Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
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([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), 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: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.3 | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.d.215.3 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.21193 | + | 1.85441i | −1.13559 | + | 0.655631i | −0.945334 | − | 0.326104i | \(-0.894264\pi\) |
−0.190253 | + | 0.981735i | \(0.560931\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.87764 | − | 4.98422i | 0.359705 | − | 0.623028i | ||||
\(5\) | −2.27338 | − | 3.93760i | −0.203337 | − | 0.352190i | 0.746265 | − | 0.665649i | \(-0.231845\pi\) |
−0.949602 | + | 0.313459i | \(0.898512\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 8.32523i | − | 0.367927i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.6038 | + | 8.43153i | 0.461814 | + | 0.266628i | ||||
\(11\) | −39.4183 | − | 22.7582i | −1.08046 | − | 0.623805i | −0.149440 | − | 0.988771i | \(-0.547747\pi\) |
−0.931021 | + | 0.364966i | \(0.881081\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.6749i | − | 0.249080i | −0.992215 | − | 0.124540i | \(-0.960255\pi\) | ||
0.992215 | − | 0.124540i | \(-0.0397455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 38.4595 | + | 66.6138i | 0.600930 | + | 1.04084i | ||||
\(17\) | 45.7579 | − | 79.2550i | 0.652818 | − | 1.13071i | −0.329618 | − | 0.944115i | \(-0.606920\pi\) |
0.982436 | − | 0.186600i | \(-0.0597469\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −121.317 | + | 70.0425i | −1.46485 | + | 0.845730i | −0.999229 | − | 0.0392566i | \(-0.987501\pi\) |
−0.465617 | + | 0.884986i | \(0.654168\pi\) | |||||||
\(20\) | −26.1679 | −0.292566 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 168.812 | 1.63594 | ||||||||
\(23\) | −38.9875 | + | 22.5094i | −0.353455 | + | 0.204067i | −0.666206 | − | 0.745768i | \(-0.732083\pi\) |
0.312751 | + | 0.949835i | \(0.398749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.1635 | − | 90.3499i | 0.417308 | − | 0.722799i | ||||
\(26\) | 21.6500 | + | 37.4989i | 0.163304 | + | 0.282852i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 47.7861i | − | 0.305988i | −0.988227 | − | 0.152994i | \(-0.951108\pi\) | ||
0.988227 | − | 0.152994i | \(-0.0488916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 206.848 | + | 119.424i | 1.19842 | + | 0.691909i | 0.960203 | − | 0.279303i | \(-0.0901033\pi\) |
0.238218 | + | 0.971212i | \(0.423437\pi\) | |||||||
\(32\) | −189.379 | − | 109.338i | −1.04618 | − | 0.604013i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 339.415i | 1.71203i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 74.4635 | + | 128.975i | 0.330858 | + | 0.573062i | 0.982680 | − | 0.185309i | \(-0.0593287\pi\) |
−0.651823 | + | 0.758371i | \(0.725995\pi\) | |||||||
\(38\) | 259.775 | − | 449.943i | 1.10897 | − | 1.92080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −32.7815 | + | 18.9264i | −0.129580 | + | 0.0748131i | ||||
\(41\) | −393.755 | −1.49986 | −0.749929 | − | 0.661518i | \(-0.769912\pi\) | ||||
−0.749929 | + | 0.661518i | \(0.769912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 412.265 | 1.46209 | 0.731045 | − | 0.682329i | \(-0.239033\pi\) | ||||
0.731045 | + | 0.682329i | \(0.239033\pi\) | |||||||
\(44\) | −226.864 | + | 130.980i | −0.777295 | + | 0.448772i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 83.4833 | − | 144.597i | 0.267586 | − | 0.463472i | ||||
\(47\) | 204.379 | + | 353.994i | 0.634292 | + | 1.09863i | 0.986665 | + | 0.162766i | \(0.0520414\pi\) |
−0.352373 | + | 0.935860i | \(0.614625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 386.929i | 1.09440i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −58.1903 | − | 33.5962i | −0.155184 | − | 0.0895953i | ||||
\(53\) | 144.687 | + | 83.5350i | 0.374986 | + | 0.216498i | 0.675635 | − | 0.737237i | \(-0.263870\pi\) |
−0.300648 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 206.952i | 0.507370i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 88.6149 | + | 153.485i | 0.200616 | + | 0.347476i | ||||
\(59\) | 68.7687 | − | 119.111i | 0.151744 | − | 0.262829i | −0.780124 | − | 0.625624i | \(-0.784844\pi\) |
0.931869 | + | 0.362795i | \(0.118178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −280.041 | + | 161.682i | −0.587797 | + | 0.339365i | −0.764226 | − | 0.644949i | \(-0.776879\pi\) |
0.176429 | + | 0.984313i | \(0.443545\pi\) | |||||||
\(62\) | −885.842 | −1.81455 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 195.677 | 0.382181 | ||||||||
\(65\) | −45.9712 | + | 26.5415i | −0.0877234 | + | 0.0506471i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −212.076 | + | 367.326i | −0.386705 | + | 0.669792i | −0.992004 | − | 0.126206i | \(-0.959720\pi\) |
0.605299 | + | 0.795998i | \(0.293053\pi\) | |||||||
\(68\) | −263.350 | − | 456.135i | −0.469644 | − | 0.813448i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 727.190i | 1.21551i | 0.794123 | + | 0.607757i | \(0.207931\pi\) | ||||
−0.794123 | + | 0.607757i | \(0.792069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −949.259 | − | 548.055i | −1.52195 | − | 0.878699i | −0.999664 | − | 0.0259286i | \(-0.991746\pi\) |
−0.522287 | − | 0.852770i | \(-0.674921\pi\) | |||||||
\(74\) | −478.343 | − | 276.171i | −0.751435 | − | 0.433841i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 806.229i | 1.21685i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 334.630 | + | 579.597i | 0.476568 | + | 0.825439i | 0.999639 | − | 0.0268493i | \(-0.00854742\pi\) |
−0.523072 | + | 0.852289i | \(0.675214\pi\) | |||||||
\(80\) | 174.866 | − | 302.877i | 0.244382 | − | 0.423283i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1264.71 | − | 730.181i | 1.70322 | − | 0.983354i | ||||
\(83\) | −199.014 | −0.263189 | −0.131594 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131594 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −416.100 | −0.530969 | ||||||||
\(86\) | −1324.16 | + | 764.507i | −1.66033 | + | 0.958592i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −189.467 | + | 328.167i | −0.229514 | + | 0.397530i | ||||
\(89\) | −403.674 | − | 699.184i | −0.480779 | − | 0.832734i | 0.518977 | − | 0.854788i | \(-0.326313\pi\) |
−0.999757 | + | 0.0220537i | \(0.992980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 259.096i | 0.293616i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1312.90 | − | 758.002i | −1.44059 | − | 0.831723i | ||||
\(95\) | 551.600 | + | 318.466i | 0.595715 | + | 0.343936i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 701.053i | − | 0.733827i | −0.930255 | − | 0.366913i | \(-0.880415\pi\) | ||
0.930255 | − | 0.366913i | \(-0.119585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −300.216 | − | 519.989i | −0.300216 | − | 0.519989i | ||||
\(101\) | −851.292 | + | 1474.48i | −0.838680 | + | 1.45264i | 0.0523187 | + | 0.998630i | \(0.483339\pi\) |
−0.890999 | + | 0.454006i | \(0.849994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −982.275 | + | 567.117i | −0.939674 | + | 0.542521i | −0.889858 | − | 0.456237i | \(-0.849197\pi\) |
−0.0498158 | + | 0.998758i | \(0.515863\pi\) | |||||||
\(104\) | −97.1963 | −0.0916431 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −619.631 | −0.567773 | ||||||||
\(107\) | −293.345 | + | 169.363i | −0.265035 | + | 0.153018i | −0.626629 | − | 0.779318i | \(-0.715566\pi\) |
0.361594 | + | 0.932336i | \(0.382233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −987.768 | + | 1710.86i | −0.867991 | + | 1.50340i | −0.00394436 | + | 0.999992i | \(0.501256\pi\) |
−0.864046 | + | 0.503412i | \(0.832078\pi\) | |||||||
