Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.w.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 9.00000 | − | 15.5885i | 0.804984 | − | 1.39427i | −0.111317 | − | 0.993785i | \(-0.535507\pi\) |
0.916302 | − | 0.400489i | \(-0.131160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.0000 | − | 31.1769i | −0.569210 | − | 0.985901i | ||||
\(11\) | −36.0000 | − | 62.3538i | −0.986764 | − | 1.70913i | −0.633817 | − | 0.773483i | \(-0.718513\pi\) |
−0.352947 | − | 0.935643i | \(-0.614820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −34.0000 | −0.725377 | −0.362689 | − | 0.931910i | \(-0.618141\pi\) | ||||
−0.362689 | + | 0.931910i | \(0.618141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.00000 | + | 5.19615i | 0.0428004 | + | 0.0741325i | 0.886632 | − | 0.462476i | \(-0.153039\pi\) |
−0.843832 | + | 0.536608i | \(0.819705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −46.0000 | + | 79.6743i | −0.555428 | + | 0.962029i | 0.442443 | + | 0.896797i | \(0.354112\pi\) |
−0.997870 | + | 0.0652319i | \(0.979221\pi\) | |||||||
\(20\) | −72.0000 | −0.804984 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −144.000 | −1.39550 | ||||||||
\(23\) | −90.0000 | + | 155.885i | −0.815926 | + | 1.41323i | 0.0927351 | + | 0.995691i | \(0.470439\pi\) |
−0.908661 | + | 0.417534i | \(0.862894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | − | 172.339i | −0.796000 | − | 1.37871i | ||||
\(26\) | −34.0000 | + | 58.8897i | −0.256460 | + | 0.444201i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 114.000 | 0.729975 | 0.364987 | − | 0.931012i | \(-0.381073\pi\) | ||||
0.364987 | + | 0.931012i | \(0.381073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.0000 | − | 48.4974i | −0.162224 | − | 0.280980i | 0.773442 | − | 0.633867i | \(-0.218533\pi\) |
−0.935666 | + | 0.352887i | \(0.885200\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0000 | 0.0605289 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.0000 | − | 29.4449i | 0.0755347 | − | 0.130830i | −0.825784 | − | 0.563987i | \(-0.809267\pi\) |
0.901319 | + | 0.433157i | \(0.142600\pi\) | |||||||
\(38\) | 92.0000 | + | 159.349i | 0.392747 | + | 0.680257i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −72.0000 | + | 124.708i | −0.284605 | + | 0.492950i | ||||
\(41\) | −6.00000 | −0.0228547 | −0.0114273 | − | 0.999935i | \(-0.503638\pi\) | ||||
−0.0114273 | + | 0.999935i | \(0.503638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | −144.000 | + | 249.415i | −0.493382 | + | 0.854563i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 180.000 | + | 311.769i | 0.576947 | + | 0.999301i | ||||
\(47\) | 84.0000 | − | 145.492i | 0.260695 | − | 0.451537i | −0.705732 | − | 0.708479i | \(-0.749382\pi\) |
0.966427 | + | 0.256942i | \(0.0827150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −398.000 | −1.12571 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 68.0000 | + | 117.779i | 0.181344 | + | 0.314098i | ||||
\(53\) | 327.000 | + | 566.381i | 0.847489 | + | 1.46789i | 0.883442 | + | 0.468540i | \(0.155220\pi\) |
−0.0359535 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1296.00 | −3.17732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 114.000 | − | 197.454i | 0.258085 | − | 0.447016i | ||||
\(59\) | −246.000 | − | 426.084i | −0.542822 | − | 0.940195i | −0.998741 | − | 0.0501732i | \(-0.984023\pi\) |
0.455919 | − | 0.890021i | \(-0.349311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 125.000 | − | 216.506i | 0.262371 | − | 0.454439i | −0.704501 | − | 0.709703i | \(-0.748829\pi\) |
0.966871 | + | 0.255264i | \(0.0821624\pi\) | |||||||
\(62\) | −112.000 | −0.229420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −306.000 | + | 530.008i | −0.583917 | + | 1.01137i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62.0000 | + | 107.387i | 0.113052 | + | 0.195812i | 0.917000 | − | 0.398888i | \(-0.130604\pi\) |
−0.803947 | + | 0.594701i | \(0.797271\pi\) | |||||||
\(68\) | 12.0000 | − | 20.7846i | 0.0214002 | − | 0.0370662i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36.0000 | −0.0601748 | −0.0300874 | − | 0.999547i | \(-0.509579\pi\) | ||||
−0.0300874 | + | 0.999547i | \(0.509579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −505.000 | − | 874.686i | −0.809668 | − | 1.40239i | −0.913094 | − | 0.407749i | \(-0.866314\pi\) |
0.103426 | − | 0.994637i | \(-0.467020\pi\) | |||||||
\(74\) | −34.0000 | − | 58.8897i | −0.0534111 | − | 0.0925107i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 368.000 | 0.555428 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −28.0000 | + | 48.4974i | −0.0398765 | + | 0.0690682i | −0.885275 | − | 0.465068i | \(-0.846030\pi\) |
0.845398 | + | 0.534136i | \(0.179363\pi\) | |||||||
\(80\) | 144.000 | + | 249.415i | 0.201246 | + | 0.348569i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | + | 10.3923i | −0.00808036 | + | 0.0139956i | ||||
\(83\) | −228.000 | −0.301521 | −0.150761 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150761 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 108.000 | 0.137815 | ||||||||
\(86\) | 164.000 | − | 284.056i | 0.205635 | − | 0.356170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 288.000 | + | 498.831i | 0.348874 | + | 0.604267i | ||||
\(89\) | 195.000 | − | 337.750i | 0.232247 | − | 0.402263i | −0.726222 | − | 0.687460i | \(-0.758726\pi\) |
0.958469 | + | 0.285197i | \(0.0920590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 720.000 | 0.815926 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −168.000 | − | 290.985i | −0.184339 | − | 0.319285i | ||||
\(95\) | 828.000 | + | 1434.14i | 0.894221 | + | 1.54884i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70.0000 | −0.0732724 | −0.0366362 | − | 0.999329i | \(-0.511664\pi\) | ||||
−0.0366362 | + | 0.999329i | \(0.511664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −398.000 | + | 689.356i | −0.398000 | + | 0.689356i | ||||
\(101\) | −675.000 | − | 1169.13i | −0.665000 | − | 1.15181i | −0.979285 | − | 0.202485i | \(-0.935098\pi\) |
0.314285 | − | 0.949329i | \(-0.398235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1000.00 | + | 1732.05i | −0.956630 | + | 1.65693i | −0.226038 | + | 0.974118i | \(0.572577\pi\) |
−0.730592 | + | 0.682814i | \(0.760756\pi\) | |||||||
\(104\) | 272.000 | 0.256460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1308.00 | 1.19853 | ||||||||
\(107\) | 348.000 | − | 602.754i | 0.314415 | − | 0.544583i | −0.664898 | − | 0.746934i | \(-0.731525\pi\) |
0.979313 | + | 0.202351i | \(0.0648582\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 557.000 | + | 964.752i | 0.489458 | + | 0.847766i | 0.999926 | − | 0.0121304i | \(-0.00386131\pi\) |
−0.510468 | + | 0.859897i | \(0.670528\pi\) | |||||||
\(110\) | −1296.00 | + | 2244.74i | −1.12335 | + | 1.94570i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 462.000 | 0.384613 | 0.192307 | − | 0.981335i | \(-0.438403\pi\) | ||||
0.192307 | + | 0.981335i | \(0.438403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1620.00 | + | 2805.92i | 1.31362 | + | 2.27525i | ||||
\(116\) | −228.000 | − | 394.908i | −0.182494 | − | 0.316088i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −984.000 | −0.767666 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1926.50 | + | 3336.80i | −1.44741 | + | 2.50698i | ||||
\(122\) | −250.000 | − | 433.013i | −0.185524 | − | 0.321337i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −112.000 | + | 193.990i | −0.0811121 | + | 0.140490i | ||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1064.00 | 0.743423 | 0.371712 | − | 0.928348i | \(-0.378771\pi\) | ||||
