Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44940 | −1.73199 | −0.865994 | − | 0.500055i | \(-0.833313\pi\) | ||||
−0.865994 | + | 0.500055i | \(0.833313\pi\) | |||||||
\(3\) | 0.192595 | 0.111195 | 0.0555974 | − | 0.998453i | \(-0.482294\pi\) | ||||
0.0555974 | + | 0.998453i | \(0.482294\pi\) | |||||||
\(4\) | 3.99956 | 1.99978 | ||||||||
\(5\) | 1.46027 | 0.653053 | 0.326526 | − | 0.945188i | \(-0.394122\pi\) | ||||
0.326526 | + | 0.945188i | \(0.394122\pi\) | |||||||
\(6\) | −0.471742 | −0.192588 | ||||||||
\(7\) | −3.96634 | −1.49913 | −0.749567 | − | 0.661928i | \(-0.769738\pi\) | ||||
−0.749567 | + | 0.661928i | \(0.769738\pi\) | |||||||
\(8\) | −4.89773 | −1.73161 | ||||||||
\(9\) | −2.96291 | −0.987636 | ||||||||
\(10\) | −3.57679 | −1.13108 | ||||||||
\(11\) | 3.20898 | 0.967542 | 0.483771 | − | 0.875194i | \(-0.339267\pi\) | ||||
0.483771 | + | 0.875194i | \(0.339267\pi\) | |||||||
\(12\) | 0.770296 | 0.222365 | ||||||||
\(13\) | 5.11663 | 1.41910 | 0.709550 | − | 0.704655i | \(-0.248898\pi\) | ||||
0.709550 | + | 0.704655i | \(0.248898\pi\) | |||||||
\(14\) | 9.71515 | 2.59648 | ||||||||
\(15\) | 0.281241 | 0.0726161 | ||||||||
\(16\) | 3.99737 | 0.999343 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 7.25735 | 1.71057 | ||||||||
\(19\) | 3.67372 | 0.842808 | 0.421404 | − | 0.906873i | \(-0.361537\pi\) | ||||
0.421404 | + | 0.906873i | \(0.361537\pi\) | |||||||
\(20\) | 5.84044 | 1.30596 | ||||||||
\(21\) | −0.763897 | −0.166696 | ||||||||
\(22\) | −7.86007 | −1.67577 | ||||||||
\(23\) | −8.14798 | −1.69897 | −0.849486 | − | 0.527611i | \(-0.823088\pi\) | ||||
−0.849486 | + | 0.527611i | \(0.823088\pi\) | |||||||
\(24\) | −0.943278 | −0.192546 | ||||||||
\(25\) | −2.86761 | −0.573522 | ||||||||
\(26\) | −12.5327 | −2.45786 | ||||||||
\(27\) | −1.14843 | −0.221015 | ||||||||
\(28\) | −15.8636 | −2.99794 | ||||||||
\(29\) | 9.62795 | 1.78787 | 0.893933 | − | 0.448201i | \(-0.147935\pi\) | ||||
0.893933 | + | 0.448201i | \(0.147935\pi\) | |||||||
\(30\) | −0.688871 | −0.125770 | ||||||||
\(31\) | 8.17471 | 1.46822 | 0.734111 | − | 0.679030i | \(-0.237599\pi\) | ||||
0.734111 | + | 0.679030i | \(0.237599\pi\) | |||||||
\(32\) | 0.00429093 | 0.000758537 0 | ||||||||
\(33\) | 0.618033 | 0.107586 | ||||||||
\(34\) | 2.44940 | 0.420069 | ||||||||
\(35\) | −5.79192 | −0.979014 | ||||||||
\(36\) | −11.8503 | −1.97506 | ||||||||
\(37\) | −7.45724 | −1.22596 | −0.612981 | − | 0.790098i | \(-0.710030\pi\) | ||||
−0.612981 | + | 0.790098i | \(0.710030\pi\) | |||||||
\(38\) | −8.99840 | −1.45973 | ||||||||
\(39\) | 0.985438 | 0.157796 | ||||||||
\(40\) | −7.15201 | −1.13083 | ||||||||
\(41\) | 8.24516 | 1.28768 | 0.643839 | − | 0.765161i | \(-0.277341\pi\) | ||||
0.643839 | + | 0.765161i | \(0.277341\pi\) | |||||||
\(42\) | 1.87109 | 0.288715 | ||||||||
\(43\) | 5.68052 | 0.866271 | 0.433136 | − | 0.901329i | \(-0.357407\pi\) | ||||
0.433136 | + | 0.901329i | \(0.357407\pi\) | |||||||
\(44\) | 12.8345 | 1.93487 | ||||||||
\(45\) | −4.32665 | −0.644978 | ||||||||
\(46\) | 19.9577 | 2.94260 | ||||||||
\(47\) | 9.11914 | 1.33016 | 0.665082 | − | 0.746771i | \(-0.268397\pi\) | ||||
0.665082 | + | 0.746771i | \(0.268397\pi\) | |||||||
\(48\) | 0.769874 | 0.111122 | ||||||||
\(49\) | 8.73182 | 1.24740 | ||||||||
\(50\) | 7.02392 | 0.993333 | ||||||||
\(51\) | −0.192595 | −0.0269687 | ||||||||
\(52\) | 20.4643 | 2.83789 | ||||||||
\(53\) | −12.4719 | −1.71315 | −0.856575 | − | 0.516022i | \(-0.827412\pi\) | ||||
−0.856575 | + | 0.516022i | \(0.827412\pi\) | |||||||
\(54\) | 2.81296 | 0.382795 | ||||||||
\(55\) | 4.68597 | 0.631856 | ||||||||
\(56\) | 19.4260 | 2.59591 | ||||||||
\(57\) | 0.707539 | 0.0937159 | ||||||||
\(58\) | −23.5827 | −3.09656 | ||||||||
\(59\) | −6.11265 | −0.795799 | −0.397900 | − | 0.917429i | \(-0.630261\pi\) | ||||
−0.397900 | + | 0.917429i | \(0.630261\pi\) | |||||||
\(60\) | 1.12484 | 0.145216 | ||||||||
\(61\) | 0.888772 | 0.113796 | 0.0568978 | − | 0.998380i | \(-0.481879\pi\) | ||||
0.0568978 | + | 0.998380i | \(0.481879\pi\) | |||||||
\(62\) | −20.0231 | −2.54294 | ||||||||
\(63\) | 11.7519 | 1.48060 | ||||||||
\(64\) | −8.00525 | −1.00066 | ||||||||
\(65\) | 7.47167 | 0.926747 | ||||||||
\(66\) | −1.51381 | −0.186337 | ||||||||
\(67\) | −3.67281 | −0.448705 | −0.224353 | − | 0.974508i | \(-0.572027\pi\) | ||||
−0.224353 | + | 0.974508i | \(0.572027\pi\) | |||||||
\(68\) | −3.99956 | −0.485018 | ||||||||
\(69\) | −1.56926 | −0.188917 | ||||||||
\(70\) | 14.1867 | 1.69564 | ||||||||
\(71\) | −9.69117 | −1.15013 | −0.575065 | − | 0.818108i | \(-0.695023\pi\) | ||||
−0.575065 | + | 0.818108i | \(0.695023\pi\) | |||||||
\(72\) | 14.5115 | 1.71020 | ||||||||
\(73\) | −10.2746 | −1.20255 | −0.601274 | − | 0.799043i | \(-0.705340\pi\) | ||||
−0.601274 | + | 0.799043i | \(0.705340\pi\) | |||||||
\(74\) | 18.2658 | 2.12335 | ||||||||
\(75\) | −0.552287 | −0.0637727 | ||||||||
\(76\) | 14.6933 | 1.68543 | ||||||||
\(77\) | −12.7279 | −1.45048 | ||||||||
\(78\) | −2.41373 | −0.273301 | ||||||||
\(79\) | 0.518576 | 0.0583444 | 0.0291722 | − | 0.999574i | \(-0.490713\pi\) | ||||
0.0291722 | + | 0.999574i | \(0.490713\pi\) | |||||||
\(80\) | 5.83724 | 0.652624 | ||||||||
\(81\) | 8.66754 | 0.963060 | ||||||||
\(82\) | −20.1957 | −2.23024 | ||||||||
\(83\) | −7.30712 | −0.802060 | −0.401030 | − | 0.916065i | \(-0.631348\pi\) | ||||
−0.401030 | + | 0.916065i | \(0.631348\pi\) | |||||||
\(84\) | −3.05525 | −0.333355 | ||||||||
\(85\) | −1.46027 | −0.158389 | ||||||||
\(86\) | −13.9139 | −1.50037 | ||||||||
\(87\) | 1.85429 | 0.198801 | ||||||||
\(88\) | −15.7167 | −1.67540 | ||||||||
\(89\) | 15.7459 | 1.66906 | 0.834532 | − | 0.550960i | \(-0.185738\pi\) | ||||
0.834532 | + | 0.550960i | \(0.185738\pi\) | |||||||
\(90\) | 10.5977 | 1.11709 | ||||||||
\(91\) | −20.2943 | −2.12742 | ||||||||
\(92\) | −32.5884 | −3.39757 | ||||||||
\(93\) | 1.57441 | 0.163259 | ||||||||
\(94\) | −22.3364 | −2.30383 | ||||||||
\(95\) | 5.36462 | 0.550398 | ||||||||
\(96\) | 0.000826413 0 | 8.43454e−5 0 | ||||||||
\(97\) | −2.59386 | −0.263367 | −0.131683 | − | 0.991292i | \(-0.542038\pi\) | ||||
−0.131683 | + | 0.991292i | \(0.542038\pi\) | |||||||
\(98\) | −21.3877 | −2.16049 | ||||||||
\(99\) | −9.50790 | −0.955579 | ||||||||
\(100\) | −11.4692 | −1.14692 | ||||||||
\(101\) | 3.14698 | 0.313136 | 0.156568 | − | 0.987667i | \(-0.449957\pi\) | ||||
0.156568 | + | 0.987667i | \(0.449957\pi\) | |||||||
\(102\) | 0.471742 | 0.0467094 | ||||||||
\(103\) | 19.4025 | 1.91178 | 0.955892 | − | 0.293719i | \(-0.0948931\pi\) | ||||
0.955892 | + | 0.293719i | \(0.0948931\pi\) | |||||||
\(104\) | −25.0599 | −2.45732 | ||||||||
\(105\) | −1.11550 | −0.108861 | ||||||||
\(106\) | 30.5487 | 2.96715 | ||||||||
\(107\) | 0.957453 | 0.0925605 | 0.0462802 | − | 0.998928i | \(-0.485263\pi\) | ||||
0.0462802 | + | 0.998928i | \(0.485263\pi\) | |||||||
\(108\) | −4.59320 | −0.441981 | ||||||||
\(109\) | −19.6585 | −1.88294 | −0.941470 | − | 0.337098i | \(-0.890555\pi\) | ||||
−0.941470 | + | 0.337098i | \(0.890555\pi\) | |||||||
\(110\) | −11.4778 | −1.09437 | ||||||||
\(111\) | −1.43623 | −0.136321 | ||||||||
