Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.841269 | −0.485707 | −0.242854 | − | 0.970063i | \(-0.578083\pi\) | ||||
−0.242854 | + | 0.970063i | \(0.578083\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.88225 | −0.841768 | −0.420884 | − | 0.907114i | \(-0.638280\pi\) | ||||
−0.420884 | + | 0.907114i | \(0.638280\pi\) | |||||||
\(6\) | 0.841269 | 0.343447 | ||||||||
\(7\) | −4.21612 | −1.59355 | −0.796773 | − | 0.604279i | \(-0.793461\pi\) | ||||
−0.796773 | + | 0.604279i | \(0.793461\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.29227 | −0.764089 | ||||||||
\(10\) | 1.88225 | 0.595220 | ||||||||
\(11\) | −4.82481 | −1.45474 | −0.727368 | − | 0.686248i | \(-0.759257\pi\) | ||||
−0.727368 | + | 0.686248i | \(0.759257\pi\) | |||||||
\(12\) | −0.841269 | −0.242854 | ||||||||
\(13\) | 5.72931 | 1.58902 | 0.794512 | − | 0.607248i | \(-0.207727\pi\) | ||||
0.794512 | + | 0.607248i | \(0.207727\pi\) | |||||||
\(14\) | 4.21612 | 1.12681 | ||||||||
\(15\) | 1.58348 | 0.408853 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.08937 | −0.264211 | −0.132106 | − | 0.991236i | \(-0.542174\pi\) | ||||
−0.132106 | + | 0.991236i | \(0.542174\pi\) | |||||||
\(18\) | 2.29227 | 0.540292 | ||||||||
\(19\) | 3.42362 | 0.785433 | 0.392716 | − | 0.919660i | \(-0.371535\pi\) | ||||
0.392716 | + | 0.919660i | \(0.371535\pi\) | |||||||
\(20\) | −1.88225 | −0.420884 | ||||||||
\(21\) | 3.54690 | 0.773996 | ||||||||
\(22\) | 4.82481 | 1.02865 | ||||||||
\(23\) | 3.34454 | 0.697386 | 0.348693 | − | 0.937237i | \(-0.386626\pi\) | ||||
0.348693 | + | 0.937237i | \(0.386626\pi\) | |||||||
\(24\) | 0.841269 | 0.171723 | ||||||||
\(25\) | −1.45713 | −0.291426 | ||||||||
\(26\) | −5.72931 | −1.12361 | ||||||||
\(27\) | 4.45222 | 0.856830 | ||||||||
\(28\) | −4.21612 | −0.796773 | ||||||||
\(29\) | 6.98169 | 1.29647 | 0.648234 | − | 0.761441i | \(-0.275508\pi\) | ||||
0.648234 | + | 0.761441i | \(0.275508\pi\) | |||||||
\(30\) | −1.58348 | −0.289103 | ||||||||
\(31\) | −1.44739 | −0.259960 | −0.129980 | − | 0.991517i | \(-0.541491\pi\) | ||||
−0.129980 | + | 0.991517i | \(0.541491\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.05897 | 0.706576 | ||||||||
\(34\) | 1.08937 | 0.186826 | ||||||||
\(35\) | 7.93580 | 1.34140 | ||||||||
\(36\) | −2.29227 | −0.382044 | ||||||||
\(37\) | 2.43857 | 0.400899 | 0.200450 | − | 0.979704i | \(-0.435760\pi\) | ||||
0.200450 | + | 0.979704i | \(0.435760\pi\) | |||||||
\(38\) | −3.42362 | −0.555385 | ||||||||
\(39\) | −4.81989 | −0.771800 | ||||||||
\(40\) | 1.88225 | 0.297610 | ||||||||
\(41\) | 10.5413 | 1.64627 | 0.823135 | − | 0.567846i | \(-0.192223\pi\) | ||||
0.823135 | + | 0.567846i | \(0.192223\pi\) | |||||||
\(42\) | −3.54690 | −0.547298 | ||||||||
\(43\) | −4.80820 | −0.733243 | −0.366622 | − | 0.930370i | \(-0.619486\pi\) | ||||
−0.366622 | + | 0.930370i | \(0.619486\pi\) | |||||||
\(44\) | −4.82481 | −0.727368 | ||||||||
\(45\) | 4.31462 | 0.643186 | ||||||||
\(46\) | −3.34454 | −0.493126 | ||||||||
\(47\) | 9.61304 | 1.40221 | 0.701103 | − | 0.713060i | \(-0.252691\pi\) | ||||
0.701103 | + | 0.713060i | \(0.252691\pi\) | |||||||
\(48\) | −0.841269 | −0.121427 | ||||||||
\(49\) | 10.7757 | 1.53939 | ||||||||
\(50\) | 1.45713 | 0.206069 | ||||||||
\(51\) | 0.916455 | 0.128329 | ||||||||
\(52\) | 5.72931 | 0.794512 | ||||||||
\(53\) | −0.675316 | −0.0927617 | −0.0463809 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463809 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(54\) | −4.45222 | −0.605871 | ||||||||
\(55\) | 9.08151 | 1.22455 | ||||||||
\(56\) | 4.21612 | 0.563403 | ||||||||
\(57\) | −2.88019 | −0.381490 | ||||||||
\(58\) | −6.98169 | −0.916741 | ||||||||
\(59\) | −7.24193 | −0.942819 | −0.471410 | − | 0.881914i | \(-0.656255\pi\) | ||||
−0.471410 | + | 0.881914i | \(0.656255\pi\) | |||||||
\(60\) | 1.58348 | 0.204426 | ||||||||
\(61\) | −3.66784 | −0.469619 | −0.234810 | − | 0.972041i | \(-0.575447\pi\) | ||||
−0.234810 | + | 0.972041i | \(0.575447\pi\) | |||||||
\(62\) | 1.44739 | 0.183819 | ||||||||
\(63\) | 9.66448 | 1.21761 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.7840 | −1.33759 | ||||||||
\(66\) | −4.05897 | −0.499624 | ||||||||
\(67\) | −6.78487 | −0.828903 | −0.414452 | − | 0.910071i | \(-0.636027\pi\) | ||||
−0.414452 | + | 0.910071i | \(0.636027\pi\) | |||||||
\(68\) | −1.08937 | −0.132106 | ||||||||
\(69\) | −2.81366 | −0.338725 | ||||||||
\(70\) | −7.93580 | −0.948510 | ||||||||
\(71\) | 8.42340 | 0.999673 | 0.499837 | − | 0.866120i | \(-0.333393\pi\) | ||||
0.499837 | + | 0.866120i | \(0.333393\pi\) | |||||||
\(72\) | 2.29227 | 0.270146 | ||||||||
\(73\) | −9.24909 | −1.08252 | −0.541262 | − | 0.840854i | \(-0.682053\pi\) | ||||
−0.541262 | + | 0.840854i | \(0.682053\pi\) | |||||||
\(74\) | −2.43857 | −0.283479 | ||||||||
\(75\) | 1.22584 | 0.141548 | ||||||||
\(76\) | 3.42362 | 0.392716 | ||||||||
\(77\) | 20.3420 | 2.31819 | ||||||||
\(78\) | 4.81989 | 0.545745 | ||||||||
\(79\) | −13.6584 | −1.53669 | −0.768344 | − | 0.640037i | \(-0.778919\pi\) | ||||
−0.768344 | + | 0.640037i | \(0.778919\pi\) | |||||||
\(80\) | −1.88225 | −0.210442 | ||||||||
\(81\) | 3.13128 | 0.347920 | ||||||||
\(82\) | −10.5413 | −1.16409 | ||||||||
\(83\) | 12.3940 | 1.36042 | 0.680210 | − | 0.733017i | \(-0.261889\pi\) | ||||
0.680210 | + | 0.733017i | \(0.261889\pi\) | |||||||
\(84\) | 3.54690 | 0.386998 | ||||||||
\(85\) | 2.05047 | 0.222405 | ||||||||
\(86\) | 4.80820 | 0.518481 | ||||||||
\(87\) | −5.87348 | −0.629704 | ||||||||
\(88\) | 4.82481 | 0.514327 | ||||||||
\(89\) | 4.99591 | 0.529565 | 0.264783 | − | 0.964308i | \(-0.414700\pi\) | ||||
0.264783 | + | 0.964308i | \(0.414700\pi\) | |||||||
\(90\) | −4.31462 | −0.454801 | ||||||||
\(91\) | −24.1555 | −2.53218 | ||||||||
\(92\) | 3.34454 | 0.348693 | ||||||||
\(93\) | 1.21765 | 0.126264 | ||||||||
\(94\) | −9.61304 | −0.991509 | ||||||||
\(95\) | −6.44412 | −0.661153 | ||||||||
\(96\) | 0.841269 | 0.0858617 | ||||||||
\(97\) | −8.10568 | −0.823007 | −0.411503 | − | 0.911408i | \(-0.634996\pi\) | ||||
−0.411503 | + | 0.911408i | \(0.634996\pi\) | |||||||
\(98\) | −10.7757 | −1.08851 | ||||||||
\(99\) | 11.0598 | 1.11155 | ||||||||
\(100\) | −1.45713 | −0.145713 | ||||||||
\(101\) | 16.1791 | 1.60988 | 0.804940 | − | 0.593356i | \(-0.202197\pi\) | ||||
0.804940 | + | 0.593356i | \(0.202197\pi\) | |||||||
\(102\) | −0.916455 | −0.0907425 | ||||||||
\(103\) | 0.329723 | 0.0324886 | 0.0162443 | − | 0.999868i | \(-0.494829\pi\) | ||||
0.0162443 | + | 0.999868i | \(0.494829\pi\) | |||||||
\(104\) | −5.72931 | −0.561805 | ||||||||
\(105\) | −6.67615 | −0.651526 | ||||||||
\(106\) | 0.675316 | 0.0655924 | ||||||||
\(107\) | −15.4568 | −1.49426 | −0.747130 | − | 0.664678i | \(-0.768569\pi\) | ||||
−0.747130 | + | 0.664678i | \(0.768569\pi\) | |||||||
\(108\) | 4.45222 | 0.428415 | ||||||||
\(109\) | −18.6885 | −1.79003 | −0.895015 | − | 0.446037i | \(-0.852835\pi\) | ||||
−0.895015 | + | 0.446037i | \(0.852835\pi\) | |||||||
\(110\) | −9.08151 | −0.865888 | ||||||||
\(111\) | −2.05150 | −0.194720 | ||||||||
\(112\) | −4.21612 | −0.398386 | ||||||||
