Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} - 1007 x^{5} - 384 x^{4} + 579 x^{3} + 44 x^{2} - 112 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.68292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68292 | 1.19000 | 0.595002 | − | 0.803724i | \(-0.297151\pi\) | ||||
0.595002 | + | 0.803724i | \(0.297151\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.832222 | 0.416111 | ||||||||
\(5\) | −3.40481 | −1.52268 | −0.761338 | − | 0.648355i | \(-0.775457\pi\) | ||||
−0.761338 | + | 0.648355i | \(0.775457\pi\) | |||||||
\(6\) | 1.68292 | 0.687049 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.96528 | −0.694831 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.73002 | −1.81199 | ||||||||
\(11\) | 1.02548 | 0.309193 | 0.154597 | − | 0.987978i | \(-0.450592\pi\) | ||||
0.154597 | + | 0.987978i | \(0.450592\pi\) | |||||||
\(12\) | 0.832222 | 0.240242 | ||||||||
\(13\) | 3.49993 | 0.970705 | 0.485353 | − | 0.874318i | \(-0.338691\pi\) | ||||
0.485353 | + | 0.874318i | \(0.338691\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.40481 | −0.879118 | ||||||||
\(16\) | −4.97185 | −1.24296 | ||||||||
\(17\) | 0.830651 | 0.201462 | 0.100731 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100731 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(18\) | 1.68292 | 0.396668 | ||||||||
\(19\) | 1.63689 | 0.375529 | 0.187765 | − | 0.982214i | \(-0.439876\pi\) | ||||
0.187765 | + | 0.982214i | \(0.439876\pi\) | |||||||
\(20\) | −2.83356 | −0.633602 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.72580 | 0.367941 | ||||||||
\(23\) | −1.51995 | −0.316931 | −0.158465 | − | 0.987365i | \(-0.550655\pi\) | ||||
−0.158465 | + | 0.987365i | \(0.550655\pi\) | |||||||
\(24\) | −1.96528 | −0.401161 | ||||||||
\(25\) | 6.59272 | 1.31854 | ||||||||
\(26\) | 5.89010 | 1.15514 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17009 | −0.217280 | −0.108640 | − | 0.994081i | \(-0.534649\pi\) | ||||
−0.108640 | + | 0.994081i | \(0.534649\pi\) | |||||||
\(30\) | −5.73002 | −1.04615 | ||||||||
\(31\) | −8.40087 | −1.50884 | −0.754421 | − | 0.656391i | \(-0.772082\pi\) | ||||
−0.754421 | + | 0.656391i | \(0.772082\pi\) | |||||||
\(32\) | −4.43667 | −0.784301 | ||||||||
\(33\) | 1.02548 | 0.178513 | ||||||||
\(34\) | 1.39792 | 0.239741 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.832222 | 0.138704 | ||||||||
\(37\) | 8.14512 | 1.33905 | 0.669524 | − | 0.742790i | \(-0.266498\pi\) | ||||
0.669524 | + | 0.742790i | \(0.266498\pi\) | |||||||
\(38\) | 2.75476 | 0.446881 | ||||||||
\(39\) | 3.49993 | 0.560437 | ||||||||
\(40\) | 6.69139 | 1.05800 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.80082 | 1.34211 | 0.671056 | − | 0.741407i | \(-0.265841\pi\) | ||||
0.671056 | + | 0.741407i | \(0.265841\pi\) | |||||||
\(44\) | 0.853425 | 0.128659 | ||||||||
\(45\) | −3.40481 | −0.507559 | ||||||||
\(46\) | −2.55795 | −0.377149 | ||||||||
\(47\) | −10.3255 | −1.50612 | −0.753061 | − | 0.657951i | \(-0.771423\pi\) | ||||
−0.753061 | + | 0.657951i | \(0.771423\pi\) | |||||||
\(48\) | −4.97185 | −0.717625 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.0950 | 1.56907 | ||||||||
\(51\) | 0.830651 | 0.116314 | ||||||||
\(52\) | 2.91272 | 0.403921 | ||||||||
\(53\) | −0.417313 | −0.0573224 | −0.0286612 | − | 0.999589i | \(-0.509124\pi\) | ||||
−0.0286612 | + | 0.999589i | \(0.509124\pi\) | |||||||
\(54\) | 1.68292 | 0.229016 | ||||||||
\(55\) | −3.49155 | −0.470801 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.63689 | 0.216812 | ||||||||
\(58\) | −1.96916 | −0.258564 | ||||||||
\(59\) | −14.7168 | −1.91597 | −0.957983 | − | 0.286826i | \(-0.907400\pi\) | ||||
−0.957983 | + | 0.286826i | \(0.907400\pi\) | |||||||
\(60\) | −2.83356 | −0.365810 | ||||||||
\(61\) | −11.6289 | −1.48892 | −0.744461 | − | 0.667665i | \(-0.767294\pi\) | ||||
−0.744461 | + | 0.667665i | \(0.767294\pi\) | |||||||
\(62\) | −14.1380 | −1.79553 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.47713 | 0.309641 | ||||||||
\(65\) | −11.9166 | −1.47807 | ||||||||
\(66\) | 1.72580 | 0.212431 | ||||||||
\(67\) | −2.21248 | −0.270297 | −0.135149 | − | 0.990825i | \(-0.543151\pi\) | ||||
−0.135149 | + | 0.990825i | \(0.543151\pi\) | |||||||
\(68\) | 0.691286 | 0.0838307 | ||||||||
\(69\) | −1.51995 | −0.182980 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.00451 | −0.119213 | −0.0596067 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596067 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(72\) | −1.96528 | −0.231610 | ||||||||
\(73\) | −12.7925 | −1.49725 | −0.748626 | − | 0.662993i | \(-0.769286\pi\) | ||||
−0.748626 | + | 0.662993i | \(0.769286\pi\) | |||||||
\(74\) | 13.7076 | 1.59347 | ||||||||
\(75\) | 6.59272 | 0.761261 | ||||||||
\(76\) | 1.36226 | 0.156262 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.89010 | 0.666923 | ||||||||
\(79\) | −9.00439 | −1.01307 | −0.506536 | − | 0.862219i | \(-0.669074\pi\) | ||||
−0.506536 | + | 0.862219i | \(0.669074\pi\) | |||||||
\(80\) | 16.9282 | 1.89263 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.68292 | −0.185847 | ||||||||
\(83\) | −1.44935 | −0.159087 | −0.0795437 | − | 0.996831i | \(-0.525346\pi\) | ||||
−0.0795437 | + | 0.996831i | \(0.525346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82821 | −0.306762 | ||||||||
\(86\) | 14.8111 | 1.59712 | ||||||||
\(87\) | −1.17009 | −0.125446 | ||||||||
\(88\) | −2.01535 | −0.214837 | ||||||||
\(89\) | −10.4048 | −1.10290 | −0.551451 | − | 0.834207i | \(-0.685926\pi\) | ||||
−0.551451 | + | 0.834207i | \(0.685926\pi\) | |||||||
\(90\) | −5.73002 | −0.603997 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.26493 | −0.131878 | ||||||||
\(93\) | −8.40087 | −0.871130 | ||||||||
\(94\) | −17.3769 | −1.79229 | ||||||||
\(95\) | −5.57331 | −0.571809 | ||||||||
\(96\) | −4.43667 | −0.452816 | ||||||||
\(97\) | −2.85223 | −0.289600 | −0.144800 | − | 0.989461i | \(-0.546254\pi\) | ||||
−0.144800 | + | 0.989461i | \(0.546254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.02548 | 0.103064 | ||||||||
\(100\) | 5.48660 | 0.548660 | ||||||||
\(101\) | −2.50244 | −0.249003 | −0.124501 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124501 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(102\) | 1.39792 | 0.138415 | ||||||||
\(103\) | −1.62814 | −0.160426 | −0.0802129 | − | 0.996778i | \(-0.525560\pi\) | ||||
−0.0802129 | + | 0.996778i | \(0.525560\pi\) | |||||||
\(104\) | −6.87833 | −0.674476 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.702305 | −0.0682139 | ||||||||
\(107\) | −13.0578 | −1.26234 | −0.631170 | − | 0.775644i | \(-0.717425\pi\) | ||||
−0.631170 | + | 0.775644i | \(0.717425\pi\) | |||||||
\(108\) | 0.832222 | 0.0800806 | ||||||||
\(109\) | −10.1224 | −0.969555 | −0.484777 | − | 0.874638i | \(-0.661099\pi\) | ||||
−0.484777 | + | 0.874638i | \(0.661099\pi\) | |||||||
\(110\) | −5.87601 | −0.560255 | ||||||||
