Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
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, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (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 | 49.2 | ||
Root | \(1.22306 - 0.710021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.f.849.2 |
$q$-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 | 0.317908 | − | 0.948122i | \(-0.397020\pi\) |
−0.948122 | + | 0.317908i | \(0.897020\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.973926 | −0.368109 | −0.184055 | − | 0.982916i | \(-0.558922\pi\) | ||||
−0.184055 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(8\) | 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 | 0.942510 | + | 0.334179i | \(0.108459\pi\) |
0.334179 | + | 0.942510i | \(0.391541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.490104i | 0.118868i | 0.998232 | + | 0.0594338i | \(0.0189295\pi\) | ||||
−0.998232 | + | 0.0594338i | \(0.981070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54863 | − | 4.54863i | 1.04353 | − | 1.04353i | 0.0445187 | − | 0.999009i | \(-0.485825\pi\) |
0.999009 | − | 0.0445187i | \(-0.0141754\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06310 | + | 1.06310i | 0.231988 | + | 0.231988i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94308 | 0.405160 | 0.202580 | − | 0.979266i | \(-0.435067\pi\) | ||||
0.202580 | + | 0.979266i | \(0.435067\pi\) | |||||||
\(24\) | 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 | −0.267827 | − | 0.963467i | \(-0.586306\pi\) |
0.963467 | + | 0.267827i | \(0.0863057\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29021 | −0.770545 | −0.385272 | − | 0.922803i | \(-0.625893\pi\) | ||||
−0.385272 | + | 0.922803i | \(0.625893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.07405i | 0.535124i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55320 | + | 4.55320i | −0.748542 | + | 0.748542i | −0.974205 | − | 0.225663i | \(-0.927545\pi\) |
0.225663 | + | 0.974205i | \(0.427545\pi\) | |||||||
\(38\) | 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 | \(-0.688152\pi\) |
0.830329 | + | 0.557273i | \(0.188152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.0162i | − | 1.46102i | −0.682902 | − | 0.730510i | \(-0.739283\pi\) | ||
0.682902 | − | 0.730510i | \(-0.260717\pi\) | |||||||
\(48\) | 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 | \(-0.566419\pi\) |
0.978309 | + | 0.207151i | \(0.0664190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.93022 | −1.31529 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.44185 | + | 8.44185i | 1.09904 | + | 1.09904i | 0.994524 | + | 0.104512i | \(0.0333281\pi\) |
0.104512 | + | 0.994524i | \(0.466672\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0.600897i | 0.0757060i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.07504 | − | 7.07504i | −0.864354 | − | 0.864354i | 0.127486 | − | 0.991840i | \(-0.459309\pi\) |
−0.991840 | + | 0.127486i | \(0.959309\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | −9.71555 | −1.13712 | −0.568559 | − | 0.822642i | \(-0.692499\pi\) | ||||
−0.568559 | + | 0.822642i | \(0.692499\pi\) | |||||||
\(74\) | 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 | \(-0.812666\pi\) | ||||
−0.831760 | + | 0.555135i | \(0.812666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.76838 | 0.752042 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.815000 | + | 0.815000i | 0.0894579 | + | 0.0894579i | 0.750420 | − | 0.660962i | \(-0.229851\pi\) |
−0.660962 | + | 0.750420i | \(0.729851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.17827 | −0.876803 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.12404i | − | 0.119148i | −0.998224 | − | 0.0595739i | \(-0.981026\pi\) | ||
0.998224 | − | 0.0595739i | \(-0.0189742\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | − | 7.54442i | − | 0.766019i | −0.923744 | − | 0.383010i | \(-0.874888\pi\) | ||
0.923744 | − | 0.383010i | \(-0.125112\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 13.8146 | 1.36120 | 0.680598 | − | 0.732657i | \(-0.261720\pi\) | ||||
0.680598 | + | 0.732657i | \(0.261720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.89124 | + | 9.89124i | −0.956222 | + | 0.956222i | −0.999081 | − | 0.0428589i | \(-0.986353\pi\) |
0.0428589 | + | 0.999081i | \(0.486353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5454 | − | 11.5454i | 1.10584 | − | 1.10584i | 0.112154 | − | 0.993691i | \(-0.464225\pi\) |
