Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6011,2,Mod(1,6011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6011.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: | \(47.9980766550\) |
Analytic rank: | \(1\) |
Dimension: | \(221\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73985 | −1.93737 | −0.968684 | − | 0.248298i | \(-0.920129\pi\) | ||||
−0.968684 | + | 0.248298i | \(0.920129\pi\) | |||||||
\(3\) | 2.92308 | 1.68764 | 0.843821 | − | 0.536624i | \(-0.180301\pi\) | ||||
0.843821 | + | 0.536624i | \(0.180301\pi\) | |||||||
\(4\) | 5.50679 | 2.75339 | ||||||||
\(5\) | −0.916253 | −0.409761 | −0.204880 | − | 0.978787i | \(-0.565681\pi\) | ||||
−0.204880 | + | 0.978787i | \(0.565681\pi\) | |||||||
\(6\) | −8.00881 | −3.26958 | ||||||||
\(7\) | 0.545086 | 0.206023 | 0.103012 | − | 0.994680i | \(-0.467152\pi\) | ||||
0.103012 | + | 0.994680i | \(0.467152\pi\) | |||||||
\(8\) | −9.60807 | −3.39697 | ||||||||
\(9\) | 5.54441 | 1.84814 | ||||||||
\(10\) | 2.51040 | 0.793857 | ||||||||
\(11\) | 5.86455 | 1.76823 | 0.884114 | − | 0.467270i | \(-0.154763\pi\) | ||||
0.884114 | + | 0.467270i | \(0.154763\pi\) | |||||||
\(12\) | 16.0968 | 4.64674 | ||||||||
\(13\) | −3.87648 | −1.07514 | −0.537571 | − | 0.843218i | \(-0.680658\pi\) | ||||
−0.537571 | + | 0.843218i | \(0.680658\pi\) | |||||||
\(14\) | −1.49346 | −0.399143 | ||||||||
\(15\) | −2.67828 | −0.691530 | ||||||||
\(16\) | 15.3111 | 3.82778 | ||||||||
\(17\) | −2.35034 | −0.570040 | −0.285020 | − | 0.958522i | \(-0.592000\pi\) | ||||
−0.285020 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(18\) | −15.1909 | −3.58052 | ||||||||
\(19\) | −4.57651 | −1.04992 | −0.524962 | − | 0.851126i | \(-0.675921\pi\) | ||||
−0.524962 | + | 0.851126i | \(0.675921\pi\) | |||||||
\(20\) | −5.04561 | −1.12823 | ||||||||
\(21\) | 1.59333 | 0.347694 | ||||||||
\(22\) | −16.0680 | −3.42571 | ||||||||
\(23\) | 5.22753 | 1.09001 | 0.545007 | − | 0.838431i | \(-0.316527\pi\) | ||||
0.545007 | + | 0.838431i | \(0.316527\pi\) | |||||||
\(24\) | −28.0852 | −5.73287 | ||||||||
\(25\) | −4.16048 | −0.832096 | ||||||||
\(26\) | 10.6210 | 2.08295 | ||||||||
\(27\) | 7.43752 | 1.43135 | ||||||||
\(28\) | 3.00167 | 0.567263 | ||||||||
\(29\) | −10.2015 | −1.89438 | −0.947189 | − | 0.320677i | \(-0.896090\pi\) | ||||
−0.947189 | + | 0.320677i | \(0.896090\pi\) | |||||||
\(30\) | 7.33810 | 1.33975 | ||||||||
\(31\) | 3.44066 | 0.617960 | 0.308980 | − | 0.951068i | \(-0.400012\pi\) | ||||
0.308980 | + | 0.951068i | \(0.400012\pi\) | |||||||
\(32\) | −22.7340 | −4.01885 | ||||||||
\(33\) | 17.1426 | 2.98414 | ||||||||
\(34\) | 6.43957 | 1.10438 | ||||||||
\(35\) | −0.499437 | −0.0844203 | ||||||||
\(36\) | 30.5319 | 5.08865 | ||||||||
\(37\) | −9.65415 | −1.58713 | −0.793566 | − | 0.608484i | \(-0.791778\pi\) | ||||
−0.793566 | + | 0.608484i | \(0.791778\pi\) | |||||||
\(38\) | 12.5390 | 2.03409 | ||||||||
\(39\) | −11.3313 | −1.81446 | ||||||||
\(40\) | 8.80342 | 1.39194 | ||||||||
\(41\) | −8.52783 | −1.33182 | −0.665912 | − | 0.746030i | \(-0.731957\pi\) | ||||
−0.665912 | + | 0.746030i | \(0.731957\pi\) | |||||||
\(42\) | −4.36549 | −0.673610 | ||||||||
\(43\) | 11.1616 | 1.70213 | 0.851063 | − | 0.525063i | \(-0.175958\pi\) | ||||
0.851063 | + | 0.525063i | \(0.175958\pi\) | |||||||
\(44\) | 32.2948 | 4.86863 | ||||||||
\(45\) | −5.08008 | −0.757294 | ||||||||
\(46\) | −14.3226 | −2.11176 | ||||||||
\(47\) | −4.82469 | −0.703754 | −0.351877 | − | 0.936046i | \(-0.614456\pi\) | ||||
−0.351877 | + | 0.936046i | \(0.614456\pi\) | |||||||
\(48\) | 44.7557 | 6.45992 | ||||||||
\(49\) | −6.70288 | −0.957554 | ||||||||
\(50\) | 11.3991 | 1.61208 | ||||||||
\(51\) | −6.87022 | −0.962024 | ||||||||
\(52\) | −21.3469 | −2.96029 | ||||||||
\(53\) | −5.52216 | −0.758527 | −0.379263 | − | 0.925289i | \(-0.623823\pi\) | ||||
−0.379263 | + | 0.925289i | \(0.623823\pi\) | |||||||
\(54\) | −20.3777 | −2.77306 | ||||||||
\(55\) | −5.37341 | −0.724551 | ||||||||
\(56\) | −5.23723 | −0.699854 | ||||||||
\(57\) | −13.3775 | −1.77190 | ||||||||
\(58\) | 27.9507 | 3.67010 | ||||||||
\(59\) | −4.39156 | −0.571733 | −0.285866 | − | 0.958269i | \(-0.592281\pi\) | ||||
−0.285866 | + | 0.958269i | \(0.592281\pi\) | |||||||
\(60\) | −14.7487 | −1.90405 | ||||||||
\(61\) | −14.8397 | −1.90003 | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||||
−0.950014 | + | 0.312207i | \(0.898932\pi\) | |||||||
\(62\) | −9.42689 | −1.19722 | ||||||||
\(63\) | 3.02218 | 0.380759 | ||||||||
\(64\) | 31.6657 | 3.95821 | ||||||||
\(65\) | 3.55184 | 0.440551 | ||||||||
\(66\) | −46.9681 | −5.78137 | ||||||||
\(67\) | −10.8837 | −1.32966 | −0.664831 | − | 0.746994i | \(-0.731496\pi\) | ||||
−0.664831 | + | 0.746994i | \(0.731496\pi\) | |||||||
\(68\) | −12.9428 | −1.56954 | ||||||||
\(69\) | 15.2805 | 1.83956 | ||||||||
\(70\) | 1.36838 | 0.163553 | ||||||||
\(71\) | 6.69850 | 0.794965 | 0.397483 | − | 0.917610i | \(-0.369884\pi\) | ||||
0.397483 | + | 0.917610i | \(0.369884\pi\) | |||||||
\(72\) | −53.2711 | −6.27806 | ||||||||
\(73\) | −2.02065 | −0.236499 | −0.118250 | − | 0.992984i | \(-0.537728\pi\) | ||||
−0.118250 | + | 0.992984i | \(0.537728\pi\) | |||||||
\(74\) | 26.4509 | 3.07486 | ||||||||
\(75\) | −12.1614 | −1.40428 | ||||||||
\(76\) | −25.2019 | −2.89085 | ||||||||
\(77\) | 3.19669 | 0.364296 | ||||||||
\(78\) | 31.0460 | 3.51527 | ||||||||
\(79\) | −12.4402 | −1.39963 | −0.699816 | − | 0.714324i | \(-0.746734\pi\) | ||||
−0.699816 | + | 0.714324i | \(0.746734\pi\) | |||||||
\(80\) | −14.0289 | −1.56847 | ||||||||
\(81\) | 5.10726 | 0.567473 | ||||||||
\(82\) | 23.3650 | 2.58023 | ||||||||
\(83\) | 7.09019 | 0.778249 | 0.389124 | − | 0.921185i | \(-0.372778\pi\) | ||||
0.389124 | + | 0.921185i | \(0.372778\pi\) | |||||||
\(84\) | 8.77414 | 0.957337 | ||||||||
\(85\) | 2.15350 | 0.233580 | ||||||||
\(86\) | −30.5811 | −3.29764 | ||||||||
\(87\) | −29.8199 | −3.19703 | ||||||||
\(88\) | −56.3470 | −6.00661 | ||||||||
\(89\) | −6.91660 | −0.733158 | −0.366579 | − | 0.930387i | \(-0.619471\pi\) | ||||
−0.366579 | + | 0.930387i | \(0.619471\pi\) | |||||||
\(90\) | 13.9187 | 1.46716 | ||||||||
\(91\) | −2.11302 | −0.221504 | ||||||||
\(92\) | 28.7869 | 3.00124 | ||||||||
\(93\) | 10.0573 | 1.04290 | ||||||||
\(94\) | 13.2189 | 1.36343 | ||||||||
\(95\) | 4.19325 | 0.430218 | ||||||||
\(96\) | −66.4535 | −6.78238 | ||||||||
\(97\) | −2.81900 | −0.286226 | −0.143113 | − | 0.989706i | \(-0.545711\pi\) | ||||
−0.143113 | + | 0.989706i | \(0.545711\pi\) | |||||||
\(98\) | 18.3649 | 1.85513 | ||||||||
\(99\) | 32.5155 | 3.26793 | ||||||||
\(100\) | −22.9109 | −2.29109 | ||||||||
\(101\) | 15.6347 | 1.55571 | 0.777855 | − | 0.628444i | \(-0.216308\pi\) | ||||
0.777855 | + | 0.628444i | \(0.216308\pi\) | |||||||
\(102\) | 18.8234 | 1.86379 | ||||||||
\(103\) | −3.99598 | −0.393736 | −0.196868 | − | 0.980430i | \(-0.563077\pi\) | ||||
−0.196868 | + | 0.980430i | \(0.563077\pi\) | |||||||
\(104\) | 37.2455 | 3.65222 | ||||||||
\(105\) | −1.45990 | −0.142471 | ||||||||
\(106\) | 15.1299 | 1.46955 | ||||||||
\(107\) | 2.78775 | 0.269502 | 0.134751 | − | 0.990879i | \(-0.456976\pi\) | ||||
