Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2169,2,Mod(1,2169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2169, 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("2169.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2169 = 3^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2169.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: | \(17.3195521984\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.0822506\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0822506 | −0.0581599 | −0.0290800 | − | 0.999577i | \(-0.509258\pi\) | ||||
−0.0290800 | + | 0.999577i | \(0.509258\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99323 | −0.996617 | ||||||||
\(5\) | −4.31963 | −1.93180 | −0.965899 | − | 0.258920i | \(-0.916633\pi\) | ||||
−0.965899 | + | 0.258920i | \(0.916633\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.690569 | 0.261010 | 0.130505 | − | 0.991448i | \(-0.458340\pi\) | ||||
0.130505 | + | 0.991448i | \(0.458340\pi\) | |||||||
\(8\) | 0.328446 | 0.116123 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.355292 | 0.112353 | ||||||||
\(11\) | 2.95833 | 0.891970 | 0.445985 | − | 0.895040i | \(-0.352853\pi\) | ||||
0.445985 | + | 0.895040i | \(0.352853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.93470 | −0.536591 | −0.268295 | − | 0.963337i | \(-0.586460\pi\) | ||||
−0.268295 | + | 0.963337i | \(0.586460\pi\) | |||||||
\(14\) | −0.0567997 | −0.0151803 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95945 | 0.989864 | ||||||||
\(17\) | 2.07477 | 0.503206 | 0.251603 | − | 0.967830i | \(-0.419042\pi\) | ||||
0.251603 | + | 0.967830i | \(0.419042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.74689 | 0.859595 | 0.429797 | − | 0.902925i | \(-0.358585\pi\) | ||||
0.429797 | + | 0.902925i | \(0.358585\pi\) | |||||||
\(20\) | 8.61004 | 1.92526 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.243324 | −0.0518769 | ||||||||
\(23\) | −4.34832 | −0.906688 | −0.453344 | − | 0.891336i | \(-0.649769\pi\) | ||||
−0.453344 | + | 0.891336i | \(0.649769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.6592 | 2.73184 | ||||||||
\(26\) | 0.159131 | 0.0312081 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.37647 | −0.260127 | ||||||||
\(29\) | 8.10772 | 1.50557 | 0.752783 | − | 0.658269i | \(-0.228711\pi\) | ||||
0.752783 | + | 0.658269i | \(0.228711\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.80197 | −0.503249 | −0.251624 | − | 0.967825i | \(-0.580965\pi\) | ||||
−0.251624 | + | 0.967825i | \(0.580965\pi\) | |||||||
\(32\) | −0.982559 | −0.173694 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.170651 | −0.0292664 | ||||||||
\(35\) | −2.98300 | −0.504219 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.72312 | −1.59847 | −0.799236 | − | 0.601018i | \(-0.794762\pi\) | ||||
−0.799236 | + | 0.601018i | \(0.794762\pi\) | |||||||
\(38\) | −0.308183 | −0.0499940 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.41876 | −0.224326 | ||||||||
\(41\) | 4.09401 | 0.639378 | 0.319689 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319689 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.02779 | 0.461733 | 0.230867 | − | 0.972985i | \(-0.425844\pi\) | ||||
0.230867 | + | 0.972985i | \(0.425844\pi\) | |||||||
\(44\) | −5.89665 | −0.888953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.357652 | 0.0527329 | ||||||||
\(47\) | −6.71240 | −0.979104 | −0.489552 | − | 0.871974i | \(-0.662840\pi\) | ||||
−0.489552 | + | 0.871974i | \(0.662840\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.52312 | −0.931874 | ||||||||
\(50\) | −1.12348 | −0.158884 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.85632 | 0.534776 | ||||||||
\(53\) | 0.0484656 | 0.00665726 | 0.00332863 | − | 0.999994i | \(-0.498940\pi\) | ||||
0.00332863 | + | 0.999994i | \(0.498940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.7789 | −1.72311 | ||||||||
\(56\) | 0.226814 | 0.0303093 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.666864 | −0.0875636 | ||||||||
\(59\) | −4.50676 | −0.586730 | −0.293365 | − | 0.956000i | \(-0.594775\pi\) | ||||
−0.293365 | + | 0.956000i | \(0.594775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.62232 | −1.23201 | −0.616006 | − | 0.787742i | \(-0.711250\pi\) | ||||
−0.616006 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(62\) | 0.230464 | 0.0292689 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.83809 | −0.979762 | ||||||||
\(65\) | 8.35721 | 1.03658 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.964160 | −0.117791 | −0.0588954 | − | 0.998264i | \(-0.518758\pi\) | ||||
−0.0588954 | + | 0.998264i | \(0.518758\pi\) | |||||||
\(68\) | −4.13551 | −0.501504 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.245353 | 0.0293254 | ||||||||
\(71\) | −7.76289 | −0.921286 | −0.460643 | − | 0.887586i | \(-0.652381\pi\) | ||||
−0.460643 | + | 0.887586i | \(0.652381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.4250 | 1.92241 | 0.961203 | − | 0.275841i | \(-0.0889563\pi\) | ||||
0.961203 | + | 0.275841i | \(0.0889563\pi\) | |||||||
\(74\) | 0.799732 | 0.0929670 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.46842 | −0.856687 | ||||||||
\(77\) | 2.04293 | 0.232813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.83310 | −0.768783 | −0.384392 | − | 0.923170i | \(-0.625589\pi\) | ||||
−0.384392 | + | 0.923170i | \(0.625589\pi\) | |||||||
\(80\) | −17.1034 | −1.91222 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.336735 | −0.0371862 | ||||||||
\(83\) | 9.15477 | 1.00487 | 0.502433 | − | 0.864616i | \(-0.332438\pi\) | ||||
0.502433 | + | 0.864616i | \(0.332438\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.96225 | −0.972092 | ||||||||
\(86\) | −0.249037 | −0.0268544 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.971651 | 0.103578 | ||||||||
\(89\) | 2.36597 | 0.250793 | 0.125396 | − | 0.992107i | \(-0.459980\pi\) | ||||
0.125396 | + | 0.992107i | \(0.459980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.33605 | −0.140056 | ||||||||
\(92\) | 8.66723 | 0.903621 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.552099 | 0.0569447 | ||||||||
\(95\) | −16.1852 | −1.66056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.25335 | −0.533396 | −0.266698 | − | 0.963780i | \(-0.585933\pi\) | ||||
−0.266698 | + | 0.963780i | \(0.585933\pi\) | |||||||
\(98\) | 0.536530 | 0.0541977 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −27.2260 | −2.72260 | ||||||||
\(101\) | −9.93584 | −0.988653 | −0.494327 | − | 0.869276i | \(-0.664585\pi\) | ||||
−0.494327 | + | 0.869276i | \(0.664585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.2644 | 1.89818 | 0.949090 | − | 0.315005i | \(-0.102006\pi\) | ||||
0.949090 | + | 0.315005i | \(0.102006\pi\) | |||||||
