Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(442,1323)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.442");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.f (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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 883.5 | ||
Root | \(-1.82904 + 1.05600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.883 |
Dual form | 1323.2.f.g.442.5 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23025 | − | 2.13086i | 0.869920 | − | 1.50675i | 0.00784213 | − | 0.999969i | \(-0.497504\pi\) |
0.862078 | − | 0.506776i | \(-0.169163\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.02704 | − | 3.51094i | −1.01352 | − | 1.75547i | ||||
\(5\) | −1.82904 | − | 3.16799i | −0.817970 | − | 1.41677i | −0.907175 | − | 0.420753i | \(-0.861766\pi\) |
0.0892047 | − | 0.996013i | \(-0.471567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.05408 | −1.78689 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.00071 | −2.84628 | ||||||||
\(11\) | 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 | \(-0.145162\pi\) |
−0.830297 | + | 0.557322i | \(0.811829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.16372 | + | 3.74766i | −0.540929 | + | 0.936916i | ||||
\(17\) | −4.85584 | −1.17771 | −0.588857 | − | 0.808237i | \(-0.700422\pi\) | ||||
−0.588857 | + | 0.808237i | \(0.700422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.97351 | −0.452755 | −0.226378 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226378 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(20\) | −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 | ||||
\(26\) | 1.19777 | 0.234901 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.82383 | − | 6.62307i | 0.710068 | − | 1.22987i | −0.254764 | − | 0.967003i | \(-0.581998\pi\) |
0.964831 | − | 0.262870i | \(-0.0846690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.51360 | − | 6.08573i | −0.631061 | − | 1.09303i | −0.987335 | − | 0.158648i | \(-0.949286\pi\) |
0.356274 | − | 0.934381i | \(-0.384047\pi\) | |||||||
\(32\) | 0.269748 | + | 0.467216i | 0.0476851 | + | 0.0825930i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.97391 | + | 10.3471i | −1.02452 | + | 1.77452i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.32743 | 0.382627 | 0.191314 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191314 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(38\) | −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 | 0.994655 | + | 0.103249i | \(0.0329240\pi\) |
−0.407911 | + | 0.913022i | \(0.633743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16372 | − | 2.01561i | 0.177465 | − | 0.307378i | −0.763547 | − | 0.645753i | \(-0.776544\pi\) |
0.941012 | + | 0.338374i | \(0.109877\pi\) | |||||||
\(44\) | −1.64766 | −0.248395 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.4356 | 1.68609 | ||||||||
\(47\) | −3.15811 | + | 5.47002i | −0.460658 | + | 0.797884i | −0.998994 | − | 0.0448469i | \(-0.985720\pi\) |
0.538335 | + | 0.842731i | \(0.319053\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | 3.56867 | 0.490195 | 0.245097 | − | 0.969498i | \(-0.421180\pi\) | ||||
0.245097 | + | 0.969498i | \(0.421180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.48672 | −0.200469 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.40856 | − | 16.2961i | −1.23540 | − | 2.13978i | ||||
\(59\) | 3.05919 | + | 5.29868i | 0.398273 | + | 0.689829i | 0.993513 | − | 0.113719i | \(-0.0362763\pi\) |
−0.595240 | + | 0.803548i | \(0.702943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.01356 | − | 6.95169i | 0.513884 | − | 0.890073i | −0.485987 | − | 0.873966i | \(-0.661540\pi\) |
0.999870 | − | 0.0161063i | \(-0.00512703\pi\) | |||||||
\(62\) | −17.2905 | −2.19589 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.32743 | −0.915929 | ||||||||
\(65\) | 0.890369 | − | 1.54216i | 0.110437 | − | 0.191282i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.80039 | − | 3.11836i | −0.219952 | − | 0.380969i | 0.734841 | − | 0.678240i | \(-0.237257\pi\) |
−0.954793 | + | 0.297271i | \(0.903924\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 1.97351 | 0.230982 | 0.115491 | − | 0.993309i | \(-0.463156\pi\) | ||||
0.115491 | + | 0.993309i | \(0.463156\pi\) | |||||||
\(74\) | 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 | ||||||||
\(79\) | −4.08113 | + | 7.06872i | −0.459163 | + | 0.795293i | −0.998917 | − | 0.0465297i | \(-0.985184\pi\) |
0.539754 | + | 0.841823i | \(0.318517\pi\) | |||||||
\(80\) | 15.8301 | 1.76986 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.4882 | 2.04168 | ||||||||
\(83\) | 6.08600 | − | 10.5413i | 0.668025 | − | 1.15705i | −0.310431 | − | 0.950596i | \(-0.600473\pi\) |
0.978456 | − | 0.206457i | \(-0.0661933\pi\) | |||||||
\(84\) | 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 | ||||
\(89\) | −14.8301 | −1.57199 | −0.785996 | − | 0.618231i | \(-0.787849\pi\) | ||||
−0.785996 | + | 0.618231i | \(0.787849\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.42101 | − | 16.3177i | 0.982208 | − | 1.70123i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.77056 | + | 13.4590i | 0.801472 | + | 1.38819i | ||||
\(95\) | 3.60963 | + | 6.25206i | 0.370340 | + | 0.641448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.74375 | − | 8.21642i | 0.481655 | − | 0.834251i | −0.518123 | − | 0.855306i | \(-0.673369\pi\) |
0.999778 | + | 0.0210547i | \(0.00670241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 33.9794 | 3.39794 | ||||||||
\(101\) | 4.35588 | − | 7.54461i | 0.433426 | − | 0.750716i | −0.563739 | − | 0.825953i | \(-0.690638\pi\) |
0.997166 | + | 0.0752364i | \(0.0239711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.01356 | − | 6.95169i | −0.395468 | − | 0.684970i | 0.597693 | − | 0.801725i | \(-0.296084\pi\) |
−0.993161 | + | 0.116755i | \(0.962751\pi\) | |||||||
\(104\) | −1.23016 | − | 2.13069i | −0.120627 | − | 0.208931i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.39037 | − | 7.60434i | 0.426430 | − | 0.738599i | ||||
\(107\) | −12.8420 | −1.24148 | −0.620742 | − | 0.784015i | \(-0.713169\pi\) | ||||
−0.620742 | + | 0.784015i | \(0.713169\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.60078 | 0.249109 | 0.124555 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124555 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(110\) | −1.82904 | + | 3.16799i | −0.174392 | + | 0.302056i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.97509 | − | 12.0812i | −0.656162 | − | 1.13651i | −0.981601 | − | 0.190942i | \(-0.938846\pi\) |
