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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 442.2 | ||
Character | \(\chi\) | \(=\) | 1323.442 |
Dual form | 1323.2.f.h.883.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35757 | − | 2.35137i | −0.959944 | − | 1.66267i | −0.722624 | − | 0.691241i | \(-0.757064\pi\) |
−0.237320 | − | 0.971432i | \(-0.576269\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.68597 | + | 4.65224i | −1.34299 | + | 2.32612i | ||||
\(5\) | −0.793197 | + | 1.37386i | −0.354728 | + | 0.614407i | −0.987071 | − | 0.160281i | \(-0.948760\pi\) |
0.632343 | + | 0.774688i | \(0.282093\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.15528 | 3.23688 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.30727 | 1.36208 | ||||||||
\(11\) | −0.674376 | − | 1.16805i | −0.203332 | − | 0.352181i | 0.746268 | − | 0.665646i | \(-0.231844\pi\) |
−0.949600 | + | 0.313464i | \(0.898510\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58916 | − | 2.75251i | 0.440754 | − | 0.763409i | −0.556991 | − | 0.830518i | \(-0.688044\pi\) |
0.997746 | + | 0.0671096i | \(0.0213777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.05696 | − | 12.2230i | −1.76424 | − | 3.05575i | ||||
\(17\) | −2.80054 | −0.679230 | −0.339615 | − | 0.940565i | \(-0.610297\pi\) | ||||
−0.339615 | + | 0.940565i | \(0.610297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.625693 | 0.143544 | 0.0717719 | − | 0.997421i | \(-0.477135\pi\) | ||||
0.0717719 | + | 0.997421i | \(0.477135\pi\) | |||||||
\(20\) | −4.26101 | − | 7.38028i | −0.952791 | − | 1.65028i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.83102 | + | 3.17142i | −0.390375 | + | 0.676149i | ||||
\(23\) | −0.142434 | + | 0.246702i | −0.0296995 | + | 0.0514410i | −0.880493 | − | 0.474059i | \(-0.842788\pi\) |
0.850794 | + | 0.525500i | \(0.176122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24168 | + | 2.15065i | 0.248336 | + | 0.430130i | ||||
\(26\) | −8.62957 | −1.69240 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27396 | − | 3.93861i | −0.422264 | − | 0.731382i | 0.573897 | − | 0.818928i | \(-0.305431\pi\) |
−0.996161 | + | 0.0875454i | \(0.972098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.71502 | + | 6.43461i | −0.667238 | + | 1.15569i | 0.311435 | + | 0.950267i | \(0.399190\pi\) |
−0.978673 | + | 0.205423i | \(0.934143\pi\) | |||||||
\(32\) | −10.0053 | + | 17.3297i | −1.76870 | + | 3.06348i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.80191 | + | 6.58511i | 0.652023 | + | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.02252 | 1.31889 | 0.659447 | − | 0.751751i | \(-0.270791\pi\) | ||||
0.659447 | + | 0.751751i | \(0.270791\pi\) | |||||||
\(38\) | −0.849420 | − | 1.47124i | −0.137794 | − | 0.238666i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.26194 | + | 12.5780i | −1.14821 | + | 1.98876i | ||||
\(41\) | −5.01329 | + | 8.68327i | −0.782944 | + | 1.35610i | 0.147275 | + | 0.989096i | \(0.452950\pi\) |
−0.930219 | + | 0.367004i | \(0.880384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | − | 5.42022i | −0.477224 | − | 0.826576i | 0.522435 | − | 0.852679i | \(-0.325024\pi\) |
−0.999659 | + | 0.0261027i | \(0.991690\pi\) | |||||||
\(44\) | 7.24542 | 1.09229 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.773452 | 0.114039 | ||||||||
\(47\) | 5.57383 | + | 9.65415i | 0.813026 | + | 1.40820i | 0.910737 | + | 0.412988i | \(0.135515\pi\) |
−0.0977106 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.37132 | − | 5.83930i | 0.476777 | − | 0.825802i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.53689 | + | 14.7863i | 1.18385 | + | 2.05049i | ||||
\(53\) | −2.78698 | −0.382821 | −0.191410 | − | 0.981510i | \(-0.561306\pi\) | ||||
−0.191410 | + | 0.981510i | \(0.561306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13965 | 0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.17410 | + | 10.6939i | −0.810699 | + | 1.40417i | ||||
\(59\) | 2.28734 | − | 3.96180i | 0.297787 | − | 0.515782i | −0.677842 | − | 0.735207i | \(-0.737085\pi\) |
0.975629 | + | 0.219425i | \(0.0704182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.192507 | + | 0.333432i | 0.0246480 | + | 0.0426916i | 0.878086 | − | 0.478502i | \(-0.158820\pi\) |
−0.853438 | + | 0.521194i | \(0.825487\pi\) | |||||||
\(62\) | 20.1736 | 2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | 2.52104 | + | 4.36656i | 0.312696 | + | 0.541605i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.26958 | − | 2.19898i | 0.155104 | − | 0.268648i | −0.777993 | − | 0.628273i | \(-0.783762\pi\) |
0.933097 | + | 0.359625i | \(0.117095\pi\) | |||||||
\(68\) | 7.52217 | − | 13.0288i | 0.912197 | − | 1.57997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.45208 | 0.172330 | 0.0861651 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861651 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.468134 | −0.0547909 | −0.0273955 | − | 0.999625i | \(-0.508721\pi\) | ||||
−0.0273955 | + | 0.999625i | \(0.508721\pi\) | |||||||
\(74\) | −10.8911 | − | 18.8639i | −1.26606 | − | 2.19289i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.68059 | + | 2.91087i | −0.192777 | + | 0.333900i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.85620 | + | 13.6073i | 0.883892 | + | 1.53095i | 0.846978 | + | 0.531627i | \(0.178419\pi\) |
0.0369135 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(80\) | 22.3902 | 2.50330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 27.2235 | 3.00633 | ||||||||
\(83\) | 6.99338 | + | 12.1129i | 0.767623 | + | 1.32956i | 0.938848 | + | 0.344331i | \(0.111894\pi\) |
−0.171225 | + | 0.985232i | \(0.554772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22138 | − | 3.84754i | 0.240942 | − | 0.417324i | ||||
\(86\) | −8.49665 | + | 14.7166i | −0.916217 | + | 1.58693i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.17410 | − | 10.6939i | −0.658162 | − | 1.13997i | ||||
\(89\) | 2.58706 | 0.274228 | 0.137114 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137114 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.765146 | − | 1.32527i | −0.0797719 | − | 0.138169i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.1337 | − | 26.2123i | 1.56092 | − | 2.70359i | ||||
\(95\) | −0.496297 | + | 0.859612i | −0.0509190 | + | 0.0881944i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.22962 | + | 12.5221i | 0.734057 | + | 1.27142i | 0.955136 | + | 0.296168i | \(0.0957089\pi\) |
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3405 | −1.33405 | ||||||||
\(101\) | 4.91888 | + | 8.51975i | 0.489447 | + | 0.847747i | 0.999926 | − | 0.0121430i | \(-0.00386534\pi\) |
−0.510479 | + | 0.859890i | \(0.670532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.52897 | + | 9.57646i | −0.544786 | + | 0.943597i | 0.453834 | + | 0.891086i | \(0.350056\pi\) |
−0.998620 | + | 0.0525110i | \(0.983278\pi\) | |||||||
\(104\) | 14.5492 | − | 25.2000i | 1.42667 | − | 2.47106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.78350 | + | 6.55322i | 0.367486 | + | 0.636505i | ||||
\(107\) | 1.92431 | 0.186030 | 0.0930149 | − | 0.995665i | \(-0.470350\pi\) | ||||
0.0930149 | + | 0.995665i | \(0.470350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6068 | −1.78221 | −0.891105 | − | 0.453797i | \(-0.850069\pi\) | ||||
−0.891105 | + | 0.453797i | \(0.850069\pi\) | |||||||
\(110\) | −2.90472 | − | 5.03112i | −0.276954 | − | 0.479698i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.59338 | + | 2.75982i | −0.149893 | + | 0.259622i | −0.931188 | − | 0.364540i | \(-0.881226\pi\) |
