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 | 883.1 | ||
Character | \(\chi\) | \(=\) | 1323.883 |
Dual form | 1323.2.f.h.442.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35757 | + | 2.35137i | −0.959944 | + | 1.66267i | −0.237320 | + | 0.971432i | \(0.576269\pi\) |
−0.722624 | + | 0.691241i | \(0.757064\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.68597 | − | 4.65224i | −1.34299 | − | 2.32612i | ||||
\(5\) | 0.793197 | + | 1.37386i | 0.354728 | + | 0.614407i | 0.987071 | − | 0.160281i | \(-0.0512400\pi\) |
−0.632343 | + | 0.774688i | \(0.717907\pi\) | |||||||
\(6\) | 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 | −0.949600 | − | 0.313464i | \(-0.898510\pi\) |
0.746268 | + | 0.665646i | \(0.231844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58916 | − | 2.75251i | −0.440754 | − | 0.763409i | 0.556991 | − | 0.830518i | \(-0.311956\pi\) |
−0.997746 | + | 0.0671096i | \(0.978622\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.05696 | + | 12.2230i | −1.76424 | + | 3.05575i | ||||
\(17\) | 2.80054 | 0.679230 | 0.339615 | − | 0.940565i | \(-0.389703\pi\) | ||||
0.339615 | + | 0.940565i | \(0.389703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.625693 | −0.143544 | −0.0717719 | − | 0.997421i | \(-0.522865\pi\) | ||||
−0.0717719 | + | 0.997421i | \(0.522865\pi\) | |||||||
\(20\) | 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 | 0.850794 | − | 0.525500i | \(-0.176122\pi\) |
−0.880493 | + | 0.474059i | \(0.842788\pi\) | |||||||
\(24\) | 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 | −0.996161 | − | 0.0875454i | \(-0.972098\pi\) |
0.573897 | + | 0.818928i | \(0.305431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.71502 | + | 6.43461i | 0.667238 | + | 1.15569i | 0.978673 | + | 0.205423i | \(0.0658569\pi\) |
−0.311435 | + | 0.950267i | \(0.600810\pi\) | |||||||
\(32\) | −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 | 0.930219 | + | 0.367004i | \(0.119616\pi\) |
−0.147275 | + | 0.989096i | \(0.547050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | + | 5.42022i | −0.477224 | + | 0.826576i | −0.999659 | − | 0.0261027i | \(-0.991690\pi\) |
0.522435 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(44\) | 7.24542 | 1.09229 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.773452 | 0.114039 | ||||||||
\(47\) | −5.57383 | + | 9.65415i | −0.813026 | + | 1.40820i | 0.0977106 | + | 0.995215i | \(0.468848\pi\) |
−0.910737 | + | 0.412988i | \(0.864485\pi\) | |||||||
\(48\) | 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 | \(-0.262915\pi\) |
−0.975629 | + | 0.219425i | \(0.929582\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.192507 | + | 0.333432i | −0.0246480 | + | 0.0426916i | −0.878086 | − | 0.478502i | \(-0.841180\pi\) |
0.853438 | + | 0.521194i | \(0.174513\pi\) | |||||||
\(62\) | −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 | 0.933097 | − | 0.359625i | \(-0.117095\pi\) |
−0.777993 | + | 0.628273i | \(0.783762\pi\) | |||||||
\(68\) | −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 | \(-0.491279\pi\) | ||||
0.0273955 | + | 0.999625i | \(0.491279\pi\) | |||||||
\(74\) | −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 | 0.0369135 | − | 0.999318i | \(-0.488247\pi\) |
0.846978 | − | 0.531627i | \(-0.178419\pi\) | |||||||
\(80\) | −22.3902 | −2.50330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −27.2235 | −3.00633 | ||||||||
\(83\) | −6.99338 | + | 12.1129i | −0.767623 | + | 1.32956i | 0.171225 | + | 0.985232i | \(0.445228\pi\) |
−0.938848 | + | 0.344331i | \(0.888106\pi\) | |||||||
\(84\) | 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 | \(-0.543783\pi\) | ||||
−0.137114 | + | 0.990555i | \(0.543783\pi\) | |||||||
