Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(1,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 320) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1 |
$q$-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 | ||||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.9282 | −2.82117 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19615 | −0.457929 | −0.228965 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228965 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53590 | 0.455461 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.46410 | −1.64749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.73205 | −0.799863 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.46410 | 1.51547 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.46410 | −1.47804 | −0.739022 | − | 0.673681i | \(-0.764712\pi\) | ||||
−0.739022 | + | 0.673681i | \(0.764712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.196152 | −0.0299130 | −0.0149565 | − | 0.999888i | \(-0.504761\pi\) | ||||
−0.0149565 | + | 0.999888i | \(0.504761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.46410 | −0.665469 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.19615 | −0.320342 | −0.160171 | − | 0.987089i | \(-0.551205\pi\) | ||||
−0.160171 | + | 0.987089i | \(0.551205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.46410 | 1.32524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.46410 | −0.723738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.928203 | 0.118844 | 0.0594221 | − | 0.998233i | \(-0.481074\pi\) | ||||
0.0594221 | + | 0.998233i | \(0.481074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.1244 | 2.66142 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.196152 | 0.0239638 | 0.0119819 | − | 0.999928i | \(-0.496186\pi\) | ||||
0.0119819 | + | 0.999928i | \(0.496186\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3923 | 1.94541 | 0.972704 | − | 0.232048i | \(-0.0745426\pi\) | ||||
0.972704 | + | 0.232048i | \(0.0745426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.39230 | −0.748163 | −0.374081 | − | 0.927396i | \(-0.622042\pi\) | ||||
−0.374081 | + | 0.927396i | \(0.622042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.73205 | −0.315470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3923 | 1.86808 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.26795 | −0.139176 | −0.0695878 | − | 0.997576i | \(-0.522168\pi\) | ||||
−0.0695878 | + | 0.997576i | \(0.522168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.3923 | −1.71838 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3923 | 1.46132 | 0.730659 | − | 0.682743i | \(-0.239213\pi\) | ||||
0.730659 | + | 0.682743i | \(0.239213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.4641 | 1.55420 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19615 | −0.216393 | −0.108197 | − | 0.994130i | \(-0.534508\pi\) | ||||
−0.108197 | + | 0.994130i | \(0.534508\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.9282 | 1.26166 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2679 | −1.28266 | −0.641331 | − | 0.767265i | \(-0.721617\pi\) | ||||
−0.641331 | + | 0.767265i | \(0.721617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9282 | 1.23830 | 0.619149 | − | 0.785274i | \(-0.287478\pi\) | ||||
0.619149 | + | 0.785274i | \(0.287478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.3923 | −1.55589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9282 | −1.21618 | −0.608092 | − | 0.793867i | \(-0.708065\pi\) | ||||
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.4641 | −1.42966 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.3923 | −1.50268 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.8564 | 2.33139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1962 | 1.25970 | 0.629852 | − | 0.776715i | \(-0.283115\pi\) | ||||
0.629852 | + | 0.776715i | \(0.283115\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.535898 | 0.0471832 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3923 | −0.907980 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.46410 | 0.820642 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.928203 | 0.0793018 | 0.0396509 | − | 0.999214i | \(-0.487375\pi\) | ||||
0.0396509 | + | 0.999214i | \(0.487375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −42.0526 | −3.46844 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.46410 | 0.770178 | 0.385089 | − | 0.922880i | \(-0.374171\pi\) | ||||
0.385089 | + | 0.922880i | \(0.374171\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.4641 | −1.25020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.53590 | −0.203688 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9282 | −1.03178 | −0.515891 | − | 0.856654i | \(-0.672539\pi\) | ||||
−0.515891 | + | 0.856654i | \(0.672539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.3923 | −2.25166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3923 | −0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1962 | 1.26858 | 0.634290 | − | 0.773095i | \(-0.281292\pi\) | ||||
0.634290 | + | 0.773095i | \(0.281292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.46410 | 0.736779 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.19615 | 0.169943 | 0.0849717 | − | 0.996383i | \(-0.472920\pi\) | ||||
