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: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.21848308.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 4x^{4} + 9x^{3} + 6x^{2} - 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.712460\) 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 | ||||||||
\(5\) | 1.82997 | 0.818388 | 0.409194 | − | 0.912447i | \(-0.365810\pi\) | ||||
0.409194 | + | 0.912447i | \(0.365810\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.67867 | 0.634478 | 0.317239 | − | 0.948346i | \(-0.397244\pi\) | ||||
0.317239 | + | 0.948346i | \(0.397244\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.82997 | −0.578688 | ||||||||
\(11\) | 2.01624 | 0.607920 | 0.303960 | − | 0.952685i | \(-0.401691\pi\) | ||||
0.303960 | + | 0.952685i | \(0.401691\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.91732 | −1.36382 | −0.681910 | − | 0.731436i | \(-0.738850\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738850\pi\) | |||||||
\(14\) | −1.67867 | −0.448644 | ||||||||
\(15\) | 1.82997 | 0.472497 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.76353 | −1.64040 | −0.820199 | − | 0.572078i | \(-0.806137\pi\) | ||||
−0.820199 | + | 0.572078i | \(0.806137\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.82997 | 0.409194 | ||||||||
\(21\) | 1.67867 | 0.366316 | ||||||||
\(22\) | −2.01624 | −0.429864 | ||||||||
\(23\) | −3.81454 | −0.795387 | −0.397693 | − | 0.917518i | \(-0.630189\pi\) | ||||
−0.397693 | + | 0.917518i | \(0.630189\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.65120 | −0.330241 | ||||||||
\(26\) | 4.91732 | 0.964366 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.67867 | 0.317239 | ||||||||
\(29\) | 2.88565 | 0.535852 | 0.267926 | − | 0.963440i | \(-0.413662\pi\) | ||||
0.267926 | + | 0.963440i | \(0.413662\pi\) | |||||||
\(30\) | −1.82997 | −0.334106 | ||||||||
\(31\) | −4.78519 | −0.859445 | −0.429723 | − | 0.902961i | \(-0.641389\pi\) | ||||
−0.429723 | + | 0.902961i | \(0.641389\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.01624 | 0.350983 | ||||||||
\(34\) | 6.76353 | 1.15994 | ||||||||
\(35\) | 3.07192 | 0.519249 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.07868 | −1.16373 | −0.581864 | − | 0.813286i | \(-0.697676\pi\) | ||||
−0.581864 | + | 0.813286i | \(0.697676\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −4.91732 | −0.787401 | ||||||||
\(40\) | −1.82997 | −0.289344 | ||||||||
\(41\) | −9.22847 | −1.44124 | −0.720622 | − | 0.693328i | \(-0.756144\pi\) | ||||
−0.720622 | + | 0.693328i | \(0.756144\pi\) | |||||||
\(42\) | −1.67867 | −0.259025 | ||||||||
\(43\) | 5.31931 | 0.811187 | 0.405593 | − | 0.914054i | \(-0.367065\pi\) | ||||
0.405593 | + | 0.914054i | \(0.367065\pi\) | |||||||
\(44\) | 2.01624 | 0.303960 | ||||||||
\(45\) | 1.82997 | 0.272796 | ||||||||
\(46\) | 3.81454 | 0.562423 | ||||||||
\(47\) | −0.326577 | −0.0476362 | −0.0238181 | − | 0.999716i | \(-0.507582\pi\) | ||||
−0.0238181 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.18206 | −0.597438 | ||||||||
\(50\) | 1.65120 | 0.233516 | ||||||||
\(51\) | −6.76353 | −0.947084 | ||||||||
\(52\) | −4.91732 | −0.681910 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.68966 | 0.497514 | ||||||||
\(56\) | −1.67867 | −0.224322 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −2.88565 | −0.378904 | ||||||||
\(59\) | −1.93626 | −0.252079 | −0.126040 | − | 0.992025i | \(-0.540227\pi\) | ||||
−0.126040 | + | 0.992025i | \(0.540227\pi\) | |||||||
\(60\) | 1.82997 | 0.236248 | ||||||||
\(61\) | −2.19824 | −0.281456 | −0.140728 | − | 0.990048i | \(-0.544944\pi\) | ||||
−0.140728 | + | 0.990048i | \(0.544944\pi\) | |||||||
\(62\) | 4.78519 | 0.607720 | ||||||||
\(63\) | 1.67867 | 0.211493 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.99856 | −1.11613 | ||||||||
