Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.2 | ||
Root | \(1.22306 + 0.710021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.g.401.2 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.09156 | + | 1.09156i | −0.630214 | + | 0.630214i | −0.948122 | − | 0.317908i | \(-0.897020\pi\) |
0.317908 | + | 0.948122i | \(0.397020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.973926i | − | 0.368109i | −0.982916 | − | 0.184055i | \(-0.941078\pi\) | ||
0.982916 | − | 0.184055i | \(-0.0589224\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.616985i | 0.205662i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.40810 | − | 1.40810i | −0.424558 | − | 0.424558i | 0.462212 | − | 0.886769i | \(-0.347056\pi\) |
−0.886769 | + | 0.462212i | \(0.847056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60317 | − | 4.60317i | 1.27669 | − | 1.27669i | 0.334179 | − | 0.942510i | \(-0.391541\pi\) |
0.942510 | − | 0.334179i | \(-0.108459\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.490104 | −0.118868 | −0.0594338 | − | 0.998232i | \(-0.518930\pi\) | ||||
−0.0594338 | + | 0.998232i | \(0.518930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.54863 | + | 4.54863i | −1.04353 | + | 1.04353i | −0.0445187 | + | 0.999009i | \(0.514175\pi\) |
−0.999009 | + | 0.0445187i | \(0.985825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06310 | + | 1.06310i | 0.231988 | + | 0.231988i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.94308i | − | 0.405160i | −0.979266 | − | 0.202580i | \(-0.935067\pi\) | ||
0.979266 | − | 0.202580i | \(-0.0649325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.94816 | − | 3.94816i | −0.759824 | − | 0.759824i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.74613 | + | 3.74613i | −0.695640 | + | 0.695640i | −0.963467 | − | 0.267827i | \(-0.913694\pi\) |
0.267827 | + | 0.963467i | \(0.413694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29021 | −0.770545 | −0.385272 | − | 0.922803i | \(-0.625893\pi\) | ||||
−0.385272 | + | 0.922803i | \(0.625893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.07405 | 0.535124 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55320 | − | 4.55320i | −0.748542 | − | 0.748542i | 0.225663 | − | 0.974205i | \(-0.427545\pi\) |
−0.974205 | + | 0.225663i | \(0.927545\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.0493i | 1.60917i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.1542i | − | 1.58582i | −0.609341 | − | 0.792908i | \(-0.708566\pi\) | ||
0.609341 | − | 0.792908i | \(-0.291434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.79055 | − | 1.79055i | −0.273057 | − | 0.273057i | 0.557273 | − | 0.830329i | \(-0.311848\pi\) |
−0.830329 | + | 0.557273i | \(0.811848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0162 | 1.46102 | 0.730510 | − | 0.682902i | \(-0.239283\pi\) | ||||
0.730510 | + | 0.682902i | \(0.239283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.05147 | 0.864495 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.534979 | − | 0.534979i | 0.0749120 | − | 0.0749120i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.61412 | − | 5.61412i | −0.771158 | − | 0.771158i | 0.207151 | − | 0.978309i | \(-0.433581\pi\) |
−0.978309 | + | 0.207151i | \(0.933581\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.93022i | − | 1.31529i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.44185 | − | 8.44185i | −1.09904 | − | 1.09904i | −0.994524 | − | 0.104512i | \(-0.966672\pi\) |
−0.104512 | − | 0.994524i | \(-0.533328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01095 | − | 3.01095i | 0.385513 | − | 0.385513i | −0.487571 | − | 0.873084i | \(-0.662117\pi\) |
0.873084 | + | 0.487571i | \(0.162117\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.600897 | 0.0757060 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.07504 | − | 7.07504i | 0.864354 | − | 0.864354i | −0.127486 | − | 0.991840i | \(-0.540691\pi\) |
0.991840 | + | 0.127486i | \(0.0406908\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.12099 | + | 2.12099i | 0.255337 | + | 0.255337i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.897891i | − | 0.106560i | −0.998580 | − | 0.0532800i | \(-0.983032\pi\) | ||
0.998580 | − | 0.0532800i | \(-0.0169676\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.71555i | 1.13712i | 0.822642 | + | 0.568559i | \(0.192499\pi\) | ||||
−0.822642 | + | 0.568559i | \(0.807501\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.37138 | + | 1.37138i | −0.156284 | + | 0.156284i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7857 | 1.66352 | 0.831760 | − | 0.555135i | \(-0.187334\pi\) | ||||
0.831760 | + | 0.555135i | \(0.187334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.76838 | 0.752042 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.815000 | − | 0.815000i | 0.0894579 | − | 0.0894579i | −0.660962 | − | 0.750420i | \(-0.729851\pi\) |
0.750420 | + | 0.660962i | \(0.229851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.17827i | − | 0.876803i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12404i | 0.119148i | 0.998224 | + | 0.0595739i | \(0.0189742\pi\) | ||||
−0.998224 | + | 0.0595739i | \(0.981026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.48314 | − | 4.48314i | −0.469961 | − | 0.469961i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.68303 | − | 4.68303i | 0.485608 | − | 0.485608i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.54442 | 0.766019 | 0.383010 | − | 0.923744i | \(-0.374888\pi\) | ||||
0.383010 | + | 0.923744i | \(0.374888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.868775 | − | 0.868775i | 0.0873152 | − | 0.0873152i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.60535 | − | 2.60535i | −0.259242 | − | 0.259242i | 0.565504 | − | 0.824746i | \(-0.308682\pi\) |
−0.824746 | + | 0.565504i | \(0.808682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.8146i | − | 1.36120i | −0.732657 | − | 0.680598i | \(-0.761720\pi\) | ||
0.732657 | − | 0.680598i | \(-0.238280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.89124 | − | 9.89124i | −0.956222 | − | 0.956222i | 0.0428589 | − | 0.999081i | \(-0.486353\pi\) |
−0.999081 | + | 0.0428589i | \(0.986353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5454 | + | 11.5454i | −1.10584 | + | 1.10584i | −0.112154 | + | 0.993691i | \(0.535775\pi\) |
