Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4536,2,Mod(1,4536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4536 = 2^{3} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4536.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: | \(36.2201423569\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.45729.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 11x^{2} + 12x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.399463\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4536.1 |
$q$-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 | ||||||||
\(5\) | −0.600537 | −0.268568 | −0.134284 | − | 0.990943i | \(-0.542873\pi\) | ||||
−0.134284 | + | 0.990943i | \(0.542873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.60054 | 0.482580 | 0.241290 | − | 0.970453i | \(-0.422430\pi\) | ||||
0.241290 | + | 0.970453i | \(0.422430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.330355 | 0.0916240 | 0.0458120 | − | 0.998950i | \(-0.485412\pi\) | ||||
0.0458120 | + | 0.998950i | \(0.485412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.44990 | 0.351652 | 0.175826 | − | 0.984421i | \(-0.443740\pi\) | ||||
0.175826 | + | 0.984421i | \(0.443740\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57918 | 0.591705 | 0.295852 | − | 0.955234i | \(-0.404396\pi\) | ||||
0.295852 | + | 0.955234i | \(0.404396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.84936 | −0.385619 | −0.192809 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192809 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.63936 | −0.927871 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.51901 | −0.653463 | −0.326732 | − | 0.945117i | \(-0.605947\pi\) | ||||
−0.326732 | + | 0.945117i | \(0.605947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.62068 | −1.72793 | −0.863963 | − | 0.503555i | \(-0.832025\pi\) | ||||
−0.863963 | + | 0.503555i | \(0.832025\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.600537 | 0.101509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.600537 | 0.0987276 | 0.0493638 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493638 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.62068 | −1.03398 | −0.516989 | − | 0.855992i | \(-0.672947\pi\) | ||||
−0.516989 | + | 0.855992i | \(0.672947\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.62962 | 0.553512 | 0.276756 | − | 0.960940i | \(-0.410741\pi\) | ||||
0.276756 | + | 0.960940i | \(0.410741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.90954 | −0.570265 | −0.285132 | − | 0.958488i | \(-0.592038\pi\) | ||||
−0.285132 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.27166 | 1.27356 | 0.636780 | − | 0.771046i | \(-0.280266\pi\) | ||||
0.636780 | + | 0.771046i | \(0.280266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.961181 | −0.129606 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.8695 | 1.80566 | 0.902828 | − | 0.430001i | \(-0.141487\pi\) | ||||
0.902828 | + | 0.430001i | \(0.141487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.18865 | −0.664339 | −0.332169 | − | 0.943220i | \(-0.607781\pi\) | ||||
−0.332169 | + | 0.943220i | \(0.607781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.198390 | −0.0246073 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8093 | −1.44274 | −0.721370 | − | 0.692550i | \(-0.756487\pi\) | ||||
−0.721370 | + | 0.692550i | \(0.756487\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17972 | 0.496041 | 0.248021 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248021 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.13969 | 0.484514 | 0.242257 | − | 0.970212i | \(-0.422112\pi\) | ||||
0.242257 | + | 0.970212i | \(0.422112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.60054 | −0.182398 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.13076 | 0.914782 | 0.457391 | − | 0.889266i | \(-0.348784\pi\) | ||||
0.457391 | + | 0.889266i | \(0.348784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.57918 | 0.612395 | 0.306197 | − | 0.951968i | \(-0.400943\pi\) | ||||
0.306197 | + | 0.951968i | \(0.400943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.870718 | −0.0944426 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.83069 | 0.406053 | 0.203026 | − | 0.979173i | \(-0.434922\pi\) | ||||
0.203026 | + | 0.979173i | \(0.434922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.330355 | −0.0346306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.54889 | −0.158913 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.94956 | −0.197948 | −0.0989741 | − | 0.995090i | \(-0.531556\pi\) | ||||
−0.0989741 | + | 0.995090i | \(0.531556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5904 | −1.75031 | −0.875155 | − | 0.483843i | \(-0.839241\pi\) | ||||
−0.875155 | + | 0.483843i | \(0.839241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6109 | −1.04553 | −0.522764 | − | 0.852478i | \(-0.675099\pi\) | ||||