\(66\) | −2.01624 | −0.248182 | ||||||||
\(67\) | 1.21471 | 0.148401 | 0.0742004 | − | 0.997243i | \(-0.476360\pi\) | ||||
0.0742004 | + | 0.997243i | \(0.476360\pi\) | |||||||
\(68\) | −6.76353 | −0.820199 | ||||||||
\(69\) | −3.81454 | −0.459217 | ||||||||
\(70\) | −3.07192 | −0.367165 | ||||||||
\(71\) | 5.02747 | 0.596650 | 0.298325 | − | 0.954464i | \(-0.403572\pi\) | ||||
0.298325 | + | 0.954464i | \(0.403572\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.3454 | −1.67900 | −0.839501 | − | 0.543358i | \(-0.817153\pi\) | ||||
−0.839501 | + | 0.543358i | \(0.817153\pi\) | |||||||
\(74\) | 7.07868 | 0.822879 | ||||||||
\(75\) | −1.65120 | −0.190665 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 3.38461 | 0.385712 | ||||||||
\(78\) | 4.91732 | 0.556777 | ||||||||
\(79\) | −5.68004 | −0.639055 | −0.319527 | − | 0.947577i | \(-0.603524\pi\) | ||||
−0.319527 | + | 0.947577i | \(0.603524\pi\) | |||||||
\(80\) | 1.82997 | 0.204597 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.22847 | 1.01911 | ||||||||
\(83\) | 3.63268 | 0.398738 | 0.199369 | − | 0.979924i | \(-0.436111\pi\) | ||||
0.199369 | + | 0.979924i | \(0.436111\pi\) | |||||||
\(84\) | 1.67867 | 0.183158 | ||||||||
\(85\) | −12.3771 | −1.34248 | ||||||||
\(86\) | −5.31931 | −0.573596 | ||||||||
\(87\) | 2.88565 | 0.309374 | ||||||||
\(88\) | −2.01624 | −0.214932 | ||||||||
\(89\) | −11.9694 | −1.26876 | −0.634379 | − | 0.773022i | \(-0.718744\pi\) | ||||
−0.634379 | + | 0.773022i | \(0.718744\pi\) | |||||||
\(90\) | −1.82997 | −0.192896 | ||||||||
\(91\) | −8.25456 | −0.865313 | ||||||||
\(92\) | −3.81454 | −0.397693 | ||||||||
\(93\) | −4.78519 | −0.496201 | ||||||||
\(94\) | 0.326577 | 0.0336839 | ||||||||
\(95\) | 1.82997 | 0.187751 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 14.3188 | 1.45386 | 0.726929 | − | 0.686713i | \(-0.240947\pi\) | ||||
0.726929 | + | 0.686713i | \(0.240947\pi\) | |||||||
\(98\) | 4.18206 | 0.422452 | ||||||||
\(99\) | 2.01624 | 0.202640 | ||||||||
\(100\) | −1.65120 | −0.165120 | ||||||||
\(101\) | 11.7632 | 1.17048 | 0.585241 | − | 0.810859i | \(-0.301000\pi\) | ||||
0.585241 | + | 0.810859i | \(0.301000\pi\) | |||||||
\(102\) | 6.76353 | 0.669690 | ||||||||
\(103\) | 0.462585 | 0.0455799 | 0.0227899 | − | 0.999740i | \(-0.492745\pi\) | ||||
0.0227899 | + | 0.999740i | \(0.492745\pi\) | |||||||
\(104\) | 4.91732 | 0.482183 | ||||||||
\(105\) | 3.07192 | 0.299789 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −16.0364 | −1.55030 | −0.775150 | − | 0.631777i | \(-0.782326\pi\) | ||||
−0.775150 | + | 0.631777i | \(0.782326\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −16.5947 | −1.58949 | −0.794743 | − | 0.606946i | \(-0.792394\pi\) | ||||
−0.794743 | + | 0.606946i | \(0.792394\pi\) | |||||||
\(110\) | −3.68966 | −0.351796 | ||||||||
\(111\) | −7.07868 | −0.671878 | ||||||||
\(112\) | 1.67867 | 0.158619 | ||||||||
\(113\) | −10.0659 | −0.946923 | −0.473461 | − | 0.880815i | \(-0.656996\pi\) | ||||
−0.473461 | + | 0.880815i | \(0.656996\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −6.98050 | −0.650935 | ||||||||
\(116\) | 2.88565 | 0.267926 | ||||||||
\(117\) | −4.91732 | −0.454606 | ||||||||
\(118\) | 1.93626 | 0.178247 | ||||||||
\(119\) | −11.3537 | −1.04080 | ||||||||
\(120\) | −1.82997 | −0.167053 | ||||||||
\(121\) | −6.93477 | −0.630434 | ||||||||
\(122\) | 2.19824 | 0.199019 | ||||||||
\(123\) | −9.22847 | −0.832103 | ||||||||
\(124\) | −4.78519 | −0.429723 | ||||||||
\(125\) | −12.1715 | −1.08865 | ||||||||
\(126\) | −1.67867 | −0.149548 | ||||||||
\(127\) | −12.4778 | −1.10722 | −0.553612 | − | 0.832775i | \(-0.686751\pi\) | ||||
−0.553612 | + | 0.832775i | \(0.686751\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.31931 | 0.468339 | ||||||||
\(130\) | 8.99856 | 0.789226 | ||||||||
\(131\) | 1.18571 | 0.103596 | 0.0517979 | − | 0.998658i | \(-0.483505\pi\) | ||||
