Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.h.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.00000 | + | 5.19615i | 0.268328 | + | 0.464758i | 0.968430 | − | 0.249285i | \(-0.0801955\pi\) |
−0.700102 | + | 0.714043i | \(0.746862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | − | 10.3923i | 0.189737 | − | 0.328634i | ||||
\(11\) | −15.0000 | + | 25.9808i | −0.411152 | + | 0.712136i | −0.995016 | − | 0.0997155i | \(-0.968207\pi\) |
0.583864 | + | 0.811851i | \(0.301540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.0426692 | −0.0213346 | − | 0.999772i | \(-0.506792\pi\) | ||||
−0.0213346 | + | 0.999772i | \(0.506792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 33.0000 | − | 57.1577i | 0.470804 | − | 0.815457i | −0.528638 | − | 0.848847i | \(-0.677297\pi\) |
0.999442 | + | 0.0333902i | \(0.0106304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.0000 | − | 45.0333i | −0.313937 | − | 0.543755i | 0.665274 | − | 0.746600i | \(-0.268315\pi\) |
−0.979211 | + | 0.202844i | \(0.934982\pi\) | |||||||
\(20\) | −24.0000 | −0.268328 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | −57.0000 | − | 98.7269i | −0.516753 | − | 0.895043i | −0.999811 | − | 0.0194541i | \(-0.993807\pi\) |
0.483058 | − | 0.875589i | \(-0.339526\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.5000 | − | 77.0763i | 0.356000 | − | 0.616610i | ||||
\(26\) | 2.00000 | + | 3.46410i | 0.0150859 | + | 0.0261295i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 72.0000 | 0.461037 | 0.230518 | − | 0.973068i | \(-0.425958\pi\) | ||||
0.230518 | + | 0.973068i | \(0.425958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −98.0000 | + | 169.741i | −0.567785 | + | 0.983432i | 0.429000 | + | 0.903304i | \(0.358866\pi\) |
−0.996785 | + | 0.0801272i | \(0.974467\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −132.000 | −0.665818 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 143.000 | + | 247.683i | 0.635380 | + | 1.10051i | 0.986435 | + | 0.164155i | \(0.0524898\pi\) |
−0.351055 | + | 0.936355i | \(0.614177\pi\) | |||||||
\(38\) | −52.0000 | + | 90.0666i | −0.221987 | + | 0.384493i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0000 | + | 41.5692i | 0.0948683 | + | 0.164317i | ||||
\(41\) | 378.000 | 1.43985 | 0.719923 | − | 0.694054i | \(-0.244177\pi\) | ||||
0.719923 | + | 0.694054i | \(0.244177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | −60.0000 | − | 103.923i | −0.205576 | − | 0.356068i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −114.000 | + | 197.454i | −0.365400 | + | 0.632891i | ||||
\(47\) | −114.000 | − | 197.454i | −0.353800 | − | 0.612800i | 0.633112 | − | 0.774060i | \(-0.281777\pi\) |
−0.986912 | + | 0.161261i | \(0.948444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −178.000 | −0.503460 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | − | 6.92820i | 0.0106673 | − | 0.0184763i | ||||
\(53\) | 174.000 | − | 301.377i | 0.450957 | − | 0.781081i | −0.547488 | − | 0.836813i | \(-0.684416\pi\) |
0.998446 | + | 0.0557323i | \(0.0177493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −180.000 | −0.441294 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −72.0000 | − | 124.708i | −0.163001 | − | 0.282326i | ||||
\(59\) | −174.000 | + | 301.377i | −0.383947 | + | 0.665016i | −0.991622 | − | 0.129170i | \(-0.958769\pi\) |
0.607676 | + | 0.794185i | \(0.292102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.0000 | − | 91.7987i | −0.111245 | − | 0.192682i | 0.805027 | − | 0.593238i | \(-0.202151\pi\) |
−0.916273 | + | 0.400555i | \(0.868817\pi\) | |||||||
\(62\) | 392.000 | 0.802969 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.0114494 | − | 0.0198309i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −298.000 | + | 516.151i | −0.543381 | + | 0.941163i | 0.455326 | + | 0.890325i | \(0.349523\pi\) |
−0.998707 | + | 0.0508381i | \(0.983811\pi\) | |||||||
\(68\) | 132.000 | + | 228.631i | 0.235402 | + | 0.407729i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 630.000 | 1.05306 | 0.526530 | − | 0.850157i | \(-0.323493\pi\) | ||||
0.526530 | + | 0.850157i | \(0.323493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −521.000 | + | 902.398i | −0.835321 | + | 1.44682i | 0.0584477 | + | 0.998290i | \(0.481385\pi\) |
−0.893769 | + | 0.448528i | \(0.851948\pi\) | |||||||
\(74\) | 286.000 | − | 495.367i | 0.449281 | − | 0.778178i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 208.000 | 0.313937 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44.0000 | + | 76.2102i | 0.0626631 | + | 0.108536i | 0.895655 | − | 0.444750i | \(-0.146707\pi\) |
−0.832992 | + | 0.553285i | \(0.813374\pi\) | |||||||
\(80\) | 48.0000 | − | 83.1384i | 0.0670820 | − | 0.116190i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −378.000 | − | 654.715i | −0.509062 | − | 0.881722i | ||||
\(83\) | 1440.00 | 1.90434 | 0.952172 | − | 0.305563i | \(-0.0988446\pi\) | ||||
0.952172 | + | 0.305563i | \(0.0988446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 396.000 | 0.505320 | ||||||||
\(86\) | −164.000 | − | 284.056i | −0.205635 | − | 0.356170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −120.000 | + | 207.846i | −0.145364 | + | 0.251778i | ||||
\(89\) | 687.000 | + | 1189.92i | 0.818223 | + | 1.41720i | 0.906990 | + | 0.421152i | \(0.138374\pi\) |
−0.0887672 | + | 0.996052i | \(0.528293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 456.000 | 0.516753 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −228.000 | + | 394.908i | −0.250175 | + | 0.433315i | ||||
\(95\) | 156.000 | − | 270.200i | 0.168476 | − | 0.291810i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 34.0000 | 0.0355895 | 0.0177947 | − | 0.999842i | \(-0.494335\pi\) | ||||
0.0177947 | + | 0.999842i | \(0.494335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 178.000 | + | 308.305i | 0.178000 | + | 0.308305i | ||||
\(101\) | −219.000 | + | 379.319i | −0.215756 | + | 0.373700i | −0.953506 | − | 0.301374i | \(-0.902555\pi\) |
0.737750 | + | 0.675074i | \(0.235888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 838.000 | + | 1451.46i | 0.801656 | + | 1.38851i | 0.918525 | + | 0.395362i | \(0.129381\pi\) |
−0.116869 | + | 0.993147i | \(0.537286\pi\) | |||||||
\(104\) | −16.0000 | −0.0150859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −696.000 | −0.637750 | ||||||||
\(107\) | −1011.00 | − | 1751.10i | −0.913430 | − | 1.58211i | −0.809183 | − | 0.587557i | \(-0.800090\pi\) |
−0.104247 | − | 0.994551i | \(-0.533243\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 251.000 | − | 434.745i | 0.220564 | − | 0.382027i | −0.734416 | − | 0.678700i | \(-0.762544\pi\) |
0.954979 | + | 0.296673i | \(0.0958770\pi\) | |||||||
\(110\) | 180.000 | + | 311.769i | 0.156021 | + | 0.270237i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2016.00 | 1.67831 | 0.839156 | − | 0.543890i | \(-0.183049\pi\) | ||||
0.839156 | + | 0.543890i | \(0.183049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 342.000 | − | 592.361i | 0.277319 | − | 0.480330i | ||||
\(116\) | −144.000 | + | 249.415i | −0.115259 | + | 0.199635i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 696.000 | 0.542983 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.500 | + | 373.257i | 0.161908 | + | 0.280433i | ||||
\(122\) | −106.000 | + | 183.597i | −0.0786622 | + | 0.136247i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −392.000 | − | 678.964i | −0.283892 | − | 0.491716i | ||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1784.00 | 1.24649 | 0.623246 | − | 0.782026i | \(-0.285814\pi\) | ||||
