Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + \cdots + 1200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.312107\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.312107 | −0.139578 | −0.0697892 | − | 0.997562i | \(-0.522233\pi\) | ||||
−0.0697892 | + | 0.997562i | \(0.522233\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.12710 | −0.426004 | −0.213002 | − | 0.977052i | \(-0.568324\pi\) | ||||
−0.213002 | + | 0.977052i | \(0.568324\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.312107 | −0.0986969 | ||||||||
\(11\) | 4.84000 | 1.45932 | 0.729658 | − | 0.683813i | \(-0.239679\pi\) | ||||
0.729658 | + | 0.683813i | \(0.239679\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.90027 | −0.804391 | −0.402195 | − | 0.915554i | \(-0.631753\pi\) | ||||
−0.402195 | + | 0.915554i | \(0.631753\pi\) | |||||||
\(14\) | −1.12710 | −0.301230 | ||||||||
\(15\) | −0.312107 | −0.0805857 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.37248 | −0.575411 | −0.287705 | − | 0.957719i | \(-0.592892\pi\) | ||||
−0.287705 | + | 0.957719i | \(0.592892\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.312107 | −0.0697892 | ||||||||
\(21\) | −1.12710 | −0.245954 | ||||||||
\(22\) | 4.84000 | 1.03189 | ||||||||
\(23\) | 7.43281 | 1.54985 | 0.774924 | − | 0.632055i | \(-0.217788\pi\) | ||||
0.774924 | + | 0.632055i | \(0.217788\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.90259 | −0.980518 | ||||||||
\(26\) | −2.90027 | −0.568790 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.12710 | −0.213002 | ||||||||
\(29\) | 2.54808 | 0.473167 | 0.236583 | − | 0.971611i | \(-0.423972\pi\) | ||||
0.236583 | + | 0.971611i | \(0.423972\pi\) | |||||||
\(30\) | −0.312107 | −0.0569827 | ||||||||
\(31\) | −1.67878 | −0.301519 | −0.150759 | − | 0.988571i | \(-0.548172\pi\) | ||||
−0.150759 | + | 0.988571i | \(0.548172\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.84000 | 0.842536 | ||||||||
\(34\) | −2.37248 | −0.406877 | ||||||||
\(35\) | 0.351776 | 0.0594610 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.39807 | −0.723038 | −0.361519 | − | 0.932365i | \(-0.617742\pi\) | ||||
−0.361519 | + | 0.932365i | \(0.617742\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −2.90027 | −0.464415 | ||||||||
\(40\) | −0.312107 | −0.0493484 | ||||||||
\(41\) | 10.4714 | 1.63535 | 0.817677 | − | 0.575677i | \(-0.195262\pi\) | ||||
0.817677 | + | 0.575677i | \(0.195262\pi\) | |||||||
\(42\) | −1.12710 | −0.173915 | ||||||||
\(43\) | 6.43770 | 0.981741 | 0.490870 | − | 0.871233i | \(-0.336679\pi\) | ||||
0.490870 | + | 0.871233i | \(0.336679\pi\) | |||||||
\(44\) | 4.84000 | 0.729658 | ||||||||
\(45\) | −0.312107 | −0.0465262 | ||||||||
\(46\) | 7.43281 | 1.09591 | ||||||||
\(47\) | 9.40984 | 1.37257 | 0.686283 | − | 0.727334i | \(-0.259241\pi\) | ||||
0.686283 | + | 0.727334i | \(0.259241\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.72964 | −0.818521 | ||||||||
\(50\) | −4.90259 | −0.693331 | ||||||||
\(51\) | −2.37248 | −0.332214 | ||||||||
\(52\) | −2.90027 | −0.402195 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.51060 | −0.203689 | ||||||||
\(56\) | −1.12710 | −0.150615 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 2.54808 | 0.334579 | ||||||||
\(59\) | 1.03474 | 0.134711 | 0.0673557 | − | 0.997729i | \(-0.478544\pi\) | ||||
0.0673557 | + | 0.997729i | \(0.478544\pi\) | |||||||
\(60\) | −0.312107 | −0.0402928 | ||||||||
\(61\) | 12.9276 | 1.65521 | 0.827605 | − | 0.561310i | \(-0.189703\pi\) | ||||
0.827605 | + | 0.561310i | \(0.189703\pi\) | |||||||
\(62\) | −1.67878 | −0.213206 | ||||||||
\(63\) | −1.12710 | −0.142001 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.905195 | 0.112276 | ||||||||
\(66\) | 4.84000 | 0.595763 | ||||||||
\(67\) | −3.92221 | −0.479174 | −0.239587 | − | 0.970875i | \(-0.577012\pi\) | ||||
−0.239587 | + | 0.970875i | \(0.577012\pi\) | |||||||
\(68\) | −2.37248 | −0.287705 | ||||||||
\(69\) | 7.43281 | 0.894805 | ||||||||
\(70\) | 0.351776 | 0.0420453 | ||||||||
\(71\) | 12.6875 | 1.50573 | 0.752863 | − | 0.658178i | \(-0.228672\pi\) | ||||
0.752863 | + | 0.658178i | \(0.228672\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.56841 | −0.417650 | −0.208825 | − | 0.977953i | \(-0.566964\pi\) | ||||
−0.208825 | + | 0.977953i | \(0.566964\pi\) | |||||||
\(74\) | −4.39807 | −0.511265 | ||||||||
\(75\) | −4.90259 | −0.566102 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −5.45517 | −0.621674 | ||||||||
\(78\) | −2.90027 | −0.328391 | ||||||||
\(79\) | −2.83255 | −0.318687 | −0.159343 | − | 0.987223i | \(-0.550938\pi\) | ||||
−0.159343 | + | 0.987223i | \(0.550938\pi\) | |||||||
\(80\) | −0.312107 | −0.0348946 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.4714 | 1.15637 | ||||||||
\(83\) | 9.84132 | 1.08023 | 0.540113 | − | 0.841593i | \(-0.318382\pi\) | ||||
0.540113 | + | 0.841593i | \(0.318382\pi\) | |||||||
\(84\) | −1.12710 | −0.122977 | ||||||||
\(85\) | 0.740467 | 0.0803149 | ||||||||
\(86\) | 6.43770 | 0.694195 | ||||||||
\(87\) | 2.54808 | 0.273183 | ||||||||
\(88\) | 4.84000 | 0.515946 | ||||||||
\(89\) | −4.79561 | −0.508334 | −0.254167 | − | 0.967160i | \(-0.581801\pi\) | ||||
−0.254167 | + | 0.967160i | \(0.581801\pi\) | |||||||
\(90\) | −0.312107 | −0.0328990 | ||||||||
\(91\) | 3.26890 | 0.342674 | ||||||||
\(92\) | 7.43281 | 0.774924 | ||||||||
\(93\) | −1.67878 | −0.174082 | ||||||||
\(94\) | 9.40984 | 0.970551 | ||||||||
\(95\) | −0.312107 | −0.0320215 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.44071 | 0.450886 | 0.225443 | − | 0.974256i | \(-0.427617\pi\) | ||||
0.225443 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(98\) | −5.72964 | −0.578781 | ||||||||
\(99\) | 4.84000 | 0.486438 | ||||||||
\(100\) | −4.90259 | −0.490259 | ||||||||
\(101\) | −13.2891 | −1.32231 | −0.661156 | − | 0.750248i | \(-0.729934\pi\) | ||||
−0.661156 | + | 0.750248i | \(0.729934\pi\) | |||||||
\(102\) | −2.37248 | −0.234910 | ||||||||
\(103\) | 18.5115 | 1.82399 | 0.911994 | − | 0.410203i | \(-0.134542\pi\) | ||||
0.911994 | + | 0.410203i | \(0.134542\pi\) | |||||||
\(104\) | −2.90027 | −0.284395 | ||||||||
\(105\) | 0.351776 | 0.0343298 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −6.18950 | −0.598362 | −0.299181 | − | 0.954196i | \(-0.596713\pi\) | ||||
−0.299181 | + | 0.954196i | \(0.596713\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −13.0943 | −1.25421 | −0.627104 | − | 0.778936i | \(-0.715760\pi\) | ||||
−0.627104 | + | 0.778936i | \(0.715760\pi\) | |||||||
\(110\) | −1.51060 | −0.144030 | ||||||||
\(111\) | −4.39807 | −0.417446 | ||||||||
\(112\) | −1.12710 | −0.106501 | ||||||||
\(113\) | 6.55174 | 0.616336 | 0.308168 | − | 0.951332i | \(-0.400284\pi\) | ||||
0.308168 | + | 0.951332i | \(0.400284\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −2.31983 | −0.216325 | ||||||||
\(116\) | 2.54808 | 0.236583 | ||||||||
\(117\) | −2.90027 | −0.268130 | ||||||||
\(118\) | 1.03474 | 0.0952554 | ||||||||
\(119\) | 2.67402 | 0.245127 | ||||||||
\(120\) | −0.312107 | −0.0284913 | ||||||||
\(121\) | 12.4256 | 1.12960 | ||||||||