\(113\) | −12.7969 | −1.20383 | −0.601915 | − | 0.798560i | \(-0.705595\pi\) | ||||
−0.601915 | + | 0.798560i | \(0.705595\pi\) | |||||||
\(114\) | 2.88019 | 0.269754 | ||||||||
\(115\) | −6.29527 | −0.587037 | ||||||||
\(116\) | 6.98169 | 0.648234 | ||||||||
\(117\) | −13.1331 | −1.21416 | ||||||||
\(118\) | 7.24193 | 0.666674 | ||||||||
\(119\) | 4.59292 | 0.421033 | ||||||||
\(120\) | −1.58348 | −0.144551 | ||||||||
\(121\) | 12.2788 | 1.11626 | ||||||||
\(122\) | 3.66784 | 0.332071 | ||||||||
\(123\) | −8.86804 | −0.799605 | ||||||||
\(124\) | −1.44739 | −0.129980 | ||||||||
\(125\) | 12.1539 | 1.08708 | ||||||||
\(126\) | −9.66448 | −0.860980 | ||||||||
\(127\) | 3.48412 | 0.309166 | 0.154583 | − | 0.987980i | \(-0.450597\pi\) | ||||
0.154583 | + | 0.987980i | \(0.450597\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.04499 | 0.356141 | ||||||||
\(130\) | 10.7840 | 0.945819 | ||||||||
\(131\) | −12.8713 | −1.12457 | −0.562287 | − | 0.826942i | \(-0.690078\pi\) | ||||
−0.562287 | + | 0.826942i | \(0.690078\pi\) | |||||||
\(132\) | 4.05897 | 0.353288 | ||||||||
\(133\) | −14.4344 | −1.25162 | ||||||||
\(134\) | 6.78487 | 0.586123 | ||||||||
\(135\) | −8.38020 | −0.721253 | ||||||||
\(136\) | 1.08937 | 0.0934128 | ||||||||
\(137\) | −2.81809 | −0.240766 | −0.120383 | − | 0.992728i | \(-0.538412\pi\) | ||||
−0.120383 | + | 0.992728i | \(0.538412\pi\) | |||||||
\(138\) | 2.81366 | 0.239515 | ||||||||
\(139\) | −11.5121 | −0.976443 | −0.488221 | − | 0.872720i | \(-0.662354\pi\) | ||||
−0.488221 | + | 0.872720i | \(0.662354\pi\) | |||||||
\(140\) | 7.93580 | 0.670698 | ||||||||
\(141\) | −8.08716 | −0.681061 | ||||||||
\(142\) | −8.42340 | −0.706876 | ||||||||
\(143\) | −27.6428 | −2.31161 | ||||||||
\(144\) | −2.29227 | −0.191022 | ||||||||
\(145\) | −13.1413 | −1.09133 | ||||||||
\(146\) | 9.24909 | 0.765460 | ||||||||
\(147\) | −9.06527 | −0.747691 | ||||||||
\(148\) | 2.43857 | 0.200450 | ||||||||
\(149\) | 1.59309 | 0.130511 | 0.0652555 | − | 0.997869i | \(-0.479214\pi\) | ||||
0.0652555 | + | 0.997869i | \(0.479214\pi\) | |||||||
\(150\) | −1.22584 | −0.100089 | ||||||||
\(151\) | 3.71839 | 0.302598 | 0.151299 | − | 0.988488i | \(-0.451654\pi\) | ||||
0.151299 | + | 0.988488i | \(0.451654\pi\) | |||||||
\(152\) | −3.42362 | −0.277692 | ||||||||
\(153\) | 2.49713 | 0.201881 | ||||||||
\(154\) | −20.3420 | −1.63921 | ||||||||
\(155\) | 2.72436 | 0.218826 | ||||||||
\(156\) | −4.81989 | −0.385900 | ||||||||
\(157\) | 7.02202 | 0.560418 | 0.280209 | − | 0.959939i | \(-0.409596\pi\) | ||||
0.280209 | + | 0.959939i | \(0.409596\pi\) | |||||||
\(158\) | 13.6584 | 1.08660 | ||||||||
\(159\) | 0.568122 | 0.0450550 | ||||||||
\(160\) | 1.88225 | 0.148805 | ||||||||
\(161\) | −14.1010 | −1.11132 | ||||||||
\(162\) | −3.13128 | −0.246016 | ||||||||
\(163\) | −4.57079 | −0.358012 | −0.179006 | − | 0.983848i | \(-0.557288\pi\) | ||||
−0.179006 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(164\) | 10.5413 | 0.823135 | ||||||||
\(165\) | −7.64000 | −0.594773 | ||||||||
\(166\) | −12.3940 | −0.961962 | ||||||||
\(167\) | −3.09616 | −0.239588 | −0.119794 | − | 0.992799i | \(-0.538223\pi\) | ||||
−0.119794 | + | 0.992799i | \(0.538223\pi\) | |||||||
\(168\) | −3.54690 | −0.273649 | ||||||||
\(169\) | 19.8250 | 1.52500 | ||||||||
\(170\) | −2.05047 | −0.157264 | ||||||||
\(171\) | −7.84785 | −0.600140 | ||||||||
\(172\) | −4.80820 | −0.366622 | ||||||||
\(173\) | 16.7004 | 1.26971 | 0.634854 | − | 0.772632i | \(-0.281060\pi\) | ||||
0.634854 | + | 0.772632i | \(0.281060\pi\) | |||||||
\(174\) | 5.87348 | 0.445268 | ||||||||
\(175\) | 6.14344 | 0.464401 | ||||||||
\(176\) | −4.82481 | −0.363684 | ||||||||
\(177\) | 6.09242 | 0.457934 | ||||||||
\(178\) | −4.99591 | −0.374459 | ||||||||
\(179\) | −5.79649 | −0.433250 | −0.216625 | − | 0.976255i | \(-0.569505\pi\) | ||||
−0.216625 | + | 0.976255i | \(0.569505\pi\) | |||||||
\(180\) | 4.31462 | 0.321593 | ||||||||
\(181\) | −1.60336 | −0.119177 | −0.0595883 | − | 0.998223i | \(-0.518979\pi\) | ||||
−0.0595883 | + | 0.998223i | \(0.518979\pi\) | |||||||
\(182\) | 24.1555 | 1.79052 | ||||||||
\(183\) | 3.08564 | 0.228097 | ||||||||
\(184\) | −3.34454 | −0.246563 | ||||||||
\(185\) | −4.59001 | −0.337464 | ||||||||
\(186\) | −1.21765 | −0.0892823 | ||||||||
\(187\) | 5.25601 | 0.384358 | ||||||||
\(188\) | 9.61304 | 0.701103 | ||||||||
\(189\) | −18.7711 | −1.36540 | ||||||||
\(190\) | 6.44412 | 0.467505 | ||||||||
\(191\) | 16.5291 | 1.19600 | 0.598002 | − | 0.801494i | \(-0.295961\pi\) | ||||
0.598002 | + | 0.801494i | \(0.295961\pi\) | |||||||
\(192\) | −0.841269 | −0.0607134 | ||||||||
\(193\) | 16.4414 | 1.18348 | 0.591739 | − | 0.806130i | \(-0.298442\pi\) | ||||
0.591739 | + | 0.806130i | \(0.298442\pi\) | |||||||
\(194\) | 8.10568 | 0.581954 | ||||||||
\(195\) | 9.07225 | 0.649677 | ||||||||
\(196\) | 10.7757 | 0.769693 | ||||||||
\(197\) | 22.3038 | 1.58908 | 0.794538 | − | 0.607214i | \(-0.207713\pi\) | ||||
0.794538 | + | 0.607214i | \(0.207713\pi\) | |||||||
\(198\) | −11.0598 | −0.785982 | ||||||||
\(199\) | 15.8172 | 1.12125 | 0.560627 | − | 0.828069i | \(-0.310560\pi\) | ||||
0.560627 | + | 0.828069i | \(0.310560\pi\) | |||||||
\(200\) | 1.45713 | 0.103035 | ||||||||
\(201\) | 5.70790 | 0.402604 | ||||||||
\(202\) | −16.1791 | −1.13836 | ||||||||
\(203\) | −29.4357 | −2.06598 | ||||||||
\(204\) | 0.916455 | 0.0641647 | ||||||||
\(205\) | −19.8413 | −1.38578 | ||||||||
\(206\) | −0.329723 | −0.0229729 | ||||||||
\(207\) | −7.66658 | −0.532864 | ||||||||
\(208\) | 5.72931 | 0.397256 | ||||||||
\(209\) | −16.5183 | −1.14260 | ||||||||
\(210\) | 6.67615 | 0.460698 | ||||||||
\(211\) | −10.4508 | −0.719463 | −0.359732 | − | 0.933056i | \(-0.617132\pi\) | ||||
−0.359732 | + | 0.933056i | \(0.617132\pi\) | |||||||
\(212\) | −0.675316 | −0.0463809 | ||||||||
\(213\) | −7.08635 | −0.485548 | ||||||||
\(214\) | 15.4568 | 1.05660 | ||||||||
\(215\) | 9.05023 | 0.617221 | ||||||||
\(216\) | −4.45222 | −0.302935 | ||||||||
\(217\) | 6.10239 | 0.414258 | ||||||||
\(218\) | 18.6885 | 1.26574 | ||||||||
\(219\) | 7.78098 | 0.525790 | ||||||||
\(220\) | 9.08151 | 0.612275 | ||||||||
\(221\) | −6.24134 | −0.419838 | ||||||||
\(222\) | 2.05150 | 0.137688 | ||||||||
\(223\) | −4.03071 | −0.269916 | −0.134958 | − | 0.990851i | \(-0.543090\pi\) | ||||
−0.134958 | + | 0.990851i | \(0.543090\pi\) | |||||||
\(224\) | 4.21612 | 0.281702 | ||||||||
\(225\) | 3.34013 | 0.222675 | ||||||||
\(226\) | 12.7969 | 0.851236 | ||||||||
\(227\) | 25.1961 | 1.67232 | 0.836161 | − | 0.548484i | \(-0.184795\pi\) | ||||
0.836161 | + | 0.548484i | \(0.184795\pi\) | |||||||
\(228\) | −2.88019 | −0.190745 | ||||||||
\(229\) | −22.4179 | −1.48142 | −0.740708 | − | 0.671827i | \(-0.765510\pi\) | ||||
−0.740708 | + | 0.671827i | \(0.765510\pi\) | |||||||
\(230\) | 6.29527 | 0.415098 | ||||||||
\(231\) | −17.1131 | −1.12596 | ||||||||
\(232\) | −6.98169 | −0.458371 | ||||||||
\(233\) | −11.6626 | −0.764041 | −0.382020 | − | 0.924154i | \(-0.624772\pi\) | ||||
−0.382020 | + | 0.924154i | \(0.624772\pi\) | |||||||
\(234\) | 13.1331 | 0.858537 | ||||||||
\(235\) | −18.0942 | −1.18033 | ||||||||
