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: | \(3\) |
Coefficient field: | 3.3.1765.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 1080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.89055\) 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 | ||||||||
\(7\) | 5.60585 | 0.302688 | 0.151344 | − | 0.988481i | \(-0.451640\pi\) | ||||
0.151344 | + | 0.988481i | \(0.451640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 53.5556 | 1.46796 | 0.733982 | − | 0.679168i | \(-0.237659\pi\) | ||||
0.733982 | + | 0.679168i | \(0.237659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.6866 | 0.633352 | 0.316676 | − | 0.948534i | \(-0.397433\pi\) | ||||
0.316676 | + | 0.948534i | \(0.397433\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 109.192 | 1.55782 | 0.778909 | − | 0.627137i | \(-0.215773\pi\) | ||||
0.778909 | + | 0.627137i | \(0.215773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 67.6070 | 0.816322 | 0.408161 | − | 0.912910i | \(-0.366170\pi\) | ||||
0.408161 | + | 0.912910i | \(0.366170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −87.4550 | −0.792854 | −0.396427 | − | 0.918066i | \(-0.629750\pi\) | ||||
−0.396427 | + | 0.918066i | \(0.629750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −141.980 | −0.909140 | −0.454570 | − | 0.890711i | \(-0.650207\pi\) | ||||
−0.454570 | + | 0.890711i | \(0.650207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 219.193 | 1.26994 | 0.634971 | − | 0.772536i | \(-0.281012\pi\) | ||||
0.634971 | + | 0.772536i | \(0.281012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 28.0293 | 0.135366 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 436.534 | 1.93961 | 0.969806 | − | 0.243876i | \(-0.0784190\pi\) | ||||
0.969806 | + | 0.243876i | \(0.0784190\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −68.7309 | −0.261804 | −0.130902 | − | 0.991395i | \(-0.541787\pi\) | ||||
−0.130902 | + | 0.991395i | \(0.541787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16.9311 | −0.0600456 | −0.0300228 | − | 0.999549i | \(-0.509558\pi\) | ||||
−0.0300228 | + | 0.999549i | \(0.509558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 566.322 | 1.75759 | 0.878793 | − | 0.477203i | \(-0.158349\pi\) | ||||
0.878793 | + | 0.477203i | \(0.158349\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −311.574 | −0.908380 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −95.0703 | −0.246395 | −0.123197 | − | 0.992382i | \(-0.539315\pi\) | ||||
−0.123197 | + | 0.992382i | \(0.539315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 267.778 | 0.656494 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 306.600 | 0.676541 | 0.338271 | − | 0.941049i | \(-0.390158\pi\) | ||||
0.338271 | + | 0.941049i | \(0.390158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −744.914 | −1.56355 | −0.781774 | − | 0.623562i | \(-0.785685\pi\) | ||||
−0.781774 | + | 0.623562i | \(0.785685\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 148.433 | 0.283243 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −521.489 | −0.950896 | −0.475448 | − | 0.879744i | \(-0.657714\pi\) | ||||
−0.475448 | + | 0.879744i | \(0.657714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −678.577 | −1.13426 | −0.567129 | − | 0.823629i | \(-0.691946\pi\) | ||||
−0.567129 | + | 0.823629i | \(0.691946\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −879.486 | −1.41008 | −0.705041 | − | 0.709166i | \(-0.749071\pi\) | ||||
−0.705041 | + | 0.709166i | \(0.749071\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 300.225 | 0.444335 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 698.634 | 0.994968 | 0.497484 | − | 0.867473i | \(-0.334257\pi\) | ||||
0.497484 | + | 0.867473i | \(0.334257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1191.92 | −1.57627 | −0.788134 | − | 0.615504i | \(-0.788952\pi\) | ||||
−0.788134 | + | 0.615504i | \(0.788952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 545.959 | 0.696678 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 840.998 | 1.00164 | 0.500818 | − | 0.865553i | \(-0.333033\pi\) | ||||
0.500818 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 166.419 | 0.191708 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 338.035 | 0.365070 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1045.59 | −1.09447 | −0.547234 | − | 0.836980i | \(-0.684319\pi\) | ||||
−0.547234 | + | 0.836980i | \(0.684319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 754.304 | 0.743129 | 0.371565 | − | 0.928407i | \(-0.378821\pi\) | ||||
0.371565 | + | 0.928407i | \(0.378821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1807.06 | 1.72869 | 0.864346 | − | 0.502898i | \(-0.167733\pi\) | ||||
0.864346 | + | 0.502898i | \(0.167733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 657.832 | 0.594346 | 0.297173 | − | 0.954824i | \(-0.403956\pi\) | ||||
