Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (of order \(3\), 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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(-1.82904 - 1.05600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.226 |
Dual form | 1323.2.h.g.802.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.46050 | −1.73984 | −0.869920 | − | 0.493193i | \(-0.835830\pi\) | ||||
−0.869920 | + | 0.493193i | \(0.835830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.05408 | 2.02704 | ||||||||
\(5\) | 1.82904 | + | 3.16799i | 0.817970 | + | 1.41677i | 0.907175 | + | 0.420753i | \(0.138234\pi\) |
−0.0892047 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.05408 | −1.78689 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.50036 | − | 7.79485i | −1.42314 | − | 2.46495i | ||||
\(11\) | 0.203210 | − | 0.351971i | 0.0612702 | − | 0.106123i | −0.833763 | − | 0.552122i | \(-0.813818\pi\) |
0.895033 | + | 0.445999i | \(0.147152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.243398 | + | 0.421578i | −0.0675065 | + | 0.116925i | −0.897803 | − | 0.440397i | \(-0.854838\pi\) |
0.830297 | + | 0.557322i | \(0.188171\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.32743 | 1.08186 | ||||||||
\(17\) | −2.42792 | − | 4.20528i | −0.588857 | − | 1.01993i | −0.994382 | − | 0.105847i | \(-0.966245\pi\) |
0.405525 | − | 0.914084i | \(-0.367089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.986757 | + | 1.70911i | −0.226378 | + | 0.392097i | −0.956732 | − | 0.290971i | \(-0.906022\pi\) |
0.730354 | + | 0.683069i | \(0.239355\pi\) | |||||||
\(20\) | 7.41507 | + | 12.8433i | 1.65806 | + | 2.87185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | 2.32383 | + | 4.02499i | 0.484552 | + | 0.839269i | 0.999843 | − | 0.0177464i | \(-0.00564915\pi\) |
−0.515290 | + | 0.857016i | \(0.672316\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.19076 | + | 7.25860i | −0.838151 | + | 1.45172i | ||||
\(26\) | 0.598883 | − | 1.03729i | 0.117451 | − | 0.203430i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.82383 | + | 6.62307i | 0.710068 | + | 1.22987i | 0.964831 | + | 0.262870i | \(0.0846690\pi\) |
−0.254764 | + | 0.967003i | \(0.581998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.02720 | −1.26212 | −0.631061 | − | 0.775733i | \(-0.717380\pi\) | ||||
−0.631061 | + | 0.775733i | \(0.717380\pi\) | |||||||
\(32\) | −0.539495 | −0.0953702 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.97391 | + | 10.3471i | 1.02452 | + | 1.77452i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16372 | + | 2.01561i | −0.191314 | + | 0.331365i | −0.945686 | − | 0.325082i | \(-0.894608\pi\) |
0.754372 | + | 0.656447i | \(0.227941\pi\) | |||||||
\(38\) | 2.42792 | − | 4.20528i | 0.393861 | − | 0.682187i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.24411 | − | 16.0113i | −1.46162 | − | 2.53160i | ||||
\(41\) | −3.75700 | + | 6.50731i | −0.586744 | + | 1.01627i | 0.407911 | + | 0.913022i | \(0.366257\pi\) |
−0.994655 | + | 0.103249i | \(0.967076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16372 | + | 2.01561i | 0.177465 | + | 0.307378i | 0.941012 | − | 0.338374i | \(-0.109877\pi\) |
−0.763547 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(44\) | 0.823832 | − | 1.42692i | 0.124197 | − | 0.215116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.71780 | − | 9.90352i | −0.843044 | − | 1.46019i | ||||
\(47\) | −6.31623 | −0.921317 | −0.460658 | − | 0.887578i | \(-0.652387\pi\) | ||||
−0.460658 | + | 0.887578i | \(0.652387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.3114 | − | 17.8598i | 1.45825 | − | 2.52576i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.986757 | + | 1.70911i | −0.136839 | + | 0.237011i | ||||
\(53\) | −1.78434 | − | 3.09056i | −0.245097 | − | 0.424521i | 0.717062 | − | 0.697010i | \(-0.245487\pi\) |
−0.962159 | + | 0.272489i | \(0.912153\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48672 | 0.200469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.40856 | − | 16.2961i | −1.23540 | − | 2.13978i | ||||
\(59\) | 6.11839 | 0.796546 | 0.398273 | − | 0.917267i | \(-0.369610\pi\) | ||||
0.398273 | + | 0.917267i | \(0.369610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.02712 | 1.02777 | 0.513884 | − | 0.857860i | \(-0.328206\pi\) | ||||
0.513884 | + | 0.857860i | \(0.328206\pi\) | |||||||
\(62\) | 17.2905 | 2.19589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.32743 | −0.915929 | ||||||||
\(65\) | −1.78074 | −0.220873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.60078 | 0.439905 | 0.219952 | − | 0.975511i | \(-0.429410\pi\) | ||||
0.219952 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(68\) | −9.84299 | − | 17.0486i | −1.19364 | − | 2.06744i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.46050 | −1.00408 | −0.502039 | − | 0.864845i | \(-0.667416\pi\) | ||||
−0.502039 | + | 0.864845i | \(0.667416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.986757 | + | 1.70911i | 0.115491 | + | 0.200037i | 0.917976 | − | 0.396636i | \(-0.129822\pi\) |
−0.802485 | + | 0.596673i | \(0.796489\pi\) | |||||||
\(74\) | 2.86333 | − | 4.95943i | 0.332855 | − | 0.576522i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00040 | + | 6.92889i | −0.458877 | + | 0.794798i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.16225 | 0.918325 | 0.459163 | − | 0.888352i | \(-0.348150\pi\) | ||||
0.459163 | + | 0.888352i | \(0.348150\pi\) | |||||||
\(80\) | 7.91503 | + | 13.7092i | 0.884928 | + | 1.53274i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.24411 | − | 16.0113i | 1.02084 | − | 1.76815i | ||||
\(83\) | −6.08600 | − | 10.5413i | −0.668025 | − | 1.15705i | −0.978456 | − | 0.206457i | \(-0.933807\pi\) |
0.310431 | − | 0.950596i | \(-0.399527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.88151 | − | 15.3832i | 0.963336 | − | 1.66855i | ||||
\(86\) | −2.86333 | − | 4.95943i | −0.308760 | − | 0.534789i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.02704 | + | 1.77889i | −0.109483 | + | 0.189630i | ||||
\(89\) | −7.41507 | + | 12.8433i | −0.785996 | + | 1.36139i | 0.142406 | + | 0.989808i | \(0.454516\pi\) |
−0.928402 | + | 0.371577i | \(0.878817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.42101 | + | 16.3177i | 0.982208 | + | 1.70123i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.5411 | 1.60294 | ||||||||
\(95\) | −7.21926 | −0.740681 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.74375 | − | 8.21642i | −0.481655 | − | 0.834251i | 0.518123 | − | 0.855306i | \(-0.326631\pi\) |
−0.999778 | + | 0.0210547i | \(0.993298\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.9897 | + | 29.4270i | −1.69897 | + | 2.94270i | ||||
\(101\) | −4.35588 | + | 7.54461i | −0.433426 | + | 0.750716i | −0.997166 | − | 0.0752364i | \(-0.976029\pi\) |
0.563739 | + | 0.825953i | \(0.309362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.01356 | + | 6.95169i | 0.395468 | + | 0.684970i | 0.993161 | − | 0.116755i | \(-0.0372492\pi\) |
−0.597693 | + | 0.801725i | \(0.703916\pi\) | |||||||
\(104\) | 1.23016 | − | 2.13069i | 0.120627 | − | 0.208931i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.39037 | + | 7.60434i | 0.426430 | + | 0.738599i | ||||
\(107\) | 6.42101 | − | 11.1215i | 0.620742 | − | 1.07516i | −0.368605 | − | 0.929586i | \(-0.620165\pi\) |
0.989348 | − | 0.145571i | \(-0.0465021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.30039 | − | 2.25234i | −0.124555 | − | 0.215735i | 0.797004 | − | 0.603974i | \(-0.206417\pi\) |
−0.921559 | + | 0.388239i | \(0.873084\pi\) | |||||||
\(110\) | −3.65808 | −0.348784 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.97509 | + | 12.0812i | −0.656162 | + | 1.13651i | 0.325440 | + | 0.945563i | \(0.394488\pi\) |