\(112\) | −15.8549 | −1.49815 | ||||||||
\(113\) | −7.20070 | −0.677384 | −0.338692 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338692 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(114\) | −1.73305 | −0.162315 | ||||||||
\(115\) | −11.8983 | −1.10952 | ||||||||
\(116\) | 38.5076 | 3.57534 | ||||||||
\(117\) | −15.1601 | −1.40155 | ||||||||
\(118\) | 14.9723 | 1.37831 | ||||||||
\(119\) | 3.96634 | 0.363593 | ||||||||
\(120\) | −1.37744 | −0.125743 | ||||||||
\(121\) | −0.702477 | −0.0638616 | ||||||||
\(122\) | −2.17696 | −0.197093 | ||||||||
\(123\) | 1.58798 | 0.143183 | ||||||||
\(124\) | 32.6953 | 2.93612 | ||||||||
\(125\) | −11.4888 | −1.02759 | ||||||||
\(126\) | −28.7851 | −2.56438 | ||||||||
\(127\) | 19.6904 | 1.74724 | 0.873622 | − | 0.486606i | \(-0.161765\pi\) | ||||
0.873622 | + | 0.486606i | \(0.161765\pi\) | |||||||
\(128\) | 19.5995 | 1.73237 | ||||||||
\(129\) | 1.09404 | 0.0963249 | ||||||||
\(130\) | −18.3011 | −1.60511 | ||||||||
\(131\) | −8.78926 | −0.767921 | −0.383961 | − | 0.923349i | \(-0.625440\pi\) | ||||
−0.383961 | + | 0.923349i | \(0.625440\pi\) | |||||||
\(132\) | 2.47186 | 0.215148 | ||||||||
\(133\) | −14.5712 | −1.26348 | ||||||||
\(134\) | 8.99619 | 0.777152 | ||||||||
\(135\) | −1.67701 | −0.144334 | ||||||||
\(136\) | 4.89773 | 0.419977 | ||||||||
\(137\) | 14.7787 | 1.26263 | 0.631313 | − | 0.775528i | \(-0.282516\pi\) | ||||
0.631313 | + | 0.775528i | \(0.282516\pi\) | |||||||
\(138\) | 3.84375 | 0.327202 | ||||||||
\(139\) | 15.2365 | 1.29234 | 0.646172 | − | 0.763192i | \(-0.276369\pi\) | ||||
0.646172 | + | 0.763192i | \(0.276369\pi\) | |||||||
\(140\) | −23.1652 | −1.95781 | ||||||||
\(141\) | 1.75630 | 0.147907 | ||||||||
\(142\) | 23.7376 | 1.99201 | ||||||||
\(143\) | 16.4192 | 1.37304 | ||||||||
\(144\) | −11.8438 | −0.986987 | ||||||||
\(145\) | 14.0594 | 1.16757 | ||||||||
\(146\) | 25.1665 | 2.08280 | ||||||||
\(147\) | 1.68171 | 0.138705 | ||||||||
\(148\) | −29.8257 | −2.45166 | ||||||||
\(149\) | 4.33872 | 0.355442 | 0.177721 | − | 0.984081i | \(-0.443128\pi\) | ||||
0.177721 | + | 0.984081i | \(0.443128\pi\) | |||||||
\(150\) | 1.35277 | 0.110453 | ||||||||
\(151\) | −12.3066 | −1.00149 | −0.500747 | − | 0.865594i | \(-0.666941\pi\) | ||||
−0.500747 | + | 0.865594i | \(0.666941\pi\) | |||||||
\(152\) | −17.9929 | −1.45941 | ||||||||
\(153\) | 2.96291 | 0.239537 | ||||||||
\(154\) | 31.1757 | 2.51221 | ||||||||
\(155\) | 11.9373 | 0.958826 | ||||||||
\(156\) | 3.94132 | 0.315558 | ||||||||
\(157\) | 4.68624 | 0.374003 | 0.187002 | − | 0.982360i | \(-0.440123\pi\) | ||||
0.187002 | + | 0.982360i | \(0.440123\pi\) | |||||||
\(158\) | −1.27020 | −0.101052 | ||||||||
\(159\) | −2.40203 | −0.190493 | ||||||||
\(160\) | 0.00626592 | 0.000495365 0 | ||||||||
\(161\) | 32.3176 | 2.54699 | ||||||||
\(162\) | −21.2303 | −1.66801 | ||||||||
\(163\) | −19.4567 | −1.52397 | −0.761983 | − | 0.647597i | \(-0.775774\pi\) | ||||
−0.761983 | + | 0.647597i | \(0.775774\pi\) | |||||||
\(164\) | 32.9770 | 2.57507 | ||||||||
\(165\) | 0.902495 | 0.0702591 | ||||||||
\(166\) | 17.8981 | 1.38916 | ||||||||
\(167\) | −11.6378 | −0.900562 | −0.450281 | − | 0.892887i | \(-0.648676\pi\) | ||||
−0.450281 | + | 0.892887i | \(0.648676\pi\) | |||||||
\(168\) | 3.74136 | 0.288652 | ||||||||
\(169\) | 13.1800 | 1.01384 | ||||||||
\(170\) | 3.57679 | 0.274327 | ||||||||
\(171\) | −10.8849 | −0.832388 | ||||||||
\(172\) | 22.7196 | 1.73235 | ||||||||
\(173\) | −0.290572 | −0.0220918 | −0.0110459 | − | 0.999939i | \(-0.503516\pi\) | ||||
−0.0110459 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(174\) | −4.54191 | −0.344321 | ||||||||
\(175\) | 11.3739 | 0.859786 | ||||||||
\(176\) | 12.8275 | 0.966907 | ||||||||
\(177\) | −1.17727 | −0.0884887 | ||||||||
\(178\) | −38.5680 | −2.89080 | ||||||||
\(179\) | 14.4316 | 1.07867 | 0.539333 | − | 0.842093i | \(-0.318676\pi\) | ||||
0.539333 | + | 0.842093i | \(0.318676\pi\) | |||||||
\(180\) | −17.3047 | −1.28982 | ||||||||
\(181\) | 16.3780 | 1.21737 | 0.608684 | − | 0.793412i | \(-0.291698\pi\) | ||||
0.608684 | + | 0.793412i | \(0.291698\pi\) | |||||||
\(182\) | 49.7089 | 3.68467 | ||||||||
\(183\) | 0.171173 | 0.0126535 | ||||||||
\(184\) | 39.9066 | 2.94195 | ||||||||
\(185\) | −10.8896 | −0.800618 | ||||||||
\(186\) | −3.85636 | −0.282762 | ||||||||
\(187\) | −3.20898 | −0.234664 | ||||||||
\(188\) | 36.4726 | 2.66003 | ||||||||
\(189\) | 4.55504 | 0.331331 | ||||||||
\(190\) | −13.1401 | −0.953283 | ||||||||
\(191\) | −17.4776 | −1.26463 | −0.632316 | − | 0.774711i | \(-0.717896\pi\) | ||||
−0.632316 | + | 0.774711i | \(0.717896\pi\) | |||||||
\(192\) | −1.54177 | −0.111268 | ||||||||
\(193\) | 5.09520 | 0.366761 | 0.183380 | − | 0.983042i | \(-0.441296\pi\) | ||||
0.183380 | + | 0.983042i | \(0.441296\pi\) | |||||||
\(194\) | 6.35340 | 0.456148 | ||||||||
\(195\) | 1.43901 | 0.103049 | ||||||||
\(196\) | 34.9235 | 2.49453 | ||||||||
\(197\) | 14.6220 | 1.04178 | 0.520888 | − | 0.853625i | \(-0.325601\pi\) | ||||
0.520888 | + | 0.853625i | \(0.325601\pi\) | |||||||
\(198\) | 23.2886 | 1.65505 | ||||||||
\(199\) | 14.5609 | 1.03220 | 0.516099 | − | 0.856529i | \(-0.327384\pi\) | ||||
0.516099 | + | 0.856529i | \(0.327384\pi\) | |||||||
\(200\) | 14.0448 | 0.993115 | ||||||||
\(201\) | −0.707365 | −0.0498937 | ||||||||
\(202\) | −7.70821 | −0.542348 | ||||||||
\(203\) | −38.1877 | −2.68025 | ||||||||
\(204\) | −0.770296 | −0.0539315 | ||||||||
\(205\) | 12.0402 | 0.840921 | ||||||||
\(206\) | −47.5244 | −3.31119 | ||||||||
\(207\) | 24.1417 | 1.67797 | ||||||||
\(208\) | 20.4531 | 1.41817 | ||||||||
\(209\) | 11.7889 | 0.815453 | ||||||||
\(210\) | 2.73230 | 0.188546 | ||||||||
\(211\) | 7.28189 | 0.501306 | 0.250653 | − | 0.968077i | \(-0.419355\pi\) | ||||
0.250653 | + | 0.968077i | \(0.419355\pi\) | |||||||
\(212\) | −49.8822 | −3.42592 | ||||||||
\(213\) | −1.86647 | −0.127888 | ||||||||
\(214\) | −2.34519 | −0.160314 | ||||||||
\(215\) | 8.29510 | 0.565721 | ||||||||
\(216\) | 5.62468 | 0.382711 | ||||||||
\(217\) | −32.4237 | −2.20106 | ||||||||
\(218\) | 48.1514 | 3.26123 | ||||||||
\(219\) | −1.97883 | −0.133717 | ||||||||
\(220\) | 18.7418 | 1.26357 | ||||||||
\(221\) | −5.11663 | −0.344182 | ||||||||
\(222\) | 3.51789 | 0.236106 | ||||||||
\(223\) | 13.4328 | 0.899527 | 0.449764 | − | 0.893148i | \(-0.351508\pi\) | ||||
0.449764 | + | 0.893148i | \(0.351508\pi\) | |||||||
\(224\) | −0.0170193 | −0.00113715 | ||||||||
\(225\) | 8.49646 | 0.566431 | ||||||||
\(226\) | 17.6374 | 1.17322 | ||||||||
\(227\) | 21.2888 | 1.41299 | 0.706493 | − | 0.707720i | \(-0.250276\pi\) | ||||
0.706493 | + | 0.707720i | \(0.250276\pi\) | |||||||
\(228\) | 2.82985 | 0.187411 | ||||||||
\(229\) | −22.0249 | −1.45545 | −0.727724 | − | 0.685870i | \(-0.759422\pi\) | ||||
−0.727724 | + | 0.685870i | \(0.759422\pi\) | |||||||
\(230\) | 29.1436 | 1.92167 | ||||||||
\(231\) | −2.45133 | −0.161285 | ||||||||
\(232\) | −47.1551 | −3.09588 | ||||||||
\(233\) | 7.16295 | 0.469260 | 0.234630 | − | 0.972085i | \(-0.424612\pi\) | ||||
0.234630 | + | 0.972085i | \(0.424612\pi\) | |||||||
