Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(127.444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 141x^{2} + 200x + 3500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 1080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-10.9094\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.5942 | −1.92191 | −0.960953 | − | 0.276713i | \(-0.910755\pi\) | ||||
−0.960953 | + | 0.276713i | \(0.910755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.7641 | 1.22699 | 0.613495 | − | 0.789699i | \(-0.289763\pi\) | ||||
0.613495 | + | 0.789699i | \(0.289763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 77.8220 | 1.66030 | 0.830152 | − | 0.557538i | \(-0.188254\pi\) | ||||
0.830152 | + | 0.557538i | \(0.188254\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −120.489 | −1.71899 | −0.859495 | − | 0.511145i | \(-0.829222\pi\) | ||||
−0.859495 | + | 0.511145i | \(0.829222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −121.319 | −1.46487 | −0.732433 | − | 0.680839i | \(-0.761615\pi\) | ||||
−0.732433 | + | 0.680839i | \(0.761615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −152.855 | −1.38576 | −0.692880 | − | 0.721053i | \(-0.743659\pi\) | ||||
−0.692880 | + | 0.721053i | \(0.743659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 187.926 | 1.20334 | 0.601672 | − | 0.798743i | \(-0.294501\pi\) | ||||
0.601672 | + | 0.798743i | \(0.294501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 161.365 | 0.934903 | 0.467452 | − | 0.884019i | \(-0.345172\pi\) | ||||
0.467452 | + | 0.884019i | \(0.345172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −177.971 | −0.859502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.3350 | 0.0592501 | 0.0296251 | − | 0.999561i | \(-0.490569\pi\) | ||||
0.0296251 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 188.065 | 0.716360 | 0.358180 | − | 0.933653i | \(-0.383397\pi\) | ||||
0.358180 | + | 0.933653i | \(0.383397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 81.5584 | 0.289245 | 0.144623 | − | 0.989487i | \(-0.453803\pi\) | ||||
0.144623 | + | 0.989487i | \(0.453803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −48.6219 | −0.150899 | −0.0754493 | − | 0.997150i | \(-0.524039\pi\) | ||||
−0.0754493 | + | 0.997150i | \(0.524039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 923.946 | 2.69372 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −707.373 | −1.83331 | −0.916653 | − | 0.399685i | \(-0.869120\pi\) | ||||
−0.916653 | + | 0.399685i | \(0.869120\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 223.821 | 0.548727 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −16.4774 | −0.0363589 | −0.0181795 | − | 0.999835i | \(-0.505787\pi\) | ||||
−0.0181795 | + | 0.999835i | \(0.505787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −743.868 | −1.56135 | −0.780676 | − | 0.624936i | \(-0.785125\pi\) | ||||
−0.780676 | + | 0.624936i | \(0.785125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 389.110 | 0.742510 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59.2676 | 0.108070 | 0.0540350 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540350 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −144.370 | −0.241317 | −0.120659 | − | 0.992694i | \(-0.538501\pi\) | ||||
−0.120659 | + | 0.992694i | \(0.538501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 657.273 | 1.05381 | 0.526904 | − | 0.849925i | \(-0.323353\pi\) | ||||
0.526904 | + | 0.849925i | \(0.323353\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1593.34 | −2.35816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 454.297 | 0.646992 | 0.323496 | − | 0.946230i | \(-0.395142\pi\) | ||||
0.323496 | + | 0.946230i | \(0.395142\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 165.513 | 0.218885 | 0.109442 | − | 0.993993i | \(-0.465093\pi\) | ||||
0.109442 | + | 0.993993i | \(0.465093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −602.444 | −0.768755 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 535.743 | 0.638074 | 0.319037 | − | 0.947742i | \(-0.396641\pi\) | ||||
0.319037 | + | 0.947742i | \(0.396641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2770.01 | −3.19094 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −606.594 | −0.655108 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −436.761 | −0.457179 | −0.228590 | − | 0.973523i | \(-0.573411\pi\) | ||||
−0.228590 | + | 0.973523i | \(0.573411\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1376.74 | 1.35635 | 0.678174 | − | 0.734901i | \(-0.262771\pi\) | ||||
0.678174 | + | 0.734901i | \(0.262771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.2617 | 0.0193830 | 0.00969149 | − | 0.999953i | \(-0.496915\pi\) | ||||
0.00969149 | + | 0.999953i | \(0.496915\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 359.961 | 0.325222 | 0.162611 | − | 0.986690i | \(-0.448008\pi\) | ||||
