Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + 376 x^{3} + 136 x^{2} + 48 x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(0.112275 + 0.345546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.u.729.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10296 | + | 0.801344i | 0.779907 | + | 0.566636i | 0.904951 | − | 0.425515i | \(-0.139907\pi\) |
−0.125044 | + | 0.992151i | \(0.539907\pi\) | |||||||
\(3\) | 0.112275 | − | 0.345546i | 0.0648218 | − | 0.199501i | −0.913400 | − | 0.407063i | \(-0.866553\pi\) |
0.978222 | + | 0.207562i | \(0.0665529\pi\) | |||||||
\(4\) | −0.0436753 | − | 0.134419i | −0.0218376 | − | 0.0672093i | ||||
\(5\) | −2.54139 | + | 1.84643i | −1.13655 | + | 0.825749i | −0.986634 | − | 0.162950i | \(-0.947899\pi\) |
−0.149912 | + | 0.988699i | \(0.547899\pi\) | |||||||
\(6\) | 0.400735 | − | 0.291151i | 0.163599 | − | 0.118862i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.902127 | − | 2.77646i | 0.318950 | − | 0.981627i | ||||
\(9\) | 2.32025 | + | 1.68576i | 0.773418 | + | 0.561921i | ||||
\(10\) | −4.28267 | −1.35430 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.0513514 | −0.0148239 | ||||||||
\(13\) | 3.86549 | + | 2.80844i | 1.07209 | + | 0.778922i | 0.976287 | − | 0.216478i | \(-0.0694570\pi\) |
0.0958065 | + | 0.995400i | \(0.469457\pi\) | |||||||
\(14\) | 0.421292 | − | 1.29660i | 0.112595 | − | 0.346532i | ||||
\(15\) | 0.352692 | + | 1.08548i | 0.0910647 | + | 0.280268i | ||||
\(16\) | 2.99122 | − | 2.17325i | 0.747805 | − | 0.543312i | ||||
\(17\) | 3.86549 | − | 2.80844i | 0.937519 | − | 0.681147i | −0.0103032 | − | 0.999947i | \(-0.503280\pi\) |
0.947822 | + | 0.318800i | \(0.103280\pi\) | |||||||
\(18\) | 1.20826 | + | 3.71865i | 0.284790 | + | 0.876493i | ||||
\(19\) | −2.16600 | + | 6.66627i | −0.496915 | + | 1.52935i | 0.317036 | + | 0.948413i | \(0.397312\pi\) |
−0.813951 | + | 0.580933i | \(0.802688\pi\) | |||||||
\(20\) | 0.359191 | + | 0.260967i | 0.0803175 | + | 0.0583541i | ||||
\(21\) | −0.363328 | −0.0792847 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.14134 | 1.07204 | 0.536021 | − | 0.844204i | \(-0.319927\pi\) | ||||
0.536021 | + | 0.844204i | \(0.319927\pi\) | |||||||
\(24\) | −0.858108 | − | 0.623452i | −0.175161 | − | 0.127262i | ||||
\(25\) | 1.50429 | − | 4.62974i | 0.300858 | − | 0.925947i | ||||
\(26\) | 2.01293 | + | 6.19518i | 0.394769 | + | 1.21497i | ||||
\(27\) | 1.72483 | − | 1.25316i | 0.331944 | − | 0.241171i | ||||
\(28\) | −0.114343 | + | 0.0830753i | −0.0216089 | + | 0.0156998i | ||||
\(29\) | 2.16600 | + | 6.66627i | 0.402216 | + | 1.23789i | 0.923197 | + | 0.384326i | \(0.125566\pi\) |
−0.520981 | + | 0.853568i | \(0.674434\pi\) | |||||||
\(30\) | −0.480835 | + | 1.47986i | −0.0877881 | + | 0.270184i | ||||
\(31\) | 2.94213 | + | 2.13758i | 0.528422 | + | 0.383921i | 0.819767 | − | 0.572697i | \(-0.194103\pi\) |
−0.291345 | + | 0.956618i | \(0.594103\pi\) | |||||||
\(32\) | −0.797984 | −0.141065 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.51399 | 1.11714 | ||||||||
\(35\) | 2.54139 | + | 1.84643i | 0.429574 | + | 0.312104i | ||||
\(36\) | 0.125260 | − | 0.385512i | 0.0208767 | − | 0.0642519i | ||||
\(37\) | −3.04938 | − | 9.38502i | −0.501315 | − | 1.54289i | −0.806879 | − | 0.590716i | \(-0.798845\pi\) |
0.305565 | − | 0.952171i | \(-0.401155\pi\) | |||||||
\(38\) | −7.73098 | + | 5.61689i | −1.25413 | + | 0.911179i | ||||
\(39\) | 1.40444 | − | 1.02039i | 0.224891 | − | 0.163393i | ||||
\(40\) | 2.83388 | + | 8.72180i | 0.448076 | + | 1.37904i | ||||
\(41\) | −0.995650 | + | 3.06430i | −0.155494 | + | 0.478563i | −0.998211 | − | 0.0597953i | \(-0.980955\pi\) |
0.842716 | + | 0.538358i | \(0.180955\pi\) | |||||||
\(42\) | −0.400735 | − | 0.291151i | −0.0618347 | − | 0.0449256i | ||||
\(43\) | 4.28267 | 0.653101 | 0.326551 | − | 0.945180i | \(-0.394114\pi\) | ||||
0.326551 | + | 0.945180i | \(0.394114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.00933 | −1.34303 | ||||||||
\(46\) | 5.67067 | + | 4.11998i | 0.836094 | + | 0.607458i | ||||
\(47\) | −0.240418 | + | 0.739929i | −0.0350685 | + | 0.107930i | −0.967059 | − | 0.254554i | \(-0.918071\pi\) |
0.931990 | + | 0.362484i | \(0.118071\pi\) | |||||||
\(48\) | −0.415119 | − | 1.27760i | −0.0599172 | − | 0.184406i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 5.36918 | − | 3.90094i | 0.759317 | − | 0.551676i | ||||
\(51\) | −0.536449 | − | 1.65102i | −0.0751179 | − | 0.231189i | ||||
\(52\) | 0.208681 | − | 0.642253i | 0.0289388 | − | 0.0890645i | ||||
\(53\) | −1.84672 | − | 1.34172i | −0.253667 | − | 0.184300i | 0.453684 | − | 0.891163i | \(-0.350110\pi\) |
−0.707350 | + | 0.706863i | \(0.750110\pi\) | |||||||
\(54\) | 2.90663 | 0.395542 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.91934 | −0.390114 | ||||||||
\(57\) | 2.06031 | + | 1.49691i | 0.272895 | + | 0.198270i | ||||
\(58\) | −2.95297 | + | 9.08831i | −0.387744 | + | 1.19335i | ||||
\(59\) | −0.112275 | − | 0.345546i | −0.0146169 | − | 0.0449862i | 0.943482 | − | 0.331424i | \(-0.107529\pi\) |
−0.958099 | + | 0.286437i | \(0.907529\pi\) | |||||||
\(60\) | 0.130504 | − | 0.0948168i | 0.0168480 | − | 0.0122408i | ||||
\(61\) | −2.60665 | + | 1.89384i | −0.333747 | + | 0.242481i | −0.742019 | − | 0.670379i | \(-0.766132\pi\) |
0.408272 | + | 0.912860i | \(0.366132\pi\) | |||||||
\(62\) | 1.53210 | + | 4.71532i | 0.194577 | + | 0.598846i | ||||
\(63\) | 0.886258 | − | 2.72762i | 0.111658 | − | 0.343648i | ||||
\(64\) | −6.86258 | − | 4.98596i | −0.857823 | − | 0.623245i | ||||
\(65\) | −15.0093 | −1.86168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.59465 | −0.805665 | −0.402832 | − | 0.915274i | \(-0.631974\pi\) | ||||
−0.402832 | + | 0.915274i | \(0.631974\pi\) | |||||||
\(68\) | −0.546333 | − | 0.396934i | −0.0662526 | − | 0.0481354i | ||||
\(69\) | 0.577241 | − | 1.77657i | 0.0694917 | − | 0.213873i | ||||
\(70\) | 1.32342 | + | 4.07306i | 0.158179 | + | 0.486824i | ||||
\(71\) | 12.2647 | − | 8.91082i | 1.45555 | − | 1.05752i | 0.471057 | − | 0.882103i | \(-0.343873\pi\) |
0.984494 | − | 0.175417i | \(-0.0561274\pi\) | |||||||
\(72\) | 6.77362 | − | 4.92132i | 0.798279 | − | 0.579984i | ||||
\(73\) | −0.995650 | − | 3.06430i | −0.116532 | − | 0.358649i | 0.875731 | − | 0.482799i | \(-0.160380\pi\) |
−0.992263 | + | 0.124150i | \(0.960380\pi\) | |||||||
\(74\) | 4.15730 | − | 12.7949i | 0.483277 | − | 1.48737i | ||||
\(75\) | −1.43089 | − | 1.03960i | −0.165225 | − | 0.120043i | ||||
\(76\) | 0.990671 | 0.113638 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.36672 | 0.267978 | ||||||||
\(79\) | 3.00738 | + | 2.18499i | 0.338357 | + | 0.245831i | 0.743968 | − | 0.668215i | \(-0.232941\pi\) |
−0.405611 | + | 0.914046i | \(0.632941\pi\) | |||||||
\(80\) | −3.58912 | + | 11.0462i | −0.401275 | + | 1.23500i | ||||
\(81\) | 2.41941 | + | 7.44616i | 0.268823 | + | 0.827351i | ||||
\(82\) | −3.55371 | + | 2.58192i | −0.392442 | + | 0.285126i | ||||
\(83\) | −1.25884 | + | 0.914603i | −0.138176 | + | 0.100391i | −0.654726 | − | 0.755866i | \(-0.727216\pi\) |
0.516550 | + | 0.856257i | \(0.327216\pi\) | |||||||
\(84\) | 0.0158685 | + | 0.0488381i | 0.00173139 | + | 0.00532867i | ||||
\(85\) | −4.63814 | + | 14.2747i | −0.503077 | + | 1.54831i | ||||
\(86\) | 4.72360 | + | 3.43189i | 0.509359 | + | 0.370071i | ||||
\(87\) | 2.54669 | 0.273034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.58532 | −0.592043 | −0.296021 | − | 0.955181i | \(-0.595660\pi\) | ||||
−0.296021 | + | 0.955181i | \(0.595660\pi\) | |||||||
\(90\) | −9.93689 | − | 7.21957i | −1.04744 | − | 0.761010i | ||||
\(91\) | 1.47649 | − | 4.54416i | 0.154778 | − | 0.476357i | ||||
\(92\) | −0.224549 | − | 0.691091i | −0.0234109 | − | 0.0720513i | ||||
\(93\) | 1.06896 | − | 0.776644i | 0.110846 | − | 0.0805342i | ||||
\(94\) | −0.858108 | + | 0.623452i | −0.0885071 | + | 0.0643042i | ||||
\(95\) | −6.80414 | − | 20.9410i | −0.698090 | − | 2.14850i | ||||
\(96\) | −0.0895933 | + | 0.275740i | −0.00914408 | + | 0.0281426i | ||||
\(97\) | −4.97599 | − | 3.61527i | −0.505235 | − | 0.367075i | 0.305778 | − | 0.952103i | \(-0.401084\pi\) |
−0.811013 | + | 0.585028i | \(0.801084\pi\) | |||||||
\(98\) | −1.36333 | −0.137717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.688023 | −0.0688023 | ||||||||
\(101\) | 8.73469 | + | 6.34612i | 0.869134 | + | 0.631463i | 0.930354 | − | 0.366662i | \(-0.119499\pi\) |
−0.0612206 | + | 0.998124i | \(0.519499\pi\) | |||||||
\(102\) | 0.731356 | − | 2.25088i | 0.0724150 | − | 0.222871i | ||||
\(103\) | −4.09159 | − | 12.5926i | −0.403156 | − | 1.24079i | −0.922425 | − | 0.386176i | \(-0.873796\pi\) |
0.519269 | − | 0.854611i | \(-0.326204\pi\) | |||||||
\(104\) | 11.2847 | − | 8.19881i | 1.10656 | − | 0.803959i | ||||
\(105\) | 0.923360 | − | 0.670861i | 0.0901107 | − | 0.0654693i | ||||
\(106\) | −0.961671 | − | 2.95972i | −0.0934057 | − | 0.287473i | ||||
\(107\) | 4.33200 | − | 13.3325i | 0.418791 | − | 1.28890i | −0.490026 | − | 0.871708i | \(-0.663013\pi\) |
0.908816 | − | 0.417197i | \(-0.136987\pi\) | |||||||
\(108\) | −0.243781 | − | 0.177117i | −0.0234578 | − | 0.0170431i | ||||
\(109\) | −15.5747 | −1.49178 | −0.745892 | − | 0.666067i | \(-0.767976\pi\) | ||||
−0.745892 | + | 0.666067i | \(0.767976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.58532 | −0.340304 | ||||||||
\(112\) | −2.99122 | − | 2.17325i | −0.282644 | − | 0.205353i | ||||
\(113\) | 1.27686 | − | 3.92977i | 0.120117 | − | 0.369682i | −0.872863 | − | 0.487965i | \(-0.837739\pi\) |
0.992980 | + | 0.118284i | \(0.0377392\pi\) | |||||||
\(114\) | 1.07290 | + | 3.30204i | 0.100486 | + | 0.309264i | ||||
\(115\) | −13.0662 | + | 9.49312i | −1.21843 | + | 0.885238i | ||||
