Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1248,2,Mod(1,1248)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1248, 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("1248.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.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: | \(9.96533017226\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1248.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.34017 | 1.94098 | 0.970492 | − | 0.241133i | \(-0.0775189\pi\) | ||||
0.970492 | + | 0.241133i | \(0.0775189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.07838 | 0.407588 | 0.203794 | − | 0.979014i | \(-0.434673\pi\) | ||||
0.203794 | + | 0.979014i | \(0.434673\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41855 | 1.03073 | 0.515366 | − | 0.856970i | \(-0.327656\pi\) | ||||
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.34017 | −1.12063 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.07838 | −0.247397 | −0.123698 | − | 0.992320i | \(-0.539476\pi\) | ||||
−0.123698 | + | 0.992320i | \(0.539476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.07838 | −0.235321 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.15676 | −0.449715 | −0.224857 | − | 0.974392i | \(-0.572192\pi\) | ||||
−0.224857 | + | 0.974392i | \(0.572192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.8371 | 2.76742 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.75872 | −1.03430 | −0.517149 | − | 0.855896i | \(-0.673007\pi\) | ||||
−0.517149 | + | 0.855896i | \(0.673007\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41855 | −0.595093 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.68035 | 0.791123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.68035 | −1.09824 | −0.549121 | − | 0.835743i | \(-0.685037\pi\) | ||||
−0.549121 | + | 0.835743i | \(0.685037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.340173 | −0.0531261 | −0.0265630 | − | 0.999647i | \(-0.508456\pi\) | ||||
−0.0265630 | + | 0.999647i | \(0.508456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8371 | −1.65264 | −0.826321 | − | 0.563199i | \(-0.809570\pi\) | ||||
−0.826321 | + | 0.563199i | \(0.809570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.34017 | 0.646995 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.41855 | 1.08211 | 0.541053 | − | 0.840988i | \(-0.318026\pi\) | ||||
0.541053 | + | 0.840988i | \(0.318026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.68035 | −0.368174 | −0.184087 | − | 0.982910i | \(-0.558933\pi\) | ||||
−0.184087 | + | 0.982910i | \(0.558933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.8371 | 2.00063 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.07838 | 0.142835 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.26180 | −1.20578 | −0.602892 | − | 0.797823i | \(-0.705985\pi\) | ||||
−0.602892 | + | 0.797823i | \(0.705985\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.52359 | −0.579186 | −0.289593 | − | 0.957150i | \(-0.593520\pi\) | ||||
−0.289593 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.07838 | 0.135863 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.34017 | 0.538332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.9155 | 1.94439 | 0.972193 | − | 0.234183i | \(-0.0752414\pi\) | ||||
0.972193 | + | 0.234183i | \(0.0752414\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.15676 | 0.259643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.26180 | 0.624460 | 0.312230 | − | 0.950007i | \(-0.398924\pi\) | ||||
0.312230 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6803 | 1.71820 | 0.859102 | − | 0.511804i | \(-0.171023\pi\) | ||||
0.859102 | + | 0.511804i | \(0.171023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.8371 | −1.59777 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68649 | 0.420114 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.26180 | 0.138500 | 0.0692500 | − | 0.997599i | \(-0.477939\pi\) | ||||
0.0692500 | + | 0.997599i | \(0.477939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.68035 | 0.941516 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0205 | −1.38017 | −0.690086 | − | 0.723727i | \(-0.742427\pi\) | ||||
−0.690086 | + | 0.723727i | \(0.742427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07838 | 0.113045 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.75872 | 0.597152 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.68035 | −0.480193 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.68035 | 0.678286 | 0.339143 | − | 0.940735i | \(-0.389863\pi\) | ||||
0.339143 | + | 0.940735i | \(0.389863\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41855 | 0.343577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.31351 | 0.628218 | 0.314109 | − | 0.949387i | \(-0.398294\pi\) | ||||
0.314109 | + | 0.949387i | \(0.398294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5236 | 1.43105 | 0.715526 | − | 0.698586i | \(-0.246187\pi\) | ||||
0.715526 | + | 0.698586i | \(0.246187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.68035 | −0.456755 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.2039 | −1.85651 | −0.928257 | − | 0.371939i | \(-0.878693\pi\) | ||||
−0.928257 | + | 0.371939i | \(0.878693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31351 | −0.604725 | −0.302362 | − | 0.953193i | \(-0.597775\pi\) | ||||
−0.302362 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.68035 | 0.634070 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9939 | −1.41050 | −0.705252 | − | 0.708957i | \(-0.749166\pi\) | ||||
−0.705252 | + | 0.708957i | \(0.749166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.36069 | −0.872889 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.15676 | 0.197709 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.686489 | 0.0624081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.340173 | 0.0306724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 38.3545 | 3.43054 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.84324 | 0.873447 | 0.436723 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436723 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.8371 | 0.954154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5174 | −1.35577 | −0.677883 | − | 0.735170i | \(-0.737102\pi\) | ||||