−0.993691 | + | 0.112154i | \(0.964225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.94021 | 0.943483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.2057 | −1.61857 | −0.809286 | − | 0.587415i | \(-0.800146\pi\) | ||||
−0.809286 | + | 0.587415i | \(0.800146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.84008 | + | 2.84008i | 0.262566 | + | 0.262566i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.477325i | 0.0437563i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.03452i | − | 0.639502i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.0839 | + | 11.0839i | 0.999403 | + | 0.999403i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.37608 | −0.122107 | −0.0610535 | − | 0.998134i | \(-0.519446\pi\) | ||||
−0.0610535 | + | 0.998134i | \(0.519446\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.90900 | 0.344168 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.03973 | − | 9.03973i | 0.789804 | − | 0.789804i | −0.191657 | − | 0.981462i | \(-0.561386\pi\) |
0.981462 | + | 0.191657i | \(0.0613863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.43003 | + | 4.43003i | 0.384132 | + | 0.384132i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.3056i | − | 1.30764i | −0.756649 | − | 0.653822i | \(-0.773165\pi\) | ||
0.756649 | − | 0.653822i | \(-0.226835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.346824 | + | 0.346824i | 0.0294173 | + | 0.0294173i | 0.721662 | − | 0.692245i | \(-0.243378\pi\) |
−0.692245 | + | 0.721662i | \(0.743378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9334 | + | 10.9334i | −0.920754 | + | 0.920754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.9634 | −1.08406 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.60555 | + | 6.60555i | −0.544817 | + | 0.544817i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.30028 | + | 4.30028i | 0.352293 | + | 0.352293i | 0.860962 | − | 0.508669i | \(-0.169862\pi\) |
−0.508669 | + | 0.860962i | \(0.669862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.02102i | − | 0.164468i | −0.996613 | − | 0.0822341i | \(-0.973794\pi\) | ||
0.996613 | − | 0.0822341i | \(-0.0262055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.302387i | − | 0.0244465i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.93327 | − | 2.93327i | 0.234101 | − | 0.234101i | −0.580301 | − | 0.814402i | \(-0.697065\pi\) |
0.814402 | + | 0.580301i | \(0.197065\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2563 | 0.971989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89241 | −0.149143 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.74697 | − | 5.74697i | 0.450137 | − | 0.450137i | −0.445263 | − | 0.895400i | \(-0.646890\pi\) |
0.895400 | + | 0.445263i | \(0.146890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.41553i | 0.496449i | 0.968703 | + | 0.248224i | \(0.0798470\pi\) | ||||
−0.968703 | + | 0.248224i | \(0.920153\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 29.3783i | − | 2.25987i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.80644 | − | 2.80644i | −0.214613 | − | 0.214613i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.545724 | + | 0.545724i | −0.0414907 | + | 0.0414907i | −0.727548 | − | 0.686057i | \(-0.759340\pi\) |
0.686057 | + | 0.727548i | \(0.259340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.4296 | 1.38525 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.57757 | − | 3.57757i | 0.267400 | − | 0.267400i | −0.560652 | − | 0.828052i | \(-0.689449\pi\) |
0.828052 | + | 0.560652i | \(0.189449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.64176 | − | 1.64176i | −0.122031 | − | 0.122031i | 0.643454 | − | 0.765485i | \(-0.277501\pi\) |
−0.765485 | + | 0.643454i | \(0.777501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.57328i | 0.485911i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.690114 | + | 0.690114i | 0.0504662 | + | 0.0504662i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.84522 | + | 3.84522i | −0.279698 | + | 0.279698i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.3359 | 1.10967 | 0.554835 | − | 0.831960i | \(-0.312781\pi\) | ||||
0.554835 | + | 0.831960i | \(0.312781\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0812703 | −0.00584996 | −0.00292498 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292498 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.40711 | + | 1.40711i | 0.100252 | + | 0.100252i | 0.755454 | − | 0.655202i | \(-0.227416\pi\) |
−0.655202 | + | 0.755454i | \(0.727416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3046i | 1.01402i | 0.861939 | + | 0.507011i | \(0.169250\pi\) | ||||
−0.861939 | + | 0.507011i | \(0.830750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.4457i | 1.08946i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.64846 | + | 3.64846i | 0.256071 | + | 0.256071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.19885 | 0.0833258 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.8098 | 0.886075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.70115 | + | 8.70115i | −0.599012 | + | 0.599012i | −0.940050 | − | 0.341038i | \(-0.889222\pi\) |
0.341038 | + | 0.940050i | \(0.389222\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.980103 | + | 0.980103i | 0.0671556 | + | 0.0671556i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.17835i | 0.283645i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.6051 | − | 10.6051i | −0.716628 | − | 0.716628i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.25603 | + | 2.25603i | −0.151757 | + | 0.151757i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.78095 | −0.521051 | −0.260525 | − | 0.965467i | \(-0.583896\pi\) | ||||
−0.260525 | + | 0.965467i | \(0.583896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.15443 | + | 2.15443i | −0.142995 | + | 0.142995i | −0.774980 | − | 0.631986i | \(-0.782240\pi\) |
0.631986 | + | 0.774980i | \(0.282240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.63865 | − | 7.63865i | −0.504776 | − | 0.504776i | 0.408142 | − | 0.912918i | \(-0.366177\pi\) |
−0.912918 | + | 0.408142i | \(0.866177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.99390i | − | 0.196984i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.51503i | − | 0.492326i | −0.969228 | − | 0.246163i | \(-0.920830\pi\) | ||