0.134751 | + | 0.990879i | \(0.456976\pi\) | |||||||
\(108\) | 40.9569 | 3.94107 | ||||||||
\(109\) | −15.5250 | −1.48702 | −0.743511 | − | 0.668724i | \(-0.766841\pi\) | ||||
−0.743511 | + | 0.668724i | \(0.766841\pi\) | |||||||
\(110\) | 14.7224 | 1.40372 | ||||||||
\(111\) | −28.2199 | −2.67851 | ||||||||
\(112\) | 8.34588 | 0.788612 | ||||||||
\(113\) | 11.1473 | 1.04865 | 0.524325 | − | 0.851519i | \(-0.324318\pi\) | ||||
0.524325 | + | 0.851519i | \(0.324318\pi\) | |||||||
\(114\) | 36.6524 | 3.43282 | ||||||||
\(115\) | −4.78974 | −0.446645 | ||||||||
\(116\) | −56.1777 | −5.21596 | ||||||||
\(117\) | −21.4928 | −1.98701 | ||||||||
\(118\) | 12.0322 | 1.10766 | ||||||||
\(119\) | −1.28114 | −0.117442 | ||||||||
\(120\) | 25.7331 | 2.34910 | ||||||||
\(121\) | 23.3930 | 2.12663 | ||||||||
\(122\) | 40.6586 | 3.68105 | ||||||||
\(123\) | −24.9276 | −2.24764 | ||||||||
\(124\) | 18.9470 | 1.70149 | ||||||||
\(125\) | 8.39332 | 0.750721 | ||||||||
\(126\) | −8.28033 | −0.737671 | ||||||||
\(127\) | 6.37229 | 0.565449 | 0.282725 | − | 0.959201i | \(-0.408762\pi\) | ||||
0.282725 | + | 0.959201i | \(0.408762\pi\) | |||||||
\(128\) | −41.2912 | −3.64966 | ||||||||
\(129\) | 32.6262 | 2.87258 | ||||||||
\(130\) | −9.73150 | −0.853509 | ||||||||
\(131\) | 1.83947 | 0.160716 | 0.0803578 | − | 0.996766i | \(-0.474394\pi\) | ||||
0.0803578 | + | 0.996766i | \(0.474394\pi\) | |||||||
\(132\) | 94.4005 | 8.21651 | ||||||||
\(133\) | −2.49460 | −0.216309 | ||||||||
\(134\) | 29.8198 | 2.57604 | ||||||||
\(135\) | −6.81465 | −0.586512 | ||||||||
\(136\) | 22.5822 | 1.93641 | ||||||||
\(137\) | 16.5783 | 1.41638 | 0.708190 | − | 0.706022i | \(-0.249512\pi\) | ||||
0.708190 | + | 0.706022i | \(0.249512\pi\) | |||||||
\(138\) | −41.8663 | −3.56389 | ||||||||
\(139\) | −0.364167 | −0.0308882 | −0.0154441 | − | 0.999881i | \(-0.504916\pi\) | ||||
−0.0154441 | + | 0.999881i | \(0.504916\pi\) | |||||||
\(140\) | −2.75029 | −0.232442 | ||||||||
\(141\) | −14.1030 | −1.18769 | ||||||||
\(142\) | −18.3529 | −1.54014 | ||||||||
\(143\) | −22.7338 | −1.90110 | ||||||||
\(144\) | 84.8911 | 7.07426 | ||||||||
\(145\) | 9.34718 | 0.776241 | ||||||||
\(146\) | 5.53628 | 0.458186 | ||||||||
\(147\) | −19.5931 | −1.61601 | ||||||||
\(148\) | −53.1634 | −4.37000 | ||||||||
\(149\) | 5.54054 | 0.453899 | 0.226949 | − | 0.973907i | \(-0.427125\pi\) | ||||
0.226949 | + | 0.973907i | \(0.427125\pi\) | |||||||
\(150\) | 33.3205 | 2.72061 | ||||||||
\(151\) | −10.3356 | −0.841102 | −0.420551 | − | 0.907269i | \(-0.638163\pi\) | ||||
−0.420551 | + | 0.907269i | \(0.638163\pi\) | |||||||
\(152\) | 43.9715 | 3.56656 | ||||||||
\(153\) | −13.0312 | −1.05351 | ||||||||
\(154\) | −8.75845 | −0.705776 | ||||||||
\(155\) | −3.15251 | −0.253216 | ||||||||
\(156\) | −62.3989 | −4.99591 | ||||||||
\(157\) | −9.98297 | −0.796728 | −0.398364 | − | 0.917227i | \(-0.630422\pi\) | ||||
−0.398364 | + | 0.917227i | \(0.630422\pi\) | |||||||
\(158\) | 34.0843 | 2.71160 | ||||||||
\(159\) | −16.1417 | −1.28012 | ||||||||
\(160\) | 20.8301 | 1.64677 | ||||||||
\(161\) | 2.84945 | 0.224568 | ||||||||
\(162\) | −13.9931 | −1.09940 | ||||||||
\(163\) | 8.48013 | 0.664215 | 0.332107 | − | 0.943242i | \(-0.392240\pi\) | ||||
0.332107 | + | 0.943242i | \(0.392240\pi\) | |||||||
\(164\) | −46.9609 | −3.66703 | ||||||||
\(165\) | −15.7069 | −1.22278 | ||||||||
\(166\) | −19.4261 | −1.50775 | ||||||||
\(167\) | 4.18144 | 0.323570 | 0.161785 | − | 0.986826i | \(-0.448275\pi\) | ||||
0.161785 | + | 0.986826i | \(0.448275\pi\) | |||||||
\(168\) | −15.3089 | −1.18110 | ||||||||
\(169\) | 2.02709 | 0.155930 | ||||||||
\(170\) | −5.90028 | −0.452530 | ||||||||
\(171\) | −25.3741 | −1.94040 | ||||||||
\(172\) | 61.4645 | 4.68662 | ||||||||
\(173\) | 7.10529 | 0.540205 | 0.270102 | − | 0.962832i | \(-0.412942\pi\) | ||||
0.270102 | + | 0.962832i | \(0.412942\pi\) | |||||||
\(174\) | 81.7022 | 6.19382 | ||||||||
\(175\) | −2.26782 | −0.171431 | ||||||||
\(176\) | 89.7929 | 6.76839 | ||||||||
\(177\) | −12.8369 | −0.964881 | ||||||||
\(178\) | 18.9505 | 1.42040 | ||||||||
\(179\) | −8.95552 | −0.669367 | −0.334684 | − | 0.942331i | \(-0.608629\pi\) | ||||
−0.334684 | + | 0.942331i | \(0.608629\pi\) | |||||||
\(180\) | −27.9749 | −2.08513 | ||||||||
\(181\) | 4.11486 | 0.305855 | 0.152927 | − | 0.988237i | \(-0.451130\pi\) | ||||
0.152927 | + | 0.988237i | \(0.451130\pi\) | |||||||
\(182\) | 5.78935 | 0.429135 | ||||||||
\(183\) | −43.3777 | −3.20657 | ||||||||
\(184\) | −50.2265 | −3.70274 | ||||||||
\(185\) | 8.84565 | 0.650345 | ||||||||
\(186\) | −27.5556 | −2.02047 | ||||||||
\(187\) | −13.7837 | −1.00796 | ||||||||
\(188\) | −26.5686 | −1.93771 | ||||||||
\(189\) | 4.05409 | 0.294892 | ||||||||
\(190\) | −11.4889 | −0.833490 | ||||||||
\(191\) | −12.8406 | −0.929115 | −0.464557 | − | 0.885543i | \(-0.653787\pi\) | ||||
−0.464557 | + | 0.885543i | \(0.653787\pi\) | |||||||
\(192\) | 92.5614 | 6.68004 | ||||||||
\(193\) | 27.0529 | 1.94731 | 0.973656 | − | 0.228021i | \(-0.0732254\pi\) | ||||
0.973656 | + | 0.228021i | \(0.0732254\pi\) | |||||||
\(194\) | 7.72364 | 0.554525 | ||||||||
\(195\) | 10.3823 | 0.743493 | ||||||||
\(196\) | −36.9113 | −2.63652 | ||||||||
\(197\) | −3.15842 | −0.225028 | −0.112514 | − | 0.993650i | \(-0.535890\pi\) | ||||
−0.112514 | + | 0.993650i | \(0.535890\pi\) | |||||||
\(198\) | −89.0876 | −6.33118 | ||||||||
\(199\) | 4.06423 | 0.288106 | 0.144053 | − | 0.989570i | \(-0.453986\pi\) | ||||
0.144053 | + | 0.989570i | \(0.453986\pi\) | |||||||
\(200\) | 39.9742 | 2.82660 | ||||||||
\(201\) | −31.8141 | −2.24399 | ||||||||
\(202\) | −42.8367 | −3.01398 | ||||||||
\(203\) | −5.56072 | −0.390286 | ||||||||
\(204\) | −37.8329 | −2.64883 | ||||||||
\(205\) | 7.81365 | 0.545729 | ||||||||
\(206\) | 10.9484 | 0.762811 | ||||||||
\(207\) | 28.9836 | 2.01450 | ||||||||
\(208\) | −59.3532 | −4.11541 | ||||||||
\(209\) | −26.8392 | −1.85651 | ||||||||
\(210\) | 3.99990 | 0.276019 | ||||||||
\(211\) | 6.01082 | 0.413802 | 0.206901 | − | 0.978362i | \(-0.433662\pi\) | ||||
0.206901 | + | 0.978362i | \(0.433662\pi\) | |||||||
\(212\) | −30.4093 | −2.08852 | ||||||||
\(213\) | 19.5803 | 1.34162 | ||||||||
\(214\) | −7.63803 | −0.522125 | ||||||||
\(215\) | −10.2268 | −0.697465 | ||||||||
\(216\) | −71.4603 | −4.86226 | ||||||||
\(217\) | 1.87546 | 0.127314 | ||||||||
\(218\) | 42.5361 | 2.88091 | ||||||||
\(219\) | −5.90653 | −0.399126 | ||||||||
\(220\) | −29.5902 | −1.99497 | ||||||||
\(221\) | 9.11103 | 0.612874 | ||||||||
\(222\) | 77.3183 | 5.18926 | ||||||||
\(223\) | 12.1672 | 0.814778 | 0.407389 | − | 0.913255i | \(-0.366439\pi\) | ||||
0.407389 | + | 0.913255i | \(0.366439\pi\) | |||||||
\(224\) | −12.3920 | −0.827977 | ||||||||
\(225\) | −23.0674 | −1.53783 | ||||||||
\(226\) | −30.5419 | −2.03162 | ||||||||
\(227\) | −15.0682 | −1.00011 | −0.500057 | − | 0.865992i | \(-0.666688\pi\) | ||||
−0.500057 | + | 0.865992i | \(0.666688\pi\) | |||||||
\(228\) | −73.6672 | −4.87873 | ||||||||
\(229\) | −5.94827 | −0.393073 | −0.196536 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196536 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(230\) | 13.1232 | 0.865316 | ||||||||