0.0849717 | + | 0.996383i | \(0.472920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.92820 | 0.682757 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.73205 | 0.357709 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.3923 | −1.23212 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.85641 | −0.587215 | −0.293608 | − | 0.955926i | \(-0.594856\pi\) | ||||
−0.293608 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820 | 0.514969 | 0.257485 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257485 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.53590 | −0.187459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.9282 | −1.37682 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.39230 | 0.317816 | 0.158908 | − | 0.987293i | \(-0.449203\pi\) | ||||
0.158908 | + | 0.987293i | \(0.449203\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3923 | −1.03598 | −0.517990 | − | 0.855386i | \(-0.673320\pi\) | ||||
−0.517990 | + | 0.855386i | \(0.673320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.46410 | −0.677738 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3923 | −0.740421 | −0.370211 | − | 0.928948i | \(-0.620714\pi\) | ||||
−0.370211 | + | 0.928948i | \(0.620714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.535898 | −0.0377994 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.46410 | 0.661002 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.80385 | −0.681415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3923 | 0.990807 | 0.495404 | − | 0.868663i | \(-0.335020\pi\) | ||||
0.495404 | + | 0.868663i | \(0.335020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −44.7846 | −3.06859 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.196152 | 0.0133775 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4641 | 1.18011 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.12436 | −0.611012 | −0.305506 | − | 0.952190i | \(-0.598826\pi\) | ||||
−0.305506 | + | 0.952190i | \(0.598826\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5885 | 0.835525 | 0.417763 | − | 0.908556i | \(-0.362814\pi\) | ||||
0.417763 | + | 0.908556i | \(0.362814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.07180 | 0.335154 | 0.167577 | − | 0.985859i | \(-0.446406\pi\) | ||||
0.167577 | + | 0.985859i | \(0.446406\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −44.7846 | −2.94661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.3923 | 1.46697 | 0.733484 | − | 0.679706i | \(-0.237893\pi\) | ||||
0.733484 | + | 0.679706i | \(0.237893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.19615 | 0.143261 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.7846 | −2.12959 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7846 | 1.34444 | 0.672222 | − | 0.740349i | \(-0.265340\pi\) | ||||
0.672222 | + | 0.740349i | \(0.265340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.392305 | 0.0252706 | 0.0126353 | − | 0.999920i | \(-0.495978\pi\) | ||||
0.0126353 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3923 | −0.983378 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | −0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46410 | 0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.53590 | 0.538781 | 0.269391 | − | 0.963031i | \(-0.413178\pi\) | ||||
0.269391 | + | 0.963031i | \(0.413178\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.60770 | −0.478292 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.46410 | −0.592665 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.3923 | 1.76421 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.80385 | −0.604531 | −0.302266 | − | 0.953224i | \(-0.597743\pi\) | ||||
−0.302266 | + | 0.953224i | \(0.597743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.3923 | −0.638394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.3205 | −2.16158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.7846 | −1.63309 | −0.816543 | − | 0.577284i | \(-0.804112\pi\) | ||||
−0.816543 | + | 0.577284i | \(0.804112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3923 | 0.995762 | 0.497881 | − | 0.867245i | \(-0.334112\pi\) | ||||
0.497881 | + | 0.867245i | \(0.334112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 44.7846 | 2.71049 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.46410 | 0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.85641 | 0.472046 | 0.236023 | − | 0.971748i | \(-0.424156\pi\) | ||||
0.236023 | + | 0.971748i | \(0.424156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.3205 | 0.677741 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.60770 | 0.453837 | 0.226919 | − | 0.973914i | \(-0.427135\pi\) | ||||
0.226919 | + | 0.973914i | \(0.427135\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5885 | −1.22386 | −0.611928 | − | 0.790913i | \(-0.709606\pi\) | ||||
−0.611928 | + | 0.790913i | \(0.709606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.46410 | 0.323665 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −44.7846 | −2.64355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.3205 | −2.30501 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0000 | 1.75262 | 0.876309 | − | 0.481749i | \(-0.159998\pi\) | ||||
