Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(149,400)]
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, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(3.19401608085\) |
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: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
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 | 349.2 | ||
Root | \(1.22306 + 0.710021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.349 |
Dual form | 400.2.q.f.149.2 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.710021 | − | 1.22306i | −0.502061 | − | 0.864832i | ||||
\(3\) | 1.09156 | − | 1.09156i | 0.630214 | − | 0.630214i | −0.317908 | − | 0.948122i | \(-0.602980\pi\) |
0.948122 | + | 0.317908i | \(0.102980\pi\) | |||||||
\(4\) | −0.991741 | + | 1.73679i | −0.495870 | + | 0.868396i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.11008 | − | 0.560012i | −0.861435 | − | 0.228624i | ||||
\(7\) | 0.973926 | 0.368109 | 0.184055 | − | 0.982916i | \(-0.441078\pi\) | ||||
0.184055 | + | 0.982916i | \(0.441078\pi\) | |||||||
\(8\) | 2.82835 | − | 0.0202025i | 0.999974 | − | 0.00714267i | ||||
\(9\) | 0.616985i | 0.205662i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40810 | − | 1.40810i | 0.424558 | − | 0.424558i | −0.462212 | − | 0.886769i | \(-0.652944\pi\) |
0.886769 | + | 0.462212i | \(0.152944\pi\) | |||||||
\(12\) | 0.813270 | + | 2.97836i | 0.234771 | + | 0.859780i | ||||
\(13\) | 4.60317 | − | 4.60317i | 1.27669 | − | 1.27669i | 0.334179 | − | 0.942510i | \(-0.391541\pi\) |
0.942510 | − | 0.334179i | \(-0.108459\pi\) | |||||||
\(14\) | −0.691508 | − | 1.19117i | −0.184813 | − | 0.318353i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.03290 | − | 3.44490i | −0.508225 | − | 0.861224i | ||||
\(17\) | − | 0.490104i | − | 0.118868i | −0.998232 | − | 0.0594338i | \(-0.981070\pi\) | ||
0.998232 | − | 0.0594338i | \(-0.0189295\pi\) | |||||||
\(18\) | 0.754608 | − | 0.438072i | 0.177863 | − | 0.103255i | ||||
\(19\) | −4.54863 | − | 4.54863i | −1.04353 | − | 1.04353i | −0.999009 | − | 0.0445187i | \(-0.985825\pi\) |
−0.0445187 | − | 0.999009i | \(-0.514175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06310 | − | 1.06310i | 0.231988 | − | 0.231988i | ||||
\(22\) | −2.72196 | − | 0.722406i | −0.580325 | − | 0.154018i | ||||
\(23\) | −1.94308 | −0.405160 | −0.202580 | − | 0.979266i | \(-0.564933\pi\) | ||||
−0.202580 | + | 0.979266i | \(0.564933\pi\) | |||||||
\(24\) | 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 | ||||
\(28\) | −0.965882 | + | 1.69151i | −0.182535 | + | 0.319665i | ||||
\(29\) | 3.74613 | + | 3.74613i | 0.695640 | + | 0.695640i | 0.963467 | − | 0.267827i | \(-0.0863057\pi\) |
−0.267827 | + | 0.963467i | \(0.586306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.29021 | 0.770545 | 0.385272 | − | 0.922803i | \(-0.374107\pi\) | ||||
0.385272 | + | 0.922803i | \(0.374107\pi\) | |||||||
\(32\) | −2.76991 | + | 4.93230i | −0.489655 | + | 0.871916i | ||||
\(33\) | − | 3.07405i | − | 0.535124i | ||||||
\(34\) | −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 | 0.225663 | − | 0.974205i | \(-0.427545\pi\) |
−0.974205 | + | 0.225663i | \(0.927545\pi\) | |||||||
\(38\) | −2.33362 | + | 8.79286i | −0.378562 | + | 1.42639i | ||||
\(39\) | − | 10.0493i | − | 1.60917i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1542i | 1.58582i | 0.609341 | + | 0.792908i | \(0.291434\pi\) | ||||
−0.609341 | + | 0.792908i | \(0.708566\pi\) | |||||||
\(42\) | −2.05506 | − | 0.545410i | −0.317102 | − | 0.0841586i | ||||
\(43\) | −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 | ||||
\(47\) | − | 10.0162i | − | 1.46102i | −0.682902 | − | 0.730510i | \(-0.739283\pi\) | ||
0.682902 | − | 0.730510i | \(-0.260717\pi\) | |||||||
\(48\) | −5.97936 | − | 1.54128i | −0.863046 | − | 0.222465i | ||||
\(49\) | −6.05147 | −0.864495 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.534979 | − | 0.534979i | −0.0749120 | − | 0.0749120i | ||||
\(52\) | 3.42960 | + | 12.5599i | 0.475600 | + | 1.74174i | ||||
\(53\) | 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 | ||||
\(57\) | −9.93022 | −1.31529 | ||||||||
\(58\) | 1.92191 | − | 7.24157i | 0.252359 | − | 0.950865i | ||||
\(59\) | −8.44185 | + | 8.44185i | −1.09904 | + | 1.09904i | −0.104512 | + | 0.994524i | \(0.533328\pi\) |
−0.994524 | + | 0.104512i | \(0.966672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01095 | + | 3.01095i | 0.385513 | + | 0.385513i | 0.873084 | − | 0.487571i | \(-0.162117\pi\) |
−0.487571 | + | 0.873084i | \(0.662117\pi\) | |||||||
\(62\) | −3.04614 | − | 5.24718i | −0.386860 | − | 0.666392i | ||||
\(63\) | 0.600897i | 0.0757060i | ||||||||
\(64\) | 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 | \(0.0406908\pi\) | |||||||
\(68\) | 0.851209 | + | 0.486056i | 0.103224 | + | 0.0589430i | ||||
\(69\) | −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 | \(-0.0169676\pi\) | |||||||
\(72\) | 0.0124646 | + | 1.74505i | 0.00146897 | + | 0.205656i | ||||
\(73\) | −9.71555 | −1.13712 | −0.568559 | − | 0.822642i | \(-0.692499\pi\) | ||||
−0.568559 | + | 0.822642i | \(0.692499\pi\) | |||||||
\(74\) | −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 | ||||
\(78\) | −12.2909 | + | 7.13520i | −1.39166 | + | 0.807902i | ||||
\(79\) | 14.7857 | 1.66352 | 0.831760 | − | 0.555135i | \(-0.187334\pi\) | ||||
0.831760 | + | 0.555135i | \(0.187334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.76838 | 0.752042 | ||||||||
\(82\) | 12.4192 | − | 7.20968i | 1.37147 | − | 0.796176i | ||||
\(83\) | −0.815000 | + | 0.815000i | −0.0894579 | + | 0.0894579i | −0.750420 | − | 0.660962i | \(-0.770149\pi\) |
0.660962 | + | 0.750420i | \(0.270149\pi\) | |||||||
\(84\) | 0.792065 | + | 2.90071i | 0.0864214 | + | 0.316493i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.918620 | + | 3.46128i | −0.0990573 | + | 0.373239i | ||||
\(87\) | 8.17827 | 0.876803 | ||||||||
\(88\) | 3.95415 | − | 4.01105i | 0.421514 | − | 0.427579i | ||||
\(89\) | 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 | ||||
\(92\) | 1.92703 | − | 3.37472i | 0.200907 | − | 0.351839i | ||||
\(93\) | 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 | ||||
\(97\) | 7.54442i | 0.766019i | 0.923744 | + | 0.383010i | \(0.125112\pi\) | ||||
−0.923744 | + | 0.383010i | \(0.874888\pi\) | |||||||
\(98\) | 4.29667 | + | 7.40130i | 0.434029 | + | 0.747644i | ||||
\(99\) | 0.868775 | + | 0.868775i | 0.0873152 | + | 0.0873152i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.60535 | + | 2.60535i | −0.259242 | + | 0.259242i | −0.824746 | − | 0.565504i | \(-0.808682\pi\) |
0.565504 | + | 0.824746i | \(0.308682\pi\) | |||||||
\(102\) | −0.274464 | + | 1.03416i | −0.0271760 | + | 0.102397i | ||||
