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 | 226.11 | ||
Character | \(\chi\) | \(=\) | 1323.226 |
Dual form | 1323.2.h.h.802.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71513 | 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 | \(-0.0512400\pi\) |
−0.632343 | + | 0.774688i | \(0.717907\pi\) | |||||||
\(6\) | 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 | −0.949600 | − | 0.313464i | \(-0.898510\pi\) |
0.746268 | + | 0.665646i | \(0.231844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58916 | + | 2.75251i | −0.440754 | + | 0.763409i | −0.997746 | − | 0.0671096i | \(-0.978622\pi\) |
0.556991 | + | 0.830518i | \(0.311956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1139 | 3.52848 | ||||||||
\(17\) | −1.40027 | − | 2.42534i | −0.339615 | − | 0.588230i | 0.644745 | − | 0.764397i | \(-0.276963\pi\) |
−0.984360 | + | 0.176167i | \(0.943630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.312846 | − | 0.541866i | 0.0717719 | − | 0.124313i | −0.827906 | − | 0.560867i | \(-0.810468\pi\) |
0.899678 | + | 0.436554i | \(0.143801\pi\) | |||||||
\(20\) | 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 | ||||
\(26\) | −4.31479 | + | 7.47343i | −0.846199 | + | 1.46566i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27396 | − | 3.93861i | −0.422264 | − | 0.731382i | 0.573897 | − | 0.818928i | \(-0.305431\pi\) |
−0.996161 | + | 0.0875454i | \(0.972098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43005 | −1.33448 | −0.667238 | − | 0.744845i | \(-0.732524\pi\) | ||||
−0.667238 | + | 0.744845i | \(0.732524\pi\) | |||||||
\(32\) | 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 | 0.321312 | + | 0.946973i | \(0.395876\pi\) |
−0.980759 | + | 0.195222i | \(0.937457\pi\) | |||||||
\(38\) | 0.849420 | − | 1.47124i | 0.137794 | − | 0.238666i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.26194 | + | 12.5780i | 1.14821 | + | 1.98876i | ||||
\(41\) | 5.01329 | − | 8.68327i | 0.782944 | − | 1.35610i | −0.147275 | − | 0.989096i | \(-0.547050\pi\) |
0.930219 | − | 0.367004i | \(-0.119616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12937 | − | 5.42022i | −0.477224 | − | 0.826576i | 0.522435 | − | 0.852679i | \(-0.325024\pi\) |
−0.999659 | + | 0.0261027i | \(0.991690\pi\) | |||||||
\(44\) | −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 | \(-0.197819\pi\) | ||||
0.813026 | + | 0.582227i | \(0.197819\pi\) | |||||||
\(48\) | 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 | 0.945718 | − | 0.324989i | \(-0.105361\pi\) |
−0.754308 | + | 0.656521i | \(0.772027\pi\) | |||||||
\(54\) | 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 | \(-0.403752\pi\) | ||||
0.297787 | + | 0.954632i | \(0.403752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.385014 | 0.0492960 | 0.0246480 | − | 0.999696i | \(-0.492154\pi\) | ||||
0.0246480 | + | 0.999696i | \(0.492154\pi\) | |||||||
\(62\) | −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 | \(-0.175388\pi\) |
−0.879398 | + | 0.476087i | \(0.842055\pi\) | |||||||
\(74\) | −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 | −0.938848 | − | 0.344331i | \(-0.888106\pi\) |
0.171225 | − | 0.985232i | \(-0.445228\pi\) | |||||||
\(84\) | 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 | \(-0.789551\pi\) |
0.926403 | + | 0.376534i | \(0.122884\pi\) | |||||||
\(90\) | 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 | −0.955136 | − | 0.296168i | \(-0.904291\pi\) |
0.221079 | − | 0.975256i | \(-0.429042\pi\) | |||||||
\(98\) | 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 | \(-0.996135\pi\) |
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 | ||||
\(107\) | −0.962153 | + | 1.66650i | −0.0930149 | + | 0.161106i | −0.908778 | − | 0.417279i | \(-0.862984\pi\) |
