Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6041 = 7 \cdot 863 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6041.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: | \(48.2376278611\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41440 | −1.70724 | −0.853621 | − | 0.520895i | \(-0.825598\pi\) | ||||
−0.853621 | + | 0.520895i | \(0.825598\pi\) | |||||||
\(3\) | 0.0560859 | 0.0323812 | 0.0161906 | − | 0.999869i | \(-0.494846\pi\) | ||||
0.0161906 | + | 0.999869i | \(0.494846\pi\) | |||||||
\(4\) | 3.82935 | 1.91467 | ||||||||
\(5\) | 0.0819711 | 0.0366586 | 0.0183293 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183293 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(6\) | −0.135414 | −0.0552826 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.41678 | −1.56157 | ||||||||
\(9\) | −2.99685 | −0.998951 | ||||||||
\(10\) | −0.197911 | −0.0625851 | ||||||||
\(11\) | 3.15377 | 0.950899 | 0.475449 | − | 0.879743i | \(-0.342286\pi\) | ||||
0.475449 | + | 0.879743i | \(0.342286\pi\) | |||||||
\(12\) | 0.214772 | 0.0619994 | ||||||||
\(13\) | 4.29773 | 1.19198 | 0.595988 | − | 0.802993i | \(-0.296761\pi\) | ||||
0.595988 | + | 0.802993i | \(0.296761\pi\) | |||||||
\(14\) | 2.41440 | 0.645277 | ||||||||
\(15\) | 0.00459743 | 0.00118705 | ||||||||
\(16\) | 3.00520 | 0.751299 | ||||||||
\(17\) | −0.551630 | −0.133790 | −0.0668949 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668949 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(18\) | 7.23562 | 1.70545 | ||||||||
\(19\) | 1.49915 | 0.343929 | 0.171964 | − | 0.985103i | \(-0.444989\pi\) | ||||
0.171964 | + | 0.985103i | \(0.444989\pi\) | |||||||
\(20\) | 0.313896 | 0.0701892 | ||||||||
\(21\) | −0.0560859 | −0.0122389 | ||||||||
\(22\) | −7.61448 | −1.62341 | ||||||||
\(23\) | 8.04809 | 1.67814 | 0.839071 | − | 0.544022i | \(-0.183099\pi\) | ||||
0.839071 | + | 0.544022i | \(0.183099\pi\) | |||||||
\(24\) | −0.247719 | −0.0505654 | ||||||||
\(25\) | −4.99328 | −0.998656 | ||||||||
\(26\) | −10.3765 | −2.03499 | ||||||||
\(27\) | −0.336339 | −0.0647285 | ||||||||
\(28\) | −3.82935 | −0.723678 | ||||||||
\(29\) | −4.31245 | −0.800803 | −0.400401 | − | 0.916340i | \(-0.631129\pi\) | ||||
−0.400401 | + | 0.916340i | \(0.631129\pi\) | |||||||
\(30\) | −0.0111000 | −0.00202658 | ||||||||
\(31\) | 1.10509 | 0.198480 | 0.0992398 | − | 0.995064i | \(-0.468359\pi\) | ||||
0.0992398 | + | 0.995064i | \(0.468359\pi\) | |||||||
\(32\) | 1.57780 | 0.278918 | ||||||||
\(33\) | 0.176882 | 0.0307913 | ||||||||
\(34\) | 1.33186 | 0.228412 | ||||||||
\(35\) | −0.0819711 | −0.0138556 | ||||||||
\(36\) | −11.4760 | −1.91267 | ||||||||
\(37\) | 0.672899 | 0.110624 | 0.0553119 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553119 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(38\) | −3.61956 | −0.587170 | ||||||||
\(39\) | 0.241042 | 0.0385976 | ||||||||
\(40\) | −0.362048 | −0.0572449 | ||||||||
\(41\) | −10.1240 | −1.58110 | −0.790552 | − | 0.612395i | \(-0.790206\pi\) | ||||
−0.790552 | + | 0.612395i | \(0.790206\pi\) | |||||||
\(42\) | 0.135414 | 0.0208948 | ||||||||
\(43\) | −9.67718 | −1.47576 | −0.737878 | − | 0.674934i | \(-0.764172\pi\) | ||||
−0.737878 | + | 0.674934i | \(0.764172\pi\) | |||||||
\(44\) | 12.0769 | 1.82066 | ||||||||
\(45\) | −0.245656 | −0.0366202 | ||||||||
\(46\) | −19.4313 | −2.86499 | ||||||||
\(47\) | −10.9562 | −1.59813 | −0.799063 | − | 0.601247i | \(-0.794671\pi\) | ||||
−0.799063 | + | 0.601247i | \(0.794671\pi\) | |||||||
\(48\) | 0.168549 | 0.0243280 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 12.0558 | 1.70495 | ||||||||
\(51\) | −0.0309387 | −0.00433228 | ||||||||
\(52\) | 16.4575 | 2.28224 | ||||||||
\(53\) | −9.48952 | −1.30349 | −0.651743 | − | 0.758440i | \(-0.725962\pi\) | ||||
−0.651743 | + | 0.758440i | \(0.725962\pi\) | |||||||
\(54\) | 0.812058 | 0.110507 | ||||||||
\(55\) | 0.258518 | 0.0348586 | ||||||||
\(56\) | 4.41678 | 0.590217 | ||||||||
\(57\) | 0.0840813 | 0.0111368 | ||||||||
\(58\) | 10.4120 | 1.36716 | ||||||||
\(59\) | 13.0712 | 1.70173 | 0.850866 | − | 0.525383i | \(-0.176078\pi\) | ||||
0.850866 | + | 0.525383i | \(0.176078\pi\) | |||||||
\(60\) | 0.0176051 | 0.00227281 | ||||||||
\(61\) | 10.3213 | 1.32150 | 0.660751 | − | 0.750605i | \(-0.270238\pi\) | ||||
0.660751 | + | 0.750605i | \(0.270238\pi\) | |||||||
\(62\) | −2.66813 | −0.338853 | ||||||||
\(63\) | 2.99685 | 0.377568 | ||||||||
\(64\) | −9.81984 | −1.22748 | ||||||||
\(65\) | 0.352290 | 0.0436962 | ||||||||
\(66\) | −0.427065 | −0.0525681 | ||||||||
\(67\) | −6.59342 | −0.805515 | −0.402757 | − | 0.915307i | \(-0.631948\pi\) | ||||
−0.402757 | + | 0.915307i | \(0.631948\pi\) | |||||||
\(68\) | −2.11238 | −0.256164 | ||||||||
\(69\) | 0.451384 | 0.0543403 | ||||||||
\(70\) | 0.197911 | 0.0236549 | ||||||||
\(71\) | 4.97738 | 0.590706 | 0.295353 | − | 0.955388i | \(-0.404563\pi\) | ||||
0.295353 | + | 0.955388i | \(0.404563\pi\) | |||||||
\(72\) | 13.2364 | 1.55993 | ||||||||
\(73\) | −1.21658 | −0.142390 | −0.0711949 | − | 0.997462i | \(-0.522681\pi\) | ||||
−0.0711949 | + | 0.997462i | \(0.522681\pi\) | |||||||
\(74\) | −1.62465 | −0.188862 | ||||||||
\(75\) | −0.280053 | −0.0323377 | ||||||||
\(76\) | 5.74077 | 0.658511 | ||||||||
\(77\) | −3.15377 | −0.359406 | ||||||||
\(78\) | −0.581973 | −0.0658955 | ||||||||
\(79\) | −11.9439 | −1.34379 | −0.671896 | − | 0.740645i | \(-0.734520\pi\) | ||||
−0.671896 | + | 0.740645i | \(0.734520\pi\) | |||||||
\(80\) | 0.246339 | 0.0275416 | ||||||||
\(81\) | 8.97170 | 0.996855 | ||||||||
\(82\) | 24.4434 | 2.69933 | ||||||||
\(83\) | 1.13422 | 0.124496 | 0.0622482 | − | 0.998061i | \(-0.480173\pi\) | ||||
0.0622482 | + | 0.998061i | \(0.480173\pi\) | |||||||
\(84\) | −0.214772 | −0.0234336 | ||||||||
\(85\) | −0.0452177 | −0.00490455 | ||||||||
\(86\) | 23.3646 | 2.51947 | ||||||||
\(87\) | −0.241868 | −0.0259310 | ||||||||
\(88\) | −13.9295 | −1.48489 | ||||||||
\(89\) | −6.27688 | −0.665348 | −0.332674 | − | 0.943042i | \(-0.607951\pi\) | ||||
−0.332674 | + | 0.943042i | \(0.607951\pi\) | |||||||
\(90\) | 0.593112 | 0.0625195 | ||||||||
\(91\) | −4.29773 | −0.450524 | ||||||||
\(92\) | 30.8189 | 3.21309 | ||||||||
\(93\) | 0.0619799 | 0.00642701 | ||||||||
\(94\) | 26.4527 | 2.72839 | ||||||||
\(95\) | 0.122887 | 0.0126080 | ||||||||
\(96\) | 0.0884924 | 0.00903172 | ||||||||
\(97\) | −1.10396 | −0.112091 | −0.0560453 | − | 0.998428i | \(-0.517849\pi\) | ||||
−0.0560453 | + | 0.998428i | \(0.517849\pi\) | |||||||
\(98\) | −2.41440 | −0.243892 | ||||||||
\(99\) | −9.45140 | −0.949902 | ||||||||
\(100\) | −19.1210 | −1.91210 | ||||||||
\(101\) | 8.62256 | 0.857976 | 0.428988 | − | 0.903310i | \(-0.358870\pi\) | ||||
0.428988 | + | 0.903310i | \(0.358870\pi\) | |||||||
\(102\) | 0.0746984 | 0.00739625 | ||||||||
\(103\) | 14.2294 | 1.40207 | 0.701033 | − | 0.713128i | \(-0.252722\pi\) | ||||
0.701033 | + | 0.713128i | \(0.252722\pi\) | |||||||
\(104\) | −18.9821 | −1.86135 | ||||||||
\(105\) | −0.00459743 | −0.000448663 0 | ||||||||
\(106\) | 22.9115 | 2.22537 | ||||||||
\(107\) | 7.21146 | 0.697159 | 0.348579 | − | 0.937279i | \(-0.386664\pi\) | ||||
0.348579 | + | 0.937279i | \(0.386664\pi\) | |||||||
\(108\) | −1.28796 | −0.123934 | ||||||||
