Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.35 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.431567 | 0.305164 | 0.152582 | − | 0.988291i | \(-0.451241\pi\) | ||||
0.152582 | + | 0.988291i | \(0.451241\pi\) | |||||||
\(3\) | 0.116041 | 0.0669964 | 0.0334982 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334982 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(4\) | −1.81375 | −0.906875 | ||||||||
\(5\) | −0.280770 | −0.125564 | −0.0627820 | − | 0.998027i | \(-0.519997\pi\) | ||||
−0.0627820 | + | 0.998027i | \(0.519997\pi\) | |||||||
\(6\) | 0.0500795 | 0.0204449 | ||||||||
\(7\) | 1.12936 | 0.426858 | 0.213429 | − | 0.976959i | \(-0.431537\pi\) | ||||
0.213429 | + | 0.976959i | \(0.431537\pi\) | |||||||
\(8\) | −1.64589 | −0.581909 | ||||||||
\(9\) | −2.98653 | −0.995511 | ||||||||
\(10\) | −0.121171 | −0.0383176 | ||||||||
\(11\) | 2.54903 | 0.768560 | 0.384280 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384280 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(12\) | −0.210470 | −0.0607574 | ||||||||
\(13\) | 0.311426 | 0.0863739 | 0.0431870 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431870 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(14\) | 0.487394 | 0.130262 | ||||||||
\(15\) | −0.0325809 | −0.00841234 | ||||||||
\(16\) | 2.91719 | 0.729298 | ||||||||
\(17\) | −3.83202 | −0.929401 | −0.464700 | − | 0.885468i | \(-0.653838\pi\) | ||||
−0.464700 | + | 0.885468i | \(0.653838\pi\) | |||||||
\(18\) | −1.28889 | −0.303794 | ||||||||
\(19\) | 1.16861 | 0.268097 | 0.134049 | − | 0.990975i | \(-0.457202\pi\) | ||||
0.134049 | + | 0.990975i | \(0.457202\pi\) | |||||||
\(20\) | 0.509246 | 0.113871 | ||||||||
\(21\) | 0.131052 | 0.0285980 | ||||||||
\(22\) | 1.10007 | 0.234537 | ||||||||
\(23\) | 2.97492 | 0.620313 | 0.310157 | − | 0.950685i | \(-0.399618\pi\) | ||||
0.310157 | + | 0.950685i | \(0.399618\pi\) | |||||||
\(24\) | −0.190991 | −0.0389858 | ||||||||
\(25\) | −4.92117 | −0.984234 | ||||||||
\(26\) | 0.134401 | 0.0263582 | ||||||||
\(27\) | −0.694684 | −0.133692 | ||||||||
\(28\) | −2.04838 | −0.387107 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.0140608 | −0.00256714 | ||||||||
\(31\) | 9.18623 | 1.64990 | 0.824948 | − | 0.565209i | \(-0.191204\pi\) | ||||
0.824948 | + | 0.565209i | \(0.191204\pi\) | |||||||
\(32\) | 4.55074 | 0.804464 | ||||||||
\(33\) | 0.295792 | 0.0514908 | ||||||||
\(34\) | −1.65377 | −0.283619 | ||||||||
\(35\) | −0.317091 | −0.0535981 | ||||||||
\(36\) | 5.41683 | 0.902805 | ||||||||
\(37\) | 9.69082 | 1.59316 | 0.796581 | − | 0.604532i | \(-0.206640\pi\) | ||||
0.796581 | + | 0.604532i | \(0.206640\pi\) | |||||||
\(38\) | 0.504332 | 0.0818135 | ||||||||
\(39\) | 0.0361382 | 0.00578674 | ||||||||
\(40\) | 0.462115 | 0.0730668 | ||||||||
\(41\) | 11.6305 | 1.81638 | 0.908191 | − | 0.418555i | \(-0.137463\pi\) | ||||
0.908191 | + | 0.418555i | \(0.137463\pi\) | |||||||
\(42\) | 0.0565578 | 0.00872706 | ||||||||
\(43\) | −8.94047 | −1.36341 | −0.681705 | − | 0.731628i | \(-0.738761\pi\) | ||||
−0.681705 | + | 0.731628i | \(0.738761\pi\) | |||||||
\(44\) | −4.62330 | −0.696988 | ||||||||
\(45\) | 0.838529 | 0.125000 | ||||||||
\(46\) | 1.28388 | 0.189297 | ||||||||
\(47\) | −12.7996 | −1.86702 | −0.933508 | − | 0.358557i | \(-0.883269\pi\) | ||||
−0.933508 | + | 0.358557i | \(0.883269\pi\) | |||||||
\(48\) | 0.338514 | 0.0488603 | ||||||||
\(49\) | −5.72454 | −0.817792 | ||||||||
\(50\) | −2.12381 | −0.300352 | ||||||||
\(51\) | −0.444672 | −0.0622665 | ||||||||
\(52\) | −0.564848 | −0.0783304 | ||||||||
\(53\) | −4.10544 | −0.563926 | −0.281963 | − | 0.959425i | \(-0.590986\pi\) | ||||
−0.281963 | + | 0.959425i | \(0.590986\pi\) | |||||||
\(54\) | −0.299803 | −0.0407980 | ||||||||
\(55\) | −0.715689 | −0.0965035 | ||||||||
\(56\) | −1.85880 | −0.248393 | ||||||||
\(57\) | 0.135607 | 0.0179615 | ||||||||
\(58\) | −0.431567 | −0.0566675 | ||||||||
\(59\) | 2.96172 | 0.385584 | 0.192792 | − | 0.981240i | \(-0.438246\pi\) | ||||
0.192792 | + | 0.981240i | \(0.438246\pi\) | |||||||
\(60\) | 0.0590935 | 0.00762894 | ||||||||
\(61\) | −14.6369 | −1.87406 | −0.937031 | − | 0.349246i | \(-0.886438\pi\) | ||||
−0.937031 | + | 0.349246i | \(0.886438\pi\) | |||||||
\(62\) | 3.96447 | 0.503488 | ||||||||
\(63\) | −3.37288 | −0.424942 | ||||||||
\(64\) | −3.87044 | −0.483805 | ||||||||
\(65\) | −0.0874389 | −0.0108455 | ||||||||
\(66\) | 0.127654 | 0.0157131 | ||||||||
\(67\) | −7.57315 | −0.925207 | −0.462603 | − | 0.886565i | \(-0.653085\pi\) | ||||
−0.462603 | + | 0.886565i | \(0.653085\pi\) | |||||||
\(68\) | 6.95032 | 0.842850 | ||||||||
\(69\) | 0.345213 | 0.0415588 | ||||||||
\(70\) | −0.136846 | −0.0163562 | ||||||||
\(71\) | −13.0047 | −1.54338 | −0.771690 | − | 0.635999i | \(-0.780588\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(72\) | 4.91550 | 0.579297 | ||||||||
\(73\) | −1.93842 | −0.226875 | −0.113437 | − | 0.993545i | \(-0.536186\pi\) | ||||
−0.113437 | + | 0.993545i | \(0.536186\pi\) | |||||||
\(74\) | 4.18223 | 0.486175 | ||||||||
\(75\) | −0.571058 | −0.0659401 | ||||||||
\(76\) | −2.11956 | −0.243131 | ||||||||
\(77\) | 2.87877 | 0.328066 | ||||||||
\(78\) | 0.0155960 | 0.00176590 | ||||||||
\(79\) | −3.60852 | −0.405990 | −0.202995 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202995 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(80\) | −0.819059 | −0.0915736 | ||||||||
\(81\) | 8.87899 | 0.986555 | ||||||||
\(82\) | 5.01934 | 0.554294 | ||||||||
\(83\) | −5.22878 | −0.573933 | −0.286966 | − | 0.957941i | \(-0.592647\pi\) | ||||
−0.286966 | + | 0.957941i | \(0.592647\pi\) | |||||||
\(84\) | −0.237696 | −0.0259348 | ||||||||
\(85\) | 1.07591 | 0.116699 | ||||||||
\(86\) | −3.85841 | −0.416063 | ||||||||
\(87\) | −0.116041 | −0.0124409 | ||||||||
\(88\) | −4.19541 | −0.447232 | ||||||||
\(89\) | −8.11999 | −0.860718 | −0.430359 | − | 0.902658i | \(-0.641613\pi\) | ||||
−0.430359 | + | 0.902658i | \(0.641613\pi\) | |||||||
\(90\) | 0.361881 | 0.0381456 | ||||||||
\(91\) | 0.351712 | 0.0368694 | ||||||||
\(92\) | −5.39576 | −0.562547 | ||||||||
\(93\) | 1.06598 | 0.110537 | ||||||||
\(94\) | −5.52389 | −0.569745 | ||||||||
\(95\) | −0.328110 | −0.0336634 | ||||||||
\(96\) | 0.528073 | 0.0538962 | ||||||||
\(97\) | 6.72429 | 0.682749 | 0.341374 | − | 0.939927i | \(-0.389108\pi\) | ||||
0.341374 | + | 0.939927i | \(0.389108\pi\) | |||||||
\(98\) | −2.47052 | −0.249560 | ||||||||
\(99\) | −7.61275 | −0.765111 | ||||||||
\(100\) | 8.92577 | 0.892577 | ||||||||
\(101\) | 1.97020 | 0.196042 | 0.0980211 | − | 0.995184i | \(-0.468749\pi\) | ||||
0.0980211 | + | 0.995184i | \(0.468749\pi\) | |||||||
\(102\) | −0.191905 | −0.0190015 | ||||||||
\(103\) | 2.22516 | 0.219252 | 0.109626 | − | 0.993973i | \(-0.465035\pi\) | ||||
0.109626 | + | 0.993973i | \(0.465035\pi\) | |||||||
\(104\) | −0.512571 | −0.0502617 | ||||||||
\(105\) | −0.0367956 | −0.00359088 | ||||||||
\(106\) | −1.77177 | −0.172090 | ||||||||
\(107\) | 18.0345 | 1.74346 | 0.871728 | − | 0.489989i | \(-0.162999\pi\) | ||||
0.871728 | + | 0.489989i | \(0.162999\pi\) | |||||||
\(108\) | 1.25998 | 0.121242 | ||||||||
\(109\) | 9.79190 | 0.937894 | 0.468947 | − | 0.883226i | \(-0.344634\pi\) | ||||
