Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} - 206 x^{7} - 16453 x^{6} + 637 x^{5} + 16290 x^{4} + 1068 x^{3} - 4992 x^{2} + \cdots - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.75508\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 | ||||||||
\(3\) | 2.75508 | 1.59065 | 0.795324 | − | 0.606184i | \(-0.207300\pi\) | ||||
0.795324 | + | 0.606184i | \(0.207300\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.75508 | 1.12476 | ||||||||
\(7\) | 4.44855 | 1.68139 | 0.840696 | − | 0.541507i | \(-0.182146\pi\) | ||||
0.840696 | + | 0.541507i | \(0.182146\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.59049 | 1.53016 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.40211 | 1.32729 | 0.663643 | − | 0.748050i | \(-0.269009\pi\) | ||||
0.663643 | + | 0.748050i | \(0.269009\pi\) | |||||||
\(12\) | 2.75508 | 0.795324 | ||||||||
\(13\) | 2.45989 | 0.682249 | 0.341125 | − | 0.940018i | \(-0.389192\pi\) | ||||
0.341125 | + | 0.940018i | \(0.389192\pi\) | |||||||
\(14\) | 4.44855 | 1.18892 | ||||||||
\(15\) | −2.75508 | −0.711360 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.98238 | −1.69348 | −0.846738 | − | 0.532010i | \(-0.821437\pi\) | ||||
−0.846738 | + | 0.532010i | \(0.821437\pi\) | |||||||
\(18\) | 4.59049 | 1.08199 | ||||||||
\(19\) | −3.42347 | −0.785399 | −0.392699 | − | 0.919667i | \(-0.628459\pi\) | ||||
−0.392699 | + | 0.919667i | \(0.628459\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 12.2561 | 2.67451 | ||||||||
\(22\) | 4.40211 | 0.938533 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 2.75508 | 0.562379 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.45989 | 0.482423 | ||||||||
\(27\) | 4.38194 | 0.843305 | ||||||||
\(28\) | 4.44855 | 0.840696 | ||||||||
\(29\) | 5.51384 | 1.02389 | 0.511947 | − | 0.859017i | \(-0.328924\pi\) | ||||
0.511947 | + | 0.859017i | \(0.328924\pi\) | |||||||
\(30\) | −2.75508 | −0.503007 | ||||||||
\(31\) | −2.05611 | −0.369288 | −0.184644 | − | 0.982805i | \(-0.559113\pi\) | ||||
−0.184644 | + | 0.982805i | \(0.559113\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 12.1282 | 2.11125 | ||||||||
\(34\) | −6.98238 | −1.19747 | ||||||||
\(35\) | −4.44855 | −0.751942 | ||||||||
\(36\) | 4.59049 | 0.765082 | ||||||||
\(37\) | −6.73053 | −1.10649 | −0.553246 | − | 0.833018i | \(-0.686611\pi\) | ||||
−0.553246 | + | 0.833018i | \(0.686611\pi\) | |||||||
\(38\) | −3.42347 | −0.555361 | ||||||||
\(39\) | 6.77719 | 1.08522 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.15936 | 0.493410 | 0.246705 | − | 0.969091i | \(-0.420652\pi\) | ||||
0.246705 | + | 0.969091i | \(0.420652\pi\) | |||||||
\(42\) | 12.2561 | 1.89116 | ||||||||
\(43\) | −2.76141 | −0.421111 | −0.210555 | − | 0.977582i | \(-0.567527\pi\) | ||||
−0.210555 | + | 0.977582i | \(0.567527\pi\) | |||||||
\(44\) | 4.40211 | 0.663643 | ||||||||
\(45\) | −4.59049 | −0.684310 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.18748 | 0.902537 | 0.451268 | − | 0.892388i | \(-0.350972\pi\) | ||||
0.451268 | + | 0.892388i | \(0.350972\pi\) | |||||||
\(48\) | 2.75508 | 0.397662 | ||||||||
\(49\) | 12.7896 | 1.82708 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −19.2371 | −2.69373 | ||||||||
\(52\) | 2.45989 | 0.341125 | ||||||||
\(53\) | −1.99036 | −0.273397 | −0.136698 | − | 0.990613i | \(-0.543649\pi\) | ||||
−0.136698 | + | 0.990613i | \(0.543649\pi\) | |||||||
\(54\) | 4.38194 | 0.596307 | ||||||||
\(55\) | −4.40211 | −0.593580 | ||||||||
\(56\) | 4.44855 | 0.594462 | ||||||||
\(57\) | −9.43196 | −1.24929 | ||||||||
\(58\) | 5.51384 | 0.724003 | ||||||||
\(59\) | 2.00254 | 0.260708 | 0.130354 | − | 0.991467i | \(-0.458389\pi\) | ||||
0.130354 | + | 0.991467i | \(0.458389\pi\) | |||||||
\(60\) | −2.75508 | −0.355680 | ||||||||
\(61\) | −13.8042 | −1.76744 | −0.883721 | − | 0.468014i | \(-0.844970\pi\) | ||||
−0.883721 | + | 0.468014i | \(0.844970\pi\) | |||||||
\(62\) | −2.05611 | −0.261126 | ||||||||
\(63\) | 20.4210 | 2.57281 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.45989 | −0.305111 | ||||||||
\(66\) | 12.1282 | 1.49288 | ||||||||
\(67\) | 8.90067 | 1.08739 | 0.543695 | − | 0.839283i | \(-0.317025\pi\) | ||||
0.543695 | + | 0.839283i | \(0.317025\pi\) | |||||||
\(68\) | −6.98238 | −0.846738 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.44855 | −0.531703 | ||||||||
\(71\) | −10.8705 | −1.29010 | −0.645048 | − | 0.764142i | \(-0.723162\pi\) | ||||
−0.645048 | + | 0.764142i | \(0.723162\pi\) | |||||||
\(72\) | 4.59049 | 0.540995 | ||||||||
\(73\) | −8.57546 | −1.00368 | −0.501841 | − | 0.864960i | \(-0.667344\pi\) | ||||
−0.501841 | + | 0.864960i | \(0.667344\pi\) | |||||||
\(74\) | −6.73053 | −0.782408 | ||||||||
\(75\) | 2.75508 | 0.318130 | ||||||||
\(76\) | −3.42347 | −0.392699 | ||||||||
\(77\) | 19.5830 | 2.23169 | ||||||||
\(78\) | 6.77719 | 0.767366 | ||||||||
\(79\) | −11.8628 | −1.33466 | −0.667332 | − | 0.744760i | \(-0.732564\pi\) | ||||
−0.667332 | + | 0.744760i | \(0.732564\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −1.69886 | −0.188762 | ||||||||
\(82\) | 3.15936 | 0.348893 | ||||||||
\(83\) | 0.319840 | 0.0351069 | 0.0175535 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175535 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(84\) | 12.2561 | 1.33725 | ||||||||
\(85\) | 6.98238 | 0.757345 | ||||||||
\(86\) | −2.76141 | −0.297770 | ||||||||
\(87\) | 15.1911 | 1.62866 | ||||||||
\(88\) | 4.40211 | 0.469266 | ||||||||
\(89\) | 8.69820 | 0.922008 | 0.461004 | − | 0.887398i | \(-0.347489\pi\) | ||||
0.461004 | + | 0.887398i | \(0.347489\pi\) | |||||||
\(90\) | −4.59049 | −0.483880 | ||||||||
\(91\) | 10.9429 | 1.14713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.66475 | −0.587408 | ||||||||
\(94\) | 6.18748 | 0.638190 | ||||||||
\(95\) | 3.42347 | 0.351241 | ||||||||
\(96\) | 2.75508 | 0.281190 | ||||||||
\(97\) | 7.30395 | 0.741603 | 0.370802 | − | 0.928712i | \(-0.379083\pi\) | ||||
0.370802 | + | 0.928712i | \(0.379083\pi\) | |||||||
\(98\) | 12.7896 | 1.29194 | ||||||||
\(99\) | 20.2078 | 2.03097 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.08953 | −0.904442 | −0.452221 | − | 0.891906i | \(-0.649368\pi\) | ||||
−0.452221 | + | 0.891906i | \(0.649368\pi\) | |||||||
\(102\) | −19.2371 | −1.90475 | ||||||||
\(103\) | 1.49900 | 0.147701 | 0.0738504 | − | 0.997269i | \(-0.476471\pi\) | ||||
0.0738504 | + | 0.997269i | \(0.476471\pi\) | |||||||
\(104\) | 2.45989 | 0.241212 | ||||||||
\(105\) | −12.2561 | −1.19608 | ||||||||
\(106\) | −1.99036 | −0.193321 | ||||||||
\(107\) | −17.7755 | −1.71842 | −0.859211 | − | 0.511622i | \(-0.829045\pi\) | ||||
−0.859211 | + | 0.511622i | \(0.829045\pi\) | |||||||
\(108\) | 4.38194 | 0.421653 | ||||||||
\(109\) | 18.9672 | 1.81673 | 0.908364 | − | 0.418181i | \(-0.137332\pi\) | ||||
0.908364 | + | 0.418181i | \(0.137332\pi\) | |||||||
\(110\) | −4.40211 | −0.419725 | ||||||||
\(111\) | −18.5432 | −1.76004 | ||||||||
\(112\) | 4.44855 | 0.420348 | ||||||||
\(113\) | −3.38804 | −0.318720 | −0.159360 | − | 0.987221i | \(-0.550943\pi\) | ||||
