Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.37210 | −1.36953 | −0.684766 | − | 0.728763i | \(-0.740096\pi\) | ||||
−0.684766 | + | 0.728763i | \(0.740096\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.30761 | −1.03200 | −0.515998 | − | 0.856590i | \(-0.672579\pi\) | ||||
−0.515998 | + | 0.856590i | \(0.672579\pi\) | |||||||
\(6\) | 2.37210 | 0.968406 | ||||||||
\(7\) | 0.129234 | 0.0488457 | 0.0244229 | − | 0.999702i | \(-0.492225\pi\) | ||||
0.0244229 | + | 0.999702i | \(0.492225\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.62686 | 0.875620 | ||||||||
\(10\) | 2.30761 | 0.729731 | ||||||||
\(11\) | 5.58164 | 1.68293 | 0.841464 | − | 0.540312i | \(-0.181694\pi\) | ||||
0.841464 | + | 0.540312i | \(0.181694\pi\) | |||||||
\(12\) | −2.37210 | −0.684766 | ||||||||
\(13\) | 2.97992 | 0.826480 | 0.413240 | − | 0.910622i | \(-0.364397\pi\) | ||||
0.413240 | + | 0.910622i | \(0.364397\pi\) | |||||||
\(14\) | −0.129234 | −0.0345391 | ||||||||
\(15\) | 5.47389 | 1.41335 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.801585 | −0.194413 | −0.0972065 | − | 0.995264i | \(-0.530991\pi\) | ||||
−0.0972065 | + | 0.995264i | \(0.530991\pi\) | |||||||
\(18\) | −2.62686 | −0.619157 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.30761 | −0.515998 | ||||||||
\(21\) | −0.306555 | −0.0668958 | ||||||||
\(22\) | −5.58164 | −1.19001 | ||||||||
\(23\) | −0.622860 | −0.129875 | −0.0649376 | − | 0.997889i | \(-0.520685\pi\) | ||||
−0.0649376 | + | 0.997889i | \(0.520685\pi\) | |||||||
\(24\) | 2.37210 | 0.484203 | ||||||||
\(25\) | 0.325080 | 0.0650161 | ||||||||
\(26\) | −2.97992 | −0.584410 | ||||||||
\(27\) | 0.885125 | 0.170342 | ||||||||
\(28\) | 0.129234 | 0.0244229 | ||||||||
\(29\) | −2.21051 | −0.410481 | −0.205240 | − | 0.978712i | \(-0.565798\pi\) | ||||
−0.205240 | + | 0.978712i | \(0.565798\pi\) | |||||||
\(30\) | −5.47389 | −0.999391 | ||||||||
\(31\) | 1.01037 | 0.181467 | 0.0907337 | − | 0.995875i | \(-0.471079\pi\) | ||||
0.0907337 | + | 0.995875i | \(0.471079\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −13.2402 | −2.30483 | ||||||||
\(34\) | 0.801585 | 0.137471 | ||||||||
\(35\) | −0.298221 | −0.0504086 | ||||||||
\(36\) | 2.62686 | 0.437810 | ||||||||
\(37\) | −5.12381 | −0.842350 | −0.421175 | − | 0.906979i | \(-0.638382\pi\) | ||||
−0.421175 | + | 0.906979i | \(0.638382\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −7.06866 | −1.13189 | ||||||||
\(40\) | 2.30761 | 0.364866 | ||||||||
\(41\) | −10.1635 | −1.58728 | −0.793638 | − | 0.608390i | \(-0.791816\pi\) | ||||
−0.793638 | + | 0.608390i | \(0.791816\pi\) | |||||||
\(42\) | 0.306555 | 0.0473025 | ||||||||
\(43\) | −2.32824 | −0.355054 | −0.177527 | − | 0.984116i | \(-0.556810\pi\) | ||||
−0.177527 | + | 0.984116i | \(0.556810\pi\) | |||||||
\(44\) | 5.58164 | 0.841464 | ||||||||
\(45\) | −6.06178 | −0.903637 | ||||||||
\(46\) | 0.622860 | 0.0918357 | ||||||||
\(47\) | 11.3413 | 1.65430 | 0.827150 | − | 0.561981i | \(-0.189961\pi\) | ||||
0.827150 | + | 0.561981i | \(0.189961\pi\) | |||||||
\(48\) | −2.37210 | −0.342383 | ||||||||
\(49\) | −6.98330 | −0.997614 | ||||||||
\(50\) | −0.325080 | −0.0459733 | ||||||||
\(51\) | 1.90144 | 0.266255 | ||||||||
\(52\) | 2.97992 | 0.413240 | ||||||||
\(53\) | −2.55489 | −0.350942 | −0.175471 | − | 0.984485i | \(-0.556145\pi\) | ||||
−0.175471 | + | 0.984485i | \(0.556145\pi\) | |||||||
\(54\) | −0.885125 | −0.120450 | ||||||||
\(55\) | −12.8803 | −1.73678 | ||||||||
\(56\) | −0.129234 | −0.0172696 | ||||||||
\(57\) | −2.37210 | −0.314192 | ||||||||
\(58\) | 2.21051 | 0.290254 | ||||||||
\(59\) | 8.14745 | 1.06071 | 0.530354 | − | 0.847776i | \(-0.322059\pi\) | ||||
0.530354 | + | 0.847776i | \(0.322059\pi\) | |||||||
\(60\) | 5.47389 | 0.706676 | ||||||||
\(61\) | −12.4457 | −1.59351 | −0.796756 | − | 0.604301i | \(-0.793453\pi\) | ||||
−0.796756 | + | 0.604301i | \(0.793453\pi\) | |||||||
\(62\) | −1.01037 | −0.128317 | ||||||||
\(63\) | 0.339479 | 0.0427703 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.87650 | −0.852925 | ||||||||
\(66\) | 13.2402 | 1.62976 | ||||||||
\(67\) | 3.73408 | 0.456191 | 0.228095 | − | 0.973639i | \(-0.426750\pi\) | ||||
0.228095 | + | 0.973639i | \(0.426750\pi\) | |||||||
\(68\) | −0.801585 | −0.0972065 | ||||||||
\(69\) | 1.47749 | 0.177868 | ||||||||
\(70\) | 0.298221 | 0.0356443 | ||||||||
\(71\) | 4.94171 | 0.586473 | 0.293237 | − | 0.956040i | \(-0.405268\pi\) | ||||
0.293237 | + | 0.956040i | \(0.405268\pi\) | |||||||
\(72\) | −2.62686 | −0.309578 | ||||||||
\(73\) | 0.583139 | 0.0682513 | 0.0341256 | − | 0.999418i | \(-0.489135\pi\) | ||||
0.0341256 | + | 0.999418i | \(0.489135\pi\) | |||||||
\(74\) | 5.12381 | 0.595631 | ||||||||
\(75\) | −0.771123 | −0.0890416 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.721336 | 0.0822039 | ||||||||
\(78\) | 7.06866 | 0.800369 | ||||||||
\(79\) | −2.00030 | −0.225051 | −0.112525 | − | 0.993649i | \(-0.535894\pi\) | ||||
−0.112525 | + | 0.993649i | \(0.535894\pi\) | |||||||
\(80\) | −2.30761 | −0.257999 | ||||||||
\(81\) | −9.98019 | −1.10891 | ||||||||
\(82\) | 10.1635 | 1.12237 | ||||||||
\(83\) | −17.2842 | −1.89719 | −0.948594 | − | 0.316496i | \(-0.897494\pi\) | ||||
−0.948594 | + | 0.316496i | \(0.897494\pi\) | |||||||
\(84\) | −0.306555 | −0.0334479 | ||||||||
\(85\) | 1.84975 | 0.200633 | ||||||||
\(86\) | 2.32824 | 0.251061 | ||||||||
\(87\) | 5.24354 | 0.562167 | ||||||||
\(88\) | −5.58164 | −0.595005 | ||||||||
\(89\) | 13.0624 | 1.38462 | 0.692308 | − | 0.721602i | \(-0.256594\pi\) | ||||
0.692308 | + | 0.721602i | \(0.256594\pi\) | |||||||
\(90\) | 6.06178 | 0.638968 | ||||||||
\(91\) | 0.385106 | 0.0403700 | ||||||||
\(92\) | −0.622860 | −0.0649376 | ||||||||
\(93\) | −2.39669 | −0.248526 | ||||||||
\(94\) | −11.3413 | −1.16977 | ||||||||
\(95\) | −2.30761 | −0.236756 | ||||||||
\(96\) | 2.37210 | 0.242101 | ||||||||
\(97\) | 1.54557 | 0.156929 | 0.0784645 | − | 0.996917i | \(-0.474998\pi\) | ||||
0.0784645 | + | 0.996917i | \(0.474998\pi\) | |||||||
\(98\) | 6.98330 | 0.705420 | ||||||||
\(99\) | 14.6622 | 1.47361 | ||||||||
\(100\) | 0.325080 | 0.0325080 | ||||||||
\(101\) | 5.15007 | 0.512451 | 0.256226 | − | 0.966617i | \(-0.417521\pi\) | ||||
0.256226 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(102\) | −1.90144 | −0.188271 | ||||||||
\(103\) | 10.8934 | 1.07335 | 0.536677 | − | 0.843788i | \(-0.319679\pi\) | ||||
0.536677 | + | 0.843788i | \(0.319679\pi\) | |||||||
\(104\) | −2.97992 | −0.292205 | ||||||||
\(105\) | 0.707411 | 0.0690362 | ||||||||
\(106\) | 2.55489 | 0.248153 | ||||||||
\(107\) | −15.6812 | −1.51596 | −0.757980 | − | 0.652278i | \(-0.773814\pi\) | ||||
−0.757980 | + | 0.652278i | \(0.773814\pi\) | |||||||
\(108\) | 0.885125 | 0.0851712 | ||||||||
\(109\) | 1.52087 | 0.145672 | 0.0728362 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728362 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(110\) | 12.8803 | 1.22809 | ||||||||
\(111\) | 12.1542 | 1.15363 | ||||||||
\(112\) | 0.129234 | 0.0122114 | ||||||||
\(113\) | 9.94313 | 0.935371 | 0.467685 | − | 0.883895i | \(-0.345088\pi\) | ||||
