Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(81\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 | ||||||||
\(3\) | −2.39342 | −1.38184 | −0.690922 | − | 0.722929i | \(-0.742795\pi\) | ||||
−0.690922 | + | 0.722929i | \(0.742795\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.94313 | 0.868993 | 0.434496 | − | 0.900674i | \(-0.356926\pi\) | ||||
0.434496 | + | 0.900674i | \(0.356926\pi\) | |||||||
\(6\) | 2.39342 | 0.977111 | ||||||||
\(7\) | 4.16913 | 1.57578 | 0.787892 | − | 0.615813i | \(-0.211172\pi\) | ||||
0.787892 | + | 0.615813i | \(0.211172\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.72848 | 0.909493 | ||||||||
\(10\) | −1.94313 | −0.614471 | ||||||||
\(11\) | −4.33125 | −1.30592 | −0.652960 | − | 0.757393i | \(-0.726473\pi\) | ||||
−0.652960 | + | 0.757393i | \(0.726473\pi\) | |||||||
\(12\) | −2.39342 | −0.690922 | ||||||||
\(13\) | 2.71319 | 0.752503 | 0.376251 | − | 0.926518i | \(-0.377213\pi\) | ||||
0.376251 | + | 0.926518i | \(0.377213\pi\) | |||||||
\(14\) | −4.16913 | −1.11425 | ||||||||
\(15\) | −4.65073 | −1.20081 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.68203 | 1.37809 | 0.689047 | − | 0.724717i | \(-0.258029\pi\) | ||||
0.689047 | + | 0.724717i | \(0.258029\pi\) | |||||||
\(18\) | −2.72848 | −0.643109 | ||||||||
\(19\) | −2.95964 | −0.678987 | −0.339494 | − | 0.940608i | \(-0.610256\pi\) | ||||
−0.339494 | + | 0.940608i | \(0.610256\pi\) | |||||||
\(20\) | 1.94313 | 0.434496 | ||||||||
\(21\) | −9.97851 | −2.17749 | ||||||||
\(22\) | 4.33125 | 0.923425 | ||||||||
\(23\) | −7.44769 | −1.55295 | −0.776476 | − | 0.630147i | \(-0.782994\pi\) | ||||
−0.776476 | + | 0.630147i | \(0.782994\pi\) | |||||||
\(24\) | 2.39342 | 0.488556 | ||||||||
\(25\) | −1.22426 | −0.244851 | ||||||||
\(26\) | −2.71319 | −0.532100 | ||||||||
\(27\) | 0.649863 | 0.125066 | ||||||||
\(28\) | 4.16913 | 0.787892 | ||||||||
\(29\) | 6.89202 | 1.27982 | 0.639908 | − | 0.768452i | \(-0.278973\pi\) | ||||
0.639908 | + | 0.768452i | \(0.278973\pi\) | |||||||
\(30\) | 4.65073 | 0.849103 | ||||||||
\(31\) | −1.08928 | −0.195641 | −0.0978203 | − | 0.995204i | \(-0.531187\pi\) | ||||
−0.0978203 | + | 0.995204i | \(0.531187\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.3665 | 1.80458 | ||||||||
\(34\) | −5.68203 | −0.974459 | ||||||||
\(35\) | 8.10116 | 1.36935 | ||||||||
\(36\) | 2.72848 | 0.454747 | ||||||||
\(37\) | 5.48734 | 0.902113 | 0.451056 | − | 0.892496i | \(-0.351047\pi\) | ||||
0.451056 | + | 0.892496i | \(0.351047\pi\) | |||||||
\(38\) | 2.95964 | 0.480117 | ||||||||
\(39\) | −6.49381 | −1.03984 | ||||||||
\(40\) | −1.94313 | −0.307235 | ||||||||
\(41\) | −5.76373 | −0.900143 | −0.450072 | − | 0.892993i | \(-0.648602\pi\) | ||||
−0.450072 | + | 0.892993i | \(0.648602\pi\) | |||||||
\(42\) | 9.97851 | 1.53972 | ||||||||
\(43\) | −4.99002 | −0.760972 | −0.380486 | − | 0.924787i | \(-0.624243\pi\) | ||||
−0.380486 | + | 0.924787i | \(0.624243\pi\) | |||||||
\(44\) | −4.33125 | −0.652960 | ||||||||
\(45\) | 5.30178 | 0.790343 | ||||||||
\(46\) | 7.44769 | 1.09810 | ||||||||
\(47\) | −11.4557 | −1.67098 | −0.835490 | − | 0.549506i | \(-0.814816\pi\) | ||||
−0.835490 | + | 0.549506i | \(0.814816\pi\) | |||||||
\(48\) | −2.39342 | −0.345461 | ||||||||
\(49\) | 10.3817 | 1.48310 | ||||||||
\(50\) | 1.22426 | 0.173136 | ||||||||
\(51\) | −13.5995 | −1.90431 | ||||||||
\(52\) | 2.71319 | 0.376251 | ||||||||
\(53\) | −2.97190 | −0.408222 | −0.204111 | − | 0.978948i | \(-0.565430\pi\) | ||||
−0.204111 | + | 0.978948i | \(0.565430\pi\) | |||||||
\(54\) | −0.649863 | −0.0884352 | ||||||||
\(55\) | −8.41616 | −1.13483 | ||||||||
\(56\) | −4.16913 | −0.557124 | ||||||||
\(57\) | 7.08367 | 0.938255 | ||||||||
\(58\) | −6.89202 | −0.904966 | ||||||||
\(59\) | −0.0542823 | −0.00706696 | −0.00353348 | − | 0.999994i | \(-0.501125\pi\) | ||||
−0.00353348 | + | 0.999994i | \(0.501125\pi\) | |||||||
\(60\) | −4.65073 | −0.600406 | ||||||||
\(61\) | 9.99674 | 1.27995 | 0.639975 | − | 0.768395i | \(-0.278945\pi\) | ||||
0.639975 | + | 0.768395i | \(0.278945\pi\) | |||||||
\(62\) | 1.08928 | 0.138339 | ||||||||
\(63\) | 11.3754 | 1.43317 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.27207 | 0.653919 | ||||||||
\(66\) | −10.3665 | −1.27603 | ||||||||
\(67\) | −14.2464 | −1.74048 | −0.870240 | − | 0.492628i | \(-0.836036\pi\) | ||||
−0.870240 | + | 0.492628i | \(0.836036\pi\) | |||||||
\(68\) | 5.68203 | 0.689047 | ||||||||
\(69\) | 17.8255 | 2.14594 | ||||||||
\(70\) | −8.10116 | −0.968274 | ||||||||
\(71\) | −6.90714 | −0.819726 | −0.409863 | − | 0.912147i | \(-0.634424\pi\) | ||||
−0.409863 | + | 0.912147i | \(0.634424\pi\) | |||||||
\(72\) | −2.72848 | −0.321554 | ||||||||
\(73\) | −4.68009 | −0.547763 | −0.273882 | − | 0.961763i | \(-0.588308\pi\) | ||||
−0.273882 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(74\) | −5.48734 | −0.637890 | ||||||||
\(75\) | 2.93017 | 0.338346 | ||||||||
\(76\) | −2.95964 | −0.339494 | ||||||||
\(77\) | −18.0575 | −2.05785 | ||||||||
\(78\) | 6.49381 | 0.735279 | ||||||||
\(79\) | 8.28729 | 0.932393 | 0.466196 | − | 0.884681i | \(-0.345624\pi\) | ||||
0.466196 | + | 0.884681i | \(0.345624\pi\) | |||||||
\(80\) | 1.94313 | 0.217248 | ||||||||
\(81\) | −9.74084 | −1.08232 | ||||||||
\(82\) | 5.76373 | 0.636497 | ||||||||
\(83\) | 10.5633 | 1.15947 | 0.579737 | − | 0.814804i | \(-0.303155\pi\) | ||||
0.579737 | + | 0.814804i | \(0.303155\pi\) | |||||||
\(84\) | −9.97851 | −1.08874 | ||||||||
\(85\) | 11.0409 | 1.19755 | ||||||||
\(86\) | 4.99002 | 0.538088 | ||||||||
\(87\) | −16.4955 | −1.76851 | ||||||||
\(88\) | 4.33125 | 0.461712 | ||||||||
\(89\) | 1.92493 | 0.204042 | 0.102021 | − | 0.994782i | \(-0.467469\pi\) | ||||
0.102021 | + | 0.994782i | \(0.467469\pi\) | |||||||
\(90\) | −5.30178 | −0.558857 | ||||||||
\(91\) | 11.3116 | 1.18578 | ||||||||
\(92\) | −7.44769 | −0.776476 | ||||||||
\(93\) | 2.60711 | 0.270345 | ||||||||
\(94\) | 11.4557 | 1.18156 | ||||||||
\(95\) | −5.75095 | −0.590035 | ||||||||
\(96\) | 2.39342 | 0.244278 | ||||||||
\(97\) | −3.23525 | −0.328489 | −0.164245 | − | 0.986420i | \(-0.552519\pi\) | ||||
−0.164245 | + | 0.986420i | \(0.552519\pi\) | |||||||
\(98\) | −10.3817 | −1.04871 | ||||||||
\(99\) | −11.8177 | −1.18772 | ||||||||
\(100\) | −1.22426 | −0.122426 | ||||||||
\(101\) | −16.3914 | −1.63101 | −0.815504 | − | 0.578751i | \(-0.803540\pi\) | ||||
−0.815504 | + | 0.578751i | \(0.803540\pi\) | |||||||
\(102\) | 13.5995 | 1.34655 | ||||||||
\(103\) | −0.0361654 | −0.00356348 | −0.00178174 | − | 0.999998i | \(-0.500567\pi\) | ||||
−0.00178174 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(104\) | −2.71319 | −0.266050 | ||||||||
\(105\) | −19.3895 | −1.89222 | ||||||||
\(106\) | 2.97190 | 0.288657 | ||||||||
\(107\) | −19.0988 | −1.84635 | −0.923174 | − | 0.384383i | \(-0.874414\pi\) | ||||
−0.923174 | + | 0.384383i | \(0.874414\pi\) | |||||||
\(108\) | 0.649863 | 0.0625331 | ||||||||
\(109\) | −19.7760 | −1.89419 | −0.947097 | − | 0.320947i | \(-0.895999\pi\) | ||||
−0.947097 | + | 0.320947i | \(0.895999\pi\) | |||||||
\(110\) | 8.41616 | 0.802449 | ||||||||