0.876309 | + | 0.481749i | \(0.159998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.8564 | −0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.60770 | 0.439964 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.928203 | −0.0535007 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.7846 | −1.88343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.928203 | −0.0531488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.8038 | −1.35856 | −0.679279 | − | 0.733880i | \(-0.737707\pi\) | ||||
−0.679279 | + | 0.733880i | \(0.737707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | 0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3923 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.1244 | −1.19022 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.60770 | −0.0902972 | −0.0451486 | − | 0.998980i | \(-0.514376\pi\) | ||||
−0.0451486 | + | 0.998980i | \(0.514376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.2487 | 2.02321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.92820 | −0.385496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46410 | −0.192154 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −35.3205 | −1.95323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3923 | −0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3923 | 1.45065 | 0.725326 | − | 0.688405i | \(-0.241689\pi\) | ||||
0.725326 | + | 0.688405i | \(0.241689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.7846 | 1.46779 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.196152 | −0.0107170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 35.3205 | 1.91835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.78461 | 0.475713 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | −0.323029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0526 | 0.539650 | 0.269825 | − | 0.962909i | \(-0.413034\pi\) | ||||
0.269825 | + | 0.962909i | \(0.413034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.7846 | 1.75492 | 0.877460 | − | 0.479650i | \(-0.159236\pi\) | ||||
0.877460 | + | 0.479650i | \(0.159236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564 | 0.739600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7846 | 1.42560 | 0.712800 | − | 0.701367i | \(-0.247427\pi\) | ||||
0.712800 | + | 0.701367i | \(0.247427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3923 | −0.870013 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.7846 | 2.37025 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.7846 | −1.73031 | −0.865153 | − | 0.501508i | \(-0.832779\pi\) | ||||
−0.865153 | + | 0.501508i | \(0.832779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.73205 | −0.143395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.39230 | 0.334589 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0526 | 1.46433 | 0.732166 | − | 0.681126i | \(-0.238510\pi\) | ||||
0.732166 | + | 0.681126i | \(0.238510\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −42.2487 | −2.19938 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 49.1769 | 2.55314 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8564 | −1.02813 | −0.514063 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514063 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73205 | 0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.7846 | −1.98700 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1962 | −0.725390 | −0.362695 | − | 0.931908i | \(-0.618143\pi\) | ||||
−0.362695 | + | 0.931908i | \(0.618143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3923 | −0.835429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.875644 | −0.0445115 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7846 | 0.749609 | 0.374805 | − | 0.927104i | \(-0.377710\pi\) | ||||
0.374805 | + | 0.927104i | \(0.377710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.60770 | 0.384738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.3923 | 1.43220 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5359 | 1.03067 | 0.515334 | − | 0.856990i | \(-0.327668\pi\) | ||||
0.515334 | + | 0.856990i | \(0.327668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.8564 | −1.29444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.8564 | −1.59083 | −0.795417 | − | 0.606063i | \(-0.792748\pi\) | ||||
−0.795417 | + | 0.606063i | \(0.792748\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.78461 | −0.437593 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.46410 | 0.122442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7846 | 1.03025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3923 | −1.20612 | −0.603061 | − | 0.797695i | \(-0.706052\pi\) | ||||
−0.603061 | + | 0.797695i | \(0.706052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.53590 | −0.125087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.3923 | 1.39709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.26795 | 0.0622412 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.3205 | −1.33789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.9282 | −0.631584 | −0.315792 | − | 0.948828i | \(-0.602270\pi\) | ||||
−0.315792 | + | 0.948828i | \(0.602270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.80385 | −0.476679 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.39230 | 0.212559 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.7846 | 1.58286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.60770 | −0.366450 | −0.183225 | − | 0.983071i | \(-0.558654\pi\) | ||||
−0.183225 | + | 0.983071i | \(0.558654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.60770 | 0.269489 | 0.134744 | − | 0.990880i | \(-0.456979\pi\) | ||||
