Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62861 | −1.15160 | −0.575799 | − | 0.817591i | \(-0.695309\pi\) | ||||
−0.575799 | + | 0.817591i | \(0.695309\pi\) | |||||||
\(3\) | −2.08850 | −1.20579 | −0.602897 | − | 0.797819i | \(-0.705987\pi\) | ||||
−0.602897 | + | 0.797819i | \(0.705987\pi\) | |||||||
\(4\) | 0.652359 | 0.326180 | ||||||||
\(5\) | −3.32951 | −1.48900 | −0.744501 | − | 0.667621i | \(-0.767313\pi\) | ||||
−0.744501 | + | 0.667621i | \(0.767313\pi\) | |||||||
\(6\) | 3.40134 | 1.38859 | ||||||||
\(7\) | −5.07571 | −1.91844 | −0.959219 | − | 0.282663i | \(-0.908782\pi\) | ||||
−0.959219 | + | 0.282663i | \(0.908782\pi\) | |||||||
\(8\) | 2.19478 | 0.775971 | ||||||||
\(9\) | 1.36181 | 0.453937 | ||||||||
\(10\) | 5.42246 | 1.71473 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.36245 | −0.393305 | ||||||||
\(13\) | −0.291030 | −0.0807171 | −0.0403586 | − | 0.999185i | \(-0.512850\pi\) | ||||
−0.0403586 | + | 0.999185i | \(0.512850\pi\) | |||||||
\(14\) | 8.26634 | 2.20927 | ||||||||
\(15\) | 6.95367 | 1.79543 | ||||||||
\(16\) | −4.87915 | −1.21979 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.21786 | −0.522754 | ||||||||
\(19\) | 7.07744 | 1.62368 | 0.811838 | − | 0.583883i | \(-0.198467\pi\) | ||||
0.811838 | + | 0.583883i | \(0.198467\pi\) | |||||||
\(20\) | −2.17204 | −0.485682 | ||||||||
\(21\) | 10.6006 | 2.31324 | ||||||||
\(22\) | −1.62861 | −0.347220 | ||||||||
\(23\) | 1.66635 | 0.347459 | 0.173729 | − | 0.984793i | \(-0.444418\pi\) | ||||
0.173729 | + | 0.984793i | \(0.444418\pi\) | |||||||
\(24\) | −4.58378 | −0.935660 | ||||||||
\(25\) | 6.08564 | 1.21713 | ||||||||
\(26\) | 0.473973 | 0.0929537 | ||||||||
\(27\) | 3.42135 | 0.658439 | ||||||||
\(28\) | −3.31119 | −0.625756 | ||||||||
\(29\) | −4.92017 | −0.913654 | −0.456827 | − | 0.889556i | \(-0.651014\pi\) | ||||
−0.456827 | + | 0.889556i | \(0.651014\pi\) | |||||||
\(30\) | −11.3248 | −2.06761 | ||||||||
\(31\) | −5.61097 | −1.00776 | −0.503880 | − | 0.863774i | \(-0.668095\pi\) | ||||
−0.503880 | + | 0.863774i | \(0.668095\pi\) | |||||||
\(32\) | 3.55666 | 0.628734 | ||||||||
\(33\) | −2.08850 | −0.363560 | ||||||||
\(34\) | −1.62861 | −0.279304 | ||||||||
\(35\) | 16.8996 | 2.85656 | ||||||||
\(36\) | 0.888390 | 0.148065 | ||||||||
\(37\) | 8.06861 | 1.32647 | 0.663236 | − | 0.748410i | \(-0.269183\pi\) | ||||
0.663236 | + | 0.748410i | \(0.269183\pi\) | |||||||
\(38\) | −11.5264 | −1.86982 | ||||||||
\(39\) | 0.607814 | 0.0973281 | ||||||||
\(40\) | −7.30753 | −1.15542 | ||||||||
\(41\) | −2.39391 | −0.373866 | −0.186933 | − | 0.982373i | \(-0.559855\pi\) | ||||
−0.186933 | + | 0.982373i | \(0.559855\pi\) | |||||||
\(42\) | −17.2642 | −2.66392 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0.652359 | 0.0983468 | ||||||||
\(45\) | −4.53417 | −0.675914 | ||||||||
\(46\) | −2.71383 | −0.400133 | ||||||||
\(47\) | 6.60547 | 0.963507 | 0.481753 | − | 0.876307i | \(-0.340000\pi\) | ||||
0.481753 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(48\) | 10.1901 | 1.47081 | ||||||||
\(49\) | 18.7629 | 2.68041 | ||||||||
\(50\) | −9.91112 | −1.40164 | ||||||||
\(51\) | −2.08850 | −0.292448 | ||||||||
\(52\) | −0.189856 | −0.0263283 | ||||||||
\(53\) | 9.64367 | 1.32466 | 0.662330 | − | 0.749212i | \(-0.269568\pi\) | ||||
0.662330 | + | 0.749212i | \(0.269568\pi\) | |||||||
\(54\) | −5.57203 | −0.758257 | ||||||||
\(55\) | −3.32951 | −0.448951 | ||||||||
\(56\) | −11.1401 | −1.48865 | ||||||||
\(57\) | −14.7812 | −1.95782 | ||||||||
\(58\) | 8.01303 | 1.05216 | ||||||||
\(59\) | 13.7484 | 1.78989 | 0.894947 | − | 0.446173i | \(-0.147213\pi\) | ||||
0.894947 | + | 0.446173i | \(0.147213\pi\) | |||||||
\(60\) | 4.53629 | 0.585632 | ||||||||
\(61\) | 14.9930 | 1.91966 | 0.959828 | − | 0.280590i | \(-0.0905302\pi\) | ||||
0.959828 | + | 0.280590i | \(0.0905302\pi\) | |||||||
\(62\) | 9.13806 | 1.16054 | ||||||||
\(63\) | −6.91216 | −0.870851 | ||||||||
\(64\) | 3.96590 | 0.495737 | ||||||||
\(65\) | 0.968986 | 0.120188 | ||||||||
\(66\) | 3.40134 | 0.418676 | ||||||||
\(67\) | 1.40254 | 0.171347 | 0.0856735 | − | 0.996323i | \(-0.472696\pi\) | ||||
0.0856735 | + | 0.996323i | \(0.472696\pi\) | |||||||
\(68\) | 0.652359 | 0.0791102 | ||||||||
\(69\) | −3.48017 | −0.418963 | ||||||||
\(70\) | −27.5229 | −3.28961 | ||||||||
\(71\) | 7.30119 | 0.866492 | 0.433246 | − | 0.901276i | \(-0.357368\pi\) | ||||
0.433246 | + | 0.901276i | \(0.357368\pi\) | |||||||
\(72\) | 2.98887 | 0.352242 | ||||||||
\(73\) | −12.2232 | −1.43061 | −0.715307 | − | 0.698810i | \(-0.753713\pi\) | ||||
−0.715307 | + | 0.698810i | \(0.753713\pi\) | |||||||
\(74\) | −13.1406 | −1.52756 | ||||||||
\(75\) | −12.7098 | −1.46761 | ||||||||
\(76\) | 4.61703 | 0.529610 | ||||||||
\(77\) | −5.07571 | −0.578431 | ||||||||
\(78\) | −0.989890 | −0.112083 | ||||||||
\(79\) | −6.07658 | −0.683668 | −0.341834 | − | 0.939760i | \(-0.611048\pi\) | ||||
−0.341834 | + | 0.939760i | \(0.611048\pi\) | |||||||
\(80\) | 16.2452 | 1.81627 | ||||||||
\(81\) | −11.2309 | −1.24788 | ||||||||
\(82\) | 3.89874 | 0.430544 | ||||||||
\(83\) | −1.31345 | −0.144170 | −0.0720851 | − | 0.997398i | \(-0.522965\pi\) | ||||
−0.0720851 | + | 0.997398i | \(0.522965\pi\) | |||||||
\(84\) | 6.91540 | 0.754532 | ||||||||
\(85\) | −3.32951 | −0.361136 | ||||||||
\(86\) | −1.62861 | −0.175617 | ||||||||
\(87\) | 10.2758 | 1.10168 | ||||||||
\(88\) | 2.19478 | 0.233964 | ||||||||
\(89\) | −4.77370 | −0.506011 | −0.253006 | − | 0.967465i | \(-0.581419\pi\) | ||||
−0.253006 | + | 0.967465i | \(0.581419\pi\) | |||||||
\(90\) | 7.38437 | 0.778381 | ||||||||
\(91\) | 1.47718 | 0.154851 | ||||||||
\(92\) | 1.08706 | 0.113334 | ||||||||
\(93\) | 11.7185 | 1.21515 | ||||||||
\(94\) | −10.7577 | −1.10957 | ||||||||
\(95\) | −23.5644 | −2.41766 | ||||||||
\(96\) | −7.42806 | −0.758123 | ||||||||
\(97\) | 1.25500 | 0.127426 | 0.0637130 | − | 0.997968i | \(-0.479706\pi\) | ||||
0.0637130 | + | 0.997968i | \(0.479706\pi\) | |||||||
\(98\) | −30.5573 | −3.08675 | ||||||||
\(99\) | 1.36181 | 0.136867 | ||||||||
\(100\) | 3.97003 | 0.397003 | ||||||||
\(101\) | 10.9162 | 1.08620 | 0.543099 | − | 0.839669i | \(-0.317251\pi\) | ||||
0.543099 | + | 0.839669i | \(0.317251\pi\) | |||||||
\(102\) | 3.40134 | 0.336783 | ||||||||
\(103\) | −11.9102 | −1.17355 | −0.586775 | − | 0.809750i | \(-0.699603\pi\) | ||||
−0.586775 | + | 0.809750i | \(0.699603\pi\) | |||||||
\(104\) | −0.638745 | −0.0626341 | ||||||||
\(105\) | −35.2948 | −3.44442 | ||||||||
\(106\) | −15.7057 | −1.52548 | ||||||||
\(107\) | −12.9562 | −1.25252 | −0.626262 | − | 0.779613i | \(-0.715416\pi\) | ||||
−0.626262 | + | 0.779613i | \(0.715416\pi\) | |||||||
\(108\) | 2.23195 | 0.214769 | ||||||||
\(109\) | 19.3440 | 1.85281 | 0.926407 | − | 0.376523i | \(-0.122880\pi\) | ||||
0.926407 | + | 0.376523i | \(0.122880\pi\) | |||||||
\(110\) | 5.42246 | 0.517012 | ||||||||
\(111\) | −16.8513 | −1.59945 | ||||||||
\(112\) | 24.7651 | 2.34009 | ||||||||
\(113\) | −10.0690 | −0.947209 | −0.473605 | − | 0.880738i | \(-0.657047\pi\) | ||||
−0.473605 | + | 0.880738i | \(0.657047\pi\) | |||||||
\(114\) | 24.0727 | 2.25462 | ||||||||
