Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(78.0595269376\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{5}, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 189) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.684742\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.15688 | −1.82323 | −0.911616 | − | 0.411043i | \(-0.865164\pi\) | ||||
−0.911616 | + | 0.411043i | \(0.865164\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 18.5934 | 2.32417 | ||||||||
\(5\) | 17.0220 | 1.52249 | 0.761245 | − | 0.648464i | \(-0.224588\pi\) | ||||
0.761245 | + | 0.648464i | \(0.224588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −54.6288 | −2.41427 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −87.7802 | −2.77585 | ||||||||
\(11\) | 30.3531 | 0.831982 | 0.415991 | − | 0.909369i | \(-0.363435\pi\) | ||||
0.415991 | + | 0.909369i | \(0.363435\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 89.5603 | 1.91074 | 0.955368 | − | 0.295419i | \(-0.0954592\pi\) | ||||
0.955368 | + | 0.295419i | \(0.0954592\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 132.967 | 2.07761 | ||||||||
\(17\) | 13.4164 | 0.191409 | 0.0957046 | − | 0.995410i | \(-0.469490\pi\) | ||||
0.0957046 | + | 0.995410i | \(0.469490\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.37355 | 0.0648830 | 0.0324415 | − | 0.999474i | \(-0.489672\pi\) | ||||
0.0324415 | + | 0.999474i | \(0.489672\pi\) | |||||||
\(20\) | 316.496 | 3.53853 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −156.527 | −1.51690 | ||||||||
\(23\) | −167.449 | −1.51807 | −0.759035 | − | 0.651050i | \(-0.774329\pi\) | ||||
−0.759035 | + | 0.651050i | \(0.774329\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 164.747 | 1.31798 | ||||||||
\(26\) | −461.852 | −3.48371 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 135.085 | 0.864986 | 0.432493 | − | 0.901637i | \(-0.357634\pi\) | ||||
0.432493 | + | 0.901637i | \(0.357634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.9339 | 0.109698 | 0.0548488 | − | 0.998495i | \(-0.482532\pi\) | ||||
0.0548488 | + | 0.998495i | \(0.482532\pi\) | |||||||
\(32\) | −248.664 | −1.37369 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −69.1868 | −0.348983 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 402.560 | 1.78866 | 0.894331 | − | 0.447406i | \(-0.147652\pi\) | ||||
0.894331 | + | 0.447406i | \(0.147652\pi\) | |||||||
\(38\) | −27.7107 | −0.118297 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −929.889 | −3.67571 | ||||||||
\(41\) | −434.345 | −1.65447 | −0.827236 | − | 0.561855i | \(-0.810088\pi\) | ||||
−0.827236 | + | 0.561855i | \(0.810088\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 53.1868 | 0.188626 | 0.0943129 | − | 0.995543i | \(-0.469935\pi\) | ||||
0.0943129 | + | 0.995543i | \(0.469935\pi\) | |||||||
\(44\) | 564.367 | 1.93367 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 863.516 | 2.76779 | ||||||||
\(47\) | −155.218 | −0.481720 | −0.240860 | − | 0.970560i | \(-0.577430\pi\) | ||||
−0.240860 | + | 0.970560i | \(0.577430\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −849.581 | −2.40298 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1665.23 | 4.44088 | ||||||||
\(53\) | 301.707 | 0.781938 | 0.390969 | − | 0.920404i | \(-0.372140\pi\) | ||||
0.390969 | + | 0.920404i | \(0.372140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 516.669 | 1.26669 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −696.615 | −1.57707 | ||||||||
\(59\) | 412.635 | 0.910518 | 0.455259 | − | 0.890359i | \(-0.349547\pi\) | ||||
0.455259 | + | 0.890359i | \(0.349547\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 571.253 | 1.19904 | 0.599520 | − | 0.800360i | \(-0.295358\pi\) | ||||
0.599520 | + | 0.800360i | \(0.295358\pi\) | |||||||
\(62\) | −97.6396 | −0.200004 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 218.593 | 0.426940 | ||||||||
\(65\) | 1524.49 | 2.90908 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 820.549 | 1.49621 | 0.748104 | − | 0.663581i | \(-0.230964\pi\) | ||||
0.748104 | + | 0.663581i | \(0.230964\pi\) | |||||||
\(68\) | 249.456 | 0.444868 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.95825 | 0.0149739 | 0.00748696 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748696 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.9339 | −0.0351666 | −0.0175833 | − | 0.999845i | \(-0.505597\pi\) | ||||
−0.0175833 | + | 0.999845i | \(0.505597\pi\) | |||||||
\(74\) | −2075.95 | −3.26115 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 99.9124 | 0.150799 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 619.428 | 0.882166 | 0.441083 | − | 0.897466i | \(-0.354594\pi\) | ||||
0.441083 | + | 0.897466i | \(0.354594\pi\) | |||||||
\(80\) | 2263.36 | 3.16314 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2239.87 | 3.01649 | ||||||||
\(83\) | −259.532 | −0.343221 | −0.171610 | − | 0.985165i | \(-0.554897\pi\) | ||||
−0.171610 | + | 0.985165i | \(0.554897\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 228.374 | 0.291419 | ||||||||
\(86\) | −274.278 | −0.343908 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1658.15 | −2.00863 | ||||||||
\(89\) | −484.329 | −0.576840 | −0.288420 | − | 0.957504i | \(-0.593130\pi\) | ||||
−0.288420 | + | 0.957504i | \(0.593130\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3113.45 | −3.52826 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 800.440 | 0.878288 | ||||||||
\(95\) | 91.4683 | 0.0987837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 252.747 | 0.264563 | 0.132281 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132281 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3063.21 | 3.06321 | ||||||||
\(101\) | 629.378 | 0.620054 | 0.310027 | − | 0.950728i | \(-0.399662\pi\) | ||||
0.310027 | + | 0.950728i | \(0.399662\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1172.54 | −1.12168 | −0.560842 | − | 0.827923i | \(-0.689523\pi\) | ||||
−0.560842 | + | 0.827923i | \(0.689523\pi\) | |||||||
\(104\) | −4892.57 | −4.61304 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1555.87 | −1.42565 | ||||||||
\(107\) | −1002.87 | −0.906087 | −0.453044 | − | 0.891488i | \(-0.649662\pi\) | ||||