0.815764 | + | 0.578386i | \(0.196317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.30341 | + | 16.1140i | 0.891105 | + | 1.54344i | 0.838553 | + | 0.544821i | \(0.183402\pi\) |
0.0525523 | + | 0.998618i | \(0.483264\pi\) | |||||||
\(110\) | −5.80944 | −0.553908 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.59338 | + | 2.75982i | −0.149893 | + | 0.259622i | −0.931188 | − | 0.364540i | \(-0.881226\pi\) |
0.781295 | + | 0.624162i | \(0.214560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.225956 | − | 0.391367i | 0.0210705 | − | 0.0364951i | ||||
\(116\) | −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 | 0.999641 | + | 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 | ||||||||
\(136\) | −12.8199 | − | 22.2046i | −1.09929 | − | 1.90403i | ||||
\(137\) | 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 | −0.983511 | − | 0.180849i | \(-0.942116\pi\) |
0.648375 | + | 0.761321i | \(0.275449\pi\) | |||||||
\(140\) | 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 | −0.997505 | − | 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 | \(0.217389\pi\) | |||||||
\(152\) | 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 | \(-0.496261\pi\) | ||||
0.0117459 | + | 0.999931i | \(0.496261\pi\) | |||||||
\(158\) | −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 | −0.995879 | − | 0.0906886i | \(-0.971093\pi\) |
0.576478 | + | 0.817112i | \(0.304427\pi\) | |||||||
\(164\) | 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 | \(-0.793853\pi\) |
0.921229 | + | 0.389020i | \(0.127186\pi\) | |||||||
\(168\) | 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 | \(-0.643177\pi\) | ||||
−0.434789 | + | 0.900533i | \(0.643177\pi\) | |||||||
\(174\) | 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 | 0.885823 | − | 0.464024i | \(-0.153595\pi\) |
−0.844768 | + | 0.535133i | \(0.820262\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | −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 | \(-0.0947083\pi\) |
−0.731919 | + | 0.681392i | \(0.761375\pi\) | |||||||
\(200\) | 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 | −0.599589 | − | 0.800308i | \(-0.704669\pi\) |
0.992882 | + | 0.119105i | \(0.0380025\pi\) | |||||||
\(212\) | 7.48574 | + | 12.9657i | 0.514123 | + | 0.890487i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.61237 | + | 4.52476i | −0.178578 | + | 0.309307i | ||||
\(215\) | 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 | −0.997513 | − | 0.0704822i | \(-0.977546\pi\) |
0.437717 | − | 0.899113i | \(-0.355787\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.32625 | + | 7.49328i | −0.287778 | + | 0.498446i | ||||
\(227\) | −8.53501 | + | 14.7831i | −0.566489 | + | 0.981187i | 0.430421 | + | 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 | ||||
\(233\) | 2.96579 | − | 5.13691i | 0.194296 | − | 0.336530i | −0.752374 | − | 0.658736i | \(-0.771091\pi\) |
0.946669 | + | 0.322207i | \(0.104425\pi\) | |||||||
\(234\) | 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 | −0.334812 | − | 0.942285i | \(-0.608673\pi\) |
0.983449 | − | 0.181187i | \(-0.0579939\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6444 | − | 25.3648i | 0.943326 | − | 1.63389i | 0.184256 | − | 0.982878i | \(-0.441012\pi\) |
0.759069 | − | 0.651010i | \(-0.225654\pi\) | |||||||
\(242\) | 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 | \(-0.755448\pi\) | ||||
−0.719106 | + | 0.694901i | \(0.755448\pi\) | |||||||
\(252\) | 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 | 0.944097 | + | 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 | ||||||||
\(262\) | 16.2536 | + | 28.1520i | 1.00415 | + | 1.73924i | ||||
\(263\) | −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 | ||||||||
\(268\) | −13.6402 | −0.833209 | ||||||||
\(269\) | 7.61561 | + | 13.1906i | 0.464332 | + | 0.804247i | 0.999171 | − | 0.0407073i | \(-0.0129611\pi\) |