\(109\) | −7.16991 | −0.686753 | −0.343376 | − | 0.939198i | \(-0.611571\pi\) | ||||
−0.343376 | + | 0.939198i | \(0.611571\pi\) | |||||||
\(110\) | −0.624168 | −0.0595121 | ||||||||
\(111\) | 0.0377401 | 0.00358214 | ||||||||
\(112\) | −3.00520 | −0.283964 | ||||||||
\(113\) | −2.22752 | −0.209548 | −0.104774 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104774 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(114\) | −0.203006 | −0.0190133 | ||||||||
\(115\) | 0.659711 | 0.0615183 | ||||||||
\(116\) | −16.5139 | −1.53328 | ||||||||
\(117\) | −12.8797 | −1.19073 | ||||||||
\(118\) | −31.5593 | −2.90527 | ||||||||
\(119\) | 0.551630 | 0.0505678 | ||||||||
\(120\) | −0.0203058 | −0.00185366 | ||||||||
\(121\) | −1.05371 | −0.0957918 | ||||||||
\(122\) | −24.9197 | −2.25612 | ||||||||
\(123\) | −0.567814 | −0.0511981 | ||||||||
\(124\) | 4.23176 | 0.380024 | ||||||||
\(125\) | −0.819160 | −0.0732679 | ||||||||
\(126\) | −7.23562 | −0.644600 | ||||||||
\(127\) | 17.1362 | 1.52059 | 0.760295 | − | 0.649578i | \(-0.225054\pi\) | ||||
0.760295 | + | 0.649578i | \(0.225054\pi\) | |||||||
\(128\) | 20.5535 | 1.81669 | ||||||||
\(129\) | −0.542753 | −0.0477868 | ||||||||
\(130\) | −0.850570 | −0.0745999 | ||||||||
\(131\) | 6.79906 | 0.594037 | 0.297018 | − | 0.954872i | \(-0.404008\pi\) | ||||
0.297018 | + | 0.954872i | \(0.404008\pi\) | |||||||
\(132\) | 0.677343 | 0.0589552 | ||||||||
\(133\) | −1.49915 | −0.129993 | ||||||||
\(134\) | 15.9192 | 1.37521 | ||||||||
\(135\) | −0.0275701 | −0.00237286 | ||||||||
\(136\) | 2.43643 | 0.208922 | ||||||||
\(137\) | −15.8412 | −1.35340 | −0.676702 | − | 0.736257i | \(-0.736591\pi\) | ||||
−0.676702 | + | 0.736257i | \(0.736591\pi\) | |||||||
\(138\) | −1.08982 | −0.0927720 | ||||||||
\(139\) | −21.3759 | −1.81308 | −0.906539 | − | 0.422122i | \(-0.861285\pi\) | ||||
−0.906539 | + | 0.422122i | \(0.861285\pi\) | |||||||
\(140\) | −0.313896 | −0.0265290 | ||||||||
\(141\) | −0.614489 | −0.0517493 | ||||||||
\(142\) | −12.0174 | −1.00848 | ||||||||
\(143\) | 13.5541 | 1.13345 | ||||||||
\(144\) | −9.00614 | −0.750511 | ||||||||
\(145\) | −0.353497 | −0.0293563 | ||||||||
\(146\) | 2.93731 | 0.243094 | ||||||||
\(147\) | 0.0560859 | 0.00462589 | ||||||||
\(148\) | 2.57676 | 0.211809 | ||||||||
\(149\) | 20.5007 | 1.67948 | 0.839741 | − | 0.542987i | \(-0.182707\pi\) | ||||
0.839741 | + | 0.542987i | \(0.182707\pi\) | |||||||
\(150\) | 0.676160 | 0.0552083 | ||||||||
\(151\) | −10.6366 | −0.865593 | −0.432796 | − | 0.901492i | \(-0.642473\pi\) | ||||
−0.432796 | + | 0.901492i | \(0.642473\pi\) | |||||||
\(152\) | −6.62142 | −0.537068 | ||||||||
\(153\) | 1.65315 | 0.133650 | ||||||||
\(154\) | 7.61448 | 0.613593 | ||||||||
\(155\) | 0.0905853 | 0.00727599 | ||||||||
\(156\) | 0.923033 | 0.0739018 | ||||||||
\(157\) | −8.37693 | −0.668552 | −0.334276 | − | 0.942475i | \(-0.608492\pi\) | ||||
−0.334276 | + | 0.942475i | \(0.608492\pi\) | |||||||
\(158\) | 28.8374 | 2.29418 | ||||||||
\(159\) | −0.532229 | −0.0422085 | ||||||||
\(160\) | 0.129334 | 0.0102248 | ||||||||
\(161\) | −8.04809 | −0.634278 | ||||||||
\(162\) | −21.6613 | −1.70187 | ||||||||
\(163\) | −1.95682 | −0.153270 | −0.0766349 | − | 0.997059i | \(-0.524418\pi\) | ||||
−0.0766349 | + | 0.997059i | \(0.524418\pi\) | |||||||
\(164\) | −38.7683 | −3.02730 | ||||||||
\(165\) | 0.0144992 | 0.00112876 | ||||||||
\(166\) | −2.73846 | −0.212546 | ||||||||
\(167\) | 14.8763 | 1.15116 | 0.575580 | − | 0.817745i | \(-0.304776\pi\) | ||||
0.575580 | + | 0.817745i | \(0.304776\pi\) | |||||||
\(168\) | 0.247719 | 0.0191119 | ||||||||
\(169\) | 5.47048 | 0.420806 | ||||||||
\(170\) | 0.109174 | 0.00837325 | ||||||||
\(171\) | −4.49274 | −0.343568 | ||||||||
\(172\) | −37.0573 | −2.82559 | ||||||||
\(173\) | 1.13517 | 0.0863052 | 0.0431526 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431526 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(174\) | 0.583967 | 0.0442704 | ||||||||
\(175\) | 4.99328 | 0.377457 | ||||||||
\(176\) | 9.47771 | 0.714409 | ||||||||
\(177\) | 0.733113 | 0.0551041 | ||||||||
\(178\) | 15.1549 | 1.13591 | ||||||||
\(179\) | 10.9609 | 0.819256 | 0.409628 | − | 0.912253i | \(-0.365659\pi\) | ||||
0.409628 | + | 0.912253i | \(0.365659\pi\) | |||||||
\(180\) | −0.940700 | −0.0701156 | ||||||||
\(181\) | −15.4773 | −1.15042 | −0.575210 | − | 0.818005i | \(-0.695080\pi\) | ||||
−0.575210 | + | 0.818005i | \(0.695080\pi\) | |||||||
\(182\) | 10.3765 | 0.769154 | ||||||||
\(183\) | 0.578877 | 0.0427918 | ||||||||
\(184\) | −35.5466 | −2.62053 | ||||||||
\(185\) | 0.0551583 | 0.00405532 | ||||||||
\(186\) | −0.149644 | −0.0109725 | ||||||||
\(187\) | −1.73972 | −0.127221 | ||||||||
\(188\) | −41.9551 | −3.05989 | ||||||||
\(189\) | 0.336339 | 0.0244651 | ||||||||
\(190\) | −0.296699 | −0.0215248 | ||||||||
\(191\) | −1.92433 | −0.139240 | −0.0696198 | − | 0.997574i | \(-0.522179\pi\) | ||||
−0.0696198 | + | 0.997574i | \(0.522179\pi\) | |||||||
\(192\) | −0.550755 | −0.0397473 | ||||||||
\(193\) | −15.6916 | −1.12951 | −0.564754 | − | 0.825259i | \(-0.691029\pi\) | ||||
−0.564754 | + | 0.825259i | \(0.691029\pi\) | |||||||
\(194\) | 2.66542 | 0.191366 | ||||||||
\(195\) | 0.0197585 | 0.00141493 | ||||||||
\(196\) | 3.82935 | 0.273525 | ||||||||
\(197\) | −9.76693 | −0.695865 | −0.347932 | − | 0.937520i | \(-0.613116\pi\) | ||||
−0.347932 | + | 0.937520i | \(0.613116\pi\) | |||||||
\(198\) | 22.8195 | 1.62171 | ||||||||
\(199\) | 0.135391 | 0.00959761 | 0.00479880 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00479880 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(200\) | 22.0542 | 1.55947 | ||||||||
\(201\) | −0.369798 | −0.0260836 | ||||||||
\(202\) | −20.8183 | −1.46477 | ||||||||
\(203\) | 4.31245 | 0.302675 | ||||||||
\(204\) | −0.118475 | −0.00829490 | ||||||||
\(205\) | −0.829876 | −0.0579611 | ||||||||
\(206\) | −34.3556 | −2.39367 | ||||||||
\(207\) | −24.1189 | −1.67638 | ||||||||
\(208\) | 12.9155 | 0.895530 | ||||||||
\(209\) | 4.72799 | 0.327042 | ||||||||
\(210\) | 0.0111000 | 0.000765976 0 | ||||||||
\(211\) | 0.819139 | 0.0563919 | 0.0281959 | − | 0.999602i | \(-0.491024\pi\) | ||||
0.0281959 | + | 0.999602i | \(0.491024\pi\) | |||||||
\(212\) | −36.3387 | −2.49575 | ||||||||
\(213\) | 0.279161 | 0.0191278 | ||||||||
\(214\) | −17.4114 | −1.19022 | ||||||||
\(215\) | −0.793249 | −0.0540992 | ||||||||
\(216\) | 1.48554 | 0.101078 | ||||||||
\(217\) | −1.10509 | −0.0750183 | ||||||||
\(218\) | 17.3111 | 1.17245 | ||||||||
\(219\) | −0.0682329 | −0.00461075 | ||||||||
\(220\) | 0.989956 | 0.0667428 | ||||||||
\(221\) | −2.37076 | −0.159474 | ||||||||
\(222\) | −0.0911199 | −0.00611557 | ||||||||
\(223\) | 9.55532 | 0.639872 | 0.319936 | − | 0.947439i | \(-0.396339\pi\) | ||||
0.319936 | + | 0.947439i | \(0.396339\pi\) | |||||||
\(224\) | −1.57780 | −0.105421 | ||||||||
\(225\) | 14.9641 | 0.997609 | ||||||||
\(226\) | 5.37814 | 0.357749 | ||||||||
\(227\) | −29.7144 | −1.97222 | −0.986108 | − | 0.166103i | \(-0.946882\pi\) | ||||
−0.986108 | + | 0.166103i | \(0.946882\pi\) | |||||||
\(228\) | 0.321976 | 0.0213234 | ||||||||
\(229\) | 24.0175 | 1.58712 | 0.793561 | − | 0.608490i | \(-0.208224\pi\) | ||||
0.793561 | + | 0.608490i | \(0.208224\pi\) | |||||||
\(230\) | −1.59281 | −0.105027 | ||||||||
\(231\) | −0.176882 | −0.0116380 | ||||||||