−0.159360 | + | 0.987221i | \(0.550943\pi\) | |||||||
\(114\) | −9.43196 | −0.883384 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.51384 | 0.511947 | ||||||||
\(117\) | 11.2921 | 1.04395 | ||||||||
\(118\) | 2.00254 | 0.184349 | ||||||||
\(119\) | −31.0614 | −2.84740 | ||||||||
\(120\) | −2.75508 | −0.251504 | ||||||||
\(121\) | 8.37857 | 0.761688 | ||||||||
\(122\) | −13.8042 | −1.24977 | ||||||||
\(123\) | 8.70432 | 0.784842 | ||||||||
\(124\) | −2.05611 | −0.184644 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 20.4210 | 1.81925 | ||||||||
\(127\) | −5.73551 | −0.508945 | −0.254472 | − | 0.967080i | \(-0.581902\pi\) | ||||
−0.254472 | + | 0.967080i | \(0.581902\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.60792 | −0.669840 | ||||||||
\(130\) | −2.45989 | −0.215746 | ||||||||
\(131\) | −10.6514 | −0.930620 | −0.465310 | − | 0.885148i | \(-0.654057\pi\) | ||||
−0.465310 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(132\) | 12.1282 | 1.05562 | ||||||||
\(133\) | −15.2295 | −1.32056 | ||||||||
\(134\) | 8.90067 | 0.768901 | ||||||||
\(135\) | −4.38194 | −0.377137 | ||||||||
\(136\) | −6.98238 | −0.598734 | ||||||||
\(137\) | 13.7187 | 1.17207 | 0.586035 | − | 0.810285i | \(-0.300688\pi\) | ||||
0.586035 | + | 0.810285i | \(0.300688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.55749 | −0.301742 | −0.150871 | − | 0.988553i | \(-0.548208\pi\) | ||||
−0.150871 | + | 0.988553i | \(0.548208\pi\) | |||||||
\(140\) | −4.44855 | −0.375971 | ||||||||
\(141\) | 17.0470 | 1.43562 | ||||||||
\(142\) | −10.8705 | −0.912235 | ||||||||
\(143\) | 10.8287 | 0.905540 | ||||||||
\(144\) | 4.59049 | 0.382541 | ||||||||
\(145\) | −5.51384 | −0.457899 | ||||||||
\(146\) | −8.57546 | −0.709710 | ||||||||
\(147\) | 35.2363 | 2.90624 | ||||||||
\(148\) | −6.73053 | −0.553246 | ||||||||
\(149\) | −8.65572 | −0.709104 | −0.354552 | − | 0.935036i | \(-0.615367\pi\) | ||||
−0.354552 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(150\) | 2.75508 | 0.224952 | ||||||||
\(151\) | −1.76370 | −0.143528 | −0.0717640 | − | 0.997422i | \(-0.522863\pi\) | ||||
−0.0717640 | + | 0.997422i | \(0.522863\pi\) | |||||||
\(152\) | −3.42347 | −0.277680 | ||||||||
\(153\) | −32.0526 | −2.59130 | ||||||||
\(154\) | 19.5830 | 1.57804 | ||||||||
\(155\) | 2.05611 | 0.165151 | ||||||||
\(156\) | 6.77719 | 0.542610 | ||||||||
\(157\) | −12.6015 | −1.00571 | −0.502856 | − | 0.864370i | \(-0.667717\pi\) | ||||
−0.502856 | + | 0.864370i | \(0.667717\pi\) | |||||||
\(158\) | −11.8628 | −0.943750 | ||||||||
\(159\) | −5.48361 | −0.434878 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.69886 | −0.133475 | ||||||||
\(163\) | 2.07678 | 0.162666 | 0.0813329 | − | 0.996687i | \(-0.474082\pi\) | ||||
0.0813329 | + | 0.996687i | \(0.474082\pi\) | |||||||
\(164\) | 3.15936 | 0.246705 | ||||||||
\(165\) | −12.1282 | −0.944178 | ||||||||
\(166\) | 0.319840 | 0.0248244 | ||||||||
\(167\) | 3.48524 | 0.269696 | 0.134848 | − | 0.990866i | \(-0.456945\pi\) | ||||
0.134848 | + | 0.990866i | \(0.456945\pi\) | |||||||
\(168\) | 12.2561 | 0.945580 | ||||||||
\(169\) | −6.94896 | −0.534536 | ||||||||
\(170\) | 6.98238 | 0.535524 | ||||||||
\(171\) | −15.7154 | −1.20179 | ||||||||
\(172\) | −2.76141 | −0.210555 | ||||||||
\(173\) | 23.1699 | 1.76157 | 0.880787 | − | 0.473513i | \(-0.157014\pi\) | ||||
0.880787 | + | 0.473513i | \(0.157014\pi\) | |||||||
\(174\) | 15.1911 | 1.15163 | ||||||||
\(175\) | 4.44855 | 0.336278 | ||||||||
\(176\) | 4.40211 | 0.331821 | ||||||||
\(177\) | 5.51717 | 0.414696 | ||||||||
\(178\) | 8.69820 | 0.651958 | ||||||||
\(179\) | 1.26603 | 0.0946279 | 0.0473139 | − | 0.998880i | \(-0.484934\pi\) | ||||
0.0473139 | + | 0.998880i | \(0.484934\pi\) | |||||||
\(180\) | −4.59049 | −0.342155 | ||||||||
\(181\) | −18.3728 | −1.36564 | −0.682822 | − | 0.730585i | \(-0.739247\pi\) | ||||
−0.682822 | + | 0.730585i | \(0.739247\pi\) | |||||||
\(182\) | 10.9429 | 0.811143 | ||||||||
\(183\) | −38.0316 | −2.81138 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.73053 | 0.494838 | ||||||||
\(186\) | −5.66475 | −0.415360 | ||||||||
\(187\) | −30.7372 | −2.24773 | ||||||||
\(188\) | 6.18748 | 0.451268 | ||||||||
\(189\) | 19.4933 | 1.41793 | ||||||||
\(190\) | 3.42347 | 0.248365 | ||||||||
\(191\) | 5.84116 | 0.422652 | 0.211326 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211326 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(192\) | 2.75508 | 0.198831 | ||||||||
\(193\) | −0.726448 | −0.0522908 | −0.0261454 | − | 0.999658i | \(-0.508323\pi\) | ||||
−0.0261454 | + | 0.999658i | \(0.508323\pi\) | |||||||
\(194\) | 7.30395 | 0.524393 | ||||||||
\(195\) | −6.77719 | −0.485325 | ||||||||
\(196\) | 12.7896 | 0.913540 | ||||||||
\(197\) | 10.1195 | 0.720987 | 0.360493 | − | 0.932762i | \(-0.382608\pi\) | ||||
0.360493 | + | 0.932762i | \(0.382608\pi\) | |||||||
\(198\) | 20.2078 | 1.43611 | ||||||||
\(199\) | 18.5869 | 1.31759 | 0.658795 | − | 0.752322i | \(-0.271066\pi\) | ||||
0.658795 | + | 0.752322i | \(0.271066\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 24.5221 | 1.72966 | ||||||||
\(202\) | −9.08953 | −0.639537 | ||||||||
\(203\) | 24.5286 | 1.72157 | ||||||||
\(204\) | −19.2371 | −1.34686 | ||||||||
\(205\) | −3.15936 | −0.220660 | ||||||||
\(206\) | 1.49900 | 0.104440 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.45989 | 0.170562 | ||||||||
\(209\) | −15.0705 | −1.04245 | ||||||||
\(210\) | −12.2561 | −0.845753 | ||||||||
\(211\) | 4.90443 | 0.337635 | 0.168817 | − | 0.985647i | \(-0.446005\pi\) | ||||
0.168817 | + | 0.985647i | \(0.446005\pi\) | |||||||
\(212\) | −1.99036 | −0.136698 | ||||||||
\(213\) | −29.9492 | −2.05209 | ||||||||
\(214\) | −17.7755 | −1.21511 | ||||||||
\(215\) | 2.76141 | 0.188327 | ||||||||
\(216\) | 4.38194 | 0.298153 | ||||||||
\(217\) | −9.14670 | −0.620918 | ||||||||
\(218\) | 18.9672 | 1.28462 | ||||||||
\(219\) | −23.6261 | −1.59651 | ||||||||
\(220\) | −4.40211 | −0.296790 | ||||||||
\(221\) | −17.1759 | −1.15537 | ||||||||
\(222\) | −18.5432 | −1.24454 | ||||||||
\(223\) | 9.71984 | 0.650888 | 0.325444 | − | 0.945561i | \(-0.394486\pi\) | ||||
0.325444 | + | 0.945561i | \(0.394486\pi\) | |||||||
\(224\) | 4.44855 | 0.297231 | ||||||||
\(225\) | 4.59049 | 0.306033 | ||||||||
\(226\) | −3.38804 | −0.225369 | ||||||||
\(227\) | 21.5002 | 1.42702 | 0.713509 | − | 0.700646i | \(-0.247105\pi\) | ||||
0.713509 | + | 0.700646i | \(0.247105\pi\) | |||||||
\(228\) | −9.43196 | −0.624647 | ||||||||
\(229\) | −5.38568 | −0.355896 | −0.177948 | − | 0.984040i | \(-0.556946\pi\) | ||||
−0.177948 | + | 0.984040i | \(0.556946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 53.9528 | 3.54983 | ||||||||
\(232\) | 5.51384 | 0.362001 | ||||||||
\(233\) | −29.3533 | −1.92300 | −0.961498 | − | 0.274811i | \(-0.911385\pi\) | ||||
−0.961498 | + | 0.274811i | \(0.911385\pi\) | |||||||
\(234\) | 11.2921 | 0.738187 | ||||||||
\(235\) | −6.18748 | −0.403627 | ||||||||
\(236\) | 2.00254 | 0.130354 | ||||||||
\(237\) | −32.6829 | −2.12298 | ||||||||
\(238\) | −31.0614 | −2.01341 | ||||||||