0.623246 | + | 0.782026i | \(0.285814\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0000 | + | 20.7846i | −0.00809592 | + | 0.0140225i | ||||
\(131\) | 804.000 | + | 1392.57i | 0.536228 | + | 0.928773i | 0.999103 | + | 0.0423499i | \(0.0134844\pi\) |
−0.462875 | + | 0.886423i | \(0.653182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1192.00 | 0.768456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 264.000 | − | 457.261i | 0.166455 | − | 0.288308i | ||||
\(137\) | 1290.00 | − | 2234.35i | 0.804468 | − | 1.39338i | −0.112181 | − | 0.993688i | \(-0.535784\pi\) |
0.916650 | − | 0.399692i | \(-0.130883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2144.00 | −1.30829 | −0.654143 | − | 0.756371i | \(-0.726970\pi\) | ||||
−0.654143 | + | 0.756371i | \(0.726970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −630.000 | − | 1091.19i | −0.372313 | − | 0.644865i | ||||
\(143\) | 30.0000 | − | 51.9615i | 0.0175435 | − | 0.0303863i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 216.000 | + | 374.123i | 0.123709 | + | 0.214270i | ||||
\(146\) | 2084.00 | 1.18132 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1144.00 | −0.635380 | ||||||||
\(149\) | −750.000 | − | 1299.04i | −0.412365 | − | 0.714237i | 0.582783 | − | 0.812628i | \(-0.301964\pi\) |
−0.995148 | + | 0.0983907i | \(0.968631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 620.000 | − | 1073.87i | 0.334138 | − | 0.578745i | −0.649181 | − | 0.760634i | \(-0.724888\pi\) |
0.983319 | + | 0.181890i | \(0.0582214\pi\) | |||||||
\(152\) | −208.000 | − | 360.267i | −0.110994 | − | 0.192247i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1176.00 | −0.609410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 307.000 | − | 531.740i | 0.156059 | − | 0.270302i | −0.777385 | − | 0.629025i | \(-0.783454\pi\) |
0.933444 | + | 0.358723i | \(0.116788\pi\) | |||||||
\(158\) | 88.0000 | − | 152.420i | 0.0443095 | − | 0.0767463i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −192.000 | −0.0948683 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −46.0000 | − | 79.6743i | −0.0221043 | − | 0.0382857i | 0.854762 | − | 0.519021i | \(-0.173703\pi\) |
−0.876866 | + | 0.480735i | \(0.840370\pi\) | |||||||
\(164\) | −756.000 | + | 1309.43i | −0.359961 | + | 0.623472i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1440.00 | − | 2494.15i | −0.673287 | − | 1.16617i | ||||
\(167\) | 3924.00 | 1.81825 | 0.909126 | − | 0.416520i | \(-0.136750\pi\) | ||||
0.909126 | + | 0.416520i | \(0.136750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2193.00 | −0.998179 | ||||||||
\(170\) | −396.000 | − | 685.892i | −0.178658 | − | 0.309444i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −328.000 | + | 568.113i | −0.145406 | + | 0.251850i | ||||
\(173\) | −951.000 | − | 1647.18i | −0.417938 | − | 0.723889i | 0.577794 | − | 0.816182i | \(-0.303914\pi\) |
−0.995732 | + | 0.0922934i | \(0.970580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 480.000 | 0.205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1374.00 | − | 2379.84i | 0.578571 | − | 1.00211i | ||||
\(179\) | 3.00000 | − | 5.19615i | 0.00125268 | − | 0.00216971i | −0.865398 | − | 0.501084i | \(-0.832935\pi\) |
0.866651 | + | 0.498915i | \(0.166268\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2878.00 | 1.18188 | 0.590939 | − | 0.806716i | \(-0.298757\pi\) | ||||
0.590939 | + | 0.806716i | \(0.298757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −456.000 | − | 789.815i | −0.182700 | − | 0.316445i | ||||
\(185\) | −858.000 | + | 1486.10i | −0.340981 | + | 0.590596i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 990.000 | + | 1714.73i | 0.387144 | + | 0.670553i | ||||
\(188\) | 912.000 | 0.353800 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −624.000 | −0.238262 | ||||||||
\(191\) | 177.000 | + | 306.573i | 0.0670538 | + | 0.116141i | 0.897603 | − | 0.440804i | \(-0.145307\pi\) |
−0.830549 | + | 0.556945i | \(0.811973\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2429.00 | − | 4207.15i | 0.905924 | − | 1.56911i | 0.0862509 | − | 0.996273i | \(-0.472511\pi\) |
0.819673 | − | 0.572832i | \(-0.194155\pi\) | |||||||
\(194\) | −34.0000 | − | 58.8897i | −0.0125828 | − | 0.0217940i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −396.000 | −0.143217 | −0.0716087 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716087 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 856.000 | − | 1482.64i | 0.304926 | − | 0.528147i | −0.672319 | − | 0.740262i | \(-0.734702\pi\) |
0.977245 | + | 0.212115i | \(0.0680350\pi\) | |||||||
\(200\) | 356.000 | − | 616.610i | 0.125865 | − | 0.218005i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 876.000 | 0.305124 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1134.00 | + | 1964.15i | 0.386351 | + | 0.669180i | ||||
\(206\) | 1676.00 | − | 2902.92i | 0.566857 | − | 0.981824i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.0000 | + | 27.7128i | 0.00533366 | + | 0.00923816i | ||||
\(209\) | 1560.00 | 0.516304 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −772.000 | −0.251880 | −0.125940 | − | 0.992038i | \(-0.540195\pi\) | ||||
−0.125940 | + | 0.992038i | \(0.540195\pi\) | |||||||
\(212\) | 696.000 | + | 1205.51i | 0.225479 | + | 0.390540i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2022.00 | + | 3502.21i | −0.645893 | + | 1.11872i | ||||
\(215\) | 492.000 | + | 852.169i | 0.156066 | + | 0.270314i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1004.00 | −0.311924 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 360.000 | − | 623.538i | 0.110324 | − | 0.191086i | ||||
\(221\) | −66.0000 | + | 114.315i | −0.0200889 | + | 0.0347949i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −776.000 | −0.233026 | −0.116513 | − | 0.993189i | \(-0.537172\pi\) | ||||
−0.116513 | + | 0.993189i | \(0.537172\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2016.00 | − | 3491.81i | −0.593373 | − | 1.02775i | ||||
\(227\) | −894.000 | + | 1548.45i | −0.261396 | + | 0.452751i | −0.966613 | − | 0.256240i | \(-0.917516\pi\) |
0.705217 | + | 0.708991i | \(0.250849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2701.00 | + | 4678.27i | 0.779420 | + | 1.34999i | 0.932277 | + | 0.361746i | \(0.117819\pi\) |
−0.152857 | + | 0.988248i | \(0.548847\pi\) | |||||||
\(230\) | −1368.00 | −0.392188 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 576.000 | 0.163001 | ||||||||
\(233\) | −1506.00 | − | 2608.47i | −0.423439 | − | 0.733418i | 0.572834 | − | 0.819671i | \(-0.305844\pi\) |
−0.996273 | + | 0.0862531i | \(0.972511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 684.000 | − | 1184.72i | 0.189869 | − | 0.328863i | ||||
\(236\) | −696.000 | − | 1205.51i | −0.191973 | − | 0.332508i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3546.00 | 0.959714 | 0.479857 | − | 0.877347i | \(-0.340689\pi\) | ||||
0.479857 | + | 0.877347i | \(0.340689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1781.00 | + | 3084.78i | −0.476034 | + | 0.824516i | −0.999623 | − | 0.0274554i | \(-0.991260\pi\) |
0.523589 | + | 0.851971i | \(0.324593\pi\) | |||||||
\(242\) | 431.000 | − | 746.514i | 0.114486 | − | 0.198296i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 424.000 | 0.111245 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 52.0000 | + | 90.0666i | 0.0133955 | + | 0.0232016i | ||||
\(248\) | −784.000 | + | 1357.93i | −0.200742 | + | 0.347696i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1284.00 | − | 2223.95i | −0.324829 | − | 0.562621i | ||||