\(115\) | −5.54814 | −0.517367 | ||||||||
\(116\) | −3.20972 | −0.298015 | ||||||||
\(117\) | −0.396328 | −0.0366405 | ||||||||
\(118\) | −22.3908 | −2.06124 | ||||||||
\(119\) | −5.07571 | −0.465290 | ||||||||
\(120\) | 15.2617 | 1.39320 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −24.4177 | −2.21067 | ||||||||
\(123\) | 4.99967 | 0.450805 | ||||||||
\(124\) | −3.66037 | −0.328711 | ||||||||
\(125\) | −3.61466 | −0.323305 | ||||||||
\(126\) | 11.2572 | 1.00287 | ||||||||
\(127\) | 14.7795 | 1.31147 | 0.655733 | − | 0.754993i | \(-0.272360\pi\) | ||||
0.655733 | + | 0.754993i | \(0.272360\pi\) | |||||||
\(128\) | −13.5722 | −1.19962 | ||||||||
\(129\) | −2.08850 | −0.183882 | ||||||||
\(130\) | −1.57810 | −0.138408 | ||||||||
\(131\) | −21.9985 | −1.92202 | −0.961010 | − | 0.276514i | \(-0.910821\pi\) | ||||
−0.961010 | + | 0.276514i | \(0.910821\pi\) | |||||||
\(132\) | −1.36245 | −0.118586 | ||||||||
\(133\) | −35.9230 | −3.11492 | ||||||||
\(134\) | −2.28418 | −0.197323 | ||||||||
\(135\) | −11.3914 | −0.980417 | ||||||||
\(136\) | 2.19478 | 0.188201 | ||||||||
\(137\) | −11.4506 | −0.978294 | −0.489147 | − | 0.872201i | \(-0.662692\pi\) | ||||
−0.489147 | + | 0.872201i | \(0.662692\pi\) | |||||||
\(138\) | 5.66783 | 0.482478 | ||||||||
\(139\) | −6.06668 | −0.514569 | −0.257284 | − | 0.966336i | \(-0.582828\pi\) | ||||
−0.257284 | + | 0.966336i | \(0.582828\pi\) | |||||||
\(140\) | 11.0246 | 0.931752 | ||||||||
\(141\) | −13.7955 | −1.16179 | ||||||||
\(142\) | −11.8908 | −0.997851 | ||||||||
\(143\) | −0.291030 | −0.0243371 | ||||||||
\(144\) | −6.64448 | −0.553706 | ||||||||
\(145\) | 16.3818 | 1.36043 | ||||||||
\(146\) | 19.9067 | 1.64749 | ||||||||
\(147\) | −39.1861 | −3.23202 | ||||||||
\(148\) | 5.26363 | 0.432668 | ||||||||
\(149\) | −6.38373 | −0.522975 | −0.261488 | − | 0.965207i | \(-0.584213\pi\) | ||||
−0.261488 | + | 0.965207i | \(0.584213\pi\) | |||||||
\(150\) | 20.6993 | 1.69009 | ||||||||
\(151\) | 1.42651 | 0.116088 | 0.0580439 | − | 0.998314i | \(-0.481514\pi\) | ||||
0.0580439 | + | 0.998314i | \(0.481514\pi\) | |||||||
\(152\) | 15.5334 | 1.25992 | ||||||||
\(153\) | 1.36181 | 0.110096 | ||||||||
\(154\) | 8.26634 | 0.666120 | ||||||||
\(155\) | 18.6818 | 1.50056 | ||||||||
\(156\) | 0.396513 | 0.0317464 | ||||||||
\(157\) | −1.02272 | −0.0816221 | −0.0408110 | − | 0.999167i | \(-0.512994\pi\) | ||||
−0.0408110 | + | 0.999167i | \(0.512994\pi\) | |||||||
\(158\) | 9.89635 | 0.787311 | ||||||||
\(159\) | −20.1408 | −1.59727 | ||||||||
\(160\) | −11.8419 | −0.936186 | ||||||||
\(161\) | −8.45793 | −0.666578 | ||||||||
\(162\) | 18.2907 | 1.43705 | ||||||||
\(163\) | 19.0310 | 1.49063 | 0.745313 | − | 0.666715i | \(-0.232300\pi\) | ||||
0.745313 | + | 0.666715i | \(0.232300\pi\) | |||||||
\(164\) | −1.56169 | −0.121947 | ||||||||
\(165\) | 6.95367 | 0.541342 | ||||||||
\(166\) | 2.13910 | 0.166026 | ||||||||
\(167\) | 1.56173 | 0.120850 | 0.0604252 | − | 0.998173i | \(-0.480754\pi\) | ||||
0.0604252 | + | 0.998173i | \(0.480754\pi\) | |||||||
\(168\) | 23.2659 | 1.79501 | ||||||||
\(169\) | −12.9153 | −0.993485 | ||||||||
\(170\) | 5.42246 | 0.415884 | ||||||||
\(171\) | 9.63814 | 0.737047 | ||||||||
\(172\) | 0.652359 | 0.0497419 | ||||||||
\(173\) | 9.72343 | 0.739259 | 0.369629 | − | 0.929179i | \(-0.379485\pi\) | ||||
0.369629 | + | 0.929179i | \(0.379485\pi\) | |||||||
\(174\) | −16.7352 | −1.26869 | ||||||||
\(175\) | −30.8890 | −2.33499 | ||||||||
\(176\) | −4.87915 | −0.367779 | ||||||||
\(177\) | −28.7135 | −2.15824 | ||||||||
\(178\) | 7.77448 | 0.582722 | ||||||||
\(179\) | 3.23929 | 0.242116 | 0.121058 | − | 0.992645i | \(-0.461371\pi\) | ||||
0.121058 | + | 0.992645i | \(0.461371\pi\) | |||||||
\(180\) | −2.95791 | −0.220469 | ||||||||
\(181\) | 11.2818 | 0.838572 | 0.419286 | − | 0.907854i | \(-0.362280\pi\) | ||||
0.419286 | + | 0.907854i | \(0.362280\pi\) | |||||||
\(182\) | −2.40575 | −0.178326 | ||||||||
\(183\) | −31.3128 | −2.31471 | ||||||||
\(184\) | 3.65727 | 0.269618 | ||||||||
\(185\) | −26.8645 | −1.97512 | ||||||||
\(186\) | −19.0848 | −1.39937 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 4.30914 | 0.314276 | ||||||||
\(189\) | −17.3658 | −1.26317 | ||||||||
\(190\) | 38.3771 | 2.78417 | ||||||||
\(191\) | 19.3859 | 1.40271 | 0.701357 | − | 0.712810i | \(-0.252578\pi\) | ||||
0.701357 | + | 0.712810i | \(0.252578\pi\) | |||||||
\(192\) | −8.28276 | −0.597757 | ||||||||
\(193\) | −14.8428 | −1.06841 | −0.534205 | − | 0.845355i | \(-0.679389\pi\) | ||||
−0.534205 | + | 0.845355i | \(0.679389\pi\) | |||||||
\(194\) | −2.04390 | −0.146744 | ||||||||
\(195\) | −2.02372 | −0.144922 | ||||||||
\(196\) | 12.2401 | 0.874294 | ||||||||
\(197\) | 11.5745 | 0.824653 | 0.412326 | − | 0.911036i | \(-0.364716\pi\) | ||||
0.412326 | + | 0.911036i | \(0.364716\pi\) | |||||||
\(198\) | −2.21786 | −0.157616 | ||||||||
\(199\) | −8.60612 | −0.610072 | −0.305036 | − | 0.952341i | \(-0.598668\pi\) | ||||
−0.305036 | + | 0.952341i | \(0.598668\pi\) | |||||||
\(200\) | 13.3566 | 0.944456 | ||||||||
\(201\) | −2.92919 | −0.206609 | ||||||||
\(202\) | −17.7781 | −1.25086 | ||||||||
\(203\) | 24.9734 | 1.75279 | ||||||||
\(204\) | −1.36245 | −0.0953905 | ||||||||
\(205\) | 7.97055 | 0.556687 | ||||||||
\(206\) | 19.3971 | 1.35146 | ||||||||
\(207\) | 2.26926 | 0.157724 | ||||||||
\(208\) | 1.41998 | 0.0984576 | ||||||||
\(209\) | 7.07744 | 0.489557 | ||||||||
\(210\) | 57.4814 | 3.96659 | ||||||||
\(211\) | −4.22581 | −0.290916 | −0.145458 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145458 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(212\) | 6.29114 | 0.432077 | ||||||||
\(213\) | −15.2485 | −1.04481 | ||||||||
\(214\) | 21.1005 | 1.44240 | ||||||||
\(215\) | −3.32951 | −0.227071 | ||||||||
\(216\) | 7.50910 | 0.510929 | ||||||||
\(217\) | 28.4797 | 1.93333 | ||||||||
\(218\) | −31.5037 | −2.13370 | ||||||||
\(219\) | 25.5280 | 1.72503 | ||||||||
\(220\) | −2.17204 | −0.146439 | ||||||||
\(221\) | −0.291030 | −0.0195768 | ||||||||
\(222\) | 27.4441 | 1.84193 | ||||||||
\(223\) | −27.5315 | −1.84364 | −0.921822 | − | 0.387613i | \(-0.873300\pi\) | ||||
−0.921822 | + | 0.387613i | \(0.873300\pi\) | |||||||
\(224\) | −18.0526 | −1.20619 | ||||||||
\(225\) | 8.28750 | 0.552500 | ||||||||
\(226\) | 16.3984 | 1.09080 | ||||||||
\(227\) | 12.0603 | 0.800473 | 0.400236 | − | 0.916412i | \(-0.368928\pi\) | ||||
0.400236 | + | 0.916412i | \(0.368928\pi\) | |||||||
\(228\) | −9.64265 | −0.638600 | ||||||||
\(229\) | 10.5284 | 0.695734 | 0.347867 | − | 0.937544i | \(-0.386906\pi\) | ||||
0.347867 | + | 0.937544i | \(0.386906\pi\) | |||||||
\(230\) | 9.03574 | 0.595799 | ||||||||
\(231\) | 10.6006 | 0.697468 | ||||||||
\(232\) | −10.7987 | −0.708968 | ||||||||
\(233\) | −9.44338 | −0.618656 | −0.309328 | − | 0.950955i | \(-0.600104\pi\) | ||||
−0.309328 | + | 0.950955i | \(0.600104\pi\) | |||||||
\(234\) | 0.645462 | 0.0421952 | ||||||||
\(235\) | −21.9930 | −1.43466 | ||||||||
\(236\) | 8.96892 | 0.583827 | ||||||||
\(237\) | 12.6909 | 0.824363 | ||||||||
\(238\) | 8.26634 | 0.535827 | ||||||||
