Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(25,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.q (of order \(3\), degree \(2\), 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: | \(1.34148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(-1.63746 - 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.25 |
Dual form | 168.2.q.c.121.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.63746 | − | 2.83616i | −0.732294 | − | 1.26837i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) |
0.223607 | − | 0.974679i | \(-0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 2.17945i | −0.566947 | − | 0.823754i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.63746 | + | 2.83616i | −0.493712 | + | 0.855135i | −0.999974 | − | 0.00724520i | \(-0.997694\pi\) |
0.506261 | + | 0.862380i | \(0.331027\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.27492 | 1.74035 | 0.870174 | − | 0.492744i | \(-0.164006\pi\) | ||||
0.870174 | + | 0.492744i | \(0.164006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.27492 | −0.845580 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.13746 | + | 5.43424i | 0.719782 | + | 1.24670i | 0.961086 | + | 0.276250i | \(0.0890918\pi\) |
−0.241303 | + | 0.970450i | \(0.577575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.63746 | + | 0.209313i | −0.575541 | + | 0.0456759i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.86254 | + | 4.95807i | −0.572508 | + | 0.991613i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.27492 | 0.979528 | 0.489764 | − | 0.871855i | \(-0.337083\pi\) | ||||
0.489764 | + | 0.871855i | \(0.337083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | − | 0.866025i | 0.0898027 | − | 0.155543i | −0.817625 | − | 0.575751i | \(-0.804710\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.63746 | + | 2.83616i | 0.285045 | + | 0.493712i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.72508 | + | 7.82300i | −0.629654 | + | 1.32233i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.13746 | + | 1.97014i | 0.186997 | + | 0.323888i | 0.944248 | − | 0.329236i | \(-0.106791\pi\) |
−0.757251 | + | 0.653124i | \(0.773458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.13746 | − | 5.43424i | 0.502395 | − | 0.870174i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.54983 | −0.710565 | −0.355282 | − | 0.934759i | \(-0.615615\pi\) | ||||
−0.355282 | + | 0.934759i | \(0.615615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.274917 | 0.0419245 | 0.0209622 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209622 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.63746 | + | 2.83616i | −0.244098 | + | 0.422790i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.50000 | + | 6.53835i | −0.357143 | + | 0.934050i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.63746 | + | 8.03231i | −0.637004 | + | 1.10332i | 0.349083 | + | 0.937092i | \(0.386493\pi\) |
−0.986087 | + | 0.166231i | \(0.946840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7251 | 1.44617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.27492 | 0.831133 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.637459 | − | 1.10411i | 0.0829900 | − | 0.143743i | −0.821543 | − | 0.570147i | \(-0.806886\pi\) |
0.904533 | + | 0.426404i | \(0.140220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | − | 8.66025i | −0.640184 | − | 1.10883i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.345207 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.13746 | + | 2.38876i | −0.143306 | + | 0.300956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.2749 | − | 17.7967i | −1.27445 | − | 2.20741i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.137459 | − | 0.238085i | 0.0167932 | − | 0.0290867i | −0.857507 | − | 0.514473i | \(-0.827988\pi\) |
0.874300 | + | 0.485386i | \(0.161321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.13746 | − | 3.70219i | 0.250171 | − | 0.433308i | −0.713402 | − | 0.700755i | \(-0.752847\pi\) |
0.963573 | + | 0.267447i | \(0.0861800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.86254 | + | 4.95807i | 0.330538 | + | 0.572508i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.63746 | − | 0.685484i | 0.984330 | − | 0.0781181i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.77492 | − | 10.0025i | −0.649729 | − | 1.12536i | −0.983188 | − | 0.182599i | \(-0.941549\pi\) |
0.333459 | − | 0.942765i | \(-0.391784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.27492 | 0.798526 | 0.399263 | − | 0.916836i | \(-0.369266\pi\) | ||||
0.399263 | + | 0.916836i | \(0.369266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0997 | −1.42086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.63746 | − | 4.56821i | 0.282765 | − | 0.489764i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.27492 | + | 9.13642i | 0.559140 | + | 0.968459i | 0.997568 | + | 0.0696929i | \(0.0222020\pi\) |
−0.438428 | + | 0.898766i | \(0.644465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.41238 | − | 13.6759i | −0.986685 | − | 1.43362i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.500000 | − | 0.866025i | −0.0518476 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2749 | − | 17.7967i | 1.05418 | − | 1.82590i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.72508 | 0.885898 | 0.442949 | − | 0.896547i | \(-0.353932\pi\) | ||||
0.442949 | + | 0.896547i | \(0.353932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.27492 | 0.329142 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.41238 | − | 9.37451i | −0.533297 | − | 0.923698i | −0.999244 | − | 0.0388850i | \(-0.987619\pi\) |
0.465946 | − | 0.884813i | \(-0.345714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.91238 | + | 7.13752i | 0.479399 | + | 0.696550i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.91238 | + | 13.7046i | 0.764918 | + | 1.32488i | 0.940290 | + | 0.340375i | \(0.110554\pi\) |
−0.175372 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.41238 | + | 14.5707i | −0.805759 | + | 1.39562i | 0.110018 | + | 0.993930i | \(0.464909\pi\) |
−0.915777 | + | 0.401687i | \(0.868424\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.27492 | 0.215926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.54983 | −0.428012 | −0.214006 | − | 0.976832i | \(-0.568651\pi\) | ||||
−0.214006 | + | 0.976832i | \(0.568651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.54983 | + | 11.3446i | −0.610775 | + | 1.05789i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.13746 | − | 5.43424i | −0.290058 | − | 0.502395i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.5498 | + | 0.837253i | −0.967102 | + | 0.0767509i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.137459 | + | 0.238085i | 0.0124962 | + | 0.0216441i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.27492 | + | 3.94027i | −0.205122 | + | 0.355282i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.37459 | 0.212389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.45017 | −0.572360 | −0.286180 | − | 0.958176i | \(-0.592385\pi\) | ||||
−0.286180 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.137459 | − | 0.238085i | 0.0121026 | − | 0.0209622i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.63746 | − | 6.30026i | −0.317806 | − | 0.550457i | 0.662224 | − | 0.749306i | \(-0.269613\pi\) |
