Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(33,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 95x^{6} + 756x^{4} + 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.6 | ||
Root | \(1.60125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.33 |
Dual form | 136.4.b.b.33.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.95309i | 0.568322i | 0.958777 | + | 0.284161i | \(0.0917150\pi\) | ||||
−0.958777 | + | 0.284161i | \(0.908285\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.89575i | 0.437889i | 0.975737 | + | 0.218944i | \(0.0702614\pi\) | ||||
−0.975737 | + | 0.218944i | \(0.929739\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.46235i | − | 0.240944i | −0.992717 | − | 0.120472i | \(-0.961559\pi\) | ||
0.992717 | − | 0.120472i | \(-0.0384408\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 18.2793 | 0.677010 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.3865i | 1.65520i | 0.561318 | + | 0.827600i | \(0.310294\pi\) | ||||
−0.561318 | + | 0.827600i | \(0.689706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −56.1938 | −1.19887 | −0.599437 | − | 0.800422i | \(-0.704609\pi\) | ||||
−0.599437 | + | 0.800422i | \(0.704609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.4576 | −0.248862 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.6861 | + | 65.2168i | 0.366458 | + | 0.930435i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −134.845 | −1.62819 | −0.814095 | − | 0.580731i | \(-0.802767\pi\) | ||||
−0.814095 | + | 0.580731i | \(0.802767\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.1777 | 0.136934 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 39.1633i | 0.355049i | 0.984116 | + | 0.177524i | \(0.0568088\pi\) | ||||
−0.984116 | + | 0.177524i | \(0.943191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 101.032 | 0.808253 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 133.714i | 0.953082i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 113.700i | − | 0.728053i | −0.931389 | − | 0.364027i | \(-0.881402\pi\) | ||
0.931389 | − | 0.364027i | \(-0.118598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 306.516i | 1.77587i | 0.459969 | + | 0.887935i | \(0.347861\pi\) | ||||
−0.459969 | + | 0.887935i | \(0.652139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −178.326 | −0.940686 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.8465 | 0.105507 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 61.9621i | − | 0.275311i | −0.990480 | − | 0.137656i | \(-0.956043\pi\) | ||
0.990480 | − | 0.137656i | \(-0.0439567\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 165.945i | − | 0.681346i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 317.272i | − | 1.20853i | −0.796785 | − | 0.604263i | \(-0.793468\pi\) | ||
0.796785 | − | 0.604263i | \(-0.206532\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 122.660 | 0.435009 | 0.217505 | − | 0.976059i | \(-0.430208\pi\) | ||||
0.217505 | + | 0.976059i | \(0.430208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 89.4907i | 0.296455i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 303.233 | 0.941086 | 0.470543 | − | 0.882377i | \(-0.344058\pi\) | ||||
0.470543 | + | 0.882377i | \(0.344058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 323.087 | 0.941946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −192.591 | + | 75.8532i | −0.528786 | + | 0.208266i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 133.743 | 0.346623 | 0.173311 | − | 0.984867i | \(-0.444553\pi\) | ||||
0.173311 | + | 0.984867i | \(0.444553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −295.637 | −0.724794 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 398.210i | − | 0.925336i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −130.660 | −0.288312 | −0.144156 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144156 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 772.618i | − | 1.62170i | −0.585256 | − | 0.810849i | \(-0.699006\pi\) | ||
0.585256 | − | 0.810849i | \(-0.300994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 81.5685i | − | 0.163122i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 275.111i | − | 0.524974i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 378.907 | 0.690909 | 0.345455 | − | 0.938435i | \(-0.387725\pi\) | ||||
0.345455 | + | 0.938435i | \(0.387725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −115.653 | −0.201782 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 465.116i | − | 0.777452i | −0.921353 | − | 0.388726i | \(-0.872915\pi\) | ||
0.921353 | − | 0.388726i | \(-0.127085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 664.801i | 1.06588i | 0.846154 | + | 0.532939i | \(0.178913\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 298.355i | 0.459348i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 269.466 | 0.398811 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 925.763i | − | 1.31844i | −0.751952 | − | 0.659218i | \(-0.770887\pi\) | ||
0.751952 | − | 0.659218i | \(-0.229113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 98.6724 | 0.135353 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −723.561 | −0.956882 | −0.478441 | − | 0.878120i | \(-0.658798\pi\) | ||||
−0.478441 | + | 0.878120i | \(0.658798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −319.285 | + | 125.752i | −0.407427 | + | 0.160468i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 335.766 | 0.413769 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 889.439 | 1.05933 | 0.529665 | − | 0.848207i | \(-0.322318\pi\) | ||||
0.529665 | + | 0.848207i | \(0.322318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 250.757i | 0.288862i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −905.170 | −1.00927 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 660.168i | − | 0.712967i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1506.43i | 1.57686i | 0.615127 | + | 0.788428i | \(0.289105\pi\) | ||||
−0.615127 | + | 0.788428i | \(0.710895\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1103.82i | 1.12059i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 606.815 | 0.597825 | 0.298912 | − | 0.954281i | \(-0.403376\pi\) | ||||
0.298912 | + | 0.954281i | \(0.403376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 582.633 | 0.557364 | 0.278682 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278682 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64.5147i | 0.0599619i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1057i | 0.0127444i | 0.999980 | + | 0.00637221i | \(0.00202835\pi\) | ||||
−0.999980 | + | 0.00637221i | \(0.997972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1599.48i | 1.40553i | 0.711422 | + | 0.702765i | \(0.248051\pi\) | ||||