−0.453044 | + | 0.891488i | \(0.649662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 542.802 | 0.476981 | 0.238491 | − | 0.971145i | \(-0.423347\pi\) | ||||
0.238491 | + | 0.971145i | \(0.423347\pi\) | |||||||
\(110\) | −2664.40 | −2.30946 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1388.74 | −1.15612 | −0.578062 | − | 0.815993i | \(-0.696191\pi\) | ||||
−0.578062 | + | 0.815993i | \(0.696191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2850.32 | −2.31125 | ||||||||
\(116\) | 2511.68 | 2.01038 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2127.91 | −1.66009 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −409.689 | −0.307805 | ||||||||
\(122\) | −2945.88 | −2.18613 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 352.045 | 0.254956 | ||||||||
\(125\) | 676.573 | 0.484117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2330.00 | −1.62798 | −0.813991 | − | 0.580877i | \(-0.802710\pi\) | ||||
−0.813991 | + | 0.580877i | \(0.802710\pi\) | |||||||
\(128\) | 862.051 | 0.595276 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7861.62 | −5.30392 | ||||||||
\(131\) | −226.817 | −0.151276 | −0.0756379 | − | 0.997135i | \(-0.524099\pi\) | ||||
−0.0756379 | + | 0.997135i | \(0.524099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4231.47 | −2.72793 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −732.922 | −0.462114 | ||||||||
\(137\) | 1900.83 | 1.18540 | 0.592698 | − | 0.805425i | \(-0.298063\pi\) | ||||
0.592698 | + | 0.805425i | \(0.298063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1958.99 | −1.19539 | −0.597695 | − | 0.801724i | \(-0.703917\pi\) | ||||
−0.597695 | + | 0.801724i | \(0.703917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −46.1966 | −0.0273009 | ||||||||
\(143\) | 2718.43 | 1.58970 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2299.40 | 1.31693 | ||||||||
\(146\) | 113.110 | 0.0641169 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7484.96 | 4.15716 | ||||||||
\(149\) | −1518.37 | −0.834831 | −0.417416 | − | 0.908716i | \(-0.637064\pi\) | ||||
−0.417416 | + | 0.908716i | \(0.637064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1815.18 | −0.978262 | −0.489131 | − | 0.872210i | \(-0.662686\pi\) | ||||
−0.489131 | + | 0.872210i | \(0.662686\pi\) | |||||||
\(152\) | −293.550 | −0.156645 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 322.291 | 0.167013 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1858.79 | 0.944889 | 0.472445 | − | 0.881360i | \(-0.343372\pi\) | ||||
0.472445 | + | 0.881360i | \(0.343372\pi\) | |||||||
\(158\) | −3194.31 | −1.60839 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4232.75 | −2.09142 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 870.089 | 0.418102 | 0.209051 | − | 0.977905i | \(-0.432962\pi\) | ||||
0.209051 | + | 0.977905i | \(0.432962\pi\) | |||||||
\(164\) | −8075.95 | −3.84528 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1338.37 | 0.625771 | ||||||||
\(167\) | 1749.13 | 0.810488 | 0.405244 | − | 0.914209i | \(-0.367187\pi\) | ||||
0.405244 | + | 0.914209i | \(0.367187\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5824.05 | 2.65091 | ||||||||
\(170\) | −1177.69 | −0.531324 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 988.922 | 0.438399 | ||||||||
\(173\) | 39.3374 | 0.0172877 | 0.00864383 | − | 0.999963i | \(-0.497249\pi\) | ||||
0.00864383 | + | 0.999963i | \(0.497249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4035.96 | 1.72853 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2497.62 | 1.05171 | ||||||||
\(179\) | 2650.58 | 1.10678 | 0.553391 | − | 0.832922i | \(-0.313334\pi\) | ||||
0.553391 | + | 0.832922i | \(0.313334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2719.71 | −1.11688 | −0.558438 | − | 0.829546i | \(-0.688599\pi\) | ||||
−0.558438 | + | 0.829546i | \(0.688599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9147.55 | 3.66504 | ||||||||
\(185\) | 6852.37 | 2.72322 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 407.230 | 0.159249 | ||||||||
\(188\) | −2886.03 | −1.11960 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −471.691 | −0.180106 | ||||||||
\(191\) | −4339.00 | −1.64376 | −0.821881 | − | 0.569659i | \(-0.807075\pi\) | ||||
−0.821881 | + | 0.569659i | \(0.807075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 977.689 | 0.364640 | 0.182320 | − | 0.983239i | \(-0.441639\pi\) | ||||
0.182320 | + | 0.983239i | \(0.441639\pi\) | |||||||
\(194\) | −1303.39 | −0.482359 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1556.32 | 0.562859 | 0.281430 | − | 0.959582i | \(-0.409191\pi\) | ||||
0.281430 | + | 0.959582i | \(0.409191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1723.21 | −0.613846 | −0.306923 | − | 0.951734i | \(-0.599299\pi\) | ||||
−0.306923 | + | 0.951734i | \(0.599299\pi\) | |||||||
\(200\) | −8999.94 | −3.18196 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3245.62 | −1.13050 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7393.41 | −2.51892 | ||||||||
\(206\) | 6046.63 | 2.04509 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11908.6 | 3.96976 | ||||||||
\(209\) | 163.104 | 0.0539815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1295.19 | 0.422581 | 0.211290 | − | 0.977423i | \(-0.432233\pi\) | ||||
0.211290 | + | 0.977423i | \(0.432233\pi\) | |||||||
\(212\) | 5609.76 | 1.81736 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5171.69 | 1.65201 | ||||||||
\(215\) | 905.343 | 0.287181 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2799.16 | −0.869647 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9606.63 | 2.94400 | ||||||||
\(221\) | 1201.58 | 0.365732 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 483.611 | 0.145224 | 0.0726121 | − | 0.997360i | \(-0.476866\pi\) | ||||
0.0726121 | + | 0.997360i | \(0.476866\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7161.58 | 2.10788 | ||||||||
\(227\) | −4019.86 | −1.17536 | −0.587681 | − | 0.809092i | \(-0.699959\pi\) | ||||
−0.587681 | + | 0.809092i | \(0.699959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5070.37 | −1.46314 | −0.731570 | − | 0.681766i | \(-0.761212\pi\) | ||||
−0.731570 | + | 0.681766i | \(0.761212\pi\) | |||||||
