Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 823.3 | ||
Root | \(-1.07992 + 0.623490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.823 |
Dual form | 1014.2.i.g.361.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.692021i | 0.309481i | 0.987955 | + | 0.154741i | \(0.0494542\pi\) | ||||
−0.987955 | + | 0.154741i | \(0.950546\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | 0.309081 | − | 0.178448i | 0.116822 | − | 0.0674470i | −0.440451 | − | 0.897777i | \(-0.645181\pi\) |
0.557272 | + | 0.830330i | \(0.311848\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.346011 | − | 0.599308i | 0.109418 | − | 0.189518i | ||||
\(11\) | −2.54525 | − | 1.46950i | −0.767422 | − | 0.443071i | 0.0645324 | − | 0.997916i | \(-0.479444\pi\) |
−0.831954 | + | 0.554845i | \(0.812778\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.356896 | −0.0953844 | ||||||||
\(15\) | −0.599308 | − | 0.346011i | −0.154741 | − | 0.0893396i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.35690 | + | 5.81431i | 0.814167 | + | 1.41018i | 0.909925 | + | 0.414774i | \(0.136139\pi\) |
−0.0957578 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.24210 | − | 3.60388i | 1.43203 | − | 0.826786i | 0.434759 | − | 0.900547i | \(-0.356834\pi\) |
0.997276 | + | 0.0737611i | \(0.0235002\pi\) | |||||||
\(20\) | −0.599308 | + | 0.346011i | −0.134009 | + | 0.0773704i | ||||
\(21\) | 0.356896i | 0.0778811i | ||||||||
\(22\) | 1.46950 | + | 2.54525i | 0.313299 | + | 0.542649i | ||||
\(23\) | 1.19806 | − | 2.07510i | 0.249813 | − | 0.432689i | −0.713661 | − | 0.700492i | \(-0.752964\pi\) |
0.963474 | + | 0.267802i | \(0.0862974\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 4.52111 | 0.904221 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.309081 | + | 0.178448i | 0.0584108 | + | 0.0337235i | ||||
\(29\) | −3.91454 | + | 6.78019i | −0.726912 | + | 1.25905i | 0.231270 | + | 0.972890i | \(0.425712\pi\) |
−0.958182 | + | 0.286159i | \(0.907621\pi\) | |||||||
\(30\) | 0.346011 | + | 0.599308i | 0.0631726 | + | 0.109418i | ||||
\(31\) | 2.76271i | 0.496197i | 0.968735 | + | 0.248099i | \(0.0798057\pi\) | ||||
−0.968735 | + | 0.248099i | \(0.920194\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 2.54525 | − | 1.46950i | 0.443071 | − | 0.255807i | ||||
\(34\) | − | 6.71379i | − | 1.15141i | ||||||
\(35\) | 0.123490 | + | 0.213891i | 0.0208736 | + | 0.0361541i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | −8.74498 | − | 5.04892i | −1.43767 | − | 0.830037i | −0.439979 | − | 0.898008i | \(-0.645014\pi\) |
−0.997687 | + | 0.0679713i | \(0.978347\pi\) | |||||||
\(38\) | −7.20775 | −1.16925 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.692021 | 0.109418 | ||||||||
\(41\) | 4.23494 | + | 2.44504i | 0.661386 | + | 0.381851i | 0.792805 | − | 0.609476i | \(-0.208620\pi\) |
−0.131419 | + | 0.991327i | \(0.541953\pi\) | |||||||
\(42\) | 0.178448 | − | 0.309081i | 0.0275351 | − | 0.0476922i | ||||
\(43\) | 3.29590 | + | 5.70866i | 0.502620 | + | 0.870563i | 0.999995 | + | 0.00302747i | \(0.000963674\pi\) |
−0.497376 | + | 0.867535i | \(0.665703\pi\) | |||||||
\(44\) | − | 2.93900i | − | 0.443071i | ||||||
\(45\) | 0.599308 | − | 0.346011i | 0.0893396 | − | 0.0515802i | ||||
\(46\) | −2.07510 | + | 1.19806i | −0.305957 | + | 0.176645i | ||||
\(47\) | 4.98792i | 0.727563i | 0.931484 | + | 0.363781i | \(0.118514\pi\) | ||||
−0.931484 | + | 0.363781i | \(0.881486\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −3.43631 | + | 5.95187i | −0.490902 | + | 0.850267i | ||||
\(50\) | −3.91539 | − | 2.26055i | −0.553720 | − | 0.319690i | ||||
\(51\) | −6.71379 | −0.940119 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.88769 | −1.22082 | −0.610409 | − | 0.792086i | \(-0.708995\pi\) | ||||
−0.610409 | + | 0.792086i | \(0.708995\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 1.01693 | − | 1.76137i | 0.137122 | − | 0.237503i | ||||
\(56\) | −0.178448 | − | 0.309081i | −0.0238461 | − | 0.0413027i | ||||
\(57\) | 7.20775i | 0.954690i | ||||||||
\(58\) | 6.78019 | − | 3.91454i | 0.890282 | − | 0.514005i | ||||
\(59\) | 1.42297 | − | 0.821552i | 0.185255 | − | 0.106957i | −0.404504 | − | 0.914536i | \(-0.632556\pi\) |
0.589759 | + | 0.807579i | \(0.299223\pi\) | |||||||
\(60\) | − | 0.692021i | − | 0.0893396i | ||||||
\(61\) | 3.24698 | + | 5.62393i | 0.415733 | + | 0.720071i | 0.995505 | − | 0.0947079i | \(-0.0301917\pi\) |
−0.579772 | + | 0.814779i | \(0.696858\pi\) | |||||||
\(62\) | 1.38135 | − | 2.39258i | 0.175432 | − | 0.303857i | ||||
\(63\) | −0.309081 | − | 0.178448i | −0.0389405 | − | 0.0224823i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.93900 | −0.361766 | ||||||||
\(67\) | 11.7134 | + | 6.76271i | 1.43101 | + | 0.826196i | 0.997198 | − | 0.0748051i | \(-0.0238335\pi\) |
0.433816 | + | 0.901001i | \(0.357167\pi\) | |||||||
\(68\) | −3.35690 | + | 5.81431i | −0.407083 | + | 0.705089i | ||||
\(69\) | 1.19806 | + | 2.07510i | 0.144230 | + | 0.249813i | ||||
\(70\) | − | 0.246980i | − | 0.0295197i | ||||||
\(71\) | −5.89904 | + | 3.40581i | −0.700087 | + | 0.404196i | −0.807380 | − | 0.590032i | \(-0.799115\pi\) |
0.107293 | + | 0.994227i | \(0.465782\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 3.18598i | 0.372891i | 0.982465 | + | 0.186445i | \(0.0596968\pi\) | ||||
−0.982465 | + | 0.186445i | \(0.940303\pi\) | |||||||
\(74\) | 5.04892 | + | 8.74498i | 0.586925 | + | 1.01658i | ||||
\(75\) | −2.26055 | + | 3.91539i | −0.261026 | + | 0.452111i | ||||
\(76\) | 6.24210 | + | 3.60388i | 0.716017 | + | 0.413393i | ||||
\(77\) | −1.04892 | −0.119535 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0465 | 1.69287 | 0.846433 | − | 0.532495i | \(-0.178745\pi\) | ||||
0.846433 | + | 0.532495i | \(0.178745\pi\) | |||||||
\(80\) | −0.599308 | − | 0.346011i | −0.0670047 | − | 0.0386852i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.44504 | − | 4.23494i | −0.270010 | − | 0.467671i | ||||
\(83\) | 14.8267i | 1.62744i | 0.581256 | + | 0.813720i | \(0.302561\pi\) | ||||
−0.581256 | + | 0.813720i | \(0.697439\pi\) | |||||||
\(84\) | −0.309081 | + | 0.178448i | −0.0337235 | + | 0.0194703i | ||||
\(85\) | −4.02363 | + | 2.32304i | −0.436424 | + | 0.251970i | ||||
\(86\) | − | 6.59179i | − | 0.710811i | ||||||
\(87\) | −3.91454 | − | 6.78019i | −0.419683 | − | 0.726912i | ||||
\(88\) | −1.46950 | + | 2.54525i | −0.156649 | + | 0.271325i | ||||
\(89\) | −0.343054 | − | 0.198062i | −0.0363636 | − | 0.0209946i | 0.481708 | − | 0.876332i | \(-0.340017\pi\) |
−0.518072 | + | 0.855337i | \(0.673350\pi\) | |||||||
\(90\) | −0.692021 | −0.0729455 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.39612 | 0.249813 | ||||||||
\(93\) | −2.39258 | − | 1.38135i | −0.248099 | − | 0.143240i | ||||
\(94\) | 2.49396 | − | 4.31966i | 0.257232 | − | 0.445539i | ||||
\(95\) | 2.49396 | + | 4.31966i | 0.255875 | + | 0.443188i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 0.361908 | − | 0.208947i | 0.0367461 | − | 0.0212154i | −0.481514 | − | 0.876438i | \(-0.659913\pi\) |
0.518261 | + | 0.855223i | \(0.326580\pi\) | |||||||
\(98\) | 5.95187 | − | 3.43631i | 0.601229 | − | 0.347120i | ||||
\(99\) | 2.93900i | 0.295381i | ||||||||
\(100\) | 2.26055 | + | 3.91539i | 0.226055 | + | 0.391539i | ||||
\(101\) | 5.00753 | − | 8.67330i | 0.498268 | − | 0.863026i | −0.501730 | − | 0.865024i | \(-0.667303\pi\) |
0.999998 | + | 0.00199864i | \(0.000636186\pi\) | |||||||
\(102\) | 5.81431 | + | 3.35690i | 0.575703 | + | 0.332382i | ||||
\(103\) | 9.62565 | 0.948443 | 0.474222 | − | 0.880406i | \(-0.342730\pi\) | ||||
0.474222 | + | 0.880406i | \(0.342730\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.246980 | −0.0241027 | ||||||||
\(106\) | 7.69697 | + | 4.44385i | 0.747595 | + | 0.431624i | ||||
\(107\) | 3.31551 | − | 5.74263i | 0.320523 | − | 0.555161i | −0.660073 | − | 0.751201i | \(-0.729475\pi\) |
0.980596 | + | 0.196040i | \(0.0628082\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 12.9879i | − | 1.24402i | −0.783011 | − | 0.622008i | \(-0.786317\pi\) | ||
0.783011 | − | 0.622008i | \(-0.213683\pi\) | |||||||
\(110\) | −1.76137 | + | 1.01693i | −0.167940 | + | 0.0969601i | ||||
\(111\) | 8.74498 | − | 5.04892i | 0.830037 | − | 0.479222i | ||||
\(112\) | 0.356896i | 0.0337235i | ||||||||
\(113\) | −0.396125 | − | 0.686108i | −0.0372643 | − | 0.0645436i | 0.846792 | − | 0.531925i | \(-0.178531\pi\) |
−0.884056 | + | 0.467381i | \(0.845198\pi\) | |||||||
\(114\) | 3.60388 | − | 6.24210i | 0.337534 | − | 0.584626i | ||||
\(115\) | 1.43602 | + | 0.829085i | 0.133909 | + | 0.0773126i | ||||
\(116\) | −7.82908 | −0.726912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.64310 | −0.151260 | ||||||||
\(119\) | 2.07510 | + | 1.19806i | 0.190225 | + | 0.109826i | ||||
\(120\) | −0.346011 | + | 0.599308i | −0.0315863 | + | 0.0547091i | ||||
\(121\) | −1.18114 | − | 2.04579i | −0.107376 | − | 0.185981i | ||||
\(122\) | − | 6.49396i | − | 0.587935i | ||||||
\(123\) | −4.23494 | + | 2.44504i | −0.381851 | + | 0.220462i | ||||
\(124\) | −2.39258 | + | 1.38135i | −0.214860 | + | 0.124049i | ||||
\(125\) | 6.58881i | 0.589321i | ||||||||
\(126\) | 0.178448 | + | 0.309081i | 0.0158974 | + | 0.0275351i | ||||
\(127\) | −9.10872 | + | 15.7768i | −0.808268 | + | 1.39996i | 0.105794 | + | 0.994388i | \(0.466262\pi\) |