0.468947 | + | 0.883226i | \(0.344634\pi\) | |||||||
\(110\) | −0.308868 | −0.0294494 | ||||||||
\(111\) | 1.12453 | 0.106736 | ||||||||
\(112\) | 3.29456 | 0.311307 | ||||||||
\(113\) | −11.9240 | −1.12171 | −0.560857 | − | 0.827913i | \(-0.689528\pi\) | ||||
−0.560857 | + | 0.827913i | \(0.689528\pi\) | |||||||
\(114\) | 0.0585233 | 0.00548121 | ||||||||
\(115\) | −0.835267 | −0.0778891 | ||||||||
\(116\) | 1.81375 | 0.168402 | ||||||||
\(117\) | −0.930083 | −0.0859862 | ||||||||
\(118\) | 1.27818 | 0.117666 | ||||||||
\(119\) | −4.32773 | −0.396723 | ||||||||
\(120\) | 0.0536244 | 0.00489522 | ||||||||
\(121\) | −4.50247 | −0.409315 | ||||||||
\(122\) | −6.31679 | −0.571896 | ||||||||
\(123\) | 1.34962 | 0.121691 | ||||||||
\(124\) | −16.6615 | −1.49625 | ||||||||
\(125\) | 2.78556 | 0.249148 | ||||||||
\(126\) | −1.45562 | −0.129677 | ||||||||
\(127\) | 8.25496 | 0.732510 | 0.366255 | − | 0.930515i | \(-0.380640\pi\) | ||||
0.366255 | + | 0.930515i | \(0.380640\pi\) | |||||||
\(128\) | −10.7718 | −0.952104 | ||||||||
\(129\) | −1.03746 | −0.0913435 | ||||||||
\(130\) | −0.0377357 | −0.00330964 | ||||||||
\(131\) | 1.09618 | 0.0957737 | 0.0478869 | − | 0.998853i | \(-0.484751\pi\) | ||||
0.0478869 | + | 0.998853i | \(0.484751\pi\) | |||||||
\(132\) | −0.536493 | −0.0466957 | ||||||||
\(133\) | 1.31978 | 0.114440 | ||||||||
\(134\) | −3.26832 | −0.282339 | ||||||||
\(135\) | 0.195046 | 0.0167869 | ||||||||
\(136\) | 6.30707 | 0.540827 | ||||||||
\(137\) | 2.81083 | 0.240146 | 0.120073 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120073 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(138\) | 0.148982 | 0.0126822 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 0.575123 | 0.0486068 | ||||||||
\(141\) | −1.48528 | −0.125083 | ||||||||
\(142\) | −5.61241 | −0.470983 | ||||||||
\(143\) | 0.793832 | 0.0663835 | ||||||||
\(144\) | −8.71229 | −0.726024 | ||||||||
\(145\) | 0.280770 | 0.0233167 | ||||||||
\(146\) | −0.836556 | −0.0692339 | ||||||||
\(147\) | −0.664283 | −0.0547891 | ||||||||
\(148\) | −17.5767 | −1.44480 | ||||||||
\(149\) | 4.46322 | 0.365641 | 0.182821 | − | 0.983146i | \(-0.441477\pi\) | ||||
0.182821 | + | 0.983146i | \(0.441477\pi\) | |||||||
\(150\) | −0.246450 | −0.0201225 | ||||||||
\(151\) | −11.0675 | −0.900660 | −0.450330 | − | 0.892862i | \(-0.648694\pi\) | ||||
−0.450330 | + | 0.892862i | \(0.648694\pi\) | |||||||
\(152\) | −1.92340 | −0.156008 | ||||||||
\(153\) | 11.4445 | 0.925229 | ||||||||
\(154\) | 1.24238 | 0.100114 | ||||||||
\(155\) | −2.57922 | −0.207168 | ||||||||
\(156\) | −0.0655456 | −0.00524785 | ||||||||
\(157\) | −21.1341 | −1.68668 | −0.843342 | − | 0.537377i | \(-0.819415\pi\) | ||||
−0.843342 | + | 0.537377i | \(0.819415\pi\) | |||||||
\(158\) | −1.55731 | −0.123893 | ||||||||
\(159\) | −0.476400 | −0.0377810 | ||||||||
\(160\) | −1.27771 | −0.101012 | ||||||||
\(161\) | 3.35976 | 0.264786 | ||||||||
\(162\) | 3.83188 | 0.301061 | ||||||||
\(163\) | −9.12904 | −0.715042 | −0.357521 | − | 0.933905i | \(-0.616378\pi\) | ||||
−0.357521 | + | 0.933905i | \(0.616378\pi\) | |||||||
\(164\) | −21.0949 | −1.64723 | ||||||||
\(165\) | −0.0830494 | −0.00646539 | ||||||||
\(166\) | −2.25657 | −0.175143 | ||||||||
\(167\) | 9.27906 | 0.718036 | 0.359018 | − | 0.933331i | \(-0.383112\pi\) | ||||
0.359018 | + | 0.933331i | \(0.383112\pi\) | |||||||
\(168\) | −0.215697 | −0.0166414 | ||||||||
\(169\) | −12.9030 | −0.992540 | ||||||||
\(170\) | 0.464329 | 0.0356124 | ||||||||
\(171\) | −3.49009 | −0.266894 | ||||||||
\(172\) | 16.2158 | 1.23644 | ||||||||
\(173\) | −22.4225 | −1.70475 | −0.852374 | − | 0.522932i | \(-0.824838\pi\) | ||||
−0.852374 | + | 0.522932i | \(0.824838\pi\) | |||||||
\(174\) | −0.0500795 | −0.00379652 | ||||||||
\(175\) | −5.55778 | −0.420128 | ||||||||
\(176\) | 7.43600 | 0.560509 | ||||||||
\(177\) | 0.343682 | 0.0258327 | ||||||||
\(178\) | −3.50432 | −0.262660 | ||||||||
\(179\) | −17.7203 | −1.32447 | −0.662237 | − | 0.749294i | \(-0.730393\pi\) | ||||
−0.662237 | + | 0.749294i | \(0.730393\pi\) | |||||||
\(180\) | −1.52088 | −0.113360 | ||||||||
\(181\) | −15.8944 | −1.18142 | −0.590712 | − | 0.806882i | \(-0.701153\pi\) | ||||
−0.590712 | + | 0.806882i | \(0.701153\pi\) | |||||||
\(182\) | 0.151787 | 0.0112512 | ||||||||
\(183\) | −1.69848 | −0.125555 | ||||||||
\(184\) | −4.89638 | −0.360966 | ||||||||
\(185\) | −2.72089 | −0.200044 | ||||||||
\(186\) | 0.460042 | 0.0337319 | ||||||||
\(187\) | −9.76791 | −0.714300 | ||||||||
\(188\) | 23.2153 | 1.69315 | ||||||||
\(189\) | −0.784550 | −0.0570676 | ||||||||
\(190\) | −0.141601 | −0.0102728 | ||||||||
\(191\) | −11.4817 | −0.830783 | −0.415392 | − | 0.909643i | \(-0.636355\pi\) | ||||
−0.415392 | + | 0.909643i | \(0.636355\pi\) | |||||||
\(192\) | −0.449130 | −0.0324132 | ||||||||
\(193\) | −4.94728 | −0.356113 | −0.178056 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178056 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(194\) | 2.90198 | 0.208350 | ||||||||
\(195\) | −0.0101465 | −0.000726607 0 | ||||||||
\(196\) | 10.3829 | 0.741635 | ||||||||
\(197\) | 25.4620 | 1.81409 | 0.907045 | − | 0.421033i | \(-0.138332\pi\) | ||||
0.907045 | + | 0.421033i | \(0.138332\pi\) | |||||||
\(198\) | −3.28541 | −0.233484 | ||||||||
\(199\) | −26.3113 | −1.86516 | −0.932579 | − | 0.360967i | \(-0.882447\pi\) | ||||
−0.932579 | + | 0.360967i | \(0.882447\pi\) | |||||||
\(200\) | 8.09969 | 0.572734 | ||||||||
\(201\) | −0.878797 | −0.0619855 | ||||||||
\(202\) | 0.850272 | 0.0598249 | ||||||||
\(203\) | −1.12936 | −0.0792656 | ||||||||
\(204\) | 0.806524 | 0.0564679 | ||||||||
\(205\) | −3.26550 | −0.228072 | ||||||||
\(206\) | 0.960304 | 0.0669076 | ||||||||
\(207\) | −8.88470 | −0.617529 | ||||||||
\(208\) | 0.908488 | 0.0629923 | ||||||||
\(209\) | 2.97881 | 0.206049 | ||||||||
\(210\) | −0.0158797 | −0.00109581 | ||||||||
\(211\) | −16.9608 | −1.16763 | −0.583815 | − | 0.811887i | \(-0.698441\pi\) | ||||
−0.583815 | + | 0.811887i | \(0.698441\pi\) | |||||||
\(212\) | 7.44625 | 0.511410 | ||||||||
\(213\) | −1.50909 | −0.103401 | ||||||||
\(214\) | 7.78307 | 0.532040 | ||||||||
\(215\) | 2.51021 | 0.171195 | ||||||||
\(216\) | 1.14337 | 0.0777966 | ||||||||
\(217\) | 10.3746 | 0.704272 | ||||||||
\(218\) | 4.22585 | 0.286211 | ||||||||
\(219\) | −0.224936 | −0.0151998 | ||||||||
\(220\) | 1.29808 | 0.0875167 | ||||||||
\(221\) | −1.19339 | −0.0802760 | ||||||||
\(222\) | 0.485311 | 0.0325720 | ||||||||
\(223\) | −7.78604 | −0.521392 | −0.260696 | − | 0.965421i | \(-0.583952\pi\) | ||||
−0.260696 | + | 0.965421i | \(0.583952\pi\) | |||||||
\(224\) | 5.13942 | 0.343392 | ||||||||
\(225\) | 14.6972 | 0.979816 | ||||||||
\(226\) | −5.14599 | −0.342306 | ||||||||
\(227\) | −19.5733 | −1.29913 | −0.649564 | − | 0.760307i | \(-0.725048\pi\) | ||||
−0.649564 | + | 0.760307i | \(0.725048\pi\) | |||||||
\(228\) | −0.245957 | −0.0162889 | ||||||||
\(229\) | −1.30739 | −0.0863951 | −0.0431975 | − | 0.999067i | \(-0.513754\pi\) | ||||
−0.0431975 | + | 0.999067i | \(0.513754\pi\) | |||||||
\(230\) | −0.360473 | −0.0237689 | ||||||||
\(231\) | 0.334056 | 0.0219793 | ||||||||
\(232\) | 1.64589 | 0.108058 | ||||||||
\(233\) | 24.0625 | 1.57639 | 0.788193 | − | 0.615428i | \(-0.211017\pi\) | ||||