\(239\) | −8.09013 | −0.523307 | −0.261653 | − | 0.965162i | \(-0.584268\pi\) | ||||
−0.261653 | + | 0.965162i | \(0.584268\pi\) | |||||||
\(240\) | −2.75508 | −0.177840 | ||||||||
\(241\) | 11.4116 | 0.735088 | 0.367544 | − | 0.930006i | \(-0.380199\pi\) | ||||
0.367544 | + | 0.930006i | \(0.380199\pi\) | |||||||
\(242\) | 8.37857 | 0.538595 | ||||||||
\(243\) | −17.8263 | −1.14356 | ||||||||
\(244\) | −13.8042 | −0.883721 | ||||||||
\(245\) | −12.7896 | −0.817095 | ||||||||
\(246\) | 8.70432 | 0.554967 | ||||||||
\(247\) | −8.42135 | −0.535838 | ||||||||
\(248\) | −2.05611 | −0.130563 | ||||||||
\(249\) | 0.881185 | 0.0558428 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 11.7941 | 0.744436 | 0.372218 | − | 0.928145i | \(-0.378597\pi\) | ||||
0.372218 | + | 0.928145i | \(0.378597\pi\) | |||||||
\(252\) | 20.4210 | 1.28640 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.73551 | −0.359878 | ||||||||
\(255\) | 19.2371 | 1.20467 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.03939 | 0.127214 | 0.0636069 | − | 0.997975i | \(-0.479740\pi\) | ||||
0.0636069 | + | 0.997975i | \(0.479740\pi\) | |||||||
\(258\) | −7.60792 | −0.473648 | ||||||||
\(259\) | −29.9411 | −1.86045 | ||||||||
\(260\) | −2.45989 | −0.152556 | ||||||||
\(261\) | 25.3112 | 1.56673 | ||||||||
\(262\) | −10.6514 | −0.658047 | ||||||||
\(263\) | 24.7269 | 1.52473 | 0.762364 | − | 0.647149i | \(-0.224039\pi\) | ||||
0.762364 | + | 0.647149i | \(0.224039\pi\) | |||||||
\(264\) | 12.1282 | 0.746438 | ||||||||
\(265\) | 1.99036 | 0.122267 | ||||||||
\(266\) | −15.2295 | −0.933779 | ||||||||
\(267\) | 23.9643 | 1.46659 | ||||||||
\(268\) | 8.90067 | 0.543695 | ||||||||
\(269\) | 14.4785 | 0.882770 | 0.441385 | − | 0.897318i | \(-0.354487\pi\) | ||||
0.441385 | + | 0.897318i | \(0.354487\pi\) | |||||||
\(270\) | −4.38194 | −0.266676 | ||||||||
\(271\) | 19.7153 | 1.19762 | 0.598811 | − | 0.800890i | \(-0.295640\pi\) | ||||
0.598811 | + | 0.800890i | \(0.295640\pi\) | |||||||
\(272\) | −6.98238 | −0.423369 | ||||||||
\(273\) | 30.1487 | 1.82468 | ||||||||
\(274\) | 13.7187 | 0.828779 | ||||||||
\(275\) | 4.40211 | 0.265457 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.7803 | −1.36874 | −0.684368 | − | 0.729136i | \(-0.739922\pi\) | ||||
−0.684368 | + | 0.729136i | \(0.739922\pi\) | |||||||
\(278\) | −3.55749 | −0.213364 | ||||||||
\(279\) | −9.43855 | −0.565071 | ||||||||
\(280\) | −4.44855 | −0.265851 | ||||||||
\(281\) | 13.2608 | 0.791073 | 0.395536 | − | 0.918450i | \(-0.370559\pi\) | ||||
0.395536 | + | 0.918450i | \(0.370559\pi\) | |||||||
\(282\) | 17.0470 | 1.01514 | ||||||||
\(283\) | 7.87321 | 0.468014 | 0.234007 | − | 0.972235i | \(-0.424816\pi\) | ||||
0.234007 | + | 0.972235i | \(0.424816\pi\) | |||||||
\(284\) | −10.8705 | −0.645048 | ||||||||
\(285\) | 9.43196 | 0.558701 | ||||||||
\(286\) | 10.8287 | 0.640314 | ||||||||
\(287\) | 14.0546 | 0.829616 | ||||||||
\(288\) | 4.59049 | 0.270497 | ||||||||
\(289\) | 31.7536 | 1.86786 | ||||||||
\(290\) | −5.51384 | −0.323784 | ||||||||
\(291\) | 20.1230 | 1.17963 | ||||||||
\(292\) | −8.57546 | −0.501841 | ||||||||
\(293\) | 10.7456 | 0.627763 | 0.313881 | − | 0.949462i | \(-0.398371\pi\) | ||||
0.313881 | + | 0.949462i | \(0.398371\pi\) | |||||||
\(294\) | 35.2363 | 2.05502 | ||||||||
\(295\) | −2.00254 | −0.116592 | ||||||||
\(296\) | −6.73053 | −0.391204 | ||||||||
\(297\) | 19.2898 | 1.11931 | ||||||||
\(298\) | −8.65572 | −0.501412 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.75508 | 0.159065 | ||||||||
\(301\) | −12.2843 | −0.708053 | ||||||||
\(302\) | −1.76370 | −0.101490 | ||||||||
\(303\) | −25.0424 | −1.43865 | ||||||||
\(304\) | −3.42347 | −0.196350 | ||||||||
\(305\) | 13.8042 | 0.790424 | ||||||||
\(306\) | −32.0526 | −1.83232 | ||||||||
\(307\) | 1.33735 | 0.0763266 | 0.0381633 | − | 0.999272i | \(-0.487849\pi\) | ||||
0.0381633 | + | 0.999272i | \(0.487849\pi\) | |||||||
\(308\) | 19.5830 | 1.11584 | ||||||||
\(309\) | 4.12987 | 0.234940 | ||||||||
\(310\) | 2.05611 | 0.116779 | ||||||||
\(311\) | 7.12911 | 0.404255 | 0.202128 | − | 0.979359i | \(-0.435214\pi\) | ||||
0.202128 | + | 0.979359i | \(0.435214\pi\) | |||||||
\(312\) | 6.77719 | 0.383683 | ||||||||
\(313\) | −13.1855 | −0.745289 | −0.372645 | − | 0.927974i | \(-0.621549\pi\) | ||||
−0.372645 | + | 0.927974i | \(0.621549\pi\) | |||||||
\(314\) | −12.6015 | −0.711146 | ||||||||
\(315\) | −20.4210 | −1.15059 | ||||||||
\(316\) | −11.8628 | −0.667332 | ||||||||
\(317\) | 11.9822 | 0.672989 | 0.336494 | − | 0.941685i | \(-0.390759\pi\) | ||||
0.336494 | + | 0.941685i | \(0.390759\pi\) | |||||||
\(318\) | −5.48361 | −0.307505 | ||||||||
\(319\) | 24.2725 | 1.35900 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −48.9730 | −2.73341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.9040 | 1.33005 | ||||||||
\(324\) | −1.69886 | −0.0943809 | ||||||||
\(325\) | 2.45989 | 0.136450 | ||||||||
\(326\) | 2.07678 | 0.115022 | ||||||||
\(327\) | 52.2562 | 2.88978 | ||||||||
\(328\) | 3.15936 | 0.174447 | ||||||||
\(329\) | 27.5253 | 1.51752 | ||||||||
\(330\) | −12.1282 | −0.667635 | ||||||||
\(331\) | 11.5934 | 0.637229 | 0.318615 | − | 0.947884i | \(-0.396782\pi\) | ||||
0.318615 | + | 0.947884i | \(0.396782\pi\) | |||||||
\(332\) | 0.319840 | 0.0175535 | ||||||||
\(333\) | −30.8964 | −1.69311 | ||||||||
\(334\) | 3.48524 | 0.190704 | ||||||||
\(335\) | −8.90067 | −0.486296 | ||||||||
\(336\) | 12.2561 | 0.668626 | ||||||||
\(337\) | 6.87330 | 0.374412 | 0.187206 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187206 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(338\) | −6.94896 | −0.377974 | ||||||||
\(339\) | −9.33434 | −0.506972 | ||||||||
\(340\) | 6.98238 | 0.378673 | ||||||||
\(341\) | −9.05122 | −0.490151 | ||||||||
\(342\) | −15.7154 | −0.849793 | ||||||||
\(343\) | 25.7551 | 1.39065 | ||||||||
\(344\) | −2.76141 | −0.148885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.1699 | 1.24562 | ||||||||
\(347\) | 5.76727 | 0.309603 | 0.154802 | − | 0.987946i | \(-0.450526\pi\) | ||||
0.154802 | + | 0.987946i | \(0.450526\pi\) | |||||||
\(348\) | 15.1911 | 0.814328 | ||||||||
\(349\) | −16.4626 | −0.881220 | −0.440610 | − | 0.897699i | \(-0.645238\pi\) | ||||
−0.440610 | + | 0.897699i | \(0.645238\pi\) | |||||||
\(350\) | 4.44855 | 0.237785 | ||||||||
\(351\) | 10.7791 | 0.575344 | ||||||||
\(352\) | 4.40211 | 0.234633 | ||||||||
\(353\) | −22.8572 | −1.21657 | −0.608283 | − | 0.793720i | \(-0.708142\pi\) | ||||
−0.608283 | + | 0.793720i | \(0.708142\pi\) | |||||||
\(354\) | 5.51717 | 0.293234 | ||||||||
\(355\) | 10.8705 | 0.576948 | ||||||||
\(356\) | 8.69820 | 0.461004 | ||||||||
\(357\) | −85.5769 | −4.52921 | ||||||||
\(358\) | 1.26603 | 0.0669120 | ||||||||
\(359\) | 21.1272 | 1.11505 | 0.557526 | − | 0.830159i | \(-0.311751\pi\) | ||||
0.557526 | + | 0.830159i | \(0.311751\pi\) | |||||||
\(360\) | −4.59049 | −0.241940 | ||||||||
\(361\) | −7.27983 | −0.383149 | ||||||||
\(362\) | −18.3728 | −0.965655 | ||||||||
\(363\) | 23.0837 | 1.21158 | ||||||||
\(364\) | 10.9429 | 0.573565 | ||||||||
\(365\) | 8.57546 | 0.448860 | ||||||||
