Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34491 | −1.65810 | −0.829052 | − | 0.559171i | \(-0.811119\pi\) | ||||
−0.829052 | + | 0.559171i | \(0.811119\pi\) | |||||||
\(3\) | −2.19404 | −1.26673 | −0.633365 | − | 0.773853i | \(-0.718327\pi\) | ||||
−0.633365 | + | 0.773853i | \(0.718327\pi\) | |||||||
\(4\) | 3.49862 | 1.74931 | ||||||||
\(5\) | 1.59097 | 0.711504 | 0.355752 | − | 0.934580i | \(-0.384225\pi\) | ||||
0.355752 | + | 0.934580i | \(0.384225\pi\) | |||||||
\(6\) | 5.14484 | 2.10037 | ||||||||
\(7\) | −2.37576 | −0.897955 | −0.448977 | − | 0.893543i | \(-0.648212\pi\) | ||||
−0.448977 | + | 0.893543i | \(0.648212\pi\) | |||||||
\(8\) | −3.51413 | −1.24243 | ||||||||
\(9\) | 1.81381 | 0.604605 | ||||||||
\(10\) | −3.73069 | −1.17975 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −7.67611 | −2.21590 | ||||||||
\(13\) | −5.53511 | −1.53516 | −0.767582 | − | 0.640951i | \(-0.778540\pi\) | ||||
−0.767582 | + | 0.640951i | \(0.778540\pi\) | |||||||
\(14\) | 5.57096 | 1.48890 | ||||||||
\(15\) | −3.49066 | −0.901284 | ||||||||
\(16\) | 1.24310 | 0.310775 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −4.25324 | −1.00250 | ||||||||
\(19\) | −1.91161 | −0.438553 | −0.219277 | − | 0.975663i | \(-0.570370\pi\) | ||||
−0.219277 | + | 0.975663i | \(0.570370\pi\) | |||||||
\(20\) | 5.56620 | 1.24464 | ||||||||
\(21\) | 5.21252 | 1.13747 | ||||||||
\(22\) | 2.34491 | 0.499937 | ||||||||
\(23\) | −0.773032 | −0.161188 | −0.0805942 | − | 0.996747i | \(-0.525682\pi\) | ||||
−0.0805942 | + | 0.996747i | \(0.525682\pi\) | |||||||
\(24\) | 7.71015 | 1.57383 | ||||||||
\(25\) | −2.46881 | −0.493762 | ||||||||
\(26\) | 12.9794 | 2.54546 | ||||||||
\(27\) | 2.60254 | 0.500859 | ||||||||
\(28\) | −8.31190 | −1.57080 | ||||||||
\(29\) | −9.38899 | −1.74349 | −0.871745 | − | 0.489959i | \(-0.837012\pi\) | ||||
−0.871745 | + | 0.489959i | \(0.837012\pi\) | |||||||
\(30\) | 8.18529 | 1.49442 | ||||||||
\(31\) | −4.00423 | −0.719181 | −0.359591 | − | 0.933110i | \(-0.617084\pi\) | ||||
−0.359591 | + | 0.933110i | \(0.617084\pi\) | |||||||
\(32\) | 4.11331 | 0.727137 | ||||||||
\(33\) | 2.19404 | 0.381933 | ||||||||
\(34\) | 2.34491 | 0.402149 | ||||||||
\(35\) | −3.77977 | −0.638898 | ||||||||
\(36\) | 6.34585 | 1.05764 | ||||||||
\(37\) | 9.93142 | 1.63272 | 0.816358 | − | 0.577546i | \(-0.195990\pi\) | ||||
0.816358 | + | 0.577546i | \(0.195990\pi\) | |||||||
\(38\) | 4.48256 | 0.727167 | ||||||||
\(39\) | 12.1443 | 1.94464 | ||||||||
\(40\) | −5.59089 | −0.883997 | ||||||||
\(41\) | −1.96661 | −0.307133 | −0.153566 | − | 0.988138i | \(-0.549076\pi\) | ||||
−0.153566 | + | 0.988138i | \(0.549076\pi\) | |||||||
\(42\) | −12.2229 | −1.88604 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −3.49862 | −0.527437 | ||||||||
\(45\) | 2.88573 | 0.430179 | ||||||||
\(46\) | 1.81269 | 0.267267 | ||||||||
\(47\) | 9.42033 | 1.37410 | 0.687048 | − | 0.726612i | \(-0.258906\pi\) | ||||
0.687048 | + | 0.726612i | \(0.258906\pi\) | |||||||
\(48\) | −2.72741 | −0.393668 | ||||||||
\(49\) | −1.35574 | −0.193677 | ||||||||
\(50\) | 5.78914 | 0.818709 | ||||||||
\(51\) | 2.19404 | 0.307227 | ||||||||
\(52\) | −19.3652 | −2.68548 | ||||||||
\(53\) | 12.4080 | 1.70436 | 0.852182 | − | 0.523246i | \(-0.175279\pi\) | ||||
0.852182 | + | 0.523246i | \(0.175279\pi\) | |||||||
\(54\) | −6.10273 | −0.830476 | ||||||||
\(55\) | −1.59097 | −0.214527 | ||||||||
\(56\) | 8.34875 | 1.11565 | ||||||||
\(57\) | 4.19415 | 0.555528 | ||||||||
\(58\) | 22.0164 | 2.89089 | ||||||||
\(59\) | 10.4087 | 1.35510 | 0.677549 | − | 0.735477i | \(-0.263042\pi\) | ||||
0.677549 | + | 0.735477i | \(0.263042\pi\) | |||||||
\(60\) | −12.2125 | −1.57662 | ||||||||
\(61\) | 4.26777 | 0.546432 | 0.273216 | − | 0.961953i | \(-0.411913\pi\) | ||||
0.273216 | + | 0.961953i | \(0.411913\pi\) | |||||||
\(62\) | 9.38958 | 1.19248 | ||||||||
\(63\) | −4.30920 | −0.542908 | ||||||||
\(64\) | −12.1315 | −1.51644 | ||||||||
\(65\) | −8.80621 | −1.09228 | ||||||||
\(66\) | −5.14484 | −0.633285 | ||||||||
\(67\) | 12.6223 | 1.54205 | 0.771027 | − | 0.636803i | \(-0.219743\pi\) | ||||
0.771027 | + | 0.636803i | \(0.219743\pi\) | |||||||
\(68\) | −3.49862 | −0.424270 | ||||||||
\(69\) | 1.69606 | 0.204182 | ||||||||
\(70\) | 8.86324 | 1.05936 | ||||||||
\(71\) | 2.28947 | 0.271710 | 0.135855 | − | 0.990729i | \(-0.456622\pi\) | ||||
0.135855 | + | 0.990729i | \(0.456622\pi\) | |||||||
\(72\) | −6.37398 | −0.751181 | ||||||||
\(73\) | 6.33403 | 0.741342 | 0.370671 | − | 0.928764i | \(-0.379128\pi\) | ||||
0.370671 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(74\) | −23.2883 | −2.70721 | ||||||||
\(75\) | 5.41667 | 0.625463 | ||||||||
\(76\) | −6.68799 | −0.767165 | ||||||||
\(77\) | 2.37576 | 0.270744 | ||||||||
\(78\) | −28.4772 | −3.22441 | ||||||||
\(79\) | −6.22362 | −0.700212 | −0.350106 | − | 0.936710i | \(-0.613855\pi\) | ||||
−0.350106 | + | 0.936710i | \(0.613855\pi\) | |||||||
\(80\) | 1.97773 | 0.221117 | ||||||||
\(81\) | −11.1515 | −1.23906 | ||||||||
\(82\) | 4.61153 | 0.509258 | ||||||||
\(83\) | −8.00954 | −0.879161 | −0.439581 | − | 0.898203i | \(-0.644873\pi\) | ||||
−0.439581 | + | 0.898203i | \(0.644873\pi\) | |||||||
\(84\) | 18.2366 | 1.98978 | ||||||||
\(85\) | −1.59097 | −0.172565 | ||||||||
\(86\) | 2.34491 | 0.252859 | ||||||||
\(87\) | 20.5998 | 2.20853 | ||||||||
\(88\) | 3.51413 | 0.374608 | ||||||||
\(89\) | 16.2151 | 1.71879 | 0.859396 | − | 0.511310i | \(-0.170840\pi\) | ||||
0.859396 | + | 0.511310i | \(0.170840\pi\) | |||||||
\(90\) | −6.76678 | −0.713281 | ||||||||
\(91\) | 13.1501 | 1.37851 | ||||||||
\(92\) | −2.70454 | −0.281968 | ||||||||
\(93\) | 8.78545 | 0.911008 | ||||||||
\(94\) | −22.0899 | −2.27840 | ||||||||
\(95\) | −3.04132 | −0.312032 | ||||||||
\(96\) | −9.02476 | −0.921086 | ||||||||
\(97\) | −0.975893 | −0.0990870 | −0.0495435 | − | 0.998772i | \(-0.515777\pi\) | ||||
−0.0495435 | + | 0.998772i | \(0.515777\pi\) | |||||||
\(98\) | 3.17910 | 0.321137 | ||||||||
\(99\) | −1.81381 | −0.182295 | ||||||||
\(100\) | −8.63742 | −0.863742 | ||||||||
\(101\) | 16.0598 | 1.59801 | 0.799007 | − | 0.601322i | \(-0.205359\pi\) | ||||
0.799007 | + | 0.601322i | \(0.205359\pi\) | |||||||
\(102\) | −5.14484 | −0.509415 | ||||||||
\(103\) | −15.6825 | −1.54524 | −0.772620 | − | 0.634869i | \(-0.781054\pi\) | ||||
−0.772620 | + | 0.634869i | \(0.781054\pi\) | |||||||
\(104\) | 19.4511 | 1.90734 | ||||||||
\(105\) | 8.29298 | 0.809312 | ||||||||
\(106\) | −29.0956 | −2.82601 | ||||||||
\(107\) | −11.1554 | −1.07843 | −0.539217 | − | 0.842167i | \(-0.681280\pi\) | ||||
−0.539217 | + | 0.842167i | \(0.681280\pi\) | |||||||
\(108\) | 9.10530 | 0.876157 | ||||||||
\(109\) | 9.34647 | 0.895229 | 0.447615 | − | 0.894227i | \(-0.352274\pi\) | ||||
0.447615 | + | 0.894227i | \(0.352274\pi\) | |||||||
\(110\) | 3.73069 | 0.355707 | ||||||||
\(111\) | −21.7899 | −2.06821 | ||||||||
\(112\) | −2.95331 | −0.279062 | ||||||||
\(113\) | 10.2119 | 0.960652 | 0.480326 | − | 0.877090i | \(-0.340518\pi\) | ||||
0.480326 | + | 0.877090i | \(0.340518\pi\) | |||||||
\(114\) | −9.83491 | −0.921124 | ||||||||