−0.711422 | + | 0.702765i | \(0.751949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 182.980 | 0.156465 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 620.655i | − | 0.516693i | −0.966052 | − | 0.258347i | \(-0.916822\pi\) | ||
0.966052 | − | 0.258347i | \(-0.0831777\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −191.734 | −0.155472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1027.18 | −0.811650 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 291.020 | − | 114.620i | 0.224183 | − | 0.0882960i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2315.52 | −1.73969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 936.932 | 0.686832 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1106.59i | 0.791814i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −970.396 | −0.678021 | −0.339011 | − | 0.940783i | \(-0.610092\pi\) | ||||
−0.339011 | + | 0.940783i | \(0.610092\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 362.224i | 0.247225i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 705.717i | 0.470678i | 0.971913 | + | 0.235339i | \(0.0756200\pi\) | ||||
−0.971913 | + | 0.235339i | \(0.924380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 601.727i | 0.392303i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −654.628 | −0.417344 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2470.01 | −1.54035 | −0.770173 | − | 0.637835i | \(-0.779830\pi\) | ||||
−0.770173 | + | 0.637835i | \(0.779830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 435.484i | 0.265736i | 0.991134 | + | 0.132868i | \(0.0424186\pi\) | ||||
−0.991134 | + | 0.132868i | \(0.957581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 895.473i | 0.534840i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3393.35i | − | 1.98438i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 556.646 | 0.318806 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 954.105i | 0.535328i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2428.83 | 1.33542 | 0.667709 | − | 0.744422i | \(-0.267275\pi\) | ||||
0.667709 | + | 0.744422i | \(0.267275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2608.09 | 1.40558 | 0.702792 | − | 0.711396i | \(-0.251937\pi\) | ||||
0.702792 | + | 0.711396i | \(0.251937\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 469.523 | + | 1192.12i | 0.248096 | + | 0.629914i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1500.63 | −0.777634 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 164.006 | 0.0833703 | 0.0416851 | − | 0.999131i | \(-0.486727\pi\) | ||||
0.0416851 | + | 0.999131i | \(0.486727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 394.955i | 0.196993i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 174.760 | 0.0855469 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 289.416i | 0.139072i | 0.997579 | + | 0.0695362i | \(0.0221519\pi\) | ||||
−0.997579 | + | 0.0695362i | \(0.977848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 873.041i | − | 0.411916i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2147.52i | − | 0.995090i | −0.867438 | − | 0.497545i | \(-0.834235\pi\) | ||
0.867438 | − | 0.497545i | \(-0.165765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 960.747 | 0.437299 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2464.87 | −1.10230 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4383.99i | − | 1.92664i | −0.268357 | − | 0.963320i | \(-0.586481\pi\) | ||
0.268357 | − | 0.963320i | \(-0.413519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 450.839i | − | 0.194744i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 385.849i | − | 0.163854i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3793.10 | 1.58385 | 0.791926 | − | 0.610617i | \(-0.209079\pi\) | ||||
0.791926 | + | 0.610617i | \(0.209079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1726.75i | 0.709108i | 0.935036 | + | 0.354554i | \(0.115367\pi\) | ||||
−0.935036 | + | 0.354554i | \(0.884633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2281.61 | 0.921646 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 303.351 | 0.120556 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3938.21 | + | 1551.09i | −1.54006 | + | 0.606561i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 596.677 | 0.229640 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1286.01 | 0.487184 | 0.243592 | − | 0.969878i | \(-0.421674\pi\) | ||||
0.243592 | + | 0.969878i | \(0.421674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1682.07i | − | 0.627349i | −0.949531 | − | 0.313674i | \(-0.898440\pi\) | ||
0.949531 | − | 0.313674i | \(-0.101560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 812.426 | 0.298354 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 415.578i | 0.150298i | 0.997172 | + | 0.0751489i | \(0.0239432\pi\) | ||||
−0.997172 | + | 0.0751489i | \(0.976057\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2761.31i | − | 0.983637i | −0.870698 | − | 0.491819i | \(-0.836332\pi\) | ||
0.870698 | − | 0.491819i | \(-0.163668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1118.95i | 0.392659i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −507.369 | −0.175420 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1553.28 | 0.529200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 715.877i | 0.240372i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8142.83i | − | 2.69498i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2713.80i | − | 0.885431i | −0.896662 | − | 0.442715i | \(-0.854015\pi\) | ||
0.896662 | − | 0.442715i | \(-0.145985\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1373.53 | 0.441843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 600.510i | 0.190486i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1367.78 | 0.427886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1963.22 | −0.605762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1443.40 | − | 3664.78i | −0.439337 | − | 1.11547i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6395.76 | −1.92059 | −0.960296 | − | 0.278984i | \(-0.910002\pi\) | ||||
−0.960296 | + | 0.278984i | \(0.910002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1846.79 | 0.547196 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3844.30i | 1.12403i | 0.827127 | + | 0.562016i | \(0.189974\pi\) | ||||
−0.827127 | + | 0.562016i | \(0.810026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4849.35 | −1.39936 | −0.699682 | − | 0.714455i | \(-0.746675\pi\) | ||||
−0.699682 | + | 0.714455i | \(0.746675\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 795.755i | 0.226653i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2719.86i | 0.764738i | 0.924010 | + | 0.382369i | \(0.124892\pi\) | ||||