−0.522764 | + | 0.852478i | \(0.675099\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.43949 | 0.332508 | 0.166254 | − | 0.986083i | \(-0.446833\pi\) | ||||
0.166254 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55010 | −0.531603 | −0.265802 | − | 0.964028i | \(-0.585637\pi\) | ||||
−0.265802 | + | 0.964028i | \(0.585637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.76158 | −0.824220 | −0.412110 | − | 0.911134i | \(-0.635208\pi\) | ||||
−0.412110 | + | 0.911134i | \(0.635208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11061 | 0.103565 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.44990 | −0.132912 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.43828 | −0.767117 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.78879 | 0.517765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1521 | −0.989590 | −0.494795 | − | 0.869010i | \(-0.664757\pi\) | ||||
−0.494795 | + | 0.869010i | \(0.664757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.19987 | 0.454314 | 0.227157 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227157 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.57918 | −0.223643 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.78798 | −0.750808 | −0.375404 | − | 0.926861i | \(-0.622496\pi\) | ||||
−0.375404 | + | 0.926861i | \(0.622496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.01867 | −0.764954 | −0.382477 | − | 0.923965i | \(-0.624929\pi\) | ||||
−0.382477 | + | 0.923965i | \(0.624929\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.528746 | 0.0442159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.11329 | 0.175499 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.05124 | 0.0861209 | 0.0430604 | − | 0.999072i | \(-0.486289\pi\) | ||||
0.0430604 | + | 0.999072i | \(0.486289\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9786 | −1.05619 | −0.528094 | − | 0.849186i | \(-0.677093\pi\) | ||||
−0.528094 | + | 0.849186i | \(0.677093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.77757 | 0.464066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.7340 | −1.57494 | −0.787471 | − | 0.616351i | \(-0.788610\pi\) | ||||
−0.787471 | + | 0.616351i | \(0.788610\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.84936 | 0.145750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9214 | −1.79534 | −0.897672 | − | 0.440664i | \(-0.854743\pi\) | ||||
−0.897672 | + | 0.440664i | \(0.854743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.23016 | −0.249957 | −0.124978 | − | 0.992159i | \(-0.539886\pi\) | ||||
−0.124978 | + | 0.992159i | \(0.539886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8909 | −0.991605 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1610 | −1.07664 | −0.538322 | − | 0.842739i | \(-0.680942\pi\) | ||||
−0.538322 | + | 0.842739i | \(0.680942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.63936 | 0.350702 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.06790 | −0.528280 | −0.264140 | − | 0.964484i | \(-0.585088\pi\) | ||||
−0.264140 | + | 0.964484i | \(0.585088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6207 | −1.45839 | −0.729197 | − | 0.684304i | \(-0.760106\pi\) | ||||
−0.729197 | + | 0.684304i | \(0.760106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.360644 | −0.0265151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.32062 | 0.169700 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.2192 | 1.46301 | 0.731505 | − | 0.681836i | \(-0.238818\pi\) | ||||
0.731505 | + | 0.681836i | \(0.238818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7895 | 1.28051 | 0.640257 | − | 0.768161i | \(-0.278828\pi\) | ||||
0.640257 | + | 0.768161i | \(0.278828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.04150 | −0.572933 | −0.286467 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286467 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0332 | 0.994790 | 0.497395 | − | 0.867524i | \(-0.334290\pi\) | ||||
0.497395 | + | 0.867524i | \(0.334290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.51901 | 0.246986 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.97596 | 0.277693 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.12808 | 0.285545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6524 | 1.00872 | 0.504358 | − | 0.863495i | \(-0.331729\pi\) | ||||
0.504358 | + | 0.863495i | \(0.331729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.17972 | −0.148656 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.62068 | 0.653095 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.478982 | 0.0322198 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0539 | −0.941120 | −0.470560 | − | 0.882368i | \(-0.655948\pi\) | ||||
−0.470560 | + | 0.882368i | \(0.655948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.81202 | −0.319385 | −0.159692 | − | 0.987167i | \(-0.551050\pi\) | ||||
−0.159692 | + | 0.987167i | \(0.551050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.36837 | 0.222588 | 0.111294 | − | 0.993788i | \(-0.464500\pi\) | ||||
