Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.358038 | −0.206713 | −0.103357 | − | 0.994644i | \(-0.532958\pi\) | ||||
−0.103357 | + | 0.994644i | \(0.532958\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.12453 | 1.39733 | 0.698665 | − | 0.715449i | \(-0.253778\pi\) | ||||
0.698665 | + | 0.715449i | \(0.253778\pi\) | |||||||
\(6\) | 0.358038 | 0.146168 | ||||||||
\(7\) | −3.38298 | −1.27864 | −0.639322 | − | 0.768939i | \(-0.720785\pi\) | ||||
−0.639322 | + | 0.768939i | \(0.720785\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.87181 | −0.957270 | ||||||||
\(10\) | −3.12453 | −0.988062 | ||||||||
\(11\) | −3.00081 | −0.904778 | −0.452389 | − | 0.891821i | \(-0.649428\pi\) | ||||
−0.452389 | + | 0.891821i | \(0.649428\pi\) | |||||||
\(12\) | −0.358038 | −0.103357 | ||||||||
\(13\) | 5.58343 | 1.54856 | 0.774282 | − | 0.632841i | \(-0.218111\pi\) | ||||
0.774282 | + | 0.632841i | \(0.218111\pi\) | |||||||
\(14\) | 3.38298 | 0.904138 | ||||||||
\(15\) | −1.11870 | −0.288847 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.615120 | 0.149188 | 0.0745942 | − | 0.997214i | \(-0.476234\pi\) | ||||
0.0745942 | + | 0.997214i | \(0.476234\pi\) | |||||||
\(18\) | 2.87181 | 0.676892 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.12453 | 0.698665 | ||||||||
\(21\) | 1.21123 | 0.264313 | ||||||||
\(22\) | 3.00081 | 0.639774 | ||||||||
\(23\) | 7.17487 | 1.49606 | 0.748032 | − | 0.663663i | \(-0.230999\pi\) | ||||
0.748032 | + | 0.663663i | \(0.230999\pi\) | |||||||
\(24\) | 0.358038 | 0.0730841 | ||||||||
\(25\) | 4.76266 | 0.952532 | ||||||||
\(26\) | −5.58343 | −1.09500 | ||||||||
\(27\) | 2.10233 | 0.404593 | ||||||||
\(28\) | −3.38298 | −0.639322 | ||||||||
\(29\) | −1.35524 | −0.251662 | −0.125831 | − | 0.992052i | \(-0.540160\pi\) | ||||
−0.125831 | + | 0.992052i | \(0.540160\pi\) | |||||||
\(30\) | 1.11870 | 0.204245 | ||||||||
\(31\) | −6.18047 | −1.11004 | −0.555022 | − | 0.831835i | \(-0.687290\pi\) | ||||
−0.555022 | + | 0.831835i | \(0.687290\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.07440 | 0.187029 | ||||||||
\(34\) | −0.615120 | −0.105492 | ||||||||
\(35\) | −10.5702 | −1.78669 | ||||||||
\(36\) | −2.87181 | −0.478635 | ||||||||
\(37\) | 4.34611 | 0.714497 | 0.357248 | − | 0.934009i | \(-0.383715\pi\) | ||||
0.357248 | + | 0.934009i | \(0.383715\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −1.99908 | −0.320109 | ||||||||
\(40\) | −3.12453 | −0.494031 | ||||||||
\(41\) | −4.36696 | −0.682005 | −0.341002 | − | 0.940062i | \(-0.610766\pi\) | ||||
−0.341002 | + | 0.940062i | \(0.610766\pi\) | |||||||
\(42\) | −1.21123 | −0.186897 | ||||||||
\(43\) | −1.24575 | −0.189975 | −0.0949876 | − | 0.995478i | \(-0.530281\pi\) | ||||
−0.0949876 | + | 0.995478i | \(0.530281\pi\) | |||||||
\(44\) | −3.00081 | −0.452389 | ||||||||
\(45\) | −8.97304 | −1.33762 | ||||||||
\(46\) | −7.17487 | −1.05788 | ||||||||
\(47\) | −6.56595 | −0.957742 | −0.478871 | − | 0.877885i | \(-0.658954\pi\) | ||||
−0.478871 | + | 0.877885i | \(0.658954\pi\) | |||||||
\(48\) | −0.358038 | −0.0516783 | ||||||||
\(49\) | 4.44452 | 0.634932 | ||||||||
\(50\) | −4.76266 | −0.673542 | ||||||||
\(51\) | −0.220236 | −0.0308392 | ||||||||
\(52\) | 5.58343 | 0.774282 | ||||||||
\(53\) | 2.38333 | 0.327376 | 0.163688 | − | 0.986512i | \(-0.447661\pi\) | ||||
0.163688 | + | 0.986512i | \(0.447661\pi\) | |||||||
\(54\) | −2.10233 | −0.286091 | ||||||||
\(55\) | −9.37610 | −1.26427 | ||||||||
\(56\) | 3.38298 | 0.452069 | ||||||||
\(57\) | 0.358038 | 0.0474233 | ||||||||
\(58\) | 1.35524 | 0.177952 | ||||||||
\(59\) | −0.0783359 | −0.0101985 | −0.00509923 | − | 0.999987i | \(-0.501623\pi\) | ||||
−0.00509923 | + | 0.999987i | \(0.501623\pi\) | |||||||
\(60\) | −1.11870 | −0.144423 | ||||||||
\(61\) | −11.8770 | −1.52069 | −0.760346 | − | 0.649519i | \(-0.774970\pi\) | ||||
−0.760346 | + | 0.649519i | \(0.774970\pi\) | |||||||
\(62\) | 6.18047 | 0.784920 | ||||||||
\(63\) | 9.71526 | 1.22401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 17.4456 | 2.16386 | ||||||||
\(66\) | −1.07440 | −0.132250 | ||||||||
\(67\) | 1.93235 | 0.236074 | 0.118037 | − | 0.993009i | \(-0.462340\pi\) | ||||
0.118037 | + | 0.993009i | \(0.462340\pi\) | |||||||
\(68\) | 0.615120 | 0.0745942 | ||||||||
\(69\) | −2.56887 | −0.309256 | ||||||||
\(70\) | 10.5702 | 1.26338 | ||||||||
\(71\) | −8.93518 | −1.06041 | −0.530205 | − | 0.847869i | \(-0.677885\pi\) | ||||
−0.530205 | + | 0.847869i | \(0.677885\pi\) | |||||||
\(72\) | 2.87181 | 0.338446 | ||||||||
\(73\) | 2.99156 | 0.350136 | 0.175068 | − | 0.984556i | \(-0.443986\pi\) | ||||
0.175068 | + | 0.984556i | \(0.443986\pi\) | |||||||
\(74\) | −4.34611 | −0.505225 | ||||||||
\(75\) | −1.70521 | −0.196901 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 10.1517 | 1.15689 | ||||||||
\(78\) | 1.99908 | 0.226351 | ||||||||
\(79\) | 4.20610 | 0.473223 | 0.236611 | − | 0.971604i | \(-0.423963\pi\) | ||||
0.236611 | + | 0.971604i | \(0.423963\pi\) | |||||||
\(80\) | 3.12453 | 0.349333 | ||||||||
\(81\) | 7.86271 | 0.873635 | ||||||||
\(82\) | 4.36696 | 0.482250 | ||||||||
\(83\) | 7.46260 | 0.819127 | 0.409564 | − | 0.912282i | \(-0.365681\pi\) | ||||
0.409564 | + | 0.912282i | \(0.365681\pi\) | |||||||
\(84\) | 1.21123 | 0.132156 | ||||||||
\(85\) | 1.92196 | 0.208465 | ||||||||
\(86\) | 1.24575 | 0.134333 | ||||||||
\(87\) | 0.485227 | 0.0520218 | ||||||||
\(88\) | 3.00081 | 0.319887 | ||||||||
\(89\) | 4.41557 | 0.468050 | 0.234025 | − | 0.972231i | \(-0.424810\pi\) | ||||
0.234025 | + | 0.972231i | \(0.424810\pi\) | |||||||
\(90\) | 8.97304 | 0.945841 | ||||||||
\(91\) | −18.8886 | −1.98006 | ||||||||
\(92\) | 7.17487 | 0.748032 | ||||||||
\(93\) | 2.21284 | 0.229461 | ||||||||
\(94\) | 6.56595 | 0.677226 | ||||||||
\(95\) | −3.12453 | −0.320570 | ||||||||
\(96\) | 0.358038 | 0.0365421 | ||||||||
\(97\) | 13.5539 | 1.37619 | 0.688096 | − | 0.725620i | \(-0.258447\pi\) | ||||
0.688096 | + | 0.725620i | \(0.258447\pi\) | |||||||
\(98\) | −4.44452 | −0.448965 | ||||||||
\(99\) | 8.61775 | 0.866116 | ||||||||
\(100\) | 4.76266 | 0.476266 | ||||||||
\(101\) | 2.45726 | 0.244506 | 0.122253 | − | 0.992499i | \(-0.460988\pi\) | ||||
0.122253 | + | 0.992499i | \(0.460988\pi\) | |||||||
\(102\) | 0.220236 | 0.0218066 | ||||||||
\(103\) | −7.74280 | −0.762921 | −0.381461 | − | 0.924385i | \(-0.624579\pi\) | ||||
−0.381461 | + | 0.924385i | \(0.624579\pi\) | |||||||
\(104\) | −5.58343 | −0.547500 | ||||||||
\(105\) | 3.78453 | 0.369332 | ||||||||
\(106\) | −2.38333 | −0.231490 | ||||||||
\(107\) | 9.74932 | 0.942502 | 0.471251 | − | 0.881999i | \(-0.343803\pi\) | ||||
0.471251 | + | 0.881999i | \(0.343803\pi\) | |||||||
\(108\) | 2.10233 | 0.202297 | ||||||||
\(109\) | −1.84992 | −0.177191 | −0.0885953 | − | 0.996068i | \(-0.528238\pi\) | ||||
−0.0885953 | + | 0.996068i | \(0.528238\pi\) | |||||||
\(110\) | 9.37610 | 0.893976 | ||||||||
\(111\) | −1.55607 | −0.147696 | ||||||||
\(112\) | −3.38298 | −0.319661 | ||||||||
\(113\) | −10.8551 | −1.02117 | −0.510583 | − | 0.859828i | \(-0.670570\pi\) | ||||
−0.510583 | + | 0.859828i | \(0.670570\pi\) | |||||||