0.0517979 | + | 0.998658i | \(0.483505\pi\) | |||||||
\(132\) | 2.01624 | 0.175491 | ||||||||
\(133\) | 1.67867 | 0.145559 | ||||||||
\(134\) | −1.21471 | −0.104935 | ||||||||
\(135\) | 1.82997 | 0.157499 | ||||||||
\(136\) | 6.76353 | 0.579968 | ||||||||
\(137\) | 18.5007 | 1.58062 | 0.790310 | − | 0.612708i | \(-0.209920\pi\) | ||||
0.790310 | + | 0.612708i | \(0.209920\pi\) | |||||||
\(138\) | 3.81454 | 0.324715 | ||||||||
\(139\) | 20.6993 | 1.75570 | 0.877848 | − | 0.478939i | \(-0.158979\pi\) | ||||
0.877848 | + | 0.478939i | \(0.158979\pi\) | |||||||
\(140\) | 3.07192 | 0.259625 | ||||||||
\(141\) | −0.326577 | −0.0275028 | ||||||||
\(142\) | −5.02747 | −0.421896 | ||||||||
\(143\) | −9.91450 | −0.829093 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.28066 | 0.438535 | ||||||||
\(146\) | 14.3454 | 1.18723 | ||||||||
\(147\) | −4.18206 | −0.344931 | ||||||||
\(148\) | −7.07868 | −0.581864 | ||||||||
\(149\) | 9.67726 | 0.792792 | 0.396396 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(150\) | 1.65120 | 0.134820 | ||||||||
\(151\) | 15.6367 | 1.27249 | 0.636246 | − | 0.771486i | \(-0.280486\pi\) | ||||
0.636246 | + | 0.771486i | \(0.280486\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −6.76353 | −0.546799 | ||||||||
\(154\) | −3.38461 | −0.272739 | ||||||||
\(155\) | −8.75676 | −0.703360 | ||||||||
\(156\) | −4.91732 | −0.393701 | ||||||||
\(157\) | −13.0127 | −1.03853 | −0.519264 | − | 0.854614i | \(-0.673794\pi\) | ||||
−0.519264 | + | 0.854614i | \(0.673794\pi\) | |||||||
\(158\) | 5.68004 | 0.451880 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | −1.82997 | −0.144672 | ||||||||
\(161\) | −6.40336 | −0.504655 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 14.4971 | 1.13550 | 0.567752 | − | 0.823200i | \(-0.307813\pi\) | ||||
0.567752 | + | 0.823200i | \(0.307813\pi\) | |||||||
\(164\) | −9.22847 | −0.720622 | ||||||||
\(165\) | 3.68966 | 0.287240 | ||||||||
\(166\) | −3.63268 | −0.281951 | ||||||||
\(167\) | 13.7105 | 1.06095 | 0.530474 | − | 0.847701i | \(-0.322014\pi\) | ||||
0.530474 | + | 0.847701i | \(0.322014\pi\) | |||||||
\(168\) | −1.67867 | −0.129512 | ||||||||
\(169\) | 11.1800 | 0.860003 | ||||||||
\(170\) | 12.3771 | 0.949278 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 5.31931 | 0.405593 | ||||||||
\(173\) | 16.9629 | 1.28966 | 0.644832 | − | 0.764324i | \(-0.276927\pi\) | ||||
0.644832 | + | 0.764324i | \(0.276927\pi\) | |||||||
\(174\) | −2.88565 | −0.218761 | ||||||||
\(175\) | −2.77183 | −0.209531 | ||||||||
\(176\) | 2.01624 | 0.151980 | ||||||||
\(177\) | −1.93626 | −0.145538 | ||||||||
\(178\) | 11.9694 | 0.897147 | ||||||||
\(179\) | 15.6436 | 1.16926 | 0.584630 | − | 0.811300i | \(-0.301240\pi\) | ||||
0.584630 | + | 0.811300i | \(0.301240\pi\) | |||||||
\(180\) | 1.82997 | 0.136398 | ||||||||
\(181\) | −13.6802 | −1.01684 | −0.508421 | − | 0.861109i | \(-0.669770\pi\) | ||||
−0.508421 | + | 0.861109i | \(0.669770\pi\) | |||||||
\(182\) | 8.25456 | 0.611869 | ||||||||
\(183\) | −2.19824 | −0.162499 | ||||||||
\(184\) | 3.81454 | 0.281212 | ||||||||
\(185\) | −12.9538 | −0.952381 | ||||||||
\(186\) | 4.78519 | 0.350867 | ||||||||
\(187\) | −13.6369 | −0.997230 | ||||||||
\(188\) | −0.326577 | −0.0238181 | ||||||||
\(189\) | 1.67867 | 0.122105 | ||||||||
\(190\) | −1.82997 | −0.132760 | ||||||||
\(191\) | 3.79372 | 0.274504 | 0.137252 | − | 0.990536i | \(-0.456173\pi\) | ||||
0.137252 | + | 0.990536i | \(0.456173\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −12.1220 | −0.872559 | −0.436280 | − | 0.899811i | \(-0.643704\pi\) | ||||
−0.436280 | + | 0.899811i | \(0.643704\pi\) | |||||||
\(194\) | −14.3188 | −1.02803 | ||||||||
\(195\) | −8.99856 | −0.644400 | ||||||||
\(196\) | −4.18206 | −0.298719 | ||||||||
\(197\) | −15.7107 | −1.11934 | −0.559671 | − | 0.828715i | \(-0.689073\pi\) | ||||
