.6023 | 2.17111 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.74794 | 0.472438 | 0.236219 | − | 0.971700i | \(-0.424092\pi\) | ||||
0.236219 | + | 0.971700i | \(0.424092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 12.6304i | − 1.24451i | −0.782814 | − | 0.622255i | \(-0.786217\pi\) | ||||
0.782814 | − | 0.622255i | \(-0.213783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.9658i | − 1.25345i | −0.779239 | − | 0.626727i | \(-0.784394\pi\) | ||||
0.779239 | − | 0.626727i | \(-0.215606\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0040 | 1.43712 | 0.718562 | − | 0.695463i | \(-0.244801\pi\) | ||||
0.718562 | + | 0.695463i | \(0.244801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.16671 | 0.110739 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.13496i | − 0.200840i | −0.994945 | − | 0.100420i | \(-0.967981\pi\) | ||||
0.994945 | − | 0.100420i | \(-0.0320187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 56.5326i | 5.22644i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35659 | 0.216029 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.58454 | −0.325867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 14.3523i | − 1.29411i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.54181i | − 0.314285i | −0.987576 | − | 0.157142i | \(-0.949772\pi\) | ||||
0.987576 | − | 0.157142i | \(-0.0502282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5499 | 1.70808 | 0.854042 | − | 0.520205i | \(-0.174144\pi\) | ||||
0.854042 | + | 0.520205i | \(0.174144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.1694i | 1.66220i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.41544i | 0.377236i | 0.982051 | + | 0.188618i | \(0.0604008\pi\) | ||||
−0.982051 | + | 0.188618i | \(0.939599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.9954 | −1.86563 | −0.932814 | − | 0.360358i | \(-0.882655\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −44.0554 | −3.71013 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.4061i | 1.62282i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.63828i | − 0.135123i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.0780 | −1.56293 | −0.781466 | − | 0.623947i | \(-0.785528\pi\) | ||||
−0.781466 | + | 0.623947i | \(0.785528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.75273 | −0.630908 | −0.315454 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315454 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 7.33006i | − 0.592600i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5129i | 1.39768i | 0.715277 | + | 0.698841i | \(0.246300\pi\) | ||||
−0.715277 | + | 0.698841i | \(0.753700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.2016 | −1.04695 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.55040 | 0.200999 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55491i | 0.200116i | 0.994982 | + | 0.100058i | \(0.0319028\pi\) | ||||
−0.994982 | + | 0.100058i | \(0.968097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3.61301i | − 0.279583i | −0.990181 | − | 0.139791i | \(-0.955357\pi\) | ||||
0.990181 | − | 0.139791i | \(-0.0446432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.7852 | −2.90655 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 59.6253 | 4.55966 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 12.7824i | − 0.971827i | −0.874007 | − | 0.485913i | \(-0.838487\pi\) | ||||
0.874007 | − | 0.485913i | \(-0.161513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 12.6990i | − 0.954519i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0149 | −0.748546 | −0.374273 | − | 0.927318i | \(-0.622108\pi\) | ||||
−0.374273 | + | 0.927318i | \(0.622108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.96248 | 0.740505 | 0.370252 | − | 0.928931i | \(-0.379271\pi\) | ||||
0.370252 | + | 0.928931i | \(0.379271\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.2300i | 2.23466i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.51621i | − 0.184003i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41.5983 | 3.02583 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.61298 | −0.478498 | −0.239249 | − | 0.970958i | \(-0.576901\pi\) | ||||
−0.239249 | + | 0.970958i | \(0.576901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0540i | 1.37154i | 0.727820 | + | 0.685768i | \(0.240534\pi\) | ||||
−0.727820 | + | 0.685768i | \(0.759466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.0886i | − 0.790030i | −0.918675 | − | 0.395015i | \(-0.870739\pi\) | ||||
0.918675 | − | 0.395015i | \(-0.129261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.71377 | −0.263263 | −0.131631 | − | 0.991299i | \(-0.542021\pi\) | ||||
−0.131631 | + | 0.991299i | \(0.542021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.4463 | −0.736825 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 6.07627i | − 0.426471i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 7.93288i | − 0.551373i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.4677 | 1.41578 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.7656 | −1.49841 | −0.749204 | − | 0.662339i | \(-0.769564\pi\) | ||||