\(234\) | 37.1332 | 2.42747 | ||||||||
\(235\) | 13.3164 | 0.868667 | ||||||||
\(236\) | −24.4479 | −1.59142 | ||||||||
\(237\) | 0.0998752 | 0.00648759 | ||||||||
\(238\) | −9.71515 | −0.629739 | ||||||||
\(239\) | 8.22604 | 0.532098 | 0.266049 | − | 0.963959i | \(-0.414282\pi\) | ||||
0.266049 | + | 0.963959i | \(0.414282\pi\) | |||||||
\(240\) | 1.12422 | 0.0725684 | ||||||||
\(241\) | 2.97682 | 0.191754 | 0.0958768 | − | 0.995393i | \(-0.469435\pi\) | ||||
0.0958768 | + | 0.995393i | \(0.469435\pi\) | |||||||
\(242\) | 1.72065 | 0.110607 | ||||||||
\(243\) | 5.11460 | 0.328102 | ||||||||
\(244\) | 3.55470 | 0.227566 | ||||||||
\(245\) | 12.7508 | 0.814620 | ||||||||
\(246\) | −3.88959 | −0.247991 | ||||||||
\(247\) | 18.7971 | 1.19603 | ||||||||
\(248\) | −40.0375 | −2.54238 | ||||||||
\(249\) | −1.40731 | −0.0891849 | ||||||||
\(250\) | 28.1408 | 1.77978 | ||||||||
\(251\) | −10.7948 | −0.681364 | −0.340682 | − | 0.940179i | \(-0.610658\pi\) | ||||
−0.340682 | + | 0.940179i | \(0.610658\pi\) | |||||||
\(252\) | 47.0024 | 2.96087 | ||||||||
\(253\) | −26.1467 | −1.64383 | ||||||||
\(254\) | −48.2297 | −3.02620 | ||||||||
\(255\) | −0.281241 | −0.0176120 | ||||||||
\(256\) | −31.9965 | −1.99978 | ||||||||
\(257\) | 9.59353 | 0.598428 | 0.299214 | − | 0.954186i | \(-0.403276\pi\) | ||||
0.299214 | + | 0.954186i | \(0.403276\pi\) | |||||||
\(258\) | −2.67974 | −0.166833 | ||||||||
\(259\) | 29.5779 | 1.83788 | ||||||||
\(260\) | 29.8834 | 1.85329 | ||||||||
\(261\) | −28.5267 | −1.76576 | ||||||||
\(262\) | 21.5284 | 1.33003 | ||||||||
\(263\) | 17.7044 | 1.09170 | 0.545850 | − | 0.837883i | \(-0.316207\pi\) | ||||
0.545850 | + | 0.837883i | \(0.316207\pi\) | |||||||
\(264\) | −3.02696 | −0.186296 | ||||||||
\(265\) | −18.2124 | −1.11878 | ||||||||
\(266\) | 35.6907 | 2.18834 | ||||||||
\(267\) | 3.03258 | 0.185591 | ||||||||
\(268\) | −14.6896 | −0.897313 | ||||||||
\(269\) | 0.243516 | 0.0148474 | 0.00742372 | − | 0.999972i | \(-0.497637\pi\) | ||||
0.00742372 | + | 0.999972i | \(0.497637\pi\) | |||||||
\(270\) | 4.10768 | 0.249985 | ||||||||
\(271\) | 10.9093 | 0.662694 | 0.331347 | − | 0.943509i | \(-0.392497\pi\) | ||||
0.331347 | + | 0.943509i | \(0.392497\pi\) | |||||||
\(272\) | −3.99737 | −0.242376 | ||||||||
\(273\) | −3.90858 | −0.236558 | ||||||||
\(274\) | −36.1988 | −2.18685 | ||||||||
\(275\) | −9.20209 | −0.554907 | ||||||||
\(276\) | −6.27636 | −0.377792 | ||||||||
\(277\) | −5.64987 | −0.339468 | −0.169734 | − | 0.985490i | \(-0.554291\pi\) | ||||
−0.169734 | + | 0.985490i | \(0.554291\pi\) | |||||||
\(278\) | −37.3203 | −2.23832 | ||||||||
\(279\) | −24.2209 | −1.45007 | ||||||||
\(280\) | 28.3673 | 1.69527 | ||||||||
\(281\) | −0.214539 | −0.0127983 | −0.00639916 | − | 0.999980i | \(-0.502037\pi\) | ||||
−0.00639916 | + | 0.999980i | \(0.502037\pi\) | |||||||
\(282\) | −4.30188 | −0.256173 | ||||||||
\(283\) | −21.0437 | −1.25092 | −0.625458 | − | 0.780258i | \(-0.715088\pi\) | ||||
−0.625458 | + | 0.780258i | \(0.715088\pi\) | |||||||
\(284\) | −38.7604 | −2.30001 | ||||||||
\(285\) | 1.03320 | 0.0612014 | ||||||||
\(286\) | −40.2171 | −2.37809 | ||||||||
\(287\) | −32.7031 | −1.93040 | ||||||||
\(288\) | −0.0127136 | −0.000749158 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −34.4371 | −2.02222 | ||||||||
\(291\) | −0.499564 | −0.0292850 | ||||||||
\(292\) | −41.0938 | −2.40483 | ||||||||
\(293\) | −8.94936 | −0.522827 | −0.261414 | − | 0.965227i | \(-0.584189\pi\) | ||||
−0.261414 | + | 0.965227i | \(0.584189\pi\) | |||||||
\(294\) | −4.11917 | −0.240235 | ||||||||
\(295\) | −8.92612 | −0.519699 | ||||||||
\(296\) | 36.5235 | 2.12289 | ||||||||
\(297\) | −3.68527 | −0.213841 | ||||||||
\(298\) | −10.6273 | −0.615621 | ||||||||
\(299\) | −41.6903 | −2.41101 | ||||||||
\(300\) | −2.20891 | −0.127531 | ||||||||
\(301\) | −22.5309 | −1.29866 | ||||||||
\(302\) | 30.1437 | 1.73458 | ||||||||
\(303\) | 0.606093 | 0.0348191 | ||||||||
\(304\) | 14.6852 | 0.842255 | ||||||||
\(305\) | 1.29785 | 0.0743145 | ||||||||
\(306\) | −7.25735 | −0.414875 | ||||||||
\(307\) | −12.8837 | −0.735311 | −0.367656 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367656 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(308\) | −50.9059 | −2.90063 | ||||||||
\(309\) | 3.73682 | 0.212580 | ||||||||
\(310\) | −29.2392 | −1.66068 | ||||||||
\(311\) | 29.9964 | 1.70094 | 0.850469 | − | 0.526024i | \(-0.176318\pi\) | ||||
0.850469 | + | 0.526024i | \(0.176318\pi\) | |||||||
\(312\) | −4.82641 | −0.273242 | ||||||||
\(313\) | −11.8376 | −0.669100 | −0.334550 | − | 0.942378i | \(-0.608584\pi\) | ||||
−0.334550 | + | 0.942378i | \(0.608584\pi\) | |||||||
\(314\) | −11.4785 | −0.647769 | ||||||||
\(315\) | 17.1609 | 0.966909 | ||||||||
\(316\) | 2.07408 | 0.116676 | ||||||||
\(317\) | 3.25428 | 0.182779 | 0.0913893 | − | 0.995815i | \(-0.470869\pi\) | ||||
0.0913893 | + | 0.995815i | \(0.470869\pi\) | |||||||
\(318\) | 5.88353 | 0.329932 | ||||||||
\(319\) | 30.8958 | 1.72984 | ||||||||
\(320\) | −11.6898 | −0.653482 | ||||||||
\(321\) | 0.184401 | 0.0102922 | ||||||||
\(322\) | −79.1588 | −4.41135 | ||||||||
\(323\) | −3.67372 | −0.204411 | ||||||||
\(324\) | 34.6664 | 1.92591 | ||||||||
\(325\) | −14.6725 | −0.813885 | ||||||||
\(326\) | 47.6573 | 2.63949 | ||||||||
\(327\) | −3.78612 | −0.209373 | ||||||||
\(328\) | −40.3825 | −2.22975 | ||||||||
\(329\) | −36.1696 | −1.99409 | ||||||||
\(330\) | −2.21057 | −0.121688 | ||||||||
\(331\) | 27.3326 | 1.50234 | 0.751168 | − | 0.660111i | \(-0.229491\pi\) | ||||
0.751168 | + | 0.660111i | \(0.229491\pi\) | |||||||
\(332\) | −29.2253 | −1.60394 | ||||||||
\(333\) | 22.0951 | 1.21080 | ||||||||
\(334\) | 28.5057 | 1.55976 | ||||||||
\(335\) | −5.36330 | −0.293028 | ||||||||
\(336\) | −3.05358 | −0.166586 | ||||||||
\(337\) | −6.08818 | −0.331644 | −0.165822 | − | 0.986156i | \(-0.553028\pi\) | ||||
−0.165822 | + | 0.986156i | \(0.553028\pi\) | |||||||
\(338\) | −32.2830 | −1.75596 | ||||||||
\(339\) | −1.38682 | −0.0753216 | ||||||||
\(340\) | −5.84044 | −0.316742 | ||||||||
\(341\) | 26.2324 | 1.42057 | ||||||||
\(342\) | 26.6614 | 1.44168 | ||||||||
\(343\) | −6.86900 | −0.370891 | ||||||||
\(344\) | −27.8216 | −1.50004 | ||||||||
\(345\) | −2.29155 | −0.123373 | ||||||||
\(346\) | 0.711727 | 0.0382627 | ||||||||
\(347\) | 36.4223 | 1.95525 | 0.977627 | − | 0.210347i | \(-0.0674594\pi\) | ||||
0.977627 | + | 0.210347i | \(0.0674594\pi\) | |||||||
\(348\) | 7.41637 | 0.397559 | ||||||||
\(349\) | 2.94554 | 0.157671 | 0.0788356 | − | 0.996888i | \(-0.474880\pi\) | ||||
0.0788356 | + | 0.996888i | \(0.474880\pi\) | |||||||
\(350\) | −27.8592 | −1.48914 | ||||||||
\(351\) | −5.87608 | −0.313642 | ||||||||
\(352\) | 0.0137695 | 0.000733917 0 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 2.88360 | 0.153261 | ||||||||
\(355\) | −14.1517 | −0.751096 | ||||||||
\(356\) | 62.9768 | 3.33776 | ||||||||
\(357\) | 0.763897 | 0.0404297 | ||||||||
\(358\) | −35.3487 | −1.86824 | ||||||||
\(359\) | 4.15379 | 0.219229 | 0.109614 | − | 0.993974i | \(-0.465038\pi\) | ||||
0.109614 | + | 0.993974i | \(0.465038\pi\) | |||||||
\(360\) | 21.1907 | 1.11685 | ||||||||
