Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(1,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, 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("4410.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.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: | \(35.2140272914\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82843 | −1.89386 | −0.946932 | − | 0.321433i | \(-0.895836\pi\) | ||||
−0.946932 | + | 0.321433i | \(0.895836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.585786 | 0.142074 | 0.0710370 | − | 0.997474i | \(-0.477369\pi\) | ||||
0.0710370 | + | 0.997474i | \(0.477369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.828427 | 0.190054 | 0.0950271 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950271 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.585786 | −0.124890 | ||||||||
\(23\) | 7.65685 | 1.59656 | 0.798282 | − | 0.602284i | \(-0.205742\pi\) | ||||
0.798282 | + | 0.602284i | \(0.205742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.82843 | 1.33916 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58579 | 0.480168 | 0.240084 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240084 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58579 | −0.823632 | −0.411816 | − | 0.911267i | \(-0.635105\pi\) | ||||
−0.411816 | + | 0.911267i | \(0.635105\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.585786 | −0.100462 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.585786 | −0.0963027 | −0.0481513 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481513 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(38\) | −0.828427 | −0.134389 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.07107 | 1.07833 | 0.539164 | − | 0.842201i | \(-0.318740\pi\) | ||||
0.539164 | + | 0.842201i | \(0.318740\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.65685 | −1.12894 | ||||||||
\(47\) | 5.41421 | 0.789744 | 0.394872 | − | 0.918736i | \(-0.370789\pi\) | ||||
0.394872 | + | 0.918736i | \(0.370789\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.82843 | −0.946932 | ||||||||
\(53\) | −10.4853 | −1.44026 | −0.720132 | − | 0.693837i | \(-0.755919\pi\) | ||||
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.58579 | −0.339530 | ||||||||
\(59\) | 4.82843 | 0.628608 | 0.314304 | − | 0.949322i | \(-0.398229\pi\) | ||||
0.314304 | + | 0.949322i | \(0.398229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.65685 | −1.23643 | −0.618217 | − | 0.786008i | \(-0.712145\pi\) | ||||
−0.618217 | + | 0.786008i | \(0.712145\pi\) | |||||||
\(62\) | 4.58579 | 0.582395 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.82843 | 0.846962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.8995 | −1.69809 | −0.849047 | − | 0.528318i | \(-0.822823\pi\) | ||||
−0.849047 | + | 0.528318i | \(0.822823\pi\) | |||||||
\(68\) | 0.585786 | 0.0710370 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.48528 | 0.769661 | 0.384831 | − | 0.922987i | \(-0.374260\pi\) | ||||
0.384831 | + | 0.922987i | \(0.374260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.17157 | −0.839369 | −0.419685 | − | 0.907670i | \(-0.637859\pi\) | ||||
−0.419685 | + | 0.907670i | \(0.637859\pi\) | |||||||
\(74\) | 0.585786 | 0.0680963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.828427 | 0.0950271 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.65685 | −0.845558 | ||||||||
\(83\) | −16.4853 | −1.80949 | −0.904747 | − | 0.425949i | \(-0.859940\pi\) | ||||
−0.904747 | + | 0.425949i | \(0.859940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.585786 | −0.0635375 | ||||||||
\(86\) | −7.07107 | −0.762493 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.585786 | −0.0624450 | ||||||||
\(89\) | −2.48528 | −0.263439 | −0.131720 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131720 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.65685 | 0.798282 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.41421 | −0.558433 | ||||||||
\(95\) | −0.828427 | −0.0849948 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.48528 | 0.252342 | 0.126171 | − | 0.992009i | \(-0.459731\pi\) | ||||
0.126171 | + | 0.992009i | \(0.459731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.65685 | −0.164863 | −0.0824316 | − | 0.996597i | \(-0.526269\pi\) | ||||
−0.0824316 | + | 0.996597i | \(0.526269\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65685 | 0.557386 | 0.278693 | − | 0.960380i | \(-0.410099\pi\) | ||||
0.278693 | + | 0.960380i | \(0.410099\pi\) | |||||||
\(104\) | 6.82843 | 0.669582 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4853 | 1.01842 | ||||||||
\(107\) | −5.17157 | −0.499955 | −0.249977 | − | 0.968252i | \(-0.580423\pi\) | ||||
−0.249977 | + | 0.968252i | \(0.580423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.48528 | −0.238047 | −0.119023 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(110\) | 0.585786 | 0.0558525 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6569 | −1.47287 | −0.736436 | − | 0.676507i | \(-0.763493\pi\) | ||||
−0.736436 | + | 0.676507i | \(0.763493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.65685 | −0.714005 | ||||||||
\(116\) | 2.58579 | 0.240084 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.82843 | −0.444493 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 9.65685 | 0.874291 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.58579 | −0.411816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1421 | 1.25491 | 0.627456 | − | 0.778652i | \(-0.284096\pi\) | ||||
0.627456 | + | 0.778652i | \(0.284096\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.82843 | −0.598893 | ||||||||
\(131\) | 10.4853 | 0.916103 | 0.458052 | − | 0.888926i | \(-0.348547\pi\) | ||||
