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: | \(30\) |
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 | ||||||||
\(3\) | −2.39570 | −1.38316 | −0.691578 | − | 0.722302i | \(-0.743084\pi\) | ||||
−0.691578 | + | 0.722302i | \(0.743084\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.46674 | −1.55037 | −0.775187 | − | 0.631732i | \(-0.782344\pi\) | ||||
−0.775187 | + | 0.631732i | \(0.782344\pi\) | |||||||
\(6\) | −2.39570 | −0.978039 | ||||||||
\(7\) | −3.11450 | −1.17717 | −0.588586 | − | 0.808435i | \(-0.700315\pi\) | ||||
−0.588586 | + | 0.808435i | \(0.700315\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.73936 | 0.913121 | ||||||||
\(10\) | −3.46674 | −1.09628 | ||||||||
\(11\) | −4.76297 | −1.43609 | −0.718045 | − | 0.695997i | \(-0.754963\pi\) | ||||
−0.718045 | + | 0.695997i | \(0.754963\pi\) | |||||||
\(12\) | −2.39570 | −0.691578 | ||||||||
\(13\) | −3.60047 | −0.998590 | −0.499295 | − | 0.866432i | \(-0.666408\pi\) | ||||
−0.499295 | + | 0.866432i | \(0.666408\pi\) | |||||||
\(14\) | −3.11450 | −0.832386 | ||||||||
\(15\) | 8.30526 | 2.14441 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.91860 | 0.707864 | 0.353932 | − | 0.935271i | \(-0.384844\pi\) | ||||
0.353932 | + | 0.935271i | \(0.384844\pi\) | |||||||
\(18\) | 2.73936 | 0.645674 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −3.46674 | −0.775187 | ||||||||
\(21\) | 7.46140 | 1.62821 | ||||||||
\(22\) | −4.76297 | −1.01547 | ||||||||
\(23\) | 4.74786 | 0.989998 | 0.494999 | − | 0.868894i | \(-0.335168\pi\) | ||||
0.494999 | + | 0.868894i | \(0.335168\pi\) | |||||||
\(24\) | −2.39570 | −0.489020 | ||||||||
\(25\) | 7.01829 | 1.40366 | ||||||||
\(26\) | −3.60047 | −0.706110 | ||||||||
\(27\) | 0.624410 | 0.120168 | ||||||||
\(28\) | −3.11450 | −0.588586 | ||||||||
\(29\) | −4.17660 | −0.775576 | −0.387788 | − | 0.921749i | \(-0.626761\pi\) | ||||
−0.387788 | + | 0.921749i | \(0.626761\pi\) | |||||||
\(30\) | 8.30526 | 1.51633 | ||||||||
\(31\) | 6.99380 | 1.25612 | 0.628062 | − | 0.778163i | \(-0.283848\pi\) | ||||
0.628062 | + | 0.778163i | \(0.283848\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 11.4106 | 1.98634 | ||||||||
\(34\) | 2.91860 | 0.500535 | ||||||||
\(35\) | 10.7972 | 1.82506 | ||||||||
\(36\) | 2.73936 | 0.456560 | ||||||||
\(37\) | 0.716100 | 0.117726 | 0.0588630 | − | 0.998266i | \(-0.481252\pi\) | ||||
0.0588630 | + | 0.998266i | \(0.481252\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 8.62563 | 1.38121 | ||||||||
\(40\) | −3.46674 | −0.548140 | ||||||||
\(41\) | −3.08255 | −0.481413 | −0.240707 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240707 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(42\) | 7.46140 | 1.15132 | ||||||||
\(43\) | 0.576373 | 0.0878961 | 0.0439480 | − | 0.999034i | \(-0.486006\pi\) | ||||
0.0439480 | + | 0.999034i | \(0.486006\pi\) | |||||||
\(44\) | −4.76297 | −0.718045 | ||||||||
\(45\) | −9.49666 | −1.41568 | ||||||||
\(46\) | 4.74786 | 0.700034 | ||||||||
\(47\) | 1.44855 | 0.211293 | 0.105646 | − | 0.994404i | \(-0.466309\pi\) | ||||
0.105646 | + | 0.994404i | \(0.466309\pi\) | |||||||
\(48\) | −2.39570 | −0.345789 | ||||||||
\(49\) | 2.70013 | 0.385733 | ||||||||
\(50\) | 7.01829 | 0.992536 | ||||||||
\(51\) | −6.99207 | −0.979086 | ||||||||
\(52\) | −3.60047 | −0.499295 | ||||||||
\(53\) | 13.7109 | 1.88333 | 0.941667 | − | 0.336545i | \(-0.109258\pi\) | ||||
0.941667 | + | 0.336545i | \(0.109258\pi\) | |||||||
\(54\) | 0.624410 | 0.0849715 | ||||||||
\(55\) | 16.5120 | 2.22648 | ||||||||
\(56\) | −3.11450 | −0.416193 | ||||||||
\(57\) | −2.39570 | −0.317318 | ||||||||
\(58\) | −4.17660 | −0.548415 | ||||||||
\(59\) | 10.0759 | 1.31177 | 0.655887 | − | 0.754859i | \(-0.272295\pi\) | ||||
0.655887 | + | 0.754859i | \(0.272295\pi\) | |||||||
\(60\) | 8.30526 | 1.07220 | ||||||||
\(61\) | −1.24194 | −0.159014 | −0.0795070 | − | 0.996834i | \(-0.525335\pi\) | ||||
−0.0795070 | + | 0.996834i | \(0.525335\pi\) | |||||||
\(62\) | 6.99380 | 0.888214 | ||||||||
\(63\) | −8.53175 | −1.07490 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.4819 | 1.54819 | ||||||||
\(66\) | 11.4106 | 1.40455 | ||||||||
\(67\) | −0.735972 | −0.0899133 | −0.0449567 | − | 0.998989i | \(-0.514315\pi\) | ||||
−0.0449567 | + | 0.998989i | \(0.514315\pi\) | |||||||
\(68\) | 2.91860 | 0.353932 | ||||||||
\(69\) | −11.3744 | −1.36932 | ||||||||
\(70\) | 10.7972 | 1.29051 | ||||||||
\(71\) | −15.1244 | −1.79494 | −0.897471 | − | 0.441074i | \(-0.854598\pi\) | ||||
−0.897471 | + | 0.441074i | \(0.854598\pi\) | |||||||
\(72\) | 2.73936 | 0.322837 | ||||||||
\(73\) | 5.48450 | 0.641912 | 0.320956 | − | 0.947094i | \(-0.395996\pi\) | ||||
0.320956 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(74\) | 0.716100 | 0.0832449 | ||||||||
\(75\) | −16.8137 | −1.94148 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 14.8343 | 1.69052 | ||||||||
\(78\) | 8.62563 | 0.976660 | ||||||||
\(79\) | −3.39442 | −0.381902 | −0.190951 | − | 0.981600i | \(-0.561157\pi\) | ||||
−0.190951 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(80\) | −3.46674 | −0.387593 | ||||||||
\(81\) | −9.71398 | −1.07933 | ||||||||
\(82\) | −3.08255 | −0.340411 | ||||||||
\(83\) | −9.99910 | −1.09754 | −0.548772 | − | 0.835972i | \(-0.684904\pi\) | ||||
−0.548772 | + | 0.835972i | \(0.684904\pi\) | |||||||
\(84\) | 7.46140 | 0.814106 | ||||||||
\(85\) | −10.1180 | −1.09745 | ||||||||
\(86\) | 0.576373 | 0.0621519 | ||||||||
\(87\) | 10.0059 | 1.07274 | ||||||||
\(88\) | −4.76297 | −0.507734 | ||||||||
\(89\) | 6.54901 | 0.694194 | 0.347097 | − | 0.937829i | \(-0.387167\pi\) | ||||
0.347097 | + | 0.937829i | \(0.387167\pi\) | |||||||
\(90\) | −9.49666 | −1.00104 | ||||||||
\(91\) | 11.2137 | 1.17551 | ||||||||
\(92\) | 4.74786 | 0.494999 | ||||||||
\(93\) | −16.7550 | −1.73742 | ||||||||
\(94\) | 1.44855 | 0.149406 | ||||||||
\(95\) | −3.46674 | −0.355680 | ||||||||
\(96\) | −2.39570 | −0.244510 | ||||||||
\(97\) | 3.66525 | 0.372150 | 0.186075 | − | 0.982536i | \(-0.440423\pi\) | ||||
0.186075 | + | 0.982536i | \(0.440423\pi\) | |||||||
\(98\) | 2.70013 | 0.272754 | ||||||||
\(99\) | −13.0475 | −1.31132 | ||||||||
\(100\) | 7.01829 | 0.701829 | ||||||||
\(101\) | 8.68367 | 0.864058 | 0.432029 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432029 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(102\) | −6.99207 | −0.692318 | ||||||||
\(103\) | −8.26186 | −0.814065 | −0.407032 | − | 0.913414i | \(-0.633436\pi\) | ||||
−0.407032 | + | 0.913414i | \(0.633436\pi\) | |||||||
\(104\) | −3.60047 | −0.353055 | ||||||||
\(105\) | −25.8668 | −2.52434 | ||||||||
\(106\) | 13.7109 | 1.33172 | ||||||||
\(107\) | 2.09800 | 0.202822 | 0.101411 | − | 0.994845i | \(-0.467664\pi\) | ||||
0.101411 | + | 0.994845i | \(0.467664\pi\) | |||||||
\(108\) | 0.624410 | 0.0600839 | ||||||||
\(109\) | −6.85539 | −0.656627 | −0.328313 | − | 0.944569i | \(-0.606480\pi\) | ||||
−0.328313 | + | 0.944569i | \(0.606480\pi\) | |||||||
\(110\) | 16.5120 | 1.57436 | ||||||||
\(111\) | −1.71556 | −0.162833 | ||||||||
\(112\) | −3.11450 | −0.294293 | ||||||||
