Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49549 | −1.76458 | −0.882291 | − | 0.470705i | \(-0.844000\pi\) | ||||
−0.882291 | + | 0.470705i | \(0.844000\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.22749 | 2.11375 | ||||||||
\(5\) | 2.28895 | 1.02365 | 0.511825 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511825 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(6\) | 2.49549 | 1.01878 | ||||||||
\(7\) | −3.97589 | −1.50275 | −0.751373 | − | 0.659878i | \(-0.770608\pi\) | ||||
−0.751373 | + | 0.659878i | \(0.770608\pi\) | |||||||
\(8\) | −5.55870 | −1.96530 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.71206 | −1.80631 | ||||||||
\(11\) | −2.09788 | −0.632534 | −0.316267 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(12\) | −4.22749 | −1.22037 | ||||||||
\(13\) | 4.13048 | 1.14559 | 0.572795 | − | 0.819699i | \(-0.305859\pi\) | ||||
0.572795 | + | 0.819699i | \(0.305859\pi\) | |||||||
\(14\) | 9.92181 | 2.65172 | ||||||||
\(15\) | −2.28895 | −0.591005 | ||||||||
\(16\) | 5.41671 | 1.35418 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.49549 | −0.588194 | ||||||||
\(19\) | 0.596243 | 0.136788 | 0.0683938 | − | 0.997658i | \(-0.478213\pi\) | ||||
0.0683938 | + | 0.997658i | \(0.478213\pi\) | |||||||
\(20\) | 9.67652 | 2.16374 | ||||||||
\(21\) | 3.97589 | 0.867610 | ||||||||
\(22\) | 5.23524 | 1.11616 | ||||||||
\(23\) | −0.899600 | −0.187580 | −0.0937898 | − | 0.995592i | \(-0.529898\pi\) | ||||
−0.0937898 | + | 0.995592i | \(0.529898\pi\) | |||||||
\(24\) | 5.55870 | 1.13466 | ||||||||
\(25\) | 0.239296 | 0.0478592 | ||||||||
\(26\) | −10.3076 | −2.02149 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −16.8080 | −3.17642 | ||||||||
\(29\) | −4.90674 | −0.911159 | −0.455580 | − | 0.890195i | \(-0.650568\pi\) | ||||
−0.455580 | + | 0.890195i | \(0.650568\pi\) | |||||||
\(30\) | 5.71206 | 1.04288 | ||||||||
\(31\) | 4.24984 | 0.763295 | 0.381647 | − | 0.924308i | \(-0.375357\pi\) | ||||
0.381647 | + | 0.924308i | \(0.375357\pi\) | |||||||
\(32\) | −2.39997 | −0.424259 | ||||||||
\(33\) | 2.09788 | 0.365194 | ||||||||
\(34\) | 2.49549 | 0.427974 | ||||||||
\(35\) | −9.10062 | −1.53829 | ||||||||
\(36\) | 4.22749 | 0.704582 | ||||||||
\(37\) | 7.90469 | 1.29952 | 0.649761 | − | 0.760138i | \(-0.274869\pi\) | ||||
0.649761 | + | 0.760138i | \(0.274869\pi\) | |||||||
\(38\) | −1.48792 | −0.241373 | ||||||||
\(39\) | −4.13048 | −0.661406 | ||||||||
\(40\) | −12.7236 | −2.01177 | ||||||||
\(41\) | 2.12540 | 0.331932 | 0.165966 | − | 0.986131i | \(-0.446926\pi\) | ||||
0.165966 | + | 0.986131i | \(0.446926\pi\) | |||||||
\(42\) | −9.92181 | −1.53097 | ||||||||
\(43\) | −1.92823 | −0.294052 | −0.147026 | − | 0.989133i | \(-0.546970\pi\) | ||||
−0.147026 | + | 0.989133i | \(0.546970\pi\) | |||||||
\(44\) | −8.86876 | −1.33702 | ||||||||
\(45\) | 2.28895 | 0.341217 | ||||||||
\(46\) | 2.24495 | 0.330999 | ||||||||
\(47\) | 2.28987 | 0.334012 | 0.167006 | − | 0.985956i | \(-0.446590\pi\) | ||||
0.167006 | + | 0.985956i | \(0.446590\pi\) | |||||||
\(48\) | −5.41671 | −0.781834 | ||||||||
\(49\) | 8.80771 | 1.25824 | ||||||||
\(50\) | −0.597161 | −0.0844514 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 17.4616 | 2.42149 | ||||||||
\(53\) | 9.86265 | 1.35474 | 0.677369 | − | 0.735643i | \(-0.263120\pi\) | ||||
0.677369 | + | 0.735643i | \(0.263120\pi\) | |||||||
\(54\) | 2.49549 | 0.339594 | ||||||||
\(55\) | −4.80194 | −0.647493 | ||||||||
\(56\) | 22.1008 | 2.95334 | ||||||||
\(57\) | −0.596243 | −0.0789743 | ||||||||
\(58\) | 12.2448 | 1.60781 | ||||||||
\(59\) | 9.79550 | 1.27527 | 0.637633 | − | 0.770340i | \(-0.279914\pi\) | ||||
0.637633 | + | 0.770340i | \(0.279914\pi\) | |||||||
\(60\) | −9.67652 | −1.24923 | ||||||||
\(61\) | −11.6143 | −1.48706 | −0.743530 | − | 0.668702i | \(-0.766850\pi\) | ||||
−0.743530 | + | 0.668702i | \(0.766850\pi\) | |||||||
\(62\) | −10.6055 | −1.34690 | ||||||||
\(63\) | −3.97589 | −0.500915 | ||||||||
\(64\) | −4.84429 | −0.605537 | ||||||||
\(65\) | 9.45447 | 1.17268 | ||||||||
\(66\) | −5.23524 | −0.644414 | ||||||||
\(67\) | −16.3430 | −1.99661 | −0.998305 | − | 0.0581999i | \(-0.981464\pi\) | ||||
−0.998305 | + | 0.0581999i | \(0.981464\pi\) | |||||||
\(68\) | −4.22749 | −0.512659 | ||||||||
\(69\) | 0.899600 | 0.108299 | ||||||||
\(70\) | 22.7105 | 2.71443 | ||||||||
\(71\) | −11.7706 | −1.39691 | −0.698455 | − | 0.715654i | \(-0.746129\pi\) | ||||
−0.698455 | + | 0.715654i | \(0.746129\pi\) | |||||||
\(72\) | −5.55870 | −0.655098 | ||||||||
\(73\) | −0.392144 | −0.0458970 | −0.0229485 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229485 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(74\) | −19.7261 | −2.29311 | ||||||||
\(75\) | −0.239296 | −0.0276315 | ||||||||
\(76\) | 2.52061 | 0.289134 | ||||||||
\(77\) | 8.34093 | 0.950537 | ||||||||
\(78\) | 10.3076 | 1.16710 | ||||||||
\(79\) | 3.46759 | 0.390135 | 0.195067 | − | 0.980790i | \(-0.437507\pi\) | ||||
0.195067 | + | 0.980790i | \(0.437507\pi\) | |||||||
\(80\) | 12.3986 | 1.38620 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.30393 | −0.585721 | ||||||||
\(83\) | 2.58974 | 0.284261 | 0.142131 | − | 0.989848i | \(-0.454605\pi\) | ||||
0.142131 | + | 0.989848i | \(0.454605\pi\) | |||||||
\(84\) | 16.8080 | 1.83391 | ||||||||
\(85\) | −2.28895 | −0.248272 | ||||||||
\(86\) | 4.81188 | 0.518878 | ||||||||
\(87\) | 4.90674 | 0.526058 | ||||||||
\(88\) | 11.6615 | 1.24312 | ||||||||
\(89\) | −11.6634 | −1.23632 | −0.618160 | − | 0.786052i | \(-0.712122\pi\) | ||||
−0.618160 | + | 0.786052i | \(0.712122\pi\) | |||||||
\(90\) | −5.71206 | −0.602104 | ||||||||
\(91\) | −16.4223 | −1.72153 | ||||||||
\(92\) | −3.80305 | −0.396496 | ||||||||
\(93\) | −4.24984 | −0.440688 | ||||||||
\(94\) | −5.71436 | −0.589392 | ||||||||
\(95\) | 1.36477 | 0.140023 | ||||||||
\(96\) | 2.39997 | 0.244946 | ||||||||
\(97\) | 14.0736 | 1.42896 | 0.714479 | − | 0.699657i | \(-0.246664\pi\) | ||||
0.714479 | + | 0.699657i | \(0.246664\pi\) | |||||||
\(98\) | −21.9796 | −2.22027 | ||||||||
\(99\) | −2.09788 | −0.210845 | ||||||||
\(100\) | 1.01162 | 0.101162 | ||||||||
\(101\) | −13.9363 | −1.38671 | −0.693354 | − | 0.720597i | \(-0.743868\pi\) | ||||
−0.693354 | + | 0.720597i | \(0.743868\pi\) | |||||||
\(102\) | −2.49549 | −0.247091 | ||||||||
\(103\) | 9.21081 | 0.907568 | 0.453784 | − | 0.891112i | \(-0.350074\pi\) | ||||
0.453784 | + | 0.891112i | \(0.350074\pi\) | |||||||
\(104\) | −22.9601 | −2.25142 | ||||||||
\(105\) | 9.10062 | 0.888129 | ||||||||
\(106\) | −24.6122 | −2.39055 | ||||||||
\(107\) | −8.16871 | −0.789699 | −0.394849 | − | 0.918746i | \(-0.629203\pi\) | ||||
−0.394849 | + | 0.918746i | \(0.629203\pi\) | |||||||
\(108\) | −4.22749 | −0.406791 | ||||||||
\(109\) | 15.5969 | 1.49391 | 0.746957 | − | 0.664873i | \(-0.231514\pi\) | ||||
0.746957 | + | 0.664873i | \(0.231514\pi\) | |||||||
\(110\) | 11.9832 | 1.14255 | ||||||||
\(111\) | −7.90469 | −0.750280 | ||||||||
\(112\) | −21.5362 | −2.03498 | ||||||||
\(113\) | 14.9837 | 1.40955 | 0.704773 | − | 0.709433i | \(-0.251049\pi\) | ||||