\(116\) | 0.801470 | − | 0.582302i | 0.0744146 | − | 0.0540654i | ||||
\(117\) | 4.23455 | + | 13.0326i | 0.391484 | + | 1.20486i | ||||
\(118\) | 0.153067 | − | 0.471092i | 0.0140910 | − | 0.0433676i | ||||
\(119\) | −3.86549 | − | 2.80844i | −0.354349 | − | 0.257450i | ||||
\(120\) | 3.33195 | 0.304164 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.39263 | −0.397690 | ||||||||
\(123\) | 0.947068 | + | 0.688085i | 0.0853943 | + | 0.0620426i | ||||
\(124\) | 0.158833 | − | 0.488836i | 0.0142636 | − | 0.0438988i | ||||
\(125\) | −0.128143 | − | 0.394384i | −0.0114615 | − | 0.0352748i | ||||
\(126\) | 3.16327 | − | 2.29825i | 0.281806 | − | 0.204744i | ||||
\(127\) | −17.8135 | + | 12.9422i | −1.58069 | + | 1.14844i | −0.664791 | + | 0.747030i | \(0.731479\pi\) |
−0.915899 | + | 0.401408i | \(0.868521\pi\) | |||||||
\(128\) | −3.08047 | − | 9.48073i | −0.272278 | − | 0.837986i | ||||
\(129\) | 0.480835 | − | 1.47986i | 0.0423352 | − | 0.130294i | ||||
\(130\) | −16.5546 | − | 12.0276i | −1.45194 | − | 1.05489i | ||||
\(131\) | 15.0093 | 1.31137 | 0.655686 | − | 0.755034i | \(-0.272380\pi\) | ||||
0.655686 | + | 0.755034i | \(0.272380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00933 | 0.607786 | ||||||||
\(134\) | −7.27361 | − | 5.28458i | −0.628344 | − | 0.456519i | ||||
\(135\) | −2.06960 | + | 6.36956i | −0.178122 | + | 0.548204i | ||||
\(136\) | −4.31037 | − | 13.2660i | −0.369611 | − | 1.13755i | ||||
\(137\) | 8.65434 | − | 6.28775i | 0.739390 | − | 0.537198i | −0.153130 | − | 0.988206i | \(-0.548935\pi\) |
0.892520 | + | 0.451008i | \(0.148935\pi\) | |||||||
\(138\) | 2.06031 | − | 1.49691i | 0.175385 | − | 0.127425i | ||||
\(139\) | 1.26780 | + | 3.90190i | 0.107534 | + | 0.330955i | 0.990317 | − | 0.138826i | \(-0.0443329\pi\) |
−0.882783 | + | 0.469781i | \(0.844333\pi\) | |||||||
\(140\) | 0.137199 | − | 0.422254i | 0.0115954 | − | 0.0356870i | ||||
\(141\) | 0.228687 | + | 0.166151i | 0.0192589 | + | 0.0139924i | ||||
\(142\) | 20.6680 | 1.73442 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.6040 | 0.883665 | ||||||||
\(145\) | −17.8135 | − | 12.9422i | −1.47933 | − | 1.07479i | ||||
\(146\) | 1.35740 | − | 4.17764i | 0.112339 | − | 0.345744i | ||||
\(147\) | 0.112275 | + | 0.345546i | 0.00926025 | + | 0.0285001i | ||||
\(148\) | −1.12834 | + | 0.819786i | −0.0927489 | + | 0.0673860i | ||||
\(149\) | −11.3413 | + | 8.23996i | −0.929118 | + | 0.675044i | −0.945777 | − | 0.324817i | \(-0.894697\pi\) |
0.0166586 | + | 0.999861i | \(0.494697\pi\) | |||||||
\(150\) | −0.745130 | − | 2.29327i | −0.0608396 | − | 0.187245i | ||||
\(151\) | −2.11039 | + | 6.49511i | −0.171741 | + | 0.528564i | −0.999470 | − | 0.0325642i | \(-0.989633\pi\) |
0.827729 | + | 0.561129i | \(0.189633\pi\) | |||||||
\(152\) | 16.5546 | + | 12.0276i | 1.34276 | + | 0.975570i | ||||
\(153\) | 13.7033 | 1.10785 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4240 | −0.917598 | ||||||||
\(156\) | −0.198498 | − | 0.144217i | −0.0158926 | − | 0.0115466i | ||||
\(157\) | −7.24418 | + | 22.2953i | −0.578149 | + | 1.77936i | 0.0470494 | + | 0.998893i | \(0.485018\pi\) |
−0.625198 | + | 0.780466i | \(0.714982\pi\) | |||||||
\(158\) | 1.56608 | + | 4.81990i | 0.124591 | + | 0.383450i | ||||
\(159\) | −0.670966 | + | 0.487485i | −0.0532110 | + | 0.0386601i | ||||
\(160\) | 2.02799 | − | 1.47342i | 0.160327 | − | 0.116484i | ||||
\(161\) | −1.58876 | − | 4.88970i | −0.125212 | − | 0.385362i | ||||
\(162\) | −3.29844 | + | 10.1516i | −0.259150 | + | 0.797582i | ||||
\(163\) | 0.801470 | + | 0.582302i | 0.0627760 | + | 0.0456094i | 0.618731 | − | 0.785603i | \(-0.287647\pi\) |
−0.555955 | + | 0.831213i | \(0.687647\pi\) | |||||||
\(164\) | 0.455384 | 0.0355595 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.12136 | −0.164649 | ||||||||
\(167\) | −0.457373 | − | 0.332301i | −0.0353926 | − | 0.0257142i | 0.569948 | − | 0.821681i | \(-0.306963\pi\) |
−0.605341 | + | 0.795966i | \(0.706963\pi\) | |||||||
\(168\) | −0.327768 | + | 1.00877i | −0.0252879 | + | 0.0778280i | ||||
\(169\) | 3.03744 | + | 9.34828i | 0.233649 | + | 0.719098i | ||||
\(170\) | −16.5546 | + | 12.0276i | −1.26968 | + | 0.922478i | ||||
\(171\) | −16.2634 | + | 11.8161i | −1.24370 | + | 0.903598i | ||||
\(172\) | −0.187047 | − | 0.575671i | −0.0142622 | − | 0.0438945i | ||||
\(173\) | −5.32765 | + | 16.3968i | −0.405054 | + | 1.24663i | 0.515796 | + | 0.856711i | \(0.327496\pi\) |
−0.920850 | + | 0.389917i | \(0.872504\pi\) | |||||||
\(174\) | 2.80888 | + | 2.04077i | 0.212941 | + | 0.154711i | ||||
\(175\) | −4.86799 | −0.367986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.132007 | −0.00992228 | ||||||||
\(178\) | −6.16036 | − | 4.47576i | −0.461739 | − | 0.335473i | ||||
\(179\) | 3.49848 | − | 10.7672i | 0.261488 | − | 0.804778i | −0.730993 | − | 0.682385i | \(-0.760943\pi\) |
0.992482 | − | 0.122394i | \(-0.0390571\pi\) | |||||||
\(180\) | 0.393485 | + | 1.21102i | 0.0293286 | + | 0.0902642i | ||||
\(181\) | −12.0360 | + | 8.74467i | −0.894629 | + | 0.649986i | −0.937081 | − | 0.349112i | \(-0.886483\pi\) |
0.0424516 | + | 0.999099i | \(0.486483\pi\) | |||||||
\(182\) | 5.26993 | − | 3.82883i | 0.390633 | − | 0.283812i | ||||
\(183\) | 0.361748 | + | 1.11335i | 0.0267412 | + | 0.0823009i | ||||
\(184\) | 4.63814 | − | 14.2747i | 0.341928 | − | 1.05235i | ||||
\(185\) | 25.0785 | + | 18.2206i | 1.84381 | + | 1.33960i | ||||
\(186\) | 1.80137 | 0.132083 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.109961 | 0.00801970 | ||||||||
\(189\) | −1.72483 | − | 1.25316i | −0.125463 | − | 0.0911542i | ||||
\(190\) | 9.27628 | − | 28.5494i | 0.672972 | − | 2.07119i | ||||
\(191\) | 1.18951 | + | 3.66094i | 0.0860699 | + | 0.264896i | 0.984824 | − | 0.173558i | \(-0.0555263\pi\) |
−0.898754 | + | 0.438454i | \(0.855526\pi\) | |||||||
\(192\) | −2.49337 | + | 1.81154i | −0.179943 | + | 0.130737i | ||||
\(193\) | 2.06031 | − | 1.49691i | 0.148305 | − | 0.107750i | −0.511159 | − | 0.859486i | \(-0.670784\pi\) |
0.659463 | + | 0.751737i | \(0.270784\pi\) | |||||||
\(194\) | −2.59122 | − | 7.97497i | −0.186039 | − | 0.572569i | ||||
\(195\) | −1.68517 | + | 5.18641i | −0.120677 | + | 0.371406i | ||||
\(196\) | 0.114343 | + | 0.0830753i | 0.00816738 | + | 0.00593395i | ||||
\(197\) | −10.5467 | −0.751420 | −0.375710 | − | 0.926737i | \(-0.622601\pi\) | ||||
−0.375710 | + | 0.926737i | \(0.622601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6846 | 0.828302 | 0.414151 | − | 0.910208i | \(-0.364079\pi\) | ||||
0.414151 | + | 0.910208i | \(0.364079\pi\) | |||||||
\(200\) | −11.4972 | − | 8.35322i | −0.812976 | − | 0.590662i | ||||
\(201\) | −0.740412 | + | 2.27875i | −0.0522246 | + | 0.160731i | ||||
\(202\) | 4.54854 | + | 13.9990i | 0.320034 | + | 0.984965i | ||||
\(203\) | 5.67067 | − | 4.11998i | 0.398003 | − | 0.289166i | ||||
\(204\) | −0.198498 | + | 0.144217i | −0.0138977 | + | 0.0100972i | ||||
\(205\) | −3.12767 | − | 9.62599i | −0.218446 | − | 0.672308i | ||||
\(206\) | 5.57817 | − | 17.1679i | 0.388650 | − | 1.19614i | ||||
\(207\) | 11.9292 | + | 8.66708i | 0.829137 | + | 0.602404i | ||||
\(208\) | 17.6660 | 1.22492 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.55602 | 0.107375 | ||||||||
\(211\) | −8.98982 | − | 6.53149i | −0.618885 | − | 0.449646i | 0.233647 | − | 0.972322i | \(-0.424934\pi\) |
−0.852532 | + | 0.522675i | \(0.824934\pi\) | |||||||
\(212\) | −0.0996963 | + | 0.306834i | −0.00684717 | + | 0.0210734i | ||||
\(213\) | −1.70208 | − | 5.23847i | −0.116625 | − | 0.358934i | ||||
\(214\) | 15.4620 | − | 11.2338i | 1.05696 | − | 0.767925i | ||||
\(215\) | −10.8840 | + | 7.90766i | −0.742280 | + | 0.539298i | ||||
\(216\) | −1.92334 | − | 5.91944i | −0.130867 | − | 0.402767i | ||||
\(217\) | 1.12379 | − | 3.45868i | 0.0762881 | − | 0.234791i | ||||
\(218\) | −17.1782 | − | 12.4807i | −1.16345 | − | 0.845298i | ||||
\(219\) | −1.17064 | −0.0791046 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8294 | 1.53567 | ||||||||
\(222\) | −3.95445 | − | 2.87308i | −0.265405 | − | 0.192828i | ||||
\(223\) | 8.66505 | − | 26.6683i | 0.580255 | − | 1.78584i | −0.0372888 | − | 0.999305i | \(-0.511872\pi\) |
0.617544 | − | 0.786537i | \(-0.288128\pi\) | |||||||
\(224\) | 0.246591 | + | 0.758928i | 0.0164760 | + | 0.0507080i | ||||
\(225\) | 11.2950 | − | 8.20629i | 0.752999 | − | 0.547086i | ||||
\(226\) | 4.55742 | − | 3.31116i | 0.303155 | − | 0.220255i | ||||
\(227\) | −7.11027 | − | 21.8832i | −0.471925 | − | 1.45244i | −0.850060 | − | 0.526686i | \(-0.823434\pi\) |
0.378134 | − | 0.925751i | \(-0.376566\pi\) | |||||||
\(228\) | 0.111227 | − | 0.342322i | 0.00736620 | − | 0.0226708i | ||||
\(229\) | −10.8603 | − | 7.89043i | −0.717666 | − | 0.521415i | 0.167972 | − | 0.985792i | \(-0.446278\pi\) |
−0.885638 | + | 0.464377i | \(0.846278\pi\) | |||||||
\(230\) | −22.0187 | −1.45187 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.4626 | 1.34344 | ||||||||
\(233\) | 2.86178 | + | 2.07921i | 0.187482 | + | 0.136213i | 0.677567 | − | 0.735461i | \(-0.263034\pi\) |
−0.490085 | + | 0.871674i | \(0.663034\pi\) | |||||||
\(234\) | −5.77308 | + | 17.7677i | −0.377398 | + | 1.16151i | ||||
\(235\) | −0.755233 | − | 2.32437i | −0.0492659 | − | 0.151625i | ||||
\(236\) | −0.0415442 | + | 0.0301836i | −0.00270429 | + | 0.00196478i | ||||
\(237\) | 1.09267 | − | 0.793869i | 0.0709763 | − | 0.0515673i | ||||
\(238\) | −2.01293 | − | 6.19518i | −0.130479 | − | 0.401574i | ||||
\(239\) | 6.80414 | − | 20.9410i | 0.440123 | − | 1.35456i | −0.447621 | − | 0.894223i | \(-0.647729\pi\) |
0.887744 | − | 0.460337i | \(-0.152271\pi\) | |||||||
\(240\) | 3.41399 | + | 2.48041i | 0.220372 | + | 0.160110i | ||||
