Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.07305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07305 | −0.758764 | −0.379382 | − | 0.925240i | \(-0.623863\pi\) | ||||
−0.379382 | + | 0.925240i | \(0.623863\pi\) | |||||||
\(3\) | −2.43140 | −1.40377 | −0.701886 | − | 0.712289i | \(-0.747658\pi\) | ||||
−0.701886 | + | 0.712289i | \(0.747658\pi\) | |||||||
\(4\) | −0.848553 | −0.424277 | ||||||||
\(5\) | 0.625432 | 0.279702 | 0.139851 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139851 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(6\) | 2.60903 | 1.06513 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.05665 | 1.08069 | ||||||||
\(9\) | 2.91173 | 0.970576 | ||||||||
\(10\) | −0.671123 | −0.212228 | ||||||||
\(11\) | −0.708521 | −0.213627 | −0.106814 | − | 0.994279i | \(-0.534065\pi\) | ||||
−0.106814 | + | 0.994279i | \(0.534065\pi\) | |||||||
\(12\) | 2.06318 | 0.595588 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52068 | −0.392637 | ||||||||
\(16\) | −1.58285 | −0.395713 | ||||||||
\(17\) | −3.34313 | −0.810829 | −0.405414 | − | 0.914133i | \(-0.632873\pi\) | ||||
−0.405414 | + | 0.914133i | \(0.632873\pi\) | |||||||
\(18\) | −3.12445 | −0.736439 | ||||||||
\(19\) | −5.20276 | −1.19360 | −0.596798 | − | 0.802392i | \(-0.703561\pi\) | ||||
−0.596798 | + | 0.802392i | \(0.703561\pi\) | |||||||
\(20\) | −0.530712 | −0.118671 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.760282 | 0.162093 | ||||||||
\(23\) | −4.43140 | −0.924012 | −0.462006 | − | 0.886877i | \(-0.652870\pi\) | ||||
−0.462006 | + | 0.886877i | \(0.652870\pi\) | |||||||
\(24\) | −7.43196 | −1.51704 | ||||||||
\(25\) | −4.60883 | −0.921767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.214623 | 0.0413042 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.59711 | −1.22505 | −0.612526 | − | 0.790450i | \(-0.709847\pi\) | ||||
−0.612526 | + | 0.790450i | \(0.709847\pi\) | |||||||
\(30\) | 1.63177 | 0.297919 | ||||||||
\(31\) | −4.39061 | −0.788576 | −0.394288 | − | 0.918987i | \(-0.629009\pi\) | ||||
−0.394288 | + | 0.918987i | \(0.629009\pi\) | |||||||
\(32\) | −4.41482 | −0.780437 | ||||||||
\(33\) | 1.72270 | 0.299884 | ||||||||
\(34\) | 3.58737 | 0.615228 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.47076 | −0.411793 | ||||||||
\(37\) | 0.423409 | 0.0696080 | 0.0348040 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348040 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(38\) | 5.58285 | 0.905658 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.91173 | 0.302271 | ||||||||
\(41\) | −5.01604 | −0.783374 | −0.391687 | − | 0.920099i | \(-0.628108\pi\) | ||||
−0.391687 | + | 0.920099i | \(0.628108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2059 | −1.70889 | −0.854445 | − | 0.519542i | \(-0.826103\pi\) | ||||
−0.854445 | + | 0.519542i | \(0.826103\pi\) | |||||||
\(44\) | 0.601218 | 0.0906370 | ||||||||
\(45\) | 1.82109 | 0.271472 | ||||||||
\(46\) | 4.75514 | 0.701107 | ||||||||
\(47\) | 8.07269 | 1.17752 | 0.588762 | − | 0.808307i | \(-0.299616\pi\) | ||||
0.588762 | + | 0.808307i | \(0.299616\pi\) | |||||||
\(48\) | 3.84855 | 0.555491 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.94553 | 0.699404 | ||||||||
\(51\) | 8.12851 | 1.13822 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.697106 | −0.0957549 | −0.0478774 | − | 0.998853i | \(-0.515246\pi\) | ||||
−0.0478774 | + | 0.998853i | \(0.515246\pi\) | |||||||
\(54\) | −0.230302 | −0.0313401 | ||||||||
\(55\) | −0.443132 | −0.0597519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.6500 | 1.67554 | ||||||||
\(58\) | 7.07906 | 0.929526 | ||||||||
\(59\) | 9.86319 | 1.28408 | 0.642039 | − | 0.766672i | \(-0.278089\pi\) | ||||
0.642039 | + | 0.766672i | \(0.278089\pi\) | |||||||
\(60\) | 1.29038 | 0.166587 | ||||||||
\(61\) | 4.69711 | 0.601403 | 0.300701 | − | 0.953718i | \(-0.402779\pi\) | ||||
0.300701 | + | 0.953718i | \(0.402779\pi\) | |||||||
\(62\) | 4.71136 | 0.598344 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.90305 | 0.987881 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.84855 | −0.227541 | ||||||||
\(67\) | 10.4208 | 1.27311 | 0.636553 | − | 0.771233i | \(-0.280360\pi\) | ||||
0.636553 | + | 0.771233i | \(0.280360\pi\) | |||||||
\(68\) | 2.83683 | 0.344016 | ||||||||
\(69\) | 10.7745 | 1.29710 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0876 | −1.67189 | −0.835946 | − | 0.548812i | \(-0.815080\pi\) | ||||
−0.835946 | + | 0.548812i | \(0.815080\pi\) | |||||||
\(72\) | 8.90015 | 1.04889 | ||||||||
\(73\) | −5.08383 | −0.595017 | −0.297509 | − | 0.954719i | \(-0.596156\pi\) | ||||
−0.297509 | + | 0.954719i | \(0.596156\pi\) | |||||||
\(74\) | −0.454341 | −0.0528161 | ||||||||
\(75\) | 11.2059 | 1.29395 | ||||||||
\(76\) | 4.41482 | 0.506415 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.91173 | −0.440104 | −0.220052 | − | 0.975488i | \(-0.570623\pi\) | ||||
−0.220052 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(80\) | −0.989966 | −0.110682 | ||||||||
\(81\) | −9.25702 | −1.02856 | ||||||||
\(82\) | 5.38249 | 0.594396 | ||||||||
\(83\) | 10.2035 | 1.11998 | 0.559990 | − | 0.828499i | \(-0.310805\pi\) | ||||
0.559990 | + | 0.828499i | \(0.310805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.09090 | −0.226790 | ||||||||
\(86\) | 12.0246 | 1.29665 | ||||||||
\(87\) | 16.0402 | 1.71969 | ||||||||
\(88\) | −2.16570 | −0.230865 | ||||||||
\(89\) | −13.3791 | −1.41818 | −0.709090 | − | 0.705117i | \(-0.750894\pi\) | ||||
−0.709090 | + | 0.705117i | \(0.750894\pi\) | |||||||
\(90\) | −1.95413 | −0.205983 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.76028 | 0.392036 | ||||||||
\(93\) | 10.6753 | 1.10698 | ||||||||
\(94\) | −8.66244 | −0.893463 | ||||||||
\(95\) | −3.25397 | −0.333851 | ||||||||
\(96\) | 10.7342 | 1.09556 | ||||||||
\(97\) | −0.202023 | −0.0205123 | −0.0102562 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102562 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.06302 | −0.207341 | ||||||||
\(100\) | 3.91084 | 0.391084 | ||||||||
\(101\) | −17.3345 | −1.72484 | −0.862421 | − | 0.506191i | \(-0.831053\pi\) | ||||
−0.862421 | + | 0.506191i | \(0.831053\pi\) | |||||||
\(102\) | −8.72234 | −0.863640 | ||||||||
\(103\) | −10.8148 | −1.06561 | −0.532806 | − | 0.846237i | \(-0.678862\pi\) | ||||
−0.532806 | + | 0.846237i | \(0.678862\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.748033 | 0.0726554 | ||||||||
\(107\) | −6.11678 | −0.591332 | −0.295666 | − | 0.955291i | \(-0.595542\pi\) | ||||
−0.295666 | + | 0.955291i | \(0.595542\pi\) | |||||||
\(108\) | −0.182119 | −0.0175244 | ||||||||
\(109\) | 11.3992 | 1.09184 | 0.545921 | − | 0.837837i | \(-0.316180\pi\) | ||||
0.545921 | + | 0.837837i | \(0.316180\pi\) | |||||||
\(110\) | 0.475505 | 0.0453376 | ||||||||
\(111\) | −1.02948 | −0.0977137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.923456 | −0.0868714 | −0.0434357 | − | 0.999056i | \(-0.513830\pi\) | ||||
−0.0434357 | + | 0.999056i | \(0.513830\pi\) | |||||||
\(114\) | −13.5742 | −1.27134 | ||||||||