\(230\) | 14698.7 | 4.21394 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7379.51 | −2.08831 | ||||||||
\(233\) | 4418.26 | 1.24227 | 0.621137 | − | 0.783702i | \(-0.286671\pi\) | ||||
0.621137 | + | 0.783702i | \(0.286671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2642.11 | −0.733415 | ||||||||
\(236\) | 7672.29 | 2.11620 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3228.15 | 0.873690 | 0.436845 | − | 0.899537i | \(-0.356096\pi\) | ||||
0.436845 | + | 0.899537i | \(0.356096\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1537.14 | 0.410854 | 0.205427 | − | 0.978672i | \(-0.434142\pi\) | ||||
0.205427 | + | 0.978672i | \(0.434142\pi\) | |||||||
\(242\) | 2112.72 | 0.561200 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10621.5 | 2.78678 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 481.257 | 0.123974 | ||||||||
\(248\) | −1034.33 | −0.264840 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3489.01 | −0.882657 | ||||||||
\(251\) | 178.384 | 0.0448587 | 0.0224293 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224293 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5082.61 | −1.26301 | ||||||||
\(254\) | 12015.5 | 2.96819 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6194.24 | −1.51227 | ||||||||
\(257\) | 3271.92 | 0.794152 | 0.397076 | − | 0.917786i | \(-0.370025\pi\) | ||||
0.397076 | + | 0.917786i | \(0.370025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 28345.5 | 6.76120 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1169.67 | 0.275811 | ||||||||
\(263\) | 4738.45 | 1.11097 | 0.555486 | − | 0.831526i | \(-0.312532\pi\) | ||||
0.555486 | + | 0.831526i | \(0.312532\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5135.65 | 1.19049 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15256.8 | 3.47745 | ||||||||
\(269\) | 418.456 | 0.0948466 | 0.0474233 | − | 0.998875i | \(-0.484899\pi\) | ||||
0.0474233 | + | 0.998875i | \(0.484899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5263.95 | −1.17993 | −0.589967 | − | 0.807428i | \(-0.700859\pi\) | ||||
−0.589967 | + | 0.807428i | \(0.700859\pi\) | |||||||
\(272\) | 1783.94 | 0.397673 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9802.37 | −2.16125 | ||||||||
\(275\) | 5000.59 | 1.09653 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2855.61 | 0.619412 | 0.309706 | − | 0.950832i | \(-0.399769\pi\) | ||||
0.309706 | + | 0.950832i | \(0.399769\pi\) | |||||||
\(278\) | 10102.3 | 2.17947 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8589.72 | −1.82356 | −0.911779 | − | 0.410682i | \(-0.865291\pi\) | ||||
−0.911779 | + | 0.410682i | \(0.865291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3681.18 | −0.773228 | −0.386614 | − | 0.922242i | \(-0.626355\pi\) | ||||
−0.386614 | + | 0.922242i | \(0.626355\pi\) | |||||||
\(284\) | 166.564 | 0.0348020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14018.6 | −2.89839 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4733.00 | −0.963363 | ||||||||
\(290\) | −11857.7 | −2.40107 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −407.825 | −0.0817334 | ||||||||
\(293\) | 1958.68 | 0.390536 | 0.195268 | − | 0.980750i | \(-0.437442\pi\) | ||||
0.195268 | + | 0.980750i | \(0.437442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7023.86 | 1.38625 | ||||||||
\(296\) | −21991.4 | −4.31832 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7830.06 | 1.52209 | ||||||||
\(299\) | −14996.8 | −2.90063 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9360.68 | 1.78360 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 714.504 | 0.134801 | ||||||||
\(305\) | 9723.84 | 1.82553 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5672.32 | 1.05452 | 0.527258 | − | 0.849706i | \(-0.323220\pi\) | ||||
0.527258 | + | 0.849706i | \(0.323220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1662.02 | −0.304504 | ||||||||
\(311\) | 1271.71 | 0.231872 | 0.115936 | − | 0.993257i | \(-0.463013\pi\) | ||||
0.115936 | + | 0.993257i | \(0.463013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4868.38 | 0.879160 | 0.439580 | − | 0.898204i | \(-0.355127\pi\) | ||||
0.439580 | + | 0.898204i | \(0.355127\pi\) | |||||||
\(314\) | −9585.55 | −1.72275 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11517.3 | 2.05031 | ||||||||
\(317\) | −3224.18 | −0.571256 | −0.285628 | − | 0.958341i | \(-0.592202\pi\) | ||||
−0.285628 | + | 0.958341i | \(0.592202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4100.24 | 0.719653 | ||||||||
\(320\) | 3720.89 | 0.650012 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 72.0937 | 0.0124192 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14754.8 | 2.51831 | ||||||||
\(326\) | −4486.94 | −0.762297 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23727.8 | 3.99435 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5309.27 | 0.881643 | 0.440821 | − | 0.897595i | \(-0.354687\pi\) | ||||
0.440821 | + | 0.897595i | \(0.354687\pi\) | |||||||
\(332\) | −4825.57 | −0.797704 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9020.04 | −1.47771 | ||||||||
\(335\) | 13967.3 | 2.27796 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2304.33 | −0.372478 | −0.186239 | − | 0.982505i | \(-0.559630\pi\) | ||||
−0.186239 | + | 0.982505i | \(0.559630\pi\) | |||||||
\(338\) | −30033.9 | −4.83322 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4246.24 | 0.677308 | ||||||||
\(341\) | 574.702 | 0.0912664 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2905.53 | −0.455394 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −202.858 | −0.0315194 | ||||||||
\(347\) | 5196.20 | 0.803881 | 0.401940 | − | 0.915666i | \(-0.368336\pi\) | ||||
0.401940 | + | 0.915666i | \(0.368336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9030.60 | 1.38509 | 0.692546 | − | 0.721374i | \(-0.256489\pi\) | ||||
0.692546 | + | 0.721374i | \(0.256489\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7547.72 | −1.14288 | ||||||||
\(353\) | −8885.51 | −1.33974 | −0.669869 | − | 0.742479i | \(-0.733650\pi\) | ||||
−0.669869 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 152.487 | 0.0227976 | ||||||||
\(356\) | −9005.31 | −1.34068 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13668.7 | −2.01792 | ||||||||