0.704773 | + | 0.709433i | \(0.251049\pi\) | |||||||
\(114\) | 1.48792 | 0.139357 | ||||||||
\(115\) | −2.05914 | −0.192016 | ||||||||
\(116\) | −20.7432 | −1.92596 | ||||||||
\(117\) | 4.13048 | 0.381863 | ||||||||
\(118\) | −24.4446 | −2.25031 | ||||||||
\(119\) | 3.97589 | 0.364469 | ||||||||
\(120\) | 12.7236 | 1.16150 | ||||||||
\(121\) | −6.59891 | −0.599901 | ||||||||
\(122\) | 28.9835 | 2.62404 | ||||||||
\(123\) | −2.12540 | −0.191641 | ||||||||
\(124\) | 17.9662 | 1.61341 | ||||||||
\(125\) | −10.8970 | −0.974659 | ||||||||
\(126\) | 9.92181 | 0.883905 | ||||||||
\(127\) | −2.35845 | −0.209278 | −0.104639 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104639 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(128\) | 16.8889 | 1.49278 | ||||||||
\(129\) | 1.92823 | 0.169771 | ||||||||
\(130\) | −23.5936 | −2.06929 | ||||||||
\(131\) | −22.1737 | −1.93732 | −0.968661 | − | 0.248388i | \(-0.920099\pi\) | ||||
−0.968661 | + | 0.248388i | \(0.920099\pi\) | |||||||
\(132\) | 8.86876 | 0.771926 | ||||||||
\(133\) | −2.37060 | −0.205557 | ||||||||
\(134\) | 40.7838 | 3.52318 | ||||||||
\(135\) | −2.28895 | −0.197002 | ||||||||
\(136\) | 5.55870 | 0.476654 | ||||||||
\(137\) | 0.226761 | 0.0193735 | 0.00968676 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968676 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(138\) | −2.24495 | −0.191103 | ||||||||
\(139\) | −8.38054 | −0.710828 | −0.355414 | − | 0.934709i | \(-0.615660\pi\) | ||||
−0.355414 | + | 0.934709i | \(0.615660\pi\) | |||||||
\(140\) | −38.4728 | −3.25154 | ||||||||
\(141\) | −2.28987 | −0.192842 | ||||||||
\(142\) | 29.3734 | 2.46496 | ||||||||
\(143\) | −8.66524 | −0.724624 | ||||||||
\(144\) | 5.41671 | 0.451392 | ||||||||
\(145\) | −11.2313 | −0.932708 | ||||||||
\(146\) | 0.978592 | 0.0809889 | ||||||||
\(147\) | −8.80771 | −0.726447 | ||||||||
\(148\) | 33.4170 | 2.74686 | ||||||||
\(149\) | −3.47861 | −0.284979 | −0.142489 | − | 0.989796i | \(-0.545511\pi\) | ||||
−0.142489 | + | 0.989796i | \(0.545511\pi\) | |||||||
\(150\) | 0.597161 | 0.0487580 | ||||||||
\(151\) | 11.2622 | 0.916506 | 0.458253 | − | 0.888822i | \(-0.348475\pi\) | ||||
0.458253 | + | 0.888822i | \(0.348475\pi\) | |||||||
\(152\) | −3.31433 | −0.268828 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −20.8147 | −1.67730 | ||||||||
\(155\) | 9.72768 | 0.781346 | ||||||||
\(156\) | −17.4616 | −1.39805 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −8.65336 | −0.688424 | ||||||||
\(159\) | −9.86265 | −0.782159 | ||||||||
\(160\) | −5.49342 | −0.434293 | ||||||||
\(161\) | 3.57671 | 0.281884 | ||||||||
\(162\) | −2.49549 | −0.196065 | ||||||||
\(163\) | 19.3240 | 1.51358 | 0.756788 | − | 0.653661i | \(-0.226768\pi\) | ||||
0.756788 | + | 0.653661i | \(0.226768\pi\) | |||||||
\(164\) | 8.98512 | 0.701620 | ||||||||
\(165\) | 4.80194 | 0.373830 | ||||||||
\(166\) | −6.46269 | −0.501602 | ||||||||
\(167\) | 7.97629 | 0.617224 | 0.308612 | − | 0.951188i | \(-0.400136\pi\) | ||||
0.308612 | + | 0.951188i | \(0.400136\pi\) | |||||||
\(168\) | −22.1008 | −1.70511 | ||||||||
\(169\) | 4.06087 | 0.312375 | ||||||||
\(170\) | 5.71206 | 0.438095 | ||||||||
\(171\) | 0.596243 | 0.0455958 | ||||||||
\(172\) | −8.15156 | −0.621551 | ||||||||
\(173\) | 11.7731 | 0.895093 | 0.447547 | − | 0.894261i | \(-0.352298\pi\) | ||||
0.447547 | + | 0.894261i | \(0.352298\pi\) | |||||||
\(174\) | −12.2448 | −0.928272 | ||||||||
\(175\) | −0.951414 | −0.0719201 | ||||||||
\(176\) | −11.3636 | −0.856563 | ||||||||
\(177\) | −9.79550 | −0.736275 | ||||||||
\(178\) | 29.1060 | 2.18159 | ||||||||
\(179\) | −13.9082 | −1.03954 | −0.519772 | − | 0.854305i | \(-0.673983\pi\) | ||||
−0.519772 | + | 0.854305i | \(0.673983\pi\) | |||||||
\(180\) | 9.67652 | 0.721245 | ||||||||
\(181\) | 15.1208 | 1.12392 | 0.561960 | − | 0.827164i | \(-0.310047\pi\) | ||||
0.561960 | + | 0.827164i | \(0.310047\pi\) | |||||||
\(182\) | 40.9819 | 3.03778 | ||||||||
\(183\) | 11.6143 | 0.858555 | ||||||||
\(184\) | 5.00060 | 0.368649 | ||||||||
\(185\) | 18.0934 | 1.33026 | ||||||||
\(186\) | 10.6055 | 0.777630 | ||||||||
\(187\) | 2.09788 | 0.153412 | ||||||||
\(188\) | 9.68042 | 0.706017 | ||||||||
\(189\) | 3.97589 | 0.289203 | ||||||||
\(190\) | −3.40578 | −0.247081 | ||||||||
\(191\) | −8.25236 | −0.597120 | −0.298560 | − | 0.954391i | \(-0.596506\pi\) | ||||
−0.298560 | + | 0.954391i | \(0.596506\pi\) | |||||||
\(192\) | 4.84429 | 0.349607 | ||||||||
\(193\) | 2.14887 | 0.154679 | 0.0773395 | − | 0.997005i | \(-0.475357\pi\) | ||||
0.0773395 | + | 0.997005i | \(0.475357\pi\) | |||||||
\(194\) | −35.1206 | −2.52151 | ||||||||
\(195\) | −9.45447 | −0.677048 | ||||||||
\(196\) | 37.2345 | 2.65961 | ||||||||
\(197\) | −1.78795 | −0.127386 | −0.0636932 | − | 0.997970i | \(-0.520288\pi\) | ||||
−0.0636932 | + | 0.997970i | \(0.520288\pi\) | |||||||
\(198\) | 5.23524 | 0.372052 | ||||||||
\(199\) | 13.7859 | 0.977253 | 0.488627 | − | 0.872493i | \(-0.337498\pi\) | ||||
0.488627 | + | 0.872493i | \(0.337498\pi\) | |||||||
\(200\) | −1.33017 | −0.0940574 | ||||||||
\(201\) | 16.3430 | 1.15274 | ||||||||
\(202\) | 34.7778 | 2.44696 | ||||||||
\(203\) | 19.5087 | 1.36924 | ||||||||
\(204\) | 4.22749 | 0.295984 | ||||||||
\(205\) | 4.86494 | 0.339782 | ||||||||
\(206\) | −22.9855 | −1.60148 | ||||||||
\(207\) | −0.899600 | −0.0625265 | ||||||||
\(208\) | 22.3736 | 1.55133 | ||||||||
\(209\) | −1.25084 | −0.0865227 | ||||||||
\(210\) | −22.7105 | −1.56718 | ||||||||
\(211\) | 7.90745 | 0.544371 | 0.272185 | − | 0.962245i | \(-0.412254\pi\) | ||||
0.272185 | + | 0.962245i | \(0.412254\pi\) | |||||||
\(212\) | 41.6943 | 2.86357 | ||||||||
\(213\) | 11.7706 | 0.806507 | ||||||||
\(214\) | 20.3850 | 1.39349 | ||||||||
\(215\) | −4.41361 | −0.301006 | ||||||||
\(216\) | 5.55870 | 0.378221 | ||||||||
\(217\) | −16.8969 | −1.14704 | ||||||||
\(218\) | −38.9220 | −2.63613 | ||||||||
\(219\) | 0.392144 | 0.0264986 | ||||||||
\(220\) | −20.3002 | −1.36864 | ||||||||
\(221\) | −4.13048 | −0.277846 | ||||||||
\(222\) | 19.7261 | 1.32393 | ||||||||
\(223\) | 9.37569 | 0.627843 | 0.313921 | − | 0.949449i | \(-0.398357\pi\) | ||||
0.313921 | + | 0.949449i | \(0.398357\pi\) | |||||||
\(224\) | 9.54203 | 0.637554 | ||||||||
\(225\) | 0.239296 | 0.0159531 | ||||||||
\(226\) | −37.3917 | −2.48726 | ||||||||
\(227\) | −15.3381 | −1.01803 | −0.509013 | − | 0.860759i | \(-0.669989\pi\) | ||||
−0.509013 | + | 0.860759i | \(0.669989\pi\) | |||||||
\(228\) | −2.52061 | −0.166932 | ||||||||
\(229\) | 8.45160 | 0.558497 | 0.279249 | − | 0.960219i | \(-0.409915\pi\) | ||||
0.279249 | + | 0.960219i | \(0.409915\pi\) | |||||||
\(230\) | 5.13857 | 0.338827 | ||||||||
\(231\) | −8.34093 | −0.548793 | ||||||||
\(232\) | 27.2751 | 1.79070 | ||||||||
\(233\) | 20.5443 | 1.34590 | 0.672950 | − | 0.739688i | \(-0.265027\pi\) | ||||
0.672950 | + | 0.739688i | \(0.265027\pi\) | |||||||
\(234\) | −10.3076 | −0.673828 | ||||||||
\(235\) | 5.24140 | 0.341912 | ||||||||
\(236\) | 41.4104 | 2.69559 | ||||||||
\(237\) | −3.46759 | −0.225244 | ||||||||
\(238\) | −9.92181 | −0.643136 | ||||||||