0.969228 | − | 0.246163i | \(-0.0791699\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.1395 | + | 16.1395i | −1.04837 | + | 1.04837i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5776 | −1.33105 | −0.665526 | − | 0.746375i | \(-0.731793\pi\) | ||||
−0.665526 | + | 0.746375i | \(0.731793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.2914 | −1.50033 | −0.750166 | − | 0.661250i | \(-0.770026\pi\) | ||||
−0.750166 | + | 0.661250i | \(0.770026\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.45639 | − | 4.45639i | 0.285877 | − | 0.285877i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.8762i | 2.66452i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.77925i | 0.112755i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.34230 | + | 3.34230i | 0.210964 | + | 0.210964i | 0.804677 | − | 0.593713i | \(-0.202339\pi\) |
−0.593713 | + | 0.804677i | \(0.702339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.73604 | + | 2.73604i | −0.172014 | + | 0.172014i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.4537 | −1.40062 | −0.700311 | − | 0.713838i | \(-0.746955\pi\) | ||||
−0.700311 | + | 0.713838i | \(0.746955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.43448 | + | 4.43448i | −0.275545 | + | 0.275545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.31131 | − | 2.31131i | −0.143066 | − | 0.143066i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.23670i | 0.507897i | 0.967218 | + | 0.253948i | \(0.0817294\pi\) | ||||
−0.967218 | + | 0.253948i | \(0.918271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.22696 | − | 1.22696i | −0.0750885 | − | 0.0750885i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.2960 | + | 17.2960i | −1.05455 | + | 1.05455i | −0.0561306 | + | 0.998423i | \(0.517876\pi\) |
−0.998423 | + | 0.0561306i | \(0.982124\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4753 | 0.757822 | 0.378911 | − | 0.925433i | \(-0.376299\pi\) | ||||
0.378911 | + | 0.925433i | \(0.376299\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.78726 | 0.592352 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2583 | + | 10.2583i | 0.616363 | + | 0.616363i | 0.944597 | − | 0.328234i | \(-0.106453\pi\) |
−0.328234 | + | 0.944597i | \(0.606453\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.64700i | − | 0.158472i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4066i | 1.27701i | 0.769618 | + | 0.638505i | \(0.220447\pi\) | ||||
−0.769618 | + | 0.638505i | \(0.779553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.39635 | + | 7.39635i | 0.439668 | + | 0.439668i | 0.891900 | − | 0.452232i | \(-0.149372\pi\) |
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.88942 | −0.583754 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7598 | −0.985870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.23520 | + | 8.23520i | −0.482756 | + | 0.482756i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.556728 | − | 0.556728i | −0.0325244 | − | 0.0325244i | 0.690658 | − | 0.723182i | \(-0.257321\pi\) |
−0.723182 | + | 0.690658i | \(0.757321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1188i | 0.645178i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.94430 | − | 8.94430i | −0.517263 | − | 0.517263i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.74387 | + | 1.74387i | −0.100515 | + | 0.100515i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.68781 | 0.326756 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.76852 | + | 9.76852i | −0.557519 | + | 0.557519i | −0.928600 | − | 0.371082i | \(-0.878987\pi\) |
0.371082 | + | 0.928600i | \(0.378987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0795 | + | 15.0795i | 0.857844 | + | 0.857844i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6874i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.71127i | − | 0.0967268i | −0.998830 | − | 0.0483634i | \(-0.984599\pi\) | ||
0.998830 | − | 0.0483634i | \(-0.0154006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0380 | + | 10.0380i | −0.563790 | + | 0.563790i | −0.930382 | − | 0.366592i | \(-0.880524\pi\) |
0.366592 | + | 0.930382i | \(0.380524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.5498 | 0.590678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5938 | 1.20525 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.22930 | − | 2.22930i | 0.124042 | − | 0.124042i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 25.2049i | − | 1.39384i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.75508i | − | 0.537815i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.89713 | − | 7.89713i | −0.434066 | − | 0.434066i | 0.455943 | − | 0.890009i | \(-0.349302\pi\) |
−0.890009 | + | 0.455943i | \(0.849302\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.80926 | − | 2.80926i | 0.153946 | − | 0.153946i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.46077 | −0.188520 | −0.0942601 | − | 0.995548i | \(-0.530049\pi\) | ||||
−0.0942601 | + | 0.995548i | \(0.530049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.7810 | − | 18.7810i | 1.02005 | − | 1.02005i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.04104 | + | 6.04104i | 0.327141 | + | 0.327141i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.7112i | − | 0.686338i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4637 | + | 17.4637i | 0.937498 | + | 0.937498i | 0.998158 | − | 0.0606600i | \(-0.0193205\pi\) |
−0.0606600 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2159 | − | 24.2159i | 1.29625 | − | 1.29625i | 0.365397 | − | 0.930852i | \(-0.380933\pi\) |
0.930852 | − | 0.365397i | \(-0.119067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.3481 | −1.94012 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7028 | −0.569650 | −0.284825 | − | 0.958580i | \(-0.591935\pi\) | ||||
−0.284825 | + | 0.958580i | \(0.591935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.521030 | − | 0.521030i | −0.0275758 | − | 0.0275758i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.6390i | − | 1.24762i | −0.781577 | − | 0.623809i | \(-0.785584\pi\) | ||
0.781577 | − | 0.623809i | \(-0.214416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 22.3801i | − | 1.17790i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.67861 | + | 7.67861i | 0.403023 | + | 0.403023i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7431 | 0.717386 | 0.358693 | − | 0.933456i | \(-0.383223\pi\) | ||||