0.297173 | + | 0.954824i | \(0.403956\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −981.839 | −0.862781 | −0.431390 | − | 0.902165i | \(-0.641977\pi\) | ||||
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −850.655 | −0.708167 | −0.354084 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354084 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −437.275 | −0.354575 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 612.113 | 0.471532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1537.20 | 1.15492 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 226.985 | 0.158596 | 0.0792978 | − | 0.996851i | \(-0.474732\pi\) | ||||
0.0792978 | + | 0.996851i | \(0.474732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1217.09 | 0.811735 | 0.405867 | − | 0.913932i | \(-0.366969\pi\) | ||||
0.405867 | + | 0.913932i | \(0.366969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 378.995 | 0.247090 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 509.696 | 0.317856 | 0.158928 | − | 0.987290i | \(-0.449196\pi\) | ||||
0.158928 | + | 0.987290i | \(0.449196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 845.621 | 0.516005 | 0.258002 | − | 0.966144i | \(-0.416936\pi\) | ||||
0.258002 | + | 0.966144i | \(0.416936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1589.88 | 0.929738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −709.901 | −0.406580 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1036.04 | 0.569638 | 0.284819 | − | 0.958581i | \(-0.408066\pi\) | ||||
0.284819 | + | 0.958581i | \(0.408066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1837.56 | 0.990321 | 0.495161 | − | 0.868801i | \(-0.335109\pi\) | ||||
0.495161 | + | 0.868801i | \(0.335109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1095.97 | 0.567936 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3080.72 | −1.56604 | −0.783020 | − | 0.621996i | \(-0.786322\pi\) | ||||
−0.783020 | + | 0.621996i | \(0.786322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −490.260 | −0.239987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 606.209 | 0.291300 | 0.145650 | − | 0.989336i | \(-0.453473\pi\) | ||||
0.145650 | + | 0.989336i | \(0.453473\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −250.692 | −0.116162 | −0.0580812 | − | 0.998312i | \(-0.518498\pi\) | ||||
−0.0580812 | + | 0.998312i | \(0.518498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1315.71 | −0.598866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1264.31 | −0.555629 | −0.277815 | − | 0.960635i | \(-0.589610\pi\) | ||||
−0.277815 | + | 0.960635i | \(0.589610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 140.146 | 0.0605375 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 558.174 | 0.233072 | 0.116536 | − | 0.993186i | \(-0.462821\pi\) | ||||
0.116536 | + | 0.993186i | \(0.462821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4377.85 | −1.79781 | −0.898904 | − | 0.438146i | \(-0.855635\pi\) | ||||
−0.898904 | + | 0.438146i | \(0.855635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2182.67 | 0.867421 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5847.83 | 2.28682 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1983.68 | −0.751489 | −0.375744 | − | 0.926723i | \(-0.622613\pi\) | ||||
−0.375744 | + | 0.926723i | \(0.622613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1092.75 | 0.407555 | 0.203778 | − | 0.979017i | \(-0.434678\pi\) | ||||
0.203778 | + | 0.979017i | \(0.434678\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −917.082 | −0.331672 | −0.165836 | − | 0.986153i | \(-0.553032\pi\) | ||||
−0.165836 | + | 0.986153i | \(0.553032\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1672.55 | −0.595797 | −0.297899 | − | 0.954598i | \(-0.596286\pi\) | ||||
−0.297899 | + | 0.954598i | \(0.596286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −795.920 | −0.275185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −343.655 | −0.117082 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3620.73 | 1.19833 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4890.34 | −1.59557 | −0.797785 | − | 0.602942i | \(-0.793995\pi\) | ||||
−0.797785 | + | 0.602942i | \(0.793995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −84.6553 | −0.0268532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1228.76 | 0.384396 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3241.53 | 0.986647 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4162 | −0.00763227 | −0.00381614 | − | 0.999993i | \(-0.501215\pi\) | ||||
−0.00381614 | + | 0.999993i | \(0.501215\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6185.05 | 1.80844 | 0.904220 | − | 0.427067i | \(-0.140453\pi\) | ||||
0.904220 | + | 0.427067i | \(0.140453\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −633.968 | −0.182942 | −0.0914712 | − | 0.995808i | \(-0.529157\pi\) | ||||
−0.0914712 | + | 0.995808i | \(0.529157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5585.10 | 1.57035 | 0.785176 | − | 0.619273i | \(-0.212573\pi\) | ||||