−0.980030 | + | 0.198850i | \(0.936279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.13746 | − | 14.9893i | 0.618896 | − | 1.29974i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.63746 | + | 2.83616i | 0.140930 | + | 0.244098i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.725083 | + | 1.25588i | −0.0619480 | + | 0.107297i | −0.895336 | − | 0.445391i | \(-0.853065\pi\) |
0.833388 | + | 0.552688i | \(0.186398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.27492 | 0.701869 | 0.350935 | − | 0.936400i | \(-0.385864\pi\) | ||||
0.350935 | + | 0.936400i | \(0.385864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2749 | + | 17.7967i | −0.859232 | + | 1.48823i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.63746 | − | 14.9605i | −0.717302 | − | 1.24240i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.41238 | + | 5.43424i | 0.363927 | + | 0.448208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.27492 | + | 12.6005i | 0.595984 | + | 1.03228i | 0.993407 | + | 0.114640i | \(0.0365713\pi\) |
−0.397423 | + | 0.917636i | \(0.630095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1873 | + | 19.3770i | −0.910409 | + | 1.57687i | −0.0969217 | + | 0.995292i | \(0.530900\pi\) |
−0.813487 | + | 0.581583i | \(0.802434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.27492 | −0.263048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.274917 | − | 0.476171i | 0.0219408 | − | 0.0380026i | −0.854847 | − | 0.518881i | \(-0.826349\pi\) |
0.876787 | + | 0.480878i | \(0.159682\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.63746 | + | 8.03231i | 0.367774 | + | 0.637004i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.54983 | + | 9.55505i | −0.358577 | + | 0.753044i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 10.3923i | 0.469956 | + | 0.813988i | 0.999410 | − | 0.0343508i | \(-0.0109363\pi\) |
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.36254 | − | 9.28819i | 0.417473 | − | 0.723085i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.00000 | −0.464294 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.3746 | 2.02881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.13746 | − | 5.43424i | 0.239927 | − | 0.415567i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2749 | + | 19.5287i | 0.857216 | + | 1.48474i | 0.874574 | + | 0.484892i | \(0.161141\pi\) |
−0.0173577 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0997 | − | 1.19834i | 1.14143 | − | 0.0905857i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.637459 | − | 1.10411i | −0.0479143 | − | 0.0829900i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.27492 | − | 14.3326i | 0.618496 | − | 1.07127i | −0.371264 | − | 0.928527i | \(-0.621075\pi\) |
0.989760 | − | 0.142740i | \(-0.0455912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8248 | −1.39923 | −0.699616 | − | 0.714519i | \(-0.746646\pi\) | ||||
−0.699616 | + | 0.714519i | \(0.746646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.72508 | − | 6.45203i | 0.273874 | − | 0.474363i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.54983 | + | 11.3446i | 0.478971 | + | 0.829603i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.50000 | + | 2.17945i | 0.109109 | + | 0.158532i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.27492 | − | 3.94027i | −0.164607 | − | 0.285108i | 0.771909 | − | 0.635734i | \(-0.219302\pi\) |
−0.936516 | + | 0.350626i | \(0.885969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.225083 | + | 0.389855i | −0.0162018 | + | 0.0280624i | −0.874013 | − | 0.485903i | \(-0.838491\pi\) |
0.857811 | + | 0.513966i | \(0.171824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.5498 | −1.47160 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.45017 | −0.103320 | −0.0516600 | − | 0.998665i | \(-0.516451\pi\) | ||||
−0.0516600 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.54983 | − | 4.41644i | 0.180753 | − | 0.313073i | −0.761384 | − | 0.648301i | \(-0.775480\pi\) |
0.942137 | + | 0.335228i | \(0.108813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.137459 | − | 0.238085i | −0.00969558 | − | 0.0167932i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.91238 | − | 11.4964i | −0.555340 | − | 0.806890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.45017 | + | 12.9041i | 0.520342 | + | 0.901259i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | + | 3.46410i | −0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.5498 | −1.42146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.6495 | −1.90347 | −0.951735 | − | 0.306921i | \(-0.900701\pi\) | ||||
−0.951735 | + | 0.306921i | \(0.900701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00000 | − | 1.73205i | 0.0685189 | − | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.450166 | − | 0.779710i | −0.0307010 | − | 0.0531758i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.63746 | + | 0.209313i | −0.179042 | + | 0.0142091i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.13746 | − | 3.70219i | −0.144436 | − | 0.250171i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.5498 | − | 21.7370i | 0.844193 | − | 1.46219i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.27492 | −0.0853748 | −0.0426874 | − | 0.999088i | \(-0.513592\pi\) | ||||
−0.0426874 | + | 0.999088i | \(0.513592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.72508 | 0.381672 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.63746 | − | 9.76436i | 0.374171 | − | 0.648084i | −0.616031 | − | 0.787722i | \(-0.711261\pi\) |
0.990203 | + | 0.139638i | \(0.0445939\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.13746 | − | 15.8265i | −0.603820 | − | 1.04585i | −0.992237 | − | 0.124363i | \(-0.960311\pi\) |
0.388416 | − | 0.921484i | \(-0.373022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.72508 | − | 7.82300i | 0.245092 | − | 0.514716i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.274917 | + | 0.476171i | 0.0180104 | + | 0.0311950i | 0.874890 | − | 0.484321i | \(-0.160933\pi\) |
−0.856880 | + | 0.515516i | \(0.827600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.82475 | − | 17.0170i | 0.640896 | − | 1.11006i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.5498 | −0.750242 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4502 | 0.999388 | 0.499694 | − | 0.866202i | \(-0.333446\pi\) | ||||
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.91238 | + | 8.50848i | −0.316434 | + | 0.548080i | −0.979741 | − | 0.200267i | \(-0.935819\pi\) |
0.663307 | + | 0.748347i | \(0.269152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.6375 | − | 3.61587i | 1.44625 | − | 0.231010i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.6873 | + | 34.0994i | 1.25267 | + | 2.16969i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.63746 | − | 6.30026i | 0.230515 | − | 0.399263i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.3746 | −1.15979 | −0.579897 | − | 0.814690i | \(-0.696907\pi\) | ||||
−0.579897 | + | 0.814690i | \(0.696907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0997 | 0.823569 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.54983 | + | 11.3446i | −0.410167 | + | 0.710429i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.54983 | − | 9.61260i | −0.346189 | − | 0.599617i | 0.639380 | − | 0.768891i | \(-0.279191\pi\) |
−0.985569 | + | 0.169274i | \(0.945858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.58762 | − | 5.43424i | 0.160787 | − | 0.337667i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.63746 | − | 4.56821i | −0.163255 | − | 0.282765i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.72508 | − | 8.18408i | 0.291361 | − | 0.504652i | −0.682771 | − | 0.730633i | \(-0.739225\pi\) |