\(90\) | 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 | 0.221079 | + | 0.975256i | \(0.429042\pi\) |
−0.955136 | + | 0.296168i | \(0.904291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.3405 | −1.33405 | ||||||||
\(101\) | −4.91888 | + | 8.51975i | −0.489447 | + | 0.847747i | −0.999926 | − | 0.0121430i | \(-0.996135\pi\) |
0.510479 | + | 0.859890i | \(0.329468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.52897 | + | 9.57646i | 0.544786 | + | 0.943597i | 0.998620 | + | 0.0525110i | \(0.0167225\pi\) |
−0.453834 | + | 0.891086i | \(0.649944\pi\) | |||||||
\(104\) | −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 | 0.781295 | − | 0.624162i | \(-0.214560\pi\) |
−0.931188 | + | 0.364540i | \(0.881226\pi\) | |||||||
\(114\) | 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 | 0.999641 | + | 0.0267937i | \(0.00852971\pi\) |
−0.476616 | + | 0.879111i | \(0.658137\pi\) | |||||||
\(132\) | 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 | −0.258961 | − | 0.965888i | \(-0.583380\pi\) |
0.965964 | − | 0.258677i | \(-0.0832865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.95119 | − | 6.84367i | −0.335136 | − | 0.580472i | 0.648375 | − | 0.761321i | \(-0.275449\pi\) |
−0.983511 | + | 0.180849i | \(0.942116\pi\) | |||||||
\(140\) | 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 | −0.997505 | − | 0.0705895i | \(-0.977512\pi\) |
0.437620 | − | 0.899160i | \(-0.355821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.94982 | + | 3.37718i | −0.158674 | + | 0.274831i | −0.934391 | − | 0.356250i | \(-0.884055\pi\) |
0.775717 | + | 0.631081i | \(0.217389\pi\) | |||||||
\(152\) | −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 | \(-0.170406\pi\) |
−0.871839 | + | 0.489793i | \(0.837072\pi\) | |||||||
\(158\) | 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 | \(-0.127186\pi\) |
−0.797516 | + | 0.603298i | \(0.793853\pi\) | |||||||
\(168\) | 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 | \(-0.690156\pi\) |
0.997278 | + | 0.0737284i | \(0.0234898\pi\) | |||||||
\(174\) | 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 | \(-0.537828\pi\) | ||||
−0.118560 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(182\) | 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 | −0.787531 | − | 0.616275i | \(-0.788641\pi\) |
0.927475 | + | 0.373884i | \(0.121974\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.06793 | + | 3.58175i | 0.148853 | + | 0.257820i | 0.930804 | − | 0.365520i | \(-0.119109\pi\) |
−0.781951 | + | 0.623340i | \(0.785775\pi\) | |||||||
\(194\) | −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 | \(-0.571958\pi\) | ||||
−0.224143 | + | 0.974556i | \(0.571958\pi\) | |||||||
\(200\) | 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 | 0.992882 | − | 0.119105i | \(-0.0380025\pi\) |
−0.599589 | + | 0.800308i | \(0.704669\pi\) | |||||||
\(212\) | 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 | 0.437717 | + | 0.899113i | \(0.355787\pi\) |
−0.997513 | + | 0.0704822i | \(0.977546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.65250 | 0.575555 | ||||||||
\(227\) | −8.53501 | + | 14.7831i | −0.566489 | + | 0.981187i | 0.430421 | + | 0.902628i | \(0.358365\pi\) |
−0.996909 | + | 0.0785588i | \(0.974968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.89471 | + | 17.1381i | 0.653861 | + | 1.13252i | 0.982178 | + | 0.187953i | \(0.0601851\pi\) |
−0.328317 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(230\) | 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 | 0.983449 | + | 0.181187i | \(0.0579939\pi\) |
−0.334812 | + | 0.942285i | \(0.608673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6444 | − | 25.3648i | 0.943326 | − | 1.63389i | 0.184256 | − | 0.982878i | \(-0.441012\pi\) |
