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: | \( x^{12} - x^{11} + 7 x^{10} - 15 x^{9} + 59 x^{8} + 118 x^{7} + 266 x^{6} + 324 x^{5} + 1036 x^{4} + \cdots + 16 \) |
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 | 729.2 | ||
Root | \(0.112275 - 0.345546i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.t.323.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 | \(-0.860093\pi\) |
0.125044 | + | 0.992151i | \(0.460093\pi\) | |||||||
\(3\) | 0.112275 | + | 0.345546i | 0.0648218 | + | 0.199501i | 0.978222 | − | 0.207562i | \(-0.0665529\pi\) |
−0.913400 | + | 0.407063i | \(0.866553\pi\) | |||||||
\(4\) | −0.0436753 | + | 0.134419i | −0.0218376 | + | 0.0672093i | ||||
\(5\) | −2.54139 | − | 1.84643i | −1.13655 | − | 0.825749i | −0.149912 | − | 0.988699i | \(-0.547899\pi\) |
−0.986634 | + | 0.162950i | \(0.947899\pi\) | |||||||
\(6\) | −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 | \(-0.930543\pi\) |
−0.0958065 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(14\) | 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 | \(-0.496720\pi\) |
−0.947822 | + | 0.318800i | \(0.896720\pi\) | |||||||
\(18\) | −1.20826 | + | 3.71865i | −0.284790 | + | 0.876493i | ||||
\(19\) | 2.16600 | + | 6.66627i | 0.496915 | + | 1.52935i | 0.813951 | + | 0.580933i | \(0.197312\pi\) |
−0.317036 | + | 0.948413i | \(0.602688\pi\) | |||||||
\(20\) | 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 | 0.520981 | + | 0.853568i | \(0.325566\pi\) |
−0.923197 | + | 0.384326i | \(0.874434\pi\) | |||||||
\(30\) | 0.480835 | + | 1.47986i | 0.0877881 | + | 0.270184i | ||||
\(31\) | 2.94213 | − | 2.13758i | 0.528422 | − | 0.383921i | −0.291345 | − | 0.956618i | \(-0.594103\pi\) |
0.819767 | + | 0.572697i | \(0.194103\pi\) | |||||||
\(32\) | 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 | 0.305565 | + | 0.952171i | \(0.401155\pi\) |
−0.806879 | + | 0.590716i | \(0.798845\pi\) | |||||||
\(38\) | −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 | \(-0.0190448\pi\) |
−0.842716 | + | 0.538358i | \(0.819045\pi\) | |||||||
\(42\) | −0.400735 | + | 0.291151i | −0.0618347 | + | 0.0449256i | ||||
\(43\) | −4.28267 | −0.653101 | −0.326551 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326551 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(44\) | 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 | 0.931990 | − | 0.362484i | \(-0.118071\pi\) |
−0.967059 | + | 0.254554i | \(0.918071\pi\) | |||||||
\(48\) | −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 | −0.707350 | − | 0.706863i | \(-0.750110\pi\) |
0.453684 | + | 0.891163i | \(0.350110\pi\) | |||||||
\(54\) | −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 | −0.958099 | − | 0.286437i | \(-0.907529\pi\) |
0.943482 | + | 0.331424i | \(0.107529\pi\) | |||||||
\(60\) | 0.130504 | + | 0.0948168i | 0.0168480 | + | 0.0122408i | ||||
\(61\) | 2.60665 | + | 1.89384i | 0.333747 | + | 0.242481i | 0.742019 | − | 0.670379i | \(-0.233868\pi\) |
−0.408272 | + | 0.912860i | \(0.633868\pi\) | |||||||
\(62\) | −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 | 0.984494 | + | 0.175417i | \(0.0561274\pi\) |
0.471057 | + | 0.882103i | \(0.343873\pi\) | |||||||
\(72\) | −6.77362 | − | 4.92132i | −0.798279 | − | 0.579984i | ||||
\(73\) | 0.995650 | − | 3.06430i | 0.116532 | − | 0.358649i | −0.875731 | − | 0.482799i | \(-0.839620\pi\) |