0.162611 | + | 0.986690i | \(0.448008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 377.931 | 0.332103 | 0.166052 | − | 0.986117i | \(-0.446898\pi\) | ||||
0.166052 | + | 0.986117i | \(0.446898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −21.3449 | −0.0177696 | −0.00888478 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888478 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −764.276 | −0.619731 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4288.70 | 3.30373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 672.826 | 0.505504 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1756.10 | −1.22700 | −0.613499 | − | 0.789696i | \(-0.710238\pi\) | ||||
−0.613499 | + | 0.789696i | \(0.710238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2388.31 | −1.59288 | −0.796441 | − | 0.604716i | \(-0.793287\pi\) | ||||
−0.796441 | + | 0.604716i | \(0.793287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4318.24 | 2.81533 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1124.94 | 0.701534 | 0.350767 | − | 0.936463i | \(-0.385921\pi\) | ||||
0.350767 | + | 0.936463i | \(0.385921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −795.105 | −0.485179 | −0.242590 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242590 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3483.63 | 2.03718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 939.630 | 0.538152 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2933.56 | 1.61293 | 0.806466 | − | 0.591281i | \(-0.201378\pi\) | ||||
0.806466 | + | 0.591281i | \(0.201378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1645.26 | −0.886686 | −0.443343 | − | 0.896352i | \(-0.646208\pi\) | ||||
−0.443343 | + | 0.896352i | \(0.646208\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 806.825 | 0.418101 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1001.96 | −0.509330 | −0.254665 | − | 0.967029i | \(-0.581965\pi\) | ||||
−0.254665 | + | 0.967029i | \(0.581965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5440.75 | 2.66330 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2135.60 | 1.02622 | 0.513108 | − | 0.858324i | \(-0.328494\pi\) | ||||
0.513108 | + | 0.858324i | \(0.328494\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3612.36 | 1.67385 | 0.836925 | − | 0.547318i | \(-0.184351\pi\) | ||||
0.836925 | + | 0.547318i | \(0.184351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3859.26 | 1.75661 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2684.80 | 1.17989 | 0.589947 | − | 0.807442i | \(-0.299149\pi\) | ||||
0.589947 | + | 0.807442i | \(0.299149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −889.854 | −0.384381 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2182.63 | 0.911382 | 0.455691 | − | 0.890138i | \(-0.349392\pi\) | ||||
0.455691 | + | 0.890138i | \(0.349392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3117.86 | 1.28038 | 0.640189 | − | 0.768217i | \(-0.278856\pi\) | ||||
0.640189 | + | 0.768217i | \(0.278856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 66.6748 | 0.0264975 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5393.57 | −2.10918 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −76.0912 | −0.0288260 | −0.0144130 | − | 0.999896i | \(-0.504588\pi\) | ||||
−0.0144130 | + | 0.999896i | \(0.504588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 533.717 | 0.199056 | 0.0995280 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995280 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2729.47 | 0.987142 | 0.493571 | − | 0.869706i | \(-0.335691\pi\) | ||||
0.493571 | + | 0.869706i | \(0.335691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3196.27 | 1.13858 | 0.569290 | − | 0.822137i | \(-0.307218\pi\) | ||||
0.569290 | + | 0.822137i | \(0.307218\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6689.07 | −2.31271 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 940.323 | 0.320366 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5430.73 | −1.79738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4325.59 | 1.41131 | 0.705654 | − | 0.708557i | \(-0.250653\pi\) | ||||
0.705654 | + | 0.708557i | \(0.250653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 407.792 | 0.129354 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5743.65 | −1.79680 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9376.68 | −2.85404 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1370.87 | −0.411660 | −0.205830 | − | 0.978588i | \(-0.565989\pi\) | ||||
−0.205830 | + | 0.978588i | \(0.565989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2676.95 | −0.782711 | −0.391356 | − | 0.920240i | \(-0.627994\pi\) | ||||
−0.391356 | + | 0.920240i | \(0.627994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2641.40 | −0.762222 | −0.381111 | − | 0.924529i | \(-0.624459\pi\) | ||||
−0.381111 | + | 0.924529i | \(0.624459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1719.93 | −0.483589 | −0.241795 | − | 0.970327i | \(-0.577736\pi\) | ||||