\(241\) | −0.315366 | −0.0203145 | −0.0101573 | − | 0.999948i | \(-0.503233\pi\) | ||||
−0.0101573 | + | 0.999948i | \(0.503233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065 | 0.592788 | ||||||||
\(244\) | 0.368413 | + | 0.267668i | 0.0235852 | + | 0.0171357i | ||||
\(245\) | 0.970726 | − | 2.98759i | 0.0620174 | − | 0.190870i | ||||
\(246\) | 0.493181 | + | 1.51786i | 0.0314441 | + | 0.0967749i | ||||
\(247\) | −27.0945 | + | 19.6853i | −1.72398 | + | 1.25255i | ||||
\(248\) | 8.58909 | − | 6.24034i | 0.545408 | − | 0.396262i | ||||
\(249\) | 0.174701 | + | 0.537675i | 0.0110712 | + | 0.0340737i | ||||
\(250\) | 0.174701 | − | 0.537675i | 0.0110491 | − | 0.0340055i | ||||
\(251\) | −15.0849 | − | 10.9598i | −0.952152 | − | 0.691779i | −0.000837449 | − | 1.00000i | \(-0.500267\pi\) |
−0.951315 | + | 0.308220i | \(0.900267\pi\) | |||||||
\(252\) | −0.405351 | −0.0255347 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −30.0187 | −1.88354 | ||||||||
\(255\) | 4.41182 | + | 3.20538i | 0.276279 | + | 0.200728i | ||||
\(256\) | −1.04285 | + | 3.20956i | −0.0651780 | + | 0.200597i | ||||
\(257\) | −2.64107 | − | 8.12838i | −0.164746 | − | 0.507035i | 0.834272 | − | 0.551353i | \(-0.185888\pi\) |
−0.999017 | + | 0.0443186i | \(0.985888\pi\) | |||||||
\(258\) | 1.71622 | − | 1.24690i | 0.106847 | − | 0.0776289i | ||||
\(259\) | −7.98337 | + | 5.80026i | −0.496063 | + | 0.360411i | ||||
\(260\) | 0.655536 | + | 2.01753i | 0.0406546 | + | 0.125122i | ||||
\(261\) | −6.21208 | + | 19.1188i | −0.384518 | + | 1.18342i | ||||
\(262\) | 16.5546 | + | 12.0276i | 1.02275 | + | 0.743070i | ||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.17064 | 0.440489 | ||||||||
\(266\) | 7.73098 | + | 5.61689i | 0.474017 | + | 0.344393i | ||||
\(267\) | −0.627090 | + | 1.92998i | −0.0383773 | + | 0.118113i | ||||
\(268\) | 0.288023 | + | 0.886444i | 0.0175938 | + | 0.0541482i | ||||
\(269\) | −6.11295 | + | 4.44131i | −0.372713 | + | 0.270792i | −0.758335 | − | 0.651865i | \(-0.773987\pi\) |
0.385622 | + | 0.922657i | \(0.373987\pi\) | |||||||
\(270\) | −7.38688 | + | 5.36688i | −0.449551 | + | 0.326618i | ||||
\(271\) | 4.33200 | + | 13.3325i | 0.263150 | + | 0.809894i | 0.992114 | + | 0.125341i | \(0.0400025\pi\) |
−0.728963 | + | 0.684553i | \(0.759998\pi\) | |||||||
\(272\) | 5.45909 | − | 16.8013i | 0.331006 | − | 1.01873i | ||||
\(273\) | −1.40444 | − | 1.02039i | −0.0850007 | − | 0.0617566i | ||||
\(274\) | 14.5840 | 0.881052 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.264015 | −0.0158918 | ||||||||
\(277\) | 4.86920 | + | 3.53768i | 0.292562 | + | 0.212558i | 0.724378 | − | 0.689403i | \(-0.242127\pi\) |
−0.431816 | + | 0.901962i | \(0.642127\pi\) | |||||||
\(278\) | −1.72843 | + | 5.31957i | −0.103665 | + | 0.319047i | ||||
\(279\) | 3.22303 | + | 9.91947i | 0.192958 | + | 0.593863i | ||||
\(280\) | 7.41920 | − | 5.39037i | 0.443382 | − | 0.322136i | ||||
\(281\) | 16.7208 | − | 12.1484i | 0.997479 | − | 0.724711i | 0.0359331 | − | 0.999354i | \(-0.488560\pi\) |
0.961546 | + | 0.274643i | \(0.0885597\pi\) | |||||||
\(282\) | 0.119087 | + | 0.366513i | 0.00709155 | + | 0.0218256i | ||||
\(283\) | 3.06420 | − | 9.43063i | 0.182148 | − | 0.560593i | −0.817740 | − | 0.575588i | \(-0.804773\pi\) |
0.999888 | + | 0.0149950i | \(0.00477324\pi\) | |||||||
\(284\) | −1.73344 | − | 1.25942i | −0.102861 | − | 0.0747329i | ||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.22199 | 0.190188 | ||||||||
\(288\) | −1.85153 | − | 1.34521i | −0.109102 | − | 0.0792674i | ||||
\(289\) | 1.80137 | − | 5.54405i | 0.105963 | − | 0.326121i | ||||
\(290\) | −9.27628 | − | 28.5494i | −0.544722 | − | 1.67648i | ||||
\(291\) | −1.80792 | + | 1.31353i | −0.105982 | + | 0.0770005i | ||||
\(292\) | −0.368413 | + | 0.267668i | −0.0215598 | + | 0.0156641i | ||||
\(293\) | −8.28062 | − | 25.4851i | −0.483759 | − | 1.48886i | −0.833770 | − | 0.552112i | \(-0.813822\pi\) |
0.350011 | − | 0.936746i | \(-0.386178\pi\) | |||||||
\(294\) | −0.153067 | + | 0.471092i | −0.00892706 | + | 0.0274747i | ||||
\(295\) | 0.923360 | + | 0.670861i | 0.0537601 | + | 0.0390590i | ||||
\(296\) | −28.8081 | −1.67443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1120 | −1.10713 | ||||||||
\(299\) | 19.8738 | + | 14.4391i | 1.14933 | + | 0.835037i | ||||
\(300\) | −0.0772475 | + | 0.237743i | −0.00445989 | + | 0.0137261i | ||||
\(301\) | −1.32342 | − | 4.07306i | −0.0762806 | − | 0.234767i | ||||
\(302\) | −7.53248 | + | 5.47267i | −0.433446 | + | 0.314917i | ||||
\(303\) | 3.17356 | − | 2.30572i | 0.182316 | − | 0.132460i | ||||
\(304\) | 8.00847 | + | 24.6475i | 0.459317 | + | 1.41363i | ||||
\(305\) | 3.12767 | − | 9.62599i | 0.179090 | − | 0.551182i | ||||
\(306\) | 15.1141 | + | 10.9811i | 0.864017 | + | 0.627745i | ||||
\(307\) | 11.8973 | 0.679015 | 0.339507 | − | 0.940603i | \(-0.389740\pi\) | ||||
0.339507 | + | 0.940603i | \(0.389740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.81070 | −0.273671 | ||||||||
\(310\) | −12.6002 | − | 9.15456i | −0.715642 | − | 0.519944i | ||||
\(311\) | −6.56372 | + | 20.2011i | −0.372195 | + | 1.14550i | 0.573157 | + | 0.819445i | \(0.305718\pi\) |
−0.945352 | + | 0.326052i | \(0.894282\pi\) | |||||||
\(312\) | −1.56608 | − | 4.81990i | −0.0886618 | − | 0.272873i | ||||
\(313\) | 10.2724 | − | 7.46332i | 0.580629 | − | 0.421852i | −0.258322 | − | 0.966059i | \(-0.583170\pi\) |
0.838951 | + | 0.544207i | \(0.183170\pi\) | |||||||
\(314\) | −25.8562 | + | 18.7856i | −1.45915 | + | 1.06014i | ||||
\(315\) | 2.78404 | + | 8.56838i | 0.156863 | + | 0.482774i | ||||
\(316\) | 0.162355 | − | 0.499678i | 0.00913320 | − | 0.0281091i | ||||
\(317\) | 9.60141 | + | 6.97583i | 0.539269 | + | 0.391802i | 0.823813 | − | 0.566861i | \(-0.191842\pi\) |
−0.284545 | + | 0.958663i | \(0.591842\pi\) | |||||||
\(318\) | −1.13069 | −0.0634059 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.6468 | 1.48960 | ||||||||
\(321\) | −4.12063 | − | 2.99381i | −0.229991 | − | 0.167098i | ||||
\(322\) | 2.16600 | − | 6.66627i | 0.120707 | − | 0.371497i | ||||
\(323\) | 10.3492 | + | 31.8515i | 0.575843 | + | 1.77226i | ||||
\(324\) | 0.895235 | − | 0.650426i | 0.0497353 | − | 0.0361348i | ||||
\(325\) | 18.8172 | − | 13.6715i | 1.04379 | − | 0.758357i | ||||
\(326\) | 0.417361 | + | 1.28451i | 0.0231155 | + | 0.0711422i | ||||
\(327\) | −1.74864 | + | 5.38176i | −0.0967000 | + | 0.297612i | ||||
\(328\) | 7.60970 | + | 5.52877i | 0.420175 | + | 0.305275i | ||||
\(329\) | 0.778008 | 0.0428930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8867 | −0.653349 | −0.326675 | − | 0.945137i | \(-0.605928\pi\) | ||||
−0.326675 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(332\) | 0.177920 | + | 0.129266i | 0.00976463 | + | 0.00709442i | ||||
\(333\) | 8.74559 | − | 26.9162i | 0.479255 | − | 1.47500i | ||||
\(334\) | −0.238175 | − | 0.733027i | −0.0130323 | − | 0.0401094i | ||||
\(335\) | 16.7596 | − | 12.1766i | 0.915675 | − | 0.665277i | ||||
\(336\) | −1.08679 | + | 0.789603i | −0.0592895 | + | 0.0430764i | ||||
\(337\) | 0.306134 | + | 0.942184i | 0.0166762 | + | 0.0513241i | 0.959048 | − | 0.283242i | \(-0.0914101\pi\) |
−0.942372 | + | 0.334567i | \(0.891410\pi\) | |||||||
\(338\) | −4.14103 | + | 12.7448i | −0.225242 | + | 0.693224i | ||||
\(339\) | −1.21456 | − | 0.882427i | −0.0659657 | − | 0.0479269i | ||||
\(340\) | 2.12136 | 0.115047 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −27.4066 | −1.48198 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 3.86351 | − | 11.8907i | 0.208307 | − | 0.641102i | ||||
\(345\) | 1.81331 | + | 5.58079i | 0.0976253 | + | 0.300460i | ||||
\(346\) | −19.0157 | + | 13.8157i | −1.02229 | + | 0.742736i | ||||
\(347\) | 12.2884 | − | 8.92805i | 0.659676 | − | 0.479283i | −0.206878 | − | 0.978367i | \(-0.566330\pi\) |
0.866553 | + | 0.499084i | \(0.166330\pi\) | |||||||
\(348\) | −0.111227 | − | 0.342322i | −0.00596241 | − | 0.0183504i | ||||
\(349\) | −9.17882 | + | 28.2495i | −0.491331 | + | 1.51216i | 0.331266 | + | 0.943537i | \(0.392524\pi\) |
−0.822597 | + | 0.568624i | \(0.807476\pi\) | |||||||
\(350\) | −5.36918 | − | 3.90094i | −0.286995 | − | 0.208514i | ||||
\(351\) | 10.1867 | 0.543728 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.71601 | −0.357457 | −0.178729 | − | 0.983898i | \(-0.557198\pi\) | ||||
−0.178729 | + | 0.983898i | \(0.557198\pi\) | |||||||
\(354\) | −0.145598 | − | 0.105783i | −0.00773846 | − | 0.00562232i | ||||
\(355\) | −14.7162 | + | 45.2918i | −0.781055 | + | 2.40384i | ||||
\(356\) | 0.243940 | + | 0.750771i | 0.0129288 | + | 0.0397908i | ||||
\(357\) | −1.40444 | + | 1.02039i | −0.0743309 | + | 0.0540046i | ||||
\(358\) | 12.4869 | − | 9.07226i | 0.659953 | − | 0.479484i | ||||
\(359\) | 5.48072 | + | 16.8679i | 0.289261 | + | 0.890255i | 0.985089 | + | 0.172046i | \(0.0550378\pi\) |
−0.695828 | + | 0.718209i | \(0.744962\pi\) | |||||||
\(360\) | −8.12756 | + | 25.0141i | −0.428360 | + | 1.31836i | ||||
\(361\) | −24.3762 | − | 17.7104i | −1.28296 | − | 0.932125i | ||||
\(362\) | −20.2827 | −1.06603 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.675305 | −0.0353956 | ||||||||
\(365\) | 8.18835 | + | 5.94919i | 0.428598 | + | 0.311395i | ||||
\(366\) | −0.493181 | + | 1.51786i | −0.0257790 | + | 0.0793396i | ||||
\(367\) | −2.50283 | − | 7.70290i | −0.130646 | − | 0.402088i | 0.864241 | − | 0.503078i | \(-0.167799\pi\) |
−0.994887 | + | 0.100990i | \(0.967799\pi\) | |||||||
\(368\) | 15.3789 | − | 11.1734i | 0.801679 | − | 0.582454i | ||||
\(369\) | −7.47584 | + | 5.43152i | −0.389177 | + | 0.282754i | ||||
\(370\) | 13.0595 | + | 40.1930i | 0.678930 | + | 2.08953i | ||||
\(371\) | −0.705385 | + | 2.17095i | −0.0366217 | + | 0.112710i | ||||