−0.924010 | + | 0.382369i | \(0.875108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1484.55i | 0.412091i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2733.86 | 0.749296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2524.92 | 0.683362 | 0.341681 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341681 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1943.29i | 0.519413i | 0.965688 | + | 0.259706i | \(0.0836258\pi\) | ||||
−0.965688 | + | 0.259706i | \(0.916374\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3901.66i | 1.03001i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1581.75i | 0.412468i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7577.47 | 1.95200 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2136.74i | − | 0.543817i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2332.58 | 0.586578 | 0.293289 | − | 0.956024i | \(-0.405250\pi\) | ||||
0.293289 | + | 0.956024i | \(0.405250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2364.93 | −0.587676 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −371.358 | − | 942.876i | −0.0911974 | − | 0.231550i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −807.810 | −0.196069 | −0.0980346 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980346 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −276.497 | −0.0663347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2078.35i | − | 0.492900i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6420.82 | −1.50542 | −0.752708 | − | 0.658354i | \(-0.771253\pi\) | ||||
−0.752708 | + | 0.658354i | \(0.771253\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 654.772i | 0.151782i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2626.59i | 0.602040i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6335.06i | − | 1.43589i | −0.696097 | − | 0.717947i | \(-0.745082\pi\) | ||
0.696097 | − | 0.717947i | \(-0.254918\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1429.35 | −0.320394 | −0.160197 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160197 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −740.506 | −0.164167 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6100.94i | 1.33782i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7878.89i | 1.70901i | 0.519441 | + | 0.854506i | \(0.326140\pi\) | ||||
−0.519441 | + | 0.854506i | \(0.673860\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5602.90i | 1.20228i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2967.99 | 0.630090 | 0.315045 | − | 0.949077i | \(-0.397980\pi\) | ||||
0.315045 | + | 0.949077i | \(0.397980\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 401.204i | 0.0842725i | 0.999112 | + | 0.0421363i | \(0.0134164\pi\) | ||||
−0.999112 | + | 0.0421363i | \(0.986584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1949.53 | 0.405195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1415.78 | −0.291188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3593.45 | + | 3350.32i | −0.731417 | + | 0.681930i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4448.63 | −0.896162 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7390.62 | 1.47360 | 0.736800 | − | 0.676111i | \(-0.236336\pi\) | ||||
0.736800 | + | 0.676111i | \(0.236336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 639.676i | − | 0.126249i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8074.49 | −1.57754 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2200.74i | − | 0.425659i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 547.350i | − | 0.104813i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1791.98i | 0.339757i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3782.54 | 0.710123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −50.2688 | −0.00934524 | −0.00467262 | − | 0.999989i | \(-0.501487\pi\) | ||||
−0.00467262 | + | 0.999989i | \(0.501487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1720.57i | 0.316762i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 215.028i | 0.0392062i | 0.999808 | + | 0.0196031i | \(0.00624026\pi\) | ||||
−0.999808 | + | 0.0196031i | \(0.993760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4639.52i | 0.837831i | 0.908025 | + | 0.418915i | \(0.137590\pi\) | ||||
−0.908025 | + | 0.418915i | \(0.862410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 399.339 | 0.0714292 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3965.63i | 0.702624i | 0.936259 | + | 0.351312i | \(0.114264\pi\) | ||||
−0.936259 | + | 0.351312i | \(0.885736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6865.94 | 1.20507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −41.6554 | −0.00724293 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3463.64 | − | 8794.17i | −0.596663 | − | 1.51492i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5677.36 | −0.968994 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4723.41 | −0.798793 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1353.13i | − | 0.226749i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7497.94 | 1.24509 | 0.622544 | − | 0.782585i | \(-0.286099\pi\) | ||||
0.622544 | + | 0.782585i | \(0.286099\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1132.62i | − | 0.186388i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1855.03i | 0.302541i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 798.500i | − | 0.129071i | −0.997915 | − | 0.0645357i | \(-0.979443\pi\) | ||
0.997915 | − | 0.0645357i | \(-0.0205567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1832.85 | 0.293648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18509.4 | −2.93942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2972.32i | − | 0.467901i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 566.206i | − | 0.0883581i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4014.43i | 0.621054i | 0.950564 | + | 0.310527i | \(0.100506\pi\) | ||||
−0.950564 | + | 0.310527i | \(0.899494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4747.53 | 0.728165 | 0.364083 | − | 0.931367i | \(-0.381383\pi\) | ||||
0.364083 | + | 0.931367i | \(0.381383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7513.88i | − | 1.14262i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9653.02 | 1.45546 | 0.727731 | − | 0.685862i | \(-0.240575\pi\) | ||||
0.727731 | + | 0.685862i | \(0.240575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2277.09 | 0.340438 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 338.484 | + | 859.408i | 0.0501805 | + | 0.127408i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6641.04 | −0.976325 | −0.488162 | − | 0.872753i | \(-0.662333\pi\) | ||||