\(115\) | −1.22987 | −0.114686 | ||||||||
\(116\) | −32.8485 | −3.04991 | ||||||||
\(117\) | −10.0397 | −0.928167 | ||||||||
\(118\) | −24.4075 | −2.24689 | ||||||||
\(119\) | 2.37576 | 0.217786 | ||||||||
\(120\) | 12.2666 | 1.11978 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −10.0076 | −0.906042 | ||||||||
\(123\) | 4.31482 | 0.389054 | ||||||||
\(124\) | −14.0093 | −1.25807 | ||||||||
\(125\) | −11.8827 | −1.06282 | ||||||||
\(126\) | 10.1047 | 0.900197 | ||||||||
\(127\) | 15.6960 | 1.39280 | 0.696398 | − | 0.717656i | \(-0.254785\pi\) | ||||
0.696398 | + | 0.717656i | \(0.254785\pi\) | |||||||
\(128\) | 20.2208 | 1.78728 | ||||||||
\(129\) | 2.19404 | 0.193175 | ||||||||
\(130\) | 20.6498 | 1.81111 | ||||||||
\(131\) | 19.7724 | 1.72752 | 0.863760 | − | 0.503904i | \(-0.168103\pi\) | ||||
0.863760 | + | 0.503904i | \(0.168103\pi\) | |||||||
\(132\) | 7.67611 | 0.668120 | ||||||||
\(133\) | 4.54153 | 0.393801 | ||||||||
\(134\) | −29.5981 | −2.55689 | ||||||||
\(135\) | 4.14057 | 0.356363 | ||||||||
\(136\) | 3.51413 | 0.301334 | ||||||||
\(137\) | −0.240622 | −0.0205578 | −0.0102789 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102789 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(138\) | −3.97712 | −0.338555 | ||||||||
\(139\) | −8.31531 | −0.705295 | −0.352648 | − | 0.935756i | \(-0.614719\pi\) | ||||
−0.352648 | + | 0.935756i | \(0.614719\pi\) | |||||||
\(140\) | −13.2240 | −1.11763 | ||||||||
\(141\) | −20.6686 | −1.74061 | ||||||||
\(142\) | −5.36860 | −0.450523 | ||||||||
\(143\) | 5.53511 | 0.462869 | ||||||||
\(144\) | 2.25475 | 0.187896 | ||||||||
\(145\) | −14.9376 | −1.24050 | ||||||||
\(146\) | −14.8527 | −1.22922 | ||||||||
\(147\) | 2.97455 | 0.245337 | ||||||||
\(148\) | 34.7463 | 2.85613 | ||||||||
\(149\) | −16.0036 | −1.31107 | −0.655533 | − | 0.755167i | \(-0.727556\pi\) | ||||
−0.655533 | + | 0.755167i | \(0.727556\pi\) | |||||||
\(150\) | −12.7016 | −1.03708 | ||||||||
\(151\) | −7.21937 | −0.587504 | −0.293752 | − | 0.955882i | \(-0.594904\pi\) | ||||
−0.293752 | + | 0.955882i | \(0.594904\pi\) | |||||||
\(152\) | 6.71765 | 0.544873 | ||||||||
\(153\) | −1.81381 | −0.146638 | ||||||||
\(154\) | −5.57096 | −0.448921 | ||||||||
\(155\) | −6.37062 | −0.511700 | ||||||||
\(156\) | 42.4881 | 3.40177 | ||||||||
\(157\) | 0.315637 | 0.0251906 | 0.0125953 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125953 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(158\) | 14.5939 | 1.16103 | ||||||||
\(159\) | −27.2236 | −2.15897 | ||||||||
\(160\) | 6.54415 | 0.517361 | ||||||||
\(161\) | 1.83654 | 0.144740 | ||||||||
\(162\) | 26.1494 | 2.05449 | ||||||||
\(163\) | −13.3783 | −1.04787 | −0.523936 | − | 0.851758i | \(-0.675537\pi\) | ||||
−0.523936 | + | 0.851758i | \(0.675537\pi\) | |||||||
\(164\) | −6.88042 | −0.537270 | ||||||||
\(165\) | 3.49066 | 0.271747 | ||||||||
\(166\) | 18.7817 | 1.45774 | ||||||||
\(167\) | 0.808183 | 0.0625391 | 0.0312695 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312695 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(168\) | −18.3175 | −1.41323 | ||||||||
\(169\) | 17.6375 | 1.35673 | ||||||||
\(170\) | 3.73069 | 0.286131 | ||||||||
\(171\) | −3.46730 | −0.265151 | ||||||||
\(172\) | −3.49862 | −0.266767 | ||||||||
\(173\) | −13.1291 | −0.998189 | −0.499095 | − | 0.866547i | \(-0.666334\pi\) | ||||
−0.499095 | + | 0.866547i | \(0.666334\pi\) | |||||||
\(174\) | −48.3048 | −3.66198 | ||||||||
\(175\) | 5.86531 | 0.443376 | ||||||||
\(176\) | −1.24310 | −0.0937021 | ||||||||
\(177\) | −22.8371 | −1.71654 | ||||||||
\(178\) | −38.0229 | −2.84994 | ||||||||
\(179\) | −18.2225 | −1.36201 | −0.681006 | − | 0.732278i | \(-0.738457\pi\) | ||||
−0.681006 | + | 0.732278i | \(0.738457\pi\) | |||||||
\(180\) | 10.0961 | 0.752516 | ||||||||
\(181\) | −2.66599 | −0.198162 | −0.0990808 | − | 0.995079i | \(-0.531590\pi\) | ||||
−0.0990808 | + | 0.995079i | \(0.531590\pi\) | |||||||
\(182\) | −30.8359 | −2.28571 | ||||||||
\(183\) | −9.36367 | −0.692182 | ||||||||
\(184\) | 2.71654 | 0.200266 | ||||||||
\(185\) | 15.8006 | 1.16168 | ||||||||
\(186\) | −20.6011 | −1.51055 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 32.9582 | 2.40372 | ||||||||
\(189\) | −6.18302 | −0.449749 | ||||||||
\(190\) | 7.13162 | 0.517382 | ||||||||
\(191\) | −6.94712 | −0.502676 | −0.251338 | − | 0.967899i | \(-0.580871\pi\) | ||||
−0.251338 | + | 0.967899i | \(0.580871\pi\) | |||||||
\(192\) | 26.6171 | 1.92092 | ||||||||
\(193\) | 25.0618 | 1.80399 | 0.901994 | − | 0.431748i | \(-0.142103\pi\) | ||||
0.901994 | + | 0.431748i | \(0.142103\pi\) | |||||||
\(194\) | 2.28839 | 0.164297 | ||||||||
\(195\) | 19.3212 | 1.38362 | ||||||||
\(196\) | −4.74323 | −0.338802 | ||||||||
\(197\) | 4.84872 | 0.345457 | 0.172729 | − | 0.984969i | \(-0.444742\pi\) | ||||
0.172729 | + | 0.984969i | \(0.444742\pi\) | |||||||
\(198\) | 4.25324 | 0.302264 | ||||||||
\(199\) | 4.56775 | 0.323799 | 0.161899 | − | 0.986807i | \(-0.448238\pi\) | ||||
0.161899 | + | 0.986807i | \(0.448238\pi\) | |||||||
\(200\) | 8.67572 | 0.613466 | ||||||||
\(201\) | −27.6937 | −1.95337 | ||||||||
\(202\) | −37.6589 | −2.64967 | ||||||||
\(203\) | 22.3060 | 1.56558 | ||||||||
\(204\) | 7.67611 | 0.537435 | ||||||||
\(205\) | −3.12882 | −0.218526 | ||||||||
\(206\) | 36.7740 | 2.56217 | ||||||||
\(207\) | −1.40214 | −0.0974552 | ||||||||
\(208\) | −6.88069 | −0.477090 | ||||||||
\(209\) | 1.91161 | 0.132229 | ||||||||
\(210\) | −19.4463 | −1.34192 | ||||||||
\(211\) | −22.0323 | −1.51677 | −0.758384 | − | 0.651808i | \(-0.774011\pi\) | ||||
−0.758384 | + | 0.651808i | \(0.774011\pi\) | |||||||
\(212\) | 43.4107 | 2.98146 | ||||||||
\(213\) | −5.02318 | −0.344183 | ||||||||
\(214\) | 26.1585 | 1.78816 | ||||||||
\(215\) | −1.59097 | −0.108503 | ||||||||
\(216\) | −9.14567 | −0.622284 | ||||||||
\(217\) | 9.51311 | 0.645792 | ||||||||
\(218\) | −21.9167 | −1.48438 | ||||||||
\(219\) | −13.8971 | −0.939080 | ||||||||
\(220\) | −5.56620 | −0.375273 | ||||||||
\(221\) | 5.53511 | 0.372332 | ||||||||
\(222\) | 51.0955 | 3.42931 | ||||||||
\(223\) | −16.6504 | −1.11500 | −0.557498 | − | 0.830178i | \(-0.688239\pi\) | ||||
−0.557498 | + | 0.830178i | \(0.688239\pi\) | |||||||
\(224\) | −9.77225 | −0.652936 | ||||||||
\(225\) | −4.47796 | −0.298531 | ||||||||
\(226\) | −23.9459 | −1.59286 | ||||||||
\(227\) | −11.9907 | −0.795850 | −0.397925 | − | 0.917418i | \(-0.630270\pi\) | ||||
−0.397925 | + | 0.917418i | \(0.630270\pi\) | |||||||
\(228\) | 14.6737 | 0.971791 | ||||||||
\(229\) | −19.6798 | −1.30048 | −0.650238 | − | 0.759731i | \(-0.725331\pi\) | ||||
−0.650238 | + | 0.759731i | \(0.725331\pi\) | |||||||
\(230\) | 2.88394 | 0.190162 | ||||||||
\(231\) | −5.21252 | −0.342959 | ||||||||
\(232\) | 32.9941 | 2.16617 | ||||||||
\(233\) | −7.11002 | −0.465793 | −0.232896 | − | 0.972502i | \(-0.574820\pi\) | ||||
−0.232896 | + | 0.972502i | \(0.574820\pi\) | |||||||
\(234\) | 23.5421 | 1.53900 | ||||||||
\(235\) | 14.9875 | 0.977676 | ||||||||
\(236\) | 36.4161 | 2.37049 | ||||||||
\(237\) | 13.6549 | 0.886980 | ||||||||