0.788193 | + | 0.615428i | \(0.211017\pi\) | |||||||
\(234\) | −0.401393 | −0.0262399 | ||||||||
\(235\) | 3.59375 | 0.234430 | ||||||||
\(236\) | −5.37183 | −0.349676 | ||||||||
\(237\) | −0.418736 | −0.0271999 | ||||||||
\(238\) | −1.86770 | −0.121065 | ||||||||
\(239\) | 6.86902 | 0.444320 | 0.222160 | − | 0.975010i | \(-0.428689\pi\) | ||||
0.222160 | + | 0.975010i | \(0.428689\pi\) | |||||||
\(240\) | −0.0950446 | −0.00613510 | ||||||||
\(241\) | 23.8266 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(242\) | −1.94311 | −0.124908 | ||||||||
\(243\) | 3.11438 | 0.199788 | ||||||||
\(244\) | 26.5477 | 1.69954 | ||||||||
\(245\) | 1.60728 | 0.102685 | ||||||||
\(246\) | 0.582451 | 0.0371357 | ||||||||
\(247\) | 0.363935 | 0.0231566 | ||||||||
\(248\) | −15.1195 | −0.960089 | ||||||||
\(249\) | −0.606754 | −0.0384514 | ||||||||
\(250\) | 1.20216 | 0.0760310 | ||||||||
\(251\) | −7.50291 | −0.473580 | −0.236790 | − | 0.971561i | \(-0.576095\pi\) | ||||
−0.236790 | + | 0.971561i | \(0.576095\pi\) | |||||||
\(252\) | 6.11756 | 0.385370 | ||||||||
\(253\) | 7.58314 | 0.476748 | ||||||||
\(254\) | 3.56257 | 0.223535 | ||||||||
\(255\) | 0.124850 | 0.00781844 | ||||||||
\(256\) | 3.09212 | 0.193257 | ||||||||
\(257\) | 0.825996 | 0.0515242 | 0.0257621 | − | 0.999668i | \(-0.491799\pi\) | ||||
0.0257621 | + | 0.999668i | \(0.491799\pi\) | |||||||
\(258\) | −0.447734 | −0.0278747 | ||||||||
\(259\) | 10.9444 | 0.680054 | ||||||||
\(260\) | 0.158592 | 0.00983548 | ||||||||
\(261\) | 2.98653 | 0.184862 | ||||||||
\(262\) | 0.473075 | 0.0292267 | ||||||||
\(263\) | −28.1850 | −1.73796 | −0.868979 | − | 0.494848i | \(-0.835224\pi\) | ||||
−0.868979 | + | 0.494848i | \(0.835224\pi\) | |||||||
\(264\) | −0.486840 | −0.0299629 | ||||||||
\(265\) | 1.15268 | 0.0708088 | ||||||||
\(266\) | 0.569573 | 0.0349228 | ||||||||
\(267\) | −0.942253 | −0.0576650 | ||||||||
\(268\) | 13.7358 | 0.839047 | ||||||||
\(269\) | −2.59357 | −0.158133 | −0.0790664 | − | 0.996869i | \(-0.525194\pi\) | ||||
−0.0790664 | + | 0.996869i | \(0.525194\pi\) | |||||||
\(270\) | 0.0841755 | 0.00512276 | ||||||||
\(271\) | −5.62276 | −0.341558 | −0.170779 | − | 0.985309i | \(-0.554628\pi\) | ||||
−0.170779 | + | 0.985309i | \(0.554628\pi\) | |||||||
\(272\) | −11.1787 | −0.677810 | ||||||||
\(273\) | 0.0408131 | 0.00247012 | ||||||||
\(274\) | 1.21306 | 0.0732838 | ||||||||
\(275\) | −12.5442 | −0.756443 | ||||||||
\(276\) | −0.626130 | −0.0376886 | ||||||||
\(277\) | 27.4068 | 1.64672 | 0.823358 | − | 0.567522i | \(-0.192098\pi\) | ||||
0.823358 | + | 0.567522i | \(0.192098\pi\) | |||||||
\(278\) | −0.431567 | −0.0258836 | ||||||||
\(279\) | −27.4350 | −1.64249 | ||||||||
\(280\) | 0.521895 | 0.0311892 | ||||||||
\(281\) | −18.6189 | −1.11071 | −0.555355 | − | 0.831614i | \(-0.687418\pi\) | ||||
−0.555355 | + | 0.831614i | \(0.687418\pi\) | |||||||
\(282\) | −0.640998 | −0.0381709 | ||||||||
\(283\) | −15.7528 | −0.936405 | −0.468202 | − | 0.883621i | \(-0.655098\pi\) | ||||
−0.468202 | + | 0.883621i | \(0.655098\pi\) | |||||||
\(284\) | 23.5874 | 1.39965 | ||||||||
\(285\) | −0.0380743 | −0.00225532 | ||||||||
\(286\) | 0.342591 | 0.0202578 | ||||||||
\(287\) | 13.1351 | 0.775338 | ||||||||
\(288\) | −13.5909 | −0.800853 | ||||||||
\(289\) | −2.31564 | −0.136214 | ||||||||
\(290\) | 0.121171 | 0.00711540 | ||||||||
\(291\) | 0.780295 | 0.0457417 | ||||||||
\(292\) | 3.51581 | 0.205747 | ||||||||
\(293\) | 3.48485 | 0.203587 | 0.101794 | − | 0.994806i | \(-0.467542\pi\) | ||||
0.101794 | + | 0.994806i | \(0.467542\pi\) | |||||||
\(294\) | −0.286682 | −0.0167196 | ||||||||
\(295\) | −0.831563 | −0.0484154 | ||||||||
\(296\) | −15.9500 | −0.927075 | ||||||||
\(297\) | −1.77077 | −0.102750 | ||||||||
\(298\) | 1.92618 | 0.111580 | ||||||||
\(299\) | 0.926466 | 0.0535789 | ||||||||
\(300\) | 1.03576 | 0.0597995 | ||||||||
\(301\) | −10.0970 | −0.581983 | ||||||||
\(302\) | −4.77636 | −0.274849 | ||||||||
\(303\) | 0.228624 | 0.0131341 | ||||||||
\(304\) | 3.40905 | 0.195523 | ||||||||
\(305\) | 4.10960 | 0.235315 | ||||||||
\(306\) | 4.93904 | 0.282346 | ||||||||
\(307\) | −19.0494 | −1.08721 | −0.543603 | − | 0.839342i | \(-0.682940\pi\) | ||||
−0.543603 | + | 0.839342i | \(0.682940\pi\) | |||||||
\(308\) | −5.22137 | −0.297515 | ||||||||
\(309\) | 0.258210 | 0.0146891 | ||||||||
\(310\) | −1.11310 | −0.0632200 | ||||||||
\(311\) | 10.4189 | 0.590801 | 0.295400 | − | 0.955374i | \(-0.404547\pi\) | ||||
0.295400 | + | 0.955374i | \(0.404547\pi\) | |||||||
\(312\) | −0.0594794 | −0.00336736 | ||||||||
\(313\) | 24.4100 | 1.37974 | 0.689868 | − | 0.723935i | \(-0.257669\pi\) | ||||
0.689868 | + | 0.723935i | \(0.257669\pi\) | |||||||
\(314\) | −9.12077 | −0.514715 | ||||||||
\(315\) | 0.947002 | 0.0533575 | ||||||||
\(316\) | 6.54495 | 0.368182 | ||||||||
\(317\) | −20.8736 | −1.17238 | −0.586190 | − | 0.810173i | \(-0.699373\pi\) | ||||
−0.586190 | + | 0.810173i | \(0.699373\pi\) | |||||||
\(318\) | −0.205598 | −0.0115294 | ||||||||
\(319\) | −2.54903 | −0.142718 | ||||||||
\(320\) | 1.08670 | 0.0607485 | ||||||||
\(321\) | 2.09274 | 0.116805 | ||||||||
\(322\) | 1.44996 | 0.0808030 | ||||||||
\(323\) | −4.47813 | −0.249170 | ||||||||
\(324\) | −16.1043 | −0.894682 | ||||||||
\(325\) | −1.53258 | −0.0850121 | ||||||||
\(326\) | −3.93979 | −0.218205 | ||||||||
\(327\) | 1.13626 | 0.0628355 | ||||||||
\(328\) | −19.1425 | −1.05697 | ||||||||
\(329\) | −14.4554 | −0.796951 | ||||||||
\(330\) | −0.0358414 | −0.00197300 | ||||||||
\(331\) | 30.3297 | 1.66707 | 0.833535 | − | 0.552466i | \(-0.186313\pi\) | ||||
0.833535 | + | 0.552466i | \(0.186313\pi\) | |||||||
\(332\) | 9.48370 | 0.520486 | ||||||||
\(333\) | −28.9420 | −1.58601 | ||||||||
\(334\) | 4.00453 | 0.219118 | ||||||||
\(335\) | 2.12631 | 0.116173 | ||||||||
\(336\) | 0.382305 | 0.0208564 | ||||||||
\(337\) | 25.8839 | 1.40999 | 0.704994 | − | 0.709214i | \(-0.250950\pi\) | ||||
0.704994 | + | 0.709214i | \(0.250950\pi\) | |||||||
\(338\) | −5.56851 | −0.302887 | ||||||||
\(339\) | −1.38367 | −0.0751508 | ||||||||
\(340\) | −1.95144 | −0.105832 | ||||||||
\(341\) | 23.4159 | 1.26804 | ||||||||
\(342\) | −1.50621 | −0.0814463 | ||||||||
\(343\) | −14.3706 | −0.775940 | ||||||||
\(344\) | 14.7150 | 0.793380 | ||||||||
\(345\) | −0.0969254 | −0.00521829 | ||||||||
\(346\) | −9.67678 | −0.520227 | ||||||||
\(347\) | 24.2007 | 1.29916 | 0.649580 | − | 0.760293i | \(-0.274945\pi\) | ||||
0.649580 | + | 0.760293i | \(0.274945\pi\) | |||||||
\(348\) | 0.210470 | 0.0112824 | ||||||||
\(349\) | 18.3078 | 0.979992 | 0.489996 | − | 0.871725i | \(-0.336998\pi\) | ||||
0.489996 | + | 0.871725i | \(0.336998\pi\) | |||||||
\(350\) | −2.39855 | −0.128208 | ||||||||
\(351\) | −0.216342 | −0.0115475 | ||||||||
\(352\) | 11.5999 | 0.618279 | ||||||||
\(353\) | −9.11915 | −0.485364 | −0.242682 | − | 0.970106i | \(-0.578027\pi\) | ||||
−0.242682 | + | 0.970106i | \(0.578027\pi\) | |||||||
\(354\) | 0.148322 | 0.00788320 | ||||||||
\(355\) | 3.65134 | 0.193793 | ||||||||
\(356\) | 14.7276 | 0.780563 | ||||||||
\(357\) | −0.502195 | −0.0265790 | ||||||||
\(358\) | −7.64747 | −0.404182 | ||||||||
\(359\) | −35.3388 | −1.86511 | −0.932555 | − | 0.361028i | \(-0.882426\pi\) | ||||
