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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1345})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(-8.91856 + 15.4474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.bf.361.2 |
$q$-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 | ||||
\(5\) | 7.91856 | − | 13.7153i | 0.708258 | − | 1.22674i | −0.257245 | − | 0.966346i | \(-0.582815\pi\) |
0.965503 | − | 0.260392i | \(-0.0838518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.8371 | − | 27.4307i | −0.500814 | − | 0.867435i | ||||
\(11\) | 25.9186 | + | 44.8923i | 0.710431 | + | 1.23050i | 0.964696 | + | 0.263368i | \(0.0848333\pi\) |
−0.254265 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.8371 | −0.828575 | −0.414288 | − | 0.910146i | \(-0.635969\pi\) | ||||
−0.414288 | + | 0.910146i | \(0.635969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −13.6742 | − | 23.6845i | −0.195088 | − | 0.337902i | 0.751842 | − | 0.659344i | \(-0.229166\pi\) |
−0.946929 | + | 0.321442i | \(0.895832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.2557 | − | 66.2608i | 0.461919 | − | 0.800067i | −0.537138 | − | 0.843494i | \(-0.680495\pi\) |
0.999057 | + | 0.0434278i | \(0.0138279\pi\) | |||||||
\(20\) | −63.3485 | −0.708258 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 103.674 | 1.00470 | ||||||||
\(23\) | 73.6742 | − | 127.608i | 0.667919 | − | 1.15687i | −0.310566 | − | 0.950552i | \(-0.600519\pi\) |
0.978485 | − | 0.206318i | \(-0.0661482\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −62.9072 | − | 108.958i | −0.503258 | − | 0.871668i | ||||
\(26\) | −38.8371 | + | 67.2679i | −0.292946 | + | 0.507397i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −240.208 | −1.53812 | −0.769061 | − | 0.639175i | \(-0.779276\pi\) | ||||
−0.769061 | + | 0.639175i | \(0.779276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −148.337 | − | 256.927i | −0.859424 | − | 1.48857i | −0.872480 | − | 0.488651i | \(-0.837489\pi\) |
0.0130559 | − | 0.999915i | \(-0.495844\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −54.6970 | −0.275896 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 80.7670 | − | 139.893i | 0.358865 | − | 0.621573i | −0.628906 | − | 0.777481i | \(-0.716497\pi\) |
0.987772 | + | 0.155908i | \(0.0498304\pi\) | |||||||
\(38\) | −76.5114 | − | 132.522i | −0.326626 | − | 0.565733i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −63.3485 | + | 109.723i | −0.250407 | + | 0.433717i | ||||
\(41\) | −102.977 | −0.392252 | −0.196126 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196126 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −328.557 | −1.16522 | −0.582610 | − | 0.812752i | \(-0.697968\pi\) | ||||
−0.582610 | + | 0.812752i | \(0.697968\pi\) | |||||||
\(44\) | 103.674 | − | 179.569i | 0.355215 | − | 0.615251i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −147.348 | − | 255.215i | −0.472290 | − | 0.818031i | ||||
\(47\) | −33.9773 | + | 58.8504i | −0.105449 | + | 0.182643i | −0.913921 | − | 0.405891i | \(-0.866961\pi\) |
0.808473 | + | 0.588534i | \(0.200295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −251.629 | −0.711714 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 77.6742 | + | 134.536i | 0.207144 | + | 0.358784i | ||||
\(53\) | −33.2443 | − | 57.5808i | −0.0861596 | − | 0.149233i | 0.819725 | − | 0.572757i | \(-0.194126\pi\) |
−0.905885 | + | 0.423524i | \(0.860793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 820.951 | 2.01267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −240.208 | + | 416.053i | −0.543809 | + | 0.941904i | ||||
\(59\) | 230.964 | + | 400.041i | 0.509643 | + | 0.882728i | 0.999938 | + | 0.0111711i | \(0.00355595\pi\) |
−0.490294 | + | 0.871557i | \(0.663111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 92.6742 | − | 160.516i | 0.194520 | − | 0.336919i | −0.752223 | − | 0.658909i | \(-0.771018\pi\) |
0.946743 | + | 0.321990i | \(0.104352\pi\) | |||||||
\(62\) | −593.348 | −1.21541 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −307.534 | + | 532.665i | −0.586845 | + | 1.01644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −272.604 | − | 472.164i | −0.497073 | − | 0.860956i | 0.502921 | − | 0.864332i | \(-0.332259\pi\) |
−0.999994 | + | 0.00337637i | \(0.998925\pi\) | |||||||
\(68\) | −54.6970 | + | 94.7379i | −0.0975438 | + | 0.168951i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 130.742 | 0.218539 | 0.109270 | − | 0.994012i | \(-0.465149\pi\) | ||||
0.109270 | + | 0.994012i | \(0.465149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.6496 | + | 157.010i | 0.145339 | + | 0.251734i | 0.929499 | − | 0.368824i | \(-0.120239\pi\) |
−0.784160 | + | 0.620558i | \(0.786906\pi\) | |||||||
\(74\) | −161.534 | − | 279.785i | −0.253756 | − | 0.439519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −306.045 | −0.461919 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 204.848 | − | 354.808i | 0.291737 | − | 0.505304i | −0.682483 | − | 0.730901i | \(-0.739100\pi\) |
0.974221 | + | 0.225597i | \(0.0724333\pi\) | |||||||
\(80\) | 126.697 | + | 219.446i | 0.177064 | + | 0.306685i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −102.977 | + | 178.362i | −0.138682 | + | 0.240205i | ||||
\(83\) | 347.928 | 0.460121 | 0.230061 | − | 0.973176i | \(-0.426108\pi\) | ||||
0.230061 | + | 0.973176i | \(0.426108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −433.121 | −0.552689 | ||||||||
\(86\) | −328.557 | + | 569.077i | −0.411967 | + | 0.713548i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −207.348 | − | 359.138i | −0.251175 | − | 0.435048i | ||||
\(89\) | −578.580 | + | 1002.13i | −0.689093 | + | 1.19354i | 0.283038 | + | 0.959109i | \(0.408658\pi\) |
−0.972132 | + | 0.234436i | \(0.924676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −589.394 | −0.667919 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 67.9546 | + | 117.701i | 0.0745636 | + | 0.129148i | ||||
\(95\) | −605.860 | − | 1049.38i | −0.654315 | − | 1.13331i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1618.30 | −1.69395 | −0.846976 | − | 0.531631i | \(-0.821579\pi\) | ||||
−0.846976 | + | 0.531631i | \(0.821579\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −251.629 | + | 435.834i | −0.251629 | + | 0.435834i | ||||
\(101\) | −359.371 | − | 622.449i | −0.354047 | − | 0.613228i | 0.632907 | − | 0.774228i | \(-0.281861\pi\) |
−0.986954 | + | 0.161000i | \(0.948528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −805.790 | + | 1395.67i | −0.770843 | + | 1.33514i | 0.166259 | + | 0.986082i | \(0.446831\pi\) |
−0.937102 | + | 0.349057i | \(0.886502\pi\) | |||||||
\(104\) | 310.697 | 0.292946 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −132.977 | −0.121848 | ||||||||
\(107\) | 467.335 | − | 809.448i | 0.422234 | − | 0.731330i | −0.573924 | − | 0.818909i | \(-0.694580\pi\) |
0.996158 | + | 0.0875784i | \(0.0279128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 598.509 | + | 1036.65i | 0.525934 | + | 0.910944i | 0.999544 | + | 0.0302095i | \(0.00961746\pi\) |
−0.473610 | + | 0.880735i | \(0.657049\pi\) | |||||||
\(110\) | 820.951 | − | 1421.93i | 0.711587 | − | 1.23251i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2384.64 | 1.98521 | 0.992604 | − | 0.121400i | \(-0.0387384\pi\) | ||||
0.992604 | + | 0.121400i | \(0.0387384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1166.79 | − | 2020.94i | −0.946118 | − | 1.63872i | ||||
\(116\) | 480.417 | + | 832.106i | 0.384531 | + | 0.666027i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 923.856 | 0.720744 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −678.044 | + | 1174.41i | −0.509424 | + | 0.882349i | ||||