\(111\) | −13.1335 | −1.24658 | ||||||||
\(112\) | 4.16913 | 0.393946 | ||||||||
\(113\) | 2.28462 | 0.214919 | 0.107460 | − | 0.994209i | \(-0.465728\pi\) | ||||
0.107460 | + | 0.994209i | \(0.465728\pi\) | |||||||
\(114\) | −7.08367 | −0.663446 | ||||||||
\(115\) | −14.4718 | −1.34950 | ||||||||
\(116\) | 6.89202 | 0.639908 | ||||||||
\(117\) | 7.40287 | 0.684396 | ||||||||
\(118\) | 0.0542823 | 0.00499709 | ||||||||
\(119\) | 23.6891 | 2.17158 | ||||||||
\(120\) | 4.65073 | 0.424551 | ||||||||
\(121\) | 7.75968 | 0.705426 | ||||||||
\(122\) | −9.99674 | −0.905062 | ||||||||
\(123\) | 13.7950 | 1.24386 | ||||||||
\(124\) | −1.08928 | −0.0978203 | ||||||||
\(125\) | −12.0945 | −1.08177 | ||||||||
\(126\) | −11.3754 | −1.01340 | ||||||||
\(127\) | −14.1060 | −1.25170 | −0.625852 | − | 0.779942i | \(-0.715249\pi\) | ||||
−0.625852 | + | 0.779942i | \(0.715249\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.9432 | 1.05154 | ||||||||
\(130\) | −5.27207 | −0.462391 | ||||||||
\(131\) | 6.78064 | 0.592428 | 0.296214 | − | 0.955122i | \(-0.404276\pi\) | ||||
0.296214 | + | 0.955122i | \(0.404276\pi\) | |||||||
\(132\) | 10.3665 | 0.902289 | ||||||||
\(133\) | −12.3391 | −1.06994 | ||||||||
\(134\) | 14.2464 | 1.23071 | ||||||||
\(135\) | 1.26277 | 0.108682 | ||||||||
\(136\) | −5.68203 | −0.487230 | ||||||||
\(137\) | −11.7616 | −1.00486 | −0.502429 | − | 0.864618i | \(-0.667560\pi\) | ||||
−0.502429 | + | 0.864618i | \(0.667560\pi\) | |||||||
\(138\) | −17.8255 | −1.51741 | ||||||||
\(139\) | −17.5545 | −1.48895 | −0.744475 | − | 0.667650i | \(-0.767300\pi\) | ||||
−0.744475 | + | 0.667650i | \(0.767300\pi\) | |||||||
\(140\) | 8.10116 | 0.684673 | ||||||||
\(141\) | 27.4182 | 2.30903 | ||||||||
\(142\) | 6.90714 | 0.579634 | ||||||||
\(143\) | −11.7515 | −0.982708 | ||||||||
\(144\) | 2.72848 | 0.227373 | ||||||||
\(145\) | 13.3921 | 1.11215 | ||||||||
\(146\) | 4.68009 | 0.387327 | ||||||||
\(147\) | −24.8478 | −2.04941 | ||||||||
\(148\) | 5.48734 | 0.451056 | ||||||||
\(149\) | 13.0283 | 1.06732 | 0.533659 | − | 0.845700i | \(-0.320817\pi\) | ||||
0.533659 | + | 0.845700i | \(0.320817\pi\) | |||||||
\(150\) | −2.93017 | −0.239247 | ||||||||
\(151\) | −2.92373 | −0.237930 | −0.118965 | − | 0.992898i | \(-0.537958\pi\) | ||||
−0.118965 | + | 0.992898i | \(0.537958\pi\) | |||||||
\(152\) | 2.95964 | 0.240058 | ||||||||
\(153\) | 15.5033 | 1.25337 | ||||||||
\(154\) | 18.0575 | 1.45512 | ||||||||
\(155\) | −2.11661 | −0.170010 | ||||||||
\(156\) | −6.49381 | −0.519921 | ||||||||
\(157\) | 4.91322 | 0.392118 | 0.196059 | − | 0.980592i | \(-0.437186\pi\) | ||||
0.196059 | + | 0.980592i | \(0.437186\pi\) | |||||||
\(158\) | −8.28729 | −0.659301 | ||||||||
\(159\) | 7.11303 | 0.564100 | ||||||||
\(160\) | −1.94313 | −0.153618 | ||||||||
\(161\) | −31.0504 | −2.44712 | ||||||||
\(162\) | 9.74084 | 0.765312 | ||||||||
\(163\) | 6.54567 | 0.512696 | 0.256348 | − | 0.966585i | \(-0.417481\pi\) | ||||
0.256348 | + | 0.966585i | \(0.417481\pi\) | |||||||
\(164\) | −5.76373 | −0.450072 | ||||||||
\(165\) | 20.1434 | 1.56816 | ||||||||
\(166\) | −10.5633 | −0.819872 | ||||||||
\(167\) | −5.09402 | −0.394187 | −0.197093 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197093 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(168\) | 9.97851 | 0.769858 | ||||||||
\(169\) | −5.63862 | −0.433740 | ||||||||
\(170\) | −11.0409 | −0.846798 | ||||||||
\(171\) | −8.07531 | −0.617534 | ||||||||
\(172\) | −4.99002 | −0.380486 | ||||||||
\(173\) | −17.0495 | −1.29625 | −0.648124 | − | 0.761535i | \(-0.724446\pi\) | ||||
−0.648124 | + | 0.761535i | \(0.724446\pi\) | |||||||
\(174\) | 16.4955 | 1.25052 | ||||||||
\(175\) | −5.10409 | −0.385833 | ||||||||
\(176\) | −4.33125 | −0.326480 | ||||||||
\(177\) | 0.129921 | 0.00976543 | ||||||||
\(178\) | −1.92493 | −0.144280 | ||||||||
\(179\) | −25.3592 | −1.89543 | −0.947717 | − | 0.319112i | \(-0.896616\pi\) | ||||
−0.947717 | + | 0.319112i | \(0.896616\pi\) | |||||||
\(180\) | 5.30178 | 0.395172 | ||||||||
\(181\) | 11.1103 | 0.825820 | 0.412910 | − | 0.910772i | \(-0.364512\pi\) | ||||
0.412910 | + | 0.910772i | \(0.364512\pi\) | |||||||
\(182\) | −11.3116 | −0.838474 | ||||||||
\(183\) | −23.9264 | −1.76869 | ||||||||
\(184\) | 7.44769 | 0.549051 | ||||||||
\(185\) | 10.6626 | 0.783929 | ||||||||
\(186\) | −2.60711 | −0.191163 | ||||||||
\(187\) | −24.6102 | −1.79968 | ||||||||
\(188\) | −11.4557 | −0.835490 | ||||||||
\(189\) | 2.70937 | 0.197078 | ||||||||
\(190\) | 5.75095 | 0.417218 | ||||||||
\(191\) | 18.4000 | 1.33138 | 0.665689 | − | 0.746229i | \(-0.268138\pi\) | ||||
0.665689 | + | 0.746229i | \(0.268138\pi\) | |||||||
\(192\) | −2.39342 | −0.172731 | ||||||||
\(193\) | 10.4867 | 0.754851 | 0.377426 | − | 0.926040i | \(-0.376809\pi\) | ||||
0.377426 | + | 0.926040i | \(0.376809\pi\) | |||||||
\(194\) | 3.23525 | 0.232277 | ||||||||
\(195\) | −12.6183 | −0.903615 | ||||||||
\(196\) | 10.3817 | 0.741548 | ||||||||
\(197\) | 12.6056 | 0.898111 | 0.449056 | − | 0.893504i | \(-0.351761\pi\) | ||||
0.449056 | + | 0.893504i | \(0.351761\pi\) | |||||||
\(198\) | 11.8177 | 0.839848 | ||||||||
\(199\) | 14.7240 | 1.04376 | 0.521879 | − | 0.853020i | \(-0.325231\pi\) | ||||
0.521879 | + | 0.853020i | \(0.325231\pi\) | |||||||
\(200\) | 1.22426 | 0.0865680 | ||||||||
\(201\) | 34.0978 | 2.40507 | ||||||||
\(202\) | 16.3914 | 1.15330 | ||||||||
\(203\) | 28.7337 | 2.01671 | ||||||||
\(204\) | −13.5995 | −0.952155 | ||||||||
\(205\) | −11.1997 | −0.782218 | ||||||||
\(206\) | 0.0361654 | 0.00251976 | ||||||||
\(207\) | −20.3209 | −1.41240 | ||||||||
\(208\) | 2.71319 | 0.188126 | ||||||||
\(209\) | 12.8189 | 0.886703 | ||||||||
\(210\) | 19.3895 | 1.33800 | ||||||||
\(211\) | 14.6438 | 1.00812 | 0.504061 | − | 0.863668i | \(-0.331839\pi\) | ||||
0.504061 | + | 0.863668i | \(0.331839\pi\) | |||||||
\(212\) | −2.97190 | −0.204111 | ||||||||
\(213\) | 16.5317 | 1.13273 | ||||||||
\(214\) | 19.0988 | 1.30556 | ||||||||
\(215\) | −9.69625 | −0.661279 | ||||||||
\(216\) | −0.649863 | −0.0442176 | ||||||||
\(217\) | −4.54136 | −0.308287 | ||||||||
\(218\) | 19.7760 | 1.33940 | ||||||||
\(219\) | 11.2014 | 0.756923 | ||||||||
\(220\) | −8.41616 | −0.567417 | ||||||||
\(221\) | 15.4164 | 1.03702 | ||||||||
\(222\) | 13.1335 | 0.881464 | ||||||||
\(223\) | 20.2733 | 1.35760 | 0.678800 | − | 0.734323i | \(-0.262500\pi\) | ||||
0.678800 | + | 0.734323i | \(0.262500\pi\) | |||||||
\(224\) | −4.16913 | −0.278562 | ||||||||
\(225\) | −3.34036 | −0.222691 | ||||||||
\(226\) | −2.28462 | −0.151971 | ||||||||
\(227\) | 27.3365 | 1.81439 | 0.907193 | − | 0.420715i | \(-0.138221\pi\) | ||||
0.907193 | + | 0.420715i | \(0.138221\pi\) | |||||||
\(228\) | 7.08367 | 0.469127 | ||||||||
\(229\) | −11.1327 | −0.735669 | −0.367834 | − | 0.929891i | \(-0.619901\pi\) | ||||
−0.367834 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(230\) | 14.4718 | 0.954243 | ||||||||
\(231\) | 43.2194 | 2.84362 | ||||||||
\(232\) | −6.89202 | −0.452483 | ||||||||
\(233\) | 0.215687 | 0.0141301 | 0.00706505 | − | 0.999975i | \(-0.497751\pi\) | ||||
0.00706505 | + | 0.999975i | \(0.497751\pi\) | |||||||