\(359\) | 37.2983 | 0.00548337 | 0.00274169 | − | 0.999996i | \(-0.499127\pi\) | ||||
0.00274169 | + | 0.999996i | \(0.499127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6830.12 | −0.995790 | ||||||||
\(362\) | 14025.2 | 2.03632 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −373.357 | −0.0535409 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3335.79 | −0.474460 | −0.237230 | − | 0.971454i | \(-0.576240\pi\) | ||||
−0.237230 | + | 0.971454i | \(0.576240\pi\) | |||||||
\(368\) | −22265.2 | −3.15395 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35336.8 | −4.96506 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3935.81 | 0.546349 | 0.273175 | − | 0.961964i | \(-0.411926\pi\) | ||||
0.273175 | + | 0.961964i | \(0.411926\pi\) | |||||||
\(374\) | −2100.03 | −0.290348 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8479.37 | 1.16301 | ||||||||
\(377\) | 12098.2 | 1.65276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2308.00 | 0.312808 | 0.156404 | − | 0.987693i | \(-0.450010\pi\) | ||||
0.156404 | + | 0.987693i | \(0.450010\pi\) | |||||||
\(380\) | 1700.71 | 0.229590 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22375.7 | 2.99696 | ||||||||
\(383\) | −2931.62 | −0.391119 | −0.195559 | − | 0.980692i | \(-0.562652\pi\) | ||||
−0.195559 | + | 0.980692i | \(0.562652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5041.82 | −0.664824 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4699.42 | 0.614890 | ||||||||
\(389\) | 7610.12 | 0.991898 | 0.495949 | − | 0.868352i | \(-0.334820\pi\) | ||||
0.495949 | + | 0.868352i | \(0.334820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2246.57 | −0.290572 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8025.76 | −1.02622 | ||||||||
\(395\) | 10543.9 | 1.34309 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4269.74 | 0.539778 | 0.269889 | − | 0.962891i | \(-0.413013\pi\) | ||||
0.269889 | + | 0.962891i | \(0.413013\pi\) | |||||||
\(398\) | 8886.41 | 1.11918 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21905.9 | 2.73824 | ||||||||
\(401\) | 11128.8 | 1.38590 | 0.692948 | − | 0.720988i | \(-0.256312\pi\) | ||||
0.692948 | + | 0.720988i | \(0.256312\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1695.72 | 0.209603 | ||||||||
\(404\) | 11702.3 | 1.44111 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12219.0 | 1.48814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7220.39 | −0.872922 | −0.436461 | − | 0.899723i | \(-0.643768\pi\) | ||||
−0.436461 | + | 0.899723i | \(0.643768\pi\) | |||||||
\(410\) | 38126.9 | 4.59257 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21801.4 | −2.60699 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4417.74 | −0.522550 | ||||||||
\(416\) | −22270.4 | −2.62475 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −841.106 | −0.0984207 | ||||||||
\(419\) | −16631.2 | −1.93911 | −0.969556 | − | 0.244870i | \(-0.921255\pi\) | ||||
−0.969556 | + | 0.244870i | \(0.921255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −654.498 | −0.0757679 | −0.0378839 | − | 0.999282i | \(-0.512062\pi\) | ||||
−0.0378839 | + | 0.999282i | \(0.512062\pi\) | |||||||
\(422\) | −6679.14 | −0.770463 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16481.9 | −1.88781 | ||||||||
\(425\) | 2210.31 | 0.252273 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18646.8 | −2.10590 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4668.74 | −0.523597 | ||||||||
\(431\) | 3049.91 | 0.340856 | 0.170428 | − | 0.985370i | \(-0.445485\pi\) | ||||
0.170428 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1599.41 | 0.177512 | 0.0887562 | − | 0.996053i | \(-0.471711\pi\) | ||||
0.0887562 | + | 0.996053i | \(0.471711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10092.5 | 1.10859 | ||||||||
\(437\) | −899.797 | −0.0984968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15893.9 | 1.72796 | 0.863979 | − | 0.503528i | \(-0.167965\pi\) | ||||
0.863979 | + | 0.503528i | \(0.167965\pi\) | |||||||
\(440\) | −28225.0 | −3.05813 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6196.39 | −0.666815 | ||||||||
\(443\) | 6160.22 | 0.660679 | 0.330339 | − | 0.943862i | \(-0.392837\pi\) | ||||
0.330339 | + | 0.943862i | \(0.392837\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8244.23 | −0.878233 | ||||||||
\(446\) | −2493.92 | −0.264777 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8742.47 | −0.918892 | −0.459446 | − | 0.888206i | \(-0.651952\pi\) | ||||
−0.459446 | + | 0.888206i | \(0.651952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13183.7 | −1.37649 | ||||||||
\(452\) | −25821.4 | −2.68703 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20729.9 | 2.14296 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −580.112 | −0.0593796 | −0.0296898 | − | 0.999559i | \(-0.509452\pi\) | ||||
−0.0296898 | + | 0.999559i | \(0.509452\pi\) | |||||||
\(458\) | 26147.3 | 2.66764 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −52997.0 | −5.37174 | ||||||||
\(461\) | 1957.05 | 0.197720 | 0.0988599 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988599 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8111.80 | 0.814227 | 0.407114 | − | 0.913378i | \(-0.366535\pi\) | ||||
0.407114 | + | 0.913378i | \(0.366535\pi\) | |||||||
\(464\) | 17961.8 | 1.79710 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22784.4 | −2.26495 | ||||||||
\(467\) | 1240.29 | 0.122899 | 0.0614493 | − | 0.998110i | \(-0.480428\pi\) | ||||
0.0614493 | + | 0.998110i | \(0.480428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 13625.1 | 1.33718 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22541.8 | −2.19824 | ||||||||
\(473\) | 1614.38 | 0.156933 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 885.276 | 0.0855142 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16647.2 | −1.59294 | ||||||||
\(479\) | 18605.0 | 1.77470 | 0.887352 | − | 0.461092i | \(-0.152542\pi\) | ||||
0.887352 | + | 0.461092i | \(0.152542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36053.4 | 3.41766 | ||||||||
\(482\) | −7926.84 | −0.749083 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7617.51 | −0.715393 | ||||||||