−0.677883 | + | 0.735170i | \(0.737102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.16290 | −0.100836 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.34017 | −0.373543 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3340 | 1.13920 | 0.569602 | − | 0.821921i | \(-0.307098\pi\) | ||||
0.569602 | + | 0.821921i | \(0.307098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.680346 | 0.0577062 | 0.0288531 | − | 0.999584i | \(-0.490814\pi\) | ||||
0.0288531 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.41855 | −0.624755 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.41855 | 0.285874 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.68035 | 0.720863 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.83710 | 0.481436 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.02052 | 0.738990 | 0.369495 | − | 0.929233i | \(-0.379531\pi\) | ||||
0.369495 | + | 0.929233i | \(0.379531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.60197 | −0.293124 | −0.146562 | − | 0.989201i | \(-0.546821\pi\) | ||||
−0.146562 | + | 0.989201i | \(0.546821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.9939 | −2.00755 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1978 | −1.45234 | −0.726171 | − | 0.687514i | \(-0.758702\pi\) | ||||
−0.726171 | + | 0.687514i | \(0.758702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.68035 | 0.212565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.32580 | −0.183298 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1256 | 1.10640 | 0.553200 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553200 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.8371 | −1.15507 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.7792 | 1.29842 | 0.649208 | − | 0.760611i | \(-0.275100\pi\) | ||||
0.649208 | + | 0.760611i | \(0.275100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.07838 | −0.0824656 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.36069 | −0.559623 | −0.279812 | − | 0.960055i | \(-0.590272\pi\) | ||||
−0.279812 | + | 0.960055i | \(0.590272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.9216 | 1.12797 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.26180 | 0.696159 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.31965 | −0.547097 | −0.273548 | − | 0.961858i | \(-0.588197\pi\) | ||||
−0.273548 | + | 0.961858i | \(0.588197\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.523590 | 0.0389182 | 0.0194591 | − | 0.999811i | \(-0.493806\pi\) | ||||
0.0194591 | + | 0.999811i | \(0.493806\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.52359 | 0.334393 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.9939 | −2.13167 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.83710 | 0.499978 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.07838 | −0.0784404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.0410 | −1.59483 | −0.797417 | − | 0.603429i | \(-0.793801\pi\) | ||||
−0.797417 | + | 0.603429i | \(0.793801\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0472 | −1.37105 | −0.685523 | − | 0.728051i | \(-0.740426\pi\) | ||||
−0.685523 | + | 0.728051i | \(0.740426\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.34017 | −0.310806 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3340 | −1.23500 | −0.617499 | − | 0.786571i | \(-0.711854\pi\) | ||||
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5174 | 1.10000 | 0.550001 | − | 0.835164i | \(-0.314627\pi\) | ||||
0.550001 | + | 0.835164i | \(0.314627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.9155 | −1.12259 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.15676 | 0.151375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.47641 | −0.103117 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.15676 | −0.149905 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.68649 | −0.255000 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.26180 | −0.360532 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −47.0349 | −3.20775 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.21008 | −0.421568 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.6803 | −0.992006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.1194 | −1.54819 | −0.774095 | − | 0.633069i | \(-0.781795\pi\) | ||||
−0.774095 | + | 0.633069i | \(0.781795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.8371 | 0.922473 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.41855 | −0.226897 | −0.113449 | − | 0.993544i | \(-0.536190\pi\) | ||||
−0.113449 | + | 0.993544i | \(0.536190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.68649 | −0.242553 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6803 | 0.961741 | 0.480871 | − | 0.876792i | \(-0.340321\pi\) | ||||
0.480871 | + | 0.876792i | \(0.340321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.1978 | 2.10035 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | −0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.57531 | 0.619375 | 0.309688 | − | 0.950838i | \(-0.399776\pi\) | ||||
0.309688 | + | 0.950838i | \(0.399776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0410 | −1.80628 | −0.903141 | − | 0.429344i | \(-0.858745\pi\) | ||||
−0.903141 | + | 0.429344i | \(0.858745\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −25.3340 | −1.61853 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.07838 | −0.0686155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.26180 | −0.0799630 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.16290 | −0.325879 | −0.162940 | − | 0.986636i | \(-0.552098\pi\) | ||||
−0.162940 | + | 0.986636i | \(0.552098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.37298 | −0.463535 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.68035 | −0.543584 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.6803 | −1.16525 | −0.582624 | − | 0.812742i | \(-0.697974\pi\) | ||||