−0.914062 | + | 0.405574i | \(0.867072\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −6.59179 | −0.580375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.73556 | 0.239007 | 0.119504 | − | 0.992834i | \(-0.461870\pi\) | ||||
0.119504 | + | 0.992834i | \(0.461870\pi\) | |||||||
\(132\) | 2.54525 | + | 1.46950i | 0.221536 | + | 0.127904i | ||||
\(133\) | 1.28621 | − | 2.22778i | 0.111528 | − | 0.193173i | ||||
\(134\) | −6.76271 | − | 11.7134i | −0.584209 | − | 1.01188i | ||||
\(135\) | 0.692021i | 0.0595597i | ||||||||
\(136\) | 5.81431 | − | 3.35690i | 0.498573 | − | 0.287851i | ||||
\(137\) | −6.62286 | + | 3.82371i | −0.565829 | + | 0.326681i | −0.755482 | − | 0.655170i | \(-0.772597\pi\) |
0.189653 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(138\) | − | 2.39612i | − | 0.203972i | ||||||
\(139\) | −1.69202 | − | 2.93067i | −0.143515 | − | 0.248576i | 0.785303 | − | 0.619112i | \(-0.212507\pi\) |
−0.928818 | + | 0.370536i | \(0.879174\pi\) | |||||||
\(140\) | −0.123490 | + | 0.213891i | −0.0104368 | + | 0.0180771i | ||||
\(141\) | −4.31966 | − | 2.49396i | −0.363781 | − | 0.210029i | ||||
\(142\) | 6.81163 | 0.571619 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.69203 | − | 2.70895i | −0.389652 | − | 0.224966i | ||||
\(146\) | 1.59299 | − | 2.75914i | 0.131837 | − | 0.228348i | ||||
\(147\) | −3.43631 | − | 5.95187i | −0.283422 | − | 0.490902i | ||||
\(148\) | − | 10.0978i | − | 0.830037i | ||||||
\(149\) | −18.0281 | + | 10.4085i | −1.47692 | + | 0.852698i | −0.999660 | − | 0.0260669i | \(-0.991702\pi\) |
−0.477255 | + | 0.878765i | \(0.658368\pi\) | |||||||
\(150\) | 3.91539 | − | 2.26055i | 0.319690 | − | 0.184573i | ||||
\(151\) | 0.895461i | 0.0728715i | 0.999336 | + | 0.0364358i | \(0.0116004\pi\) | ||||
−0.999336 | + | 0.0364358i | \(0.988400\pi\) | |||||||
\(152\) | −3.60388 | − | 6.24210i | −0.292313 | − | 0.506301i | ||||
\(153\) | 3.35690 | − | 5.81431i | 0.271389 | − | 0.470059i | ||||
\(154\) | 0.908389 | + | 0.524459i | 0.0732001 | + | 0.0422621i | ||||
\(155\) | −1.91185 | −0.153564 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.59179 | 0.685700 | 0.342850 | − | 0.939390i | \(-0.388608\pi\) | ||||
0.342850 | + | 0.939390i | \(0.388608\pi\) | |||||||
\(158\) | −13.0307 | − | 7.52326i | −1.03666 | − | 0.598519i | ||||
\(159\) | 4.44385 | − | 7.69697i | 0.352420 | − | 0.610409i | ||||
\(160\) | 0.346011 | + | 0.599308i | 0.0273546 | + | 0.0473795i | ||||
\(161\) | − | 0.855167i | − | 0.0673966i | ||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −1.49465 | + | 0.862937i | −0.117070 | + | 0.0675904i | −0.557392 | − | 0.830250i | \(-0.688198\pi\) |
0.440322 | + | 0.897840i | \(0.354864\pi\) | |||||||
\(164\) | 4.89008i | 0.381851i | ||||||||
\(165\) | 1.01693 | + | 1.76137i | 0.0791676 | + | 0.137122i | ||||
\(166\) | 7.41335 | − | 12.8403i | 0.575387 | − | 0.996600i | ||||
\(167\) | 18.3078 | + | 10.5700i | 1.41670 | + | 0.817933i | 0.996007 | − | 0.0892696i | \(-0.0284533\pi\) |
0.420694 | + | 0.907203i | \(0.361787\pi\) | |||||||
\(168\) | 0.356896 | 0.0275351 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.64609 | 0.356339 | ||||||||
\(171\) | −6.24210 | − | 3.60388i | −0.477345 | − | 0.275595i | ||||
\(172\) | −3.29590 | + | 5.70866i | −0.251310 | + | 0.435281i | ||||
\(173\) | 4.67725 | + | 8.10124i | 0.355605 | + | 0.615926i | 0.987221 | − | 0.159355i | \(-0.0509416\pi\) |
−0.631616 | + | 0.775281i | \(0.717608\pi\) | |||||||
\(174\) | 7.82908i | 0.593521i | ||||||||
\(175\) | 1.39739 | − | 0.806782i | 0.105633 | − | 0.0609870i | ||||
\(176\) | 2.54525 | − | 1.46950i | 0.191855 | − | 0.110768i | ||||
\(177\) | 1.64310i | 0.123503i | ||||||||
\(178\) | 0.198062 | + | 0.343054i | 0.0148454 | + | 0.0257130i | ||||
\(179\) | 1.58761 | − | 2.74983i | 0.118664 | − | 0.205532i | −0.800575 | − | 0.599233i | \(-0.795472\pi\) |
0.919238 | + | 0.393701i | \(0.128806\pi\) | |||||||
\(180\) | 0.599308 | + | 0.346011i | 0.0446698 | + | 0.0257901i | ||||
\(181\) | 19.7995 | 1.47169 | 0.735844 | − | 0.677151i | \(-0.236786\pi\) | ||||
0.735844 | + | 0.677151i | \(0.236786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.49396 | −0.480047 | ||||||||
\(184\) | −2.07510 | − | 1.19806i | −0.152979 | − | 0.0883223i | ||||
\(185\) | 3.49396 | − | 6.05171i | 0.256881 | − | 0.444931i | ||||
\(186\) | 1.38135 | + | 2.39258i | 0.101286 | + | 0.175432i | ||||
\(187\) | − | 19.7318i | − | 1.44294i | ||||||
\(188\) | −4.31966 | + | 2.49396i | −0.315044 | + | 0.181891i | ||||
\(189\) | 0.309081 | − | 0.178448i | 0.0224823 | − | 0.0129802i | ||||
\(190\) | − | 4.98792i | − | 0.361862i | ||||||
\(191\) | −7.63102 | − | 13.2173i | −0.552161 | − | 0.956372i | −0.998118 | − | 0.0613172i | \(-0.980470\pi\) |
0.445957 | − | 0.895054i | \(-0.352863\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 4.12928 | + | 2.38404i | 0.297232 | + | 0.171607i | 0.641199 | − | 0.767375i | \(-0.278437\pi\) |
−0.343967 | + | 0.938982i | \(0.611771\pi\) | |||||||
\(194\) | −0.417895 | −0.0300031 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.87263 | −0.490902 | ||||||||
\(197\) | −10.5957 | − | 6.11745i | −0.754915 | − | 0.435850i | 0.0725523 | − | 0.997365i | \(-0.476886\pi\) |
−0.827467 | + | 0.561514i | \(0.810219\pi\) | |||||||
\(198\) | 1.46950 | − | 2.54525i | 0.104433 | − | 0.180883i | ||||
\(199\) | −5.92423 | − | 10.2611i | −0.419958 | − | 0.727388i | 0.575977 | − | 0.817466i | \(-0.304622\pi\) |
−0.995935 | + | 0.0900779i | \(0.971288\pi\) | |||||||
\(200\) | − | 4.52111i | − | 0.319690i | ||||||
\(201\) | −11.7134 | + | 6.76271i | −0.826196 | + | 0.477005i | ||||
\(202\) | −8.67330 | + | 5.00753i | −0.610251 | + | 0.352329i | ||||
\(203\) | 2.79417i | 0.196112i | ||||||||
\(204\) | −3.35690 | − | 5.81431i | −0.235030 | − | 0.407083i | ||||
\(205\) | −1.69202 | + | 2.93067i | −0.118176 | + | 0.204687i | ||||
\(206\) | −8.33605 | − | 4.81282i | −0.580800 | − | 0.335325i | ||||
\(207\) | −2.39612 | −0.166542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1836 | −1.46530 | ||||||||
\(210\) | 0.213891 | + | 0.123490i | 0.0147599 | + | 0.00852161i | ||||
\(211\) | 8.63102 | − | 14.9494i | 0.594184 | − | 1.02916i | −0.399477 | − | 0.916743i | \(-0.630808\pi\) |
0.993661 | − | 0.112414i | \(-0.0358583\pi\) | |||||||
\(212\) | −4.44385 | − | 7.69697i | −0.305205 | − | 0.528630i | ||||
\(213\) | − | 6.81163i | − | 0.466725i | ||||||
\(214\) | −5.74263 | + | 3.31551i | −0.392558 | + | 0.226644i | ||||
\(215\) | −3.95052 | + | 2.28083i | −0.269423 | + | 0.155551i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0.493000 | + | 0.853901i | 0.0334670 | + | 0.0579665i | ||||
\(218\) | −6.49396 | + | 11.2479i | −0.439826 | + | 0.761802i | ||||
\(219\) | −2.75914 | − | 1.59299i | −0.186445 | − | 0.107644i | ||||
\(220\) | 2.03385 | 0.137122 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.0978 | −0.677722 | ||||||||
\(223\) | −5.86133 | − | 3.38404i | −0.392504 | − | 0.226612i | 0.290741 | − | 0.956802i | \(-0.406098\pi\) |
−0.683245 | + | 0.730190i | \(0.739432\pi\) | |||||||
\(224\) | 0.178448 | − | 0.309081i | 0.0119231 | − | 0.0206513i | ||||
\(225\) | −2.26055 | − | 3.91539i | −0.150704 | − | 0.261026i | ||||
\(226\) | 0.792249i | 0.0526996i | ||||||||
\(227\) | 20.5074 | − | 11.8400i | 1.36113 | − | 0.785846i | 0.371352 | − | 0.928492i | \(-0.378894\pi\) |
0.989774 | + | 0.142646i | \(0.0455610\pi\) | |||||||
\(228\) | −6.24210 | + | 3.60388i | −0.413393 | + | 0.238672i | ||||
\(229\) | 8.29829i | 0.548366i | 0.961677 | + | 0.274183i | \(0.0884075\pi\) | ||||
−0.961677 | + | 0.274183i | \(0.911593\pi\) | |||||||
\(230\) | −0.829085 | − | 1.43602i | −0.0546682 | − | 0.0946882i | ||||
\(231\) | 0.524459 | − | 0.908389i | 0.0345068 | − | 0.0597676i | ||||
\(232\) | 6.78019 | + | 3.91454i | 0.445141 | + | 0.257002i | ||||
\(233\) | 23.9651 | 1.57000 | 0.785002 | − | 0.619493i | \(-0.212662\pi\) | ||||
0.785002 | + | 0.619493i | \(0.212662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.45175 | −0.225167 | ||||||||
\(236\) | 1.42297 | + | 0.821552i | 0.0926275 | + | 0.0534785i | ||||
\(237\) | −7.52326 | + | 13.0307i | −0.488688 | + | 0.846433i | ||||
\(238\) | −1.19806 | − | 2.07510i | −0.0776588 | − | 0.134509i | ||||
\(239\) | 12.6160i | 0.816058i | 0.912969 | + | 0.408029i | \(0.133784\pi\) | ||||
−0.912969 | + | 0.408029i | \(0.866216\pi\) | |||||||
\(240\) | 0.599308 | − | 0.346011i | 0.0386852 | − | 0.0223349i | ||||
\(241\) | −22.8576 | + | 13.1969i | −1.47239 | + | 0.850085i | −0.999518 | − | 0.0310462i | \(-0.990116\pi\) |
−0.472872 | + | 0.881131i | \(0.656783\pi\) | |||||||
\(242\) | 2.36227i | 0.151853i | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.24698 | + | 5.62393i | −0.207867 | + | 0.360035i | ||||
\(245\) | −4.11882 | − | 2.37800i | −0.263142 | − | 0.151925i | ||||
\(246\) | 4.89008 | 0.311780 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.76271 | 0.175432 | ||||||||
\(249\) | −12.8403 | − | 7.41335i | −0.813720 | − | 0.469802i | ||||
\(250\) | 3.29440 | − | 5.70608i | 0.208356 | − | 0.360884i | ||||
\(251\) | −15.0172 | − | 26.0106i | −0.947879 | − | 1.64177i | −0.749882 | − | 0.661571i | \(-0.769890\pi\) |
−0.197996 | − | 0.980203i | \(-0.563443\pi\) | |||||||
\(252\) | − | 0.356896i | − | 0.0224823i | ||||||