\(372\) | −0.151082 | − | 0.109768i | −0.00783326 | − | 0.00569120i | ||||
\(373\) | 0.565344 | 0.0292724 | 0.0146362 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146362 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.150665 | −0.00778030 | ||||||||
\(376\) | 1.83750 | + | 1.33502i | 0.0947617 | + | 0.0688484i | ||||
\(377\) | −10.3492 | + | 31.8515i | −0.533010 | + | 1.64043i | ||||
\(378\) | −0.898197 | − | 2.76437i | −0.0461983 | − | 0.142184i | ||||
\(379\) | 18.2320 | − | 13.2464i | 0.936517 | − | 0.680419i | −0.0110628 | − | 0.999939i | \(-0.503521\pi\) |
0.947580 | + | 0.319519i | \(0.103521\pi\) | |||||||
\(380\) | −2.51769 | + | 1.82921i | −0.129155 | + | 0.0938363i | ||||
\(381\) | 2.47214 | + | 7.60845i | 0.126651 | + | 0.389793i | ||||
\(382\) | −1.62169 | + | 4.99106i | −0.0829730 | + | 0.255365i | ||||
\(383\) | −17.3059 | − | 12.5735i | −0.884292 | − | 0.642476i | 0.0500914 | − | 0.998745i | \(-0.484049\pi\) |
−0.934383 | + | 0.356269i | \(0.884049\pi\) | |||||||
\(384\) | −3.62188 | −0.184828 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.47197 | 0.176719 | ||||||||
\(387\) | 9.93689 | + | 7.21957i | 0.505121 | + | 0.366992i | ||||
\(388\) | −0.268632 | + | 0.826764i | −0.0136377 | + | 0.0419726i | ||||
\(389\) | 3.29990 | + | 10.1560i | 0.167311 | + | 0.514932i | 0.999199 | − | 0.0400122i | \(-0.0127397\pi\) |
−0.831888 | + | 0.554944i | \(0.812740\pi\) | |||||||
\(390\) | −6.01476 | + | 4.36998i | −0.304569 | + | 0.221283i | ||||
\(391\) | 19.8738 | − | 14.4391i | 1.00506 | − | 0.730219i | ||||
\(392\) | 0.902127 | + | 2.77646i | 0.0455643 | + | 0.140232i | ||||
\(393\) | 1.68517 | − | 5.18641i | 0.0850054 | − | 0.261620i | ||||
\(394\) | −11.6325 | − | 8.45153i | −0.586038 | − | 0.425782i | ||||
\(395\) | −11.6774 | −0.587553 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9160 | −1.20031 | −0.600154 | − | 0.799885i | \(-0.704894\pi\) | ||||
−0.600154 | + | 0.799885i | \(0.704894\pi\) | |||||||
\(398\) | 12.8876 | + | 9.36341i | 0.645999 | + | 0.469346i | ||||
\(399\) | 0.786970 | − | 2.42204i | 0.0393978 | − | 0.121254i | ||||
\(400\) | −5.56190 | − | 17.1178i | −0.278095 | − | 0.855888i | ||||
\(401\) | −9.43210 | + | 6.85282i | −0.471017 | + | 0.342214i | −0.797837 | − | 0.602873i | \(-0.794023\pi\) |
0.326821 | + | 0.945086i | \(0.394023\pi\) | |||||||
\(402\) | −2.64271 | + | 1.92004i | −0.131806 | + | 0.0957628i | ||||
\(403\) | 5.36949 | + | 16.5256i | 0.267474 | + | 0.823199i | ||||
\(404\) | 0.471547 | − | 1.45127i | 0.0234603 | − | 0.0722035i | ||||
\(405\) | −19.8975 | − | 14.4564i | −0.988714 | − | 0.718343i | ||||
\(406\) | 9.55602 | 0.474257 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.06794 | −0.250900 | ||||||||
\(409\) | −26.5482 | − | 19.2884i | −1.31272 | − | 0.953748i | −0.999992 | − | 0.00390587i | \(-0.998757\pi\) |
−0.312729 | − | 0.949842i | \(-0.601243\pi\) | |||||||
\(410\) | 4.26404 | − | 13.1234i | 0.210586 | − | 0.648117i | ||||
\(411\) | −1.20104 | − | 3.69642i | −0.0592430 | − | 0.182331i | ||||
\(412\) | −1.51398 | + | 1.09997i | −0.0745884 | + | 0.0541917i | ||||
\(413\) | −0.293939 | + | 0.213559i | −0.0144638 | + | 0.0105086i | ||||
\(414\) | 6.21208 | + | 19.1188i | 0.305307 | + | 0.939638i | ||||
\(415\) | 1.51047 | − | 4.64873i | 0.0741458 | − | 0.228197i | ||||
\(416\) | −3.08460 | − | 2.24109i | −0.151235 | − | 0.109879i | ||||
\(417\) | 1.49063 | 0.0729964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7967 | 0.527452 | 0.263726 | − | 0.964598i | \(-0.415049\pi\) | ||||
0.263726 | + | 0.964598i | \(0.415049\pi\) | |||||||
\(420\) | −0.130504 | − | 0.0948168i | −0.00636795 | − | 0.00462659i | ||||
\(421\) | −0.355982 | + | 1.09560i | −0.0173495 | + | 0.0533963i | −0.959356 | − | 0.282197i | \(-0.908937\pi\) |
0.942007 | + | 0.335593i | \(0.108937\pi\) | |||||||
\(422\) | −4.68141 | − | 14.4079i | −0.227887 | − | 0.701365i | ||||
\(423\) | −1.80518 | + | 1.31154i | −0.0877707 | + | 0.0637691i | ||||
\(424\) | −5.39121 | + | 3.91695i | −0.261820 | + | 0.190224i | ||||
\(425\) | −7.18752 | − | 22.1209i | −0.348646 | − | 1.07302i | ||||
\(426\) | 2.32050 | − | 7.14175i | 0.112428 | − | 0.346019i | ||||
\(427\) | 2.60665 | + | 1.89384i | 0.126144 | + | 0.0916493i | ||||
\(428\) | −1.98134 | −0.0957718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3413 | −0.884495 | ||||||||
\(431\) | 25.8562 | + | 18.7856i | 1.24545 | + | 0.904873i | 0.997949 | − | 0.0640148i | \(-0.0203905\pi\) |
0.247501 | + | 0.968888i | \(0.420391\pi\) | |||||||
\(432\) | 2.43591 | − | 7.49697i | 0.117198 | − | 0.360698i | ||||
\(433\) | −1.36998 | − | 4.21635i | −0.0658369 | − | 0.202625i | 0.912726 | − | 0.408571i | \(-0.133973\pi\) |
−0.978563 | + | 0.205946i | \(0.933973\pi\) | |||||||
\(434\) | 4.01109 | − | 2.91423i | 0.192538 | − | 0.139887i | ||||
\(435\) | −6.47214 | + | 4.70228i | −0.310315 | + | 0.225457i | ||||
\(436\) | 0.680228 | + | 2.09353i | 0.0325770 | + | 0.100262i | ||||
\(437\) | −11.1361 | + | 34.2735i | −0.532714 | + | 1.63952i | ||||
\(438\) | −1.29116 | − | 0.938086i | −0.0616942 | − | 0.0448235i | ||||
\(439\) | −27.4720 | −1.31117 | −0.655583 | − | 0.755123i | \(-0.727577\pi\) | ||||
−0.655583 | + | 0.755123i | \(0.727577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86799 | −0.136571 | ||||||||
\(442\) | 25.1798 | + | 18.2942i | 1.19768 | + | 0.870165i | ||||
\(443\) | −2.40747 | + | 7.40942i | −0.114382 | + | 0.352032i | −0.991818 | − | 0.127662i | \(-0.959253\pi\) |
0.877435 | + | 0.479695i | \(0.159253\pi\) | |||||||
\(444\) | 0.156590 | + | 0.481934i | 0.00743142 | + | 0.0228716i | ||||
\(445\) | 14.1945 | − | 10.3129i | 0.672884 | − | 0.488879i | ||||
\(446\) | 30.9277 | − | 22.4703i | 1.46447 | − | 1.06400i | ||||
\(447\) | 1.57394 | + | 4.84409i | 0.0744448 | + | 0.229117i | ||||
\(448\) | −2.62127 | + | 8.06745i | −0.123844 | + | 0.381151i | ||||
\(449\) | −16.5934 | − | 12.0558i | −0.783092 | − | 0.568950i | 0.122813 | − | 0.992430i | \(-0.460808\pi\) |
−0.905905 | + | 0.423480i | \(0.860808\pi\) | |||||||
\(450\) | 19.0339 | 0.897268 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.584002 | −0.0274691 | ||||||||
\(453\) | 2.00741 | + | 1.45847i | 0.0943165 | + | 0.0685249i | ||||
\(454\) | 9.69364 | − | 29.8339i | 0.454945 | − | 1.40018i | ||||
\(455\) | 4.63814 | + | 14.2747i | 0.217439 | + | 0.669209i | ||||
\(456\) | 6.01476 | − | 4.36998i | 0.281667 | − | 0.204643i | ||||
\(457\) | 6.92951 | − | 5.03458i | 0.324149 | − | 0.235508i | −0.413795 | − | 0.910370i | \(-0.635797\pi\) |
0.737944 | + | 0.674862i | \(0.235797\pi\) | |||||||
\(458\) | −5.65542 | − | 17.4056i | −0.264261 | − | 0.813310i | ||||
\(459\) | 3.14788 | − | 9.68817i | 0.146930 | − | 0.452205i | ||||
\(460\) | 1.84672 | + | 1.34172i | 0.0861038 | + | 0.0625581i | ||||
\(461\) | 9.66598 | 0.450189 | 0.225095 | − | 0.974337i | \(-0.427731\pi\) | ||||
0.225095 | + | 0.974337i | \(0.427731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4240 | 0.530919 | 0.265459 | − | 0.964122i | \(-0.414476\pi\) | ||||
0.265459 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(464\) | 20.9664 | + | 15.2330i | 0.973343 | + | 0.707175i | ||||
\(465\) | −1.28263 | + | 3.94752i | −0.0594804 | + | 0.183062i | ||||
\(466\) | 1.49026 | + | 4.58655i | 0.0690349 | + | 0.212468i | ||||
\(467\) | −14.7408 | + | 10.7098i | −0.682124 | + | 0.495592i | −0.874062 | − | 0.485815i | \(-0.838523\pi\) |
0.191937 | + | 0.981407i | \(0.438523\pi\) | |||||||
\(468\) | 1.56688 | − | 1.13840i | 0.0724290 | − | 0.0526228i | ||||
\(469\) | 2.03786 | + | 6.27188i | 0.0940996 | + | 0.289609i | ||||
\(470\) | 1.02963 | − | 3.16888i | 0.0474933 | − | 0.146169i | ||||
\(471\) | 6.89071 | + | 5.00639i | 0.317507 | + | 0.230682i | ||||
\(472\) | −1.06068 | −0.0488218 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.84132 | 0.0845749 | ||||||||
\(475\) | 27.6048 | + | 20.0560i | 1.26659 | + | 0.920234i | ||||
\(476\) | −0.208681 | + | 0.642253i | −0.00956487 | + | 0.0294376i | ||||
\(477\) | −2.02304 | − | 6.22627i | −0.0926285 | − | 0.285081i | ||||
\(478\) | 24.2856 | − | 17.6445i | 1.11080 | − | 0.807042i | ||||
\(479\) | −2.80888 | + | 2.04077i | −0.128341 | + | 0.0932453i | −0.650104 | − | 0.759845i | \(-0.725275\pi\) |
0.521763 | + | 0.853091i | \(0.325275\pi\) | |||||||
\(480\) | −0.281443 | − | 0.866192i | −0.0128460 | − | 0.0395361i | ||||
\(481\) | 14.5699 | − | 44.8417i | 0.664333 | − | 2.04461i | ||||
\(482\) | −0.347835 | − | 0.252717i | −0.0158434 | − | 0.0115109i | ||||
\(483\) | −1.86799 | −0.0849966 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.3213 | 0.877335 | ||||||||
\(486\) | 10.1920 | + | 7.40494i | 0.462320 | + | 0.335895i | ||||
\(487\) | −8.48602 | + | 26.1173i | −0.384538 | + | 1.18349i | 0.552277 | + | 0.833661i | \(0.313759\pi\) |
−0.936815 | + | 0.349826i | \(0.886241\pi\) | |||||||
\(488\) | 2.90665 | + | 8.94574i | 0.131578 | + | 0.404954i | ||||
\(489\) | 0.291197 | − | 0.211567i | 0.0131684 | − | 0.00956738i | ||||
\(490\) | 3.46475 | − | 2.51729i | 0.156522 | − | 0.113720i | ||||
\(491\) | −1.93569 | − | 5.95743i | −0.0873563 | − | 0.268855i | 0.897830 | − | 0.440342i | \(-0.145143\pi\) |
−0.985186 | + | 0.171487i | \(0.945143\pi\) | |||||||
\(492\) | 0.0511280 | − | 0.157356i | 0.00230503 | − | 0.00709415i | ||||
\(493\) | 27.0945 | + | 19.6853i | 1.22027 | + | 0.886581i | ||||
\(494\) | −45.6587 | −2.05428 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.4461 | 0.603746 | ||||||||
\(497\) | −12.2647 | − | 8.91082i | −0.550147 | − | 0.399705i | ||||
\(498\) | −0.238175 | + | 0.733027i | −0.0106729 | + | 0.0328477i | ||||