0.325440 | − | 0.945563i | \(-0.394488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.50075 | − | 14.7237i | 0.792699 | − | 1.37300i | ||||
\(116\) | −31.0043 | −2.87867 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0543 | 1.38586 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.41741 | + | 9.38323i | 0.492492 | + | 0.853021i | ||||
\(122\) | −9.87538 | − | 17.1047i | −0.894075 | − | 1.54858i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.2444 | + | 24.6721i | −1.27919 | + | 2.21562i | ||||
\(125\) | 12.3698 | 1.10639 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5438 | −1.37929 | −0.689643 | − | 0.724149i | \(-0.742233\pi\) | ||||
−0.689643 | + | 0.724149i | \(0.742233\pi\) | |||||||
\(128\) | −9.55408 | + | 16.5482i | −0.844470 | + | 1.46266i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.19076 | − | 3.79450i | −0.192142 | − | 0.332800i | ||||
\(131\) | −4.25696 | − | 7.37327i | −0.371932 | − | 0.644205i | 0.617931 | − | 0.786233i | \(-0.287971\pi\) |
−0.989863 | + | 0.142027i | \(0.954638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.85973 | −0.765364 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.5418 | 2.10444 | ||||||||
\(137\) | 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 | 0.915725 | + | 0.401806i | \(0.131617\pi\) |
−0.109888 | + | 0.993944i | \(0.535049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4086 | + | 18.0281i | −0.873467 | + | 1.51289i | ||||
\(143\) | 0.197844 | 0.0165446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27.9757 | −2.32326 | ||||||||
\(146\) | 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 | \(-0.00823738\pi\) | |||||||
\(152\) | 9.97430 | 0.809023 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.8530 | + | 22.2621i | −1.03238 | + | 1.78813i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4743 | − | 18.1420i | −0.835937 | − | 1.44789i | −0.893265 | − | 0.449531i | \(-0.851591\pi\) |
0.0573276 | − | 0.998355i | \(-0.481742\pi\) | |||||||
\(158\) | 10.0416 | + | 17.3926i | 0.798869 | + | 1.38368i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.986757 | − | 1.70911i | 0.0780100 | − | 0.135117i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1623 | −0.874295 | −0.437148 | − | 0.899390i | \(-0.644011\pi\) | ||||
−0.437148 | + | 0.899390i | \(0.644011\pi\) | |||||||
\(164\) | 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 | \(-0.123923\pi\) |
−0.791289 | + | 0.611443i | \(0.790590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38151 | − | 11.0531i | 0.490886 | − | 0.850239i | ||||
\(170\) | 43.7060 | 3.35210 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.43560 | −0.719458 | ||||||||
\(173\) | −3.02680 | + | 5.24258i | −0.230124 | + | 0.398586i | −0.957844 | − | 0.287288i | \(-0.907246\pi\) |
0.727721 | + | 0.685874i | \(0.240580\pi\) | |||||||
\(174\) | 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 | ||||
\(179\) | −9.13307 | −0.682638 | −0.341319 | − | 0.939948i | \(-0.610874\pi\) | ||||
−0.341319 | + | 0.939948i | \(0.610874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9478 | 0.888074 | 0.444037 | − | 0.896008i | \(-0.353546\pi\) | ||||
0.444037 | + | 0.896008i | \(0.353546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.7448 | − | 20.3427i | −0.865841 | − | 1.49968i | ||||
\(185\) | −4.25696 | − | 7.37327i | −0.312978 | − | 0.542093i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.986757 | + | 1.70911i | −0.0721588 | + | 0.124983i | ||||
\(188\) | 25.6065 | 1.86755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7630 | 1.28867 | ||||||||
\(191\) | 4.57014 | − | 7.91571i | 0.330683 | − | 0.572760i | −0.651963 | − | 0.758251i | \(-0.726054\pi\) |
0.982646 | + | 0.185491i | \(0.0593874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.47150 | − | 14.6731i | −0.609792 | − | 1.05619i | −0.991274 | − | 0.131814i | \(-0.957920\pi\) |
0.381483 | − | 0.924376i | \(-0.375414\pi\) | |||||||
\(194\) | −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 | ||||||||
\(199\) | 9.97430 | 0.707060 | 0.353530 | − | 0.935423i | \(-0.384981\pi\) | ||||
0.353530 | + | 0.935423i | \(0.384981\pi\) | |||||||
\(200\) | 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 | ||||||||
\(205\) | 13.7434 | − | 23.8042i | 0.959879 | − | 1.66256i | ||||
\(206\) | −19.7508 | −1.37610 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.10658 | −0.146065 | ||||||||
\(209\) | −0.401038 | + | 0.694619i | −0.0277404 | + | 0.0480478i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44592 | − | 4.23645i | −0.168384 | − | 0.291649i | 0.769468 | − | 0.638685i | \(-0.220521\pi\) |
−0.937852 | + | 0.347036i | \(0.887188\pi\) | |||||||
\(212\) | −7.23385 | − | 12.5294i | −0.496823 | − | 0.860523i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.7989 | + | 27.3645i | −1.07999 | + | 1.87060i | ||||
\(215\) | −8.51392 | −0.580644 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.19961 | − | 5.54189i | 0.216705 | − | 0.375344i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.01364 | + | 5.21978i | 0.203179 | + | 0.351917i | ||||
\(221\) | −1.18190 | − | 2.04712i | −0.0795034 | − | 0.137704i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.7044 | − | 20.2727i | 0.783786 | − | 1.35756i | −0.145936 | − | 0.989294i | \(-0.546619\pi\) |
0.929722 | − | 0.368263i | \(-0.120047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −34.3245 | −2.28323 | ||||||||
\(227\) | −3.05919 | + | 5.29868i | −0.203046 | + | 0.351686i | −0.949508 | − | 0.313742i | \(-0.898417\pi\) |
0.746463 | + | 0.665427i | \(0.231751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.730195 | − | 1.26473i | −0.0482526 | − | 0.0835760i | 0.840890 | − | 0.541206i | \(-0.182032\pi\) |
−0.889143 | + | 0.457630i | \(0.848699\pi\) | |||||||
\(230\) | −20.9161 | − | 36.2278i | −1.37917 | − | 2.38879i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3260 | + | 33.4736i | −1.26881 | + | 2.19765i | ||||
\(233\) | 13.2484 | 0.867934 | 0.433967 | − | 0.900929i | \(-0.357113\pi\) | ||||
0.433967 | + | 0.900929i | \(0.357113\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1052 | 1.50722 | ||||||||