\(253\) | −6.09873 | + | 3.52111i | −0.383424 | + | 0.221370i | ||||
\(254\) | 15.7768 | − | 9.10872i | 0.989922 | − | 0.571532i | ||||
\(255\) | − | 4.64609i | − | 0.290949i | ||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.63102 | − | 9.75322i | 0.351254 | − | 0.608389i | −0.635216 | − | 0.772335i | \(-0.719089\pi\) |
0.986469 | + | 0.163946i | \(0.0524222\pi\) | |||||||
\(258\) | 5.70866 | + | 3.29590i | 0.355406 | + | 0.205194i | ||||
\(259\) | −3.60388 | −0.223934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.82908 | 0.484608 | ||||||||
\(262\) | −2.36907 | − | 1.36778i | −0.146361 | − | 0.0845018i | ||||
\(263\) | 2.77479 | − | 4.80608i | 0.171101 | − | 0.296355i | −0.767704 | − | 0.640804i | \(-0.778601\pi\) |
0.938805 | + | 0.344449i | \(0.111934\pi\) | |||||||
\(264\) | −1.46950 | − | 2.54525i | −0.0904415 | − | 0.156649i | ||||
\(265\) | − | 6.15047i | − | 0.377821i | ||||||
\(266\) | −2.22778 | + | 1.28621i | −0.136594 | + | 0.0788625i | ||||
\(267\) | 0.343054 | − | 0.198062i | 0.0209946 | − | 0.0121212i | ||||
\(268\) | 13.5254i | 0.826196i | ||||||||
\(269\) | −8.34362 | − | 14.4516i | −0.508719 | − | 0.881128i | −0.999949 | − | 0.0100977i | \(-0.996786\pi\) |
0.491230 | − | 0.871030i | \(-0.336548\pi\) | |||||||
\(270\) | 0.346011 | − | 0.599308i | 0.0210575 | − | 0.0364727i | ||||
\(271\) | −5.72751 | − | 3.30678i | −0.347922 | − | 0.200873i | 0.315848 | − | 0.948810i | \(-0.397711\pi\) |
−0.663770 | + | 0.747937i | \(0.731044\pi\) | |||||||
\(272\) | −6.71379 | −0.407083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.64742 | 0.461997 | ||||||||
\(275\) | −11.5073 | − | 6.64377i | −0.693919 | − | 0.400634i | ||||
\(276\) | −1.19806 | + | 2.07510i | −0.0721149 | + | 0.124907i | ||||
\(277\) | −10.8998 | − | 18.8790i | −0.654904 | − | 1.13433i | −0.981918 | − | 0.189307i | \(-0.939376\pi\) |
0.327014 | − | 0.945019i | \(-0.393958\pi\) | |||||||
\(278\) | 3.38404i | 0.202961i | ||||||||
\(279\) | 2.39258 | − | 1.38135i | 0.143240 | − | 0.0826995i | ||||
\(280\) | 0.213891 | − | 0.123490i | 0.0127824 | − | 0.00737993i | ||||
\(281\) | − | 20.5918i | − | 1.22840i | −0.789149 | − | 0.614202i | \(-0.789478\pi\) | ||
0.789149 | − | 0.614202i | \(-0.210522\pi\) | |||||||
\(282\) | 2.49396 | + | 4.31966i | 0.148513 | + | 0.257232i | ||||
\(283\) | −6.50604 | + | 11.2688i | −0.386744 | + | 0.669860i | −0.992009 | − | 0.126163i | \(-0.959734\pi\) |
0.605265 | + | 0.796024i | \(0.293067\pi\) | |||||||
\(284\) | −5.89904 | − | 3.40581i | −0.350044 | − | 0.202098i | ||||
\(285\) | −4.98792 | −0.295459 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.74525 | 0.103019 | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −14.0375 | + | 24.3137i | −0.825735 | + | 1.43022i | ||||
\(290\) | 2.70895 | + | 4.69203i | 0.159075 | + | 0.275526i | ||||
\(291\) | 0.417895i | 0.0244974i | ||||||||
\(292\) | −2.75914 | + | 1.59299i | −0.161466 | + | 0.0932227i | ||||
\(293\) | 12.9376 | − | 7.46950i | 0.755820 | − | 0.436373i | −0.0719730 | − | 0.997407i | \(-0.522930\pi\) |
0.827793 | + | 0.561034i | \(0.189596\pi\) | |||||||
\(294\) | 6.87263i | 0.400820i | ||||||||
\(295\) | 0.568532 | + | 0.984726i | 0.0331012 | + | 0.0573329i | ||||
\(296\) | −5.04892 | + | 8.74498i | −0.293462 | + | 0.508292i | ||||
\(297\) | −2.54525 | − | 1.46950i | −0.147690 | − | 0.0852691i | ||||
\(298\) | 20.8170 | 1.20590 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.52111 | −0.261026 | ||||||||
\(301\) | 2.03740 | + | 1.17629i | 0.117434 | + | 0.0678003i | ||||
\(302\) | 0.447730 | − | 0.775492i | 0.0257640 | − | 0.0446245i | ||||
\(303\) | 5.00753 | + | 8.67330i | 0.287675 | + | 0.498268i | ||||
\(304\) | 7.20775i | 0.413393i | ||||||||
\(305\) | −3.89188 | + | 2.24698i | −0.222849 | + | 0.128662i | ||||
\(306\) | −5.81431 | + | 3.35690i | −0.332382 | + | 0.191901i | ||||
\(307\) | − | 26.0301i | − | 1.48562i | −0.669503 | − | 0.742809i | \(-0.733493\pi\) | ||
0.669503 | − | 0.742809i | \(-0.266507\pi\) | |||||||
\(308\) | −0.524459 | − | 0.908389i | −0.0298838 | − | 0.0517603i | ||||
\(309\) | −4.81282 | + | 8.33605i | −0.273792 | + | 0.474222i | ||||
\(310\) | 1.65571 | + | 0.955927i | 0.0940382 | + | 0.0542930i | ||||
\(311\) | 4.81163 | 0.272842 | 0.136421 | − | 0.990651i | \(-0.456440\pi\) | ||||
0.136421 | + | 0.990651i | \(0.456440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0411 | −1.47193 | −0.735966 | − | 0.677018i | \(-0.763272\pi\) | ||||
−0.735966 | + | 0.677018i | \(0.763272\pi\) | |||||||
\(314\) | −7.44071 | − | 4.29590i | −0.419904 | − | 0.242431i | ||||
\(315\) | 0.123490 | − | 0.213891i | 0.00695786 | − | 0.0120514i | ||||
\(316\) | 7.52326 | + | 13.0307i | 0.423217 | + | 0.733033i | ||||
\(317\) | − | 11.5211i | − | 0.647090i | −0.946213 | − | 0.323545i | \(-0.895125\pi\) | ||
0.946213 | − | 0.323545i | \(-0.104875\pi\) | |||||||
\(318\) | −7.69697 | + | 4.44385i | −0.431624 | + | 0.249198i | ||||
\(319\) | 19.9270 | − | 11.5048i | 1.11570 | − | 0.644148i | ||||
\(320\) | − | 0.692021i | − | 0.0386852i | ||||||
\(321\) | 3.31551 | + | 5.74263i | 0.185054 | + | 0.320523i | ||||
\(322\) | −0.427583 | + | 0.740596i | −0.0238283 | + | 0.0412718i | ||||
\(323\) | 41.9081 | + | 24.1957i | 2.33183 | + | 1.34628i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.72587 | 0.0955873 | ||||||||
\(327\) | 11.2479 | + | 6.49396i | 0.622008 | + | 0.359117i | ||||
\(328\) | 2.44504 | − | 4.23494i | 0.135005 | − | 0.233835i | ||||
\(329\) | 0.890084 | + | 1.54167i | 0.0490719 | + | 0.0849950i | ||||
\(330\) | − | 2.03385i | − | 0.111960i | ||||||
\(331\) | 2.97769 | − | 1.71917i | 0.163668 | − | 0.0944940i | −0.415928 | − | 0.909397i | \(-0.636543\pi\) |
0.579597 | + | 0.814903i | \(0.303210\pi\) | |||||||
\(332\) | −12.8403 | + | 7.41335i | −0.704703 | + | 0.406860i | ||||
\(333\) | 10.0978i | 0.553358i | ||||||||
\(334\) | −10.5700 | − | 18.3078i | −0.578366 | − | 1.00176i | ||||
\(335\) | −4.67994 | + | 8.10589i | −0.255692 | + | 0.442872i | ||||
\(336\) | −0.309081 | − | 0.178448i | −0.0168617 | − | 0.00973513i | ||||
\(337\) | −8.20105 | −0.446739 | −0.223370 | − | 0.974734i | \(-0.571706\pi\) | ||||
−0.223370 | + | 0.974734i | \(0.571706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.792249 | 0.0430291 | ||||||||
\(340\) | −4.02363 | − | 2.32304i | −0.218212 | − | 0.125985i | ||||
\(341\) | 4.05980 | − | 7.03178i | 0.219851 | − | 0.380792i | ||||
\(342\) | 3.60388 | + | 6.24210i | 0.194875 | + | 0.337534i | ||||
\(343\) | 4.95108i | 0.267333i | ||||||||
\(344\) | 5.70866 | − | 3.29590i | 0.307790 | − | 0.177703i | ||||
\(345\) | −1.43602 | + | 0.829085i | −0.0773126 | + | 0.0446364i | ||||
\(346\) | − | 9.35450i | − | 0.502901i | ||||||
\(347\) | −3.93147 | − | 6.80950i | −0.211052 | − | 0.365553i | 0.740992 | − | 0.671514i | \(-0.234356\pi\) |
−0.952044 | + | 0.305961i | \(0.901022\pi\) | |||||||
\(348\) | 3.91454 | − | 6.78019i | 0.209841 | − | 0.363456i | ||||
\(349\) | −16.2159 | − | 9.36227i | −0.868019 | − | 0.501151i | −0.00132953 | − | 0.999999i | \(-0.500423\pi\) |
−0.866689 | + | 0.498848i | \(0.833757\pi\) | |||||||
\(350\) | −1.61356 | −0.0862486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.93900 | −0.156649 | ||||||||
\(353\) | 27.3186 | + | 15.7724i | 1.45402 | + | 0.839480i | 0.998706 | − | 0.0508500i | \(-0.0161930\pi\) |
0.455316 | + | 0.890330i | \(0.349526\pi\) | |||||||
\(354\) | 0.821552 | − | 1.42297i | 0.0436650 | − | 0.0756300i | ||||
\(355\) | −2.35690 | − | 4.08226i | −0.125091 | − | 0.216664i | ||||
\(356\) | − | 0.396125i | − | 0.0209946i | ||||||
\(357\) | −2.07510 | + | 1.19806i | −0.109826 | + | 0.0634082i | ||||
\(358\) | −2.74983 | + | 1.58761i | −0.145333 | + | 0.0839080i | ||||
\(359\) | − | 2.39612i | − | 0.126463i | −0.997999 | − | 0.0632313i | \(-0.979859\pi\) | ||
0.997999 | − | 0.0632313i | \(-0.0201406\pi\) | |||||||
\(360\) | −0.346011 | − | 0.599308i | −0.0182364 | − | 0.0315863i | ||||
\(361\) | 16.4758 | − | 28.5370i | 0.867149 | − | 1.50195i | ||||
\(362\) | −17.1469 | − | 9.89977i | −0.901222 | − | 0.520320i | ||||
\(363\) | 2.36227 | 0.123987 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.20477 | −0.115403 | ||||||||
\(366\) | 5.62393 | + | 3.24698i | 0.293968 | + | 0.169722i | ||||
\(367\) | 0.00215593 | − | 0.00373419i | 0.000112539 | − | 0.000194923i | −0.865969 | − | 0.500097i | \(-0.833298\pi\) |
0.866082 | + | 0.499903i | \(0.166631\pi\) | |||||||
\(368\) | 1.19806 | + | 2.07510i | 0.0624533 | + | 0.108172i | ||||
\(369\) | − | 4.89008i | − | 0.254568i | ||||||
\(370\) | −6.05171 | + | 3.49396i | −0.314614 | + | 0.181642i | ||||
\(371\) | −2.74702 | + | 1.58599i | −0.142618 | + | 0.0823405i | ||||
\(372\) | − | 2.76271i | − | 0.143240i | ||||||
\(373\) | 16.1564 | + | 27.9838i | 0.836549 | + | 1.44895i | 0.892763 | + | 0.450526i | \(0.148764\pi\) |
−0.0562144 | + | 0.998419i | \(0.517903\pi\) | |||||||
\(374\) | −9.86592 | + | 17.0883i | −0.510155 | + | 0.883614i | ||||
\(375\) | −5.70608 | − | 3.29440i | −0.294661 | − | 0.170122i | ||||
\(376\) | 4.98792 | 0.257232 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.356896 | −0.0183567 | ||||||||
\(379\) | −17.1092 | − | 9.87800i | −0.878841 | − | 0.507399i | −0.00856468 | − | 0.999963i | \(-0.502726\pi\) |