\(239\) | −5.66979 | −0.366748 | −0.183374 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183374 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(240\) | −12.3986 | −0.800325 | ||||||||
\(241\) | 26.3181 | 1.69530 | 0.847648 | − | 0.530559i | \(-0.178018\pi\) | ||||
0.847648 | + | 0.530559i | \(0.178018\pi\) | |||||||
\(242\) | 16.4675 | 1.05857 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −49.0994 | −3.14327 | ||||||||
\(245\) | 20.1604 | 1.28800 | ||||||||
\(246\) | 5.30393 | 0.338166 | ||||||||
\(247\) | 2.46277 | 0.156702 | ||||||||
\(248\) | −23.6236 | −1.50010 | ||||||||
\(249\) | −2.58974 | −0.164118 | ||||||||
\(250\) | 27.1934 | 1.71986 | ||||||||
\(251\) | −15.9749 | −1.00833 | −0.504163 | − | 0.863608i | \(-0.668199\pi\) | ||||
−0.504163 | + | 0.863608i | \(0.668199\pi\) | |||||||
\(252\) | −16.8080 | −1.05881 | ||||||||
\(253\) | 1.88725 | 0.118650 | ||||||||
\(254\) | 5.88549 | 0.369288 | ||||||||
\(255\) | 2.28895 | 0.143340 | ||||||||
\(256\) | −32.4575 | −2.02859 | ||||||||
\(257\) | 1.22344 | 0.0763158 | 0.0381579 | − | 0.999272i | \(-0.487851\pi\) | ||||
0.0381579 | + | 0.999272i | \(0.487851\pi\) | |||||||
\(258\) | −4.81188 | −0.299574 | ||||||||
\(259\) | −31.4282 | −1.95285 | ||||||||
\(260\) | 39.9687 | 2.47875 | ||||||||
\(261\) | −4.90674 | −0.303720 | ||||||||
\(262\) | 55.3342 | 3.41856 | ||||||||
\(263\) | 1.42930 | 0.0881345 | 0.0440672 | − | 0.999029i | \(-0.485968\pi\) | ||||
0.0440672 | + | 0.999029i | \(0.485968\pi\) | |||||||
\(264\) | −11.6615 | −0.717713 | ||||||||
\(265\) | 22.5751 | 1.38678 | ||||||||
\(266\) | 5.91581 | 0.362722 | ||||||||
\(267\) | 11.6634 | 0.713790 | ||||||||
\(268\) | −69.0897 | −4.22033 | ||||||||
\(269\) | −1.18644 | −0.0723386 | −0.0361693 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361693 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(270\) | 5.71206 | 0.347625 | ||||||||
\(271\) | 9.17310 | 0.557226 | 0.278613 | − | 0.960403i | \(-0.410125\pi\) | ||||
0.278613 | + | 0.960403i | \(0.410125\pi\) | |||||||
\(272\) | −5.41671 | −0.328436 | ||||||||
\(273\) | 16.4223 | 0.993925 | ||||||||
\(274\) | −0.565881 | −0.0341861 | ||||||||
\(275\) | −0.502013 | −0.0302725 | ||||||||
\(276\) | 3.80305 | 0.228917 | ||||||||
\(277\) | 17.7208 | 1.06474 | 0.532371 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532371 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(278\) | 20.9136 | 1.25431 | ||||||||
\(279\) | 4.24984 | 0.254432 | ||||||||
\(280\) | 50.5876 | 3.02319 | ||||||||
\(281\) | −21.3320 | −1.27256 | −0.636281 | − | 0.771458i | \(-0.719528\pi\) | ||||
−0.636281 | + | 0.771458i | \(0.719528\pi\) | |||||||
\(282\) | 5.71436 | 0.340285 | ||||||||
\(283\) | −9.29149 | −0.552322 | −0.276161 | − | 0.961111i | \(-0.589062\pi\) | ||||
−0.276161 | + | 0.961111i | \(0.589062\pi\) | |||||||
\(284\) | −49.7600 | −2.95271 | ||||||||
\(285\) | −1.36477 | −0.0808421 | ||||||||
\(286\) | 21.6241 | 1.27866 | ||||||||
\(287\) | −8.45037 | −0.498810 | ||||||||
\(288\) | −2.39997 | −0.141420 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 28.0276 | 1.64584 | ||||||||
\(291\) | −14.0736 | −0.825009 | ||||||||
\(292\) | −1.65778 | −0.0970145 | ||||||||
\(293\) | −10.1040 | −0.590283 | −0.295142 | − | 0.955454i | \(-0.595367\pi\) | ||||
−0.295142 | + | 0.955454i | \(0.595367\pi\) | |||||||
\(294\) | 21.9796 | 1.28188 | ||||||||
\(295\) | 22.4214 | 1.30543 | ||||||||
\(296\) | −43.9398 | −2.55395 | ||||||||
\(297\) | 2.09788 | 0.121731 | ||||||||
\(298\) | 8.68084 | 0.502868 | ||||||||
\(299\) | −3.71578 | −0.214889 | ||||||||
\(300\) | −1.01162 | −0.0584060 | ||||||||
\(301\) | 7.66642 | 0.441885 | ||||||||
\(302\) | −28.1048 | −1.61725 | ||||||||
\(303\) | 13.9363 | 0.800617 | ||||||||
\(304\) | 3.22967 | 0.185235 | ||||||||
\(305\) | −26.5846 | −1.52223 | ||||||||
\(306\) | 2.49549 | 0.142658 | ||||||||
\(307\) | −21.0143 | −1.19935 | −0.599675 | − | 0.800244i | \(-0.704703\pi\) | ||||
−0.599675 | + | 0.800244i | \(0.704703\pi\) | |||||||
\(308\) | 35.2612 | 2.00919 | ||||||||
\(309\) | −9.21081 | −0.523984 | ||||||||
\(310\) | −24.2754 | −1.37875 | ||||||||
\(311\) | 8.34780 | 0.473360 | 0.236680 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236680 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(312\) | 22.9601 | 1.29986 | ||||||||
\(313\) | −10.6184 | −0.600188 | −0.300094 | − | 0.953910i | \(-0.597018\pi\) | ||||
−0.300094 | + | 0.953910i | \(0.597018\pi\) | |||||||
\(314\) | −2.49549 | −0.140829 | ||||||||
\(315\) | −9.10062 | −0.512762 | ||||||||
\(316\) | 14.6592 | 0.824646 | ||||||||
\(317\) | 3.76018 | 0.211193 | 0.105597 | − | 0.994409i | \(-0.466325\pi\) | ||||
0.105597 | + | 0.994409i | \(0.466325\pi\) | |||||||
\(318\) | 24.6122 | 1.38018 | ||||||||
\(319\) | 10.2937 | 0.576339 | ||||||||
\(320\) | −11.0884 | −0.619858 | ||||||||
\(321\) | 8.16871 | 0.455933 | ||||||||
\(322\) | −8.92566 | −0.497408 | ||||||||
\(323\) | −0.596243 | −0.0331758 | ||||||||
\(324\) | 4.22749 | 0.234861 | ||||||||
\(325\) | 0.988407 | 0.0548269 | ||||||||
\(326\) | −48.2230 | −2.67083 | ||||||||
\(327\) | −15.5969 | −0.862511 | ||||||||
\(328\) | −11.8145 | −0.652345 | ||||||||
\(329\) | −9.10428 | −0.501935 | ||||||||
\(330\) | −11.9832 | −0.659654 | ||||||||
\(331\) | 21.3573 | 1.17390 | 0.586950 | − | 0.809623i | \(-0.300328\pi\) | ||||
0.586950 | + | 0.809623i | \(0.300328\pi\) | |||||||
\(332\) | 10.9481 | 0.600856 | ||||||||
\(333\) | 7.90469 | 0.433174 | ||||||||
\(334\) | −19.9048 | −1.08914 | ||||||||
\(335\) | −37.4082 | −2.04383 | ||||||||
\(336\) | 21.5362 | 1.17490 | ||||||||
\(337\) | 0.693705 | 0.0377885 | 0.0188943 | − | 0.999821i | \(-0.493985\pi\) | ||||
0.0188943 | + | 0.999821i | \(0.493985\pi\) | |||||||
\(338\) | −10.1339 | −0.551211 | ||||||||
\(339\) | −14.9837 | −0.813802 | ||||||||
\(340\) | −9.67652 | −0.524783 | ||||||||
\(341\) | −8.91565 | −0.482810 | ||||||||
\(342\) | −1.48792 | −0.0804576 | ||||||||
\(343\) | −7.18725 | −0.388075 | ||||||||
\(344\) | 10.7184 | 0.577899 | ||||||||
\(345\) | 2.05914 | 0.110860 | ||||||||
\(346\) | −29.3797 | −1.57946 | ||||||||
\(347\) | 4.23048 | 0.227104 | 0.113552 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(348\) | 20.7432 | 1.11195 | ||||||||
\(349\) | −11.3269 | −0.606315 | −0.303158 | − | 0.952940i | \(-0.598041\pi\) | ||||
−0.303158 | + | 0.952940i | \(0.598041\pi\) | |||||||
\(350\) | 2.37425 | 0.126909 | ||||||||
\(351\) | −4.13048 | −0.220469 | ||||||||
\(352\) | 5.03485 | 0.268358 | ||||||||
\(353\) | 10.6126 | 0.564854 | 0.282427 | − | 0.959289i | \(-0.408860\pi\) | ||||
0.282427 | + | 0.959289i | \(0.408860\pi\) | |||||||
\(354\) | 24.4446 | 1.29922 | ||||||||
\(355\) | −26.9423 | −1.42995 | ||||||||
\(356\) | −49.3070 | −2.61327 | ||||||||
\(357\) | −3.97589 | −0.210426 | ||||||||
\(358\) | 34.7077 | 1.83436 | ||||||||
\(359\) | −32.7552 | −1.72875 | −0.864377 | − | 0.502844i | \(-0.832287\pi\) | ||||
−0.864377 | + | 0.502844i | \(0.832287\pi\) | |||||||
\(360\) | −12.7236 | −0.670592 | ||||||||
\(361\) | −18.6445 | −0.981289 | ||||||||
\(362\) | −37.7339 | −1.98325 | ||||||||