\(485\) | 4302.25 | 0.402794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 874.431 | 0.0813640 | 0.0406820 | − | 0.999172i | \(-0.487047\pi\) | ||||
0.0406820 | + | 0.999172i | \(0.487047\pi\) | |||||||
\(488\) | −31206.9 | −2.89481 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5849.95 | −0.537688 | −0.268844 | − | 0.963184i | \(-0.586642\pi\) | ||||
−0.268844 | + | 0.963184i | \(0.586642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1812.35 | 0.165566 | ||||||||
\(494\) | −2481.78 | −0.226034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2517.58 | 0.227908 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1095.76 | −0.0983029 | −0.0491514 | − | 0.998791i | \(-0.515652\pi\) | ||||
−0.0491514 | + | 0.998791i | \(0.515652\pi\) | |||||||
\(500\) | 12579.8 | 1.12517 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −919.907 | −0.0817878 | ||||||||
\(503\) | 4988.25 | 0.442177 | 0.221088 | − | 0.975254i | \(-0.429039\pi\) | ||||
0.221088 | + | 0.975254i | \(0.429039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10713.2 | 0.944025 | ||||||||
\(506\) | 26210.4 | 2.30275 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −43322.5 | −3.78371 | ||||||||
\(509\) | −16831.7 | −1.46572 | −0.732859 | − | 0.680381i | \(-0.761814\pi\) | ||||
−0.732859 | + | 0.680381i | \(0.761814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25046.5 | 2.16193 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16872.9 | −1.44792 | ||||||||
\(515\) | −19958.9 | −1.70775 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4711.35 | −0.400783 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −83281.2 | −7.02331 | ||||||||
\(521\) | −12826.2 | −1.07855 | −0.539277 | − | 0.842129i | \(-0.681302\pi\) | ||||
−0.539277 | + | 0.842129i | \(0.681302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3377.82 | 0.282412 | 0.141206 | − | 0.989980i | \(-0.454902\pi\) | ||||
0.141206 | + | 0.989980i | \(0.454902\pi\) | |||||||
\(524\) | −4217.30 | −0.351591 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24435.6 | −2.02556 | ||||||||
\(527\) | 254.024 | 0.0209971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15872.3 | 1.30453 | ||||||||
\(530\) | −26483.9 | −2.17054 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38900.1 | −3.16126 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17070.8 | −1.37951 | ||||||||
\(536\) | −44825.6 | −3.61226 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2157.93 | −0.172927 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4866.90 | 0.386774 | 0.193387 | − | 0.981123i | \(-0.438053\pi\) | ||||
0.193387 | + | 0.981123i | \(0.438053\pi\) | |||||||
\(542\) | 27145.5 | 2.15129 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3336.18 | −0.262936 | ||||||||
\(545\) | 9239.55 | 0.726199 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6870.41 | 0.537034 | 0.268517 | − | 0.963275i | \(-0.413467\pi\) | ||||
0.268517 | + | 0.963275i | \(0.413467\pi\) | |||||||
\(548\) | 35342.9 | 2.75506 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25787.4 | −1.99923 | ||||||||
\(551\) | 725.883 | 0.0561228 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14726.0 | −1.12933 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36424.2 | −2.77829 | ||||||||
\(557\) | 19795.9 | 1.50589 | 0.752943 | − | 0.658086i | \(-0.228634\pi\) | ||||
0.752943 | + | 0.658086i | \(0.228634\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4763.42 | 0.360414 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 44296.1 | 3.32477 | ||||||||
\(563\) | 6981.58 | 0.522626 | 0.261313 | − | 0.965254i | \(-0.415844\pi\) | ||||
0.261313 | + | 0.965254i | \(0.415844\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23639.1 | −1.76019 | ||||||||
\(566\) | 18983.4 | 1.40977 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −489.378 | −0.0361512 | ||||||||
\(569\) | 3412.25 | 0.251404 | 0.125702 | − | 0.992068i | \(-0.459882\pi\) | ||||
0.125702 | + | 0.992068i | \(0.459882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20647.3 | 1.51325 | 0.756624 | − | 0.653850i | \(-0.226847\pi\) | ||||
0.756624 | + | 0.653850i | \(0.226847\pi\) | |||||||
\(572\) | 50544.9 | 3.69473 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27586.8 | −2.00078 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12938.7 | −0.933530 | −0.466765 | − | 0.884381i | \(-0.654581\pi\) | ||||
−0.466765 | + | 0.884381i | \(0.654581\pi\) | |||||||
\(578\) | 24407.5 | 1.75643 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 42753.7 | 3.06078 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9157.75 | 0.650558 | ||||||||
\(584\) | 1198.22 | 0.0849019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10100.7 | −0.712038 | ||||||||
\(587\) | 14032.4 | 0.986676 | 0.493338 | − | 0.869838i | \(-0.335777\pi\) | ||||
0.493338 | + | 0.869838i | \(0.335777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 101.742 | 0.00711750 | ||||||||
\(590\) | −36221.2 | −2.52746 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 53527.2 | 3.71614 | ||||||||
\(593\) | 23344.9 | 1.61663 | 0.808313 | − | 0.588752i | \(-0.200381\pi\) | ||||
0.808313 | + | 0.588752i | \(0.200381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28231.7 | −1.94029 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 77336.7 | 5.28852 | ||||||||
\(599\) | −21813.4 | −1.48793 | −0.743966 | − | 0.668217i | \(-0.767058\pi\) | ||||
−0.743966 | + | 0.668217i | \(0.767058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1010.28 | −0.0685690 | −0.0342845 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342845 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33750.4 | −2.27365 | ||||||||
\(605\) | −6973.71 | −0.468631 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1763.19 | 0.117901 | 0.0589504 | − | 0.998261i | \(-0.481225\pi\) | ||||
0.0589504 | + | 0.998261i | \(0.481225\pi\) | |||||||
\(608\) | −1336.21 | −0.0891288 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −50144.7 | −3.32836 | ||||||||
\(611\) | −13901.4 | −0.920440 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 264.802 | 0.0174474 | 0.00872368 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872368 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(614\) | −29251.4 | −1.92263 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17930.8 | 1.16996 | 0.584980 | − | 0.811048i | \(-0.301102\pi\) | ||||