\(122\) | 12.9276 | 1.17041 | ||||||||
\(123\) | 10.4714 | 0.944172 | ||||||||
\(124\) | −1.67878 | −0.150759 | ||||||||
\(125\) | 3.09067 | 0.276438 | ||||||||
\(126\) | −1.12710 | −0.100410 | ||||||||
\(127\) | −4.97721 | −0.441656 | −0.220828 | − | 0.975313i | \(-0.570876\pi\) | ||||
−0.220828 | + | 0.975313i | \(0.570876\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.43770 | 0.566808 | ||||||||
\(130\) | 0.905195 | 0.0793908 | ||||||||
\(131\) | 10.7157 | 0.936232 | 0.468116 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468116 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(132\) | 4.84000 | 0.421268 | ||||||||
\(133\) | −1.12710 | −0.0977320 | ||||||||
\(134\) | −3.92221 | −0.338827 | ||||||||
\(135\) | −0.312107 | −0.0268619 | ||||||||
\(136\) | −2.37248 | −0.203438 | ||||||||
\(137\) | −5.43456 | −0.464306 | −0.232153 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232153 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(138\) | 7.43281 | 0.632723 | ||||||||
\(139\) | −18.9143 | −1.60429 | −0.802143 | − | 0.597132i | \(-0.796307\pi\) | ||||
−0.802143 | + | 0.597132i | \(0.796307\pi\) | |||||||
\(140\) | 0.351776 | 0.0297305 | ||||||||
\(141\) | 9.40984 | 0.792452 | ||||||||
\(142\) | 12.6875 | 1.06471 | ||||||||
\(143\) | −14.0373 | −1.17386 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.795274 | −0.0660439 | ||||||||
\(146\) | −3.56841 | −0.295323 | ||||||||
\(147\) | −5.72964 | −0.472573 | ||||||||
\(148\) | −4.39807 | −0.361519 | ||||||||
\(149\) | −9.36511 | −0.767220 | −0.383610 | − | 0.923495i | \(-0.625319\pi\) | ||||
−0.383610 | + | 0.923495i | \(0.625319\pi\) | |||||||
\(150\) | −4.90259 | −0.400295 | ||||||||
\(151\) | 19.7763 | 1.60938 | 0.804688 | − | 0.593698i | \(-0.202332\pi\) | ||||
0.804688 | + | 0.593698i | \(0.202332\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.37248 | −0.191804 | ||||||||
\(154\) | −5.45517 | −0.439590 | ||||||||
\(155\) | 0.523960 | 0.0420855 | ||||||||
\(156\) | −2.90027 | −0.232208 | ||||||||
\(157\) | 6.96594 | 0.555942 | 0.277971 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277971 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(158\) | −2.83255 | −0.225345 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | −0.312107 | −0.0246742 | ||||||||
\(161\) | −8.37752 | −0.660241 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.93881 | 0.151859 | 0.0759296 | − | 0.997113i | \(-0.475808\pi\) | ||||
0.0759296 | + | 0.997113i | \(0.475808\pi\) | |||||||
\(164\) | 10.4714 | 0.817677 | ||||||||
\(165\) | −1.51060 | −0.117600 | ||||||||
\(166\) | 9.84132 | 0.763834 | ||||||||
\(167\) | 24.3879 | 1.88719 | 0.943595 | − | 0.331102i | \(-0.107420\pi\) | ||||
0.943595 | + | 0.331102i | \(0.107420\pi\) | |||||||
\(168\) | −1.12710 | −0.0869577 | ||||||||
\(169\) | −4.58842 | −0.352956 | ||||||||
\(170\) | 0.740467 | 0.0567912 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 6.43770 | 0.490870 | ||||||||
\(173\) | −10.5054 | −0.798709 | −0.399355 | − | 0.916797i | \(-0.630766\pi\) | ||||
−0.399355 | + | 0.916797i | \(0.630766\pi\) | |||||||
\(174\) | 2.54808 | 0.193170 | ||||||||
\(175\) | 5.52571 | 0.417705 | ||||||||
\(176\) | 4.84000 | 0.364829 | ||||||||
\(177\) | 1.03474 | 0.0777757 | ||||||||
\(178\) | −4.79561 | −0.359446 | ||||||||
\(179\) | −5.23975 | −0.391637 | −0.195819 | − | 0.980640i | \(-0.562736\pi\) | ||||
−0.195819 | + | 0.980640i | \(0.562736\pi\) | |||||||
\(180\) | −0.312107 | −0.0232631 | ||||||||
\(181\) | 0.0286803 | 0.00213179 | 0.00106590 | − | 0.999999i | \(-0.499661\pi\) | ||||
0.00106590 | + | 0.999999i | \(0.499661\pi\) | |||||||
\(182\) | 3.26890 | 0.242307 | ||||||||
\(183\) | 12.9276 | 0.955636 | ||||||||
\(184\) | 7.43281 | 0.547954 | ||||||||
\(185\) | 1.37267 | 0.100921 | ||||||||
\(186\) | −1.67878 | −0.123094 | ||||||||
\(187\) | −11.4828 | −0.839705 | ||||||||
\(188\) | 9.40984 | 0.686283 | ||||||||
\(189\) | −1.12710 | −0.0819845 | ||||||||
\(190\) | −0.312107 | −0.0226426 | ||||||||
\(191\) | −20.7273 | −1.49977 | −0.749887 | − | 0.661566i | \(-0.769892\pi\) | ||||
−0.749887 | + | 0.661566i | \(0.769892\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.95443 | −0.644554 | −0.322277 | − | 0.946645i | \(-0.604448\pi\) | ||||
−0.322277 | + | 0.946645i | \(0.604448\pi\) | |||||||
\(194\) | 4.44071 | 0.318825 | ||||||||
\(195\) | 0.905195 | 0.0648224 | ||||||||
\(196\) | −5.72964 | −0.409260 | ||||||||
\(197\) | 15.2265 | 1.08484 | 0.542420 | − | 0.840107i | \(-0.317508\pi\) | ||||
0.542420 | + | 0.840107i | \(0.317508\pi\) | |||||||
\(198\) | 4.84000 | 0.343964 | ||||||||
\(199\) | 18.7897 | 1.33197 | 0.665984 | − | 0.745966i | \(-0.268012\pi\) | ||||
0.665984 | + | 0.745966i | \(0.268012\pi\) | |||||||
\(200\) | −4.90259 | −0.346665 | ||||||||
\(201\) | −3.92221 | −0.276651 | ||||||||
\(202\) | −13.2891 | −0.935016 | ||||||||
\(203\) | −2.87194 | −0.201571 | ||||||||
\(204\) | −2.37248 | −0.166107 | ||||||||
\(205\) | −3.26819 | −0.228260 | ||||||||
\(206\) | 18.5115 | 1.28975 | ||||||||
\(207\) | 7.43281 | 0.516616 | ||||||||
\(208\) | −2.90027 | −0.201098 | ||||||||
\(209\) | 4.84000 | 0.334790 | ||||||||
\(210\) | 0.351776 | 0.0242748 | ||||||||
\(211\) | 15.6590 | 1.07801 | 0.539004 | − | 0.842303i | \(-0.318801\pi\) | ||||
0.539004 | + | 0.842303i | \(0.318801\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 12.6875 | 0.869331 | ||||||||
\(214\) | −6.18950 | −0.423106 | ||||||||
\(215\) | −2.00925 | −0.137030 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.89216 | 0.128448 | ||||||||
\(218\) | −13.0943 | −0.886859 | ||||||||
\(219\) | −3.56841 | −0.241131 | ||||||||
\(220\) | −1.51060 | −0.101844 | ||||||||
\(221\) | 6.88083 | 0.462855 | ||||||||
\(222\) | −4.39807 | −0.295179 | ||||||||
\(223\) | 1.69152 | 0.113273 | 0.0566364 | − | 0.998395i | \(-0.481962\pi\) | ||||
0.0566364 | + | 0.998395i | \(0.481962\pi\) | |||||||
\(224\) | −1.12710 | −0.0753076 | ||||||||
\(225\) | −4.90259 | −0.326839 | ||||||||
\(226\) | 6.55174 | 0.435815 | ||||||||
\(227\) | 19.5295 | 1.29622 | 0.648108 | − | 0.761548i | \(-0.275560\pi\) | ||||
0.648108 | + | 0.761548i | \(0.275560\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | −12.1019 | −0.799718 | −0.399859 | − | 0.916577i | \(-0.630941\pi\) | ||||
−0.399859 | + | 0.916577i | \(0.630941\pi\) | |||||||
\(230\) | −2.31983 | −0.152965 | ||||||||
\(231\) | −5.45517 | −0.358924 | ||||||||
\(232\) | 2.54808 | 0.167290 | ||||||||
\(233\) | −19.3946 | −1.27058 | −0.635292 | − | 0.772272i | \(-0.719120\pi\) | ||||
−0.635292 | + | 0.772272i | \(0.719120\pi\) | |||||||
\(234\) | −2.90027 | −0.189597 | ||||||||
\(235\) | −2.93688 | −0.191581 | ||||||||
\(236\) | 1.03474 | 0.0673557 | ||||||||
\(237\) | −2.83255 | −0.183994 | ||||||||
\(238\) | 2.67402 | 0.173331 | ||||||||
\(239\) | 13.2720 | 0.858493 | 0.429246 | − | 0.903187i | \(-0.358779\pi\) | ||||
0.429246 | + | 0.903187i | \(0.358779\pi\) | |||||||
\(240\) | −0.312107 | −0.0201464 | ||||||||
\(241\) | −19.4649 | −1.25384 | −0.626922 | − | 0.779082i | \(-0.715686\pi\) | ||||