\(113\) | −7.58937 | −0.713948 | −0.356974 | − | 0.934114i | \(-0.616191\pi\) | ||||
−0.356974 | + | 0.934114i | \(0.616191\pi\) | |||||||
\(114\) | −2.39570 | −0.224378 | ||||||||
\(115\) | −16.4596 | −1.53487 | ||||||||
\(116\) | −4.17660 | −0.387788 | ||||||||
\(117\) | −9.86299 | −0.911833 | ||||||||
\(118\) | 10.0759 | 0.927564 | ||||||||
\(119\) | −9.08998 | −0.833277 | ||||||||
\(120\) | 8.30526 | 0.758163 | ||||||||
\(121\) | 11.6859 | 1.06235 | ||||||||
\(122\) | −1.24194 | −0.112440 | ||||||||
\(123\) | 7.38485 | 0.665870 | ||||||||
\(124\) | 6.99380 | 0.628062 | ||||||||
\(125\) | −6.99687 | −0.625819 | ||||||||
\(126\) | −8.53175 | −0.760069 | ||||||||
\(127\) | 5.20294 | 0.461687 | 0.230843 | − | 0.972991i | \(-0.425852\pi\) | ||||
0.230843 | + | 0.972991i | \(0.425852\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.38082 | −0.121574 | ||||||||
\(130\) | 12.4819 | 1.09473 | ||||||||
\(131\) | 1.27464 | 0.111366 | 0.0556830 | − | 0.998448i | \(-0.482266\pi\) | ||||
0.0556830 | + | 0.998448i | \(0.482266\pi\) | |||||||
\(132\) | 11.4106 | 0.993168 | ||||||||
\(133\) | −3.11450 | −0.270062 | ||||||||
\(134\) | −0.735972 | −0.0635783 | ||||||||
\(135\) | −2.16467 | −0.186305 | ||||||||
\(136\) | 2.91860 | 0.250268 | ||||||||
\(137\) | −3.81237 | −0.325713 | −0.162856 | − | 0.986650i | \(-0.552071\pi\) | ||||
−0.162856 | + | 0.986650i | \(0.552071\pi\) | |||||||
\(138\) | −11.3744 | −0.968257 | ||||||||
\(139\) | 5.87770 | 0.498540 | 0.249270 | − | 0.968434i | \(-0.419809\pi\) | ||||
0.249270 | + | 0.968434i | \(0.419809\pi\) | |||||||
\(140\) | 10.7972 | 0.912528 | ||||||||
\(141\) | −3.47028 | −0.292251 | ||||||||
\(142\) | −15.1244 | −1.26922 | ||||||||
\(143\) | 17.1489 | 1.43407 | ||||||||
\(144\) | 2.73936 | 0.228280 | ||||||||
\(145\) | 14.4792 | 1.20243 | ||||||||
\(146\) | 5.48450 | 0.453900 | ||||||||
\(147\) | −6.46870 | −0.533529 | ||||||||
\(148\) | 0.716100 | 0.0588630 | ||||||||
\(149\) | 4.21051 | 0.344938 | 0.172469 | − | 0.985015i | \(-0.444826\pi\) | ||||
0.172469 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(150\) | −16.8137 | −1.37283 | ||||||||
\(151\) | 17.5187 | 1.42565 | 0.712824 | − | 0.701343i | \(-0.247416\pi\) | ||||
0.712824 | + | 0.701343i | \(0.247416\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 7.99509 | 0.646365 | ||||||||
\(154\) | 14.8343 | 1.19538 | ||||||||
\(155\) | −24.2457 | −1.94746 | ||||||||
\(156\) | 8.62563 | 0.690603 | ||||||||
\(157\) | −10.0118 | −0.799025 | −0.399512 | − | 0.916728i | \(-0.630821\pi\) | ||||
−0.399512 | + | 0.916728i | \(0.630821\pi\) | |||||||
\(158\) | −3.39442 | −0.270045 | ||||||||
\(159\) | −32.8471 | −2.60495 | ||||||||
\(160\) | −3.46674 | −0.274070 | ||||||||
\(161\) | −14.7872 | −1.16540 | ||||||||
\(162\) | −9.71398 | −0.763203 | ||||||||
\(163\) | −6.70898 | −0.525488 | −0.262744 | − | 0.964866i | \(-0.584627\pi\) | ||||
−0.262744 | + | 0.964866i | \(0.584627\pi\) | |||||||
\(164\) | −3.08255 | −0.240707 | ||||||||
\(165\) | −39.5577 | −3.07956 | ||||||||
\(166\) | −9.99910 | −0.776081 | ||||||||
\(167\) | 4.55028 | 0.352111 | 0.176056 | − | 0.984380i | \(-0.443666\pi\) | ||||
0.176056 | + | 0.984380i | \(0.443666\pi\) | |||||||
\(168\) | 7.46140 | 0.575660 | ||||||||
\(169\) | −0.0366224 | −0.00281711 | ||||||||
\(170\) | −10.1180 | −0.776017 | ||||||||
\(171\) | 2.73936 | 0.209484 | ||||||||
\(172\) | 0.576373 | 0.0439480 | ||||||||
\(173\) | −1.75815 | −0.133669 | −0.0668347 | − | 0.997764i | \(-0.521290\pi\) | ||||
−0.0668347 | + | 0.997764i | \(0.521290\pi\) | |||||||
\(174\) | 10.0059 | 0.758543 | ||||||||
\(175\) | −21.8585 | −1.65235 | ||||||||
\(176\) | −4.76297 | −0.359022 | ||||||||
\(177\) | −24.1389 | −1.81439 | ||||||||
\(178\) | 6.54901 | 0.490869 | ||||||||
\(179\) | −13.5938 | −1.01605 | −0.508025 | − | 0.861342i | \(-0.669624\pi\) | ||||
−0.508025 | + | 0.861342i | \(0.669624\pi\) | |||||||
\(180\) | −9.49666 | −0.707839 | ||||||||
\(181\) | −15.0394 | −1.11787 | −0.558936 | − | 0.829211i | \(-0.688790\pi\) | ||||
−0.558936 | + | 0.829211i | \(0.688790\pi\) | |||||||
\(182\) | 11.2137 | 0.831213 | ||||||||
\(183\) | 2.97531 | 0.219941 | ||||||||
\(184\) | 4.74786 | 0.350017 | ||||||||
\(185\) | −2.48253 | −0.182519 | ||||||||
\(186\) | −16.7550 | −1.22854 | ||||||||
\(187\) | −13.9012 | −1.01656 | ||||||||
\(188\) | 1.44855 | 0.105646 | ||||||||
\(189\) | −1.94473 | −0.141458 | ||||||||
\(190\) | −3.46674 | −0.251504 | ||||||||
\(191\) | 16.7799 | 1.21415 | 0.607077 | − | 0.794643i | \(-0.292342\pi\) | ||||
0.607077 | + | 0.794643i | \(0.292342\pi\) | |||||||
\(192\) | −2.39570 | −0.172895 | ||||||||
\(193\) | −5.72740 | −0.412267 | −0.206133 | − | 0.978524i | \(-0.566088\pi\) | ||||
−0.206133 | + | 0.978524i | \(0.566088\pi\) | |||||||
\(194\) | 3.66525 | 0.263150 | ||||||||
\(195\) | −29.9028 | −2.14139 | ||||||||
\(196\) | 2.70013 | 0.192867 | ||||||||
\(197\) | 4.17820 | 0.297684 | 0.148842 | − | 0.988861i | \(-0.452445\pi\) | ||||
0.148842 | + | 0.988861i | \(0.452445\pi\) | |||||||
\(198\) | −13.0475 | −0.927245 | ||||||||
\(199\) | 9.50199 | 0.673578 | 0.336789 | − | 0.941580i | \(-0.390659\pi\) | ||||
0.336789 | + | 0.941580i | \(0.390659\pi\) | |||||||
\(200\) | 7.01829 | 0.496268 | ||||||||
\(201\) | 1.76317 | 0.124364 | ||||||||
\(202\) | 8.68367 | 0.610981 | ||||||||
\(203\) | 13.0080 | 0.912985 | ||||||||
\(204\) | −6.99207 | −0.489543 | ||||||||
\(205\) | 10.6864 | 0.746370 | ||||||||
\(206\) | −8.26186 | −0.575631 | ||||||||
\(207\) | 13.0061 | 0.903987 | ||||||||
\(208\) | −3.60047 | −0.249648 | ||||||||
\(209\) | −4.76297 | −0.329462 | ||||||||
\(210\) | −25.8668 | −1.78498 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 13.7109 | 0.941667 | ||||||||
\(213\) | 36.2336 | 2.48268 | ||||||||
\(214\) | 2.09800 | 0.143417 | ||||||||
\(215\) | −1.99814 | −0.136272 | ||||||||
\(216\) | 0.624410 | 0.0424857 | ||||||||
\(217\) | −21.7822 | −1.47867 | ||||||||
\(218\) | −6.85539 | −0.464305 | ||||||||
\(219\) | −13.1392 | −0.887864 | ||||||||
\(220\) | 16.5120 | 1.11324 | ||||||||
\(221\) | −10.5083 | −0.706866 | ||||||||
\(222\) | −1.71556 | −0.115141 | ||||||||
\(223\) | −0.264142 | −0.0176883 | −0.00884413 | − | 0.999961i | \(-0.502815\pi\) | ||||
−0.00884413 | + | 0.999961i | \(0.502815\pi\) | |||||||
\(224\) | −3.11450 | −0.208097 | ||||||||
\(225\) | 19.2256 | 1.28171 | ||||||||
\(226\) | −7.58937 | −0.504837 | ||||||||
\(227\) | 12.5929 | 0.835821 | 0.417910 | − | 0.908488i | \(-0.362763\pi\) | ||||
0.417910 | + | 0.908488i | \(0.362763\pi\) | |||||||
\(228\) | −2.39570 | −0.158659 | ||||||||
\(229\) | 3.05372 | 0.201796 | 0.100898 | − | 0.994897i | \(-0.467828\pi\) | ||||
0.100898 | + | 0.994897i | \(0.467828\pi\) | |||||||
\(230\) | −16.4596 | −1.08531 | ||||||||
\(231\) | −35.5385 | −2.33826 | ||||||||
\(232\) | −4.17660 | −0.274207 | ||||||||
\(233\) | −24.2585 | −1.58923 | −0.794613 | − | 0.607117i | \(-0.792326\pi\) | ||||
−0.794613 | + | 0.607117i | \(0.792326\pi\) | |||||||
\(234\) | −9.86299 | −0.644764 | ||||||||
\(235\) | −5.02174 | −0.327582 | ||||||||
\(236\) | 10.0759 | 0.655887 | ||||||||
