Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(8,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.j (of order \(10\), degree \(4\), 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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.556839 - 1.81878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.17 |
Dual form | 99.2.j.a.35.1 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.726437 | − | 2.23574i | −0.513668 | − | 1.58091i | −0.785692 | − | 0.618618i | \(-0.787693\pi\) |
0.272023 | − | 0.962291i | \(-0.412307\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.85280 | + | 2.07268i | −1.42640 | + | 1.03634i | ||||
\(5\) | −2.13811 | − | 0.694712i | −0.956190 | − | 0.310685i | −0.210962 | − | 0.977494i | \(-0.567659\pi\) |
−0.745228 | + | 0.666809i | \(0.767659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.38116 | − | 3.27739i | −0.899995 | − | 1.23874i | −0.970470 | − | 0.241223i | \(-0.922452\pi\) |
0.0704753 | − | 0.997514i | \(-0.477548\pi\) | |||||||
\(8\) | 2.90269 | + | 2.10893i | 1.02626 | + | 0.745618i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.28492i | 1.67124i | ||||||||
\(11\) | 3.31656 | + | 0.0200544i | 0.999982 | + | 0.00604662i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.42495 | − | 1.43775i | 1.22726 | − | 0.398761i | 0.377538 | − | 0.925994i | \(-0.376771\pi\) |
0.849721 | + | 0.527233i | \(0.176771\pi\) | |||||||
\(14\) | −5.59763 | + | 7.70448i | −1.49603 | + | 2.05911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.427051 | − | 1.31433i | 0.106763 | − | 0.328582i | ||||
\(17\) | 0.0235753 | − | 0.0725574i | 0.00571786 | − | 0.0175978i | −0.948157 | − | 0.317803i | \(-0.897055\pi\) |
0.953875 | + | 0.300205i | \(0.0970551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.40822 | − | 1.93825i | 0.323068 | − | 0.444665i | −0.616333 | − | 0.787486i | \(-0.711382\pi\) |
0.939401 | + | 0.342821i | \(0.111382\pi\) | |||||||
\(20\) | 7.53950 | − | 2.44973i | 1.68588 | − | 0.547777i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.36444 | − | 7.42955i | −0.504100 | − | 1.58399i | ||||
\(23\) | − | 3.22717i | − | 0.672912i | −0.941699 | − | 0.336456i | \(-0.890772\pi\) | ||
0.941699 | − | 0.336456i | \(-0.109228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0437835 | + | 0.0318106i | 0.00875670 | + | 0.00636211i | ||||
\(26\) | −6.42889 | − | 8.84860i | −1.26081 | − | 1.73535i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.5860 | + | 4.41435i | 2.56750 | + | 0.834233i | ||||
\(29\) | −1.48796 | + | 1.08107i | −0.276307 | + | 0.200749i | −0.717305 | − | 0.696759i | \(-0.754625\pi\) |
0.440998 | + | 0.897508i | \(0.354625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.517528 | + | 1.59279i | 0.0929508 | + | 0.286073i | 0.986714 | − | 0.162466i | \(-0.0519446\pi\) |
−0.893763 | + | 0.448539i | \(0.851945\pi\) | |||||||
\(32\) | 3.92711 | 0.694222 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.179346 | −0.0307575 | ||||||||
\(35\) | 2.81433 | + | 8.66162i | 0.475709 | + | 1.46408i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.87906 | + | 4.27138i | −0.966511 | + | 0.702211i | −0.954654 | − | 0.297718i | \(-0.903774\pi\) |
−0.0118571 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(38\) | −5.35641 | − | 1.74040i | −0.868925 | − | 0.282331i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.74115 | − | 6.52564i | −0.749642 | − | 1.03179i | ||||
\(41\) | 6.82980 | + | 4.96214i | 1.06664 | + | 0.774956i | 0.975305 | − | 0.220864i | \(-0.0708878\pi\) |
0.0913313 | + | 0.995821i | \(0.470888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.28086i | − | 0.652825i | −0.945227 | − | 0.326413i | \(-0.894160\pi\) | ||
0.945227 | − | 0.326413i | \(-0.105840\pi\) | |||||||
\(44\) | −9.50306 | + | 6.81697i | −1.43264 | + | 1.02770i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.21513 | + | 2.34434i | −1.06381 | + | 0.345654i | ||||
\(47\) | 3.65360 | − | 5.02874i | 0.532932 | − | 0.733518i | −0.454642 | − | 0.890674i | \(-0.650233\pi\) |
0.987574 | + | 0.157157i | \(0.0502328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.90822 | + | 8.95058i | −0.415460 | + | 1.27865i | ||||
\(50\) | 0.0393143 | − | 0.120997i | 0.00555988 | − | 0.0171116i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.64348 | + | 13.2731i | −1.33731 | + | 1.84065i | ||||
\(53\) | −1.16884 | + | 0.379779i | −0.160552 | + | 0.0521666i | −0.388190 | − | 0.921579i | \(-0.626900\pi\) |
0.227638 | + | 0.973746i | \(0.426900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.07723 | − | 2.34694i | −0.954294 | − | 0.316461i | ||||
\(56\) | − | 14.5349i | − | 1.94231i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.49789 | + | 2.54137i | 0.459296 | + | 0.333698i | ||||
\(59\) | 0.341086 | + | 0.469465i | 0.0444056 | + | 0.0611191i | 0.830642 | − | 0.556806i | \(-0.187973\pi\) |
−0.786237 | + | 0.617925i | \(0.787973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.59710 | − | 1.16877i | −0.460561 | − | 0.149645i | 0.0695411 | − | 0.997579i | \(-0.477847\pi\) |
−0.530102 | + | 0.847934i | \(0.677847\pi\) | |||||||
\(62\) | 3.18511 | − | 2.31412i | 0.404510 | − | 0.293893i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.70690 | − | 11.4087i | −0.463363 | − | 1.42608i | ||||
\(65\) | −10.4598 | −1.29738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9984 | 1.58801 | 0.794003 | − | 0.607914i | \(-0.207993\pi\) | ||||
0.794003 | + | 0.607914i | \(0.207993\pi\) | |||||||
\(68\) | 0.0831326 | + | 0.255856i | 0.0100813 | + | 0.0310271i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.3207 | − | 12.5842i | 2.07022 | − | 1.50410i | ||||
\(71\) | −1.06563 | − | 0.346245i | −0.126467 | − | 0.0410917i | 0.245100 | − | 0.969498i | \(-0.421179\pi\) |
−0.371567 | + | 0.928406i | \(0.621179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.82153 | + | 10.7654i | 0.915441 | + | 1.26000i | 0.965274 | + | 0.261239i | \(0.0841309\pi\) |
−0.0498335 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(74\) | 13.8205 | + | 10.0412i | 1.60660 | + | 1.16726i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.44824i | 0.969079i | ||||||||
\(77\) | −7.83155 | − | 10.9174i | −0.892488 | − | 1.24416i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.627566 | − | 0.203908i | 0.0706066 | − | 0.0229415i | −0.273501 | − | 0.961872i | \(-0.588182\pi\) |
0.344107 | + | 0.938930i | \(0.388182\pi\) | |||||||
\(80\) | −1.82616 | + | 2.51349i | −0.204171 | + | 0.281017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.13265 | − | 18.8744i | 0.677238 | − | 2.08432i | ||||
\(83\) | 3.15542 | − | 9.71138i | 0.346352 | − | 1.06596i | −0.614504 | − | 0.788914i | \(-0.710644\pi\) |
0.960856 | − | 0.277048i | \(-0.0893562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.100813 | + | 0.138757i | −0.0109347 | + | 0.0150503i | ||||
\(86\) | −9.57090 | + | 3.10977i | −1.03206 | + | 0.335336i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.58466 | + | 7.05260i | 1.02173 | + | 0.751810i | ||||
\(89\) | 6.58983i | 0.698520i | 0.937026 | + | 0.349260i | \(0.113567\pi\) | ||||
−0.937026 | + | 0.349260i | \(0.886433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.2486 | − | 11.0787i | −1.59849 | − | 1.16137i | ||||
\(92\) | 6.68890 | + | 9.20649i | 0.697366 | + | 0.959843i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.8971 | − | 4.51544i | −1.43337 | − | 0.465732i | ||||
\(95\) | −4.35745 | + | 3.16587i | −0.447065 | + | 0.324812i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.08168 | + | 15.6398i | 0.515966 | + | 1.58798i | 0.781517 | + | 0.623883i | \(0.214446\pi\) |
−0.265551 | + | 0.964097i | \(0.585554\pi\) | |||||||
\(98\) | 22.1238 | 2.23485 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.190839 | −0.0190839 | ||||||||
\(101\) | −0.532095 | − | 1.63762i | −0.0529455 | − | 0.162949i | 0.921087 | − | 0.389356i | \(-0.127302\pi\) |
−0.974033 | + | 0.226406i | \(0.927302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.61382 | − | 1.89905i | 0.257548 | − | 0.187119i | −0.451518 | − | 0.892262i | \(-0.649117\pi\) |
0.709065 | + | 0.705143i | \(0.249117\pi\) | |||||||
\(104\) | 15.8763 | + | 5.15854i | 1.55680 | + | 0.505836i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.69818 | + | 2.33734i | 0.164941 | + | 0.227022i | ||||
\(107\) | −11.9884 | − | 8.71006i | −1.15896 | − | 0.842034i | −0.169314 | − | 0.985562i | \(-0.554155\pi\) |
−0.989646 | + | 0.143529i | \(0.954155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.9258i | − | 1.42963i | −0.699313 | − | 0.714815i | \(-0.746511\pi\) | ||
0.699313 | − | 0.714815i | \(-0.253489\pi\) | |||||||
\(110\) | −0.105986 | + | 17.5278i | −0.0101053 | + | 1.67121i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.32444 | + | 1.73002i | −0.503112 | + | 0.163471i | ||||