0.358693 | + | 0.933456i | \(0.383223\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.26498 | 0.326142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.46773 | + | 5.46773i | −0.283871 | + | 0.283871i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4703 | + | 18.4703i | 0.956355 | + | 0.956355i | 0.999087 | − | 0.0427313i | \(-0.0136059\pi\) |
−0.0427313 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.4881i | 1.77623i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1028 | + | 16.1028i | 0.827143 | + | 0.827143i | 0.987121 | − | 0.159978i | \(-0.0511423\pi\) |
−0.159978 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50207 | − | 1.50207i | 0.0769535 | − | 0.0769535i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.1255 | −1.18166 | −0.590830 | − | 0.806796i | \(-0.701200\pi\) | ||||
−0.590830 | + | 0.806796i | \(0.701200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.10474 | − | 1.10474i | 0.0561573 | − | 0.0561573i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4044 | − | 19.4044i | −0.983842 | − | 0.983842i | 0.0160295 | − | 0.999872i | \(-0.494897\pi\) |
−0.999872 | + | 0.0160295i | \(0.994897\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.952310i | 0.0481604i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.7348i | 0.995491i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00102 | + | 4.00102i | −0.200806 | + | 0.200806i | −0.800345 | − | 0.599540i | \(-0.795350\pi\) |
0.599540 | + | 0.800345i | \(0.295350\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.67130 | −0.484171 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.9287 | 1.94401 | 0.972003 | − | 0.234967i | \(-0.0754980\pi\) | ||||
0.972003 | + | 0.234967i | \(0.0754980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7486 | + | 19.7486i | −0.983746 | + | 0.983746i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8227i | 0.635598i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.59845i | 0.227379i | 0.993516 | + | 0.113689i | \(0.0362669\pi\) | ||||
−0.993516 | + | 0.113689i | \(0.963733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.7070 | + | 16.7070i | 0.824095 | + | 0.824095i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.22174 | + | 8.22174i | −0.404565 | + | 0.404565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.757161 | −0.0370783 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.6774 | + | 16.6774i | −0.814746 | + | 0.814746i | −0.985341 | − | 0.170595i | \(-0.945431\pi\) |
0.170595 | + | 0.985341i | \(0.445431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4169 | + | 15.4169i | 0.751372 | + | 0.751372i | 0.974735 | − | 0.223364i | \(-0.0717037\pi\) |
−0.223364 | + | 0.974735i | \(0.571704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.17987i | 0.300476i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.93244 | − | 2.93244i | −0.141911 | − | 0.141911i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.1504 | − | 14.1504i | 0.683186 | − | 0.683186i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.2234 | −0.974126 | −0.487063 | − | 0.873367i | \(-0.661932\pi\) | ||||
−0.487063 | + | 0.873367i | \(0.661932\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.676118 | 0.0324922 | 0.0162461 | − | 0.999868i | \(-0.494828\pi\) | ||||
0.0162461 | + | 0.999868i | \(0.494828\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.83834 | + | 8.83834i | 0.422795 | + | 0.422795i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.3550i | − | 0.637400i | −0.947856 | − | 0.318700i | \(-0.896754\pi\) | ||
0.947856 | − | 0.318700i | \(-0.103246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.73366i | 0.177794i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1262 | − | 28.1262i | −1.33631 | − | 1.33631i | −0.899600 | − | 0.436714i | \(-0.856142\pi\) |
−0.436714 | − | 0.899600i | \(-0.643858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.38805 | −0.444039 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.37972 | −0.395464 | −0.197732 | − | 0.980256i | \(-0.563358\pi\) | ||||
−0.197732 | + | 0.980256i | \(0.563358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2981 | + | 14.2981i | −0.673271 | + | 0.673271i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.20607 | + | 2.20607i | 0.103650 | + | 0.103650i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.66561i | − | 0.265026i | −0.991181 | − | 0.132513i | \(-0.957695\pi\) | ||
0.991181 | − | 0.132513i | \(-0.0423046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.93501 | + | 1.93501i | 0.0903186 | + | 0.0903186i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6375 | − | 16.6375i | 0.774887 | − | 0.774887i | −0.204069 | − | 0.978956i | \(-0.565417\pi\) |
0.978956 | + | 0.204069i | \(0.0654168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.6835 | 1.93720 | 0.968598 | − | 0.248631i | \(-0.0799808\pi\) | ||||
0.968598 | + | 0.248631i | \(0.0799808\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.11020 | + | 3.11020i | −0.143923 | + | 0.143923i | −0.775397 | − | 0.631474i | \(-0.782450\pi\) |
0.631474 | + | 0.775397i | \(0.282450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.89057 | − | 6.89057i | −0.318177 | − | 0.318177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.40370i | 0.295067i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.04255i | 0.231857i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.46383 | − | 3.46383i | 0.158598 | − | 0.158598i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.32325 | 0.380299 | 0.190149 | − | 0.981755i | \(-0.439103\pi\) | ||||
0.190149 | + | 0.981755i | \(0.439103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.9183 | −1.91131 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.06569 | − | 2.06569i | 0.0939920 | − | 0.0939920i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.29577i | − | 0.330603i | −0.986243 | − | 0.165301i | \(-0.947140\pi\) | ||
0.986243 | − | 0.165301i | \(-0.0528597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5463i | 0.567365i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.57528 | − | 3.57528i | −0.161350 | − | 0.161350i | 0.621815 | − | 0.783165i | \(-0.286396\pi\) |
−0.783165 | + | 0.621815i | \(0.786396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.83600 | − | 1.83600i | 0.0826891 | − | 0.0826891i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.874479 | −0.0392257 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8833 | − | 10.8833i | 0.487203 | − | 0.487203i | −0.420220 | − | 0.907422i | \(-0.638047\pi\) |
