Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.a (trivial) |
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: | yes |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1345}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 336 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(18.8371\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −15.8371 | −1.41652 | −0.708258 | − | 0.705954i | \(-0.750518\pi\) | ||||
−0.708258 | + | 0.705954i | \(0.750518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 31.6742 | 1.00163 | ||||||||
\(11\) | −51.8371 | −1.42086 | −0.710431 | − | 0.703767i | \(-0.751500\pi\) | ||||
−0.710431 | + | 0.703767i | \(0.751500\pi\) | |||||||
\(12\) | 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 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 27.3485 | 0.390175 | 0.195088 | − | 0.980786i | \(-0.437501\pi\) | ||||
0.195088 | + | 0.980786i | \(0.437501\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.5114 | −0.923837 | −0.461919 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461919 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(20\) | −63.3485 | −0.708258 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 103.674 | 1.00470 | ||||||||
\(23\) | −147.348 | −1.33584 | −0.667919 | − | 0.744234i | \(-0.732815\pi\) | ||||
−0.667919 | + | 0.744234i | \(0.732815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.814 | 1.00652 | ||||||||
\(26\) | 77.6742 | 0.585891 | ||||||||
\(27\) | 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 | ||||||||
\(31\) | 296.674 | 1.71885 | 0.859424 | − | 0.511264i | \(-0.170823\pi\) | ||||
0.859424 | + | 0.511264i | \(0.170823\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −54.6970 | −0.275896 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −161.534 | −0.717731 | −0.358865 | − | 0.933389i | \(-0.616836\pi\) | ||||
−0.358865 | + | 0.933389i | \(0.616836\pi\) | |||||||
\(38\) | 153.023 | 0.653252 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 126.697 | 0.500814 | ||||||||
\(41\) | −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 | \(0.697968\pi\) | |||||||
\(44\) | −207.348 | −0.710431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 294.697 | 0.944580 | ||||||||
\(47\) | 67.9546 | 0.210898 | 0.105449 | − | 0.994425i | \(-0.466372\pi\) | ||||
0.105449 | + | 0.994425i | \(0.466372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −251.629 | −0.711714 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −155.348 | −0.414288 | ||||||||
\(53\) | 66.4886 | 0.172319 | 0.0861596 | − | 0.996281i | \(-0.472541\pi\) | ||||
0.0861596 | + | 0.996281i | \(0.472541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 820.951 | 2.01267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 480.417 | 1.08762 | ||||||||
\(59\) | −461.928 | −1.01929 | −0.509643 | − | 0.860386i | \(-0.670223\pi\) | ||||
−0.509643 | + | 0.860386i | \(0.670223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.348 | −0.389040 | −0.194520 | − | 0.980899i | \(-0.562315\pi\) | ||||
−0.194520 | + | 0.980899i | \(0.562315\pi\) | |||||||
\(62\) | −593.348 | −1.21541 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 615.068 | 1.17369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 545.208 | 0.994146 | 0.497073 | − | 0.867709i | \(-0.334408\pi\) | ||||
0.497073 | + | 0.867709i | \(0.334408\pi\) | |||||||
\(68\) | 109.394 | 0.195088 | ||||||||
\(69\) | 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 | ||||||||
\(73\) | −181.299 | −0.290678 | −0.145339 | − | 0.989382i | \(-0.546427\pi\) | ||||
−0.145339 | + | 0.989382i | \(0.546427\pi\) | |||||||
\(74\) | 323.068 | 0.507512 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −306.045 | −0.461919 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −409.697 | −0.583475 | −0.291737 | − | 0.956498i | \(-0.594233\pi\) | ||||
−0.291737 | + | 0.956498i | \(0.594233\pi\) | |||||||
\(80\) | −253.394 | −0.354129 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 205.955 | 0.277364 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 657.114 | 0.823935 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 414.697 | 0.502351 | ||||||||
\(89\) | 1157.16 | 1.37819 | 0.689093 | − | 0.724673i | \(-0.258009\pi\) | ||||
0.689093 | + | 0.724673i | \(0.258009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −589.394 | −0.667919 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −135.909 | −0.149127 | ||||||||
\(95\) | 1211.72 | 1.30863 | ||||||||
\(96\) | 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 | ||||||||
\(100\) | 503.258 | 0.503258 | ||||||||
\(101\) | 718.742 | 0.708094 | 0.354047 | − | 0.935228i | \(-0.384805\pi\) | ||||
0.354047 | + | 0.935228i | \(0.384805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1611.58 | 1.54169 | 0.770843 | − | 0.637025i | \(-0.219835\pi\) | ||||
0.770843 | + | 0.637025i | \(0.219835\pi\) | |||||||
\(104\) | 310.697 | 0.292946 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −132.977 | −0.121848 | ||||||||
\(107\) | −934.670 | −0.844467 | −0.422234 | − | 0.906487i | \(-0.638754\pi\) | ||||
−0.422234 | + | 0.906487i | \(0.638754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1197.02 | −1.05187 | −0.525934 | − | 0.850525i | \(-0.676284\pi\) | ||||
−0.525934 | + | 0.850525i | \(0.676284\pi\) | |||||||
\(110\) | −1641.90 | −1.42317 | ||||||||
\(111\) | 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 | ||||||||
\(115\) | 2333.58 | 1.89224 | ||||||||
