Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.5922408960000.19 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 54x^{6} + 176x^{5} + 1307x^{4} - 2912x^{3} - 15314x^{2} + 16800x + 86044 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 49) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.3 | ||
Root | \(5.23824 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.y.361.3 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26556 | − | 3.92407i | 0.800998 | − | 1.38737i | −0.117962 | − | 0.993018i | \(-0.537636\pi\) |
0.918960 | − | 0.394351i | \(-0.129031\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.26556 | − | 10.8523i | −0.783196 | − | 1.35653i | ||||
\(5\) | −6.73953 | + | 11.6732i | −0.602802 | + | 1.04408i | 0.389593 | + | 0.920987i | \(0.372616\pi\) |
−0.992395 | + | 0.123096i | \(0.960718\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −20.5311 | −0.907356 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 30.5377 | + | 52.8928i | 0.965686 | + | 1.67262i | ||||
\(11\) | 0.406613 | + | 0.704275i | 0.0111453 | + | 0.0193043i | 0.871544 | − | 0.490317i | \(-0.163119\pi\) |
−0.860399 | + | 0.509621i | \(0.829786\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.9564 | 0.745781 | 0.372891 | − | 0.927875i | \(-0.378367\pi\) | ||||
0.372891 | + | 0.927875i | \(0.378367\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.60992 | − | 6.25256i | 0.0564050 | − | 0.0976963i | ||||
\(17\) | 58.8660 | + | 101.959i | 0.839829 | + | 1.45463i | 0.890037 | + | 0.455888i | \(0.150678\pi\) |
−0.0502085 | + | 0.998739i | \(0.515989\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 46.6457 | − | 80.7927i | 0.563224 | − | 0.975532i | −0.433989 | − | 0.900918i | \(-0.642894\pi\) |
0.997213 | − | 0.0746138i | \(-0.0237724\pi\) | |||||||
\(20\) | 168.908 | 1.88845 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.68484 | 0.0357095 | ||||||||
\(23\) | 60.1245 | − | 104.139i | 0.545079 | − | 0.944105i | −0.453522 | − | 0.891245i | \(-0.649833\pi\) |
0.998602 | − | 0.0528605i | \(-0.0168339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −28.3424 | − | 49.0905i | −0.226739 | − | 0.392724i | ||||
\(26\) | 79.1960 | − | 137.171i | 0.597369 | − | 1.03467i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.56420 | −0.0548390 | −0.0274195 | − | 0.999624i | \(-0.508729\pi\) | ||||
−0.0274195 | + | 0.999624i | \(0.508729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.0535 | + | 71.1067i | 0.237852 | + | 0.411972i | 0.960098 | − | 0.279665i | \(-0.0902232\pi\) |
−0.722245 | + | 0.691637i | \(0.756890\pi\) | |||||||
\(32\) | −98.4815 | − | 170.575i | −0.544039 | − | 0.942303i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 533.458 | 2.69080 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.4066 | + | 24.9530i | −0.0640117 | + | 0.110872i | −0.896255 | − | 0.443539i | \(-0.853723\pi\) |
0.832243 | + | 0.554410i | \(0.187056\pi\) | |||||||
\(38\) | −211.358 | − | 366.082i | −0.902282 | − | 1.56280i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 138.370 | − | 239.664i | 0.546956 | − | 0.947355i | ||||
\(41\) | 70.5291 | 0.268654 | 0.134327 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134327 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 417.179 | 1.47952 | 0.739758 | − | 0.672873i | \(-0.234940\pi\) | ||||
0.739758 | + | 0.672873i | \(0.234940\pi\) | |||||||
\(44\) | 5.09532 | − | 8.82536i | 0.0174579 | − | 0.0302380i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −272.432 | − | 471.866i | −0.873215 | − | 1.51245i | ||||
\(47\) | 169.131 | − | 292.943i | 0.524899 | − | 0.909151i | −0.474681 | − | 0.880158i | \(-0.657437\pi\) |
0.999580 | − | 0.0289931i | \(-0.00923008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −256.846 | −0.726471 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −219.022 | − | 379.356i | −0.584093 | − | 1.01168i | ||||
\(53\) | 74.5603 | + | 129.142i | 0.193239 | + | 0.334699i | 0.946322 | − | 0.323226i | \(-0.104768\pi\) |
−0.753083 | + | 0.657925i | \(0.771434\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9615 | −0.0268737 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.4027 | + | 33.6065i | −0.0439259 | + | 0.0760820i | ||||
\(59\) | −47.0914 | − | 81.5647i | −0.103911 | − | 0.179980i | 0.809382 | − | 0.587283i | \(-0.199803\pi\) |
−0.913293 | + | 0.407303i | \(0.866469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.2623 | − | 104.377i | 0.126488 | − | 0.219084i | −0.795825 | − | 0.605526i | \(-0.792963\pi\) |
0.922314 | + | 0.386442i | \(0.126296\pi\) | |||||||
\(62\) | 372.037 | 0.762077 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −834.706 | −1.63029 | ||||||||
\(65\) | −235.590 | + | 408.053i | −0.449558 | + | 0.778658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 396.183 | + | 686.209i | 0.722410 | + | 1.25125i | 0.960031 | + | 0.279892i | \(0.0902988\pi\) |
−0.237622 | + | 0.971358i | \(0.576368\pi\) | |||||||
\(68\) | 737.657 | − | 1277.66i | 1.31550 | − | 2.27851i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −449.128 | −0.750729 | −0.375364 | − | 0.926877i | \(-0.622482\pi\) | ||||
−0.375364 | + | 0.926877i | \(0.622482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 234.710 | + | 406.530i | 0.376311 | + | 0.651790i | 0.990522 | − | 0.137352i | \(-0.0438590\pi\) |
−0.614211 | + | 0.789142i | \(0.710526\pi\) | |||||||
\(74\) | 65.2782 | + | 113.065i | 0.102546 | + | 0.177616i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1169.05 | −1.76446 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 509.926 | − | 883.218i | 0.726217 | − | 1.25785i | −0.232254 | − | 0.972655i | \(-0.574610\pi\) |
0.958471 | − | 0.285190i | \(-0.0920567\pi\) | |||||||
\(80\) | 48.6583 | + | 84.2786i | 0.0680020 | + | 0.117783i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 159.788 | − | 276.761i | 0.215191 | − | 0.372722i | ||||
\(83\) | 104.253 | 0.137870 | 0.0689352 | − | 0.997621i | \(-0.478040\pi\) | ||||
0.0689352 | + | 0.997621i | \(0.478040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1586.91 | −2.02500 | ||||||||
\(86\) | 945.146 | − | 1637.04i | 1.18509 | − | 2.05264i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.34823 | − | 14.4596i | −0.0101128 | − | 0.0175158i | ||||
\(89\) | −786.460 | + | 1362.19i | −0.936680 | + | 1.62238i | −0.165071 | + | 0.986282i | \(0.552785\pi\) |
−0.771610 | + | 0.636096i | \(0.780548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1506.86 | −1.70762 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −766.352 | − | 1327.36i | −0.840885 | − | 1.45646i | ||||
\(95\) | 628.739 | + | 1089.01i | 0.679024 | + | 1.17610i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 550.057 | 0.575772 | 0.287886 | − | 0.957665i | \(-0.407048\pi\) | ||||
0.287886 | + | 0.957665i | \(0.407048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −355.162 | + | 615.159i | −0.355162 | + | 0.615159i | ||||
\(101\) | −32.8585 | − | 56.9125i | −0.0323717 | − | 0.0560694i | 0.849386 | − | 0.527773i | \(-0.176973\pi\) |
−0.881757 | + | 0.471703i | \(0.843639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −914.674 | + | 1584.26i | −0.875005 | + | 1.51555i | −0.0182480 | + | 0.999833i | \(0.505809\pi\) |
−0.856757 | + | 0.515720i | \(0.827524\pi\) | |||||||
\(104\) | −717.694 | −0.676689 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 675.685 | 0.619135 | ||||||||
\(107\) | 430.689 | − | 745.975i | 0.389124 | − | 0.673982i | −0.603208 | − | 0.797584i | \(-0.706111\pi\) |
0.992332 | + | 0.123602i | \(0.0394445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 810.259 | + | 1403.41i | 0.712007 | + | 1.23323i | 0.964103 | + | 0.265529i | \(0.0855467\pi\) |
−0.252096 | + | 0.967702i | \(0.581120\pi\) | |||||||