−0.534839 | + | 0.844954i | \(0.679628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.33910 | + | 4.05144i | −0.142090 | + | 0.246108i | −0.928284 | − | 0.371873i | \(-0.878716\pi\) |
0.786193 | + | 0.617981i | \(0.212049\pi\) | |||||||
\(272\) | −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 | \(0.00278202\pi\) | |||||||
\(278\) | −10.7280 | + | 18.5815i | −0.643423 | + | 1.11444i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75702 | − | 3.04325i | −0.104815 | − | 0.181545i | 0.808848 | − | 0.588018i | \(-0.200092\pi\) |
−0.913663 | + | 0.406473i | \(0.866758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.0708 | −1.54975 | −0.774874 | − | 0.632116i | \(-0.782187\pi\) | ||||
−0.774874 | + | 0.632116i | \(0.782187\pi\) | |||||||
\(284\) | 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 | 0.446556 | + | 0.894756i | \(0.352650\pi\) |
−0.998159 | + | 0.0606487i | \(0.980683\pi\) | |||||||
\(294\) | 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 | \(-0.288125\pi\) | ||||
0.617551 | + | 0.786531i | \(0.288125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.0016 | − | 27.7156i | −0.908830 | − | 1.57414i | ||||
\(311\) | 4.49448 | 0.254859 | 0.127429 | − | 0.991848i | \(-0.459327\pi\) | ||||
0.127429 | + | 0.991848i | \(0.459327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.60204 | −0.486216 | −0.243108 | − | 0.969999i | \(-0.578167\pi\) | ||||
−0.243108 | + | 0.969999i | \(0.578167\pi\) | |||||||
\(314\) | 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 | −0.989789 | − | 0.142542i | \(-0.954472\pi\) |
0.618339 | + | 0.785911i | \(0.287806\pi\) | |||||||
\(338\) | 3.93458 | + | 6.81489i | 0.214013 | + | 0.370681i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.9331 | − | 20.6688i | 0.647164 | − | 1.12092i | ||||
\(341\) | 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 | \(-0.135744\pi\) |
−0.813444 | + | 0.581643i | \(0.802410\pi\) | |||||||
\(350\) | 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 | \(-0.809983\pi\) |
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 | ||||
\(359\) | −8.40076 | + | 14.5505i | −0.443375 | + | 0.767948i | −0.997937 | − | 0.0641941i | \(-0.979552\pi\) |
0.554562 | + | 0.832142i | \(0.312886\pi\) | |||||||
\(360\) | 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 | 0.363934 | + | 0.931425i | \(0.381433\pi\) |
−0.988605 | + | 0.150536i | \(0.951900\pi\) | |||||||
\(368\) | −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 | 0.999990 | − | 0.00455622i | \(-0.00145030\pi\) |
−0.503941 | + | 0.863738i | \(0.668117\pi\) | |||||||
\(374\) | 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 | 0.999856 | + | 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 | ||||||||
\(388\) | −38.8372 | − | 67.2679i | −1.97166 | − | 3.41501i | ||||
\(389\) | 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 | ||||||||
\(394\) | 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 | \(-0.982634\pi\) |
0.546482 | + | 0.837471i | \(0.315967\pi\) | |||||||
\(398\) | 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 | ||||
\(404\) | −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 | \(-0.413484\pi\) | ||||
0.268465 | + | 0.963289i | \(0.413484\pi\) | |||||||
\(410\) | 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 | \(-0.837183\pi\) |
0.859915 | + | 0.510438i | \(0.170517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.50320 | + | 16.4600i | 0.463158 | + | 0.802212i | 0.999116 | − | 0.0420318i | \(-0.0133831\pi\) |
−0.535959 | + | 0.844244i | \(0.680050\pi\) | |||||||
\(422\) | 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 | 0.587074 | − | 0.809533i | \(-0.300280\pi\) |
−0.994613 | + | 0.103655i | \(0.966946\pi\) | |||||||
\(432\) | 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 | ||||
