Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
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 | 802.12 | ||
Character | \(\chi\) | \(=\) | 1323.802 |
Dual form | 1323.2.h.h.226.12 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71513 | 1.91989 | 0.959944 | − | 0.280191i | \(-0.0903976\pi\) | ||||
0.959944 | + | 0.280191i | \(0.0903976\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.37195 | 2.68597 | ||||||||
\(5\) | −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 | ||||||||
\(10\) | −2.15363 | + | 3.73020i | −0.681039 | + | 1.17959i | ||||
\(11\) | −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 | 0.997746 | − | 0.0671096i | \(-0.0213777\pi\) |
−0.556991 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1139 | 3.52848 | ||||||||
\(17\) | 1.40027 | − | 2.42534i | 0.339615 | − | 0.588230i | −0.644745 | − | 0.764397i | \(-0.723037\pi\) |
0.984360 | + | 0.176167i | \(0.0563699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.312846 | − | 0.541866i | −0.0717719 | − | 0.124313i | 0.827906 | − | 0.560867i | \(-0.189532\pi\) |
−0.899678 | + | 0.436554i | \(0.856199\pi\) | |||||||
\(20\) | −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 | ||||
\(26\) | 4.31479 | + | 7.47343i | 0.846199 | + | 1.46566i | ||||
\(27\) | 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 | ||||||||
\(31\) | 7.43005 | 1.33448 | 0.667238 | − | 0.744845i | \(-0.267476\pi\) | ||||
0.667238 | + | 0.744845i | \(0.267476\pi\) | |||||||
\(32\) | 20.0106 | 3.53741 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.80191 | − | 6.58511i | 0.652023 | − | 1.12934i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.01126 | − | 6.94770i | −0.659447 | − | 1.14220i | −0.980759 | − | 0.195222i | \(-0.937457\pi\) |
0.321312 | − | 0.946973i | \(-0.395876\pi\) | |||||||
\(38\) | −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 | \(-0.880384\pi\) |
0.147275 | − | 0.989096i | \(-0.452950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | + | 5.42022i | −0.477224 | + | 0.826576i | −0.999659 | − | 0.0261027i | \(-0.991690\pi\) |
0.522435 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(44\) | −3.62271 | − | 6.27472i | −0.546144 | − | 0.945950i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.386726 | + | 0.669829i | −0.0570197 | + | 0.0987609i | ||||
\(47\) | −11.1477 | −1.62605 | −0.813026 | − | 0.582227i | \(-0.802181\pi\) | ||||
−0.813026 | + | 0.582227i | \(0.802181\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | 1.39349 | − | 2.41359i | 0.191410 | − | 0.331532i | −0.754308 | − | 0.656521i | \(-0.772027\pi\) |
0.945718 | + | 0.324989i | \(0.105361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13965 | 0.288510 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.17410 | + | 10.6939i | −0.810699 | + | 1.40417i | ||||
\(59\) | −4.57469 | −0.595574 | −0.297787 | − | 0.954632i | \(-0.596248\pi\) | ||||
−0.297787 | + | 0.954632i | \(0.596248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.385014 | −0.0492960 | −0.0246480 | − | 0.999696i | \(-0.507846\pi\) | ||||
−0.0246480 | + | 0.999696i | \(0.507846\pi\) | |||||||
\(62\) | 20.1736 | 2.56205 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1036 | 3.26295 | ||||||||
\(65\) | −5.04207 | −0.625392 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.53916 | −0.310208 | −0.155104 | − | 0.987898i | \(-0.549571\pi\) | ||||
−0.155104 | + | 0.987898i | \(0.549571\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 0.234067 | − | 0.405416i | 0.0273955 | − | 0.0474503i | −0.852003 | − | 0.523538i | \(-0.824612\pi\) |
0.879398 | + | 0.476087i | \(0.157945\pi\) | |||||||
\(74\) | −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 | ||||||||
\(79\) | −15.7124 | −1.76778 | −0.883892 | − | 0.467691i | \(-0.845086\pi\) | ||||
−0.883892 | + | 0.467691i | \(0.845086\pi\) | |||||||
\(80\) | −11.1951 | + | 19.3905i | −1.25165 | + | 2.16792i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.6117 | − | 23.5762i | −1.50317 | − | 2.60356i | ||||
\(83\) | 6.99338 | − | 12.1129i | 0.767623 | − | 1.32956i | −0.171225 | − | 0.985232i | \(-0.554772\pi\) |
0.938848 | − | 0.344331i | \(-0.111894\pi\) | |||||||
\(84\) | 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 | ||||
\(89\) | −1.29353 | − | 2.24046i | −0.137114 | − | 0.237488i | 0.789289 | − | 0.614022i | \(-0.210449\pi\) |
−0.926403 | + | 0.376534i | \(0.877116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.765146 | + | 1.32527i | −0.0797719 | + | 0.138169i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −30.2674 | −3.12184 | ||||||||
\(95\) | 0.992595 | 0.101838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.22962 | − | 12.5221i | 0.734057 | − | 1.27142i | −0.221079 | − | 0.975256i | \(-0.570958\pi\) |
0.955136 | − | 0.296168i | \(-0.0957089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.67023 | + | 11.5532i | 0.667023 | + | 1.15532i | ||||
\(101\) | 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 | ||||
\(107\) | −0.962153 | − | 1.66650i | −0.0930149 | − | 0.161106i | 0.815764 | − | 0.578386i | \(-0.196317\pi\) |
−0.908778 | + | 0.417279i | \(0.862984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.30341 | − | 16.1140i | 0.891105 | − | 1.54344i | 0.0525523 | − | 0.998618i | \(-0.483264\pi\) |