\(363\) | 6.59891 | 0.346353 | ||||||||
\(364\) | −69.4253 | −3.63888 | ||||||||
\(365\) | −0.897598 | −0.0469824 | ||||||||
\(366\) | −28.9835 | −1.51499 | ||||||||
\(367\) | −16.5337 | −0.863051 | −0.431525 | − | 0.902101i | \(-0.642024\pi\) | ||||
−0.431525 | + | 0.902101i | \(0.642024\pi\) | |||||||
\(368\) | −4.87287 | −0.254016 | ||||||||
\(369\) | 2.12540 | 0.110644 | ||||||||
\(370\) | −45.1521 | −2.34735 | ||||||||
\(371\) | −39.2128 | −2.03583 | ||||||||
\(372\) | −17.9662 | −0.931503 | ||||||||
\(373\) | 13.7181 | 0.710298 | 0.355149 | − | 0.934810i | \(-0.384430\pi\) | ||||
0.355149 | + | 0.934810i | \(0.384430\pi\) | |||||||
\(374\) | −5.23524 | −0.270708 | ||||||||
\(375\) | 10.8970 | 0.562720 | ||||||||
\(376\) | −12.7287 | −0.656433 | ||||||||
\(377\) | −20.2672 | −1.04381 | ||||||||
\(378\) | −9.92181 | −0.510323 | ||||||||
\(379\) | 20.5527 | 1.05572 | 0.527862 | − | 0.849330i | \(-0.322994\pi\) | ||||
0.527862 | + | 0.849330i | \(0.322994\pi\) | |||||||
\(380\) | 5.76956 | 0.295972 | ||||||||
\(381\) | 2.35845 | 0.120827 | ||||||||
\(382\) | 20.5937 | 1.05367 | ||||||||
\(383\) | 10.2040 | 0.521401 | 0.260701 | − | 0.965420i | \(-0.416046\pi\) | ||||
0.260701 | + | 0.965420i | \(0.416046\pi\) | |||||||
\(384\) | −16.8889 | −0.861856 | ||||||||
\(385\) | 19.0920 | 0.973017 | ||||||||
\(386\) | −5.36249 | −0.272944 | ||||||||
\(387\) | −1.92823 | −0.0980172 | ||||||||
\(388\) | 59.4961 | 3.02045 | ||||||||
\(389\) | −6.73322 | −0.341388 | −0.170694 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170694 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(390\) | 23.5936 | 1.19471 | ||||||||
\(391\) | 0.899600 | 0.0454947 | ||||||||
\(392\) | −48.9594 | −2.47282 | ||||||||
\(393\) | 22.1737 | 1.11851 | ||||||||
\(394\) | 4.46183 | 0.224784 | ||||||||
\(395\) | 7.93715 | 0.399361 | ||||||||
\(396\) | −8.86876 | −0.445672 | ||||||||
\(397\) | −11.3217 | −0.568221 | −0.284111 | − | 0.958791i | \(-0.591698\pi\) | ||||
−0.284111 | + | 0.958791i | \(0.591698\pi\) | |||||||
\(398\) | −34.4025 | −1.72444 | ||||||||
\(399\) | 2.37060 | 0.118678 | ||||||||
\(400\) | 1.29620 | 0.0648098 | ||||||||
\(401\) | −25.6960 | −1.28320 | −0.641599 | − | 0.767040i | \(-0.721729\pi\) | ||||
−0.641599 | + | 0.767040i | \(0.721729\pi\) | |||||||
\(402\) | −40.7838 | −2.03411 | ||||||||
\(403\) | 17.5539 | 0.874422 | ||||||||
\(404\) | −58.9154 | −2.93115 | ||||||||
\(405\) | 2.28895 | 0.113739 | ||||||||
\(406\) | −48.6838 | −2.41614 | ||||||||
\(407\) | −16.5831 | −0.821992 | ||||||||
\(408\) | −5.55870 | −0.275196 | ||||||||
\(409\) | 7.20371 | 0.356200 | 0.178100 | − | 0.984012i | \(-0.443005\pi\) | ||||
0.178100 | + | 0.984012i | \(0.443005\pi\) | |||||||
\(410\) | −12.1404 | −0.599573 | ||||||||
\(411\) | −0.226761 | −0.0111853 | ||||||||
\(412\) | 38.9386 | 1.91837 | ||||||||
\(413\) | −38.9458 | −1.91640 | ||||||||
\(414\) | 2.24495 | 0.110333 | ||||||||
\(415\) | 5.92780 | 0.290984 | ||||||||
\(416\) | −9.91304 | −0.486027 | ||||||||
\(417\) | 8.38054 | 0.410397 | ||||||||
\(418\) | 3.12148 | 0.152676 | ||||||||
\(419\) | 14.6594 | 0.716156 | 0.358078 | − | 0.933692i | \(-0.383432\pi\) | ||||
0.358078 | + | 0.933692i | \(0.383432\pi\) | |||||||
\(420\) | 38.4728 | 1.87728 | ||||||||
\(421\) | 28.3421 | 1.38131 | 0.690655 | − | 0.723185i | \(-0.257322\pi\) | ||||
0.690655 | + | 0.723185i | \(0.257322\pi\) | |||||||
\(422\) | −19.7330 | −0.960587 | ||||||||
\(423\) | 2.28987 | 0.111337 | ||||||||
\(424\) | −54.8235 | −2.66246 | ||||||||
\(425\) | −0.239296 | −0.0116076 | ||||||||
\(426\) | −29.3734 | −1.42315 | ||||||||
\(427\) | 46.1773 | 2.23467 | ||||||||
\(428\) | −34.5332 | −1.66922 | ||||||||
\(429\) | 8.66524 | 0.418362 | ||||||||
\(430\) | 11.0142 | 0.531150 | ||||||||
\(431\) | 17.6699 | 0.851131 | 0.425566 | − | 0.904928i | \(-0.360075\pi\) | ||||
0.425566 | + | 0.904928i | \(0.360075\pi\) | |||||||
\(432\) | −5.41671 | −0.260611 | ||||||||
\(433\) | 11.9186 | 0.572771 | 0.286385 | − | 0.958115i | \(-0.407546\pi\) | ||||
0.286385 | + | 0.958115i | \(0.407546\pi\) | |||||||
\(434\) | 42.1662 | 2.02404 | ||||||||
\(435\) | 11.2313 | 0.538499 | ||||||||
\(436\) | 65.9358 | 3.15775 | ||||||||
\(437\) | −0.536380 | −0.0256585 | ||||||||
\(438\) | −0.978592 | −0.0467590 | ||||||||
\(439\) | 39.7031 | 1.89492 | 0.947462 | − | 0.319869i | \(-0.103639\pi\) | ||||
0.947462 | + | 0.319869i | \(0.103639\pi\) | |||||||
\(440\) | 26.6925 | 1.27252 | ||||||||
\(441\) | 8.80771 | 0.419415 | ||||||||
\(442\) | 10.3076 | 0.490282 | ||||||||
\(443\) | 6.45246 | 0.306566 | 0.153283 | − | 0.988182i | \(-0.451015\pi\) | ||||
0.153283 | + | 0.988182i | \(0.451015\pi\) | |||||||
\(444\) | −33.4170 | −1.58590 | ||||||||
\(445\) | −26.6970 | −1.26556 | ||||||||
\(446\) | −23.3970 | −1.10788 | ||||||||
\(447\) | 3.47861 | 0.164532 | ||||||||
\(448\) | 19.2604 | 0.909968 | ||||||||
\(449\) | 24.8339 | 1.17199 | 0.585993 | − | 0.810316i | \(-0.300705\pi\) | ||||
0.585993 | + | 0.810316i | \(0.300705\pi\) | |||||||
\(450\) | −0.597161 | −0.0281505 | ||||||||
\(451\) | −4.45883 | −0.209958 | ||||||||
\(452\) | 63.3434 | 2.97942 | ||||||||
\(453\) | −11.2622 | −0.529145 | ||||||||
\(454\) | 38.2761 | 1.79639 | ||||||||
\(455\) | −37.5899 | −1.76224 | ||||||||
\(456\) | 3.31433 | 0.155208 | ||||||||
\(457\) | −25.8728 | −1.21028 | −0.605139 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605139 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(458\) | −21.0909 | −0.985514 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −8.70500 | −0.405873 | ||||||||
\(461\) | 6.11593 | 0.284847 | 0.142424 | − | 0.989806i | \(-0.454510\pi\) | ||||
0.142424 | + | 0.989806i | \(0.454510\pi\) | |||||||
\(462\) | 20.8147 | 0.968390 | ||||||||
\(463\) | −31.2996 | −1.45462 | −0.727308 | − | 0.686312i | \(-0.759229\pi\) | ||||
−0.727308 | + | 0.686312i | \(0.759229\pi\) | |||||||
\(464\) | −26.5784 | −1.23387 | ||||||||
\(465\) | −9.72768 | −0.451111 | ||||||||
\(466\) | −51.2681 | −2.37495 | ||||||||
\(467\) | −27.0814 | −1.25318 | −0.626588 | − | 0.779351i | \(-0.715549\pi\) | ||||
−0.626588 | + | 0.779351i | \(0.715549\pi\) | |||||||
\(468\) | 17.4616 | 0.807162 | ||||||||
\(469\) | 64.9778 | 3.00040 | ||||||||
\(470\) | −13.0799 | −0.603331 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −54.4502 | −2.50627 | ||||||||
\(473\) | 4.04518 | 0.185998 | ||||||||
\(474\) | 8.65336 | 0.397462 | ||||||||
\(475\) | 0.142678 | 0.00654654 | ||||||||
\(476\) | 16.8080 | 0.770396 | ||||||||
\(477\) | 9.86265 | 0.451580 | ||||||||
\(478\) | 14.1489 | 0.647157 | ||||||||
\(479\) | −17.9859 | −0.821798 | −0.410899 | − | 0.911681i | \(-0.634785\pi\) | ||||
−0.410899 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(480\) | 5.49342 | 0.250739 | ||||||||
\(481\) | 32.6502 | 1.48872 | ||||||||
\(482\) | −65.6766 | −2.99149 | ||||||||
\(483\) | −3.57671 | −0.162746 | ||||||||
\(484\) | −27.8968 | −1.26804 | ||||||||
\(485\) | 32.2138 | 1.46275 | ||||||||
\(486\) | 2.49549 | 0.113198 | ||||||||
\(487\) | −18.4562 | −0.836329 | −0.418164 | − | 0.908371i | \(-0.637326\pi\) | ||||