\(115\) | −2.77154 | −0.258448 | ||||||||
\(116\) | 5.59800 | 0.519761 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.5837 | −0.974312 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.64819 | −0.424319 | ||||||||
\(121\) | −10.4980 | −0.954363 | ||||||||
\(122\) | −5.04025 | −0.456323 | ||||||||
\(123\) | 12.1960 | 1.09968 | ||||||||
\(124\) | 3.72566 | 0.334574 | ||||||||
\(125\) | −6.00967 | −0.537521 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.50972 | −0.755116 | −0.377558 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377558 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(128\) | 0.349236 | 0.0308684 | ||||||||
\(129\) | 27.2462 | 2.39889 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00305 | −0.611859 | −0.305930 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305930 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(132\) | −1.46180 | −0.127234 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.1821 | −0.965988 | ||||||||
\(135\) | 0.134232 | 0.0115528 | ||||||||
\(136\) | −10.2188 | −0.876255 | ||||||||
\(137\) | −6.21694 | −0.531149 | −0.265575 | − | 0.964090i | \(-0.585562\pi\) | ||||
−0.265575 | + | 0.964090i | \(0.585562\pi\) | |||||||
\(138\) | −11.5617 | −0.984195 | ||||||||
\(139\) | 6.53140 | 0.553986 | 0.276993 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276993 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.6280 | −1.65297 | ||||||||
\(142\) | 15.1168 | 1.26857 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.60883 | −0.384070 | ||||||||
\(145\) | −4.12604 | −0.342649 | ||||||||
\(146\) | 5.45523 | 0.451478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.359285 | −0.0295330 | ||||||||
\(149\) | −3.69738 | −0.302901 | −0.151451 | − | 0.988465i | \(-0.548394\pi\) | ||||
−0.151451 | + | 0.988465i | \(0.548394\pi\) | |||||||
\(150\) | −12.0246 | −0.981804 | ||||||||
\(151\) | −4.87774 | −0.396945 | −0.198473 | − | 0.980106i | \(-0.563598\pi\) | ||||
−0.198473 | + | 0.980106i | \(0.563598\pi\) | |||||||
\(152\) | −15.9030 | −1.28991 | ||||||||
\(153\) | −9.73430 | −0.786971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.74603 | −0.220566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.51968 | −0.759753 | −0.379876 | − | 0.925037i | \(-0.624033\pi\) | ||||
−0.379876 | + | 0.925037i | \(0.624033\pi\) | |||||||
\(158\) | 4.19750 | 0.333935 | ||||||||
\(159\) | 1.69495 | 0.134418 | ||||||||
\(160\) | −2.76117 | −0.218290 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.93329 | 0.780433 | ||||||||
\(163\) | −23.7089 | −1.85702 | −0.928511 | − | 0.371305i | \(-0.878910\pi\) | ||||
−0.928511 | + | 0.371305i | \(0.878910\pi\) | |||||||
\(164\) | 4.25637 | 0.332367 | ||||||||
\(165\) | 1.07743 | 0.0838780 | ||||||||
\(166\) | −10.9489 | −0.849801 | ||||||||
\(167\) | 1.13193 | 0.0875914 | 0.0437957 | − | 0.999041i | \(-0.486055\pi\) | ||||
0.0437957 | + | 0.999041i | \(0.486055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.24365 | 0.172080 | ||||||||
\(171\) | −15.1490 | −1.15848 | ||||||||
\(172\) | 9.50884 | 0.725042 | ||||||||
\(173\) | 11.9892 | 0.911519 | 0.455760 | − | 0.890103i | \(-0.349368\pi\) | ||||
0.455760 | + | 0.890103i | \(0.349368\pi\) | |||||||
\(174\) | −17.2121 | −1.30484 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.12148 | 0.0845350 | ||||||||
\(177\) | −23.9814 | −1.80255 | ||||||||
\(178\) | 14.3565 | 1.07607 | ||||||||
\(179\) | 9.47076 | 0.707878 | 0.353939 | − | 0.935269i | \(-0.384842\pi\) | ||||
0.353939 | + | 0.935269i | \(0.384842\pi\) | |||||||
\(180\) | −1.54529 | −0.115179 | ||||||||
\(181\) | 11.4314 | 0.849690 | 0.424845 | − | 0.905266i | \(-0.360329\pi\) | ||||
0.424845 | + | 0.905266i | \(0.360329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4206 | −0.844233 | ||||||||
\(184\) | −13.5453 | −0.998571 | ||||||||
\(185\) | 0.264813 | 0.0194695 | ||||||||
\(186\) | −11.4552 | −0.839938 | ||||||||
\(187\) | 2.36868 | 0.173215 | ||||||||
\(188\) | −6.85011 | −0.499595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.49169 | 0.253314 | ||||||||
\(191\) | 15.6875 | 1.13511 | 0.567555 | − | 0.823335i | \(-0.307889\pi\) | ||||
0.567555 | + | 0.823335i | \(0.307889\pi\) | |||||||
\(192\) | −19.2155 | −1.38676 | ||||||||
\(193\) | 23.0071 | 1.65609 | 0.828045 | − | 0.560662i | \(-0.189453\pi\) | ||||
0.828045 | + | 0.560662i | \(0.189453\pi\) | |||||||
\(194\) | 0.216782 | 0.0155640 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.2035 | −0.726970 | −0.363485 | − | 0.931600i | \(-0.618413\pi\) | ||||
−0.363485 | + | 0.931600i | \(0.618413\pi\) | |||||||
\(198\) | 2.21373 | 0.157323 | ||||||||
\(199\) | 11.9235 | 0.845231 | 0.422616 | − | 0.906309i | \(-0.361112\pi\) | ||||
0.422616 | + | 0.906309i | \(0.361112\pi\) | |||||||
\(200\) | −14.0876 | −0.996145 | ||||||||
\(201\) | −25.3372 | −1.78715 | ||||||||
\(202\) | 18.6008 | 1.30875 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.89747 | −0.482920 | ||||||||
\(205\) | −3.13719 | −0.219111 | ||||||||
\(206\) | 11.6049 | 0.808548 | ||||||||
\(207\) | −12.9030 | −0.896824 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.68627 | 0.254984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5893 | −1.07321 | −0.536606 | − | 0.843833i | \(-0.680294\pi\) | ||||
−0.536606 | + | 0.843833i | \(0.680294\pi\) | |||||||
\(212\) | 0.591531 | 0.0406265 | ||||||||
\(213\) | 34.2527 | 2.34696 | ||||||||
\(214\) | 6.56365 | 0.448682 | ||||||||
\(215\) | −7.00855 | −0.477979 | ||||||||
\(216\) | 0.656028 | 0.0446370 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.2319 | −0.828451 | ||||||||
\(219\) | 12.3608 | 0.835269 | ||||||||
\(220\) | 0.376021 | 0.0253513 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.10469 | 0.0741417 | ||||||||
\(223\) | 6.76662 | 0.453126 | 0.226563 | − | 0.973996i | \(-0.427251\pi\) | ||||
0.226563 | + | 0.973996i | \(0.427251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.4197 | −0.894645 | ||||||||
\(226\) | 0.990919 | 0.0659149 | ||||||||
\(227\) | −16.8245 | −1.11668 | −0.558340 | − | 0.829612i | \(-0.688562\pi\) | ||||
−0.558340 | + | 0.829612i | \(0.688562\pi\) | |||||||
\(228\) | −10.7342 | −0.710891 | ||||||||
\(229\) | −11.0257 | −0.728599 | −0.364300 | − | 0.931282i | \(-0.618692\pi\) | ||||
−0.364300 | + | 0.931282i | \(0.618692\pi\) | |||||||
\(230\) | 2.97402 | 0.196101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20.1651 | −1.32390 | ||||||||
\(233\) | 17.3549 | 1.13695 | 0.568477 | − | 0.822699i | \(-0.307533\pi\) | ||||
0.568477 | + | 0.822699i | \(0.307533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.04892 | 0.329355 | ||||||||
\(236\) | −8.36944 | −0.544804 | ||||||||
\(237\) | 9.51100 | 0.617806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.7223 | −1.27573 | −0.637865 | − | 0.770148i | \(-0.720182\pi\) | ||||
−0.637865 | + | 0.770148i | \(0.720182\pi\) | |||||||
\(240\) | 2.40701 | 0.155372 | ||||||||
\(241\) | −2.78413 | −0.179341 | −0.0896706 | − | 0.995971i | \(-0.528581\pi\) | ||||