0.781295 | + | 0.624162i | \(0.214560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.225956 | − | 0.391367i | −0.0210705 | − | 0.0364951i | ||||
\(116\) | 24.4312 | 2.26838 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4209 | −1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.59043 | − | 7.95086i | 0.417312 | − | 0.722806i | ||||
\(122\) | 0.522682 | − | 0.905312i | 0.0473214 | − | 0.0819631i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −19.9569 | − | 34.5664i | −1.79218 | − | 3.10415i | ||||
\(125\) | −11.8715 | −1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | −15.4267 | − | 26.7199i | −1.36354 | − | 2.36173i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.84495 | − | 11.8558i | 0.600341 | − | 1.03982i | ||||
\(131\) | −5.98629 | + | 10.3686i | −0.523024 | + | 0.905905i | 0.476616 | + | 0.879111i | \(0.341863\pi\) |
−0.999641 | + | 0.0267937i | \(0.991470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.89415 | −0.595564 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −25.6397 | −2.19859 | ||||||||
\(137\) | 8.27525 | + | 14.3332i | 0.707003 | + | 1.22456i | 0.965964 | + | 0.258677i | \(0.0832865\pi\) |
−0.258961 | + | 0.965888i | \(0.583380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.95119 | − | 6.84367i | 0.335136 | − | 0.580472i | −0.648375 | − | 0.761321i | \(-0.724551\pi\) |
0.983511 | + | 0.180849i | \(0.0578845\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.97130 | − | 3.41438i | −0.165427 | − | 0.286529i | ||||
\(143\) | −4.28677 | −0.358478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.21479 | 0.599156 | ||||||||
\(146\) | 0.635523 | + | 1.10076i | 0.0525962 | + | 0.0910994i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −21.5483 | + | 37.3227i | −1.77126 | + | 3.06791i | ||||
\(149\) | −6.83427 | + | 11.8373i | −0.559885 | + | 0.969749i | 0.437620 | + | 0.899160i | \(0.355821\pi\) |
−0.997505 | + | 0.0705895i | \(0.977512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.94982 | − | 3.37718i | −0.158674 | − | 0.274831i | 0.775717 | − | 0.631081i | \(-0.217389\pi\) |
−0.934391 | + | 0.356250i | \(0.884055\pi\) | |||||||
\(152\) | 5.72839 | 0.464634 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.89349 | − | 10.2078i | −0.473376 | − | 0.819912i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.147176 | − | 0.254917i | 0.0117459 | − | 0.0203446i | −0.860093 | − | 0.510138i | \(-0.829594\pi\) |
0.871839 | + | 0.489793i | \(0.162928\pi\) | |||||||
\(158\) | 21.3306 | − | 36.9457i | 1.69697 | − | 2.93925i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.8723 | − | 27.4917i | −1.25482 | − | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7091 | 0.838802 | 0.419401 | − | 0.907801i | \(-0.362240\pi\) | ||||
0.419401 | + | 0.907801i | \(0.362240\pi\) | |||||||
\(164\) | −26.9311 | − | 46.6461i | −2.10297 | − | 3.64245i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.9880 | − | 32.8881i | 1.47375 | − | 2.55261i | ||||
\(167\) | −1.59872 | + | 2.76907i | −0.123713 | + | 0.214277i | −0.921229 | − | 0.389020i | \(-0.872814\pi\) |
0.797516 | + | 0.603298i | \(0.206147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | + | 2.50997i | 0.111472 | + | 0.193074i | ||||
\(170\) | −12.0627 | −0.925164 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 33.6216 | 2.56362 | ||||||||
\(173\) | −5.71875 | − | 9.90517i | −0.434789 | − | 0.753076i | 0.562490 | − | 0.826804i | \(-0.309844\pi\) |
−0.997278 | + | 0.0737284i | \(0.976510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.51809 | + | 16.4858i | −0.717453 | + | 1.24266i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.51210 | − | 6.08314i | −0.263243 | − | 0.455951i | ||||
\(179\) | −1.09855 | −0.0821095 | −0.0410547 | − | 0.999157i | \(-0.513072\pi\) | ||||
−0.0410547 | + | 0.999157i | \(0.513072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.19013 | 0.237120 | 0.118560 | − | 0.992947i | \(-0.462172\pi\) | ||||
0.118560 | + | 0.992947i | \(0.462172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.30402 | + | 2.25863i | −0.0961336 | + | 0.166508i | ||||
\(185\) | −6.36343 | + | 11.0218i | −0.467849 | + | 0.810338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88861 | + | 3.27118i | 0.138109 | + | 0.239212i | ||||
\(188\) | −59.8846 | −4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | 1.93407 | + | 3.34992i | 0.139945 | + | 0.242391i | 0.927475 | − | 0.373884i | \(-0.121974\pi\) |
−0.787531 | + | 0.616275i | \(0.788641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.06793 | − | 3.58175i | 0.148853 | − | 0.257820i | −0.781951 | − | 0.623340i | \(-0.785775\pi\) |
0.930804 | + | 0.365520i | \(0.119109\pi\) | |||||||
\(194\) | 19.6294 | − | 33.9991i | 1.40931 | − | 2.44099i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.889267 | 0.0633576 | 0.0316788 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316788 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.32386 | 0.448287 | 0.224143 | − | 0.974556i | \(-0.428042\pi\) | ||||
0.224143 | + | 0.974556i | \(0.428042\pi\) | |||||||
\(200\) | 11.3679 | + | 19.6898i | 0.803833 | + | 1.39228i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.3554 | − | 23.1323i | 0.939684 | − | 1.62758i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.95305 | − | 13.7751i | −0.555465 | − | 0.962093i | ||||
\(206\) | 30.0238 | 2.09186 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −44.8586 | −3.11038 | ||||||||
\(209\) | −0.421952 | − | 0.730843i | −0.0291870 | − | 0.0505535i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71291 | − | 9.89505i | 0.393293 | − | 0.681204i | −0.599589 | − | 0.800308i | \(-0.704669\pi\) |
0.992882 | + | 0.119105i | \(0.0380025\pi\) | |||||||
\(212\) | 7.48574 | − | 12.9657i | 0.514123 | − | 0.890487i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.61237 | − | 4.52476i | −0.178578 | − | 0.309307i | ||||
\(215\) | 9.92881 | 0.677139 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.2600 | + | 43.7516i | 1.71082 | + | 2.96323i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.74705 | + | 9.95417i | −0.387466 | + | 0.671110i | ||||
\(221\) | −4.45051 | + | 7.70850i | −0.299373 | + | 0.518530i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.35953 | + | 14.4791i | 0.559796 | + | 0.969595i | 0.997513 | + | 0.0704822i | \(0.0224538\pi\) |
−0.437717 | + | 0.899113i | \(0.644213\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.65250 | 0.575555 | ||||||||
\(227\) | 8.53501 | + | 14.7831i | 0.566489 | + | 0.981187i | 0.996909 | + | 0.0785588i | \(0.0250318\pi\) |
−0.430421 | + | 0.902628i | \(0.641635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.89471 | + | 17.1381i | −0.653861 | + | 1.13252i | 0.328317 | + | 0.944567i | \(0.393518\pi\) |
−0.982178 | + | 0.187953i | \(0.939815\pi\) | |||||||
\(230\) | −0.613500 | + | 1.06261i | −0.0404530 | + | 0.0700666i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.8187 | − | 36.0591i | −1.36682 | − | 2.36740i | ||||
\(233\) | −5.93159 | −0.388591 | −0.194296 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194296 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.6846 | −1.15361 | ||||||||
\(236\) | 12.2875 | + | 21.2826i | 0.799847 | + | 1.38538i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0277 | − | 17.3685i | 0.648637 | − | 1.12347i | −0.334812 | − | 0.942285i | \(-0.608673\pi\) |
0.983449 | − | 0.181187i | \(-0.0579939\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6444 | − | 25.3648i | −0.943326 | − | 1.63389i | −0.759069 | − | 0.651010i | \(-0.774346\pi\) |
−0.184256 | − | 0.982878i | \(-0.558988\pi\) | |||||||