0.458052 | + | 0.888926i | \(0.348547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.8995 | 1.20073 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.585786 | −0.0502308 | ||||||||
\(137\) | −12.4853 | −1.06669 | −0.533345 | − | 0.845898i | \(-0.679065\pi\) | ||||
−0.533345 | + | 0.845898i | \(0.679065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.3137 | −1.80781 | −0.903903 | − | 0.427738i | \(-0.859310\pi\) | ||||
−0.903903 | + | 0.427738i | \(0.859310\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.48528 | −0.544233 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.58579 | −0.214738 | ||||||||
\(146\) | 7.17157 | 0.593524 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.585786 | −0.0481513 | ||||||||
\(149\) | 12.7279 | 1.04271 | 0.521356 | − | 0.853339i | \(-0.325426\pi\) | ||||
0.521356 | + | 0.853339i | \(0.325426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.82843 | 0.718447 | 0.359224 | − | 0.933252i | \(-0.383042\pi\) | ||||
0.359224 | + | 0.933252i | \(0.383042\pi\) | |||||||
\(152\) | −0.828427 | −0.0671943 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.58579 | 0.368339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | −2.34315 | −0.186411 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.07107 | −0.553849 | −0.276924 | − | 0.960892i | \(-0.589315\pi\) | ||||
−0.276924 | + | 0.960892i | \(0.589315\pi\) | |||||||
\(164\) | 7.65685 | 0.597900 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.4853 | 1.27951 | ||||||||
\(167\) | −9.41421 | −0.728494 | −0.364247 | − | 0.931302i | \(-0.618674\pi\) | ||||
−0.364247 | + | 0.931302i | \(0.618674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | 0.585786 | 0.0449278 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.07107 | 0.539164 | ||||||||
\(173\) | 8.14214 | 0.619035 | 0.309518 | − | 0.950894i | \(-0.399832\pi\) | ||||
0.309518 | + | 0.950894i | \(0.399832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.585786 | 0.0441553 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.48528 | 0.186280 | ||||||||
\(179\) | −14.7279 | −1.10082 | −0.550408 | − | 0.834896i | \(-0.685528\pi\) | ||||
−0.550408 | + | 0.834896i | \(0.685528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4853 | −1.52266 | −0.761329 | − | 0.648365i | \(-0.775453\pi\) | ||||
−0.761329 | + | 0.648365i | \(0.775453\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.65685 | −0.564471 | ||||||||
\(185\) | 0.585786 | 0.0430679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.343146 | 0.0250933 | ||||||||
\(188\) | 5.41421 | 0.394872 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.828427 | 0.0601004 | ||||||||
\(191\) | 13.3137 | 0.963346 | 0.481673 | − | 0.876351i | \(-0.340029\pi\) | ||||
0.481673 | + | 0.876351i | \(0.340029\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.14214 | −0.586084 | −0.293042 | − | 0.956100i | \(-0.594668\pi\) | ||||
−0.293042 | + | 0.956100i | \(0.594668\pi\) | |||||||
\(194\) | −2.48528 | −0.178433 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6569 | −0.830516 | −0.415258 | − | 0.909704i | \(-0.636309\pi\) | ||||
−0.415258 | + | 0.909704i | \(0.636309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.75736 | −0.691681 | −0.345840 | − | 0.938293i | \(-0.612406\pi\) | ||||
−0.345840 | + | 0.938293i | \(0.612406\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.65685 | 0.116576 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.65685 | −0.534778 | ||||||||
\(206\) | −5.65685 | −0.394132 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.82843 | −0.473466 | ||||||||
\(209\) | 0.485281 | 0.0335676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7990 | 1.08765 | 0.543824 | − | 0.839200i | \(-0.316976\pi\) | ||||
0.543824 | + | 0.839200i | \(0.316976\pi\) | |||||||
\(212\) | −10.4853 | −0.720132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.17157 | 0.353521 | ||||||||
\(215\) | −7.07107 | −0.482243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.48528 | 0.168324 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.585786 | −0.0394937 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.17157 | 0.346314 | 0.173157 | − | 0.984894i | \(-0.444603\pi\) | ||||
0.173157 | + | 0.984894i | \(0.444603\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.6569 | 1.04148 | ||||||||
\(227\) | 8.97056 | 0.595397 | 0.297699 | − | 0.954660i | \(-0.403781\pi\) | ||||
0.297699 | + | 0.954660i | \(0.403781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.8284 | 0.715563 | 0.357781 | − | 0.933805i | \(-0.383533\pi\) | ||||
0.357781 | + | 0.933805i | \(0.383533\pi\) | |||||||
\(230\) | 7.65685 | 0.504878 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.58579 | −0.169765 | ||||||||
\(233\) | −12.3431 | −0.808626 | −0.404313 | − | 0.914621i | \(-0.632489\pi\) | ||||
−0.404313 | + | 0.914621i | \(0.632489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.41421 | −0.353184 | ||||||||
\(236\) | 4.82843 | 0.314304 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.34315 | 0.539673 | 0.269837 | − | 0.962906i | \(-0.413030\pi\) | ||||
0.269837 | + | 0.962906i | \(0.413030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.92893 | −0.317500 | −0.158750 | − | 0.987319i | \(-0.550746\pi\) | ||||
−0.158750 | + | 0.987319i | \(0.550746\pi\) | |||||||
\(242\) | 10.6569 | 0.685049 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.65685 | −0.618217 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.65685 | −0.359937 | ||||||||
\(248\) | 4.58579 | 0.291198 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −25.6569 | −1.61945 | −0.809723 | − | 0.586812i | \(-0.800383\pi\) | ||||
−0.809723 | + | 0.586812i | \(0.800383\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.48528 | 0.281987 | ||||||||