0.371712 | + | 0.928348i | \(0.378771\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 612.000 | + | 1060.02i | 0.412892 | + | 0.715150i | ||||
\(131\) | 90.0000 | − | 155.885i | 0.0600255 | − | 0.103967i | −0.834451 | − | 0.551082i | \(-0.814215\pi\) |
0.894477 | + | 0.447115i | \(0.147548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 248.000 | 0.159880 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.0000 | − | 41.5692i | −0.0151322 | − | 0.0262098i | ||||
\(137\) | −1359.00 | − | 2353.86i | −0.847498 | − | 1.46791i | −0.883434 | − | 0.468555i | \(-0.844775\pi\) |
0.0359363 | − | 0.999354i | \(-0.488559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1348.00 | −0.822560 | −0.411280 | − | 0.911509i | \(-0.634918\pi\) | ||||
−0.411280 | + | 0.911509i | \(0.634918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −36.0000 | + | 62.3538i | −0.0212750 | + | 0.0368494i | ||||
\(143\) | 1224.00 | + | 2120.03i | 0.715776 | + | 1.23976i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1026.00 | − | 1777.08i | 0.587618 | − | 1.01778i | ||||
\(146\) | −2020.00 | −1.14504 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −136.000 | −0.0755347 | ||||||||
\(149\) | 279.000 | − | 483.242i | 0.153400 | − | 0.265696i | −0.779075 | − | 0.626930i | \(-0.784311\pi\) |
0.932475 | + | 0.361234i | \(0.117644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −964.000 | − | 1669.70i | −0.519531 | − | 0.899854i | −0.999742 | − | 0.0227014i | \(-0.992773\pi\) |
0.480211 | − | 0.877153i | \(-0.340560\pi\) | |||||||
\(152\) | 368.000 | − | 637.395i | 0.196373 | − | 0.340129i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1205.00 | + | 2087.12i | 0.612544 | + | 1.06096i | 0.990810 | + | 0.135261i | \(0.0431873\pi\) |
−0.378266 | + | 0.925697i | \(0.623479\pi\) | |||||||
\(158\) | 56.0000 | + | 96.9948i | 0.0281970 | + | 0.0488386i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 576.000 | 0.284605 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −370.000 | + | 640.859i | −0.177795 | + | 0.307951i | −0.941125 | − | 0.338058i | \(-0.890230\pi\) |
0.763330 | + | 0.646009i | \(0.223563\pi\) | |||||||
\(164\) | 12.0000 | + | 20.7846i | 0.00571367 | + | 0.00989637i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −228.000 | + | 394.908i | −0.106604 | + | 0.184643i | ||||
\(167\) | −3984.00 | −1.84605 | −0.923027 | − | 0.384734i | \(-0.874293\pi\) | ||||
−0.923027 | + | 0.384734i | \(0.874293\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 108.000 | − | 187.061i | 0.0487248 | − | 0.0843939i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −328.000 | − | 568.113i | −0.145406 | − | 0.251850i | ||||
\(173\) | −519.000 | + | 898.934i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1152.00 | 0.493382 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −390.000 | − | 675.500i | −0.164223 | − | 0.284443i | ||||
\(179\) | −1284.00 | − | 2223.95i | −0.536149 | − | 0.928637i | −0.999107 | − | 0.0422569i | \(-0.986545\pi\) |
0.462958 | − | 0.886380i | \(-0.346788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2698.00 | −1.10796 | −0.553980 | − | 0.832530i | \(-0.686892\pi\) | ||||
−0.553980 | + | 0.832530i | \(0.686892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 720.000 | − | 1247.08i | 0.288473 | − | 0.499651i | ||||
\(185\) | −306.000 | − | 530.008i | −0.121608 | − | 0.210632i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 216.000 | − | 374.123i | 0.0844678 | − | 0.146303i | ||||
\(188\) | −672.000 | −0.260695 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3312.00 | 1.26462 | ||||||||
\(191\) | −2058.00 | + | 3564.56i | −0.779642 | + | 1.35038i | 0.152506 | + | 0.988303i | \(0.451266\pi\) |
−0.932148 | + | 0.362077i | \(0.882068\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1655.00 | + | 2866.54i | 0.617251 | + | 1.06911i | 0.989985 | + | 0.141172i | \(0.0450872\pi\) |
−0.372734 | + | 0.927938i | \(0.621580\pi\) | |||||||
\(194\) | −70.0000 | + | 121.244i | −0.0259057 | + | 0.0448700i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1278.00 | −0.462202 | −0.231101 | − | 0.972930i | \(-0.574233\pi\) | ||||
−0.231101 | + | 0.972930i | \(0.574233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1468.00 | − | 2542.65i | −0.522933 | − | 0.905747i | −0.999644 | − | 0.0266869i | \(-0.991504\pi\) |
0.476710 | − | 0.879060i | \(-0.341829\pi\) | |||||||
\(200\) | 796.000 | + | 1378.71i | 0.281428 | + | 0.487448i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2700.00 | −0.940452 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54.0000 | + | 93.5307i | −0.0183977 | + | 0.0318657i | ||||
\(206\) | 2000.00 | + | 3464.10i | 0.676440 | + | 1.17163i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 272.000 | − | 471.118i | 0.0906721 | − | 0.157049i | ||||
\(209\) | 6624.00 | 2.19230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3508.00 | −1.14455 | −0.572276 | − | 0.820061i | \(-0.693940\pi\) | ||||
−0.572276 | + | 0.820061i | \(0.693940\pi\) | |||||||
\(212\) | 1308.00 | − | 2265.52i | 0.423744 | − | 0.733947i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −696.000 | − | 1205.51i | −0.222325 | − | 0.385078i | ||||
\(215\) | 1476.00 | − | 2556.51i | 0.468197 | − | 0.810941i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2228.00 | 0.692198 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2592.00 | + | 4489.48i | 0.794330 | + | 1.37582i | ||||
\(221\) | −102.000 | − | 176.669i | −0.0310464 | − | 0.0537740i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1888.00 | −0.566950 | −0.283475 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283475 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 462.000 | − | 800.207i | 0.135981 | − | 0.235527i | ||||
\(227\) | 1782.00 | + | 3086.51i | 0.521037 | + | 0.902463i | 0.999701 | + | 0.0244647i | \(0.00778814\pi\) |
−0.478663 | + | 0.877999i | \(0.658879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −667.000 | + | 1155.28i | −0.192474 | + | 0.333375i | −0.946070 | − | 0.323963i | \(-0.894985\pi\) |
0.753595 | + | 0.657339i | \(0.228318\pi\) | |||||||
\(230\) | 6480.00 | 1.85773 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −912.000 | −0.258085 | ||||||||
\(233\) | 1329.00 | − | 2301.90i | 0.373672 | − | 0.647220i | −0.616455 | − | 0.787390i | \(-0.711432\pi\) |
0.990127 | + | 0.140171i | \(0.0447651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1512.00 | − | 2618.86i | −0.419711 | − | 0.726960i | ||||
\(236\) | −984.000 | + | 1704.34i | −0.271411 | + | 0.470097i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 588.000 | 0.159140 | 0.0795702 | − | 0.996829i | \(-0.474645\pi\) | ||||
0.0795702 | + | 0.996829i | \(0.474645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2845.00 | − | 4927.68i | −0.760426 | − | 1.31710i | −0.942631 | − | 0.333835i | \(-0.891657\pi\) |
0.182206 | − | 0.983260i | \(-0.441676\pi\) | |||||||
\(242\) | 3853.00 | + | 6673.59i | 1.02347 | + | 1.77271i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1000.00 | −0.262371 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1564.00 | − | 2708.93i | 0.402894 | − | 0.697834i | ||||
\(248\) | 224.000 | + | 387.979i | 0.0573549 | + | 0.0993416i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1332.00 | + | 2307.09i | −0.336972 | + | 0.583653i | ||||
\(251\) | −180.000 | −0.0452649 | −0.0226325 | − | 0.999744i | \(-0.507205\pi\) | ||||
−0.0226325 | + | 0.999744i | \(0.507205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12960.0 | 3.22051 | ||||||||