−0.418164 | + | 0.908371i | \(0.637326\pi\) | |||||||
\(488\) | 64.5604 | 2.92251 | ||||||||
\(489\) | −19.3240 | −0.873863 | ||||||||
\(490\) | −50.3102 | −2.27278 | ||||||||
\(491\) | 22.9380 | 1.03518 | 0.517590 | − | 0.855629i | \(-0.326829\pi\) | ||||
0.517590 | + | 0.855629i | \(0.326829\pi\) | |||||||
\(492\) | −8.98512 | −0.405081 | ||||||||
\(493\) | 4.90674 | 0.220989 | ||||||||
\(494\) | −6.14583 | −0.276514 | ||||||||
\(495\) | −4.80194 | −0.215831 | ||||||||
\(496\) | 23.0202 | 1.03364 | ||||||||
\(497\) | 46.7985 | 2.09920 | ||||||||
\(498\) | 6.46269 | 0.289600 | ||||||||
\(499\) | 14.3853 | 0.643975 | 0.321988 | − | 0.946744i | \(-0.395649\pi\) | ||||
0.321988 | + | 0.946744i | \(0.395649\pi\) | |||||||
\(500\) | −46.0671 | −2.06018 | ||||||||
\(501\) | −7.97629 | −0.356354 | ||||||||
\(502\) | 39.8653 | 1.77927 | ||||||||
\(503\) | 24.4206 | 1.08886 | 0.544430 | − | 0.838806i | \(-0.316746\pi\) | ||||
0.544430 | + | 0.838806i | \(0.316746\pi\) | |||||||
\(504\) | 22.1008 | 0.984446 | ||||||||
\(505\) | −31.8994 | −1.41950 | ||||||||
\(506\) | −4.70962 | −0.209368 | ||||||||
\(507\) | −4.06087 | −0.180350 | ||||||||
\(508\) | −9.97031 | −0.442361 | ||||||||
\(509\) | 1.86289 | 0.0825710 | 0.0412855 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412855 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(510\) | −5.71206 | −0.252934 | ||||||||
\(511\) | 1.55912 | 0.0689714 | ||||||||
\(512\) | 47.2197 | 2.08684 | ||||||||
\(513\) | −0.596243 | −0.0263248 | ||||||||
\(514\) | −3.05308 | −0.134665 | ||||||||
\(515\) | 21.0831 | 0.929032 | ||||||||
\(516\) | 8.15156 | 0.358853 | ||||||||
\(517\) | −4.80387 | −0.211274 | ||||||||
\(518\) | 78.4289 | 3.44597 | ||||||||
\(519\) | −11.7731 | −0.516782 | ||||||||
\(520\) | −52.5545 | −2.30467 | ||||||||
\(521\) | −21.8144 | −0.955708 | −0.477854 | − | 0.878439i | \(-0.658585\pi\) | ||||
−0.477854 | + | 0.878439i | \(0.658585\pi\) | |||||||
\(522\) | 12.2448 | 0.535938 | ||||||||
\(523\) | 21.3018 | 0.931462 | 0.465731 | − | 0.884926i | \(-0.345791\pi\) | ||||
0.465731 | + | 0.884926i | \(0.345791\pi\) | |||||||
\(524\) | −93.7390 | −4.09501 | ||||||||
\(525\) | 0.951414 | 0.0415231 | ||||||||
\(526\) | −3.56681 | −0.155520 | ||||||||
\(527\) | −4.24984 | −0.185126 | ||||||||
\(528\) | 11.3636 | 0.494537 | ||||||||
\(529\) | −22.1907 | −0.964814 | ||||||||
\(530\) | −56.3361 | −2.44708 | ||||||||
\(531\) | 9.79550 | 0.425088 | ||||||||
\(532\) | −10.0217 | −0.434495 | ||||||||
\(533\) | 8.77894 | 0.380258 | ||||||||
\(534\) | −29.1060 | −1.25954 | ||||||||
\(535\) | −18.6978 | −0.808375 | ||||||||
\(536\) | 90.8455 | 3.92393 | ||||||||
\(537\) | 13.9082 | 0.600181 | ||||||||
\(538\) | 2.96076 | 0.127647 | ||||||||
\(539\) | −18.4775 | −0.795882 | ||||||||
\(540\) | −9.67652 | −0.416411 | ||||||||
\(541\) | −22.0891 | −0.949683 | −0.474842 | − | 0.880071i | \(-0.657495\pi\) | ||||
−0.474842 | + | 0.880071i | \(0.657495\pi\) | |||||||
\(542\) | −22.8914 | −0.983271 | ||||||||
\(543\) | −15.1208 | −0.648896 | ||||||||
\(544\) | 2.39997 | 0.102898 | ||||||||
\(545\) | 35.7006 | 1.52924 | ||||||||
\(546\) | −40.9819 | −1.75386 | ||||||||
\(547\) | 22.4546 | 0.960090 | 0.480045 | − | 0.877244i | \(-0.340620\pi\) | ||||
0.480045 | + | 0.877244i | \(0.340620\pi\) | |||||||
\(548\) | 0.958631 | 0.0409507 | ||||||||
\(549\) | −11.6143 | −0.495687 | ||||||||
\(550\) | 1.25277 | 0.0534183 | ||||||||
\(551\) | −2.92561 | −0.124635 | ||||||||
\(552\) | −5.00060 | −0.212840 | ||||||||
\(553\) | −13.7868 | −0.586273 | ||||||||
\(554\) | −44.2223 | −1.87882 | ||||||||
\(555\) | −18.0934 | −0.768024 | ||||||||
\(556\) | −35.4287 | −1.50251 | ||||||||
\(557\) | −27.8557 | −1.18028 | −0.590142 | − | 0.807300i | \(-0.700928\pi\) | ||||
−0.590142 | + | 0.807300i | \(0.700928\pi\) | |||||||
\(558\) | −10.6055 | −0.448965 | ||||||||
\(559\) | −7.96450 | −0.336863 | ||||||||
\(560\) | −49.2954 | −2.08311 | ||||||||
\(561\) | −2.09788 | −0.0885724 | ||||||||
\(562\) | 53.2339 | 2.24554 | ||||||||
\(563\) | −40.7299 | −1.71656 | −0.858280 | − | 0.513182i | \(-0.828466\pi\) | ||||
−0.858280 | + | 0.513182i | \(0.828466\pi\) | |||||||
\(564\) | −9.68042 | −0.407619 | ||||||||
\(565\) | 34.2969 | 1.44288 | ||||||||
\(566\) | 23.1869 | 0.974616 | ||||||||
\(567\) | −3.97589 | −0.166972 | ||||||||
\(568\) | 65.4291 | 2.74534 | ||||||||
\(569\) | 39.2807 | 1.64673 | 0.823366 | − | 0.567510i | \(-0.192093\pi\) | ||||
0.823366 | + | 0.567510i | \(0.192093\pi\) | |||||||
\(570\) | 3.40578 | 0.142652 | ||||||||
\(571\) | −22.7897 | −0.953718 | −0.476859 | − | 0.878980i | \(-0.658225\pi\) | ||||
−0.476859 | + | 0.878980i | \(0.658225\pi\) | |||||||
\(572\) | −36.6322 | −1.53167 | ||||||||
\(573\) | 8.25236 | 0.344747 | ||||||||
\(574\) | 21.0879 | 0.880190 | ||||||||
\(575\) | −0.215270 | −0.00897740 | ||||||||
\(576\) | −4.84429 | −0.201846 | ||||||||
\(577\) | 24.7742 | 1.03136 | 0.515682 | − | 0.856780i | \(-0.327539\pi\) | ||||
0.515682 | + | 0.856780i | \(0.327539\pi\) | |||||||
\(578\) | −2.49549 | −0.103799 | ||||||||
\(579\) | −2.14887 | −0.0893040 | ||||||||
\(580\) | −47.4802 | −1.97151 | ||||||||
\(581\) | −10.2965 | −0.427172 | ||||||||
\(582\) | 35.1206 | 1.45580 | ||||||||
\(583\) | −20.6906 | −0.856918 | ||||||||
\(584\) | 2.17981 | 0.0902011 | ||||||||
\(585\) | 9.45447 | 0.390894 | ||||||||
\(586\) | 25.2145 | 1.04160 | ||||||||
\(587\) | 23.8272 | 0.983454 | 0.491727 | − | 0.870749i | \(-0.336366\pi\) | ||||
0.491727 | + | 0.870749i | \(0.336366\pi\) | |||||||
\(588\) | −37.2345 | −1.53553 | ||||||||
\(589\) | 2.53394 | 0.104409 | ||||||||
\(590\) | −55.9525 | −2.30353 | ||||||||
\(591\) | 1.78795 | 0.0735465 | ||||||||
\(592\) | 42.8174 | 1.75978 | ||||||||
\(593\) | 31.1570 | 1.27947 | 0.639733 | − | 0.768598i | \(-0.279045\pi\) | ||||
0.639733 | + | 0.768598i | \(0.279045\pi\) | |||||||
\(594\) | −5.23524 | −0.214805 | ||||||||
\(595\) | 9.10062 | 0.373089 | ||||||||
\(596\) | −14.7058 | −0.602372 | ||||||||
\(597\) | −13.7859 | −0.564217 | ||||||||
\(598\) | 9.27271 | 0.379189 | ||||||||
\(599\) | −8.58770 | −0.350884 | −0.175442 | − | 0.984490i | \(-0.556135\pi\) | ||||
−0.175442 | + | 0.984490i | \(0.556135\pi\) | |||||||
\(600\) | 1.33017 | 0.0543041 | ||||||||
\(601\) | −35.0826 | −1.43105 | −0.715525 | − | 0.698587i | \(-0.753813\pi\) | ||||
−0.715525 | + | 0.698587i | \(0.753813\pi\) | |||||||
\(602\) | −19.1315 | −0.779742 | ||||||||
\(603\) | −16.3430 | −0.665537 | ||||||||
\(604\) | 47.6109 | 1.93726 | ||||||||
\(605\) | −15.1046 | −0.614089 | ||||||||
\(606\) | −34.7778 | −1.41275 | ||||||||
\(607\) | 27.1225 | 1.10087 | 0.550434 | − | 0.834879i | \(-0.314462\pi\) | ||||
0.550434 | + | 0.834879i | \(0.314462\pi\) | |||||||
\(608\) | −1.43097 | −0.0580334 | ||||||||
\(609\) | −19.5087 | −0.790532 | ||||||||
\(610\) | 66.3417 | 2.68610 | ||||||||
\(611\) | 9.45827 | 0.382641 | ||||||||
\(612\) | −4.22749 | −0.170886 | ||||||||
\(613\) | −36.9362 | −1.49184 | −0.745919 | − | 0.666036i | \(-0.767990\pi\) | ||||
−0.745919 | + | 0.666036i | \(0.767990\pi\) | |||||||
\(614\) | 52.4411 | 2.11635 | ||||||||