−0.749204 | + | 0.662339i | \(0.769564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.0996i | 1.37720i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.20928i | − 0.149975i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.4424 | 2.53012 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.58484 | 0.442944 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.90730i | − 0.462547i | −0.972889 | − | 0.231273i | \(-0.925711\pi\) | ||||
0.972889 | − | 0.231273i | \(-0.0742892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.0325i | − 1.52872i | −0.644791 | − | 0.764359i | \(-0.723055\pi\) | ||||
0.644791 | − | 0.764359i | \(-0.276945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9665 | −0.856854 | −0.428427 | − | 0.903576i | \(-0.640932\pi\) | ||||
−0.428427 | + | 0.903576i | \(0.640932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.9638 | 1.51091 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.80934i | 0.315071i | 0.987513 | + | 0.157535i | \(0.0503548\pi\) | ||||
−0.987513 | + | 0.157535i | \(0.949645\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 39.8738i | − 2.59008i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4661 | 1.32384 | 0.661922 | − | 0.749573i | \(-0.269741\pi\) | ||||
0.661922 | + | 0.749573i | \(0.269741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8657 | 1.73057 | 0.865287 | − | 0.501277i | \(-0.167136\pi\) | ||||
0.865287 | + | 0.501277i | \(0.167136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 50.6993i | − 3.25236i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 53.5635i | 3.40816i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.0057 | 1.33118 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.9625 | −1.00754 | −0.503771 | − | 0.863837i | \(-0.668055\pi\) | ||||
−0.503771 | + | 0.863837i | \(0.668055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.72314i | − 0.171202i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.33867i | 0.208261i | 0.994564 | + | 0.104130i | \(0.0332059\pi\) | ||||
−0.994564 | + | 0.104130i | \(0.966794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.899919 | 0.0559183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.8999 | −1.16988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3880i | 1.44217i | 0.692849 | + | 0.721083i | \(0.256355\pi\) | ||||
−0.692849 | + | 0.721083i | \(0.743645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 32.1185i | − 1.96562i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.1378 | −0.861995 | −0.430998 | − | 0.902353i | \(-0.641838\pi\) | ||||
−0.430998 | + | 0.902353i | \(0.641838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9283 | 1.57503 | 0.787517 | − | 0.616293i | \(-0.211366\pi\) | ||||
0.787517 | + | 0.616293i | \(0.211366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 60.0957i | 3.63716i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.07117i | 0.0643603i | 0.999482 | + | 0.0321802i | \(0.0102450\pi\) | ||||
−0.999482 | + | 0.0321802i | \(0.989755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.87184 | −0.411406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2260 | 0.729341 | 0.364671 | − | 0.931137i | \(-0.381182\pi\) | ||||
0.364671 | + | 0.931137i | \(0.381182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.5454i | 1.81573i | 0.419259 | + | 0.907867i | \(0.362290\pi\) | ||||
−0.419259 | + | 0.907867i | \(0.637710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 11.0704i | − 0.653465i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.1462 | 0.949777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.9802 | 1.69885 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.46838i | 0.494728i | 0.968923 | + | 0.247364i | \(0.0795644\pi\) | ||||
−0.968923 | + | 0.247364i | \(0.920436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 44.4157i | − 2.57726i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.12637 | 0.412129 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 15.6990i | − 0.901885i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.32802i | − 0.0757942i | −0.999282 | − | 0.0378971i | \(-0.987934\pi\) | ||||
0.999282 | − | 0.0378971i | \(-0.0120659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −41.7623 | −2.37578 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2971 | 1.37776 | 0.688882 | − | 0.724874i | \(-0.258102\pi\) | ||||
0.688882 | + | 0.724874i | \(0.258102\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 20.3478i | − 1.15013i | −0.818109 | − | 0.575063i | \(-0.804977\pi\) | ||||
0.818109 | − | 0.575063i | \(-0.195023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.57309i | − 0.481513i | −0.970586 | − | 0.240756i | \(-0.922604\pi\) | ||||