\(103\) | −13.8146 | −1.36120 | −0.680598 | − | 0.732657i | \(-0.738280\pi\) | ||||
−0.680598 | + | 0.732657i | \(0.738280\pi\) | |||||||
\(104\) | 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 | 0.999081 | − | 0.0428589i | \(-0.0136466\pi\) |
−0.0428589 | + | 0.999081i | \(0.513647\pi\) | |||||||
\(108\) | −10.7727 | + | 2.94159i | −1.03660 | + | 0.283054i | ||||
\(109\) | 11.5454 | + | 11.5454i | 1.10584 | + | 1.10584i | 0.993691 | + | 0.112154i | \(0.0357750\pi\) |
0.112154 | + | 0.993691i | \(0.464225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.94021 | −0.943483 | ||||||||
\(112\) | −1.97989 | − | 3.35507i | −0.187082 | − | 0.317025i | ||||
\(113\) | 17.2057i | 1.61857i | 0.587415 | + | 0.809286i | \(0.300146\pi\) | ||||
−0.587415 | + | 0.809286i | \(0.699854\pi\) | |||||||
\(114\) | 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 | ||||
\(118\) | 16.3188 | + | 4.33098i | 1.50226 | + | 0.398699i | ||||
\(119\) | − | 0.477325i | − | 0.0437563i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.03452i | 0.639502i | ||||||||
\(122\) | 1.54473 | − | 5.82041i | 0.139853 | − | 0.526955i | ||||
\(123\) | 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 | ||||
\(127\) | 1.37608i | 0.122107i | 0.998134 | + | 0.0610535i | \(0.0194460\pi\) | ||||
−0.998134 | + | 0.0610535i | \(0.980554\pi\) | |||||||
\(128\) | −5.81936 | − | 9.70232i | −0.514363 | − | 0.857572i | ||||
\(129\) | −3.90900 | −0.344168 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.03973 | − | 9.03973i | −0.789804 | − | 0.789804i | 0.191657 | − | 0.981462i | \(-0.438614\pi\) |
−0.981462 | + | 0.191657i | \(0.938614\pi\) | |||||||
\(132\) | 5.33899 | + | 3.04866i | 0.464700 | + | 0.265352i | ||||
\(133\) | −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 | ||||
\(137\) | −15.3056 | −1.30764 | −0.653822 | − | 0.756649i | \(-0.726835\pi\) | ||||
−0.653822 | + | 0.756649i | \(0.726835\pi\) | |||||||
\(138\) | 4.10004 | + | 1.08815i | 0.349018 | + | 0.0926291i | ||||
\(139\) | 0.346824 | − | 0.346824i | 0.0294173 | − | 0.0294173i | −0.692245 | − | 0.721662i | \(-0.743378\pi\) |
0.721662 | + | 0.692245i | \(0.243378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9334 | − | 10.9334i | −0.920754 | − | 0.920754i | ||||
\(142\) | −1.09817 | + | 0.637521i | −0.0921566 | + | 0.0534996i | ||||
\(143\) | − | 12.9634i | − | 1.08406i | ||||||
\(144\) | 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 | ||||
\(148\) | 12.4236 | − | 3.39237i | 1.02121 | − | 0.278851i | ||||
\(149\) | −4.30028 | + | 4.30028i | −0.352293 | + | 0.352293i | −0.860962 | − | 0.508669i | \(-0.830138\pi\) |
0.508669 | + | 0.860962i | \(0.330138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.02102i | − | 0.164468i | −0.996613 | − | 0.0822341i | \(-0.973794\pi\) | ||
0.996613 | − | 0.0822341i | \(-0.0262055\pi\) | |||||||
\(152\) | −12.9570 | − | 12.7732i | −1.05095 | − | 1.03605i | ||||
\(153\) | 0.302387 | 0.0244465 | ||||||||
\(154\) | −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 | \(0.302935\pi\) | |||||||
\(158\) | −10.4981 | − | 18.0838i | −0.835188 | − | 1.43867i | ||||
\(159\) | 12.2563 | 0.971989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89241 | −0.149143 | ||||||||
\(162\) | −4.80569 | − | 8.27811i | −0.377570 | − | 0.650390i | ||||
\(163\) | −5.74697 | + | 5.74697i | −0.450137 | + | 0.450137i | −0.895400 | − | 0.445263i | \(-0.853110\pi\) |
0.445263 | + | 0.895400i | \(0.353110\pi\) | |||||||
\(164\) | −17.6357 | − | 10.0703i | −1.37712 | − | 0.786360i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.57546 | + | 0.418125i | 0.122279 | + | 0.0324528i | ||||
\(167\) | −6.41553 | −0.496449 | −0.248224 | − | 0.968703i | \(-0.579847\pi\) | ||||
−0.248224 | + | 0.968703i | \(0.579847\pi\) | |||||||
\(168\) | 2.98535 | − | 3.02830i | 0.230325 | − | 0.233639i | ||||
\(169\) | − | 29.3783i | − | 2.25987i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.80644 | − | 2.80644i | 0.214613 | − | 0.214613i | ||||
\(172\) | 4.88558 | − | 1.33405i | 0.372522 | − | 0.101721i | ||||
\(173\) | −0.545724 | + | 0.545724i | −0.0414907 | + | 0.0414907i | −0.727548 | − | 0.686057i | \(-0.759340\pi\) |
0.686057 | + | 0.727548i | \(0.259340\pi\) | |||||||
\(174\) | −5.80674 | − | 10.0025i | −0.440208 | − | 0.758288i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.71328 | − | 1.98823i | −0.581410 | − | 0.149869i | ||||
\(177\) | 18.4296i | 1.38525i | ||||||||
\(178\) | 1.37476 | − | 0.798090i | 0.103043 | − | 0.0598194i | ||||
\(179\) | 3.57757 | + | 3.57757i | 0.267400 | + | 0.267400i | 0.828052 | − | 0.560652i | \(-0.189449\pi\) |
−0.560652 | + | 0.828052i | \(0.689449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.64176 | + | 1.64176i | −0.122031 | + | 0.122031i | −0.765485 | − | 0.643454i | \(-0.777501\pi\) |
0.643454 | + | 0.765485i | \(0.277501\pi\) | |||||||
\(182\) | −8.66627 | − | 2.30002i | −0.642386 | − | 0.170489i | ||||
\(183\) | 6.57328 | 0.485911 | ||||||||
\(184\) | −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 | ||||
\(188\) | 17.3961 | + | 9.93352i | 1.26874 | + | 0.724476i | ||||
\(189\) | 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 | \(0.687219\pi\) | |||||||
\(192\) | 8.60686 | − | 8.85635i | 0.621147 | − | 0.639152i | ||||
\(193\) | 0.0812703i | 0.00584996i | 0.999996 | + | 0.00292498i | \(0.000931052\pi\) | ||||
−0.999996 | + | 0.00292498i | \(0.999069\pi\) | |||||||
\(194\) | 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 | 0.755454 | − | 0.655202i | \(-0.227416\pi\) |
−0.655202 | + | 0.755454i | \(0.727416\pi\) | |||||||
\(198\) | 0.445714 | − | 1.67941i | 0.0316755 | − | 0.119351i | ||||
\(199\) | − | 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 | ||||||
\(202\) | 5.03635 | + | 1.33664i | 0.354356 | + | 0.0940458i | ||||
\(203\) | 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 | ||||
\(207\) | − | 1.19885i | − | 0.0833258i | ||||||
\(208\) | −25.2152 | − | 6.49966i | −1.74836 | − | 0.450670i | ||||
\(209\) | −12.8098 | −0.886075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70115 | + | 8.70115i | 0.599012 | + | 0.599012i | 0.940050 | − | 0.341038i | \(-0.110778\pi\) |
−0.341038 | + | 0.940050i | \(0.610778\pi\) | |||||||
\(212\) | −15.3183 | + | 4.18281i | −1.05207 | + | 0.287277i | ||||
\(213\) | −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 | ||||
\(217\) | 4.17835 | 0.283645 | ||||||||
\(218\) | 5.92320 | − | 22.3181i | 0.401169 | − | 1.51157i | ||||
\(219\) | −10.6051 | + | 10.6051i | −0.716628 | + | 0.716628i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.25603 | − | 2.25603i | −0.151757 | − | 0.151757i | ||||
\(222\) | 7.05776 | + | 12.1575i | 0.473686 | + | 0.815955i | ||||