−0.582624 | + | 0.812742i | \(0.697974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.20394 | −0.447631 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.8371 | −1.40820 | −0.704098 | − | 0.710103i | \(-0.748648\pi\) | ||||
−0.704098 | + | 0.710103i | \(0.748648\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6332 | −0.714620 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.0205 | 0.796843 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.36069 | −0.448789 | −0.224395 | − | 0.974498i | \(-0.572040\pi\) | ||||
−0.224395 | + | 0.974498i | \(0.572040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4391 | 1.60606 | 0.803030 | − | 0.595939i | \(-0.203220\pi\) | ||||
0.803030 | + | 0.595939i | \(0.203220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.07838 | −0.0652664 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 47.3028 | 2.85247 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3607 | 0.922935 | 0.461467 | − | 0.887157i | \(-0.347323\pi\) | ||||
0.461467 | + | 0.887157i | \(0.347323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.75872 | −0.344766 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6537 | −0.754855 | −0.377428 | − | 0.926039i | \(-0.623191\pi\) | ||||
−0.377428 | + | 0.926039i | \(0.623191\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.2039 | −1.61711 | −0.808553 | − | 0.588423i | \(-0.799749\pi\) | ||||
−0.808553 | + | 0.588423i | \(0.799749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.68035 | 0.277240 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.366835 | −0.0216536 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.68035 | −0.391609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6537 | −0.739236 | −0.369618 | − | 0.929184i | \(-0.620511\pi\) | ||||
−0.369618 | + | 0.929184i | \(0.620511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −40.1978 | −2.34041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41855 | −0.198364 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.15676 | −0.124728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.6865 | −0.673598 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.31351 | −0.362702 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.6332 | −1.12419 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.08452 | 0.461408 | 0.230704 | − | 0.973024i | \(-0.425897\pi\) | ||||
0.230704 | + | 0.973024i | \(0.425897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5236 | −0.826218 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8310 | 1.35133 | 0.675665 | − | 0.737209i | \(-0.263857\pi\) | ||||
0.675665 | + | 0.737209i | \(0.263857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.68649 | 0.321419 | 0.160710 | − | 0.987002i | \(-0.448622\pi\) | ||||
0.160710 | + | 0.987002i | \(0.448622\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.68035 | 0.263708 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.65368 | 0.486039 | 0.243020 | − | 0.970021i | \(-0.421862\pi\) | ||||
0.243020 | + | 0.970021i | \(0.421862\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.83710 | 0.382804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.2039 | 1.07186 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.15676 | −0.120005 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8371 | 0.767544 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.31351 | 0.349138 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.75872 | −0.316528 | −0.158264 | − | 0.987397i | \(-0.550590\pi\) | ||||
−0.158264 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.68035 | −0.366081 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 69.0759 | 3.77402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3135 | 1.21549 | 0.607747 | − | 0.794131i | \(-0.292073\pi\) | ||||
0.607747 | + | 0.794131i | \(0.292073\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.9939 | 0.814355 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.6865 | −1.06608 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8432 | −0.747465 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.36069 | 0.503963 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.0472 | 0.915141 | 0.457570 | − | 0.889173i | \(-0.348720\pi\) | ||||
0.457570 | + | 0.889173i | \(0.348720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.31965 | −0.284755 | −0.142377 | − | 0.989812i | \(-0.545475\pi\) | ||||
−0.142377 | + | 0.989812i | \(0.545475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.65368 | −0.247691 | −0.123845 | − | 0.992302i | \(-0.539523\pi\) | ||||
−0.123845 | + | 0.992302i | \(0.539523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.8371 | 1.21207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.15676 | −0.114148 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.5692 | −1.82449 | −0.912245 | − | 0.409644i | \(-0.865653\pi\) | ||||
−0.912245 | + | 0.409644i | \(0.865653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8371 | −0.938795 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.686489 | −0.0360313 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63.7152 | 3.33501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.36683 | 0.227947 | 0.113973 | − | 0.993484i | \(-0.463642\pi\) | ||||
0.113973 | + | 0.993484i | \(0.463642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.340173 | −0.0177087 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.89043 | −0.150063 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.7214 | 1.69425 | 0.847125 | − | 0.531394i | \(-0.178332\pi\) | ||||
0.847125 | + | 0.531394i | \(0.178332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −38.3545 | −1.98062 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000 | 0.103005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3919 | −0.687895 | −0.343948 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343948 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.84324 | −0.504285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5814 | 0.847272 | 0.423636 | − | 0.905832i | \(-0.360753\pi\) | ||||