\(116\) | −960.833 | −0.769061 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 923.856 | 0.720744 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1356.09 | 1.01885 | ||||||||
\(122\) | 370.697 | 0.275093 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1186.70 | 0.859424 | ||||||||
\(125\) | −12.8977 | −0.00922883 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2673.92 | −1.86829 | −0.934143 | − | 0.356898i | \(-0.883834\pi\) | ||||
−0.934143 | + | 0.356898i | \(0.883834\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1230.14 | −0.829924 | ||||||||
\(131\) | −38.8598 | −0.0259176 | −0.0129588 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129588 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1090.42 | −0.702968 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −218.788 | −0.137948 | ||||||||
\(137\) | 768.144 | 0.479029 | 0.239514 | − | 0.970893i | \(-0.423012\pi\) | ||||
0.239514 | + | 0.970893i | \(0.423012\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −261.485 | −0.154530 | ||||||||
\(143\) | 2013.20 | 1.17729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3804.21 | 2.17877 | ||||||||
\(146\) | 362.598 | 0.205540 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −646.136 | −0.358865 | ||||||||
\(149\) | −360.977 | −0.198473 | −0.0992363 | − | 0.995064i | \(-0.531640\pi\) | ||||
−0.0992363 | + | 0.995064i | \(0.531640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1548.39 | 0.834478 | 0.417239 | − | 0.908797i | \(-0.362998\pi\) | ||||
0.417239 | + | 0.908797i | \(0.362998\pi\) | |||||||
\(152\) | 612.091 | 0.326626 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4698.47 | −2.43477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 967.068 | 0.491595 | 0.245798 | − | 0.969321i | \(-0.420950\pi\) | ||||
0.245798 | + | 0.969321i | \(0.420950\pi\) | |||||||
\(158\) | 819.394 | 0.412579 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 506.788 | 0.250407 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1326.50 | −0.637420 | −0.318710 | − | 0.947852i | \(-0.603250\pi\) | ||||
−0.318710 | + | 0.947852i | \(0.603250\pi\) | |||||||
\(164\) | −411.909 | −0.196126 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −695.856 | −0.325355 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 866.242 | 0.390810 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1314.23 | −0.582610 | ||||||||
\(173\) | −1036.60 | −0.455556 | −0.227778 | − | 0.973713i | \(-0.573146\pi\) | ||||
−0.227778 | + | 0.973713i | \(0.573146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −829.394 | −0.355215 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2314.32 | −0.974525 | ||||||||
\(179\) | 767.432 | 0.320450 | 0.160225 | − | 0.987081i | \(-0.448778\pi\) | ||||
0.160225 | + | 0.987081i | \(0.448778\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | 1178.79 | 0.472290 | ||||||||
\(185\) | 2558.23 | 1.01668 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1417.67 | −0.554385 | ||||||||
\(188\) | 271.818 | 0.105449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2423.44 | −0.925341 | ||||||||
\(191\) | 1805.30 | 0.683909 | 0.341954 | − | 0.939717i | \(-0.388911\pi\) | ||||
0.341954 | + | 0.939717i | \(0.388911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3370.84 | 1.25719 | 0.628597 | − | 0.777731i | \(-0.283630\pi\) | ||||
0.628597 | + | 0.777731i | \(0.283630\pi\) | |||||||
\(194\) | 3236.60 | 1.19781 | ||||||||
\(195\) | 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 | ||||||||
\(199\) | 2229.86 | 0.794326 | 0.397163 | − | 0.917748i | \(-0.369995\pi\) | ||||
0.397163 | + | 0.917748i | \(0.369995\pi\) | |||||||
\(200\) | −1006.52 | −0.355857 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1437.48 | −0.500698 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1630.86 | 0.555631 | ||||||||
\(206\) | −3223.16 | −1.09014 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −621.394 | −0.207144 | ||||||||
\(209\) | 3966.13 | 1.31265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 912.614 | 0.297758 | 0.148879 | − | 0.988855i | \(-0.452434\pi\) | ||||
0.148879 | + | 0.988855i | \(0.452434\pi\) | |||||||
\(212\) | 265.955 | 0.0861596 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1869.34 | 0.597129 | ||||||||
\(215\) | 5203.39 | 1.65055 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2394.04 | 0.743783 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3283.80 | 1.00634 | ||||||||
\(221\) | −1062.14 | −0.323290 | ||||||||
\(222\) | 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 | ||||||||
\(226\) | −4769.29 | −1.40375 | ||||||||
\(227\) | 2061.28 | 0.602697 | 0.301349 | − | 0.953514i | \(-0.402563\pi\) | ||||
0.301349 | + | 0.953514i | \(0.402563\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3474.63 | 1.00266 | 0.501332 | − | 0.865255i | \(-0.332843\pi\) | ||||
0.501332 | + | 0.865255i | \(0.332843\pi\) | |||||||
\(230\) | −4667.15 | −1.33801 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1921.67 | 0.543809 | ||||||||
\(233\) | −776.099 | −0.218214 | −0.109107 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109107 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1076.20 | −0.298740 | ||||||||
\(236\) | −1847.71 | −0.509643 | ||||||||
\(237\) | 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 | ||||||||
\(241\) | −805.648 | −0.215337 | −0.107669 | − | 0.994187i | \(-0.534339\pi\) | ||||
−0.107669 | + | 0.994187i | \(0.534339\pi\) | |||||||
\(242\) | −2712.17 | −0.720435 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −741.394 | −0.194520 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2971.48 | 0.765469 | ||||||||