\(499\) | −6.38678 | − | 19.6565i | −0.285911 | − | 0.879945i | −0.986124 | − | 0.166010i | \(-0.946911\pi\) |
0.700213 | − | 0.713934i | \(-0.253089\pi\) | |||||||
\(500\) | −0.0474158 | + | 0.0344496i | −0.00212050 | + | 0.00154063i | ||||
\(501\) | −0.166177 | + | 0.120734i | −0.00742422 | + | 0.00539401i | ||||
\(502\) | −7.85540 | − | 24.1764i | −0.350604 | − | 1.07905i | ||||
\(503\) | 6.80414 | − | 20.9410i | 0.303382 | − | 0.933712i | −0.676895 | − | 0.736080i | \(-0.736675\pi\) |
0.980276 | − | 0.197633i | \(-0.0633253\pi\) | |||||||
\(504\) | −6.77362 | − | 4.92132i | −0.301721 | − | 0.219213i | ||||
\(505\) | −33.9160 | −1.50924 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.57128 | 0.158606 | ||||||||
\(508\) | 2.51769 | + | 1.82921i | 0.111704 | + | 0.0811579i | ||||
\(509\) | 6.62038 | − | 20.3754i | 0.293443 | − | 0.903126i | −0.690297 | − | 0.723527i | \(-0.742520\pi\) |
0.983740 | − | 0.179599i | \(-0.0574801\pi\) | |||||||
\(510\) | 2.29743 | + | 7.07078i | 0.101732 | + | 0.313099i | ||||
\(511\) | −2.60665 | + | 1.89384i | −0.115311 | + | 0.0837785i | ||||
\(512\) | −19.8517 | + | 14.4231i | −0.877332 | + | 0.637419i | ||||
\(513\) | 4.61793 | + | 14.2125i | 0.203887 | + | 0.627499i | ||||
\(514\) | 3.60065 | − | 11.0817i | 0.158818 | − | 0.488791i | ||||
\(515\) | 33.6497 | + | 24.4479i | 1.48278 | + | 1.07731i | ||||
\(516\) | −0.219921 | −0.00968149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.4533 | −0.591105 | ||||||||
\(519\) | 5.06769 | + | 3.68190i | 0.222447 | + | 0.161617i | ||||
\(520\) | −13.5403 | + | 41.6728i | −0.593782 | + | 1.82747i | ||||
\(521\) | 4.30932 | + | 13.2627i | 0.188795 | + | 0.581051i | 0.999993 | − | 0.00372050i | \(-0.00118427\pi\) |
−0.811198 | + | 0.584771i | \(0.801184\pi\) | |||||||
\(522\) | −22.1724 | + | 16.1092i | −0.970459 | + | 0.705080i | ||||
\(523\) | 14.9517 | − | 10.8630i | 0.653792 | − | 0.475007i | −0.210769 | − | 0.977536i | \(-0.567597\pi\) |
0.864561 | + | 0.502529i | \(0.167597\pi\) | |||||||
\(524\) | −0.655536 | − | 2.01753i | −0.0286372 | − | 0.0881364i | ||||
\(525\) | −0.546552 | + | 1.68211i | −0.0238535 | + | 0.0734135i | ||||
\(526\) | 17.6473 | + | 12.8215i | 0.769458 | + | 0.559044i | ||||
\(527\) | 17.3760 | 0.756912 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.43334 | 0.149276 | ||||||||
\(530\) | 7.90890 | + | 5.74615i | 0.343541 | + | 0.249597i | ||||
\(531\) | 0.322003 | − | 0.991022i | 0.0139737 | − | 0.0430067i | ||||
\(532\) | −0.306134 | − | 0.942184i | −0.0132726 | − | 0.0408489i | ||||
\(533\) | −12.4546 | + | 9.04878i | −0.539468 | + | 0.391946i | ||||
\(534\) | −2.23823 | + | 1.62617i | −0.0968578 | + | 0.0703713i | ||||
\(535\) | 13.6083 | + | 41.8820i | 0.588337 | + | 1.81072i | ||||
\(536\) | −5.94921 | + | 18.3098i | −0.256967 | + | 0.790862i | ||||
\(537\) | −3.32777 | − | 2.41777i | −0.143604 | − | 0.104334i | ||||
\(538\) | −10.3013 | −0.444122 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.946578 | 0.0407342 | ||||||||
\(541\) | −30.3004 | − | 22.0145i | −1.30271 | − | 0.946477i | −0.302736 | − | 0.953074i | \(-0.597900\pi\) |
−0.999978 | + | 0.00659687i | \(0.997900\pi\) | |||||||
\(542\) | −5.90594 | + | 18.1766i | −0.253682 | + | 0.780753i | ||||
\(543\) | 1.67035 | + | 5.14079i | 0.0716814 | + | 0.220613i | ||||
\(544\) | −3.08460 | + | 2.24109i | −0.132251 | + | 0.0960860i | ||||
\(545\) | 39.5814 | − | 28.7576i | 1.69548 | − | 1.23184i | ||||
\(546\) | −0.731356 | − | 2.25088i | −0.0312991 | − | 0.0963289i | ||||
\(547\) | −5.29367 | + | 16.2923i | −0.226341 | + | 0.696606i | 0.771812 | + | 0.635851i | \(0.219351\pi\) |
−0.998153 | + | 0.0607551i | \(0.980649\pi\) | |||||||
\(548\) | −1.22317 | − | 0.888686i | −0.0522513 | − | 0.0379628i | ||||
\(549\) | −9.24065 | −0.394381 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.1307 | −2.09304 | ||||||||
\(552\) | −4.41182 | − | 3.20538i | −0.187780 | − | 0.136430i | ||||
\(553\) | 1.14872 | − | 3.53539i | 0.0488484 | − | 0.150340i | ||||
\(554\) | 2.53561 | + | 7.80380i | 0.107728 | + | 0.331552i | ||||
\(555\) | 9.11171 | − | 6.62005i | 0.386771 | − | 0.281005i | ||||
\(556\) | 0.469117 | − | 0.340833i | 0.0198950 | − | 0.0144545i | ||||
\(557\) | 7.59111 | + | 23.3630i | 0.321646 | + | 0.989923i | 0.972932 | + | 0.231091i | \(0.0742296\pi\) |
−0.651286 | + | 0.758832i | \(0.725770\pi\) | |||||||
\(558\) | −4.39405 | + | 13.5235i | −0.186015 | + | 0.572495i | ||||
\(559\) | 16.5546 | + | 12.0276i | 0.700186 | + | 0.508715i | ||||
\(560\) | 11.6146 | 0.490807 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.1773 | 1.18859 | ||||||||
\(563\) | 12.1428 | + | 8.82226i | 0.511758 | + | 0.371814i | 0.813490 | − | 0.581579i | \(-0.197565\pi\) |
−0.301732 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(564\) | 0.0123458 | − | 0.0379964i | 0.000519851 | − | 0.00159994i | ||||
\(565\) | 4.01105 | + | 12.3447i | 0.168746 | + | 0.519347i | ||||
\(566\) | 10.9369 | − | 7.94609i | 0.459710 | − | 0.333999i | ||||
\(567\) | 6.33408 | − | 4.60198i | 0.266007 | − | 0.193265i | ||||
\(568\) | −13.6762 | − | 42.0911i | −0.573842 | − | 1.76610i | ||||
\(569\) | 3.73994 | − | 11.5104i | 0.156786 | − | 0.482539i | −0.841551 | − | 0.540178i | \(-0.818357\pi\) |
0.998338 | + | 0.0576384i | \(0.0183571\pi\) | |||||||
\(570\) | −8.82365 | − | 6.41075i | −0.369582 | − | 0.268517i | ||||
\(571\) | 38.9439 | 1.62975 | 0.814877 | − | 0.579634i | \(-0.196805\pi\) | ||||
0.814877 | + | 0.579634i | \(0.196805\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39857 | 0.0584262 | ||||||||
\(574\) | 3.55371 | + | 2.58192i | 0.148329 | + | 0.107767i | ||||
\(575\) | 7.73407 | − | 23.8030i | 0.322533 | − | 0.992655i | ||||
\(576\) | −7.51779 | − | 23.1374i | −0.313241 | − | 0.964058i | ||||
\(577\) | −30.8645 | + | 22.4244i | −1.28491 | + | 0.933540i | −0.999689 | − | 0.0249227i | \(-0.992066\pi\) |
−0.285218 | + | 0.958463i | \(0.592066\pi\) | |||||||
\(578\) | 6.42953 | − | 4.67132i | 0.267433 | − | 0.194301i | ||||
\(579\) | −0.285928 | − | 0.879997i | −0.0118828 | − | 0.0365714i | ||||
\(580\) | −0.961671 | + | 2.95972i | −0.0399312 | + | 0.122896i | ||||
\(581\) | 1.25884 | + | 0.914603i | 0.0522256 | + | 0.0379441i | ||||
\(582\) | −3.04664 | −0.126287 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.40610 | −0.389227 | ||||||||
\(585\) | −34.8255 | − | 25.3022i | −1.43986 | − | 1.04612i | ||||
\(586\) | 11.2892 | − | 34.7446i | 0.466353 | − | 1.43529i | ||||
\(587\) | −10.7528 | − | 33.0936i | −0.443814 | − | 1.36592i | −0.883779 | − | 0.467904i | \(-0.845009\pi\) |
0.439965 | − | 0.898015i | \(-0.354991\pi\) | |||||||
\(588\) | 0.0415442 | − | 0.0301836i | 0.00171325 | − | 0.00124475i | ||||
\(589\) | −20.6224 | + | 14.9830i | −0.849729 | + | 0.617364i | ||||
\(590\) | 0.480835 | + | 1.47986i | 0.0197957 | + | 0.0609248i | ||||
\(591\) | −1.18413 | + | 3.64436i | −0.0487084 | + | 0.149909i | ||||
\(592\) | −29.5173 | − | 21.4456i | −1.21316 | − | 0.881409i | ||||
\(593\) | −18.5913 | −0.763452 | −0.381726 | − | 0.924276i | \(-0.624670\pi\) | ||||
−0.381726 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0093 | 0.615322 | ||||||||
\(596\) | 1.60294 | + | 1.16460i | 0.0656590 | + | 0.0477040i | ||||
\(597\) | 1.31189 | − | 4.03757i | 0.0536920 | − | 0.165247i | ||||
\(598\) | 10.3492 | + | 31.8515i | 0.423209 | + | 1.30250i | ||||
\(599\) | −19.9569 | + | 14.4995i | −0.815416 | + | 0.592434i | −0.915396 | − | 0.402555i | \(-0.868122\pi\) |
0.0999801 | + | 0.994989i | \(0.468122\pi\) | |||||||
\(600\) | −4.17726 | + | 3.03496i | −0.170536 | + | 0.123902i | ||||
\(601\) | −9.31025 | − | 28.6540i | −0.379773 | − | 1.16882i | −0.940201 | − | 0.340619i | \(-0.889363\pi\) |
0.560428 | − | 0.828203i | \(-0.310637\pi\) | |||||||
\(602\) | 1.80425 | − | 5.55292i | 0.0735359 | − | 0.226320i | ||||
\(603\) | −15.3013 | − | 11.1170i | −0.623116 | − | 0.452720i | ||||
\(604\) | 0.965235 | 0.0392749 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.34797 | 0.217247 | ||||||||
\(607\) | 11.0501 | + | 8.02839i | 0.448511 | + | 0.325862i | 0.789008 | − | 0.614383i | \(-0.210595\pi\) |
−0.340497 | + | 0.940246i | \(0.610595\pi\) | |||||||
\(608\) | 1.72843 | − | 5.31957i | 0.0700973 | − | 0.215737i | ||||
\(609\) | −0.786970 | − | 2.42204i | −0.0318896 | − | 0.0981461i | ||||
\(610\) | 11.1634 | − | 8.11069i | 0.451993 | − | 0.328392i | ||||
\(611\) | −3.00738 | + | 2.18499i | −0.121666 | + | 0.0883953i | ||||
\(612\) | −0.598495 | − | 1.84198i | −0.0241927 | − | 0.0744575i | ||||
\(613\) | −13.9144 | + | 42.8242i | −0.561998 | + | 1.72965i | 0.114709 | + | 0.993399i | \(0.463406\pi\) |
−0.676707 | + | 0.736252i | \(0.736594\pi\) | |||||||
\(614\) | 13.1222 | + | 9.53383i | 0.529569 | + | 0.384754i | ||||
\(615\) | −3.67738 | −0.148286 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.26401 | −0.332697 | −0.166348 | − | 0.986067i | \(-0.553198\pi\) | ||||
−0.166348 | + | 0.986067i | \(0.553198\pi\) | |||||||
\(618\) | −5.30599 | − | 3.85503i | −0.213438 | − | 0.155072i | ||||
\(619\) | 13.3032 | − | 40.9430i | 0.534700 | − | 1.64564i | −0.209595 | − | 0.977788i | \(-0.567215\pi\) |
0.744296 | − | 0.667850i | \(-0.232785\pi\) | |||||||
\(620\) | 0.498947 | + | 1.53560i | 0.0200382 | + | 0.0616712i | ||||
\(621\) | 8.86793 | − | 6.44293i | 0.355858 | − | 0.258546i | ||||
\(622\) | −23.4275 | + | 17.0211i | −0.939357 | + | 0.682483i | ||||
\(623\) | 1.72596 | + | 5.31196i | 0.0691491 | + | 0.212819i | ||||
\(624\) | 1.98344 | − | 6.10440i | 0.0794012 | − | 0.244372i | ||||
\(625\) | 20.7453 | + | 15.0723i | 0.829812 | + | 0.602894i | ||||
\(626\) | 17.3107 | 0.691873 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.31330 | 0.132215 | ||||||||