\(113\) | −6.61055 | + | 9.09864i | −0.621868 | + | 0.855928i | −0.997487 | − | 0.0708461i | \(-0.977430\pi\) |
0.375619 | + | 0.926774i | \(0.377430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.24196 | + | 6.90004i | −0.209064 | + | 0.643432i | ||||
\(116\) | 2.00415 | − | 6.16813i | 0.186080 | − | 0.572697i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.801825 | − | 1.10362i | 0.0738139 | − | 0.101596i | ||||
\(119\) | −0.293935 | + | 0.0955054i | −0.0269450 | + | 0.00875497i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9992 | + | 0.133023i | 0.999927 | + | 0.0120930i | ||||
\(122\) | 8.89122i | 0.804973i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.77775 | − | 3.47124i | −0.429054 | − | 0.311726i | ||||
\(125\) | 6.53559 | + | 8.99547i | 0.584561 | + | 0.804580i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.76481 | − | 1.87310i | −0.511544 | − | 0.166211i | 0.0418604 | − | 0.999123i | \(-0.486672\pi\) |
−0.553404 | + | 0.832913i | \(0.686672\pi\) | |||||||
\(128\) | −16.4598 | + | 11.9588i | −1.45486 | + | 1.05701i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.59840 | + | 23.3855i | 0.666424 | + | 2.05104i | ||||
\(131\) | 7.15083 | 0.624771 | 0.312385 | − | 0.949955i | \(-0.398872\pi\) | ||||
0.312385 | + | 0.949955i | \(0.398872\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.70560 | −0.841582 | ||||||||
\(134\) | −9.44251 | − | 29.0611i | −0.815709 | − | 2.51049i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.221450 | − | 0.160893i | 0.0189892 | − | 0.0137964i | ||||
\(137\) | −10.1026 | − | 3.28252i | −0.863120 | − | 0.280445i | −0.156189 | − | 0.987727i | \(-0.549921\pi\) |
−0.706931 | + | 0.707283i | \(0.749921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0311975 | − | 0.0429397i | −0.00264614 | − | 0.00364210i | 0.807692 | − | 0.589605i | \(-0.200716\pi\) |
−0.810338 | + | 0.585963i | \(0.800716\pi\) | |||||||
\(140\) | −25.9815 | − | 18.8767i | −2.19584 | − | 1.59537i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.63400i | 0.221041i | ||||||||
\(143\) | 14.7044 | − | 4.67966i | 1.22965 | − | 0.391333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93244 | − | 1.27773i | 0.326572 | − | 0.106110i | ||||
\(146\) | 18.3868 | − | 25.3073i | 1.52171 | − | 2.09445i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.91856 | − | 24.3708i | 0.650901 | − | 2.00327i | ||||
\(149\) | 6.30238 | − | 19.3967i | 0.516311 | − | 1.58904i | −0.264572 | − | 0.964366i | \(-0.585231\pi\) |
0.780883 | − | 0.624677i | \(-0.214769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.698980 | − | 0.962063i | 0.0568822 | − | 0.0782916i | −0.779628 | − | 0.626243i | \(-0.784592\pi\) |
0.836510 | + | 0.547951i | \(0.184592\pi\) | |||||||
\(152\) | 8.17525 | − | 2.65630i | 0.663101 | − | 0.215454i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.7194 | + | 25.4401i | −1.50845 | + | 2.05003i | ||||
\(155\) | − | 3.76508i | − | 0.302419i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.40210 | + | 1.01868i | 0.111900 | + | 0.0812998i | 0.642328 | − | 0.766430i | \(-0.277969\pi\) |
−0.530428 | + | 0.847730i | \(0.677969\pi\) | |||||||
\(158\) | −0.911773 | − | 1.25495i | −0.0725368 | − | 0.0998383i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.39658 | − | 2.72822i | −0.663808 | − | 0.215684i | ||||
\(161\) | −10.5767 | + | 7.68443i | −0.833561 | + | 0.605618i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.309821 | − | 0.953532i | −0.0242671 | − | 0.0746864i | 0.938190 | − | 0.346122i | \(-0.112502\pi\) |
−0.962457 | + | 0.271435i | \(0.912502\pi\) | |||||||
\(164\) | −29.7690 | −2.32457 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.0044 | −1.86310 | ||||||||
\(167\) | 4.17734 | + | 12.8565i | 0.323252 | + | 0.994868i | 0.972223 | + | 0.234055i | \(0.0751996\pi\) |
−0.648971 | + | 0.760813i | \(0.724800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.99579 | − | 5.08274i | 0.538138 | − | 0.390980i | ||||
\(170\) | 0.383460 | + | 0.124594i | 0.0294100 | + | 0.00955590i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.87286 | + | 12.2124i | 0.676549 | + | 0.931190i | ||||
\(173\) | 6.08619 | + | 4.42188i | 0.462724 | + | 0.336189i | 0.794599 | − | 0.607135i | \(-0.207681\pi\) |
−0.331875 | + | 0.943324i | \(0.607681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.219242i | − | 0.0165731i | ||||||
\(176\) | 1.44270 | − | 4.35049i | 0.108748 | − | 0.327930i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.7332 | − | 4.78709i | 1.10430 | − | 0.358808i | ||||
\(179\) | −7.34750 | + | 10.1130i | −0.549178 | + | 0.755879i | −0.989900 | − | 0.141765i | \(-0.954722\pi\) |
0.440722 | + | 0.897643i | \(0.354722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.56261 | + | 17.1200i | −0.413466 | + | 1.27252i | 0.500150 | + | 0.865939i | \(0.333278\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(182\) | −13.6921 | + | 42.1399i | −1.01492 | + | 3.12362i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.80587 | − | 9.36748i | 0.501736 | − | 0.690580i | ||||
\(185\) | 15.5374 | − | 5.04842i | 1.14233 | − | 0.371167i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0796442 | − | 0.240168i | 0.00582416 | − | 0.0175629i | ||||
\(188\) | 21.9187i | 1.59859i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.2435 | + | 7.44233i | 0.743141 | + | 0.539924i | ||||
\(191\) | 12.7297 | + | 17.5209i | 0.921085 | + | 1.26777i | 0.963237 | + | 0.268654i | \(0.0865788\pi\) |
−0.0421514 | + | 0.999111i | \(0.513421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.93306 | − | 1.60285i | −0.355090 | − | 0.115376i | 0.126040 | − | 0.992025i | \(-0.459773\pi\) |
−0.481129 | + | 0.876650i | \(0.659773\pi\) | |||||||
\(194\) | 31.2750 | − | 22.7226i | 2.24542 | − | 1.63139i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.2551 | − | 31.5620i | −0.732509 | − | 2.25443i | ||||
\(197\) | 5.14679 | 0.366693 | 0.183347 | − | 0.983048i | \(-0.441307\pi\) | ||||
0.183347 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.2595 | 1.71971 | 0.859855 | − | 0.510539i | \(-0.170554\pi\) | ||||
0.859855 | + | 0.510539i | \(0.170554\pi\) | |||||||
\(200\) | 0.0600037 | + | 0.184672i | 0.00424290 | + | 0.0130583i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.27477 | + | 2.37926i | −0.230412 | + | 0.167404i | ||||
\(203\) | 7.08615 | + | 2.30243i | 0.497350 | + | 0.161599i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1556 | − | 15.3543i | −0.779139 | − | 1.07239i | ||||
\(206\) | −6.14457 | − | 4.46429i | −0.428113 | − | 0.311042i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.42982i | − | 0.445828i | ||||||
\(209\) | 4.70933 | − | 6.40009i | 0.325751 | − | 0.442704i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8262 | + | 5.79210i | −1.22721 | + | 0.398744i | −0.849702 | − | 0.527263i | \(-0.823218\pi\) |
−0.377506 | + | 0.926007i | \(0.623218\pi\) | |||||||
\(212\) | 2.54730 | − | 3.50606i | 0.174950 | − | 0.240797i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.7647 | + | 33.1302i | −0.735857 | + | 2.26474i | ||||
\(215\) | −2.97397 | + | 9.15293i | −0.202823 | + | 0.624225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.98787 | − | 5.48883i | 0.270714 | − | 0.372606i | ||||
\(218\) | −33.3702 | + | 10.8426i | −2.26012 | + | 0.734356i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.0544 | − | 7.97350i | 1.68917 | − | 0.537573i | ||||
\(221\) | − | 0.354958i | − | 0.0238771i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.44037 | + | 3.22612i | 0.297349 | + | 0.216037i | 0.726449 | − | 0.687220i | \(-0.241169\pi\) |
−0.429100 | + | 0.903257i | \(0.641169\pi\) | |||||||
\(224\) | −9.35109 | − | 12.8707i | −0.624796 | − | 0.859958i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.1444 | + | 8.16990i | 1.67258 | + | 0.543454i | ||||
\(227\) | 11.1352 | − | 8.09016i | 0.739066 | − | 0.536963i | −0.153352 | − | 0.988172i | \(-0.549007\pi\) |
0.892419 | + | 0.451209i | \(0.149007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.53035 | − | 20.0983i | −0.431538 | − | 1.32814i | −0.896593 | − | 0.442855i | \(-0.853966\pi\) |
0.465056 | − | 0.885281i | \(-0.346034\pi\) | |||||||
\(230\) | 17.0554 | 1.12460 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.59897 | −0.433244 | ||||||||
\(233\) | 4.62458 | + | 14.2330i | 0.302967 | + | 0.932435i | 0.980428 | + | 0.196877i | \(0.0630800\pi\) |
−0.677462 | + | 0.735558i | \(0.736920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3053 | + | 8.21378i | −0.737477 | + | 0.535808i | ||||
\(236\) | −1.94610 | − | 0.632327i | −0.126680 | − | 0.0411610i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.427051 | + | 0.587785i | 0.0276816 | + | 0.0381005i | ||||
\(239\) | −4.37274 | − | 3.17698i | −0.282849 | − | 0.205502i | 0.437310 | − | 0.899311i | \(-0.355931\pi\) |