\(234\) | −7.40287 | −0.483941 | ||||||||
\(235\) | −22.2598 | −1.45207 | ||||||||
\(236\) | −0.0542823 | −0.00353348 | ||||||||
\(237\) | −19.8350 | −1.28842 | ||||||||
\(238\) | −23.6891 | −1.53554 | ||||||||
\(239\) | 16.5435 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(240\) | −4.65073 | −0.300203 | ||||||||
\(241\) | 27.1229 | 1.74714 | 0.873569 | − | 0.486700i | \(-0.161799\pi\) | ||||
0.873569 | + | 0.486700i | \(0.161799\pi\) | |||||||
\(242\) | −7.75968 | −0.498811 | ||||||||
\(243\) | 21.3644 | 1.37052 | ||||||||
\(244\) | 9.99674 | 0.639975 | ||||||||
\(245\) | 20.1729 | 1.28880 | ||||||||
\(246\) | −13.7950 | −0.879540 | ||||||||
\(247\) | −8.03005 | −0.510940 | ||||||||
\(248\) | 1.08928 | 0.0691694 | ||||||||
\(249\) | −25.2825 | −1.60221 | ||||||||
\(250\) | 12.0945 | 0.764925 | ||||||||
\(251\) | −1.72214 | −0.108700 | −0.0543502 | − | 0.998522i | \(-0.517309\pi\) | ||||
−0.0543502 | + | 0.998522i | \(0.517309\pi\) | |||||||
\(252\) | 11.3754 | 0.716583 | ||||||||
\(253\) | 32.2578 | 2.02803 | ||||||||
\(254\) | 14.1060 | 0.885088 | ||||||||
\(255\) | −26.4256 | −1.65483 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.47780 | −0.279318 | −0.139659 | − | 0.990200i | \(-0.544601\pi\) | ||||
−0.139659 | + | 0.990200i | \(0.544601\pi\) | |||||||
\(258\) | −11.9432 | −0.743554 | ||||||||
\(259\) | 22.8774 | 1.42153 | ||||||||
\(260\) | 5.27207 | 0.326960 | ||||||||
\(261\) | 18.8047 | 1.16398 | ||||||||
\(262\) | −6.78064 | −0.418910 | ||||||||
\(263\) | −15.5812 | −0.960780 | −0.480390 | − | 0.877055i | \(-0.659505\pi\) | ||||
−0.480390 | + | 0.877055i | \(0.659505\pi\) | |||||||
\(264\) | −10.3665 | −0.638014 | ||||||||
\(265\) | −5.77479 | −0.354742 | ||||||||
\(266\) | 12.3391 | 0.756560 | ||||||||
\(267\) | −4.60718 | −0.281955 | ||||||||
\(268\) | −14.2464 | −0.870240 | ||||||||
\(269\) | 1.15183 | 0.0702281 | 0.0351140 | − | 0.999383i | \(-0.488821\pi\) | ||||
0.0351140 | + | 0.999383i | \(0.488821\pi\) | |||||||
\(270\) | −1.26277 | −0.0768496 | ||||||||
\(271\) | 23.5103 | 1.42815 | 0.714075 | − | 0.700069i | \(-0.246848\pi\) | ||||
0.714075 | + | 0.700069i | \(0.246848\pi\) | |||||||
\(272\) | 5.68203 | 0.344523 | ||||||||
\(273\) | −27.0735 | −1.63857 | ||||||||
\(274\) | 11.7616 | 0.710542 | ||||||||
\(275\) | 5.30255 | 0.319756 | ||||||||
\(276\) | 17.8255 | 1.07297 | ||||||||
\(277\) | −11.7967 | −0.708796 | −0.354398 | − | 0.935095i | \(-0.615314\pi\) | ||||
−0.354398 | + | 0.935095i | \(0.615314\pi\) | |||||||
\(278\) | 17.5545 | 1.05285 | ||||||||
\(279\) | −2.97208 | −0.177934 | ||||||||
\(280\) | −8.10116 | −0.484137 | ||||||||
\(281\) | −20.0725 | −1.19742 | −0.598712 | − | 0.800964i | \(-0.704321\pi\) | ||||
−0.598712 | + | 0.800964i | \(0.704321\pi\) | |||||||
\(282\) | −27.4182 | −1.63273 | ||||||||
\(283\) | 7.09054 | 0.421489 | 0.210744 | − | 0.977541i | \(-0.432411\pi\) | ||||
0.210744 | + | 0.977541i | \(0.432411\pi\) | |||||||
\(284\) | −6.90714 | −0.409863 | ||||||||
\(285\) | 13.7645 | 0.815337 | ||||||||
\(286\) | 11.7515 | 0.694879 | ||||||||
\(287\) | −24.0298 | −1.41843 | ||||||||
\(288\) | −2.72848 | −0.160777 | ||||||||
\(289\) | 15.2854 | 0.899142 | ||||||||
\(290\) | −13.3921 | −0.786409 | ||||||||
\(291\) | 7.74331 | 0.453921 | ||||||||
\(292\) | −4.68009 | −0.273882 | ||||||||
\(293\) | −7.50039 | −0.438177 | −0.219089 | − | 0.975705i | \(-0.570308\pi\) | ||||
−0.219089 | + | 0.975705i | \(0.570308\pi\) | |||||||
\(294\) | 24.8478 | 1.44915 | ||||||||
\(295\) | −0.105477 | −0.00614113 | ||||||||
\(296\) | −5.48734 | −0.318945 | ||||||||
\(297\) | −2.81472 | −0.163326 | ||||||||
\(298\) | −13.0283 | −0.754708 | ||||||||
\(299\) | −20.2070 | −1.16860 | ||||||||
\(300\) | 2.93017 | 0.169173 | ||||||||
\(301\) | −20.8041 | −1.19913 | ||||||||
\(302\) | 2.92373 | 0.168242 | ||||||||
\(303\) | 39.2317 | 2.25380 | ||||||||
\(304\) | −2.95964 | −0.169747 | ||||||||
\(305\) | 19.4249 | 1.11227 | ||||||||
\(306\) | −15.5033 | −0.886264 | ||||||||
\(307\) | 11.2203 | 0.640374 | 0.320187 | − | 0.947354i | \(-0.396254\pi\) | ||||
0.320187 | + | 0.947354i | \(0.396254\pi\) | |||||||
\(308\) | −18.0575 | −1.02892 | ||||||||
\(309\) | 0.0865592 | 0.00492418 | ||||||||
\(310\) | 2.11661 | 0.120215 | ||||||||
\(311\) | 1.87274 | 0.106193 | 0.0530966 | − | 0.998589i | \(-0.483091\pi\) | ||||
0.0530966 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(312\) | 6.49381 | 0.367639 | ||||||||
\(313\) | −26.8274 | −1.51637 | −0.758187 | − | 0.652037i | \(-0.773915\pi\) | ||||
−0.758187 | + | 0.652037i | \(0.773915\pi\) | |||||||
\(314\) | −4.91322 | −0.277269 | ||||||||
\(315\) | 22.1038 | 1.24541 | ||||||||
\(316\) | 8.28729 | 0.466196 | ||||||||
\(317\) | −34.2630 | −1.92440 | −0.962200 | − | 0.272345i | \(-0.912201\pi\) | ||||
−0.962200 | + | 0.272345i | \(0.912201\pi\) | |||||||
\(318\) | −7.11303 | −0.398879 | ||||||||
\(319\) | −29.8510 | −1.67134 | ||||||||
\(320\) | 1.94313 | 0.108624 | ||||||||
\(321\) | 45.7114 | 2.55136 | ||||||||
\(322\) | 31.0504 | 1.73037 | ||||||||
\(323\) | −16.8167 | −0.935708 | ||||||||
\(324\) | −9.74084 | −0.541158 | ||||||||
\(325\) | −3.32164 | −0.184251 | ||||||||
\(326\) | −6.54567 | −0.362531 | ||||||||
\(327\) | 47.3323 | 2.61748 | ||||||||
\(328\) | 5.76373 | 0.318249 | ||||||||
\(329\) | −47.7602 | −2.63310 | ||||||||
\(330\) | −20.1434 | −1.10886 | ||||||||
\(331\) | 3.34434 | 0.183821 | 0.0919107 | − | 0.995767i | \(-0.470703\pi\) | ||||
0.0919107 | + | 0.995767i | \(0.470703\pi\) | |||||||
\(332\) | 10.5633 | 0.579737 | ||||||||
\(333\) | 14.9721 | 0.820465 | ||||||||
\(334\) | 5.09402 | 0.278732 | ||||||||
\(335\) | −27.6826 | −1.51246 | ||||||||
\(336\) | −9.97851 | −0.544372 | ||||||||
\(337\) | 26.9648 | 1.46887 | 0.734433 | − | 0.678682i | \(-0.237448\pi\) | ||||
0.734433 | + | 0.678682i | \(0.237448\pi\) | |||||||
\(338\) | 5.63862 | 0.306700 | ||||||||
\(339\) | −5.46807 | −0.296985 | ||||||||
\(340\) | 11.0409 | 0.598777 | ||||||||
\(341\) | 4.71794 | 0.255491 | ||||||||
\(342\) | 8.07531 | 0.436663 | ||||||||
\(343\) | 14.0987 | 0.761257 | ||||||||
\(344\) | 4.99002 | 0.269044 | ||||||||
\(345\) | 34.6372 | 1.86480 | ||||||||
\(346\) | 17.0495 | 0.916586 | ||||||||
\(347\) | −12.2128 | −0.655618 | −0.327809 | − | 0.944744i | \(-0.606310\pi\) | ||||
−0.327809 | + | 0.944744i | \(0.606310\pi\) | |||||||
\(348\) | −16.4955 | −0.884253 | ||||||||
\(349\) | 2.33229 | 0.124844 | 0.0624222 | − | 0.998050i | \(-0.480117\pi\) | ||||
0.0624222 | + | 0.998050i | \(0.480117\pi\) | |||||||
\(350\) | 5.10409 | 0.272825 | ||||||||
\(351\) | 1.76320 | 0.0941127 | ||||||||
\(352\) | 4.33125 | 0.230856 | ||||||||
\(353\) | −13.9573 | −0.742872 | −0.371436 | − | 0.928458i | \(-0.621135\pi\) | ||||
−0.371436 | + | 0.928458i | \(0.621135\pi\) | |||||||
\(354\) | −0.129921 | −0.00690520 | ||||||||
\(355\) | −13.4214 | −0.712336 | ||||||||
\(356\) | 1.92493 | 0.102021 | ||||||||
\(357\) | −56.6981 | −3.00078 | ||||||||
\(358\) | 25.3592 | 1.34027 | ||||||||
\(359\) | 21.0099 | 1.10886 | 0.554430 | − | 0.832230i | \(-0.312936\pi\) | ||||
0.554430 | + | 0.832230i | \(0.312936\pi\) | |||||||
\(360\) | −5.30178 | −0.279429 | ||||||||