0.993691 | − | 0.112154i | \(-0.0357750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.94021 | 0.943483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.2057i | − | 1.61857i | −0.587415 | − | 0.809286i | \(-0.699854\pi\) | ||
0.587415 | − | 0.809286i | \(-0.300146\pi\) | |||||||
\(114\) | 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 | ||||||||
\(127\) | 1.37608i | 0.122107i | 0.998134 | + | 0.0610535i | \(0.0194460\pi\) | ||||
−0.998134 | + | 0.0610535i | \(0.980554\pi\) | |||||||
\(128\) | 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 | ||||||||
\(137\) | −15.3056 | −1.30764 | −0.653822 | − | 0.756649i | \(-0.726835\pi\) | ||||
−0.653822 | + | 0.756649i | \(0.726835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.346824 | − | 0.346824i | −0.0294173 | − | 0.0294173i | 0.692245 | − | 0.721662i | \(-0.256622\pi\) |
−0.721662 | + | 0.692245i | \(0.756622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9334 | + | 10.9334i | −0.920754 | + | 0.920754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.9634i | − | 1.08406i | ||||||
\(144\) | 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 | 0.508669 | − | 0.860962i | \(-0.330138\pi\) |
−0.860962 | + | 0.508669i | \(0.830138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.02102i | − | 0.164468i | −0.996613 | − | 0.0822341i | \(-0.973794\pi\) | ||
0.996613 | − | 0.0822341i | \(-0.0262055\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.302387 | 0.0244465 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.93327 | − | 2.93327i | −0.234101 | − | 0.234101i | 0.580301 | − | 0.814402i | \(-0.302935\pi\) |
−0.814402 | + | 0.580301i | \(0.802935\pi\) | |||||||
\(158\) | 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 | 0.895400 | − | 0.445263i | \(-0.146890\pi\) |
−0.445263 | + | 0.895400i | \(0.646890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.41553 | 0.496449 | 0.248224 | − | 0.968703i | \(-0.420153\pi\) | ||||
0.248224 | + | 0.968703i | \(0.420153\pi\) | |||||||
\(168\) | 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 | 0.686057 | − | 0.727548i | \(-0.259340\pi\) |
−0.727548 | + | 0.686057i | \(0.759340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 18.4296i | − | 1.38525i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.57757 | + | 3.57757i | −0.267400 | + | 0.267400i | −0.828052 | − | 0.560652i | \(-0.810551\pi\) |
0.560652 | + | 0.828052i | \(0.310551\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | −6.57328 | −0.485911 | ||||||||
\(184\) | 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 | ||||||||
\(193\) | − | 0.0812703i | − | 0.00584996i | −0.999996 | − | 0.00292498i | \(-0.999069\pi\) | ||
0.999996 | − | 0.00292498i | \(-0.000931052\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.40711 | − | 1.40711i | 0.100252 | − | 0.100252i | −0.655202 | − | 0.755454i | \(-0.727416\pi\) |
0.755454 | + | 0.655202i | \(0.227416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.3046i | − | 1.01402i | −0.861939 | − | 0.507011i | \(-0.830750\pi\) | ||
0.861939 | − | 0.507011i | \(-0.169250\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | − | 1.19885i | − | 0.0833258i | ||||||
\(208\) | 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 | ||||||||
\(217\) | 4.17835 | 0.283645 | ||||||||
\(218\) | 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 | ||||||||
\(223\) | − | 7.78095i | − | 0.521051i | −0.965467 | − | 0.260525i | \(-0.916104\pi\) | ||
0.965467 | − | 0.260525i | \(-0.0838958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.15443 | + | 2.15443i | 0.142995 | + | 0.142995i | 0.774980 | − | 0.631986i | \(-0.217760\pi\) |
−0.631986 | + | 0.774980i | \(0.717760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.63865 | + | 7.63865i | 0.504776 | + | 0.504776i | 0.912918 | − | 0.408142i | \(-0.133823\pi\) |
−0.408142 | + | 0.912918i | \(0.633823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.99390i | − | 0.196984i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.51503 | 0.492326 | 0.246163 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246163 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(234\) | 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 | \(-0.268207\pi\) | ||||
0.665526 | + | 0.746375i | \(0.268207\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | 41.8762 | 2.66452 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | 22.4537i | 1.40062i | 0.713838 | + | 0.700311i | \(0.246955\pi\) | ||||
