Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(101,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.l (of order \(4\), degree \(2\), 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: | \(3.19401608085\) |
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: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 101.5 | ||
Root | \(1.22306 + 0.710021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.101 |
Dual form | 400.2.l.g.301.5 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22306 | + | 0.710021i | 0.864832 | + | 0.502061i | ||||
\(3\) | −1.09156 | + | 1.09156i | −0.630214 | + | 0.630214i | −0.948122 | − | 0.317908i | \(-0.897020\pi\) |
0.317908 | + | 0.948122i | \(0.397020\pi\) | |||||||
\(4\) | 0.991741 | + | 1.73679i | 0.495870 | + | 0.868396i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.11008 | + | 0.560012i | −0.861435 | + | 0.228624i | ||||
\(7\) | − | 0.973926i | − | 0.368109i | −0.982916 | − | 0.184055i | \(-0.941078\pi\) | ||
0.982916 | − | 0.184055i | \(-0.0589224\pi\) | |||||||
\(8\) | −0.0202025 | + | 2.82835i | −0.00714267 | + | 0.999974i | ||||
\(9\) | 0.616985i | 0.205662i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40810 | + | 1.40810i | 0.424558 | + | 0.424558i | 0.886769 | − | 0.462212i | \(-0.152944\pi\) |
−0.462212 | + | 0.886769i | \(0.652944\pi\) | |||||||
\(12\) | −2.97836 | − | 0.813270i | −0.859780 | − | 0.234771i | ||||
\(13\) | −4.60317 | + | 4.60317i | −1.27669 | + | 1.27669i | −0.334179 | + | 0.942510i | \(0.608459\pi\) |
−0.942510 | + | 0.334179i | \(0.891541\pi\) | |||||||
\(14\) | 0.691508 | − | 1.19117i | 0.184813 | − | 0.318353i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.03290 | + | 3.44490i | −0.508225 | + | 0.861224i | ||||
\(17\) | 0.490104 | 0.118868 | 0.0594338 | − | 0.998232i | \(-0.481070\pi\) | ||||
0.0594338 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(18\) | −0.438072 | + | 0.754608i | −0.103255 | + | 0.177863i | ||||
\(19\) | 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 | ||||
\(22\) | 0.722406 | + | 2.72196i | 0.154018 | + | 0.580325i | ||||
\(23\) | − | 1.94308i | − | 0.405160i | −0.979266 | − | 0.202580i | \(-0.935067\pi\) | ||
0.979266 | − | 0.202580i | \(-0.0649325\pi\) | |||||||
\(24\) | −3.06527 | − | 3.10938i | −0.625696 | − | 0.634699i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.89828 | + | 2.36159i | −1.74510 | + | 0.463147i | ||||
\(27\) | −3.94816 | − | 3.94816i | −0.759824 | − | 0.759824i | ||||
\(28\) | 1.69151 | − | 0.965882i | 0.319665 | − | 0.182535i | ||||
\(29\) | −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 | \(-0.374107\pi\) | ||||
0.385272 | + | 0.922803i | \(0.374107\pi\) | |||||||
\(32\) | −4.93230 | + | 2.76991i | −0.871916 | + | 0.489655i | ||||
\(33\) | −3.07405 | −0.535124 | ||||||||
\(34\) | 0.599426 | + | 0.347984i | 0.102801 | + | 0.0596788i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.07157 | + | 0.611889i | −0.178596 | + | 0.101982i | ||||
\(37\) | 4.55320 | + | 4.55320i | 0.748542 | + | 0.748542i | 0.974205 | − | 0.225663i | \(-0.0724549\pi\) |
−0.225663 | + | 0.974205i | \(0.572455\pi\) | |||||||
\(38\) | 8.79286 | − | 2.33362i | 1.42639 | − | 0.378562i | ||||
\(39\) | − | 10.0493i | − | 1.60917i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.1542i | − | 1.58582i | −0.609341 | − | 0.792908i | \(-0.708566\pi\) | ||
0.609341 | − | 0.792908i | \(-0.291434\pi\) | |||||||
\(42\) | 0.545410 | + | 2.05506i | 0.0841586 | + | 0.317102i | ||||
\(43\) | −1.79055 | − | 1.79055i | −0.273057 | − | 0.273057i | 0.557273 | − | 0.830329i | \(-0.311848\pi\) |
−0.830329 | + | 0.557273i | \(0.811848\pi\) | |||||||
\(44\) | −1.04911 | + | 3.84204i | −0.158159 | + | 0.579210i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.37963 | − | 2.37650i | 0.203415 | − | 0.350395i | ||||
\(47\) | 10.0162 | 1.46102 | 0.730510 | − | 0.682902i | \(-0.239283\pi\) | ||||
0.730510 | + | 0.682902i | \(0.239283\pi\) | |||||||
\(48\) | −1.54128 | − | 5.97936i | −0.222465 | − | 0.863046i | ||||
\(49\) | 6.05147 | 0.864495 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.534979 | + | 0.534979i | −0.0749120 | + | 0.0749120i | ||||
\(52\) | −12.5599 | − | 3.42960i | −1.74174 | − | 0.475600i | ||||
\(53\) | 5.61412 | + | 5.61412i | 0.771158 | + | 0.771158i | 0.978309 | − | 0.207151i | \(-0.0664190\pi\) |
−0.207151 | + | 0.978309i | \(0.566419\pi\) | |||||||
\(54\) | −2.02555 | − | 7.63211i | −0.275643 | − | 1.03860i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.75461 | + | 0.0196757i | 0.368100 | + | 0.00262928i | ||||
\(57\) | 9.93022i | 1.31529i | ||||||||
\(58\) | −7.24157 | + | 1.92191i | −0.950865 | + | 0.252359i | ||||
\(59\) | 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 | \(0.162117\pi\) | |||||||
\(62\) | 5.24718 | + | 3.04614i | 0.666392 | + | 0.386860i | ||||
\(63\) | 0.600897 | 0.0757060 | ||||||||
\(64\) | −7.99918 | − | 0.114280i | −0.999898 | − | 0.0142850i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.75974 | − | 2.18264i | −0.462793 | − | 0.268665i | ||||
\(67\) | 7.07504 | − | 7.07504i | 0.864354 | − | 0.864354i | −0.127486 | − | 0.991840i | \(-0.540691\pi\) |
0.991840 | + | 0.127486i | \(0.0406908\pi\) | |||||||
\(68\) | 0.486056 | + | 0.851209i | 0.0589430 | + | 0.103224i | ||||
\(69\) | 2.12099 | + | 2.12099i | 0.255337 | + | 0.255337i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.897891i | 0.106560i | 0.998580 | + | 0.0532800i | \(0.0169676\pi\) | ||||
−0.998580 | + | 0.0532800i | \(0.983032\pi\) | |||||||
\(72\) | −1.74505 | − | 0.0124646i | −0.205656 | − | 0.00146897i | ||||
\(73\) | − | 9.71555i | − | 1.13712i | −0.822642 | − | 0.568559i | \(-0.807501\pi\) | ||
0.822642 | − | 0.568559i | \(-0.192499\pi\) | |||||||
\(74\) | 2.33596 | + | 8.80170i | 0.271550 | + | 1.02318i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.4111 | + | 3.38897i | 1.42365 | + | 0.388741i | ||||
\(77\) | 1.37138 | − | 1.37138i | 0.156284 | − | 0.156284i | ||||
\(78\) | 7.13520 | − | 12.2909i | 0.807902 | − | 1.39166i | ||||
\(79\) | −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 | ||||||||
\(82\) | 7.20968 | − | 12.4192i | 0.796176 | − | 1.37147i | ||||
\(83\) | 0.815000 | − | 0.815000i | 0.0894579 | − | 0.0894579i | −0.660962 | − | 0.750420i | \(-0.729851\pi\) |
0.750420 | + | 0.660962i | \(0.229851\pi\) | |||||||
\(84\) | −0.792065 | + | 2.90071i | −0.0864214 | + | 0.316493i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.918620 | − | 3.46128i | −0.0990573 | − | 0.373239i | ||||
\(87\) | − | 8.17827i | − | 0.876803i | ||||||
\(88\) | −4.01105 | + | 3.95415i | −0.427579 | + | 0.421514i | ||||
\(89\) | 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 | ||||
\(92\) | 3.37472 | − | 1.92703i | 0.351839 | − | 0.200907i | ||||
\(93\) | −4.68303 | + | 4.68303i | −0.485608 | + | 0.485608i | ||||
\(94\) | 12.2504 | + | 7.11174i | 1.26354 | + | 0.733520i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.36039 | − | 8.40744i | 0.240906 | − | 0.858081i | ||||
\(97\) | −7.54442 | −0.766019 | −0.383010 | − | 0.923744i | \(-0.625112\pi\) | ||||
−0.383010 | + | 0.923744i | \(0.625112\pi\) | |||||||
\(98\) | 7.40130 | + | 4.29667i | 0.747644 | + | 0.434029i | ||||
\(99\) | −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 | \(0.808682\pi\) | |||||||
\(102\) | −1.03416 | + | 0.274464i | −0.102397 | + | 0.0271760i | ||||
\(103\) | − | 13.8146i | − | 1.36120i | −0.732657 | − | 0.680598i | \(-0.761720\pi\) | ||
0.732657 | − | 0.680598i | \(-0.238280\pi\) | |||||||
\(104\) | −12.9264 | − | 13.1124i | −1.26754 | − | 1.28577i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.88025 | + | 10.8525i | 0.279755 | + | 1.05409i | ||||
\(107\) | −9.89124 | − | 9.89124i | −0.956222 | − | 0.956222i | 0.0428589 | − | 0.999081i | \(-0.486353\pi\) |
−0.999081 | + | 0.0428589i | \(0.986353\pi\) | |||||||
\(108\) | 2.94159 | − | 10.7727i | 0.283054 | − | 1.03660i | ||||
\(109\) | −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 | ||||||||
\(112\) | 3.35507 | + | 1.97989i | 0.317025 | + | 0.187082i | ||||
\(113\) | 17.2057 | 1.61857 | 0.809286 | − | 0.587415i | \(-0.199854\pi\) | ||||
0.809286 | + | 0.587415i | \(0.199854\pi\) | |||||||
\(114\) | −7.05066 | + | 12.1452i | −0.660355 | + | 1.13751i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.2215 | − | 2.79106i | −0.949038 | − | 0.259144i | ||||