\(237\) | 8.13199 | 0.528230 | ||||||||
\(238\) | −9.08998 | −0.589216 | ||||||||
\(239\) | 16.6046 | 1.07406 | 0.537031 | − | 0.843562i | \(-0.319546\pi\) | ||||
0.537031 | + | 0.843562i | \(0.319546\pi\) | |||||||
\(240\) | 8.30526 | 0.536102 | ||||||||
\(241\) | 27.3688 | 1.76298 | 0.881489 | − | 0.472205i | \(-0.156542\pi\) | ||||
0.881489 | + | 0.472205i | \(0.156542\pi\) | |||||||
\(242\) | 11.6859 | 0.751198 | ||||||||
\(243\) | 21.3985 | 1.37272 | ||||||||
\(244\) | −1.24194 | −0.0795070 | ||||||||
\(245\) | −9.36065 | −0.598030 | ||||||||
\(246\) | 7.38485 | 0.470841 | ||||||||
\(247\) | −3.60047 | −0.229092 | ||||||||
\(248\) | 6.99380 | 0.444107 | ||||||||
\(249\) | 23.9548 | 1.51807 | ||||||||
\(250\) | −6.99687 | −0.442521 | ||||||||
\(251\) | −0.744054 | −0.0469643 | −0.0234821 | − | 0.999724i | \(-0.507475\pi\) | ||||
−0.0234821 | + | 0.999724i | \(0.507475\pi\) | |||||||
\(252\) | −8.53175 | −0.537450 | ||||||||
\(253\) | −22.6139 | −1.42173 | ||||||||
\(254\) | 5.20294 | 0.326462 | ||||||||
\(255\) | 24.2397 | 1.51795 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.7949 | 1.67142 | 0.835710 | − | 0.549172i | \(-0.185057\pi\) | ||||
0.835710 | + | 0.549172i | \(0.185057\pi\) | |||||||
\(258\) | −1.38082 | −0.0859658 | ||||||||
\(259\) | −2.23029 | −0.138584 | ||||||||
\(260\) | 12.4819 | 0.774094 | ||||||||
\(261\) | −11.4412 | −0.708194 | ||||||||
\(262\) | 1.27464 | 0.0787477 | ||||||||
\(263\) | 2.17017 | 0.133818 | 0.0669092 | − | 0.997759i | \(-0.478686\pi\) | ||||
0.0669092 | + | 0.997759i | \(0.478686\pi\) | |||||||
\(264\) | 11.4106 | 0.702276 | ||||||||
\(265\) | −47.5321 | −2.91987 | ||||||||
\(266\) | −3.11450 | −0.190962 | ||||||||
\(267\) | −15.6894 | −0.960178 | ||||||||
\(268\) | −0.735972 | −0.0449567 | ||||||||
\(269\) | −15.2664 | −0.930811 | −0.465406 | − | 0.885097i | \(-0.654092\pi\) | ||||
−0.465406 | + | 0.885097i | \(0.654092\pi\) | |||||||
\(270\) | −2.16467 | −0.131737 | ||||||||
\(271\) | −6.40444 | −0.389042 | −0.194521 | − | 0.980898i | \(-0.562315\pi\) | ||||
−0.194521 | + | 0.980898i | \(0.562315\pi\) | |||||||
\(272\) | 2.91860 | 0.176966 | ||||||||
\(273\) | −26.8646 | −1.62592 | ||||||||
\(274\) | −3.81237 | −0.230314 | ||||||||
\(275\) | −33.4279 | −2.01578 | ||||||||
\(276\) | −11.3744 | −0.684661 | ||||||||
\(277\) | −29.4586 | −1.77000 | −0.884999 | − | 0.465593i | \(-0.845841\pi\) | ||||
−0.884999 | + | 0.465593i | \(0.845841\pi\) | |||||||
\(278\) | 5.87770 | 0.352521 | ||||||||
\(279\) | 19.1586 | 1.14699 | ||||||||
\(280\) | 10.7972 | 0.645255 | ||||||||
\(281\) | −2.35803 | −0.140668 | −0.0703342 | − | 0.997523i | \(-0.522407\pi\) | ||||
−0.0703342 | + | 0.997523i | \(0.522407\pi\) | |||||||
\(282\) | −3.47028 | −0.206652 | ||||||||
\(283\) | −10.0881 | −0.599673 | −0.299837 | − | 0.953991i | \(-0.596932\pi\) | ||||
−0.299837 | + | 0.953991i | \(0.596932\pi\) | |||||||
\(284\) | −15.1244 | −0.897471 | ||||||||
\(285\) | 8.30526 | 0.491961 | ||||||||
\(286\) | 17.1489 | 1.01404 | ||||||||
\(287\) | 9.60061 | 0.566706 | ||||||||
\(288\) | 2.73936 | 0.161418 | ||||||||
\(289\) | −8.48179 | −0.498929 | ||||||||
\(290\) | 14.4792 | 0.850248 | ||||||||
\(291\) | −8.78083 | −0.514742 | ||||||||
\(292\) | 5.48450 | 0.320956 | ||||||||
\(293\) | 11.3310 | 0.661967 | 0.330983 | − | 0.943637i | \(-0.392620\pi\) | ||||
0.330983 | + | 0.943637i | \(0.392620\pi\) | |||||||
\(294\) | −6.46870 | −0.377262 | ||||||||
\(295\) | −34.9306 | −2.03374 | ||||||||
\(296\) | 0.716100 | 0.0416224 | ||||||||
\(297\) | −2.97405 | −0.172572 | ||||||||
\(298\) | 4.21051 | 0.243908 | ||||||||
\(299\) | −17.0945 | −0.988602 | ||||||||
\(300\) | −16.8137 | −0.970739 | ||||||||
\(301\) | −1.79512 | −0.103469 | ||||||||
\(302\) | 17.5187 | 1.00809 | ||||||||
\(303\) | −20.8034 | −1.19513 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 4.30548 | 0.246531 | ||||||||
\(306\) | 7.99509 | 0.457049 | ||||||||
\(307\) | −20.0815 | −1.14611 | −0.573055 | − | 0.819517i | \(-0.694242\pi\) | ||||
−0.573055 | + | 0.819517i | \(0.694242\pi\) | |||||||
\(308\) | 14.8343 | 0.845262 | ||||||||
\(309\) | 19.7929 | 1.12598 | ||||||||
\(310\) | −24.2457 | −1.37706 | ||||||||
\(311\) | 22.7007 | 1.28724 | 0.643619 | − | 0.765346i | \(-0.277432\pi\) | ||||
0.643619 | + | 0.765346i | \(0.277432\pi\) | |||||||
\(312\) | 8.62563 | 0.488330 | ||||||||
\(313\) | 19.0345 | 1.07589 | 0.537945 | − | 0.842980i | \(-0.319201\pi\) | ||||
0.537945 | + | 0.842980i | \(0.319201\pi\) | |||||||
\(314\) | −10.0118 | −0.564996 | ||||||||
\(315\) | 29.5774 | 1.66650 | ||||||||
\(316\) | −3.39442 | −0.190951 | ||||||||
\(317\) | −1.34673 | −0.0756400 | −0.0378200 | − | 0.999285i | \(-0.512041\pi\) | ||||
−0.0378200 | + | 0.999285i | \(0.512041\pi\) | |||||||
\(318\) | −32.8471 | −1.84197 | ||||||||
\(319\) | 19.8930 | 1.11380 | ||||||||
\(320\) | −3.46674 | −0.193797 | ||||||||
\(321\) | −5.02618 | −0.280534 | ||||||||
\(322\) | −14.7872 | −0.824060 | ||||||||
\(323\) | 2.91860 | 0.162395 | ||||||||
\(324\) | −9.71398 | −0.539666 | ||||||||
\(325\) | −25.2691 | −1.40168 | ||||||||
\(326\) | −6.70898 | −0.371576 | ||||||||
\(327\) | 16.4234 | 0.908217 | ||||||||
\(328\) | −3.08255 | −0.170205 | ||||||||
\(329\) | −4.51151 | −0.248728 | ||||||||
\(330\) | −39.5577 | −2.17758 | ||||||||
\(331\) | −7.28727 | −0.400545 | −0.200272 | − | 0.979740i | \(-0.564183\pi\) | ||||
−0.200272 | + | 0.979740i | \(0.564183\pi\) | |||||||
\(332\) | −9.99910 | −0.548772 | ||||||||
\(333\) | 1.96166 | 0.107498 | ||||||||
\(334\) | 4.55028 | 0.248980 | ||||||||
\(335\) | 2.55142 | 0.139399 | ||||||||
\(336\) | 7.46140 | 0.407053 | ||||||||
\(337\) | −8.73141 | −0.475630 | −0.237815 | − | 0.971310i | \(-0.576431\pi\) | ||||
−0.237815 | + | 0.971310i | \(0.576431\pi\) | |||||||
\(338\) | −0.0366224 | −0.00199199 | ||||||||
\(339\) | 18.1818 | 0.987501 | ||||||||
\(340\) | −10.1180 | −0.548727 | ||||||||
\(341\) | −33.3113 | −1.80391 | ||||||||
\(342\) | 2.73936 | 0.148128 | ||||||||
\(343\) | 13.3920 | 0.723098 | ||||||||
\(344\) | 0.576373 | 0.0310760 | ||||||||
\(345\) | 39.4322 | 2.12296 | ||||||||
\(346\) | −1.75815 | −0.0945186 | ||||||||
\(347\) | 18.7884 | 1.00862 | 0.504308 | − | 0.863524i | \(-0.331748\pi\) | ||||
0.504308 | + | 0.863524i | \(0.331748\pi\) | |||||||
\(348\) | 10.0059 | 0.536371 | ||||||||
\(349\) | 22.0275 | 1.17910 | 0.589552 | − | 0.807730i | \(-0.299304\pi\) | ||||
0.589552 | + | 0.807730i | \(0.299304\pi\) | |||||||
\(350\) | −21.8585 | −1.16838 | ||||||||
\(351\) | −2.24817 | −0.119998 | ||||||||
\(352\) | −4.76297 | −0.253867 | ||||||||
\(353\) | −23.7823 | −1.26581 | −0.632903 | − | 0.774231i | \(-0.718137\pi\) | ||||
−0.632903 | + | 0.774231i | \(0.718137\pi\) | |||||||
\(354\) | −24.1389 | −1.28297 | ||||||||
\(355\) | 52.4325 | 2.78283 | ||||||||
\(356\) | 6.54901 | 0.347097 | ||||||||
\(357\) | 21.7768 | 1.15255 | ||||||||
\(358\) | −13.5938 | −0.718456 | ||||||||
\(359\) | 3.73402 | 0.197074 | 0.0985371 | − | 0.995133i | \(-0.468584\pi\) | ||||
0.0985371 | + | 0.995133i | \(0.468584\pi\) | |||||||
\(360\) | −9.49666 | −0.500518 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −15.0394 | −0.790454 | ||||||||