\(361\) | −10.2405 | −0.538976 | ||||||||
\(362\) | −11.1103 | −0.583943 | ||||||||
\(363\) | −18.5722 | −0.974789 | ||||||||
\(364\) | 11.3116 | 0.592891 | ||||||||
\(365\) | −9.09401 | −0.476002 | ||||||||
\(366\) | 23.9264 | 1.25065 | ||||||||
\(367\) | 17.9655 | 0.937793 | 0.468897 | − | 0.883253i | \(-0.344652\pi\) | ||||
0.468897 | + | 0.883253i | \(0.344652\pi\) | |||||||
\(368\) | −7.44769 | −0.388238 | ||||||||
\(369\) | −15.7262 | −0.818674 | ||||||||
\(370\) | −10.6626 | −0.554322 | ||||||||
\(371\) | −12.3903 | −0.643270 | ||||||||
\(372\) | 2.60711 | 0.135172 | ||||||||
\(373\) | −9.07032 | −0.469643 | −0.234822 | − | 0.972038i | \(-0.575451\pi\) | ||||
−0.234822 | + | 0.972038i | \(0.575451\pi\) | |||||||
\(374\) | 24.6102 | 1.27257 | ||||||||
\(375\) | 28.9473 | 1.49483 | ||||||||
\(376\) | 11.4557 | 0.590780 | ||||||||
\(377\) | 18.6993 | 0.963064 | ||||||||
\(378\) | −2.70937 | −0.139355 | ||||||||
\(379\) | −28.4905 | −1.46346 | −0.731730 | − | 0.681595i | \(-0.761287\pi\) | ||||
−0.731730 | + | 0.681595i | \(0.761287\pi\) | |||||||
\(380\) | −5.75095 | −0.295018 | ||||||||
\(381\) | 33.7616 | 1.72966 | ||||||||
\(382\) | −18.4000 | −0.941426 | ||||||||
\(383\) | 29.1766 | 1.49086 | 0.745428 | − | 0.666586i | \(-0.232245\pi\) | ||||
0.745428 | + | 0.666586i | \(0.232245\pi\) | |||||||
\(384\) | 2.39342 | 0.122139 | ||||||||
\(385\) | −35.0881 | −1.78826 | ||||||||
\(386\) | −10.4867 | −0.533760 | ||||||||
\(387\) | −13.6152 | −0.692098 | ||||||||
\(388\) | −3.23525 | −0.164245 | ||||||||
\(389\) | −16.6747 | −0.845442 | −0.422721 | − | 0.906260i | \(-0.638925\pi\) | ||||
−0.422721 | + | 0.906260i | \(0.638925\pi\) | |||||||
\(390\) | 12.6183 | 0.638952 | ||||||||
\(391\) | −42.3180 | −2.14011 | ||||||||
\(392\) | −10.3817 | −0.524354 | ||||||||
\(393\) | −16.2290 | −0.818642 | ||||||||
\(394\) | −12.6056 | −0.635060 | ||||||||
\(395\) | 16.1033 | 0.810243 | ||||||||
\(396\) | −11.8177 | −0.593862 | ||||||||
\(397\) | 10.0850 | 0.506150 | 0.253075 | − | 0.967447i | \(-0.418558\pi\) | ||||
0.253075 | + | 0.967447i | \(0.418558\pi\) | |||||||
\(398\) | −14.7240 | −0.738048 | ||||||||
\(399\) | 29.5328 | 1.47849 | ||||||||
\(400\) | −1.22426 | −0.0612128 | ||||||||
\(401\) | −9.05638 | −0.452254 | −0.226127 | − | 0.974098i | \(-0.572606\pi\) | ||||
−0.226127 | + | 0.974098i | \(0.572606\pi\) | |||||||
\(402\) | −34.0978 | −1.70064 | ||||||||
\(403\) | −2.95542 | −0.147220 | ||||||||
\(404\) | −16.3914 | −0.815504 | ||||||||
\(405\) | −18.9277 | −0.940524 | ||||||||
\(406\) | −28.7337 | −1.42603 | ||||||||
\(407\) | −23.7670 | −1.17809 | ||||||||
\(408\) | 13.5995 | 0.673276 | ||||||||
\(409\) | −28.8539 | −1.42674 | −0.713368 | − | 0.700790i | \(-0.752831\pi\) | ||||
−0.713368 | + | 0.700790i | \(0.752831\pi\) | |||||||
\(410\) | 11.1997 | 0.553112 | ||||||||
\(411\) | 28.1504 | 1.38856 | ||||||||
\(412\) | −0.0361654 | −0.00178174 | ||||||||
\(413\) | −0.226310 | −0.0111360 | ||||||||
\(414\) | 20.3209 | 0.998717 | ||||||||
\(415\) | 20.5259 | 1.00758 | ||||||||
\(416\) | −2.71319 | −0.133025 | ||||||||
\(417\) | 42.0153 | 2.05750 | ||||||||
\(418\) | −12.8189 | −0.626994 | ||||||||
\(419\) | −36.0868 | −1.76295 | −0.881477 | − | 0.472227i | \(-0.843450\pi\) | ||||
−0.881477 | + | 0.472227i | \(0.843450\pi\) | |||||||
\(420\) | −19.3895 | −0.946111 | ||||||||
\(421\) | 23.2510 | 1.13318 | 0.566592 | − | 0.823999i | \(-0.308262\pi\) | ||||
0.566592 | + | 0.823999i | \(0.308262\pi\) | |||||||
\(422\) | −14.6438 | −0.712850 | ||||||||
\(423\) | −31.2565 | −1.51974 | ||||||||
\(424\) | 2.97190 | 0.144328 | ||||||||
\(425\) | −6.95626 | −0.337428 | ||||||||
\(426\) | −16.5317 | −0.800964 | ||||||||
\(427\) | 41.6777 | 2.01693 | ||||||||
\(428\) | −19.0988 | −0.923174 | ||||||||
\(429\) | 28.1263 | 1.35795 | ||||||||
\(430\) | 9.69625 | 0.467595 | ||||||||
\(431\) | 27.2496 | 1.31257 | 0.656283 | − | 0.754515i | \(-0.272128\pi\) | ||||
0.656283 | + | 0.754515i | \(0.272128\pi\) | |||||||
\(432\) | 0.649863 | 0.0312666 | ||||||||
\(433\) | 25.0898 | 1.20574 | 0.602868 | − | 0.797841i | \(-0.294024\pi\) | ||||
0.602868 | + | 0.797841i | \(0.294024\pi\) | |||||||
\(434\) | 4.54136 | 0.217992 | ||||||||
\(435\) | −32.0529 | −1.53682 | ||||||||
\(436\) | −19.7760 | −0.947097 | ||||||||
\(437\) | 22.0425 | 1.05443 | ||||||||
\(438\) | −11.2014 | −0.535226 | ||||||||
\(439\) | −15.7084 | −0.749721 | −0.374861 | − | 0.927081i | \(-0.622309\pi\) | ||||
−0.374861 | + | 0.927081i | \(0.622309\pi\) | |||||||
\(440\) | 8.41616 | 0.401225 | ||||||||
\(441\) | 28.3262 | 1.34887 | ||||||||
\(442\) | −15.4164 | −0.733283 | ||||||||
\(443\) | −35.2775 | −1.67609 | −0.838043 | − | 0.545604i | \(-0.816300\pi\) | ||||
−0.838043 | + | 0.545604i | \(0.816300\pi\) | |||||||
\(444\) | −13.1335 | −0.623289 | ||||||||
\(445\) | 3.74039 | 0.177311 | ||||||||
\(446\) | −20.2733 | −0.959968 | ||||||||
\(447\) | −31.1822 | −1.47487 | ||||||||
\(448\) | 4.16913 | 0.196973 | ||||||||
\(449\) | −31.7244 | −1.49717 | −0.748583 | − | 0.663041i | \(-0.769265\pi\) | ||||
−0.748583 | + | 0.663041i | \(0.769265\pi\) | |||||||
\(450\) | 3.34036 | 0.157466 | ||||||||
\(451\) | 24.9641 | 1.17551 | ||||||||
\(452\) | 2.28462 | 0.107460 | ||||||||
\(453\) | 6.99773 | 0.328782 | ||||||||
\(454\) | −27.3365 | −1.28296 | ||||||||
\(455\) | 21.9800 | 1.03044 | ||||||||
\(456\) | −7.08367 | −0.331723 | ||||||||
\(457\) | 12.6934 | 0.593771 | 0.296886 | − | 0.954913i | \(-0.404052\pi\) | ||||
0.296886 | + | 0.954913i | \(0.404052\pi\) | |||||||
\(458\) | 11.1327 | 0.520197 | ||||||||
\(459\) | 3.69254 | 0.172353 | ||||||||
\(460\) | −14.4718 | −0.674752 | ||||||||
\(461\) | 10.0120 | 0.466304 | 0.233152 | − | 0.972440i | \(-0.425096\pi\) | ||||
0.233152 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(462\) | −43.2194 | −2.01075 | ||||||||
\(463\) | 39.4617 | 1.83394 | 0.916970 | − | 0.398956i | \(-0.130628\pi\) | ||||
0.916970 | + | 0.398956i | \(0.130628\pi\) | |||||||
\(464\) | 6.89202 | 0.319954 | ||||||||
\(465\) | 5.06595 | 0.234928 | ||||||||
\(466\) | −0.215687 | −0.00999149 | ||||||||
\(467\) | 35.1410 | 1.62613 | 0.813066 | − | 0.582172i | \(-0.197797\pi\) | ||||
0.813066 | + | 0.582172i | \(0.197797\pi\) | |||||||
\(468\) | 7.40287 | 0.342198 | ||||||||
\(469\) | −59.3953 | −2.74262 | ||||||||
\(470\) | 22.2598 | 1.02677 | ||||||||
\(471\) | −11.7594 | −0.541846 | ||||||||
\(472\) | 0.0542823 | 0.00249855 | ||||||||
\(473\) | 21.6130 | 0.993768 | ||||||||
\(474\) | 19.8350 | 0.911052 | ||||||||
\(475\) | 3.62336 | 0.166251 | ||||||||
\(476\) | 23.6891 | 1.08579 | ||||||||
\(477\) | −8.10878 | −0.371275 | ||||||||
\(478\) | −16.5435 | −0.756681 | ||||||||
\(479\) | 18.8847 | 0.862863 | 0.431432 | − | 0.902146i | \(-0.358009\pi\) | ||||
0.431432 | + | 0.902146i | \(0.358009\pi\) | |||||||
\(480\) | 4.65073 | 0.212276 | ||||||||
\(481\) | 14.8882 | 0.678842 | ||||||||
\(482\) | −27.1229 | −1.23541 | ||||||||
\(483\) | 74.3168 | 3.38153 | ||||||||
\(484\) | 7.75968 | 0.352713 | ||||||||
\(485\) | −6.28649 | −0.285455 | ||||||||
\(486\) | −21.3644 | −0.969107 | ||||||||