\(104\) | −0.635446 | −0.0623106 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.00398632 | −0.000387186 0 | ||||||||
\(107\) | 7.88030 | 0.761817 | 0.380909 | − | 0.924613i | \(-0.375611\pi\) | ||||
0.380909 | + | 0.924613i | \(0.375611\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.72728 | −0.165443 | −0.0827215 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827215 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(110\) | 1.05107 | 0.100216 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.73427 | 0.258365 | ||||||||
\(113\) | −14.0431 | −1.32107 | −0.660533 | − | 0.750797i | \(-0.729670\pi\) | ||||
−0.660533 | + | 0.750797i | \(0.729670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.7831 | 1.75154 | ||||||||
\(116\) | −16.1606 | −1.50047 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.370684 | 0.0341242 | ||||||||
\(119\) | 1.43277 | 0.131342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.24829 | −0.204390 | ||||||||
\(122\) | 0.791441 | 0.0716537 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.58499 | 0.501547 | ||||||||
\(125\) | −37.4046 | −3.34557 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65498 | −0.146856 | −0.0734278 | − | 0.997301i | \(-0.523394\pi\) | ||||
−0.0734278 | + | 0.997301i | \(0.523394\pi\) | |||||||
\(128\) | 2.60981 | 0.230676 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.687385 | −0.0602877 | ||||||||
\(131\) | −17.1541 | −1.49876 | −0.749381 | − | 0.662139i | \(-0.769649\pi\) | ||||
−0.749381 | + | 0.662139i | \(0.769649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.58748 | 0.224363 | ||||||||
\(134\) | 0.0793027 | 0.00685071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.681450 | 0.0584339 | ||||||||
\(137\) | −14.7651 | −1.26147 | −0.630733 | − | 0.776000i | \(-0.717245\pi\) | ||||
−0.630733 | + | 0.776000i | \(0.717245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.3570 | 1.72666 | 0.863329 | − | 0.504641i | \(-0.168375\pi\) | ||||
0.863329 | + | 0.504641i | \(0.168375\pi\) | |||||||
\(140\) | 5.94582 | 0.502514 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.638502 | 0.0535819 | ||||||||
\(143\) | −5.72349 | −0.478623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.0223 | −2.90845 | ||||||||
\(146\) | −1.35097 | −0.111807 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.3805 | 1.59306 | ||||||||
\(149\) | −8.37820 | −0.686369 | −0.343185 | − | 0.939268i | \(-0.611506\pi\) | ||||
−0.343185 | + | 0.939268i | \(0.611506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0074 | −1.79093 | −0.895467 | − | 0.445128i | \(-0.853158\pi\) | ||||
−0.895467 | + | 0.445128i | \(0.853158\pi\) | |||||||
\(152\) | 1.23065 | 0.0998188 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.168032 | −0.0135404 | ||||||||
\(155\) | 12.1035 | 0.972175 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.208187 | −0.0166151 | −0.00830757 | − | 0.999965i | \(-0.502644\pi\) | ||||
−0.00830757 | + | 0.999965i | \(0.502644\pi\) | |||||||
\(158\) | 0.562026 | 0.0447124 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.24429 | 0.335541 | ||||||||
\(161\) | −3.00281 | −0.236655 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.85060 | 0.614906 | 0.307453 | − | 0.951563i | \(-0.400523\pi\) | ||||
0.307453 | + | 0.951563i | \(0.400523\pi\) | |||||||
\(164\) | −8.16033 | −0.637215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.752985 | −0.0584430 | ||||||||
\(167\) | 13.8766 | 1.07380 | 0.536900 | − | 0.843646i | \(-0.319595\pi\) | ||||
0.536900 | + | 0.843646i | \(0.319595\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.25692 | −0.712071 | ||||||||
\(170\) | 0.737150 | 0.0565368 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.03509 | −0.460171 | ||||||||
\(173\) | −19.3500 | −1.47115 | −0.735577 | − | 0.677441i | \(-0.763089\pi\) | ||||
−0.735577 | + | 0.677441i | \(0.763089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.43262 | 0.713039 | ||||||||
\(176\) | 11.7134 | 0.882929 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.194603 | −0.0145861 | ||||||||
\(179\) | 7.02479 | 0.525057 | 0.262529 | − | 0.964924i | \(-0.415444\pi\) | ||||
0.262529 | + | 0.964924i | \(0.415444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.22067 | 0.536708 | 0.268354 | − | 0.963320i | \(-0.413520\pi\) | ||||
0.268354 | + | 0.963320i | \(0.413520\pi\) | |||||||
\(182\) | 0.109891 | 0.00814563 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.42819 | −0.105287 | ||||||||
\(185\) | 42.0003 | 3.08792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.13786 | 0.448845 | ||||||||
\(188\) | 13.3794 | 0.975793 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.33124 | 0.0965782 | ||||||||
\(191\) | −20.7694 | −1.50282 | −0.751412 | − | 0.659834i | \(-0.770627\pi\) | ||||
−0.751412 | + | 0.659834i | \(0.770627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.7206 | −1.41952 | −0.709762 | − | 0.704442i | \(-0.751197\pi\) | ||||
−0.709762 | + | 0.704442i | \(0.751197\pi\) | |||||||
\(194\) | 0.432091 | 0.0310223 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0021 | 0.928721 | ||||||||
\(197\) | 16.2977 | 1.16116 | 0.580582 | − | 0.814201i | \(-0.302825\pi\) | ||||
0.580582 | + | 0.814201i | \(0.302825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.79014 | 0.339564 | 0.169782 | − | 0.985482i | \(-0.445694\pi\) | ||||
0.169782 | + | 0.985482i | \(0.445694\pi\) | |||||||
\(200\) | 4.48631 | 0.317230 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.817229 | 0.0575000 | ||||||||
\(203\) | 5.59893 | 0.392968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.6846 | −1.23515 | ||||||||
\(206\) | −1.58451 | −0.110398 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.66038 | −0.531152 | ||||||||
\(209\) | 11.0845 | 0.766733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.30473 | −0.296350 | −0.148175 | − | 0.988961i | \(-0.547340\pi\) | ||||
−0.148175 | + | 0.988961i | \(0.547340\pi\) | |||||||
\(212\) | −0.0966033 | −0.00663474 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.648159 | −0.0443072 | ||||||||
\(215\) | −13.0789 | −0.891975 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.93495 | −0.131353 | ||||||||
\(218\) | 0.142069 | 0.00962215 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.4713 | 1.71728 | ||||||||
\(221\) | −4.01407 | −0.270016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8068 | 0.991540 | 0.495770 | − | 0.868454i | \(-0.334886\pi\) | ||||
0.495770 | + | 0.868454i | \(0.334886\pi\) | |||||||
\(224\) | −0.678524 | −0.0453358 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.15505 | 0.0768331 | ||||||||
\(227\) | 11.9026 | 0.790000 | 0.395000 | − | 0.918681i | \(-0.370745\pi\) | ||||