0.134744 | + | 0.990880i | \(0.456979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.39230 | −0.210112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.07180 | 0.242064 | 0.121032 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121032 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 68.7128 | 3.27204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6603 | −0.839064 | −0.419532 | − | 0.907741i | \(-0.637806\pi\) | ||||
−0.419532 | + | 0.907741i | \(0.637806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.9282 | −0.612856 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49.1769 | 2.32599 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.46410 | −0.446639 | −0.223319 | − | 0.974745i | \(-0.571689\pi\) | ||||
−0.223319 | + | 0.974745i | \(0.571689\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.7846 | −1.54377 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.8564 | −1.21484 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.3923 | 0.768483 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7846 | 0.878707 | 0.439353 | − | 0.898314i | \(-0.355208\pi\) | ||||
0.439353 | + | 0.898314i | \(0.355208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8564 | 0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1962 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.92820 | 0.321288 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9808 | −1.34107 | −0.670535 | − | 0.741878i | \(-0.733935\pi\) | ||||
−0.670535 | + | 0.741878i | \(0.733935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.928203 | 0.0428604 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.3205 | 1.62748 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.679492 | −0.0312431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 46.3923 | 2.12416 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7846 | −0.947697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.3923 | 1.29189 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.3923 | −0.653521 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.8756 | 0.674080 | 0.337040 | − | 0.941490i | \(-0.390574\pi\) | ||||
0.337040 | + | 0.941490i | \(0.390574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.2487 | −2.00100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.60770 | 0.0725543 | 0.0362771 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362771 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.4641 | −0.695060 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 77.5692 | 3.47946 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.5692 | −1.95043 | −0.975213 | − | 0.221268i | \(-0.928980\pi\) | ||||
−0.975213 | + | 0.221268i | \(0.928980\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.19615 | −0.0979216 | −0.0489608 | − | 0.998801i | \(-0.515591\pi\) | ||||
−0.0489608 | + | 0.998801i | \(0.515591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.73205 | 0.121335 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.7846 | −1.45315 | −0.726576 | − | 0.687086i | \(-0.758890\pi\) | ||||
−0.726576 | + | 0.687086i | \(0.758890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.2487 | −1.33812 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.19615 | 0.0967740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.60770 | −0.334586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.14359 | −0.181534 | −0.0907671 | − | 0.995872i | \(-0.528932\pi\) | ||||
−0.0907671 | + | 0.995872i | \(0.528932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.9808 | 1.61706 | 0.808528 | − | 0.588458i | \(-0.200265\pi\) | ||||
0.808528 | + | 0.588458i | \(0.200265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9282 | −0.564233 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.78461 | −0.382664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.7846 | 1.16235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.7846 | 1.42006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2679 | 0.573623 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.4641 | 0.926244 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 53.3205 | 2.29668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.7128 | −1.70739 | −0.853694 | − | 0.520776i | \(-0.825643\pi\) | ||||
−0.853694 | + | 0.520776i | \(0.825643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9282 | −0.812287 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9282 | −0.553783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1962 | −0.521470 | −0.260735 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260735 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.14359 | 0.176844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.7846 | 2.41473 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.3923 | 0.695815 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.7846 | 1.13490 | 0.567450 | − | 0.823408i | \(-0.307930\pi\) | ||||
0.567450 | + | 0.823408i | \(0.307930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.679492 | 0.0287394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.7846 | 1.38417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.8038 | −0.666053 | −0.333026 | − | 0.942918i | \(-0.608070\pi\) | ||||