−0.488162 | + | 0.872753i | \(0.662333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11324.2 | 1.65100 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6837.94i | − | 0.988703i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3254.70 | −0.466736 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3305.96i | 0.470217i | 0.971969 | + | 0.235108i | \(0.0755445\pi\) | ||||
−0.971969 | + | 0.235108i | \(0.924455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5799.50i | − | 0.818185i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 596.808i | − | 0.0835168i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 238.635 | 0.0331261 | 0.0165631 | − | 0.999863i | \(-0.494728\pi\) | ||||
0.0165631 | + | 0.999863i | \(0.494728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3267.87 | −0.450005 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6389.23i | 0.872844i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11081.6i | − | 1.50191i | −0.660353 | − | 0.750955i | \(-0.729593\pi\) | ||
0.660353 | − | 0.750955i | \(-0.270407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2865.66i | − | 0.385334i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7956.45 | 1.06150 | 0.530752 | − | 0.847527i | \(-0.321910\pi\) | ||||
0.530752 | + | 0.847527i | \(0.321910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1319.24i | 0.174635i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2242.13 | 0.294506 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5128.06 | 0.668388 | 0.334194 | − | 0.942504i | \(-0.391536\pi\) | ||||
0.334194 | + | 0.942504i | \(0.391536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2554.11 | + | 1005.95i | −0.330349 | + | 0.130110i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2084.04 | −0.267496 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4532.30 | 0.577329 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2933.96i | − | 0.370910i | −0.982653 | − | 0.185455i | \(-0.940624\pi\) | ||
0.982653 | − | 0.185455i | \(-0.0593759\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1776.95 | −0.222955 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5278.07i | 0.657293i | 0.944453 | + | 0.328646i | \(0.106592\pi\) | ||||
−0.944453 | + | 0.328646i | \(0.893408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 17224.3i | − | 2.12904i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 483.075i | 0.0592696i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3741.67 | 0.455695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6880.00 | −0.831770 | −0.415885 | − | 0.909417i | \(-0.636528\pi\) | ||||
−0.415885 | + | 0.909417i | \(0.636528\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7294.16i | − | 0.875412i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 583.049i | 0.0694672i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3542.37i | − | 0.419008i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1286.02 | −0.151024 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3048.43i | − | 0.355431i | −0.984082 | − | 0.177715i | \(-0.943129\pi\) | ||
0.984082 | − | 0.177715i | \(-0.0568707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3607.83 | 0.417660 | 0.208830 | − | 0.977952i | \(-0.433034\pi\) | ||||
0.208830 | + | 0.977952i | \(0.433034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5542.88 | 0.637125 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2595.11 | + | 6588.96i | 0.296191 | + | 0.752027i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3447.69 | −0.390739 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10020.8 | 1.12776 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8866.93i | 0.990962i | 0.868619 | + | 0.495481i | \(0.165008\pi\) | ||||
−0.868619 | + | 0.495481i | \(0.834992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11353.2 | −1.26005 | −0.630024 | − | 0.776575i | \(-0.716955\pi\) | ||||
−0.630024 | + | 0.776575i | \(0.716955\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1643.82i | 0.181185i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5280.99i | − | 0.578087i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2786.53i | − | 0.302947i | −0.988461 | − | 0.151474i | \(-0.951598\pi\) | ||
0.988461 | − | 0.151474i | \(-0.0484019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5905.80 | 0.637707 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15244.4 | 1.63495 | 0.817474 | − | 0.575965i | \(-0.195374\pi\) | ||||
0.817474 | + | 0.575965i | \(0.195374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4354.47i | 0.463869i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7172.54i | 0.758947i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17473.1i | − | 1.83654i | −0.395958 | − | 0.918269i | \(-0.629587\pi\) | ||
0.395958 | − | 0.918269i | \(-0.370413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19158.9 | 2.00035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7701.91i | 0.798824i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1227.64 | −0.126489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16422.8 | −1.68102 | −0.840508 | − | 0.541800i | \(-0.817743\pi\) | ||||
−0.840508 | + | 0.541800i | \(0.817743\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8720.37 | + | 3434.58i | −0.886780 | + | 0.349264i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12802.9 | −1.29347 | −0.646737 | − | 0.762713i | \(-0.723867\pi\) | ||||
−0.646737 | + | 0.762713i | \(0.723867\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2291.00 | −0.229961 | −0.114980 | − | 0.993368i | \(-0.536680\pi\) | ||||
−0.114980 | + | 0.993368i | \(0.536680\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 4431.48i | − | 0.441946i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14464.0 | −1.43322 | −0.716610 | − | 0.697474i | \(-0.754307\pi\) | ||||
−0.716610 | + | 0.697474i | \(0.754307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1690.82i | − | 0.166471i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 484.325i | 0.0473812i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7406.97i | 0.720028i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13623.6 | −1.31599 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2444.72 | 0.234667 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6988.15i | 0.666590i | 0.942823 | + | 0.333295i | \(0.108161\pi\) | ||||
−0.942823 | + | 0.333295i | \(0.891839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3481.89i | 0.330063i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 516.083i | 0.0486182i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7375.11 | −0.690488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8494.76i | 0.790420i | 0.918591 | + | 0.395210i | \(0.129328\pi\) | ||||