\(251\) | −3348.00 | −0.841928 | −0.420964 | − | 0.907077i | \(-0.638308\pi\) | ||||
−0.420964 | + | 0.907077i | \(0.638308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3420.00 | 0.849856 | ||||||||
\(254\) | −1784.00 | − | 3089.98i | −0.440701 | − | 0.763317i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 183.000 | + | 316.965i | 0.0444172 | + | 0.0769329i | 0.887379 | − | 0.461040i | \(-0.152524\pi\) |
−0.842962 | + | 0.537973i | \(0.819190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 48.0000 | 0.0114494 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1608.00 | − | 2785.14i | 0.379170 | − | 0.656742i | ||||
\(263\) | −2085.00 | + | 3611.33i | −0.488846 | + | 0.846707i | −0.999918 | − | 0.0128315i | \(-0.995915\pi\) |
0.511071 | + | 0.859538i | \(0.329249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2088.00 | 0.484018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1192.00 | − | 2064.60i | −0.271690 | − | 0.470581i | ||||
\(269\) | 3039.00 | − | 5263.70i | 0.688814 | − | 1.19306i | −0.283407 | − | 0.959000i | \(-0.591465\pi\) |
0.972222 | − | 0.234062i | \(-0.0752019\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1234.00 | + | 2137.35i | 0.276606 | + | 0.479095i | 0.970539 | − | 0.240944i | \(-0.0774571\pi\) |
−0.693933 | + | 0.720039i | \(0.744124\pi\) | |||||||
\(272\) | −1056.00 | −0.235402 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5160.00 | −1.13769 | ||||||||
\(275\) | 1335.00 | + | 2312.29i | 0.292740 | + | 0.507041i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 197.000 | − | 341.214i | 0.0427313 | − | 0.0740129i | −0.843869 | − | 0.536550i | \(-0.819727\pi\) |
0.886600 | + | 0.462537i | \(0.153061\pi\) | |||||||
\(278\) | 2144.00 | + | 3713.52i | 0.462549 | + | 0.801158i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −396.000 | −0.0840690 | −0.0420345 | − | 0.999116i | \(-0.513384\pi\) | ||||
−0.0420345 | + | 0.999116i | \(0.513384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −674.000 | + | 1167.40i | −0.141573 | + | 0.245212i | −0.928089 | − | 0.372358i | \(-0.878549\pi\) |
0.786516 | + | 0.617570i | \(0.211883\pi\) | |||||||
\(284\) | −1260.00 | + | 2182.38i | −0.263265 | + | 0.455988i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −120.000 | −0.0248103 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 278.500 | + | 482.376i | 0.0566863 | + | 0.0981836i | ||||
\(290\) | 432.000 | − | 748.246i | 0.0874756 | − | 0.151512i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2084.00 | − | 3609.59i | −0.417661 | − | 0.723409i | ||||
\(293\) | −7506.00 | −1.49660 | −0.748302 | − | 0.663358i | \(-0.769131\pi\) | ||||
−0.748302 | + | 0.663358i | \(0.769131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2088.00 | −0.412095 | ||||||||
\(296\) | 1144.00 | + | 1981.47i | 0.224641 | + | 0.389089i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1500.00 | + | 2598.08i | −0.291586 | + | 0.505042i | ||||
\(299\) | 114.000 | + | 197.454i | 0.0220495 | + | 0.0381908i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2480.00 | −0.472543 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −416.000 | + | 720.533i | −0.0784843 | + | 0.135939i | ||||
\(305\) | 318.000 | − | 550.792i | 0.0597004 | − | 0.103404i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1748.00 | −0.324963 | −0.162481 | − | 0.986712i | \(-0.551950\pi\) | ||||
−0.162481 | + | 0.986712i | \(0.551950\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1176.00 | + | 2036.89i | 0.215459 | + | 0.373186i | ||||
\(311\) | −570.000 | + | 987.269i | −0.103928 | + | 0.180009i | −0.913300 | − | 0.407288i | \(-0.866475\pi\) |
0.809371 | + | 0.587297i | \(0.199808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 73.0000 | + | 126.440i | 0.0131828 | + | 0.0228332i | 0.872542 | − | 0.488540i | \(-0.162470\pi\) |
−0.859359 | + | 0.511373i | \(0.829137\pi\) | |||||||
\(314\) | −1228.00 | −0.220701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −352.000 | −0.0626631 | ||||||||
\(317\) | 4074.00 | + | 7056.37i | 0.721825 | + | 1.25024i | 0.960267 | + | 0.279081i | \(0.0900300\pi\) |
−0.238442 | + | 0.971157i | \(0.576637\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1080.00 | + | 1870.61i | −0.189556 | + | 0.328321i | ||||
\(320\) | 192.000 | + | 332.554i | 0.0335410 | + | 0.0580948i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3432.00 | −0.591212 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −89.0000 | + | 154.153i | −0.0151903 | + | 0.0263103i | ||||
\(326\) | −92.0000 | + | 159.349i | −0.0156301 | + | 0.0270721i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3024.00 | 0.509062 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4850.00 | + | 8400.45i | 0.805378 | + | 1.39496i | 0.916036 | + | 0.401097i | \(0.131371\pi\) |
−0.110658 | + | 0.993859i | \(0.535296\pi\) | |||||||
\(332\) | −2880.00 | + | 4988.31i | −0.476086 | + | 0.824605i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3924.00 | − | 6796.57i | −0.642849 | − | 1.11345i | ||||
\(335\) | −3576.00 | −0.583217 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8174.00 | 1.32126 | 0.660632 | − | 0.750710i | \(-0.270288\pi\) | ||||
0.660632 | + | 0.750710i | \(0.270288\pi\) | |||||||
\(338\) | 2193.00 | + | 3798.39i | 0.352910 | + | 0.611258i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −792.000 | + | 1371.78i | −0.126330 | + | 0.218810i | ||||
\(341\) | −2940.00 | − | 5092.23i | −0.466891 | − | 0.808679i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1312.00 | 0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1902.00 | + | 3294.36i | −0.295526 | + | 0.511867i | ||||
\(347\) | 2019.00 | − | 3497.01i | 0.312350 | − | 0.541007i | −0.666520 | − | 0.745487i | \(-0.732217\pi\) |
0.978871 | + | 0.204480i | \(0.0655504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10766.0 | −1.65126 | −0.825631 | − | 0.564210i | \(-0.809181\pi\) | ||||
−0.825631 | + | 0.564210i | \(0.809181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −480.000 | − | 831.384i | −0.0726821 | − | 0.125889i | ||||
\(353\) | 1833.00 | − | 3174.85i | 0.276376 | − | 0.478697i | −0.694105 | − | 0.719873i | \(-0.744200\pi\) |
0.970481 | + | 0.241176i | \(0.0775331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1890.00 | + | 3273.58i | 0.282566 | + | 0.489418i | ||||
\(356\) | −5496.00 | −0.818223 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.00177156 | ||||||||
\(359\) | 2553.00 | + | 4421.93i | 0.375326 | + | 0.650084i | 0.990376 | − | 0.138404i | \(-0.0441973\pi\) |
−0.615049 | + | 0.788489i | \(0.710864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2077.50 | − | 3598.34i | 0.302887 | − | 0.524615i | ||||
\(362\) | −2878.00 | − | 4984.84i | −0.417857 | − | 0.723750i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6252.00 | −0.896561 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2888.00 | + | 5002.16i | −0.410769 | + | 0.711473i | −0.994974 | − | 0.100133i | \(-0.968073\pi\) |
0.584205 | + | 0.811606i | \(0.301407\pi\) | |||||||
\(368\) | −912.000 | + | 1579.63i | −0.129188 | + | 0.223761i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3432.00 | 0.482219 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4231.00 | − | 7328.31i | −0.587327 | − | 1.01728i | −0.994581 | − | 0.103965i | \(-0.966847\pi\) |
0.407254 | − | 0.913315i | \(-0.366486\pi\) | |||||||
\(374\) | 1980.00 | − | 3429.46i | 0.273752 | − | 0.474153i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −912.000 | − | 1579.63i | −0.125087 | − | 0.216657i | ||||