\(231\) | 9.34418 | 0.614802 | ||||||||
\(232\) | 98.0171 | 6.43514 | ||||||||
\(233\) | −22.9544 | −1.50380 | −0.751898 | − | 0.659280i | \(-0.770861\pi\) | ||||
−0.751898 | + | 0.659280i | \(0.770861\pi\) | |||||||
\(234\) | 58.8871 | 3.84957 | ||||||||
\(235\) | 4.42064 | 0.288371 | ||||||||
\(236\) | −24.1834 | −1.57421 | ||||||||
\(237\) | −36.3637 | −2.36208 | ||||||||
\(238\) | 3.51012 | 0.227527 | ||||||||
\(239\) | −27.2132 | −1.76027 | −0.880137 | − | 0.474719i | \(-0.842550\pi\) | ||||
−0.880137 | + | 0.474719i | \(0.842550\pi\) | |||||||
\(240\) | −41.0075 | −2.64702 | ||||||||
\(241\) | −11.9121 | −0.767327 | −0.383663 | − | 0.923473i | \(-0.625338\pi\) | ||||
−0.383663 | + | 0.923473i | \(0.625338\pi\) | |||||||
\(242\) | −64.0933 | −4.12007 | ||||||||
\(243\) | −7.38362 | −0.473660 | ||||||||
\(244\) | −81.7190 | −5.23152 | ||||||||
\(245\) | 6.14153 | 0.392368 | ||||||||
\(246\) | 68.2978 | 4.35451 | ||||||||
\(247\) | 17.7408 | 1.12882 | ||||||||
\(248\) | −33.0581 | −2.09919 | ||||||||
\(249\) | 20.7252 | 1.31341 | ||||||||
\(250\) | −22.9964 | −1.45442 | ||||||||
\(251\) | 20.7787 | 1.31154 | 0.655771 | − | 0.754959i | \(-0.272343\pi\) | ||||
0.655771 | + | 0.754959i | \(0.272343\pi\) | |||||||
\(252\) | 16.6425 | 1.04838 | ||||||||
\(253\) | 30.6571 | 1.92740 | ||||||||
\(254\) | −17.4591 | −1.09548 | ||||||||
\(255\) | 6.29486 | 0.394200 | ||||||||
\(256\) | 49.8003 | 3.11252 | ||||||||
\(257\) | 26.5827 | 1.65818 | 0.829092 | − | 0.559113i | \(-0.188858\pi\) | ||||
0.829092 | + | 0.559113i | \(0.188858\pi\) | |||||||
\(258\) | −89.3911 | −5.56524 | ||||||||
\(259\) | −5.26235 | −0.326986 | ||||||||
\(260\) | 19.5592 | 1.21301 | ||||||||
\(261\) | −56.5615 | −3.50107 | ||||||||
\(262\) | −5.03989 | −0.311365 | ||||||||
\(263\) | 15.7267 | 0.969747 | 0.484874 | − | 0.874584i | \(-0.338866\pi\) | ||||
0.484874 | + | 0.874584i | \(0.338866\pi\) | |||||||
\(264\) | −164.707 | −10.1370 | ||||||||
\(265\) | 5.05969 | 0.310815 | ||||||||
\(266\) | 6.83482 | 0.419070 | ||||||||
\(267\) | −20.2178 | −1.23731 | ||||||||
\(268\) | −59.9345 | −3.66108 | ||||||||
\(269\) | 22.3317 | 1.36159 | 0.680793 | − | 0.732476i | \(-0.261635\pi\) | ||||
0.680793 | + | 0.732476i | \(0.261635\pi\) | |||||||
\(270\) | 18.6711 | 1.13629 | ||||||||
\(271\) | −14.9954 | −0.910906 | −0.455453 | − | 0.890260i | \(-0.650523\pi\) | ||||
−0.455453 | + | 0.890260i | \(0.650523\pi\) | |||||||
\(272\) | −35.9863 | −2.18199 | ||||||||
\(273\) | −6.17652 | −0.373820 | ||||||||
\(274\) | −45.4221 | −2.74405 | ||||||||
\(275\) | −24.3994 | −1.47134 | ||||||||
\(276\) | 84.1464 | 5.06502 | ||||||||
\(277\) | 4.24351 | 0.254968 | 0.127484 | − | 0.991841i | \(-0.459310\pi\) | ||||
0.127484 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(278\) | 0.997763 | 0.0598419 | ||||||||
\(279\) | 19.0764 | 1.14208 | ||||||||
\(280\) | 4.79863 | 0.286773 | ||||||||
\(281\) | 0.760954 | 0.0453947 | 0.0226974 | − | 0.999742i | \(-0.492775\pi\) | ||||
0.0226974 | + | 0.999742i | \(0.492775\pi\) | |||||||
\(282\) | 38.6401 | 2.30098 | ||||||||
\(283\) | −0.322950 | −0.0191974 | −0.00959870 | − | 0.999954i | \(-0.503055\pi\) | ||||
−0.00959870 | + | 0.999954i | \(0.503055\pi\) | |||||||
\(284\) | 36.8872 | 2.18885 | ||||||||
\(285\) | 12.2572 | 0.726054 | ||||||||
\(286\) | 62.2873 | 3.68312 | ||||||||
\(287\) | −4.64841 | −0.274387 | ||||||||
\(288\) | −126.047 | −7.42739 | ||||||||
\(289\) | −11.4759 | −0.675054 | ||||||||
\(290\) | −25.6099 | −1.50386 | ||||||||
\(291\) | −8.24017 | −0.483047 | ||||||||
\(292\) | −11.1273 | −0.651175 | ||||||||
\(293\) | −25.2193 | −1.47332 | −0.736662 | − | 0.676261i | \(-0.763599\pi\) | ||||
−0.736662 | + | 0.676261i | \(0.763599\pi\) | |||||||
\(294\) | 53.6821 | 3.13080 | ||||||||
\(295\) | 4.02378 | 0.234274 | ||||||||
\(296\) | 92.7578 | 5.39144 | ||||||||
\(297\) | 43.6177 | 2.53096 | ||||||||
\(298\) | −15.1803 | −0.879368 | ||||||||
\(299\) | −20.2644 | −1.17192 | ||||||||
\(300\) | −66.9704 | −3.86654 | ||||||||
\(301\) | 6.08403 | 0.350678 | ||||||||
\(302\) | 28.3181 | 1.62952 | ||||||||
\(303\) | 45.7015 | 2.62548 | ||||||||
\(304\) | −70.0716 | −4.01888 | ||||||||
\(305\) | 13.5969 | 0.778557 | ||||||||
\(306\) | 35.7036 | 2.04104 | ||||||||
\(307\) | −1.67713 | −0.0957191 | −0.0478595 | − | 0.998854i | \(-0.515240\pi\) | ||||
−0.0478595 | + | 0.998854i | \(0.515240\pi\) | |||||||
\(308\) | 17.6035 | 1.00305 | ||||||||
\(309\) | −11.6806 | −0.664485 | ||||||||
\(310\) | 8.63742 | 0.490572 | ||||||||
\(311\) | 31.3850 | 1.77968 | 0.889841 | − | 0.456271i | \(-0.150815\pi\) | ||||
0.889841 | + | 0.456271i | \(0.150815\pi\) | |||||||
\(312\) | 108.872 | 6.16364 | ||||||||
\(313\) | 28.8819 | 1.63250 | 0.816250 | − | 0.577699i | \(-0.196049\pi\) | ||||
0.816250 | + | 0.577699i | \(0.196049\pi\) | |||||||
\(314\) | 27.3519 | 1.54355 | ||||||||
\(315\) | −2.76908 | −0.156020 | ||||||||
\(316\) | −68.5055 | −3.85373 | ||||||||
\(317\) | 23.9069 | 1.34275 | 0.671373 | − | 0.741119i | \(-0.265705\pi\) | ||||
0.671373 | + | 0.741119i | \(0.265705\pi\) | |||||||
\(318\) | 44.2259 | 2.48007 | ||||||||
\(319\) | −59.8274 | −3.34969 | ||||||||
\(320\) | −29.0138 | −1.62192 | ||||||||
\(321\) | 8.14884 | 0.454824 | ||||||||
\(322\) | −7.80708 | −0.435072 | ||||||||
\(323\) | 10.7563 | 0.598499 | ||||||||
\(324\) | 28.1246 | 1.56248 | ||||||||
\(325\) | 16.1280 | 0.894621 | ||||||||
\(326\) | −23.2343 | −1.28683 | ||||||||
\(327\) | −45.3807 | −2.50956 | ||||||||
\(328\) | 81.9360 | 4.52416 | ||||||||
\(329\) | −2.62988 | −0.144990 | ||||||||
\(330\) | 43.0347 | 2.36898 | ||||||||
\(331\) | −7.91150 | −0.434855 | −0.217428 | − | 0.976076i | \(-0.569767\pi\) | ||||
−0.217428 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(332\) | 39.0441 | 2.14283 | ||||||||
\(333\) | −53.5266 | −2.93324 | ||||||||
\(334\) | −11.4565 | −0.626873 | ||||||||
\(335\) | 9.97226 | 0.544843 | ||||||||
\(336\) | 24.3957 | 1.33089 | ||||||||
\(337\) | 17.4752 | 0.951936 | 0.475968 | − | 0.879462i | \(-0.342098\pi\) | ||||
0.475968 | + | 0.879462i | \(0.342098\pi\) | |||||||
\(338\) | −5.55394 | −0.302094 | ||||||||
\(339\) | 32.5845 | 1.76974 | ||||||||
\(340\) | 11.8589 | 0.643138 | ||||||||
\(341\) | 20.1779 | 1.09270 | ||||||||
\(342\) | 69.5212 | 3.75928 | ||||||||
\(343\) | −7.46925 | −0.403302 | ||||||||
\(344\) | −107.241 | −5.78207 | ||||||||
\(345\) | −14.0008 | −0.753778 | ||||||||
\(346\) | −19.4674 | −1.04658 | ||||||||
\(347\) | 33.3476 | 1.79019 | 0.895096 | − | 0.445873i | \(-0.147107\pi\) | ||||
0.895096 | + | 0.445873i | \(0.147107\pi\) | |||||||
\(348\) | −164.212 | −8.80268 | ||||||||
\(349\) | 30.3305 | 1.62355 | 0.811777 | − | 0.583967i | \(-0.198500\pi\) | ||||
0.811777 | + | 0.583967i | \(0.198500\pi\) | |||||||
\(350\) | 6.21349 | 0.332125 | ||||||||
\(351\) | −28.8314 | −1.53891 | ||||||||
\(352\) | −133.325 | −7.10625 | ||||||||
\(353\) | −17.3069 | −0.921153 | −0.460576 | − | 0.887620i | \(-0.652357\pi\) | ||||
−0.460576 | + | 0.887620i | \(0.652357\pi\) | |||||||
\(354\) | 35.1712 | 1.86933 | ||||||||
\(355\) | −6.13752 | −0.325746 | ||||||||