\(110\) | −383.772 | − | 664.713i | −0.332648 | − | 0.576163i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1685.74i | 1.40337i | 0.712488 | + | 0.701685i | \(0.247568\pi\) | ||||
−0.712488 | + | 0.701685i | \(0.752432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 177.267 | + | 102.345i | 0.143741 | + | 0.0829888i | ||||
\(116\) | −238.177 | − | 137.511i | −0.190639 | − | 0.110066i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 510.100i | 0.397954i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 370.370 | + | 641.499i | 0.278264 | + | 0.481968i | ||||
\(122\) | 599.648 | − | 1038.62i | 0.444996 | − | 0.770756i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1190.47 | − | 687.319i | 0.862157 | − | 0.497767i | ||||
\(125\) | −1042.69 | −0.746091 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1155.98 | −0.807691 | −0.403846 | − | 0.914827i | \(-0.632327\pi\) | ||||
−0.403846 | + | 0.914827i | \(0.632327\pi\) | |||||||
\(128\) | 886.534 | − | 511.840i | 0.612181 | − | 0.353443i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 98.4373 | − | 170.498i | 0.0664117 | − | 0.115028i | ||||
\(131\) | 317.534 | + | 549.984i | 0.211779 | + | 0.366812i | 0.952271 | − | 0.305253i | \(-0.0987410\pi\) |
−0.740492 | + | 0.672065i | \(0.765408\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1573.10i | − | 1.01414i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −659.816 | − | 380.945i | −0.416020 | − | 0.240189i | ||||
\(137\) | 2128.80 | + | 1229.06i | 1.32756 | + | 0.766466i | 0.984921 | − | 0.173002i | \(-0.0553468\pi\) |
0.342636 | + | 0.939468i | \(0.388680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1094.81i | − | 0.668062i | −0.942562 | − | 0.334031i | \(-0.891591\pi\) | ||
0.942562 | − | 0.334031i | \(-0.108409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1348.50 | − | 2335.68i | −0.796930 | − | 1.38032i | ||||
\(143\) | −265.700 | + | 460.205i | −0.155377 | + | 0.269121i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −188.163 | + | 108.636i | −0.107766 | + | 0.0622187i | ||||
\(146\) | 4065.27 | 2.30441 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 857.117 | 0.476045 | ||||||||
\(149\) | 837.026 | − | 483.257i | 0.460214 | − | 0.265704i | −0.251921 | − | 0.967748i | \(-0.581062\pi\) |
0.712134 | + | 0.702044i | \(0.247729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1164.94 | − | 2017.74i | 0.627825 | − | 1.08743i | −0.360162 | − | 0.932890i | \(-0.617279\pi\) |
0.987987 | − | 0.154536i | \(-0.0493881\pi\) | |||||||
\(152\) | 583.120 | + | 1009.99i | 0.311166 | + | 0.538956i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1085.98i | − | 0.562763i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2957.39 | + | 1707.45i | 1.50334 | + | 0.867956i | 0.999992 | + | 0.00387483i | \(0.00123340\pi\) |
0.503352 | + | 0.864081i | \(0.332100\pi\) | |||||||
\(158\) | −2149.61 | − | 1241.08i | −1.08237 | − | 0.624905i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 994.267i | 0.491273i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 180.834 | + | 313.214i | 0.0868960 | + | 0.150508i | 0.906198 | − | 0.422855i | \(-0.138972\pi\) |
−0.819302 | + | 0.573363i | \(0.805639\pi\) | |||||||
\(164\) | −1133.09 | + | 1962.56i | −0.539507 | + | 0.934453i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 639.219 | − | 369.053i | 0.298874 | − | 0.172555i | ||||
\(167\) | −1605.57 | −0.743969 | −0.371984 | − | 0.928239i | \(-0.621322\pi\) | ||||
−0.371984 | + | 0.928239i | \(0.621322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2060.70 | 0.937959 | ||||||||
\(170\) | 1336.48 | − | 771.617i | 0.602961 | − | 0.348120i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1186.35 | − | 2054.82i | 0.525921 | − | 0.910922i | ||||
\(173\) | 733.434 | + | 1270.35i | 0.322324 | + | 0.558281i | 0.980967 | − | 0.194174i | \(-0.0622028\pi\) |
−0.658644 | + | 0.752455i | \(0.728869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3501.07i | − | 1.49945i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2593.14 | + | 1497.15i | 1.09193 | + | 0.630428i | ||||
\(179\) | 850.303 | + | 490.923i | 0.355054 | + | 0.204990i | 0.666909 | − | 0.745139i | \(-0.267617\pi\) |
−0.311855 | + | 0.950130i | \(0.600950\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1547.32i | − | 0.635422i | −0.948188 | − | 0.317711i | \(-0.897086\pi\) | ||
0.948188 | − | 0.317711i | \(-0.102914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 187.396 | + | 324.580i | 0.0750817 | + | 0.130045i | ||||
\(185\) | 338.567 | − | 586.416i | 0.134551 | − | 0.233049i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3607.40 | + | 2082.73i | −1.41069 | + | 0.814462i | ||||
\(188\) | 2352.52 | 0.912632 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2362.26 | −0.901982 | ||||||||
\(191\) | 4143.61 | − | 2392.32i | 1.56975 | − | 0.906293i | 0.573548 | − | 0.819172i | \(-0.305567\pi\) |
0.996198 | − | 0.0871206i | \(-0.0277666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 638.186 | − | 1105.37i | 0.238019 | − | 0.412261i | −0.722127 | − | 0.691761i | \(-0.756835\pi\) |
0.960146 | + | 0.279500i | \(0.0901687\pi\) | |||||||
\(194\) | 1300.04 | + | 2251.73i | 0.481120 | + | 0.833324i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 491.111i | − | 0.177615i | −0.996049 | − | 0.0888076i | \(-0.971694\pi\) | ||
0.996049 | − | 0.0888076i | \(-0.0283056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2588.06 | + | 1494.22i | 0.921924 | + | 0.532273i | 0.884248 | − | 0.467017i | \(-0.154671\pi\) |
0.0376759 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(200\) | −752.183 | − | 434.273i | −0.265937 | − | 0.153539i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6314.56i | − | 2.19946i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 895.153 | + | 1550.45i | 0.304977 | + | 0.528235i | ||||
\(206\) | 2103.33 | − | 3643.07i | 0.711388 | − | 1.23216i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 777.710 | − | 449.011i | 0.259252 | − | 0.149679i | ||||
\(209\) | 6376.16 | 2.11028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 978.467 | 0.319244 | 0.159622 | − | 0.987178i | \(-0.448972\pi\) | ||||
0.159622 | + | 0.987178i | \(0.448972\pi\) | |||||||
\(212\) | 832.714 | − | 480.768i | 0.269769 | − | 0.155751i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 628.135 | − | 1087.96i | 0.200647 | − | 0.347531i | ||||
\(215\) | −937.234 | − | 1623.34i | −0.297297 | − | 0.514933i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 7326.89i | − | 2.27633i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1031.49 | + | 595.533i | 0.316106 | + | 0.182504i | ||||
\(221\) | −925.294 | − | 534.219i | −0.281638 | − | 0.162604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 727.150i | 0.218357i | 0.994022 | + | 0.109178i | \(0.0348220\pi\) | ||||
−0.994022 | + | 0.109178i | \(0.965178\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3126.04 | − | 5414.46i | −0.920093 | − | 1.59365i | ||||
\(227\) | −3115.04 | + | 5395.40i | −0.910803 | + | 1.57756i | −0.0978711 | + | 0.995199i | \(0.531203\pi\) |
−0.812932 | + | 0.582358i | \(0.802130\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4910.42 | + | 2835.03i | −1.41699 | + | 0.818097i | −0.996033 | − | 0.0889858i | \(-0.971637\pi\) |
−0.420952 | + | 0.907083i | \(0.638304\pi\) | |||||||
\(230\) | −759.156 | −0.217640 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −397.830 | −0.112581 | ||||||||
\(233\) | −3424.06 | + | 1976.88i | −0.962737 | + | 0.555836i | −0.897014 | − | 0.442002i | \(-0.854268\pi\) |
−0.0657224 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 929.260 | − | 1609.53i | 0.257950 | − | 0.446782i | ||||