\(363\) | −27.9959 | −1.46940 | ||||||||
\(364\) | 11.2137 | 0.587756 | ||||||||
\(365\) | −19.0133 | −0.995203 | ||||||||
\(366\) | 2.97531 | 0.155522 | ||||||||
\(367\) | 14.5365 | 0.758799 | 0.379399 | − | 0.925233i | \(-0.376131\pi\) | ||||
0.379399 | + | 0.925233i | \(0.376131\pi\) | |||||||
\(368\) | 4.74786 | 0.247499 | ||||||||
\(369\) | −8.44422 | −0.439588 | ||||||||
\(370\) | −2.48253 | −0.129061 | ||||||||
\(371\) | −42.7026 | −2.21701 | ||||||||
\(372\) | −16.7550 | −0.868708 | ||||||||
\(373\) | 3.93186 | 0.203584 | 0.101792 | − | 0.994806i | \(-0.467542\pi\) | ||||
0.101792 | + | 0.994806i | \(0.467542\pi\) | |||||||
\(374\) | −13.9012 | −0.718814 | ||||||||
\(375\) | 16.7624 | 0.865606 | ||||||||
\(376\) | 1.44855 | 0.0747032 | ||||||||
\(377\) | 15.0377 | 0.774482 | ||||||||
\(378\) | −1.94473 | −0.100026 | ||||||||
\(379\) | 11.1988 | 0.575242 | 0.287621 | − | 0.957744i | \(-0.407136\pi\) | ||||
0.287621 | + | 0.957744i | \(0.407136\pi\) | |||||||
\(380\) | −3.46674 | −0.177840 | ||||||||
\(381\) | −12.4647 | −0.638585 | ||||||||
\(382\) | 16.7799 | 0.858536 | ||||||||
\(383\) | 25.4159 | 1.29869 | 0.649346 | − | 0.760493i | \(-0.275043\pi\) | ||||
0.649346 | + | 0.760493i | \(0.275043\pi\) | |||||||
\(384\) | −2.39570 | −0.122255 | ||||||||
\(385\) | −51.4266 | −2.62094 | ||||||||
\(386\) | −5.72740 | −0.291517 | ||||||||
\(387\) | 1.57889 | 0.0802597 | ||||||||
\(388\) | 3.66525 | 0.186075 | ||||||||
\(389\) | −22.9851 | −1.16539 | −0.582694 | − | 0.812691i | \(-0.698002\pi\) | ||||
−0.582694 | + | 0.812691i | \(0.698002\pi\) | |||||||
\(390\) | −29.9028 | −1.51419 | ||||||||
\(391\) | 13.8571 | 0.700784 | ||||||||
\(392\) | 2.70013 | 0.136377 | ||||||||
\(393\) | −3.05366 | −0.154037 | ||||||||
\(394\) | 4.17820 | 0.210495 | ||||||||
\(395\) | 11.7676 | 0.592090 | ||||||||
\(396\) | −13.0475 | −0.655662 | ||||||||
\(397\) | −26.3767 | −1.32381 | −0.661904 | − | 0.749589i | \(-0.730251\pi\) | ||||
−0.661904 | + | 0.749589i | \(0.730251\pi\) | |||||||
\(398\) | 9.50199 | 0.476292 | ||||||||
\(399\) | 7.46140 | 0.373537 | ||||||||
\(400\) | 7.01829 | 0.350914 | ||||||||
\(401\) | 14.0205 | 0.700150 | 0.350075 | − | 0.936722i | \(-0.386156\pi\) | ||||
0.350075 | + | 0.936722i | \(0.386156\pi\) | |||||||
\(402\) | 1.76317 | 0.0879387 | ||||||||
\(403\) | −25.1810 | −1.25435 | ||||||||
\(404\) | 8.68367 | 0.432029 | ||||||||
\(405\) | 33.6759 | 1.67337 | ||||||||
\(406\) | 13.0080 | 0.645578 | ||||||||
\(407\) | −3.41076 | −0.169065 | ||||||||
\(408\) | −6.99207 | −0.346159 | ||||||||
\(409\) | 7.58354 | 0.374982 | 0.187491 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187491 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(410\) | 10.6864 | 0.527764 | ||||||||
\(411\) | 9.13328 | 0.450511 | ||||||||
\(412\) | −8.26186 | −0.407032 | ||||||||
\(413\) | −31.3815 | −1.54418 | ||||||||
\(414\) | 13.0061 | 0.639216 | ||||||||
\(415\) | 34.6643 | 1.70160 | ||||||||
\(416\) | −3.60047 | −0.176528 | ||||||||
\(417\) | −14.0812 | −0.689559 | ||||||||
\(418\) | −4.76297 | −0.232965 | ||||||||
\(419\) | −2.08611 | −0.101913 | −0.0509567 | − | 0.998701i | \(-0.516227\pi\) | ||||
−0.0509567 | + | 0.998701i | \(0.516227\pi\) | |||||||
\(420\) | −25.8668 | −1.26217 | ||||||||
\(421\) | −11.5154 | −0.561225 | −0.280613 | − | 0.959821i | \(-0.590538\pi\) | ||||
−0.280613 | + | 0.959821i | \(0.590538\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 3.96810 | 0.192936 | ||||||||
\(424\) | 13.7109 | 0.665859 | ||||||||
\(425\) | 20.4836 | 0.993598 | ||||||||
\(426\) | 36.2336 | 1.75552 | ||||||||
\(427\) | 3.86802 | 0.187187 | ||||||||
\(428\) | 2.09800 | 0.101411 | ||||||||
\(429\) | −41.0836 | −1.98354 | ||||||||
\(430\) | −1.99814 | −0.0963587 | ||||||||
\(431\) | −9.52295 | −0.458704 | −0.229352 | − | 0.973343i | \(-0.573661\pi\) | ||||
−0.229352 | + | 0.973343i | \(0.573661\pi\) | |||||||
\(432\) | 0.624410 | 0.0300419 | ||||||||
\(433\) | 1.75745 | 0.0844574 | 0.0422287 | − | 0.999108i | \(-0.486554\pi\) | ||||
0.0422287 | + | 0.999108i | \(0.486554\pi\) | |||||||
\(434\) | −21.7822 | −1.04558 | ||||||||
\(435\) | −34.6878 | −1.66315 | ||||||||
\(436\) | −6.85539 | −0.328313 | ||||||||
\(437\) | 4.74786 | 0.227121 | ||||||||
\(438\) | −13.1392 | −0.627815 | ||||||||
\(439\) | −14.5340 | −0.693668 | −0.346834 | − | 0.937927i | \(-0.612743\pi\) | ||||
−0.346834 | + | 0.937927i | \(0.612743\pi\) | |||||||
\(440\) | 16.5120 | 0.787178 | ||||||||
\(441\) | 7.39664 | 0.352221 | ||||||||
\(442\) | −10.5083 | −0.499830 | ||||||||
\(443\) | −19.7877 | −0.940142 | −0.470071 | − | 0.882629i | \(-0.655772\pi\) | ||||
−0.470071 | + | 0.882629i | \(0.655772\pi\) | |||||||
\(444\) | −1.71556 | −0.0814167 | ||||||||
\(445\) | −22.7037 | −1.07626 | ||||||||
\(446\) | −0.264142 | −0.0125075 | ||||||||
\(447\) | −10.0871 | −0.477103 | ||||||||
\(448\) | −3.11450 | −0.147146 | ||||||||
\(449\) | −36.7356 | −1.73366 | −0.866830 | − | 0.498603i | \(-0.833847\pi\) | ||||
−0.866830 | + | 0.498603i | \(0.833847\pi\) | |||||||
\(450\) | 19.2256 | 0.906305 | ||||||||
\(451\) | 14.6821 | 0.691353 | ||||||||
\(452\) | −7.58937 | −0.356974 | ||||||||
\(453\) | −41.9694 | −1.97189 | ||||||||
\(454\) | 12.5929 | 0.591014 | ||||||||
\(455\) | −38.8749 | −1.82248 | ||||||||
\(456\) | −2.39570 | −0.112189 | ||||||||
\(457\) | 21.2778 | 0.995332 | 0.497666 | − | 0.867369i | \(-0.334191\pi\) | ||||
0.497666 | + | 0.867369i | \(0.334191\pi\) | |||||||
\(458\) | 3.05372 | 0.142691 | ||||||||
\(459\) | 1.82240 | 0.0850624 | ||||||||
\(460\) | −16.4596 | −0.767433 | ||||||||
\(461\) | 15.0555 | 0.701204 | 0.350602 | − | 0.936525i | \(-0.385977\pi\) | ||||
0.350602 | + | 0.936525i | \(0.385977\pi\) | |||||||
\(462\) | −35.5385 | −1.65340 | ||||||||
\(463\) | 31.3140 | 1.45529 | 0.727643 | − | 0.685956i | \(-0.240616\pi\) | ||||
0.727643 | + | 0.685956i | \(0.240616\pi\) | |||||||
\(464\) | −4.17660 | −0.193894 | ||||||||
\(465\) | 58.0853 | 2.69364 | ||||||||
\(466\) | −24.2585 | −1.12375 | ||||||||
\(467\) | 3.29466 | 0.152459 | 0.0762294 | − | 0.997090i | \(-0.475712\pi\) | ||||
0.0762294 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(468\) | −9.86299 | −0.455917 | ||||||||
\(469\) | 2.29219 | 0.105843 | ||||||||
\(470\) | −5.02174 | −0.231636 | ||||||||
\(471\) | 23.9851 | 1.10518 | ||||||||
\(472\) | 10.0759 | 0.463782 | ||||||||
\(473\) | −2.74525 | −0.126227 | ||||||||
\(474\) | 8.13199 | 0.373515 | ||||||||
\(475\) | 7.01829 | 0.322021 | ||||||||
\(476\) | −9.08998 | −0.416639 | ||||||||
\(477\) | 37.5591 | 1.71971 | ||||||||
\(478\) | 16.6046 | 0.759477 | ||||||||
\(479\) | 34.0016 | 1.55357 | 0.776786 | − | 0.629764i | \(-0.216849\pi\) | ||||
0.776786 | + | 0.629764i | \(0.216849\pi\) | |||||||
\(480\) | 8.30526 | 0.379081 | ||||||||
\(481\) | −2.57829 | −0.117560 | ||||||||
\(482\) | 27.3688 | 1.24661 | ||||||||
\(483\) | 35.4257 | 1.61193 | ||||||||
\(484\) | 11.6859 | 0.531177 | ||||||||
\(485\) | −12.7065 | −0.576971 | ||||||||
\(486\) | 21.3985 | 0.970657 | ||||||||
\(487\) | −13.9227 | −0.630898 | −0.315449 | − | 0.948943i | \(-0.602155\pi\) | ||||