0.992263 | + | 0.124150i | \(0.0396203\pi\) | |||||||
\(74\) | −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 | \(-0.767059\pi\) |
0.405611 | + | 0.914046i | \(0.367059\pi\) | |||||||
\(80\) | −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 | \(-0.272784\pi\) |
−0.516550 | + | 0.856257i | \(0.672784\pi\) | |||||||
\(84\) | −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 | −0.811013 | − | 0.585028i | \(-0.801084\pi\) |
0.305778 | + | 0.952103i | \(0.401084\pi\) | |||||||
\(98\) | 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 | \(-0.880501\pi\) |
0.0612206 | + | 0.998124i | \(0.480501\pi\) | |||||||
\(102\) | 0.731356 | + | 2.25088i | 0.0724150 | + | 0.222871i | ||||
\(103\) | −4.09159 | + | 12.5926i | −0.403156 | + | 1.24079i | 0.519269 | + | 0.854611i | \(0.326204\pi\) |
−0.922425 | + | 0.386176i | \(0.873796\pi\) | |||||||
\(104\) | 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 | −0.908816 | − | 0.417197i | \(-0.863013\pi\) |
0.490026 | − | 0.871708i | \(-0.336987\pi\) | |||||||
\(108\) | −0.243781 | + | 0.177117i | −0.0234578 | + | 0.0170431i | ||||
\(109\) | 15.5747 | 1.49178 | 0.745892 | − | 0.666067i | \(-0.232024\pi\) | ||||
0.745892 | + | 0.666067i | \(0.232024\pi\) | |||||||
\(110\) | 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 | 0.992980 | − | 0.118284i | \(-0.0377392\pi\) |
−0.872863 | + | 0.487965i | \(0.837739\pi\) | |||||||
\(114\) | 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 | 0.915899 | + | 0.401408i | \(0.131479\pi\) |
0.664791 | + | 0.747030i | \(0.268521\pi\) | |||||||
\(128\) | 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 | \(-0.727620\pi\) | ||||
−0.655686 | + | 0.755034i | \(0.727620\pi\) | |||||||
\(132\) | 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 | 0.892520 | − | 0.451008i | \(-0.148935\pi\) |
−0.153130 | + | 0.988206i | \(0.548935\pi\) | |||||||
\(138\) | −2.06031 | − | 1.49691i | −0.175385 | − | 0.127425i | ||||
\(139\) | −1.26780 | + | 3.90190i | −0.107534 | + | 0.330955i | −0.990317 | − | 0.138826i | \(-0.955667\pi\) |
0.882783 | + | 0.469781i | \(0.155667\pi\) | |||||||
\(140\) | −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 | \(-0.105303\pi\) |
−0.0166586 | + | 0.999861i | \(0.505303\pi\) | |||||||
\(150\) | 0.745130 | − | 2.29327i | 0.0608396 | − | 0.187245i | ||||
\(151\) | 2.11039 | + | 6.49511i | 0.171741 | + | 0.528564i | 0.999470 | − | 0.0325642i | \(-0.0103673\pi\) |
−0.827729 | + | 0.561129i | \(0.810367\pi\) | |||||||
\(152\) | 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 | −0.625198 | − | 0.780466i | \(-0.714982\pi\) |
0.0470494 | − | 0.998893i | \(-0.485018\pi\) | |||||||
\(158\) | 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 | −0.555955 | − | 0.831213i | \(-0.687647\pi\) |
0.618731 | + | 0.785603i | \(0.287647\pi\) | |||||||
\(164\) | −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 | \(-0.693037\pi\) |
0.605341 | + | 0.795966i | \(0.293037\pi\) | |||||||
\(168\) | −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 | 0.920850 | + | 0.389917i | \(0.127496\pi\) |
−0.515796 | + | 0.856711i | \(0.672504\pi\) | |||||||
\(174\) | 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 | 0.992482 | + | 0.122394i | \(0.0390571\pi\) |
−0.730993 | + | 0.682385i | \(0.760943\pi\) | |||||||
\(180\) | 0.393485 | − | 1.21102i | 0.0293286 | − | 0.0902642i | ||||