\(377\) | −144.000 | −0.0196721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6860.00 | 0.929748 | 0.464874 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464874 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(380\) | 624.000 | + | 1080.80i | 0.0842382 | + | 0.145905i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 354.000 | − | 613.146i | 0.0474142 | − | 0.0821238i | ||||
\(383\) | −348.000 | − | 602.754i | −0.0464281 | − | 0.0804159i | 0.841877 | − | 0.539669i | \(-0.181451\pi\) |
−0.888306 | + | 0.459253i | \(0.848117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9716.00 | −1.28117 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −68.0000 | + | 117.779i | −0.00889736 | + | 0.0154107i | ||||
\(389\) | −5568.00 | + | 9644.06i | −0.725730 | + | 1.25700i | 0.232943 | + | 0.972490i | \(0.425164\pi\) |
−0.958673 | + | 0.284510i | \(0.908169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7524.00 | −0.973159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 396.000 | + | 685.892i | 0.0506350 | + | 0.0877024i | ||||
\(395\) | −264.000 | + | 457.261i | −0.0336286 | + | 0.0582464i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5419.00 | + | 9385.98i | 0.685068 | + | 1.18657i | 0.973416 | + | 0.229046i | \(0.0735607\pi\) |
−0.288348 | + | 0.957526i | \(0.593106\pi\) | |||||||
\(398\) | −3424.00 | −0.431230 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1424.00 | −0.178000 | ||||||||
\(401\) | 4182.00 | + | 7243.44i | 0.520796 | + | 0.902045i | 0.999708 | + | 0.0241817i | \(0.00769804\pi\) |
−0.478912 | + | 0.877863i | \(0.658969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 196.000 | − | 339.482i | 0.0242269 | − | 0.0419623i | ||||
\(404\) | −876.000 | − | 1517.28i | −0.107878 | − | 0.186850i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8580.00 | −1.04495 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −881.000 | + | 1525.94i | −0.106510 | + | 0.184481i | −0.914354 | − | 0.404915i | \(-0.867301\pi\) |
0.807844 | + | 0.589396i | \(0.200634\pi\) | |||||||
\(410\) | 2268.00 | − | 3928.29i | 0.273192 | − | 0.473182i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6704.00 | −0.801656 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4320.00 | + | 7482.46i | 0.510989 | + | 0.885059i | ||||
\(416\) | 32.0000 | − | 55.4256i | 0.00377146 | − | 0.00653237i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1560.00 | − | 2702.00i | −0.182541 | − | 0.316170i | ||||
\(419\) | −14580.0 | −1.69995 | −0.849976 | − | 0.526822i | \(-0.823383\pi\) | ||||
−0.849976 | + | 0.526822i | \(0.823383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8534.00 | 0.987938 | 0.493969 | − | 0.869480i | \(-0.335546\pi\) | ||||
0.493969 | + | 0.869480i | \(0.335546\pi\) | |||||||
\(422\) | 772.000 | + | 1337.14i | 0.0890530 | + | 0.154244i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1392.00 | − | 2411.01i | 0.159437 | − | 0.276154i | ||||
\(425\) | −2937.00 | − | 5087.03i | −0.335213 | − | 0.580606i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8088.00 | 0.913430 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 984.000 | − | 1704.34i | 0.110355 | − | 0.191141i | ||||
\(431\) | −2967.00 | + | 5138.99i | −0.331590 | + | 0.574331i | −0.982824 | − | 0.184546i | \(-0.940918\pi\) |
0.651234 | + | 0.758877i | \(0.274252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14758.0 | 1.63793 | 0.818966 | − | 0.573843i | \(-0.194548\pi\) | ||||
0.818966 | + | 0.573843i | \(0.194548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1004.00 | + | 1738.98i | 0.110282 | + | 0.191014i | ||||
\(437\) | −2964.00 | + | 5133.80i | −0.324456 | + | 0.561975i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5696.00 | − | 9865.76i | −0.619260 | − | 1.07259i | −0.989621 | − | 0.143702i | \(-0.954099\pi\) |
0.370361 | − | 0.928888i | \(-0.379234\pi\) | |||||||
\(440\) | −1440.00 | −0.156021 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 264.000 | 0.0284100 | ||||||||
\(443\) | −3513.00 | − | 6084.69i | −0.376767 | − | 0.652579i | 0.613823 | − | 0.789444i | \(-0.289631\pi\) |
−0.990590 | + | 0.136865i | \(0.956298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4122.00 | + | 7139.51i | −0.439105 | + | 0.760551i | ||||
\(446\) | 776.000 | + | 1344.07i | 0.0823871 | + | 0.142699i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3384.00 | −0.355681 | −0.177841 | − | 0.984059i | \(-0.556911\pi\) | ||||
−0.177841 | + | 0.984059i | \(0.556911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5670.00 | + | 9820.73i | −0.591995 | + | 1.02537i | ||||
\(452\) | −4032.00 | + | 6983.63i | −0.419578 | + | 0.726731i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3576.00 | 0.369670 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2141.00 | + | 3708.32i | 0.219150 | + | 0.379580i | 0.954548 | − | 0.298056i | \(-0.0963381\pi\) |
−0.735398 | + | 0.677635i | \(0.763005\pi\) | |||||||
\(458\) | 5402.00 | − | 9356.54i | 0.551133 | − | 0.954590i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1368.00 | + | 2369.45i | 0.138659 | + | 0.240165i | ||||
\(461\) | −16650.0 | −1.68214 | −0.841071 | − | 0.540924i | \(-0.818075\pi\) | ||||
−0.841071 | + | 0.540924i | \(0.818075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9664.00 | −0.970031 | −0.485015 | − | 0.874506i | \(-0.661186\pi\) | ||||
−0.485015 | + | 0.874506i | \(0.661186\pi\) | |||||||
\(464\) | −576.000 | − | 997.661i | −0.0576296 | − | 0.0998174i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3012.00 | + | 5216.94i | −0.299417 | + | 0.518605i | ||||
\(467\) | −6162.00 | − | 10672.9i | −0.610585 | − | 1.05756i | −0.991142 | − | 0.132807i | \(-0.957601\pi\) |
0.380557 | − | 0.924758i | \(-0.375732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2736.00 | −0.268515 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1392.00 | + | 2411.01i | −0.135746 | + | 0.235119i | ||||
\(473\) | −2460.00 | + | 4260.84i | −0.239135 | + | 0.414194i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4628.00 | −0.447047 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3546.00 | − | 6141.85i | −0.339310 | − | 0.587702i | ||||
\(479\) | 9330.00 | − | 16160.0i | 0.889976 | − | 1.54148i | 0.0500744 | − | 0.998745i | \(-0.484054\pi\) |
0.839902 | − | 0.542738i | \(-0.182613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −286.000 | − | 495.367i | −0.0271112 | − | 0.0469579i | ||||
\(482\) | 7124.00 | 0.673214 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1724.00 | −0.161908 | ||||||||
\(485\) | 102.000 | + | 176.669i | 0.00954965 | + | 0.0165405i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1700.00 | − | 2944.49i | 0.158181 | − | 0.273978i | −0.776031 | − | 0.630694i | \(-0.782770\pi\) |
0.934213 | + | 0.356716i | \(0.116104\pi\) | |||||||
\(488\) | −424.000 | − | 734.390i | −0.0393311 | − | 0.0681235i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2970.00 | 0.272982 | 0.136491 | − | 0.990641i | \(-0.456418\pi\) | ||||
0.136491 | + | 0.990641i | \(0.456418\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2376.00 | − | 4115.35i | 0.217058 | − | 0.375956i | ||||
\(494\) | 104.000 | − | 180.133i | 0.00947203 | − | 0.0164060i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3136.00 | 0.283892 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 494.000 | + | 855.633i | 0.0443176 | + | 0.0767603i | 0.887333 | − | 0.461129i | \(-0.152555\pi\) |
−0.843016 | + | 0.537889i | \(0.819222\pi\) | |||||||
\(500\) | −2568.00 | + | 4447.91i | −0.229689 | + | 0.397833i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3348.00 | + | 5798.91i | 0.297666 | + | 0.515573i | ||||