\(615\) | −4.86494 | −0.196173 | ||||||||
\(616\) | −46.3647 | −1.86809 | ||||||||
\(617\) | −18.9504 | −0.762915 | −0.381458 | − | 0.924386i | \(-0.624578\pi\) | ||||
−0.381458 | + | 0.924386i | \(0.624578\pi\) | |||||||
\(618\) | 22.9855 | 0.924613 | ||||||||
\(619\) | 32.7318 | 1.31560 | 0.657802 | − | 0.753191i | \(-0.271486\pi\) | ||||
0.657802 | + | 0.753191i | \(0.271486\pi\) | |||||||
\(620\) | 41.1237 | 1.65157 | ||||||||
\(621\) | 0.899600 | 0.0360997 | ||||||||
\(622\) | −20.8319 | −0.835283 | ||||||||
\(623\) | 46.3725 | 1.85788 | ||||||||
\(624\) | −22.3736 | −0.895661 | ||||||||
\(625\) | −26.1392 | −1.04557 | ||||||||
\(626\) | 26.4982 | 1.05908 | ||||||||
\(627\) | 1.25084 | 0.0499539 | ||||||||
\(628\) | 4.22749 | 0.168695 | ||||||||
\(629\) | −7.90469 | −0.315181 | ||||||||
\(630\) | 22.7105 | 0.904810 | ||||||||
\(631\) | 8.05952 | 0.320844 | 0.160422 | − | 0.987048i | \(-0.448714\pi\) | ||||
0.160422 | + | 0.987048i | \(0.448714\pi\) | |||||||
\(632\) | −19.2753 | −0.766730 | ||||||||
\(633\) | −7.90745 | −0.314293 | ||||||||
\(634\) | −9.38352 | −0.372667 | ||||||||
\(635\) | −5.39837 | −0.214228 | ||||||||
\(636\) | −41.6943 | −1.65329 | ||||||||
\(637\) | 36.3801 | 1.44143 | ||||||||
\(638\) | −25.6880 | −1.01700 | ||||||||
\(639\) | −11.7706 | −0.465637 | ||||||||
\(640\) | 38.6578 | 1.52808 | ||||||||
\(641\) | 26.0860 | 1.03034 | 0.515168 | − | 0.857089i | \(-0.327729\pi\) | ||||
0.515168 | + | 0.857089i | \(0.327729\pi\) | |||||||
\(642\) | −20.3850 | −0.804531 | ||||||||
\(643\) | −8.46999 | −0.334024 | −0.167012 | − | 0.985955i | \(-0.553412\pi\) | ||||
−0.167012 | + | 0.985955i | \(0.553412\pi\) | |||||||
\(644\) | 15.1205 | 0.595832 | ||||||||
\(645\) | 4.41361 | 0.173786 | ||||||||
\(646\) | 1.48792 | 0.0585415 | ||||||||
\(647\) | 9.54660 | 0.375315 | 0.187658 | − | 0.982234i | \(-0.439910\pi\) | ||||
0.187658 | + | 0.982234i | \(0.439910\pi\) | |||||||
\(648\) | −5.55870 | −0.218366 | ||||||||
\(649\) | −20.5498 | −0.806649 | ||||||||
\(650\) | −2.46656 | −0.0967466 | ||||||||
\(651\) | 16.8969 | 0.662242 | ||||||||
\(652\) | 81.6922 | 3.19931 | ||||||||
\(653\) | 39.4107 | 1.54226 | 0.771130 | − | 0.636678i | \(-0.219692\pi\) | ||||
0.771130 | + | 0.636678i | \(0.219692\pi\) | |||||||
\(654\) | 38.9220 | 1.52197 | ||||||||
\(655\) | −50.7544 | −1.98314 | ||||||||
\(656\) | 11.5127 | 0.449495 | ||||||||
\(657\) | −0.392144 | −0.0152990 | ||||||||
\(658\) | 22.7197 | 0.885705 | ||||||||
\(659\) | 35.9160 | 1.39909 | 0.699544 | − | 0.714589i | \(-0.253386\pi\) | ||||
0.699544 | + | 0.714589i | \(0.253386\pi\) | |||||||
\(660\) | 20.3002 | 0.790182 | ||||||||
\(661\) | 0.756861 | 0.0294385 | 0.0147192 | − | 0.999892i | \(-0.495315\pi\) | ||||
0.0147192 | + | 0.999892i | \(0.495315\pi\) | |||||||
\(662\) | −53.2969 | −2.07144 | ||||||||
\(663\) | 4.13048 | 0.160415 | ||||||||
\(664\) | −14.3956 | −0.558657 | ||||||||
\(665\) | −5.42618 | −0.210418 | ||||||||
\(666\) | −19.7261 | −0.764371 | ||||||||
\(667\) | 4.41411 | 0.170915 | ||||||||
\(668\) | 33.7197 | 1.30465 | ||||||||
\(669\) | −9.37569 | −0.362485 | ||||||||
\(670\) | 93.3520 | 3.60650 | ||||||||
\(671\) | 24.3654 | 0.940616 | ||||||||
\(672\) | −9.54203 | −0.368092 | ||||||||
\(673\) | 46.9803 | 1.81096 | 0.905478 | − | 0.424393i | \(-0.139513\pi\) | ||||
0.905478 | + | 0.424393i | \(0.139513\pi\) | |||||||
\(674\) | −1.73114 | −0.0666809 | ||||||||
\(675\) | −0.239296 | −0.00921050 | ||||||||
\(676\) | 17.1673 | 0.660281 | ||||||||
\(677\) | 29.7466 | 1.14325 | 0.571627 | − | 0.820514i | \(-0.306313\pi\) | ||||
0.571627 | + | 0.820514i | \(0.306313\pi\) | |||||||
\(678\) | 37.3917 | 1.43602 | ||||||||
\(679\) | −55.9551 | −2.14736 | ||||||||
\(680\) | 12.7236 | 0.487927 | ||||||||
\(681\) | 15.3381 | 0.587757 | ||||||||
\(682\) | 22.2490 | 0.851957 | ||||||||
\(683\) | −28.5625 | −1.09291 | −0.546457 | − | 0.837487i | \(-0.684024\pi\) | ||||
−0.546457 | + | 0.837487i | \(0.684024\pi\) | |||||||
\(684\) | 2.52061 | 0.0963780 | ||||||||
\(685\) | 0.519045 | 0.0198317 | ||||||||
\(686\) | 17.9357 | 0.684790 | ||||||||
\(687\) | −8.45160 | −0.322449 | ||||||||
\(688\) | −10.4446 | −0.398198 | ||||||||
\(689\) | 40.7375 | 1.55197 | ||||||||
\(690\) | −5.13857 | −0.195622 | ||||||||
\(691\) | 40.0576 | 1.52386 | 0.761931 | − | 0.647658i | \(-0.224252\pi\) | ||||
0.761931 | + | 0.647658i | \(0.224252\pi\) | |||||||
\(692\) | 49.7707 | 1.89200 | ||||||||
\(693\) | 8.34093 | 0.316846 | ||||||||
\(694\) | −10.5571 | −0.400744 | ||||||||
\(695\) | −19.1826 | −0.727639 | ||||||||
\(696\) | −27.2751 | −1.03386 | ||||||||
\(697\) | −2.12540 | −0.0805054 | ||||||||
\(698\) | 28.2662 | 1.06989 | ||||||||
\(699\) | −20.5443 | −0.777055 | ||||||||
\(700\) | −4.02210 | −0.152021 | ||||||||
\(701\) | 37.2628 | 1.40740 | 0.703699 | − | 0.710498i | \(-0.251530\pi\) | ||||
0.703699 | + | 0.710498i | \(0.251530\pi\) | |||||||
\(702\) | 10.3076 | 0.389035 | ||||||||
\(703\) | 4.71312 | 0.177759 | ||||||||
\(704\) | 10.1627 | 0.383023 | ||||||||
\(705\) | −5.24140 | −0.197403 | ||||||||
\(706\) | −26.4838 | −0.996731 | ||||||||
\(707\) | 55.4090 | 2.08387 | ||||||||
\(708\) | −41.4104 | −1.55630 | ||||||||
\(709\) | 29.5209 | 1.10868 | 0.554340 | − | 0.832290i | \(-0.312971\pi\) | ||||
0.554340 | + | 0.832290i | \(0.312971\pi\) | |||||||
\(710\) | 67.2343 | 2.52326 | ||||||||
\(711\) | 3.46759 | 0.130045 | ||||||||
\(712\) | 64.8334 | 2.42974 | ||||||||
\(713\) | −3.82316 | −0.143178 | ||||||||
\(714\) | 9.92181 | 0.371315 | ||||||||
\(715\) | −19.8343 | −0.741761 | ||||||||
\(716\) | −58.7966 | −2.19733 | ||||||||
\(717\) | 5.66979 | 0.211742 | ||||||||
\(718\) | 81.7405 | 3.05053 | ||||||||
\(719\) | 1.07639 | 0.0401426 | 0.0200713 | − | 0.999799i | \(-0.493611\pi\) | ||||
0.0200713 | + | 0.999799i | \(0.493611\pi\) | |||||||
\(720\) | 12.3986 | 0.462068 | ||||||||
\(721\) | −36.6212 | −1.36384 | ||||||||
\(722\) | 46.5272 | 1.73156 | ||||||||
\(723\) | −26.3181 | −0.978780 | ||||||||
\(724\) | 63.9231 | 2.37568 | ||||||||
\(725\) | −1.17416 | −0.0436073 | ||||||||
\(726\) | −16.4675 | −0.611168 | ||||||||
\(727\) | 21.7500 | 0.806665 | 0.403332 | − | 0.915054i | \(-0.367852\pi\) | ||||
0.403332 | + | 0.915054i | \(0.367852\pi\) | |||||||
\(728\) | 91.2868 | 3.38331 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.23995 | 0.0829043 | ||||||||
\(731\) | 1.92823 | 0.0713180 | ||||||||
\(732\) | 49.0994 | 1.81477 | ||||||||
\(733\) | 10.9645 | 0.404983 | 0.202492 | − | 0.979284i | \(-0.435096\pi\) | ||||
0.202492 | + | 0.979284i | \(0.435096\pi\) | |||||||
\(734\) | 41.2597 | 1.52292 | ||||||||
\(735\) | −20.1604 | −0.743628 | ||||||||
\(736\) | 2.15902 | 0.0795824 | ||||||||
\(737\) | 34.2855 | 1.26292 | ||||||||
\(738\) | −5.30393 | −0.195240 | ||||||||
\(739\) | −27.9372 | −1.02769 | −0.513844 | − | 0.857884i | \(-0.671779\pi\) | ||||
−0.513844 | + | 0.857884i | \(0.671779\pi\) | |||||||
\(740\) | 76.4899 | 2.81182 | ||||||||
\(741\) | −2.46277 | −0.0904721 | ||||||||
\(742\) | 97.8554 | 3.59238 | ||||||||
\(743\) | −17.1717 | −0.629969 | −0.314984 | − | 0.949097i | \(-0.601999\pi\) | ||||