0.907422 | + | 0.420220i | \(0.138047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00295 | − | 7.00295i | −0.312869 | − | 0.312869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.3781i | 1.30991i | 0.755670 | + | 0.654953i | \(0.227312\pi\) | ||||
−0.755670 | + | 0.654953i | \(0.772688\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.0682 | + | 32.0682i | 1.42420 | + | 1.42420i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4592 | − | 17.4592i | 0.773863 | − | 0.773863i | −0.204916 | − | 0.978780i | \(-0.565692\pi\) |
0.978780 | + | 0.204916i | \(0.0656922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.46222 | 0.418584 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.9175 | 1.58579 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1039 | − | 14.1039i | −0.620287 | − | 0.620287i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.19138i | − | 0.0522959i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.48578i | 0.415580i | 0.978174 | + | 0.207790i | \(0.0666270\pi\) | ||||
−0.978174 | + | 0.207790i | \(0.933373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2705 | − | 16.2705i | −0.711460 | − | 0.711460i | 0.255380 | − | 0.966841i | \(-0.417799\pi\) |
−0.966841 | + | 0.255380i | \(0.917799\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.10265 | 0.0915929 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2245 | 0.835846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.20849 | − | 5.20849i | 0.226029 | − | 0.226029i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.7414 | − | 46.7414i | −2.02459 | − | 2.02459i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.81028i | 0.337039i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.52106 | − | 8.52106i | −0.367028 | − | 0.367028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.55686 | + | 2.55686i | −0.109928 | + | 0.109928i | −0.759931 | − | 0.650003i | \(-0.774767\pi\) |
0.650003 | + | 0.759931i | \(0.274767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.58416 | 0.153811 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9660 | − | 21.9660i | 0.939197 | − | 0.939197i | −0.0590579 | − | 0.998255i | \(-0.518810\pi\) |
0.998255 | + | 0.0590579i | \(0.0188097\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.85771 | + | 1.85771i | 0.0792852 | + | 0.0792852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.0796i | − | 1.45184i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.4002i | − | 0.612357i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5409 | − | 17.5409i | 0.743234 | − | 0.743234i | −0.229965 | − | 0.973199i | \(-0.573861\pi\) |
0.973199 | + | 0.229965i | \(0.0738612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.4844 | −0.697217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.50661 | −0.0636089 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.5975 | + | 27.5975i | −1.16309 | + | 1.16309i | −0.179300 | + | 0.983794i | \(0.557383\pi\) |
−0.983794 | + | 0.179300i | \(0.942617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 6.59190i | − | 0.276834i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6390i | 0.990998i | 0.868608 | + | 0.495499i | \(0.165015\pi\) | ||||
−0.868608 | + | 0.495499i | \(0.834985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.7518 | + | 21.7518i | 0.910284 | + | 0.910284i | 0.996294 | − | 0.0860105i | \(-0.0274118\pi\) |
−0.0860105 | + | 0.996294i | \(0.527412\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7401 | + | 16.7401i | −0.699329 | + | 0.699329i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.69585 | −0.153860 | −0.0769302 | − | 0.997036i | \(-0.524512\pi\) | ||||
−0.0769302 | + | 0.997036i | \(0.524512\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0887116 | − | 0.0887116i | 0.00368673 | − | 0.00368673i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.793750 | − | 0.793750i | −0.0329303 | − | 0.0329303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.8105i | 0.654802i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0313 | − | 27.0313i | −1.11570 | − | 1.11570i | −0.992365 | − | 0.123335i | \(-0.960641\pi\) |
−0.123335 | − | 0.992365i | \(-0.539359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.5146 | − | 19.5146i | 0.804085 | − | 0.804085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.07189 | −0.126361 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.55524 | −0.187061 | −0.0935306 | − | 0.995616i | \(-0.529815\pi\) | ||||
−0.0935306 | + | 0.995616i | \(0.529815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.6143 | − | 15.6143i | −0.639051 | − | 0.639051i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.46846i | − | 0.305153i | −0.988292 | − | 0.152576i | \(-0.951243\pi\) | ||
0.988292 | − | 0.152576i | \(-0.0487570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.2638i | − | 0.500250i | −0.968214 | − | 0.250125i | \(-0.919528\pi\) | ||
0.968214 | − | 0.250125i | \(-0.0804717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.36519 | + | 4.36519i | 0.177764 | + | 0.177764i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.23884 | −0.212638 | −0.106319 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106319 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.96503 | −0.322759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.1064 | − | 46.1064i | 1.86527 | − | 1.86527i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.7209 | + | 20.7209i | 0.836910 | + | 0.836910i | 0.988451 | − | 0.151541i | \(-0.0484235\pi\) |
−0.151541 | + | 0.988451i | \(0.548424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.20286i | 0.0886838i | 0.999016 | + | 0.0443419i | \(0.0141191\pi\) | ||||
−0.999016 | + | 0.0443419i | \(0.985881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4569 | + | 31.4569i | 1.26436 | + | 1.26436i | 0.948958 | + | 0.315404i | \(0.102140\pi\) |
0.315404 | + | 0.948958i | \(0.397860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.67158 | + | 7.67158i | −0.307850 | + | 0.307850i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.09473 | 0.0438594 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.9827 | + | 13.9827i | −0.558416 | + | 0.558416i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.23154 | + | 2.23154i | 0.0889775 | + | 0.0889775i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.8215i | − | 0.669655i | −0.942279 | − | 0.334828i | \(-0.891322\pi\) | ||