−0.0896706 | + | 0.995971i | \(0.528581\pi\) | |||||||
\(242\) | 11.2649 | 0.724137 | ||||||||
\(243\) | 21.8637 | 1.40256 | ||||||||
\(244\) | −3.98574 | −0.255161 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.0870 | −0.834397 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −13.4206 | −0.852207 | ||||||||
\(249\) | −24.8088 | −1.57220 | ||||||||
\(250\) | 6.44871 | 0.407852 | ||||||||
\(251\) | 23.5608 | 1.48714 | 0.743572 | − | 0.668655i | \(-0.233130\pi\) | ||||
0.743572 | + | 0.668655i | \(0.233130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.13974 | 0.197394 | ||||||||
\(254\) | 9.13140 | 0.572955 | ||||||||
\(255\) | 5.08383 | 0.318362 | ||||||||
\(256\) | −16.1808 | −1.01130 | ||||||||
\(257\) | −3.43229 | −0.214101 | −0.107050 | − | 0.994254i | \(-0.534141\pi\) | ||||
−0.107050 | + | 0.994254i | \(0.534141\pi\) | |||||||
\(258\) | −29.2367 | −1.82019 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.2090 | −1.18901 | ||||||||
\(262\) | 7.51465 | 0.464257 | ||||||||
\(263\) | −21.4491 | −1.32261 | −0.661303 | − | 0.750119i | \(-0.729996\pi\) | ||||
−0.661303 | + | 0.750119i | \(0.729996\pi\) | |||||||
\(264\) | 5.26570 | 0.324082 | ||||||||
\(265\) | −0.435992 | −0.0267828 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.5300 | 1.99080 | ||||||||
\(268\) | −8.84262 | −0.540149 | ||||||||
\(269\) | 14.6569 | 0.893645 | 0.446822 | − | 0.894623i | \(-0.352556\pi\) | ||||
0.446822 | + | 0.894623i | \(0.352556\pi\) | |||||||
\(270\) | −0.144038 | −0.00876589 | ||||||||
\(271\) | 2.04366 | 0.124143 | 0.0620717 | − | 0.998072i | \(-0.480229\pi\) | ||||
0.0620717 | + | 0.998072i | \(0.480229\pi\) | |||||||
\(272\) | 5.29168 | 0.320856 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.67112 | 0.403017 | ||||||||
\(275\) | 3.26546 | 0.196914 | ||||||||
\(276\) | −9.14277 | −0.550330 | ||||||||
\(277\) | −5.43356 | −0.326471 | −0.163236 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163236 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(278\) | −7.00855 | −0.420345 | ||||||||
\(279\) | −12.7843 | −0.765373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2356 | −1.20715 | −0.603577 | − | 0.797305i | \(-0.706258\pi\) | ||||
−0.603577 | + | 0.797305i | \(0.706258\pi\) | |||||||
\(282\) | 21.0619 | 1.25422 | ||||||||
\(283\) | 1.73519 | 0.103146 | 0.0515731 | − | 0.998669i | \(-0.483576\pi\) | ||||
0.0515731 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(284\) | 11.9541 | 0.709345 | ||||||||
\(285\) | 7.91173 | 0.468650 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.8548 | −0.757474 | ||||||||
\(289\) | −5.82346 | −0.342556 | ||||||||
\(290\) | 4.42747 | 0.259990 | ||||||||
\(291\) | 0.491200 | 0.0287947 | ||||||||
\(292\) | 4.31390 | 0.252452 | ||||||||
\(293\) | −27.2441 | −1.59162 | −0.795810 | − | 0.605547i | \(-0.792954\pi\) | ||||
−0.795810 | + | 0.605547i | \(0.792954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16875 | 0.359159 | ||||||||
\(296\) | 1.29421 | 0.0752247 | ||||||||
\(297\) | −0.152065 | −0.00882369 | ||||||||
\(298\) | 3.96750 | 0.229831 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.50884 | −0.548993 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.23409 | 0.301188 | ||||||||
\(303\) | 42.1471 | 2.42129 | ||||||||
\(304\) | 8.23520 | 0.472321 | ||||||||
\(305\) | 2.93772 | 0.168213 | ||||||||
\(306\) | 10.4454 | 0.597126 | ||||||||
\(307\) | −12.7138 | −0.725612 | −0.362806 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362806 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.2951 | 1.49588 | ||||||||
\(310\) | 2.94664 | 0.167358 | ||||||||
\(311\) | 9.61879 | 0.545431 | 0.272716 | − | 0.962095i | \(-0.412078\pi\) | ||||
0.272716 | + | 0.962095i | \(0.412078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.02547 | −0.510149 | −0.255075 | − | 0.966921i | \(-0.582100\pi\) | ||||
−0.255075 | + | 0.966921i | \(0.582100\pi\) | |||||||
\(314\) | 10.2151 | 0.576473 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.31931 | 0.186726 | ||||||||
\(317\) | −24.6262 | −1.38314 | −0.691572 | − | 0.722307i | \(-0.743082\pi\) | ||||
−0.691572 | + | 0.722307i | \(0.743082\pi\) | |||||||
\(318\) | −1.81877 | −0.101992 | ||||||||
\(319\) | 4.67419 | 0.261704 | ||||||||
\(320\) | 4.94282 | 0.276312 | ||||||||
\(321\) | 14.8724 | 0.830095 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.3935 | 0.967802 | ||||||||
\(324\) | 7.85507 | 0.436393 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.4409 | 1.40904 | ||||||||
\(327\) | −27.7160 | −1.53270 | ||||||||
\(328\) | −15.3323 | −0.846584 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.15614 | −0.0636436 | ||||||||
\(331\) | −13.1718 | −0.723989 | −0.361994 | − | 0.932180i | \(-0.617904\pi\) | ||||
−0.361994 | + | 0.932180i | \(0.617904\pi\) | |||||||
\(332\) | −8.65821 | −0.475181 | ||||||||
\(333\) | 1.23285 | 0.0675599 | ||||||||
\(334\) | −1.21462 | −0.0664612 | ||||||||
\(335\) | 6.51752 | 0.356090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0307 | −0.927720 | −0.463860 | − | 0.885909i | \(-0.653536\pi\) | ||||
−0.463860 | + | 0.885909i | \(0.653536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.24529 | 0.121948 | ||||||||
\(340\) | 1.77424 | 0.0962218 | ||||||||
\(341\) | 3.11084 | 0.168461 | ||||||||
\(342\) | 16.2558 | 0.879010 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −34.2527 | −1.84678 | ||||||||
\(345\) | 6.73874 | 0.362802 | ||||||||
\(346\) | −12.8650 | −0.691628 | ||||||||
\(347\) | 0.459917 | 0.0246897 | 0.0123448 | − | 0.999924i | \(-0.496070\pi\) | ||||
0.0123448 | + | 0.999924i | \(0.496070\pi\) | |||||||
\(348\) | −13.6110 | −0.729626 | ||||||||
\(349\) | 6.87822 | 0.368183 | 0.184091 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184091 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.12799 | 0.166723 | ||||||||
\(353\) | −1.53326 | −0.0816073 | −0.0408036 | − | 0.999167i | \(-0.512992\pi\) | ||||
−0.0408036 | + | 0.999167i | \(0.512992\pi\) | |||||||
\(354\) | 25.7334 | 1.36771 | ||||||||
\(355\) | −8.81084 | −0.467631 | ||||||||
\(356\) | 11.3529 | 0.601701 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.1626 | −0.537112 | ||||||||
\(359\) | 27.2068 | 1.43592 | 0.717959 | − | 0.696085i | \(-0.245077\pi\) | ||||
0.717959 | + | 0.696085i | \(0.245077\pi\) | |||||||
\(360\) | 5.56644 | 0.293377 | ||||||||
\(361\) | 8.06875 | 0.424671 | ||||||||
\(362\) | −12.2665 | −0.644714 | ||||||||
\(363\) | 25.5249 | 1.33971 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.17959 | −0.166427 | ||||||||
\(366\) | 12.2549 | 0.640574 | ||||||||
\(367\) | 26.9814 | 1.40842 | 0.704208 | − | 0.709994i | \(-0.251302\pi\) | ||||
0.704208 | + | 0.709994i | \(0.251302\pi\) | |||||||
\(368\) | 7.01426 | 0.365643 | ||||||||
\(369\) | −14.6053 | −0.760324 | ||||||||
\(370\) | −0.284159 | −0.0147727 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.05859 | −0.469666 | ||||||||
\(373\) | 3.97238 | 0.205682 | 0.102841 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102841 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(374\) | −2.54172 | −0.131429 | ||||||||