\(239\) | 21.1275 | 1.36662 | 0.683312 | − | 0.730126i | \(-0.260539\pi\) | ||||
0.683312 | + | 0.730126i | \(0.260539\pi\) | |||||||
\(240\) | −33.9280 | −2.19004 | ||||||||
\(241\) | 10.9561 | 0.705741 | 0.352871 | − | 0.935672i | \(-0.385206\pi\) | ||||
0.352871 | + | 0.935672i | \(0.385206\pi\) | |||||||
\(242\) | −1.62861 | −0.104691 | ||||||||
\(243\) | 13.1916 | 0.846244 | ||||||||
\(244\) | 9.78081 | 0.626152 | ||||||||
\(245\) | −62.4711 | −3.99113 | ||||||||
\(246\) | −8.14249 | −0.519146 | ||||||||
\(247\) | −2.05974 | −0.131058 | ||||||||
\(248\) | −12.3148 | −0.781992 | ||||||||
\(249\) | 2.74314 | 0.173839 | ||||||||
\(250\) | 5.88686 | 0.372318 | ||||||||
\(251\) | 14.5228 | 0.916673 | 0.458336 | − | 0.888779i | \(-0.348446\pi\) | ||||
0.458336 | + | 0.888779i | \(0.348446\pi\) | |||||||
\(252\) | −4.50921 | −0.284054 | ||||||||
\(253\) | 1.66635 | 0.104763 | ||||||||
\(254\) | −24.0700 | −1.51028 | ||||||||
\(255\) | 6.95367 | 0.435456 | ||||||||
\(256\) | 14.1720 | 0.885748 | ||||||||
\(257\) | −21.4777 | −1.33974 | −0.669872 | − | 0.742476i | \(-0.733651\pi\) | ||||
−0.669872 | + | 0.742476i | \(0.733651\pi\) | |||||||
\(258\) | 3.40134 | 0.211758 | ||||||||
\(259\) | −40.9540 | −2.54476 | ||||||||
\(260\) | 0.632127 | 0.0392029 | ||||||||
\(261\) | −6.70035 | −0.414741 | ||||||||
\(262\) | 35.8269 | 2.21340 | ||||||||
\(263\) | −5.46042 | −0.336704 | −0.168352 | − | 0.985727i | \(-0.553844\pi\) | ||||
−0.168352 | + | 0.985727i | \(0.553844\pi\) | |||||||
\(264\) | −4.58378 | −0.282112 | ||||||||
\(265\) | −32.1087 | −1.97242 | ||||||||
\(266\) | 58.5045 | 3.58714 | ||||||||
\(267\) | 9.96985 | 0.610145 | ||||||||
\(268\) | 0.914957 | 0.0558899 | ||||||||
\(269\) | −0.0887634 | −0.00541200 | −0.00270600 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270600 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(270\) | 18.5521 | 1.12905 | ||||||||
\(271\) | −16.3443 | −0.992843 | −0.496422 | − | 0.868082i | \(-0.665353\pi\) | ||||
−0.496422 | + | 0.868082i | \(0.665353\pi\) | |||||||
\(272\) | −4.87915 | −0.295842 | ||||||||
\(273\) | −3.08509 | −0.186718 | ||||||||
\(274\) | 18.6486 | 1.12660 | ||||||||
\(275\) | 6.08564 | 0.366978 | ||||||||
\(276\) | −2.27032 | −0.136657 | ||||||||
\(277\) | 21.8189 | 1.31097 | 0.655486 | − | 0.755207i | \(-0.272464\pi\) | ||||
0.655486 | + | 0.755207i | \(0.272464\pi\) | |||||||
\(278\) | 9.88023 | 0.592577 | ||||||||
\(279\) | −7.64108 | −0.457460 | ||||||||
\(280\) | 37.0909 | 2.21661 | ||||||||
\(281\) | 11.3532 | 0.677276 | 0.338638 | − | 0.940917i | \(-0.390034\pi\) | ||||
0.338638 | + | 0.940917i | \(0.390034\pi\) | |||||||
\(282\) | 22.4674 | 1.33792 | ||||||||
\(283\) | 27.6296 | 1.64241 | 0.821203 | − | 0.570636i | \(-0.193303\pi\) | ||||
0.821203 | + | 0.570636i | \(0.193303\pi\) | |||||||
\(284\) | 4.76300 | 0.282632 | ||||||||
\(285\) | 49.2141 | 2.91519 | ||||||||
\(286\) | 0.473973 | 0.0280266 | ||||||||
\(287\) | 12.1508 | 0.717239 | ||||||||
\(288\) | 4.84349 | 0.285406 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −26.6795 | −1.56667 | ||||||||
\(291\) | −2.62106 | −0.153649 | ||||||||
\(292\) | −7.97390 | −0.466637 | ||||||||
\(293\) | 13.6011 | 0.794584 | 0.397292 | − | 0.917692i | \(-0.369950\pi\) | ||||
0.397292 | + | 0.917692i | \(0.369950\pi\) | |||||||
\(294\) | 63.8188 | 3.72199 | ||||||||
\(295\) | −45.7756 | −2.66516 | ||||||||
\(296\) | 17.7088 | 1.02930 | ||||||||
\(297\) | 3.42135 | 0.198527 | ||||||||
\(298\) | 10.3966 | 0.602258 | ||||||||
\(299\) | −0.484958 | −0.0280459 | ||||||||
\(300\) | −8.29138 | −0.478703 | ||||||||
\(301\) | −5.07571 | −0.292559 | ||||||||
\(302\) | −2.32323 | −0.133687 | ||||||||
\(303\) | −22.7983 | −1.30973 | ||||||||
\(304\) | −34.5318 | −1.98054 | ||||||||
\(305\) | −49.9193 | −2.85837 | ||||||||
\(306\) | −2.21786 | −0.126786 | ||||||||
\(307\) | −24.0368 | −1.37185 | −0.685926 | − | 0.727671i | \(-0.740603\pi\) | ||||
−0.685926 | + | 0.727671i | \(0.740603\pi\) | |||||||
\(308\) | −3.31119 | −0.188672 | ||||||||
\(309\) | 24.8745 | 1.41506 | ||||||||
\(310\) | −30.4253 | −1.72804 | ||||||||
\(311\) | 32.4528 | 1.84023 | 0.920115 | − | 0.391648i | \(-0.128095\pi\) | ||||
0.920115 | + | 0.391648i | \(0.128095\pi\) | |||||||
\(312\) | 1.33402 | 0.0755238 | ||||||||
\(313\) | 0.741689 | 0.0419227 | 0.0209614 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209614 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(314\) | 1.66561 | 0.0939959 | ||||||||
\(315\) | 23.0141 | 1.29670 | ||||||||
\(316\) | −3.96411 | −0.222999 | ||||||||
\(317\) | −22.9895 | −1.29122 | −0.645609 | − | 0.763668i | \(-0.723396\pi\) | ||||
−0.645609 | + | 0.763668i | \(0.723396\pi\) | |||||||
\(318\) | 32.8014 | 1.83941 | ||||||||
\(319\) | −4.92017 | −0.275477 | ||||||||
\(320\) | −13.2045 | −0.738154 | ||||||||
\(321\) | 27.0590 | 1.51028 | ||||||||
\(322\) | 13.7746 | 0.767631 | ||||||||
\(323\) | 7.07744 | 0.393799 | ||||||||
\(324\) | −7.32658 | −0.407032 | ||||||||
\(325\) | −1.77110 | −0.0982431 | ||||||||
\(326\) | −30.9941 | −1.71660 | ||||||||
\(327\) | −40.3998 | −2.23411 | ||||||||
\(328\) | −5.25410 | −0.290109 | ||||||||
\(329\) | −33.5275 | −1.84843 | ||||||||
\(330\) | −11.3248 | −0.623409 | ||||||||
\(331\) | 8.56674 | 0.470870 | 0.235435 | − | 0.971890i | \(-0.424348\pi\) | ||||
0.235435 | + | 0.971890i | \(0.424348\pi\) | |||||||
\(332\) | −0.856843 | −0.0470254 | ||||||||
\(333\) | 10.9879 | 0.602135 | ||||||||
\(334\) | −2.54344 | −0.139171 | ||||||||
\(335\) | −4.66976 | −0.255136 | ||||||||
\(336\) | −51.7219 | −2.82166 | ||||||||
\(337\) | −9.85838 | −0.537020 | −0.268510 | − | 0.963277i | \(-0.586531\pi\) | ||||
−0.268510 | + | 0.963277i | \(0.586531\pi\) | |||||||
\(338\) | 21.0339 | 1.14410 | ||||||||
\(339\) | 21.0290 | 1.14214 | ||||||||
\(340\) | −2.17204 | −0.117795 | ||||||||
\(341\) | −5.61097 | −0.303851 | ||||||||
\(342\) | −15.6967 | −0.848782 | ||||||||
\(343\) | −59.7048 | −3.22376 | ||||||||
\(344\) | 2.19478 | 0.118334 | ||||||||
\(345\) | 11.5873 | 0.623837 | ||||||||
\(346\) | −15.8356 | −0.851330 | ||||||||
\(347\) | −32.9701 | −1.76993 | −0.884963 | − | 0.465661i | \(-0.845817\pi\) | ||||
−0.884963 | + | 0.465661i | \(0.845817\pi\) | |||||||
\(348\) | 6.70349 | 0.359345 | ||||||||
\(349\) | −6.16526 | −0.330019 | −0.165009 | − | 0.986292i | \(-0.552765\pi\) | ||||
−0.165009 | + | 0.986292i | \(0.552765\pi\) | |||||||
\(350\) | 50.3060 | 2.68897 | ||||||||
\(351\) | −0.995714 | −0.0531473 | ||||||||
\(352\) | 3.55666 | 0.189570 | ||||||||
\(353\) | 9.70048 | 0.516304 | 0.258152 | − | 0.966104i | \(-0.416886\pi\) | ||||
0.258152 | + | 0.966104i | \(0.416886\pi\) | |||||||
\(354\) | 46.7631 | 2.48543 | ||||||||
\(355\) | −24.3094 | −1.29021 | ||||||||
\(356\) | −3.11417 | −0.165051 | ||||||||
\(357\) | 10.6006 | 0.561043 | ||||||||
\(358\) | −5.27553 | −0.278821 | ||||||||
\(359\) | 22.9708 | 1.21235 | 0.606176 | − | 0.795331i | \(-0.292703\pi\) | ||||
0.606176 | + | 0.795331i | \(0.292703\pi\) | |||||||
\(360\) | −9.95148 | −0.524489 | ||||||||
\(361\) | 31.0901 | 1.63632 | ||||||||
\(362\) | −18.3737 | −0.965698 | ||||||||
\(363\) | −2.08850 | −0.109618 | ||||||||