−0.981601 | + | 0.190942i | \(0.938846\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.50075 | + | 14.7237i | −0.792699 | + | 1.37300i | ||||
\(116\) | 15.5021 | + | 26.8505i | 1.43934 | + | 2.49301i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.0543 | −1.38586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.41741 | + | 9.38323i | 0.492492 | + | 0.853021i | ||||
\(122\) | −19.7508 | −1.78815 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −28.4889 | −2.55837 | ||||||||
\(125\) | −12.3698 | −1.10639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5438 | −1.37929 | −0.689643 | − | 0.724149i | \(-0.742233\pi\) | ||||
−0.689643 | + | 0.724149i | \(0.742233\pi\) | |||||||
\(128\) | 19.1082 | 1.68894 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.38151 | 0.384284 | ||||||||
\(131\) | 4.25696 | + | 7.37327i | 0.371932 | + | 0.644205i | 0.989863 | − | 0.142027i | \(-0.0453621\pi\) |
−0.617931 | + | 0.786233i | \(0.712029\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.85973 | −0.765364 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.2709 | + | 21.2538i | 1.05222 | + | 1.82250i | ||||
\(137\) | 0.188621 | − | 0.326702i | 0.0161150 | − | 0.0279120i | −0.857855 | − | 0.513891i | \(-0.828204\pi\) |
0.873970 | + | 0.485979i | \(0.161537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.50067 | + | 16.4556i | −0.805837 | + | 1.39575i | 0.109888 | + | 0.993944i | \(0.464951\pi\) |
−0.915725 | + | 0.401806i | \(0.868383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.8171 | 1.74693 | ||||||||
\(143\) | 0.0989221 | + | 0.171338i | 0.00827228 | + | 0.0143280i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.9879 | + | 24.2277i | −1.16163 | + | 2.01200i | ||||
\(146\) | −2.42792 | − | 4.20528i | −0.200936 | − | 0.348032i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.71780 | + | 8.17147i | −0.387801 | + | 0.671691i | ||||
\(149\) | −4.85087 | − | 8.40196i | −0.397399 | − | 0.688315i | 0.596005 | − | 0.802981i | \(-0.296754\pi\) |
−0.993404 | + | 0.114665i | \(0.963420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.41741 | − | 11.1153i | 0.522242 | − | 0.904549i | −0.477424 | − | 0.878673i | \(-0.658429\pi\) |
0.999665 | − | 0.0258756i | \(-0.00823738\pi\) | |||||||
\(152\) | 4.98715 | − | 8.63800i | 0.404511 | − | 0.700634i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.8530 | − | 22.2621i | −1.03238 | − | 1.78813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.9485 | −1.67187 | −0.835937 | − | 0.548825i | \(-0.815075\pi\) | ||||
−0.835937 | + | 0.548825i | \(0.815075\pi\) | |||||||
\(158\) | −20.0833 | −1.59774 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.986757 | − | 1.70911i | −0.0780100 | − | 0.135117i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.58113 | − | 9.66679i | 0.437148 | − | 0.757162i | −0.560321 | − | 0.828276i | \(-0.689322\pi\) |
0.997468 | + | 0.0711140i | \(0.0226554\pi\) | |||||||
\(164\) | −15.2312 | + | 26.3812i | −1.18936 | + | 2.06002i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.9746 | + | 25.9368i | 1.16226 | + | 2.01309i | ||||
\(167\) | −1.73012 | + | 2.99665i | −0.133880 | + | 0.231888i | −0.925169 | − | 0.379555i | \(-0.876077\pi\) |
0.791289 | + | 0.611443i | \(0.209410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38151 | + | 11.0531i | 0.490886 | + | 0.850239i | ||||
\(170\) | −21.8530 | + | 37.8505i | −1.67605 | + | 2.90300i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.71780 | + | 8.17147i | 0.359729 | + | 0.623069i | ||||
\(173\) | −6.05361 | −0.460247 | −0.230124 | − | 0.973161i | \(-0.573913\pi\) | ||||
−0.230124 | + | 0.973161i | \(0.573913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.879379 | − | 1.52313i | 0.0662857 | − | 0.114810i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.2448 | − | 31.6010i | 1.36751 | − | 2.36859i | ||||
\(179\) | 4.56654 | + | 7.90947i | 0.341319 | + | 0.591182i | 0.984678 | − | 0.174383i | \(-0.0557930\pi\) |
−0.643359 | + | 0.765565i | \(0.722460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9478 | −0.888074 | −0.444037 | − | 0.896008i | \(-0.646454\pi\) | ||||
−0.444037 | + | 0.896008i | \(0.646454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.7448 | − | 20.3427i | −0.865841 | − | 1.49968i | ||||
\(185\) | −8.51392 | −0.625956 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.97351 | −0.144318 | ||||||||
\(188\) | −25.6065 | −1.86755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7630 | 1.28867 | ||||||||
\(191\) | −9.14027 | −0.661367 | −0.330683 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330683 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9430 | 1.21958 | 0.609792 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609792 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(194\) | 11.6720 | + | 20.2165i | 0.838003 | + | 1.45146i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3173 | 1.51880 | 0.759398 | − | 0.650627i | \(-0.225494\pi\) | ||||
0.759398 | + | 0.650627i | \(0.225494\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.98715 | + | 8.63800i | 0.353530 | + | 0.612332i | 0.986865 | − | 0.161546i | \(-0.0516479\pi\) |
−0.633335 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(200\) | 21.1804 | − | 36.6856i | 1.49768 | − | 2.59406i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.7177 | − | 18.5635i | 0.754092 | − | 1.30613i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.4868 | −1.91976 | ||||||||
\(206\) | −9.87538 | − | 17.1047i | −0.688051 | − | 1.19174i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.05329 | + | 1.82435i | −0.0730324 | + | 0.126496i | ||||
\(209\) | 0.401038 | + | 0.694619i | 0.0277404 | + | 0.0480478i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44592 | + | 4.23645i | −0.168384 | + | 0.291649i | −0.937852 | − | 0.347036i | \(-0.887188\pi\) |
0.769468 | + | 0.638685i | \(0.220521\pi\) | |||||||
\(212\) | −7.23385 | − | 12.5294i | −0.496823 | − | 0.860523i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.7989 | + | 27.3645i | −1.07999 | + | 1.87060i | ||||
\(215\) | −4.25696 | + | 7.37327i | −0.290322 | + | 0.502853i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.19961 | + | 5.54189i | 0.216705 | + | 0.375344i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.02728 | 0.406359 | ||||||||
\(221\) | 2.36381 | 0.159007 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7044 | − | 20.2727i | −0.783786 | − | 1.35756i | −0.929722 | − | 0.368263i | \(-0.879953\pi\) |
0.145936 | − | 0.989294i | \(-0.453381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.1623 | − | 29.7259i | 1.14162 | − | 1.97734i | ||||
\(227\) | 3.05919 | − | 5.29868i | 0.203046 | − | 0.351686i | −0.746463 | − | 0.665427i | \(-0.768249\pi\) |
0.949508 | + | 0.313742i | \(0.101583\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.730195 | + | 1.26473i | 0.0482526 | + | 0.0835760i | 0.889143 | − | 0.457630i | \(-0.151301\pi\) |
−0.840890 | + | 0.541206i | \(0.817968\pi\) | |||||||
\(230\) | 20.9161 | − | 36.2278i | 1.37917 | − | 2.38879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3260 | − | 33.4736i | −1.26881 | − | 2.19765i | ||||
\(233\) | −6.62422 | + | 11.4735i | −0.433967 | + | 0.751653i | −0.997211 | − | 0.0746378i | \(-0.976220\pi\) |
0.563244 | + | 0.826291i | \(0.309553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5526 | − | 20.0097i | −0.753610 | − | 1.30529i | ||||
\(236\) | 24.8045 | 1.61463 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.69436 | − | 16.7911i | 0.627076 | − | 1.08613i | −0.361060 | − | 0.932543i | \(-0.617585\pi\) |
0.988136 | − | 0.153584i | \(-0.0490817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.52684 | + | 4.37662i | −0.162768 | + | 0.281923i | −0.935860 | − | 0.352371i | \(-0.885376\pi\) |