\(232\) | 19.0472 | 1.25051 | ||||||||
\(233\) | −5.08403 | −0.333066 | −0.166533 | − | 0.986036i | \(-0.553257\pi\) | ||||
−0.166533 | + | 0.986036i | \(0.553257\pi\) | |||||||
\(234\) | 31.0967 | 2.03286 | ||||||||
\(235\) | −0.898092 | −0.0585851 | ||||||||
\(236\) | 50.0543 | 3.25826 | ||||||||
\(237\) | −0.669884 | −0.0435137 | ||||||||
\(238\) | −1.33186 | −0.0863315 | ||||||||
\(239\) | −7.01350 | −0.453666 | −0.226833 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226833 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(240\) | 0.0138162 | 0.000891830 0 | ||||||||
\(241\) | −18.7569 | −1.20824 | −0.604120 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604120 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(242\) | 2.54408 | 0.163540 | ||||||||
\(243\) | 1.51220 | 0.0970079 | ||||||||
\(244\) | 39.5237 | 2.53024 | ||||||||
\(245\) | 0.0819711 | 0.00523694 | ||||||||
\(246\) | 1.37093 | 0.0874075 | ||||||||
\(247\) | 6.44295 | 0.409955 | ||||||||
\(248\) | −4.88093 | −0.309939 | ||||||||
\(249\) | 0.0636136 | 0.00403135 | ||||||||
\(250\) | 1.97778 | 0.125086 | ||||||||
\(251\) | −26.5570 | −1.67626 | −0.838130 | − | 0.545470i | \(-0.816351\pi\) | ||||
−0.838130 | + | 0.545470i | \(0.816351\pi\) | |||||||
\(252\) | 11.4760 | 0.722919 | ||||||||
\(253\) | 25.3818 | 1.59574 | ||||||||
\(254\) | −41.3736 | −2.59601 | ||||||||
\(255\) | −0.00253608 | −0.000158815 0 | ||||||||
\(256\) | −29.9847 | −1.87404 | ||||||||
\(257\) | 15.1895 | 0.947498 | 0.473749 | − | 0.880660i | \(-0.342900\pi\) | ||||
0.473749 | + | 0.880660i | \(0.342900\pi\) | |||||||
\(258\) | 1.31043 | 0.0815836 | ||||||||
\(259\) | −0.672899 | −0.0418119 | ||||||||
\(260\) | 1.34904 | 0.0836639 | ||||||||
\(261\) | 12.9238 | 0.799963 | ||||||||
\(262\) | −16.4157 | −1.01416 | ||||||||
\(263\) | 28.1462 | 1.73557 | 0.867785 | − | 0.496939i | \(-0.165543\pi\) | ||||
0.867785 | + | 0.496939i | \(0.165543\pi\) | |||||||
\(264\) | −0.781250 | −0.0480826 | ||||||||
\(265\) | −0.777867 | −0.0477840 | ||||||||
\(266\) | 3.61956 | 0.221929 | ||||||||
\(267\) | −0.352045 | −0.0215448 | ||||||||
\(268\) | −25.2485 | −1.54230 | ||||||||
\(269\) | −5.63250 | −0.343420 | −0.171710 | − | 0.985148i | \(-0.554929\pi\) | ||||
−0.171710 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(270\) | 0.0665653 | 0.00405104 | ||||||||
\(271\) | −14.0654 | −0.854413 | −0.427207 | − | 0.904154i | \(-0.640502\pi\) | ||||
−0.427207 | + | 0.904154i | \(0.640502\pi\) | |||||||
\(272\) | −1.65776 | −0.100516 | ||||||||
\(273\) | −0.241042 | −0.0145885 | ||||||||
\(274\) | 38.2470 | 2.31059 | ||||||||
\(275\) | −15.7477 | −0.949621 | ||||||||
\(276\) | 1.72851 | 0.104044 | ||||||||
\(277\) | 3.44564 | 0.207029 | 0.103514 | − | 0.994628i | \(-0.466991\pi\) | ||||
0.103514 | + | 0.994628i | \(0.466991\pi\) | |||||||
\(278\) | 51.6100 | 3.09536 | ||||||||
\(279\) | −3.31179 | −0.198272 | ||||||||
\(280\) | 0.362048 | 0.0216365 | ||||||||
\(281\) | −2.96343 | −0.176783 | −0.0883916 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883916 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(282\) | 1.48362 | 0.0883485 | ||||||||
\(283\) | 29.6443 | 1.76217 | 0.881085 | − | 0.472959i | \(-0.156814\pi\) | ||||
0.881085 | + | 0.472959i | \(0.156814\pi\) | |||||||
\(284\) | 19.0601 | 1.13101 | ||||||||
\(285\) | 0.00689224 | 0.000408261 0 | ||||||||
\(286\) | −32.7250 | −1.93507 | ||||||||
\(287\) | 10.1240 | 0.597601 | ||||||||
\(288\) | −4.72844 | −0.278626 | ||||||||
\(289\) | −16.6957 | −0.982100 | ||||||||
\(290\) | 0.853484 | 0.0501183 | ||||||||
\(291\) | −0.0619168 | −0.00362963 | ||||||||
\(292\) | −4.65870 | −0.272630 | ||||||||
\(293\) | −5.71006 | −0.333585 | −0.166793 | − | 0.985992i | \(-0.553341\pi\) | ||||
−0.166793 | + | 0.985992i | \(0.553341\pi\) | |||||||
\(294\) | −0.135414 | −0.00789751 | ||||||||
\(295\) | 1.07147 | 0.0623831 | ||||||||
\(296\) | −2.97204 | −0.172747 | ||||||||
\(297\) | −1.06074 | −0.0615502 | ||||||||
\(298\) | −49.4970 | −2.86728 | ||||||||
\(299\) | 34.5885 | 2.00030 | ||||||||
\(300\) | −1.07242 | −0.0619161 | ||||||||
\(301\) | 9.67718 | 0.557783 | ||||||||
\(302\) | 25.6810 | 1.47778 | ||||||||
\(303\) | 0.483604 | 0.0277823 | ||||||||
\(304\) | 4.50524 | 0.258393 | ||||||||
\(305\) | 0.846045 | 0.0484444 | ||||||||
\(306\) | −3.99138 | −0.228172 | ||||||||
\(307\) | 9.48632 | 0.541413 | 0.270706 | − | 0.962662i | \(-0.412743\pi\) | ||||
0.270706 | + | 0.962662i | \(0.412743\pi\) | |||||||
\(308\) | −12.0769 | −0.688145 | ||||||||
\(309\) | 0.798070 | 0.0454006 | ||||||||
\(310\) | −0.218710 | −0.0124219 | ||||||||
\(311\) | −17.1321 | −0.971474 | −0.485737 | − | 0.874105i | \(-0.661449\pi\) | ||||
−0.485737 | + | 0.874105i | \(0.661449\pi\) | |||||||
\(312\) | −1.06463 | −0.0602728 | ||||||||
\(313\) | −21.4207 | −1.21077 | −0.605385 | − | 0.795933i | \(-0.706981\pi\) | ||||
−0.605385 | + | 0.795933i | \(0.706981\pi\) | |||||||
\(314\) | 20.2253 | 1.14138 | ||||||||
\(315\) | 0.245656 | 0.0138411 | ||||||||
\(316\) | −45.7373 | −2.57292 | ||||||||
\(317\) | −1.31458 | −0.0738340 | −0.0369170 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369170 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(318\) | 1.28501 | 0.0720600 | ||||||||
\(319\) | −13.6005 | −0.761482 | ||||||||
\(320\) | −0.804943 | −0.0449977 | ||||||||
\(321\) | 0.404462 | 0.0225748 | ||||||||
\(322\) | 19.4313 | 1.08287 | ||||||||
\(323\) | −0.826977 | −0.0460142 | ||||||||
\(324\) | 34.3557 | 1.90865 | ||||||||
\(325\) | −21.4598 | −1.19037 | ||||||||
\(326\) | 4.72455 | 0.261669 | ||||||||
\(327\) | −0.402131 | −0.0222379 | ||||||||
\(328\) | 44.7155 | 2.46900 | ||||||||
\(329\) | 10.9562 | 0.604035 | ||||||||
\(330\) | −0.0350070 | −0.00192707 | ||||||||
\(331\) | −6.00091 | −0.329840 | −0.164920 | − | 0.986307i | \(-0.552737\pi\) | ||||
−0.164920 | + | 0.986307i | \(0.552737\pi\) | |||||||
\(332\) | 4.34331 | 0.238370 | ||||||||
\(333\) | −2.01658 | −0.110508 | ||||||||
\(334\) | −35.9173 | −1.96531 | ||||||||
\(335\) | −0.540470 | −0.0295291 | ||||||||
\(336\) | −0.168549 | −0.00919511 | ||||||||
\(337\) | −28.9489 | −1.57695 | −0.788475 | − | 0.615067i | \(-0.789129\pi\) | ||||
−0.788475 | + | 0.615067i | \(0.789129\pi\) | |||||||
\(338\) | −13.2079 | −0.718417 | ||||||||
\(339\) | −0.124933 | −0.00678542 | ||||||||
\(340\) | −0.173154 | −0.00939061 | ||||||||
\(341\) | 3.48520 | 0.188734 | ||||||||
\(342\) | 10.8473 | 0.586554 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 42.7420 | 2.30449 | ||||||||
\(345\) | 0.0370005 | 0.00199204 | ||||||||
\(346\) | −2.74075 | −0.147344 | ||||||||
\(347\) | 22.5157 | 1.20871 | 0.604354 | − | 0.796716i | \(-0.293431\pi\) | ||||
0.604354 | + | 0.796716i | \(0.293431\pi\) | |||||||
\(348\) | −0.926196 | −0.0496493 | ||||||||
\(349\) | 5.94338 | 0.318142 | 0.159071 | − | 0.987267i | \(-0.449150\pi\) | ||||
0.159071 | + | 0.987267i | \(0.449150\pi\) | |||||||
\(350\) | −12.0558 | −0.644409 | ||||||||
\(351\) | −1.44549 | −0.0771548 | ||||||||
\(352\) | 4.97603 | 0.265223 | ||||||||
\(353\) | 7.95562 | 0.423435 | 0.211718 | − | 0.977331i | \(-0.432094\pi\) | ||||
0.211718 | + | 0.977331i | \(0.432094\pi\) | |||||||
\(354\) | −1.77003 | −0.0940761 | ||||||||
\(355\) | 0.408001 | 0.0216545 | ||||||||