\(248\) | −2373.39 | −0.607704 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 25.7954 | 0.00652577 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 5347.85 | 1.32108 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1465.82 | −0.355779 | −0.177890 | − | 0.984050i | \(-0.556927\pi\) | ||||
−0.177890 | + | 0.984050i | \(0.556927\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2460.27 | 0.586845 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 77.7197 | 0.0183265 | ||||||||
\(263\) | −6991.39 | −1.63919 | −0.819596 | − | 0.572942i | \(-0.805802\pi\) | ||||
−0.819596 | + | 0.572942i | \(0.805802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1052.99 | −0.244093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2180.83 | 0.497073 | ||||||||
\(269\) | 808.958 | 0.183357 | 0.0916786 | − | 0.995789i | \(-0.470777\pi\) | ||||
0.0916786 | + | 0.995789i | \(0.470777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6661.77 | −1.49326 | −0.746630 | − | 0.665239i | \(-0.768330\pi\) | ||||
−0.746630 | + | 0.665239i | \(0.768330\pi\) | |||||||
\(272\) | 437.576 | 0.0975438 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1536.29 | −0.338725 | ||||||||
\(275\) | −6521.86 | −1.43012 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7531.47 | −1.63365 | −0.816827 | − | 0.576883i | \(-0.804269\pi\) | ||||
−0.816827 | + | 0.576883i | \(0.804269\pi\) | |||||||
\(278\) | 2105.10 | 0.454156 | ||||||||
\(279\) | 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 | ||||||||
\(283\) | −3178.23 | −0.667584 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(284\) | 522.970 | 0.109270 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4026.41 | −0.832470 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4165.06 | −0.847763 | ||||||||
\(290\) | −7608.42 | −1.54063 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −725.197 | −0.145339 | ||||||||
\(293\) | −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 | ||||||||
\(296\) | 1292.27 | 0.253756 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 721.955 | 0.140341 | ||||||||
\(299\) | 5722.59 | 1.10684 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3096.78 | −0.590065 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1224.18 | −0.230959 | ||||||||
\(305\) | 2935.39 | 0.551081 | ||||||||
\(306\) | 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 | ||||||||
\(310\) | 9396.93 | 1.72164 | ||||||||
\(311\) | 467.992 | 0.0853293 | 0.0426647 | − | 0.999089i | \(-0.486415\pi\) | ||||
0.0426647 | + | 0.999089i | \(0.486415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3612.81 | −0.652422 | −0.326211 | − | 0.945297i | \(-0.605772\pi\) | ||||
−0.326211 | + | 0.945297i | \(0.605772\pi\) | |||||||
\(314\) | −1934.14 | −0.347610 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1638.79 | −0.291737 | ||||||||
\(317\) | −4531.74 | −0.802927 | −0.401463 | − | 0.915875i | \(-0.631498\pi\) | ||||
−0.401463 | + | 0.915875i | \(0.631498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12451.7 | 2.18546 | ||||||||
\(320\) | −1013.58 | −0.177064 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2092.47 | −0.360459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4886.27 | −0.833974 | ||||||||
\(326\) | 2653.00 | 0.450724 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 823.818 | 0.138682 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1237.06 | −0.205422 | −0.102711 | − | 0.994711i | \(-0.532752\pi\) | ||||
−0.102711 | + | 0.994711i | \(0.532752\pi\) | |||||||
\(332\) | 1391.71 | 0.230061 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2833.39 | −0.464181 | ||||||||
\(335\) | −8634.53 | −1.40822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1867.83 | −0.301921 | −0.150960 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(338\) | 1377.36 | 0.221652 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1732.48 | −0.276345 | ||||||||
\(341\) | −15378.7 | −2.44224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2628.45 | 0.411967 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2073.20 | 0.322126 | ||||||||
\(347\) | 63.3637 | 0.00980271 | 0.00490136 | − | 0.999988i | \(-0.498440\pi\) | ||||
0.00490136 | + | 0.999988i | \(0.498440\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 1658.79 | 0.251175 | ||||||||
\(353\) | −4515.61 | −0.680855 | −0.340428 | − | 0.940271i | \(-0.610572\pi\) | ||||
−0.340428 | + | 0.940271i | \(0.610572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2070.58 | −0.309564 | ||||||||
\(356\) | 4628.64 | 0.689093 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1534.86 | −0.226592 | ||||||||
\(359\) | −2228.49 | −0.327619 | −0.163810 | − | 0.986492i | \(-0.552378\pi\) | ||||
−0.163810 | + | 0.986492i | \(0.552378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1005.01 | −0.146524 | ||||||||
\(362\) | −7915.42 | −1.14924 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2871.26 | 0.411749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1437.34 | 0.204438 | 0.102219 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102219 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(368\) | −2357.58 | −0.333960 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5116.47 | −0.718899 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12237.4 | −1.69874 | −0.849370 | − | 0.527798i | \(-0.823018\pi\) | ||||
−0.849370 | + | 0.527798i | \(0.823018\pi\) | |||||||
\(374\) | 2835.33 | 0.392010 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −543.636 | −0.0745636 | ||||||||