\(356\) | −38.0882 | −2.01867 | ||||||||
\(357\) | −3.74487 | −0.198199 | ||||||||
\(358\) | 24.5368 | 1.29681 | ||||||||
\(359\) | −25.5922 | −1.35070 | −0.675351 | − | 0.737496i | \(-0.736008\pi\) | ||||
−0.675351 | + | 0.737496i | \(0.736008\pi\) | |||||||
\(360\) | 48.8098 | 2.57250 | ||||||||
\(361\) | 1.94449 | 0.102341 | ||||||||
\(362\) | −11.2741 | −0.592553 | ||||||||
\(363\) | 68.3796 | 3.58900 | ||||||||
\(364\) | −11.6359 | −0.609888 | ||||||||
\(365\) | 1.85143 | 0.0969081 | ||||||||
\(366\) | 118.848 | 6.21230 | ||||||||
\(367\) | 7.35748 | 0.384058 | 0.192029 | − | 0.981389i | \(-0.438493\pi\) | ||||
0.192029 | + | 0.981389i | \(0.438493\pi\) | |||||||
\(368\) | 80.0393 | 4.17234 | ||||||||
\(369\) | −47.2818 | −2.46139 | ||||||||
\(370\) | −24.2358 | −1.25996 | ||||||||
\(371\) | −3.01005 | −0.156274 | ||||||||
\(372\) | 55.3835 | 2.87150 | ||||||||
\(373\) | −1.10095 | −0.0570050 | −0.0285025 | − | 0.999594i | \(-0.509074\pi\) | ||||
−0.0285025 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(374\) | 37.7652 | 1.95279 | ||||||||
\(375\) | 24.5344 | 1.26695 | ||||||||
\(376\) | 46.3560 | 2.39063 | ||||||||
\(377\) | 39.5460 | 2.03672 | ||||||||
\(378\) | −11.1076 | −0.571314 | ||||||||
\(379\) | 5.57938 | 0.286593 | 0.143297 | − | 0.989680i | \(-0.454230\pi\) | ||||
0.143297 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(380\) | 23.0913 | 1.18456 | ||||||||
\(381\) | 18.6267 | 0.954276 | ||||||||
\(382\) | 35.1814 | 1.80004 | ||||||||
\(383\) | 27.7922 | 1.42012 | 0.710058 | − | 0.704144i | \(-0.248669\pi\) | ||||
0.710058 | + | 0.704144i | \(0.248669\pi\) | |||||||
\(384\) | −120.697 | −6.15932 | ||||||||
\(385\) | −2.92897 | −0.149274 | ||||||||
\(386\) | −74.1210 | −3.77266 | ||||||||
\(387\) | 61.8844 | 3.14576 | ||||||||
\(388\) | −15.5236 | −0.788093 | ||||||||
\(389\) | −19.9616 | −1.01210 | −0.506048 | − | 0.862506i | \(-0.668894\pi\) | ||||
−0.506048 | + | 0.862506i | \(0.668894\pi\) | |||||||
\(390\) | −28.4460 | −1.44042 | ||||||||
\(391\) | −12.2864 | −0.621352 | ||||||||
\(392\) | 64.4018 | 3.25278 | ||||||||
\(393\) | 5.37693 | 0.271230 | ||||||||
\(394\) | 8.65359 | 0.435962 | ||||||||
\(395\) | 11.3984 | 0.573514 | ||||||||
\(396\) | 179.056 | 8.99789 | ||||||||
\(397\) | −10.5885 | −0.531420 | −0.265710 | − | 0.964053i | \(-0.585606\pi\) | ||||
−0.265710 | + | 0.964053i | \(0.585606\pi\) | |||||||
\(398\) | −11.1354 | −0.558167 | ||||||||
\(399\) | −7.29191 | −0.365052 | ||||||||
\(400\) | −63.7016 | −3.18508 | ||||||||
\(401\) | −20.5049 | −1.02396 | −0.511982 | − | 0.858996i | \(-0.671089\pi\) | ||||
−0.511982 | + | 0.858996i | \(0.671089\pi\) | |||||||
\(402\) | 87.1659 | 4.34744 | ||||||||
\(403\) | −13.3376 | −0.664395 | ||||||||
\(404\) | 86.0969 | 4.28348 | ||||||||
\(405\) | −4.67954 | −0.232528 | ||||||||
\(406\) | 15.2355 | 0.756127 | ||||||||
\(407\) | −56.6173 | −2.80641 | ||||||||
\(408\) | 66.0096 | 3.26796 | ||||||||
\(409\) | −3.38467 | −0.167361 | −0.0836806 | − | 0.996493i | \(-0.526668\pi\) | ||||
−0.0836806 | + | 0.996493i | \(0.526668\pi\) | |||||||
\(410\) | −21.4082 | −1.05728 | ||||||||
\(411\) | 48.4598 | 2.39034 | ||||||||
\(412\) | −22.0050 | −1.08411 | ||||||||
\(413\) | −2.39378 | −0.117790 | ||||||||
\(414\) | −79.4107 | −3.90282 | ||||||||
\(415\) | −6.49640 | −0.318896 | ||||||||
\(416\) | 88.1281 | 4.32083 | ||||||||
\(417\) | −1.06449 | −0.0521283 | ||||||||
\(418\) | 73.5354 | 3.59674 | ||||||||
\(419\) | 32.8087 | 1.60281 | 0.801405 | − | 0.598122i | \(-0.204086\pi\) | ||||
0.801405 | + | 0.598122i | \(0.204086\pi\) | |||||||
\(420\) | −8.03933 | −0.392279 | ||||||||
\(421\) | −31.2389 | −1.52249 | −0.761245 | − | 0.648464i | \(-0.775412\pi\) | ||||
−0.761245 | + | 0.648464i | \(0.775412\pi\) | |||||||
\(422\) | −16.4688 | −0.801687 | ||||||||
\(423\) | −26.7501 | −1.30063 | ||||||||
\(424\) | 53.0573 | 2.57669 | ||||||||
\(425\) | 9.77853 | 0.474328 | ||||||||
\(426\) | −53.6470 | −2.59921 | ||||||||
\(427\) | −8.08892 | −0.391450 | ||||||||
\(428\) | 15.3516 | 0.742046 | ||||||||
\(429\) | −66.4528 | −3.20837 | ||||||||
\(430\) | 28.0200 | 1.35125 | ||||||||
\(431\) | 5.08888 | 0.245123 | 0.122561 | − | 0.992461i | \(-0.460889\pi\) | ||||
0.122561 | + | 0.992461i | \(0.460889\pi\) | |||||||
\(432\) | 113.877 | 5.47890 | ||||||||
\(433\) | 23.4864 | 1.12868 | 0.564342 | − | 0.825541i | \(-0.309130\pi\) | ||||
0.564342 | + | 0.825541i | \(0.309130\pi\) | |||||||
\(434\) | −5.13847 | −0.246654 | ||||||||
\(435\) | 27.3226 | 1.31002 | ||||||||
\(436\) | −85.4926 | −4.09436 | ||||||||
\(437\) | −23.9239 | −1.14443 | ||||||||
\(438\) | 16.1830 | 0.773254 | ||||||||
\(439\) | 35.6818 | 1.70300 | 0.851499 | − | 0.524356i | \(-0.175694\pi\) | ||||
0.851499 | + | 0.524356i | \(0.175694\pi\) | |||||||
\(440\) | 51.6281 | 2.46128 | ||||||||
\(441\) | −37.1635 | −1.76969 | ||||||||
\(442\) | −24.9629 | −1.18736 | ||||||||
\(443\) | 20.1264 | 0.956233 | 0.478116 | − | 0.878297i | \(-0.341320\pi\) | ||||
0.478116 | + | 0.878297i | \(0.341320\pi\) | |||||||
\(444\) | −155.401 | −7.37500 | ||||||||
\(445\) | 6.33736 | 0.300419 | ||||||||
\(446\) | −33.3364 | −1.57852 | ||||||||
\(447\) | 16.1954 | 0.766018 | ||||||||
\(448\) | 17.2605 | 0.815483 | ||||||||
\(449\) | 13.7896 | 0.650769 | 0.325385 | − | 0.945582i | \(-0.394506\pi\) | ||||
0.325385 | + | 0.945582i | \(0.394506\pi\) | |||||||
\(450\) | 63.2013 | 2.97934 | ||||||||
\(451\) | −50.0119 | −2.35497 | ||||||||
\(452\) | 61.3858 | 2.88734 | ||||||||
\(453\) | −30.2119 | −1.41948 | ||||||||
\(454\) | 41.2848 | 1.93759 | ||||||||
\(455\) | 1.93606 | 0.0907638 | ||||||||
\(456\) | 128.532 | 6.01908 | ||||||||
\(457\) | −26.8320 | −1.25515 | −0.627575 | − | 0.778556i | \(-0.715952\pi\) | ||||
−0.627575 | + | 0.778556i | \(0.715952\pi\) | |||||||
\(458\) | 16.2974 | 0.761526 | ||||||||
\(459\) | −17.4807 | −0.815928 | ||||||||
\(460\) | −26.3761 | −1.22979 | ||||||||
\(461\) | 4.99412 | 0.232600 | 0.116300 | − | 0.993214i | \(-0.462897\pi\) | ||||
0.116300 | + | 0.993214i | \(0.462897\pi\) | |||||||
\(462\) | −25.6017 | −1.19110 | ||||||||
\(463\) | −11.4776 | −0.533410 | −0.266705 | − | 0.963778i | \(-0.585935\pi\) | ||||
−0.266705 | + | 0.963778i | \(0.585935\pi\) | |||||||
\(464\) | −156.197 | −7.25126 | ||||||||
\(465\) | −9.21505 | −0.427338 | ||||||||
\(466\) | 62.8918 | 2.91340 | ||||||||
\(467\) | −9.24481 | −0.427799 | −0.213899 | − | 0.976856i | \(-0.568616\pi\) | ||||
−0.213899 | + | 0.976856i | \(0.568616\pi\) | |||||||
\(468\) | −118.356 | −5.47102 | ||||||||
\(469\) | −5.93258 | −0.273941 | ||||||||
\(470\) | −12.1119 | −0.558680 | ||||||||
\(471\) | −29.1810 | −1.34459 | ||||||||
\(472\) | 42.1945 | 1.94216 | ||||||||
\(473\) | 65.4577 | 3.00975 | ||||||||
\(474\) | 99.6312 | 4.57621 | ||||||||
\(475\) | 19.0405 | 0.873638 | ||||||||
\(476\) | −7.05494 | −0.323363 | ||||||||
\(477\) | −30.6171 | −1.40186 | ||||||||
\(478\) | 74.5601 | 3.41030 | ||||||||
\(479\) | −20.2692 | −0.926123 | −0.463061 | − | 0.886326i | \(-0.653249\pi\) | ||||
−0.463061 | + | 0.886326i | \(0.653249\pi\) | |||||||
\(480\) | 60.8882 | 2.77915 | ||||||||
\(481\) | 37.4241 | 1.70639 | ||||||||