\(356\) | −24.0364 | −1.27392 | ||||||||
\(357\) | 0.0309387 | 0.00163745 | ||||||||
\(358\) | −26.4640 | −1.39867 | ||||||||
\(359\) | 33.8130 | 1.78458 | 0.892291 | − | 0.451460i | \(-0.149097\pi\) | ||||
0.892291 | + | 0.451460i | \(0.149097\pi\) | |||||||
\(360\) | 1.08501 | 0.0571848 | ||||||||
\(361\) | −16.7525 | −0.881713 | ||||||||
\(362\) | 37.3685 | 1.96405 | ||||||||
\(363\) | −0.0590983 | −0.00310186 | ||||||||
\(364\) | −16.4575 | −0.862607 | ||||||||
\(365\) | −0.0997243 | −0.00521981 | ||||||||
\(366\) | −1.39764 | −0.0730560 | ||||||||
\(367\) | 20.0561 | 1.04692 | 0.523460 | − | 0.852050i | \(-0.324641\pi\) | ||||
0.523460 | + | 0.852050i | \(0.324641\pi\) | |||||||
\(368\) | 24.1861 | 1.26079 | ||||||||
\(369\) | 30.3402 | 1.57945 | ||||||||
\(370\) | −0.133174 | −0.00692340 | ||||||||
\(371\) | 9.48952 | 0.492672 | ||||||||
\(372\) | 0.237342 | 0.0123056 | ||||||||
\(373\) | −31.4212 | −1.62693 | −0.813463 | − | 0.581617i | \(-0.802420\pi\) | ||||
−0.813463 | + | 0.581617i | \(0.802420\pi\) | |||||||
\(374\) | 4.20038 | 0.217196 | ||||||||
\(375\) | −0.0459434 | −0.00237251 | ||||||||
\(376\) | 48.3911 | 2.49558 | ||||||||
\(377\) | −18.5338 | −0.954537 | ||||||||
\(378\) | −0.812058 | −0.0417678 | ||||||||
\(379\) | −3.80824 | −0.195616 | −0.0978081 | − | 0.995205i | \(-0.531183\pi\) | ||||
−0.0978081 | + | 0.995205i | \(0.531183\pi\) | |||||||
\(380\) | 0.470577 | 0.0241401 | ||||||||
\(381\) | 0.961098 | 0.0492385 | ||||||||
\(382\) | 4.64611 | 0.237716 | ||||||||
\(383\) | 22.8584 | 1.16801 | 0.584004 | − | 0.811751i | \(-0.301485\pi\) | ||||
0.584004 | + | 0.811751i | \(0.301485\pi\) | |||||||
\(384\) | 1.15276 | 0.0588265 | ||||||||
\(385\) | −0.258518 | −0.0131753 | ||||||||
\(386\) | 37.8859 | 1.92834 | ||||||||
\(387\) | 29.0011 | 1.47421 | ||||||||
\(388\) | −4.22746 | −0.214617 | ||||||||
\(389\) | −6.78685 | −0.344107 | −0.172054 | − | 0.985088i | \(-0.555040\pi\) | ||||
−0.172054 | + | 0.985088i | \(0.555040\pi\) | |||||||
\(390\) | −0.0477050 | −0.00241564 | ||||||||
\(391\) | −4.43956 | −0.224518 | ||||||||
\(392\) | −4.41678 | −0.223081 | ||||||||
\(393\) | 0.381331 | 0.0192356 | ||||||||
\(394\) | 23.5813 | 1.18801 | ||||||||
\(395\) | −0.979054 | −0.0492616 | ||||||||
\(396\) | −36.1927 | −1.81875 | ||||||||
\(397\) | −19.4657 | −0.976955 | −0.488478 | − | 0.872576i | \(-0.662448\pi\) | ||||
−0.488478 | + | 0.872576i | \(0.662448\pi\) | |||||||
\(398\) | −0.326888 | −0.0163854 | ||||||||
\(399\) | −0.0840813 | −0.00420933 | ||||||||
\(400\) | −15.0058 | −0.750289 | ||||||||
\(401\) | 34.5712 | 1.72641 | 0.863203 | − | 0.504857i | \(-0.168455\pi\) | ||||
0.863203 | + | 0.504857i | \(0.168455\pi\) | |||||||
\(402\) | 0.892842 | 0.0445309 | ||||||||
\(403\) | 4.74937 | 0.236583 | ||||||||
\(404\) | 33.0187 | 1.64274 | ||||||||
\(405\) | 0.735420 | 0.0365433 | ||||||||
\(406\) | −10.4120 | −0.516739 | ||||||||
\(407\) | 2.12217 | 0.105192 | ||||||||
\(408\) | 0.136649 | 0.00676514 | ||||||||
\(409\) | 26.9808 | 1.33411 | 0.667057 | − | 0.745007i | \(-0.267554\pi\) | ||||
0.667057 | + | 0.745007i | \(0.267554\pi\) | |||||||
\(410\) | 2.00366 | 0.0989535 | ||||||||
\(411\) | −0.888467 | −0.0438249 | ||||||||
\(412\) | 54.4894 | 2.68450 | ||||||||
\(413\) | −13.0712 | −0.643194 | ||||||||
\(414\) | 58.2329 | 2.86199 | ||||||||
\(415\) | 0.0929730 | 0.00456387 | ||||||||
\(416\) | 6.78096 | 0.332464 | ||||||||
\(417\) | −1.19889 | −0.0587097 | ||||||||
\(418\) | −11.4153 | −0.558339 | ||||||||
\(419\) | −19.4415 | −0.949779 | −0.474889 | − | 0.880046i | \(-0.657512\pi\) | ||||
−0.474889 | + | 0.880046i | \(0.657512\pi\) | |||||||
\(420\) | −0.0176051 | −0.000859042 0 | ||||||||
\(421\) | −13.4138 | −0.653748 | −0.326874 | − | 0.945068i | \(-0.605995\pi\) | ||||
−0.326874 | + | 0.945068i | \(0.605995\pi\) | |||||||
\(422\) | −1.97773 | −0.0962745 | ||||||||
\(423\) | 32.8341 | 1.59645 | ||||||||
\(424\) | 41.9131 | 2.03548 | ||||||||
\(425\) | 2.75444 | 0.133610 | ||||||||
\(426\) | −0.674007 | −0.0326557 | ||||||||
\(427\) | −10.3213 | −0.499481 | ||||||||
\(428\) | 27.6152 | 1.33483 | ||||||||
\(429\) | 0.760192 | 0.0367024 | ||||||||
\(430\) | 1.91522 | 0.0923603 | ||||||||
\(431\) | 2.07220 | 0.0998145 | 0.0499073 | − | 0.998754i | \(-0.484107\pi\) | ||||
0.0499073 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(432\) | −1.01076 | −0.0486304 | ||||||||
\(433\) | 11.0911 | 0.533003 | 0.266502 | − | 0.963834i | \(-0.414132\pi\) | ||||
0.266502 | + | 0.963834i | \(0.414132\pi\) | |||||||
\(434\) | 2.66813 | 0.128074 | ||||||||
\(435\) | −0.0198262 | −0.000950593 0 | ||||||||
\(436\) | −27.4561 | −1.31491 | ||||||||
\(437\) | 12.0653 | 0.577162 | ||||||||
\(438\) | 0.164742 | 0.00787167 | ||||||||
\(439\) | −29.7983 | −1.42220 | −0.711098 | − | 0.703093i | \(-0.751802\pi\) | ||||
−0.711098 | + | 0.703093i | \(0.751802\pi\) | |||||||
\(440\) | −1.14182 | −0.0544341 | ||||||||
\(441\) | −2.99685 | −0.142707 | ||||||||
\(442\) | 5.72396 | 0.272261 | ||||||||
\(443\) | 38.2754 | 1.81852 | 0.909259 | − | 0.416231i | \(-0.136649\pi\) | ||||
0.909259 | + | 0.416231i | \(0.136649\pi\) | |||||||
\(444\) | 0.144520 | 0.00685862 | ||||||||
\(445\) | −0.514523 | −0.0243907 | ||||||||
\(446\) | −23.0704 | −1.09242 | ||||||||
\(447\) | 1.14980 | 0.0543837 | ||||||||
\(448\) | 9.81984 | 0.463944 | ||||||||
\(449\) | −13.6143 | −0.642498 | −0.321249 | − | 0.946995i | \(-0.604103\pi\) | ||||
−0.321249 | + | 0.946995i | \(0.604103\pi\) | |||||||
\(450\) | −36.1295 | −1.70316 | ||||||||
\(451\) | −31.9288 | −1.50347 | ||||||||
\(452\) | −8.52996 | −0.401216 | ||||||||
\(453\) | −0.596562 | −0.0280289 | ||||||||
\(454\) | 71.7427 | 3.36705 | ||||||||
\(455\) | −0.352290 | −0.0165156 | ||||||||
\(456\) | −0.371368 | −0.0173909 | ||||||||
\(457\) | −13.2829 | −0.621349 | −0.310675 | − | 0.950516i | \(-0.600555\pi\) | ||||
−0.310675 | + | 0.950516i | \(0.600555\pi\) | |||||||
\(458\) | −57.9880 | −2.70960 | ||||||||
\(459\) | 0.185535 | 0.00866002 | ||||||||
\(460\) | 2.52626 | 0.117788 | ||||||||
\(461\) | −25.1599 | −1.17181 | −0.585907 | − | 0.810378i | \(-0.699262\pi\) | ||||
−0.585907 | + | 0.810378i | \(0.699262\pi\) | |||||||
\(462\) | 0.427065 | 0.0198689 | ||||||||
\(463\) | −24.1655 | −1.12306 | −0.561532 | − | 0.827455i | \(-0.689788\pi\) | ||||
−0.561532 | + | 0.827455i | \(0.689788\pi\) | |||||||
\(464\) | −12.9598 | −0.601642 | ||||||||
\(465\) | 0.00508056 | 0.000235605 0 | ||||||||
\(466\) | 12.2749 | 0.568624 | ||||||||
\(467\) | 18.5509 | 0.858435 | 0.429217 | − | 0.903201i | \(-0.358789\pi\) | ||||
0.429217 | + | 0.903201i | \(0.358789\pi\) | |||||||
\(468\) | −49.3207 | −2.27985 | ||||||||
\(469\) | 6.59342 | 0.304456 | ||||||||
\(470\) | 2.16836 | 0.100019 | ||||||||
\(471\) | −0.469828 | −0.0216485 | ||||||||
\(472\) | −57.7328 | −2.65737 | ||||||||
\(473\) | −30.5196 | −1.40329 | ||||||||
\(474\) | 1.61737 | 0.0742883 | ||||||||
\(475\) | −7.48568 | −0.343467 | ||||||||
\(476\) | 2.11238 | 0.0968208 | ||||||||
\(477\) | 28.4387 | 1.30212 | ||||||||
\(478\) | 16.9334 | 0.774517 | ||||||||
\(479\) | −37.6934 | −1.72226 | −0.861129 | − | 0.508387i | \(-0.830242\pi\) | ||||
−0.861129 | + | 0.508387i | \(0.830242\pi\) | |||||||
\(480\) | 0.00725382 | 0.000331090 0 | ||||||||
\(481\) | 2.89194 | 0.131861 | ||||||||