0.759069 | − | 0.651010i | \(-0.225654\pi\) | |||||||
\(242\) | −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 | \(-0.755448\pi\) | ||||
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(252\) | 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 | 0.944097 | + | 0.329668i | \(0.106937\pi\) |
−0.186547 | + | 0.982446i | \(0.559730\pi\) | |||||||
\(258\) | 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 | −0.967696 | − | 0.252120i | \(-0.918872\pi\) |
0.702190 | + | 0.711989i | \(0.252206\pi\) | |||||||
\(264\) | 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 | \(-0.653706\pi\) | ||||
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.67820 | 0.284181 | 0.142090 | − | 0.989854i | \(-0.454618\pi\) | ||||
0.142090 | + | 0.989854i | \(0.454618\pi\) | |||||||
\(272\) | −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 | −0.507550 | − | 0.861622i | \(-0.669449\pi\) |
0.999962 | + | 0.00873986i | \(0.00278202\pi\) | |||||||
\(278\) | 21.4560 | 1.28685 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75702 | + | 3.04325i | −0.104815 | + | 0.181545i | −0.913663 | − | 0.406473i | \(-0.866758\pi\) |
0.808848 | + | 0.588018i | \(0.200092\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0354 | + | 22.5780i | 0.774874 | + | 1.34212i | 0.934865 | + | 0.355002i | \(0.115520\pi\) |
−0.159992 | + | 0.987118i | \(0.551147\pi\) | |||||||
\(284\) | −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 | −0.998159 | − | 0.0606487i | \(-0.980683\pi\) |
0.446556 | − | 0.894756i | \(-0.352650\pi\) | |||||||
\(294\) | 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 | \(-0.288125\pi\) | ||||
0.617551 | + | 0.786531i | \(0.288125\pi\) | |||||||
\(308\) | 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 | \(-0.207339\pi\) |
−0.922680 | + | 0.385567i | \(0.874006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30102 | − | 7.44958i | 0.243108 | − | 0.421075i | −0.718490 | − | 0.695537i | \(-0.755166\pi\) |
0.961598 | + | 0.274462i | \(0.0884997\pi\) | |||||||
\(314\) | 0.799206 | 0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | −4.03128 | + | 6.98237i | −0.226419 | + | 0.392169i | −0.956744 | − | 0.290930i | \(-0.906035\pi\) |
0.730325 | + | 0.683100i | \(0.239369\pi\) | |||||||
\(318\) | 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 | −0.358249 | − | 0.933626i | \(-0.616626\pi\) |
0.987668 | − | 0.156560i | \(-0.0500405\pi\) | |||||||
\(332\) | 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 | 0.618339 | − | 0.785911i | \(-0.287806\pi\) |
−0.989789 | + | 0.142542i | \(0.954472\pi\) | |||||||
\(338\) | 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 | 0.825609 | − | 0.564243i | \(-0.190832\pi\) |
−0.901453 | + | 0.432877i | \(0.857498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.81202 | − | 3.13851i | 0.0969951 | − | 0.168000i | −0.813444 | − | 0.581643i | \(-0.802410\pi\) |
0.910440 | + | 0.413642i | \(0.135744\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.9893 | 1.43854 | ||||||||
\(353\) | 1.37701 | − | 2.38504i | 0.0732907 | − | 0.126943i | −0.827051 | − | 0.562127i | \(-0.809983\pi\) |
0.900342 | + | 0.435184i | \(0.143317\pi\) | |||||||
\(354\) | 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 | 0.363934 | + | 0.931425i | \(0.381433\pi\) |
−0.988605 | + | 0.150536i | \(0.951900\pi\) | |||||||
\(368\) | 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 | 0.999990 | − | 0.00455622i | \(-0.00145030\pi\) |
−0.503941 | + | 0.863738i | \(0.668117\pi\) | |||||||
\(374\) | −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 | 0.999856 | + | 0.0169915i | \(0.00540883\pi\) |
−0.485213 | + | 0.874396i | \(0.661258\pi\) | |||||||
\(384\) | 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 | −0.644782 | − | 0.764366i | \(-0.723052\pi\) |