−0.241795 | + | 0.970327i | \(0.577736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −243.109 | −0.0674839 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5162.21 | 1.39714 | 0.698568 | − | 0.715543i | \(-0.253821\pi\) | ||||
0.698568 | + | 0.715543i | \(0.253821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −717.935 | −0.191893 | −0.0959465 | − | 0.995386i | \(-0.530588\pi\) | ||||
−0.0959465 | + | 0.995386i | \(0.530588\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4619.73 | 1.20467 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9441.27 | −2.43212 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1101.95 | 0.277110 | 0.138555 | − | 0.990355i | \(-0.455754\pi\) | ||||
0.138555 | + | 0.990355i | \(0.455754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6842.43 | −1.70031 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2922.73 | 0.709396 | 0.354698 | − | 0.934981i | \(-0.384584\pi\) | ||||
0.354698 | + | 0.934981i | \(0.384584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −474.647 | −0.113873 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1380.33 | 0.323631 | 0.161815 | − | 0.986821i | \(-0.448265\pi\) | ||||
0.161815 | + | 0.986821i | \(0.448265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3536.87 | −0.819879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −85.9555 | −0.0194825 | −0.00974126 | − | 0.999953i | \(-0.503101\pi\) | ||||
−0.00974126 | + | 0.999953i | \(0.503101\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2676.24 | 0.599889 | 0.299944 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299944 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1119.10 | 0.245398 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6135.26 | 1.33080 | 0.665400 | − | 0.746487i | \(-0.268261\pi\) | ||||
0.665400 | + | 0.746487i | \(0.268261\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2899.29 | −0.615505 | −0.307753 | − | 0.951466i | \(-0.599577\pi\) | ||||
−0.307753 | + | 0.951466i | \(0.599577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3584.20 | 0.752857 | 0.376429 | − | 0.926446i | \(-0.377152\pi\) | ||||
0.376429 | + | 0.926446i | \(0.377152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6694.00 | −1.37678 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9604.55 | 1.95492 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7592.52 | 1.51386 | 0.756928 | − | 0.653498i | \(-0.226699\pi\) | ||||
0.756928 | + | 0.653498i | \(0.226699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −82.3871 | −0.0162602 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11895.5 | −2.30078 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2903.01 | −0.555902 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3719.34 | −0.698258 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5539.62 | −1.02985 | −0.514923 | − | 0.857237i | \(-0.672179\pi\) | ||||
−0.514923 | + | 0.857237i | \(0.672179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8862.85 | 1.61597 | 0.807984 | − | 0.589204i | \(-0.200559\pi\) | ||||
0.807984 | + | 0.589204i | \(0.200559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6028.49 | 1.08866 | 0.544329 | − | 0.838872i | \(-0.316784\pi\) | ||||
0.544329 | + | 0.838872i | \(0.316784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10578.3 | 1.87425 | 0.937126 | − | 0.348991i | \(-0.113476\pi\) | ||||
0.937126 | + | 0.348991i | \(0.113476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8412.34 | 1.47649 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14617.6 | 2.51809 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1945.55 | 0.332061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1730.66 | 0.290013 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8051.25 | −1.33697 | −0.668484 | − | 0.743726i | \(-0.733057\pi\) | ||||
−0.668484 | + | 0.743726i | \(0.733057\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 296.338 | 0.0483304 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3573.37 | −0.577608 | −0.288804 | − | 0.957388i | \(-0.593258\pi\) | ||||
−0.288804 | + | 0.957388i | \(0.593258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7223.36 | 1.14712 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20678.3 | −3.25517 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3268.28 | 0.505621 | 0.252811 | − | 0.967516i | \(-0.418645\pi\) | ||||
0.252811 | + | 0.967516i | \(0.418645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5831.57 | 0.894432 | 0.447216 | − | 0.894426i | \(-0.352415\pi\) | ||||
0.447216 | + | 0.894426i | \(0.352415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12021.4 | −1.81257 | −0.906285 | − | 0.422667i | \(-0.861094\pi\) | ||||
−0.906285 | + | 0.422667i | \(0.861094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −721.849 | −0.107920 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1598.32 | 0.234975 | 0.117487 | − | 0.993074i | \(-0.462516\pi\) | ||||