\(223\) | − | 7.78095i | − | 0.521051i | −0.965467 | − | 0.260525i | \(-0.916104\pi\) | ||
0.965467 | − | 0.260525i | \(-0.0838958\pi\) | |||||||
\(224\) | −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 | \(0.282240\pi\) | |||||||
\(228\) | 9.84821 | − | 17.2467i | 0.652214 | − | 1.14219i | ||||
\(229\) | 7.63865 | − | 7.63865i | 0.504776 | − | 0.504776i | −0.408142 | − | 0.912918i | \(-0.633823\pi\) |
0.912918 | + | 0.408142i | \(0.133823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.99390i | − | 0.196984i | ||||||
\(232\) | 10.6711 | + | 10.5197i | 0.700591 | + | 0.690653i | ||||
\(233\) | 7.51503 | 0.492326 | 0.246163 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246163 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(234\) | 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 | ||||
\(238\) | −0.583796 | + | 0.338911i | −0.0378419 | + | 0.0219683i | ||||
\(239\) | −20.5776 | −1.33105 | −0.665526 | − | 0.746375i | \(-0.731793\pi\) | ||||
−0.665526 | + | 0.746375i | \(0.731793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.2914 | −1.50033 | −0.750166 | − | 0.661250i | \(-0.770026\pi\) | ||||
−0.750166 | + | 0.661250i | \(0.770026\pi\) | |||||||
\(242\) | 8.60362 | − | 4.99466i | 0.553062 | − | 0.321069i | ||||
\(243\) | −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 | ||||
\(247\) | −41.8762 | −2.66452 | ||||||||
\(248\) | 12.1342 | − | 0.0866731i | 0.770525 | − | 0.00550375i | ||||
\(249\) | 1.77925i | 0.112755i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.34230 | + | 3.34230i | −0.210964 | + | 0.210964i | −0.804677 | − | 0.593713i | \(-0.797661\pi\) |
0.593713 | + | 0.804677i | \(0.297661\pi\) | |||||||
\(252\) | −1.04363 | − | 0.595935i | −0.0657428 | − | 0.0375404i | ||||
\(253\) | −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 | ||||
\(257\) | − | 22.4537i | − | 1.40062i | −0.713838 | − | 0.700311i | \(-0.753045\pi\) | ||
0.713838 | − | 0.700311i | \(-0.246955\pi\) | |||||||
\(258\) | 2.77547 | + | 4.78093i | 0.172793 | + | 0.297648i | ||||
\(259\) | −4.43448 | − | 4.43448i | −0.275545 | − | 0.275545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.31131 | + | 2.31131i | −0.143066 | + | 0.143066i | ||||
\(262\) | −4.63771 | + | 17.4745i | −0.286519 | + | 1.07958i | ||||
\(263\) | 8.23670 | 0.507897 | 0.253948 | − | 0.967218i | \(-0.418271\pi\) | ||||
0.253948 | + | 0.967218i | \(0.418271\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | 5.27128 | + | 19.3045i | 0.321994 | + | 1.17921i | ||||
\(269\) | 17.2960 | + | 17.2960i | 1.05455 | + | 1.05455i | 0.998423 | + | 0.0561306i | \(0.0178763\pi\) |
0.0561306 | + | 0.998423i | \(0.482124\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.4753 | −0.757822 | −0.378911 | − | 0.925433i | \(-0.623701\pi\) | ||||
−0.378911 | + | 0.925433i | \(0.623701\pi\) | |||||||
\(272\) | −1.68836 | + | 0.996332i | −0.102372 | + | 0.0604115i | ||||
\(273\) | − | 9.78726i | − | 0.592352i | ||||||
\(274\) | 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 | 0.944597 | − | 0.328234i | \(-0.106453\pi\) |
−0.328234 | + | 0.944597i | \(0.606453\pi\) | |||||||
\(278\) | −0.670439 | − | 0.177934i | −0.0402103 | − | 0.0106718i | ||||
\(279\) | 2.64700i | 0.158472i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.4066i | − | 1.27701i | −0.769618 | − | 0.638505i | \(-0.779553\pi\) | ||
0.769618 | − | 0.638505i | \(-0.220447\pi\) | |||||||
\(282\) | −5.60922 | + | 21.1350i | −0.334024 | + | 1.25857i | ||||
\(283\) | 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 | ||||
\(287\) | 9.88942i | 0.583754i | ||||||||
\(288\) | −3.04316 | − | 1.70899i | −0.179320 | − | 0.100703i | ||||
\(289\) | 16.7598 | 0.985870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.23520 | + | 8.23520i | 0.482756 | + | 0.482756i | ||||
\(292\) | 9.63531 | − | 16.8739i | 0.563864 | − | 0.987470i | ||||
\(293\) | 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 | ||||
\(297\) | 11.1188 | 0.645178 | ||||||||
\(298\) | 8.31278 | + | 2.20620i | 0.481546 | + | 0.127802i | ||||
\(299\) | −8.94430 | + | 8.94430i | −0.517263 | + | 0.517263i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.74387 | − | 1.74387i | −0.100515 | − | 0.100515i | ||||
\(302\) | −2.47182 | + | 1.43497i | −0.142238 | + | 0.0825730i | ||||
\(303\) | 5.68781i | 0.326756i | ||||||||
\(304\) | −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 | \(0.378987\pi\) | |||||||
\(308\) | 1.02175 | + | 3.74187i | 0.0582197 | + | 0.213213i | ||||
\(309\) | −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 | \(0.664078\pi\) | |||||||
\(312\) | −0.203021 | − | 28.4229i | −0.0114938 | − | 1.60913i | ||||
\(313\) | 1.71127 | 0.0967268 | 0.0483634 | − | 0.998830i | \(-0.484599\pi\) | ||||
0.0483634 | + | 0.998830i | \(0.484599\pi\) | |||||||
\(314\) | 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 | \(0.119476\pi\) | |||||||
\(318\) | −8.70224 | − | 14.9902i | −0.487997 | − | 0.840608i | ||||
\(319\) | 10.5498 | 0.590678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5938 | 1.20525 | ||||||||
\(322\) | 1.34365 | + | 2.31453i | 0.0748788 | + | 0.128984i | ||||
\(323\) | −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 | ||||
\(327\) | 25.2049 | 1.39384 | ||||||||
\(328\) | 0.205140 | + | 28.7196i | 0.0113270 | + | 1.58578i | ||||
\(329\) | − | 9.75508i | − | 0.537815i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.89713 | − | 7.89713i | 0.434066 | − | 0.434066i | −0.455943 | − | 0.890009i | \(-0.650698\pi\) |
0.890009 | + | 0.455943i | \(0.150698\pi\) | |||||||
\(332\) | −0.607218 | − | 2.22376i | −0.0333254 | − | 0.122044i | ||||
\(333\) | 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 | ||||
\(337\) | − | 3.46077i | − | 0.188520i | −0.995548 | − | 0.0942601i | \(-0.969951\pi\) | ||
0.995548 | − | 0.0942601i | \(-0.0300485\pi\) | |||||||
\(338\) | −35.9313 | + | 20.8592i | −1.95441 | + | 1.13459i | ||||
\(339\) | 18.7810 | + | 18.7810i | 1.02005 | + | 1.02005i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.04104 | − | 6.04104i | 0.327141 | − | 0.327141i | ||||
\(342\) | −5.42506 | − | 1.43981i | −0.293354 | − | 0.0778558i | ||||
\(343\) | −12.7112 | −0.686338 | ||||||||
\(344\) | −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 | 0.0606600 | − | 0.998158i | \(-0.480679\pi\) |
−0.998158 | + | 0.0606600i | \(0.980679\pi\) | |||||||
\(348\) | −8.11073 | + | 14.2040i | −0.434781 | + | 0.761413i | ||||
\(349\) | −24.2159 | − | 24.2159i | −1.29625 | − | 1.29625i | −0.930852 | − | 0.365397i | \(-0.880933\pi\) |
−0.365397 | − | 0.930852i | \(-0.619067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.3481 | 1.94012 | ||||||||
\(352\) | 3.04486 | + | 10.8455i | 0.162292 | + | 0.578065i | ||||