\(482\) | 32.6374 | 1.48659 | ||||||||
\(483\) | 8.32919 | 0.378991 | ||||||||
\(484\) | 128.820 | 5.85546 | ||||||||
\(485\) | 2.58292 | 0.117284 | ||||||||
\(486\) | 20.2300 | 0.917653 | ||||||||
\(487\) | −25.5738 | −1.15886 | −0.579430 | − | 0.815022i | \(-0.696725\pi\) | ||||
−0.579430 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(488\) | 142.581 | 6.45433 | ||||||||
\(489\) | 24.7881 | 1.12096 | ||||||||
\(490\) | −16.8269 | −0.760161 | ||||||||
\(491\) | 7.80394 | 0.352187 | 0.176093 | − | 0.984373i | \(-0.443654\pi\) | ||||
0.176093 | + | 0.984373i | \(0.443654\pi\) | |||||||
\(492\) | −137.271 | −6.18864 | ||||||||
\(493\) | 23.9770 | 1.07987 | ||||||||
\(494\) | −48.6071 | −2.18694 | ||||||||
\(495\) | −29.7924 | −1.33907 | ||||||||
\(496\) | 52.6803 | 2.36542 | ||||||||
\(497\) | 3.65126 | 0.163781 | ||||||||
\(498\) | −56.7840 | −2.54455 | ||||||||
\(499\) | −7.87630 | −0.352592 | −0.176296 | − | 0.984337i | \(-0.556412\pi\) | ||||
−0.176296 | + | 0.984337i | \(0.556412\pi\) | |||||||
\(500\) | 46.2202 | 2.06703 | ||||||||
\(501\) | 12.2227 | 0.546070 | ||||||||
\(502\) | −56.9307 | −2.54094 | ||||||||
\(503\) | 9.26750 | 0.413217 | 0.206609 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(504\) | −29.0374 | −1.29343 | ||||||||
\(505\) | −14.3253 | −0.637469 | ||||||||
\(506\) | −83.9959 | −3.73407 | ||||||||
\(507\) | 5.92536 | 0.263155 | ||||||||
\(508\) | 35.0908 | 1.55690 | ||||||||
\(509\) | −4.05963 | −0.179940 | −0.0899700 | − | 0.995944i | \(-0.528677\pi\) | ||||
−0.0899700 | + | 0.995944i | \(0.528677\pi\) | |||||||
\(510\) | −17.2470 | −0.763710 | ||||||||
\(511\) | −1.10143 | −0.0487243 | ||||||||
\(512\) | −53.8631 | −2.38043 | ||||||||
\(513\) | −34.0379 | −1.50281 | ||||||||
\(514\) | −72.8327 | −3.21251 | ||||||||
\(515\) | 3.66133 | 0.161338 | ||||||||
\(516\) | 179.666 | 7.90934 | ||||||||
\(517\) | −28.2947 | −1.24440 | ||||||||
\(518\) | 14.4180 | 0.633493 | ||||||||
\(519\) | 20.7693 | 0.911673 | ||||||||
\(520\) | −34.1263 | −1.49654 | ||||||||
\(521\) | 11.8568 | 0.519458 | 0.259729 | − | 0.965682i | \(-0.416367\pi\) | ||||
0.259729 | + | 0.965682i | \(0.416367\pi\) | |||||||
\(522\) | 154.970 | 6.78286 | ||||||||
\(523\) | −35.5475 | −1.55438 | −0.777192 | − | 0.629263i | \(-0.783357\pi\) | ||||
−0.777192 | + | 0.629263i | \(0.783357\pi\) | |||||||
\(524\) | 10.1296 | 0.442513 | ||||||||
\(525\) | −6.62903 | −0.289315 | ||||||||
\(526\) | −43.0887 | −1.87876 | ||||||||
\(527\) | −8.08670 | −0.352262 | ||||||||
\(528\) | 262.472 | 11.4226 | ||||||||
\(529\) | 4.32704 | 0.188132 | ||||||||
\(530\) | −13.8628 | −0.602162 | ||||||||
\(531\) | −24.3486 | −1.05664 | ||||||||
\(532\) | −13.7372 | −0.595583 | ||||||||
\(533\) | 33.0580 | 1.43190 | ||||||||
\(534\) | 55.3938 | 2.39712 | ||||||||
\(535\) | −2.55429 | −0.110432 | ||||||||
\(536\) | 104.572 | 4.51681 | ||||||||
\(537\) | −26.1777 | −1.12965 | ||||||||
\(538\) | −61.1855 | −2.63789 | ||||||||
\(539\) | −39.3094 | −1.69318 | ||||||||
\(540\) | −37.5268 | −1.61490 | ||||||||
\(541\) | −0.893073 | −0.0383962 | −0.0191981 | − | 0.999816i | \(-0.506111\pi\) | ||||
−0.0191981 | + | 0.999816i | \(0.506111\pi\) | |||||||
\(542\) | 41.0852 | 1.76476 | ||||||||
\(543\) | 12.0281 | 0.516174 | ||||||||
\(544\) | 53.4326 | 2.29091 | ||||||||
\(545\) | 14.2248 | 0.609323 | ||||||||
\(546\) | 16.9228 | 0.724227 | ||||||||
\(547\) | 3.69493 | 0.157984 | 0.0789919 | − | 0.996875i | \(-0.474830\pi\) | ||||
0.0789919 | + | 0.996875i | \(0.474830\pi\) | |||||||
\(548\) | 91.2932 | 3.89985 | ||||||||
\(549\) | −82.2774 | −3.51151 | ||||||||
\(550\) | 66.8506 | 2.85052 | ||||||||
\(551\) | 46.6875 | 1.98895 | ||||||||
\(552\) | −146.816 | −6.24891 | ||||||||
\(553\) | −6.78098 | −0.288357 | ||||||||
\(554\) | −11.6266 | −0.493966 | ||||||||
\(555\) | 25.8566 | 1.09755 | ||||||||
\(556\) | −2.00539 | −0.0850474 | ||||||||
\(557\) | 1.59478 | 0.0675731 | 0.0337865 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337865 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(558\) | −52.2666 | −2.21262 | ||||||||
\(559\) | −43.2677 | −1.83003 | ||||||||
\(560\) | −7.64694 | −0.323142 | ||||||||
\(561\) | −40.2908 | −1.70108 | ||||||||
\(562\) | −2.08490 | −0.0879463 | ||||||||
\(563\) | 33.3487 | 1.40548 | 0.702740 | − | 0.711447i | \(-0.251960\pi\) | ||||
0.702740 | + | 0.711447i | \(0.251960\pi\) | |||||||
\(564\) | −77.6621 | −3.27016 | ||||||||
\(565\) | −10.2137 | −0.429695 | ||||||||
\(566\) | 0.884835 | 0.0371924 | ||||||||
\(567\) | 2.78390 | 0.116913 | ||||||||
\(568\) | −64.3597 | −2.70047 | ||||||||
\(569\) | −27.6045 | −1.15724 | −0.578620 | − | 0.815597i | \(-0.696409\pi\) | ||||
−0.578620 | + | 0.815597i | \(0.696409\pi\) | |||||||
\(570\) | −33.5829 | −1.40663 | ||||||||
\(571\) | −18.3660 | −0.768592 | −0.384296 | − | 0.923210i | \(-0.625556\pi\) | ||||
−0.384296 | + | 0.923210i | \(0.625556\pi\) | |||||||
\(572\) | −125.190 | −5.23447 | ||||||||
\(573\) | −37.5342 | −1.56801 | ||||||||
\(574\) | 12.7359 | 0.531588 | ||||||||
\(575\) | −21.7490 | −0.906997 | ||||||||
\(576\) | 175.568 | 7.31531 | ||||||||
\(577\) | 9.50682 | 0.395774 | 0.197887 | − | 0.980225i | \(-0.436592\pi\) | ||||
0.197887 | + | 0.980225i | \(0.436592\pi\) | |||||||
\(578\) | 31.4423 | 1.30783 | ||||||||
\(579\) | 79.0779 | 3.28637 | ||||||||
\(580\) | 51.4729 | 2.13730 | ||||||||
\(581\) | 3.86476 | 0.160337 | ||||||||
\(582\) | 22.5768 | 0.935840 | ||||||||
\(583\) | −32.3850 | −1.34125 | ||||||||
\(584\) | 19.4146 | 0.803380 | ||||||||
\(585\) | 19.6928 | 0.814199 | ||||||||
\(586\) | 69.0970 | 2.85437 | ||||||||
\(587\) | −8.63875 | −0.356560 | −0.178280 | − | 0.983980i | \(-0.557053\pi\) | ||||
−0.178280 | + | 0.983980i | \(0.557053\pi\) | |||||||
\(588\) | −107.895 | −4.44951 | ||||||||
\(589\) | −15.7462 | −0.648812 | ||||||||
\(590\) | −11.0246 | −0.453874 | ||||||||
\(591\) | −9.23231 | −0.379766 | ||||||||
\(592\) | −147.816 | −6.07520 | ||||||||
\(593\) | −27.3750 | −1.12415 | −0.562077 | − | 0.827085i | \(-0.689998\pi\) | ||||
−0.562077 | + | 0.827085i | \(0.689998\pi\) | |||||||
\(594\) | −119.506 | −4.90340 | ||||||||
\(595\) | 1.17384 | 0.0481229 | ||||||||
\(596\) | 30.5106 | 1.24976 | ||||||||
\(597\) | 11.8801 | 0.486220 | ||||||||
\(598\) | 55.5215 | 2.27044 | ||||||||
\(599\) | −22.9673 | −0.938417 | −0.469209 | − | 0.883087i | \(-0.655461\pi\) | ||||
−0.469209 | + | 0.883087i | \(0.655461\pi\) | |||||||
\(600\) | 116.848 | 4.77029 | ||||||||
\(601\) | −37.4650 | −1.52823 | −0.764115 | − | 0.645080i | \(-0.776824\pi\) | ||||
−0.764115 | + | 0.645080i | \(0.776824\pi\) | |||||||
\(602\) | −16.6693 | −0.679392 | ||||||||
\(603\) | −60.3440 | −2.45740 | ||||||||
\(604\) | −56.9161 | −2.31588 | ||||||||
\(605\) | −21.4339 | −0.871411 | ||||||||
\(606\) | −125.215 | −5.08652 | ||||||||
\(607\) | −20.9734 | −0.851283 | −0.425642 | − | 0.904892i | \(-0.639952\pi\) | ||||
−0.425642 | + | 0.904892i | \(0.639952\pi\) | |||||||
\(608\) | 104.043 | 4.21949 | ||||||||
\(609\) | −16.2544 | −0.658663 | ||||||||
\(610\) | −37.2535 | −1.50835 | ||||||||
\(611\) | 18.7028 | 0.756635 | ||||||||
\(612\) | −71.7602 | −2.90073 | ||||||||