−0.932555 | + | 0.361028i | \(0.882426\pi\) | |||||||
\(360\) | −1.38012 | −0.0727389 | ||||||||
\(361\) | −17.6344 | −0.928124 | ||||||||
\(362\) | −6.85951 | −0.360528 | ||||||||
\(363\) | −0.522472 | −0.0274226 | ||||||||
\(364\) | −0.637918 | −0.0334360 | ||||||||
\(365\) | 0.544249 | 0.0284873 | ||||||||
\(366\) | −0.733008 | −0.0383149 | ||||||||
\(367\) | 1.25934 | 0.0657369 | 0.0328684 | − | 0.999460i | \(-0.489536\pi\) | ||||
0.0328684 | + | 0.999460i | \(0.489536\pi\) | |||||||
\(368\) | 8.67840 | 0.452393 | ||||||||
\(369\) | −34.7350 | −1.80823 | ||||||||
\(370\) | −1.17425 | −0.0610461 | ||||||||
\(371\) | −4.63653 | −0.240717 | ||||||||
\(372\) | −1.93342 | −0.100243 | ||||||||
\(373\) | −17.7386 | −0.918469 | −0.459234 | − | 0.888315i | \(-0.651876\pi\) | ||||
−0.459234 | + | 0.888315i | \(0.651876\pi\) | |||||||
\(374\) | −4.21550 | −0.217978 | ||||||||
\(375\) | 0.323240 | 0.0166920 | ||||||||
\(376\) | 21.0667 | 1.08643 | ||||||||
\(377\) | −0.311426 | −0.0160392 | ||||||||
\(378\) | −0.338585 | −0.0174150 | ||||||||
\(379\) | −12.9268 | −0.664004 | −0.332002 | − | 0.943279i | \(-0.607724\pi\) | ||||
−0.332002 | + | 0.943279i | \(0.607724\pi\) | |||||||
\(380\) | 0.595110 | 0.0305285 | ||||||||
\(381\) | 0.957916 | 0.0490755 | ||||||||
\(382\) | −4.95510 | −0.253525 | ||||||||
\(383\) | 18.9617 | 0.968899 | 0.484449 | − | 0.874819i | \(-0.339020\pi\) | ||||
0.484449 | + | 0.874819i | \(0.339020\pi\) | |||||||
\(384\) | −1.24997 | −0.0637875 | ||||||||
\(385\) | −0.808272 | −0.0411934 | ||||||||
\(386\) | −2.13508 | −0.108673 | ||||||||
\(387\) | 26.7010 | 1.35729 | ||||||||
\(388\) | −12.1962 | −0.619168 | ||||||||
\(389\) | −30.4863 | −1.54572 | −0.772858 | − | 0.634580i | \(-0.781173\pi\) | ||||
−0.772858 | + | 0.634580i | \(0.781173\pi\) | |||||||
\(390\) | −0.00437889 | −0.000221734 0 | ||||||||
\(391\) | −11.3999 | −0.576520 | ||||||||
\(392\) | 9.42195 | 0.475880 | ||||||||
\(393\) | 0.127202 | 0.00641650 | ||||||||
\(394\) | 10.9885 | 0.553594 | ||||||||
\(395\) | 1.01316 | 0.0509777 | ||||||||
\(396\) | 13.8076 | 0.693860 | ||||||||
\(397\) | 12.9002 | 0.647443 | 0.323722 | − | 0.946152i | \(-0.395066\pi\) | ||||
0.323722 | + | 0.946152i | \(0.395066\pi\) | |||||||
\(398\) | −11.3551 | −0.569178 | ||||||||
\(399\) | 0.153149 | 0.00766704 | ||||||||
\(400\) | −14.3560 | −0.717799 | ||||||||
\(401\) | 11.0575 | 0.552185 | 0.276093 | − | 0.961131i | \(-0.410960\pi\) | ||||
0.276093 | + | 0.961131i | \(0.410960\pi\) | |||||||
\(402\) | −0.379259 | −0.0189157 | ||||||||
\(403\) | 2.86083 | 0.142508 | ||||||||
\(404\) | −3.57345 | −0.177786 | ||||||||
\(405\) | −2.49295 | −0.123876 | ||||||||
\(406\) | −0.487394 | −0.0241890 | ||||||||
\(407\) | 24.7022 | 1.22444 | ||||||||
\(408\) | 0.731879 | 0.0362334 | ||||||||
\(409\) | 31.1882 | 1.54216 | 0.771079 | − | 0.636740i | \(-0.219717\pi\) | ||||
0.771079 | + | 0.636740i | \(0.219717\pi\) | |||||||
\(410\) | −1.40928 | −0.0695994 | ||||||||
\(411\) | 0.326173 | 0.0160889 | ||||||||
\(412\) | −4.03588 | −0.198834 | ||||||||
\(413\) | 3.34486 | 0.164590 | ||||||||
\(414\) | −3.83434 | −0.188447 | ||||||||
\(415\) | 1.46808 | 0.0720654 | ||||||||
\(416\) | 1.41722 | 0.0694847 | ||||||||
\(417\) | −0.116041 | −0.00568256 | ||||||||
\(418\) | 1.28556 | 0.0628786 | ||||||||
\(419\) | −19.4368 | −0.949549 | −0.474774 | − | 0.880108i | \(-0.657470\pi\) | ||||
−0.474774 | + | 0.880108i | \(0.657470\pi\) | |||||||
\(420\) | 0.0667379 | 0.00325648 | ||||||||
\(421\) | −7.74411 | −0.377425 | −0.188712 | − | 0.982032i | \(-0.560431\pi\) | ||||
−0.188712 | + | 0.982032i | \(0.560431\pi\) | |||||||
\(422\) | −7.31971 | −0.356318 | ||||||||
\(423\) | 38.2265 | 1.85864 | ||||||||
\(424\) | 6.75709 | 0.328154 | ||||||||
\(425\) | 18.8580 | 0.914747 | ||||||||
\(426\) | −0.651271 | −0.0315542 | ||||||||
\(427\) | −16.5303 | −0.799959 | ||||||||
\(428\) | −32.7100 | −1.58110 | ||||||||
\(429\) | 0.0921172 | 0.00444746 | ||||||||
\(430\) | 1.08332 | 0.0522425 | ||||||||
\(431\) | 40.5225 | 1.95190 | 0.975949 | − | 0.217999i | \(-0.0699529\pi\) | ||||
0.975949 | + | 0.217999i | \(0.0699529\pi\) | |||||||
\(432\) | −2.02653 | −0.0975013 | ||||||||
\(433\) | 15.4784 | 0.743846 | 0.371923 | − | 0.928264i | \(-0.378698\pi\) | ||||
0.371923 | + | 0.928264i | \(0.378698\pi\) | |||||||
\(434\) | 4.47732 | 0.214918 | ||||||||
\(435\) | 0.0325809 | 0.00156213 | ||||||||
\(436\) | −17.7601 | −0.850552 | ||||||||
\(437\) | 3.47651 | 0.166304 | ||||||||
\(438\) | −0.0970750 | −0.00463842 | ||||||||
\(439\) | 3.44487 | 0.164415 | 0.0822073 | − | 0.996615i | \(-0.473803\pi\) | ||||
0.0822073 | + | 0.996615i | \(0.473803\pi\) | |||||||
\(440\) | 1.17794 | 0.0561563 | ||||||||
\(441\) | 17.0965 | 0.814121 | ||||||||
\(442\) | −0.515026 | −0.0244973 | ||||||||
\(443\) | 26.2142 | 1.24547 | 0.622737 | − | 0.782431i | \(-0.286021\pi\) | ||||
0.622737 | + | 0.782431i | \(0.286021\pi\) | |||||||
\(444\) | −2.03962 | −0.0967963 | ||||||||
\(445\) | 2.27985 | 0.108075 | ||||||||
\(446\) | −3.36019 | −0.159110 | ||||||||
\(447\) | 0.517917 | 0.0244966 | ||||||||
\(448\) | −4.37112 | −0.206516 | ||||||||
\(449\) | 19.7732 | 0.933153 | 0.466576 | − | 0.884481i | \(-0.345487\pi\) | ||||
0.466576 | + | 0.884481i | \(0.345487\pi\) | |||||||
\(450\) | 6.34284 | 0.299004 | ||||||||
\(451\) | 29.6465 | 1.39600 | ||||||||
\(452\) | 21.6271 | 1.01725 | ||||||||
\(453\) | −1.28429 | −0.0603410 | ||||||||
\(454\) | −8.44719 | −0.396446 | ||||||||
\(455\) | −0.0987501 | −0.00462948 | ||||||||
\(456\) | −0.223193 | −0.0104520 | ||||||||
\(457\) | −38.0468 | −1.77976 | −0.889878 | − | 0.456200i | \(-0.849210\pi\) | ||||
−0.889878 | + | 0.456200i | \(0.849210\pi\) | |||||||
\(458\) | −0.564228 | −0.0263646 | ||||||||
\(459\) | 2.66204 | 0.124254 | ||||||||
\(460\) | 1.51497 | 0.0706357 | ||||||||
\(461\) | 32.5625 | 1.51659 | 0.758293 | − | 0.651914i | \(-0.226034\pi\) | ||||
0.758293 | + | 0.651914i | \(0.226034\pi\) | |||||||
\(462\) | 0.144167 | 0.00670727 | ||||||||
\(463\) | −24.7790 | −1.15158 | −0.575788 | − | 0.817599i | \(-0.695305\pi\) | ||||
−0.575788 | + | 0.817599i | \(0.695305\pi\) | |||||||
\(464\) | −2.91719 | −0.135427 | ||||||||
\(465\) | −0.299295 | −0.0138795 | ||||||||
\(466\) | 10.3846 | 0.481056 | ||||||||
\(467\) | −1.37883 | −0.0638045 | −0.0319022 | − | 0.999491i | \(-0.510157\pi\) | ||||
−0.0319022 | + | 0.999491i | \(0.510157\pi\) | |||||||
\(468\) | 1.68694 | 0.0779788 | ||||||||
\(469\) | −8.55282 | −0.394932 | ||||||||
\(470\) | 1.55094 | 0.0715395 | ||||||||
\(471\) | −2.45243 | −0.113002 | ||||||||
\(472\) | −4.87466 | −0.224375 | ||||||||
\(473\) | −22.7895 | −1.04786 | ||||||||
\(474\) | −0.180713 | −0.00830041 | ||||||||
\(475\) | −5.75092 | −0.263870 | ||||||||
\(476\) | 7.84942 | 0.359778 | ||||||||
\(477\) | 12.2610 | 0.561395 | ||||||||
\(478\) | 2.96444 | 0.135590 | ||||||||
\(479\) | 24.0021 | 1.09668 | 0.548341 | − | 0.836255i | \(-0.315259\pi\) | ||||
0.548341 | + | 0.836255i | \(0.315259\pi\) | |||||||
\(480\) | −0.148267 | −0.00676743 | ||||||||
\(481\) | 3.01797 | 0.137608 | ||||||||
\(482\) | 10.2828 | 0.468368 | ||||||||
\(483\) | 0.389870 | 0.0177397 | ||||||||
\(484\) | 8.16635 | 0.371198 | ||||||||
\(485\) | −1.88798 | −0.0857287 | ||||||||