−0.626922 | + | 0.779082i | \(0.715686\pi\) | |||||||
\(242\) | 12.4256 | 0.798748 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.9276 | 0.827605 | ||||||||
\(245\) | 1.78826 | 0.114248 | ||||||||
\(246\) | 10.4714 | 0.667630 | ||||||||
\(247\) | −2.90027 | −0.184540 | ||||||||
\(248\) | −1.67878 | −0.106603 | ||||||||
\(249\) | 9.84132 | 0.623668 | ||||||||
\(250\) | 3.09067 | 0.195471 | ||||||||
\(251\) | 13.5545 | 0.855555 | 0.427777 | − | 0.903884i | \(-0.359297\pi\) | ||||
0.427777 | + | 0.903884i | \(0.359297\pi\) | |||||||
\(252\) | −1.12710 | −0.0710007 | ||||||||
\(253\) | 35.9748 | 2.26172 | ||||||||
\(254\) | −4.97721 | −0.312298 | ||||||||
\(255\) | 0.740467 | 0.0463699 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.07788 | −0.566263 | −0.283131 | − | 0.959081i | \(-0.591373\pi\) | ||||
−0.283131 | + | 0.959081i | \(0.591373\pi\) | |||||||
\(258\) | 6.43770 | 0.400794 | ||||||||
\(259\) | 4.95707 | 0.308017 | ||||||||
\(260\) | 0.905195 | 0.0561378 | ||||||||
\(261\) | 2.54808 | 0.157722 | ||||||||
\(262\) | 10.7157 | 0.662016 | ||||||||
\(263\) | 3.49362 | 0.215426 | 0.107713 | − | 0.994182i | \(-0.465647\pi\) | ||||
0.107713 | + | 0.994182i | \(0.465647\pi\) | |||||||
\(264\) | 4.84000 | 0.297881 | ||||||||
\(265\) | 0.312107 | 0.0191726 | ||||||||
\(266\) | −1.12710 | −0.0691070 | ||||||||
\(267\) | −4.79561 | −0.293487 | ||||||||
\(268\) | −3.92221 | −0.239587 | ||||||||
\(269\) | −10.7773 | −0.657103 | −0.328552 | − | 0.944486i | \(-0.606561\pi\) | ||||
−0.328552 | + | 0.944486i | \(0.606561\pi\) | |||||||
\(270\) | −0.312107 | −0.0189942 | ||||||||
\(271\) | −30.7063 | −1.86527 | −0.932637 | − | 0.360817i | \(-0.882498\pi\) | ||||
−0.932637 | + | 0.360817i | \(0.882498\pi\) | |||||||
\(272\) | −2.37248 | −0.143853 | ||||||||
\(273\) | 3.26890 | 0.197843 | ||||||||
\(274\) | −5.43456 | −0.328314 | ||||||||
\(275\) | −23.7285 | −1.43088 | ||||||||
\(276\) | 7.43281 | 0.447402 | ||||||||
\(277\) | −0.0124079 | −0.000745520 0 | −0.000372760 | − | 1.00000i | \(-0.500119\pi\) | ||||
−0.000372760 | 1.00000i | \(0.500119\pi\) | ||||||||
\(278\) | −18.9143 | −1.13440 | ||||||||
\(279\) | −1.67878 | −0.100506 | ||||||||
\(280\) | 0.351776 | 0.0210226 | ||||||||
\(281\) | 9.13583 | 0.544998 | 0.272499 | − | 0.962156i | \(-0.412150\pi\) | ||||
0.272499 | + | 0.962156i | \(0.412150\pi\) | |||||||
\(282\) | 9.40984 | 0.560348 | ||||||||
\(283\) | −9.25049 | −0.549884 | −0.274942 | − | 0.961461i | \(-0.588659\pi\) | ||||
−0.274942 | + | 0.961461i | \(0.588659\pi\) | |||||||
\(284\) | 12.6875 | 0.752863 | ||||||||
\(285\) | −0.312107 | −0.0184876 | ||||||||
\(286\) | −14.0373 | −0.830044 | ||||||||
\(287\) | −11.8023 | −0.696667 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.3713 | −0.668903 | ||||||||
\(290\) | −0.795274 | −0.0467001 | ||||||||
\(291\) | 4.44071 | 0.260319 | ||||||||
\(292\) | −3.56841 | −0.208825 | ||||||||
\(293\) | 14.4344 | 0.843265 | 0.421632 | − | 0.906767i | \(-0.361457\pi\) | ||||
0.421632 | + | 0.906767i | \(0.361457\pi\) | |||||||
\(294\) | −5.72964 | −0.334160 | ||||||||
\(295\) | −0.322949 | −0.0188028 | ||||||||
\(296\) | −4.39807 | −0.255633 | ||||||||
\(297\) | 4.84000 | 0.280845 | ||||||||
\(298\) | −9.36511 | −0.542506 | ||||||||
\(299\) | −21.5572 | −1.24668 | ||||||||
\(300\) | −4.90259 | −0.283051 | ||||||||
\(301\) | −7.25594 | −0.418225 | ||||||||
\(302\) | 19.7763 | 1.13800 | ||||||||
\(303\) | −13.2891 | −0.763438 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −4.03480 | −0.231032 | ||||||||
\(306\) | −2.37248 | −0.135626 | ||||||||
\(307\) | 25.1928 | 1.43783 | 0.718914 | − | 0.695099i | \(-0.244640\pi\) | ||||
0.718914 | + | 0.695099i | \(0.244640\pi\) | |||||||
\(308\) | −5.45517 | −0.310837 | ||||||||
\(309\) | 18.5115 | 1.05308 | ||||||||
\(310\) | 0.523960 | 0.0297589 | ||||||||
\(311\) | −0.712485 | −0.0404013 | −0.0202007 | − | 0.999796i | \(-0.506431\pi\) | ||||
−0.0202007 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(312\) | −2.90027 | −0.164196 | ||||||||
\(313\) | 6.85218 | 0.387308 | 0.193654 | − | 0.981070i | \(-0.437966\pi\) | ||||
0.193654 | + | 0.981070i | \(0.437966\pi\) | |||||||
\(314\) | 6.96594 | 0.393111 | ||||||||
\(315\) | 0.351776 | 0.0198203 | ||||||||
\(316\) | −2.83255 | −0.159343 | ||||||||
\(317\) | −14.4900 | −0.813837 | −0.406919 | − | 0.913464i | \(-0.633397\pi\) | ||||
−0.406919 | + | 0.913464i | \(0.633397\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | 12.3327 | 0.690499 | ||||||||
\(320\) | −0.312107 | −0.0174473 | ||||||||
\(321\) | −6.18950 | −0.345464 | ||||||||
\(322\) | −8.37752 | −0.466861 | ||||||||
\(323\) | −2.37248 | −0.132008 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 14.2188 | 0.788719 | ||||||||
\(326\) | 1.93881 | 0.107381 | ||||||||
\(327\) | −13.0943 | −0.724117 | ||||||||
\(328\) | 10.4714 | 0.578185 | ||||||||
\(329\) | −10.6058 | −0.584719 | ||||||||
\(330\) | −1.51060 | −0.0831557 | ||||||||
\(331\) | 19.0040 | 1.04456 | 0.522279 | − | 0.852775i | \(-0.325082\pi\) | ||||
0.522279 | + | 0.852775i | \(0.325082\pi\) | |||||||
\(332\) | 9.84132 | 0.540113 | ||||||||
\(333\) | −4.39807 | −0.241013 | ||||||||
\(334\) | 24.3879 | 1.33444 | ||||||||
\(335\) | 1.22415 | 0.0668824 | ||||||||
\(336\) | −1.12710 | −0.0614884 | ||||||||
\(337\) | −8.22592 | −0.448095 | −0.224047 | − | 0.974578i | \(-0.571927\pi\) | ||||
−0.224047 | + | 0.974578i | \(0.571927\pi\) | |||||||
\(338\) | −4.58842 | −0.249577 | ||||||||
\(339\) | 6.55174 | 0.355842 | ||||||||
\(340\) | 0.740467 | 0.0401575 | ||||||||
\(341\) | −8.12532 | −0.440011 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 14.3476 | 0.774697 | ||||||||
\(344\) | 6.43770 | 0.347098 | ||||||||
\(345\) | −2.31983 | −0.124896 | ||||||||
\(346\) | −10.5054 | −0.564773 | ||||||||
\(347\) | 2.98107 | 0.160032 | 0.0800161 | − | 0.996794i | \(-0.474503\pi\) | ||||
0.0800161 | + | 0.996794i | \(0.474503\pi\) | |||||||
\(348\) | 2.54808 | 0.136591 | ||||||||
\(349\) | 11.7132 | 0.626992 | 0.313496 | − | 0.949590i | \(-0.398500\pi\) | ||||
0.313496 | + | 0.949590i | \(0.398500\pi\) | |||||||
\(350\) | 5.52571 | 0.295362 | ||||||||
\(351\) | −2.90027 | −0.154805 | ||||||||
\(352\) | 4.84000 | 0.257973 | ||||||||
\(353\) | −1.11039 | −0.0591003 | −0.0295501 | − | 0.999563i | \(-0.509407\pi\) | ||||
−0.0295501 | + | 0.999563i | \(0.509407\pi\) | |||||||
\(354\) | 1.03474 | 0.0549957 | ||||||||
\(355\) | −3.95985 | −0.210167 | ||||||||
\(356\) | −4.79561 | −0.254167 | ||||||||
\(357\) | 2.67402 | 0.141524 | ||||||||
\(358\) | −5.23975 | −0.276929 | ||||||||
\(359\) | −0.00864373 | −0.000456199 0 | −0.000228099 | − | 1.00000i | \(-0.500073\pi\) | ||||
−0.000228099 | 1.00000i | \(0.500073\pi\) | ||||||||
\(360\) | −0.312107 | −0.0164495 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0.0286803 | 0.00150741 | ||||||||
\(363\) | 12.4256 | 0.652175 | ||||||||
\(364\) | 3.26890 | 0.171337 | ||||||||
\(365\) | 1.11372 | 0.0582950 | ||||||||
\(366\) | 12.9276 | 0.675737 | ||||||||
\(367\) | 25.1528 | 1.31297 | 0.656483 | − | 0.754341i | \(-0.272044\pi\) | ||||