\(503\) | −5184.00 | −0.459529 | −0.229765 | − | 0.973246i | \(-0.573796\pi\) | ||||
−0.229765 | + | 0.973246i | \(0.573796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2628.00 | −0.231573 | ||||||||
\(506\) | −3420.00 | − | 5923.61i | −0.300469 | − | 0.520428i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3568.00 | + | 6179.96i | −0.311623 | + | 0.539747i | ||||
\(509\) | 8427.00 | + | 14596.0i | 0.733831 | + | 1.27103i | 0.955234 | + | 0.295851i | \(0.0956032\pi\) |
−0.221403 | + | 0.975182i | \(0.571064\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 366.000 | − | 633.931i | 0.0314077 | − | 0.0543998i | ||||
\(515\) | −5028.00 | + | 8708.75i | −0.430214 | + | 0.745152i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6840.00 | 0.581862 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −48.0000 | − | 83.1384i | −0.00404796 | − | 0.00701127i | ||||
\(521\) | −2199.00 | + | 3808.78i | −0.184914 | + | 0.320280i | −0.943547 | − | 0.331238i | \(-0.892534\pi\) |
0.758634 | + | 0.651517i | \(0.225867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5336.00 | − | 9242.22i | −0.446132 | − | 0.772723i | 0.551998 | − | 0.833845i | \(-0.313865\pi\) |
−0.998130 | + | 0.0611220i | \(0.980532\pi\) | |||||||
\(524\) | −6432.00 | −0.536228 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8340.00 | 0.691333 | ||||||||
\(527\) | 6468.00 | + | 11202.9i | 0.534631 | + | 0.926008i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −414.500 | + | 717.935i | −0.0340676 | + | 0.0590067i | ||||
\(530\) | −2088.00 | − | 3616.52i | −0.171126 | − | 0.296399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −756.000 | −0.0614371 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6066.00 | − | 10506.6i | 0.490198 | − | 0.849048i | ||||
\(536\) | −2384.00 | + | 4129.21i | −0.192114 | + | 0.332751i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12156.0 | −0.974131 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10351.0 | − | 17928.5i | −0.822596 | − | 1.42478i | −0.903743 | − | 0.428075i | \(-0.859192\pi\) |
0.0811474 | − | 0.996702i | \(-0.474142\pi\) | |||||||
\(542\) | 2468.00 | − | 4274.70i | 0.195590 | − | 0.338771i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1056.00 | + | 1829.05i | 0.0832273 | + | 0.144154i | ||||
\(545\) | 3012.00 | 0.236734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22876.0 | −1.78813 | −0.894065 | − | 0.447937i | \(-0.852159\pi\) | ||||
−0.894065 | + | 0.447937i | \(0.852159\pi\) | |||||||
\(548\) | 5160.00 | + | 8937.38i | 0.402234 | + | 0.696690i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2670.00 | − | 4624.58i | 0.206999 | − | 0.358532i | ||||
\(551\) | −1872.00 | − | 3242.40i | −0.144737 | − | 0.250691i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −788.000 | −0.0604312 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4288.00 | − | 7427.03i | 0.327071 | − | 0.566504i | ||||
\(557\) | 6438.00 | − | 11150.9i | 0.489743 | − | 0.848260i | −0.510187 | − | 0.860063i | \(-0.670424\pi\) |
0.999930 | + | 0.0118036i | \(0.00375730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −328.000 | −0.0248174 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 396.000 | + | 685.892i | 0.0297229 | + | 0.0514815i | ||||
\(563\) | −3450.00 | + | 5975.58i | −0.258260 | + | 0.447319i | −0.965776 | − | 0.259378i | \(-0.916482\pi\) |
0.707516 | + | 0.706697i | \(0.249816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6048.00 | + | 10475.4i | 0.450339 | + | 0.780009i | ||||
\(566\) | 2696.00 | 0.200214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5040.00 | 0.372313 | ||||||||
\(569\) | −7338.00 | − | 12709.8i | −0.540641 | − | 0.936418i | −0.998867 | − | 0.0475826i | \(-0.984848\pi\) |
0.458226 | − | 0.888836i | \(-0.348485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −190.000 | + | 329.090i | −0.0139251 | + | 0.0241190i | −0.872904 | − | 0.487892i | \(-0.837766\pi\) |
0.858979 | + | 0.512011i | \(0.171099\pi\) | |||||||
\(572\) | 120.000 | + | 207.846i | 0.00877177 | + | 0.0151932i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10146.0 | −0.735856 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5903.00 | + | 10224.3i | −0.425901 | + | 0.737683i | −0.996504 | − | 0.0835434i | \(-0.973376\pi\) |
0.570603 | + | 0.821226i | \(0.306710\pi\) | |||||||
\(578\) | 557.000 | − | 964.752i | 0.0400833 | − | 0.0694263i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1728.00 | −0.123709 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5220.00 | + | 9041.31i | 0.370824 | + | 0.642286i | ||||
\(584\) | −4168.00 | + | 7219.19i | −0.295331 | + | 0.511528i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7506.00 | + | 13000.8i | 0.529130 | + | 0.916480i | ||||
\(587\) | 19188.0 | 1.34919 | 0.674594 | − | 0.738189i | \(-0.264319\pi\) | ||||
0.674594 | + | 0.738189i | \(0.264319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10192.0 | 0.712995 | ||||||||
\(590\) | 2088.00 | + | 3616.52i | 0.145698 | + | 0.252356i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2288.00 | − | 3962.93i | 0.158845 | − | 0.275128i | ||||
\(593\) | 345.000 | + | 597.558i | 0.0238912 | + | 0.0413807i | 0.877724 | − | 0.479167i | \(-0.159061\pi\) |
−0.853833 | + | 0.520548i | \(0.825728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6000.00 | 0.412365 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 228.000 | − | 394.908i | 0.0155913 | − | 0.0270050i | ||||
\(599\) | 10245.0 | − | 17744.9i | 0.698830 | − | 1.21041i | −0.270042 | − | 0.962849i | \(-0.587038\pi\) |
0.968872 | − | 0.247561i | \(-0.0796291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11590.0 | 0.786632 | 0.393316 | − | 0.919403i | \(-0.371328\pi\) | ||||
0.393316 | + | 0.919403i | \(0.371328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2480.00 | + | 4295.49i | 0.167069 | + | 0.289372i | ||||
\(605\) | −1293.00 | + | 2239.54i | −0.0868891 | + | 0.150496i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3212.00 | − | 5563.35i | −0.214779 | − | 0.372009i | 0.738425 | − | 0.674336i | \(-0.235570\pi\) |
−0.953204 | + | 0.302327i | \(0.902237\pi\) | |||||||
\(608\) | 1664.00 | 0.110994 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1272.00 | −0.0844291 | ||||||||
\(611\) | 228.000 | + | 394.908i | 0.0150964 | + | 0.0261477i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4841.00 | − | 8384.86i | 0.318966 | − | 0.552465i | −0.661307 | − | 0.750116i | \(-0.729998\pi\) |
0.980273 | + | 0.197650i | \(0.0633311\pi\) | |||||||
\(614\) | 1748.00 | + | 3027.62i | 0.114892 | + | 0.198998i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5076.00 | 0.331203 | 0.165601 | − | 0.986193i | \(-0.447044\pi\) | ||||
0.165601 | + | 0.986193i | \(0.447044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11332.0 | − | 19627.6i | 0.735818 | − | 1.27447i | −0.218545 | − | 0.975827i | \(-0.570131\pi\) |
0.954363 | − | 0.298648i | \(-0.0965356\pi\) | |||||||
\(620\) | 2352.00 | − | 4073.78i | 0.152353 | − | 0.263882i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2280.00 | 0.146977 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1710.50 | − | 2962.67i | −0.109472 | − | 0.189611i | ||||
\(626\) | 146.000 | − | 252.879i | 0.00932162 | − | 0.0161455i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1228.00 | + | 2126.96i | 0.0780295 | + | 0.135151i | ||||
\(629\) | 18876.0 | 1.19656 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8584.00 | −0.541559 | −0.270779 | − | 0.962641i | \(-0.587281\pi\) | ||||
−0.270779 | + | 0.962641i | \(0.587281\pi\) | |||||||