0.838553 | − | 0.544821i | \(-0.183402\pi\) | |||||||
\(110\) | 5.80944 | 0.553908 | ||||||||
\(111\) | 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 | ||||
\(116\) | −12.2156 | + | 21.1580i | −1.13419 | + | 1.96447i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4209 | −1.14344 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.59043 | − | 7.95086i | 0.417312 | − | 0.722806i | ||||
\(122\) | −1.04536 | −0.0946428 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 39.9138 | 3.58437 | ||||||||
\(125\) | −11.8715 | −1.06182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37387 | −0.743061 | −0.371530 | − | 0.928421i | \(-0.621167\pi\) | ||||
−0.371530 | + | 0.928421i | \(0.621167\pi\) | |||||||
\(128\) | 30.8535 | 2.72709 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −13.6899 | −1.20068 | ||||||||
\(131\) | −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 | ||||||||
\(136\) | 12.8199 | − | 22.2046i | 1.09929 | − | 1.90403i | ||||
\(137\) | 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 | 0.983511 | − | 0.180849i | \(-0.0578845\pi\) |
−0.648375 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.94259 | 0.330855 | ||||||||
\(143\) | 2.14339 | − | 3.71245i | 0.179239 | − | 0.310451i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.60739 | − | 6.24819i | −0.299578 | − | 0.518884i | ||||
\(146\) | 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 | \(0.884055\pi\) | |||||||
\(152\) | −2.86420 | − | 4.96093i | −0.232317 | − | 0.402385i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.89349 | + | 10.2078i | −0.473376 | + | 0.819912i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.294352 | −0.0234919 | −0.0117459 | − | 0.999931i | \(-0.503739\pi\) | ||||
−0.0117459 | + | 0.999931i | \(0.503739\pi\) | |||||||
\(158\) | −42.6613 | −3.39395 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.8723 | + | 27.4917i | −1.25482 | + | 2.17341i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.35455 | − | 9.27436i | −0.419401 | − | 0.726424i | 0.576478 | − | 0.817112i | \(-0.304427\pi\) |
−0.995879 | + | 0.0906886i | \(0.971093\pi\) | |||||||
\(164\) | −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 | 0.797516 | − | 0.603298i | \(-0.206147\pi\) |
−0.921229 | + | 0.389020i | \(0.872814\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.44913 | − | 2.50997i | 0.111472 | − | 0.193074i | ||||
\(170\) | 6.03133 | + | 10.4466i | 0.462582 | + | 0.801215i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.8108 | + | 29.1171i | −1.28181 | + | 2.22016i | ||||
\(173\) | 11.4375 | 0.869577 | 0.434789 | − | 0.900533i | \(-0.356823\pi\) | ||||
0.434789 | + | 0.900533i | \(0.356823\pi\) | |||||||
\(174\) | 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 | ||||
\(179\) | 0.549275 | − | 0.951372i | 0.0410547 | − | 0.0711089i | −0.844768 | − | 0.535133i | \(-0.820262\pi\) |
0.885823 | + | 0.464024i | \(0.153595\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | 12.7269 | 0.935698 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.77723 | −0.276218 | ||||||||
\(188\) | −59.8846 | −4.36753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.69503 | 0.195518 | ||||||||
\(191\) | −3.86815 | −0.279889 | −0.139945 | − | 0.990159i | \(-0.544692\pi\) | ||||
−0.139945 | + | 0.990159i | \(0.544692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.13585 | −0.297705 | −0.148853 | − | 0.988859i | \(-0.547558\pi\) | ||||
−0.148853 | + | 0.988859i | \(0.547558\pi\) | |||||||
\(194\) | 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 | ||||||||
\(199\) | −3.16193 | + | 5.47663i | −0.224143 | + | 0.388228i | −0.956062 | − | 0.293164i | \(-0.905292\pi\) |
0.731919 | + | 0.681392i | \(0.238625\pi\) | |||||||
\(200\) | 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 | ||||||||
\(205\) | 15.9061 | 1.11093 | ||||||||
\(206\) | −15.0119 | + | 26.0014i | −1.04593 | + | 1.81160i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.4293 | + | 38.8487i | 1.55519 | + | 2.69367i | ||||
\(209\) | −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 | ||||
\(215\) | −4.96441 | − | 8.59860i | −0.338570 | − | 0.586420i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.2600 | − | 43.7516i | 1.71082 | − | 2.96323i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.4941 | 0.774931 | ||||||||
\(221\) | 8.90101 | 0.598747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.35953 | − | 14.4791i | 0.559796 | − | 0.969595i | −0.437717 | − | 0.899113i | \(-0.644213\pi\) |
0.997513 | − | 0.0704822i | \(-0.0224538\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.32625 | − | 7.49328i | −0.287778 | − | 0.498446i | ||||
\(227\) | 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 | ||||
\(233\) | 2.96579 | + | 5.13691i | 0.194296 | + | 0.336530i | 0.946669 | − | 0.322207i | \(-0.104425\pi\) |
−0.752374 | + | 0.658736i | \(0.771091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.84228 | − | 15.3153i | 0.576807 | − | 0.999058i | ||||
\(236\) | −24.5750 | −1.59969 | ||||||||
\(237\) | 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 | −0.759069 | − | 0.651010i | \(-0.774346\pi\) |
−0.184256 | − | 0.982878i | \(-0.558988\pi\) | |||||||