0.974132 | + | 0.225980i | \(0.0725586\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.3746 | 1.86590 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5498 | 0.645639 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3625 | + | 17.9484i | −0.631815 | + | 1.09434i | 0.355365 | + | 0.934728i | \(0.384357\pi\) |
−0.987180 | + | 0.159609i | \(0.948977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.637459 | − | 1.10411i | −0.0387229 | − | 0.0670699i | 0.846014 | − | 0.533160i | \(-0.178996\pi\) |
−0.884737 | + | 0.466090i | \(0.845662\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.5498 | + | 1.31342i | −1.00164 | + | 0.0794920i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.37459 | − | 16.2373i | −0.565309 | − | 0.979144i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4124 | − | 23.2309i | 0.805872 | − | 1.39581i | −0.109830 | − | 0.993950i | \(-0.535030\pi\) |
0.915701 | − | 0.401860i | \(-0.131636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.5498 | −1.58383 | −0.791915 | − | 0.610631i | \(-0.790916\pi\) | ||||
−0.791915 | + | 0.610631i | \(0.790916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9622 | − | 22.4512i | 0.770523 | − | 1.33459i | −0.166753 | − | 0.985999i | \(-0.553328\pi\) |
0.937276 | − | 0.348587i | \(-0.113338\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.2749 | − | 17.7967i | −0.608634 | − | 1.05418i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.82475 | + | 9.91613i | 0.402852 | + | 0.585331i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.36254 | − | 7.55614i | 0.255737 | − | 0.442949i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.8248 | −1.62554 | −0.812770 | − | 0.582585i | \(-0.802041\pi\) | ||||
−0.812770 | + | 0.582585i | \(0.802041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.17525 | −0.243092 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.63746 | − | 2.83616i | 0.0950150 | − | 0.164571i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.5498 | − | 21.7370i | −0.725776 | − | 1.25708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.412376 | − | 0.599168i | −0.0237689 | − | 0.0345355i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | − | 5.19615i | −0.172345 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.3746 | + | 28.3616i | −0.937606 | + | 1.62398i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3746 | 0.649182 | 0.324591 | − | 0.945854i | \(-0.394773\pi\) | ||||
0.324591 | + | 0.945854i | \(0.394773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.8248 | −0.615799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.27492 | − | 3.94027i | 0.128999 | − | 0.223432i | −0.794290 | − | 0.607539i | \(-0.792157\pi\) |
0.923289 | + | 0.384106i | \(0.125490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.77492 | + | 16.9307i | 0.552511 | + | 0.956977i | 0.998093 | + | 0.0617357i | \(0.0196636\pi\) |
−0.445582 | + | 0.895241i | \(0.647003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.63746 | − | 0.685484i | 0.486666 | − | 0.0386226i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9124 | + | 24.0969i | 0.781397 | + | 1.35342i | 0.931128 | + | 0.364692i | \(0.118826\pi\) |
−0.149731 | + | 0.988727i | \(0.547841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.63746 | + | 14.9605i | −0.483605 | + | 0.837628i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.8248 | 0.883252 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.0997 | 1.39658 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9622 | + | 31.1115i | −0.996364 | + | 1.72575i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.41238 | + | 14.5707i | 0.465205 | + | 0.805759i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.82475 | − | 14.3326i | 0.376261 | − | 0.790181i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.587624 | − | 1.01779i | −0.0322987 | − | 0.0559431i | 0.849424 | − | 0.527711i | \(-0.176949\pi\) |
−0.881723 | + | 0.471768i | \(0.843616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.13746 | − | 1.97014i | 0.0623323 | − | 0.107963i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.900331 | −0.0491903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0997 | −1.31279 | −0.656396 | − | 0.754416i | \(-0.727920\pi\) | ||||
−0.656396 | + | 0.754416i | \(0.727920\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.27492 | + | 3.94027i | −0.123557 | + | 0.214006i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.63746 | + | 2.83616i | 0.0886734 | + | 0.153587i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0000 | − | 4.35890i | 0.971909 | − | 0.235358i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.54983 | + | 11.3446i | 0.352631 | + | 0.610775i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0997 | + | 26.1534i | −0.810593 | + | 1.40399i | 0.101857 | + | 0.994799i | \(0.467522\pi\) |
−0.912450 | + | 0.409189i | \(0.865812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.27492 | −0.334930 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.2749 | − | 17.7967i | 0.546879 | − | 0.947222i | −0.451607 | − | 0.892217i | \(-0.649149\pi\) |
0.998486 | − | 0.0550049i | \(-0.0175174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.27492 | − | 5.67232i | −0.173815 | − | 0.301056i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.54983 | + | 9.55505i | −0.240803 | + | 0.505707i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.82475 | + | 17.0170i | 0.518531 | + | 0.898121i | 0.999768 | + | 0.0215311i | \(0.00685409\pi\) |
−0.481238 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1873 | + | 17.6449i | −0.536173 | + | 0.928679i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.274917 | 0.0144294 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0498 | + | 19.1389i | −0.576797 | + | 0.999041i | 0.419047 | + | 0.907964i | \(0.362364\pi\) |
−0.995844 | + | 0.0910767i | \(0.970969\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.27492 | + | 3.94027i | 0.118427 | + | 0.205122i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4622 | − | 1.94136i | 1.27001 | − | 0.100791i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.13746 | + | 5.43424i | 0.162451 | + | 0.281374i | 0.935747 | − | 0.352671i | \(-0.114727\pi\) |
−0.773296 | + | 0.634045i | \(0.781393\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.18729 | − | 2.05645i | 0.0613115 | − | 0.106195i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.0997 | 1.70472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1752 | 0.676767 | 0.338384 | − | 0.941008i | \(-0.390120\pi\) | ||||
0.338384 | + | 0.941008i | \(0.390120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.22508 | + | 5.58601i | −0.165226 | + | 0.286180i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.27492 | − | 9.13642i | −0.269536 | − | 0.466849i | 0.699206 | − | 0.714920i | \(-0.253537\pi\) |
−0.968742 | + | 0.248070i | \(0.920204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0876 | − | 23.3748i | −0.819901 | − | 1.19129i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.137459 | − | 0.238085i | −0.00698741 | − | 0.0121026i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.00000 | − | 1.73205i | 0.0507020 | − | 0.0878185i | −0.839561 | − | 0.543266i | \(-0.817187\pi\) |