\(236\) | −395.783 | − | 685.517i | −0.109167 | − | 0.189082i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3916.55i | 1.06000i | 0.847997 | + | 0.530001i | \(0.177808\pi\) | ||||
−0.847997 | + | 0.530001i | \(0.822192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2833.37 | + | 1635.85i | 0.757316 | + | 0.437237i | 0.828331 | − | 0.560238i | \(-0.189290\pi\) |
−0.0710150 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(242\) | −2379.20 | − | 1373.63i | −0.631987 | − | 0.364878i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1861.05i | 0.488285i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 817.740 | + | 1416.37i | 0.210654 | + | 0.364863i | ||||
\(248\) | 994.232 | − | 1722.06i | 0.254572 | − | 0.440931i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3349.05 | − | 1933.58i | 0.847251 | − | 0.489161i | ||||
\(251\) | 1401.75 | 0.352502 | 0.176251 | − | 0.984345i | \(-0.443603\pi\) | ||||
0.176251 | + | 0.984345i | \(0.443603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2049.10 | 0.509192 | ||||||||
\(254\) | 3712.93 | − | 2143.66i | 0.917204 | − | 0.529548i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2681.03 | + | 4643.67i | −0.654548 | + | 1.13371i | ||||
\(257\) | −2044.17 | − | 3540.61i | −0.496155 | − | 0.859366i | 0.503835 | − | 0.863800i | \(-0.331922\pi\) |
−0.999990 | + | 0.00443389i | \(0.998589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 305.507i | 0.0728721i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2039.79 | − | 1177.67i | −0.480987 | − | 0.277698i | ||||
\(263\) | 3994.32 | + | 2306.12i | 0.936503 | + | 0.540690i | 0.888863 | − | 0.458174i | \(-0.151496\pi\) |
0.0476409 | + | 0.998865i | \(0.484830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 759.626i | − | 0.176089i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1220.56 | + | 2114.07i | 0.278199 | + | 0.481855i | ||||
\(269\) | −1839.16 | + | 3185.51i | −0.416860 | + | 0.722023i | −0.995622 | − | 0.0934741i | \(-0.970203\pi\) |
0.578762 | + | 0.815497i | \(0.303536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6200.70 | − | 3579.98i | 1.38991 | − | 0.802465i | 0.396606 | − | 0.917989i | \(-0.370188\pi\) |
0.993305 | + | 0.115524i | \(0.0368547\pi\) | |||||||
\(272\) | 7039.30 | 1.56919 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9116.72 | −2.01008 | ||||||||
\(275\) | −4112.40 | + | 2374.29i | −0.901770 | + | 0.520637i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −565.348 | + | 979.212i | −0.122630 | + | 0.212401i | −0.920804 | − | 0.390026i | \(-0.872466\pi\) |
0.798174 | + | 0.602427i | \(0.205799\pi\) | |||||||
\(278\) | 2030.22 | + | 3516.45i | 0.438003 | + | 0.758643i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3919.67i | − | 0.832128i | −0.909335 | − | 0.416064i | \(-0.863409\pi\) | ||
0.909335 | − | 0.416064i | \(-0.136591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3902.97 | − | 2253.38i | −0.819815 | − | 0.473320i | 0.0305379 | − | 0.999534i | \(-0.490278\pi\) |
−0.850353 | + | 0.526213i | \(0.823611\pi\) | |||||||
\(284\) | 3624.47 | + | 2092.59i | 0.757299 | + | 0.437227i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1970.86i | − | 0.407480i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1731.06 | − | 2998.29i | −0.352344 | − | 0.610277i | ||||
\(290\) | 402.910 | − | 697.860i | 0.0815851 | − | 0.141310i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5463.26 | + | 3154.21i | −1.09491 | + | 0.632145i | ||||
\(293\) | −8956.63 | −1.78584 | −0.892922 | − | 0.450212i | \(-0.851348\pi\) | ||||
−0.892922 | + | 0.450212i | \(0.851348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −625.349 | −0.123421 | ||||||||
\(296\) | 1073.74 | − | 619.926i | 0.210845 | − | 0.121731i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1792.31 | + | 3104.37i | −0.348408 | + | 0.603461i | ||||
\(299\) | 262.796 | + | 455.175i | 0.0508290 | + | 0.0880383i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8641.10i | 1.64649i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9331.60 | − | 5387.60i | −1.76054 | − | 1.01645i | ||||
\(305\) | 1273.28 | + | 735.128i | 0.239042 | + | 0.138011i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3522.69i | 0.654888i | 0.944871 | + | 0.327444i | \(0.106187\pi\) | ||||
−0.944871 | + | 0.327444i | \(0.893813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2013.85 | + | 3488.10i | 0.368965 | + | 0.639066i | ||||
\(311\) | −1777.91 | + | 3079.43i | −0.324168 | + | 0.561475i | −0.981344 | − | 0.192262i | \(-0.938418\pi\) |
0.657176 | + | 0.753737i | \(0.271751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5490.40 | − | 3169.88i | 0.991488 | − | 0.572436i | 0.0857693 | − | 0.996315i | \(-0.472665\pi\) |
0.905719 | + | 0.423879i | \(0.139332\pi\) | |||||||
\(314\) | −12665.2 | −2.27624 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3851.78 | 0.685695 | ||||||||
\(317\) | 2203.91 | − | 1272.43i | 0.390486 | − | 0.225447i | −0.291885 | − | 0.956454i | \(-0.594282\pi\) |
0.682371 | + | 0.731006i | \(0.260949\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1087.53 | + | 1883.65i | −0.190877 | + | 0.330608i | ||||
\(320\) | −444.847 | − | 770.498i | −0.0777116 | − | 0.134600i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12820.0i | 2.20843i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1054.83 | − | 609.004i | −0.180035 | − | 0.103943i | ||||
\(326\) | −1161.65 | − | 670.681i | −0.197356 | − | 0.113943i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3278.10i | 0.551838i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5699.21 | − | 9871.33i | −0.946396 | − | 1.63921i | −0.752931 | − | 0.658099i | \(-0.771361\pi\) |
−0.193465 | − | 0.981107i | \(-0.561973\pi\) | |||||||
\(332\) | −572.692 | + | 991.932i | −0.0946704 | + | 0.163974i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5156.97 | − | 2977.38i | 0.844841 | − | 0.487769i | ||||
\(335\) | 1928.52 | 0.314525 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −551.119 | −0.0890842 | −0.0445421 | − | 0.999008i | \(-0.514183\pi\) | ||||
−0.0445421 | + | 0.999008i | \(0.514183\pi\) | |||||||
\(338\) | −6618.80 | + | 3821.37i | −1.06513 | + | 0.614956i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1197.39 | + | 2073.93i | −0.190992 | + | 0.330808i | ||||
\(341\) | −5435.74 | − | 9414.99i | −0.863232 | − | 1.49516i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3432.20i | − | 0.537942i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4711.47 | − | 2720.17i | −0.732053 | − | 0.422651i | ||||
\(347\) | 2500.59 | + | 1443.72i | 0.386855 | + | 0.223351i | 0.680797 | − | 0.732472i | \(-0.261634\pi\) |
−0.293941 | + | 0.955823i | \(0.594967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2290.34i | 0.351286i | 0.984454 | + | 0.175643i | \(0.0562005\pi\) | ||||
−0.984454 | + | 0.175643i | \(0.943800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4976.67 | + | 8619.85i | 0.753572 | + | 1.30523i | ||||
\(353\) | −704.760 | + | 1220.68i | −0.106262 | + | 0.184052i | −0.914253 | − | 0.405143i | \(-0.867222\pi\) |
0.807991 | + | 0.589195i | \(0.200555\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2863.38 | − | 1653.18i | 0.428092 | − | 0.247159i | ||||
\(356\) | −4646.52 | −0.691755 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3641.48 | −0.537593 | ||||||||
\(359\) | −6021.18 | + | 3476.33i | −0.885196 | + | 0.511068i | −0.872368 | − | 0.488849i | \(-0.837417\pi\) |
−0.0128282 | + | 0.999918i | \(0.504083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6382.42 | − | 11054.7i | 0.930517 | − | 1.61170i | ||||