−0.559671 | + | 0.828715i | \(0.689073\pi\) | |||||||
\(198\) | −2.01624 | −0.143288 | ||||||||
\(199\) | −9.53375 | −0.675830 | −0.337915 | − | 0.941177i | \(-0.609722\pi\) | ||||
−0.337915 | + | 0.941177i | \(0.609722\pi\) | |||||||
\(200\) | 1.65120 | 0.116758 | ||||||||
\(201\) | 1.21471 | 0.0856793 | ||||||||
\(202\) | −11.7632 | −0.827656 | ||||||||
\(203\) | 4.84406 | 0.339986 | ||||||||
\(204\) | −6.76353 | −0.473542 | ||||||||
\(205\) | −16.8878 | −1.17950 | ||||||||
\(206\) | −0.462585 | −0.0322298 | ||||||||
\(207\) | −3.81454 | −0.265129 | ||||||||
\(208\) | −4.91732 | −0.340955 | ||||||||
\(209\) | 2.01624 | 0.139466 | ||||||||
\(210\) | −3.07192 | −0.211983 | ||||||||
\(211\) | −5.22430 | −0.359655 | −0.179828 | − | 0.983698i | \(-0.557554\pi\) | ||||
−0.179828 | + | 0.983698i | \(0.557554\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 5.02747 | 0.344476 | ||||||||
\(214\) | 16.0364 | 1.09623 | ||||||||
\(215\) | 9.73418 | 0.663866 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.03276 | −0.545299 | ||||||||
\(218\) | 16.5947 | 1.12394 | ||||||||
\(219\) | −14.3454 | −0.969372 | ||||||||
\(220\) | 3.68966 | 0.248757 | ||||||||
\(221\) | 33.2585 | 2.23721 | ||||||||
\(222\) | 7.07868 | 0.475090 | ||||||||
\(223\) | 8.03389 | 0.537989 | 0.268995 | − | 0.963142i | \(-0.413309\pi\) | ||||
0.268995 | + | 0.963142i | \(0.413309\pi\) | |||||||
\(224\) | −1.67867 | −0.112161 | ||||||||
\(225\) | −1.65120 | −0.110080 | ||||||||
\(226\) | 10.0659 | 0.669575 | ||||||||
\(227\) | 23.5491 | 1.56301 | 0.781504 | − | 0.623900i | \(-0.214453\pi\) | ||||
0.781504 | + | 0.623900i | \(0.214453\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 13.4028 | 0.885680 | 0.442840 | − | 0.896601i | \(-0.353971\pi\) | ||||
0.442840 | + | 0.896601i | \(0.353971\pi\) | |||||||
\(230\) | 6.98050 | 0.460281 | ||||||||
\(231\) | 3.38461 | 0.222691 | ||||||||
\(232\) | −2.88565 | −0.189452 | ||||||||
\(233\) | 1.75466 | 0.114951 | 0.0574757 | − | 0.998347i | \(-0.481695\pi\) | ||||
0.0574757 | + | 0.998347i | \(0.481695\pi\) | |||||||
\(234\) | 4.91732 | 0.321455 | ||||||||
\(235\) | −0.597627 | −0.0389849 | ||||||||
\(236\) | −1.93626 | −0.126040 | ||||||||
\(237\) | −5.68004 | −0.368958 | ||||||||
\(238\) | 11.3537 | 0.735954 | ||||||||
\(239\) | −7.06655 | −0.457097 | −0.228549 | − | 0.973533i | \(-0.573398\pi\) | ||||
−0.228549 | + | 0.973533i | \(0.573398\pi\) | |||||||
\(240\) | 1.82997 | 0.118124 | ||||||||
\(241\) | 22.3701 | 1.44098 | 0.720491 | − | 0.693464i | \(-0.243917\pi\) | ||||
0.720491 | + | 0.693464i | \(0.243917\pi\) | |||||||
\(242\) | 6.93477 | 0.445784 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.19824 | −0.140728 | ||||||||
\(245\) | −7.65306 | −0.488936 | ||||||||
\(246\) | 9.22847 | 0.588386 | ||||||||
\(247\) | −4.91732 | −0.312882 | ||||||||
\(248\) | 4.78519 | 0.303860 | ||||||||
\(249\) | 3.63268 | 0.230212 | ||||||||
\(250\) | 12.1715 | 0.769794 | ||||||||
\(251\) | 19.4392 | 1.22699 | 0.613496 | − | 0.789698i | \(-0.289763\pi\) | ||||
0.613496 | + | 0.789698i | \(0.289763\pi\) | |||||||
\(252\) | 1.67867 | 0.105746 | ||||||||
\(253\) | −7.69104 | −0.483531 | ||||||||
\(254\) | 12.4778 | 0.782926 | ||||||||
\(255\) | −12.3771 | −0.775082 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.8818 | −1.05306 | −0.526529 | − | 0.850157i | \(-0.676507\pi\) | ||||
−0.526529 | + | 0.850157i | \(0.676507\pi\) | |||||||
\(258\) | −5.31931 | −0.331166 | ||||||||
\(259\) | −11.8828 | −0.738359 | ||||||||
\(260\) | −8.99856 | −0.558067 | ||||||||
\(261\) | 2.88565 | 0.178617 | ||||||||
\(262\) | −1.18571 | −0.0732532 | ||||||||
\(263\) | −11.3054 | −0.697121 | −0.348561 | − | 0.937286i | \(-0.613329\pi\) | ||||
−0.348561 | + | 0.937286i | \(0.613329\pi\) | |||||||
\(264\) | −2.01624 | −0.124091 | ||||||||