\(236\) | −7.24193 | −0.471410 | ||||||||
\(237\) | 11.4904 | 0.746381 | ||||||||
\(238\) | −4.59292 | −0.297715 | ||||||||
\(239\) | −24.8251 | −1.60580 | −0.802902 | − | 0.596111i | \(-0.796712\pi\) | ||||
−0.802902 | + | 0.596111i | \(0.796712\pi\) | |||||||
\(240\) | 1.58348 | 0.102213 | ||||||||
\(241\) | 12.5505 | 0.808447 | 0.404223 | − | 0.914660i | \(-0.367542\pi\) | ||||
0.404223 | + | 0.914660i | \(0.367542\pi\) | |||||||
\(242\) | −12.2788 | −0.789312 | ||||||||
\(243\) | −15.9909 | −1.02582 | ||||||||
\(244\) | −3.66784 | −0.234810 | ||||||||
\(245\) | −20.2826 | −1.29581 | ||||||||
\(246\) | 8.86804 | 0.565406 | ||||||||
\(247\) | 19.6150 | 1.24807 | ||||||||
\(248\) | 1.44739 | 0.0919096 | ||||||||
\(249\) | −10.4267 | −0.660766 | ||||||||
\(250\) | −12.1539 | −0.768683 | ||||||||
\(251\) | 16.4964 | 1.04124 | 0.520620 | − | 0.853788i | \(-0.325701\pi\) | ||||
0.520620 | + | 0.853788i | \(0.325701\pi\) | |||||||
\(252\) | 9.66448 | 0.608805 | ||||||||
\(253\) | −16.1368 | −1.01451 | ||||||||
\(254\) | −3.48412 | −0.218613 | ||||||||
\(255\) | −1.72500 | −0.108024 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.7888 | 0.860121 | 0.430060 | − | 0.902800i | \(-0.358492\pi\) | ||||
0.430060 | + | 0.902800i | \(0.358492\pi\) | |||||||
\(258\) | −4.04499 | −0.251830 | ||||||||
\(259\) | −10.2813 | −0.638851 | ||||||||
\(260\) | −10.7840 | −0.668795 | ||||||||
\(261\) | −16.0039 | −0.990616 | ||||||||
\(262\) | 12.8713 | 0.795193 | ||||||||
\(263\) | −4.32499 | −0.266691 | −0.133345 | − | 0.991070i | \(-0.542572\pi\) | ||||
−0.133345 | + | 0.991070i | \(0.542572\pi\) | |||||||
\(264\) | −4.05897 | −0.249812 | ||||||||
\(265\) | 1.27111 | 0.0780839 | ||||||||
\(266\) | 14.4344 | 0.885031 | ||||||||
\(267\) | −4.20291 | −0.257214 | ||||||||
\(268\) | −6.78487 | −0.414452 | ||||||||
\(269\) | −11.0027 | −0.670844 | −0.335422 | − | 0.942068i | \(-0.608879\pi\) | ||||
−0.335422 | + | 0.942068i | \(0.608879\pi\) | |||||||
\(270\) | 8.38020 | 0.510003 | ||||||||
\(271\) | 2.35759 | 0.143213 | 0.0716066 | − | 0.997433i | \(-0.477187\pi\) | ||||
0.0716066 | + | 0.997433i | \(0.477187\pi\) | |||||||
\(272\) | −1.08937 | −0.0660528 | ||||||||
\(273\) | 20.3213 | 1.22990 | ||||||||
\(274\) | 2.81809 | 0.170247 | ||||||||
\(275\) | 7.03038 | 0.423948 | ||||||||
\(276\) | −2.81366 | −0.169363 | ||||||||
\(277\) | 21.4480 | 1.28868 | 0.644342 | − | 0.764738i | \(-0.277131\pi\) | ||||
0.644342 | + | 0.764738i | \(0.277131\pi\) | |||||||
\(278\) | 11.5121 | 0.690449 | ||||||||
\(279\) | 3.31781 | 0.198632 | ||||||||
\(280\) | −7.93580 | −0.474255 | ||||||||
\(281\) | 25.9927 | 1.55059 | 0.775297 | − | 0.631597i | \(-0.217600\pi\) | ||||
0.775297 | + | 0.631597i | \(0.217600\pi\) | |||||||
\(282\) | 8.08716 | 0.481583 | ||||||||
\(283\) | 5.87483 | 0.349222 | 0.174611 | − | 0.984637i | \(-0.444133\pi\) | ||||
0.174611 | + | 0.984637i | \(0.444133\pi\) | |||||||
\(284\) | 8.42340 | 0.499837 | ||||||||
\(285\) | 5.42124 | 0.321127 | ||||||||
\(286\) | 27.6428 | 1.63456 | ||||||||
\(287\) | −44.4433 | −2.62340 | ||||||||
\(288\) | 2.29227 | 0.135073 | ||||||||
\(289\) | −15.8133 | −0.930192 | ||||||||
\(290\) | 13.1413 | 0.771684 | ||||||||
\(291\) | 6.81906 | 0.399740 | ||||||||
\(292\) | −9.24909 | −0.541262 | ||||||||
\(293\) | 13.6295 | 0.796245 | 0.398122 | − | 0.917332i | \(-0.369662\pi\) | ||||
0.398122 | + | 0.917332i | \(0.369662\pi\) | |||||||
\(294\) | 9.06527 | 0.528697 | ||||||||
\(295\) | 13.6311 | 0.793635 | ||||||||
\(296\) | −2.43857 | −0.141739 | ||||||||
\(297\) | −21.4811 | −1.24646 | ||||||||
\(298\) | −1.59309 | −0.0922852 | ||||||||
\(299\) | 19.1619 | 1.10816 | ||||||||
\(300\) | 1.22584 | 0.0707739 | ||||||||
\(301\) | 20.2720 | 1.16846 | ||||||||
\(302\) | −3.71839 | −0.213969 | ||||||||
\(303\) | −13.6110 | −0.781930 | ||||||||
\(304\) | 3.42362 | 0.196358 | ||||||||
\(305\) | 6.90380 | 0.395311 | ||||||||
\(306\) | −2.49713 | −0.142751 | ||||||||
\(307\) | 13.4101 | 0.765354 | 0.382677 | − | 0.923882i | \(-0.375002\pi\) | ||||
0.382677 | + | 0.923882i | \(0.375002\pi\) | |||||||
\(308\) | 20.3420 | 1.15909 | ||||||||
\(309\) | −0.277386 | −0.0157799 | ||||||||
\(310\) | −2.72436 | −0.154733 | ||||||||
\(311\) | −21.1385 | −1.19866 | −0.599328 | − | 0.800504i | \(-0.704565\pi\) | ||||
−0.599328 | + | 0.800504i | \(0.704565\pi\) | |||||||
\(312\) | 4.81989 | 0.272873 | ||||||||
\(313\) | 2.40819 | 0.136119 | 0.0680594 | − | 0.997681i | \(-0.478319\pi\) | ||||
0.0680594 | + | 0.997681i | \(0.478319\pi\) | |||||||
\(314\) | −7.02202 | −0.396275 | ||||||||
\(315\) | −18.1910 | −1.02495 | ||||||||
\(316\) | −13.6584 | −0.768344 | ||||||||
\(317\) | −21.6410 | −1.21548 | −0.607739 | − | 0.794137i | \(-0.707923\pi\) | ||||
−0.607739 | + | 0.794137i | \(0.707923\pi\) | |||||||
\(318\) | −0.568122 | −0.0318587 | ||||||||
\(319\) | −33.6854 | −1.88602 | ||||||||
\(320\) | −1.88225 | −0.105221 | ||||||||
\(321\) | 13.0033 | 0.725773 | ||||||||
\(322\) | 14.1010 | 0.785819 | ||||||||
\(323\) | −3.72960 | −0.207520 | ||||||||
\(324\) | 3.13128 | 0.173960 | ||||||||
\(325\) | −8.34835 | −0.463083 | ||||||||
\(326\) | 4.57079 | 0.253153 | ||||||||
\(327\) | 15.7220 | 0.869430 | ||||||||
\(328\) | −10.5413 | −0.582044 | ||||||||
\(329\) | −40.5298 | −2.23448 | ||||||||
\(330\) | 7.64000 | 0.420568 | ||||||||
\(331\) | 0.855744 | 0.0470360 | 0.0235180 | − | 0.999723i | \(-0.492513\pi\) | ||||
0.0235180 | + | 0.999723i | \(0.492513\pi\) | |||||||
\(332\) | 12.3940 | 0.680210 | ||||||||
\(333\) | −5.58986 | −0.306322 | ||||||||
\(334\) | 3.09616 | 0.169414 | ||||||||
\(335\) | 12.7708 | 0.697745 | ||||||||
\(336\) | 3.54690 | 0.193499 | ||||||||
\(337\) | −34.5078 | −1.87976 | −0.939881 | − | 0.341502i | \(-0.889064\pi\) | ||||
−0.939881 | + | 0.341502i | \(0.889064\pi\) | |||||||
\(338\) | −19.8250 | −1.07834 | ||||||||
\(339\) | 10.7656 | 0.584709 | ||||||||
\(340\) | 2.05047 | 0.111202 | ||||||||
\(341\) | 6.98341 | 0.378173 | ||||||||
\(342\) | 7.84785 | 0.424363 | ||||||||
\(343\) | −15.9188 | −0.859536 | ||||||||
\(344\) | 4.80820 | 0.259241 | ||||||||
\(345\) | 5.29602 | 0.285128 | ||||||||
\(346\) | −16.7004 | −0.897820 | ||||||||
\(347\) | −22.2428 | −1.19405 | −0.597027 | − | 0.802221i | \(-0.703651\pi\) | ||||
−0.597027 | + | 0.802221i | \(0.703651\pi\) | |||||||
\(348\) | −5.87348 | −0.314852 | ||||||||
\(349\) | 32.4327 | 1.73608 | 0.868042 | − | 0.496490i | \(-0.165378\pi\) | ||||
0.868042 | + | 0.496490i | \(0.165378\pi\) | |||||||
\(350\) | −6.14344 | −0.328381 | ||||||||
\(351\) | 25.5081 | 1.36152 | ||||||||
\(352\) | 4.82481 | 0.257163 | ||||||||
\(353\) | 32.9861 | 1.75567 | 0.877837 | − | 0.478960i | \(-0.158986\pi\) | ||||
0.877837 | + | 0.478960i | \(0.158986\pi\) | |||||||
\(354\) | −6.09242 | −0.323808 | ||||||||
\(355\) | −15.8549 | −0.841493 | ||||||||
\(356\) | 4.99591 | 0.264783 | ||||||||
\(357\) | −3.86389 | −0.204499 | ||||||||
\(358\) | 5.79649 | 0.306354 | ||||||||
\(359\) | −13.4018 | −0.707320 | −0.353660 | − | 0.935374i | \(-0.615063\pi\) | ||||
−0.353660 | + | 0.935374i | \(0.615063\pi\) | |||||||
\(360\) | −4.31462 | −0.227400 | ||||||||
\(361\) | −7.27881 | −0.383095 | ||||||||