\(236\) | 12.4022 | − | 21.4813i | 0.807316 | − | 1.39831i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.69436 | + | 16.7911i | 0.627076 | + | 1.08613i | 0.988136 | + | 0.153584i | \(0.0490817\pi\) |
−0.361060 | + | 0.932543i | \(0.617585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.52684 | − | 4.37662i | 0.162768 | − | 0.281923i | −0.773092 | − | 0.634294i | \(-0.781291\pi\) |
0.935860 | + | 0.352371i | \(0.114624\pi\) | |||||||
\(242\) | 26.6591 | 1.71371 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −32.5426 | −2.08333 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.480350 | − | 0.831990i | −0.0305639 | − | 0.0529383i | ||||
\(248\) | 17.7580 | + | 30.7578i | 1.12764 | + | 1.95312i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.2180 | − | 26.3584i | 0.962472 | − | 1.66705i | ||||
\(251\) | 15.0928 | 0.952647 | 0.476324 | − | 0.879270i | \(-0.341969\pi\) | ||||
0.476324 | + | 0.879270i | \(0.341969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88891 | 0.118755 | ||||||||
\(254\) | −19.1228 | + | 33.1216i | −1.19987 | + | 2.07823i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1804 | + | 28.0253i | 1.01128 | + | 1.75158i | ||||
\(257\) | −3.85592 | − | 6.67865i | −0.240526 | − | 0.416603i | 0.720338 | − | 0.693623i | \(-0.243986\pi\) |
−0.960864 | + | 0.277020i | \(0.910653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.21926 | −0.447720 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9485 | −1.29420 | ||||||||
\(263\) | 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 | ||||||||
\(268\) | −7.29893 | + | 12.6421i | −0.445853 | + | 0.772240i | ||||
\(269\) | 20.7507 | 1.26519 | 0.632596 | − | 0.774482i | \(-0.281989\pi\) | ||||
0.632596 | + | 0.774482i | \(0.281989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.4889 | 1.73057 | 0.865287 | − | 0.501276i | \(-0.167136\pi\) | ||||
0.865287 | + | 0.501276i | \(0.167136\pi\) | |||||||
\(272\) | 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 | \(0.994239\pi\) | |||||||
\(278\) | 46.7529 | 2.80405 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.72140 | − | 8.17770i | 0.281655 | − | 0.487841i | −0.690138 | − | 0.723678i | \(-0.742450\pi\) |
0.971793 | + | 0.235837i | \(0.0757833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.43422 | + | 14.6085i | 0.501362 | + | 0.868385i | 0.999999 | + | 0.00157378i | \(0.000500949\pi\) |
−0.498636 | + | 0.866811i | \(0.666166\pi\) | |||||||
\(284\) | 17.1498 | + | 29.7043i | 1.01765 | + | 1.76263i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.243398 | − | 0.421578i | 0.0143924 | − | 0.0249284i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.57918 | 0.387011 | ||||||||
\(290\) | −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 | \(-0.131983\pi\) |
−0.806517 | + | 0.591211i | \(0.798650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1908 | − | 19.3830i | 0.651551 | − | 1.12852i | ||||
\(296\) | −11.7630 | −0.683712 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.8712 | −1.38282 | ||||||||
\(299\) | −1.13123 | + | 1.95935i | −0.0654209 | + | 0.113312i | ||||
\(300\) | 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 | ||||
\(305\) | −29.3638 | −1.68137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.5691 | −1.74467 | −0.872335 | − | 0.488908i | \(-0.837395\pi\) | ||||
−0.872335 | + | 0.488908i | \(0.837395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.6249 | + | 54.7759i | 1.79617 | + | 3.11106i | ||||
\(311\) | 5.21739 | + | 9.03678i | 0.295851 | + | 0.512429i | 0.975182 | − | 0.221403i | \(-0.0710635\pi\) |
−0.679332 | + | 0.733831i | \(0.737730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.309930 | + | 0.536815i | −0.0175183 | + | 0.0303426i | −0.874652 | − | 0.484752i | \(-0.838910\pi\) |
0.857133 | + | 0.515095i | \(0.172243\pi\) | |||||||
\(314\) | −51.5440 | −2.90879 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.0905 | 1.86148 | ||||||||
\(317\) | 5.12422 | − | 8.87541i | 0.287805 | − | 0.498493i | −0.685481 | − | 0.728091i | \(-0.740408\pi\) |
0.973285 | + | 0.229598i | \(0.0737412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.55408 | − | 2.69175i | −0.0870120 | − | 0.150709i | ||||
\(320\) | 13.4021 | + | 23.2132i | 0.749203 | + | 1.29766i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.58307 | 0.533216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.08009 | −0.226323 | ||||||||
\(326\) | −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 | ||||||||
\(331\) | 10.1819 | − | 17.6356i | 0.559648 | − | 0.969339i | −0.437878 | − | 0.899035i | \(-0.644270\pi\) |
0.997526 | − | 0.0703042i | \(-0.0223970\pi\) | |||||||
\(332\) | −49.3463 | −2.70823 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.51392 | 0.465861 | ||||||||
\(335\) | −6.58596 | + | 11.4072i | −0.359829 | + | 0.623242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.85594 | + | 4.94662i | 0.155573 | + | 0.269460i | 0.933267 | − | 0.359182i | \(-0.116944\pi\) |
−0.777695 | + | 0.628642i | \(0.783611\pi\) | |||||||
\(338\) | −15.7017 | − | 27.1962i | −0.854062 | − | 1.47928i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.0064 | − | 62.3649i | 1.95272 | − | 3.38221i | ||||
\(341\) | −2.85600 | −0.154661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.88151 | + | 10.1871i | −0.317110 | + | 0.549251i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.44746 | + | 12.8994i | 0.400378 | + | 0.693475i | ||||
\(347\) | 4.44066 | + | 7.69145i | 0.238387 | + | 0.412899i | 0.960252 | − | 0.279136i | \(-0.0900480\pi\) |
−0.721865 | + | 0.692034i | \(0.756715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4874 | + | 18.1648i | −0.561379 | + | 0.972337i | 0.435997 | + | 0.899948i | \(0.356396\pi\) |
−0.997376 | + | 0.0723893i | \(0.976938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.219262 | 0.0116867 | ||||||||
\(353\) | −7.38268 | + | 12.7872i | −0.392941 | + | 0.680593i | −0.992836 | − | 0.119485i | \(-0.961876\pi\) |
0.599895 | + | 0.800078i | \(0.295209\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | −7.21206 | −0.380638 | −0.190319 | − | 0.981722i | \(-0.560952\pi\) | ||||
−0.190319 | + | 0.981722i | \(0.560952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1052 | −0.795013 | ||||||||
\(362\) | 14.6988 | − | 25.4591i | 0.772554 | − | 1.33810i | ||||