\(242\) | 12.4636 | − | 21.5877i | 0.801193 | − | 1.38771i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.06827 | −0.132408 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.994327 | − | 1.72223i | 0.0632675 | − | 0.109583i | ||||
\(248\) | 68.0242 | 4.31954 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −32.2328 | −2.03858 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | −22.7362 | −1.42659 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 31.5642 | 1.97276 | ||||||||
\(257\) | −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 | ||||||||
\(262\) | −16.2536 | + | 28.1520i | −1.00415 | + | 1.73924i | ||||
\(263\) | −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 | ||||||||
\(268\) | −13.6402 | −0.833209 | ||||||||
\(269\) | −7.61561 | + | 13.1906i | −0.464332 | + | 0.804247i | −0.999171 | − | 0.0407073i | \(-0.987039\pi\) |
0.534839 | + | 0.844954i | \(0.320372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.33910 | + | 4.05144i | 0.142090 | + | 0.246108i | 0.928284 | − | 0.371873i | \(-0.121284\pi\) |
−0.786193 | + | 0.617981i | \(0.787951\pi\) | |||||||
\(272\) | 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 | \(0.669449\pi\) | |||||||
\(278\) | 10.7280 | + | 18.5815i | 0.643423 | + | 1.11444i | ||||
\(279\) | 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 | ||||||||
\(283\) | 26.0708 | 1.54975 | 0.774874 | − | 0.632116i | \(-0.217813\pi\) | ||||
0.774874 | + | 0.632116i | \(0.217813\pi\) | |||||||
\(284\) | 7.80050 | 0.462874 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.81958 | − | 10.0798i | 0.344119 | − | 0.596031i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.57850 | + | 7.93019i | 0.269323 | + | 0.466482i | ||||
\(290\) | −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 | \(0.0193169\pi\) |
−0.446556 | + | 0.894756i | \(0.647350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.62863 | − | 6.28497i | 0.211267 | − | 0.365925i | ||||
\(296\) | −36.7242 | − | 63.6082i | −2.13455 | − | 3.69715i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.5559 | + | 32.1398i | −1.07492 | + | 1.86181i | ||||
\(299\) | −0.905400 | −0.0523606 | ||||||||
\(300\) | 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 | ||||
\(305\) | 0.305392 | − | 0.528954i | 0.0174867 | − | 0.0302878i | ||||
\(306\) | 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 | ||||
\(311\) | −4.49448 | −0.254859 | −0.127429 | − | 0.991848i | \(-0.540673\pi\) | ||||
−0.127429 | + | 0.991848i | \(0.540673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.60204 | 0.486216 | 0.243108 | − | 0.969999i | \(-0.421833\pi\) | ||||
0.243108 | + | 0.969999i | \(0.421833\pi\) | |||||||
\(314\) | −0.799206 | −0.0451018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.4062 | −4.74822 | ||||||||
\(317\) | 8.06255 | 0.452838 | 0.226419 | − | 0.974030i | \(-0.427298\pi\) | ||||
0.226419 | + | 0.974030i | \(0.427298\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.13402 | 0.343439 | ||||||||
\(320\) | −20.7053 | + | 35.8626i | −1.15746 | + | 2.00478i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.75228 | −0.0974992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.94646 | + | 6.83546i | −0.218910 | + | 0.379163i | ||||
\(326\) | −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 | ||||||||
\(331\) | −22.9026 | −1.25884 | −0.629419 | − | 0.777066i | \(-0.716707\pi\) | ||||
−0.629419 | + | 0.777066i | \(0.716707\pi\) | |||||||
\(332\) | 37.5681 | − | 65.0698i | 2.06182 | − | 3.57117i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.34075 | − | 7.51840i | −0.237515 | − | 0.411388i | ||||
\(335\) | 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 | ||||
\(341\) | −5.01065 | − | 8.67869i | −0.271342 | − | 0.469978i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −28.6502 | + | 49.6237i | −1.54472 | + | 2.67553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.0543 | 1.66949 | ||||||||
\(347\) | 2.82563 | 0.151688 | 0.0758440 | − | 0.997120i | \(-0.475835\pi\) | ||||
0.0758440 | + | 0.997120i | \(0.475835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81202 | + | 3.13851i | −0.0969951 | + | 0.168000i | −0.910440 | − | 0.413642i | \(-0.864256\pi\) |
0.813444 | + | 0.581643i | \(0.197590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.4947 | − | 23.3734i | −0.719268 | − | 1.24581i | ||||
\(353\) | −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 | ||||
\(359\) | −8.40076 | − | 14.5505i | −0.443375 | − | 0.767948i | 0.554562 | − | 0.832142i | \(-0.312886\pi\) |
−0.997937 | + | 0.0641941i | \(0.979552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.30425 | − | 16.1154i | 0.489698 | − | 0.848181i | ||||
\(362\) | 8.66163 | 0.455245 | ||||||||
\(363\) | 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 | \(0.618567\pi\) | |||||||
\(368\) | −2.01030 | + | 3.48193i | −0.104794 | + | 0.181508i | ||||
\(369\) | 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 | \(0.00145030\pi\) | |||||||
\(374\) | −10.2557 | −0.530309 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −102.060 | −5.26334 | ||||||||
\(377\) | −14.4548 | −0.744458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0770 | 0.517622 | 0.258811 | − | 0.965928i | \(-0.416669\pi\) | ||||
0.258811 | + | 0.965928i | \(0.416669\pi\) | |||||||