\(377\) | 9329.00 | 1.27445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10647.0 | −1.44301 | −0.721503 | − | 0.692411i | \(-0.756549\pi\) | ||||
−0.721503 | + | 0.692411i | \(0.756549\pi\) | |||||||
\(380\) | 4846.88 | 0.654315 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3610.59 | −0.483597 | ||||||||
\(383\) | −6714.81 | −0.895851 | −0.447925 | − | 0.894071i | \(-0.647837\pi\) | ||||
−0.447925 | + | 0.894071i | \(0.647837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6741.68 | −0.888970 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6473.20 | −0.846976 | ||||||||
\(389\) | 10653.1 | 1.38852 | 0.694258 | − | 0.719727i | \(-0.255733\pi\) | ||||
0.694258 | + | 0.719727i | \(0.255733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4029.76 | −0.521211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9224.62 | −1.17952 | ||||||||
\(395\) | 6488.42 | 0.826501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3221.04 | −0.407203 | −0.203601 | − | 0.979054i | \(-0.565265\pi\) | ||||
−0.203601 | + | 0.979054i | \(0.565265\pi\) | |||||||
\(398\) | −4459.73 | −0.561673 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2013.03 | 0.251629 | ||||||||
\(401\) | −12485.0 | −1.55479 | −0.777395 | − | 0.629012i | \(-0.783460\pi\) | ||||
−0.777395 | + | 0.629012i | \(0.783460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11522.0 | −1.42419 | ||||||||
\(404\) | 2874.97 | 0.354047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8373.46 | 1.01980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7037.39 | −0.850798 | −0.425399 | − | 0.905006i | \(-0.639866\pi\) | ||||
−0.425399 | + | 0.905006i | \(0.639866\pi\) | |||||||
\(410\) | −3261.73 | −0.392891 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6446.32 | 0.770843 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5510.18 | −0.651769 | ||||||||
\(416\) | 1242.79 | 0.146473 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7932.26 | −0.928180 | ||||||||
\(419\) | −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 | \(0.396255\pi\) | |||||||
\(422\) | −1825.23 | −0.210547 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −531.909 | −0.0609240 | ||||||||
\(425\) | 3440.83 | 0.392717 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3738.68 | −0.422234 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10406.8 | −1.16712 | ||||||||
\(431\) | 2029.93 | 0.226864 | 0.113432 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113432 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −4788.08 | −0.525934 | ||||||||
\(437\) | 11273.8 | 1.23410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7908.68 | −0.859819 | −0.429910 | − | 0.902872i | \(-0.641455\pi\) | ||||
−0.429910 | + | 0.902872i | \(0.641455\pi\) | |||||||
\(440\) | −6567.61 | −0.711587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2124.27 | 0.228600 | ||||||||
\(443\) | 2920.82 | 0.313256 | 0.156628 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156628 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18326.1 | −1.95222 | ||||||||
\(446\) | −8638.93 | −0.917187 | ||||||||
\(447\) | 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 | ||||||||
\(451\) | 5338.05 | 0.557336 | ||||||||
\(452\) | 9538.58 | 0.992604 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4122.57 | −0.426171 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5892.63 | 0.603163 | 0.301582 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301582 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(458\) | −6949.26 | −0.708991 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9334.30 | 0.946118 | ||||||||
\(461\) | −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 | \(0.226423\pi\) | |||||||
\(464\) | −3843.33 | −0.384531 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1552.20 | 0.154301 | ||||||||
\(467\) | −2820.23 | −0.279454 | −0.139727 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139727 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2152.41 | 0.211241 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3695.42 | 0.360372 | ||||||||
\(473\) | 17031.4 | 1.65562 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9626.23 | −0.929856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4013.59 | 0.384053 | ||||||||
\(479\) | −16448.5 | −1.56900 | −0.784500 | − | 0.620129i | \(-0.787080\pi\) | ||||
−0.784500 | + | 0.620129i | \(0.787080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6273.52 | 0.594694 | ||||||||
\(482\) | 1611.30 | 0.152267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5424.35 | 0.509424 | ||||||||
\(485\) | 25629.2 | 2.39951 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6331.07 | 0.589093 | 0.294546 | − | 0.955637i | \(-0.404831\pi\) | ||||
0.294546 | + | 0.955637i | \(0.404831\pi\) | |||||||
\(488\) | 1482.79 | 0.137546 | ||||||||
\(489\) | 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 | ||||||||
\(493\) | −6569.33 | −0.600138 | ||||||||
\(494\) | −5942.96 | −0.541268 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4746.79 | 0.429712 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −243.451 | −0.0218404 | −0.0109202 | − | 0.999940i | \(-0.503476\pi\) | ||||
−0.0109202 | + | 0.999940i | \(0.503476\pi\) | |||||||
\(500\) | −51.5907 | −0.00461442 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2843.57 | −0.252818 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | −15276.2 | −1.34212 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10695.7 | −0.934143 | ||||||||