−0.713838 | + | 0.700311i | \(0.753045\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | −8.23670 | −0.507897 | −0.253948 | − | 0.967218i | \(-0.581729\pi\) | ||||
−0.253948 | + | 0.967218i | \(0.581729\pi\) | |||||||
\(264\) | 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 | \(-0.482124\pi\) |
0.998423 | − | 0.0561306i | \(-0.0178763\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4753 | 0.757822 | 0.378911 | − | 0.925433i | \(-0.376299\pi\) | ||||
0.378911 | + | 0.925433i | \(0.376299\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.78726i | 0.592352i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2583 | − | 10.2583i | 0.616363 | − | 0.616363i | −0.328234 | − | 0.944597i | \(-0.606453\pi\) |
0.944597 | + | 0.328234i | \(0.106453\pi\) | |||||||
\(278\) | 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 | \(-0.850628\pi\) |
0.452232 | + | 0.891900i | \(0.350628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.88942i | 0.583754i | ||||||||
\(288\) | 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 | \(-0.742679\pi\) |
0.723182 | + | 0.690658i | \(0.242679\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1188 | 0.645178 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 5.68781i | 0.326756i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.76852 | + | 9.76852i | 0.557519 | + | 0.557519i | 0.928600 | − | 0.371082i | \(-0.121013\pi\) |
−0.371082 | + | 0.928600i | \(0.621013\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 1.71127 | 0.0967268 | 0.0483634 | − | 0.998830i | \(-0.484599\pi\) | ||||
0.0483634 | + | 0.998830i | \(0.484599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0380 | + | 10.0380i | 0.563790 | + | 0.563790i | 0.930382 | − | 0.366592i | \(-0.119476\pi\) |
−0.366592 | + | 0.930382i | \(0.619476\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −25.2049 | −1.39384 | ||||||||
\(328\) | 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 | ||||||||
\(337\) | 3.46077i | 0.188520i | 0.995548 | + | 0.0942601i | \(0.0300485\pi\) | ||||
−0.995548 | + | 0.0942601i | \(0.969951\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 12.7112 | 0.686338 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4637 | − | 17.4637i | 0.937498 | − | 0.937498i | −0.0606600 | − | 0.998158i | \(-0.519321\pi\) |
0.998158 | + | 0.0606600i | \(0.0193205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2159 | + | 24.2159i | −1.29625 | + | 1.29625i | −0.365397 | + | 0.930852i | \(0.619067\pi\) |
−0.930852 | + | 0.365397i | \(0.880933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.3481 | −1.94012 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.7028i | − | 0.569650i | −0.958580 | − | 0.284825i | \(-0.908065\pi\) | ||
0.958580 | − | 0.284825i | \(-0.0919355\pi\) | |||||||
\(354\) | 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 | \(0.214416\pi\) | ||||
−0.781577 | + | 0.623809i | \(0.785584\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | − | 13.7431i | − | 0.717386i | −0.933456 | − | 0.358693i | \(-0.883223\pi\) | ||
0.933456 | − | 0.358693i | \(-0.116777\pi\) | |||||||
\(368\) | 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 | \(-0.986394\pi\) |
0.0427313 | + | 0.999087i | \(0.486394\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.4881 | 1.77623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1028 | − | 16.1028i | −0.827143 | − | 0.827143i | 0.159978 | − | 0.987121i | \(-0.448858\pi\) |
−0.987121 | + | 0.159978i | \(0.948858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50207 | − | 1.50207i | 0.0769535 | − | 0.0769535i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 23.1255i | − | 1.18166i | −0.806796 | − | 0.590830i | \(-0.798800\pi\) | ||
0.806796 | − | 0.590830i | \(-0.201200\pi\) | |||||||
\(384\) | 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 | 0.999872 | − | 0.0160295i | \(-0.00510257\pi\) |
−0.0160295 | + | 0.999872i | \(0.505103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.952310i | 0.0481604i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.7348 | −0.995491 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00102 | + | 4.00102i | 0.200806 | + | 0.200806i | 0.800345 | − | 0.599540i | \(-0.204650\pi\) |
−0.599540 | + | 0.800345i | \(0.704650\pi\) | |||||||
\(398\) | 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 | ||||||||