−0.315449 | + | 0.948943i | \(0.602155\pi\) | |||||||
\(488\) | −1.24194 | −0.0562199 | ||||||||
\(489\) | 16.0727 | 0.726831 | ||||||||
\(490\) | −9.36065 | −0.422871 | ||||||||
\(491\) | 34.9576 | 1.57762 | 0.788808 | − | 0.614640i | \(-0.210699\pi\) | ||||
0.788808 | + | 0.614640i | \(0.210699\pi\) | |||||||
\(492\) | 7.38485 | 0.332935 | ||||||||
\(493\) | −12.1898 | −0.549002 | ||||||||
\(494\) | −3.60047 | −0.161993 | ||||||||
\(495\) | 45.2323 | 2.03304 | ||||||||
\(496\) | 6.99380 | 0.314031 | ||||||||
\(497\) | 47.1051 | 2.11295 | ||||||||
\(498\) | 23.9548 | 1.07344 | ||||||||
\(499\) | 33.8912 | 1.51718 | 0.758590 | − | 0.651568i | \(-0.225888\pi\) | ||||
0.758590 | + | 0.651568i | \(0.225888\pi\) | |||||||
\(500\) | −6.99687 | −0.312910 | ||||||||
\(501\) | −10.9011 | −0.487025 | ||||||||
\(502\) | −0.744054 | −0.0332088 | ||||||||
\(503\) | −34.9088 | −1.55651 | −0.778253 | − | 0.627950i | \(-0.783894\pi\) | ||||
−0.778253 | + | 0.627950i | \(0.783894\pi\) | |||||||
\(504\) | −8.53175 | −0.380034 | ||||||||
\(505\) | −30.1040 | −1.33961 | ||||||||
\(506\) | −22.6139 | −1.00531 | ||||||||
\(507\) | 0.0877361 | 0.00389650 | ||||||||
\(508\) | 5.20294 | 0.230843 | ||||||||
\(509\) | 2.61476 | 0.115897 | 0.0579486 | − | 0.998320i | \(-0.481544\pi\) | ||||
0.0579486 | + | 0.998320i | \(0.481544\pi\) | |||||||
\(510\) | 24.2397 | 1.07335 | ||||||||
\(511\) | −17.0815 | −0.755640 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.624410 | 0.0275684 | ||||||||
\(514\) | 26.7949 | 1.18187 | ||||||||
\(515\) | 28.6417 | 1.26210 | ||||||||
\(516\) | −1.38082 | −0.0607870 | ||||||||
\(517\) | −6.89940 | −0.303435 | ||||||||
\(518\) | −2.23029 | −0.0979935 | ||||||||
\(519\) | 4.21199 | 0.184886 | ||||||||
\(520\) | 12.4819 | 0.547367 | ||||||||
\(521\) | −19.1821 | −0.840385 | −0.420192 | − | 0.907435i | \(-0.638037\pi\) | ||||
−0.420192 | + | 0.907435i | \(0.638037\pi\) | |||||||
\(522\) | −11.4412 | −0.500769 | ||||||||
\(523\) | −21.7511 | −0.951107 | −0.475554 | − | 0.879687i | \(-0.657752\pi\) | ||||
−0.475554 | + | 0.879687i | \(0.657752\pi\) | |||||||
\(524\) | 1.27464 | 0.0556830 | ||||||||
\(525\) | 52.3663 | 2.28545 | ||||||||
\(526\) | 2.17017 | 0.0946238 | ||||||||
\(527\) | 20.4121 | 0.889165 | ||||||||
\(528\) | 11.4106 | 0.496584 | ||||||||
\(529\) | −0.457794 | −0.0199041 | ||||||||
\(530\) | −47.5321 | −2.06466 | ||||||||
\(531\) | 27.6016 | 1.19781 | ||||||||
\(532\) | −3.11450 | −0.135031 | ||||||||
\(533\) | 11.0986 | 0.480735 | ||||||||
\(534\) | −15.6894 | −0.678949 | ||||||||
\(535\) | −7.27324 | −0.314449 | ||||||||
\(536\) | −0.735972 | −0.0317892 | ||||||||
\(537\) | 32.5667 | 1.40536 | ||||||||
\(538\) | −15.2664 | −0.658183 | ||||||||
\(539\) | −12.8606 | −0.553947 | ||||||||
\(540\) | −2.16467 | −0.0931525 | ||||||||
\(541\) | −39.8063 | −1.71141 | −0.855703 | − | 0.517468i | \(-0.826875\pi\) | ||||
−0.855703 | + | 0.517468i | \(0.826875\pi\) | |||||||
\(542\) | −6.40444 | −0.275094 | ||||||||
\(543\) | 36.0299 | 1.54619 | ||||||||
\(544\) | 2.91860 | 0.125134 | ||||||||
\(545\) | 23.7658 | 1.01802 | ||||||||
\(546\) | −26.8646 | −1.14970 | ||||||||
\(547\) | 8.40901 | 0.359543 | 0.179772 | − | 0.983708i | \(-0.442464\pi\) | ||||
0.179772 | + | 0.983708i | \(0.442464\pi\) | |||||||
\(548\) | −3.81237 | −0.162856 | ||||||||
\(549\) | −3.40212 | −0.145199 | ||||||||
\(550\) | −33.4279 | −1.42537 | ||||||||
\(551\) | −4.17660 | −0.177929 | ||||||||
\(552\) | −11.3744 | −0.484128 | ||||||||
\(553\) | 10.5719 | 0.449564 | ||||||||
\(554\) | −29.4586 | −1.25158 | ||||||||
\(555\) | 5.94739 | 0.252453 | ||||||||
\(556\) | 5.87770 | 0.249270 | ||||||||
\(557\) | −22.8979 | −0.970215 | −0.485107 | − | 0.874455i | \(-0.661219\pi\) | ||||
−0.485107 | + | 0.874455i | \(0.661219\pi\) | |||||||
\(558\) | 19.1586 | 0.811047 | ||||||||
\(559\) | −2.07521 | −0.0877722 | ||||||||
\(560\) | 10.7972 | 0.456264 | ||||||||
\(561\) | 33.3030 | 1.40606 | ||||||||
\(562\) | −2.35803 | −0.0994676 | ||||||||
\(563\) | −7.50282 | −0.316206 | −0.158103 | − | 0.987423i | \(-0.550538\pi\) | ||||
−0.158103 | + | 0.987423i | \(0.550538\pi\) | |||||||
\(564\) | −3.47028 | −0.146125 | ||||||||
\(565\) | 26.3104 | 1.10689 | ||||||||
\(566\) | −10.0881 | −0.424033 | ||||||||
\(567\) | 30.2542 | 1.27056 | ||||||||
\(568\) | −15.1244 | −0.634608 | ||||||||
\(569\) | −40.2358 | −1.68677 | −0.843387 | − | 0.537307i | \(-0.819442\pi\) | ||||
−0.843387 | + | 0.537307i | \(0.819442\pi\) | |||||||
\(570\) | 8.30526 | 0.347869 | ||||||||
\(571\) | −34.6012 | −1.44801 | −0.724007 | − | 0.689792i | \(-0.757702\pi\) | ||||
−0.724007 | + | 0.689792i | \(0.757702\pi\) | |||||||
\(572\) | 17.1489 | 0.717033 | ||||||||
\(573\) | −40.1996 | −1.67936 | ||||||||
\(574\) | 9.60061 | 0.400722 | ||||||||
\(575\) | 33.3219 | 1.38962 | ||||||||
\(576\) | 2.73936 | 0.114140 | ||||||||
\(577\) | −14.3364 | −0.596833 | −0.298416 | − | 0.954436i | \(-0.596458\pi\) | ||||
−0.298416 | + | 0.954436i | \(0.596458\pi\) | |||||||
\(578\) | −8.48179 | −0.352796 | ||||||||
\(579\) | 13.7211 | 0.570229 | ||||||||
\(580\) | 14.4792 | 0.601216 | ||||||||
\(581\) | 31.1422 | 1.29200 | ||||||||
\(582\) | −8.78083 | −0.363977 | ||||||||
\(583\) | −65.3045 | −2.70464 | ||||||||
\(584\) | 5.48450 | 0.226950 | ||||||||
\(585\) | 34.1924 | 1.41368 | ||||||||
\(586\) | 11.3310 | 0.468081 | ||||||||
\(587\) | −31.4574 | −1.29839 | −0.649193 | − | 0.760624i | \(-0.724893\pi\) | ||||
−0.649193 | + | 0.760624i | \(0.724893\pi\) | |||||||
\(588\) | −6.46870 | −0.266764 | ||||||||
\(589\) | 6.99380 | 0.288175 | ||||||||
\(590\) | −34.9306 | −1.43807 | ||||||||
\(591\) | −10.0097 | −0.411744 | ||||||||
\(592\) | 0.716100 | 0.0294315 | ||||||||
\(593\) | 11.1381 | 0.457386 | 0.228693 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228693 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(594\) | −2.97405 | −0.122027 | ||||||||
\(595\) | 31.5126 | 1.29189 | ||||||||
\(596\) | 4.21051 | 0.172469 | ||||||||
\(597\) | −22.7639 | −0.931663 | ||||||||
\(598\) | −17.0945 | −0.699048 | ||||||||
\(599\) | 13.2168 | 0.540025 | 0.270012 | − | 0.962857i | \(-0.412972\pi\) | ||||
0.270012 | + | 0.962857i | \(0.412972\pi\) | |||||||
\(600\) | −16.8137 | −0.686416 | ||||||||
\(601\) | −22.6203 | −0.922702 | −0.461351 | − | 0.887218i | \(-0.652635\pi\) | ||||
−0.461351 | + | 0.887218i | \(0.652635\pi\) | |||||||
\(602\) | −1.79512 | −0.0731635 | ||||||||
\(603\) | −2.01609 | −0.0821017 | ||||||||
\(604\) | 17.5187 | 0.712824 | ||||||||
\(605\) | −40.5119 | −1.64704 | ||||||||
\(606\) | −20.8034 | −0.845082 | ||||||||
\(607\) | 3.54583 | 0.143921 | 0.0719604 | − | 0.997407i | \(-0.477074\pi\) | ||||
0.0719604 | + | 0.997407i | \(0.477074\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −31.1633 | −1.26280 | ||||||||
\(610\) | 4.30548 | 0.174324 | ||||||||
\(611\) | −5.21546 | −0.210995 | ||||||||
\(612\) | 7.99509 | 0.323183 | ||||||||
\(613\) | −22.4850 | −0.908159 | −0.454080 | − | 0.890961i | \(-0.650032\pi\) | ||||
−0.454080 | + | 0.890961i | \(0.650032\pi\) | |||||||