0.117487 | + | 0.993074i | \(0.462516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7859.26 | 1.14583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3286.37 | 0.471277 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12200.7 | 1.73534 | 0.867671 | − | 0.497138i | \(-0.165616\pi\) | ||||
0.867671 | + | 0.497138i | \(0.165616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25178.4 | 3.52344 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7613.13 | −1.05682 | −0.528409 | − | 0.848990i | \(-0.677211\pi\) | ||||
−0.528409 | + | 0.848990i | \(0.677211\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14624.8 | 1.99792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7463.85 | 1.01159 | 0.505794 | − | 0.862654i | \(-0.331200\pi\) | ||||
0.505794 | + | 0.862654i | \(0.331200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4064.01 | 0.542196 | 0.271098 | − | 0.962552i | \(-0.412613\pi\) | ||||
0.271098 | + | 0.962552i | \(0.412613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7966.71 | −1.05460 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1258.30 | 0.164006 | 0.0820028 | − | 0.996632i | \(-0.473868\pi\) | ||||
0.0820028 | + | 0.996632i | \(0.473868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18417.3 | 2.38211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2271.48 | 0.289344 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8486.66 | −1.07288 | −0.536440 | − | 0.843938i | \(-0.680231\pi\) | ||||
−0.536440 | + | 0.843938i | \(0.680231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −829.986 | −0.103360 | −0.0516802 | − | 0.998664i | \(-0.516458\pi\) | ||||
−0.0516802 | + | 0.998664i | \(0.516458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12557.7 | 1.55222 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 596.928 | 0.0726993 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8600.00 | −1.03971 | −0.519857 | − | 0.854254i | \(-0.674015\pi\) | ||||
−0.519857 | + | 0.854254i | \(0.674015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 586.500 | 0.0698784 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 827.566 | 0.0978882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2926.84 | 0.341254 | 0.170627 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170627 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −707.503 | −0.0819041 | −0.0409520 | − | 0.999161i | \(-0.513039\pi\) | ||||
−0.0409520 | + | 0.999161i | \(0.513039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3012.22 | −0.343798 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26477.4 | 3.00077 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4693.17 | −0.524506 | −0.262253 | − | 0.964999i | \(-0.584465\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584465\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −279.149 | −0.0309816 | −0.0154908 | − | 0.999880i | \(-0.504931\pi\) | ||||
−0.0154908 | + | 0.999880i | \(0.504931\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18544.2 | 2.02995 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2651.13 | 0.288226 | 0.144113 | − | 0.989561i | \(-0.453967\pi\) | ||||
0.144113 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1899.98 | −0.203771 | −0.101886 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101886 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2678.71 | 0.285355 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6033.52 | 0.634164 | 0.317082 | − | 0.948398i | \(-0.397297\pi\) | ||||
0.317082 | + | 0.948398i | \(0.397297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8418.54 | 0.878966 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13850.1 | −1.42703 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7920.25 | −0.810708 | −0.405354 | − | 0.914160i | \(-0.632852\pi\) | ||||
−0.405354 | + | 0.914160i | \(0.632852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3754.65 | 0.379331 | 0.189666 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189666 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3094.28 | 0.310591 | 0.155295 | − | 0.987868i | \(-0.450367\pi\) | ||||
0.155295 | + | 0.987868i | \(0.450367\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13827.8 | −1.37018 | −0.685092 | − | 0.728457i | \(-0.740238\pi\) | ||||
−0.685092 | + | 0.728457i | \(0.740238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2109.58 | −0.207700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3650.89 | 0.354901 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3032.97 | −0.292973 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1776.55 | 0.169463 | 0.0847313 | − | 0.996404i | \(-0.472997\pi\) | ||||