−0.870276 | + | 0.492564i | \(0.836060\pi\) | |||||||
\(380\) | −2.49396 | + | 4.31966i | −0.127937 | + | 0.221594i | ||||
\(381\) | −9.10872 | − | 15.7768i | −0.466654 | − | 0.808268i | ||||
\(382\) | 15.2620i | 0.780874i | ||||||||
\(383\) | 24.9516 | − | 14.4058i | 1.27497 | − | 0.736103i | 0.299049 | − | 0.954238i | \(-0.403331\pi\) |
0.975919 | + | 0.218135i | \(0.0699974\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | − | 0.725873i | − | 0.0369939i | ||||||
\(386\) | −2.38404 | − | 4.12928i | −0.121345 | − | 0.210175i | ||||
\(387\) | 3.29590 | − | 5.70866i | 0.167540 | − | 0.290188i | ||||
\(388\) | 0.361908 | + | 0.208947i | 0.0183731 | + | 0.0106077i | ||||
\(389\) | −34.7821 | −1.76352 | −0.881761 | − | 0.471697i | \(-0.843642\pi\) | ||||
−0.881761 | + | 0.471697i | \(0.843642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0871 | 0.813559 | ||||||||
\(392\) | 5.95187 | + | 3.43631i | 0.300615 | + | 0.173560i | ||||
\(393\) | −1.36778 | + | 2.36907i | −0.0689954 | + | 0.119504i | ||||
\(394\) | 6.11745 | + | 10.5957i | 0.308193 | + | 0.533805i | ||||
\(395\) | 10.4125i | 0.523911i | ||||||||
\(396\) | −2.54525 | + | 1.46950i | −0.127904 | + | 0.0738452i | ||||
\(397\) | 4.46302 | − | 2.57673i | 0.223993 | − | 0.129322i | −0.383805 | − | 0.923414i | \(-0.625386\pi\) |
0.607798 | + | 0.794092i | \(0.292053\pi\) | |||||||
\(398\) | 11.8485i | 0.593910i | ||||||||
\(399\) | 1.28621 | + | 2.22778i | 0.0643910 | + | 0.111528i | ||||
\(400\) | −2.26055 | + | 3.91539i | −0.113028 | + | 0.195770i | ||||
\(401\) | 11.5398 | + | 6.66248i | 0.576268 | + | 0.332708i | 0.759649 | − | 0.650333i | \(-0.225371\pi\) |
−0.183381 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(402\) | 13.5254 | 0.674587 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.0151 | 0.498268 | ||||||||
\(405\) | −0.599308 | − | 0.346011i | −0.0297799 | − | 0.0171934i | ||||
\(406\) | 1.39708 | − | 2.41982i | 0.0693361 | − | 0.120094i | ||||
\(407\) | 14.8388 | + | 25.7015i | 0.735531 | + | 1.27398i | ||||
\(408\) | 6.71379i | 0.332382i | ||||||||
\(409\) | −20.8051 | + | 12.0118i | −1.02875 | + | 0.593947i | −0.916626 | − | 0.399747i | \(-0.869098\pi\) |
−0.112122 | + | 0.993694i | \(0.535765\pi\) | |||||||
\(410\) | 2.93067 | − | 1.69202i | 0.144735 | − | 0.0835630i | ||||
\(411\) | − | 7.64742i | − | 0.377219i | ||||||
\(412\) | 4.81282 | + | 8.33605i | 0.237111 | + | 0.410688i | ||||
\(413\) | 0.293209 | − | 0.507852i | 0.0144278 | − | 0.0249898i | ||||
\(414\) | 2.07510 | + | 1.19806i | 0.101986 | + | 0.0588815i | ||||
\(415\) | −10.2604 | −0.503663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.38404 | 0.165717 | ||||||||
\(418\) | 18.3455 | + | 10.5918i | 0.897309 | + | 0.518062i | ||||
\(419\) | −6.90246 | + | 11.9554i | −0.337207 | + | 0.584060i | −0.983906 | − | 0.178685i | \(-0.942816\pi\) |
0.646699 | + | 0.762745i | \(0.276149\pi\) | |||||||
\(420\) | −0.123490 | − | 0.213891i | −0.00602569 | − | 0.0104368i | ||||
\(421\) | 7.72587i | 0.376536i | 0.982118 | + | 0.188268i | \(0.0602874\pi\) | ||||
−0.982118 | + | 0.188268i | \(0.939713\pi\) | |||||||
\(422\) | −14.9494 | + | 8.63102i | −0.727724 | + | 0.420152i | ||||
\(423\) | 4.31966 | − | 2.49396i | 0.210029 | − | 0.121260i | ||||
\(424\) | 8.88769i | 0.431624i | ||||||||
\(425\) | 15.1769 | + | 26.2871i | 0.736187 | + | 1.27511i | ||||
\(426\) | −3.40581 | + | 5.89904i | −0.165012 | + | 0.285809i | ||||
\(427\) | 2.00716 | + | 1.15883i | 0.0971332 | + | 0.0560799i | ||||
\(428\) | 6.63102 | 0.320523 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.56166 | 0.219983 | ||||||||
\(431\) | −0.554360 | − | 0.320060i | −0.0267026 | − | 0.0154168i | 0.486589 | − | 0.873631i | \(-0.338241\pi\) |
−0.513292 | + | 0.858214i | \(0.671574\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 10.6380 | + | 18.4256i | 0.511231 | + | 0.885478i | 0.999915 | + | 0.0130171i | \(0.00414358\pi\) |
−0.488685 | + | 0.872461i | \(0.662523\pi\) | |||||||
\(434\) | − | 0.985999i | − | 0.0473295i | ||||||
\(435\) | 4.69203 | − | 2.70895i | 0.224966 | − | 0.129884i | ||||
\(436\) | 11.2479 | − | 6.49396i | 0.538675 | − | 0.311004i | ||||
\(437\) | − | 17.2707i | − | 0.826168i | ||||||
\(438\) | 1.59299 | + | 2.75914i | 0.0761160 | + | 0.131837i | ||||
\(439\) | 6.35905 | − | 11.0142i | 0.303501 | − | 0.525679i | −0.673425 | − | 0.739255i | \(-0.735178\pi\) |
0.976926 | + | 0.213576i | \(0.0685111\pi\) | |||||||
\(440\) | −1.76137 | − | 1.01693i | −0.0839699 | − | 0.0484800i | ||||
\(441\) | 6.87263 | 0.327268 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.5972 | 1.07362 | 0.536812 | − | 0.843702i | \(-0.319628\pi\) | ||||
0.536812 | + | 0.843702i | \(0.319628\pi\) | |||||||
\(444\) | 8.74498 | + | 5.04892i | 0.415018 | + | 0.239611i | ||||
\(445\) | 0.137063 | − | 0.237401i | 0.00649743 | − | 0.0112539i | ||||
\(446\) | 3.38404 | + | 5.86133i | 0.160239 | + | 0.277542i | ||||
\(447\) | − | 20.8170i | − | 0.984610i | ||||||
\(448\) | −0.309081 | + | 0.178448i | −0.0146027 | + | 0.00843087i | ||||
\(449\) | −10.0870 | + | 5.82371i | −0.476033 | + | 0.274838i | −0.718762 | − | 0.695256i | \(-0.755291\pi\) |
0.242729 | + | 0.970094i | \(0.421957\pi\) | |||||||
\(450\) | 4.52111i | 0.213127i | ||||||||
\(451\) | −7.18598 | − | 12.4465i | −0.338375 | − | 0.586082i | ||||
\(452\) | 0.396125 | − | 0.686108i | 0.0186321 | − | 0.0322718i | ||||
\(453\) | −0.775492 | − | 0.447730i | −0.0364358 | − | 0.0210362i | ||||
\(454\) | −23.6799 | −1.11135 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.20775 | 0.337534 | ||||||||
\(457\) | 18.3502 | + | 10.5945i | 0.858385 | + | 0.495589i | 0.863471 | − | 0.504398i | \(-0.168286\pi\) |
−0.00508594 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(458\) | 4.14914 | − | 7.18653i | 0.193877 | − | 0.335804i | ||||
\(459\) | 3.35690 | + | 5.81431i | 0.156686 | + | 0.271389i | ||||
\(460\) | 1.65817i | 0.0773126i | ||||||||
\(461\) | 20.8447 | − | 12.0347i | 0.970833 | − | 0.560511i | 0.0713432 | − | 0.997452i | \(-0.477271\pi\) |
0.899490 | + | 0.436941i | \(0.143938\pi\) | |||||||
\(462\) | −0.908389 | + | 0.524459i | −0.0422621 | + | 0.0244000i | ||||
\(463\) | 18.1715i | 0.844502i | 0.906479 | + | 0.422251i | \(0.138760\pi\) | ||||
−0.906479 | + | 0.422251i | \(0.861240\pi\) | |||||||
\(464\) | −3.91454 | − | 6.78019i | −0.181728 | − | 0.314762i | ||||
\(465\) | 0.955927 | − | 1.65571i | 0.0443301 | − | 0.0767819i | ||||
\(466\) | −20.7544 | − | 11.9825i | −0.961428 | − | 0.555081i | ||||
\(467\) | 2.93123 | 0.135641 | 0.0678206 | − | 0.997698i | \(-0.478395\pi\) | ||||
0.0678206 | + | 0.997698i | \(0.478395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82717 | 0.222898 | ||||||||
\(470\) | 2.98930 | + | 1.72587i | 0.137886 | + | 0.0796086i | ||||
\(471\) | −4.29590 | + | 7.44071i | −0.197944 | + | 0.342850i | ||||
\(472\) | −0.821552 | − | 1.42297i | −0.0378150 | − | 0.0654975i | ||||
\(473\) | − | 19.3733i | − | 0.890785i | ||||||
\(474\) | 13.0307 | − | 7.52326i | 0.598519 | − | 0.345555i | ||||
\(475\) | 28.2212 | − | 16.2935i | 1.29488 | − | 0.747597i | ||||
\(476\) | 2.39612i | 0.109826i | ||||||||
\(477\) | 4.44385 | + | 7.69697i | 0.203470 | + | 0.352420i | ||||
\(478\) | 6.30798 | − | 10.9257i | 0.288520 | − | 0.499732i | ||||
\(479\) | −26.5948 | − | 15.3545i | −1.21515 | − | 0.701565i | −0.251271 | − | 0.967917i | \(-0.580848\pi\) |
−0.963876 | + | 0.266352i | \(0.914182\pi\) | |||||||
\(480\) | −0.692021 | −0.0315863 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26.3937 | 1.20220 | ||||||||
\(483\) | 0.740596 | + | 0.427583i | 0.0336983 | + | 0.0194557i | ||||
\(484\) | 1.18114 | − | 2.04579i | 0.0536880 | − | 0.0929904i | ||||
\(485\) | 0.144596 | + | 0.250448i | 0.00656577 | + | 0.0113722i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 20.9143 | − | 12.0749i | 0.947717 | − | 0.547164i | 0.0553458 | − | 0.998467i | \(-0.482374\pi\) |
0.892371 | + | 0.451303i | \(0.149041\pi\) | |||||||
\(488\) | 5.62393 | − | 3.24698i | 0.254584 | − | 0.146984i | ||||
\(489\) | − | 1.72587i | − | 0.0780467i | ||||||
\(490\) | 2.37800 | + | 4.11882i | 0.107427 | + | 0.186069i | ||||
\(491\) | 7.29859 | − | 12.6415i | 0.329381 | − | 0.570504i | −0.653009 | − | 0.757351i | \(-0.726493\pi\) |
0.982389 | + | 0.186847i | \(0.0598268\pi\) | |||||||
\(492\) | −4.23494 | − | 2.44504i | −0.190926 | − | 0.110231i | ||||
\(493\) | −52.5628 | −2.36731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.03385 | −0.0914148 | ||||||||
\(496\) | −2.39258 | − | 1.38135i | −0.107430 | − | 0.0620246i | ||||
\(497\) | −1.21552 | + | 2.10534i | −0.0545236 | + | 0.0944376i | ||||
\(498\) | 7.41335 | + | 12.8403i | 0.332200 | + | 0.575387i | ||||
\(499\) | 6.85517i | 0.306879i | 0.988158 | + | 0.153440i | \(0.0490351\pi\) | ||||
−0.988158 | + | 0.153440i | \(0.950965\pi\) | |||||||
\(500\) | −5.70608 | + | 3.29440i | −0.255184 | + | 0.147330i | ||||
\(501\) | −18.3078 | + | 10.5700i | −0.817933 | + | 0.472234i | ||||
\(502\) | 30.0344i | 1.34050i | ||||||||
\(503\) | 13.3666 | + | 23.1516i | 0.595987 | + | 1.03228i | 0.993407 | + | 0.114642i | \(0.0365722\pi\) |
−0.397420 | + | 0.917637i | \(0.630094\pi\) | |||||||
\(504\) | −0.178448 | + | 0.309081i | −0.00794870 | + | 0.0137676i | ||||
\(505\) | 6.00211 | + | 3.46532i | 0.267090 | + | 0.154205i | ||||