\(265\) | −1.82997 | −0.112414 | ||||||||
\(266\) | −1.67867 | −0.102926 | ||||||||
\(267\) | −11.9694 | −0.732518 | ||||||||
\(268\) | 1.21471 | 0.0742004 | ||||||||
\(269\) | 22.7265 | 1.38566 | 0.692831 | − | 0.721100i | \(-0.256363\pi\) | ||||
0.692831 | + | 0.721100i | \(0.256363\pi\) | |||||||
\(270\) | −1.82997 | −0.111369 | ||||||||
\(271\) | −25.0006 | −1.51868 | −0.759338 | − | 0.650696i | \(-0.774477\pi\) | ||||
−0.759338 | + | 0.650696i | \(0.774477\pi\) | |||||||
\(272\) | −6.76353 | −0.410099 | ||||||||
\(273\) | −8.25456 | −0.499589 | ||||||||
\(274\) | −18.5007 | −1.11767 | ||||||||
\(275\) | −3.32923 | −0.200760 | ||||||||
\(276\) | −3.81454 | −0.229608 | ||||||||
\(277\) | 18.4958 | 1.11130 | 0.555652 | − | 0.831415i | \(-0.312469\pi\) | ||||
0.555652 | + | 0.831415i | \(0.312469\pi\) | |||||||
\(278\) | −20.6993 | −1.24146 | ||||||||
\(279\) | −4.78519 | −0.286482 | ||||||||
\(280\) | −3.07192 | −0.183582 | ||||||||
\(281\) | −26.7049 | −1.59308 | −0.796540 | − | 0.604586i | \(-0.793339\pi\) | ||||
−0.796540 | + | 0.604586i | \(0.793339\pi\) | |||||||
\(282\) | 0.326577 | 0.0194474 | ||||||||
\(283\) | −0.720726 | −0.0428427 | −0.0214214 | − | 0.999771i | \(-0.506819\pi\) | ||||
−0.0214214 | + | 0.999771i | \(0.506819\pi\) | |||||||
\(284\) | 5.02747 | 0.298325 | ||||||||
\(285\) | 1.82997 | 0.108398 | ||||||||
\(286\) | 9.91450 | 0.586257 | ||||||||
\(287\) | −15.4916 | −0.914438 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 28.7454 | 1.69090 | ||||||||
\(290\) | −5.28066 | −0.310091 | ||||||||
\(291\) | 14.3188 | 0.839385 | ||||||||
\(292\) | −14.3454 | −0.839501 | ||||||||
\(293\) | 9.39722 | 0.548992 | 0.274496 | − | 0.961588i | \(-0.411489\pi\) | ||||
0.274496 | + | 0.961588i | \(0.411489\pi\) | |||||||
\(294\) | 4.18206 | 0.243903 | ||||||||
\(295\) | −3.54330 | −0.206299 | ||||||||
\(296\) | 7.07868 | 0.411440 | ||||||||
\(297\) | 2.01624 | 0.116994 | ||||||||
\(298\) | −9.67726 | −0.560589 | ||||||||
\(299\) | 18.7573 | 1.08476 | ||||||||
\(300\) | −1.65120 | −0.0953323 | ||||||||
\(301\) | 8.92937 | 0.514680 | ||||||||
\(302\) | −15.6367 | −0.899788 | ||||||||
\(303\) | 11.7632 | 0.675778 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −4.02272 | −0.230340 | ||||||||
\(306\) | 6.76353 | 0.386645 | ||||||||
\(307\) | −20.7864 | −1.18634 | −0.593171 | − | 0.805077i | \(-0.702124\pi\) | ||||
−0.593171 | + | 0.805077i | \(0.702124\pi\) | |||||||
\(308\) | 3.38461 | 0.192856 | ||||||||
\(309\) | 0.462585 | 0.0263155 | ||||||||
\(310\) | 8.75676 | 0.497350 | ||||||||
\(311\) | 20.5249 | 1.16386 | 0.581932 | − | 0.813238i | \(-0.302297\pi\) | ||||
0.581932 | + | 0.813238i | \(0.302297\pi\) | |||||||
\(312\) | 4.91732 | 0.278388 | ||||||||
\(313\) | −24.1449 | −1.36475 | −0.682375 | − | 0.731002i | \(-0.739053\pi\) | ||||
−0.682375 | + | 0.731002i | \(0.739053\pi\) | |||||||
\(314\) | 13.0127 | 0.734350 | ||||||||
\(315\) | 3.07192 | 0.173083 | ||||||||
\(316\) | −5.68004 | −0.319527 | ||||||||
\(317\) | 13.5367 | 0.760299 | 0.380150 | − | 0.924925i | \(-0.375872\pi\) | ||||
0.380150 | + | 0.924925i | \(0.375872\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | 5.81817 | 0.325755 | ||||||||
\(320\) | 1.82997 | 0.102299 | ||||||||
\(321\) | −16.0364 | −0.895067 | ||||||||
\(322\) | 6.40336 | 0.356845 | ||||||||
\(323\) | −6.76353 | −0.376333 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.11950 | 0.450389 | ||||||||
\(326\) | −14.4971 | −0.802922 | ||||||||
\(327\) | −16.5947 | −0.917690 | ||||||||
\(328\) | 9.22847 | 0.509557 | ||||||||
\(329\) | −0.548216 | −0.0302241 | ||||||||
\(330\) | −3.68966 | −0.203109 | ||||||||
\(331\) | 19.8754 | 1.09245 | 0.546224 | − | 0.837639i | \(-0.316065\pi\) | ||||
0.546224 | + | 0.837639i | \(0.316065\pi\) | |||||||
\(332\) | 3.63268 | 0.199369 | ||||||||
\(333\) | −7.07868 | −0.387909 | ||||||||