\(375\) | 14.6119 | 0.754558 | ||||||||
\(376\) | 24.6754 | 1.27254 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4059 | 0.585884 | 0.292942 | − | 0.956130i | \(-0.405366\pi\) | ||||
0.292942 | + | 0.956130i | \(0.405366\pi\) | |||||||
\(380\) | 2.76117 | 0.141645 | ||||||||
\(381\) | 20.6906 | 1.06001 | ||||||||
\(382\) | −16.8336 | −0.861281 | ||||||||
\(383\) | 23.7920 | 1.21571 | 0.607856 | − | 0.794047i | \(-0.292030\pi\) | ||||
0.607856 | + | 0.794047i | \(0.292030\pi\) | |||||||
\(384\) | −0.849134 | −0.0433322 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.6879 | −1.25658 | ||||||||
\(387\) | −32.6287 | −1.65861 | ||||||||
\(388\) | 0.171427 | 0.00870290 | ||||||||
\(389\) | −28.4110 | −1.44049 | −0.720247 | − | 0.693717i | \(-0.755972\pi\) | ||||
−0.720247 | + | 0.693717i | \(0.755972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8148 | 0.749216 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0272 | 0.858911 | ||||||||
\(394\) | 10.9489 | 0.551599 | ||||||||
\(395\) | −2.44652 | −0.123098 | ||||||||
\(396\) | 1.75058 | 0.0879701 | ||||||||
\(397\) | 9.85912 | 0.494815 | 0.247408 | − | 0.968912i | \(-0.420421\pi\) | ||||
0.247408 | + | 0.968912i | \(0.420421\pi\) | |||||||
\(398\) | −12.7945 | −0.641332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.29510 | 0.364755 | ||||||||
\(401\) | −12.6194 | −0.630184 | −0.315092 | − | 0.949061i | \(-0.602035\pi\) | ||||
−0.315092 | + | 0.949061i | \(0.602035\pi\) | |||||||
\(402\) | 27.1883 | 1.35603 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.7092 | 0.731810 | ||||||||
\(405\) | −5.78964 | −0.287689 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.299994 | −0.0148701 | ||||||||
\(408\) | 24.8460 | 1.23006 | ||||||||
\(409\) | 18.0573 | 0.892878 | 0.446439 | − | 0.894814i | \(-0.352692\pi\) | ||||
0.446439 | + | 0.894814i | \(0.352692\pi\) | |||||||
\(410\) | 3.36638 | 0.166254 | ||||||||
\(411\) | 15.1159 | 0.745613 | ||||||||
\(412\) | 9.17691 | 0.452114 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 13.8457 | 0.680478 | ||||||||
\(415\) | 6.38160 | 0.313260 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.8805 | −0.777671 | ||||||||
\(418\) | −3.95557 | −0.193473 | ||||||||
\(419\) | 14.2805 | 0.697647 | 0.348823 | − | 0.937188i | \(-0.386581\pi\) | ||||
0.348823 | + | 0.937188i | \(0.386581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.27439 | −0.208321 | −0.104160 | − | 0.994561i | \(-0.533216\pi\) | ||||
−0.104160 | + | 0.994561i | \(0.533216\pi\) | |||||||
\(422\) | 16.7282 | 0.814316 | ||||||||
\(423\) | 23.5055 | 1.14288 | ||||||||
\(424\) | −2.13081 | −0.103481 | ||||||||
\(425\) | 15.4080 | 0.747395 | ||||||||
\(426\) | −36.7550 | −1.78079 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.19042 | 0.250888 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.52056 | 0.362674 | ||||||||
\(431\) | −14.6067 | −0.703580 | −0.351790 | − | 0.936079i | \(-0.614427\pi\) | ||||
−0.351790 | + | 0.936079i | \(0.614427\pi\) | |||||||
\(432\) | −0.339716 | −0.0163446 | ||||||||
\(433\) | −28.0099 | −1.34607 | −0.673035 | − | 0.739611i | \(-0.735009\pi\) | ||||
−0.673035 | + | 0.739611i | \(0.735009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.0321 | 0.481001 | ||||||||
\(436\) | −9.67279 | −0.463243 | ||||||||
\(437\) | 23.0556 | 1.10290 | ||||||||
\(438\) | −13.2639 | −0.633772 | ||||||||
\(439\) | 17.0774 | 0.815061 | 0.407531 | − | 0.913192i | \(-0.366390\pi\) | ||||
0.407531 | + | 0.913192i | \(0.366390\pi\) | |||||||
\(440\) | −1.35450 | −0.0645733 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8157 | 0.656402 | 0.328201 | − | 0.944608i | \(-0.393558\pi\) | ||||
0.328201 | + | 0.944608i | \(0.393558\pi\) | |||||||
\(444\) | 0.873567 | 0.0414576 | ||||||||
\(445\) | −8.36771 | −0.396668 | ||||||||
\(446\) | −7.26096 | −0.343816 | ||||||||
\(447\) | 8.98984 | 0.425205 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.6410 | −1.54042 | −0.770211 | − | 0.637789i | \(-0.779849\pi\) | ||||
−0.770211 | + | 0.637789i | \(0.779849\pi\) | |||||||
\(450\) | 14.4001 | 0.678825 | ||||||||
\(451\) | 3.55397 | 0.167350 | ||||||||
\(452\) | 0.783601 | 0.0368575 | ||||||||
\(453\) | 11.8598 | 0.557220 | ||||||||
\(454\) | 18.0536 | 0.847298 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.6667 | 1.81074 | ||||||||
\(457\) | 3.17034 | 0.148302 | 0.0741511 | − | 0.997247i | \(-0.476375\pi\) | ||||
0.0741511 | + | 0.997247i | \(0.476375\pi\) | |||||||
\(458\) | 11.8312 | 0.552835 | ||||||||
\(459\) | −0.717513 | −0.0334906 | ||||||||
\(460\) | 2.35180 | 0.109653 | ||||||||
\(461\) | 0.202023 | 0.00940915 | 0.00470458 | − | 0.999989i | \(-0.498502\pi\) | ||||
0.00470458 | + | 0.999989i | \(0.498502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2121 | 0.799912 | 0.399956 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399956 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(464\) | 10.4422 | 0.484769 | ||||||||
\(465\) | 6.67670 | 0.309625 | ||||||||
\(466\) | −18.6227 | −0.862681 | ||||||||
\(467\) | −0.191169 | −0.00884625 | −0.00442312 | − | 0.999990i | \(-0.501408\pi\) | ||||
−0.00442312 | + | 0.999990i | \(0.501408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.41777 | −0.249903 | ||||||||
\(471\) | 23.1462 | 1.06652 | ||||||||
\(472\) | 30.1483 | 1.38769 | ||||||||
\(473\) | 7.93965 | 0.365065 | ||||||||
\(474\) | −10.2058 | −0.468769 | ||||||||
\(475\) | 23.9787 | 1.10022 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.02978 | −0.0929374 | ||||||||
\(478\) | 21.1631 | 0.967978 | ||||||||
\(479\) | −21.4785 | −0.981377 | −0.490688 | − | 0.871335i | \(-0.663255\pi\) | ||||
−0.490688 | + | 0.871335i | \(0.663255\pi\) | |||||||
\(480\) | 6.71352 | 0.306429 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.98752 | 0.136078 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.90811 | 0.404914 | ||||||||
\(485\) | −0.126352 | −0.00573733 | ||||||||
\(486\) | −23.4609 | −1.06421 | ||||||||
\(487\) | −19.0484 | −0.863167 | −0.431584 | − | 0.902073i | \(-0.642045\pi\) | ||||
−0.431584 | + | 0.902073i | \(0.642045\pi\) | |||||||
\(488\) | 14.3574 | 0.649930 | ||||||||
\(489\) | 57.6458 | 2.60684 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.7559 | 1.61364 | 0.806821 | − | 0.590796i | \(-0.201186\pi\) | ||||
0.806821 | + | 0.590796i | \(0.201186\pi\) | |||||||
\(492\) | −10.3490 | −0.466568 | ||||||||
\(493\) | 22.0550 | 0.993308 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.29028 | −0.0579937 | ||||||||
\(496\) | 6.94968 | 0.312050 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26.6213 | 1.19293 | ||||||||
\(499\) | −17.6891 | −0.791875 | −0.395937 | − | 0.918277i | \(-0.629580\pi\) | ||||
−0.395937 | + | 0.918277i | \(0.629580\pi\) | |||||||
\(500\) | 5.09953 | 0.228058 | ||||||||
\(501\) | −2.75218 | −0.122958 | ||||||||
\(502\) | −25.2820 | −1.12839 | ||||||||
\(503\) | 11.3305 | 0.505203 | 0.252601 | − | 0.967570i | \(-0.418714\pi\) | ||||