\(254\) | 1064.00 | − | 1842.90i | 0.262840 | − | 0.455252i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2655.00 | − | 4598.59i | 0.644414 | − | 1.11616i | −0.340023 | − | 0.940417i | \(-0.610435\pi\) |
0.984437 | − | 0.175740i | \(-0.0562319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2448.00 | 0.583917 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −180.000 | − | 311.769i | −0.0424444 | − | 0.0735159i | ||||
\(263\) | 414.000 | + | 717.069i | 0.0970659 | + | 0.168123i | 0.910469 | − | 0.413577i | \(-0.135721\pi\) |
−0.813403 | + | 0.581701i | \(0.802388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11772.0 | 2.72886 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 248.000 | − | 429.549i | 0.0565262 | − | 0.0979062i | ||||
\(269\) | −2067.00 | − | 3580.15i | −0.468503 | − | 0.811470i | 0.530849 | − | 0.847466i | \(-0.321873\pi\) |
−0.999352 | + | 0.0359958i | \(0.988540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1484.00 | − | 2570.36i | 0.332644 | − | 0.576157i | −0.650385 | − | 0.759605i | \(-0.725393\pi\) |
0.983029 | + | 0.183448i | \(0.0587259\pi\) | |||||||
\(272\) | −96.0000 | −0.0214002 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5436.00 | −1.19854 | ||||||||
\(275\) | −7164.00 | + | 12408.4i | −1.57093 | + | 2.72093i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2393.00 | + | 4144.80i | 0.519067 | + | 0.899050i | 0.999754 | + | 0.0221579i | \(0.00705366\pi\) |
−0.480688 | + | 0.876892i | \(0.659613\pi\) | |||||||
\(278\) | −1348.00 | + | 2334.80i | −0.290819 | + | 0.503713i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4398.00 | 0.933675 | 0.466838 | − | 0.884343i | \(-0.345393\pi\) | ||||
0.466838 | + | 0.884343i | \(0.345393\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2386.00 | − | 4132.67i | −0.501177 | − | 0.868063i | −0.999999 | − | 0.00135915i | \(-0.999567\pi\) |
0.498822 | − | 0.866704i | \(-0.333766\pi\) | |||||||
\(284\) | 72.0000 | + | 124.708i | 0.0150437 | + | 0.0260565i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4896.00 | 1.01226 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2438.50 | − | 4223.61i | 0.496336 | − | 0.859680i | ||||
\(290\) | −2052.00 | − | 3554.17i | −0.415509 | − | 0.719683i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2020.00 | + | 3498.74i | −0.404834 | + | 0.701193i | ||||
\(293\) | −6522.00 | −1.30041 | −0.650204 | − | 0.759760i | \(-0.725316\pi\) | ||||
−0.650204 | + | 0.759760i | \(0.725316\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8856.00 | −1.74785 | ||||||||
\(296\) | −136.000 | + | 235.559i | −0.0267055 | + | 0.0462553i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −558.000 | − | 966.484i | −0.108470 | − | 0.187876i | ||||
\(299\) | 3060.00 | − | 5300.08i | 0.591854 | − | 1.02512i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3856.00 | −0.734728 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −736.000 | − | 1274.79i | −0.138857 | − | 0.240507i | ||||
\(305\) | −2250.00 | − | 3897.11i | −0.422409 | − | 0.731633i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6244.00 | −1.16079 | −0.580397 | − | 0.814333i | \(-0.697103\pi\) | ||||
−0.580397 | + | 0.814333i | \(0.697103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1008.00 | + | 1745.91i | −0.184679 | + | 0.319874i | ||||
\(311\) | −264.000 | − | 457.261i | −0.0481353 | − | 0.0833727i | 0.840954 | − | 0.541107i | \(-0.181995\pi\) |
−0.889089 | + | 0.457734i | \(0.848661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2915.00 | − | 5048.93i | 0.526407 | − | 0.911765i | −0.473119 | − | 0.880998i | \(-0.656872\pi\) |
0.999527 | − | 0.0307660i | \(-0.00979468\pi\) | |||||||
\(314\) | 4820.00 | 0.866269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 224.000 | 0.0398765 | ||||||||
\(317\) | 2523.00 | − | 4369.96i | 0.447021 | − | 0.774264i | −0.551169 | − | 0.834394i | \(-0.685818\pi\) |
0.998191 | + | 0.0601297i | \(0.0191514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4104.00 | − | 7108.34i | −0.720313 | − | 1.24762i | ||||
\(320\) | 576.000 | − | 997.661i | 0.100623 | − | 0.174284i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −552.000 | −0.0950901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3383.00 | + | 5859.53i | 0.577400 | + | 1.00009i | ||||
\(326\) | 740.000 | + | 1281.72i | 0.125720 | + | 0.217754i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 48.0000 | 0.00808036 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2510.00 | − | 4347.45i | 0.416804 | − | 0.721925i | −0.578812 | − | 0.815461i | \(-0.696484\pi\) |
0.995616 | + | 0.0935355i | \(0.0298169\pi\) | |||||||
\(332\) | 456.000 | + | 789.815i | 0.0753803 | + | 0.130562i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3984.00 | + | 6900.49i | −0.652679 | + | 1.13047i | ||||
\(335\) | 2232.00 | 0.364021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7486.00 | −1.21005 | −0.605027 | − | 0.796205i | \(-0.706838\pi\) | ||||
−0.605027 | + | 0.796205i | \(0.706838\pi\) | |||||||
\(338\) | −1041.00 | + | 1803.06i | −0.167523 | + | 0.290159i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −216.000 | − | 374.123i | −0.0344537 | − | 0.0596755i | ||||
\(341\) | −2016.00 | + | 3491.81i | −0.320154 | + | 0.554523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1312.00 | −0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1038.00 | + | 1797.87i | 0.161281 | + | 0.279347i | ||||
\(347\) | −5016.00 | − | 8687.97i | −0.776003 | − | 1.34408i | −0.934229 | − | 0.356673i | \(-0.883911\pi\) |
0.158226 | − | 0.987403i | \(-0.449422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5942.00 | 0.911370 | 0.455685 | − | 0.890141i | \(-0.349394\pi\) | ||||
0.455685 | + | 0.890141i | \(0.349394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1152.00 | − | 1995.32i | 0.174437 | − | 0.302134i | ||||
\(353\) | −45.0000 | − | 77.9423i | −0.00678501 | − | 0.0117520i | 0.862613 | − | 0.505864i | \(-0.168826\pi\) |
−0.869398 | + | 0.494113i | \(0.835493\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −324.000 | + | 561.184i | −0.0484398 | + | 0.0839002i | ||||
\(356\) | −1560.00 | −0.232247 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5136.00 | −0.758229 | ||||||||
\(359\) | 5298.00 | − | 9176.41i | 0.778880 | − | 1.34906i | −0.153708 | − | 0.988116i | \(-0.549122\pi\) |
0.932588 | − | 0.360943i | \(-0.117545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −802.500 | − | 1389.97i | −0.117000 | − | 0.202649i | ||||
\(362\) | −2698.00 | + | 4673.07i | −0.391723 | + | 0.678484i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18180.0 | −2.60708 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2008.00 | − | 3477.96i | −0.285604 | − | 0.494681i | 0.687151 | − | 0.726514i | \(-0.258861\pi\) |
−0.972756 | + | 0.231833i | \(0.925528\pi\) | |||||||
\(368\) | −1440.00 | − | 2494.15i | −0.203981 | − | 0.353306i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1224.00 | −0.171980 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1639.00 | + | 2838.83i | −0.227518 | + | 0.394073i | −0.957072 | − | 0.289851i | \(-0.906394\pi\) |
0.729554 | + | 0.683923i | \(0.239728\pi\) | |||||||
\(374\) | −432.000 | − | 748.246i | −0.0597278 | − | 0.103452i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −672.000 | + | 1163.94i | −0.0921696 | + | 0.159642i | ||||
\(377\) | −3876.00 | −0.529507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4628.00 | 0.627241 | 0.313621 | − | 0.949548i | \(-0.398458\pi\) | ||||
0.313621 | + | 0.949548i | \(0.398458\pi\) | |||||||
\(380\) | 3312.00 | − | 5736.55i | 0.447111 | − | 0.774418i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4116.00 | + | 7129.12i | 0.551290 | + | 0.954863i | ||||