\(254\) | −14.1421 | −0.887357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.8995 | −0.991783 | −0.495892 | − | 0.868384i | \(-0.665159\pi\) | ||||
−0.495892 | + | 0.868384i | \(0.665159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.82843 | 0.423481 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.4853 | −0.647783 | ||||||||
\(263\) | 10.0000 | 0.616626 | 0.308313 | − | 0.951285i | \(-0.400236\pi\) | ||||
0.308313 | + | 0.951285i | \(0.400236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4853 | 0.644106 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.8995 | −0.849047 | ||||||||
\(269\) | 18.9706 | 1.15666 | 0.578328 | − | 0.815804i | \(-0.303705\pi\) | ||||
0.578328 | + | 0.815804i | \(0.303705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2426 | −0.622196 | −0.311098 | − | 0.950378i | \(-0.600697\pi\) | ||||
−0.311098 | + | 0.950378i | \(0.600697\pi\) | |||||||
\(272\) | 0.585786 | 0.0355185 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4853 | 0.754263 | ||||||||
\(275\) | 0.585786 | 0.0353243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.5858 | −1.71755 | −0.858777 | − | 0.512350i | \(-0.828775\pi\) | ||||
−0.858777 | + | 0.512350i | \(0.828775\pi\) | |||||||
\(278\) | 21.3137 | 1.27831 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4558 | −1.75719 | −0.878594 | − | 0.477569i | \(-0.841518\pi\) | ||||
−0.878594 | + | 0.477569i | \(0.841518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9706 | −1.12768 | −0.563841 | − | 0.825883i | \(-0.690677\pi\) | ||||
−0.563841 | + | 0.825883i | \(0.690677\pi\) | |||||||
\(284\) | 6.48528 | 0.384831 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6569 | −0.979815 | ||||||||
\(290\) | 2.58579 | 0.151843 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.17157 | −0.419685 | ||||||||
\(293\) | 2.68629 | 0.156935 | 0.0784674 | − | 0.996917i | \(-0.474997\pi\) | ||||
0.0784674 | + | 0.996917i | \(0.474997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.82843 | −0.281122 | ||||||||
\(296\) | 0.585786 | 0.0340481 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.7279 | −0.737309 | ||||||||
\(299\) | −52.2843 | −3.02368 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.82843 | −0.508019 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.828427 | 0.0475136 | ||||||||
\(305\) | 9.65685 | 0.552950 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6274 | 1.06312 | 0.531561 | − | 0.847020i | \(-0.321605\pi\) | ||||
0.531561 | + | 0.847020i | \(0.321605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.58579 | −0.260455 | ||||||||
\(311\) | −29.4558 | −1.67029 | −0.835144 | − | 0.550032i | \(-0.814616\pi\) | ||||
−0.835144 | + | 0.550032i | \(0.814616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.65685 | 0.206698 | 0.103349 | − | 0.994645i | \(-0.467044\pi\) | ||||
0.103349 | + | 0.994645i | \(0.467044\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.34315 | 0.131812 | ||||||||
\(317\) | 18.9706 | 1.06549 | 0.532746 | − | 0.846275i | \(-0.321160\pi\) | ||||
0.532746 | + | 0.846275i | \(0.321160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.51472 | 0.0848080 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.485281 | 0.0270018 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.82843 | −0.378773 | ||||||||
\(326\) | 7.07107 | 0.391630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.65685 | −0.422779 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7990 | −1.30811 | −0.654055 | − | 0.756447i | \(-0.726934\pi\) | ||||
−0.654055 | + | 0.756447i | \(0.726934\pi\) | |||||||
\(332\) | −16.4853 | −0.904747 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.41421 | 0.515123 | ||||||||
\(335\) | 13.8995 | 0.759411 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.51472 | −0.518300 | −0.259150 | − | 0.965837i | \(-0.583442\pi\) | ||||
−0.259150 | + | 0.965837i | \(0.583442\pi\) | |||||||
\(338\) | −33.6274 | −1.82909 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.585786 | −0.0317687 | ||||||||
\(341\) | −2.68629 | −0.145471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.07107 | −0.381246 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.14214 | −0.437724 | ||||||||
\(347\) | −6.34315 | −0.340518 | −0.170259 | − | 0.985399i | \(-0.554460\pi\) | ||||
−0.170259 | + | 0.985399i | \(0.554460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.51472 | 0.188139 | 0.0940693 | − | 0.995566i | \(-0.470012\pi\) | ||||
0.0940693 | + | 0.995566i | \(0.470012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.585786 | −0.0312225 | ||||||||
\(353\) | −7.89949 | −0.420448 | −0.210224 | − | 0.977653i | \(-0.567419\pi\) | ||||
−0.210224 | + | 0.977653i | \(0.567419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48528 | −0.344203 | ||||||||
\(356\) | −2.48528 | −0.131720 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7279 | 0.778395 | ||||||||
\(359\) | 27.1716 | 1.43406 | 0.717030 | − | 0.697042i | \(-0.245501\pi\) | ||||
0.717030 | + | 0.697042i | \(0.245501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 20.4853 | 1.07668 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.17157 | 0.375377 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4853 | −0.860525 | −0.430262 | − | 0.902704i | \(-0.641579\pi\) | ||||
−0.430262 | + | 0.902704i | \(0.641579\pi\) | |||||||
\(368\) | 7.65685 | 0.399141 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.585786 | −0.0304536 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.2426 | 1.56590 | 0.782952 | − | 0.622082i | \(-0.213713\pi\) | ||||
0.782952 | + | 0.622082i | \(0.213713\pi\) | |||||||
\(374\) | −0.343146 | −0.0177436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.41421 | −0.279217 | ||||||||
\(377\) | −17.6569 | −0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4853 | −0.641326 | −0.320663 | − | 0.947193i | \(-0.603906\pi\) | ||||