\(111\) | 8.14512 | 0.773100 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3018 | −1.34540 | −0.672701 | − | 0.739914i | \(-0.734866\pi\) | ||||
−0.672701 | + | 0.739914i | \(0.734866\pi\) | |||||||
\(114\) | 2.75476 | 0.258007 | ||||||||
\(115\) | 5.17512 | 0.482583 | ||||||||
\(116\) | −0.973771 | −0.0904124 | ||||||||
\(117\) | 3.49993 | 0.323568 | ||||||||
\(118\) | −24.7672 | −2.28001 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.69139 | 0.610838 | ||||||||
\(121\) | −9.94840 | −0.904400 | ||||||||
\(122\) | −19.5704 | −1.77183 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −6.99139 | −0.627846 | ||||||||
\(125\) | −5.42289 | −0.485038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.21842 | −0.196853 | −0.0984266 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984266 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(128\) | 13.0422 | 1.15278 | ||||||||
\(129\) | 8.80082 | 0.774869 | ||||||||
\(130\) | −20.0547 | −1.75891 | ||||||||
\(131\) | 8.00260 | 0.699190 | 0.349595 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349595 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(132\) | 0.853425 | 0.0742811 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.72343 | −0.321655 | ||||||||
\(135\) | −3.40481 | −0.293039 | ||||||||
\(136\) | −1.63246 | −0.139982 | ||||||||
\(137\) | 5.55967 | 0.474995 | 0.237497 | − | 0.971388i | \(-0.423673\pi\) | ||||
0.237497 | + | 0.971388i | \(0.423673\pi\) | |||||||
\(138\) | −2.55795 | −0.217747 | ||||||||
\(139\) | 12.3095 | 1.04408 | 0.522040 | − | 0.852921i | \(-0.325171\pi\) | ||||
0.522040 | + | 0.852921i | \(0.325171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3255 | −0.869560 | ||||||||
\(142\) | −1.69051 | −0.141864 | ||||||||
\(143\) | 3.58910 | 0.300135 | ||||||||
\(144\) | −4.97185 | −0.414321 | ||||||||
\(145\) | 3.98392 | 0.330846 | ||||||||
\(146\) | −21.5288 | −1.78174 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.77854 | 0.557193 | ||||||||
\(149\) | 17.9547 | 1.47090 | 0.735452 | − | 0.677577i | \(-0.236970\pi\) | ||||
0.735452 | + | 0.677577i | \(0.236970\pi\) | |||||||
\(150\) | 11.0950 | 0.905904 | ||||||||
\(151\) | 10.8220 | 0.880684 | 0.440342 | − | 0.897830i | \(-0.354857\pi\) | ||||
0.440342 | + | 0.897830i | \(0.354857\pi\) | |||||||
\(152\) | −3.21695 | −0.260929 | ||||||||
\(153\) | 0.830651 | 0.0671541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.6034 | 2.29748 | ||||||||
\(156\) | 2.91272 | 0.233204 | ||||||||
\(157\) | 8.60868 | 0.687047 | 0.343524 | − | 0.939144i | \(-0.388379\pi\) | ||||
0.343524 | + | 0.939144i | \(0.388379\pi\) | |||||||
\(158\) | −15.1537 | −1.20556 | ||||||||
\(159\) | −0.417313 | −0.0330951 | ||||||||
\(160\) | 15.1060 | 1.19424 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.68292 | 0.132223 | ||||||||
\(163\) | 17.3793 | 1.36125 | 0.680627 | − | 0.732630i | \(-0.261708\pi\) | ||||
0.680627 | + | 0.732630i | \(0.261708\pi\) | |||||||
\(164\) | −0.832222 | −0.0649856 | ||||||||
\(165\) | −3.49155 | −0.271817 | ||||||||
\(166\) | −2.43915 | −0.189315 | ||||||||
\(167\) | −2.73619 | −0.211733 | −0.105866 | − | 0.994380i | \(-0.533762\pi\) | ||||
−0.105866 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.750505 | −0.0577311 | ||||||||
\(170\) | −4.75965 | −0.365048 | ||||||||
\(171\) | 1.63689 | 0.125176 | ||||||||
\(172\) | 7.32423 | 0.558467 | ||||||||
\(173\) | −17.2827 | −1.31398 | −0.656988 | − | 0.753901i | \(-0.728170\pi\) | ||||
−0.656988 | + | 0.753901i | \(0.728170\pi\) | |||||||
\(174\) | −1.96916 | −0.149282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.09852 | −0.384315 | ||||||||
\(177\) | −14.7168 | −1.10618 | ||||||||
\(178\) | −17.5104 | −1.31246 | ||||||||
\(179\) | 11.7765 | 0.880214 | 0.440107 | − | 0.897945i | \(-0.354940\pi\) | ||||
0.440107 | + | 0.897945i | \(0.354940\pi\) | |||||||
\(180\) | −2.83356 | −0.211201 | ||||||||
\(181\) | 1.80377 | 0.134073 | 0.0670366 | − | 0.997751i | \(-0.478646\pi\) | ||||
0.0670366 | + | 0.997751i | \(0.478646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6289 | −0.859630 | ||||||||
\(184\) | 2.98712 | 0.220213 | ||||||||
\(185\) | −27.7326 | −2.03894 | ||||||||
\(186\) | −14.1380 | −1.03665 | ||||||||
\(187\) | 0.851813 | 0.0622908 | ||||||||
\(188\) | −8.59307 | −0.626714 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.37943 | −0.680456 | ||||||||
\(191\) | −19.2126 | −1.39018 | −0.695089 | − | 0.718924i | \(-0.744635\pi\) | ||||
−0.695089 | + | 0.718924i | \(0.744635\pi\) | |||||||
\(192\) | 2.47713 | 0.178771 | ||||||||
\(193\) | 15.9487 | 1.14801 | 0.574006 | − | 0.818851i | \(-0.305388\pi\) | ||||
0.574006 | + | 0.818851i | \(0.305388\pi\) | |||||||
\(194\) | −4.80008 | −0.344625 | ||||||||
\(195\) | −11.9166 | −0.853364 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.49324 | 0.391377 | 0.195689 | − | 0.980666i | \(-0.437306\pi\) | ||||
0.195689 | + | 0.980666i | \(0.437306\pi\) | |||||||
\(198\) | 1.72580 | 0.122647 | ||||||||
\(199\) | 0.785333 | 0.0556708 | 0.0278354 | − | 0.999613i | \(-0.491139\pi\) | ||||
0.0278354 | + | 0.999613i | \(0.491139\pi\) | |||||||
\(200\) | −12.9565 | −0.916164 | ||||||||
\(201\) | −2.21248 | −0.156056 | ||||||||
\(202\) | −4.21142 | −0.296314 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.691286 | 0.0483997 | ||||||||
\(205\) | 3.40481 | 0.237802 | ||||||||
\(206\) | −2.74004 | −0.190907 | ||||||||
\(207\) | −1.51995 | −0.105644 | ||||||||
\(208\) | −17.4011 | −1.20655 | ||||||||
\(209\) | 1.67860 | 0.116111 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7215 | −1.35769 | −0.678843 | − | 0.734284i | \(-0.737518\pi\) | ||||
−0.678843 | + | 0.734284i | \(0.737518\pi\) | |||||||
\(212\) | −0.347297 | −0.0238525 | ||||||||
\(213\) | −1.00451 | −0.0688278 | ||||||||
\(214\) | −21.9752 | −1.50219 | ||||||||
\(215\) | −29.9651 | −2.04360 | ||||||||
\(216\) | −1.96528 | −0.133720 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −17.0353 | −1.15377 | ||||||||
\(219\) | −12.7925 | −0.864439 | ||||||||
\(220\) | −2.90575 | −0.195905 | ||||||||
\(221\) | 2.90722 | 0.195561 | ||||||||
\(222\) | 13.7076 | 0.919993 | ||||||||
\(223\) | 14.0160 | 0.938579 | 0.469290 | − | 0.883044i | \(-0.344510\pi\) | ||||
0.469290 | + | 0.883044i | \(0.344510\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.59272 | 0.439514 | ||||||||
\(226\) | −24.0688 | −1.60103 | ||||||||
\(227\) | 13.5192 | 0.897299 | 0.448649 | − | 0.893708i | \(-0.351905\pi\) | ||||
0.448649 | + | 0.893708i | \(0.351905\pi\) | |||||||
\(228\) | 1.36226 | 0.0902178 | ||||||||
\(229\) | 0.208217 | 0.0137594 | 0.00687969 | − | 0.999976i | \(-0.497810\pi\) | ||||
0.00687969 | + | 0.999976i | \(0.497810\pi\) | |||||||
\(230\) | 8.70932 | 0.574276 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.29954 | 0.150972 | ||||||||
\(233\) | 15.6507 | 1.02531 | 0.512655 | − | 0.858595i | \(-0.328662\pi\) | ||||
0.512655 | + | 0.858595i | \(0.328662\pi\) | |||||||
\(234\) | 5.89010 | 0.385048 | ||||||||
\(235\) | 35.1562 | 2.29334 | ||||||||