\(437\) | −0.178239 | −0.00852634 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9315 | −0.999005 | −0.499502 | − | 0.866313i | \(-0.666484\pi\) | ||||
−0.499502 | + | 0.866313i | \(0.666484\pi\) | |||||||
\(440\) | −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 | \(-0.0366005\pi\) |
−0.596058 | + | 0.802941i | \(0.703267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1243 | − | 31.3922i | 0.842306 | − | 1.45892i | −0.0456338 | − | 0.998958i | \(-0.514531\pi\) |
0.887940 | − | 0.459959i | \(-0.152136\pi\) | |||||||
\(464\) | −32.0945 | − | 55.5893i | −1.48995 | − | 2.58067i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.05253 | − | 13.9474i | 0.373026 | − | 0.646100i | ||||
\(467\) | 4.09580 | − | 7.09413i | 0.189531 | − | 0.328277i | −0.755563 | − | 0.655076i | \(-0.772637\pi\) |
0.945094 | + | 0.326799i | \(0.105970\pi\) | |||||||
\(468\) | 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 | −0.411205 | − | 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 | ||||
\(485\) | 11.4690 | − | 19.8649i | 0.520782 | − | 0.902020i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.46140 | + | 5.99533i | 0.156851 | + | 0.271674i | 0.933732 | − | 0.357974i | \(-0.116532\pi\) |
−0.776880 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(488\) | 3.52491 | 0.159565 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7262 | + | 32.4348i | −0.845103 | + | 1.46376i | 0.0404294 | + | 0.999182i | \(0.487127\pi\) |
−0.885532 | + | 0.464578i | \(0.846206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.36831 | + | 11.0302i | −0.286814 | + | 0.496777i | ||||
\(494\) | 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 | −0.996196 | − | 0.0871432i | \(-0.972226\pi\) |
0.422630 | − | 0.906302i | \(-0.361107\pi\) | |||||||
\(500\) | 63.7733 | 2.85203 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −61.8658 | −2.76121 | ||||||||
\(503\) | −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 | ||||||||
\(506\) | 1.04320 | 0.0463757 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.9840 | −1.99584 | ||||||||
\(509\) | −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 | ||||||||
\(514\) | 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 | \(-0.217763\pi\) |
−0.934809 | + | 0.355152i | \(0.884429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.38637 | − | 14.5256i | 0.366710 | − | 0.635161i | −0.622339 | − | 0.782748i | \(-0.713817\pi\) |
0.989049 | + | 0.147587i | \(0.0471506\pi\) | |||||||
\(524\) | 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 | −0.803444 | − | 0.595381i | \(-0.797001\pi\) |
0.917337 | + | 0.398112i | \(0.130335\pi\) | |||||||
\(542\) | −6.35097 | + | 11.0002i | −0.272798 | + | 0.472499i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.0202 | − | 48.5324i | −1.20136 | − | 2.08081i | ||||
\(545\) | −14.7589 | + | 25.5631i | −0.632200 | + | 1.09500i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4325 | + | 28.4619i | 0.702603 | + | 1.21694i | 0.967550 | + | 0.252681i | \(0.0813123\pi\) |
−0.264947 | + | 0.964263i | \(0.585354\pi\) | |||||||
\(548\) | 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 | 0.594928 | − | 0.803779i | \(-0.297181\pi\) |
−0.993557 | + | 0.113333i | \(0.963847\pi\) | |||||||
\(558\) | 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 | \(-0.301891\pi\) | ||||
0.582970 | + | 0.812494i | \(0.301891\pi\) | |||||||
\(564\) | 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 | −0.943799 | − | 0.330519i | \(-0.892776\pi\) |
0.185661 | − | 0.982614i | \(-0.440557\pi\) | |||||||
\(578\) | 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 | \(-0.0927000\pi\) |
−0.727605 | + | 0.685996i | \(0.759367\pi\) | |||||||
\(588\) | 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 | \(-0.966661\pi\) |
0.587800 | + | 0.809006i | \(0.299994\pi\) | |||||||