0.423636 | + | 0.905832i | \(0.360753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.8371 | −0.550881 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.63317 | 0.0828048 | 0.0414024 | − | 0.999143i | \(-0.486817\pi\) | ||||
0.0414024 | + | 0.999143i | \(0.486817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.31351 | −0.218144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.5174 | 0.782752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.0821 | 2.62053 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6803 | 0.536031 | 0.268016 | − | 0.963415i | \(-0.413632\pi\) | ||||
0.268016 | + | 0.963415i | \(0.413632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.16290 | 0.0582177 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0144 | 0.500094 | 0.250047 | − | 0.968234i | \(-0.419554\pi\) | ||||
0.250047 | + | 0.968234i | \(0.419554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.75872 | −0.286862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.34017 | 0.215665 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.8371 | −1.13199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.31965 | −0.0652527 | −0.0326263 | − | 0.999468i | \(-0.510387\pi\) | ||||
−0.0326263 | + | 0.999468i | \(0.510387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.3340 | −0.657719 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.98771 | −0.491463 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.47641 | 0.268826 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.680346 | −0.0333167 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.8781 | −0.824551 | −0.412276 | − | 0.911059i | \(-0.635266\pi\) | ||||
−0.412276 | + | 0.911059i | \(0.635266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.3135 | −1.47739 | −0.738695 | − | 0.674040i | \(-0.764558\pi\) | ||||
−0.738695 | + | 0.674040i | \(0.764558\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.41855 | 0.360702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.6742 | 1.34240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.87814 | −0.236070 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.41855 | −0.165049 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.37137 | −0.114225 | −0.0571124 | − | 0.998368i | \(-0.518189\pi\) | ||||
−0.0571124 | + | 0.998368i | \(0.518189\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.19779 | −0.297847 | −0.148923 | − | 0.988849i | \(-0.547581\pi\) | ||||
−0.148923 | + | 0.988849i | \(0.547581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.68035 | −0.416191 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.32580 | 0.111258 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.8843 | −0.758115 | −0.379058 | − | 0.925373i | \(-0.623752\pi\) | ||||
−0.379058 | + | 0.925373i | \(0.623752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.83710 | −0.277957 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5174 | −0.737256 | −0.368628 | − | 0.929577i | \(-0.620172\pi\) | ||||
−0.368628 | + | 0.929577i | \(0.620172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −56.5113 | −2.67889 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.02052 | −0.426656 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.97334 | −0.376285 | −0.188143 | − | 0.982142i | \(-0.560247\pi\) | ||||
−0.188143 | + | 0.982142i | \(0.560247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.16290 | −0.0547588 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.60197 | 0.169235 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.68035 | 0.219418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.9939 | 1.63694 | 0.818472 | − | 0.574547i | \(-0.194822\pi\) | ||||
0.818472 | + | 0.574547i | \(0.194822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.0205 | −1.35162 | −0.675810 | − | 0.737076i | \(-0.736206\pi\) | ||||
−0.675810 | + | 0.737076i | \(0.736206\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.4740 | 1.55567 | 0.777834 | − | 0.628470i | \(-0.216319\pi\) | ||||
0.777834 | + | 0.628470i | \(0.216319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.9939 | 1.15906 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.52359 | −0.301876 | −0.150938 | − | 0.988543i | \(-0.548229\pi\) | ||||
−0.150938 | + | 0.988543i | \(0.548229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.1629 | 0.792509 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.1978 | 0.838510 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.0472 | −1.70343 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9216 | −0.684651 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.68035 | −0.122725 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.47187 | 0.158634 | 0.0793170 | − | 0.996849i | \(-0.474726\pi\) | ||||
0.0793170 | + | 0.996849i | \(0.474726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.68035 | −0.304598 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.32580 | 0.105827 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.9939 | 1.31654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2290 | 0.916663 | 0.458332 | − | 0.888781i | \(-0.348447\pi\) | ||||
0.458332 | + | 0.888781i | \(0.348447\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.1256 | −0.638780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.21008 | −0.0997395 | −0.0498697 | − | 0.998756i | \(-0.515881\pi\) | ||||
−0.0498697 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.8371 | 0.666878 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.67420 | 0.254523 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7587 | −0.615925 | −0.307963 | − | 0.951398i | \(-0.599647\pi\) | ||||
−0.307963 | + | 0.951398i | \(0.599647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.7792 | −0.749641 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.5113 | 1.27126 | 0.635628 | − | 0.771995i | \(-0.280741\pi\) | ||||