0.252601 | + | 0.967570i | \(0.418714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.8415 | −0.482441 | ||||||||
\(506\) | −3.36912 | −0.149776 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.22095 | 0.320378 | ||||||||
\(509\) | 19.3514 | 0.857735 | 0.428868 | − | 0.903367i | \(-0.358913\pi\) | ||||
0.428868 | + | 0.903367i | \(0.358913\pi\) | |||||||
\(510\) | −5.45523 | −0.241562 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.6645 | 0.736472 | ||||||||
\(513\) | −1.11663 | −0.0493005 | ||||||||
\(514\) | 3.68304 | 0.162452 | ||||||||
\(515\) | −6.76391 | −0.298053 | ||||||||
\(516\) | −23.1198 | −1.01779 | ||||||||
\(517\) | −5.71967 | −0.251551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.1505 | −1.27957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.71099 | −0.337825 | −0.168912 | − | 0.985631i | \(-0.554025\pi\) | ||||
−0.168912 | + | 0.985631i | \(0.554025\pi\) | |||||||
\(522\) | 20.6123 | 0.902176 | ||||||||
\(523\) | −35.0501 | −1.53263 | −0.766317 | − | 0.642462i | \(-0.777913\pi\) | ||||
−0.766317 | + | 0.642462i | \(0.777913\pi\) | |||||||
\(524\) | 5.94246 | 0.259597 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.0160 | 1.00355 | ||||||||
\(527\) | 14.6784 | 0.639401 | ||||||||
\(528\) | −2.72678 | −0.118668 | ||||||||
\(529\) | −3.36265 | −0.146202 | ||||||||
\(530\) | 0.467844 | 0.0203218 | ||||||||
\(531\) | 28.7189 | 1.24630 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −34.9065 | −1.51055 | ||||||||
\(535\) | −3.82563 | −0.165396 | ||||||||
\(536\) | 31.8529 | 1.37583 | ||||||||
\(537\) | −23.0272 | −0.993699 | ||||||||
\(538\) | −15.7276 | −0.678066 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.113903 | −0.00490160 | ||||||||
\(541\) | −12.1335 | −0.521659 | −0.260829 | − | 0.965385i | \(-0.583996\pi\) | ||||
−0.260829 | + | 0.965385i | \(0.583996\pi\) | |||||||
\(542\) | −2.19296 | −0.0941956 | ||||||||
\(543\) | −27.7944 | −1.19277 | ||||||||
\(544\) | 14.7593 | 0.632801 | ||||||||
\(545\) | 7.12940 | 0.305390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12546 | −0.219149 | −0.109575 | − | 0.993979i | \(-0.534949\pi\) | ||||
−0.109575 | + | 0.993979i | \(0.534949\pi\) | |||||||
\(548\) | 5.27541 | 0.225354 | ||||||||
\(549\) | 13.6767 | 0.583707 | ||||||||
\(550\) | −3.50401 | −0.149412 | ||||||||
\(551\) | 34.3232 | 1.46222 | ||||||||
\(552\) | 32.9340 | 1.40177 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.83051 | 0.247715 | ||||||||
\(555\) | −0.643868 | −0.0273307 | ||||||||
\(556\) | −5.54224 | −0.235043 | ||||||||
\(557\) | −37.5586 | −1.59141 | −0.795705 | − | 0.605685i | \(-0.792899\pi\) | ||||
−0.795705 | + | 0.605685i | \(0.792899\pi\) | |||||||
\(558\) | 13.7182 | 0.580738 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.75922 | −0.243154 | ||||||||
\(562\) | 21.7139 | 0.915945 | ||||||||
\(563\) | 28.7009 | 1.20960 | 0.604799 | − | 0.796378i | \(-0.293253\pi\) | ||||
0.604799 | + | 0.796378i | \(0.293253\pi\) | |||||||
\(564\) | 16.6554 | 0.701318 | ||||||||
\(565\) | −0.577559 | −0.0242981 | ||||||||
\(566\) | −1.86195 | −0.0782636 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.0610 | −1.80680 | ||||||||
\(569\) | 17.9483 | 0.752434 | 0.376217 | − | 0.926532i | \(-0.377225\pi\) | ||||
0.376217 | + | 0.926532i | \(0.377225\pi\) | |||||||
\(570\) | −8.48972 | −0.355595 | ||||||||
\(571\) | 17.8274 | 0.746053 | 0.373027 | − | 0.927821i | \(-0.378320\pi\) | ||||
0.373027 | + | 0.927821i | \(0.378320\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −38.1428 | −1.59344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4236 | 0.851724 | ||||||||
\(576\) | 23.0115 | 0.958814 | ||||||||
\(577\) | −33.0570 | −1.37618 | −0.688091 | − | 0.725624i | \(-0.741551\pi\) | ||||
−0.688091 | + | 0.725624i | \(0.741551\pi\) | |||||||
\(578\) | 6.24889 | 0.259920 | ||||||||
\(579\) | −55.9396 | −2.32477 | ||||||||
\(580\) | 3.50117 | 0.145378 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.527085 | −0.0218484 | ||||||||
\(583\) | 0.493914 | 0.0204558 | ||||||||
\(584\) | −15.5395 | −0.643029 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.2345 | 1.20766 | ||||||||
\(587\) | −14.7295 | −0.607953 | −0.303976 | − | 0.952680i | \(-0.598314\pi\) | ||||
−0.303976 | + | 0.952680i | \(0.598314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.8433 | 0.941241 | ||||||||
\(590\) | −6.61941 | −0.272517 | ||||||||
\(591\) | 24.8088 | 1.02050 | ||||||||
\(592\) | −0.670193 | −0.0275448 | ||||||||
\(593\) | 9.20987 | 0.378204 | 0.189102 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189102 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(594\) | 0.163174 | 0.00669510 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.13743 | 0.128514 | ||||||||
\(597\) | −28.9907 | −1.18651 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5745 | −0.432064 | −0.216032 | − | 0.976386i | \(-0.569312\pi\) | ||||
−0.216032 | + | 0.976386i | \(0.569312\pi\) | |||||||
\(600\) | 34.2527 | 1.39836 | ||||||||
\(601\) | 4.08916 | 0.166800 | 0.0834001 | − | 0.996516i | \(-0.473422\pi\) | ||||
0.0834001 | + | 0.996516i | \(0.473422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.3426 | 1.23565 | ||||||||
\(604\) | 4.13902 | 0.168414 | ||||||||
\(605\) | −6.56578 | −0.266937 | ||||||||
\(606\) | −45.2261 | −1.83719 | ||||||||
\(607\) | 3.60706 | 0.146406 | 0.0732030 | − | 0.997317i | \(-0.476678\pi\) | ||||
0.0732030 | + | 0.997317i | \(0.476678\pi\) | |||||||
\(608\) | 22.9693 | 0.931527 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.15233 | −0.127634 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.26007 | 0.333893 | ||||||||
\(613\) | 38.4845 | 1.55437 | 0.777186 | − | 0.629271i | \(-0.216646\pi\) | ||||
0.777186 | + | 0.629271i | \(0.216646\pi\) | |||||||
\(614\) | 13.6426 | 0.550569 | ||||||||
\(615\) | 7.62778 | 0.307582 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.09503 | 0.124601 | 0.0623007 | − | 0.998057i | \(-0.480156\pi\) | ||||
0.0623007 | + | 0.998057i | \(0.480156\pi\) | |||||||
\(618\) | −28.2161 | −1.13502 | ||||||||
\(619\) | −12.2692 | −0.493142 | −0.246571 | − | 0.969125i | \(-0.579304\pi\) | ||||
−0.246571 | + | 0.969125i | \(0.579304\pi\) | |||||||
\(620\) | 2.33015 | 0.0935810 | ||||||||
\(621\) | −0.951081 | −0.0381655 | ||||||||
\(622\) | −10.3215 | −0.413854 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2855 | 0.771421 | ||||||||
\(626\) | 9.68482 | 0.387083 | ||||||||
\(627\) | −8.96281 | −0.357940 | ||||||||
\(628\) | 8.07795 | 0.322345 | ||||||||
\(629\) | −1.41551 | −0.0564402 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.31780 | 0.211698 | 0.105849 | − | 0.994382i | \(-0.466244\pi\) | ||||
0.105849 | + | 0.994382i | \(0.466244\pi\) | |||||||
\(632\) | −11.9568 | −0.475616 | ||||||||
\(633\) | 37.9039 | 1.50655 | ||||||||
\(634\) | 26.4253 | 1.04948 | ||||||||
\(635\) | −5.32225 | −0.211207 | ||||||||
\(636\) | −1.43825 | −0.0570304 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.01566 | −0.198572 | ||||||||
\(639\) | −41.0193 | −1.62270 | ||||||||