\(114\) | −0.358038 | −0.0335333 | ||||||||
\(115\) | 22.4181 | 2.09049 | ||||||||
\(116\) | −1.35524 | −0.125831 | ||||||||
\(117\) | −16.0345 | −1.48239 | ||||||||
\(118\) | 0.0783359 | 0.00721140 | ||||||||
\(119\) | −2.08093 | −0.190759 | ||||||||
\(120\) | 1.11870 | 0.102123 | ||||||||
\(121\) | −1.99515 | −0.181377 | ||||||||
\(122\) | 11.8770 | 1.07529 | ||||||||
\(123\) | 1.56354 | 0.140979 | ||||||||
\(124\) | −6.18047 | −0.555022 | ||||||||
\(125\) | −0.741577 | −0.0663287 | ||||||||
\(126\) | −9.71526 | −0.865504 | ||||||||
\(127\) | 3.98375 | 0.353500 | 0.176750 | − | 0.984256i | \(-0.443442\pi\) | ||||
0.176750 | + | 0.984256i | \(0.443442\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.446026 | 0.0392704 | ||||||||
\(130\) | −17.4456 | −1.53008 | ||||||||
\(131\) | −3.90039 | −0.340779 | −0.170389 | − | 0.985377i | \(-0.554503\pi\) | ||||
−0.170389 | + | 0.985377i | \(0.554503\pi\) | |||||||
\(132\) | 1.07440 | 0.0935147 | ||||||||
\(133\) | 3.38298 | 0.293341 | ||||||||
\(134\) | −1.93235 | −0.166929 | ||||||||
\(135\) | 6.56878 | 0.565351 | ||||||||
\(136\) | −0.615120 | −0.0527461 | ||||||||
\(137\) | −4.07235 | −0.347925 | −0.173962 | − | 0.984752i | \(-0.555657\pi\) | ||||
−0.173962 | + | 0.984752i | \(0.555657\pi\) | |||||||
\(138\) | 2.56887 | 0.218677 | ||||||||
\(139\) | −5.65075 | −0.479290 | −0.239645 | − | 0.970861i | \(-0.577031\pi\) | ||||
−0.239645 | + | 0.970861i | \(0.577031\pi\) | |||||||
\(140\) | −10.5702 | −0.893344 | ||||||||
\(141\) | 2.35086 | 0.197978 | ||||||||
\(142\) | 8.93518 | 0.749823 | ||||||||
\(143\) | −16.7548 | −1.40111 | ||||||||
\(144\) | −2.87181 | −0.239317 | ||||||||
\(145\) | −4.23448 | −0.351655 | ||||||||
\(146\) | −2.99156 | −0.247583 | ||||||||
\(147\) | −1.59131 | −0.131249 | ||||||||
\(148\) | 4.34611 | 0.357248 | ||||||||
\(149\) | 4.46885 | 0.366103 | 0.183051 | − | 0.983103i | \(-0.441403\pi\) | ||||
0.183051 | + | 0.983103i | \(0.441403\pi\) | |||||||
\(150\) | 1.70521 | 0.139230 | ||||||||
\(151\) | −3.01879 | −0.245665 | −0.122833 | − | 0.992427i | \(-0.539198\pi\) | ||||
−0.122833 | + | 0.992427i | \(0.539198\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −1.76651 | −0.142814 | ||||||||
\(154\) | −10.1517 | −0.818044 | ||||||||
\(155\) | −19.3110 | −1.55110 | ||||||||
\(156\) | −1.99908 | −0.160054 | ||||||||
\(157\) | 14.3364 | 1.14417 | 0.572084 | − | 0.820195i | \(-0.306135\pi\) | ||||
0.572084 | + | 0.820195i | \(0.306135\pi\) | |||||||
\(158\) | −4.20610 | −0.334619 | ||||||||
\(159\) | −0.853324 | −0.0676730 | ||||||||
\(160\) | −3.12453 | −0.247015 | ||||||||
\(161\) | −24.2724 | −1.91293 | ||||||||
\(162\) | −7.86271 | −0.617753 | ||||||||
\(163\) | −16.1862 | −1.26780 | −0.633902 | − | 0.773413i | \(-0.718548\pi\) | ||||
−0.633902 | + | 0.773413i | \(0.718548\pi\) | |||||||
\(164\) | −4.36696 | −0.341002 | ||||||||
\(165\) | 3.35700 | 0.261342 | ||||||||
\(166\) | −7.46260 | −0.579210 | ||||||||
\(167\) | −16.2282 | −1.25578 | −0.627888 | − | 0.778304i | \(-0.716080\pi\) | ||||
−0.627888 | + | 0.778304i | \(0.716080\pi\) | |||||||
\(168\) | −1.21123 | −0.0934486 | ||||||||
\(169\) | 18.1747 | 1.39805 | ||||||||
\(170\) | −1.92196 | −0.147407 | ||||||||
\(171\) | 2.87181 | 0.219613 | ||||||||
\(172\) | −1.24575 | −0.0949876 | ||||||||
\(173\) | 12.7558 | 0.969804 | 0.484902 | − | 0.874568i | \(-0.338855\pi\) | ||||
0.484902 | + | 0.874568i | \(0.338855\pi\) | |||||||
\(174\) | −0.485227 | −0.0367850 | ||||||||
\(175\) | −16.1120 | −1.21795 | ||||||||
\(176\) | −3.00081 | −0.226194 | ||||||||
\(177\) | 0.0280472 | 0.00210816 | ||||||||
\(178\) | −4.41557 | −0.330961 | ||||||||
\(179\) | −4.28228 | −0.320073 | −0.160036 | − | 0.987111i | \(-0.551161\pi\) | ||||
−0.160036 | + | 0.987111i | \(0.551161\pi\) | |||||||
\(180\) | −8.97304 | −0.668811 | ||||||||
\(181\) | −0.0191058 | −0.00142012 | −0.000710061 | − | 1.00000i | \(-0.500226\pi\) | ||||
−0.000710061 | 1.00000i | \(0.500226\pi\) | ||||||||
\(182\) | 18.8886 | 1.40012 | ||||||||
\(183\) | 4.25241 | 0.314347 | ||||||||
\(184\) | −7.17487 | −0.528938 | ||||||||
\(185\) | 13.5795 | 0.998388 | ||||||||
\(186\) | −2.21284 | −0.162253 | ||||||||
\(187\) | −1.84586 | −0.134982 | ||||||||
\(188\) | −6.56595 | −0.478871 | ||||||||
\(189\) | −7.11213 | −0.517331 | ||||||||
\(190\) | 3.12453 | 0.226677 | ||||||||
\(191\) | −27.2759 | −1.97361 | −0.986807 | − | 0.161903i | \(-0.948237\pi\) | ||||
−0.986807 | + | 0.161903i | \(0.948237\pi\) | |||||||
\(192\) | −0.358038 | −0.0258391 | ||||||||
\(193\) | −17.1033 | −1.23113 | −0.615563 | − | 0.788088i | \(-0.711071\pi\) | ||||
−0.615563 | + | 0.788088i | \(0.711071\pi\) | |||||||
\(194\) | −13.5539 | −0.973115 | ||||||||
\(195\) | −6.24617 | −0.447297 | ||||||||
\(196\) | 4.44452 | 0.317466 | ||||||||
\(197\) | −6.67123 | −0.475305 | −0.237653 | − | 0.971350i | \(-0.576378\pi\) | ||||
−0.237653 | + | 0.971350i | \(0.576378\pi\) | |||||||
\(198\) | −8.61775 | −0.612437 | ||||||||
\(199\) | −11.7554 | −0.833321 | −0.416661 | − | 0.909062i | \(-0.636800\pi\) | ||||
−0.416661 | + | 0.909062i | \(0.636800\pi\) | |||||||
\(200\) | −4.76266 | −0.336771 | ||||||||
\(201\) | −0.691853 | −0.0487996 | ||||||||
\(202\) | −2.45726 | −0.172892 | ||||||||
\(203\) | 4.58475 | 0.321786 | ||||||||
\(204\) | −0.220236 | −0.0154196 | ||||||||
\(205\) | −13.6447 | −0.952986 | ||||||||
\(206\) | 7.74280 | 0.539467 | ||||||||
\(207\) | −20.6048 | −1.43214 | ||||||||
\(208\) | 5.58343 | 0.387141 | ||||||||
\(209\) | 3.00081 | 0.207570 | ||||||||
\(210\) | −3.78453 | −0.261157 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 2.38333 | 0.163688 | ||||||||
\(213\) | 3.19913 | 0.219201 | ||||||||
\(214\) | −9.74932 | −0.666450 | ||||||||
\(215\) | −3.89238 | −0.265458 | ||||||||
\(216\) | −2.10233 | −0.143045 | ||||||||
\(217\) | 20.9084 | 1.41935 | ||||||||
\(218\) | 1.84992 | 0.125293 | ||||||||
\(219\) | −1.07109 | −0.0723776 | ||||||||
\(220\) | −9.37610 | −0.632137 | ||||||||
\(221\) | 3.43448 | 0.231028 | ||||||||
\(222\) | 1.55607 | 0.104437 | ||||||||
\(223\) | 4.71137 | 0.315497 | 0.157748 | − | 0.987479i | \(-0.449577\pi\) | ||||
0.157748 | + | 0.987479i | \(0.449577\pi\) | |||||||
\(224\) | 3.38298 | 0.226035 | ||||||||
\(225\) | −13.6774 | −0.911830 | ||||||||
\(226\) | 10.8551 | 0.722074 | ||||||||
\(227\) | 23.1619 | 1.53731 | 0.768655 | − | 0.639663i | \(-0.220926\pi\) | ||||
0.768655 | + | 0.639663i | \(0.220926\pi\) | |||||||
\(228\) | 0.358038 | 0.0237116 | ||||||||
\(229\) | −12.7547 | −0.842854 | −0.421427 | − | 0.906862i | \(-0.638471\pi\) | ||||
−0.421427 | + | 0.906862i | \(0.638471\pi\) | |||||||
\(230\) | −22.4181 | −1.47820 | ||||||||
\(231\) | −3.63468 | −0.239144 | ||||||||
\(232\) | 1.35524 | 0.0889759 | ||||||||
\(233\) | 14.8648 | 0.973827 | 0.486914 | − | 0.873450i | \(-0.338123\pi\) | ||||
0.486914 | + | 0.873450i | \(0.338123\pi\) | |||||||
\(234\) | 16.0345 | 1.04821 | ||||||||
\(235\) | −20.5155 | −1.33828 | ||||||||
\(236\) | −0.0783359 | −0.00509923 | ||||||||
\(237\) | −1.50594 | −0.0978214 | ||||||||
\(238\) | 2.08093 | 0.134887 | ||||||||
\(239\) | 4.70178 | 0.304133 | 0.152066 | − | 0.988370i | \(-0.451407\pi\) | ||||