\(613\) | −24.3587 | −0.983839 | −0.491919 | − | 0.870641i | \(-0.663705\pi\) | ||||
−0.491919 | + | 0.870641i | \(0.663705\pi\) | |||||||
\(614\) | 4.59510 | 0.185443 | ||||||||
\(615\) | 22.8399 | 0.920996 | ||||||||
\(616\) | −30.7140 | −1.23750 | ||||||||
\(617\) | 21.1918 | 0.853150 | 0.426575 | − | 0.904452i | \(-0.359720\pi\) | ||||
0.426575 | + | 0.904452i | \(0.359720\pi\) | |||||||
\(618\) | 32.0031 | 1.28735 | ||||||||
\(619\) | −15.7267 | −0.632111 | −0.316055 | − | 0.948741i | \(-0.602359\pi\) | ||||
−0.316055 | + | 0.948741i | \(0.602359\pi\) | |||||||
\(620\) | −17.3602 | −0.697203 | ||||||||
\(621\) | 38.8799 | 1.56020 | ||||||||
\(622\) | −85.9903 | −3.44790 | ||||||||
\(623\) | −3.77014 | −0.151048 | ||||||||
\(624\) | −173.494 | −6.94534 | ||||||||
\(625\) | 13.1120 | 0.524480 | ||||||||
\(626\) | −79.1320 | −3.16275 | ||||||||
\(627\) | −78.4532 | −3.13312 | ||||||||
\(628\) | −54.9741 | −2.19370 | ||||||||
\(629\) | 22.6905 | 0.904729 | ||||||||
\(630\) | 7.58688 | 0.302269 | ||||||||
\(631\) | 38.8715 | 1.54745 | 0.773724 | − | 0.633522i | \(-0.218392\pi\) | ||||
0.773724 | + | 0.633522i | \(0.218392\pi\) | |||||||
\(632\) | 119.526 | 4.75450 | ||||||||
\(633\) | 17.5701 | 0.698350 | ||||||||
\(634\) | −65.5014 | −2.60139 | ||||||||
\(635\) | −5.83863 | −0.231699 | ||||||||
\(636\) | −88.8890 | −3.52468 | ||||||||
\(637\) | 25.9836 | 1.02951 | ||||||||
\(638\) | 163.918 | 6.48959 | ||||||||
\(639\) | 37.1392 | 1.46921 | ||||||||
\(640\) | 37.8331 | 1.49549 | ||||||||
\(641\) | 14.8719 | 0.587406 | 0.293703 | − | 0.955897i | \(-0.405112\pi\) | ||||
0.293703 | + | 0.955897i | \(0.405112\pi\) | |||||||
\(642\) | −22.3266 | −0.881161 | ||||||||
\(643\) | 37.2237 | 1.46796 | 0.733979 | − | 0.679172i | \(-0.237661\pi\) | ||||
0.733979 | + | 0.679172i | \(0.237661\pi\) | |||||||
\(644\) | 15.6913 | 0.618325 | ||||||||
\(645\) | −29.8939 | −1.17707 | ||||||||
\(646\) | −29.4708 | −1.15951 | ||||||||
\(647\) | 12.7835 | 0.502571 | 0.251285 | − | 0.967913i | \(-0.419147\pi\) | ||||
0.251285 | + | 0.967913i | \(0.419147\pi\) | |||||||
\(648\) | −49.0709 | −1.92769 | ||||||||
\(649\) | −25.7546 | −1.01095 | ||||||||
\(650\) | −44.1884 | −1.73321 | ||||||||
\(651\) | 5.48211 | 0.214861 | ||||||||
\(652\) | 46.6982 | 1.82884 | ||||||||
\(653\) | 4.48109 | 0.175359 | 0.0876794 | − | 0.996149i | \(-0.472055\pi\) | ||||
0.0876794 | + | 0.996149i | \(0.472055\pi\) | |||||||
\(654\) | 124.336 | 4.86194 | ||||||||
\(655\) | −1.68542 | −0.0658549 | ||||||||
\(656\) | −130.571 | −5.09793 | ||||||||
\(657\) | −11.2033 | −0.437083 | ||||||||
\(658\) | 7.20547 | 0.280898 | ||||||||
\(659\) | −48.9351 | −1.90624 | −0.953121 | − | 0.302590i | \(-0.902149\pi\) | ||||
−0.953121 | + | 0.302590i | \(0.902149\pi\) | |||||||
\(660\) | −86.4947 | −3.36680 | ||||||||
\(661\) | 24.4952 | 0.952753 | 0.476376 | − | 0.879242i | \(-0.341950\pi\) | ||||
0.476376 | + | 0.879242i | \(0.341950\pi\) | |||||||
\(662\) | 21.6763 | 0.842475 | ||||||||
\(663\) | 26.6323 | 1.03431 | ||||||||
\(664\) | −68.1230 | −2.64369 | ||||||||
\(665\) | 2.28568 | 0.0886349 | ||||||||
\(666\) | 146.655 | 5.68276 | ||||||||
\(667\) | −53.3288 | −2.06490 | ||||||||
\(668\) | 23.0263 | 0.890914 | ||||||||
\(669\) | 35.5658 | 1.37505 | ||||||||
\(670\) | −27.3225 | −1.05556 | ||||||||
\(671\) | −87.0282 | −3.35969 | ||||||||
\(672\) | −36.2229 | −1.39733 | ||||||||
\(673\) | 43.5949 | 1.68046 | 0.840229 | − | 0.542232i | \(-0.182420\pi\) | ||||
0.840229 | + | 0.542232i | \(0.182420\pi\) | |||||||
\(674\) | −47.8795 | −1.84425 | ||||||||
\(675\) | −30.9437 | −1.19102 | ||||||||
\(676\) | 11.1628 | 0.429338 | ||||||||
\(677\) | 48.7047 | 1.87187 | 0.935936 | − | 0.352170i | \(-0.114556\pi\) | ||||
0.935936 | + | 0.352170i | \(0.114556\pi\) | |||||||
\(678\) | −89.2766 | −3.42865 | ||||||||
\(679\) | −1.53660 | −0.0589692 | ||||||||
\(680\) | −20.6910 | −0.793464 | ||||||||
\(681\) | −44.0457 | −1.68784 | ||||||||
\(682\) | −55.2845 | −2.11695 | ||||||||
\(683\) | −33.6476 | −1.28749 | −0.643746 | − | 0.765240i | \(-0.722620\pi\) | ||||
−0.643746 | + | 0.765240i | \(0.722620\pi\) | |||||||
\(684\) | −139.730 | −5.34270 | ||||||||
\(685\) | −15.1899 | −0.580377 | ||||||||
\(686\) | 20.4646 | 0.781344 | ||||||||
\(687\) | −17.3873 | −0.663366 | ||||||||
\(688\) | 170.896 | 6.51537 | ||||||||
\(689\) | 21.4065 | 0.815524 | ||||||||
\(690\) | 38.3601 | 1.46034 | ||||||||
\(691\) | 26.6702 | 1.01458 | 0.507291 | − | 0.861775i | \(-0.330647\pi\) | ||||
0.507291 | + | 0.861775i | \(0.330647\pi\) | |||||||
\(692\) | 39.1273 | 1.48740 | ||||||||
\(693\) | 17.7238 | 0.673270 | ||||||||
\(694\) | −91.3675 | −3.46826 | ||||||||
\(695\) | 0.333669 | 0.0126568 | ||||||||
\(696\) | 286.512 | 10.8602 | ||||||||
\(697\) | 20.0433 | 0.759193 | ||||||||
\(698\) | −83.1011 | −3.14542 | ||||||||
\(699\) | −67.0977 | −2.53787 | ||||||||
\(700\) | −12.4884 | −0.472017 | ||||||||
\(701\) | −32.8004 | −1.23885 | −0.619427 | − | 0.785054i | \(-0.712635\pi\) | ||||
−0.619427 | + | 0.785054i | \(0.712635\pi\) | |||||||
\(702\) | 78.9938 | 2.98143 | ||||||||
\(703\) | 44.1824 | 1.66637 | ||||||||
\(704\) | 185.705 | 6.99902 | ||||||||
\(705\) | 12.9219 | 0.486667 | ||||||||
\(706\) | 47.4183 | 1.78461 | ||||||||
\(707\) | 8.52226 | 0.320512 | ||||||||
\(708\) | −70.6901 | −2.65670 | ||||||||
\(709\) | −3.02062 | −0.113442 | −0.0567209 | − | 0.998390i | \(-0.518065\pi\) | ||||
−0.0567209 | + | 0.998390i | \(0.518065\pi\) | |||||||
\(710\) | 16.8159 | 0.631089 | ||||||||
\(711\) | −68.9735 | −2.58671 | ||||||||
\(712\) | 66.4552 | 2.49051 | ||||||||
\(713\) | 17.9861 | 0.673586 | ||||||||
\(714\) | 10.2604 | 0.383985 | ||||||||
\(715\) | 20.8299 | 0.778995 | ||||||||
\(716\) | −49.3161 | −1.84303 | ||||||||
\(717\) | −79.5464 | −2.97071 | ||||||||
\(718\) | 70.1187 | 2.61681 | ||||||||
\(719\) | −13.0183 | −0.485501 | −0.242751 | − | 0.970089i | \(-0.578050\pi\) | ||||
−0.242751 | + | 0.970089i | \(0.578050\pi\) | |||||||
\(720\) | −77.7818 | −2.89876 | ||||||||
\(721\) | −2.17816 | −0.0811188 | ||||||||
\(722\) | −5.32761 | −0.198273 | ||||||||
\(723\) | −34.8201 | −1.29497 | ||||||||
\(724\) | 22.6596 | 0.842139 | ||||||||
\(725\) | 42.4433 | 1.57630 | ||||||||
\(726\) | −187.350 | −6.95321 | ||||||||
\(727\) | 3.17522 | 0.117762 | 0.0588811 | − | 0.998265i | \(-0.481247\pi\) | ||||
0.0588811 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(728\) | 20.3020 | 0.752443 | ||||||||
\(729\) | −36.9047 | −1.36684 | ||||||||
\(730\) | −5.07263 | −0.187747 | ||||||||
\(731\) | −26.2335 | −0.970280 | ||||||||
\(732\) | −238.871 | −8.82894 | ||||||||
\(733\) | −33.9909 | −1.25548 | −0.627742 | − | 0.778422i | \(-0.716021\pi\) | ||||
−0.627742 | + | 0.778422i | \(0.716021\pi\) | |||||||
\(734\) | −20.1584 | −0.744061 | ||||||||
\(735\) | 17.9522 | 0.662177 | ||||||||
\(736\) | −118.843 | −4.38061 | ||||||||
\(737\) | −63.8283 | −2.35115 | ||||||||
\(738\) | 129.545 | 4.76862 | ||||||||
\(739\) | 20.1546 | 0.741400 | 0.370700 | − | 0.928753i | \(-0.379118\pi\) | ||||
0.370700 | + | 0.928753i | \(0.379118\pi\) | |||||||
\(740\) | 48.7111 | 1.79065 | ||||||||
\(741\) | 51.8577 | 1.90504 | ||||||||