0.656483 | + | 0.754341i | \(0.272044\pi\) | |||||||
\(368\) | 7.43281 | 0.387462 | ||||||||
\(369\) | 10.4714 | 0.545118 | ||||||||
\(370\) | 1.37267 | 0.0713616 | ||||||||
\(371\) | 1.12710 | 0.0585162 | ||||||||
\(372\) | −1.67878 | −0.0870409 | ||||||||
\(373\) | −11.8013 | −0.611049 | −0.305525 | − | 0.952184i | \(-0.598832\pi\) | ||||
−0.305525 | + | 0.952184i | \(0.598832\pi\) | |||||||
\(374\) | −11.4828 | −0.593761 | ||||||||
\(375\) | 3.09067 | 0.159601 | ||||||||
\(376\) | 9.40984 | 0.485275 | ||||||||
\(377\) | −7.39013 | −0.380611 | ||||||||
\(378\) | −1.12710 | −0.0579718 | ||||||||
\(379\) | −19.9045 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(380\) | −0.312107 | −0.0160107 | ||||||||
\(381\) | −4.97721 | −0.254990 | ||||||||
\(382\) | −20.7273 | −1.06050 | ||||||||
\(383\) | 25.5615 | 1.30613 | 0.653066 | − | 0.757301i | \(-0.273482\pi\) | ||||
0.653066 | + | 0.757301i | \(0.273482\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.70260 | 0.0867723 | ||||||||
\(386\) | −8.95443 | −0.455769 | ||||||||
\(387\) | 6.43770 | 0.327247 | ||||||||
\(388\) | 4.44071 | 0.225443 | ||||||||
\(389\) | −4.98592 | −0.252796 | −0.126398 | − | 0.991980i | \(-0.540342\pi\) | ||||
−0.126398 | + | 0.991980i | \(0.540342\pi\) | |||||||
\(390\) | 0.905195 | 0.0458363 | ||||||||
\(391\) | −17.6342 | −0.891799 | ||||||||
\(392\) | −5.72964 | −0.289391 | ||||||||
\(393\) | 10.7157 | 0.540534 | ||||||||
\(394\) | 15.2265 | 0.767098 | ||||||||
\(395\) | 0.884058 | 0.0444818 | ||||||||
\(396\) | 4.84000 | 0.243219 | ||||||||
\(397\) | 4.44779 | 0.223228 | 0.111614 | − | 0.993752i | \(-0.464398\pi\) | ||||
0.111614 | + | 0.993752i | \(0.464398\pi\) | |||||||
\(398\) | 18.7897 | 0.941843 | ||||||||
\(399\) | −1.12710 | −0.0564256 | ||||||||
\(400\) | −4.90259 | −0.245129 | ||||||||
\(401\) | −2.92809 | −0.146222 | −0.0731110 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731110 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(402\) | −3.92221 | −0.195622 | ||||||||
\(403\) | 4.86893 | 0.242539 | ||||||||
\(404\) | −13.2891 | −0.661156 | ||||||||
\(405\) | −0.312107 | −0.0155087 | ||||||||
\(406\) | −2.87194 | −0.142532 | ||||||||
\(407\) | −21.2867 | −1.05514 | ||||||||
\(408\) | −2.37248 | −0.117455 | ||||||||
\(409\) | 19.7987 | 0.978985 | 0.489492 | − | 0.872008i | \(-0.337182\pi\) | ||||
0.489492 | + | 0.872008i | \(0.337182\pi\) | |||||||
\(410\) | −3.26819 | −0.161404 | ||||||||
\(411\) | −5.43456 | −0.268067 | ||||||||
\(412\) | 18.5115 | 0.911994 | ||||||||
\(413\) | −1.16625 | −0.0573876 | ||||||||
\(414\) | 7.43281 | 0.365303 | ||||||||
\(415\) | −3.07154 | −0.150776 | ||||||||
\(416\) | −2.90027 | −0.142198 | ||||||||
\(417\) | −18.9143 | −0.926235 | ||||||||
\(418\) | 4.84000 | 0.236732 | ||||||||
\(419\) | −15.8532 | −0.774479 | −0.387240 | − | 0.921979i | \(-0.626571\pi\) | ||||
−0.387240 | + | 0.921979i | \(0.626571\pi\) | |||||||
\(420\) | 0.351776 | 0.0171649 | ||||||||
\(421\) | 22.0991 | 1.07704 | 0.538521 | − | 0.842612i | \(-0.318983\pi\) | ||||
0.538521 | + | 0.842612i | \(0.318983\pi\) | |||||||
\(422\) | 15.6590 | 0.762266 | ||||||||
\(423\) | 9.40984 | 0.457522 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 11.6313 | 0.564200 | ||||||||
\(426\) | 12.6875 | 0.614710 | ||||||||
\(427\) | −14.5707 | −0.705126 | ||||||||
\(428\) | −6.18950 | −0.299181 | ||||||||
\(429\) | −14.0373 | −0.677728 | ||||||||
\(430\) | −2.00925 | −0.0968947 | ||||||||
\(431\) | −8.57113 | −0.412857 | −0.206428 | − | 0.978462i | \(-0.566184\pi\) | ||||
−0.206428 | + | 0.978462i | \(0.566184\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −15.7372 | −0.756281 | −0.378140 | − | 0.925748i | \(-0.623436\pi\) | ||||
−0.378140 | + | 0.925748i | \(0.623436\pi\) | |||||||
\(434\) | 1.89216 | 0.0908265 | ||||||||
\(435\) | −0.795274 | −0.0381305 | ||||||||
\(436\) | −13.0943 | −0.627104 | ||||||||
\(437\) | 7.43281 | 0.355559 | ||||||||
\(438\) | −3.56841 | −0.170505 | ||||||||
\(439\) | −4.07960 | −0.194709 | −0.0973544 | − | 0.995250i | \(-0.531038\pi\) | ||||
−0.0973544 | + | 0.995250i | \(0.531038\pi\) | |||||||
\(440\) | −1.51060 | −0.0720149 | ||||||||
\(441\) | −5.72964 | −0.272840 | ||||||||
\(442\) | 6.88083 | 0.327288 | ||||||||
\(443\) | −11.3643 | −0.539934 | −0.269967 | − | 0.962870i | \(-0.587013\pi\) | ||||
−0.269967 | + | 0.962870i | \(0.587013\pi\) | |||||||
\(444\) | −4.39807 | −0.208723 | ||||||||
\(445\) | 1.49674 | 0.0709525 | ||||||||
\(446\) | 1.69152 | 0.0800960 | ||||||||
\(447\) | −9.36511 | −0.442955 | ||||||||
\(448\) | −1.12710 | −0.0532505 | ||||||||
\(449\) | −4.01659 | −0.189554 | −0.0947772 | − | 0.995499i | \(-0.530214\pi\) | ||||
−0.0947772 | + | 0.995499i | \(0.530214\pi\) | |||||||
\(450\) | −4.90259 | −0.231110 | ||||||||
\(451\) | 50.6815 | 2.38650 | ||||||||
\(452\) | 6.55174 | 0.308168 | ||||||||
\(453\) | 19.7763 | 0.929174 | ||||||||
\(454\) | 19.5295 | 0.916564 | ||||||||
\(455\) | −1.02025 | −0.0478299 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 5.36089 | 0.250772 | 0.125386 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125386 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(458\) | −12.1019 | −0.565486 | ||||||||
\(459\) | −2.37248 | −0.110738 | ||||||||
\(460\) | −2.31983 | −0.108163 | ||||||||
\(461\) | 9.48494 | 0.441758 | 0.220879 | − | 0.975301i | \(-0.429107\pi\) | ||||
0.220879 | + | 0.975301i | \(0.429107\pi\) | |||||||
\(462\) | −5.45517 | −0.253797 | ||||||||
\(463\) | −28.1321 | −1.30741 | −0.653704 | − | 0.756750i | \(-0.726786\pi\) | ||||
−0.653704 | + | 0.756750i | \(0.726786\pi\) | |||||||
\(464\) | 2.54808 | 0.118292 | ||||||||
\(465\) | 0.523960 | 0.0242981 | ||||||||
\(466\) | −19.3946 | −0.898438 | ||||||||
\(467\) | −1.03823 | −0.0480437 | −0.0240219 | − | 0.999711i | \(-0.507647\pi\) | ||||
−0.0240219 | + | 0.999711i | \(0.507647\pi\) | |||||||
\(468\) | −2.90027 | −0.134065 | ||||||||
\(469\) | 4.42073 | 0.204130 | ||||||||
\(470\) | −2.93688 | −0.135468 | ||||||||
\(471\) | 6.96594 | 0.320973 | ||||||||
\(472\) | 1.03474 | 0.0476277 | ||||||||
\(473\) | 31.1585 | 1.43267 | ||||||||
\(474\) | −2.83255 | −0.130103 | ||||||||
\(475\) | −4.90259 | −0.224946 | ||||||||
\(476\) | 2.67402 | 0.122564 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 13.2720 | 0.607046 | ||||||||
\(479\) | −29.5296 | −1.34924 | −0.674620 | − | 0.738165i | \(-0.735693\pi\) | ||||
−0.674620 | + | 0.738165i | \(0.735693\pi\) | |||||||
\(480\) | −0.312107 | −0.0142457 | ||||||||
\(481\) | 12.7556 | 0.581605 | ||||||||
\(482\) | −19.4649 | −0.886602 | ||||||||
\(483\) | −8.37752 | −0.381191 | ||||||||
\(484\) | 12.4256 | 0.564800 | ||||||||
\(485\) | −1.38598 | −0.0629340 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −38.8021 | −1.75829 | −0.879145 | − | 0.476554i | \(-0.841886\pi\) | ||||
−0.879145 | + | 0.476554i | \(0.841886\pi\) | |||||||
\(488\) | 12.9276 | 0.585205 | ||||||||
\(489\) | 1.93881 | 0.0876759 | ||||||||
\(490\) | 1.78826 | 0.0807854 | ||||||||
\(491\) | −20.0880 | −0.906558 | −0.453279 | − | 0.891369i | \(-0.649746\pi\) | ||||