\(380\) | 5.33217 | 0.273534 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5025 | −0.537357 | ||||||||
\(383\) | −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 | ||||||||
\(388\) | 38.8372 | − | 67.2679i | 1.97166 | − | 3.41501i | ||||
\(389\) | 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 | ||||||||
\(394\) | 2.41448 | 0.121640 | ||||||||
\(395\) | 12.4630 | − | 21.5866i | 0.627083 | − | 1.08614i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00664 | + | 15.6000i | 0.452031 | + | 0.782940i | 0.998512 | − | 0.0545313i | \(-0.0173665\pi\) |
−0.546482 | + | 0.837471i | \(0.684033\pi\) | |||||||
\(398\) | −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 | ||||
\(404\) | 26.4240 | + | 45.7676i | 1.31464 | + | 2.27703i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.41019 | + | 9.37073i | −0.268173 | + | 0.464490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8587 | −0.536931 | −0.268465 | − | 0.963289i | \(-0.586516\pi\) | ||||
−0.268465 | + | 0.963289i | \(0.586516\pi\) | |||||||
\(410\) | 43.1872 | 2.13286 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.7014 | + | 51.4443i | −1.46328 | + | 2.53448i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0943 | + | 19.2158i | 0.544595 | + | 0.943267i | ||||
\(416\) | 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 | 0.872009 | − | 0.489489i | \(-0.162817\pi\) |
−0.859915 | + | 0.510438i | \(0.829483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | − | 16.4600i | 0.463158 | − | 0.802212i | −0.535959 | − | 0.844244i | \(-0.680050\pi\) |
0.999116 | + | 0.0420318i | \(0.0133831\pi\) | |||||||
\(422\) | 15.5113 | + | 26.8664i | 0.755079 | + | 1.30784i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.7578 | − | 22.0971i | 0.619572 | − | 1.07313i | ||||
\(425\) | 6.95473 | 0.337354 | ||||||||
\(426\) | 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 | ||||
\(431\) | −8.46073 | + | 14.6544i | −0.407539 | + | 0.705878i | −0.994613 | − | 0.103655i | \(-0.966946\pi\) |
0.587074 | + | 0.809533i | \(0.300280\pi\) | |||||||
\(432\) | 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 | ||||
\(437\) | 0.178239 | 0.00852634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9315 | 0.999005 | 0.499502 | − | 0.866313i | \(-0.333516\pi\) | ||||
0.499502 | + | 0.866313i | \(0.333516\pi\) | |||||||
\(440\) | 19.5891 | 0.933874 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.1674 | 1.14953 | ||||||||
\(443\) | 30.8580 | 1.46611 | 0.733054 | − | 0.680170i | \(-0.238094\pi\) | ||||
0.733054 | + | 0.680170i | \(0.238094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.10409 | 0.194553 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | −6.76168 | + | 11.7116i | −0.318395 | + | 0.551477i | ||||
\(452\) | −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 | ||||||||
\(457\) | 23.7904 | 1.11287 | 0.556434 | − | 0.830892i | \(-0.312169\pi\) | ||||
0.556434 | + | 0.830892i | \(0.312169\pi\) | |||||||
\(458\) | −26.8654 | + | 46.5323i | −1.25534 | + | 2.17431i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.21382 | − | 2.10240i | −0.0565947 | − | 0.0980249i | ||||
\(461\) | −8.53122 | + | 14.7765i | −0.397339 | + | 0.688211i | −0.993397 | − | 0.114731i | \(-0.963400\pi\) |
0.596058 | + | 0.802941i | \(0.296733\pi\) | |||||||
\(462\) | 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 | ||||
\(467\) | −4.09580 | − | 7.09413i | −0.189531 | − | 0.328277i | 0.755563 | − | 0.655076i | \(-0.227363\pi\) |
−0.945094 | + | 0.326799i | \(0.894030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 24.0080 | − | 41.5830i | 1.10740 | − | 1.91808i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −41.8826 | −1.92780 | ||||||||
\(473\) | 8.44148 | 0.388140 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.776909 | − | 1.34565i | 0.0356470 | − | 0.0617425i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.2265 | + | 47.1577i | 1.24531 | + | 2.15694i | ||||
\(479\) | −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 | ||||
\(485\) | 11.4690 | + | 19.8649i | 0.520782 | + | 0.902020i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.46140 | − | 5.99533i | 0.156851 | − | 0.271674i | −0.776880 | − | 0.629648i | \(-0.783199\pi\) |
0.933732 | + | 0.357974i | \(0.116532\pi\) | |||||||
\(488\) | −3.52491 | −0.159565 | ||||||||
\(489\) | 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 | ||||
\(494\) | 2.69973 | − | 4.67607i | 0.121467 | − | 0.210386i | ||||
\(495\) | 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 | \(0.972226\pi\) | |||||||
\(500\) | −63.7733 | −2.85203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 61.8658 | 2.76121 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 1.04320 | 0.0463757 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.9840 | −1.99584 | ||||||||
\(509\) | 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 | ||||||||
\(514\) | −32.9738 | + | 57.1123i | −1.45441 | + | 2.51911i | ||||
\(515\) | −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 | ||||||||
\(520\) | −46.1616 | −2.02432 | ||||||||
\(521\) | 3.64828 | − | 6.31900i | 0.159834 | − | 0.276841i | −0.774975 | − | 0.631992i | \(-0.782237\pi\) |
0.934809 | + | 0.355152i | \(0.115571\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.38637 | − | 14.5256i | −0.366710 | − | 0.635161i | 0.622339 | − | 0.782748i | \(-0.286183\pi\) |