\(122\) | −185.348 | − | 321.033i | −0.137546 | − | 0.238237i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −593.348 | + | 1027.71i | −0.429712 | + | 0.744283i | ||||
\(125\) | −12.8977 | −0.00922883 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2673.92 | −1.86829 | −0.934143 | − | 0.356898i | \(-0.883834\pi\) | ||||
−0.934143 | + | 0.356898i | \(0.883834\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 615.068 | + | 1065.33i | 0.414962 | + | 0.718735i | ||||
\(131\) | 19.4299 | − | 33.6536i | 0.0129588 | − | 0.0224453i | −0.859473 | − | 0.511181i | \(-0.829208\pi\) |
0.872432 | + | 0.488735i | \(0.162542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1090.42 | −0.702968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 109.394 | + | 189.476i | 0.0689739 | + | 0.119466i | ||||
\(137\) | −384.072 | − | 665.232i | −0.239514 | − | 0.414851i | 0.721061 | − | 0.692872i | \(-0.243655\pi\) |
−0.960575 | + | 0.278021i | \(0.910322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1052.55 | −0.642274 | −0.321137 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321137 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 130.742 | − | 226.453i | 0.0772652 | − | 0.133827i | ||||
\(143\) | −1006.60 | − | 1743.49i | −0.588646 | − | 1.01956i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1902.10 | + | 3294.54i | −1.08939 | + | 1.88687i | ||||
\(146\) | 362.598 | 0.205540 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −646.136 | −0.358865 | ||||||||
\(149\) | 180.489 | − | 312.615i | 0.0992363 | − | 0.171882i | −0.812132 | − | 0.583473i | \(-0.801693\pi\) |
0.911369 | + | 0.411591i | \(0.135027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −774.195 | − | 1340.95i | −0.417239 | − | 0.722679i | 0.578422 | − | 0.815738i | \(-0.303669\pi\) |
−0.995661 | + | 0.0930587i | \(0.970336\pi\) | |||||||
\(152\) | −306.045 | + | 530.086i | −0.163313 | + | 0.282866i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4698.47 | −2.43477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −483.534 | − | 837.506i | −0.245798 | − | 0.425734i | 0.716558 | − | 0.697528i | \(-0.245717\pi\) |
−0.962356 | + | 0.271794i | \(0.912383\pi\) | |||||||
\(158\) | −409.697 | − | 709.616i | −0.206289 | − | 0.357304i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 506.788 | 0.250407 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 663.250 | − | 1148.78i | 0.318710 | − | 0.552022i | −0.661509 | − | 0.749937i | \(-0.730084\pi\) |
0.980219 | + | 0.197915i | \(0.0634170\pi\) | |||||||
\(164\) | 205.955 | + | 356.724i | 0.0980631 | + | 0.169850i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 347.928 | − | 602.629i | 0.162677 | − | 0.281766i | ||||
\(167\) | 1416.70 | 0.656451 | 0.328225 | − | 0.944599i | \(-0.393549\pi\) | ||||
0.328225 | + | 0.944599i | \(0.393549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −688.678 | −0.313463 | ||||||||
\(170\) | −433.121 | + | 750.188i | −0.195405 | + | 0.338452i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 657.114 | + | 1138.15i | 0.291305 | + | 0.504555i | ||||
\(173\) | 518.299 | − | 897.721i | 0.227778 | − | 0.394523i | −0.729371 | − | 0.684118i | \(-0.760187\pi\) |
0.957149 | + | 0.289595i | \(0.0935207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −829.394 | −0.355215 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1157.16 | + | 2004.26i | 0.487263 | + | 0.843964i | ||||
\(179\) | −383.716 | − | 664.615i | −0.160225 | − | 0.277518i | 0.774724 | − | 0.632299i | \(-0.217889\pi\) |
−0.934949 | + | 0.354781i | \(0.884555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3957.71 | 1.62527 | 0.812636 | − | 0.582772i | \(-0.198032\pi\) | ||||
0.812636 | + | 0.582772i | \(0.198032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −589.394 | + | 1020.86i | −0.236145 | + | 0.409015i | ||||
\(185\) | −1279.12 | − | 2215.50i | −0.508338 | − | 0.880468i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 708.833 | − | 1227.74i | 0.277193 | − | 0.480112i | ||||
\(188\) | 271.818 | 0.105449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2423.44 | −0.925341 | ||||||||
\(191\) | −902.648 | + | 1563.43i | −0.341954 | + | 0.592282i | −0.984796 | − | 0.173717i | \(-0.944422\pi\) |
0.642841 | + | 0.765999i | \(0.277756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1685.42 | − | 2919.23i | −0.628597 | − | 1.08876i | −0.987833 | − | 0.155515i | \(-0.950296\pi\) |
0.359237 | − | 0.933247i | \(-0.383037\pi\) | |||||||
\(194\) | −1618.30 | + | 2802.98i | −0.598903 | + | 1.03733i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4612.31 | 1.66809 | 0.834044 | − | 0.551697i | \(-0.186020\pi\) | ||||
0.834044 | + | 0.551697i | \(0.186020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1114.93 | − | 1931.12i | −0.397163 | − | 0.687906i | 0.596212 | − | 0.802827i | \(-0.296672\pi\) |
−0.993375 | + | 0.114921i | \(0.963339\pi\) | |||||||
\(200\) | 503.258 | + | 871.668i | 0.177928 | + | 0.308181i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1437.48 | −0.500698 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −815.432 | + | 1412.37i | −0.277816 | + | 0.481191i | ||||
\(206\) | 1611.58 | + | 2791.34i | 0.545068 | + | 0.944086i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 310.697 | − | 538.143i | 0.103572 | − | 0.179392i | ||||
\(209\) | 3966.13 | 1.31265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 912.614 | 0.297758 | 0.148879 | − | 0.988855i | \(-0.452434\pi\) | ||||
0.148879 | + | 0.988855i | \(0.452434\pi\) | |||||||
\(212\) | −132.977 | + | 230.323i | −0.0430798 | + | 0.0746164i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −934.670 | − | 1618.90i | −0.298564 | − | 0.517129i | ||||
\(215\) | −2601.70 | + | 4506.27i | −0.825276 | + | 1.42942i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2394.04 | 0.743783 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1641.90 | − | 2843.86i | −0.503168 | − | 0.871513i | ||||
\(221\) | 531.068 | + | 919.837i | 0.161645 | + | 0.279977i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4319.47 | 1.29710 | 0.648549 | − | 0.761173i | \(-0.275376\pi\) | ||||
0.648549 | + | 0.761173i | \(0.275376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2384.64 | − | 4130.32i | 0.701877 | − | 1.21569i | ||||
\(227\) | −1030.64 | − | 1785.12i | −0.301349 | − | 0.521951i | 0.675093 | − | 0.737733i | \(-0.264103\pi\) |
−0.976442 | + | 0.215782i | \(0.930770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1737.32 | + | 3009.12i | −0.501332 | + | 0.868333i | 0.498667 | + | 0.866794i | \(0.333823\pi\) |
−0.999999 | + | 0.00153905i | \(0.999510\pi\) | |||||||
\(230\) | −4667.15 | −1.33801 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1921.67 | 0.543809 | ||||||||
\(233\) | 388.049 | − | 672.121i | 0.109107 | − | 0.188979i | −0.806302 | − | 0.591505i | \(-0.798534\pi\) |
0.915409 | + | 0.402525i | \(0.131868\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 538.102 | + | 932.020i | 0.149370 | + | 0.258716i | ||||
\(236\) | 923.856 | − | 1600.17i | 0.254822 | − | 0.441364i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2006.80 | −0.543133 | −0.271567 | − | 0.962420i | \(-0.587542\pi\) | ||||
−0.271567 | + | 0.962420i | \(0.587542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 402.824 | + | 697.711i | 0.107669 | + | 0.186488i | 0.914825 | − | 0.403850i | \(-0.132328\pi\) |
−0.807157 | + | 0.590337i | \(0.798995\pi\) | |||||||