\(110\) | −24.8340 | + | 43.0138i | −0.0215258 | + | 0.0372837i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −380.409 | −0.316689 | −0.158344 | − | 0.987384i | \(-0.550616\pi\) | ||||
−0.158344 | + | 0.987384i | \(0.550616\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 810.421 | + | 1403.69i | 0.657149 | + | 1.13822i | ||||
\(116\) | 53.6595 | + | 92.9410i | 0.0429497 | + | 0.0743910i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −426.754 | −0.332931 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 665.169 | − | 1152.11i | 0.499752 | − | 0.865595i | ||||
\(122\) | −273.056 | − | 472.947i | −0.202634 | − | 0.350972i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 514.446 | − | 891.047i | 0.372570 | − | 0.645310i | ||||
\(125\) | −920.824 | −0.658888 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 958.358 | 0.669610 | 0.334805 | − | 0.942287i | \(-0.391329\pi\) | ||||
0.334805 | + | 0.942287i | \(0.391329\pi\) | |||||||
\(128\) | −1103.23 | + | 1910.85i | −0.761817 | + | 1.31951i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1067.49 | + | 1848.94i | 0.720190 | + | 1.24741i | ||||
\(131\) | 576.079 | − | 997.798i | 0.384216 | − | 0.665481i | −0.607444 | − | 0.794362i | \(-0.707805\pi\) |
0.991660 | + | 0.128881i | \(0.0411386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3590.31 | 2.31459 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1208.58 | − | 2093.33i | −0.762024 | − | 1.31986i | ||||
\(137\) | 178.689 | + | 309.498i | 0.111434 | + | 0.193009i | 0.916349 | − | 0.400382i | \(-0.131122\pi\) |
−0.804915 | + | 0.593390i | \(0.797789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2736.29 | −1.66970 | −0.834852 | − | 0.550475i | \(-0.814447\pi\) | ||||
−0.834852 | + | 0.550475i | \(0.814447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1017.53 | + | 1762.41i | −0.601332 | + | 1.04154i | ||||
\(143\) | 14.2137 | + | 24.6189i | 0.00831197 | + | 0.0143968i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 57.7186 | − | 99.9716i | 0.0330570 | − | 0.0572565i | ||||
\(146\) | 2127.00 | 1.20570 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 361.062 | 0.200535 | ||||||||
\(149\) | 704.969 | − | 1221.04i | 0.387606 | − | 0.671353i | −0.604521 | − | 0.796589i | \(-0.706635\pi\) |
0.992127 | + | 0.125236i | \(0.0399687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1176.18 | − | 2037.20i | −0.633879 | − | 1.09791i | −0.986751 | − | 0.162240i | \(-0.948128\pi\) |
0.352872 | − | 0.935672i | \(-0.385205\pi\) | |||||||
\(152\) | −957.688 | + | 1658.76i | −0.511045 | + | 0.885155i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1106.72 | −0.573511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −606.911 | − | 1051.20i | −0.308514 | − | 0.534363i | 0.669523 | − | 0.742791i | \(-0.266498\pi\) |
−0.978038 | + | 0.208429i | \(0.933165\pi\) | |||||||
\(158\) | −2310.54 | − | 4001.97i | −1.16340 | − | 2.01506i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2654.88 | 1.31179 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 361.387 | − | 625.941i | 0.173657 | − | 0.300782i | −0.766039 | − | 0.642794i | \(-0.777775\pi\) |
0.939696 | + | 0.342012i | \(0.111108\pi\) | |||||||
\(164\) | −441.905 | − | 765.401i | −0.210408 | − | 0.364438i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 236.192 | − | 409.096i | 0.110434 | − | 0.191277i | ||||
\(167\) | −753.016 | −0.348923 | −0.174462 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174462 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −975.051 | −0.443810 | ||||||||
\(170\) | −3595.26 | + | 6227.17i | −1.62202 | + | 2.80942i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2613.86 | − | 4527.34i | −1.15875 | − | 2.00702i | ||||
\(173\) | −929.569 | + | 1610.06i | −0.408519 | + | 0.707576i | −0.994724 | − | 0.102587i | \(-0.967288\pi\) |
0.586205 | + | 0.810163i | \(0.300621\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.87137 | 0.00251461 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3563.55 | + | 6172.25i | 1.50056 | + | 2.59904i | ||||
\(179\) | −261.413 | − | 452.780i | −0.109156 | − | 0.189063i | 0.806273 | − | 0.591544i | \(-0.201481\pi\) |
−0.915429 | + | 0.402481i | \(0.868148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2901.38 | 1.19148 | 0.595740 | − | 0.803177i | \(-0.296859\pi\) | ||||
0.595740 | + | 0.803177i | \(0.296859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1234.42 | + | 2138.09i | −0.494581 | + | 0.856640i | ||||
\(185\) | −194.187 | − | 336.343i | −0.0771727 | − | 0.133667i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −47.8714 | + | 82.9156i | −0.0187203 | + | 0.0324246i | ||||
\(188\) | −4238.79 | −1.64439 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5697.80 | 2.17559 | ||||||||
\(191\) | 1302.18 | − | 2255.43i | 0.493309 | − | 0.854437i | −0.506661 | − | 0.862145i | \(-0.669120\pi\) |
0.999970 | + | 0.00770854i | \(0.00245373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −338.123 | − | 585.646i | −0.126107 | − | 0.218423i | 0.796058 | − | 0.605220i | \(-0.206915\pi\) |
−0.922165 | + | 0.386797i | \(0.873582\pi\) | |||||||
\(194\) | 1246.19 | − | 2158.47i | 0.461192 | − | 0.798808i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3685.99 | 1.33308 | 0.666538 | − | 0.745471i | \(-0.267775\pi\) | ||||
0.666538 | + | 0.745471i | \(0.267775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 399.901 | + | 692.648i | 0.142453 | + | 0.246736i | 0.928420 | − | 0.371533i | \(-0.121168\pi\) |
−0.785967 | + | 0.618269i | \(0.787834\pi\) | |||||||
\(200\) | 581.902 | + | 1007.88i | 0.205733 | + | 0.356341i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −297.772 | −0.103719 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −475.333 | + | 823.300i | −0.161945 | + | 0.280497i | ||||
\(206\) | 4144.51 | + | 7178.50i | 1.40175 | + | 2.42791i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 126.190 | − | 218.567i | 0.0420658 | − | 0.0728601i | ||||
\(209\) | 75.8670 | 0.0251092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −667.385 | −0.217747 | −0.108874 | − | 0.994056i | \(-0.534724\pi\) | ||||
−0.108874 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(212\) | 934.325 | − | 1618.30i | 0.302687 | − | 0.524270i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1951.51 | − | 3380.11i | −0.623375 | − | 1.07972i | ||||
\(215\) | −2811.59 | + | 4869.81i | −0.891855 | + | 1.54474i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7342.77 | 2.28126 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 68.6801 | + | 118.957i | 0.0210473 | + | 0.0364551i | ||||
\(221\) | 2057.74 | + | 3564.11i | 0.626329 | + | 1.08483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2646.82 | 0.794818 | 0.397409 | − | 0.917642i | \(-0.369909\pi\) | ||||
0.397409 | + | 0.917642i | \(0.369909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −861.840 | + | 1492.75i | −0.253667 | + | 0.439364i | ||||
\(227\) | 2060.56 | + | 3568.99i | 0.602485 | + | 1.04353i | 0.992444 | + | 0.122702i | \(0.0391558\pi\) |
−0.389959 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2033.46 | + | 3522.06i | −0.586790 | + | 1.01635i | 0.407860 | + | 0.913045i | \(0.366275\pi\) |
−0.994650 | + | 0.103306i | \(0.967058\pi\) | |||||||
\(230\) | 7344.25 | 2.10550 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 175.833 | 0.0497585 | ||||||||
\(233\) | −1952.33 | + | 3381.54i | −0.548934 | + | 0.950782i | 0.449414 | + | 0.893324i | \(0.351633\pi\) |
−0.998348 | + | 0.0574584i | \(0.981700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2279.72 | + | 3948.59i | 0.632819 | + | 1.09608i | ||||