\(362\) | 2869.36 | + | 4969.88i | 0.416603 | + | 0.721577i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4983.74i | 0.714688i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1300.86 | − | 751.049i | −0.185025 | − | 0.106824i | 0.404627 | − | 0.914482i | \(-0.367402\pi\) |
−0.589651 | + | 0.807658i | \(0.700735\pi\) | |||||||
\(368\) | −2998.88 | − | 1731.40i | −0.424802 | − | 0.245260i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2511.37i | 0.352864i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3527.52 | + | 6109.84i | 0.489673 | + | 0.848138i | 0.999929 | − | 0.0118844i | \(-0.00378300\pi\) |
−0.510257 | + | 0.860022i | \(0.670450\pi\) | |||||||
\(374\) | 7724.46 | − | 13379.2i | 1.06797 | − | 1.84979i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2947.08 | − | 1701.50i | 0.404214 | − | 0.233373i | ||||
\(377\) | −557.898 | −0.0762155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5163.51 | 0.699820 | 0.349910 | − | 0.936783i | \(-0.386212\pi\) | ||||
0.349910 | + | 0.936783i | \(0.386212\pi\) | |||||||
\(380\) | 3174.61 | − | 1832.86i | 0.428564 | − | 0.247431i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8872.65 | + | 15367.9i | −1.18839 | + | 2.05835i | ||||
\(383\) | −1258.96 | − | 2180.58i | −0.167963 | − | 0.290921i | 0.769740 | − | 0.638357i | \(-0.220386\pi\) |
−0.937704 | + | 0.347436i | \(0.887052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4733.82i | 0.624210i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3494.21 | − | 2017.38i | −0.457194 | − | 0.263961i | ||||
\(389\) | −4145.43 | − | 2393.37i | −0.540313 | − | 0.311950i | 0.204893 | − | 0.978784i | \(-0.434315\pi\) |
−0.745206 | + | 0.666834i | \(0.767649\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4119.94i | 0.532875i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 910.718 | + | 1577.41i | 0.116450 | + | 0.201697i | ||||
\(395\) | 1521.48 | − | 2635.28i | 0.193808 | − | 0.335685i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8309.07 | + | 4797.25i | −1.05043 | + | 0.606466i | −0.922770 | − | 0.385352i | \(-0.874080\pi\) |
−0.127660 | + | 0.991818i | \(0.540747\pi\) | |||||||
\(398\) | −11083.6 | −1.39590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8024.73 | 1.00309 | ||||||||
\(401\) | −11732.4 | + | 6773.68i | −1.46106 | + | 0.843544i | −0.999061 | − | 0.0433348i | \(-0.986202\pi\) |
−0.462001 | + | 0.886879i | \(0.652868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1394.26 | − | 2414.93i | 0.172340 | − | 0.298502i | ||||
\(404\) | 4899.42 | + | 8486.05i | 0.603355 | + | 1.04504i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6778.62i | − | 0.825562i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1872.55 | + | 1081.12i | 0.226386 | + | 0.130704i | 0.608904 | − | 0.793244i | \(-0.291610\pi\) |
−0.382518 | + | 0.923948i | \(0.624943\pi\) | |||||||
\(410\) | −5750.33 | − | 3319.95i | −0.692655 | − | 0.399905i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6527.83i | 0.780590i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 452.435 | + | 783.640i | 0.0535160 | + | 0.0926925i | ||||
\(416\) | −1276.51 | + | 2210.98i | −0.150447 | + | 0.260583i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20479.8 | + | 11824.0i | −2.39641 | + | 1.38357i | ||||
\(419\) | −4907.59 | −0.572199 | −0.286099 | − | 0.958200i | \(-0.592359\pi\) | ||||
−0.286099 | + | 0.958200i | \(0.592359\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5719.49 | 0.662116 | 0.331058 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331058 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(422\) | −3142.76 | + | 1814.48i | −0.362529 | + | 0.209306i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 695.448 | − | 1204.55i | 0.0796555 | − | 0.137967i | ||||
\(425\) | −4773.78 | − | 8268.43i | −0.544853 | − | 0.943713i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1949.46i | 0.220166i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6020.65 | + | 3476.03i | 0.675213 | + | 0.389834i | ||||
\(431\) | −3314.11 | − | 1913.41i | −0.370384 | − | 0.213841i | 0.303242 | − | 0.952913i | \(-0.401931\pi\) |
−0.673626 | + | 0.739072i | \(0.735264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9120.21i | 1.01222i | 0.862470 | + | 0.506108i | \(0.168916\pi\) | ||||
−0.862470 | + | 0.506108i | \(0.831084\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5684.88 | + | 9846.51i | 0.624442 | + | 1.08156i | ||||
\(437\) | 3153.24 | − | 5461.57i | 0.345171 | − | 0.597854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2550.00 | − | 1472.24i | 0.277232 | − | 0.160060i | −0.354938 | − | 0.934890i | \(-0.615498\pi\) |
0.632170 | + | 0.774830i | \(0.282165\pi\) | |||||||
\(440\) | 1722.92 | 0.186675 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3962.63 | 0.426433 | ||||||||
\(443\) | 3692.44 | − | 2131.83i | 0.396011 | − | 0.228637i | −0.288750 | − | 0.957404i | \(-0.593240\pi\) |
0.684762 | + | 0.728767i | \(0.259906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1835.41 | + | 3179.02i | −0.195520 | + | 0.338651i | ||||
\(446\) | −1348.43 | − | 2335.55i | −0.143162 | − | 0.247963i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1608.94i | − | 0.169110i | −0.996419 | − | 0.0845550i | \(-0.973053\pi\) | ||
0.996419 | − | 0.0845550i | \(-0.0269469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15521.2 | + | 8961.14i | 1.62054 | + | 0.935618i | ||||
\(452\) | 8402.08 | + | 4850.94i | 0.874338 | + | 0.504799i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23106.2i | − | 2.38861i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2626.91 | + | 4549.94i | 0.268887 | + | 0.465727i | 0.968575 | − | 0.248723i | \(-0.0800107\pi\) |
−0.699687 | + | 0.714449i | \(0.746677\pi\) | |||||||
\(458\) | 10514.6 | − | 18211.8i | 1.07274 | − | 1.85804i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1020.22 | − | 589.024i | 0.103409 | − | 0.0597030i | ||||
\(461\) | 19229.1 | 1.94271 | 0.971356 | − | 0.237627i | \(-0.0763696\pi\) | ||||
0.971356 | + | 0.237627i | \(0.0763696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6539.63 | 0.656420 | 0.328210 | − | 0.944605i | \(-0.393555\pi\) | ||||
0.328210 | + | 0.944605i | \(0.393555\pi\) | |||||||
\(464\) | 3183.21 | − | 1837.83i | 0.318485 | − | 0.183877i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7331.88 | − | 12699.2i | 0.728847 | − | 1.26240i | ||||
\(467\) | 4508.88 | + | 7809.61i | 0.446780 | + | 0.773845i | 0.998174 | − | 0.0603995i | \(-0.0192375\pi\) |
−0.551395 | + | 0.834245i | \(0.685904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6892.90i | 0.676480i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −991.626 | − | 572.515i | −0.0967018 | − | 0.0558308i | ||||
\(473\) | −16250.8 | − | 9382.41i | −1.57973 | − | 0.912058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14614.7i | 1.41172i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7262.87 | − | 12579.7i | −0.694971 | − | 1.20372i | ||||
\(479\) | 4112.88 | − | 7123.71i | 0.392322 | − | 0.679521i | −0.600434 | − | 0.799675i | \(-0.705005\pi\) |
0.992755 | + | 0.120153i | \(0.0383387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1505.77 | − | 869.355i | 0.142738 | − | 0.0824099i | ||||
\(482\) | −12134.1 | −1.14666 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4263.17 | 0.400372 | ||||||||
\(485\) | −2760.47 | + | 1593.76i | −0.258446 | + | 0.149214i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9017.38 | − | 15618.6i | 0.839048 | − | 1.45327i | −0.0516439 | − | 0.998666i | \(-0.516446\pi\) |
0.890692 | − | 0.454608i | \(-0.150221\pi\) | |||||||
\(488\) | 1346.04 | + | 2331.41i | 0.124861 | + | 0.216266i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12148.2i | − | 1.11658i | −0.829646 | − | 0.558290i | \(-0.811458\pi\) | ||