\(640\) | 0.218423 | 0.00863394 | ||||||||
\(641\) | 12.1904 | 0.481493 | 0.240746 | − | 0.970588i | \(-0.422608\pi\) | ||||
0.240746 | + | 0.970588i | \(0.422608\pi\) | |||||||
\(642\) | −15.9589 | −0.629847 | ||||||||
\(643\) | 18.9733 | 0.748235 | 0.374117 | − | 0.927381i | \(-0.377946\pi\) | ||||
0.374117 | + | 0.927381i | \(0.377946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.0406 | 0.670974 | ||||||||
\(646\) | −18.6642 | −0.734334 | ||||||||
\(647\) | 19.7117 | 0.774948 | 0.387474 | − | 0.921881i | \(-0.373348\pi\) | ||||
0.387474 | + | 0.921881i | \(0.373348\pi\) | |||||||
\(648\) | −28.2955 | −1.11155 | ||||||||
\(649\) | −6.98827 | −0.274314 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.1182 | 0.787891 | ||||||||
\(653\) | −20.3973 | −0.798206 | −0.399103 | − | 0.916906i | \(-0.630678\pi\) | ||||
−0.399103 | + | 0.916906i | \(0.630678\pi\) | |||||||
\(654\) | 29.7408 | 1.16296 | ||||||||
\(655\) | −4.37993 | −0.171138 | ||||||||
\(656\) | 7.93965 | 0.309991 | ||||||||
\(657\) | −14.8027 | −0.577510 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6628 | 1.27236 | 0.636181 | − | 0.771540i | \(-0.280513\pi\) | ||||
0.636181 | + | 0.771540i | \(0.280513\pi\) | |||||||
\(660\) | −0.914258 | −0.0355875 | ||||||||
\(661\) | 9.73692 | 0.378722 | 0.189361 | − | 0.981908i | \(-0.439358\pi\) | ||||
0.189361 | + | 0.981908i | \(0.439358\pi\) | |||||||
\(662\) | 14.1341 | 0.549337 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 31.1886 | 1.21035 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.32292 | −0.0512620 | ||||||||
\(667\) | 29.2345 | 1.13196 | ||||||||
\(668\) | −0.960502 | −0.0371630 | ||||||||
\(669\) | −16.4524 | −0.636086 | ||||||||
\(670\) | −6.99365 | −0.270188 | ||||||||
\(671\) | −3.32800 | −0.128476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.4512 | 1.52073 | 0.760367 | − | 0.649494i | \(-0.225019\pi\) | ||||
0.760367 | + | 0.649494i | \(0.225019\pi\) | |||||||
\(674\) | 18.2748 | 0.703921 | ||||||||
\(675\) | −0.989161 | −0.0380728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.6339 | −1.86915 | −0.934576 | − | 0.355764i | \(-0.884221\pi\) | ||||
−0.934576 | + | 0.355764i | \(0.884221\pi\) | |||||||
\(678\) | −2.40932 | −0.0925296 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.39117 | −0.245090 | ||||||||
\(681\) | 40.9072 | 1.56757 | ||||||||
\(682\) | −3.33810 | −0.127822 | ||||||||
\(683\) | −5.70773 | −0.218400 | −0.109200 | − | 0.994020i | \(-0.534829\pi\) | ||||
−0.109200 | + | 0.994020i | \(0.534829\pi\) | |||||||
\(684\) | 12.8548 | 0.491514 | ||||||||
\(685\) | −3.88828 | −0.148563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.8080 | 1.02279 | ||||||||
\(688\) | 17.7373 | 0.676230 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.23104 | −0.275281 | ||||||||
\(691\) | 41.7732 | 1.58913 | 0.794563 | − | 0.607182i | \(-0.207700\pi\) | ||||
0.794563 | + | 0.607182i | \(0.207700\pi\) | |||||||
\(692\) | −10.1734 | −0.386736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.493517 | −0.0187336 | ||||||||
\(695\) | 4.08495 | 0.154951 | ||||||||
\(696\) | 49.0295 | 1.85846 | ||||||||
\(697\) | 16.7693 | 0.635182 | ||||||||
\(698\) | −7.38071 | −0.279364 | ||||||||
\(699\) | −42.1967 | −1.59603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.4361 | −0.847399 | −0.423700 | − | 0.905803i | \(-0.639269\pi\) | ||||
−0.423700 | + | 0.905803i | \(0.639269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.20290 | −0.0830838 | ||||||||
\(704\) | −5.59948 | −0.211038 | ||||||||
\(705\) | −12.2760 | −0.462340 | ||||||||
\(706\) | 1.64527 | 0.0619207 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20.3495 | 0.764780 | ||||||||
\(709\) | 28.7468 | 1.07961 | 0.539804 | − | 0.841790i | \(-0.318498\pi\) | ||||
0.539804 | + | 0.841790i | \(0.318498\pi\) | |||||||
\(710\) | 9.45452 | 0.354822 | ||||||||
\(711\) | −11.3899 | −0.427154 | ||||||||
\(712\) | −40.8953 | −1.53261 | ||||||||
\(713\) | 19.4566 | 0.728654 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.03644 | −0.300336 | ||||||||
\(717\) | 47.9529 | 1.79083 | ||||||||
\(718\) | −29.1944 | −1.08952 | ||||||||
\(719\) | −4.20899 | −0.156969 | −0.0784844 | − | 0.996915i | \(-0.525008\pi\) | ||||
−0.0784844 | + | 0.996915i | \(0.525008\pi\) | |||||||
\(720\) | −2.88251 | −0.107425 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.65821 | −0.322225 | ||||||||
\(723\) | 6.76934 | 0.251754 | ||||||||
\(724\) | −9.70015 | −0.360503 | ||||||||
\(725\) | 30.4050 | 1.12921 | ||||||||
\(726\) | −27.3896 | −1.01652 | ||||||||
\(727\) | 43.4680 | 1.61214 | 0.806070 | − | 0.591820i | \(-0.201591\pi\) | ||||
0.806070 | + | 0.591820i | \(0.201591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3884 | −0.940312 | ||||||||
\(730\) | 3.41187 | 0.126279 | ||||||||
\(731\) | 37.4630 | 1.38562 | ||||||||
\(732\) | 9.69096 | 0.358188 | ||||||||
\(733\) | 9.09421 | 0.335902 | 0.167951 | − | 0.985795i | \(-0.446285\pi\) | ||||
0.167951 | + | 0.985795i | \(0.446285\pi\) | |||||||
\(734\) | −28.9525 | −1.06866 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5639 | 0.721133 | ||||||||
\(737\) | −7.38337 | −0.271970 | ||||||||
\(738\) | 15.6723 | 0.576907 | ||||||||
\(739\) | 9.60867 | 0.353461 | 0.176730 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176730 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(740\) | −0.224708 | −0.00826044 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.1771 | 1.18046 | 0.590231 | − | 0.807234i | \(-0.299036\pi\) | ||||
0.590231 | + | 0.807234i | \(0.299036\pi\) | |||||||
\(744\) | 32.6308 | 1.19630 | ||||||||
\(745\) | −2.31246 | −0.0847220 | ||||||||
\(746\) | −4.26258 | −0.156064 | ||||||||
\(747\) | 29.7098 | 1.08703 | ||||||||
\(748\) | −2.00995 | −0.0734911 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −15.6794 | −0.572531 | ||||||||
\(751\) | 7.79784 | 0.284547 | 0.142274 | − | 0.989827i | \(-0.454559\pi\) | ||||
0.142274 | + | 0.989827i | \(0.454559\pi\) | |||||||
\(752\) | −12.7779 | −0.465961 | ||||||||
\(753\) | −57.2858 | −2.08761 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.05070 | −0.111026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.9970 | 0.654110 | 0.327055 | − | 0.945005i | \(-0.393944\pi\) | ||||
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(758\) | −12.2392 | −0.444548 | ||||||||
\(759\) | −7.63399 | −0.277096 | ||||||||
\(760\) | −9.94627 | −0.360789 | ||||||||
\(761\) | 40.6790 | 1.47461 | 0.737306 | − | 0.675559i | \(-0.236098\pi\) | ||||
0.737306 | + | 0.675559i | \(0.236098\pi\) | |||||||
\(762\) | −22.2021 | −0.804299 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.3117 | −0.481601 | ||||||||
\(765\) | −6.08814 | −0.220117 | ||||||||
\(766\) | −25.5301 | −0.922439 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 39.3422 | 1.41964 | ||||||||
\(769\) | −39.3098 | −1.41755 | −0.708774 | − | 0.705435i | \(-0.750752\pi\) | ||||
−0.708774 | + | 0.705435i | \(0.750752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.34529 | 0.300548 | ||||||||
\(772\) | −19.5228 | −0.702640 | ||||||||