\(482\) | 45.2868 | 2.06276 | ||||||||
\(483\) | −0.451384 | −0.0205387 | ||||||||
\(484\) | −4.03502 | −0.183410 | ||||||||
\(485\) | −0.0904932 | −0.00410908 | ||||||||
\(486\) | −3.65107 | −0.165616 | ||||||||
\(487\) | −37.2945 | −1.68997 | −0.844987 | − | 0.534786i | \(-0.820392\pi\) | ||||
−0.844987 | + | 0.534786i | \(0.820392\pi\) | |||||||
\(488\) | −45.5867 | −2.06361 | ||||||||
\(489\) | −0.109750 | −0.00496306 | ||||||||
\(490\) | −0.197911 | −0.00894073 | ||||||||
\(491\) | −10.2577 | −0.462922 | −0.231461 | − | 0.972844i | \(-0.574351\pi\) | ||||
−0.231461 | + | 0.972844i | \(0.574351\pi\) | |||||||
\(492\) | −2.17436 | −0.0980276 | ||||||||
\(493\) | 2.37888 | 0.107139 | ||||||||
\(494\) | −15.5559 | −0.699892 | ||||||||
\(495\) | −0.774742 | −0.0348221 | ||||||||
\(496\) | 3.32101 | 0.149118 | ||||||||
\(497\) | −4.97738 | −0.223266 | ||||||||
\(498\) | −0.153589 | −0.00688248 | ||||||||
\(499\) | −18.9967 | −0.850408 | −0.425204 | − | 0.905098i | \(-0.639798\pi\) | ||||
−0.425204 | + | 0.905098i | \(0.639798\pi\) | |||||||
\(500\) | −3.13685 | −0.140284 | ||||||||
\(501\) | 0.834350 | 0.0372760 | ||||||||
\(502\) | 64.1192 | 2.86178 | ||||||||
\(503\) | 31.0533 | 1.38460 | 0.692300 | − | 0.721610i | \(-0.256598\pi\) | ||||
0.692300 | + | 0.721610i | \(0.256598\pi\) | |||||||
\(504\) | −13.2364 | −0.589598 | ||||||||
\(505\) | 0.706801 | 0.0314522 | ||||||||
\(506\) | −61.2820 | −2.72432 | ||||||||
\(507\) | 0.306817 | 0.0136262 | ||||||||
\(508\) | 65.6203 | 2.91143 | ||||||||
\(509\) | −0.858249 | −0.0380412 | −0.0190206 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190206 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(510\) | 0.00612311 | 0.000271136 0 | ||||||||
\(511\) | 1.21658 | 0.0538183 | ||||||||
\(512\) | 31.2882 | 1.38275 | ||||||||
\(513\) | −0.504223 | −0.0222620 | ||||||||
\(514\) | −36.6737 | −1.61761 | ||||||||
\(515\) | 1.16640 | 0.0513978 | ||||||||
\(516\) | −2.07839 | −0.0914960 | ||||||||
\(517\) | −34.5534 | −1.51966 | ||||||||
\(518\) | 1.62465 | 0.0713830 | ||||||||
\(519\) | 0.0636669 | 0.00279467 | ||||||||
\(520\) | −1.55599 | −0.0682345 | ||||||||
\(521\) | −9.48521 | −0.415555 | −0.207777 | − | 0.978176i | \(-0.566623\pi\) | ||||
−0.207777 | + | 0.978176i | \(0.566623\pi\) | |||||||
\(522\) | −31.2033 | −1.36573 | ||||||||
\(523\) | −27.8802 | −1.21912 | −0.609559 | − | 0.792741i | \(-0.708653\pi\) | ||||
−0.609559 | + | 0.792741i | \(0.708653\pi\) | |||||||
\(524\) | 26.0359 | 1.13739 | ||||||||
\(525\) | 0.280053 | 0.0122225 | ||||||||
\(526\) | −67.9564 | −2.96304 | ||||||||
\(527\) | −0.609599 | −0.0265546 | ||||||||
\(528\) | 0.531566 | 0.0231334 | ||||||||
\(529\) | 41.7717 | 1.81616 | ||||||||
\(530\) | 1.87808 | 0.0815788 | ||||||||
\(531\) | −39.1726 | −1.69995 | ||||||||
\(532\) | −5.74077 | −0.248894 | ||||||||
\(533\) | −43.5102 | −1.88464 | ||||||||
\(534\) | 0.849978 | 0.0367822 | ||||||||
\(535\) | 0.591132 | 0.0255569 | ||||||||
\(536\) | 29.1217 | 1.25787 | ||||||||
\(537\) | 0.614752 | 0.0265285 | ||||||||
\(538\) | 13.5991 | 0.586300 | ||||||||
\(539\) | 3.15377 | 0.135843 | ||||||||
\(540\) | −0.105575 | −0.00454324 | ||||||||
\(541\) | 1.66474 | 0.0715726 | 0.0357863 | − | 0.999359i | \(-0.488606\pi\) | ||||
0.0357863 | + | 0.999359i | \(0.488606\pi\) | |||||||
\(542\) | 33.9596 | 1.45869 | ||||||||
\(543\) | −0.868060 | −0.0372520 | ||||||||
\(544\) | −0.870362 | −0.0373165 | ||||||||
\(545\) | −0.587726 | −0.0251754 | ||||||||
\(546\) | 0.581973 | 0.0249061 | ||||||||
\(547\) | −6.97421 | −0.298196 | −0.149098 | − | 0.988822i | \(-0.547637\pi\) | ||||
−0.149098 | + | 0.988822i | \(0.547637\pi\) | |||||||
\(548\) | −60.6614 | −2.59132 | ||||||||
\(549\) | −30.9313 | −1.32012 | ||||||||
\(550\) | 38.0213 | 1.62123 | ||||||||
\(551\) | −6.46502 | −0.275419 | ||||||||
\(552\) | −1.99366 | −0.0848560 | ||||||||
\(553\) | 11.9439 | 0.507906 | ||||||||
\(554\) | −8.31918 | −0.353448 | ||||||||
\(555\) | 0.00309360 | 0.000131316 0 | ||||||||
\(556\) | −81.8556 | −3.47145 | ||||||||
\(557\) | −14.1799 | −0.600824 | −0.300412 | − | 0.953810i | \(-0.597124\pi\) | ||||
−0.300412 | + | 0.953810i | \(0.597124\pi\) | |||||||
\(558\) | 7.99599 | 0.338497 | ||||||||
\(559\) | −41.5899 | −1.75907 | ||||||||
\(560\) | −0.246339 | −0.0104097 | ||||||||
\(561\) | −0.0975735 | −0.00411956 | ||||||||
\(562\) | 7.15491 | 0.301812 | ||||||||
\(563\) | 32.4036 | 1.36565 | 0.682825 | − | 0.730582i | \(-0.260751\pi\) | ||||
0.682825 | + | 0.730582i | \(0.260751\pi\) | |||||||
\(564\) | −2.35309 | −0.0990829 | ||||||||
\(565\) | −0.182593 | −0.00768173 | ||||||||
\(566\) | −71.5732 | −3.00845 | ||||||||
\(567\) | −8.97170 | −0.376776 | ||||||||
\(568\) | −21.9840 | −0.922427 | ||||||||
\(569\) | 6.88989 | 0.288839 | 0.144420 | − | 0.989517i | \(-0.453868\pi\) | ||||
0.144420 | + | 0.989517i | \(0.453868\pi\) | |||||||
\(570\) | −0.0166406 | −0.000697000 0 | ||||||||
\(571\) | −45.3534 | −1.89798 | −0.948991 | − | 0.315303i | \(-0.897894\pi\) | ||||
−0.948991 | + | 0.315303i | \(0.897894\pi\) | |||||||
\(572\) | 51.9032 | 2.17018 | ||||||||
\(573\) | −0.107928 | −0.00450875 | ||||||||
\(574\) | −24.4434 | −1.02025 | ||||||||
\(575\) | −40.1864 | −1.67589 | ||||||||
\(576\) | 29.4286 | 1.22619 | ||||||||
\(577\) | −11.5503 | −0.480847 | −0.240423 | − | 0.970668i | \(-0.577286\pi\) | ||||
−0.240423 | + | 0.970668i | \(0.577286\pi\) | |||||||
\(578\) | 40.3102 | 1.67668 | ||||||||
\(579\) | −0.880079 | −0.0365748 | ||||||||
\(580\) | −1.35366 | −0.0562077 | ||||||||
\(581\) | −1.13422 | −0.0470552 | ||||||||
\(582\) | 0.149492 | 0.00619665 | ||||||||
\(583\) | −29.9278 | −1.23948 | ||||||||
\(584\) | 5.37336 | 0.222351 | ||||||||
\(585\) | −1.05576 | −0.0436503 | ||||||||
\(586\) | 13.7864 | 0.569510 | ||||||||
\(587\) | −24.4168 | −1.00779 | −0.503895 | − | 0.863765i | \(-0.668100\pi\) | ||||
−0.503895 | + | 0.863765i | \(0.668100\pi\) | |||||||
\(588\) | 0.214772 | 0.00885706 | ||||||||
\(589\) | 1.65669 | 0.0682629 | ||||||||
\(590\) | −2.58695 | −0.106503 | ||||||||
\(591\) | −0.547787 | −0.0225329 | ||||||||
\(592\) | 2.02219 | 0.0831116 | ||||||||
\(593\) | −0.958541 | −0.0393626 | −0.0196813 | − | 0.999806i | \(-0.506265\pi\) | ||||
−0.0196813 | + | 0.999806i | \(0.506265\pi\) | |||||||
\(594\) | 2.56105 | 0.105081 | ||||||||
\(595\) | 0.0452177 | 0.00185375 | ||||||||
\(596\) | 78.5042 | 3.21566 | ||||||||
\(597\) | 0.00759352 | 0.000310782 0 | ||||||||
\(598\) | −83.5106 | −3.41500 | ||||||||
\(599\) | −27.6161 | −1.12836 | −0.564182 | − | 0.825651i | \(-0.690808\pi\) | ||||
−0.564182 | + | 0.825651i | \(0.690808\pi\) | |||||||
\(600\) | 1.23693 | 0.0504975 | ||||||||
\(601\) | −9.10119 | −0.371245 | −0.185623 | − | 0.982621i | \(-0.559430\pi\) | ||||
−0.185623 | + | 0.982621i | \(0.559430\pi\) | |||||||
\(602\) | −23.3646 | −0.952271 | ||||||||
\(603\) | 19.7595 | 0.804670 | ||||||||
\(604\) | −40.7311 | −1.65733 | ||||||||
\(605\) | −0.0863738 | −0.00351159 | ||||||||
\(606\) | −1.16762 | −0.0474311 | ||||||||
\(607\) | 11.2104 | 0.455015 | 0.227508 | − | 0.973776i | \(-0.426942\pi\) | ||||
0.227508 | + | 0.973776i | \(0.426942\pi\) | |||||||
\(608\) | 2.36536 | 0.0959281 | ||||||||
\(609\) | 0.241868 | 0.00980098 | ||||||||
\(610\) | −2.04269 | −0.0827063 | ||||||||