−0.918591 | + | 0.395210i | \(0.870672\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −854.670 | −0.0790379 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5195.82 | −0.477565 | −0.238782 | − | 0.971073i | \(-0.576748\pi\) | ||||
−0.238782 | + | 0.971073i | \(0.576748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7415.14 | − | 2920.50i | 0.677406 | − | 0.266801i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5404.03 | −0.490693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2075.51 | −0.187323 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8790.68i | − | 0.788627i | −0.918976 | − | 0.394313i | \(-0.870982\pi\) | ||
0.918976 | − | 0.394313i | \(-0.129018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6341.81 | 0.565531 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7764.74i | 0.688295i | 0.938916 | + | 0.344148i | \(0.111832\pi\) | ||||
−0.938916 | + | 0.344148i | \(0.888168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2970.81i | 0.261781i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2837.17i | 0.248527i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9919.29 | 0.863782 | 0.431891 | − | 0.901926i | \(-0.357847\pi\) | ||||
0.431891 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2966.58 | 0.256817 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 18030.6i | − | 1.55180i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2852.42i | 0.244064i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18311.2i | 1.55769i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12946.3 | 1.09495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4230.44i | 0.355737i | 0.984054 | + | 0.177868i | \(0.0569201\pi\) | ||||
−0.984054 | + | 0.177868i | \(0.943080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10566.8 | 0.883465 | 0.441732 | − | 0.897147i | \(-0.354364\pi\) | ||||
0.441732 | + | 0.897147i | \(0.354364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1331.37 | 0.110677 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19990.0 | + | 7873.20i | −1.65233 | + | 0.650782i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10633.2 | 0.873941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2388.36 | −0.195190 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17828.7i | 1.44887i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −69.0581 | −0.00558064 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11201.3i | 0.900138i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19510.1i | 1.55911i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1980.86i | − | 0.157419i | −0.996898 | − | 0.0787094i | \(-0.974920\pi\) | ||
0.996898 | − | 0.0787094i | \(-0.0250799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5099.25 | −0.403001 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7830.67 | −0.615466 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3940.22i | 0.307992i | 0.988071 | + | 0.153996i | \(0.0492143\pi\) | ||||
−0.988071 | + | 0.153996i | \(0.950786\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 14122.9i | − | 1.09791i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15331.9i | 1.18541i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4131.08 | −0.317670 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 895.822i | 0.0685145i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3709.12 | 0.282155 | 0.141077 | − | 0.989999i | \(-0.454943\pi\) | ||||
0.141077 | + | 0.989999i | \(0.454943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6892.71 | −0.521522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4580.50 | − | 11629.9i | −0.344722 | − | 0.875247i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3393.34 | −0.254018 | −0.127009 | − | 0.991902i | \(-0.540538\pi\) | ||||
−0.127009 | + | 0.991902i | \(0.540538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3038.57 | 0.226254 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 440.311i | − | 0.0326125i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2927.65 | −0.215700 | −0.107850 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107850 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 19781.8i | − | 1.44981i | −0.688846 | − | 0.724907i | \(-0.741883\pi\) | ||
0.688846 | − | 0.724907i | \(-0.258117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3797.69i | 0.276877i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3956.74i | 0.286969i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17520.1 | 1.26407 | 0.632037 | − | 0.774938i | \(-0.282219\pi\) | ||||
0.632037 | + | 0.774938i | \(0.282219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4967.31 | 0.356536 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3228.79i | 0.230555i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8076.26i | 0.573730i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5028.83i | − | 0.355413i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7846.90 | 0.551748 | 0.275874 | − | 0.961194i | \(-0.411033\pi\) | ||||
0.275874 | + | 0.961194i | \(0.411033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 41332.3i | − | 2.89145i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1227.24 | −0.0854175 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10572.9 | 0.732173 | 0.366086 | − | 0.930581i | \(-0.380697\pi\) | ||||
0.366086 | + | 0.930581i | \(0.380697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 561.152 | + | 1424.76i | 0.0386638 | + | 0.0981672i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8154.38 | 0.559023 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27156.5 | −1.85240 | −0.926198 | − | 0.377038i | \(-0.876943\pi\) | ||||
−0.926198 | + | 0.377038i | \(0.876943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11180.6i | 0.758849i | 0.925223 | + | 0.379424i | \(0.123878\pi\) | ||||
−0.925223 | + | 0.379424i | \(0.876122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6926.15 | 0.467752 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 11336.2i | − | 0.761790i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19444.2i | 1.30019i | 0.759851 | + | 0.650097i | \(0.225272\pi\) | ||||
−0.759851 | + | 0.650097i | \(0.774728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1498.30i | − | 0.0996952i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17039.8 | −1.12824 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16630.9 | −1.09579 | −0.547893 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547893 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4586.98i | 0.300756i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8035.03i | 0.524276i | 0.965030 | + | 0.262138i | \(0.0844275\pi\) | ||||
−0.965030 | + | 0.262138i | \(0.915572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16161.6i | − | 1.04942i | −0.851282 | − | 0.524709i | \(-0.824174\pi\) | ||