0.152066 | + | 0.988370i | \(0.451407\pi\) | |||||||
\(240\) | −1.11870 | −0.0722116 | ||||||||
\(241\) | 1.84635 | 0.118934 | 0.0594671 | − | 0.998230i | \(-0.481060\pi\) | ||||
0.0594671 | + | 0.998230i | \(0.481060\pi\) | |||||||
\(242\) | 1.99515 | 0.128253 | ||||||||
\(243\) | −9.12214 | −0.585185 | ||||||||
\(244\) | −11.8770 | −0.760346 | ||||||||
\(245\) | 13.8870 | 0.887209 | ||||||||
\(246\) | −1.56354 | −0.0996875 | ||||||||
\(247\) | −5.58343 | −0.355265 | ||||||||
\(248\) | 6.18047 | 0.392460 | ||||||||
\(249\) | −2.67189 | −0.169324 | ||||||||
\(250\) | 0.741577 | 0.0469015 | ||||||||
\(251\) | −10.7902 | −0.681069 | −0.340534 | − | 0.940232i | \(-0.610608\pi\) | ||||
−0.340534 | + | 0.940232i | \(0.610608\pi\) | |||||||
\(252\) | 9.71526 | 0.612004 | ||||||||
\(253\) | −21.5304 | −1.35360 | ||||||||
\(254\) | −3.98375 | −0.249963 | ||||||||
\(255\) | −0.688133 | −0.0430926 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.57704 | −0.535021 | −0.267510 | − | 0.963555i | \(-0.586201\pi\) | ||||
−0.267510 | + | 0.963555i | \(0.586201\pi\) | |||||||
\(258\) | −0.446026 | −0.0277684 | ||||||||
\(259\) | −14.7028 | −0.913587 | ||||||||
\(260\) | 17.4456 | 1.08193 | ||||||||
\(261\) | 3.89199 | 0.240908 | ||||||||
\(262\) | 3.90039 | 0.240967 | ||||||||
\(263\) | 6.01493 | 0.370896 | 0.185448 | − | 0.982654i | \(-0.440626\pi\) | ||||
0.185448 | + | 0.982654i | \(0.440626\pi\) | |||||||
\(264\) | −1.07440 | −0.0661249 | ||||||||
\(265\) | 7.44679 | 0.457453 | ||||||||
\(266\) | −3.38298 | −0.207424 | ||||||||
\(267\) | −1.58094 | −0.0967521 | ||||||||
\(268\) | 1.93235 | 0.118037 | ||||||||
\(269\) | −8.11925 | −0.495039 | −0.247520 | − | 0.968883i | \(-0.579615\pi\) | ||||
−0.247520 | + | 0.968883i | \(0.579615\pi\) | |||||||
\(270\) | −6.56878 | −0.399763 | ||||||||
\(271\) | 4.06018 | 0.246638 | 0.123319 | − | 0.992367i | \(-0.460646\pi\) | ||||
0.123319 | + | 0.992367i | \(0.460646\pi\) | |||||||
\(272\) | 0.615120 | 0.0372971 | ||||||||
\(273\) | 6.76283 | 0.409305 | ||||||||
\(274\) | 4.07235 | 0.246020 | ||||||||
\(275\) | −14.2918 | −0.861829 | ||||||||
\(276\) | −2.56887 | −0.154628 | ||||||||
\(277\) | −8.51449 | −0.511586 | −0.255793 | − | 0.966732i | \(-0.582337\pi\) | ||||
−0.255793 | + | 0.966732i | \(0.582337\pi\) | |||||||
\(278\) | 5.65075 | 0.338909 | ||||||||
\(279\) | 17.7491 | 1.06261 | ||||||||
\(280\) | 10.5702 | 0.631690 | ||||||||
\(281\) | 3.50678 | 0.209197 | 0.104599 | − | 0.994515i | \(-0.466644\pi\) | ||||
0.104599 | + | 0.994515i | \(0.466644\pi\) | |||||||
\(282\) | −2.35086 | −0.139992 | ||||||||
\(283\) | −16.1688 | −0.961137 | −0.480568 | − | 0.876957i | \(-0.659570\pi\) | ||||
−0.480568 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(284\) | −8.93518 | −0.530205 | ||||||||
\(285\) | 1.11870 | 0.0662659 | ||||||||
\(286\) | 16.7548 | 0.990732 | ||||||||
\(287\) | 14.7733 | 0.872042 | ||||||||
\(288\) | 2.87181 | 0.169223 | ||||||||
\(289\) | −16.6216 | −0.977743 | ||||||||
\(290\) | 4.23448 | 0.248657 | ||||||||
\(291\) | −4.85281 | −0.284477 | ||||||||
\(292\) | 2.99156 | 0.175068 | ||||||||
\(293\) | −10.2467 | −0.598617 | −0.299308 | − | 0.954156i | \(-0.596756\pi\) | ||||
−0.299308 | + | 0.954156i | \(0.596756\pi\) | |||||||
\(294\) | 1.59131 | 0.0928069 | ||||||||
\(295\) | −0.244763 | −0.0142506 | ||||||||
\(296\) | −4.34611 | −0.252613 | ||||||||
\(297\) | −6.30869 | −0.366067 | ||||||||
\(298\) | −4.46885 | −0.258874 | ||||||||
\(299\) | 40.0604 | 2.31675 | ||||||||
\(300\) | −1.70521 | −0.0984504 | ||||||||
\(301\) | 4.21434 | 0.242911 | ||||||||
\(302\) | 3.01879 | 0.173712 | ||||||||
\(303\) | −0.879791 | −0.0505426 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −37.1099 | −2.12491 | ||||||||
\(306\) | 1.76651 | 0.100984 | ||||||||
\(307\) | 3.54653 | 0.202411 | 0.101206 | − | 0.994866i | \(-0.467730\pi\) | ||||
0.101206 | + | 0.994866i | \(0.467730\pi\) | |||||||
\(308\) | 10.1517 | 0.578444 | ||||||||
\(309\) | 2.77222 | 0.157706 | ||||||||
\(310\) | 19.3110 | 1.09679 | ||||||||
\(311\) | −10.8457 | −0.615003 | −0.307501 | − | 0.951548i | \(-0.599493\pi\) | ||||
−0.307501 | + | 0.951548i | \(0.599493\pi\) | |||||||
\(312\) | 1.99908 | 0.113175 | ||||||||
\(313\) | −4.14525 | −0.234303 | −0.117152 | − | 0.993114i | \(-0.537376\pi\) | ||||
−0.117152 | + | 0.993114i | \(0.537376\pi\) | |||||||
\(314\) | −14.3364 | −0.809050 | ||||||||
\(315\) | 30.3556 | 1.71034 | ||||||||
\(316\) | 4.20610 | 0.236611 | ||||||||
\(317\) | 20.3736 | 1.14430 | 0.572148 | − | 0.820150i | \(-0.306110\pi\) | ||||
0.572148 | + | 0.820150i | \(0.306110\pi\) | |||||||
\(318\) | 0.853324 | 0.0478520 | ||||||||
\(319\) | 4.06682 | 0.227698 | ||||||||
\(320\) | 3.12453 | 0.174666 | ||||||||
\(321\) | −3.49062 | −0.194828 | ||||||||
\(322\) | 24.2724 | 1.35265 | ||||||||
\(323\) | −0.615120 | −0.0342262 | ||||||||
\(324\) | 7.86271 | 0.436817 | ||||||||
\(325\) | 26.5920 | 1.47506 | ||||||||
\(326\) | 16.1862 | 0.896473 | ||||||||
\(327\) | 0.662343 | 0.0366276 | ||||||||
\(328\) | 4.36696 | 0.241125 | ||||||||
\(329\) | 22.2124 | 1.22461 | ||||||||
\(330\) | −3.35700 | −0.184797 | ||||||||
\(331\) | −15.1441 | −0.832394 | −0.416197 | − | 0.909274i | \(-0.636637\pi\) | ||||
−0.416197 | + | 0.909274i | \(0.636637\pi\) | |||||||
\(332\) | 7.46260 | 0.409564 | ||||||||
\(333\) | −12.4812 | −0.683966 | ||||||||
\(334\) | 16.2282 | 0.887968 | ||||||||
\(335\) | 6.03767 | 0.329873 | ||||||||
\(336\) | 1.21123 | 0.0660782 | ||||||||
\(337\) | −13.4583 | −0.733122 | −0.366561 | − | 0.930394i | \(-0.619465\pi\) | ||||
−0.366561 | + | 0.930394i | \(0.619465\pi\) | |||||||
\(338\) | −18.1747 | −0.988572 | ||||||||
\(339\) | 3.88655 | 0.211089 | ||||||||
\(340\) | 1.92196 | 0.104233 | ||||||||
\(341\) | 18.5464 | 1.00434 | ||||||||
\(342\) | −2.87181 | −0.155290 | ||||||||
\(343\) | 8.64512 | 0.466793 | ||||||||
\(344\) | 1.24575 | 0.0671664 | ||||||||
\(345\) | −8.02651 | −0.432133 | ||||||||
\(346\) | −12.7558 | −0.685755 | ||||||||
\(347\) | −32.6416 | −1.75229 | −0.876147 | − | 0.482043i | \(-0.839895\pi\) | ||||
−0.876147 | + | 0.482043i | \(0.839895\pi\) | |||||||
\(348\) | 0.485227 | 0.0260109 | ||||||||
\(349\) | −18.0042 | −0.963742 | −0.481871 | − | 0.876242i | \(-0.660043\pi\) | ||||
−0.481871 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(350\) | 16.1120 | 0.861220 | ||||||||
\(351\) | 11.7382 | 0.626539 | ||||||||
\(352\) | 3.00081 | 0.159944 | ||||||||
\(353\) | −29.7728 | −1.58465 | −0.792323 | − | 0.610102i | \(-0.791128\pi\) | ||||
−0.792323 | + | 0.610102i | \(0.791128\pi\) | |||||||
\(354\) | −0.0280472 | −0.00149069 | ||||||||
\(355\) | −27.9182 | −1.48174 | ||||||||
\(356\) | 4.41557 | 0.234025 | ||||||||
\(357\) | 0.745053 | 0.0394324 | ||||||||
\(358\) | 4.28228 | 0.226325 | ||||||||
\(359\) | −32.1488 | −1.69675 | −0.848373 | − | 0.529398i | \(-0.822418\pi\) | ||||
−0.848373 | + | 0.529398i | \(0.822418\pi\) | |||||||
\(360\) | 8.97304 | 0.472921 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.0191058 | 0.00100418 | ||||||||
\(363\) | 0.714340 | 0.0374931 | ||||||||
\(364\) | −18.8886 | −0.990032 | ||||||||