\(334\) | −13.7105 | −0.750204 | ||||||||
\(335\) | 2.22289 | 0.121450 | ||||||||
\(336\) | 1.67867 | 0.0915790 | ||||||||
\(337\) | −24.2650 | −1.32180 | −0.660899 | − | 0.750475i | \(-0.729825\pi\) | ||||
−0.660899 | + | 0.750475i | \(0.729825\pi\) | |||||||
\(338\) | −11.1800 | −0.608114 | ||||||||
\(339\) | −10.0659 | −0.546706 | ||||||||
\(340\) | −12.3771 | −0.671241 | ||||||||
\(341\) | −9.64810 | −0.522474 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −18.7710 | −1.01354 | ||||||||
\(344\) | −5.31931 | −0.286798 | ||||||||
\(345\) | −6.98050 | −0.375818 | ||||||||
\(346\) | −16.9629 | −0.911930 | ||||||||
\(347\) | 26.6638 | 1.43139 | 0.715694 | − | 0.698414i | \(-0.246110\pi\) | ||||
0.715694 | + | 0.698414i | \(0.246110\pi\) | |||||||
\(348\) | 2.88565 | 0.154687 | ||||||||
\(349\) | 12.8924 | 0.690113 | 0.345056 | − | 0.938582i | \(-0.387860\pi\) | ||||
0.345056 | + | 0.938582i | \(0.387860\pi\) | |||||||
\(350\) | 2.77183 | 0.148160 | ||||||||
\(351\) | −4.91732 | −0.262467 | ||||||||
\(352\) | −2.01624 | −0.107466 | ||||||||
\(353\) | 6.26395 | 0.333396 | 0.166698 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166698 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(354\) | 1.93626 | 0.102911 | ||||||||
\(355\) | 9.20012 | 0.488292 | ||||||||
\(356\) | −11.9694 | −0.634379 | ||||||||
\(357\) | −11.3537 | −0.600904 | ||||||||
\(358\) | −15.6436 | −0.826792 | ||||||||
\(359\) | 8.33428 | 0.439866 | 0.219933 | − | 0.975515i | \(-0.429416\pi\) | ||||
0.219933 | + | 0.975515i | \(0.429416\pi\) | |||||||
\(360\) | −1.82997 | −0.0964480 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.6802 | 0.719015 | ||||||||
\(363\) | −6.93477 | −0.363981 | ||||||||
\(364\) | −8.25456 | −0.432657 | ||||||||
\(365\) | −26.2517 | −1.37408 | ||||||||
\(366\) | 2.19824 | 0.114904 | ||||||||
\(367\) | −9.60416 | −0.501333 | −0.250667 | − | 0.968074i | \(-0.580650\pi\) | ||||
−0.250667 | + | 0.968074i | \(0.580650\pi\) | |||||||
\(368\) | −3.81454 | −0.198847 | ||||||||
\(369\) | −9.22847 | −0.480415 | ||||||||
\(370\) | 12.9538 | 0.673435 | ||||||||
\(371\) | −1.67867 | −0.0871522 | ||||||||
\(372\) | −4.78519 | −0.248100 | ||||||||
\(373\) | −14.6242 | −0.757213 | −0.378607 | − | 0.925558i | \(-0.623597\pi\) | ||||
−0.378607 | + | 0.925558i | \(0.623597\pi\) | |||||||
\(374\) | 13.6369 | 0.705148 | ||||||||
\(375\) | −12.1715 | −0.628534 | ||||||||
\(376\) | 0.326577 | 0.0168419 | ||||||||
\(377\) | −14.1897 | −0.730805 | ||||||||
\(378\) | −1.67867 | −0.0863415 | ||||||||
\(379\) | 29.1960 | 1.49970 | 0.749848 | − | 0.661610i | \(-0.230127\pi\) | ||||
0.749848 | + | 0.661610i | \(0.230127\pi\) | |||||||
\(380\) | 1.82997 | 0.0938756 | ||||||||
\(381\) | −12.4778 | −0.639256 | ||||||||
\(382\) | −3.79372 | −0.194104 | ||||||||
\(383\) | 13.4192 | 0.685688 | 0.342844 | − | 0.939392i | \(-0.388610\pi\) | ||||
0.342844 | + | 0.939392i | \(0.388610\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 6.19373 | 0.315662 | ||||||||
\(386\) | 12.1220 | 0.616992 | ||||||||
\(387\) | 5.31931 | 0.270396 | ||||||||
\(388\) | 14.3188 | 0.726929 | ||||||||
\(389\) | 17.8705 | 0.906072 | 0.453036 | − | 0.891492i | \(-0.350341\pi\) | ||||
0.453036 | + | 0.891492i | \(0.350341\pi\) | |||||||
\(390\) | 8.99856 | 0.455660 | ||||||||
\(391\) | 25.7998 | 1.30475 | ||||||||
\(392\) | 4.18206 | 0.211226 | ||||||||
\(393\) | 1.18571 | 0.0598110 | ||||||||
\(394\) | 15.7107 | 0.791495 | ||||||||
\(395\) | −10.3943 | −0.522995 | ||||||||
\(396\) | 2.01624 | 0.101320 | ||||||||
\(397\) | −6.69808 | −0.336167 | −0.168084 | − | 0.985773i | \(-0.553758\pi\) | ||||
−0.168084 | + | 0.985773i | \(0.553758\pi\) | |||||||
\(398\) | 9.53375 | 0.477884 | ||||||||
\(399\) | 1.67867 | 0.0840386 | ||||||||
\(400\) | −1.65120 | −0.0825602 | ||||||||
\(401\) | −16.2790 | −0.812936 | −0.406468 | − | 0.913665i | \(-0.633240\pi\) | ||||