−0.453279 | + | 0.891369i | \(0.649746\pi\) | |||||||
\(492\) | 10.4714 | 0.472086 | ||||||||
\(493\) | −6.04527 | −0.272265 | ||||||||
\(494\) | −2.90027 | −0.130489 | ||||||||
\(495\) | −1.51060 | −0.0678963 | ||||||||
\(496\) | −1.67878 | −0.0753796 | ||||||||
\(497\) | −14.3001 | −0.641445 | ||||||||
\(498\) | 9.84132 | 0.441000 | ||||||||
\(499\) | −6.79610 | −0.304235 | −0.152118 | − | 0.988362i | \(-0.548609\pi\) | ||||
−0.152118 | + | 0.988362i | \(0.548609\pi\) | |||||||
\(500\) | 3.09067 | 0.138219 | ||||||||
\(501\) | 24.3879 | 1.08957 | ||||||||
\(502\) | 13.5545 | 0.604969 | ||||||||
\(503\) | −14.8344 | −0.661431 | −0.330716 | − | 0.943730i | \(-0.607290\pi\) | ||||
−0.330716 | + | 0.943730i | \(0.607290\pi\) | |||||||
\(504\) | −1.12710 | −0.0502051 | ||||||||
\(505\) | 4.14761 | 0.184566 | ||||||||
\(506\) | 35.9748 | 1.59927 | ||||||||
\(507\) | −4.58842 | −0.203779 | ||||||||
\(508\) | −4.97721 | −0.220828 | ||||||||
\(509\) | 2.89253 | 0.128209 | 0.0641045 | − | 0.997943i | \(-0.479581\pi\) | ||||
0.0641045 | + | 0.997943i | \(0.479581\pi\) | |||||||
\(510\) | 0.740467 | 0.0327884 | ||||||||
\(511\) | 4.02195 | 0.177921 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −9.07788 | −0.400408 | ||||||||
\(515\) | −5.77755 | −0.254589 | ||||||||
\(516\) | 6.43770 | 0.283404 | ||||||||
\(517\) | 45.5436 | 2.00301 | ||||||||
\(518\) | 4.95707 | 0.217801 | ||||||||
\(519\) | −10.5054 | −0.461135 | ||||||||
\(520\) | 0.905195 | 0.0396954 | ||||||||
\(521\) | −33.1033 | −1.45028 | −0.725142 | − | 0.688600i | \(-0.758226\pi\) | ||||
−0.725142 | + | 0.688600i | \(0.758226\pi\) | |||||||
\(522\) | 2.54808 | 0.111526 | ||||||||
\(523\) | −4.44257 | −0.194260 | −0.0971300 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971300 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(524\) | 10.7157 | 0.468116 | ||||||||
\(525\) | 5.52571 | 0.241162 | ||||||||
\(526\) | 3.49362 | 0.152329 | ||||||||
\(527\) | 3.98288 | 0.173497 | ||||||||
\(528\) | 4.84000 | 0.210634 | ||||||||
\(529\) | 32.2466 | 1.40203 | ||||||||
\(530\) | 0.312107 | 0.0135571 | ||||||||
\(531\) | 1.03474 | 0.0449038 | ||||||||
\(532\) | −1.12710 | −0.0488660 | ||||||||
\(533\) | −30.3698 | −1.31546 | ||||||||
\(534\) | −4.79561 | −0.207526 | ||||||||
\(535\) | 1.93179 | 0.0835184 | ||||||||
\(536\) | −3.92221 | −0.169414 | ||||||||
\(537\) | −5.23975 | −0.226112 | ||||||||
\(538\) | −10.7773 | −0.464642 | ||||||||
\(539\) | −27.7315 | −1.19448 | ||||||||
\(540\) | −0.312107 | −0.0134309 | ||||||||
\(541\) | −2.23297 | −0.0960029 | −0.0480015 | − | 0.998847i | \(-0.515285\pi\) | ||||
−0.0480015 | + | 0.998847i | \(0.515285\pi\) | |||||||
\(542\) | −30.7063 | −1.31895 | ||||||||
\(543\) | 0.0286803 | 0.00123079 | ||||||||
\(544\) | −2.37248 | −0.101719 | ||||||||
\(545\) | 4.08682 | 0.175060 | ||||||||
\(546\) | 3.26890 | 0.139896 | ||||||||
\(547\) | 8.84662 | 0.378254 | 0.189127 | − | 0.981953i | \(-0.439434\pi\) | ||||
0.189127 | + | 0.981953i | \(0.439434\pi\) | |||||||
\(548\) | −5.43456 | −0.232153 | ||||||||
\(549\) | 12.9276 | 0.551737 | ||||||||
\(550\) | −23.7285 | −1.01179 | ||||||||
\(551\) | 2.54808 | 0.108552 | ||||||||
\(552\) | 7.43281 | 0.316361 | ||||||||
\(553\) | 3.19257 | 0.135762 | ||||||||
\(554\) | −0.0124079 | −0.000527162 0 | ||||||||
\(555\) | 1.37267 | 0.0582665 | ||||||||
\(556\) | −18.9143 | −0.802143 | ||||||||
\(557\) | −31.4547 | −1.33278 | −0.666389 | − | 0.745604i | \(-0.732161\pi\) | ||||
−0.666389 | + | 0.745604i | \(0.732161\pi\) | |||||||
\(558\) | −1.67878 | −0.0710686 | ||||||||
\(559\) | −18.6711 | −0.789703 | ||||||||
\(560\) | 0.351776 | 0.0148652 | ||||||||
\(561\) | −11.4828 | −0.484804 | ||||||||
\(562\) | 9.13583 | 0.385372 | ||||||||
\(563\) | −24.1511 | −1.01785 | −0.508923 | − | 0.860812i | \(-0.669956\pi\) | ||||
−0.508923 | + | 0.860812i | \(0.669956\pi\) | |||||||
\(564\) | 9.40984 | 0.396226 | ||||||||
\(565\) | −2.04484 | −0.0860273 | ||||||||
\(566\) | −9.25049 | −0.388827 | ||||||||
\(567\) | −1.12710 | −0.0473338 | ||||||||
\(568\) | 12.6875 | 0.532354 | ||||||||
\(569\) | −37.2824 | −1.56296 | −0.781480 | − | 0.623931i | \(-0.785535\pi\) | ||||
−0.781480 | + | 0.623931i | \(0.785535\pi\) | |||||||
\(570\) | −0.312107 | −0.0130727 | ||||||||
\(571\) | −41.1691 | −1.72287 | −0.861436 | − | 0.507866i | \(-0.830435\pi\) | ||||
−0.861436 | + | 0.507866i | \(0.830435\pi\) | |||||||
\(572\) | −14.0373 | −0.586930 | ||||||||
\(573\) | −20.7273 | −0.865895 | ||||||||
\(574\) | −11.8023 | −0.492618 | ||||||||
\(575\) | −36.4400 | −1.51965 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.3871 | −0.723833 | −0.361916 | − | 0.932211i | \(-0.617877\pi\) | ||||
−0.361916 | + | 0.932211i | \(0.617877\pi\) | |||||||
\(578\) | −11.3713 | −0.472986 | ||||||||
\(579\) | −8.95443 | −0.372134 | ||||||||
\(580\) | −0.795274 | −0.0330219 | ||||||||
\(581\) | −11.0922 | −0.460180 | ||||||||
\(582\) | 4.44071 | 0.184073 | ||||||||
\(583\) | −4.84000 | −0.200452 | ||||||||
\(584\) | −3.56841 | −0.147662 | ||||||||
\(585\) | 0.905195 | 0.0374252 | ||||||||
\(586\) | 14.4344 | 0.596278 | ||||||||
\(587\) | −33.8883 | −1.39872 | −0.699359 | − | 0.714770i | \(-0.746531\pi\) | ||||
−0.699359 | + | 0.714770i | \(0.746531\pi\) | |||||||
\(588\) | −5.72964 | −0.236287 | ||||||||
\(589\) | −1.67878 | −0.0691731 | ||||||||
\(590\) | −0.322949 | −0.0132956 | ||||||||
\(591\) | 15.2265 | 0.626333 | ||||||||
\(592\) | −4.39807 | −0.180760 | ||||||||
\(593\) | 16.9261 | 0.695073 | 0.347536 | − | 0.937666i | \(-0.387018\pi\) | ||||
0.347536 | + | 0.937666i | \(0.387018\pi\) | |||||||
\(594\) | 4.84000 | 0.198588 | ||||||||
\(595\) | −0.834581 | −0.0342145 | ||||||||
\(596\) | −9.36511 | −0.383610 | ||||||||
\(597\) | 18.7897 | 0.769012 | ||||||||
\(598\) | −21.5572 | −0.881538 | ||||||||
\(599\) | −12.3523 | −0.504703 | −0.252351 | − | 0.967636i | \(-0.581204\pi\) | ||||
−0.252351 | + | 0.967636i | \(0.581204\pi\) | |||||||
\(600\) | −4.90259 | −0.200147 | ||||||||
\(601\) | −33.6317 | −1.37187 | −0.685933 | − | 0.727665i | \(-0.740606\pi\) | ||||
−0.685933 | + | 0.727665i | \(0.740606\pi\) | |||||||
\(602\) | −7.25594 | −0.295730 | ||||||||
\(603\) | −3.92221 | −0.159725 | ||||||||
\(604\) | 19.7763 | 0.804688 | ||||||||
\(605\) | −3.87812 | −0.157668 | ||||||||
\(606\) | −13.2891 | −0.539832 | ||||||||
\(607\) | 26.5653 | 1.07825 | 0.539126 | − | 0.842225i | \(-0.318755\pi\) | ||||
0.539126 | + | 0.842225i | \(0.318755\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −2.87194 | −0.116377 | ||||||||
\(610\) | −4.03480 | −0.163364 | ||||||||
\(611\) | −27.2911 | −1.10408 | ||||||||
\(612\) | −2.37248 | −0.0959018 | ||||||||
\(613\) | −32.9423 | −1.33053 | −0.665264 | − | 0.746608i | \(-0.731681\pi\) | ||||
−0.665264 | + | 0.746608i | \(0.731681\pi\) | |||||||
\(614\) | 25.1928 | 1.01670 | ||||||||
\(615\) | −3.26819 | −0.131786 | ||||||||
\(616\) | −5.45517 | −0.219795 | ||||||||
\(617\) | −12.9819 | −0.522633 | −0.261316 | − | 0.965253i | \(-0.584157\pi\) | ||||
−0.261316 | + | 0.965253i | \(0.584157\pi\) | |||||||