\(117\) | −2.84008 | − | 2.84008i | −0.262566 | − | 0.262566i | ||||
\(118\) | 4.33098 | + | 16.3188i | 0.398699 | + | 1.50226i | ||||
\(119\) | − | 0.477325i | − | 0.0437563i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.03452i | − | 0.639502i | ||||||
\(122\) | 5.82041 | − | 1.54473i | 0.526955 | − | 0.139853i | ||||
\(123\) | 11.0839 | + | 11.0839i | 0.999403 | + | 0.999403i | ||||
\(124\) | 4.25478 | + | 7.45121i | 0.382091 | + | 0.669139i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.734932 | + | 0.426650i | 0.0654730 | + | 0.0380090i | ||||
\(127\) | −1.37608 | −0.122107 | −0.0610535 | − | 0.998134i | \(-0.519446\pi\) | ||||
−0.0610535 | + | 0.998134i | \(0.519446\pi\) | |||||||
\(128\) | −9.70232 | − | 5.81936i | −0.857572 | − | 0.514363i | ||||
\(129\) | 3.90900 | 0.344168 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.03973 | + | 9.03973i | −0.789804 | + | 0.789804i | −0.981462 | − | 0.191657i | \(-0.938614\pi\) |
0.191657 | + | 0.981462i | \(0.438614\pi\) | |||||||
\(132\) | −3.04866 | − | 5.33899i | −0.265352 | − | 0.464700i | ||||
\(133\) | −4.43003 | − | 4.43003i | −0.384132 | − | 0.384132i | ||||
\(134\) | 13.6766 | − | 3.62976i | 1.18148 | − | 0.313563i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.00990133 | + | 1.38619i | −0.000849032 | + | 0.118865i | ||||
\(137\) | 15.3056i | 1.30764i | 0.756649 | + | 0.653822i | \(0.226835\pi\) | ||||
−0.756649 | + | 0.653822i | \(0.773165\pi\) | |||||||
\(138\) | 1.08815 | + | 4.10004i | 0.0926291 | + | 0.349018i | ||||
\(139\) | −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 | ||||
\(142\) | −0.637521 | + | 1.09817i | −0.0534996 | + | 0.0921566i | ||||
\(143\) | −12.9634 | −1.08406 | ||||||||
\(144\) | −2.12545 | − | 1.25427i | −0.177121 | − | 0.104522i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.89824 | − | 11.8827i | 0.570902 | − | 0.983417i | ||||
\(147\) | −6.60555 | + | 6.60555i | −0.544817 | + | 0.544817i | ||||
\(148\) | −3.39237 | + | 12.4236i | −0.278851 | + | 1.02121i | ||||
\(149\) | 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 | \(0.0262055\pi\) | ||||
−0.996613 | + | 0.0822341i | \(0.973794\pi\) | |||||||
\(152\) | 12.7732 | + | 12.9570i | 1.03605 | + | 1.05095i | ||||
\(153\) | 0.302387i | 0.0244465i | ||||||||
\(154\) | 2.65099 | − | 0.703570i | 0.213623 | − | 0.0566953i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 17.4535 | − | 9.96628i | 1.39740 | − | 0.797941i | ||||
\(157\) | −2.93327 | + | 2.93327i | −0.234101 | + | 0.234101i | −0.814402 | − | 0.580301i | \(-0.802935\pi\) |
0.580301 | + | 0.814402i | \(0.302935\pi\) | |||||||
\(158\) | −18.0838 | − | 10.4981i | −1.43867 | − | 0.835188i | ||||
\(159\) | −12.2563 | −0.971989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89241 | −0.149143 | ||||||||
\(162\) | 8.27811 | + | 4.80569i | 0.650390 | + | 0.377570i | ||||
\(163\) | 5.74697 | − | 5.74697i | 0.450137 | − | 0.450137i | −0.445263 | − | 0.895400i | \(-0.646890\pi\) |
0.895400 | + | 0.445263i | \(0.146890\pi\) | |||||||
\(164\) | 17.6357 | − | 10.0703i | 1.37712 | − | 0.786360i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.57546 | − | 0.418125i | 0.122279 | − | 0.0324528i | ||||
\(167\) | 6.41553i | 0.496449i | 0.968703 | + | 0.248224i | \(0.0798470\pi\) | ||||
−0.968703 | + | 0.248224i | \(0.920153\pi\) | |||||||
\(168\) | −3.02830 | + | 2.98535i | −0.233639 | + | 0.230325i | ||||
\(169\) | − | 29.3783i | − | 2.25987i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.80644 | + | 2.80644i | 0.214613 | + | 0.214613i | ||||
\(172\) | 1.33405 | − | 4.88558i | 0.101721 | − | 0.372522i | ||||
\(173\) | 0.545724 | − | 0.545724i | 0.0414907 | − | 0.0414907i | −0.686057 | − | 0.727548i | \(-0.740660\pi\) |
0.727548 | + | 0.686057i | \(0.240660\pi\) | |||||||
\(174\) | 5.80674 | − | 10.0025i | 0.440208 | − | 0.758288i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.71328 | + | 1.98823i | −0.581410 | + | 0.149869i | ||||
\(177\) | −18.4296 | −1.38525 | ||||||||
\(178\) | −0.798090 | + | 1.37476i | −0.0598194 | + | 0.103043i | ||||
\(179\) | −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 | \(0.777501\pi\) | |||||||
\(182\) | 2.30002 | + | 8.66627i | 0.170489 | + | 0.642386i | ||||
\(183\) | 6.57328i | 0.485911i | ||||||||
\(184\) | 5.49571 | + | 0.0392550i | 0.405149 | + | 0.00289392i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.05267 | + | 2.40257i | −0.663774 | + | 0.176165i | ||||
\(187\) | 0.690114 | + | 0.690114i | 0.0504662 | + | 0.0504662i | ||||
\(188\) | 9.93352 | + | 17.3961i | 0.724476 | + | 1.26874i | ||||
\(189\) | −3.84522 | + | 3.84522i | −0.279698 | + | 0.279698i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3359 | −1.10967 | −0.554835 | − | 0.831960i | \(-0.687219\pi\) | ||||
−0.554835 | + | 0.831960i | \(0.687219\pi\) | |||||||
\(192\) | 8.85635 | − | 8.60686i | 0.639152 | − | 0.621147i | ||||
\(193\) | 0.0812703 | 0.00584996 | 0.00292498 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292498 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(194\) | −9.22726 | − | 5.35669i | −0.662478 | − | 0.384588i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00149 | + | 10.5101i | 0.428678 | + | 0.750725i | ||||
\(197\) | −1.40711 | − | 1.40711i | −0.100252 | − | 0.100252i | 0.655202 | − | 0.755454i | \(-0.272584\pi\) |
−0.755454 | + | 0.655202i | \(0.772584\pi\) | |||||||
\(198\) | −1.67941 | + | 0.445714i | −0.119351 | + | 0.0316755i | ||||
\(199\) | − | 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 | ||||||||
\(202\) | −1.33664 | − | 5.03635i | −0.0940458 | − | 0.354356i | ||||
\(203\) | 3.64846 | + | 3.64846i | 0.256071 | + | 0.256071i | ||||
\(204\) | −1.45971 | − | 0.398587i | −0.102200 | − | 0.0279067i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.80868 | − | 16.8961i | 0.683403 | − | 1.17721i | ||||
\(207\) | 1.19885 | 0.0833258 | ||||||||
\(208\) | −6.49966 | − | 25.2152i | −0.450670 | − | 1.74836i | ||||
\(209\) | 12.8098 | 0.886075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70115 | − | 8.70115i | 0.599012 | − | 0.599012i | −0.341038 | − | 0.940050i | \(-0.610778\pi\) |
0.940050 | + | 0.341038i | \(0.110778\pi\) | |||||||
\(212\) | −4.18281 | + | 15.3183i | −0.287277 | + | 1.05207i | ||||
\(213\) | −0.980103 | − | 0.980103i | −0.0671556 | − | 0.0671556i | ||||
\(214\) | −5.07457 | − | 19.1205i | −0.346891 | − | 1.30705i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.2466 | − | 11.0870i | 0.765232 | − | 0.754378i | ||||
\(217\) | − | 4.17835i | − | 0.283645i | ||||||
\(218\) | −22.3181 | + | 5.92320i | −1.51157 | + | 0.401169i | ||||
\(219\) | 10.6051 | + | 10.6051i | 0.716628 | + | 0.716628i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.25603 | + | 2.25603i | −0.151757 | + | 0.151757i | ||||
\(222\) | −12.1575 | − | 7.05776i | −0.815955 | − | 0.473686i | ||||
\(223\) | −7.78095 | −0.521051 | −0.260525 | − | 0.965467i | \(-0.583896\pi\) | ||||
−0.260525 | + | 0.965467i | \(0.583896\pi\) | |||||||
\(224\) | 2.69769 | + | 4.80370i | 0.180247 | + | 0.320961i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.0435 | + | 12.2164i | 1.39979 | + | 0.812621i | ||||
\(227\) | −2.15443 | + | 2.15443i | −0.142995 | + | 0.142995i | −0.774980 | − | 0.631986i | \(-0.782240\pi\) |
0.631986 | + | 0.774980i | \(0.282240\pi\) | |||||||
\(228\) | −17.2467 | + | 9.84821i | −1.14219 | + | 0.652214i | ||||
\(229\) | −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 | ||||||||
\(232\) | −10.5197 | − | 10.6711i | −0.690653 | − | 0.700591i | ||||
\(233\) | 7.51503i | 0.492326i | 0.969228 | + | 0.246163i | \(0.0791699\pi\) | ||||
−0.969228 | + | 0.246163i | \(0.920830\pi\) | |||||||
\(234\) | −1.45707 | − | 5.49010i | −0.0952515 | − | 0.358899i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.28962 | + | 23.0339i | −0.409419 | + | 1.49938i | ||||
\(237\) | 16.1395 | − | 16.1395i | 1.04837 | − | 1.04837i | ||||
\(238\) | 0.338911 | − | 0.583796i | 0.0219683 | − | 0.0378419i | ||||
\(239\) | 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 | \(0.770026\pi\) | |||||||
\(242\) | 4.99466 | − | 8.60362i | 0.321069 | − | 0.553062i | ||||
\(243\) | 4.45639 | − | 4.45639i | 0.285877 | − | 0.285877i | ||||