\(236\) | −590.108 | + | 1022.10i | −0.162766 | + | 0.281919i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5425.12 | −1.46829 | −0.734146 | − | 0.678991i | \(-0.762417\pi\) | ||||
−0.734146 | + | 0.678991i | \(0.762417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 801.446 | + | 1388.15i | 0.214215 | + | 0.371030i | 0.953029 | − | 0.302878i | \(-0.0979475\pi\) |
−0.738815 | + | 0.673909i | \(0.764614\pi\) | |||||||
\(242\) | −3013.97 | − | 5220.35i | −0.800600 | − | 1.38668i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1510.31 | −0.396261 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1630.56 | − | 2824.22i | 0.420042 | − | 0.727534i | ||||
\(248\) | −842.874 | − | 1459.90i | −0.215817 | − | 0.373806i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2086.19 | + | 3613.38i | −0.527768 | + | 0.914121i | ||||
\(251\) | −3805.93 | −0.957085 | −0.478542 | − | 0.878064i | \(-0.658835\pi\) | ||||
−0.478542 | + | 0.878064i | \(0.658835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 97.7897 | 0.0243003 | ||||||||
\(254\) | 2171.22 | − | 3760.67i | 0.536357 | − | 0.928997i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1660.05 | + | 2875.28i | 0.405285 | + | 0.701974i | ||||
\(257\) | 2294.67 | − | 3974.49i | 0.556956 | − | 0.964676i | −0.440792 | − | 0.897609i | \(-0.645303\pi\) |
0.997748 | − | 0.0670671i | \(-0.0213641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5904.41 | 1.40837 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2610.29 | − | 4521.15i | −0.615512 | − | 1.06610i | ||||
\(263\) | 438.587 | + | 759.656i | 0.102831 | + | 0.178108i | 0.912850 | − | 0.408295i | \(-0.133877\pi\) |
−0.810019 | + | 0.586403i | \(0.800543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2010.00 | −0.465938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4964.62 | − | 8598.97i | 1.13158 | − | 1.95995i | ||||
\(269\) | −3061.78 | − | 5303.15i | −0.693977 | − | 1.20200i | −0.970524 | − | 0.241003i | \(-0.922524\pi\) |
0.276547 | − | 0.961000i | \(-0.410810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1744.88 | − | 3022.22i | 0.391122 | − | 0.677443i | −0.601476 | − | 0.798891i | \(-0.705421\pi\) |
0.992598 | + | 0.121448i | \(0.0387538\pi\) | |||||||
\(272\) | 850.006 | 0.189482 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1619.32 | 0.357032 | ||||||||
\(275\) | 23.0488 | − | 39.9217i | 0.00505417 | − | 0.00875407i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2445.85 | + | 4236.33i | 0.530530 | + | 0.918905i | 0.999365 | + | 0.0356193i | \(0.0113404\pi\) |
−0.468836 | + | 0.883285i | \(0.655326\pi\) | |||||||
\(278\) | −6199.23 | + | 10737.4i | −1.33743 | + | 2.31649i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6914.46 | −1.46791 | −0.733954 | − | 0.679199i | \(-0.762327\pi\) | ||||
−0.733954 | + | 0.679199i | \(0.762327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1779.92 | − | 3082.92i | −0.373871 | − | 0.647564i | 0.616286 | − | 0.787522i | \(-0.288636\pi\) |
−0.990157 | + | 0.139959i | \(0.955303\pi\) | |||||||
\(284\) | 2814.04 | + | 4874.07i | 0.587967 | + | 1.01839i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 128.809 | 0.0266315 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4473.90 | + | 7749.02i | −0.910625 | + | 1.57725i | ||||
\(290\) | −261.531 | − | 452.984i | −0.0529572 | − | 0.0917246i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2941.18 | − | 5094.27i | 0.589451 | − | 1.02096i | ||||
\(293\) | −3285.11 | −0.655011 | −0.327505 | − | 0.944849i | \(-0.606208\pi\) | ||||
−0.327505 | + | 0.944849i | \(0.606208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1269.49 | 0.250552 | ||||||||
\(296\) | 295.784 | − | 512.313i | 0.0580814 | − | 0.100600i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3194.31 | − | 5532.70i | −0.620943 | − | 1.07551i | ||||
\(299\) | 2101.74 | − | 3640.31i | 0.406510 | − | 0.704096i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10658.8 | −2.03094 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −336.774 | − | 583.310i | −0.0635373 | − | 0.110050i | ||||
\(305\) | 812.278 | + | 1406.91i | 0.152495 | + | 0.264129i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9094.65 | −1.69075 | −0.845373 | − | 0.534176i | \(-0.820622\pi\) | ||||
−0.845373 | + | 0.534176i | \(0.820622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2507.35 | + | 4342.86i | −0.459381 | + | 0.795671i | ||||
\(311\) | −4081.53 | − | 7069.42i | −0.744188 | − | 1.28897i | −0.950573 | − | 0.310500i | \(-0.899503\pi\) |
0.206386 | − | 0.978471i | \(-0.433830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1489.81 | + | 2580.42i | −0.269038 | + | 0.465988i | −0.968614 | − | 0.248571i | \(-0.920039\pi\) |
0.699576 | + | 0.714559i | \(0.253372\pi\) | |||||||
\(314\) | −5499.98 | −0.988478 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12779.9 | −2.27508 | ||||||||
\(317\) | −1944.05 | + | 3367.20i | −0.344445 | + | 0.596596i | −0.985253 | − | 0.171105i | \(-0.945266\pi\) |
0.640808 | + | 0.767701i | \(0.278599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.48232 | − | 6.03155i | −0.000611198 | − | 0.00105863i | ||||
\(320\) | 5625.52 | − | 9743.69i | 0.982739 | − | 1.70215i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10983.4 | 1.89205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −990.749 | − | 1716.03i | −0.169098 | − | 0.292886i | ||||
\(326\) | −1637.49 | − | 2836.22i | −0.278197 | − | 0.481852i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1448.04 | −0.243764 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2446.52 | − | 4237.49i | 0.406262 | − | 0.703666i | −0.588206 | − | 0.808711i | \(-0.700165\pi\) |
0.994467 | + | 0.105045i | \(0.0334988\pi\) | |||||||
\(332\) | −653.203 | − | 1131.38i | −0.107979 | − | 0.187026i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1706.01 | + | 2954.89i | −0.279487 | + | 0.484085i | ||||
\(335\) | −10680.3 | −1.74188 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1722.10 | −0.278364 | −0.139182 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139182 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(338\) | −2209.04 | + | 3826.17i | −0.355491 | + | 0.615728i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9942.91 | + | 17221.6i | 1.58597 | + | 2.74698i | ||||
\(341\) | −33.3858 | + | 57.8259i | −0.00530188 | + | 0.00918313i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8565.16 | −1.34245 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4212.00 | + | 7295.39i | 0.654446 | + | 1.13353i | ||||
\(347\) | −119.029 | − | 206.165i | −0.0184145 | − | 0.0318948i | 0.856671 | − | 0.515863i | \(-0.172529\pi\) |
−0.875086 | + | 0.483968i | \(0.839195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10053.1 | −1.54192 | −0.770959 | − | 0.636884i | \(-0.780223\pi\) | ||||
−0.770959 | + | 0.636884i | \(0.780223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 80.0878 | − | 138.716i | 0.0121270 | − | 0.0210045i | ||||
\(353\) | −1735.08 | − | 3005.25i | −0.261612 | − | 0.453125i | 0.705058 | − | 0.709149i | \(-0.250921\pi\) |
−0.966670 | + | 0.256024i | \(0.917587\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3026.91 | − | 5242.77i | 0.452540 | − | 0.783823i | ||||
\(356\) | 19710.5 | 2.93442 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2368.99 | −0.349734 | ||||||||
\(359\) | 703.770 | − | 1218.97i | 0.103464 | − | 0.179205i | −0.809646 | − | 0.586919i | \(-0.800341\pi\) |
0.913110 | + | 0.407714i | \(0.133674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −922.136 | − | 1597.19i | −0.134442 | − | 0.232860i | ||||
\(362\) | 6573.26 | − | 11385.2i | 0.954373 | − | 1.65302i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6327.34 | −0.907364 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5566.51 | − | 9641.48i | −0.791742 | − | 1.37134i | −0.924887 | − | 0.380242i | \(-0.875841\pi\) |