\(383\) | −1440.00 | + | 2494.15i | −0.192116 | + | 0.332755i | −0.945951 | − | 0.324308i | \(-0.894868\pi\) |
0.753835 | + | 0.657064i | \(0.228202\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6620.00 | 0.872925 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 140.000 | + | 242.487i | 0.0183181 | + | 0.0317279i | ||||
\(389\) | 3987.00 | + | 6905.69i | 0.519663 | + | 0.900083i | 0.999739 | + | 0.0228557i | \(0.00727584\pi\) |
−0.480076 | + | 0.877227i | \(0.659391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1080.00 | −0.139688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1278.00 | + | 2213.56i | −0.163413 | + | 0.283040i | ||||
\(395\) | 504.000 | + | 872.954i | 0.0642000 | + | 0.111198i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6173.00 | − | 10691.9i | 0.780388 | − | 1.35167i | −0.151328 | − | 0.988484i | \(-0.548355\pi\) |
0.931716 | − | 0.363188i | \(-0.118312\pi\) | |||||||
\(398\) | −5872.00 | −0.739540 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3184.00 | 0.398000 | ||||||||
\(401\) | 4869.00 | − | 8433.36i | 0.606350 | − | 1.05023i | −0.385487 | − | 0.922713i | \(-0.625966\pi\) |
0.991837 | − | 0.127515i | \(-0.0407002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 952.000 | + | 1648.91i | 0.117674 | + | 0.203817i | ||||
\(404\) | −2700.00 | + | 4676.54i | −0.332500 | + | 0.575907i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2448.00 | −0.298140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 215.000 | + | 372.391i | 0.0259928 | + | 0.0450209i | 0.878729 | − | 0.477321i | \(-0.158392\pi\) |
−0.852736 | + | 0.522342i | \(0.825059\pi\) | |||||||
\(410\) | 108.000 | + | 187.061i | 0.0130091 | + | 0.0225325i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8000.00 | 0.956630 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2052.00 | + | 3554.17i | −0.242720 | + | 0.420403i | ||||
\(416\) | −544.000 | − | 942.236i | −0.0641149 | − | 0.111050i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6624.00 | − | 11473.1i | 0.775097 | − | 1.34251i | ||||
\(419\) | 1812.00 | 0.211270 | 0.105635 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105635 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10690.0 | −1.23753 | −0.618763 | − | 0.785577i | \(-0.712366\pi\) | ||||
−0.618763 | + | 0.785577i | \(0.712366\pi\) | |||||||
\(422\) | −3508.00 | + | 6076.03i | −0.404661 | + | 0.700893i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2616.00 | − | 4531.04i | −0.299633 | − | 0.518979i | ||||
\(425\) | 597.000 | − | 1034.03i | 0.0681382 | − | 0.118019i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2784.00 | −0.314415 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2952.00 | − | 5113.01i | −0.331065 | − | 0.573422i | ||||
\(431\) | −2058.00 | − | 3564.56i | −0.230001 | − | 0.398373i | 0.727807 | − | 0.685782i | \(-0.240540\pi\) |
−0.957808 | + | 0.287409i | \(0.907206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9938.00 | 1.10298 | 0.551489 | − | 0.834182i | \(-0.314060\pi\) | ||||
0.551489 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2228.00 | − | 3859.01i | 0.244729 | − | 0.423883i | ||||
\(437\) | −8280.00 | − | 14341.4i | −0.906376 | − | 1.56989i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −892.000 | + | 1544.99i | −0.0969769 | + | 0.167969i | −0.910432 | − | 0.413659i | \(-0.864251\pi\) |
0.813455 | + | 0.581628i | \(0.197584\pi\) | |||||||
\(440\) | 10368.0 | 1.12335 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −408.000 | −0.0439063 | ||||||||
\(443\) | −5856.00 | + | 10142.9i | −0.628052 | + | 1.08782i | 0.359890 | + | 0.932995i | \(0.382814\pi\) |
−0.987942 | + | 0.154823i | \(0.950519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3510.00 | − | 6079.50i | −0.373910 | − | 0.647631i | ||||
\(446\) | −1888.00 | + | 3270.11i | −0.200447 | + | 0.347185i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7650.00 | −0.804066 | −0.402033 | − | 0.915625i | \(-0.631696\pi\) | ||||
−0.402033 | + | 0.915625i | \(0.631696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 216.000 | + | 374.123i | 0.0225522 | + | 0.0390616i | ||||
\(452\) | −924.000 | − | 1600.41i | −0.0961533 | − | 0.166542i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7128.00 | 0.736858 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1837.00 | + | 3181.78i | −0.188033 | + | 0.325683i | −0.944594 | − | 0.328240i | \(-0.893545\pi\) |
0.756561 | + | 0.653923i | \(0.226878\pi\) | |||||||
\(458\) | 1334.00 | + | 2310.56i | 0.136100 | + | 0.235732i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6480.00 | − | 11223.7i | 0.656808 | − | 1.13762i | ||||
\(461\) | 3102.00 | 0.313394 | 0.156697 | − | 0.987647i | \(-0.449915\pi\) | ||||
0.156697 | + | 0.987647i | \(0.449915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8984.00 | 0.901775 | 0.450888 | − | 0.892581i | \(-0.351108\pi\) | ||||
0.450888 | + | 0.892581i | \(0.351108\pi\) | |||||||
\(464\) | −912.000 | + | 1579.63i | −0.0912468 | + | 0.158044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2658.00 | − | 4603.79i | −0.264226 | − | 0.457653i | ||||
\(467\) | 1806.00 | − | 3128.08i | 0.178954 | − | 0.309958i | −0.762568 | − | 0.646908i | \(-0.776062\pi\) |
0.941523 | + | 0.336950i | \(0.109395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6048.00 | −0.593561 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1968.00 | + | 3408.68i | 0.191916 | + | 0.332409i | ||||
\(473\) | −5904.00 | − | 10226.0i | −0.573924 | − | 0.994066i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18308.0 | 1.76848 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 588.000 | − | 1018.45i | 0.0562646 | − | 0.0974532i | ||||
\(479\) | −4644.00 | − | 8043.64i | −0.442985 | − | 0.767272i | 0.554924 | − | 0.831901i | \(-0.312747\pi\) |
−0.997909 | + | 0.0646283i | \(0.979414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −578.000 | + | 1001.13i | −0.0547911 | + | 0.0949010i | ||||
\(482\) | −11380.0 | −1.07540 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15412.0 | 1.44741 | ||||||||
\(485\) | −630.000 | + | 1091.19i | −0.0589831 | + | 0.102162i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2924.00 | + | 5064.52i | 0.272072 | + | 0.471243i | 0.969392 | − | 0.245517i | \(-0.0789578\pi\) |
−0.697320 | + | 0.716760i | \(0.745624\pi\) | |||||||
\(488\) | −1000.00 | + | 1732.05i | −0.0927620 | + | 0.160669i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5952.00 | 0.547067 | 0.273534 | − | 0.961862i | \(-0.411808\pi\) | ||||
0.273534 | + | 0.961862i | \(0.411808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 342.000 | + | 592.361i | 0.0312432 | + | 0.0541148i | ||||
\(494\) | −3128.00 | − | 5417.85i | −0.284889 | − | 0.493443i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 896.000 | 0.0811121 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5374.00 | + | 9308.04i | −0.482111 | + | 0.835040i | −0.999789 | − | 0.0205349i | \(-0.993463\pi\) |
0.517678 | + | 0.855575i | \(0.326796\pi\) | |||||||
\(500\) | 2664.00 | + | 4614.18i | 0.238275 | + | 0.412705i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −180.000 | + | 311.769i | −0.0160036 | + | 0.0277190i | ||||
\(503\) | 16488.0 | 1.46156 | 0.730779 | − | 0.682614i | \(-0.239157\pi\) | ||||
0.730779 | + | 0.682614i | \(0.239157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24300.0 | −2.14126 | ||||||||
\(506\) | 12960.0 | − | 22447.4i | 1.13862 | − | 1.97215i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2128.00 | − | 3685.80i | −0.185856 | − | 0.321912i | ||||