\(242\) | 1356.09 | + | 2348.81i | 0.360217 | + | 0.623915i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −741.394 | −0.194520 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1485.74 | + | 2573.38i | −0.382734 | + | 0.662915i | ||||
\(248\) | 1186.70 | + | 2055.42i | 0.303852 | + | 0.526287i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.8977 | + | 22.3394i | −0.00326289 | + | 0.00565148i | ||||
\(251\) | 1421.78 | 0.357539 | 0.178769 | − | 0.983891i | \(-0.442788\pi\) | ||||
0.178769 | + | 0.983891i | \(0.442788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7638.12 | 1.89804 | ||||||||
\(254\) | −2673.92 | + | 4631.37i | −0.660539 | + | 1.14409i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 732.909 | − | 1269.44i | 0.177890 | − | 0.308114i | −0.763268 | − | 0.646082i | \(-0.776406\pi\) |
0.941157 | + | 0.337968i | \(0.109740\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2460.27 | 0.586845 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −38.8598 | − | 67.3072i | −0.00916324 | − | 0.0158712i | ||||
\(263\) | 3495.69 | + | 6054.72i | 0.819596 | + | 1.41958i | 0.905980 | + | 0.423320i | \(0.139135\pi\) |
−0.0863847 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1052.99 | −0.244093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1090.42 | + | 1888.66i | −0.248537 | + | 0.430478i | ||||
\(269\) | −404.479 | − | 700.578i | −0.0916786 | − | 0.158792i | 0.816539 | − | 0.577290i | \(-0.195890\pi\) |
−0.908218 | + | 0.418498i | \(0.862557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3330.88 | − | 5769.26i | 0.746630 | − | 1.29320i | −0.202799 | − | 0.979220i | \(-0.565004\pi\) |
0.949429 | − | 0.313981i | \(-0.101663\pi\) | |||||||
\(272\) | 437.576 | 0.0975438 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1536.29 | −0.338725 | ||||||||
\(275\) | 3260.93 | − | 5648.09i | 0.715059 | − | 1.23852i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3765.73 | + | 6522.44i | 0.816827 | + | 1.41479i | 0.908009 | + | 0.418951i | \(0.137602\pi\) |
−0.0911823 | + | 0.995834i | \(0.529065\pi\) | |||||||
\(278\) | −1052.55 | + | 1823.07i | −0.227078 | + | 0.393311i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1690.19 | −0.358819 | −0.179410 | − | 0.983774i | \(-0.557419\pi\) | ||||
−0.179410 | + | 0.983774i | \(0.557419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1589.12 | + | 2752.43i | 0.333792 | + | 0.578145i | 0.983252 | − | 0.182251i | \(-0.0583384\pi\) |
−0.649460 | + | 0.760396i | \(0.725005\pi\) | |||||||
\(284\) | −261.485 | − | 452.905i | −0.0546348 | − | 0.0946302i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4026.41 | −0.832470 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2082.53 | − | 3607.05i | 0.423882 | − | 0.734184i | ||||
\(290\) | 3804.21 | + | 6589.08i | 0.770313 | + | 1.33422i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 362.598 | − | 628.039i | 0.0726694 | − | 0.125867i | ||||
\(293\) | −2176.53 | −0.433974 | −0.216987 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7315.61 | 1.44383 | ||||||||
\(296\) | −646.136 | + | 1119.14i | −0.126878 | + | 0.219759i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −360.977 | − | 625.231i | −0.0701706 | − | 0.121539i | ||||
\(299\) | −2861.30 | + | 4955.91i | −0.553421 | + | 0.958554i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3096.78 | −0.590065 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 612.091 | + | 1060.17i | 0.115480 | + | 0.200017i | ||||
\(305\) | −1467.69 | − | 2542.12i | −0.275541 | − | 0.477250i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −623.504 | −0.115913 | −0.0579564 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579564 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4698.47 | + | 8137.98i | −0.860822 | + | 1.49099i | ||||
\(311\) | −233.996 | − | 405.293i | −0.0426647 | − | 0.0738973i | 0.843905 | − | 0.536493i | \(-0.180251\pi\) |
−0.886569 | + | 0.462596i | \(0.846918\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1806.41 | − | 3128.79i | 0.326211 | − | 0.565014i | −0.655546 | − | 0.755156i | \(-0.727561\pi\) |
0.981757 | + | 0.190141i | \(0.0608946\pi\) | |||||||
\(314\) | −1934.14 | −0.347610 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1638.79 | −0.291737 | ||||||||
\(317\) | 2265.87 | − | 3924.60i | 0.401463 | − | 0.695355i | −0.592439 | − | 0.805615i | \(-0.701835\pi\) |
0.993903 | + | 0.110260i | \(0.0351684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6225.85 | − | 10783.5i | −1.09273 | − | 1.89266i | ||||
\(320\) | 506.788 | − | 877.782i | 0.0885322 | − | 0.153342i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2092.47 | −0.360459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2443.13 | + | 4231.63i | 0.416987 | + | 0.722242i | ||||
\(326\) | −1326.50 | − | 2297.57i | −0.225362 | − | 0.390339i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 823.818 | 0.138682 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 618.528 | − | 1071.32i | 0.102711 | − | 0.177901i | −0.810090 | − | 0.586306i | \(-0.800582\pi\) |
0.912801 | + | 0.408405i | \(0.133915\pi\) | |||||||
\(332\) | −695.856 | − | 1205.26i | −0.115030 | − | 0.199238i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1416.70 | − | 2453.79i | 0.232090 | − | 0.401992i | ||||
\(335\) | −8634.53 | −1.40822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1867.83 | −0.301921 | −0.150960 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(338\) | −688.678 | + | 1192.83i | −0.110826 | + | 0.191956i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 866.242 | + | 1500.38i | 0.138172 | + | 0.239322i | ||||
\(341\) | 7689.37 | − | 13318.4i | 1.22112 | − | 2.11505i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2628.45 | 0.411967 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1036.60 | − | 1795.44i | −0.161063 | − | 0.278970i | ||||
\(347\) | −31.6819 | − | 54.8746i | −0.00490136 | − | 0.00848940i | 0.863564 | − | 0.504239i | \(-0.168227\pi\) |
−0.868466 | + | 0.495749i | \(0.834893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1223.79 | −0.187702 | −0.0938508 | − | 0.995586i | \(-0.529918\pi\) | ||||
−0.0938508 | + | 0.995586i | \(0.529918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −829.394 | + | 1436.55i | −0.125588 | + | 0.217524i | ||||
\(353\) | 2257.81 | + | 3910.64i | 0.340428 | + | 0.589638i | 0.984512 | − | 0.175316i | \(-0.0560949\pi\) |
−0.644085 | + | 0.764954i | \(0.722762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1035.29 | − | 1793.18i | 0.154782 | − | 0.268090i | ||||
\(356\) | 4628.64 | 0.689093 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1534.86 | −0.226592 | ||||||||
\(359\) | 1114.25 | − | 1929.93i | 0.163810 | − | 0.283727i | −0.772422 | − | 0.635109i | \(-0.780955\pi\) |
0.936232 | + | 0.351383i | \(0.114288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 502.506 | + | 870.365i | 0.0732622 | + | 0.126894i | ||||
\(362\) | 3957.71 | − | 6854.95i | 0.574620 | − | 0.995271i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2871.26 | 0.411749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −718.670 | − | 1244.77i | −0.102219 | − | 0.177048i | 0.810380 | − | 0.585905i | \(-0.199261\pi\) |
−0.912598 | + | 0.408857i | \(0.865928\pi\) | |||||||
\(368\) | 1178.79 | + | 2041.72i | 0.166980 | + | 0.289217i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5116.47 | −0.718899 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6118.71 | − | 10597.9i | 0.849370 | − | 1.47115i | −0.0324014 | − | 0.999475i | \(-0.510315\pi\) |
0.881771 | − | 0.471677i | \(-0.156351\pi\) | |||||||