\(236\) | −12.2477 | −0.797254 | ||||||||
\(237\) | −9.00439 | −0.584898 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7846 | −0.956334 | −0.478167 | − | 0.878269i | \(-0.658699\pi\) | ||||
−0.478167 | + | 0.878269i | \(0.658699\pi\) | |||||||
\(240\) | 16.9282 | 1.09271 | ||||||||
\(241\) | 6.77989 | 0.436731 | 0.218366 | − | 0.975867i | \(-0.429927\pi\) | ||||
0.218366 | + | 0.975867i | \(0.429927\pi\) | |||||||
\(242\) | −16.7424 | −1.07624 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.67779 | −0.619557 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.68292 | −0.107299 | ||||||||
\(247\) | 5.72901 | 0.364528 | ||||||||
\(248\) | 16.5101 | 1.04839 | ||||||||
\(249\) | −1.44935 | −0.0918491 | ||||||||
\(250\) | −9.12630 | −0.577198 | ||||||||
\(251\) | 28.5862 | 1.80434 | 0.902171 | − | 0.431379i | \(-0.141973\pi\) | ||||
0.902171 | + | 0.431379i | \(0.141973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.55867 | −0.0979927 | ||||||||
\(254\) | −3.73343 | −0.234256 | ||||||||
\(255\) | −2.82821 | −0.177109 | ||||||||
\(256\) | 16.9947 | 1.06217 | ||||||||
\(257\) | −24.5785 | −1.53316 | −0.766582 | − | 0.642147i | \(-0.778044\pi\) | ||||
−0.766582 | + | 0.642147i | \(0.778044\pi\) | |||||||
\(258\) | 14.8111 | 0.922097 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.91724 | −0.615041 | ||||||||
\(261\) | −1.17009 | −0.0724265 | ||||||||
\(262\) | 13.4677 | 0.832040 | ||||||||
\(263\) | 2.67564 | 0.164987 | 0.0824936 | − | 0.996592i | \(-0.473712\pi\) | ||||
0.0824936 | + | 0.996592i | \(0.473712\pi\) | |||||||
\(264\) | −2.01535 | −0.124036 | ||||||||
\(265\) | 1.42087 | 0.0872834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.4048 | −0.636761 | ||||||||
\(268\) | −1.84127 | −0.112474 | ||||||||
\(269\) | −20.4028 | −1.24398 | −0.621990 | − | 0.783026i | \(-0.713675\pi\) | ||||
−0.621990 | + | 0.783026i | \(0.713675\pi\) | |||||||
\(270\) | −5.73002 | −0.348718 | ||||||||
\(271\) | −25.9779 | −1.57805 | −0.789023 | − | 0.614364i | \(-0.789413\pi\) | ||||
−0.789023 | + | 0.614364i | \(0.789413\pi\) | |||||||
\(272\) | −4.12987 | −0.250410 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.35648 | 0.565246 | ||||||||
\(275\) | 6.76068 | 0.407684 | ||||||||
\(276\) | −1.26493 | −0.0761400 | ||||||||
\(277\) | −11.8244 | −0.710461 | −0.355230 | − | 0.934779i | \(-0.615598\pi\) | ||||
−0.355230 | + | 0.934779i | \(0.615598\pi\) | |||||||
\(278\) | 20.7160 | 1.24246 | ||||||||
\(279\) | −8.40087 | −0.502947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.86950 | −0.469455 | −0.234727 | − | 0.972061i | \(-0.575420\pi\) | ||||
−0.234727 | + | 0.972061i | \(0.575420\pi\) | |||||||
\(282\) | −17.3769 | −1.03478 | ||||||||
\(283\) | 16.7613 | 0.996353 | 0.498177 | − | 0.867076i | \(-0.334003\pi\) | ||||
0.498177 | + | 0.867076i | \(0.334003\pi\) | |||||||
\(284\) | −0.835975 | −0.0496060 | ||||||||
\(285\) | −5.57331 | −0.330134 | ||||||||
\(286\) | 6.04016 | 0.357162 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.43667 | −0.261434 | ||||||||
\(289\) | −16.3100 | −0.959413 | ||||||||
\(290\) | 6.70462 | 0.393709 | ||||||||
\(291\) | −2.85223 | −0.167201 | ||||||||
\(292\) | −10.6462 | −0.623023 | ||||||||
\(293\) | 13.3389 | 0.779270 | 0.389635 | − | 0.920969i | \(-0.372601\pi\) | ||||
0.389635 | + | 0.920969i | \(0.372601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 50.1079 | 2.91740 | ||||||||
\(296\) | −16.0074 | −0.930412 | ||||||||
\(297\) | 1.02548 | 0.0595042 | ||||||||
\(298\) | 30.2163 | 1.75038 | ||||||||
\(299\) | −5.31970 | −0.307646 | ||||||||
\(300\) | 5.48660 | 0.316769 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.2126 | 1.04802 | ||||||||
\(303\) | −2.50244 | −0.143762 | ||||||||
\(304\) | −8.13839 | −0.466769 | ||||||||
\(305\) | 39.5940 | 2.26715 | ||||||||
\(306\) | 1.39792 | 0.0799137 | ||||||||
\(307\) | 0.258573 | 0.0147575 | 0.00737877 | − | 0.999973i | \(-0.497651\pi\) | ||||
0.00737877 | + | 0.999973i | \(0.497651\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.62814 | −0.0926218 | ||||||||
\(310\) | 48.1372 | 2.73401 | ||||||||
\(311\) | 22.9830 | 1.30325 | 0.651624 | − | 0.758542i | \(-0.274088\pi\) | ||||
0.651624 | + | 0.758542i | \(0.274088\pi\) | |||||||
\(312\) | −6.87833 | −0.389409 | ||||||||
\(313\) | 5.78960 | 0.327247 | 0.163624 | − | 0.986523i | \(-0.447682\pi\) | ||||
0.163624 | + | 0.986523i | \(0.447682\pi\) | |||||||
\(314\) | 14.4877 | 0.817590 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.49365 | −0.421551 | ||||||||
\(317\) | −25.7608 | −1.44687 | −0.723434 | − | 0.690393i | \(-0.757438\pi\) | ||||
−0.723434 | + | 0.690393i | \(0.757438\pi\) | |||||||
\(318\) | −0.702305 | −0.0393833 | ||||||||
\(319\) | −1.19990 | −0.0671813 | ||||||||
\(320\) | −8.43415 | −0.471483 | ||||||||
\(321\) | −13.0578 | −0.728813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.35969 | 0.0756550 | ||||||||
\(324\) | 0.832222 | 0.0462346 | ||||||||
\(325\) | 23.0740 | 1.27992 | ||||||||
\(326\) | 29.2480 | 1.61990 | ||||||||
\(327\) | −10.1224 | −0.559773 | ||||||||
\(328\) | 1.96528 | 0.108514 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.87601 | −0.323464 | ||||||||
\(331\) | −12.0711 | −0.663490 | −0.331745 | − | 0.943369i | \(-0.607637\pi\) | ||||
−0.331745 | + | 0.943369i | \(0.607637\pi\) | |||||||
\(332\) | −1.20618 | −0.0661980 | ||||||||
\(333\) | 8.14512 | 0.446350 | ||||||||
\(334\) | −4.60479 | −0.251963 | ||||||||
\(335\) | 7.53307 | 0.411576 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7963 | 1.35074 | 0.675371 | − | 0.737478i | \(-0.263983\pi\) | ||||
0.675371 | + | 0.737478i | \(0.263983\pi\) | |||||||
\(338\) | −1.26304 | −0.0687003 | ||||||||
\(339\) | −14.3018 | −0.776768 | ||||||||
\(340\) | −2.35370 | −0.127647 | ||||||||
\(341\) | −8.61491 | −0.466523 | ||||||||
\(342\) | 2.75476 | 0.148960 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.2960 | −0.932540 | ||||||||
\(345\) | 5.17512 | 0.278619 | ||||||||
\(346\) | −29.0853 | −1.56364 | ||||||||
\(347\) | −5.85866 | −0.314509 | −0.157255 | − | 0.987558i | \(-0.550264\pi\) | ||||
−0.157255 | + | 0.987558i | \(0.550264\pi\) | |||||||
\(348\) | −0.973771 | −0.0521996 | ||||||||
\(349\) | −36.1859 | −1.93699 | −0.968494 | − | 0.249038i | \(-0.919886\pi\) | ||||
−0.968494 | + | 0.249038i | \(0.919886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.49993 | 0.186812 | ||||||||
\(352\) | −4.54971 | −0.242500 | ||||||||
\(353\) | −5.24732 | −0.279287 | −0.139643 | − | 0.990202i | \(-0.544596\pi\) | ||||
−0.139643 | + | 0.990202i | \(0.544596\pi\) | |||||||
\(354\) | −24.7672 | −1.31636 | ||||||||
\(355\) | 3.42016 | 0.181523 | ||||||||
\(356\) | −8.65907 | −0.458930 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.8189 | 1.04746 | ||||||||
\(359\) | −4.84702 | −0.255816 | −0.127908 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127908 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(360\) | 6.69139 | 0.352667 | ||||||||