\(244\) | 8.21549 | + | 2.24332i | 0.525943 | + | 0.143614i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.68646 | + | 21.4261i | 0.362556 | + | 1.36608i | ||||
\(247\) | 41.8762i | 2.66452i | ||||||||
\(248\) | −0.0866731 | + | 12.1342i | −0.00550375 | + | 0.770525i | ||||
\(249\) | 1.77925i | 0.112755i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.34230 | − | 3.34230i | −0.210964 | − | 0.210964i | 0.593713 | − | 0.804677i | \(-0.297661\pi\) |
−0.804677 | + | 0.593713i | \(0.797661\pi\) | |||||||
\(252\) | 0.595935 | + | 1.04363i | 0.0375404 | + | 0.0657428i | ||||
\(253\) | 2.73604 | − | 2.73604i | 0.172014 | − | 0.172014i | ||||
\(254\) | −1.68302 | − | 0.977043i | −0.105602 | − | 0.0613051i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.73464 | − | 14.0063i | −0.483415 | − | 0.875391i | ||||
\(257\) | 22.4537 | 1.40062 | 0.700311 | − | 0.713838i | \(-0.253045\pi\) | ||||
0.700311 | + | 0.713838i | \(0.253045\pi\) | |||||||
\(258\) | 4.78093 | + | 2.77547i | 0.297648 | + | 0.172793i | ||||
\(259\) | 4.43448 | − | 4.43448i | 0.275545 | − | 0.275545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.31131 | − | 2.31131i | −0.143066 | − | 0.143066i | ||||
\(262\) | −17.4745 | + | 4.63771i | −1.07958 | + | 0.286519i | ||||
\(263\) | 8.23670i | 0.507897i | 0.967218 | + | 0.253948i | \(0.0817294\pi\) | ||||
−0.967218 | + | 0.253948i | \(0.918271\pi\) | |||||||
\(264\) | 0.0621036 | − | 8.69451i | 0.00382221 | − | 0.535110i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.27277 | − | 8.56359i | −0.139352 | − | 0.525068i | ||||
\(267\) | −1.22696 | − | 1.22696i | −0.0750885 | − | 0.0750885i | ||||
\(268\) | 19.3045 | + | 5.27128i | 1.17921 | + | 0.321994i | ||||
\(269\) | −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 | \(-0.623701\pi\) | ||||
−0.378911 | + | 0.925433i | \(0.623701\pi\) | |||||||
\(272\) | −0.996332 | + | 1.68836i | −0.0604115 | + | 0.102372i | ||||
\(273\) | −9.78726 | −0.592352 | ||||||||
\(274\) | −10.8673 | + | 18.7196i | −0.656516 | + | 1.13089i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.58025 | + | 5.78719i | −0.0951197 | + | 0.348348i | ||||
\(277\) | −10.2583 | − | 10.2583i | −0.616363 | − | 0.616363i | 0.328234 | − | 0.944597i | \(-0.393547\pi\) |
−0.944597 | + | 0.328234i | \(0.893547\pi\) | |||||||
\(278\) | −0.177934 | − | 0.670439i | −0.0106718 | − | 0.0402103i | ||||
\(279\) | 2.64700i | 0.158472i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4066i | 1.27701i | 0.769618 | + | 0.638505i | \(0.220447\pi\) | ||||
−0.769618 | + | 0.638505i | \(0.779553\pi\) | |||||||
\(282\) | −21.1350 | + | 5.60922i | −1.25857 | + | 0.334024i | ||||
\(283\) | 7.39635 | + | 7.39635i | 0.439668 | + | 0.439668i | 0.891900 | − | 0.452232i | \(-0.149372\pi\) |
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(284\) | −1.55945 | + | 0.890475i | −0.0925363 | + | 0.0528400i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.8550 | − | 9.20430i | −0.937526 | − | 0.544261i | ||||
\(287\) | −9.88942 | −0.583754 | ||||||||
\(288\) | −1.70899 | − | 3.04316i | −0.100703 | − | 0.179320i | ||||
\(289\) | −16.7598 | −0.985870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.23520 | − | 8.23520i | 0.482756 | − | 0.482756i | ||||
\(292\) | 16.8739 | − | 9.63531i | 0.987470 | − | 0.563864i | ||||
\(293\) | 0.556728 | + | 0.556728i | 0.0325244 | + | 0.0325244i | 0.723182 | − | 0.690658i | \(-0.242679\pi\) |
−0.690658 | + | 0.723182i | \(0.742679\pi\) | |||||||
\(294\) | −12.7691 | + | 3.38889i | −0.744706 | + | 0.197644i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.9701 | + | 12.7861i | −0.753870 | + | 0.743177i | ||||
\(297\) | − | 11.1188i | − | 0.645178i | ||||||
\(298\) | 2.20620 | + | 8.31278i | 0.127802 | + | 0.481546i | ||||
\(299\) | 8.94430 | + | 8.94430i | 0.517263 | + | 0.517263i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.74387 | + | 1.74387i | −0.100515 | + | 0.100515i | ||||
\(302\) | −1.43497 | + | 2.47182i | −0.0825730 | + | 0.142238i | ||||
\(303\) | 5.68781 | 0.326756 | ||||||||
\(304\) | 6.42266 | + | 24.9165i | 0.368365 | + | 1.42906i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.214701 | + | 0.369836i | −0.0122736 | + | 0.0211421i | ||||
\(307\) | −9.76852 | + | 9.76852i | −0.557519 | + | 0.557519i | −0.928600 | − | 0.371082i | \(-0.878987\pi\) |
0.371082 | + | 0.928600i | \(0.378987\pi\) | |||||||
\(308\) | 3.74187 | + | 1.02175i | 0.213213 | + | 0.0582197i | ||||
\(309\) | 15.0795 | + | 15.0795i | 0.857844 | + | 0.857844i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 30.6874i | − | 1.74013i | −0.492941 | − | 0.870063i | \(-0.664078\pi\) | ||
0.492941 | − | 0.870063i | \(-0.335922\pi\) | |||||||
\(312\) | 28.4229 | + | 0.203021i | 1.60913 | + | 0.0114938i | ||||
\(313\) | 1.71127i | 0.0967268i | 0.998830 | + | 0.0483634i | \(0.0154006\pi\) | ||||
−0.998830 | + | 0.0483634i | \(0.984599\pi\) | |||||||
\(314\) | −5.67024 | + | 1.50488i | −0.319990 | + | 0.0849251i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.6636 | − | 25.6797i | −0.824891 | − | 1.44460i | ||||
\(317\) | 10.0380 | − | 10.0380i | 0.563790 | − | 0.563790i | −0.366592 | − | 0.930382i | \(-0.619476\pi\) |
0.930382 | + | 0.366592i | \(0.119476\pi\) | |||||||
\(318\) | −14.9902 | − | 8.70224i | −0.840608 | − | 0.487997i | ||||
\(319\) | −10.5498 | −0.590678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5938 | 1.20525 | ||||||||
\(322\) | −2.31453 | − | 1.34365i | −0.128984 | − | 0.0748788i | ||||
\(323\) | 2.22930 | − | 2.22930i | 0.124042 | − | 0.124042i | ||||
\(324\) | 6.71248 | + | 11.7553i | 0.372915 | + | 0.653070i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.1093 | − | 2.94841i | 0.615290 | − | 0.163297i | ||||
\(327\) | − | 25.2049i | − | 1.39384i | ||||||
\(328\) | 28.7196 | + | 0.205140i | 1.58578 | + | 0.0113270i | ||||
\(329\) | − | 9.75508i | − | 0.537815i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.89713 | + | 7.89713i | 0.434066 | + | 0.434066i | 0.890009 | − | 0.455943i | \(-0.150698\pi\) |
−0.455943 | + | 0.890009i | \(0.650698\pi\) | |||||||
\(332\) | 2.22376 | + | 0.607218i | 0.122044 | + | 0.0333254i | ||||
\(333\) | −2.80926 | + | 2.80926i | −0.153946 | + | 0.153946i | ||||
\(334\) | −4.55516 | + | 7.84656i | −0.249247 | + | 0.429345i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.82345 | + | 1.50110i | −0.317695 | + | 0.0818915i | ||||
\(337\) | 3.46077 | 0.188520 | 0.0942601 | − | 0.995548i | \(-0.469951\pi\) | ||||
0.0942601 | + | 0.995548i | \(0.469951\pi\) | |||||||
\(338\) | 20.8592 | − | 35.9313i | 1.13459 | − | 1.95441i | ||||
\(339\) | −18.7810 | + | 18.7810i | −1.02005 | + | 1.02005i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.04104 | + | 6.04104i | 0.327141 | + | 0.327141i | ||||
\(342\) | 1.43981 | + | 5.42506i | 0.0778558 | + | 0.293354i | ||||
\(343\) | − | 12.7112i | − | 0.686338i | ||||||
\(344\) | 5.10049 | − | 5.02814i | 0.275000 | − | 0.271099i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.05493 | − | 0.279977i | 0.0567133 | − | 0.0150516i | ||||
\(347\) | 17.4637 | + | 17.4637i | 0.937498 | + | 0.937498i | 0.998158 | − | 0.0606600i | \(-0.0193205\pi\) |
−0.0606600 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(348\) | 14.2040 | − | 8.11073i | 0.761413 | − | 0.434781i | ||||
\(349\) | 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 | ||||||||
\(352\) | −10.8455 | − | 3.04486i | −0.578065 | − | 0.162292i | ||||
\(353\) | 10.7028 | 0.569650 | 0.284825 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284825 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(354\) | −22.5405 | − | 13.0854i | −1.19801 | − | 0.695482i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.95222 | + | 1.11475i | −0.103467 | + | 0.0590818i | ||||
\(357\) | 0.521030 | + | 0.521030i | 0.0275758 | + | 0.0275758i | ||||
\(358\) | −6.91573 | + | 1.83543i | −0.365507 | + | 0.0970053i | ||||
\(359\) | 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 | ||||||
\(362\) | −0.842282 | − | 3.17364i | −0.0442693 | − | 0.166803i | ||||
\(363\) | 7.67861 | + | 7.67861i | 0.403023 | + | 0.403023i | ||||
\(364\) | −3.34017 | + | 12.2324i | −0.175073 | + | 0.641152i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.66717 | + | 8.03950i | −0.243957 | + | 0.420232i | ||||