0.829646 | − | 0.558290i | \(-0.188542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3787.29 | − | 2186.59i | −0.345985 | − | 0.199755i | ||||
\(494\) | −5253.04 | − | 3032.84i | −0.478432 | − | 0.276223i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18371.9i | 1.66315i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1473.28 | + | 2551.79i | 0.132170 | + | 0.228925i | 0.924513 | − | 0.381151i | \(-0.124472\pi\) |
−0.792343 | + | 0.610076i | \(0.791139\pi\) | |||||||
\(500\) | −3000.50 | + | 5197.02i | −0.268373 | + | 0.464835i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4502.33 | + | 2599.42i | −0.400296 | + | 0.231111i | ||||
\(503\) | −11290.2 | −1.00080 | −0.500402 | − | 0.865793i | \(-0.666814\pi\) | ||||
−0.500402 | + | 0.865793i | \(0.666814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7741.23 | 0.682139 | ||||||||
\(506\) | −6581.54 | + | 3799.85i | −0.578232 | + | 0.333842i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3326.50 | + | 5761.67i | −0.290531 | + | 0.503214i | ||||
\(509\) | 3214.41 | + | 5567.52i | 0.279914 | + | 0.484825i | 0.971363 | − | 0.237600i | \(-0.0763608\pi\) |
−0.691449 | + | 0.722425i | \(0.743027\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11697.4i | − | 1.00968i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13131.4 | + | 7581.45i | 1.12685 | + | 0.650590i | ||||
\(515\) | 4466.16 | + | 2578.54i | 0.382141 | + | 0.220629i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 18605.2i | − | 1.58270i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 220.964 | + | 382.720i | 0.0186344 | + | 0.0322758i | ||||
\(521\) | −3150.38 | + | 5456.62i | −0.264915 | + | 0.458846i | −0.967541 | − | 0.252713i | \(-0.918677\pi\) |
0.702626 | + | 0.711559i | \(0.252011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11423.1 | − | 6595.13i | 0.955061 | − | 0.551405i | 0.0604118 | − | 0.998174i | \(-0.480759\pi\) |
0.894650 | + | 0.446769i | \(0.147425\pi\) | |||||||
\(524\) | 3654.99 | 0.304712 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17105.9 | −1.41797 | ||||||||
\(527\) | 18929.9 | − | 10929.2i | 1.56470 | − | 0.903382i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5070.15 | + | 8781.76i | −0.416713 | + | 0.721769i | ||||
\(530\) | 1408.66 | + | 2439.86i | 0.115449 | + | 0.199964i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4597.05i | 0.373584i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1333.77 | + | 770.051i | 0.107783 | + | 0.0622285i | ||||
\(536\) | 3058.08 | + | 1765.58i | 0.246434 | + | 0.142279i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13642.2i | − | 1.09323i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5946.49 | − | 10299.6i | −0.472568 | − | 0.818513i | 0.526939 | − | 0.849903i | \(-0.323340\pi\) |
−0.999507 | + | 0.0313907i | \(0.990006\pi\) | |||||||
\(542\) | −13277.5 | + | 22997.2i | −1.05224 | + | 1.82254i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17331.2 | + | 10006.2i | −1.36593 | + | 0.788622i | ||||
\(545\) | 8982.27 | 0.705979 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1348.19 | 0.105383 | 0.0526915 | − | 0.998611i | \(-0.483220\pi\) | ||||
0.0526915 | + | 0.998611i | \(0.483220\pi\) | |||||||
\(548\) | 12251.8 | − | 7073.60i | 0.955059 | − | 0.551404i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8805.81 | − | 15252.1i | 0.682693 | − | 1.18246i | ||||
\(551\) | 3347.06 | + | 5797.28i | 0.258783 | + | 0.448226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 4193.54i | − | 0.321600i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5456.78 | − | 3150.47i | −0.416221 | − | 0.240305i | ||||
\(557\) | 16461.7 | + | 9504.16i | 1.25225 | + | 0.722988i | 0.971556 | − | 0.236809i | \(-0.0761016\pi\) |
0.280695 | + | 0.959797i | \(0.409435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4813.16i | − | 0.364177i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7268.66 | + | 12589.7i | 0.545569 | + | 0.944953i | ||||
\(563\) | 1365.26 | − | 2364.70i | 0.102201 | − | 0.177017i | −0.810390 | − | 0.585890i | \(-0.800745\pi\) |
0.912591 | + | 0.408874i | \(0.134078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6637.76 | − | 3832.31i | 0.494253 | − | 0.285357i | ||||
\(566\) | 16714.7 | 1.24129 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6054.02 | 0.447220 | ||||||||
\(569\) | 1334.77 | − | 770.632i | 0.0983421 | − | 0.0567778i | −0.450022 | − | 0.893017i | \(-0.648584\pi\) |
0.548364 | + | 0.836239i | \(0.315251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1735.00 | − | 3005.11i | 0.127158 | − | 0.220245i | −0.795416 | − | 0.606064i | \(-0.792748\pi\) |
0.922575 | + | 0.385819i | \(0.126081\pi\) | |||||||
\(572\) | 1529.18 | + | 2648.61i | 0.111780 | + | 0.193608i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4696.69i | 0.340635i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4030.32 | − | 2326.91i | −0.290788 | − | 0.167886i | 0.347509 | − | 0.937676i | \(-0.387027\pi\) |
−0.638297 | + | 0.769790i | \(0.720361\pi\) | |||||||
\(578\) | 11120.1 | + | 6420.19i | 0.800234 | + | 0.462015i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1250.46i | 0.0895216i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3802.21 | − | 6585.62i | −0.270105 | − | 0.467836i | ||||
\(584\) | −4562.68 | + | 7902.80i | −0.323297 | + | 0.559966i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28768.0 | − | 16609.2i | 2.02798 | − | 1.17086i | ||||
\(587\) | −12056.1 | −0.847717 | −0.423858 | − | 0.905728i | \(-0.639325\pi\) | ||||
−0.423858 | + | 0.905728i | \(0.639325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33459.0 | −2.34067 | ||||||||
\(590\) | 2008.57 | − | 1159.65i | 0.140155 | − | 0.0809187i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5727.66 | + | 9920.60i | −0.397644 | + | 0.688740i | ||||
\(593\) | −6450.02 | − | 11171.8i | −0.446662 | − | 0.773641i | 0.551505 | − | 0.834172i | \(-0.314054\pi\) |
−0.998166 | + | 0.0605310i | \(0.980721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5562.56i | − | 0.382301i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1688.16 | − | 974.659i | −0.115441 | − | 0.0666501i | ||||
\(599\) | 3037.85 | + | 1753.90i | 0.207217 | + | 0.119637i | 0.600017 | − | 0.799987i | \(-0.295160\pi\) |
−0.392800 | + | 0.919624i | \(0.628494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1767.94i | 0.119993i | 0.998199 | + | 0.0599966i | \(0.0191090\pi\) | ||||
−0.998199 | + | 0.0599966i | \(0.980891\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6704.57 | − | 11612.7i | −0.451664 | − | 0.782305i | ||||
\(605\) | 1683.98 | − | 2916.74i | 0.113163 | − | 0.196004i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12027.1 | + | 6943.85i | −0.804225 | + | 0.464320i | −0.844946 | − | 0.534851i | \(-0.820368\pi\) |
0.0407213 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(608\) | 30633.3 | 2.04333 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5452.90 | −0.361937 | ||||||||
\(611\) | 4132.85 | − | 2386.10i | 0.273645 | − | 0.157989i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11254.9 | + | 19494.1i | −0.741569 | + | 1.28443i | 0.210212 | + | 0.977656i | \(0.432584\pi\) |
−0.951781 | + | 0.306779i | \(0.900749\pi\) | |||||||
\(614\) | −6532.50 | − | 11314.6i | −0.429365 | − | 0.743682i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1591.00i | 0.103811i | 0.998652 | + | 0.0519053i | \(0.0165294\pi\) | ||||
−0.998652 | + | 0.0519053i | \(0.983471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11495.2 | − | 6636.75i | −0.746415 | − | 0.430943i | 0.0779820 | − | 0.996955i | \(-0.475152\pi\) |
−0.824397 | + | 0.566012i | \(0.808486\pi\) | |||||||