\(611\) | −47.0868 | −1.90493 | ||||||||
\(612\) | 6.33050 | 0.255895 | ||||||||
\(613\) | −37.2292 | −1.50367 | −0.751837 | − | 0.659349i | \(-0.770832\pi\) | ||||
−0.751837 | + | 0.659349i | \(0.770832\pi\) | |||||||
\(614\) | −22.9038 | −0.924322 | ||||||||
\(615\) | −0.0465444 | −0.00187685 | ||||||||
\(616\) | 13.9295 | 0.561236 | ||||||||
\(617\) | 24.4563 | 0.984574 | 0.492287 | − | 0.870433i | \(-0.336161\pi\) | ||||
0.492287 | + | 0.870433i | \(0.336161\pi\) | |||||||
\(618\) | −1.92686 | −0.0775098 | ||||||||
\(619\) | −25.6117 | −1.02942 | −0.514711 | − | 0.857364i | \(-0.672101\pi\) | ||||
−0.514711 | + | 0.857364i | \(0.672101\pi\) | |||||||
\(620\) | 0.346882 | 0.0139311 | ||||||||
\(621\) | −2.70689 | −0.108624 | ||||||||
\(622\) | 41.3639 | 1.65854 | ||||||||
\(623\) | 6.27688 | 0.251478 | ||||||||
\(624\) | 0.724379 | 0.0289984 | ||||||||
\(625\) | 24.8993 | 0.995970 | ||||||||
\(626\) | 51.7182 | 2.06708 | ||||||||
\(627\) | 0.265173 | 0.0105900 | ||||||||
\(628\) | −32.0781 | −1.28006 | ||||||||
\(629\) | −0.371191 | −0.0148004 | ||||||||
\(630\) | −0.593112 | −0.0236301 | ||||||||
\(631\) | 7.07244 | 0.281549 | 0.140775 | − | 0.990042i | \(-0.455041\pi\) | ||||
0.140775 | + | 0.990042i | \(0.455041\pi\) | |||||||
\(632\) | 52.7535 | 2.09842 | ||||||||
\(633\) | 0.0459422 | 0.00182604 | ||||||||
\(634\) | 3.17392 | 0.126052 | ||||||||
\(635\) | 1.40467 | 0.0557427 | ||||||||
\(636\) | −2.03809 | −0.0808154 | ||||||||
\(637\) | 4.29773 | 0.170282 | ||||||||
\(638\) | 32.8371 | 1.30003 | ||||||||
\(639\) | −14.9165 | −0.590086 | ||||||||
\(640\) | 1.68479 | 0.0665972 | ||||||||
\(641\) | −49.0316 | −1.93663 | −0.968317 | − | 0.249726i | \(-0.919659\pi\) | ||||
−0.968317 | + | 0.249726i | \(0.919659\pi\) | |||||||
\(642\) | −0.976534 | −0.0385407 | ||||||||
\(643\) | −48.7332 | −1.92185 | −0.960924 | − | 0.276812i | \(-0.910722\pi\) | ||||
−0.960924 | + | 0.276812i | \(0.910722\pi\) | |||||||
\(644\) | −30.8189 | −1.21444 | ||||||||
\(645\) | −0.0444901 | −0.00175180 | ||||||||
\(646\) | 1.99666 | 0.0785574 | ||||||||
\(647\) | −20.2375 | −0.795617 | −0.397809 | − | 0.917468i | \(-0.630229\pi\) | ||||
−0.397809 | + | 0.917468i | \(0.630229\pi\) | |||||||
\(648\) | −39.6260 | −1.55666 | ||||||||
\(649\) | 41.2238 | 1.61817 | ||||||||
\(650\) | 51.8125 | 2.03226 | ||||||||
\(651\) | −0.0619799 | −0.00242918 | ||||||||
\(652\) | −7.49333 | −0.293462 | ||||||||
\(653\) | 23.1701 | 0.906715 | 0.453357 | − | 0.891329i | \(-0.350226\pi\) | ||||
0.453357 | + | 0.891329i | \(0.350226\pi\) | |||||||
\(654\) | 0.970906 | 0.0379654 | ||||||||
\(655\) | 0.557327 | 0.0217766 | ||||||||
\(656\) | −30.4246 | −1.18788 | ||||||||
\(657\) | 3.64591 | 0.142240 | ||||||||
\(658\) | −26.4527 | −1.03123 | ||||||||
\(659\) | −42.9127 | −1.67164 | −0.835820 | − | 0.549003i | \(-0.815008\pi\) | ||||
−0.835820 | + | 0.549003i | \(0.815008\pi\) | |||||||
\(660\) | 0.0555226 | 0.00216121 | ||||||||
\(661\) | 4.68953 | 0.182402 | 0.0912009 | − | 0.995833i | \(-0.470929\pi\) | ||||
0.0912009 | + | 0.995833i | \(0.470929\pi\) | |||||||
\(662\) | 14.4886 | 0.563116 | ||||||||
\(663\) | −0.132966 | −0.00516397 | ||||||||
\(664\) | −5.00959 | −0.194410 | ||||||||
\(665\) | −0.122887 | −0.00476536 | ||||||||
\(666\) | 4.86884 | 0.188664 | ||||||||
\(667\) | −34.7070 | −1.34386 | ||||||||
\(668\) | 56.9664 | 2.20410 | ||||||||
\(669\) | 0.535919 | 0.0207198 | ||||||||
\(670\) | 1.30491 | 0.0504132 | ||||||||
\(671\) | 32.5509 | 1.25661 | ||||||||
\(672\) | −0.0884924 | −0.00341367 | ||||||||
\(673\) | 29.2236 | 1.12649 | 0.563243 | − | 0.826291i | \(-0.309553\pi\) | ||||
0.563243 | + | 0.826291i | \(0.309553\pi\) | |||||||
\(674\) | 69.8945 | 2.69223 | ||||||||
\(675\) | 1.67944 | 0.0646415 | ||||||||
\(676\) | 20.9483 | 0.805706 | ||||||||
\(677\) | −29.6696 | −1.14029 | −0.570147 | − | 0.821543i | \(-0.693114\pi\) | ||||
−0.570147 | + | 0.821543i | \(0.693114\pi\) | |||||||
\(678\) | 0.301638 | 0.0115843 | ||||||||
\(679\) | 1.10396 | 0.0423663 | ||||||||
\(680\) | 0.199717 | 0.00765878 | ||||||||
\(681\) | −1.66656 | −0.0638628 | ||||||||
\(682\) | −8.41467 | −0.322215 | ||||||||
\(683\) | −11.2066 | −0.428807 | −0.214404 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214404 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(684\) | −17.2042 | −0.657821 | ||||||||
\(685\) | −1.29852 | −0.0496139 | ||||||||
\(686\) | 2.41440 | 0.0921824 | ||||||||
\(687\) | 1.34704 | 0.0513930 | ||||||||
\(688\) | −29.0818 | −1.10873 | ||||||||
\(689\) | −40.7834 | −1.55372 | ||||||||
\(690\) | −0.0893341 | −0.00340089 | ||||||||
\(691\) | 13.8607 | 0.527287 | 0.263643 | − | 0.964620i | \(-0.415076\pi\) | ||||
0.263643 | + | 0.964620i | \(0.415076\pi\) | |||||||
\(692\) | 4.34695 | 0.165246 | ||||||||
\(693\) | 9.45140 | 0.359029 | ||||||||
\(694\) | −54.3621 | −2.06356 | ||||||||
\(695\) | −1.75220 | −0.0664649 | ||||||||
\(696\) | 1.06828 | 0.0404929 | ||||||||
\(697\) | 5.58470 | 0.211536 | ||||||||
\(698\) | −14.3497 | −0.543145 | ||||||||
\(699\) | −0.285142 | −0.0107851 | ||||||||
\(700\) | 19.1210 | 0.722706 | ||||||||
\(701\) | −27.7333 | −1.04747 | −0.523737 | − | 0.851880i | \(-0.675462\pi\) | ||||
−0.523737 | + | 0.851880i | \(0.675462\pi\) | |||||||
\(702\) | 3.49001 | 0.131722 | ||||||||
\(703\) | 1.00878 | 0.0380467 | ||||||||
\(704\) | −30.9696 | −1.16721 | ||||||||
\(705\) | −0.0503703 | −0.00189706 | ||||||||
\(706\) | −19.2081 | −0.722906 | ||||||||
\(707\) | −8.62256 | −0.324285 | ||||||||
\(708\) | 2.80734 | 0.105506 | ||||||||
\(709\) | 2.99495 | 0.112478 | 0.0562388 | − | 0.998417i | \(-0.482089\pi\) | ||||
0.0562388 | + | 0.998417i | \(0.482089\pi\) | |||||||
\(710\) | −0.985079 | −0.0369694 | ||||||||
\(711\) | 35.7941 | 1.34238 | ||||||||
\(712\) | 27.7236 | 1.03899 | ||||||||
\(713\) | 8.89384 | 0.333077 | ||||||||
\(714\) | −0.0746984 | −0.00279552 | ||||||||
\(715\) | 1.11104 | 0.0415506 | ||||||||
\(716\) | 41.9731 | 1.56861 | ||||||||
\(717\) | −0.393359 | −0.0146902 | ||||||||
\(718\) | −81.6383 | −3.04671 | ||||||||
\(719\) | 18.6326 | 0.694877 | 0.347438 | − | 0.937703i | \(-0.387052\pi\) | ||||
0.347438 | + | 0.937703i | \(0.387052\pi\) | |||||||
\(720\) | −0.738243 | −0.0275127 | ||||||||
\(721\) | −14.2294 | −0.529931 | ||||||||
\(722\) | 40.4474 | 1.50530 | ||||||||
\(723\) | −1.05200 | −0.0391243 | ||||||||
\(724\) | −59.2680 | −2.20268 | ||||||||
\(725\) | 21.5333 | 0.799727 | ||||||||
\(726\) | 0.142687 | 0.00529562 | ||||||||
\(727\) | −8.40706 | −0.311801 | −0.155900 | − | 0.987773i | \(-0.549828\pi\) | ||||
−0.155900 | + | 0.987773i | \(0.549828\pi\) | |||||||
\(728\) | 18.9821 | 0.703524 | ||||||||
\(729\) | −26.8303 | −0.993714 | ||||||||
\(730\) | 0.240775 | 0.00891148 | ||||||||
\(731\) | 5.33822 | 0.197441 | ||||||||
\(732\) | 2.21672 | 0.0819323 | ||||||||
\(733\) | 26.4109 | 0.975508 | 0.487754 | − | 0.872981i | \(-0.337816\pi\) | ||||
0.487754 | + | 0.872981i | \(0.337816\pi\) | |||||||
\(734\) | −48.4236 | −1.78735 | ||||||||
\(735\) | 0.00459743 | 0.000169579 0 | ||||||||
\(736\) | 12.6983 | 0.468065 | ||||||||
\(737\) | −20.7942 | −0.765963 | ||||||||
\(738\) | −73.2534 | −2.69650 | ||||||||
\(739\) | −42.4791 | −1.56262 | −0.781310 | − | 0.624144i | \(-0.785448\pi\) | ||||