0.890263 | + | 0.455448i | \(0.150521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.27492 | −0.366971 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.9124 | + | 32.7572i | −0.951585 | + | 1.64819i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.68729 | + | 2.92248i | 0.0846828 | + | 0.146675i | 0.905256 | − | 0.424867i | \(-0.139679\pi\) |
−0.820573 | + | 0.571541i | \(0.806346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.41238 | − | 13.6759i | −0.471208 | − | 0.684650i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.13746 | − | 5.43424i | 0.156288 | − | 0.270699i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.27492 | 0.162732 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.45017 | −0.369291 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.22508 | + | 9.05011i | −0.258364 | + | 0.447499i | −0.965804 | − | 0.259274i | \(-0.916517\pi\) |
0.707440 | + | 0.706773i | \(0.249850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.725083 | + | 1.25588i | 0.0357657 | + | 0.0619480i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.36254 | + | 0.266857i | −0.165460 | + | 0.0131312i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9124 | − | 20.6328i | −0.584756 | − | 1.01283i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.13746 | − | 7.16629i | 0.202612 | − | 0.350935i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.5498 | 1.39475 | 0.697375 | − | 0.716706i | \(-0.254351\pi\) | ||||
0.697375 | + | 0.716706i | \(0.254351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.82475 | 0.430092 | 0.215046 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215046 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.4502 | + | 19.8323i | 0.555415 | + | 0.962006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3746 | + | 23.8876i | −0.550455 | + | 1.15600i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.2749 | + | 17.7967i | 0.496078 | + | 0.859232i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.82475 | − | 15.2849i | 0.425073 | − | 0.736249i | −0.571354 | − | 0.820704i | \(-0.693582\pi\) |
0.996427 | + | 0.0844552i | \(0.0269150\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.17525 | 0.152593 | 0.0762963 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762963 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.2749 | −0.828269 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.5498 | − | 21.7370i | 0.600340 | − | 1.03982i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.63746 | − | 14.9605i | −0.412243 | − | 0.714027i | 0.582891 | − | 0.812550i | \(-0.301921\pi\) |
−0.995135 | + | 0.0985236i | \(0.968588\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.91238 | − | 1.10411i | 0.329161 | − | 0.0525767i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.18729 | + | 5.52055i | 0.151433 | + | 0.262289i | 0.931754 | − | 0.363089i | \(-0.118278\pi\) |
−0.780322 | + | 0.625378i | \(0.784945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2749 | − | 29.9210i | 0.818910 | − | 1.41839i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.5498 | 0.688184 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.5498 | 0.969807 | 0.484903 | − | 0.874568i | \(-0.338855\pi\) | ||||
0.484903 | + | 0.874568i | \(0.338855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.45017 | − | 12.9041i | 0.350815 | − | 0.607629i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1873 | + | 19.3770i | 0.525625 | + | 0.910409i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.3746 | + | 49.0887i | −1.09582 | + | 2.30131i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.3248 | − | 31.7394i | −0.857196 | − | 1.48471i | −0.874593 | − | 0.484858i | \(-0.838871\pi\) |
0.0173972 | − | 0.999849i | \(-0.494462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.64950 | −0.169974 | −0.0849872 | − | 0.996382i | \(-0.527085\pi\) | ||||
−0.0849872 | + | 0.996382i | \(0.527085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1752 | 0.612306 | 0.306153 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306153 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.63746 | + | 2.83616i | −0.0759353 | + | 0.131524i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.2749 | − | 35.1172i | −0.938211 | − | 1.62503i | −0.768805 | − | 0.639483i | \(-0.779148\pi\) |
−0.169406 | − | 0.985546i | \(-0.554185\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.725083 | + | 0.0575438i | −0.0334812 | + | 0.00265713i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.274917 | − | 0.476171i | −0.0126675 | − | 0.0219408i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.450166 | + | 0.779710i | −0.0206986 | + | 0.0358511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.9244 | −1.64833 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.27492 | 0.424669 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.72508 | − | 4.71998i | 0.124512 | − | 0.215661i | −0.797030 | − | 0.603940i | \(-0.793597\pi\) |
0.921542 | + | 0.388278i | \(0.126930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.13746 | + | 12.3624i | 0.325440 | + | 0.563679i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | + | 8.71780i | 0.273009 | + | 0.396674i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.2870 | − | 24.7457i | −0.648738 | − | 1.12365i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | + | 0.866025i | −0.0226572 | + | 0.0392434i | −0.877132 | − | 0.480250i | \(-0.840546\pi\) |
0.854475 | + | 0.519493i | \(0.173879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.9244 | 1.66638 | 0.833188 | − | 0.552990i | \(-0.186513\pi\) | ||||
0.833188 | + | 0.552990i | \(0.186513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.5498 | − | 18.2728i | 0.475141 | − | 0.822968i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.36254 | − | 9.28819i | −0.241028 | − | 0.417473i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | − | 4.35890i | −0.134568 | − | 0.195523i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1375 | − | 27.9509i | −0.722412 | − | 1.25125i | −0.960030 | − | 0.279896i | \(-0.909700\pi\) |
0.237619 | − | 0.971359i | \(-0.423633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.00000 | + | 5.19615i | −0.134030 | + | 0.232147i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.6495 | −1.67871 | −0.839354 | − | 0.543585i | \(-0.817067\pi\) | ||||
−0.839354 | + | 0.543585i | \(0.817067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.6495 | −0.874391 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.1873 | − | 22.8411i | 0.585668 | − | 1.01441i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.63746 | + | 9.76436i | 0.249876 | + | 0.432798i | 0.963491 | − | 0.267740i | \(-0.0862768\pi\) |
−0.713615 | + | 0.700538i | \(0.752943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2749 | + | 0.894797i | −0.498773 | + | 0.0395835i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.13746 | − | 5.43424i | −0.138522 | − | 0.239927i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.7251 | + | 30.7007i | −0.781060 | + | 1.35284i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.6495 | −0.864184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.5498 | 0.989828 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.27492 | − | 12.6005i | 0.318720 | − | 0.552039i | −0.661501 | − | 0.749944i | \(-0.730080\pi\) |
0.980221 | + | 0.197905i | \(0.0634137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.86254 | + | 15.3504i | 0.387532 | + | 0.671225i | 0.992117 | − | 0.125316i | \(-0.0399944\pi\) |