\(181\) | −12.0360 | − | 8.74467i | −0.894629 | − | 0.649986i | 0.0424516 | − | 0.999099i | \(-0.486483\pi\) |
−0.937081 | + | 0.349112i | \(0.886483\pi\) | |||||||
\(182\) | −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 | −0.898754 | − | 0.438454i | \(-0.855526\pi\) |
0.984824 | + | 0.173558i | \(0.0555263\pi\) | |||||||
\(192\) | −2.49337 | − | 1.81154i | −0.179943 | − | 0.130737i | ||||
\(193\) | −2.06031 | − | 1.49691i | −0.148305 | − | 0.107750i | 0.511159 | − | 0.859486i | \(-0.329216\pi\) |
−0.659463 | + | 0.751737i | \(0.729216\pi\) | |||||||
\(194\) | 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 | \(-0.377399\pi\) | ||||
0.375710 | + | 0.926737i | \(0.377399\pi\) | |||||||
\(198\) | 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 | \(-0.575066\pi\) |
0.852532 | + | 0.522675i | \(0.175066\pi\) | |||||||
\(212\) | −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 | 0.617544 | + | 0.786537i | \(0.288128\pi\) |
−0.0372888 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(224\) | 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 | −0.378134 | − | 0.925751i | \(-0.623434\pi\) |
0.850060 | − | 0.526686i | \(-0.176566\pi\) | |||||||
\(228\) | −0.111227 | − | 0.342322i | −0.00736620 | − | 0.0226708i | ||||
\(229\) | −10.8603 | + | 7.89043i | −0.717666 | + | 0.521415i | −0.885638 | − | 0.464377i | \(-0.846278\pi\) |
0.167972 | + | 0.985792i | \(0.446278\pi\) | |||||||
\(230\) | 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 | \(-0.736966\pi\) |
0.490085 | + | 0.871674i | \(0.336966\pi\) | |||||||
\(234\) | −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 | −0.887744 | − | 0.460337i | \(-0.847729\pi\) |
0.447621 | − | 0.894223i | \(-0.352271\pi\) | |||||||
\(240\) | 3.41399 | − | 2.48041i | 0.220372 | − | 0.160110i | ||||
\(241\) | 0.315366 | 0.0203145 | 0.0101573 | − | 0.999948i | \(-0.496767\pi\) | ||||
0.0101573 | + | 0.999948i | \(0.496767\pi\) | |||||||
\(242\) | 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 | −0.951315 | − | 0.308220i | \(-0.900267\pi\) |
−0.000837449 | 1.00000i | \(0.500267\pi\) | ||||||||
\(252\) | 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 | −0.999017 | − | 0.0443186i | \(-0.985888\pi\) |
0.834272 | + | 0.551353i | \(0.185888\pi\) | |||||||
\(258\) | 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 | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 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 | 0.385622 | − | 0.922657i | \(-0.373987\pi\) |
−0.758335 | + | 0.651865i | \(0.773987\pi\) | |||||||
\(270\) | 7.38688 | + | 5.36688i | 0.449551 | + | 0.326618i | ||||
\(271\) | −4.33200 | + | 13.3325i | −0.263150 | + | 0.809894i | 0.728963 | + | 0.684553i | \(0.240002\pi\) |
−0.992114 | + | 0.125341i | \(0.959998\pi\) | |||||||
\(272\) | −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 | \(-0.757873\pi\) |
0.431816 | + | 0.901962i | \(0.357873\pi\) | |||||||
\(278\) | −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 | \(-0.511440\pi\) |
−0.961546 | + | 0.274643i | \(0.911440\pi\) | |||||||
\(282\) | −0.119087 | + | 0.366513i | −0.00709155 | + | 0.0218256i | ||||
\(283\) | −3.06420 | − | 9.43063i | −0.182148 | − | 0.560593i | 0.817740 | − | 0.575588i | \(-0.195227\pi\) |
−0.999888 | + | 0.0149950i | \(0.995227\pi\) | |||||||
\(284\) | −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 | −0.350011 | − | 0.936746i | \(-0.613822\pi\) |