0.395000 | + | 0.918681i | \(0.370745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.11465 | −0.337985 | −0.168993 | − | 0.985617i | \(-0.554051\pi\) | ||||
−0.168993 | + | 0.985617i | \(0.554051\pi\) | |||||||
\(230\) | −1.54492 | −0.101869 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.66295 | 0.174831 | ||||||||
\(233\) | 14.9300 | 0.978097 | 0.489048 | − | 0.872257i | \(-0.337344\pi\) | ||||
0.489048 | + | 0.872257i | \(0.337344\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.9951 | 1.89143 | ||||||||
\(236\) | 8.98303 | 0.584746 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.117846 | −0.00763884 | ||||||||
\(239\) | −29.8624 | −1.93164 | −0.965820 | − | 0.259215i | \(-0.916536\pi\) | ||||
−0.965820 | + | 0.259215i | \(0.916536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 0.184923 | 0.0118873 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.1795 | 1.22784 | ||||||||
\(245\) | 28.1774 | 1.80019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.24912 | −0.461250 | ||||||||
\(248\) | −0.920296 | −0.0584388 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.07655 | 0.194578 | ||||||||
\(251\) | −13.0620 | −0.824464 | −0.412232 | − | 0.911079i | \(-0.635251\pi\) | ||||
−0.412232 | + | 0.911079i | \(0.635251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8638 | −0.808738 | ||||||||
\(254\) | 0.136123 | 0.00854111 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4615 | 0.966346 | ||||||||
\(257\) | −6.35830 | −0.396620 | −0.198310 | − | 0.980139i | \(-0.563545\pi\) | ||||
−0.198310 | + | 0.980139i | \(0.563545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.71448 | −0.417218 | ||||||||
\(260\) | −16.6579 | −1.03308 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.41094 | 0.0871679 | ||||||||
\(263\) | −4.66189 | −0.287465 | −0.143732 | − | 0.989617i | \(-0.545910\pi\) | ||||
−0.143732 | + | 0.989617i | \(0.545910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.209353 | −0.0128605 | ||||||||
\(266\) | −0.212822 | −0.0130489 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.92180 | 0.117392 | ||||||||
\(269\) | 10.5251 | 0.641728 | 0.320864 | − | 0.947125i | \(-0.396027\pi\) | ||||
0.320864 | + | 0.947125i | \(0.396027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3212 | 0.626968 | 0.313484 | − | 0.949593i | \(-0.398504\pi\) | ||||
0.313484 | + | 0.949593i | \(0.398504\pi\) | |||||||
\(272\) | 8.21497 | 0.498106 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.21444 | 0.0733667 | ||||||||
\(275\) | 40.4084 | 2.43672 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1023 | 1.32800 | 0.663999 | − | 0.747734i | \(-0.268858\pi\) | ||||
0.663999 | + | 0.747734i | \(0.268858\pi\) | |||||||
\(278\) | −1.67437 | −0.100422 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.979754 | −0.0585515 | ||||||||
\(281\) | −4.22803 | −0.252223 | −0.126111 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126111 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.06769 | −0.182355 | −0.0911776 | − | 0.995835i | \(-0.529063\pi\) | ||||
−0.0911776 | + | 0.995835i | \(0.529063\pi\) | |||||||
\(284\) | 15.4733 | 0.918169 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.470761 | 0.0278367 | ||||||||
\(287\) | 2.82720 | 0.166884 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.6953 | −0.746783 | ||||||||
\(290\) | 2.88061 | 0.169155 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32.7390 | −1.91590 | ||||||||
\(293\) | 15.4694 | 0.903735 | 0.451867 | − | 0.892085i | \(-0.350758\pi\) | ||||
0.451867 | + | 0.892085i | \(0.350758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.4675 | 1.13344 | ||||||||
\(296\) | −3.19352 | −0.185619 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.689112 | 0.0399192 | ||||||||
\(299\) | 8.41272 | 0.486520 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09089 | 0.120517 | ||||||||
\(302\) | 1.81012 | 0.104161 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.8356 | 0.850881 | ||||||||
\(305\) | 41.5648 | 2.38000 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2412 | −1.15523 | −0.577614 | − | 0.816310i | \(-0.696016\pi\) | ||||
−0.577614 | + | 0.816310i | \(0.696016\pi\) | |||||||
\(308\) | −4.07204 | −0.232026 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.995518 | −0.0565416 | ||||||||
\(311\) | −1.49434 | −0.0847363 | −0.0423681 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423681 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6470 | −1.22356 | −0.611780 | − | 0.791028i | \(-0.709546\pi\) | ||||
−0.611780 | + | 0.791028i | \(0.709546\pi\) | |||||||
\(314\) | 0.0171235 | 0.000966335 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6200 | 0.766183 | ||||||||
\(317\) | −28.9329 | −1.62504 | −0.812518 | − | 0.582936i | \(-0.801904\pi\) | ||||
−0.812518 | + | 0.582936i | \(0.801904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9853 | 1.34292 | ||||||||
\(320\) | 33.8577 | 1.89270 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.246983 | 0.0137638 | ||||||||
\(323\) | 7.77394 | 0.432553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4265 | −1.46588 | ||||||||
\(326\) | −0.645716 | −0.0357629 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.34466 | 0.0742465 | ||||||||
\(329\) | −4.63537 | −0.255556 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5701 | −1.51539 | −0.757695 | − | 0.652609i | \(-0.773675\pi\) | ||||
−0.757695 | + | 0.652609i | \(0.773675\pi\) | |||||||
\(332\) | −18.2476 | −1.00147 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.14135 | −0.0624521 | ||||||||
\(335\) | 4.16481 | 0.227548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.25450 | −0.449651 | −0.224826 | − | 0.974399i | \(-0.572181\pi\) | ||||
−0.224826 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(338\) | 0.761387 | 0.0414140 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 17.8639 | 0.968804 | ||||||||
\(341\) | −8.28915 | −0.448883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.33864 | −0.504239 | ||||||||
\(344\) | 0.994464 | 0.0536179 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.59155 | 0.0855622 | ||||||||
\(347\) | −21.2018 | −1.13817 | −0.569085 | − | 0.822278i | \(-0.692703\pi\) | ||||
−0.569085 | + | 0.822278i | \(0.692703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3257 | 1.14154 | 0.570770 | − | 0.821110i | \(-0.306645\pi\) | ||||
0.570770 | + | 0.821110i | \(0.306645\pi\) | |||||||
\(350\) | −0.775838 | −0.0414703 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.90673 | −0.154929 | ||||||||
\(353\) | −2.80184 | −0.149127 | −0.0745635 | − | 0.997216i | \(-0.523756\pi\) | ||||
−0.0745635 | + | 0.997216i | \(0.523756\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.5328 | 1.77974 | ||||||||