\(242\) | −24.9273 | −1.60239 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.06827 | −0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.994327 | − | 1.72223i | 0.0632675 | − | 0.109583i | ||||
\(248\) | −34.0121 | + | 58.9107i | −2.15977 | + | 3.74083i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.1164 | + | 27.9144i | 1.01929 | + | 1.76546i | ||||
\(251\) | 22.7856 | 1.43821 | 0.719106 | − | 0.694901i | \(-0.244552\pi\) | ||||
0.719106 | + | 0.694901i | \(0.244552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384215 | 0.0241554 | ||||||||
\(254\) | 11.3681 | + | 19.6901i | 0.713297 | + | 1.23547i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7821 | + | 27.3354i | −0.986381 | + | 1.70846i | ||||
\(257\) | −12.1444 | + | 21.0348i | −0.757550 | + | 1.31211i | 0.186547 | + | 0.982446i | \(0.440270\pi\) |
−0.944097 | + | 0.329668i | \(0.893063\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.0857 | −1.67979 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 32.5071 | 2.00830 | ||||||||
\(263\) | −4.30578 | − | 7.45782i | −0.265506 | − | 0.459869i | 0.702190 | − | 0.711989i | \(-0.252206\pi\) |
−0.967696 | + | 0.252120i | \(0.918872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.21062 | − | 3.82890i | 0.135797 | − | 0.235208i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.82011 | + | 11.8128i | 0.416605 | + | 0.721581i | ||||
\(269\) | 15.2312 | 0.928664 | 0.464332 | − | 0.885661i | \(-0.346294\pi\) | ||||
0.464332 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.67820 | −0.284181 | −0.142090 | − | 0.989854i | \(-0.545382\pi\) | ||||
−0.142090 | + | 0.989854i | \(0.545382\pi\) | |||||||
\(272\) | 19.7633 | + | 34.2310i | 1.19832 | + | 2.07556i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.4684 | − | 38.9164i | 1.35737 | − | 2.35103i | ||||
\(275\) | 1.67472 | − | 2.90069i | 0.100989 | − | 0.174918i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.19537 | + | 14.1948i | 0.492412 | + | 0.852883i | 0.999962 | − | 0.00873986i | \(-0.00278202\pi\) |
−0.507550 | + | 0.861622i | \(0.669449\pi\) | |||||||
\(278\) | −21.4560 | −1.28685 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75702 | − | 3.04325i | −0.104815 | − | 0.181545i | 0.808848 | − | 0.588018i | \(-0.200092\pi\) |
−0.913663 | + | 0.406473i | \(0.866758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0354 | + | 22.5780i | −0.774874 | + | 1.34212i | 0.159992 | + | 0.987118i | \(0.448853\pi\) |
−0.934865 | + | 0.355002i | \(0.884480\pi\) | |||||||
\(284\) | −3.90025 | + | 6.75543i | −0.231437 | + | 0.400861i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.81958 | + | 10.0798i | 0.344119 | + | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.15699 | −0.538647 | ||||||||
\(290\) | −9.79455 | − | 16.9647i | −0.575156 | − | 0.996199i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.25740 | − | 2.17787i | 0.0735835 | − | 0.127450i | ||||
\(293\) | 9.44192 | − | 16.3539i | 0.551603 | − | 0.955404i | −0.446556 | − | 0.894756i | \(-0.647350\pi\) |
0.998159 | − | 0.0606487i | \(-0.0193169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | + | 6.28497i | 0.211267 | + | 0.365925i | ||||
\(296\) | 73.4484 | 4.26910 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 37.1119 | 2.14983 | ||||||||
\(299\) | 0.452700 | + | 0.784099i | 0.0261803 | + | 0.0453456i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.29401 | + | 9.16950i | −0.304636 | + | 0.527645i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.41549 | − | 7.64785i | −0.253246 | − | 0.438634i | ||||
\(305\) | −0.610783 | −0.0349734 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6407 | −1.23510 | −0.617551 | − | 0.786531i | \(-0.711875\pi\) | ||||
−0.617551 | + | 0.786531i | \(0.711875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0016 | + | 27.7156i | −0.908830 | + | 1.57414i | ||||
\(311\) | 2.24724 | − | 3.89234i | 0.127429 | − | 0.220714i | −0.795251 | − | 0.606281i | \(-0.792661\pi\) |
0.922680 | + | 0.385567i | \(0.125994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.30102 | − | 7.44958i | −0.243108 | − | 0.421075i | 0.718490 | − | 0.695537i | \(-0.244834\pi\) |
−0.961598 | + | 0.274462i | \(0.911500\pi\) | |||||||
\(314\) | −0.799206 | −0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | −4.03128 | − | 6.98237i | −0.226419 | − | 0.392169i | 0.730325 | − | 0.683100i | \(-0.239369\pi\) |
−0.956744 | + | 0.290930i | \(0.906035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.06701 | + | 5.31221i | −0.171719 | + | 0.297427i | ||||
\(320\) | −20.7053 | + | 35.8626i | −1.15746 | + | 2.00478i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.75228 | −0.0974992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.89291 | 0.437820 | ||||||||
\(326\) | −14.5383 | − | 25.1811i | −0.805203 | − | 1.39465i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −45.8981 | + | 79.4978i | −2.53430 | + | 4.38953i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4513 | + | 19.8342i | 0.629419 | + | 1.09019i | 0.987668 | + | 0.156560i | \(0.0500405\pi\) |
−0.358249 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(332\) | −75.1361 | −4.12363 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.68150 | 0.475030 | ||||||||
\(335\) | 2.01405 | + | 3.48844i | 0.110039 | + | 0.190594i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.81891 | + | 11.8107i | −0.371450 | + | 0.643369i | −0.989789 | − | 0.142542i | \(-0.954472\pi\) |
0.618339 | + | 0.785911i | \(0.287806\pi\) | |||||||
\(338\) | 3.93458 | − | 6.81489i | 0.214013 | − | 0.370681i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.9331 | + | 20.6688i | 0.647164 | + | 1.12092i | ||||
\(341\) | 10.0213 | 0.542683 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −28.6502 | − | 49.6237i | −1.54472 | − | 2.67553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5272 | + | 26.8938i | −0.834746 | + | 1.44582i | ||||
\(347\) | −1.41282 | + | 2.44707i | −0.0758440 | + | 0.131366i | −0.901453 | − | 0.432877i | \(-0.857498\pi\) |
0.825609 | + | 0.564243i | \(0.190832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81202 | − | 3.13851i | −0.0969951 | − | 0.168000i | 0.813444 | − | 0.581643i | \(-0.197590\pi\) |
−0.910440 | + | 0.413642i | \(0.864256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.9893 | 1.43854 | ||||||||
\(353\) | −1.37701 | − | 2.38504i | −0.0732907 | − | 0.126943i | 0.827051 | − | 0.562127i | \(-0.190017\pi\) |
−0.900342 | + | 0.435184i | \(0.856683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.15179 | + | 1.99495i | −0.0611304 | + | 0.105881i | ||||
\(356\) | −6.94877 | + | 12.0356i | −0.368284 | + | 0.637887i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.49135 | + | 2.58310i | 0.0788205 | + | 0.136521i | ||||
\(359\) | 16.8015 | 0.886750 | 0.443375 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443375 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6085 | −0.979395 | ||||||||
\(362\) | −4.33081 | − | 7.50119i | −0.227622 | − | 0.394254i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.371322 | − | 0.643149i | 0.0194359 | − | 0.0336640i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.9670 | + | 20.7274i | 0.624670 | + | 1.08196i | 0.988605 | + | 0.150536i | \(0.0480999\pi\) |
−0.363934 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(368\) | 4.02059 | 0.209588 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.5551 | 1.79644 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.58030 | − | 16.5936i | 0.496049 | − | 0.859182i | −0.503941 | − | 0.863738i | \(-0.668117\pi\) |
0.999990 | + | 0.00455622i | \(0.00145030\pi\) | |||||||