−0.320663 | + | 0.947193i | \(0.603906\pi\) | |||||||
\(380\) | −0.828427 | −0.0424974 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.3137 | −0.681189 | ||||||||
\(383\) | 29.6985 | 1.51752 | 0.758761 | − | 0.651369i | \(-0.225805\pi\) | ||||
0.758761 | + | 0.651369i | \(0.225805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.14214 | 0.414424 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.48528 | 0.126171 | ||||||||
\(389\) | 32.0416 | 1.62458 | 0.812288 | − | 0.583257i | \(-0.198222\pi\) | ||||
0.812288 | + | 0.583257i | \(0.198222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.48528 | 0.226830 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.6569 | 0.587264 | ||||||||
\(395\) | −2.34315 | −0.117896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6569 | −0.986549 | −0.493275 | − | 0.869874i | \(-0.664200\pi\) | ||||
−0.493275 | + | 0.869874i | \(0.664200\pi\) | |||||||
\(398\) | 9.75736 | 0.489092 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 28.9706 | 1.44672 | 0.723360 | − | 0.690471i | \(-0.242597\pi\) | ||||
0.723360 | + | 0.690471i | \(0.242597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.3137 | 1.55985 | ||||||||
\(404\) | −1.65685 | −0.0824316 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.343146 | −0.0170091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.8701 | 1.32864 | 0.664319 | − | 0.747449i | \(-0.268721\pi\) | ||||
0.664319 | + | 0.747449i | \(0.268721\pi\) | |||||||
\(410\) | 7.65685 | 0.378145 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.65685 | 0.278693 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.4853 | 0.809231 | ||||||||
\(416\) | 6.82843 | 0.334791 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.485281 | −0.0237359 | ||||||||
\(419\) | 16.2843 | 0.795539 | 0.397769 | − | 0.917485i | \(-0.369784\pi\) | ||||
0.397769 | + | 0.917485i | \(0.369784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.17157 | 0.154573 | 0.0772865 | − | 0.997009i | \(-0.475374\pi\) | ||||
0.0772865 | + | 0.997009i | \(0.475374\pi\) | |||||||
\(422\) | −15.7990 | −0.769083 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4853 | 0.509210 | ||||||||
\(425\) | 0.585786 | 0.0284148 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.17157 | −0.249977 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.07107 | 0.340997 | ||||||||
\(431\) | −12.1421 | −0.584866 | −0.292433 | − | 0.956286i | \(-0.594465\pi\) | ||||
−0.292433 | + | 0.956286i | \(0.594465\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.1716 | −1.30578 | −0.652891 | − | 0.757452i | \(-0.726444\pi\) | ||||
−0.652891 | + | 0.757452i | \(0.726444\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.48528 | −0.119023 | ||||||||
\(437\) | 6.34315 | 0.303434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.75736 | −0.274784 | −0.137392 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137392 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(440\) | 0.585786 | 0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | −32.9706 | −1.56648 | −0.783239 | − | 0.621720i | \(-0.786434\pi\) | ||||
−0.783239 | + | 0.621720i | \(0.786434\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48528 | 0.117814 | ||||||||
\(446\) | −5.17157 | −0.244881 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1716 | 1.56546 | 0.782732 | − | 0.622359i | \(-0.213826\pi\) | ||||
0.782732 | + | 0.622359i | \(0.213826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.48528 | 0.211204 | ||||||||
\(452\) | −15.6569 | −0.736436 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.97056 | −0.421009 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.1421 | −1.31643 | −0.658217 | − | 0.752828i | \(-0.728689\pi\) | ||||
−0.658217 | + | 0.752828i | \(0.728689\pi\) | |||||||
\(458\) | −10.8284 | −0.505979 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.65685 | −0.357003 | ||||||||
\(461\) | −25.3137 | −1.17898 | −0.589488 | − | 0.807777i | \(-0.700671\pi\) | ||||
−0.589488 | + | 0.807777i | \(0.700671\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.0000 | 1.67306 | 0.836531 | − | 0.547920i | \(-0.184580\pi\) | ||||
0.836531 | + | 0.547920i | \(0.184580\pi\) | |||||||
\(464\) | 2.58579 | 0.120042 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.3431 | 0.571785 | ||||||||
\(467\) | −33.1716 | −1.53500 | −0.767499 | − | 0.641051i | \(-0.778499\pi\) | ||||
−0.767499 | + | 0.641051i | \(0.778499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.41421 | 0.249739 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.82843 | −0.222246 | ||||||||
\(473\) | 4.14214 | 0.190456 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.828427 | 0.0380108 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.34315 | −0.381607 | ||||||||
\(479\) | −25.1716 | −1.15012 | −0.575059 | − | 0.818112i | \(-0.695021\pi\) | ||||
−0.575059 | + | 0.818112i | \(0.695021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 4.92893 | 0.224507 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6569 | −0.484402 | ||||||||
\(485\) | −2.48528 | −0.112851 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.8284 | −0.671940 | −0.335970 | − | 0.941873i | \(-0.609064\pi\) | ||||
−0.335970 | + | 0.941873i | \(0.609064\pi\) | |||||||
\(488\) | 9.65685 | 0.437145 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.0711 | −1.49248 | −0.746238 | − | 0.665679i | \(-0.768142\pi\) | ||||
−0.746238 | + | 0.665679i | \(0.768142\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.51472 | 0.0682195 | ||||||||
\(494\) | 5.65685 | 0.254514 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.58579 | −0.205908 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.1127 | 1.39280 | 0.696398 | − | 0.717656i | \(-0.254785\pi\) | ||||