\(407\) | 12.8227 | 0.635598 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.59845i | − | 0.227379i | −0.993516 | − | 0.113689i | \(-0.963733\pi\) | ||
0.993516 | − | 0.113689i | \(-0.0362669\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | 0.757161i | 0.0370783i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.6774 | − | 16.6774i | 0.814746 | − | 0.814746i | −0.170595 | − | 0.985341i | \(-0.554569\pi\) |
0.985341 | + | 0.170595i | \(0.0545689\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −6.17987 | −0.300476 | ||||||||
\(424\) | 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 | ||||||||
\(433\) | 0.676118i | 0.0324922i | 0.999868 | + | 0.0162461i | \(0.00517152\pi\) | ||||
−0.999868 | + | 0.0162461i | \(0.994828\pi\) | |||||||
\(434\) | 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 | \(0.103246\pi\) | ||||
−0.947856 | + | 0.318700i | \(0.896754\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.73366i | 0.177794i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.1262 | − | 28.1262i | 1.33631 | − | 1.33631i | 0.436714 | − | 0.899600i | \(-0.356142\pi\) |
0.899600 | − | 0.436714i | \(-0.143858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.38805i | 0.444039i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.37972 | 0.395464 | 0.197732 | − | 0.980256i | \(-0.436642\pi\) | ||||
0.197732 | + | 0.980256i | \(0.436642\pi\) | |||||||
\(450\) | 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 | ||||||||
\(457\) | −5.66561 | −0.265026 | −0.132513 | − | 0.991181i | \(-0.542305\pi\) | ||||
−0.132513 | + | 0.991181i | \(0.542305\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 41.6835i | 1.93720i | 0.248631 | + | 0.968598i | \(0.420019\pi\) | ||||
−0.248631 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.11020 | + | 3.11020i | 0.143923 | + | 0.143923i | 0.775397 | − | 0.631474i | \(-0.217550\pi\) |
−0.631474 | + | 0.775397i | \(0.717550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.89057 | + | 6.89057i | 0.318177 | + | 0.318177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.40370i | 0.295067i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.04255 | −0.231857 | ||||||||
\(474\) | 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 | \(-0.560897\pi\) | ||||
−0.190149 | + | 0.981755i | \(0.560897\pi\) | |||||||
\(480\) | 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 | ||||||||
\(487\) | −7.29577 | −0.330603 | −0.165301 | − | 0.986243i | \(-0.552860\pi\) | ||||
−0.165301 | + | 0.986243i | \(0.552860\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | 0.874479i | 0.0392257i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8833 | + | 10.8833i | −0.487203 | + | 0.487203i | −0.907422 | − | 0.420220i | \(-0.861953\pi\) |
0.420220 | + | 0.907422i | \(0.361953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00295 | − | 7.00295i | −0.312869 | − | 0.312869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.3781 | −1.30991 | −0.654953 | − | 0.755670i | \(-0.727312\pi\) | ||||
−0.654953 | + | 0.755670i | \(0.727312\pi\) | |||||||
\(504\) | 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 | −0.978780 | − | 0.204916i | \(-0.934308\pi\) |
0.204916 | + | 0.978780i | \(0.434308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.46222 | 0.418584 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.9175i | 1.58579i | ||||||||
\(514\) | 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 | \(-0.582201\pi\) |
0.966841 | + | 0.255380i | \(0.0822006\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.10265i | − | 0.0915929i | ||||||
\(528\) | 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 | ||||||||
\(537\) | 7.81028 | 0.337039 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 3.58416i | 0.153811i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.9660 | − | 21.9660i | −0.939197 | − | 0.939197i | 0.0590579 | − | 0.998255i | \(-0.481190\pi\) |
−0.998255 | + | 0.0590579i | \(0.981190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.85771 | − | 1.85771i | −0.0792852 | − | 0.0792852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.0796i | − | 1.45184i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4002 | 0.612357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.5409 | − | 17.5409i | −0.743234 | − | 0.743234i | 0.229965 | − | 0.973199i | \(-0.426139\pi\) |
−0.973199 | + | 0.229965i | \(0.926139\pi\) | |||||||
\(558\) | 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 | −0.983794 | − | 0.179300i | \(-0.942617\pi\) |