\(486\) | 1.34406 | 0.0609679 | ||||||||
\(487\) | 12.7714 | 0.578727 | 0.289363 | − | 0.957219i | \(-0.406556\pi\) | ||||
0.289363 | + | 0.957219i | \(0.406556\pi\) | |||||||
\(488\) | 24.0907 | 1.09053 | ||||||||
\(489\) | −1.05934 | −0.0479052 | ||||||||
\(490\) | 0.693648 | 0.0313358 | ||||||||
\(491\) | −34.8491 | −1.57272 | −0.786359 | − | 0.617770i | \(-0.788036\pi\) | ||||
−0.786359 | + | 0.617770i | \(0.788036\pi\) | |||||||
\(492\) | −2.44787 | −0.110359 | ||||||||
\(493\) | 3.83202 | 0.172585 | ||||||||
\(494\) | 0.157062 | 0.00706655 | ||||||||
\(495\) | 2.13743 | 0.0960704 | ||||||||
\(496\) | 26.7980 | 1.20327 | ||||||||
\(497\) | −14.6871 | −0.658804 | ||||||||
\(498\) | −0.261854 | −0.0117340 | ||||||||
\(499\) | 37.2423 | 1.66719 | 0.833596 | − | 0.552374i | \(-0.186278\pi\) | ||||
0.833596 | + | 0.552374i | \(0.186278\pi\) | |||||||
\(500\) | −5.05232 | −0.225947 | ||||||||
\(501\) | 1.07675 | 0.0481058 | ||||||||
\(502\) | −3.23801 | −0.144519 | ||||||||
\(503\) | −14.5353 | −0.648098 | −0.324049 | − | 0.946040i | \(-0.605044\pi\) | ||||
−0.324049 | + | 0.946040i | \(0.605044\pi\) | |||||||
\(504\) | 5.55137 | 0.247278 | ||||||||
\(505\) | −0.553172 | −0.0246158 | ||||||||
\(506\) | 3.27263 | 0.145486 | ||||||||
\(507\) | −1.49728 | −0.0664966 | ||||||||
\(508\) | −14.9724 | −0.664295 | ||||||||
\(509\) | −38.4949 | −1.70626 | −0.853128 | − | 0.521702i | \(-0.825297\pi\) | ||||
−0.853128 | + | 0.521702i | \(0.825297\pi\) | |||||||
\(510\) | 0.0538813 | 0.00238590 | ||||||||
\(511\) | −2.18917 | −0.0968434 | ||||||||
\(512\) | 22.8781 | 1.01108 | ||||||||
\(513\) | −0.811814 | −0.0358425 | ||||||||
\(514\) | 0.356472 | 0.0157233 | ||||||||
\(515\) | −0.624758 | −0.0275301 | ||||||||
\(516\) | 1.88170 | 0.0828372 | ||||||||
\(517\) | −32.6265 | −1.43491 | ||||||||
\(518\) | 4.72325 | 0.207528 | ||||||||
\(519\) | −2.60193 | −0.114212 | ||||||||
\(520\) | 0.143915 | 0.00631107 | ||||||||
\(521\) | −32.3780 | −1.41851 | −0.709253 | − | 0.704954i | \(-0.750968\pi\) | ||||
−0.709253 | + | 0.704954i | \(0.750968\pi\) | |||||||
\(522\) | 1.28889 | 0.0564131 | ||||||||
\(523\) | 16.3398 | 0.714489 | 0.357245 | − | 0.934011i | \(-0.383716\pi\) | ||||
0.357245 | + | 0.934011i | \(0.383716\pi\) | |||||||
\(524\) | −1.98820 | −0.0868548 | ||||||||
\(525\) | −0.644931 | −0.0281471 | ||||||||
\(526\) | −12.1637 | −0.530362 | ||||||||
\(527\) | −35.2018 | −1.53341 | ||||||||
\(528\) | 0.862882 | 0.0375521 | ||||||||
\(529\) | −14.1499 | −0.615211 | ||||||||
\(530\) | 0.497460 | 0.0216083 | ||||||||
\(531\) | −8.84529 | −0.383853 | ||||||||
\(532\) | −2.39375 | −0.103782 | ||||||||
\(533\) | 3.62204 | 0.156888 | ||||||||
\(534\) | −0.406645 | −0.0175973 | ||||||||
\(535\) | −5.06353 | −0.218916 | ||||||||
\(536\) | 12.4645 | 0.538386 | ||||||||
\(537\) | −2.05628 | −0.0887351 | ||||||||
\(538\) | −1.11930 | −0.0482564 | ||||||||
\(539\) | −14.5920 | −0.628522 | ||||||||
\(540\) | −0.353765 | −0.0152236 | ||||||||
\(541\) | −25.2154 | −1.08410 | −0.542048 | − | 0.840348i | \(-0.682351\pi\) | ||||
−0.542048 | + | 0.840348i | \(0.682351\pi\) | |||||||
\(542\) | −2.42659 | −0.104231 | ||||||||
\(543\) | −1.84441 | −0.0791512 | ||||||||
\(544\) | −17.4385 | −0.747669 | ||||||||
\(545\) | −2.74927 | −0.117766 | ||||||||
\(546\) | 0.0176136 | 0.000753790 0 | ||||||||
\(547\) | −5.07760 | −0.217103 | −0.108551 | − | 0.994091i | \(-0.534621\pi\) | ||||
−0.108551 | + | 0.994091i | \(0.534621\pi\) | |||||||
\(548\) | −5.09815 | −0.217782 | ||||||||
\(549\) | 43.7136 | 1.86565 | ||||||||
\(550\) | −5.41365 | −0.230839 | ||||||||
\(551\) | −1.16861 | −0.0497844 | ||||||||
\(552\) | −0.568182 | −0.0241834 | ||||||||
\(553\) | −4.07532 | −0.173300 | ||||||||
\(554\) | 11.8279 | 0.502518 | ||||||||
\(555\) | −0.315735 | −0.0134022 | ||||||||
\(556\) | 1.81375 | 0.0769201 | ||||||||
\(557\) | −20.4536 | −0.866647 | −0.433324 | − | 0.901238i | \(-0.642659\pi\) | ||||
−0.433324 | + | 0.901238i | \(0.642659\pi\) | |||||||
\(558\) | −11.8400 | −0.501228 | ||||||||
\(559\) | −2.78429 | −0.117763 | ||||||||
\(560\) | −0.925014 | −0.0390890 | ||||||||
\(561\) | −1.13348 | −0.0478556 | ||||||||
\(562\) | −8.03529 | −0.338948 | ||||||||
\(563\) | 21.7928 | 0.918459 | 0.459229 | − | 0.888318i | \(-0.348126\pi\) | ||||
0.459229 | + | 0.888318i | \(0.348126\pi\) | |||||||
\(564\) | 2.69393 | 0.113435 | ||||||||
\(565\) | 3.34789 | 0.140847 | ||||||||
\(566\) | −6.79837 | −0.285757 | ||||||||
\(567\) | 10.0276 | 0.421119 | ||||||||
\(568\) | 21.4043 | 0.898106 | ||||||||
\(569\) | 37.9762 | 1.59204 | 0.796022 | − | 0.605268i | \(-0.206934\pi\) | ||||
0.796022 | + | 0.605268i | \(0.206934\pi\) | |||||||
\(570\) | −0.0164316 | −0.000688243 0 | ||||||||
\(571\) | −7.06087 | −0.295488 | −0.147744 | − | 0.989026i | \(-0.547201\pi\) | ||||
−0.147744 | + | 0.989026i | \(0.547201\pi\) | |||||||
\(572\) | −1.43981 | −0.0602016 | ||||||||
\(573\) | −1.33234 | −0.0556595 | ||||||||
\(574\) | 5.66865 | 0.236605 | ||||||||
\(575\) | −14.6401 | −0.610533 | ||||||||
\(576\) | 11.5592 | 0.481633 | ||||||||
\(577\) | −4.96325 | −0.206623 | −0.103311 | − | 0.994649i | \(-0.532944\pi\) | ||||
−0.103311 | + | 0.994649i | \(0.532944\pi\) | |||||||
\(578\) | −0.999354 | −0.0415677 | ||||||||
\(579\) | −0.574088 | −0.0238583 | ||||||||
\(580\) | −0.509246 | −0.0211453 | ||||||||
\(581\) | −5.90518 | −0.244988 | ||||||||
\(582\) | 0.336749 | 0.0139587 | ||||||||
\(583\) | −10.4649 | −0.433411 | ||||||||
\(584\) | 3.19042 | 0.132020 | ||||||||
\(585\) | 0.261139 | 0.0107968 | ||||||||
\(586\) | 1.50395 | 0.0621275 | ||||||||
\(587\) | 35.1554 | 1.45102 | 0.725509 | − | 0.688213i | \(-0.241605\pi\) | ||||
0.725509 | + | 0.688213i | \(0.241605\pi\) | |||||||
\(588\) | 1.20484 | 0.0496869 | ||||||||
\(589\) | 10.7351 | 0.442332 | ||||||||
\(590\) | −0.358875 | −0.0147746 | ||||||||
\(591\) | 2.95464 | 0.121538 | ||||||||
\(592\) | 28.2700 | 1.16189 | ||||||||
\(593\) | 30.1770 | 1.23922 | 0.619611 | − | 0.784909i | \(-0.287290\pi\) | ||||
0.619611 | + | 0.784909i | \(0.287290\pi\) | |||||||
\(594\) | −0.764204 | −0.0313557 | ||||||||
\(595\) | 1.21510 | 0.0498141 | ||||||||
\(596\) | −8.09516 | −0.331591 | ||||||||
\(597\) | −3.05319 | −0.124959 | ||||||||
\(598\) | 0.399832 | 0.0163503 | ||||||||
\(599\) | 34.7234 | 1.41876 | 0.709379 | − | 0.704827i | \(-0.248975\pi\) | ||||
0.709379 | + | 0.704827i | \(0.248975\pi\) | |||||||
\(600\) | 0.939897 | 0.0383711 | ||||||||
\(601\) | −11.8372 | −0.482849 | −0.241425 | − | 0.970420i | \(-0.577615\pi\) | ||||
−0.241425 | + | 0.970420i | \(0.577615\pi\) | |||||||
\(602\) | −4.35754 | −0.177600 | ||||||||
\(603\) | 22.6175 | 0.921054 | ||||||||
\(604\) | 20.0737 | 0.816786 | ||||||||
\(605\) | 1.26416 | 0.0513953 | ||||||||
\(606\) | 0.0986665 | 0.00400805 | ||||||||
\(607\) | −14.9512 | −0.606852 | −0.303426 | − | 0.952855i | \(-0.598131\pi\) | ||||
−0.303426 | + | 0.952855i | \(0.598131\pi\) | |||||||
\(608\) | 5.31803 | 0.215675 | ||||||||
\(609\) | −0.131052 | −0.00531051 | ||||||||
\(610\) | 1.77356 | 0.0718095 | ||||||||
\(611\) | −3.98613 | −0.161261 | ||||||||
\(612\) | −20.7574 | −0.839067 | ||||||||
\(613\) | 45.0690 | 1.82032 | 0.910159 | − | 0.414259i | \(-0.135959\pi\) | ||||