0.696398 | + | 0.717656i | \(0.254785\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.6569 | 1.14512 | ||||||||
\(503\) | −22.5858 | −1.00705 | −0.503525 | − | 0.863981i | \(-0.667964\pi\) | ||||
−0.503525 | + | 0.863981i | \(0.667964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.65685 | 0.0737290 | ||||||||
\(506\) | −4.48528 | −0.199395 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1421 | 0.627456 | ||||||||
\(509\) | −43.5980 | −1.93245 | −0.966223 | − | 0.257707i | \(-0.917033\pi\) | ||||
−0.966223 | + | 0.257707i | \(0.917033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.8995 | 0.701297 | ||||||||
\(515\) | −5.65685 | −0.249271 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.17157 | 0.139486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.82843 | −0.299446 | ||||||||
\(521\) | −15.1716 | −0.664679 | −0.332339 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332339 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.6274 | 0.901974 | 0.450987 | − | 0.892531i | \(-0.351072\pi\) | ||||
0.450987 | + | 0.892531i | \(0.351072\pi\) | |||||||
\(524\) | 10.4853 | 0.458052 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0000 | −0.436021 | ||||||||
\(527\) | −2.68629 | −0.117017 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | −10.4853 | −0.455452 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.2843 | −2.26468 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.17157 | 0.223587 | ||||||||
\(536\) | 13.8995 | 0.600367 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.9706 | −0.817879 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.9411 | 1.02931 | 0.514655 | − | 0.857398i | \(-0.327920\pi\) | ||||
0.514655 | + | 0.857398i | \(0.327920\pi\) | |||||||
\(542\) | 10.2426 | 0.439959 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.585786 | −0.0251154 | ||||||||
\(545\) | 2.48528 | 0.106458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.7279 | −1.39934 | −0.699672 | − | 0.714464i | \(-0.746671\pi\) | ||||
−0.699672 | + | 0.714464i | \(0.746671\pi\) | |||||||
\(548\) | −12.4853 | −0.533345 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.585786 | −0.0249780 | ||||||||
\(551\) | 2.14214 | 0.0912580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.5858 | 1.21449 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.3137 | −0.903903 | ||||||||
\(557\) | 29.3137 | 1.24206 | 0.621031 | − | 0.783786i | \(-0.286714\pi\) | ||||
0.621031 | + | 0.783786i | \(0.286714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.2843 | −2.04221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.4558 | 1.24252 | ||||||||
\(563\) | −23.7990 | −1.00301 | −0.501504 | − | 0.865155i | \(-0.667220\pi\) | ||||
−0.501504 | + | 0.865155i | \(0.667220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.6569 | 0.658689 | ||||||||
\(566\) | 18.9706 | 0.797392 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.48528 | −0.272116 | ||||||||
\(569\) | 23.3137 | 0.977362 | 0.488681 | − | 0.872463i | \(-0.337478\pi\) | ||||
0.488681 | + | 0.872463i | \(0.337478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3137 | −1.14304 | −0.571522 | − | 0.820587i | \(-0.693647\pi\) | ||||
−0.571522 | + | 0.820587i | \(0.693647\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.65685 | 0.319313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.62742 | −0.359164 | −0.179582 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179582 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(578\) | 16.6569 | 0.692834 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.58579 | −0.107369 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.14214 | −0.254381 | ||||||||
\(584\) | 7.17157 | 0.296762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.68629 | −0.110970 | ||||||||
\(587\) | −18.1421 | −0.748806 | −0.374403 | − | 0.927266i | \(-0.622152\pi\) | ||||
−0.374403 | + | 0.927266i | \(0.622152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.79899 | −0.156535 | ||||||||
\(590\) | 4.82843 | 0.198783 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.585786 | −0.0240757 | ||||||||
\(593\) | 19.6985 | 0.808920 | 0.404460 | − | 0.914556i | \(-0.367460\pi\) | ||||
0.404460 | + | 0.914556i | \(0.367460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.7279 | 0.521356 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 52.2843 | 2.13806 | ||||||||
\(599\) | −12.6274 | −0.515942 | −0.257971 | − | 0.966153i | \(-0.583054\pi\) | ||||
−0.257971 | + | 0.966153i | \(0.583054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.61522 | 0.392213 | 0.196107 | − | 0.980583i | \(-0.437170\pi\) | ||||
0.196107 | + | 0.980583i | \(0.437170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.82843 | 0.359224 | ||||||||
\(605\) | 10.6569 | 0.433263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.1127 | −1.26283 | −0.631413 | − | 0.775447i | \(-0.717525\pi\) | ||||
−0.631413 | + | 0.775447i | \(0.717525\pi\) | |||||||
\(608\) | −0.828427 | −0.0335972 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.65685 | −0.390995 | ||||||||
\(611\) | −36.9706 | −1.49567 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5858 | 0.669894 | 0.334947 | − | 0.942237i | \(-0.391282\pi\) | ||||
0.334947 | + | 0.942237i | \(0.391282\pi\) | |||||||
\(614\) | −18.6274 | −0.751741 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.1127 | −0.930482 | −0.465241 | − | 0.885184i | \(-0.654032\pi\) | ||||
−0.465241 | + | 0.885184i | \(0.654032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.82843 | 0.194071 | 0.0970354 | − | 0.995281i | \(-0.469064\pi\) | ||||
0.0970354 | + | 0.995281i | \(0.469064\pi\) | |||||||
\(620\) | 4.58579 | 0.184170 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.4558 | 1.18107 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.65685 | −0.146157 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | −0.399043 | ||||||||