\(362\) | 1.60336 | 0.0842705 | ||||||||
\(363\) | −10.3298 | −0.542173 | ||||||||
\(364\) | −24.1555 | −1.26609 | ||||||||
\(365\) | 17.4091 | 0.911235 | ||||||||
\(366\) | −3.08564 | −0.161289 | ||||||||
\(367\) | 19.7119 | 1.02895 | 0.514477 | − | 0.857504i | \(-0.327986\pi\) | ||||
0.514477 | + | 0.857504i | \(0.327986\pi\) | |||||||
\(368\) | 3.34454 | 0.174346 | ||||||||
\(369\) | −24.1634 | −1.25790 | ||||||||
\(370\) | 4.59001 | 0.238623 | ||||||||
\(371\) | 2.84721 | 0.147820 | ||||||||
\(372\) | 1.21765 | 0.0631322 | ||||||||
\(373\) | −22.9719 | −1.18944 | −0.594719 | − | 0.803933i | \(-0.702737\pi\) | ||||
−0.594719 | + | 0.803933i | \(0.702737\pi\) | |||||||
\(374\) | −5.25601 | −0.271782 | ||||||||
\(375\) | −10.2247 | −0.528003 | ||||||||
\(376\) | −9.61304 | −0.495755 | ||||||||
\(377\) | 40.0003 | 2.06012 | ||||||||
\(378\) | 18.7711 | 0.965482 | ||||||||
\(379\) | −32.5199 | −1.67044 | −0.835218 | − | 0.549919i | \(-0.814658\pi\) | ||||
−0.835218 | + | 0.549919i | \(0.814658\pi\) | |||||||
\(380\) | −6.44412 | −0.330576 | ||||||||
\(381\) | −2.93108 | −0.150164 | ||||||||
\(382\) | −16.5291 | −0.845703 | ||||||||
\(383\) | −29.4514 | −1.50490 | −0.752448 | − | 0.658651i | \(-0.771127\pi\) | ||||
−0.752448 | + | 0.658651i | \(0.771127\pi\) | |||||||
\(384\) | 0.841269 | 0.0429309 | ||||||||
\(385\) | −38.2888 | −1.95138 | ||||||||
\(386\) | −16.4414 | −0.836845 | ||||||||
\(387\) | 11.0217 | 0.560263 | ||||||||
\(388\) | −8.10568 | −0.411503 | ||||||||
\(389\) | −33.4454 | −1.69575 | −0.847874 | − | 0.530198i | \(-0.822118\pi\) | ||||
−0.847874 | + | 0.530198i | \(0.822118\pi\) | |||||||
\(390\) | −9.07225 | −0.459391 | ||||||||
\(391\) | −3.64345 | −0.184257 | ||||||||
\(392\) | −10.7757 | −0.544255 | ||||||||
\(393\) | 10.8283 | 0.546213 | ||||||||
\(394\) | −22.3038 | −1.12365 | ||||||||
\(395\) | 25.7085 | 1.29354 | ||||||||
\(396\) | 11.0598 | 0.555773 | ||||||||
\(397\) | −2.19143 | −0.109985 | −0.0549923 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549923 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(398\) | −15.8172 | −0.792846 | ||||||||
\(399\) | 12.1432 | 0.607922 | ||||||||
\(400\) | −1.45713 | −0.0728565 | ||||||||
\(401\) | 19.6058 | 0.979068 | 0.489534 | − | 0.871984i | \(-0.337167\pi\) | ||||
0.489534 | + | 0.871984i | \(0.337167\pi\) | |||||||
\(402\) | −5.70790 | −0.284684 | ||||||||
\(403\) | −8.29257 | −0.413082 | ||||||||
\(404\) | 16.1791 | 0.804940 | ||||||||
\(405\) | −5.89385 | −0.292868 | ||||||||
\(406\) | 29.4357 | 1.46087 | ||||||||
\(407\) | −11.7657 | −0.583202 | ||||||||
\(408\) | −0.916455 | −0.0453713 | ||||||||
\(409\) | −6.19236 | −0.306192 | −0.153096 | − | 0.988211i | \(-0.548924\pi\) | ||||
−0.153096 | + | 0.988211i | \(0.548924\pi\) | |||||||
\(410\) | 19.8413 | 0.979892 | ||||||||
\(411\) | 2.37078 | 0.116942 | ||||||||
\(412\) | 0.329723 | 0.0162443 | ||||||||
\(413\) | 30.5329 | 1.50242 | ||||||||
\(414\) | 7.66658 | 0.376792 | ||||||||
\(415\) | −23.3287 | −1.14516 | ||||||||
\(416\) | −5.72931 | −0.280902 | ||||||||
\(417\) | 9.68477 | 0.474265 | ||||||||
\(418\) | 16.5183 | 0.807938 | ||||||||
\(419\) | −21.1687 | −1.03416 | −0.517079 | − | 0.855938i | \(-0.672981\pi\) | ||||
−0.517079 | + | 0.855938i | \(0.672981\pi\) | |||||||
\(420\) | −6.67615 | −0.325763 | ||||||||
\(421\) | −12.1390 | −0.591617 | −0.295809 | − | 0.955247i | \(-0.595589\pi\) | ||||
−0.295809 | + | 0.955247i | \(0.595589\pi\) | |||||||
\(422\) | 10.4508 | 0.508737 | ||||||||
\(423\) | −22.0356 | −1.07141 | ||||||||
\(424\) | 0.675316 | 0.0327962 | ||||||||
\(425\) | 1.58736 | 0.0769980 | ||||||||
\(426\) | 7.08635 | 0.343335 | ||||||||
\(427\) | 15.4641 | 0.748359 | ||||||||
\(428\) | −15.4568 | −0.747130 | ||||||||
\(429\) | 23.2551 | 1.12277 | ||||||||
\(430\) | −9.05023 | −0.436441 | ||||||||
\(431\) | −9.81860 | −0.472945 | −0.236473 | − | 0.971638i | \(-0.575991\pi\) | ||||
−0.236473 | + | 0.971638i | \(0.575991\pi\) | |||||||
\(432\) | 4.45222 | 0.214208 | ||||||||
\(433\) | 11.0706 | 0.532019 | 0.266009 | − | 0.963970i | \(-0.414295\pi\) | ||||
0.266009 | + | 0.963970i | \(0.414295\pi\) | |||||||
\(434\) | −6.10239 | −0.292924 | ||||||||
\(435\) | 11.0554 | 0.530065 | ||||||||
\(436\) | −18.6885 | −0.895015 | ||||||||
\(437\) | 11.4505 | 0.547750 | ||||||||
\(438\) | −7.78098 | −0.371790 | ||||||||
\(439\) | 26.2880 | 1.25466 | 0.627330 | − | 0.778754i | \(-0.284148\pi\) | ||||
0.627330 | + | 0.778754i | \(0.284148\pi\) | |||||||
\(440\) | −9.08151 | −0.432944 | ||||||||
\(441\) | −24.7008 | −1.17623 | ||||||||
\(442\) | 6.24134 | 0.296870 | ||||||||
\(443\) | 5.19550 | 0.246846 | 0.123423 | − | 0.992354i | \(-0.460613\pi\) | ||||
0.123423 | + | 0.992354i | \(0.460613\pi\) | |||||||
\(444\) | −2.05150 | −0.0973598 | ||||||||
\(445\) | −9.40356 | −0.445771 | ||||||||
\(446\) | 4.03071 | 0.190859 | ||||||||
\(447\) | −1.34022 | −0.0633901 | ||||||||
\(448\) | −4.21612 | −0.199193 | ||||||||
\(449\) | −37.2659 | −1.75869 | −0.879343 | − | 0.476188i | \(-0.842018\pi\) | ||||
−0.879343 | + | 0.476188i | \(0.842018\pi\) | |||||||
\(450\) | −3.34013 | −0.157455 | ||||||||
\(451\) | −50.8596 | −2.39489 | ||||||||
\(452\) | −12.7969 | −0.601915 | ||||||||
\(453\) | −3.12817 | −0.146974 | ||||||||
\(454\) | −25.1961 | −1.18251 | ||||||||
\(455\) | 45.4667 | 2.13151 | ||||||||
\(456\) | 2.88019 | 0.134877 | ||||||||
\(457\) | 2.71322 | 0.126919 | 0.0634596 | − | 0.997984i | \(-0.479787\pi\) | ||||
0.0634596 | + | 0.997984i | \(0.479787\pi\) | |||||||
\(458\) | 22.4179 | 1.04752 | ||||||||
\(459\) | −4.85012 | −0.226384 | ||||||||
\(460\) | −6.29527 | −0.293519 | ||||||||
\(461\) | −19.6834 | −0.916750 | −0.458375 | − | 0.888759i | \(-0.651568\pi\) | ||||
−0.458375 | + | 0.888759i | \(0.651568\pi\) | |||||||
\(462\) | 17.1131 | 0.796174 | ||||||||
\(463\) | 22.2994 | 1.03634 | 0.518170 | − | 0.855278i | \(-0.326614\pi\) | ||||
0.518170 | + | 0.855278i | \(0.326614\pi\) | |||||||
\(464\) | 6.98169 | 0.324117 | ||||||||
\(465\) | −2.29192 | −0.106285 | ||||||||
\(466\) | 11.6626 | 0.540258 | ||||||||
\(467\) | −0.279514 | −0.0129343 | −0.00646717 | − | 0.999979i | \(-0.502059\pi\) | ||||
−0.00646717 | + | 0.999979i | \(0.502059\pi\) | |||||||
\(468\) | −13.1331 | −0.607078 | ||||||||
\(469\) | 28.6058 | 1.32089 | ||||||||
\(470\) | 18.0942 | 0.834621 | ||||||||
\(471\) | −5.90741 | −0.272199 | ||||||||
\(472\) | 7.24193 | 0.333337 | ||||||||
\(473\) | 23.1986 | 1.06667 | ||||||||
\(474\) | −11.4904 | −0.527771 | ||||||||
\(475\) | −4.98866 | −0.228896 | ||||||||
\(476\) | 4.59292 | 0.210516 | ||||||||
\(477\) | 1.54800 | 0.0708782 | ||||||||
\(478\) | 24.8251 | 1.13548 | ||||||||
\(479\) | −38.7175 | −1.76905 | −0.884524 | − | 0.466494i | \(-0.845517\pi\) | ||||
−0.884524 | + | 0.466494i | \(0.845517\pi\) | |||||||
\(480\) | −1.58348 | −0.0722757 | ||||||||
\(481\) | 13.9713 | 0.637038 | ||||||||
\(482\) | −12.5505 | −0.571658 | ||||||||
\(483\) | 11.8628 | 0.539774 | ||||||||
\(484\) | 12.2788 | 0.558128 | ||||||||
\(485\) | 15.2569 | 0.692781 | ||||||||
\(486\) | 15.9909 | 0.725363 | ||||||||
\(487\) | 24.8964 | 1.12816 | 0.564082 | − | 0.825718i | \(-0.309230\pi\) | ||||