−0.333026 | + | 0.942918i | \(0.608070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.9282 | 0.543894 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.6603 | −0.489685 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.24871 | −0.261960 | −0.130980 | − | 0.991385i | \(-0.541812\pi\) | ||||
−0.130980 | + | 0.991385i | \(0.541812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.60770 | −0.402070 | −0.201035 | − | 0.979584i | \(-0.564430\pi\) | ||||
−0.201035 | + | 0.979584i | \(0.564430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.19615 | −0.0915859 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.3205 | 1.63410 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000 | 1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.4641 | 0.639362 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.5167 | −1.30083 | −0.650416 | − | 0.759578i | \(-0.725405\pi\) | ||||
−0.650416 | + | 0.759578i | \(0.725405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.07180 | 0.208980 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.3923 | 1.16790 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9282 | 0.530898 | 0.265449 | − | 0.964125i | \(-0.414480\pi\) | ||||
0.265449 | + | 0.964125i | \(0.414480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3923 | 0.672019 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.9282 | −0.774680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.392305 | −0.0160024 | −0.00800122 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800122 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.875644 | 0.0356590 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.19615 | −0.0891391 | −0.0445695 | − | 0.999006i | \(-0.514192\pi\) | ||||
−0.0445695 | + | 0.999006i | \(0.514192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.60770 | 0.307774 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3923 | −1.38909 | −0.694546 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694546 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −25.8564 | −1.04263 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.3923 | −1.38458 | −0.692291 | − | 0.721618i | \(-0.743399\pi\) | ||||
−0.692291 | + | 0.721618i | \(0.743399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.7846 | −1.39811 | −0.699056 | − | 0.715067i | \(-0.746396\pi\) | ||||
−0.699056 | + | 0.715067i | \(0.746396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.78461 | 0.352514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 61.1769 | 2.45100 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.9282 | −0.755920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.7846 | −0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5359 | 0.578665 | 0.289332 | − | 0.957229i | \(-0.406567\pi\) | ||||
0.289332 | + | 0.957229i | \(0.406567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.3205 | −1.56285 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.1962 | −0.563357 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53.3205 | −2.11264 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 73.1769 | 2.89483 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3923 | 0.647457 | 0.323729 | − | 0.946150i | \(-0.395064\pi\) | ||||
0.323729 | + | 0.946150i | \(0.395064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5885 | 0.811929 | 0.405965 | − | 0.913889i | \(-0.366936\pi\) | ||||
0.405965 | + | 0.913889i | \(0.366936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.535898 | −0.0211010 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.41154 | −0.212750 | −0.106375 | − | 0.994326i | \(-0.533924\pi\) | ||||
−0.106375 | + | 0.994326i | \(0.533924\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7846 | 0.815867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.7846 | −1.28493 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.1769 | −1.68964 | −0.844822 | − | 0.535048i | \(-0.820293\pi\) | ||||
−0.844822 | + | 0.535048i | \(0.820293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3923 | 0.406061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.5359 | −1.11329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.6410 | 1.11570 | 0.557848 | − | 0.829943i | \(-0.311627\pi\) | ||||
0.557848 | + | 0.829943i | \(0.311627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.5692 | −1.85023 | −0.925114 | − | 0.379689i | \(-0.876031\pi\) | ||||
−0.925114 | + | 0.379689i | \(0.876031\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −32.7846 | −1.27325 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.46410 | −0.367002 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.9282 | 0.963780 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.21539 | 0.124129 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1769 | 0.893404 | 0.446702 | − | 0.894683i | \(-0.352598\pi\) | ||||
0.446702 | + | 0.894683i | \(0.352598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.1769 | −0.737029 | −0.368514 | − | 0.929622i | \(-0.620133\pi\) | ||||
−0.368514 | + | 0.929622i | \(0.620133\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 68.1051 | 2.61363 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.3923 | −1.31792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.66025 | 0.216584 | 0.108292 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108292 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.928203 | −0.0354648 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8564 | −0.528655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3923 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 73.1769 | 2.77976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0000 | −0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.7846 | 1.24181 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −61.1769 | −2.31392 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7846 | 1.01164 | 0.505820 | − | 0.862639i | \(-0.331190\pi\) | ||||