0.970586 | − | 0.240756i | \(-0.0773955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.48781 | −0.363248 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.8714 | −2.39285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.94508i | − 0.386434i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 49.6106i | − 2.74347i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.9813 | −1.87345 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.9767 | −1.15299 | −0.576493 | − | 0.817102i | \(-0.695579\pi\) | ||||
−0.576493 | + | 0.817102i | \(0.695579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.79915i | − 0.153393i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.17314i | − 0.118379i | −0.998247 | − | 0.0591894i | \(-0.981148\pi\) | ||||
0.998247 | − | 0.0591894i | \(-0.0188516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.05922 | −0.383404 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.35891 | −0.127742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 19.1164i | − 1.03219i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 32.1335i | − 1.72502i | −0.506042 | − | 0.862509i | \(-0.668892\pi\) | ||||
0.506042 | − | 0.862509i | \(-0.331108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5157 | −0.723479 | −0.361740 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361740 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 116.235 | 6.20415 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0645i | 1.49372i | 0.664981 | + | 0.746861i | \(0.268440\pi\) | ||||
−0.664981 | + | 0.746861i | \(0.731560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 7.79205i | − 0.412399i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.2340 | −1.06791 | −0.533956 | − | 0.845513i | \(-0.679295\pi\) | ||||
−0.533956 | + | 0.845513i | \(0.679295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.4937 | 1.97336 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8522i | 0.622081i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.76666i | 0.248818i | 0.992231 | + | 0.124409i | \(0.0397034\pi\) | ||||
−0.992231 | + | 0.124409i | \(0.960297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −34.4339 | −1.79256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1828 | −0.528663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.1510i | 1.50938i | 0.656082 | + | 0.754690i | \(0.272213\pi\) | ||||
−0.656082 | + | 0.754690i | \(0.727787\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 16.9784i | − 0.874434i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.20856 | −0.216179 | −0.108090 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108090 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7110 | −0.599971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 3.55206i | − 0.181502i | −0.995874 | − | 0.0907508i | \(-0.971073\pi\) | ||||
0.995874 | − | 0.0907508i | \(-0.0289267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.2515 | 1.48311 | 0.741554 | − | 0.670893i | \(-0.234089\pi\) | ||||
0.741554 | + | 0.670893i | \(0.234089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.924010 | −0.0467292 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 64.6416i | − 3.26074i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 17.8000i | − 0.893356i | −0.894695 | − | 0.446678i | \(-0.852607\pi\) | ||||
0.894695 | − | 0.446678i | \(-0.147393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 63.3834 | 3.17314 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.6210 | −0.580327 | −0.290164 | − | 0.956977i | \(-0.593710\pi\) | ||||
−0.290164 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.17320i | − 0.307509i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 0.960871i | − 0.0476286i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5710 | 0.671041 | 0.335521 | − | 0.942033i | \(-0.391088\pi\) | ||||
0.335521 | + | 0.942033i | \(0.391088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5996 | 0.720145 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 9.79516i | − 0.481988i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 72.7277i | 3.56149i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4959 | −0.659317 | −0.329658 | − | 0.944100i | \(-0.606934\pi\) | ||||
−0.329658 | + | 0.944100i | \(0.606934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.6495 | 1.83492 | 0.917462 | − | 0.397824i | \(-0.130234\pi\) | ||||
0.917462 | + | 0.397824i | \(0.130234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 105.697i | 5.13916i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.3173i | 1.12840i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 64.1660 | 3.09796 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0568 | 0.484421 | 0.242210 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242210 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 2.30001i | − 0.110531i | −0.998472 | − | 0.0552657i | \(-0.982399\pi\) | ||||