\(361\) | −5.50381 | −0.289674 | ||||||||
\(362\) | −40.1163 | −2.10847 | ||||||||
\(363\) | −0.135294 | −0.00710108 | ||||||||
\(364\) | −81.1683 | −4.25437 | ||||||||
\(365\) | −15.0037 | −0.785327 | ||||||||
\(366\) | −0.419271 | −0.0219157 | ||||||||
\(367\) | 4.33551 | 0.226312 | 0.113156 | − | 0.993577i | \(-0.463904\pi\) | ||||
0.113156 | + | 0.993577i | \(0.463904\pi\) | |||||||
\(368\) | −32.5705 | −1.69786 | ||||||||
\(369\) | −24.4296 | −1.27176 | ||||||||
\(370\) | 26.6729 | 1.38666 | ||||||||
\(371\) | 49.4678 | 2.56824 | ||||||||
\(372\) | 6.29695 | 0.326481 | ||||||||
\(373\) | −28.5247 | −1.47695 | −0.738476 | − | 0.674279i | \(-0.764454\pi\) | ||||
−0.738476 | + | 0.674279i | \(0.764454\pi\) | |||||||
\(374\) | 7.86007 | 0.406434 | ||||||||
\(375\) | −2.21269 | −0.114263 | ||||||||
\(376\) | −44.6631 | −2.30332 | ||||||||
\(377\) | 49.2627 | 2.53716 | ||||||||
\(378\) | −11.1571 | −0.573861 | ||||||||
\(379\) | −15.5883 | −0.800717 | −0.400359 | − | 0.916359i | \(-0.631114\pi\) | ||||
−0.400359 | + | 0.916359i | \(0.631114\pi\) | |||||||
\(380\) | 21.4561 | 1.10068 | ||||||||
\(381\) | 3.79228 | 0.194284 | ||||||||
\(382\) | 42.8095 | 2.19033 | ||||||||
\(383\) | 34.2414 | 1.74966 | 0.874828 | − | 0.484434i | \(-0.160974\pi\) | ||||
0.874828 | + | 0.484434i | \(0.160974\pi\) | |||||||
\(384\) | 3.77476 | 0.192630 | ||||||||
\(385\) | −18.5861 | −0.947237 | ||||||||
\(386\) | −12.4802 | −0.635225 | ||||||||
\(387\) | −16.8309 | −0.855561 | ||||||||
\(388\) | −10.3743 | −0.526675 | ||||||||
\(389\) | 15.6035 | 0.791130 | 0.395565 | − | 0.918438i | \(-0.370549\pi\) | ||||
0.395565 | + | 0.918438i | \(0.370549\pi\) | |||||||
\(390\) | −3.52470 | −0.178480 | ||||||||
\(391\) | 8.14798 | 0.412061 | ||||||||
\(392\) | −42.7661 | −2.16001 | ||||||||
\(393\) | −1.69277 | −0.0853889 | ||||||||
\(394\) | −35.8152 | −1.80434 | ||||||||
\(395\) | 0.757262 | 0.0381020 | ||||||||
\(396\) | −38.0274 | −1.91095 | ||||||||
\(397\) | 32.8191 | 1.64714 | 0.823571 | − | 0.567213i | \(-0.191978\pi\) | ||||
0.823571 | + | 0.567213i | \(0.191978\pi\) | |||||||
\(398\) | −35.6655 | −1.78775 | ||||||||
\(399\) | −2.80634 | −0.140493 | ||||||||
\(400\) | −11.4629 | −0.573145 | ||||||||
\(401\) | 37.2479 | 1.86007 | 0.930037 | − | 0.367466i | \(-0.119775\pi\) | ||||
0.930037 | + | 0.367466i | \(0.119775\pi\) | |||||||
\(402\) | 1.73262 | 0.0864153 | ||||||||
\(403\) | 41.8270 | 2.08355 | ||||||||
\(404\) | 12.5865 | 0.626204 | ||||||||
\(405\) | 12.6570 | 0.628929 | ||||||||
\(406\) | 93.5369 | 4.64216 | ||||||||
\(407\) | −23.9301 | −1.18617 | ||||||||
\(408\) | 0.943278 | 0.0466992 | ||||||||
\(409\) | −9.29099 | −0.459410 | −0.229705 | − | 0.973260i | \(-0.573776\pi\) | ||||
−0.229705 | + | 0.973260i | \(0.573776\pi\) | |||||||
\(410\) | −29.4912 | −1.45647 | ||||||||
\(411\) | 2.84630 | 0.140397 | ||||||||
\(412\) | 77.6014 | 3.82315 | ||||||||
\(413\) | 24.2448 | 1.19301 | ||||||||
\(414\) | −59.1327 | −2.90622 | ||||||||
\(415\) | −10.6704 | −0.523788 | ||||||||
\(416\) | 0.0219551 | 0.00107644 | ||||||||
\(417\) | 2.93447 | 0.143702 | ||||||||
\(418\) | −28.8756 | −1.41235 | ||||||||
\(419\) | 6.23699 | 0.304697 | 0.152348 | − | 0.988327i | \(-0.451316\pi\) | ||||
0.152348 | + | 0.988327i | \(0.451316\pi\) | |||||||
\(420\) | −4.46149 | −0.217699 | ||||||||
\(421\) | −4.13653 | −0.201602 | −0.100801 | − | 0.994907i | \(-0.532141\pi\) | ||||
−0.100801 | + | 0.994907i | \(0.532141\pi\) | |||||||
\(422\) | −17.8363 | −0.868256 | ||||||||
\(423\) | −27.0192 | −1.31372 | ||||||||
\(424\) | 61.0841 | 2.96650 | ||||||||
\(425\) | 2.86761 | 0.139100 | ||||||||
\(426\) | 4.57173 | 0.221501 | ||||||||
\(427\) | −3.52517 | −0.170595 | ||||||||
\(428\) | 3.82939 | 0.185101 | ||||||||
\(429\) | 3.16225 | 0.152675 | ||||||||
\(430\) | −20.3180 | −0.979822 | ||||||||
\(431\) | −3.87001 | −0.186412 | −0.0932059 | − | 0.995647i | \(-0.529711\pi\) | ||||
−0.0932059 | + | 0.995647i | \(0.529711\pi\) | |||||||
\(432\) | −4.59069 | −0.220870 | ||||||||
\(433\) | 0.720491 | 0.0346246 | 0.0173123 | − | 0.999850i | \(-0.494489\pi\) | ||||
0.0173123 | + | 0.999850i | \(0.494489\pi\) | |||||||
\(434\) | 79.4185 | 3.81221 | ||||||||
\(435\) | 2.70777 | 0.129828 | ||||||||
\(436\) | −78.6252 | −3.76547 | ||||||||
\(437\) | −29.9334 | −1.43191 | ||||||||
\(438\) | 4.84695 | 0.231596 | ||||||||
\(439\) | −34.7771 | −1.65982 | −0.829911 | − | 0.557896i | \(-0.811609\pi\) | ||||
−0.829911 | + | 0.557896i | \(0.811609\pi\) | |||||||
\(440\) | −22.9506 | −1.09413 | ||||||||
\(441\) | −25.8716 | −1.23198 | ||||||||
\(442\) | 12.5327 | 0.596119 | ||||||||
\(443\) | −15.8554 | −0.753315 | −0.376657 | − | 0.926353i | \(-0.622927\pi\) | ||||
−0.376657 | + | 0.926353i | \(0.622927\pi\) | |||||||
\(444\) | −5.74428 | −0.272611 | ||||||||
\(445\) | 22.9933 | 1.08999 | ||||||||
\(446\) | −32.9023 | −1.55797 | ||||||||
\(447\) | 0.835617 | 0.0395233 | ||||||||
\(448\) | 31.7515 | 1.50012 | ||||||||
\(449\) | −6.79290 | −0.320577 | −0.160288 | − | 0.987070i | \(-0.551242\pi\) | ||||
−0.160288 | + | 0.987070i | \(0.551242\pi\) | |||||||
\(450\) | −20.8112 | −0.981051 | ||||||||
\(451\) | 26.4585 | 1.24588 | ||||||||
\(452\) | −28.7996 | −1.35462 | ||||||||
\(453\) | −2.37018 | −0.111361 | ||||||||
\(454\) | −52.1447 | −2.44727 | ||||||||
\(455\) | −29.6352 | −1.38932 | ||||||||
\(456\) | −3.46534 | −0.162279 | ||||||||
\(457\) | −4.69497 | −0.219621 | −0.109811 | − | 0.993953i | \(-0.535024\pi\) | ||||
−0.109811 | + | 0.993953i | \(0.535024\pi\) | |||||||
\(458\) | 53.9479 | 2.52082 | ||||||||
\(459\) | 1.14843 | 0.0536039 | ||||||||
\(460\) | −47.5878 | −2.21879 | ||||||||
\(461\) | −13.0849 | −0.609427 | −0.304713 | − | 0.952444i | \(-0.598561\pi\) | ||||
−0.304713 | + | 0.952444i | \(0.598561\pi\) | |||||||
\(462\) | 6.00428 | 0.279344 | ||||||||
\(463\) | 6.07716 | 0.282429 | 0.141215 | − | 0.989979i | \(-0.454899\pi\) | ||||
0.141215 | + | 0.989979i | \(0.454899\pi\) | |||||||
\(464\) | 38.4865 | 1.78669 | ||||||||
\(465\) | 2.29906 | 0.106616 | ||||||||
\(466\) | −17.5449 | −0.812753 | ||||||||
\(467\) | 36.6402 | 1.69550 | 0.847752 | − | 0.530392i | \(-0.177955\pi\) | ||||
0.847752 | + | 0.530392i | \(0.177955\pi\) | |||||||
\(468\) | −60.6338 | −2.80280 | ||||||||
\(469\) | 14.5676 | 0.672670 | ||||||||
\(470\) | −32.6172 | −1.50452 | ||||||||
\(471\) | 0.902547 | 0.0415872 | ||||||||
\(472\) | 29.9381 | 1.37801 | ||||||||
\(473\) | 18.2287 | 0.838154 | ||||||||
\(474\) | −0.244634 | −0.0112364 | ||||||||
\(475\) | −10.5348 | −0.483369 | ||||||||
\(476\) | 15.8636 | 0.727107 | ||||||||
\(477\) | 36.9531 | 1.69197 | ||||||||
\(478\) | −20.1489 | −0.921588 | ||||||||
\(479\) | 39.3934 | 1.79993 | 0.899966 | − | 0.435960i | \(-0.143591\pi\) | ||||
0.899966 | + | 0.435960i | \(0.143591\pi\) | |||||||
\(480\) | 0.00120679 | 5.50820e−5 0 | ||||||||
\(481\) | −38.1560 | −1.73976 | ||||||||
\(482\) | −7.29142 | −0.332115 | ||||||||
\(483\) | 6.22422 | 0.283212 | ||||||||
\(484\) | −2.80960 | −0.127709 | ||||||||
\(485\) | −3.78774 | −0.171992 | ||||||||
\(486\) | −12.5277 | −0.568269 | ||||||||