\(629\) | −38.1446 | − | 27.7137i | −1.52093 | − | 1.10502i | ||||
\(630\) | −3.79555 | + | 11.6815i | −0.151219 | + | 0.465403i | ||||
\(631\) | 0.320955 | + | 0.987799i | 0.0127770 | + | 0.0393237i | 0.957242 | − | 0.289289i | \(-0.0934189\pi\) |
−0.944465 | + | 0.328613i | \(0.893419\pi\) | |||||||
\(632\) | 8.77958 | − | 6.37874i | 0.349233 | − | 0.253733i | ||||
\(633\) | −3.26626 | + | 2.37307i | −0.129822 | + | 0.0943212i | ||||
\(634\) | 4.99989 | + | 15.3881i | 0.198571 | + | 0.611138i | ||||
\(635\) | 21.3741 | − | 65.7827i | 0.848205 | − | 2.61051i | ||||
\(636\) | 0.0948317 | + | 0.0688993i | 0.00376032 | + | 0.00273203i | ||||
\(637\) | −4.77801 | −0.189312 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.4787 | 1.71999 | ||||||||
\(640\) | 25.3342 | + | 18.4064i | 1.00142 | + | 0.727576i | ||||
\(641\) | 10.3957 | − | 31.9948i | 0.410607 | − | 1.26372i | −0.505515 | − | 0.862818i | \(-0.668698\pi\) |
0.916122 | − | 0.400900i | \(-0.131302\pi\) | |||||||
\(642\) | −2.14580 | − | 6.60408i | −0.0846878 | − | 0.260642i | ||||
\(643\) | 17.0147 | − | 12.3619i | 0.670996 | − | 0.487507i | −0.199363 | − | 0.979926i | \(-0.563887\pi\) |
0.870358 | + | 0.492419i | \(0.163887\pi\) | |||||||
\(644\) | −0.587877 | + | 0.427118i | −0.0231656 | + | 0.0168308i | ||||
\(645\) | 1.51047 | + | 4.64873i | 0.0594745 | + | 0.183044i | ||||
\(646\) | −14.1093 | + | 43.4240i | −0.555124 | + | 1.70850i | ||||
\(647\) | −20.4115 | − | 14.8298i | −0.802459 | − | 0.583021i | 0.109176 | − | 0.994022i | \(-0.465179\pi\) |
−0.911634 | + | 0.411002i | \(0.865179\pi\) | |||||||
\(648\) | 22.8566 | 0.897892 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 31.7101 | 1.24377 | ||||||||
\(651\) | −1.06896 | − | 0.776644i | −0.0418958 | − | 0.0304391i | ||||
\(652\) | 0.0432678 | − | 0.133165i | 0.00169450 | − | 0.00521513i | ||||
\(653\) | 6.37772 | + | 19.6286i | 0.249580 | + | 0.768127i | 0.994849 | + | 0.101364i | \(0.0323207\pi\) |
−0.745270 | + | 0.666763i | \(0.767679\pi\) | |||||||
\(654\) | −6.24132 | + | 4.53458i | −0.244055 | + | 0.177316i | ||||
\(655\) | −38.1446 | + | 27.7137i | −1.49043 | + | 1.08286i | ||||
\(656\) | 3.68127 | + | 11.3298i | 0.143729 | + | 0.442354i | ||||
\(657\) | 2.85552 | − | 8.78838i | 0.111404 | − | 0.342867i | ||||
\(658\) | 0.858108 | + | 0.623452i | 0.0334525 | + | 0.0243047i | ||||
\(659\) | −18.5067 | −0.720920 | −0.360460 | − | 0.932775i | \(-0.617380\pi\) | ||||
−0.360460 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8001 | 0.653446 | 0.326723 | − | 0.945120i | \(-0.394056\pi\) | ||||
0.326723 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(662\) | −13.1104 | − | 9.52530i | −0.509552 | − | 0.370211i | ||||
\(663\) | 2.56316 | − | 7.88859i | 0.0995448 | − | 0.306367i | ||||
\(664\) | 1.40372 | + | 4.32022i | 0.0544750 | + | 0.167657i | ||||
\(665\) | −17.8135 | + | 12.9422i | −0.690777 | + | 0.501879i | ||||
\(666\) | 31.2151 | − | 22.6791i | 1.20956 | − | 0.878798i | ||||
\(667\) | 11.1361 | + | 34.2735i | 0.431193 | + | 1.32708i | ||||
\(668\) | −0.0246916 | + | 0.0759928i | −0.000955345 | + | 0.00294025i | ||||
\(669\) | −8.24225 | − | 5.98834i | −0.318664 | − | 0.231523i | ||||
\(670\) | 28.2427 | 1.09111 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.289930 | 0.0111843 | ||||||||
\(673\) | −14.2031 | − | 10.3192i | −0.547490 | − | 0.397775i | 0.279369 | − | 0.960184i | \(-0.409875\pi\) |
−0.826859 | + | 0.562409i | \(0.809875\pi\) | |||||||
\(674\) | −0.417361 | + | 1.28451i | −0.0160762 | + | 0.0494773i | ||||
\(675\) | −3.20716 | − | 9.87063i | −0.123444 | − | 0.379921i | ||||
\(676\) | 1.12392 | − | 0.816577i | 0.0432278 | − | 0.0314068i | ||||
\(677\) | 2.95074 | − | 2.14384i | 0.113406 | − | 0.0823945i | −0.529637 | − | 0.848225i | \(-0.677672\pi\) |
0.643043 | + | 0.765830i | \(0.277672\pi\) | |||||||
\(678\) | −0.632475 | − | 1.94656i | −0.0242900 | − | 0.0747570i | ||||
\(679\) | −1.90066 | + | 5.84963i | −0.0729406 | + | 0.224488i | ||||
\(680\) | 35.4490 | + | 25.7552i | 1.35941 | + | 0.987668i | ||||
\(681\) | −8.35994 | −0.320354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4720 | 1.05119 | 0.525593 | − | 0.850736i | \(-0.323844\pi\) | ||||
0.525593 | + | 0.850736i | \(0.323844\pi\) | |||||||
\(684\) | 2.29861 | + | 1.67004i | 0.0878895 | + | 0.0638555i | ||||
\(685\) | −10.3842 | + | 31.9593i | −0.396760 | + | 1.22110i | ||||
\(686\) | 0.421292 | + | 1.29660i | 0.0160850 | + | 0.0495045i | ||||
\(687\) | −3.94584 | + | 2.86682i | −0.150543 | + | 0.109376i | ||||
\(688\) | 12.8104 | − | 9.30731i | 0.488393 | − | 0.354838i | ||||
\(689\) | −3.37033 | − | 10.3728i | −0.128399 | − | 0.395173i | ||||
\(690\) | −2.47214 | + | 7.60845i | −0.0941126 | + | 0.289649i | ||||
\(691\) | 4.81904 | + | 3.50124i | 0.183325 | + | 0.133193i | 0.675663 | − | 0.737211i | \(-0.263858\pi\) |
−0.492338 | + | 0.870404i | \(0.663858\pi\) | |||||||
\(692\) | 2.43673 | 0.0926304 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.7080 | 0.786065 | ||||||||
\(695\) | −10.4266 | − | 7.57536i | −0.395503 | − | 0.287350i | ||||
\(696\) | 2.29743 | − | 7.07078i | 0.0870840 | − | 0.268017i | ||||
\(697\) | 4.75723 | + | 14.6412i | 0.180193 | + | 0.554576i | ||||
\(698\) | −32.7614 | + | 23.8026i | −1.24004 | + | 0.900940i | ||||
\(699\) | 1.03977 | − | 0.755435i | 0.0393276 | − | 0.0285732i | ||||
\(700\) | 0.212611 | + | 0.654349i | 0.00803593 | + | 0.0247321i | ||||
\(701\) | 2.27723 | − | 7.00859i | 0.0860097 | − | 0.264711i | −0.898797 | − | 0.438365i | \(-0.855558\pi\) |
0.984807 | + | 0.173655i | \(0.0555576\pi\) | |||||||
\(702\) | 11.2355 | + | 8.16309i | 0.424058 | + | 0.308096i | ||||
\(703\) | 69.1680 | 2.60872 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.887968 | −0.0334428 | ||||||||
\(706\) | −7.40746 | − | 5.38184i | −0.278783 | − | 0.202548i | ||||
\(707\) | 3.33635 | − | 10.2682i | 0.125476 | − | 0.386177i | ||||
\(708\) | 0.00576546 | + | 0.0177443i | 0.000216679 | + | 0.000666870i | ||||
\(709\) | 28.0858 | − | 20.4056i | 1.05479 | − | 0.766347i | 0.0816692 | − | 0.996659i | \(-0.473975\pi\) |
0.973117 | + | 0.230313i | \(0.0739749\pi\) | |||||||
\(710\) | −52.5257 | + | 38.1621i | −1.97125 | + | 1.43220i | ||||
\(711\) | 3.29451 | + | 10.1395i | 0.123554 | + | 0.380260i | ||||
\(712\) | −5.03867 | + | 15.5074i | −0.188832 | + | 0.581165i | ||||
\(713\) | 15.1265 | + | 10.9900i | 0.566491 | + | 0.411580i | ||||
\(714\) | −2.36672 | −0.0885722 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.60011 | −0.0597989 | ||||||||
\(717\) | −6.47214 | − | 4.70228i | −0.241706 | − | 0.175610i | ||||
\(718\) | −7.47202 | + | 22.9965i | −0.278853 | + | 0.858222i | ||||
\(719\) | −1.25523 | − | 3.86319i | −0.0468121 | − | 0.144073i | 0.924918 | − | 0.380166i | \(-0.124133\pi\) |
−0.971730 | + | 0.236093i | \(0.924133\pi\) | |||||||
\(720\) | −26.9489 | + | 19.5795i | −1.00433 | + | 0.729685i | ||||
\(721\) | −10.7119 | + | 7.78266i | −0.398932 | + | 0.289841i | ||||
\(722\) | −12.6938 | − | 39.0675i | −0.472415 | − | 1.45394i | ||||
\(723\) | −0.0354076 | + | 0.108973i | −0.00131682 | + | 0.00405277i | ||||
\(724\) | 1.70112 | + | 1.23594i | 0.0632217 | + | 0.0459333i | ||||
\(725\) | 34.1214 | 1.26724 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5433 | −1.13279 | −0.566394 | − | 0.824135i | \(-0.691662\pi\) | ||||
−0.566394 | + | 0.824135i | \(0.691662\pi\) | |||||||
\(728\) | −11.2847 | − | 8.19881i | −0.418239 | − | 0.303868i | ||||
\(729\) | −6.22072 | + | 19.1454i | −0.230397 | + | 0.709090i | ||||
\(730\) | 4.26404 | + | 13.1234i | 0.157819 | + | 0.485718i | ||||
\(731\) | 16.5546 | − | 12.0276i | 0.612295 | − | 0.444858i | ||||
\(732\) | 0.133855 | − | 0.0972513i | 0.00494742 | − | 0.00359451i | ||||
\(733\) | −9.52822 | − | 29.3249i | −0.351933 | − | 1.08314i | −0.957767 | − | 0.287547i | \(-0.907160\pi\) |
0.605834 | − | 0.795591i | \(-0.292840\pi\) | |||||||
\(734\) | 3.41217 | − | 10.5016i | 0.125946 | − | 0.387621i | ||||
\(735\) | −0.923360 | − | 0.670861i | −0.0340587 | − | 0.0247451i | ||||
\(736\) | −4.10270 | −0.151228 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.5980 | −0.463740 | ||||||||
\(739\) | −17.9796 | − | 13.0630i | −0.661392 | − | 0.480529i | 0.205741 | − | 0.978607i | \(-0.434040\pi\) |
−0.867133 | + | 0.498077i | \(0.834040\pi\) | |||||||
\(740\) | 1.35388 | − | 4.16680i | 0.0497695 | − | 0.153175i | ||||
\(741\) | 3.76015 | + | 11.5725i | 0.138132 | + | 0.425128i | ||||
\(742\) | −2.51769 | + | 1.82921i | −0.0924272 | + | 0.0671523i | ||||
\(743\) | 25.2004 | − | 18.3091i | 0.924511 | − | 0.671697i | −0.0201316 | − | 0.999797i | \(-0.506409\pi\) |
0.944643 | + | 0.328101i | \(0.106409\pi\) | |||||||
\(744\) | −1.19199 | − | 3.66855i | −0.0437003 | − | 0.134496i | ||||
\(745\) | 13.6083 | − | 41.8820i | 0.498569 | − | 1.53444i | ||||
\(746\) | 0.623550 | + | 0.453036i | 0.0228298 | + | 0.0165868i | ||||
\(747\) | −4.46264 | −0.163280 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0187 | −0.512231 | ||||||||
\(750\) | −0.166177 | − | 0.120734i | −0.00606791 | − | 0.00440860i | ||||
\(751\) | 3.70491 | − | 11.4026i | 0.135194 | − | 0.416085i | −0.860426 | − | 0.509575i | \(-0.829802\pi\) |
0.995620 | + | 0.0934905i | \(0.0298025\pi\) | |||||||
\(752\) | 0.888909 | + | 2.73578i | 0.0324152 | + | 0.0997636i | ||||
\(753\) | −5.48078 | + | 3.98202i | −0.199731 | + | 0.145113i | ||||
\(754\) | −36.9387 | + | 26.8375i | −1.34523 | + | 0.977365i | ||||
\(755\) | −6.62944 | − | 20.4033i | −0.241270 | − | 0.742553i | ||||
\(756\) | −0.0931160 | + | 0.286582i | −0.00338660 | + | 0.0104229i | ||||
\(757\) | 9.26592 | + | 6.73209i | 0.336776 | + | 0.244682i | 0.743300 | − | 0.668958i | \(-0.233259\pi\) |