\(374\) | 5.12784 | − | 8.88168i | 0.265154 | − | 0.459261i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 51.0299 | + | 88.3865i | 2.63167 | + | 4.55818i | ||||
\(377\) | −14.4548 | −0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | −2.66608 | − | 4.61779i | −0.136767 | − | 0.236888i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.25127 | − | 9.09546i | 0.268678 | − | 0.465364i | ||||
\(383\) | −10.0718 | + | 17.4448i | −0.514643 | + | 0.891388i | 0.485213 | + | 0.874396i | \(0.338742\pi\) |
−0.999856 | + | 0.0169915i | \(0.994591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.2294 | −0.571561 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −77.6743 | −3.94332 | ||||||||
\(389\) | 6.69736 | + | 11.6002i | 0.339570 | + | 0.588152i | 0.984352 | − | 0.176215i | \(-0.0563853\pi\) |
−0.644782 | + | 0.764366i | \(0.723052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.398891 | − | 0.690899i | 0.0201728 | − | 0.0349402i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.20724 | − | 2.09100i | −0.0608198 | − | 0.105343i | ||||
\(395\) | −24.9261 | −1.25417 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0133 | −0.904061 | −0.452031 | − | 0.892002i | \(-0.649300\pi\) | ||||
−0.452031 | + | 0.892002i | \(0.649300\pi\) | |||||||
\(398\) | −8.58506 | − | 14.8698i | −0.430330 | − | 0.745354i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.5249 | − | 30.3541i | 0.876247 | − | 1.51770i | ||||
\(401\) | 14.4337 | − | 25.0000i | 0.720787 | − | 1.24844i | −0.239898 | − | 0.970798i | \(-0.577114\pi\) |
0.960685 | − | 0.277642i | \(-0.0895528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8075 | + | 20.4513i | 0.588176 | + | 1.01875i | ||||
\(404\) | −52.8479 | −2.62928 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.41019 | − | 9.37073i | −0.268173 | − | 0.464490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.42937 | − | 9.40395i | 0.268465 | − | 0.464995i | −0.700000 | − | 0.714142i | \(-0.746817\pi\) |
0.968466 | + | 0.249147i | \(0.0801502\pi\) | |||||||
\(410\) | −21.5936 | + | 37.4012i | −1.06643 | + | 1.84711i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.7014 | − | 51.4443i | −1.46328 | − | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.1885 | −1.08919 | ||||||||
\(416\) | 31.8001 | + | 55.0793i | 1.55913 | + | 2.70049i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.14566 | + | 1.98434i | −0.0560359 | + | 0.0970570i | ||||
\(419\) | 0.247572 | − | 0.428807i | 0.0120947 | − | 0.0209486i | −0.859915 | − | 0.510438i | \(-0.829483\pi\) |
0.872009 | + | 0.489489i | \(0.162817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | + | 16.4600i | 0.463158 | + | 0.802212i | 0.999116 | − | 0.0420318i | \(-0.0133831\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(422\) | −31.0226 | −1.51016 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.5155 | −1.23914 | ||||||||
\(425\) | −3.47737 | − | 6.02298i | −0.168677 | − | 0.292157i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.16864 | + | 8.95234i | −0.249835 | + | 0.432728i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4790 | − | 23.3464i | −0.650016 | − | 1.12586i | ||||
\(431\) | 16.9215 | 0.815078 | 0.407539 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407539 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.4740 | −1.60866 | −0.804330 | − | 0.594183i | \(-0.797476\pi\) | ||||
−0.804330 | + | 0.594183i | \(0.797476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 49.9774 | − | 86.5634i | 2.39348 | − | 4.14564i | ||||
\(437\) | −0.0891197 | + | 0.154360i | −0.00426317 | + | 0.00738403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4657 | − | 18.1272i | −0.499502 | − | 0.865163i | 0.500498 | − | 0.865738i | \(-0.333150\pi\) |
−1.00000 | 0.000574559i | \(0.999817\pi\) | ||||||||
\(440\) | 19.5891 | 0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | −15.4290 | − | 26.7238i | −0.733054 | − | 1.26969i | −0.955572 | − | 0.294759i | \(-0.904761\pi\) |
0.222517 | − | 0.974929i | \(-0.428573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.05205 | + | 3.55425i | −0.0972763 | + | 0.168487i | ||||
\(446\) | 22.6972 | − | 39.3128i | 1.07475 | − | 1.86151i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.2789 | 1.57053 | 0.785263 | − | 0.619162i | \(-0.212528\pi\) | ||||
0.785263 | + | 0.619162i | \(0.212528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5234 | 0.636791 | ||||||||
\(452\) | −8.55957 | − | 14.8256i | −0.402608 | − | 0.697338i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.1737 | − | 40.1380i | 1.08760 | − | 1.88377i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8952 | − | 20.6031i | −0.556434 | − | 0.963772i | −0.997790 | − | 0.0664402i | \(-0.978836\pi\) |
0.441356 | − | 0.897332i | \(-0.354498\pi\) | |||||||
\(458\) | 53.7309 | 2.51068 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.42764 | 0.113189 | ||||||||
\(461\) | −8.53122 | − | 14.7765i | −0.397339 | − | 0.688211i | 0.596058 | − | 0.802941i | \(-0.296733\pi\) |
−0.993397 | + | 0.114731i | \(0.963400\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | − | 31.3922i | 0.842306 | − | 1.45892i | −0.0456338 | − | 0.998958i | \(-0.514531\pi\) |
0.887940 | − | 0.459959i | \(-0.152136\pi\) | |||||||
\(464\) | −32.0945 | + | 55.5893i | −1.48995 | + | 2.58067i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.05253 | + | 13.9474i | 0.373026 | + | 0.646100i | ||||
\(467\) | 8.19160 | 0.379062 | 0.189531 | − | 0.981875i | \(-0.439303\pi\) | ||||
0.189531 | + | 0.981875i | \(0.439303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.0080 | + | 41.5830i | 1.10740 | + | 1.91808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.9413 | − | 36.2714i | 0.963900 | − | 1.66952i | ||||
\(473\) | −4.22074 | + | 7.31054i | −0.194070 | + | 0.336139i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.776909 | + | 1.34565i | 0.0356470 | + | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −54.4530 | −2.49062 | ||||||||
\(479\) | −12.7775 | − | 22.1312i | −0.583817 | − | 1.01120i | −0.995022 | − | 0.0996574i | \(-0.968225\pi\) |
0.411205 | − | 0.911543i | \(-0.365108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.7491 | − | 22.0820i | 0.581308 | − | 1.00685i | ||||
\(482\) | −39.7614 | + | 68.8687i | −1.81108 | + | 3.13688i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.6596 | + | 42.7116i | 1.12089 | + | 1.94144i | ||||
\(485\) | −22.9381 | −1.04156 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.92281 | −0.313702 | −0.156851 | − | 0.987622i | \(-0.550134\pi\) | ||||
−0.156851 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(488\) | 1.76246 | + | 3.05266i | 0.0797826 | + | 0.138188i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7262 | + | 32.4348i | −0.845103 | + | 1.46376i | 0.0404294 | + | 0.999182i | \(0.487127\pi\) |
−0.885532 | + | 0.464578i | \(0.846206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.36831 | + | 11.0302i | 0.286814 | + | 0.496777i | ||||
\(494\) | −5.39946 | −0.242933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 104.867 | 4.70867 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8125 | + | 22.1919i | −0.573566 | + | 0.993446i | 0.422630 | + | 0.906302i | \(0.361107\pi\) |
−0.996196 | + | 0.0871432i | \(0.972226\pi\) | |||||||
\(500\) | 31.8867 | − | 55.2293i | 1.42601 | − | 2.46993i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.9329 | − | 53.5774i | −1.38060 | − | 2.39127i | ||||
\(503\) | 5.79692 | 0.258472 | 0.129236 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129236 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6066 | −0.694483 | ||||||||