0.851282 | − | 0.524709i | \(-0.175826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5236.67 | −0.338390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3968.99i | − | 0.255239i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7211.35 | 0.461527 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24046.5 | 1.53162 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4040.97 | − | 1591.56i | 0.256159 | − | 0.100890i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10043.9 | −0.633665 | −0.316833 | − | 0.948481i | \(-0.602619\pi\) | ||||
−0.316833 | + | 0.948481i | \(0.602619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8014.09 | 0.503210 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 4750.81i | − | 0.296898i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18155.5 | −1.12927 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8501.98i | − | 0.526343i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15316.1i | − | 0.943757i | −0.881664 | − | 0.471879i | \(-0.843576\pi\) | ||
0.881664 | − | 0.471879i | \(-0.156424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24684.6i | − | 1.51394i | −0.653449 | − | 0.756970i | \(-0.726679\pi\) | ||
0.653449 | − | 0.756970i | \(-0.273321\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1773.36 | −0.108257 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7774.11 | 0.472383 | 0.236192 | − | 0.971707i | \(-0.424101\pi\) | ||||
0.236192 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7890.07i | − | 0.477214i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4039.18i | 0.243177i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 752.623i | − | 0.0451032i | −0.999746 | − | 0.0225516i | \(-0.992821\pi\) | ||
0.999746 | − | 0.0225516i | \(-0.00717901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3455.01 | −0.206105 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12152.1i | 0.721611i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4887.68 | −0.288918 | −0.144459 | − | 0.989511i | \(-0.546144\pi\) | ||||
−0.144459 | + | 0.989511i | \(0.546144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7122.91 | −0.419136 | −0.209568 | − | 0.977794i | \(-0.567206\pi\) | ||||
−0.209568 | + | 0.977794i | \(0.567206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10822.4 | − | 4262.48i | 0.633948 | − | 0.249685i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2945.90 | −0.171785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4452.87 | 0.258494 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 18887.2i | − | 1.09151i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46655.6 | 2.68423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32249.6i | − | 1.84715i | −0.383421 | − | 0.923574i | \(-0.625254\pi\) | ||
0.383421 | − | 0.923574i | \(-0.374746\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13509.3i | 0.770331i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17447.9i | 0.990511i | 0.868748 | + | 0.495255i | \(0.164925\pi\) | ||||
−0.868748 | + | 0.495255i | \(0.835075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6722.23 | 0.379934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11352.6 | −0.638812 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 13935.3i | − | 0.780701i | −0.920666 | − | 0.390351i | \(-0.872354\pi\) | ||
0.920666 | − | 0.390351i | \(-0.127646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12092.6i | − | 0.674500i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14320.6i | − | 0.795289i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7515.53 | −0.415557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22358.6i | 1.23092i | 0.788170 | + | 0.615458i | \(0.211029\pi\) | ||||
−0.788170 | + | 0.615458i | \(0.788971\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4925.64 | 0.269999 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2132.02 | −0.116363 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20691.5 | − | 8149.47i | 1.12445 | − | 0.442874i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8031.99 | −0.434617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30456.5 | 1.64098 | 0.820491 | − | 0.571660i | \(-0.193700\pi\) | ||||
0.820491 | + | 0.571660i | \(0.193700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8355.30i | 0.448259i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4384.01 | −0.234201 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2707.82i | − | 0.144042i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36945.7i | 1.95702i | 0.206210 | + | 0.978508i | \(0.433887\pi\) | ||||
−0.206210 | + | 0.978508i | \(0.566113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 16922.3i | − | 0.892595i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12004.2 | −0.630520 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16613.0 | 0.868937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7456.31i | 0.388369i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 12442.4i | − | 0.645375i | −0.946506 | − | 0.322687i | \(-0.895414\pi\) | ||
0.946506 | − | 0.322687i | \(-0.104586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2599.91i | − | 0.134294i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5738.71 | −0.295194 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 11487.3i | − | 0.588451i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29943.3 | −1.52756 | −0.763780 | − | 0.645477i | \(-0.776659\pi\) | ||||
−0.763780 | + | 0.645477i | \(0.776659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8857.78 | −0.450022 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3150.64 | + | 7999.46i | 0.159413 | + | 0.404748i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19615.5 | 0.988423 | 0.494212 | − | 0.869342i | \(-0.335457\pi\) | ||||
0.494212 | + | 0.869342i | \(0.335457\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4671.06 | −0.234414 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22880.9i | 1.14359i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3459.26 | −0.172194 | −0.0860968 | − | 0.996287i | \(-0.527439\pi\) | ||||
−0.0860968 | + | 0.996287i | \(0.527439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22376.9i | 1.10936i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 37392.9i | − | 1.84632i | −0.384421 | − | 0.923158i | \(-0.625599\pi\) | ||
0.384421 | − | 0.923158i | \(-0.374401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11890.9i | 0.584765i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13226.2 | −0.647819 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.9447 | 0.00307069 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34379.7i | − | 1.67048i | −0.549884 | − | 0.835241i | \(-0.685328\pi\) | ||