\(487\) | −21.9048 | −0.992603 | −0.496301 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496301 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(488\) | −4.35296 | −0.197049 | ||||||||
\(489\) | −3.74726 | −0.169457 | ||||||||
\(490\) | −31.2319 | −1.41091 | ||||||||
\(491\) | 14.7880 | 0.667371 | 0.333686 | − | 0.942684i | \(-0.391708\pi\) | ||||
0.333686 | + | 0.942684i | \(0.391708\pi\) | |||||||
\(492\) | 6.35121 | 0.286335 | ||||||||
\(493\) | −9.62795 | −0.433621 | ||||||||
\(494\) | −46.0415 | −2.07151 | ||||||||
\(495\) | −13.8841 | −0.624044 | ||||||||
\(496\) | 32.6774 | 1.46726 | ||||||||
\(497\) | 38.4384 | 1.72420 | ||||||||
\(498\) | 3.44708 | 0.154467 | ||||||||
\(499\) | −13.5733 | −0.607626 | −0.303813 | − | 0.952732i | \(-0.598260\pi\) | ||||
−0.303813 | + | 0.952732i | \(0.598260\pi\) | |||||||
\(500\) | −45.9503 | −2.05496 | ||||||||
\(501\) | −2.24139 | −0.100138 | ||||||||
\(502\) | 26.4409 | 1.18011 | ||||||||
\(503\) | −0.962694 | −0.0429244 | −0.0214622 | − | 0.999770i | \(-0.506832\pi\) | ||||
−0.0214622 | + | 0.999770i | \(0.506832\pi\) | |||||||
\(504\) | −57.5575 | −2.56382 | ||||||||
\(505\) | 4.59544 | 0.204494 | ||||||||
\(506\) | 64.0437 | 2.84709 | ||||||||
\(507\) | 2.53839 | 0.112734 | ||||||||
\(508\) | 78.7531 | 3.49410 | ||||||||
\(509\) | −33.6953 | −1.49352 | −0.746759 | − | 0.665095i | \(-0.768391\pi\) | ||||
−0.746759 | + | 0.665095i | \(0.768391\pi\) | |||||||
\(510\) | 0.688871 | 0.0305037 | ||||||||
\(511\) | 40.7524 | 1.80278 | ||||||||
\(512\) | 39.1732 | 1.73123 | ||||||||
\(513\) | −4.21899 | −0.186273 | ||||||||
\(514\) | −23.4984 | −1.03647 | ||||||||
\(515\) | 28.3329 | 1.24850 | ||||||||
\(516\) | 4.37568 | 0.192629 | ||||||||
\(517\) | 29.2631 | 1.28699 | ||||||||
\(518\) | −72.4481 | −3.18319 | ||||||||
\(519\) | −0.0559627 | −0.00245649 | ||||||||
\(520\) | −36.5942 | −1.60476 | ||||||||
\(521\) | 1.48409 | 0.0650192 | 0.0325096 | − | 0.999471i | \(-0.489650\pi\) | ||||
0.0325096 | + | 0.999471i | \(0.489650\pi\) | |||||||
\(522\) | 69.8734 | 3.05827 | ||||||||
\(523\) | −10.9555 | −0.479053 | −0.239526 | − | 0.970890i | \(-0.576992\pi\) | ||||
−0.239526 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(524\) | −35.1532 | −1.53567 | ||||||||
\(525\) | 2.19056 | 0.0956038 | ||||||||
\(526\) | −43.3651 | −1.89081 | ||||||||
\(527\) | −8.17471 | −0.356096 | ||||||||
\(528\) | 2.47051 | 0.107515 | ||||||||
\(529\) | 43.3896 | 1.88651 | ||||||||
\(530\) | 44.6094 | 1.93771 | ||||||||
\(531\) | 18.1112 | 0.785960 | ||||||||
\(532\) | −58.2784 | −2.52669 | ||||||||
\(533\) | 42.1875 | 1.82734 | ||||||||
\(534\) | −7.42801 | −0.321442 | ||||||||
\(535\) | 1.39814 | 0.0604469 | ||||||||
\(536\) | 17.9884 | 0.776982 | ||||||||
\(537\) | 2.77945 | 0.119942 | ||||||||
\(538\) | −0.596469 | −0.0257156 | ||||||||
\(539\) | 28.0202 | 1.20692 | ||||||||
\(540\) | −6.70732 | −0.288637 | ||||||||
\(541\) | −3.19187 | −0.137229 | −0.0686147 | − | 0.997643i | \(-0.521858\pi\) | ||||
−0.0686147 | + | 0.997643i | \(0.521858\pi\) | |||||||
\(542\) | −26.7213 | −1.14778 | ||||||||
\(543\) | 3.15433 | 0.135365 | ||||||||
\(544\) | −0.00429093 | −0.000183972 0 | ||||||||
\(545\) | −28.7067 | −1.22966 | ||||||||
\(546\) | 9.57368 | 0.409716 | ||||||||
\(547\) | 26.5735 | 1.13620 | 0.568101 | − | 0.822959i | \(-0.307678\pi\) | ||||
0.568101 | + | 0.822959i | \(0.307678\pi\) | |||||||
\(548\) | 59.1081 | 2.52497 | ||||||||
\(549\) | −2.63335 | −0.112389 | ||||||||
\(550\) | 22.5396 | 0.961092 | ||||||||
\(551\) | 35.3703 | 1.50683 | ||||||||
\(552\) | 7.68581 | 0.327130 | ||||||||
\(553\) | −2.05685 | −0.0874661 | ||||||||
\(554\) | 13.8388 | 0.587954 | ||||||||
\(555\) | −2.09728 | −0.0890245 | ||||||||
\(556\) | 60.9393 | 2.58440 | ||||||||
\(557\) | 20.6929 | 0.876785 | 0.438392 | − | 0.898784i | \(-0.355548\pi\) | ||||
0.438392 | + | 0.898784i | \(0.355548\pi\) | |||||||
\(558\) | 59.3267 | 2.51150 | ||||||||
\(559\) | 29.0652 | 1.22933 | ||||||||
\(560\) | −23.1525 | −0.978371 | ||||||||
\(561\) | −0.618033 | −0.0260934 | ||||||||
\(562\) | 0.525492 | 0.0221665 | ||||||||
\(563\) | −29.5380 | −1.24488 | −0.622439 | − | 0.782669i | \(-0.713858\pi\) | ||||
−0.622439 | + | 0.782669i | \(0.713858\pi\) | |||||||
\(564\) | 7.02443 | 0.295782 | ||||||||
\(565\) | −10.5150 | −0.442368 | ||||||||
\(566\) | 51.5444 | 2.16657 | ||||||||
\(567\) | −34.3784 | −1.44376 | ||||||||
\(568\) | 47.4647 | 1.99157 | ||||||||
\(569\) | −3.92157 | −0.164401 | −0.0822004 | − | 0.996616i | \(-0.526195\pi\) | ||||
−0.0822004 | + | 0.996616i | \(0.526195\pi\) | |||||||
\(570\) | −2.53072 | −0.106000 | ||||||||
\(571\) | −30.4936 | −1.27612 | −0.638058 | − | 0.769988i | \(-0.720262\pi\) | ||||
−0.638058 | + | 0.769988i | \(0.720262\pi\) | |||||||
\(572\) | 65.6694 | 2.74578 | ||||||||
\(573\) | −3.36609 | −0.140620 | ||||||||
\(574\) | 80.1029 | 3.34343 | ||||||||
\(575\) | 23.3652 | 0.974398 | ||||||||
\(576\) | 23.7188 | 0.988284 | ||||||||
\(577\) | −21.7812 | −0.906762 | −0.453381 | − | 0.891317i | \(-0.649782\pi\) | ||||
−0.453381 | + | 0.891317i | \(0.649782\pi\) | |||||||
\(578\) | −2.44940 | −0.101882 | ||||||||
\(579\) | 0.981310 | 0.0407819 | ||||||||
\(580\) | 56.2315 | 2.33489 | ||||||||
\(581\) | 28.9825 | 1.20240 | ||||||||
\(582\) | 1.22363 | 0.0507212 | ||||||||
\(583\) | −40.0221 | −1.65755 | ||||||||
\(584\) | 50.3221 | 2.08234 | ||||||||
\(585\) | −22.1379 | −0.915288 | ||||||||
\(586\) | 21.9206 | 0.905530 | ||||||||
\(587\) | −42.7786 | −1.76566 | −0.882831 | − | 0.469690i | \(-0.844366\pi\) | ||||
−0.882831 | + | 0.469690i | \(0.844366\pi\) | |||||||
\(588\) | 6.72609 | 0.277379 | ||||||||
\(589\) | 30.0316 | 1.23743 | ||||||||
\(590\) | 21.8636 | 0.900112 | ||||||||
\(591\) | 2.81613 | 0.115840 | ||||||||
\(592\) | −29.8093 | −1.22516 | ||||||||
\(593\) | 47.0717 | 1.93300 | 0.966501 | − | 0.256663i | \(-0.0826230\pi\) | ||||
0.966501 | + | 0.256663i | \(0.0826230\pi\) | |||||||
\(594\) | 9.02670 | 0.370370 | ||||||||
\(595\) | 5.79192 | 0.237446 | ||||||||
\(596\) | 17.3530 | 0.710806 | ||||||||
\(597\) | 2.80436 | 0.114775 | ||||||||
\(598\) | 102.116 | 4.17584 | ||||||||
\(599\) | 28.6998 | 1.17264 | 0.586320 | − | 0.810079i | \(-0.300576\pi\) | ||||
0.586320 | + | 0.810079i | \(0.300576\pi\) | |||||||
\(600\) | 2.70495 | 0.110429 | ||||||||
\(601\) | −3.70833 | −0.151266 | −0.0756330 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756330 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(602\) | 55.1871 | 2.24926 | ||||||||
\(603\) | 10.8822 | 0.443158 | ||||||||
\(604\) | −49.2209 | −2.00277 | ||||||||
\(605\) | −1.02581 | −0.0417050 | ||||||||
\(606\) | −1.48456 | −0.0603063 | ||||||||
\(607\) | −5.41113 | −0.219631 | −0.109816 | − | 0.993952i | \(-0.535026\pi\) | ||||
−0.109816 | + | 0.993952i | \(0.535026\pi\) | |||||||
\(608\) | 0.0157637 | 0.000639301 0 | ||||||||
\(609\) | −7.35476 | −0.298030 | ||||||||
\(610\) | −3.17895 | −0.128712 | ||||||||
\(611\) | 46.6593 | 1.88763 | ||||||||
\(612\) | 11.8503 | 0.479021 | ||||||||
\(613\) | 28.8506 | 1.16526 | 0.582631 | − | 0.812736i | \(-0.302023\pi\) | ||||
0.582631 | + | 0.812736i | \(0.302023\pi\) | |||||||