\(364\) | 0.963654 | 0.0505092 | ||||||||
\(365\) | 40.6972 | 2.13019 | ||||||||
\(366\) | 50.9962 | 2.66561 | ||||||||
\(367\) | 17.4307 | 0.909875 | 0.454938 | − | 0.890523i | \(-0.349662\pi\) | ||||
0.454938 | + | 0.890523i | \(0.349662\pi\) | |||||||
\(368\) | −8.13038 | −0.423825 | ||||||||
\(369\) | −3.26005 | −0.169712 | ||||||||
\(370\) | 43.7518 | 2.27455 | ||||||||
\(371\) | −48.9485 | −2.54128 | ||||||||
\(372\) | 7.64466 | 0.396357 | ||||||||
\(373\) | −6.92606 | −0.358618 | −0.179309 | − | 0.983793i | \(-0.557386\pi\) | ||||
−0.179309 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(374\) | −1.62861 | −0.0842132 | ||||||||
\(375\) | 7.54920 | 0.389839 | ||||||||
\(376\) | 14.4975 | 0.747653 | ||||||||
\(377\) | 1.43192 | 0.0737475 | ||||||||
\(378\) | 28.2820 | 1.45467 | ||||||||
\(379\) | 14.6675 | 0.753419 | 0.376709 | − | 0.926331i | \(-0.377056\pi\) | ||||
0.376709 | + | 0.926331i | \(0.377056\pi\) | |||||||
\(380\) | −15.3725 | −0.788590 | ||||||||
\(381\) | −30.8669 | −1.58136 | ||||||||
\(382\) | −31.5720 | −1.61536 | ||||||||
\(383\) | −0.404206 | −0.0206540 | −0.0103270 | − | 0.999947i | \(-0.503287\pi\) | ||||
−0.0103270 | + | 0.999947i | \(0.503287\pi\) | |||||||
\(384\) | 28.3455 | 1.44650 | ||||||||
\(385\) | 16.8996 | 0.861285 | ||||||||
\(386\) | 24.1731 | 1.23038 | ||||||||
\(387\) | 1.36181 | 0.0692248 | ||||||||
\(388\) | 0.818711 | 0.0415637 | ||||||||
\(389\) | 11.7715 | 0.596837 | 0.298418 | − | 0.954435i | \(-0.403541\pi\) | ||||
0.298418 | + | 0.954435i | \(0.403541\pi\) | |||||||
\(390\) | 3.29585 | 0.166892 | ||||||||
\(391\) | 1.66635 | 0.0842711 | ||||||||
\(392\) | 41.1803 | 2.07992 | ||||||||
\(393\) | 45.9438 | 2.31756 | ||||||||
\(394\) | −18.8504 | −0.949669 | ||||||||
\(395\) | 20.2320 | 1.01798 | ||||||||
\(396\) | 0.888390 | 0.0446433 | ||||||||
\(397\) | −14.7110 | −0.738325 | −0.369162 | − | 0.929365i | \(-0.620355\pi\) | ||||
−0.369162 | + | 0.929365i | \(0.620355\pi\) | |||||||
\(398\) | 14.0160 | 0.702558 | ||||||||
\(399\) | 75.0251 | 3.75595 | ||||||||
\(400\) | −29.6927 | −1.48464 | ||||||||
\(401\) | 36.0545 | 1.80048 | 0.900238 | − | 0.435398i | \(-0.143392\pi\) | ||||
0.900238 | + | 0.435398i | \(0.143392\pi\) | |||||||
\(402\) | 4.77049 | 0.237931 | ||||||||
\(403\) | 1.63296 | 0.0813435 | ||||||||
\(404\) | 7.12125 | 0.354296 | ||||||||
\(405\) | 37.3934 | 1.85809 | ||||||||
\(406\) | −40.6718 | −2.01851 | ||||||||
\(407\) | 8.06861 | 0.399946 | ||||||||
\(408\) | −4.58378 | −0.226931 | ||||||||
\(409\) | 26.8478 | 1.32754 | 0.663770 | − | 0.747937i | \(-0.268956\pi\) | ||||
0.663770 | + | 0.747937i | \(0.268956\pi\) | |||||||
\(410\) | −12.9809 | −0.641080 | ||||||||
\(411\) | 23.9146 | 1.17962 | ||||||||
\(412\) | −7.76975 | −0.382788 | ||||||||
\(413\) | −69.7831 | −3.43380 | ||||||||
\(414\) | −3.69573 | −0.181635 | ||||||||
\(415\) | 4.37316 | 0.214670 | ||||||||
\(416\) | −1.03509 | −0.0507496 | ||||||||
\(417\) | 12.6702 | 0.620464 | ||||||||
\(418\) | −11.5264 | −0.563773 | ||||||||
\(419\) | −7.71081 | −0.376698 | −0.188349 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188349 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(420\) | −23.0249 | −1.12350 | ||||||||
\(421\) | 21.0274 | 1.02481 | 0.512405 | − | 0.858744i | \(-0.328755\pi\) | ||||
0.512405 | + | 0.858744i | \(0.328755\pi\) | |||||||
\(422\) | 6.88217 | 0.335019 | ||||||||
\(423\) | 8.99541 | 0.437372 | ||||||||
\(424\) | 21.1657 | 1.02790 | ||||||||
\(425\) | 6.08564 | 0.295197 | ||||||||
\(426\) | 24.8338 | 1.20320 | ||||||||
\(427\) | −76.1001 | −3.68274 | ||||||||
\(428\) | −8.45209 | −0.408547 | ||||||||
\(429\) | 0.607814 | 0.0293455 | ||||||||
\(430\) | 5.42246 | 0.261494 | ||||||||
\(431\) | 9.31784 | 0.448824 | 0.224412 | − | 0.974494i | \(-0.427954\pi\) | ||||
0.224412 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(432\) | −16.6933 | −0.803155 | ||||||||
\(433\) | −2.56641 | −0.123334 | −0.0616669 | − | 0.998097i | \(-0.519642\pi\) | ||||
−0.0616669 | + | 0.998097i | \(0.519642\pi\) | |||||||
\(434\) | −46.3822 | −2.22642 | ||||||||
\(435\) | −34.2133 | −1.64040 | ||||||||
\(436\) | 12.6192 | 0.604350 | ||||||||
\(437\) | 11.7935 | 0.564160 | ||||||||
\(438\) | −41.5751 | −1.98654 | ||||||||
\(439\) | 3.05425 | 0.145772 | 0.0728858 | − | 0.997340i | \(-0.476779\pi\) | ||||
0.0728858 | + | 0.997340i | \(0.476779\pi\) | |||||||
\(440\) | −7.30753 | −0.348373 | ||||||||
\(441\) | 25.5515 | 1.21674 | ||||||||
\(442\) | 0.473973 | 0.0225446 | ||||||||
\(443\) | 33.9273 | 1.61194 | 0.805968 | − | 0.591960i | \(-0.201645\pi\) | ||||
0.805968 | + | 0.591960i | \(0.201645\pi\) | |||||||
\(444\) | −10.9931 | −0.521708 | ||||||||
\(445\) | 15.8941 | 0.753452 | ||||||||
\(446\) | 44.8380 | 2.12314 | ||||||||
\(447\) | 13.3324 | 0.630600 | ||||||||
\(448\) | −20.1298 | −0.951042 | ||||||||
\(449\) | 4.81672 | 0.227315 | 0.113657 | − | 0.993520i | \(-0.463743\pi\) | ||||
0.113657 | + | 0.993520i | \(0.463743\pi\) | |||||||
\(450\) | −13.4971 | −0.636258 | ||||||||
\(451\) | −2.39391 | −0.112725 | ||||||||
\(452\) | −6.56859 | −0.308960 | ||||||||
\(453\) | −2.97926 | −0.139978 | ||||||||
\(454\) | −19.6415 | −0.921823 | ||||||||
\(455\) | −4.91830 | −0.230573 | ||||||||
\(456\) | −32.4414 | −1.51921 | ||||||||
\(457\) | 14.9884 | 0.701129 | 0.350565 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350565 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(458\) | −17.1466 | −0.801206 | ||||||||
\(459\) | 3.42135 | 0.159695 | ||||||||
\(460\) | −3.61938 | −0.168755 | ||||||||
\(461\) | −27.4947 | −1.28056 | −0.640279 | − | 0.768142i | \(-0.721181\pi\) | ||||
−0.640279 | + | 0.768142i | \(0.721181\pi\) | |||||||
\(462\) | −17.2642 | −0.803204 | ||||||||
\(463\) | −38.9588 | −1.81057 | −0.905284 | − | 0.424808i | \(-0.860342\pi\) | ||||
−0.905284 | + | 0.424808i | \(0.860342\pi\) | |||||||
\(464\) | 24.0063 | 1.11446 | ||||||||
\(465\) | −39.0168 | −1.80936 | ||||||||
\(466\) | 15.3795 | 0.712444 | ||||||||
\(467\) | 19.1118 | 0.884388 | 0.442194 | − | 0.896919i | \(-0.354200\pi\) | ||||
0.442194 | + | 0.896919i | \(0.354200\pi\) | |||||||
\(468\) | −0.258548 | −0.0119514 | ||||||||
\(469\) | −7.11886 | −0.328719 | ||||||||
\(470\) | 35.8179 | 1.65216 | ||||||||
\(471\) | 2.13595 | 0.0984193 | ||||||||
\(472\) | 30.1747 | 1.38891 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −20.6685 | −0.949335 | ||||||||
\(475\) | 43.0708 | 1.97622 | ||||||||
\(476\) | −3.31119 | −0.151768 | ||||||||
\(477\) | 13.1329 | 0.601312 | ||||||||
\(478\) | −34.4084 | −1.57380 | ||||||||
\(479\) | 15.3476 | 0.701250 | 0.350625 | − | 0.936516i | \(-0.385969\pi\) | ||||
0.350625 | + | 0.936516i | \(0.385969\pi\) | |||||||
\(480\) | 24.7318 | 1.12885 | ||||||||
\(481\) | −2.34821 | −0.107069 | ||||||||
\(482\) | −17.8431 | −0.812731 | ||||||||
\(483\) | 17.6643 | 0.803755 | ||||||||
\(484\) | 0.652359 | 0.0296527 | ||||||||
\(485\) | −4.17854 | −0.189738 | ||||||||
\(486\) | −21.4840 | −0.974534 | ||||||||
\(487\) | 8.22456 | 0.372690 | 0.186345 | − | 0.982484i | \(-0.440336\pi\) | ||||
0.186345 | + | 0.982484i | \(0.440336\pi\) | |||||||