\(367\) | 13.7431 | 0.717386 | 0.358693 | − | 0.933456i | \(-0.383223\pi\) | ||||
0.358693 | + | 0.933456i | \(0.383223\pi\) | |||||||
\(368\) | 6.69370 | + | 3.95008i | 0.348933 | + | 0.205912i | ||||
\(369\) | 6.26498 | 0.326142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.46773 | − | 5.46773i | 0.283871 | − | 0.283871i | ||||
\(372\) | −12.7778 | − | 3.48910i | −0.662499 | − | 0.180902i | ||||
\(373\) | −18.4703 | − | 18.4703i | −0.956355 | − | 0.956355i | 0.0427313 | − | 0.999087i | \(-0.486394\pi\) |
−0.999087 | + | 0.0427313i | \(0.986394\pi\) | |||||||
\(374\) | 0.354054 | + | 1.33405i | 0.0183077 | + | 0.0689819i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.202353 | + | 28.3295i | −0.0104356 | + | 1.46098i | ||||
\(377\) | − | 34.4881i | − | 1.77623i | ||||||
\(378\) | −7.43311 | + | 1.97274i | −0.382318 | + | 0.101467i | ||||
\(379\) | −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 | ||||
\(382\) | −18.7568 | − | 10.8888i | −0.959679 | − | 0.557122i | ||||
\(383\) | −23.1255 | −1.18166 | −0.590830 | − | 0.806796i | \(-0.701200\pi\) | ||||
−0.590830 | + | 0.806796i | \(0.701200\pi\) | |||||||
\(384\) | 16.9429 | − | 4.23850i | 0.864613 | − | 0.216295i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0993983 | + | 0.0577036i | 0.00505924 | + | 0.00293704i | ||||
\(387\) | 1.10474 | − | 1.10474i | 0.0561573 | − | 0.0561573i | ||||
\(388\) | −7.48211 | − | 13.1031i | −0.379846 | − | 0.665209i | ||||
\(389\) | −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 | ||||||
\(392\) | −0.122255 | + | 17.1157i | −0.00617480 | + | 0.864473i | ||||
\(393\) | − | 19.7348i | − | 0.995491i | ||||||
\(394\) | −0.721898 | − | 2.72005i | −0.0363687 | − | 0.137034i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.37048 | − | 0.647283i | −0.119121 | − | 0.0325272i | ||||
\(397\) | 4.00102 | − | 4.00102i | 0.200806 | − | 0.200806i | −0.599540 | − | 0.800345i | \(-0.704650\pi\) |
0.800345 | + | 0.599540i | \(0.204650\pi\) | |||||||
\(398\) | 10.1565 | − | 17.4953i | 0.509101 | − | 0.876960i | ||||
\(399\) | 9.67130 | 0.484171 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.9287 | 1.94401 | 0.972003 | − | 0.234967i | \(-0.0754980\pi\) | ||||
0.972003 | + | 0.234967i | \(0.0754980\pi\) | |||||||
\(402\) | −10.9668 | + | 18.8910i | −0.546973 | + | 0.942197i | ||||
\(403\) | −19.7486 | + | 19.7486i | −0.983746 | + | 0.983746i | ||||
\(404\) | 1.94112 | − | 7.10879i | 0.0965745 | − | 0.353676i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.87179 | + | 7.05275i | 0.0928955 | + | 0.350022i | ||||
\(407\) | 12.8227i | 0.635598i | ||||||||
\(408\) | −1.50230 | − | 1.52392i | −0.0743750 | − | 0.0754452i | ||||
\(409\) | 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 | ||||
\(412\) | 23.9932 | − | 13.7005i | 1.18206 | − | 0.674977i | ||||
\(413\) | 8.22174 | − | 8.22174i | 0.404565 | − | 0.404565i | ||||
\(414\) | 1.46626 | + | 0.851208i | 0.0720628 | + | 0.0418346i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.95386 | − | 35.4546i | 0.488028 | − | 1.73830i | ||||
\(417\) | 0.757161 | 0.0370783 | ||||||||
\(418\) | 15.6672 | + | 9.09525i | 0.766306 | + | 0.444863i | ||||
\(419\) | 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 | \(0.571704\pi\) | |||||||
\(422\) | 16.8200 | − | 4.46401i | 0.818786 | − | 0.217305i | ||||
\(423\) | 6.17987i | 0.300476i | ||||||||
\(424\) | −15.9921 | + | 15.7653i | −0.776647 | + | 0.765631i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.502829 | − | 1.89462i | −0.0243622 | − | 0.0917945i | ||||
\(427\) | −2.93244 | − | 2.93244i | −0.141911 | − | 0.141911i | ||||
\(428\) | 7.36949 | − | 26.9886i | 0.356218 | − | 1.30454i | ||||
\(429\) | 14.1504 | − | 14.1504i | 0.683186 | − | 0.683186i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2234 | 0.974126 | 0.487063 | − | 0.873367i | \(-0.338068\pi\) | ||||
0.487063 | + | 0.873367i | \(0.338068\pi\) | |||||||
\(432\) | 21.6272 | − | 5.57480i | 1.04054 | − | 0.268218i | ||||
\(433\) | −0.676118 | −0.0324922 | −0.0162461 | − | 0.999868i | \(-0.505172\pi\) | ||||
−0.0162461 | + | 0.999868i | \(0.505172\pi\) | |||||||
\(434\) | 2.96671 | − | 5.11036i | 0.142407 | − | 0.245305i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.5019 | − | 8.60189i | −1.50867 | − | 0.411956i | ||||
\(437\) | −8.83834 | − | 8.83834i | −0.422795 | − | 0.422795i | ||||
\(438\) | 5.44082 | + | 20.5005i | 0.259972 | + | 0.979553i | ||||
\(439\) | 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 | ||||||||
\(442\) | −4.36108 | + | 1.15743i | −0.207436 | + | 0.0550532i | ||||
\(443\) | −28.1262 | − | 28.1262i | −1.33631 | − | 1.33631i | −0.899600 | − | 0.436714i | \(-0.856142\pi\) |
−0.436714 | − | 0.899600i | \(-0.643858\pi\) | |||||||
\(444\) | −9.85811 | − | 17.2641i | −0.467845 | − | 0.819317i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.51655 | − | 5.52464i | −0.450622 | − | 0.261599i | ||||
\(447\) | −9.38805 | −0.444039 | ||||||||
\(448\) | −0.111300 | + | 7.79061i | −0.00525843 | + | 0.368072i | ||||
\(449\) | −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 | ||||
\(452\) | 17.0635 | + | 29.8827i | 0.802602 | + | 1.40556i | ||||
\(453\) | −2.20607 | − | 2.20607i | −0.103650 | − | 0.103650i | ||||
\(454\) | −4.16469 | + | 1.10530i | −0.195458 | + | 0.0518745i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.0862 | − | 0.200615i | −1.31526 | − | 0.00939468i | ||||
\(457\) | 5.66561i | 0.265026i | 0.991181 | + | 0.132513i | \(0.0423046\pi\) | ||||
−0.991181 | + | 0.132513i | \(0.957695\pi\) | |||||||
\(458\) | −3.91891 | − | 14.7661i | −0.183119 | − | 0.689975i | ||||
\(459\) | −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 | \(0.0654168\pi\) | |||||||
\(462\) | −2.12573 | + | 3.66171i | −0.0988979 | + | 0.170358i | ||||
\(463\) | 41.6835 | 1.93720 | 0.968598 | − | 0.248631i | \(-0.0799808\pi\) | ||||
0.968598 | + | 0.248631i | \(0.0799808\pi\) | |||||||
\(464\) | −5.28953 | − | 20.5206i | −0.245560 | − | 0.952643i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.33583 | + | 9.19132i | −0.247178 | + | 0.425780i | ||||
\(467\) | −3.11020 | + | 3.11020i | −0.143923 | + | 0.143923i | −0.775397 | − | 0.631474i | \(-0.782450\pi\) |
0.631474 | + | 0.775397i | \(0.282450\pi\) | |||||||
\(468\) | 2.11601 | − | 7.74926i | 0.0978126 | − | 0.358210i | ||||
\(469\) | −6.89057 | − | 6.89057i | −0.318177 | − | 0.318177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.40370i | − | 0.295067i | ||||||
\(472\) | −24.0471 | + | 23.7060i | −1.10686 | + | 1.09116i | ||||
\(473\) | − | 5.04255i | − | 0.231857i | ||||||
\(474\) | 31.1989 | − | 8.28016i | 1.43301 | − | 0.380320i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.829015 | − | 0.473383i | 0.0379978 | − | 0.0216975i | ||||
\(477\) | −3.46383 | + | 3.46383i | −0.158598 | + | 0.158598i | ||||
\(478\) | 25.1675 | + | 14.6105i | 1.15114 | + | 0.668268i | ||||
\(479\) | −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 | ||||||||
\(482\) | −28.4868 | − | 16.5374i | −1.29754 | − | 0.753257i | ||||
\(483\) | 2.06569 | − | 2.06569i | 0.0939920 | − | 0.0939920i | ||||
\(484\) | 12.2175 | − | 6.97642i | 0.555341 | − | 0.317110i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.61455 | − | 2.28629i | 0.390764 | − | 0.103708i | ||||
\(487\) | − | 7.29577i | − | 0.330603i | −0.986243 | − | 0.165301i | \(-0.947140\pi\) | ||
0.986243 | − | 0.165301i | \(-0.0528597\pi\) | |||||||
\(488\) | 8.45521 | + | 8.57687i | 0.382750 | + | 0.388257i | ||||
\(489\) | 12.5463i | 0.567365i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.57528 | + | 3.57528i | 0.161350 | + | 0.161350i | 0.783165 | − | 0.621815i | \(-0.213604\pi\) |
−0.621815 | + | 0.783165i | \(0.713604\pi\) | |||||||
\(492\) | −8.25810 | + | 30.2429i | −0.372304 | + | 1.36345i | ||||
\(493\) | −1.83600 | + | 1.83600i | −0.0826891 | + | 0.0826891i | ||||
\(494\) | −29.7330 | + | 51.2170i | −1.33775 | + | 2.30436i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.72157 | + | 14.7793i | −0.391610 | + | 0.663612i | ||||
\(497\) | 0.874479 | 0.0392257 | ||||||||
\(498\) | −1.26330 | + | 2.17612i | −0.0566099 | + | 0.0975143i | ||||
\(499\) | −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 | ||||
\(502\) | −1.71472 | − | 6.46093i | −0.0765318 | − | 0.288365i | ||||
\(503\) | 29.3781i | 1.30991i | 0.755670 | + | 0.654953i | \(0.227312\pi\) | ||||