−0.406468 | + | 0.913665i | \(0.633240\pi\) | |||||||
\(402\) | −1.21471 | −0.0605844 | ||||||||
\(403\) | 23.5303 | 1.17213 | ||||||||
\(404\) | 11.7632 | 0.585241 | ||||||||
\(405\) | 1.82997 | 0.0909320 | ||||||||
\(406\) | −4.84406 | −0.240406 | ||||||||
\(407\) | −14.2723 | −0.707453 | ||||||||
\(408\) | 6.76353 | 0.334845 | ||||||||
\(409\) | −36.0746 | −1.78377 | −0.891887 | − | 0.452259i | \(-0.850618\pi\) | ||||
−0.891887 | + | 0.452259i | \(0.850618\pi\) | |||||||
\(410\) | 16.8878 | 0.834031 | ||||||||
\(411\) | 18.5007 | 0.912571 | ||||||||
\(412\) | 0.462585 | 0.0227899 | ||||||||
\(413\) | −3.25034 | −0.159939 | ||||||||
\(414\) | 3.81454 | 0.187474 | ||||||||
\(415\) | 6.64770 | 0.326323 | ||||||||
\(416\) | 4.91732 | 0.241091 | ||||||||
\(417\) | 20.6993 | 1.01365 | ||||||||
\(418\) | −2.01624 | −0.0986176 | ||||||||
\(419\) | 13.0160 | 0.635873 | 0.317937 | − | 0.948112i | \(-0.397010\pi\) | ||||
0.317937 | + | 0.948112i | \(0.397010\pi\) | |||||||
\(420\) | 3.07192 | 0.149894 | ||||||||
\(421\) | −11.2940 | −0.550438 | −0.275219 | − | 0.961382i | \(-0.588750\pi\) | ||||
−0.275219 | + | 0.961382i | \(0.588750\pi\) | |||||||
\(422\) | 5.22430 | 0.254315 | ||||||||
\(423\) | −0.326577 | −0.0158787 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 11.1680 | 0.541726 | ||||||||
\(426\) | −5.02747 | −0.243582 | ||||||||
\(427\) | −3.69012 | −0.178578 | ||||||||
\(428\) | −16.0364 | −0.775150 | ||||||||
\(429\) | −9.91450 | −0.478677 | ||||||||
\(430\) | −9.73418 | −0.469424 | ||||||||
\(431\) | −6.00406 | −0.289206 | −0.144603 | − | 0.989490i | \(-0.546190\pi\) | ||||
−0.144603 | + | 0.989490i | \(0.546190\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −12.1053 | −0.581741 | −0.290871 | − | 0.956762i | \(-0.593945\pi\) | ||||
−0.290871 | + | 0.956762i | \(0.593945\pi\) | |||||||
\(434\) | 8.03276 | 0.385585 | ||||||||
\(435\) | 5.28066 | 0.253188 | ||||||||
\(436\) | −16.5947 | −0.794743 | ||||||||
\(437\) | −3.81454 | −0.182474 | ||||||||
\(438\) | 14.3454 | 0.685450 | ||||||||
\(439\) | 15.4987 | 0.739711 | 0.369856 | − | 0.929089i | \(-0.379407\pi\) | ||||
0.369856 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(440\) | −3.68966 | −0.175898 | ||||||||
\(441\) | −4.18206 | −0.199146 | ||||||||
\(442\) | −33.2585 | −1.58194 | ||||||||
\(443\) | −15.4339 | −0.733287 | −0.366643 | − | 0.930362i | \(-0.619493\pi\) | ||||
−0.366643 | + | 0.930362i | \(0.619493\pi\) | |||||||
\(444\) | −7.07868 | −0.335939 | ||||||||
\(445\) | −21.9037 | −1.03834 | ||||||||
\(446\) | −8.03389 | −0.380416 | ||||||||
\(447\) | 9.67726 | 0.457719 | ||||||||
\(448\) | 1.67867 | 0.0793097 | ||||||||
\(449\) | 23.3945 | 1.10406 | 0.552028 | − | 0.833825i | \(-0.313854\pi\) | ||||
0.552028 | + | 0.833825i | \(0.313854\pi\) | |||||||
\(450\) | 1.65120 | 0.0778385 | ||||||||
\(451\) | −18.6068 | −0.876161 | ||||||||
\(452\) | −10.0659 | −0.473461 | ||||||||
\(453\) | 15.6367 | 0.734674 | ||||||||
\(454\) | −23.5491 | −1.10521 | ||||||||
\(455\) | −15.1056 | −0.708162 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −7.37685 | −0.345074 | −0.172537 | − | 0.985003i | \(-0.555196\pi\) | ||||
−0.172537 | + | 0.985003i | \(0.555196\pi\) | |||||||
\(458\) | −13.4028 | −0.626270 | ||||||||
\(459\) | −6.76353 | −0.315695 | ||||||||
\(460\) | −6.98050 | −0.325468 | ||||||||
\(461\) | 19.0342 | 0.886511 | 0.443256 | − | 0.896395i | \(-0.353823\pi\) | ||||
0.443256 | + | 0.896395i | \(0.353823\pi\) | |||||||
\(462\) | −3.38461 | −0.157466 | ||||||||
\(463\) | 18.9218 | 0.879372 | 0.439686 | − | 0.898152i | \(-0.355090\pi\) | ||||
0.439686 | + | 0.898152i | \(0.355090\pi\) | |||||||
\(464\) | 2.88565 | 0.133963 | ||||||||
\(465\) | −8.75676 | −0.406085 | ||||||||
\(466\) | −1.75466 | −0.0812830 | ||||||||
\(467\) | −6.93699 | −0.321006 | −0.160503 | − | 0.987035i | \(-0.551312\pi\) | ||||