\(594\) | 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 | 0.999994 | + | 0.00333942i | \(0.00106297\pi\) |
−0.497105 | + | 0.867690i | \(0.665604\pi\) | |||||||
\(602\) | 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 | \(-0.0526319\pi\) |
−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 | ||||
\(611\) | −17.7154 | + | 30.6840i | −0.716689 | + | 1.24134i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.77828 | − | 16.9365i | −0.394941 | − | 0.684058i | 0.598153 | − | 0.801382i | \(-0.295902\pi\) |
−0.993094 | + | 0.117324i | \(0.962568\pi\) | |||||||
\(614\) | 58.7575 | 2.37126 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8723 | + | 18.8314i | −0.437702 | + | 0.758122i | −0.997512 | − | 0.0704988i | \(-0.977541\pi\) |
0.559810 | + | 0.828621i | \(0.310874\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9024 | − | 29.2758i | 0.679366 | − | 1.17670i | −0.295807 | − | 0.955248i | \(-0.595588\pi\) |
0.975172 | − | 0.221448i | \(-0.0710782\pi\) | |||||||
\(620\) | −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 | −0.664940 | − | 0.746897i | \(-0.731543\pi\) |
0.979302 | + | 0.202406i | \(0.0648760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.2527 | − | 22.9544i | 0.522636 | − | 0.905231i | −0.477017 | − | 0.878894i | \(-0.658282\pi\) |
0.999653 | − | 0.0263376i | \(-0.00838450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.75766 | −0.187188 | ||||||||
\(647\) | −0.00801958 | − | 0.0138903i | −0.000315282 | − | 0.000546085i | 0.865868 | − | 0.500273i | \(-0.166767\pi\) |
−0.866183 | + | 0.499727i | \(0.833434\pi\) | |||||||
\(648\) | 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 | −0.982801 | − | 0.184669i | \(-0.940879\pi\) |
0.331473 | − | 0.943465i | \(-0.392455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.49661 | + | 16.4486i | −0.371063 | + | 0.642700i | ||||
\(656\) | 70.7571 | − | 122.555i | 2.76260 | − | 4.78497i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4156 | − | 33.6288i | −0.756324 | − | 1.30999i | −0.944713 | − | 0.327897i | \(-0.893660\pi\) |
0.188389 | − | 0.982094i | \(-0.439673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.30644 | −0.206397 | −0.103198 | − | 0.994661i | \(-0.532908\pi\) | ||||
−0.103198 | + | 0.994661i | \(0.532908\pi\) | |||||||
\(662\) | −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 | 0.801568 | − | 0.597903i | \(-0.203999\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(674\) | −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 | \(-0.733041\pi\) | ||||
−0.668449 | + | 0.743758i | \(0.733041\pi\) | |||||||
\(678\) | 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 | 0.989815 | − | 0.142358i | \(-0.0454686\pi\) |
−0.618194 | + | 0.786026i | \(0.712135\pi\) | |||||||
\(684\) | 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 | \(-0.459710\pi\) | ||||
0.126237 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(692\) | −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 | −0.0753825 | − | 0.997155i | \(-0.524018\pi\) |
0.901253 | − | 0.433294i | \(-0.142649\pi\) | |||||||
\(720\) | 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 | −0.999614 | − | 0.0277700i | \(-0.991159\pi\) |
0.475758 | − | 0.879576i | \(-0.342174\pi\) | |||||||
\(728\) | 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 | \(-0.319538\pi\) |
−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 | ||||
\(737\) | 1.71235 | − | 2.96587i | 0.0630752 | − | 0.109249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0115 | − | 27.7327i | −0.588992 | − | 1.02016i | −0.994365 | − | 0.106013i | \(-0.966192\pi\) |
0.405373 | − | 0.914151i | \(-0.367142\pi\) | |||||||
\(740\) | −68.3680 | −2.51326 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4031 | + | 33.6072i | −0.711833 | + | 1.23293i | 0.252336 | + | 0.967640i | \(0.418801\pi\) |