−0.179300 | − | 0.983794i | \(-0.557383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.59190 | −0.276834 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.6390i | − | 0.990998i | −0.868608 | − | 0.495499i | \(-0.834985\pi\) | ||
0.868608 | − | 0.495499i | \(-0.165015\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | 3.69585i | 0.153860i | 0.997036 | + | 0.0769302i | \(0.0245119\pi\) | ||||
−0.997036 | + | 0.0769302i | \(0.975488\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −15.8105 | −0.654802 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.0313 | + | 27.0313i | −1.11570 | + | 1.11570i | −0.123335 | + | 0.992365i | \(0.539359\pi\) |
−0.992365 | + | 0.123335i | \(0.960641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.5146 | + | 19.5146i | −0.804085 | + | 0.804085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.07189 | −0.126361 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.55524i | − | 0.187061i | −0.995616 | − | 0.0935306i | \(-0.970185\pi\) | ||
0.995616 | − | 0.0935306i | \(-0.0298153\pi\) | |||||||
\(594\) | 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 | \(0.0487570\pi\) | ||||
−0.988292 | + | 0.152576i | \(0.951243\pi\) | |||||||
\(600\) | 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 | ||||||||
\(607\) | 5.23884i | 0.212638i | 0.994332 | + | 0.106319i | \(0.0339065\pi\) | ||||
−0.994332 | + | 0.106319i | \(0.966094\pi\) | |||||||
\(608\) | 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 | \(-0.951576\pi\) |
0.151541 | + | 0.988451i | \(0.451576\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.20286 | 0.0886838 | 0.0443419 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443419 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.4569 | − | 31.4569i | −1.26436 | − | 1.26436i | −0.948958 | − | 0.315404i | \(-0.897860\pi\) |
−0.315404 | − | 0.948958i | \(-0.602140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.67158 | + | 7.67158i | −0.307850 | + | 0.307850i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.09473i | 0.0438594i | ||||||||
\(624\) | 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 | ||||||||
\(633\) | 18.9957 | 0.755011 | ||||||||
\(634\) | 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 | 0.717710 | − | 0.696342i | \(-0.245190\pi\) |
−0.696342 | + | 0.717710i | \(0.745190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.6391 | −1.28318 | −0.641588 | − | 0.767049i | \(-0.721724\pi\) | ||||
−0.641588 | + | 0.767049i | \(0.721724\pi\) | |||||||
\(648\) | 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 | 0.871491 | − | 0.490412i | \(-0.163154\pi\) |
−0.490412 | + | 0.871491i | \(0.663154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.99434i | 0.233862i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.26445 | − | 1.26445i | 0.0492560 | − | 0.0492560i | −0.682050 | − | 0.731306i | \(-0.738911\pi\) |
0.731306 | + | 0.682050i | \(0.238911\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 4.92519 | 0.191279 | ||||||||
\(664\) | 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 | ||||||||
\(673\) | 3.58765i | 0.138294i | 0.997606 | + | 0.0691469i | \(0.0220277\pi\) | ||||
−0.997606 | + | 0.0691469i | \(0.977972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.1507 | − | 10.1507i | 0.390124 | − | 0.390124i | −0.484608 | − | 0.874731i | \(-0.661038\pi\) |
0.874731 | + | 0.484608i | \(0.161038\pi\) | |||||||
\(678\) | 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 | \(-0.600954\pi\) |
0.950126 | + | 0.311866i | \(0.100954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16.6761i | − | 0.636234i | ||||||
\(688\) | 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 | ||||||||
\(697\) | 4.97661 | 0.188502 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 41.4217i | 1.56225i | ||||||||
\(704\) | 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 | 0.522628 | − | 0.852561i | \(-0.324952\pi\) |
−0.852561 | + | 0.522628i | \(0.824952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.12255i | 0.342122i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.33621 | −0.312194 | ||||||||
\(714\) | 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 | \(-0.169150\pi\) | ||||
0.862099 | + | 0.506740i | \(0.169150\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | 17.4640 | 0.647703 | 0.323852 | − | 0.946108i | \(-0.395022\pi\) | ||||
0.323852 | + | 0.946108i | \(0.395022\pi\) | |||||||