0.833770 | − | 0.552112i | \(-0.186178\pi\) | |||||||
\(294\) | 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 | \(-0.610260\pi\) | ||||
−0.339507 | + | 0.940603i | \(0.610260\pi\) | |||||||
\(308\) | 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 | −0.945352 | − | 0.326052i | \(-0.894282\pi\) |
0.573157 | − | 0.819445i | \(-0.305718\pi\) | |||||||
\(312\) | −1.56608 | + | 4.81990i | −0.0886618 | + | 0.272873i | ||||
\(313\) | 10.2724 | + | 7.46332i | 0.580629 | + | 0.421852i | 0.838951 | − | 0.544207i | \(-0.183170\pi\) |
−0.258322 | + | 0.966059i | \(0.583170\pi\) | |||||||
\(314\) | 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 | −0.284545 | − | 0.958663i | \(-0.591842\pi\) |
0.823813 | + | 0.566861i | \(0.191842\pi\) | |||||||
\(318\) | 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 | \(-0.908590\pi\) |
0.942372 | + | 0.334567i | \(0.108590\pi\) | |||||||
\(338\) | 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 | \(-0.433670\pi\) |
−0.866553 | + | 0.499084i | \(0.833670\pi\) | |||||||
\(348\) | 0.111227 | − | 0.342322i | 0.00596241 | − | 0.0183504i | ||||
\(349\) | 9.17882 | + | 28.2495i | 0.491331 | + | 1.51216i | 0.822597 | + | 0.568624i | \(0.192524\pi\) |
−0.331266 | + | 0.943537i | \(0.607476\pi\) | |||||||
\(350\) | −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 | 0.695828 | + | 0.718209i | \(0.255038\pi\) |
−0.985089 | + | 0.172046i | \(0.944962\pi\) | |||||||
\(360\) | 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 | −0.994887 | − | 0.100990i | \(-0.967799\pi\) |
0.864241 | + | 0.503078i | \(0.167799\pi\) | |||||||
\(368\) | 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 | \(-0.504659\pi\) | ||||
−0.0146362 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(374\) | 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 | 0.947580 | − | 0.319519i | \(-0.103521\pi\) |
−0.0110628 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(380\) | 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 | −0.934383 | − | 0.356269i | \(-0.884049\pi\) |
0.0500914 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(384\) | 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 | −0.831888 | − | 0.554944i | \(-0.812740\pi\) |
0.999199 | + | 0.0400122i | \(0.0127397\pi\) | |||||||
\(390\) | −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 | 0.326821 | − | 0.945086i | \(-0.394023\pi\) |
−0.797837 | + | 0.602873i | \(0.794023\pi\) | |||||||
\(402\) | 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 | 0.312729 | − | 0.949842i | \(-0.398757\pi\) |
0.999992 | − | 0.00390587i | \(-0.00124328\pi\) | |||||||
\(410\) | 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 | 0.942007 | − | 0.335593i | \(-0.108937\pi\) |
−0.959356 | + | 0.282197i | \(0.908937\pi\) | |||||||
\(422\) | −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 | \(-0.979609\pi\) |
−0.247501 | + | 0.968888i | \(0.579609\pi\) | |||||||
\(432\) | 2.43591 | + | 7.49697i | 0.117198 | + | 0.360698i | ||||
\(433\) | −1.36998 | + | 4.21635i | −0.0658369 | + | 0.202625i | −0.978563 | − | 0.205946i | \(-0.933973\pi\) |
0.912726 | + | 0.408571i | \(0.133973\pi\) | |||||||
\(434\) | 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 | \(-0.272423\pi\) | ||||
0.655583 | + | 0.755123i | \(0.272423\pi\) | |||||||