0.505820 | + | 0.862639i | \(0.331190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.7846 | 2.13561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.8564 | −1.42173 | −0.710864 | − | 0.703330i | \(-0.751696\pi\) | ||||
−0.710864 | + | 0.703330i | \(0.751696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 53.5692 | 2.00900 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.56922 | −0.208569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −56.7846 | −2.12066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.21539 | −0.119914 | −0.0599569 | − | 0.998201i | \(-0.519096\pi\) | ||||
−0.0599569 | + | 0.998201i | \(0.519096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3923 | −0.387030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.07180 | −0.0398606 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.05256 | −0.150301 | −0.0751505 | − | 0.997172i | \(-0.523944\pi\) | ||||
−0.0751505 | + | 0.997172i | \(0.523944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.679492 | 0.0251319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.78461 | −0.102852 | −0.0514260 | − | 0.998677i | \(-0.516377\pi\) | ||||
−0.0514260 | + | 0.998677i | \(0.516377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 42.0526 | 1.55113 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.679492 | 0.0250294 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.00000 | −0.0735712 | −0.0367856 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367856 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.9282 | 0.695345 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.41154 | 0.198530 | 0.0992651 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992651 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | 0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.66025 | −0.207098 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −62.7846 | −2.29410 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6077 | 0.715495 | 0.357747 | − | 0.933818i | \(-0.383545\pi\) | ||||
0.357747 | + | 0.933818i | \(0.383545\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.3205 | −0.849847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.46410 | −0.344434 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9282 | 1.34218 | 0.671089 | − | 0.741377i | \(-0.265827\pi\) | ||||
0.671089 | + | 0.741377i | \(0.265827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7128 | −1.22209 | −0.611044 | − | 0.791596i | \(-0.709250\pi\) | ||||
−0.611044 | + | 0.791596i | \(0.709250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 61.1769 | 2.21475 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.4641 | 0.559106 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7846 | −0.750489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7846 | 1.25437 | 0.627183 | − | 0.778872i | \(-0.284208\pi\) | ||||
0.627183 | + | 0.778872i | \(0.284208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3923 | −0.590354 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6077 | −0.921045 | −0.460522 | − | 0.887648i | \(-0.652338\pi\) | ||||
−0.460522 | + | 0.887648i | \(0.652338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.53590 | 0.0910922 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −77.5692 | −2.78278 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.9282 | −0.678173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.7846 | 2.03191 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9282 | 0.461427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1962 | 0.577330 | 0.288665 | − | 0.957430i | \(-0.406789\pi\) | ||||
0.288665 | + | 0.957430i | \(0.406789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.7846 | 0.953557 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −61.1769 | −2.17520 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.21539 | −0.114182 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.3923 | 1.00697 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3923 | 0.793176 | 0.396588 | − | 0.917997i | \(-0.370194\pi\) | ||||
0.396588 | + | 0.917997i | \(0.370194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.60770 | 0.269141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.7128 | 2.03918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.1436 | −0.781430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923 | 0.366281 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 73.1769 | 2.57595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.5692 | 1.67244 | 0.836222 | − | 0.548391i | \(-0.184759\pi\) | ||||
0.836222 | + | 0.548391i | \(0.184759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.6077 | −0.618290 | −0.309145 | − | 0.951015i | \(-0.600043\pi\) | ||||
−0.309145 | + | 0.951015i | \(0.600043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.7846 | −1.57066 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1962 | −0.567326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.392305 | −0.0137250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −73.1769 | −2.55701 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.21539 | 0.321619 | 0.160810 | − | 0.986985i | \(-0.448589\pi\) | ||||