\(618\) | 18.5115 | 0.744640 | ||||||||
\(619\) | −22.9877 | −0.923953 | −0.461976 | − | 0.886892i | \(-0.652860\pi\) | ||||
−0.461976 | + | 0.886892i | \(0.652860\pi\) | |||||||
\(620\) | 0.523960 | 0.0210427 | ||||||||
\(621\) | 7.43281 | 0.298268 | ||||||||
\(622\) | −0.712485 | −0.0285681 | ||||||||
\(623\) | 5.40514 | 0.216552 | ||||||||
\(624\) | −2.90027 | −0.116104 | ||||||||
\(625\) | 23.5483 | 0.941933 | ||||||||
\(626\) | 6.85218 | 0.273868 | ||||||||
\(627\) | 4.84000 | 0.193291 | ||||||||
\(628\) | 6.96594 | 0.277971 | ||||||||
\(629\) | 10.4343 | 0.416044 | ||||||||
\(630\) | 0.351776 | 0.0140151 | ||||||||
\(631\) | −22.6885 | −0.903213 | −0.451607 | − | 0.892217i | \(-0.649149\pi\) | ||||
−0.451607 | + | 0.892217i | \(0.649149\pi\) | |||||||
\(632\) | −2.83255 | −0.112673 | ||||||||
\(633\) | 15.6590 | 0.622388 | ||||||||
\(634\) | −14.4900 | −0.575470 | ||||||||
\(635\) | 1.55342 | 0.0616456 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 16.6175 | 0.658410 | ||||||||
\(638\) | 12.3327 | 0.488257 | ||||||||
\(639\) | 12.6875 | 0.501908 | ||||||||
\(640\) | −0.312107 | −0.0123371 | ||||||||
\(641\) | 4.94747 | 0.195413 | 0.0977066 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977066 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(642\) | −6.18950 | −0.244280 | ||||||||
\(643\) | 3.64025 | 0.143558 | 0.0717788 | − | 0.997421i | \(-0.477132\pi\) | ||||
0.0717788 | + | 0.997421i | \(0.477132\pi\) | |||||||
\(644\) | −8.37752 | −0.330121 | ||||||||
\(645\) | −2.00925 | −0.0791142 | ||||||||
\(646\) | −2.37248 | −0.0933439 | ||||||||
\(647\) | 23.6656 | 0.930391 | 0.465196 | − | 0.885208i | \(-0.345984\pi\) | ||||
0.465196 | + | 0.885208i | \(0.345984\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.00813 | 0.196586 | ||||||||
\(650\) | 14.2188 | 0.557709 | ||||||||
\(651\) | 1.89216 | 0.0741595 | ||||||||
\(652\) | 1.93881 | 0.0759296 | ||||||||
\(653\) | −33.3328 | −1.30441 | −0.652206 | − | 0.758042i | \(-0.726156\pi\) | ||||
−0.652206 | + | 0.758042i | \(0.726156\pi\) | |||||||
\(654\) | −13.0943 | −0.512028 | ||||||||
\(655\) | −3.34443 | −0.130678 | ||||||||
\(656\) | 10.4714 | 0.408838 | ||||||||
\(657\) | −3.56841 | −0.139217 | ||||||||
\(658\) | −10.6058 | −0.413459 | ||||||||
\(659\) | 7.43691 | 0.289701 | 0.144850 | − | 0.989454i | \(-0.453730\pi\) | ||||
0.144850 | + | 0.989454i | \(0.453730\pi\) | |||||||
\(660\) | −1.51060 | −0.0587999 | ||||||||
\(661\) | 30.9982 | 1.20569 | 0.602845 | − | 0.797858i | \(-0.294034\pi\) | ||||
0.602845 | + | 0.797858i | \(0.294034\pi\) | |||||||
\(662\) | 19.0040 | 0.738613 | ||||||||
\(663\) | 6.88083 | 0.267229 | ||||||||
\(664\) | 9.84132 | 0.381917 | ||||||||
\(665\) | 0.351776 | 0.0136413 | ||||||||
\(666\) | −4.39807 | −0.170422 | ||||||||
\(667\) | 18.9394 | 0.733336 | ||||||||
\(668\) | 24.3879 | 0.943595 | ||||||||
\(669\) | 1.69152 | 0.0653981 | ||||||||
\(670\) | 1.22415 | 0.0472930 | ||||||||
\(671\) | 62.5696 | 2.41547 | ||||||||
\(672\) | −1.12710 | −0.0434789 | ||||||||
\(673\) | 10.0610 | 0.387822 | 0.193911 | − | 0.981019i | \(-0.437883\pi\) | ||||
0.193911 | + | 0.981019i | \(0.437883\pi\) | |||||||
\(674\) | −8.22592 | −0.316851 | ||||||||
\(675\) | −4.90259 | −0.188701 | ||||||||
\(676\) | −4.58842 | −0.176478 | ||||||||
\(677\) | 17.2255 | 0.662030 | 0.331015 | − | 0.943625i | \(-0.392609\pi\) | ||||
0.331015 | + | 0.943625i | \(0.392609\pi\) | |||||||
\(678\) | 6.55174 | 0.251618 | ||||||||
\(679\) | −5.00513 | −0.192079 | ||||||||
\(680\) | 0.740467 | 0.0283956 | ||||||||
\(681\) | 19.5295 | 0.748371 | ||||||||
\(682\) | −8.12532 | −0.311134 | ||||||||
\(683\) | 36.6898 | 1.40390 | 0.701949 | − | 0.712228i | \(-0.252314\pi\) | ||||
0.701949 | + | 0.712228i | \(0.252314\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 1.69617 | 0.0648071 | ||||||||
\(686\) | 14.3476 | 0.547794 | ||||||||
\(687\) | −12.1019 | −0.461718 | ||||||||
\(688\) | 6.43770 | 0.245435 | ||||||||
\(689\) | 2.90027 | 0.110492 | ||||||||
\(690\) | −2.31983 | −0.0883145 | ||||||||
\(691\) | −15.9653 | −0.607348 | −0.303674 | − | 0.952776i | \(-0.598213\pi\) | ||||
−0.303674 | + | 0.952776i | \(0.598213\pi\) | |||||||
\(692\) | −10.5054 | −0.399355 | ||||||||
\(693\) | −5.45517 | −0.207225 | ||||||||
\(694\) | 2.98107 | 0.113160 | ||||||||
\(695\) | 5.90327 | 0.223924 | ||||||||
\(696\) | 2.54808 | 0.0965848 | ||||||||
\(697\) | −24.8431 | −0.941000 | ||||||||
\(698\) | 11.7132 | 0.443350 | ||||||||
\(699\) | −19.3946 | −0.733572 | ||||||||
\(700\) | 5.52571 | 0.208852 | ||||||||
\(701\) | 0.219659 | 0.00829641 | 0.00414820 | − | 0.999991i | \(-0.498680\pi\) | ||||
0.00414820 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(702\) | −2.90027 | −0.109464 | ||||||||
\(703\) | −4.39807 | −0.165876 | ||||||||
\(704\) | 4.84000 | 0.182414 | ||||||||
\(705\) | −2.93688 | −0.110609 | ||||||||
\(706\) | −1.11039 | −0.0417902 | ||||||||
\(707\) | 14.9781 | 0.563310 | ||||||||
\(708\) | 1.03474 | 0.0388878 | ||||||||
\(709\) | −13.0944 | −0.491771 | −0.245886 | − | 0.969299i | \(-0.579079\pi\) | ||||
−0.245886 | + | 0.969299i | \(0.579079\pi\) | |||||||
\(710\) | −3.95985 | −0.148610 | ||||||||
\(711\) | −2.83255 | −0.106229 | ||||||||
\(712\) | −4.79561 | −0.179723 | ||||||||
\(713\) | −12.4781 | −0.467308 | ||||||||
\(714\) | 2.67402 | 0.100073 | ||||||||
\(715\) | 4.38114 | 0.163845 | ||||||||
\(716\) | −5.23975 | −0.195819 | ||||||||
\(717\) | 13.2720 | 0.495651 | ||||||||
\(718\) | −0.00864373 | −0.000322581 0 | ||||||||
\(719\) | 32.8022 | 1.22332 | 0.611658 | − | 0.791122i | \(-0.290503\pi\) | ||||
0.611658 | + | 0.791122i | \(0.290503\pi\) | |||||||
\(720\) | −0.312107 | −0.0116315 | ||||||||
\(721\) | −20.8643 | −0.777026 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −19.4649 | −0.723907 | ||||||||
\(724\) | 0.0286803 | 0.00106590 | ||||||||
\(725\) | −12.4922 | −0.463948 | ||||||||
\(726\) | 12.4256 | 0.461157 | ||||||||
\(727\) | −3.16192 | −0.117269 | −0.0586346 | − | 0.998280i | \(-0.518675\pi\) | ||||
−0.0586346 | + | 0.998280i | \(0.518675\pi\) | |||||||
\(728\) | 3.26890 | 0.121153 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.11372 | 0.0412208 | ||||||||
\(731\) | −15.2733 | −0.564904 | ||||||||
\(732\) | 12.9276 | 0.477818 | ||||||||
\(733\) | −27.9626 | −1.03282 | −0.516411 | − | 0.856341i | \(-0.672732\pi\) | ||||
−0.516411 | + | 0.856341i | \(0.672732\pi\) | |||||||
\(734\) | 25.1528 | 0.928407 | ||||||||
\(735\) | 1.78826 | 0.0659610 | ||||||||
\(736\) | 7.43281 | 0.273977 | ||||||||
\(737\) | −18.9835 | −0.699266 | ||||||||
\(738\) | 10.4714 | 0.385457 | ||||||||
\(739\) | −17.6904 | −0.650754 | −0.325377 | − | 0.945584i | \(-0.605491\pi\) | ||||
−0.325377 | + | 0.945584i | \(0.605491\pi\) | |||||||
\(740\) | 1.37267 | 0.0504603 | ||||||||
\(741\) | −2.90027 | −0.106544 | ||||||||
\(742\) | 1.12710 | 0.0413772 | ||||||||
\(743\) | −1.86526 | −0.0684298 | −0.0342149 | − | 0.999414i | \(-0.510893\pi\) | ||||
−0.0342149 | + | 0.999414i | \(0.510893\pi\) | |||||||
\(744\) | −1.67878 | −0.0615472 | ||||||||