0.910159 | + | 0.414259i | \(0.135959\pi\) | |||||||
\(614\) | −8.22108 | −0.331776 | ||||||||
\(615\) | −0.378932 | −0.0152800 | ||||||||
\(616\) | −4.73813 | −0.190905 | ||||||||
\(617\) | −8.91275 | −0.358814 | −0.179407 | − | 0.983775i | \(-0.557418\pi\) | ||||
−0.179407 | + | 0.983775i | \(0.557418\pi\) | |||||||
\(618\) | 0.111435 | 0.00448257 | ||||||||
\(619\) | 5.91521 | 0.237752 | 0.118876 | − | 0.992909i | \(-0.462071\pi\) | ||||
0.118876 | + | 0.992909i | \(0.462071\pi\) | |||||||
\(620\) | 4.67805 | 0.187875 | ||||||||
\(621\) | −2.06663 | −0.0829310 | ||||||||
\(622\) | 4.49644 | 0.180291 | ||||||||
\(623\) | −9.17040 | −0.367405 | ||||||||
\(624\) | 0.105422 | 0.00422026 | ||||||||
\(625\) | 23.8237 | 0.952950 | ||||||||
\(626\) | 10.5345 | 0.421045 | ||||||||
\(627\) | 0.345665 | 0.0138045 | ||||||||
\(628\) | 38.3320 | 1.52961 | ||||||||
\(629\) | −37.1354 | −1.48069 | ||||||||
\(630\) | 0.408694 | 0.0162828 | ||||||||
\(631\) | −25.2393 | −1.00476 | −0.502381 | − | 0.864646i | \(-0.667543\pi\) | ||||
−0.502381 | + | 0.864646i | \(0.667543\pi\) | |||||||
\(632\) | 5.93921 | 0.236249 | ||||||||
\(633\) | −1.96815 | −0.0782270 | ||||||||
\(634\) | −9.00836 | −0.357768 | ||||||||
\(635\) | −2.31774 | −0.0919769 | ||||||||
\(636\) | 0.864071 | 0.0342627 | ||||||||
\(637\) | −1.78277 | −0.0706359 | ||||||||
\(638\) | −1.10007 | −0.0435524 | ||||||||
\(639\) | 38.8391 | 1.53645 | ||||||||
\(640\) | 3.02440 | 0.119550 | ||||||||
\(641\) | 29.7548 | 1.17525 | 0.587623 | − | 0.809135i | \(-0.300064\pi\) | ||||
0.587623 | + | 0.809135i | \(0.300064\pi\) | |||||||
\(642\) | 0.903156 | 0.0356447 | ||||||||
\(643\) | 5.99954 | 0.236599 | 0.118299 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118299 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(644\) | −6.09376 | −0.240128 | ||||||||
\(645\) | 0.291288 | 0.0114695 | ||||||||
\(646\) | −1.93261 | −0.0760375 | ||||||||
\(647\) | 31.0120 | 1.21921 | 0.609604 | − | 0.792706i | \(-0.291328\pi\) | ||||
0.609604 | + | 0.792706i | \(0.291328\pi\) | |||||||
\(648\) | −14.6138 | −0.574085 | ||||||||
\(649\) | 7.54951 | 0.296344 | ||||||||
\(650\) | −0.661409 | −0.0259426 | ||||||||
\(651\) | 1.20388 | 0.0471837 | ||||||||
\(652\) | 16.5578 | 0.648453 | ||||||||
\(653\) | 15.9197 | 0.622988 | 0.311494 | − | 0.950248i | \(-0.399171\pi\) | ||||
0.311494 | + | 0.950248i | \(0.399171\pi\) | |||||||
\(654\) | 0.490373 | 0.0191751 | ||||||||
\(655\) | −0.307774 | −0.0120257 | ||||||||
\(656\) | 33.9285 | 1.32468 | ||||||||
\(657\) | 5.78915 | 0.225856 | ||||||||
\(658\) | −6.23846 | −0.243201 | ||||||||
\(659\) | −1.80806 | −0.0704320 | −0.0352160 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352160 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(660\) | 0.150631 | 0.00586330 | ||||||||
\(661\) | 35.8856 | 1.39579 | 0.697894 | − | 0.716201i | \(-0.254121\pi\) | ||||
0.697894 | + | 0.716201i | \(0.254121\pi\) | |||||||
\(662\) | 13.0893 | 0.508729 | ||||||||
\(663\) | −0.138482 | −0.00537820 | ||||||||
\(664\) | 8.60598 | 0.333977 | ||||||||
\(665\) | −0.370555 | −0.0143695 | ||||||||
\(666\) | −12.4904 | −0.483993 | ||||||||
\(667\) | −2.97492 | −0.115189 | ||||||||
\(668\) | −16.8299 | −0.651169 | ||||||||
\(669\) | −0.903501 | −0.0349314 | ||||||||
\(670\) | 0.917644 | 0.0354517 | ||||||||
\(671\) | −37.3098 | −1.44033 | ||||||||
\(672\) | 0.596385 | 0.0230060 | ||||||||
\(673\) | −28.9362 | −1.11541 | −0.557704 | − | 0.830040i | \(-0.688318\pi\) | ||||
−0.557704 | + | 0.830040i | \(0.688318\pi\) | |||||||
\(674\) | 11.1706 | 0.430277 | ||||||||
\(675\) | 3.41866 | 0.131584 | ||||||||
\(676\) | 23.4028 | 0.900109 | ||||||||
\(677\) | −26.7757 | −1.02907 | −0.514537 | − | 0.857468i | \(-0.672036\pi\) | ||||
−0.514537 | + | 0.857468i | \(0.672036\pi\) | |||||||
\(678\) | −0.597147 | −0.0229333 | ||||||||
\(679\) | 7.59416 | 0.291437 | ||||||||
\(680\) | −1.77083 | −0.0679084 | ||||||||
\(681\) | −2.27131 | −0.0870368 | ||||||||
\(682\) | 10.1055 | 0.386961 | ||||||||
\(683\) | 5.76437 | 0.220567 | 0.110284 | − | 0.993900i | \(-0.464824\pi\) | ||||
0.110284 | + | 0.993900i | \(0.464824\pi\) | |||||||
\(684\) | 6.33015 | 0.242039 | ||||||||
\(685\) | −0.789198 | −0.0301537 | ||||||||
\(686\) | −6.20187 | −0.236789 | ||||||||
\(687\) | −0.151712 | −0.00578816 | ||||||||
\(688\) | −26.0811 | −0.994331 | ||||||||
\(689\) | −1.27854 | −0.0487085 | ||||||||
\(690\) | −0.0418297 | −0.00159243 | ||||||||
\(691\) | −8.22389 | −0.312852 | −0.156426 | − | 0.987690i | \(-0.549997\pi\) | ||||
−0.156426 | + | 0.987690i | \(0.549997\pi\) | |||||||
\(692\) | 40.6688 | 1.54599 | ||||||||
\(693\) | −8.59755 | −0.326594 | ||||||||
\(694\) | 10.4442 | 0.396456 | ||||||||
\(695\) | 0.280770 | 0.0106502 | ||||||||
\(696\) | 0.190991 | 0.00723948 | ||||||||
\(697\) | −44.5684 | −1.68815 | ||||||||
\(698\) | 7.90102 | 0.299058 | ||||||||
\(699\) | 2.79224 | 0.105612 | ||||||||
\(700\) | 10.0804 | 0.381004 | ||||||||
\(701\) | 8.97999 | 0.339169 | 0.169585 | − | 0.985516i | \(-0.445757\pi\) | ||||
0.169585 | + | 0.985516i | \(0.445757\pi\) | |||||||
\(702\) | −0.0933662 | −0.00352388 | ||||||||
\(703\) | 11.3248 | 0.427122 | ||||||||
\(704\) | −9.86584 | −0.371833 | ||||||||
\(705\) | 0.417022 | 0.0157060 | ||||||||
\(706\) | −3.93552 | −0.148115 | ||||||||
\(707\) | 2.22507 | 0.0836822 | ||||||||
\(708\) | −0.623353 | −0.0234270 | ||||||||
\(709\) | −33.6896 | −1.26524 | −0.632619 | − | 0.774463i | \(-0.718020\pi\) | ||||
−0.632619 | + | 0.774463i | \(0.718020\pi\) | |||||||
\(710\) | 1.57580 | 0.0591386 | ||||||||
\(711\) | 10.7770 | 0.404168 | ||||||||
\(712\) | 13.3646 | 0.500859 | ||||||||
\(713\) | 27.3283 | 1.02345 | ||||||||
\(714\) | −0.216731 | −0.00811094 | ||||||||
\(715\) | −0.222884 | −0.00833539 | ||||||||
\(716\) | 32.1401 | 1.20113 | ||||||||
\(717\) | 0.797089 | 0.0297678 | ||||||||
\(718\) | −15.2510 | −0.569164 | ||||||||
\(719\) | 8.53294 | 0.318225 | 0.159112 | − | 0.987260i | \(-0.449137\pi\) | ||||
0.159112 | + | 0.987260i | \(0.449137\pi\) | |||||||
\(720\) | 2.44615 | 0.0911626 | ||||||||
\(721\) | 2.51301 | 0.0935894 | ||||||||
\(722\) | −7.61040 | −0.283230 | ||||||||
\(723\) | 2.76487 | 0.102827 | ||||||||
\(724\) | 28.8286 | 1.07140 | ||||||||
\(725\) | 4.92117 | 0.182768 | ||||||||
\(726\) | −0.225481 | −0.00836839 | ||||||||
\(727\) | −10.6639 | −0.395501 | −0.197751 | − | 0.980252i | \(-0.563364\pi\) | ||||
−0.197751 | + | 0.980252i | \(0.563364\pi\) | |||||||
\(728\) | −0.578878 | −0.0214546 | ||||||||
\(729\) | −26.2756 | −0.973170 | ||||||||
\(730\) | 0.234880 | 0.00869329 | ||||||||
\(731\) | 34.2600 | 1.26715 | ||||||||
\(732\) | 3.08062 | 0.113863 | ||||||||
\(733\) | −3.39646 | −0.125451 | −0.0627255 | − | 0.998031i | \(-0.519979\pi\) | ||||
−0.0627255 | + | 0.998031i | \(0.519979\pi\) | |||||||
\(734\) | 0.543488 | 0.0200605 | ||||||||
\(735\) | 0.186511 | 0.00687954 | ||||||||
\(736\) | 13.5381 | 0.499020 | ||||||||
\(737\) | −19.3041 | −0.711077 | ||||||||
\(738\) | −14.9904 | −0.551806 | ||||||||
\(739\) | 12.1503 | 0.446957 | 0.223478 | − | 0.974709i | \(-0.428259\pi\) | ||||
0.223478 | + | 0.974709i | \(0.428259\pi\) | |||||||
\(740\) | 4.93502 | 0.181415 | ||||||||
\(741\) | 0.0422314 | 0.00155141 | ||||||||