0.111294 | + | 0.993788i | \(0.464500\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9137 | −1.37010 | −0.685051 | − | 0.728495i | \(-0.740220\pi\) | ||||
−0.685051 | + | 0.728495i | \(0.740220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.34782 | 0.153155 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.2123 | −1.24274 | −0.621370 | − | 0.783517i | \(-0.713423\pi\) | ||||
−0.621370 | + | 0.783517i | \(0.713423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7782 | −1.14520 | −0.572599 | − | 0.819836i | \(-0.694065\pi\) | ||||
−0.572599 | + | 0.819836i | \(0.694065\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.600537 | −0.0383669 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.852046 | 0.0542144 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5531 | −1.29730 | −0.648649 | − | 0.761088i | \(-0.724665\pi\) | ||||
−0.648649 | + | 0.761088i | \(0.724665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.95997 | −0.186092 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3885 | 1.58369 | 0.791846 | − | 0.610721i | \(-0.209120\pi\) | ||||
0.791846 | + | 0.610721i | \(0.209120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.600537 | −0.0373155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.7114 | 1.89375 | 0.946874 | − | 0.321606i | \(-0.104223\pi\) | ||||
0.946874 | + | 0.321606i | \(0.104223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.56797 | −0.342038 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7402 | −0.837757 | −0.418878 | − | 0.908042i | \(-0.637577\pi\) | ||||
−0.418878 | + | 0.908042i | \(0.637577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.64977 | 0.464690 | 0.232345 | − | 0.972633i | \(-0.425360\pi\) | ||||
0.232345 | + | 0.972633i | \(0.425360\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.42546 | −0.447772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.38347 | −0.503714 | −0.251857 | − | 0.967764i | \(-0.581041\pi\) | ||||
−0.251857 | + | 0.967764i | \(0.581041\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.5573 | 1.52462 | 0.762310 | − | 0.647212i | \(-0.224065\pi\) | ||||
0.762310 | + | 0.647212i | \(0.224065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9226 | 0.649283 | 0.324641 | − | 0.945837i | \(-0.394756\pi\) | ||||
0.324641 | + | 0.945837i | \(0.394756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.62068 | 0.390807 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8978 | −0.876341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.9988 | −1.63571 | −0.817853 | − | 0.575427i | \(-0.804836\pi\) | ||||
−0.817853 | + | 0.575427i | \(0.804836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.32915 | −0.484942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.610947 | −0.0353320 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.62962 | −0.209208 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.11598 | 0.178420 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.0259 | −1.88489 | −0.942443 | − | 0.334367i | \(-0.891477\pi\) | ||||
−0.942443 | + | 0.334367i | \(0.891477\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0287 | 1.47595 | 0.737975 | − | 0.674828i | \(-0.235782\pi\) | ||||
0.737975 | + | 0.674828i | \(0.235782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.9324 | −0.617934 | −0.308967 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308967 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9719 | 0.672407 | 0.336203 | − | 0.941789i | \(-0.390857\pi\) | ||||
0.336203 | + | 0.941789i | \(0.390857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.63230 | −0.315348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.73956 | 0.208074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53264 | −0.0850153 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.90954 | 0.215540 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2352 | 1.27712 | 0.638561 | − | 0.769571i | \(-0.279530\pi\) | ||||
0.638561 | + | 0.769571i | \(0.279530\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.09194 | 0.387474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.79187 | 0.424450 | 0.212225 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212225 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3983 | −0.833862 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.5240 | 0.994419 | 0.497209 | − | 0.867631i | \(-0.334358\pi\) | ||||
0.497209 | + | 0.867631i | \(0.334358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.91700 | −0.102614 | −0.0513072 | − | 0.998683i | \(-0.516339\pi\) | ||||
−0.0513072 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.73956 | 0.0925872 | 0.0462936 | − | 0.998928i | \(-0.485259\pi\) | ||||