0.584980 | + | 0.811048i | \(0.301102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19581.1 | 1.27146 | 0.635729 | − | 0.771912i | \(-0.280700\pi\) | ||||
0.635729 | + | 0.771912i | \(0.280700\pi\) | |||||||
\(620\) | 5992.49 | 0.388168 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6558.07 | −0.422757 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9076.78 | −0.580914 | ||||||||
\(626\) | −25105.6 | −1.60291 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34561.2 | 2.19609 | ||||||||
\(629\) | 5400.91 | 0.342366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13595.9 | 0.857754 | 0.428877 | − | 0.903363i | \(-0.358909\pi\) | ||||
0.428877 | + | 0.903363i | \(0.358909\pi\) | |||||||
\(632\) | −33838.6 | −2.12979 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16626.7 | 1.04153 | ||||||||
\(635\) | −39661.1 | −2.47859 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21144.4 | −1.31209 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14673.8 | 0.906301 | ||||||||
\(641\) | 9626.58 | 0.593178 | 0.296589 | − | 0.955005i | \(-0.404151\pi\) | ||||
0.296589 | + | 0.955005i | \(0.404151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26571.5 | −1.62967 | −0.814834 | − | 0.579695i | \(-0.803172\pi\) | ||||
−0.814834 | + | 0.579695i | \(0.803172\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −371.778 | −0.0226431 | ||||||||
\(647\) | −29729.0 | −1.80644 | −0.903220 | − | 0.429179i | \(-0.858803\pi\) | ||||
−0.903220 | + | 0.429179i | \(0.858803\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12524.8 | 0.757535 | ||||||||
\(650\) | −76088.7 | −4.59145 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16177.9 | 0.971742 | ||||||||
\(653\) | 16796.1 | 1.00656 | 0.503278 | − | 0.864125i | \(-0.332127\pi\) | ||||
0.503278 | + | 0.864125i | \(0.332127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3860.88 | −0.230316 | ||||||||
\(656\) | −57753.6 | −3.43734 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2078.96 | 0.122891 | 0.0614453 | − | 0.998110i | \(-0.480429\pi\) | ||||
0.0614453 | + | 0.998110i | \(0.480429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6600.40 | 0.388390 | 0.194195 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194195 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(662\) | −27379.2 | −1.60744 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14177.9 | 0.828629 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22619.8 | −1.31311 | ||||||||
\(668\) | 32522.2 | 1.88372 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −72027.9 | −4.15325 | ||||||||
\(671\) | 17339.3 | 0.997580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21644.8 | −1.23974 | −0.619871 | − | 0.784704i | \(-0.712815\pi\) | ||||
−0.619871 | + | 0.784704i | \(0.712815\pi\) | |||||||
\(674\) | 11883.2 | 0.679113 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 108289. | 6.16118 | ||||||||
\(677\) | 349.464 | 0.0198390 | 0.00991949 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00991949 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12475.8 | −0.703565 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2963.67 | −0.166400 | ||||||||
\(683\) | 14807.9 | 0.829589 | 0.414795 | − | 0.909915i | \(-0.363853\pi\) | ||||
0.414795 | + | 0.909915i | \(0.363853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32355.9 | 1.80475 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7072.08 | 0.391890 | ||||||||
\(689\) | 27021.0 | 1.49408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21679.4 | −1.19352 | −0.596760 | − | 0.802420i | \(-0.703546\pi\) | ||||
−0.596760 | + | 0.802420i | \(0.703546\pi\) | |||||||
\(692\) | 731.415 | 0.0401795 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26796.2 | −1.46566 | ||||||||
\(695\) | −33345.8 | −1.81997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5827.35 | −0.316681 | ||||||||
\(698\) | −46569.7 | −2.52534 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5065.92 | −0.272949 | −0.136474 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136474 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2163.18 | 0.116054 | ||||||||
\(704\) | 6634.99 | 0.355207 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45821.5 | 2.44265 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16981.8 | −0.899527 | −0.449764 | − | 0.893148i | \(-0.648492\pi\) | ||||
−0.449764 | + | 0.893148i | \(0.648492\pi\) | |||||||
\(710\) | −786.356 | −0.0415654 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 26458.3 | 1.39265 | ||||||||
\(713\) | −3170.46 | −0.166528 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46273.1 | 2.42030 | ||||||||
\(716\) | 49283.3 | 2.57235 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −192.343 | −0.00999746 | ||||||||
\(719\) | −31450.6 | −1.63130 | −0.815652 | − | 0.578543i | \(-0.803622\pi\) | ||||
−0.815652 | + | 0.578543i | \(0.803622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 35222.1 | 1.81556 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −50568.7 | −2.59581 | ||||||||
\(725\) | 22254.8 | 1.14003 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14930.2 | −0.761665 | −0.380833 | − | 0.924644i | \(-0.624363\pi\) | ||||
−0.380833 | + | 0.924644i | \(0.624363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1925.36 | 0.0976174 | ||||||||
\(731\) | 713.575 | 0.0361047 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26799.5 | −1.35043 | −0.675213 | − | 0.737623i | \(-0.735948\pi\) | ||||
−0.675213 | + | 0.737623i | \(0.735948\pi\) | |||||||
\(734\) | 17202.3 | 0.865050 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41638.6 | 2.08535 | ||||||||
\(737\) | 24906.2 | 1.24482 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22511.2 | 1.12055 | 0.560275 | − | 0.828307i | \(-0.310695\pi\) | ||||
0.560275 | + | 0.828307i | \(0.310695\pi\) | |||||||
\(740\) | 127409. | 6.32924 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23783.0 | 1.17431 | 0.587155 | − | 0.809474i | \(-0.300248\pi\) | ||||
0.587155 | + | 0.809474i | \(0.300248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25845.7 | −1.27102 | ||||||||