\(238\) | −5.57096 | −0.361112 | ||||||||
\(239\) | 17.9261 | 1.15955 | 0.579773 | − | 0.814778i | \(-0.303141\pi\) | ||||
0.579773 | + | 0.814778i | \(0.303141\pi\) | |||||||
\(240\) | −4.33923 | −0.280096 | ||||||||
\(241\) | −0.335908 | −0.0216378 | −0.0108189 | − | 0.999941i | \(-0.503444\pi\) | ||||
−0.0108189 | + | 0.999941i | \(0.503444\pi\) | |||||||
\(242\) | −2.34491 | −0.150737 | ||||||||
\(243\) | 16.6593 | 1.06869 | ||||||||
\(244\) | 14.9313 | 0.955879 | ||||||||
\(245\) | −2.15695 | −0.137802 | ||||||||
\(246\) | −10.1179 | −0.645093 | ||||||||
\(247\) | 10.5810 | 0.673251 | ||||||||
\(248\) | 14.0714 | 0.893535 | ||||||||
\(249\) | 17.5733 | 1.11366 | ||||||||
\(250\) | 27.8638 | 1.76226 | ||||||||
\(251\) | −8.79768 | −0.555304 | −0.277652 | − | 0.960682i | \(-0.589556\pi\) | ||||
−0.277652 | + | 0.960682i | \(0.589556\pi\) | |||||||
\(252\) | −15.0762 | −0.949714 | ||||||||
\(253\) | 0.773032 | 0.0486001 | ||||||||
\(254\) | −36.8058 | −2.30940 | ||||||||
\(255\) | 3.49066 | 0.218593 | ||||||||
\(256\) | −23.1530 | −1.44706 | ||||||||
\(257\) | 13.3127 | 0.830422 | 0.415211 | − | 0.909725i | \(-0.363708\pi\) | ||||
0.415211 | + | 0.909725i | \(0.363708\pi\) | |||||||
\(258\) | −5.14484 | −0.320303 | ||||||||
\(259\) | −23.5947 | −1.46610 | ||||||||
\(260\) | −30.8096 | −1.91073 | ||||||||
\(261\) | −17.0299 | −1.05412 | ||||||||
\(262\) | −46.3645 | −2.86441 | ||||||||
\(263\) | 1.27144 | 0.0784001 | 0.0392000 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0392000 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(264\) | −7.71015 | −0.474527 | ||||||||
\(265\) | 19.7407 | 1.21266 | ||||||||
\(266\) | −10.6495 | −0.652963 | ||||||||
\(267\) | −35.5765 | −2.17725 | ||||||||
\(268\) | 44.1605 | 2.69753 | ||||||||
\(269\) | −9.93394 | −0.605683 | −0.302841 | − | 0.953041i | \(-0.597935\pi\) | ||||
−0.302841 | + | 0.953041i | \(0.597935\pi\) | |||||||
\(270\) | −9.70927 | −0.590887 | ||||||||
\(271\) | 23.1776 | 1.40794 | 0.703970 | − | 0.710229i | \(-0.251409\pi\) | ||||
0.703970 | + | 0.710229i | \(0.251409\pi\) | |||||||
\(272\) | −1.24310 | −0.0753739 | ||||||||
\(273\) | −28.8519 | −1.74620 | ||||||||
\(274\) | 0.564239 | 0.0340869 | ||||||||
\(275\) | 2.46881 | 0.148875 | ||||||||
\(276\) | 5.93388 | 0.357178 | ||||||||
\(277\) | 9.30533 | 0.559103 | 0.279552 | − | 0.960131i | \(-0.409814\pi\) | ||||
0.279552 | + | 0.960131i | \(0.409814\pi\) | |||||||
\(278\) | 19.4987 | 1.16945 | ||||||||
\(279\) | −7.26293 | −0.434820 | ||||||||
\(280\) | 13.2826 | 0.793789 | ||||||||
\(281\) | 14.6979 | 0.876801 | 0.438400 | − | 0.898780i | \(-0.355545\pi\) | ||||
0.438400 | + | 0.898780i | \(0.355545\pi\) | |||||||
\(282\) | 48.4661 | 2.88611 | ||||||||
\(283\) | 1.00619 | 0.0598119 | 0.0299060 | − | 0.999553i | \(-0.490479\pi\) | ||||
0.0299060 | + | 0.999553i | \(0.490479\pi\) | |||||||
\(284\) | 8.00997 | 0.475304 | ||||||||
\(285\) | 6.67277 | 0.395261 | ||||||||
\(286\) | −12.9794 | −0.767486 | ||||||||
\(287\) | 4.67220 | 0.275791 | ||||||||
\(288\) | 7.46077 | 0.439630 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 35.0274 | 2.05688 | ||||||||
\(291\) | 2.14115 | 0.125516 | ||||||||
\(292\) | 22.1603 | 1.29684 | ||||||||
\(293\) | −15.9111 | −0.929537 | −0.464769 | − | 0.885432i | \(-0.653862\pi\) | ||||
−0.464769 | + | 0.885432i | \(0.653862\pi\) | |||||||
\(294\) | −6.97507 | −0.406794 | ||||||||
\(295\) | 16.5600 | 0.964158 | ||||||||
\(296\) | −34.9003 | −2.02854 | ||||||||
\(297\) | −2.60254 | −0.151015 | ||||||||
\(298\) | 37.5270 | 2.17388 | ||||||||
\(299\) | 4.27882 | 0.247450 | ||||||||
\(300\) | 18.9509 | 1.09413 | ||||||||
\(301\) | 2.37576 | 0.136937 | ||||||||
\(302\) | 16.9288 | 0.974143 | ||||||||
\(303\) | −35.2359 | −2.02425 | ||||||||
\(304\) | −2.37632 | −0.136291 | ||||||||
\(305\) | 6.78991 | 0.388789 | ||||||||
\(306\) | 4.25324 | 0.243141 | ||||||||
\(307\) | 28.4272 | 1.62243 | 0.811214 | − | 0.584749i | \(-0.198807\pi\) | ||||
0.811214 | + | 0.584749i | \(0.198807\pi\) | |||||||
\(308\) | 8.31190 | 0.473614 | ||||||||
\(309\) | 34.4080 | 1.95740 | ||||||||
\(310\) | 14.9386 | 0.848453 | ||||||||
\(311\) | 11.0735 | 0.627920 | 0.313960 | − | 0.949436i | \(-0.398344\pi\) | ||||
0.313960 | + | 0.949436i | \(0.398344\pi\) | |||||||
\(312\) | −42.6765 | −2.41608 | ||||||||
\(313\) | 5.04811 | 0.285336 | 0.142668 | − | 0.989771i | \(-0.454432\pi\) | ||||
0.142668 | + | 0.989771i | \(0.454432\pi\) | |||||||
\(314\) | −0.740142 | −0.0417686 | ||||||||
\(315\) | −6.85581 | −0.386281 | ||||||||
\(316\) | −21.7741 | −1.22489 | ||||||||
\(317\) | 10.4228 | 0.585405 | 0.292702 | − | 0.956204i | \(-0.405445\pi\) | ||||
0.292702 | + | 0.956204i | \(0.405445\pi\) | |||||||
\(318\) | 63.8369 | 3.57979 | ||||||||
\(319\) | 9.38899 | 0.525682 | ||||||||
\(320\) | −19.3009 | −1.07896 | ||||||||
\(321\) | 24.4754 | 1.36609 | ||||||||
\(322\) | −4.30653 | −0.239994 | ||||||||
\(323\) | 1.91161 | 0.106365 | ||||||||
\(324\) | −39.0149 | −2.16750 | ||||||||
\(325\) | 13.6651 | 0.758005 | ||||||||
\(326\) | 31.3710 | 1.73748 | ||||||||
\(327\) | −20.5065 | −1.13401 | ||||||||
\(328\) | 6.91093 | 0.381592 | ||||||||
\(329\) | −22.3805 | −1.23388 | ||||||||
\(330\) | −8.18529 | −0.450585 | ||||||||
\(331\) | 6.71947 | 0.369336 | 0.184668 | − | 0.982801i | \(-0.440879\pi\) | ||||
0.184668 | + | 0.982801i | \(0.440879\pi\) | |||||||
\(332\) | −28.0223 | −1.53793 | ||||||||
\(333\) | 18.0138 | 0.987148 | ||||||||
\(334\) | −1.89512 | −0.103696 | ||||||||
\(335\) | 20.0816 | 1.09718 | ||||||||
\(336\) | 6.47968 | 0.353496 | ||||||||
\(337\) | 26.3681 | 1.43636 | 0.718181 | − | 0.695857i | \(-0.244975\pi\) | ||||
0.718181 | + | 0.695857i | \(0.244975\pi\) | |||||||
\(338\) | −41.3583 | −2.24960 | ||||||||
\(339\) | −22.4053 | −1.21689 | ||||||||
\(340\) | −5.56620 | −0.301870 | ||||||||
\(341\) | 4.00423 | 0.216841 | ||||||||
\(342\) | 8.13053 | 0.439649 | ||||||||
\(343\) | 19.8513 | 1.07187 | ||||||||
\(344\) | 3.51413 | 0.189469 | ||||||||
\(345\) | 2.69839 | 0.145276 | ||||||||
\(346\) | 30.7867 | 1.65510 | ||||||||
\(347\) | 1.93372 | 0.103808 | 0.0519038 | − | 0.998652i | \(-0.483471\pi\) | ||||
0.0519038 | + | 0.998652i | \(0.483471\pi\) | |||||||
\(348\) | 72.0709 | 3.86341 | ||||||||
\(349\) | 3.93316 | 0.210537 | 0.105269 | − | 0.994444i | \(-0.466430\pi\) | ||||
0.105269 | + | 0.994444i | \(0.466430\pi\) | |||||||
\(350\) | −13.7536 | −0.735163 | ||||||||
\(351\) | −14.4053 | −0.768901 | ||||||||
\(352\) | −4.11331 | −0.219240 | ||||||||
\(353\) | 18.0015 | 0.958122 | 0.479061 | − | 0.877782i | \(-0.340977\pi\) | ||||
0.479061 | + | 0.877782i | \(0.340977\pi\) | |||||||
\(354\) | 53.5511 | 2.84621 | ||||||||
\(355\) | 3.64248 | 0.193323 | ||||||||
\(356\) | 56.7303 | 3.00670 | ||||||||
\(357\) | −5.21252 | −0.275876 | ||||||||
\(358\) | 42.7301 | 2.25836 | ||||||||
\(359\) | −21.5735 | −1.13861 | −0.569304 | − | 0.822127i | \(-0.692787\pi\) | ||||
−0.569304 | + | 0.822127i | \(0.692787\pi\) | |||||||
\(360\) | −10.1408 | −0.534469 | ||||||||
\(361\) | −15.3458 | −0.807671 | ||||||||
\(362\) | 6.25152 | 0.328573 | ||||||||