\(487\) | −5.29030 | −0.239726 | −0.119863 | − | 0.992790i | \(-0.538246\pi\) | ||||
−0.119863 | + | 0.992790i | \(0.538246\pi\) | |||||||
\(488\) | −9.99674 | −0.452531 | ||||||||
\(489\) | −15.6666 | −0.708466 | ||||||||
\(490\) | −20.1729 | −0.911320 | ||||||||
\(491\) | −24.3784 | −1.10018 | −0.550090 | − | 0.835105i | \(-0.685407\pi\) | ||||
−0.550090 | + | 0.835105i | \(0.685407\pi\) | |||||||
\(492\) | 13.7950 | 0.621929 | ||||||||
\(493\) | 39.1606 | 1.76371 | ||||||||
\(494\) | 8.03005 | 0.361289 | ||||||||
\(495\) | −22.9633 | −1.03212 | ||||||||
\(496\) | −1.08928 | −0.0489101 | ||||||||
\(497\) | −28.7968 | −1.29171 | ||||||||
\(498\) | 25.2825 | 1.13294 | ||||||||
\(499\) | −37.5239 | −1.67980 | −0.839901 | − | 0.542740i | \(-0.817387\pi\) | ||||
−0.839901 | + | 0.542740i | \(0.817387\pi\) | |||||||
\(500\) | −12.0945 | −0.540883 | ||||||||
\(501\) | 12.1921 | 0.544705 | ||||||||
\(502\) | 1.72214 | 0.0768628 | ||||||||
\(503\) | −31.2489 | −1.39332 | −0.696660 | − | 0.717402i | \(-0.745331\pi\) | ||||
−0.696660 | + | 0.717402i | \(0.745331\pi\) | |||||||
\(504\) | −11.3754 | −0.506700 | ||||||||
\(505\) | −31.8506 | −1.41734 | ||||||||
\(506\) | −32.2578 | −1.43403 | ||||||||
\(507\) | 13.4956 | 0.599361 | ||||||||
\(508\) | −14.1060 | −0.625852 | ||||||||
\(509\) | −19.1345 | −0.848120 | −0.424060 | − | 0.905634i | \(-0.639395\pi\) | ||||
−0.424060 | + | 0.905634i | \(0.639395\pi\) | |||||||
\(510\) | 26.4256 | 1.17014 | ||||||||
\(511\) | −19.5119 | −0.863157 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.92336 | −0.0849184 | ||||||||
\(514\) | 4.47780 | 0.197507 | ||||||||
\(515\) | −0.0702740 | −0.00309664 | ||||||||
\(516\) | 11.9432 | 0.525772 | ||||||||
\(517\) | 49.6173 | 2.18216 | ||||||||
\(518\) | −22.8774 | −1.00518 | ||||||||
\(519\) | 40.8067 | 1.79121 | ||||||||
\(520\) | −5.27207 | −0.231195 | ||||||||
\(521\) | 3.10270 | 0.135932 | 0.0679659 | − | 0.997688i | \(-0.478349\pi\) | ||||
0.0679659 | + | 0.997688i | \(0.478349\pi\) | |||||||
\(522\) | −18.8047 | −0.823061 | ||||||||
\(523\) | −19.0531 | −0.833132 | −0.416566 | − | 0.909105i | \(-0.636767\pi\) | ||||
−0.416566 | + | 0.909105i | \(0.636767\pi\) | |||||||
\(524\) | 6.78064 | 0.296214 | ||||||||
\(525\) | 12.2163 | 0.533161 | ||||||||
\(526\) | 15.5812 | 0.679374 | ||||||||
\(527\) | −6.18932 | −0.269611 | ||||||||
\(528\) | 10.3665 | 0.451144 | ||||||||
\(529\) | 32.4681 | 1.41166 | ||||||||
\(530\) | 5.77479 | 0.250841 | ||||||||
\(531\) | −0.148108 | −0.00642735 | ||||||||
\(532\) | −12.3391 | −0.534969 | ||||||||
\(533\) | −15.6381 | −0.677360 | ||||||||
\(534\) | 4.60718 | 0.199372 | ||||||||
\(535\) | −37.1113 | −1.60446 | ||||||||
\(536\) | 14.2464 | 0.615353 | ||||||||
\(537\) | 60.6953 | 2.61919 | ||||||||
\(538\) | −1.15183 | −0.0496588 | ||||||||
\(539\) | −44.9656 | −1.93681 | ||||||||
\(540\) | 1.26277 | 0.0543409 | ||||||||
\(541\) | −42.7976 | −1.84001 | −0.920006 | − | 0.391904i | \(-0.871816\pi\) | ||||
−0.920006 | + | 0.391904i | \(0.871816\pi\) | |||||||
\(542\) | −23.5103 | −1.00985 | ||||||||
\(543\) | −26.5916 | −1.14115 | ||||||||
\(544\) | −5.68203 | −0.243615 | ||||||||
\(545\) | −38.4272 | −1.64604 | ||||||||
\(546\) | 27.0735 | 1.15864 | ||||||||
\(547\) | −18.9667 | −0.810956 | −0.405478 | − | 0.914105i | \(-0.632895\pi\) | ||||
−0.405478 | + | 0.914105i | \(0.632895\pi\) | |||||||
\(548\) | −11.7616 | −0.502429 | ||||||||
\(549\) | 27.2759 | 1.16411 | ||||||||
\(550\) | −5.30255 | −0.226102 | ||||||||
\(551\) | −20.3979 | −0.868979 | ||||||||
\(552\) | −17.8255 | −0.758703 | ||||||||
\(553\) | 34.5508 | 1.46925 | ||||||||
\(554\) | 11.7967 | 0.501195 | ||||||||
\(555\) | −25.5201 | −1.08327 | ||||||||
\(556\) | −17.5545 | −0.744475 | ||||||||
\(557\) | −22.6603 | −0.960149 | −0.480074 | − | 0.877228i | \(-0.659390\pi\) | ||||
−0.480074 | + | 0.877228i | \(0.659390\pi\) | |||||||
\(558\) | 2.97208 | 0.125818 | ||||||||
\(559\) | −13.5389 | −0.572633 | ||||||||
\(560\) | 8.10116 | 0.342336 | ||||||||
\(561\) | 58.9028 | 2.48688 | ||||||||
\(562\) | 20.0725 | 0.846707 | ||||||||
\(563\) | 2.52568 | 0.106445 | 0.0532223 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532223 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(564\) | 27.4182 | 1.15452 | ||||||||
\(565\) | 4.43931 | 0.186763 | ||||||||
\(566\) | −7.09054 | −0.298038 | ||||||||
\(567\) | −40.6109 | −1.70550 | ||||||||
\(568\) | 6.90714 | 0.289817 | ||||||||
\(569\) | 34.2535 | 1.43598 | 0.717991 | − | 0.696052i | \(-0.245062\pi\) | ||||
0.717991 | + | 0.696052i | \(0.245062\pi\) | |||||||
\(570\) | −13.7645 | −0.576530 | ||||||||
\(571\) | −43.4271 | −1.81737 | −0.908683 | − | 0.417486i | \(-0.862911\pi\) | ||||
−0.908683 | + | 0.417486i | \(0.862911\pi\) | |||||||
\(572\) | −11.7515 | −0.491354 | ||||||||
\(573\) | −44.0390 | −1.83976 | ||||||||
\(574\) | 24.0298 | 1.00298 | ||||||||
\(575\) | 9.11789 | 0.380242 | ||||||||
\(576\) | 2.72848 | 0.113687 | ||||||||
\(577\) | −0.861400 | −0.0358605 | −0.0179303 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179303 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(578\) | −15.2854 | −0.635790 | ||||||||
\(579\) | −25.0992 | −1.04309 | ||||||||
\(580\) | 13.3921 | 0.556075 | ||||||||
\(581\) | 44.0399 | 1.82708 | ||||||||
\(582\) | −7.74331 | −0.320971 | ||||||||
\(583\) | 12.8720 | 0.533106 | ||||||||
\(584\) | 4.68009 | 0.193664 | ||||||||
\(585\) | 14.3847 | 0.594735 | ||||||||
\(586\) | 7.50039 | 0.309838 | ||||||||
\(587\) | 15.8166 | 0.652819 | 0.326410 | − | 0.945228i | \(-0.394161\pi\) | ||||
0.326410 | + | 0.945228i | \(0.394161\pi\) | |||||||
\(588\) | −24.8478 | −1.02470 | ||||||||
\(589\) | 3.22388 | 0.132837 | ||||||||
\(590\) | 0.105477 | 0.00434244 | ||||||||
\(591\) | −30.1705 | −1.24105 | ||||||||
\(592\) | 5.48734 | 0.225528 | ||||||||
\(593\) | 3.26147 | 0.133933 | 0.0669663 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669663 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(594\) | 2.81472 | 0.115489 | ||||||||
\(595\) | 46.0310 | 1.88709 | ||||||||
\(596\) | 13.0283 | 0.533659 | ||||||||
\(597\) | −35.2408 | −1.44231 | ||||||||
\(598\) | 20.2070 | 0.826325 | ||||||||
\(599\) | −11.3760 | −0.464811 | −0.232405 | − | 0.972619i | \(-0.574660\pi\) | ||||
−0.232405 | + | 0.972619i | \(0.574660\pi\) | |||||||
\(600\) | −2.93017 | −0.119623 | ||||||||
\(601\) | 40.6685 | 1.65890 | 0.829450 | − | 0.558580i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558580i | \(0.188654\pi\) | |||||||
\(602\) | 20.8041 | 0.847911 | ||||||||
\(603\) | −38.8711 | −1.58295 | ||||||||
\(604\) | −2.92373 | −0.118965 | ||||||||
\(605\) | 15.0781 | 0.613010 | ||||||||
\(606\) | −39.2317 | −1.59368 | ||||||||
\(607\) | 8.86610 | 0.359864 | 0.179932 | − | 0.983679i | \(-0.442412\pi\) | ||||
0.179932 | + | 0.983679i | \(0.442412\pi\) | |||||||
\(608\) | 2.95964 | 0.120029 | ||||||||
\(609\) | −68.7720 | −2.78678 | ||||||||
\(610\) | −19.4249 | −0.786492 | ||||||||
\(611\) | −31.0813 | −1.25742 | ||||||||
\(612\) | 15.5033 | 0.626683 | ||||||||
\(613\) | 30.3652 | 1.22644 | 0.613219 | − | 0.789913i | \(-0.289874\pi\) | ||||
0.613219 | + | 0.789913i | \(0.289874\pi\) | |||||||