−0.406524 | + | 0.913640i | \(0.633259\pi\) | |||||||
\(758\) | 30.7240 | 1.11595 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64.2800 | −2.33168 | ||||||||
\(761\) | −6.38318 | − | 4.63765i | −0.231390 | − | 0.168115i | 0.466049 | − | 0.884759i | \(-0.345677\pi\) |
−0.697439 | + | 0.716644i | \(0.745677\pi\) | |||||||
\(762\) | −3.37033 | + | 10.3728i | −0.122094 | + | 0.375768i | ||||
\(763\) | 4.81284 | + | 14.8124i | 0.174236 | + | 0.536245i | ||||
\(764\) | 0.440146 | − | 0.319785i | 0.0159239 | − | 0.0115694i | ||||
\(765\) | −34.8255 | + | 25.3022i | −1.25912 | + | 0.914802i | ||||
\(766\) | −9.01198 | − | 27.7360i | −0.325616 | − | 1.00214i | ||||
\(767\) | 0.536449 | − | 1.65102i | 0.0193700 | − | 0.0596149i | ||||
\(768\) | 0.991963 | + | 0.720703i | 0.0357944 | + | 0.0260061i | ||||
\(769\) | −48.8153 | −1.76033 | −0.880163 | − | 0.474672i | \(-0.842567\pi\) | ||||
−0.880163 | + | 0.474672i | \(0.842567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.10525 | −0.111833 | ||||||||
\(772\) | −0.291197 | − | 0.211567i | −0.0104804 | − | 0.00761445i | ||||
\(773\) | −0.987642 | + | 3.03965i | −0.0355230 | + | 0.109329i | −0.967246 | − | 0.253842i | \(-0.918306\pi\) |
0.931723 | + | 0.363170i | \(0.118306\pi\) | |||||||
\(774\) | 5.17459 | + | 15.9257i | 0.185997 | + | 0.572439i | ||||
\(775\) | 14.3223 | − | 10.4057i | 0.514471 | − | 0.373785i | ||||
\(776\) | −14.5266 | + | 10.5542i | −0.521476 | + | 0.378874i | ||||
\(777\) | 1.10792 | + | 3.40984i | 0.0397466 | + | 0.122327i | ||||
\(778\) | −4.49884 | + | 13.8460i | −0.161291 | + | 0.496404i | ||||
\(779\) | −18.2708 | − | 13.2745i | −0.654621 | − | 0.475610i | ||||
\(780\) | 0.770750 | 0.0275973 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 33.4906 | 1.19762 | ||||||||
\(783\) | 12.0899 | + | 8.78383i | 0.432058 | + | 0.313908i | ||||
\(784\) | −1.14254 | + | 3.51639i | −0.0408052 | + | 0.125585i | ||||
\(785\) | −22.7564 | − | 70.0370i | −0.812211 | − | 2.49973i | ||||
\(786\) | 6.01476 | − | 4.36998i | 0.214539 | − | 0.155872i | ||||
\(787\) | 34.3681 | − | 24.9699i | 1.22509 | − | 0.890080i | 0.228578 | − | 0.973526i | \(-0.426592\pi\) |
0.996512 | + | 0.0834455i | \(0.0265925\pi\) | |||||||
\(788\) | 0.460629 | + | 1.41767i | 0.0164092 | + | 0.0505024i | ||||
\(789\) | 1.79639 | − | 5.52873i | 0.0639533 | − | 0.196828i | ||||
\(790\) | −12.8796 | − | 9.35760i | −0.458237 | − | 0.332928i | ||||
\(791\) | −4.13201 | −0.146917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.3947 | −0.546682 | ||||||||
\(794\) | −26.3782 | − | 19.1649i | −0.936129 | − | 0.680137i | ||||
\(795\) | 0.805081 | − | 2.47778i | 0.0285533 | − | 0.0878779i | ||||
\(796\) | −0.510329 | − | 1.57063i | −0.0180881 | − | 0.0556696i | ||||
\(797\) | 23.3471 | − | 16.9627i | 0.826998 | − | 0.600850i | −0.0917101 | − | 0.995786i | \(-0.529233\pi\) |
0.918709 | + | 0.394936i | \(0.129233\pi\) | |||||||
\(798\) | 2.80888 | − | 2.04077i | 0.0994334 | − | 0.0722426i | ||||
\(799\) | 1.14872 | + | 3.53539i | 0.0406387 | + | 0.125073i | ||||
\(800\) | −1.20040 | + | 3.69445i | −0.0424406 | + | 0.130619i | ||||
\(801\) | −12.9594 | − | 9.41553i | −0.457897 | − | 0.332681i | ||||
\(802\) | −15.8947 | −0.561260 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.338644 | 0.0119431 | ||||||||
\(805\) | 13.0662 | + | 9.49312i | 0.460522 | + | 0.334589i | ||||
\(806\) | −7.32038 | + | 22.5298i | −0.257849 | + | 0.793579i | ||||
\(807\) | 0.848349 | + | 2.61095i | 0.0298633 | + | 0.0919097i | ||||
\(808\) | 25.4996 | − | 18.5265i | 0.897071 | − | 0.651760i | ||||
\(809\) | 23.8282 | − | 17.3122i | 0.837756 | − | 0.608665i | −0.0839869 | − | 0.996467i | \(-0.526765\pi\) |
0.921743 | + | 0.387802i | \(0.126765\pi\) | |||||||
\(810\) | −10.3615 | − | 31.8895i | −0.364067 | − | 1.12048i | ||||
\(811\) | −0.766764 | + | 2.35986i | −0.0269247 | + | 0.0828657i | −0.963616 | − | 0.267291i | \(-0.913872\pi\) |
0.936691 | + | 0.350156i | \(0.113872\pi\) | |||||||
\(812\) | −0.801470 | − | 0.582302i | −0.0281261 | − | 0.0204348i | ||||
\(813\) | 5.09337 | 0.178632 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.11203 | −0.109010 | ||||||||
\(816\) | −5.19271 | − | 3.77273i | −0.181781 | − | 0.132072i | ||||
\(817\) | −9.27628 | + | 28.5494i | −0.324536 | + | 0.998818i | ||||
\(818\) | −13.8248 | − | 42.5484i | −0.483373 | − | 1.48767i | ||||
\(819\) | 11.0862 | − | 8.05459i | 0.387383 | − | 0.281450i | ||||
\(820\) | −1.15731 | + | 0.840835i | −0.0404150 | + | 0.0293632i | ||||
\(821\) | −4.33200 | − | 13.3325i | −0.151188 | − | 0.465309i | 0.846567 | − | 0.532283i | \(-0.178666\pi\) |
−0.997755 | + | 0.0669738i | \(0.978666\pi\) | |||||||
\(822\) | 1.63741 | − | 5.03944i | 0.0571113 | − | 0.175771i | ||||
\(823\) | 34.6205 | + | 25.1533i | 1.20679 | + | 0.876787i | 0.994936 | − | 0.100513i | \(-0.0320484\pi\) |
0.211859 | + | 0.977300i | \(0.432048\pi\) | |||||||
\(824\) | −38.6540 | −1.34658 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.495336 | −0.0172349 | ||||||||
\(827\) | −7.41920 | − | 5.39037i | −0.257991 | − | 0.187441i | 0.451270 | − | 0.892388i | \(-0.350971\pi\) |
−0.709261 | + | 0.704946i | \(0.750971\pi\) | |||||||
\(828\) | 0.644005 | − | 1.98204i | 0.0223807 | − | 0.0688808i | ||||
\(829\) | 9.02246 | + | 27.7683i | 0.313363 | + | 0.964433i | 0.976423 | + | 0.215866i | \(0.0692575\pi\) |
−0.663060 | + | 0.748566i | \(0.730743\pi\) | |||||||
\(830\) | 5.39121 | − | 3.91695i | 0.187132 | − | 0.135959i | ||||
\(831\) | 1.76912 | − | 1.28534i | 0.0613700 | − | 0.0445879i | ||||
\(832\) | −12.5245 | − | 38.5463i | −0.434208 | − | 1.33635i | ||||
\(833\) | −1.47649 | + | 4.54416i | −0.0511572 | + | 0.157446i | ||||
\(834\) | 1.64410 | + | 1.19451i | 0.0569304 | + | 0.0413624i | ||||
\(835\) | 1.77594 | 0.0614588 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.75341 | 0.267997 | ||||||||
\(838\) | 11.9082 | + | 8.65185i | 0.411363 | + | 0.298873i | ||||
\(839\) | 6.09771 | − | 18.7668i | 0.210516 | − | 0.647902i | −0.788925 | − | 0.614489i | \(-0.789362\pi\) |
0.999442 | − | 0.0334134i | \(-0.0106378\pi\) | |||||||
\(840\) | −1.02963 | − | 3.16888i | −0.0355256 | − | 0.109337i | ||||
\(841\) | −16.2861 | + | 11.8325i | −0.561589 | + | 0.408018i | ||||
\(842\) | −1.27059 | + | 0.923135i | −0.0437873 | + | 0.0318133i | ||||
\(843\) | −2.32050 | − | 7.14175i | −0.0799222 | − | 0.245975i | ||||
\(844\) | −0.485321 | + | 1.49366i | −0.0167054 | + | 0.0514140i | ||||
\(845\) | −24.9803 | − | 18.1492i | −0.859348 | − | 0.624353i | ||||
\(846\) | −3.04202 | −0.104587 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.43984 | −0.289825 | ||||||||
\(849\) | −2.91468 | − | 2.11764i | −0.100032 | − | 0.0726773i | ||||
\(850\) | 9.79895 | − | 30.1581i | 0.336101 | − | 1.03441i | ||||
\(851\) | −15.6779 | − | 48.2515i | −0.537431 | − | 1.65404i | ||||
\(852\) | −0.629809 | + | 0.457583i | −0.0215769 | + | 0.0156765i | ||||
\(853\) | −22.9378 | + | 16.6653i | −0.785375 | + | 0.570609i | −0.906587 | − | 0.422018i | \(-0.861322\pi\) |
0.121212 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(854\) | 1.35740 | + | 4.17764i | 0.0464492 | + | 0.142956i | ||||
\(855\) | 19.5142 | − | 60.0586i | 0.667372 | − | 2.05396i | ||||
\(856\) | −33.1092 | − | 24.0553i | −1.13165 | − | 0.822192i | ||||
\(857\) | −13.2033 | −0.451017 | −0.225509 | − | 0.974241i | \(-0.572404\pi\) | ||||
−0.225509 | + | 0.974241i | \(0.572404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.8260 | −0.710573 | −0.355286 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355286 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(860\) | 1.53830 | + | 1.11764i | 0.0524555 | + | 0.0381111i | ||||
\(861\) | 0.361748 | − | 1.11335i | 0.0123283 | − | 0.0379427i | ||||
\(862\) | 13.4645 | + | 41.4395i | 0.458603 | + | 1.41143i | ||||
\(863\) | −28.2702 | + | 20.5395i | −0.962330 | + | 0.699174i | −0.953691 | − | 0.300789i | \(-0.902750\pi\) |
−0.00863946 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(864\) | −1.37639 | + | 1.00000i | −0.0468256 | + | 0.0340208i | ||||
\(865\) | −16.7360 | − | 51.5080i | −0.569039 | − | 1.75132i | ||||
\(866\) | 1.86773 | − | 5.74827i | 0.0634680 | − | 0.195334i | ||||
\(867\) | −1.71347 | − | 1.24491i | −0.0581926 | − | 0.0422794i | ||||
\(868\) | −0.513993 | −0.0174461 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.9066 | −0.369769 | ||||||||
\(871\) | −25.4915 | − | 18.5207i | −0.863748 | − | 0.627550i | ||||
\(872\) | −14.0503 | + | 43.2425i | −0.475804 | + | 1.46437i | ||||
\(873\) | −5.45108 | − | 16.7767i | −0.184491 | − | 0.567805i | ||||
\(874\) | −39.7476 | + | 28.8783i | −1.34448 | + | 0.976823i | ||||
\(875\) | −0.335483 | + | 0.243743i | −0.0113414 | + | 0.00824000i | ||||
\(876\) | 0.0511280 | + | 0.157356i | 0.00172746 | + | 0.00531656i | ||||
\(877\) | 8.18317 | − | 25.1852i | 0.276326 | − | 0.850444i | −0.712539 | − | 0.701632i | \(-0.752455\pi\) |
0.988865 | − | 0.148812i | \(-0.0475450\pi\) | |||||||
\(878\) | −30.3004 | − | 22.0145i | −1.02259 | − | 0.742954i | ||||
\(879\) | −9.73599 | −0.328387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2627 | 0.581595 | 0.290798 | − | 0.956785i | \(-0.406079\pi\) | ||||
0.290798 | + | 0.956785i | \(0.406079\pi\) | |||||||
\(882\) | −3.16327 | − | 2.29825i | −0.106513 | − | 0.0773861i | ||||
\(883\) | −13.7830 | + | 42.4196i | −0.463834 | + | 1.42753i | 0.396609 | + | 0.917988i | \(0.370187\pi\) |
−0.860443 | + | 0.509547i | \(0.829813\pi\) | |||||||
\(884\) | −0.997078 | − | 3.06869i | −0.0335354 | − | 0.103211i | ||||
\(885\) | 0.335483 | − | 0.243743i | 0.0112771 | − | 0.00819332i | ||||
\(886\) | −8.59283 | + | 6.24305i | −0.288682 | + | 0.209739i | ||||