\(746\) | −20296.5 | −0.996121 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7571.78 | 0.370123 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6729.39 | −0.326976 | −0.163488 | − | 0.986545i | \(-0.552274\pi\) | ||||
−0.163488 | + | 0.986545i | \(0.552274\pi\) | |||||||
\(752\) | −20638.8 | −1.00083 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −62389.0 | −3.01336 | ||||||||
\(755\) | −30898.0 | −1.48939 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34646.1 | 1.66345 | 0.831726 | − | 0.555187i | \(-0.187353\pi\) | ||||
0.831726 | + | 0.555187i | \(0.187353\pi\) | |||||||
\(758\) | −11902.1 | −0.570321 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4996.80 | −0.238491 | ||||||||
\(761\) | 24096.3 | 1.14782 | 0.573908 | − | 0.818919i | \(-0.305427\pi\) | ||||
0.573908 | + | 0.818919i | \(0.305427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −80676.6 | −3.82039 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15118.0 | 0.713100 | ||||||||
\(767\) | 36955.8 | 1.73976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28099.8 | 1.31769 | 0.658846 | − | 0.752278i | \(-0.271045\pi\) | ||||
0.658846 | + | 0.752278i | \(0.271045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18178.5 | 0.847487 | ||||||||
\(773\) | 9455.98 | 0.439984 | 0.219992 | − | 0.975502i | \(-0.429397\pi\) | ||||
0.219992 | + | 0.975502i | \(0.429397\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3119.30 | 0.144579 | ||||||||
\(776\) | −13807.3 | −0.638727 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39244.5 | −1.80846 | ||||||||
\(779\) | −2333.98 | −0.107347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 271.911 | 0.0124580 | ||||||||
\(782\) | 11585.3 | 0.529781 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31640.2 | 1.43858 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16846.0 | 0.763017 | 0.381509 | − | 0.924365i | \(-0.375405\pi\) | ||||
0.381509 | + | 0.924365i | \(0.375405\pi\) | |||||||
\(788\) | 28937.3 | 1.30818 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −54373.5 | −2.44876 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51161.6 | 2.29105 | ||||||||
\(794\) | −22018.5 | −0.984140 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32040.4 | −1.42669 | ||||||||
\(797\) | −35955.5 | −1.59801 | −0.799003 | − | 0.601327i | \(-0.794639\pi\) | ||||
−0.799003 | + | 0.601327i | \(0.794639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2082.47 | −0.0922057 | ||||||||
\(800\) | −40966.6 | −1.81049 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −57389.7 | −2.52681 | ||||||||
\(803\) | −665.761 | −0.0292580 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8744.64 | −0.382155 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −34382.1 | −1.49698 | ||||||||
\(809\) | −13680.6 | −0.594543 | −0.297272 | − | 0.954793i | \(-0.596077\pi\) | ||||
−0.297272 | + | 0.954793i | \(0.596077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10215.1 | −0.442294 | −0.221147 | − | 0.975241i | \(-0.570980\pi\) | ||||
−0.221147 | + | 0.975241i | \(0.570980\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −63011.7 | −2.71322 | ||||||||
\(815\) | 14810.6 | 0.636557 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 285.802 | 0.0122386 | ||||||||
\(818\) | 37234.6 | 1.59154 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −137469. | −5.85440 | ||||||||
\(821\) | −14255.6 | −0.605996 | −0.302998 | − | 0.952991i | \(-0.597988\pi\) | ||||
−0.302998 | + | 0.952991i | \(0.597988\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31349.9 | −1.32781 | −0.663905 | − | 0.747817i | \(-0.731102\pi\) | ||||
−0.663905 | + | 0.747817i | \(0.731102\pi\) | |||||||
\(824\) | 64054.3 | 2.70805 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6114.87 | 0.257116 | 0.128558 | − | 0.991702i | \(-0.458965\pi\) | ||||
0.128558 | + | 0.991702i | \(0.458965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32418.4 | −1.35819 | −0.679093 | − | 0.734052i | \(-0.737627\pi\) | ||||
−0.679093 | + | 0.734052i | \(0.737627\pi\) | |||||||
\(830\) | 22781.7 | 0.952730 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19577.3 | 0.815770 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29773.6 | 1.23396 | ||||||||
\(836\) | 3032.65 | 0.125462 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 85765.1 | 3.53545 | ||||||||
\(839\) | −44683.5 | −1.83867 | −0.919336 | − | 0.393474i | \(-0.871273\pi\) | ||||
−0.919336 | + | 0.393474i | \(0.871273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6141.15 | −0.251800 | ||||||||
\(842\) | 3375.17 | 0.138142 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24082.0 | 0.982151 | ||||||||
\(845\) | 99136.8 | 4.03599 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40117.1 | 1.62456 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11398.3 | −0.459952 | ||||||||
\(851\) | −67408.4 | −2.71531 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9965.17 | 0.400001 | 0.200001 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200001 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 54785.7 | 2.18754 | ||||||||
\(857\) | 8639.89 | 0.344379 | 0.172190 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172190 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15551.5 | −0.617707 | −0.308853 | − | 0.951110i | \(-0.599945\pi\) | ||||
−0.308853 | + | 0.951110i | \(0.599945\pi\) | |||||||
\(860\) | 16833.4 | 0.667458 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15728.0 | −0.621460 | ||||||||
\(863\) | 47746.4 | 1.88332 | 0.941661 | − | 0.336563i | \(-0.109265\pi\) | ||||
0.941661 | + | 0.336563i | \(0.109265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 669.599 | 0.0263203 | ||||||||
\(866\) | −8247.97 | −0.323646 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18801.6 | 0.733946 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73488.6 | 2.85886 | ||||||||
\(872\) | −29652.6 | −1.15156 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4640.14 | 0.179583 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37958.8 | −1.46155 | −0.730773 | − | 0.682620i | \(-0.760840\pi\) | ||||
−0.730773 | + | 0.682620i | \(0.760840\pi\) | |||||||