0.635628 | + | 0.771995i | \(0.280741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.4017 | 1.21936 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.0144 | 1.50766 | 0.753830 | − | 0.657069i | \(-0.228204\pi\) | ||||
0.753830 | + | 0.657069i | \(0.228204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.8310 | 0.700320 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.07838 | 0.0476115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 63.0349 | 2.77765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.3607 | 1.11536 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.36069 | 0.323099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.35455 | −0.366019 | −0.183010 | − | 0.983111i | \(-0.558584\pi\) | ||||
−0.183010 | + | 0.983111i | \(0.558584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3668 | 0.890580 | 0.445290 | − | 0.895387i | \(-0.353101\pi\) | ||||
0.445290 | + | 0.895387i | \(0.353101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.9216 | −0.651233 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.5174 | −0.501708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3484 | −0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.26180 | −0.401928 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.340173 | −0.0147345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −83.3484 | −3.60347 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.31965 | 0.315866 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.9544 | −0.859498 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.63931 | 0.199459 | 0.0997297 | − | 0.995015i | \(-0.468202\pi\) | ||||
0.0997297 | + | 0.995015i | \(0.468202\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.523590 | −0.0224694 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.4017 | −1.17376 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0410 | −0.771379 | −0.385690 | − | 0.922629i | \(-0.626036\pi\) | ||||
−0.385690 | + | 0.922629i | \(0.626036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.52359 | −0.193062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.15676 | −0.0918809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9405 | 0.550287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.9939 | 1.23072 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0205 | 0.721183 | 0.360591 | − | 0.932724i | \(-0.382575\pi\) | ||||
0.360591 | + | 0.932724i | \(0.382575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.8371 | −0.458361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.83710 | −0.288663 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.7152 | −1.33664 | −0.668319 | − | 0.743875i | \(-0.732986\pi\) | ||||
−0.668319 | + | 0.743875i | \(0.732986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −65.0759 | −2.73777 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.07838 | 0.0452876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.7152 | 1.91648 | 0.958241 | − | 0.285961i | \(-0.0923127\pi\) | ||||
0.958241 | + | 0.285961i | \(0.0923127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8781 | 0.706328 | 0.353164 | − | 0.935561i | \(-0.385106\pi\) | ||||
0.353164 | + | 0.935561i | \(0.385106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.0410 | 0.920778 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.8432 | −1.24455 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.3484 | −1.72136 | −0.860678 | − | 0.509149i | \(-0.829960\pi\) | ||||
−0.860678 | + | 0.509149i | \(0.829960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.0472 | 0.791574 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36069 | 0.0564510 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.16290 | −0.379488 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.34017 | 0.179444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.5753 | 1.55090 | 0.775449 | − | 0.631410i | \(-0.217523\pi\) | ||||
0.775449 | + | 0.631410i | \(0.217523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.21008 | 0.255882 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.3340 | 0.713027 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.9672 | 1.18954 | 0.594770 | − | 0.803896i | \(-0.297243\pi\) | ||||
0.594770 | + | 0.803896i | \(0.297243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.36069 | 0.383751 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.5174 | −0.635087 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.21008 | −0.253737 | −0.126868 | − | 0.991920i | \(-0.540493\pi\) | ||||
−0.126868 | + | 0.991920i | \(0.540493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.3135 | −1.07335 | −0.536675 | − | 0.843789i | \(-0.680320\pi\) | ||||
−0.536675 | + | 0.843789i | \(0.680320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.9155 | 0.648128 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.97948 | 0.121133 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6803 | −1.00174 | −0.500872 | − | 0.865521i | \(-0.666987\pi\) | ||||
−0.500872 | + | 0.865521i | \(0.666987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.15676 | −0.0873961 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.41855 | 0.300122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3545 | −0.822112 | −0.411056 | − | 0.911610i | \(-0.634840\pi\) | ||||
−0.411056 | + | 0.911610i | \(0.634840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.47641 | 0.0595346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0616 | −1.08946 | −0.544729 | − | 0.838612i | \(-0.683367\pi\) | ||||
−0.544729 | + | 0.838612i | \(0.683367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.9155 | −0.639697 | −0.319849 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319849 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.15676 | 0.0865476 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.0410 | −0.562542 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 97.2799 | 3.89119 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.68649 | 0.147224 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.3607 | −0.532726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.2413 | −0.407699 | −0.203849 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203849 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.7214 | 1.69535 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.83710 | −0.231274 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.26180 | 0.208153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3607 | 0.448720 | 0.224360 | − | 0.974506i | \(-0.427971\pi\) | ||||