\(363\) | −2.19404 | −0.115157 | ||||||||
\(364\) | 46.0073 | 2.41144 | ||||||||
\(365\) | 10.0773 | 0.527468 | ||||||||
\(366\) | 21.9570 | 1.14771 | ||||||||
\(367\) | 17.2403 | 0.899936 | 0.449968 | − | 0.893045i | \(-0.351435\pi\) | ||||
0.449968 | + | 0.893045i | \(0.351435\pi\) | |||||||
\(368\) | −0.960955 | −0.0500932 | ||||||||
\(369\) | −3.56706 | −0.185694 | ||||||||
\(370\) | −37.0511 | −1.92619 | ||||||||
\(371\) | −29.4784 | −1.53044 | ||||||||
\(372\) | 30.7369 | 1.59364 | ||||||||
\(373\) | 2.79102 | 0.144514 | 0.0722569 | − | 0.997386i | \(-0.476980\pi\) | ||||
0.0722569 | + | 0.997386i | \(0.476980\pi\) | |||||||
\(374\) | −2.34491 | −0.121253 | ||||||||
\(375\) | 26.0710 | 1.34630 | ||||||||
\(376\) | −33.1043 | −1.70722 | ||||||||
\(377\) | 51.9691 | 2.67654 | ||||||||
\(378\) | 14.4987 | 0.745730 | ||||||||
\(379\) | 18.5682 | 0.953783 | 0.476891 | − | 0.878962i | \(-0.341764\pi\) | ||||
0.476891 | + | 0.878962i | \(0.341764\pi\) | |||||||
\(380\) | −10.6404 | −0.545841 | ||||||||
\(381\) | −34.4377 | −1.76430 | ||||||||
\(382\) | 16.2904 | 0.833489 | ||||||||
\(383\) | −18.6607 | −0.953515 | −0.476757 | − | 0.879035i | \(-0.658188\pi\) | ||||
−0.476757 | + | 0.879035i | \(0.658188\pi\) | |||||||
\(384\) | −44.3653 | −2.26401 | ||||||||
\(385\) | 3.77977 | 0.192635 | ||||||||
\(386\) | −58.7678 | −2.99120 | ||||||||
\(387\) | −1.81381 | −0.0922014 | ||||||||
\(388\) | −3.41428 | −0.173334 | ||||||||
\(389\) | −2.55867 | −0.129730 | −0.0648648 | − | 0.997894i | \(-0.520662\pi\) | ||||
−0.0648648 | + | 0.997894i | \(0.520662\pi\) | |||||||
\(390\) | −45.3065 | −2.29418 | ||||||||
\(391\) | 0.773032 | 0.0390939 | ||||||||
\(392\) | 4.76426 | 0.240631 | ||||||||
\(393\) | −43.3814 | −2.18830 | ||||||||
\(394\) | −11.3698 | −0.572804 | ||||||||
\(395\) | −9.90161 | −0.498204 | ||||||||
\(396\) | −6.34585 | −0.318891 | ||||||||
\(397\) | −7.60085 | −0.381476 | −0.190738 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190738 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(398\) | −10.7110 | −0.536892 | ||||||||
\(399\) | −9.96431 | −0.498839 | ||||||||
\(400\) | −3.06897 | −0.153449 | ||||||||
\(401\) | 11.5518 | 0.576868 | 0.288434 | − | 0.957500i | \(-0.406865\pi\) | ||||
0.288434 | + | 0.957500i | \(0.406865\pi\) | |||||||
\(402\) | 64.9394 | 3.23888 | ||||||||
\(403\) | 22.1639 | 1.10406 | ||||||||
\(404\) | 56.1873 | 2.79542 | ||||||||
\(405\) | −17.7418 | −0.881595 | ||||||||
\(406\) | −52.3057 | −2.59589 | ||||||||
\(407\) | −9.93142 | −0.492282 | ||||||||
\(408\) | −7.71015 | −0.381709 | ||||||||
\(409\) | −23.4594 | −1.15999 | −0.579997 | − | 0.814619i | \(-0.696946\pi\) | ||||
−0.579997 | + | 0.814619i | \(0.696946\pi\) | |||||||
\(410\) | 7.33681 | 0.362339 | ||||||||
\(411\) | 0.527935 | 0.0260411 | ||||||||
\(412\) | −54.8670 | −2.70310 | ||||||||
\(413\) | −24.7286 | −1.21682 | ||||||||
\(414\) | 3.28789 | 0.161591 | ||||||||
\(415\) | −12.7430 | −0.625527 | ||||||||
\(416\) | −22.7676 | −1.11627 | ||||||||
\(417\) | 18.2441 | 0.893418 | ||||||||
\(418\) | −4.48256 | −0.219249 | ||||||||
\(419\) | −36.5491 | −1.78554 | −0.892770 | − | 0.450513i | \(-0.851241\pi\) | ||||
−0.892770 | + | 0.450513i | \(0.851241\pi\) | |||||||
\(420\) | 29.0140 | 1.41574 | ||||||||
\(421\) | 17.7712 | 0.866117 | 0.433058 | − | 0.901366i | \(-0.357434\pi\) | ||||
0.433058 | + | 0.901366i | \(0.357434\pi\) | |||||||
\(422\) | 51.6639 | 2.51496 | ||||||||
\(423\) | 17.0867 | 0.830785 | ||||||||
\(424\) | −43.6032 | −2.11756 | ||||||||
\(425\) | 2.46881 | 0.119755 | ||||||||
\(426\) | 11.7789 | 0.570691 | ||||||||
\(427\) | −10.1392 | −0.490672 | ||||||||
\(428\) | −39.0286 | −1.88652 | ||||||||
\(429\) | −12.1443 | −0.586330 | ||||||||
\(430\) | 3.73069 | 0.179910 | ||||||||
\(431\) | −27.1863 | −1.30952 | −0.654759 | − | 0.755838i | \(-0.727230\pi\) | ||||
−0.654759 | + | 0.755838i | \(0.727230\pi\) | |||||||
\(432\) | 3.23521 | 0.155654 | ||||||||
\(433\) | 15.6651 | 0.752816 | 0.376408 | − | 0.926454i | \(-0.377159\pi\) | ||||
0.376408 | + | 0.926454i | \(0.377159\pi\) | |||||||
\(434\) | −22.3074 | −1.07079 | ||||||||
\(435\) | 32.7737 | 1.57138 | ||||||||
\(436\) | 32.6997 | 1.56603 | ||||||||
\(437\) | 1.47773 | 0.0706896 | ||||||||
\(438\) | 32.5875 | 1.55709 | ||||||||
\(439\) | −6.47146 | −0.308866 | −0.154433 | − | 0.988003i | \(-0.549355\pi\) | ||||
−0.154433 | + | 0.988003i | \(0.549355\pi\) | |||||||
\(440\) | 5.59089 | 0.266535 | ||||||||
\(441\) | −2.45906 | −0.117098 | ||||||||
\(442\) | −12.9794 | −0.617365 | ||||||||
\(443\) | 1.96090 | 0.0931651 | 0.0465825 | − | 0.998914i | \(-0.485167\pi\) | ||||
0.0465825 | + | 0.998914i | \(0.485167\pi\) | |||||||
\(444\) | −76.2347 | −3.61794 | ||||||||
\(445\) | 25.7977 | 1.22293 | ||||||||
\(446\) | 39.0439 | 1.84878 | ||||||||
\(447\) | 35.1125 | 1.66077 | ||||||||
\(448\) | 28.8217 | 1.36170 | ||||||||
\(449\) | −20.2192 | −0.954204 | −0.477102 | − | 0.878848i | \(-0.658313\pi\) | ||||
−0.477102 | + | 0.878848i | \(0.658313\pi\) | |||||||
\(450\) | 10.5004 | 0.494995 | ||||||||
\(451\) | 1.96661 | 0.0926040 | ||||||||
\(452\) | 35.7274 | 1.68048 | ||||||||
\(453\) | 15.8396 | 0.744209 | ||||||||
\(454\) | 28.1171 | 1.31960 | ||||||||
\(455\) | 20.9215 | 0.980814 | ||||||||
\(456\) | −14.7388 | −0.690207 | ||||||||
\(457\) | −27.3829 | −1.28092 | −0.640459 | − | 0.767992i | \(-0.721256\pi\) | ||||
−0.640459 | + | 0.767992i | \(0.721256\pi\) | |||||||
\(458\) | 46.1474 | 2.15632 | ||||||||
\(459\) | −2.60254 | −0.121476 | ||||||||
\(460\) | −4.30285 | −0.200622 | ||||||||
\(461\) | 1.61879 | 0.0753946 | 0.0376973 | − | 0.999289i | \(-0.487998\pi\) | ||||
0.0376973 | + | 0.999289i | \(0.487998\pi\) | |||||||
\(462\) | 12.2229 | 0.568662 | ||||||||
\(463\) | 28.9366 | 1.34480 | 0.672399 | − | 0.740189i | \(-0.265264\pi\) | ||||
0.672399 | + | 0.740189i | \(0.265264\pi\) | |||||||
\(464\) | −11.6714 | −0.541833 | ||||||||
\(465\) | 13.9774 | 0.648186 | ||||||||
\(466\) | 16.6724 | 0.772333 | ||||||||
\(467\) | 9.71543 | 0.449577 | 0.224788 | − | 0.974408i | \(-0.427831\pi\) | ||||
0.224788 | + | 0.974408i | \(0.427831\pi\) | |||||||
\(468\) | −35.1250 | −1.62365 | ||||||||
\(469\) | −29.9875 | −1.38469 | ||||||||
\(470\) | −35.1443 | −1.62109 | ||||||||
\(471\) | −0.692520 | −0.0319097 | ||||||||
\(472\) | −36.5776 | −1.68362 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −32.0195 | −1.47071 | ||||||||
\(475\) | 4.71940 | 0.216541 | ||||||||
\(476\) | 8.31190 | 0.380975 | ||||||||
\(477\) | 22.5057 | 1.03047 | ||||||||
\(478\) | −42.0353 | −1.92265 | ||||||||
\(479\) | −2.14941 | −0.0982091 | −0.0491046 | − | 0.998794i | \(-0.515637\pi\) | ||||
−0.0491046 | + | 0.998794i | \(0.515637\pi\) | |||||||
\(480\) | −14.3581 | −0.655356 | ||||||||
\(481\) | −54.9715 | −2.50649 | ||||||||
\(482\) | 0.787676 | 0.0358777 | ||||||||
\(483\) | −4.02945 | −0.183346 | ||||||||
\(484\) | 3.49862 | 0.159028 | ||||||||
\(485\) | −1.55262 | −0.0705008 | ||||||||
\(486\) | −39.0645 | −1.77200 | ||||||||
\(487\) | −24.3608 | −1.10389 | −0.551946 | − | 0.833880i | \(-0.686115\pi\) | ||||
−0.551946 | + | 0.833880i | \(0.686115\pi\) | |||||||