−0.989049 | + | 0.147587i | \(0.952849\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | 6.00212 | + | 10.3960i | 0.260716 | + | 0.451573i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9339 | − | 27.5982i | 0.690172 | − | 1.19541i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.05271 | 0.131980 | ||||||||
\(536\) | −23.2467 | −1.00411 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.6774 | + | 35.8143i | −0.891466 | + | 1.54406i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.64908 | + | 4.58834i | 0.113893 | + | 0.197268i | 0.917337 | − | 0.398112i | \(-0.130335\pi\) |
−0.803444 | + | 0.595381i | \(0.797001\pi\) | |||||||
\(542\) | 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 | \(-0.0813123\pi\) | |||||||
\(548\) | 44.4542 | + | 76.9970i | 1.89899 | + | 3.28915i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.54708 | − | 7.87577i | 0.193888 | − | 0.335824i | ||||
\(551\) | 2.84560 | 0.121227 | ||||||||
\(552\) | 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 | ||||
\(557\) | −9.40798 | + | 16.2951i | −0.398629 | + | 0.690446i | −0.993557 | − | 0.113333i | \(-0.963847\pi\) |
0.594928 | + | 0.803779i | \(0.297181\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.8923 | −0.841354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.77054 | + | 8.26282i | −0.201233 | + | 0.348546i | ||||
\(563\) | −27.6650 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698109\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.05547 | 0.212685 | ||||||||
\(566\) | 70.7856 | 2.97534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.2942 | 0.557812 | ||||||||
\(569\) | 40.1831 | 1.68456 | 0.842282 | − | 0.539037i | \(-0.181212\pi\) | ||||
0.842282 | + | 0.539037i | \(0.181212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.81129 | −0.285044 | −0.142522 | − | 0.989792i | \(-0.545521\pi\) | ||||
−0.142522 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(572\) | 11.5142 | − | 19.9431i | 0.481431 | − | 0.833863i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.707427 | −0.0295017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2111 | − | 31.5425i | 0.758138 | − | 1.31313i | −0.185661 | − | 0.982614i | \(-0.559443\pi\) |
0.943799 | − | 0.330519i | \(-0.107224\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −3.75894 | −0.155679 | ||||||||
\(584\) | 2.14295 | − | 3.71170i | 0.0886759 | − | 0.153591i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.6361 | + | 44.4030i | 1.05902 | + | 1.83427i | ||||
\(587\) | −5.57943 | + | 9.66385i | −0.230288 | + | 0.398870i | −0.957893 | − | 0.287126i | \(-0.907300\pi\) |
0.727605 | + | 0.685996i | \(0.240633\pi\) | |||||||
\(588\) | 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 | ||||
\(593\) | 9.90427 | + | 17.1547i | 0.406720 | + | 0.704459i | 0.994520 | − | 0.104547i | \(-0.0333392\pi\) |
−0.587800 | + | 0.809006i | \(0.700006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −36.7133 | + | 63.5893i | −1.50384 | + | 2.60472i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.45828 | −0.100527 | ||||||||
\(599\) | 18.1320 | 0.740853 | 0.370427 | − | 0.928862i | \(-0.379211\pi\) | ||||
0.370427 | + | 0.928862i | \(0.379211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3285 | + | 21.3536i | −0.502889 | + | 0.871030i | 0.497105 | + | 0.867690i | \(0.334396\pi\) |
−0.999994 | + | 0.00333942i | \(0.998937\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.4743 | − | 18.1420i | −0.426194 | − | 0.738189i | ||||
\(605\) | 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 | ||||
\(611\) | −17.7154 | − | 30.6840i | −0.716689 | − | 1.24134i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.77828 | + | 16.9365i | −0.394941 | + | 0.684058i | −0.993094 | − | 0.117324i | \(-0.962568\pi\) |
0.598153 | + | 0.801382i | \(0.295902\pi\) | |||||||
\(614\) | −58.7575 | −2.37126 | ||||||||
\(615\) | 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 | −0.975172 | − | 0.221448i | \(-0.928922\pi\) |
0.295807 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(620\) | −31.6595 | + | 54.8359i | −1.27148 | + | 2.20226i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.2031 | −0.489300 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.20808 | − | 5.55655i | 0.128323 | − | 0.222262i | ||||
\(626\) | 23.3557 | 0.933481 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.58125 | −0.0630986 | ||||||||
\(629\) | −22.4674 | −0.895832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6410 | −0.941134 | −0.470567 | − | 0.882364i | \(-0.655951\pi\) | ||||
−0.470567 | + | 0.882364i | \(0.655951\pi\) | |||||||
\(632\) | −143.852 | −5.72211 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.8909 | 0.869399 | ||||||||
\(635\) | 6.64213 | − | 11.5045i | 0.263585 | − | 0.456542i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.6547 | 0.659365 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.4729 | + | 42.3883i | −0.967375 | + | 1.67554i | ||||
\(641\) | 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 | −0.999653 | − | 0.0263376i | \(-0.991616\pi\) |
0.477017 | − | 0.878894i | \(-0.341718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.75766 | −0.187188 | ||||||||