0.467685 | + | 0.883895i | \(0.345088\pi\) | |||||||
\(114\) | 2.37210 | 0.222168 | ||||||||
\(115\) | 1.43732 | 0.134031 | ||||||||
\(116\) | −2.21051 | −0.205240 | ||||||||
\(117\) | 7.82783 | 0.723683 | ||||||||
\(118\) | −8.14745 | −0.750034 | ||||||||
\(119\) | −0.103592 | −0.00949624 | ||||||||
\(120\) | −5.47389 | −0.499696 | ||||||||
\(121\) | 20.1547 | 1.83225 | ||||||||
\(122\) | 12.4457 | 1.12678 | ||||||||
\(123\) | 24.1089 | 2.17383 | ||||||||
\(124\) | 1.01037 | 0.0907337 | ||||||||
\(125\) | 10.7879 | 0.964900 | ||||||||
\(126\) | −0.339479 | −0.0302432 | ||||||||
\(127\) | −11.4861 | −1.01923 | −0.509614 | − | 0.860403i | \(-0.670212\pi\) | ||||
−0.509614 | + | 0.860403i | \(0.670212\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.52283 | 0.486258 | ||||||||
\(130\) | 6.87650 | 0.603109 | ||||||||
\(131\) | −17.2685 | −1.50876 | −0.754378 | − | 0.656440i | \(-0.772062\pi\) | ||||
−0.754378 | + | 0.656440i | \(0.772062\pi\) | |||||||
\(132\) | −13.2402 | −1.15241 | ||||||||
\(133\) | 0.129234 | 0.0112060 | ||||||||
\(134\) | −3.73408 | −0.322576 | ||||||||
\(135\) | −2.04253 | −0.175793 | ||||||||
\(136\) | 0.801585 | 0.0687354 | ||||||||
\(137\) | 7.83325 | 0.669240 | 0.334620 | − | 0.942353i | \(-0.391392\pi\) | ||||
0.334620 | + | 0.942353i | \(0.391392\pi\) | |||||||
\(138\) | −1.47749 | −0.125772 | ||||||||
\(139\) | 19.6350 | 1.66542 | 0.832710 | − | 0.553709i | \(-0.186788\pi\) | ||||
0.832710 | + | 0.553709i | \(0.186788\pi\) | |||||||
\(140\) | −0.298221 | −0.0252043 | ||||||||
\(141\) | −26.9027 | −2.26562 | ||||||||
\(142\) | −4.94171 | −0.414699 | ||||||||
\(143\) | 16.6328 | 1.39091 | ||||||||
\(144\) | 2.62686 | 0.218905 | ||||||||
\(145\) | 5.10099 | 0.423614 | ||||||||
\(146\) | −0.583139 | −0.0482609 | ||||||||
\(147\) | 16.5651 | 1.36627 | ||||||||
\(148\) | −5.12381 | −0.421175 | ||||||||
\(149\) | 0.281926 | 0.0230963 | 0.0115481 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115481 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(150\) | 0.771123 | 0.0629619 | ||||||||
\(151\) | 5.05857 | 0.411660 | 0.205830 | − | 0.978588i | \(-0.434011\pi\) | ||||
0.205830 | + | 0.978588i | \(0.434011\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −2.10565 | −0.170232 | ||||||||
\(154\) | −0.721336 | −0.0581269 | ||||||||
\(155\) | −2.33154 | −0.187274 | ||||||||
\(156\) | −7.06866 | −0.565946 | ||||||||
\(157\) | −14.6778 | −1.17142 | −0.585708 | − | 0.810522i | \(-0.699183\pi\) | ||||
−0.585708 | + | 0.810522i | \(0.699183\pi\) | |||||||
\(158\) | 2.00030 | 0.159135 | ||||||||
\(159\) | 6.06046 | 0.480626 | ||||||||
\(160\) | 2.30761 | 0.182433 | ||||||||
\(161\) | −0.0804944 | −0.00634385 | ||||||||
\(162\) | 9.98019 | 0.784117 | ||||||||
\(163\) | 4.94513 | 0.387332 | 0.193666 | − | 0.981067i | \(-0.437962\pi\) | ||||
0.193666 | + | 0.981067i | \(0.437962\pi\) | |||||||
\(164\) | −10.1635 | −0.793638 | ||||||||
\(165\) | 30.5533 | 2.37857 | ||||||||
\(166\) | 17.2842 | 1.34151 | ||||||||
\(167\) | 0.0773168 | 0.00598295 | 0.00299148 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299148 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(168\) | 0.306555 | 0.0236512 | ||||||||
\(169\) | −4.12009 | −0.316930 | ||||||||
\(170\) | −1.84975 | −0.141869 | ||||||||
\(171\) | 2.62686 | 0.200881 | ||||||||
\(172\) | −2.32824 | −0.177527 | ||||||||
\(173\) | 15.0036 | 1.14070 | 0.570349 | − | 0.821402i | \(-0.306808\pi\) | ||||
0.570349 | + | 0.821402i | \(0.306808\pi\) | |||||||
\(174\) | −5.24354 | −0.397512 | ||||||||
\(175\) | 0.0420113 | 0.00317576 | ||||||||
\(176\) | 5.58164 | 0.420732 | ||||||||
\(177\) | −19.3266 | −1.45267 | ||||||||
\(178\) | −13.0624 | −0.979072 | ||||||||
\(179\) | 17.6441 | 1.31878 | 0.659392 | − | 0.751800i | \(-0.270814\pi\) | ||||
0.659392 | + | 0.751800i | \(0.270814\pi\) | |||||||
\(180\) | −6.06178 | −0.451818 | ||||||||
\(181\) | 20.5425 | 1.52691 | 0.763454 | − | 0.645862i | \(-0.223502\pi\) | ||||
0.763454 | + | 0.645862i | \(0.223502\pi\) | |||||||
\(182\) | −0.385106 | −0.0285459 | ||||||||
\(183\) | 29.5225 | 2.18237 | ||||||||
\(184\) | 0.622860 | 0.0459178 | ||||||||
\(185\) | 11.8238 | 0.869302 | ||||||||
\(186\) | 2.39669 | 0.175734 | ||||||||
\(187\) | −4.47416 | −0.327183 | ||||||||
\(188\) | 11.3413 | 0.827150 | ||||||||
\(189\) | 0.114388 | 0.00832049 | ||||||||
\(190\) | 2.30761 | 0.167412 | ||||||||
\(191\) | 3.51326 | 0.254211 | 0.127105 | − | 0.991889i | \(-0.459431\pi\) | ||||
0.127105 | + | 0.991889i | \(0.459431\pi\) | |||||||
\(192\) | −2.37210 | −0.171192 | ||||||||
\(193\) | −25.2223 | −1.81554 | −0.907770 | − | 0.419469i | \(-0.862216\pi\) | ||||
−0.907770 | + | 0.419469i | \(0.862216\pi\) | |||||||
\(194\) | −1.54557 | −0.110966 | ||||||||
\(195\) | 16.3117 | 1.16811 | ||||||||
\(196\) | −6.98330 | −0.498807 | ||||||||
\(197\) | −21.7650 | −1.55069 | −0.775345 | − | 0.631538i | \(-0.782424\pi\) | ||||
−0.775345 | + | 0.631538i | \(0.782424\pi\) | |||||||
\(198\) | −14.6622 | −1.04200 | ||||||||
\(199\) | −12.0030 | −0.850869 | −0.425435 | − | 0.904989i | \(-0.639879\pi\) | ||||
−0.425435 | + | 0.904989i | \(0.639879\pi\) | |||||||
\(200\) | −0.325080 | −0.0229866 | ||||||||
\(201\) | −8.85762 | −0.624768 | ||||||||
\(202\) | −5.15007 | −0.362358 | ||||||||
\(203\) | −0.285672 | −0.0200502 | ||||||||
\(204\) | 1.90144 | 0.133127 | ||||||||
\(205\) | 23.4535 | 1.63806 | ||||||||
\(206\) | −10.8934 | −0.758976 | ||||||||
\(207\) | −1.63617 | −0.113721 | ||||||||
\(208\) | 2.97992 | 0.206620 | ||||||||
\(209\) | 5.58164 | 0.386090 | ||||||||
\(210\) | −0.707411 | −0.0488160 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −2.55489 | −0.175471 | ||||||||
\(213\) | −11.7222 | −0.803194 | ||||||||
\(214\) | 15.6812 | 1.07195 | ||||||||
\(215\) | 5.37269 | 0.366414 | ||||||||
\(216\) | −0.885125 | −0.0602251 | ||||||||
\(217\) | 0.130573 | 0.00886391 | ||||||||
\(218\) | −1.52087 | −0.103006 | ||||||||
\(219\) | −1.38326 | −0.0934724 | ||||||||
\(220\) | −12.8803 | −0.868388 | ||||||||
\(221\) | −2.38866 | −0.160679 | ||||||||
\(222\) | −12.1542 | −0.815737 | ||||||||
\(223\) | −21.9021 | −1.46667 | −0.733337 | − | 0.679865i | \(-0.762038\pi\) | ||||
−0.733337 | + | 0.679865i | \(0.762038\pi\) | |||||||
\(224\) | −0.129234 | −0.00863478 | ||||||||
\(225\) | 0.853941 | 0.0569294 | ||||||||
\(226\) | −9.94313 | −0.661407 | ||||||||
\(227\) | −18.3678 | −1.21911 | −0.609556 | − | 0.792743i | \(-0.708652\pi\) | ||||
−0.609556 | + | 0.792743i | \(0.708652\pi\) | |||||||
\(228\) | −2.37210 | −0.157096 | ||||||||
\(229\) | −25.1732 | −1.66349 | −0.831745 | − | 0.555158i | \(-0.812658\pi\) | ||||
−0.831745 | + | 0.555158i | \(0.812658\pi\) | |||||||
\(230\) | −1.43732 | −0.0947741 | ||||||||
\(231\) | −1.71108 | −0.112581 | ||||||||
\(232\) | 2.21051 | 0.145127 | ||||||||
\(233\) | 11.4777 | 0.751929 | 0.375964 | − | 0.926634i | \(-0.377312\pi\) | ||||
0.375964 | + | 0.926634i | \(0.377312\pi\) | |||||||
\(234\) | −7.82783 | −0.511721 | ||||||||
\(235\) | −26.1714 | −1.70723 | ||||||||
\(236\) | 8.14745 | 0.530354 | ||||||||
\(237\) | 4.74490 | 0.308215 | ||||||||
\(238\) | 0.103592 | 0.00671486 | ||||||||