\(742\) | 8.24710 | 0.302761 | ||||||||
\(743\) | 37.0387 | 1.35882 | 0.679409 | − | 0.733760i | \(-0.262236\pi\) | ||||
0.679409 | + | 0.733760i | \(0.262236\pi\) | |||||||
\(744\) | −96.6315 | −3.54268 | ||||||||
\(745\) | −5.07653 | −0.185990 | ||||||||
\(746\) | 3.01644 | 0.110440 | ||||||||
\(747\) | 39.3109 | 1.43831 | ||||||||
\(748\) | −75.9037 | −2.77531 | ||||||||
\(749\) | 1.51957 | 0.0555238 | ||||||||
\(750\) | −67.2205 | −2.45455 | ||||||||
\(751\) | −15.9750 | −0.582935 | −0.291467 | − | 0.956581i | \(-0.594143\pi\) | ||||
−0.291467 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(752\) | −73.8715 | −2.69382 | ||||||||
\(753\) | 60.7380 | 2.21342 | ||||||||
\(754\) | −108.350 | −3.94588 | ||||||||
\(755\) | 9.47005 | 0.344650 | ||||||||
\(756\) | 22.3250 | 0.811953 | ||||||||
\(757\) | −36.6991 | −1.33385 | −0.666926 | − | 0.745124i | \(-0.732390\pi\) | ||||
−0.666926 | + | 0.745124i | \(0.732390\pi\) | |||||||
\(758\) | −15.2867 | −0.555237 | ||||||||
\(759\) | 89.6133 | 3.25275 | ||||||||
\(760\) | −40.2890 | −1.46144 | ||||||||
\(761\) | 18.4039 | 0.667142 | 0.333571 | − | 0.942725i | \(-0.391746\pi\) | ||||
0.333571 | + | 0.942725i | \(0.391746\pi\) | |||||||
\(762\) | −51.0345 | −1.84878 | ||||||||
\(763\) | −8.46245 | −0.306361 | ||||||||
\(764\) | −70.7105 | −2.55822 | ||||||||
\(765\) | 11.9399 | 0.431688 | ||||||||
\(766\) | −76.1465 | −2.75129 | ||||||||
\(767\) | 17.0238 | 0.614694 | ||||||||
\(768\) | 145.570 | 5.25282 | ||||||||
\(769\) | 26.6869 | 0.962354 | 0.481177 | − | 0.876624i | \(-0.340210\pi\) | ||||
0.481177 | + | 0.876624i | \(0.340210\pi\) | |||||||
\(770\) | 8.02495 | 0.289199 | ||||||||
\(771\) | 77.7034 | 2.79842 | ||||||||
\(772\) | 148.975 | 5.36172 | ||||||||
\(773\) | −27.9068 | −1.00374 | −0.501869 | − | 0.864943i | \(-0.667354\pi\) | ||||
−0.501869 | + | 0.864943i | \(0.667354\pi\) | |||||||
\(774\) | −169.554 | −6.09450 | ||||||||
\(775\) | −14.3148 | −0.514202 | ||||||||
\(776\) | 27.0852 | 0.972300 | ||||||||
\(777\) | −15.3823 | −0.551836 | ||||||||
\(778\) | 54.6919 | 1.96080 | ||||||||
\(779\) | 39.0277 | 1.39831 | ||||||||
\(780\) | 57.1732 | 2.04713 | ||||||||
\(781\) | 39.2837 | 1.40568 | ||||||||
\(782\) | 33.6630 | 1.20379 | ||||||||
\(783\) | −75.8741 | −2.71152 | ||||||||
\(784\) | −102.629 | −3.66531 | ||||||||
\(785\) | 9.14693 | 0.326468 | ||||||||
\(786\) | −14.7320 | −0.525473 | ||||||||
\(787\) | −5.29070 | −0.188593 | −0.0942966 | − | 0.995544i | \(-0.530060\pi\) | ||||
−0.0942966 | + | 0.995544i | \(0.530060\pi\) | |||||||
\(788\) | −17.3927 | −0.619590 | ||||||||
\(789\) | 45.9703 | 1.63659 | ||||||||
\(790\) | −31.2298 | −1.11111 | ||||||||
\(791\) | 6.07624 | 0.216046 | ||||||||
\(792\) | −312.411 | −11.1010 | ||||||||
\(793\) | 57.5258 | 2.04280 | ||||||||
\(794\) | 29.0108 | 1.02956 | ||||||||
\(795\) | 14.7899 | 0.524544 | ||||||||
\(796\) | 22.3809 | 0.793268 | ||||||||
\(797\) | −13.7665 | −0.487634 | −0.243817 | − | 0.969821i | \(-0.578400\pi\) | ||||
−0.243817 | + | 0.969821i | \(0.578400\pi\) | |||||||
\(798\) | 19.9787 | 0.707240 | ||||||||
\(799\) | 11.3397 | 0.401168 | ||||||||
\(800\) | 94.5846 | 3.34407 | ||||||||
\(801\) | −38.3485 | −1.35498 | ||||||||
\(802\) | 56.1803 | 1.98380 | ||||||||
\(803\) | −11.8502 | −0.418185 | ||||||||
\(804\) | −175.193 | −6.17859 | ||||||||
\(805\) | −2.61082 | −0.0920193 | ||||||||
\(806\) | 36.5432 | 1.28718 | ||||||||
\(807\) | 65.2773 | 2.29787 | ||||||||
\(808\) | −150.219 | −5.28469 | ||||||||
\(809\) | −9.50637 | −0.334226 | −0.167113 | − | 0.985938i | \(-0.553444\pi\) | ||||
−0.167113 | + | 0.985938i | \(0.553444\pi\) | |||||||
\(810\) | 12.8213 | 0.450493 | ||||||||
\(811\) | −12.1087 | −0.425195 | −0.212597 | − | 0.977140i | \(-0.568192\pi\) | ||||
−0.212597 | + | 0.977140i | \(0.568192\pi\) | |||||||
\(812\) | −30.6217 | −1.07461 | ||||||||
\(813\) | −43.8328 | −1.53728 | ||||||||
\(814\) | 155.123 | 5.43706 | ||||||||
\(815\) | −7.76994 | −0.272169 | ||||||||
\(816\) | −105.191 | −3.68242 | ||||||||
\(817\) | −51.0812 | −1.78710 | ||||||||
\(818\) | 9.27349 | 0.324240 | ||||||||
\(819\) | −11.7154 | −0.409370 | ||||||||
\(820\) | 43.0281 | 1.50261 | ||||||||
\(821\) | 10.3757 | 0.362114 | 0.181057 | − | 0.983473i | \(-0.442048\pi\) | ||||
0.181057 | + | 0.983473i | \(0.442048\pi\) | |||||||
\(822\) | −132.773 | −4.63097 | ||||||||
\(823\) | −14.8316 | −0.516998 | −0.258499 | − | 0.966011i | \(-0.583228\pi\) | ||||
−0.258499 | + | 0.966011i | \(0.583228\pi\) | |||||||
\(824\) | 38.3937 | 1.33751 | ||||||||
\(825\) | −71.3213 | −2.48309 | ||||||||
\(826\) | 6.55861 | 0.228203 | ||||||||
\(827\) | −43.3145 | −1.50619 | −0.753096 | − | 0.657911i | \(-0.771440\pi\) | ||||
−0.753096 | + | 0.657911i | \(0.771440\pi\) | |||||||
\(828\) | 159.606 | 5.54670 | ||||||||
\(829\) | 9.89858 | 0.343792 | 0.171896 | − | 0.985115i | \(-0.445011\pi\) | ||||
0.171896 | + | 0.985115i | \(0.445011\pi\) | |||||||
\(830\) | 17.7992 | 0.617819 | ||||||||
\(831\) | 12.4041 | 0.430294 | ||||||||
\(832\) | −122.751 | −4.25564 | ||||||||
\(833\) | 15.7540 | 0.545844 | ||||||||
\(834\) | 2.91654 | 0.100992 | ||||||||
\(835\) | −3.83126 | −0.132586 | ||||||||
\(836\) | −147.798 | −5.11169 | ||||||||
\(837\) | 25.5900 | 0.884519 | ||||||||
\(838\) | −89.8910 | −3.10523 | ||||||||
\(839\) | 5.23421 | 0.180705 | 0.0903525 | − | 0.995910i | \(-0.471201\pi\) | ||||
0.0903525 | + | 0.995910i | \(0.471201\pi\) | |||||||
\(840\) | 14.0268 | 0.483970 | ||||||||
\(841\) | 75.0713 | 2.58866 | ||||||||
\(842\) | 85.5899 | 2.94962 | ||||||||
\(843\) | 2.22433 | 0.0766101 | ||||||||
\(844\) | 33.1003 | 1.13936 | ||||||||
\(845\) | −1.85733 | −0.0638941 | ||||||||
\(846\) | 73.2913 | 2.51981 | ||||||||
\(847\) | 12.7512 | 0.438136 | ||||||||
\(848\) | −84.5504 | −2.90347 | ||||||||
\(849\) | −0.944010 | −0.0323983 | ||||||||
\(850\) | −26.7917 | −0.918948 | ||||||||
\(851\) | −50.4673 | −1.73000 | ||||||||
\(852\) | 107.824 | 3.69400 | ||||||||
\(853\) | 18.8471 | 0.645311 | 0.322656 | − | 0.946516i | \(-0.395424\pi\) | ||||
0.322656 | + | 0.946516i | \(0.395424\pi\) | |||||||
\(854\) | 22.1624 | 0.758383 | ||||||||
\(855\) | 23.2491 | 0.795102 | ||||||||
\(856\) | −26.7850 | −0.915491 | ||||||||
\(857\) | 10.5391 | 0.360008 | 0.180004 | − | 0.983666i | \(-0.442389\pi\) | ||||
0.180004 | + | 0.983666i | \(0.442389\pi\) | |||||||
\(858\) | 182.071 | 6.21580 | ||||||||
\(859\) | 21.7268 | 0.741308 | 0.370654 | − | 0.928771i | \(-0.379134\pi\) | ||||
0.370654 | + | 0.928771i | \(0.379134\pi\) | |||||||
\(860\) | −56.3170 | −1.92039 | ||||||||
\(861\) | −13.5877 | −0.463067 | ||||||||
\(862\) | −13.9428 | −0.474892 | ||||||||
\(863\) | −18.0073 | −0.612976 | −0.306488 | − | 0.951875i | \(-0.599154\pi\) | ||||
−0.306488 | + | 0.951875i | \(0.599154\pi\) | |||||||
\(864\) | −169.085 | −5.75239 | ||||||||
\(865\) | −6.51024 | −0.221355 | ||||||||
\(866\) | −64.3493 | −2.18668 | ||||||||
\(867\) | −33.5451 | −1.13925 | ||||||||
\(868\) | 10.3277 | 0.350546 | ||||||||
\(869\) | −72.9562 | −2.47487 | ||||||||
\(870\) | −74.8598 | −2.53799 | ||||||||
\(871\) | 42.1906 | 1.42957 | ||||||||
\(872\) | 149.165 | 5.05136 | ||||||||