0.224360 | + | 0.974506i | \(0.427971\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.77101 | −0.148714 | −0.0743571 | − | 0.997232i | \(-0.523690\pi\) | ||||
−0.0743571 | + | 0.997232i | \(0.523690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 47.0349 | 1.85200 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9877 | −1.33619 | −0.668097 | − | 0.744074i | \(-0.732891\pi\) | ||||
−0.668097 | + | 0.744074i | \(0.732891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.6619 | −1.24284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.21008 | 0.243392 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.3135 | −0.403599 | −0.201799 | − | 0.979427i | \(-0.564679\pi\) | ||||
−0.201799 | + | 0.979427i | \(0.564679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −67.3484 | −2.63152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6803 | 0.572735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3607 | −0.520459 | −0.260229 | − | 0.965547i | \(-0.583798\pi\) | ||||
−0.260229 | + | 0.965547i | \(0.583798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.3074 | 1.06213 | 0.531067 | − | 0.847330i | \(-0.321791\pi\) | ||||
0.531067 | + | 0.847330i | \(0.321791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.04718 | −0.195721 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.31351 | −0.167020 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1194 | 0.893848 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.4641 | −0.596986 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.5113 | 1.79288 | 0.896440 | − | 0.443166i | \(-0.146145\pi\) | ||||
0.896440 | + | 0.443166i | \(0.146145\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.8371 | −0.532590 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.6803 | 1.79407 | 0.897036 | − | 0.441958i | \(-0.145716\pi\) | ||||
0.897036 | + | 0.441958i | \(0.145716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.20394 | 0.276462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.41855 | 0.130999 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.2905 | −1.88605 | −0.943025 | − | 0.332721i | \(-0.892033\pi\) | ||||
−0.943025 | + | 0.332721i | \(0.892033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.8720 | 2.21118 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.00000 | −0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.68035 | −0.102113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2762 | 0.657217 | 0.328608 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328608 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.68649 | 0.140038 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.95282 | 0.112007 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.680346 | −0.0257699 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.6803 | −0.555262 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.68035 | 0.252313 | 0.126157 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126157 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.20394 | 0.271702 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.1978 | −1.21264 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.80835 | 0.256054 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6742 | 1.33977 | 0.669886 | − | 0.742464i | \(-0.266343\pi\) | ||||
0.669886 | + | 0.742464i | \(0.266343\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4202 | 0.465139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.8371 | 0.554876 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.57531 | −0.357596 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2039 | −0.567011 | −0.283506 | − | 0.958971i | \(-0.591497\pi\) | ||||
−0.283506 | + | 0.958971i | \(0.591497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6619 | 0.583280 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.0410 | 1.04286 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.6742 | 1.02779 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.8904 | 1.14566 | 0.572831 | − | 0.819673i | \(-0.305845\pi\) | ||||
0.572831 | + | 0.819673i | \(0.305845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.6742 | −0.801649 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.37298 | −0.346199 | −0.173099 | − | 0.984904i | \(-0.555378\pi\) | ||||
−0.173099 | + | 0.984904i | \(0.555378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.3340 | 0.934460 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.4079 | 2.00414 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.8059 | 0.986071 | 0.493036 | − | 0.870009i | \(-0.335887\pi\) | ||||
0.493036 | + | 0.870009i | \(0.335887\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.07838 | 0.0396152 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0989 | −0.443865 | −0.221933 | − | 0.975062i | \(-0.571237\pi\) | ||||
−0.221933 | + | 0.975062i | \(0.571237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.1506 | 1.43437 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.26180 | 0.0461667 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.7091 | −0.756694 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4764 | 0.929647 | 0.464824 | − | 0.885403i | \(-0.346118\pi\) | ||||
0.464824 | + | 0.885403i | \(0.346118\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.16290 | 0.188146 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.6332 | −0.568949 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.5113 | 0.672805 | 0.336402 | − | 0.941718i | \(-0.390790\pi\) | ||||
0.336402 | + | 0.941718i | \(0.390790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.37298 | 0.267622 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.96719 | −0.325061 | −0.162530 | − | 0.986704i | \(-0.551966\pi\) | ||||