0.0847313 | + | 0.996404i | \(0.472997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1037.75 | 0.0983732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2183.81 | −0.204457 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3223.84 | 0.299971 | 0.149986 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149986 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8699.20 | 0.799571 | 0.399786 | − | 0.916609i | \(-0.369085\pi\) | ||||
0.399786 | + | 0.916609i | \(0.369085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22643.0 | −2.06854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5138.72 | 0.463789 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11833.7 | −1.06163 | −0.530813 | − | 0.847489i | \(-0.678113\pi\) | ||||
−0.530813 | + | 0.847489i | \(0.678113\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15882.5 | 1.40789 | 0.703943 | − | 0.710256i | \(-0.251421\pi\) | ||||
0.703943 | + | 0.710256i | \(0.251421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6883.72 | 0.606577 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20662.8 | −1.79934 | −0.899670 | − | 0.436570i | \(-0.856193\pi\) | ||||
−0.899670 | + | 0.436570i | \(0.856193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23395.1 | −2.02532 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 101.309 | 0.00866834 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2176.52 | −0.185151 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13333.8 | 1.12124 | 0.560618 | − | 0.828075i | \(-0.310564\pi\) | ||||
0.560618 | + | 0.828075i | \(0.310564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8822.73 | 0.737650 | 0.368825 | − | 0.929499i | \(-0.379760\pi\) | ||||
0.368825 | + | 0.929499i | \(0.379760\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19442.7 | −1.60709 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11197.7 | 0.920333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14635.6 | 1.18937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1799.80 | 0.145444 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41359.6 | 3.30517 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16975.6 | −1.34905 | −0.674527 | − | 0.738250i | \(-0.735652\pi\) | ||||
−0.674527 | + | 0.738250i | \(0.735652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1889.66 | 0.148521 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9986.07 | −0.780573 | −0.390287 | − | 0.920693i | \(-0.627624\pi\) | ||||
−0.390287 | + | 0.920693i | \(0.627624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22799.0 | −1.76274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16170.3 | −1.24346 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15740.3 | −1.19737 | −0.598686 | − | 0.800984i | \(-0.704310\pi\) | ||||
−0.598686 | + | 0.800984i | \(0.704310\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6347.04 | 0.480235 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10829.5 | 0.810674 | 0.405337 | − | 0.914167i | \(-0.367154\pi\) | ||||
0.405337 | + | 0.914167i | \(0.367154\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −106.725 | −0.00794679 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11858.7 | −0.873711 | −0.436855 | − | 0.899532i | \(-0.643908\pi\) | ||||
−0.436855 | + | 0.899532i | \(0.643908\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16839.3 | −1.23415 | −0.617077 | − | 0.786903i | \(-0.711683\pi\) | ||||
−0.617077 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3821.38 | −0.277152 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2182.04 | 0.157434 | 0.0787169 | − | 0.996897i | \(-0.474918\pi\) | ||||
0.0787169 | + | 0.996897i | \(0.474918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5891.31 | −0.420676 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31664.9 | −2.24945 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2121.16 | −0.149148 | −0.0745739 | − | 0.997215i | \(-0.523760\pi\) | ||||
−0.0745739 | + | 0.997215i | \(0.523760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19576.6 | −1.36951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1602.22 | 0.110953 | 0.0554766 | − | 0.998460i | \(-0.482332\pi\) | ||||
0.0554766 | + | 0.998460i | \(0.482332\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21443.5 | 1.47748 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18383.4 | 1.25396 | 0.626982 | − | 0.779033i | \(-0.284290\pi\) | ||||
0.626982 | + | 0.779033i | \(0.284290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25606.2 | −1.73793 | −0.868967 | − | 0.494870i | \(-0.835216\pi\) | ||||
−0.868967 | + | 0.494870i | \(0.835216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3364.13 | 0.226068 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28967.2 | 1.93697 | 0.968487 | − | 0.249065i | \(-0.0801232\pi\) | ||||
0.968487 | + | 0.249065i | \(0.0801232\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3783.85 | −0.250537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9101.21 | 0.599665 | 0.299832 | − | 0.953992i | \(-0.403069\pi\) | ||||