\(239\) | 7.31317 | 0.473050 | 0.236525 | − | 0.971625i | \(-0.423991\pi\) | ||||
0.236525 | + | 0.971625i | \(0.423991\pi\) | |||||||
\(240\) | 5.47389 | 0.353338 | ||||||||
\(241\) | 24.2493 | 1.56204 | 0.781018 | − | 0.624508i | \(-0.214701\pi\) | ||||
0.781018 | + | 0.624508i | \(0.214701\pi\) | |||||||
\(242\) | −20.1547 | −1.29560 | ||||||||
\(243\) | 21.0186 | 1.34835 | ||||||||
\(244\) | −12.4457 | −0.796756 | ||||||||
\(245\) | 16.1148 | 1.02953 | ||||||||
\(246\) | −24.1089 | −1.53713 | ||||||||
\(247\) | 2.97992 | 0.189608 | ||||||||
\(248\) | −1.01037 | −0.0641584 | ||||||||
\(249\) | 40.9999 | 2.59826 | ||||||||
\(250\) | −10.7879 | −0.682287 | ||||||||
\(251\) | 9.33387 | 0.589149 | 0.294574 | − | 0.955629i | \(-0.404822\pi\) | ||||
0.294574 | + | 0.955629i | \(0.404822\pi\) | |||||||
\(252\) | 0.339479 | 0.0213851 | ||||||||
\(253\) | −3.47658 | −0.218571 | ||||||||
\(254\) | 11.4861 | 0.720703 | ||||||||
\(255\) | −4.38779 | −0.274774 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4864 | −0.716500 | −0.358250 | − | 0.933626i | \(-0.616626\pi\) | ||||
−0.358250 | + | 0.933626i | \(0.616626\pi\) | |||||||
\(258\) | −5.52283 | −0.343836 | ||||||||
\(259\) | −0.662169 | −0.0411452 | ||||||||
\(260\) | −6.87650 | −0.426462 | ||||||||
\(261\) | −5.80669 | −0.359425 | ||||||||
\(262\) | 17.2685 | 1.06685 | ||||||||
\(263\) | 22.6393 | 1.39600 | 0.697999 | − | 0.716098i | \(-0.254074\pi\) | ||||
0.697999 | + | 0.716098i | \(0.254074\pi\) | |||||||
\(264\) | 13.2402 | 0.814879 | ||||||||
\(265\) | 5.89571 | 0.362170 | ||||||||
\(266\) | −0.129234 | −0.00792382 | ||||||||
\(267\) | −30.9854 | −1.89628 | ||||||||
\(268\) | 3.73408 | 0.228095 | ||||||||
\(269\) | 12.7878 | 0.779687 | 0.389843 | − | 0.920881i | \(-0.372529\pi\) | ||||
0.389843 | + | 0.920881i | \(0.372529\pi\) | |||||||
\(270\) | 2.04253 | 0.124304 | ||||||||
\(271\) | −14.2202 | −0.863818 | −0.431909 | − | 0.901917i | \(-0.642160\pi\) | ||||
−0.431909 | + | 0.901917i | \(0.642160\pi\) | |||||||
\(272\) | −0.801585 | −0.0486032 | ||||||||
\(273\) | −0.913509 | −0.0552881 | ||||||||
\(274\) | −7.83325 | −0.473224 | ||||||||
\(275\) | 1.81448 | 0.109417 | ||||||||
\(276\) | 1.47749 | 0.0889342 | ||||||||
\(277\) | −1.20237 | −0.0722435 | −0.0361217 | − | 0.999347i | \(-0.511500\pi\) | ||||
−0.0361217 | + | 0.999347i | \(0.511500\pi\) | |||||||
\(278\) | −19.6350 | −1.17763 | ||||||||
\(279\) | 2.65410 | 0.158897 | ||||||||
\(280\) | 0.298221 | 0.0178221 | ||||||||
\(281\) | 18.9818 | 1.13236 | 0.566179 | − | 0.824283i | \(-0.308421\pi\) | ||||
0.566179 | + | 0.824283i | \(0.308421\pi\) | |||||||
\(282\) | 26.9027 | 1.60203 | ||||||||
\(283\) | −9.36990 | −0.556983 | −0.278491 | − | 0.960439i | \(-0.589834\pi\) | ||||
−0.278491 | + | 0.960439i | \(0.589834\pi\) | |||||||
\(284\) | 4.94171 | 0.293237 | ||||||||
\(285\) | 5.47389 | 0.324245 | ||||||||
\(286\) | −16.6328 | −0.983520 | ||||||||
\(287\) | −1.31347 | −0.0775317 | ||||||||
\(288\) | −2.62686 | −0.154789 | ||||||||
\(289\) | −16.3575 | −0.962204 | ||||||||
\(290\) | −5.10099 | −0.299541 | ||||||||
\(291\) | −3.66625 | −0.214919 | ||||||||
\(292\) | 0.583139 | 0.0341256 | ||||||||
\(293\) | 27.4042 | 1.60097 | 0.800484 | − | 0.599354i | \(-0.204576\pi\) | ||||
0.800484 | + | 0.599354i | \(0.204576\pi\) | |||||||
\(294\) | −16.5651 | −0.966095 | ||||||||
\(295\) | −18.8012 | −1.09465 | ||||||||
\(296\) | 5.12381 | 0.297816 | ||||||||
\(297\) | 4.94045 | 0.286674 | ||||||||
\(298\) | −0.281926 | −0.0163315 | ||||||||
\(299\) | −1.85607 | −0.107339 | ||||||||
\(300\) | −0.771123 | −0.0445208 | ||||||||
\(301\) | −0.300887 | −0.0173429 | ||||||||
\(302\) | −5.05857 | −0.291088 | ||||||||
\(303\) | −12.2165 | −0.701819 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 28.7199 | 1.64450 | ||||||||
\(306\) | 2.10565 | 0.120372 | ||||||||
\(307\) | −14.3611 | −0.819629 | −0.409814 | − | 0.912169i | \(-0.634407\pi\) | ||||
−0.409814 | + | 0.912169i | \(0.634407\pi\) | |||||||
\(308\) | 0.721336 | 0.0411019 | ||||||||
\(309\) | −25.8401 | −1.46999 | ||||||||
\(310\) | 2.33154 | 0.132422 | ||||||||
\(311\) | −5.93100 | −0.336316 | −0.168158 | − | 0.985760i | \(-0.553782\pi\) | ||||
−0.168158 | + | 0.985760i | \(0.553782\pi\) | |||||||
\(312\) | 7.06866 | 0.400184 | ||||||||
\(313\) | −16.2381 | −0.917834 | −0.458917 | − | 0.888479i | \(-0.651763\pi\) | ||||
−0.458917 | + | 0.888479i | \(0.651763\pi\) | |||||||
\(314\) | 14.6778 | 0.828316 | ||||||||
\(315\) | −0.783386 | −0.0441388 | ||||||||
\(316\) | −2.00030 | −0.112525 | ||||||||
\(317\) | −24.7840 | −1.39201 | −0.696005 | − | 0.718037i | \(-0.745041\pi\) | ||||
−0.696005 | + | 0.718037i | \(0.745041\pi\) | |||||||
\(318\) | −6.06046 | −0.339854 | ||||||||
\(319\) | −12.3383 | −0.690810 | ||||||||
\(320\) | −2.30761 | −0.129000 | ||||||||
\(321\) | 37.1974 | 2.07616 | ||||||||
\(322\) | 0.0804944 | 0.00448578 | ||||||||
\(323\) | −0.801585 | −0.0446014 | ||||||||
\(324\) | −9.98019 | −0.554455 | ||||||||
\(325\) | 0.968713 | 0.0537345 | ||||||||
\(326\) | −4.94513 | −0.273885 | ||||||||
\(327\) | −3.60765 | −0.199503 | ||||||||
\(328\) | 10.1635 | 0.561187 | ||||||||
\(329\) | 1.46568 | 0.0808055 | ||||||||
\(330\) | −30.5533 | −1.68190 | ||||||||
\(331\) | 4.86006 | 0.267133 | 0.133566 | − | 0.991040i | \(-0.457357\pi\) | ||||
0.133566 | + | 0.991040i | \(0.457357\pi\) | |||||||
\(332\) | −17.2842 | −0.948594 | ||||||||
\(333\) | −13.4595 | −0.737579 | ||||||||
\(334\) | −0.0773168 | −0.00423059 | ||||||||
\(335\) | −8.61682 | −0.470787 | ||||||||
\(336\) | −0.306555 | −0.0167240 | ||||||||
\(337\) | −21.8159 | −1.18839 | −0.594195 | − | 0.804321i | \(-0.702529\pi\) | ||||
−0.594195 | + | 0.804321i | \(0.702529\pi\) | |||||||
\(338\) | 4.12009 | 0.224103 | ||||||||
\(339\) | −23.5861 | −1.28102 | ||||||||
\(340\) | 1.84975 | 0.100317 | ||||||||
\(341\) | 5.63951 | 0.305397 | ||||||||
\(342\) | −2.62686 | −0.142044 | ||||||||
\(343\) | −1.80711 | −0.0975749 | ||||||||
\(344\) | 2.32824 | 0.125531 | ||||||||
\(345\) | −3.40947 | −0.183560 | ||||||||
\(346\) | −15.0036 | −0.806596 | ||||||||
\(347\) | 3.29941 | 0.177122 | 0.0885609 | − | 0.996071i | \(-0.471773\pi\) | ||||
0.0885609 | + | 0.996071i | \(0.471773\pi\) | |||||||
\(348\) | 5.24354 | 0.281083 | ||||||||
\(349\) | 21.8699 | 1.17067 | 0.585336 | − | 0.810791i | \(-0.300963\pi\) | ||||
0.585336 | + | 0.810791i | \(0.300963\pi\) | |||||||
\(350\) | −0.0420113 | −0.00224560 | ||||||||
\(351\) | 2.63760 | 0.140785 | ||||||||
\(352\) | −5.58164 | −0.297503 | ||||||||
\(353\) | −19.7130 | −1.04922 | −0.524610 | − | 0.851343i | \(-0.675789\pi\) | ||||
−0.524610 | + | 0.851343i | \(0.675789\pi\) | |||||||
\(354\) | 19.3266 | 1.02720 | ||||||||
\(355\) | −11.4036 | −0.605238 | ||||||||
\(356\) | 13.0624 | 0.692308 | ||||||||
\(357\) | 0.245730 | 0.0130054 | ||||||||
\(358\) | −17.6441 | −0.932521 | ||||||||
\(359\) | 10.4907 | 0.553676 | 0.276838 | − | 0.960917i | \(-0.410713\pi\) | ||||
0.276838 | + | 0.960917i | \(0.410713\pi\) | |||||||
\(360\) | 6.06178 | 0.319484 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −20.5425 | −1.07969 | ||||||||