\(440\) | 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 | 0.877435 | − | 0.479695i | \(-0.159253\pi\) |
−0.991818 | + | 0.127662i | \(0.959253\pi\) | |||||||
\(444\) | 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 | −0.905905 | − | 0.423480i | \(-0.860808\pi\) |
0.122813 | + | 0.992430i | \(0.460808\pi\) | |||||||
\(450\) | −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 | \(-0.364203\pi\) |
−0.737944 | + | 0.674862i | \(0.764203\pi\) | |||||||
\(458\) | 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 | \(-0.572269\pi\) | ||||
−0.225095 | + | 0.974337i | \(0.572269\pi\) | |||||||
\(462\) | 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 | 0.191937 | − | 0.981407i | \(-0.438523\pi\) |
−0.874062 | + | 0.485815i | \(0.838523\pi\) | |||||||
\(468\) | −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 | \(-0.274725\pi\) |
−0.521763 | + | 0.853091i | \(0.674725\pi\) | |||||||
\(480\) | 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 | −0.936815 | − | 0.349826i | \(-0.886241\pi\) |
0.552277 | − | 0.833661i | \(-0.313759\pi\) | |||||||
\(488\) | 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 | \(-0.854857\pi\) |
0.985186 | + | 0.171487i | \(0.0548572\pi\) | |||||||
\(492\) | −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 | 0.700213 | + | 0.713934i | \(0.253089\pi\) |
−0.986124 | + | 0.166010i | \(0.946911\pi\) | |||||||
\(500\) | −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 | −0.980276 | − | 0.197633i | \(-0.936675\pi\) |
0.676895 | − | 0.736080i | \(-0.263325\pi\) | |||||||
\(504\) | −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 | 0.983740 | + | 0.179599i | \(0.0574801\pi\) |
−0.690297 | + | 0.723527i | \(0.742520\pi\) | |||||||
\(510\) | 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 | −0.811198 | − | 0.584771i | \(-0.801184\pi\) |
0.999993 | + | 0.00372050i | \(0.00118427\pi\) | |||||||
\(522\) | −22.1724 | − | 16.1092i | −0.970459 | − | 0.705080i | ||||
\(523\) | −14.9517 | − | 10.8630i | −0.653792 | − | 0.475007i | 0.210769 | − | 0.977536i | \(-0.432403\pi\) |
−0.864561 | + | 0.502529i | \(0.832403\pi\) | |||||||
\(524\) | 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 | \(-0.402100\pi\) |
0.999978 | + | 0.00659687i | \(0.00209986\pi\) | |||||||
\(542\) | −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 | 0.998153 | + | 0.0607551i | \(0.0193509\pi\) |
−0.771812 | + | 0.635851i | \(0.780649\pi\) | |||||||
\(548\) | −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 | 0.651286 | + | 0.758832i | \(0.274230\pi\) |
−0.972932 | + | 0.231091i | \(0.925770\pi\) | |||||||
\(558\) | 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 | \(-0.802435\pi\) |
0.301732 | + | 0.953393i | \(0.402435\pi\) | |||||||
\(564\) | 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 | \(-0.181643\pi\) |
−0.998338 | + | 0.0576384i | \(0.981643\pi\) | |||||||
\(570\) | −8.82365 | + | 6.41075i | −0.369582 | + | 0.268517i | ||||
\(571\) | −38.9439 | −1.62975 | −0.814877 | − | 0.579634i | \(-0.803195\pi\) | ||||
−0.814877 | + | 0.579634i | \(0.803195\pi\) | |||||||
\(572\) | 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 | −0.285218 | − | 0.958463i | \(-0.592066\pi\) |
−0.999689 | + | 0.0249227i | \(0.992066\pi\) | |||||||
\(578\) | −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 | 0.439965 | + | 0.898015i | \(0.354991\pi\) |