\(363\) | 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 | −0.686529 | − | 0.727103i | \(-0.740866\pi\) |
0.972954 | + | 0.231000i | \(0.0741998\pi\) | |||||||
\(368\) | −20.1124 | −1.04843 | ||||||||
\(369\) | 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 | \(0.828852\pi\) | |||||||
\(374\) | 2.42792 | + | 4.20528i | 0.125545 | + | 0.217450i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.9614 | − | 27.6459i | 0.823145 | − | 1.42573i | ||||
\(377\) | 3.72286 | 0.191737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6912 | −1.16557 | −0.582785 | − | 0.812626i | \(-0.698037\pi\) | ||||
−0.582785 | + | 0.812626i | \(0.698037\pi\) | |||||||
\(380\) | 14.6337 | − | 25.3464i | 0.750695 | − | 1.30024i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.2448 | − | 19.4766i | −0.575336 | − | 0.996511i | ||||
\(383\) | 17.8569 | + | 30.9291i | 0.912447 | + | 1.58041i | 0.810596 | + | 0.585606i | \(0.199143\pi\) |
0.101851 | + | 0.994800i | \(0.467523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.6883 | −2.12188 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −38.4632 | −1.95267 | ||||||||
\(389\) | 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 | ||||||||
\(394\) | 26.2257 | − | 45.4242i | 1.32123 | − | 2.28844i | ||||
\(395\) | 29.8581 | 1.50233 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9478 | −0.599644 | −0.299822 | − | 0.953995i | \(-0.596927\pi\) | ||||
−0.299822 | + | 0.953995i | \(0.596927\pi\) | |||||||
\(398\) | 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 | ||||
\(404\) | −35.3182 | −1.75715 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.472958 | − | 0.819187i | 0.0234437 | − | 0.0406056i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.48751 | − | 16.4328i | −0.469127 | − | 0.812552i | 0.530250 | − | 0.847841i | \(-0.322098\pi\) |
−0.999377 | + | 0.0352893i | \(0.988765\pi\) | |||||||
\(410\) | −33.8157 | − | 58.5704i | −1.67004 | − | 2.89259i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.2713 | + | 28.1827i | −0.801630 | + | 1.38846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −44.5261 | −2.18570 | ||||||||
\(416\) | −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 | \(-0.305460\pi\) |
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.30039 | + | 16.1087i | −0.453273 | + | 0.785092i | −0.998587 | − | 0.0531397i | \(-0.983077\pi\) |
0.545314 | + | 0.838232i | \(0.316410\pi\) | |||||||
\(422\) | −12.0364 | −0.585922 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0364 | −0.875924 | ||||||||
\(425\) | 20.3496 | − | 35.2466i | 0.987103 | − | 1.70971i | ||||
\(426\) | 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 | ||||
\(431\) | 15.8784 | 0.764835 | 0.382418 | − | 0.923990i | \(-0.375092\pi\) | ||||
0.382418 | + | 0.923990i | \(0.375092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.4367 | 1.94326 | 0.971631 | − | 0.236501i | \(-0.0760007\pi\) | ||||
0.971631 | + | 0.236501i | \(0.0760007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.27188 | − | 9.13117i | −0.252477 | − | 0.437304i | ||||
\(437\) | −4.58611 | − | 7.94338i | −0.219384 | − | 0.379984i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.23047 | + | 10.7915i | −0.297364 | + | 0.515050i | −0.975532 | − | 0.219857i | \(-0.929441\pi\) |
0.678168 | + | 0.734907i | \(0.262774\pi\) | |||||||
\(440\) | 7.51399 | 0.358216 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.81616 | −0.276646 | ||||||||
\(443\) | −4.11537 | + | 7.12802i | −0.195527 | + | 0.338663i | −0.947073 | − | 0.321018i | \(-0.895975\pi\) |
0.751546 | + | 0.659680i | \(0.229308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.1249 | + | 46.9817i | 1.28584 | + | 2.22715i | ||||
\(446\) | −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 | ||||||||
\(451\) | 3.05384 | 0.143800 | ||||||||
\(452\) | −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 | ||||||||
\(457\) | −2.53443 | + | 4.38977i | −0.118556 | + | 0.205345i | −0.919196 | − | 0.393801i | \(-0.871160\pi\) |
0.800640 | + | 0.599146i | \(0.204493\pi\) | |||||||
\(458\) | −3.59330 | −0.167904 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −68.9255 | −3.21367 | ||||||||
\(461\) | −3.88831 | + | 6.73475i | −0.181097 | + | 0.313669i | −0.942254 | − | 0.334898i | \(-0.891298\pi\) |
0.761158 | + | 0.648567i | \(0.224631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.58998 | + | 7.95008i | 0.213314 | + | 0.369472i | 0.952750 | − | 0.303756i | \(-0.0982408\pi\) |
−0.739435 | + | 0.673228i | \(0.764907\pi\) | |||||||
\(464\) | 16.5474 | + | 28.6609i | 0.768192 | + | 1.33055i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.2989 | − | 28.2306i | 0.755033 | − | 1.30776i | ||||
\(467\) | 13.7654 | 0.636989 | 0.318494 | − | 0.947925i | \(-0.396823\pi\) | ||||
0.318494 | + | 0.947925i | \(0.396823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 28.4253 | − | 49.2340i | 1.31116 | − | 2.27100i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4614 | − | 26.7800i | −0.711669 | − | 1.23265i | ||||
\(473\) | −0.472958 | − | 0.819187i | −0.0217466 | − | 0.0376663i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.27052 | − | 14.3250i | 0.379477 | − | 0.657274i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 47.7060 | 2.18202 | ||||||||
\(479\) | 4.35588 | − | 7.54461i | 0.199025 | − | 0.344722i | −0.749187 | − | 0.662358i | \(-0.769556\pi\) |
0.948213 | + | 0.317636i | \(0.102889\pi\) | |||||||
\(480\) | 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 | ||||
\(485\) | −34.7060 | −1.57592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.0364 | −0.817306 | −0.408653 | − | 0.912690i | \(-0.634001\pi\) | ||||
−0.408653 | + | 0.912690i | \(0.634001\pi\) | |||||||
\(488\) | −20.2849 | + | 35.1344i | −0.918253 | + | 1.59046i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02344 | + | 1.77266i | 0.0461874 | + | 0.0799989i | 0.888195 | − | 0.459467i | \(-0.151960\pi\) |
−0.842007 | + | 0.539466i | \(0.818626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.5679 | + | 32.1606i | −0.836257 | + | 1.44844i | ||||
\(494\) | −2.36381 | −0.106353 | ||||||||
\(495\) | 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 | \(0.494261\pi\) | |||||||
\(500\) | −25.0742 | − | 43.4297i | −1.12135 | − | 1.94224i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.5679 | − | 32.1606i | 0.828727 | − | 1.43540i | ||||