0.785176 | + | 0.619273i | \(0.212573\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2831.61 | 0.786016 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2686.83 | 0.727181 | 0.363591 | − | 0.931559i | \(-0.381551\pi\) | ||||
0.363591 | + | 0.931559i | \(0.381551\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1601.60 | −0.428084 | −0.214042 | − | 0.976824i | \(-0.568663\pi\) | ||||
−0.214042 | + | 0.976824i | \(0.568663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1557.87 | −0.406240 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2007.02 | 0.517019 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4955.28 | 1.24611 | 0.623057 | − | 0.782177i | \(-0.285891\pi\) | ||||
0.623057 | + | 0.782177i | \(0.285891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4683.70 | −1.16388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6161.72 | −1.49556 | −0.747778 | − | 0.663949i | \(-0.768879\pi\) | ||||
−0.747778 | + | 0.663949i | \(0.768879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2447.14 | 0.587097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 768.688 | 0.180226 | 0.0901128 | − | 0.995932i | \(-0.471277\pi\) | ||||
0.0901128 | + | 0.995932i | \(0.471277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −475.351 | −0.110191 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7989.19 | 1.81082 | 0.905408 | − | 0.424542i | \(-0.139565\pi\) | ||||
0.905408 | + | 0.424542i | \(0.139565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3875.39 | 0.868683 | 0.434341 | − | 0.900748i | \(-0.356981\pi\) | ||||
0.434341 | + | 0.900748i | \(0.356981\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1338.89 | 0.293593 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1121.71 | 0.243311 | 0.121656 | − | 0.992572i | \(-0.461180\pi\) | ||||
0.121656 | + | 0.992572i | \(0.461180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5681.52 | −1.20616 | −0.603081 | − | 0.797680i | \(-0.706060\pi\) | ||||
−0.603081 | + | 0.797680i | \(0.706060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6366.11 | −1.33719 | −0.668597 | − | 0.743625i | \(-0.733105\pi\) | ||||
−0.668597 | + | 0.743625i | \(0.733105\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −385.296 | −0.0792449 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7009.86 | 1.42680 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5316.63 | 1.06007 | 0.530035 | − | 0.847976i | \(-0.322179\pi\) | ||||
0.530035 | + | 0.847976i | \(0.322179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1533.00 | 0.302558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2596.24 | −0.502155 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −94.9130 | −0.0181751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3724.57 | −0.699240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2310.21 | −0.429480 | −0.214740 | − | 0.976671i | \(-0.568890\pi\) | ||||
−0.214740 | + | 0.976671i | \(0.568890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2874.98 | 0.524197 | 0.262099 | − | 0.965041i | \(-0.415585\pi\) | ||||
0.262099 | + | 0.965041i | \(0.415585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7587.20 | −1.37014 | −0.685070 | − | 0.728478i | \(-0.740228\pi\) | ||||
−0.685070 | + | 0.728478i | \(0.740228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7699.56 | 1.36420 | 0.682099 | − | 0.731260i | \(-0.261067\pi\) | ||||
0.682099 | + | 0.731260i | \(0.261067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7603.83 | −1.33459 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7382.14 | 1.27168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 742.164 | 0.126670 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3174.72 | 0.531999 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5469.00 | 0.908168 | 0.454084 | − | 0.890959i | \(-0.349967\pi\) | ||||
0.454084 | + | 0.890959i | \(0.349967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2607.45 | −0.425254 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6073.73 | 0.981772 | 0.490886 | − | 0.871224i | \(-0.336673\pi\) | ||||
0.490886 | + | 0.871224i | \(0.336673\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11739.0 | 1.86423 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3669.45 | −0.577643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6463.73 | −0.999975 | −0.499988 | − | 0.866033i | \(-0.666662\pi\) | ||||
−0.499988 | + | 0.866033i | \(0.666662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1630.31 | −0.250053 | −0.125026 | − | 0.992153i | \(-0.539902\pi\) | ||||
−0.125026 | + | 0.992153i | \(0.539902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8136.15 | 1.22675 | 0.613376 | − | 0.789791i | \(-0.289811\pi\) | ||||
0.613376 | + | 0.789791i | \(0.289811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3392.88 | −0.507255 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8847.53 | 1.30071 | 0.650355 | − | 0.759631i | \(-0.274620\pi\) | ||||