−0.883779 | + | 0.467904i | \(0.845009\pi\) | |||||||
\(588\) | 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 | \(-0.375330\pi\) | ||||
0.381726 | + | 0.924276i | \(0.375330\pi\) | |||||||
\(594\) | 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 | 0.0999801 | − | 0.994989i | \(-0.468122\pi\) |
−0.915396 | + | 0.402555i | \(0.868122\pi\) | |||||||
\(600\) | 4.17726 | + | 3.03496i | 0.170536 | + | 0.123902i | ||||
\(601\) | 9.31025 | − | 28.6540i | 0.379773 | − | 1.16882i | −0.560428 | − | 0.828203i | \(-0.689363\pi\) |
0.940201 | − | 0.340619i | \(-0.110637\pi\) | |||||||
\(602\) | −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 | \(-0.789405\pi\) |
0.340497 | + | 0.940246i | \(0.389405\pi\) | |||||||
\(608\) | 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 | 0.676707 | + | 0.736252i | \(0.263406\pi\) |
−0.114709 | + | 0.993399i | \(0.536594\pi\) | |||||||
\(614\) | 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 | 0.744296 | + | 0.667850i | \(0.232785\pi\) |
−0.209595 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(620\) | 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 | −0.944465 | − | 0.328613i | \(-0.893419\pi\) |
0.957242 | + | 0.289289i | \(0.0934189\pi\) | |||||||
\(632\) | 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 | 0.916122 | + | 0.400900i | \(0.131302\pi\) |
−0.505515 | + | 0.862818i | \(0.668698\pi\) | |||||||
\(642\) | −2.14580 | + | 6.60408i | −0.0846878 | + | 0.260642i | ||||
\(643\) | 17.0147 | + | 12.3619i | 0.670996 | + | 0.487507i | 0.870358 | − | 0.492419i | \(-0.163887\pi\) |
−0.199363 | + | 0.979926i | \(0.563887\pi\) | |||||||
\(644\) | 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 | −0.911634 | − | 0.411002i | \(-0.865179\pi\) |
0.109176 | + | 0.994022i | \(0.465179\pi\) | |||||||
\(648\) | −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 | −0.745270 | − | 0.666763i | \(-0.767679\pi\) |
0.994849 | − | 0.101364i | \(-0.0323207\pi\) | |||||||
\(654\) | −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 | \(-0.382620\pi\) | ||||
0.360460 | + | 0.932775i | \(0.382620\pi\) | |||||||
\(660\) | 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 | \(-0.590125\pi\) |
0.826859 | + | 0.562409i | \(0.190125\pi\) | |||||||
\(674\) | −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 | \(-0.322328\pi\) |
−0.643043 | + | 0.765830i | \(0.722328\pi\) | |||||||
\(678\) | 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 | −0.492338 | − | 0.870404i | \(-0.663858\pi\) |
0.675663 | + | 0.737211i | \(0.263858\pi\) | |||||||
\(692\) | −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 | \(-0.144442\pi\) |
−0.984807 | + | 0.173655i | \(0.944442\pi\) | |||||||
\(702\) | 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 | 0.973117 | − | 0.230313i | \(-0.0739749\pi\) |
0.0816692 | + | 0.996659i | \(0.473975\pi\) | |||||||
\(710\) | 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 | −0.971730 | − | 0.236093i | \(-0.924133\pi\) |
0.924918 | + | 0.380166i | \(0.124133\pi\) | |||||||
\(720\) | −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 | −0.605834 | − | 0.795591i | \(-0.707160\pi\) |
0.957767 | − | 0.287547i | \(-0.0928397\pi\) | |||||||
\(734\) | −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 | \(-0.565960\pi\) |
0.867133 | + | 0.498077i | \(0.165960\pi\) | |||||||