\(647\) | 0.00801958 | − | 0.0138903i | 0.000315282 | − | 0.000546085i | −0.865868 | − | 0.500273i | \(-0.833233\pi\) |
0.866183 | + | 0.499727i | \(0.166566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.08506 | + | 5.34348i | 0.121099 | + | 0.209750i | ||||
\(650\) | −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 | ||||
\(656\) | −70.7571 | − | 122.555i | −2.76260 | − | 4.78497i | ||||
\(657\) | 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 | ||||||||
\(661\) | 5.30644 | 0.206397 | 0.103198 | − | 0.994661i | \(-0.467092\pi\) | ||||
0.103198 | + | 0.994661i | \(0.467092\pi\) | |||||||
\(662\) | −62.1835 | −2.41683 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64.0264 | − | 110.897i | 2.48471 | − | 4.30364i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.647777 | − | 1.12198i | −0.0250820 | − | 0.0434433i | ||||
\(668\) | −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 | \(0.203999\pi\) | |||||||
\(674\) | −18.5142 | − | 32.0676i | −0.713142 | − | 1.23520i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.78465 | − | 13.4834i | 0.299410 | − | 0.518593i | ||||
\(677\) | 34.7850 | 1.33690 | 0.668449 | − | 0.743758i | \(-0.266959\pi\) | ||||
0.668449 | + | 0.743758i | \(0.266959\pi\) | |||||||
\(678\) | 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 | ||||
\(683\) | 9.71206 | − | 16.8218i | 0.371622 | − | 0.643667i | −0.618194 | − | 0.786026i | \(-0.712135\pi\) |
0.989815 | + | 0.142358i | \(0.0454686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.2556 | −1.00318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.1676 | + | 76.5006i | −1.68387 | + | 2.91656i | ||||
\(689\) | 8.85791 | 0.337459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.63675 | −0.252474 | −0.126237 | − | 0.992000i | \(-0.540290\pi\) | ||||
−0.126237 | + | 0.992000i | \(0.540290\pi\) | |||||||
\(692\) | 61.4416 | 2.33566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67197 | 0.291224 | ||||||||
\(695\) | −12.5363 | −0.475529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0798 | −1.06360 | ||||||||
\(698\) | −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 | ||||||||
\(703\) | −2.50982 | + | 4.34713i | −0.0946595 | + | 0.163955i | ||||
\(704\) | −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 | ||||||||
\(709\) | 34.1556 | 1.28274 | 0.641370 | − | 0.767231i | \(-0.278366\pi\) | ||||
0.641370 | + | 0.767231i | \(0.278366\pi\) | |||||||
\(710\) | −3.12725 | + | 5.41655i | −0.117364 | + | 0.203280i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.8426 | − | 20.5120i | −0.443821 | − | 0.768721i | ||||
\(713\) | −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 | ||||
\(719\) | −22.1450 | − | 38.3563i | −0.825870 | − | 1.43045i | −0.901253 | − | 0.433294i | \(-0.857351\pi\) |
0.0753825 | − | 0.997155i | \(-0.475982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.2623 | − | 43.7556i | 0.940165 | − | 1.62841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.1372 | 0.636899 | ||||||||
\(725\) | −11.2941 | −0.419453 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1247 | − | 24.4647i | 0.523857 | − | 0.907346i | −0.475758 | − | 0.879576i | \(-0.657826\pi\) |
0.999614 | − | 0.0277700i | \(-0.00884060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.00819 | + | 1.74623i | 0.0373147 | + | 0.0646310i | ||||
\(731\) | 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 | ||||
\(737\) | 1.71235 | + | 2.96587i | 0.0630752 | + | 0.109249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0115 | + | 27.7327i | −0.588992 | + | 1.02016i | 0.405373 | + | 0.914151i | \(0.367142\pi\) |
−0.994365 | + | 0.106013i | \(0.966192\pi\) | |||||||
\(740\) | 68.3680 | 2.51326 | ||||||||
\(741\) | 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 | ||||
\(746\) | 26.0118 | − | 45.0537i | 0.952359 | − | 1.64953i | ||||
\(747\) | 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 | \(0.296236\pi\) | |||||||
\(752\) | −157.337 | −5.73749 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −39.2466 | −1.42928 | ||||||||
\(755\) | 6.18635 | 0.225144 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5242 | 1.21846 | 0.609229 | − | 0.792995i | \(-0.291479\pi\) | ||||
0.609229 | + | 0.792995i | \(0.291479\pi\) | |||||||
\(758\) | 27.3605 | 0.993778 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.08748 | 0.329638 | ||||||||
\(761\) | −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 | ||||||||
\(766\) | −27.3462 | + | 47.3649i | −0.988057 | + | 1.71137i | ||||
\(767\) | −7.26992 | − | 12.5919i | −0.262502 | − | 0.454666i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.3568 | + | 47.3833i | 0.986510 | + | 1.70869i | 0.635022 | + | 0.772494i | \(0.280991\pi\) |
0.351488 | + | 0.936192i | \(0.385676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.2176 | −0.799628 | ||||||||
\(773\) | 1.18021 | − | 2.04418i | 0.0424491 | − | 0.0735240i | −0.844020 | − | 0.536311i | \(-0.819817\pi\) |
0.886469 | + | 0.462787i | \(0.153151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.22573 | + | 15.9794i | 0.331398 | + | 0.573998i | ||||
\(776\) | 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 | ||||