\(745\) | 2.92292 | 0.107087 | ||||||||
\(746\) | −11.8013 | −0.432077 | ||||||||
\(747\) | 9.84132 | 0.360075 | ||||||||
\(748\) | −11.4828 | −0.419853 | ||||||||
\(749\) | 6.97619 | 0.254904 | ||||||||
\(750\) | 3.09067 | 0.112855 | ||||||||
\(751\) | −11.6483 | −0.425054 | −0.212527 | − | 0.977155i | \(-0.568169\pi\) | ||||
−0.212527 | + | 0.977155i | \(0.568169\pi\) | |||||||
\(752\) | 9.40984 | 0.343142 | ||||||||
\(753\) | 13.5545 | 0.493955 | ||||||||
\(754\) | −7.39013 | −0.269133 | ||||||||
\(755\) | −6.17234 | −0.224634 | ||||||||
\(756\) | −1.12710 | −0.0409923 | ||||||||
\(757\) | −12.9957 | −0.472338 | −0.236169 | − | 0.971712i | \(-0.575892\pi\) | ||||
−0.236169 | + | 0.971712i | \(0.575892\pi\) | |||||||
\(758\) | −19.9045 | −0.722964 | ||||||||
\(759\) | 35.9748 | 1.30580 | ||||||||
\(760\) | −0.312107 | −0.0113213 | ||||||||
\(761\) | −24.7997 | −0.898989 | −0.449494 | − | 0.893283i | \(-0.648396\pi\) | ||||
−0.449494 | + | 0.893283i | \(0.648396\pi\) | |||||||
\(762\) | −4.97721 | −0.180305 | ||||||||
\(763\) | 14.7586 | 0.534297 | ||||||||
\(764\) | −20.7273 | −0.749887 | ||||||||
\(765\) | 0.740467 | 0.0267716 | ||||||||
\(766\) | 25.5615 | 0.923575 | ||||||||
\(767\) | −3.00102 | −0.108361 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 35.6344 | 1.28501 | 0.642504 | − | 0.766282i | \(-0.277895\pi\) | ||||
0.642504 | + | 0.766282i | \(0.277895\pi\) | |||||||
\(770\) | 1.70260 | 0.0613573 | ||||||||
\(771\) | −9.07788 | −0.326932 | ||||||||
\(772\) | −8.95443 | −0.322277 | ||||||||
\(773\) | 3.56567 | 0.128248 | 0.0641241 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641241 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(774\) | 6.43770 | 0.231398 | ||||||||
\(775\) | 8.23039 | 0.295644 | ||||||||
\(776\) | 4.44071 | 0.159412 | ||||||||
\(777\) | 4.95707 | 0.177834 | ||||||||
\(778\) | −4.98592 | −0.178754 | ||||||||
\(779\) | 10.4714 | 0.375176 | ||||||||
\(780\) | 0.905195 | 0.0324112 | ||||||||
\(781\) | 61.4073 | 2.19733 | ||||||||
\(782\) | −17.6342 | −0.630597 | ||||||||
\(783\) | 2.54808 | 0.0910610 | ||||||||
\(784\) | −5.72964 | −0.204630 | ||||||||
\(785\) | −2.17412 | −0.0775976 | ||||||||
\(786\) | 10.7157 | 0.382215 | ||||||||
\(787\) | −25.2464 | −0.899938 | −0.449969 | − | 0.893044i | \(-0.648565\pi\) | ||||
−0.449969 | + | 0.893044i | \(0.648565\pi\) | |||||||
\(788\) | 15.2265 | 0.542420 | ||||||||
\(789\) | 3.49362 | 0.124376 | ||||||||
\(790\) | 0.884058 | 0.0314534 | ||||||||
\(791\) | −7.38447 | −0.262562 | ||||||||
\(792\) | 4.84000 | 0.171982 | ||||||||
\(793\) | −37.4936 | −1.33144 | ||||||||
\(794\) | 4.44779 | 0.157846 | ||||||||
\(795\) | 0.312107 | 0.0110693 | ||||||||
\(796\) | 18.7897 | 0.665984 | ||||||||
\(797\) | 52.3040 | 1.85270 | 0.926351 | − | 0.376662i | \(-0.122928\pi\) | ||||
0.926351 | + | 0.376662i | \(0.122928\pi\) | |||||||
\(798\) | −1.12710 | −0.0398989 | ||||||||
\(799\) | −22.3246 | −0.789789 | ||||||||
\(800\) | −4.90259 | −0.173333 | ||||||||
\(801\) | −4.79561 | −0.169445 | ||||||||
\(802\) | −2.92809 | −0.103395 | ||||||||
\(803\) | −17.2711 | −0.609484 | ||||||||
\(804\) | −3.92221 | −0.138326 | ||||||||
\(805\) | 2.61468 | 0.0921555 | ||||||||
\(806\) | 4.86893 | 0.171501 | ||||||||
\(807\) | −10.7773 | −0.379379 | ||||||||
\(808\) | −13.2891 | −0.467508 | ||||||||
\(809\) | 13.1451 | 0.462157 | 0.231079 | − | 0.972935i | \(-0.425775\pi\) | ||||
0.231079 | + | 0.972935i | \(0.425775\pi\) | |||||||
\(810\) | −0.312107 | −0.0109663 | ||||||||
\(811\) | 1.01350 | 0.0355888 | 0.0177944 | − | 0.999842i | \(-0.494336\pi\) | ||||
0.0177944 | + | 0.999842i | \(0.494336\pi\) | |||||||
\(812\) | −2.87194 | −0.100785 | ||||||||
\(813\) | −30.7063 | −1.07692 | ||||||||
\(814\) | −21.2867 | −0.746097 | ||||||||
\(815\) | −0.605115 | −0.0211963 | ||||||||
\(816\) | −2.37248 | −0.0830534 | ||||||||
\(817\) | 6.43770 | 0.225227 | ||||||||
\(818\) | 19.7987 | 0.692247 | ||||||||
\(819\) | 3.26890 | 0.114225 | ||||||||
\(820\) | −3.26819 | −0.114130 | ||||||||
\(821\) | −13.1364 | −0.458463 | −0.229232 | − | 0.973372i | \(-0.573621\pi\) | ||||
−0.229232 | + | 0.973372i | \(0.573621\pi\) | |||||||
\(822\) | −5.43456 | −0.189552 | ||||||||
\(823\) | −36.4883 | −1.27190 | −0.635951 | − | 0.771730i | \(-0.719392\pi\) | ||||
−0.635951 | + | 0.771730i | \(0.719392\pi\) | |||||||
\(824\) | 18.5115 | 0.644877 | ||||||||
\(825\) | −23.7285 | −0.826122 | ||||||||
\(826\) | −1.16625 | −0.0405792 | ||||||||
\(827\) | −6.01078 | −0.209015 | −0.104508 | − | 0.994524i | \(-0.533327\pi\) | ||||
−0.104508 | + | 0.994524i | \(0.533327\pi\) | |||||||
\(828\) | 7.43281 | 0.258308 | ||||||||
\(829\) | 40.9935 | 1.42376 | 0.711881 | − | 0.702300i | \(-0.247844\pi\) | ||||
0.711881 | + | 0.702300i | \(0.247844\pi\) | |||||||
\(830\) | −3.07154 | −0.106615 | ||||||||
\(831\) | −0.0124079 | −0.000430426 0 | ||||||||
\(832\) | −2.90027 | −0.100549 | ||||||||
\(833\) | 13.5935 | 0.470985 | ||||||||
\(834\) | −18.9143 | −0.654947 | ||||||||
\(835\) | −7.61162 | −0.263411 | ||||||||
\(836\) | 4.84000 | 0.167395 | ||||||||
\(837\) | −1.67878 | −0.0580273 | ||||||||
\(838\) | −15.8532 | −0.547639 | ||||||||
\(839\) | −39.4686 | −1.36261 | −0.681304 | − | 0.732000i | \(-0.738587\pi\) | ||||
−0.681304 | + | 0.732000i | \(0.738587\pi\) | |||||||
\(840\) | 0.351776 | 0.0121374 | ||||||||
\(841\) | −22.5073 | −0.776113 | ||||||||
\(842\) | 22.0991 | 0.761584 | ||||||||
\(843\) | 9.13583 | 0.314655 | ||||||||
\(844\) | 15.6590 | 0.539004 | ||||||||
\(845\) | 1.43208 | 0.0492650 | ||||||||
\(846\) | 9.40984 | 0.323517 | ||||||||
\(847\) | −14.0049 | −0.481214 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | −9.25049 | −0.317476 | ||||||||
\(850\) | 11.6313 | 0.398950 | ||||||||
\(851\) | −32.6900 | −1.12060 | ||||||||
\(852\) | 12.6875 | 0.434665 | ||||||||
\(853\) | 46.0837 | 1.57788 | 0.788938 | − | 0.614473i | \(-0.210631\pi\) | ||||
0.788938 | + | 0.614473i | \(0.210631\pi\) | |||||||
\(854\) | −14.5707 | −0.498600 | ||||||||
\(855\) | −0.312107 | −0.0106738 | ||||||||
\(856\) | −6.18950 | −0.211553 | ||||||||
\(857\) | −33.1700 | −1.13307 | −0.566533 | − | 0.824039i | \(-0.691716\pi\) | ||||
−0.566533 | + | 0.824039i | \(0.691716\pi\) | |||||||
\(858\) | −14.0373 | −0.479226 | ||||||||
\(859\) | −7.92260 | −0.270315 | −0.135158 | − | 0.990824i | \(-0.543154\pi\) | ||||
−0.135158 | + | 0.990824i | \(0.543154\pi\) | |||||||
\(860\) | −2.00925 | −0.0685149 | ||||||||
\(861\) | −11.8023 | −0.402221 | ||||||||
\(862\) | −8.57113 | −0.291934 | ||||||||
\(863\) | 56.9252 | 1.93776 | 0.968879 | − | 0.247536i | \(-0.0796209\pi\) | ||||
0.968879 | + | 0.247536i | \(0.0796209\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 3.27880 | 0.111483 | ||||||||
\(866\) | −15.7372 | −0.534771 | ||||||||
\(867\) | −11.3713 | −0.386191 | ||||||||
\(868\) | 1.89216 | 0.0642241 | ||||||||
\(869\) | −13.7095 | −0.465064 | ||||||||
\(870\) | −0.795274 | −0.0269623 | ||||||||
\(871\) | 11.3755 | 0.385443 | ||||||||
\(872\) | −13.0943 | −0.443429 | ||||||||
\(873\) | 4.44071 | 0.150295 | ||||||||
\(874\) | 7.43281 | 0.251418 | ||||||||