\(632\) | 352.000 | + | 609.682i | 0.0221548 | + | 0.0383732i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8148.00 | − | 14112.7i | 0.510408 | − | 0.884052i | ||||
\(635\) | 5352.00 | + | 9269.94i | 0.334469 | + | 0.579317i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4320.00 | 0.268073 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 384.000 | − | 665.108i | 0.0237171 | − | 0.0410792i | ||||
\(641\) | −186.000 | + | 322.161i | −0.0114611 | + | 0.0198512i | −0.871699 | − | 0.490042i | \(-0.836982\pi\) |
0.860238 | + | 0.509893i | \(0.170315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3188.00 | −0.195525 | −0.0977624 | − | 0.995210i | \(-0.531169\pi\) | ||||
−0.0977624 | + | 0.995210i | \(0.531169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3432.00 | + | 5944.40i | 0.209025 | + | 0.362042i | ||||
\(647\) | −6366.00 | + | 11026.2i | −0.386821 | + | 0.669994i | −0.992020 | − | 0.126080i | \(-0.959760\pi\) |
0.605199 | + | 0.796074i | \(0.293094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5220.00 | − | 9041.31i | −0.315721 | − | 0.546845i | ||||
\(650\) | 356.000 | 0.0214823 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 368.000 | 0.0221043 | ||||||||
\(653\) | 1788.00 | + | 3096.91i | 0.107151 | + | 0.185592i | 0.914615 | − | 0.404326i | \(-0.132494\pi\) |
−0.807464 | + | 0.589917i | \(0.799160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4824.00 | + | 8355.41i | −0.287770 | + | 0.498432i | ||||
\(656\) | −3024.00 | − | 5237.72i | −0.179981 | − | 0.311736i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11430.0 | 0.675644 | 0.337822 | − | 0.941210i | \(-0.390310\pi\) | ||||
0.337822 | + | 0.941210i | \(0.390310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11323.0 | − | 19612.0i | 0.666284 | − | 1.15404i | −0.312652 | − | 0.949868i | \(-0.601217\pi\) |
0.978936 | − | 0.204170i | \(-0.0654494\pi\) | |||||||
\(662\) | 9700.00 | − | 16800.9i | 0.569488 | − | 0.986383i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11520.0 | 0.673287 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4104.00 | − | 7108.34i | −0.238242 | − | 0.412648i | ||||
\(668\) | −7848.00 | + | 13593.1i | −0.454563 | + | 0.787327i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3576.00 | + | 6193.81i | 0.206198 | + | 0.357146i | ||||
\(671\) | 3180.00 | 0.182955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13570.0 | −0.777244 | −0.388622 | − | 0.921397i | \(-0.627049\pi\) | ||||
−0.388622 | + | 0.921397i | \(0.627049\pi\) | |||||||
\(674\) | −8174.00 | − | 14157.8i | −0.467138 | − | 0.809106i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4386.00 | − | 7596.77i | 0.249545 | − | 0.432224i | ||||
\(677\) | −1419.00 | − | 2457.78i | −0.0805563 | − | 0.139528i | 0.822933 | − | 0.568139i | \(-0.192336\pi\) |
−0.903489 | + | 0.428611i | \(0.859003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3168.00 | 0.178658 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5880.00 | + | 10184.5i | −0.330142 | + | 0.571823i | ||||
\(683\) | 3279.00 | − | 5679.39i | 0.183701 | − | 0.318179i | −0.759437 | − | 0.650580i | \(-0.774526\pi\) |
0.943138 | + | 0.332402i | \(0.107859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15480.0 | 0.863446 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1312.00 | − | 2272.45i | −0.0727028 | − | 0.125925i | ||||
\(689\) | −348.000 | + | 602.754i | −0.0192420 | + | 0.0333281i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10916.0 | − | 18907.1i | −0.600961 | − | 1.04090i | −0.992676 | − | 0.120809i | \(-0.961451\pi\) |
0.391715 | − | 0.920087i | \(-0.371882\pi\) | |||||||
\(692\) | 7608.00 | 0.417938 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8076.00 | −0.441730 | ||||||||
\(695\) | −6432.00 | − | 11140.6i | −0.351050 | − | 0.608036i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12474.0 | − | 21605.6i | 0.677886 | − | 1.17413i | ||||
\(698\) | 10766.0 | + | 18647.3i | 0.583810 | + | 1.01119i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16200.0 | 0.872847 | 0.436423 | − | 0.899741i | \(-0.356245\pi\) | ||||
0.436423 | + | 0.899741i | \(0.356245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7436.00 | − | 12879.5i | 0.398939 | − | 0.690982i | ||||
\(704\) | −960.000 | + | 1662.77i | −0.0513940 | + | 0.0890170i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7332.00 | −0.390855 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18361.0 | − | 31802.2i | −0.972584 | − | 1.68456i | −0.687689 | − | 0.726006i | \(-0.741375\pi\) |
−0.284895 | − | 0.958559i | \(-0.591959\pi\) | |||||||
\(710\) | 3780.00 | − | 6547.15i | 0.199804 | − | 0.346071i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5496.00 | + | 9519.35i | 0.289286 | + | 0.501057i | ||||
\(713\) | 22344.0 | 1.17362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 360.000 | 0.0188297 | ||||||||
\(716\) | 12.0000 | + | 20.7846i | 0.000626342 | + | 0.00108486i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5106.00 | − | 8843.85i | 0.265396 | − | 0.459679i | ||||
\(719\) | 6888.00 | + | 11930.4i | 0.357273 | + | 0.618814i | 0.987504 | − | 0.157593i | \(-0.0503734\pi\) |
−0.630231 | + | 0.776407i | \(0.717040\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8310.00 | −0.428347 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5756.00 | + | 9969.68i | −0.295470 | + | 0.511769i | ||||
\(725\) | 3204.00 | − | 5549.49i | 0.164129 | − | 0.284280i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34220.0 | −1.74574 | −0.872868 | − | 0.487957i | \(-0.837742\pi\) | ||||
−0.872868 | + | 0.487957i | \(0.837742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6252.00 | + | 10828.8i | 0.316982 | + | 0.549029i | ||||
\(731\) | 5412.00 | − | 9373.86i | 0.273830 | − | 0.474288i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6875.00 | − | 11907.8i | −0.346431 | − | 0.600036i | 0.639182 | − | 0.769056i | \(-0.279273\pi\) |
−0.985613 | + | 0.169020i | \(0.945940\pi\) | |||||||
\(734\) | 11552.0 | 0.580916 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3648.00 | 0.182700 | ||||||||
\(737\) | −8940.00 | − | 15484.5i | −0.446824 | − | 0.773922i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19918.0 | + | 34499.0i | −0.991469 | + | 1.71727i | −0.382853 | + | 0.923809i | \(0.625059\pi\) |
−0.608616 | + | 0.793465i | \(0.708275\pi\) | |||||||
\(740\) | −3432.00 | − | 5944.40i | −0.170490 | − | 0.295298i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34470.0 | 1.70199 | 0.850997 | − | 0.525170i | \(-0.175998\pi\) | ||||
0.850997 | + | 0.525170i | \(0.175998\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4500.00 | − | 7794.23i | 0.221298 | − | 0.383300i | ||||
\(746\) | −8462.00 | + | 14656.6i | −0.415303 | + | 0.719325i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7920.00 | −0.387144 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2620.00 | − | 4537.97i | −0.127304 | − | 0.220497i | 0.795327 | − | 0.606180i | \(-0.207299\pi\) |
−0.922631 | + | 0.385684i | \(0.873966\pi\) | |||||||
\(752\) | −1824.00 | + | 3159.26i | −0.0884500 | + | 0.153200i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 144.000 | + | 249.415i | 0.00695513 | + | 0.0120466i | ||||
\(755\) | 7440.00 | 0.358635 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18578.0 | 0.891980 | 0.445990 | − | 0.895038i | \(-0.352852\pi\) | ||||
0.445990 | + | 0.895038i | \(0.352852\pi\) | |||||||
\(758\) | −6860.00 | − | 11881.9i | −0.328716 | − | 0.569352i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1248.00 | − | 2161.60i | 0.0595654 | − | 0.103170i | ||||