0.998472 | − | 0.0552657i | \(-0.0176006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.51623i | − 0.359550i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4273 | −0.593124 | −0.296562 | − | 0.955014i | \(-0.595840\pi\) | ||||
−0.296562 | + | 0.955014i | \(0.595840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.93053 | −0.187168 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.18268i | − 0.103702i | −0.998655 | − | 0.0518510i | \(-0.983488\pi\) | ||||
0.998655 | − | 0.0518510i | \(-0.0165121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 63.0813i | 2.98364i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.09603 | −0.146111 | −0.0730554 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730554 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8202 | −0.556591 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.6343i | 1.20441i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 0.320363i | − 0.0149860i | −0.999972 | − | 0.00749298i | \(-0.997615\pi\) | ||||
0.999972 | − | 0.00749298i | \(-0.00238511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.0711 | −0.703458 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3239 | −0.713706 | −0.356853 | − | 0.934161i | \(-0.616150\pi\) | ||||
−0.356853 | + | 0.934161i | \(0.616150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.81556i | − 0.316746i | −0.987379 | − | 0.158373i | \(-0.949375\pi\) | ||||
0.987379 | − | 0.158373i | \(-0.0506248\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.2444i | 1.26072i | 0.776303 | + | 0.630360i | \(0.217093\pi\) | ||||
−0.776303 | + | 0.630360i | \(0.782907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.05755 | −0.372063 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 57.9062 | 2.66818 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.6730i | 1.45021i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.5031 | −1.07388 | −0.536942 | − | 0.843619i | \(-0.680421\pi\) | ||||
−0.536942 | + | 0.843619i | \(0.680421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.51457 | 0.114655 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8.43286i | − 0.383709i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.63058i | 0.345774i | 0.984942 | + | 0.172887i | \(0.0553096\pi\) | ||||
−0.984942 | + | 0.172887i | \(0.944690\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.44779 | 0.382022 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1206 | −0.862902 | −0.431451 | − | 0.902136i | \(-0.641998\pi\) | ||||
−0.431451 | + | 0.902136i | \(0.641998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.20144i | 0.0991477i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5034i | 0.695424i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6581 | 1.14861 | 0.574306 | − | 0.818641i | \(-0.305272\pi\) | ||||
0.574306 | + | 0.818641i | \(0.305272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.9464 | −0.533725 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.42282i | 0.375555i | 0.982212 | + | 0.187777i | \(0.0601284\pi\) | ||||
−0.982212 | + | 0.187777i | \(0.939872\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 124.936i | 5.54862i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.2328 | −0.808153 | −0.404076 | − | 0.914725i | \(-0.632407\pi\) | ||||
−0.404076 | + | 0.914725i | \(0.632407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.8805 | 1.27760 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 122.594i | − 5.41264i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.2828i | 1.59572i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.2648 | −1.85522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8738 | 0.870689 | 0.435345 | − | 0.900264i | \(-0.356627\pi\) | ||||
0.435345 | + | 0.900264i | \(0.356627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7228i | 0.862418i | 0.902252 | + | 0.431209i | \(0.141913\pi\) | ||||
−0.902252 | + | 0.431209i | \(0.858087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.800422i | 0.0348669i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.4673 | −1.32217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 30.9331i | − 1.33986i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.1141i | 1.42898i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.34924 | −0.0581160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.4662 | −0.707938 | −0.353969 | − | 0.935257i | \(-0.615168\pi\) | ||||
−0.353969 | + | 0.935257i | \(0.615168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 32.9408i | − 1.41363i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 38.3286i | − 1.63881i | −0.573215 | − | 0.819405i | \(-0.694304\pi\) | ||||
0.573215 | − | 0.819405i | \(-0.305696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 72.5273 | 3.09539 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.9073 | −0.762875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 30.7559i | − 1.30787i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20.3973i | − 0.864263i | −0.901811 | − | 0.432132i | \(-0.857762\pi\) | ||||