0.650355 | + | 0.759631i | \(0.274620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2288.29 | −0.333619 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4397.43 | −0.630608 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6938.76 | −0.986922 | −0.493461 | − | 0.869768i | \(-0.664268\pi\) | ||||
−0.493461 | + | 0.869768i | \(0.664268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −532.950 | −0.0745806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7950.83 | 1.10369 | 0.551847 | − | 0.833945i | \(-0.313923\pi\) | ||||
0.551847 | + | 0.833945i | \(0.313923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4214.90 | −0.575805 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11947.9 | 1.61932 | 0.809659 | − | 0.586901i | \(-0.199652\pi\) | ||||
0.809659 | + | 0.586901i | \(0.199652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1499.09 | −0.199999 | −0.0999997 | − | 0.994987i | \(-0.531884\pi\) | ||||
−0.0999997 | + | 0.994987i | \(0.531884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1501.12 | 0.198713 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −708.852 | −0.0923913 | −0.0461956 | − | 0.998932i | \(-0.514710\pi\) | ||||
−0.0461956 | + | 0.998932i | \(0.514710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9549.38 | −1.23512 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3493.17 | 0.444963 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2541.17 | 0.321253 | 0.160626 | − | 0.987015i | \(-0.448649\pi\) | ||||
0.160626 | + | 0.987015i | \(0.448649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2135.53 | 0.265944 | 0.132972 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132972 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6507.09 | 0.804321 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23378.8 | 2.84728 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7921.49 | 0.957684 | 0.478842 | − | 0.877901i | \(-0.341057\pi\) | ||||
0.478842 | + | 0.877901i | \(0.341057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1718.76 | 0.204781 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5959.60 | −0.704928 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13067.7 | −1.52362 | −0.761811 | − | 0.647799i | \(-0.775690\pi\) | ||||
−0.761811 | + | 0.647799i | \(0.775690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14532.5 | 1.68235 | 0.841175 | − | 0.540762i | \(-0.181864\pi\) | ||||
0.841175 | + | 0.540762i | \(0.181864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2729.80 | 0.311564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4175.88 | −0.473267 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1363.94 | 0.152433 | 0.0762164 | − | 0.997091i | \(-0.475716\pi\) | ||||
0.0762164 | + | 0.997091i | \(0.475716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10621.2 | 1.17880 | 0.589401 | − | 0.807841i | \(-0.299364\pi\) | ||||
0.589401 | + | 0.807841i | \(0.299364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5912.57 | −0.647224 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9505.12 | 1.03338 | 0.516691 | − | 0.856172i | \(-0.327164\pi\) | ||||
0.516691 | + | 0.856172i | \(0.327164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 377.897 | 0.0405292 | 0.0202646 | − | 0.999795i | \(-0.493549\pi\) | ||||
0.0202646 | + | 0.999795i | \(0.493549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4204.99 | 0.447945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1424.29 | 0.149703 | 0.0748513 | − | 0.997195i | \(-0.476152\pi\) | ||||
0.0748513 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3680.93 | −0.384319 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 832.093 | 0.0857343 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10979.1 | −1.12381 | −0.561903 | − | 0.827203i | \(-0.689931\pi\) | ||||
−0.561903 | + | 0.827203i | \(0.689931\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10729.6 | 1.08401 | 0.542003 | − | 0.840377i | \(-0.317666\pi\) | ||||
0.542003 | + | 0.840377i | \(0.317666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1314.85 | −0.131979 | −0.0659895 | − | 0.997820i | \(-0.521020\pi\) | ||||
−0.0659895 | + | 0.997820i | \(0.521020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7772.33 | 0.770151 | 0.385075 | − | 0.922885i | \(-0.374175\pi\) | ||||
0.385075 | + | 0.922885i | \(0.374175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2923.39 | −0.287824 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −906.753 | −0.0881449 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1690.18 | 0.163264 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17266.5 | −1.64702 | −0.823512 | − | 0.567299i | \(-0.807988\pi\) | ||||