0.564082 | + | 0.825718i | \(0.309230\pi\) | |||||||
\(488\) | 3.66784 | 0.166035 | ||||||||
\(489\) | 3.84527 | 0.173889 | ||||||||
\(490\) | 20.2826 | 0.916273 | ||||||||
\(491\) | −23.7423 | −1.07147 | −0.535737 | − | 0.844385i | \(-0.679966\pi\) | ||||
−0.535737 | + | 0.844385i | \(0.679966\pi\) | |||||||
\(492\) | −8.86804 | −0.399802 | ||||||||
\(493\) | −7.60565 | −0.342541 | ||||||||
\(494\) | −19.6150 | −0.882520 | ||||||||
\(495\) | −20.8172 | −0.935665 | ||||||||
\(496\) | −1.44739 | −0.0649899 | ||||||||
\(497\) | −35.5141 | −1.59302 | ||||||||
\(498\) | 10.4267 | 0.467232 | ||||||||
\(499\) | −1.12134 | −0.0501983 | −0.0250991 | − | 0.999685i | \(-0.507990\pi\) | ||||
−0.0250991 | + | 0.999685i | \(0.507990\pi\) | |||||||
\(500\) | 12.1539 | 0.543541 | ||||||||
\(501\) | 2.60471 | 0.116370 | ||||||||
\(502\) | −16.4964 | −0.736268 | ||||||||
\(503\) | 1.55759 | 0.0694496 | 0.0347248 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347248 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(504\) | −9.66448 | −0.430490 | ||||||||
\(505\) | −30.4531 | −1.35515 | ||||||||
\(506\) | 16.1368 | 0.717368 | ||||||||
\(507\) | −16.6781 | −0.740702 | ||||||||
\(508\) | 3.48412 | 0.154583 | ||||||||
\(509\) | −8.05217 | −0.356906 | −0.178453 | − | 0.983948i | \(-0.557109\pi\) | ||||
−0.178453 | + | 0.983948i | \(0.557109\pi\) | |||||||
\(510\) | 1.72500 | 0.0763842 | ||||||||
\(511\) | 38.9953 | 1.72505 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 15.2427 | 0.672983 | ||||||||
\(514\) | −13.7888 | −0.608197 | ||||||||
\(515\) | −0.620621 | −0.0273478 | ||||||||
\(516\) | 4.04499 | 0.178071 | ||||||||
\(517\) | −46.3811 | −2.03984 | ||||||||
\(518\) | 10.2813 | 0.451736 | ||||||||
\(519\) | −14.0495 | −0.616707 | ||||||||
\(520\) | 10.7840 | 0.472910 | ||||||||
\(521\) | 23.6403 | 1.03570 | 0.517851 | − | 0.855471i | \(-0.326732\pi\) | ||||
0.517851 | + | 0.855471i | \(0.326732\pi\) | |||||||
\(522\) | 16.0039 | 0.700471 | ||||||||
\(523\) | −19.8303 | −0.867118 | −0.433559 | − | 0.901125i | \(-0.642742\pi\) | ||||
−0.433559 | + | 0.901125i | \(0.642742\pi\) | |||||||
\(524\) | −12.8713 | −0.562287 | ||||||||
\(525\) | −5.16829 | −0.225563 | ||||||||
\(526\) | 4.32499 | 0.188579 | ||||||||
\(527\) | 1.57675 | 0.0686843 | ||||||||
\(528\) | 4.05897 | 0.176644 | ||||||||
\(529\) | −11.8140 | −0.513653 | ||||||||
\(530\) | −1.27111 | −0.0552136 | ||||||||
\(531\) | 16.6004 | 0.720397 | ||||||||
\(532\) | −14.4344 | −0.625811 | ||||||||
\(533\) | 60.3942 | 2.61596 | ||||||||
\(534\) | 4.20291 | 0.181878 | ||||||||
\(535\) | 29.0935 | 1.25782 | ||||||||
\(536\) | 6.78487 | 0.293062 | ||||||||
\(537\) | 4.87641 | 0.210433 | ||||||||
\(538\) | 11.0027 | 0.474358 | ||||||||
\(539\) | −51.9907 | −2.23940 | ||||||||
\(540\) | −8.38020 | −0.360626 | ||||||||
\(541\) | 12.1772 | 0.523540 | 0.261770 | − | 0.965130i | \(-0.415694\pi\) | ||||
0.261770 | + | 0.965130i | \(0.415694\pi\) | |||||||
\(542\) | −2.35759 | −0.101267 | ||||||||
\(543\) | 1.34885 | 0.0578849 | ||||||||
\(544\) | 1.08937 | 0.0467064 | ||||||||
\(545\) | 35.1764 | 1.50679 | ||||||||
\(546\) | −20.3213 | −0.869670 | ||||||||
\(547\) | −37.2881 | −1.59433 | −0.797163 | − | 0.603764i | \(-0.793667\pi\) | ||||
−0.797163 | + | 0.603764i | \(0.793667\pi\) | |||||||
\(548\) | −2.81809 | −0.120383 | ||||||||
\(549\) | 8.40767 | 0.358831 | ||||||||
\(550\) | −7.03038 | −0.299776 | ||||||||
\(551\) | 23.9027 | 1.01829 | ||||||||
\(552\) | 2.81366 | 0.119757 | ||||||||
\(553\) | 57.5855 | 2.44878 | ||||||||
\(554\) | −21.4480 | −0.911237 | ||||||||
\(555\) | 3.86144 | 0.163909 | ||||||||
\(556\) | −11.5121 | −0.488221 | ||||||||
\(557\) | −44.7533 | −1.89626 | −0.948129 | − | 0.317885i | \(-0.897027\pi\) | ||||
−0.948129 | + | 0.317885i | \(0.897027\pi\) | |||||||
\(558\) | −3.31781 | −0.140454 | ||||||||
\(559\) | −27.5476 | −1.16514 | ||||||||
\(560\) | 7.93580 | 0.335349 | ||||||||
\(561\) | −4.42172 | −0.186685 | ||||||||
\(562\) | −25.9927 | −1.09644 | ||||||||
\(563\) | 4.21839 | 0.177784 | 0.0888919 | − | 0.996041i | \(-0.471667\pi\) | ||||
0.0888919 | + | 0.996041i | \(0.471667\pi\) | |||||||
\(564\) | −8.08716 | −0.340531 | ||||||||
\(565\) | 24.0870 | 1.01335 | ||||||||
\(566\) | −5.87483 | −0.246938 | ||||||||
\(567\) | −13.2019 | −0.554426 | ||||||||
\(568\) | −8.42340 | −0.353438 | ||||||||
\(569\) | −18.3444 | −0.769035 | −0.384518 | − | 0.923118i | \(-0.625632\pi\) | ||||
−0.384518 | + | 0.923118i | \(0.625632\pi\) | |||||||
\(570\) | −5.42124 | −0.227071 | ||||||||
\(571\) | 2.17978 | 0.0912208 | 0.0456104 | − | 0.998959i | \(-0.485477\pi\) | ||||
0.0456104 | + | 0.998959i | \(0.485477\pi\) | |||||||
\(572\) | −27.6428 | −1.15581 | ||||||||
\(573\) | −13.9054 | −0.580908 | ||||||||
\(574\) | 44.4433 | 1.85503 | ||||||||
\(575\) | −4.87344 | −0.203236 | ||||||||
\(576\) | −2.29227 | −0.0955111 | ||||||||
\(577\) | −17.0901 | −0.711472 | −0.355736 | − | 0.934587i | \(-0.615770\pi\) | ||||
−0.355736 | + | 0.934587i | \(0.615770\pi\) | |||||||
\(578\) | 15.8133 | 0.657745 | ||||||||
\(579\) | −13.8316 | −0.574823 | ||||||||
\(580\) | −13.1413 | −0.545663 | ||||||||
\(581\) | −52.2547 | −2.16789 | ||||||||
\(582\) | −6.81906 | −0.282659 | ||||||||
\(583\) | 3.25827 | 0.134944 | ||||||||
\(584\) | 9.24909 | 0.382730 | ||||||||
\(585\) | 24.7198 | 1.02204 | ||||||||
\(586\) | −13.6295 | −0.563030 | ||||||||
\(587\) | 26.5055 | 1.09400 | 0.547000 | − | 0.837133i | \(-0.315770\pi\) | ||||
0.547000 | + | 0.837133i | \(0.315770\pi\) | |||||||
\(588\) | −9.06527 | −0.373845 | ||||||||
\(589\) | −4.95533 | −0.204181 | ||||||||
\(590\) | −13.6311 | −0.561185 | ||||||||
\(591\) | −18.7635 | −0.771826 | ||||||||
\(592\) | 2.43857 | 0.100225 | ||||||||
\(593\) | −12.7116 | −0.522002 | −0.261001 | − | 0.965339i | \(-0.584053\pi\) | ||||
−0.261001 | + | 0.965339i | \(0.584053\pi\) | |||||||
\(594\) | 21.4811 | 0.881382 | ||||||||
\(595\) | −8.64504 | −0.354412 | ||||||||
\(596\) | 1.59309 | 0.0652555 | ||||||||
\(597\) | −13.3065 | −0.544601 | ||||||||
\(598\) | −19.1619 | −0.783589 | ||||||||
\(599\) | −6.48987 | −0.265169 | −0.132584 | − | 0.991172i | \(-0.542328\pi\) | ||||
−0.132584 | + | 0.991172i | \(0.542328\pi\) | |||||||
\(600\) | −1.22584 | −0.0500447 | ||||||||
\(601\) | −6.21476 | −0.253505 | −0.126753 | − | 0.991934i | \(-0.540455\pi\) | ||||
−0.126753 | + | 0.991934i | \(0.540455\pi\) | |||||||
\(602\) | −20.2720 | −0.826223 | ||||||||
\(603\) | 15.5527 | 0.633356 | ||||||||
\(604\) | 3.71839 | 0.151299 | ||||||||
\(605\) | −23.1118 | −0.939629 | ||||||||
\(606\) | 13.6110 | 0.552908 | ||||||||
\(607\) | 16.5887 | 0.673314 | 0.336657 | − | 0.941627i | \(-0.390704\pi\) | ||||
0.336657 | + | 0.941627i | \(0.390704\pi\) | |||||||
\(608\) | −3.42362 | −0.138846 | ||||||||
\(609\) | 24.7633 | 1.00346 | ||||||||
\(610\) | −6.90380 | −0.279527 | ||||||||
\(611\) | 55.0761 | 2.22814 | ||||||||
\(612\) | 2.49713 | 0.100940 | ||||||||
\(613\) | 42.5422 | 1.71826 | 0.859132 | − | 0.511754i | \(-0.171004\pi\) | ||||
0.859132 | + | 0.511754i | \(0.171004\pi\) | |||||||
\(614\) | −13.4101 | −0.541187 | ||||||||