\(353\) | 10.7028i | 0.569650i | 0.958580 | + | 0.284825i | \(0.0919355\pi\) | ||||
−0.958580 | + | 0.284825i | \(0.908065\pi\) | |||||||
\(354\) | 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 | ||||
\(358\) | 1.83543 | − | 6.91573i | 0.0970053 | − | 0.365507i | ||||
\(359\) | 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 | ||||||||
\(362\) | 3.17364 | + | 0.842282i | 0.166803 | + | 0.0442693i | ||||
\(363\) | 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 | ||||
\(367\) | − | 13.7431i | − | 0.717386i | −0.933456 | − | 0.358693i | \(-0.883223\pi\) | ||
0.933456 | − | 0.358693i | \(-0.116777\pi\) | |||||||
\(368\) | 3.95008 | + | 6.69370i | 0.205912 | + | 0.348933i | ||||
\(369\) | −6.26498 | −0.326142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.46773 | + | 5.46773i | 0.283871 | + | 0.283871i | ||||
\(372\) | 3.48910 | + | 12.7778i | 0.180902 | + | 0.662499i | ||||
\(373\) | −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 | ||||
\(377\) | 34.4881 | 1.77623 | ||||||||
\(378\) | 1.97274 | − | 7.43311i | 0.101467 | − | 0.382318i | ||||
\(379\) | 16.1028 | − | 16.1028i | 0.827143 | − | 0.827143i | −0.159978 | − | 0.987121i | \(-0.551142\pi\) |
0.987121 | + | 0.159978i | \(0.0511423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.50207 | + | 1.50207i | 0.0769535 | + | 0.0769535i | ||||
\(382\) | 10.8888 | + | 18.7568i | 0.557122 | + | 0.959679i | ||||
\(383\) | − | 23.1255i | − | 1.18166i | −0.806796 | − | 0.590830i | \(-0.798800\pi\) | ||
0.806796 | − | 0.590830i | \(-0.201200\pi\) | |||||||
\(384\) | −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 | ||||
\(388\) | −13.1031 | − | 7.48211i | −0.665209 | − | 0.379846i | ||||
\(389\) | 19.4044 | − | 19.4044i | 0.983842 | − | 0.983842i | −0.0160295 | − | 0.999872i | \(-0.505103\pi\) |
0.999872 | + | 0.0160295i | \(0.00510257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.952310i | 0.0481604i | ||||||||
\(392\) | −17.1157 | + | 0.122255i | −0.864473 | + | 0.00617480i | ||||
\(393\) | −19.7348 | −0.995491 | ||||||||
\(394\) | 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 | \(0.204650\pi\) | |||||||
\(398\) | −17.4953 | + | 10.1565i | −0.876960 | + | 0.509101i | ||||
\(399\) | −9.67130 | −0.484171 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.9287 | 1.94401 | 0.972003 | − | 0.234967i | \(-0.0754980\pi\) | ||||
0.972003 | + | 0.234967i | \(0.0754980\pi\) | |||||||
\(402\) | −18.8910 | + | 10.9668i | −0.942197 | + | 0.546973i | ||||
\(403\) | 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 | ||||
\(407\) | −12.8227 | −0.635598 | ||||||||
\(408\) | −1.52392 | − | 1.50230i | −0.0754452 | − | 0.0743750i | ||||
\(409\) | 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 | ||||
\(412\) | 13.7005 | − | 23.9932i | 0.674977 | − | 1.18206i | ||||
\(413\) | −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 | ||||
\(417\) | − | 0.757161i | − | 0.0370783i | ||||||
\(418\) | 9.09525 | + | 15.6672i | 0.444863 | + | 0.766306i | ||||
\(419\) | −16.6774 | − | 16.6774i | −0.814746 | − | 0.814746i | 0.170595 | − | 0.985341i | \(-0.445431\pi\) |
−0.985341 | + | 0.170595i | \(0.945431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4169 | − | 15.4169i | 0.751372 | − | 0.751372i | −0.223364 | − | 0.974735i | \(-0.571704\pi\) |
0.974735 | + | 0.223364i | \(0.0717037\pi\) | |||||||
\(422\) | 4.46401 | − | 16.8200i | 0.217305 | − | 0.818786i | ||||
\(423\) | 6.17987 | 0.300476 | ||||||||
\(424\) | 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 | ||||
\(428\) | −26.9886 | + | 7.36949i | −1.30454 | + | 0.356218i | ||||
\(429\) | −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 | \(0.338068\pi\) | |||||||
\(432\) | 5.57480 | − | 21.6272i | 0.268218 | − | 1.04054i | ||||
\(433\) | − | 0.676118i | − | 0.0324922i | −0.999868 | − | 0.0162461i | \(-0.994828\pi\) | ||
0.999868 | − | 0.0162461i | \(-0.00517152\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 20.5005 | + | 5.44082i | 0.979553 | + | 0.259972i | ||||
\(439\) | 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 | ||||||
\(442\) | −1.15743 | + | 4.36108i | −0.0550532 | + | 0.207436i | ||||
\(443\) | −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 | ||||
\(447\) | 9.38805i | 0.444039i | ||||||||
\(448\) | 7.79061 | − | 0.111300i | 0.368072 | − | 0.00525843i | ||||
\(449\) | 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 | ||||
\(452\) | −29.8827 | − | 17.0635i | −1.40556 | − | 0.802602i | ||||
\(453\) | −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 | ||||
\(457\) | −5.66561 | −0.265026 | −0.132513 | − | 0.991181i | \(-0.542305\pi\) | ||||
−0.132513 | + | 0.991181i | \(0.542305\pi\) | |||||||
\(458\) | −14.7661 | − | 3.91891i | −0.689975 | − | 0.183119i | ||||
\(459\) | 1.93501 | − | 1.93501i | 0.0903186 | − | 0.0903186i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6375 | + | 16.6375i | 0.774887 | + | 0.774887i | 0.978956 | − | 0.204069i | \(-0.0654168\pi\) |
−0.204069 | + | 0.978956i | \(0.565417\pi\) | |||||||
\(462\) | −3.66171 | + | 2.12573i | −0.170358 | + | 0.0988979i | ||||
\(463\) | 41.6835i | 1.93720i | 0.248631 | + | 0.968598i | \(0.420019\pi\) | ||||
−0.248631 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(464\) | 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 | \(0.282450\pi\) | |||||||
\(468\) | −7.74926 | + | 2.11601i | −0.358210 | + | 0.0978126i | ||||
\(469\) | 6.89057 | − | 6.89057i | 0.318177 | − | 0.318177i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.40370i | 0.295067i | ||||||||
\(472\) | −23.7060 | + | 24.0471i | −1.09116 | + | 1.10686i | ||||
\(473\) | −5.04255 | −0.231857 | ||||||||
\(474\) | −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 | ||||
\(478\) | 14.6105 | + | 25.1675i | 0.668268 | + | 1.15114i | ||||
\(479\) | 8.32325 | 0.380299 | 0.190149 | − | 0.981755i | \(-0.439103\pi\) | ||||
0.190149 | + | 0.981755i | \(0.439103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.9183 | −1.91131 | ||||||||
\(482\) | 16.5374 | + | 28.4868i | 0.753257 | + | 1.29754i | ||||
\(483\) | −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 | ||||
\(487\) | 7.29577 | 0.330603 | 0.165301 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165301 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(488\) | 8.57687 | + | 8.45521i | 0.388257 | + | 0.382750i | ||||
\(489\) | 12.5463i | 0.567365i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.57528 | − | 3.57528i | 0.161350 | − | 0.161350i | −0.621815 | − | 0.783165i | \(-0.713604\pi\) |
0.783165 | + | 0.621815i | \(0.213604\pi\) | |||||||
\(492\) | −30.2429 | + | 8.25810i | −1.36345 | + | 0.372304i | ||||
\(493\) | 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 | ||||