\(728\) | 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 | 0.837744 | − | 0.546063i | \(-0.183874\pi\) |
−0.546063 | + | 0.837744i | \(0.683874\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.9247i | 0.733936i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.1724 | − | 26.1724i | 0.962769 | − | 0.962769i | −0.0365624 | − | 0.999331i | \(-0.511641\pi\) |
0.999331 | + | 0.0365624i | \(0.0116408\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.7105 | − | 45.7105i | −1.67922 | − | 1.67922i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.7660 | 1.82574 | 0.912868 | − | 0.408254i | \(-0.133862\pi\) | ||||
0.912868 | + | 0.408254i | \(0.133862\pi\) | |||||||
\(744\) | 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 | ||||||||
\(753\) | − | 7.29665i | − | 0.265905i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4872 | + | 15.4872i | −0.562890 | + | 0.562890i | −0.930127 | − | 0.367237i | \(-0.880304\pi\) |
0.367237 | + | 0.930127i | \(0.380304\pi\) | |||||||
\(758\) | 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 | ||||||||
\(767\) | 77.7185i | 2.80625i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.9737 | 0.900573 | 0.450287 | − | 0.892884i | \(-0.351322\pi\) | ||||
0.450287 | + | 0.892884i | \(0.351322\pi\) | |||||||
\(770\) | 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 | \(-0.739272\pi\) |
0.730533 | + | 0.682878i | \(0.239272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.68103 | −0.347305 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 29.5807i | 1.05713i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.647036 | + | 0.647036i | 0.0230644 | + | 0.0230644i | 0.718545 | − | 0.695481i | \(-0.244808\pi\) |
−0.695481 | + | 0.718545i | \(0.744808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.99087 | + | 8.99087i | 0.320084 | + | 0.320084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7570i | 0.595811i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7198 | 0.984360 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.3024 | − | 18.3024i | −0.648303 | − | 0.648303i | 0.304280 | − | 0.952583i | \(-0.401584\pi\) |
−0.952583 | + | 0.304280i | \(0.901584\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | −37.7593 | −1.32919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.4845i | − | 1.14209i | −0.820917 | − | 0.571047i | \(-0.806537\pi\) | ||
0.820917 | − | 0.571047i | \(-0.193463\pi\) | |||||||
\(810\) | 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 | ||||||||
\(817\) | − | 16.2891i | − | 0.569884i | ||||||
\(818\) | 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 | ||||||||
\(823\) | −4.85817 | −0.169345 | −0.0846726 | − | 0.996409i | \(-0.526984\pi\) | ||||
−0.0846726 | + | 0.996409i | \(0.526984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.02757 | + | 8.02757i | −0.279146 | + | 0.279146i | −0.832768 | − | 0.553622i | \(-0.813245\pi\) |
0.553622 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3613 | − | 24.3613i | 0.846102 | − | 0.846102i | −0.143542 | − | 0.989644i | \(-0.545849\pi\) |
0.989644 | + | 0.143542i | \(0.0458493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.3952 | −0.776881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 2.96585i | − | 0.102761i | ||||||
\(834\) | 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 | \(-0.732761\pi\) | ||
0.667794 | − | 0.744346i | \(-0.267239\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 6.85110i | 0.235407i | ||||||||
\(848\) | 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 | \(-0.894057\pi\) |
0.326720 | + | 0.945121i | \(0.394057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.8346 | −1.22409 | −0.612043 | − | 0.790825i | \(-0.709652\pi\) | ||||
−0.612043 | + | 0.790825i | \(0.709652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.619460 | − | 0.619460i | −0.0211357 | − | 0.0211357i | 0.696460 | − | 0.717596i | \(-0.254757\pi\) |
−0.717596 | + | 0.696460i | \(0.754757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7949 | − | 10.7949i | 0.367890 | − | 0.367890i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.8270i | − | 0.640878i | −0.947269 | − | 0.320439i | \(-0.896170\pi\) | ||
0.947269 | − | 0.320439i | \(-0.103830\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −4.65479 | −0.157541 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.77833 | + | 7.77833i | 0.262656 | + | 0.262656i | 0.826132 | − | 0.563476i | \(-0.190536\pi\) |