0.0462936 | + | 0.998928i | \(0.485259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.51007 | −0.133221 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07616 | 0.162354 | 0.0811768 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811768 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3478 | −0.649885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.48604 | −0.130125 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.3574 | −0.645052 | −0.322526 | − | 0.946561i | \(-0.604532\pi\) | ||||
−0.322526 | + | 0.946561i | \(0.604532\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.27166 | −0.481360 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7999 | 1.28409 | 0.642044 | − | 0.766668i | \(-0.278087\pi\) | ||||
0.642044 | + | 0.766668i | \(0.278087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.16252 | −0.0598730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9650 | −0.614602 | −0.307301 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307301 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7162 | −0.598669 | −0.299335 | − | 0.954148i | \(-0.596765\pi\) | ||||
−0.299335 | + | 0.954148i | \(0.596765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.961181 | 0.0489863 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −38.2719 | −1.94046 | −0.970232 | − | 0.242178i | \(-0.922138\pi\) | ||||
−0.970232 | + | 0.242178i | \(0.922138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.68139 | −0.135604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.88282 | −0.245681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8396 | 0.644402 | 0.322201 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322201 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3140 | −1.11431 | −0.557155 | − | 0.830408i | \(-0.688107\pi\) | ||||
−0.557155 | + | 0.830408i | \(0.688107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.17824 | −0.158320 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.961181 | 0.0476440 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.53210 | −0.372438 | −0.186219 | − | 0.982508i | \(-0.559623\pi\) | ||||
−0.186219 | + | 0.982508i | \(0.559623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.8695 | −0.682474 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.35050 | −0.164470 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2491 | 1.38006 | 0.690029 | − | 0.723781i | \(-0.257598\pi\) | ||||
0.690029 | + | 0.723781i | \(0.257598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0679 | 0.929313 | 0.464656 | − | 0.885491i | \(-0.346178\pi\) | ||||
0.464656 | + | 0.885491i | \(0.346178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.72660 | −0.326288 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.18865 | 0.251097 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9786 | 1.10684 | 0.553421 | − | 0.832902i | \(-0.313322\pi\) | ||||
0.553421 | + | 0.832902i | \(0.313322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.0806 | −1.39752 | −0.698762 | − | 0.715354i | \(-0.746265\pi\) | ||||
−0.698762 | + | 0.715354i | \(0.746265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.76984 | −0.228173 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7355 | −0.703289 | −0.351644 | − | 0.936134i | \(-0.614377\pi\) | ||||
−0.351644 | + | 0.936134i | \(0.614377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5095 | 1.63960 | 0.819799 | − | 0.572652i | \(-0.194085\pi\) | ||||
0.819799 | + | 0.572652i | \(0.194085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.30047 | −0.109053 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5508 | −0.545115 | −0.272557 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272557 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5966 | −0.498977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.198390 | 0.00930068 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.3989 | 1.74945 | 0.874724 | − | 0.484621i | \(-0.161043\pi\) | ||||
0.874724 | + | 0.484621i | \(0.161043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2786 | 0.851318 | 0.425659 | − | 0.904884i | \(-0.360042\pi\) | ||||
0.425659 | + | 0.904884i | \(0.360042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.49220 | 0.394666 | 0.197333 | − | 0.980336i | \(-0.436772\pi\) | ||||
0.197333 | + | 0.980336i | \(0.436772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6746 | 0.679060 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8093 | 0.545305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.80934 | 0.267114 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.9657 | −0.549026 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.4303 | −1.71023 | −0.855117 | − | 0.518435i | \(-0.826515\pi\) | ||||
−0.855117 | + | 0.518435i | \(0.826515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.198390 | 0.00904582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.17078 | 0.0531626 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.3216 | 1.50994 | 0.754972 | − | 0.655757i | \(-0.227650\pi\) | ||||