−0.781310 | + | 0.624144i | \(0.785448\pi\) | |||||||
\(740\) | 0.211220 | 0.00776460 | ||||||||
\(741\) | 0.361359 | 0.0132748 | ||||||||
\(742\) | −22.9115 | −0.841109 | ||||||||
\(743\) | 16.5269 | 0.606314 | 0.303157 | − | 0.952941i | \(-0.401959\pi\) | ||||
0.303157 | + | 0.952941i | \(0.401959\pi\) | |||||||
\(744\) | −0.273751 | −0.0100362 | ||||||||
\(745\) | 1.68047 | 0.0615675 | ||||||||
\(746\) | 75.8633 | 2.77755 | ||||||||
\(747\) | −3.39908 | −0.124366 | ||||||||
\(748\) | −6.66197 | −0.243586 | ||||||||
\(749\) | −7.21146 | −0.263501 | ||||||||
\(750\) | 0.110926 | 0.00405044 | ||||||||
\(751\) | −27.3920 | −0.999548 | −0.499774 | − | 0.866156i | \(-0.666584\pi\) | ||||
−0.499774 | + | 0.866156i | \(0.666584\pi\) | |||||||
\(752\) | −32.9255 | −1.20067 | ||||||||
\(753\) | −1.48947 | −0.0542794 | ||||||||
\(754\) | 44.7480 | 1.62963 | ||||||||
\(755\) | −0.871893 | −0.0317314 | ||||||||
\(756\) | 1.28796 | 0.0468426 | ||||||||
\(757\) | 54.5074 | 1.98111 | 0.990553 | − | 0.137127i | \(-0.0437869\pi\) | ||||
0.990553 | + | 0.137127i | \(0.0437869\pi\) | |||||||
\(758\) | 9.19463 | 0.333964 | ||||||||
\(759\) | 1.42356 | 0.0516721 | ||||||||
\(760\) | −0.542765 | −0.0196882 | ||||||||
\(761\) | −7.88285 | −0.285753 | −0.142876 | − | 0.989741i | \(-0.545635\pi\) | ||||
−0.142876 | + | 0.989741i | \(0.545635\pi\) | |||||||
\(762\) | −2.32048 | −0.0840621 | ||||||||
\(763\) | 7.16991 | 0.259568 | ||||||||
\(764\) | −7.36892 | −0.266598 | ||||||||
\(765\) | 0.135511 | 0.00489941 | ||||||||
\(766\) | −55.1893 | −1.99407 | ||||||||
\(767\) | 56.1767 | 2.02842 | ||||||||
\(768\) | −1.68172 | −0.0606837 | ||||||||
\(769\) | 10.8798 | 0.392336 | 0.196168 | − | 0.980570i | \(-0.437150\pi\) | ||||
0.196168 | + | 0.980570i | \(0.437150\pi\) | |||||||
\(770\) | 0.624168 | 0.0224934 | ||||||||
\(771\) | 0.851920 | 0.0306811 | ||||||||
\(772\) | −60.0886 | −2.16264 | ||||||||
\(773\) | 41.0549 | 1.47664 | 0.738321 | − | 0.674450i | \(-0.235619\pi\) | ||||
0.738321 | + | 0.674450i | \(0.235619\pi\) | |||||||
\(774\) | −70.0204 | −2.51683 | ||||||||
\(775\) | −5.51801 | −0.198213 | ||||||||
\(776\) | 4.87597 | 0.175037 | ||||||||
\(777\) | −0.0377401 | −0.00135392 | ||||||||
\(778\) | 16.3862 | 0.587474 | ||||||||
\(779\) | −15.1774 | −0.543788 | ||||||||
\(780\) | 0.0756621 | 0.00270914 | ||||||||
\(781\) | 15.6975 | 0.561701 | ||||||||
\(782\) | 10.7189 | 0.383307 | ||||||||
\(783\) | 1.45045 | 0.0518347 | ||||||||
\(784\) | 3.00520 | 0.107328 | ||||||||
\(785\) | −0.686666 | −0.0245082 | ||||||||
\(786\) | −0.920688 | −0.0328399 | ||||||||
\(787\) | −21.4170 | −0.763434 | −0.381717 | − | 0.924279i | \(-0.624667\pi\) | ||||
−0.381717 | + | 0.924279i | \(0.624667\pi\) | |||||||
\(788\) | −37.4009 | −1.33235 | ||||||||
\(789\) | 1.57861 | 0.0561999 | ||||||||
\(790\) | 2.36383 | 0.0841014 | ||||||||
\(791\) | 2.22752 | 0.0792017 | ||||||||
\(792\) | 41.7447 | 1.48334 | ||||||||
\(793\) | 44.3580 | 1.57520 | ||||||||
\(794\) | 46.9981 | 1.66790 | ||||||||
\(795\) | −0.0436274 | −0.00154730 | ||||||||
\(796\) | 0.518459 | 0.0183763 | ||||||||
\(797\) | −4.20032 | −0.148783 | −0.0743914 | − | 0.997229i | \(-0.523701\pi\) | ||||
−0.0743914 | + | 0.997229i | \(0.523701\pi\) | |||||||
\(798\) | 0.203006 | 0.00718634 | ||||||||
\(799\) | 6.04377 | 0.213813 | ||||||||
\(800\) | −7.87840 | −0.278544 | ||||||||
\(801\) | 18.8109 | 0.664651 | ||||||||
\(802\) | −83.4689 | −2.94739 | ||||||||
\(803\) | −3.83681 | −0.135398 | ||||||||
\(804\) | −1.41609 | −0.0499415 | ||||||||
\(805\) | −0.659711 | −0.0232517 | ||||||||
\(806\) | −11.4669 | −0.403904 | ||||||||
\(807\) | −0.315904 | −0.0111203 | ||||||||
\(808\) | −38.0839 | −1.33979 | ||||||||
\(809\) | −50.8669 | −1.78838 | −0.894192 | − | 0.447683i | \(-0.852249\pi\) | ||||
−0.894192 | + | 0.447683i | \(0.852249\pi\) | |||||||
\(810\) | −1.77560 | −0.0623883 | ||||||||
\(811\) | −26.5180 | −0.931173 | −0.465587 | − | 0.885002i | \(-0.654157\pi\) | ||||
−0.465587 | + | 0.885002i | \(0.654157\pi\) | |||||||
\(812\) | 16.5139 | 0.579524 | ||||||||
\(813\) | −0.788872 | −0.0276669 | ||||||||
\(814\) | −5.12378 | −0.179588 | ||||||||
\(815\) | −0.160403 | −0.00561866 | ||||||||
\(816\) | −0.0929767 | −0.00325484 | ||||||||
\(817\) | −14.5076 | −0.507555 | ||||||||
\(818\) | −65.1425 | −2.27765 | ||||||||
\(819\) | 12.8797 | 0.450052 | ||||||||
\(820\) | −3.17788 | −0.110976 | ||||||||
\(821\) | −35.3221 | −1.23275 | −0.616376 | − | 0.787452i | \(-0.711400\pi\) | ||||
−0.616376 | + | 0.787452i | \(0.711400\pi\) | |||||||
\(822\) | 2.14512 | 0.0748196 | ||||||||
\(823\) | 27.6666 | 0.964399 | 0.482199 | − | 0.876061i | \(-0.339838\pi\) | ||||
0.482199 | + | 0.876061i | \(0.339838\pi\) | |||||||
\(824\) | −62.8482 | −2.18942 | ||||||||
\(825\) | −0.883223 | −0.0307499 | ||||||||
\(826\) | 31.5593 | 1.09809 | ||||||||
\(827\) | −20.6867 | −0.719347 | −0.359674 | − | 0.933078i | \(-0.617112\pi\) | ||||
−0.359674 | + | 0.933078i | \(0.617112\pi\) | |||||||
\(828\) | −92.3598 | −3.20972 | ||||||||
\(829\) | 37.6166 | 1.30648 | 0.653240 | − | 0.757151i | \(-0.273409\pi\) | ||||
0.653240 | + | 0.757151i | \(0.273409\pi\) | |||||||
\(830\) | −0.224474 | −0.00779162 | ||||||||
\(831\) | 0.193252 | 0.00670384 | ||||||||
\(832\) | −42.2030 | −1.46313 | ||||||||
\(833\) | −0.551630 | −0.0191128 | ||||||||
\(834\) | 2.89459 | 0.100232 | ||||||||
\(835\) | 1.21943 | 0.0421999 | ||||||||
\(836\) | 18.1051 | 0.626178 | ||||||||
\(837\) | −0.371684 | −0.0128473 | ||||||||
\(838\) | 46.9396 | 1.62150 | ||||||||
\(839\) | 14.5068 | 0.500832 | 0.250416 | − | 0.968138i | \(-0.419433\pi\) | ||||
0.250416 | + | 0.968138i | \(0.419433\pi\) | |||||||
\(840\) | 0.0203058 | 0.000700617 0 | ||||||||
\(841\) | −10.4027 | −0.358715 | ||||||||
\(842\) | 32.3863 | 1.11610 | ||||||||
\(843\) | −0.166206 | −0.00572445 | ||||||||
\(844\) | 3.13677 | 0.107972 | ||||||||
\(845\) | 0.448421 | 0.0154262 | ||||||||
\(846\) | −79.2749 | −2.72553 | ||||||||
\(847\) | 1.05371 | 0.0362059 | ||||||||
\(848\) | −28.5179 | −0.979308 | ||||||||
\(849\) | 1.66263 | 0.0570612 | ||||||||
\(850\) | −6.65034 | −0.228105 | ||||||||
\(851\) | 5.41555 | 0.185643 | ||||||||
\(852\) | 1.06900 | 0.0366234 | ||||||||
\(853\) | −12.1159 | −0.414841 | −0.207421 | − | 0.978252i | \(-0.566507\pi\) | ||||
−0.207421 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(854\) | 24.9197 | 0.852734 | ||||||||
\(855\) | −0.368275 | −0.0125947 | ||||||||
\(856\) | −31.8514 | −1.08866 | ||||||||
\(857\) | 1.88506 | 0.0643923 | 0.0321961 | − | 0.999482i | \(-0.489750\pi\) | ||||
0.0321961 | + | 0.999482i | \(0.489750\pi\) | |||||||
\(858\) | −1.83541 | −0.0626599 | ||||||||
\(859\) | −49.6659 | −1.69458 | −0.847290 | − | 0.531131i | \(-0.821767\pi\) | ||||
−0.847290 | + | 0.531131i | \(0.821767\pi\) | |||||||
\(860\) | −3.03763 | −0.103582 | ||||||||
\(861\) | 0.567814 | 0.0193511 | ||||||||
\(862\) | −5.00314 | −0.170407 | ||||||||
\(863\) | −1.00000 | −0.0340404 | ||||||||
\(864\) | −0.530676 | −0.0180540 | ||||||||
\(865\) | 0.0930510 | 0.00316383 | ||||||||
\(866\) | −26.7784 | −0.909965 | ||||||||
\(867\) | −0.936394 | −0.0318016 | ||||||||
\(868\) | −4.23176 | −0.143635 | ||||||||
\(869\) | −37.6683 | −1.27781 | ||||||||
\(870\) | 0.0478684 | 0.00162289 | ||||||||
\(871\) | −28.3368 | −0.960154 | ||||||||