\(620\) | −5412.78 | − | 3125.07i | −0.350617 | − | 0.202429i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 13187.9i | − | 0.850138i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4150.00 | − | 7188.02i | −0.265600 | − | 0.460033i | ||||
\(626\) | −11756.5 | + | 20362.9i | −0.750614 | + | 1.30010i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17020.6 | − | 9826.84i | 1.08152 | − | 0.624417i | ||||
\(629\) | 13629.2 | 0.863960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11933.2 | −0.752860 | −0.376430 | − | 0.926445i | \(-0.622848\pi\) | ||||
−0.376430 | + | 0.926445i | \(0.622848\pi\) | |||||||
\(632\) | 4825.27 | − | 2785.87i | 0.303701 | − | 0.175342i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4719.21 | + | 8173.90i | −0.295621 | + | 0.512030i | ||||
\(635\) | 2627.98 | + | 4551.80i | 0.164234 | + | 0.284461i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 8066.85i | − | 0.500580i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4030.85 | − | 2327.21i | −0.248958 | − | 0.143736i | ||||
\(641\) | −23852.5 | − | 13771.2i | −1.46976 | − | 0.848566i | −0.470335 | − | 0.882488i | \(-0.655867\pi\) |
−0.999424 | + | 0.0339218i | \(0.989200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 19003.1i | − | 1.16549i | −0.812655 | − | 0.582746i | \(-0.801978\pi\) | ||
0.812655 | − | 0.582746i | \(-0.198022\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23773.5 | − | 41176.8i | −1.44792 | − | 2.50787i | ||||
\(647\) | −12524.2 | + | 21692.6i | −0.761016 | + | 1.31812i | 0.181312 | + | 0.983426i | \(0.441966\pi\) |
−0.942327 | + | 0.334692i | \(0.891368\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5421.49 | + | 3130.10i | −0.327908 | + | 0.189318i | ||||
\(650\) | 4517.36 | 0.272593 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2081.51 | 0.125028 | ||||||||
\(653\) | −11903.6 | + | 6872.56i | −0.713361 | + | 0.411859i | −0.812304 | − | 0.583234i | \(-0.801787\pi\) |
0.0989433 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1443.75 | − | 2500.64i | 0.0861250 | − | 0.149173i | ||||
\(656\) | −15143.6 | − | 26229.5i | −0.901309 | − | 1.56111i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6965.25i | − | 0.411726i | −0.978581 | − | 0.205863i | \(-0.934000\pi\) | ||
0.978581 | − | 0.205863i | \(-0.0660002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10265.5 | − | 5926.78i | −0.604056 | − | 0.348752i | 0.166579 | − | 0.986028i | \(-0.446728\pi\) |
−0.770636 | + | 0.637276i | \(0.780061\pi\) | |||||||
\(662\) | 36610.9 | + | 21137.3i | 2.14943 | + | 1.24097i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1656.84i | 0.0968342i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1075.64 | + | 1863.06i | 0.0624421 | + | 0.108153i | ||||
\(668\) | −4620.26 | + | 8002.52i | −0.267609 | + | 0.463513i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6194.25 | + | 3576.25i | −0.357171 | + | 0.206213i | ||||
\(671\) | 14718.3 | 0.846789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30769.5 | −1.76238 | −0.881188 | − | 0.472766i | \(-0.843255\pi\) | ||||
−0.881188 | + | 0.472766i | \(0.843255\pi\) | |||||||
\(674\) | 1770.15 | − | 1022.00i | 0.101163 | − | 0.0584064i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5929.95 | − | 10271.0i | 0.337389 | − | 0.584375i | ||||
\(677\) | 654.744 | + | 1134.05i | 0.0371696 | + | 0.0643797i | 0.884012 | − | 0.467465i | \(-0.154832\pi\) |
−0.846842 | + | 0.531844i | \(0.821499\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3464.12i | 0.195358i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 34918.4 | + | 20160.2i | 1.96055 | + | 1.13192i | ||||
\(683\) | 20035.2 | + | 11567.3i | 1.12244 | + | 0.648041i | 0.942023 | − | 0.335549i | \(-0.108922\pi\) |
0.180417 | + | 0.983590i | \(0.442255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11176.5i | − | 0.623403i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15855.5 | + | 27462.5i | 0.878613 | + | 1.52180i | ||||
\(689\) | 975.263 | − | 1689.21i | 0.0539254 | − | 0.0934015i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21031.0 | − | 12142.3i | 1.15782 | − | 0.668471i | 0.207043 | − | 0.978332i | \(-0.433616\pi\) |
0.950782 | + | 0.309861i | \(0.100283\pi\) | |||||||
\(692\) | 8442.24 | 0.463766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10708.9 | −0.585744 | ||||||||
\(695\) | −4310.93 | + | 2488.92i | −0.235285 | + | 0.135842i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18017.4 | + | 31207.0i | −0.979135 | + | 1.69591i | ||||
\(698\) | −4247.21 | − | 7356.39i | −0.230314 | − | 0.398916i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 20398.8i | − | 1.09907i | −0.835469 | − | 0.549537i | \(-0.814804\pi\) | ||
0.835469 | − | 0.549537i | \(-0.185196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18067.4 | − | 10431.2i | −0.969311 | − | 0.559632i | ||||
\(704\) | −7713.25 | − | 4453.25i | −0.412932 | − | 0.238406i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 5227.65i | − | 0.278676i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15428.5 | + | 26723.0i | 0.817250 | + | 1.41552i | 0.907701 | + | 0.419617i | \(0.137836\pi\) |
−0.0904511 | + | 0.995901i | \(0.528831\pi\) | |||||||
\(710\) | −6131.32 | + | 10619.8i | −0.324091 | + | 0.561341i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5820.87 | + | 3360.68i | −0.306385 | + | 0.176892i | ||||
\(713\) | −10752.7 | −0.564783 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2416.14 | 0.126376 | ||||||||
\(716\) | 4893.74 | − | 2825.40i | 0.255430 | − | 0.147472i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12893.0 | − | 22331.4i | 0.670145 | − | 1.16073i | ||||
\(719\) | 17203.6 | + | 29797.5i | 0.892332 | + | 1.54556i | 0.837072 | + | 0.547092i | \(0.184265\pi\) |
0.0552599 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 47342.4i | 2.44030i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7712.18 | − | 4452.63i | −0.395885 | − | 0.228565i | ||||
\(725\) | −4317.47 | − | 2492.69i | −0.221168 | − | 0.127691i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11996.1i | − | 0.611983i | −0.952034 | − | 0.305992i | \(-0.901012\pi\) | ||
0.952034 | − | 0.305992i | \(-0.0989880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9241.88 | − | 16007.4i | −0.468572 | − | 0.811590i | ||||
\(731\) | 18864.4 | − | 32674.1i | 0.954479 | − | 1.65321i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27819.5 | + | 16061.6i | −1.40182 | + | 0.809342i | −0.994580 | − | 0.103978i | \(-0.966843\pi\) |
−0.407242 | + | 0.913320i | \(0.633510\pi\) | |||||||
\(734\) | 5571.00 | 0.280149 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9844.55 | 0.493037 | ||||||||
\(737\) | 16719.4 | − | 9652.93i | 0.835639 | − | 0.482456i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11436.0 | + | 19807.7i | −0.569254 | + | 0.985977i | 0.427386 | + | 0.904069i | \(0.359435\pi\) |
−0.996640 | + | 0.0819076i | \(0.973899\pi\) | |||||||
\(740\) | −1948.55 | − | 3374.99i | −0.0967975 | − | 0.167658i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20982.3i | − | 1.03602i | −0.855373 | − | 0.518012i | \(-0.826672\pi\) | ||
0.855373 | − | 0.518012i | \(-0.173328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3805.75 | − | 2197.25i | −0.187157 | − | 0.108055i | ||||
\(746\) | −22660.2 | − | 13082.9i | −1.11213 | − | 0.642089i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23973.4i | 1.17187i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9321.27 | − | 16144.9i | −0.452914 | − | 0.784469i | 0.545652 | − | 0.838012i | \(-0.316282\pi\) |
−0.998566 | + | 0.0535425i | \(0.982949\pi\) | |||||||
\(752\) | −15720.6 | + | 27228.9i | −0.762329 | + | 1.32039i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1791.93 | − | 1034.57i | 0.0865493 | − | 0.0499692i | ||||