0.901811 | − | 0.432132i | \(-0.142238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.31981 | −0.351263 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.72270i | 0.0726032i | 0.999341 | + | 0.0363016i | \(0.0115577\pi\) | ||||
−0.999341 | + | 0.0363016i | \(0.988442\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 76.8483i | − 3.22733i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.3283 | −1.06182 | −0.530909 | − | 0.847429i | \(-0.678150\pi\) | ||||
−0.530909 | + | 0.847429i | \(0.678150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.68968 | −0.238106 | −0.119053 | − | 0.992888i | \(-0.537986\pi\) | ||||
−0.119053 | + | 0.992888i | \(0.537986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.8658i | 0.913455i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 18.0377i | − 0.750918i | −0.926839 | − | 0.375459i | \(-0.877485\pi\) | ||||
0.926839 | − | 0.375459i | \(-0.122515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 63.0019 | 2.61827 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2023 | 0.672185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8724i | 0.450291i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.1894i | 0.544383i | 0.962243 | + | 0.272192i | \(0.0877485\pi\) | ||||
−0.962243 | + | 0.272192i | \(0.912252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51092 | −0.268278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.6643 | −1.50817 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.326755i | 0.0134182i | 0.999977 | + | 0.00670911i | \(0.00213559\pi\) | ||||
−0.999977 | + | 0.00670911i | \(0.997864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.2796i | 0.502569i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.49619 | 0.306286 | 0.153143 | − | 0.988204i | \(-0.451061\pi\) | ||||
0.153143 | + | 0.988204i | \(0.451061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.121724 | 0.00496523 | 0.00248262 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248262 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.0626i | 1.02063i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.52992i | 0.0620975i | 0.999518 | + | 0.0310488i | \(0.00988471\pi\) | ||||
−0.999518 | + | 0.0310488i | \(0.990115\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0911 | −0.814134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −94.9512 | −3.84131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24.3927i | − 0.985211i | −0.870253 | − | 0.492605i | \(-0.836045\pi\) | ||||
0.870253 | − | 0.492605i | \(-0.163955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.8906i | 1.12283i | 0.827534 | + | 0.561416i | \(0.189743\pi\) | ||||
−0.827534 | + | 0.561416i | \(0.810257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8617 | −0.516957 | −0.258478 | − | 0.966017i | \(-0.583221\pi\) | ||||
−0.258478 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.3105 | −0.654518 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 24.7740i | − 0.992549i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 67.6763i | − 2.70273i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.326041 | −0.0130001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.9518 | −0.475794 | −0.237897 | − | 0.971290i | \(-0.576458\pi\) | ||||
−0.237897 | + | 0.971290i | \(0.576458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 71.9679i | 2.86047i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.53093i | − 0.139901i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48.2226 | 1.90766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.9139 | −0.944544 | −0.472272 | − | 0.881453i | \(-0.656566\pi\) | ||||
−0.472272 | + | 0.881453i | \(0.656566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.87313i | − 0.152741i | −0.997079 | − | 0.0763707i | \(-0.975667\pi\) | ||||
0.997079 | − | 0.0763707i | \(-0.0243333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 10.3330i | − 0.406231i | −0.979155 | − | 0.203115i | \(-0.934893\pi\) | ||||
0.979155 | − | 0.203115i | \(-0.0651067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4586 | −0.410535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.30495 | −0.286303 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 21.6319i | − 0.846522i | −0.906008 | − | 0.423261i | \(-0.860885\pi\) | ||||
0.906008 | − | 0.423261i | \(-0.139115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 89.8312i | − 3.50465i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.7168 | −0.612238 | −0.306119 | − | 0.951993i | \(-0.599030\pi\) | ||||
−0.306119 | + | 0.951993i | \(0.599030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.3002 | −1.56750 | −0.783749 | − | 0.621078i | \(-0.786695\pi\) | ||||