\(506\) | −0.521598 | − | 0.903434i | −0.0231878 | − | 0.0401625i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.4920 | − | 38.9573i | 0.997921 | − | 1.72845i | ||||
\(509\) | 12.5697 | − | 21.7714i | 0.557144 | − | 0.965002i | −0.440589 | − | 0.897709i | \(-0.645230\pi\) |
0.997733 | − | 0.0672931i | \(-0.0214363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 23.9940 | 1.06039 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 65.9475 | 2.90882 | ||||||||
\(515\) | −8.77113 | − | 15.1920i | −0.386502 | − | 0.669441i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.51771 | − | 13.0211i | 0.330629 | − | 0.572665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.0808 | + | 39.9771i | 1.01216 | + | 1.75311i | ||||
\(521\) | −7.29656 | −0.319668 | −0.159834 | − | 0.987144i | \(-0.551096\pi\) | ||||
−0.159834 | + | 0.987144i | \(0.551096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7727 | 0.733421 | 0.366710 | − | 0.930335i | \(-0.380484\pi\) | ||||
0.366710 | + | 0.930335i | \(0.380484\pi\) | |||||||
\(524\) | −32.1580 | − | 55.6993i | −1.40483 | − | 2.43324i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6908 | + | 20.2490i | −0.509741 | + | 0.882898i | ||||
\(527\) | 10.4041 | − | 18.0204i | 0.453208 | − | 0.784979i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4594 | + | 19.8483i | 0.498236 | + | 0.862970i | ||||
\(530\) | −12.0042 | −0.521431 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9339 | + | 27.5982i | 0.690172 | + | 1.19541i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.52635 | + | 2.64372i | −0.0659900 | + | 0.114298i | ||||
\(536\) | 11.6234 | − | 20.1322i | 0.502053 | − | 0.869581i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.6774 | − | 35.8143i | −0.891466 | − | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.29816 | −0.227786 | −0.113893 | − | 0.993493i | \(-0.536332\pi\) | ||||
−0.113893 | + | 0.993493i | \(0.536332\pi\) | |||||||
\(542\) | 6.35097 | + | 11.0002i | 0.272798 | + | 0.472499i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.0202 | − | 48.5324i | 1.20136 | − | 2.08081i | ||||
\(545\) | 14.7589 | − | 25.5631i | 0.632200 | − | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | + | 28.4619i | 0.702603 | + | 1.21694i | 0.967550 | + | 0.252681i | \(0.0813123\pi\) |
−0.264947 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(548\) | −88.9084 | −3.79798 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.09416 | −0.387776 | ||||||||
\(551\) | −1.42280 | − | 2.46436i | −0.0606133 | − | 0.104985i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.2515 | − | 38.5408i | 0.945376 | − | 1.63744i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.2256 | + | 36.7638i | 0.900166 | + | 1.55913i | ||||
\(557\) | 18.8160 | 0.797258 | 0.398629 | − | 0.917112i | \(-0.369486\pi\) | ||||
0.398629 | + | 0.917112i | \(0.369486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8923 | −0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.77054 | + | 8.26282i | −0.201233 | + | 0.348546i | ||||
\(563\) | 13.8325 | − | 23.9586i | 0.582970 | − | 1.00973i | −0.412155 | − | 0.911114i | \(-0.635224\pi\) |
0.995125 | − | 0.0986197i | \(-0.0314427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.52773 | − | 4.37816i | −0.106343 | − | 0.184191i | ||||
\(566\) | 70.7856 | 2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | −20.0916 | − | 34.7996i | −0.842282 | − | 1.45888i | −0.887961 | − | 0.459920i | \(-0.847878\pi\) |
0.0456782 | − | 0.998956i | \(-0.485455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.40565 | − | 5.89875i | 0.142522 | − | 0.246855i | −0.785924 | − | 0.618323i | \(-0.787812\pi\) |
0.928446 | + | 0.371468i | \(0.121146\pi\) | |||||||
\(572\) | 11.5142 | − | 19.9431i | 0.481431 | − | 0.833863i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.707427 | −0.0295017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.4222 | −1.51628 | −0.758138 | − | 0.652094i | \(-0.773891\pi\) | ||||
−0.758138 | + | 0.652094i | \(0.773891\pi\) | |||||||
\(578\) | 12.4312 | + | 21.5315i | 0.517071 | + | 0.895593i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.3787 | + | 33.5649i | −0.804658 | + | 1.39371i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.87947 | + | 3.25534i | 0.0778397 | + | 0.134822i | ||||
\(584\) | −4.28590 | −0.177352 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51.2721 | −2.11803 | ||||||||
\(587\) | −5.57943 | − | 9.66385i | −0.230288 | − | 0.398870i | 0.727605 | − | 0.685996i | \(-0.240633\pi\) |
−0.957893 | + | 0.287126i | \(0.907300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.32446 | + | 4.02609i | −0.0957779 | + | 0.165892i | ||||
\(590\) | 9.85220 | − | 17.0645i | 0.405609 | − | 0.702535i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −56.6145 | − | 98.0593i | −2.32684 | − | 4.03021i | ||||
\(593\) | −19.8085 | −0.813439 | −0.406720 | − | 0.913553i | \(-0.633327\pi\) | ||||
−0.406720 | + | 0.913553i | \(0.633327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.7133 | − | 63.5893i | −1.50384 | − | 2.60472i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.22914 | − | 2.12893i | 0.0502633 | − | 0.0870586i | ||||
\(599\) | −9.06600 | + | 15.7028i | −0.370427 | + | 0.641598i | −0.989631 | − | 0.143632i | \(-0.954122\pi\) |
0.619204 | + | 0.785230i | \(0.287455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3285 | − | 21.3536i | −0.502889 | − | 0.871030i | −0.999994 | − | 0.00333942i | \(-0.998937\pi\) |
0.497105 | − | 0.867690i | \(-0.334396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.9486 | 0.852387 | ||||||||
\(605\) | 7.28223 | + | 12.6132i | 0.296065 | + | 0.512799i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.63876 | + | 14.9628i | −0.350637 | + | 0.607320i | −0.986361 | − | 0.164596i | \(-0.947368\pi\) |
0.635725 | + | 0.771916i | \(0.280701\pi\) | |||||||
\(608\) | −6.26024 | + | 10.8431i | −0.253886 | + | 0.439744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.829179 | + | 1.43618i | 0.0335725 | + | 0.0581492i | ||||
\(611\) | 35.4308 | 1.43338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5566 | 0.789882 | 0.394941 | − | 0.918707i | \(-0.370765\pi\) | ||||
0.394941 | + | 0.918707i | \(0.370765\pi\) | |||||||
\(614\) | 29.3787 | + | 50.8855i | 1.18563 | + | 2.05357i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8723 | + | 18.8314i | −0.437702 | + | 0.758122i | −0.997512 | − | 0.0704988i | \(-0.977541\pi\) |
0.559810 | + | 0.828621i | \(0.310874\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.9024 | − | 29.2758i | −0.679366 | − | 1.17670i | −0.975172 | − | 0.221448i | \(-0.928922\pi\) |
0.295807 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(620\) | 63.3190 | 2.54295 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.2031 | −0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.20808 | − | 5.55655i | 0.128323 | − | 0.222262i | ||||
\(626\) | −11.6778 | + | 20.2266i | −0.466740 | + | 0.808418i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.790623 | + | 1.36940i | 0.0315493 | + | 0.0546450i | ||||
\(629\) | −22.4674 | −0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | 71.9258 | + | 124.579i | 2.86105 | + | 4.95549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.9454 | + | 18.9581i | −0.434699 | + | 0.752921i | ||||
\(635\) | 6.64213 | − | 11.5045i | 0.263585 | − | 0.456542i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6547 | 0.659365 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.9458 | 1.93475 | ||||||||
\(641\) | 7.95901 | + | 13.7854i | 0.314362 | + | 0.544491i | 0.979302 | − | 0.202406i | \(-0.0648760\pi\) |