\(497\) | − | 0.874479i | − | 0.0392257i | ||||||
\(498\) | 2.17612 | − | 1.26330i | 0.0975143 | − | 0.0566099i | ||||
\(499\) | 10.8833 | + | 10.8833i | 0.487203 | + | 0.487203i | 0.907422 | − | 0.420220i | \(-0.138047\pi\) |
−0.420220 | + | 0.907422i | \(0.638047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00295 | + | 7.00295i | −0.312869 | + | 0.312869i | ||||
\(502\) | 6.46093 | + | 1.71472i | 0.288365 | + | 0.0765318i | ||||
\(503\) | 29.3781 | 1.30991 | 0.654953 | − | 0.755670i | \(-0.272688\pi\) | ||||
0.654953 | + | 0.755670i | \(0.272688\pi\) | |||||||
\(504\) | 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 | ||||
\(508\) | −2.38996 | − | 1.36471i | −0.106037 | − | 0.0605493i | ||||
\(509\) | −17.4592 | − | 17.4592i | −0.773863 | − | 0.773863i | 0.204916 | − | 0.978780i | \(-0.434308\pi\) |
−0.978780 | + | 0.204916i | \(0.934308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.46222 | −0.418584 | ||||||||
\(512\) | 22.6222 | − | 0.484827i | 0.999770 | − | 0.0214265i | ||||
\(513\) | − | 35.9175i | − | 1.58579i | ||||||
\(514\) | −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 | ||||
\(518\) | −2.27505 | + | 8.57221i | −0.0999602 | + | 0.376641i | ||||
\(519\) | 1.19138i | 0.0522959i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.48578i | − | 0.415580i | −0.978174 | − | 0.207790i | \(-0.933373\pi\) | ||
0.978174 | − | 0.207790i | \(-0.0666270\pi\) | |||||||
\(522\) | 4.46794 | + | 1.18579i | 0.195556 | + | 0.0519005i | ||||
\(523\) | −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 | ||||
\(527\) | − | 2.10265i | − | 0.0915929i | ||||||
\(528\) | −10.5898 | + | 6.24924i | −0.460862 | + | 0.271963i | ||||
\(529\) | −19.2245 | −0.835846 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.20849 | − | 5.20849i | −0.226029 | − | 0.226029i | ||||
\(532\) | 12.0875 | − | 3.30060i | 0.524059 | − | 0.143099i | ||||
\(533\) | 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 | ||||
\(537\) | 7.81028 | 0.337039 | ||||||||
\(538\) | 8.87348 | − | 33.4345i | 0.382563 | − | 1.44146i | ||||
\(539\) | −8.52106 | + | 8.52106i | −0.367028 | + | 0.367028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.55686 | − | 2.55686i | −0.109928 | − | 0.109928i | 0.650003 | − | 0.759931i | \(-0.274767\pi\) |
−0.759931 | + | 0.650003i | \(0.774767\pi\) | |||||||
\(542\) | 8.85774 | + | 15.2580i | 0.380472 | + | 0.655389i | ||||
\(543\) | 3.58416i | 0.153811i | ||||||||
\(544\) | 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 | \(0.0188097\pi\) | |||||||
\(548\) | 15.1792 | − | 26.5826i | 0.648422 | − | 1.13555i | ||||
\(549\) | −1.85771 | + | 1.85771i | −0.0792852 | + | 0.0792852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.0796i | − | 1.45184i | ||||||
\(552\) | −5.95606 | + | 6.04176i | −0.253507 | + | 0.257154i | ||||
\(553\) | 14.4002 | 0.612357 | ||||||||
\(554\) | 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 | \(0.426139\pi\) | |||||||
\(558\) | 3.23743 | − | 1.87942i | 0.137051 | − | 0.0795623i | ||||
\(559\) | −16.4844 | −0.697217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.50661 | −0.0636089 | ||||||||
\(562\) | −26.1815 | + | 15.1991i | −1.10440 | + | 0.641136i | ||||
\(563\) | 27.5975 | − | 27.5975i | 1.16309 | − | 1.16309i | 0.179300 | − | 0.983794i | \(-0.442617\pi\) |
0.983794 | − | 0.179300i | \(-0.0573833\pi\) | |||||||
\(564\) | 29.8320 | − | 8.14592i | 1.25615 | − | 0.343005i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.79460 | − | 14.2977i | 0.159499 | − | 0.600979i | ||||
\(567\) | 6.59190 | 0.276834 | ||||||||
\(568\) | −0.0181396 | − | 2.53955i | −0.000761123 | − | 0.106557i | ||||
\(569\) | 23.6390i | 0.990998i | 0.868608 | + | 0.495499i | \(0.165015\pi\) | ||||
−0.868608 | + | 0.495499i | \(0.834985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7518 | + | 21.7518i | −0.910284 | + | 0.910284i | −0.996294 | − | 0.0860105i | \(-0.972588\pi\) |
0.0860105 | + | 0.996294i | \(0.472588\pi\) | |||||||
\(572\) | 22.5148 | + | 12.8564i | 0.941390 | + | 0.537551i | ||||
\(573\) | −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 | ||||
\(577\) | − | 3.69585i | − | 0.153860i | −0.997036 | − | 0.0769302i | \(-0.975488\pi\) | ||
0.997036 | − | 0.0769302i | \(-0.0245119\pi\) | |||||||
\(578\) | −11.8998 | − | 20.4982i | −0.494967 | − | 0.852613i | ||||
\(579\) | 0.0887116 | + | 0.0887116i | 0.00368673 | + | 0.00368673i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.793750 | + | 0.793750i | −0.0329303 | + | 0.0329303i | ||||
\(582\) | 4.22496 | − | 15.9193i | 0.175130 | − | 0.659876i | ||||
\(583\) | 15.8105 | 0.654802 | ||||||||
\(584\) | −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 | \(0.0393590\pi\) |
0.123335 | + | 0.992365i | \(0.460641\pi\) | |||||||
\(588\) | −4.92148 | − | 18.0235i | −0.202958 | − | 0.743276i | ||||
\(589\) | −19.5146 | − | 19.5146i | −0.804085 | − | 0.804085i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.07189 | 0.126361 | ||||||||
\(592\) | −6.42912 | + | 24.9415i | −0.264235 | + | 1.02509i | ||||
\(593\) | 4.55524i | 0.187061i | 0.995616 | + | 0.0935306i | \(0.0298153\pi\) | ||||
−0.995616 | + | 0.0935306i | \(0.970185\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | 17.2900 | + | 4.58876i | 0.707043 | + | 0.187648i | ||||
\(599\) | 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 | \(0.0804717\pi\) | ||||
−0.968214 | + | 0.250125i | \(0.919528\pi\) | |||||||
\(602\) | −0.894668 | + | 3.37103i | −0.0364639 | + | 0.137393i | ||||
\(603\) | 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 | ||||
\(607\) | 5.23884i | 0.212638i | 0.994332 | + | 0.106319i | \(0.0339065\pi\) | ||||
−0.994332 | + | 0.106319i | \(0.966094\pi\) | |||||||
\(608\) | 35.0345 | − | 9.83593i | 1.42084 | − | 0.398900i | ||||
\(609\) | 7.96503 | 0.322759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.1064 | − | 46.1064i | −1.86527 | − | 1.86527i | ||||
\(612\) | −0.299889 | + | 0.525183i | −0.0121223 | + | 0.0212293i | ||||
\(613\) | −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 | ||||
\(617\) | 2.20286 | 0.0886838 | 0.0443419 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443419 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(618\) | 29.1499 | + | 7.73636i | 1.17258 | + | 0.311202i | ||||
\(619\) | 31.4569 | − | 31.4569i | 1.26436 | − | 1.26436i | 0.315404 | − | 0.948958i | \(-0.397860\pi\) |
0.948958 | − | 0.315404i | \(-0.102140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.67158 | − | 7.67158i | −0.307850 | − | 0.307850i | ||||
\(622\) | 37.5325 | − | 21.7887i | 1.50492 | − | 0.873648i | ||||
\(623\) | 1.09473i | 0.0438594i | ||||||||
\(624\) | −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 | ||||
\(628\) | −2.18544 | − | 8.00353i | −0.0872085 | − | 0.319376i | ||||