\(773\) | −13.4736 | −0.484611 | −0.242306 | − | 0.970200i | \(-0.577904\pi\) | ||||
−0.242306 | + | 0.970200i | \(0.577904\pi\) | |||||||
\(774\) | 35.0124 | 1.25849 | ||||||||
\(775\) | 20.2356 | 0.726884 | ||||||||
\(776\) | −0.617515 | −0.0221675 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.4866 | 1.09300 | ||||||||
\(779\) | 26.0973 | 0.935032 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.98137 | 0.357161 | ||||||||
\(782\) | −15.8971 | −0.568478 | ||||||||
\(783\) | −1.41589 | −0.0505998 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.95391 | −0.212504 | ||||||||
\(786\) | −18.2712 | −0.651711 | ||||||||
\(787\) | −39.8291 | −1.41975 | −0.709877 | − | 0.704326i | \(-0.751249\pi\) | ||||
−0.709877 | + | 0.704326i | \(0.751249\pi\) | |||||||
\(788\) | 8.65821 | 0.308436 | ||||||||
\(789\) | 52.1514 | 1.85664 | ||||||||
\(790\) | 2.62525 | 0.0934022 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.30594 | −0.224072 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.5794 | −0.375448 | ||||||||
\(795\) | 1.06007 | 0.0375969 | ||||||||
\(796\) | −10.1177 | −0.358612 | ||||||||
\(797\) | −21.2530 | −0.752821 | −0.376410 | − | 0.926453i | \(-0.622842\pi\) | ||||
−0.376410 | + | 0.926453i | \(0.622842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.9881 | −0.954770 | ||||||||
\(800\) | 20.3472 | 0.719382 | ||||||||
\(801\) | −38.9563 | −1.37645 | ||||||||
\(802\) | 13.5413 | 0.478161 | ||||||||
\(803\) | 3.60200 | 0.127112 | ||||||||
\(804\) | 21.5000 | 0.758246 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.6368 | −1.25447 | ||||||||
\(808\) | −52.9854 | −1.86402 | ||||||||
\(809\) | 21.4175 | 0.753000 | 0.376500 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376500 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(810\) | 6.21260 | 0.218288 | ||||||||
\(811\) | 11.0116 | 0.386669 | 0.193335 | − | 0.981133i | \(-0.438070\pi\) | ||||
0.193335 | + | 0.981133i | \(0.438070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.96896 | −0.174269 | ||||||||
\(814\) | 0.321910 | 0.0112829 | ||||||||
\(815\) | −14.8283 | −0.519412 | ||||||||
\(816\) | −12.8662 | −0.450408 | ||||||||
\(817\) | 58.3019 | 2.03972 | ||||||||
\(818\) | −19.3765 | −0.677484 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.66207 | 0.0929636 | ||||||||
\(821\) | 38.6685 | 1.34954 | 0.674769 | − | 0.738029i | \(-0.264243\pi\) | ||||
0.674769 | + | 0.738029i | \(0.264243\pi\) | |||||||
\(822\) | −16.2202 | −0.565744 | ||||||||
\(823\) | −20.4566 | −0.713073 | −0.356537 | − | 0.934281i | \(-0.616043\pi\) | ||||
−0.356537 | + | 0.934281i | \(0.616043\pi\) | |||||||
\(824\) | −33.0570 | −1.15160 | ||||||||
\(825\) | −7.93965 | −0.276423 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.3451 | −0.950881 | −0.475440 | − | 0.879748i | \(-0.657711\pi\) | ||||
−0.475440 | + | 0.879748i | \(0.657711\pi\) | |||||||
\(828\) | 10.9489 | 0.380501 | ||||||||
\(829\) | −25.0086 | −0.868585 | −0.434292 | − | 0.900772i | \(-0.643002\pi\) | ||||
−0.434292 | + | 0.900772i | \(0.643002\pi\) | |||||||
\(830\) | −6.84780 | −0.237691 | ||||||||
\(831\) | 13.2112 | 0.458291 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.0406 | 0.590069 | ||||||||
\(835\) | 0.707945 | 0.0244994 | ||||||||
\(836\) | −3.12799 | −0.108184 | ||||||||
\(837\) | −0.942324 | −0.0325715 | ||||||||
\(838\) | −15.3237 | −0.529350 | ||||||||
\(839\) | −8.76981 | −0.302768 | −0.151384 | − | 0.988475i | \(-0.548373\pi\) | ||||
−0.151384 | + | 0.988475i | \(0.548373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5218 | 0.500753 | ||||||||
\(842\) | 4.58665 | 0.158066 | ||||||||
\(843\) | 49.2009 | 1.69457 | ||||||||
\(844\) | 13.2284 | 0.455339 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.2227 | −0.867174 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.10342 | 0.0378914 | ||||||||
\(849\) | −4.21894 | −0.144794 | ||||||||
\(850\) | −16.5336 | −0.567097 | ||||||||
\(851\) | −1.87630 | −0.0643186 | ||||||||
\(852\) | −29.0652 | −0.995758 | ||||||||
\(853\) | −19.8232 | −0.678734 | −0.339367 | − | 0.940654i | \(-0.610213\pi\) | ||||
−0.339367 | + | 0.940654i | \(0.610213\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.47469 | −0.324028 | ||||||||
\(856\) | −18.6969 | −0.639047 | ||||||||
\(857\) | −2.67037 | −0.0912181 | −0.0456090 | − | 0.998959i | \(-0.514523\pi\) | ||||
−0.0456090 | + | 0.998959i | \(0.514523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9597 | −1.32929 | −0.664644 | − | 0.747160i | \(-0.731417\pi\) | ||||
−0.664644 | + | 0.747160i | \(0.731417\pi\) | |||||||
\(860\) | 5.94713 | 0.202795 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.6738 | 0.533851 | ||||||||
\(863\) | 24.7976 | 0.844121 | 0.422060 | − | 0.906568i | \(-0.361307\pi\) | ||||
0.422060 | + | 0.906568i | \(0.361307\pi\) | |||||||
\(864\) | −0.947521 | −0.0322353 | ||||||||
\(865\) | 7.49840 | 0.254953 | ||||||||
\(866\) | 30.0561 | 1.02135 | ||||||||
\(867\) | 14.1592 | 0.480871 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.77154 | 0.0940181 | ||||||||
\(870\) | −10.7650 | −0.364967 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 34.8433 | 1.17994 | ||||||||
\(873\) | −0.588237 | −0.0199088 | ||||||||
\(874\) | −24.7399 | −0.836839 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.4888 | −0.354385 | ||||||||
\(877\) | −1.97840 | −0.0668059 | −0.0334029 | − | 0.999442i | \(-0.510634\pi\) | ||||
−0.0334029 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(878\) | −18.3250 | −0.618440 | ||||||||
\(879\) | 66.2415 | 2.23427 | ||||||||
\(880\) | 0.701412 | 0.0236446 | ||||||||
\(881\) | 17.1466 | 0.577683 | 0.288841 | − | 0.957377i | \(-0.406730\pi\) | ||||
0.288841 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.2168 | −0.343822 | −0.171911 | − | 0.985112i | \(-0.554994\pi\) | ||||
−0.171911 | + | 0.985112i | \(0.554994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.9987 | −0.504177 | ||||||||
\(886\) | −14.8250 | −0.498055 | ||||||||
\(887\) | 50.9931 | 1.71218 | 0.856090 | − | 0.516826i | \(-0.172887\pi\) | ||||
0.856090 | + | 0.516826i | \(0.172887\pi\) | |||||||
\(888\) | −3.14676 | −0.105598 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.97901 | 0.300977 | ||||||||
\(891\) | 6.55879 | 0.219728 | ||||||||
\(892\) | −5.74184 | −0.192251 | ||||||||
\(893\) | −42.0003 | −1.40549 | ||||||||
\(894\) | −9.64659 | −0.322630 | ||||||||
\(895\) | 5.92331 | 0.197995 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.0255 | 1.16882 | ||||||||
\(899\) | 28.9653 | 0.966047 | ||||||||
\(900\) | 11.3873 | 0.379577 | ||||||||
\(901\) | 2.33052 | 0.0776408 | ||||||||
\(902\) | −3.81360 | −0.126979 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.82268 | −0.0938811 | ||||||||
\(905\) | 7.14957 | 0.237660 | ||||||||
\(906\) | −12.7262 | −0.422799 | ||||||||
\(907\) | −5.78538 | −0.192100 | −0.0960501 | − | 0.995376i | \(-0.530621\pi\) | ||||
−0.0960501 | + | 0.995376i | \(0.530621\pi\) | |||||||
\(908\) | 14.2765 | 0.473782 | ||||||||