\(629\) | −0.343146 | −0.0136821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.4558 | −1.41147 | −0.705737 | − | 0.708473i | \(-0.749384\pi\) | ||||
−0.705737 | + | 0.708473i | \(0.749384\pi\) | |||||||
\(632\) | −2.34315 | −0.0932053 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.9706 | −0.753417 | ||||||||
\(635\) | −14.1421 | −0.561214 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.51472 | −0.0599683 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 26.6274 | 1.05172 | 0.525860 | − | 0.850571i | \(-0.323744\pi\) | ||||
0.525860 | + | 0.850571i | \(0.323744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.9706 | 1.06362 | 0.531808 | − | 0.846865i | \(-0.321513\pi\) | ||||
0.531808 | + | 0.846865i | \(0.321513\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.485281 | −0.0190931 | ||||||||
\(647\) | −50.3848 | −1.98083 | −0.990415 | − | 0.138124i | \(-0.955893\pi\) | ||||
−0.990415 | + | 0.138124i | \(0.955893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82843 | 0.111025 | ||||||||
\(650\) | 6.82843 | 0.267833 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.07107 | −0.276924 | ||||||||
\(653\) | 17.1127 | 0.669672 | 0.334836 | − | 0.942276i | \(-0.391319\pi\) | ||||
0.334836 | + | 0.942276i | \(0.391319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4853 | −0.409694 | ||||||||
\(656\) | 7.65685 | 0.298950 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.4142 | 1.22372 | 0.611862 | − | 0.790965i | \(-0.290421\pi\) | ||||
0.611862 | + | 0.790965i | \(0.290421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.6569 | 1.30910 | 0.654550 | − | 0.756019i | \(-0.272858\pi\) | ||||
0.654550 | + | 0.756019i | \(0.272858\pi\) | |||||||
\(662\) | 23.7990 | 0.924974 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.4853 | 0.639753 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.7990 | 0.766620 | ||||||||
\(668\) | −9.41421 | −0.364247 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.8995 | −0.536984 | ||||||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.9706 | −0.885450 | −0.442725 | − | 0.896657i | \(-0.645988\pi\) | ||||
−0.442725 | + | 0.896657i | \(0.645988\pi\) | |||||||
\(674\) | 9.51472 | 0.366493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.6274 | 1.29336 | ||||||||
\(677\) | 35.4558 | 1.36268 | 0.681339 | − | 0.731968i | \(-0.261398\pi\) | ||||
0.681339 | + | 0.731968i | \(0.261398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.585786 | 0.0224639 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.68629 | 0.102863 | ||||||||
\(683\) | −37.6569 | −1.44090 | −0.720450 | − | 0.693507i | \(-0.756065\pi\) | ||||
−0.720450 | + | 0.693507i | \(0.756065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4853 | 0.477038 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.07107 | 0.269582 | ||||||||
\(689\) | 71.5980 | 2.72767 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.9706 | 1.33034 | 0.665171 | − | 0.746691i | \(-0.268358\pi\) | ||||
0.665171 | + | 0.746691i | \(0.268358\pi\) | |||||||
\(692\) | 8.14214 | 0.309518 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.34315 | 0.240783 | ||||||||
\(695\) | 21.3137 | 0.808475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.48528 | 0.169892 | ||||||||
\(698\) | −3.51472 | −0.133034 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.2426 | −0.613476 | −0.306738 | − | 0.951794i | \(-0.599238\pi\) | ||||
−0.306738 | + | 0.951794i | \(0.599238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.485281 | −0.0183027 | ||||||||
\(704\) | 0.585786 | 0.0220777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.89949 | 0.297301 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.1127 | −1.54402 | −0.772010 | − | 0.635611i | \(-0.780748\pi\) | ||||
−0.772010 | + | 0.635611i | \(0.780748\pi\) | |||||||
\(710\) | 6.48528 | 0.243388 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.48528 | 0.0931399 | ||||||||
\(713\) | −35.1127 | −1.31498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | 0.149592 | ||||||||
\(716\) | −14.7279 | −0.550408 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27.1716 | −1.01403 | ||||||||
\(719\) | −17.4558 | −0.650993 | −0.325497 | − | 0.945543i | \(-0.605531\pi\) | ||||
−0.325497 | + | 0.945543i | \(0.605531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.3137 | 0.681566 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.4853 | −0.761329 | ||||||||
\(725\) | 2.58579 | 0.0960337 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.4558 | 1.38916 | 0.694580 | − | 0.719415i | \(-0.255590\pi\) | ||||
0.694580 | + | 0.719415i | \(0.255590\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.17157 | −0.265432 | ||||||||
\(731\) | 4.14214 | 0.153202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.9706 | −0.996180 | −0.498090 | − | 0.867125i | \(-0.665965\pi\) | ||||
−0.498090 | + | 0.867125i | \(0.665965\pi\) | |||||||
\(734\) | 16.4853 | 0.608483 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.65685 | −0.282235 | ||||||||
\(737\) | −8.14214 | −0.299919 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.82843 | 0.104045 | 0.0520227 | − | 0.998646i | \(-0.483433\pi\) | ||||
0.0520227 | + | 0.998646i | \(0.483433\pi\) | |||||||
\(740\) | 0.585786 | 0.0215339 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.3431 | −1.25993 | −0.629964 | − | 0.776624i | \(-0.716930\pi\) | ||||
−0.629964 | + | 0.776624i | \(0.716930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7279 | −0.466315 | ||||||||
\(746\) | −30.2426 | −1.10726 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.343146 | 0.0125467 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.20101 | −0.0803160 | −0.0401580 | − | 0.999193i | \(-0.512786\pi\) | ||||