\(361\) | −16.3206 | −0.858978 | ||||||||
\(362\) | 3.03560 | 0.159548 | ||||||||
\(363\) | −9.94840 | −0.522155 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.5561 | 2.27983 | ||||||||
\(366\) | −19.5704 | −1.02296 | ||||||||
\(367\) | 24.3441 | 1.27075 | 0.635375 | − | 0.772204i | \(-0.280846\pi\) | ||||
0.635375 | + | 0.772204i | \(0.280846\pi\) | |||||||
\(368\) | 7.55694 | 0.393933 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −46.6717 | −2.42635 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.99139 | −0.362487 | ||||||||
\(373\) | −9.41811 | −0.487651 | −0.243826 | − | 0.969819i | \(-0.578402\pi\) | ||||
−0.243826 | + | 0.969819i | \(0.578402\pi\) | |||||||
\(374\) | 1.43353 | 0.0741263 | ||||||||
\(375\) | −5.42289 | −0.280037 | ||||||||
\(376\) | 20.2924 | 1.04650 | ||||||||
\(377\) | −4.09522 | −0.210914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5719 | 0.902606 | 0.451303 | − | 0.892371i | \(-0.350959\pi\) | ||||
0.451303 | + | 0.892371i | \(0.350959\pi\) | |||||||
\(380\) | −4.63823 | −0.237936 | ||||||||
\(381\) | −2.21842 | −0.113653 | ||||||||
\(382\) | −32.3334 | −1.65432 | ||||||||
\(383\) | −36.4451 | −1.86226 | −0.931130 | − | 0.364688i | \(-0.881176\pi\) | ||||
−0.931130 | + | 0.364688i | \(0.881176\pi\) | |||||||
\(384\) | 13.0422 | 0.665555 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.8404 | 1.36614 | ||||||||
\(387\) | 8.80082 | 0.447371 | ||||||||
\(388\) | −2.37369 | −0.120506 | ||||||||
\(389\) | 5.42387 | 0.275001 | 0.137500 | − | 0.990502i | \(-0.456093\pi\) | ||||
0.137500 | + | 0.990502i | \(0.456093\pi\) | |||||||
\(390\) | −20.0547 | −1.01551 | ||||||||
\(391\) | −1.26254 | −0.0638496 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00260 | 0.403678 | ||||||||
\(394\) | 9.24468 | 0.465740 | ||||||||
\(395\) | 30.6582 | 1.54258 | ||||||||
\(396\) | 0.853425 | 0.0428862 | ||||||||
\(397\) | 33.0276 | 1.65761 | 0.828803 | − | 0.559540i | \(-0.189022\pi\) | ||||
0.828803 | + | 0.559540i | \(0.189022\pi\) | |||||||
\(398\) | 1.32165 | 0.0662485 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −32.7780 | −1.63890 | ||||||||
\(401\) | −4.18181 | −0.208830 | −0.104415 | − | 0.994534i | \(-0.533297\pi\) | ||||
−0.104415 | + | 0.994534i | \(0.533297\pi\) | |||||||
\(402\) | −3.72343 | −0.185708 | ||||||||
\(403\) | −29.4025 | −1.46464 | ||||||||
\(404\) | −2.08259 | −0.103613 | ||||||||
\(405\) | −3.40481 | −0.169186 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.35263 | 0.414025 | ||||||||
\(408\) | −1.63246 | −0.0808188 | ||||||||
\(409\) | −11.7978 | −0.583365 | −0.291682 | − | 0.956515i | \(-0.594215\pi\) | ||||
−0.291682 | + | 0.956515i | \(0.594215\pi\) | |||||||
\(410\) | 5.73002 | 0.282986 | ||||||||
\(411\) | 5.55967 | 0.274238 | ||||||||
\(412\) | −1.35498 | −0.0667549 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.55795 | −0.125716 | ||||||||
\(415\) | 4.93477 | 0.242238 | ||||||||
\(416\) | −15.5280 | −0.761325 | ||||||||
\(417\) | 12.3095 | 0.602800 | ||||||||
\(418\) | 2.82495 | 0.138173 | ||||||||
\(419\) | −28.0765 | −1.37163 | −0.685813 | − | 0.727777i | \(-0.740553\pi\) | ||||
−0.685813 | + | 0.727777i | \(0.740553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7916 | 0.720899 | 0.360450 | − | 0.932779i | \(-0.382623\pi\) | ||||
0.360450 | + | 0.932779i | \(0.382623\pi\) | |||||||
\(422\) | −33.1897 | −1.61565 | ||||||||
\(423\) | −10.3255 | −0.502041 | ||||||||
\(424\) | 0.820136 | 0.0398293 | ||||||||
\(425\) | 5.47625 | 0.265637 | ||||||||
\(426\) | −1.69051 | −0.0819054 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −10.8670 | −0.525274 | ||||||||
\(429\) | 3.58910 | 0.173283 | ||||||||
\(430\) | −50.4289 | −2.43190 | ||||||||
\(431\) | −2.77927 | −0.133873 | −0.0669364 | − | 0.997757i | \(-0.521322\pi\) | ||||
−0.0669364 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(432\) | −4.97185 | −0.239208 | ||||||||
\(433\) | −27.8722 | −1.33945 | −0.669727 | − | 0.742607i | \(-0.733589\pi\) | ||||
−0.669727 | + | 0.742607i | \(0.733589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.98392 | 0.191014 | ||||||||
\(436\) | −8.42412 | −0.403442 | ||||||||
\(437\) | −2.48799 | −0.119017 | ||||||||
\(438\) | −21.5288 | −1.02869 | ||||||||
\(439\) | 18.9919 | 0.906435 | 0.453218 | − | 0.891400i | \(-0.350276\pi\) | ||||
0.453218 | + | 0.891400i | \(0.350276\pi\) | |||||||
\(440\) | 6.86187 | 0.327127 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.89262 | 0.232718 | ||||||||
\(443\) | −17.4345 | −0.828339 | −0.414170 | − | 0.910200i | \(-0.635928\pi\) | ||||
−0.414170 | + | 0.910200i | \(0.635928\pi\) | |||||||
\(444\) | 6.77854 | 0.321696 | ||||||||
\(445\) | 35.4262 | 1.67936 | ||||||||
\(446\) | 23.5878 | 1.11691 | ||||||||
\(447\) | 17.9547 | 0.849226 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.12272 | 0.336142 | 0.168071 | − | 0.985775i | \(-0.446246\pi\) | ||||
0.168071 | + | 0.985775i | \(0.446246\pi\) | |||||||
\(450\) | 11.0950 | 0.523024 | ||||||||
\(451\) | −1.02548 | −0.0482878 | ||||||||
\(452\) | −11.9023 | −0.559837 | ||||||||
\(453\) | 10.8220 | 0.508463 | ||||||||
\(454\) | 22.7517 | 1.06779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.21695 | −0.150647 | ||||||||
\(457\) | 38.4769 | 1.79987 | 0.899936 | − | 0.436021i | \(-0.143613\pi\) | ||||
0.899936 | + | 0.436021i | \(0.143613\pi\) | |||||||
\(458\) | 0.350413 | 0.0163737 | ||||||||
\(459\) | 0.830651 | 0.0387715 | ||||||||
\(460\) | 4.30685 | 0.200808 | ||||||||
\(461\) | −6.67458 | −0.310866 | −0.155433 | − | 0.987846i | \(-0.549677\pi\) | ||||
−0.155433 | + | 0.987846i | \(0.549677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.7433 | −1.38229 | −0.691144 | − | 0.722717i | \(-0.742893\pi\) | ||||
−0.691144 | + | 0.722717i | \(0.742893\pi\) | |||||||
\(464\) | 5.81749 | 0.270070 | ||||||||
\(465\) | 28.6034 | 1.32645 | ||||||||
\(466\) | 26.3388 | 1.22012 | ||||||||
\(467\) | −34.5371 | −1.59819 | −0.799094 | − | 0.601206i | \(-0.794687\pi\) | ||||
−0.799094 | + | 0.601206i | \(0.794687\pi\) | |||||||
\(468\) | 2.91272 | 0.134640 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 59.1651 | 2.72908 | ||||||||
\(471\) | 8.60868 | 0.396667 | ||||||||
\(472\) | 28.9226 | 1.33127 | ||||||||
\(473\) | 9.02504 | 0.414972 | ||||||||
\(474\) | −15.1537 | −0.696031 | ||||||||
\(475\) | 10.7916 | 0.495151 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.417313 | −0.0191075 | ||||||||
\(478\) | −24.8813 | −1.13804 | ||||||||
\(479\) | −26.2082 | −1.19748 | −0.598742 | − | 0.800942i | \(-0.704333\pi\) | ||||
−0.598742 | + | 0.800942i | \(0.704333\pi\) | |||||||
\(480\) | 15.1060 | 0.689492 | ||||||||
\(481\) | 28.5073 | 1.29982 | ||||||||
\(482\) | 11.4100 | 0.519712 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.27927 | −0.376331 | ||||||||
\(485\) | 9.71129 | 0.440967 | ||||||||
\(486\) | 1.68292 | 0.0763388 | ||||||||
\(487\) | −4.32368 | −0.195924 | −0.0979622 | − | 0.995190i | \(-0.531232\pi\) | ||||