−0.823512 | + | 0.567299i | \(0.807988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12959.2 | 1.22846 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5227.94 | −0.489461 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 123.244 | 0.0114676 | 0.00573380 | − | 0.999984i | \(-0.498175\pi\) | ||||
0.00573380 | + | 0.999984i | \(0.498175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13322.6 | 1.22453 | 0.612263 | − | 0.790654i | \(-0.290259\pi\) | ||||
0.612263 | + | 0.790654i | \(0.290259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15503.1 | −1.41627 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3804.00 | −0.343326 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5106.10 | −0.458077 | −0.229039 | − | 0.973417i | \(-0.573558\pi\) | ||||
−0.229039 | + | 0.973417i | \(0.573558\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −856.862 | −0.0759554 | −0.0379777 | − | 0.999279i | \(-0.512092\pi\) | ||||
−0.0379777 | + | 0.999279i | \(0.512092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3771.52 | 0.332338 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −568.382 | −0.0494953 | −0.0247476 | − | 0.999694i | \(-0.507878\pi\) | ||||
−0.0247476 | + | 0.999694i | \(0.507878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4930.27 | −0.426814 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9035.32 | 0.773095 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30329.7 | 2.58007 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3341.28 | −0.280968 | −0.140484 | − | 0.990083i | \(-0.544866\pi\) | ||||
−0.140484 | + | 0.990083i | \(0.544866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20342.2 | −1.70077 | −0.850383 | − | 0.526165i | \(-0.823630\pi\) | ||||
−0.850383 | + | 0.526165i | \(0.823630\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23934.1 | 1.97834 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4518.62 | −0.371383 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2040.39 | −0.165814 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3289.16 | 0.265800 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16686.5 | −1.33347 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5490.90 | 0.436363 | 0.218181 | − | 0.975908i | \(-0.429988\pi\) | ||||
0.218181 | + | 0.975908i | \(0.429988\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4909.19 | −0.385847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13539.2 | −1.05831 | −0.529153 | − | 0.848527i | \(-0.677490\pi\) | ||||
−0.529153 | + | 0.848527i | \(0.677490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9598.86 | −0.742151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3916.44 | 0.301164 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9817.92 | 0.746856 | 0.373428 | − | 0.927659i | \(-0.378182\pi\) | ||||
0.373428 | + | 0.927659i | \(0.378182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −502.625 | −0.0380300 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8971.81 | −0.671610 | −0.335805 | − | 0.941931i | \(-0.609008\pi\) | ||||
−0.335805 | + | 0.941931i | \(0.609008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4253.28 | −0.316702 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13876.7 | −1.02239 | −0.511195 | − | 0.859464i | \(-0.670797\pi\) | ||||
−0.511195 | + | 0.859464i | \(0.670797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3513.33 | 0.257492 | 0.128746 | − | 0.991678i | \(-0.458905\pi\) | ||||
0.128746 | + | 0.991678i | \(0.458905\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2186.38 | −0.158571 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17636.6 | −1.27248 | −0.636241 | − | 0.771491i | \(-0.719511\pi\) | ||||
−0.636241 | + | 0.771491i | \(0.719511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6681.73 | −0.477117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5091.54 | −0.361698 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1129.54 | −0.0794229 | −0.0397114 | − | 0.999211i | \(-0.512644\pi\) | ||||
−0.0397114 | + | 0.999211i | \(0.512644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14819.0 | 1.03668 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25431.4 | 1.76111 | 0.880557 | − | 0.473940i | \(-0.157169\pi\) | ||||
0.880557 | + | 0.473940i | \(0.157169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3060.57 | 0.210876 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24719.7 | −1.68618 | −0.843089 | − | 0.537775i | \(-0.819265\pi\) | ||||
−0.843089 | + | 0.537775i | \(0.819265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24379.3 | −1.65466 | −0.827331 | − | 0.561714i | \(-0.810142\pi\) | ||||
−0.827331 | + | 0.561714i | \(0.810142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7686.00 | 0.516496 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16258.8 | −1.08719 | −0.543596 | − | 0.839347i | \(-0.682937\pi\) | ||||
−0.543596 | + | 0.839347i | \(0.682937\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16812.2 | 1.11317 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13069.4 | −0.861124 | −0.430562 | − | 0.902561i | \(-0.641685\pi\) | ||||