\(374\) | −1417.67 | − | 2455.47i | −0.196005 | − | 0.339490i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 271.818 | − | 470.803i | 0.0372818 | − | 0.0645740i | ||||
\(377\) | 9329.00 | 1.27445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10647.0 | −1.44301 | −0.721503 | − | 0.692411i | \(-0.756549\pi\) | ||||
−0.721503 | + | 0.692411i | \(0.756549\pi\) | |||||||
\(380\) | −2423.44 | + | 4197.52i | −0.327157 | + | 0.566653i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1805.30 | + | 3126.86i | 0.241798 | + | 0.418807i | ||||
\(383\) | 3357.41 | − | 5815.20i | 0.447925 | − | 0.775829i | −0.550326 | − | 0.834950i | \(-0.685496\pi\) |
0.998251 | + | 0.0591208i | \(0.0188297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6741.68 | −0.888970 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3236.60 | + | 5605.95i | 0.423488 | + | 0.733503i | ||||
\(389\) | −5326.54 | − | 9225.83i | −0.694258 | − | 1.20249i | −0.970430 | − | 0.241381i | \(-0.922400\pi\) |
0.276173 | − | 0.961108i | \(-0.410934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4029.76 | −0.521211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4612.31 | − | 7988.76i | 0.589758 | − | 1.02149i | ||||
\(395\) | −3244.21 | − | 5619.14i | −0.413250 | − | 0.715771i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1610.52 | − | 2789.50i | 0.203601 | − | 0.352648i | −0.746085 | − | 0.665851i | \(-0.768069\pi\) |
0.949686 | + | 0.313203i | \(0.101402\pi\) | |||||||
\(398\) | −4459.73 | −0.561673 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2013.03 | 0.251629 | ||||||||
\(401\) | 6242.50 | − | 10812.3i | 0.777395 | − | 1.34649i | −0.156043 | − | 0.987750i | \(-0.549874\pi\) |
0.933438 | − | 0.358738i | \(-0.116793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5760.99 | + | 9978.32i | 0.712097 | + | 1.23339i | ||||
\(404\) | −1437.48 | + | 2489.80i | −0.177024 | + | 0.306614i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8373.46 | 1.01980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3518.69 | + | 6094.56i | 0.425399 | + | 0.736813i | 0.996458 | − | 0.0840967i | \(-0.0268004\pi\) |
−0.571059 | + | 0.820909i | \(0.693467\pi\) | |||||||
\(410\) | 1630.86 | + | 2824.74i | 0.196445 | + | 0.340253i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6446.32 | 0.770843 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2755.09 | − | 4771.95i | 0.325884 | − | 0.564448i | ||||
\(416\) | −621.394 | − | 1076.29i | −0.0732364 | − | 0.126849i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3966.13 | − | 6869.54i | 0.464090 | − | 0.803828i | ||||
\(419\) | −1549.66 | −0.180682 | −0.0903410 | − | 0.995911i | \(-0.528796\pi\) | ||||
−0.0903410 | + | 0.995911i | \(0.528796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5531.63 | 0.640369 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(422\) | 912.614 | − | 1580.69i | 0.105273 | − | 0.182339i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 265.955 | + | 460.647i | 0.0304620 | + | 0.0527618i | ||||
\(425\) | −1720.42 | + | 2979.85i | −0.196359 | + | 0.340103i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3738.68 | −0.422234 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5203.39 | + | 9012.54i | 0.583558 | + | 1.01075i | ||||
\(431\) | −1014.97 | − | 1757.97i | −0.113432 | − | 0.196470i | 0.803720 | − | 0.595008i | \(-0.202851\pi\) |
−0.917152 | + | 0.398538i | \(0.869518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 327.739 | 0.0363744 | 0.0181872 | − | 0.999835i | \(-0.494211\pi\) | ||||
0.0181872 | + | 0.999835i | \(0.494211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2394.04 | − | 4146.60i | 0.262967 | − | 0.455472i | ||||
\(437\) | −5636.92 | − | 9763.43i | −0.617049 | − | 1.06876i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3954.34 | − | 6849.12i | 0.429910 | − | 0.744625i | −0.566955 | − | 0.823749i | \(-0.691879\pi\) |
0.996865 | + | 0.0791234i | \(0.0252121\pi\) | |||||||
\(440\) | −6567.61 | −0.711587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2124.27 | 0.228600 | ||||||||
\(443\) | −1460.41 | + | 2529.51i | −0.156628 | + | 0.271288i | −0.933651 | − | 0.358185i | \(-0.883396\pi\) |
0.777023 | + | 0.629473i | \(0.216729\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9163.03 | + | 15870.8i | 0.976111 | + | 1.69067i | ||||
\(446\) | 4319.47 | − | 7481.53i | 0.458593 | − | 0.794307i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10240.2 | 1.07631 | 0.538156 | − | 0.842845i | \(-0.319121\pi\) | ||||
0.538156 | + | 0.842845i | \(0.319121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2669.02 | − | 4622.88i | −0.278668 | − | 0.482668i | ||||
\(452\) | −4769.29 | − | 8260.65i | −0.496302 | − | 0.859620i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4122.57 | −0.426171 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2946.31 | + | 5103.17i | −0.301582 | + | 0.522355i | −0.976494 | − | 0.215543i | \(-0.930848\pi\) |
0.674913 | + | 0.737897i | \(0.264181\pi\) | |||||||
\(458\) | 3474.63 | + | 6018.24i | 0.354495 | + | 0.614004i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4667.15 | + | 8083.74i | −0.473059 | + | 0.819362i | ||||
\(461\) | −12643.4 | −1.27735 | −0.638677 | − | 0.769475i | \(-0.720518\pi\) | ||||
−0.638677 | + | 0.769475i | \(0.720518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15093.2 | 1.51499 | 0.757494 | − | 0.652842i | \(-0.226423\pi\) | ||||
0.757494 | + | 0.652842i | \(0.226423\pi\) | |||||||
\(464\) | 1921.67 | − | 3328.42i | 0.192265 | − | 0.333013i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −776.099 | − | 1344.24i | −0.0771504 | − | 0.133628i | ||||
\(467\) | 1410.12 | − | 2442.39i | 0.139727 | − | 0.242014i | −0.787666 | − | 0.616102i | \(-0.788711\pi\) |
0.927393 | + | 0.374088i | \(0.122044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2152.41 | 0.211241 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1847.71 | − | 3200.33i | −0.180186 | − | 0.312091i | ||||
\(473\) | −8515.72 | − | 14749.7i | −0.827808 | − | 1.43381i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9626.23 | −0.929856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2006.80 | + | 3475.87i | −0.192027 | + | 0.332600i | ||||
\(479\) | 8224.25 | + | 14244.8i | 0.784500 | + | 1.35879i | 0.929297 | + | 0.369332i | \(0.120414\pi\) |
−0.144798 | + | 0.989461i | \(0.546253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3136.76 | + | 5433.03i | −0.297347 | + | 0.515020i | ||||
\(482\) | 1611.30 | 0.152267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5424.35 | 0.509424 | ||||||||
\(485\) | −12814.6 | + | 22195.5i | −1.19975 | + | 2.07804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3165.53 | − | 5482.87i | −0.294546 | − | 0.510169i | 0.680333 | − | 0.732903i | \(-0.261835\pi\) |
−0.974879 | + | 0.222734i | \(0.928502\pi\) | |||||||
\(488\) | −741.394 | + | 1284.13i | −0.0687732 | + | 0.119119i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9286.90 | 0.853588 | 0.426794 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426794 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3284.67 | + | 5689.21i | 0.300069 | + | 0.519735i | ||||
\(494\) | 2971.48 | + | 5146.76i | 0.270634 | + | 0.468752i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4746.79 | 0.429712 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 121.725 | − | 210.835i | 0.0109202 | − | 0.0189143i | −0.860514 | − | 0.509427i | \(-0.829857\pi\) |
0.871434 | + | 0.490513i | \(0.163191\pi\) | |||||||