0.160810 | + | 0.986985i | \(0.448589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.8372 | −1.70236 | −0.851178 | − | 0.524877i | \(-0.824111\pi\) | ||||
−0.851178 | + | 0.524877i | \(0.824111\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.46410 | −0.329498 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.26795 | 0.0440909 | 0.0220455 | − | 0.999757i | \(-0.492982\pi\) | ||||
0.0220455 | + | 0.999757i | \(0.492982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.21539 | −0.320064 | −0.160032 | − | 0.987112i | \(-0.551160\pi\) | ||||
−0.160032 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.4641 | −0.744581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.3205 | −1.84745 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.19615 | −0.0760010 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.1436 | −0.350614 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.7846 | −1.13185 | −0.565925 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565925 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.7846 | −0.715860 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.73205 | 0.162595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 56.2487 | 1.93045 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1769 | −0.451699 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.46410 | 0.118609 | 0.0593043 | − | 0.998240i | \(-0.481112\pi\) | ||||
0.0593043 | + | 0.998240i | \(0.481112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.92820 | −0.305338 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.8564 | 1.49811 | 0.749053 | − | 0.662510i | \(-0.230509\pi\) | ||||
0.749053 | + | 0.662510i | \(0.230509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.5692 | 1.07713 | 0.538564 | − | 0.842585i | \(-0.318967\pi\) | ||||
0.538564 | + | 0.842585i | \(0.318967\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.354 | 4.16981 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.9808 | 0.373789 | 0.186895 | − | 0.982380i | \(-0.440158\pi\) | ||||
0.186895 | + | 0.982380i | \(0.440158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6603 | 0.463927 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.5692 | 1.41014 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.679492 | −0.0230237 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 64.2487 | 2.17449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.73205 | −0.159973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.8564 | 0.670503 | 0.335252 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335252 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81.9615 | −2.76449 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3923 | −0.956561 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.1962 | 0.545044 | 0.272522 | − | 0.962150i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3923 | 0.551021 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.3731 | 1.72494 | 0.862469 | − | 0.506109i | \(-0.168917\pi\) | ||||
0.862469 | + | 0.506109i | \(0.168917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.1769 | 2.25304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.53590 | −0.285963 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.39230 | −0.146983 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.85641 | 0.262611 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.7846 | −0.693978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.53590 | 0.0843894 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.92820 | −0.230301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5885 | 1.08208 | 0.541041 | − | 0.840996i | \(-0.318030\pi\) | ||||
0.541041 | + | 0.840996i | \(0.318030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 53.5692 | 1.77678 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1769 | −0.834148 | −0.417074 | − | 0.908872i | \(-0.636944\pi\) | ||||
−0.417074 | + | 0.908872i | \(0.636944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.39230 | −0.145364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.53590 | 0.0838342 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.1769 | −1.62396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7128 | −0.518318 | −0.259159 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259159 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 65.0333 | 2.14292 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.7846 | −1.86909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.80385 | −0.322001 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3923 | 0.931521 | 0.465761 | − | 0.884911i | \(-0.345781\pi\) | ||||
0.465761 | + | 0.884911i | \(0.345781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.7846 | 1.00892 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 77.5692 | 2.53950 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.3923 | 0.992873 | 0.496437 | − | 0.868073i | \(-0.334641\pi\) | ||||
0.496437 | + | 0.868073i | \(0.334641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.1051 | 1.96146 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7846 | −0.677559 | −0.338779 | − | 0.940866i | \(-0.610014\pi\) | ||||