0.984352 | + | 0.176215i | \(0.0563853\pi\) | |||||||
\(390\) | 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 | \(-0.350700\pi\) | ||||
0.452031 | + | 0.892002i | \(0.350700\pi\) | |||||||
\(398\) | 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 | 0.960685 | + | 0.277642i | \(0.0895528\pi\) |
−0.239898 | + | 0.970798i | \(0.577114\pi\) | |||||||
\(402\) | 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 | \(-0.253183\pi\) |
−0.968466 | + | 0.249147i | \(0.919850\pi\) | |||||||
\(410\) | −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 | \(-0.170517\pi\) |
−0.872009 | + | 0.489489i | \(0.837183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | − | 16.4600i | 0.463158 | − | 0.802212i | −0.535959 | − | 0.844244i | \(-0.680050\pi\) |
0.999116 | + | 0.0420318i | \(0.0133831\pi\) | |||||||
\(422\) | −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 | \(-0.202524\pi\) | ||||
0.804330 | + | 0.594183i | \(0.202524\pi\) | |||||||
\(434\) | 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 | \(-0.666850\pi\) |
1.00000 | 0.000574559i | \(0.000182888\pi\) | ||||||||
\(440\) | −19.5891 | −0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | −15.4290 | + | 26.7238i | −0.733054 | + | 1.26969i | 0.222517 | + | 0.974929i | \(0.428573\pi\) |
−0.955572 | + | 0.294759i | \(0.904761\pi\) | |||||||
\(444\) | 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 | 0.441356 | + | 0.897332i | \(0.354498\pi\) |
−0.997790 | + | 0.0664402i | \(0.978836\pi\) | |||||||
\(458\) | −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 | \(-0.703267\pi\) |
0.993397 | + | 0.114731i | \(0.0366005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | + | 31.3922i | 0.842306 | + | 1.45892i | 0.887940 | + | 0.459959i | \(0.152136\pi\) |
−0.0456338 | + | 0.998958i | \(0.514531\pi\) | |||||||
\(464\) | −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 | \(-0.560697\pi\) | ||||
−0.189531 | + | 0.981875i | \(0.560697\pi\) | |||||||
\(468\) | 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 | −0.411205 | − | 0.911543i | \(-0.634892\pi\) |
0.995022 | − | 0.0996574i | \(-0.0317747\pi\) | |||||||
\(480\) | 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 | −0.885532 | − | 0.464578i | \(-0.846206\pi\) |
0.0404294 | − | 0.999182i | \(-0.487127\pi\) | |||||||
\(492\) | 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 | −0.996196 | − | 0.0871432i | \(-0.972226\pi\) |
0.422630 | − | 0.906302i | \(-0.361107\pi\) | |||||||
\(500\) | −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 | \(-0.541252\pi\) | ||||
−0.129236 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(504\) | 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 | −0.997733 | − | 0.0672931i | \(-0.978564\pi\) |
0.440589 | − | 0.897709i | \(-0.354770\pi\) | |||||||
\(510\) | 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 | \(-0.448904\pi\) | ||||
0.159834 | + | 0.987144i | \(0.448904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7727 | −0.733421 | −0.366710 | − | 0.930335i | \(-0.619516\pi\) | ||||
−0.366710 | + | 0.930335i | \(0.619516\pi\) | |||||||
\(524\) | 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 | −0.264947 | − | 0.964263i | \(-0.585354\pi\) |
0.967550 | − | 0.252681i | \(-0.0813123\pi\) | |||||||
\(548\) | −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 | −0.995125 | − | 0.0986197i | \(-0.968557\pi\) |
0.412155 | − | 0.911114i | \(-0.364776\pi\) | |||||||
\(564\) | 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 | 0.0456782 | + | 0.998956i | \(0.485455\pi\) |
−0.887961 | + | 0.459920i | \(0.847878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.40565 | + | 5.89875i | 0.142522 | + | 0.246855i | 0.928446 | − | 0.371468i | \(-0.121146\pi\) |