−0.720159 | + | 0.693809i | \(0.755931\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.7091i | − | 0.754252i | −0.926162 | − | 0.377126i | \(-0.876912\pi\) | ||
0.926162 | − | 0.377126i | \(-0.123088\pi\) | |||||||
\(242\) | −7.69281 | − | 24.6880i | −0.494513 | − | 1.58700i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6843 | − | 4.12137i | 0.812028 | − | 0.263844i | ||||
\(245\) | 12.4362 | − | 17.1169i | 0.794518 | − | 1.09356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.44458 | − | 10.6013i | 0.219173 | − | 0.674546i | ||||
\(248\) | −1.85685 | + | 5.71479i | −0.117910 | + | 0.362890i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.3639 | − | 21.1465i | 0.971696 | − | 1.33743i | ||||
\(251\) | −21.4920 | + | 6.98319i | −1.35657 | + | 0.440775i | −0.894895 | − | 0.446276i | \(-0.852750\pi\) |
−0.461671 | + | 0.887051i | \(0.652750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0647190 | − | 10.7031i | 0.00406885 | − | 0.672900i | ||||
\(254\) | 14.2493i | 0.894081i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.2841 | + | 14.0107i | 1.20526 | + | 0.875671i | ||||
\(257\) | −16.1737 | − | 22.2612i | −1.00889 | − | 1.38862i | −0.919709 | − | 0.392601i | \(-0.871575\pi\) |
−0.0891801 | − | 0.996016i | \(-0.528425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.9980 | + | 9.09709i | 1.73971 | + | 0.565266i | ||||
\(260\) | 29.8398 | − | 21.6799i | 1.85059 | − | 1.34453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.19462 | − | 15.9874i | −0.320925 | − | 0.987705i | ||||
\(263\) | −32.0386 | −1.97559 | −0.987793 | − | 0.155773i | \(-0.950213\pi\) | ||||
−0.987793 | + | 0.155773i | \(0.950213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76294 | 0.169726 | ||||||||
\(266\) | 7.05051 | + | 21.6992i | 0.432294 | + | 1.33046i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −37.0818 | + | 26.9415i | −2.26513 | + | 1.64572i | ||||
\(269\) | 25.7177 | + | 8.35619i | 1.56804 | + | 0.509486i | 0.958940 | − | 0.283610i | \(-0.0915322\pi\) |
0.609097 | + | 0.793096i | \(0.291532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.74690 | + | 12.0391i | 0.531336 | + | 0.731322i | 0.987333 | − | 0.158660i | \(-0.0507172\pi\) |
−0.455997 | + | 0.889981i | \(0.650717\pi\) | |||||||
\(272\) | −0.0852963 | − | 0.0619714i | −0.00517185 | − | 0.00375757i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.9713i | 1.50857i | ||||||||
\(275\) | 0.144573 | + | 0.106380i | 0.00871807 | + | 0.00641495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.49418 | + | 2.43501i | −0.450282 | + | 0.146305i | −0.525374 | − | 0.850871i | \(-0.676075\pi\) |
0.0750927 | + | 0.997177i | \(0.476075\pi\) | |||||||
\(278\) | −0.0733391 | + | 0.100943i | −0.00439859 | + | 0.00605414i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.0976 | + | 31.0772i | −0.603447 | + | 1.85722i | ||||
\(281\) | −6.56034 | + | 20.1906i | −0.391357 | + | 1.20447i | 0.540406 | + | 0.841405i | \(0.318271\pi\) |
−0.931763 | + | 0.363068i | \(0.881729\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.52460 | + | 3.47482i | −0.150072 | + | 0.206556i | −0.877434 | − | 0.479698i | \(-0.840746\pi\) |
0.727362 | + | 0.686254i | \(0.240746\pi\) | |||||||
\(284\) | 3.75769 | − | 1.22095i | 0.222978 | − | 0.0724499i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.1444 | − | 29.4759i | −1.25029 | − | 1.74295i | ||||
\(287\) | − | 34.1996i | − | 2.01874i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7486 | + | 9.98893i | 0.808740 | + | 0.587584i | ||||
\(290\) | −5.71335 | − | 7.86374i | −0.335499 | − | 0.461775i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −44.6265 | − | 14.5000i | −2.61157 | − | 0.848550i | ||||
\(293\) | −15.4486 | + | 11.2241i | −0.902518 | + | 0.655717i | −0.939111 | − | 0.343613i | \(-0.888349\pi\) |
0.0365938 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.403135 | − | 1.24072i | −0.0234714 | − | 0.0722376i | ||||
\(296\) | −26.0731 | −1.51547 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −47.9444 | −2.77735 | ||||||||
\(299\) | −4.63988 | − | 14.2801i | −0.268331 | − | 0.825838i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0300 | + | 10.1934i | −0.808678 | + | 0.587539i | ||||
\(302\) | −2.65869 | − | 0.863861i | −0.152990 | − | 0.0497096i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.94611 | − | 2.67860i | −0.111617 | − | 0.153628i | ||||
\(305\) | 6.87902 | + | 4.99790i | 0.393891 | + | 0.286179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.86240i | − | 0.106293i | −0.998587 | − | 0.0531463i | \(-0.983075\pi\) | ||
0.998587 | − | 0.0531463i | \(-0.0169250\pi\) | |||||||
\(308\) | 44.9702 | + | 14.9129i | 2.56241 | + | 0.849742i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.41775 | + | 2.73509i | −0.478096 | + | 0.155343i | ||||
\(311\) | −5.26339 | + | 7.24443i | −0.298459 | + | 0.410794i | −0.931739 | − | 0.363129i | \(-0.881708\pi\) |
0.633279 | + | 0.773923i | \(0.281708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.29558 | − | 16.2981i | 0.299324 | − | 0.921224i | −0.682411 | − | 0.730969i | \(-0.739068\pi\) |
0.981735 | − | 0.190255i | \(-0.0609316\pi\) | |||||||
\(314\) | 1.25898 | − | 3.87474i | 0.0710483 | − | 0.218664i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.36768 | + | 1.88245i | −0.0769381 | + | 0.105896i | ||||
\(317\) | 25.9678 | − | 8.43746i | 1.45850 | − | 0.473895i | 0.530888 | − | 0.847442i | \(-0.321859\pi\) |
0.927611 | + | 0.373547i | \(0.121859\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.95659 | + | 3.55558i | −0.277516 | + | 0.199075i | ||||
\(320\) | 26.9682i | 1.50757i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.8637 | + | 18.0645i | 1.38560 | + | 1.00670i | ||||
\(323\) | −0.107435 | − | 0.147872i | −0.00597785 | − | 0.00822781i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.239475 | + | 0.0778102i | 0.0132837 | + | 0.00431614i | ||||
\(326\) | −1.90679 | + | 1.38536i | −0.105607 | + | 0.0767281i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.35999 | + | 28.8071i | 0.516819 | + | 1.59061i | ||||
\(329\) | −25.1809 | −1.38827 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.87217 | −0.322764 | −0.161382 | − | 0.986892i | \(-0.551595\pi\) | ||||
−0.161382 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(332\) | 11.1268 | + | 34.2448i | 0.610663 | + | 1.87943i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.7093 | − | 18.6789i | 1.40675 | − | 1.02206i | ||||
\(335\) | −27.7919 | − | 9.03014i | −1.51844 | − | 0.493370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.74004 | − | 13.4060i | −0.530574 | − | 0.730272i | 0.456644 | − | 0.889650i | \(-0.349051\pi\) |
−0.987218 | + | 0.159377i | \(0.949051\pi\) | |||||||
\(338\) | −16.4457 | − | 11.9485i | −0.894528 | − | 0.649912i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 0.604800i | − | 0.0327999i | ||||||
\(341\) | 1.68447 | + | 5.29296i | 0.0912193 | + | 0.286630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.28988 | − | 3.01847i | 0.501606 | − | 0.162982i | ||||
\(344\) | 9.02802 | − | 12.4260i | 0.486758 | − | 0.669965i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.46494 | − | 16.8194i | 0.293797 | − | 0.904215i | ||||
\(347\) | −0.778158 | + | 2.39492i | −0.0417737 | + | 0.128566i | −0.969768 | − | 0.244027i | \(-0.921531\pi\) |
0.927995 | + | 0.372593i | \(0.121531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.13104 | − | 7.06228i | 0.274658 | − | 0.378035i | −0.649297 | − | 0.760535i | \(-0.724937\pi\) |
0.923955 | + | 0.382500i | \(0.124937\pi\) | |||||||
\(350\) | −0.490168 | + | 0.159265i | −0.0262006 | + | 0.00851308i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.0245 | + | 0.0787558i | 0.694210 | + | 0.00419770i | ||||
\(353\) | − | 0.536500i | − | 0.0285550i | −0.999898 | − | 0.0142775i | \(-0.995455\pi\) | ||
0.999898 | − | 0.0142775i | \(-0.00454483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.03789 | + | 1.48062i | 0.108160 | + | 0.0785829i | ||||
\(356\) | −13.6586 | − | 18.7995i | −0.723905 | − | 0.996370i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.9475 | + | 9.08069i | 1.47707 | + | 0.479929i | ||||
\(359\) | 12.7871 | − | 9.29040i | 0.674880 | − | 0.490329i | −0.196775 | − | 0.980449i | \(-0.563047\pi\) |
0.871655 | + | 0.490120i | \(0.163047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.09760 | + | 12.6111i | 0.215663 | + | 0.663742i | ||||
\(362\) | 42.3167 | 2.22412 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 66.4639 | 3.48365 | ||||||||
\(365\) | −9.24439 | − | 28.4513i | −0.483873 | − | 1.48921i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.4075 | + | 17.0065i | −1.22186 | + | 0.887734i | −0.996253 | − | 0.0864843i | \(-0.972437\pi\) |
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(368\) | −4.24157 | − | 1.37817i | −0.221107 | − | 0.0718420i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.5739 | − | 31.0703i | −1.17356 | − | 1.61527i | ||||