\(761\) | 15267.0 | + | 26443.2i | 0.727238 | + | 1.25961i | 0.958046 | + | 0.286614i | \(0.0925298\pi\) |
−0.230808 | + | 0.972999i | \(0.574137\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1416.00 | −0.0670538 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −696.000 | + | 1205.51i | −0.0328296 | + | 0.0568626i | ||||
\(767\) | 348.000 | − | 602.754i | 0.0163827 | − | 0.0283757i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39958.0 | 1.87376 | 0.936881 | − | 0.349650i | \(-0.113699\pi\) | ||||
0.936881 | + | 0.349650i | \(0.113699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9716.00 | + | 16828.6i | 0.452962 | + | 0.784553i | ||||
\(773\) | −1983.00 | + | 3434.66i | −0.0922685 | + | 0.159814i | −0.908465 | − | 0.417960i | \(-0.862745\pi\) |
0.816197 | + | 0.577774i | \(0.196078\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8722.00 | + | 15106.9i | 0.404263 | + | 0.700203i | ||||
\(776\) | 272.000 | 0.0125828 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22272.0 | 1.02634 | ||||||||
\(779\) | −9828.00 | − | 17022.6i | −0.452021 | − | 0.782924i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9450.00 | + | 16367.9i | −0.432967 | + | 0.749922i | ||||
\(782\) | 7524.00 | + | 13032.0i | 0.344064 | + | 0.595936i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3684.00 | 0.167500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1880.00 | + | 3256.26i | −0.0851522 | + | 0.147488i | −0.905456 | − | 0.424440i | \(-0.860471\pi\) |
0.820304 | + | 0.571928i | \(0.193804\pi\) | |||||||
\(788\) | 792.000 | − | 1371.78i | 0.0358044 | − | 0.0620150i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1056.00 | 0.0475580 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 106.000 | + | 183.597i | 0.00474675 | + | 0.00822161i | ||||
\(794\) | 10838.0 | − | 18772.0i | 0.484416 | − | 0.839033i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3424.00 | + | 5930.54i | 0.152463 | + | 0.264073i | ||||
\(797\) | 24102.0 | 1.07119 | 0.535594 | − | 0.844476i | \(-0.320088\pi\) | ||||
0.535594 | + | 0.844476i | \(0.320088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15048.0 | −0.666283 | ||||||||
\(800\) | 1424.00 | + | 2466.44i | 0.0629325 | + | 0.109002i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8364.00 | − | 14486.9i | 0.368258 | − | 0.637842i | ||||
\(803\) | −15630.0 | − | 27072.0i | −0.686888 | − | 1.18972i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −784.000 | −0.0342621 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1752.00 | + | 3034.55i | −0.0762811 | + | 0.132123i | ||||
\(809\) | −5856.00 | + | 10142.9i | −0.254494 | + | 0.440797i | −0.964758 | − | 0.263138i | \(-0.915242\pi\) |
0.710264 | + | 0.703936i | \(0.248576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37424.0 | −1.62039 | −0.810194 | − | 0.586162i | \(-0.800638\pi\) | ||||
−0.810194 | + | 0.586162i | \(0.800638\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8580.00 | + | 14861.0i | 0.369446 | + | 0.639899i | ||||
\(815\) | 276.000 | − | 478.046i | 0.0118624 | − | 0.0205463i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4264.00 | − | 7385.46i | −0.182593 | − | 0.316260i | ||||
\(818\) | 3524.00 | 0.150628 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9072.00 | −0.386351 | ||||||||
\(821\) | −6726.00 | − | 11649.8i | −0.285918 | − | 0.495225i | 0.686913 | − | 0.726740i | \(-0.258965\pi\) |
−0.972831 | + | 0.231514i | \(0.925632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10216.0 | + | 17694.6i | −0.432694 | + | 0.749448i | −0.997104 | − | 0.0760461i | \(-0.975770\pi\) |
0.564410 | + | 0.825495i | \(0.309104\pi\) | |||||||
\(824\) | 6704.00 | + | 11611.7i | 0.283428 | + | 0.490912i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24390.0 | 1.02554 | 0.512771 | − | 0.858525i | \(-0.328619\pi\) | ||||
0.512771 | + | 0.858525i | \(0.328619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14255.0 | + | 24690.4i | −0.597221 | + | 1.03442i | 0.396008 | + | 0.918247i | \(0.370395\pi\) |
−0.993229 | + | 0.116171i | \(0.962938\pi\) | |||||||
\(830\) | 8640.00 | − | 14964.9i | 0.361324 | − | 0.625831i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −128.000 | −0.00533366 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11772.0 | + | 20389.7i | 0.487888 | + | 0.845048i | ||||
\(836\) | −3120.00 | + | 5404.00i | −0.129076 | + | 0.223566i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14580.0 | + | 25253.3i | 0.601024 | + | 1.04100i | ||||
\(839\) | 36972.0 | 1.52135 | 0.760677 | − | 0.649131i | \(-0.224867\pi\) | ||||
0.760677 | + | 0.649131i | \(0.224867\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19205.0 | −0.787445 | ||||||||
\(842\) | −8534.00 | − | 14781.3i | −0.349289 | − | 0.604986i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1544.00 | − | 2674.29i | 0.0629700 | − | 0.109067i | ||||
\(845\) | −6579.00 | − | 11395.2i | −0.267840 | − | 0.463912i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5568.00 | −0.225479 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5874.00 | + | 10174.1i | −0.237031 | + | 0.410550i | ||||
\(851\) | 16302.0 | − | 28235.9i | 0.656669 | − | 1.13738i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14074.0 | 0.564929 | 0.282465 | − | 0.959278i | \(-0.408848\pi\) | ||||
0.282465 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8088.00 | − | 14008.8i | −0.322946 | − | 0.559360i | ||||
\(857\) | −4413.00 | + | 7643.54i | −0.175899 | + | 0.304666i | −0.940472 | − | 0.339871i | \(-0.889616\pi\) |
0.764573 | + | 0.644537i | \(0.222950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10250.0 | − | 17753.5i | −0.407131 | − | 0.705171i | 0.587436 | − | 0.809271i | \(-0.300137\pi\) |
−0.994567 | + | 0.104099i | \(0.966804\pi\) | |||||||
\(860\) | −3936.00 | −0.156066 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11868.0 | 0.468939 | ||||||||
\(863\) | −3837.00 | − | 6645.88i | −0.151348 | − | 0.262142i | 0.780375 | − | 0.625311i | \(-0.215028\pi\) |
−0.931723 | + | 0.363169i | \(0.881695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5706.00 | − | 9883.08i | 0.224289 | − | 0.388480i | ||||
\(866\) | −14758.0 | − | 25561.6i | −0.579096 | − | 1.00302i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2640.00 | −0.103056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 596.000 | − | 1032.30i | 0.0231856 | − | 0.0401587i | ||||
\(872\) | 2008.00 | − | 3477.96i | 0.0779810 | − | 0.135067i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11856.0 | 0.458850 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4445.00 | + | 7698.97i | 0.171148 | + | 0.296437i | 0.938822 | − | 0.344404i | \(-0.111919\pi\) |
−0.767673 | + | 0.640841i | \(0.778586\pi\) | |||||||
\(878\) | −11392.0 | + | 19731.5i | −0.437883 | + | 0.758436i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1440.00 | + | 2494.15i | 0.0551618 | + | 0.0955431i | ||||
\(881\) | −738.000 | −0.0282223 | −0.0141112 | − | 0.999900i | \(-0.504492\pi\) | ||||
−0.0141112 | + | 0.999900i | \(0.504492\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.000762235 | 0.000381118 | − | 1.00000i | \(-0.499879\pi\) | ||||
0.000381118 | 1.00000i | \(0.499879\pi\) | ||||||||
\(884\) | −264.000 | − | 457.261i | −0.0100444 | − | 0.0173975i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7026.00 | + | 12169.4i | −0.266414 | + | 0.461443i | ||||
\(887\) | 19902.0 | + | 34471.3i | 0.753375 | + | 1.30488i | 0.946178 | + | 0.323647i | \(0.104909\pi\) |