\(614\) | −20.0815 | −0.810422 | ||||||||
\(615\) | −25.6014 | −1.03235 | ||||||||
\(616\) | 14.8343 | 0.597691 | ||||||||
\(617\) | 20.6460 | 0.831177 | 0.415588 | − | 0.909553i | \(-0.363576\pi\) | ||||
0.415588 | + | 0.909553i | \(0.363576\pi\) | |||||||
\(618\) | 19.7929 | 0.796187 | ||||||||
\(619\) | −23.9668 | −0.963306 | −0.481653 | − | 0.876362i | \(-0.659963\pi\) | ||||
−0.481653 | + | 0.876362i | \(0.659963\pi\) | |||||||
\(620\) | −24.2457 | −0.973731 | ||||||||
\(621\) | 2.96461 | 0.118966 | ||||||||
\(622\) | 22.7007 | 0.910214 | ||||||||
\(623\) | −20.3969 | −0.817185 | ||||||||
\(624\) | 8.62563 | 0.345302 | ||||||||
\(625\) | −10.8351 | −0.433403 | ||||||||
\(626\) | 19.0345 | 0.760770 | ||||||||
\(627\) | 11.4106 | 0.455697 | ||||||||
\(628\) | −10.0118 | −0.399512 | ||||||||
\(629\) | 2.09001 | 0.0833340 | ||||||||
\(630\) | 29.5774 | 1.17839 | ||||||||
\(631\) | 33.5332 | 1.33494 | 0.667468 | − | 0.744638i | \(-0.267378\pi\) | ||||
0.667468 | + | 0.744638i | \(0.267378\pi\) | |||||||
\(632\) | −3.39442 | −0.135023 | ||||||||
\(633\) | 2.39570 | 0.0952204 | ||||||||
\(634\) | −1.34673 | −0.0534856 | ||||||||
\(635\) | −18.0373 | −0.715787 | ||||||||
\(636\) | −32.8471 | −1.30247 | ||||||||
\(637\) | −9.72174 | −0.385189 | ||||||||
\(638\) | 19.8930 | 0.787573 | ||||||||
\(639\) | −41.4313 | −1.63900 | ||||||||
\(640\) | −3.46674 | −0.137035 | ||||||||
\(641\) | 5.40276 | 0.213396 | 0.106698 | − | 0.994291i | \(-0.465972\pi\) | ||||
0.106698 | + | 0.994291i | \(0.465972\pi\) | |||||||
\(642\) | −5.02618 | −0.198368 | ||||||||
\(643\) | 8.77311 | 0.345978 | 0.172989 | − | 0.984924i | \(-0.444658\pi\) | ||||
0.172989 | + | 0.984924i | \(0.444658\pi\) | |||||||
\(644\) | −14.7872 | −0.582699 | ||||||||
\(645\) | 4.78693 | 0.188485 | ||||||||
\(646\) | 2.91860 | 0.114831 | ||||||||
\(647\) | 31.4847 | 1.23779 | 0.618895 | − | 0.785473i | \(-0.287581\pi\) | ||||
0.618895 | + | 0.785473i | \(0.287581\pi\) | |||||||
\(648\) | −9.71398 | −0.381601 | ||||||||
\(649\) | −47.9913 | −1.88382 | ||||||||
\(650\) | −25.2691 | −0.991137 | ||||||||
\(651\) | 52.1836 | 2.04524 | ||||||||
\(652\) | −6.70898 | −0.262744 | ||||||||
\(653\) | −13.0862 | −0.512101 | −0.256050 | − | 0.966663i | \(-0.582421\pi\) | ||||
−0.256050 | + | 0.966663i | \(0.582421\pi\) | |||||||
\(654\) | 16.4234 | 0.642207 | ||||||||
\(655\) | −4.41886 | −0.172659 | ||||||||
\(656\) | −3.08255 | −0.120353 | ||||||||
\(657\) | 15.0240 | 0.586143 | ||||||||
\(658\) | −4.51151 | −0.175877 | ||||||||
\(659\) | −41.3855 | −1.61215 | −0.806074 | − | 0.591814i | \(-0.798412\pi\) | ||||
−0.806074 | + | 0.591814i | \(0.798412\pi\) | |||||||
\(660\) | −39.5577 | −1.53978 | ||||||||
\(661\) | 2.68407 | 0.104398 | 0.0521991 | − | 0.998637i | \(-0.483377\pi\) | ||||
0.0521991 | + | 0.998637i | \(0.483377\pi\) | |||||||
\(662\) | −7.28727 | −0.283228 | ||||||||
\(663\) | 25.1747 | 0.977706 | ||||||||
\(664\) | −9.99910 | −0.388040 | ||||||||
\(665\) | 10.7972 | 0.418696 | ||||||||
\(666\) | 1.96166 | 0.0760126 | ||||||||
\(667\) | −19.8299 | −0.767818 | ||||||||
\(668\) | 4.55028 | 0.176056 | ||||||||
\(669\) | 0.632804 | 0.0244656 | ||||||||
\(670\) | 2.55142 | 0.0985701 | ||||||||
\(671\) | 5.91532 | 0.228358 | ||||||||
\(672\) | 7.46140 | 0.287830 | ||||||||
\(673\) | −29.2692 | −1.12825 | −0.564123 | − | 0.825691i | \(-0.690786\pi\) | ||||
−0.564123 | + | 0.825691i | \(0.690786\pi\) | |||||||
\(674\) | −8.73141 | −0.336322 | ||||||||
\(675\) | 4.38229 | 0.168674 | ||||||||
\(676\) | −0.0366224 | −0.00140855 | ||||||||
\(677\) | −0.312598 | −0.0120141 | −0.00600707 | − | 0.999982i | \(-0.501912\pi\) | ||||
−0.00600707 | + | 0.999982i | \(0.501912\pi\) | |||||||
\(678\) | 18.1818 | 0.698269 | ||||||||
\(679\) | −11.4154 | −0.438084 | ||||||||
\(680\) | −10.1180 | −0.388008 | ||||||||
\(681\) | −30.1688 | −1.15607 | ||||||||
\(682\) | −33.3113 | −1.27556 | ||||||||
\(683\) | −27.8757 | −1.06663 | −0.533317 | − | 0.845915i | \(-0.679055\pi\) | ||||
−0.533317 | + | 0.845915i | \(0.679055\pi\) | |||||||
\(684\) | 2.73936 | 0.104742 | ||||||||
\(685\) | 13.2165 | 0.504976 | ||||||||
\(686\) | 13.3920 | 0.511307 | ||||||||
\(687\) | −7.31580 | −0.279115 | ||||||||
\(688\) | 0.576373 | 0.0219740 | ||||||||
\(689\) | −49.3656 | −1.88068 | ||||||||
\(690\) | 39.4322 | 1.50116 | ||||||||
\(691\) | −14.7712 | −0.561922 | −0.280961 | − | 0.959719i | \(-0.590653\pi\) | ||||
−0.280961 | + | 0.959719i | \(0.590653\pi\) | |||||||
\(692\) | −1.75815 | −0.0668347 | ||||||||
\(693\) | 40.6365 | 1.54365 | ||||||||
\(694\) | 18.7884 | 0.713199 | ||||||||
\(695\) | −20.3765 | −0.772924 | ||||||||
\(696\) | 10.0059 | 0.379272 | ||||||||
\(697\) | −8.99672 | −0.340775 | ||||||||
\(698\) | 22.0275 | 0.833753 | ||||||||
\(699\) | 58.1159 | 2.19815 | ||||||||
\(700\) | −21.8585 | −0.826173 | ||||||||
\(701\) | 32.3364 | 1.22133 | 0.610664 | − | 0.791890i | \(-0.290903\pi\) | ||||
0.610664 | + | 0.791890i | \(0.290903\pi\) | |||||||
\(702\) | −2.24817 | −0.0848517 | ||||||||
\(703\) | 0.716100 | 0.0270082 | ||||||||
\(704\) | −4.76297 | −0.179511 | ||||||||
\(705\) | 12.0306 | 0.453098 | ||||||||
\(706\) | −23.7823 | −0.895060 | ||||||||
\(707\) | −27.0453 | −1.01714 | ||||||||
\(708\) | −24.1389 | −0.907194 | ||||||||
\(709\) | 19.8481 | 0.745412 | 0.372706 | − | 0.927949i | \(-0.378430\pi\) | ||||
0.372706 | + | 0.927949i | \(0.378430\pi\) | |||||||
\(710\) | 52.4325 | 1.96776 | ||||||||
\(711\) | −9.29854 | −0.348722 | ||||||||
\(712\) | 6.54901 | 0.245435 | ||||||||
\(713\) | 33.2056 | 1.24356 | ||||||||
\(714\) | 21.7768 | 0.814978 | ||||||||
\(715\) | −59.4509 | −2.22334 | ||||||||
\(716\) | −13.5938 | −0.508025 | ||||||||
\(717\) | −39.7796 | −1.48560 | ||||||||
\(718\) | 3.73402 | 0.139353 | ||||||||
\(719\) | 26.7083 | 0.996050 | 0.498025 | − | 0.867163i | \(-0.334059\pi\) | ||||
0.498025 | + | 0.867163i | \(0.334059\pi\) | |||||||
\(720\) | −9.49666 | −0.353919 | ||||||||
\(721\) | 25.7316 | 0.958294 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −65.5673 | −2.43847 | ||||||||
\(724\) | −15.0394 | −0.558936 | ||||||||
\(725\) | −29.3126 | −1.08864 | ||||||||
\(726\) | −27.9959 | −1.03902 | ||||||||
\(727\) | −19.6278 | −0.727956 | −0.363978 | − | 0.931407i | \(-0.618582\pi\) | ||||
−0.363978 | + | 0.931407i | \(0.618582\pi\) | |||||||
\(728\) | 11.2137 | 0.415606 | ||||||||
\(729\) | −22.1224 | −0.819349 | ||||||||
\(730\) | −19.0133 | −0.703715 | ||||||||
\(731\) | 1.68220 | 0.0622185 | ||||||||
\(732\) | 2.97531 | 0.109971 | ||||||||
\(733\) | −51.2301 | −1.89223 | −0.946113 | − | 0.323836i | \(-0.895028\pi\) | ||||
−0.946113 | + | 0.323836i | \(0.895028\pi\) | |||||||
\(734\) | 14.5365 | 0.536552 | ||||||||
\(735\) | 22.4253 | 0.827169 | ||||||||
\(736\) | 4.74786 | 0.175009 | ||||||||
\(737\) | 3.50541 | 0.129124 | ||||||||
\(738\) | −8.44422 | −0.310836 | ||||||||
\(739\) | 41.3831 | 1.52230 | 0.761151 | − | 0.648575i | \(-0.224635\pi\) | ||||
0.761151 | + | 0.648575i | \(0.224635\pi\) | |||||||
\(740\) | −2.48253 | −0.0912596 | ||||||||
\(741\) | 8.62563 | 0.316870 | ||||||||
\(742\) | −42.7026 | −1.56766 | ||||||||