−0.604585 | + | 0.796541i | \(0.706661\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.51204 | − | 13.6759i | 0.284209 | − | 0.596864i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.00000 | − | 3.46410i | −0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.27492 | −0.0553267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.5498 | −1.23663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.9124 | − | 44.8816i | 1.12029 | − | 1.94040i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.27492 | − | 14.3326i | −0.357089 | − | 0.618496i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.4502 | − | 17.7967i | −0.622413 | − | 0.766557i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.13746 | + | 7.16629i | 0.177883 | + | 0.308103i | 0.941155 | − | 0.337974i | \(-0.109742\pi\) |
−0.763272 | + | 0.646077i | \(0.776408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.41238 | + | 16.3027i | −0.403924 | + | 0.699616i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.0997 | 2.36021 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00000 | + | 8.66025i | −0.213395 | + | 0.369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5498 | + | 28.6652i | 0.705047 | + | 1.22118i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1375 | + | 27.5898i | −0.558662 | + | 1.17324i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.72508 | − | 6.45203i | −0.158121 | − | 0.273874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9124 | − | 25.8290i | 0.631858 | − | 1.09441i | −0.355314 | − | 0.934747i | \(-0.615626\pi\) |
0.987172 | − | 0.159663i | \(-0.0510406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.72508 | 0.0729632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0997 | 0.553068 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.63746 | + | 13.2285i | −0.321881 | + | 0.557513i | −0.980876 | − | 0.194633i | \(-0.937648\pi\) |
0.658996 | + | 0.752147i | \(0.270982\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.45017 | + | 12.9041i | 0.313431 | + | 0.542878i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.63746 | − | 0.209313i | 0.110763 | − | 0.00879034i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.72508 | − | 9.91613i | −0.240008 | − | 0.415706i | 0.720708 | − | 0.693238i | \(-0.243817\pi\) |
−0.960716 | + | 0.277532i | \(0.910483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.13746 | + | 7.16629i | −0.173147 | + | 0.299900i | −0.939519 | − | 0.342498i | \(-0.888727\pi\) |
0.766371 | + | 0.642398i | \(0.222060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.54983 | −0.190072 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9003 | 0.955010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5000 | − | 21.6506i | 0.520382 | − | 0.901328i | −0.479337 | − | 0.877631i | \(-0.659123\pi\) |
0.999719 | − | 0.0236970i | \(-0.00754370\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.225083 | + | 0.389855i | 0.00935412 | + | 0.0162018i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9124 | − | 15.8553i | −0.452722 | − | 0.657789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1873 | − | 26.3052i | −0.628993 | − | 1.08945i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.2749 | + | 17.7967i | −0.424816 | + | 0.735802i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.27492 | 0.382817 | 0.191408 | − | 0.981510i | \(-0.438695\pi\) | ||||
0.191408 | + | 0.981510i | \(0.438695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.27492 | 0.258553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.725083 | + | 1.25588i | −0.0298259 | + | 0.0516600i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.274917 | + | 0.476171i | 0.0112895 | + | 0.0195540i | 0.871615 | − | 0.490191i | \(-0.163073\pi\) |
−0.860325 | + | 0.509745i | \(0.829740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.6495 | + | 28.5501i | 0.805551 | + | 1.17044i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.54983 | − | 4.41644i | −0.104358 | − | 0.180753i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.2749 | + | 19.5287i | −0.460681 | + | 0.797922i | −0.998995 | − | 0.0448219i | \(-0.985728\pi\) |
0.538314 | + | 0.842744i | \(0.319061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.09967 | 0.167229 | 0.0836145 | − | 0.996498i | \(-0.473354\pi\) | ||||
0.0836145 | + | 0.996498i | \(0.473354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.274917 | −0.0111955 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.450166 | − | 0.779710i | 0.0183018 | − | 0.0316997i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50000 | + | 6.06218i | 0.142061 | + | 0.246056i | 0.928272 | − | 0.371901i | \(-0.121294\pi\) |
−0.786212 | + | 0.617957i | \(0.787961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.9124 | + | 1.10411i | −0.563758 | + | 0.0447408i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.8248 | + | 32.6054i | 0.761568 | + | 1.31907i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.27492 | − | 7.40437i | 0.172662 | − | 0.299060i | −0.766688 | − | 0.642020i | \(-0.778096\pi\) |
0.939350 | + | 0.342961i | \(0.111430\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.9003 | 0.600839 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4124 | + | 24.9630i | −0.579282 | + | 1.00335i | 0.416280 | + | 0.909237i | \(0.363334\pi\) |
−0.995562 | + | 0.0941097i | \(0.970000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | − | 25.2011i | 0.480770 | − | 1.00966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.4244 | + | 18.0556i | 0.416977 | + | 0.722225i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.2749 | + | 17.7967i | −0.410341 | + | 0.710731i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.09967 | 0.362828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8248 | 0.789211 | 0.394605 | − | 0.918851i | \(-0.370881\pi\) | ||||
0.394605 | + | 0.918851i | \(0.370881\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.8248 | + | 23.9452i | −0.549485 | + | 0.951735i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.5619 | + | 18.2937i | 0.419135 | + | 0.725964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6873 | + | 41.0276i | −0.621553 | + | 1.62557i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.82475 | − | 3.16056i | 0.0720734 | − | 0.124835i | −0.827736 | − | 0.561117i | \(-0.810372\pi\) |
0.899810 | + | 0.436282i | \(0.143705\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.37459 | 0.211953 | 0.105976 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105976 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.900331 | −0.0354505 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.0000 | − | 29.4449i | 0.668339 | − | 1.15760i | −0.310029 | − | 0.950727i | \(-0.600339\pi\) |
0.978368 | − | 0.206870i | \(-0.0663277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.08762 | + | 3.61587i | 0.0819464 | + | 0.141935i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.13746 | + | 2.38876i | −0.0445805 | + | 0.0936230i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.46221 | + | 5.99672i | 0.135487 | + | 0.234670i | 0.925783 | − | 0.378055i | \(-0.123407\pi\) |
−0.790297 | + | 0.612725i | \(0.790074\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9124 | + | 20.6328i | −0.465455 | + | 0.806192i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.27492 | −0.166780 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.1993 | −1.64385 | −0.821926 | − | 0.569594i | \(-0.807101\pi\) | ||||