0.754972 | + | 0.655757i | \(0.227650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.8911 | 1.80026 | 0.900131 | − | 0.435620i | \(-0.143471\pi\) | ||||
0.900131 | + | 0.435620i | \(0.143471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.10221 | −0.229792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.17972 | −0.187486 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0741 | 0.988171 | 0.494086 | − | 0.869413i | \(-0.335503\pi\) | ||||
0.494086 | + | 0.869413i | \(0.335503\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.30820 | 0.415032 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5637 | 0.470077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.76931 | 0.255720 | 0.127860 | − | 0.991792i | \(-0.459189\pi\) | ||||
0.127860 | + | 0.991792i | \(0.459189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.13969 | −0.183129 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.37226 | 0.280795 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.25736 | −0.275198 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2989 | 0.582634 | 0.291317 | − | 0.956627i | \(-0.405907\pi\) | ||||
0.291317 | + | 0.956627i | \(0.405907\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.27523 | 0.186943 | 0.0934713 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934713 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.9490 | −0.607629 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5799 | −0.851298 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18718 | −0.0947372 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.06554 | −0.0893011 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.60054 | 0.0689400 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2130 | −0.525076 | −0.262538 | − | 0.964922i | \(-0.584560\pi\) | ||||
−0.262538 | + | 0.964922i | \(0.584560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.33304 | 0.142772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.1820 | 1.63254 | 0.816272 | − | 0.577668i | \(-0.196037\pi\) | ||||
0.816272 | + | 0.577668i | \(0.196037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.07616 | −0.386658 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.13076 | −0.345755 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.8404 | −1.56098 | −0.780490 | − | 0.625169i | \(-0.785030\pi\) | ||||
−0.780490 | + | 0.625169i | \(0.785030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.19906 | 0.0507150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.1253 | −0.806036 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.26165 | 0.221359 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9153 | 1.08642 | 0.543212 | − | 0.839596i | \(-0.317208\pi\) | ||||
0.543212 | + | 0.839596i | \(0.317208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.1357 | −1.63778 | −0.818889 | − | 0.573951i | \(-0.805410\pi\) | ||||
−0.818889 | + | 0.573951i | \(0.805410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.57985 | 0.357805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.72008 | 0.404652 | 0.202326 | − | 0.979318i | \(-0.435150\pi\) | ||||
0.202326 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.57918 | −0.231463 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8396 | 0.614595 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8218 | −0.570485 | −0.285242 | − | 0.958455i | \(-0.592074\pi\) | ||||
−0.285242 | + | 0.958455i | \(0.592074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8135 | −1.02242 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1361 | 0.909022 | 0.454511 | − | 0.890741i | \(-0.349814\pi\) | ||||
0.454511 | + | 0.890741i | \(0.349814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.870718 | 0.0356960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.56118 | −0.186365 | −0.0931824 | − | 0.995649i | \(-0.529704\pi\) | ||||
−0.0931824 | + | 0.995649i | \(0.529704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4232 | 0.833081 | 0.416541 | − | 0.909117i | \(-0.363242\pi\) | ||||
0.416541 | + | 0.909117i | \(0.363242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.06750 | 0.206023 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2241 | 0.577339 | 0.288670 | − | 0.957429i | \(-0.406787\pi\) | ||||
0.288670 | + | 0.957429i | \(0.406787\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.29154 | −0.0522499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.3892 | −1.26780 | −0.633899 | − | 0.773416i | \(-0.718546\pi\) | ||||
−0.633899 | + | 0.773416i | \(0.718546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.03533 | −0.202715 | −0.101357 | − | 0.994850i | \(-0.532319\pi\) | ||||
−0.101357 | + | 0.994850i | \(0.532319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.3605 | −1.54184 | −0.770920 | − | 0.636933i | \(-0.780203\pi\) | ||||
−0.770920 | + | 0.636933i | \(0.780203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.83069 | −0.153473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.7204 | 0.788816 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.870718 | 0.0347178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0768 | 0.958480 | 0.479240 | − | 0.877684i | \(-0.340912\pi\) | ||||