−0.783749 | + | 0.621078i | \(0.786695\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 21.7727i | − 0.845582i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.38248i | 0.0922500i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8389 | −0.883003 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.8966 | 0.961122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.69888i | 0.258223i | 0.991630 | + | 0.129111i | \(0.0412125\pi\) | ||||
−0.991630 | + | 0.129111i | \(0.958788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 22.5812i | − 0.867866i | −0.900945 | − | 0.433933i | \(-0.857125\pi\) | ||||
0.900945 | − | 0.433933i | \(-0.142875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.3533 | 0.857843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −76.1566 | −2.91833 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.42797i | 0.0546398i | 0.999627 | + | 0.0273199i | \(0.00869728\pi\) | ||||
−0.999627 | + | 0.0273199i | \(0.991303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.8738i | 1.63574i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.4529 | −1.08397 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.50255 | −0.0571595 | −0.0285798 | − | 0.999592i | \(-0.509098\pi\) | ||||
−0.0285798 | + | 0.999592i | \(0.509098\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 55.0944i | − 2.09286i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.01081i | 0.151920i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9020 | 0.601471 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.7341 | 0.707577 | 0.353789 | − | 0.935325i | \(-0.384893\pi\) | ||||
0.353789 | + | 0.935325i | \(0.384893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.65214i | − 0.100027i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 12.1091i | − 0.455411i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5052 | 0.507199 | 0.253599 | − | 0.967309i | \(-0.418385\pi\) | ||||
0.253599 | + | 0.967309i | \(0.418385\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −95.6646 | −3.58770 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.866248i | 0.0324412i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 67.6711i | − 2.52722i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7496 | −1.18406 | −0.592030 | − | 0.805916i | \(-0.701673\pi\) | ||||
−0.592030 | + | 0.805916i | \(0.701673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.2126 | −1.19966 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 88.8313i | − 3.30367i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6531i | 0.803070i | 0.915844 | + | 0.401535i | \(0.131523\pi\) | ||||
−0.915844 | + | 0.401535i | \(0.868477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −77.2411 | −2.86078 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 0.640507i | − 0.0236577i | −0.999930 | − | 0.0118288i | \(-0.996235\pi\) | ||||
0.999930 | − | 0.0118288i | \(-0.00376533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.60329i | 0.316906i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8191 | −0.618700 | −0.309350 | − | 0.950948i | \(-0.600111\pi\) | ||||
−0.309350 | + | 0.950948i | \(0.600111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 177.107 | 6.50619 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.9691i | 0.585851i | 0.956135 | + | 0.292925i | \(0.0946288\pi\) | ||||
−0.956135 | + | 0.292925i | \(0.905371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 50.3964i | − 1.84391i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.0680 | −1.20828 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.09841 | −0.295515 | −0.147758 | − | 0.989024i | \(-0.547206\pi\) | ||||
−0.147758 | + | 0.989024i | \(0.547206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 52.7798i | 1.92340i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.5691i | 0.747598i | 0.927510 | + | 0.373799i | \(0.121945\pi\) | ||||
−0.927510 | + | 0.373799i | \(0.878055\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00402 | −0.326825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1840 | −0.622919 | −0.311459 | − | 0.950259i | \(-0.600818\pi\) | ||||
−0.311459 | + | 0.950259i | \(0.600818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 38.2662i | − 1.38533i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 27.3698i | − 0.988268i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.8648 | −1.50968 | −0.754841 | − | 0.655908i | \(-0.772286\pi\) | ||||
−0.754841 | + | 0.655908i | \(0.772286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0393 | 0.397570 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.7639i | 1.28634i | 0.765724 | + | 0.643170i | \(0.222381\pi\) | ||||
−0.765724 | + | 0.643170i | \(0.777619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 2.97557i | − 0.106748i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.6254 | −1.16893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.5535 | 0.592330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.8595i | 1.38872i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9835i | 0.961858i | 0.876759 | + | 0.480929i | \(0.159701\pi\) | ||||