\(503\) | −5.11846 | −0.228221 | −0.114111 | − | 0.993468i | \(-0.536402\pi\) | ||||
−0.114111 | + | 0.993468i | \(0.536402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8683 | −1.41812 | ||||||||
\(506\) | 2.32383 | − | 4.02499i | 0.103307 | − | 0.178933i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 31.5079 | + | 54.5732i | 1.39794 | + | 2.42130i | ||||
\(509\) | −14.7636 | − | 25.5713i | −0.654386 | − | 1.13343i | −0.982047 | − | 0.188634i | \(-0.939594\pi\) |
0.327662 | − | 0.944795i | \(-0.393739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 41.4078 | 1.82998 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.9750 | −0.836952 | ||||||||
\(515\) | −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 | ||||||||
\(520\) | −4.50000 | + | 7.79423i | −0.197338 | + | 0.341800i | ||||
\(521\) | −1.06470 | −0.0466454 | −0.0233227 | − | 0.999728i | \(-0.507425\pi\) | ||||
−0.0233227 | + | 0.999728i | \(0.507425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3819 | 0.585149 | 0.292574 | − | 0.956243i | \(-0.405488\pi\) | ||||
0.292574 | + | 0.956243i | \(0.405488\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −32.1206 | −1.39523 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.82889 | + | 3.16774i | −0.0792181 | + | 0.137210i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.4885 | + | 40.6833i | 1.01550 | + | 1.75889i | ||||
\(536\) | 9.09931 | + | 15.7605i | 0.393031 | + | 0.680749i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.5286 | − | 44.2168i | 1.10062 | − | 1.90632i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0875 | −1.46554 | −0.732769 | − | 0.680478i | \(-0.761772\pi\) | ||||
−0.732769 | + | 0.680478i | \(0.761772\pi\) | |||||||
\(542\) | 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 | −0.795481 | − | 0.605978i | \(-0.792782\pi\) |
0.922533 | + | 0.385918i | \(0.126115\pi\) | |||||||
\(548\) | −1.52937 | −0.0653316 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.38151 | 0.357389 | ||||||||
\(551\) | −7.54638 | + | 13.0707i | −0.321487 | + | 0.556831i | ||||
\(552\) | 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 | ||||
\(557\) | 30.0803 | 1.27454 | 0.637272 | − | 0.770639i | \(-0.280063\pi\) | ||||
0.637272 | + | 0.770639i | \(0.280063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.13298 | 0.0479202 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.6170 | − | 20.1213i | −0.490035 | − | 0.848765i | ||||
\(563\) | 9.81060 | + | 16.9925i | 0.413468 | + | 0.716147i | 0.995266 | − | 0.0971860i | \(-0.0309842\pi\) |
−0.581799 | + | 0.813333i | \(0.697651\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.5154 | + | 44.1940i | −1.07344 | + | 1.85926i | ||||
\(566\) | 41.5049 | 1.74458 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.7601 | 1.79417 | ||||||||
\(569\) | −0.687159 | + | 1.19019i | −0.0288072 | + | 0.0498955i | −0.880070 | − | 0.474845i | \(-0.842504\pi\) |
0.851262 | + | 0.524740i | \(0.175838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.69076 | − | 15.0528i | −0.363697 | − | 0.629941i | 0.624869 | − | 0.780729i | \(-0.285152\pi\) |
−0.988566 | + | 0.150788i | \(0.951819\pi\) | |||||||
\(572\) | −0.401038 | − | 0.694619i | −0.0167683 | − | 0.0290435i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.9545 | −1.62451 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0548 | 1.12631 | 0.563153 | − | 0.826353i | \(-0.309588\pi\) | ||||
0.563153 | + | 0.826353i | \(0.309588\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 0.725191 | − | 1.25607i | 0.0300344 | − | 0.0520210i | ||||
\(584\) | −9.97430 | −0.412740 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.16010 | 0.378400 | ||||||||
\(587\) | −3.75700 | + | 6.50731i | −0.155068 | + | 0.268585i | −0.933084 | − | 0.359659i | \(-0.882893\pi\) |
0.778016 | + | 0.628245i | \(0.216226\pi\) | |||||||
\(588\) | 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 | ||||
\(593\) | 35.5808 | 1.46113 | 0.730565 | − | 0.682843i | \(-0.239257\pi\) | ||||
0.730565 | + | 0.682843i | \(0.239257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.6659 | + | 34.0623i | −0.805545 | + | 1.39524i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.78340 | + | 4.82100i | 0.113822 | + | 0.197145i | ||||
\(599\) | −5.74105 | − | 9.94379i | −0.234573 | − | 0.406292i | 0.724576 | − | 0.689195i | \(-0.242036\pi\) |
−0.959148 | + | 0.282903i | \(0.908702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.190030 | + | 0.329142i | −0.00775150 | + | 0.0134260i | −0.869875 | − | 0.493272i | \(-0.835801\pi\) |
0.862124 | + | 0.506698i | \(0.169134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −52.0335 | −2.11721 | ||||||||
\(605\) | 19.8173 | − | 34.3246i | 0.805688 | − | 1.39549i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.27044 | − | 16.0569i | −0.376275 | − | 0.651728i | 0.614242 | − | 0.789118i | \(-0.289462\pi\) |
−0.990517 | + | 0.137390i | \(0.956129\pi\) | |||||||
\(608\) | −0.532351 | − | 0.922058i | −0.0215897 | − | 0.0373944i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.1249 | + | 62.5702i | −1.46265 | + | 2.53339i | ||||
\(611\) | −3.07472 | −0.124390 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.32451 | 0.295834 | 0.147917 | − | 0.989000i | \(-0.452743\pi\) | ||||
0.147917 | + | 0.989000i | \(0.452743\pi\) | |||||||
\(614\) | −37.6077 | + | 65.1385i | −1.51772 | + | 2.62877i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.7427 | − | 22.0710i | −0.513002 | − | 0.888546i | −0.999886 | − | 0.0150791i | \(-0.995200\pi\) |
0.486884 | − | 0.873466i | \(-0.338133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4482 | − | 28.4891i | 0.661108 | − | 1.14507i | −0.319217 | − | 0.947682i | \(-0.603420\pi\) |
0.980325 | − | 0.197391i | \(-0.0632468\pi\) | |||||||
\(620\) | 104.214 | 4.18535 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.6748 | 1.02947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.67111 | − | 2.89444i | −0.0668443 | − | 0.115778i | ||||
\(626\) | 0.762585 | + | 1.32084i | 0.0304790 | + | 0.0527912i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42.4636 | + | 73.5490i | −1.69448 | + | 2.93493i | ||||
\(629\) | −11.3016 | −0.450626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8683 | 1.18904 | 0.594519 | − | 0.804082i | \(-0.297343\pi\) | ||||
0.594519 | + | 0.804082i | \(0.297343\pi\) | |||||||