0.479240 | + | 0.877684i | \(0.340912\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.69725 | 0.265772 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.330355 | 0.0130891 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.5600 | −1.64152 | −0.820760 | − | 0.571273i | \(-0.806450\pi\) | ||||
−0.820760 | + | 0.571273i | \(0.806450\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.84869 | −0.0729052 | −0.0364526 | − | 0.999335i | \(-0.511606\pi\) | ||||
−0.0364526 | + | 0.999335i | \(0.511606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.8480 | 1.52727 | 0.763637 | − | 0.645646i | \(-0.223412\pi\) | ||||
0.763637 | + | 0.645646i | \(0.223412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1987 | 0.871374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.6450 | −1.59056 | −0.795281 | − | 0.606241i | \(-0.792677\pi\) | ||||
−0.795281 | + | 0.606241i | \(0.792677\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.12271 | −0.122014 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.4280 | −1.49694 | −0.748471 | − | 0.663167i | \(-0.769212\pi\) | ||||
−0.748471 | + | 0.663167i | \(0.769212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.4568 | −0.445619 | −0.222809 | − | 0.974862i | \(-0.571523\pi\) | ||||
−0.222809 | + | 0.974862i | \(0.571523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.54889 | 0.0600635 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.50793 | 0.251988 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.30463 | −0.320597 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.9866 | 1.81120 | 0.905601 | − | 0.424131i | \(-0.139420\pi\) | ||||
0.905601 | + | 0.424131i | \(0.139420\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0788 | 0.617960 | 0.308980 | − | 0.951068i | \(-0.400012\pi\) | ||||
0.308980 | + | 0.951068i | \(0.400012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94956 | 0.0748174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.20464 | 0.199150 | 0.0995750 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995750 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.27750 | 0.201643 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.06294 | 0.116689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.56676 | 0.0596024 | 0.0298012 | − | 0.999556i | \(-0.490513\pi\) | ||||
0.0298012 | + | 0.999556i | \(0.490513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.41604 | 0.205442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.59933 | −0.363601 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.94479 | −0.224532 | −0.112266 | − | 0.993678i | \(-0.535811\pi\) | ||||
−0.112266 | + | 0.993678i | \(0.535811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.54889 | 0.0584176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.5904 | 0.661555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0783 | −0.491166 | −0.245583 | − | 0.969376i | \(-0.578979\pi\) | ||||
−0.245583 | + | 0.969376i | \(0.578979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.7921 | 0.666321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.317531 | −0.0118750 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5600 | 0.393821 | 0.196910 | − | 0.980422i | \(-0.436909\pi\) | ||||
0.196910 | + | 0.980422i | \(0.436909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6109 | 0.395172 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.3259 | 0.606330 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1610 | −0.376852 | −0.188426 | − | 0.982087i | \(-0.560339\pi\) | ||||
−0.188426 | + | 0.982087i | \(0.560339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.26258 | 0.194644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.4561 | 0.977177 | 0.488589 | − | 0.872514i | \(-0.337512\pi\) | ||||
0.488589 | + | 0.872514i | \(0.337512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.9013 | −0.696237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.3880 | 0.897127 | 0.448563 | − | 0.893751i | \(-0.351936\pi\) | ||||
0.448563 | + | 0.893751i | \(0.351936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.4392 | −0.603097 | −0.301548 | − | 0.953451i | \(-0.597503\pi\) | ||||
−0.301548 | + | 0.953451i | \(0.597503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.631308 | −0.0231293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.43949 | −0.125676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.130758 | −0.00477142 | −0.00238571 | − | 0.999997i | \(-0.500759\pi\) | ||||
−0.00238571 | + | 0.999997i | \(0.500759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.79415 | 0.283658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.1017 | 1.31214 | 0.656069 | − | 0.754701i | \(-0.272218\pi\) | ||||