0.549884 | − | 0.835241i | \(-0.314672\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6888.31i | 0.333365i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12768.5i | 0.615489i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20120.9 | −0.966057 | −0.483028 | − | 0.875605i | \(-0.660463\pi\) | ||||
−0.483028 | + | 0.875605i | \(0.660463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 6983.86i | − | 0.333989i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21739.7 | −1.03556 | −0.517781 | − | 0.855513i | \(-0.673242\pi\) | ||||
−0.517781 | + | 0.855513i | \(0.673242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7137.46 | 0.338654 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5836.29 | + | 2298.66i | −0.275832 | + | 0.108638i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7342.26 | 0.345650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26884.9 | 1.26072 | 0.630360 | − | 0.776303i | \(-0.282907\pi\) | ||||
0.630360 | + | 0.776303i | \(0.282907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2385.53i | − | 0.111430i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21927.0 | −1.02026 | −0.510128 | − | 0.860099i | \(-0.670402\pi\) | ||||
−0.510128 | + | 0.860099i | \(0.670402\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30967.9i | 1.43535i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 816.519i | − | 0.0376994i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42782.6i | 1.96771i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28086.7 | 1.28684 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15203.2 | 0.693894 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 802.934i | 0.0365069i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28401.4i | − | 1.28641i | −0.765695 | − | 0.643203i | \(-0.777605\pi\) | ||
0.765695 | − | 0.643203i | \(-0.222395\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 18961.2i | − | 0.855561i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2769.58 | −0.124494 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43416.3i | 1.94421i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1933.60 | −0.0862612 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19462.7 | −0.864999 | −0.432499 | − | 0.901634i | \(-0.642368\pi\) | ||||
−0.432499 | + | 0.901634i | \(0.642368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7788.86 | + | 19775.9i | 0.344869 | + | 0.875619i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16258.3 | 0.717177 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40145.0 | −1.76424 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 855.583i | 0.0374601i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18708.0 | 0.816050 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11073.0i | 0.481220i | 0.970622 | + | 0.240610i | \(0.0773474\pi\) | ||||
−0.970622 | + | 0.240610i | \(0.922653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8512.57i | − | 0.368578i | −0.982872 | − | 0.184289i | \(-0.941002\pi\) | ||
0.982872 | − | 0.184289i | \(-0.0589982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4220.99i | − | 0.182087i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1416.91 | −0.0608983 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16540.1 | −0.708278 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4583.65i | 0.195562i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26291.2i | 1.11762i | 0.829294 | + | 0.558812i | \(0.188743\pi\) | ||||
−0.829294 | + | 0.558812i | \(0.811257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4379.37i | − | 0.185486i | −0.995690 | − | 0.0927432i | \(-0.970436\pi\) | ||
0.995690 | − | 0.0927432i | \(-0.0295636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18016.6 | −0.760313 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2994.98i | − | 0.125932i | −0.998016 | − | 0.0629659i | \(-0.979944\pi\) | ||
0.998016 | − | 0.0629659i | \(-0.0200559\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33497.1 | −1.40338 | −0.701690 | − | 0.712482i | \(-0.747571\pi\) | ||||
−0.701690 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23267.0 | −0.971269 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8298.84 | + | 21070.7i | 0.345184 | + | 0.876419i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10513.7 | 0.435739 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40985.4 | −1.69255 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 25588.9i | − | 1.05295i | −0.850189 | − | 0.526477i | \(-0.823513\pi\) | ||
0.850189 | − | 0.526477i | \(-0.176487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11461.3 | 0.469938 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8764.73i | 0.358094i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4703.57i | 0.191489i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10332.7i | 0.419168i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1184.79 | −0.0478939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2426.64 | 0.0977488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31609.1i | 1.26879i | 0.773010 | + | 0.634394i | \(0.218750\pi\) | ||||
−0.773010 | + | 0.634394i | \(0.781250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 12067.4i | − | 0.482686i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7519.34i | − | 0.299715i | −0.988708 | − | 0.149858i | \(-0.952119\pi\) | ||
0.988708 | − | 0.149858i | \(-0.0478815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3923.30 | −0.155834 | −0.0779169 | − | 0.996960i | \(-0.524827\pi\) | ||||
−0.0779169 | + | 0.996960i | \(0.524827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4180.92i | − | 0.165488i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32254.8 | 1.27227 | 0.636133 | − | 0.771580i | \(-0.280533\pi\) | ||||
0.636133 | + | 0.771580i | \(0.280533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21462.9 | 0.843654 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9893.80 | − | 10611.8i | −0.387556 | − | 0.415680i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55903.5 | 2.18228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21292.3 | −0.828313 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27536.5i | 1.06755i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4938.01 | 0.190783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9587.97i | − | 0.369171i | −0.982816 | − | 0.184585i | \(-0.940906\pi\) | ||
0.982816 | − | 0.184585i | \(-0.0590942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21825.2i | 0.837479i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10243.5i | − | 0.391726i | −0.980631 | − | 0.195863i | \(-0.937249\pi\) | ||