\(632\) | 20.6264 | − | 35.7259i | 0.820472 | − | 1.42110i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.6082 | − | 21.8380i | −0.500734 | − | 0.867297i | ||||
\(635\) | 28.4301 | + | 49.2424i | 1.12822 | + | 1.95413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.64766 | −0.302774 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 69.8991 | 2.76301 | ||||||||
\(641\) | 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 | \(-0.278019\pi\) |
−0.984939 | + | 0.172903i | \(0.944685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.7896 | − | 20.4202i | 0.463855 | − | 0.803421i | ||||
\(647\) | 25.3439 | 0.996372 | 0.498186 | − | 0.867070i | \(-0.334000\pi\) | ||||
0.498186 | + | 0.867070i | \(0.334000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.48664 | 0.0976091 | ||||||||
\(650\) | −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 | ||||
\(656\) | −32.5163 | −1.26955 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0854 | − | 33.0569i | 0.743462 | − | 1.28771i | −0.207449 | − | 0.978246i | \(-0.566516\pi\) |
0.950910 | − | 0.309467i | \(-0.100151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.176866 | − | 0.306341i | −0.00687930 | − | 0.0119153i | 0.862565 | − | 0.505946i | \(-0.168856\pi\) |
−0.869445 | + | 0.494031i | \(0.835523\pi\) | |||||||
\(662\) | −25.0526 | − | 43.3924i | −0.973698 | − | 1.68649i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.7591 | + | 53.2764i | −1.19369 | + | 2.06752i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.5438 | 1.37626 | ||||||||
\(668\) | 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 | −0.587653 | − | 0.809113i | \(-0.699948\pi\) |
0.994539 | + | 0.104365i | \(0.0332811\pi\) | |||||||
\(674\) | 14.0541 | 0.541343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.7424 | −1.99009 | ||||||||
\(677\) | −10.5732 | + | 18.3133i | −0.406361 | + | 0.703837i | −0.994479 | − | 0.104938i | \(-0.966536\pi\) |
0.588118 | + | 0.808775i | \(0.299869\pi\) | |||||||
\(678\) | 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 | ||||
\(683\) | −34.7716 | −1.33050 | −0.665249 | − | 0.746622i | \(-0.731674\pi\) | ||||
−0.665249 | + | 0.746622i | \(0.731674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.37998 | −0.0527264 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.03590 | + | 8.72243i | 0.191992 | + | 0.332539i | ||||
\(689\) | 0.868609 | + | 1.50447i | 0.0330914 | + | 0.0573159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3246 | − | 30.0071i | 0.659059 | − | 1.14152i | −0.321801 | − | 0.946807i | \(-0.604288\pi\) |
0.980860 | − | 0.194716i | \(-0.0623785\pi\) | |||||||
\(692\) | 24.5418 | 0.932940 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.8525 | 0.829511 | ||||||||
\(695\) | 34.7542 | − | 60.1960i | 1.31830 | − | 2.28336i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.2434 | − | 31.5985i | −0.691017 | − | 1.19688i | ||||
\(698\) | 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 | ||||||||
\(703\) | −4.59322 | −0.173236 | ||||||||
\(704\) | −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 | ||||||||
\(709\) | −2.05408 | + | 3.55778i | −0.0771428 | + | 0.133615i | −0.902016 | − | 0.431702i | \(-0.857913\pi\) |
0.824873 | + | 0.565318i | \(0.191246\pi\) | |||||||
\(710\) | 76.1506 | 2.85788 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 74.9528 | 2.80898 | ||||||||
\(713\) | 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 | ||||
\(719\) | 48.2816 | 1.80060 | 0.900299 | − | 0.435271i | \(-0.143347\pi\) | ||||
0.900299 | + | 0.435271i | \(0.143347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.5833 | + | 32.1872i | −0.691597 | + | 1.19788i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.2187 | − | 41.9481i | −0.900082 | − | 1.55899i | ||||
\(725\) | 32.0495 | + | 55.5114i | 1.19029 | + | 2.06164i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5151 | + | 35.5332i | −0.760863 | + | 1.31785i | 0.181543 | + | 0.983383i | \(0.441891\pi\) |
−0.942406 | + | 0.334470i | \(0.891443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7630 | −0.657439 | ||||||||
\(731\) | −5.65082 | + | 9.78750i | −0.209003 | + | 0.362004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.2714 | + | 26.4508i | 0.564062 | + | 0.976983i | 0.997136 | + | 0.0756253i | \(0.0240953\pi\) |
−0.433075 | + | 0.901358i | \(0.642571\pi\) | |||||||
\(734\) | −13.5011 | − | 23.3845i | −0.498334 | − | 0.863139i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.25370 | + | 2.17147i | −0.0462118 | + | 0.0800413i | ||||
\(737\) | −1.46343 | −0.0539061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8200 | 0.876234 | 0.438117 | − | 0.898918i | \(-0.355646\pi\) | ||||
0.438117 | + | 0.898918i | \(0.355646\pi\) | |||||||
\(740\) | −17.2581 | + | 29.8918i | −0.634419 | + | 1.09885i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.26089 | + | 9.11213i | 0.193003 | + | 0.334292i | 0.946244 | − | 0.323453i | \(-0.104844\pi\) |
−0.753241 | + | 0.657745i | \(0.771510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.7449 | + | 30.7350i | −0.650121 | + | 1.12604i | ||||
\(746\) | 1.33794 | 0.0489855 | ||||||||
\(747\) | 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 | \(0.773332\pi\) | |||||||
\(752\) | −13.6665 | − | 23.6711i | −0.498367 | − | 0.863197i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.58005 | − | 7.93288i | 0.166796 | − | 0.288899i | ||||
\(755\) | −46.9507 | −1.70871 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.03930 | 0.292193 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(758\) | −27.9159 | + | 48.3518i | −1.01395 | + | 1.75622i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.2434 | − | 31.5985i | −0.661757 | − | 1.14620i | ||||
\(761\) | −13.8302 | − | 23.9547i | −0.501345 | − | 0.868355i | −0.999999 | − | 0.00155404i | \(-0.999505\pi\) |
0.498654 | − | 0.866801i | \(-0.333828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −37.0554 | −1.34062 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 87.8742 | 3.17502 | ||||||||
\(767\) | −1.48920 | + | 2.57938i | −0.0537720 | + | 0.0931359i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9613 | − | 29.3778i | −0.611640 | − | 1.05939i | −0.990964 | − | 0.134128i | \(-0.957177\pi\) |
0.379324 | − | 0.925264i | \(-0.376157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −34.3442 | + | 59.4858i | −1.23607 | + | 2.14094i | ||||