0.656069 | + | 0.754701i | \(0.272218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.22055 | 0.334245 | 0.167122 | − | 0.985936i | \(-0.446553\pi\) | ||||
0.167122 | + | 0.985936i | \(0.446553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.55010 | 0.200927 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.58186 | 0.165442 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.7320 | −1.64914 | −0.824568 | − | 0.565762i | \(-0.808582\pi\) | ||||
−0.824568 | + | 0.565762i | \(0.808582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.9709 | −0.934109 | −0.467054 | − | 0.884229i | \(-0.654685\pi\) | ||||
−0.467054 | + | 0.884229i | \(0.654685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.6338 | 1.60329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.0759 | −0.611809 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.68979 | 0.239380 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8510 | 0.422979 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.7641 | 1.80955 | 0.904773 | − | 0.425894i | \(-0.140040\pi\) | ||||
0.904773 | + | 0.425894i | \(0.140040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.76158 | 0.311526 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.71410 | −0.0608694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.5953 | −0.942054 | −0.471027 | − | 0.882119i | \(-0.656117\pi\) | ||||
−0.471027 | + | 0.882119i | \(0.656117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.66844 | −0.200535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.62573 | 0.233817 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.11061 | −0.0391439 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1540 | 0.743735 | 0.371867 | − | 0.928286i | \(-0.378718\pi\) | ||||
0.371867 | + | 0.928286i | \(0.378718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4615 | −0.542927 | −0.271464 | − | 0.962449i | \(-0.587508\pi\) | ||||
−0.271464 | + | 0.962449i | \(0.587508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.7652 | 0.482172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.36145 | 0.327516 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.5686 | −0.927252 | −0.463626 | − | 0.886031i | \(-0.653452\pi\) | ||||
−0.463626 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0938 | −0.874714 | −0.437357 | − | 0.899288i | \(-0.644085\pi\) | ||||
−0.437357 | + | 0.899288i | \(0.644085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8156 | −0.445642 | −0.222821 | − | 0.974859i | \(-0.571526\pi\) | ||||
−0.222821 | + | 0.974859i | \(0.571526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9832 | 1.31921 | 0.659605 | − | 0.751613i | \(-0.270724\pi\) | ||||
0.659605 | + | 0.751613i | \(0.270724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.44990 | 0.0502361 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.93983 | 0.0671305 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.91275 | 0.204131 | 0.102065 | − | 0.994778i | \(-0.467455\pi\) | ||||
0.102065 | + | 0.994778i | \(0.467455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6166 | −0.572986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.74144 | 0.266313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.43828 | 0.289943 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.11061 | −0.0380712 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4522 | −0.666030 | −0.333015 | − | 0.942922i | \(-0.608066\pi\) | ||||
−0.333015 | + | 0.942922i | \(0.608066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.85004 | 0.233993 | 0.116996 | − | 0.993132i | \(-0.462673\pi\) | ||||
0.116996 | + | 0.993132i | \(0.462673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.09483 | 0.207953 | 0.103977 | − | 0.994580i | \(-0.466843\pi\) | ||||
0.103977 | + | 0.994580i | \(0.466843\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.6568 | 1.14569 | 0.572846 | − | 0.819663i | \(-0.305839\pi\) | ||||
0.572846 | + | 0.819663i | \(0.305839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.50423 | 0.289152 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0136 | 0.441455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.90128 | −0.132190 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.78879 | −0.195697 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.3781 | 0.553049 | 0.276525 | − | 0.961007i | \(-0.410817\pi\) | ||||
0.276525 | + | 0.961007i | \(0.410817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0864 | −0.744108 | −0.372054 | − | 0.928211i | \(-0.621346\pi\) | ||||
−0.372054 | + | 0.928211i | \(0.621346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1872 | 0.443784 | 0.221892 | − | 0.975071i | \(-0.428777\pi\) | ||||
0.221892 | + | 0.975071i | \(0.428777\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.4347 | −0.988321 | −0.494160 | − | 0.869371i | \(-0.664524\pi\) | ||||