−0.314984 | + | 0.949097i | \(0.601999\pi\) | |||||||
\(744\) | 23.6236 | 0.866083 | ||||||||
\(745\) | −7.96236 | −0.291718 | ||||||||
\(746\) | −34.2335 | −1.25338 | ||||||||
\(747\) | 2.58974 | 0.0947538 | ||||||||
\(748\) | 8.86876 | 0.324274 | ||||||||
\(749\) | 32.4779 | 1.18672 | ||||||||
\(750\) | −27.1934 | −0.992964 | ||||||||
\(751\) | 34.5845 | 1.26201 | 0.631003 | − | 0.775781i | \(-0.282644\pi\) | ||||
0.631003 | + | 0.775781i | \(0.282644\pi\) | |||||||
\(752\) | 12.4036 | 0.452312 | ||||||||
\(753\) | 15.9749 | 0.582158 | ||||||||
\(754\) | 50.5767 | 1.84190 | ||||||||
\(755\) | 25.7787 | 0.938182 | ||||||||
\(756\) | 16.8080 | 0.611303 | ||||||||
\(757\) | −37.7428 | −1.37178 | −0.685892 | − | 0.727703i | \(-0.740588\pi\) | ||||
−0.685892 | + | 0.727703i | \(0.740588\pi\) | |||||||
\(758\) | −51.2893 | −1.86291 | ||||||||
\(759\) | −1.88725 | −0.0685028 | ||||||||
\(760\) | −7.58635 | −0.275186 | ||||||||
\(761\) | 1.57113 | 0.0569535 | 0.0284767 | − | 0.999594i | \(-0.490934\pi\) | ||||
0.0284767 | + | 0.999594i | \(0.490934\pi\) | |||||||
\(762\) | −5.88549 | −0.213209 | ||||||||
\(763\) | −62.0116 | −2.24497 | ||||||||
\(764\) | −34.8868 | −1.26216 | ||||||||
\(765\) | −2.28895 | −0.0827572 | ||||||||
\(766\) | −25.4641 | −0.920054 | ||||||||
\(767\) | 40.4601 | 1.46093 | ||||||||
\(768\) | 32.4575 | 1.17121 | ||||||||
\(769\) | 47.0999 | 1.69847 | 0.849233 | − | 0.528019i | \(-0.177065\pi\) | ||||
0.849233 | + | 0.528019i | \(0.177065\pi\) | |||||||
\(770\) | −47.6439 | −1.71697 | ||||||||
\(771\) | −1.22344 | −0.0440609 | ||||||||
\(772\) | 9.08433 | 0.326952 | ||||||||
\(773\) | 44.3393 | 1.59477 | 0.797387 | − | 0.603468i | \(-0.206215\pi\) | ||||
0.797387 | + | 0.603468i | \(0.206215\pi\) | |||||||
\(774\) | 4.81188 | 0.172959 | ||||||||
\(775\) | 1.01697 | 0.0365306 | ||||||||
\(776\) | −78.2309 | −2.80832 | ||||||||
\(777\) | 31.4282 | 1.12748 | ||||||||
\(778\) | 16.8027 | 0.602406 | ||||||||
\(779\) | 1.26726 | 0.0454042 | ||||||||
\(780\) | −39.9687 | −1.43111 | ||||||||
\(781\) | 24.6932 | 0.883593 | ||||||||
\(782\) | −2.24495 | −0.0802791 | ||||||||
\(783\) | 4.90674 | 0.175353 | ||||||||
\(784\) | 47.7088 | 1.70388 | ||||||||
\(785\) | 2.28895 | 0.0816962 | ||||||||
\(786\) | −55.3342 | −1.97371 | ||||||||
\(787\) | −4.97973 | −0.177508 | −0.0887540 | − | 0.996054i | \(-0.528289\pi\) | ||||
−0.0887540 | + | 0.996054i | \(0.528289\pi\) | |||||||
\(788\) | −7.55856 | −0.269262 | ||||||||
\(789\) | −1.42930 | −0.0508845 | ||||||||
\(790\) | −19.8071 | −0.704706 | ||||||||
\(791\) | −59.5735 | −2.11819 | ||||||||
\(792\) | 11.6615 | 0.414372 | ||||||||
\(793\) | −47.9727 | −1.70356 | ||||||||
\(794\) | 28.2533 | 1.00267 | ||||||||
\(795\) | −22.5751 | −0.800657 | ||||||||
\(796\) | 58.2796 | 2.06566 | ||||||||
\(797\) | 33.6541 | 1.19209 | 0.596045 | − | 0.802951i | \(-0.296738\pi\) | ||||
0.596045 | + | 0.802951i | \(0.296738\pi\) | |||||||
\(798\) | −5.91581 | −0.209417 | ||||||||
\(799\) | −2.28987 | −0.0810098 | ||||||||
\(800\) | −0.574304 | −0.0203047 | ||||||||
\(801\) | −11.6634 | −0.412107 | ||||||||
\(802\) | 64.1242 | 2.26431 | ||||||||
\(803\) | 0.822669 | 0.0290314 | ||||||||
\(804\) | 69.0897 | 2.43661 | ||||||||
\(805\) | 8.18691 | 0.288551 | ||||||||
\(806\) | −43.8057 | −1.54299 | ||||||||
\(807\) | 1.18644 | 0.0417647 | ||||||||
\(808\) | 77.4674 | 2.72529 | ||||||||
\(809\) | −10.9571 | −0.385231 | −0.192615 | − | 0.981274i | \(-0.561697\pi\) | ||||
−0.192615 | + | 0.981274i | \(0.561697\pi\) | |||||||
\(810\) | −5.71206 | −0.200701 | ||||||||
\(811\) | −20.2163 | −0.709890 | −0.354945 | − | 0.934887i | \(-0.615500\pi\) | ||||
−0.354945 | + | 0.934887i | \(0.615500\pi\) | |||||||
\(812\) | 82.4728 | 2.89423 | ||||||||
\(813\) | −9.17310 | −0.321715 | ||||||||
\(814\) | 41.3830 | 1.45047 | ||||||||
\(815\) | 44.2318 | 1.54937 | ||||||||
\(816\) | 5.41671 | 0.189623 | ||||||||
\(817\) | −1.14969 | −0.0402226 | ||||||||
\(818\) | −17.9768 | −0.628545 | ||||||||
\(819\) | −16.4223 | −0.573843 | ||||||||
\(820\) | 20.5665 | 0.718214 | ||||||||
\(821\) | 21.2270 | 0.740827 | 0.370413 | − | 0.928867i | \(-0.379216\pi\) | ||||
0.370413 | + | 0.928867i | \(0.379216\pi\) | |||||||
\(822\) | 0.565881 | 0.0197374 | ||||||||
\(823\) | 24.1802 | 0.842869 | 0.421435 | − | 0.906859i | \(-0.361527\pi\) | ||||
0.421435 | + | 0.906859i | \(0.361527\pi\) | |||||||
\(824\) | −51.2001 | −1.78364 | ||||||||
\(825\) | 0.502013 | 0.0174779 | ||||||||
\(826\) | 97.1891 | 3.38164 | ||||||||
\(827\) | −10.0475 | −0.349386 | −0.174693 | − | 0.984623i | \(-0.555893\pi\) | ||||
−0.174693 | + | 0.984623i | \(0.555893\pi\) | |||||||
\(828\) | −3.80305 | −0.132165 | ||||||||
\(829\) | 27.2764 | 0.947348 | 0.473674 | − | 0.880700i | \(-0.342927\pi\) | ||||
0.473674 | + | 0.880700i | \(0.342927\pi\) | |||||||
\(830\) | −14.7928 | −0.513465 | ||||||||
\(831\) | −17.7208 | −0.614729 | ||||||||
\(832\) | −20.0093 | −0.693696 | ||||||||
\(833\) | −8.80771 | −0.305169 | ||||||||
\(834\) | −20.9136 | −0.724178 | ||||||||
\(835\) | 18.2573 | 0.631821 | ||||||||
\(836\) | −5.28794 | −0.182887 | ||||||||
\(837\) | −4.24984 | −0.146896 | ||||||||
\(838\) | −36.5823 | −1.26372 | ||||||||
\(839\) | 48.9554 | 1.69013 | 0.845065 | − | 0.534664i | \(-0.179562\pi\) | ||||
0.845065 | + | 0.534664i | \(0.179562\pi\) | |||||||
\(840\) | −50.5876 | −1.74544 | ||||||||
\(841\) | −4.92386 | −0.169788 | ||||||||
\(842\) | −70.7276 | −2.43743 | ||||||||
\(843\) | 21.3320 | 0.734714 | ||||||||
\(844\) | 33.4287 | 1.15066 | ||||||||
\(845\) | 9.29514 | 0.319762 | ||||||||
\(846\) | −5.71436 | −0.196464 | ||||||||
\(847\) | 26.2365 | 0.901499 | ||||||||
\(848\) | 53.4231 | 1.83456 | ||||||||
\(849\) | 9.29149 | 0.318883 | ||||||||
\(850\) | 0.597161 | 0.0204825 | ||||||||
\(851\) | −7.11106 | −0.243764 | ||||||||
\(852\) | 49.7600 | 1.70475 | ||||||||
\(853\) | 10.0226 | 0.343168 | 0.171584 | − | 0.985170i | \(-0.445112\pi\) | ||||
0.171584 | + | 0.985170i | \(0.445112\pi\) | |||||||
\(854\) | −115.235 | −3.94326 | ||||||||
\(855\) | 1.36477 | 0.0466742 | ||||||||
\(856\) | 45.4074 | 1.55199 | ||||||||
\(857\) | −22.9102 | −0.782597 | −0.391299 | − | 0.920264i | \(-0.627974\pi\) | ||||
−0.391299 | + | 0.920264i | \(0.627974\pi\) | |||||||
\(858\) | −21.6241 | −0.738233 | ||||||||
\(859\) | 2.94992 | 0.100650 | 0.0503250 | − | 0.998733i | \(-0.483974\pi\) | ||||
0.0503250 | + | 0.998733i | \(0.483974\pi\) | |||||||
\(860\) | −18.6585 | −0.636250 | ||||||||
\(861\) | 8.45037 | 0.287988 | ||||||||
\(862\) | −44.0952 | −1.50189 | ||||||||
\(863\) | 11.2571 | 0.383198 | 0.191599 | − | 0.981473i | \(-0.438633\pi\) | ||||
0.191599 | + | 0.981473i | \(0.438633\pi\) | |||||||
\(864\) | 2.39997 | 0.0816488 | ||||||||
\(865\) | 26.9481 | 0.916262 | ||||||||
\(866\) | −29.7428 | −1.01070 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −71.4316 | −2.42455 | ||||||||
\(869\) | −7.27459 | −0.246773 | ||||||||
\(870\) | −28.0276 | −0.950226 | ||||||||
\(871\) | −67.5043 | −2.28729 | ||||||||
\(872\) | −86.6985 | −2.93598 | ||||||||