\(743\) | −18.8532 | −0.691657 | −0.345829 | − | 0.938298i | \(-0.612402\pi\) | ||||
−0.345829 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(744\) | −16.7550 | −0.614269 | ||||||||
\(745\) | −14.5967 | −0.534783 | ||||||||
\(746\) | 3.93186 | 0.143956 | ||||||||
\(747\) | −27.3911 | −1.00219 | ||||||||
\(748\) | −13.9012 | −0.508278 | ||||||||
\(749\) | −6.53424 | −0.238756 | ||||||||
\(750\) | 16.7624 | 0.612076 | ||||||||
\(751\) | −5.65452 | −0.206337 | −0.103168 | − | 0.994664i | \(-0.532898\pi\) | ||||
−0.103168 | + | 0.994664i | \(0.532898\pi\) | |||||||
\(752\) | 1.44855 | 0.0528232 | ||||||||
\(753\) | 1.78253 | 0.0649589 | ||||||||
\(754\) | 15.0377 | 0.547642 | ||||||||
\(755\) | −60.7326 | −2.21029 | ||||||||
\(756\) | −1.94473 | −0.0707291 | ||||||||
\(757\) | 15.5648 | 0.565713 | 0.282856 | − | 0.959162i | \(-0.408718\pi\) | ||||
0.282856 | + | 0.959162i | \(0.408718\pi\) | |||||||
\(758\) | 11.1988 | 0.406757 | ||||||||
\(759\) | 54.1761 | 1.96647 | ||||||||
\(760\) | −3.46674 | −0.125752 | ||||||||
\(761\) | −20.0597 | −0.727165 | −0.363583 | − | 0.931562i | \(-0.618447\pi\) | ||||
−0.363583 | + | 0.931562i | \(0.618447\pi\) | |||||||
\(762\) | −12.4647 | −0.451547 | ||||||||
\(763\) | 21.3511 | 0.772963 | ||||||||
\(764\) | 16.7799 | 0.607077 | ||||||||
\(765\) | −27.7169 | −1.00211 | ||||||||
\(766\) | 25.4159 | 0.918314 | ||||||||
\(767\) | −36.2781 | −1.30992 | ||||||||
\(768\) | −2.39570 | −0.0864473 | ||||||||
\(769\) | 33.8449 | 1.22048 | 0.610240 | − | 0.792217i | \(-0.291073\pi\) | ||||
0.610240 | + | 0.792217i | \(0.291073\pi\) | |||||||
\(770\) | −51.4266 | −1.85329 | ||||||||
\(771\) | −64.1924 | −2.31183 | ||||||||
\(772\) | −5.72740 | −0.206133 | ||||||||
\(773\) | 3.33000 | 0.119772 | 0.0598859 | − | 0.998205i | \(-0.480926\pi\) | ||||
0.0598859 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(774\) | 1.57889 | 0.0567522 | ||||||||
\(775\) | 49.0845 | 1.76317 | ||||||||
\(776\) | 3.66525 | 0.131575 | ||||||||
\(777\) | 5.34311 | 0.191683 | ||||||||
\(778\) | −22.9851 | −0.824054 | ||||||||
\(779\) | −3.08255 | −0.110444 | ||||||||
\(780\) | −29.9028 | −1.07069 | ||||||||
\(781\) | 72.0373 | 2.57770 | ||||||||
\(782\) | 13.8571 | 0.495529 | ||||||||
\(783\) | −2.60791 | −0.0931992 | ||||||||
\(784\) | 2.70013 | 0.0964333 | ||||||||
\(785\) | 34.7081 | 1.23879 | ||||||||
\(786\) | −3.05366 | −0.108920 | ||||||||
\(787\) | 43.9440 | 1.56643 | 0.783217 | − | 0.621748i | \(-0.213577\pi\) | ||||
0.783217 | + | 0.621748i | \(0.213577\pi\) | |||||||
\(788\) | 4.17820 | 0.148842 | ||||||||
\(789\) | −5.19906 | −0.185092 | ||||||||
\(790\) | 11.7676 | 0.418671 | ||||||||
\(791\) | 23.6371 | 0.840439 | ||||||||
\(792\) | −13.0475 | −0.463623 | ||||||||
\(793\) | 4.47156 | 0.158790 | ||||||||
\(794\) | −26.3767 | −0.936074 | ||||||||
\(795\) | 113.872 | 4.03864 | ||||||||
\(796\) | 9.50199 | 0.336789 | ||||||||
\(797\) | −41.4672 | −1.46884 | −0.734421 | − | 0.678694i | \(-0.762546\pi\) | ||||
−0.734421 | + | 0.678694i | \(0.762546\pi\) | |||||||
\(798\) | 7.46140 | 0.264131 | ||||||||
\(799\) | 4.22773 | 0.149566 | ||||||||
\(800\) | 7.01829 | 0.248134 | ||||||||
\(801\) | 17.9401 | 0.633883 | ||||||||
\(802\) | 14.0205 | 0.495081 | ||||||||
\(803\) | −26.1225 | −0.921843 | ||||||||
\(804\) | 1.76317 | 0.0621821 | ||||||||
\(805\) | 51.2635 | 1.80680 | ||||||||
\(806\) | −25.1810 | −0.886962 | ||||||||
\(807\) | 36.5738 | 1.28746 | ||||||||
\(808\) | 8.68367 | 0.305490 | ||||||||
\(809\) | 46.9593 | 1.65100 | 0.825501 | − | 0.564401i | \(-0.190893\pi\) | ||||
0.825501 | + | 0.564401i | \(0.190893\pi\) | |||||||
\(810\) | 33.6759 | 1.18325 | ||||||||
\(811\) | 9.54285 | 0.335095 | 0.167547 | − | 0.985864i | \(-0.446415\pi\) | ||||
0.167547 | + | 0.985864i | \(0.446415\pi\) | |||||||
\(812\) | 13.0080 | 0.456493 | ||||||||
\(813\) | 15.3431 | 0.538106 | ||||||||
\(814\) | −3.41076 | −0.119547 | ||||||||
\(815\) | 23.2583 | 0.814702 | ||||||||
\(816\) | −6.99207 | −0.244772 | ||||||||
\(817\) | 0.576373 | 0.0201647 | ||||||||
\(818\) | 7.58354 | 0.265152 | ||||||||
\(819\) | 30.7183 | 1.07338 | ||||||||
\(820\) | 10.6864 | 0.373185 | ||||||||
\(821\) | 35.7091 | 1.24626 | 0.623128 | − | 0.782120i | \(-0.285861\pi\) | ||||
0.623128 | + | 0.782120i | \(0.285861\pi\) | |||||||
\(822\) | 9.13328 | 0.318560 | ||||||||
\(823\) | −33.9380 | −1.18300 | −0.591501 | − | 0.806304i | \(-0.701465\pi\) | ||||
−0.591501 | + | 0.806304i | \(0.701465\pi\) | |||||||
\(824\) | −8.26186 | −0.287815 | ||||||||
\(825\) | 80.0831 | 2.78814 | ||||||||
\(826\) | −31.3815 | −1.09190 | ||||||||
\(827\) | −31.2810 | −1.08775 | −0.543874 | − | 0.839167i | \(-0.683043\pi\) | ||||
−0.543874 | + | 0.839167i | \(0.683043\pi\) | |||||||
\(828\) | 13.0061 | 0.451994 | ||||||||
\(829\) | −24.0426 | −0.835034 | −0.417517 | − | 0.908669i | \(-0.637100\pi\) | ||||
−0.417517 | + | 0.908669i | \(0.637100\pi\) | |||||||
\(830\) | 34.6643 | 1.20321 | ||||||||
\(831\) | 70.5739 | 2.44818 | ||||||||
\(832\) | −3.60047 | −0.124824 | ||||||||
\(833\) | 7.88060 | 0.273046 | ||||||||
\(834\) | −14.0812 | −0.487592 | ||||||||
\(835\) | −15.7746 | −0.545904 | ||||||||
\(836\) | −4.76297 | −0.164731 | ||||||||
\(837\) | 4.36700 | 0.150946 | ||||||||
\(838\) | −2.08611 | −0.0720636 | ||||||||
\(839\) | 9.46822 | 0.326879 | 0.163440 | − | 0.986553i | \(-0.447741\pi\) | ||||
0.163440 | + | 0.986553i | \(0.447741\pi\) | |||||||
\(840\) | −25.8668 | −0.892488 | ||||||||
\(841\) | −11.5560 | −0.398483 | ||||||||
\(842\) | −11.5154 | −0.396846 | ||||||||
\(843\) | 5.64913 | 0.194566 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 0.126960 | 0.00436756 | ||||||||
\(846\) | 3.96810 | 0.136426 | ||||||||
\(847\) | −36.3957 | −1.25057 | ||||||||
\(848\) | 13.7109 | 0.470834 | ||||||||
\(849\) | 24.1679 | 0.829441 | ||||||||
\(850\) | 20.4836 | 0.702580 | ||||||||
\(851\) | 3.39994 | 0.116549 | ||||||||
\(852\) | 36.2336 | 1.24134 | ||||||||
\(853\) | −2.30635 | −0.0789681 | −0.0394840 | − | 0.999220i | \(-0.512571\pi\) | ||||
−0.0394840 | + | 0.999220i | \(0.512571\pi\) | |||||||
\(854\) | 3.86802 | 0.132361 | ||||||||
\(855\) | −9.49666 | −0.324779 | ||||||||
\(856\) | 2.09800 | 0.0717083 | ||||||||
\(857\) | −45.5345 | −1.55543 | −0.777714 | − | 0.628618i | \(-0.783621\pi\) | ||||
−0.777714 | + | 0.628618i | \(0.783621\pi\) | |||||||
\(858\) | −41.0836 | −1.40257 | ||||||||
\(859\) | 2.77452 | 0.0946654 | 0.0473327 | − | 0.998879i | \(-0.484928\pi\) | ||||
0.0473327 | + | 0.998879i | \(0.484928\pi\) | |||||||
\(860\) | −1.99814 | −0.0681359 | ||||||||
\(861\) | −23.0002 | −0.783843 | ||||||||
\(862\) | −9.52295 | −0.324353 | ||||||||
\(863\) | 3.11531 | 0.106047 | 0.0530233 | − | 0.998593i | \(-0.483114\pi\) | ||||
0.0530233 | + | 0.998593i | \(0.483114\pi\) | |||||||
\(864\) | 0.624410 | 0.0212429 | ||||||||
\(865\) | 6.09504 | 0.207238 | ||||||||
\(866\) | 1.75745 | 0.0597204 | ||||||||
\(867\) | 20.3198 | 0.690096 | ||||||||
\(868\) | −21.7822 | −0.739337 | ||||||||
\(869\) | 16.1675 | 0.548445 | ||||||||
\(870\) | −34.6878 | −1.17602 | ||||||||
\(871\) | 2.64984 | 0.0897866 | ||||||||