\(500\) | 25.7954 | + | 44.6789i | 0.00230721 | + | 0.00399620i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1421.78 | − | 2462.60i | 0.126409 | − | 0.218947i | ||||
\(503\) | 8499.30 | 0.753409 | 0.376705 | − | 0.926333i | \(-0.377057\pi\) | ||||
0.376705 | + | 0.926333i | \(0.377057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11382.8 | −1.00303 | ||||||||
\(506\) | 7638.12 | − | 13229.6i | 0.671059 | − | 1.16231i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5347.85 | + | 9262.75i | 0.467072 | + | 0.808992i | ||||
\(509\) | 3841.55 | − | 6653.76i | 0.334526 | − | 0.579416i | −0.648868 | − | 0.760901i | \(-0.724757\pi\) |
0.983394 | + | 0.181485i | \(0.0580904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1465.82 | − | 2538.87i | −0.125787 | − | 0.217869i | ||||
\(515\) | 12761.4 | + | 22103.4i | 1.09191 | + | 1.89124i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3522.57 | −0.299656 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2460.27 | − | 4261.32i | 0.207481 | − | 0.359368i | ||||
\(521\) | 10765.3 | + | 18646.1i | 0.905253 | + | 1.56794i | 0.820578 | + | 0.571535i | \(0.193652\pi\) |
0.0846750 | + | 0.996409i | \(0.473015\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8423.53 | + | 14590.0i | −0.704274 | + | 1.21984i | 0.262679 | + | 0.964883i | \(0.415394\pi\) |
−0.966953 | + | 0.254955i | \(0.917939\pi\) | |||||||
\(524\) | −155.439 | −0.0129588 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13982.8 | 1.15908 | ||||||||
\(527\) | −4056.80 | + | 7026.58i | −0.335326 | + | 0.580802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4772.29 | − | 8265.84i | −0.392232 | − | 0.679366i | ||||
\(530\) | −1052.99 | + | 1823.83i | −0.0862998 | + | 0.149476i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3999.34 | 0.325011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7401.24 | − | 12819.3i | −0.598100 | − | 1.03594i | ||||
\(536\) | 2180.83 | + | 3777.31i | 0.175742 | + | 0.304394i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1617.92 | −0.129653 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8720.02 | + | 15103.5i | −0.692981 | + | 1.20028i | 0.277875 | + | 0.960617i | \(0.410370\pi\) |
−0.970856 | + | 0.239662i | \(0.922963\pi\) | |||||||
\(542\) | −6661.77 | − | 11538.5i | −0.527947 | − | 0.914432i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 437.576 | − | 757.903i | 0.0344870 | − | 0.0597332i | ||||
\(545\) | 18957.3 | 1.48999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11520.7 | 0.900530 | 0.450265 | − | 0.892895i | \(-0.351329\pi\) | ||||
0.450265 | + | 0.892895i | \(0.351329\pi\) | |||||||
\(548\) | −1536.29 | + | 2660.93i | −0.119757 | + | 0.207426i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6521.86 | − | 11296.2i | −0.505623 | − | 0.875765i | ||||
\(551\) | −9189.33 | + | 15916.4i | −0.710488 | + | 1.23060i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15062.9 | 1.15517 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2105.10 | + | 3646.14i | 0.160568 | + | 0.278113i | ||||
\(557\) | 5746.51 | + | 9953.25i | 0.437141 | + | 0.757151i | 0.997468 | − | 0.0711212i | \(-0.0226577\pi\) |
−0.560327 | + | 0.828272i | \(0.689324\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12760.2 | 0.965472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1690.19 | + | 2927.49i | −0.126862 | + | 0.219731i | ||||
\(563\) | −9055.65 | − | 15684.8i | −0.677886 | − | 1.17413i | −0.975616 | − | 0.219483i | \(-0.929563\pi\) |
0.297730 | − | 0.954650i | \(-0.403770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18882.9 | − | 32706.2i | 1.40604 | − | 2.43533i | ||||
\(566\) | 6356.46 | 0.472053 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1045.94 | −0.0772652 | ||||||||
\(569\) | 2208.81 | − | 3825.77i | 0.162738 | − | 0.281871i | −0.773112 | − | 0.634270i | \(-0.781301\pi\) |
0.935850 | + | 0.352399i | \(0.114634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6609.87 | − | 11448.6i | −0.484439 | − | 0.839073i | 0.515401 | − | 0.856949i | \(-0.327643\pi\) |
−0.999840 | + | 0.0178762i | \(0.994310\pi\) | |||||||
\(572\) | −4026.41 | + | 6973.95i | −0.294323 | + | 0.509782i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18538.6 | −1.34454 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8748.20 | − | 15152.3i | −0.631182 | − | 1.09324i | −0.987310 | − | 0.158803i | \(-0.949237\pi\) |
0.356128 | − | 0.934437i | \(-0.384097\pi\) | |||||||
\(578\) | −4165.06 | − | 7214.10i | −0.299730 | − | 0.519147i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15216.8 | 1.08939 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1723.29 | − | 2984.83i | 0.122421 | − | 0.212039i | ||||
\(584\) | −725.197 | − | 1256.08i | −0.0513850 | − | 0.0890015i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2176.53 | + | 3769.87i | −0.153433 | + | 0.265754i | ||||
\(587\) | −4280.53 | −0.300982 | −0.150491 | − | 0.988611i | \(-0.548085\pi\) | ||||
−0.150491 | + | 0.988611i | \(0.548085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22699.0 | −1.58794 | ||||||||
\(590\) | 7315.61 | − | 12671.0i | 0.510473 | − | 0.884165i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1292.27 | + | 2238.28i | 0.0897164 | + | 0.155393i | ||||
\(593\) | 795.466 | − | 1377.79i | 0.0550858 | − | 0.0954114i | −0.837168 | − | 0.546946i | \(-0.815790\pi\) |
0.892253 | + | 0.451535i | \(0.149123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1443.91 | −0.0992363 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5722.59 | + | 9911.82i | 0.391328 | + | 0.677800i | ||||
\(599\) | −6961.42 | − | 12057.5i | −0.474851 | − | 0.822467i | 0.524734 | − | 0.851266i | \(-0.324165\pi\) |
−0.999585 | + | 0.0287997i | \(0.990831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12559.7 | −0.852446 | −0.426223 | − | 0.904618i | \(-0.640156\pi\) | ||||
−0.426223 | + | 0.904618i | \(0.640156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3096.78 | + | 5363.78i | −0.208620 | + | 0.361340i | ||||
\(605\) | 10738.3 | + | 18599.2i | 0.721607 | + | 1.24986i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3839.19 | − | 6649.66i | 0.256718 | − | 0.444648i | −0.708643 | − | 0.705567i | \(-0.750692\pi\) |
0.965361 | + | 0.260919i | \(0.0840256\pi\) | |||||||
\(608\) | 2448.36 | 0.163313 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5870.77 | −0.389673 | ||||||||
\(611\) | 1319.58 | − | 2285.58i | 0.0873723 | − | 0.151333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3079.19 | − | 5333.31i | −0.202883 | − | 0.351403i | 0.746573 | − | 0.665303i | \(-0.231698\pi\) |
−0.949456 | + | 0.313900i | \(0.898364\pi\) | |||||||
\(614\) | −623.504 | + | 1079.94i | −0.0409814 | + | 0.0709818i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8813.12 | −0.575045 | −0.287523 | − | 0.957774i | \(-0.592832\pi\) | ||||
−0.287523 | + | 0.957774i | \(0.592832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11595.0 | + | 20083.1i | 0.752894 | + | 1.30405i | 0.946415 | + | 0.322954i | \(0.104676\pi\) |
−0.193521 | + | 0.981096i | \(0.561991\pi\) | |||||||
\(620\) | 9396.93 | + | 16276.0i | 0.608693 | + | 1.05429i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −935.985 | −0.0603369 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7761.27 | − | 13442.9i | 0.496721 | − | 0.860346i | ||||
\(626\) | −3612.81 | − | 6257.57i | −0.230666 | − | 0.399525i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1934.14 | + | 3350.02i | −0.122899 | + | 0.212867i | ||||
\(629\) | −4417.71 | −0.280041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7936.94 | 0.500736 | 0.250368 | − | 0.968151i | \(-0.419448\pi\) | ||||