\(363\) | −47.8091 | −2.50933 | ||||||||
\(364\) | 0.385106 | 0.0201850 | ||||||||
\(365\) | −1.34566 | −0.0704351 | ||||||||
\(366\) | −29.5225 | −1.54317 | ||||||||
\(367\) | 9.60866 | 0.501568 | 0.250784 | − | 0.968043i | \(-0.419312\pi\) | ||||
0.250784 | + | 0.968043i | \(0.419312\pi\) | |||||||
\(368\) | −0.622860 | −0.0324688 | ||||||||
\(369\) | −26.6982 | −1.38985 | ||||||||
\(370\) | −11.8238 | −0.614689 | ||||||||
\(371\) | −0.330178 | −0.0171420 | ||||||||
\(372\) | −2.39669 | −0.124263 | ||||||||
\(373\) | 8.01561 | 0.415032 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(374\) | 4.47416 | 0.231353 | ||||||||
\(375\) | −25.5900 | −1.32146 | ||||||||
\(376\) | −11.3413 | −0.584883 | ||||||||
\(377\) | −6.58713 | −0.339254 | ||||||||
\(378\) | −0.114388 | −0.00588348 | ||||||||
\(379\) | −1.12368 | −0.0577197 | −0.0288599 | − | 0.999583i | \(-0.509188\pi\) | ||||
−0.0288599 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(380\) | −2.30761 | −0.118378 | ||||||||
\(381\) | 27.2462 | 1.39587 | ||||||||
\(382\) | −3.51326 | −0.179754 | ||||||||
\(383\) | −32.8370 | −1.67789 | −0.838945 | − | 0.544216i | \(-0.816827\pi\) | ||||
−0.838945 | + | 0.544216i | \(0.816827\pi\) | |||||||
\(384\) | 2.37210 | 0.121051 | ||||||||
\(385\) | −1.66456 | −0.0848341 | ||||||||
\(386\) | 25.2223 | 1.28378 | ||||||||
\(387\) | −6.11597 | −0.310892 | ||||||||
\(388\) | 1.54557 | 0.0784645 | ||||||||
\(389\) | 15.4191 | 0.781780 | 0.390890 | − | 0.920437i | \(-0.372167\pi\) | ||||
0.390890 | + | 0.920437i | \(0.372167\pi\) | |||||||
\(390\) | −16.3117 | −0.825977 | ||||||||
\(391\) | 0.499275 | 0.0252494 | ||||||||
\(392\) | 6.98330 | 0.352710 | ||||||||
\(393\) | 40.9626 | 2.06629 | ||||||||
\(394\) | 21.7650 | 1.09650 | ||||||||
\(395\) | 4.61591 | 0.232252 | ||||||||
\(396\) | 14.6622 | 0.736803 | ||||||||
\(397\) | 11.8721 | 0.595844 | 0.297922 | − | 0.954590i | \(-0.403706\pi\) | ||||
0.297922 | + | 0.954590i | \(0.403706\pi\) | |||||||
\(398\) | 12.0030 | 0.601656 | ||||||||
\(399\) | −0.306555 | −0.0153470 | ||||||||
\(400\) | 0.325080 | 0.0162540 | ||||||||
\(401\) | 3.78310 | 0.188919 | 0.0944595 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944595 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(402\) | 8.85762 | 0.441778 | ||||||||
\(403\) | 3.01081 | 0.149979 | ||||||||
\(404\) | 5.15007 | 0.256226 | ||||||||
\(405\) | 23.0304 | 1.14439 | ||||||||
\(406\) | 0.285672 | 0.0141776 | ||||||||
\(407\) | −28.5993 | −1.41762 | ||||||||
\(408\) | −1.90144 | −0.0941353 | ||||||||
\(409\) | 4.53713 | 0.224347 | 0.112173 | − | 0.993689i | \(-0.464219\pi\) | ||||
0.112173 | + | 0.993689i | \(0.464219\pi\) | |||||||
\(410\) | −23.4535 | −1.15829 | ||||||||
\(411\) | −18.5813 | −0.916546 | ||||||||
\(412\) | 10.8934 | 0.536677 | ||||||||
\(413\) | 1.05292 | 0.0518110 | ||||||||
\(414\) | 1.63617 | 0.0804132 | ||||||||
\(415\) | 39.8853 | 1.95789 | ||||||||
\(416\) | −2.97992 | −0.146102 | ||||||||
\(417\) | −46.5762 | −2.28085 | ||||||||
\(418\) | −5.58164 | −0.273007 | ||||||||
\(419\) | −37.3366 | −1.82401 | −0.912007 | − | 0.410175i | \(-0.865468\pi\) | ||||
−0.912007 | + | 0.410175i | \(0.865468\pi\) | |||||||
\(420\) | 0.707411 | 0.0345181 | ||||||||
\(421\) | 9.85092 | 0.480105 | 0.240052 | − | 0.970760i | \(-0.422835\pi\) | ||||
0.240052 | + | 0.970760i | \(0.422835\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 29.7920 | 1.44854 | ||||||||
\(424\) | 2.55489 | 0.124077 | ||||||||
\(425\) | −0.260580 | −0.0126400 | ||||||||
\(426\) | 11.7222 | 0.567944 | ||||||||
\(427\) | −1.60841 | −0.0778363 | ||||||||
\(428\) | −15.6812 | −0.757980 | ||||||||
\(429\) | −39.4548 | −1.90489 | ||||||||
\(430\) | −5.37269 | −0.259094 | ||||||||
\(431\) | 10.2991 | 0.496092 | 0.248046 | − | 0.968748i | \(-0.420212\pi\) | ||||
0.248046 | + | 0.968748i | \(0.420212\pi\) | |||||||
\(432\) | 0.885125 | 0.0425856 | ||||||||
\(433\) | −38.9898 | −1.87373 | −0.936865 | − | 0.349691i | \(-0.886287\pi\) | ||||
−0.936865 | + | 0.349691i | \(0.886287\pi\) | |||||||
\(434\) | −0.130573 | −0.00626773 | ||||||||
\(435\) | −12.1001 | −0.580154 | ||||||||
\(436\) | 1.52087 | 0.0728362 | ||||||||
\(437\) | −0.622860 | −0.0297954 | ||||||||
\(438\) | 1.38326 | 0.0660949 | ||||||||
\(439\) | −7.31729 | −0.349235 | −0.174618 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174618 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(440\) | 12.8803 | 0.614043 | ||||||||
\(441\) | −18.3442 | −0.873531 | ||||||||
\(442\) | 2.38866 | 0.113617 | ||||||||
\(443\) | −11.9408 | −0.567324 | −0.283662 | − | 0.958924i | \(-0.591549\pi\) | ||||
−0.283662 | + | 0.958924i | \(0.591549\pi\) | |||||||
\(444\) | 12.1542 | 0.576813 | ||||||||
\(445\) | −30.1431 | −1.42892 | ||||||||
\(446\) | 21.9021 | 1.03710 | ||||||||
\(447\) | −0.668757 | −0.0316311 | ||||||||
\(448\) | 0.129234 | 0.00610571 | ||||||||
\(449\) | 4.60064 | 0.217118 | 0.108559 | − | 0.994090i | \(-0.465376\pi\) | ||||
0.108559 | + | 0.994090i | \(0.465376\pi\) | |||||||
\(450\) | −0.853941 | −0.0402551 | ||||||||
\(451\) | −56.7292 | −2.67127 | ||||||||
\(452\) | 9.94313 | 0.467685 | ||||||||
\(453\) | −11.9994 | −0.563782 | ||||||||
\(454\) | 18.3678 | 0.862042 | ||||||||
\(455\) | −0.888675 | −0.0416617 | ||||||||
\(456\) | 2.37210 | 0.111084 | ||||||||
\(457\) | 1.03784 | 0.0485481 | 0.0242740 | − | 0.999705i | \(-0.492273\pi\) | ||||
0.0242740 | + | 0.999705i | \(0.492273\pi\) | |||||||
\(458\) | 25.1732 | 1.17627 | ||||||||
\(459\) | −0.709503 | −0.0331168 | ||||||||
\(460\) | 1.43732 | 0.0670154 | ||||||||
\(461\) | −7.79244 | −0.362930 | −0.181465 | − | 0.983397i | \(-0.558084\pi\) | ||||
−0.181465 | + | 0.983397i | \(0.558084\pi\) | |||||||
\(462\) | 1.71108 | 0.0796067 | ||||||||
\(463\) | −32.5424 | −1.51237 | −0.756187 | − | 0.654355i | \(-0.772940\pi\) | ||||
−0.756187 | + | 0.654355i | \(0.772940\pi\) | |||||||
\(464\) | −2.21051 | −0.102620 | ||||||||
\(465\) | 5.53064 | 0.256477 | ||||||||
\(466\) | −11.4777 | −0.531694 | ||||||||
\(467\) | 0.107350 | 0.00496756 | 0.00248378 | − | 0.999997i | \(-0.499209\pi\) | ||||
0.00248378 | + | 0.999997i | \(0.499209\pi\) | |||||||
\(468\) | 7.82783 | 0.361841 | ||||||||
\(469\) | 0.482569 | 0.0222830 | ||||||||
\(470\) | 26.1714 | 1.20719 | ||||||||
\(471\) | 34.8172 | 1.60429 | ||||||||
\(472\) | −8.14745 | −0.375017 | ||||||||
\(473\) | −12.9954 | −0.597530 | ||||||||
\(474\) | −4.74490 | −0.217941 | ||||||||
\(475\) | 0.325080 | 0.0149157 | ||||||||
\(476\) | −0.103592 | −0.00474812 | ||||||||
\(477\) | −6.71135 | −0.307292 | ||||||||
\(478\) | −7.31317 | −0.334497 | ||||||||
\(479\) | 3.45727 | 0.157966 | 0.0789832 | − | 0.996876i | \(-0.474833\pi\) | ||||
0.0789832 | + | 0.996876i | \(0.474833\pi\) | |||||||
\(480\) | −5.47389 | −0.249848 | ||||||||
\(481\) | −15.2685 | −0.696186 | ||||||||
\(482\) | −24.2493 | −1.10453 | ||||||||
\(483\) | 0.190941 | 0.00868811 | ||||||||
\(484\) | 20.1547 | 0.916125 | ||||||||
\(485\) | −3.56658 | −0.161950 | ||||||||
\(486\) | −21.0186 | −0.953424 | ||||||||
\(487\) | −19.0364 | −0.862620 | −0.431310 | − | 0.902204i | \(-0.641948\pi\) | ||||