\(909\) | −50.4732 | −1.67409 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.70706 | −0.0565573 | −0.0282787 | − | 0.999600i | \(-0.509003\pi\) | ||||
−0.0282787 | + | 0.999600i | \(0.509003\pi\) | |||||||
\(912\) | −20.0231 | −0.663032 | ||||||||
\(913\) | −7.22940 | −0.239258 | ||||||||
\(914\) | −3.40195 | −0.112526 | ||||||||
\(915\) | −7.14279 | −0.236133 | ||||||||
\(916\) | 9.35590 | 0.309128 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.769931 | 0.0254115 | ||||||||
\(919\) | 37.2050 | 1.22728 | 0.613640 | − | 0.789586i | \(-0.289705\pi\) | ||||
0.613640 | + | 0.789586i | \(0.289705\pi\) | |||||||
\(920\) | −8.47164 | −0.279302 | ||||||||
\(921\) | 30.9123 | 1.01859 | ||||||||
\(922\) | −0.216782 | −0.00713933 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.95142 | −0.0641623 | ||||||||
\(926\) | −18.4695 | −0.606945 | ||||||||
\(927\) | −31.4897 | −1.03426 | ||||||||
\(928\) | 29.1251 | 0.956077 | ||||||||
\(929\) | 19.9046 | 0.653048 | 0.326524 | − | 0.945189i | \(-0.394123\pi\) | ||||
0.326524 | + | 0.945189i | \(0.394123\pi\) | |||||||
\(930\) | −7.16447 | −0.234932 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.7265 | −0.482383 | ||||||||
\(933\) | −23.3872 | −0.765661 | ||||||||
\(934\) | 0.205135 | 0.00671222 | ||||||||
\(935\) | 1.48145 | 0.0484485 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.16949 | 0.234217 | 0.117109 | − | 0.993119i | \(-0.462637\pi\) | ||||
0.117109 | + | 0.993119i | \(0.462637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9446 | 0.716134 | ||||||||
\(940\) | −4.28428 | −0.139738 | ||||||||
\(941\) | 3.06072 | 0.0997766 | 0.0498883 | − | 0.998755i | \(-0.484113\pi\) | ||||
0.0498883 | + | 0.998755i | \(0.484113\pi\) | |||||||
\(942\) | −24.8371 | −0.809237 | ||||||||
\(943\) | 22.2281 | 0.723846 | ||||||||
\(944\) | −15.6120 | −0.508126 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.51968 | −0.276999 | ||||||||
\(947\) | −44.2056 | −1.43649 | −0.718244 | − | 0.695791i | \(-0.755054\pi\) | ||||
−0.718244 | + | 0.695791i | \(0.755054\pi\) | |||||||
\(948\) | −8.07058 | −0.262120 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −25.7304 | −0.834806 | ||||||||
\(951\) | 59.8762 | 1.94162 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7002 | −0.443791 | −0.221896 | − | 0.975070i | \(-0.571224\pi\) | ||||
−0.221896 | + | 0.975070i | \(0.571224\pi\) | |||||||
\(954\) | 2.17807 | 0.0705176 | ||||||||
\(955\) | 9.81149 | 0.317492 | ||||||||
\(956\) | 16.7354 | 0.541262 | ||||||||
\(957\) | −11.3648 | −0.367373 | ||||||||
\(958\) | 23.0476 | 0.744634 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −12.0180 | −0.387879 | ||||||||
\(961\) | −11.7226 | −0.378147 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.8104 | −0.573933 | ||||||||
\(964\) | 2.36248 | 0.0760903 | ||||||||
\(965\) | 14.3894 | 0.463211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.9429 | −1.41311 | −0.706554 | − | 0.707659i | \(-0.749751\pi\) | ||||
−0.706554 | + | 0.707659i | \(0.749751\pi\) | |||||||
\(968\) | −32.0887 | −1.03137 | ||||||||
\(969\) | −42.2907 | −1.35857 | ||||||||
\(970\) | 0.135582 | 0.00435329 | ||||||||
\(971\) | −21.3171 | −0.684098 | −0.342049 | − | 0.939682i | \(-0.611121\pi\) | ||||
−0.342049 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(972\) | −18.5525 | −0.595072 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.4400 | 0.654941 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.43482 | −0.237983 | ||||||||
\(977\) | −16.4466 | −0.526173 | −0.263087 | − | 0.964772i | \(-0.584740\pi\) | ||||
−0.263087 | + | 0.964772i | \(0.584740\pi\) | |||||||
\(978\) | −61.8572 | −1.97797 | ||||||||
\(979\) | 9.47937 | 0.302962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1913 | 1.05972 | ||||||||
\(982\) | −38.3681 | −1.22437 | ||||||||
\(983\) | 11.7104 | 0.373504 | 0.186752 | − | 0.982407i | \(-0.440204\pi\) | ||||
0.186752 | + | 0.982407i | \(0.440204\pi\) | |||||||
\(984\) | 37.2790 | 1.18841 | ||||||||
\(985\) | −6.38160 | −0.203335 | ||||||||
\(986\) | −23.6662 | −0.753687 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.6581 | 1.57903 | ||||||||
\(990\) | 1.38454 | 0.0440036 | ||||||||
\(991\) | −31.3747 | −0.996650 | −0.498325 | − | 0.866990i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866990i | \(0.666051\pi\) | |||||||
\(992\) | 19.3837 | 0.615434 | ||||||||
\(993\) | 32.0260 | 1.01632 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.45731 | 0.236413 | ||||||||
\(996\) | 21.0516 | 0.667046 | ||||||||
\(997\) | −4.69711 | −0.148759 | −0.0743794 | − | 0.997230i | \(-0.523698\pi\) | ||||
−0.0743794 | + | 0.997230i | \(0.523698\pi\) | |||||||
\(998\) | 18.9814 | 0.600847 | ||||||||
\(999\) | 0.0908732 | 0.00287510 |
(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 | 8281.2.a.ck.1.3 | 8 | ||
7.2 | even | 3 | 1183.2.e.i.508.6 | 16 | |||
7.4 | even | 3 | 1183.2.e.i.170.6 | 16 | |||
7.6 | odd | 2 | 8281.2.a.cj.1.3 | 8 | |||
13.5 | odd | 4 | 637.2.c.f.246.6 | 8 | |||
13.8 | odd | 4 | 637.2.c.f.246.3 | 8 | |||
13.12 | even | 2 | inner | 8281.2.a.ck.1.6 | 8 | ||
91.5 | even | 12 | 637.2.r.f.116.6 | 16 | |||
91.18 | odd | 12 | 91.2.r.a.51.3 | yes | 16 | ||
91.25 | even | 6 | 1183.2.e.i.170.3 | 16 | |||
91.31 | even | 12 | 637.2.r.f.324.3 | 16 | |||
91.34 | even | 4 | 637.2.c.e.246.3 | 8 | |||
91.44 | odd | 12 | 91.2.r.a.25.6 | yes | 16 | ||
91.47 | even | 12 | 637.2.r.f.116.3 | 16 | |||
91.51 | even | 6 | 1183.2.e.i.508.3 | 16 | |||
91.60 | odd | 12 | 91.2.r.a.51.6 | yes | 16 | ||
91.73 | even | 12 | 637.2.r.f.324.6 | 16 | |||
91.83 | even | 4 | 637.2.c.e.246.6 | 8 | |||
91.86 | odd | 12 | 91.2.r.a.25.3 | ✓ | 16 | ||
91.90 | odd | 2 | 8281.2.a.cj.1.6 | 8 | |||
273.44 | even | 12 | 819.2.dl.e.298.3 | 16 | |||
273.86 | even | 12 | 819.2.dl.e.298.6 | 16 | |||
273.200 | even | 12 | 819.2.dl.e.415.6 | 16 | |||
273.242 | even | 12 | 819.2.dl.e.415.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.3 | ✓ | 16 | 91.86 | odd | 12 | ||
91.2.r.a.25.6 | yes | 16 | 91.44 | odd | 12 | ||
91.2.r.a.51.3 | yes | 16 | 91.18 | odd | 12 | ||
91.2.r.a.51.6 | yes | 16 | 91.60 | odd | 12 | ||
637.2.c.e.246.3 | 8 | 91.34 | even | 4 | |||
637.2.c.e.246.6 | 8 | 91.83 | even | 4 | |||
637.2.c.f.246.3 | 8 | 13.8 | odd | 4 | |||
637.2.c.f.246.6 | 8 | 13.5 | odd | 4 | |||
637.2.r.f.116.3 | 16 | 91.47 | even | 12 | |||
637.2.r.f.116.6 | 16 | 91.5 | even | 12 | |||
637.2.r.f.324.3 | 16 | 91.31 | even | 12 | |||
637.2.r.f.324.6 | 16 | 91.73 | even | 12 | |||
819.2.dl.e.298.3 | 16 | 273.44 | even | 12 | |||
819.2.dl.e.298.6 | 16 | 273.86 | even | 12 | |||
819.2.dl.e.415.3 | 16 | 273.242 | even | 12 | |||
819.2.dl.e.415.6 | 16 | 273.200 | even | 12 | |||
1183.2.e.i.170.3 | 16 | 91.25 | even | 6 | |||
1183.2.e.i.170.6 | 16 | 7.4 | even | 3 | |||
1183.2.e.i.508.3 | 16 | 91.51 | even | 6 | |||
1183.2.e.i.508.6 | 16 | 7.2 | even | 3 | |||
8281.2.a.cj.1.3 | 8 | 7.6 | odd | 2 | |||
8281.2.a.cj.1.6 | 8 | 91.90 | odd | 2 | |||
8281.2.a.ck.1.3 | 8 | 1.1 | even | 1 | trivial | ||
8281.2.a.ck.1.6 | 8 | 13.12 | even | 2 | inner |