\(365\) | 9.34721 | 0.489255 | ||||||||
\(366\) | −4.25241 | −0.222277 | ||||||||
\(367\) | 24.4044 | 1.27390 | 0.636951 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636951 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(368\) | 7.17487 | 0.374016 | ||||||||
\(369\) | 12.5411 | 0.652863 | ||||||||
\(370\) | −13.5795 | −0.705967 | ||||||||
\(371\) | −8.06276 | −0.418598 | ||||||||
\(372\) | 2.21284 | 0.114730 | ||||||||
\(373\) | −24.2893 | −1.25765 | −0.628826 | − | 0.777546i | \(-0.716464\pi\) | ||||
−0.628826 | + | 0.777546i | \(0.716464\pi\) | |||||||
\(374\) | 1.84586 | 0.0954469 | ||||||||
\(375\) | 0.265513 | 0.0137110 | ||||||||
\(376\) | 6.56595 | 0.338613 | ||||||||
\(377\) | −7.56689 | −0.389715 | ||||||||
\(378\) | 7.11213 | 0.365808 | ||||||||
\(379\) | 10.7478 | 0.552077 | 0.276038 | − | 0.961147i | \(-0.410978\pi\) | ||||
0.276038 | + | 0.961147i | \(0.410978\pi\) | |||||||
\(380\) | −3.12453 | −0.160285 | ||||||||
\(381\) | −1.42633 | −0.0730732 | ||||||||
\(382\) | 27.2759 | 1.39556 | ||||||||
\(383\) | −21.1458 | −1.08050 | −0.540249 | − | 0.841505i | \(-0.681670\pi\) | ||||
−0.540249 | + | 0.841505i | \(0.681670\pi\) | |||||||
\(384\) | 0.358038 | 0.0182710 | ||||||||
\(385\) | 31.7191 | 1.61656 | ||||||||
\(386\) | 17.1033 | 0.870537 | ||||||||
\(387\) | 3.57756 | 0.181858 | ||||||||
\(388\) | 13.5539 | 0.688096 | ||||||||
\(389\) | 10.0628 | 0.510206 | 0.255103 | − | 0.966914i | \(-0.417891\pi\) | ||||
0.255103 | + | 0.966914i | \(0.417891\pi\) | |||||||
\(390\) | 6.24617 | 0.316287 | ||||||||
\(391\) | 4.41340 | 0.223195 | ||||||||
\(392\) | −4.44452 | −0.224482 | ||||||||
\(393\) | 1.39649 | 0.0704434 | ||||||||
\(394\) | 6.67123 | 0.336091 | ||||||||
\(395\) | 13.1421 | 0.661248 | ||||||||
\(396\) | 8.61775 | 0.433058 | ||||||||
\(397\) | 16.9112 | 0.848748 | 0.424374 | − | 0.905487i | \(-0.360494\pi\) | ||||
0.424374 | + | 0.905487i | \(0.360494\pi\) | |||||||
\(398\) | 11.7554 | 0.589247 | ||||||||
\(399\) | −1.21123 | −0.0606375 | ||||||||
\(400\) | 4.76266 | 0.238133 | ||||||||
\(401\) | 26.5788 | 1.32728 | 0.663641 | − | 0.748051i | \(-0.269010\pi\) | ||||
0.663641 | + | 0.748051i | \(0.269010\pi\) | |||||||
\(402\) | 0.691853 | 0.0345065 | ||||||||
\(403\) | −34.5082 | −1.71898 | ||||||||
\(404\) | 2.45726 | 0.122253 | ||||||||
\(405\) | 24.5672 | 1.22076 | ||||||||
\(406\) | −4.58475 | −0.227537 | ||||||||
\(407\) | −13.0419 | −0.646461 | ||||||||
\(408\) | 0.220236 | 0.0109033 | ||||||||
\(409\) | −8.32028 | −0.411412 | −0.205706 | − | 0.978614i | \(-0.565949\pi\) | ||||
−0.205706 | + | 0.978614i | \(0.565949\pi\) | |||||||
\(410\) | 13.6447 | 0.673863 | ||||||||
\(411\) | 1.45806 | 0.0719206 | ||||||||
\(412\) | −7.74280 | −0.381461 | ||||||||
\(413\) | 0.265008 | 0.0130402 | ||||||||
\(414\) | 20.6048 | 1.01267 | ||||||||
\(415\) | 23.3171 | 1.14459 | ||||||||
\(416\) | −5.58343 | −0.273750 | ||||||||
\(417\) | 2.02318 | 0.0990756 | ||||||||
\(418\) | −3.00081 | −0.146774 | ||||||||
\(419\) | −32.8304 | −1.60387 | −0.801935 | − | 0.597411i | \(-0.796196\pi\) | ||||
−0.801935 | + | 0.597411i | \(0.796196\pi\) | |||||||
\(420\) | 3.78453 | 0.184666 | ||||||||
\(421\) | 2.12978 | 0.103799 | 0.0518994 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0518994 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(422\) | 1.00000 | 0.0486792 | ||||||||
\(423\) | 18.8562 | 0.916817 | ||||||||
\(424\) | −2.38333 | −0.115745 | ||||||||
\(425\) | 2.92960 | 0.142107 | ||||||||
\(426\) | −3.19913 | −0.154998 | ||||||||
\(427\) | 40.1795 | 1.94442 | ||||||||
\(428\) | 9.74932 | 0.471251 | ||||||||
\(429\) | 5.99885 | 0.289627 | ||||||||
\(430\) | 3.89238 | 0.187707 | ||||||||
\(431\) | −33.8992 | −1.63286 | −0.816432 | − | 0.577441i | \(-0.804051\pi\) | ||||
−0.816432 | + | 0.577441i | \(0.804051\pi\) | |||||||
\(432\) | 2.10233 | 0.101148 | ||||||||
\(433\) | 0.554211 | 0.0266337 | 0.0133168 | − | 0.999911i | \(-0.495761\pi\) | ||||
0.0133168 | + | 0.999911i | \(0.495761\pi\) | |||||||
\(434\) | −20.9084 | −1.00363 | ||||||||
\(435\) | 1.51610 | 0.0726917 | ||||||||
\(436\) | −1.84992 | −0.0885953 | ||||||||
\(437\) | −7.17487 | −0.343220 | ||||||||
\(438\) | 1.07109 | 0.0511787 | ||||||||
\(439\) | 21.5358 | 1.02785 | 0.513923 | − | 0.857837i | \(-0.328192\pi\) | ||||
0.513923 | + | 0.857837i | \(0.328192\pi\) | |||||||
\(440\) | 9.37610 | 0.446988 | ||||||||
\(441\) | −12.7638 | −0.607801 | ||||||||
\(442\) | −3.43448 | −0.163361 | ||||||||
\(443\) | −19.3598 | −0.919812 | −0.459906 | − | 0.887968i | \(-0.652117\pi\) | ||||
−0.459906 | + | 0.887968i | \(0.652117\pi\) | |||||||
\(444\) | −1.55607 | −0.0738479 | ||||||||
\(445\) | 13.7966 | 0.654020 | ||||||||
\(446\) | −4.71137 | −0.223090 | ||||||||
\(447\) | −1.60002 | −0.0756783 | ||||||||
\(448\) | −3.38298 | −0.159831 | ||||||||
\(449\) | −28.3635 | −1.33855 | −0.669277 | − | 0.743013i | \(-0.733396\pi\) | ||||
−0.669277 | + | 0.743013i | \(0.733396\pi\) | |||||||
\(450\) | 13.6774 | 0.644761 | ||||||||
\(451\) | 13.1044 | 0.617063 | ||||||||
\(452\) | −10.8551 | −0.510583 | ||||||||
\(453\) | 1.08084 | 0.0507823 | ||||||||
\(454\) | −23.1619 | −1.08704 | ||||||||
\(455\) | −59.0179 | −2.76680 | ||||||||
\(456\) | −0.358038 | −0.0167667 | ||||||||
\(457\) | −1.65460 | −0.0773989 | −0.0386994 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386994 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(458\) | 12.7547 | 0.595988 | ||||||||
\(459\) | 1.29318 | 0.0603606 | ||||||||
\(460\) | 22.4181 | 1.04525 | ||||||||
\(461\) | 39.2786 | 1.82939 | 0.914693 | − | 0.404149i | \(-0.132432\pi\) | ||||
0.914693 | + | 0.404149i | \(0.132432\pi\) | |||||||
\(462\) | 3.63468 | 0.169100 | ||||||||
\(463\) | 15.0384 | 0.698892 | 0.349446 | − | 0.936957i | \(-0.386370\pi\) | ||||
0.349446 | + | 0.936957i | \(0.386370\pi\) | |||||||
\(464\) | −1.35524 | −0.0629155 | ||||||||
\(465\) | 6.91408 | 0.320633 | ||||||||
\(466\) | −14.8648 | −0.688600 | ||||||||
\(467\) | −13.5231 | −0.625773 | −0.312886 | − | 0.949791i | \(-0.601296\pi\) | ||||
−0.312886 | + | 0.949791i | \(0.601296\pi\) | |||||||
\(468\) | −16.0345 | −0.741197 | ||||||||
\(469\) | −6.53709 | −0.301855 | ||||||||
\(470\) | 20.5155 | 0.946308 | ||||||||
\(471\) | −5.13297 | −0.236515 | ||||||||
\(472\) | 0.0783359 | 0.00360570 | ||||||||
\(473\) | 3.73826 | 0.171885 | ||||||||
\(474\) | 1.50594 | 0.0691702 | ||||||||
\(475\) | −4.76266 | −0.218526 | ||||||||
\(476\) | −2.08093 | −0.0953795 | ||||||||
\(477\) | −6.84448 | −0.313387 | ||||||||
\(478\) | −4.70178 | −0.215054 | ||||||||
\(479\) | −16.7659 | −0.766055 | −0.383027 | − | 0.923737i | \(-0.625118\pi\) | ||||
−0.383027 | + | 0.923737i | \(0.625118\pi\) | |||||||
\(480\) | 1.11870 | 0.0510613 | ||||||||
\(481\) | 24.2662 | 1.10644 | ||||||||
\(482\) | −1.84635 | −0.0840992 | ||||||||
\(483\) | 8.69043 | 0.395428 | ||||||||
\(484\) | −1.99515 | −0.0906887 | ||||||||
\(485\) | 42.3496 | 1.92299 | ||||||||
\(486\) | 9.12214 | 0.413788 | ||||||||
\(487\) | −21.8167 | −0.988611 | −0.494305 | − | 0.869288i | \(-0.664578\pi\) | ||||
−0.494305 | + | 0.869288i | \(0.664578\pi\) | |||||||
\(488\) | 11.8770 | 0.537646 | ||||||||