0.250368 | + | 0.968151i | \(0.419448\pi\) | |||||||
\(632\) | −1638.79 | + | 2838.46i | −0.103145 | + | 0.178652i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4531.74 | − | 7849.20i | −0.283877 | − | 0.491690i | ||||
\(635\) | −21173.6 | + | 36673.8i | −1.32323 | + | 2.29190i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24903.4 | −1.54535 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1013.58 | − | 1755.56i | −0.0626017 | − | 0.108429i | ||||
\(641\) | 16057.3 | + | 27812.1i | 0.989432 | + | 1.71375i | 0.620286 | + | 0.784376i | \(0.287016\pi\) |
0.369146 | + | 0.929371i | \(0.379650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24786.7 | 1.52021 | 0.760104 | − | 0.649802i | \(-0.225148\pi\) | ||||
0.760104 | + | 0.649802i | \(0.225148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2092.47 | + | 3624.26i | −0.127441 | + | 0.220735i | ||||
\(647\) | −3772.80 | − | 6534.67i | −0.229249 | − | 0.397070i | 0.728337 | − | 0.685219i | \(-0.240294\pi\) |
−0.957586 | + | 0.288149i | \(0.906960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11972.5 | + | 20737.0i | −0.724133 | + | 1.25423i | ||||
\(650\) | 9772.54 | 0.589708 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5306.00 | −0.318710 | ||||||||
\(653\) | −2444.49 | + | 4233.99i | −0.146494 | + | 0.253735i | −0.929929 | − | 0.367738i | \(-0.880132\pi\) |
0.783435 | + | 0.621473i | \(0.213466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −307.714 | − | 532.976i | −0.0183563 | − | 0.0317941i | ||||
\(656\) | 823.818 | − | 1426.89i | 0.0490316 | − | 0.0849251i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25895.9 | −1.53075 | −0.765374 | − | 0.643586i | \(-0.777446\pi\) | ||||
−0.765374 | + | 0.643586i | \(0.777446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4091.68 | + | 7087.00i | 0.240769 | + | 0.417023i | 0.960933 | − | 0.276780i | \(-0.0892672\pi\) |
−0.720165 | + | 0.693803i | \(0.755934\pi\) | |||||||
\(662\) | −1237.06 | − | 2142.65i | −0.0726278 | − | 0.125795i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2783.42 | −0.162677 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17697.2 | + | 30652.4i | −1.02734 | + | 1.77941i | ||||
\(668\) | −2833.39 | − | 4907.58i | −0.164113 | − | 0.284252i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8634.53 | + | 14955.4i | −0.497882 | + | 0.862357i | ||||
\(671\) | 9607.93 | 0.552772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4635.02 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(674\) | −1867.83 | + | 3235.18i | −0.106745 | + | 0.184888i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1377.36 | + | 2385.65i | 0.0783657 | + | 0.135733i | ||||
\(677\) | 12192.9 | − | 21118.7i | 0.692187 | − | 1.19890i | −0.278932 | − | 0.960311i | \(-0.589980\pi\) |
0.971120 | − | 0.238593i | \(-0.0766862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3464.97 | 0.195405 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15378.7 | − | 26636.8i | −0.863464 | − | 1.49556i | ||||
\(683\) | −9196.71 | − | 15929.2i | −0.515230 | − | 0.892405i | −0.999844 | − | 0.0176767i | \(-0.994373\pi\) |
0.484613 | − | 0.874728i | \(-0.338960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12165.2 | −0.678552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2628.45 | − | 4552.62i | 0.145652 | − | 0.252277i | ||||
\(689\) | 1291.11 | + | 2236.27i | 0.0713897 | + | 0.123651i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7449.44 | + | 12902.8i | −0.410116 | + | 0.710341i | −0.994902 | − | 0.100846i | \(-0.967845\pi\) |
0.584786 | + | 0.811187i | \(0.301178\pi\) | |||||||
\(692\) | −4146.39 | −0.227778 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −126.727 | −0.00693157 | ||||||||
\(695\) | −8334.67 | + | 14436.1i | −0.454895 | + | 0.787902i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1408.14 | + | 2438.96i | 0.0765236 | + | 0.132543i | ||||
\(698\) | −1223.79 | + | 2119.66i | −0.0663625 | + | 0.114943i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5725.70 | 0.308497 | 0.154249 | − | 0.988032i | \(-0.450704\pi\) | ||||
0.154249 | + | 0.988032i | \(0.450704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6179.60 | − | 10703.4i | −0.331533 | − | 0.574232i | ||||
\(704\) | 1658.79 | + | 2873.10i | 0.0888039 | + | 0.153813i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9031.23 | 0.481437 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11728.4 | − | 20314.2i | 0.621255 | − | 1.07604i | −0.367998 | − | 0.929827i | \(-0.619957\pi\) |
0.989252 | − | 0.146218i | \(-0.0467101\pi\) | |||||||
\(710\) | −2070.58 | − | 3586.36i | −0.109447 | − | 0.189568i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4628.64 | − | 8017.03i | 0.243631 | − | 0.421982i | ||||
\(713\) | −43714.5 | −2.29610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31883.4 | −1.66765 | ||||||||
\(716\) | −1534.86 | + | 2658.46i | −0.0801125 | + | 0.138759i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2228.49 | − | 3859.86i | −0.115831 | − | 0.200625i | ||||
\(719\) | 4229.50 | − | 7325.71i | 0.219379 | − | 0.379976i | −0.735239 | − | 0.677808i | \(-0.762930\pi\) |
0.954618 | + | 0.297832i | \(0.0962634\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2010.02 | 0.103608 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7915.42 | − | 13709.9i | −0.406318 | − | 0.703763i | ||||
\(725\) | 15110.8 | + | 26172.7i | 0.774072 | + | 1.34073i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11822.2 | 0.603111 | 0.301555 | − | 0.953449i | \(-0.402494\pi\) | ||||
0.301555 | + | 0.953449i | \(0.402494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2871.26 | − | 4973.16i | 0.145575 | − | 0.252144i | ||||
\(731\) | 4492.77 | + | 7781.70i | 0.227320 | + | 0.393730i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2514.48 | − | 4355.20i | 0.126704 | − | 0.219458i | −0.795694 | − | 0.605699i | \(-0.792893\pi\) |
0.922398 | + | 0.386241i | \(0.126227\pi\) | |||||||
\(734\) | −2874.68 | −0.144559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4715.15 | 0.236145 | ||||||||
\(737\) | 14131.0 | − | 24475.6i | 0.706272 | − | 1.22330i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8871.95 | + | 15366.7i | 0.441624 | + | 0.764914i | 0.997810 | − | 0.0661431i | \(-0.0210694\pi\) |
−0.556187 | + | 0.831057i | \(0.687736\pi\) | |||||||
\(740\) | −5116.47 | + | 8861.99i | −0.254169 | + | 0.440234i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13202.3 | 0.651877 | 0.325938 | − | 0.945391i | \(-0.394320\pi\) | ||||
0.325938 | + | 0.945391i | \(0.394320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2858.42 | − | 4950.93i | −0.140570 | − | 0.243474i | ||||
\(746\) | −12237.4 | − | 21195.8i | −0.600595 | − | 1.04026i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5670.67 | −0.277193 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7800.49 | + | 13510.8i | −0.379020 | + | 0.656482i | −0.990920 | − | 0.134453i | \(-0.957072\pi\) |
0.611900 | + | 0.790935i | \(0.290406\pi\) | |||||||
\(752\) | −543.636 | − | 941.606i | −0.0263622 | − | 0.0456607i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9329.00 | − | 16158.3i | 0.450586 | − | 0.780439i | ||||
\(755\) | −24522.0 | −1.18205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2948.08 | 0.141545 | 0.0707725 | − | 0.997492i | \(-0.477454\pi\) | ||||
0.0707725 | + | 0.997492i | \(0.477454\pi\) | |||||||
\(758\) | −10647.0 | + | 18441.1i | −0.510180 | + | 0.883657i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4846.88 | + | 8395.04i | 0.231335 | + | 0.400684i | ||||