\(488\) | 32.9063 | 1.48960 | ||||||||
\(489\) | −39.7462 | −1.79739 | ||||||||
\(490\) | 101.741 | 4.59618 | ||||||||
\(491\) | 36.4639 | 1.64559 | 0.822797 | − | 0.568335i | \(-0.192412\pi\) | ||||
0.822797 | + | 0.568335i | \(0.192412\pi\) | |||||||
\(492\) | 3.26158 | 0.147043 | ||||||||
\(493\) | −4.92017 | −0.221594 | ||||||||
\(494\) | 3.35451 | 0.150927 | ||||||||
\(495\) | −4.53417 | −0.203796 | ||||||||
\(496\) | 27.3767 | 1.22925 | ||||||||
\(497\) | −37.0588 | −1.66231 | ||||||||
\(498\) | −4.46750 | −0.200193 | ||||||||
\(499\) | −33.1026 | −1.48188 | −0.740938 | − | 0.671573i | \(-0.765619\pi\) | ||||
−0.740938 | + | 0.671573i | \(0.765619\pi\) | |||||||
\(500\) | −2.35806 | −0.105456 | ||||||||
\(501\) | −3.26167 | −0.145721 | ||||||||
\(502\) | −23.6520 | −1.05564 | ||||||||
\(503\) | −0.683501 | −0.0304758 | −0.0152379 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152379 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(504\) | −15.1707 | −0.675755 | ||||||||
\(505\) | −36.3455 | −1.61735 | ||||||||
\(506\) | −2.71383 | −0.120645 | ||||||||
\(507\) | 26.9735 | 1.19794 | ||||||||
\(508\) | 9.64153 | 0.427774 | ||||||||
\(509\) | −34.2606 | −1.51857 | −0.759286 | − | 0.650757i | \(-0.774452\pi\) | ||||
−0.759286 | + | 0.650757i | \(0.774452\pi\) | |||||||
\(510\) | −11.3248 | −0.501470 | ||||||||
\(511\) | 62.0413 | 2.74455 | ||||||||
\(512\) | 4.06383 | 0.179598 | ||||||||
\(513\) | 24.2144 | 1.06909 | ||||||||
\(514\) | 34.9788 | 1.54285 | ||||||||
\(515\) | 39.6553 | 1.74742 | ||||||||
\(516\) | −1.36245 | −0.0599785 | ||||||||
\(517\) | 6.60547 | 0.290508 | ||||||||
\(518\) | 66.6979 | 2.93054 | ||||||||
\(519\) | −20.3073 | −0.891393 | ||||||||
\(520\) | 2.12671 | 0.0932624 | ||||||||
\(521\) | 8.32135 | 0.364565 | 0.182283 | − | 0.983246i | \(-0.441651\pi\) | ||||
0.182283 | + | 0.983246i | \(0.441651\pi\) | |||||||
\(522\) | 10.9122 | 0.477616 | ||||||||
\(523\) | 21.8533 | 0.955578 | 0.477789 | − | 0.878475i | \(-0.341438\pi\) | ||||
0.477789 | + | 0.878475i | \(0.341438\pi\) | |||||||
\(524\) | −14.3509 | −0.626924 | ||||||||
\(525\) | 64.5115 | 2.81551 | ||||||||
\(526\) | 8.89287 | 0.387747 | ||||||||
\(527\) | −5.61097 | −0.244418 | ||||||||
\(528\) | 10.1901 | 0.443466 | ||||||||
\(529\) | −20.2233 | −0.879272 | ||||||||
\(530\) | 52.2924 | 2.27144 | ||||||||
\(531\) | 18.7228 | 0.812499 | ||||||||
\(532\) | −23.4347 | −1.01602 | ||||||||
\(533\) | 0.696699 | 0.0301774 | ||||||||
\(534\) | −16.2370 | −0.702642 | ||||||||
\(535\) | 43.1378 | 1.86501 | ||||||||
\(536\) | 3.07825 | 0.132960 | ||||||||
\(537\) | −6.76525 | −0.291942 | ||||||||
\(538\) | 0.144561 | 0.00623245 | ||||||||
\(539\) | 18.7629 | 0.808173 | ||||||||
\(540\) | −7.43129 | −0.319792 | ||||||||
\(541\) | −43.2293 | −1.85857 | −0.929287 | − | 0.369358i | \(-0.879578\pi\) | ||||
−0.929287 | + | 0.369358i | \(0.879578\pi\) | |||||||
\(542\) | 26.6184 | 1.14336 | ||||||||
\(543\) | −23.5621 | −1.01114 | ||||||||
\(544\) | 3.55666 | 0.152490 | ||||||||
\(545\) | −64.4059 | −2.75885 | ||||||||
\(546\) | 5.02440 | 0.215024 | ||||||||
\(547\) | 12.9473 | 0.553585 | 0.276792 | − | 0.960930i | \(-0.410729\pi\) | ||||
0.276792 | + | 0.960930i | \(0.410729\pi\) | |||||||
\(548\) | −7.46993 | −0.319099 | ||||||||
\(549\) | 20.4176 | 0.871403 | ||||||||
\(550\) | −9.91112 | −0.422612 | ||||||||
\(551\) | −34.8222 | −1.48348 | ||||||||
\(552\) | −7.63820 | −0.325103 | ||||||||
\(553\) | 30.8430 | 1.31158 | ||||||||
\(554\) | −35.5344 | −1.50971 | ||||||||
\(555\) | 56.1065 | 2.38159 | ||||||||
\(556\) | −3.95765 | −0.167842 | ||||||||
\(557\) | −45.2180 | −1.91595 | −0.957975 | − | 0.286852i | \(-0.907391\pi\) | ||||
−0.957975 | + | 0.286852i | \(0.907391\pi\) | |||||||
\(558\) | 12.4443 | 0.526810 | ||||||||
\(559\) | −0.291030 | −0.0123092 | ||||||||
\(560\) | −82.4558 | −3.48439 | ||||||||
\(561\) | −2.08850 | −0.0881763 | ||||||||
\(562\) | −18.4899 | −0.779950 | ||||||||
\(563\) | 28.6961 | 1.20940 | 0.604698 | − | 0.796455i | \(-0.293294\pi\) | ||||
0.604698 | + | 0.796455i | \(0.293294\pi\) | |||||||
\(564\) | −8.99962 | −0.378952 | ||||||||
\(565\) | 33.5248 | 1.41040 | ||||||||
\(566\) | −44.9977 | −1.89139 | ||||||||
\(567\) | 57.0048 | 2.39398 | ||||||||
\(568\) | 16.0245 | 0.672373 | ||||||||
\(569\) | 43.7394 | 1.83365 | 0.916826 | − | 0.399288i | \(-0.130743\pi\) | ||||
0.916826 | + | 0.399288i | \(0.130743\pi\) | |||||||
\(570\) | −80.1505 | −3.35713 | ||||||||
\(571\) | −45.5937 | −1.90804 | −0.954019 | − | 0.299747i | \(-0.903098\pi\) | ||||
−0.954019 | + | 0.299747i | \(0.903098\pi\) | |||||||
\(572\) | −0.189856 | −0.00793827 | ||||||||
\(573\) | −40.4873 | −1.69138 | ||||||||
\(574\) | −19.7889 | −0.825971 | ||||||||
\(575\) | 10.1408 | 0.422902 | ||||||||
\(576\) | 5.40081 | 0.225034 | ||||||||
\(577\) | −21.6913 | −0.903020 | −0.451510 | − | 0.892266i | \(-0.649115\pi\) | ||||
−0.451510 | + | 0.892266i | \(0.649115\pi\) | |||||||
\(578\) | −1.62861 | −0.0677411 | ||||||||
\(579\) | 30.9992 | 1.28828 | ||||||||
\(580\) | 10.6868 | 0.443745 | ||||||||
\(581\) | 6.66671 | 0.276582 | ||||||||
\(582\) | 4.26868 | 0.176942 | ||||||||
\(583\) | 9.64367 | 0.399400 | ||||||||
\(584\) | −26.8271 | −1.11011 | ||||||||
\(585\) | 1.31958 | 0.0545578 | ||||||||
\(586\) | −22.1508 | −0.915042 | ||||||||
\(587\) | −46.4306 | −1.91640 | −0.958198 | − | 0.286106i | \(-0.907639\pi\) | ||||
−0.958198 | + | 0.286106i | \(0.907639\pi\) | |||||||
\(588\) | −25.5634 | −1.05422 | ||||||||
\(589\) | −39.7113 | −1.63628 | ||||||||
\(590\) | 74.5504 | 3.06919 | ||||||||
\(591\) | −24.1734 | −0.994360 | ||||||||
\(592\) | −39.3679 | −1.61801 | ||||||||
\(593\) | 7.37552 | 0.302876 | 0.151438 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151438 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(594\) | −5.57203 | −0.228623 | ||||||||
\(595\) | 16.8996 | 0.692818 | ||||||||
\(596\) | −4.16448 | −0.170584 | ||||||||
\(597\) | 17.9738 | 0.735620 | ||||||||
\(598\) | 0.789806 | 0.0322976 | ||||||||
\(599\) | −5.20415 | −0.212636 | −0.106318 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106318 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(600\) | −27.8953 | −1.13882 | ||||||||
\(601\) | −3.93573 | −0.160542 | −0.0802709 | − | 0.996773i | \(-0.525579\pi\) | ||||
−0.0802709 | + | 0.996773i | \(0.525579\pi\) | |||||||
\(602\) | 8.26634 | 0.336911 | ||||||||
\(603\) | 1.90999 | 0.0777808 | ||||||||
\(604\) | 0.930598 | 0.0378655 | ||||||||
\(605\) | −3.32951 | −0.135364 | ||||||||
\(606\) | 37.1295 | 1.50828 | ||||||||
\(607\) | 10.2445 | 0.415813 | 0.207906 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207906 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(608\) | 25.1720 | 1.02086 | ||||||||
\(609\) | −52.1568 | −2.11350 | ||||||||
\(610\) | 81.2989 | 3.29170 | ||||||||
\(611\) | −1.92239 | −0.0777715 | ||||||||
\(612\) | 0.888390 | 0.0359110 | ||||||||
\(613\) | 26.3194 | 1.06303 | 0.531515 | − | 0.847049i | \(-0.321623\pi\) | ||||
0.531515 | + | 0.847049i | \(0.321623\pi\) | |||||||
\(614\) | 39.1465 | 1.57982 | ||||||||
\(615\) | −16.6465 | −0.671250 | ||||||||