−0.430562 | + | 0.902561i | \(0.641685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20592.5 | −1.34363 | −0.671816 | − | 0.740718i | \(-0.734485\pi\) | ||||
−0.671816 | + | 0.740718i | \(0.734485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24687.2 | −1.60301 | −0.801504 | − | 0.597989i | \(-0.795967\pi\) | ||||
−0.801504 | + | 0.597989i | \(0.795967\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4714.51 | 0.303183 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47665.9 | 3.02157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18847.2 | −1.18906 | −0.594529 | − | 0.804074i | \(-0.702662\pi\) | ||||
−0.594529 | + | 0.804074i | \(0.702662\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1134.92 | 0.0709261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9249.57 | −0.575324 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3418.42 | 0.210639 | 0.105319 | − | 0.994438i | \(-0.466414\pi\) | ||||
0.105319 | + | 0.994438i | \(0.466414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20369.8 | −1.24931 | −0.624656 | − | 0.780900i | \(-0.714761\pi\) | ||||
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15267.3 | 0.927699 | 0.463849 | − | 0.885914i | \(-0.346468\pi\) | ||||
0.463849 | + | 0.885914i | \(0.346468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16420.1 | 0.993139 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10839.6 | 0.649595 | 0.324797 | − | 0.945784i | \(-0.394704\pi\) | ||||
0.324797 | + | 0.945784i | \(0.394704\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6085.43 | 0.363019 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1589.00 | −0.0939282 | −0.0469641 | − | 0.998897i | \(-0.514955\pi\) | ||||
−0.0469641 | + | 0.998897i | \(0.514955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15061.5 | −0.886272 | −0.443136 | − | 0.896454i | \(-0.646134\pi\) | ||||
−0.443136 | + | 0.896454i | \(0.646134\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1894.98 | 0.110502 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12416.9 | 0.720815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39894.3 | −2.29523 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18477.3 | 1.05832 | 0.529159 | − | 0.848523i | \(-0.322508\pi\) | ||||
0.529159 | + | 0.848523i | \(0.322508\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28782.1 | −1.63395 | −0.816975 | − | 0.576673i | \(-0.804351\pi\) | ||||
−0.816975 | + | 0.576673i | \(0.804351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5861.42 | −0.331282 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1542.58 | −0.0864205 | −0.0432103 | − | 0.999066i | \(-0.513759\pi\) | ||||
−0.0432103 | + | 0.999066i | \(0.513759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2548.48 | 0.142149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2822.31 | −0.156054 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8037.73 | 0.442503 | 0.221252 | − | 0.975217i | \(-0.428986\pi\) | ||||
0.221252 | + | 0.975217i | \(0.428986\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4228.11 | 0.230764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7504.86 | −0.407843 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3686.72 | 0.198639 | 0.0993193 | − | 0.995056i | \(-0.468333\pi\) | ||||
0.0993193 | + | 0.995056i | \(0.468333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29512.7 | 1.58335 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4228.52 | 0.224936 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20887.3 | 1.10640 | 0.553200 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553200 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19169.5 | −1.00688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7949.41 | 0.415791 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30381.8 | 1.57587 | 0.787935 | − | 0.615758i | \(-0.211150\pi\) | ||||
0.787935 | + | 0.615758i | \(0.211150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10130.1 | 0.523254 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3549.50 | −0.181828 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36256.3 | 1.84962 | 0.924810 | − | 0.380430i | \(-0.124224\pi\) | ||||
0.924810 | + | 0.380430i | \(0.124224\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1848.73 | −0.0935402 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 206.568 | 0.0104089 | 0.00520447 | − | 0.999986i | \(-0.498343\pi\) | ||||
0.00520447 | + | 0.999986i | \(0.498343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27928.7 | −1.39588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28859.8 | 1.43657 | 0.718285 | − | 0.695749i | \(-0.244927\pi\) | ||||
0.718285 | + | 0.695749i | \(0.244927\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9452.34 | −0.466720 | −0.233360 | − | 0.972390i | \(-0.574972\pi\) | ||||