\(506\) | 7.04221 | 0.313065 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.2174 | −0.808268 | ||||||||
\(509\) | 17.8916 | + | 10.3297i | 0.793033 | + | 0.457858i | 0.841029 | − | 0.540989i | \(-0.181950\pi\) |
−0.0479959 | + | 0.998848i | \(0.515283\pi\) | |||||||
\(510\) | −2.32304 | + | 4.02363i | −0.102866 | + | 0.178169i | ||||
\(511\) | 0.568532 | + | 0.984726i | 0.0251504 | + | 0.0435617i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.24210 | − | 3.60388i | 0.275595 | − | 0.159115i | ||||
\(514\) | −9.75322 | + | 5.63102i | −0.430196 | + | 0.248374i | ||||
\(515\) | 6.66115i | 0.293525i | ||||||||
\(516\) | −3.29590 | − | 5.70866i | −0.145094 | − | 0.251310i | ||||
\(517\) | 7.32975 | − | 12.6955i | 0.322362 | − | 0.558347i | ||||
\(518\) | 3.12105 | + | 1.80194i | 0.137131 | + | 0.0791726i | ||||
\(519\) | −9.35450 | −0.410617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0965 | −0.661390 | −0.330695 | − | 0.943738i | \(-0.607283\pi\) | ||||
−0.330695 | + | 0.943738i | \(0.607283\pi\) | |||||||
\(522\) | −6.78019 | − | 3.91454i | −0.296761 | − | 0.171335i | ||||
\(523\) | −0.0174584 | + | 0.0302388i | −0.000763402 | + | 0.00132225i | −0.866407 | − | 0.499339i | \(-0.833576\pi\) |
0.865643 | + | 0.500661i | \(0.166910\pi\) | |||||||
\(524\) | 1.36778 | + | 2.36907i | 0.0597518 | + | 0.103493i | ||||
\(525\) | 1.61356i | 0.0704217i | ||||||||
\(526\) | −4.80608 | + | 2.77479i | −0.209555 | + | 0.120987i | ||||
\(527\) | −16.0633 | + | 9.27413i | −0.699727 | + | 0.403987i | ||||
\(528\) | 2.93900i | 0.127904i | ||||||||
\(529\) | 8.62929 | + | 14.9464i | 0.375187 | + | 0.649842i | ||||
\(530\) | −3.07524 | + | 5.32647i | −0.133580 | + | 0.231367i | ||||
\(531\) | −1.42297 | − | 0.821552i | −0.0617516 | − | 0.0356523i | ||||
\(532\) | 2.57242 | 0.111528 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.396125 | −0.0171420 | ||||||||
\(535\) | 3.97403 | + | 2.29440i | 0.171812 | + | 0.0991958i | ||||
\(536\) | 6.76271 | − | 11.7134i | 0.292105 | − | 0.505940i | ||||
\(537\) | 1.58761 | + | 2.74983i | 0.0685106 | + | 0.118664i | ||||
\(538\) | 16.6872i | 0.719438i | ||||||||
\(539\) | 17.4925 | − | 10.0993i | 0.753457 | − | 0.435009i | ||||
\(540\) | −0.599308 | + | 0.346011i | −0.0257901 | + | 0.0148899i | ||||
\(541\) | − | 13.0858i | − | 0.562600i | −0.959620 | − | 0.281300i | \(-0.909234\pi\) | ||
0.959620 | − | 0.281300i | \(-0.0907657\pi\) | |||||||
\(542\) | 3.30678 | + | 5.72751i | 0.142038 | + | 0.246018i | ||||
\(543\) | −9.89977 | + | 17.1469i | −0.424840 | + | 0.735844i | ||||
\(544\) | 5.81431 | + | 3.35690i | 0.249287 | + | 0.143926i | ||||
\(545\) | 8.98792 | 0.385000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.97584 | −0.255508 | −0.127754 | − | 0.991806i | \(-0.540777\pi\) | ||||
−0.127754 | + | 0.991806i | \(0.540777\pi\) | |||||||
\(548\) | −6.62286 | − | 3.82371i | −0.282914 | − | 0.163341i | ||||
\(549\) | 3.24698 | − | 5.62393i | 0.138578 | − | 0.240024i | ||||
\(550\) | 6.64377 | + | 11.5073i | 0.283291 | + | 0.490675i | ||||
\(551\) | 56.4301i | 2.40400i | ||||||||
\(552\) | 2.07510 | − | 1.19806i | 0.0883223 | − | 0.0509929i | ||||
\(553\) | 4.65059 | − | 2.68502i | 0.197763 | − | 0.114179i | ||||
\(554\) | 21.7995i | 0.926174i | ||||||||
\(555\) | 3.49396 | + | 6.05171i | 0.148310 | + | 0.256881i | ||||
\(556\) | 1.69202 | − | 2.93067i | 0.0717577 | − | 0.124288i | ||||
\(557\) | −9.04102 | − | 5.21983i | −0.383080 | − | 0.221171i | 0.296077 | − | 0.955164i | \(-0.404321\pi\) |
−0.679158 | + | 0.733993i | \(0.737655\pi\) | |||||||
\(558\) | −2.76271 | −0.116955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.246980 | −0.0104368 | ||||||||
\(561\) | 17.0883 | + | 9.86592i | 0.721468 | + | 0.416539i | ||||
\(562\) | −10.2959 | + | 17.8330i | −0.434306 | + | 0.752240i | ||||
\(563\) | −2.83028 | − | 4.90219i | −0.119282 | − | 0.206603i | 0.800201 | − | 0.599732i | \(-0.204726\pi\) |
−0.919483 | + | 0.393129i | \(0.871393\pi\) | |||||||
\(564\) | − | 4.98792i | − | 0.210029i | ||||||
\(565\) | 0.474801 | − | 0.274127i | 0.0199750 | − | 0.0115326i | ||||
\(566\) | 11.2688 | − | 6.50604i | 0.473663 | − | 0.273469i | ||||
\(567\) | 0.356896i | 0.0149882i | ||||||||
\(568\) | 3.40581 | + | 5.89904i | 0.142905 | + | 0.247518i | ||||
\(569\) | 10.3284 | − | 17.8893i | 0.432990 | − | 0.749961i | −0.564139 | − | 0.825680i | \(-0.690792\pi\) |
0.997129 | + | 0.0757191i | \(0.0241252\pi\) | |||||||
\(570\) | 4.31966 | + | 2.49396i | 0.180931 | + | 0.104460i | ||||
\(571\) | −44.3672 | −1.85671 | −0.928354 | − | 0.371697i | \(-0.878776\pi\) | ||||
−0.928354 | + | 0.371697i | \(0.878776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2620 | 0.637581 | ||||||||
\(574\) | −1.51143 | − | 0.872625i | −0.0630859 | − | 0.0364227i | ||||
\(575\) | 5.41657 | − | 9.38177i | 0.225886 | − | 0.391247i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 29.4426i | 1.22571i | 0.790194 | + | 0.612857i | \(0.209980\pi\) | ||||
−0.790194 | + | 0.612857i | \(0.790020\pi\) | |||||||
\(578\) | 24.3137 | − | 14.0375i | 1.01132 | − | 0.583883i | ||||
\(579\) | −4.12928 | + | 2.38404i | −0.171607 | + | 0.0990774i | ||||
\(580\) | − | 5.41789i | − | 0.224966i | ||||||
\(581\) | 2.64579 | + | 4.58265i | 0.109766 | + | 0.190120i | ||||
\(582\) | 0.208947 | − | 0.361908i | 0.00866115 | − | 0.0150015i | ||||
\(583\) | 22.6214 | + | 13.0605i | 0.936882 | + | 0.540909i | ||||
\(584\) | 3.18598 | 0.131837 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.9390 | −0.617124 | ||||||||
\(587\) | 16.9426 | + | 9.78179i | 0.699294 | + | 0.403738i | 0.807085 | − | 0.590436i | \(-0.201044\pi\) |
−0.107790 | + | 0.994174i | \(0.534377\pi\) | |||||||
\(588\) | 3.43631 | − | 5.95187i | 0.141711 | − | 0.245451i | ||||
\(589\) | 9.95646 | + | 17.2451i | 0.410249 | + | 0.710572i | ||||
\(590\) | − | 1.13706i | − | 0.0468122i | ||||||
\(591\) | 10.5957 | − | 6.11745i | 0.435850 | − | 0.251638i | ||||
\(592\) | 8.74498 | − | 5.04892i | 0.359417 | − | 0.207509i | ||||
\(593\) | 10.8793i | 0.446761i | 0.974731 | + | 0.223380i | \(0.0717092\pi\) | ||||
−0.974731 | + | 0.223380i | \(0.928291\pi\) | |||||||
\(594\) | 1.46950 | + | 2.54525i | 0.0602943 | + | 0.104433i | ||||
\(595\) | −0.829085 | + | 1.43602i | −0.0339892 | + | 0.0588710i | ||||
\(596\) | −18.0281 | − | 10.4085i | −0.738458 | − | 0.426349i | ||||
\(597\) | 11.8485 | 0.484925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0543 | 0.655961 | 0.327980 | − | 0.944685i | \(-0.393632\pi\) | ||||
0.327980 | + | 0.944685i | \(0.393632\pi\) | |||||||
\(600\) | 3.91539 | + | 2.26055i | 0.159845 | + | 0.0922867i | ||||
\(601\) | −6.44773 | + | 11.1678i | −0.263008 | + | 0.455544i | −0.967040 | − | 0.254625i | \(-0.918048\pi\) |
0.704032 | + | 0.710169i | \(0.251381\pi\) | |||||||
\(602\) | −1.17629 | − | 2.03740i | −0.0479421 | − | 0.0830381i | ||||
\(603\) | − | 13.5254i | − | 0.550798i | ||||||
\(604\) | −0.775492 | + | 0.447730i | −0.0315543 | + | 0.0182179i | ||||
\(605\) | 1.41573 | − | 0.817372i | 0.0575576 | − | 0.0332309i | ||||
\(606\) | − | 10.0151i | − | 0.406834i | ||||||
\(607\) | −22.2371 | − | 38.5157i | −0.902574 | − | 1.56330i | −0.824141 | − | 0.566385i | \(-0.808342\pi\) |
−0.0784334 | − | 0.996919i | \(-0.524992\pi\) | |||||||
\(608\) | 3.60388 | − | 6.24210i | 0.146156 | − | 0.253150i | ||||
\(609\) | −2.41982 | − | 1.39708i | −0.0980561 | − | 0.0566127i | ||||
\(610\) | 4.49396 | 0.181955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.71379 | 0.271389 | ||||||||
\(613\) | −36.3950 | − | 21.0127i | −1.46998 | − | 0.848694i | −0.470548 | − | 0.882374i | \(-0.655944\pi\) |
−0.999433 | + | 0.0336804i | \(0.989277\pi\) | |||||||
\(614\) | −13.0151 | + | 22.5428i | −0.525245 | + | 0.909752i | ||||
\(615\) | −1.69202 | − | 2.93067i | −0.0682289 | − | 0.118176i | ||||
\(616\) | 1.04892i | 0.0422621i | ||||||||
\(617\) | −14.4327 | + | 8.33273i | −0.581039 | + | 0.335463i | −0.761546 | − | 0.648111i | \(-0.775559\pi\) |
0.180507 | + | 0.983574i | \(0.442226\pi\) | |||||||
\(618\) | 8.33605 | − | 4.81282i | 0.335325 | − | 0.193600i | ||||
\(619\) | − | 39.7512i | − | 1.59774i | −0.601506 | − | 0.798868i | \(-0.705432\pi\) | ||
0.601506 | − | 0.798868i | \(-0.294568\pi\) | |||||||
\(620\) | −0.955927 | − | 1.65571i | −0.0383910 | − | 0.0664951i | ||||
\(621\) | 1.19806 | − | 2.07510i | 0.0480766 | − | 0.0832711i | ||||
\(622\) | −4.16699 | − | 2.40581i | −0.167081 | − | 0.0964643i | ||||
\(623\) | −0.141375 | −0.00566408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0459 | 0.721837 | ||||||||
\(626\) | 22.5523 | + | 13.0206i | 0.901371 | + | 0.520407i | ||||
\(627\) | 10.5918 | − | 18.3455i | 0.422996 | − | 0.732650i | ||||
\(628\) | 4.29590 | + | 7.44071i | 0.171425 | + | 0.296917i | ||||
\(629\) | − | 67.7948i | − | 2.70315i | ||||||
\(630\) | −0.213891 | + | 0.123490i | −0.00852161 | + | 0.00491995i | ||||
\(631\) | −12.6238 | + | 7.28836i | −0.502546 | + | 0.290145i | −0.729764 | − | 0.683699i | \(-0.760370\pi\) |
0.227218 | + | 0.973844i | \(0.427037\pi\) | |||||||
\(632\) | − | 15.0465i | − | 0.598519i | ||||||
\(633\) | 8.63102 | + | 14.9494i | 0.343052 | + | 0.594184i | ||||
\(634\) | −5.76055 | + | 9.97757i | −0.228781 | + | 0.396260i | ||||
\(635\) | −10.9179 | − | 6.30343i | −0.433262 | − | 0.250144i | ||||