−0.785924 | + | 0.618323i | \(0.787812\pi\) | |||||||
\(572\) | −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 | \(-0.226109\pi\) | ||||
0.758138 | + | 0.652094i | \(0.226109\pi\) | |||||||
\(578\) | 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 | \(-0.759367\pi\) |
0.957893 | + | 0.287126i | \(0.0927000\pi\) | |||||||
\(588\) | 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 | \(-0.366673\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366673\pi\) | |||||||
\(594\) | 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 | 0.619204 | − | 0.785230i | \(-0.287455\pi\) |
−0.989631 | + | 0.143632i | \(0.954122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3285 | − | 21.3536i | 0.502889 | − | 0.871030i | −0.497105 | − | 0.867690i | \(-0.665604\pi\) |
0.999994 | − | 0.00333942i | \(-0.00106297\pi\) | |||||||
\(602\) | 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 | \(-0.0526319\pi\) |
−0.635725 | + | 0.771916i | \(0.719299\pi\) | |||||||
\(608\) | 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 | 0.559810 | − | 0.828621i | \(-0.310874\pi\) |
−0.997512 | + | 0.0704988i | \(0.977541\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9024 | − | 29.2758i | 0.679366 | − | 1.17670i | −0.295807 | − | 0.955248i | \(-0.595588\pi\) |
0.975172 | − | 0.221448i | \(-0.0710782\pi\) | |||||||
\(620\) | 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 | −0.664940 | − | 0.746897i | \(-0.731543\pi\) |
0.979302 | + | 0.202406i | \(0.0648760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2527 | + | 22.9544i | 0.522636 | + | 0.905231i | 0.999653 | + | 0.0263376i | \(0.00838450\pi\) |
−0.477017 | + | 0.878894i | \(0.658282\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.37883 | − | 4.12026i | 0.0935938 | − | 0.162109i | ||||
\(647\) | 0.0160392 | 0.000630565 | 0.000315282 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000315282 | 1.00000i | \(0.499900\pi\) | ||||||||
\(648\) | 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 | −0.982801 | − | 0.184669i | \(-0.940879\pi\) |
0.331473 | − | 0.943465i | \(-0.392455\pi\) | |||||||
\(654\) | 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 | 0.188389 | + | 0.982094i | \(0.439673\pi\) |
−0.944713 | + | 0.327897i | \(0.893660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.65322 | + | 4.59551i | 0.103198 | + | 0.178745i | 0.913001 | − | 0.407958i | \(-0.133759\pi\) |
−0.809802 | + | 0.586703i | \(0.800426\pi\) | |||||||
\(662\) | 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 | −0.918584 | − | 0.395227i | \(-0.870666\pi\) |
0.801568 | + | 0.597903i | \(0.203999\pi\) | |||||||
\(674\) | 37.0285 | 1.42628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.5693 | −0.598819 | ||||||||
\(677\) | 17.3925 | − | 30.1247i | 0.668449 | − | 1.15779i | −0.309889 | − | 0.950773i | \(-0.600292\pi\) |
0.978338 | − | 0.207014i | \(-0.0663747\pi\) | |||||||
\(678\) | 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 | \(-0.873623\pi\) |
0.795979 | + | 0.605324i | \(0.206957\pi\) | |||||||
\(692\) | −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 | 0.343757 | + | 0.939059i | \(0.388300\pi\) |
−0.985127 | + | 0.171827i | \(0.945033\pi\) | |||||||
\(710\) | −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 | \(-0.809316\pi\) | ||||
−0.825870 | + | 0.563861i | \(0.809316\pi\) | |||||||
\(720\) | 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 | 0.475758 | + | 0.879576i | \(0.342174\pi\) |
−0.999614 | + | 0.0277700i | \(0.991159\pi\) | |||||||
\(728\) | 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 | \(-0.319538\pi\) |
−0.999061 | + | 0.0433249i | \(0.986205\pi\) | |||||||