\(629\) | −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 | \(-0.108678\pi\) | |||||||
\(632\) | 41.8192 | − | 0.298708i | 1.66348 | − | 0.0118820i | ||||
\(633\) | 18.9957 | 0.755011 | ||||||||
\(634\) | −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 | ||||
\(638\) | −7.49061 | − | 12.9031i | −0.296556 | − | 0.510838i | ||||
\(639\) | 0.553985 | 0.0219153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9208 | −0.589336 | −0.294668 | − | 0.955600i | \(-0.595209\pi\) | ||||
−0.294668 | + | 0.955600i | \(0.595209\pi\) | |||||||
\(642\) | −15.3320 | − | 26.4105i | −0.605108 | − | 1.04234i | ||||
\(643\) | −0.541845 | + | 0.541845i | −0.0213683 | + | 0.0213683i | −0.717710 | − | 0.696342i | \(-0.754810\pi\) |
0.696342 | + | 0.717710i | \(0.254810\pi\) | |||||||
\(644\) | 1.87678 | − | 3.28673i | 0.0739556 | − | 0.129515i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.30942 | + | 1.14371i | 0.169552 | + | 0.0449988i | ||||
\(647\) | 32.6391 | 1.28318 | 0.641588 | − | 0.767049i | \(-0.278276\pi\) | ||||
0.641588 | + | 0.767049i | \(0.278276\pi\) | |||||||
\(648\) | 19.1434 | − | 0.136738i | 0.752023 | − | 0.00537158i | ||||
\(649\) | 23.7739i | 0.933208i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.56093 | − | 4.56093i | 0.178757 | − | 0.178757i | ||||
\(652\) | −4.28179 | − | 15.6808i | −0.167688 | − | 0.614108i | ||||
\(653\) | 9.73805 | − | 9.73805i | 0.381079 | − | 0.381079i | −0.490412 | − | 0.871491i | \(-0.663154\pi\) |
0.871491 | + | 0.490412i | \(0.163154\pi\) | |||||||
\(654\) | −17.8960 | − | 30.8271i | −0.699790 | − | 1.20544i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.9801 | − | 20.6424i | 1.36574 | − | 0.805952i | ||||
\(657\) | − | 5.99434i | − | 0.233862i | ||||||
\(658\) | −11.9310 | + | 6.92631i | −0.465120 | + | 0.270016i | ||||
\(659\) | −1.26445 | − | 1.26445i | −0.0492560 | − | 0.0492560i | 0.682050 | − | 0.731306i | \(-0.261089\pi\) |
−0.731306 | + | 0.682050i | \(0.761089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6701 | − | 22.6701i | 0.881763 | − | 0.881763i | −0.111951 | − | 0.993714i | \(-0.535710\pi\) |
0.993714 | + | 0.111951i | \(0.0357099\pi\) | |||||||
\(662\) | −15.2658 | − | 4.05152i | −0.593321 | − | 0.157467i | ||||
\(663\) | −4.92519 | −0.191279 | ||||||||
\(664\) | −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 | ||||
\(668\) | 6.36254 | − | 11.1424i | 0.246174 | − | 0.431114i | ||||
\(669\) | −8.49339 | − | 8.49339i | −0.328373 | − | 0.328373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.47943 | 0.327345 | ||||||||
\(672\) | 2.29884 | + | 8.18822i | 0.0886798 | + | 0.315868i | ||||
\(673\) | − | 3.58765i | − | 0.138294i | −0.997606 | − | 0.0691469i | \(-0.977972\pi\) | ||
0.997606 | − | 0.0691469i | \(-0.0220277\pi\) | |||||||
\(674\) | −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 | 0.874731 | − | 0.484608i | \(-0.161038\pi\) |
−0.484608 | + | 0.874731i | \(0.661038\pi\) | |||||||
\(678\) | 9.63537 | − | 36.3052i | 0.370044 | − | 1.39429i | ||||
\(679\) | 7.34770i | 0.281979i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.70339i | 0.180234i | ||||||||
\(682\) | −11.6778 | − | 3.09928i | −0.447166 | − | 0.118677i | ||||
\(683\) | −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 | ||||
\(687\) | − | 16.6761i | − | 0.636234i | ||||||
\(688\) | −2.52826 | + | 9.80828i | −0.0963889 | + | 0.373937i | ||||
\(689\) | 51.6854 | 1.96906 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4781 | + | 12.4781i | 0.474689 | + | 0.474689i | 0.903428 | − | 0.428739i | \(-0.141042\pi\) |
−0.428739 | + | 0.903428i | \(0.641042\pi\) | |||||||
\(692\) | −0.406593 | − | 1.48903i | −0.0154563 | − | 0.0566043i | ||||
\(693\) | 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 | ||||
\(697\) | 4.97661 | 0.188502 | ||||||||
\(698\) | −12.4237 | + | 46.8113i | −0.470243 | + | 1.77183i | ||||
\(699\) | 8.20312 | − | 8.20312i | 0.310271 | − | 0.310271i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.40945 | + | 6.40945i | 0.242082 | + | 0.242082i | 0.817711 | − | 0.575629i | \(-0.195243\pi\) |
−0.575629 | + | 0.817711i | \(0.695243\pi\) | |||||||
\(702\) | −25.8079 | − | 44.4558i | −0.974057 | − | 1.67788i | ||||
\(703\) | 41.4217i | 1.56225i | ||||||||
\(704\) | 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 | ||||
\(708\) | −32.0084 | − | 18.2774i | −1.20295 | − | 0.686907i | ||||
\(709\) | −8.78514 | + | 8.78514i | −0.329933 | + | 0.329933i | −0.852561 | − | 0.522628i | \(-0.824952\pi\) |
0.522628 | + | 0.852561i | \(0.324952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.12255i | 0.342122i | ||||||||
\(712\) | 0.0227084 | + | 3.17918i | 0.000851033 | + | 0.119145i | ||||
\(713\) | −8.33621 | −0.312194 | ||||||||
\(714\) | −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 | ||||
\(718\) | 28.9119 | − | 16.7842i | 1.07898 | − | 0.626380i | ||||
\(719\) | −46.2329 | −1.72420 | −0.862099 | − | 0.506740i | \(-0.830850\pi\) | ||||
−0.862099 | + | 0.506740i | \(0.830850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4544 | −0.501069 | ||||||||
\(722\) | 27.3721 | − | 15.8903i | 1.01868 | − | 0.591376i | ||||
\(723\) | −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 | ||||
\(727\) | −17.4640 | −0.647703 | −0.323852 | − | 0.946108i | \(-0.604978\pi\) | ||||
−0.323852 | + | 0.946108i | \(0.604978\pi\) | |||||||
\(728\) | 12.5893 | − | 12.7705i | 0.466592 | − | 0.473306i | ||||
\(729\) | 30.0340i | 1.11237i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.877557 | + | 0.877557i | −0.0324576 | + | 0.0324576i | ||||
\(732\) | −6.51899 | + | 11.4164i | −0.240949 | + | 0.421963i | ||||
\(733\) | 7.89695 | − | 7.89695i | 0.291680 | − | 0.291680i | −0.546063 | − | 0.837744i | \(-0.683874\pi\) |
0.837744 | + | 0.546063i | \(0.183874\pi\) | |||||||
\(734\) | −16.8086 | + | 9.75791i | −0.620419 | + | 0.360171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.38214 | − | 9.58384i | 0.198388 | − | 0.353265i | ||||
\(737\) | − | 19.9247i | − | 0.733936i | ||||||
\(738\) | 4.44826 | + | 7.66243i | 0.163743 | + | 0.282058i | ||||
\(739\) | −26.1724 | − | 26.1724i | −0.962769 | − | 0.962769i | 0.0365624 | − | 0.999331i | \(-0.488359\pi\) |
−0.999331 | + | 0.0365624i | \(0.988359\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.7105 | + | 45.7105i | −1.67922 | + | 1.67922i | ||||
\(742\) | 2.80515 | − | 10.5696i | 0.102980 | − | 0.388021i | ||||
\(743\) | −49.7660 | −1.82574 | −0.912868 | − | 0.408254i | \(-0.866138\pi\) | ||||
−0.912868 | + | 0.408254i | \(0.866138\pi\) | |||||||
\(744\) | 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 | ||||
\(748\) | 1.88300 | − | 0.514171i | 0.0688493 | − | 0.0188000i | ||||