\(873\) | −15.6297 | −0.528985 | ||||||||
\(874\) | 65.5478 | 2.21719 | ||||||||
\(875\) | 4.57508 | 0.154666 | ||||||||
\(876\) | −32.5260 | −1.09895 | ||||||||
\(877\) | −9.26703 | −0.312925 | −0.156463 | − | 0.987684i | \(-0.550009\pi\) | ||||
−0.156463 | + | 0.987684i | \(0.550009\pi\) | |||||||
\(878\) | −97.7628 | −3.29933 | ||||||||
\(879\) | −73.7180 | −2.48644 | ||||||||
\(880\) | −82.2730 | −2.77342 | ||||||||
\(881\) | −11.7422 | −0.395605 | −0.197803 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197803 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(882\) | 101.823 | 3.42854 | ||||||||
\(883\) | −16.7432 | −0.563452 | −0.281726 | − | 0.959495i | \(-0.590907\pi\) | ||||
−0.281726 | + | 0.959495i | \(0.590907\pi\) | |||||||
\(884\) | 50.1725 | 1.68748 | ||||||||
\(885\) | 11.7619 | 0.395370 | ||||||||
\(886\) | −55.1433 | −1.85257 | ||||||||
\(887\) | 35.0011 | 1.17522 | 0.587610 | − | 0.809144i | \(-0.300069\pi\) | ||||
0.587610 | + | 0.809144i | \(0.300069\pi\) | |||||||
\(888\) | 271.139 | 9.09882 | ||||||||
\(889\) | 3.47345 | 0.116496 | ||||||||
\(890\) | −17.3634 | −0.582023 | ||||||||
\(891\) | 29.9518 | 1.00342 | ||||||||
\(892\) | 67.0023 | 2.24340 | ||||||||
\(893\) | 22.0803 | 0.738889 | ||||||||
\(894\) | −44.3731 | −1.48406 | ||||||||
\(895\) | 8.20552 | 0.274280 | ||||||||
\(896\) | −22.5072 | −0.751914 | ||||||||
\(897\) | −59.2345 | −1.97778 | ||||||||
\(898\) | −37.7813 | −1.26078 | ||||||||
\(899\) | −35.1000 | −1.17065 | ||||||||
\(900\) | −127.027 | −4.23424 | ||||||||
\(901\) | 12.9789 | 0.432391 | ||||||||
\(902\) | 137.025 | 4.56244 | ||||||||
\(903\) | 17.7841 | 0.591819 | ||||||||
\(904\) | −107.104 | −3.56223 | ||||||||
\(905\) | −3.77025 | −0.125327 | ||||||||
\(906\) | 82.7761 | 2.75005 | ||||||||
\(907\) | −43.1837 | −1.43389 | −0.716945 | − | 0.697129i | \(-0.754460\pi\) | ||||
−0.716945 | + | 0.697129i | \(0.754460\pi\) | |||||||
\(908\) | −82.9776 | −2.75371 | ||||||||
\(909\) | 86.6852 | 2.87516 | ||||||||
\(910\) | −5.30451 | −0.175843 | ||||||||
\(911\) | −0.0291155 | −0.000964640 0 | −0.000482320 | − | 1.00000i | \(-0.500154\pi\) | ||||
−0.000482320 | 1.00000i | \(0.500154\pi\) | ||||||||
\(912\) | −204.825 | −6.78243 | ||||||||
\(913\) | 41.5808 | 1.37612 | ||||||||
\(914\) | 73.5158 | 2.43169 | ||||||||
\(915\) | 39.7449 | 1.31393 | ||||||||
\(916\) | −32.7558 | −1.08228 | ||||||||
\(917\) | 1.00267 | 0.0331112 | ||||||||
\(918\) | 47.8945 | 1.58075 | ||||||||
\(919\) | 3.03602 | 0.100149 | 0.0500745 | − | 0.998745i | \(-0.484054\pi\) | ||||
0.0500745 | + | 0.998745i | \(0.484054\pi\) | |||||||
\(920\) | 46.0201 | 1.51724 | ||||||||
\(921\) | −4.90240 | −0.161540 | ||||||||
\(922\) | −13.6832 | −0.450631 | ||||||||
\(923\) | −25.9666 | −0.854701 | ||||||||
\(924\) | 51.4564 | 1.69279 | ||||||||
\(925\) | 40.1659 | 1.32065 | ||||||||
\(926\) | 31.4469 | 1.03341 | ||||||||
\(927\) | −22.1554 | −0.727678 | ||||||||
\(928\) | 231.922 | 7.61322 | ||||||||
\(929\) | −27.6216 | −0.906236 | −0.453118 | − | 0.891451i | \(-0.649688\pi\) | ||||
−0.453118 | + | 0.891451i | \(0.649688\pi\) | |||||||
\(930\) | 25.2479 | 0.827911 | ||||||||
\(931\) | 30.6758 | 1.00536 | ||||||||
\(932\) | −126.405 | −4.14054 | ||||||||
\(933\) | 91.7411 | 3.00347 | ||||||||
\(934\) | 25.3294 | 0.828804 | ||||||||
\(935\) | 12.6293 | 0.413023 | ||||||||
\(936\) | 206.504 | 6.74981 | ||||||||
\(937\) | 17.4891 | 0.571344 | 0.285672 | − | 0.958327i | \(-0.407783\pi\) | ||||
0.285672 | + | 0.958327i | \(0.407783\pi\) | |||||||
\(938\) | 16.2544 | 0.530725 | ||||||||
\(939\) | 84.4241 | 2.75508 | ||||||||
\(940\) | 24.3435 | 0.793998 | ||||||||
\(941\) | −39.3899 | −1.28407 | −0.642037 | − | 0.766674i | \(-0.721910\pi\) | ||||
−0.642037 | + | 0.766674i | \(0.721910\pi\) | |||||||
\(942\) | 79.9517 | 2.60497 | ||||||||
\(943\) | −44.5795 | −1.45171 | ||||||||
\(944\) | −67.2398 | −2.18847 | ||||||||
\(945\) | −3.71457 | −0.120835 | ||||||||
\(946\) | −179.344 | −5.83099 | ||||||||
\(947\) | −6.71251 | −0.218127 | −0.109064 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109064 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(948\) | −200.247 | −6.50373 | ||||||||
\(949\) | 7.83301 | 0.254270 | ||||||||
\(950\) | −52.1681 | −1.69256 | ||||||||
\(951\) | 69.8819 | 2.26608 | ||||||||
\(952\) | 12.3092 | 0.398945 | ||||||||
\(953\) | −19.1723 | −0.621052 | −0.310526 | − | 0.950565i | \(-0.600505\pi\) | ||||
−0.310526 | + | 0.950565i | \(0.600505\pi\) | |||||||
\(954\) | 83.8863 | 2.71592 | ||||||||
\(955\) | 11.7653 | 0.380715 | ||||||||
\(956\) | −149.857 | −4.84673 | ||||||||
\(957\) | −174.880 | −5.65308 | ||||||||
\(958\) | 55.5346 | 1.79424 | ||||||||
\(959\) | 9.03661 | 0.291807 | ||||||||
\(960\) | −84.8096 | −2.73722 | ||||||||
\(961\) | −19.1619 | −0.618125 | ||||||||
\(962\) | −102.537 | −3.30591 | ||||||||
\(963\) | 15.4565 | 0.498077 | ||||||||
\(964\) | −65.5975 | −2.11275 | ||||||||
\(965\) | −24.7873 | −0.797932 | ||||||||
\(966\) | −22.8207 | −0.734245 | ||||||||
\(967\) | 23.3973 | 0.752405 | 0.376202 | − | 0.926537i | \(-0.377230\pi\) | ||||
0.376202 | + | 0.926537i | \(0.377230\pi\) | |||||||
\(968\) | −224.761 | −7.22410 | ||||||||
\(969\) | 31.4417 | 1.01005 | ||||||||
\(970\) | −7.07681 | −0.227223 | ||||||||
\(971\) | −15.9214 | −0.510942 | −0.255471 | − | 0.966817i | \(-0.582230\pi\) | ||||
−0.255471 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(972\) | −40.6600 | −1.30417 | ||||||||
\(973\) | −0.198502 | −0.00636370 | ||||||||
\(974\) | 70.0685 | 2.24514 | ||||||||
\(975\) | 47.1435 | 1.50980 | ||||||||
\(976\) | −227.212 | −7.27289 | ||||||||
\(977\) | −22.8197 | −0.730066 | −0.365033 | − | 0.930995i | \(-0.618942\pi\) | ||||
−0.365033 | + | 0.930995i | \(0.618942\pi\) | |||||||
\(978\) | −67.9157 | −2.17171 | ||||||||
\(979\) | −40.5628 | −1.29639 | ||||||||
\(980\) | 33.8201 | 1.08034 | ||||||||
\(981\) | −86.0768 | −2.74822 | ||||||||
\(982\) | −21.3816 | −0.682315 | ||||||||
\(983\) | −31.6106 | −1.00822 | −0.504110 | − | 0.863639i | \(-0.668179\pi\) | ||||
−0.504110 | + | 0.863639i | \(0.668179\pi\) | |||||||
\(984\) | 239.506 | 7.63517 | ||||||||
\(985\) | 2.89391 | 0.0922076 | ||||||||
\(986\) | −65.6935 | −2.09211 | ||||||||
\(987\) | −7.68734 | −0.244691 | ||||||||
\(988\) | 97.6946 | 3.10808 | ||||||||
\(989\) | 58.3475 | 1.85534 | ||||||||
\(990\) | 81.6268 | 2.59427 | ||||||||
\(991\) | −4.99185 | −0.158571 | −0.0792857 | − | 0.996852i | \(-0.525264\pi\) | ||||
−0.0792857 | + | 0.996852i | \(0.525264\pi\) | |||||||
\(992\) | −78.2201 | −2.48349 | ||||||||
\(993\) | −23.1260 | −0.733881 | ||||||||
\(994\) | −10.0039 | −0.317305 | ||||||||
\(995\) | −3.72386 | −0.118054 | ||||||||
\(996\) | 114.129 | 3.61632 | ||||||||
\(997\) | −14.5680 | −0.461374 | −0.230687 | − | 0.973028i | \(-0.574097\pi\) | ||||
−0.230687 | + | 0.973028i | \(0.574097\pi\) | |||||||
\(998\) | 21.5799 | 0.683100 | ||||||||
\(999\) | −71.8030 | −2.27175 |
(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 | 6011.2.a.e.1.3 | ✓ | 221 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6011.2.a.e.1.3 | ✓ | 221 | 1.1 | even | 1 | trivial |