0.942279 | − | 0.334828i | \(-0.108678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 18.9957i | − | 0.755011i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.8559 | − | 27.8559i | 1.10369 | − | 1.10369i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.553985 | 0.0219153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9208 | −0.589336 | −0.294668 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294668 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.541845 | − | 0.541845i | 0.0213683 | − | 0.0213683i | −0.696342 | − | 0.717710i | \(-0.745190\pi\) |
0.717710 | + | 0.696342i | \(0.245190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.6391i | − | 1.28318i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) | ||
0.767049 | − | 0.641588i | \(-0.221724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.7739i | 0.933208i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.56093 | − | 4.56093i | −0.178757 | − | 0.178757i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.73805 | − | 9.73805i | 0.381079 | − | 0.381079i | −0.490412 | − | 0.871491i | \(-0.663154\pi\) |
0.871491 | + | 0.490412i | \(0.163154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.99434 | −0.233862 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.26445 | + | 1.26445i | −0.0492560 | + | 0.0492560i | −0.731306 | − | 0.682050i | \(-0.761089\pi\) |
0.682050 | + | 0.731306i | \(0.261089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6701 | + | 22.6701i | 0.881763 | + | 0.881763i | 0.993714 | − | 0.111951i | \(-0.0357099\pi\) |
−0.111951 | + | 0.993714i | \(0.535710\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.92519i | − | 0.191279i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.27903 | + | 7.27903i | 0.281845 | + | 0.281845i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.49339 | − | 8.49339i | 0.328373 | − | 0.328373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.47943 | −0.327345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.58765 | 0.138294 | 0.0691469 | − | 0.997606i | \(-0.477972\pi\) | ||||
0.0691469 | + | 0.997606i | \(0.477972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.1507 | + | 10.1507i | 0.390124 | + | 0.390124i | 0.874731 | − | 0.484608i | \(-0.161038\pi\) |
−0.484608 | + | 0.874731i | \(0.661038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 7.34770i | − | 0.281979i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.70339i | − | 0.180234i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.6805 | − | 16.6805i | −0.638260 | − | 0.638260i | 0.311866 | − | 0.950126i | \(-0.399046\pi\) |
−0.950126 | + | 0.311866i | \(0.899046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.6761 | 0.636234 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −51.6854 | −1.96906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4781 | + | 12.4781i | −0.474689 | + | 0.474689i | −0.903428 | − | 0.428739i | \(-0.858958\pi\) |
0.428739 | + | 0.903428i | \(0.358958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.846123 | − | 0.846123i | −0.0321415 | − | 0.0321415i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.97661i | 0.188502i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.20312 | + | 8.20312i | 0.310271 | + | 0.310271i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.40945 | − | 6.40945i | 0.242082 | − | 0.242082i | −0.575629 | − | 0.817711i | \(-0.695243\pi\) |
0.817711 | + | 0.575629i | \(0.195243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.4217 | 1.56225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.53742 | + | 2.53742i | −0.0954295 | + | 0.0954295i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.78514 | + | 8.78514i | 0.329933 | + | 0.329933i | 0.852561 | − | 0.522628i | \(-0.175048\pi\) |
−0.522628 | + | 0.852561i | \(0.675048\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.12255i | 0.342122i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.33621i | 0.312194i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.4617 | − | 22.4617i | 0.838847 | − | 0.838847i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.2329 | −1.72420 | −0.862099 | − | 0.506740i | \(-0.830850\pi\) | ||||
−0.862099 | + | 0.506740i | \(0.830850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4544 | −0.501069 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.4240 | − | 25.4240i | 0.945530 | − | 0.945530i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.4640i | 0.647703i | 0.946108 | + | 0.323852i | \(0.104978\pi\) | ||||
−0.946108 | + | 0.323852i | \(0.895022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0340i | 1.11237i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.877557 | + | 0.877557i | 0.0324576 | + | 0.0324576i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.89695 | − | 7.89695i | 0.291680 | − | 0.291680i | −0.546063 | − | 0.837744i | \(-0.683874\pi\) |
0.837744 | + | 0.546063i | \(0.183874\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.9247 | −0.733936 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.1724 | + | 26.1724i | −0.962769 | + | 0.962769i | −0.999331 | − | 0.0365624i | \(-0.988359\pi\) |
0.0365624 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.7105 | − | 45.7105i | −1.67922 | − | 1.67922i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 49.7660i | − | 1.82574i | −0.408254 | − | 0.912868i | \(-0.633862\pi\) | ||
0.408254 | − | 0.912868i | \(-0.366138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.502843 | + | 0.502843i | 0.0183981 | + | 0.0183981i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.63333 | + | 9.63333i | −0.351994 | + | 0.351994i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2379 | 0.884454 | 0.442227 | − | 0.896903i | \(-0.354189\pi\) | ||||
0.442227 | + | 0.896903i | \(0.354189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.29665 | −0.265905 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4872 | − | 15.4872i | −0.562890 | − | 0.562890i | 0.367237 | − | 0.930127i | \(-0.380304\pi\) |
−0.930127 | + | 0.367237i | \(0.880304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.97312i | − | 0.216811i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9821i | 0.941849i | 0.882174 | + | 0.470924i | \(0.156080\pi\) | ||||