−0.755670 | + | 0.654953i | \(0.772688\pi\) | |||||||
\(504\) | −0.0121396 | + | 1.69955i | −0.000540742 | + | 0.0757040i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.28899 | − | 1.40369i | 0.235124 | − | 0.0624017i | ||||
\(507\) | 32.0682 | + | 32.0682i | 1.42420 | + | 1.42420i | ||||
\(508\) | −1.36471 | − | 2.38996i | −0.0605493 | − | 0.106037i | ||||
\(509\) | 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 | ||||||||
\(512\) | 0.484827 | − | 22.6222i | 0.0214265 | − | 0.999770i | ||||
\(513\) | −35.9175 | −1.58579 | ||||||||
\(514\) | 27.4621 | + | 15.9426i | 1.21130 | + | 0.703197i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.87671 | + | 6.78912i | 0.170663 | + | 0.298874i | ||||
\(517\) | 14.1039 | + | 14.1039i | 0.620287 | + | 0.620287i | ||||
\(518\) | 8.57221 | − | 2.27505i | 0.376641 | − | 0.0999602i | ||||
\(519\) | 1.19138i | 0.0522959i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.48578i | 0.415580i | 0.978174 | + | 0.207790i | \(0.0666270\pi\) | ||||
−0.978174 | + | 0.207790i | \(0.933373\pi\) | |||||||
\(522\) | −1.18579 | − | 4.46794i | −0.0519005 | − | 0.195556i | ||||
\(523\) | −16.2705 | − | 16.2705i | −0.711460 | − | 0.711460i | 0.255380 | − | 0.966841i | \(-0.417799\pi\) |
−0.966841 | + | 0.255380i | \(0.917799\pi\) | |||||||
\(524\) | −24.6652 | − | 6.73507i | −1.07750 | − | 0.294223i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.84823 | + | 10.0740i | −0.254995 | + | 0.439246i | ||||
\(527\) | 2.10265 | 0.0915929 | ||||||||
\(528\) | 6.24924 | − | 10.5898i | 0.271963 | − | 0.460862i | ||||
\(529\) | 19.2245 | 0.835846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.20849 | + | 5.20849i | −0.226029 | + | 0.226029i | ||||
\(532\) | 3.30060 | − | 12.0875i | 0.143099 | − | 0.524059i | ||||
\(533\) | 46.7414 | + | 46.7414i | 2.02459 | + | 2.02459i | ||||
\(534\) | −0.629474 | − | 2.37180i | −0.0272400 | − | 0.102638i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 19.8678 | + | 20.1537i | 0.858158 | + | 0.870506i | ||||
\(537\) | − | 7.81028i | − | 0.337039i | ||||||
\(538\) | −33.4345 | + | 8.87348i | −1.44146 | + | 0.382563i | ||||
\(539\) | 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 | \(0.274767\pi\) | |||||||
\(542\) | −15.2580 | − | 8.85774i | −0.655389 | − | 0.380472i | ||||
\(543\) | 3.58416 | 0.153811 | ||||||||
\(544\) | −2.41734 | + | 1.35754i | −0.103643 | + | 0.0582042i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.9704 | − | 6.94915i | −0.512285 | − | 0.297396i | ||||
\(547\) | 21.9660 | − | 21.9660i | 0.939197 | − | 0.939197i | −0.0590579 | − | 0.998255i | \(-0.518810\pi\) |
0.998255 | + | 0.0590579i | \(0.0188097\pi\) | |||||||
\(548\) | −26.5826 | + | 15.1792i | −1.13555 | + | 0.648422i | ||||
\(549\) | 1.85771 | + | 1.85771i | 0.0792852 | + | 0.0792852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.0796i | 1.45184i | ||||||||
\(552\) | −6.04176 | + | 5.95606i | −0.257154 | + | 0.253507i | ||||
\(553\) | 14.4002i | 0.612357i | ||||||||
\(554\) | −5.26290 | − | 19.8301i | −0.223599 | − | 0.842502i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.258402 | − | 0.946322i | 0.0109587 | − | 0.0401330i | ||||
\(557\) | −17.5409 | + | 17.5409i | −0.743234 | + | 0.743234i | −0.973199 | − | 0.229965i | \(-0.926139\pi\) |
0.229965 | + | 0.973199i | \(0.426139\pi\) | |||||||
\(558\) | −1.87942 | + | 3.23743i | −0.0795623 | + | 0.137051i | ||||
\(559\) | 16.4844 | 0.697217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.50661 | −0.0636089 | ||||||||
\(562\) | −15.1991 | + | 26.1815i | −0.641136 | + | 1.10440i | ||||
\(563\) | −27.5975 | + | 27.5975i | −1.16309 | + | 1.16309i | −0.179300 | + | 0.983794i | \(0.557383\pi\) |
−0.983794 | + | 0.179300i | \(0.942617\pi\) | |||||||
\(564\) | −29.8320 | − | 8.14592i | −1.25615 | − | 0.343005i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.79460 | + | 14.2977i | 0.159499 | + | 0.600979i | ||||
\(567\) | − | 6.59190i | − | 0.276834i | ||||||
\(568\) | −2.53955 | − | 0.0181396i | −0.106557 | − | 0.000761123i | ||||
\(569\) | 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 | 0.0860105 | − | 0.996294i | \(-0.472588\pi\) |
−0.996294 | + | 0.0860105i | \(0.972588\pi\) | |||||||
\(572\) | −12.8564 | − | 22.5148i | −0.537551 | − | 0.941390i | ||||
\(573\) | 16.7401 | − | 16.7401i | 0.699329 | − | 0.699329i | ||||
\(574\) | −12.0953 | − | 7.02169i | −0.504850 | − | 0.293080i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0705089 | − | 4.93537i | 0.00293787 | − | 0.205641i | ||||
\(577\) | 3.69585 | 0.153860 | 0.0769302 | − | 0.997036i | \(-0.475488\pi\) | ||||
0.0769302 | + | 0.997036i | \(0.475488\pi\) | |||||||
\(578\) | −20.4982 | − | 11.8998i | −0.852613 | − | 0.494967i | ||||
\(579\) | −0.0887116 | + | 0.0887116i | −0.00368673 | + | 0.00368673i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.793750 | − | 0.793750i | −0.0329303 | − | 0.0329303i | ||||
\(582\) | 15.9193 | − | 4.22496i | 0.659876 | − | 0.175130i | ||||
\(583\) | 15.8105i | 0.654802i | ||||||||
\(584\) | 27.4790 | + | 0.196278i | 1.13709 | + | 0.00812206i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.285622 | + | 1.07620i | 0.0117989 | + | 0.0444573i | ||||
\(587\) | −27.0313 | − | 27.0313i | −1.11570 | − | 1.11570i | −0.992365 | − | 0.123335i | \(-0.960641\pi\) |
−0.123335 | − | 0.992365i | \(-0.539359\pi\) | |||||||
\(588\) | −18.0235 | − | 4.92148i | −0.743276 | − | 0.202958i | ||||
\(589\) | 19.5146 | − | 19.5146i | 0.804085 | − | 0.804085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.07189 | 0.126361 | ||||||||
\(592\) | −24.9415 | + | 6.42912i | −1.02509 | + | 0.264235i | ||||
\(593\) | 4.55524 | 0.187061 | 0.0935306 | − | 0.995616i | \(-0.470185\pi\) | ||||
0.0935306 | + | 0.995616i | \(0.470185\pi\) | |||||||
\(594\) | 7.89458 | − | 13.5989i | 0.323919 | − | 0.557971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.20393 | + | 11.7335i | −0.131238 | + | 0.480621i | ||||
\(597\) | 15.6143 | + | 15.6143i | 0.639051 | + | 0.639051i | ||||
\(598\) | 4.58876 | + | 17.2900i | 0.187648 | + | 0.707043i | ||||
\(599\) | 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 | \(-0.0804717\pi\) | |||||||
\(602\) | −3.37103 | + | 0.894668i | −0.137393 | + | 0.0364639i | ||||
\(603\) | 4.36519 | + | 4.36519i | 0.177764 | + | 0.177764i | ||||
\(604\) | −3.51009 | + | 2.00433i | −0.142824 | + | 0.0815550i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.95652 | + | 4.03846i | 0.282589 | + | 0.164051i | ||||
\(607\) | −5.23884 | −0.212638 | −0.106319 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106319 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(608\) | −9.83593 | + | 35.0345i | −0.398900 | + | 1.42084i | ||||
\(609\) | −7.96503 | −0.322759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.1064 | + | 46.1064i | −1.86527 | + | 1.86527i | ||||
\(612\) | −0.525183 | + | 0.299889i | −0.0212293 | + | 0.0121223i | ||||
\(613\) | −20.7209 | − | 20.7209i | −0.836910 | − | 0.836910i | 0.151541 | − | 0.988451i | \(-0.451576\pi\) |
−0.988451 | + | 0.151541i | \(0.951576\pi\) | |||||||
\(614\) | −18.8833 | + | 5.01161i | −0.762068 | + | 0.202252i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.85105 | + | 3.90646i | 0.155163 | + | 0.157396i | ||||
\(617\) | − | 2.20286i | − | 0.0886838i | −0.999016 | − | 0.0443419i | \(-0.985881\pi\) | ||
0.999016 | − | 0.0443419i | \(-0.0141191\pi\) | |||||||
\(618\) | 7.73636 | + | 29.1499i | 0.311202 | + | 1.17258i | ||||
\(619\) | −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 | ||||
\(622\) | 21.7887 | − | 37.5325i | 0.873648 | − | 1.50492i | ||||
\(623\) | 1.09473 | 0.0438594 | ||||||||
\(624\) | 34.6187 | + | 20.4292i | 1.38586 | + | 0.817822i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.21504 | + | 2.09298i | −0.0485627 | + | 0.0836525i | ||||
\(627\) | −13.9827 | + | 13.9827i | −0.558416 | + | 0.558416i | ||||
\(628\) | −8.00353 | − | 2.18544i | −0.319376 | − | 0.0872085i | ||||
\(629\) | 2.23154 | + | 2.23154i | 0.0889775 | + | 0.0889775i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8215i | 0.669655i | 0.942279 | + | 0.334828i | \(0.108678\pi\) | ||||
−0.942279 | + | 0.334828i | \(0.891322\pi\) | |||||||
\(632\) | 0.298708 | − | 41.8192i | 0.0118820 | − | 1.66348i | ||||