0.133145 | − | 0.991097i | \(-0.457492\pi\) | |||||||
\(368\) | −434.089 | − | 751.865i | −0.0614904 | − | 0.106505i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1759.78 | −0.247261 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4512.97 | + | 7816.69i | −0.626468 | + | 1.08507i | 0.361787 | + | 0.932261i | \(0.382167\pi\) |
−0.988255 | + | 0.152814i | \(0.951166\pi\) | |||||||
\(374\) | 216.911 | + | 375.701i | 0.0299899 | + | 0.0519440i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3472.44 | + | 6014.45i | −0.476270 | + | 0.824924i | ||||
\(377\) | −299.373 | −0.0408979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5855.75 | −0.793640 | −0.396820 | − | 0.917896i | \(-0.629886\pi\) | ||||
−0.396820 | + | 0.917896i | \(0.629886\pi\) | |||||||
\(380\) | 7878.81 | − | 13646.5i | 1.06362 | − | 1.84224i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5900.32 | − | 10219.7i | −0.790280 | − | 1.36880i | ||||
\(383\) | −3894.01 | + | 6744.63i | −0.519517 | + | 0.899829i | 0.480226 | + | 0.877145i | \(0.340555\pi\) |
−0.999743 | + | 0.0226844i | \(0.992779\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3064.16 | −0.404045 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3446.42 | − | 5969.38i | −0.450942 | − | 0.781054i | ||||
\(389\) | −1907.03 | − | 3303.07i | −0.248560 | − | 0.430519i | 0.714566 | − | 0.699568i | \(-0.246624\pi\) |
−0.963127 | + | 0.269048i | \(0.913291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14157.1 | 1.83109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8350.85 | − | 14464.1i | 1.06779 | − | 1.84947i | ||||
\(395\) | 6873.32 | + | 11904.9i | 0.875530 | + | 1.51646i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5082.64 | − | 8803.39i | 0.642545 | − | 1.11292i | −0.342318 | − | 0.939584i | \(-0.611212\pi\) |
0.984863 | − | 0.173336i | \(-0.0554547\pi\) | |||||||
\(398\) | 3624.00 | 0.456419 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −409.255 | −0.0511569 | ||||||||
\(401\) | 5751.27 | − | 9961.50i | 0.716222 | − | 1.24053i | −0.246265 | − | 0.969203i | \(-0.579203\pi\) |
0.962486 | − | 0.271330i | \(-0.0874634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1435.08 | + | 2485.63i | 0.177386 | + | 0.307241i | ||||
\(404\) | −411.754 | + | 713.178i | −0.0507067 | + | 0.0878266i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.4317 | −0.00285372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1633.14 | − | 2828.67i | −0.197441 | − | 0.341978i | 0.750257 | − | 0.661146i | \(-0.229930\pi\) |
−0.947698 | + | 0.319168i | \(0.896596\pi\) | |||||||
\(410\) | 2153.79 | + | 3730.48i | 0.259435 | + | 0.449354i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22923.8 | 2.74120 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −702.615 | + | 1216.96i | −0.0831084 | + | 0.143948i | ||||
\(416\) | −3442.56 | − | 5962.69i | −0.405734 | − | 0.702752i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 171.882 | − | 297.708i | 0.0201124 | − | 0.0348358i | ||||
\(419\) | 6822.93 | 0.795518 | 0.397759 | − | 0.917490i | \(-0.369788\pi\) | ||||
0.397759 | + | 0.917490i | \(0.369788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1431.63 | 0.165733 | 0.0828665 | − | 0.996561i | \(-0.473592\pi\) | ||||
0.0828665 | + | 0.996561i | \(0.473592\pi\) | |||||||
\(422\) | −1512.00 | + | 2618.87i | −0.174415 | + | 0.302096i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1530.81 | − | 2651.44i | −0.175336 | − | 0.303691i | ||||
\(425\) | 3336.81 | − | 5779.52i | 0.380844 | − | 0.659642i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10794.0 | −1.21904 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12739.7 | + | 22065.8i | 1.42875 | + | 2.47466i | ||||
\(431\) | 7571.10 | + | 13113.5i | 0.846141 | + | 1.46556i | 0.884626 | + | 0.466301i | \(0.154414\pi\) |
−0.0384849 | + | 0.999259i | \(0.512253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5475.65 | −0.607721 | −0.303860 | − | 0.952717i | \(-0.598276\pi\) | ||||
−0.303860 | + | 0.952717i | \(0.598276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10153.5 | − | 17586.3i | 1.11528 | − | 1.93172i | ||||
\(437\) | −5609.10 | − | 9715.24i | −0.614003 | − | 1.06348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −890.272 | + | 1542.00i | −0.0967890 | + | 0.167643i | −0.910354 | − | 0.413831i | \(-0.864191\pi\) |
0.813565 | + | 0.581474i | \(0.197524\pi\) | |||||||
\(440\) | 225.052 | 0.0243840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18647.8 | 2.00675 | ||||||||
\(443\) | −1629.82 | + | 2822.93i | −0.174797 | + | 0.302757i | −0.940091 | − | 0.340924i | \(-0.889260\pi\) |
0.765294 | + | 0.643681i | \(0.222594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10600.7 | − | 18361.0i | −1.12926 | − | 1.95594i | ||||
\(446\) | 5996.55 | − | 10386.3i | 0.636648 | − | 1.10271i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6826.19 | 0.717478 | 0.358739 | − | 0.933438i | \(-0.383207\pi\) | ||||
0.358739 | + | 0.933438i | \(0.383207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.6781 | + | 49.6719i | 0.00299423 | + | 0.00518616i | ||||
\(452\) | 2383.48 | + | 4128.30i | 0.248029 | + | 0.429599i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18673.3 | 1.93036 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1850.01 | + | 3204.32i | −0.189365 | + | 0.327991i | −0.945039 | − | 0.326958i | \(-0.893976\pi\) |
0.755673 | + | 0.654949i | \(0.227310\pi\) | |||||||
\(458\) | 9213.88 | + | 15958.9i | 0.940035 | + | 1.62819i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10155.5 | − | 17589.8i | 1.02935 | − | 1.78289i | ||||
\(461\) | 9400.80 | 0.949759 | 0.474880 | − | 0.880051i | \(-0.342492\pi\) | ||||
0.474880 | + | 0.880051i | \(0.342492\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15483.9 | 1.55420 | 0.777102 | − | 0.629374i | \(-0.216689\pi\) | ||||
0.777102 | + | 0.629374i | \(0.216689\pi\) | |||||||
\(464\) | −30.9161 | + | 53.5482i | −0.00309319 | + | 0.00535757i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8846.28 | + | 15322.2i | 0.879391 | + | 1.52315i | ||||
\(467\) | −1102.81 | + | 1910.12i | −0.109276 | + | 0.189272i | −0.915477 | − | 0.402370i | \(-0.868187\pi\) |
0.806201 | + | 0.591642i | \(0.201520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 20659.4 | 2.02755 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 966.839 | + | 1674.61i | 0.0942847 | + | 0.163306i | ||||
\(473\) | 169.631 | + | 293.809i | 0.0164897 | + | 0.0285610i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5288.20 | −0.510820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12291.0 | + | 21288.6i | −1.17610 | + | 2.03706i | ||||
\(479\) | 1174.66 | + | 2034.57i | 0.112049 | + | 0.194075i | 0.916596 | − | 0.399814i | \(-0.130925\pi\) |
−0.804547 | + | 0.593889i | \(0.797592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −503.603 | + | 872.266i | −0.0477387 | + | 0.0826859i | ||||
\(482\) | 7262.91 | 0.686342 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16670.6 | −1.56561 | ||||||||
\(485\) | −3707.13 | + | 6420.93i | −0.347076 | + | 0.601154i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5197.14 | − | 9001.72i | −0.483583 | − | 0.837591i | 0.516239 | − | 0.856445i | \(-0.327332\pi\) |
−0.999822 | + | 0.0188537i | \(0.993998\pi\) | |||||||
\(488\) | −1237.25 | + | 2142.98i | −0.114770 | + | 0.198788i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12586.7 | −1.15689 | −0.578444 | − | 0.815722i | \(-0.696340\pi\) | ||||
−0.578444 | + | 0.815722i | \(0.696340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −504.140 | − | 873.195i | −0.0460554 | − | 0.0797703i | ||||