\(356\) | −4.71594 | −0.249944 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.577793 | −0.0305373 | ||||||||
\(359\) | −4.62788 | −0.244250 | −0.122125 | − | 0.992515i | \(-0.538971\pi\) | ||||
−0.122125 | + | 0.992515i | \(0.538971\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.96085 | −0.261097 | ||||||||
\(362\) | −0.593904 | −0.0312149 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.66305 | 0.139582 | ||||||||
\(365\) | −70.9501 | −3.71370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.106183 | −0.00554270 | −0.00277135 | − | 0.999996i | \(-0.500882\pi\) | ||||
−0.00277135 | + | 0.999996i | \(0.500882\pi\) | |||||||
\(368\) | −17.2170 | −0.897497 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.45455 | −0.179593 | ||||||||
\(371\) | 0.0334688 | 0.00173761 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.6703 | −0.863157 | −0.431579 | − | 0.902075i | \(-0.642043\pi\) | ||||
−0.431579 | + | 0.902075i | \(0.642043\pi\) | |||||||
\(374\) | −0.504843 | −0.0261048 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.20466 | −0.113697 | ||||||||
\(377\) | −15.6860 | −0.807872 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.5660 | −0.850939 | −0.425469 | − | 0.904973i | \(-0.639891\pi\) | ||||
−0.425469 | + | 0.904973i | \(0.639891\pi\) | |||||||
\(380\) | 32.2608 | 1.65495 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.70830 | 0.0874041 | ||||||||
\(383\) | 25.0198 | 1.27845 | 0.639226 | − | 0.769019i | \(-0.279255\pi\) | ||||
0.639226 | + | 0.769019i | \(0.279255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.82470 | −0.449748 | ||||||||
\(386\) | 1.62203 | 0.0825594 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.4712 | 0.531592 | ||||||||
\(389\) | 32.6696 | 1.65641 | 0.828207 | − | 0.560423i | \(-0.189361\pi\) | ||||
0.828207 | + | 0.560423i | \(0.189361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.02178 | −0.456251 | ||||||||
\(392\) | −2.14249 | −0.108212 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.34050 | −0.0675333 | ||||||||
\(395\) | 29.5165 | 1.48513 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9103 | −1.09964 | −0.549822 | − | 0.835282i | \(-0.685305\pi\) | ||||
−0.549822 | + | 0.835282i | \(0.685305\pi\) | |||||||
\(398\) | −0.393992 | −0.0197490 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 54.0830 | 2.70415 | ||||||||
\(401\) | −10.2229 | −0.510508 | −0.255254 | − | 0.966874i | \(-0.582159\pi\) | ||||
−0.255254 | + | 0.966874i | \(0.582159\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.42099 | 0.270039 | ||||||||
\(404\) | 19.8045 | 0.985309 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.460516 | −0.0228550 | ||||||||
\(407\) | −28.7642 | −1.42579 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.7739 | −0.829417 | −0.414709 | − | 0.909954i | \(-0.636117\pi\) | ||||
−0.414709 | + | 0.909954i | \(0.636117\pi\) | |||||||
\(410\) | 1.45457 | 0.0718361 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −38.3985 | −1.89176 | ||||||||
\(413\) | −3.11223 | −0.153143 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.5452 | −1.94120 | ||||||||
\(416\) | 1.90096 | 0.0932023 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.911708 | −0.0445931 | ||||||||
\(419\) | −32.5790 | −1.59159 | −0.795793 | − | 0.605569i | \(-0.792946\pi\) | ||||
−0.795793 | + | 0.605569i | \(0.792946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5346 | 0.562163 | 0.281082 | − | 0.959684i | \(-0.409307\pi\) | ||||
0.281082 | + | 0.959684i | \(0.409307\pi\) | |||||||
\(422\) | 0.354066 | 0.0172357 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0159183 | 0.000773062 0 | ||||||||
\(425\) | 28.3397 | 1.37468 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.64487 | −0.321568 | ||||||||
\(428\) | −15.7073 | −0.759240 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.07575 | 0.0518772 | ||||||||
\(431\) | −15.2713 | −0.735590 | −0.367795 | − | 0.929907i | \(-0.619887\pi\) | ||||
−0.367795 | + | 0.929907i | \(0.619887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.69941 | 0.418067 | 0.209034 | − | 0.977908i | \(-0.432968\pi\) | ||||
0.209034 | + | 0.977908i | \(0.432968\pi\) | |||||||
\(434\) | 0.159151 | 0.00763949 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.44287 | 0.164883 | ||||||||
\(437\) | −16.2927 | −0.779384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.4040 | 1.40338 | 0.701689 | − | 0.712484i | \(-0.252430\pi\) | ||||
0.701689 | + | 0.712484i | \(0.252430\pi\) | |||||||
\(440\) | −4.19717 | −0.200092 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.330160 | 0.0157041 | ||||||||
\(443\) | 35.7878 | 1.70033 | 0.850164 | − | 0.526518i | \(-0.176503\pi\) | ||||
0.850164 | + | 0.526518i | \(0.176503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2201 | −0.484481 | ||||||||
\(446\) | −1.21787 | −0.0576679 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.41274 | −0.255728 | ||||||||
\(449\) | 7.50777 | 0.354314 | 0.177157 | − | 0.984183i | \(-0.443310\pi\) | ||||
0.177157 | + | 0.984183i | \(0.443310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.1114 | 0.570306 | ||||||||
\(452\) | 27.9912 | 1.31660 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.978992 | −0.0459464 | ||||||||
\(455\) | 5.77123 | 0.270559 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.7902 | −1.48708 | −0.743540 | − | 0.668691i | \(-0.766855\pi\) | ||||
−0.743540 | + | 0.668691i | \(0.766855\pi\) | |||||||
\(458\) | 0.420683 | 0.0196572 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −37.4392 | −1.74561 | ||||||||
\(461\) | 12.8715 | 0.599487 | 0.299743 | − | 0.954020i | \(-0.403099\pi\) | ||||
0.299743 | + | 0.954020i | \(0.403099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8687 | −0.551587 | −0.275794 | − | 0.961217i | \(-0.588941\pi\) | ||||
−0.275794 | + | 0.961217i | \(0.588941\pi\) | |||||||
\(464\) | 32.1021 | 1.49030 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22800 | −0.0568860 | ||||||||
\(467\) | 18.9191 | 0.875473 | 0.437736 | − | 0.899103i | \(-0.355780\pi\) | ||||
0.437736 | + | 0.899103i | \(0.355780\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.665818 | −0.0307446 | ||||||||
\(470\) | −2.38486 | −0.110006 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.48023 | −0.0681329 | ||||||||
\(473\) | 8.95719 | 0.411852 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 51.1795 | 2.34828 | ||||||||
\(476\) | −2.85585 | −0.130898 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.45620 | 0.112344 | ||||||||
\(479\) | −23.7911 | −1.08704 | −0.543522 | − | 0.839395i | \(-0.682909\pi\) | ||||
−0.543522 | + | 0.839395i | \(0.682909\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.8114 | 0.857725 | ||||||||