\(636\) | 8.88769 | 0.352420 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.0097 | −0.910962 | ||||||||
\(639\) | 5.89904 | + | 3.40581i | 0.233362 | + | 0.134732i | ||||
\(640\) | −0.346011 | + | 0.599308i | −0.0136773 | + | 0.0236897i | ||||
\(641\) | 19.2174 | + | 33.2856i | 0.759043 | + | 1.31470i | 0.943339 | + | 0.331831i | \(0.107666\pi\) |
−0.184296 | + | 0.982871i | \(0.559000\pi\) | |||||||
\(642\) | − | 6.63102i | − | 0.261706i | ||||||
\(643\) | −0.902583 | + | 0.521106i | −0.0355944 | + | 0.0205504i | −0.517692 | − | 0.855567i | \(-0.673209\pi\) |
0.482097 | + | 0.876118i | \(0.339875\pi\) | |||||||
\(644\) | 0.740596 | − | 0.427583i | 0.0291836 | − | 0.0168491i | ||||
\(645\) | − | 4.56166i | − | 0.179615i | ||||||
\(646\) | −24.1957 | − | 41.9081i | −0.951966 | − | 1.64885i | ||||
\(647\) | −14.0804 | + | 24.3879i | −0.553557 | + | 0.958788i | 0.444458 | + | 0.895800i | \(0.353396\pi\) |
−0.998014 | + | 0.0629884i | \(0.979937\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −4.82908 | −0.189558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.985999 | −0.0386444 | ||||||||
\(652\) | −1.49465 | − | 0.862937i | −0.0585350 | − | 0.0337952i | ||||
\(653\) | −5.31013 | + | 9.19742i | −0.207802 | + | 0.359923i | −0.951022 | − | 0.309124i | \(-0.899964\pi\) |
0.743220 | + | 0.669047i | \(0.233298\pi\) | |||||||
\(654\) | −6.49396 | − | 11.2479i | −0.253934 | − | 0.439826i | ||||
\(655\) | 1.89307i | 0.0739683i | ||||||||
\(656\) | −4.23494 | + | 2.44504i | −0.165347 | + | 0.0954628i | ||||
\(657\) | 2.75914 | − | 1.59299i | 0.107644 | − | 0.0621485i | ||||
\(658\) | − | 1.78017i | − | 0.0693982i | ||||||
\(659\) | 20.1814 | + | 34.9553i | 0.786157 | + | 1.36166i | 0.928305 | + | 0.371818i | \(0.121266\pi\) |
−0.142148 | + | 0.989845i | \(0.545401\pi\) | |||||||
\(660\) | −1.01693 | + | 1.76137i | −0.0395838 | + | 0.0685611i | ||||
\(661\) | −27.6407 | − | 15.9584i | −1.07510 | − | 0.620709i | −0.145529 | − | 0.989354i | \(-0.546488\pi\) |
−0.929570 | + | 0.368645i | \(0.879822\pi\) | |||||||
\(662\) | −3.43834 | −0.133635 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.8267 | 0.575387 | ||||||||
\(665\) | 1.54167 | + | 0.890084i | 0.0597834 | + | 0.0345160i | ||||
\(666\) | 5.04892 | − | 8.74498i | 0.195642 | − | 0.338861i | ||||
\(667\) | 9.37973 | + | 16.2462i | 0.363185 | + | 0.629054i | ||||
\(668\) | 21.1400i | 0.817933i | ||||||||
\(669\) | 5.86133 | − | 3.38404i | 0.226612 | − | 0.130835i | ||||
\(670\) | 8.10589 | − | 4.67994i | 0.313158 | − | 0.180802i | ||||
\(671\) | − | 19.0858i | − | 0.736797i | ||||||
\(672\) | 0.178448 | + | 0.309081i | 0.00688378 | + | 0.0119231i | ||||
\(673\) | 1.91401 | − | 3.31516i | 0.0737797 | − | 0.127790i | −0.826775 | − | 0.562532i | \(-0.809827\pi\) |
0.900555 | + | 0.434742i | \(0.143161\pi\) | |||||||
\(674\) | 7.10231 | + | 4.10052i | 0.273571 | + | 0.157946i | ||||
\(675\) | 4.52111 | 0.174017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.78927 | 0.0687670 | 0.0343835 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343835 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(678\) | −0.686108 | − | 0.396125i | −0.0263498 | − | 0.0152131i | ||||
\(679\) | 0.0745725 | − | 0.129163i | 0.00286183 | − | 0.00495683i | ||||
\(680\) | 2.32304 | + | 4.02363i | 0.0890847 | + | 0.154299i | ||||
\(681\) | 23.6799i | 0.907417i | ||||||||
\(682\) | −7.03178 | + | 4.05980i | −0.269261 | + | 0.155458i | ||||
\(683\) | −0.657941 | + | 0.379863i | −0.0251754 | + | 0.0145350i | −0.512535 | − | 0.858666i | \(-0.671293\pi\) |
0.487359 | + | 0.873201i | \(0.337960\pi\) | |||||||
\(684\) | − | 7.20775i | − | 0.275595i | ||||||
\(685\) | −2.64609 | − | 4.58316i | −0.101102 | − | 0.175114i | ||||
\(686\) | 2.47554 | − | 4.28776i | 0.0945166 | − | 0.163708i | ||||
\(687\) | −7.18653 | − | 4.14914i | −0.274183 | − | 0.158300i | ||||
\(688\) | −6.59179 | −0.251310 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.65817 | 0.0631254 | ||||||||
\(691\) | −4.03524 | − | 2.32975i | −0.153508 | − | 0.0886278i | 0.421278 | − | 0.906931i | \(-0.361582\pi\) |
−0.574786 | + | 0.818304i | \(0.694915\pi\) | |||||||
\(692\) | −4.67725 | + | 8.10124i | −0.177802 | + | 0.307963i | ||||
\(693\) | 0.524459 | + | 0.908389i | 0.0199225 | + | 0.0345068i | ||||
\(694\) | 7.86294i | 0.298473i | ||||||||
\(695\) | 2.02808 | − | 1.17092i | 0.0769296 | − | 0.0444153i | ||||
\(696\) | −6.78019 | + | 3.91454i | −0.257002 | + | 0.148380i | ||||
\(697\) | 32.8310i | 1.24356i | ||||||||
\(698\) | 9.36227 | + | 16.2159i | 0.354367 | + | 0.613782i | ||||
\(699\) | −11.9825 | + | 20.7544i | −0.453221 | + | 0.785002i | ||||
\(700\) | 1.39739 | + | 0.806782i | 0.0528163 | + | 0.0304935i | ||||
\(701\) | 24.3284 | 0.918872 | 0.459436 | − | 0.888211i | \(-0.348052\pi\) | ||||
0.459436 | + | 0.888211i | \(0.348052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.7827 | −2.74505 | ||||||||
\(704\) | 2.54525 | + | 1.46950i | 0.0959277 | + | 0.0553839i | ||||
\(705\) | 1.72587 | − | 2.98930i | 0.0650001 | − | 0.112584i | ||||
\(706\) | −15.7724 | − | 27.3186i | −0.593602 | − | 1.02815i | ||||
\(707\) | − | 3.57434i | − | 0.134427i | ||||||
\(708\) | −1.42297 | + | 0.821552i | −0.0534785 | + | 0.0308758i | ||||
\(709\) | 25.4548 | − | 14.6963i | 0.955975 | − | 0.551932i | 0.0610430 | − | 0.998135i | \(-0.480557\pi\) |
0.894932 | + | 0.446203i | \(0.147224\pi\) | |||||||
\(710\) | 4.71379i | 0.176905i | ||||||||
\(711\) | −7.52326 | − | 13.0307i | −0.282144 | − | 0.488688i | ||||
\(712\) | −0.198062 | + | 0.343054i | −0.00742270 | + | 0.0128565i | ||||
\(713\) | 5.73291 | + | 3.30990i | 0.214699 | + | 0.123957i | ||||
\(714\) | 2.39612 | 0.0896727 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.17523 | 0.118664 | ||||||||
\(717\) | −10.9257 | − | 6.30798i | −0.408029 | − | 0.235576i | ||||
\(718\) | −1.19806 | + | 2.07510i | −0.0447113 | + | 0.0774422i | ||||
\(719\) | −25.7439 | − | 44.5898i | −0.960086 | − | 1.66292i | −0.722274 | − | 0.691607i | \(-0.756903\pi\) |
−0.237812 | − | 0.971311i | \(-0.576430\pi\) | |||||||
\(720\) | 0.692021i | 0.0257901i | ||||||||
\(721\) | 2.97510 | − | 1.71768i | 0.110799 | − | 0.0639696i | ||||
\(722\) | −28.5370 | + | 16.4758i | −1.06204 | + | 0.613167i | ||||
\(723\) | − | 26.3937i | − | 0.981593i | ||||||
\(724\) | 9.89977 | + | 17.1469i | 0.367922 | + | 0.637260i | ||||
\(725\) | −17.6981 | + | 30.6539i | −0.657290 | + | 1.13846i | ||||
\(726\) | −2.04579 | − | 1.18114i | −0.0759263 | − | 0.0438361i | ||||
\(727\) | 3.67324 | 0.136233 | 0.0681164 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681164 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.90938 | + | 1.10238i | 0.0706695 | + | 0.0408010i | ||||
\(731\) | −22.1280 | + | 38.3268i | −0.818432 | + | 1.41757i | ||||
\(732\) | −3.24698 | − | 5.62393i | −0.120012 | − | 0.207867i | ||||
\(733\) | 18.3612i | 0.678187i | 0.940753 | + | 0.339093i | \(0.110120\pi\) | ||||
−0.940753 | + | 0.339093i | \(0.889880\pi\) | |||||||
\(734\) | −0.00373419 | + | 0.00215593i | −0.000137831 | + | 7.95770e-5i | ||||
\(735\) | 4.11882 | − | 2.37800i | 0.151925 | − | 0.0877139i | ||||
\(736\) | − | 2.39612i | − | 0.0883223i | ||||||
\(737\) | −19.8756 | − | 34.4256i | −0.732127 | − | 1.26808i | ||||
\(738\) | −2.44504 | + | 4.23494i | −0.0900032 | + | 0.155890i | ||||
\(739\) | 1.45694 | + | 0.841166i | 0.0535945 | + | 0.0309428i | 0.526558 | − | 0.850139i | \(-0.323482\pi\) |
−0.472963 | + | 0.881082i | \(0.656816\pi\) | |||||||
\(740\) | 6.98792 | 0.256881 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.17198 | 0.116447 | ||||||||
\(743\) | −41.8234 | − | 24.1468i | −1.53435 | − | 0.885858i | −0.999154 | − | 0.0411318i | \(-0.986904\pi\) |
−0.535198 | − | 0.844727i | \(-0.679763\pi\) | |||||||
\(744\) | −1.38135 | + | 2.39258i | −0.0506429 | + | 0.0877161i | ||||
\(745\) | −7.20291 | − | 12.4758i | −0.263894 | − | 0.457078i | ||||
\(746\) | − | 32.3129i | − | 1.18306i | ||||||
\(747\) | 12.8403 | − | 7.41335i | 0.469802 | − | 0.271240i | ||||
\(748\) | 17.0883 | − | 9.86592i | 0.624809 | − | 0.360734i | ||||
\(749\) | − | 2.36658i | − | 0.0864731i | ||||||
\(750\) | 3.29440 | + | 5.70608i | 0.120295 | + | 0.208356i | ||||
\(751\) | 5.85056 | − | 10.1335i | 0.213490 | − | 0.369775i | −0.739314 | − | 0.673360i | \(-0.764850\pi\) |
0.952804 | + | 0.303585i | \(0.0981836\pi\) | |||||||
\(752\) | −4.31966 | − | 2.49396i | −0.157522 | − | 0.0909453i | ||||
\(753\) | 30.0344 | 1.09452 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.619678 | −0.0225524 | ||||||||
\(756\) | 0.309081 | + | 0.178448i | 0.0112412 | + | 0.00649009i | ||||
\(757\) | −12.5918 | + | 21.8096i | −0.457657 | + | 0.792684i | −0.998837 | − | 0.0482223i | \(-0.984644\pi\) |
0.541180 | + | 0.840907i | \(0.317978\pi\) | |||||||
\(758\) | 9.87800 | + | 17.1092i | 0.358785 | + | 0.621434i | ||||
\(759\) | − | 7.04221i | − | 0.255616i | ||||||
\(760\) | 4.31966 | − | 2.49396i | 0.156691 | − | 0.0904654i | ||||
\(761\) | −19.4124 | + | 11.2078i | −0.703699 | + | 0.406281i | −0.808724 | − | 0.588189i | \(-0.799841\pi\) |
0.105025 | + | 0.994470i | \(0.466508\pi\) | |||||||
\(762\) | 18.2174i | 0.659948i | ||||||||
\(763\) | −2.31767 | − | 4.01432i | −0.0839052 | − | 0.145328i | ||||