−0.338779 | + | 0.940866i | \(0.610014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846 | 0.676840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.9282 | 0.615734 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.1962 | 1.82613 | 0.913065 | − | 0.407815i | \(-0.133709\pi\) | ||||
0.913065 | + | 0.407815i | \(0.133709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1436 | 0.718811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.39230 | 0.142430 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.0718 | −0.358651 | −0.179325 | − | 0.983790i | \(-0.557391\pi\) | ||||
−0.179325 | + | 0.983790i | \(0.557391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.39230 | −0.142132 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.39230 | 0.141835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5692 | −0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −59.2295 | −1.90864 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3923 | 0.463305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.19615 | 0.0706235 | 0.0353118 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353118 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9282 | 0.608061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0333 | 1.83029 | 0.915143 | − | 0.403129i | \(-0.132077\pi\) | ||||
0.915143 | + | 0.403129i | \(0.132077\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3205 | 1.51703 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.46410 | 0.303094 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.3205 | −0.938046 | −0.469023 | − | 0.883186i | \(-0.655394\pi\) | ||||
−0.469023 | + | 0.883186i | \(0.655394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.7846 | 1.43132 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.7128 | 1.84263 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.5885 | −1.35836 | −0.679180 | − | 0.733971i | \(-0.737665\pi\) | ||||
−0.679180 | + | 0.733971i | \(0.737665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.3923 | 0.331126 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.3923 | 0.903737 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.430781 | 0.0136980 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.1051 | 1.01985 | 0.509926 | − | 0.860218i | \(-0.329673\pi\) | ||||
0.509926 | + | 0.860218i | \(0.329673\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.1051 | −2.28819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.92820 | −0.219639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.3923 | −1.46926 | −0.734630 | − | 0.678468i | \(-0.762644\pi\) | ||||
−0.734630 | + | 0.678468i | \(0.762644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0000 | −0.759326 |
(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 | 1280.2.a.b.1.1 | 2 | ||
4.3 | odd | 2 | 1280.2.a.m.1.2 | 2 | |||
5.4 | even | 2 | 6400.2.a.cd.1.2 | 2 | |||
8.3 | odd | 2 | 1280.2.a.c.1.1 | 2 | |||
8.5 | even | 2 | 1280.2.a.p.1.2 | 2 | |||
16.3 | odd | 4 | 320.2.d.b.161.4 | yes | 4 | ||
16.5 | even | 4 | 320.2.d.a.161.4 | yes | 4 | ||
16.11 | odd | 4 | 320.2.d.b.161.1 | yes | 4 | ||
16.13 | even | 4 | 320.2.d.a.161.1 | ✓ | 4 | ||
20.19 | odd | 2 | 6400.2.a.bf.1.1 | 2 | |||
40.19 | odd | 2 | 6400.2.a.ck.1.2 | 2 | |||
40.29 | even | 2 | 6400.2.a.y.1.1 | 2 | |||
48.5 | odd | 4 | 2880.2.k.e.1441.3 | 4 | |||
48.11 | even | 4 | 2880.2.k.l.1441.4 | 4 | |||
48.29 | odd | 4 | 2880.2.k.e.1441.1 | 4 | |||
48.35 | even | 4 | 2880.2.k.l.1441.2 | 4 | |||
80.3 | even | 4 | 1600.2.f.d.1249.1 | 4 | |||
80.13 | odd | 4 | 1600.2.f.i.1249.4 | 4 | |||
80.19 | odd | 4 | 1600.2.d.b.801.1 | 4 | |||
80.27 | even | 4 | 1600.2.f.d.1249.2 | 4 | |||
80.29 | even | 4 | 1600.2.d.h.801.4 | 4 | |||
80.37 | odd | 4 | 1600.2.f.i.1249.3 | 4 | |||
80.43 | even | 4 | 1600.2.f.h.1249.3 | 4 | |||
80.53 | odd | 4 | 1600.2.f.e.1249.2 | 4 | |||
80.59 | odd | 4 | 1600.2.d.b.801.4 | 4 | |||
80.67 | even | 4 | 1600.2.f.h.1249.4 | 4 | |||
80.69 | even | 4 | 1600.2.d.h.801.1 | 4 | |||
80.77 | odd | 4 | 1600.2.f.e.1249.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.1 | ✓ | 4 | 16.13 | even | 4 | ||
320.2.d.a.161.4 | yes | 4 | 16.5 | even | 4 | ||
320.2.d.b.161.1 | yes | 4 | 16.11 | odd | 4 | ||
320.2.d.b.161.4 | yes | 4 | 16.3 | odd | 4 | ||
1280.2.a.b.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1280.2.a.c.1.1 | 2 | 8.3 | odd | 2 | |||
1280.2.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
1280.2.a.p.1.2 | 2 | 8.5 | even | 2 | |||
1600.2.d.b.801.1 | 4 | 80.19 | odd | 4 | |||
1600.2.d.b.801.4 | 4 | 80.59 | odd | 4 | |||
1600.2.d.h.801.1 | 4 | 80.69 | even | 4 | |||
1600.2.d.h.801.4 | 4 | 80.29 | even | 4 | |||
1600.2.f.d.1249.1 | 4 | 80.3 | even | 4 | |||
1600.2.f.d.1249.2 | 4 | 80.27 | even | 4 | |||
1600.2.f.e.1249.1 | 4 | 80.77 | odd | 4 | |||
1600.2.f.e.1249.2 | 4 | 80.53 | odd | 4 | |||
1600.2.f.h.1249.3 | 4 | 80.43 | even | 4 | |||
1600.2.f.h.1249.4 | 4 | 80.67 | even | 4 | |||
1600.2.f.i.1249.3 | 4 | 80.37 | odd | 4 | |||
1600.2.f.i.1249.4 | 4 | 80.13 | odd | 4 | |||
2880.2.k.e.1441.1 | 4 | 48.29 | odd | 4 | |||
2880.2.k.e.1441.3 | 4 | 48.5 | odd | 4 | |||
2880.2.k.l.1441.2 | 4 | 48.35 | even | 4 | |||
2880.2.k.l.1441.4 | 4 | 48.11 | even | 4 | |||
6400.2.a.y.1.1 | 2 | 40.29 | even | 2 | |||
6400.2.a.bf.1.1 | 2 | 20.19 | odd | 2 | |||
6400.2.a.cd.1.2 | 2 | 5.4 | even | 2 | |||
6400.2.a.ck.1.2 | 2 | 40.19 | odd | 2 |