\(488\) | −14.9975 | −0.678906 | ||||||||
\(489\) | 29.3526 | 1.32737 | ||||||||
\(490\) | 5.05786 | 0.228491 | ||||||||
\(491\) | −38.3450 | −1.73048 | −0.865242 | − | 0.501355i | \(-0.832835\pi\) | ||||
−0.865242 | + | 0.501355i | \(0.832835\pi\) | |||||||
\(492\) | 15.0959 | 0.680576 | ||||||||
\(493\) | 9.38899 | 0.422859 | ||||||||
\(494\) | −24.8115 | −1.11632 | ||||||||
\(495\) | −2.88573 | −0.129704 | ||||||||
\(496\) | −4.97765 | −0.223503 | ||||||||
\(497\) | −5.43923 | −0.243983 | ||||||||
\(498\) | −41.2078 | −1.84656 | ||||||||
\(499\) | −11.4766 | −0.513762 | −0.256881 | − | 0.966443i | \(-0.582695\pi\) | ||||
−0.256881 | + | 0.966443i | \(0.582695\pi\) | |||||||
\(500\) | −41.5729 | −1.85920 | ||||||||
\(501\) | −1.77319 | −0.0792201 | ||||||||
\(502\) | 20.6298 | 0.920752 | ||||||||
\(503\) | −4.05706 | −0.180895 | −0.0904477 | − | 0.995901i | \(-0.528830\pi\) | ||||
−0.0904477 | + | 0.995901i | \(0.528830\pi\) | |||||||
\(504\) | 15.1431 | 0.674527 | ||||||||
\(505\) | 25.5507 | 1.13699 | ||||||||
\(506\) | −1.81269 | −0.0805840 | ||||||||
\(507\) | −38.6973 | −1.71861 | ||||||||
\(508\) | 54.9144 | 2.43643 | ||||||||
\(509\) | −11.6767 | −0.517562 | −0.258781 | − | 0.965936i | \(-0.583321\pi\) | ||||
−0.258781 | + | 0.965936i | \(0.583321\pi\) | |||||||
\(510\) | −8.18529 | −0.362451 | ||||||||
\(511\) | −15.0482 | −0.665691 | ||||||||
\(512\) | 13.8501 | 0.612092 | ||||||||
\(513\) | −4.97504 | −0.219653 | ||||||||
\(514\) | −31.2171 | −1.37693 | ||||||||
\(515\) | −24.9504 | −1.09944 | ||||||||
\(516\) | 7.67611 | 0.337922 | ||||||||
\(517\) | −9.42033 | −0.414306 | ||||||||
\(518\) | 55.3276 | 2.43095 | ||||||||
\(519\) | 28.8058 | 1.26444 | ||||||||
\(520\) | 30.9462 | 1.35708 | ||||||||
\(521\) | −7.47951 | −0.327683 | −0.163842 | − | 0.986487i | \(-0.552389\pi\) | ||||
−0.163842 | + | 0.986487i | \(0.552389\pi\) | |||||||
\(522\) | 39.9336 | 1.74785 | ||||||||
\(523\) | −6.58250 | −0.287833 | −0.143916 | − | 0.989590i | \(-0.545970\pi\) | ||||
−0.143916 | + | 0.989590i | \(0.545970\pi\) | |||||||
\(524\) | 69.1760 | 3.02197 | ||||||||
\(525\) | −12.8687 | −0.561637 | ||||||||
\(526\) | −2.98141 | −0.129995 | ||||||||
\(527\) | 4.00423 | 0.174427 | ||||||||
\(528\) | 2.72741 | 0.118695 | ||||||||
\(529\) | −22.4024 | −0.974018 | ||||||||
\(530\) | −46.2902 | −2.01072 | ||||||||
\(531\) | 18.8795 | 0.819299 | ||||||||
\(532\) | 15.8891 | 0.688880 | ||||||||
\(533\) | 10.8854 | 0.471499 | ||||||||
\(534\) | 83.4238 | 3.61010 | ||||||||
\(535\) | −17.7480 | −0.767311 | ||||||||
\(536\) | −44.3563 | −1.91590 | ||||||||
\(537\) | 39.9809 | 1.72530 | ||||||||
\(538\) | 23.2942 | 1.00429 | ||||||||
\(539\) | 1.35574 | 0.0583960 | ||||||||
\(540\) | 14.4863 | 0.623390 | ||||||||
\(541\) | 39.1193 | 1.68187 | 0.840936 | − | 0.541135i | \(-0.182005\pi\) | ||||
0.840936 | + | 0.541135i | \(0.182005\pi\) | |||||||
\(542\) | −54.3495 | −2.33451 | ||||||||
\(543\) | 5.84930 | 0.251017 | ||||||||
\(544\) | −4.11331 | −0.176357 | ||||||||
\(545\) | 14.8700 | 0.636959 | ||||||||
\(546\) | 67.6552 | 2.89538 | ||||||||
\(547\) | −7.97157 | −0.340840 | −0.170420 | − | 0.985372i | \(-0.554512\pi\) | ||||
−0.170420 | + | 0.985372i | \(0.554512\pi\) | |||||||
\(548\) | −0.841846 | −0.0359619 | ||||||||
\(549\) | 7.74095 | 0.330376 | ||||||||
\(550\) | −5.78914 | −0.246850 | ||||||||
\(551\) | 17.9481 | 0.764613 | ||||||||
\(552\) | −5.96019 | −0.253683 | ||||||||
\(553\) | 14.7859 | 0.628759 | ||||||||
\(554\) | −21.8202 | −0.927051 | ||||||||
\(555\) | −34.6672 | −1.47154 | ||||||||
\(556\) | −29.0921 | −1.23378 | ||||||||
\(557\) | 34.1259 | 1.44596 | 0.722981 | − | 0.690867i | \(-0.242771\pi\) | ||||
0.722981 | + | 0.690867i | \(0.242771\pi\) | |||||||
\(558\) | 17.0309 | 0.720978 | ||||||||
\(559\) | 5.53511 | 0.234110 | ||||||||
\(560\) | −4.69863 | −0.198553 | ||||||||
\(561\) | −2.19404 | −0.0926325 | ||||||||
\(562\) | −34.4652 | −1.45383 | ||||||||
\(563\) | −23.7317 | −1.00017 | −0.500086 | − | 0.865975i | \(-0.666698\pi\) | ||||
−0.500086 | + | 0.865975i | \(0.666698\pi\) | |||||||
\(564\) | −72.3115 | −3.04487 | ||||||||
\(565\) | 16.2468 | 0.683508 | ||||||||
\(566\) | −2.35943 | −0.0991744 | ||||||||
\(567\) | 26.4934 | 1.11262 | ||||||||
\(568\) | −8.04549 | −0.337581 | ||||||||
\(569\) | 8.43984 | 0.353816 | 0.176908 | − | 0.984227i | \(-0.443390\pi\) | ||||
0.176908 | + | 0.984227i | \(0.443390\pi\) | |||||||
\(570\) | −15.6471 | −0.655384 | ||||||||
\(571\) | −3.10617 | −0.129989 | −0.0649947 | − | 0.997886i | \(-0.520703\pi\) | ||||
−0.0649947 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(572\) | 19.3652 | 0.809702 | ||||||||
\(573\) | 15.2423 | 0.636755 | ||||||||
\(574\) | −10.9559 | −0.457291 | ||||||||
\(575\) | 1.90847 | 0.0795886 | ||||||||
\(576\) | −22.0044 | −0.916849 | ||||||||
\(577\) | 31.9577 | 1.33042 | 0.665208 | − | 0.746658i | \(-0.268343\pi\) | ||||
0.665208 | + | 0.746658i | \(0.268343\pi\) | |||||||
\(578\) | −2.34491 | −0.0975355 | ||||||||
\(579\) | −54.9866 | −2.28517 | ||||||||
\(580\) | −52.2610 | −2.17002 | ||||||||
\(581\) | 19.0288 | 0.789447 | ||||||||
\(582\) | −5.02081 | −0.208119 | ||||||||
\(583\) | −12.4080 | −0.513885 | ||||||||
\(584\) | −22.2586 | −0.921068 | ||||||||
\(585\) | −15.9728 | −0.660395 | ||||||||
\(586\) | 37.3102 | 1.54127 | ||||||||
\(587\) | 2.13224 | 0.0880071 | 0.0440036 | − | 0.999031i | \(-0.485989\pi\) | ||||
0.0440036 | + | 0.999031i | \(0.485989\pi\) | |||||||
\(588\) | 10.4068 | 0.429171 | ||||||||
\(589\) | 7.65453 | 0.315399 | ||||||||
\(590\) | −38.8317 | −1.59867 | ||||||||
\(591\) | −10.6383 | −0.437601 | ||||||||
\(592\) | 12.3457 | 0.507407 | ||||||||
\(593\) | −23.1831 | −0.952016 | −0.476008 | − | 0.879441i | \(-0.657917\pi\) | ||||
−0.476008 | + | 0.879441i | \(0.657917\pi\) | |||||||
\(594\) | 6.10273 | 0.250398 | ||||||||
\(595\) | 3.77977 | 0.154956 | ||||||||
\(596\) | −55.9905 | −2.29346 | ||||||||
\(597\) | −10.0218 | −0.410166 | ||||||||
\(598\) | −10.0335 | −0.410299 | ||||||||
\(599\) | −40.5055 | −1.65501 | −0.827504 | − | 0.561459i | \(-0.810240\pi\) | ||||
−0.827504 | + | 0.561459i | \(0.810240\pi\) | |||||||
\(600\) | −19.0349 | −0.777096 | ||||||||
\(601\) | −12.6775 | −0.517125 | −0.258562 | − | 0.965995i | \(-0.583249\pi\) | ||||
−0.258562 | + | 0.965995i | \(0.583249\pi\) | |||||||
\(602\) | −5.57096 | −0.227055 | ||||||||
\(603\) | 22.8944 | 0.932333 | ||||||||
\(604\) | −25.2578 | −1.02773 | ||||||||
\(605\) | 1.59097 | 0.0646822 | ||||||||
\(606\) | 82.6252 | 3.35642 | ||||||||
\(607\) | −13.2614 | −0.538264 | −0.269132 | − | 0.963103i | \(-0.586737\pi\) | ||||
−0.269132 | + | 0.963103i | \(0.586737\pi\) | |||||||
\(608\) | −7.86303 | −0.318888 | ||||||||
\(609\) | −48.9403 | −1.98316 | ||||||||
\(610\) | −15.9217 | −0.644653 | ||||||||
\(611\) | −52.1426 | −2.10946 | ||||||||
\(612\) | −6.34585 | −0.256516 | ||||||||
\(613\) | −6.99889 | −0.282683 | −0.141341 | − | 0.989961i | \(-0.545142\pi\) | ||||
−0.141341 | + | 0.989961i | \(0.545142\pi\) | |||||||
\(614\) | −66.6594 | −2.69016 | ||||||||
\(615\) | 6.86476 | 0.276814 | ||||||||