\(749\) | 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 | \(0.645811\pi\) | |||||||
\(752\) | −34.5049 | + | 20.3620i | −1.25827 | + | 0.742527i | ||||
\(753\) | 7.29665i | 0.265905i | ||||||||
\(754\) | −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 | 0.367237 | − | 0.930127i | \(-0.380304\pi\) |
−0.930127 | + | 0.367237i | \(0.880304\pi\) | |||||||
\(758\) | −31.1279 | − | 8.26131i | −1.13062 | − | 0.300064i | ||||
\(759\) | 5.97312i | 0.216811i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.9821i | − | 0.941849i | −0.882174 | − | 0.470924i | \(-0.843920\pi\) | ||
0.882174 | − | 0.470924i | \(-0.156080\pi\) | |||||||
\(762\) | 0.770619 | − | 2.90363i | 0.0279166 | − | 0.105187i | ||||
\(763\) | 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 | ||||
\(767\) | 77.7185i | 2.80625i | ||||||||
\(768\) | 6.84587 | + | 23.7315i | 0.247029 | + | 0.856338i | ||||
\(769\) | 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 | ||||
\(772\) | −0.141150 | − | 0.0805991i | −0.00508009 | − | 0.00290082i | ||||
\(773\) | 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 | ||||
\(777\) | −9.68103 | −0.347305 | ||||||||
\(778\) | −37.5102 | − | 9.95518i | −1.34481 | − | 0.356910i | ||||
\(779\) | 46.1876 | − | 46.1876i | 1.65484 | − | 1.65484i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26432 | − | 1.26432i | −0.0452409 | − | 0.0452409i | ||||
\(782\) | 1.16473 | − | 0.676160i | 0.0416507 | − | 0.0241794i | ||||
\(783\) | 29.5807i | 1.05713i | ||||||||
\(784\) | 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 | \(0.255192\pi\) | |||||||
\(788\) | −3.83934 | + | 1.04837i | −0.136771 | + | 0.0373466i | ||||
\(789\) | 8.99087 | − | 8.99087i | 0.320084 | − | 0.320084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7570i | 0.595811i | ||||||||
\(792\) | 2.47476 | + | 2.43965i | 0.0879366 | + | 0.0866893i | ||||
\(793\) | 27.7198 | 0.984360 | ||||||||
\(794\) | −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 | \(0.401584\pi\) | |||||||
\(798\) | 6.86682 | + | 11.8286i | 0.243083 | + | 0.418727i | ||||
\(799\) | −4.90900 | −0.173668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.693514 | −0.0245041 | ||||||||
\(802\) | −27.6402 | − | 47.6121i | −0.976009 | − | 1.68124i | ||||
\(803\) | −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 | ||||
\(807\) | 37.7593 | 1.32919 | ||||||||
\(808\) | −7.31623 | + | 7.42150i | −0.257384 | + | 0.261087i | ||||
\(809\) | 32.4845i | 1.14209i | 0.820917 | + | 0.571047i | \(0.193463\pi\) | ||||
−0.820917 | + | 0.571047i | \(0.806537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.69149 | − | 7.69149i | 0.270085 | − | 0.270085i | −0.559049 | − | 0.829134i | \(-0.688834\pi\) |
0.829134 | + | 0.559049i | \(0.188834\pi\) | |||||||
\(812\) | −9.95494 | + | 2.71829i | −0.349350 | + | 0.0953933i | ||||
\(813\) | −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 | ||||
\(817\) | 16.2891i | 0.569884i | ||||||||
\(818\) | 5.62417 | − | 3.26499i | 0.196644 | − | 0.114158i | ||||
\(819\) | 2.76603 | + | 2.76603i | 0.0966529 | + | 0.0966529i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5798 | + | 10.5798i | −0.369238 | + | 0.369238i | −0.867199 | − | 0.497961i | \(-0.834082\pi\) |
0.497961 | + | 0.867199i | \(0.334082\pi\) | |||||||
\(822\) | 32.2959 | + | 8.57130i | 1.12645 | + | 0.298958i | ||||
\(823\) | 4.85817 | 0.169345 | 0.0846726 | − | 0.996409i | \(-0.473016\pi\) | ||||
0.0846726 | + | 0.996409i | \(0.473016\pi\) | |||||||
\(824\) | −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 | 0.832768 | − | 0.553622i | \(-0.186755\pi\) |
−0.553622 | + | 0.832768i | \(0.686755\pi\) | |||||||
\(828\) | 2.08215 | + | 1.18895i | 0.0723598 | + | 0.0413188i | ||||
\(829\) | 24.3613 | + | 24.3613i | 0.846102 | + | 0.846102i | 0.989644 | − | 0.143542i | \(-0.0458493\pi\) |
−0.143542 | + | 0.989644i | \(0.545849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.3952 | 0.776881 | ||||||||
\(832\) | 36.2955 | − | 37.3476i | 1.25832 | − | 1.29480i | ||||
\(833\) | 2.96585i | 0.102761i | ||||||||
\(834\) | −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 | ||||
\(838\) | −8.55615 | + | 32.2388i | −0.295567 | + | 1.11367i | ||||
\(839\) | − | 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 | ||||||
\(842\) | −29.8020 | − | 7.90942i | −1.02704 | − | 0.272577i | ||||
\(843\) | −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 | ||||
\(847\) | 6.85110i | 0.235407i | ||||||||
\(848\) | 7.92712 | − | 30.7530i | 0.272219 | − | 1.05606i | ||||
\(849\) | 16.1472 | 0.554169 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.84723 | + | 8.84723i | 0.303279 | + | 0.303279i | ||||
\(852\) | 2.67425 | − | 0.730228i | 0.0916181 | − | 0.0250172i | ||||
\(853\) | −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 | ||||
\(857\) | −35.8346 | −1.22409 | −0.612043 | − | 0.790825i | \(-0.709652\pi\) | ||||
−0.612043 | + | 0.790825i | \(0.709652\pi\) | |||||||
\(858\) | −7.25967 | + | 27.3538i | −0.247841 | + | 0.933843i | ||||
\(859\) | 0.619460 | − | 0.619460i | 0.0211357 | − | 0.0211357i | −0.696460 | − | 0.717596i | \(-0.745243\pi\) |
0.717596 | + | 0.696460i | \(0.245243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7949 | + | 10.7949i | 0.367890 | + | 0.367890i | ||||
\(862\) | −14.3590 | − | 24.7344i | −0.489070 | − | 0.842456i | ||||
\(863\) | − | 18.8270i | − | 0.640878i | −0.947269 | − | 0.320439i | \(-0.896170\pi\) | ||
0.947269 | − | 0.320439i | \(-0.103830\pi\) | |||||||
\(864\) | −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 | ||||
\(868\) | −4.14384 | + | 7.25693i | −0.140651 | + | 0.246316i | ||||
\(869\) | 20.8197 | − | 20.8197i | 0.706260 | − | 0.706260i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 65.1352i | − | 2.20702i | ||||||
\(872\) | 32.8876 | + | 32.4211i | 1.11372 | + | 1.09792i | ||||
\(873\) | −4.65479 | −0.157541 | ||||||||
\(874\) | 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 | \(0.190536\pi\) | |||||||
\(878\) | 16.3339 | − | 9.48233i | 0.551244 | − | 0.320013i | ||||
\(879\) | 1.21541 | 0.0409946 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6551 | 0.460052 | 0.230026 | − | 0.973184i | \(-0.426119\pi\) | ||||
0.230026 | + | 0.973184i | \(0.426119\pi\) | |||||||
\(882\) | −4.56649 | + | 2.65098i | −0.153762 | + | 0.0892631i | ||||
\(883\) | −25.7585 | + | 25.7585i | −0.866844 | + | 0.866844i | −0.992122 | − | 0.125278i | \(-0.960018\pi\) |
0.125278 | + | 0.992122i | \(0.460018\pi\) | |||||||
\(884\) | 6.15565 | − | 1.68086i | 0.207037 | − | 0.0565334i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.4298 | + | 54.3701i | −0.484777 | + | 1.82660i | ||||
\(887\) | 38.8982 | 1.30607 | 0.653037 | − | 0.757326i | \(-0.273495\pi\) | ||||