\(615\) | 16.6919 | 0.673082 | ||||||||
\(616\) | −20.3420 | −0.819603 | ||||||||
\(617\) | 36.7530 | 1.47962 | 0.739810 | − | 0.672815i | \(-0.234915\pi\) | ||||
0.739810 | + | 0.672815i | \(0.234915\pi\) | |||||||
\(618\) | 0.277386 | 0.0111581 | ||||||||
\(619\) | 12.9809 | 0.521746 | 0.260873 | − | 0.965373i | \(-0.415990\pi\) | ||||
0.260873 | + | 0.965373i | \(0.415990\pi\) | |||||||
\(620\) | 2.72436 | 0.109413 | ||||||||
\(621\) | 14.8907 | 0.597541 | ||||||||
\(622\) | 21.1385 | 0.847578 | ||||||||
\(623\) | −21.0634 | −0.843886 | ||||||||
\(624\) | −4.81989 | −0.192950 | ||||||||
\(625\) | −15.5911 | −0.623645 | ||||||||
\(626\) | −2.40819 | −0.0962505 | ||||||||
\(627\) | 13.8964 | 0.554968 | ||||||||
\(628\) | 7.02202 | 0.280209 | ||||||||
\(629\) | −2.65651 | −0.105922 | ||||||||
\(630\) | 18.1910 | 0.724746 | ||||||||
\(631\) | 10.4456 | 0.415832 | 0.207916 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207916 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(632\) | 13.6584 | 0.543302 | ||||||||
\(633\) | 8.79194 | 0.349448 | ||||||||
\(634\) | 21.6410 | 0.859472 | ||||||||
\(635\) | −6.55799 | −0.260246 | ||||||||
\(636\) | 0.568122 | 0.0225275 | ||||||||
\(637\) | 61.7373 | 2.44612 | ||||||||
\(638\) | 33.6854 | 1.33362 | ||||||||
\(639\) | −19.3087 | −0.763839 | ||||||||
\(640\) | 1.88225 | 0.0744025 | ||||||||
\(641\) | −7.70732 | −0.304421 | −0.152210 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152210 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(642\) | −13.0033 | −0.513199 | ||||||||
\(643\) | −0.243674 | −0.00960956 | −0.00480478 | − | 0.999988i | \(-0.501529\pi\) | ||||
−0.00480478 | + | 0.999988i | \(0.501529\pi\) | |||||||
\(644\) | −14.1010 | −0.555658 | ||||||||
\(645\) | −7.61369 | −0.299789 | ||||||||
\(646\) | 3.72960 | 0.146739 | ||||||||
\(647\) | −22.3444 | −0.878450 | −0.439225 | − | 0.898377i | \(-0.644747\pi\) | ||||
−0.439225 | + | 0.898377i | \(0.644747\pi\) | |||||||
\(648\) | −3.13128 | −0.123008 | ||||||||
\(649\) | 34.9410 | 1.37155 | ||||||||
\(650\) | 8.34835 | 0.327449 | ||||||||
\(651\) | −5.13376 | −0.201208 | ||||||||
\(652\) | −4.57079 | −0.179006 | ||||||||
\(653\) | −3.83956 | −0.150254 | −0.0751268 | − | 0.997174i | \(-0.523936\pi\) | ||||
−0.0751268 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(654\) | −15.7220 | −0.614780 | ||||||||
\(655\) | 24.2271 | 0.946630 | ||||||||
\(656\) | 10.5413 | 0.411567 | ||||||||
\(657\) | 21.2014 | 0.827144 | ||||||||
\(658\) | 40.5298 | 1.58001 | ||||||||
\(659\) | 6.40909 | 0.249663 | 0.124831 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124831 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(660\) | −7.64000 | −0.297386 | ||||||||
\(661\) | −10.4490 | −0.406418 | −0.203209 | − | 0.979135i | \(-0.565137\pi\) | ||||
−0.203209 | + | 0.979135i | \(0.565137\pi\) | |||||||
\(662\) | −0.855744 | −0.0332594 | ||||||||
\(663\) | 5.25065 | 0.203918 | ||||||||
\(664\) | −12.3940 | −0.480981 | ||||||||
\(665\) | 27.1692 | 1.05358 | ||||||||
\(666\) | 5.58986 | 0.216603 | ||||||||
\(667\) | 23.3506 | 0.904138 | ||||||||
\(668\) | −3.09616 | −0.119794 | ||||||||
\(669\) | 3.39091 | 0.131100 | ||||||||
\(670\) | −12.7708 | −0.493380 | ||||||||
\(671\) | 17.6967 | 0.683172 | ||||||||
\(672\) | −3.54690 | −0.136825 | ||||||||
\(673\) | −38.6084 | −1.48824 | −0.744122 | − | 0.668044i | \(-0.767132\pi\) | ||||
−0.744122 | + | 0.668044i | \(0.767132\pi\) | |||||||
\(674\) | 34.5078 | 1.32919 | ||||||||
\(675\) | −6.48747 | −0.249703 | ||||||||
\(676\) | 19.8250 | 0.762499 | ||||||||
\(677\) | 5.45005 | 0.209463 | 0.104731 | − | 0.994501i | \(-0.466602\pi\) | ||||
0.104731 | + | 0.994501i | \(0.466602\pi\) | |||||||
\(678\) | −10.7656 | −0.413452 | ||||||||
\(679\) | 34.1745 | 1.31150 | ||||||||
\(680\) | −2.05047 | −0.0786319 | ||||||||
\(681\) | −21.1967 | −0.812259 | ||||||||
\(682\) | −6.98341 | −0.267408 | ||||||||
\(683\) | −1.23732 | −0.0473446 | −0.0236723 | − | 0.999720i | \(-0.507536\pi\) | ||||
−0.0236723 | + | 0.999720i | \(0.507536\pi\) | |||||||
\(684\) | −7.84785 | −0.300070 | ||||||||
\(685\) | 5.30436 | 0.202669 | ||||||||
\(686\) | 15.9188 | 0.607784 | ||||||||
\(687\) | 18.8595 | 0.719534 | ||||||||
\(688\) | −4.80820 | −0.183311 | ||||||||
\(689\) | −3.86909 | −0.147401 | ||||||||
\(690\) | −5.29602 | −0.201616 | ||||||||
\(691\) | 23.4044 | 0.890347 | 0.445174 | − | 0.895444i | \(-0.353142\pi\) | ||||
0.445174 | + | 0.895444i | \(0.353142\pi\) | |||||||
\(692\) | 16.7004 | 0.634854 | ||||||||
\(693\) | −46.6293 | −1.77130 | ||||||||
\(694\) | 22.2428 | 0.844324 | ||||||||
\(695\) | 21.6686 | 0.821939 | ||||||||
\(696\) | 5.87348 | 0.222634 | ||||||||
\(697\) | −11.4833 | −0.434963 | ||||||||
\(698\) | −32.4327 | −1.22760 | ||||||||
\(699\) | 9.81137 | 0.371100 | ||||||||
\(700\) | 6.14344 | 0.232200 | ||||||||
\(701\) | −39.0654 | −1.47548 | −0.737739 | − | 0.675086i | \(-0.764107\pi\) | ||||
−0.737739 | + | 0.675086i | \(0.764107\pi\) | |||||||
\(702\) | −25.5081 | −0.962743 | ||||||||
\(703\) | 8.34876 | 0.314879 | ||||||||
\(704\) | −4.82481 | −0.181842 | ||||||||
\(705\) | 15.2221 | 0.573296 | ||||||||
\(706\) | −32.9861 | −1.24145 | ||||||||
\(707\) | −68.2131 | −2.56542 | ||||||||
\(708\) | 6.09242 | 0.228967 | ||||||||
\(709\) | −20.9689 | −0.787504 | −0.393752 | − | 0.919217i | \(-0.628823\pi\) | ||||
−0.393752 | + | 0.919217i | \(0.628823\pi\) | |||||||
\(710\) | 15.8549 | 0.595026 | ||||||||
\(711\) | 31.3087 | 1.17417 | ||||||||
\(712\) | −4.99591 | −0.187230 | ||||||||
\(713\) | −4.84088 | −0.181292 | ||||||||
\(714\) | 3.86389 | 0.144602 | ||||||||
\(715\) | 52.0308 | 1.94584 | ||||||||
\(716\) | −5.79649 | −0.216625 | ||||||||
\(717\) | 20.8846 | 0.779951 | ||||||||
\(718\) | 13.4018 | 0.500151 | ||||||||
\(719\) | 7.68056 | 0.286436 | 0.143218 | − | 0.989691i | \(-0.454255\pi\) | ||||
0.143218 | + | 0.989691i | \(0.454255\pi\) | |||||||
\(720\) | 4.31462 | 0.160796 | ||||||||
\(721\) | −1.39015 | −0.0517720 | ||||||||
\(722\) | 7.27881 | 0.270889 | ||||||||
\(723\) | −10.5583 | −0.392668 | ||||||||
\(724\) | −1.60336 | −0.0595883 | ||||||||
\(725\) | −10.1732 | −0.377824 | ||||||||
\(726\) | 10.3298 | 0.383375 | ||||||||
\(727\) | 22.8897 | 0.848932 | 0.424466 | − | 0.905444i | \(-0.360462\pi\) | ||||
0.424466 | + | 0.905444i | \(0.360462\pi\) | |||||||
\(728\) | 24.1555 | 0.895261 | ||||||||
\(729\) | 4.05883 | 0.150327 | ||||||||
\(730\) | −17.4091 | −0.644340 | ||||||||
\(731\) | 5.23791 | 0.193731 | ||||||||
\(732\) | 3.08564 | 0.114049 | ||||||||
\(733\) | −9.73597 | −0.359606 | −0.179803 | − | 0.983703i | \(-0.557546\pi\) | ||||
−0.179803 | + | 0.983703i | \(0.557546\pi\) | |||||||
\(734\) | −19.7119 | −0.727580 | ||||||||
\(735\) | 17.0631 | 0.629382 | ||||||||
\(736\) | −3.34454 | −0.123282 | ||||||||
\(737\) | 32.7357 | 1.20584 | ||||||||
\(738\) | 24.1634 | 0.889466 | ||||||||
\(739\) | −7.70807 | −0.283546 | −0.141773 | − | 0.989899i | \(-0.545280\pi\) | ||||
−0.141773 | + | 0.989899i | \(0.545280\pi\) | |||||||
\(740\) | −4.59001 | −0.168732 | ||||||||
\(741\) | −16.5015 | −0.606197 | ||||||||
\(742\) | −2.84721 | −0.104525 | ||||||||