−0.882174 | + | 0.470924i | \(0.843920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.2443 | + | 11.2443i | 0.407072 | + | 0.407072i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −77.7185 | −2.80625 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.9737 | −0.900573 | −0.450287 | − | 0.892884i | \(-0.648678\pi\) | ||||
−0.450287 | + | 0.892884i | \(0.648678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.5096 | − | 24.5096i | 0.882691 | − | 0.882691i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.32495 | − | 1.32495i | −0.0476550 | − | 0.0476550i | 0.682878 | − | 0.730533i | \(-0.260728\pi\) |
−0.730533 | + | 0.682878i | \(0.760728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.68103i | − | 0.347305i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.1876 | + | 46.1876i | 1.65484 | + | 1.65484i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26432 | + | 1.26432i | −0.0452409 | + | 0.0452409i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.5807 | 1.05713 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.647036 | + | 0.647036i | −0.0230644 | + | 0.0230644i | −0.718545 | − | 0.695481i | \(-0.755192\pi\) |
0.695481 | + | 0.718545i | \(0.255192\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.99087 | − | 8.99087i | −0.320084 | − | 0.320084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7570i | 0.595811i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.7198i | − | 0.984360i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.3024 | − | 18.3024i | 0.648303 | − | 0.648303i | −0.304280 | − | 0.952583i | \(-0.598416\pi\) |
0.952583 | + | 0.304280i | \(0.0984158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.90900 | −0.173668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.693514 | −0.0245041 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6804 | − | 13.6804i | 0.482772 | − | 0.482772i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 37.7593i | − | 1.32919i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.4845i | 1.14209i | 0.820917 | + | 0.571047i | \(0.193463\pi\) | ||||
−0.820917 | + | 0.571047i | \(0.806537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.69149 | − | 7.69149i | −0.270085 | − | 0.270085i | 0.559049 | − | 0.829134i | \(-0.311166\pi\) |
−0.829134 | + | 0.559049i | \(0.811166\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.6176 | + | 13.6176i | −0.477590 | + | 0.477590i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2891 | 0.569884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.76603 | − | 2.76603i | 0.0966529 | − | 0.0966529i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5798 | − | 10.5798i | −0.369238 | − | 0.369238i | 0.497961 | − | 0.867199i | \(-0.334082\pi\) |
−0.867199 | + | 0.497961i | \(0.834082\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.85817i | 0.169345i | 0.996409 | + | 0.0846726i | \(0.0269844\pi\) | ||||
−0.996409 | + | 0.0846726i | \(0.973016\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.02757 | − | 8.02757i | −0.279146 | − | 0.279146i | 0.553622 | − | 0.832768i | \(-0.313245\pi\) |
−0.832768 | + | 0.553622i | \(0.813245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3613 | + | 24.3613i | −0.846102 | + | 0.846102i | −0.989644 | − | 0.143542i | \(-0.954151\pi\) |
0.143542 | + | 0.989644i | \(0.454151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.3952 | −0.776881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.96585 | −0.102761 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.9385 | + | 16.9385i | 0.585479 | + | 0.585479i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.1207i | 1.48869i | 0.667794 | + | 0.744346i | \(0.267239\pi\) | ||||
−0.667794 | + | 0.744346i | \(0.732761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.932964i | 0.0321712i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.3666 | − | 23.3666i | −0.804789 | − | 0.804789i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.85110 | −0.235407 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.1472 | −0.554169 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.84723 | + | 8.84723i | −0.303279 | + | 0.303279i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0611 | + | 18.0611i | 0.618401 | + | 0.618401i | 0.945121 | − | 0.326720i | \(-0.105943\pi\) |
−0.326720 | + | 0.945121i | \(0.605943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 35.8346i | − | 1.22409i | −0.790825 | − | 0.612043i | \(-0.790348\pi\) | ||
0.790825 | − | 0.612043i | \(-0.209652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.619460 | + | 0.619460i | 0.0211357 | + | 0.0211357i | 0.717596 | − | 0.696460i | \(-0.245243\pi\) |
−0.696460 | + | 0.717596i | \(0.745243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7949 | − | 10.7949i | 0.367890 | − | 0.367890i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.8270 | −0.640878 | −0.320439 | − | 0.947269i | \(-0.603830\pi\) | ||||
−0.320439 | + | 0.947269i | \(0.603830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.2944 | − | 18.2944i | 0.621309 | − | 0.621309i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.8197 | − | 20.8197i | −0.706260 | − | 0.706260i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 65.1352i | − | 2.20702i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.65479i | 0.157541i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.77833 | + | 7.77833i | −0.262656 | + | 0.262656i | −0.826132 | − | 0.563476i | \(-0.809464\pi\) |
0.563476 | + | 0.826132i | \(0.309464\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.21541 | 0.0409946 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6551 | 0.460052 | 0.230026 | − | 0.973184i | \(-0.426119\pi\) | ||||
0.230026 | + | 0.973184i | \(0.426119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7585 | − | 25.7585i | 0.866844 | − | 0.866844i | −0.125278 | − | 0.992122i | \(-0.539982\pi\) |
0.992122 | + | 0.125278i | \(0.0399823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 38.8982i | − | 1.30607i | −0.757326 | − | 0.653037i | \(-0.773495\pi\) | ||