−0.821926 | + | 0.569594i | \(0.807101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.58762 | + | 6.21395i | −0.139542 | + | 0.241695i | −0.927323 | − | 0.374261i | \(-0.877896\pi\) |
0.787781 | + | 0.615955i | \(0.211230\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.5498 | − | 21.7370i | −0.487395 | − | 0.844193i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −54.1993 | + | 4.30136i | −2.10176 | + | 0.166799i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5498 | − | 18.2728i | −0.408491 | − | 0.707528i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.637459 | + | 1.10411i | −0.0246456 | + | 0.0426874i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.7492 | 1.26427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.5498 | 1.60163 | 0.800814 | − | 0.598913i | \(-0.204400\pi\) | ||||
0.800814 | + | 0.598913i | \(0.204400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.86254 | − | 4.95807i | 0.110179 | − | 0.190836i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.63746 | + | 11.4964i | 0.255098 | + | 0.441843i | 0.964922 | − | 0.262536i | \(-0.0845588\pi\) |
−0.709824 | + | 0.704379i | \(0.751226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0876 | − | 19.0159i | −0.502257 | − | 0.729762i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.63746 | − | 9.76436i | −0.216028 | − | 0.374171i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.08762 | + | 10.5441i | −0.232936 | + | 0.403458i | −0.958671 | − | 0.284517i | \(-0.908167\pi\) |
0.725735 | + | 0.687975i | \(0.241500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.74917 | 0.181457 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.2749 | −0.697232 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.0997 | + | 50.4021i | −1.10861 | + | 1.92017i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.41238 | + | 9.37451i | 0.205896 | + | 0.356623i | 0.950418 | − | 0.310975i | \(-0.100656\pi\) |
−0.744522 | + | 0.667598i | \(0.767322\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.91238 | − | 7.13752i | −0.186606 | − | 0.271132i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.5498 | − | 23.4690i | −0.513975 | − | 0.890230i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.09967 | + | 15.7611i | −0.344675 | + | 0.596994i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.549834 | 0.0207966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9244 | −0.488149 | −0.244074 | − | 0.969757i | \(-0.578484\pi\) | ||||
−0.244074 | + | 0.969757i | \(0.578484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.13746 | + | 12.3624i | −0.269194 | + | 0.466258i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.82475 | − | 17.0170i | −0.370022 | − | 0.640896i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.8248 | + | 1.25588i | −0.595151 | + | 0.0472322i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0997 | + | 24.4213i | 0.529524 | + | 0.917163i | 0.999407 | + | 0.0344340i | \(0.0109628\pi\) |
−0.469883 | + | 0.882729i | \(0.655704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.77492 | + | 10.0025i | −0.216576 | + | 0.375121i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 67.2990 | 2.51684 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.72508 | − | 13.3802i | 0.288499 | − | 0.499694i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0997 | − | 24.4213i | −0.525829 | − | 0.910762i | −0.999547 | − | 0.0300860i | \(-0.990422\pi\) |
0.473718 | − | 0.880676i | \(-0.342911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3127 | + | 25.8578i | −0.458549 | + | 0.962993i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.91238 | + | 8.50848i | 0.182693 | + | 0.316434i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0997 | + | 26.1534i | −0.560788 | + | 0.971313i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5498 | 1.17012 | 0.585059 | − | 0.810991i | \(-0.301071\pi\) | ||||
0.585059 | + | 0.810991i | \(0.301071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.549834 | − | 0.952341i | 0.0203364 | − | 0.0352236i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.96221 | − | 5.13070i | −0.109412 | − | 0.189507i | 0.806120 | − | 0.591752i | \(-0.201563\pi\) |
−0.915532 | + | 0.402245i | \(0.868230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.18729 | − | 21.4125i | 0.301993 | − | 0.789814i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.450166 | + | 0.779710i | 0.0165821 | + | 0.0287210i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.687293 | + | 1.19043i | −0.0252825 | + | 0.0437905i | −0.878390 | − | 0.477945i | \(-0.841382\pi\) |
0.853107 | + | 0.521735i | \(0.174715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.3746 | 1.44646 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.1993 | −1.62152 | −0.810758 | − | 0.585381i | \(-0.800945\pi\) | ||||
−0.810758 | + | 0.585381i | \(0.800945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8248 | − | 41.2657i | 0.872871 | − | 1.51186i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.63746 | − | 6.30026i | −0.133088 | − | 0.230515i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | − | 37.8016i | 0.657706 | − | 1.38124i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.22508 | + | 9.05011i | 0.190666 | + | 0.330243i | 0.945471 | − | 0.325706i | \(-0.105602\pi\) |
−0.754805 | + | 0.655949i | \(0.772269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.18729 | + | 15.9129i | −0.334804 | + | 0.579897i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 73.2749 | 2.66675 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.54983 | − | 11.3446i | 0.237744 | − | 0.411785i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5498 | + | 21.7370i | 0.454931 | + | 0.787964i | 0.998684 | − | 0.0512814i | \(-0.0163305\pi\) |
−0.543753 | + | 0.839245i | \(0.682997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.3746 | − | 3.52165i | 1.60647 | − | 0.127492i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.54983 | + | 11.3446i | 0.236810 | + | 0.410167i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | − | 6.92820i | 0.144432 | − | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.6495 | −1.17737 | −0.588686 | − | 0.808362i | \(-0.700354\pi\) | ||||
−0.588686 | + | 0.808362i | \(0.700354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0997 | −0.399745 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.54983 | + | 2.68439i | −0.0557437 | + | 0.0965509i | −0.892551 | − | 0.450947i | \(-0.851086\pi\) |
0.836807 | + | 0.547498i | \(0.184420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.86254 | + | 4.95807i | 0.102826 | + | 0.178099i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.41238 | − | 4.95807i | −0.122418 | − | 0.177870i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.2749 | − | 24.7249i | −0.511452 | − | 0.885861i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.27492 | + | 5.67232i | −0.117186 | + | 0.202972i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.27492 | −0.188510 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.80066 | −0.0642684 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27492 | + | 2.20822i | −0.0454459 | + | 0.0787146i | −0.887854 | − | 0.460126i | \(-0.847804\pi\) |