0.773092 | + | 0.634294i | \(0.218709\pi\) | |||||||
\(242\) | −13.3296 | − | 23.0875i | −0.856857 | − | 1.48412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.5426 | 2.08333 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.480350 | − | 0.831990i | −0.0305639 | − | 0.0529383i | ||||
\(248\) | 35.5161 | 2.25527 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 30.4360 | 1.92494 | ||||||||
\(251\) | −15.0928 | −0.952647 | −0.476324 | − | 0.879270i | \(-0.658031\pi\) | ||||
−0.476324 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88891 | 0.118755 | ||||||||
\(254\) | 38.2455 | 2.39974 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.3609 | −2.02256 | ||||||||
\(257\) | 3.85592 | + | 6.67865i | 0.240526 | + | 0.416603i | 0.960864 | − | 0.277020i | \(-0.0893469\pi\) |
−0.720338 | + | 0.693623i | \(0.756014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.21926 | −0.447720 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.4743 | − | 18.1420i | −0.647102 | − | 1.12081i | ||||
\(263\) | 2.10603 | − | 3.64776i | 0.129864 | − | 0.224930i | −0.793760 | − | 0.608231i | \(-0.791879\pi\) |
0.923624 | + | 0.383301i | \(0.125213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.52724 | − | 11.3055i | 0.400965 | − | 0.694492i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.5979 | 0.891706 | ||||||||
\(269\) | 10.3753 | + | 17.9706i | 0.632596 | + | 1.09569i | 0.987019 | + | 0.160603i | \(0.0513439\pi\) |
−0.354423 | + | 0.935085i | \(0.615323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2444 | − | 24.6721i | 0.865287 | − | 1.49872i | −0.00147433 | − | 0.999999i | \(-0.500469\pi\) |
0.866762 | − | 0.498723i | \(-0.166197\pi\) | |||||||
\(272\) | −10.5067 | − | 18.1981i | −0.637060 | − | 1.10342i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.464103 | + | 0.803851i | −0.0280375 | + | 0.0485624i | ||||
\(275\) | 1.70321 | + | 2.95005i | 0.102707 | + | 0.177895i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.58113 | + | 14.8629i | −0.515590 | + | 0.893028i | 0.484246 | + | 0.874932i | \(0.339094\pi\) |
−0.999836 | + | 0.0180962i | \(0.994239\pi\) | |||||||
\(278\) | 23.3765 | − | 40.4892i | 1.40203 | − | 2.42838i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.72140 | + | 8.17770i | 0.281655 | + | 0.487841i | 0.971793 | − | 0.235837i | \(-0.0757833\pi\) |
−0.690138 | + | 0.723678i | \(0.742450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8684 | 1.00272 | 0.501362 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501362 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(284\) | −34.2996 | −2.03531 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.243398 | − | 0.421578i | −0.0143924 | − | 0.0249284i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.28959 | + | 5.69774i | −0.193505 | + | 0.335161i | ||||
\(290\) | 34.4172 | − | 59.6124i | 2.02105 | − | 3.50056i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.00040 | + | 6.92889i | 0.234105 | + | 0.405483i | ||||
\(293\) | −1.86143 | + | 3.22409i | −0.108746 | + | 0.188353i | −0.915262 | − | 0.402858i | \(-0.868017\pi\) |
0.806517 | + | 0.591211i | \(0.201350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1908 | + | 19.3830i | 0.651551 | + | 1.12852i | ||||
\(296\) | 5.88151 | − | 10.1871i | 0.341856 | − | 0.592112i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.9356 | + | 20.6731i | 0.691411 | + | 1.19756i | ||||
\(299\) | −2.26247 | −0.130842 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.7901 | + | 27.3492i | −0.908617 | + | 1.57377i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.27012 | + | 7.39607i | −0.244908 | + | 0.424194i | ||||
\(305\) | 14.6819 | + | 25.4298i | 0.840683 | + | 1.45611i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.5691 | 1.74467 | 0.872335 | − | 0.488908i | \(-0.162605\pi\) | ||||
0.872335 | + | 0.488908i | \(0.162605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.6249 | + | 54.7759i | 1.79617 | + | 3.11106i | ||||
\(311\) | 10.4348 | 0.591702 | 0.295851 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295851 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.619860 | −0.0350366 | −0.0175183 | − | 0.999847i | \(-0.505577\pi\) | ||||
−0.0175183 | + | 0.999847i | \(0.505577\pi\) | |||||||
\(314\) | 51.5440 | 2.90879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0905 | 1.86148 | ||||||||
\(317\) | −10.2484 | −0.575610 | −0.287805 | − | 0.957689i | \(-0.592925\pi\) | ||||
−0.287805 | + | 0.957689i | \(0.592925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.10817 | 0.174024 | ||||||||
\(320\) | −13.4021 | − | 23.2132i | −0.749203 | − | 1.29766i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.58307 | 0.533216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.04005 | − | 3.53346i | −0.113161 | − | 0.196001i | ||||
\(326\) | −13.7324 | + | 23.7852i | −0.760567 | + | 1.31734i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.9882 | − | 32.8885i | 1.04845 | − | 1.81596i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3638 | −1.11930 | −0.559648 | − | 0.828730i | \(-0.689064\pi\) | ||||
−0.559648 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(332\) | −24.6731 | − | 42.7351i | −1.35411 | − | 2.34539i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.25696 | − | 7.37327i | 0.232930 | − | 0.403447i | ||||
\(335\) | 6.58596 | + | 11.4072i | 0.359829 | + | 0.623242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.85594 | − | 4.94662i | 0.155573 | − | 0.269460i | −0.777695 | − | 0.628642i | \(-0.783611\pi\) |
0.933267 | + | 0.359182i | \(0.116944\pi\) | |||||||
\(338\) | −15.7017 | − | 27.1962i | −0.854062 | − | 1.47928i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.0064 | − | 62.3649i | 1.95272 | − | 3.38221i | ||||
\(341\) | −1.42800 | + | 2.47337i | −0.0773305 | + | 0.133940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.88151 | − | 10.1871i | −0.317110 | − | 0.549251i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.8949 | 0.800756 | ||||||||
\(347\) | −8.88132 | −0.476774 | −0.238387 | − | 0.971170i | \(-0.576619\pi\) | ||||
−0.238387 | + | 0.971170i | \(0.576619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4874 | + | 18.1648i | 0.561379 | + | 0.972337i | 0.997376 | + | 0.0723893i | \(0.0230624\pi\) |
−0.435997 | + | 0.899948i | \(0.643604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.109631 | + | 0.189886i | −0.00584335 | + | 0.0101210i | ||||
\(353\) | 7.38268 | − | 12.7872i | 0.392941 | − | 0.680593i | −0.599895 | − | 0.800078i | \(-0.704791\pi\) |
0.992836 | + | 0.119485i | \(0.0381245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4746 | − | 26.8028i | −0.821306 | − | 1.42254i | ||||
\(356\) | −30.0613 | + | 52.0677i | −1.59325 | + | 2.75959i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2360 | − | 19.4613i | −0.593840 | − | 1.02856i | ||||
\(359\) | 3.60603 | − | 6.24583i | 0.190319 | − | 0.329642i | −0.755037 | − | 0.655682i | \(-0.772381\pi\) |
0.945356 | + | 0.326040i | \(0.105714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.55262 | + | 13.0815i | 0.397506 | + | 0.688501i | ||||
\(362\) | 29.3977 | 1.54511 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.60963 | + | 6.25206i | −0.188937 | + | 0.327248i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.48711 | + | 9.50396i | −0.286425 | + | 0.496103i | −0.972954 | − | 0.231000i | \(-0.925800\pi\) |
0.686529 | + | 0.727103i | \(0.259134\pi\) | |||||||
\(368\) | 10.0562 | + | 17.4179i | 0.524217 | + | 0.907970i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.9485 | 1.08906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.271884 | + | 0.470916i | 0.0140776 | + | 0.0243831i | 0.872978 | − | 0.487759i | \(-0.162185\pi\) |