\(761\) | −848.515 | + | 1469.67i | −0.0404187 | + | 0.0700073i | −0.885527 | − | 0.464588i | \(-0.846203\pi\) |
0.845108 | + | 0.534595i | \(0.179536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7221.18 | 0.341954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6714.81 | − | 11630.4i | −0.316731 | − | 0.548594i | ||||
\(767\) | −8969.98 | − | 15536.5i | −0.422278 | − | 0.731407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 96.7799 | 0.00453833 | 0.00226916 | − | 0.999997i | \(-0.499278\pi\) | ||||
0.00226916 | + | 0.999997i | \(0.499278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6741.68 | + | 11676.9i | −0.314298 | + | 0.544381i | ||||
\(773\) | −18163.4 | − | 31459.9i | −0.845138 | − | 1.46382i | −0.885501 | − | 0.464637i | \(-0.846185\pi\) |
0.0403629 | − | 0.999185i | \(-0.487149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18662.9 | + | 32325.2i | −0.865023 | + | 1.49826i | ||||
\(776\) | 12946.4 | 0.598903 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21306.2 | −0.981828 | ||||||||
\(779\) | −3939.47 | + | 6823.35i | −0.181189 | + | 0.313828i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3388.66 | + | 5869.32i | 0.155257 | + | 0.268913i | ||||
\(782\) | −4029.76 | + | 6979.74i | −0.184276 | + | 0.319175i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15315.6 | −0.696352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3548.23 | + | 6145.72i | 0.160713 | + | 0.278362i | 0.935124 | − | 0.354319i | \(-0.115287\pi\) |
−0.774412 | + | 0.632682i | \(0.781954\pi\) | |||||||
\(788\) | −9224.62 | − | 15977.5i | −0.417022 | − | 0.722304i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12976.8 | −0.584424 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3599.20 | + | 6234.00i | −0.161174 | + | 0.279162i | ||||
\(794\) | −3221.04 | − | 5579.01i | −0.143968 | − | 0.249360i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4459.73 | + | 7724.47i | −0.198581 | + | 0.343953i | ||||
\(797\) | 40289.6 | 1.79063 | 0.895314 | − | 0.445436i | \(-0.146951\pi\) | ||||
0.895314 | + | 0.445436i | \(0.146951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1858.45 | 0.0822871 | ||||||||
\(800\) | 2013.03 | − | 3486.67i | 0.0889642 | − | 0.154091i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12485.0 | − | 21624.7i | −0.549702 | − | 0.952111i | ||||
\(803\) | −4699.02 | + | 8138.93i | −0.206506 | + | 0.357680i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23043.9 | 1.00706 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2874.97 | + | 4979.59i | 0.125175 | + | 0.216809i | ||||
\(809\) | −5782.98 | − | 10016.4i | −0.251321 | − | 0.435301i | 0.712569 | − | 0.701602i | \(-0.247532\pi\) |
−0.963890 | + | 0.266301i | \(0.914198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18014.2 | −0.779981 | −0.389991 | − | 0.920819i | \(-0.627522\pi\) | ||||
−0.389991 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8373.46 | − | 14503.3i | 0.360552 | − | 0.624495i | ||||
\(815\) | −10504.0 | − | 18193.4i | −0.451458 | − | 0.781948i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12569.2 | + | 21770.4i | −0.538237 | + | 0.932253i | ||||
\(818\) | 14074.8 | 0.601605 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6523.45 | 0.277816 | ||||||||
\(821\) | −8396.22 | + | 14542.7i | −0.356918 | + | 0.618201i | −0.987444 | − | 0.157967i | \(-0.949506\pi\) |
0.630526 | + | 0.776168i | \(0.282839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4409.52 | + | 7637.50i | 0.186763 | + | 0.323483i | 0.944169 | − | 0.329461i | \(-0.106867\pi\) |
−0.757406 | + | 0.652944i | \(0.773534\pi\) | |||||||
\(824\) | 6446.32 | − | 11165.4i | 0.272534 | − | 0.472043i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8250.13 | −0.346898 | −0.173449 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173449 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10775.2 | − | 18663.3i | −0.451435 | − | 0.781909i | 0.547040 | − | 0.837106i | \(-0.315754\pi\) |
−0.998475 | + | 0.0551975i | \(0.982421\pi\) | |||||||
\(830\) | −5510.18 | − | 9543.91i | −0.230435 | − | 0.399125i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2485.58 | −0.103572 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11218.2 | − | 19430.5i | 0.464936 | − | 0.805293i | ||||
\(836\) | −7932.26 | − | 13739.1i | −0.328161 | − | 0.568392i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1549.66 | + | 2684.09i | −0.0638808 | + | 0.110645i | ||||
\(839\) | 30130.4 | 1.23983 | 0.619916 | − | 0.784669i | \(-0.287167\pi\) | ||||
0.619916 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33311.0 | 1.36582 | ||||||||
\(842\) | 5531.63 | − | 9581.07i | 0.226405 | − | 0.392144i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1825.23 | − | 3161.39i | −0.0744395 | − | 0.128933i | ||||
\(845\) | −5453.34 | + | 9445.46i | −0.222012 | + | 0.384537i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1063.82 | 0.0430798 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3440.83 | + | 5959.70i | 0.138847 | + | 0.240489i | ||||
\(851\) | −11900.9 | − | 20613.0i | −0.479386 | − | 0.830321i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40738.6 | 1.63525 | 0.817623 | − | 0.575754i | \(-0.195291\pi\) | ||||
0.817623 | + | 0.575754i | \(0.195291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3738.68 | + | 6475.59i | −0.149282 | + | 0.258564i | ||||
\(857\) | 18254.1 | + | 31617.0i | 0.727594 | + | 1.26023i | 0.957897 | + | 0.287111i | \(0.0926949\pi\) |
−0.230303 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10990.4 | + | 19036.0i | −0.436541 | + | 0.756110i | −0.997420 | − | 0.0717871i | \(-0.977130\pi\) |
0.560879 | + | 0.827897i | \(0.310463\pi\) | |||||||
\(860\) | 20813.6 | 0.825276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4059.86 | −0.160417 | ||||||||
\(863\) | −11713.0 | + | 20287.6i | −0.462012 | + | 0.800228i | −0.999061 | − | 0.0433226i | \(-0.986206\pi\) |
0.537049 | + | 0.843551i | \(0.319539\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8208.37 | − | 14217.3i | −0.322651 | − | 0.558847i | ||||
\(866\) | 327.739 | − | 567.660i | 0.0128603 | − | 0.0222747i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21237.5 | 0.829037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10587.2 | + | 18337.5i | 0.411863 | + | 0.713367i | ||||
\(872\) | −4788.08 | − | 8293.19i | −0.185946 | − | 0.322068i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −22547.7 | −0.872639 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −153.701 | + | 266.217i | −0.00591802 | + | 0.0102503i | −0.868969 | − | 0.494866i | \(-0.835217\pi\) |
0.863051 | + | 0.505116i | \(0.168550\pi\) | |||||||
\(878\) | −7908.68 | − | 13698.2i | −0.303992 | − | 0.526530i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6567.61 | + | 11375.4i | −0.251584 | + | 0.435756i | ||||
\(881\) | −19941.7 | −0.762605 | −0.381302 | − | 0.924450i | \(-0.624524\pi\) | ||||
−0.381302 | + | 0.924450i | \(0.624524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37524.1 | −1.43011 | −0.715056 | − | 0.699068i | \(-0.753599\pi\) | ||||
−0.715056 | + | 0.699068i | \(0.753599\pi\) | |||||||
\(884\) | 2124.27 | − | 3679.35i | 0.0808224 | − | 0.139989i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2920.82 | + | 5059.01i | 0.110753 | + | 0.191829i | ||||
\(887\) | 1440.10 | − | 2494.33i | 0.0545140 | − | 0.0944210i | −0.837481 | − | 0.546467i | \(-0.815972\pi\) |
0.891995 | + | 0.452046i | \(0.149306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36652.1 | 1.38043 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8638.93 | − | 14963.1i | −0.324274 | − | 0.561660i | ||||