−0.494160 | + | 0.869371i | \(0.664524\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.1521 | 0.374030 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0834 | −0.337428 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.24453 | 0.141879 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.8553 | 1.12914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4430 | 0.447850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.7829 | 0.391678 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0783 | 0.600280 | 0.300140 | − | 0.953895i | \(-0.402967\pi\) | ||||
0.300140 | + | 0.953895i | \(0.402967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.48099 | −0.280988 | −0.140494 | − | 0.990082i | \(-0.544869\pi\) | ||||
−0.140494 | + | 0.990082i | \(0.544869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.92968 | 0.295529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.19987 | −0.171715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.0092 | 0.726017 | 0.363008 | − | 0.931786i | \(-0.381750\pi\) | ||||
0.363008 | + | 0.931786i | \(0.381750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.38079 | 0.0454493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.78610 | −0.0916065 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.8215 | −1.40493 | −0.702464 | − | 0.711719i | \(-0.747917\pi\) | ||||
−0.702464 | + | 0.711719i | \(0.747917\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.57918 | 0.0845293 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39362 | −0.0455761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.65749 | 0.282828 | 0.141414 | − | 0.989951i | \(-0.454835\pi\) | ||||
0.141414 | + | 0.989951i | \(0.454835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.8947 | −1.69172 | −0.845859 | − | 0.533406i | \(-0.820912\pi\) | ||||
−0.845859 | + | 0.533406i | \(0.820912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2441 | 0.398721 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0788 | 0.749962 | 0.374981 | − | 0.927033i | \(-0.377649\pi\) | ||||
0.374981 | + | 0.927033i | \(0.377649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.36757 | 0.0443932 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9656 | 0.743927 | 0.371964 | − | 0.928247i | \(-0.378685\pi\) | ||||
0.371964 | + | 0.928247i | \(0.378685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1424 | −0.392918 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.78798 | 0.283779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.5576 | 1.98573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6832 | −0.343905 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.9393 | 1.89536 | 0.947680 | − | 0.319222i | \(-0.103422\pi\) | ||||
0.947680 | + | 0.319222i | \(0.103422\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8074 | −0.828198 | −0.414099 | − | 0.910232i | \(-0.635903\pi\) | ||||
−0.414099 | + | 0.910232i | \(0.635903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01867 | 0.289125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.9549 | 1.43823 | 0.719117 | − | 0.694889i | \(-0.244547\pi\) | ||||
0.719117 | + | 0.694889i | \(0.244547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.13116 | 0.195953 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.67152 | 0.276579 | 0.138289 | − | 0.990392i | \(-0.455840\pi\) | ||||
0.138289 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.82922 | 0.153872 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.71248 | −0.213445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.39241 | −0.107763 | −0.0538817 | − | 0.998547i | \(-0.517159\pi\) | ||||
−0.0538817 | + | 0.998547i | \(0.517159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.42747 | −0.267169 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0403 | 0.888045 | 0.444023 | − | 0.896016i | \(-0.353551\pi\) | ||||
0.444023 | + | 0.896016i | \(0.353551\pi\) | |||||||
\(998\) | 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 | 4536.2.a.y.1.2 | 4 | ||
3.2 | odd | 2 | 4536.2.a.z.1.3 | 4 | |||
4.3 | odd | 2 | 9072.2.a.cg.1.2 | 4 | |||
9.2 | odd | 6 | 504.2.r.e.337.4 | yes | 8 | ||
9.4 | even | 3 | 1512.2.r.e.505.3 | 8 | |||
9.5 | odd | 6 | 504.2.r.e.169.4 | ✓ | 8 | ||
9.7 | even | 3 | 1512.2.r.e.1009.3 | 8 | |||
12.11 | even | 2 | 9072.2.a.cj.1.3 | 4 | |||
36.7 | odd | 6 | 3024.2.r.m.1009.3 | 8 | |||
36.11 | even | 6 | 1008.2.r.l.337.1 | 8 | |||
36.23 | even | 6 | 1008.2.r.l.673.1 | 8 | |||
36.31 | odd | 6 | 3024.2.r.m.2017.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.e.169.4 | ✓ | 8 | 9.5 | odd | 6 | ||
504.2.r.e.337.4 | yes | 8 | 9.2 | odd | 6 | ||
1008.2.r.l.337.1 | 8 | 36.11 | even | 6 | |||
1008.2.r.l.673.1 | 8 | 36.23 | even | 6 | |||
1512.2.r.e.505.3 | 8 | 9.4 | even | 3 | |||
1512.2.r.e.1009.3 | 8 | 9.7 | even | 3 | |||
3024.2.r.m.1009.3 | 8 | 36.7 | odd | 6 | |||
3024.2.r.m.2017.3 | 8 | 36.31 | odd | 6 | |||
4536.2.a.y.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4536.2.a.z.1.3 | 4 | 3.2 | odd | 2 | |||
9072.2.a.cg.1.2 | 4 | 4.3 | odd | 2 | |||
9072.2.a.cj.1.3 | 4 | 12.11 | even | 2 |