\(755\) | −10593.4 | −0.510641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4135.46 | 0.198555 | 0.0992774 | − | 0.995060i | \(-0.468347\pi\) | ||||
0.0992774 | + | 0.995060i | \(0.468347\pi\) | |||||||
\(758\) | −16584.8 | + | 9575.25i | −0.794707 | + | 0.458824i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2651.30 | − | 4592.19i | 0.126543 | − | 0.219179i | ||||
\(761\) | −1790.84 | − | 3101.83i | −0.0853062 | − | 0.147755i | 0.820215 | − | 0.572055i | \(-0.193854\pi\) |
−0.905522 | + | 0.424300i | \(0.860520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 27536.9i | − | 1.30399i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8087.37 | + | 4669.25i | 0.381474 | + | 0.220244i | ||||
\(767\) | −1390.61 | − | 802.868i | −0.0654654 | − | 0.0377965i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11427.1i | − | 0.535852i | −0.963439 | − | 0.267926i | \(-0.913662\pi\) | ||
0.963439 | − | 0.267926i | \(-0.0863383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3672.94 | − | 6361.72i | −0.171233 | − | 0.296585i | ||||
\(773\) | 741.803 | − | 1284.84i | 0.0345159 | − | 0.0597833i | −0.848251 | − | 0.529594i | \(-0.822344\pi\) |
0.882767 | + | 0.469810i | \(0.155678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21579.9 | − | 12459.1i | 1.00022 | − | 0.577478i | ||||
\(776\) | −5836.43 | −0.269994 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17753.1 | 0.818097 | ||||||||
\(779\) | 47769.2 | − | 27579.6i | 2.19706 | − | 1.26847i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16549.5 | − | 28664.6i | 0.758243 | − | 1.31332i | ||||
\(782\) | −7640.03 | − | 13232.9i | −0.349370 | − | 0.605126i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15526.7i | − | 0.705951i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15173.0 | + | 8760.12i | 0.687240 | + | 0.396778i | 0.802577 | − | 0.596548i | \(-0.203462\pi\) |
−0.115337 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(788\) | −2447.80 | − | 1413.24i | −0.110659 | − | 0.0638891i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11285.8i | 0.508266i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1887.62 | + | 3269.46i | 0.0845289 | + | 0.146408i | ||||
\(794\) | 17792.1 | − | 30816.8i | 0.795236 | − | 1.37739i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14895.0 | − | 8599.65i | 0.663242 | − | 0.382923i | ||||
\(797\) | 2687.85 | 0.119459 | 0.0597293 | − | 0.998215i | \(-0.480976\pi\) | ||||
0.0597293 | + | 0.998215i | \(0.480976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37407.7 | 1.65631 | ||||||||
\(800\) | −19757.4 | + | 11406.9i | −0.873160 | + | 0.504119i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25122.3 | − | 43513.1i | 1.10611 | − | 1.91584i | ||||
\(803\) | 24945.5 | + | 43206.8i | 1.09627 | + | 1.89880i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10342.1i | 0.451967i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12275.4 | + | 7087.20i | 0.534464 | + | 0.308573i | ||||
\(809\) | 728.881 | + | 420.819i | 0.0316762 | + | 0.0182883i | 0.515754 | − | 0.856736i | \(-0.327512\pi\) |
−0.484078 | + | 0.875025i | \(0.660845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37115.6i | 1.60704i | 0.595281 | + | 0.803518i | \(0.297041\pi\) | ||||
−0.595281 | + | 0.803518i | \(0.702959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12570.3 | + | 21772.4i | 0.541264 | + | 0.937497i | ||||
\(815\) | 822.209 | − | 1424.11i | 0.0353383 | − | 0.0612078i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50014.9 | + | 28876.1i | −2.14174 | + | 1.23653i | ||||
\(818\) | −8019.33 | −0.342774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10303.7 | 0.438807 | ||||||||
\(821\) | −23903.7 | + | 13800.8i | −1.01613 | + | 0.586664i | −0.912981 | − | 0.408002i | \(-0.866226\pi\) |
−0.103151 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3682.60 | + | 6378.45i | −0.155975 | + | 0.270156i | −0.933414 | − | 0.358802i | \(-0.883185\pi\) |
0.777439 | + | 0.628959i | \(0.216519\pi\) | |||||||
\(824\) | 4721.38 | + | 8177.66i | 0.199608 | + | 0.345731i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46801.3i | 1.96789i | 0.178485 | + | 0.983943i | \(0.442880\pi\) | ||||
−0.178485 | + | 0.983943i | \(0.557120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8806.68 | − | 5084.54i | −0.368961 | − | 0.213020i | 0.304044 | − | 0.952658i | \(-0.401663\pi\) |
−0.673004 | + | 0.739638i | \(0.734997\pi\) | |||||||
\(830\) | −2906.37 | − | 1678.00i | −0.121544 | − | 0.0701736i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2284.51i | − | 0.0951936i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3650.07 | + | 6322.10i | 0.151276 | + | 0.262018i | ||||
\(836\) | 18348.3 | − | 31780.2i | 0.759079 | − | 1.31476i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15762.8 | − | 9100.66i | 0.649782 | − | 0.375152i | ||||
\(839\) | −45477.6 | −1.87135 | −0.935674 | − | 0.352864i | \(-0.885208\pi\) | ||||
−0.935674 | + | 0.352864i | \(0.885208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22105.5 | 0.906371 | ||||||||
\(842\) | −18370.6 | + | 10606.3i | −0.751891 | + | 0.434104i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2815.68 | − | 4876.90i | 0.114834 | − | 0.198898i | ||||
\(845\) | −4684.74 | − | 8114.21i | −0.190722 | − | 0.330340i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12850.9i | 0.520401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30666.1 | + | 17705.1i | 1.23746 | + | 0.714445i | ||||
\(851\) | −5806.29 | − | 3352.26i | −0.233886 | − | 0.135034i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3005.89i | 0.120656i | 0.998179 | + | 0.0603281i | \(0.0192147\pi\) | ||||
−0.998179 | + | 0.0603281i | \(0.980785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1409.99 | + | 2442.17i | 0.0562994 | + | 0.0975135i | ||||
\(857\) | 22426.6 | − | 38844.0i | 0.893907 | − | 1.54829i | 0.0587561 | − | 0.998272i | \(-0.481287\pi\) |
0.835151 | − | 0.550020i | \(-0.185380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11337.0 | + | 6545.40i | −0.450305 | + | 0.259984i | −0.707959 | − | 0.706253i | \(-0.750384\pi\) |
0.257654 | + | 0.966237i | \(0.417051\pi\) | |||||||
\(860\) | −10788.1 | −0.427757 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14192.9 | 0.560804 | ||||||||
\(863\) | 18376.4 | − | 10609.6i | 0.724843 | − | 0.418488i | −0.0916894 | − | 0.995788i | \(-0.529227\pi\) |
0.816533 | + | 0.577299i | \(0.195893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3334.74 | − | 5775.95i | 0.131081 | − | 0.227038i | ||||
\(866\) | −16912.6 | − | 29293.4i | −0.663641 | − | 1.14946i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 30462.3i | − | 1.18914i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4288.50 | + | 2475.97i | 0.166832 | + | 0.0963203i | ||||
\(872\) | 14243.3 | + | 8223.40i | 0.553143 | + | 0.319357i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23389.5i | 0.905220i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20938.2 | + | 36266.1i | 0.806195 | + | 1.39637i | 0.915481 | + | 0.402361i | \(0.131810\pi\) |
−0.109286 | + | 0.994010i | \(0.534856\pi\) | |||||||
\(878\) | −5460.27 | + | 9457.47i | −0.209881 | + | 0.363524i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13785.8 | + | 7959.26i | −0.528091 | + | 0.304894i | ||||
\(881\) | 16277.8 | 0.622490 | 0.311245 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311245 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32041.9 | −1.22117 | −0.610586 | − | 0.791950i | \(-0.709066\pi\) | ||||
−0.610586 | + | 0.791950i | \(0.709066\pi\) | |||||||
\(884\) | −5325.33 | + | 3074.58i | −0.202613 | + | 0.116979i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7906.56 | + | 13694.6i | −0.299804 | + | 0.519275i | ||||