\(366\) | −38.0316 | −1.98795 | ||||||||
\(367\) | 12.1222 | 0.632773 | 0.316386 | − | 0.948630i | \(-0.397530\pi\) | ||||
0.316386 | + | 0.948630i | \(0.397530\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.5030 | 0.754998 | ||||||||
\(370\) | 6.73053 | 0.349904 | ||||||||
\(371\) | −8.85420 | −0.459687 | ||||||||
\(372\) | −5.66475 | −0.293704 | ||||||||
\(373\) | −18.1236 | −0.938402 | −0.469201 | − | 0.883091i | \(-0.655458\pi\) | ||||
−0.469201 | + | 0.883091i | \(0.655458\pi\) | |||||||
\(374\) | −30.7372 | −1.58938 | ||||||||
\(375\) | −2.75508 | −0.142272 | ||||||||
\(376\) | 6.18748 | 0.319095 | ||||||||
\(377\) | 13.5634 | 0.698551 | ||||||||
\(378\) | 19.4933 | 1.00263 | ||||||||
\(379\) | 18.0644 | 0.927906 | 0.463953 | − | 0.885860i | \(-0.346431\pi\) | ||||
0.463953 | + | 0.885860i | \(0.346431\pi\) | |||||||
\(380\) | 3.42347 | 0.175620 | ||||||||
\(381\) | −15.8018 | −0.809552 | ||||||||
\(382\) | 5.84116 | 0.298860 | ||||||||
\(383\) | 20.5709 | 1.05112 | 0.525561 | − | 0.850756i | \(-0.323855\pi\) | ||||
0.525561 | + | 0.850756i | \(0.323855\pi\) | |||||||
\(384\) | 2.75508 | 0.140595 | ||||||||
\(385\) | −19.5830 | −0.998041 | ||||||||
\(386\) | −0.726448 | −0.0369752 | ||||||||
\(387\) | −12.6762 | −0.644369 | ||||||||
\(388\) | 7.30395 | 0.370802 | ||||||||
\(389\) | −4.21880 | −0.213902 | −0.106951 | − | 0.994264i | \(-0.534109\pi\) | ||||
−0.106951 | + | 0.994264i | \(0.534109\pi\) | |||||||
\(390\) | −6.77719 | −0.343177 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 12.7896 | 0.645970 | ||||||||
\(393\) | −29.3456 | −1.48029 | ||||||||
\(394\) | 10.1195 | 0.509815 | ||||||||
\(395\) | 11.8628 | 0.596880 | ||||||||
\(396\) | 20.2078 | 1.01548 | ||||||||
\(397\) | 22.9773 | 1.15320 | 0.576598 | − | 0.817028i | \(-0.304380\pi\) | ||||
0.576598 | + | 0.817028i | \(0.304380\pi\) | |||||||
\(398\) | 18.5869 | 0.931677 | ||||||||
\(399\) | −41.9585 | −2.10055 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −30.9372 | −1.54493 | −0.772465 | − | 0.635057i | \(-0.780977\pi\) | ||||
−0.772465 | + | 0.635057i | \(0.780977\pi\) | |||||||
\(402\) | 24.5221 | 1.22305 | ||||||||
\(403\) | −5.05779 | −0.251947 | ||||||||
\(404\) | −9.08953 | −0.452221 | ||||||||
\(405\) | 1.69886 | 0.0844169 | ||||||||
\(406\) | 24.5286 | 1.21733 | ||||||||
\(407\) | −29.6285 | −1.46863 | ||||||||
\(408\) | −19.2371 | −0.952376 | ||||||||
\(409\) | 0.576257 | 0.0284941 | 0.0142470 | − | 0.999899i | \(-0.495465\pi\) | ||||
0.0142470 | + | 0.999899i | \(0.495465\pi\) | |||||||
\(410\) | −3.15936 | −0.156030 | ||||||||
\(411\) | 37.7963 | 1.86435 | ||||||||
\(412\) | 1.49900 | 0.0738504 | ||||||||
\(413\) | 8.90839 | 0.438353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.319840 | −0.0157003 | ||||||||
\(416\) | 2.45989 | 0.120606 | ||||||||
\(417\) | −9.80118 | −0.479966 | ||||||||
\(418\) | −15.0705 | −0.737122 | ||||||||
\(419\) | 7.93865 | 0.387828 | 0.193914 | − | 0.981018i | \(-0.437882\pi\) | ||||
0.193914 | + | 0.981018i | \(0.437882\pi\) | |||||||
\(420\) | −12.2561 | −0.598038 | ||||||||
\(421\) | 3.08985 | 0.150590 | 0.0752951 | − | 0.997161i | \(-0.476010\pi\) | ||||
0.0752951 | + | 0.997161i | \(0.476010\pi\) | |||||||
\(422\) | 4.90443 | 0.238744 | ||||||||
\(423\) | 28.4036 | 1.38103 | ||||||||
\(424\) | −1.99036 | −0.0966603 | ||||||||
\(425\) | −6.98238 | −0.338695 | ||||||||
\(426\) | −29.9492 | −1.45105 | ||||||||
\(427\) | −61.4085 | −2.97176 | ||||||||
\(428\) | −17.7755 | −0.859211 | ||||||||
\(429\) | 29.8339 | 1.44040 | ||||||||
\(430\) | 2.76141 | 0.133167 | ||||||||
\(431\) | 3.77328 | 0.181752 | 0.0908762 | − | 0.995862i | \(-0.471033\pi\) | ||||
0.0908762 | + | 0.995862i | \(0.471033\pi\) | |||||||
\(432\) | 4.38194 | 0.210826 | ||||||||
\(433\) | 8.51858 | 0.409377 | 0.204689 | − | 0.978827i | \(-0.434382\pi\) | ||||
0.204689 | + | 0.978827i | \(0.434382\pi\) | |||||||
\(434\) | −9.14670 | −0.439055 | ||||||||
\(435\) | −15.1911 | −0.728357 | ||||||||
\(436\) | 18.9672 | 0.908364 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −23.6261 | −1.12890 | ||||||||
\(439\) | −31.7255 | −1.51417 | −0.757087 | − | 0.653314i | \(-0.773378\pi\) | ||||
−0.757087 | + | 0.653314i | \(0.773378\pi\) | |||||||
\(440\) | −4.40211 | −0.209862 | ||||||||
\(441\) | 58.7104 | 2.79573 | ||||||||
\(442\) | −17.1759 | −0.816972 | ||||||||
\(443\) | 3.57155 | 0.169690 | 0.0848448 | − | 0.996394i | \(-0.472961\pi\) | ||||
0.0848448 | + | 0.996394i | \(0.472961\pi\) | |||||||
\(444\) | −18.5432 | −0.880020 | ||||||||
\(445\) | −8.69820 | −0.412334 | ||||||||
\(446\) | 9.71984 | 0.460248 | ||||||||
\(447\) | −23.8472 | −1.12794 | ||||||||
\(448\) | 4.44855 | 0.210174 | ||||||||
\(449\) | 31.6916 | 1.49562 | 0.747810 | − | 0.663913i | \(-0.231106\pi\) | ||||
0.747810 | + | 0.663913i | \(0.231106\pi\) | |||||||
\(450\) | 4.59049 | 0.216398 | ||||||||
\(451\) | 13.9079 | 0.654896 | ||||||||
\(452\) | −3.38804 | −0.159360 | ||||||||
\(453\) | −4.85915 | −0.228303 | ||||||||
\(454\) | 21.5002 | 1.00905 | ||||||||
\(455\) | −10.9429 | −0.513012 | ||||||||
\(456\) | −9.43196 | −0.441692 | ||||||||
\(457\) | −35.5083 | −1.66101 | −0.830503 | − | 0.557014i | \(-0.811947\pi\) | ||||
−0.830503 | + | 0.557014i | \(0.811947\pi\) | |||||||
\(458\) | −5.38568 | −0.251656 | ||||||||
\(459\) | −30.5964 | −1.42812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.4649 | −1.65177 | −0.825883 | − | 0.563842i | \(-0.809323\pi\) | ||||
−0.825883 | + | 0.563842i | \(0.809323\pi\) | |||||||
\(462\) | 53.9528 | 2.51011 | ||||||||
\(463\) | 3.37272 | 0.156744 | 0.0783719 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783719 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(464\) | 5.51384 | 0.255974 | ||||||||
\(465\) | 5.66475 | 0.262697 | ||||||||
\(466\) | −29.3533 | −1.35976 | ||||||||
\(467\) | 17.6398 | 0.816273 | 0.408136 | − | 0.912921i | \(-0.366179\pi\) | ||||
0.408136 | + | 0.912921i | \(0.366179\pi\) | |||||||
\(468\) | 11.2921 | 0.521977 | ||||||||
\(469\) | 39.5951 | 1.82833 | ||||||||
\(470\) | −6.18748 | −0.285407 | ||||||||
\(471\) | −34.7183 | −1.59973 | ||||||||
\(472\) | 2.00254 | 0.0921744 | ||||||||
\(473\) | −12.1560 | −0.558935 | ||||||||
\(474\) | −32.6829 | −1.50118 | ||||||||
\(475\) | −3.42347 | −0.157080 | ||||||||
\(476\) | −31.0614 | −1.42370 | ||||||||
\(477\) | −9.13673 | −0.418342 | ||||||||
\(478\) | −8.09013 | −0.370034 | ||||||||
\(479\) | −31.4181 | −1.43553 | −0.717766 | − | 0.696285i | \(-0.754835\pi\) | ||||
−0.717766 | + | 0.696285i | \(0.754835\pi\) | |||||||
\(480\) | −2.75508 | −0.125752 | ||||||||
\(481\) | −16.5563 | −0.754904 | ||||||||
\(482\) | 11.4116 | 0.519786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.37857 | 0.380844 | ||||||||
\(485\) | −7.30395 | −0.331655 | ||||||||
\(486\) | −17.8263 | −0.808618 | ||||||||
\(487\) | −2.67284 | −0.121118 | −0.0605590 | − | 0.998165i | \(-0.519288\pi\) | ||||
−0.0605590 | + | 0.998165i | \(0.519288\pi\) | |||||||
\(488\) | −13.8042 | −0.624885 | ||||||||
\(489\) | 5.72170 | 0.258744 | ||||||||