\(773\) | −28.5956 | −1.02851 | −0.514256 | − | 0.857637i | \(-0.671932\pi\) | ||||
−0.514256 | + | 0.857637i | \(0.671932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58.8986 | 2.11570 | ||||||||
\(776\) | −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 | ||||
\(782\) | −55.5294 | −1.98573 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.3157 | + | 66.3647i | −1.36754 | + | 2.36866i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0017 | + | 39.8402i | 0.819923 | + | 1.42015i | 0.905738 | + | 0.423838i | \(0.139317\pi\) |
−0.0858145 | + | 0.996311i | \(0.527349\pi\) | |||||||
\(788\) | −43.2111 | − | 74.8438i | −1.53933 | − | 2.66620i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 36.7330 | − | 63.6235i | 1.30690 | − | 2.26362i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.90757 | 0.138762 | ||||||||
\(794\) | −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 | 0.982208 | + | 0.187795i | \(0.0601339\pi\) |
−0.328469 | + | 0.944515i | \(0.606533\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3353 | − | 26.5615i | 0.542524 | − | 0.939679i | ||||
\(800\) | −4.52179 | −0.159869 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 79.6136 | 2.81125 | ||||||||
\(803\) | 0.401038 | − | 0.694619i | 0.0141523 | − | 0.0245126i | ||||
\(804\) | 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 | ||||
\(809\) | −47.6887 | −1.67665 | −0.838323 | − | 0.545174i | \(-0.816463\pi\) | ||||
−0.838323 | + | 0.545174i | \(0.816463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.02728 | 0.211646 | 0.105823 | − | 0.994385i | \(-0.466252\pi\) | ||||
0.105823 | + | 0.994385i | \(0.466252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.16372 | − | 2.01561i | −0.0407882 | − | 0.0706472i | ||||
\(815\) | 20.4162 | + | 35.3619i | 0.715148 | + | 1.23867i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.29661 | + | 3.97784i | −0.0803481 | + | 0.139167i | ||||
\(818\) | −46.6881 | −1.63241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.434 | −3.89143 | ||||||||
\(821\) | −19.6321 | + | 34.0038i | −0.685165 | + | 1.18674i | 0.288220 | + | 0.957564i | \(0.406936\pi\) |
−0.973385 | + | 0.229176i | \(0.926397\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3815 | − | 19.7134i | −0.396735 | − | 0.687165i | 0.596586 | − | 0.802549i | \(-0.296523\pi\) |
−0.993321 | + | 0.115384i | \(0.963190\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | −33.9767 | −1.18006 | −0.590029 | − | 0.807382i | \(-0.700884\pi\) | ||||
−0.590029 | + | 0.807382i | \(0.700884\pi\) | |||||||
\(830\) | −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 | ||||||||
\(835\) | 6.32889 | − | 10.9620i | 0.219020 | − | 0.379354i | ||||
\(836\) | 3.25169 | 0.112462 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −42.5432 | −1.46963 | ||||||||
\(839\) | 19.0206 | − | 32.9446i | 0.656663 | − | 1.13737i | −0.324811 | − | 0.945779i | \(-0.605301\pi\) |
0.981474 | − | 0.191595i | \(-0.0613659\pi\) | |||||||
\(840\) | 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 | ||||
\(845\) | −46.6881 | −1.60612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.72159 | + | 13.3742i | −0.265161 | + | 0.459272i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −50.0704 | − | 86.7245i | −1.71740 | − | 2.97463i | ||||
\(851\) | 5.40856 | + | 9.36790i | 0.185403 | + | 0.321127i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.90746 | + | 8.49996i | −0.168028 | + | 0.291033i | −0.937726 | − | 0.347374i | \(-0.887073\pi\) |
0.769698 | + | 0.638408i | \(0.220407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 64.9046 | 2.21840 | ||||||||
\(857\) | 13.3680 | − | 23.1541i | 0.456642 | − | 0.790928i | −0.542139 | − | 0.840289i | \(-0.682385\pi\) |
0.998781 | + | 0.0493613i | \(0.0157186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.24411 | + | 16.0113i | 0.315405 | + | 0.546297i | 0.979523 | − | 0.201330i | \(-0.0645263\pi\) |
−0.664119 | + | 0.747627i | \(0.731193\pi\) | |||||||
\(860\) | 17.2581 | + | 29.8918i | 0.588495 | + | 1.01930i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5344 | − | 33.8346i | 0.665345 | − | 1.15241i | ||||
\(863\) | 9.14786 | 0.311397 | 0.155698 | − | 0.987805i | \(-0.450237\pi\) | ||||
0.155698 | + | 0.987805i | \(0.450237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1445 | 0.752937 | ||||||||
\(866\) | 49.7473 | − | 86.1649i | 1.69048 | − | 2.92800i | ||||
\(867\) | 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 | ||||
\(872\) | −13.1445 | −0.445130 | ||||||||
\(873\) | 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 | \(0.958465\pi\) | |||||||
\(878\) | 15.3301 | + | 26.5525i | 0.517366 | + | 0.896104i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.21683 | − | 5.57172i | 0.108439 | − | 0.187823i | ||||
\(881\) | −15.3696 | −0.517815 | −0.258907 | − | 0.965902i | \(-0.583362\pi\) | ||||
−0.258907 | + | 0.965902i | \(0.583362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6372 | 0.997370 | 0.498685 | − | 0.866783i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333817\pi\) | |||||||
\(884\) | −4.79153 | + | 8.29918i | −0.161157 | + | 0.279132i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.1259 | + | 17.5385i | 0.340185 | + | 0.589219i | ||||
\(887\) | −9.38252 | − | 16.2510i | −0.315034 | − | 0.545655i | 0.664410 | − | 0.747368i | \(-0.268683\pi\) |
−0.979445 | + | 0.201712i | \(0.935349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 133.482 | 4.47432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −94.9014 | −3.17753 | ||||||||
\(893\) | 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 | ||||||||
\(898\) | −6.94445 | + | 12.0281i | −0.231739 | + | 0.401384i | ||||
\(899\) | −53.7416 | −1.79238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.3289 | −0.577310 | ||||||||
\(902\) | 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 | \(-0.00608567\pi\) | |||||||
\(908\) | 24.8045 | 0.823165 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.73764 | − | 15.1340i | 0.289491 | − | 0.501413i | −0.684197 | − | 0.729297i | \(-0.739847\pi\) |
0.973688 | + | 0.227884i | \(0.0731806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.47347 | − | 4.28418i | −0.0818600 | − | 0.141786i | ||||