0.842408 | + | 0.538841i | \(0.181138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.72508 | − | 8.18408i | −0.168217 | − | 0.291361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.82475 | + | 9.91613i | 0.242660 | + | 0.352577i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.3746 | − | 54.3424i | −1.11414 | − | 1.92975i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.1873 | − | 26.3052i | 0.538638 | − | 0.932948i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.4743 | −1.11488 | −0.557438 | − | 0.830219i | \(-0.688215\pi\) | ||||
−0.557438 | + | 0.830219i | \(0.688215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.27492 | − | 9.13642i | 0.186380 | − | 0.322820i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.00000 | + | 12.1244i | 0.247025 | + | 0.427859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.5498 | − | 2.74194i | 1.21772 | − | 0.0966405i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.3625 | + | 17.9484i | 0.364779 | + | 0.631815i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.8248 | − | 25.6772i | 0.521211 | − | 0.902763i | −0.478485 | − | 0.878096i | \(-0.658814\pi\) |
0.999696 | − | 0.0246675i | \(-0.00785270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.5498 | −1.49413 | −0.747063 | − | 0.664753i | \(-0.768537\pi\) | ||||
−0.747063 | + | 0.664753i | \(0.768537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.27492 | −0.0447133 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.6495 | − | 34.0339i | 0.688292 | − | 1.19216i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.862541 | + | 1.49397i | 0.0301765 | + | 0.0522672i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.13746 | + | 14.9893i | −0.249403 | + | 0.523768i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.36254 | − | 11.0202i | −0.222054 | − | 0.384609i | 0.733377 | − | 0.679822i | \(-0.237943\pi\) |
−0.955432 | + | 0.295213i | \(0.904610\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0997 | − | 29.6175i | 0.596057 | − | 1.03240i | −0.397340 | − | 0.917672i | \(-0.630067\pi\) |
0.993397 | − | 0.114729i | \(-0.0366001\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.7492 | −0.652762 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.0241 | −1.53087 | −0.765434 | − | 0.643515i | \(-0.777476\pi\) | ||||
−0.765434 | + | 0.643515i | \(0.777476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1375 | + | 26.2188i | −0.525746 | + | 0.910618i | 0.473805 | + | 0.880630i | \(0.342880\pi\) |
−0.999550 | + | 0.0299882i | \(0.990453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4124 | − | 23.2309i | −0.465270 | − | 0.805872i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.6495 | + | 21.7370i | 0.611519 | + | 0.753141i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.82475 | + | 17.0170i | 0.340000 | + | 0.588896i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.500000 | + | 0.866025i | −0.0172825 | + | 0.0299342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1993 | −1.04260 | −0.521298 | − | 0.853374i | \(-0.674552\pi\) | ||||
−0.521298 | + | 0.853374i | \(0.674552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.17525 | −0.0405258 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.2749 | + | 22.9928i | −0.457212 | + | 0.791915i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.1873 | − | 74.8026i | −1.48569 | − | 2.57329i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.312707 | − | 0.656712i | 0.0107447 | − | 0.0225649i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9622 | − | 22.4512i | −0.444862 | − | 0.770523i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.54983 | − | 7.88054i | 0.155966 | − | 0.270142i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.3746 | 0.457937 | 0.228969 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228969 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.5498 | −0.702790 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.72508 | − | 11.6482i | 0.229724 | − | 0.397894i | −0.728002 | − | 0.685575i | \(-0.759551\pi\) |
0.957726 | + | 0.287681i | \(0.0928842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8248 | + | 48.1939i | 0.949368 | + | 1.64435i | 0.746759 | + | 0.665094i | \(0.231609\pi\) |
0.202609 | + | 0.979260i | \(0.435058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0000 | − | 0.952341i | 0.408959 | − | 0.0324557i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.54983 | − | 16.5408i | −0.325080 | − | 0.563055i | 0.656448 | − | 0.754371i | \(-0.272058\pi\) |
−0.981529 | + | 0.191316i | \(0.938725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.9244 | − | 63.9550i | 1.25547 | − | 2.17453i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.8248 | 1.28312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.862541 | − | 1.49397i | 0.0292261 | − | 0.0506211i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.36254 | − | 7.55614i | −0.147650 | − | 0.255737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.56188 | − | 5.17529i | −0.120413 | − | 0.174957i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3746 | − | 40.4860i | −0.789304 | − | 1.36711i | −0.926394 | − | 0.376556i | \(-0.877108\pi\) |
0.137090 | − | 0.990559i | \(-0.456225\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.9124 | + | 24.0969i | −0.469253 | + | 0.812770i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.45017 | 0.318384 | 0.159192 | − | 0.987248i | \(-0.449111\pi\) | ||||
0.159192 | + | 0.987248i | \(0.449111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.37459 | 0.248175 | 0.124087 | − | 0.992271i | \(-0.460400\pi\) | ||||
0.124087 | + | 0.992271i | \(0.460400\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.08762 | + | 3.61587i | −0.0701747 | + | 0.121546i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8248 | − | 29.1413i | −0.564920 | − | 0.978470i | −0.997057 | − | 0.0766621i | \(-0.975574\pi\) |
0.432137 | − | 0.901808i | \(-0.357760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.67525 | + | 14.0578i | 0.324497 | + | 0.471484i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.63746 | − | 2.83616i | −0.0548569 | − | 0.0950150i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8248 | + | 32.6054i | −0.629946 | + | 1.09110i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.1993 | −1.81168 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.0997 | −0.838054 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.63746 | − | 4.56821i | 0.0879642 | − | 0.152358i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.5498 | + | 32.1293i | 0.617985 | + | 1.07038i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.725083 | + | 0.0575438i | −0.0241292 | + | 0.00191494i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.8248 | + | 53.3900i | 1.02465 | + | 1.77474i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.8625 | − | 25.7427i | 0.493503 | − | 0.854772i | −0.506469 | − | 0.862258i | \(-0.669050\pi\) |
0.999972 | + | 0.00748639i | \(0.00238301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.8488 | 1.78409 | 0.892046 | − | 0.451945i | \(-0.149270\pi\) | ||||
0.892046 | + | 0.451945i | \(0.149270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.9124 | + | 20.6328i | −0.394242 | + | 0.682847i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.3746 | + | 28.3616i | 0.541327 | + | 0.937606i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.27492 | + | 17.3781i | −0.273262 | + | 0.573874i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.41238 | + | 2.44631i | 0.0465900 | + | 0.0806962i | 0.888380 | − | 0.459109i | \(-0.151831\pi\) |