\(509\) | 7029.00 | − | 12174.6i | 0.612092 | − | 1.06017i | −0.378795 | − | 0.925481i | \(-0.623661\pi\) |
0.990887 | − | 0.134694i | \(-0.0430052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5310.00 | − | 9197.19i | −0.455669 | − | 0.789243i | ||||
\(515\) | 18000.0 | + | 31176.9i | 1.54015 | + | 2.66761i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12096.0 | −1.02898 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2448.00 | − | 4240.06i | 0.206446 | − | 0.357575i | ||||
\(521\) | −7233.00 | − | 12527.9i | −0.608222 | − | 1.05347i | −0.991533 | − | 0.129852i | \(-0.958550\pi\) |
0.383312 | − | 0.923619i | \(-0.374783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9262.00 | + | 16042.3i | −0.774377 | + | 1.34126i | 0.160768 | + | 0.986992i | \(0.448603\pi\) |
−0.935144 | + | 0.354267i | \(0.884730\pi\) | |||||||
\(524\) | −720.000 | −0.0600255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1656.00 | 0.137272 | ||||||||
\(527\) | 168.000 | − | 290.985i | 0.0138865 | − | 0.0240522i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10116.5 | − | 17522.3i | −0.831470 | − | 1.44015i | ||||
\(530\) | 11772.0 | − | 20389.7i | 0.964798 | − | 1.67108i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 204.000 | 0.0165783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6264.00 | − | 10849.6i | −0.506199 | − | 0.876762i | ||||
\(536\) | −496.000 | − | 859.097i | −0.0399700 | − | 0.0692301i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8268.00 | −0.662563 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2179.00 | + | 3774.14i | −0.173165 | + | 0.299931i | −0.939525 | − | 0.342481i | \(-0.888733\pi\) |
0.766359 | + | 0.642412i | \(0.222066\pi\) | |||||||
\(542\) | −2968.00 | − | 5140.73i | −0.235215 | − | 0.407404i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −96.0000 | + | 166.277i | −0.00756611 | + | 0.0131049i | ||||
\(545\) | 20052.0 | 1.57602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2140.00 | −0.167276 | −0.0836378 | − | 0.996496i | \(-0.526654\pi\) | ||||
−0.0836378 | + | 0.996496i | \(0.526654\pi\) | |||||||
\(548\) | −5436.00 | + | 9415.43i | −0.423749 | + | 0.733955i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14328.0 | + | 24816.8i | 1.11081 | + | 1.92399i | ||||
\(551\) | −5244.00 | + | 9082.87i | −0.405448 | + | 0.702257i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9572.00 | 0.734071 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2696.00 | + | 4669.61i | 0.205640 | + | 0.356179i | ||||
\(557\) | 1011.00 | + | 1751.10i | 0.0769074 | + | 0.133208i | 0.901914 | − | 0.431915i | \(-0.142162\pi\) |
−0.825007 | + | 0.565123i | \(0.808829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5576.00 | −0.421896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4398.00 | − | 7617.56i | 0.330104 | − | 0.571757i | ||||
\(563\) | 3678.00 | + | 6370.48i | 0.275327 | + | 0.476881i | 0.970218 | − | 0.242235i | \(-0.0778805\pi\) |
−0.694890 | + | 0.719116i | \(0.744547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4158.00 | − | 7201.87i | 0.309608 | − | 0.536256i | ||||
\(566\) | −9544.00 | −0.708771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 288.000 | 0.0212750 | ||||||||
\(569\) | 5601.00 | − | 9701.22i | 0.412665 | − | 0.714756i | −0.582516 | − | 0.812820i | \(-0.697932\pi\) |
0.995180 | + | 0.0980635i | \(0.0312648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5282.00 | + | 9148.69i | 0.387119 | + | 0.670509i | 0.992061 | − | 0.125760i | \(-0.0401370\pi\) |
−0.604942 | + | 0.796270i | \(0.706804\pi\) | |||||||
\(572\) | 4896.00 | − | 8480.12i | 0.357888 | − | 0.619881i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35820.0 | 2.59791 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9287.00 | + | 16085.6i | 0.670057 | + | 1.16057i | 0.977888 | + | 0.209132i | \(0.0670637\pi\) |
−0.307831 | + | 0.951441i | \(0.599603\pi\) | |||||||
\(578\) | −4877.00 | − | 8447.21i | −0.350963 | − | 0.607885i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8208.00 | −0.587618 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23544.0 | − | 40779.4i | 1.67254 | − | 2.89693i | ||||
\(584\) | 4040.00 | + | 6997.49i | 0.286261 | + | 0.495818i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6522.00 | + | 11296.4i | −0.459763 | + | 0.796334i | ||||
\(587\) | −13188.0 | −0.927303 | −0.463652 | − | 0.886018i | \(-0.653461\pi\) | ||||
−0.463652 | + | 0.886018i | \(0.653461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5152.00 | 0.360415 | ||||||||
\(590\) | −8856.00 | + | 15339.0i | −0.617959 | + | 1.07034i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 272.000 | + | 471.118i | 0.0188837 | + | 0.0327075i | ||||
\(593\) | −11253.0 | + | 19490.8i | −0.779267 | + | 1.34973i | 0.153098 | + | 0.988211i | \(0.451075\pi\) |
−0.932365 | + | 0.361519i | \(0.882258\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2232.00 | −0.153400 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6120.00 | − | 10600.2i | −0.418504 | − | 0.724870i | ||||
\(599\) | 5298.00 | + | 9176.41i | 0.361386 | + | 0.625939i | 0.988189 | − | 0.153238i | \(-0.0489702\pi\) |
−0.626803 | + | 0.779178i | \(0.715637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14618.0 | 0.992148 | 0.496074 | − | 0.868280i | \(-0.334775\pi\) | ||||
0.496074 | + | 0.868280i | \(0.334775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3856.00 | + | 6678.79i | −0.259766 | + | 0.449927i | ||||
\(605\) | 34677.0 | + | 60062.3i | 2.33028 | + | 4.03617i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2584.00 | + | 4475.62i | −0.172786 | + | 0.299275i | −0.939393 | − | 0.342842i | \(-0.888610\pi\) |
0.766607 | + | 0.642117i | \(0.221944\pi\) | |||||||
\(608\) | −2944.00 | −0.196373 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9000.00 | −0.597376 | ||||||||
\(611\) | −2856.00 | + | 4946.74i | −0.189102 | + | 0.327534i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2863.00 | − | 4958.86i | −0.188639 | − | 0.326732i | 0.756158 | − | 0.654389i | \(-0.227074\pi\) |
−0.944797 | + | 0.327657i | \(0.893741\pi\) | |||||||
\(614\) | −6244.00 | + | 10814.9i | −0.410403 | + | 0.710839i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7806.00 | 0.509332 | 0.254666 | − | 0.967029i | \(-0.418035\pi\) | ||||
0.254666 | + | 0.967029i | \(0.418035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9026.00 | + | 15633.5i | 0.586083 | + | 1.01513i | 0.994739 | + | 0.102438i | \(0.0326642\pi\) |
−0.408656 | + | 0.912688i | \(0.634002\pi\) | |||||||
\(620\) | 2016.00 | + | 3491.81i | 0.130588 | + | 0.226185i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1056.00 | −0.0680735 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 449.500 | − | 778.557i | 0.0287680 | − | 0.0498276i | ||||
\(626\) | −5830.00 | − | 10097.9i | −0.372226 | − | 0.644715i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4820.00 | − | 8348.48i | 0.306272 | − | 0.530479i | ||||
\(629\) | 204.000 | 0.0129317 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6208.00 | −0.391659 | −0.195829 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195829 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(632\) | 224.000 | − | 387.979i | 0.0140985 | − | 0.0244193i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5046.00 | − | 8739.93i | −0.316092 | − | 0.547487i | ||||
\(635\) | 9576.00 | − | 16586.1i | 0.598444 | − | 1.03654i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16416.0 | −1.01868 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1152.00 | − | 1995.32i | −0.0711512 | − | 0.123238i | ||||