\(616\) | −11.1401 | −0.448846 | ||||||||
\(617\) | −9.39245 | −0.378126 | −0.189063 | − | 0.981965i | \(-0.560545\pi\) | ||||
−0.189063 | + | 0.981965i | \(0.560545\pi\) | |||||||
\(618\) | −40.5107 | −1.62958 | ||||||||
\(619\) | 0.610849 | 0.0245521 | 0.0122761 | − | 0.999925i | \(-0.496092\pi\) | ||||
0.0122761 | + | 0.999925i | \(0.496092\pi\) | |||||||
\(620\) | 12.1872 | 0.489451 | ||||||||
\(621\) | 5.70118 | 0.228780 | ||||||||
\(622\) | −52.8529 | −2.11921 | ||||||||
\(623\) | 24.2299 | 0.970752 | ||||||||
\(624\) | −2.96561 | −0.118720 | ||||||||
\(625\) | −18.3932 | −0.735726 | ||||||||
\(626\) | −1.20792 | −0.0482782 | ||||||||
\(627\) | −14.7812 | −0.590304 | ||||||||
\(628\) | −0.667182 | −0.0266235 | ||||||||
\(629\) | 8.06861 | 0.321717 | ||||||||
\(630\) | −37.4810 | −1.49328 | ||||||||
\(631\) | 12.2961 | 0.489501 | 0.244751 | − | 0.969586i | \(-0.421294\pi\) | ||||
0.244751 | + | 0.969586i | \(0.421294\pi\) | |||||||
\(632\) | −13.3367 | −0.530507 | ||||||||
\(633\) | 8.82557 | 0.350785 | ||||||||
\(634\) | 37.4408 | 1.48696 | ||||||||
\(635\) | −49.2084 | −1.95278 | ||||||||
\(636\) | −13.1390 | −0.520996 | ||||||||
\(637\) | −5.46055 | −0.216355 | ||||||||
\(638\) | 8.01303 | 0.317239 | ||||||||
\(639\) | 9.94285 | 0.393333 | ||||||||
\(640\) | 45.1888 | 1.78624 | ||||||||
\(641\) | 9.14232 | 0.361100 | 0.180550 | − | 0.983566i | \(-0.442212\pi\) | ||||
0.180550 | + | 0.983566i | \(0.442212\pi\) | |||||||
\(642\) | −44.0684 | −1.73924 | ||||||||
\(643\) | 14.0019 | 0.552179 | 0.276090 | − | 0.961132i | \(-0.410961\pi\) | ||||
0.276090 | + | 0.961132i | \(0.410961\pi\) | |||||||
\(644\) | −5.51761 | −0.217424 | ||||||||
\(645\) | 6.95367 | 0.273800 | ||||||||
\(646\) | −11.5264 | −0.453499 | ||||||||
\(647\) | −26.7200 | −1.05047 | −0.525235 | − | 0.850957i | \(-0.676023\pi\) | ||||
−0.525235 | + | 0.850957i | \(0.676023\pi\) | |||||||
\(648\) | −24.6493 | −0.968317 | ||||||||
\(649\) | 13.7484 | 0.539673 | ||||||||
\(650\) | 2.88443 | 0.113137 | ||||||||
\(651\) | −59.4796 | −2.33119 | ||||||||
\(652\) | 12.4151 | 0.486212 | ||||||||
\(653\) | 9.86080 | 0.385883 | 0.192941 | − | 0.981210i | \(-0.438197\pi\) | ||||
0.192941 | + | 0.981210i | \(0.438197\pi\) | |||||||
\(654\) | 65.7953 | 2.57280 | ||||||||
\(655\) | 73.2443 | 2.86189 | ||||||||
\(656\) | 11.6802 | 0.456037 | ||||||||
\(657\) | −16.6457 | −0.649409 | ||||||||
\(658\) | 54.6030 | 2.12865 | ||||||||
\(659\) | −27.6231 | −1.07604 | −0.538022 | − | 0.842931i | \(-0.680828\pi\) | ||||
−0.538022 | + | 0.842931i | \(0.680828\pi\) | |||||||
\(660\) | 4.53629 | 0.176575 | ||||||||
\(661\) | −14.3226 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589852\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589852\pi\) | |||||||
\(662\) | −13.9518 | −0.542254 | ||||||||
\(663\) | 0.607814 | 0.0236055 | ||||||||
\(664\) | −2.88274 | −0.111872 | ||||||||
\(665\) | 119.606 | 4.63813 | ||||||||
\(666\) | −17.8950 | −0.693418 | ||||||||
\(667\) | −8.19875 | −0.317457 | ||||||||
\(668\) | 1.01881 | 0.0394189 | ||||||||
\(669\) | 57.4994 | 2.22305 | ||||||||
\(670\) | 7.60520 | 0.293814 | ||||||||
\(671\) | 14.9930 | 0.578798 | ||||||||
\(672\) | 37.7027 | 1.45441 | ||||||||
\(673\) | −38.2857 | −1.47581 | −0.737903 | − | 0.674907i | \(-0.764184\pi\) | ||||
−0.737903 | + | 0.674907i | \(0.764184\pi\) | |||||||
\(674\) | 16.0554 | 0.618432 | ||||||||
\(675\) | 20.8211 | 0.801405 | ||||||||
\(676\) | −8.42542 | −0.324054 | ||||||||
\(677\) | 25.7670 | 0.990307 | 0.495154 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495154 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(678\) | −34.2480 | −1.31529 | ||||||||
\(679\) | −6.37002 | −0.244459 | ||||||||
\(680\) | −7.30753 | −0.280231 | ||||||||
\(681\) | −25.1880 | −0.965205 | ||||||||
\(682\) | 9.13806 | 0.349914 | ||||||||
\(683\) | 22.4740 | 0.859944 | 0.429972 | − | 0.902842i | \(-0.358523\pi\) | ||||
0.429972 | + | 0.902842i | \(0.358523\pi\) | |||||||
\(684\) | 6.28753 | 0.240410 | ||||||||
\(685\) | 38.1250 | 1.45668 | ||||||||
\(686\) | 97.2357 | 3.71248 | ||||||||
\(687\) | −21.9884 | −0.838911 | ||||||||
\(688\) | −4.87915 | −0.186016 | ||||||||
\(689\) | −2.80659 | −0.106923 | ||||||||
\(690\) | −18.8711 | −0.718410 | ||||||||
\(691\) | 10.1459 | 0.385970 | 0.192985 | − | 0.981202i | \(-0.438183\pi\) | ||||
0.192985 | + | 0.981202i | \(0.438183\pi\) | |||||||
\(692\) | 6.34317 | 0.241131 | ||||||||
\(693\) | −6.91216 | −0.262571 | ||||||||
\(694\) | 53.6953 | 2.03824 | ||||||||
\(695\) | 20.1991 | 0.766194 | ||||||||
\(696\) | 22.5530 | 0.854869 | ||||||||
\(697\) | −2.39391 | −0.0906758 | ||||||||
\(698\) | 10.0408 | 0.380049 | ||||||||
\(699\) | 19.7224 | 0.745971 | ||||||||
\(700\) | −20.1507 | −0.761625 | ||||||||
\(701\) | 38.8986 | 1.46918 | 0.734589 | − | 0.678512i | \(-0.237375\pi\) | ||||
0.734589 | + | 0.678512i | \(0.237375\pi\) | |||||||
\(702\) | 1.62163 | 0.0612043 | ||||||||
\(703\) | 57.1051 | 2.15376 | ||||||||
\(704\) | 3.96590 | 0.149470 | ||||||||
\(705\) | 45.9322 | 1.72991 | ||||||||
\(706\) | −15.7983 | −0.594576 | ||||||||
\(707\) | −55.4073 | −2.08380 | ||||||||
\(708\) | −18.7315 | −0.703974 | ||||||||
\(709\) | −39.1055 | −1.46864 | −0.734318 | − | 0.678805i | \(-0.762498\pi\) | ||||
−0.734318 | + | 0.678805i | \(0.762498\pi\) | |||||||
\(710\) | 39.5905 | 1.48580 | ||||||||
\(711\) | −8.27515 | −0.310342 | ||||||||
\(712\) | −10.4772 | −0.392650 | ||||||||
\(713\) | −9.34986 | −0.350155 | ||||||||
\(714\) | −17.2642 | −0.646097 | ||||||||
\(715\) | 0.968986 | 0.0362380 | ||||||||
\(716\) | 2.11318 | 0.0789733 | ||||||||
\(717\) | −44.1247 | −1.64787 | ||||||||
\(718\) | −37.4104 | −1.39614 | ||||||||
\(719\) | 34.7211 | 1.29488 | 0.647439 | − | 0.762117i | \(-0.275840\pi\) | ||||
0.647439 | + | 0.762117i | \(0.275840\pi\) | |||||||
\(720\) | 22.1229 | 0.824470 | ||||||||
\(721\) | 60.4529 | 2.25138 | ||||||||
\(722\) | −50.6336 | −1.88439 | ||||||||
\(723\) | −22.8817 | −0.850978 | ||||||||
\(724\) | 7.35981 | 0.273525 | ||||||||
\(725\) | −29.9424 | −1.11203 | ||||||||
\(726\) | 3.40134 | 0.126235 | ||||||||
\(727\) | 7.13207 | 0.264514 | 0.132257 | − | 0.991215i | \(-0.457778\pi\) | ||||
0.132257 | + | 0.991215i | \(0.457778\pi\) | |||||||
\(728\) | 3.24209 | 0.120160 | ||||||||
\(729\) | 6.14203 | 0.227483 | ||||||||
\(730\) | −66.2797 | −2.45312 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −20.4272 | −0.755010 | ||||||||
\(733\) | −36.6739 | −1.35458 | −0.677291 | − | 0.735716i | \(-0.736846\pi\) | ||||
−0.677291 | + | 0.735716i | \(0.736846\pi\) | |||||||
\(734\) | −28.3878 | −1.04781 | ||||||||
\(735\) | 130.471 | 4.81248 | ||||||||
\(736\) | 5.92664 | 0.218459 | ||||||||
\(737\) | 1.40254 | 0.0516630 | ||||||||
\(738\) | 5.30935 | 0.195440 | ||||||||
\(739\) | −1.61499 | −0.0594084 | −0.0297042 | − | 0.999559i | \(-0.509457\pi\) | ||||
−0.0297042 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(740\) | −17.5253 | −0.644244 | ||||||||
\(741\) | 4.30177 | 0.158029 | ||||||||
\(742\) | 79.7178 | 2.92653 | ||||||||
\(743\) | −3.21151 | −0.117819 | −0.0589094 | − | 0.998263i | \(-0.518762\pi\) | ||||