\(764\) | 7.63102 | − | 13.2173i | 0.276081 | − | 0.478186i | ||||
\(765\) | 4.02363 | + | 2.32304i | 0.145475 | + | 0.0839898i | ||||
\(766\) | −28.8116 | −1.04101 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 0.114966 | + | 0.0663757i | 0.00414579 | + | 0.00239357i | 0.502071 | − | 0.864826i | \(-0.332571\pi\) |
−0.497926 | + | 0.867220i | \(0.665905\pi\) | |||||||
\(770\) | −0.362937 | + | 0.628625i | −0.0130793 | + | 0.0226541i | ||||
\(771\) | 5.63102 | + | 9.75322i | 0.202796 | + | 0.351254i | ||||
\(772\) | 4.76809i | 0.171607i | ||||||||
\(773\) | −41.6293 | + | 24.0347i | −1.49730 | + | 0.864467i | −0.999995 | − | 0.00310775i | \(-0.999011\pi\) |
−0.497306 | + | 0.867575i | \(0.665677\pi\) | |||||||
\(774\) | −5.70866 | + | 3.29590i | −0.205194 | + | 0.118469i | ||||
\(775\) | 12.4905i | 0.448672i | ||||||||
\(776\) | −0.208947 | − | 0.361908i | −0.00750077 | − | 0.0129917i | ||||
\(777\) | 1.80194 | − | 3.12105i | 0.0646442 | − | 0.111967i | ||||
\(778\) | 30.1222 | + | 17.3910i | 1.07993 | + | 0.623499i | ||||
\(779\) | 35.2465 | 1.26284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0194 | 0.716350 | ||||||||
\(782\) | −13.9318 | − | 8.04354i | −0.498201 | − | 0.287636i | ||||
\(783\) | −3.91454 | + | 6.78019i | −0.139894 | + | 0.242304i | ||||
\(784\) | −3.43631 | − | 5.95187i | −0.122725 | − | 0.212567i | ||||
\(785\) | 5.94571i | 0.212211i | ||||||||
\(786\) | 2.36907 | − | 1.36778i | 0.0845018 | − | 0.0487871i | ||||
\(787\) | −5.37722 | + | 3.10454i | −0.191677 | + | 0.110665i | −0.592767 | − | 0.805374i | \(-0.701965\pi\) |
0.401090 | + | 0.916039i | \(0.368631\pi\) | |||||||
\(788\) | − | 12.2349i | − | 0.435850i | ||||||
\(789\) | 2.77479 | + | 4.80608i | 0.0987852 | + | 0.171101i | ||||
\(790\) | 5.20626 | − | 9.01751i | 0.185230 | − | 0.320828i | ||||
\(791\) | −0.244869 | − | 0.141375i | −0.00870654 | − | 0.00502672i | ||||
\(792\) | 2.93900 | 0.104433 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.15346 | −0.182889 | ||||||||
\(795\) | 5.32647 | + | 3.07524i | 0.188910 | + | 0.109067i | ||||
\(796\) | 5.92423 | − | 10.2611i | 0.209979 | − | 0.363694i | ||||
\(797\) | 0.163915 | + | 0.283909i | 0.00580616 | + | 0.0100566i | 0.868914 | − | 0.494963i | \(-0.164818\pi\) |
−0.863108 | + | 0.505020i | \(0.831485\pi\) | |||||||
\(798\) | − | 2.57242i | − | 0.0910626i | ||||||
\(799\) | −29.0013 | + | 16.7439i | −1.02599 | + | 0.592357i | ||||
\(800\) | 3.91539 | − | 2.26055i | 0.138430 | − | 0.0799226i | ||||
\(801\) | 0.396125i | 0.0139964i | ||||||||
\(802\) | −6.66248 | − | 11.5398i | −0.235260 | − | 0.407483i | ||||
\(803\) | 4.68180 | − | 8.10912i | 0.165217 | − | 0.286164i | ||||
\(804\) | −11.7134 | − | 6.76271i | −0.413098 | − | 0.238502i | ||||
\(805\) | 0.591794 | 0.0208580 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.6872 | 0.587419 | ||||||||
\(808\) | −8.67330 | − | 5.00753i | −0.305126 | − | 0.176164i | ||||
\(809\) | 18.7192 | − | 32.4226i | 0.658131 | − | 1.13992i | −0.322968 | − | 0.946410i | \(-0.604681\pi\) |
0.981099 | − | 0.193506i | \(-0.0619860\pi\) | |||||||
\(810\) | 0.346011 | + | 0.599308i | 0.0121576 | + | 0.0210575i | ||||
\(811\) | 17.1448i | 0.602037i | 0.953618 | + | 0.301018i | \(0.0973265\pi\) | ||||
−0.953618 | + | 0.301018i | \(0.902673\pi\) | |||||||
\(812\) | −2.41982 | + | 1.39708i | −0.0849191 | + | 0.0490280i | ||||
\(813\) | 5.72751 | − | 3.30678i | 0.200873 | − | 0.115974i | ||||
\(814\) | − | 29.6775i | − | 1.04020i | ||||||
\(815\) | −0.597171 | − | 1.03433i | −0.0209180 | − | 0.0362310i | ||||
\(816\) | 3.35690 | − | 5.81431i | 0.117515 | − | 0.203542i | ||||
\(817\) | 41.1466 | + | 23.7560i | 1.43954 | + | 0.831117i | ||||
\(818\) | 24.0237 | 0.839969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.38404 | −0.118176 | ||||||||
\(821\) | 15.4053 | + | 8.89426i | 0.537649 | + | 0.310412i | 0.744126 | − | 0.668040i | \(-0.232866\pi\) |
−0.206476 | + | 0.978452i | \(0.566200\pi\) | |||||||
\(822\) | −3.82371 | + | 6.62286i | −0.133367 | + | 0.230999i | ||||
\(823\) | 6.11506 | + | 10.5916i | 0.213157 | + | 0.369200i | 0.952701 | − | 0.303909i | \(-0.0982919\pi\) |
−0.739544 | + | 0.673109i | \(0.764959\pi\) | |||||||
\(824\) | − | 9.62565i | − | 0.335325i | ||||||
\(825\) | 11.5073 | − | 6.64377i | 0.400634 | − | 0.231306i | ||||
\(826\) | −0.507852 | + | 0.293209i | −0.0176704 | + | 0.0102020i | ||||
\(827\) | − | 20.5623i | − | 0.715020i | −0.933909 | − | 0.357510i | \(-0.883626\pi\) | ||
0.933909 | − | 0.357510i | \(-0.116374\pi\) | |||||||
\(828\) | −1.19806 | − | 2.07510i | −0.0416355 | − | 0.0721149i | ||||
\(829\) | −12.7235 | + | 22.0377i | −0.441905 | + | 0.765401i | −0.997831 | − | 0.0658303i | \(-0.979030\pi\) |
0.555926 | + | 0.831232i | \(0.312364\pi\) | |||||||
\(830\) | 8.88576 | + | 5.13019i | 0.308429 | + | 0.178072i | ||||
\(831\) | 21.7995 | 0.756218 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.1414 | −1.59870 | ||||||||
\(834\) | −2.93067 | − | 1.69202i | −0.101481 | − | 0.0585899i | ||||
\(835\) | −7.31468 | + | 12.6694i | −0.253135 | + | 0.438443i | ||||
\(836\) | −10.5918 | − | 18.3455i | −0.366325 | − | 0.634493i | ||||
\(837\) | 2.76271i | 0.0954932i | ||||||||
\(838\) | 11.9554 | − | 6.90246i | 0.412993 | − | 0.238442i | ||||
\(839\) | −4.99416 | + | 2.88338i | −0.172418 | + | 0.0995453i | −0.583725 | − | 0.811951i | \(-0.698405\pi\) |
0.411308 | + | 0.911497i | \(0.365072\pi\) | |||||||
\(840\) | 0.246980i | 0.00852161i | ||||||||
\(841\) | −16.1473 | − | 27.9679i | −0.556803 | − | 0.964411i | ||||
\(842\) | 3.86294 | − | 6.69080i | 0.133126 | − | 0.230580i | ||||
\(843\) | 17.8330 | + | 10.2959i | 0.614202 | + | 0.354610i | ||||
\(844\) | 17.2620 | 0.594184 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.98792 | −0.171488 | ||||||||
\(847\) | −0.730133 | − | 0.421543i | −0.0250877 | − | 0.0144844i | ||||
\(848\) | 4.44385 | − | 7.69697i | 0.152602 | − | 0.264315i | ||||
\(849\) | −6.50604 | − | 11.2688i | −0.223287 | − | 0.386744i | ||||
\(850\) | − | 30.3538i | − | 1.04113i | ||||||
\(851\) | −20.9541 | + | 12.0978i | −0.718296 | + | 0.414708i | ||||
\(852\) | 5.89904 | − | 3.40581i | 0.202098 | − | 0.116681i | ||||
\(853\) | 21.1728i | 0.724944i | 0.931995 | + | 0.362472i | \(0.118067\pi\) | ||||
−0.931995 | + | 0.362472i | \(0.881933\pi\) | |||||||
\(854\) | −1.15883 | − | 2.00716i | −0.0396545 | − | 0.0686836i | ||||
\(855\) | 2.49396 | − | 4.31966i | 0.0852916 | − | 0.147729i | ||||
\(856\) | −5.74263 | − | 3.31551i | −0.196279 | − | 0.113322i | ||||
\(857\) | −12.0086 | −0.410207 | −0.205103 | − | 0.978740i | \(-0.565753\pi\) | ||||
−0.205103 | + | 0.978740i | \(0.565753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.66296 | −0.0567393 | −0.0283697 | − | 0.999598i | \(-0.509032\pi\) | ||||
−0.0283697 | + | 0.999598i | \(0.509032\pi\) | |||||||
\(860\) | −3.95052 | − | 2.28083i | −0.134711 | − | 0.0777757i | ||||
\(861\) | −0.872625 | + | 1.51143i | −0.0297390 | + | 0.0515094i | ||||
\(862\) | 0.320060 | + | 0.554360i | 0.0109013 | + | 0.0188816i | ||||
\(863\) | − | 23.8323i | − | 0.811262i | −0.914037 | − | 0.405631i | \(-0.867052\pi\) | ||
0.914037 | − | 0.405631i | \(-0.132948\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −5.60623 | + | 3.23676i | −0.190618 | + | 0.110053i | ||||
\(866\) | − | 21.2760i | − | 0.722989i | ||||||
\(867\) | −14.0375 | − | 24.3137i | −0.476738 | − | 0.825735i | ||||
\(868\) | −0.493000 | + | 0.853901i | −0.0167335 | + | 0.0289833i | ||||
\(869\) | −38.2972 | − | 22.1109i | −1.29914 | − | 0.750060i | ||||
\(870\) | −5.41789 | −0.183684 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −12.9879 | −0.439826 | ||||||||
\(873\) | −0.361908 | − | 0.208947i | −0.0122487 | − | 0.00707180i | ||||
\(874\) | −8.63533 | + | 14.9568i | −0.292095 | + | 0.505923i | ||||
\(875\) | 1.17576 | + | 2.03648i | 0.0397479 | + | 0.0688454i | ||||
\(876\) | − | 3.18598i | − | 0.107644i | ||||||
\(877\) | −36.6482 | + | 21.1588i | −1.23752 | + | 0.714483i | −0.968587 | − | 0.248676i | \(-0.920005\pi\) |
−0.268934 | + | 0.963159i | \(0.586671\pi\) | |||||||
\(878\) | −11.0142 | + | 6.35905i | −0.371711 | + | 0.214608i | ||||
\(879\) | 14.9390i | 0.503880i | ||||||||
\(880\) | 1.01693 | + | 1.76137i | 0.0342806 | + | 0.0593757i | ||||
\(881\) | 11.1371 | − | 19.2900i | 0.375217 | − | 0.649895i | −0.615142 | − | 0.788416i | \(-0.710901\pi\) |
0.990360 | + | 0.138521i | \(0.0442348\pi\) | |||||||
\(882\) | −5.95187 | − | 3.43631i | −0.200410 | − | 0.115707i | ||||
\(883\) | 8.54229 | 0.287471 | 0.143735 | − | 0.989616i | \(-0.454089\pi\) | ||||
0.143735 | + | 0.989616i | \(0.454089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.13706 | −0.0382220 | ||||||||
\(886\) | −19.5697 | − | 11.2986i | −0.657458 | − | 0.379583i | ||||
\(887\) | 9.45712 | − | 16.3802i | 0.317539 | − | 0.549994i | −0.662435 | − | 0.749120i | \(-0.730477\pi\) |
0.979974 | + | 0.199126i | \(0.0638102\pi\) | |||||||
\(888\) | −5.04892 | − | 8.74498i | −0.169431 | − | 0.293462i | ||||
\(889\) | 6.50173i | 0.218061i | ||||||||
\(890\) | −0.237401 | + | 0.137063i | −0.00795769 | + | 0.00459437i | ||||
\(891\) | 2.54525 | − | 1.46950i | 0.0852691 | − | 0.0492301i | ||||
\(892\) | − | 6.76809i | − | 0.226612i | ||||||
\(893\) | 17.9758 | + | 31.1351i | 0.601538 | + | 1.04190i | ||||