−0.664940 | + | 0.746897i | \(0.731543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.2527 | + | 22.9544i | −0.522636 | + | 0.905231i | 0.477017 | + | 0.878894i | \(0.341718\pi\) |
−0.999653 | + | 0.0263376i | \(0.991616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.37883 | + | 4.12026i | 0.0935938 | + | 0.162109i | ||||
\(647\) | −0.0160392 | −0.000630565 | −0.000315282 | − | 1.00000i | \(-0.500100\pi\) | ||||
−0.000315282 | 1.00000i | \(0.500100\pi\) | ||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.17012 | −0.242198 | ||||||||
\(650\) | −10.7152 | − | 18.5592i | −0.420283 | − | 0.727951i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.7644 | + | 49.8214i | −1.12650 | + | 1.95115i | ||||
\(653\) | −16.6440 | + | 28.8282i | −0.651328 | + | 1.12813i | 0.331473 | + | 0.943465i | \(0.392455\pi\) |
−0.982801 | + | 0.184669i | \(0.940879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.49661 | − | 16.4486i | −0.371063 | − | 0.642700i | ||||
\(656\) | 141.514 | 5.52520 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4156 | − | 33.6288i | −0.756324 | − | 1.30999i | −0.944713 | − | 0.327897i | \(-0.893660\pi\) |
0.188389 | − | 0.982094i | \(-0.439673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.65322 | + | 4.59551i | −0.103198 | + | 0.178745i | −0.913001 | − | 0.407958i | \(-0.866241\pi\) |
0.809802 | + | 0.586703i | \(0.199574\pi\) | |||||||
\(662\) | 31.0917 | − | 53.8525i | 1.20842 | − | 2.09304i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64.0264 | + | 110.897i | 2.48471 | + | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29555 | 0.0501640 | ||||||||
\(668\) | −8.58826 | − | 14.8753i | −0.332290 | − | 0.575543i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.46842 | − | 9.47158i | 0.211263 | − | 0.365919i | ||||
\(671\) | 0.259644 | − | 0.449717i | 0.0100235 | − | 0.0173611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03565 | − | 5.25789i | −0.117016 | − | 0.202677i | 0.801568 | − | 0.597903i | \(-0.203999\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(674\) | 37.0285 | 1.42628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.5693 | −0.598819 | ||||||||
\(677\) | −17.3925 | − | 30.1247i | −0.668449 | − | 1.15779i | −0.978338 | − | 0.207014i | \(-0.933625\pi\) |
0.309889 | − | 0.950773i | \(-0.399708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20.3373 | − | 35.2253i | 0.779901 | − | 1.35083i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.6046 | − | 23.5638i | −0.520946 | − | 0.902305i | ||||
\(683\) | −19.4241 | −0.743243 | −0.371622 | − | 0.928384i | \(-0.621198\pi\) | ||||
−0.371622 | + | 0.928384i | \(0.621198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.2556 | −1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.1676 | + | 76.5006i | −1.68387 | + | 2.91656i | ||||
\(689\) | −4.42895 | + | 7.67117i | −0.168730 | + | 0.292248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.31837 | + | 5.74759i | 0.126237 | + | 0.218649i | 0.922216 | − | 0.386676i | \(-0.126377\pi\) |
−0.795979 | + | 0.605324i | \(0.793043\pi\) | |||||||
\(692\) | 61.4416 | 2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | 6.26814 | + | 10.8567i | 0.237764 | + | 0.411820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.0399 | − | 24.3178i | 0.531799 | − | 0.921103i | ||||
\(698\) | −4.91987 | + | 8.52147i | −0.186220 | + | 0.322542i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.9153 | 0.525574 | 0.262787 | − | 0.964854i | \(-0.415358\pi\) | ||||
0.262787 | + | 0.964854i | \(0.415358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.01963 | 0.189319 | ||||||||
\(704\) | −17.6036 | − | 30.4904i | −0.663462 | − | 1.14915i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.73876 | + | 6.47571i | −0.140710 | + | 0.243717i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0778 | − | 29.5796i | −0.641370 | − | 1.11089i | −0.985127 | − | 0.171827i | \(-0.945033\pi\) |
0.343757 | − | 0.939059i | \(-0.388300\pi\) | |||||||
\(710\) | 6.25450 | 0.234727 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.6852 | 0.887642 | ||||||||
\(713\) | −1.05829 | − | 1.83301i | −0.0396332 | − | 0.0686467i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.40025 | − | 5.88941i | 0.127162 | − | 0.220251i | ||||
\(716\) | 2.95068 | − | 5.11072i | 0.110272 | − | 0.190997i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.8092 | − | 39.5066i | −0.851231 | − | 1.47437i | ||||
\(719\) | 44.2900 | 1.65174 | 0.825870 | − | 0.563861i | \(-0.190684\pi\) | ||||
0.825870 | + | 0.563861i | \(0.190684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.2623 | + | 43.7556i | 0.940165 | + | 1.62841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.56860 | + | 14.8413i | −0.318450 | + | 0.551571i | ||||
\(725\) | 5.64705 | − | 9.78099i | 0.209726 | − | 0.363257i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1247 | + | 24.4647i | 0.523857 | + | 0.907346i | 0.999614 | + | 0.0277700i | \(0.00884060\pi\) |
−0.475758 | + | 0.879576i | \(0.657826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.01638 | −0.0746295 | ||||||||
\(731\) | 8.76391 | + | 15.1795i | 0.324145 | + | 0.561435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5084 | − | 21.6653i | 0.462010 | − | 0.800225i | −0.537051 | − | 0.843550i | \(-0.680462\pi\) |
0.999061 | + | 0.0433249i | \(0.0137951\pi\) | |||||||
\(734\) | 32.4919 | − | 56.2776i | 1.19930 | − | 2.07724i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.85018 | − | 4.93666i | −0.105059 | − | 0.181968i | ||||
\(737\) | −3.42470 | −0.126150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0230 | 1.17798 | 0.588992 | − | 0.808139i | \(-0.299525\pi\) | ||||
0.588992 | + | 0.808139i | \(0.299525\pi\) | |||||||
\(740\) | −34.1840 | − | 59.2084i | −1.25663 | − | 2.17655i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4031 | + | 33.6072i | −0.711833 | + | 1.23293i | 0.252336 | + | 0.967640i | \(0.418801\pi\) |
−0.964169 | + | 0.265290i | \(0.914532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.8418 | − | 18.7786i | −0.397214 | − | 0.687995i | ||||
\(746\) | −52.0236 | −1.90472 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.2911 | −0.741915 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8495 | + | 18.7920i | −0.395905 | + | 0.685728i | −0.993216 | − | 0.116282i | \(-0.962903\pi\) |
0.597311 | + | 0.802010i | \(0.296236\pi\) | |||||||
\(752\) | 78.6685 | − | 136.258i | 2.86874 | − | 4.96881i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.6233 | + | 33.9885i | 0.714638 | + | 1.23779i | ||||
\(755\) | 6.18635 | 0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | −13.6802 | − | 23.6949i | −0.496889 | − | 0.860637i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.54374 | + | 7.86999i | −0.164819 | + | 0.285475i | ||||
\(761\) | −6.66048 | + | 11.5363i | −0.241442 | + | 0.418190i | −0.961125 | − | 0.276113i | \(-0.910954\pi\) |
0.719683 | + | 0.694303i | \(0.244287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.7795 | −0.751775 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54.6923 | 1.97611 | ||||||||
\(767\) | −7.26992 | − | 12.5919i | −0.262502 | − | 0.454666i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.3568 | − | 47.3833i | 0.986510 | − | 1.70869i | 0.351488 | − | 0.936192i | \(-0.385676\pi\) |
0.635022 | − | 0.772494i | \(-0.280991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.1088 | + | 19.2410i | 0.399814 | + | 0.692498i | ||||
\(773\) | −2.36042 | −0.0848983 | −0.0424491 | − | 0.999099i | \(-0.513516\pi\) | ||||
−0.0424491 | + | 0.999099i | \(0.513516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.4515 | −0.662796 | ||||||||