\(490\) | −12.7896 | −0.577774 | ||||||||
\(491\) | 6.39355 | 0.288537 | 0.144268 | − | 0.989539i | \(-0.453917\pi\) | ||||
0.144268 | + | 0.989539i | \(0.453917\pi\) | |||||||
\(492\) | 8.70432 | 0.392421 | ||||||||
\(493\) | −38.4997 | −1.73394 | ||||||||
\(494\) | −8.42135 | −0.378895 | ||||||||
\(495\) | −20.2078 | −0.908275 | ||||||||
\(496\) | −2.05611 | −0.0923220 | ||||||||
\(497\) | −48.3581 | −2.16916 | ||||||||
\(498\) | 0.881185 | 0.0394868 | ||||||||
\(499\) | −2.98791 | −0.133757 | −0.0668785 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668785 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 9.60214 | 0.428992 | ||||||||
\(502\) | 11.7941 | 0.526396 | ||||||||
\(503\) | −32.6689 | −1.45663 | −0.728316 | − | 0.685241i | \(-0.759697\pi\) | ||||
−0.728316 | + | 0.685241i | \(0.759697\pi\) | |||||||
\(504\) | 20.4210 | 0.909624 | ||||||||
\(505\) | 9.08953 | 0.404479 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1450 | −0.850259 | ||||||||
\(508\) | −5.73551 | −0.254472 | ||||||||
\(509\) | 6.90839 | 0.306209 | 0.153105 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153105 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(510\) | 19.2371 | 0.851831 | ||||||||
\(511\) | −38.1483 | −1.68758 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −15.0015 | −0.662331 | ||||||||
\(514\) | 2.03939 | 0.0899538 | ||||||||
\(515\) | −1.49900 | −0.0660538 | ||||||||
\(516\) | −7.60792 | −0.334920 | ||||||||
\(517\) | 27.2380 | 1.19792 | ||||||||
\(518\) | −29.9411 | −1.31554 | ||||||||
\(519\) | 63.8350 | 2.80205 | ||||||||
\(520\) | −2.45989 | −0.107873 | ||||||||
\(521\) | −25.5985 | −1.12149 | −0.560746 | − | 0.827988i | \(-0.689485\pi\) | ||||
−0.560746 | + | 0.827988i | \(0.689485\pi\) | |||||||
\(522\) | 25.3112 | 1.10784 | ||||||||
\(523\) | −38.7838 | −1.69590 | −0.847948 | − | 0.530080i | \(-0.822162\pi\) | ||||
−0.847948 | + | 0.530080i | \(0.822162\pi\) | |||||||
\(524\) | −10.6514 | −0.465310 | ||||||||
\(525\) | 12.2561 | 0.534901 | ||||||||
\(526\) | 24.7269 | 1.07815 | ||||||||
\(527\) | 14.3565 | 0.625380 | ||||||||
\(528\) | 12.1282 | 0.527811 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1.99036 | 0.0864556 | ||||||||
\(531\) | 9.19264 | 0.398927 | ||||||||
\(532\) | −15.2295 | −0.660282 | ||||||||
\(533\) | 7.77168 | 0.336629 | ||||||||
\(534\) | 23.9643 | 1.03704 | ||||||||
\(535\) | 17.7755 | 0.768501 | ||||||||
\(536\) | 8.90067 | 0.384451 | ||||||||
\(537\) | 3.48803 | 0.150520 | ||||||||
\(538\) | 14.4785 | 0.624213 | ||||||||
\(539\) | 56.3011 | 2.42506 | ||||||||
\(540\) | −4.38194 | −0.188569 | ||||||||
\(541\) | −12.2853 | −0.528186 | −0.264093 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264093 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(542\) | 19.7153 | 0.846847 | ||||||||
\(543\) | −50.6188 | −2.17226 | ||||||||
\(544\) | −6.98238 | −0.299367 | ||||||||
\(545\) | −18.9672 | −0.812465 | ||||||||
\(546\) | 30.1487 | 1.29024 | ||||||||
\(547\) | −40.4153 | −1.72803 | −0.864016 | − | 0.503465i | \(-0.832058\pi\) | ||||
−0.864016 | + | 0.503465i | \(0.832058\pi\) | |||||||
\(548\) | 13.7187 | 0.586035 | ||||||||
\(549\) | −63.3679 | −2.70448 | ||||||||
\(550\) | 4.40211 | 0.187707 | ||||||||
\(551\) | −18.8765 | −0.804165 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.7720 | −2.24409 | ||||||||
\(554\) | −22.7803 | −0.967843 | ||||||||
\(555\) | 18.5432 | 0.787114 | ||||||||
\(556\) | −3.55749 | −0.150871 | ||||||||
\(557\) | 20.7658 | 0.879874 | 0.439937 | − | 0.898029i | \(-0.355001\pi\) | ||||
0.439937 | + | 0.898029i | \(0.355001\pi\) | |||||||
\(558\) | −9.43855 | −0.399566 | ||||||||
\(559\) | −6.79275 | −0.287303 | ||||||||
\(560\) | −4.44855 | −0.187985 | ||||||||
\(561\) | −84.6836 | −3.57534 | ||||||||
\(562\) | 13.2608 | 0.559373 | ||||||||
\(563\) | −9.46288 | −0.398813 | −0.199406 | − | 0.979917i | \(-0.563901\pi\) | ||||
−0.199406 | + | 0.979917i | \(0.563901\pi\) | |||||||
\(564\) | 17.0470 | 0.717809 | ||||||||
\(565\) | 3.38804 | 0.142536 | ||||||||
\(566\) | 7.87321 | 0.330936 | ||||||||
\(567\) | −7.55744 | −0.317383 | ||||||||
\(568\) | −10.8705 | −0.456118 | ||||||||
\(569\) | 21.9043 | 0.918276 | 0.459138 | − | 0.888365i | \(-0.348158\pi\) | ||||
0.459138 | + | 0.888365i | \(0.348158\pi\) | |||||||
\(570\) | 9.43196 | 0.395061 | ||||||||
\(571\) | 15.5220 | 0.649575 | 0.324788 | − | 0.945787i | \(-0.394707\pi\) | ||||
0.324788 | + | 0.945787i | \(0.394707\pi\) | |||||||
\(572\) | 10.8287 | 0.452770 | ||||||||
\(573\) | 16.0929 | 0.672291 | ||||||||
\(574\) | 14.0546 | 0.586627 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.59049 | 0.191271 | ||||||||
\(577\) | −42.9640 | −1.78862 | −0.894308 | − | 0.447452i | \(-0.852331\pi\) | ||||
−0.894308 | + | 0.447452i | \(0.852331\pi\) | |||||||
\(578\) | 31.7536 | 1.32078 | ||||||||
\(579\) | −2.00142 | −0.0831764 | ||||||||
\(580\) | −5.51384 | −0.228950 | ||||||||
\(581\) | 1.42282 | 0.0590286 | ||||||||
\(582\) | 20.1230 | 0.834125 | ||||||||
\(583\) | −8.76178 | −0.362876 | ||||||||
\(584\) | −8.57546 | −0.354855 | ||||||||
\(585\) | −11.2921 | −0.466870 | ||||||||
\(586\) | 10.7456 | 0.443895 | ||||||||
\(587\) | 35.7584 | 1.47591 | 0.737954 | − | 0.674852i | \(-0.235792\pi\) | ||||
0.737954 | + | 0.674852i | \(0.235792\pi\) | |||||||
\(588\) | 35.2363 | 1.45312 | ||||||||
\(589\) | 7.03903 | 0.290038 | ||||||||
\(590\) | −2.00254 | −0.0824433 | ||||||||
\(591\) | 27.8802 | 1.14684 | ||||||||
\(592\) | −6.73053 | −0.276623 | ||||||||
\(593\) | −35.7883 | −1.46965 | −0.734824 | − | 0.678258i | \(-0.762735\pi\) | ||||
−0.734824 | + | 0.678258i | \(0.762735\pi\) | |||||||
\(594\) | 19.2898 | 0.791469 | ||||||||
\(595\) | 31.0614 | 1.27339 | ||||||||
\(596\) | −8.65572 | −0.354552 | ||||||||
\(597\) | 51.2085 | 2.09582 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.5055 | 1.77759 | 0.888794 | − | 0.458307i | \(-0.151544\pi\) | ||||
0.888794 | + | 0.458307i | \(0.151544\pi\) | |||||||
\(600\) | 2.75508 | 0.112476 | ||||||||
\(601\) | −34.9867 | −1.42714 | −0.713569 | − | 0.700585i | \(-0.752923\pi\) | ||||
−0.713569 | + | 0.700585i | \(0.752923\pi\) | |||||||
\(602\) | −12.2843 | −0.500669 | ||||||||
\(603\) | 40.8585 | 1.66389 | ||||||||
\(604\) | −1.76370 | −0.0717640 | ||||||||
\(605\) | −8.37857 | −0.340637 | ||||||||
\(606\) | −25.0424 | −1.01728 | ||||||||
\(607\) | 18.5267 | 0.751974 | 0.375987 | − | 0.926625i | \(-0.377304\pi\) | ||||
0.375987 | + | 0.926625i | \(0.377304\pi\) | |||||||
\(608\) | −3.42347 | −0.138840 | ||||||||
\(609\) | 67.5783 | 2.73841 | ||||||||
\(610\) | 13.8042 | 0.558914 | ||||||||
\(611\) | 15.2205 | 0.615755 | ||||||||
\(612\) | −32.0526 | −1.29565 | ||||||||
\(613\) | 16.0330 | 0.647568 | 0.323784 | − | 0.946131i | \(-0.395045\pi\) | ||||
0.323784 | + | 0.946131i | \(0.395045\pi\) | |||||||
\(614\) | 1.33735 | 0.0539711 | ||||||||
\(615\) | −8.70432 | −0.350992 | ||||||||
\(616\) | 19.5830 | 0.789021 | ||||||||
\(617\) | 11.4406 | 0.460581 | 0.230291 | − | 0.973122i | \(-0.426032\pi\) | ||||
0.230291 | + | 0.973122i | \(0.426032\pi\) | |||||||