\(782\) | 1.08304 | + | 1.87588i | 0.0387295 | + | 0.0670814i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.233479 | − | 0.404398i | 0.00833323 | − | 0.0144336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.66794 | −0.0594557 | −0.0297278 | − | 0.999558i | \(-0.509464\pi\) | ||||
−0.0297278 | + | 0.999558i | \(0.509464\pi\) | |||||||
\(788\) | 4.77709 | 0.170177 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.8388 | − | 58.6105i | 1.20393 | − | 2.08527i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.611849 | − | 1.05975i | −0.0217274 | − | 0.0376330i | ||||
\(794\) | 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 | \(0.00259906\pi\) |
−0.492912 | + | 0.870079i | \(0.664068\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.6097 | + | 27.0368i | −0.552232 | + | 0.956493i | ||||
\(800\) | 24.8467 | + | 43.0358i | 0.878464 | + | 1.52154i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.1895 | − | 67.8783i | 1.38383 | − | 2.39687i | ||||
\(803\) | −0.631397 | −0.0222815 | ||||||||
\(804\) | 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 | ||||
\(809\) | −1.42846 | + | 2.47416i | −0.0502219 | + | 0.0869868i | −0.890043 | − | 0.455876i | \(-0.849326\pi\) |
0.839822 | + | 0.542862i | \(0.182660\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | 16.9889 | 0.595094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.91605 | 0.137005 | ||||||||
\(818\) | −29.4829 | −1.03085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4467 | 2.98393 | ||||||||
\(821\) | 2.65849 | 0.0927821 | 0.0463910 | − | 0.998923i | \(-0.485228\pi\) | ||||
0.0463910 | + | 0.998923i | \(0.485228\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2154 | −0.425801 | −0.212901 | − | 0.977074i | \(-0.568291\pi\) | ||||
−0.212901 | + | 0.977074i | \(0.568291\pi\) | |||||||
\(824\) | −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 | ||||||||
\(829\) | −9.17156 | + | 15.8856i | −0.318541 | + | 0.551730i | −0.980184 | − | 0.198089i | \(-0.936526\pi\) |
0.661642 | + | 0.749819i | \(0.269860\pi\) | |||||||
\(830\) | 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 | ||||||||
\(835\) | 5.07241 | 0.175538 | ||||||||
\(836\) | −2.26670 | + | 3.92605i | −0.0783956 | + | 0.135785i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.672190 | + | 1.16427i | 0.0232204 | + | 0.0402190i | ||||
\(839\) | 9.47055 | − | 16.4035i | 0.326960 | − | 0.566311i | −0.654947 | − | 0.755675i | \(-0.727309\pi\) |
0.981907 | + | 0.189364i | \(0.0606425\pi\) | |||||||
\(840\) | 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 | ||||
\(845\) | 2.29889 | + | 3.98179i | 0.0790842 | + | 0.136978i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.6676 | − | 34.0652i | 0.675387 | − | 1.16980i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.8830 | 0.647682 | ||||||||
\(851\) | 2.28535 | 0.0783408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.97922 | + | 17.2845i | −0.341682 | + | 0.591811i | −0.984745 | − | 0.174002i | \(-0.944330\pi\) |
0.643063 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.80878 | − | 15.2573i | −0.301078 | − | 0.521482i | ||||
\(857\) | −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 | ||||
\(863\) | −14.3415 | − | 24.8403i | −0.488191 | − | 0.845572i | 0.511716 | − | 0.859154i | \(-0.329010\pi\) |
−0.999908 | + | 0.0135822i | \(0.995677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.07219 | + | 15.7135i | −0.308464 | + | 0.534275i | ||||
\(866\) | −90.8865 | −3.08845 | ||||||||
\(867\) | 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 | ||||
\(872\) | 85.1753 | − | 147.528i | 2.88440 | − | 4.99593i | ||||
\(873\) | 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 | \(0.000557684\pi\) | |||||||
\(878\) | 56.8317 | 1.91798 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 30.1988 | 1.01800 | ||||||||
\(881\) | −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 | \(0.391478\pi\) | |||||||
\(884\) | 47.8158 | 1.60822 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.7836 | 2.81477 | ||||||||
\(887\) | 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 | ||||||||
\(892\) | 44.9070 | − | 77.7812i | 1.50360 | − | 2.60431i | ||||
\(893\) | 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 | ||||||||
\(898\) | 90.3565 | 3.01524 | ||||||||
\(899\) | −16.8956 | + | 29.2641i | −0.563501 | + | 0.976012i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.90251 | − | 6.75935i | −0.130012 | − | 0.225187i | ||||
\(902\) | −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 | \(0.966145\pi\) | |||||||
\(908\) | 45.8496 | + | 79.4139i | 1.52157 | + | 2.63544i | ||||
\(909\) | 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 | ||||||||
\(913\) | −18.8647 | −0.624330 | ||||||||
\(914\) | 64.5941 | 2.13658 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.1538 | + | 92.0652i | −1.75625 | + | 3.04192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2988 | + | 24.7662i | 0.471674 | + | 0.816963i | 0.999475 | − | 0.0324050i | \(-0.0103167\pi\) |
−0.527801 | + | 0.849368i | \(0.676983\pi\) | |||||||
\(920\) | −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 | ||||
\(926\) | 49.2098 | + | 85.2339i | 1.61713 | + | 2.80096i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.5033 | + | 78.8140i | −1.49372 | + | 2.58720i | ||||