\(509\) | −7683.10 | −0.669052 | −0.334526 | − | 0.942387i | \(-0.608576\pi\) | ||||
−0.334526 | + | 0.942387i | \(0.608576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2931.64 | 0.251574 | ||||||||
\(515\) | −25522.8 | −2.18382 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3522.57 | −0.299656 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4920.55 | −0.414962 | ||||||||
\(521\) | −21530.6 | −1.81051 | −0.905253 | − | 0.424874i | \(-0.860319\pi\) | ||||
−0.905253 | + | 0.424874i | \(0.860319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16847.1 | 1.40855 | 0.704274 | − | 0.709929i | \(-0.251273\pi\) | ||||
0.704274 | + | 0.709929i | \(0.251273\pi\) | |||||||
\(524\) | −155.439 | −0.0129588 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13982.8 | 1.15908 | ||||||||
\(527\) | 8113.59 | 0.670652 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9544.58 | 0.784464 | ||||||||
\(530\) | 2105.98 | 0.172600 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3999.34 | 0.325011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14802.5 | 1.19620 | ||||||||
\(536\) | −4361.67 | −0.351484 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1617.92 | −0.129653 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17440.0 | 1.38596 | 0.692981 | − | 0.720955i | \(-0.256297\pi\) | ||||
0.692981 | + | 0.720955i | \(0.256297\pi\) | |||||||
\(542\) | 13323.5 | 1.05589 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −875.151 | −0.0689739 | ||||||||
\(545\) | 18957.3 | 1.48999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11520.7 | 0.900530 | 0.450265 | − | 0.892895i | \(-0.351329\pi\) | ||||
0.450265 | + | 0.892895i | \(0.351329\pi\) | |||||||
\(548\) | 3072.58 | 0.239514 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13043.7 | 1.01125 | ||||||||
\(551\) | 18378.7 | 1.42098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15062.9 | 1.15517 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4210.20 | −0.321137 | ||||||||
\(557\) | −11493.0 | −0.874282 | −0.437141 | − | 0.899393i | \(-0.644009\pi\) | ||||
−0.437141 | + | 0.899393i | \(0.644009\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12760.2 | 0.965472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3380.38 | 0.253724 | ||||||||
\(563\) | 18111.3 | 1.35577 | 0.677886 | − | 0.735167i | \(-0.262896\pi\) | ||||
0.677886 | + | 0.735167i | \(0.262896\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37765.9 | −2.81208 | ||||||||
\(566\) | 6356.46 | 0.472053 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1045.94 | −0.0772652 | ||||||||
\(569\) | −4417.61 | −0.325476 | −0.162738 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162738 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13219.7 | 0.968878 | 0.484439 | − | 0.874825i | \(-0.339024\pi\) | ||||
0.484439 | + | 0.874825i | \(0.339024\pi\) | |||||||
\(572\) | 8052.82 | 0.588646 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18538.6 | −1.34454 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17496.4 | 1.26236 | 0.631182 | − | 0.775634i | \(-0.282570\pi\) | ||||
0.631182 | + | 0.775634i | \(0.282570\pi\) | |||||||
\(578\) | 8330.12 | 0.599459 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15216.8 | 1.08939 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3446.58 | −0.244842 | ||||||||
\(584\) | 1450.39 | 0.102770 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4353.07 | 0.306866 | ||||||||
\(587\) | −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 | ||||||||
\(590\) | −14631.2 | −1.02095 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2584.55 | −0.179433 | ||||||||
\(593\) | −1590.93 | −0.110172 | −0.0550858 | − | 0.998482i | \(-0.517543\pi\) | ||||
−0.0550858 | + | 0.998482i | \(0.517543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1443.91 | −0.0992363 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11445.2 | −0.782656 | ||||||||
\(599\) | 13922.8 | 0.949703 | 0.474851 | − | 0.880066i | \(-0.342502\pi\) | ||||
0.474851 | + | 0.880066i | \(0.342502\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 6193.56 | 0.417239 | ||||||||
\(605\) | −21476.5 | −1.44321 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7678.37 | −0.513436 | −0.256718 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256718 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(608\) | 2448.36 | 0.163313 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5870.77 | −0.389673 | ||||||||
\(611\) | −2639.16 | −0.174745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6158.37 | 0.405766 | 0.202883 | − | 0.979203i | \(-0.434969\pi\) | ||||
0.202883 | + | 0.979203i | \(0.434969\pi\) | |||||||
\(614\) | 1247.01 | 0.0819628 | ||||||||
\(615\) | 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 | ||||||||
\(619\) | −23189.9 | −1.50579 | −0.752894 | − | 0.658142i | \(-0.771342\pi\) | ||||
−0.752894 | + | 0.658142i | \(0.771342\pi\) | |||||||
\(620\) | −18793.9 | −1.21739 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −935.985 | −0.0603369 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15522.5 | −0.993442 | ||||||||
\(626\) | 7225.62 | 0.461332 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3868.27 | 0.245798 | ||||||||
\(629\) | −4417.71 | −0.280041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7936.94 | 0.500736 | 0.250368 | − | 0.968151i | \(-0.419448\pi\) | ||||
0.250368 | + | 0.968151i | \(0.419448\pi\) | |||||||
\(632\) | 3277.58 | 0.206289 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9063.48 | 0.567755 | ||||||||