\(887\) | 23076.8 | + | 39970.2i | 0.873555 | + | 1.51304i | 0.858294 | + | 0.513158i | \(0.171524\pi\) |
0.0152603 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 13614.4i | − | 0.512758i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3624.28 | + | 2092.48i | 0.136042 | + | 0.0785441i | ||||
\(893\) | −49589.3 | − | 28630.4i | −1.85828 | − | 1.07288i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4464.21i | − | 0.166729i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2983.62 | + | 5167.78i | 0.110874 | + | 0.192039i | ||||
\(899\) | 5706.81 | − | 9884.48i | 0.211716 | − | 0.366703i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13241.1 | − | 7644.77i | 0.489596 | − | 0.282668i | ||||
\(902\) | −66470.4 | −2.45368 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14034.1 | 0.516337 | ||||||||
\(905\) | −6092.73 | + | 3517.64i | −0.223789 | + | 0.129205i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13614.8 | + | 23581.6i | −0.498427 | + | 0.863301i | −0.999998 | − | 0.00181559i | \(-0.999422\pi\) |
0.501572 | + | 0.865116i | \(0.332755\pi\) | |||||||
\(908\) | 17927.9 | + | 31052.1i | 0.655241 | + | 1.13491i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11012.2i | 0.400494i | 0.979745 | + | 0.200247i | \(0.0641745\pi\) | ||||
−0.979745 | + | 0.200247i | \(0.935826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7844.82 | + | 4529.21i | 0.284365 | + | 0.164178i | ||||
\(914\) | −16874.9 | − | 9742.70i | −0.610690 | − | 0.352582i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32632.8i | 1.17709i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10888.8 | − | 18859.9i | −0.390846 | − | 0.676965i | 0.601715 | − | 0.798711i | \(-0.294484\pi\) |
−0.992561 | + | 0.121745i | \(0.961151\pi\) | |||||||
\(920\) | 852.045 | − | 1475.78i | 0.0305338 | − | 0.0528861i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −61762.6 | + | 35658.6i | −2.20612 | + | 1.27370i | ||||
\(923\) | 8489.87 | 0.302760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15537.1 | 0.552278 | ||||||||
\(926\) | −21004.8 | + | 12127.1i | −0.745422 | + | 0.430370i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5224.84 | + | 9049.69i | −0.184821 | + | 0.320119i | ||||
\(929\) | 6186.14 | + | 10714.7i | 0.218472 | + | 0.378405i | 0.954341 | − | 0.298719i | \(-0.0965593\pi\) |
−0.735869 | + | 0.677124i | \(0.763226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22755.0i | 0.799749i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28964.4 | − | 16722.6i | −1.01471 | − | 0.585846i | ||||
\(935\) | 16401.9 | + | 9469.67i | 0.573691 | + | 0.331221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41577.7i | − | 1.44961i | −0.688954 | − | 0.724806i | \(-0.741930\pi\) | ||
0.688954 | − | 0.724806i | \(-0.258070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5348.15 | − | 9263.27i | −0.185572 | − | 0.321420i | ||||
\(941\) | 16245.4 | − | 28137.8i | 0.562789 | − | 0.974779i | −0.434463 | − | 0.900690i | \(-0.643062\pi\) |
0.997252 | − | 0.0740893i | \(-0.0236050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15351.5 | − | 8863.20i | 0.530131 | − | 0.306072i | ||||
\(944\) | 10579.2 | 0.364751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69595.2 | 2.39190 | ||||||||
\(947\) | −44020.7 | + | 25415.4i | −1.51054 | + | 0.872110i | −0.510615 | + | 0.859809i | \(0.670582\pi\) |
−0.999924 | + | 0.0123009i | \(0.996084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6398.49 | + | 11082.5i | −0.218866 | + | 0.379087i | ||||
\(950\) | −27101.5 | − | 46941.2i | −0.925568 | − | 1.60313i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4892.40i | − | 0.166296i | −0.996537 | − | 0.0831482i | \(-0.973503\pi\) | ||
0.996537 | − | 0.0831482i | \(-0.0264975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18840.0 | − | 10877.3i | −0.638375 | − | 0.368566i | ||||
\(956\) | 19521.0 | + | 11270.4i | 0.660411 | + | 0.381288i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30507.8i | 1.02887i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13628.7 | + | 23605.5i | 0.457476 | + | 0.792372i | ||||
\(962\) | −3224.27 | + | 5584.60i | −0.108061 | + | 0.187167i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16306.8 | − | 9414.76i | 0.544821 | − | 0.314553i | ||||
\(965\) | −5803.35 | −0.193592 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41170.9 | −1.36915 | −0.684575 | − | 0.728943i | \(-0.740012\pi\) | ||||
−0.684575 | + | 0.728943i | \(0.740012\pi\) | |||||||
\(968\) | 5340.63 | − | 3083.41i | 0.177329 | − | 0.102381i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5910.95 | − | 10238.1i | 0.195659 | − | 0.338891i | ||||
\(971\) | −21643.8 | − | 37488.1i | −0.715327 | − | 1.23898i | −0.962833 | − | 0.270096i | \(-0.912945\pi\) |
0.247507 | − | 0.968886i | \(-0.420389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 66887.5i | 2.20042i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21540.5 | − | 12436.4i | −0.706449 | − | 0.407869i | ||||
\(977\) | −15651.8 | − | 9036.54i | −0.512532 | − | 0.295911i | 0.221342 | − | 0.975196i | \(-0.428956\pi\) |
−0.733874 | + | 0.679286i | \(0.762290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36747.5i | 1.19965i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22527.7 | + | 39019.1i | 0.732065 | + | 1.26797i | ||||
\(983\) | 9865.31 | − | 17087.2i | 0.320096 | − | 0.554423i | −0.660411 | − | 0.750904i | \(-0.729618\pi\) |
0.980508 | + | 0.196481i | \(0.0629514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1933.80 | + | 1116.48i | −0.0625543 | + | 0.0361157i | ||||
\(986\) | 16219.3 | 0.523862 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9412.65 | 0.303093 | ||||||||
\(989\) | −16073.2 | + | 9279.86i | −0.516782 | + | 0.298364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6846.14 | − | 11857.9i | 0.219450 | − | 0.380098i | −0.735190 | − | 0.677861i | \(-0.762907\pi\) |
0.954640 | + | 0.297763i | \(0.0962405\pi\) | |||||||
\(992\) | −26115.2 | − | 45232.8i | −0.835844 | − | 1.44772i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13587.7i | − | 0.432923i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2672.18 | + | 1542.78i | 0.0848833 | + | 0.0490074i | 0.541841 | − | 0.840481i | \(-0.317728\pi\) |
−0.456958 | + | 0.889489i | \(0.651061\pi\) | |||||||
\(998\) | −9464.11 | − | 5464.10i | −0.300181 | − | 0.173310i | ||||
\(999\) | 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.p.d.80.3 | 48 | ||
3.2 | odd | 2 | inner | 441.4.p.d.80.22 | 48 | ||
7.2 | even | 3 | inner | 441.4.p.d.215.21 | 48 | ||
7.3 | odd | 6 | 441.4.c.b.440.7 | ✓ | 24 | ||
7.4 | even | 3 | 441.4.c.b.440.17 | yes | 24 | ||
7.5 | odd | 6 | inner | 441.4.p.d.215.22 | 48 | ||
7.6 | odd | 2 | inner | 441.4.p.d.80.4 | 48 | ||
21.2 | odd | 6 | inner | 441.4.p.d.215.4 | 48 | ||
21.5 | even | 6 | inner | 441.4.p.d.215.3 | 48 | ||
21.11 | odd | 6 | 441.4.c.b.440.8 | yes | 24 | ||
21.17 | even | 6 | 441.4.c.b.440.18 | yes | 24 | ||
21.20 | even | 2 | inner | 441.4.p.d.80.21 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.7 | ✓ | 24 | 7.3 | odd | 6 | ||
441.4.c.b.440.8 | yes | 24 | 21.11 | odd | 6 | ||
441.4.c.b.440.17 | yes | 24 | 7.4 | even | 3 | ||
441.4.c.b.440.18 | yes | 24 | 21.17 | even | 6 | ||
441.4.p.d.80.3 | 48 | 1.1 | even | 1 | trivial | ||
441.4.p.d.80.4 | 48 | 7.6 | odd | 2 | inner | ||
441.4.p.d.80.21 | 48 | 21.20 | even | 2 | inner | ||
441.4.p.d.80.22 | 48 | 3.2 | odd | 2 | inner | ||
441.4.p.d.215.3 | 48 | 21.5 | even | 6 | inner | ||
441.4.p.d.215.4 | 48 | 21.2 | odd | 6 | inner | ||
441.4.p.d.215.21 | 48 | 7.2 | even | 3 | inner | ||
441.4.p.d.215.22 | 48 | 7.5 | odd | 6 | inner |