−0.858901 | + | 0.512142i | \(0.828852\pi\) | |||||||
\(374\) | 4.85584 | 0.251090 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.9228 | 1.64629 | ||||||||
\(377\) | −3.72286 | −0.191737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6912 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(380\) | −29.2675 | −1.50139 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.4897 | 1.15067 | ||||||||
\(383\) | −17.8569 | − | 30.9291i | −0.912447 | − | 1.58041i | −0.810596 | − | 0.585606i | \(-0.800857\pi\) |
−0.101851 | − | 0.994800i | \(-0.532477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.6883 | −2.12188 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19.2316 | − | 33.3101i | −0.976336 | − | 1.69106i | ||||
\(389\) | 19.3296 | − | 33.4798i | 0.980048 | − | 1.69749i | 0.317892 | − | 0.948127i | \(-0.397025\pi\) |
0.662156 | − | 0.749366i | \(-0.269641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2842 | − | 19.5447i | 0.570664 | − | 0.988420i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.4513 | −2.64246 | ||||||||
\(395\) | 14.9291 | + | 25.8579i | 0.751163 | + | 1.30105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.97391 | + | 10.3471i | −0.299822 | + | 0.519307i | −0.976095 | − | 0.217344i | \(-0.930261\pi\) |
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(398\) | −12.2709 | − | 21.2538i | −0.615085 | − | 1.06536i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.1352 | + | 31.4111i | −0.906761 | + | 1.57056i | ||||
\(401\) | 16.1783 | + | 28.0216i | 0.807906 | + | 1.39933i | 0.914312 | + | 0.405011i | \(0.132732\pi\) |
−0.106406 | + | 0.994323i | \(0.533934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.71041 | − | 2.96251i | 0.0852015 | − | 0.147573i | ||||
\(404\) | −17.6591 | + | 30.5865i | −0.878573 | + | 1.52173i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.472958 | + | 0.819187i | 0.0234437 | + | 0.0406056i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9750 | −0.938254 | −0.469127 | − | 0.883131i | \(-0.655431\pi\) | ||||
−0.469127 | + | 0.883131i | \(0.655431\pi\) | |||||||
\(410\) | 67.6313 | 3.34007 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.2713 | + | 28.1827i | 0.801630 | + | 1.38846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.2630 | − | 38.5607i | 1.09285 | − | 1.89287i | ||||
\(416\) | 0.131312 | − | 0.227439i | 0.00643811 | − | 0.0111511i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.986757 | − | 1.70911i | −0.0482639 | − | 0.0835955i | ||||
\(419\) | 8.64523 | − | 14.9740i | 0.422347 | − | 0.731526i | −0.573822 | − | 0.818980i | \(-0.694540\pi\) |
0.996169 | + | 0.0874539i | \(0.0278730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.30039 | − | 16.1087i | −0.453273 | − | 0.785092i | 0.545314 | − | 0.838232i | \(-0.316410\pi\) |
−0.998587 | + | 0.0531397i | \(0.983077\pi\) | |||||||
\(422\) | 6.01819 | − | 10.4238i | 0.292961 | − | 0.507423i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.01819 | + | 15.6200i | 0.437962 | + | 0.758572i | ||||
\(425\) | 40.6993 | 1.97421 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26.0313 | − | 45.0876i | 1.25827 | − | 2.17939i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.4743 | − | 18.1420i | 0.505114 | − | 0.874883i | ||||
\(431\) | −7.93920 | − | 13.7511i | −0.382418 | − | 0.662367i | 0.608990 | − | 0.793178i | \(-0.291575\pi\) |
−0.991407 | + | 0.130811i | \(0.958242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.4367 | −1.94326 | −0.971631 | − | 0.236501i | \(-0.923999\pi\) | ||||
−0.971631 | + | 0.236501i | \(0.923999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.27188 | − | 9.13117i | −0.252477 | − | 0.437304i | ||||
\(437\) | −9.17223 | −0.438767 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4609 | −0.594728 | −0.297364 | − | 0.954764i | \(-0.596108\pi\) | ||||
−0.297364 | + | 0.954764i | \(0.596108\pi\) | |||||||
\(440\) | −7.51399 | −0.358216 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.81616 | −0.276646 | ||||||||
\(443\) | 8.23073 | 0.391054 | 0.195527 | − | 0.980698i | \(-0.437358\pi\) | ||||
0.195527 | + | 0.980698i | \(0.437358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −54.2498 | −2.57169 | ||||||||
\(446\) | 28.7988 | + | 49.8810i | 1.36366 | + | 2.36193i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.64474 | −0.266392 | −0.133196 | − | 0.991090i | \(-0.542524\pi\) | ||||
−0.133196 | + | 0.991090i | \(0.542524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.52692 | + | 2.64471i | 0.0718999 | + | 0.124534i | ||||
\(452\) | −28.2776 | + | 48.9783i | −1.33007 | + | 2.30374i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.52716 | + | 13.0374i | −0.353267 | + | 0.611876i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.06887 | 0.237112 | 0.118556 | − | 0.992947i | \(-0.462174\pi\) | ||||
0.118556 | + | 0.992947i | \(0.462174\pi\) | |||||||
\(458\) | −1.79665 | − | 3.11188i | −0.0839518 | − | 0.145409i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −34.4628 | + | 59.6913i | −1.60683 | + | 2.78312i | ||||
\(461\) | 3.88831 | + | 6.73475i | 0.181097 | + | 0.313669i | 0.942254 | − | 0.334898i | \(-0.108702\pi\) |
−0.761158 | + | 0.648567i | \(0.775369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58998 | − | 7.95008i | 0.213314 | − | 0.369472i | −0.739435 | − | 0.673228i | \(-0.764907\pi\) |
0.952750 | + | 0.303756i | \(0.0982408\pi\) | |||||||
\(464\) | 16.5474 | + | 28.6609i | 0.768192 | + | 1.33055i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.2989 | − | 28.2306i | 0.755033 | − | 1.30776i | ||||
\(467\) | 6.88272 | − | 11.9212i | 0.318494 | − | 0.551648i | −0.661680 | − | 0.749787i | \(-0.730156\pi\) |
0.980174 | + | 0.198138i | \(0.0634895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28.4253 | + | 49.2340i | 1.31116 | + | 2.27100i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −30.9228 | −1.42334 | ||||||||
\(473\) | 0.945916 | 0.0434933 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.27052 | − | 14.3250i | −0.379477 | − | 0.657274i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.8530 | + | 41.3146i | −1.09101 | + | 1.88969i | ||||
\(479\) | −4.35588 | + | 7.54461i | −0.199025 | + | 0.344722i | −0.948213 | − | 0.317636i | \(-0.897111\pi\) |
0.749187 | + | 0.662358i | \(0.230444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.566492 | − | 0.981194i | −0.0258298 | − | 0.0447386i | ||||
\(482\) | 6.21731 | − | 10.7687i | 0.283191 | − | 0.490501i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.9626 | + | 38.0404i | 0.998302 | + | 1.72911i | ||||
\(485\) | 17.3530 | − | 30.0563i | 0.787960 | − | 1.36479i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.01819 | + | 15.6200i | 0.408653 | + | 0.707808i | 0.994739 | − | 0.102441i | \(-0.0326653\pi\) |
−0.586086 | + | 0.810249i | \(0.699332\pi\) | |||||||
\(488\) | −40.5697 | −1.83651 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02344 | − | 1.77266i | 0.0461874 | − | 0.0799989i | −0.842007 | − | 0.539466i | \(-0.818626\pi\) |
0.888195 | + | 0.459467i | \(0.151960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.5679 | − | 32.1606i | 0.836257 | − | 1.44844i | ||||
\(494\) | 1.18190 | + | 2.04712i | 0.0531763 | + | 0.0921041i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.4097 | −1.36544 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.5438 | + | 33.8508i | 0.874899 | + | 1.51537i | 0.856870 | + | 0.515532i | \(0.172406\pi\) |
0.0180291 | + | 0.999837i | \(0.494261\pi\) | |||||||
\(500\) | −50.1484 | −2.24270 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 37.1358 | 1.65745 | ||||||||
\(503\) | 5.11846 | 0.228221 | 0.114111 | − | 0.993468i | \(-0.463598\pi\) | ||||
0.114111 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8683 | −1.41812 | ||||||||