\(371\) | 4.02788 | + | 2.92642i | 0.209117 | + | 0.151932i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.60935i | 0.342219i | 0.985252 | + | 0.171109i | \(0.0547352\pi\) | ||||
−0.985252 | + | 0.171109i | \(0.945265\pi\) | |||||||
\(374\) | −0.594811 | − | 0.00359666i | −0.0307570 | − | 0.000185979i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.2105 | − | 6.89171i | 1.09385 | − | 0.355413i | ||||
\(377\) | −5.02984 | + | 6.92297i | −0.259050 | + | 0.356551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.478524 | − | 1.47275i | 0.0245801 | − | 0.0756498i | −0.938014 | − | 0.346597i | \(-0.887337\pi\) |
0.962594 | + | 0.270948i | \(0.0873370\pi\) | |||||||
\(380\) | 5.86909 | − | 18.0632i | 0.301078 | − | 0.926623i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29.9249 | − | 41.1880i | 1.53109 | − | 2.10736i | ||||
\(383\) | 12.8467 | − | 4.17415i | 0.656436 | − | 0.213289i | 0.0381861 | − | 0.999271i | \(-0.487842\pi\) |
0.618250 | + | 0.785982i | \(0.287842\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.16021 | + | 28.7833i | 0.466847 | + | 1.46693i | ||||
\(386\) | 12.1934i | 0.620629i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −46.9133 | − | 34.0845i | −2.38166 | − | 1.73038i | ||||
\(389\) | 8.80471 | + | 12.1186i | 0.446416 | + | 0.614440i | 0.971623 | − | 0.236535i | \(-0.0760119\pi\) |
−0.525206 | + | 0.850975i | \(0.676012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.234155 | − | 0.0760817i | −0.0118417 | − | 0.00384762i | ||||
\(392\) | −27.3178 | + | 19.8475i | −1.37976 | + | 1.00245i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.73882 | − | 11.5069i | −0.188359 | − | 0.579709i | ||||
\(395\) | −1.48346 | −0.0746409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.7132 | −1.03956 | −0.519782 | − | 0.854299i | \(-0.673987\pi\) | ||||
−0.519782 | + | 0.854299i | \(0.673987\pi\) | |||||||
\(398\) | −17.6230 | − | 54.2380i | −0.883360 | − | 2.71870i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0605073 | − | 0.0439611i | 0.00302537 | − | 0.00219806i | ||||
\(401\) | 25.7211 | + | 8.35730i | 1.28445 | + | 0.417343i | 0.870146 | − | 0.492795i | \(-0.164025\pi\) |
0.414305 | + | 0.910138i | \(0.364025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.58007 | + | 6.30392i | 0.228149 | + | 0.314021i | ||||
\(404\) | 4.91223 | + | 3.56894i | 0.244392 | + | 0.177561i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 17.5154i | − | 0.869273i | ||||||
\(407\) | −19.5839 | + | 14.0484i | −0.970739 | + | 0.696354i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.80668 | + | 1.88670i | −0.287122 | + | 0.0932915i | −0.449037 | − | 0.893513i | \(-0.648233\pi\) |
0.161915 | + | 0.986805i | \(0.448233\pi\) | |||||||
\(410\) | −26.2245 | + | 36.0949i | −1.29514 | + | 1.78260i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.52058 | + | 10.8352i | −0.173447 | + | 0.533814i | ||||
\(413\) | 0.726437 | − | 2.23574i | 0.0357456 | − | 0.110014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4932 | + | 18.5718i | −0.662357 | + | 0.911656i | ||||
\(416\) | 17.3773 | − | 5.64622i | 0.851991 | − | 0.276829i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.7300 | − | 5.87958i | −0.867202 | − | 0.287580i | ||||
\(419\) | 35.6619i | 1.74220i | 0.491110 | + | 0.871098i | \(0.336591\pi\) | ||||
−0.491110 | + | 0.871098i | \(0.663409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5751 | − | 8.40982i | −0.564137 | − | 0.409870i | 0.268834 | − | 0.963187i | \(-0.413362\pi\) |
−0.832971 | + | 0.553317i | \(0.813362\pi\) | |||||||
\(422\) | 25.8993 | + | 35.6473i | 1.26076 | + | 1.73528i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19370 | − | 1.36262i | −0.203664 | − | 0.0661745i | ||||
\(425\) | 0.00334030 | − | 0.00242687i | 0.000162028 | − | 0.000117721i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.73477 | + | 14.5721i | 0.229131 | + | 0.705194i | ||||
\(428\) | 52.2536 | 2.52577 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.6240 | 1.09103 | ||||||||
\(431\) | 2.68944 | + | 8.27725i | 0.129546 | + | 0.398701i | 0.994702 | − | 0.102802i | \(-0.0327807\pi\) |
−0.865156 | + | 0.501503i | \(0.832781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3812 | − | 22.0733i | 1.46003 | − | 1.06077i | 0.476673 | − | 0.879080i | \(-0.341842\pi\) |
0.983355 | − | 0.181693i | \(-0.0581576\pi\) | |||||||
\(434\) | −15.1685 | − | 4.92856i | −0.728113 | − | 0.236578i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.9364 | + | 42.5803i | 1.48158 | + | 2.03923i | ||||
\(437\) | −6.25507 | − | 4.54458i | −0.299221 | − | 0.217397i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.4669i | 1.54956i | 0.632232 | + | 0.774779i | \(0.282139\pi\) | ||||
−0.632232 | + | 0.774779i | \(0.717861\pi\) | |||||||
\(440\) | −15.5935 | − | 21.7378i | −0.743390 | − | 1.03631i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.793595 | + | 0.257855i | −0.0377474 | + | 0.0122649i | ||||
\(443\) | −11.0630 | + | 15.2269i | −0.525618 | + | 0.723451i | −0.986455 | − | 0.164034i | \(-0.947549\pi\) |
0.460837 | + | 0.887485i | \(0.347549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57804 | − | 14.0897i | 0.217020 | − | 0.667918i | ||||
\(446\) | 3.98712 | − | 12.2711i | 0.188796 | − | 0.581053i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −28.5639 | + | 39.3149i | −1.34952 | + | 1.85745i | ||||
\(449\) | −6.86840 | + | 2.23168i | −0.324140 | + | 0.105319i | −0.466567 | − | 0.884486i | \(-0.654509\pi\) |
0.142427 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5520 | + | 16.5942i | 1.06193 | + | 0.781392i | ||||
\(452\) | − | 39.6582i | − | 1.86536i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.1765 | − | 19.0183i | −1.22852 | − | 0.892575i | ||||
\(455\) | 24.9065 | + | 34.2809i | 1.16764 | + | 1.60711i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.01554 | + | 1.30473i | 0.187839 | + | 0.0610326i | 0.401426 | − | 0.915891i | \(-0.368515\pi\) |
−0.213587 | + | 0.976924i | \(0.568515\pi\) | |||||||
\(458\) | −40.1908 | + | 29.2004i | −1.87799 | + | 1.36444i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.90572 | − | 24.3313i | −0.368606 | − | 1.13445i | ||||
\(461\) | 14.1922 | 0.660997 | 0.330499 | − | 0.943806i | \(-0.392783\pi\) | ||||
0.330499 | + | 0.943806i | \(0.392783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.3784 | −1.87654 | −0.938271 | − | 0.345902i | \(-0.887573\pi\) | ||||
−0.938271 | + | 0.345902i | \(0.887573\pi\) | |||||||
\(464\) | 0.785440 | + | 2.41734i | 0.0364632 | + | 0.112222i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.4619 | − | 20.6788i | 1.31847 | − | 0.957925i | ||||
\(467\) | −10.7476 | − | 3.49210i | −0.497338 | − | 0.161595i | 0.0495980 | − | 0.998769i | \(-0.484206\pi\) |
−0.546936 | + | 0.837174i | \(0.684206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.9513 | − | 42.6008i | −1.42920 | − | 1.96712i | ||||
\(470\) | 26.5765 | + | 19.3090i | 1.22588 | + | 0.890656i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.08203i | 0.0958334i | ||||||||
\(473\) | 0.0858500 | − | 14.1977i | 0.00394739 | − | 0.652813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.123314 | − | 0.0400671i | 0.00565802 | − | 0.00183840i | ||||
\(476\) | 0.640587 | − | 0.881692i | 0.0293612 | − | 0.0404123i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.92639 | + | 12.0842i | −0.179589 | + | 0.552718i | ||||
\(479\) | 7.07597 | − | 21.7776i | 0.323309 | − | 0.995044i | −0.648889 | − | 0.760883i | \(-0.724766\pi\) |
0.972198 | − | 0.234161i | \(-0.0752341\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.8733 | + | 27.3533i | −0.906145 | + | 1.24720i | ||||
\(482\) | −26.1786 | + | 8.50595i | −1.19240 | + | 0.387436i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.6542 | + | 22.4183i | −1.43883 | + | 1.01902i | ||||
\(485\) | − | 36.9698i | − | 1.67871i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.10169 | + | 4.43314i | 0.276494 | + | 0.200885i | 0.717387 | − | 0.696675i | \(-0.245338\pi\) |
−0.440893 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(488\) | −7.97641 | − | 10.9786i | −0.361075 | − | 0.496977i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −47.3031 | − | 15.3697i | −2.13694 | − | 0.694333i | ||||
\(491\) | 30.8965 | − | 22.4476i | 1.39434 | − | 1.01305i | 0.398967 | − | 0.916965i | \(-0.369369\pi\) |
0.995373 | − | 0.0960820i | \(-0.0306311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0433602 | + | 0.133449i | 0.00195285 | + | 0.00601024i | ||||
\(494\) | −26.2041 | −1.17898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.31446 | 0.103922 | ||||||||
\(497\) | 1.40266 | + | 4.31695i | 0.0629181 | + | 0.193642i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.51994 | − | 4.73701i | 0.291873 | − | 0.212058i | −0.432207 | − | 0.901775i | \(-0.642265\pi\) |