−0.0589094 | + | 0.998263i | \(0.518762\pi\) | |||||||
\(744\) | 25.7195 | 0.942921 | ||||||||
\(745\) | 21.2547 | 0.778712 | ||||||||
\(746\) | 11.2798 | 0.412984 | ||||||||
\(747\) | −1.78868 | −0.0654442 | ||||||||
\(748\) | 0.652359 | 0.0238526 | ||||||||
\(749\) | 65.7619 | 2.40289 | ||||||||
\(750\) | −12.2947 | −0.448938 | ||||||||
\(751\) | 31.7034 | 1.15687 | 0.578436 | − | 0.815728i | \(-0.303663\pi\) | ||||
0.578436 | + | 0.815728i | \(0.303663\pi\) | |||||||
\(752\) | −32.2291 | −1.17527 | ||||||||
\(753\) | −30.3308 | −1.10532 | ||||||||
\(754\) | −2.33203 | −0.0849275 | ||||||||
\(755\) | −4.74958 | −0.172855 | ||||||||
\(756\) | −11.3287 | −0.412022 | ||||||||
\(757\) | −17.5773 | −0.638857 | −0.319429 | − | 0.947610i | \(-0.603491\pi\) | ||||
−0.319429 | + | 0.947610i | \(0.603491\pi\) | |||||||
\(758\) | −23.8876 | −0.867636 | ||||||||
\(759\) | −3.48017 | −0.126322 | ||||||||
\(760\) | −51.7186 | −1.87603 | ||||||||
\(761\) | −18.6364 | −0.675569 | −0.337784 | − | 0.941223i | \(-0.609677\pi\) | ||||
−0.337784 | + | 0.941223i | \(0.609677\pi\) | |||||||
\(762\) | 50.2700 | 1.82109 | ||||||||
\(763\) | −98.1843 | −3.55451 | ||||||||
\(764\) | 12.6466 | 0.457537 | ||||||||
\(765\) | −4.53417 | −0.163933 | ||||||||
\(766\) | 0.658293 | 0.0237851 | ||||||||
\(767\) | −4.00120 | −0.144475 | ||||||||
\(768\) | −29.5981 | −1.06803 | ||||||||
\(769\) | 4.64011 | 0.167327 | 0.0836633 | − | 0.996494i | \(-0.473338\pi\) | ||||
0.0836633 | + | 0.996494i | \(0.473338\pi\) | |||||||
\(770\) | −27.5229 | −0.991855 | ||||||||
\(771\) | 44.8562 | 1.61546 | ||||||||
\(772\) | −9.68286 | −0.348494 | ||||||||
\(773\) | −18.9078 | −0.680068 | −0.340034 | − | 0.940413i | \(-0.610439\pi\) | ||||
−0.340034 | + | 0.940413i | \(0.610439\pi\) | |||||||
\(774\) | −2.21786 | −0.0797192 | ||||||||
\(775\) | −34.1464 | −1.22657 | ||||||||
\(776\) | 2.75445 | 0.0988788 | ||||||||
\(777\) | 85.5321 | 3.06845 | ||||||||
\(778\) | −19.1711 | −0.687316 | ||||||||
\(779\) | −16.9427 | −0.607037 | ||||||||
\(780\) | −1.32019 | −0.0472705 | ||||||||
\(781\) | 7.30119 | 0.261257 | ||||||||
\(782\) | −2.71383 | −0.0970465 | ||||||||
\(783\) | −16.8336 | −0.601585 | ||||||||
\(784\) | −91.5467 | −3.26952 | ||||||||
\(785\) | 3.40516 | 0.121535 | ||||||||
\(786\) | −74.8244 | −2.66890 | ||||||||
\(787\) | 30.0731 | 1.07199 | 0.535994 | − | 0.844222i | \(-0.319937\pi\) | ||||
0.535994 | + | 0.844222i | \(0.319937\pi\) | |||||||
\(788\) | 7.55076 | 0.268985 | ||||||||
\(789\) | 11.4041 | 0.405995 | ||||||||
\(790\) | −32.9500 | −1.17231 | ||||||||
\(791\) | 51.1072 | 1.81716 | ||||||||
\(792\) | 2.98887 | 0.106205 | ||||||||
\(793\) | −4.36340 | −0.154949 | ||||||||
\(794\) | 23.9585 | 0.850254 | ||||||||
\(795\) | 67.0589 | 2.37833 | ||||||||
\(796\) | −5.61428 | −0.198993 | ||||||||
\(797\) | 31.1217 | 1.10239 | 0.551194 | − | 0.834377i | \(-0.314172\pi\) | ||||
0.551194 | + | 0.834377i | \(0.314172\pi\) | |||||||
\(798\) | −122.186 | −4.32535 | ||||||||
\(799\) | 6.60547 | 0.233685 | ||||||||
\(800\) | 21.6445 | 0.765250 | ||||||||
\(801\) | −6.50088 | −0.229697 | ||||||||
\(802\) | −58.7186 | −2.07343 | ||||||||
\(803\) | −12.2232 | −0.431347 | ||||||||
\(804\) | −1.91088 | −0.0673916 | ||||||||
\(805\) | 28.1608 | 0.992537 | ||||||||
\(806\) | −2.65945 | −0.0936750 | ||||||||
\(807\) | 0.185382 | 0.00652575 | ||||||||
\(808\) | 23.9585 | 0.842858 | ||||||||
\(809\) | 25.7767 | 0.906262 | 0.453131 | − | 0.891444i | \(-0.350307\pi\) | ||||
0.453131 | + | 0.891444i | \(0.350307\pi\) | |||||||
\(810\) | −60.8992 | −2.13978 | ||||||||
\(811\) | 13.1142 | 0.460501 | 0.230250 | − | 0.973131i | \(-0.426046\pi\) | ||||
0.230250 | + | 0.973131i | \(0.426046\pi\) | |||||||
\(812\) | 16.2916 | 0.571724 | ||||||||
\(813\) | 34.1349 | 1.19716 | ||||||||
\(814\) | −13.1406 | −0.460578 | ||||||||
\(815\) | −63.3640 | −2.21955 | ||||||||
\(816\) | 10.1901 | 0.356724 | ||||||||
\(817\) | 7.07744 | 0.247608 | ||||||||
\(818\) | −43.7245 | −1.52879 | ||||||||
\(819\) | 2.01164 | 0.0702926 | ||||||||
\(820\) | 5.19966 | 0.181580 | ||||||||
\(821\) | 20.0522 | 0.699828 | 0.349914 | − | 0.936782i | \(-0.386211\pi\) | ||||
0.349914 | + | 0.936782i | \(0.386211\pi\) | |||||||
\(822\) | −38.9475 | −1.35845 | ||||||||
\(823\) | 13.8477 | 0.482702 | 0.241351 | − | 0.970438i | \(-0.422410\pi\) | ||||
0.241351 | + | 0.970438i | \(0.422410\pi\) | |||||||
\(824\) | −26.1403 | −0.910641 | ||||||||
\(825\) | −12.7098 | −0.442500 | ||||||||
\(826\) | 113.649 | 3.95436 | ||||||||
\(827\) | −32.5826 | −1.13301 | −0.566503 | − | 0.824059i | \(-0.691704\pi\) | ||||
−0.566503 | + | 0.824059i | \(0.691704\pi\) | |||||||
\(828\) | 1.48037 | 0.0514465 | ||||||||
\(829\) | −20.0534 | −0.696482 | −0.348241 | − | 0.937405i | \(-0.613221\pi\) | ||||
−0.348241 | + | 0.937405i | \(0.613221\pi\) | |||||||
\(830\) | −7.12215 | −0.247214 | ||||||||
\(831\) | −45.5687 | −1.58076 | ||||||||
\(832\) | −1.15419 | −0.0400145 | ||||||||
\(833\) | 18.7629 | 0.650094 | ||||||||
\(834\) | −20.6348 | −0.714525 | ||||||||
\(835\) | −5.19980 | −0.179946 | ||||||||
\(836\) | 4.61703 | 0.159683 | ||||||||
\(837\) | −19.1971 | −0.663548 | ||||||||
\(838\) | 12.5579 | 0.433805 | ||||||||
\(839\) | −8.47812 | −0.292697 | −0.146349 | − | 0.989233i | \(-0.546752\pi\) | ||||
−0.146349 | + | 0.989233i | \(0.546752\pi\) | |||||||
\(840\) | −77.4642 | −2.67277 | ||||||||
\(841\) | −4.79188 | −0.165237 | ||||||||
\(842\) | −34.2453 | −1.18017 | ||||||||
\(843\) | −23.7111 | −0.816654 | ||||||||
\(844\) | −2.75674 | −0.0948910 | ||||||||
\(845\) | 43.0016 | 1.47930 | ||||||||
\(846\) | −14.6500 | −0.503677 | ||||||||
\(847\) | −5.07571 | −0.174404 | ||||||||
\(848\) | −47.0529 | −1.61580 | ||||||||
\(849\) | −57.7042 | −1.98040 | ||||||||
\(850\) | −9.91112 | −0.339949 | ||||||||
\(851\) | 13.4452 | 0.460894 | ||||||||
\(852\) | −9.94750 | −0.340796 | ||||||||
\(853\) | −47.7144 | −1.63371 | −0.816855 | − | 0.576842i | \(-0.804285\pi\) | ||||
−0.816855 | + | 0.576842i | \(0.804285\pi\) | |||||||
\(854\) | 123.937 | 4.24104 | ||||||||
\(855\) | −32.0903 | −1.09746 | ||||||||
\(856\) | −28.4360 | −0.971921 | ||||||||
\(857\) | −24.3088 | −0.830373 | −0.415186 | − | 0.909736i | \(-0.636284\pi\) | ||||
−0.415186 | + | 0.909736i | \(0.636284\pi\) | |||||||
\(858\) | −0.989890 | −0.0337943 | ||||||||
\(859\) | 9.53462 | 0.325317 | 0.162658 | − | 0.986682i | \(-0.447993\pi\) | ||||
0.162658 | + | 0.986682i | \(0.447993\pi\) | |||||||
\(860\) | −2.17204 | −0.0740658 | ||||||||
\(861\) | −25.3769 | −0.864842 | ||||||||
\(862\) | −15.1751 | −0.516866 | ||||||||
\(863\) | 29.5973 | 1.00750 | 0.503752 | − | 0.863848i | \(-0.331953\pi\) | ||||
0.503752 | + | 0.863848i | \(0.331953\pi\) | |||||||
\(864\) | 12.1686 | 0.413983 | ||||||||
\(865\) | −32.3743 | −1.10076 | ||||||||
\(866\) | 4.17968 | 0.142031 | ||||||||
\(867\) | −2.08850 | −0.0709290 | ||||||||
\(868\) | 18.5790 | 0.630611 | ||||||||
\(869\) | −6.07658 | −0.206134 | ||||||||
\(870\) | 55.7199 | 1.88908 | ||||||||
\(871\) | −0.408179 | −0.0138306 | ||||||||
\(872\) | 42.4557 | 1.43773 | ||||||||