\(872\) | −6.85539 | −0.232153 | ||||||||
\(873\) | 10.0405 | 0.339818 | ||||||||
\(874\) | 4.74786 | 0.160599 | ||||||||
\(875\) | 21.7918 | 0.736697 | ||||||||
\(876\) | −13.1392 | −0.443932 | ||||||||
\(877\) | −36.4019 | −1.22920 | −0.614602 | − | 0.788837i | \(-0.710683\pi\) | ||||
−0.614602 | + | 0.788837i | \(0.710683\pi\) | |||||||
\(878\) | −14.5340 | −0.490497 | ||||||||
\(879\) | −27.1457 | −0.915603 | ||||||||
\(880\) | 16.5120 | 0.556619 | ||||||||
\(881\) | −10.2607 | −0.345692 | −0.172846 | − | 0.984949i | \(-0.555296\pi\) | ||||
−0.172846 | + | 0.984949i | \(0.555296\pi\) | |||||||
\(882\) | 7.39664 | 0.249058 | ||||||||
\(883\) | −58.1186 | −1.95585 | −0.977924 | − | 0.208962i | \(-0.932992\pi\) | ||||
−0.977924 | + | 0.208962i | \(0.932992\pi\) | |||||||
\(884\) | −10.5083 | −0.353433 | ||||||||
\(885\) | 83.6831 | 2.81298 | ||||||||
\(886\) | −19.7877 | −0.664781 | ||||||||
\(887\) | 45.9652 | 1.54336 | 0.771681 | − | 0.636010i | \(-0.219416\pi\) | ||||
0.771681 | + | 0.636010i | \(0.219416\pi\) | |||||||
\(888\) | −1.71556 | −0.0575703 | ||||||||
\(889\) | −16.2046 | −0.543484 | ||||||||
\(890\) | −22.7037 | −0.761030 | ||||||||
\(891\) | 46.2674 | 1.55002 | ||||||||
\(892\) | −0.264142 | −0.00884413 | ||||||||
\(893\) | 1.44855 | 0.0484738 | ||||||||
\(894\) | −10.0871 | −0.337363 | ||||||||
\(895\) | 47.1263 | 1.57526 | ||||||||
\(896\) | −3.11450 | −0.104048 | ||||||||
\(897\) | 40.9533 | 1.36739 | ||||||||
\(898\) | −36.7356 | −1.22588 | ||||||||
\(899\) | −29.2103 | −0.974219 | ||||||||
\(900\) | 19.2256 | 0.640854 | ||||||||
\(901\) | 40.0165 | 1.33314 | ||||||||
\(902\) | 14.6821 | 0.488860 | ||||||||
\(903\) | 4.30055 | 0.143113 | ||||||||
\(904\) | −7.58937 | −0.252419 | ||||||||
\(905\) | 52.1378 | 1.73312 | ||||||||
\(906\) | −41.9694 | −1.39434 | ||||||||
\(907\) | 9.20336 | 0.305592 | 0.152796 | − | 0.988258i | \(-0.451172\pi\) | ||||
0.152796 | + | 0.988258i | \(0.451172\pi\) | |||||||
\(908\) | 12.5929 | 0.417910 | ||||||||
\(909\) | 23.7877 | 0.788989 | ||||||||
\(910\) | −38.8749 | −1.28869 | ||||||||
\(911\) | 47.9069 | 1.58722 | 0.793612 | − | 0.608424i | \(-0.208198\pi\) | ||||
0.793612 | + | 0.608424i | \(0.208198\pi\) | |||||||
\(912\) | −2.39570 | −0.0793294 | ||||||||
\(913\) | 47.6254 | 1.57617 | ||||||||
\(914\) | 21.2778 | 0.703806 | ||||||||
\(915\) | −10.3146 | −0.340991 | ||||||||
\(916\) | 3.05372 | 0.100898 | ||||||||
\(917\) | −3.96988 | −0.131097 | ||||||||
\(918\) | 1.82240 | 0.0601482 | ||||||||
\(919\) | −2.11610 | −0.0698038 | −0.0349019 | − | 0.999391i | \(-0.511112\pi\) | ||||
−0.0349019 | + | 0.999391i | \(0.511112\pi\) | |||||||
\(920\) | −16.4596 | −0.542657 | ||||||||
\(921\) | 48.1091 | 1.58525 | ||||||||
\(922\) | 15.0555 | 0.495826 | ||||||||
\(923\) | 54.4551 | 1.79241 | ||||||||
\(924\) | −35.5385 | −1.16913 | ||||||||
\(925\) | 5.02579 | 0.165247 | ||||||||
\(926\) | 31.3140 | 1.02904 | ||||||||
\(927\) | −22.6322 | −0.743339 | ||||||||
\(928\) | −4.17660 | −0.137104 | ||||||||
\(929\) | 59.1023 | 1.93908 | 0.969542 | − | 0.244925i | \(-0.0787632\pi\) | ||||
0.969542 | + | 0.244925i | \(0.0787632\pi\) | |||||||
\(930\) | 58.0853 | 1.90469 | ||||||||
\(931\) | 2.70013 | 0.0884932 | ||||||||
\(932\) | −24.2585 | −0.794613 | ||||||||
\(933\) | −54.3839 | −1.78045 | ||||||||
\(934\) | 3.29466 | 0.107805 | ||||||||
\(935\) | 48.1918 | 1.57604 | ||||||||
\(936\) | −9.86299 | −0.322382 | ||||||||
\(937\) | 53.9137 | 1.76128 | 0.880642 | − | 0.473782i | \(-0.157112\pi\) | ||||
0.880642 | + | 0.473782i | \(0.157112\pi\) | |||||||
\(938\) | 2.29219 | 0.0748426 | ||||||||
\(939\) | −45.6008 | −1.48812 | ||||||||
\(940\) | −5.02174 | −0.163791 | ||||||||
\(941\) | −1.22707 | −0.0400013 | −0.0200007 | − | 0.999800i | \(-0.506367\pi\) | ||||
−0.0200007 | + | 0.999800i | \(0.506367\pi\) | |||||||
\(942\) | 23.9851 | 0.781477 | ||||||||
\(943\) | −14.6355 | −0.476598 | ||||||||
\(944\) | 10.0759 | 0.327943 | ||||||||
\(945\) | 6.74186 | 0.219313 | ||||||||
\(946\) | −2.74525 | −0.0892557 | ||||||||
\(947\) | 43.1175 | 1.40113 | 0.700566 | − | 0.713588i | \(-0.252931\pi\) | ||||
0.700566 | + | 0.713588i | \(0.252931\pi\) | |||||||
\(948\) | 8.13199 | 0.264115 | ||||||||
\(949\) | −19.7468 | −0.641007 | ||||||||
\(950\) | 7.01829 | 0.227703 | ||||||||
\(951\) | 3.22636 | 0.104622 | ||||||||
\(952\) | −9.08998 | −0.294608 | ||||||||
\(953\) | −3.33059 | −0.107888 | −0.0539442 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539442 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(954\) | 37.5591 | 1.21602 | ||||||||
\(955\) | −58.1717 | −1.88239 | ||||||||
\(956\) | 16.6046 | 0.537031 | ||||||||
\(957\) | −47.6577 | −1.54055 | ||||||||
\(958\) | 34.0016 | 1.09854 | ||||||||
\(959\) | 11.8736 | 0.383420 | ||||||||
\(960\) | 8.30526 | 0.268051 | ||||||||
\(961\) | 17.9133 | 0.577848 | ||||||||
\(962\) | −2.57829 | −0.0831275 | ||||||||
\(963\) | 5.74719 | 0.185201 | ||||||||
\(964\) | 27.3688 | 0.881489 | ||||||||
\(965\) | 19.8554 | 0.639168 | ||||||||
\(966\) | 35.4257 | 1.13980 | ||||||||
\(967\) | 33.5724 | 1.07962 | 0.539808 | − | 0.841788i | \(-0.318497\pi\) | ||||
0.539808 | + | 0.841788i | \(0.318497\pi\) | |||||||
\(968\) | 11.6859 | 0.375599 | ||||||||
\(969\) | −6.99207 | −0.224618 | ||||||||
\(970\) | −12.7065 | −0.407980 | ||||||||
\(971\) | 5.37828 | 0.172597 | 0.0862986 | − | 0.996269i | \(-0.472496\pi\) | ||||
0.0862986 | + | 0.996269i | \(0.472496\pi\) | |||||||
\(972\) | 21.3985 | 0.686358 | ||||||||
\(973\) | −18.3061 | −0.586868 | ||||||||
\(974\) | −13.9227 | −0.446112 | ||||||||
\(975\) | 60.5372 | 1.93874 | ||||||||
\(976\) | −1.24194 | −0.0397535 | ||||||||
\(977\) | 11.7975 | 0.377434 | 0.188717 | − | 0.982031i | \(-0.439567\pi\) | ||||
0.188717 | + | 0.982031i | \(0.439567\pi\) | |||||||
\(978\) | 16.0727 | 0.513947 | ||||||||
\(979\) | −31.1928 | −0.996925 | ||||||||
\(980\) | −9.36065 | −0.299015 | ||||||||
\(981\) | −18.7794 | −0.599580 | ||||||||
\(982\) | 34.9576 | 1.11554 | ||||||||
\(983\) | 57.1198 | 1.82184 | 0.910920 | − | 0.412584i | \(-0.135374\pi\) | ||||
0.910920 | + | 0.412584i | \(0.135374\pi\) | |||||||
\(984\) | 7.38485 | 0.235421 | ||||||||
\(985\) | −14.4847 | −0.461522 | ||||||||
\(986\) | −12.1898 | −0.388203 | ||||||||
\(987\) | 10.8082 | 0.344029 | ||||||||
\(988\) | −3.60047 | −0.114546 | ||||||||
\(989\) | 2.73654 | 0.0870169 | ||||||||
\(990\) | 45.2323 | 1.43758 | ||||||||
\(991\) | −51.0080 | −1.62032 | −0.810161 | − | 0.586207i | \(-0.800621\pi\) | ||||
−0.810161 | + | 0.586207i | \(0.800621\pi\) | |||||||
\(992\) | 6.99380 | 0.222054 | ||||||||
\(993\) | 17.4581 | 0.554016 | ||||||||
\(994\) | 47.1051 | 1.49408 | ||||||||
\(995\) | −32.9409 | −1.04430 | ||||||||
\(996\) | 23.9548 | 0.759037 | ||||||||
\(997\) | 13.0379 | 0.412916 | 0.206458 | − | 0.978455i | \(-0.433806\pi\) | ||||
0.206458 | + | 0.978455i | \(0.433806\pi\) | |||||||
\(998\) | 33.8912 | 1.07281 | ||||||||
\(999\) | 0.447140 | 0.0141469 |
(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.d.1.7 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.7 | ✓ | 30 | 1.1 | even | 1 | trivial |