\(506\) | −4.64766 | −0.206614 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −63.0157 | −2.79587 | ||||||||
\(509\) | 14.7636 | + | 25.5713i | 0.654386 | + | 1.13343i | 0.982047 | + | 0.188634i | \(0.0604060\pi\) |
−0.327662 | + | 0.944795i | \(0.606261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 41.4078 | 1.82998 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.48751 | − | 16.4328i | −0.418476 | − | 0.724822i | ||||
\(515\) | −14.6819 | + | 25.4298i | −0.646962 | + | 1.12057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.28352 | + | 2.22313i | −0.0564493 | + | 0.0977730i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | −0.532351 | − | 0.922058i | −0.0233227 | − | 0.0403961i | 0.854128 | − | 0.520062i | \(-0.174091\pi\) |
−0.877451 | + | 0.479666i | \(0.840758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.69094 | − | 11.5890i | 0.292574 | − | 0.506754i | −0.681843 | − | 0.731498i | \(-0.738821\pi\) |
0.974418 | + | 0.224745i | \(0.0721548\pi\) | |||||||
\(524\) | 17.2581 | + | 29.8918i | 0.753922 | + | 1.30583i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.18190 | + | 8.97532i | −0.225942 | + | 0.391343i | ||||
\(527\) | 17.0615 | + | 29.5513i | 0.743210 | + | 1.28728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.699612 | − | 1.21176i | 0.0304179 | − | 0.0526853i | ||||
\(530\) | −16.0603 | + | 27.8173i | −0.697615 | + | 1.20830i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.82889 | − | 3.16774i | −0.0792181 | − | 0.137210i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.9771 | 2.03100 | ||||||||
\(536\) | −18.1986 | −0.786061 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.5286 | − | 44.2168i | −1.10062 | − | 1.90632i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0438 | − | 29.5207i | 0.732769 | − | 1.26919i | −0.222927 | − | 0.974835i | \(-0.571561\pi\) |
0.955695 | − | 0.294358i | \(-0.0951056\pi\) | |||||||
\(542\) | −35.0485 | + | 60.7058i | −1.50546 | + | 2.60754i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.30985 | + | 2.26873i | 0.0561594 | + | 0.0972709i | ||||
\(545\) | 4.75692 | − | 8.23922i | 0.203764 | − | 0.352930i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.97150 | + | 5.14678i | 0.127052 | + | 0.220060i | 0.922533 | − | 0.385918i | \(-0.126115\pi\) |
−0.795481 | + | 0.605978i | \(0.792782\pi\) | |||||||
\(548\) | 0.764686 | − | 1.32448i | 0.0326658 | − | 0.0565788i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.19076 | − | 7.25860i | −0.178694 | − | 0.309508i | ||||
\(551\) | −15.0928 | −0.642974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.1139 | − | 36.5704i | 0.897044 | − | 1.55373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −38.5165 | + | 66.7126i | −1.63346 | + | 2.82924i | ||||
\(557\) | −15.0402 | − | 26.0503i | −0.637272 | − | 1.10379i | −0.986029 | − | 0.166575i | \(-0.946729\pi\) |
0.348756 | − | 0.937213i | \(-0.386604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.13298 | −0.0479202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.6170 | − | 20.1213i | −0.490035 | − | 0.848765i | ||||
\(563\) | 19.6212 | 0.826935 | 0.413468 | − | 0.910519i | \(-0.364317\pi\) | ||||
0.413468 | + | 0.910519i | \(0.364317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −51.0308 | −2.14688 | ||||||||
\(566\) | −41.5049 | −1.74458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7601 | 1.79417 | ||||||||
\(569\) | 1.37432 | 0.0576144 | 0.0288072 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288072 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3815 | 0.727394 | 0.363697 | − | 0.931517i | \(-0.381514\pi\) | ||||
0.363697 | + | 0.931517i | \(0.381514\pi\) | |||||||
\(572\) | 0.401038 | + | 0.694619i | 0.0167683 | + | 0.0290435i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.9545 | −1.62451 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5274 | + | 23.4301i | 0.563153 | + | 0.975409i | 0.997219 | + | 0.0745283i | \(0.0237451\pi\) |
−0.434066 | + | 0.900881i | \(0.642922\pi\) | |||||||
\(578\) | 8.09406 | − | 14.0193i | 0.336668 | − | 0.583127i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −56.7080 | + | 98.2211i | −2.35467 | + | 4.07841i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.45038 | −0.0600687 | ||||||||
\(584\) | −4.98715 | − | 8.63800i | −0.206370 | − | 0.357443i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.58005 | − | 7.93288i | 0.189200 | − | 0.327704i | ||||
\(587\) | 3.75700 | + | 6.50731i | 0.155068 | + | 0.268585i | 0.933084 | − | 0.359659i | \(-0.117107\pi\) |
−0.778016 | + | 0.628245i | \(0.783774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93414 | − | 12.0103i | 0.285716 | − | 0.494875i | ||||
\(590\) | −27.5349 | − | 47.6919i | −1.13359 | − | 1.96344i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.03590 | + | 8.72243i | −0.206974 | + | 0.358490i | ||||
\(593\) | 17.7904 | − | 30.8139i | 0.730565 | − | 1.26538i | −0.226077 | − | 0.974109i | \(-0.572590\pi\) |
0.956642 | − | 0.291266i | \(-0.0940765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.6659 | − | 34.0623i | −0.805545 | − | 1.39524i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.56681 | 0.227644 | ||||||||
\(599\) | 11.4821 | 0.469146 | 0.234573 | − | 0.972099i | \(-0.424631\pi\) | ||||
0.234573 | + | 0.972099i | \(0.424631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.190030 | + | 0.329142i | 0.00775150 | + | 0.0134260i | 0.869875 | − | 0.493272i | \(-0.164199\pi\) |
−0.862124 | + | 0.506698i | \(0.830866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 26.0167 | − | 45.0623i | 1.05861 | − | 1.83356i | ||||
\(605\) | −19.8173 | + | 34.3246i | −0.805688 | + | 1.39549i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.27044 | + | 16.0569i | 0.376275 | + | 0.651728i | 0.990517 | − | 0.137390i | \(-0.0438713\pi\) |
−0.614242 | + | 0.789118i | \(0.710538\pi\) | |||||||
\(608\) | 0.532351 | − | 0.922058i | 0.0215897 | − | 0.0373944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.1249 | − | 62.5702i | −1.46265 | − | 2.53339i | ||||
\(611\) | 1.53736 | − | 2.66278i | 0.0621949 | − | 0.107725i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.66225 | − | 6.34321i | −0.147917 | − | 0.256200i | 0.782540 | − | 0.622600i | \(-0.213924\pi\) |
−0.930457 | + | 0.366400i | \(0.880590\pi\) | |||||||
\(614\) | −75.2154 | −3.03545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.7427 | + | 22.0710i | −0.513002 | + | 0.888546i | 0.486884 | + | 0.873466i | \(0.338133\pi\) |
−0.999886 | + | 0.0150791i | \(0.995200\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4482 | + | 28.4891i | −0.661108 | + | 1.14507i | 0.319217 | + | 0.947682i | \(0.396580\pi\) |
−0.980325 | + | 0.197391i | \(0.936753\pi\) | |||||||
\(620\) | −52.1072 | − | 90.2523i | −2.09267 | − | 3.62462i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.6748 | −1.02947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.67111 | − | 2.89444i | −0.0668443 | − | 0.115778i | ||||
\(626\) | 1.52517 | 0.0609580 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −84.9271 | −3.38896 | ||||||||
\(629\) | 11.3016 | 0.450626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8683 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(632\) | −41.2527 | −1.64094 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.2163 | 1.00147 | ||||||||
\(635\) | −28.4301 | − | 49.2424i | −1.12822 | − | 1.95413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.64766 | −0.302774 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 34.9496 | + | 60.5344i | 1.38150 | + | 2.39283i | ||||
\(641\) | 5.73025 | − | 9.92509i | 0.226331 | − | 0.392017i | −0.730387 | − | 0.683034i | \(-0.760660\pi\) |