\(614\) | 31.5573 | 1.27355 | ||||||||
\(615\) | 2.31887 | 0.0935061 | ||||||||
\(616\) | 62.3377 | 2.51166 | ||||||||
\(617\) | 10.5288 | 0.423874 | 0.211937 | − | 0.977283i | \(-0.432023\pi\) | ||||
0.211937 | + | 0.977283i | \(0.432023\pi\) | |||||||
\(618\) | −9.15297 | −0.368187 | ||||||||
\(619\) | −1.60767 | −0.0646177 | −0.0323089 | − | 0.999478i | \(-0.510286\pi\) | ||||
−0.0323089 | + | 0.999478i | \(0.510286\pi\) | |||||||
\(620\) | 47.7439 | 1.91744 | ||||||||
\(621\) | 9.35736 | 0.375498 | ||||||||
\(622\) | −73.4732 | −2.94601 | ||||||||
\(623\) | −62.4536 | −2.50215 | ||||||||
\(624\) | 3.93916 | 0.157693 | ||||||||
\(625\) | −2.43876 | −0.0975505 | ||||||||
\(626\) | 28.9950 | 1.15887 | ||||||||
\(627\) | 2.27048 | 0.0906741 | ||||||||
\(628\) | 18.7429 | 0.747924 | ||||||||
\(629\) | 7.45724 | 0.297339 | ||||||||
\(630\) | −42.0340 | −1.67467 | ||||||||
\(631\) | 37.8451 | 1.50659 | 0.753294 | − | 0.657683i | \(-0.228464\pi\) | ||||
0.753294 | + | 0.657683i | \(0.228464\pi\) | |||||||
\(632\) | −2.53985 | −0.101030 | ||||||||
\(633\) | 1.40246 | 0.0557426 | ||||||||
\(634\) | −7.97104 | −0.316570 | ||||||||
\(635\) | 28.7534 | 1.14104 | ||||||||
\(636\) | −9.60707 | −0.380945 | ||||||||
\(637\) | 44.6776 | 1.77019 | ||||||||
\(638\) | −75.6763 | −2.99605 | ||||||||
\(639\) | 28.7140 | 1.13591 | ||||||||
\(640\) | 28.6206 | 1.13133 | ||||||||
\(641\) | 30.5735 | 1.20758 | 0.603791 | − | 0.797143i | \(-0.293656\pi\) | ||||
0.603791 | + | 0.797143i | \(0.293656\pi\) | |||||||
\(642\) | −0.451671 | −0.0178260 | ||||||||
\(643\) | 24.9713 | 0.984771 | 0.492385 | − | 0.870377i | \(-0.336125\pi\) | ||||
0.492385 | + | 0.870377i | \(0.336125\pi\) | |||||||
\(644\) | 129.256 | 5.09342 | ||||||||
\(645\) | 1.59759 | 0.0629052 | ||||||||
\(646\) | 8.99840 | 0.354037 | ||||||||
\(647\) | 49.1413 | 1.93194 | 0.965971 | − | 0.258649i | \(-0.0832773\pi\) | ||||
0.965971 | + | 0.258649i | \(0.0832773\pi\) | |||||||
\(648\) | −42.4513 | −1.66764 | ||||||||
\(649\) | −19.6153 | −0.769969 | ||||||||
\(650\) | 35.9389 | 1.40964 | ||||||||
\(651\) | −6.24464 | −0.244747 | ||||||||
\(652\) | −77.8183 | −3.04760 | ||||||||
\(653\) | −10.1484 | −0.397138 | −0.198569 | − | 0.980087i | \(-0.563629\pi\) | ||||
−0.198569 | + | 0.980087i | \(0.563629\pi\) | |||||||
\(654\) | 9.27373 | 0.362631 | ||||||||
\(655\) | −12.8347 | −0.501493 | ||||||||
\(656\) | 32.9590 | 1.28683 | ||||||||
\(657\) | 30.4426 | 1.18768 | ||||||||
\(658\) | 88.5938 | 3.45374 | ||||||||
\(659\) | 47.3753 | 1.84548 | 0.922740 | − | 0.385423i | \(-0.125944\pi\) | ||||
0.922740 | + | 0.385423i | \(0.125944\pi\) | |||||||
\(660\) | 3.60958 | 0.140503 | ||||||||
\(661\) | −30.9698 | −1.20458 | −0.602292 | − | 0.798276i | \(-0.705746\pi\) | ||||
−0.602292 | + | 0.798276i | \(0.705746\pi\) | |||||||
\(662\) | −66.9485 | −2.60203 | ||||||||
\(663\) | −0.985438 | −0.0382713 | ||||||||
\(664\) | 35.7883 | 1.38885 | ||||||||
\(665\) | −21.2779 | −0.825121 | ||||||||
\(666\) | −54.1197 | −2.09710 | ||||||||
\(667\) | −78.4484 | −3.03753 | ||||||||
\(668\) | −46.5462 | −1.80093 | ||||||||
\(669\) | 2.58709 | 0.100023 | ||||||||
\(670\) | 13.1369 | 0.507522 | ||||||||
\(671\) | 2.85205 | 0.110102 | ||||||||
\(672\) | −0.00327783 | −0.000126445 0 | ||||||||
\(673\) | −4.09240 | −0.157750 | −0.0788752 | − | 0.996884i | \(-0.525133\pi\) | ||||
−0.0788752 | + | 0.996884i | \(0.525133\pi\) | |||||||
\(674\) | 14.9124 | 0.574404 | ||||||||
\(675\) | 3.29324 | 0.126757 | ||||||||
\(676\) | 52.7140 | 2.02746 | ||||||||
\(677\) | 14.2216 | 0.546582 | 0.273291 | − | 0.961931i | \(-0.411888\pi\) | ||||
0.273291 | + | 0.961931i | \(0.411888\pi\) | |||||||
\(678\) | 3.39687 | 0.130456 | ||||||||
\(679\) | 10.2881 | 0.394822 | ||||||||
\(680\) | 7.15201 | 0.274267 | ||||||||
\(681\) | 4.10011 | 0.157117 | ||||||||
\(682\) | −64.2538 | −2.46040 | ||||||||
\(683\) | 48.4610 | 1.85431 | 0.927153 | − | 0.374682i | \(-0.122248\pi\) | ||||
0.927153 | + | 0.374682i | \(0.122248\pi\) | |||||||
\(684\) | −43.5347 | −1.66459 | ||||||||
\(685\) | 21.5808 | 0.824561 | ||||||||
\(686\) | 16.8249 | 0.642379 | ||||||||
\(687\) | −4.24189 | −0.161838 | ||||||||
\(688\) | 22.7072 | 0.865702 | ||||||||
\(689\) | −63.8143 | −2.43113 | ||||||||
\(690\) | 5.61291 | 0.213680 | ||||||||
\(691\) | 7.95233 | 0.302521 | 0.151260 | − | 0.988494i | \(-0.451667\pi\) | ||||
0.151260 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(692\) | −1.16216 | −0.0441787 | ||||||||
\(693\) | 37.7115 | 1.43254 | ||||||||
\(694\) | −89.2129 | −3.38647 | ||||||||
\(695\) | 22.2494 | 0.843969 | ||||||||
\(696\) | −9.08183 | −0.344246 | ||||||||
\(697\) | −8.24516 | −0.312308 | ||||||||
\(698\) | −7.21481 | −0.273084 | ||||||||
\(699\) | 1.37955 | 0.0521793 | ||||||||
\(700\) | 45.4906 | 1.71938 | ||||||||
\(701\) | 21.3897 | 0.807879 | 0.403939 | − | 0.914786i | \(-0.367641\pi\) | ||||
0.403939 | + | 0.914786i | \(0.367641\pi\) | |||||||
\(702\) | 14.3929 | 0.543224 | ||||||||
\(703\) | −27.3958 | −1.03325 | ||||||||
\(704\) | −25.6887 | −0.968178 | ||||||||
\(705\) | 2.56467 | 0.0965912 | ||||||||
\(706\) | −2.44940 | −0.0921844 | ||||||||
\(707\) | −12.4820 | −0.469433 | ||||||||
\(708\) | −4.70855 | −0.176958 | ||||||||
\(709\) | 10.9413 | 0.410909 | 0.205454 | − | 0.978667i | \(-0.434133\pi\) | ||||
0.205454 | + | 0.978667i | \(0.434133\pi\) | |||||||
\(710\) | 34.6632 | 1.30089 | ||||||||
\(711\) | −1.53649 | −0.0576230 | ||||||||
\(712\) | −77.1192 | −2.89016 | ||||||||
\(713\) | −66.6074 | −2.49447 | ||||||||
\(714\) | −1.87109 | −0.0700237 | ||||||||
\(715\) | 23.9764 | 0.896667 | ||||||||
\(716\) | 57.7200 | 2.15710 | ||||||||
\(717\) | 1.58429 | 0.0591666 | ||||||||
\(718\) | −10.1743 | −0.379702 | ||||||||
\(719\) | 8.79119 | 0.327856 | 0.163928 | − | 0.986472i | \(-0.447584\pi\) | ||||
0.163928 | + | 0.986472i | \(0.447584\pi\) | |||||||
\(720\) | −17.2952 | −0.644555 | ||||||||
\(721\) | −76.9568 | −2.86602 | ||||||||
\(722\) | 13.4810 | 0.501712 | ||||||||
\(723\) | 0.573320 | 0.0213220 | ||||||||
\(724\) | 65.5049 | 2.43447 | ||||||||
\(725\) | −27.6092 | −1.02538 | ||||||||
\(726\) | 0.331388 | 0.0122990 | ||||||||
\(727\) | 30.0643 | 1.11502 | 0.557512 | − | 0.830169i | \(-0.311756\pi\) | ||||
0.557512 | + | 0.830169i | \(0.311756\pi\) | |||||||
\(728\) | 99.3959 | 3.68386 | ||||||||
\(729\) | −25.0176 | −0.926577 | ||||||||
\(730\) | 36.7500 | 1.36018 | ||||||||
\(731\) | −5.68052 | −0.210102 | ||||||||
\(732\) | 0.684617 | 0.0253042 | ||||||||
\(733\) | 12.2030 | 0.450728 | 0.225364 | − | 0.974275i | \(-0.427643\pi\) | ||||
0.225364 | + | 0.974275i | \(0.427643\pi\) | |||||||
\(734\) | −10.6194 | −0.391969 | ||||||||
\(735\) | 2.45575 | 0.0905815 | ||||||||
\(736\) | −0.0349625 | −0.00128873 | ||||||||
\(737\) | −11.7860 | −0.434142 | ||||||||
\(738\) | 59.8380 | 2.20267 | ||||||||
\(739\) | −21.7569 | −0.800342 | −0.400171 | − | 0.916441i | \(-0.631049\pi\) | ||||
−0.400171 | + | 0.916441i | \(0.631049\pi\) | |||||||
\(740\) | −43.5536 | −1.60106 | ||||||||
\(741\) | 3.62022 | 0.132992 | ||||||||
\(742\) | −121.167 | −4.44816 | ||||||||