\(635\) | 42347.3 | 2.64646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24903.4 | −1.54535 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2027.15 | 0.125203 | ||||||||
\(641\) | −32114.6 | −1.97886 | −0.989432 | − | 0.144996i | \(-0.953683\pi\) | ||||
−0.989432 | + | 0.144996i | \(0.953683\pi\) | |||||||
\(642\) | 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 | ||||||||
\(646\) | 4184.94 | 0.254883 | ||||||||
\(647\) | 7545.59 | 0.458497 | 0.229249 | − | 0.973368i | \(-0.426373\pi\) | ||||
0.229249 | + | 0.973368i | \(0.426373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23945.0 | 1.44827 | ||||||||
\(650\) | 9772.54 | 0.589708 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5306.00 | −0.318710 | ||||||||
\(653\) | 4888.99 | 0.292988 | 0.146494 | − | 0.989212i | \(-0.453201\pi\) | ||||
0.146494 | + | 0.989212i | \(0.453201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 615.428 | 0.0367126 | ||||||||
\(656\) | −1647.64 | −0.0980631 | ||||||||
\(657\) | 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 | ||||||||
\(661\) | −8183.37 | −0.481537 | −0.240769 | − | 0.970583i | \(-0.577399\pi\) | ||||
−0.240769 | + | 0.970583i | \(0.577399\pi\) | |||||||
\(662\) | 2474.11 | 0.145256 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2783.42 | −0.162677 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35394.3 | 2.05468 | ||||||||
\(668\) | 5666.79 | 0.328225 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17269.1 | 0.995764 | ||||||||
\(671\) | 9607.93 | 0.552772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4635.02 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(674\) | 3735.67 | 0.213490 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2754.71 | −0.156731 | ||||||||
\(677\) | −24385.8 | −1.38437 | −0.692187 | − | 0.721718i | \(-0.743353\pi\) | ||||
−0.692187 | + | 0.721718i | \(0.743353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3464.97 | 0.195405 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30757.5 | 1.72693 | ||||||||
\(683\) | 18393.4 | 1.03046 | 0.515230 | − | 0.857052i | \(-0.327706\pi\) | ||||
0.515230 | + | 0.857052i | \(0.327706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12165.2 | −0.678552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5256.91 | −0.291305 | ||||||||
\(689\) | −2582.23 | −0.142779 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14898.9 | 0.820231 | 0.410116 | − | 0.912034i | \(-0.365488\pi\) | ||||
0.410116 | + | 0.912034i | \(0.365488\pi\) | |||||||
\(692\) | −4146.39 | −0.227778 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −126.727 | −0.00693157 | ||||||||
\(695\) | 16669.3 | 0.909791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2816.27 | −0.153047 | ||||||||
\(698\) | 2447.58 | 0.132725 | ||||||||
\(699\) | 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 | ||||||||
\(703\) | 12359.2 | 0.663067 | ||||||||
\(704\) | −3317.58 | −0.177608 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9031.23 | 0.481437 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23456.8 | −1.24251 | −0.621255 | − | 0.783609i | \(-0.713377\pi\) | ||||
−0.621255 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(710\) | 4141.17 | 0.218895 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9257.27 | −0.487263 | ||||||||
\(713\) | −43714.5 | −2.29610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31883.4 | −1.66765 | ||||||||
\(716\) | 3069.73 | 0.160225 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4456.98 | 0.231662 | ||||||||
\(719\) | −8459.00 | −0.438759 | −0.219379 | − | 0.975640i | \(-0.570403\pi\) | ||||
−0.219379 | + | 0.975640i | \(0.570403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2010.02 | 0.103608 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15830.8 | 0.812636 | ||||||||
\(725\) | −30221.7 | −1.54814 | ||||||||
\(726\) | 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 | ||||||||
\(730\) | −5742.52 | −0.291151 | ||||||||
\(731\) | −8985.53 | −0.454640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5028.95 | −0.253409 | −0.126704 | − | 0.991941i | \(-0.540440\pi\) | ||||
−0.126704 | + | 0.991941i | \(0.540440\pi\) | |||||||
\(734\) | −2874.68 | −0.144559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4715.15 | 0.236145 | ||||||||
\(737\) | −28262.0 | −1.41254 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17743.9 | −0.883247 | −0.441624 | − | 0.897200i | \(-0.645597\pi\) | ||||
−0.441624 | + | 0.897200i | \(0.645597\pi\) | |||||||
\(740\) | 10232.9 | 0.508338 | ||||||||
\(741\) | 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 | ||||||||
\(745\) | 5716.84 | 0.281139 | ||||||||
\(746\) | 24474.9 | 1.20119 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5670.67 | −0.277193 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15601.0 | 0.758040 | 0.379020 | − | 0.925388i | \(-0.376261\pi\) | ||||
0.379020 | + | 0.925388i | \(0.376261\pi\) | |||||||
\(752\) | 1087.27 | 0.0527244 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18658.0 | −0.901173 | ||||||||
\(755\) | −24522.0 | −1.18205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2948.08 | 0.141545 | 0.0707725 | − | 0.997492i | \(-0.477454\pi\) | ||||
0.0707725 | + | 0.997492i | \(0.477454\pi\) | |||||||
\(758\) | 21294.0 | 1.02036 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9693.76 | −0.462670 | ||||||||
\(761\) | 1697.03 | 0.0808375 | 0.0404187 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404187 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7221.18 | 0.341954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13429.6 | 0.633462 | ||||||||