−0.876759 | + | 0.480929i | \(0.840299\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 77.3321 | 2.75310 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.44500 | −0.193602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.1537i | 2.31368i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.7226i | 0.946561i | 0.880912 | + | 0.473281i | \(0.156930\pi\) | ||||
−0.880912 | + | 0.473281i | \(0.843070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.3114 | 0.435547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −77.0582 | −2.72272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 30.8366i | − 1.08820i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.7464i | 1.64555i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.0319 | −1.75903 | −0.879513 | − | 0.475874i | \(-0.842132\pi\) | ||||
−0.879513 | + | 0.475874i | \(0.842132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5774 | 1.17906 | 0.589531 | − | 0.807746i | \(-0.299313\pi\) | ||||
0.589531 | + | 0.807746i | \(0.299313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 85.7318i | − 3.00675i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 144.181 | 5.03808 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.1429 | 0.947295 | 0.473647 | − | 0.880715i | \(-0.342937\pi\) | ||||
0.473647 | + | 0.880715i | \(0.342937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 32.6392i | − 1.13773i | −0.822431 | − | 0.568866i | \(-0.807382\pi\) | ||||
0.822431 | − | 0.568866i | \(-0.192618\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37.0828i | − 1.28949i | −0.764396 | − | 0.644747i | \(-0.776963\pi\) | ||||
0.764396 | − | 0.644747i | \(-0.223037\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9405 | −1.17880 | −0.589401 | − | 0.807841i | \(-0.700636\pi\) | ||||
−0.589401 | + | 0.807841i | \(0.700636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.54181 | 0.122864 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.457823i | 0.0158626i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.1289i | 0.488368i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.36929 | 0.0472730 | 0.0236365 | − | 0.999721i | \(-0.492476\pi\) | ||||
0.0236365 | + | 0.999721i | \(0.492476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3238 | −0.804269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 40.4251i | − 1.39231i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.14199i | 0.314122i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 100.998 | 3.46624 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.352855 | −0.0120957 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 9.21382i | − 0.315475i | −0.987481 | − | 0.157738i | \(-0.949580\pi\) | ||||
0.987481 | − | 0.157738i | \(-0.0504200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.3564i | 0.490405i | 0.969472 | + | 0.245202i | \(0.0788544\pi\) | ||||
−0.969472 | + | 0.245202i | \(0.921146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3758 | −1.07053 | −0.535264 | − | 0.844685i | \(-0.679788\pi\) | ||||
−0.535264 | + | 0.844685i | \(0.679788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.6042 | −1.24747 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 26.1214i | − 0.889182i | −0.895734 | − | 0.444591i | \(-0.853349\pi\) | ||||
0.895734 | − | 0.444591i | \(-0.146651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 53.3873i | − 1.81313i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.8390 | −1.11399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.5146 | −0.762877 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 69.5289i | − 2.35320i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 11.5530i | − 0.390118i | −0.980792 | − | 0.195059i | \(-0.937510\pi\) | ||||
0.980792 | − | 0.195059i | \(-0.0624898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0006 | 0.944437 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3559 | −1.15748 | −0.578740 | − | 0.815512i | \(-0.696456\pi\) | ||||
−0.578740 | + | 0.815512i | \(0.696456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12.8316i | − 0.431818i | −0.976414 | − | 0.215909i | \(-0.930729\pi\) | ||||
0.976414 | − | 0.215909i | \(-0.0692714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1.46724i | − 0.0492652i | −0.999697 | − | 0.0246326i | \(-0.992158\pi\) | ||||
0.999697 | − | 0.0246326i | \(-0.00784159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.03303 | −0.302958 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −82.0533 | −2.74889 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 100.146i | 3.35125i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 23.5633i | − 0.786755i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.06382 | 0.0688322 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.68922 | 0.122906 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.44558i | 0.147613i | 0.997273 | + | 0.0738066i | \(0.0235147\pi\) | ||||