\(489\) | 5.79529 | 0.262072 | ||||||||
\(490\) | −13.8870 | −0.627352 | ||||||||
\(491\) | 18.8936 | 0.852657 | 0.426329 | − | 0.904568i | \(-0.359807\pi\) | ||||
0.426329 | + | 0.904568i | \(0.359807\pi\) | |||||||
\(492\) | 1.56354 | 0.0704897 | ||||||||
\(493\) | −0.833635 | −0.0375450 | ||||||||
\(494\) | 5.58343 | 0.251210 | ||||||||
\(495\) | 26.9264 | 1.21025 | ||||||||
\(496\) | −6.18047 | −0.277511 | ||||||||
\(497\) | 30.2275 | 1.35589 | ||||||||
\(498\) | 2.67189 | 0.119730 | ||||||||
\(499\) | −19.8282 | −0.887634 | −0.443817 | − | 0.896117i | \(-0.646376\pi\) | ||||
−0.443817 | + | 0.896117i | \(0.646376\pi\) | |||||||
\(500\) | −0.741577 | −0.0331643 | ||||||||
\(501\) | 5.81031 | 0.259586 | ||||||||
\(502\) | 10.7902 | 0.481588 | ||||||||
\(503\) | −8.98579 | −0.400657 | −0.200328 | − | 0.979729i | \(-0.564201\pi\) | ||||
−0.200328 | + | 0.979729i | \(0.564201\pi\) | |||||||
\(504\) | −9.71526 | −0.432752 | ||||||||
\(505\) | 7.67776 | 0.341656 | ||||||||
\(506\) | 21.5304 | 0.957143 | ||||||||
\(507\) | −6.50722 | −0.288996 | ||||||||
\(508\) | 3.98375 | 0.176750 | ||||||||
\(509\) | −12.9747 | −0.575093 | −0.287546 | − | 0.957767i | \(-0.592840\pi\) | ||||
−0.287546 | + | 0.957767i | \(0.592840\pi\) | |||||||
\(510\) | 0.688133 | 0.0304710 | ||||||||
\(511\) | −10.1204 | −0.447699 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.10233 | −0.0928201 | ||||||||
\(514\) | 8.57704 | 0.378317 | ||||||||
\(515\) | −24.1926 | −1.06605 | ||||||||
\(516\) | 0.446026 | 0.0196352 | ||||||||
\(517\) | 19.7032 | 0.866544 | ||||||||
\(518\) | 14.7028 | 0.646004 | ||||||||
\(519\) | −4.56705 | −0.200471 | ||||||||
\(520\) | −17.4456 | −0.765039 | ||||||||
\(521\) | −29.2714 | −1.28240 | −0.641201 | − | 0.767373i | \(-0.721563\pi\) | ||||
−0.641201 | + | 0.767373i | \(0.721563\pi\) | |||||||
\(522\) | −3.89199 | −0.170348 | ||||||||
\(523\) | −3.09694 | −0.135420 | −0.0677099 | − | 0.997705i | \(-0.521569\pi\) | ||||
−0.0677099 | + | 0.997705i | \(0.521569\pi\) | |||||||
\(524\) | −3.90039 | −0.170389 | ||||||||
\(525\) | 5.76869 | 0.251766 | ||||||||
\(526\) | −6.01493 | −0.262263 | ||||||||
\(527\) | −3.80173 | −0.165606 | ||||||||
\(528\) | 1.07440 | 0.0467574 | ||||||||
\(529\) | 28.4787 | 1.23821 | ||||||||
\(530\) | −7.44679 | −0.323468 | ||||||||
\(531\) | 0.224966 | 0.00976268 | ||||||||
\(532\) | 3.38298 | 0.146671 | ||||||||
\(533\) | −24.3826 | −1.05613 | ||||||||
\(534\) | 1.58094 | 0.0684141 | ||||||||
\(535\) | 30.4620 | 1.31699 | ||||||||
\(536\) | −1.93235 | −0.0834647 | ||||||||
\(537\) | 1.53322 | 0.0661632 | ||||||||
\(538\) | 8.11925 | 0.350046 | ||||||||
\(539\) | −13.3372 | −0.574472 | ||||||||
\(540\) | 6.56878 | 0.282675 | ||||||||
\(541\) | 28.7730 | 1.23705 | 0.618524 | − | 0.785766i | \(-0.287731\pi\) | ||||
0.618524 | + | 0.785766i | \(0.287731\pi\) | |||||||
\(542\) | −4.06018 | −0.174400 | ||||||||
\(543\) | 0.00684059 | 0.000293558 0 | ||||||||
\(544\) | −0.615120 | −0.0263730 | ||||||||
\(545\) | −5.78014 | −0.247594 | ||||||||
\(546\) | −6.76283 | −0.289422 | ||||||||
\(547\) | −36.6068 | −1.56519 | −0.782597 | − | 0.622529i | \(-0.786105\pi\) | ||||
−0.782597 | + | 0.622529i | \(0.786105\pi\) | |||||||
\(548\) | −4.07235 | −0.173962 | ||||||||
\(549\) | 34.1084 | 1.45571 | ||||||||
\(550\) | 14.2918 | 0.609405 | ||||||||
\(551\) | 1.35524 | 0.0577352 | ||||||||
\(552\) | 2.56887 | 0.109338 | ||||||||
\(553\) | −14.2291 | −0.605084 | ||||||||
\(554\) | 8.51449 | 0.361746 | ||||||||
\(555\) | −4.86199 | −0.206380 | ||||||||
\(556\) | −5.65075 | −0.239645 | ||||||||
\(557\) | −0.621524 | −0.0263348 | −0.0131674 | − | 0.999913i | \(-0.504191\pi\) | ||||
−0.0131674 | + | 0.999913i | \(0.504191\pi\) | |||||||
\(558\) | −17.7491 | −0.751380 | ||||||||
\(559\) | −6.95556 | −0.294189 | ||||||||
\(560\) | −10.5702 | −0.446672 | ||||||||
\(561\) | 0.660886 | 0.0279026 | ||||||||
\(562\) | −3.50678 | −0.147925 | ||||||||
\(563\) | −27.1266 | −1.14325 | −0.571625 | − | 0.820515i | \(-0.693687\pi\) | ||||
−0.571625 | + | 0.820515i | \(0.693687\pi\) | |||||||
\(564\) | 2.35086 | 0.0989890 | ||||||||
\(565\) | −33.9172 | −1.42691 | ||||||||
\(566\) | 16.1688 | 0.679626 | ||||||||
\(567\) | −26.5994 | −1.11707 | ||||||||
\(568\) | 8.93518 | 0.374912 | ||||||||
\(569\) | 12.7725 | 0.535451 | 0.267726 | − | 0.963495i | \(-0.413728\pi\) | ||||
0.267726 | + | 0.963495i | \(0.413728\pi\) | |||||||
\(570\) | −1.11870 | −0.0468571 | ||||||||
\(571\) | 16.4930 | 0.690209 | 0.345104 | − | 0.938564i | \(-0.387844\pi\) | ||||
0.345104 | + | 0.938564i | \(0.387844\pi\) | |||||||
\(572\) | −16.7548 | −0.700553 | ||||||||
\(573\) | 9.76579 | 0.407972 | ||||||||
\(574\) | −14.7733 | −0.616627 | ||||||||
\(575\) | 34.1714 | 1.42505 | ||||||||
\(576\) | −2.87181 | −0.119659 | ||||||||
\(577\) | 16.2653 | 0.677132 | 0.338566 | − | 0.940943i | \(-0.390058\pi\) | ||||
0.338566 | + | 0.940943i | \(0.390058\pi\) | |||||||
\(578\) | 16.6216 | 0.691369 | ||||||||
\(579\) | 6.12364 | 0.254490 | ||||||||
\(580\) | −4.23448 | −0.175827 | ||||||||
\(581\) | −25.2458 | −1.04737 | ||||||||
\(582\) | 4.85281 | 0.201156 | ||||||||
\(583\) | −7.15193 | −0.296203 | ||||||||
\(584\) | −2.99156 | −0.123792 | ||||||||
\(585\) | −50.1003 | −2.07139 | ||||||||
\(586\) | 10.2467 | 0.423286 | ||||||||
\(587\) | 47.0653 | 1.94259 | 0.971296 | − | 0.237873i | \(-0.0764501\pi\) | ||||
0.971296 | + | 0.237873i | \(0.0764501\pi\) | |||||||
\(588\) | −1.59131 | −0.0656244 | ||||||||
\(589\) | 6.18047 | 0.254662 | ||||||||
\(590\) | 0.244763 | 0.0100767 | ||||||||
\(591\) | 2.38855 | 0.0982518 | ||||||||
\(592\) | 4.34611 | 0.178624 | ||||||||
\(593\) | 16.7663 | 0.688508 | 0.344254 | − | 0.938876i | \(-0.388132\pi\) | ||||
0.344254 | + | 0.938876i | \(0.388132\pi\) | |||||||
\(594\) | 6.30869 | 0.258849 | ||||||||
\(595\) | −6.50193 | −0.266553 | ||||||||
\(596\) | 4.46885 | 0.183051 | ||||||||
\(597\) | 4.20889 | 0.172258 | ||||||||
\(598\) | −40.0604 | −1.63819 | ||||||||
\(599\) | −7.65934 | −0.312952 | −0.156476 | − | 0.987682i | \(-0.550013\pi\) | ||||
−0.156476 | + | 0.987682i | \(0.550013\pi\) | |||||||
\(600\) | 1.70521 | 0.0696150 | ||||||||
\(601\) | −1.79716 | −0.0733078 | −0.0366539 | − | 0.999328i | \(-0.511670\pi\) | ||||
−0.0366539 | + | 0.999328i | \(0.511670\pi\) | |||||||
\(602\) | −4.21434 | −0.171764 | ||||||||
\(603\) | −5.54933 | −0.225986 | ||||||||
\(604\) | −3.01879 | −0.122833 | ||||||||
\(605\) | −6.23390 | −0.253444 | ||||||||
\(606\) | 0.879791 | 0.0357390 | ||||||||
\(607\) | 3.69879 | 0.150129 | 0.0750647 | − | 0.997179i | \(-0.476084\pi\) | ||||
0.0750647 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −1.64151 | −0.0665174 | ||||||||
\(610\) | 37.1099 | 1.50254 | ||||||||
\(611\) | −36.6605 | −1.48313 | ||||||||
\(612\) | −1.76651 | −0.0714068 | ||||||||
\(613\) | 12.5828 | 0.508216 | 0.254108 | − | 0.967176i | \(-0.418218\pi\) | ||||
0.254108 | + | 0.967176i | \(0.418218\pi\) | |||||||
\(614\) | −3.54653 | −0.143126 | ||||||||
\(615\) | 4.88531 | 0.196995 | ||||||||
\(616\) | −10.1517 | −0.409022 | ||||||||
\(617\) | 25.3603 | 1.02097 | 0.510484 | − | 0.859887i | \(-0.329466\pi\) | ||||