−0.0979622 | + | 0.995190i | \(0.531232\pi\) | |||||||
\(488\) | 22.8539 | 1.03455 | ||||||||
\(489\) | 17.3793 | 0.785920 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.30432 | −0.0588630 | −0.0294315 | − | 0.999567i | \(-0.509370\pi\) | ||||
−0.0294315 | + | 0.999567i | \(0.509370\pi\) | |||||||
\(492\) | −0.832222 | −0.0375195 | ||||||||
\(493\) | −0.971933 | −0.0437737 | ||||||||
\(494\) | 9.64147 | 0.433790 | ||||||||
\(495\) | −3.49155 | −0.156934 | ||||||||
\(496\) | 41.7679 | 1.87543 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.43915 | −0.109301 | ||||||||
\(499\) | 2.10363 | 0.0941713 | 0.0470857 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470857 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(500\) | −4.51305 | −0.201830 | ||||||||
\(501\) | −2.73619 | −0.122244 | ||||||||
\(502\) | 48.1082 | 2.14718 | ||||||||
\(503\) | 33.4139 | 1.48985 | 0.744926 | − | 0.667147i | \(-0.232485\pi\) | ||||
0.744926 | + | 0.667147i | \(0.232485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.52034 | 0.379150 | ||||||||
\(506\) | −2.62312 | −0.116612 | ||||||||
\(507\) | −0.750505 | −0.0333311 | ||||||||
\(508\) | −1.84622 | −0.0819128 | ||||||||
\(509\) | −14.0498 | −0.622745 | −0.311373 | − | 0.950288i | \(-0.600789\pi\) | ||||
−0.311373 | + | 0.950288i | \(0.600789\pi\) | |||||||
\(510\) | −4.75965 | −0.210761 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.51635 | 0.111208 | ||||||||
\(513\) | 1.63689 | 0.0722706 | ||||||||
\(514\) | −41.3636 | −1.82447 | ||||||||
\(515\) | 5.54352 | 0.244276 | ||||||||
\(516\) | 7.32423 | 0.322431 | ||||||||
\(517\) | −10.5885 | −0.465682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2827 | −0.758624 | ||||||||
\(520\) | 23.4194 | 1.02701 | ||||||||
\(521\) | −8.62481 | −0.377860 | −0.188930 | − | 0.981991i | \(-0.560502\pi\) | ||||
−0.188930 | + | 0.981991i | \(0.560502\pi\) | |||||||
\(522\) | −1.96916 | −0.0861879 | ||||||||
\(523\) | 8.15795 | 0.356722 | 0.178361 | − | 0.983965i | \(-0.442920\pi\) | ||||
0.178361 | + | 0.983965i | \(0.442920\pi\) | |||||||
\(524\) | 6.65994 | 0.290941 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.50290 | 0.196336 | ||||||||
\(527\) | −6.97819 | −0.303975 | ||||||||
\(528\) | −5.09852 | −0.221885 | ||||||||
\(529\) | −20.6898 | −0.899555 | ||||||||
\(530\) | 2.39121 | 0.103868 | ||||||||
\(531\) | −14.7168 | −0.638655 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.49993 | −0.151599 | ||||||||
\(534\) | −17.5104 | −0.757748 | ||||||||
\(535\) | 44.4591 | 1.92214 | ||||||||
\(536\) | 4.34814 | 0.187811 | ||||||||
\(537\) | 11.7765 | 0.508192 | ||||||||
\(538\) | −34.3362 | −1.48034 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.83356 | −0.121937 | ||||||||
\(541\) | 7.04980 | 0.303095 | 0.151547 | − | 0.988450i | \(-0.451574\pi\) | ||||
0.151547 | + | 0.988450i | \(0.451574\pi\) | |||||||
\(542\) | −43.7188 | −1.87788 | ||||||||
\(543\) | 1.80377 | 0.0774072 | ||||||||
\(544\) | −3.68533 | −0.158007 | ||||||||
\(545\) | 34.4650 | 1.47632 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.1767 | 1.58956 | 0.794781 | − | 0.606896i | \(-0.207585\pi\) | ||||
0.794781 | + | 0.606896i | \(0.207585\pi\) | |||||||
\(548\) | 4.62688 | 0.197650 | ||||||||
\(549\) | −11.6289 | −0.496308 | ||||||||
\(550\) | 11.3777 | 0.485146 | ||||||||
\(551\) | −1.91531 | −0.0815948 | ||||||||
\(552\) | 2.98712 | 0.127140 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19.8996 | −0.845451 | ||||||||
\(555\) | −27.7326 | −1.17718 | ||||||||
\(556\) | 10.2443 | 0.434453 | ||||||||
\(557\) | −4.16417 | −0.176441 | −0.0882207 | − | 0.996101i | \(-0.528118\pi\) | ||||
−0.0882207 | + | 0.996101i | \(0.528118\pi\) | |||||||
\(558\) | −14.1380 | −0.598509 | ||||||||
\(559\) | 30.8022 | 1.30280 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.851813 | 0.0359636 | ||||||||
\(562\) | −13.2437 | −0.558653 | ||||||||
\(563\) | −8.11995 | −0.342215 | −0.171108 | − | 0.985252i | \(-0.554735\pi\) | ||||
−0.171108 | + | 0.985252i | \(0.554735\pi\) | |||||||
\(564\) | −8.59307 | −0.361833 | ||||||||
\(565\) | 48.6950 | 2.04861 | ||||||||
\(566\) | 28.2079 | 1.18566 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.97414 | 0.0828331 | ||||||||
\(569\) | 1.33633 | 0.0560217 | 0.0280109 | − | 0.999608i | \(-0.491083\pi\) | ||||
0.0280109 | + | 0.999608i | \(0.491083\pi\) | |||||||
\(570\) | −9.37943 | −0.392861 | ||||||||
\(571\) | −41.0462 | −1.71773 | −0.858866 | − | 0.512201i | \(-0.828830\pi\) | ||||
−0.858866 | + | 0.512201i | \(0.828830\pi\) | |||||||
\(572\) | 2.98692 | 0.124890 | ||||||||
\(573\) | −19.2126 | −0.802620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.0206 | −0.417887 | ||||||||
\(576\) | 2.47713 | 0.103214 | ||||||||
\(577\) | −19.1094 | −0.795534 | −0.397767 | − | 0.917487i | \(-0.630215\pi\) | ||||
−0.397767 | + | 0.917487i | \(0.630215\pi\) | |||||||
\(578\) | −27.4485 | −1.14171 | ||||||||
\(579\) | 15.9487 | 0.662806 | ||||||||
\(580\) | 3.31550 | 0.137669 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.80008 | −0.198970 | ||||||||
\(583\) | −0.427945 | −0.0177237 | ||||||||
\(584\) | 25.1409 | 1.04034 | ||||||||
\(585\) | −11.9166 | −0.492690 | ||||||||
\(586\) | 22.4484 | 0.927334 | ||||||||
\(587\) | 2.30359 | 0.0950794 | 0.0475397 | − | 0.998869i | \(-0.484862\pi\) | ||||
0.0475397 | + | 0.998869i | \(0.484862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7513 | −0.566614 | ||||||||
\(590\) | 84.3276 | 3.47171 | ||||||||
\(591\) | 5.49324 | 0.225962 | ||||||||
\(592\) | −40.4963 | −1.66439 | ||||||||
\(593\) | 15.7840 | 0.648169 | 0.324085 | − | 0.946028i | \(-0.394944\pi\) | ||||
0.324085 | + | 0.946028i | \(0.394944\pi\) | |||||||
\(594\) | 1.72580 | 0.0708103 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.9423 | 0.612059 | ||||||||
\(597\) | 0.785333 | 0.0321415 | ||||||||
\(598\) | −8.95263 | −0.366100 | ||||||||
\(599\) | −22.0285 | −0.900061 | −0.450030 | − | 0.893013i | \(-0.648587\pi\) | ||||
−0.450030 | + | 0.893013i | \(0.648587\pi\) | |||||||
\(600\) | −12.9565 | −0.528948 | ||||||||
\(601\) | 40.6668 | 1.65883 | 0.829416 | − | 0.558632i | \(-0.188674\pi\) | ||||
0.829416 | + | 0.558632i | \(0.188674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.21248 | −0.0900991 | ||||||||
\(604\) | 9.00633 | 0.366462 | ||||||||
\(605\) | 33.8724 | 1.37711 | ||||||||
\(606\) | −4.21142 | −0.171077 | ||||||||
\(607\) | −12.5914 | −0.511069 | −0.255534 | − | 0.966800i | \(-0.582251\pi\) | ||||
−0.255534 | + | 0.966800i | \(0.582251\pi\) | |||||||
\(608\) | −7.26236 | −0.294528 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 66.6336 | 2.69792 | ||||||||
\(611\) | −36.1383 | −1.46200 | ||||||||
\(612\) | 0.691286 | 0.0279436 | ||||||||
\(613\) | −26.8645 | −1.08505 | −0.542523 | − | 0.840041i | \(-0.682531\pi\) | ||||
−0.542523 | + | 0.840041i | \(0.682531\pi\) | |||||||
\(614\) | 0.435158 | 0.0175615 | ||||||||