\(893\) | 2599.65 | + | 4502.72i | 0.0974176 | + | 0.168732i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12153.9 | −0.453922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10240.2 | − | 17736.5i | 0.380534 | − | 0.659104i | ||||
\(899\) | 35631.8 | + | 61716.1i | 1.32190 | + | 2.28960i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −909.182 | + | 1574.75i | −0.0336174 | + | 0.0582270i | ||||
\(902\) | −10676.1 | −0.394096 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19077.2 | −0.701877 | ||||||||
\(905\) | 31339.4 | − | 54281.4i | 1.15111 | − | 1.99378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9159.62 | − | 15864.9i | −0.335326 | − | 0.580801i | 0.648222 | − | 0.761452i | \(-0.275513\pi\) |
−0.983547 | + | 0.180651i | \(0.942180\pi\) | |||||||
\(908\) | −4122.57 | + | 7140.50i | −0.150674 | + | 0.260975i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46150.7 | −1.67842 | −0.839210 | − | 0.543807i | \(-0.816982\pi\) | ||||
−0.839210 | + | 0.543807i | \(0.816982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9017.79 | + | 15619.3i | 0.326884 | + | 0.566180i | ||||
\(914\) | 5892.63 | + | 10206.3i | 0.213250 | + | 0.369360i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13898.5 | 0.501332 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23632.1 | + | 40932.1i | −0.848261 | + | 1.46923i | 0.0344969 | + | 0.999405i | \(0.489017\pi\) |
−0.882758 | + | 0.469827i | \(0.844316\pi\) | |||||||
\(920\) | 9334.30 | + | 16167.5i | 0.334503 | + | 0.579376i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12643.4 | + | 21899.0i | −0.451613 | + | 0.782217i | ||||
\(923\) | −5077.66 | −0.181076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20323.3 | −0.722407 | ||||||||
\(926\) | 15093.2 | − | 26142.2i | 0.535629 | − | 0.927737i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3843.33 | − | 6656.85i | −0.135952 | − | 0.235476i | ||||
\(929\) | 26635.7 | − | 46134.4i | 0.940678 | − | 1.62930i | 0.176496 | − | 0.984301i | \(-0.443524\pi\) |
0.764182 | − | 0.645001i | \(-0.223143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3104.39 | −0.109107 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2820.23 | − | 4884.79i | −0.0988018 | − | 0.171130i | ||||
\(935\) | −11225.9 | − | 19443.8i | −0.392648 | − | 0.680086i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17197.8 | −0.599602 | −0.299801 | − | 0.954002i | \(-0.596920\pi\) | ||||
−0.299801 | + | 0.954002i | \(0.596920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2152.41 | − | 3728.08i | 0.0746849 | − | 0.129358i | ||||
\(941\) | −14417.4 | − | 24971.7i | −0.499463 | − | 0.865096i | 0.500537 | − | 0.865715i | \(-0.333136\pi\) |
−1.00000 | 0.000619696i | \(0.999803\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7586.77 | + | 13140.7i | −0.261993 | + | 0.453785i | ||||
\(944\) | −7390.85 | −0.254822 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34062.9 | −1.17070 | ||||||||
\(947\) | −25920.6 | + | 44895.8i | −0.889448 | + | 1.54057i | −0.0489180 | + | 0.998803i | \(0.515577\pi\) |
−0.840530 | + | 0.541766i | \(0.817756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3520.57 | − | 6097.81i | −0.120424 | − | 0.208581i | ||||
\(950\) | −9626.23 | + | 16673.1i | −0.328754 | + | 0.569418i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5887.31 | 0.200114 | 0.100057 | − | 0.994982i | \(-0.468097\pi\) | ||||
0.100057 | + | 0.994982i | \(0.468097\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14295.3 | + | 24760.3i | 0.484384 | + | 0.838977i | ||||
\(956\) | 4013.59 | + | 6951.74i | 0.135783 | + | 0.235184i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32897.0 | 1.10945 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29112.3 | + | 50424.0i | −0.977218 | + | 1.69259i | ||||
\(962\) | 6273.52 | + | 10866.1i | 0.210256 | + | 0.364174i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1611.30 | − | 2790.85i | 0.0538344 | − | 0.0932439i | ||||
\(965\) | −53384.4 | −1.78083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36620.0 | −1.21781 | −0.608904 | − | 0.793244i | \(-0.708391\pi\) | ||||
−0.608904 | + | 0.793244i | \(0.708391\pi\) | |||||||
\(968\) | 5424.35 | − | 9395.25i | 0.180109 | − | 0.311957i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25629.2 | + | 44391.1i | 0.848355 | + | 1.46939i | ||||
\(971\) | 21182.4 | − | 36689.1i | 0.700079 | − | 1.21257i | −0.268359 | − | 0.963319i | \(-0.586481\pi\) |
0.968438 | − | 0.249254i | \(-0.0801853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12662.1 | −0.416551 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1482.79 | + | 2568.26i | 0.0486300 | + | 0.0842296i | ||||
\(977\) | 2511.16 | + | 4349.46i | 0.0822304 | + | 0.142427i | 0.904208 | − | 0.427093i | \(-0.140462\pi\) |
−0.821977 | + | 0.569520i | \(0.807129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59983.8 | −1.95821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9286.90 | − | 16085.4i | 0.301789 | − | 0.522714i | ||||
\(983\) | −14146.4 | − | 24502.3i | −0.459003 | − | 0.795016i | 0.539906 | − | 0.841725i | \(-0.318460\pi\) |
−0.998909 | + | 0.0467095i | \(0.985127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36522.9 | − | 63259.4i | 1.18144 | − | 2.04631i | ||||
\(986\) | 13138.7 | 0.424361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11885.9 | 0.382734 | ||||||||
\(989\) | −24206.2 | + | 41926.3i | −0.778273 | + | 1.34801i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18200.5 | − | 31524.2i | −0.583410 | − | 1.01050i | −0.995072 | − | 0.0991586i | \(-0.968385\pi\) |
0.411662 | − | 0.911337i | \(-0.364948\pi\) | |||||||
\(992\) | 4746.79 | − | 8221.68i | 0.151926 | − | 0.263144i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35314.6 | −1.12517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1178.60 | − | 2041.39i | −0.0374389 | − | 0.0648460i | 0.846699 | − | 0.532072i | \(-0.178587\pi\) |
−0.884138 | + | 0.467226i | \(0.845253\pi\) | |||||||
\(998\) | −243.451 | − | 421.669i | −0.00772174 | − | 0.0133745i | ||||
\(999\) | 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.bf.667.2 | 4 | ||
3.2 | odd | 2 | 294.4.e.l.79.1 | 4 | |||
7.2 | even | 3 | 882.4.a.z.1.1 | 2 | |||
7.3 | odd | 6 | 126.4.g.g.109.1 | 4 | |||
7.4 | even | 3 | inner | 882.4.g.bf.361.2 | 4 | ||
7.5 | odd | 6 | 882.4.a.v.1.2 | 2 | |||
7.6 | odd | 2 | 126.4.g.g.37.1 | 4 | |||
21.2 | odd | 6 | 294.4.a.m.1.2 | 2 | |||
21.5 | even | 6 | 294.4.a.n.1.1 | 2 | |||
21.11 | odd | 6 | 294.4.e.l.67.1 | 4 | |||
21.17 | even | 6 | 42.4.e.c.25.2 | ✓ | 4 | ||
21.20 | even | 2 | 42.4.e.c.37.2 | yes | 4 | ||
84.23 | even | 6 | 2352.4.a.ca.1.2 | 2 | |||
84.47 | odd | 6 | 2352.4.a.bq.1.1 | 2 | |||
84.59 | odd | 6 | 336.4.q.j.193.2 | 4 | |||
84.83 | odd | 2 | 336.4.q.j.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.2 | ✓ | 4 | 21.17 | even | 6 | ||
42.4.e.c.37.2 | yes | 4 | 21.20 | even | 2 | ||
126.4.g.g.37.1 | 4 | 7.6 | odd | 2 | |||
126.4.g.g.109.1 | 4 | 7.3 | odd | 6 | |||
294.4.a.m.1.2 | 2 | 21.2 | odd | 6 | |||
294.4.a.n.1.1 | 2 | 21.5 | even | 6 | |||
294.4.e.l.67.1 | 4 | 21.11 | odd | 6 | |||
294.4.e.l.79.1 | 4 | 3.2 | odd | 2 | |||
336.4.q.j.193.2 | 4 | 84.59 | odd | 6 | |||
336.4.q.j.289.2 | 4 | 84.83 | odd | 2 | |||
882.4.a.v.1.2 | 2 | 7.5 | odd | 6 | |||
882.4.a.z.1.1 | 2 | 7.2 | even | 3 | |||
882.4.g.bf.361.2 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.bf.667.2 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.bq.1.1 | 2 | 84.47 | odd | 6 | |||
2352.4.a.ca.1.2 | 2 | 84.23 | even | 6 |