\(482\) | −0.0822506 | −0.00374641 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.48136 | 0.203698 | ||||||||
\(485\) | 22.6925 | 1.03041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.59589 | 0.0723165 | 0.0361583 | − | 0.999346i | \(-0.488488\pi\) | ||||
0.0361583 | + | 0.999346i | \(0.488488\pi\) | |||||||
\(488\) | −3.16041 | −0.143065 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.31761 | −0.104699 | ||||||||
\(491\) | 31.8604 | 1.43784 | 0.718920 | − | 0.695093i | \(-0.244637\pi\) | ||||
0.718920 | + | 0.695093i | \(0.244637\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8217 | 0.757610 | ||||||||
\(494\) | 0.596244 | 0.0268263 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.0943 | −0.498148 | ||||||||
\(497\) | −5.36081 | −0.240465 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3389 | 0.776194 | 0.388097 | − | 0.921619i | \(-0.373133\pi\) | ||||
0.388097 | + | 0.921619i | \(0.373133\pi\) | |||||||
\(500\) | 74.5561 | 3.33425 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.07435 | 0.0479508 | ||||||||
\(503\) | 13.8066 | 0.615607 | 0.307803 | − | 0.951450i | \(-0.400406\pi\) | ||||
0.307803 | + | 0.951450i | \(0.400406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.9192 | 1.90988 | ||||||||
\(506\) | 1.05805 | 0.0470362 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.29876 | 0.146359 | ||||||||
\(509\) | −37.2876 | −1.65274 | −0.826372 | − | 0.563124i | \(-0.809599\pi\) | ||||
−0.826372 | + | 0.563124i | \(0.809599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.3426 | 0.501768 | ||||||||
\(512\) | −6.49133 | −0.286879 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.522974 | 0.0230674 | ||||||||
\(515\) | −83.2152 | −3.66690 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.8575 | −0.873332 | ||||||||
\(518\) | 0.552270 | 0.0242653 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.74489 | 0.120371 | ||||||||
\(521\) | −35.4359 | −1.55248 | −0.776238 | − | 0.630439i | \(-0.782875\pi\) | ||||
−0.776238 | + | 0.630439i | \(0.782875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2983 | −0.975036 | −0.487518 | − | 0.873113i | \(-0.662098\pi\) | ||||
−0.487518 | + | 0.873113i | \(0.662098\pi\) | |||||||
\(524\) | 34.1922 | 1.49369 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.383443 | 0.0167189 | ||||||||
\(527\) | −5.81345 | −0.253238 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.09210 | −0.177917 | ||||||||
\(530\) | 0.0172194 | 0.000747964 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.15746 | −0.223604 | ||||||||
\(533\) | −7.92071 | −0.343084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.0400 | −1.47168 | ||||||||
\(536\) | −0.316674 | −0.0136782 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.865698 | −0.0373229 | ||||||||
\(539\) | −19.2975 | −0.831203 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.0367 | −1.20539 | −0.602697 | − | 0.797970i | \(-0.705907\pi\) | ||||
−0.602697 | + | 0.797970i | \(0.705907\pi\) | |||||||
\(542\) | −0.848925 | −0.0364644 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.03859 | −0.0874037 | ||||||||
\(545\) | 7.46119 | 0.319602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.1556 | −0.562491 | −0.281245 | − | 0.959636i | \(-0.590747\pi\) | ||||
−0.281245 | + | 0.959636i | \(0.590747\pi\) | |||||||
\(548\) | 29.4303 | 1.25720 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.32362 | −0.141719 | ||||||||
\(551\) | 30.3787 | 1.29418 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.71872 | −0.200660 | ||||||||
\(554\) | −1.81793 | −0.0772363 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.5763 | −1.72082 | ||||||||
\(557\) | 20.1003 | 0.851678 | 0.425839 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425839 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.85787 | −0.247762 | ||||||||
\(560\) | −11.8111 | −0.499108 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.347757 | 0.0146693 | ||||||||
\(563\) | 1.97240 | 0.0831268 | 0.0415634 | − | 0.999136i | \(-0.486766\pi\) | ||||
0.0415634 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 60.6611 | 2.55203 | ||||||||
\(566\) | 0.252319 | 0.0106058 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.54969 | −0.106983 | ||||||||
\(569\) | −19.0863 | −0.800139 | −0.400070 | − | 0.916485i | \(-0.631014\pi\) | ||||
−0.400070 | + | 0.916485i | \(0.631014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.1484 | 0.424697 | 0.212348 | − | 0.977194i | \(-0.431889\pi\) | ||||
0.212348 | + | 0.977194i | \(0.431889\pi\) | |||||||
\(572\) | 11.4083 | 0.477004 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.232539 | −0.00970597 | ||||||||
\(575\) | −59.3946 | −2.47693 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.2993 | 0.470395 | 0.235198 | − | 0.971948i | \(-0.424426\pi\) | ||||
0.235198 | + | 0.971948i | \(0.424426\pi\) | |||||||
\(578\) | 1.04420 | 0.0434329 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 69.8078 | 2.89861 | ||||||||
\(581\) | 6.32200 | 0.262281 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.143377 | 0.00593807 | ||||||||
\(584\) | 5.39474 | 0.223236 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.27237 | −0.0525611 | ||||||||
\(587\) | −36.1850 | −1.49352 | −0.746758 | − | 0.665095i | \(-0.768391\pi\) | ||||
−0.746758 | + | 0.665095i | \(0.768391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4987 | −0.432590 | ||||||||
\(590\) | −1.60122 | −0.0659210 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −38.4983 | −1.58227 | ||||||||
\(593\) | 28.2897 | 1.16172 | 0.580858 | − | 0.814005i | \(-0.302717\pi\) | ||||
0.580858 | + | 0.814005i | \(0.302717\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.18905 | −0.253726 | ||||||||
\(596\) | 16.6997 | 0.684047 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.691951 | −0.0282960 | ||||||||
\(599\) | 10.9989 | 0.449404 | 0.224702 | − | 0.974427i | \(-0.427859\pi\) | ||||
0.224702 | + | 0.974427i | \(0.427859\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3224 | −0.421058 | −0.210529 | − | 0.977588i | \(-0.567519\pi\) | ||||
−0.210529 | + | 0.977588i | \(0.567519\pi\) | |||||||
\(602\) | −0.171977 | −0.00700927 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 43.8658 | 1.78488 | ||||||||
\(605\) | 9.71176 | 0.394839 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.4559 | −1.07381 | −0.536906 | − | 0.843642i | \(-0.680407\pi\) | ||||
−0.536906 | + | 0.843642i | \(0.680407\pi\) | |||||||
\(608\) | −3.68154 | −0.149306 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.41873 | −0.138420 | ||||||||
\(611\) | 12.9865 | 0.525378 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8484 | 1.36712 | 0.683561 | − | 0.729893i | \(-0.260430\pi\) | ||||