0.980631 | − | 0.195863i | \(-0.0627508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17802.2 | −0.678474 | −0.339237 | − | 0.940701i | \(-0.610169\pi\) | ||||
−0.339237 | + | 0.940701i | \(0.610169\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1889.02 | 0.0717499 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5409.67i | 0.204779i | 0.994744 | + | 0.102389i | \(0.0326488\pi\) | ||||
−0.994744 | + | 0.102389i | \(0.967351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4330.25i | 0.163365i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5958.47i | 0.224036i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40889.5 | −1.53227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18570.1i | 0.693551i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6498.97 | 0.241911 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34850.9 | 1.29293 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3435.33 | + | 8722.28i | 0.127023 | + | 0.322510i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1616.37 | 0.0595675 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8453.74 | −0.310510 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27596.6i | 1.01029i | 0.863036 | + | 0.505143i | \(0.168560\pi\) | ||||
−0.863036 | + | 0.505143i | \(0.831440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11092.1 | 0.404733 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 47306.9i | − | 1.72047i | −0.509898 | − | 0.860235i | \(-0.670317\pi\) | ||
0.509898 | − | 0.860235i | \(-0.329683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 43693.3i | − | 1.58383i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11170.2i | 0.403579i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3149.16 | 0.113407 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40635.5 | 1.45859 | 0.729293 | − | 0.684202i | \(-0.239849\pi\) | ||||
0.729293 | + | 0.684202i | \(0.239849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 148.448i | − | 0.00531111i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26136.6i | 0.932067i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6260.14i | − | 0.222521i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10650.1 | 0.377341 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 34143.2i | − | 1.20582i | −0.797811 | − | 0.602908i | \(-0.794009\pi\) | ||
0.797811 | − | 0.602908i | \(-0.205991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43566.8 | −1.53367 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −634.997 | −0.0222817 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7593.75 | − | 19280.5i | −0.265606 | − | 0.674373i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4097.67 | 0.142865 | 0.0714327 | − | 0.997445i | \(-0.477243\pi\) | ||||
0.0714327 | + | 0.997445i | \(0.477243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13700.9 | −0.476157 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 32801.4i | − | 1.13634i | −0.822912 | − | 0.568169i | \(-0.807652\pi\) | ||
0.822912 | − | 0.568169i | \(-0.192348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12425.4 | 0.429086 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2921.18i | 0.100557i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 32528.3i | − | 1.11618i | −0.829779 | − | 0.558092i | \(-0.811534\pi\) | ||
0.829779 | − | 0.558092i | \(-0.188466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 37357.7i | − | 1.27785i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11710.8 | −0.399316 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14335.6 | 0.487276 | 0.243638 | − | 0.969866i | \(-0.421659\pi\) | ||||
0.243638 | + | 0.969866i | \(0.421659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6295.96i | 0.213332i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20275.7i | 0.684870i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11022.1i | 0.371138i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −64161.3 | −2.15371 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 257.842i | 0.00862810i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8235.01 | 0.274709 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −688.081 | −0.0228823 | −0.0114412 | − | 0.999935i | \(-0.503642\pi\) | ||||
−0.0114412 | + | 0.999935i | \(0.503642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25970.0 | − | 10228.4i | 0.860965 | − | 0.339097i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49985.2 | 1.65201 | 0.826005 | − | 0.563663i | \(-0.190609\pi\) | ||||
0.826005 | + | 0.563663i | \(0.190609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1943.28 | 0.0640276 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 16765.7i | − | 0.550701i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38752.4 | 1.26899 | 0.634493 | − | 0.772929i | \(-0.281209\pi\) | ||||
0.634493 | + | 0.772929i | \(0.281209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53710.1i | 1.75340i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29237.4i | 0.951558i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 21516.4i | − | 0.698135i | −0.937098 | − | 0.349067i | \(-0.886498\pi\) | ||
0.937098 | − | 0.349067i | \(-0.113502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2034.56 | −0.0658138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3995.92 | 0.128867 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4803.75i | 0.154449i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6941.00i | − | 0.222491i | −0.993793 | − | 0.111245i | \(-0.964516\pi\) | ||
0.993793 | − | 0.111245i | \(-0.0354839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22142.1i | 0.707611i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13518.7 | 0.430724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44135.5i | − | 1.40199i | −0.713165 | − | 0.700996i | \(-0.752739\pi\) | ||
0.713165 | − | 0.700996i | \(-0.247261\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8285.18 | 0.262394 |
(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 | 136.4.b.b.33.6 | yes | 8 | |
3.2 | odd | 2 | 1224.4.c.e.577.4 | 8 | |||
4.3 | odd | 2 | 272.4.b.f.33.3 | 8 | |||
17.4 | even | 4 | 2312.4.a.k.1.6 | 8 | |||
17.13 | even | 4 | 2312.4.a.k.1.3 | 8 | |||
17.16 | even | 2 | inner | 136.4.b.b.33.3 | ✓ | 8 | |
51.50 | odd | 2 | 1224.4.c.e.577.5 | 8 | |||
68.67 | odd | 2 | 272.4.b.f.33.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.3 | ✓ | 8 | 17.16 | even | 2 | inner | |
136.4.b.b.33.6 | yes | 8 | 1.1 | even | 1 | trivial | |
272.4.b.f.33.3 | 8 | 4.3 | odd | 2 | |||
272.4.b.f.33.6 | 8 | 68.67 | odd | 2 | |||
1224.4.c.e.577.4 | 8 | 3.2 | odd | 2 | |||
1224.4.c.e.577.5 | 8 | 51.50 | odd | 2 | |||
2312.4.a.k.1.3 | 8 | 17.13 | even | 4 | |||
2312.4.a.k.1.6 | 8 | 17.4 | even | 4 |