0.724079 | + | 0.689717i | \(0.242265\pi\) | |||||||
\(500\) | −37.2895 | − | 12.1161i | −1.66764 | − | 0.541848i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.2252 | + | 42.9778i | 1.39365 | + | 1.91820i | ||||
\(503\) | −21.0846 | − | 15.3188i | −0.940115 | − | 0.683033i | 0.00833362 | − | 0.999965i | \(-0.497347\pi\) |
−0.948448 | + | 0.316932i | \(0.897347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.87106i | 0.172260i | ||||||||
\(506\) | −23.9765 | + | 7.63045i | −1.06588 | + | 0.339215i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.3282 | − | 6.60503i | 0.901917 | − | 0.293051i | ||||
\(509\) | 16.4364 | − | 22.6228i | 0.728531 | − | 1.00274i | −0.270666 | − | 0.962673i | \(-0.587244\pi\) |
0.999197 | − | 0.0400639i | \(-0.0127561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6581 | − | 51.2684i | 0.736911 | − | 2.26798i | ||||
\(512\) | 4.74153 | − | 14.5929i | 0.209548 | − | 0.644922i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.0212 | + | 52.3316i | −1.67704 | + | 2.30825i | ||||
\(515\) | −6.90792 | + | 2.24452i | −0.304399 | + | 0.0989054i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2182 | − | 16.6049i | 0.537357 | − | 0.730282i | ||||
\(518\) | − | 69.2047i | − | 3.04068i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −30.3616 | − | 22.0590i | −1.33144 | − | 0.967351i | ||||
\(521\) | −18.9804 | − | 26.1242i | −0.831545 | − | 1.14452i | −0.987633 | − | 0.156781i | \(-0.949888\pi\) |
0.156088 | − | 0.987743i | \(-0.450112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5104 | + | 5.36454i | 0.721948 | + | 0.234575i | 0.646868 | − | 0.762602i | \(-0.276079\pi\) |
0.0750804 | + | 0.997177i | \(0.476079\pi\) | |||||||
\(524\) | −20.3999 | + | 14.8214i | −0.891173 | + | 0.647475i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.2740 | + | 71.6301i | 1.01480 | + | 3.12322i | ||||
\(527\) | 0.127769 | 0.00556572 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5853 | 0.547189 | ||||||||
\(530\) | −2.00710 | − | 6.17722i | −0.0871828 | − | 0.268321i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.6881 | − | 20.1166i | 1.20043 | − | 0.872166i | ||||
\(533\) | 37.3558 | + | 12.1376i | 1.61806 | + | 0.525740i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.5814 | + | 26.9515i | 0.846578 | + | 1.16522i | ||||
\(536\) | 37.7303 | + | 27.4126i | 1.62970 | + | 1.18405i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 63.5684i | − | 2.74063i | ||||||
\(539\) | −9.82480 | + | 29.6269i | −0.423184 | + | 1.27612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58312 | + | 3.11375i | −0.412011 | + | 0.133870i | −0.507686 | − | 0.861542i | \(-0.669499\pi\) |
0.0956753 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(542\) | 20.5622 | − | 28.3014i | 0.883222 | − | 1.21565i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0925830 | − | 0.284941i | 0.00396946 | − | 0.0122168i | ||||
\(545\) | −10.3691 | + | 31.9129i | −0.444165 | + | 1.36700i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0244 | − | 19.3029i | 0.599639 | − | 0.825333i | −0.396036 | − | 0.918235i | \(-0.629614\pi\) |
0.995675 | + | 0.0929023i | \(0.0296144\pi\) | |||||||
\(548\) | 35.6242 | − | 11.5750i | 1.52179 | − | 0.494460i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.132815 | − | 0.400506i | 0.00566325 | − | 0.0170776i | ||||
\(551\) | 4.40642i | 0.187720i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.16262 | − | 1.57124i | −0.0919640 | − | 0.0668158i | ||||
\(554\) | 10.8881 | + | 14.9862i | 0.462591 | + | 0.636702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.178001 | + | 0.0578359i | 0.00754891 | + | 0.00245279i | ||||
\(557\) | −31.6776 | + | 23.0151i | −1.34222 | + | 0.975181i | −0.342862 | + | 0.939386i | \(0.611396\pi\) |
−0.999359 | + | 0.0357950i | \(0.988604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.15482 | − | 18.9426i | −0.260321 | − | 0.801185i | ||||
\(560\) | 12.5861 | 0.531859 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 49.9068 | 2.10519 | ||||||||
\(563\) | 1.55147 | + | 4.77494i | 0.0653868 | + | 0.201240i | 0.978412 | − | 0.206663i | \(-0.0662603\pi\) |
−0.913025 | + | 0.407903i | \(0.866260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.4550 | − | 14.8614i | 0.860548 | − | 0.625225i | ||||
\(566\) | 9.60276 | + | 3.12012i | 0.403634 | + | 0.131149i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.36299 | − | 3.25238i | −0.0991489 | − | 0.136467i | ||||
\(569\) | 7.69308 | + | 5.58935i | 0.322511 | + | 0.234318i | 0.737246 | − | 0.675624i | \(-0.236126\pi\) |
−0.414735 | + | 0.909942i | \(0.636126\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 39.8291i | − | 1.66680i | −0.552673 | − | 0.833398i | \(-0.686392\pi\) | ||
0.552673 | − | 0.833398i | \(-0.313608\pi\) | |||||||
\(572\) | −32.2494 | + | 43.8278i | −1.34842 | + | 1.83253i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −76.4614 | + | 24.8438i | −3.19144 | + | 1.03696i | ||||
\(575\) | 0.102658 | − | 0.141297i | 0.00428115 | − | 0.00589249i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.03506 | + | 12.4186i | −0.167982 | + | 0.516994i | −0.999244 | − | 0.0388866i | \(-0.987619\pi\) |
0.831262 | + | 0.555881i | \(0.187619\pi\) | |||||||
\(578\) | 12.3452 | − | 37.9946i | 0.513493 | − | 1.58037i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.57016 | + | 11.7958i | −0.355856 | + | 0.489794i | ||||
\(581\) | −39.3415 | + | 12.7828i | −1.63216 | + | 0.530321i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.88415 | + | 1.23612i | −0.160865 | + | 0.0511949i | ||||
\(584\) | 47.7437i | 1.97565i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.3166 | + | 26.3855i | 1.50022 | + | 1.08998i | ||||
\(587\) | −13.9608 | − | 19.2153i | −0.576222 | − | 0.793102i | 0.417053 | − | 0.908882i | \(-0.363063\pi\) |
−0.993275 | + | 0.115780i | \(0.963063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.81602 | + | 1.23990i | 0.157236 | + | 0.0510891i | ||||
\(590\) | −2.48108 | + | 1.80261i | −0.102145 | + | 0.0742123i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.10334 | + | 9.55111i | 0.127547 | + | 0.392548i | ||||
\(593\) | 37.1489 | 1.52552 | 0.762761 | − | 0.646680i | \(-0.223843\pi\) | ||||
0.762761 | + | 0.646680i | \(0.223843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.694814 | 0.0284846 | ||||||||
\(596\) | 22.2238 | + | 68.3979i | 0.910323 | + | 2.80169i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.5560 | + | 20.7471i | −1.16774 | + | 0.848414i | ||||
\(599\) | 2.26902 | + | 0.737248i | 0.0927095 | + | 0.0301231i | 0.355004 | − | 0.934865i | \(-0.384479\pi\) |
−0.262295 | + | 0.964988i | \(0.584479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.99333 | + | 5.49635i | 0.162891 | + | 0.224201i | 0.882658 | − | 0.470015i | \(-0.155751\pi\) |
−0.719767 | + | 0.694216i | \(0.755751\pi\) | |||||||
\(602\) | 32.9818 | + | 23.9627i | 1.34424 | + | 0.976646i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.19334i | 0.170624i | ||||||||
\(605\) | −23.4250 | − | 7.92570i | −0.952363 | − | 0.322225i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.5143 | + | 12.5141i | −1.56325 | + | 0.507930i | −0.957673 | − | 0.287859i | \(-0.907057\pi\) |
−0.605575 | + | 0.795788i | \(0.707057\pi\) | |||||||
\(608\) | 5.53025 | − | 7.61173i | 0.224281 | − | 0.308696i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.17684 | − | 19.0104i | 0.250093 | − | 0.769707i | ||||
\(611\) | 8.93688 | − | 27.5049i | 0.361547 | − | 1.11273i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.119072 | − | 0.163888i | 0.00480926 | − | 0.00661938i | −0.806606 | − | 0.591090i | \(-0.798698\pi\) |
0.811415 | + | 0.584471i | \(0.198698\pi\) | |||||||
\(614\) | −4.16384 | + | 1.35291i | −0.168039 | + | 0.0545991i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.291489 | − | 48.2060i | 0.0117444 | − | 1.94228i | ||||
\(617\) | 8.08426i | 0.325460i | 0.986671 | + | 0.162730i | \(0.0520299\pi\) | ||||
−0.986671 | + | 0.162730i | \(0.947970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.9785 | − | 12.3356i | −0.682424 | − | 0.495810i | 0.191737 | − | 0.981446i | \(-0.438588\pi\) |
−0.874161 | + | 0.485636i | \(0.838588\pi\) | |||||||
\(620\) | 7.80381 | + | 10.7410i | 0.313409 | + | 0.431370i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.0202 | + | 6.50496i | 0.802737 | + | 0.260825i | ||||
\(623\) | 21.5974 | − | 15.6914i | 0.865282 | − | 0.628664i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.80814 | − | 24.0310i | −0.312326 | − | 0.961239i | ||||
\(626\) | −40.2853 | −1.61012 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.11131 | −0.243868 | ||||||||
\(629\) | 0.171320 | + | 0.527268i | 0.00683097 | + | 0.0210236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6268 | − | 14.2597i | 0.781332 | − | 0.567671i | −0.124047 | − | 0.992276i | \(-0.539587\pi\) |