\(618\) | 4.12987 | 0.166128 | ||||||||
\(619\) | −9.90379 | −0.398067 | −0.199033 | − | 0.979993i | \(-0.563780\pi\) | ||||
−0.199033 | + | 0.979993i | \(0.563780\pi\) | |||||||
\(620\) | 2.05611 | 0.0825753 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.12911 | 0.285851 | ||||||||
\(623\) | 38.6944 | 1.55026 | ||||||||
\(624\) | 6.77719 | 0.271305 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.1855 | −0.526999 | ||||||||
\(627\) | −41.5205 | −1.65817 | ||||||||
\(628\) | −12.6015 | −0.502856 | ||||||||
\(629\) | 46.9951 | 1.87382 | ||||||||
\(630\) | −20.4210 | −0.813593 | ||||||||
\(631\) | −23.1560 | −0.921828 | −0.460914 | − | 0.887445i | \(-0.652478\pi\) | ||||
−0.460914 | + | 0.887445i | \(0.652478\pi\) | |||||||
\(632\) | −11.8628 | −0.471875 | ||||||||
\(633\) | 13.5121 | 0.537058 | ||||||||
\(634\) | 11.9822 | 0.475875 | ||||||||
\(635\) | 5.73551 | 0.227607 | ||||||||
\(636\) | −5.48361 | −0.217439 | ||||||||
\(637\) | 31.4609 | 1.24652 | ||||||||
\(638\) | 24.2725 | 0.960958 | ||||||||
\(639\) | −49.9011 | −1.97406 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 10.8851 | 0.429938 | 0.214969 | − | 0.976621i | \(-0.431035\pi\) | ||||
0.214969 | + | 0.976621i | \(0.431035\pi\) | |||||||
\(642\) | −48.9730 | −1.93281 | ||||||||
\(643\) | −38.3078 | −1.51071 | −0.755356 | − | 0.655315i | \(-0.772536\pi\) | ||||
−0.755356 | + | 0.655315i | \(0.772536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.60792 | 0.299561 | ||||||||
\(646\) | 23.9040 | 0.940490 | ||||||||
\(647\) | −31.6382 | −1.24382 | −0.621912 | − | 0.783087i | \(-0.713644\pi\) | ||||
−0.621912 | + | 0.783087i | \(0.713644\pi\) | |||||||
\(648\) | −1.69886 | −0.0667374 | ||||||||
\(649\) | 8.81540 | 0.346035 | ||||||||
\(650\) | 2.45989 | 0.0964846 | ||||||||
\(651\) | −25.1999 | −0.987663 | ||||||||
\(652\) | 2.07678 | 0.0813329 | ||||||||
\(653\) | −21.8844 | −0.856404 | −0.428202 | − | 0.903683i | \(-0.640853\pi\) | ||||
−0.428202 | + | 0.903683i | \(0.640853\pi\) | |||||||
\(654\) | 52.2562 | 2.04338 | ||||||||
\(655\) | 10.6514 | 0.416186 | ||||||||
\(656\) | 3.15936 | 0.123352 | ||||||||
\(657\) | −39.3656 | −1.53580 | ||||||||
\(658\) | 27.5253 | 1.07305 | ||||||||
\(659\) | 14.4063 | 0.561191 | 0.280595 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280595 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(660\) | −12.1282 | −0.472089 | ||||||||
\(661\) | −2.90302 | −0.112914 | −0.0564571 | − | 0.998405i | \(-0.517980\pi\) | ||||
−0.0564571 | + | 0.998405i | \(0.517980\pi\) | |||||||
\(662\) | 11.5934 | 0.450589 | ||||||||
\(663\) | −47.3209 | −1.83779 | ||||||||
\(664\) | 0.319840 | 0.0124122 | ||||||||
\(665\) | 15.2295 | 0.590574 | ||||||||
\(666\) | −30.8964 | −1.19721 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 3.48524 | 0.134848 | ||||||||
\(669\) | 26.7790 | 1.03533 | ||||||||
\(670\) | −8.90067 | −0.343863 | ||||||||
\(671\) | −60.7674 | −2.34590 | ||||||||
\(672\) | 12.2561 | 0.472790 | ||||||||
\(673\) | 13.9422 | 0.537433 | 0.268717 | − | 0.963219i | \(-0.413400\pi\) | ||||
0.268717 | + | 0.963219i | \(0.413400\pi\) | |||||||
\(674\) | 6.87330 | 0.264749 | ||||||||
\(675\) | 4.38194 | 0.168661 | ||||||||
\(676\) | −6.94896 | −0.267268 | ||||||||
\(677\) | −14.1958 | −0.545591 | −0.272795 | − | 0.962072i | \(-0.587948\pi\) | ||||
−0.272795 | + | 0.962072i | \(0.587948\pi\) | |||||||
\(678\) | −9.33434 | −0.358483 | ||||||||
\(679\) | 32.4919 | 1.24693 | ||||||||
\(680\) | 6.98238 | 0.267762 | ||||||||
\(681\) | 59.2349 | 2.26988 | ||||||||
\(682\) | −9.05122 | −0.346589 | ||||||||
\(683\) | −0.587432 | −0.0224775 | −0.0112387 | − | 0.999937i | \(-0.503577\pi\) | ||||
−0.0112387 | + | 0.999937i | \(0.503577\pi\) | |||||||
\(684\) | −15.7154 | −0.600894 | ||||||||
\(685\) | −13.7187 | −0.524166 | ||||||||
\(686\) | 25.7551 | 0.983336 | ||||||||
\(687\) | −14.8380 | −0.566105 | ||||||||
\(688\) | −2.76141 | −0.105278 | ||||||||
\(689\) | −4.89605 | −0.186525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.3834 | −1.42213 | −0.711066 | − | 0.703126i | \(-0.751787\pi\) | ||||
−0.711066 | + | 0.703126i | \(0.751787\pi\) | |||||||
\(692\) | 23.1699 | 0.880787 | ||||||||
\(693\) | 89.8955 | 3.41485 | ||||||||
\(694\) | 5.76727 | 0.218923 | ||||||||
\(695\) | 3.55749 | 0.134943 | ||||||||
\(696\) | 15.1911 | 0.575817 | ||||||||
\(697\) | −22.0599 | −0.835578 | ||||||||
\(698\) | −16.4626 | −0.623117 | ||||||||
\(699\) | −80.8707 | −3.05881 | ||||||||
\(700\) | 4.44855 | 0.168139 | ||||||||
\(701\) | 18.6885 | 0.705857 | 0.352928 | − | 0.935650i | \(-0.385186\pi\) | ||||
0.352928 | + | 0.935650i | \(0.385186\pi\) | |||||||
\(702\) | 10.7791 | 0.406830 | ||||||||
\(703\) | 23.0418 | 0.869037 | ||||||||
\(704\) | 4.40211 | 0.165911 | ||||||||
\(705\) | −17.0470 | −0.642028 | ||||||||
\(706\) | −22.8572 | −0.860243 | ||||||||
\(707\) | −40.4352 | −1.52072 | ||||||||
\(708\) | 5.51717 | 0.207348 | ||||||||
\(709\) | 41.3053 | 1.55125 | 0.775627 | − | 0.631192i | \(-0.217434\pi\) | ||||
0.775627 | + | 0.631192i | \(0.217434\pi\) | |||||||
\(710\) | 10.8705 | 0.407964 | ||||||||
\(711\) | −54.4559 | −2.04226 | ||||||||
\(712\) | 8.69820 | 0.325979 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −85.5769 | −3.20264 | ||||||||
\(715\) | −10.8287 | −0.404970 | ||||||||
\(716\) | 1.26603 | 0.0473139 | ||||||||
\(717\) | −22.2890 | −0.832397 | ||||||||
\(718\) | 21.1272 | 0.788461 | ||||||||
\(719\) | 36.3270 | 1.35477 | 0.677383 | − | 0.735630i | \(-0.263114\pi\) | ||||
0.677383 | + | 0.735630i | \(0.263114\pi\) | |||||||
\(720\) | −4.59049 | −0.171078 | ||||||||
\(721\) | 6.66837 | 0.248343 | ||||||||
\(722\) | −7.27983 | −0.270927 | ||||||||
\(723\) | 31.4400 | 1.16927 | ||||||||
\(724\) | −18.3728 | −0.682822 | ||||||||
\(725\) | 5.51384 | 0.204779 | ||||||||
\(726\) | 23.0837 | 0.856715 | ||||||||
\(727\) | −5.17645 | −0.191984 | −0.0959920 | − | 0.995382i | \(-0.530602\pi\) | ||||
−0.0959920 | + | 0.995382i | \(0.530602\pi\) | |||||||
\(728\) | 10.9429 | 0.405571 | ||||||||
\(729\) | −44.0165 | −1.63024 | ||||||||
\(730\) | 8.57546 | 0.317392 | ||||||||
\(731\) | 19.2812 | 0.713141 | ||||||||
\(732\) | −38.0316 | −1.40569 | ||||||||
\(733\) | −3.74165 | −0.138201 | −0.0691006 | − | 0.997610i | \(-0.522013\pi\) | ||||
−0.0691006 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(734\) | 12.1222 | 0.447438 | ||||||||
\(735\) | −35.2363 | −1.29971 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.1817 | 1.44328 | ||||||||
\(738\) | 14.5030 | 0.533864 | ||||||||
\(739\) | −15.7153 | −0.578097 | −0.289049 | − | 0.957314i | \(-0.593339\pi\) | ||||
−0.289049 | + | 0.957314i | \(0.593339\pi\) | |||||||
\(740\) | 6.73053 | 0.247419 | ||||||||
\(741\) | −23.2015 | −0.852330 | ||||||||
\(742\) | −8.85420 | −0.325048 | ||||||||
\(743\) | 48.5703 | 1.78187 | 0.890936 | − | 0.454130i | \(-0.150050\pi\) | ||||
0.890936 | + | 0.454130i | \(0.150050\pi\) | |||||||
\(744\) | −5.66475 | −0.207680 | ||||||||
\(745\) | 8.65572 | 0.317121 | ||||||||
\(746\) | −18.1236 | −0.663551 | ||||||||
\(747\) | 1.46822 | 0.0537194 | ||||||||