\(743\) | −23.2599 | −0.853322 | −0.426661 | − | 0.904412i | \(-0.640310\pi\) | ||||
−0.426661 | + | 0.904412i | \(0.640310\pi\) | |||||||
\(744\) | −7.71103 | −0.282700 | ||||||||
\(745\) | 6.33571 | 0.232122 | ||||||||
\(746\) | 69.8684 | 2.55806 | ||||||||
\(747\) | 21.6503 | 0.792143 | ||||||||
\(748\) | −12.8345 | −0.469276 | ||||||||
\(749\) | −3.79758 | −0.138761 | ||||||||
\(750\) | 5.41977 | 0.197902 | ||||||||
\(751\) | −29.2394 | −1.06696 | −0.533481 | − | 0.845812i | \(-0.679116\pi\) | ||||
−0.533481 | + | 0.845812i | \(0.679116\pi\) | |||||||
\(752\) | 36.4526 | 1.32929 | ||||||||
\(753\) | −2.07903 | −0.0757641 | ||||||||
\(754\) | −120.664 | −4.39433 | ||||||||
\(755\) | −17.9709 | −0.654029 | ||||||||
\(756\) | 18.2182 | 0.662589 | ||||||||
\(757\) | −14.1482 | −0.514226 | −0.257113 | − | 0.966381i | \(-0.582771\pi\) | ||||
−0.257113 | + | 0.966381i | \(0.582771\pi\) | |||||||
\(758\) | 38.1820 | 1.38683 | ||||||||
\(759\) | −5.03572 | −0.182785 | ||||||||
\(760\) | −26.2744 | −0.953074 | ||||||||
\(761\) | −4.14378 | −0.150212 | −0.0751059 | − | 0.997176i | \(-0.523929\pi\) | ||||
−0.0751059 | + | 0.997176i | \(0.523929\pi\) | |||||||
\(762\) | −9.28881 | −0.336498 | ||||||||
\(763\) | 77.9721 | 2.82278 | ||||||||
\(764\) | −69.9026 | −2.52899 | ||||||||
\(765\) | 4.32665 | 0.156430 | ||||||||
\(766\) | −83.8710 | −3.03038 | ||||||||
\(767\) | −31.2762 | −1.12932 | ||||||||
\(768\) | −6.16236 | −0.222365 | ||||||||
\(769\) | 40.2774 | 1.45244 | 0.726220 | − | 0.687463i | \(-0.241275\pi\) | ||||
0.726220 | + | 0.687463i | \(0.241275\pi\) | |||||||
\(770\) | 45.5249 | 1.64060 | ||||||||
\(771\) | 1.84767 | 0.0665421 | ||||||||
\(772\) | 20.3786 | 0.733441 | ||||||||
\(773\) | −28.6055 | −1.02887 | −0.514433 | − | 0.857530i | \(-0.671998\pi\) | ||||
−0.514433 | + | 0.857530i | \(0.671998\pi\) | |||||||
\(774\) | 41.2255 | 1.48182 | ||||||||
\(775\) | −23.4419 | −0.842057 | ||||||||
\(776\) | 12.7040 | 0.456048 | ||||||||
\(777\) | 5.69656 | 0.204363 | ||||||||
\(778\) | −38.2193 | −1.37023 | ||||||||
\(779\) | 30.2904 | 1.08526 | ||||||||
\(780\) | 5.75540 | 0.206076 | ||||||||
\(781\) | −31.0987 | −1.11280 | ||||||||
\(782\) | −19.9577 | −0.713685 | ||||||||
\(783\) | −11.0570 | −0.395145 | ||||||||
\(784\) | 34.9044 | 1.24658 | ||||||||
\(785\) | 6.84318 | 0.244244 | ||||||||
\(786\) | 4.14627 | 0.147892 | ||||||||
\(787\) | 44.8561 | 1.59895 | 0.799473 | − | 0.600702i | \(-0.205112\pi\) | ||||
0.799473 | + | 0.600702i | \(0.205112\pi\) | |||||||
\(788\) | 58.4817 | 2.08332 | ||||||||
\(789\) | 3.40978 | 0.121391 | ||||||||
\(790\) | −1.85484 | −0.0659921 | ||||||||
\(791\) | 28.5604 | 1.01549 | ||||||||
\(792\) | 46.5671 | 1.65469 | ||||||||
\(793\) | 4.54752 | 0.161487 | ||||||||
\(794\) | −80.3871 | −2.85283 | ||||||||
\(795\) | −3.50761 | −0.124402 | ||||||||
\(796\) | 58.2373 | 2.06417 | ||||||||
\(797\) | 23.4702 | 0.831358 | 0.415679 | − | 0.909511i | \(-0.363544\pi\) | ||||
0.415679 | + | 0.909511i | \(0.363544\pi\) | |||||||
\(798\) | 6.87385 | 0.243332 | ||||||||
\(799\) | −9.11914 | −0.322612 | ||||||||
\(800\) | −0.0123047 | −0.000435038 0 | ||||||||
\(801\) | −46.6537 | −1.64843 | ||||||||
\(802\) | −91.2351 | −3.22162 | ||||||||
\(803\) | −32.9709 | −1.16352 | ||||||||
\(804\) | −2.82915 | −0.0997765 | ||||||||
\(805\) | 47.1925 | 1.66332 | ||||||||
\(806\) | −102.451 | −3.60869 | ||||||||
\(807\) | 0.0469000 | 0.00165096 | ||||||||
\(808\) | −15.4130 | −0.542229 | ||||||||
\(809\) | −19.3807 | −0.681387 | −0.340694 | − | 0.940174i | \(-0.610662\pi\) | ||||
−0.340694 | + | 0.940174i | \(0.610662\pi\) | |||||||
\(810\) | −31.0019 | −1.08930 | ||||||||
\(811\) | 5.17798 | 0.181823 | 0.0909117 | − | 0.995859i | \(-0.471022\pi\) | ||||
0.0909117 | + | 0.995859i | \(0.471022\pi\) | |||||||
\(812\) | −152.734 | −5.35991 | ||||||||
\(813\) | 2.10108 | 0.0736881 | ||||||||
\(814\) | 58.6144 | 2.05443 | ||||||||
\(815\) | −28.4120 | −0.995231 | ||||||||
\(816\) | −0.769874 | −0.0269510 | ||||||||
\(817\) | 20.8686 | 0.730101 | ||||||||
\(818\) | 22.7574 | 0.795693 | ||||||||
\(819\) | 60.1301 | 2.10112 | ||||||||
\(820\) | 48.1554 | 1.68166 | ||||||||
\(821\) | −23.4297 | −0.817701 | −0.408851 | − | 0.912601i | \(-0.634070\pi\) | ||||
−0.408851 | + | 0.912601i | \(0.634070\pi\) | |||||||
\(822\) | −6.97172 | −0.243167 | ||||||||
\(823\) | 34.4428 | 1.20060 | 0.600300 | − | 0.799775i | \(-0.295048\pi\) | ||||
0.600300 | + | 0.799775i | \(0.295048\pi\) | |||||||
\(824\) | −95.0281 | −3.31046 | ||||||||
\(825\) | −1.77228 | −0.0617028 | ||||||||
\(826\) | −59.3853 | −2.06628 | ||||||||
\(827\) | 27.0627 | 0.941063 | 0.470531 | − | 0.882383i | \(-0.344062\pi\) | ||||
0.470531 | + | 0.882383i | \(0.344062\pi\) | |||||||
\(828\) | 96.5563 | 3.35556 | ||||||||
\(829\) | −32.3660 | −1.12412 | −0.562060 | − | 0.827097i | \(-0.689991\pi\) | ||||
−0.562060 | + | 0.827097i | \(0.689991\pi\) | |||||||
\(830\) | 26.1360 | 0.907194 | ||||||||
\(831\) | −1.08814 | −0.0377471 | ||||||||
\(832\) | −40.9600 | −1.42003 | ||||||||
\(833\) | −8.73182 | −0.302540 | ||||||||
\(834\) | −7.18770 | −0.248890 | ||||||||
\(835\) | −16.9944 | −0.588114 | ||||||||
\(836\) | 47.1503 | 1.63073 | ||||||||
\(837\) | −9.38805 | −0.324499 | ||||||||
\(838\) | −15.2769 | −0.527731 | ||||||||
\(839\) | 38.2524 | 1.32062 | 0.660310 | − | 0.750993i | \(-0.270425\pi\) | ||||
0.660310 | + | 0.750993i | \(0.270425\pi\) | |||||||
\(840\) | 5.46339 | 0.188505 | ||||||||
\(841\) | 63.6974 | 2.19646 | ||||||||
\(842\) | 10.1320 | 0.349172 | ||||||||
\(843\) | −0.0413192 | −0.00142311 | ||||||||
\(844\) | 29.1244 | 1.00250 | ||||||||
\(845\) | 19.2463 | 0.662093 | ||||||||
\(846\) | 66.1807 | 2.27534 | ||||||||
\(847\) | 2.78626 | 0.0957371 | ||||||||
\(848\) | −49.8549 | −1.71202 | ||||||||
\(849\) | −4.05290 | −0.139095 | ||||||||
\(850\) | −7.02392 | −0.240919 | ||||||||
\(851\) | 60.7614 | 2.08287 | ||||||||
\(852\) | −7.46507 | −0.255749 | ||||||||
\(853\) | −15.2598 | −0.522486 | −0.261243 | − | 0.965273i | \(-0.584132\pi\) | ||||
−0.261243 | + | 0.965273i | \(0.584132\pi\) | |||||||
\(854\) | 8.63455 | 0.295468 | ||||||||
\(855\) | −15.8949 | −0.543593 | ||||||||
\(856\) | −4.68934 | −0.160278 | ||||||||
\(857\) | 54.0751 | 1.84717 | 0.923584 | − | 0.383395i | \(-0.125245\pi\) | ||||
0.923584 | + | 0.383395i | \(0.125245\pi\) | |||||||
\(858\) | −7.74561 | −0.264431 | ||||||||
\(859\) | 7.34739 | 0.250690 | 0.125345 | − | 0.992113i | \(-0.459996\pi\) | ||||
0.125345 | + | 0.992113i | \(0.459996\pi\) | |||||||
\(860\) | 33.1768 | 1.13132 | ||||||||
\(861\) | −6.29845 | −0.214651 | ||||||||
\(862\) | 9.47920 | 0.322863 | ||||||||
\(863\) | 9.13833 | 0.311073 | 0.155536 | − | 0.987830i | \(-0.450289\pi\) | ||||
0.155536 | + | 0.987830i | \(0.450289\pi\) | |||||||
\(864\) | −0.00492782 | −0.000167648 0 | ||||||||
\(865\) | −0.424313 | −0.0144271 | ||||||||
\(866\) | −1.76477 | −0.0599694 | ||||||||
\(867\) | 0.192595 | 0.00654087 | ||||||||
\(868\) | −129.680 | −4.40164 | ||||||||
\(869\) | 1.66410 | 0.0564507 | ||||||||
\(870\) | −6.63242 | −0.224860 | ||||||||
\(871\) | −18.7924 | −0.636758 | ||||||||