\(633\) | 18.9957i | 0.755011i | ||||||||
\(634\) | 19.4042 | − | 5.14986i | 0.770640 | − | 0.204527i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.1551 | − | 21.2867i | −0.481981 | − | 0.844072i | ||||
\(637\) | −27.8559 | + | 27.8559i | −1.10369 | + | 1.10369i | ||||
\(638\) | −12.9031 | − | 7.49061i | −0.510838 | − | 0.296556i | ||||
\(639\) | −0.553985 | −0.0219153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9208 | −0.589336 | −0.294668 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294668 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(642\) | 26.4105 | + | 15.3320i | 1.04234 | + | 0.605108i | ||||
\(643\) | 0.541845 | − | 0.541845i | 0.0213683 | − | 0.0213683i | −0.696342 | − | 0.717710i | \(-0.745190\pi\) |
0.717710 | + | 0.696342i | \(0.245190\pi\) | |||||||
\(644\) | −1.87678 | − | 3.28673i | −0.0739556 | − | 0.129515i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.30942 | − | 1.14371i | 0.169552 | − | 0.0449988i | ||||
\(647\) | − | 32.6391i | − | 1.28318i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) | ||
0.767049 | − | 0.641588i | \(-0.221724\pi\) | |||||||
\(648\) | −0.136738 | + | 19.1434i | −0.00537158 | + | 0.752023i | ||||
\(649\) | 23.7739i | 0.933208i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.56093 | + | 4.56093i | 0.178757 | + | 0.178757i | ||||
\(652\) | 15.6808 | + | 4.28179i | 0.614108 | + | 0.167688i | ||||
\(653\) | −9.73805 | + | 9.73805i | −0.381079 | + | 0.381079i | −0.871491 | − | 0.490412i | \(-0.836846\pi\) |
0.490412 | + | 0.871491i | \(0.336846\pi\) | |||||||
\(654\) | 17.8960 | − | 30.8271i | 0.699790 | − | 1.20544i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.9801 | + | 20.6424i | 1.36574 | + | 0.805952i | ||||
\(657\) | 5.99434 | 0.233862 | ||||||||
\(658\) | 6.92631 | − | 11.9310i | 0.270016 | − | 0.465120i | ||||
\(659\) | 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 | \(0.535710\pi\) | |||||||
\(662\) | 4.05152 | + | 15.2658i | 0.157467 | + | 0.593321i | ||||
\(663\) | − | 4.92519i | − | 0.191279i | ||||||
\(664\) | 2.28865 | + | 2.32158i | 0.0888167 | + | 0.0900946i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.43052 | + | 1.44125i | −0.210428 | + | 0.0558474i | ||||
\(667\) | 7.27903 | + | 7.27903i | 0.281845 | + | 0.281845i | ||||
\(668\) | −11.1424 | + | 6.36254i | −0.431114 | + | 0.246174i | ||||
\(669\) | 8.49339 | − | 8.49339i | 0.328373 | − | 0.328373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.47943 | 0.327345 | ||||||||
\(672\) | −8.18822 | − | 2.29884i | −0.315868 | − | 0.0886798i | ||||
\(673\) | −3.58765 | −0.138294 | −0.0691469 | − | 0.997606i | \(-0.522028\pi\) | ||||
−0.0691469 | + | 0.997606i | \(0.522028\pi\) | |||||||
\(674\) | 4.23273 | + | 2.45722i | 0.163038 | + | 0.0946486i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.0240 | − | 29.1356i | 1.96246 | − | 1.12060i | ||||
\(677\) | −10.1507 | − | 10.1507i | −0.390124 | − | 0.390124i | 0.484608 | − | 0.874731i | \(-0.338962\pi\) |
−0.874731 | + | 0.484608i | \(0.838962\pi\) | |||||||
\(678\) | −36.3052 | + | 9.63537i | −1.39429 | + | 0.370044i | ||||
\(679\) | 7.34770i | 0.281979i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.70339i | − | 0.180234i | ||||||
\(682\) | 3.09928 | + | 11.6778i | 0.118677 | + | 0.447166i | ||||
\(683\) | −16.6805 | − | 16.6805i | −0.638260 | − | 0.638260i | 0.311866 | − | 0.950126i | \(-0.399046\pi\) |
−0.950126 | + | 0.311866i | \(0.899046\pi\) | |||||||
\(684\) | −2.09094 | + | 7.65745i | −0.0799491 | + | 0.292790i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.02519 | − | 15.5465i | 0.344583 | − | 0.593568i | ||||
\(687\) | 16.6761 | 0.636234 | ||||||||
\(688\) | 9.80828 | − | 2.52826i | 0.373937 | − | 0.0963889i | ||||
\(689\) | −51.6854 | −1.96906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4781 | − | 12.4781i | 0.474689 | − | 0.474689i | −0.428739 | − | 0.903428i | \(-0.641042\pi\) |
0.903428 | + | 0.428739i | \(0.141042\pi\) | |||||||
\(692\) | 1.48903 | + | 0.406593i | 0.0566043 | + | 0.0154563i | ||||
\(693\) | 0.846123 | + | 0.846123i | 0.0321415 | + | 0.0321415i | ||||
\(694\) | 8.95951 | + | 33.7586i | 0.340098 | + | 1.28146i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 23.1311 | + | 0.165222i | 0.876781 | + | 0.00626271i | ||||
\(697\) | − | 4.97661i | − | 0.188502i | ||||||
\(698\) | 46.8113 | − | 12.4237i | 1.77183 | − | 0.470243i | ||||
\(699\) | −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 | \(0.195243\pi\) | |||||||
\(702\) | 44.4558 | + | 25.8079i | 1.67788 | + | 0.974057i | ||||
\(703\) | 41.4217 | 1.56225 | ||||||||
\(704\) | −11.1027 | − | 11.4246i | −0.418449 | − | 0.430579i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.0901 | + | 7.59918i | 0.492652 | + | 0.285999i | ||||
\(707\) | −2.53742 | + | 2.53742i | −0.0954295 | + | 0.0954295i | ||||
\(708\) | −18.2774 | − | 32.0084i | −0.686907 | − | 1.20295i | ||||
\(709\) | 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 | ||||||
\(712\) | −3.17918 | − | 0.0227084i | −0.119145 | − | 0.000851033i | ||||
\(713\) | − | 8.33621i | − | 0.312194i | ||||||
\(714\) | 0.267308 | + | 1.00719i | 0.0100037 | + | 0.0376932i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.76152 | − | 2.66548i | −0.364805 | − | 0.0996135i | ||||
\(717\) | −22.4617 | + | 22.4617i | −0.838847 | + | 0.838847i | ||||
\(718\) | −16.7842 | + | 28.9119i | −0.626380 | + | 1.07898i | ||||
\(719\) | 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 | ||||||||
\(722\) | 15.8903 | − | 27.3721i | 0.591376 | − | 1.01868i | ||||
\(723\) | 25.4240 | − | 25.4240i | 0.945530 | − | 0.945530i | ||||
\(724\) | 1.22319 | − | 4.47959i | 0.0454596 | − | 0.166483i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.93941 | + | 14.8434i | 0.146205 | + | 0.550889i | ||||
\(727\) | 17.4640i | 0.647703i | 0.946108 | + | 0.323852i | \(0.104978\pi\) | ||||
−0.946108 | + | 0.323852i | \(0.895022\pi\) | |||||||
\(728\) | −12.7705 | + | 12.5893i | −0.473306 | + | 0.466592i | ||||
\(729\) | 30.0340i | 1.11237i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.877557 | − | 0.877557i | −0.0324576 | − | 0.0324576i | ||||
\(732\) | −11.4164 | + | 6.51899i | −0.421963 | + | 0.240949i | ||||
\(733\) | −7.89695 | + | 7.89695i | −0.291680 | + | 0.291680i | −0.837744 | − | 0.546063i | \(-0.816126\pi\) |
0.546063 | + | 0.837744i | \(0.316126\pi\) | |||||||
\(734\) | 16.8086 | + | 9.75791i | 0.620419 | + | 0.360171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.38214 | + | 9.58384i | 0.198388 | + | 0.353265i | ||||
\(737\) | 19.9247 | 0.733936 | ||||||||
\(738\) | 7.66243 | + | 4.44826i | 0.282058 | + | 0.163743i | ||||
\(739\) | 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 | ||||
\(742\) | 10.5696 | − | 2.80515i | 0.388021 | − | 0.102980i | ||||
\(743\) | − | 49.7660i | − | 1.82574i | −0.408254 | − | 0.912868i | \(-0.633862\pi\) | ||
0.408254 | − | 0.912868i | \(-0.366138\pi\) | |||||||
\(744\) | −13.1507 | − | 13.3399i | −0.482127 | − | 0.489064i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.47594 | − | 35.7045i | −0.346939 | − | 1.30724i | ||||
\(747\) | 0.502843 | + | 0.502843i | 0.0183981 | + | 0.0183981i | ||||
\(748\) | −0.514171 | + | 1.88300i | −0.0188000 | + | 0.0688493i | ||||
\(749\) | −9.63333 | + | 9.63333i | −0.351994 | + | 0.351994i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2379 | −0.884454 | −0.442227 | − | 0.896903i | \(-0.645811\pi\) | ||||
−0.442227 | + | 0.896903i | \(0.645811\pi\) | |||||||
\(752\) | −20.3620 | + | 34.5049i | −0.742527 | + | 1.25827i | ||||
\(753\) | 7.29665 | 0.265905 | ||||||||
\(754\) | 24.4873 | − | 42.1810i | 0.891775 | − | 1.53614i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.4918 | − | 2.86489i | −0.381583 | − | 0.104195i | ||||
\(757\) | 15.4872 | + | 15.4872i | 0.562890 | + | 0.562890i | 0.930127 | − | 0.367237i | \(-0.119696\pi\) |
−0.367237 | + | 0.930127i | \(0.619696\pi\) | |||||||
\(758\) | −8.26131 | − | 31.1279i | −0.300064 | − | 1.13062i | ||||
\(759\) | 5.97312i | 0.216811i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9821i | 0.941849i | 0.882174 | + | 0.470924i | \(0.156080\pi\) | ||||
−0.882174 | + | 0.470924i | \(0.843920\pi\) | |||||||
\(762\) | 2.90363 | − | 0.770619i | 0.105187 | − | 0.0279166i | ||||