\(887\) | −9.51445 | − | 29.2825i | −0.319464 | − | 0.983209i | −0.973878 | − | 0.227072i | \(-0.927085\pi\) |
0.654414 | − | 0.756137i | \(-0.272915\pi\) | |||||||
\(888\) | −3.23441 | + | 9.95450i | −0.108540 | + | 0.334051i | ||||
\(889\) | 17.8135 | + | 12.9422i | 0.597445 | + | 0.434069i | ||||
\(890\) | 23.9201 | 0.801803 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.96316 | −0.132697 | ||||||||
\(893\) | −4.41182 | − | 3.20538i | −0.147636 | − | 0.107264i | ||||
\(894\) | −2.14580 | + | 6.60408i | −0.0717661 | + | 0.220873i | ||||
\(895\) | 10.9899 | + | 33.8234i | 0.367351 | + | 1.13059i | ||||
\(896\) | −8.06479 | + | 5.85941i | −0.269426 | + | 0.195749i | ||||
\(897\) | 7.22071 | − | 5.24615i | 0.241092 | − | 0.175164i | ||||
\(898\) | −8.64094 | − | 26.5941i | −0.288352 | − | 0.887456i | ||||
\(899\) | −7.87704 | + | 24.2430i | −0.262714 | + | 0.808550i | ||||
\(900\) | −1.59639 | − | 1.15984i | −0.0532130 | − | 0.0386615i | ||||
\(901\) | −10.9066 | −0.363352 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55602 | −0.0517810 | ||||||||
\(904\) | −9.75897 | − | 7.09031i | −0.324579 | − | 0.235820i | ||||
\(905\) | 14.4418 | − | 44.4473i | 0.480062 | − | 1.47748i | ||||
\(906\) | 1.04535 | + | 3.21726i | 0.0347294 | + | 0.106886i | ||||
\(907\) | −19.2385 | + | 13.9776i | −0.638804 | + | 0.464118i | −0.859439 | − | 0.511238i | \(-0.829187\pi\) |
0.220635 | + | 0.975356i | \(0.429187\pi\) | |||||||
\(908\) | −2.63096 | + | 1.91151i | −0.0873116 | + | 0.0634356i | ||||
\(909\) | 9.56864 | + | 29.4492i | 0.317372 | + | 0.976769i | ||||
\(910\) | −6.32330 | + | 19.4611i | −0.209615 | + | 0.645130i | ||||
\(911\) | −39.6645 | − | 28.8179i | −1.31414 | − | 0.954781i | −0.999985 | − | 0.00540957i | \(-0.998278\pi\) |
−0.314157 | − | 0.949371i | \(-0.601722\pi\) | |||||||
\(912\) | 9.41600 | 0.311795 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.6774 | 0.386253 | ||||||||
\(915\) | −2.97506 | − | 2.16151i | −0.0983524 | − | 0.0714572i | ||||
\(916\) | −0.586297 | + | 1.80444i | −0.0193718 | + | 0.0596203i | ||||
\(917\) | −4.63814 | − | 14.2747i | −0.153165 | − | 0.471393i | ||||
\(918\) | 11.2355 | − | 8.16309i | 0.370828 | − | 0.269422i | ||||
\(919\) | −32.3607 | + | 23.5114i | −1.06748 | + | 0.775570i | −0.975458 | − | 0.220187i | \(-0.929333\pi\) |
−0.0920227 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(920\) | 14.5699 | + | 44.8417i | 0.480357 | + | 1.47839i | ||||
\(921\) | 1.33576 | − | 4.11106i | 0.0440149 | − | 0.135464i | ||||
\(922\) | 10.6611 | + | 7.74577i | 0.351106 | + | 0.255093i | ||||
\(923\) | 72.4346 | 2.38421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.0373 | −1.57946 | ||||||||
\(926\) | 12.6002 | + | 9.15456i | 0.414067 | + | 0.300838i | ||||
\(927\) | 11.7346 | − | 36.1155i | 0.385416 | − | 1.18619i | ||||
\(928\) | −1.72843 | − | 5.31957i | −0.0567386 | − | 0.174624i | ||||
\(929\) | 45.7774 | − | 33.2592i | 1.50191 | − | 1.09120i | 0.532295 | − | 0.846559i | \(-0.321330\pi\) |
0.969614 | − | 0.244641i | \(-0.0786702\pi\) | |||||||
\(930\) | −4.57800 | + | 3.32611i | −0.150119 | + | 0.109067i | ||||
\(931\) | −2.16600 | − | 6.66627i | −0.0709878 | − | 0.218478i | ||||
\(932\) | 0.154495 | − | 0.475487i | 0.00506065 | − | 0.0155751i | ||||
\(933\) | 6.24345 | + | 4.53613i | 0.204401 | + | 0.148506i | ||||
\(934\) | −24.8408 | −0.812814 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40.0046 | 1.30759 | ||||||||
\(937\) | 13.6039 | + | 9.88380i | 0.444419 | + | 0.322890i | 0.787389 | − | 0.616457i | \(-0.211433\pi\) |
−0.342969 | + | 0.939347i | \(0.611433\pi\) | |||||||
\(938\) | −2.77827 | + | 8.55064i | −0.0907137 | + | 0.279188i | ||||
\(939\) | −1.42559 | − | 4.38752i | −0.0465224 | − | 0.143181i | ||||
\(940\) | −0.279453 | + | 0.203035i | −0.00911476 | + | 0.00662226i | ||||
\(941\) | −5.87290 | + | 4.26691i | −0.191451 | + | 0.139097i | −0.679382 | − | 0.733785i | \(-0.737752\pi\) |
0.487931 | + | 0.872882i | \(0.337752\pi\) | |||||||
\(942\) | 3.58830 | + | 11.0437i | 0.116913 | + | 0.359822i | ||||
\(943\) | −5.11897 | + | 15.7546i | −0.166697 | + | 0.513040i | ||||
\(944\) | −1.08679 | − | 0.789603i | −0.0353722 | − | 0.0256994i | ||||
\(945\) | 6.69735 | 0.217865 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6040 | −0.832017 | −0.416009 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416009 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(948\) | −0.154433 | − | 0.112202i | −0.00501576 | − | 0.00364416i | ||||
\(949\) | 4.75723 | − | 14.6412i | 0.154426 | − | 0.475275i | ||||
\(950\) | 14.3750 | + | 44.2418i | 0.466388 | + | 1.43539i | ||||
\(951\) | 3.48846 | − | 2.53452i | 0.113121 | − | 0.0821873i | ||||
\(952\) | −11.2847 | + | 8.19881i | −0.365739 | + | 0.265725i | ||||
\(953\) | 2.20927 | + | 6.79943i | 0.0715653 | + | 0.220255i | 0.980442 | − | 0.196811i | \(-0.0630584\pi\) |
−0.908876 | + | 0.417066i | \(0.863058\pi\) | |||||||
\(954\) | 2.75806 | − | 8.48845i | 0.0892956 | − | 0.274824i | ||||
\(955\) | −9.78268 | − | 7.10753i | −0.316560 | − | 0.229994i | ||||
\(956\) | −3.11203 | −0.100650 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.73344 | −0.152930 | ||||||||
\(959\) | −8.65434 | − | 6.28775i | −0.279463 | − | 0.203042i | ||||
\(960\) | 2.99175 | − | 9.20767i | 0.0965584 | − | 0.297176i | ||||
\(961\) | −5.49266 | − | 16.9047i | −0.177183 | − | 0.545312i | ||||
\(962\) | 52.0036 | − | 37.7829i | 1.67666 | − | 1.21817i | ||||
\(963\) | 32.5269 | − | 23.6321i | 1.04816 | − | 0.761535i | ||||
\(964\) | 0.0137737 | + | 0.0423911i | 0.000443621 | + | 0.00136533i | ||||
\(965\) | −2.47214 | + | 7.60845i | −0.0795809 | + | 0.244925i | ||||
\(966\) | −2.06031 | − | 1.49691i | −0.0662895 | − | 0.0481621i | ||||
\(967\) | 15.9600 | 0.513241 | 0.256620 | − | 0.966512i | \(-0.417391\pi\) | ||||
0.256620 | + | 0.966512i | \(0.417391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.1681 | 0.390895 | ||||||||
\(970\) | 21.3105 | + | 15.4830i | 0.684240 | + | 0.497130i | ||||
\(971\) | −9.41819 | + | 28.9862i | −0.302244 | + | 0.930212i | 0.678447 | + | 0.734649i | \(0.262653\pi\) |
−0.980691 | + | 0.195563i | \(0.937347\pi\) | |||||||
\(972\) | −0.403588 | − | 1.24212i | −0.0129451 | − | 0.0398409i | ||||
\(973\) | 3.31916 | − | 2.41151i | 0.106407 | − | 0.0773094i | ||||
\(974\) | −30.2886 | + | 22.0060i | −0.970510 | + | 0.705117i | ||||
\(975\) | −2.61143 | − | 8.03715i | −0.0836327 | − | 0.257395i | ||||
\(976\) | −3.68127 | + | 11.3298i | −0.117835 | + | 0.362658i | ||||
\(977\) | −3.34286 | − | 2.42873i | −0.106948 | − | 0.0777021i | 0.533026 | − | 0.846099i | \(-0.321055\pi\) |
−0.639974 | + | 0.768397i | \(0.721055\pi\) | |||||||
\(978\) | 0.490715 | 0.0156913 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.443984 | −0.0141826 | ||||||||
\(981\) | −36.1372 | − | 26.2552i | −1.15377 | − | 0.838265i | ||||
\(982\) | 2.63898 | − | 8.12194i | 0.0842131 | − | 0.259181i | ||||
\(983\) | −7.73303 | − | 23.7998i | −0.246645 | − | 0.759096i | −0.995362 | − | 0.0962053i | \(-0.969329\pi\) |
0.748716 | − | 0.662891i | \(-0.230671\pi\) | |||||||
\(984\) | 2.76482 | − | 2.00876i | 0.0881392 | − | 0.0640369i | ||||
\(985\) | 26.8033 | − | 19.4737i | 0.854024 | − | 0.620485i | ||||
\(986\) | 14.1093 | + | 43.4240i | 0.449332 | + | 1.38290i | ||||
\(987\) | 0.0873505 | − | 0.268837i | 0.00278040 | − | 0.00855718i | ||||
\(988\) | 3.82943 | + | 2.78224i | 0.121830 | + | 0.0885150i | ||||
\(989\) | 22.0187 | 0.700153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5747 | −0.875938 | −0.437969 | − | 0.898990i | \(-0.644302\pi\) | ||||
−0.437969 | + | 0.898990i | \(0.644302\pi\) | |||||||
\(992\) | −2.34777 | − | 1.70576i | −0.0745418 | − | 0.0541578i | ||||
\(993\) | −1.33457 | + | 4.10738i | −0.0423513 | + | 0.130344i | ||||
\(994\) | −6.38678 | − | 19.6565i | −0.202576 | − | 0.623466i | ||||
\(995\) | −29.6953 | + | 21.5749i | −0.941403 | + | 0.683969i | ||||
\(996\) | 0.0646434 | − | 0.0469662i | 0.00204830 | − | 0.00148818i | ||||
\(997\) | 7.31895 | + | 22.5254i | 0.231794 | + | 0.713387i | 0.997531 | + | 0.0702335i | \(0.0223744\pi\) |
−0.765737 | + | 0.643154i | \(0.777626\pi\) | |||||||
\(998\) | 8.70727 | − | 26.7982i | 0.275624 | − | 0.848283i | ||||
\(999\) | −17.0206 | − | 12.3662i | −0.538508 | − | 0.391249i |
(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 | 847.2.f.u.323.2 | 12 | ||
11.2 | odd | 10 | 847.2.f.t.148.2 | 12 | |||
11.3 | even | 5 | inner | 847.2.f.u.729.2 | 12 | ||
11.4 | even | 5 | inner | 847.2.f.u.372.2 | 12 | ||
11.5 | even | 5 | 847.2.a.i.1.2 | ✓ | 3 | ||
11.6 | odd | 10 | 847.2.a.j.1.2 | yes | 3 | ||
11.7 | odd | 10 | 847.2.f.t.372.2 | 12 | |||
11.8 | odd | 10 | 847.2.f.t.729.2 | 12 | |||
11.9 | even | 5 | inner | 847.2.f.u.148.2 | 12 | ||
11.10 | odd | 2 | 847.2.f.t.323.2 | 12 | |||
33.5 | odd | 10 | 7623.2.a.ce.1.2 | 3 | |||
33.17 | even | 10 | 7623.2.a.bz.1.2 | 3 | |||
77.6 | even | 10 | 5929.2.a.y.1.2 | 3 | |||
77.27 | odd | 10 | 5929.2.a.t.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.2 | ✓ | 3 | 11.5 | even | 5 | ||
847.2.a.j.1.2 | yes | 3 | 11.6 | odd | 10 | ||
847.2.f.t.148.2 | 12 | 11.2 | odd | 10 | |||
847.2.f.t.323.2 | 12 | 11.10 | odd | 2 | |||
847.2.f.t.372.2 | 12 | 11.7 | odd | 10 | |||
847.2.f.t.729.2 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.148.2 | 12 | 11.9 | even | 5 | inner | ||
847.2.f.u.323.2 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.372.2 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.u.729.2 | 12 | 11.3 | even | 5 | inner | ||
5929.2.a.t.1.2 | 3 | 77.27 | odd | 10 | |||
5929.2.a.y.1.2 | 3 | 77.6 | even | 10 | |||
7623.2.a.bz.1.2 | 3 | 33.17 | even | 10 | |||
7623.2.a.ce.1.2 | 3 | 33.5 | odd | 10 |