\(614\) | −11.2203 | −0.452813 | ||||||||
\(615\) | 26.8055 | 1.08090 | ||||||||
\(616\) | 18.0575 | 0.727559 | ||||||||
\(617\) | −38.5220 | −1.55084 | −0.775419 | − | 0.631447i | \(-0.782462\pi\) | ||||
−0.775419 | + | 0.631447i | \(0.782462\pi\) | |||||||
\(618\) | −0.0865592 | −0.00348192 | ||||||||
\(619\) | −30.2580 | −1.21617 | −0.608087 | − | 0.793871i | \(-0.708063\pi\) | ||||
−0.608087 | + | 0.793871i | \(0.708063\pi\) | |||||||
\(620\) | −2.11661 | −0.0850051 | ||||||||
\(621\) | −4.83998 | −0.194222 | ||||||||
\(622\) | −1.87274 | −0.0750900 | ||||||||
\(623\) | 8.02530 | 0.321527 | ||||||||
\(624\) | −6.49381 | −0.259960 | ||||||||
\(625\) | −17.3799 | −0.695197 | ||||||||
\(626\) | 26.8274 | 1.07224 | ||||||||
\(627\) | −30.6811 | −1.22529 | ||||||||
\(628\) | 4.91322 | 0.196059 | ||||||||
\(629\) | 31.1792 | 1.24320 | ||||||||
\(630\) | −22.1038 | −0.880638 | ||||||||
\(631\) | −35.7124 | −1.42169 | −0.710844 | − | 0.703350i | \(-0.751687\pi\) | ||||
−0.710844 | + | 0.703350i | \(0.751687\pi\) | |||||||
\(632\) | −8.28729 | −0.329651 | ||||||||
\(633\) | −35.0489 | −1.39307 | ||||||||
\(634\) | 34.2630 | 1.36076 | ||||||||
\(635\) | −27.4097 | −1.08772 | ||||||||
\(636\) | 7.11303 | 0.282050 | ||||||||
\(637\) | 28.1674 | 1.11603 | ||||||||
\(638\) | 29.8510 | 1.18181 | ||||||||
\(639\) | −18.8460 | −0.745535 | ||||||||
\(640\) | −1.94313 | −0.0768088 | ||||||||
\(641\) | −36.0350 | −1.42330 | −0.711649 | − | 0.702535i | \(-0.752051\pi\) | ||||
−0.711649 | + | 0.702535i | \(0.752051\pi\) | |||||||
\(642\) | −45.7114 | −1.80409 | ||||||||
\(643\) | 25.2333 | 0.995106 | 0.497553 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497553 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(644\) | −31.0504 | −1.22356 | ||||||||
\(645\) | 23.2072 | 0.913784 | ||||||||
\(646\) | 16.8167 | 0.661646 | ||||||||
\(647\) | −23.1262 | −0.909184 | −0.454592 | − | 0.890700i | \(-0.650215\pi\) | ||||
−0.454592 | + | 0.890700i | \(0.650215\pi\) | |||||||
\(648\) | 9.74084 | 0.382656 | ||||||||
\(649\) | 0.235110 | 0.00922888 | ||||||||
\(650\) | 3.32164 | 0.130285 | ||||||||
\(651\) | 10.8694 | 0.426005 | ||||||||
\(652\) | 6.54567 | 0.256348 | ||||||||
\(653\) | 17.4034 | 0.681048 | 0.340524 | − | 0.940236i | \(-0.389396\pi\) | ||||
0.340524 | + | 0.940236i | \(0.389396\pi\) | |||||||
\(654\) | −47.3323 | −1.85084 | ||||||||
\(655\) | 13.1757 | 0.514815 | ||||||||
\(656\) | −5.76373 | −0.225036 | ||||||||
\(657\) | −12.7695 | −0.498187 | ||||||||
\(658\) | 47.7602 | 1.86189 | ||||||||
\(659\) | −12.7356 | −0.496108 | −0.248054 | − | 0.968746i | \(-0.579791\pi\) | ||||
−0.248054 | + | 0.968746i | \(0.579791\pi\) | |||||||
\(660\) | 20.1434 | 0.784082 | ||||||||
\(661\) | 25.7885 | 1.00306 | 0.501528 | − | 0.865141i | \(-0.332771\pi\) | ||||
0.501528 | + | 0.865141i | \(0.332771\pi\) | |||||||
\(662\) | −3.34434 | −0.129981 | ||||||||
\(663\) | −36.8980 | −1.43300 | ||||||||
\(664\) | −10.5633 | −0.409936 | ||||||||
\(665\) | −23.9765 | −0.929768 | ||||||||
\(666\) | −14.9721 | −0.580157 | ||||||||
\(667\) | −51.3296 | −1.98749 | ||||||||
\(668\) | −5.09402 | −0.197093 | ||||||||
\(669\) | −48.5226 | −1.87599 | ||||||||
\(670\) | 27.6826 | 1.06947 | ||||||||
\(671\) | −43.2983 | −1.67151 | ||||||||
\(672\) | 9.97851 | 0.384929 | ||||||||
\(673\) | −39.5163 | −1.52324 | −0.761621 | − | 0.648023i | \(-0.775596\pi\) | ||||
−0.761621 | + | 0.648023i | \(0.775596\pi\) | |||||||
\(674\) | −26.9648 | −1.03864 | ||||||||
\(675\) | −0.795600 | −0.0306226 | ||||||||
\(676\) | −5.63862 | −0.216870 | ||||||||
\(677\) | 4.46518 | 0.171611 | 0.0858054 | − | 0.996312i | \(-0.472654\pi\) | ||||
0.0858054 | + | 0.996312i | \(0.472654\pi\) | |||||||
\(678\) | 5.46807 | 0.210000 | ||||||||
\(679\) | −13.4882 | −0.517628 | ||||||||
\(680\) | −11.0409 | −0.423399 | ||||||||
\(681\) | −65.4278 | −2.50720 | ||||||||
\(682\) | −4.71794 | −0.180659 | ||||||||
\(683\) | 28.1324 | 1.07646 | 0.538228 | − | 0.842799i | \(-0.319094\pi\) | ||||
0.538228 | + | 0.842799i | \(0.319094\pi\) | |||||||
\(684\) | −8.07531 | −0.308767 | ||||||||
\(685\) | −22.8542 | −0.873215 | ||||||||
\(686\) | −14.0987 | −0.538290 | ||||||||
\(687\) | 26.6453 | 1.01658 | ||||||||
\(688\) | −4.99002 | −0.190243 | ||||||||
\(689\) | −8.06333 | −0.307188 | ||||||||
\(690\) | −34.6372 | −1.31862 | ||||||||
\(691\) | 18.5205 | 0.704555 | 0.352277 | − | 0.935896i | \(-0.385407\pi\) | ||||
0.352277 | + | 0.935896i | \(0.385407\pi\) | |||||||
\(692\) | −17.0495 | −0.648124 | ||||||||
\(693\) | −49.2696 | −1.87160 | ||||||||
\(694\) | 12.2128 | 0.463592 | ||||||||
\(695\) | −34.1106 | −1.29389 | ||||||||
\(696\) | 16.4955 | 0.625261 | ||||||||
\(697\) | −32.7497 | −1.24048 | ||||||||
\(698\) | −2.33229 | −0.0882784 | ||||||||
\(699\) | −0.516230 | −0.0195256 | ||||||||
\(700\) | −5.10409 | −0.192916 | ||||||||
\(701\) | 16.8389 | 0.635997 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(702\) | −1.76320 | −0.0665477 | ||||||||
\(703\) | −16.2405 | −0.612523 | ||||||||
\(704\) | −4.33125 | −0.163240 | ||||||||
\(705\) | 53.2771 | 2.00653 | ||||||||
\(706\) | 13.9573 | 0.525290 | ||||||||
\(707\) | −68.3381 | −2.57012 | ||||||||
\(708\) | 0.129921 | 0.00488272 | ||||||||
\(709\) | −39.9157 | −1.49907 | −0.749533 | − | 0.661967i | \(-0.769722\pi\) | ||||
−0.749533 | + | 0.661967i | \(0.769722\pi\) | |||||||
\(710\) | 13.4214 | 0.503698 | ||||||||
\(711\) | 22.6117 | 0.848005 | ||||||||
\(712\) | −1.92493 | −0.0721398 | ||||||||
\(713\) | 8.11263 | 0.303820 | ||||||||
\(714\) | 56.6981 | 2.12187 | ||||||||
\(715\) | −22.8346 | −0.853966 | ||||||||
\(716\) | −25.3592 | −0.947717 | ||||||||
\(717\) | −39.5956 | −1.47872 | ||||||||
\(718\) | −21.0099 | −0.784083 | ||||||||
\(719\) | 10.6302 | 0.396440 | 0.198220 | − | 0.980158i | \(-0.436484\pi\) | ||||
0.198220 | + | 0.980158i | \(0.436484\pi\) | |||||||
\(720\) | 5.30178 | 0.197586 | ||||||||
\(721\) | −0.150778 | −0.00561528 | ||||||||
\(722\) | 10.2405 | 0.381114 | ||||||||
\(723\) | −64.9166 | −2.41427 | ||||||||
\(724\) | 11.1103 | 0.412910 | ||||||||
\(725\) | −8.43760 | −0.313364 | ||||||||
\(726\) | 18.5722 | 0.689280 | ||||||||
\(727\) | 30.8953 | 1.14584 | 0.572921 | − | 0.819611i | \(-0.305810\pi\) | ||||
0.572921 | + | 0.819611i | \(0.305810\pi\) | |||||||
\(728\) | −11.3116 | −0.419237 | ||||||||
\(729\) | −21.9115 | −0.811536 | ||||||||
\(730\) | 9.09401 | 0.336585 | ||||||||
\(731\) | −28.3534 | −1.04869 | ||||||||
\(732\) | −23.9264 | −0.884346 | ||||||||
\(733\) | −45.0743 | −1.66486 | −0.832428 | − | 0.554133i | \(-0.813050\pi\) | ||||
−0.832428 | + | 0.554133i | \(0.813050\pi\) | |||||||
\(734\) | −17.9655 | −0.663120 | ||||||||
\(735\) | −48.2824 | −1.78092 | ||||||||
\(736\) | 7.44769 | 0.274526 | ||||||||
\(737\) | 61.7048 | 2.27293 | ||||||||
\(738\) | 15.7262 | 0.578890 | ||||||||
\(739\) | 19.5871 | 0.720522 | 0.360261 | − | 0.932852i | \(-0.382688\pi\) | ||||
0.360261 | + | 0.932852i | \(0.382688\pi\) | |||||||
\(740\) | 10.6626 | 0.391965 | ||||||||
\(741\) | 19.2193 | 0.706039 | ||||||||
\(742\) | 12.3903 | 0.454861 | ||||||||