−0.841790 | + | 0.539805i | \(0.818498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.68729 | − | 9.85068i | 0.187403 | − | 0.324591i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.5498 | 0.413083 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0241 | −0.428229 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.41238 | + | 9.37451i | −0.177766 | + | 0.307899i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0997 | + | 34.8136i | 0.659449 | + | 1.14220i | 0.980759 | + | 0.195225i | \(0.0625436\pi\) |
−0.321310 | + | 0.946974i | \(0.604123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.3746 | + | 6.92820i | −1.42154 | + | 0.227063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.27492 | − | 3.94027i | −0.0744774 | − | 0.128999i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.4502 | − | 37.1528i | 0.701495 | − | 1.21503i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.09967 | −0.199267 | −0.0996337 | − | 0.995024i | \(-0.531767\pi\) | ||||
−0.0996337 | + | 0.995024i | \(0.531767\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.5498 | 0.637985 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.9124 | + | 44.8816i | −0.844719 | + | 1.46310i | 0.0411454 | + | 0.999153i | \(0.486899\pi\) |
−0.885865 | + | 0.463944i | \(0.846434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.09967 | + | 15.7611i | 0.296326 | + | 0.513252i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.72508 | − | 7.82300i | 0.121177 | − | 0.254482i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.72508 | + | 16.8443i | 0.316023 | + | 0.547367i | 0.979654 | − | 0.200692i | \(-0.0643191\pi\) |
−0.663632 | + | 0.748060i | \(0.730986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4124 | − | 23.2309i | 0.435384 | − | 0.754107i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.8248 | 0.902279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.6495 | 1.80266 | 0.901332 | − | 0.433129i | \(-0.142590\pi\) | ||||
0.901332 | + | 0.433129i | \(0.142590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.45017 | + | 12.9041i | −0.241082 | + | 0.417566i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.63746 | + | 14.9605i | 0.279209 | + | 0.483605i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.82475 | − | 0.303539i | 0.123508 | − | 0.00980179i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | + | 25.9808i | 0.483871 | + | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.91238 | − | 13.7046i | 0.254973 | − | 0.441626i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.47425 | 0.0474579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.5498 | −1.72205 | −0.861023 | − | 0.508566i | \(-0.830176\pi\) | ||||
−0.861023 | + | 0.508566i | \(0.830176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.5498 | − | 21.7370i | 0.403159 | − | 0.698291i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.2870 | − | 48.9945i | −0.907772 | − | 1.57231i | −0.817153 | − | 0.576421i | \(-0.804449\pi\) |
−0.0906191 | − | 0.995886i | \(-0.528885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.4124 | − | 18.0348i | −0.397923 | − | 0.578168i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.9622 | + | 31.1115i | 0.575251 | + | 0.996364i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.45017 | + | 7.70791i | −0.142373 | + | 0.246598i | −0.928390 | − | 0.371608i | \(-0.878807\pi\) |
0.786017 | + | 0.618205i | \(0.212140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.5498 | −1.10422 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8248 | 0.537173 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.6495 | + | 34.0339i | −0.626722 | + | 1.08551i | 0.361483 | + | 0.932379i | \(0.382270\pi\) |
−0.988205 | + | 0.153135i | \(0.951063\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.37459 | + | 4.11290i | 0.0756606 | + | 0.131048i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.00000 | − | 13.0767i | −0.286473 | − | 0.416236i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.549834 | − | 0.952341i | −0.0174837 | − | 0.0302827i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.04983 | − | 12.2107i | 0.223945 | − | 0.387885i | −0.732057 | − | 0.681243i | \(-0.761440\pi\) |
0.956003 | + | 0.293358i | \(0.0947729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.17525 | −0.0372954 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.7010 | −0.529457 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4124 | − | 38.8194i | 0.709807 | − | 1.22942i | −0.255121 | − | 0.966909i | \(-0.582115\pi\) |
0.964928 | − | 0.262513i | \(-0.0845512\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.13746 | − | 1.97014i | −0.0359876 | − | 0.0623323i |
(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 | 168.2.q.c.25.1 | ✓ | 4 | |
3.2 | odd | 2 | 504.2.s.i.361.2 | 4 | |||
4.3 | odd | 2 | 336.2.q.g.193.1 | 4 | |||
7.2 | even | 3 | inner | 168.2.q.c.121.1 | yes | 4 | |
7.3 | odd | 6 | 1176.2.a.n.1.1 | 2 | |||
7.4 | even | 3 | 1176.2.a.k.1.2 | 2 | |||
7.5 | odd | 6 | 1176.2.q.l.961.2 | 4 | |||
7.6 | odd | 2 | 1176.2.q.l.361.2 | 4 | |||
8.3 | odd | 2 | 1344.2.q.x.193.2 | 4 | |||
8.5 | even | 2 | 1344.2.q.w.193.2 | 4 | |||
12.11 | even | 2 | 1008.2.s.r.865.2 | 4 | |||
21.2 | odd | 6 | 504.2.s.i.289.2 | 4 | |||
21.5 | even | 6 | 3528.2.s.bk.3313.1 | 4 | |||
21.11 | odd | 6 | 3528.2.a.bk.1.1 | 2 | |||
21.17 | even | 6 | 3528.2.a.bd.1.2 | 2 | |||
21.20 | even | 2 | 3528.2.s.bk.361.1 | 4 | |||
28.3 | even | 6 | 2352.2.a.ba.1.1 | 2 | |||
28.11 | odd | 6 | 2352.2.a.bf.1.2 | 2 | |||
28.19 | even | 6 | 2352.2.q.bf.961.2 | 4 | |||
28.23 | odd | 6 | 336.2.q.g.289.1 | 4 | |||
28.27 | even | 2 | 2352.2.q.bf.1537.2 | 4 | |||
56.3 | even | 6 | 9408.2.a.dw.1.2 | 2 | |||
56.11 | odd | 6 | 9408.2.a.dp.1.1 | 2 | |||
56.37 | even | 6 | 1344.2.q.w.961.2 | 4 | |||
56.45 | odd | 6 | 9408.2.a.dj.1.2 | 2 | |||
56.51 | odd | 6 | 1344.2.q.x.961.2 | 4 | |||
56.53 | even | 6 | 9408.2.a.ec.1.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.cu.1.1 | 2 | |||
84.23 | even | 6 | 1008.2.s.r.289.2 | 4 | |||
84.59 | odd | 6 | 7056.2.a.ch.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.q.c.25.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
168.2.q.c.121.1 | yes | 4 | 7.2 | even | 3 | inner | |
336.2.q.g.193.1 | 4 | 4.3 | odd | 2 | |||
336.2.q.g.289.1 | 4 | 28.23 | odd | 6 | |||
504.2.s.i.289.2 | 4 | 21.2 | odd | 6 | |||
504.2.s.i.361.2 | 4 | 3.2 | odd | 2 | |||
1008.2.s.r.289.2 | 4 | 84.23 | even | 6 | |||
1008.2.s.r.865.2 | 4 | 12.11 | even | 2 | |||
1176.2.a.k.1.2 | 2 | 7.4 | even | 3 | |||
1176.2.a.n.1.1 | 2 | 7.3 | odd | 6 | |||
1176.2.q.l.361.2 | 4 | 7.6 | odd | 2 | |||
1176.2.q.l.961.2 | 4 | 7.5 | odd | 6 | |||
1344.2.q.w.193.2 | 4 | 8.5 | even | 2 | |||
1344.2.q.w.961.2 | 4 | 56.37 | even | 6 | |||
1344.2.q.x.193.2 | 4 | 8.3 | odd | 2 | |||
1344.2.q.x.961.2 | 4 | 56.51 | odd | 6 | |||
2352.2.a.ba.1.1 | 2 | 28.3 | even | 6 | |||
2352.2.a.bf.1.2 | 2 | 28.11 | odd | 6 | |||
2352.2.q.bf.961.2 | 4 | 28.19 | even | 6 | |||
2352.2.q.bf.1537.2 | 4 | 28.27 | even | 2 | |||
3528.2.a.bd.1.2 | 2 | 21.17 | even | 6 | |||
3528.2.a.bk.1.1 | 2 | 21.11 | odd | 6 | |||
3528.2.s.bk.361.1 | 4 | 21.20 | even | 2 | |||
3528.2.s.bk.3313.1 | 4 | 21.5 | even | 6 | |||
7056.2.a.ch.1.2 | 2 | 84.59 | odd | 6 | |||
7056.2.a.cu.1.1 | 2 | 84.11 | even | 6 | |||
9408.2.a.dj.1.2 | 2 | 56.45 | odd | 6 | |||
9408.2.a.dp.1.1 | 2 | 56.11 | odd | 6 | |||
9408.2.a.dw.1.2 | 2 | 56.3 | even | 6 | |||
9408.2.a.ec.1.1 | 2 | 56.53 | even | 6 |