\(641\) | −10755.0 | − | 18628.2i | −0.662710 | − | 1.14785i | −0.979901 | − | 0.199485i | \(-0.936073\pi\) |
0.317191 | − | 0.948362i | \(-0.397260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11140.0 | −0.683233 | −0.341616 | − | 0.939839i | \(-0.610974\pi\) | ||||
−0.341616 | + | 0.939839i | \(0.610974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −552.000 | + | 956.092i | −0.0336194 | + | 0.0582306i | ||||
\(647\) | 4656.00 | + | 8064.43i | 0.282915 | + | 0.490024i | 0.972102 | − | 0.234561i | \(-0.0753651\pi\) |
−0.689186 | + | 0.724584i | \(0.742032\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17712.0 | + | 30678.1i | −1.07127 | + | 1.85550i | ||||
\(650\) | 13532.0 | 0.816567 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2960.00 | 0.177795 | ||||||||
\(653\) | 2439.00 | − | 4224.47i | 0.146165 | − | 0.253164i | −0.783642 | − | 0.621212i | \(-0.786640\pi\) |
0.929807 | + | 0.368048i | \(0.119974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1620.00 | − | 2805.92i | −0.0966391 | − | 0.167384i | ||||
\(656\) | 48.0000 | − | 83.1384i | 0.00285684 | − | 0.00494819i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9744.00 | 0.575982 | 0.287991 | − | 0.957633i | \(-0.407013\pi\) | ||||
0.287991 | + | 0.957633i | \(0.407013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1495.00 | − | 2589.42i | −0.0879709 | − | 0.152370i | 0.818682 | − | 0.574247i | \(-0.194705\pi\) |
−0.906653 | + | 0.421876i | \(0.861372\pi\) | |||||||
\(662\) | −5020.00 | − | 8694.90i | −0.294725 | − | 0.510478i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1824.00 | 0.106604 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10260.0 | + | 17770.8i | −0.595605 | + | 1.03162i | ||||
\(668\) | 7968.00 | + | 13801.0i | 0.461514 | + | 0.799365i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2232.00 | − | 3865.94i | 0.128701 | − | 0.222917i | ||||
\(671\) | −18000.0 | −1.03559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33266.0 | 1.90536 | 0.952682 | − | 0.303969i | \(-0.0983118\pi\) | ||||
0.952682 | + | 0.303969i | \(0.0983118\pi\) | |||||||
\(674\) | −7486.00 | + | 12966.1i | −0.427819 | + | 0.741004i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2082.00 | + | 3606.13i | 0.118457 | + | 0.205174i | ||||
\(677\) | 2685.00 | − | 4650.56i | 0.152427 | − | 0.264011i | −0.779692 | − | 0.626163i | \(-0.784625\pi\) |
0.932119 | + | 0.362152i | \(0.117958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −864.000 | −0.0487248 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4032.00 | + | 6983.63i | 0.226383 | + | 0.392107i | ||||
\(683\) | 192.000 | + | 332.554i | 0.0107565 | + | 0.0186308i | 0.871354 | − | 0.490656i | \(-0.163243\pi\) |
−0.860597 | + | 0.509286i | \(0.829909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48924.0 | −2.72889 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1312.00 | + | 2272.45i | −0.0727028 | + | 0.125925i | ||||
\(689\) | −11118.0 | − | 19256.9i | −0.614749 | − | 1.06478i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7262.00 | − | 12578.2i | 0.399797 | − | 0.692468i | −0.593904 | − | 0.804536i | \(-0.702414\pi\) |
0.993701 | + | 0.112068i | \(0.0357474\pi\) | |||||||
\(692\) | 4152.00 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20064.0 | −1.09743 | ||||||||
\(695\) | −12132.0 | + | 21013.2i | −0.662148 | + | 1.14687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 31.1769i | −0.000978190 | − | 0.00169428i | ||||
\(698\) | 5942.00 | − | 10291.8i | 0.322218 | − | 0.558098i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24750.0 | −1.33352 | −0.666758 | − | 0.745274i | \(-0.732318\pi\) | ||||
−0.666758 | + | 0.745274i | \(0.732318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1564.00 | + | 2708.93i | 0.0839081 | + | 0.145333i | ||||
\(704\) | −2304.00 | − | 3990.65i | −0.123346 | − | 0.213641i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −180.000 | −0.00959545 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 521.000 | − | 902.398i | 0.0275974 | − | 0.0478001i | −0.851897 | − | 0.523710i | \(-0.824548\pi\) |
0.879494 | + | 0.475909i | \(0.157881\pi\) | |||||||
\(710\) | 648.000 | + | 1122.37i | 0.0342521 | + | 0.0593264i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1560.00 | + | 2702.00i | −0.0821116 | + | 0.142221i | ||||
\(713\) | 10080.0 | 0.529452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44064.0 | 2.30476 | ||||||||
\(716\) | −5136.00 | + | 8895.81i | −0.268074 | + | 0.464319i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10596.0 | − | 18352.8i | −0.550751 | − | 0.953929i | ||||
\(719\) | −18480.0 | + | 32008.3i | −0.958536 | + | 1.66023i | −0.232477 | + | 0.972602i | \(0.574683\pi\) |
−0.726059 | + | 0.687632i | \(0.758650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3210.00 | −0.165462 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5396.00 | + | 9346.15i | 0.276990 | + | 0.479761i | ||||
\(725\) | −11343.0 | − | 19646.7i | −0.581060 | − | 1.00643i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16288.0 | −0.830933 | −0.415467 | − | 0.909608i | \(-0.636382\pi\) | ||||
−0.415467 | + | 0.909608i | \(0.636382\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18180.0 | + | 31488.7i | −0.921742 | + | 1.59650i | ||||
\(731\) | 492.000 | + | 852.169i | 0.0248937 | + | 0.0431171i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3905.00 | − | 6763.66i | 0.196773 | − | 0.340820i | −0.750707 | − | 0.660635i | \(-0.770287\pi\) |
0.947480 | + | 0.319814i | \(0.103621\pi\) | |||||||
\(734\) | −8032.00 | −0.403905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5760.00 | −0.288473 | ||||||||
\(737\) | 4464.00 | − | 7731.87i | 0.223112 | − | 0.386441i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18350.0 | + | 31783.1i | 0.913418 | + | 1.58209i | 0.809202 | + | 0.587531i | \(0.199900\pi\) |
0.104216 | + | 0.994555i | \(0.466767\pi\) | |||||||
\(740\) | −1224.00 | + | 2120.03i | −0.0608042 | + | 0.105316i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29508.0 | −1.45699 | −0.728495 | − | 0.685051i | \(-0.759780\pi\) | ||||
−0.728495 | + | 0.685051i | \(0.759780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5022.00 | − | 8698.36i | −0.246969 | − | 0.427763i | ||||
\(746\) | 3278.00 | + | 5677.66i | 0.160880 | + | 0.278651i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1728.00 | −0.0844678 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7568.00 | − | 13108.2i | 0.367723 | − | 0.636916i | −0.621486 | − | 0.783425i | \(-0.713471\pi\) |
0.989209 | + | 0.146510i | \(0.0468040\pi\) | |||||||
\(752\) | 1344.00 | + | 2327.88i | 0.0651737 | + | 0.112884i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3876.00 | + | 6713.43i | −0.187209 | + | 0.324256i | ||||
\(755\) | −34704.0 | −1.67286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3422.00 | 0.164299 | 0.0821497 | − | 0.996620i | \(-0.473821\pi\) | ||||
0.0821497 | + | 0.996620i | \(0.473821\pi\) | |||||||
\(758\) | 4628.00 | − | 8015.93i | 0.221763 | − | 0.384105i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6624.00 | − | 11473.1i | −0.316155 | − | 0.547596i | ||||
\(761\) | 15723.0 | − | 27233.0i | 0.748960 | − | 1.29724i | −0.199362 | − | 0.979926i | \(-0.563887\pi\) |
0.948322 | − | 0.317310i | \(-0.102780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16464.0 | 0.779642 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2880.00 | + | 4988.31i | 0.135847 | + | 0.235294i | ||||
\(767\) | 8364.00 | + | 14486.9i | 0.393750 | + | 0.681996i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18718.0 | −0.877748 | −0.438874 | − | 0.898549i | \(-0.644623\pi\) | ||||