\(734\) | −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 | −0.964169 | − | 0.265290i | \(-0.914532\pi\) |
0.252336 | − | 0.967640i | \(-0.418801\pi\) | |||||||
\(744\) | 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 | 0.597311 | − | 0.802010i | \(-0.296236\pi\) |
−0.993216 | + | 0.116282i | \(0.962903\pi\) | |||||||
\(752\) | −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 | \(-0.0890462\pi\) |
−0.719683 | + | 0.694303i | \(0.755713\pi\) | |||||||
\(762\) | 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 | −0.635022 | − | 0.772494i | \(-0.719009\pi\) |
−0.351488 | − | 0.936192i | \(-0.614324\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.1088 | − | 19.2410i | 0.399814 | − | 0.692498i | ||||
\(773\) | 2.36042 | 0.0848983 | 0.0424491 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424491 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(774\) | 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 | \(-0.176131\pi\) |
−0.880507 | + | 0.474034i | \(0.842797\pi\) | |||||||
\(788\) | −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 | −0.999967 | − | 0.00816511i | \(-0.997401\pi\) |
0.492912 | − | 0.870079i | \(-0.335932\pi\) | |||||||
\(798\) | 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 | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887082i | \(0.652729\pi\) | |||||||
\(812\) | 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 | −0.888289 | − | 0.459286i | \(-0.848105\pi\) |
0.841897 | + | 0.539638i | \(0.181439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.10769 | + | 10.5788i | 0.212901 | + | 0.368755i | 0.952621 | − | 0.304160i | \(-0.0983756\pi\) |
−0.739721 | + | 0.672914i | \(0.765042\pi\) | |||||||
\(824\) | 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 | \(-0.603193\pi\) | ||||
−0.318541 | + | 0.947909i | \(0.603193\pi\) | |||||||
\(830\) | 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 | \(-0.939357\pi\) |
0.654947 | + | 0.755675i | \(0.272691\pi\) | |||||||
\(840\) | 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 | \(-0.722337\pi\) |
0.984745 | + | 0.174002i | \(0.0556701\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.6176 | 0.602156 | ||||||||
\(857\) | 8.20001 | − | 14.2028i | 0.280107 | − | 0.485159i | −0.691304 | − | 0.722564i | \(-0.742963\pi\) |
0.971411 | + | 0.237405i | \(0.0762967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8575 | + | 29.1981i | 0.575172 | + | 0.996226i | 0.996023 | + | 0.0890968i | \(0.0283980\pi\) |
−0.420851 | + | 0.907130i | \(0.638269\pi\) | |||||||
\(860\) | 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 | 0.999998 | − | 0.00175202i | \(-0.000557684\pi\) |
−0.501517 | + | 0.865148i | \(0.667224\pi\) | |||||||
\(878\) | 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 | \(-0.0798934\pi\) | ||||
0.968666 | + | 0.248366i | \(0.0798934\pi\) | |||||||
\(882\) | 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 | −0.988968 | − | 0.148127i | \(-0.952676\pi\) |
0.366203 | − | 0.930535i | \(-0.380658\pi\) | |||||||
\(888\) | 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 | −0.994349 | − | 0.106157i | \(-0.966145\pi\) |
0.589110 | + | 0.808053i | \(0.299479\pi\) | |||||||
\(908\) | 91.6993 | 3.04315 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5493 | − | 21.7360i | 0.415776 | − | 0.720146i | −0.579733 | − | 0.814806i | \(-0.696843\pi\) |
0.995510 | + | 0.0946604i | \(0.0301765\pi\) | |||||||
\(912\) | 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 | −0.204170 | − | 0.978935i | \(-0.565450\pi\) |
0.949868 | − | 0.312651i | \(-0.101217\pi\) | |||||||
\(930\) | 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 | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(938\) | 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 | \(-0.233108\pi\) |