0.299832 | + | 0.953992i | \(0.403069\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13945.3 | −0.909913 | −0.454957 | − | 0.890514i | \(-0.650345\pi\) | ||||
−0.454957 | + | 0.890514i | \(0.650345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4276.76 | 0.277702 | 0.138851 | − | 0.990313i | \(-0.455659\pi\) | ||||
0.138851 | + | 0.990313i | \(0.455659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19069.3 | −1.22632 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1606.71 | −0.101850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18459.0 | 1.16457 | 0.582283 | − | 0.812987i | \(-0.302160\pi\) | ||||
0.582283 | + | 0.812987i | \(0.302160\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8780.50 | −0.548730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 71903.3 | 4.47239 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25102.1 | −1.54676 | −0.773381 | − | 0.633941i | \(-0.781436\pi\) | ||||
−0.773381 | + | 0.633941i | \(0.781436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14935.1 | 0.915991 | 0.457996 | − | 0.888954i | \(-0.348568\pi\) | ||||
0.457996 | + | 0.888954i | \(0.348568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18764.3 | 1.14019 | 0.570093 | − | 0.821580i | \(-0.306907\pi\) | ||||
0.570093 | + | 0.821580i | \(0.306907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −737.597 | −0.0446121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10200.0 | 0.611264 | 0.305632 | − | 0.952150i | \(-0.401132\pi\) | ||||
0.305632 | + | 0.952150i | \(0.401132\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11941.5 | −0.712359 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6908.98 | 0.408400 | 0.204200 | − | 0.978929i | \(-0.434541\pi\) | ||||
0.204200 | + | 0.978929i | \(0.434541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15449.8 | −0.909118 | −0.454559 | − | 0.890717i | \(-0.650203\pi\) | ||||
−0.454559 | + | 0.890717i | \(0.650203\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21591.2 | 1.25906 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28725.5 | −1.66755 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33298.6 | −1.91576 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15782.7 | 0.903977 | 0.451989 | − | 0.892024i | \(-0.350715\pi\) | ||||
0.451989 | + | 0.892024i | \(0.350715\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6982.32 | 0.396384 | 0.198192 | − | 0.980163i | \(-0.436493\pi\) | ||||
0.198192 | + | 0.980163i | \(0.436493\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15546.2 | 0.878655 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1267.31 | 0.0709988 | 0.0354994 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354994 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5624.71 | 0.313736 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −55049.2 | −3.04384 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24220.7 | −1.33343 | −0.666713 | − | 0.745315i | \(-0.732299\pi\) | ||||
−0.666713 | + | 0.745315i | \(0.732299\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3975.52 | −0.216979 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22659.7 | −1.23141 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11822.1 | 0.636967 | 0.318483 | − | 0.947928i | \(-0.396826\pi\) | ||||
0.318483 | + | 0.947928i | \(0.396826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1617.78 | −0.0867935 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49004.1 | −2.60677 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15140.6 | −0.801997 | −0.400998 | − | 0.916079i | \(-0.631337\pi\) | ||||
−0.400998 | + | 0.916079i | \(0.631337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24665.5 | −1.29555 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17418.2 | 0.911052 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1628.91 | 0.0844895 | 0.0422448 | − | 0.999107i | \(-0.486549\pi\) | ||||
0.0422448 | + | 0.999107i | \(0.486549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −721.200 | −0.0372523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4698.15 | 0.240669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30179.1 | 1.53959 | 0.769793 | − | 0.638293i | \(-0.220359\pi\) | ||||
0.769793 | + | 0.638293i | \(0.220359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9826.87 | −0.497209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9233.18 | 0.465260 | 0.232630 | − | 0.972565i | \(-0.425267\pi\) | ||||
0.232630 | + | 0.972565i | \(0.425267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2653.06 | 0.132601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21276.8 | −1.05911 | −0.529554 | − | 0.848276i | \(-0.677641\pi\) | ||||
−0.529554 | + | 0.848276i | \(0.677641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9647.90 | −0.476375 | −0.238188 | − | 0.971219i | \(-0.576553\pi\) | ||||