\(878\) | −81962.8 | −3.15047 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 68699.9 | 2.63168 | ||||||||
\(881\) | 32323.6 | 1.23611 | 0.618053 | − | 0.786136i | \(-0.287922\pi\) | ||||
0.618053 | + | 0.786136i | \(0.287922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27760.0 | 1.05798 | 0.528991 | − | 0.848628i | \(-0.322571\pi\) | ||||
0.528991 | + | 0.848628i | \(0.322571\pi\) | |||||||
\(884\) | 22341.4 | 0.850026 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31767.5 | −1.20457 | ||||||||
\(887\) | −32759.6 | −1.24009 | −0.620044 | − | 0.784567i | \(-0.712885\pi\) | ||||
−0.620044 | + | 0.784567i | \(0.712885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 42514.5 | 1.60122 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8991.97 | 0.337526 | ||||||||
\(893\) | −834.071 | −0.0312554 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45118.1 | 1.68506 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45083.8 | 1.67535 | ||||||||
\(899\) | 2557.67 | 0.0948868 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4047.83 | 0.149670 | ||||||||
\(902\) | 67986.9 | 2.50966 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 75865.3 | 2.79120 | ||||||||
\(905\) | −46294.8 | −1.70043 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42682.6 | −1.56257 | −0.781286 | − | 0.624174i | \(-0.785436\pi\) | ||||
−0.781286 | + | 0.624174i | \(0.785436\pi\) | |||||||
\(908\) | −74742.8 | −2.73175 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50130.0 | 1.82314 | 0.911570 | − | 0.411144i | \(-0.134871\pi\) | ||||
0.911570 | + | 0.411144i | \(0.134871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7877.60 | −0.285554 | ||||||||
\(914\) | 2991.57 | 0.108263 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −94275.3 | −3.40059 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33784.7 | −1.21268 | −0.606341 | − | 0.795205i | \(-0.707363\pi\) | ||||
−0.606341 | + | 0.795205i | \(0.707363\pi\) | |||||||
\(920\) | 155709. | 5.57998 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10092.3 | −0.360489 | ||||||||
\(923\) | 802.303 | 0.0286112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66320.6 | 2.35742 | ||||||||
\(926\) | −41831.5 | −1.48452 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −33590.7 | −1.18822 | ||||||||
\(929\) | −50854.8 | −1.79601 | −0.898004 | − | 0.439987i | \(-0.854983\pi\) | ||||
−0.898004 | + | 0.439987i | \(0.854983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 82150.4 | 2.88726 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6396.01 | −0.224073 | ||||||||
\(935\) | 6931.85 | 0.242455 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3684.00 | 0.128443 | 0.0642215 | − | 0.997936i | \(-0.479544\pi\) | ||||
0.0642215 | + | 0.997936i | \(0.479544\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −49125.8 | −1.70458 | ||||||||
\(941\) | −28660.5 | −0.992886 | −0.496443 | − | 0.868069i | \(-0.665361\pi\) | ||||
−0.496443 | + | 0.868069i | \(0.665361\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 72730.8 | 2.51160 | ||||||||
\(944\) | 54866.9 | 1.89170 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8325.18 | −0.286126 | ||||||||
\(947\) | −31873.0 | −1.09370 | −0.546849 | − | 0.837231i | \(-0.684173\pi\) | ||||
−0.546849 | + | 0.837231i | \(0.684173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1964.40 | −0.0671942 | ||||||||
\(950\) | −4565.26 | −0.155912 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3310.08 | 0.112512 | 0.0562561 | − | 0.998416i | \(-0.482084\pi\) | ||||
0.0562561 | + | 0.998416i | \(0.482084\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −73858.2 | −2.50261 | ||||||||
\(956\) | 60022.3 | 2.03061 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −95943.6 | −3.23570 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29432.5 | −0.987966 | ||||||||
\(962\) | −185923. | −6.23119 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28580.6 | 0.954897 | ||||||||
\(965\) | 16642.2 | 0.555161 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −168.413 | −0.00560061 | −0.00280031 | − | 0.999996i | \(-0.500891\pi\) | ||||
−0.00280031 | + | 0.999996i | \(0.500891\pi\) | |||||||
\(968\) | 22380.8 | 0.743127 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22186.2 | −0.734387 | ||||||||
\(971\) | 37669.9 | 1.24499 | 0.622495 | − | 0.782624i | \(-0.286119\pi\) | ||||
0.622495 | + | 0.782624i | \(0.286119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4509.33 | −0.148345 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 75957.7 | 2.49114 | ||||||||
\(977\) | −26688.7 | −0.873948 | −0.436974 | − | 0.899474i | \(-0.643950\pi\) | ||||
−0.436974 | + | 0.899474i | \(0.643950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14700.9 | −0.479921 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 30167.5 | 0.980329 | ||||||||
\(983\) | −1102.29 | −0.0357655 | −0.0178828 | − | 0.999840i | \(-0.505693\pi\) | ||||
−0.0178828 | + | 0.999840i | \(0.505693\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26491.6 | 0.856948 | ||||||||
\(986\) | −9346.07 | −0.301866 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8948.19 | 0.288137 | ||||||||
\(989\) | −8906.09 | −0.286347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16523.6 | 0.529656 | 0.264828 | − | 0.964296i | \(-0.414685\pi\) | ||||
0.264828 | + | 0.964296i | \(0.414685\pi\) | |||||||
\(992\) | −4708.17 | −0.150690 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29332.5 | −0.934575 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17994.5 | −0.571605 | −0.285802 | − | 0.958289i | \(-0.592260\pi\) | ||||
−0.285802 | + | 0.958289i | \(0.592260\pi\) | |||||||
\(998\) | 5650.72 | 0.179229 | ||||||||
\(999\) | 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 | 1323.4.a.ba.1.1 | 4 | ||
3.2 | odd | 2 | inner | 1323.4.a.ba.1.4 | 4 | ||
7.6 | odd | 2 | 189.4.a.l.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 189.4.a.l.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.4.a.l.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
189.4.a.l.1.4 | yes | 4 | 21.20 | even | 2 | ||
1323.4.a.ba.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1323.4.a.ba.1.4 | 4 | 3.2 | odd | 2 | inner |