−0.438874 | + | 0.898549i | \(0.644623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6620.00 | − | 11466.2i | 0.308626 | − | 0.534555i | ||||
\(773\) | −843.000 | − | 1460.12i | −0.0392246 | − | 0.0679390i | 0.845747 | − | 0.533585i | \(-0.179155\pi\) |
−0.884971 | + | 0.465646i | \(0.845822\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5572.00 | + | 9650.99i | −0.258261 | + | 0.447321i | ||||
\(776\) | 560.000 | 0.0259057 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15948.0 | 0.734915 | ||||||||
\(779\) | 276.000 | − | 478.046i | 0.0126941 | − | 0.0219869i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1296.00 | + | 2244.74i | 0.0593784 | + | 0.102846i | ||||
\(782\) | −1080.00 | + | 1870.61i | −0.0493871 | + | 0.0855410i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43380.0 | 1.97235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2746.00 | − | 4756.21i | −0.124377 | − | 0.215426i | 0.797113 | − | 0.603831i | \(-0.206360\pi\) |
−0.921489 | + | 0.388404i | \(0.873026\pi\) | |||||||
\(788\) | 2556.00 | + | 4427.12i | 0.115550 | + | 0.200139i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2016.00 | 0.0907925 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4250.00 | + | 7361.22i | −0.190318 | + | 0.329640i | ||||
\(794\) | −12346.0 | − | 21383.9i | −0.551818 | − | 0.955776i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5872.00 | + | 10170.6i | −0.261467 | + | 0.452874i | ||||
\(797\) | 17310.0 | 0.769325 | 0.384662 | − | 0.923057i | \(-0.374318\pi\) | ||||
0.384662 | + | 0.923057i | \(0.374318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1008.00 | 0.0446314 | ||||||||
\(800\) | 3184.00 | − | 5514.85i | 0.140714 | − | 0.243724i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9738.00 | − | 16866.7i | −0.428754 | − | 0.742624i | ||||
\(803\) | −36360.0 | + | 62977.4i | −1.59790 | + | 2.76765i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3808.00 | 0.166416 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5400.00 | + | 9353.07i | 0.235113 | + | 0.407228i | ||||
\(809\) | 17877.0 | + | 30963.9i | 0.776912 | + | 1.34565i | 0.933714 | + | 0.358021i | \(0.116548\pi\) |
−0.156801 | + | 0.987630i | \(0.550118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33644.0 | 1.45672 | 0.728360 | − | 0.685194i | \(-0.240283\pi\) | ||||
0.728360 | + | 0.685194i | \(0.240283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2448.00 | + | 4240.06i | −0.105408 | + | 0.182573i | ||||
\(815\) | 6660.00 | + | 11535.5i | 0.286245 | + | 0.495791i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7544.00 | + | 13066.6i | −0.323049 | + | 0.559538i | ||||
\(818\) | 860.000 | 0.0367594 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 432.000 | 0.0183977 | ||||||||
\(821\) | 14367.0 | − | 24884.4i | 0.610733 | − | 1.05782i | −0.380384 | − | 0.924829i | \(-0.624208\pi\) |
0.991117 | − | 0.132992i | \(-0.0424584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14336.0 | + | 24830.7i | 0.607195 | + | 1.05169i | 0.991700 | + | 0.128570i | \(0.0410387\pi\) |
−0.384505 | + | 0.923123i | \(0.625628\pi\) | |||||||
\(824\) | 8000.00 | − | 13856.4i | 0.338220 | − | 0.585814i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15912.0 | 0.669062 | 0.334531 | − | 0.942385i | \(-0.391422\pi\) | ||||
0.334531 | + | 0.942385i | \(0.391422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8767.00 | − | 15184.9i | −0.367299 | − | 0.636180i | 0.621844 | − | 0.783141i | \(-0.286384\pi\) |
−0.989142 | + | 0.146962i | \(0.953051\pi\) | |||||||
\(830\) | 4104.00 | + | 7108.34i | 0.171629 | + | 0.297270i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2176.00 | −0.0906721 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35856.0 | + | 62104.4i | −1.48605 | + | 2.57391i | ||||
\(836\) | −13248.0 | − | 22946.2i | −0.548076 | − | 0.949296i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1812.00 | − | 3138.48i | 0.0746951 | − | 0.129376i | ||||
\(839\) | −40656.0 | −1.67295 | −0.836473 | − | 0.548009i | \(-0.815386\pi\) | ||||
−0.836473 | + | 0.548009i | \(0.815386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11393.0 | −0.467137 | ||||||||
\(842\) | −10690.0 | + | 18515.6i | −0.437532 | + | 0.757827i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7016.00 | + | 12152.1i | 0.286138 | + | 0.495606i | ||||
\(845\) | −9369.00 | + | 16227.6i | −0.381424 | + | 0.660646i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10464.0 | −0.423744 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1194.00 | − | 2068.07i | −0.0481810 | − | 0.0834520i | ||||
\(851\) | 3060.00 | + | 5300.08i | 0.123261 | + | 0.213495i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23870.0 | 0.958140 | 0.479070 | − | 0.877777i | \(-0.340974\pi\) | ||||
0.479070 | + | 0.877777i | \(0.340974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2784.00 | + | 4822.03i | −0.111163 | + | 0.192539i | ||||
\(857\) | −14805.0 | − | 25643.0i | −0.590116 | − | 1.02211i | −0.994216 | − | 0.107396i | \(-0.965749\pi\) |
0.404101 | − | 0.914715i | \(-0.367585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22742.0 | − | 39390.3i | 0.903314 | − | 1.56459i | 0.0801503 | − | 0.996783i | \(-0.474460\pi\) |
0.823164 | − | 0.567804i | \(-0.192207\pi\) | |||||||
\(860\) | −11808.0 | −0.468197 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8232.00 | −0.325270 | ||||||||
\(863\) | 23082.0 | − | 39979.2i | 0.910452 | − | 1.57695i | 0.0970261 | − | 0.995282i | \(-0.469067\pi\) |
0.813426 | − | 0.581668i | \(-0.197600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9342.00 | + | 16180.8i | 0.367211 | + | 0.636028i | ||||
\(866\) | 9938.00 | − | 17213.1i | 0.389962 | − | 0.675434i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4032.00 | 0.157395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2108.00 | − | 3651.16i | −0.0820056 | − | 0.142038i | ||||
\(872\) | −4456.00 | − | 7718.02i | −0.173050 | − | 0.299731i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −33120.0 | −1.28181 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1493.00 | − | 2585.95i | 0.0574858 | − | 0.0995683i | −0.835850 | − | 0.548957i | \(-0.815025\pi\) |
0.893336 | + | 0.449389i | \(0.148358\pi\) | |||||||
\(878\) | 1784.00 | + | 3089.98i | 0.0685730 | + | 0.118772i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10368.0 | − | 17957.9i | 0.397165 | − | 0.687910i | ||||
\(881\) | −6534.00 | −0.249871 | −0.124935 | − | 0.992165i | \(-0.539872\pi\) | ||||
−0.124935 | + | 0.992165i | \(0.539872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29756.0 | 1.13405 | 0.567027 | − | 0.823699i | \(-0.308094\pi\) | ||||
0.567027 | + | 0.823699i | \(0.308094\pi\) | |||||||
\(884\) | −408.000 | + | 706.677i | −0.0155232 | + | 0.0268870i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11712.0 | + | 20285.8i | 0.444100 | + | 0.769203i | ||||
\(887\) | 14976.0 | − | 25939.2i | 0.566905 | − | 0.981909i | −0.429964 | − | 0.902846i | \(-0.641474\pi\) |
0.996870 | − | 0.0790627i | \(-0.0251927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14040.0 | −0.528789 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3776.00 | + | 6540.22i | 0.141737 | + | 0.245497i | ||||
\(893\) | 7728.00 | + | 13385.3i | 0.289594 | + | 0.501592i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46224.0 | −1.72637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7650.00 | + | 13250.2i | −0.284280 | + | 0.492388i | ||||