\(494\) | −7388.30 | − | 12796.9i | −0.672905 | − | 1.16551i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 592.799 | 0.0536642 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5313.97 | + | 9204.06i | −0.476725 | + | 0.825712i | −0.999644 | − | 0.0266703i | \(-0.991510\pi\) |
0.522919 | + | 0.852382i | \(0.324843\pi\) | |||||||
\(500\) | 5769.48 | + | 9993.03i | 0.516038 | + | 0.893804i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8622.59 | + | 14934.8i | −0.766623 | + | 1.32783i | ||||
\(503\) | 6719.02 | 0.595599 | 0.297800 | − | 0.954628i | \(-0.403747\pi\) | ||||
0.297800 | + | 0.954628i | \(0.403747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 885.802 | 0.0780548 | ||||||||
\(506\) | 221.549 | − | 383.734i | 0.0194645 | − | 0.0337136i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6004.65 | − | 10400.4i | −0.524436 | − | 0.908350i | ||||
\(509\) | 1952.17 | − | 3381.25i | 0.169997 | − | 0.294443i | −0.768422 | − | 0.639944i | \(-0.778958\pi\) |
0.938418 | + | 0.345501i | \(0.112291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2607.89 | −0.225105 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10397.5 | − | 18008.9i | −0.892241 | − | 1.54541i | ||||
\(515\) | −12328.9 | − | 21354.4i | −1.05491 | − | 1.82716i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 275.083 | 0.0234007 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4836.92 | − | 8377.79i | 0.407909 | − | 0.706520i | ||||
\(521\) | −7849.85 | − | 13596.3i | −0.660092 | − | 1.14331i | −0.980591 | − | 0.196064i | \(-0.937184\pi\) |
0.320499 | − | 0.947249i | \(-0.396150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5076.03 | + | 8791.95i | −0.424397 | + | 0.735077i | −0.996364 | − | 0.0851998i | \(-0.972847\pi\) |
0.571967 | + | 0.820277i | \(0.306180\pi\) | |||||||
\(524\) | −14437.8 | −1.20366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3974.59 | 0.329469 | ||||||||
\(527\) | −4833.30 | + | 8371.53i | −0.399510 | + | 0.691972i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1146.41 | − | 1985.65i | −0.0942233 | − | 0.163200i | ||||
\(530\) | −4553.80 | + | 7887.41i | −0.373216 | + | 0.646428i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2465.44 | 0.200357 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5805.28 | + | 10055.0i | 0.469129 | + | 0.812555i | ||||
\(536\) | −8134.08 | − | 14088.6i | −0.655483 | − | 1.13533i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27746.6 | −2.22350 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9923.32 | − | 17187.7i | 0.788608 | − | 1.36591i | −0.138212 | − | 0.990403i | \(-0.544136\pi\) |
0.926820 | − | 0.375506i | \(-0.122531\pi\) | |||||||
\(542\) | −7906.28 | − | 13694.1i | −0.626575 | − | 1.08526i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11594.4 | − | 20082.1i | 0.913799 | − | 1.58275i | ||||
\(545\) | −21843.0 | −1.71679 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22798.9 | −1.78210 | −0.891052 | − | 0.453901i | \(-0.850032\pi\) | ||||
−0.891052 | + | 0.453901i | \(0.850032\pi\) | |||||||
\(548\) | 2239.17 | − | 3878.36i | 0.174549 | − | 0.302327i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −104.437 | − | 180.890i | −0.00809675 | − | 0.0140240i | ||||
\(551\) | −399.483 | + | 691.924i | −0.0308866 | + | 0.0534972i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22164.9 | 1.69981 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17144.4 | + | 29694.9i | 1.30770 | + | 2.26501i | ||||
\(557\) | −8999.13 | − | 15586.9i | −0.684570 | − | 1.18571i | −0.973572 | − | 0.228381i | \(-0.926657\pi\) |
0.289002 | − | 0.957328i | \(-0.406677\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14583.1 | 1.10340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15665.2 | + | 27132.8i | −1.17579 | + | 2.03653i | ||||
\(563\) | 97.8182 | + | 169.426i | 0.00732246 | + | 0.0126829i | 0.869663 | − | 0.493645i | \(-0.164336\pi\) |
−0.862341 | + | 0.506328i | \(0.831002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2563.77 | − | 4440.59i | 0.190901 | − | 0.330649i | ||||
\(566\) | −16130.1 | −1.19788 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9221.11 | 0.681178 | ||||||||
\(569\) | −9830.21 | + | 17026.4i | −0.724260 | + | 1.25445i | 0.235018 | + | 0.971991i | \(0.424485\pi\) |
−0.959278 | + | 0.282464i | \(0.908848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7882.25 | + | 13652.5i | 0.577691 | + | 1.00059i | 0.995743 | + | 0.0921678i | \(0.0293796\pi\) |
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(572\) | 178.114 | − | 308.503i | 0.0130198 | − | 0.0225510i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6816.30 | −0.494364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11153.2 | − | 19317.9i | −0.804704 | − | 1.39379i | −0.916490 | − | 0.400057i | \(-0.868990\pi\) |
0.111786 | − | 0.993732i | \(-0.464343\pi\) | |||||||
\(578\) | 20271.8 | + | 35111.8i | 1.45882 | + | 2.52675i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1446.56 | −0.103560 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −60.6344 | + | 105.022i | −0.00430741 | + | 0.00746066i | ||||
\(584\) | −4818.86 | − | 8346.51i | −0.341448 | − | 0.591406i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7442.63 | + | 12891.0i | −0.524662 | + | 0.908742i | ||||
\(587\) | 15953.2 | 1.12173 | 0.560866 | − | 0.827906i | \(-0.310468\pi\) | ||||
0.560866 | + | 0.827906i | \(0.310468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7659.87 | 0.535856 | ||||||||
\(590\) | 2876.12 | − | 4981.59i | 0.200692 | − | 0.347608i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 104.013 | + | 180.157i | 0.00722116 | + | 0.0125074i | ||||
\(593\) | −1577.84 | + | 2732.90i | −0.109265 | + | 0.189253i | −0.915473 | − | 0.402380i | \(-0.868183\pi\) |
0.806208 | + | 0.591633i | \(0.201516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17668.1 | −1.21429 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9523.24 | − | 16494.7i | −0.651228 | − | 1.12796i | ||||
\(599\) | 12728.2 | + | 22045.8i | 0.868212 | + | 1.50379i | 0.863823 | + | 0.503796i | \(0.168064\pi\) |
0.00438889 | + | 0.999990i | \(0.498603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5580.96 | 0.378789 | 0.189395 | − | 0.981901i | \(-0.439347\pi\) | ||||
0.189395 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14738.8 | + | 25528.4i | −0.992903 | + | 1.71976i | ||||
\(605\) | 8965.85 | + | 15529.3i | 0.602502 | + | 1.04356i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −190.566 | + | 330.071i | −0.0127427 | + | 0.0220711i | −0.872326 | − | 0.488924i | \(-0.837390\pi\) |
0.859584 | + | 0.510995i | \(0.170723\pi\) | |||||||
\(608\) | −18374.9 | −1.22566 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7361.07 | 0.488592 | ||||||||
\(611\) | 5912.20 | − | 10240.2i | 0.391460 | − | 0.678028i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4117.99 | + | 7132.57i | 0.271328 | + | 0.469954i | 0.969202 | − | 0.246266i | \(-0.0792038\pi\) |
−0.697874 | + | 0.716220i | \(0.745871\pi\) | |||||||
\(614\) | −20604.5 | + | 35688.1i | −1.35428 | + | 2.34569i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27419.8 | 1.78911 | 0.894555 | − | 0.446958i | \(-0.147493\pi\) | ||||
0.894555 | + | 0.446958i | \(0.147493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8186.69 | + | 14179.8i | 0.531585 | + | 0.920732i | 0.999320 | + | 0.0368632i | \(0.0117366\pi\) |
−0.467736 | + | 0.883868i | \(0.654930\pi\) | |||||||
\(620\) | 6934.25 | + | 12010.5i | 0.449171 | + | 0.777987i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −36987.9 | −2.38437 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9748.72 | − | 16885.3i | 0.623918 | − | 1.08066i | ||||