0.510484 | + | 0.859887i | \(0.329466\pi\) | |||||||
\(618\) | −2.77222 | −0.111515 | ||||||||
\(619\) | −27.6129 | −1.10986 | −0.554928 | − | 0.831899i | \(-0.687254\pi\) | ||||
−0.554928 | + | 0.831899i | \(0.687254\pi\) | |||||||
\(620\) | −19.3110 | −0.775550 | ||||||||
\(621\) | 15.0839 | 0.605297 | ||||||||
\(622\) | 10.8457 | 0.434873 | ||||||||
\(623\) | −14.9378 | −0.598470 | ||||||||
\(624\) | −1.99908 | −0.0800272 | ||||||||
\(625\) | −26.1304 | −1.04521 | ||||||||
\(626\) | 4.14525 | 0.165678 | ||||||||
\(627\) | −1.07440 | −0.0429075 | ||||||||
\(628\) | 14.3364 | 0.572084 | ||||||||
\(629\) | 2.67338 | 0.106595 | ||||||||
\(630\) | −30.3556 | −1.20939 | ||||||||
\(631\) | 13.8660 | 0.551995 | 0.275998 | − | 0.961158i | \(-0.410992\pi\) | ||||
0.275998 | + | 0.961158i | \(0.410992\pi\) | |||||||
\(632\) | −4.20610 | −0.167310 | ||||||||
\(633\) | 0.358038 | 0.0142307 | ||||||||
\(634\) | −20.3736 | −0.809139 | ||||||||
\(635\) | 12.4473 | 0.493957 | ||||||||
\(636\) | −0.853324 | −0.0338365 | ||||||||
\(637\) | 24.8157 | 0.983233 | ||||||||
\(638\) | −4.06682 | −0.161007 | ||||||||
\(639\) | 25.6601 | 1.01510 | ||||||||
\(640\) | −3.12453 | −0.123508 | ||||||||
\(641\) | −32.3492 | −1.27772 | −0.638858 | − | 0.769325i | \(-0.720593\pi\) | ||||
−0.638858 | + | 0.769325i | \(0.720593\pi\) | |||||||
\(642\) | 3.49062 | 0.137764 | ||||||||
\(643\) | −39.6253 | −1.56267 | −0.781334 | − | 0.624113i | \(-0.785461\pi\) | ||||
−0.781334 | + | 0.624113i | \(0.785461\pi\) | |||||||
\(644\) | −24.2724 | −0.956466 | ||||||||
\(645\) | 1.39362 | 0.0548737 | ||||||||
\(646\) | 0.615120 | 0.0242016 | ||||||||
\(647\) | 22.3852 | 0.880052 | 0.440026 | − | 0.897985i | \(-0.354969\pi\) | ||||
0.440026 | + | 0.897985i | \(0.354969\pi\) | |||||||
\(648\) | −7.86271 | −0.308877 | ||||||||
\(649\) | 0.235071 | 0.00922734 | ||||||||
\(650\) | −26.5920 | −1.04302 | ||||||||
\(651\) | −7.48599 | −0.293399 | ||||||||
\(652\) | −16.1862 | −0.633902 | ||||||||
\(653\) | −25.3919 | −0.993662 | −0.496831 | − | 0.867847i | \(-0.665503\pi\) | ||||
−0.496831 | + | 0.867847i | \(0.665503\pi\) | |||||||
\(654\) | −0.662343 | −0.0258997 | ||||||||
\(655\) | −12.1869 | −0.476180 | ||||||||
\(656\) | −4.36696 | −0.170501 | ||||||||
\(657\) | −8.59119 | −0.335174 | ||||||||
\(658\) | −22.2124 | −0.865931 | ||||||||
\(659\) | 0.0400543 | 0.00156030 | 0.000780148 | − | 1.00000i | \(-0.499752\pi\) | ||||
0.000780148 | 1.00000i | \(0.499752\pi\) | ||||||||
\(660\) | 3.35700 | 0.130671 | ||||||||
\(661\) | −43.2027 | −1.68039 | −0.840195 | − | 0.542284i | \(-0.817560\pi\) | ||||
−0.840195 | + | 0.542284i | \(0.817560\pi\) | |||||||
\(662\) | 15.1441 | 0.588592 | ||||||||
\(663\) | −1.22967 | −0.0477565 | ||||||||
\(664\) | −7.46260 | −0.289605 | ||||||||
\(665\) | 10.5702 | 0.409894 | ||||||||
\(666\) | 12.4812 | 0.483637 | ||||||||
\(667\) | −9.72367 | −0.376502 | ||||||||
\(668\) | −16.2282 | −0.627888 | ||||||||
\(669\) | −1.68685 | −0.0652173 | ||||||||
\(670\) | −6.03767 | −0.233256 | ||||||||
\(671\) | 35.6405 | 1.37589 | ||||||||
\(672\) | −1.21123 | −0.0467243 | ||||||||
\(673\) | 12.7442 | 0.491252 | 0.245626 | − | 0.969365i | \(-0.421006\pi\) | ||||
0.245626 | + | 0.969365i | \(0.421006\pi\) | |||||||
\(674\) | 13.4583 | 0.518396 | ||||||||
\(675\) | 10.0127 | 0.385388 | ||||||||
\(676\) | 18.1747 | 0.699026 | ||||||||
\(677\) | −14.3958 | −0.553274 | −0.276637 | − | 0.960974i | \(-0.589220\pi\) | ||||
−0.276637 | + | 0.960974i | \(0.589220\pi\) | |||||||
\(678\) | −3.88655 | −0.149262 | ||||||||
\(679\) | −45.8526 | −1.75966 | ||||||||
\(680\) | −1.92196 | −0.0737037 | ||||||||
\(681\) | −8.29284 | −0.317782 | ||||||||
\(682\) | −18.5464 | −0.710178 | ||||||||
\(683\) | −13.0006 | −0.497455 | −0.248727 | − | 0.968574i | \(-0.580012\pi\) | ||||
−0.248727 | + | 0.968574i | \(0.580012\pi\) | |||||||
\(684\) | 2.87181 | 0.109806 | ||||||||
\(685\) | −12.7242 | −0.486166 | ||||||||
\(686\) | −8.64512 | −0.330072 | ||||||||
\(687\) | 4.56666 | 0.174229 | ||||||||
\(688\) | −1.24575 | −0.0474938 | ||||||||
\(689\) | 13.3072 | 0.506963 | ||||||||
\(690\) | 8.02651 | 0.305564 | ||||||||
\(691\) | 0.218049 | 0.00829499 | 0.00414749 | − | 0.999991i | \(-0.498680\pi\) | ||||
0.00414749 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(692\) | 12.7558 | 0.484902 | ||||||||
\(693\) | −29.1536 | −1.10745 | ||||||||
\(694\) | 32.6416 | 1.23906 | ||||||||
\(695\) | −17.6559 | −0.669726 | ||||||||
\(696\) | −0.485227 | −0.0183925 | ||||||||
\(697\) | −2.68620 | −0.101747 | ||||||||
\(698\) | 18.0042 | 0.681468 | ||||||||
\(699\) | −5.32217 | −0.201303 | ||||||||
\(700\) | −16.1120 | −0.608975 | ||||||||
\(701\) | 25.2798 | 0.954806 | 0.477403 | − | 0.878684i | \(-0.341578\pi\) | ||||
0.477403 | + | 0.878684i | \(0.341578\pi\) | |||||||
\(702\) | −11.7382 | −0.443030 | ||||||||
\(703\) | −4.34611 | −0.163917 | ||||||||
\(704\) | −3.00081 | −0.113097 | ||||||||
\(705\) | 7.34531 | 0.276641 | ||||||||
\(706\) | 29.7728 | 1.12051 | ||||||||
\(707\) | −8.31284 | −0.312636 | ||||||||
\(708\) | 0.0280472 | 0.00105408 | ||||||||
\(709\) | 9.79497 | 0.367858 | 0.183929 | − | 0.982940i | \(-0.441118\pi\) | ||||
0.183929 | + | 0.982940i | \(0.441118\pi\) | |||||||
\(710\) | 27.9182 | 1.04775 | ||||||||
\(711\) | −12.0791 | −0.453002 | ||||||||
\(712\) | −4.41557 | −0.165481 | ||||||||
\(713\) | −44.3440 | −1.66070 | ||||||||
\(714\) | −0.745053 | −0.0278829 | ||||||||
\(715\) | −52.3508 | −1.95781 | ||||||||
\(716\) | −4.28228 | −0.160036 | ||||||||
\(717\) | −1.68341 | −0.0628682 | ||||||||
\(718\) | 32.1488 | 1.19978 | ||||||||
\(719\) | 38.7960 | 1.44685 | 0.723424 | − | 0.690404i | \(-0.242567\pi\) | ||||
0.723424 | + | 0.690404i | \(0.242567\pi\) | |||||||
\(720\) | −8.97304 | −0.334405 | ||||||||
\(721\) | 26.1937 | 0.975505 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −0.661065 | −0.0245853 | ||||||||
\(724\) | −0.0191058 | −0.000710061 0 | ||||||||
\(725\) | −6.45455 | −0.239716 | ||||||||
\(726\) | −0.714340 | −0.0265116 | ||||||||
\(727\) | −1.53700 | −0.0570043 | −0.0285021 | − | 0.999594i | \(-0.509074\pi\) | ||||
−0.0285021 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(728\) | 18.8886 | 0.700058 | ||||||||
\(729\) | −20.3221 | −0.752669 | ||||||||
\(730\) | −9.34721 | −0.345956 | ||||||||
\(731\) | −0.766286 | −0.0283421 | ||||||||
\(732\) | 4.25241 | 0.157173 | ||||||||
\(733\) | 50.8935 | 1.87980 | 0.939898 | − | 0.341455i | \(-0.110920\pi\) | ||||
0.939898 | + | 0.341455i | \(0.110920\pi\) | |||||||
\(734\) | −24.4044 | −0.900784 | ||||||||
\(735\) | −4.97208 | −0.183398 | ||||||||
\(736\) | −7.17487 | −0.264469 | ||||||||
\(737\) | −5.79860 | −0.213594 | ||||||||
\(738\) | −12.5411 | −0.461644 | ||||||||
\(739\) | −5.83827 | −0.214764 | −0.107382 | − | 0.994218i | \(-0.534247\pi\) | ||||
−0.107382 | + | 0.994218i | \(0.534247\pi\) | |||||||
\(740\) | 13.5795 | 0.499194 | ||||||||
\(741\) | 1.99908 | 0.0734380 | ||||||||
\(742\) | 8.06276 | 0.295993 | ||||||||
\(743\) | 45.9366 | 1.68525 | 0.842625 | − | 0.538501i | \(-0.181009\pi\) | ||||
0.842625 | + | 0.538501i | \(0.181009\pi\) | |||||||