\(616\) | −8.34875 | −0.336381 | ||||||||
\(617\) | 41.0936 | 1.65437 | 0.827183 | − | 0.561933i | \(-0.189942\pi\) | ||||
0.827183 | + | 0.561933i | \(0.189942\pi\) | |||||||
\(618\) | −80.6837 | −3.24557 | ||||||||
\(619\) | 9.84611 | 0.395749 | 0.197874 | − | 0.980227i | \(-0.436596\pi\) | ||||
0.197874 | + | 0.980227i | \(0.436596\pi\) | |||||||
\(620\) | −22.2884 | −0.895122 | ||||||||
\(621\) | −2.01185 | −0.0807326 | ||||||||
\(622\) | −25.9664 | −1.04116 | ||||||||
\(623\) | −38.5232 | −1.54340 | ||||||||
\(624\) | 15.0965 | 0.604344 | ||||||||
\(625\) | −6.56093 | −0.262437 | ||||||||
\(626\) | −11.8374 | −0.473117 | ||||||||
\(627\) | −4.19415 | −0.167498 | ||||||||
\(628\) | 1.10429 | 0.0440661 | ||||||||
\(629\) | −9.93142 | −0.395992 | ||||||||
\(630\) | 16.0763 | 0.640494 | ||||||||
\(631\) | 10.8018 | 0.430012 | 0.215006 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215006 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(632\) | 21.8706 | 0.869967 | ||||||||
\(633\) | 48.3398 | 1.92133 | ||||||||
\(634\) | −24.4406 | −0.970662 | ||||||||
\(635\) | 24.9719 | 0.990980 | ||||||||
\(636\) | −95.2449 | −3.77670 | ||||||||
\(637\) | 7.50419 | 0.297327 | ||||||||
\(638\) | −22.0164 | −0.871636 | ||||||||
\(639\) | 4.15267 | 0.164277 | ||||||||
\(640\) | 32.1707 | 1.27166 | ||||||||
\(641\) | −27.5400 | −1.08776 | −0.543882 | − | 0.839162i | \(-0.683046\pi\) | ||||
−0.543882 | + | 0.839162i | \(0.683046\pi\) | |||||||
\(642\) | −57.3928 | −2.26511 | ||||||||
\(643\) | −3.11124 | −0.122695 | −0.0613477 | − | 0.998116i | \(-0.519540\pi\) | ||||
−0.0613477 | + | 0.998116i | \(0.519540\pi\) | |||||||
\(644\) | 6.42536 | 0.253195 | ||||||||
\(645\) | 3.49066 | 0.137444 | ||||||||
\(646\) | −4.48256 | −0.176364 | ||||||||
\(647\) | −6.50985 | −0.255929 | −0.127964 | − | 0.991779i | \(-0.540844\pi\) | ||||
−0.127964 | + | 0.991779i | \(0.540844\pi\) | |||||||
\(648\) | 39.1879 | 1.53945 | ||||||||
\(649\) | −10.4087 | −0.408578 | ||||||||
\(650\) | −32.0436 | −1.25685 | ||||||||
\(651\) | −20.8722 | −0.818044 | ||||||||
\(652\) | −46.8057 | −1.83305 | ||||||||
\(653\) | −31.6499 | −1.23856 | −0.619279 | − | 0.785171i | \(-0.712575\pi\) | ||||
−0.619279 | + | 0.785171i | \(0.712575\pi\) | |||||||
\(654\) | 48.0860 | 1.88031 | ||||||||
\(655\) | 31.4573 | 1.22914 | ||||||||
\(656\) | −2.44469 | −0.0954491 | ||||||||
\(657\) | 11.4887 | 0.448219 | ||||||||
\(658\) | 52.4803 | 2.04590 | ||||||||
\(659\) | −3.45044 | −0.134410 | −0.0672050 | − | 0.997739i | \(-0.521408\pi\) | ||||
−0.0672050 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(660\) | 12.2125 | 0.475370 | ||||||||
\(661\) | −8.39294 | −0.326448 | −0.163224 | − | 0.986589i | \(-0.552189\pi\) | ||||
−0.163224 | + | 0.986589i | \(0.552189\pi\) | |||||||
\(662\) | −15.7566 | −0.612397 | ||||||||
\(663\) | −12.1443 | −0.471644 | ||||||||
\(664\) | 28.1466 | 1.09230 | ||||||||
\(665\) | 7.22545 | 0.280191 | ||||||||
\(666\) | −42.2407 | −1.63679 | ||||||||
\(667\) | 7.25799 | 0.281030 | ||||||||
\(668\) | 2.82752 | 0.109400 | ||||||||
\(669\) | 36.5318 | 1.41240 | ||||||||
\(670\) | −47.0897 | −1.81923 | ||||||||
\(671\) | −4.26777 | −0.164756 | ||||||||
\(672\) | 21.4407 | 0.827093 | ||||||||
\(673\) | −25.3909 | −0.978746 | −0.489373 | − | 0.872075i | \(-0.662774\pi\) | ||||
−0.489373 | + | 0.872075i | \(0.662774\pi\) | |||||||
\(674\) | −61.8309 | −2.38164 | ||||||||
\(675\) | −6.42517 | −0.247305 | ||||||||
\(676\) | 61.7068 | 2.37334 | ||||||||
\(677\) | −24.3815 | −0.937056 | −0.468528 | − | 0.883449i | \(-0.655216\pi\) | ||||
−0.468528 | + | 0.883449i | \(0.655216\pi\) | |||||||
\(678\) | 52.5384 | 2.01772 | ||||||||
\(679\) | 2.31849 | 0.0889756 | ||||||||
\(680\) | 5.59089 | 0.214401 | ||||||||
\(681\) | 26.3081 | 1.00813 | ||||||||
\(682\) | −9.38958 | −0.359545 | ||||||||
\(683\) | −18.9799 | −0.726244 | −0.363122 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363122 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(684\) | −12.1308 | −0.463832 | ||||||||
\(685\) | −0.382823 | −0.0146269 | ||||||||
\(686\) | −46.5495 | −1.77727 | ||||||||
\(687\) | 43.1782 | 1.64735 | ||||||||
\(688\) | −1.24310 | −0.0473927 | ||||||||
\(689\) | −68.6794 | −2.61648 | ||||||||
\(690\) | −6.32749 | −0.240883 | ||||||||
\(691\) | −22.1346 | −0.842039 | −0.421019 | − | 0.907052i | \(-0.638328\pi\) | ||||
−0.421019 | + | 0.907052i | \(0.638328\pi\) | |||||||
\(692\) | −45.9338 | −1.74614 | ||||||||
\(693\) | 4.30920 | 0.163693 | ||||||||
\(694\) | −4.53441 | −0.172124 | ||||||||
\(695\) | −13.2294 | −0.501820 | ||||||||
\(696\) | −72.3905 | −2.74395 | ||||||||
\(697\) | 1.96661 | 0.0744906 | ||||||||
\(698\) | −9.22291 | −0.349092 | ||||||||
\(699\) | 15.5997 | 0.590034 | ||||||||
\(700\) | 20.5205 | 0.775602 | ||||||||
\(701\) | 17.5944 | 0.664533 | 0.332266 | − | 0.943186i | \(-0.392187\pi\) | ||||
0.332266 | + | 0.943186i | \(0.392187\pi\) | |||||||
\(702\) | 33.7793 | 1.27492 | ||||||||
\(703\) | −18.9850 | −0.716033 | ||||||||
\(704\) | 12.1315 | 0.457225 | ||||||||
\(705\) | −32.8831 | −1.23845 | ||||||||
\(706\) | −42.2119 | −1.58867 | ||||||||
\(707\) | −38.1544 | −1.43494 | ||||||||
\(708\) | −79.8984 | −3.00277 | ||||||||
\(709\) | 39.5337 | 1.48472 | 0.742359 | − | 0.670002i | \(-0.233707\pi\) | ||||
0.742359 | + | 0.670002i | \(0.233707\pi\) | |||||||
\(710\) | −8.54129 | −0.320549 | ||||||||
\(711\) | −11.2885 | −0.423352 | ||||||||
\(712\) | −56.9819 | −2.13549 | ||||||||
\(713\) | 3.09540 | 0.115924 | ||||||||
\(714\) | 12.2229 | 0.457431 | ||||||||
\(715\) | 8.80621 | 0.329333 | ||||||||
\(716\) | −63.7535 | −2.38258 | ||||||||
\(717\) | −39.3307 | −1.46883 | ||||||||
\(718\) | 50.5881 | 1.88793 | ||||||||
\(719\) | −13.0362 | −0.486170 | −0.243085 | − | 0.970005i | \(-0.578159\pi\) | ||||
−0.243085 | + | 0.970005i | \(0.578159\pi\) | |||||||
\(720\) | 3.58724 | 0.133689 | ||||||||
\(721\) | 37.2578 | 1.38755 | ||||||||
\(722\) | 35.9845 | 1.33920 | ||||||||
\(723\) | 0.736997 | 0.0274092 | ||||||||
\(724\) | −9.32729 | −0.346646 | ||||||||
\(725\) | 23.1796 | 0.860869 | ||||||||
\(726\) | 5.14484 | 0.190943 | ||||||||
\(727\) | −49.4313 | −1.83330 | −0.916652 | − | 0.399686i | \(-0.869119\pi\) | ||||
−0.916652 | + | 0.399686i | \(0.869119\pi\) | |||||||
\(728\) | −46.2113 | −1.71270 | ||||||||
\(729\) | −3.09656 | −0.114687 | ||||||||
\(730\) | −23.6303 | −0.874596 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −32.7599 | −1.21084 | ||||||||
\(733\) | 47.3777 | 1.74994 | 0.874968 | − | 0.484180i | \(-0.160882\pi\) | ||||
0.874968 | + | 0.484180i | \(0.160882\pi\) | |||||||
\(734\) | −40.4270 | −1.49219 | ||||||||
\(735\) | 4.73243 | 0.174558 | ||||||||
\(736\) | −3.17972 | −0.117206 | ||||||||
\(737\) | −12.6223 | −0.464947 | ||||||||
\(738\) | 8.36446 | 0.307900 | ||||||||
\(739\) | 24.6277 | 0.905944 | 0.452972 | − | 0.891525i | \(-0.350364\pi\) | ||||
0.452972 | + | 0.891525i | \(0.350364\pi\) | |||||||
\(740\) | 55.2803 | 2.03215 | ||||||||
\(741\) | −23.2151 | −0.852827 | ||||||||
\(742\) | 69.1243 | 2.53763 | ||||||||