−0.233360 | + | 0.972390i | \(0.574972\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5180.22 | 0.254750 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3687.71 | 0.179901 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13833.5 | 0.672160 | 0.336080 | − | 0.941833i | \(-0.390899\pi\) | ||||
0.336080 | + | 0.941833i | \(0.390899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9187.80 | 0.442885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4267.28 | −0.204884 | −0.102442 | − | 0.994739i | \(-0.532666\pi\) | ||||
−0.102442 | + | 0.994739i | \(0.532666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21502.5 | −1.02426 | −0.512131 | − | 0.858907i | \(-0.671144\pi\) | ||||
−0.512131 | + | 0.858907i | \(0.671144\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5504.04 | −0.261153 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9101.91 | 0.428489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17936.2 | 0.841086 | 0.420543 | − | 0.907273i | \(-0.361840\pi\) | ||||
0.420543 | + | 0.907273i | \(0.361840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13672.3 | −0.636167 | −0.318083 | − | 0.948063i | \(-0.603039\pi\) | ||||
−0.318083 | + | 0.948063i | \(0.603039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5479.83 | 0.253989 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4646.69 | −0.213716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36341.6 | −1.66505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15403.6 | −0.700354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14681.1 | −0.664963 | −0.332482 | − | 0.943110i | \(-0.607886\pi\) | ||||
−0.332482 | + | 0.943110i | \(0.607886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4768.65 | −0.214353 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22113.9 | −0.990276 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11761.8 | −0.522740 | −0.261370 | − | 0.965239i | \(-0.584174\pi\) | ||||
−0.261370 | + | 0.965239i | \(0.584174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 61837.7 | 2.73800 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47101.4 | −2.06995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2451.30 | −0.107325 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18821.1 | 0.817941 | 0.408971 | − | 0.912548i | \(-0.365888\pi\) | ||||
0.408971 | + | 0.912548i | \(0.365888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13804.6 | −0.597713 | −0.298856 | − | 0.954298i | \(-0.596605\pi\) | ||||
−0.298856 | + | 0.954298i | \(0.596605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3031.05 | 0.130274 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1144.66 | −0.0490166 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21364.1 | 0.908176 | 0.454088 | − | 0.890957i | \(-0.349965\pi\) | ||||
0.454088 | + | 0.890957i | \(0.349965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30739.7 | −1.30197 | −0.650983 | − | 0.759092i | \(-0.725643\pi\) | ||||
−0.650983 | + | 0.759092i | \(0.725643\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3820.31 | 0.160635 | 0.0803176 | − | 0.996769i | \(-0.474407\pi\) | ||||
0.0803176 | + | 0.996769i | \(0.474407\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22902.8 | 0.959526 | 0.479763 | − | 0.877398i | \(-0.340723\pi\) | ||||
0.479763 | + | 0.877398i | \(0.340723\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34021.4 | −1.41509 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1253.46 | −0.0519494 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32660.2 | −1.34393 | −0.671963 | − | 0.740585i | \(-0.734549\pi\) | ||||
−0.671963 | + | 0.740585i | \(0.734549\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4230.63 | −0.173465 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6578.54 | −0.267821 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8617.31 | 0.349580 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38177.1 | −1.53783 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3474.35 | 0.139460 | 0.0697301 | − | 0.997566i | \(-0.477786\pi\) | ||||
0.0697301 | + | 0.997566i | \(0.477786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36755.3 | −1.46504 | −0.732519 | − | 0.680746i | \(-0.761656\pi\) | ||||
−0.732519 | + | 0.680746i | \(0.761656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20322.2 | 0.807201 | 0.403600 | − | 0.914935i | \(-0.367759\pi\) | ||||
0.403600 | + | 0.914935i | \(0.367759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8541.33 | −0.336907 | −0.168453 | − | 0.985710i | \(-0.553877\pi\) | ||||
−0.168453 | + | 0.985710i | \(0.553877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6321.56 | −0.248485 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37415.7 | 1.46058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15481.2 | −0.602252 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 700.732 | 0.0270732 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30963.2 | −1.19219 | −0.596096 | − | 0.802913i | \(-0.703282\pi\) | ||||