−0.238188 | + | 0.971219i | \(0.576553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14667.8 | 0.721325 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12812.5 | −0.625045 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19151.6 | 0.930560 | 0.465280 | − | 0.885163i | \(-0.345954\pi\) | ||||
0.465280 | + | 0.885163i | \(0.345954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8226.31 | −0.396538 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6689.40 | 0.321176 | 0.160588 | − | 0.987022i | \(-0.448661\pi\) | ||||
0.160588 | + | 0.987022i | \(0.448661\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24594.6 | 1.17156 | 0.585779 | − | 0.810471i | \(-0.300789\pi\) | ||||
0.585779 | + | 0.810471i | \(0.300789\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13452.2 | −0.638271 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1282.31 | −0.0603669 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2631.04 | −0.123378 | −0.0616890 | − | 0.998095i | \(-0.519649\pi\) | ||||
−0.0616890 | + | 0.998095i | \(0.519649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15347.0 | −0.714091 | −0.357045 | − | 0.934087i | \(-0.616216\pi\) | ||||
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4034.12 | 0.186981 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22815.8 | −1.04937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6462.58 | −0.296094 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5009.78 | −0.227779 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42630.0 | −1.93087 | −0.965436 | − | 0.260639i | \(-0.916067\pi\) | ||||
−0.965436 | + | 0.260639i | \(0.916067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 759.755 | 0.0341514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −57889.3 | −2.59232 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10002.6 | −0.444554 | −0.222277 | − | 0.974984i | \(-0.571349\pi\) | ||||
−0.222277 | + | 0.974984i | \(0.571349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5858.39 | 0.259393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29422.3 | 1.29301 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27203.8 | 1.19106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13642.8 | 0.592898 | 0.296449 | − | 0.955049i | \(-0.404198\pi\) | ||||
0.296449 | + | 0.955049i | \(0.404198\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3786.57 | 0.163951 | 0.0819756 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819756 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10678.0 | 0.458938 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9894.57 | −0.423705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31609.5 | 1.34370 | 0.671851 | − | 0.740686i | \(-0.265499\pi\) | ||||
0.671851 | + | 0.740686i | \(0.265499\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20737.3 | −0.878320 | −0.439160 | − | 0.898409i | \(-0.644724\pi\) | ||||
−0.439160 | + | 0.898409i | \(0.644724\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10152.0 | −0.426866 | −0.213433 | − | 0.976958i | \(-0.568465\pi\) | ||||
−0.213433 | + | 0.976958i | \(0.568465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2857.26 | −0.119706 | −0.0598532 | − | 0.998207i | \(-0.519063\pi\) | ||||
−0.0598532 | + | 0.998207i | \(0.519063\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −111325. | −4.63047 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18061.8 | 0.748568 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24638.0 | 1.01382 | 0.506911 | − | 0.861998i | \(-0.330787\pi\) | ||||
0.506911 | + | 0.861998i | \(0.330787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10927.2 | 0.448037 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19296.3 | 0.785578 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23948.7 | −0.971531 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2038.32 | −0.0821065 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.13034 | 4.53719e−5 0 | 2.26860e−5 | − | 1.00000i | \(-0.499993\pi\) | ||||
2.26860e−5 | 1.00000i | \(0.499993\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37803.4 | 1.50681 | 0.753406 | − | 0.657555i | \(-0.228409\pi\) | ||||
0.753406 | + | 0.657555i | \(0.228409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23555.7 | 0.935635 | 0.467817 | − | 0.883825i | \(-0.345041\pi\) | ||||
0.467817 | + | 0.883825i | \(0.345041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9572.78 | 0.377591 | 0.188796 | − | 0.982016i | \(-0.439542\pi\) | ||||
0.188796 | + | 0.982016i | \(0.439542\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13424.0 | 0.527665 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20336.2 | 0.793853 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4612.32 | 0.179429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4449.27 | −0.171900 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1559.23 | 0.0600358 | 0.0300179 | − | 0.999549i | \(-0.490444\pi\) | ||||