−0.431310 | + | 0.902204i | \(0.641948\pi\) | |||||||
\(488\) | 12.4457 | 0.563392 | ||||||||
\(489\) | −11.7303 | −0.530464 | ||||||||
\(490\) | −16.1148 | −0.727990 | ||||||||
\(491\) | 34.7226 | 1.56701 | 0.783504 | − | 0.621387i | \(-0.213431\pi\) | ||||
0.783504 | + | 0.621387i | \(0.213431\pi\) | |||||||
\(492\) | 24.1089 | 1.08691 | ||||||||
\(493\) | 1.77191 | 0.0798028 | ||||||||
\(494\) | −2.97992 | −0.134073 | ||||||||
\(495\) | −33.8347 | −1.52076 | ||||||||
\(496\) | 1.01037 | 0.0453669 | ||||||||
\(497\) | 0.638635 | 0.0286467 | ||||||||
\(498\) | −40.9999 | −1.83725 | ||||||||
\(499\) | 38.9035 | 1.74156 | 0.870779 | − | 0.491674i | \(-0.163615\pi\) | ||||
0.870779 | + | 0.491674i | \(0.163615\pi\) | |||||||
\(500\) | 10.7879 | 0.482450 | ||||||||
\(501\) | −0.183403 | −0.00819385 | ||||||||
\(502\) | −9.33387 | −0.416591 | ||||||||
\(503\) | −28.0907 | −1.25250 | −0.626251 | − | 0.779622i | \(-0.715411\pi\) | ||||
−0.626251 | + | 0.779622i | \(0.715411\pi\) | |||||||
\(504\) | −0.339479 | −0.0151216 | ||||||||
\(505\) | −11.8844 | −0.528848 | ||||||||
\(506\) | 3.47658 | 0.154553 | ||||||||
\(507\) | 9.77327 | 0.434046 | ||||||||
\(508\) | −11.4861 | −0.509614 | ||||||||
\(509\) | 23.8570 | 1.05744 | 0.528722 | − | 0.848795i | \(-0.322671\pi\) | ||||
0.528722 | + | 0.848795i | \(0.322671\pi\) | |||||||
\(510\) | 4.38779 | 0.194295 | ||||||||
\(511\) | 0.0753612 | 0.00333378 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.885125 | 0.0390792 | ||||||||
\(514\) | 11.4864 | 0.506642 | ||||||||
\(515\) | −25.1376 | −1.10770 | ||||||||
\(516\) | 5.52283 | 0.243129 | ||||||||
\(517\) | 63.3031 | 2.78407 | ||||||||
\(518\) | 0.662169 | 0.0290940 | ||||||||
\(519\) | −35.5899 | −1.56222 | ||||||||
\(520\) | 6.87650 | 0.301554 | ||||||||
\(521\) | 40.6734 | 1.78193 | 0.890967 | − | 0.454068i | \(-0.150028\pi\) | ||||
0.890967 | + | 0.454068i | \(0.150028\pi\) | |||||||
\(522\) | 5.80669 | 0.254152 | ||||||||
\(523\) | 15.6487 | 0.684272 | 0.342136 | − | 0.939650i | \(-0.388850\pi\) | ||||
0.342136 | + | 0.939650i | \(0.388850\pi\) | |||||||
\(524\) | −17.2685 | −0.754378 | ||||||||
\(525\) | −0.0996550 | −0.00434930 | ||||||||
\(526\) | −22.6393 | −0.987120 | ||||||||
\(527\) | −0.809896 | −0.0352796 | ||||||||
\(528\) | −13.2402 | −0.576207 | ||||||||
\(529\) | −22.6120 | −0.983132 | ||||||||
\(530\) | −5.89571 | −0.256093 | ||||||||
\(531\) | 21.4022 | 0.928777 | ||||||||
\(532\) | 0.129234 | 0.00560299 | ||||||||
\(533\) | −30.2865 | −1.31185 | ||||||||
\(534\) | 30.9854 | 1.34087 | ||||||||
\(535\) | 36.1862 | 1.56446 | ||||||||
\(536\) | −3.73408 | −0.161288 | ||||||||
\(537\) | −41.8536 | −1.80612 | ||||||||
\(538\) | −12.7878 | −0.551322 | ||||||||
\(539\) | −38.9783 | −1.67891 | ||||||||
\(540\) | −2.04253 | −0.0878963 | ||||||||
\(541\) | −18.1414 | −0.779959 | −0.389979 | − | 0.920824i | \(-0.627518\pi\) | ||||
−0.389979 | + | 0.920824i | \(0.627518\pi\) | |||||||
\(542\) | 14.2202 | 0.610811 | ||||||||
\(543\) | −48.7288 | −2.09115 | ||||||||
\(544\) | 0.801585 | 0.0343677 | ||||||||
\(545\) | −3.50957 | −0.150333 | ||||||||
\(546\) | 0.913509 | 0.0390946 | ||||||||
\(547\) | 8.19147 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(548\) | 7.83325 | 0.334620 | ||||||||
\(549\) | −32.6932 | −1.39531 | ||||||||
\(550\) | −1.81448 | −0.0773698 | ||||||||
\(551\) | −2.21051 | −0.0941707 | ||||||||
\(552\) | −1.47749 | −0.0628860 | ||||||||
\(553\) | −0.258506 | −0.0109928 | ||||||||
\(554\) | 1.20237 | 0.0510838 | ||||||||
\(555\) | −28.0472 | −1.19054 | ||||||||
\(556\) | 19.6350 | 0.832710 | ||||||||
\(557\) | −31.2483 | −1.32403 | −0.662016 | − | 0.749490i | \(-0.730299\pi\) | ||||
−0.662016 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(558\) | −2.65410 | −0.112357 | ||||||||
\(559\) | −6.93798 | −0.293445 | ||||||||
\(560\) | −0.298221 | −0.0126021 | ||||||||
\(561\) | 10.6132 | 0.448088 | ||||||||
\(562\) | −18.9818 | −0.800697 | ||||||||
\(563\) | 38.3130 | 1.61470 | 0.807351 | − | 0.590072i | \(-0.200901\pi\) | ||||
0.807351 | + | 0.590072i | \(0.200901\pi\) | |||||||
\(564\) | −26.9027 | −1.13281 | ||||||||
\(565\) | −22.9449 | −0.965299 | ||||||||
\(566\) | 9.36990 | 0.393846 | ||||||||
\(567\) | −1.28978 | −0.0541655 | ||||||||
\(568\) | −4.94171 | −0.207350 | ||||||||
\(569\) | −28.7008 | −1.20320 | −0.601600 | − | 0.798797i | \(-0.705470\pi\) | ||||
−0.601600 | + | 0.798797i | \(0.705470\pi\) | |||||||
\(570\) | −5.47389 | −0.229276 | ||||||||
\(571\) | 23.5432 | 0.985251 | 0.492626 | − | 0.870241i | \(-0.336037\pi\) | ||||
0.492626 | + | 0.870241i | \(0.336037\pi\) | |||||||
\(572\) | 16.6328 | 0.695454 | ||||||||
\(573\) | −8.33382 | −0.348150 | ||||||||
\(574\) | 1.31347 | 0.0548232 | ||||||||
\(575\) | −0.202479 | −0.00844398 | ||||||||
\(576\) | 2.62686 | 0.109453 | ||||||||
\(577\) | 18.9958 | 0.790804 | 0.395402 | − | 0.918508i | \(-0.370605\pi\) | ||||
0.395402 | + | 0.918508i | \(0.370605\pi\) | |||||||
\(578\) | 16.3575 | 0.680381 | ||||||||
\(579\) | 59.8298 | 2.48644 | ||||||||
\(580\) | 5.10099 | 0.211807 | ||||||||
\(581\) | −2.23370 | −0.0926695 | ||||||||
\(582\) | 3.66625 | 0.151971 | ||||||||
\(583\) | −14.2605 | −0.590610 | ||||||||
\(584\) | −0.583139 | −0.0241305 | ||||||||
\(585\) | −18.0636 | −0.746838 | ||||||||
\(586\) | −27.4042 | −1.13206 | ||||||||
\(587\) | 0.812759 | 0.0335462 | 0.0167731 | − | 0.999859i | \(-0.494661\pi\) | ||||
0.0167731 | + | 0.999859i | \(0.494661\pi\) | |||||||
\(588\) | 16.5651 | 0.683133 | ||||||||
\(589\) | 1.01037 | 0.0416315 | ||||||||
\(590\) | 18.8012 | 0.774032 | ||||||||
\(591\) | 51.6287 | 2.12372 | ||||||||
\(592\) | −5.12381 | −0.210587 | ||||||||
\(593\) | 42.2880 | 1.73656 | 0.868279 | − | 0.496076i | \(-0.165226\pi\) | ||||
0.868279 | + | 0.496076i | \(0.165226\pi\) | |||||||
\(594\) | −4.94045 | −0.202709 | ||||||||
\(595\) | 0.239050 | 0.00980009 | ||||||||
\(596\) | 0.281926 | 0.0115481 | ||||||||
\(597\) | 28.4723 | 1.16529 | ||||||||
\(598\) | 1.85607 | 0.0759004 | ||||||||
\(599\) | −40.5198 | −1.65559 | −0.827796 | − | 0.561029i | \(-0.810406\pi\) | ||||
−0.827796 | + | 0.561029i | \(0.810406\pi\) | |||||||
\(600\) | 0.771123 | 0.0314810 | ||||||||
\(601\) | −7.54494 | −0.307765 | −0.153882 | − | 0.988089i | \(-0.549178\pi\) | ||||
−0.153882 | + | 0.988089i | \(0.549178\pi\) | |||||||
\(602\) | 0.300887 | 0.0122633 | ||||||||
\(603\) | 9.80891 | 0.399450 | ||||||||
\(604\) | 5.05857 | 0.205830 | ||||||||
\(605\) | −46.5094 | −1.89087 | ||||||||
\(606\) | 12.2165 | 0.496261 | ||||||||
\(607\) | 15.5292 | 0.630309 | 0.315155 | − | 0.949040i | \(-0.397944\pi\) | ||||
0.315155 | + | 0.949040i | \(0.397944\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0.677642 | 0.0274594 | ||||||||
\(610\) | −28.7199 | −1.16284 | ||||||||
\(611\) | 33.7962 | 1.36725 | ||||||||
\(612\) | −2.10565 | −0.0851160 | ||||||||
\(613\) | 30.3832 | 1.22717 | 0.613583 | − | 0.789630i | \(-0.289727\pi\) | ||||
0.613583 | + | 0.789630i | \(0.289727\pi\) | |||||||
\(614\) | 14.3611 | 0.579565 | ||||||||
\(615\) | −55.6341 | −2.24338 | ||||||||
\(616\) | −0.721336 | −0.0290635 | ||||||||