\(763\) | 11.2443 | + | 11.2443i | 0.407072 | + | 0.407072i | ||||
\(764\) | −15.2093 | − | 26.6354i | −0.550253 | − | 0.963634i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.2839 | − | 16.4196i | −1.02194 | − | 0.593265i | ||||
\(767\) | −77.7185 | −2.80625 | ||||||||
\(768\) | 23.7315 | + | 6.84587i | 0.856338 | + | 0.247029i | ||||
\(769\) | −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 | ||||
\(772\) | 0.0805991 | + | 0.141150i | 0.00290082 | + | 0.00508009i | ||||
\(773\) | 1.32495 | + | 1.32495i | 0.0476550 | + | 0.0476550i | 0.730533 | − | 0.682878i | \(-0.239272\pi\) |
−0.682878 | + | 0.730533i | \(0.739272\pi\) | |||||||
\(774\) | 2.13556 | − | 0.566775i | 0.0767610 | − | 0.0203723i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.152416 | − | 21.3383i | 0.00547142 | − | 0.766000i | ||||
\(777\) | 9.68103i | 0.347305i | ||||||||
\(778\) | −9.95518 | − | 37.5102i | −0.356910 | − | 1.34481i | ||||
\(779\) | −46.1876 | − | 46.1876i | −1.65484 | − | 1.65484i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26432 | + | 1.26432i | −0.0452409 | + | 0.0452409i | ||||
\(782\) | 0.676160 | − | 1.16473i | 0.0241794 | − | 0.0416507i | ||||
\(783\) | 29.5807 | 1.05713 | ||||||||
\(784\) | −12.3020 | + | 20.8467i | −0.439358 | + | 0.744525i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.0121 | − | 24.1369i | 0.499797 | − | 0.860933i | ||||
\(787\) | −0.647036 | + | 0.647036i | −0.0230644 | + | 0.0230644i | −0.718545 | − | 0.695481i | \(-0.755192\pi\) |
0.695481 | + | 0.718545i | \(0.255192\pi\) | |||||||
\(788\) | 1.04837 | − | 3.83934i | 0.0373466 | − | 0.136771i | ||||
\(789\) | −8.99087 | − | 8.99087i | −0.320084 | − | 0.320084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.7570i | − | 0.595811i | ||||||
\(792\) | −2.43965 | − | 2.47476i | −0.0866893 | − | 0.0879366i | ||||
\(793\) | 27.7198i | 0.984360i | ||||||||
\(794\) | 7.73429 | − | 2.05267i | 0.274480 | − | 0.0728466i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.8440 | − | 14.1864i | 0.880574 | − | 0.502824i | ||||
\(797\) | −18.3024 | + | 18.3024i | −0.648303 | + | 0.648303i | −0.952583 | − | 0.304280i | \(-0.901584\pi\) |
0.304280 | + | 0.952583i | \(0.401584\pi\) | |||||||
\(798\) | 11.8286 | + | 6.86682i | 0.418727 | + | 0.243083i | ||||
\(799\) | 4.90900 | 0.173668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.693514 | −0.0245041 | ||||||||
\(802\) | 47.6121 | + | 27.6402i | 1.68124 | + | 0.976009i | ||||
\(803\) | 13.6804 | − | 13.6804i | 0.482772 | − | 0.482772i | ||||
\(804\) | −26.8260 | + | 15.3181i | −0.946079 | + | 0.540229i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −38.1755 | + | 10.1317i | −1.34468 | + | 0.356875i | ||||
\(807\) | − | 37.7593i | − | 1.32919i | ||||||
\(808\) | 7.42150 | − | 7.31623i | 0.261087 | − | 0.257384i | ||||
\(809\) | 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 | 0.829134 | − | 0.559049i | \(-0.188834\pi\) |
−0.559049 | + | 0.829134i | \(0.688834\pi\) | |||||||
\(812\) | −2.71829 | + | 9.95494i | −0.0953933 | + | 0.349350i | ||||
\(813\) | 13.6176 | − | 13.6176i | 0.477590 | − | 0.477590i | ||||
\(814\) | −9.10440 | + | 15.6829i | −0.319109 | + | 0.549686i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.755389 | − | 2.93051i | −0.0264439 | − | 0.102588i | ||||
\(817\) | −16.2891 | −0.569884 | ||||||||
\(818\) | −3.26499 | + | 5.62417i | −0.114158 | + | 0.196644i | ||||
\(819\) | −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 | \(0.834082\pi\) | |||||||
\(822\) | −8.57130 | − | 32.2959i | −0.298958 | − | 1.12645i | ||||
\(823\) | 4.85817i | 0.169345i | 0.996409 | + | 0.0846726i | \(0.0269844\pi\) | ||||
−0.996409 | + | 0.0846726i | \(0.973016\pi\) | |||||||
\(824\) | 39.0727 | + | 0.279090i | 1.36116 | + | 0.00972257i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.8933 | − | 4.21806i | 0.552997 | − | 0.146765i | ||||
\(827\) | −8.02757 | − | 8.02757i | −0.279146 | − | 0.279146i | 0.553622 | − | 0.832768i | \(-0.313245\pi\) |
−0.832768 | + | 0.553622i | \(0.813245\pi\) | |||||||
\(828\) | 1.18895 | + | 2.08215i | 0.0413188 | + | 0.0723598i | ||||
\(829\) | −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 | ||||||||
\(832\) | 37.3476 | − | 36.2955i | 1.29480 | − | 1.25832i | ||||
\(833\) | 2.96585 | 0.102761 | ||||||||
\(834\) | 0.926051 | + | 0.537600i | 0.0320665 | + | 0.0186156i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.7040 | + | 22.2480i | 0.439378 | + | 0.769464i | ||||
\(837\) | −16.9385 | − | 16.9385i | −0.585479 | − | 0.585479i | ||||
\(838\) | 32.2388 | − | 8.55615i | 1.11367 | − | 0.295567i | ||||
\(839\) | − | 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 | ||||||||
\(842\) | 7.90942 | + | 29.8020i | 0.272577 | + | 1.02704i | ||||
\(843\) | −23.3666 | − | 23.3666i | −0.804789 | − | 0.804789i | ||||
\(844\) | 23.7414 | + | 6.48281i | 0.817213 | + | 0.223148i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.38784 | + | 7.55834i | −0.150857 | + | 0.259861i | ||||
\(847\) | −6.85110 | −0.235407 | ||||||||
\(848\) | −30.7530 | + | 7.92712i | −1.05606 | + | 0.272219i | ||||
\(849\) | −16.1472 | −0.554169 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.84723 | − | 8.84723i | 0.303279 | − | 0.303279i | ||||
\(852\) | 0.730228 | − | 2.67425i | 0.0250172 | − | 0.0916181i | ||||
\(853\) | −18.0611 | − | 18.0611i | −0.618401 | − | 0.618401i | 0.326720 | − | 0.945121i | \(-0.394057\pi\) |
−0.945121 | + | 0.326720i | \(0.894057\pi\) | |||||||
\(854\) | −1.50445 | − | 5.66865i | −0.0514813 | − | 0.193977i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.1758 | − | 27.7761i | 0.963028 | − | 0.949368i | ||||
\(857\) | 35.8346i | 1.22409i | 0.790825 | + | 0.612043i | \(0.209652\pi\) | ||||
−0.790825 | + | 0.612043i | \(0.790348\pi\) | |||||||
\(858\) | 27.3538 | − | 7.25967i | 0.933843 | − | 0.247841i | ||||
\(859\) | −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 | ||||
\(862\) | 24.7344 | + | 14.3590i | 0.842456 | + | 0.489070i | ||||
\(863\) | −18.8270 | −0.640878 | −0.320439 | − | 0.947269i | \(-0.603830\pi\) | ||||
−0.320439 | + | 0.947269i | \(0.603830\pi\) | |||||||
\(864\) | 30.4096 | + | 8.53749i | 1.03456 | + | 0.290451i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.826931 | − | 0.480058i | −0.0281003 | − | 0.0163130i | ||||
\(867\) | 18.2944 | − | 18.2944i | 0.621309 | − | 0.621309i | ||||
\(868\) | 7.25693 | − | 4.14384i | 0.246316 | − | 0.140651i | ||||
\(869\) | −20.8197 | − | 20.8197i | −0.706260 | − | 0.706260i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.1352i | 2.20702i | ||||||||
\(872\) | −32.4211 | − | 32.8876i | −1.09792 | − | 1.11372i | ||||
\(873\) | − | 4.65479i | − | 0.157541i | ||||||
\(874\) | −4.53439 | − | 17.0852i | −0.153378 | − | 0.577916i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.90137 | + | 28.9364i | −0.266962 | + | 0.977672i | ||||
\(877\) | 7.77833 | − | 7.77833i | 0.262656 | − | 0.262656i | −0.563476 | − | 0.826132i | \(-0.690536\pi\) |
0.826132 | + | 0.563476i | \(0.190536\pi\) | |||||||
\(878\) | −9.48233 | + | 16.3339i | −0.320013 | + | 0.551244i | ||||
\(879\) | −1.21541 | −0.0409946 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6551 | 0.460052 | 0.230026 | − | 0.973184i | \(-0.426119\pi\) | ||||
0.230026 | + | 0.973184i | \(0.426119\pi\) | |||||||
\(882\) | −2.65098 | + | 4.56649i | −0.0892631 | + | 0.153762i | ||||
\(883\) | 25.7585 | − | 25.7585i | 0.866844 | − | 0.866844i | −0.125278 | − | 0.992122i | \(-0.539982\pi\) |
0.992122 | + | 0.125278i | \(0.0399823\pi\) | |||||||
\(884\) | −6.15565 | − | 1.68086i | −0.207037 | − | 0.0565334i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.4298 | − | 54.3701i | −0.484777 | − | 1.82660i | ||||
\(887\) | − | 38.8982i | − | 1.30607i | −0.757326 | − | 0.653037i | \(-0.773495\pi\) | ||
0.757326 | − | 0.653037i | \(-0.226505\pi\) | |||||||
\(888\) | 0.200817 | − | 28.1144i | 0.00673898 | − | 0.943459i | ||||
\(889\) | 1.34020i | 0.0449488i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.53054 | + | 9.53054i | 0.319285 | + | 0.319285i | ||||
\(892\) | −7.71669 | − | 13.5139i | −0.258374 | − | 0.452479i | ||||
\(893\) | 45.5602 | − | 45.5602i | 1.52461 | − | 1.52461i | ||||
\(894\) | −11.4821 | − | 6.66571i | −0.384020 | − | 0.222935i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.66762 | + | 9.44934i | −0.189342 | + | 0.315680i | ||||