\(872\) | 31.6679 | 1.07241 | ||||||||
\(873\) | 3.30842 | 0.111973 | ||||||||
\(874\) | −29.1305 | −0.985354 | ||||||||
\(875\) | 0.819160 | 0.0276927 | ||||||||
\(876\) | −0.261287 | −0.00882809 | ||||||||
\(877\) | 31.9024 | 1.07727 | 0.538634 | − | 0.842540i | \(-0.318941\pi\) | ||||
0.538634 | + | 0.842540i | \(0.318941\pi\) | |||||||
\(878\) | 71.9451 | 2.42803 | ||||||||
\(879\) | −0.320254 | −0.0108019 | ||||||||
\(880\) | 0.776899 | 0.0261892 | ||||||||
\(881\) | 26.8097 | 0.903243 | 0.451622 | − | 0.892210i | \(-0.350846\pi\) | ||||
0.451622 | + | 0.892210i | \(0.350846\pi\) | |||||||
\(882\) | 7.23562 | 0.243636 | ||||||||
\(883\) | 40.4759 | 1.36212 | 0.681061 | − | 0.732227i | \(-0.261519\pi\) | ||||
0.681061 | + | 0.732227i | \(0.261519\pi\) | |||||||
\(884\) | −9.07844 | −0.305341 | ||||||||
\(885\) | 0.0600941 | 0.00202004 | ||||||||
\(886\) | −92.4122 | −3.10465 | ||||||||
\(887\) | 9.09625 | 0.305422 | 0.152711 | − | 0.988271i | \(-0.451200\pi\) | ||||
0.152711 | + | 0.988271i | \(0.451200\pi\) | |||||||
\(888\) | −0.166690 | −0.00559375 | ||||||||
\(889\) | −17.1362 | −0.574729 | ||||||||
\(890\) | 1.24227 | 0.0416409 | ||||||||
\(891\) | 28.2947 | 0.947908 | ||||||||
\(892\) | 36.5906 | 1.22514 | ||||||||
\(893\) | −16.4250 | −0.549642 | ||||||||
\(894\) | −2.77608 | −0.0928461 | ||||||||
\(895\) | 0.898477 | 0.0300328 | ||||||||
\(896\) | −20.5535 | −0.686643 | ||||||||
\(897\) | 1.93993 | 0.0647723 | ||||||||
\(898\) | 32.8704 | 1.09690 | ||||||||
\(899\) | −4.76564 | −0.158943 | ||||||||
\(900\) | 57.3028 | 1.91009 | ||||||||
\(901\) | 5.23470 | 0.174393 | ||||||||
\(902\) | 77.0891 | 2.56679 | ||||||||
\(903\) | 0.542753 | 0.0180617 | ||||||||
\(904\) | 9.83848 | 0.327223 | ||||||||
\(905\) | −1.26869 | −0.0421728 | ||||||||
\(906\) | 1.44034 | 0.0478522 | ||||||||
\(907\) | 18.1566 | 0.602880 | 0.301440 | − | 0.953485i | \(-0.402533\pi\) | ||||
0.301440 | + | 0.953485i | \(0.402533\pi\) | |||||||
\(908\) | −113.787 | −3.77615 | ||||||||
\(909\) | −25.8405 | −0.857077 | ||||||||
\(910\) | 0.850570 | 0.0281961 | ||||||||
\(911\) | −3.22155 | −0.106735 | −0.0533674 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533674 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(912\) | 0.252681 | 0.00836710 | ||||||||
\(913\) | 3.57706 | 0.118384 | ||||||||
\(914\) | 32.0704 | 1.06079 | ||||||||
\(915\) | 0.0474512 | 0.00156869 | ||||||||
\(916\) | 91.9714 | 3.03882 | ||||||||
\(917\) | −6.79906 | −0.224525 | ||||||||
\(918\) | −0.447956 | −0.0147847 | ||||||||
\(919\) | 21.9632 | 0.724500 | 0.362250 | − | 0.932081i | \(-0.382009\pi\) | ||||
0.362250 | + | 0.932081i | \(0.382009\pi\) | |||||||
\(920\) | −2.91380 | −0.0960650 | ||||||||
\(921\) | 0.532049 | 0.0175316 | ||||||||
\(922\) | 60.7462 | 2.00057 | ||||||||
\(923\) | 21.3914 | 0.704107 | ||||||||
\(924\) | −0.677343 | −0.0222830 | ||||||||
\(925\) | −3.35997 | −0.110475 | ||||||||
\(926\) | 58.3452 | 1.91734 | ||||||||
\(927\) | −42.6435 | −1.40060 | ||||||||
\(928\) | −6.80419 | −0.223359 | ||||||||
\(929\) | 43.0635 | 1.41287 | 0.706434 | − | 0.707778i | \(-0.250302\pi\) | ||||
0.706434 | + | 0.707778i | \(0.250302\pi\) | |||||||
\(930\) | −0.0122665 | −0.000402235 0 | ||||||||
\(931\) | 1.49915 | 0.0491327 | ||||||||
\(932\) | −19.4685 | −0.637712 | ||||||||
\(933\) | −0.960871 | −0.0314575 | ||||||||
\(934\) | −44.7894 | −1.46556 | ||||||||
\(935\) | −0.142606 | −0.00466373 | ||||||||
\(936\) | 56.8866 | 1.85940 | ||||||||
\(937\) | −49.0340 | −1.60187 | −0.800936 | − | 0.598750i | \(-0.795664\pi\) | ||||
−0.800936 | + | 0.598750i | \(0.795664\pi\) | |||||||
\(938\) | −15.9192 | −0.519780 | ||||||||
\(939\) | −1.20140 | −0.0392062 | ||||||||
\(940\) | −3.43911 | −0.112171 | ||||||||
\(941\) | 17.6625 | 0.575781 | 0.287890 | − | 0.957663i | \(-0.407046\pi\) | ||||
0.287890 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(942\) | 1.13435 | 0.0369592 | ||||||||
\(943\) | −81.4789 | −2.65332 | ||||||||
\(944\) | 39.2817 | 1.27851 | ||||||||
\(945\) | 0.0275701 | 0.000896855 0 | ||||||||
\(946\) | 73.6867 | 2.39576 | ||||||||
\(947\) | −23.6183 | −0.767493 | −0.383747 | − | 0.923438i | \(-0.625366\pi\) | ||||
−0.383747 | + | 0.923438i | \(0.625366\pi\) | |||||||
\(948\) | −2.56522 | −0.0833144 | ||||||||
\(949\) | −5.22853 | −0.169725 | ||||||||
\(950\) | 18.0735 | 0.586381 | ||||||||
\(951\) | −0.0737293 | −0.00239084 | ||||||||
\(952\) | −2.43643 | −0.0789650 | ||||||||
\(953\) | 26.0428 | 0.843609 | 0.421804 | − | 0.906687i | \(-0.361397\pi\) | ||||
0.421804 | + | 0.906687i | \(0.361397\pi\) | |||||||
\(954\) | −68.6626 | −2.22303 | ||||||||
\(955\) | −0.157739 | −0.00510433 | ||||||||
\(956\) | −26.8571 | −0.868621 | ||||||||
\(957\) | −0.762797 | −0.0246577 | ||||||||
\(958\) | 91.0072 | 2.94031 | ||||||||
\(959\) | 15.8412 | 0.511538 | ||||||||
\(960\) | −0.0451460 | −0.00145708 | ||||||||
\(961\) | −29.7788 | −0.960606 | ||||||||
\(962\) | −6.98230 | −0.225118 | ||||||||
\(963\) | −21.6117 | −0.696428 | ||||||||
\(964\) | −71.8267 | −2.31338 | ||||||||
\(965\) | −1.28626 | −0.0414062 | ||||||||
\(966\) | 1.08982 | 0.0350645 | ||||||||
\(967\) | 58.4964 | 1.88112 | 0.940559 | − | 0.339630i | \(-0.110302\pi\) | ||||
0.940559 | + | 0.339630i | \(0.110302\pi\) | |||||||
\(968\) | 4.65400 | 0.149585 | ||||||||
\(969\) | −0.0463817 | −0.00149000 | ||||||||
\(970\) | 0.218487 | 0.00701520 | ||||||||
\(971\) | 21.7832 | 0.699055 | 0.349528 | − | 0.936926i | \(-0.386342\pi\) | ||||
0.349528 | + | 0.936926i | \(0.386342\pi\) | |||||||
\(972\) | 5.79075 | 0.185738 | ||||||||
\(973\) | 21.3759 | 0.685279 | ||||||||
\(974\) | 90.0440 | 2.88519 | ||||||||
\(975\) | −1.20359 | −0.0385458 | ||||||||
\(976\) | 31.0174 | 0.992843 | ||||||||
\(977\) | −33.2853 | −1.06489 | −0.532446 | − | 0.846464i | \(-0.678727\pi\) | ||||
−0.532446 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(978\) | 0.264981 | 0.00847315 | ||||||||
\(979\) | −19.7959 | −0.632679 | ||||||||
\(980\) | 0.313896 | 0.0100270 | ||||||||
\(981\) | 21.4872 | 0.686033 | ||||||||
\(982\) | 24.7662 | 0.790320 | ||||||||
\(983\) | −51.0697 | −1.62887 | −0.814435 | − | 0.580255i | \(-0.802953\pi\) | ||||
−0.814435 | + | 0.580255i | \(0.802953\pi\) | |||||||
\(984\) | 2.50791 | 0.0799492 | ||||||||
\(985\) | −0.800606 | −0.0255094 | ||||||||
\(986\) | −5.74357 | −0.182913 | ||||||||
\(987\) | 0.614489 | 0.0195594 | ||||||||
\(988\) | 24.6723 | 0.784930 | ||||||||
\(989\) | −77.8828 | −2.47653 | ||||||||
\(990\) | 1.87054 | 0.0594497 | ||||||||
\(991\) | 32.1226 | 1.02041 | 0.510205 | − | 0.860053i | \(-0.329570\pi\) | ||||
0.510205 | + | 0.860053i | \(0.329570\pi\) | |||||||
\(992\) | 1.74361 | 0.0553596 | ||||||||
\(993\) | −0.336566 | −0.0106806 | ||||||||
\(994\) | 12.0174 | 0.381169 | ||||||||
\(995\) | 0.0110981 | 0.000351835 0 | ||||||||
\(996\) | 0.243598 | 0.00771871 | ||||||||
\(997\) | 6.92242 | 0.219235 | 0.109618 | − | 0.993974i | \(-0.465037\pi\) | ||||
0.109618 | + | 0.993974i | \(0.465037\pi\) | |||||||
\(998\) | 45.8656 | 1.45185 | ||||||||
\(999\) | −0.226322 | −0.00716052 |
(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 | 6041.2.a.d.1.9 | ✓ | 101 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6041.2.a.d.1.9 | ✓ | 101 | 1.1 | even | 1 | trivial |