\(744\) | −2.21284 | −0.0811267 | ||||||||
\(745\) | 13.9630 | 0.511567 | ||||||||
\(746\) | 24.2893 | 0.889294 | ||||||||
\(747\) | −21.4312 | −0.784126 | ||||||||
\(748\) | −1.84586 | −0.0674912 | ||||||||
\(749\) | −32.9817 | −1.20513 | ||||||||
\(750\) | −0.265513 | −0.00969515 | ||||||||
\(751\) | 16.1899 | 0.590779 | 0.295390 | − | 0.955377i | \(-0.404551\pi\) | ||||
0.295390 | + | 0.955377i | \(0.404551\pi\) | |||||||
\(752\) | −6.56595 | −0.239436 | ||||||||
\(753\) | 3.86328 | 0.140786 | ||||||||
\(754\) | 7.56689 | 0.275570 | ||||||||
\(755\) | −9.43228 | −0.343276 | ||||||||
\(756\) | −7.11213 | −0.258666 | ||||||||
\(757\) | −36.3310 | −1.32047 | −0.660236 | − | 0.751059i | \(-0.729544\pi\) | ||||
−0.660236 | + | 0.751059i | \(0.729544\pi\) | |||||||
\(758\) | −10.7478 | −0.390377 | ||||||||
\(759\) | 7.70869 | 0.279808 | ||||||||
\(760\) | 3.12453 | 0.113338 | ||||||||
\(761\) | −6.83122 | −0.247632 | −0.123816 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123816 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(762\) | 1.42633 | 0.0516706 | ||||||||
\(763\) | 6.25825 | 0.226564 | ||||||||
\(764\) | −27.2759 | −0.986807 | ||||||||
\(765\) | −5.51949 | −0.199558 | ||||||||
\(766\) | 21.1458 | 0.764028 | ||||||||
\(767\) | −0.437383 | −0.0157930 | ||||||||
\(768\) | −0.358038 | −0.0129196 | ||||||||
\(769\) | −10.3997 | −0.375024 | −0.187512 | − | 0.982262i | \(-0.560042\pi\) | ||||
−0.187512 | + | 0.982262i | \(0.560042\pi\) | |||||||
\(770\) | −31.7191 | −1.14308 | ||||||||
\(771\) | 3.07090 | 0.110596 | ||||||||
\(772\) | −17.1033 | −0.615563 | ||||||||
\(773\) | −5.54935 | −0.199596 | −0.0997981 | − | 0.995008i | \(-0.531820\pi\) | ||||
−0.0997981 | + | 0.995008i | \(0.531820\pi\) | |||||||
\(774\) | −3.57756 | −0.128593 | ||||||||
\(775\) | −29.4355 | −1.05735 | ||||||||
\(776\) | −13.5539 | −0.486557 | ||||||||
\(777\) | 5.26415 | 0.188850 | ||||||||
\(778\) | −10.0628 | −0.360770 | ||||||||
\(779\) | 4.36696 | 0.156463 | ||||||||
\(780\) | −6.24617 | −0.223649 | ||||||||
\(781\) | 26.8127 | 0.959435 | ||||||||
\(782\) | −4.41340 | −0.157823 | ||||||||
\(783\) | −2.84916 | −0.101821 | ||||||||
\(784\) | 4.44452 | 0.158733 | ||||||||
\(785\) | 44.7944 | 1.59878 | ||||||||
\(786\) | −1.39649 | −0.0498110 | ||||||||
\(787\) | −3.95969 | −0.141148 | −0.0705738 | − | 0.997507i | \(-0.522483\pi\) | ||||
−0.0705738 | + | 0.997507i | \(0.522483\pi\) | |||||||
\(788\) | −6.67123 | −0.237653 | ||||||||
\(789\) | −2.15357 | −0.0766692 | ||||||||
\(790\) | −13.1421 | −0.467573 | ||||||||
\(791\) | 36.7227 | 1.30571 | ||||||||
\(792\) | −8.61775 | −0.306218 | ||||||||
\(793\) | −66.3143 | −2.35489 | ||||||||
\(794\) | −16.9112 | −0.600155 | ||||||||
\(795\) | −2.66623 | −0.0945615 | ||||||||
\(796\) | −11.7554 | −0.416661 | ||||||||
\(797\) | −0.820786 | −0.0290737 | −0.0145369 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145369 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(798\) | 1.21123 | 0.0428772 | ||||||||
\(799\) | −4.03884 | −0.142884 | ||||||||
\(800\) | −4.76266 | −0.168385 | ||||||||
\(801\) | −12.6807 | −0.448050 | ||||||||
\(802\) | −26.5788 | −0.938530 | ||||||||
\(803\) | −8.97710 | −0.316795 | ||||||||
\(804\) | −0.691853 | −0.0243998 | ||||||||
\(805\) | −75.8397 | −2.67300 | ||||||||
\(806\) | 34.5082 | 1.21550 | ||||||||
\(807\) | 2.90700 | 0.102331 | ||||||||
\(808\) | −2.45726 | −0.0864460 | ||||||||
\(809\) | 11.5408 | 0.405753 | 0.202876 | − | 0.979204i | \(-0.434971\pi\) | ||||
0.202876 | + | 0.979204i | \(0.434971\pi\) | |||||||
\(810\) | −24.5672 | −0.863205 | ||||||||
\(811\) | −15.8151 | −0.555342 | −0.277671 | − | 0.960676i | \(-0.589563\pi\) | ||||
−0.277671 | + | 0.960676i | \(0.589563\pi\) | |||||||
\(812\) | 4.58475 | 0.160893 | ||||||||
\(813\) | −1.45370 | −0.0509834 | ||||||||
\(814\) | 13.0419 | 0.457117 | ||||||||
\(815\) | −50.5743 | −1.77154 | ||||||||
\(816\) | −0.220236 | −0.00770980 | ||||||||
\(817\) | 1.24575 | 0.0435833 | ||||||||
\(818\) | 8.32028 | 0.290912 | ||||||||
\(819\) | 54.2445 | 1.89545 | ||||||||
\(820\) | −13.6447 | −0.476493 | ||||||||
\(821\) | 7.13775 | 0.249109 | 0.124555 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124555 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(822\) | −1.45806 | −0.0508555 | ||||||||
\(823\) | 22.3234 | 0.778145 | 0.389073 | − | 0.921207i | \(-0.372796\pi\) | ||||
0.389073 | + | 0.921207i | \(0.372796\pi\) | |||||||
\(824\) | 7.74280 | 0.269733 | ||||||||
\(825\) | 5.11701 | 0.178152 | ||||||||
\(826\) | −0.265008 | −0.00922082 | ||||||||
\(827\) | −41.7018 | −1.45011 | −0.725057 | − | 0.688688i | \(-0.758187\pi\) | ||||
−0.725057 | + | 0.688688i | \(0.758187\pi\) | |||||||
\(828\) | −20.6048 | −0.716068 | ||||||||
\(829\) | −49.0713 | −1.70432 | −0.852158 | − | 0.523285i | \(-0.824706\pi\) | ||||
−0.852158 | + | 0.523285i | \(0.824706\pi\) | |||||||
\(830\) | −23.3171 | −0.809348 | ||||||||
\(831\) | 3.04851 | 0.105752 | ||||||||
\(832\) | 5.58343 | 0.193571 | ||||||||
\(833\) | 2.73391 | 0.0947244 | ||||||||
\(834\) | −2.02318 | −0.0700570 | ||||||||
\(835\) | −50.7054 | −1.75473 | ||||||||
\(836\) | 3.00081 | 0.103785 | ||||||||
\(837\) | −12.9934 | −0.449117 | ||||||||
\(838\) | 32.8304 | 1.13411 | ||||||||
\(839\) | 19.1731 | 0.661928 | 0.330964 | − | 0.943643i | \(-0.392626\pi\) | ||||
0.330964 | + | 0.943643i | \(0.392626\pi\) | |||||||
\(840\) | −3.78453 | −0.130579 | ||||||||
\(841\) | −27.1633 | −0.936666 | ||||||||
\(842\) | −2.12978 | −0.0733969 | ||||||||
\(843\) | −1.25556 | −0.0432438 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 56.7872 | 1.95354 | ||||||||
\(846\) | −18.8562 | −0.648288 | ||||||||
\(847\) | 6.74955 | 0.231917 | ||||||||
\(848\) | 2.38333 | 0.0818440 | ||||||||
\(849\) | 5.78905 | 0.198680 | ||||||||
\(850\) | −2.92960 | −0.100485 | ||||||||
\(851\) | 31.1828 | 1.06893 | ||||||||
\(852\) | 3.19913 | 0.109600 | ||||||||
\(853\) | −20.3042 | −0.695201 | −0.347601 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347601 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(854\) | −40.1795 | −1.37491 | ||||||||
\(855\) | 8.97304 | 0.306872 | ||||||||
\(856\) | −9.74932 | −0.333225 | ||||||||
\(857\) | 8.86837 | 0.302938 | 0.151469 | − | 0.988462i | \(-0.451600\pi\) | ||||
0.151469 | + | 0.988462i | \(0.451600\pi\) | |||||||
\(858\) | −5.99885 | −0.204797 | ||||||||
\(859\) | 36.6955 | 1.25203 | 0.626017 | − | 0.779809i | \(-0.284684\pi\) | ||||
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(860\) | −3.89238 | −0.132729 | ||||||||
\(861\) | −5.28941 | −0.180263 | ||||||||
\(862\) | 33.8992 | 1.15461 | ||||||||
\(863\) | 28.8863 | 0.983302 | 0.491651 | − | 0.870792i | \(-0.336394\pi\) | ||||
0.491651 | + | 0.870792i | \(0.336394\pi\) | |||||||
\(864\) | −2.10233 | −0.0715227 | ||||||||
\(865\) | 39.8558 | 1.35514 | ||||||||
\(866\) | −0.554211 | −0.0188328 | ||||||||
\(867\) | 5.95117 | 0.202112 | ||||||||
\(868\) | 20.9084 | 0.709676 | ||||||||
\(869\) | −12.6217 | −0.428161 | ||||||||
\(870\) | −1.51610 | −0.0514008 | ||||||||
\(871\) | 10.7891 | 0.365576 | ||||||||
\(872\) | 1.84992 | 0.0626463 | ||||||||