\(897\) | −19.5265 | −0.651972 | ||||||||
\(898\) | −10.2489 | − | 5.94978i | −0.342010 | − | 0.198547i | ||||
\(899\) | −16.0717 | + | 16.0717i | −0.536022 | + | 0.536022i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.75150 | + | 2.75150i | 0.0916658 | + | 0.0916658i | ||||
\(902\) | 27.6393 | − | 7.33545i | 0.920289 | − | 0.244244i | ||||
\(903\) | − | 3.80707i | − | 0.126692i | ||||||
\(904\) | −0.347597 | + | 48.6637i | −0.0115609 | + | 1.61853i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.13179 | − | 4.26450i | −0.0376014 | − | 0.141679i | ||||
\(907\) | 5.10220 | + | 5.10220i | 0.169416 | + | 0.169416i | 0.786723 | − | 0.617307i | \(-0.211776\pi\) |
−0.617307 | + | 0.786723i | \(0.711776\pi\) | |||||||
\(908\) | −5.87844 | − | 1.60516i | −0.195083 | − | 0.0532692i | ||||
\(909\) | 1.60746 | − | 1.60746i | 0.0533162 | − | 0.0533162i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.7058 | −1.54743 | −0.773716 | − | 0.633533i | \(-0.781604\pi\) | ||||
−0.773716 | + | 0.633533i | \(0.781604\pi\) | |||||||
\(912\) | −34.2086 | − | 20.1871i | −1.13276 | − | 0.668463i | ||||
\(913\) | 2.29520 | 0.0759601 | ||||||||
\(914\) | −4.02270 | + | 6.92937i | −0.133059 | + | 0.229203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.69119 | − | 20.8423i | 0.188042 | − | 0.688650i | ||||
\(917\) | 8.80402 | + | 8.80402i | 0.290734 | + | 0.290734i | ||||
\(918\) | −0.992732 | − | 3.74053i | −0.0327650 | − | 0.123456i | ||||
\(919\) | 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 | ||||||
\(922\) | 32.1617 | − | 8.53567i | 1.05919 | − | 0.281107i | ||||
\(923\) | −4.13314 | − | 4.13314i | −0.136044 | − | 0.136044i | ||||
\(924\) | −5.19978 | + | 2.96917i | −0.171060 | + | 0.0976786i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 50.9813 | + | 29.5961i | 1.67535 | + | 0.972590i | ||||
\(927\) | 8.52342 | 0.279946 | ||||||||
\(928\) | 8.10062 | − | 28.8535i | 0.265916 | − | 0.947163i | ||||
\(929\) | 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 | ||||
\(932\) | −13.0521 | + | 7.45297i | −0.427534 | + | 0.244130i | ||||
\(933\) | 33.4972 | + | 33.4972i | 1.09665 | + | 1.09665i | ||||
\(934\) | −6.01227 | + | 1.59565i | −0.196728 | + | 0.0522113i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.09014 | − | 7.97539i | 0.264434 | − | 0.260684i | ||||
\(937\) | − | 5.26656i | − | 0.172051i | −0.996293 | − | 0.0860255i | \(-0.972583\pi\) | ||
0.996293 | − | 0.0860255i | \(-0.0274166\pi\) | |||||||
\(938\) | −3.53512 | − | 13.3200i | −0.115426 | − | 0.434914i | ||||
\(939\) | −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 | \(0.107507\pi\) | |||||||
\(942\) | 4.54676 | − | 7.83209i | 0.148141 | − | 0.255183i | ||||
\(943\) | −19.7304 | −0.642509 | ||||||||
\(944\) | −46.2428 | + | 11.9199i | −1.50507 | + | 0.387959i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.58031 | − | 6.16733i | 0.116406 | − | 0.200517i | ||||
\(947\) | −3.27572 | + | 3.27572i | −0.106447 | + | 0.106447i | −0.758324 | − | 0.651878i | \(-0.773982\pi\) |
0.651878 | + | 0.758324i | \(0.273982\pi\) | |||||||
\(948\) | 44.0372 | + | 12.0248i | 1.43026 | + | 0.390546i | ||||
\(949\) | 44.7223 | + | 44.7223i | 1.45175 | + | 1.45175i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.9142i | 0.710616i | ||||||||
\(952\) | 1.35004 | + | 0.00964316i | 0.0437552 | + | 0.000312537i | ||||
\(953\) | 30.0292i | 0.972741i | 0.873753 | + | 0.486371i | \(0.161680\pi\) | ||||
−0.873753 | + | 0.486371i | \(0.838320\pi\) | |||||||
\(954\) | −6.69585 | + | 1.77707i | −0.216786 | + | 0.0575348i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.4076 | + | 35.7390i | 0.660029 | + | 1.15588i | ||||
\(957\) | 11.5158 | − | 11.5158i | 0.372253 | − | 0.372253i | ||||
\(958\) | −10.1798 | − | 5.90968i | −0.328895 | − | 0.190933i | ||||
\(959\) | 14.9065 | 0.481356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5941 | −0.406260 | ||||||||
\(962\) | −51.2685 | − | 29.7629i | −1.65296 | − | 0.959593i | ||||
\(963\) | 6.10274 | − | 6.10274i | 0.196658 | − | 0.196658i | ||||
\(964\) | −23.0991 | − | 40.4524i | −0.743970 | − | 1.30288i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.99313 | − | 1.05977i | 0.128477 | − | 0.0340977i | ||||
\(967\) | − | 15.2196i | − | 0.489429i | −0.969595 | − | 0.244715i | \(-0.921306\pi\) | ||
0.969595 | − | 0.244715i | \(-0.0786943\pi\) | |||||||
\(968\) | 19.8961 | + | 0.142115i | 0.639485 | + | 0.00456775i | ||||
\(969\) | 4.86684i | 0.156345i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4838 | − | 18.4838i | −0.593173 | − | 0.593173i | 0.345314 | − | 0.938487i | \(-0.387772\pi\) |
−0.938487 | + | 0.345314i | \(0.887772\pi\) | |||||||
\(972\) | 12.1594 | + | 3.32024i | 0.390013 | + | 0.106497i | ||||
\(973\) | −0.337781 | + | 0.337781i | −0.0108288 | + | 0.0108288i | ||||
\(974\) | 5.18014 | − | 8.92314i | 0.165983 | − | 0.285916i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.25146 | + | 16.4934i | 0.136086 | + | 0.527940i | ||||
\(977\) | 18.7912 | 0.601183 | 0.300592 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300592 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(978\) | −8.90817 | + | 15.3449i | −0.284852 | + | 0.490676i | ||||
\(979\) | −1.58276 | + | 1.58276i | −0.0505851 | + | 0.0505851i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.12331 | − | 7.12331i | −0.227430 | − | 0.227430i | ||||
\(982\) | 1.83425 | + | 6.91129i | 0.0585333 | + | 0.220548i | ||||
\(983\) | 56.5605i | 1.80400i | 0.431738 | + | 0.901999i | \(0.357901\pi\) | ||||
−0.431738 | + | 0.901999i | \(0.642099\pi\) | |||||||
\(984\) | −31.5732 | + | 31.1253i | −1.00652 | + | 0.992240i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.54912 | + | 0.941933i | −0.113027 | + | 0.0299973i | ||||
\(987\) | 10.6483 | + | 10.6483i | 0.338938 | + | 0.338938i | ||||
\(988\) | −72.7303 | + | 41.5303i | −2.31386 | + | 1.32126i | ||||
\(989\) | −3.47918 | + | 3.47918i | −0.110632 | + | 0.110632i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0866 | 1.43222 | 0.716112 | − | 0.697985i | \(-0.245920\pi\) | ||||
0.716112 | + | 0.697985i | \(0.245920\pi\) | |||||||
\(992\) | −21.1606 | + | 11.8835i | −0.671851 | + | 0.377301i | ||||
\(993\) | −17.2404 | −0.547108 | ||||||||
\(994\) | 1.06954 | + | 0.620898i | 0.0339237 | + | 0.0196937i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.09018 | + | 1.76455i | −0.0979162 | + | 0.0559120i | ||||
\(997\) | 35.1508 | + | 35.1508i | 1.11324 | + | 1.11324i | 0.992710 | + | 0.120528i | \(0.0384588\pi\) |
0.120528 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(998\) | −21.0382 | + | 5.58353i | −0.665954 | + | 0.176743i | ||||
\(999\) | − | 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 | 400.2.l.g.101.5 | yes | 12 | |
4.3 | odd | 2 | 1600.2.l.f.1201.5 | 12 | |||
5.2 | odd | 4 | 400.2.q.f.149.2 | 12 | |||
5.3 | odd | 4 | 400.2.q.e.149.5 | 12 | |||
5.4 | even | 2 | 400.2.l.f.101.2 | ✓ | 12 | ||
16.3 | odd | 4 | 1600.2.l.f.401.5 | 12 | |||
16.13 | even | 4 | inner | 400.2.l.g.301.5 | yes | 12 | |
20.3 | even | 4 | 1600.2.q.e.49.5 | 12 | |||
20.7 | even | 4 | 1600.2.q.f.49.2 | 12 | |||
20.19 | odd | 2 | 1600.2.l.g.1201.2 | 12 | |||
80.3 | even | 4 | 1600.2.q.f.849.2 | 12 | |||
80.13 | odd | 4 | 400.2.q.f.349.2 | 12 | |||
80.19 | odd | 4 | 1600.2.l.g.401.2 | 12 | |||
80.29 | even | 4 | 400.2.l.f.301.2 | yes | 12 | ||
80.67 | even | 4 | 1600.2.q.e.849.5 | 12 | |||
80.77 | odd | 4 | 400.2.q.e.349.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.2 | ✓ | 12 | 5.4 | even | 2 | ||
400.2.l.f.301.2 | yes | 12 | 80.29 | even | 4 | ||
400.2.l.g.101.5 | yes | 12 | 1.1 | even | 1 | trivial | |
400.2.l.g.301.5 | yes | 12 | 16.13 | even | 4 | inner | |
400.2.q.e.149.5 | 12 | 5.3 | odd | 4 | |||
400.2.q.e.349.5 | 12 | 80.77 | odd | 4 | |||
400.2.q.f.149.2 | 12 | 5.2 | odd | 4 | |||
400.2.q.f.349.2 | 12 | 80.13 | odd | 4 | |||
1600.2.l.f.401.5 | 12 | 16.3 | odd | 4 | |||
1600.2.l.f.1201.5 | 12 | 4.3 | odd | 2 | |||
1600.2.l.g.401.2 | 12 | 80.19 | odd | 4 | |||
1600.2.l.g.1201.2 | 12 | 20.19 | odd | 2 | |||
1600.2.q.e.49.5 | 12 | 20.3 | even | 4 | |||
1600.2.q.e.849.5 | 12 | 80.67 | even | 4 | |||
1600.2.q.f.49.2 | 12 | 20.7 | even | 4 | |||
1600.2.q.f.849.2 | 12 | 80.3 | even | 4 |