0.905378 | + | 0.424606i | \(0.139587\pi\) | |||||||
\(632\) | 2.25165 | + | 0.731607i | 0.0895660 | + | 0.0291018i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −37.7280 | − | 51.9281i | −1.49837 | − | 2.06233i | ||||
\(635\) | 11.0245 | + | 8.00977i | 0.437494 | + | 0.317858i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.7871i | 1.73491i | ||||||||
\(638\) | 11.5500 | + | 8.49876i | 0.457270 | + | 0.336469i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.5007 | − | 14.1342i | 1.71952 | − | 0.558705i | ||||
\(641\) | −9.48633 | + | 13.0568i | −0.374688 | + | 0.515713i | −0.954167 | − | 0.299273i | \(-0.903256\pi\) |
0.579480 | + | 0.814987i | \(0.303256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.88866 | − | 11.9681i | 0.153354 | − | 0.471975i | −0.844637 | − | 0.535340i | \(-0.820183\pi\) |
0.997990 | + | 0.0633656i | \(0.0201834\pi\) | |||||||
\(644\) | 14.2459 | − | 43.8443i | 0.561366 | − | 1.72771i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.252558 | + | 0.347617i | −0.00993678 | + | 0.0136768i | ||||
\(647\) | 28.7701 | − | 9.34797i | 1.13107 | − | 0.367507i | 0.317087 | − | 0.948396i | \(-0.397295\pi\) |
0.813982 | + | 0.580890i | \(0.197295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12182 | + | 1.56385i | 0.0440352 | + | 0.0613865i | ||||
\(650\) | − | 0.591929i | − | 0.0232174i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.86023 | + | 2.07808i | 0.112015 | + | 0.0813837i | ||||
\(653\) | −11.5162 | − | 15.8507i | −0.450664 | − | 0.620286i | 0.521876 | − | 0.853021i | \(-0.325232\pi\) |
−0.972540 | + | 0.232735i | \(0.925232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.2892 | − | 4.96777i | −0.597399 | − | 0.194107i | ||||
\(656\) | 9.43855 | − | 6.85751i | 0.368514 | − | 0.267741i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.2924 | + | 56.2981i | 0.713111 | + | 2.19473i | ||||
\(659\) | 1.34943 | 0.0525664 | 0.0262832 | − | 0.999655i | \(-0.491633\pi\) | ||||
0.0262832 | + | 0.999655i | \(0.491633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7859 | 1.11964 | 0.559821 | − | 0.828614i | \(-0.310870\pi\) | ||||
0.559821 | + | 0.828614i | \(0.310870\pi\) | |||||||
\(662\) | 4.26576 | + | 13.1287i | 0.165794 | + | 0.510260i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.6398 | − | 21.5346i | 1.15025 | − | 0.835703i | ||||
\(665\) | 20.7516 | + | 6.74260i | 0.804712 | + | 0.261467i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.48879 | + | 4.80191i | 0.135086 | + | 0.185931i | ||||
\(668\) | −38.5646 | − | 28.0188i | −1.49211 | − | 1.08408i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 68.6954i | 2.65394i | ||||||||
\(671\) | −11.9066 | − | 3.94843i | −0.459648 | − | 0.152428i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6864 | − | 6.72140i | 0.797400 | − | 0.259091i | 0.118148 | − | 0.992996i | \(-0.462304\pi\) |
0.679252 | + | 0.733905i | \(0.262304\pi\) | |||||||
\(674\) | −22.8969 | + | 31.5149i | −0.881955 | + | 1.21391i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.42270 | + | 29.0001i | −0.362411 | + | 1.11539i | ||||
\(677\) | −5.84208 | + | 17.9801i | −0.224529 | + | 0.691030i | 0.773810 | + | 0.633418i | \(0.218349\pi\) |
−0.998339 | + | 0.0576121i | \(0.981651\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.1574 | − | 53.8955i | 1.50272 | − | 2.06832i | ||||
\(680\) | −0.585258 | + | 0.190162i | −0.0224436 | + | 0.00729237i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.6100 | − | 7.61105i | 0.406279 | − | 0.291442i | ||||
\(683\) | − | 33.7466i | − | 1.29128i | −0.763642 | − | 0.645640i | \(-0.776591\pi\) | ||
0.763642 | − | 0.645640i | \(-0.223409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3199 | + | 14.0367i | 0.738176 | + | 0.536316i | ||||
\(686\) | −13.4970 | − | 18.5771i | −0.515319 | − | 0.709275i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.62645 | − | 1.82815i | −0.214507 | − | 0.0696974i | ||||
\(689\) | −4.62602 | + | 3.36100i | −0.176237 | + | 0.128044i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.50814 | − | 26.1854i | −0.323665 | − | 0.996138i | −0.972040 | − | 0.234817i | \(-0.924551\pi\) |
0.648375 | − | 0.761321i | \(-0.275449\pi\) | |||||||
\(692\) | −26.5278 | −1.00844 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.91971 | 0.224709 | ||||||||
\(695\) | 0.0368728 | + | 0.113483i | 0.00139867 | + | 0.00430465i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.521055 | − | 0.378569i | 0.0197364 | − | 0.0143393i | ||||
\(698\) | −19.5168 | − | 6.34140i | −0.738722 | − | 0.240025i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.454418 | + | 0.625453i | 0.0171754 | + | 0.0236399i | ||||
\(701\) | −8.43699 | − | 6.12983i | −0.318661 | − | 0.231521i | 0.416943 | − | 0.908933i | \(-0.363101\pi\) |
−0.735604 | + | 0.677412i | \(0.763101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4101i | 0.656636i | ||||||||
\(704\) | −12.0654 | − | 37.9119i | −0.454731 | − | 1.42886i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.19948 | + | 0.389734i | −0.0451429 | + | 0.0146678i | ||||
\(707\) | −4.10011 | + | 5.64332i | −0.154201 | + | 0.212239i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.19477 | + | 19.0655i | −0.232649 | + | 0.716021i | 0.764775 | + | 0.644297i | \(0.222850\pi\) |
−0.997425 | + | 0.0717239i | \(0.977150\pi\) | |||||||
\(710\) | 1.82988 | − | 5.63178i | 0.0686740 | − | 0.211357i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.8975 | + | 19.1282i | −0.520829 | + | 0.716860i | ||||
\(713\) | 5.14021 | − | 1.67015i | 0.192502 | − | 0.0625478i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34.6907 | − | 0.209765i | −1.29736 | − | 0.00784477i | ||||
\(716\) | − | 44.0793i | − | 1.64732i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.0600 | − | 21.8399i | −1.12183 | − | 0.815057i | ||||
\(719\) | −6.01752 | − | 8.28241i | −0.224416 | − | 0.308882i | 0.681931 | − | 0.731417i | \(-0.261140\pi\) |
−0.906347 | + | 0.422535i | \(0.861140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.4479 | − | 4.04456i | −0.463583 | − | 0.150627i | ||||
\(722\) | 25.2185 | − | 18.3223i | 0.938537 | − | 0.681887i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.6152 | − | 60.3694i | −0.728993 | − | 2.24361i | ||||
\(725\) | −0.0995374 | −0.00369673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.4456 | −0.535759 | −0.267880 | − | 0.963452i | \(-0.586323\pi\) | ||||
−0.267880 | + | 0.963452i | \(0.586323\pi\) | |||||||
\(728\) | −20.8976 | − | 64.3163i | −0.774517 | − | 2.38372i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −56.8943 | + | 41.3361i | −2.10575 | + | 1.52992i | ||||
\(731\) | −0.310608 | − | 0.100923i | −0.0114883 | − | 0.00373276i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.29622 | + | 5.91324i | 0.158685 | + | 0.218411i | 0.880955 | − | 0.473200i | \(-0.156901\pi\) |
−0.722270 | + | 0.691611i | \(0.756901\pi\) | |||||||
\(734\) | 55.0263 | + | 39.9789i | 2.03106 | + | 1.47565i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 12.6735i | − | 0.467151i | ||||||
\(737\) | 43.1100 | + | 0.260675i | 1.58798 | + | 0.00960207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4909 | + | 4.05854i | −0.459485 | + | 0.149296i | −0.529608 | − | 0.848243i | \(-0.677661\pi\) |
0.0701229 | + | 0.997538i | \(0.477661\pi\) | |||||||
\(740\) | −33.8614 | + | 46.6062i | −1.24477 | + | 1.71328i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.61673 | − | 11.1312i | 0.132774 | − | 0.408638i | ||||
\(743\) | −10.9307 | + | 33.6412i | −0.401008 | + | 1.23418i | 0.523175 | + | 0.852225i | \(0.324747\pi\) |
−0.924183 | + | 0.381950i | \(0.875253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9503 | + | 37.0939i | −0.987383 | + | 1.35902i | ||||
\(746\) | 14.7768 | − | 4.80127i | 0.541017 | − | 0.175787i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.270584 | + | 0.850230i | 0.00989352 | + | 0.0310875i | ||||
\(749\) | 60.0306i | 2.19347i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6629 | + | 13.5594i | 0.681018 | + | 0.494789i | 0.873695 | − | 0.486473i | \(-0.161717\pi\) |
−0.192677 | + | 0.981262i | \(0.561717\pi\) | |||||||
\(752\) | −5.04914 | − | 6.94955i | −0.184123 | − | 0.253424i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.1318 | + | 6.21631i | 0.696741 | + | 0.226385i | ||||
\(755\) | −2.16285 | + | 1.57140i | −0.0787141 | + | 0.0571892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.02640 | + | 9.31430i | 0.109996 | + | 0.338534i | 0.990871 | − | 0.134816i | \(-0.0430445\pi\) |
−0.880874 | + | 0.473350i | \(0.843044\pi\) | |||||||
\(758\) | −3.64030 | −0.132222 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.3249 | −0.700988 | ||||||||
\(761\) | −14.9642 | − | 46.0550i | −0.542452 | − | 1.66949i | −0.726973 | − | 0.686666i | \(-0.759074\pi\) |