−0.964169 | + | 0.265290i | \(0.914532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.8418 | − | 18.7786i | 0.397214 | − | 0.687995i | ||||
\(746\) | 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 | 0.597311 | − | 0.802010i | \(-0.296236\pi\) |
−0.993216 | + | 0.116282i | \(0.962903\pi\) | |||||||
\(752\) | 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 | \(-0.0890462\pi\) |
−0.719683 | + | 0.694303i | \(0.755713\pi\) | |||||||
\(762\) | 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 | −0.351488 | + | 0.936192i | \(0.614324\pi\) |
−0.635022 | + | 0.772494i | \(0.719009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.2176 | −0.799628 | ||||||||
\(773\) | −1.18021 | − | 2.04418i | −0.0424491 | − | 0.0735240i | 0.844020 | − | 0.536311i | \(-0.180183\pi\) |
−0.886469 | + | 0.462787i | \(0.846849\pi\) | |||||||
\(774\) | 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 | \(-0.490536\pi\) | ||||
0.0297278 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(788\) | 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 | 0.492912 | + | 0.870079i | \(0.335932\pi\) |
−0.999967 | + | 0.00816511i | \(0.997401\pi\) | |||||||
\(798\) | 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 | 0.839822 | − | 0.542862i | \(-0.182660\pi\) |
−0.890043 | + | 0.455876i | \(0.849326\pi\) | |||||||
\(810\) | 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 | ||||
\(815\) | −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 | \(-0.0634737\pi\) |
−0.661642 | + | 0.749819i | \(0.730140\pi\) | |||||||
\(830\) | 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 | \(-0.272691\pi\) |
−0.981907 | + | 0.189364i | \(0.939357\pi\) | |||||||
\(840\) | 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 | \(-0.0556701\pi\) |
−0.643063 | + | 0.765813i | \(0.722337\pi\) | |||||||
\(854\) | 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 | \(-0.742963\pi\) |
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 | ||||
\(863\) | −14.3415 | + | 24.8403i | −0.488191 | + | 0.845572i | −0.999908 | − | 0.0135822i | \(-0.995677\pi\) |
0.511716 | + | 0.859154i | \(0.329010\pi\) | |||||||
\(864\) | 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 | 0.999998 | − | 0.00175202i | \(-0.000557684\pi\) |
−0.501517 | + | 0.865148i | \(0.667224\pi\) | |||||||
\(878\) | −56.8317 | −1.91798 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.1988 | −1.01800 | ||||||||
\(881\) | 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 | \(0.391478\pi\) | |||||||
\(884\) | 47.8158 | 1.60822 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.7836 | 2.81477 | ||||||||
\(887\) | −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 | ||||||||
\(892\) | −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 | −0.994349 | − | 0.106157i | \(-0.966145\pi\) |
0.589110 | + | 0.808053i | \(0.299479\pi\) | |||||||
\(908\) | −45.8496 | + | 79.4139i | −1.52157 | + | 2.63544i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5493 | + | 21.7360i | 0.415776 | + | 0.720146i | 0.995510 | − | 0.0946604i | \(-0.0301765\pi\) |
−0.579733 | + | 0.814806i | \(0.696843\pi\) | |||||||
\(912\) | 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 | −0.527801 | − | 0.849368i | \(-0.676983\pi\) |
0.999475 | + | 0.0324050i | \(0.0103167\pi\) | |||||||
\(920\) | 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 | \(-0.767884\pi\) | ||||
−0.745698 | + | 0.666284i | \(0.767884\pi\) | |||||||
\(930\) | 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 | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 47.5002 | + | 82.2728i | 1.54929 | + | 2.68344i | ||||
\(941\) | 12.7131 | 0.414436 | 0.207218 | − | 0.978295i | \(-0.433559\pi\) | ||||
0.207218 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(942\) | 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 | 0.325244 | + | 0.945630i | \(0.394553\pi\) |