0.956718 | + | 0.291016i | \(0.0939934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.69078 | − | 15.0529i | 0.342731 | − | 0.593627i | −0.642208 | − | 0.766531i | \(-0.721981\pi\) |
0.984939 | + | 0.172903i | \(0.0553147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.5792 | −0.927711 | ||||||||
\(647\) | 12.6720 | + | 21.9485i | 0.498186 | + | 0.862883i | 0.999998 | − | 0.00209358i | \(-0.000666408\pi\) |
−0.501812 | + | 0.864977i | \(0.667333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.24332 | − | 2.15349i | 0.0488045 | − | 0.0845320i | ||||
\(650\) | 5.01954 | + | 8.69410i | 0.196883 | + | 0.341011i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.6264 | − | 39.1900i | 0.886116 | − | 1.53480i | ||||
\(653\) | 7.04163 | + | 12.1965i | 0.275560 | + | 0.477284i | 0.970276 | − | 0.242000i | \(-0.0778033\pi\) |
−0.694716 | + | 0.719284i | \(0.744470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.5723 | + | 26.9720i | −0.608459 | + | 1.05388i | ||||
\(656\) | −16.2581 | + | 28.1599i | −0.634774 | + | 1.09946i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0854 | + | 33.0569i | 0.743462 | + | 1.28771i | 0.950910 | + | 0.309467i | \(0.100151\pi\) |
−0.207449 | + | 0.978246i | \(0.566516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.353732 | −0.0137586 | −0.00687930 | − | 0.999976i | \(-0.502190\pi\) | ||||
−0.00687930 | + | 0.999976i | \(0.502190\pi\) | |||||||
\(662\) | 50.1052 | 1.94740 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30.7591 | + | 53.2764i | 1.19369 | + | 2.06752i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.7719 | + | 30.7818i | −0.688130 | + | 1.19188i | ||||
\(668\) | −7.01403 | + | 12.1487i | −0.271381 | + | 0.470046i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.2048 | − | 28.0675i | −0.626045 | − | 1.08434i | ||||
\(671\) | 1.63119 | − | 2.82531i | 0.0629715 | − | 0.109070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5555 | + | 18.2827i | 0.406886 | + | 0.704748i | 0.994539 | − | 0.104365i | \(-0.0332811\pi\) |
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(674\) | −7.02704 | + | 12.1712i | −0.270672 | + | 0.468817i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.8712 | + | 44.8102i | 0.995046 | + | 1.72347i | ||||
\(677\) | −21.1464 | −0.812721 | −0.406361 | − | 0.913713i | \(-0.633202\pi\) | ||||
−0.406361 | + | 0.913713i | \(0.633202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −44.8879 | + | 77.7482i | −1.72137 | + | 2.98151i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.51360 | − | 6.08573i | 0.134543 | − | 0.233035i | ||||
\(683\) | 17.3858 | + | 30.1131i | 0.665249 | + | 1.15224i | 0.979218 | + | 0.202811i | \(0.0650078\pi\) |
−0.313969 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.37998 | 0.0527264 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.03590 | + | 8.72243i | 0.191992 | + | 0.332539i | ||||
\(689\) | 1.73722 | 0.0661827 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6492 | 1.31812 | 0.659059 | − | 0.752091i | \(-0.270955\pi\) | ||||
0.659059 | + | 0.752091i | \(0.270955\pi\) | |||||||
\(692\) | −24.5418 | −0.932940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8525 | 0.829511 | ||||||||
\(695\) | −69.5083 | −2.63660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.4868 | 1.38203 | ||||||||
\(698\) | −25.8044 | − | 44.6945i | −0.976710 | − | 1.69171i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.6050 | 1.83579 | 0.917894 | − | 0.396826i | \(-0.129889\pi\) | ||||
0.917894 | + | 0.396826i | \(0.129889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.29661 | − | 3.97784i | −0.0866182 | − | 0.150027i | ||||
\(704\) | −1.48901 | + | 2.57904i | −0.0561192 | + | 0.0972012i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.1651 | + | 31.4629i | −0.683654 | + | 1.18412i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.10817 | 0.154286 | 0.0771428 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771428 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(710\) | 38.0753 | + | 65.9483i | 1.42894 | + | 2.47500i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37.4764 | − | 64.9110i | 1.40449 | − | 2.43264i | ||||
\(713\) | −16.3300 | − | 28.2844i | −0.611564 | − | 1.05926i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.361864 | + | 0.626767i | −0.0135330 | + | 0.0234398i | ||||
\(716\) | 18.5131 | + | 32.0657i | 0.691868 | + | 1.19835i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.87266 | + | 15.3679i | −0.331125 | + | 0.573525i | ||||
\(719\) | 24.1408 | − | 41.8131i | 0.900299 | − | 1.55936i | 0.0731939 | − | 0.997318i | \(-0.476681\pi\) |
0.827106 | − | 0.562047i | \(-0.189986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.5833 | − | 32.1872i | −0.691597 | − | 1.19788i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −48.4375 | −1.80016 | ||||||||
\(725\) | −64.0990 | −2.38058 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5151 | + | 35.5332i | 0.760863 | + | 1.31785i | 0.942406 | + | 0.334470i | \(0.108557\pi\) |
−0.181543 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.88151 | − | 15.3832i | 0.328720 | − | 0.569359i | ||||
\(731\) | 5.65082 | − | 9.78750i | 0.209003 | − | 0.362004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2714 | − | 26.4508i | −0.564062 | − | 0.976983i | −0.997136 | − | 0.0756253i | \(-0.975905\pi\) |
0.433075 | − | 0.901358i | \(-0.357429\pi\) | |||||||
\(734\) | 13.5011 | − | 23.3845i | 0.498334 | − | 0.863139i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.25370 | − | 2.17147i | −0.0462118 | − | 0.0800413i | ||||
\(737\) | 0.731715 | − | 1.26737i | 0.0269531 | − | 0.0466841i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.9100 | − | 20.6288i | −0.438117 | − | 0.758841i | 0.559427 | − | 0.828880i | \(-0.311021\pi\) |
−0.997544 | + | 0.0700384i | \(0.977688\pi\) | |||||||
\(740\) | −34.5161 | −1.26884 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.26089 | − | 9.11213i | 0.193003 | − | 0.334292i | −0.753241 | − | 0.657745i | \(-0.771510\pi\) |
0.946244 | + | 0.323453i | \(0.104844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7449 | − | 30.7350i | 0.650121 | − | 1.12604i | ||||
\(746\) | −0.668971 | − | 1.15869i | −0.0244928 | − | 0.0424227i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.00079 | −0.292538 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.13521 | + | 8.89445i | 0.187386 | + | 0.324563i | 0.944378 | − | 0.328862i | \(-0.106665\pi\) |
−0.756992 | + | 0.653425i | \(0.773332\pi\) | |||||||
\(752\) | −27.3330 | −0.996734 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.16010 | 0.333591 | ||||||||
\(755\) | 46.9507 | 1.70871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03930 | 0.292193 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(758\) | 55.8319 | 2.02791 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.4868 | 1.32351 | ||||||||
\(761\) | 13.8302 | + | 23.9547i | 0.501345 | + | 0.868355i | 0.999999 | + | 0.00155404i | \(0.000494668\pi\) |
−0.498654 | + | 0.866801i | \(0.666172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −37.0554 | −1.34062 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.9371 | + | 76.1013i | 1.58751 | + | 2.74965i | ||||
\(767\) | −1.48920 | + | 2.57938i | −0.0537720 | + | 0.0931359i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9613 | − | 29.3778i | 0.611640 | − | 1.05939i | −0.379324 | − | 0.925264i | \(-0.623843\pi\) |
0.990964 | − | 0.134128i | \(-0.0428233\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 68.6883 | 2.47215 | ||||||||
\(773\) | −14.2978 | − | 24.7645i | −0.514256 | − | 0.890717i | −0.999863 | − | 0.0165403i | \(-0.994735\pi\) |
0.485607 | − | 0.874177i | \(-0.338599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.4493 | − | 51.0077i | 1.05785 | − | 1.83225i | ||||