\(743\) | 11.4594 | 0.420404 | 0.210202 | − | 0.977658i | \(-0.432588\pi\) | ||||
0.210202 | + | 0.977658i | \(0.432588\pi\) | |||||||
\(744\) | −30.8732 | −1.13187 | ||||||||
\(745\) | −25.4613 | −0.932828 | ||||||||
\(746\) | −6.54471 | −0.239619 | ||||||||
\(747\) | −14.5278 | −0.531545 | ||||||||
\(748\) | 3.49862 | 0.127922 | ||||||||
\(749\) | 26.5026 | 0.968386 | ||||||||
\(750\) | −61.1343 | −2.23231 | ||||||||
\(751\) | 15.0548 | 0.549358 | 0.274679 | − | 0.961536i | \(-0.411428\pi\) | ||||
0.274679 | + | 0.961536i | \(0.411428\pi\) | |||||||
\(752\) | 11.7104 | 0.427034 | ||||||||
\(753\) | 19.3025 | 0.703421 | ||||||||
\(754\) | −121.863 | −4.43799 | ||||||||
\(755\) | −11.4858 | −0.418012 | ||||||||
\(756\) | −21.6320 | −0.786750 | ||||||||
\(757\) | 10.5360 | 0.382936 | 0.191468 | − | 0.981499i | \(-0.438675\pi\) | ||||
0.191468 | + | 0.981499i | \(0.438675\pi\) | |||||||
\(758\) | −43.5407 | −1.58147 | ||||||||
\(759\) | −1.69606 | −0.0615632 | ||||||||
\(760\) | 10.6876 | 0.387680 | ||||||||
\(761\) | 44.6574 | 1.61883 | 0.809414 | − | 0.587238i | \(-0.199785\pi\) | ||||
0.809414 | + | 0.587238i | \(0.199785\pi\) | |||||||
\(762\) | 80.7534 | 2.92539 | ||||||||
\(763\) | −22.2050 | −0.803875 | ||||||||
\(764\) | −24.3053 | −0.879336 | ||||||||
\(765\) | −2.88573 | −0.104334 | ||||||||
\(766\) | 43.7576 | 1.58103 | ||||||||
\(767\) | −57.6134 | −2.08030 | ||||||||
\(768\) | 50.7985 | 1.83303 | ||||||||
\(769\) | −20.6666 | −0.745255 | −0.372627 | − | 0.927981i | \(-0.621543\pi\) | ||||
−0.372627 | + | 0.927981i | \(0.621543\pi\) | |||||||
\(770\) | −8.86324 | −0.319409 | ||||||||
\(771\) | −29.2086 | −1.05192 | ||||||||
\(772\) | 87.6817 | 3.15573 | ||||||||
\(773\) | −33.2310 | −1.19524 | −0.597619 | − | 0.801781i | \(-0.703886\pi\) | ||||
−0.597619 | + | 0.801781i | \(0.703886\pi\) | |||||||
\(774\) | 4.25324 | 0.152879 | ||||||||
\(775\) | 9.88568 | 0.355104 | ||||||||
\(776\) | 3.42942 | 0.123109 | ||||||||
\(777\) | 51.7678 | 1.85716 | ||||||||
\(778\) | 5.99986 | 0.215105 | ||||||||
\(779\) | 3.75939 | 0.134694 | ||||||||
\(780\) | 67.5974 | 2.42038 | ||||||||
\(781\) | −2.28947 | −0.0819236 | ||||||||
\(782\) | −1.81269 | −0.0648218 | ||||||||
\(783\) | −24.4352 | −0.873243 | ||||||||
\(784\) | −1.68532 | −0.0601900 | ||||||||
\(785\) | 0.502170 | 0.0179232 | ||||||||
\(786\) | 101.726 | 3.62843 | ||||||||
\(787\) | 53.8411 | 1.91923 | 0.959614 | − | 0.281321i | \(-0.0907726\pi\) | ||||
0.959614 | + | 0.281321i | \(0.0907726\pi\) | |||||||
\(788\) | 16.9638 | 0.604312 | ||||||||
\(789\) | −2.78958 | −0.0993117 | ||||||||
\(790\) | 23.2184 | 0.826074 | ||||||||
\(791\) | −24.2610 | −0.862622 | ||||||||
\(792\) | 6.37398 | 0.226490 | ||||||||
\(793\) | −23.6226 | −0.838863 | ||||||||
\(794\) | 17.8233 | 0.632526 | ||||||||
\(795\) | −43.3119 | −1.53611 | ||||||||
\(796\) | 15.9808 | 0.566425 | ||||||||
\(797\) | −7.55164 | −0.267493 | −0.133746 | − | 0.991016i | \(-0.542701\pi\) | ||||
−0.133746 | + | 0.991016i | \(0.542701\pi\) | |||||||
\(798\) | 23.3654 | 0.827128 | ||||||||
\(799\) | −9.42033 | −0.333267 | ||||||||
\(800\) | −10.1550 | −0.359032 | ||||||||
\(801\) | 29.4111 | 1.03919 | ||||||||
\(802\) | −27.0879 | −0.956508 | ||||||||
\(803\) | −6.33403 | −0.223523 | ||||||||
\(804\) | −96.8898 | −3.41704 | ||||||||
\(805\) | 2.92189 | 0.102983 | ||||||||
\(806\) | −51.9724 | −1.83065 | ||||||||
\(807\) | 21.7955 | 0.767237 | ||||||||
\(808\) | −56.4364 | −1.98543 | ||||||||
\(809\) | 11.2585 | 0.395827 | 0.197913 | − | 0.980219i | \(-0.436583\pi\) | ||||
0.197913 | + | 0.980219i | \(0.436583\pi\) | |||||||
\(810\) | 41.6029 | 1.46178 | ||||||||
\(811\) | 3.90203 | 0.137019 | 0.0685093 | − | 0.997650i | \(-0.478176\pi\) | ||||
0.0685093 | + | 0.997650i | \(0.478176\pi\) | |||||||
\(812\) | 78.0403 | 2.73868 | ||||||||
\(813\) | −50.8527 | −1.78348 | ||||||||
\(814\) | 23.2883 | 0.816255 | ||||||||
\(815\) | −21.2846 | −0.745566 | ||||||||
\(816\) | 2.72741 | 0.0954784 | ||||||||
\(817\) | 1.91161 | 0.0668787 | ||||||||
\(818\) | 55.0103 | 1.92339 | ||||||||
\(819\) | 23.8519 | 0.833452 | ||||||||
\(820\) | −10.9465 | −0.382270 | ||||||||
\(821\) | 46.7461 | 1.63145 | 0.815726 | − | 0.578439i | \(-0.196338\pi\) | ||||
0.815726 | + | 0.578439i | \(0.196338\pi\) | |||||||
\(822\) | −1.23796 | −0.0431789 | ||||||||
\(823\) | 7.82455 | 0.272747 | 0.136373 | − | 0.990658i | \(-0.456455\pi\) | ||||
0.136373 | + | 0.990658i | \(0.456455\pi\) | |||||||
\(824\) | 55.1103 | 1.91986 | ||||||||
\(825\) | −5.41667 | −0.188584 | ||||||||
\(826\) | 57.9865 | 2.01761 | ||||||||
\(827\) | −19.0899 | −0.663822 | −0.331911 | − | 0.943311i | \(-0.607693\pi\) | ||||
−0.331911 | + | 0.943311i | \(0.607693\pi\) | |||||||
\(828\) | −4.90554 | −0.170479 | ||||||||
\(829\) | 10.9501 | 0.380313 | 0.190157 | − | 0.981754i | \(-0.439100\pi\) | ||||
0.190157 | + | 0.981754i | \(0.439100\pi\) | |||||||
\(830\) | 29.8811 | 1.03719 | ||||||||
\(831\) | −20.4163 | −0.708233 | ||||||||
\(832\) | 67.1495 | 2.32799 | ||||||||
\(833\) | 1.35574 | 0.0469737 | ||||||||
\(834\) | −42.7809 | −1.48138 | ||||||||
\(835\) | 1.28580 | 0.0444968 | ||||||||
\(836\) | 6.68799 | 0.231309 | ||||||||
\(837\) | −10.4212 | −0.360208 | ||||||||
\(838\) | 85.7044 | 2.96061 | ||||||||
\(839\) | 19.0202 | 0.656652 | 0.328326 | − | 0.944565i | \(-0.393516\pi\) | ||||
0.328326 | + | 0.944565i | \(0.393516\pi\) | |||||||
\(840\) | −29.1426 | −1.00552 | ||||||||
\(841\) | 59.1530 | 2.03976 | ||||||||
\(842\) | −41.6720 | −1.43611 | ||||||||
\(843\) | −32.2477 | −1.11067 | ||||||||
\(844\) | −77.0827 | −2.65330 | ||||||||
\(845\) | 28.0607 | 0.965318 | ||||||||
\(846\) | −40.0669 | −1.37753 | ||||||||
\(847\) | −2.37576 | −0.0816322 | ||||||||
\(848\) | 15.4243 | 0.529673 | ||||||||
\(849\) | −2.20763 | −0.0757655 | ||||||||
\(850\) | −5.78914 | −0.198566 | ||||||||
\(851\) | −7.67731 | −0.263175 | ||||||||
\(852\) | −17.5742 | −0.602082 | ||||||||
\(853\) | 15.2365 | 0.521688 | 0.260844 | − | 0.965381i | \(-0.415999\pi\) | ||||
0.260844 | + | 0.965381i | \(0.415999\pi\) | |||||||
\(854\) | 23.7756 | 0.813585 | ||||||||
\(855\) | −5.51638 | −0.188656 | ||||||||
\(856\) | 39.2016 | 1.33988 | ||||||||
\(857\) | −31.9983 | −1.09304 | −0.546521 | − | 0.837445i | \(-0.684048\pi\) | ||||
−0.546521 | + | 0.837445i | \(0.684048\pi\) | |||||||
\(858\) | 28.4772 | 0.972197 | ||||||||
\(859\) | −3.00700 | −0.102597 | −0.0512987 | − | 0.998683i | \(-0.516336\pi\) | ||||
−0.0512987 | + | 0.998683i | \(0.516336\pi\) | |||||||
\(860\) | −5.56620 | −0.189806 | ||||||||
\(861\) | −10.2510 | −0.349353 | ||||||||
\(862\) | 63.7495 | 2.17132 | ||||||||
\(863\) | 9.92154 | 0.337733 | 0.168867 | − | 0.985639i | \(-0.445989\pi\) | ||||
0.168867 | + | 0.985639i | \(0.445989\pi\) | |||||||
\(864\) | 10.7050 | 0.364193 | ||||||||
\(865\) | −20.8881 | −0.710216 | ||||||||
\(866\) | −36.7333 | −1.24825 | ||||||||
\(867\) | −2.19404 | −0.0745135 | ||||||||
\(868\) | 33.2828 | 1.12969 | ||||||||
\(869\) | 6.22362 | 0.211122 | ||||||||
\(870\) | −76.8515 | −2.60551 | ||||||||
\(871\) | −69.8656 | −2.36730 | ||||||||
\(872\) | −32.8447 | −1.11226 | ||||||||