\(929\) | 45.4570 | 1.49140 | 0.745698 | − | 0.666284i | \(-0.232116\pi\) | ||||
0.745698 | + | 0.666284i | \(0.232116\pi\) | |||||||
\(930\) | 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 | ||||
\(935\) | 2.99609 | − | 5.18937i | 0.0979825 | − | 0.169711i | ||||
\(936\) | 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 | ||||
\(941\) | −12.7131 | −0.414436 | −0.207218 | − | 0.978295i | \(-0.566441\pi\) | ||||
−0.207218 | + | 0.978295i | \(0.566441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85624 | 0.0930121 | ||||||||
\(944\) | −64.5667 | −2.10147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.9197 | 0.745185 | ||||||||
\(947\) | −47.5447 | −1.54500 | −0.772498 | − | 0.635017i | \(-0.780993\pi\) | ||||
−0.772498 | + | 0.635017i | \(0.780993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.48788 | 0.0482987 | ||||||||
\(950\) | 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 | ||||||||
\(955\) | 3.06820 | − | 5.31428i | 0.0992847 | − | 0.171966i | ||||
\(956\) | 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 | ||||||||
\(961\) | 24.2056 | 0.780826 | ||||||||
\(962\) | 34.6154 | − | 59.9557i | 1.11605 | − | 1.93305i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −78.6687 | − | 136.258i | −2.53375 | − | 4.38858i | ||||
\(965\) | 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 | ||||
\(971\) | 22.4735 | + | 38.9253i | 0.721210 | + | 1.24917i | 0.960515 | + | 0.278228i | \(0.0897470\pi\) |
−0.239305 | + | 0.970944i | \(0.576920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.39817 | − | 16.2781i | 0.301137 | − | 0.521584i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.43405 | −0.173940 | ||||||||
\(977\) | −53.5104 | −1.71195 | −0.855974 | − | 0.517018i | \(-0.827042\pi\) | ||||
−0.855974 | + | 0.517018i | \(0.827042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.74465 | + | 3.02182i | −0.0557593 | + | 0.0965779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −50.8442 | − | 88.0647i | −1.62250 | − | 2.81026i | ||||
\(983\) | 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 | ||||
\(989\) | −0.891454 | − | 1.54404i | −0.0283466 | − | 0.0490977i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0046 | + | 22.5246i | −0.413104 | + | 0.715517i | −0.995227 | − | 0.0975835i | \(-0.968889\pi\) |
0.582123 | + | 0.813100i | \(0.302222\pi\) | |||||||
\(992\) | 148.680 | 4.72058 | ||||||||
\(993\) | 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 | \(0.566895\pi\) | |||||||
\(998\) | −34.7876 | + | 60.2539i | −1.10118 | + | 1.90731i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1323.2.h.h.802.12 | 24 | ||
3.2 | odd | 2 | 441.2.h.h.214.2 | 24 | |||
7.2 | even | 3 | 1323.2.g.h.667.1 | 24 | |||
7.3 | odd | 6 | 1323.2.f.h.883.1 | 24 | |||
7.4 | even | 3 | 1323.2.f.h.883.2 | 24 | |||
7.5 | odd | 6 | 1323.2.g.h.667.2 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.h.h.802.11 | 24 | ||
9.4 | even | 3 | 1323.2.g.h.361.1 | 24 | |||
9.5 | odd | 6 | 441.2.g.h.67.11 | 24 | |||
21.2 | odd | 6 | 441.2.g.h.79.11 | 24 | |||
21.5 | even | 6 | 441.2.g.h.79.12 | 24 | |||
21.11 | odd | 6 | 441.2.f.h.295.12 | yes | 24 | ||
21.17 | even | 6 | 441.2.f.h.295.11 | yes | 24 | ||
21.20 | even | 2 | 441.2.h.h.214.1 | 24 | |||
63.4 | even | 3 | 1323.2.f.h.442.2 | 24 | |||
63.5 | even | 6 | 441.2.h.h.373.1 | 24 | |||
63.11 | odd | 6 | 3969.2.a.bh.1.1 | 12 | |||
63.13 | odd | 6 | 1323.2.g.h.361.2 | 24 | |||
63.23 | odd | 6 | 441.2.h.h.373.2 | 24 | |||
63.25 | even | 3 | 3969.2.a.bi.1.12 | 12 | |||
63.31 | odd | 6 | 1323.2.f.h.442.1 | 24 | |||
63.32 | odd | 6 | 441.2.f.h.148.12 | yes | 24 | ||
63.38 | even | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.40 | odd | 6 | inner | 1323.2.h.h.226.11 | 24 | ||
63.41 | even | 6 | 441.2.g.h.67.12 | 24 | |||
63.52 | odd | 6 | 3969.2.a.bi.1.11 | 12 | |||
63.58 | even | 3 | inner | 1323.2.h.h.226.12 | 24 | ||
63.59 | even | 6 | 441.2.f.h.148.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 63.59 | even | 6 | ||
441.2.f.h.148.12 | yes | 24 | 63.32 | odd | 6 | ||
441.2.f.h.295.11 | yes | 24 | 21.17 | even | 6 | ||
441.2.f.h.295.12 | yes | 24 | 21.11 | odd | 6 | ||
441.2.g.h.67.11 | 24 | 9.5 | odd | 6 | |||
441.2.g.h.67.12 | 24 | 63.41 | even | 6 | |||
441.2.g.h.79.11 | 24 | 21.2 | odd | 6 | |||
441.2.g.h.79.12 | 24 | 21.5 | even | 6 | |||
441.2.h.h.214.1 | 24 | 21.20 | even | 2 | |||
441.2.h.h.214.2 | 24 | 3.2 | odd | 2 | |||
441.2.h.h.373.1 | 24 | 63.5 | even | 6 | |||
441.2.h.h.373.2 | 24 | 63.23 | odd | 6 | |||
1323.2.f.h.442.1 | 24 | 63.31 | odd | 6 | |||
1323.2.f.h.442.2 | 24 | 63.4 | even | 3 | |||
1323.2.f.h.883.1 | 24 | 7.3 | odd | 6 | |||
1323.2.f.h.883.2 | 24 | 7.4 | even | 3 | |||
1323.2.g.h.361.1 | 24 | 9.4 | even | 3 | |||
1323.2.g.h.361.2 | 24 | 63.13 | odd | 6 | |||
1323.2.g.h.667.1 | 24 | 7.2 | even | 3 | |||
1323.2.g.h.667.2 | 24 | 7.5 | odd | 6 | |||
1323.2.h.h.226.11 | 24 | 63.40 | odd | 6 | inner | ||
1323.2.h.h.226.12 | 24 | 63.58 | even | 3 | inner | ||
1323.2.h.h.802.11 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.802.12 | 24 | 1.1 | even | 1 | trivial | ||
3969.2.a.bh.1.1 | 12 | 63.11 | odd | 6 | |||
3969.2.a.bh.1.2 | 12 | 63.38 | even | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.52 | odd | 6 | |||
3969.2.a.bi.1.12 | 12 | 63.25 | even | 3 |