\(742\) | −2.00097 | −0.0734579 | ||||||||
\(743\) | 25.7901 | 0.946148 | 0.473074 | − | 0.881023i | \(-0.343144\pi\) | ||||
0.473074 | + | 0.881023i | \(0.343144\pi\) | |||||||
\(744\) | −1.75448 | −0.0643225 | ||||||||
\(745\) | −1.25314 | −0.0459114 | ||||||||
\(746\) | −7.65538 | −0.280283 | ||||||||
\(747\) | 15.6159 | 0.571357 | ||||||||
\(748\) | 17.7166 | 0.647781 | ||||||||
\(749\) | 20.3674 | 0.744209 | ||||||||
\(750\) | 0.139500 | 0.00509381 | ||||||||
\(751\) | 41.6825 | 1.52102 | 0.760508 | − | 0.649328i | \(-0.224950\pi\) | ||||
0.760508 | + | 0.649328i | \(0.224950\pi\) | |||||||
\(752\) | −37.3389 | −1.36161 | ||||||||
\(753\) | −0.870647 | −0.0317281 | ||||||||
\(754\) | −0.134401 | −0.00489459 | ||||||||
\(755\) | 3.10742 | 0.113091 | ||||||||
\(756\) | 1.42298 | 0.0517532 | ||||||||
\(757\) | 37.4819 | 1.36230 | 0.681151 | − | 0.732143i | \(-0.261480\pi\) | ||||
0.681151 | + | 0.732143i | \(0.261480\pi\) | |||||||
\(758\) | −5.57876 | −0.202630 | ||||||||
\(759\) | 0.879957 | 0.0319404 | ||||||||
\(760\) | 0.540032 | 0.0195890 | ||||||||
\(761\) | 24.6396 | 0.893184 | 0.446592 | − | 0.894738i | \(-0.352638\pi\) | ||||
0.446592 | + | 0.894738i | \(0.352638\pi\) | |||||||
\(762\) | 0.413404 | 0.0149761 | ||||||||
\(763\) | 11.0586 | 0.400348 | ||||||||
\(764\) | 20.8249 | 0.753417 | ||||||||
\(765\) | −3.21326 | −0.116176 | ||||||||
\(766\) | 8.18324 | 0.295673 | ||||||||
\(767\) | 0.922356 | 0.0333044 | ||||||||
\(768\) | 0.358813 | 0.0129475 | ||||||||
\(769\) | −18.9866 | −0.684673 | −0.342337 | − | 0.939577i | \(-0.611218\pi\) | ||||
−0.342337 | + | 0.939577i | \(0.611218\pi\) | |||||||
\(770\) | −0.348823 | −0.0125707 | ||||||||
\(771\) | 0.0958495 | 0.00345194 | ||||||||
\(772\) | 8.97313 | 0.322950 | ||||||||
\(773\) | −50.1426 | −1.80351 | −0.901753 | − | 0.432252i | \(-0.857719\pi\) | ||||
−0.901753 | + | 0.432252i | \(0.857719\pi\) | |||||||
\(774\) | 11.5233 | 0.414195 | ||||||||
\(775\) | −45.2070 | −1.62388 | ||||||||
\(776\) | −11.0674 | −0.397297 | ||||||||
\(777\) | 1.27001 | 0.0455612 | ||||||||
\(778\) | −13.1569 | −0.471696 | ||||||||
\(779\) | 13.5915 | 0.486967 | ||||||||
\(780\) | 0.0184032 | 0.000658942 0 | ||||||||
\(781\) | −33.1494 | −1.18618 | ||||||||
\(782\) | −4.91983 | −0.175933 | ||||||||
\(783\) | 0.694684 | 0.0248260 | ||||||||
\(784\) | −16.6996 | −0.596414 | ||||||||
\(785\) | 5.93382 | 0.211787 | ||||||||
\(786\) | 0.0548962 | 0.00195808 | ||||||||
\(787\) | −3.90476 | −0.139190 | −0.0695949 | − | 0.997575i | \(-0.522171\pi\) | ||||
−0.0695949 | + | 0.997575i | \(0.522171\pi\) | |||||||
\(788\) | −46.1817 | −1.64515 | ||||||||
\(789\) | −3.27061 | −0.116437 | ||||||||
\(790\) | 0.437247 | 0.0155565 | ||||||||
\(791\) | −13.4665 | −0.478813 | ||||||||
\(792\) | 12.5297 | 0.445225 | ||||||||
\(793\) | −4.55830 | −0.161870 | ||||||||
\(794\) | 5.56730 | 0.197576 | ||||||||
\(795\) | 0.133759 | 0.00474394 | ||||||||
\(796\) | 47.7221 | 1.69147 | ||||||||
\(797\) | −28.0672 | −0.994192 | −0.497096 | − | 0.867696i | \(-0.665600\pi\) | ||||
−0.497096 | + | 0.867696i | \(0.665600\pi\) | |||||||
\(798\) | 0.0660940 | 0.00233970 | ||||||||
\(799\) | 49.0483 | 1.73521 | ||||||||
\(800\) | −22.3949 | −0.791781 | ||||||||
\(801\) | 24.2506 | 0.856854 | ||||||||
\(802\) | 4.77205 | 0.168507 | ||||||||
\(803\) | −4.94108 | −0.174367 | ||||||||
\(804\) | 1.59392 | 0.0562131 | ||||||||
\(805\) | −0.943318 | −0.0332476 | ||||||||
\(806\) | 1.23464 | 0.0434882 | ||||||||
\(807\) | −0.300961 | −0.0105943 | ||||||||
\(808\) | −3.24272 | −0.114079 | ||||||||
\(809\) | 17.9039 | 0.629468 | 0.314734 | − | 0.949180i | \(-0.398085\pi\) | ||||
0.314734 | + | 0.949180i | \(0.398085\pi\) | |||||||
\(810\) | −1.07587 | −0.0378024 | ||||||||
\(811\) | −14.0472 | −0.493263 | −0.246631 | − | 0.969109i | \(-0.579324\pi\) | ||||
−0.246631 | + | 0.969109i | \(0.579324\pi\) | |||||||
\(812\) | 2.04838 | 0.0718840 | ||||||||
\(813\) | −0.652471 | −0.0228832 | ||||||||
\(814\) | 10.6606 | 0.373655 | ||||||||
\(815\) | 2.56316 | 0.0897835 | ||||||||
\(816\) | −1.29719 | −0.0454108 | ||||||||
\(817\) | −10.4479 | −0.365526 | ||||||||
\(818\) | 13.4598 | 0.470610 | ||||||||
\(819\) | −1.05040 | −0.0367039 | ||||||||
\(820\) | 5.92280 | 0.206833 | ||||||||
\(821\) | −19.6144 | −0.684546 | −0.342273 | − | 0.939600i | \(-0.611197\pi\) | ||||
−0.342273 | + | 0.939600i | \(0.611197\pi\) | |||||||
\(822\) | 0.140765 | 0.00490975 | ||||||||
\(823\) | 2.22528 | 0.0775684 | 0.0387842 | − | 0.999248i | \(-0.487652\pi\) | ||||
0.0387842 | + | 0.999248i | \(0.487652\pi\) | |||||||
\(824\) | −3.66236 | −0.127584 | ||||||||
\(825\) | −1.45564 | −0.0506789 | ||||||||
\(826\) | 1.44353 | 0.0502268 | ||||||||
\(827\) | −13.8918 | −0.483067 | −0.241533 | − | 0.970393i | \(-0.577650\pi\) | ||||
−0.241533 | + | 0.970393i | \(0.577650\pi\) | |||||||
\(828\) | 16.1146 | 0.560022 | ||||||||
\(829\) | −10.9325 | −0.379700 | −0.189850 | − | 0.981813i | \(-0.560800\pi\) | ||||
−0.189850 | + | 0.981813i | \(0.560800\pi\) | |||||||
\(830\) | 0.633575 | 0.0219917 | ||||||||
\(831\) | 3.18032 | 0.110324 | ||||||||
\(832\) | −1.20535 | −0.0417881 | ||||||||
\(833\) | 21.9365 | 0.760056 | ||||||||
\(834\) | −0.0500795 | −0.00173411 | ||||||||
\(835\) | −2.60528 | −0.0901595 | ||||||||
\(836\) | −5.40282 | −0.186861 | ||||||||
\(837\) | −6.38153 | −0.220578 | ||||||||
\(838\) | −8.38826 | −0.289768 | ||||||||
\(839\) | −21.4014 | −0.738857 | −0.369429 | − | 0.929259i | \(-0.620447\pi\) | ||||
−0.369429 | + | 0.929259i | \(0.620447\pi\) | |||||||
\(840\) | 0.0605613 | 0.00208956 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −3.34210 | −0.115176 | ||||||||
\(843\) | −2.16056 | −0.0744135 | ||||||||
\(844\) | 30.7627 | 1.05889 | ||||||||
\(845\) | 3.62278 | 0.124627 | ||||||||
\(846\) | 16.4973 | 0.567188 | ||||||||
\(847\) | −5.08491 | −0.174720 | ||||||||
\(848\) | −11.9764 | −0.411270 | ||||||||
\(849\) | −1.82797 | −0.0627357 | ||||||||
\(850\) | 8.13848 | 0.279148 | ||||||||
\(851\) | 28.8294 | 0.988259 | ||||||||
\(852\) | 2.73710 | 0.0937717 | ||||||||
\(853\) | −34.3358 | −1.17564 | −0.587818 | − | 0.808993i | \(-0.700013\pi\) | ||||
−0.587818 | + | 0.808993i | \(0.700013\pi\) | |||||||
\(854\) | −7.13394 | −0.244118 | ||||||||
\(855\) | 0.979912 | 0.0335123 | ||||||||
\(856\) | −29.6827 | −1.01453 | ||||||||
\(857\) | −2.61691 | −0.0893918 | −0.0446959 | − | 0.999001i | \(-0.514232\pi\) | ||||
−0.0446959 | + | 0.999001i | \(0.514232\pi\) | |||||||
\(858\) | 0.0397547 | 0.00135720 | ||||||||
\(859\) | −14.3229 | −0.488690 | −0.244345 | − | 0.969688i | \(-0.578573\pi\) | ||||
−0.244345 | + | 0.969688i | \(0.578573\pi\) | |||||||
\(860\) | −4.55290 | −0.155253 | ||||||||
\(861\) | 1.52421 | 0.0519449 | ||||||||
\(862\) | 17.4881 | 0.595648 | ||||||||
\(863\) | −30.8938 | −1.05164 | −0.525818 | − | 0.850597i | \(-0.676241\pi\) | ||||
−0.525818 | + | 0.850597i | \(0.676241\pi\) | |||||||
\(864\) | −3.16133 | −0.107550 | ||||||||
\(865\) | 6.29555 | 0.214055 | ||||||||
\(866\) | 6.67998 | 0.226995 | ||||||||
\(867\) | −0.268710 | −0.00912587 | ||||||||
\(868\) | −18.8169 | −0.638687 | ||||||||
\(869\) | −9.19820 | −0.312028 | ||||||||
\(870\) | 0.0140608 | 0.000476706 0 | ||||||||