\(615\) | 3.40481 | 0.137295 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1864 | 0.772416 | 0.386208 | − | 0.922412i | \(-0.373785\pi\) | ||||
0.386208 | + | 0.922412i | \(0.373785\pi\) | |||||||
\(618\) | −2.74004 | −0.110220 | ||||||||
\(619\) | 30.6480 | 1.23185 | 0.615923 | − | 0.787806i | \(-0.288783\pi\) | ||||
0.615923 | + | 0.787806i | \(0.288783\pi\) | |||||||
\(620\) | 23.8043 | 0.956006 | ||||||||
\(621\) | −1.51995 | −0.0609933 | ||||||||
\(622\) | 38.6786 | 1.55087 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.4011 | −0.696602 | ||||||||
\(625\) | −14.4997 | −0.579987 | ||||||||
\(626\) | 9.74343 | 0.389426 | ||||||||
\(627\) | 1.67860 | 0.0670367 | ||||||||
\(628\) | 7.16433 | 0.285888 | ||||||||
\(629\) | 6.76575 | 0.269768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1250 | −0.721545 | −0.360772 | − | 0.932654i | \(-0.617487\pi\) | ||||
−0.360772 | + | 0.932654i | \(0.617487\pi\) | |||||||
\(632\) | 17.6961 | 0.703914 | ||||||||
\(633\) | −19.7215 | −0.783860 | ||||||||
\(634\) | −43.3533 | −1.72178 | ||||||||
\(635\) | 7.55330 | 0.299744 | ||||||||
\(636\) | −0.347297 | −0.0137712 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.01933 | −0.0799461 | ||||||||
\(639\) | −1.00451 | −0.0397378 | ||||||||
\(640\) | −44.4061 | −1.75530 | ||||||||
\(641\) | 20.3664 | 0.804424 | 0.402212 | − | 0.915546i | \(-0.368241\pi\) | ||||
0.402212 | + | 0.915546i | \(0.368241\pi\) | |||||||
\(642\) | −21.9752 | −0.867291 | ||||||||
\(643\) | 47.8847 | 1.88839 | 0.944195 | − | 0.329387i | \(-0.106842\pi\) | ||||
0.944195 | + | 0.329387i | \(0.106842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.9651 | −1.17987 | ||||||||
\(646\) | 2.28824 | 0.0900298 | ||||||||
\(647\) | 45.2884 | 1.78047 | 0.890236 | − | 0.455499i | \(-0.150539\pi\) | ||||
0.890236 | + | 0.455499i | \(0.150539\pi\) | |||||||
\(648\) | −1.96528 | −0.0772034 | ||||||||
\(649\) | −15.0918 | −0.592403 | ||||||||
\(650\) | 38.8318 | 1.52311 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.4635 | 0.566432 | ||||||||
\(653\) | 49.0869 | 1.92092 | 0.960459 | − | 0.278421i | \(-0.0898111\pi\) | ||||
0.960459 | + | 0.278421i | \(0.0898111\pi\) | |||||||
\(654\) | −17.0353 | −0.666132 | ||||||||
\(655\) | −27.2473 | −1.06464 | ||||||||
\(656\) | 4.97185 | 0.194118 | ||||||||
\(657\) | −12.7925 | −0.499084 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.8228 | 1.86291 | 0.931456 | − | 0.363853i | \(-0.118539\pi\) | ||||
0.931456 | + | 0.363853i | \(0.118539\pi\) | |||||||
\(660\) | −2.90575 | −0.113106 | ||||||||
\(661\) | −38.8838 | −1.51240 | −0.756202 | − | 0.654339i | \(-0.772947\pi\) | ||||
−0.756202 | + | 0.654339i | \(0.772947\pi\) | |||||||
\(662\) | −20.3148 | −0.789557 | ||||||||
\(663\) | 2.90722 | 0.112907 | ||||||||
\(664\) | 2.84838 | 0.110539 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.7076 | 0.531158 | ||||||||
\(667\) | 1.77847 | 0.0688625 | ||||||||
\(668\) | −2.27712 | −0.0881043 | ||||||||
\(669\) | 14.0160 | 0.541889 | ||||||||
\(670\) | 12.6776 | 0.489777 | ||||||||
\(671\) | −11.9251 | −0.460365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.8958 | 0.766926 | 0.383463 | − | 0.923556i | \(-0.374731\pi\) | ||||
0.383463 | + | 0.923556i | \(0.374731\pi\) | |||||||
\(674\) | 41.7303 | 1.60739 | ||||||||
\(675\) | 6.59272 | 0.253754 | ||||||||
\(676\) | −0.624586 | −0.0240226 | ||||||||
\(677\) | −14.7663 | −0.567514 | −0.283757 | − | 0.958896i | \(-0.591581\pi\) | ||||
−0.283757 | + | 0.958896i | \(0.591581\pi\) | |||||||
\(678\) | −24.0688 | −0.924358 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.55821 | 0.213148 | ||||||||
\(681\) | 13.5192 | 0.518056 | ||||||||
\(682\) | −14.4982 | −0.555165 | ||||||||
\(683\) | 34.9130 | 1.33591 | 0.667954 | − | 0.744203i | \(-0.267170\pi\) | ||||
0.667954 | + | 0.744203i | \(0.267170\pi\) | |||||||
\(684\) | 1.36226 | 0.0520872 | ||||||||
\(685\) | −18.9296 | −0.723263 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.208217 | 0.00794398 | ||||||||
\(688\) | −43.7563 | −1.66819 | ||||||||
\(689\) | −1.46057 | −0.0556431 | ||||||||
\(690\) | 8.70932 | 0.331558 | ||||||||
\(691\) | −26.3787 | −1.00349 | −0.501746 | − | 0.865015i | \(-0.667309\pi\) | ||||
−0.501746 | + | 0.865015i | \(0.667309\pi\) | |||||||
\(692\) | −14.3830 | −0.546760 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.85966 | −0.374268 | ||||||||
\(695\) | −41.9116 | −1.58980 | ||||||||
\(696\) | 2.29954 | 0.0871640 | ||||||||
\(697\) | −0.830651 | −0.0314631 | ||||||||
\(698\) | −60.8980 | −2.30502 | ||||||||
\(699\) | 15.6507 | 0.591963 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.5243 | −0.812962 | −0.406481 | − | 0.913659i | \(-0.633244\pi\) | ||||
−0.406481 | + | 0.913659i | \(0.633244\pi\) | |||||||
\(702\) | 5.89010 | 0.222308 | ||||||||
\(703\) | 13.3327 | 0.502852 | ||||||||
\(704\) | 2.54024 | 0.0957389 | ||||||||
\(705\) | 35.1562 | 1.32406 | ||||||||
\(706\) | −8.83083 | −0.332353 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −12.2477 | −0.460295 | ||||||||
\(709\) | 37.6979 | 1.41577 | 0.707887 | − | 0.706325i | \(-0.249648\pi\) | ||||
0.707887 | + | 0.706325i | \(0.249648\pi\) | |||||||
\(710\) | 5.75586 | 0.216014 | ||||||||
\(711\) | −9.00439 | −0.337691 | ||||||||
\(712\) | 20.4482 | 0.766330 | ||||||||
\(713\) | 12.7689 | 0.478198 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.2202 | −0.457009 | ||||||||
\(716\) | 9.80063 | 0.366267 | ||||||||
\(717\) | −14.7846 | −0.552140 | ||||||||
\(718\) | −8.15716 | −0.304422 | ||||||||
\(719\) | 41.4883 | 1.54725 | 0.773627 | − | 0.633642i | \(-0.218441\pi\) | ||||
0.773627 | + | 0.633642i | \(0.218441\pi\) | |||||||
\(720\) | 16.9282 | 0.630877 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −27.4662 | −1.02219 | ||||||||
\(723\) | 6.77989 | 0.252147 | ||||||||
\(724\) | 1.50114 | 0.0557893 | ||||||||
\(725\) | −7.71405 | −0.286492 | ||||||||
\(726\) | −16.7424 | −0.621367 | ||||||||
\(727\) | 2.82371 | 0.104726 | 0.0523629 | − | 0.998628i | \(-0.483325\pi\) | ||||
0.0523629 | + | 0.998628i | \(0.483325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 73.3014 | 2.71301 | ||||||||
\(731\) | 7.31040 | 0.270385 | ||||||||
\(732\) | −9.67779 | −0.357701 | ||||||||
\(733\) | 3.92493 | 0.144971 | 0.0724853 | − | 0.997369i | \(-0.476907\pi\) | ||||
0.0724853 | + | 0.997369i | \(0.476907\pi\) | |||||||
\(734\) | 40.9691 | 1.51220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.74350 | 0.248569 | ||||||||
\(737\) | −2.26885 | −0.0835741 | ||||||||
\(738\) | −1.68292 | −0.0619492 | ||||||||
\(739\) | 13.1283 | 0.482933 | 0.241467 | − | 0.970409i | \(-0.422372\pi\) | ||||
0.241467 | + | 0.970409i | \(0.422372\pi\) | |||||||
\(740\) | −23.0796 | −0.848425 | ||||||||
\(741\) | 5.72901 | 0.210460 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9382 | −0.768148 | −0.384074 | − | 0.923302i | \(-0.625479\pi\) | ||||
−0.384074 | + | 0.923302i | \(0.625479\pi\) | |||||||
\(744\) | 16.5101 | 0.605288 | ||||||||