\(626\) | 6750.51 | + | 11692.2i | 0.430998 | + | 0.746510i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7605.28 | + | 13172.7i | −0.483254 | + | 0.837021i | ||||
\(629\) | −3392.24 | −0.215035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4059.60 | 0.256118 | 0.128059 | − | 0.991767i | \(-0.459125\pi\) | ||||
0.128059 | + | 0.991767i | \(0.459125\pi\) | |||||||
\(632\) | −10469.4 | + | 18133.5i | −0.658938 | + | 1.14131i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8808.76 | + | 15257.2i | 0.551799 | + | 0.955744i | ||||
\(635\) | −6458.88 | + | 11187.1i | −0.403642 | + | 0.699129i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −31.5577 | −0.00195827 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14870.5 | − | 25756.4i | −0.918449 | − | 1.59080i | ||||
\(641\) | −3194.32 | − | 5532.72i | −0.196830 | − | 0.340919i | 0.750669 | − | 0.660678i | \(-0.229731\pi\) |
−0.947499 | + | 0.319759i | \(0.896398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18308.0 | −1.12286 | −0.561428 | − | 0.827525i | \(-0.689748\pi\) | ||||
−0.561428 | + | 0.827525i | \(0.689748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24883.5 | − | 43099.5i | 1.51553 | − | 2.62497i | ||||
\(647\) | 1651.95 | + | 2861.26i | 0.100379 | + | 0.173861i | 0.911841 | − | 0.410544i | \(-0.134661\pi\) |
−0.811462 | + | 0.584405i | \(0.801328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.2960 | − | 66.3306i | 0.00231625 | − | 0.00401187i | ||||
\(650\) | −8978.42 | −0.541789 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9057.18 | −0.544028 | ||||||||
\(653\) | 2185.63 | − | 3785.63i | 0.130981 | − | 0.226865i | −0.793074 | − | 0.609125i | \(-0.791521\pi\) |
0.924055 | + | 0.382260i | \(0.124854\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7765.00 | + | 13449.4i | 0.463211 | + | 0.802306i | ||||
\(656\) | 254.604 | − | 440.988i | 0.0151534 | − | 0.0262465i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6259.75 | −0.370023 | −0.185012 | − | 0.982736i | \(-0.559232\pi\) | ||||
−0.185012 | + | 0.982736i | \(0.559232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7422.87 | + | 12856.8i | 0.436787 | + | 0.756537i | 0.997440 | − | 0.0715138i | \(-0.0227830\pi\) |
−0.560653 | + | 0.828051i | \(0.689450\pi\) | |||||||
\(662\) | −11085.5 | − | 19200.6i | −0.650830 | − | 1.12727i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2140.43 | −0.125098 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −514.918 | + | 891.864i | −0.0298916 | + | 0.0517738i | ||||
\(668\) | 4718.07 | + | 8171.94i | 0.273275 | + | 0.473326i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24197.0 | + | 41910.4i | −1.39524 | + | 2.41663i | ||||
\(671\) | 98.0138 | 0.00563902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9409.13 | 0.538923 | 0.269462 | − | 0.963011i | \(-0.413154\pi\) | ||||
0.269462 | + | 0.963011i | \(0.413154\pi\) | |||||||
\(674\) | −3901.52 | + | 6757.64i | −0.222969 | + | 0.386194i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6109.24 | + | 10581.5i | 0.347590 | + | 0.602044i | ||||
\(677\) | 1475.32 | − | 2555.32i | 0.0837533 | − | 0.145065i | −0.821106 | − | 0.570776i | \(-0.806643\pi\) |
0.904859 | + | 0.425711i | \(0.139976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 32581.1 | 1.83740 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 151.275 | + | 262.016i | 0.00849359 | + | 0.0147113i | ||||
\(683\) | 3140.42 | + | 5439.38i | 0.175937 | + | 0.304732i | 0.940485 | − | 0.339835i | \(-0.110371\pi\) |
−0.764548 | + | 0.644567i | \(0.777038\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4817.11 | −0.268689 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1505.98 | − | 2608.44i | 0.0834521 | − | 0.144543i | ||||
\(689\) | 2606.36 | + | 4514.35i | 0.144114 | + | 0.249612i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16381.6 | + | 28373.8i | −0.901861 | + | 1.56207i | −0.0767837 | + | 0.997048i | \(0.524465\pi\) |
−0.825077 | + | 0.565021i | \(0.808868\pi\) | |||||||
\(692\) | 23297.1 | 1.27980 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1078.67 | −0.0589998 | ||||||||
\(695\) | 18441.3 | − | 31941.2i | 1.00650 | − | 1.74331i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4151.76 | + | 7191.06i | 0.225623 | + | 0.390791i | ||||
\(698\) | −22775.9 | + | 39449.1i | −1.23507 | + | 2.13921i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1775.97 | 0.0956883 | 0.0478442 | − | 0.998855i | \(-0.484765\pi\) | ||||
0.0478442 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1344.01 | + | 2327.90i | 0.0721058 | + | 0.124891i | ||||
\(704\) | −339.403 | − | 587.863i | −0.0181701 | − | 0.0314715i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15723.7 | −0.838203 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4431.22 | + | 7675.09i | −0.234722 | + | 0.406550i | −0.959192 | − | 0.282756i | \(-0.908751\pi\) |
0.724470 | + | 0.689306i | \(0.242085\pi\) | |||||||
\(710\) | −13715.3 | − | 23755.6i | −0.724968 | − | 1.25568i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16146.9 | − | 27967.3i | 0.849903 | − | 1.47207i | ||||
\(713\) | 9873.28 | 0.518594 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −383.175 | −0.0200419 | ||||||||
\(716\) | −3275.79 | + | 5673.84i | −0.170981 | + | 0.296147i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3188.87 | − | 5523.29i | −0.165749 | − | 0.287085i | ||||
\(719\) | 13749.6 | − | 23815.0i | 0.713177 | − | 1.23526i | −0.250481 | − | 0.968121i | \(-0.580589\pi\) |
0.963658 | − | 0.267138i | \(-0.0860778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8356.64 | −0.430750 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18178.8 | − | 31486.6i | −0.933162 | − | 1.61628i | ||||
\(725\) | 242.730 | + | 420.421i | 0.0124342 | + | 0.0215366i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25434.9 | 1.29756 | 0.648781 | − | 0.760975i | \(-0.275279\pi\) | ||||
0.648781 | + | 0.760975i | \(0.275279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14335.0 | + | 24828.9i | −0.726797 | + | 1.25885i | ||||
\(731\) | 24557.6 | + | 42535.1i | 1.24254 | + | 2.15214i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12077.8 | − | 20919.4i | 0.608600 | − | 1.05413i | −0.382871 | − | 0.923802i | \(-0.625065\pi\) |
0.991471 | − | 0.130325i | \(-0.0416020\pi\) | |||||||
\(734\) | −50445.2 | −2.53674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23684.6 | −1.18618 | ||||||||
\(737\) | −322.187 | + | 558.043i | −0.0161030 | + | 0.0278912i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13756.4 | − | 23826.9i | −0.684762 | − | 1.18604i | −0.973512 | − | 0.228638i | \(-0.926573\pi\) |
0.288750 | − | 0.957405i | \(-0.406760\pi\) | |||||||
\(740\) | −2433.39 | + | 4214.75i | −0.120883 | + | 0.209375i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5995.09 | −0.296014 | −0.148007 | − | 0.988986i | \(-0.547286\pi\) | ||||
−0.148007 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9502.31 | + | 16458.5i | 0.467299 | + | 0.809386i | ||||
\(746\) | 20448.8 | + | 35418.4i | 1.00360 | + | 1.73829i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1199.76 | 0.0586467 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −772.544 | + | 1338.09i | −0.0375373 | + | 0.0650166i | −0.884184 | − | 0.467139i | \(-0.845285\pi\) |
0.846646 | + | 0.532156i | \(0.178618\pi\) | |||||||
\(752\) | −1221.10 | − | 2115.00i | −0.0592138 | − | 0.102561i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −678.250 | + | 1174.76i | −0.0327591 | + | 0.0567405i | ||||
\(755\) | 31707.5 | 1.52841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5157.82 | −0.247641 | −0.123820 | − | 0.992305i | \(-0.539515\pi\) | ||||
−0.123820 | + | 0.992305i | \(0.539515\pi\) | |||||||