\(617\) | −10.1528 | −0.408738 | −0.204369 | − | 0.978894i | \(-0.565514\pi\) | ||||
−0.204369 | + | 0.978894i | \(0.565514\pi\) | |||||||
\(618\) | 25.8401 | 1.03944 | ||||||||
\(619\) | −33.6293 | −1.35168 | −0.675838 | − | 0.737050i | \(-0.736218\pi\) | ||||
−0.675838 | + | 0.737050i | \(0.736218\pi\) | |||||||
\(620\) | −2.33154 | −0.0936368 | ||||||||
\(621\) | −0.551309 | −0.0221233 | ||||||||
\(622\) | 5.93100 | 0.237812 | ||||||||
\(623\) | 1.68811 | 0.0676326 | ||||||||
\(624\) | −7.06866 | −0.282973 | ||||||||
\(625\) | −26.5197 | −1.06079 | ||||||||
\(626\) | 16.2381 | 0.649007 | ||||||||
\(627\) | −13.2402 | −0.528763 | ||||||||
\(628\) | −14.6778 | −0.585708 | ||||||||
\(629\) | 4.10717 | 0.163764 | ||||||||
\(630\) | 0.783386 | 0.0312108 | ||||||||
\(631\) | −30.0336 | −1.19562 | −0.597809 | − | 0.801639i | \(-0.703962\pi\) | ||||
−0.597809 | + | 0.801639i | \(0.703962\pi\) | |||||||
\(632\) | 2.00030 | 0.0795675 | ||||||||
\(633\) | −2.37210 | −0.0942825 | ||||||||
\(634\) | 24.7840 | 0.984300 | ||||||||
\(635\) | 26.5055 | 1.05184 | ||||||||
\(636\) | 6.06046 | 0.240313 | ||||||||
\(637\) | −20.8097 | −0.824509 | ||||||||
\(638\) | 12.3383 | 0.488476 | ||||||||
\(639\) | 12.9812 | 0.513528 | ||||||||
\(640\) | 2.30761 | 0.0912164 | ||||||||
\(641\) | 23.6455 | 0.933942 | 0.466971 | − | 0.884273i | \(-0.345345\pi\) | ||||
0.466971 | + | 0.884273i | \(0.345345\pi\) | |||||||
\(642\) | −37.1974 | −1.46806 | ||||||||
\(643\) | −17.9992 | −0.709821 | −0.354911 | − | 0.934900i | \(-0.615489\pi\) | ||||
−0.354911 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(644\) | −0.0804944 | −0.00317192 | ||||||||
\(645\) | −12.7446 | −0.501816 | ||||||||
\(646\) | 0.801585 | 0.0315380 | ||||||||
\(647\) | −4.73165 | −0.186020 | −0.0930102 | − | 0.995665i | \(-0.529649\pi\) | ||||
−0.0930102 | + | 0.995665i | \(0.529649\pi\) | |||||||
\(648\) | 9.98019 | 0.392059 | ||||||||
\(649\) | 45.4762 | 1.78510 | ||||||||
\(650\) | −0.968713 | −0.0379960 | ||||||||
\(651\) | −0.309733 | −0.0121394 | ||||||||
\(652\) | 4.94513 | 0.193666 | ||||||||
\(653\) | −32.9607 | −1.28985 | −0.644925 | − | 0.764246i | \(-0.723112\pi\) | ||||
−0.644925 | + | 0.764246i | \(0.723112\pi\) | |||||||
\(654\) | 3.60765 | 0.141070 | ||||||||
\(655\) | 39.8490 | 1.55703 | ||||||||
\(656\) | −10.1635 | −0.396819 | ||||||||
\(657\) | 1.53183 | 0.0597622 | ||||||||
\(658\) | −1.46568 | −0.0571381 | ||||||||
\(659\) | 33.7736 | 1.31563 | 0.657817 | − | 0.753178i | \(-0.271480\pi\) | ||||
0.657817 | + | 0.753178i | \(0.271480\pi\) | |||||||
\(660\) | 30.5533 | 1.18929 | ||||||||
\(661\) | −43.2002 | −1.68029 | −0.840146 | − | 0.542361i | \(-0.817531\pi\) | ||||
−0.840146 | + | 0.542361i | \(0.817531\pi\) | |||||||
\(662\) | −4.86006 | −0.188892 | ||||||||
\(663\) | 5.66614 | 0.220055 | ||||||||
\(664\) | 17.2842 | 0.670757 | ||||||||
\(665\) | −0.298221 | −0.0115645 | ||||||||
\(666\) | 13.4595 | 0.521547 | ||||||||
\(667\) | 1.37684 | 0.0533113 | ||||||||
\(668\) | 0.0773168 | 0.00299148 | ||||||||
\(669\) | 51.9540 | 2.00866 | ||||||||
\(670\) | 8.61682 | 0.332897 | ||||||||
\(671\) | −69.4676 | −2.68177 | ||||||||
\(672\) | 0.306555 | 0.0118256 | ||||||||
\(673\) | −40.9130 | −1.57708 | −0.788539 | − | 0.614984i | \(-0.789162\pi\) | ||||
−0.788539 | + | 0.614984i | \(0.789162\pi\) | |||||||
\(674\) | 21.8159 | 0.840318 | ||||||||
\(675\) | 0.287737 | 0.0110750 | ||||||||
\(676\) | −4.12009 | −0.158465 | ||||||||
\(677\) | −29.1685 | −1.12104 | −0.560518 | − | 0.828142i | \(-0.689398\pi\) | ||||
−0.560518 | + | 0.828142i | \(0.689398\pi\) | |||||||
\(678\) | 23.5861 | 0.905819 | ||||||||
\(679\) | 0.199740 | 0.00766531 | ||||||||
\(680\) | −1.84975 | −0.0709346 | ||||||||
\(681\) | 43.5702 | 1.66961 | ||||||||
\(682\) | −5.63951 | −0.215948 | ||||||||
\(683\) | −31.2307 | −1.19501 | −0.597505 | − | 0.801865i | \(-0.703841\pi\) | ||||
−0.597505 | + | 0.801865i | \(0.703841\pi\) | |||||||
\(684\) | 2.62686 | 0.100441 | ||||||||
\(685\) | −18.0761 | −0.690653 | ||||||||
\(686\) | 1.80711 | 0.0689959 | ||||||||
\(687\) | 59.7133 | 2.27820 | ||||||||
\(688\) | −2.32824 | −0.0887635 | ||||||||
\(689\) | −7.61337 | −0.290046 | ||||||||
\(690\) | 3.40947 | 0.129796 | ||||||||
\(691\) | 7.72699 | 0.293949 | 0.146974 | − | 0.989140i | \(-0.453047\pi\) | ||||
0.146974 | + | 0.989140i | \(0.453047\pi\) | |||||||
\(692\) | 15.0036 | 0.570349 | ||||||||
\(693\) | 1.89485 | 0.0719794 | ||||||||
\(694\) | −3.29941 | −0.125244 | ||||||||
\(695\) | −45.3100 | −1.71871 | ||||||||
\(696\) | −5.24354 | −0.198756 | ||||||||
\(697\) | 8.14694 | 0.308587 | ||||||||
\(698\) | −21.8699 | −0.827790 | ||||||||
\(699\) | −27.2262 | −1.02979 | ||||||||
\(700\) | 0.0420113 | 0.00158788 | ||||||||
\(701\) | −1.85902 | −0.0702144 | −0.0351072 | − | 0.999384i | \(-0.511177\pi\) | ||||
−0.0351072 | + | 0.999384i | \(0.511177\pi\) | |||||||
\(702\) | −2.63760 | −0.0995497 | ||||||||
\(703\) | −5.12381 | −0.193248 | ||||||||
\(704\) | 5.58164 | 0.210366 | ||||||||
\(705\) | 62.0811 | 2.33811 | ||||||||
\(706\) | 19.7130 | 0.741910 | ||||||||
\(707\) | 0.665562 | 0.0250311 | ||||||||
\(708\) | −19.3266 | −0.726337 | ||||||||
\(709\) | −5.51880 | −0.207263 | −0.103631 | − | 0.994616i | \(-0.533046\pi\) | ||||
−0.103631 | + | 0.994616i | \(0.533046\pi\) | |||||||
\(710\) | 11.4036 | 0.427968 | ||||||||
\(711\) | −5.25450 | −0.197059 | ||||||||
\(712\) | −13.0624 | −0.489536 | ||||||||
\(713\) | −0.629317 | −0.0235681 | ||||||||
\(714\) | −0.245730 | −0.00919622 | ||||||||
\(715\) | −38.3822 | −1.43541 | ||||||||
\(716\) | 17.6441 | 0.659392 | ||||||||
\(717\) | −17.3476 | −0.647857 | ||||||||
\(718\) | −10.4907 | −0.391508 | ||||||||
\(719\) | 6.11637 | 0.228102 | 0.114051 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114051 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(720\) | −6.06178 | −0.225909 | ||||||||
\(721\) | 1.40779 | 0.0524287 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −57.5218 | −2.13926 | ||||||||
\(724\) | 20.5425 | 0.763454 | ||||||||
\(725\) | −0.718592 | −0.0266878 | ||||||||
\(726\) | 47.8091 | 1.77436 | ||||||||
\(727\) | 3.99503 | 0.148167 | 0.0740836 | − | 0.997252i | \(-0.476397\pi\) | ||||
0.0740836 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(728\) | −0.385106 | −0.0142730 | ||||||||
\(729\) | −19.9177 | −0.737694 | ||||||||
\(730\) | 1.34566 | 0.0498051 | ||||||||
\(731\) | 1.86629 | 0.0690271 | ||||||||
\(732\) | 29.5225 | 1.09118 | ||||||||
\(733\) | 19.0468 | 0.703508 | 0.351754 | − | 0.936092i | \(-0.385585\pi\) | ||||
0.351754 | + | 0.936092i | \(0.385585\pi\) | |||||||
\(734\) | −9.60866 | −0.354662 | ||||||||
\(735\) | −38.2258 | −1.40998 | ||||||||
\(736\) | 0.622860 | 0.0229589 | ||||||||
\(737\) | 20.8423 | 0.767737 | ||||||||
\(738\) | 26.6982 | 0.982773 | ||||||||
\(739\) | −11.5377 | −0.424421 | −0.212210 | − | 0.977224i | \(-0.568066\pi\) | ||||
−0.212210 | + | 0.977224i | \(0.568066\pi\) | |||||||
\(740\) | 11.8238 | 0.434651 | ||||||||
\(741\) | −7.06866 | −0.259674 | ||||||||
\(742\) | 0.330178 | 0.0121212 | ||||||||
\(743\) | 18.4628 | 0.677333 | 0.338666 | − | 0.940907i | \(-0.390024\pi\) | ||||