−0.563476 | + | 0.826132i | \(0.690536\pi\) | |||||||
\(878\) | 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 | 0.992122 | − | 0.125278i | \(-0.0399823\pi\) |
−0.125278 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.8982 | −1.30607 | −0.653037 | − | 0.757326i | \(-0.726505\pi\) | ||||
−0.653037 | + | 0.757326i | \(0.726505\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | − | 19.5265i | − | 0.651972i | ||||||
\(898\) | 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 | ||||||||
\(903\) | 3.80707 | 0.126692 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.10220 | − | 5.10220i | 0.169416 | − | 0.169416i | −0.617307 | − | 0.786723i | \(-0.711776\pi\) |
0.786723 | + | 0.617307i | \(0.211776\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 2.29520i | − | 0.0759601i | ||||||
\(914\) | 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 | \(0.343731\pi\) | ||||
−0.471449 | + | 0.881893i | \(0.656269\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | − | 8.52342i | − | 0.279946i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.2098 | −0.466209 | −0.233104 | − | 0.972452i | \(-0.574888\pi\) | ||||
−0.233104 | + | 0.972452i | \(0.574888\pi\) | |||||||
\(930\) | 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 | ||||||||
\(937\) | 5.26656 | 0.172051 | 0.0860255 | − | 0.996293i | \(-0.472583\pi\) | ||||
0.0860255 | + | 0.996293i | \(0.472583\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − | 19.7304i | − | 0.642509i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.27572 | + | 3.27572i | 0.106447 | + | 0.106447i | 0.758324 | − | 0.651878i | \(-0.226018\pi\) |
−0.651878 | + | 0.758324i | \(0.726018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.7223 | − | 44.7223i | −1.45175 | − | 1.45175i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.9142i | − | 0.710616i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0292 | 0.972741 | 0.486371 | − | 0.873753i | \(-0.338320\pi\) | ||||
0.486371 | + | 0.873753i | \(0.338320\pi\) | |||||||
\(954\) | 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 | ||||||||
\(967\) | −15.2196 | −0.489429 | −0.244715 | − | 0.969595i | \(-0.578694\pi\) | ||||
−0.244715 | + | 0.969595i | \(0.578694\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | 18.7912i | 0.601183i | 0.953753 | + | 0.300592i | \(0.0971841\pi\) | ||||
−0.953753 | + | 0.300592i | \(0.902816\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | −56.5605 | −1.80400 | −0.901999 | − | 0.431738i | \(-0.857901\pi\) | ||||
−0.901999 | + | 0.431738i | \(0.857901\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | 17.2404i | 0.547108i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.1508 | + | 35.1508i | −1.11324 | + | 1.11324i | −0.120528 | + | 0.992710i | \(0.538459\pi\) |
−0.992710 | + | 0.120528i | \(0.961541\pi\) | |||||||
\(998\) | 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.q.f.49.2 | 12 | ||
4.3 | odd | 2 | 400.2.q.f.149.2 | 12 | |||
5.2 | odd | 4 | 1600.2.l.g.1201.2 | 12 | |||
5.3 | odd | 4 | 1600.2.l.f.1201.5 | 12 | |||
5.4 | even | 2 | 1600.2.q.e.49.5 | 12 | |||
16.3 | odd | 4 | 400.2.q.e.349.5 | 12 | |||
16.13 | even | 4 | 1600.2.q.e.849.5 | 12 | |||
20.3 | even | 4 | 400.2.l.g.101.5 | yes | 12 | ||
20.7 | even | 4 | 400.2.l.f.101.2 | ✓ | 12 | ||
20.19 | odd | 2 | 400.2.q.e.149.5 | 12 | |||
80.3 | even | 4 | 400.2.l.g.301.5 | yes | 12 | ||
80.13 | odd | 4 | 1600.2.l.f.401.5 | 12 | |||
80.19 | odd | 4 | 400.2.q.f.349.2 | 12 | |||
80.29 | even | 4 | inner | 1600.2.q.f.849.2 | 12 | ||
80.67 | even | 4 | 400.2.l.f.301.2 | yes | 12 | ||
80.77 | odd | 4 | 1600.2.l.g.401.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.2 | ✓ | 12 | 20.7 | even | 4 | ||
400.2.l.f.301.2 | yes | 12 | 80.67 | even | 4 | ||
400.2.l.g.101.5 | yes | 12 | 20.3 | even | 4 | ||
400.2.l.g.301.5 | yes | 12 | 80.3 | even | 4 | ||
400.2.q.e.149.5 | 12 | 20.19 | odd | 2 | |||
400.2.q.e.349.5 | 12 | 16.3 | odd | 4 | |||
400.2.q.f.149.2 | 12 | 4.3 | odd | 2 | |||
400.2.q.f.349.2 | 12 | 80.19 | odd | 4 | |||
1600.2.l.f.401.5 | 12 | 80.13 | odd | 4 | |||
1600.2.l.f.1201.5 | 12 | 5.3 | odd | 4 | |||
1600.2.l.g.401.2 | 12 | 80.77 | odd | 4 | |||
1600.2.l.g.1201.2 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.49.5 | 12 | 5.4 | even | 2 | |||
1600.2.q.e.849.5 | 12 | 16.13 | even | 4 | |||
1600.2.q.f.49.2 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.f.849.2 | 12 | 80.29 | even | 4 | inner |