\(745\) | −61.1322 | −2.23971 | ||||||||
\(746\) | −15.8499 | −0.580307 | ||||||||
\(747\) | −1.44935 | −0.0530291 | ||||||||
\(748\) | 0.708898 | 0.0259199 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.12630 | −0.333245 | ||||||||
\(751\) | −42.0676 | −1.53507 | −0.767535 | − | 0.641008i | \(-0.778517\pi\) | ||||
−0.767535 | + | 0.641008i | \(0.778517\pi\) | |||||||
\(752\) | 51.3366 | 1.87205 | ||||||||
\(753\) | 28.5862 | 1.04174 | ||||||||
\(754\) | −6.89192 | −0.250989 | ||||||||
\(755\) | −36.8469 | −1.34100 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4088 | 1.17792 | 0.588959 | − | 0.808163i | \(-0.299538\pi\) | ||||
0.588959 | + | 0.808163i | \(0.299538\pi\) | |||||||
\(758\) | 29.5720 | 1.07410 | ||||||||
\(759\) | −1.55867 | −0.0565761 | ||||||||
\(760\) | 10.9531 | 0.397311 | ||||||||
\(761\) | 44.6418 | 1.61826 | 0.809132 | − | 0.587627i | \(-0.199938\pi\) | ||||
0.809132 | + | 0.587627i | \(0.199938\pi\) | |||||||
\(762\) | −3.73343 | −0.135248 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.9892 | −0.578468 | ||||||||
\(765\) | −2.82821 | −0.102254 | ||||||||
\(766\) | −61.3343 | −2.21610 | ||||||||
\(767\) | −51.5078 | −1.85984 | ||||||||
\(768\) | 16.9947 | 0.613242 | ||||||||
\(769\) | −50.2119 | −1.81069 | −0.905344 | − | 0.424678i | \(-0.860387\pi\) | ||||
−0.905344 | + | 0.424678i | \(0.860387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.5785 | −0.885172 | ||||||||
\(772\) | 13.2729 | 0.477701 | ||||||||
\(773\) | 9.92150 | 0.356852 | 0.178426 | − | 0.983953i | \(-0.442900\pi\) | ||||
0.178426 | + | 0.983953i | \(0.442900\pi\) | |||||||
\(774\) | 14.8111 | 0.532373 | ||||||||
\(775\) | −55.3846 | −1.98947 | ||||||||
\(776\) | 5.60542 | 0.201223 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.12794 | 0.327252 | ||||||||
\(779\) | −1.63689 | −0.0586478 | ||||||||
\(780\) | −9.91724 | −0.355094 | ||||||||
\(781\) | −1.03010 | −0.0368599 | ||||||||
\(782\) | −2.12476 | −0.0759813 | ||||||||
\(783\) | −1.17009 | −0.0418155 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.3109 | −1.04615 | ||||||||
\(786\) | 13.4677 | 0.480378 | ||||||||
\(787\) | 4.64621 | 0.165619 | 0.0828097 | − | 0.996565i | \(-0.473611\pi\) | ||||
0.0828097 | + | 0.996565i | \(0.473611\pi\) | |||||||
\(788\) | 4.57159 | 0.162856 | ||||||||
\(789\) | 2.67564 | 0.0952555 | ||||||||
\(790\) | 51.5953 | 1.83568 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.01535 | −0.0716123 | ||||||||
\(793\) | −40.7002 | −1.44531 | ||||||||
\(794\) | 55.5828 | 1.97256 | ||||||||
\(795\) | 1.42087 | 0.0503931 | ||||||||
\(796\) | 0.653571 | 0.0231652 | ||||||||
\(797\) | −22.7270 | −0.805030 | −0.402515 | − | 0.915413i | \(-0.631864\pi\) | ||||
−0.402515 | + | 0.915413i | \(0.631864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.57684 | −0.303427 | ||||||||
\(800\) | −29.2497 | −1.03413 | ||||||||
\(801\) | −10.4048 | −0.367634 | ||||||||
\(802\) | −7.03766 | −0.248508 | ||||||||
\(803\) | −13.1184 | −0.462940 | ||||||||
\(804\) | −1.84127 | −0.0649367 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −49.4820 | −1.74293 | ||||||||
\(807\) | −20.4028 | −0.718212 | ||||||||
\(808\) | 4.91800 | 0.173015 | ||||||||
\(809\) | −3.74399 | −0.131632 | −0.0658159 | − | 0.997832i | \(-0.520965\pi\) | ||||
−0.0658159 | + | 0.997832i | \(0.520965\pi\) | |||||||
\(810\) | −5.73002 | −0.201332 | ||||||||
\(811\) | 28.8811 | 1.01415 | 0.507077 | − | 0.861901i | \(-0.330726\pi\) | ||||
0.507077 | + | 0.861901i | \(0.330726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.9779 | −0.911085 | ||||||||
\(814\) | 14.0568 | 0.492691 | ||||||||
\(815\) | −59.1732 | −2.07275 | ||||||||
\(816\) | −4.12987 | −0.144574 | ||||||||
\(817\) | 14.4060 | 0.504002 | ||||||||
\(818\) | −19.8548 | −0.694207 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.83356 | 0.0989521 | ||||||||
\(821\) | −22.9214 | −0.799961 | −0.399981 | − | 0.916524i | \(-0.630983\pi\) | ||||
−0.399981 | + | 0.916524i | \(0.630983\pi\) | |||||||
\(822\) | 9.35648 | 0.326345 | ||||||||
\(823\) | 48.0792 | 1.67594 | 0.837968 | − | 0.545720i | \(-0.183744\pi\) | ||||
0.837968 | + | 0.545720i | \(0.183744\pi\) | |||||||
\(824\) | 3.19975 | 0.111469 | ||||||||
\(825\) | 6.76068 | 0.235377 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9287 | 0.866856 | 0.433428 | − | 0.901188i | \(-0.357304\pi\) | ||||
0.433428 | + | 0.901188i | \(0.357304\pi\) | |||||||
\(828\) | −1.26493 | −0.0439594 | ||||||||
\(829\) | −39.6168 | −1.37595 | −0.687974 | − | 0.725736i | \(-0.741500\pi\) | ||||
−0.687974 | + | 0.725736i | \(0.741500\pi\) | |||||||
\(830\) | 8.30483 | 0.288265 | ||||||||
\(831\) | −11.8244 | −0.410185 | ||||||||
\(832\) | 8.66978 | 0.300570 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.7160 | 0.717335 | ||||||||
\(835\) | 9.31620 | 0.322401 | ||||||||
\(836\) | 1.39696 | 0.0483150 | ||||||||
\(837\) | −8.40087 | −0.290377 | ||||||||
\(838\) | −47.2505 | −1.63224 | ||||||||
\(839\) | 0.996793 | 0.0344131 | 0.0172066 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172066 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6309 | −0.952790 | ||||||||
\(842\) | 24.8931 | 0.857873 | ||||||||
\(843\) | −7.86950 | −0.271040 | ||||||||
\(844\) | −16.4127 | −0.564948 | ||||||||
\(845\) | 2.55532 | 0.0879058 | ||||||||
\(846\) | −17.3769 | −0.597431 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.07482 | 0.0712496 | ||||||||
\(849\) | 16.7613 | 0.575245 | ||||||||
\(850\) | 9.21609 | 0.316109 | ||||||||
\(851\) | −12.3801 | −0.424386 | ||||||||
\(852\) | −0.835975 | −0.0286400 | ||||||||
\(853\) | −14.9102 | −0.510517 | −0.255258 | − | 0.966873i | \(-0.582160\pi\) | ||||
−0.255258 | + | 0.966873i | \(0.582160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.57331 | −0.190603 | ||||||||
\(856\) | 25.6621 | 0.877113 | ||||||||
\(857\) | 42.8328 | 1.46314 | 0.731571 | − | 0.681765i | \(-0.238787\pi\) | ||||
0.731571 | + | 0.681765i | \(0.238787\pi\) | |||||||
\(858\) | 6.04016 | 0.206208 | ||||||||
\(859\) | −3.21511 | −0.109698 | −0.0548490 | − | 0.998495i | \(-0.517468\pi\) | ||||
−0.0548490 | + | 0.998495i | \(0.517468\pi\) | |||||||
\(860\) | −24.9376 | −0.850365 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.67730 | −0.159309 | ||||||||
\(863\) | −16.1955 | −0.551302 | −0.275651 | − | 0.961258i | \(-0.588893\pi\) | ||||
−0.275651 | + | 0.961258i | \(0.588893\pi\) | |||||||
\(864\) | −4.43667 | −0.150939 | ||||||||
\(865\) | 58.8441 | 2.00076 | ||||||||
\(866\) | −46.9068 | −1.59396 | ||||||||
\(867\) | −16.3100 | −0.553917 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.23379 | −0.313235 | ||||||||
\(870\) | 6.70462 | 0.227308 | ||||||||
\(871\) | −7.74352 | −0.262379 | ||||||||
\(872\) | 19.8934 | 0.673676 | ||||||||
\(873\) | −2.85223 | −0.0965333 | ||||||||
\(874\) | −4.18709 | −0.141630 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6462 | −0.359702 | ||||||||
\(877\) | 8.10740 | 0.273767 | 0.136884 | − | 0.990587i | \(-0.456291\pi\) | ||||