\(894\) | −10.4085 | + | 18.0281i | −0.348112 | + | 0.602948i | ||||
\(895\) | 1.90294 | + | 1.09866i | 0.0636083 | + | 0.0367242i | ||||
\(896\) | 0.356896 | 0.0119231 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.6474 | 0.388679 | ||||||||
\(899\) | −18.7317 | − | 10.8147i | −0.624737 | − | 0.360692i | ||||
\(900\) | 2.26055 | − | 3.91539i | 0.0753518 | − | 0.130513i | ||||
\(901\) | −29.8351 | − | 51.6758i | −0.993950 | − | 1.72157i | ||||
\(902\) | 14.3720i | 0.478534i | ||||||||
\(903\) | −2.03740 | + | 1.17629i | −0.0678003 | + | 0.0391445i | ||||
\(904\) | −0.686108 | + | 0.396125i | −0.0228196 | + | 0.0131749i | ||||
\(905\) | 13.7017i | 0.455460i | ||||||||
\(906\) | 0.447730 | + | 0.775492i | 0.0148748 | + | 0.0257640i | ||||
\(907\) | 6.97584 | − | 12.0825i | 0.231629 | − | 0.401193i | −0.726659 | − | 0.686999i | \(-0.758928\pi\) |
0.958288 | + | 0.285806i | \(0.0922612\pi\) | |||||||
\(908\) | 20.5074 | + | 11.8400i | 0.680563 | + | 0.392923i | ||||
\(909\) | −10.0151 | −0.332179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.0422 | 1.49232 | 0.746158 | − | 0.665769i | \(-0.231897\pi\) | ||||
0.746158 | + | 0.665769i | \(0.231897\pi\) | |||||||
\(912\) | −6.24210 | − | 3.60388i | −0.206696 | − | 0.119336i | ||||
\(913\) | 21.7878 | − | 37.7376i | 0.721072 | − | 1.24893i | ||||
\(914\) | −10.5945 | − | 18.3502i | −0.350434 | − | 0.606970i | ||||
\(915\) | − | 4.49396i | − | 0.148566i | ||||||
\(916\) | −7.18653 | + | 4.14914i | −0.237450 | + | 0.137092i | ||||
\(917\) | 0.845510 | − | 0.488155i | 0.0279212 | − | 0.0161203i | ||||
\(918\) | − | 6.71379i | − | 0.221588i | ||||||
\(919\) | −19.9988 | − | 34.6389i | −0.659700 | − | 1.14263i | −0.980693 | − | 0.195552i | \(-0.937350\pi\) |
0.320994 | − | 0.947081i | \(-0.395983\pi\) | |||||||
\(920\) | 0.829085 | − | 1.43602i | 0.0273341 | − | 0.0473441i | ||||
\(921\) | 22.5428 | + | 13.0151i | 0.742809 | + | 0.428861i | ||||
\(922\) | −24.0694 | −0.792682 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.04892 | 0.0345068 | ||||||||
\(925\) | −39.5370 | − | 22.8267i | −1.29997 | − | 0.750537i | ||||
\(926\) | 9.08575 | − | 15.7370i | 0.298576 | − | 0.517149i | ||||
\(927\) | −4.81282 | − | 8.33605i | −0.158074 | − | 0.273792i | ||||
\(928\) | 7.82908i | 0.257002i | ||||||||
\(929\) | 30.0380 | − | 17.3424i | 0.985513 | − | 0.568986i | 0.0815832 | − | 0.996667i | \(-0.474002\pi\) |
0.903930 | + | 0.427680i | \(0.140669\pi\) | |||||||
\(930\) | −1.65571 | + | 0.955927i | −0.0542930 | + | 0.0313461i | ||||
\(931\) | 49.5362i | 1.62348i | ||||||||
\(932\) | 11.9825 | + | 20.7544i | 0.392501 | + | 0.679832i | ||||
\(933\) | −2.40581 | + | 4.16699i | −0.0787628 | + | 0.136421i | ||||
\(934\) | −2.53852 | − | 1.46562i | −0.0830629 | − | 0.0479564i | ||||
\(935\) | 13.6549 | 0.446562 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1260 | −0.624821 | −0.312410 | − | 0.949947i | \(-0.601136\pi\) | ||||
−0.312410 | + | 0.949947i | \(0.601136\pi\) | |||||||
\(938\) | −4.18045 | − | 2.41358i | −0.136496 | − | 0.0788063i | ||||
\(939\) | 13.0206 | − | 22.5523i | 0.424910 | − | 0.735966i | ||||
\(940\) | −1.72587 | − | 2.98930i | −0.0562918 | − | 0.0975002i | ||||
\(941\) | − | 22.5972i | − | 0.736647i | −0.929698 | − | 0.368323i | \(-0.879932\pi\) | ||
0.929698 | − | 0.368323i | \(-0.120068\pi\) | |||||||
\(942\) | 7.44071 | − | 4.29590i | 0.242431 | − | 0.139968i | ||||
\(943\) | 10.1474 | − | 5.85862i | 0.330446 | − | 0.190783i | ||||
\(944\) | 1.64310i | 0.0534785i | ||||||||
\(945\) | 0.123490 | + | 0.213891i | 0.00401712 | + | 0.00695786i | ||||
\(946\) | −9.68664 | + | 16.7778i | −0.314940 | + | 0.545492i | ||||
\(947\) | −23.7602 | − | 13.7180i | −0.772104 | − | 0.445774i | 0.0615209 | − | 0.998106i | \(-0.480405\pi\) |
−0.833625 | + | 0.552332i | \(0.813738\pi\) | |||||||
\(948\) | −15.0465 | −0.488688 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −32.5870 | −1.05726 | ||||||||
\(951\) | 9.97757 | + | 5.76055i | 0.323545 | + | 0.186799i | ||||
\(952\) | 1.19806 | − | 2.07510i | 0.0388294 | − | 0.0672545i | ||||
\(953\) | −0.923936 | − | 1.60030i | −0.0299292 | − | 0.0518389i | 0.850673 | − | 0.525695i | \(-0.176195\pi\) |
−0.880602 | + | 0.473857i | \(0.842862\pi\) | |||||||
\(954\) | − | 8.88769i | − | 0.287750i | ||||||
\(955\) | 9.14667 | − | 5.28083i | 0.295979 | − | 0.170884i | ||||
\(956\) | −10.9257 | + | 6.30798i | −0.353364 | + | 0.204015i | ||||
\(957\) | 23.0097i | 0.743798i | ||||||||
\(958\) | 15.3545 | + | 26.5948i | 0.496081 | + | 0.859238i | ||||
\(959\) | −1.36467 | + | 2.36367i | −0.0440674 | + | 0.0763269i | ||||
\(960\) | 0.599308 | + | 0.346011i | 0.0193426 | + | 0.0111674i | ||||
\(961\) | 23.3674 | 0.753788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.63102 | −0.213682 | ||||||||
\(964\) | −22.8576 | − | 13.1969i | −0.736195 | − | 0.425042i | ||||
\(965\) | −1.64981 | + | 2.85755i | −0.0531092 | + | 0.0919879i | ||||
\(966\) | −0.427583 | − | 0.740596i | −0.0137573 | − | 0.0238283i | ||||
\(967\) | − | 8.88471i | − | 0.285713i | −0.989743 | − | 0.142856i | \(-0.954371\pi\) | ||
0.989743 | − | 0.142856i | \(-0.0456287\pi\) | |||||||
\(968\) | −2.04579 | + | 1.18114i | −0.0657541 | + | 0.0379632i | ||||
\(969\) | −41.9081 | + | 24.1957i | −1.34628 | + | 0.777277i | ||||
\(970\) | − | 0.289192i | − | 0.00928540i | ||||||
\(971\) | −17.5432 | − | 30.3857i | −0.562987 | − | 0.975122i | −0.997234 | − | 0.0743284i | \(-0.976319\pi\) |
0.434247 | − | 0.900794i | \(-0.357015\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −1.04594 | − | 0.603875i | −0.0335314 | − | 0.0193594i | ||||
\(974\) | −24.1497 | −0.773807 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.49396 | −0.207867 | ||||||||
\(977\) | 7.22009 | + | 4.16852i | 0.230991 | + | 0.133363i | 0.611029 | − | 0.791608i | \(-0.290756\pi\) |
−0.380038 | + | 0.924971i | \(0.624089\pi\) | |||||||
\(978\) | −0.862937 | + | 1.49465i | −0.0275937 | + | 0.0477936i | ||||
\(979\) | 0.582105 | + | 1.00824i | 0.0186042 | + | 0.0322234i | ||||
\(980\) | − | 4.75600i | − | 0.151925i | ||||||
\(981\) | −11.2479 | + | 6.49396i | −0.359117 | + | 0.207336i | ||||
\(982\) | −12.6415 | + | 7.29859i | −0.403407 | + | 0.232907i | ||||
\(983\) | 55.6051i | 1.77353i | 0.462224 | + | 0.886763i | \(0.347051\pi\) | ||||
−0.462224 | + | 0.886763i | \(0.652949\pi\) | |||||||
\(984\) | 2.44504 | + | 4.23494i | 0.0779451 | + | 0.135005i | ||||
\(985\) | 4.23341 | − | 7.33247i | 0.134888 | − | 0.233632i | ||||
\(986\) | 45.5208 | + | 26.2814i | 1.44968 | + | 0.836971i | ||||
\(987\) | −1.78017 | −0.0566634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7948 | 0.502244 | ||||||||
\(990\) | 1.76137 | + | 1.01693i | 0.0559799 | + | 0.0323200i | ||||
\(991\) | 21.7983 | − | 37.7558i | 0.692447 | − | 1.19935i | −0.278586 | − | 0.960411i | \(-0.589866\pi\) |
0.971034 | − | 0.238943i | \(-0.0768008\pi\) | |||||||
\(992\) | 1.38135 | + | 2.39258i | 0.0438581 | + | 0.0759644i | ||||
\(993\) | 3.43834i | 0.109112i | ||||||||
\(994\) | 2.10534 | − | 1.21552i | 0.0667774 | − | 0.0385540i | ||||
\(995\) | 7.10088 | − | 4.09970i | 0.225113 | − | 0.129969i | ||||
\(996\) | − | 14.8267i | − | 0.469802i | ||||||
\(997\) | −11.2295 | − | 19.4501i | −0.355643 | − | 0.615991i | 0.631585 | − | 0.775306i | \(-0.282405\pi\) |
−0.987228 | + | 0.159316i | \(0.949071\pi\) | |||||||
\(998\) | 3.42758 | − | 5.93675i | 0.108498 | − | 0.187924i | ||||
\(999\) | −8.74498 | − | 5.04892i | −0.276679 | − | 0.159741i |
(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 | 1014.2.i.g.823.3 | 12 | ||
13.2 | odd | 12 | 1014.2.e.k.991.3 | 6 | |||
13.3 | even | 3 | inner | 1014.2.i.g.361.6 | 12 | ||
13.4 | even | 6 | 1014.2.b.g.337.1 | 6 | |||
13.5 | odd | 4 | 1014.2.e.k.529.3 | 6 | |||
13.6 | odd | 12 | 1014.2.a.o.1.3 | yes | 3 | ||
13.7 | odd | 12 | 1014.2.a.m.1.1 | ✓ | 3 | ||
13.8 | odd | 4 | 1014.2.e.m.529.1 | 6 | |||
13.9 | even | 3 | 1014.2.b.g.337.6 | 6 | |||
13.10 | even | 6 | inner | 1014.2.i.g.361.1 | 12 | ||
13.11 | odd | 12 | 1014.2.e.m.991.1 | 6 | |||
13.12 | even | 2 | inner | 1014.2.i.g.823.4 | 12 | ||
39.17 | odd | 6 | 3042.2.b.r.1351.6 | 6 | |||
39.20 | even | 12 | 3042.2.a.be.1.3 | 3 | |||
39.32 | even | 12 | 3042.2.a.bd.1.1 | 3 | |||
39.35 | odd | 6 | 3042.2.b.r.1351.1 | 6 | |||
52.7 | even | 12 | 8112.2.a.ce.1.1 | 3 | |||
52.19 | even | 12 | 8112.2.a.bz.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.1 | ✓ | 3 | 13.7 | odd | 12 | ||
1014.2.a.o.1.3 | yes | 3 | 13.6 | odd | 12 | ||
1014.2.b.g.337.1 | 6 | 13.4 | even | 6 | |||
1014.2.b.g.337.6 | 6 | 13.9 | even | 3 | |||
1014.2.e.k.529.3 | 6 | 13.5 | odd | 4 | |||
1014.2.e.k.991.3 | 6 | 13.2 | odd | 12 | |||
1014.2.e.m.529.1 | 6 | 13.8 | odd | 4 | |||
1014.2.e.m.991.1 | 6 | 13.11 | odd | 12 | |||
1014.2.i.g.361.1 | 12 | 13.10 | even | 6 | inner | ||
1014.2.i.g.361.6 | 12 | 13.3 | even | 3 | inner | ||
1014.2.i.g.823.3 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.i.g.823.4 | 12 | 13.12 | even | 2 | inner | ||
3042.2.a.bd.1.1 | 3 | 39.32 | even | 12 | |||
3042.2.a.be.1.3 | 3 | 39.20 | even | 12 | |||
3042.2.b.r.1351.1 | 6 | 39.35 | odd | 6 | |||
3042.2.b.r.1351.6 | 6 | 39.17 | odd | 6 | |||
8112.2.a.bz.1.3 | 3 | 52.19 | even | 12 | |||
8112.2.a.ce.1.1 | 3 | 52.7 | even | 12 |