−0.981562 | + | 0.191145i | \(0.938780\pi\) | |||||||
\(968\) | 42.0267 | + | 72.7924i | 1.35079 | + | 2.33964i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.1399 | − | 53.9359i | 0.999843 | − | 1.73178i | ||||
\(971\) | −22.4735 | + | 38.9253i | −0.721210 | + | 1.24917i | 0.239305 | + | 0.970944i | \(0.423080\pi\) |
−0.960515 | + | 0.278228i | \(0.910253\pi\) | |||||||
\(972\) | 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 | \(-0.892588\pi\) |
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 | ||||
\(989\) | −0.891454 | + | 1.54404i | −0.0283466 | + | 0.0490977i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0046 | − | 22.5246i | −0.413104 | − | 0.715517i | 0.582123 | − | 0.813100i | \(-0.302222\pi\) |
−0.995227 | + | 0.0975835i | \(0.968889\pi\) | |||||||
\(992\) | −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 | 0.208612 | + | 0.977999i | \(0.433105\pi\) |
−0.951277 | + | 0.308336i | \(0.900228\pi\) | |||||||
\(998\) | −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.226.11 | 24 | ||
3.2 | odd | 2 | 441.2.h.h.373.1 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.442.1 | 24 | |||
7.3 | odd | 6 | 1323.2.g.h.361.1 | 24 | |||
7.4 | even | 3 | 1323.2.g.h.361.2 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.442.2 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.h.h.226.12 | 24 | ||
9.2 | odd | 6 | 441.2.g.h.79.12 | 24 | |||
9.7 | even | 3 | 1323.2.g.h.667.2 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.148.11 | ✓ | 24 | ||
21.5 | even | 6 | 441.2.f.h.148.12 | yes | 24 | ||
21.11 | odd | 6 | 441.2.g.h.67.12 | 24 | |||
21.17 | even | 6 | 441.2.g.h.67.11 | 24 | |||
21.20 | even | 2 | 441.2.h.h.373.2 | 24 | |||
63.2 | odd | 6 | 441.2.f.h.295.11 | yes | 24 | ||
63.5 | even | 6 | 3969.2.a.bh.1.1 | 12 | |||
63.11 | odd | 6 | 441.2.h.h.214.1 | 24 | |||
63.16 | even | 3 | 1323.2.f.h.883.1 | 24 | |||
63.20 | even | 6 | 441.2.g.h.79.11 | 24 | |||
63.23 | odd | 6 | 3969.2.a.bh.1.2 | 12 | |||
63.25 | even | 3 | inner | 1323.2.h.h.802.11 | 24 | ||
63.34 | odd | 6 | 1323.2.g.h.667.1 | 24 | |||
63.38 | even | 6 | 441.2.h.h.214.2 | 24 | |||
63.40 | odd | 6 | 3969.2.a.bi.1.12 | 12 | |||
63.47 | even | 6 | 441.2.f.h.295.12 | yes | 24 | ||
63.52 | odd | 6 | inner | 1323.2.h.h.802.12 | 24 | ||
63.58 | even | 3 | 3969.2.a.bi.1.11 | 12 | |||
63.61 | odd | 6 | 1323.2.f.h.883.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.11 | ✓ | 24 | 21.2 | odd | 6 | ||
441.2.f.h.148.12 | yes | 24 | 21.5 | even | 6 | ||
441.2.f.h.295.11 | yes | 24 | 63.2 | odd | 6 | ||
441.2.f.h.295.12 | yes | 24 | 63.47 | even | 6 | ||
441.2.g.h.67.11 | 24 | 21.17 | even | 6 | |||
441.2.g.h.67.12 | 24 | 21.11 | odd | 6 | |||
441.2.g.h.79.11 | 24 | 63.20 | even | 6 | |||
441.2.g.h.79.12 | 24 | 9.2 | odd | 6 | |||
441.2.h.h.214.1 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.214.2 | 24 | 63.38 | even | 6 | |||
441.2.h.h.373.1 | 24 | 3.2 | odd | 2 | |||
441.2.h.h.373.2 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.1 | 24 | 7.2 | even | 3 | |||
1323.2.f.h.442.2 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.883.1 | 24 | 63.16 | even | 3 | |||
1323.2.f.h.883.2 | 24 | 63.61 | odd | 6 | |||
1323.2.g.h.361.1 | 24 | 7.3 | odd | 6 | |||
1323.2.g.h.361.2 | 24 | 7.4 | even | 3 | |||
1323.2.g.h.667.1 | 24 | 63.34 | odd | 6 | |||
1323.2.g.h.667.2 | 24 | 9.7 | even | 3 | |||
1323.2.h.h.226.11 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.h.h.226.12 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.802.11 | 24 | 63.25 | even | 3 | inner | ||
1323.2.h.h.802.12 | 24 | 63.52 | odd | 6 | inner | ||
3969.2.a.bh.1.1 | 12 | 63.5 | even | 6 | |||
3969.2.a.bh.1.2 | 12 | 63.23 | odd | 6 | |||
3969.2.a.bi.1.11 | 12 | 63.58 | even | 3 | |||
3969.2.a.bi.1.12 | 12 | 63.40 | odd | 6 |