0.683561 | + | 0.729893i | \(0.260430\pi\) | |||||||
\(614\) | 1.66485 | 0.0671879 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.670992 | 0.0270350 | ||||||||
\(617\) | 0.659865 | 0.0265651 | 0.0132826 | − | 0.999912i | \(-0.495772\pi\) | ||||
0.0132826 | + | 0.999912i | \(0.495772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.8866 | −1.40221 | −0.701106 | − | 0.713057i | \(-0.747310\pi\) | ||||
−0.701106 | + | 0.713057i | \(0.747310\pi\) | |||||||
\(620\) | −24.1251 | −0.968886 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.122910 | 0.00492826 | ||||||||
\(623\) | 1.63387 | 0.0654595 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 93.2779 | 3.73111 | ||||||||
\(626\) | 1.78048 | 0.0711622 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.414966 | 0.0165589 | ||||||||
\(629\) | −20.1733 | −0.804361 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.39474 | −0.254571 | −0.127285 | − | 0.991866i | \(-0.540626\pi\) | ||||
−0.127285 | + | 0.991866i | \(0.540626\pi\) | |||||||
\(632\) | −2.24430 | −0.0892735 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.37975 | 0.0945120 | ||||||||
\(635\) | 7.14890 | 0.283695 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6203 | 0.500035 | ||||||||
\(638\) | −1.97280 | −0.0781041 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.2734 | −0.445620 | ||||||||
\(641\) | −16.9466 | −0.669352 | −0.334676 | − | 0.942333i | \(-0.608627\pi\) | ||||
−0.334676 | + | 0.942333i | \(0.608627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.3993 | 0.567852 | 0.283926 | − | 0.958846i | \(-0.408363\pi\) | ||||
0.283926 | + | 0.958846i | \(0.408363\pi\) | |||||||
\(644\) | 5.98531 | 0.235854 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.639411 | −0.0251573 | ||||||||
\(647\) | −4.38744 | −0.172488 | −0.0862441 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862441 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.3325 | −0.523346 | ||||||||
\(650\) | 2.17360 | 0.0852555 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.6481 | −0.612826 | ||||||||
\(653\) | 4.56970 | 0.178826 | 0.0894132 | − | 0.995995i | \(-0.471501\pi\) | ||||
0.0894132 | + | 0.995995i | \(0.471501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 74.0994 | 2.89530 | ||||||||
\(656\) | 16.2101 | 0.632897 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.381262 | 0.0148631 | ||||||||
\(659\) | 13.6506 | 0.531751 | 0.265875 | − | 0.964007i | \(-0.414339\pi\) | ||||
0.265875 | + | 0.964007i | \(0.414339\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.4151 | 1.26080 | 0.630401 | − | 0.776270i | \(-0.282891\pi\) | ||||
0.630401 | + | 0.776270i | \(0.282891\pi\) | |||||||
\(662\) | 2.26766 | 0.0881350 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.00685 | 0.116688 | ||||||||
\(665\) | −11.1770 | −0.433424 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.2550 | −1.36508 | ||||||||
\(668\) | −27.6592 | −1.07017 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.342558 | −0.0132342 | ||||||||
\(671\) | −28.4660 | −1.09892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.237992 | 0.00917391 | 0.00458696 | − | 0.999989i | \(-0.498540\pi\) | ||||
0.00458696 | + | 0.999989i | \(0.498540\pi\) | |||||||
\(674\) | 0.678938 | 0.0261517 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.4512 | 0.709662 | ||||||||
\(677\) | 30.9534 | 1.18964 | 0.594818 | − | 0.803860i | \(-0.297224\pi\) | ||||
0.594818 | + | 0.803860i | \(0.297224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.62780 | −0.139222 | ||||||||
\(680\) | −2.94361 | −0.112882 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.681788 | 0.0261070 | ||||||||
\(683\) | 28.5801 | 1.09359 | 0.546794 | − | 0.837267i | \(-0.315848\pi\) | ||||
0.546794 | + | 0.837267i | \(0.315848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.7796 | 2.43689 | ||||||||
\(686\) | 0.768108 | 0.0293265 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.9884 | 0.457053 | ||||||||
\(689\) | −0.0937666 | −0.00357222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.89241 | −0.262200 | −0.131100 | − | 0.991369i | \(-0.541851\pi\) | ||||
−0.131100 | + | 0.991369i | \(0.541851\pi\) | |||||||
\(692\) | 38.5691 | 1.46618 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.74386 | 0.0661959 | ||||||||
\(695\) | −87.9347 | −3.33555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.49415 | 0.321739 | ||||||||
\(698\) | −1.75405 | −0.0663919 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.8014 | −0.710627 | ||||||||
\(701\) | 29.3972 | 1.11032 | 0.555158 | − | 0.831745i | \(-0.312658\pi\) | ||||
0.555158 | + | 0.831745i | \(0.312658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.4314 | −1.37404 | ||||||||
\(704\) | −23.1877 | −0.873918 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.230453 | 0.00867321 | ||||||||
\(707\) | −6.86138 | −0.258049 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.8690 | −0.408195 | −0.204098 | − | 0.978951i | \(-0.565426\pi\) | ||||
−0.204098 | + | 0.978951i | \(0.565426\pi\) | |||||||
\(710\) | −2.75809 | −0.103509 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.777094 | 0.0291228 | ||||||||
\(713\) | 12.1839 | 0.456290 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.7234 | 0.924602 | ||||||||
\(716\) | −14.0021 | −0.523281 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.380646 | 0.0142056 | ||||||||
\(719\) | 30.8283 | 1.14970 | 0.574850 | − | 0.818259i | \(-0.305060\pi\) | ||||
0.574850 | + | 0.818259i | \(0.305060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.3034 | 0.495445 | ||||||||
\(722\) | 0.408032 | 0.0151854 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.3925 | −0.534892 | ||||||||
\(725\) | 110.745 | 4.11297 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0322 | 1.03966 | 0.519828 | − | 0.854271i | \(-0.325996\pi\) | ||||
0.519828 | + | 0.854271i | \(0.325996\pi\) | |||||||
\(728\) | −0.438819 | −0.0162637 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.83569 | 0.215989 | ||||||||
\(731\) | 6.28197 | 0.232347 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.8442 | 0.954578 | 0.477289 | − | 0.878746i | \(-0.341619\pi\) | ||||
0.477289 | + | 0.878746i | \(0.341619\pi\) | |||||||
\(734\) | 0.00873360 | 0.000322363 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.27248 | 0.157486 | ||||||||
\(737\) | −2.85230 | −0.105066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.0752 | −1.58455 | −0.792273 | − | 0.610166i | \(-0.791103\pi\) | ||||
−0.792273 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(740\) | −83.7164 | −3.07748 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.00275283 | −0.000101059 0 | ||||||||