\(767\) | 17940.0 | 0.844556 | ||||||||
\(768\) | 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 | ||||||||
\(772\) | 13483.4 | 0.628597 | ||||||||
\(773\) | 36326.8 | 1.69028 | 0.845138 | − | 0.534548i | \(-0.179518\pi\) | ||||
0.845138 | + | 0.534548i | \(0.179518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37325.9 | 1.73005 | ||||||||
\(776\) | 12946.4 | 0.598903 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21306.2 | −0.981828 | ||||||||
\(779\) | 7878.93 | 0.362377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6777.31 | −0.310514 | ||||||||
\(782\) | 8059.52 | 0.368552 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15315.6 | −0.696352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7096.46 | −0.321425 | −0.160713 | − | 0.987001i | \(-0.551379\pi\) | ||||
−0.160713 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(788\) | 18449.2 | 0.834044 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12976.8 | −0.584424 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7198.40 | 0.322349 | ||||||||
\(794\) | 6442.08 | 0.287936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8919.45 | 0.397163 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | −4026.06 | −0.177928 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24970.0 | 1.09940 | ||||||||
\(803\) | 9398.03 | 0.413013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23043.9 | 1.00706 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5749.94 | −0.250349 | ||||||||
\(809\) | 11566.0 | 0.502642 | 0.251321 | − | 0.967904i | \(-0.419135\pi\) | ||||
0.251321 | + | 0.967904i | \(0.419135\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | −16746.9 | −0.721105 | ||||||||
\(815\) | 21007.9 | 0.902915 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25138.3 | 1.07647 | ||||||||
\(818\) | 14074.8 | 0.601605 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6523.45 | 0.277816 | ||||||||
\(821\) | 16792.4 | 0.713837 | 0.356918 | − | 0.934136i | \(-0.383827\pi\) | ||||
0.356918 | + | 0.934136i | \(0.383827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8819.03 | −0.373526 | −0.186763 | − | 0.982405i | \(-0.559800\pi\) | ||||
−0.186763 | + | 0.982405i | \(0.559800\pi\) | |||||||
\(824\) | −12892.6 | −0.545068 | ||||||||
\(825\) | 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 | ||||||||
\(829\) | 21550.5 | 0.902871 | 0.451435 | − | 0.892304i | \(-0.350912\pi\) | ||||
0.451435 | + | 0.892304i | \(0.350912\pi\) | |||||||
\(830\) | 11020.4 | 0.460870 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2485.58 | −0.103572 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22436.4 | −0.929873 | ||||||||
\(836\) | 15864.5 | 0.656323 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3099.32 | 0.127762 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −11063.3 | −0.452809 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3650.45 | 0.148879 | ||||||||
\(845\) | 10906.7 | 0.444025 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1063.82 | 0.0430798 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6881.67 | −0.277693 | ||||||||
\(851\) | 23801.8 | 0.958772 | ||||||||
\(852\) | 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 | ||||||||
\(856\) | 7477.36 | 0.298564 | ||||||||
\(857\) | −36508.2 | −1.45519 | −0.727594 | − | 0.686008i | \(-0.759362\pi\) | ||||
−0.727594 | + | 0.686008i | \(0.759362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21980.8 | 0.873081 | 0.436541 | − | 0.899685i | \(-0.356204\pi\) | ||||
0.436541 | + | 0.899685i | \(0.356204\pi\) | |||||||
\(860\) | 20813.6 | 0.825276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4059.86 | −0.160417 | ||||||||
\(863\) | 23426.1 | 0.924024 | 0.462012 | − | 0.886874i | \(-0.347128\pi\) | ||||
0.462012 | + | 0.886874i | \(0.347128\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16416.7 | 0.645301 | ||||||||
\(866\) | −655.477 | −0.0257206 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21237.5 | 0.829037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21174.3 | −0.823725 | ||||||||
\(872\) | 9576.15 | 0.371892 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −22547.7 | −0.872639 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 307.401 | 0.0118360 | 0.00591802 | − | 0.999982i | \(-0.498116\pi\) | ||||
0.00591802 | + | 0.999982i | \(0.498116\pi\) | |||||||
\(878\) | 15817.4 | 0.607984 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13135.2 | 0.503168 | ||||||||
\(881\) | −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 | \(0.753599\pi\) | |||||||
\(884\) | −4248.55 | −0.161645 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5841.64 | −0.221505 | ||||||||
\(887\) | −2880.20 | −0.109028 | −0.0545140 | − | 0.998513i | \(-0.517361\pi\) | ||||
−0.0545140 | + | 0.998513i | \(0.517361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36652.1 | 1.38043 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17277.9 | 0.648549 | ||||||||
\(893\) | −5199.30 | −0.194835 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12153.9 | −0.453922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20480.4 | −0.761068 | ||||||||
\(899\) | −71263.6 | −2.64380 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1818.36 | 0.0672347 | ||||||||
\(902\) | −10676.1 | −0.394096 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19077.2 | −0.701877 | ||||||||