\(776\) | 23.9753 | + | 41.5265i | 0.860664 | + | 1.49071i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47.5605 | + | 82.3772i | −1.70513 | + | 2.95337i | ||||
\(779\) | −7.41449 | − | 12.8423i | −0.265652 | − | 0.460122i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.71926 | + | 2.97785i | −0.0615200 | + | 0.106556i | ||||
\(782\) | −27.7647 | + | 48.0899i | −0.992864 | + | 1.71969i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.3157 | − | 66.3647i | −1.36754 | − | 2.36866i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.0035 | 1.63985 | 0.819923 | − | 0.572473i | \(-0.194016\pi\) | ||||
0.819923 | + | 0.572473i | \(0.194016\pi\) | |||||||
\(788\) | 86.4222 | 3.07866 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −36.7330 | − | 63.6235i | −1.30690 | − | 2.26362i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.95379 | + | 3.38406i | −0.0693810 | + | 0.120171i | ||||
\(794\) | 14.6988 | − | 25.4591i | 0.521642 | − | 0.903511i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.2183 | + | 35.0192i | 0.716620 | + | 1.24122i | ||||
\(797\) | −18.4558 | + | 31.9664i | −0.653739 | + | 1.13231i | 0.328469 | + | 0.944515i | \(0.393467\pi\) |
−0.982208 | + | 0.187795i | \(0.939866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3353 | + | 26.5615i | 0.542524 | + | 0.939679i | ||||
\(800\) | 2.26089 | − | 3.91598i | 0.0799346 | − | 0.138451i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39.8068 | − | 68.9474i | −1.40563 | − | 2.43462i | ||||
\(803\) | 0.802077 | 0.0283047 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.20847 | + | 7.28928i | −0.148237 | + | 0.256754i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.0150 | − | 38.1311i | 0.774484 | − | 1.34145i | ||||
\(809\) | 23.8444 | + | 41.2996i | 0.838323 | + | 1.45202i | 0.891296 | + | 0.453422i | \(0.149797\pi\) |
−0.0529735 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.02728 | −0.211646 | −0.105823 | − | 0.994385i | \(-0.533748\pi\) | ||||
−0.105823 | + | 0.994385i | \(0.533748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.16372 | − | 2.01561i | −0.0407882 | − | 0.0706472i | ||||
\(815\) | 40.8324 | 1.43030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.59322 | −0.160696 | ||||||||
\(818\) | 46.6881 | 1.63241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.434 | −3.89143 | ||||||||
\(821\) | 39.2642 | 1.37033 | 0.685165 | − | 0.728388i | \(-0.259730\pi\) | ||||
0.685165 | + | 0.728388i | \(0.259730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.7630 | 0.793469 | 0.396735 | − | 0.917933i | \(-0.370143\pi\) | ||||
0.396735 | + | 0.917933i | \(0.370143\pi\) | |||||||
\(824\) | −20.2849 | − | 35.1344i | −0.706657 | − | 1.22397i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.9286 | 1.00595 | 0.502973 | − | 0.864302i | \(-0.332240\pi\) | ||||
0.502973 | + | 0.864302i | \(0.332240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.9883 | − | 29.4247i | −0.590029 | − | 1.02196i | −0.994228 | − | 0.107290i | \(-0.965783\pi\) |
0.404198 | − | 0.914671i | \(-0.367551\pi\) | |||||||
\(830\) | −54.7783 | + | 94.8788i | −1.90138 | + | 3.29329i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.78348 | − | 3.08908i | 0.0618312 | − | 0.107095i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6578 | −0.438041 | ||||||||
\(836\) | 1.62584 | + | 2.81604i | 0.0562310 | + | 0.0973949i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.2716 | + | 36.8435i | −0.734816 | + | 1.27274i | ||||
\(839\) | −19.0206 | − | 32.9446i | −0.656663 | − | 1.13737i | −0.981474 | − | 0.191595i | \(-0.938634\pi\) |
0.324811 | − | 0.945779i | \(-0.394699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7434 | + | 25.5363i | −0.508392 | + | 0.880561i | ||||
\(842\) | 22.8837 | + | 39.6356i | 0.788623 | + | 1.36593i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.91595 | + | 17.1749i | −0.341321 | + | 0.591185i | ||||
\(845\) | −23.3441 | + | 40.4331i | −0.803060 | + | 1.39094i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.72159 | − | 13.3742i | −0.265161 | − | 0.459272i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −100.141 | −3.43480 | ||||||||
\(851\) | −10.8171 | −0.370806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.90746 | + | 8.49996i | 0.168028 | + | 0.291033i | 0.937726 | − | 0.347374i | \(-0.112927\pi\) |
−0.769698 | + | 0.638408i | \(0.779593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.4523 | + | 56.2091i | −1.10920 | + | 1.92119i | ||||
\(857\) | −13.3680 | + | 23.1541i | −0.456642 | + | 0.790928i | −0.998781 | − | 0.0493613i | \(-0.984281\pi\) |
0.542139 | + | 0.840289i | \(0.317615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.24411 | − | 16.0113i | −0.315405 | − | 0.546297i | 0.664119 | − | 0.747627i | \(-0.268807\pi\) |
−0.979523 | + | 0.201330i | \(0.935474\pi\) | |||||||
\(860\) | −17.2581 | + | 29.8918i | −0.588495 | + | 1.01930i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5344 | + | 33.8346i | 0.665345 | + | 1.15241i | ||||
\(863\) | −4.57393 | + | 7.92228i | −0.155698 | + | 0.269677i | −0.933313 | − | 0.359064i | \(-0.883096\pi\) |
0.777615 | + | 0.628741i | \(0.216429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0723 | − | 19.1777i | −0.376469 | − | 0.652063i | ||||
\(866\) | 99.4946 | 3.38097 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.65865 | − | 2.87287i | 0.0562660 | − | 0.0974555i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.876423 | + | 1.51801i | −0.0296964 | + | 0.0514358i | ||||
\(872\) | 6.57227 | + | 11.3835i | 0.222565 | + | 0.385494i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.5683 | 0.763385 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3442 | − | 19.6487i | −0.383065 | − | 0.663488i | 0.608434 | − | 0.793605i | \(-0.291798\pi\) |
−0.991499 | + | 0.130117i | \(0.958465\pi\) | |||||||
\(878\) | 30.6602 | 1.03473 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.43367 | 0.216879 | ||||||||
\(881\) | 15.3696 | 0.517815 | 0.258907 | − | 0.965902i | \(-0.416638\pi\) | ||||
0.258907 | + | 0.965902i | \(0.416638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6372 | 0.997370 | 0.498685 | − | 0.866783i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333817\pi\) | |||||||
\(884\) | 9.58307 | 0.322313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.2518 | −0.680371 | ||||||||
\(887\) | 9.38252 | + | 16.2510i | 0.315034 | + | 0.545655i | 0.979445 | − | 0.201712i | \(-0.0646506\pi\) |
−0.664410 | + | 0.747368i | \(0.731317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 133.482 | 4.47432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −47.4507 | − | 82.1870i | −1.58877 | − | 2.75183i | ||||
\(893\) | 6.23258 | − | 10.7952i | 0.208565 | − | 0.361246i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.7047 | + | 28.9335i | −0.558378 | + | 0.967139i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.8889 | 0.463479 | ||||||||
\(899\) | −26.8708 | − | 46.5416i | −0.896192 | − | 1.55225i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.66445 | + | 15.0073i | −0.288655 | + | 0.499965i | ||||
\(902\) | −3.75700 | − | 6.50731i | −0.125094 | − | 0.216670i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.2527 | − | 61.0595i | 1.17249 | − | 2.03081i | ||||
\(905\) | −21.8530 | − | 37.8505i | −0.726419 | − | 1.25819i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.5541 | − | 26.9405i | 0.516465 | − | 0.894543i | −0.483352 | − | 0.875426i | \(-0.660581\pi\) |
0.999817 | − | 0.0191175i | \(-0.00608567\pi\) | |||||||
\(908\) | 12.4022 | − | 21.4813i | 0.411582 | − | 0.712881i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.73764 | + | 15.1340i | 0.289491 | + | 0.501413i | 0.973688 | − | 0.227884i | \(-0.0731806\pi\) |