0.184522 | − | 0.982828i | \(-0.440926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.9176 | + | 35.5407i | −1.77094 | + | 1.28666i | ||||
\(764\) | −72.6303 | − | 23.5990i | −2.62767 | − | 0.853783i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6646 | − | 25.6897i | −0.674381 | − | 0.928205i | ||||
\(767\) | 2.18426 | + | 1.58696i | 0.0788691 | + | 0.0573017i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.4223i | 1.20524i | 0.798029 | + | 0.602619i | \(0.205876\pi\) | ||||
−0.798029 | + | 0.602619i | \(0.794124\pi\) | |||||||
\(770\) | 57.6977 | − | 41.3891i | 2.07928 | − | 1.49156i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.3952 | − | 5.65205i | 0.626068 | − | 0.203422i | ||||
\(773\) | 3.82924 | − | 5.27050i | 0.137728 | − | 0.189567i | −0.734581 | − | 0.678521i | \(-0.762621\pi\) |
0.872310 | + | 0.488954i | \(0.162621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0280083 | + | 0.0862007i | −0.00100609 | + | 0.00309642i | ||||
\(776\) | −18.2326 | + | 56.1143i | −0.654514 | + | 2.01439i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.6981 | − | 28.4885i | 0.742063 | − | 1.02136i | ||||
\(779\) | 19.2357 | − | 6.25007i | 0.689192 | − | 0.223932i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.52729 | − | 1.16971i | −0.126216 | − | 0.0418556i | ||||
\(782\) | 0.578780i | 0.0206971i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.5220 | + | 7.64471i | 0.375787 | + | 0.273025i | ||||
\(785\) | −2.29014 | − | 3.15211i | −0.0817386 | − | 0.112503i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.5749 | + | 8.95962i | 0.982939 | + | 0.319376i | 0.756028 | − | 0.654539i | \(-0.227137\pi\) |
0.226911 | + | 0.973916i | \(0.427137\pi\) | |||||||
\(788\) | −14.6828 | + | 10.6676i | −0.523052 | + | 0.380019i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.07764 | + | 3.31663i | 0.0383407 | + | 0.118000i | ||||
\(791\) | 45.5606 | 1.61995 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5974 | −0.624901 | ||||||||
\(794\) | 15.0468 | + | 46.3093i | 0.533991 | + | 1.64346i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −69.2075 | + | 50.2822i | −2.45299 | + | 1.78220i | ||||
\(797\) | −25.7264 | − | 8.35900i | −0.911274 | − | 0.296091i | −0.184392 | − | 0.982853i | \(-0.559032\pi\) |
−0.726882 | + | 0.686762i | \(0.759032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.278738 | − | 0.383650i | −0.00986103 | − | 0.0135725i | ||||
\(800\) | 0.171943 | + | 0.124924i | 0.00607910 | + | 0.00441672i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 63.5768i | − | 2.24498i | ||||||
\(803\) | 25.7247 | + | 35.8610i | 0.907805 | + | 1.26551i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.9526 | − | 9.08234i | 0.985199 | − | 0.320110i | ||||
\(806\) | 10.7668 | − | 14.8193i | 0.379245 | − | 0.521986i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.90911 | − | 5.87565i | 0.0671624 | − | 0.206705i | ||||
\(809\) | −12.9385 | + | 39.8205i | −0.454892 | + | 1.40001i | 0.416370 | + | 0.909195i | \(0.363302\pi\) |
−0.871262 | + | 0.490818i | \(0.836698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.51871 | + | 10.3486i | −0.264018 | + | 0.363389i | −0.920359 | − | 0.391075i | \(-0.872103\pi\) |
0.656341 | + | 0.754464i | \(0.272103\pi\) | |||||||
\(812\) | −24.9876 | + | 8.11895i | −0.876891 | + | 0.284919i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.6351 | + | 33.5793i | 1.59951 | + | 1.17695i | ||||
\(815\) | 2.25399i | 0.0789538i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.29738 | − | 6.02840i | −0.290289 | − | 0.210907i | ||||
\(818\) | 8.43637 | + | 11.6117i | 0.294971 | + | 0.405992i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 63.6493 | + | 20.6809i | 2.22273 | + | 0.722208i | ||||
\(821\) | −9.59682 | + | 6.97250i | −0.334931 | + | 0.243342i | −0.742520 | − | 0.669824i | \(-0.766370\pi\) |
0.407589 | + | 0.913166i | \(0.366370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.11976 | + | 24.9900i | 0.283037 | + | 0.871098i | 0.986980 | + | 0.160842i | \(0.0514210\pi\) |
−0.703943 | + | 0.710256i | \(0.748579\pi\) | |||||||
\(824\) | 11.5921 | 0.403829 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.52626 | −0.192283 | ||||||||
\(827\) | −7.99992 | − | 24.6212i | −0.278184 | − | 0.856163i | −0.988359 | − | 0.152138i | \(-0.951384\pi\) |
0.710175 | − | 0.704025i | \(-0.248616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0195 | + | 10.1858i | −0.486918 | + | 0.353766i | −0.803998 | − | 0.594632i | \(-0.797298\pi\) |
0.317080 | + | 0.948399i | \(0.397298\pi\) | |||||||
\(830\) | 51.3238 | + | 16.6761i | 1.78148 | + | 0.578837i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32.8057 | − | 45.1531i | −1.13733 | − | 1.56540i | ||||
\(833\) | 0.580869 | + | 0.422026i | 0.0201259 | + | 0.0146223i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.3907i | − | 1.05171i | ||||||
\(836\) | −0.169424 | + | 28.0191i | −0.00585965 | + | 0.969061i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 79.7307 | − | 25.9061i | 2.75425 | − | 0.894911i | ||||
\(839\) | −18.2513 | + | 25.1207i | −0.630104 | + | 0.867264i | −0.998039 | − | 0.0625873i | \(-0.980065\pi\) |
0.367935 | + | 0.929851i | \(0.380065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.91617 | + | 24.3635i | −0.272971 | + | 0.840120i | ||||
\(842\) | −10.3936 | + | 31.9882i | −0.358187 | + | 1.10239i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.8495 | − | 53.4718i | 1.33726 | − | 1.84058i | ||||
\(845\) | −18.4888 | + | 6.00737i | −0.636033 | + | 0.206660i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.7549 | − | 36.3654i | −0.884949 | − | 1.24953i | ||||
\(848\) | 1.69842i | 0.0583241i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.00785238 | − | 0.00570509i | −0.000269334 | − | 0.000195683i | ||||
\(851\) | 13.7845 | + | 18.9727i | 0.472527 | + | 0.650377i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.303737 | + | 0.0986902i | 0.0103998 | + | 0.00337909i | 0.314212 | − | 0.949353i | \(-0.398260\pi\) |
−0.303812 | + | 0.952732i | \(0.598260\pi\) | |||||||
\(854\) | 29.1400 | − | 21.1714i | 0.997150 | − | 0.724472i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.4296 | − | 50.5652i | −0.561553 | − | 1.72828i | ||||
\(857\) | −13.2476 | −0.452528 | −0.226264 | − | 0.974066i | \(-0.572651\pi\) | ||||
−0.226264 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.58152 | −0.292798 | −0.146399 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146399 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(860\) | −10.4870 | − | 32.2756i | −0.357603 | − | 1.10059i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.5521 | − | 12.0258i | 0.563766 | − | 0.409600i | ||||
\(863\) | −51.0889 | − | 16.5998i | −1.73909 | − | 0.565063i | −0.744374 | − | 0.667763i | \(-0.767252\pi\) |
−0.994712 | + | 0.102700i | \(0.967252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.94098 | − | 13.6826i | −0.338004 | − | 0.465222i | ||||
\(866\) | −71.4202 | − | 51.8898i | −2.42696 | − | 1.76329i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.9241i | 0.812037i | ||||||||
\(869\) | 2.08545 | − | 0.663690i | 0.0707441 | − | 0.0225141i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.5172 | − | 18.6885i | 1.94889 | − | 0.633234i | ||||
\(872\) | 31.4774 | − | 43.3249i | 1.06596 | − | 1.46717i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.61659 | + | 17.2861i | −0.189984 | + | 0.584710i | ||||
\(875\) | 13.9193 | − | 42.8394i | 0.470560 | − | 1.44823i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.8716 | + | 35.6092i | −0.873623 | + | 1.20244i | 0.104524 | + | 0.994522i | \(0.466668\pi\) |
−0.978147 | + | 0.207916i | \(0.933332\pi\) | |||||||
\(878\) | 72.5876 | − | 23.5851i | 2.44971 | − | 0.795959i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.10698 | + | 8.29954i | −0.205866 | + | 0.279777i | ||||
\(881\) | − | 7.44194i | − | 0.250725i | −0.992111 | − | 0.125363i | \(-0.959991\pi\) | ||
0.992111 | − | 0.125363i | \(-0.0400095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.59369 | + | 5.51714i | 0.255548 | + | 0.185667i | 0.708182 | − | 0.706030i | \(-0.249516\pi\) |
−0.452634 | + | 0.891696i | \(0.649516\pi\) | |||||||
\(884\) | 0.735715 | + | 1.01262i | 0.0247448 | + | 0.0340582i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.0799 | + | 13.6726i | 1.41370 | + | 0.459340i | ||||
\(887\) | 19.5658 | − | 14.2154i | 0.656957 | − | 0.477307i | −0.208677 | − | 0.977985i | \(-0.566916\pi\) |
0.865634 | + | 0.500678i | \(0.166916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.58806 | + | 23.3537i | 0.254496 | + | 0.783257i | ||||
\(890\) | −34.8267 | −1.16739 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.3542 | −0.648026 | ||||||||