\(743\) | −13.1212 | −0.481372 | −0.240686 | − | 0.970603i | \(-0.577372\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.1907 | 1.32593 | ||||||||
\(746\) | 1.37114 | 0.0502012 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.2342 | −0.447327 | ||||||||
\(749\) | 5.44189 | 0.198842 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6870 | 1.22926 | 0.614629 | − | 0.788817i | \(-0.289306\pi\) | ||||
0.614629 | + | 0.788817i | \(0.289306\pi\) | |||||||
\(752\) | −26.5775 | −0.969180 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.29019 | 0.0469858 | ||||||||
\(755\) | 95.0637 | 3.45972 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0911 | −1.67521 | −0.837604 | − | 0.546278i | \(-0.816044\pi\) | ||||
−0.837604 | + | 0.546278i | \(0.816044\pi\) | |||||||
\(758\) | 1.36256 | 0.0494905 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.31595 | −0.192830 | ||||||||
\(761\) | −14.2727 | −0.517387 | −0.258693 | − | 0.965960i | \(-0.583292\pi\) | ||||
−0.258693 | + | 0.965960i | \(0.583292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.19280 | −0.0431823 | ||||||||
\(764\) | 41.3983 | 1.49774 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.05789 | −0.0743547 | ||||||||
\(767\) | 8.71925 | 0.314834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0154 | 0.469349 | 0.234674 | − | 0.972074i | \(-0.424598\pi\) | ||||
0.234674 | + | 0.972074i | \(0.424598\pi\) | |||||||
\(770\) | 0.725837 | 0.0261573 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39.3079 | 1.41472 | ||||||||
\(773\) | 29.9438 | 1.07700 | 0.538502 | − | 0.842624i | \(-0.318990\pi\) | ||||
0.538502 | + | 0.842624i | \(0.318990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38.2727 | −1.37480 | ||||||||
\(776\) | −1.72544 | −0.0619397 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.68709 | −0.0963369 | ||||||||
\(779\) | 15.3398 | 0.549606 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9652 | −0.821759 | ||||||||
\(782\) | 0.742046 | 0.0265355 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.8280 | −0.922428 | ||||||||
\(785\) | 0.899291 | 0.0320971 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7932 | 0.491676 | 0.245838 | − | 0.969311i | \(-0.420937\pi\) | ||||
0.245838 | + | 0.969311i | \(0.420937\pi\) | |||||||
\(788\) | −32.4852 | −1.15724 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.42774 | −0.0863753 | ||||||||
\(791\) | −9.69774 | −0.344812 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.6163 | 0.661086 | ||||||||
\(794\) | 1.80213 | 0.0639553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.54788 | −0.338416 | ||||||||
\(797\) | −18.4152 | −0.652300 | −0.326150 | − | 0.945318i | \(-0.605751\pi\) | ||||
−0.326150 | + | 0.945318i | \(0.605751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.9267 | −0.492691 | ||||||||
\(800\) | −13.4210 | −0.474503 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.840841 | 0.0296911 | ||||||||
\(803\) | 48.5907 | 1.71473 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.9710 | 0.457169 | ||||||||
\(806\) | −0.445879 | −0.0157054 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.26339 | −0.114806 | ||||||||
\(809\) | 14.7007 | 0.516849 | 0.258425 | − | 0.966031i | \(-0.416797\pi\) | ||||
0.258425 | + | 0.966031i | \(0.416797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3555 | −1.62776 | −0.813882 | − | 0.581031i | \(-0.802650\pi\) | ||||
−0.813882 | + | 0.581031i | \(0.802650\pi\) | |||||||
\(812\) | −11.1600 | −0.391639 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.36587 | 0.0829238 | ||||||||
\(815\) | −33.9117 | −1.18787 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.3448 | 0.396903 | ||||||||
\(818\) | 1.37967 | 0.0482389 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.2496 | 1.23097 | ||||||||
\(821\) | −39.2626 | −1.37027 | −0.685137 | − | 0.728414i | \(-0.740258\pi\) | ||||
−0.685137 | + | 0.728414i | \(0.740258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.0804 | −1.01368 | −0.506839 | − | 0.862041i | \(-0.669186\pi\) | ||||
−0.506839 | + | 0.862041i | \(0.669186\pi\) | |||||||
\(824\) | 6.32732 | 0.220423 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.255982 | 0.00890677 | ||||||||
\(827\) | −30.7270 | −1.06848 | −0.534242 | − | 0.845332i | \(-0.679403\pi\) | ||||
−0.534242 | + | 0.845332i | \(0.679403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.4599 | −0.571675 | −0.285837 | − | 0.958278i | \(-0.592272\pi\) | ||||
−0.285837 | + | 0.958278i | \(0.592272\pi\) | |||||||
\(830\) | 3.25262 | 0.112900 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.1644 | 0.525731 | ||||||||
\(833\) | −13.5340 | −0.468925 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −59.9416 | −2.07436 | ||||||||
\(836\) | −22.0941 | −0.764139 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.67964 | 0.0925665 | ||||||||
\(839\) | −43.2285 | −1.49241 | −0.746206 | − | 0.665715i | \(-0.768127\pi\) | ||||
−0.746206 | + | 0.665715i | \(0.768127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.7351 | 1.26673 | ||||||||
\(842\) | −0.948729 | −0.0326954 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.58034 | 0.295347 | ||||||||
\(845\) | 39.9865 | 1.37558 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.55260 | −0.0533478 | ||||||||
\(848\) | 0.191897 | 0.00658978 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.33096 | −0.0799513 | ||||||||
\(851\) | 42.2793 | 1.44931 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.36996 | 0.286582 | 0.143291 | − | 0.989681i | \(-0.454232\pi\) | ||||
0.143291 | + | 0.989681i | \(0.454232\pi\) | |||||||
\(854\) | 0.546544 | 0.0187024 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.58825 | 0.0884646 | ||||||||
\(857\) | −18.3641 | −0.627305 | −0.313653 | − | 0.949538i | \(-0.601553\pi\) | ||||
−0.313653 | + | 0.949538i | \(0.601553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.47499 | 0.0844457 | 0.0422228 | − | 0.999108i | \(-0.486556\pi\) | ||||
0.0422228 | + | 0.999108i | \(0.486556\pi\) | |||||||
\(860\) | 26.0694 | 0.888958 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.25607 | 0.0427819 | ||||||||
\(863\) | 10.0917 | 0.343525 | 0.171762 | − | 0.985138i | \(-0.445054\pi\) | ||||
0.171762 | + | 0.985138i | \(0.445054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 83.5849 | 2.84197 | ||||||||
\(866\) | −0.715532 | −0.0243148 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.85682 | 0.130909 | ||||||||
\(869\) | −20.2146 | −0.685732 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.86536 | 0.0632055 | ||||||||
\(872\) | −0.567316 | −0.0192118 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.34008 | 0.0453289 | ||||||||
\(875\) | −25.8304 | −0.873227 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.6453 | 1.81147 | 0.905736 | − | 0.423843i | \(-0.139319\pi\) | ||||