\(758\) | −13266.6 | + | 22978.4i | −0.635704 | + | 1.10107i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12908.7 | − | 22358.6i | −0.616117 | − | 1.06715i | ||||
\(761\) | −1644.98 | + | 2849.19i | −0.0783581 | + | 0.135720i | −0.902542 | − | 0.430602i | \(-0.858301\pi\) |
0.824184 | + | 0.566323i | \(0.191634\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32635.4 | −1.54543 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17644.3 | + | 30560.8i | 0.832264 | + | 1.44152i | ||||
\(767\) | −1646.14 | − | 2851.21i | −0.0774952 | − | 0.134226i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11146.5 | −0.522697 | −0.261348 | − | 0.965245i | \(-0.584167\pi\) | ||||
−0.261348 | + | 0.965245i | \(0.584167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4237.06 | + | 7338.80i | −0.197533 | + | 0.342136i | ||||
\(773\) | −7915.11 | − | 13709.4i | −0.368288 | − | 0.637894i | 0.621010 | − | 0.783803i | \(-0.286723\pi\) |
−0.989298 | + | 0.145909i | \(0.953389\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2327.11 | − | 4030.67i | 0.107861 | − | 0.186821i | ||||
\(776\) | −11293.3 | −0.522430 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17282.0 | −0.796386 | ||||||||
\(779\) | 3289.88 | − | 5698.23i | 0.151312 | − | 0.262080i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −182.622 | − | 316.310i | −0.00836711 | − | 0.0144923i | ||||
\(782\) | 32073.9 | − | 55553.7i | 1.46670 | − | 2.54040i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16361.2 | 0.743892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7581.72 | + | 13131.9i | 0.343404 | + | 0.594794i | 0.985063 | − | 0.172197i | \(-0.0550865\pi\) |
−0.641658 | + | 0.766991i | \(0.721753\pi\) | |||||||
\(788\) | −23094.8 | − | 40001.4i | −1.04406 | − | 1.80836i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 62287.8 | 2.80519 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2106.55 | − | 3648.65i | 0.0943327 | − | 0.163389i | ||||
\(794\) | −23030.1 | − | 39889.3i | −1.02935 | − | 1.78289i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5011.21 | − | 8679.66i | 0.223138 | − | 0.386486i | ||||
\(797\) | −29398.3 | −1.30658 | −0.653289 | − | 0.757109i | \(-0.726611\pi\) | ||||
−0.653289 | + | 0.757109i | \(0.726611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39824.1 | 1.76330 | ||||||||
\(800\) | −5582.41 | + | 9669.02i | −0.246710 | + | 0.427314i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26059.8 | − | 45136.8i | −1.14738 | − | 1.98733i | ||||
\(803\) | −190.872 | + | 330.601i | −0.00838822 | + | 0.0145288i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13005.1 | 0.568343 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 674.621 | + | 1168.48i | 0.0293726 | + | 0.0508749i | ||||
\(809\) | −10356.4 | − | 17937.9i | −0.450078 | − | 0.779557i | 0.548313 | − | 0.836273i | \(-0.315270\pi\) |
−0.998390 | + | 0.0567160i | \(0.981937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27369.9 | 1.18506 | 0.592532 | − | 0.805547i | \(-0.298128\pi\) | ||||
0.592532 | + | 0.805547i | \(0.298128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −53.0860 | + | 91.9476i | −0.00228583 | + | 0.00395917i | ||||
\(815\) | 4871.16 | + | 8437.09i | 0.209361 | + | 0.362624i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19459.6 | − | 33705.0i | 0.833299 | − | 1.44332i | ||||
\(818\) | −14799.9 | −0.632600 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11912.9 | 0.507338 | ||||||||
\(821\) | −17681.3 | + | 30625.0i | −0.751623 | + | 1.30185i | 0.195412 | + | 0.980721i | \(0.437396\pi\) |
−0.947036 | + | 0.321129i | \(0.895938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14595.2 | + | 25279.6i | 0.618174 | + | 1.07071i | 0.989819 | + | 0.142333i | \(0.0454605\pi\) |
−0.371645 | + | 0.928375i | \(0.621206\pi\) | |||||||
\(824\) | 18779.3 | − | 32526.7i | 0.793941 | − | 1.37515i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7302.08 | 0.307035 | 0.153518 | − | 0.988146i | \(-0.450940\pi\) | ||||
0.153518 | + | 0.988146i | \(0.450940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2125.38 | − | 3681.27i | −0.0890442 | − | 0.154229i | 0.818063 | − | 0.575128i | \(-0.195048\pi\) |
−0.907107 | + | 0.420899i | \(0.861715\pi\) | |||||||
\(830\) | 3183.64 | + | 5514.22i | 0.133139 | + | 0.230604i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29178.3 | −1.21584 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5074.97 | − | 8790.11i | 0.210331 | − | 0.364305i | ||||
\(836\) | −475.350 | − | 823.330i | −0.0196654 | − | 0.0340615i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15457.8 | − | 26773.7i | 0.637208 | − | 1.10368i | ||||
\(839\) | 39527.7 | 1.62652 | 0.813258 | − | 0.581903i | \(-0.197692\pi\) | ||||
0.813258 | + | 0.581903i | \(0.197692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24315.7 | −0.996993 | ||||||||
\(842\) | 3243.46 | − | 5617.84i | 0.132752 | − | 0.229933i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4181.54 | + | 7242.65i | 0.170539 | + | 0.295382i | ||||
\(845\) | 6571.38 | − | 11382.0i | 0.267529 | − | 0.463374i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1076.63 | 0.0435985 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15119.5 | − | 26187.7i | −0.610111 | − | 1.05674i | ||||
\(851\) | 1732.38 | + | 3000.57i | 0.0697829 | + | 0.120868i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31656.1 | 1.27067 | 0.635337 | − | 0.772235i | \(-0.280861\pi\) | ||||
0.635337 | + | 0.772235i | \(0.280861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8842.53 | + | 15315.7i | −0.353074 | + | 0.611542i | ||||
\(857\) | 596.579 | + | 1033.31i | 0.0237792 | + | 0.0411867i | 0.877670 | − | 0.479265i | \(-0.159097\pi\) |
−0.853891 | + | 0.520452i | \(0.825763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14530.0 | + | 25166.7i | −0.577134 | + | 0.999625i | 0.418673 | + | 0.908137i | \(0.362495\pi\) |
−0.995806 | + | 0.0914874i | \(0.970838\pi\) | |||||||
\(860\) | 70464.8 | 2.79399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 68611.2 | 2.71103 | ||||||||
\(863\) | 11531.5 | − | 19973.1i | 0.454851 | − | 0.787825i | −0.543828 | − | 0.839196i | \(-0.683026\pi\) |
0.998680 | + | 0.0513711i | \(0.0163591\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12529.7 | − | 21702.1i | −0.492512 | − | 0.853056i | ||||
\(866\) | −12405.4 | + | 21486.9i | −0.486783 | + | 0.843133i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 829.371 | 0.0323757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13849.1 | + | 23987.4i | 0.538760 | + | 0.933159i | ||||
\(872\) | −16635.5 | − | 28813.6i | −0.646044 | − | 1.11898i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −50831.1 | −1.96726 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16935.5 | + | 29333.2i | −0.652077 | + | 1.12943i | 0.330541 | + | 0.943792i | \(0.392769\pi\) |
−0.982618 | + | 0.185639i | \(0.940565\pi\) | |||||||
\(878\) | 4033.94 | + | 6986.98i | 0.155056 | + | 0.268564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −39.5702 | + | 68.5377i | −0.00151581 | + | 0.00262546i | ||||
\(881\) | 43331.1 | 1.65705 | 0.828525 | − | 0.559953i | \(-0.189181\pi\) | ||||
0.828525 | + | 0.559953i | \(0.189181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40897.3 | −1.55867 | −0.779334 | − | 0.626609i | \(-0.784442\pi\) | ||||
−0.779334 | + | 0.626609i | \(0.784442\pi\) | |||||||
\(884\) | 25785.8 | − | 44662.4i | 0.981076 | − | 1.69927i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7384.91 | + | 12791.0i | 0.280024 | + | 0.485015i | ||||
\(887\) | −22532.9 | + | 39028.1i | −0.852965 | + | 1.47738i | 0.0255550 | + | 0.999673i | \(0.491865\pi\) |