−0.950837 | + | 0.309691i | \(0.899774\pi\) | |||||||
\(942\) | 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 | −0.163692 | − | 0.986511i | \(-0.552340\pi\) |
0.936190 | − | 0.351494i | \(-0.114326\pi\) | |||||||
\(948\) | 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 | −0.981562 | − | 0.191145i | \(-0.938780\pi\) |
0.325244 | − | 0.945630i | \(-0.394553\pi\) | |||||||
\(968\) | 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 | \(-0.243586\pi\) | ||||
0.721210 | + | 0.692717i | \(0.243586\pi\) | |||||||
\(972\) | 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 | 0.875738 | + | 0.482787i | \(0.160375\pi\) |
−0.0197635 | + | 0.999805i | \(0.506291\pi\) | |||||||
\(978\) | 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 | \(-0.892588\pi\) |
0.758524 | + | 0.651646i | \(0.225921\pi\) | |||||||
\(984\) | 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 | 0.208612 | + | 0.977999i | \(0.433105\pi\) |
−0.951277 | + | 0.308336i | \(0.900228\pi\) | |||||||
\(998\) | 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.883.1 | 24 | ||
3.2 | odd | 2 | 441.2.f.h.295.11 | yes | 24 | ||
7.2 | even | 3 | 1323.2.h.h.802.11 | 24 | |||
7.3 | odd | 6 | 1323.2.g.h.667.1 | 24 | |||
7.4 | even | 3 | 1323.2.g.h.667.2 | 24 | |||
7.5 | odd | 6 | 1323.2.h.h.802.12 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.f.h.883.2 | 24 | ||
9.2 | odd | 6 | 3969.2.a.bh.1.2 | 12 | |||
9.4 | even | 3 | inner | 1323.2.f.h.442.1 | 24 | ||
9.5 | odd | 6 | 441.2.f.h.148.11 | ✓ | 24 | ||
9.7 | even | 3 | 3969.2.a.bi.1.11 | 12 | |||
21.2 | odd | 6 | 441.2.h.h.214.1 | 24 | |||
21.5 | even | 6 | 441.2.h.h.214.2 | 24 | |||
21.11 | odd | 6 | 441.2.g.h.79.12 | 24 | |||
21.17 | even | 6 | 441.2.g.h.79.11 | 24 | |||
21.20 | even | 2 | 441.2.f.h.295.12 | yes | 24 | ||
63.4 | even | 3 | 1323.2.h.h.226.11 | 24 | |||
63.5 | even | 6 | 441.2.g.h.67.11 | 24 | |||
63.13 | odd | 6 | inner | 1323.2.f.h.442.2 | 24 | ||
63.20 | even | 6 | 3969.2.a.bh.1.1 | 12 | |||
63.23 | odd | 6 | 441.2.g.h.67.12 | 24 | |||
63.31 | odd | 6 | 1323.2.h.h.226.12 | 24 | |||
63.32 | odd | 6 | 441.2.h.h.373.1 | 24 | |||
63.34 | odd | 6 | 3969.2.a.bi.1.12 | 12 | |||
63.40 | odd | 6 | 1323.2.g.h.361.1 | 24 | |||
63.41 | even | 6 | 441.2.f.h.148.12 | yes | 24 | ||
63.58 | even | 3 | 1323.2.g.h.361.2 | 24 | |||
63.59 | even | 6 | 441.2.h.h.373.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 9.5 | odd | 6 | ||
441.2.f.h.148.12 | yes | 24 | 63.41 | even | 6 | ||
441.2.f.h.295.11 | yes | 24 | 3.2 | odd | 2 | ||
441.2.f.h.295.12 | yes | 24 | 21.20 | even | 2 | ||
441.2.g.h.67.11 | 24 | 63.5 | even | 6 | |||
441.2.g.h.67.12 | 24 | 63.23 | odd | 6 | |||
441.2.g.h.79.11 | 24 | 21.17 | even | 6 | |||
441.2.g.h.79.12 | 24 | 21.11 | odd | 6 | |||
441.2.h.h.214.1 | 24 | 21.2 | odd | 6 | |||
441.2.h.h.214.2 | 24 | 21.5 | even | 6 | |||
441.2.h.h.373.1 | 24 | 63.32 | odd | 6 | |||
441.2.h.h.373.2 | 24 | 63.59 | even | 6 | |||
1323.2.f.h.442.1 | 24 | 9.4 | even | 3 | inner | ||
1323.2.f.h.442.2 | 24 | 63.13 | odd | 6 | inner | ||
1323.2.f.h.883.1 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.f.h.883.2 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.g.h.361.1 | 24 | 63.40 | odd | 6 | |||
1323.2.g.h.361.2 | 24 | 63.58 | even | 3 | |||
1323.2.g.h.667.1 | 24 | 7.3 | odd | 6 | |||
1323.2.g.h.667.2 | 24 | 7.4 | even | 3 | |||
1323.2.h.h.226.11 | 24 | 63.4 | even | 3 | |||
1323.2.h.h.226.12 | 24 | 63.31 | odd | 6 | |||
1323.2.h.h.802.11 | 24 | 7.2 | even | 3 | |||
1323.2.h.h.802.12 | 24 | 7.5 | odd | 6 | |||
3969.2.a.bh.1.1 | 12 | 63.20 | even | 6 | |||
3969.2.a.bh.1.2 | 12 | 9.2 | odd | 6 | |||
3969.2.a.bi.1.11 | 12 | 9.7 | even | 3 | |||
3969.2.a.bi.1.12 | 12 | 63.34 | odd | 6 |