\(743\) | 19.6090 | 0.719384 | 0.359692 | − | 0.933071i | \(-0.382882\pi\) | ||||
0.359692 | + | 0.933071i | \(0.382882\pi\) | |||||||
\(744\) | −2.60711 | −0.0955813 | ||||||||
\(745\) | 25.3156 | 0.927492 | ||||||||
\(746\) | 9.07032 | 0.332088 | ||||||||
\(747\) | 28.8218 | 1.05453 | ||||||||
\(748\) | −24.6102 | −0.899840 | ||||||||
\(749\) | −79.6253 | −2.90945 | ||||||||
\(750\) | −28.9473 | −1.05701 | ||||||||
\(751\) | 27.4195 | 1.00055 | 0.500276 | − | 0.865866i | \(-0.333232\pi\) | ||||
0.500276 | + | 0.865866i | \(0.333232\pi\) | |||||||
\(752\) | −11.4557 | −0.417745 | ||||||||
\(753\) | 4.12181 | 0.150207 | ||||||||
\(754\) | −18.6993 | −0.680989 | ||||||||
\(755\) | −5.68119 | −0.206760 | ||||||||
\(756\) | 2.70937 | 0.0985388 | ||||||||
\(757\) | −16.9437 | −0.615829 | −0.307915 | − | 0.951414i | \(-0.599631\pi\) | ||||
−0.307915 | + | 0.951414i | \(0.599631\pi\) | |||||||
\(758\) | 28.4905 | 1.03482 | ||||||||
\(759\) | −77.2066 | −2.80242 | ||||||||
\(760\) | 5.75095 | 0.208609 | ||||||||
\(761\) | −22.6779 | −0.822073 | −0.411037 | − | 0.911619i | \(-0.634833\pi\) | ||||
−0.411037 | + | 0.911619i | \(0.634833\pi\) | |||||||
\(762\) | −33.7616 | −1.22305 | ||||||||
\(763\) | −82.4487 | −2.98484 | ||||||||
\(764\) | 18.4000 | 0.665689 | ||||||||
\(765\) | 30.1249 | 1.08917 | ||||||||
\(766\) | −29.1766 | −1.05419 | ||||||||
\(767\) | −0.147278 | −0.00531790 | ||||||||
\(768\) | −2.39342 | −0.0863653 | ||||||||
\(769\) | 54.4430 | 1.96327 | 0.981633 | − | 0.190779i | \(-0.0611013\pi\) | ||||
0.981633 | + | 0.190779i | \(0.0611013\pi\) | |||||||
\(770\) | 35.0881 | 1.26449 | ||||||||
\(771\) | 10.7173 | 0.385973 | ||||||||
\(772\) | 10.4867 | 0.377426 | ||||||||
\(773\) | 23.7275 | 0.853421 | 0.426710 | − | 0.904388i | \(-0.359672\pi\) | ||||
0.426710 | + | 0.904388i | \(0.359672\pi\) | |||||||
\(774\) | 13.6152 | 0.489388 | ||||||||
\(775\) | 1.33356 | 0.0479028 | ||||||||
\(776\) | 3.23525 | 0.116139 | ||||||||
\(777\) | −54.7554 | −1.96434 | ||||||||
\(778\) | 16.6747 | 0.597818 | ||||||||
\(779\) | 17.0585 | 0.611186 | ||||||||
\(780\) | −12.6183 | −0.451807 | ||||||||
\(781\) | 29.9165 | 1.07050 | ||||||||
\(782\) | 42.3180 | 1.51329 | ||||||||
\(783\) | 4.47887 | 0.160062 | ||||||||
\(784\) | 10.3817 | 0.370774 | ||||||||
\(785\) | 9.54702 | 0.340748 | ||||||||
\(786\) | 16.2290 | 0.578868 | ||||||||
\(787\) | 11.2934 | 0.402567 | 0.201283 | − | 0.979533i | \(-0.435489\pi\) | ||||
0.201283 | + | 0.979533i | \(0.435489\pi\) | |||||||
\(788\) | 12.6056 | 0.449056 | ||||||||
\(789\) | 37.2925 | 1.32765 | ||||||||
\(790\) | −16.1033 | −0.572928 | ||||||||
\(791\) | 9.52490 | 0.338666 | ||||||||
\(792\) | 11.8177 | 0.419924 | ||||||||
\(793\) | 27.1230 | 0.963166 | ||||||||
\(794\) | −10.0850 | −0.357902 | ||||||||
\(795\) | 13.8215 | 0.490199 | ||||||||
\(796\) | 14.7240 | 0.521879 | ||||||||
\(797\) | −4.59914 | −0.162910 | −0.0814550 | − | 0.996677i | \(-0.525957\pi\) | ||||
−0.0814550 | + | 0.996677i | \(0.525957\pi\) | |||||||
\(798\) | −29.5328 | −1.04545 | ||||||||
\(799\) | −65.0913 | −2.30277 | ||||||||
\(800\) | 1.22426 | 0.0432840 | ||||||||
\(801\) | 5.25213 | 0.185575 | ||||||||
\(802\) | 9.05638 | 0.319792 | ||||||||
\(803\) | 20.2706 | 0.715335 | ||||||||
\(804\) | 34.0978 | 1.20254 | ||||||||
\(805\) | −60.3349 | −2.12653 | ||||||||
\(806\) | 2.95542 | 0.104100 | ||||||||
\(807\) | −2.75681 | −0.0970443 | ||||||||
\(808\) | 16.3914 | 0.576649 | ||||||||
\(809\) | 26.1697 | 0.920078 | 0.460039 | − | 0.887899i | \(-0.347835\pi\) | ||||
0.460039 | + | 0.887899i | \(0.347835\pi\) | |||||||
\(810\) | 18.9277 | 0.665051 | ||||||||
\(811\) | −6.27402 | −0.220310 | −0.110155 | − | 0.993914i | \(-0.535135\pi\) | ||||
−0.110155 | + | 0.993914i | \(0.535135\pi\) | |||||||
\(812\) | 28.7337 | 1.00836 | ||||||||
\(813\) | −56.2701 | −1.97348 | ||||||||
\(814\) | 23.7670 | 0.833033 | ||||||||
\(815\) | 12.7191 | 0.445529 | ||||||||
\(816\) | −13.5995 | −0.476078 | ||||||||
\(817\) | 14.7687 | 0.516690 | ||||||||
\(818\) | 28.8539 | 1.00885 | ||||||||
\(819\) | 30.8636 | 1.07846 | ||||||||
\(820\) | −11.1997 | −0.391109 | ||||||||
\(821\) | −30.9781 | −1.08114 | −0.540572 | − | 0.841298i | \(-0.681792\pi\) | ||||
−0.540572 | + | 0.841298i | \(0.681792\pi\) | |||||||
\(822\) | −28.1504 | −0.981859 | ||||||||
\(823\) | 30.8907 | 1.07678 | 0.538391 | − | 0.842695i | \(-0.319032\pi\) | ||||
0.538391 | + | 0.842695i | \(0.319032\pi\) | |||||||
\(824\) | 0.0361654 | 0.00125988 | ||||||||
\(825\) | −12.6913 | −0.441853 | ||||||||
\(826\) | 0.226310 | 0.00787434 | ||||||||
\(827\) | −13.7984 | −0.479818 | −0.239909 | − | 0.970795i | \(-0.577118\pi\) | ||||
−0.239909 | + | 0.970795i | \(0.577118\pi\) | |||||||
\(828\) | −20.3209 | −0.706199 | ||||||||
\(829\) | −26.6331 | −0.925005 | −0.462502 | − | 0.886618i | \(-0.653048\pi\) | ||||
−0.462502 | + | 0.886618i | \(0.653048\pi\) | |||||||
\(830\) | −20.5259 | −0.712463 | ||||||||
\(831\) | 28.2346 | 0.979446 | ||||||||
\(832\) | 2.71319 | 0.0940628 | ||||||||
\(833\) | 58.9890 | 2.04385 | ||||||||
\(834\) | −42.0153 | −1.45487 | ||||||||
\(835\) | −9.89832 | −0.342545 | ||||||||
\(836\) | 12.8189 | 0.443351 | ||||||||
\(837\) | −0.707884 | −0.0244680 | ||||||||
\(838\) | 36.0868 | 1.24660 | ||||||||
\(839\) | −20.2614 | −0.699500 | −0.349750 | − | 0.936843i | \(-0.613734\pi\) | ||||
−0.349750 | + | 0.936843i | \(0.613734\pi\) | |||||||
\(840\) | 19.3895 | 0.669002 | ||||||||
\(841\) | 18.4999 | 0.637927 | ||||||||
\(842\) | −23.2510 | −0.801282 | ||||||||
\(843\) | 48.0420 | 1.65465 | ||||||||
\(844\) | 14.6438 | 0.504061 | ||||||||
\(845\) | −10.9566 | −0.376917 | ||||||||
\(846\) | 31.2565 | 1.07462 | ||||||||
\(847\) | 32.3512 | 1.11160 | ||||||||
\(848\) | −2.97190 | −0.102056 | ||||||||
\(849\) | −16.9707 | −0.582432 | ||||||||
\(850\) | 6.95626 | 0.238598 | ||||||||
\(851\) | −40.8680 | −1.40094 | ||||||||
\(852\) | 16.5317 | 0.566367 | ||||||||
\(853\) | −21.0615 | −0.721132 | −0.360566 | − | 0.932734i | \(-0.617416\pi\) | ||||
−0.360566 | + | 0.932734i | \(0.617416\pi\) | |||||||
\(854\) | −41.6777 | −1.42618 | ||||||||
\(855\) | −15.6914 | −0.536633 | ||||||||
\(856\) | 19.0988 | 0.652782 | ||||||||
\(857\) | −21.3145 | −0.728088 | −0.364044 | − | 0.931382i | \(-0.618604\pi\) | ||||
−0.364044 | + | 0.931382i | \(0.618604\pi\) | |||||||
\(858\) | −28.1263 | −0.960215 | ||||||||
\(859\) | 3.90743 | 0.133320 | 0.0666599 | − | 0.997776i | \(-0.478766\pi\) | ||||
0.0666599 | + | 0.997776i | \(0.478766\pi\) | |||||||
\(860\) | −9.69625 | −0.330639 | ||||||||
\(861\) | 57.5134 | 1.96005 | ||||||||
\(862\) | −27.2496 | −0.928124 | ||||||||
\(863\) | 2.42849 | 0.0826666 | 0.0413333 | − | 0.999145i | \(-0.486839\pi\) | ||||
0.0413333 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(864\) | −0.649863 | −0.0221088 | ||||||||
\(865\) | −33.1293 | −1.12643 | ||||||||
\(866\) | −25.0898 | −0.852585 | ||||||||
\(867\) | −36.5845 | −1.24247 | ||||||||
\(868\) | −4.54136 | −0.154144 | ||||||||
\(869\) | −35.8943 | −1.21763 | ||||||||
\(870\) | 32.0529 | 1.08669 | ||||||||
\(871\) | −38.6533 | −1.30972 | ||||||||
\(872\) | 19.7760 | 0.669699 | ||||||||