−0.997273 | + | 0.0738066i | \(0.976485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.6648 | −1.24926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1697 | 1.33088 | 0.665440 | − | 0.746451i | \(-0.268244\pi\) | ||||
0.665440 | + | 0.746451i | \(0.268244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 17.2997i | − 0.572536i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 49.8600i | − 1.64652i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.8063 | −1.54400 | −0.771999 | − | 0.635624i | \(-0.780743\pi\) | ||||
−0.771999 | + | 0.635624i | \(0.780743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.39109 | −0.144691 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.3200i | 1.42590i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 100.195i | 3.29085i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.92145 | −0.292703 | −0.146352 | − | 0.989233i | \(-0.546753\pi\) | ||||
−0.146352 | + | 0.989233i | \(0.546753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.72409 | −0.122052 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 80.3382i | − 2.63016i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.70070i | 0.251571i | 0.992057 | + | 0.125785i | \(0.0401451\pi\) | ||||
−0.992057 | + | 0.125785i | \(0.959855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.2799 | −2.19560 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8979 | −0.550856 | −0.275428 | − | 0.961322i | \(-0.588820\pi\) | ||||
−0.275428 | + | 0.961322i | \(0.588820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.34066i | 0.141351i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 43.7150i | − 1.42055i | −0.703927 | − | 0.710273i | \(-0.748572\pi\) | ||||
0.703927 | − | 0.710273i | \(-0.251428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.6985 | 2.61958 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.3469 | −0.919210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 30.2353i | − 0.979418i | −0.871886 | − | 0.489709i | \(-0.837103\pi\) | ||||
0.871886 | − | 0.489709i | \(-0.162897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.4519i | 0.693441i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2611 | 0.363641 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2496 | −0.975794 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 102.856i | 3.31450i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2727i | 0.523296i | 0.965163 | + | 0.261648i | \(0.0842659\pi\) | ||||
−0.965163 | + | 0.261648i | \(0.915734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.9638 | −0.737704 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.21424 | 0.199424 | 0.0997122 | − | 0.995016i | \(-0.468208\pi\) | ||||
0.0997122 | + | 0.995016i | \(0.468208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.0971i | 1.79839i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.6705i | 0.821271i | 0.911800 | + | 0.410636i | \(0.134693\pi\) | ||||
−0.911800 | + | 0.410636i | \(0.865307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.4519 | −0.845407 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −119.025 | −3.80018 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.7124i | 0.979574i | 0.871842 | + | 0.489787i | \(0.162925\pi\) | ||||
−0.871842 | + | 0.489787i | \(0.837075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 112.359i | 3.57642i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4052 | 0.934086 | 0.467043 | − | 0.884235i | \(-0.345319\pi\) | ||||
0.467043 | + | 0.884235i | \(0.345319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 69.3594i | 2.20105i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.59825i | 0.177298i | 0.996063 | + | 0.0886492i | \(0.0282550\pi\) | ||||
−0.996063 | + | 0.0886492i | \(0.971745\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.75524 | −0.182088 |
(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 | 4600.2.e.u.4049.2 | 10 | ||
5.2 | odd | 4 | 4600.2.a.be.1.1 | 5 | |||
5.3 | odd | 4 | 920.2.a.j.1.5 | ✓ | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.u.4049.9 | 10 | ||
15.8 | even | 4 | 8280.2.a.bs.1.2 | 5 | |||
20.3 | even | 4 | 1840.2.a.v.1.1 | 5 | |||
20.7 | even | 4 | 9200.2.a.cu.1.5 | 5 | |||
40.3 | even | 4 | 7360.2.a.cp.1.5 | 5 | |||
40.13 | odd | 4 | 7360.2.a.co.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.j.1.5 | ✓ | 5 | 5.3 | odd | 4 | ||
1840.2.a.v.1.1 | 5 | 20.3 | even | 4 | |||
4600.2.a.be.1.1 | 5 | 5.2 | odd | 4 | |||
4600.2.e.u.4049.2 | 10 | 1.1 | even | 1 | trivial | ||
4600.2.e.u.4049.9 | 10 | 5.4 | even | 2 | inner | ||
7360.2.a.co.1.1 | 5 | 40.13 | odd | 4 | |||
7360.2.a.cp.1.5 | 5 | 40.3 | even | 4 | |||
8280.2.a.bs.1.2 | 5 | 15.8 | even | 4 | |||
9200.2.a.cu.1.5 | 5 | 20.7 | even | 4 |