\(873\) | 14.0736 | 0.476319 | ||||||||
\(874\) | 1.33853 | 0.0452766 | ||||||||
\(875\) | 43.3254 | 1.46466 | ||||||||
\(876\) | 1.65778 | 0.0560114 | ||||||||
\(877\) | −22.0202 | −0.743570 | −0.371785 | − | 0.928319i | \(-0.621254\pi\) | ||||
−0.371785 | + | 0.928319i | \(0.621254\pi\) | |||||||
\(878\) | −99.0788 | −3.34375 | ||||||||
\(879\) | 10.1040 | 0.340800 | ||||||||
\(880\) | −26.0107 | −0.876820 | ||||||||
\(881\) | 18.7679 | 0.632306 | 0.316153 | − | 0.948708i | \(-0.397609\pi\) | ||||
0.316153 | + | 0.948708i | \(0.397609\pi\) | |||||||
\(882\) | −21.9796 | −0.740091 | ||||||||
\(883\) | −48.5145 | −1.63264 | −0.816321 | − | 0.577598i | \(-0.803990\pi\) | ||||
−0.816321 | + | 0.577598i | \(0.803990\pi\) | |||||||
\(884\) | −17.4616 | −0.587296 | ||||||||
\(885\) | −22.4214 | −0.753688 | ||||||||
\(886\) | −16.1021 | −0.540960 | ||||||||
\(887\) | 38.9880 | 1.30909 | 0.654544 | − | 0.756024i | \(-0.272860\pi\) | ||||
0.654544 | + | 0.756024i | \(0.272860\pi\) | |||||||
\(888\) | 43.9398 | 1.47452 | ||||||||
\(889\) | 9.37692 | 0.314492 | ||||||||
\(890\) | 66.6222 | 2.23318 | ||||||||
\(891\) | −2.09788 | −0.0702815 | ||||||||
\(892\) | 39.6357 | 1.32710 | ||||||||
\(893\) | 1.36532 | 0.0456887 | ||||||||
\(894\) | −8.68084 | −0.290331 | ||||||||
\(895\) | −31.8351 | −1.06413 | ||||||||
\(896\) | −67.1483 | −2.24327 | ||||||||
\(897\) | 3.71578 | 0.124066 | ||||||||
\(898\) | −61.9729 | −2.06806 | ||||||||
\(899\) | −20.8529 | −0.695483 | ||||||||
\(900\) | 1.01162 | 0.0337207 | ||||||||
\(901\) | −9.86265 | −0.328572 | ||||||||
\(902\) | 11.1270 | 0.370488 | ||||||||
\(903\) | −7.66642 | −0.255122 | ||||||||
\(904\) | −83.2897 | −2.77018 | ||||||||
\(905\) | 34.6108 | 1.15050 | ||||||||
\(906\) | 28.1048 | 0.933720 | ||||||||
\(907\) | 12.4223 | 0.412475 | 0.206238 | − | 0.978502i | \(-0.433878\pi\) | ||||
0.206238 | + | 0.978502i | \(0.433878\pi\) | |||||||
\(908\) | −64.8417 | −2.15185 | ||||||||
\(909\) | −13.9363 | −0.462236 | ||||||||
\(910\) | 93.8055 | 3.10962 | ||||||||
\(911\) | −2.11142 | −0.0699543 | −0.0349772 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349772 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(912\) | −3.22967 | −0.106945 | ||||||||
\(913\) | −5.43296 | −0.179805 | ||||||||
\(914\) | 64.5654 | 2.13563 | ||||||||
\(915\) | 26.5846 | 0.878860 | ||||||||
\(916\) | 35.7291 | 1.18052 | ||||||||
\(917\) | 88.1600 | 2.91130 | ||||||||
\(918\) | −2.49549 | −0.0823636 | ||||||||
\(919\) | 28.8910 | 0.953026 | 0.476513 | − | 0.879167i | \(-0.341901\pi\) | ||||
0.476513 | + | 0.879167i | \(0.341901\pi\) | |||||||
\(920\) | 11.4461 | 0.377368 | ||||||||
\(921\) | 21.0143 | 0.692445 | ||||||||
\(922\) | −15.2623 | −0.502636 | ||||||||
\(923\) | −48.6181 | −1.60029 | ||||||||
\(924\) | −35.2612 | −1.16001 | ||||||||
\(925\) | 1.89156 | 0.0621941 | ||||||||
\(926\) | 78.1080 | 2.56679 | ||||||||
\(927\) | 9.21081 | 0.302523 | ||||||||
\(928\) | 11.7761 | 0.386568 | ||||||||
\(929\) | −16.2154 | −0.532011 | −0.266005 | − | 0.963972i | \(-0.585704\pi\) | ||||
−0.266005 | + | 0.963972i | \(0.585704\pi\) | |||||||
\(930\) | 24.2754 | 0.796021 | ||||||||
\(931\) | 5.25153 | 0.172112 | ||||||||
\(932\) | 86.8507 | 2.84489 | ||||||||
\(933\) | −8.34780 | −0.273295 | ||||||||
\(934\) | 67.5814 | 2.21133 | ||||||||
\(935\) | 4.80194 | 0.157040 | ||||||||
\(936\) | −22.9601 | −0.750474 | ||||||||
\(937\) | 38.5316 | 1.25877 | 0.629386 | − | 0.777093i | \(-0.283306\pi\) | ||||
0.629386 | + | 0.777093i | \(0.283306\pi\) | |||||||
\(938\) | −162.152 | −5.29444 | ||||||||
\(939\) | 10.6184 | 0.346519 | ||||||||
\(940\) | 22.1580 | 0.722714 | ||||||||
\(941\) | 25.3666 | 0.826929 | 0.413464 | − | 0.910520i | \(-0.364319\pi\) | ||||
0.413464 | + | 0.910520i | \(0.364319\pi\) | |||||||
\(942\) | 2.49549 | 0.0813076 | ||||||||
\(943\) | −1.91201 | −0.0622637 | ||||||||
\(944\) | 53.0594 | 1.72694 | ||||||||
\(945\) | 9.10062 | 0.296043 | ||||||||
\(946\) | −10.0947 | −0.328208 | ||||||||
\(947\) | 50.3579 | 1.63641 | 0.818205 | − | 0.574926i | \(-0.194969\pi\) | ||||
0.818205 | + | 0.574926i | \(0.194969\pi\) | |||||||
\(948\) | −14.6592 | −0.476110 | ||||||||
\(949\) | −1.61974 | −0.0525791 | ||||||||
\(950\) | −0.356053 | −0.0115519 | ||||||||
\(951\) | −3.76018 | −0.121932 | ||||||||
\(952\) | −22.1008 | −0.716290 | ||||||||
\(953\) | −43.9038 | −1.42218 | −0.711092 | − | 0.703099i | \(-0.751799\pi\) | ||||
−0.711092 | + | 0.703099i | \(0.751799\pi\) | |||||||
\(954\) | −24.6122 | −0.796849 | ||||||||
\(955\) | −18.8893 | −0.611242 | ||||||||
\(956\) | −23.9690 | −0.775213 | ||||||||
\(957\) | −10.2937 | −0.332750 | ||||||||
\(958\) | 44.8838 | 1.45013 | ||||||||
\(959\) | −0.901578 | −0.0291135 | ||||||||
\(960\) | 11.0884 | 0.357875 | ||||||||
\(961\) | −12.9388 | −0.417381 | ||||||||
\(962\) | −81.4783 | −2.62697 | ||||||||
\(963\) | −8.16871 | −0.263233 | ||||||||
\(964\) | 111.259 | 3.58343 | ||||||||
\(965\) | 4.91866 | 0.158337 | ||||||||
\(966\) | 8.92566 | 0.287178 | ||||||||
\(967\) | 26.2750 | 0.844948 | 0.422474 | − | 0.906375i | \(-0.361162\pi\) | ||||
0.422474 | + | 0.906375i | \(0.361162\pi\) | |||||||
\(968\) | 36.6813 | 1.17898 | ||||||||
\(969\) | 0.596243 | 0.0191541 | ||||||||
\(970\) | −80.3893 | −2.58115 | ||||||||
\(971\) | 8.52272 | 0.273507 | 0.136754 | − | 0.990605i | \(-0.456333\pi\) | ||||
0.136754 | + | 0.990605i | \(0.456333\pi\) | |||||||
\(972\) | −4.22749 | −0.135597 | ||||||||
\(973\) | 33.3201 | 1.06819 | ||||||||
\(974\) | 46.0573 | 1.47577 | ||||||||
\(975\) | −0.988407 | −0.0316543 | ||||||||
\(976\) | −62.9114 | −2.01374 | ||||||||
\(977\) | −33.9487 | −1.08611 | −0.543057 | − | 0.839696i | \(-0.682733\pi\) | ||||
−0.543057 | + | 0.839696i | \(0.682733\pi\) | |||||||
\(978\) | 48.2230 | 1.54200 | ||||||||
\(979\) | 24.4684 | 0.782015 | ||||||||
\(980\) | 85.2280 | 2.72251 | ||||||||
\(981\) | 15.5969 | 0.497971 | ||||||||
\(982\) | −57.2418 | −1.82666 | ||||||||
\(983\) | −0.748729 | −0.0238807 | −0.0119404 | − | 0.999929i | \(-0.503801\pi\) | ||||
−0.0119404 | + | 0.999929i | \(0.503801\pi\) | |||||||
\(984\) | 11.8145 | 0.376631 | ||||||||
\(985\) | −4.09254 | −0.130399 | ||||||||
\(986\) | −12.2448 | −0.389952 | ||||||||
\(987\) | 9.10428 | 0.289792 | ||||||||
\(988\) | 10.4113 | 0.331229 | ||||||||
\(989\) | 1.73463 | 0.0551581 | ||||||||
\(990\) | 11.9832 | 0.380851 | ||||||||
\(991\) | −28.3216 | −0.899665 | −0.449832 | − | 0.893113i | \(-0.648516\pi\) | ||||
−0.449832 | + | 0.893113i | \(0.648516\pi\) | |||||||
\(992\) | −10.1995 | −0.323835 | ||||||||
\(993\) | −21.3573 | −0.677752 | ||||||||
\(994\) | −116.785 | −3.70421 | ||||||||
\(995\) | 31.5551 | 1.00036 | ||||||||
\(996\) | −10.9481 | −0.346905 | ||||||||
\(997\) | −4.47201 | −0.141630 | −0.0708149 | − | 0.997489i | \(-0.522560\pi\) | ||||
−0.0708149 | + | 0.997489i | \(0.522560\pi\) | |||||||
\(998\) | −35.8985 | −1.13635 | ||||||||
\(999\) | −7.90469 | −0.250093 |
(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 | 8007.2.a.g.1.5 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.g.1.5 | ✓ | 56 | 1.1 | even | 1 | trivial |