\(875\) | −3.48349 | −0.117764 | ||||||||
\(876\) | −3.56841 | −0.120565 | ||||||||
\(877\) | −25.7285 | −0.868789 | −0.434394 | − | 0.900723i | \(-0.643038\pi\) | ||||
−0.434394 | + | 0.900723i | \(0.643038\pi\) | |||||||
\(878\) | −4.07960 | −0.137680 | ||||||||
\(879\) | 14.4344 | 0.486859 | ||||||||
\(880\) | −1.51060 | −0.0509222 | ||||||||
\(881\) | 7.96729 | 0.268425 | 0.134212 | − | 0.990953i | \(-0.457150\pi\) | ||||
0.134212 | + | 0.990953i | \(0.457150\pi\) | |||||||
\(882\) | −5.72964 | −0.192927 | ||||||||
\(883\) | 18.7596 | 0.631312 | 0.315656 | − | 0.948874i | \(-0.397775\pi\) | ||||
0.315656 | + | 0.948874i | \(0.397775\pi\) | |||||||
\(884\) | 6.88083 | 0.231427 | ||||||||
\(885\) | −0.322949 | −0.0108558 | ||||||||
\(886\) | −11.3643 | −0.381791 | ||||||||
\(887\) | 41.6654 | 1.39899 | 0.699494 | − | 0.714638i | \(-0.253409\pi\) | ||||
0.699494 | + | 0.714638i | \(0.253409\pi\) | |||||||
\(888\) | −4.39807 | −0.147590 | ||||||||
\(889\) | 5.60981 | 0.188147 | ||||||||
\(890\) | 1.49674 | 0.0501710 | ||||||||
\(891\) | 4.84000 | 0.162146 | ||||||||
\(892\) | 1.69152 | 0.0566364 | ||||||||
\(893\) | 9.40984 | 0.314888 | ||||||||
\(894\) | −9.36511 | −0.313216 | ||||||||
\(895\) | 1.63536 | 0.0546641 | ||||||||
\(896\) | −1.12710 | −0.0376538 | ||||||||
\(897\) | −21.5572 | −0.719773 | ||||||||
\(898\) | −4.01659 | −0.134035 | ||||||||
\(899\) | −4.27768 | −0.142669 | ||||||||
\(900\) | −4.90259 | −0.163420 | ||||||||
\(901\) | 2.37248 | 0.0790387 | ||||||||
\(902\) | 50.6815 | 1.68751 | ||||||||
\(903\) | −7.25594 | −0.241463 | ||||||||
\(904\) | 6.55174 | 0.217908 | ||||||||
\(905\) | −0.00895133 | −0.000297552 0 | ||||||||
\(906\) | 19.7763 | 0.657025 | ||||||||
\(907\) | 30.4129 | 1.00984 | 0.504921 | − | 0.863165i | \(-0.331521\pi\) | ||||
0.504921 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(908\) | 19.5295 | 0.648108 | ||||||||
\(909\) | −13.2891 | −0.440771 | ||||||||
\(910\) | −1.02025 | −0.0338208 | ||||||||
\(911\) | 27.5910 | 0.914130 | 0.457065 | − | 0.889433i | \(-0.348901\pi\) | ||||
0.457065 | + | 0.889433i | \(0.348901\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 47.6320 | 1.57639 | ||||||||
\(914\) | 5.36089 | 0.177323 | ||||||||
\(915\) | −4.03480 | −0.133386 | ||||||||
\(916\) | −12.1019 | −0.399859 | ||||||||
\(917\) | −12.0776 | −0.398838 | ||||||||
\(918\) | −2.37248 | −0.0783035 | ||||||||
\(919\) | −47.4204 | −1.56425 | −0.782127 | − | 0.623119i | \(-0.785865\pi\) | ||||
−0.782127 | + | 0.623119i | \(0.785865\pi\) | |||||||
\(920\) | −2.31983 | −0.0764826 | ||||||||
\(921\) | 25.1928 | 0.830130 | ||||||||
\(922\) | 9.48494 | 0.312370 | ||||||||
\(923\) | −36.7971 | −1.21119 | ||||||||
\(924\) | −5.45517 | −0.179462 | ||||||||
\(925\) | 21.5619 | 0.708952 | ||||||||
\(926\) | −28.1321 | −0.924477 | ||||||||
\(927\) | 18.5115 | 0.607996 | ||||||||
\(928\) | 2.54808 | 0.0836449 | ||||||||
\(929\) | −43.8078 | −1.43729 | −0.718644 | − | 0.695378i | \(-0.755237\pi\) | ||||
−0.718644 | + | 0.695378i | \(0.755237\pi\) | |||||||
\(930\) | 0.523960 | 0.0171813 | ||||||||
\(931\) | −5.72964 | −0.187781 | ||||||||
\(932\) | −19.3946 | −0.635292 | ||||||||
\(933\) | −0.712485 | −0.0233257 | ||||||||
\(934\) | −1.03823 | −0.0339720 | ||||||||
\(935\) | 3.58386 | 0.117205 | ||||||||
\(936\) | −2.90027 | −0.0947983 | ||||||||
\(937\) | 50.7683 | 1.65853 | 0.829264 | − | 0.558857i | \(-0.188760\pi\) | ||||
0.829264 | + | 0.558857i | \(0.188760\pi\) | |||||||
\(938\) | 4.42073 | 0.144342 | ||||||||
\(939\) | 6.85218 | 0.223613 | ||||||||
\(940\) | −2.93688 | −0.0957903 | ||||||||
\(941\) | −18.6305 | −0.607337 | −0.303668 | − | 0.952778i | \(-0.598212\pi\) | ||||
−0.303668 | + | 0.952778i | \(0.598212\pi\) | |||||||
\(942\) | 6.96594 | 0.226962 | ||||||||
\(943\) | 77.8317 | 2.53455 | ||||||||
\(944\) | 1.03474 | 0.0336779 | ||||||||
\(945\) | 0.351776 | 0.0114433 | ||||||||
\(946\) | 31.1585 | 1.01305 | ||||||||
\(947\) | −8.12191 | −0.263927 | −0.131963 | − | 0.991255i | \(-0.542128\pi\) | ||||
−0.131963 | + | 0.991255i | \(0.542128\pi\) | |||||||
\(948\) | −2.83255 | −0.0919969 | ||||||||
\(949\) | 10.3493 | 0.335954 | ||||||||
\(950\) | −4.90259 | −0.159061 | ||||||||
\(951\) | −14.4900 | −0.469869 | ||||||||
\(952\) | 2.67402 | 0.0866656 | ||||||||
\(953\) | 51.2723 | 1.66087 | 0.830436 | − | 0.557114i | \(-0.188092\pi\) | ||||
0.830436 | + | 0.557114i | \(0.188092\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | 6.46913 | 0.209336 | ||||||||
\(956\) | 13.2720 | 0.429246 | ||||||||
\(957\) | 12.3327 | 0.398660 | ||||||||
\(958\) | −29.5296 | −0.954057 | ||||||||
\(959\) | 6.12530 | 0.197796 | ||||||||
\(960\) | −0.312107 | −0.0100732 | ||||||||
\(961\) | −28.1817 | −0.909087 | ||||||||
\(962\) | 12.7556 | 0.411257 | ||||||||
\(963\) | −6.18950 | −0.199454 | ||||||||
\(964\) | −19.4649 | −0.626922 | ||||||||
\(965\) | 2.79474 | 0.0899659 | ||||||||
\(966\) | −8.37752 | −0.269542 | ||||||||
\(967\) | 34.5687 | 1.11165 | 0.555827 | − | 0.831298i | \(-0.312402\pi\) | ||||
0.555827 | + | 0.831298i | \(0.312402\pi\) | |||||||
\(968\) | 12.4256 | 0.399374 | ||||||||
\(969\) | −2.37248 | −0.0762150 | ||||||||
\(970\) | −1.38598 | −0.0445010 | ||||||||
\(971\) | −26.8686 | −0.862253 | −0.431127 | − | 0.902291i | \(-0.641884\pi\) | ||||
−0.431127 | + | 0.902291i | \(0.641884\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 21.3183 | 0.683432 | ||||||||
\(974\) | −38.8021 | −1.24330 | ||||||||
\(975\) | 14.2188 | 0.455367 | ||||||||
\(976\) | 12.9276 | 0.413803 | ||||||||
\(977\) | −2.54460 | −0.0814089 | −0.0407044 | − | 0.999171i | \(-0.512960\pi\) | ||||
−0.0407044 | + | 0.999171i | \(0.512960\pi\) | |||||||
\(978\) | 1.93881 | 0.0619962 | ||||||||
\(979\) | −23.2108 | −0.741819 | ||||||||
\(980\) | 1.78826 | 0.0571239 | ||||||||
\(981\) | −13.0943 | −0.418069 | ||||||||
\(982\) | −20.0880 | −0.641033 | ||||||||
\(983\) | 20.4816 | 0.653261 | 0.326631 | − | 0.945152i | \(-0.394087\pi\) | ||||
0.326631 | + | 0.945152i | \(0.394087\pi\) | |||||||
\(984\) | 10.4714 | 0.333815 | ||||||||
\(985\) | −4.75228 | −0.151420 | ||||||||
\(986\) | −6.04527 | −0.192521 | ||||||||
\(987\) | −10.6058 | −0.337588 | ||||||||
\(988\) | −2.90027 | −0.0922699 | ||||||||
\(989\) | 47.8502 | 1.52155 | ||||||||
\(990\) | −1.51060 | −0.0480099 | ||||||||
\(991\) | −30.7395 | −0.976473 | −0.488237 | − | 0.872711i | \(-0.662360\pi\) | ||||
−0.488237 | + | 0.872711i | \(0.662360\pi\) | |||||||
\(992\) | −1.67878 | −0.0533014 | ||||||||
\(993\) | 19.0040 | 0.603075 | ||||||||
\(994\) | −14.3001 | −0.453570 | ||||||||
\(995\) | −5.86440 | −0.185914 | ||||||||
\(996\) | 9.84132 | 0.311834 | ||||||||
\(997\) | 16.6078 | 0.525974 | 0.262987 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262987 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(998\) | −6.79610 | −0.215127 | ||||||||
\(999\) | −4.39807 | −0.139149 |
(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 | 6042.2.a.bh.1.6 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.bh.1.6 | ✓ | 13 | 1.1 | even | 1 | trivial |