−0.878520 | + | 0.477705i | \(0.841469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −96066.5 | −3.61816 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16583.9 | − | 28724.1i | −0.622498 | − | 1.07820i | ||||
\(893\) | −15778.4 | − | 27329.0i | −0.591271 | − | 1.02411i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7047.19 | 0.263197 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15465.2 | − | 26786.5i | 0.574699 | − | 0.995407i | ||||
\(899\) | −351.590 | − | 608.972i | −0.0130436 | − | 0.0225922i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8778.13 | + | 15204.2i | −0.324575 | + | 0.562180i | ||||
\(902\) | 259.888 | 0.00959349 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7810.22 | 0.287350 | ||||||||
\(905\) | −19553.9 | + | 33868.4i | −0.718226 | + | 1.24400i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12641.2 | − | 21895.3i | −0.462785 | − | 0.801567i | 0.536314 | − | 0.844019i | \(-0.319816\pi\) |
−0.999099 | + | 0.0424520i | \(0.986483\pi\) | |||||||
\(908\) | 25821.1 | − | 44723.5i | 0.943726 | − | 1.63458i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41646.1 | 1.51460 | 0.757298 | − | 0.653070i | \(-0.226519\pi\) | ||||
0.757298 | + | 0.653070i | \(0.226519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.3906 | + | 73.4227i | 0.00153661 | + | 0.00266149i | ||||
\(914\) | 8382.65 | + | 14519.2i | 0.303363 | + | 0.525440i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50963.1 | 1.83829 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13056.2 | − | 22614.1i | 0.468646 | − | 0.811719i | −0.530712 | − | 0.847552i | \(-0.678075\pi\) |
0.999358 | + | 0.0358337i | \(0.0114087\pi\) | |||||||
\(920\) | −16638.9 | − | 28819.4i | −0.596269 | − | 1.03277i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21298.1 | − | 36889.4i | 0.760755 | − | 1.31767i | ||||
\(923\) | −15699.9 | −0.559879 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1633.27 | 0.0580559 | ||||||||
\(926\) | 35079.7 | − | 60759.9i | 1.24491 | − | 2.15626i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 843.415 | + | 1460.84i | 0.0298345 | + | 0.0516749i | ||||
\(929\) | 16178.5 | − | 28022.0i | 0.571366 | − | 0.989636i | −0.425060 | − | 0.905165i | \(-0.639747\pi\) |
0.996426 | − | 0.0844704i | \(-0.0269198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 48929.9 | 1.71969 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4996.97 | + | 8655.01i | 0.175060 | + | 0.303213i | ||||
\(935\) | −645.261 | − | 1117.62i | −0.0225693 | − | 0.0390911i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32947.0 | 1.14870 | 0.574350 | − | 0.818610i | \(-0.305255\pi\) | ||||
0.574350 | + | 0.818610i | \(0.305255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28567.5 | − | 49480.3i | 0.991243 | − | 1.71688i | ||||
\(941\) | −250.801 | − | 434.400i | −0.00868849 | − | 0.0150489i | 0.861648 | − | 0.507506i | \(-0.169432\pi\) |
−0.870337 | + | 0.492457i | \(0.836099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4240.53 | − | 7344.81i | 0.146438 | − | 0.253637i | ||||
\(944\) | −679.984 | −0.0234445 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1537.24 | 0.0528328 | ||||||||
\(947\) | −3218.45 | + | 5574.52i | −0.110439 | + | 0.191286i | −0.915947 | − | 0.401299i | \(-0.868559\pi\) |
0.805508 | + | 0.592584i | \(0.201892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8204.61 | + | 14210.8i | 0.280646 | + | 0.486093i | ||||
\(950\) | −11980.8 | + | 20751.3i | −0.409166 | + | 0.708696i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47511.2 | −1.61494 | −0.807470 | − | 0.589908i | \(-0.799164\pi\) | ||||
−0.807470 | + | 0.589908i | \(0.799164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17552.1 | + | 30401.1i | 0.594735 | + | 1.03011i | ||||
\(956\) | 33991.4 | + | 58874.9i | 1.14996 | + | 1.99179i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10645.1 | 0.359004 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11524.7 | − | 19961.4i | 0.386853 | − | 0.670048i | ||||
\(962\) | 2281.89 | + | 3952.35i | 0.0764773 | + | 0.132462i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10043.0 | − | 17395.0i | 0.335544 | − | 0.581179i | ||||
\(965\) | 9115.15 | 0.304069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7817.32 | 0.259967 | 0.129984 | − | 0.991516i | \(-0.458508\pi\) | ||||
0.129984 | + | 0.991516i | \(0.458508\pi\) | |||||||
\(968\) | −13656.7 | + | 23654.1i | −0.453453 | + | 0.785403i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16797.5 | + | 29094.1i | 0.556015 | + | 0.963046i | ||||
\(971\) | 751.748 | − | 1302.07i | 0.0248453 | − | 0.0430332i | −0.853335 | − | 0.521362i | \(-0.825424\pi\) |
0.878181 | + | 0.478329i | \(0.158757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −47097.9 | −1.54940 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −435.084 | − | 753.587i | −0.0142692 | − | 0.0247149i | ||||
\(977\) | 16694.6 | + | 28915.8i | 0.546680 | + | 0.946877i | 0.998499 | + | 0.0547675i | \(0.0174418\pi\) |
−0.451819 | + | 0.892109i | \(0.649225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1279.14 | −0.0417584 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28516.1 | + | 49391.3i | −0.926665 | + | 1.60503i | ||||
\(983\) | −2725.51 | − | 4720.73i | −0.0884337 | − | 0.153172i | 0.818416 | − | 0.574627i | \(-0.194853\pi\) |
−0.906849 | + | 0.421455i | \(0.861519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24841.8 | + | 43027.3i | −0.803581 | + | 1.39184i | ||||
\(986\) | −4568.64 | −0.147561 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −40865.6 | −1.31590 | ||||||||
\(989\) | 25082.7 | − | 43444.5i | 0.806454 | − | 1.39682i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23265.0 | + | 40296.2i | 0.745750 | + | 1.29168i | 0.949844 | + | 0.312725i | \(0.101242\pi\) |
−0.204094 | + | 0.978951i | \(0.565425\pi\) | |||||||
\(992\) | 8086.02 | − | 14005.4i | 0.258802 | − | 0.448258i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10780.6 | −0.343484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5704.98 | − | 9881.31i | −0.181222 | − | 0.313886i | 0.761075 | − | 0.648664i | \(-0.224672\pi\) |
−0.942297 | + | 0.334778i | \(0.891339\pi\) | |||||||
\(998\) | 24078.3 | + | 41704.8i | 0.763711 | + | 1.32279i | ||||
\(999\) | 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 | 441.4.e.y.226.3 | 8 | ||
3.2 | odd | 2 | 49.4.c.e.30.1 | 8 | |||
7.2 | even | 3 | 441.4.a.u.1.2 | 4 | |||
7.3 | odd | 6 | inner | 441.4.e.y.361.4 | 8 | ||
7.4 | even | 3 | inner | 441.4.e.y.361.3 | 8 | ||
7.5 | odd | 6 | 441.4.a.u.1.1 | 4 | |||
7.6 | odd | 2 | inner | 441.4.e.y.226.4 | 8 | ||
21.2 | odd | 6 | 49.4.a.e.1.4 | yes | 4 | ||
21.5 | even | 6 | 49.4.a.e.1.3 | ✓ | 4 | ||
21.11 | odd | 6 | 49.4.c.e.18.1 | 8 | |||
21.17 | even | 6 | 49.4.c.e.18.2 | 8 | |||
21.20 | even | 2 | 49.4.c.e.30.2 | 8 | |||
84.23 | even | 6 | 784.4.a.bf.1.2 | 4 | |||
84.47 | odd | 6 | 784.4.a.bf.1.3 | 4 | |||
105.44 | odd | 6 | 1225.4.a.bb.1.1 | 4 | |||
105.89 | even | 6 | 1225.4.a.bb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.e.1.3 | ✓ | 4 | 21.5 | even | 6 | ||
49.4.a.e.1.4 | yes | 4 | 21.2 | odd | 6 | ||
49.4.c.e.18.1 | 8 | 21.11 | odd | 6 | |||
49.4.c.e.18.2 | 8 | 21.17 | even | 6 | |||
49.4.c.e.30.1 | 8 | 3.2 | odd | 2 | |||
49.4.c.e.30.2 | 8 | 21.20 | even | 2 | |||
441.4.a.u.1.1 | 4 | 7.5 | odd | 6 | |||
441.4.a.u.1.2 | 4 | 7.2 | even | 3 | |||
441.4.e.y.226.3 | 8 | 1.1 | even | 1 | trivial | ||
441.4.e.y.226.4 | 8 | 7.6 | odd | 2 | inner | ||
441.4.e.y.361.3 | 8 | 7.4 | even | 3 | inner | ||
441.4.e.y.361.4 | 8 | 7.3 | odd | 6 | inner | ||
784.4.a.bf.1.2 | 4 | 84.23 | even | 6 | |||
784.4.a.bf.1.3 | 4 | 84.47 | odd | 6 | |||
1225.4.a.bb.1.1 | 4 | 105.44 | odd | 6 | |||
1225.4.a.bb.1.2 | 4 | 105.89 | even | 6 |