\(776\) | 66.1892 | + | 114.643i | 2.37606 | + | 4.11545i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.1842 | − | 31.4960i | 0.651936 | − | 1.12919i | ||||
\(779\) | −3.13678 | + | 5.43306i | −0.112387 | + | 0.194660i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.979248 | − | 1.69611i | −0.0350403 | − | 0.0606915i | ||||
\(782\) | −2.16608 | −0.0774589 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.233479 | + | 0.404398i | 0.00833323 | + | 0.0144336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.833971 | − | 1.44448i | 0.0297278 | − | 0.0514901i | −0.850779 | − | 0.525524i | \(-0.823869\pi\) |
0.880507 | + | 0.474034i | \(0.157203\pi\) | |||||||
\(788\) | −2.38855 | + | 4.13708i | −0.0850884 | + | 0.147377i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.8388 | + | 58.6105i | 1.20393 | + | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.22370 | 0.0434548 | ||||||||
\(794\) | 24.4542 | + | 42.3560i | 0.867848 | + | 1.50316i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.9857 | + | 29.4201i | −0.602043 | + | 1.04277i | ||||
\(797\) | 14.3148 | − | 24.7939i | 0.507055 | − | 0.878244i | −0.492912 | − | 0.870079i | \(-0.664068\pi\) |
0.999967 | − | 0.00816511i | \(-0.00259906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | − | 27.0368i | −0.552232 | − | 0.956493i | ||||
\(800\) | −49.6934 | −1.75693 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −78.3791 | −2.76766 | ||||||||
\(803\) | 0.315698 | + | 0.546805i | 0.0111408 | + | 0.0192963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0591 | − | 55.5279i | 1.12923 | − | 1.95589i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.0337 | + | 78.0007i | 1.58428 | + | 2.74406i | ||||
\(809\) | 2.85691 | 0.100444 | 0.0502219 | − | 0.998738i | \(-0.484007\pi\) | ||||
0.0502219 | + | 0.998738i | \(0.484007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.2917 | 0.923225 | 0.461613 | − | 0.887082i | \(-0.347271\pi\) | ||||
0.461613 | + | 0.887082i | \(0.347271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.6894 | + | 25.4428i | −0.514863 | + | 0.891769i | ||||
\(815\) | −8.49443 | + | 14.7128i | −0.297547 | + | 0.515366i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.95802 | − | 3.39139i | −0.0685025 | − | 0.118650i | ||||
\(818\) | −29.4829 | −1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | −1.32925 | − | 2.30232i | −0.0463910 | − | 0.0803517i | 0.841897 | − | 0.539638i | \(-0.181439\pi\) |
−0.888289 | + | 0.459286i | \(0.848105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.10769 | − | 10.5788i | 0.212901 | − | 0.368755i | −0.739721 | − | 0.672914i | \(-0.765042\pi\) |
0.952621 | + | 0.304160i | \(0.0983756\pi\) | |||||||
\(824\) | −50.6193 | + | 87.6752i | −1.76341 | + | 3.05431i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.15812 | −0.318459 | −0.159230 | − | 0.987242i | \(-0.550901\pi\) | ||||
−0.159230 | + | 0.987242i | \(0.550901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3431 | 0.637083 | 0.318541 | − | 0.947909i | \(-0.396807\pi\) | ||||
0.318541 | + | 0.947909i | \(0.396807\pi\) | |||||||
\(830\) | 30.1224 | + | 52.1735i | 1.04556 | + | 1.81097i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.4828 | − | 71.8503i | 1.43816 | − | 2.49096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.53620 | − | 4.39284i | −0.0877690 | − | 0.152020i | ||||
\(836\) | 4.53341 | 0.156791 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.34438 | −0.0464409 | ||||||||
\(839\) | 9.47055 | + | 16.4035i | 0.326960 | + | 0.566311i | 0.981907 | − | 0.189364i | \(-0.0606425\pi\) |
−0.654947 | + | 0.755675i | \(0.727309\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15821 | − | 7.20224i | 0.143387 | − | 0.248353i | ||||
\(842\) | 25.8024 | − | 44.6911i | 0.889211 | − | 1.54016i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.6895 | + | 53.1557i | 1.05637 | + | 1.82969i | ||||
\(845\) | −4.59778 | −0.158168 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.6676 | + | 34.0652i | 0.675387 | + | 1.16980i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.44151 | + | 16.3532i | −0.323841 | + | 0.560909i | ||||
\(851\) | −1.14268 | + | 1.97917i | −0.0391704 | + | 0.0678452i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.97922 | − | 17.2845i | −0.341682 | − | 0.591811i | 0.643063 | − | 0.765813i | \(-0.277663\pi\) |
−0.984745 | + | 0.174002i | \(0.944330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.6176 | 0.602156 | ||||||||
\(857\) | −8.20001 | − | 14.2028i | −0.280107 | − | 0.485159i | 0.691304 | − | 0.722564i | \(-0.257037\pi\) |
−0.971411 | + | 0.237405i | \(0.923703\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8575 | + | 29.1981i | −0.575172 | + | 0.996226i | 0.420851 | + | 0.907130i | \(0.361731\pi\) |
−0.996023 | + | 0.0890968i | \(0.971602\pi\) | |||||||
\(860\) | −26.6685 | + | 46.1912i | −0.909389 | + | 1.57511i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.9720 | − | 39.7887i | −0.782429 | − | 1.35521i | ||||
\(863\) | 28.6831 | 0.976383 | 0.488191 | − | 0.872737i | \(-0.337657\pi\) | ||||
0.488191 | + | 0.872737i | \(0.337657\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.1444 | 0.616927 | ||||||||
\(866\) | 45.4432 | + | 78.7100i | 1.54422 | + | 2.67467i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.5961 | − | 18.3529i | 0.359447 | − | 0.622581i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.03513 | − | 6.98906i | −0.136725 | − | 0.236815i | ||||
\(872\) | −170.351 | −5.76880 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.483944 | 0.0163696 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.7621 | − | 25.5688i | 0.498482 | − | 0.863396i | −0.501517 | − | 0.865148i | \(-0.667224\pi\) |
0.999998 | + | 0.00175202i | \(0.000557684\pi\) | |||||||
\(878\) | −28.4159 | + | 49.2177i | −0.958989 | + | 1.66102i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.0994 | − | 26.1530i | −0.509001 | − | 0.881616i | ||||
\(881\) | −57.5032 | −1.93733 | −0.968666 | − | 0.248366i | \(-0.920107\pi\) | ||||
−0.968666 | + | 0.248366i | \(0.920107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8715 | 0.668730 | 0.334365 | − | 0.942444i | \(-0.391478\pi\) | ||||
0.334365 | + | 0.942444i | \(0.391478\pi\) | |||||||
\(884\) | −23.9079 | − | 41.4097i | −0.804109 | − | 1.39276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.8918 | + | 72.5587i | −1.40738 | + | 2.43766i | ||||
\(887\) | 18.5475 | − | 32.1253i | 0.622766 | − | 1.07866i | −0.366203 | − | 0.930535i | \(-0.619342\pi\) |
0.988968 | − | 0.148127i | \(-0.0473243\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.1432 | 0.373519 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −89.8139 | −3.00719 | ||||||||
\(893\) | 3.48750 | + | 6.04053i | 0.116705 | + | 0.202139i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.871366 | − | 1.50925i | 0.0291266 | − | 0.0504487i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.1783 | − | 78.2511i | −1.50762 | − | 2.61127i | ||||
\(899\) | 33.7913 | 1.12700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.80503 | 0.260023 | ||||||||
\(902\) | −18.3589 | − | 31.7985i | −0.611284 | − | 1.05877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.5879 | + | 25.2669i | −0.485185 | + | 0.840366i | ||||
\(905\) | −2.53040 | + | 4.38278i | −0.0841133 | + | 0.145689i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.2044 | − | 21.1386i | −0.405240 | − | 0.701896i | 0.589110 | − | 0.808053i | \(-0.299479\pi\) |
−0.994349 | + | 0.106157i | \(0.966145\pi\) | |||||||
\(908\) | −91.6993 | −3.04315 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5493 | + | 21.7360i | 0.415776 | + | 0.720146i | 0.995510 | − | 0.0946604i | \(-0.0301765\pi\) |