\(893\) | −4.60189 | − | 14.1632i | −0.153996 | − | 0.473952i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.7353 | − | 16.5182i | 0.759958 | − | 0.552142i | ||||
\(896\) | 78.3870 | + | 25.4695i | 2.61873 | + | 0.850875i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.97892 | + | 13.7348i | 0.333001 | + | 0.458336i | ||||
\(899\) | −2.49197 | − | 1.81052i | −0.0831119 | − | 0.0603843i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0937613i | 0.00312364i | ||||||||
\(902\) | 20.7178 | − | 62.4750i | 0.689829 | − | 2.08019i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.3767 | + | 12.4693i | −1.27639 | + | 0.414724i | ||||
\(905\) | 23.7869 | − | 32.7399i | 0.790703 | − | 1.08831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0734 | + | 34.0803i | −0.367685 | + | 1.13162i | 0.580597 | + | 0.814191i | \(0.302819\pi\) |
−0.948282 | + | 0.317428i | \(0.897181\pi\) | |||||||
\(908\) | −14.9980 | + | 46.1592i | −0.497728 | + | 1.53185i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 58.5502 | − | 80.5875i | 1.94092 | − | 2.67145i | ||||
\(911\) | −8.33061 | + | 2.70678i | −0.276005 | + | 0.0896796i | −0.443749 | − | 0.896151i | \(-0.646352\pi\) |
0.167744 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6599 | − | 32.1451i | 0.352791 | − | 1.06385i | ||||
\(914\) | − | 9.92552i | − | 0.328307i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 60.2872 | + | 43.8012i | 1.99195 | + | 1.44723i | ||||
\(917\) | −17.0273 | − | 23.4360i | −0.562290 | − | 0.773926i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.4876 | − | 12.8303i | −1.30258 | − | 0.423233i | −0.426100 | − | 0.904676i | \(-0.640113\pi\) |
−0.876477 | + | 0.481443i | \(0.840113\pi\) | |||||||
\(920\) | −21.0594 | + | 15.3005i | −0.694307 | + | 0.504444i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.3097 | − | 31.7301i | −0.339533 | − | 1.04498i | ||||
\(923\) | −5.21318 | −0.171594 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.393281 | −0.0129310 | ||||||||
\(926\) | 29.3323 | + | 90.2756i | 0.963920 | + | 2.96664i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.84339 | + | 4.24547i | −0.191819 | + | 0.139364i | ||||
\(929\) | −51.5363 | − | 16.7451i | −1.69085 | − | 0.549390i | −0.703883 | − | 0.710316i | \(-0.748552\pi\) |
−0.986967 | + | 0.160925i | \(0.948552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.2531 | + | 18.2413i | 0.434351 | + | 0.597833i | ||||
\(932\) | −42.6935 | − | 31.0186i | −1.39847 | − | 1.01605i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.5656i | 0.869253i | ||||||||
\(935\) | −0.337136 | + | 0.458176i | −0.0110255 | + | 0.0149839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5444 | + | 5.37559i | −0.540480 | + | 0.175613i | −0.566520 | − | 0.824048i | \(-0.691710\pi\) |
0.0260393 | + | 0.999661i | \(0.491710\pi\) | |||||||
\(938\) | −72.7602 | + | 100.146i | −2.37571 | + | 3.26988i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.2272 | − | 46.8646i | 0.496657 | − | 1.52855i | ||||
\(941\) | 6.64708 | − | 20.4576i | 0.216689 | − | 0.666899i | −0.782341 | − | 0.622851i | \(-0.785974\pi\) |
0.999029 | − | 0.0440486i | \(-0.0140256\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0137 | − | 22.0410i | 0.521478 | − | 0.717753i | ||||
\(944\) | 0.762692 | − | 0.247814i | 0.0248235 | − | 0.00806564i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.8049 | + | 10.1218i | −1.03407 | + | 0.329089i | ||||
\(947\) | 44.7887i | 1.45544i | 0.685875 | + | 0.727719i | \(0.259420\pi\) | ||||
−0.685875 | + | 0.727719i | \(0.740580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.0878 | + | 36.3909i | 1.62592 | + | 1.18130i | ||||
\(950\) | −0.179159 | − | 0.246592i | −0.00581269 | − | 0.00800049i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.05462 | − | 0.342666i | −0.0341803 | − | 0.0111059i | ||||
\(953\) | −8.11741 | + | 5.89765i | −0.262949 | + | 0.191043i | −0.711446 | − | 0.702741i | \(-0.751959\pi\) |
0.448497 | + | 0.893784i | \(0.351959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0454 | − | 46.3049i | −0.486857 | − | 1.49839i | ||||
\(956\) | 19.0594 | 0.616425 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −53.8294 | −1.73915 | ||||||||
\(959\) | 13.2977 | + | 40.9262i | 0.429406 | + | 1.32158i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.8104 | − | 16.5727i | 0.735819 | − | 0.534604i | ||||
\(962\) | 75.5916 | + | 24.5612i | 2.43717 | + | 0.791884i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2693 | + | 33.4039i | 0.781662 | + | 1.07587i | ||||
\(965\) | 9.43388 | + | 6.85412i | 0.303688 | + | 0.220642i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.32167i | 0.138976i | 0.997583 | + | 0.0694878i | \(0.0221365\pi\) | ||||
−0.997583 | + | 0.0694878i | \(0.977863\pi\) | |||||||
\(968\) | 31.6467 | + | 23.5826i | 1.01716 | + | 0.757974i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −82.6550 | + | 26.8562i | −2.65389 | + | 0.862302i | ||||
\(971\) | 33.7344 | − | 46.4314i | 1.08259 | − | 1.49005i | 0.225947 | − | 0.974140i | \(-0.427452\pi\) |
0.856640 | − | 0.515914i | \(-0.172548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0664437 | + | 0.204493i | −0.00213009 | + | 0.00655574i | ||||
\(974\) | 5.47886 | − | 16.8622i | 0.175554 | − | 0.540300i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.07229 | + | 4.22864i | −0.0983416 | + | 0.135356i | ||||
\(977\) | 3.28130 | − | 1.06616i | 0.104978 | − | 0.0341095i | −0.256057 | − | 0.966662i | \(-0.582423\pi\) |
0.361035 | + | 0.932552i | \(0.382423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.132155 | + | 21.8556i | −0.00422369 | + | 0.698508i | ||||
\(980\) | 74.6073i | 2.38324i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −72.6315 | − | 52.7699i | −2.31776 | − | 1.68395i | ||||
\(983\) | 0.608167 | + | 0.837070i | 0.0193975 | + | 0.0266984i | 0.818606 | − | 0.574356i | \(-0.194747\pi\) |
−0.799208 | + | 0.601054i | \(0.794747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0044 | − | 3.57554i | −0.350628 | − | 0.113926i | ||||
\(986\) | 0.266859 | − | 0.193884i | 0.00849853 | − | 0.00617454i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.1465 | + | 37.3830i | 0.386431 | + | 1.18931i | ||||
\(989\) | −13.8151 | −0.439294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.78910 | 0.310961 | 0.155481 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155481 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(992\) | 2.03239 | + | 6.25506i | 0.0645285 | + | 0.198598i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.63265 | − | 6.27199i | 0.273811 | − | 0.198935i | ||||
\(995\) | −51.8693 | − | 16.8534i | −1.64437 | − | 0.534288i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.82690 | − | 9.39642i | −0.216210 | − | 0.297588i | 0.687111 | − | 0.726552i | \(-0.258878\pi\) |
−0.903321 | + | 0.428965i | \(0.858878\pi\) | |||||||
\(998\) | −15.3271 | − | 11.1358i | −0.485170 | − | 0.352496i | ||||
\(999\) | 0 | 0 |
(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 | 99.2.j.a.17.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 99.2.j.a.17.4 | yes | 16 | |
4.3 | odd | 2 | 1584.2.cd.c.17.1 | 16 | |||
9.2 | odd | 6 | 891.2.u.c.215.4 | 32 | |||
9.4 | even | 3 | 891.2.u.c.512.4 | 32 | |||
9.5 | odd | 6 | 891.2.u.c.512.1 | 32 | |||
9.7 | even | 3 | 891.2.u.c.215.1 | 32 | |||
11.2 | odd | 10 | inner | 99.2.j.a.35.4 | yes | 16 | |
11.3 | even | 5 | 1089.2.d.g.1088.3 | 16 | |||
11.8 | odd | 10 | 1089.2.d.g.1088.13 | 16 | |||
12.11 | even | 2 | 1584.2.cd.c.17.4 | 16 | |||
33.2 | even | 10 | inner | 99.2.j.a.35.1 | yes | 16 | |
33.8 | even | 10 | 1089.2.d.g.1088.4 | 16 | |||
33.14 | odd | 10 | 1089.2.d.g.1088.14 | 16 | |||
44.35 | even | 10 | 1584.2.cd.c.1025.4 | 16 | |||
99.2 | even | 30 | 891.2.u.c.134.4 | 32 | |||
99.13 | odd | 30 | 891.2.u.c.431.4 | 32 | |||
99.68 | even | 30 | 891.2.u.c.431.1 | 32 | |||
99.79 | odd | 30 | 891.2.u.c.134.1 | 32 | |||
132.35 | odd | 10 | 1584.2.cd.c.1025.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
99.2.j.a.17.4 | yes | 16 | 3.2 | odd | 2 | inner | |
99.2.j.a.35.1 | yes | 16 | 33.2 | even | 10 | inner | |
99.2.j.a.35.4 | yes | 16 | 11.2 | odd | 10 | inner | |
891.2.u.c.134.1 | 32 | 99.79 | odd | 30 | |||
891.2.u.c.134.4 | 32 | 99.2 | even | 30 | |||
891.2.u.c.215.1 | 32 | 9.7 | even | 3 | |||
891.2.u.c.215.4 | 32 | 9.2 | odd | 6 | |||
891.2.u.c.431.1 | 32 | 99.68 | even | 30 | |||
891.2.u.c.431.4 | 32 | 99.13 | odd | 30 | |||
891.2.u.c.512.1 | 32 | 9.5 | odd | 6 | |||
891.2.u.c.512.4 | 32 | 9.4 | even | 3 | |||
1089.2.d.g.1088.3 | 16 | 11.3 | even | 5 | |||
1089.2.d.g.1088.4 | 16 | 33.8 | even | 10 | |||
1089.2.d.g.1088.13 | 16 | 11.8 | odd | 10 | |||
1089.2.d.g.1088.14 | 16 | 33.14 | odd | 10 | |||
1584.2.cd.c.17.1 | 16 | 4.3 | odd | 2 | |||
1584.2.cd.c.17.4 | 16 | 12.11 | even | 2 | |||
1584.2.cd.c.1025.1 | 16 | 132.35 | odd | 10 | |||
1584.2.cd.c.1025.4 | 16 | 44.35 | even | 10 |