−0.0401580 | + | 0.999193i | \(0.512786\pi\) | |||||||
\(752\) | 5.41421 | 0.197436 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.6569 | 0.643025 | ||||||||
\(755\) | −8.82843 | −0.321299 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.3553 | −1.79385 | −0.896925 | − | 0.442182i | \(-0.854204\pi\) | ||||
−0.896925 | + | 0.442182i | \(0.854204\pi\) | |||||||
\(758\) | 12.4853 | 0.453486 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.828427 | 0.0300502 | ||||||||
\(761\) | 36.6274 | 1.32774 | 0.663871 | − | 0.747847i | \(-0.268912\pi\) | ||||
0.663871 | + | 0.747847i | \(0.268912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.3137 | 0.481673 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.6985 | −1.07305 | ||||||||
\(767\) | −32.9706 | −1.19050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0711 | 0.976208 | 0.488104 | − | 0.872786i | \(-0.337689\pi\) | ||||
0.488104 | + | 0.872786i | \(0.337689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.14214 | −0.293042 | ||||||||
\(773\) | −14.9706 | −0.538454 | −0.269227 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269227 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.58579 | −0.164726 | ||||||||
\(776\) | −2.48528 | −0.0892164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −32.0416 | −1.14875 | ||||||||
\(779\) | 6.34315 | 0.227267 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.79899 | 0.135939 | ||||||||
\(782\) | −4.48528 | −0.160393 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.9706 | 1.31786 | 0.658929 | − | 0.752205i | \(-0.271010\pi\) | ||||
0.658929 | + | 0.752205i | \(0.271010\pi\) | |||||||
\(788\) | −11.6569 | −0.415258 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.34315 | 0.0833654 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.9411 | 2.34164 | ||||||||
\(794\) | 19.6569 | 0.697596 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.75736 | −0.345840 | ||||||||
\(797\) | 36.1421 | 1.28022 | 0.640110 | − | 0.768283i | \(-0.278889\pi\) | ||||
0.640110 | + | 0.768283i | \(0.278889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.17157 | 0.112202 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.9706 | −1.02299 | ||||||||
\(803\) | −4.20101 | −0.148250 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31.3137 | −1.10298 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.65685 | 0.0582879 | ||||||||
\(809\) | −0.485281 | −0.0170616 | −0.00853079 | − | 0.999964i | \(-0.502715\pi\) | ||||
−0.00853079 | + | 0.999964i | \(0.502715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6274 | −0.724327 | −0.362163 | − | 0.932115i | \(-0.617962\pi\) | ||||
−0.362163 | + | 0.932115i | \(0.617962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.343146 | 0.0120273 | ||||||||
\(815\) | 7.07107 | 0.247689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.85786 | 0.204941 | ||||||||
\(818\) | −26.8701 | −0.939490 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.65685 | −0.267389 | ||||||||
\(821\) | −43.0711 | −1.50319 | −0.751595 | − | 0.659625i | \(-0.770715\pi\) | ||||
−0.751595 | + | 0.659625i | \(0.770715\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.6569 | 0.754910 | 0.377455 | − | 0.926028i | \(-0.376799\pi\) | ||||
0.377455 | + | 0.926028i | \(0.376799\pi\) | |||||||
\(824\) | −5.65685 | −0.197066 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7990 | 0.549385 | 0.274692 | − | 0.961532i | \(-0.411424\pi\) | ||||
0.274692 | + | 0.961532i | \(0.411424\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | −16.4853 | −0.572212 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.82843 | −0.236733 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.41421 | 0.325792 | ||||||||
\(836\) | 0.485281 | 0.0167838 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.2843 | −0.562531 | ||||||||
\(839\) | 32.2843 | 1.11458 | 0.557288 | − | 0.830319i | \(-0.311842\pi\) | ||||
0.557288 | + | 0.830319i | \(0.311842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3137 | −0.769438 | ||||||||
\(842\) | −3.17157 | −0.109300 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.7990 | 0.543824 | ||||||||
\(845\) | −33.6274 | −1.15682 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.4853 | −0.360066 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.585786 | −0.0200923 | ||||||||
\(851\) | −4.48528 | −0.153753 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3431 | 1.38132 | 0.690662 | − | 0.723178i | \(-0.257319\pi\) | ||||
0.690662 | + | 0.723178i | \(0.257319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.17157 | 0.176761 | ||||||||
\(857\) | 32.1005 | 1.09653 | 0.548266 | − | 0.836304i | \(-0.315288\pi\) | ||||
0.548266 | + | 0.836304i | \(0.315288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.97056 | 0.101354 | 0.0506771 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506771 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(860\) | −7.07107 | −0.241121 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.1421 | 0.413563 | ||||||||
\(863\) | 4.97056 | 0.169200 | 0.0846000 | − | 0.996415i | \(-0.473039\pi\) | ||||
0.0846000 | + | 0.996415i | \(0.473039\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.14214 | −0.276841 | ||||||||
\(866\) | 27.1716 | 0.923328 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.37258 | 0.0465617 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 94.9117 | 3.21596 | ||||||||
\(872\) | 2.48528 | 0.0841622 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.34315 | −0.214560 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.4437 | −0.352657 | −0.176329 | − | 0.984331i | \(-0.556422\pi\) | ||||
−0.176329 | + | 0.984331i | \(0.556422\pi\) | |||||||