\(748\) | −30.7372 | −1.12386 | ||||||||
\(749\) | −79.0751 | −2.88934 | ||||||||
\(750\) | −2.75508 | −0.100601 | ||||||||
\(751\) | −36.1176 | −1.31795 | −0.658975 | − | 0.752165i | \(-0.729010\pi\) | ||||
−0.658975 | + | 0.752165i | \(0.729010\pi\) | |||||||
\(752\) | 6.18748 | 0.225634 | ||||||||
\(753\) | 32.4937 | 1.18414 | ||||||||
\(754\) | 13.5634 | 0.493950 | ||||||||
\(755\) | 1.76370 | 0.0641877 | ||||||||
\(756\) | 19.4933 | 0.708963 | ||||||||
\(757\) | 16.6016 | 0.603397 | 0.301698 | − | 0.953403i | \(-0.402446\pi\) | ||||
0.301698 | + | 0.953403i | \(0.402446\pi\) | |||||||
\(758\) | 18.0644 | 0.656129 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.42347 | 0.124182 | ||||||||
\(761\) | −10.6287 | −0.385291 | −0.192645 | − | 0.981268i | \(-0.561707\pi\) | ||||
−0.192645 | + | 0.981268i | \(0.561707\pi\) | |||||||
\(762\) | −15.8018 | −0.572440 | ||||||||
\(763\) | 84.3764 | 3.05463 | ||||||||
\(764\) | 5.84116 | 0.211326 | ||||||||
\(765\) | 32.0526 | 1.15886 | ||||||||
\(766\) | 20.5709 | 0.743256 | ||||||||
\(767\) | 4.92602 | 0.177868 | ||||||||
\(768\) | 2.75508 | 0.0994156 | ||||||||
\(769\) | −42.5639 | −1.53489 | −0.767446 | − | 0.641113i | \(-0.778473\pi\) | ||||
−0.767446 | + | 0.641113i | \(0.778473\pi\) | |||||||
\(770\) | −19.5830 | −0.705722 | ||||||||
\(771\) | 5.61870 | 0.202353 | ||||||||
\(772\) | −0.726448 | −0.0261454 | ||||||||
\(773\) | −23.6457 | −0.850475 | −0.425238 | − | 0.905082i | \(-0.639810\pi\) | ||||
−0.425238 | + | 0.905082i | \(0.639810\pi\) | |||||||
\(774\) | −12.6762 | −0.455638 | ||||||||
\(775\) | −2.05611 | −0.0738576 | ||||||||
\(776\) | 7.30395 | 0.262196 | ||||||||
\(777\) | −82.4902 | −2.95932 | ||||||||
\(778\) | −4.21880 | −0.151251 | ||||||||
\(779\) | −10.8160 | −0.387523 | ||||||||
\(780\) | −6.77719 | −0.242662 | ||||||||
\(781\) | −47.8533 | −1.71233 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.1613 | 0.863455 | ||||||||
\(784\) | 12.7896 | 0.456770 | ||||||||
\(785\) | 12.6015 | 0.449768 | ||||||||
\(786\) | −29.3456 | −1.04672 | ||||||||
\(787\) | −47.0801 | −1.67822 | −0.839112 | − | 0.543959i | \(-0.816925\pi\) | ||||
−0.839112 | + | 0.543959i | \(0.816925\pi\) | |||||||
\(788\) | 10.1195 | 0.360493 | ||||||||
\(789\) | 68.1248 | 2.42531 | ||||||||
\(790\) | 11.8628 | 0.422058 | ||||||||
\(791\) | −15.0719 | −0.535893 | ||||||||
\(792\) | 20.2078 | 0.718055 | ||||||||
\(793\) | −33.9567 | −1.20584 | ||||||||
\(794\) | 22.9773 | 0.815433 | ||||||||
\(795\) | 5.48361 | 0.194483 | ||||||||
\(796\) | 18.5869 | 0.658795 | ||||||||
\(797\) | −15.0160 | −0.531894 | −0.265947 | − | 0.963988i | \(-0.585685\pi\) | ||||
−0.265947 | + | 0.963988i | \(0.585685\pi\) | |||||||
\(798\) | −41.9585 | −1.48531 | ||||||||
\(799\) | −43.2033 | −1.52842 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 39.9290 | 1.41082 | ||||||||
\(802\) | −30.9372 | −1.09243 | ||||||||
\(803\) | −37.7501 | −1.33217 | ||||||||
\(804\) | 24.5221 | 0.864828 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.05779 | −0.178153 | ||||||||
\(807\) | 39.8895 | 1.40418 | ||||||||
\(808\) | −9.08953 | −0.319769 | ||||||||
\(809\) | −47.7657 | −1.67935 | −0.839675 | − | 0.543088i | \(-0.817255\pi\) | ||||
−0.839675 | + | 0.543088i | \(0.817255\pi\) | |||||||
\(810\) | 1.69886 | 0.0596917 | ||||||||
\(811\) | 55.8820 | 1.96228 | 0.981142 | − | 0.193289i | \(-0.0619154\pi\) | ||||
0.981142 | + | 0.193289i | \(0.0619154\pi\) | |||||||
\(812\) | 24.5286 | 0.860784 | ||||||||
\(813\) | 54.3174 | 1.90500 | ||||||||
\(814\) | −29.6285 | −1.03848 | ||||||||
\(815\) | −2.07678 | −0.0727464 | ||||||||
\(816\) | −19.2371 | −0.673431 | ||||||||
\(817\) | 9.45361 | 0.330740 | ||||||||
\(818\) | 0.576257 | 0.0201484 | ||||||||
\(819\) | 50.2334 | 1.75530 | ||||||||
\(820\) | −3.15936 | −0.110330 | ||||||||
\(821\) | −7.19232 | −0.251014 | −0.125507 | − | 0.992093i | \(-0.540056\pi\) | ||||
−0.125507 | + | 0.992093i | \(0.540056\pi\) | |||||||
\(822\) | 37.7963 | 1.31830 | ||||||||
\(823\) | 12.3438 | 0.430278 | 0.215139 | − | 0.976583i | \(-0.430980\pi\) | ||||
0.215139 | + | 0.976583i | \(0.430980\pi\) | |||||||
\(824\) | 1.49900 | 0.0522201 | ||||||||
\(825\) | 12.1282 | 0.422249 | ||||||||
\(826\) | 8.90839 | 0.309963 | ||||||||
\(827\) | 48.0835 | 1.67203 | 0.836013 | − | 0.548710i | \(-0.184881\pi\) | ||||
0.836013 | + | 0.548710i | \(0.184881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8346 | 1.27932 | 0.639658 | − | 0.768659i | \(-0.279076\pi\) | ||||
0.639658 | + | 0.768659i | \(0.279076\pi\) | |||||||
\(830\) | −0.319840 | −0.0111018 | ||||||||
\(831\) | −62.7617 | −2.17718 | ||||||||
\(832\) | 2.45989 | 0.0852812 | ||||||||
\(833\) | −89.3016 | −3.09412 | ||||||||
\(834\) | −9.80118 | −0.339387 | ||||||||
\(835\) | −3.48524 | −0.120612 | ||||||||
\(836\) | −15.0705 | −0.521224 | ||||||||
\(837\) | −9.00975 | −0.311422 | ||||||||
\(838\) | 7.93865 | 0.274236 | ||||||||
\(839\) | −15.9647 | −0.551164 | −0.275582 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275582 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(840\) | −12.2561 | −0.422876 | ||||||||
\(841\) | 1.40242 | 0.0483595 | ||||||||
\(842\) | 3.08985 | 0.106483 | ||||||||
\(843\) | 36.5346 | 1.25832 | ||||||||
\(844\) | 4.90443 | 0.168817 | ||||||||
\(845\) | 6.94896 | 0.239052 | ||||||||
\(846\) | 28.4036 | 0.976535 | ||||||||
\(847\) | 37.2724 | 1.28070 | ||||||||
\(848\) | −1.99036 | −0.0683492 | ||||||||
\(849\) | 21.6914 | 0.744446 | ||||||||
\(850\) | −6.98238 | −0.239494 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −29.9492 | −1.02604 | ||||||||
\(853\) | 28.0441 | 0.960213 | 0.480107 | − | 0.877210i | \(-0.340598\pi\) | ||||
0.480107 | + | 0.877210i | \(0.340598\pi\) | |||||||
\(854\) | −61.4085 | −2.10135 | ||||||||
\(855\) | 15.7154 | 0.537456 | ||||||||
\(856\) | −17.7755 | −0.607554 | ||||||||
\(857\) | −4.37547 | −0.149463 | −0.0747316 | − | 0.997204i | \(-0.523810\pi\) | ||||
−0.0747316 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(858\) | 29.8339 | 1.01851 | ||||||||
\(859\) | −6.77691 | −0.231225 | −0.115613 | − | 0.993294i | \(-0.536883\pi\) | ||||
−0.115613 | + | 0.993294i | \(0.536883\pi\) | |||||||
\(860\) | 2.76141 | 0.0941633 | ||||||||
\(861\) | 38.7216 | 1.31963 | ||||||||
\(862\) | 3.77328 | 0.128518 | ||||||||
\(863\) | 25.2591 | 0.859830 | 0.429915 | − | 0.902869i | \(-0.358544\pi\) | ||||
0.429915 | + | 0.902869i | \(0.358544\pi\) | |||||||
\(864\) | 4.38194 | 0.149077 | ||||||||
\(865\) | −23.1699 | −0.787800 | ||||||||
\(866\) | 8.51858 | 0.289473 | ||||||||
\(867\) | 87.4840 | 2.97111 | ||||||||
\(868\) | −9.14670 | −0.310459 | ||||||||
\(869\) | −52.2211 | −1.77148 | ||||||||
\(870\) | −15.1911 | −0.515026 | ||||||||
\(871\) | 21.8946 | 0.741872 | ||||||||
\(872\) | 18.9672 | 0.642310 | ||||||||
\(873\) | 33.5287 | 1.13478 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.44855 | −0.150388 | ||||||||
\(876\) | −23.6261 | −0.798253 | ||||||||
\(877\) | 56.1429 | 1.89581 | 0.947906 | − | 0.318550i | \(-0.103196\pi\) | ||||
0.947906 | + | 0.318550i | \(0.103196\pi\) | |||||||