\(873\) | −1.77009 | −0.0599085 | ||||||||
\(874\) | −3.46516 | −0.117211 | ||||||||
\(875\) | 28.2304 | 0.954362 | ||||||||
\(876\) | −48.6207 | −1.64274 | ||||||||
\(877\) | −17.9276 | −0.605373 | −0.302687 | − | 0.953090i | \(-0.597884\pi\) | ||||
−0.302687 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(878\) | 15.1750 | 0.512132 | ||||||||
\(879\) | 34.9096 | 1.17747 | ||||||||
\(880\) | −1.97773 | −0.0666694 | ||||||||
\(881\) | −39.9023 | −1.34434 | −0.672171 | − | 0.740396i | \(-0.734638\pi\) | ||||
−0.672171 | + | 0.740396i | \(0.734638\pi\) | |||||||
\(882\) | 5.76629 | 0.194161 | ||||||||
\(883\) | −3.65112 | −0.122870 | −0.0614350 | − | 0.998111i | \(-0.519568\pi\) | ||||
−0.0614350 | + | 0.998111i | \(0.519568\pi\) | |||||||
\(884\) | 19.3652 | 0.651324 | ||||||||
\(885\) | −36.3332 | −1.22133 | ||||||||
\(886\) | −4.59814 | −0.154477 | ||||||||
\(887\) | 18.7593 | 0.629874 | 0.314937 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314937 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(888\) | 76.5728 | 2.56961 | ||||||||
\(889\) | −37.2900 | −1.25067 | ||||||||
\(890\) | −60.4934 | −2.02774 | ||||||||
\(891\) | 11.1515 | 0.373590 | ||||||||
\(892\) | −58.2536 | −1.95047 | ||||||||
\(893\) | −18.0080 | −0.602615 | ||||||||
\(894\) | −82.3358 | −2.75372 | ||||||||
\(895\) | −28.9915 | −0.969077 | ||||||||
\(896\) | −48.0399 | −1.60490 | ||||||||
\(897\) | −9.38790 | −0.313453 | ||||||||
\(898\) | 47.4123 | 1.58217 | ||||||||
\(899\) | 37.5957 | 1.25389 | ||||||||
\(900\) | −15.6667 | −0.522223 | ||||||||
\(901\) | −12.4080 | −0.413369 | ||||||||
\(902\) | −4.61153 | −0.153547 | ||||||||
\(903\) | −5.21252 | −0.173462 | ||||||||
\(904\) | −35.8859 | −1.19355 | ||||||||
\(905\) | −4.24152 | −0.140993 | ||||||||
\(906\) | −37.1425 | −1.23398 | ||||||||
\(907\) | 4.63897 | 0.154034 | 0.0770172 | − | 0.997030i | \(-0.475460\pi\) | ||||
0.0770172 | + | 0.997030i | \(0.475460\pi\) | |||||||
\(908\) | −41.9509 | −1.39219 | ||||||||
\(909\) | 29.1296 | 0.966167 | ||||||||
\(910\) | −49.0590 | −1.62629 | ||||||||
\(911\) | −56.9117 | −1.88557 | −0.942784 | − | 0.333403i | \(-0.891803\pi\) | ||||
−0.942784 | + | 0.333403i | \(0.891803\pi\) | |||||||
\(912\) | 5.21374 | 0.172644 | ||||||||
\(913\) | 8.00954 | 0.265077 | ||||||||
\(914\) | 64.2106 | 2.12390 | ||||||||
\(915\) | −14.8973 | −0.492491 | ||||||||
\(916\) | −68.8520 | −2.27494 | ||||||||
\(917\) | −46.9745 | −1.55123 | ||||||||
\(918\) | 6.10273 | 0.201420 | ||||||||
\(919\) | 41.4529 | 1.36740 | 0.683702 | − | 0.729761i | \(-0.260369\pi\) | ||||
0.683702 | + | 0.729761i | \(0.260369\pi\) | |||||||
\(920\) | 4.32193 | 0.142490 | ||||||||
\(921\) | −62.3705 | −2.05518 | ||||||||
\(922\) | −3.79592 | −0.125012 | ||||||||
\(923\) | −12.6725 | −0.417119 | ||||||||
\(924\) | −18.2366 | −0.599941 | ||||||||
\(925\) | −24.5188 | −0.806173 | ||||||||
\(926\) | −67.8538 | −2.22982 | ||||||||
\(927\) | −28.4451 | −0.934259 | ||||||||
\(928\) | −38.6198 | −1.26776 | ||||||||
\(929\) | 57.4720 | 1.88559 | 0.942797 | − | 0.333368i | \(-0.108185\pi\) | ||||
0.942797 | + | 0.333368i | \(0.108185\pi\) | |||||||
\(930\) | −32.7758 | −1.07476 | ||||||||
\(931\) | 2.59165 | 0.0849379 | ||||||||
\(932\) | −24.8752 | −0.814816 | ||||||||
\(933\) | −24.2957 | −0.795405 | ||||||||
\(934\) | −22.7818 | −0.745445 | ||||||||
\(935\) | 1.59097 | 0.0520303 | ||||||||
\(936\) | 35.2807 | 1.15319 | ||||||||
\(937\) | 22.6074 | 0.738550 | 0.369275 | − | 0.929320i | \(-0.379606\pi\) | ||||
0.369275 | + | 0.929320i | \(0.379606\pi\) | |||||||
\(938\) | 70.3181 | 2.29597 | ||||||||
\(939\) | −11.0758 | −0.361444 | ||||||||
\(940\) | 52.4355 | 1.71026 | ||||||||
\(941\) | −49.7955 | −1.62329 | −0.811643 | − | 0.584154i | \(-0.801426\pi\) | ||||
−0.811643 | + | 0.584154i | \(0.801426\pi\) | |||||||
\(942\) | 1.62390 | 0.0529095 | ||||||||
\(943\) | 1.52025 | 0.0495062 | ||||||||
\(944\) | 12.9390 | 0.421130 | ||||||||
\(945\) | −9.83701 | −0.319998 | ||||||||
\(946\) | −2.34491 | −0.0762397 | ||||||||
\(947\) | −39.6830 | −1.28953 | −0.644763 | − | 0.764383i | \(-0.723044\pi\) | ||||
−0.644763 | + | 0.764383i | \(0.723044\pi\) | |||||||
\(948\) | 47.7732 | 1.55160 | ||||||||
\(949\) | −35.0595 | −1.13808 | ||||||||
\(950\) | −11.0666 | −0.359047 | ||||||||
\(951\) | −22.8681 | −0.741550 | ||||||||
\(952\) | −8.34875 | −0.270585 | ||||||||
\(953\) | −10.6711 | −0.345671 | −0.172836 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172836 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(954\) | −52.7740 | −1.70862 | ||||||||
\(955\) | −11.0527 | −0.357656 | ||||||||
\(956\) | 62.7168 | 2.02841 | ||||||||
\(957\) | −20.5998 | −0.665897 | ||||||||
\(958\) | 5.04018 | 0.162841 | ||||||||
\(959\) | 0.571662 | 0.0184599 | ||||||||
\(960\) | 42.3471 | 1.36675 | ||||||||
\(961\) | −14.9661 | −0.482778 | ||||||||
\(962\) | 128.903 | 4.15602 | ||||||||
\(963\) | −20.2339 | −0.652027 | ||||||||
\(964\) | −1.17522 | −0.0378511 | ||||||||
\(965\) | 39.8726 | 1.28355 | ||||||||
\(966\) | 9.44871 | 0.304007 | ||||||||
\(967\) | −28.8159 | −0.926656 | −0.463328 | − | 0.886187i | \(-0.653345\pi\) | ||||
−0.463328 | + | 0.886187i | \(0.653345\pi\) | |||||||
\(968\) | −3.51413 | −0.112949 | ||||||||
\(969\) | −4.19415 | −0.134735 | ||||||||
\(970\) | 3.64076 | 0.116898 | ||||||||
\(971\) | 33.1467 | 1.06373 | 0.531864 | − | 0.846830i | \(-0.321492\pi\) | ||||
0.531864 | + | 0.846830i | \(0.321492\pi\) | |||||||
\(972\) | 58.2844 | 1.86947 | ||||||||
\(973\) | 19.7552 | 0.633323 | ||||||||
\(974\) | 57.1239 | 1.83037 | ||||||||
\(975\) | −29.9819 | −0.960188 | ||||||||
\(976\) | 5.30526 | 0.169817 | ||||||||
\(977\) | 4.84326 | 0.154950 | 0.0774749 | − | 0.996994i | \(-0.475314\pi\) | ||||
0.0774749 | + | 0.996994i | \(0.475314\pi\) | |||||||
\(978\) | −68.8294 | −2.20092 | ||||||||
\(979\) | −16.2151 | −0.518235 | ||||||||
\(980\) | −7.54634 | −0.241059 | ||||||||
\(981\) | 16.9528 | 0.541260 | ||||||||
\(982\) | 89.9156 | 2.86932 | ||||||||
\(983\) | 33.9439 | 1.08264 | 0.541321 | − | 0.840816i | \(-0.317924\pi\) | ||||
0.541321 | + | 0.840816i | \(0.317924\pi\) | |||||||
\(984\) | −15.1629 | −0.483374 | ||||||||
\(985\) | 7.71418 | 0.245794 | ||||||||
\(986\) | −22.0164 | −0.701144 | ||||||||
\(987\) | 49.1037 | 1.56299 | ||||||||
\(988\) | 37.0188 | 1.17772 | ||||||||
\(989\) | 0.773032 | 0.0245810 | ||||||||
\(990\) | 6.76678 | 0.215062 | ||||||||
\(991\) | −40.6334 | −1.29076 | −0.645382 | − | 0.763860i | \(-0.723302\pi\) | ||||
−0.645382 | + | 0.763860i | \(0.723302\pi\) | |||||||
\(992\) | −16.4706 | −0.522943 | ||||||||
\(993\) | −14.7428 | −0.467849 | ||||||||
\(994\) | 12.7545 | 0.404549 | ||||||||
\(995\) | 7.26715 | 0.230384 | ||||||||
\(996\) | 61.4821 | 1.94814 | ||||||||
\(997\) | −43.5337 | −1.37873 | −0.689364 | − | 0.724415i | \(-0.742110\pi\) | ||||
−0.689364 | + | 0.724415i | \(0.742110\pi\) | |||||||
\(998\) | 26.9116 | 0.851872 | ||||||||
\(999\) | 25.8469 | 0.817760 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.h.1.10 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.10 | ✓ | 74 | 1.1 | even | 1 | trivial |