\(878\) | 5.75736 | 0.194301 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.585786 | −0.0197469 | ||||||||
\(881\) | 23.8579 | 0.803792 | 0.401896 | − | 0.915685i | \(-0.368351\pi\) | ||||
0.401896 | + | 0.915685i | \(0.368351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5269 | −1.49845 | −0.749225 | − | 0.662316i | \(-0.769574\pi\) | ||||
−0.749225 | + | 0.662316i | \(0.769574\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9706 | 1.10767 | ||||||||
\(887\) | 26.1005 | 0.876369 | 0.438185 | − | 0.898885i | \(-0.355622\pi\) | ||||
0.438185 | + | 0.898885i | \(0.355622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.48528 | −0.0833068 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.17157 | 0.173157 | ||||||||
\(893\) | 4.48528 | 0.150094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7279 | 0.492300 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.1716 | −1.10695 | ||||||||
\(899\) | −11.8579 | −0.395482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.14214 | −0.204624 | ||||||||
\(902\) | −4.48528 | −0.149344 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.6569 | 0.520739 | ||||||||
\(905\) | 20.4853 | 0.680954 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3259 | 1.60464 | 0.802318 | − | 0.596897i | \(-0.203600\pi\) | ||||
0.802318 | + | 0.596897i | \(0.203600\pi\) | |||||||
\(908\) | 8.97056 | 0.297699 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.5980 | 1.77578 | 0.887890 | − | 0.460056i | \(-0.152171\pi\) | ||||
0.887890 | + | 0.460056i | \(0.152171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.65685 | −0.319595 | ||||||||
\(914\) | 28.1421 | 0.930859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.8284 | 0.357781 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.4558 | 1.03763 | 0.518816 | − | 0.854886i | \(-0.326373\pi\) | ||||
0.518816 | + | 0.854886i | \(0.326373\pi\) | |||||||
\(920\) | 7.65685 | 0.252439 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.3137 | 0.833663 | ||||||||
\(923\) | −44.2843 | −1.45763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.585786 | −0.0192605 | ||||||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.58579 | −0.0848826 | ||||||||
\(929\) | −48.9117 | −1.60474 | −0.802370 | − | 0.596827i | \(-0.796428\pi\) | ||||
−0.802370 | + | 0.596827i | \(0.796428\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.3431 | −0.404313 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.1716 | 1.08541 | ||||||||
\(935\) | −0.343146 | −0.0112221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9706 | −0.489067 | −0.244533 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244533 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.41421 | −0.176592 | ||||||||
\(941\) | 56.0000 | 1.82555 | 0.912774 | − | 0.408465i | \(-0.133936\pi\) | ||||
0.912774 | + | 0.408465i | \(0.133936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.6274 | 1.90917 | ||||||||
\(944\) | 4.82843 | 0.157152 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.14214 | −0.134672 | ||||||||
\(947\) | −6.62742 | −0.215362 | −0.107681 | − | 0.994185i | \(-0.534343\pi\) | ||||
−0.107681 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.9706 | 1.58965 | ||||||||
\(950\) | −0.828427 | −0.0268777 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.8284 | −1.64649 | −0.823247 | − | 0.567683i | \(-0.807840\pi\) | ||||
−0.823247 | + | 0.567683i | \(0.807840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.3137 | −0.430821 | ||||||||
\(956\) | 8.34315 | 0.269837 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.1716 | 0.813257 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.92893 | −0.158750 | ||||||||
\(965\) | 8.14214 | 0.262105 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.02944 | 0.226051 | 0.113026 | − | 0.993592i | \(-0.463946\pi\) | ||||
0.113026 | + | 0.993592i | \(0.463946\pi\) | |||||||
\(968\) | 10.6569 | 0.342524 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.48528 | 0.0797976 | ||||||||
\(971\) | −1.65685 | −0.0531710 | −0.0265855 | − | 0.999647i | \(-0.508463\pi\) | ||||
−0.0265855 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.8284 | 0.475133 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.65685 | −0.309108 | ||||||||
\(977\) | 6.68629 | 0.213913 | 0.106957 | − | 0.994264i | \(-0.465889\pi\) | ||||
0.106957 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.45584 | −0.0465290 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.0711 | 1.05534 | ||||||||
\(983\) | −22.3848 | −0.713963 | −0.356982 | − | 0.934111i | \(-0.616194\pi\) | ||||
−0.356982 | + | 0.934111i | \(0.616194\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6569 | 0.371418 | ||||||||
\(986\) | −1.51472 | −0.0482385 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.65685 | −0.179969 | ||||||||
\(989\) | 54.1421 | 1.72162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.1421 | 0.512772 | 0.256386 | − | 0.966574i | \(-0.417468\pi\) | ||||
0.256386 | + | 0.966574i | \(0.417468\pi\) | |||||||
\(992\) | 4.58579 | 0.145599 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.75736 | 0.309329 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.6569 | 0.622539 | 0.311269 | − | 0.950322i | \(-0.399246\pi\) | ||||
0.311269 | + | 0.950322i | \(0.399246\pi\) | |||||||
\(998\) | −31.1127 | −0.984855 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4410.2.a.bp.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 4410.2.a.bx.1.2 | yes | 2 | ||
7.6 | odd | 2 | 4410.2.a.bs.1.1 | yes | 2 | ||
21.20 | even | 2 | 4410.2.a.bu.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.a.bp.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4410.2.a.bs.1.1 | yes | 2 | 7.6 | odd | 2 | ||
4410.2.a.bu.1.2 | yes | 2 | 21.20 | even | 2 | ||
4410.2.a.bx.1.2 | yes | 2 | 3.2 | odd | 2 |