−0.162530 | + | 0.986704i | \(0.551966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.80835 | −0.246479 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.68035 | 0.313839 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.26180 | −0.334424 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.4079 | 1.16866 | 0.584329 | − | 0.811517i | \(-0.301358\pi\) | ||||
0.584329 | + | 0.811517i | \(0.301358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6803 | 0.672756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.29299 | −0.118441 | −0.0592203 | − | 0.998245i | \(-0.518861\pi\) | ||||
−0.0592203 | + | 0.998245i | \(0.518861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −79.6840 | −2.86234 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.20394 | 0.258440 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.366835 | 0.0131432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9877 | 0.643651 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −78.9816 | −2.81897 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8059 | 0.670358 | 0.335179 | − | 0.942154i | \(-0.391203\pi\) | ||||
0.335179 | + | 0.942154i | \(0.391203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.8371 | 0.813022 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1690 | −0.574905 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.52359 | −0.160637 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.6332 | 0.412586 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.6803 | 1.08675 | 0.543377 | − | 0.839489i | \(-0.317146\pi\) | ||||
0.543377 | + | 0.839489i | \(0.317146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.8371 | 0.524899 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.0205 | −0.460057 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.1855 | 1.77101 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0944 | −0.355780 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.36069 | 0.259109 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.3668 | −0.786376 | −0.393188 | − | 0.919458i | \(-0.628628\pi\) | ||||
−0.393188 | + | 0.919458i | \(0.628628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.7998 | −1.53802 | −0.769009 | − | 0.639238i | \(-0.779250\pi\) | ||||
−0.769009 | + | 0.639238i | \(0.779250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.4391 | −0.927259 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 61.3074 | 2.14750 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6865 | 0.408858 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.07838 | 0.0376816 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.06770 | 0.211764 | 0.105882 | − | 0.994379i | \(-0.466233\pi\) | ||||
0.105882 | + | 0.994379i | \(0.466233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.8248 | −1.28363 | −0.641816 | − | 0.766859i | \(-0.721819\pi\) | ||||
−0.641816 | + | 0.766859i | \(0.721819\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −47.3028 | −1.64687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.9893 | −1.21670 | −0.608349 | − | 0.793670i | \(-0.708168\pi\) | ||||
−0.608349 | + | 0.793670i | \(0.708168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5113 | −0.503998 | −0.251999 | − | 0.967727i | \(-0.581088\pi\) | ||||
−0.251999 | + | 0.967727i | \(0.581088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.3607 | −0.532856 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.6742 | −0.404487 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 72.8248 | 2.52021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.75872 | 0.199051 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.4124 | 1.39519 | 0.697596 | − | 0.716492i | \(-0.254253\pi\) | ||||
0.697596 | + | 0.716492i | \(0.254253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.6537 | 0.435816 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.34017 | 0.149306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.740294 | 0.0254368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.2039 | 0.933637 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.4079 | 0.493896 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7152 | −1.01743 | −0.508715 | − | 0.860935i | \(-0.669879\pi\) | ||||
−0.508715 | + | 0.860935i | \(0.669879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.68035 | −0.160064 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.3545 | 1.78840 | 0.894199 | − | 0.447670i | \(-0.147746\pi\) | ||||
0.894199 | + | 0.447670i | \(0.147746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3730 | −0.388041 | −0.194021 | − | 0.980997i | \(-0.562153\pi\) | ||||
−0.194021 | + | 0.980997i | \(0.562153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.366835 | 0.0125017 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.20847 | 0.313460 | 0.156730 | − | 0.987641i | \(-0.449905\pi\) | ||||
0.156730 | + | 0.987641i | \(0.449905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.9467 | −1.08622 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.0226 | 1.39160 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.9155 | 0.539275 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.68035 | 0.226095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.3607 | 1.39825 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3074 | −0.787034 | −0.393517 | − | 0.919317i | \(-0.628742\pi\) | ||||
−0.393517 | + | 0.919317i | \(0.628742\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6537 | 0.426798 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.9939 | −1.31374 | −0.656868 | − | 0.754005i | \(-0.728119\pi\) | ||||
−0.656868 | + | 0.754005i | \(0.728119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.5646 | −1.23050 | −0.615249 | − | 0.788333i | \(-0.710944\pi\) | ||||
−0.615249 | + | 0.788333i | \(0.710944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.1978 | 1.35123 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.0410 | −1.00868 | −0.504340 | − | 0.863505i | \(-0.668264\pi\) | ||||