\(905\) | −62678.7 | −2.30222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18319.2 | 0.670651 | 0.335326 | − | 0.942102i | \(-0.391154\pi\) | ||||
0.335326 | + | 0.942102i | \(0.391154\pi\) | |||||||
\(908\) | 8245.14 | 0.301349 | ||||||||
\(909\) | 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 | ||||||||
\(913\) | −18035.6 | −0.653769 | ||||||||
\(914\) | −11785.3 | −0.426501 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13898.5 | 0.501332 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47264.3 | 1.69652 | 0.848261 | − | 0.529578i | \(-0.177650\pi\) | ||||
0.848261 | + | 0.529578i | \(0.177650\pi\) | |||||||
\(920\) | −18668.6 | −0.669006 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25286.7 | 0.903226 | ||||||||
\(923\) | −5077.66 | −0.181076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20323.3 | −0.722407 | ||||||||
\(926\) | −30186.4 | −1.07126 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7686.67 | 0.271904 | ||||||||
\(929\) | −53271.5 | −1.88136 | −0.940678 | − | 0.339301i | \(-0.889810\pi\) | ||||
−0.940678 | + | 0.339301i | \(0.889810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3104.39 | −0.109107 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5640.47 | 0.197604 | ||||||||
\(935\) | 22451.8 | 0.785295 | ||||||||
\(936\) | 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 | ||||||||
\(940\) | −4304.82 | −0.149370 | ||||||||
\(941\) | 28834.9 | 0.998926 | 0.499463 | − | 0.866335i | \(-0.333531\pi\) | ||||
0.499463 | + | 0.866335i | \(0.333531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15173.5 | 0.523986 | ||||||||
\(944\) | −7390.85 | −0.254822 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34062.9 | −1.17070 | ||||||||
\(947\) | 51841.2 | 1.77890 | 0.889448 | − | 0.457037i | \(-0.151089\pi\) | ||||
0.889448 | + | 0.457037i | \(0.151089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7041.14 | 0.240848 | ||||||||
\(950\) | 19252.5 | 0.657508 | ||||||||
\(951\) | 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 | ||||||||
\(955\) | −28590.7 | −0.968767 | ||||||||
\(956\) | −8027.18 | −0.271567 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32897.0 | 1.10945 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58224.6 | 1.95444 | ||||||||
\(962\) | −12547.0 | −0.420512 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3222.59 | −0.107669 | ||||||||
\(965\) | −53384.4 | −1.78083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36620.0 | −1.21781 | −0.608904 | − | 0.793244i | \(-0.708391\pi\) | ||||
−0.608904 | + | 0.793244i | \(0.708391\pi\) | |||||||
\(968\) | −10848.7 | −0.360217 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −51258.4 | −1.69671 | ||||||||
\(971\) | −42364.9 | −1.40016 | −0.700079 | − | 0.714065i | \(-0.746852\pi\) | ||||
−0.700079 | + | 0.714065i | \(0.746852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12662.1 | −0.416551 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2965.58 | −0.0972600 | ||||||||
\(977\) | −5022.32 | −0.164461 | −0.0822304 | − | 0.996613i | \(-0.526204\pi\) | ||||
−0.0822304 | + | 0.996613i | \(0.526204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59983.8 | −1.95821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18573.8 | −0.603578 | ||||||||
\(983\) | 28292.8 | 0.918005 | 0.459003 | − | 0.888435i | \(-0.348207\pi\) | ||||
0.459003 | + | 0.888435i | \(0.348207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −73045.7 | −2.36287 | ||||||||
\(986\) | 13138.7 | 0.424361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11885.9 | 0.382734 | ||||||||
\(989\) | 48412.3 | 1.55655 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36401.1 | 1.16682 | 0.583410 | − | 0.812178i | \(-0.301718\pi\) | ||||
0.583410 | + | 0.812178i | \(0.301718\pi\) | |||||||
\(992\) | −9493.58 | −0.303852 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35314.6 | −1.12517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2357.19 | 0.0748777 | 0.0374389 | − | 0.999299i | \(-0.488080\pi\) | ||||
0.0374389 | + | 0.999299i | \(0.488080\pi\) | |||||||
\(998\) | 486.902 | 0.0154435 | ||||||||
\(999\) | 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.a.z.1.1 | 2 | ||
3.2 | odd | 2 | 294.4.a.m.1.2 | 2 | |||
7.2 | even | 3 | 882.4.g.bf.361.2 | 4 | |||
7.3 | odd | 6 | 126.4.g.g.37.1 | 4 | |||
7.4 | even | 3 | 882.4.g.bf.667.2 | 4 | |||
7.5 | odd | 6 | 126.4.g.g.109.1 | 4 | |||
7.6 | odd | 2 | 882.4.a.v.1.2 | 2 | |||
12.11 | even | 2 | 2352.4.a.ca.1.2 | 2 | |||
21.2 | odd | 6 | 294.4.e.l.67.1 | 4 | |||
21.5 | even | 6 | 42.4.e.c.25.2 | ✓ | 4 | ||
21.11 | odd | 6 | 294.4.e.l.79.1 | 4 | |||
21.17 | even | 6 | 42.4.e.c.37.2 | yes | 4 | ||
21.20 | even | 2 | 294.4.a.n.1.1 | 2 | |||
84.47 | odd | 6 | 336.4.q.j.193.2 | 4 | |||
84.59 | odd | 6 | 336.4.q.j.289.2 | 4 | |||
84.83 | odd | 2 | 2352.4.a.bq.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.2 | ✓ | 4 | 21.5 | even | 6 | ||
42.4.e.c.37.2 | yes | 4 | 21.17 | even | 6 | ||
126.4.g.g.37.1 | 4 | 7.3 | odd | 6 | |||
126.4.g.g.109.1 | 4 | 7.5 | odd | 6 | |||
294.4.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
294.4.a.n.1.1 | 2 | 21.20 | even | 2 | |||
294.4.e.l.67.1 | 4 | 21.2 | odd | 6 | |||
294.4.e.l.79.1 | 4 | 21.11 | odd | 6 | |||
336.4.q.j.193.2 | 4 | 84.47 | odd | 6 | |||
336.4.q.j.289.2 | 4 | 84.59 | odd | 6 | |||
882.4.a.v.1.2 | 2 | 7.6 | odd | 2 | |||
882.4.a.z.1.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.bf.361.2 | 4 | 7.2 | even | 3 | |||
882.4.g.bf.667.2 | 4 | 7.4 | even | 3 | |||
2352.4.a.bq.1.1 | 2 | 84.83 | odd | 2 | |||
2352.4.a.ca.1.2 | 2 | 12.11 | even | 2 |