−0.579733 | + | 0.814806i | \(0.696843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.43234 | − | 16.3373i | 0.312165 | − | 0.540685i | ||||
\(914\) | −32.2971 | + | 55.9401i | −1.06829 | + | 1.85034i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.1538 | − | 92.0652i | −1.75625 | − | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5976 | −0.943348 | −0.471674 | − | 0.881773i | \(-0.656350\pi\) | ||||
−0.471674 | + | 0.881773i | \(0.656350\pi\) | |||||||
\(920\) | −2.06869 | − | 3.58307i | −0.0682026 | − | 0.118130i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.1634 | + | 40.1202i | −0.762846 | + | 1.32129i | ||||
\(923\) | 2.30759 | − | 3.99686i | 0.0759553 | − | 0.131558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.96139 | + | 17.2536i | 0.327528 | + | 0.567296i | ||||
\(926\) | −98.4196 | −3.23427 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 91.0065 | 2.98744 | ||||||||
\(929\) | −22.7285 | − | 39.3669i | −0.745698 | − | 1.29159i | −0.949868 | − | 0.312651i | \(-0.898783\pi\) |
0.204170 | − | 0.978935i | \(-0.434550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.9321 | − | 27.5952i | 0.521873 | − | 0.903910i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.1206 | − | 19.2615i | −0.363878 | − | 0.630256i | ||||
\(935\) | −5.99217 | −0.195965 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0083 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 47.5002 | − | 82.2728i | 1.54929 | − | 2.68344i | ||||
\(941\) | 6.35657 | − | 11.0099i | 0.207218 | − | 0.358912i | −0.743619 | − | 0.668604i | \(-0.766892\pi\) |
0.950837 | + | 0.309691i | \(0.100226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.42812 | − | 2.47358i | −0.0465060 | − | 0.0805508i | ||||
\(944\) | −64.5667 | −2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | 23.7724 | + | 41.1749i | 0.772498 | + | 1.33801i | 0.936190 | + | 0.351494i | \(0.114326\pi\) |
−0.163692 | + | 0.986511i | \(0.552340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.743940 | + | 1.28854i | −0.0241493 | + | 0.0418279i | ||||
\(950\) | 2.10941 | − | 3.65361i | 0.0684384 | − | 0.118539i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.2355 | −1.23857 | −0.619285 | − | 0.785166i | \(-0.712577\pi\) | ||||
−0.619285 | + | 0.785166i | \(0.712577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.13640 | −0.198569 | ||||||||
\(956\) | 53.8682 | + | 93.3024i | 1.74222 | + | 3.01762i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.6925 | + | 60.0891i | −1.12086 | + | 1.94139i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1028 | − | 20.9627i | −0.390413 | − | 0.676215i | ||||
\(962\) | −69.2309 | −2.23209 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 157.337 | 5.06749 | ||||||||
\(965\) | 3.28054 | + | 5.68207i | 0.105604 | + | 0.182912i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4093 | + | 35.3499i | −0.656317 | + | 1.13678i | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(968\) | 42.0267 | − | 72.7924i | 1.35079 | − | 2.33964i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.1399 | + | 53.9359i | 0.999843 | + | 1.73178i | ||||
\(971\) | −44.9471 | −1.44242 | −0.721210 | − | 0.692717i | \(-0.756414\pi\) | ||||
−0.721210 | + | 0.692717i | \(0.756414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.39817 | + | 16.2781i | 0.301137 | + | 0.521584i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.71703 | − | 4.70603i | 0.0869699 | − | 0.150636i | ||||
\(977\) | 26.7552 | − | 46.3414i | 0.855974 | − | 1.48259i | −0.0197635 | − | 0.999805i | \(-0.506291\pi\) |
0.875738 | − | 0.482787i | \(-0.160375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.74465 | − | 3.02182i | −0.0557593 | − | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 101.688 | 3.24501 | ||||||||
\(983\) | 5.80278 | + | 10.0507i | 0.185080 | + | 0.320568i | 0.943603 | − | 0.331078i | \(-0.107412\pi\) |
−0.758524 | + | 0.651646i | \(0.774079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.705363 | + | 1.22172i | −0.0224747 | + | 0.0389274i | ||||
\(986\) | 17.2908 | − | 29.9485i | 0.550651 | − | 0.953756i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.34147 | + | 9.25170i | 0.169935 | + | 0.294336i | ||||
\(989\) | 1.78291 | 0.0566932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0091 | 0.826208 | 0.413104 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413104 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(992\) | −74.3398 | − | 128.760i | −2.36029 | − | 4.08814i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.01607 | + | 8.68808i | −0.159020 | + | 0.275431i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4499 | + | 40.6164i | 0.742666 | + | 1.28633i | 0.951277 | + | 0.308336i | \(0.0997721\pi\) |
−0.208612 | + | 0.977999i | \(0.566895\pi\) | |||||||
\(998\) | 69.5753 | 2.20237 | ||||||||
\(999\) | 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.h.442.2 | 24 | ||
3.2 | odd | 2 | 441.2.f.h.148.12 | yes | 24 | ||
7.2 | even | 3 | 1323.2.g.h.361.1 | 24 | |||
7.3 | odd | 6 | 1323.2.h.h.226.11 | 24 | |||
7.4 | even | 3 | 1323.2.h.h.226.12 | 24 | |||
7.5 | odd | 6 | 1323.2.g.h.361.2 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.f.h.442.1 | 24 | ||
9.2 | odd | 6 | 441.2.f.h.295.12 | yes | 24 | ||
9.4 | even | 3 | 3969.2.a.bi.1.12 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bh.1.1 | 12 | |||
9.7 | even | 3 | inner | 1323.2.f.h.883.2 | 24 | ||
21.2 | odd | 6 | 441.2.g.h.67.11 | 24 | |||
21.5 | even | 6 | 441.2.g.h.67.12 | 24 | |||
21.11 | odd | 6 | 441.2.h.h.373.2 | 24 | |||
21.17 | even | 6 | 441.2.h.h.373.1 | 24 | |||
21.20 | even | 2 | 441.2.f.h.148.11 | ✓ | 24 | ||
63.2 | odd | 6 | 441.2.h.h.214.2 | 24 | |||
63.11 | odd | 6 | 441.2.g.h.79.11 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bi.1.11 | 12 | |||
63.16 | even | 3 | 1323.2.h.h.802.12 | 24 | |||
63.20 | even | 6 | 441.2.f.h.295.11 | yes | 24 | ||
63.25 | even | 3 | 1323.2.g.h.667.1 | 24 | |||
63.34 | odd | 6 | inner | 1323.2.f.h.883.1 | 24 | ||
63.38 | even | 6 | 441.2.g.h.79.12 | 24 | |||
63.41 | even | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.47 | even | 6 | 441.2.h.h.214.1 | 24 | |||
63.52 | odd | 6 | 1323.2.g.h.667.2 | 24 | |||
63.61 | odd | 6 | 1323.2.h.h.802.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 21.20 | even | 2 | ||
441.2.f.h.148.12 | yes | 24 | 3.2 | odd | 2 | ||
441.2.f.h.295.11 | yes | 24 | 63.20 | even | 6 | ||
441.2.f.h.295.12 | yes | 24 | 9.2 | odd | 6 | ||
441.2.g.h.67.11 | 24 | 21.2 | odd | 6 | |||
441.2.g.h.67.12 | 24 | 21.5 | even | 6 | |||
441.2.g.h.79.11 | 24 | 63.11 | odd | 6 | |||
441.2.g.h.79.12 | 24 | 63.38 | even | 6 | |||
441.2.h.h.214.1 | 24 | 63.47 | even | 6 | |||
441.2.h.h.214.2 | 24 | 63.2 | odd | 6 | |||
441.2.h.h.373.1 | 24 | 21.17 | even | 6 | |||
441.2.h.h.373.2 | 24 | 21.11 | odd | 6 | |||
1323.2.f.h.442.1 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.f.h.442.2 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.f.h.883.1 | 24 | 63.34 | odd | 6 | inner | ||
1323.2.f.h.883.2 | 24 | 9.7 | even | 3 | inner | ||
1323.2.g.h.361.1 | 24 | 7.2 | even | 3 | |||
1323.2.g.h.361.2 | 24 | 7.5 | odd | 6 | |||
1323.2.g.h.667.1 | 24 | 63.25 | even | 3 | |||
1323.2.g.h.667.2 | 24 | 63.52 | odd | 6 | |||
1323.2.h.h.226.11 | 24 | 7.3 | odd | 6 | |||
1323.2.h.h.226.12 | 24 | 7.4 | even | 3 | |||
1323.2.h.h.802.11 | 24 | 63.61 | odd | 6 | |||
1323.2.h.h.802.12 | 24 | 63.16 | even | 3 | |||
3969.2.a.bh.1.1 | 12 | 9.5 | odd | 6 | |||
3969.2.a.bh.1.2 | 12 | 63.41 | even | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bi.1.12 | 12 | 9.4 | even | 3 |