\(873\) | −8.82730 | −0.298759 | ||||||||
\(874\) | −22.0425 | −0.745598 | ||||||||
\(875\) | −50.4237 | −1.70463 | ||||||||
\(876\) | 11.2014 | 0.378462 | ||||||||
\(877\) | −36.3404 | −1.22713 | −0.613563 | − | 0.789646i | \(-0.710264\pi\) | ||||
−0.613563 | + | 0.789646i | \(0.710264\pi\) | |||||||
\(878\) | 15.7084 | 0.530133 | ||||||||
\(879\) | 17.9516 | 0.605493 | ||||||||
\(880\) | −8.41616 | −0.283709 | ||||||||
\(881\) | 56.7582 | 1.91223 | 0.956117 | − | 0.292985i | \(-0.0946487\pi\) | ||||
0.956117 | + | 0.292985i | \(0.0946487\pi\) | |||||||
\(882\) | −28.3262 | −0.953793 | ||||||||
\(883\) | −9.34946 | −0.314634 | −0.157317 | − | 0.987548i | \(-0.550284\pi\) | ||||
−0.157317 | + | 0.987548i | \(0.550284\pi\) | |||||||
\(884\) | 15.4164 | 0.518510 | ||||||||
\(885\) | 0.252452 | 0.00848609 | ||||||||
\(886\) | 35.2775 | 1.18517 | ||||||||
\(887\) | 45.0943 | 1.51412 | 0.757059 | − | 0.653346i | \(-0.226635\pi\) | ||||
0.757059 | + | 0.653346i | \(0.226635\pi\) | |||||||
\(888\) | 13.1335 | 0.440732 | ||||||||
\(889\) | −58.8098 | −1.97242 | ||||||||
\(890\) | −3.74039 | −0.125378 | ||||||||
\(891\) | 42.1900 | 1.41342 | ||||||||
\(892\) | 20.2733 | 0.678800 | ||||||||
\(893\) | 33.9046 | 1.13457 | ||||||||
\(894\) | 31.1822 | 1.04289 | ||||||||
\(895\) | −49.2761 | −1.64712 | ||||||||
\(896\) | −4.16913 | −0.139281 | ||||||||
\(897\) | 48.3639 | 1.61482 | ||||||||
\(898\) | 31.7244 | 1.05866 | ||||||||
\(899\) | −7.50734 | −0.250384 | ||||||||
\(900\) | −3.34036 | −0.111345 | ||||||||
\(901\) | −16.8864 | −0.562569 | ||||||||
\(902\) | −24.9641 | −0.831214 | ||||||||
\(903\) | 49.7930 | 1.65701 | ||||||||
\(904\) | −2.28462 | −0.0759854 | ||||||||
\(905\) | 21.5887 | 0.717631 | ||||||||
\(906\) | −6.99773 | −0.232484 | ||||||||
\(907\) | −19.1081 | −0.634474 | −0.317237 | − | 0.948346i | \(-0.602755\pi\) | ||||
−0.317237 | + | 0.948346i | \(0.602755\pi\) | |||||||
\(908\) | 27.3365 | 0.907193 | ||||||||
\(909\) | −44.7237 | −1.48339 | ||||||||
\(910\) | −21.9800 | −0.728628 | ||||||||
\(911\) | −30.4724 | −1.00960 | −0.504799 | − | 0.863237i | \(-0.668433\pi\) | ||||
−0.504799 | + | 0.863237i | \(0.668433\pi\) | |||||||
\(912\) | 7.08367 | 0.234564 | ||||||||
\(913\) | −45.7523 | −1.51418 | ||||||||
\(914\) | −12.6934 | −0.419860 | ||||||||
\(915\) | −46.4921 | −1.53698 | ||||||||
\(916\) | −11.1327 | −0.367834 | ||||||||
\(917\) | 28.2694 | 0.933538 | ||||||||
\(918\) | −3.69254 | −0.121872 | ||||||||
\(919\) | 8.68114 | 0.286364 | 0.143182 | − | 0.989696i | \(-0.454267\pi\) | ||||
0.143182 | + | 0.989696i | \(0.454267\pi\) | |||||||
\(920\) | 14.4718 | 0.477122 | ||||||||
\(921\) | −26.8548 | −0.884897 | ||||||||
\(922\) | −10.0120 | −0.329727 | ||||||||
\(923\) | −18.7403 | −0.616846 | ||||||||
\(924\) | 43.2194 | 1.42181 | ||||||||
\(925\) | −6.71791 | −0.220883 | ||||||||
\(926\) | −39.4617 | −1.29679 | ||||||||
\(927\) | −0.0986766 | −0.00324097 | ||||||||
\(928\) | −6.89202 | −0.226242 | ||||||||
\(929\) | −7.89059 | −0.258882 | −0.129441 | − | 0.991587i | \(-0.541318\pi\) | ||||
−0.129441 | + | 0.991587i | \(0.541318\pi\) | |||||||
\(930\) | −5.06595 | −0.166119 | ||||||||
\(931\) | −30.7260 | −1.00700 | ||||||||
\(932\) | 0.215687 | 0.00706505 | ||||||||
\(933\) | −4.48226 | −0.146743 | ||||||||
\(934\) | −35.1410 | −1.14985 | ||||||||
\(935\) | −47.8208 | −1.56391 | ||||||||
\(936\) | −7.40287 | −0.241970 | ||||||||
\(937\) | 4.17264 | 0.136314 | 0.0681570 | − | 0.997675i | \(-0.478288\pi\) | ||||
0.0681570 | + | 0.997675i | \(0.478288\pi\) | |||||||
\(938\) | 59.3953 | 1.93933 | ||||||||
\(939\) | 64.2094 | 2.09539 | ||||||||
\(940\) | −22.2598 | −0.726035 | ||||||||
\(941\) | −20.2127 | −0.658916 | −0.329458 | − | 0.944170i | \(-0.606866\pi\) | ||||
−0.329458 | + | 0.944170i | \(0.606866\pi\) | |||||||
\(942\) | 11.7594 | 0.383143 | ||||||||
\(943\) | 42.9265 | 1.39788 | ||||||||
\(944\) | −0.0542823 | −0.00176674 | ||||||||
\(945\) | 5.26465 | 0.171259 | ||||||||
\(946\) | −21.6130 | −0.702700 | ||||||||
\(947\) | 30.0721 | 0.977213 | 0.488607 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488607 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(948\) | −19.8350 | −0.644211 | ||||||||
\(949\) | −12.6980 | −0.412193 | ||||||||
\(950\) | −3.62336 | −0.117557 | ||||||||
\(951\) | 82.0058 | 2.65922 | ||||||||
\(952\) | −23.6891 | −0.767769 | ||||||||
\(953\) | 32.3158 | 1.04681 | 0.523406 | − | 0.852083i | \(-0.324661\pi\) | ||||
0.523406 | + | 0.852083i | \(0.324661\pi\) | |||||||
\(954\) | 8.10878 | 0.262531 | ||||||||
\(955\) | 35.7536 | 1.15696 | ||||||||
\(956\) | 16.5435 | 0.535054 | ||||||||
\(957\) | 71.4461 | 2.30953 | ||||||||
\(958\) | −18.8847 | −0.610136 | ||||||||
\(959\) | −49.0355 | −1.58344 | ||||||||
\(960\) | −4.65073 | −0.150102 | ||||||||
\(961\) | −29.8135 | −0.961725 | ||||||||
\(962\) | −14.8882 | −0.480014 | ||||||||
\(963\) | −52.1106 | −1.67924 | ||||||||
\(964\) | 27.1229 | 0.873569 | ||||||||
\(965\) | 20.3770 | 0.655960 | ||||||||
\(966\) | −74.3168 | −2.39111 | ||||||||
\(967\) | −16.6079 | −0.534074 | −0.267037 | − | 0.963686i | \(-0.586045\pi\) | ||||
−0.267037 | + | 0.963686i | \(0.586045\pi\) | |||||||
\(968\) | −7.75968 | −0.249406 | ||||||||
\(969\) | 40.2496 | 1.29300 | ||||||||
\(970\) | 6.28649 | 0.201847 | ||||||||
\(971\) | −11.3801 | −0.365203 | −0.182602 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182602 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(972\) | 21.3644 | 0.685262 | ||||||||
\(973\) | −73.1870 | −2.34627 | ||||||||
\(974\) | 5.29030 | 0.169512 | ||||||||
\(975\) | 7.95008 | 0.254606 | ||||||||
\(976\) | 9.99674 | 0.319988 | ||||||||
\(977\) | −34.7575 | −1.11199 | −0.555995 | − | 0.831186i | \(-0.687663\pi\) | ||||
−0.555995 | + | 0.831186i | \(0.687663\pi\) | |||||||
\(978\) | 15.6666 | 0.500961 | ||||||||
\(979\) | −8.33735 | −0.266463 | ||||||||
\(980\) | 20.1729 | 0.644400 | ||||||||
\(981\) | −53.9583 | −1.72276 | ||||||||
\(982\) | 24.3784 | 0.777945 | ||||||||
\(983\) | 51.2355 | 1.63416 | 0.817079 | − | 0.576526i | \(-0.195592\pi\) | ||||
0.817079 | + | 0.576526i | \(0.195592\pi\) | |||||||
\(984\) | −13.7950 | −0.439770 | ||||||||
\(985\) | 24.4943 | 0.780452 | ||||||||
\(986\) | −39.1606 | −1.24713 | ||||||||
\(987\) | 114.310 | 3.63854 | ||||||||
\(988\) | −8.03005 | −0.255470 | ||||||||
\(989\) | 37.1642 | 1.18175 | ||||||||
\(990\) | 22.9633 | 0.729822 | ||||||||
\(991\) | 55.2451 | 1.75492 | 0.877460 | − | 0.479650i | \(-0.159237\pi\) | ||||
0.877460 | + | 0.479650i | \(0.159237\pi\) | |||||||
\(992\) | 1.08928 | 0.0345847 | ||||||||
\(993\) | −8.00442 | −0.254013 | ||||||||
\(994\) | 28.7968 | 0.913378 | ||||||||
\(995\) | 28.6106 | 0.907018 | ||||||||
\(996\) | −25.2825 | −0.801106 | ||||||||
\(997\) | −32.2517 | −1.02142 | −0.510711 | − | 0.859753i | \(-0.670618\pi\) | ||||
−0.510711 | + | 0.859753i | \(0.670618\pi\) | |||||||
\(998\) | 37.5239 | 1.18780 | ||||||||
\(999\) | 3.56602 | 0.112824 |
(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 | 8026.2.a.b.1.15 | ✓ | 81 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.b.1.15 | ✓ | 81 | 1.1 | even | 1 | trivial |