0.757326 | − | 0.653037i | \(-0.226505\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.34020i | 0.0449488i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.53054 | − | 9.53054i | −0.319285 | − | 0.319285i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.5602 | + | 45.5602i | −1.52461 | + | 1.52461i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.5265 | 0.651972 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0717 | − | 16.0717i | 0.536022 | − | 0.536022i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.75150 | + | 2.75150i | 0.0916658 | + | 0.0916658i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.80707i | − | 0.126692i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.10220 | + | 5.10220i | 0.169416 | + | 0.169416i | 0.786723 | − | 0.617307i | \(-0.211776\pi\) |
−0.617307 | + | 0.786723i | \(0.711776\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.60746 | − | 1.60746i | 0.0533162 | − | 0.0533162i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.7058 | 1.54743 | 0.773716 | − | 0.633533i | \(-0.218396\pi\) | ||||
0.773716 | + | 0.633533i | \(0.218396\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.29520 | −0.0759601 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.80402 | − | 8.80402i | −0.290734 | − | 0.290734i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 53.4692i | − | 1.76379i | −0.471449 | − | 0.881893i | \(-0.656269\pi\) | ||
0.471449 | − | 0.881893i | \(-0.343731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 21.3259i | − | 0.702712i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.13314 | − | 4.13314i | −0.136044 | − | 0.136044i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.52342 | 0.279946 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.2098 | 0.466209 | 0.233104 | − | 0.972452i | \(-0.425112\pi\) | ||||
0.233104 | + | 0.972452i | \(0.425112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.5259 | + | 27.5259i | −0.902125 | + | 0.902125i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.4972 | − | 33.4972i | −1.09665 | − | 1.09665i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.26656i | 0.172051i | 0.996293 | + | 0.0860255i | \(0.0274166\pi\) | ||||
−0.996293 | + | 0.0860255i | \(0.972583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.86796 | + | 1.86796i | 0.0609585 | + | 0.0609585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.7780 | − | 18.7780i | 0.612145 | − | 0.612145i | −0.331359 | − | 0.943505i | \(-0.607507\pi\) |
0.943505 | + | 0.331359i | \(0.107507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7304 | −0.642509 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.27572 | + | 3.27572i | −0.106447 | + | 0.106447i | −0.758324 | − | 0.651878i | \(-0.773982\pi\) |
0.651878 | + | 0.758324i | \(0.273982\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.7223 | + | 44.7223i | 1.45175 | + | 1.45175i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.9142i | − | 0.710616i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.0292i | − | 0.972741i | −0.873753 | − | 0.486371i | \(-0.838320\pi\) | ||
0.873753 | − | 0.486371i | \(-0.161680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5158 | + | 11.5158i | −0.372253 | + | 0.372253i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.9065 | −0.481356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5941 | −0.406260 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.10274 | − | 6.10274i | 0.196658 | − | 0.196658i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.2196i | − | 0.489429i | −0.969595 | − | 0.244715i | \(-0.921306\pi\) | ||
0.969595 | − | 0.244715i | \(-0.0786943\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.86684i | 0.156345i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.4838 | + | 18.4838i | 0.593173 | + | 0.593173i | 0.938487 | − | 0.345314i | \(-0.112228\pi\) |
−0.345314 | + | 0.938487i | \(0.612228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.337781 | − | 0.337781i | 0.0108288 | − | 0.0108288i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7912 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.58276 | − | 1.58276i | 0.0505851 | − | 0.0505851i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.12331 | − | 7.12331i | −0.227430 | − | 0.227430i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.5605i | 1.80400i | 0.431738 | + | 0.901999i | \(0.357901\pi\) | ||||
−0.431738 | + | 0.901999i | \(0.642099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.6483 | + | 10.6483i | 0.338938 | + | 0.338938i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.47918 | + | 3.47918i | −0.110632 | + | 0.110632i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.0866 | −1.43222 | −0.716112 | − | 0.697985i | \(-0.754080\pi\) | ||||
−0.716112 | + | 0.697985i | \(0.754080\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2404 | 0.547108 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.1508 | − | 35.1508i | −1.11324 | − | 1.11324i | −0.992710 | − | 0.120528i | \(-0.961541\pi\) |
−0.120528 | − | 0.992710i | \(-0.538459\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.9536i | 1.13752i |
(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 | 1600.2.l.g.1201.2 | 12 | ||
4.3 | odd | 2 | 400.2.l.f.101.2 | ✓ | 12 | ||
5.2 | odd | 4 | 1600.2.q.e.49.5 | 12 | |||
5.3 | odd | 4 | 1600.2.q.f.49.2 | 12 | |||
5.4 | even | 2 | 1600.2.l.f.1201.5 | 12 | |||
16.3 | odd | 4 | 400.2.l.f.301.2 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.g.401.2 | 12 | ||
20.3 | even | 4 | 400.2.q.f.149.2 | 12 | |||
20.7 | even | 4 | 400.2.q.e.149.5 | 12 | |||
20.19 | odd | 2 | 400.2.l.g.101.5 | yes | 12 | ||
80.3 | even | 4 | 400.2.q.e.349.5 | 12 | |||
80.13 | odd | 4 | 1600.2.q.e.849.5 | 12 | |||
80.19 | odd | 4 | 400.2.l.g.301.5 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.f.401.5 | 12 | |||
80.67 | even | 4 | 400.2.q.f.349.2 | 12 | |||
80.77 | odd | 4 | 1600.2.q.f.849.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.2 | ✓ | 12 | 4.3 | odd | 2 | ||
400.2.l.f.301.2 | yes | 12 | 16.3 | odd | 4 | ||
400.2.l.g.101.5 | yes | 12 | 20.19 | odd | 2 | ||
400.2.l.g.301.5 | yes | 12 | 80.19 | odd | 4 | ||
400.2.q.e.149.5 | 12 | 20.7 | even | 4 | |||
400.2.q.e.349.5 | 12 | 80.3 | even | 4 | |||
400.2.q.f.149.2 | 12 | 20.3 | even | 4 | |||
400.2.q.f.349.2 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.401.5 | 12 | 80.29 | even | 4 | |||
1600.2.l.f.1201.5 | 12 | 5.4 | even | 2 | |||
1600.2.l.g.401.2 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.g.1201.2 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.e.49.5 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.849.5 | 12 | 80.13 | odd | 4 | |||
1600.2.q.f.49.2 | 12 | 5.3 | odd | 4 | |||
1600.2.q.f.849.2 | 12 | 80.77 | odd | 4 |