\(873\) | 1.70907 | 0.0578434 | ||||||||
\(874\) | −19.2070 | −0.649686 | ||||||||
\(875\) | 18.3470 | 0.620241 | ||||||||
\(876\) | 16.6535 | 0.562668 | ||||||||
\(877\) | −38.0420 | −1.28459 | −0.642294 | − | 0.766459i | \(-0.722017\pi\) | ||||
−0.642294 | + | 0.766459i | \(0.722017\pi\) | |||||||
\(878\) | −4.97418 | −0.167870 | ||||||||
\(879\) | −28.4058 | −0.958104 | ||||||||
\(880\) | 16.2452 | 0.547625 | ||||||||
\(881\) | −33.7151 | −1.13589 | −0.567946 | − | 0.823066i | \(-0.692262\pi\) | ||||
−0.567946 | + | 0.823066i | \(0.692262\pi\) | |||||||
\(882\) | −41.6133 | −1.40119 | ||||||||
\(883\) | −21.0002 | −0.706711 | −0.353356 | − | 0.935489i | \(-0.614959\pi\) | ||||
−0.353356 | + | 0.935489i | \(0.614959\pi\) | |||||||
\(884\) | −0.189856 | −0.00638554 | ||||||||
\(885\) | 95.6020 | 3.21363 | ||||||||
\(886\) | −55.2542 | −1.85630 | ||||||||
\(887\) | 34.0722 | 1.14403 | 0.572016 | − | 0.820243i | \(-0.306162\pi\) | ||||
0.572016 | + | 0.820243i | \(0.306162\pi\) | |||||||
\(888\) | −36.9848 | −1.24113 | ||||||||
\(889\) | −75.0164 | −2.51597 | ||||||||
\(890\) | −25.8852 | −0.867674 | ||||||||
\(891\) | −11.2309 | −0.376249 | ||||||||
\(892\) | −17.9604 | −0.601359 | ||||||||
\(893\) | 46.7498 | 1.56442 | ||||||||
\(894\) | −21.7132 | −0.726198 | ||||||||
\(895\) | −10.7853 | −0.360512 | ||||||||
\(896\) | 68.8886 | 2.30141 | ||||||||
\(897\) | 1.01283 | 0.0338175 | ||||||||
\(898\) | −7.84454 | −0.261776 | ||||||||
\(899\) | 27.6070 | 0.920743 | ||||||||
\(900\) | 5.40643 | 0.180214 | ||||||||
\(901\) | 9.64367 | 0.321277 | ||||||||
\(902\) | 3.89874 | 0.129814 | ||||||||
\(903\) | 10.6006 | 0.352766 | ||||||||
\(904\) | −22.0991 | −0.735007 | ||||||||
\(905\) | −37.5630 | −1.24864 | ||||||||
\(906\) | 4.85205 | 0.161198 | ||||||||
\(907\) | 29.4640 | 0.978337 | 0.489168 | − | 0.872189i | \(-0.337300\pi\) | ||||
0.489168 | + | 0.872189i | \(0.337300\pi\) | |||||||
\(908\) | 7.86767 | 0.261098 | ||||||||
\(909\) | 14.8657 | 0.493066 | ||||||||
\(910\) | 8.00997 | 0.265528 | ||||||||
\(911\) | 3.26857 | 0.108293 | 0.0541463 | − | 0.998533i | \(-0.482756\pi\) | ||||
0.0541463 | + | 0.998533i | \(0.482756\pi\) | |||||||
\(912\) | 72.1196 | 2.38812 | ||||||||
\(913\) | −1.31345 | −0.0434690 | ||||||||
\(914\) | −24.4103 | −0.807420 | ||||||||
\(915\) | 104.256 | 3.44661 | ||||||||
\(916\) | 6.86828 | 0.226934 | ||||||||
\(917\) | 111.658 | 3.68728 | ||||||||
\(918\) | −5.57203 | −0.183904 | ||||||||
\(919\) | −0.643250 | −0.0212189 | −0.0106094 | − | 0.999944i | \(-0.503377\pi\) | ||||
−0.0106094 | + | 0.999944i | \(0.503377\pi\) | |||||||
\(920\) | −12.1769 | −0.401462 | ||||||||
\(921\) | 50.2007 | 1.65417 | ||||||||
\(922\) | 44.7781 | 1.47469 | ||||||||
\(923\) | −2.12486 | −0.0699408 | ||||||||
\(924\) | 6.91540 | 0.227500 | ||||||||
\(925\) | 49.1027 | 1.61449 | ||||||||
\(926\) | 63.4485 | 2.08505 | ||||||||
\(927\) | −16.2195 | −0.532718 | ||||||||
\(928\) | −17.4994 | −0.574445 | ||||||||
\(929\) | 15.5564 | 0.510390 | 0.255195 | − | 0.966890i | \(-0.417860\pi\) | ||||
0.255195 | + | 0.966890i | \(0.417860\pi\) | |||||||
\(930\) | 63.5430 | 2.08366 | ||||||||
\(931\) | 132.793 | 4.35211 | ||||||||
\(932\) | −6.16047 | −0.201793 | ||||||||
\(933\) | −67.7775 | −2.21894 | ||||||||
\(934\) | −31.1256 | −1.01846 | ||||||||
\(935\) | −3.32951 | −0.108887 | ||||||||
\(936\) | −0.869851 | −0.0284320 | ||||||||
\(937\) | −52.4852 | −1.71462 | −0.857309 | − | 0.514802i | \(-0.827865\pi\) | ||||
−0.857309 | + | 0.514802i | \(0.827865\pi\) | |||||||
\(938\) | 11.5938 | 0.378552 | ||||||||
\(939\) | −1.54901 | −0.0505501 | ||||||||
\(940\) | −14.3473 | −0.467958 | ||||||||
\(941\) | −16.1525 | −0.526556 | −0.263278 | − | 0.964720i | \(-0.584804\pi\) | ||||
−0.263278 | + | 0.964720i | \(0.584804\pi\) | |||||||
\(942\) | −3.47862 | −0.113340 | ||||||||
\(943\) | −3.98910 | −0.129903 | ||||||||
\(944\) | −67.0806 | −2.18329 | ||||||||
\(945\) | 57.8195 | 1.88087 | ||||||||
\(946\) | −1.62861 | −0.0529506 | ||||||||
\(947\) | −12.8320 | −0.416984 | −0.208492 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208492 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(948\) | 8.27902 | 0.268890 | ||||||||
\(949\) | 3.55731 | 0.115475 | ||||||||
\(950\) | −70.1453 | −2.27581 | ||||||||
\(951\) | 48.0134 | 1.55694 | ||||||||
\(952\) | −11.1401 | −0.361051 | ||||||||
\(953\) | −21.9532 | −0.711133 | −0.355566 | − | 0.934651i | \(-0.615712\pi\) | ||||
−0.355566 | + | 0.934651i | \(0.615712\pi\) | |||||||
\(954\) | −21.3883 | −0.692471 | ||||||||
\(955\) | −64.5455 | −2.08864 | ||||||||
\(956\) | 13.7827 | 0.445765 | ||||||||
\(957\) | 10.2758 | 0.332168 | ||||||||
\(958\) | −24.9952 | −0.807558 | ||||||||
\(959\) | 58.1201 | 1.87680 | ||||||||
\(960\) | 27.5775 | 0.890062 | ||||||||
\(961\) | 0.482983 | 0.0155801 | ||||||||
\(962\) | 3.82430 | 0.123301 | ||||||||
\(963\) | −17.6439 | −0.568567 | ||||||||
\(964\) | 7.14728 | 0.230198 | ||||||||
\(965\) | 49.4194 | 1.59087 | ||||||||
\(966\) | −28.7683 | −0.925604 | ||||||||
\(967\) | −14.4592 | −0.464977 | −0.232488 | − | 0.972599i | \(-0.574687\pi\) | ||||
−0.232488 | + | 0.972599i | \(0.574687\pi\) | |||||||
\(968\) | 2.19478 | 0.0705428 | ||||||||
\(969\) | −14.7812 | −0.474840 | ||||||||
\(970\) | 6.80519 | 0.218502 | ||||||||
\(971\) | −37.1369 | −1.19178 | −0.595890 | − | 0.803066i | \(-0.703201\pi\) | ||||
−0.595890 | + | 0.803066i | \(0.703201\pi\) | |||||||
\(972\) | 8.60569 | 0.276028 | ||||||||
\(973\) | 30.7927 | 0.987169 | ||||||||
\(974\) | −13.3946 | −0.429190 | ||||||||
\(975\) | 3.69894 | 0.118461 | ||||||||
\(976\) | −73.1530 | −2.34157 | ||||||||
\(977\) | −40.3189 | −1.28992 | −0.644958 | − | 0.764218i | \(-0.723125\pi\) | ||||
−0.644958 | + | 0.764218i | \(0.723125\pi\) | |||||||
\(978\) | 64.7310 | 2.06987 | ||||||||
\(979\) | −4.77370 | −0.152568 | ||||||||
\(980\) | −40.7536 | −1.30183 | ||||||||
\(981\) | 26.3428 | 0.841062 | ||||||||
\(982\) | −59.3854 | −1.89506 | ||||||||
\(983\) | 28.5515 | 0.910651 | 0.455326 | − | 0.890325i | \(-0.349523\pi\) | ||||
0.455326 | + | 0.890325i | \(0.349523\pi\) | |||||||
\(984\) | 10.9732 | 0.349812 | ||||||||
\(985\) | −38.5376 | −1.22791 | ||||||||
\(986\) | 8.01303 | 0.255187 | ||||||||
\(987\) | 70.0219 | 2.22882 | ||||||||
\(988\) | −1.34369 | −0.0427486 | ||||||||
\(989\) | 1.66635 | 0.0529870 | ||||||||
\(990\) | 7.38437 | 0.234691 | ||||||||
\(991\) | 28.5652 | 0.907405 | 0.453702 | − | 0.891153i | \(-0.350103\pi\) | ||||
0.453702 | + | 0.891153i | \(0.350103\pi\) | |||||||
\(992\) | −19.9563 | −0.633613 | ||||||||
\(993\) | −17.8916 | −0.567772 | ||||||||
\(994\) | 60.3541 | 1.91432 | ||||||||
\(995\) | 28.6542 | 0.908398 | ||||||||
\(996\) | 1.78951 | 0.0567029 | ||||||||
\(997\) | 4.98477 | 0.157869 | 0.0789346 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789346 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(998\) | 53.9111 | 1.70653 | ||||||||
\(999\) | 27.6055 | 0.873401 |
(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 | 8041.2.a.j.1.20 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.20 | ✓ | 82 | 1.1 | even | 1 | trivial |