0.905736 | + | 0.423843i | \(0.139319\pi\) | |||||||
\(878\) | −2.41850 | −0.0816203 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −50.5974 | −1.70564 | ||||||||
\(881\) | −30.6985 | −1.03426 | −0.517130 | − | 0.855907i | \(-0.672999\pi\) | ||||
−0.517130 | + | 0.855907i | \(0.672999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8831 | −0.736424 | −0.368212 | − | 0.929742i | \(-0.620030\pi\) | ||||
−0.368212 | + | 0.929742i | \(0.620030\pi\) | |||||||
\(884\) | 8.00099 | 0.269102 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.94356 | −0.0988910 | ||||||||
\(887\) | 23.3921 | 0.785431 | 0.392715 | − | 0.919660i | \(-0.371536\pi\) | ||||
0.392715 | + | 0.919660i | \(0.371536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.14288 | −0.0383308 | ||||||||
\(890\) | 0.840612 | 0.0281774 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.5135 | −0.988186 | ||||||||
\(893\) | −25.1506 | −0.841633 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.3445 | −1.01430 | ||||||||
\(896\) | 1.80225 | 0.0602089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.617518 | −0.0206069 | ||||||||
\(899\) | −22.7176 | −0.757674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.100555 | 0.00334997 | ||||||||
\(902\) | −0.996173 | −0.0331689 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.61240 | −0.153406 | ||||||||
\(905\) | −31.1906 | −1.03681 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.98723 | −0.0991893 | −0.0495947 | − | 0.998769i | \(-0.515793\pi\) | ||||
−0.0495947 | + | 0.998769i | \(0.515793\pi\) | |||||||
\(908\) | −23.7246 | −0.787328 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.474687 | −0.0157357 | ||||||||
\(911\) | −42.1883 | −1.39776 | −0.698880 | − | 0.715239i | \(-0.746318\pi\) | ||||
−0.698880 | + | 0.715239i | \(0.746318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0828 | 0.896311 | ||||||||
\(914\) | 2.61476 | 0.0864885 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.1947 | 0.336842 | ||||||||
\(917\) | −11.8461 | −0.391192 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.2428 | −1.75632 | −0.878160 | − | 0.478367i | \(-0.841229\pi\) | ||||
−0.878160 | + | 0.478367i | \(0.841229\pi\) | |||||||
\(920\) | 6.16924 | 0.203394 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.05869 | −0.0348661 | ||||||||
\(923\) | 15.0189 | 0.494353 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −132.810 | −4.36677 | ||||||||
\(926\) | 0.976211 | 0.0320803 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.96631 | −0.261507 | ||||||||
\(929\) | 27.2213 | 0.893103 | 0.446552 | − | 0.894758i | \(-0.352652\pi\) | ||||
0.446552 | + | 0.894758i | \(0.352652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.4414 | −0.801033 | ||||||||
\(932\) | −29.7590 | −0.974788 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.55611 | −0.0509174 | ||||||||
\(935\) | −26.5133 | −0.867077 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.54293 | 0.246417 | 0.123208 | − | 0.992381i | \(-0.460682\pi\) | ||||
0.123208 | + | 0.992381i | \(0.460682\pi\) | |||||||
\(938\) | 0.0547639 | 0.00178811 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −57.7940 | −1.88503 | ||||||||
\(941\) | −35.4553 | −1.15581 | −0.577905 | − | 0.816104i | \(-0.696130\pi\) | ||||
−0.577905 | + | 0.816104i | \(0.696130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.8021 | −0.579716 | ||||||||
\(944\) | −17.8443 | −0.580783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.736734 | −0.0239533 | ||||||||
\(947\) | −33.0630 | −1.07440 | −0.537202 | − | 0.843454i | \(-0.680519\pi\) | ||||
−0.537202 | + | 0.843454i | \(0.680519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.7776 | −1.03155 | ||||||||
\(950\) | −4.20954 | −0.136576 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.470588 | 0.0152518 | ||||||||
\(953\) | 5.14501 | 0.166663 | 0.0833316 | − | 0.996522i | \(-0.473444\pi\) | ||||
0.0833316 | + | 0.996522i | \(0.473444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 89.7162 | 2.90315 | ||||||||
\(956\) | 59.5228 | 1.92511 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.95683 | 0.0632223 | ||||||||
\(959\) | −10.1963 | −0.329255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1490 | −0.746741 | ||||||||
\(962\) | −1.54725 | −0.0498852 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.99323 | −0.0641978 | ||||||||
\(965\) | 85.1859 | 2.74223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.82789 | 0.0909390 | 0.0454695 | − | 0.998966i | \(-0.485522\pi\) | ||||
0.0454695 | + | 0.998966i | \(0.485522\pi\) | |||||||
\(968\) | −0.738440 | −0.0237344 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.86647 | −0.0599288 | ||||||||
\(971\) | 43.0152 | 1.38042 | 0.690211 | − | 0.723608i | \(-0.257518\pi\) | ||||
0.690211 | + | 0.723608i | \(0.257518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0579 | 0.450676 | ||||||||
\(974\) | −0.131263 | −0.00420592 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.0991 | −1.21952 | ||||||||
\(977\) | 5.45876 | 0.174641 | 0.0873207 | − | 0.996180i | \(-0.472170\pi\) | ||||
0.0873207 | + | 0.996180i | \(0.472170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.99933 | 0.223700 | ||||||||
\(980\) | −56.1643 | −1.79410 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.62054 | −0.0836246 | ||||||||
\(983\) | −16.8518 | −0.537489 | −0.268745 | − | 0.963211i | \(-0.586609\pi\) | ||||
−0.268745 | + | 0.963211i | \(0.586609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.4002 | −2.24314 | ||||||||
\(986\) | −1.38359 | −0.0440625 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.4492 | 0.459690 | ||||||||
\(989\) | −13.1658 | −0.418648 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.3144 | 1.82065 | 0.910326 | − | 0.413892i | \(-0.135831\pi\) | ||||
0.910326 | + | 0.413892i | \(0.135831\pi\) | |||||||
\(992\) | 2.75310 | 0.0874111 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.440929 | 0.0139854 | ||||||||
\(995\) | −20.6916 | −0.655969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.3642 | −1.24668 | −0.623339 | − | 0.781952i | \(-0.714224\pi\) | ||||
−0.623339 | + | 0.781952i | \(0.714224\pi\) | |||||||
\(998\) | −1.42613 | −0.0451434 | ||||||||
\(999\) | 0 | 0 |
(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 | 2169.2.a.h.1.7 | 12 | ||
3.2 | odd | 2 | 241.2.a.b.1.6 | ✓ | 12 | ||
12.11 | even | 2 | 3856.2.a.n.1.4 | 12 | |||
15.14 | odd | 2 | 6025.2.a.h.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.6 | ✓ | 12 | 3.2 | odd | 2 | ||
2169.2.a.h.1.7 | 12 | 1.1 | even | 1 | trivial | ||
3856.2.a.n.1.4 | 12 | 12.11 | even | 2 | |||
6025.2.a.h.1.7 | 12 | 15.14 | odd | 2 |