0.338666 | + | 0.940907i | \(0.390024\pi\) | |||||||
\(744\) | 2.39669 | 0.0878671 | ||||||||
\(745\) | −0.650576 | −0.0238353 | ||||||||
\(746\) | −8.01561 | −0.293472 | ||||||||
\(747\) | −45.4032 | −1.66122 | ||||||||
\(748\) | −4.47416 | −0.163592 | ||||||||
\(749\) | −2.02654 | −0.0740481 | ||||||||
\(750\) | 25.5900 | 0.934415 | ||||||||
\(751\) | 52.2066 | 1.90505 | 0.952523 | − | 0.304468i | \(-0.0984787\pi\) | ||||
0.952523 | + | 0.304468i | \(0.0984787\pi\) | |||||||
\(752\) | 11.3413 | 0.413575 | ||||||||
\(753\) | −22.1409 | −0.806859 | ||||||||
\(754\) | 6.58713 | 0.239889 | ||||||||
\(755\) | −11.6732 | −0.424832 | ||||||||
\(756\) | 0.114388 | 0.00416025 | ||||||||
\(757\) | −26.8635 | −0.976371 | −0.488185 | − | 0.872740i | \(-0.662341\pi\) | ||||
−0.488185 | + | 0.872740i | \(0.662341\pi\) | |||||||
\(758\) | 1.12368 | 0.0408140 | ||||||||
\(759\) | 8.24680 | 0.299340 | ||||||||
\(760\) | 2.30761 | 0.0837059 | ||||||||
\(761\) | 47.5802 | 1.72478 | 0.862391 | − | 0.506243i | \(-0.168966\pi\) | ||||
0.862391 | + | 0.506243i | \(0.168966\pi\) | |||||||
\(762\) | −27.2462 | −0.987027 | ||||||||
\(763\) | 0.196547 | 0.00711548 | ||||||||
\(764\) | 3.51326 | 0.127105 | ||||||||
\(765\) | 4.85903 | 0.175679 | ||||||||
\(766\) | 32.8370 | 1.18645 | ||||||||
\(767\) | 24.2787 | 0.876654 | ||||||||
\(768\) | −2.37210 | −0.0855958 | ||||||||
\(769\) | −24.1209 | −0.869824 | −0.434912 | − | 0.900473i | \(-0.643220\pi\) | ||||
−0.434912 | + | 0.900473i | \(0.643220\pi\) | |||||||
\(770\) | 1.66456 | 0.0599868 | ||||||||
\(771\) | 27.2468 | 0.981270 | ||||||||
\(772\) | −25.2223 | −0.907770 | ||||||||
\(773\) | −12.5397 | −0.451022 | −0.225511 | − | 0.974241i | \(-0.572405\pi\) | ||||
−0.225511 | + | 0.974241i | \(0.572405\pi\) | |||||||
\(774\) | 6.11597 | 0.219834 | ||||||||
\(775\) | 0.328451 | 0.0117983 | ||||||||
\(776\) | −1.54557 | −0.0554828 | ||||||||
\(777\) | 1.57073 | 0.0563497 | ||||||||
\(778\) | −15.4191 | −0.552802 | ||||||||
\(779\) | −10.1635 | −0.364146 | ||||||||
\(780\) | 16.3117 | 0.584054 | ||||||||
\(781\) | 27.5829 | 0.986993 | ||||||||
\(782\) | −0.499275 | −0.0178540 | ||||||||
\(783\) | −1.95657 | −0.0699222 | ||||||||
\(784\) | −6.98330 | −0.249404 | ||||||||
\(785\) | 33.8707 | 1.20890 | ||||||||
\(786\) | −40.9626 | −1.46109 | ||||||||
\(787\) | 33.4332 | 1.19177 | 0.595883 | − | 0.803072i | \(-0.296802\pi\) | ||||
0.595883 | + | 0.803072i | \(0.296802\pi\) | |||||||
\(788\) | −21.7650 | −0.775345 | ||||||||
\(789\) | −53.7027 | −1.91187 | ||||||||
\(790\) | −4.61591 | −0.164227 | ||||||||
\(791\) | 1.28499 | 0.0456889 | ||||||||
\(792\) | −14.6622 | −0.520999 | ||||||||
\(793\) | −37.0873 | −1.31701 | ||||||||
\(794\) | −11.8721 | −0.421326 | ||||||||
\(795\) | −13.9852 | −0.496004 | ||||||||
\(796\) | −12.0030 | −0.425435 | ||||||||
\(797\) | 13.7999 | 0.488818 | 0.244409 | − | 0.969672i | \(-0.421406\pi\) | ||||
0.244409 | + | 0.969672i | \(0.421406\pi\) | |||||||
\(798\) | 0.306555 | 0.0108519 | ||||||||
\(799\) | −9.09103 | −0.321617 | ||||||||
\(800\) | −0.325080 | −0.0114933 | ||||||||
\(801\) | 34.3132 | 1.21240 | ||||||||
\(802\) | −3.78310 | −0.133586 | ||||||||
\(803\) | 3.25487 | 0.114862 | ||||||||
\(804\) | −8.85762 | −0.312384 | ||||||||
\(805\) | 0.185750 | 0.00654683 | ||||||||
\(806\) | −3.01081 | −0.106051 | ||||||||
\(807\) | −30.3340 | −1.06781 | ||||||||
\(808\) | −5.15007 | −0.181179 | ||||||||
\(809\) | −56.4095 | −1.98325 | −0.991626 | − | 0.129143i | \(-0.958777\pi\) | ||||
−0.991626 | + | 0.129143i | \(0.958777\pi\) | |||||||
\(810\) | −23.0304 | −0.809206 | ||||||||
\(811\) | −14.2172 | −0.499234 | −0.249617 | − | 0.968345i | \(-0.580305\pi\) | ||||
−0.249617 | + | 0.968345i | \(0.580305\pi\) | |||||||
\(812\) | −0.285672 | −0.0100251 | ||||||||
\(813\) | 33.7318 | 1.18303 | ||||||||
\(814\) | 28.5993 | 1.00241 | ||||||||
\(815\) | −11.4114 | −0.399726 | ||||||||
\(816\) | 1.90144 | 0.0665637 | ||||||||
\(817\) | −2.32824 | −0.0814549 | ||||||||
\(818\) | −4.53713 | −0.158637 | ||||||||
\(819\) | 1.01162 | 0.0353488 | ||||||||
\(820\) | 23.4535 | 0.819032 | ||||||||
\(821\) | −24.1925 | −0.844323 | −0.422161 | − | 0.906521i | \(-0.638728\pi\) | ||||
−0.422161 | + | 0.906521i | \(0.638728\pi\) | |||||||
\(822\) | 18.5813 | 0.648096 | ||||||||
\(823\) | 17.0192 | 0.593253 | 0.296627 | − | 0.954994i | \(-0.404138\pi\) | ||||
0.296627 | + | 0.954994i | \(0.404138\pi\) | |||||||
\(824\) | −10.8934 | −0.379488 | ||||||||
\(825\) | −4.30413 | −0.149851 | ||||||||
\(826\) | −1.05292 | −0.0366359 | ||||||||
\(827\) | −50.4370 | −1.75387 | −0.876934 | − | 0.480611i | \(-0.840415\pi\) | ||||
−0.876934 | + | 0.480611i | \(0.840415\pi\) | |||||||
\(828\) | −1.63617 | −0.0568607 | ||||||||
\(829\) | 34.8686 | 1.21104 | 0.605518 | − | 0.795832i | \(-0.292966\pi\) | ||||
0.605518 | + | 0.795832i | \(0.292966\pi\) | |||||||
\(830\) | −39.8853 | −1.38444 | ||||||||
\(831\) | 2.85214 | 0.0989398 | ||||||||
\(832\) | 2.97992 | 0.103310 | ||||||||
\(833\) | 5.59771 | 0.193949 | ||||||||
\(834\) | 46.5762 | 1.61280 | ||||||||
\(835\) | −0.178417 | −0.00617439 | ||||||||
\(836\) | 5.58164 | 0.193045 | ||||||||
\(837\) | 0.894301 | 0.0309116 | ||||||||
\(838\) | 37.3366 | 1.28977 | ||||||||
\(839\) | −28.8383 | −0.995609 | −0.497804 | − | 0.867289i | \(-0.665860\pi\) | ||||
−0.497804 | + | 0.867289i | \(0.665860\pi\) | |||||||
\(840\) | −0.707411 | −0.0244080 | ||||||||
\(841\) | −24.1137 | −0.831506 | ||||||||
\(842\) | −9.85092 | −0.339485 | ||||||||
\(843\) | −45.0266 | −1.55080 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | 9.50758 | 0.327071 | ||||||||
\(846\) | −29.7920 | −1.02427 | ||||||||
\(847\) | 2.60467 | 0.0894976 | ||||||||
\(848\) | −2.55489 | −0.0877354 | ||||||||
\(849\) | 22.2263 | 0.762806 | ||||||||
\(850\) | 0.260580 | 0.00893781 | ||||||||
\(851\) | 3.19142 | 0.109400 | ||||||||
\(852\) | −11.7222 | −0.401597 | ||||||||
\(853\) | 13.4926 | 0.461977 | 0.230988 | − | 0.972956i | \(-0.425804\pi\) | ||||
0.230988 | + | 0.972956i | \(0.425804\pi\) | |||||||
\(854\) | 1.60841 | 0.0550386 | ||||||||
\(855\) | −6.06178 | −0.207308 | ||||||||
\(856\) | 15.6812 | 0.535973 | ||||||||
\(857\) | 24.2814 | 0.829437 | 0.414718 | − | 0.909950i | \(-0.363880\pi\) | ||||
0.414718 | + | 0.909950i | \(0.363880\pi\) | |||||||
\(858\) | 39.4548 | 1.34696 | ||||||||
\(859\) | 16.3125 | 0.556574 | 0.278287 | − | 0.960498i | \(-0.410233\pi\) | ||||
0.278287 | + | 0.960498i | \(0.410233\pi\) | |||||||
\(860\) | 5.37269 | 0.183207 | ||||||||
\(861\) | 3.11568 | 0.106182 | ||||||||
\(862\) | −10.2991 | −0.350790 | ||||||||
\(863\) | −36.8429 | −1.25415 | −0.627074 | − | 0.778960i | \(-0.715748\pi\) | ||||
−0.627074 | + | 0.778960i | \(0.715748\pi\) | |||||||
\(864\) | −0.885125 | −0.0301126 | ||||||||
\(865\) | −34.6224 | −1.17720 | ||||||||
\(866\) | 38.9898 | 1.32493 | ||||||||
\(867\) | 38.8015 | 1.31777 | ||||||||
\(868\) | 0.130573 | 0.00443195 | ||||||||
\(869\) | −11.1649 | −0.378745 | ||||||||
\(870\) | 12.1001 | 0.410231 | ||||||||
\(871\) | 11.1273 | 0.377033 | ||||||||
\(872\) | −1.52087 | −0.0515030 | ||||||||