\(743\) | −52.5541 | −1.92802 | −0.964011 | − | 0.265862i | \(-0.914344\pi\) | ||||
−0.964011 | + | 0.265862i | \(0.914344\pi\) | |||||||
\(744\) | −1.21765 | −0.0446412 | ||||||||
\(745\) | −2.99860 | −0.109860 | ||||||||
\(746\) | 22.9719 | 0.841060 | ||||||||
\(747\) | −28.4104 | −1.03948 | ||||||||
\(748\) | 5.25601 | 0.192179 | ||||||||
\(749\) | 65.1676 | 2.38117 | ||||||||
\(750\) | 10.2247 | 0.373355 | ||||||||
\(751\) | 48.8917 | 1.78408 | 0.892042 | − | 0.451952i | \(-0.149272\pi\) | ||||
0.892042 | + | 0.451952i | \(0.149272\pi\) | |||||||
\(752\) | 9.61304 | 0.350551 | ||||||||
\(753\) | −13.8779 | −0.505738 | ||||||||
\(754\) | −40.0003 | −1.45672 | ||||||||
\(755\) | −6.99895 | −0.254718 | ||||||||
\(756\) | −18.7711 | −0.682699 | ||||||||
\(757\) | 15.4485 | 0.561486 | 0.280743 | − | 0.959783i | \(-0.409419\pi\) | ||||
0.280743 | + | 0.959783i | \(0.409419\pi\) | |||||||
\(758\) | 32.5199 | 1.18118 | ||||||||
\(759\) | 13.5754 | 0.492756 | ||||||||
\(760\) | 6.44412 | 0.233753 | ||||||||
\(761\) | −41.9102 | −1.51924 | −0.759622 | − | 0.650365i | \(-0.774616\pi\) | ||||
−0.759622 | + | 0.650365i | \(0.774616\pi\) | |||||||
\(762\) | 2.93108 | 0.106182 | ||||||||
\(763\) | 78.7929 | 2.85249 | ||||||||
\(764\) | 16.5291 | 0.598002 | ||||||||
\(765\) | −4.70022 | −0.169937 | ||||||||
\(766\) | 29.4514 | 1.06412 | ||||||||
\(767\) | −41.4913 | −1.49816 | ||||||||
\(768\) | −0.841269 | −0.0303567 | ||||||||
\(769\) | 7.30644 | 0.263477 | 0.131738 | − | 0.991285i | \(-0.457944\pi\) | ||||
0.131738 | + | 0.991285i | \(0.457944\pi\) | |||||||
\(770\) | 38.2888 | 1.37983 | ||||||||
\(771\) | −11.6001 | −0.417767 | ||||||||
\(772\) | 16.4414 | 0.591739 | ||||||||
\(773\) | 2.27618 | 0.0818683 | 0.0409342 | − | 0.999162i | \(-0.486967\pi\) | ||||
0.0409342 | + | 0.999162i | \(0.486967\pi\) | |||||||
\(774\) | −11.0217 | −0.396166 | ||||||||
\(775\) | 2.10904 | 0.0757590 | ||||||||
\(776\) | 8.10568 | 0.290977 | ||||||||
\(777\) | 8.64937 | 0.310294 | ||||||||
\(778\) | 33.4454 | 1.19907 | ||||||||
\(779\) | 36.0893 | 1.29303 | ||||||||
\(780\) | 9.07225 | 0.324839 | ||||||||
\(781\) | −40.6413 | −1.45426 | ||||||||
\(782\) | 3.64345 | 0.130290 | ||||||||
\(783\) | 31.0840 | 1.11085 | ||||||||
\(784\) | 10.7757 | 0.384846 | ||||||||
\(785\) | −13.2172 | −0.471742 | ||||||||
\(786\) | −10.8283 | −0.386231 | ||||||||
\(787\) | −15.8048 | −0.563379 | −0.281689 | − | 0.959506i | \(-0.590895\pi\) | ||||
−0.281689 | + | 0.959506i | \(0.590895\pi\) | |||||||
\(788\) | 22.3038 | 0.794538 | ||||||||
\(789\) | 3.63848 | 0.129533 | ||||||||
\(790\) | −25.7085 | −0.914668 | ||||||||
\(791\) | 53.9533 | 1.91836 | ||||||||
\(792\) | −11.0598 | −0.392991 | ||||||||
\(793\) | −21.0142 | −0.746236 | ||||||||
\(794\) | 2.19143 | 0.0777708 | ||||||||
\(795\) | −1.06935 | −0.0379259 | ||||||||
\(796\) | 15.8172 | 0.560627 | ||||||||
\(797\) | 39.0142 | 1.38196 | 0.690978 | − | 0.722876i | \(-0.257180\pi\) | ||||
0.690978 | + | 0.722876i | \(0.257180\pi\) | |||||||
\(798\) | −12.1432 | −0.429866 | ||||||||
\(799\) | −10.4722 | −0.370479 | ||||||||
\(800\) | 1.45713 | 0.0515173 | ||||||||
\(801\) | −11.4520 | −0.404635 | ||||||||
\(802\) | −19.6058 | −0.692306 | ||||||||
\(803\) | 44.6251 | 1.57479 | ||||||||
\(804\) | 5.70790 | 0.201302 | ||||||||
\(805\) | 26.5417 | 0.935470 | ||||||||
\(806\) | 8.29257 | 0.292093 | ||||||||
\(807\) | 9.25620 | 0.325834 | ||||||||
\(808\) | −16.1791 | −0.569179 | ||||||||
\(809\) | −20.4669 | −0.719579 | −0.359789 | − | 0.933034i | \(-0.617151\pi\) | ||||
−0.359789 | + | 0.933034i | \(0.617151\pi\) | |||||||
\(810\) | 5.89385 | 0.207089 | ||||||||
\(811\) | −41.3406 | −1.45167 | −0.725833 | − | 0.687871i | \(-0.758545\pi\) | ||||
−0.725833 | + | 0.687871i | \(0.758545\pi\) | |||||||
\(812\) | −29.4357 | −1.03299 | ||||||||
\(813\) | −1.98336 | −0.0695596 | ||||||||
\(814\) | 11.7657 | 0.412386 | ||||||||
\(815\) | 8.60338 | 0.301363 | ||||||||
\(816\) | 0.916455 | 0.0320823 | ||||||||
\(817\) | −16.4615 | −0.575913 | ||||||||
\(818\) | 6.19236 | 0.216511 | ||||||||
\(819\) | 55.3708 | 1.93481 | ||||||||
\(820\) | −19.8413 | −0.692889 | ||||||||
\(821\) | −11.7942 | −0.411621 | −0.205811 | − | 0.978592i | \(-0.565983\pi\) | ||||
−0.205811 | + | 0.978592i | \(0.565983\pi\) | |||||||
\(822\) | −2.37078 | −0.0826903 | ||||||||
\(823\) | −30.0981 | −1.04915 | −0.524577 | − | 0.851363i | \(-0.675777\pi\) | ||||
−0.524577 | + | 0.851363i | \(0.675777\pi\) | |||||||
\(824\) | −0.329723 | −0.0114864 | ||||||||
\(825\) | −5.91444 | −0.205915 | ||||||||
\(826\) | −30.5329 | −1.06237 | ||||||||
\(827\) | 17.0117 | 0.591556 | 0.295778 | − | 0.955257i | \(-0.404421\pi\) | ||||
0.295778 | + | 0.955257i | \(0.404421\pi\) | |||||||
\(828\) | −7.66658 | −0.266432 | ||||||||
\(829\) | −22.7288 | −0.789404 | −0.394702 | − | 0.918809i | \(-0.629152\pi\) | ||||
−0.394702 | + | 0.918809i | \(0.629152\pi\) | |||||||
\(830\) | 23.3287 | 0.809749 | ||||||||
\(831\) | −18.0435 | −0.625923 | ||||||||
\(832\) | 5.72931 | 0.198628 | ||||||||
\(833\) | −11.7387 | −0.406723 | ||||||||
\(834\) | −9.68477 | −0.335356 | ||||||||
\(835\) | 5.82775 | 0.201678 | ||||||||
\(836\) | −16.5183 | −0.571299 | ||||||||
\(837\) | −6.44412 | −0.222741 | ||||||||
\(838\) | 21.1687 | 0.731260 | ||||||||
\(839\) | 28.2670 | 0.975886 | 0.487943 | − | 0.872875i | \(-0.337747\pi\) | ||||
0.487943 | + | 0.872875i | \(0.337747\pi\) | |||||||
\(840\) | 6.67615 | 0.230349 | ||||||||
\(841\) | 19.7440 | 0.680829 | ||||||||
\(842\) | 12.1390 | 0.418337 | ||||||||
\(843\) | −21.8669 | −0.753135 | ||||||||
\(844\) | −10.4508 | −0.359732 | ||||||||
\(845\) | −37.3156 | −1.28369 | ||||||||
\(846\) | 22.0356 | 0.757601 | ||||||||
\(847\) | −51.7690 | −1.77880 | ||||||||
\(848\) | −0.675316 | −0.0231904 | ||||||||
\(849\) | −4.94232 | −0.169620 | ||||||||
\(850\) | −1.58736 | −0.0544458 | ||||||||
\(851\) | 8.15592 | 0.279581 | ||||||||
\(852\) | −7.08635 | −0.242774 | ||||||||
\(853\) | 2.85678 | 0.0978143 | 0.0489071 | − | 0.998803i | \(-0.484426\pi\) | ||||
0.0489071 | + | 0.998803i | \(0.484426\pi\) | |||||||
\(854\) | −15.4641 | −0.529170 | ||||||||
\(855\) | 14.7716 | 0.505179 | ||||||||
\(856\) | 15.4568 | 0.528301 | ||||||||
\(857\) | 25.4106 | 0.868009 | 0.434004 | − | 0.900911i | \(-0.357100\pi\) | ||||
0.434004 | + | 0.900911i | \(0.357100\pi\) | |||||||
\(858\) | −23.2551 | −0.793915 | ||||||||
\(859\) | −2.02573 | −0.0691171 | −0.0345585 | − | 0.999403i | \(-0.511003\pi\) | ||||
−0.0345585 | + | 0.999403i | \(0.511003\pi\) | |||||||
\(860\) | 9.05023 | 0.308610 | ||||||||
\(861\) | 37.3888 | 1.27421 | ||||||||
\(862\) | 9.81860 | 0.334423 | ||||||||
\(863\) | −29.6812 | −1.01036 | −0.505179 | − | 0.863014i | \(-0.668574\pi\) | ||||
−0.505179 | + | 0.863014i | \(0.668574\pi\) | |||||||
\(864\) | −4.45222 | −0.151468 | ||||||||
\(865\) | −31.4344 | −1.06880 | ||||||||
\(866\) | −11.0706 | −0.376194 | ||||||||
\(867\) | 13.3032 | 0.451801 | ||||||||
\(868\) | 6.10239 | 0.207129 | ||||||||
\(869\) | 65.8992 | 2.23548 | ||||||||
\(870\) | −11.0554 | −0.374812 | ||||||||
\(871\) | −38.8726 | −1.31715 | ||||||||