\(873\) | −38.9243 | −1.31739 | ||||||||
\(874\) | 7.17487 | 0.242694 | ||||||||
\(875\) | 2.50874 | 0.0848108 | ||||||||
\(876\) | −1.07109 | −0.0361888 | ||||||||
\(877\) | 19.2468 | 0.649917 | 0.324958 | − | 0.945728i | \(-0.394650\pi\) | ||||
0.324958 | + | 0.945728i | \(0.394650\pi\) | |||||||
\(878\) | −21.5358 | −0.726796 | ||||||||
\(879\) | 3.66869 | 0.123742 | ||||||||
\(880\) | −9.37610 | −0.316068 | ||||||||
\(881\) | 32.7640 | 1.10385 | 0.551924 | − | 0.833895i | \(-0.313894\pi\) | ||||
0.551924 | + | 0.833895i | \(0.313894\pi\) | |||||||
\(882\) | 12.7638 | 0.429780 | ||||||||
\(883\) | −39.0126 | −1.31288 | −0.656439 | − | 0.754379i | \(-0.727938\pi\) | ||||
−0.656439 | + | 0.754379i | \(0.727938\pi\) | |||||||
\(884\) | 3.43448 | 0.115514 | ||||||||
\(885\) | 0.0876342 | 0.00294579 | ||||||||
\(886\) | 19.3598 | 0.650405 | ||||||||
\(887\) | −40.4343 | −1.35765 | −0.678825 | − | 0.734300i | \(-0.737511\pi\) | ||||
−0.678825 | + | 0.734300i | \(0.737511\pi\) | |||||||
\(888\) | 1.55607 | 0.0522184 | ||||||||
\(889\) | −13.4769 | −0.452001 | ||||||||
\(890\) | −13.7966 | −0.462462 | ||||||||
\(891\) | −23.5945 | −0.790445 | ||||||||
\(892\) | 4.71137 | 0.157748 | ||||||||
\(893\) | 6.56595 | 0.219721 | ||||||||
\(894\) | 1.60002 | 0.0535126 | ||||||||
\(895\) | −13.3801 | −0.447247 | ||||||||
\(896\) | 3.38298 | 0.113017 | ||||||||
\(897\) | −14.3431 | −0.478903 | ||||||||
\(898\) | 28.3635 | 0.946501 | ||||||||
\(899\) | 8.37602 | 0.279356 | ||||||||
\(900\) | −13.6774 | −0.455915 | ||||||||
\(901\) | 1.46604 | 0.0488407 | ||||||||
\(902\) | −13.1044 | −0.436329 | ||||||||
\(903\) | −1.50889 | −0.0502129 | ||||||||
\(904\) | 10.8551 | 0.361037 | ||||||||
\(905\) | −0.0596965 | −0.00198438 | ||||||||
\(906\) | −1.08084 | −0.0359085 | ||||||||
\(907\) | −25.5757 | −0.849229 | −0.424614 | − | 0.905374i | \(-0.639590\pi\) | ||||
−0.424614 | + | 0.905374i | \(0.639590\pi\) | |||||||
\(908\) | 23.1619 | 0.768655 | ||||||||
\(909\) | −7.05677 | −0.234058 | ||||||||
\(910\) | 59.0179 | 1.95642 | ||||||||
\(911\) | −45.4379 | −1.50542 | −0.752712 | − | 0.658350i | \(-0.771255\pi\) | ||||
−0.752712 | + | 0.658350i | \(0.771255\pi\) | |||||||
\(912\) | 0.358038 | 0.0118558 | ||||||||
\(913\) | −22.3938 | −0.741128 | ||||||||
\(914\) | 1.65460 | 0.0547293 | ||||||||
\(915\) | 13.2868 | 0.439246 | ||||||||
\(916\) | −12.7547 | −0.421427 | ||||||||
\(917\) | 13.1949 | 0.435735 | ||||||||
\(918\) | −1.29318 | −0.0426814 | ||||||||
\(919\) | 34.4806 | 1.13741 | 0.568706 | − | 0.822541i | \(-0.307444\pi\) | ||||
0.568706 | + | 0.822541i | \(0.307444\pi\) | |||||||
\(920\) | −22.4181 | −0.739101 | ||||||||
\(921\) | −1.26979 | −0.0418410 | ||||||||
\(922\) | −39.2786 | −1.29357 | ||||||||
\(923\) | −49.8889 | −1.64211 | ||||||||
\(924\) | −3.63468 | −0.119572 | ||||||||
\(925\) | 20.6991 | 0.680581 | ||||||||
\(926\) | −15.0384 | −0.494191 | ||||||||
\(927\) | 22.2358 | 0.730321 | ||||||||
\(928\) | 1.35524 | 0.0444880 | ||||||||
\(929\) | 58.4115 | 1.91642 | 0.958210 | − | 0.286065i | \(-0.0923472\pi\) | ||||
0.958210 | + | 0.286065i | \(0.0923472\pi\) | |||||||
\(930\) | −6.91408 | −0.226722 | ||||||||
\(931\) | −4.44452 | −0.145663 | ||||||||
\(932\) | 14.8648 | 0.486914 | ||||||||
\(933\) | 3.88317 | 0.127129 | ||||||||
\(934\) | 13.5231 | 0.442488 | ||||||||
\(935\) | −5.76742 | −0.188615 | ||||||||
\(936\) | 16.0345 | 0.524105 | ||||||||
\(937\) | 2.99786 | 0.0979357 | 0.0489678 | − | 0.998800i | \(-0.484407\pi\) | ||||
0.0489678 | + | 0.998800i | \(0.484407\pi\) | |||||||
\(938\) | 6.53709 | 0.213443 | ||||||||
\(939\) | 1.48416 | 0.0484336 | ||||||||
\(940\) | −20.5155 | −0.669141 | ||||||||
\(941\) | −48.7190 | −1.58819 | −0.794097 | − | 0.607791i | \(-0.792056\pi\) | ||||
−0.794097 | + | 0.607791i | \(0.792056\pi\) | |||||||
\(942\) | 5.13297 | 0.167241 | ||||||||
\(943\) | −31.3324 | −1.02032 | ||||||||
\(944\) | −0.0783359 | −0.00254962 | ||||||||
\(945\) | −22.2220 | −0.722882 | ||||||||
\(946\) | −3.73826 | −0.121541 | ||||||||
\(947\) | 30.5376 | 0.992338 | 0.496169 | − | 0.868226i | \(-0.334740\pi\) | ||||
0.496169 | + | 0.868226i | \(0.334740\pi\) | |||||||
\(948\) | −1.50594 | −0.0489107 | ||||||||
\(949\) | 16.7032 | 0.542208 | ||||||||
\(950\) | 4.76266 | 0.154521 | ||||||||
\(951\) | −7.29452 | −0.236541 | ||||||||
\(952\) | 2.08093 | 0.0674435 | ||||||||
\(953\) | −18.2301 | −0.590532 | −0.295266 | − | 0.955415i | \(-0.595408\pi\) | ||||
−0.295266 | + | 0.955415i | \(0.595408\pi\) | |||||||
\(954\) | 6.84448 | 0.221598 | ||||||||
\(955\) | −85.2242 | −2.75779 | ||||||||
\(956\) | 4.70178 | 0.152066 | ||||||||
\(957\) | −1.45607 | −0.0470682 | ||||||||
\(958\) | 16.7659 | 0.541682 | ||||||||
\(959\) | 13.7767 | 0.444872 | ||||||||
\(960\) | −1.11870 | −0.0361058 | ||||||||
\(961\) | 7.19819 | 0.232200 | ||||||||
\(962\) | −24.2662 | −0.782374 | ||||||||
\(963\) | −27.9982 | −0.902229 | ||||||||
\(964\) | 1.84635 | 0.0594671 | ||||||||
\(965\) | −53.4398 | −1.72029 | ||||||||
\(966\) | −8.69043 | −0.279610 | ||||||||
\(967\) | −48.3574 | −1.55507 | −0.777535 | − | 0.628840i | \(-0.783530\pi\) | ||||
−0.777535 | + | 0.628840i | \(0.783530\pi\) | |||||||
\(968\) | 1.99515 | 0.0641266 | ||||||||
\(969\) | 0.220236 | 0.00707500 | ||||||||
\(970\) | −42.3496 | −1.35976 | ||||||||
\(971\) | −30.5748 | −0.981191 | −0.490595 | − | 0.871388i | \(-0.663221\pi\) | ||||
−0.490595 | + | 0.871388i | \(0.663221\pi\) | |||||||
\(972\) | −9.12214 | −0.292593 | ||||||||
\(973\) | 19.1163 | 0.612841 | ||||||||
\(974\) | 21.8167 | 0.699053 | ||||||||
\(975\) | −9.52093 | −0.304914 | ||||||||
\(976\) | −11.8770 | −0.380173 | ||||||||
\(977\) | −24.8139 | −0.793867 | −0.396933 | − | 0.917847i | \(-0.629926\pi\) | ||||
−0.396933 | + | 0.917847i | \(0.629926\pi\) | |||||||
\(978\) | −5.79529 | −0.185313 | ||||||||
\(979\) | −13.2503 | −0.423481 | ||||||||
\(980\) | 13.8870 | 0.443605 | ||||||||
\(981\) | 5.31263 | 0.169619 | ||||||||
\(982\) | −18.8936 | −0.602920 | ||||||||
\(983\) | 22.4403 | 0.715734 | 0.357867 | − | 0.933773i | \(-0.383504\pi\) | ||||
0.357867 | + | 0.933773i | \(0.383504\pi\) | |||||||
\(984\) | −1.56354 | −0.0498437 | ||||||||
\(985\) | −20.8444 | −0.664158 | ||||||||
\(986\) | 0.833635 | 0.0265483 | ||||||||
\(987\) | −7.95289 | −0.253143 | ||||||||
\(988\) | −5.58343 | −0.177633 | ||||||||
\(989\) | −8.93810 | −0.284215 | ||||||||
\(990\) | −26.9264 | −0.855776 | ||||||||
\(991\) | 17.9030 | 0.568708 | 0.284354 | − | 0.958719i | \(-0.408221\pi\) | ||||
0.284354 | + | 0.958719i | \(0.408221\pi\) | |||||||
\(992\) | 6.18047 | 0.196230 | ||||||||
\(993\) | 5.42215 | 0.172067 | ||||||||
\(994\) | −30.2275 | −0.958757 | ||||||||
\(995\) | −36.7302 | −1.16442 | ||||||||
\(996\) | −2.67189 | −0.0846622 | ||||||||
\(997\) | −37.7752 | −1.19635 | −0.598177 | − | 0.801364i | \(-0.704108\pi\) | ||||
−0.598177 | + | 0.801364i | \(0.704108\pi\) | |||||||
\(998\) | 19.8282 | 0.627652 | ||||||||
\(999\) | 9.13696 | 0.289081 |
(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 | 8018.2.a.f.1.18 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.f.1.18 | ✓ | 34 | 1.1 | even | 1 | trivial |