\(873\) | 4.06000 | 0.137410 | ||||||||
\(874\) | 0.622860 | 0.0210685 | ||||||||
\(875\) | 1.39416 | 0.0471312 | ||||||||
\(876\) | −1.38326 | −0.0467362 | ||||||||
\(877\) | −47.6415 | −1.60874 | −0.804370 | − | 0.594128i | \(-0.797497\pi\) | ||||
−0.804370 | + | 0.594128i | \(0.797497\pi\) | |||||||
\(878\) | 7.31729 | 0.246946 | ||||||||
\(879\) | −65.0054 | −2.19258 | ||||||||
\(880\) | −12.8803 | −0.434194 | ||||||||
\(881\) | −50.6020 | −1.70483 | −0.852413 | − | 0.522870i | \(-0.824861\pi\) | ||||
−0.852413 | + | 0.522870i | \(0.824861\pi\) | |||||||
\(882\) | 18.3442 | 0.617680 | ||||||||
\(883\) | −26.1128 | −0.878765 | −0.439382 | − | 0.898300i | \(-0.644803\pi\) | ||||
−0.439382 | + | 0.898300i | \(0.644803\pi\) | |||||||
\(884\) | −2.38866 | −0.0803393 | ||||||||
\(885\) | 44.5982 | 1.49915 | ||||||||
\(886\) | 11.9408 | 0.401159 | ||||||||
\(887\) | 33.8581 | 1.13685 | 0.568423 | − | 0.822737i | \(-0.307554\pi\) | ||||
0.568423 | + | 0.822737i | \(0.307554\pi\) | |||||||
\(888\) | −12.1542 | −0.407868 | ||||||||
\(889\) | −1.48439 | −0.0497849 | ||||||||
\(890\) | 30.1431 | 1.01040 | ||||||||
\(891\) | −55.7058 | −1.86622 | ||||||||
\(892\) | −21.9021 | −0.733337 | ||||||||
\(893\) | 11.3413 | 0.379522 | ||||||||
\(894\) | 0.668757 | 0.0223666 | ||||||||
\(895\) | −40.7158 | −1.36098 | ||||||||
\(896\) | −0.129234 | −0.00431739 | ||||||||
\(897\) | 4.40279 | 0.147005 | ||||||||
\(898\) | −4.60064 | −0.153525 | ||||||||
\(899\) | −2.23342 | −0.0744889 | ||||||||
\(900\) | 0.853941 | 0.0284647 | ||||||||
\(901\) | 2.04797 | 0.0682276 | ||||||||
\(902\) | 56.7292 | 1.88888 | ||||||||
\(903\) | 0.713735 | 0.0237516 | ||||||||
\(904\) | −9.94313 | −0.330703 | ||||||||
\(905\) | −47.4041 | −1.57576 | ||||||||
\(906\) | 11.9994 | 0.398654 | ||||||||
\(907\) | −54.7679 | −1.81854 | −0.909270 | − | 0.416207i | \(-0.863359\pi\) | ||||
−0.909270 | + | 0.416207i | \(0.863359\pi\) | |||||||
\(908\) | −18.3678 | −0.609556 | ||||||||
\(909\) | 13.5285 | 0.448713 | ||||||||
\(910\) | 0.888675 | 0.0294593 | ||||||||
\(911\) | 0.808514 | 0.0267873 | 0.0133936 | − | 0.999910i | \(-0.495737\pi\) | ||||
0.0133936 | + | 0.999910i | \(0.495737\pi\) | |||||||
\(912\) | −2.37210 | −0.0785481 | ||||||||
\(913\) | −96.4743 | −3.19283 | ||||||||
\(914\) | −1.03784 | −0.0343287 | ||||||||
\(915\) | −68.1266 | −2.25220 | ||||||||
\(916\) | −25.1732 | −0.831745 | ||||||||
\(917\) | −2.23167 | −0.0736963 | ||||||||
\(918\) | 0.709503 | 0.0234171 | ||||||||
\(919\) | −22.2345 | −0.733449 | −0.366725 | − | 0.930330i | \(-0.619521\pi\) | ||||
−0.366725 | + | 0.930330i | \(0.619521\pi\) | |||||||
\(920\) | −1.43732 | −0.0473870 | ||||||||
\(921\) | 34.0659 | 1.12251 | ||||||||
\(922\) | 7.79244 | 0.256630 | ||||||||
\(923\) | 14.7259 | 0.484709 | ||||||||
\(924\) | −1.71108 | −0.0562904 | ||||||||
\(925\) | −1.66565 | −0.0547663 | ||||||||
\(926\) | 32.5424 | 1.06941 | ||||||||
\(927\) | 28.6153 | 0.939850 | ||||||||
\(928\) | 2.21051 | 0.0725634 | ||||||||
\(929\) | 8.67844 | 0.284730 | 0.142365 | − | 0.989814i | \(-0.454529\pi\) | ||||
0.142365 | + | 0.989814i | \(0.454529\pi\) | |||||||
\(930\) | −5.53064 | −0.181357 | ||||||||
\(931\) | −6.98330 | −0.228868 | ||||||||
\(932\) | 11.4777 | 0.375964 | ||||||||
\(933\) | 14.0689 | 0.460596 | ||||||||
\(934\) | −0.107350 | −0.00351259 | ||||||||
\(935\) | 10.3246 | 0.337652 | ||||||||
\(936\) | −7.82783 | −0.255861 | ||||||||
\(937\) | −38.8362 | −1.26872 | −0.634362 | − | 0.773036i | \(-0.718737\pi\) | ||||
−0.634362 | + | 0.773036i | \(0.718737\pi\) | |||||||
\(938\) | −0.482569 | −0.0157564 | ||||||||
\(939\) | 38.5185 | 1.25700 | ||||||||
\(940\) | −26.1714 | −0.853615 | ||||||||
\(941\) | 14.9926 | 0.488746 | 0.244373 | − | 0.969681i | \(-0.421418\pi\) | ||||
0.244373 | + | 0.969681i | \(0.421418\pi\) | |||||||
\(942\) | −34.8172 | −1.13441 | ||||||||
\(943\) | 6.33045 | 0.206148 | ||||||||
\(944\) | 8.14745 | 0.265177 | ||||||||
\(945\) | −0.263963 | −0.00858672 | ||||||||
\(946\) | 12.9954 | 0.422518 | ||||||||
\(947\) | −39.7491 | −1.29167 | −0.645837 | − | 0.763476i | \(-0.723491\pi\) | ||||
−0.645837 | + | 0.763476i | \(0.723491\pi\) | |||||||
\(948\) | 4.74490 | 0.154107 | ||||||||
\(949\) | 1.73771 | 0.0564083 | ||||||||
\(950\) | −0.325080 | −0.0105470 | ||||||||
\(951\) | 58.7902 | 1.90640 | ||||||||
\(952\) | 0.103592 | 0.00335743 | ||||||||
\(953\) | 11.1609 | 0.361536 | 0.180768 | − | 0.983526i | \(-0.442142\pi\) | ||||
0.180768 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(954\) | 6.71135 | 0.217288 | ||||||||
\(955\) | −8.10726 | −0.262345 | ||||||||
\(956\) | 7.31317 | 0.236525 | ||||||||
\(957\) | 29.2676 | 0.946087 | ||||||||
\(958\) | −3.45727 | −0.111699 | ||||||||
\(959\) | 1.01232 | 0.0326895 | ||||||||
\(960\) | 5.47389 | 0.176669 | ||||||||
\(961\) | −29.9792 | −0.967070 | ||||||||
\(962\) | 15.2685 | 0.492278 | ||||||||
\(963\) | −41.1923 | −1.32740 | ||||||||
\(964\) | 24.2493 | 0.781018 | ||||||||
\(965\) | 58.2033 | 1.87363 | ||||||||
\(966\) | −0.190941 | −0.00614342 | ||||||||
\(967\) | −46.8485 | −1.50654 | −0.753272 | − | 0.657709i | \(-0.771526\pi\) | ||||
−0.753272 | + | 0.657709i | \(0.771526\pi\) | |||||||
\(968\) | −20.1547 | −0.647798 | ||||||||
\(969\) | 1.90144 | 0.0610831 | ||||||||
\(970\) | 3.56658 | 0.114516 | ||||||||
\(971\) | −0.952180 | −0.0305569 | −0.0152785 | − | 0.999883i | \(-0.504863\pi\) | ||||
−0.0152785 | + | 0.999883i | \(0.504863\pi\) | |||||||
\(972\) | 21.0186 | 0.674173 | ||||||||
\(973\) | 2.53750 | 0.0813486 | ||||||||
\(974\) | 19.0364 | 0.609965 | ||||||||
\(975\) | −2.29788 | −0.0735912 | ||||||||
\(976\) | −12.4457 | −0.398378 | ||||||||
\(977\) | 35.9822 | 1.15117 | 0.575587 | − | 0.817741i | \(-0.304774\pi\) | ||||
0.575587 | + | 0.817741i | \(0.304774\pi\) | |||||||
\(978\) | 11.7303 | 0.375095 | ||||||||
\(979\) | 72.9099 | 2.33021 | ||||||||
\(980\) | 16.1148 | 0.514767 | ||||||||
\(981\) | 3.99510 | 0.127554 | ||||||||
\(982\) | −34.7226 | −1.10804 | ||||||||
\(983\) | −1.18236 | −0.0377113 | −0.0188557 | − | 0.999822i | \(-0.506002\pi\) | ||||
−0.0188557 | + | 0.999822i | \(0.506002\pi\) | |||||||
\(984\) | −24.1089 | −0.768564 | ||||||||
\(985\) | 50.2251 | 1.60031 | ||||||||
\(986\) | −1.77191 | −0.0564291 | ||||||||
\(987\) | −3.47674 | −0.110666 | ||||||||
\(988\) | 2.97992 | 0.0948038 | ||||||||
\(989\) | 1.45017 | 0.0461127 | ||||||||
\(990\) | 33.8347 | 1.07534 | ||||||||
\(991\) | −36.0652 | −1.14565 | −0.572825 | − | 0.819678i | \(-0.694152\pi\) | ||||
−0.572825 | + | 0.819678i | \(0.694152\pi\) | |||||||
\(992\) | −1.01037 | −0.0320792 | ||||||||
\(993\) | −11.5285 | −0.365847 | ||||||||
\(994\) | −0.638635 | −0.0202563 | ||||||||
\(995\) | 27.6983 | 0.878094 | ||||||||
\(996\) | 40.9999 | 1.29913 | ||||||||
\(997\) | 33.6365 | 1.06528 | 0.532640 | − | 0.846342i | \(-0.321200\pi\) | ||||
0.532640 | + | 0.846342i | \(0.321200\pi\) | |||||||
\(998\) | −38.9035 | −1.23147 | ||||||||
\(999\) | −4.53521 | −0.143488 |
(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 | 8018.2.a.g.1.7 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.g.1.7 | ✓ | 34 | 1.1 | even | 1 | trivial |