\(872\) | 18.6885 | 0.632871 | ||||||||
\(873\) | 18.5804 | 0.628850 | ||||||||
\(874\) | −11.4505 | −0.387318 | ||||||||
\(875\) | −51.2425 | −1.73231 | ||||||||
\(876\) | 7.78098 | 0.262895 | ||||||||
\(877\) | −47.3190 | −1.59785 | −0.798924 | − | 0.601432i | \(-0.794597\pi\) | ||||
−0.798924 | + | 0.601432i | \(0.794597\pi\) | |||||||
\(878\) | −26.2880 | −0.887178 | ||||||||
\(879\) | −11.4661 | −0.386742 | ||||||||
\(880\) | 9.08151 | 0.306138 | ||||||||
\(881\) | 10.5126 | 0.354178 | 0.177089 | − | 0.984195i | \(-0.443332\pi\) | ||||
0.177089 | + | 0.984195i | \(0.443332\pi\) | |||||||
\(882\) | 24.7008 | 0.831718 | ||||||||
\(883\) | −18.7643 | −0.631469 | −0.315735 | − | 0.948848i | \(-0.602251\pi\) | ||||
−0.315735 | + | 0.948848i | \(0.602251\pi\) | |||||||
\(884\) | −6.24134 | −0.209919 | ||||||||
\(885\) | −11.4675 | −0.385474 | ||||||||
\(886\) | −5.19550 | −0.174546 | ||||||||
\(887\) | −6.22353 | −0.208966 | −0.104483 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104483 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(888\) | 2.05150 | 0.0688438 | ||||||||
\(889\) | −14.6895 | −0.492669 | ||||||||
\(890\) | 9.40356 | 0.315208 | ||||||||
\(891\) | −15.1078 | −0.506131 | ||||||||
\(892\) | −4.03071 | −0.134958 | ||||||||
\(893\) | 32.9114 | 1.10134 | ||||||||
\(894\) | 1.34022 | 0.0448236 | ||||||||
\(895\) | 10.9105 | 0.364696 | ||||||||
\(896\) | 4.21612 | 0.140851 | ||||||||
\(897\) | −16.1203 | −0.538243 | ||||||||
\(898\) | 37.2659 | 1.24358 | ||||||||
\(899\) | −10.1053 | −0.337029 | ||||||||
\(900\) | 3.34013 | 0.111338 | ||||||||
\(901\) | 0.735669 | 0.0245087 | ||||||||
\(902\) | 50.8596 | 1.69344 | ||||||||
\(903\) | −17.0542 | −0.567527 | ||||||||
\(904\) | 12.7969 | 0.425618 | ||||||||
\(905\) | 3.01792 | 0.100319 | ||||||||
\(906\) | 3.12817 | 0.103926 | ||||||||
\(907\) | −27.4858 | −0.912651 | −0.456326 | − | 0.889813i | \(-0.650835\pi\) | ||||
−0.456326 | + | 0.889813i | \(0.650835\pi\) | |||||||
\(908\) | 25.1961 | 0.836161 | ||||||||
\(909\) | −37.0868 | −1.23009 | ||||||||
\(910\) | −45.4667 | −1.50721 | ||||||||
\(911\) | 28.3475 | 0.939196 | 0.469598 | − | 0.882880i | \(-0.344399\pi\) | ||||
0.469598 | + | 0.882880i | \(0.344399\pi\) | |||||||
\(912\) | −2.88019 | −0.0953726 | ||||||||
\(913\) | −59.7988 | −1.97905 | ||||||||
\(914\) | −2.71322 | −0.0897454 | ||||||||
\(915\) | −5.80796 | −0.192005 | ||||||||
\(916\) | −22.4179 | −0.740708 | ||||||||
\(917\) | 54.2671 | 1.79206 | ||||||||
\(918\) | 4.85012 | 0.160078 | ||||||||
\(919\) | 22.8047 | 0.752259 | 0.376129 | − | 0.926567i | \(-0.377255\pi\) | ||||
0.376129 | + | 0.926567i | \(0.377255\pi\) | |||||||
\(920\) | 6.29527 | 0.207549 | ||||||||
\(921\) | −11.2815 | −0.371738 | ||||||||
\(922\) | 19.6834 | 0.648240 | ||||||||
\(923\) | 48.2602 | 1.58850 | ||||||||
\(924\) | −17.1131 | −0.562980 | ||||||||
\(925\) | −3.55332 | −0.116832 | ||||||||
\(926\) | −22.2994 | −0.732803 | ||||||||
\(927\) | −0.755812 | −0.0248241 | ||||||||
\(928\) | −6.98169 | −0.229185 | ||||||||
\(929\) | −47.7286 | −1.56592 | −0.782962 | − | 0.622070i | \(-0.786292\pi\) | ||||
−0.782962 | + | 0.622070i | \(0.786292\pi\) | |||||||
\(930\) | 2.29192 | 0.0751551 | ||||||||
\(931\) | 36.8919 | 1.20908 | ||||||||
\(932\) | −11.6626 | −0.382020 | ||||||||
\(933\) | 17.7832 | 0.582196 | ||||||||
\(934\) | 0.279514 | 0.00914597 | ||||||||
\(935\) | −9.89313 | −0.323540 | ||||||||
\(936\) | 13.1331 | 0.429269 | ||||||||
\(937\) | 3.29283 | 0.107572 | 0.0537860 | − | 0.998552i | \(-0.482871\pi\) | ||||
0.0537860 | + | 0.998552i | \(0.482871\pi\) | |||||||
\(938\) | −28.6058 | −0.934014 | ||||||||
\(939\) | −2.02593 | −0.0661138 | ||||||||
\(940\) | −18.0942 | −0.590166 | ||||||||
\(941\) | 0.973513 | 0.0317356 | 0.0158678 | − | 0.999874i | \(-0.494949\pi\) | ||||
0.0158678 | + | 0.999874i | \(0.494949\pi\) | |||||||
\(942\) | 5.90741 | 0.192474 | ||||||||
\(943\) | 35.2557 | 1.14808 | ||||||||
\(944\) | −7.24193 | −0.235705 | ||||||||
\(945\) | 35.3320 | 1.14935 | ||||||||
\(946\) | −23.1986 | −0.754253 | ||||||||
\(947\) | 45.0759 | 1.46477 | 0.732385 | − | 0.680891i | \(-0.238407\pi\) | ||||
0.732385 | + | 0.680891i | \(0.238407\pi\) | |||||||
\(948\) | 11.4904 | 0.373190 | ||||||||
\(949\) | −52.9909 | −1.72016 | ||||||||
\(950\) | 4.98866 | 0.161854 | ||||||||
\(951\) | 18.2059 | 0.590366 | ||||||||
\(952\) | −4.59292 | −0.148857 | ||||||||
\(953\) | 49.3118 | 1.59737 | 0.798684 | − | 0.601751i | \(-0.205530\pi\) | ||||
0.798684 | + | 0.601751i | \(0.205530\pi\) | |||||||
\(954\) | −1.54800 | −0.0501184 | ||||||||
\(955\) | −31.1119 | −1.00676 | ||||||||
\(956\) | −24.8251 | −0.802902 | ||||||||
\(957\) | 28.3385 | 0.916052 | ||||||||
\(958\) | 38.7175 | 1.25091 | ||||||||
\(959\) | 11.8814 | 0.383671 | ||||||||
\(960\) | 1.58348 | 0.0511066 | ||||||||
\(961\) | −28.9050 | −0.932421 | ||||||||
\(962\) | −13.9713 | −0.450454 | ||||||||
\(963\) | 35.4310 | 1.14175 | ||||||||
\(964\) | 12.5505 | 0.404223 | ||||||||
\(965\) | −30.9468 | −0.996213 | ||||||||
\(966\) | −11.8628 | −0.381678 | ||||||||
\(967\) | −37.9805 | −1.22137 | −0.610685 | − | 0.791874i | \(-0.709106\pi\) | ||||
−0.610685 | + | 0.791874i | \(0.709106\pi\) | |||||||
\(968\) | −12.2788 | −0.394656 | ||||||||
\(969\) | 3.13759 | 0.100794 | ||||||||
\(970\) | −15.2569 | −0.489870 | ||||||||
\(971\) | 14.0225 | 0.450005 | 0.225002 | − | 0.974358i | \(-0.427761\pi\) | ||||
0.225002 | + | 0.974358i | \(0.427761\pi\) | |||||||
\(972\) | −15.9909 | −0.512909 | ||||||||
\(973\) | 48.5364 | 1.55601 | ||||||||
\(974\) | −24.8964 | −0.797733 | ||||||||
\(975\) | 7.02321 | 0.224923 | ||||||||
\(976\) | −3.66784 | −0.117405 | ||||||||
\(977\) | 22.9616 | 0.734607 | 0.367304 | − | 0.930101i | \(-0.380281\pi\) | ||||
0.367304 | + | 0.930101i | \(0.380281\pi\) | |||||||
\(978\) | −3.84527 | −0.122958 | ||||||||
\(979\) | −24.1043 | −0.770378 | ||||||||
\(980\) | −20.2826 | −0.647903 | ||||||||
\(981\) | 42.8389 | 1.36774 | ||||||||
\(982\) | 23.7423 | 0.757646 | ||||||||
\(983\) | 12.3091 | 0.392599 | 0.196299 | − | 0.980544i | \(-0.437108\pi\) | ||||
0.196299 | + | 0.980544i | \(0.437108\pi\) | |||||||
\(984\) | 8.86804 | 0.282703 | ||||||||
\(985\) | −41.9813 | −1.33763 | ||||||||
\(986\) | 7.60565 | 0.242213 | ||||||||
\(987\) | 34.0965 | 1.08530 | ||||||||
\(988\) | 19.6150 | 0.624036 | ||||||||
\(989\) | −16.0812 | −0.511353 | ||||||||
\(990\) | 20.8172 | 0.661615 | ||||||||
\(991\) | −28.1922 | −0.895554 | −0.447777 | − | 0.894145i | \(-0.647784\pi\) | ||||
−0.447777 | + | 0.894145i | \(0.647784\pi\) | |||||||
\(992\) | 1.44739 | 0.0459548 | ||||||||
\(993\) | −0.719911 | −0.0228457 | ||||||||
\(994\) | 35.5141 | 1.12644 | ||||||||
\(995\) | −29.7720 | −0.943835 | ||||||||
\(996\) | −10.4267 | −0.330383 | ||||||||
\(997\) | 30.1377 | 0.954470 | 0.477235 | − | 0.878776i | \(-0.341639\pi\) | ||||
0.477235 | + | 0.878776i | \(0.341639\pi\) | |||||||
\(998\) | 1.12134 | 0.0354955 | ||||||||
\(999\) | 10.8571 | 0.343503 |
(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 | 4034.2.a.b.1.15 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.b.1.15 | ✓ | 35 | 1.1 | even | 1 | trivial |