\(878\) | −31.7255 | −1.07068 | ||||||||
\(879\) | 29.6050 | 0.998550 | ||||||||
\(880\) | −4.40211 | −0.148395 | ||||||||
\(881\) | −16.0725 | −0.541497 | −0.270749 | − | 0.962650i | \(-0.587271\pi\) | ||||
−0.270749 | + | 0.962650i | \(0.587271\pi\) | |||||||
\(882\) | 58.7104 | 1.97688 | ||||||||
\(883\) | −51.9366 | −1.74781 | −0.873903 | − | 0.486100i | \(-0.838419\pi\) | ||||
−0.873903 | + | 0.486100i | \(0.838419\pi\) | |||||||
\(884\) | −17.1759 | −0.577687 | ||||||||
\(885\) | −5.51717 | −0.185458 | ||||||||
\(886\) | 3.57155 | 0.119989 | ||||||||
\(887\) | 9.49221 | 0.318717 | 0.159359 | − | 0.987221i | \(-0.449057\pi\) | ||||
0.159359 | + | 0.987221i | \(0.449057\pi\) | |||||||
\(888\) | −18.5432 | −0.622268 | ||||||||
\(889\) | −25.5147 | −0.855736 | ||||||||
\(890\) | −8.69820 | −0.291564 | ||||||||
\(891\) | −7.47855 | −0.250541 | ||||||||
\(892\) | 9.71984 | 0.325444 | ||||||||
\(893\) | −21.1827 | −0.708851 | ||||||||
\(894\) | −23.8472 | −0.797571 | ||||||||
\(895\) | −1.26603 | −0.0423189 | ||||||||
\(896\) | 4.44855 | 0.148615 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.6916 | 1.05756 | ||||||||
\(899\) | −11.3371 | −0.378112 | ||||||||
\(900\) | 4.59049 | 0.153016 | ||||||||
\(901\) | 13.8974 | 0.462991 | ||||||||
\(902\) | 13.9079 | 0.463081 | ||||||||
\(903\) | −33.8442 | −1.12626 | ||||||||
\(904\) | −3.38804 | −0.112685 | ||||||||
\(905\) | 18.3728 | 0.610734 | ||||||||
\(906\) | −4.85915 | −0.161434 | ||||||||
\(907\) | 22.6681 | 0.752680 | 0.376340 | − | 0.926482i | \(-0.377182\pi\) | ||||
0.376340 | + | 0.926482i | \(0.377182\pi\) | |||||||
\(908\) | 21.5002 | 0.713509 | ||||||||
\(909\) | −41.7254 | −1.38394 | ||||||||
\(910\) | −10.9429 | −0.362754 | ||||||||
\(911\) | 18.0437 | 0.597815 | 0.298908 | − | 0.954282i | \(-0.403378\pi\) | ||||
0.298908 | + | 0.954282i | \(0.403378\pi\) | |||||||
\(912\) | −9.43196 | −0.312323 | ||||||||
\(913\) | 1.40797 | 0.0465970 | ||||||||
\(914\) | −35.5083 | −1.17451 | ||||||||
\(915\) | 38.0316 | 1.25729 | ||||||||
\(916\) | −5.38568 | −0.177948 | ||||||||
\(917\) | −47.3834 | −1.56474 | ||||||||
\(918\) | −30.5964 | −1.00983 | ||||||||
\(919\) | −3.42259 | −0.112901 | −0.0564505 | − | 0.998405i | \(-0.517978\pi\) | ||||
−0.0564505 | + | 0.998405i | \(0.517978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.68451 | 0.121409 | ||||||||
\(922\) | −35.4649 | −1.16797 | ||||||||
\(923\) | −26.7403 | −0.880167 | ||||||||
\(924\) | 53.9528 | 1.77492 | ||||||||
\(925\) | −6.73053 | −0.221298 | ||||||||
\(926\) | 3.37272 | 0.110835 | ||||||||
\(927\) | 6.88115 | 0.226007 | ||||||||
\(928\) | 5.51384 | 0.181001 | ||||||||
\(929\) | 5.28457 | 0.173381 | 0.0866906 | − | 0.996235i | \(-0.472371\pi\) | ||||
0.0866906 | + | 0.996235i | \(0.472371\pi\) | |||||||
\(930\) | 5.66475 | 0.185755 | ||||||||
\(931\) | −43.7847 | −1.43499 | ||||||||
\(932\) | −29.3533 | −0.961498 | ||||||||
\(933\) | 19.6413 | 0.643028 | ||||||||
\(934\) | 17.6398 | 0.577192 | ||||||||
\(935\) | 30.7372 | 1.00521 | ||||||||
\(936\) | 11.2921 | 0.369093 | ||||||||
\(937\) | −9.57867 | −0.312921 | −0.156461 | − | 0.987684i | \(-0.550008\pi\) | ||||
−0.156461 | + | 0.987684i | \(0.550008\pi\) | |||||||
\(938\) | 39.5951 | 1.29282 | ||||||||
\(939\) | −36.3272 | −1.18549 | ||||||||
\(940\) | −6.18748 | −0.201813 | ||||||||
\(941\) | −18.7350 | −0.610744 | −0.305372 | − | 0.952233i | \(-0.598781\pi\) | ||||
−0.305372 | + | 0.952233i | \(0.598781\pi\) | |||||||
\(942\) | −34.7183 | −1.13118 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.00254 | 0.0651771 | ||||||||
\(945\) | −19.4933 | −0.634116 | ||||||||
\(946\) | −12.1560 | −0.395226 | ||||||||
\(947\) | 48.5733 | 1.57842 | 0.789211 | − | 0.614122i | \(-0.210490\pi\) | ||||
0.789211 | + | 0.614122i | \(0.210490\pi\) | |||||||
\(948\) | −32.6829 | −1.06149 | ||||||||
\(949\) | −21.0947 | −0.684761 | ||||||||
\(950\) | −3.42347 | −0.111072 | ||||||||
\(951\) | 33.0120 | 1.07049 | ||||||||
\(952\) | −31.0614 | −1.00671 | ||||||||
\(953\) | 3.40802 | 0.110397 | 0.0551983 | − | 0.998475i | \(-0.482421\pi\) | ||||
0.0551983 | + | 0.998475i | \(0.482421\pi\) | |||||||
\(954\) | −9.13673 | −0.295812 | ||||||||
\(955\) | −5.84116 | −0.189016 | ||||||||
\(956\) | −8.09013 | −0.261653 | ||||||||
\(957\) | 66.8729 | 2.16169 | ||||||||
\(958\) | −31.4181 | −1.01507 | ||||||||
\(959\) | 61.0284 | 1.97071 | ||||||||
\(960\) | −2.75508 | −0.0889200 | ||||||||
\(961\) | −26.7724 | −0.863626 | ||||||||
\(962\) | −16.5563 | −0.533798 | ||||||||
\(963\) | −81.5982 | −2.62947 | ||||||||
\(964\) | 11.4116 | 0.367544 | ||||||||
\(965\) | 0.726448 | 0.0233852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2945 | −0.427524 | −0.213762 | − | 0.976886i | \(-0.568572\pi\) | ||||
−0.213762 | + | 0.976886i | \(0.568572\pi\) | |||||||
\(968\) | 8.37857 | 0.269297 | ||||||||
\(969\) | 65.8575 | 2.11565 | ||||||||
\(970\) | −7.30395 | −0.234516 | ||||||||
\(971\) | −9.61364 | −0.308516 | −0.154258 | − | 0.988031i | \(-0.549299\pi\) | ||||
−0.154258 | + | 0.988031i | \(0.549299\pi\) | |||||||
\(972\) | −17.8263 | −0.571779 | ||||||||
\(973\) | −15.8256 | −0.507347 | ||||||||
\(974\) | −2.67284 | −0.0856434 | ||||||||
\(975\) | 6.77719 | 0.217044 | ||||||||
\(976\) | −13.8042 | −0.441861 | ||||||||
\(977\) | −49.8942 | −1.59626 | −0.798129 | − | 0.602487i | \(-0.794177\pi\) | ||||
−0.798129 | + | 0.602487i | \(0.794177\pi\) | |||||||
\(978\) | 5.72170 | 0.182960 | ||||||||
\(979\) | 38.2904 | 1.22377 | ||||||||
\(980\) | −12.7896 | −0.408548 | ||||||||
\(981\) | 87.0688 | 2.77989 | ||||||||
\(982\) | 6.39355 | 0.204026 | ||||||||
\(983\) | −28.8271 | −0.919443 | −0.459721 | − | 0.888063i | \(-0.652051\pi\) | ||||
−0.459721 | + | 0.888063i | \(0.652051\pi\) | |||||||
\(984\) | 8.70432 | 0.277484 | ||||||||
\(985\) | −10.1195 | −0.322435 | ||||||||
\(986\) | −38.4997 | −1.22608 | ||||||||
\(987\) | 75.8345 | 2.41384 | ||||||||
\(988\) | −8.42135 | −0.267919 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −20.2078 | −0.642248 | ||||||||
\(991\) | −6.23589 | −0.198090 | −0.0990448 | − | 0.995083i | \(-0.531579\pi\) | ||||
−0.0990448 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(992\) | −2.05611 | −0.0652815 | ||||||||
\(993\) | 31.9407 | 1.01361 | ||||||||
\(994\) | −48.3581 | −1.53383 | ||||||||
\(995\) | −18.5869 | −0.589244 | ||||||||
\(996\) | 0.881185 | 0.0279214 | ||||||||
\(997\) | −43.3422 | −1.37266 | −0.686330 | − | 0.727290i | \(-0.740779\pi\) | ||||
−0.686330 | + | 0.727290i | \(0.740779\pi\) | |||||||
\(998\) | −2.98791 | −0.0945805 | ||||||||
\(999\) | −29.4928 | −0.933110 |
(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 | 5290.2.a.bk.1.12 | 15 | ||
23.3 | even | 11 | 230.2.g.d.101.1 | yes | 30 | ||
23.8 | even | 11 | 230.2.g.d.41.1 | ✓ | 30 | ||
23.22 | odd | 2 | 5290.2.a.bl.1.12 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.g.d.41.1 | ✓ | 30 | 23.8 | even | 11 | ||
230.2.g.d.101.1 | yes | 30 | 23.3 | even | 11 | ||
5290.2.a.bk.1.12 | 15 | 1.1 | even | 1 | trivial | ||
5290.2.a.bl.1.12 | 15 | 23.22 | odd | 2 |