−0.684197 | + | 0.729297i | \(0.739847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.94695 | −0.163720 | ||||||||
\(914\) | −12.4720 | −0.412536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.96027 | + | 5.12734i | 0.0978101 | + | 0.169412i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0993 | + | 36.5451i | −0.696002 | + | 1.20551i | 0.273840 | + | 0.961775i | \(0.411706\pi\) |
−0.969842 | + | 0.243736i | \(0.921627\pi\) | |||||||
\(920\) | 42.9635 | − | 74.4150i | 1.41647 | − | 2.45339i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.56720 | − | 16.5709i | −0.315079 | − | 0.545733i | ||||
\(923\) | 2.05927 | − | 3.56676i | 0.0677818 | − | 0.117401i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.75370 | − | 16.8939i | −0.320700 | − | 0.555468i | ||||
\(926\) | −11.2937 | + | 19.5612i | −0.371133 | + | 0.642821i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.06294 | − | 3.57311i | −0.0677193 | − | 0.117293i | ||||
\(929\) | 48.4111 | 1.58832 | 0.794159 | − | 0.607710i | \(-0.207912\pi\) | ||||
0.794159 | + | 0.607710i | \(0.207912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26.8551 | + | 46.5145i | −0.879670 | + | 1.52363i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.9350 | + | 29.3322i | −0.554129 | + | 0.959780i | ||||
\(935\) | −3.60963 | − | 6.25206i | −0.118048 | − | 0.204464i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6750 | 0.740762 | 0.370381 | − | 0.928880i | \(-0.379227\pi\) | ||||
0.370381 | + | 0.928880i | \(0.379227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −46.8353 | − | 81.1211i | −1.52760 | − | 2.64588i | ||||
\(941\) | −49.9505 | −1.62834 | −0.814170 | − | 0.580627i | \(-0.802808\pi\) | ||||
−0.814170 | + | 0.580627i | \(0.802808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.9225 | −1.13723 | ||||||||
\(944\) | 26.4769 | 0.861749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.32743 | −0.0756713 | ||||||||
\(947\) | −17.7123 | −0.575571 | −0.287786 | − | 0.957695i | \(-0.592919\pi\) | ||||
−0.287786 | + | 0.957695i | \(0.592919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.960699 | −0.0311856 | ||||||||
\(950\) | 20.3496 | + | 35.2466i | 0.660230 | + | 1.14355i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.0229 | −1.23168 | −0.615842 | − | 0.787870i | \(-0.711184\pi\) | ||||
−0.615842 | + | 0.787870i | \(0.711184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.7179 | − | 28.9563i | −0.540979 | − | 0.937002i | ||||
\(956\) | 39.3017 | − | 68.0726i | 1.27111 | − | 2.20163i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.7177 | − | 18.5635i | 0.346272 | − | 0.599761i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.3815 | 0.592952 | ||||||||
\(962\) | 1.39386 | + | 2.41423i | 0.0449398 | + | 0.0778380i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.2440 | + | 17.7432i | −0.329938 | + | 0.571469i | ||||
\(965\) | 30.9894 | + | 53.6752i | 0.997583 | + | 1.72786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5064 | − | 26.8579i | 0.498652 | − | 0.863691i | −0.501346 | − | 0.865247i | \(-0.667162\pi\) |
0.999999 | + | 0.00155529i | \(0.000495066\pi\) | |||||||
\(968\) | −27.3801 | − | 47.4236i | −0.880028 | − | 1.52425i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −42.6972 | + | 73.9537i | −1.37092 | + | 2.37451i | ||||
\(971\) | 7.28376 | − | 12.6158i | 0.233747 | − | 0.404862i | −0.725161 | − | 0.688580i | \(-0.758235\pi\) |
0.958908 | + | 0.283718i | \(0.0915679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.1893 | − | 38.4330i | −0.710991 | − | 1.23147i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.7368 | 1.11190 | ||||||||
\(977\) | 47.8797 | 1.53181 | 0.765904 | − | 0.642955i | \(-0.222292\pi\) | ||||
0.765904 | + | 0.642955i | \(0.222292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.01364 | + | 5.21978i | 0.0963163 | + | 0.166825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.51819 | + | 4.36163i | −0.0803586 | + | 0.139185i | ||||
\(983\) | 22.2128 | − | 38.4737i | 0.708479 | − | 1.22712i | −0.256942 | − | 0.966427i | \(-0.582715\pi\) |
0.965421 | − | 0.260695i | \(-0.0839517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.9902 | + | 67.5329i | 1.24233 | + | 2.15178i | ||||
\(986\) | −45.6864 | + | 79.1313i | −1.45495 | + | 2.52005i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.94738 | − | 3.37296i | −0.0619544 | − | 0.107308i | ||||
\(989\) | −5.40856 | + | 9.36790i | −0.171982 | + | 0.297882i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.8078 | + | 36.0401i | 0.660981 | + | 1.14485i | 0.980358 | + | 0.197225i | \(0.0631929\pi\) |
−0.319377 | + | 0.947628i | \(0.603474\pi\) | |||||||
\(992\) | 3.79114 | 0.120369 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.2434 | + | 31.5985i | −0.578354 | + | 1.00174i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.51407 | − | 11.2827i | 0.206303 | − | 0.357327i | −0.744244 | − | 0.667908i | \(-0.767190\pi\) |
0.950547 | + | 0.310581i | \(0.100523\pi\) | |||||||
\(998\) | −48.0875 | − | 83.2901i | −1.52218 | − | 2.63650i | ||||
\(999\) | 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 | 1323.2.h.g.226.2 | 12 | ||
3.2 | odd | 2 | 441.2.h.g.373.6 | 12 | |||
7.2 | even | 3 | 1323.2.f.g.442.6 | 12 | |||
7.3 | odd | 6 | 1323.2.g.g.361.6 | 12 | |||
7.4 | even | 3 | 1323.2.g.g.361.5 | 12 | |||
7.5 | odd | 6 | 1323.2.f.g.442.5 | 12 | |||
7.6 | odd | 2 | inner | 1323.2.h.g.226.1 | 12 | ||
9.2 | odd | 6 | 441.2.g.g.79.2 | 12 | |||
9.7 | even | 3 | 1323.2.g.g.667.5 | 12 | |||
21.2 | odd | 6 | 441.2.f.g.148.1 | ✓ | 12 | ||
21.5 | even | 6 | 441.2.f.g.148.2 | yes | 12 | ||
21.11 | odd | 6 | 441.2.g.g.67.2 | 12 | |||
21.17 | even | 6 | 441.2.g.g.67.1 | 12 | |||
21.20 | even | 2 | 441.2.h.g.373.5 | 12 | |||
63.2 | odd | 6 | 441.2.f.g.295.1 | yes | 12 | ||
63.5 | even | 6 | 3969.2.a.be.1.5 | 6 | |||
63.11 | odd | 6 | 441.2.h.g.214.6 | 12 | |||
63.16 | even | 3 | 1323.2.f.g.883.6 | 12 | |||
63.20 | even | 6 | 441.2.g.g.79.1 | 12 | |||
63.23 | odd | 6 | 3969.2.a.be.1.6 | 6 | |||
63.25 | even | 3 | inner | 1323.2.h.g.802.2 | 12 | ||
63.34 | odd | 6 | 1323.2.g.g.667.6 | 12 | |||
63.38 | even | 6 | 441.2.h.g.214.5 | 12 | |||
63.40 | odd | 6 | 3969.2.a.bd.1.2 | 6 | |||
63.47 | even | 6 | 441.2.f.g.295.2 | yes | 12 | ||
63.52 | odd | 6 | inner | 1323.2.h.g.802.1 | 12 | ||
63.58 | even | 3 | 3969.2.a.bd.1.1 | 6 | |||
63.61 | odd | 6 | 1323.2.f.g.883.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.1 | ✓ | 12 | 21.2 | odd | 6 | ||
441.2.f.g.148.2 | yes | 12 | 21.5 | even | 6 | ||
441.2.f.g.295.1 | yes | 12 | 63.2 | odd | 6 | ||
441.2.f.g.295.2 | yes | 12 | 63.47 | even | 6 | ||
441.2.g.g.67.1 | 12 | 21.17 | even | 6 | |||
441.2.g.g.67.2 | 12 | 21.11 | odd | 6 | |||
441.2.g.g.79.1 | 12 | 63.20 | even | 6 | |||
441.2.g.g.79.2 | 12 | 9.2 | odd | 6 | |||
441.2.h.g.214.5 | 12 | 63.38 | even | 6 | |||
441.2.h.g.214.6 | 12 | 63.11 | odd | 6 | |||
441.2.h.g.373.5 | 12 | 21.20 | even | 2 | |||
441.2.h.g.373.6 | 12 | 3.2 | odd | 2 | |||
1323.2.f.g.442.5 | 12 | 7.5 | odd | 6 | |||
1323.2.f.g.442.6 | 12 | 7.2 | even | 3 | |||
1323.2.f.g.883.5 | 12 | 63.61 | odd | 6 | |||
1323.2.f.g.883.6 | 12 | 63.16 | even | 3 | |||
1323.2.g.g.361.5 | 12 | 7.4 | even | 3 | |||
1323.2.g.g.361.6 | 12 | 7.3 | odd | 6 | |||
1323.2.g.g.667.5 | 12 | 9.7 | even | 3 | |||
1323.2.g.g.667.6 | 12 | 63.34 | odd | 6 | |||
1323.2.h.g.226.1 | 12 | 7.6 | odd | 2 | inner | ||
1323.2.h.g.226.2 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.h.g.802.1 | 12 | 63.52 | odd | 6 | inner | ||
1323.2.h.g.802.2 | 12 | 63.25 | even | 3 | inner | ||
3969.2.a.bd.1.1 | 6 | 63.58 | even | 3 | |||
3969.2.a.bd.1.2 | 6 | 63.40 | odd | 6 | |||
3969.2.a.be.1.5 | 6 | 63.5 | even | 6 | |||
3969.2.a.be.1.6 | 6 | 63.23 | odd | 6 |