−0.192803 | + | 0.981238i | \(0.561758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16488.0 | 0.620988 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1552.00 | − | 2688.14i | 0.0582565 | − | 0.100903i | ||||
\(893\) | −5928.00 | + | 10267.6i | −0.222142 | + | 0.384762i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | 0.00134452 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3384.00 | + | 5861.26i | 0.125752 | + | 0.217809i | ||||
\(899\) | −7056.00 | + | 12221.4i | −0.261769 | + | 0.453398i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11484.0 | − | 19890.9i | −0.424625 | − | 0.735473i | ||||
\(902\) | 22680.0 | 0.837208 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16128.0 | 0.593373 | ||||||||
\(905\) | 8634.00 | + | 14954.5i | 0.317131 | + | 0.549288i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14590.0 | + | 25270.6i | −0.534127 | + | 0.925135i | 0.465078 | + | 0.885270i | \(0.346026\pi\) |
−0.999205 | + | 0.0398652i | \(0.987307\pi\) | |||||||
\(908\) | −3576.00 | − | 6193.81i | −0.130698 | − | 0.226375i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48258.0 | −1.75506 | −0.877530 | − | 0.479523i | \(-0.840810\pi\) | ||||
−0.877530 | + | 0.479523i | \(0.840810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21600.0 | + | 37412.3i | −0.782974 | + | 1.35615i | ||||
\(914\) | 4282.00 | − | 7416.64i | 0.154963 | − | 0.268403i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21608.0 | −0.779420 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12880.0 | − | 22308.8i | −0.462320 | − | 0.800762i | 0.536756 | − | 0.843737i | \(-0.319649\pi\) |
−0.999076 | + | 0.0429758i | \(0.986316\pi\) | |||||||
\(920\) | 2736.00 | − | 4738.89i | 0.0980470 | − | 0.169822i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16650.0 | + | 28838.6i | 0.594727 | + | 1.03010i | ||||
\(923\) | −1260.00 | −0.0449333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25454.0 | 0.904781 | ||||||||
\(926\) | 9664.00 | + | 16738.5i | 0.342958 | + | 0.594020i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1152.00 | + | 1995.32i | −0.0407503 | + | 0.0705815i | ||||
\(929\) | −22389.0 | − | 38778.9i | −0.790699 | − | 1.36953i | −0.925535 | − | 0.378663i | \(-0.876384\pi\) |
0.134836 | − | 0.990868i | \(-0.456949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12048.0 | 0.423439 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12324.0 | + | 21345.8i | −0.431749 | + | 0.747811i | ||||
\(935\) | −5940.00 | + | 10288.4i | −0.207763 | + | 0.359857i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44494.0 | 1.55129 | 0.775643 | − | 0.631171i | \(-0.217426\pi\) | ||||
0.775643 | + | 0.631171i | \(0.217426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2736.00 | + | 4738.89i | 0.0949346 | + | 0.164431i | ||||
\(941\) | −3729.00 | + | 6458.82i | −0.129184 | + | 0.223753i | −0.923361 | − | 0.383934i | \(-0.874569\pi\) |
0.794177 | + | 0.607687i | \(0.207902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21546.0 | − | 37318.8i | −0.744045 | − | 1.28872i | ||||
\(944\) | 5568.00 | 0.191973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9840.00 | 0.338188 | ||||||||
\(947\) | −8895.00 | − | 15406.6i | −0.305226 | − | 0.528666i | 0.672086 | − | 0.740473i | \(-0.265399\pi\) |
−0.977312 | + | 0.211807i | \(0.932065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1042.00 | − | 1804.80i | 0.0356425 | − | 0.0617347i | ||||
\(950\) | 4628.00 | + | 8015.93i | 0.158055 | + | 0.273759i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5832.00 | −0.198234 | −0.0991170 | − | 0.995076i | \(-0.531602\pi\) | ||||
−0.0991170 | + | 0.995076i | \(0.531602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1062.00 | + | 1839.44i | −0.0359848 | + | 0.0623276i | ||||
\(956\) | −7092.00 | + | 12283.7i | −0.239929 | + | 0.415568i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37320.0 | −1.25862 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4312.50 | − | 7469.47i | −0.144758 | − | 0.250729i | ||||
\(962\) | −572.000 | + | 990.733i | −0.0191705 | + | 0.0332043i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7124.00 | − | 12339.1i | −0.238017 | − | 0.412258i | ||||
\(965\) | 29148.0 | 0.972339 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13264.0 | −0.441098 | −0.220549 | − | 0.975376i | \(-0.570785\pi\) | ||||
−0.220549 | + | 0.975376i | \(0.570785\pi\) | |||||||
\(968\) | 1724.00 | + | 2986.06i | 0.0572432 | + | 0.0991482i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 204.000 | − | 353.338i | 0.00675262 | − | 0.0116959i | ||||
\(971\) | 1992.00 | + | 3450.25i | 0.0658356 | + | 0.114031i | 0.897064 | − | 0.441900i | \(-0.145695\pi\) |
−0.831229 | + | 0.555931i | \(0.812362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6800.00 | −0.223702 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −848.000 | + | 1468.78i | −0.0278113 | + | 0.0481706i | ||||
\(977\) | 19470.0 | − | 33723.0i | 0.637564 | − | 1.10429i | −0.348401 | − | 0.937346i | \(-0.613275\pi\) |
0.985966 | − | 0.166949i | \(-0.0533914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41220.0 | −1.34566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2970.00 | − | 5144.19i | −0.0965138 | − | 0.167167i | ||||
\(983\) | −4404.00 | + | 7627.95i | −0.142895 | + | 0.247501i | −0.928586 | − | 0.371118i | \(-0.878974\pi\) |
0.785691 | + | 0.618620i | \(0.212308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1188.00 | − | 2057.68i | −0.0384293 | − | 0.0665614i | ||||
\(986\) | −9504.00 | −0.306967 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −416.000 | −0.0133955 | ||||||||
\(989\) | −9348.00 | − | 16191.2i | −0.300555 | − | 0.520577i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9244.00 | + | 16011.1i | −0.296312 | + | 0.513228i | −0.975289 | − | 0.220932i | \(-0.929090\pi\) |
0.678977 | + | 0.734159i | \(0.262424\pi\) | |||||||
\(992\) | −3136.00 | − | 5431.71i | −0.100371 | − | 0.173848i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10272.0 | 0.327281 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2501.00 | + | 4331.86i | −0.0794458 | + | 0.137604i | −0.903011 | − | 0.429618i | \(-0.858648\pi\) |
0.823565 | + | 0.567222i | \(0.191982\pi\) | |||||||
\(998\) | 988.000 | − | 1711.27i | 0.0313373 | − | 0.0542777i | ||||
\(999\) | 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 | 882.4.g.h.361.1 | 2 | ||
3.2 | odd | 2 | 882.4.g.q.361.1 | 2 | |||
7.2 | even | 3 | inner | 882.4.g.h.667.1 | 2 | ||
7.3 | odd | 6 | 126.4.a.g.1.1 | yes | 1 | ||
7.4 | even | 3 | 882.4.a.m.1.1 | 1 | |||
7.5 | odd | 6 | 882.4.g.e.667.1 | 2 | |||
7.6 | odd | 2 | 882.4.g.e.361.1 | 2 | |||
21.2 | odd | 6 | 882.4.g.q.667.1 | 2 | |||
21.5 | even | 6 | 882.4.g.t.667.1 | 2 | |||
21.11 | odd | 6 | 882.4.a.e.1.1 | 1 | |||
21.17 | even | 6 | 126.4.a.b.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 882.4.g.t.361.1 | 2 | |||
28.3 | even | 6 | 1008.4.a.n.1.1 | 1 | |||
84.59 | odd | 6 | 1008.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.a.b.1.1 | ✓ | 1 | 21.17 | even | 6 | ||
126.4.a.g.1.1 | yes | 1 | 7.3 | odd | 6 | ||
882.4.a.e.1.1 | 1 | 21.11 | odd | 6 | |||
882.4.a.m.1.1 | 1 | 7.4 | even | 3 | |||
882.4.g.e.361.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.e.667.1 | 2 | 7.5 | odd | 6 | |||
882.4.g.h.361.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.h.667.1 | 2 | 7.2 | even | 3 | inner | ||
882.4.g.q.361.1 | 2 | 3.2 | odd | 2 | |||
882.4.g.q.667.1 | 2 | 21.2 | odd | 6 | |||
882.4.g.t.361.1 | 2 | 21.20 | even | 2 | |||
882.4.g.t.667.1 | 2 | 21.5 | even | 6 | |||
1008.4.a.g.1.1 | 1 | 84.59 | odd | 6 | |||
1008.4.a.n.1.1 | 1 | 28.3 | even | 6 |