\(740\) | 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 | \(-0.493591\pi\) |
−0.944643 | + | 0.328101i | \(0.893591\pi\) | |||||||
\(744\) | 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 | 0.995620 | − | 0.0934905i | \(-0.0298025\pi\) |
−0.860426 | + | 0.509575i | \(0.829802\pi\) | |||||||
\(752\) | 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 | −0.406524 | − | 0.913640i | \(-0.633259\pi\) |
0.743300 | + | 0.668958i | \(0.233259\pi\) | |||||||
\(758\) | −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 | \(-0.654323\pi\) |
0.697439 | + | 0.716644i | \(0.254323\pi\) | |||||||
\(762\) | −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 | \(-0.157433\pi\) | ||||
0.880163 | + | 0.474672i | \(0.157433\pi\) | |||||||
\(770\) | 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 | 0.931723 | − | 0.363170i | \(-0.118306\pi\) |
−0.967246 | + | 0.253842i | \(0.918306\pi\) | |||||||
\(774\) | 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 | \(-0.573408\pi\) |
−0.996512 | + | 0.0834455i | \(0.973408\pi\) | |||||||
\(788\) | −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 | 0.918709 | − | 0.394936i | \(-0.129233\pi\) |
−0.0917101 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(798\) | −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 | \(-0.473235\pi\) |
−0.921743 | + | 0.387802i | \(0.873235\pi\) | |||||||
\(810\) | 10.3615 | − | 31.8895i | 0.364067 | − | 1.12048i | ||||
\(811\) | 0.766764 | + | 2.35986i | 0.0269247 | + | 0.0828657i | 0.963616 | − | 0.267291i | \(-0.0861284\pi\) |
−0.936691 | + | 0.350156i | \(0.886128\pi\) | |||||||
\(812\) | −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 | \(-0.821334\pi\) |
0.997755 | + | 0.0669738i | \(0.0213344\pi\) | |||||||
\(822\) | −1.63741 | − | 5.03944i | −0.0571113 | − | 0.175771i | ||||
\(823\) | 34.6205 | − | 25.1533i | 1.20679 | − | 0.876787i | 0.211859 | − | 0.977300i | \(-0.432048\pi\) |
0.994936 | + | 0.100513i | \(0.0320484\pi\) | |||||||
\(824\) | 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 | \(-0.649029\pi\) |
0.709261 | + | 0.704946i | \(0.249029\pi\) | |||||||
\(828\) | 0.644005 | + | 1.98204i | 0.0223807 | + | 0.0688808i | ||||
\(829\) | 9.02246 | − | 27.7683i | 0.313363 | − | 0.964433i | −0.663060 | − | 0.748566i | \(-0.730743\pi\) |
0.976423 | − | 0.215866i | \(-0.0692575\pi\) | |||||||
\(830\) | 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 | 0.999442 | + | 0.0334134i | \(0.0106378\pi\) |
−0.788925 | + | 0.614489i | \(0.789362\pi\) | |||||||
\(840\) | −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 | \(-0.138678\pi\) |
−0.121212 | + | 0.992627i | \(0.538678\pi\) | |||||||
\(854\) | −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 | \(-0.427596\pi\) | ||||
0.225509 | + | 0.974241i | \(0.427596\pi\) | |||||||
\(858\) | 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 | −0.00863946 | − | 0.999963i | \(-0.502750\pi\) |
−0.953691 | + | 0.300789i | \(0.902750\pi\) | |||||||
\(864\) | 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 | −0.988865 | − | 0.148812i | \(-0.952455\pi\) |
0.712539 | − | 0.701632i | \(-0.247545\pi\) | |||||||
\(878\) | −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 | −0.860443 | − | 0.509547i | \(-0.829813\pi\) |
0.396609 | − | 0.917988i | \(-0.370187\pi\) | |||||||
\(884\) | −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 | −0.654414 | − | 0.756137i | \(-0.727085\pi\) |