0.136884 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(878\) | 31.9619 | 1.07866 | ||||||||
\(879\) | 13.3389 | 0.449912 | ||||||||
\(880\) | 17.3595 | 0.585188 | ||||||||
\(881\) | 42.9107 | 1.44570 | 0.722849 | − | 0.691006i | \(-0.242832\pi\) | ||||
0.722849 | + | 0.691006i | \(0.242832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.6450 | 0.795718 | 0.397859 | − | 0.917446i | \(-0.369753\pi\) | ||||
0.397859 | + | 0.917446i | \(0.369753\pi\) | |||||||
\(884\) | 2.41945 | 0.0813749 | ||||||||
\(885\) | 50.1079 | 1.68436 | ||||||||
\(886\) | −29.3409 | −0.985728 | ||||||||
\(887\) | −49.4383 | −1.65998 | −0.829989 | − | 0.557780i | \(-0.811653\pi\) | ||||
−0.829989 | + | 0.557780i | \(0.811653\pi\) | |||||||
\(888\) | −16.0074 | −0.537174 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 59.6195 | 1.99845 | ||||||||
\(891\) | 1.02548 | 0.0343548 | ||||||||
\(892\) | 11.6644 | 0.390553 | ||||||||
\(893\) | −16.9017 | −0.565592 | ||||||||
\(894\) | 30.2163 | 1.01058 | ||||||||
\(895\) | −40.0966 | −1.34028 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.31970 | −0.177620 | ||||||||
\(898\) | 11.9870 | 0.400010 | ||||||||
\(899\) | 9.82975 | 0.327840 | ||||||||
\(900\) | 5.48660 | 0.182887 | ||||||||
\(901\) | −0.346641 | −0.0115483 | ||||||||
\(902\) | −1.72580 | −0.0574628 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.1071 | 0.934827 | ||||||||
\(905\) | −6.14149 | −0.204150 | ||||||||
\(906\) | 18.2126 | 0.605073 | ||||||||
\(907\) | 4.12340 | 0.136915 | 0.0684576 | − | 0.997654i | \(-0.478192\pi\) | ||||
0.0684576 | + | 0.997654i | \(0.478192\pi\) | |||||||
\(908\) | 11.2509 | 0.373376 | ||||||||
\(909\) | −2.50244 | −0.0830009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6414 | −0.485090 | −0.242545 | − | 0.970140i | \(-0.577982\pi\) | ||||
−0.242545 | + | 0.970140i | \(0.577982\pi\) | |||||||
\(912\) | −8.13839 | −0.269489 | ||||||||
\(913\) | −1.48628 | −0.0491887 | ||||||||
\(914\) | 64.7536 | 2.14186 | ||||||||
\(915\) | 39.5940 | 1.30894 | ||||||||
\(916\) | 0.173283 | 0.00572543 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.39792 | 0.0461382 | ||||||||
\(919\) | 60.1835 | 1.98527 | 0.992635 | − | 0.121147i | \(-0.0386573\pi\) | ||||
0.992635 | + | 0.121147i | \(0.0386573\pi\) | |||||||
\(920\) | −10.1706 | −0.335313 | ||||||||
\(921\) | 0.258573 | 0.00852027 | ||||||||
\(922\) | −11.2328 | −0.369932 | ||||||||
\(923\) | −3.51571 | −0.115721 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.6984 | 1.76559 | ||||||||
\(926\) | −50.0556 | −1.64493 | ||||||||
\(927\) | −1.62814 | −0.0534752 | ||||||||
\(928\) | 5.19129 | 0.170412 | ||||||||
\(929\) | 58.3675 | 1.91497 | 0.957487 | − | 0.288476i | \(-0.0931487\pi\) | ||||
0.957487 | + | 0.288476i | \(0.0931487\pi\) | |||||||
\(930\) | 48.1372 | 1.57848 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.0248 | 0.426643 | ||||||||
\(933\) | 22.9830 | 0.752430 | ||||||||
\(934\) | −58.1232 | −1.90185 | ||||||||
\(935\) | −2.90026 | −0.0948487 | ||||||||
\(936\) | −6.87833 | −0.224825 | ||||||||
\(937\) | 15.7839 | 0.515637 | 0.257818 | − | 0.966193i | \(-0.416996\pi\) | ||||
0.257818 | + | 0.966193i | \(0.416996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.78960 | 0.188936 | ||||||||
\(940\) | 29.2577 | 0.954282 | ||||||||
\(941\) | 35.9945 | 1.17339 | 0.586694 | − | 0.809809i | \(-0.300429\pi\) | ||||
0.586694 | + | 0.809809i | \(0.300429\pi\) | |||||||
\(942\) | 14.4877 | 0.472036 | ||||||||
\(943\) | 1.51995 | 0.0494962 | ||||||||
\(944\) | 73.1698 | 2.38147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.1884 | 0.493818 | ||||||||
\(947\) | −20.8209 | −0.676590 | −0.338295 | − | 0.941040i | \(-0.609850\pi\) | ||||
−0.338295 | + | 0.941040i | \(0.609850\pi\) | |||||||
\(948\) | −7.49365 | −0.243382 | ||||||||
\(949\) | −44.7729 | −1.45339 | ||||||||
\(950\) | 18.1614 | 0.589232 | ||||||||
\(951\) | −25.7608 | −0.835350 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.0984 | 0.521479 | 0.260739 | − | 0.965409i | \(-0.416034\pi\) | ||||
0.260739 | + | 0.965409i | \(0.416034\pi\) | |||||||
\(954\) | −0.702305 | −0.0227380 | ||||||||
\(955\) | 65.4154 | 2.11679 | ||||||||
\(956\) | −12.3040 | −0.397941 | ||||||||
\(957\) | −1.19990 | −0.0387872 | ||||||||
\(958\) | −44.1064 | −1.42501 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.43415 | −0.272211 | ||||||||
\(961\) | 39.5747 | 1.27660 | ||||||||
\(962\) | 47.9756 | 1.54679 | ||||||||
\(963\) | −13.0578 | −0.420780 | ||||||||
\(964\) | 5.64237 | 0.181729 | ||||||||
\(965\) | −54.3023 | −1.74805 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.604604 | −0.0194428 | −0.00972138 | − | 0.999953i | \(-0.503094\pi\) | ||||
−0.00972138 | + | 0.999953i | \(0.503094\pi\) | |||||||
\(968\) | 19.5514 | 0.628405 | ||||||||
\(969\) | 1.35969 | 0.0436794 | ||||||||
\(970\) | 16.3433 | 0.524753 | ||||||||
\(971\) | 35.7504 | 1.14728 | 0.573642 | − | 0.819106i | \(-0.305530\pi\) | ||||
0.573642 | + | 0.819106i | \(0.305530\pi\) | |||||||
\(972\) | 0.832222 | 0.0266935 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.27640 | −0.233151 | ||||||||
\(975\) | 23.0740 | 0.738960 | ||||||||
\(976\) | 57.8170 | 1.85068 | ||||||||
\(977\) | 31.1492 | 0.996550 | 0.498275 | − | 0.867019i | \(-0.333967\pi\) | ||||
0.498275 | + | 0.867019i | \(0.333967\pi\) | |||||||
\(978\) | 29.2480 | 0.935248 | ||||||||
\(979\) | −10.6698 | −0.341010 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1224 | −0.323185 | ||||||||
\(982\) | −2.19506 | −0.0700473 | ||||||||
\(983\) | −21.6780 | −0.691421 | −0.345710 | − | 0.938341i | \(-0.612362\pi\) | ||||
−0.345710 | + | 0.938341i | \(0.612362\pi\) | |||||||
\(984\) | 1.96528 | 0.0626508 | ||||||||
\(985\) | −18.7034 | −0.595941 | ||||||||
\(986\) | −1.63569 | −0.0520909 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.76781 | 0.151684 | ||||||||
\(989\) | −13.3768 | −0.425356 | ||||||||
\(990\) | −5.87601 | −0.186752 | ||||||||
\(991\) | −20.6913 | −0.657281 | −0.328641 | − | 0.944455i | \(-0.606590\pi\) | ||||
−0.328641 | + | 0.944455i | \(0.606590\pi\) | |||||||
\(992\) | 37.2719 | 1.18339 | ||||||||
\(993\) | −12.0711 | −0.383066 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.67391 | −0.0847686 | ||||||||
\(996\) | −1.20618 | −0.0382194 | ||||||||
\(997\) | 52.1527 | 1.65169 | 0.825847 | − | 0.563894i | \(-0.190697\pi\) | ||||
0.825847 | + | 0.563894i | \(0.190697\pi\) | |||||||
\(998\) | 3.54024 | 0.112064 | ||||||||
\(999\) | 8.14512 | 0.257700 |
(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 | 6027.2.a.bk.1.12 | 14 | ||
7.3 | odd | 6 | 861.2.i.g.247.3 | ✓ | 28 | ||
7.5 | odd | 6 | 861.2.i.g.739.3 | yes | 28 | ||
7.6 | odd | 2 | 6027.2.a.bj.1.12 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.3 | ✓ | 28 | 7.3 | odd | 6 | ||
861.2.i.g.739.3 | yes | 28 | 7.5 | odd | 6 | ||
6027.2.a.bj.1.12 | 14 | 7.6 | odd | 2 | |||
6027.2.a.bk.1.12 | 14 | 1.1 | even | 1 | trivial |