−0.596096 | + | 0.802913i | \(0.703282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25296.4 | −0.967376 | −0.483688 | − | 0.875241i | \(-0.660703\pi\) | ||||
−0.483688 | + | 0.875241i | \(0.660703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20261.1 | 0.772187 | 0.386094 | − | 0.922460i | \(-0.373824\pi\) | ||||
0.386094 | + | 0.922460i | \(0.373824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6869.30 | 0.260032 | 0.130016 | − | 0.991512i | \(-0.458497\pi\) | ||||
0.130016 | + | 0.991512i | \(0.458497\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1272.44 | 0.0480049 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38287.3 | 1.43476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2790.87 | 0.104233 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31121.1 | −1.15456 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10380.9 | −0.383838 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21889.3 | −0.804004 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11567.2 | −0.423465 | −0.211733 | − | 0.977328i | \(-0.567911\pi\) | ||||
−0.211733 | + | 0.977328i | \(0.567911\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27971.1 | −1.01726 | −0.508631 | − | 0.860985i | \(-0.669848\pi\) | ||||
−0.508631 | + | 0.860985i | \(0.669848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −63834.0 | −2.31391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6822.80 | 0.245702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 254.867 | 0.00914828 | 0.00457414 | − | 0.999990i | \(-0.498544\pi\) | ||||
0.00457414 | + | 0.999990i | \(0.498544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20144.6 | −0.718384 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10913.3 | 0.387923 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8347.83 | 0.294815 | 0.147408 | − | 0.989076i | \(-0.452907\pi\) | ||||
0.147408 | + | 0.989076i | \(0.452907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21064.6 | −0.741531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29239.2 | 1.02270 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4128.98 | 0.143957 | 0.0719786 | − | 0.997406i | \(-0.477069\pi\) | ||||
0.0719786 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43760.0 | −1.51598 | −0.757988 | − | 0.652268i | \(-0.773818\pi\) | ||||
−0.757988 | + | 0.652268i | \(0.773818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6010.87 | 0.207572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8035.72 | 0.275740 | 0.137870 | − | 0.990450i | \(-0.455974\pi\) | ||||
0.137870 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26108.9 | −0.893078 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10733.9 | −0.364854 | −0.182427 | − | 0.983219i | \(-0.558395\pi\) | ||||
−0.182427 | + | 0.983219i | \(0.558395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9918.42 | −0.336076 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2857.28 | 0.0962110 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18254.6 | 0.612755 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5463.77 | 0.182264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5800.85 | 0.192909 | 0.0964543 | − | 0.995337i | \(-0.469250\pi\) | ||||
0.0964543 | + | 0.995337i | \(0.469250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47046.8 | 1.55490 | 0.777448 | − | 0.628947i | \(-0.216514\pi\) | ||||
0.777448 | + | 0.628947i | \(0.216514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4740.43 | 0.156188 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32043.6 | −1.04930 | −0.524649 | − | 0.851318i | \(-0.675804\pi\) | ||||
−0.524649 | + | 0.851318i | \(0.675804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45040.1 | 1.47037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25178.5 | −0.816957 | −0.408478 | − | 0.912768i | \(-0.633940\pi\) | ||||
−0.408478 | + | 0.912768i | \(0.633940\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4585.41 | −0.148328 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1480.71 | 0.0476074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18011.8 | −0.577360 | −0.288680 | − | 0.957426i | \(-0.593216\pi\) | ||||
−0.288680 | + | 0.957426i | \(0.593216\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8362.73 | −0.266449 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31687.1 | −1.00656 | −0.503281 | − | 0.864123i | \(-0.667874\pi\) | ||||
−0.503281 | + | 0.864123i | \(0.667874\pi\) | |||||||
\(998\) | 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.bp.1.2 | 3 | ||
3.2 | odd | 2 | 2160.4.a.bh.1.2 | 3 | |||
4.3 | odd | 2 | 1080.4.a.l.1.2 | yes | 3 | ||
12.11 | even | 2 | 1080.4.a.f.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.f.1.2 | ✓ | 3 | 12.11 | even | 2 | ||
1080.4.a.l.1.2 | yes | 3 | 4.3 | odd | 2 | ||
2160.4.a.bh.1.2 | 3 | 3.2 | odd | 2 | |||
2160.4.a.bp.1.2 | 3 | 1.1 | even | 1 | trivial |