0.653037 | + | 0.757326i | \(0.273495\pi\) | |||||||
\(888\) | −28.1144 | + | 0.200817i | −0.943459 | + | 0.00673898i | ||||
\(889\) | 1.34020i | 0.0449488i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.53054 | − | 9.53054i | 0.319285 | − | 0.319285i | ||||
\(892\) | 13.5139 | + | 7.71669i | 0.452479 | + | 0.258374i | ||||
\(893\) | −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 | ||||
\(897\) | 19.5265i | 0.651972i | ||||||||
\(898\) | −5.94978 | − | 10.2489i | −0.198547 | − | 0.342010i | ||||
\(899\) | 16.0717 | + | 16.0717i | 0.536022 | + | 0.536022i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.75150 | − | 2.75150i | 0.0916658 | − | 0.0916658i | ||||
\(902\) | 7.33545 | − | 27.6393i | 0.244244 | − | 0.920289i | ||||
\(903\) | −3.80707 | −0.126692 | ||||||||
\(904\) | 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 | 0.617307 | − | 0.786723i | \(-0.288224\pi\) |
−0.786723 | + | 0.617307i | \(0.788224\pi\) | |||||||
\(908\) | −1.60516 | − | 5.87844i | −0.0532692 | − | 0.195083i | ||||
\(909\) | −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 | \(0.781604\pi\) | |||||||
\(912\) | 20.1871 | + | 34.2086i | 0.668463 | + | 1.13276i | ||||
\(913\) | 2.29520i | 0.0759601i | ||||||||
\(914\) | 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 | ||||
\(918\) | −3.74053 | − | 0.992732i | −0.123456 | − | 0.0327650i | ||||
\(919\) | 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 | ||||||||
\(922\) | 8.53567 | − | 32.1617i | 0.281107 | − | 1.05919i | ||||
\(923\) | −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 | ||||
\(927\) | − | 8.52342i | − | 0.279946i | ||||||
\(928\) | −28.8535 | + | 8.10062i | −0.947163 | + | 0.265916i | ||||
\(929\) | −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 | ||||
\(932\) | −7.45297 | + | 13.0521i | −0.244130 | + | 0.427534i | ||||
\(933\) | 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 | ||||
\(937\) | 5.26656 | 0.172051 | 0.0860255 | − | 0.996293i | \(-0.472583\pi\) | ||||
0.0860255 | + | 0.996293i | \(0.472583\pi\) | |||||||
\(938\) | −13.3200 | − | 3.53512i | −0.434914 | − | 0.115426i | ||||
\(939\) | 1.86796 | − | 1.86796i | 0.0609585 | − | 0.0609585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.7780 | + | 18.7780i | 0.612145 | + | 0.612145i | 0.943505 | − | 0.331359i | \(-0.107507\pi\) |
−0.331359 | + | 0.943505i | \(0.607507\pi\) | |||||||
\(942\) | 7.83209 | − | 4.54676i | 0.255183 | − | 0.148141i | ||||
\(943\) | − | 19.7304i | − | 0.642509i | ||||||
\(944\) | 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 | \(0.273982\pi\) | |||||||
\(948\) | 12.0248 | + | 44.0372i | 0.390546 | + | 1.43026i | ||||
\(949\) | −44.7223 | + | 44.7223i | −1.45175 | + | 1.45175i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.9142i | − | 0.710616i | ||||||
\(952\) | −0.00964316 | − | 1.35004i | −0.000312537 | − | 0.0437552i | ||||
\(953\) | 30.0292 | 0.972741 | 0.486371 | − | 0.873753i | \(-0.338320\pi\) | ||||
0.486371 | + | 0.873753i | \(0.338320\pi\) | |||||||
\(954\) | 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 | ||||
\(958\) | −5.90968 | − | 10.1798i | −0.190933 | − | 0.328895i | ||||
\(959\) | −14.9065 | −0.481356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5941 | −0.406260 | ||||||||
\(962\) | 29.7629 | + | 51.2685i | 0.959593 | + | 1.65296i | ||||
\(963\) | −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 | ||||
\(967\) | 15.2196 | 0.489429 | 0.244715 | − | 0.969595i | \(-0.421306\pi\) | ||||
0.244715 | + | 0.969595i | \(0.421306\pi\) | |||||||
\(968\) | 0.142115 | + | 19.8961i | 0.00456775 | + | 0.639485i | ||||
\(969\) | 4.86684i | 0.156345i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4838 | + | 18.4838i | −0.593173 | + | 0.593173i | −0.938487 | − | 0.345314i | \(-0.887772\pi\) |
0.345314 | + | 0.938487i | \(0.387772\pi\) | |||||||
\(972\) | −3.32024 | − | 12.1594i | −0.106497 | − | 0.390013i | ||||
\(973\) | 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 | ||||
\(977\) | − | 18.7912i | − | 0.601183i | −0.953753 | − | 0.300592i | \(-0.902816\pi\) | ||
0.953753 | − | 0.300592i | \(-0.0971841\pi\) | |||||||
\(978\) | 15.3449 | − | 8.90817i | 0.490676 | − | 0.284852i | ||||
\(979\) | 1.58276 | + | 1.58276i | 0.0505851 | + | 0.0505851i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.12331 | + | 7.12331i | −0.227430 | + | 0.227430i | ||||
\(982\) | −6.91129 | − | 1.83425i | −0.220548 | − | 0.0585333i | ||||
\(983\) | 56.5605 | 1.80400 | 0.901999 | − | 0.431738i | \(-0.142099\pi\) | ||||
0.901999 | + | 0.431738i | \(0.142099\pi\) | |||||||
\(984\) | 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 | ||||
\(988\) | 41.5303 | − | 72.7303i | 1.32126 | − | 2.31386i | ||||
\(989\) | 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 | \(0.245920\pi\) | |||||||
\(992\) | −11.8835 | + | 21.1606i | −0.377301 | + | 0.671851i | ||||
\(993\) | − | 17.2404i | − | 0.547108i | ||||||
\(994\) | −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 | \(-0.961541\pi\) |
−0.120528 | − | 0.992710i | \(-0.538459\pi\) | |||||||
\(998\) | 5.58353 | − | 21.0382i | 0.176743 | − | 0.665954i | ||||
\(999\) | − | 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.q.f.349.2 | 12 | ||
4.3 | odd | 2 | 1600.2.q.f.849.2 | 12 | |||
5.2 | odd | 4 | 400.2.l.g.301.5 | yes | 12 | ||
5.3 | odd | 4 | 400.2.l.f.301.2 | yes | 12 | ||
5.4 | even | 2 | 400.2.q.e.349.5 | 12 | |||
16.5 | even | 4 | 400.2.q.e.149.5 | 12 | |||
16.11 | odd | 4 | 1600.2.q.e.49.5 | 12 | |||
20.3 | even | 4 | 1600.2.l.g.401.2 | 12 | |||
20.7 | even | 4 | 1600.2.l.f.401.5 | 12 | |||
20.19 | odd | 2 | 1600.2.q.e.849.5 | 12 | |||
80.27 | even | 4 | 1600.2.l.f.1201.5 | 12 | |||
80.37 | odd | 4 | 400.2.l.g.101.5 | yes | 12 | ||
80.43 | even | 4 | 1600.2.l.g.1201.2 | 12 | |||
80.53 | odd | 4 | 400.2.l.f.101.2 | ✓ | 12 | ||
80.59 | odd | 4 | 1600.2.q.f.49.2 | 12 | |||
80.69 | even | 4 | inner | 400.2.q.f.149.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.2 | ✓ | 12 | 80.53 | odd | 4 | ||
400.2.l.f.301.2 | yes | 12 | 5.3 | odd | 4 | ||
400.2.l.g.101.5 | yes | 12 | 80.37 | odd | 4 | ||
400.2.l.g.301.5 | yes | 12 | 5.2 | odd | 4 | ||
400.2.q.e.149.5 | 12 | 16.5 | even | 4 | |||
400.2.q.e.349.5 | 12 | 5.4 | even | 2 | |||
400.2.q.f.149.2 | 12 | 80.69 | even | 4 | inner | ||
400.2.q.f.349.2 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.l.f.401.5 | 12 | 20.7 | even | 4 | |||
1600.2.l.f.1201.5 | 12 | 80.27 | even | 4 | |||
1600.2.l.g.401.2 | 12 | 20.3 | even | 4 | |||
1600.2.l.g.1201.2 | 12 | 80.43 | even | 4 | |||
1600.2.q.e.49.5 | 12 | 16.11 | odd | 4 | |||
1600.2.q.e.849.5 | 12 | 20.19 | odd | 2 | |||
1600.2.q.f.49.2 | 12 | 80.59 | odd | 4 | |||
1600.2.q.f.849.2 | 12 | 4.3 | odd | 2 |