0.0300179 | + | 0.999549i | \(0.490444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36729.5 | −1.40459 | −0.702297 | − | 0.711884i | \(-0.747842\pi\) | ||||
−0.702297 | + | 0.711884i | \(0.747842\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6625.31 | −0.252502 | −0.126251 | − | 0.991998i | \(-0.540294\pi\) | ||||
−0.126251 | + | 0.991998i | \(0.540294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32562.3 | −1.23262 | −0.616311 | − | 0.787503i | \(-0.711374\pi\) | ||||
−0.616311 | + | 0.787503i | \(0.711374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62506.9 | 2.35817 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5898.75 | 0.221046 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10913.1 | 0.407582 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30324.7 | 1.12501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 85230.5 | 3.15143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15589.3 | 0.572603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37343.5 | 1.36711 | 0.683556 | − | 0.729898i | \(-0.260432\pi\) | ||||
0.683556 | + | 0.729898i | \(0.260432\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13207.3 | 0.480328 | 0.240164 | − | 0.970732i | \(-0.422799\pi\) | ||||
0.240164 | + | 0.970732i | \(0.422799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7409.05 | 0.268569 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 85009.9 | 3.06137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51007.6 | −1.83089 | −0.915444 | − | 0.402445i | \(-0.868161\pi\) | ||||
−0.915444 | + | 0.402445i | \(0.868161\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11235.1 | −0.400660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 333.374 | 0.0118500 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25322.8 | −0.894311 | −0.447155 | − | 0.894456i | \(-0.647563\pi\) | ||||
−0.447155 | + | 0.894456i | \(0.647563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −112092. | −3.94594 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26967.9 | −0.943255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12667.9 | 0.441668 | 0.220834 | − | 0.975311i | \(-0.429122\pi\) | ||||
0.220834 | + | 0.975311i | \(0.429122\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25676.4 | −0.889507 | −0.444753 | − | 0.895653i | \(-0.646709\pi\) | ||||
−0.444753 | + | 0.895653i | \(0.646709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28746.6 | −0.992703 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50265.9 | −1.72484 | −0.862420 | − | 0.506193i | \(-0.831052\pi\) | ||||
−0.862420 | + | 0.506193i | \(0.831052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51150.3 | 1.74964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39606.9 | 1.34627 | 0.673134 | − | 0.739520i | \(-0.264948\pi\) | ||||
0.673134 | + | 0.739520i | \(0.264948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −380.456 | −0.0128914 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40041.4 | −1.34828 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3752.35 | −0.125956 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2668.59 | 0.0890205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13997.6 | −0.465493 | −0.232746 | − | 0.972537i | \(-0.574771\pi\) | ||||
−0.232746 | + | 0.972537i | \(0.574771\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29067.3 | 0.960675 | 0.480337 | − | 0.877084i | \(-0.340514\pi\) | ||||
0.480337 | + | 0.877084i | \(0.340514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28301.1 | 0.932468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32811.7 | −1.07445 | −0.537226 | − | 0.843438i | \(-0.680528\pi\) | ||||
−0.537226 | + | 0.843438i | \(0.680528\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23982.0 | 0.782911 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2957.58 | 0.0959635 | 0.0479818 | − | 0.998848i | \(-0.484721\pi\) | ||||
0.0479818 | + | 0.998848i | \(0.484721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13647.4 | 0.441463 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12466.6 | −0.400825 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8950.60 | 0.286907 | 0.143454 | − | 0.989657i | \(-0.454179\pi\) | ||||
0.143454 | + | 0.989657i | \(0.454179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15981.3 | 0.509188 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53211.5 | −1.69029 | −0.845147 | − | 0.534533i | \(-0.820487\pi\) | ||||
−0.845147 | + | 0.534533i | \(0.820487\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2160.4.a.bv.1.1 | 4 | ||
3.2 | odd | 2 | 2160.4.a.bu.1.1 | 4 | |||
4.3 | odd | 2 | 1080.4.a.p.1.4 | yes | 4 | ||
12.11 | even | 2 | 1080.4.a.o.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.o.1.4 | ✓ | 4 | 12.11 | even | 2 | ||
1080.4.a.p.1.4 | yes | 4 | 4.3 | odd | 2 | ||
2160.4.a.bu.1.1 | 4 | 3.2 | odd | 2 | |||
2160.4.a.bv.1.1 | 4 | 1.1 | even | 1 | trivial |