0.973878 | − | 0.227072i | \(-0.0729154\pi\) | |||||||
\(888\) | 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 | 0.220635 | − | 0.975356i | \(-0.429187\pi\) |
−0.859439 | + | 0.511238i | \(0.829187\pi\) | |||||||
\(908\) | 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 | −0.314157 | + | 0.949371i | \(0.601722\pi\) |
−0.999985 | + | 0.00540957i | \(0.998278\pi\) | |||||||
\(912\) | −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 | \(-0.0706668\pi\) |
0.0920227 | + | 0.995757i | \(0.470667\pi\) | |||||||
\(920\) | −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 | 0.969614 | + | 0.244641i | \(0.0786702\pi\) |
0.532295 | + | 0.846559i | \(0.321330\pi\) | |||||||
\(930\) | 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 | \(-0.788567\pi\) |
0.342969 | + | 0.939347i | \(0.388567\pi\) | |||||||
\(938\) | −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 | \(-0.262248\pi\) |
−0.487931 | + | 0.872882i | \(0.662248\pi\) | |||||||
\(942\) | −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 | \(-0.936942\pi\) |
0.908876 | + | 0.417066i | \(0.136942\pi\) | |||||||
\(954\) | −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 | \(-0.582609\pi\) | ||||
−0.256620 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(968\) | 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 | −0.980691 | − | 0.195563i | \(-0.937347\pi\) |
0.678447 | − | 0.734649i | \(-0.262653\pi\) | |||||||
\(972\) | −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 | −0.639974 | − | 0.768397i | \(-0.721055\pi\) |
0.533026 | + | 0.846099i | \(0.321055\pi\) | |||||||
\(978\) | −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 | 0.748716 | + | 0.662891i | \(0.230671\pi\) |
−0.995362 | + | 0.0962053i | \(0.969329\pi\) | |||||||
\(984\) | 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 | 0.765737 | + | 0.643154i | \(0.222374\pi\) |
−0.997531 | + | 0.0702335i | \(0.977626\pi\) | |||||||
\(998\) | −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.t.729.2 | 12 | ||
11.2 | odd | 10 | 847.2.a.i.1.2 | ✓ | 3 | ||
11.3 | even | 5 | inner | 847.2.f.t.148.2 | 12 | ||
11.4 | even | 5 | inner | 847.2.f.t.323.2 | 12 | ||
11.5 | even | 5 | inner | 847.2.f.t.372.2 | 12 | ||
11.6 | odd | 10 | 847.2.f.u.372.2 | 12 | |||
11.7 | odd | 10 | 847.2.f.u.323.2 | 12 | |||
11.8 | odd | 10 | 847.2.f.u.148.2 | 12 | |||
11.9 | even | 5 | 847.2.a.j.1.2 | yes | 3 | ||
11.10 | odd | 2 | 847.2.f.u.729.2 | 12 | |||
33.2 | even | 10 | 7623.2.a.ce.1.2 | 3 | |||
33.20 | odd | 10 | 7623.2.a.bz.1.2 | 3 | |||
77.13 | even | 10 | 5929.2.a.t.1.2 | 3 | |||
77.20 | odd | 10 | 5929.2.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.2 | ✓ | 3 | 11.2 | odd | 10 | ||
847.2.a.j.1.2 | yes | 3 | 11.9 | even | 5 | ||
847.2.f.t.148.2 | 12 | 11.3 | even | 5 | inner | ||
847.2.f.t.323.2 | 12 | 11.4 | even | 5 | inner | ||
847.2.f.t.372.2 | 12 | 11.5 | even | 5 | inner | ||
847.2.f.t.729.2 | 12 | 1.1 | even | 1 | trivial | ||
847.2.f.u.148.2 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.323.2 | 12 | 11.7 | odd | 10 | |||
847.2.f.u.372.2 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.729.2 | 12 | 11.10 | odd | 2 | |||
5929.2.a.t.1.2 | 3 | 77.13 | even | 10 | |||
5929.2.a.y.1.2 | 3 | 77.20 | odd | 10 | |||
7623.2.a.bz.1.2 | 3 | 33.20 | odd | 10 | |||
7623.2.a.ce.1.2 | 3 | 33.2 | even | 10 |