\(899\) | −3192.00 | − | 5528.71i | −0.118420 | − | 0.205109i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1962.00 | + | 3398.28i | −0.0725457 | + | 0.125653i | ||||
\(902\) | 864.000 | 0.0318936 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3696.00 | −0.135981 | ||||||||
\(905\) | −24282.0 | + | 42057.7i | −0.891891 | + | 1.54480i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18134.0 | + | 31409.0i | 0.663869 | + | 1.14986i | 0.979591 | + | 0.201004i | \(0.0644203\pi\) |
−0.315721 | + | 0.948852i | \(0.602246\pi\) | |||||||
\(908\) | 7128.00 | − | 12346.1i | 0.260519 | − | 0.451232i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23604.0 | 0.858436 | 0.429218 | − | 0.903201i | \(-0.358789\pi\) | ||||
0.429218 | + | 0.903201i | \(0.358789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8208.00 | + | 14216.7i | 0.297530 | + | 0.515338i | ||||
\(914\) | 3674.00 | + | 6363.55i | 0.132960 | + | 0.230293i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5336.00 | 0.192474 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17092.0 | + | 29604.2i | −0.613507 | + | 1.06263i | 0.377137 | + | 0.926157i | \(0.376908\pi\) |
−0.990644 | + | 0.136468i | \(0.956425\pi\) | |||||||
\(920\) | −12960.0 | − | 22447.4i | −0.464433 | − | 0.804422i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3102.00 | − | 5372.82i | 0.110801 | − | 0.191914i | ||||
\(923\) | 1224.00 | 0.0436495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6766.00 | −0.240502 | ||||||||
\(926\) | 8984.00 | − | 15560.7i | 0.318826 | − | 0.552222i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1824.00 | + | 3159.26i | 0.0645213 | + | 0.111754i | ||||
\(929\) | −26961.0 | + | 46697.8i | −0.952165 | + | 1.64920i | −0.211440 | + | 0.977391i | \(0.567815\pi\) |
−0.740725 | + | 0.671808i | \(0.765518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10632.0 | −0.373672 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3612.00 | − | 6256.17i | −0.126540 | − | 0.219174i | ||||
\(935\) | −3888.00 | − | 6734.21i | −0.135991 | − | 0.235543i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40538.0 | 1.41336 | 0.706680 | − | 0.707533i | \(-0.250192\pi\) | ||||
0.706680 | + | 0.707533i | \(0.250192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6048.00 | + | 10475.4i | −0.209855 | + | 0.363480i | ||||
\(941\) | −1803.00 | − | 3122.89i | −0.0624613 | − | 0.108186i | 0.833104 | − | 0.553117i | \(-0.186562\pi\) |
−0.895565 | + | 0.444931i | \(0.853228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 540.000 | − | 935.307i | 0.0186477 | − | 0.0322988i | ||||
\(944\) | 7872.00 | 0.271411 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23616.0 | −0.811652 | ||||||||
\(947\) | 7032.00 | − | 12179.8i | 0.241298 | − | 0.417941i | −0.719786 | − | 0.694196i | \(-0.755760\pi\) |
0.961084 | + | 0.276255i | \(0.0890935\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17170.0 | + | 29739.3i | 0.587315 | + | 1.01726i | ||||
\(950\) | 18308.0 | − | 31710.4i | 0.625253 | − | 1.08297i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33066.0 | −1.12394 | −0.561969 | − | 0.827158i | \(-0.689956\pi\) | ||||
−0.561969 | + | 0.827158i | \(0.689956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37044.0 | + | 64162.1i | 1.25520 | + | 2.17407i | ||||
\(956\) | −1176.00 | − | 2036.89i | −0.0397851 | − | 0.0689098i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18576.0 | −0.626475 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13327.5 | − | 23083.9i | 0.447367 | − | 0.774862i | ||||
\(962\) | 1156.00 | + | 2002.25i | 0.0387432 | + | 0.0671052i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11380.0 | + | 19710.7i | −0.380213 | + | 0.658548i | ||||
\(965\) | 59580.0 | 1.98751 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26368.0 | −0.876875 | −0.438437 | − | 0.898762i | \(-0.644468\pi\) | ||||
−0.438437 | + | 0.898762i | \(0.644468\pi\) | |||||||
\(968\) | 15412.0 | − | 26694.4i | 0.511736 | − | 0.886353i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1260.00 | + | 2182.38i | 0.0417074 | + | 0.0722393i | ||||
\(971\) | 27942.0 | − | 48397.0i | 0.923482 | − | 1.59952i | 0.129499 | − | 0.991580i | \(-0.458663\pi\) |
0.793984 | − | 0.607939i | \(-0.208003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11696.0 | 0.384768 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2000.00 | + | 3464.10i | 0.0655927 | + | 0.113610i | ||||
\(977\) | −25563.0 | − | 44276.4i | −0.837086 | − | 1.44988i | −0.892321 | − | 0.451402i | \(-0.850924\pi\) |
0.0552350 | − | 0.998473i | \(-0.482409\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28080.0 | −0.916691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5952.00 | − | 10309.2i | 0.193417 | − | 0.335009i | ||||
\(983\) | −7092.00 | − | 12283.7i | −0.230112 | − | 0.398565i | 0.727729 | − | 0.685865i | \(-0.240576\pi\) |
−0.957841 | + | 0.287300i | \(0.907242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11502.0 | + | 19922.0i | −0.372065 | + | 0.644436i | ||||
\(986\) | 1368.00 | 0.0441846 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12512.0 | −0.402894 | ||||||||
\(989\) | −14760.0 | + | 25565.1i | −0.474561 | + | 0.821964i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25840.0 | − | 44756.2i | −0.828289 | − | 1.43464i | −0.899379 | − | 0.437169i | \(-0.855981\pi\) |
0.0710900 | − | 0.997470i | \(-0.477352\pi\) | |||||||
\(992\) | 896.000 | − | 1551.92i | 0.0286774 | − | 0.0496708i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52848.0 | −1.68381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26047.0 | − | 45114.7i | −0.827399 | − | 1.43310i | −0.900072 | − | 0.435741i | \(-0.856486\pi\) |
0.0726730 | − | 0.997356i | \(-0.476847\pi\) | |||||||
\(998\) | 10748.0 | + | 18616.1i | 0.340904 | + | 0.590463i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.g.w.667.1 | 2 | ||
3.2 | odd | 2 | 294.4.e.c.79.1 | 2 | |||
7.2 | even | 3 | 126.4.a.a.1.1 | 1 | |||
7.3 | odd | 6 | 882.4.g.o.361.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.w.361.1 | 2 | ||
7.5 | odd | 6 | 882.4.a.g.1.1 | 1 | |||
7.6 | odd | 2 | 882.4.g.o.667.1 | 2 | |||
21.2 | odd | 6 | 42.4.a.a.1.1 | ✓ | 1 | ||
21.5 | even | 6 | 294.4.a.i.1.1 | 1 | |||
21.11 | odd | 6 | 294.4.e.c.67.1 | 2 | |||
21.17 | even | 6 | 294.4.e.b.67.1 | 2 | |||
21.20 | even | 2 | 294.4.e.b.79.1 | 2 | |||
28.23 | odd | 6 | 1008.4.a.b.1.1 | 1 | |||
84.23 | even | 6 | 336.4.a.l.1.1 | 1 | |||
84.47 | odd | 6 | 2352.4.a.a.1.1 | 1 | |||
105.2 | even | 12 | 1050.4.g.a.799.2 | 2 | |||
105.23 | even | 12 | 1050.4.g.a.799.1 | 2 | |||
105.44 | odd | 6 | 1050.4.a.g.1.1 | 1 | |||
168.107 | even | 6 | 1344.4.a.a.1.1 | 1 | |||
168.149 | odd | 6 | 1344.4.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.a.a.1.1 | ✓ | 1 | 21.2 | odd | 6 | ||
126.4.a.a.1.1 | 1 | 7.2 | even | 3 | |||
294.4.a.i.1.1 | 1 | 21.5 | even | 6 | |||
294.4.e.b.67.1 | 2 | 21.17 | even | 6 | |||
294.4.e.b.79.1 | 2 | 21.20 | even | 2 | |||
294.4.e.c.67.1 | 2 | 21.11 | odd | 6 | |||
294.4.e.c.79.1 | 2 | 3.2 | odd | 2 | |||
336.4.a.l.1.1 | 1 | 84.23 | even | 6 | |||
882.4.a.g.1.1 | 1 | 7.5 | odd | 6 | |||
882.4.g.o.361.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.o.667.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.w.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.w.667.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.4.a.b.1.1 | 1 | 28.23 | odd | 6 | |||
1050.4.a.g.1.1 | 1 | 105.44 | odd | 6 | |||
1050.4.g.a.799.1 | 2 | 105.23 | even | 12 | |||
1050.4.g.a.799.2 | 2 | 105.2 | even | 12 | |||
1344.4.a.a.1.1 | 1 | 168.107 | even | 6 | |||
1344.4.a.o.1.1 | 1 | 168.149 | odd | 6 | |||
2352.4.a.a.1.1 | 1 | 84.47 | odd | 6 |