\(914\) | 6.23599 | + | 10.8010i | 0.206268 | + | 0.357267i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.96027 | + | 5.12734i | −0.0978101 | + | 0.169412i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1986 | 1.39200 | 0.696002 | − | 0.718040i | \(-0.254960\pi\) | ||||
0.696002 | + | 0.718040i | \(0.254960\pi\) | |||||||
\(920\) | −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 | ||||
\(926\) | 22.5873 | 0.742266 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.12588 | 0.135439 | ||||||||
\(929\) | 24.2056 | − | 41.9253i | 0.794159 | − | 1.37552i | −0.129213 | − | 0.991617i | \(-0.541245\pi\) |
0.923372 | − | 0.383907i | \(-0.125422\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | 7.21926 | 0.236095 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6750 | −0.740762 | −0.370381 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370381 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −46.8353 | − | 81.1211i | −1.52760 | − | 2.64588i | ||||
\(941\) | −24.9753 | − | 43.2584i | −0.814170 | − | 1.41018i | −0.909922 | − | 0.414779i | \(-0.863859\pi\) |
0.0957523 | − | 0.995405i | \(-0.469474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.4613 | + | 30.2438i | −0.568617 | + | 0.984873i | ||||
\(944\) | −26.4769 | −0.861749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.32743 | −0.0756713 | ||||||||
\(947\) | 8.85613 | − | 15.3393i | 0.287786 | − | 0.498459i | −0.685495 | − | 0.728077i | \(-0.740414\pi\) |
0.973281 | + | 0.229618i | \(0.0737476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.480350 | + | 0.831990i | 0.0155928 | + | 0.0270075i | ||||
\(950\) | −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 | ||||||||
\(955\) | −33.4358 | −1.08196 | ||||||||
\(956\) | 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 | ||||||||
\(961\) | −9.19076 | + | 15.9189i | −0.296476 | + | 0.513512i | ||||
\(962\) | 2.78771 | 0.0898795 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.4881 | −0.659876 | ||||||||
\(965\) | −30.9894 | + | 53.6752i | −0.997583 | + | 1.72786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5064 | + | 26.8579i | 0.498652 | + | 0.863691i | 0.999999 | − | 0.00155529i | \(-0.000495066\pi\) |
−0.501346 | + | 0.865247i | \(0.667162\pi\) | |||||||
\(968\) | −27.3801 | − | 47.4236i | −0.880028 | − | 1.52425i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −42.6972 | + | 73.9537i | −1.37092 | + | 2.37451i | ||||
\(971\) | 14.5675 | 0.467494 | 0.233747 | − | 0.972297i | \(-0.424901\pi\) | ||||
0.233747 | + | 0.972297i | \(0.424901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.1893 | + | 38.4330i | −0.710991 | + | 1.23147i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17.3684 | + | 30.0830i | 0.555949 | + | 0.962932i | ||||
\(977\) | −23.9399 | − | 41.4651i | −0.765904 | − | 1.32659i | −0.939767 | − | 0.341815i | \(-0.888958\pi\) |
0.173863 | − | 0.984770i | \(-0.444375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.01364 | + | 5.21978i | −0.0963163 | + | 0.166825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.03638 | 0.160717 | ||||||||
\(983\) | −22.2128 | + | 38.4737i | −0.708479 | + | 1.22712i | 0.256942 | + | 0.966427i | \(0.417285\pi\) |
−0.965421 | + | 0.260695i | \(0.916048\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | 10.8171 | 0.343964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6156 | −1.32196 | −0.660981 | − | 0.750403i | \(-0.729860\pi\) | ||||
−0.660981 | + | 0.750403i | \(0.729860\pi\) | |||||||
\(992\) | 1.89557 | − | 3.28322i | 0.0601844 | − | 0.104242i | ||||
\(993\) | 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 | −0.950547 | − | 0.310581i | \(-0.899477\pi\) |
0.744244 | + | 0.667908i | \(0.232810\pi\) | |||||||
\(998\) | 96.1751 | 3.04437 | ||||||||
\(999\) | 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.f.g.883.5 | 12 | ||
3.2 | odd | 2 | 441.2.f.g.295.2 | yes | 12 | ||
7.2 | even | 3 | 1323.2.h.g.802.1 | 12 | |||
7.3 | odd | 6 | 1323.2.g.g.667.5 | 12 | |||
7.4 | even | 3 | 1323.2.g.g.667.6 | 12 | |||
7.5 | odd | 6 | 1323.2.h.g.802.2 | 12 | |||
7.6 | odd | 2 | inner | 1323.2.f.g.883.6 | 12 | ||
9.2 | odd | 6 | 3969.2.a.be.1.5 | 6 | |||
9.4 | even | 3 | inner | 1323.2.f.g.442.5 | 12 | ||
9.5 | odd | 6 | 441.2.f.g.148.2 | yes | 12 | ||
9.7 | even | 3 | 3969.2.a.bd.1.2 | 6 | |||
21.2 | odd | 6 | 441.2.h.g.214.5 | 12 | |||
21.5 | even | 6 | 441.2.h.g.214.6 | 12 | |||
21.11 | odd | 6 | 441.2.g.g.79.1 | 12 | |||
21.17 | even | 6 | 441.2.g.g.79.2 | 12 | |||
21.20 | even | 2 | 441.2.f.g.295.1 | yes | 12 | ||
63.4 | even | 3 | 1323.2.h.g.226.1 | 12 | |||
63.5 | even | 6 | 441.2.g.g.67.2 | 12 | |||
63.13 | odd | 6 | inner | 1323.2.f.g.442.6 | 12 | ||
63.20 | even | 6 | 3969.2.a.be.1.6 | 6 | |||
63.23 | odd | 6 | 441.2.g.g.67.1 | 12 | |||
63.31 | odd | 6 | 1323.2.h.g.226.2 | 12 | |||
63.32 | odd | 6 | 441.2.h.g.373.5 | 12 | |||
63.34 | odd | 6 | 3969.2.a.bd.1.1 | 6 | |||
63.40 | odd | 6 | 1323.2.g.g.361.5 | 12 | |||
63.41 | even | 6 | 441.2.f.g.148.1 | ✓ | 12 | ||
63.58 | even | 3 | 1323.2.g.g.361.6 | 12 | |||
63.59 | even | 6 | 441.2.h.g.373.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.g.148.1 | ✓ | 12 | 63.41 | even | 6 | ||
441.2.f.g.148.2 | yes | 12 | 9.5 | odd | 6 | ||
441.2.f.g.295.1 | yes | 12 | 21.20 | even | 2 | ||
441.2.f.g.295.2 | yes | 12 | 3.2 | odd | 2 | ||
441.2.g.g.67.1 | 12 | 63.23 | odd | 6 | |||
441.2.g.g.67.2 | 12 | 63.5 | even | 6 | |||
441.2.g.g.79.1 | 12 | 21.11 | odd | 6 | |||
441.2.g.g.79.2 | 12 | 21.17 | even | 6 | |||
441.2.h.g.214.5 | 12 | 21.2 | odd | 6 | |||
441.2.h.g.214.6 | 12 | 21.5 | even | 6 | |||
441.2.h.g.373.5 | 12 | 63.32 | odd | 6 | |||
441.2.h.g.373.6 | 12 | 63.59 | even | 6 | |||
1323.2.f.g.442.5 | 12 | 9.4 | even | 3 | inner | ||
1323.2.f.g.442.6 | 12 | 63.13 | odd | 6 | inner | ||
1323.2.f.g.883.5 | 12 | 1.1 | even | 1 | trivial | ||
1323.2.f.g.883.6 | 12 | 7.6 | odd | 2 | inner | ||
1323.2.g.g.361.5 | 12 | 63.40 | odd | 6 | |||
1323.2.g.g.361.6 | 12 | 63.58 | even | 3 | |||
1323.2.g.g.667.5 | 12 | 7.3 | odd | 6 | |||
1323.2.g.g.667.6 | 12 | 7.4 | even | 3 | |||
1323.2.h.g.226.1 | 12 | 63.4 | even | 3 | |||
1323.2.h.g.226.2 | 12 | 63.31 | odd | 6 | |||
1323.2.h.g.802.1 | 12 | 7.2 | even | 3 | |||
1323.2.h.g.802.2 | 12 | 7.5 | odd | 6 | |||
3969.2.a.bd.1.1 | 6 | 63.34 | odd | 6 | |||
3969.2.a.bd.1.2 | 6 | 9.7 | even | 3 | |||
3969.2.a.be.1.5 | 6 | 9.2 | odd | 6 | |||
3969.2.a.be.1.6 | 6 | 63.20 | even | 6 |