\(871\) | −2.35847 | −0.0799137 | ||||||||
\(872\) | −16.1164 | −0.545769 | ||||||||
\(873\) | −20.0823 | −0.679684 | ||||||||
\(874\) | 1.50035 | 0.0507500 | ||||||||
\(875\) | 3.14591 | 0.106351 | ||||||||
\(876\) | 0.407978 | 0.0137843 | ||||||||
\(877\) | 1.99498 | 0.0673656 | 0.0336828 | − | 0.999433i | \(-0.489276\pi\) | ||||
0.0336828 | + | 0.999433i | \(0.489276\pi\) | |||||||
\(878\) | 1.48669 | 0.0501733 | ||||||||
\(879\) | 0.404387 | 0.0136396 | ||||||||
\(880\) | −2.08780 | −0.0703798 | ||||||||
\(881\) | −23.9401 | −0.806562 | −0.403281 | − | 0.915076i | \(-0.632130\pi\) | ||||
−0.403281 | + | 0.915076i | \(0.632130\pi\) | |||||||
\(882\) | 7.37830 | 0.248440 | ||||||||
\(883\) | 47.6172 | 1.60245 | 0.801223 | − | 0.598366i | \(-0.204183\pi\) | ||||
0.801223 | + | 0.598366i | \(0.204183\pi\) | |||||||
\(884\) | 2.16451 | 0.0728003 | ||||||||
\(885\) | −0.0964955 | −0.00324366 | ||||||||
\(886\) | 11.3132 | 0.380074 | ||||||||
\(887\) | −13.7078 | −0.460262 | −0.230131 | − | 0.973160i | \(-0.573915\pi\) | ||||
−0.230131 | + | 0.973160i | \(0.573915\pi\) | |||||||
\(888\) | −1.85086 | −0.0621107 | ||||||||
\(889\) | 9.32284 | 0.312678 | ||||||||
\(890\) | 0.983906 | 0.0329806 | ||||||||
\(891\) | 22.6328 | 0.758227 | ||||||||
\(892\) | 14.1219 | 0.472837 | ||||||||
\(893\) | −14.9577 | −0.500542 | ||||||||
\(894\) | 0.223516 | 0.00747548 | ||||||||
\(895\) | 4.97532 | 0.166306 | ||||||||
\(896\) | −12.1653 | −0.406413 | ||||||||
\(897\) | 0.107508 | 0.00358959 | ||||||||
\(898\) | 8.53343 | 0.284764 | ||||||||
\(899\) | −9.18623 | −0.306378 | ||||||||
\(900\) | −26.6571 | −0.888571 | ||||||||
\(901\) | 15.7321 | 0.524113 | ||||||||
\(902\) | 12.7944 | 0.426008 | ||||||||
\(903\) | −1.17167 | −0.0389907 | ||||||||
\(904\) | 19.6255 | 0.652735 | ||||||||
\(905\) | 4.46268 | 0.148344 | ||||||||
\(906\) | −0.554254 | −0.0184139 | ||||||||
\(907\) | 1.58710 | 0.0526989 | 0.0263495 | − | 0.999653i | \(-0.491612\pi\) | ||||
0.0263495 | + | 0.999653i | \(0.491612\pi\) | |||||||
\(908\) | 35.5011 | 1.17815 | ||||||||
\(909\) | −5.88407 | −0.195162 | ||||||||
\(910\) | −0.0426172 | −0.00141275 | ||||||||
\(911\) | 9.69455 | 0.321195 | 0.160597 | − | 0.987020i | \(-0.448658\pi\) | ||||
0.160597 | + | 0.987020i | \(0.448658\pi\) | |||||||
\(912\) | 0.395591 | 0.0130993 | ||||||||
\(913\) | −13.3283 | −0.441102 | ||||||||
\(914\) | −16.4197 | −0.543116 | ||||||||
\(915\) | 0.476883 | 0.0157653 | ||||||||
\(916\) | 2.37129 | 0.0783496 | ||||||||
\(917\) | 1.23798 | 0.0408818 | ||||||||
\(918\) | 1.14885 | 0.0379177 | ||||||||
\(919\) | 15.6836 | 0.517356 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(920\) | 1.37476 | 0.0453243 | ||||||||
\(921\) | −2.21051 | −0.0728389 | ||||||||
\(922\) | 14.0529 | 0.462807 | ||||||||
\(923\) | −4.05001 | −0.133308 | ||||||||
\(924\) | −0.605894 | −0.0199325 | ||||||||
\(925\) | −47.6902 | −1.56804 | ||||||||
\(926\) | −10.6938 | −0.351419 | ||||||||
\(927\) | −6.64552 | −0.218267 | ||||||||
\(928\) | −4.55074 | −0.149385 | ||||||||
\(929\) | −47.5752 | −1.56089 | −0.780446 | − | 0.625223i | \(-0.785008\pi\) | ||||
−0.780446 | + | 0.625223i | \(0.785008\pi\) | |||||||
\(930\) | −0.129166 | −0.00423551 | ||||||||
\(931\) | −6.68975 | −0.219248 | ||||||||
\(932\) | −43.6434 | −1.42959 | ||||||||
\(933\) | 1.20902 | 0.0395815 | ||||||||
\(934\) | −0.595055 | −0.0194708 | ||||||||
\(935\) | 2.74253 | 0.0896905 | ||||||||
\(936\) | 1.53081 | 0.0500361 | ||||||||
\(937\) | −37.9607 | −1.24012 | −0.620062 | − | 0.784553i | \(-0.712892\pi\) | ||||
−0.620062 | + | 0.784553i | \(0.712892\pi\) | |||||||
\(938\) | −3.69111 | −0.120519 | ||||||||
\(939\) | 2.83257 | 0.0924373 | ||||||||
\(940\) | −6.51816 | −0.212599 | ||||||||
\(941\) | 21.3061 | 0.694560 | 0.347280 | − | 0.937761i | \(-0.387105\pi\) | ||||
0.347280 | + | 0.937761i | \(0.387105\pi\) | |||||||
\(942\) | −1.05838 | −0.0344840 | ||||||||
\(943\) | 34.5999 | 1.12673 | ||||||||
\(944\) | 8.63991 | 0.281205 | ||||||||
\(945\) | 0.220278 | 0.00716564 | ||||||||
\(946\) | −9.83518 | −0.319769 | ||||||||
\(947\) | 27.9932 | 0.909656 | 0.454828 | − | 0.890579i | \(-0.349701\pi\) | ||||
0.454828 | + | 0.890579i | \(0.349701\pi\) | |||||||
\(948\) | 0.759483 | 0.0246669 | ||||||||
\(949\) | −0.603673 | −0.0195960 | ||||||||
\(950\) | −2.48190 | −0.0805236 | ||||||||
\(951\) | −2.42220 | −0.0785453 | ||||||||
\(952\) | 7.12296 | 0.230856 | ||||||||
\(953\) | 13.3842 | 0.433557 | 0.216778 | − | 0.976221i | \(-0.430445\pi\) | ||||
0.216778 | + | 0.976221i | \(0.430445\pi\) | |||||||
\(954\) | 5.29146 | 0.171317 | ||||||||
\(955\) | 3.22370 | 0.104317 | ||||||||
\(956\) | −12.4587 | −0.402943 | ||||||||
\(957\) | −0.295792 | −0.00956160 | ||||||||
\(958\) | 10.3585 | 0.334668 | ||||||||
\(959\) | 3.17445 | 0.102508 | ||||||||
\(960\) | 0.126102 | 0.00406993 | ||||||||
\(961\) | 53.3868 | 1.72216 | ||||||||
\(962\) | 1.30245 | 0.0419928 | ||||||||
\(963\) | −53.8605 | −1.73563 | ||||||||
\(964\) | −43.2156 | −1.39188 | ||||||||
\(965\) | 1.38905 | 0.0447150 | ||||||||
\(966\) | 0.168255 | 0.00541351 | ||||||||
\(967\) | −0.229111 | −0.00736773 | −0.00368386 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368386 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(968\) | 7.41055 | 0.238184 | ||||||||
\(969\) | −0.519647 | −0.0166935 | ||||||||
\(970\) | −0.814788 | −0.0261613 | ||||||||
\(971\) | 22.3642 | 0.717703 | 0.358851 | − | 0.933395i | \(-0.383168\pi\) | ||||
0.358851 | + | 0.933395i | \(0.383168\pi\) | |||||||
\(972\) | −5.64871 | −0.181183 | ||||||||
\(973\) | −1.12936 | −0.0362057 | ||||||||
\(974\) | 5.51170 | 0.176606 | ||||||||
\(975\) | −0.177842 | −0.00569551 | ||||||||
\(976\) | −42.6986 | −1.36675 | ||||||||
\(977\) | 7.81157 | 0.249914 | 0.124957 | − | 0.992162i | \(-0.460121\pi\) | ||||
0.124957 | + | 0.992162i | \(0.460121\pi\) | |||||||
\(978\) | −0.457178 | −0.0146189 | ||||||||
\(979\) | −20.6981 | −0.661513 | ||||||||
\(980\) | −2.91520 | −0.0931227 | ||||||||
\(981\) | −29.2438 | −0.933684 | ||||||||
\(982\) | −15.0397 | −0.479936 | ||||||||
\(983\) | −1.09592 | −0.0349544 | −0.0174772 | − | 0.999847i | \(-0.505563\pi\) | ||||
−0.0174772 | + | 0.999847i | \(0.505563\pi\) | |||||||
\(984\) | −2.22132 | −0.0708131 | ||||||||
\(985\) | −7.14895 | −0.227785 | ||||||||
\(986\) | 1.65377 | 0.0526668 | ||||||||
\(987\) | −1.67742 | −0.0533929 | ||||||||
\(988\) | −0.660086 | −0.0210001 | ||||||||
\(989\) | −26.5972 | −0.845741 | ||||||||
\(990\) | 0.922444 | 0.0293172 | ||||||||
\(991\) | −61.6269 | −1.95764 | −0.978821 | − | 0.204716i | \(-0.934373\pi\) | ||||
−0.978821 | + | 0.204716i | \(0.934373\pi\) | |||||||
\(992\) | 41.8041 | 1.32728 | ||||||||
\(993\) | 3.51949 | 0.111688 | ||||||||
\(994\) | −6.33844 | −0.201043 | ||||||||
\(995\) | 7.38741 | 0.234197 | ||||||||
\(996\) | 1.10050 | 0.0348707 | ||||||||
\(997\) | 1.41529 | 0.0448226 | 0.0224113 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224113 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(998\) | 16.0725 | 0.508767 | ||||||||
\(999\) | −6.73206 | −0.212993 |
(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 | 4031.2.a.c.1.35 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.35 | ✓ | 61 | 1.1 | even | 1 | trivial |