−0.504340 | + | 0.863505i | \(0.668264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6147 | 0.356007 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41855 | 0.114526 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.00000 | −0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.7686 | −1.06191 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.15676 | 0.0720120 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.5174 | −0.384128 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.36069 | −0.178591 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.6865 | 0.388902 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.27247 | 0.0755396 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.8310 | −0.392841 | −0.196420 | − | 0.980520i | \(-0.562932\pi\) | ||||
−0.196420 | + | 0.980520i | \(0.562932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.31351 | 0.209406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.3423 | −1.46912 | −0.734562 | − | 0.678541i | \(-0.762612\pi\) | ||||
−0.734562 | + | 0.678541i | \(0.762612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.31351 | 0.142756 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.6332 | 0.649052 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.7337 | −0.552594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0821 | 1.05829 | 0.529145 | − | 0.848531i | \(-0.322513\pi\) | ||||
0.529145 | + | 0.848531i | \(0.322513\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.08452 | −0.266394 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.26180 | 0.173194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −92.4366 | −3.03930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.5236 | 0.477017 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.4345 | −1.12976 | −0.564880 | − | 0.825173i | \(-0.691078\pi\) | ||||
−0.564880 | + | 0.825173i | \(0.691078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.29460 | 0.206297 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.8310 | −0.780191 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.6742 | 0.970450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.1978 | 1.11719 | 0.558597 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558597 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.68649 | −0.185572 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7009 | −0.577032 | −0.288516 | − | 0.957475i | \(-0.593162\pi\) | ||||
−0.288516 | + | 0.957475i | \(0.593162\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.733670 | 0.0238916 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.68035 | −0.152252 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7259 | 0.543519 | 0.271760 | − | 0.962365i | \(-0.412394\pi\) | ||||
0.271760 | + | 0.962365i | \(0.412394\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6803 | 0.476544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.65368 | −0.280615 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.9939 | 0.356126 | 0.178063 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178063 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −95.6619 | −3.09555 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.83710 | −0.221012 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.3791 | 0.464326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.16290 | 0.0697709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.2039 | −0.618838 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −82.6681 | −2.66118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3111 | 1.29632 | 0.648158 | − | 0.761506i | \(-0.275540\pi\) | ||||
0.648158 | + | 0.761506i | \(0.275540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.15676 | 0.0692850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.67420 | −0.0537277 | −0.0268639 | − | 0.999639i | \(-0.508552\pi\) | ||||
−0.0268639 | + | 0.999639i | \(0.508552\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.733670 | 0.0235204 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.8371 | −0.443142 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.0328 | −0.352971 | −0.176485 | − | 0.984303i | \(-0.556473\pi\) | ||||
−0.176485 | + | 0.984303i | \(0.556473\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.5113 | −1.42259 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.31351 | −0.201575 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.4001 | 1.60751 | 0.803757 | − | 0.594958i | \(-0.202831\pi\) | ||||
0.803757 | + | 0.594958i | \(0.202831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −75.2327 | −2.39711 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.00000 | −0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.3730 | 0.743217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7152 | −0.753339 | −0.376670 | − | 0.926348i | \(-0.622931\pi\) | ||||
−0.376670 | + | 0.926348i | \(0.622931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.75872 | 0.182748 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.3484 | 2.13509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.37298 | 0.170164 | 0.0850820 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850820 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.68035 | 0.211357 |
(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 | 1248.2.a.o.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 3744.2.a.ba.1.1 | 3 | |||
4.3 | odd | 2 | 1248.2.a.p.1.3 | yes | 3 | ||
8.3 | odd | 2 | 2496.2.a.bk.1.1 | 3 | |||
8.5 | even | 2 | 2496.2.a.bl.1.1 | 3 | |||
12.11 | even | 2 | 3744.2.a.z.1.1 | 3 | |||
24.5 | odd | 2 | 7488.2.a.cx.1.3 | 3 | |||
24.11 | even | 2 | 7488.2.a.cy.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.o.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1248.2.a.p.1.3 | yes | 3 | 4.3 | odd | 2 | ||
2496.2.a.bk.1.1 | 3 | 8.3 | odd | 2 | |||
2496.2.a.bl.1.1 | 3 | 8.5 | even | 2 | |||
3744.2.a.z.1.1 | 3 | 12.11 | even | 2 | |||
3744.2.a.ba.1.1 | 3 | 3.2 | odd | 2 | |||
7488.2.a.cx.1.3 | 3 | 24.5 | odd | 2 | |||
7488.2.a.cy.1.3 | 3 | 24.11 | even | 2 |