\(872\) | 96.2818 | 3.26051 | ||||||||
\(873\) | 7.68536 | 0.260110 | ||||||||
\(874\) | 73.3188 | 2.48005 | ||||||||
\(875\) | 45.5686 | 1.54050 | ||||||||
\(876\) | −7.91446 | −0.267405 | ||||||||
\(877\) | −22.2798 | −0.752335 | −0.376168 | − | 0.926552i | \(-0.622758\pi\) | ||||
−0.376168 | + | 0.926552i | \(0.622758\pi\) | |||||||
\(878\) | 85.1831 | 2.87479 | ||||||||
\(879\) | −1.72360 | −0.0581356 | ||||||||
\(880\) | 18.7316 | 0.631441 | ||||||||
\(881\) | −25.5340 | −0.860263 | −0.430131 | − | 0.902766i | \(-0.641533\pi\) | ||||
−0.430131 | + | 0.902766i | \(0.641533\pi\) | |||||||
\(882\) | 63.3699 | 2.13377 | ||||||||
\(883\) | −5.19272 | −0.174749 | −0.0873745 | − | 0.996176i | \(-0.527848\pi\) | ||||
−0.0873745 | + | 0.996176i | \(0.527848\pi\) | |||||||
\(884\) | −20.4643 | −0.688289 | ||||||||
\(885\) | −1.71913 | −0.0577878 | ||||||||
\(886\) | 38.8363 | 1.30473 | ||||||||
\(887\) | −34.6634 | −1.16388 | −0.581942 | − | 0.813231i | \(-0.697707\pi\) | ||||
−0.581942 | + | 0.813231i | \(0.697707\pi\) | |||||||
\(888\) | 7.03425 | 0.236054 | ||||||||
\(889\) | −78.0989 | −2.61935 | ||||||||
\(890\) | −56.3198 | −1.88784 | ||||||||
\(891\) | 27.8139 | 0.931801 | ||||||||
\(892\) | 53.7253 | 1.79886 | ||||||||
\(893\) | 33.5011 | 1.12107 | ||||||||
\(894\) | −2.04676 | −0.0684539 | ||||||||
\(895\) | 21.0740 | 0.704426 | ||||||||
\(896\) | −77.7382 | −2.59705 | ||||||||
\(897\) | −8.02933 | −0.268092 | ||||||||
\(898\) | 16.6385 | 0.555235 | ||||||||
\(899\) | 78.7057 | 2.62498 | ||||||||
\(900\) | 33.9821 | 1.13274 | ||||||||
\(901\) | 12.4719 | 0.415500 | ||||||||
\(902\) | −64.8075 | −2.15785 | ||||||||
\(903\) | −4.33933 | −0.144404 | ||||||||
\(904\) | 35.2670 | 1.17296 | ||||||||
\(905\) | 23.9163 | 0.795006 | ||||||||
\(906\) | 5.80553 | 0.192876 | ||||||||
\(907\) | −27.3658 | −0.908668 | −0.454334 | − | 0.890832i | \(-0.650123\pi\) | ||||
−0.454334 | + | 0.890832i | \(0.650123\pi\) | |||||||
\(908\) | 85.1458 | 2.82566 | ||||||||
\(909\) | −9.32421 | −0.309264 | ||||||||
\(910\) | 72.5884 | 2.40628 | ||||||||
\(911\) | −15.9220 | −0.527520 | −0.263760 | − | 0.964588i | \(-0.584963\pi\) | ||||
−0.263760 | + | 0.964588i | \(0.584963\pi\) | |||||||
\(912\) | 2.82830 | 0.0936543 | ||||||||
\(913\) | −23.4484 | −0.776027 | ||||||||
\(914\) | 11.4999 | 0.380382 | ||||||||
\(915\) | 0.249959 | 0.00826339 | ||||||||
\(916\) | −88.0901 | −2.91058 | ||||||||
\(917\) | 34.8612 | 1.15122 | ||||||||
\(918\) | −2.81296 | −0.0928414 | ||||||||
\(919\) | −15.6312 | −0.515627 | −0.257814 | − | 0.966195i | \(-0.583002\pi\) | ||||
−0.257814 | + | 0.966195i | \(0.583002\pi\) | |||||||
\(920\) | 58.2744 | 1.92125 | ||||||||
\(921\) | −2.48134 | −0.0817628 | ||||||||
\(922\) | 32.0503 | 1.05552 | ||||||||
\(923\) | −49.5862 | −1.63215 | ||||||||
\(924\) | −9.80423 | −0.322535 | ||||||||
\(925\) | 21.3844 | 0.703116 | ||||||||
\(926\) | −14.8854 | −0.489164 | ||||||||
\(927\) | −57.4878 | −1.88815 | ||||||||
\(928\) | 0.0413129 | 0.00135616 | ||||||||
\(929\) | −9.40043 | −0.308418 | −0.154209 | − | 0.988038i | \(-0.549283\pi\) | ||||
−0.154209 | + | 0.988038i | \(0.549283\pi\) | |||||||
\(930\) | −5.63133 | −0.184658 | ||||||||
\(931\) | 32.0782 | 1.05132 | ||||||||
\(932\) | 28.6487 | 0.938418 | ||||||||
\(933\) | 5.77715 | 0.189136 | ||||||||
\(934\) | −89.7464 | −2.93659 | ||||||||
\(935\) | −4.68597 | −0.153248 | ||||||||
\(936\) | 74.2501 | 2.42694 | ||||||||
\(937\) | 2.48267 | 0.0811054 | 0.0405527 | − | 0.999177i | \(-0.487088\pi\) | ||||
0.0405527 | + | 0.999177i | \(0.487088\pi\) | |||||||
\(938\) | −35.6819 | −1.16506 | ||||||||
\(939\) | −2.27986 | −0.0744005 | ||||||||
\(940\) | 53.2598 | 1.73714 | ||||||||
\(941\) | −16.9931 | −0.553960 | −0.276980 | − | 0.960876i | \(-0.589334\pi\) | ||||
−0.276980 | + | 0.960876i | \(0.589334\pi\) | |||||||
\(942\) | −2.21070 | −0.0720285 | ||||||||
\(943\) | −67.1814 | −2.18773 | ||||||||
\(944\) | −24.4345 | −0.795276 | ||||||||
\(945\) | 6.65160 | 0.216376 | ||||||||
\(946\) | −44.6493 | −1.45167 | ||||||||
\(947\) | −22.2843 | −0.724143 | −0.362072 | − | 0.932150i | \(-0.617930\pi\) | ||||
−0.362072 | + | 0.932150i | \(0.617930\pi\) | |||||||
\(948\) | 0.399457 | 0.0129738 | ||||||||
\(949\) | −52.5712 | −1.70653 | ||||||||
\(950\) | 25.8039 | 0.837189 | ||||||||
\(951\) | 0.626758 | 0.0203240 | ||||||||
\(952\) | −19.4260 | −0.629601 | ||||||||
\(953\) | 27.5107 | 0.891159 | 0.445579 | − | 0.895242i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895242i | \(0.352998\pi\) | |||||||
\(954\) | −90.5130 | −2.93047 | ||||||||
\(955\) | −25.5220 | −0.825871 | ||||||||
\(956\) | 32.9006 | 1.06408 | ||||||||
\(957\) | 5.95039 | 0.192349 | ||||||||
\(958\) | −96.4903 | −3.11746 | ||||||||
\(959\) | −58.6171 | −1.89285 | ||||||||
\(960\) | −2.25140 | −0.0726638 | ||||||||
\(961\) | 35.8259 | 1.15567 | ||||||||
\(962\) | 93.4592 | 3.01325 | ||||||||
\(963\) | −2.83684 | −0.0914160 | ||||||||
\(964\) | 11.9060 | 0.383465 | ||||||||
\(965\) | 7.44037 | 0.239514 | ||||||||
\(966\) | −15.2456 | −0.490519 | ||||||||
\(967\) | 60.6327 | 1.94982 | 0.974908 | − | 0.222608i | \(-0.0714569\pi\) | ||||
0.974908 | + | 0.222608i | \(0.0714569\pi\) | |||||||
\(968\) | 3.44054 | 0.110583 | ||||||||
\(969\) | −0.707539 | −0.0227294 | ||||||||
\(970\) | 9.27768 | 0.297888 | ||||||||
\(971\) | −22.4098 | −0.719164 | −0.359582 | − | 0.933113i | \(-0.617081\pi\) | ||||
−0.359582 | + | 0.933113i | \(0.617081\pi\) | |||||||
\(972\) | 20.4562 | 0.656132 | ||||||||
\(973\) | −60.4331 | −1.93740 | ||||||||
\(974\) | 53.6537 | 1.71918 | ||||||||
\(975\) | −2.82585 | −0.0904997 | ||||||||
\(976\) | 3.55275 | 0.113721 | ||||||||
\(977\) | 10.9135 | 0.349154 | 0.174577 | − | 0.984644i | \(-0.444144\pi\) | ||||
0.174577 | + | 0.984644i | \(0.444144\pi\) | |||||||
\(978\) | 9.17855 | 0.293498 | ||||||||
\(979\) | 50.5282 | 1.61489 | ||||||||
\(980\) | 50.9977 | 1.62906 | ||||||||
\(981\) | 58.2462 | 1.85966 | ||||||||
\(982\) | −36.2216 | −1.15588 | ||||||||
\(983\) | −23.2106 | −0.740304 | −0.370152 | − | 0.928971i | \(-0.620694\pi\) | ||||
−0.370152 | + | 0.928971i | \(0.620694\pi\) | |||||||
\(984\) | −7.77748 | −0.247937 | ||||||||
\(985\) | 21.3521 | 0.680335 | ||||||||
\(986\) | 23.5827 | 0.751026 | ||||||||
\(987\) | −6.96608 | −0.221733 | ||||||||
\(988\) | 75.1800 | 2.39180 | ||||||||
\(989\) | −46.2848 | −1.47177 | ||||||||
\(990\) | 34.0077 | 1.08084 | ||||||||
\(991\) | 32.5276 | 1.03327 | 0.516636 | − | 0.856205i | \(-0.327184\pi\) | ||||
0.516636 | + | 0.856205i | \(0.327184\pi\) | |||||||
\(992\) | 0.0350772 | 0.00111370 | ||||||||
\(993\) | 5.26412 | 0.167052 | ||||||||
\(994\) | −94.1511 | −2.98629 | ||||||||
\(995\) | 21.2629 | 0.674079 | ||||||||
\(996\) | −5.62864 | −0.178350 | ||||||||
\(997\) | 13.0285 | 0.412617 | 0.206308 | − | 0.978487i | \(-0.433855\pi\) | ||||
0.206308 | + | 0.978487i | \(0.433855\pi\) | |||||||
\(998\) | 33.2466 | 1.05240 | ||||||||
\(999\) | 8.56408 | 0.270956 |
(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 | 6001.2.a.c.1.11 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.c.1.11 | ✓ | 121 | 1.1 | even | 1 | trivial |