−0.160503 | + | 0.987035i | \(0.551312\pi\) | |||||||
\(468\) | −4.91732 | −0.227303 | ||||||||
\(469\) | 2.03910 | 0.0941571 | ||||||||
\(470\) | 0.597627 | 0.0275665 | ||||||||
\(471\) | −13.0127 | −0.599594 | ||||||||
\(472\) | 1.93626 | 0.0891235 | ||||||||
\(473\) | 10.7250 | 0.493136 | ||||||||
\(474\) | 5.68004 | 0.260893 | ||||||||
\(475\) | −1.65120 | −0.0757625 | ||||||||
\(476\) | −11.3537 | −0.520398 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 7.06655 | 0.323217 | ||||||||
\(479\) | −36.7045 | −1.67707 | −0.838535 | − | 0.544848i | \(-0.816587\pi\) | ||||
−0.838535 | + | 0.544848i | \(0.816587\pi\) | |||||||
\(480\) | −1.82997 | −0.0835264 | ||||||||
\(481\) | 34.8081 | 1.58711 | ||||||||
\(482\) | −22.3701 | −1.01893 | ||||||||
\(483\) | −6.40336 | −0.291363 | ||||||||
\(484\) | −6.93477 | −0.315217 | ||||||||
\(485\) | 26.2031 | 1.18982 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −22.6007 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671121\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671121\pi\) | |||||||
\(488\) | 2.19824 | 0.0995097 | ||||||||
\(489\) | 14.4971 | 0.655583 | ||||||||
\(490\) | 7.65306 | 0.345730 | ||||||||
\(491\) | −20.2104 | −0.912081 | −0.456040 | − | 0.889959i | \(-0.650733\pi\) | ||||
−0.456040 | + | 0.889959i | \(0.650733\pi\) | |||||||
\(492\) | −9.22847 | −0.416051 | ||||||||
\(493\) | −19.5172 | −0.879010 | ||||||||
\(494\) | 4.91732 | 0.221241 | ||||||||
\(495\) | 3.68966 | 0.165838 | ||||||||
\(496\) | −4.78519 | −0.214861 | ||||||||
\(497\) | 8.43946 | 0.378562 | ||||||||
\(498\) | −3.63268 | −0.162784 | ||||||||
\(499\) | −16.5662 | −0.741605 | −0.370802 | − | 0.928712i | \(-0.620917\pi\) | ||||
−0.370802 | + | 0.928712i | \(0.620917\pi\) | |||||||
\(500\) | −12.1715 | −0.544327 | ||||||||
\(501\) | 13.7105 | 0.612539 | ||||||||
\(502\) | −19.4392 | −0.867614 | ||||||||
\(503\) | 30.5255 | 1.36106 | 0.680532 | − | 0.732719i | \(-0.261749\pi\) | ||||
0.680532 | + | 0.732719i | \(0.261749\pi\) | |||||||
\(504\) | −1.67867 | −0.0747739 | ||||||||
\(505\) | 21.5263 | 0.957909 | ||||||||
\(506\) | 7.69104 | 0.341908 | ||||||||
\(507\) | 11.1800 | 0.496523 | ||||||||
\(508\) | −12.4778 | −0.553612 | ||||||||
\(509\) | 26.8982 | 1.19224 | 0.596122 | − | 0.802894i | \(-0.296707\pi\) | ||||
0.596122 | + | 0.802894i | \(0.296707\pi\) | |||||||
\(510\) | 12.3771 | 0.548066 | ||||||||
\(511\) | −24.0812 | −1.06529 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 16.8818 | 0.744624 | ||||||||
\(515\) | 0.846518 | 0.0373020 | ||||||||
\(516\) | 5.31931 | 0.234169 | ||||||||
\(517\) | −0.658459 | −0.0289590 | ||||||||
\(518\) | 11.8828 | 0.522099 | ||||||||
\(519\) | 16.9629 | 0.744588 | ||||||||
\(520\) | 8.99856 | 0.394613 | ||||||||
\(521\) | 35.6978 | 1.56395 | 0.781975 | − | 0.623310i | \(-0.214212\pi\) | ||||
0.781975 | + | 0.623310i | \(0.214212\pi\) | |||||||
\(522\) | −2.88565 | −0.126301 | ||||||||
\(523\) | −8.47989 | −0.370800 | −0.185400 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185400 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(524\) | 1.18571 | 0.0517979 | ||||||||
\(525\) | −2.77183 | −0.120973 | ||||||||
\(526\) | 11.3054 | 0.492939 | ||||||||
\(527\) | 32.3648 | 1.40983 | ||||||||
\(528\) | 2.01624 | 0.0877456 | ||||||||
\(529\) | −8.44927 | −0.367360 | ||||||||
\(530\) | 1.82997 | 0.0794889 | ||||||||
\(531\) | −1.93626 | −0.0840264 | ||||||||
\(532\) | 1.67867 | 0.0727796 | ||||||||
\(533\) | 45.3793 | 1.96560 | ||||||||
\(534\) | 11.9694 | 0.517968 | ||||||||
\(535\) | −29.3462 | −1.26875 | ||||||||
\(536\) | −1.21471 | −0.0524676 | ||||||||
\(537\) | 15.6436 | 0.675073 | ||||||||
\(538\) | −22.7265 | −0.979811 | ||||||||
\(539\) | −8.43205 | −0.363194 | ||||||||
\(540\) | 1.82997 | 0.0787494 | ||||||||
\(541\) | −21.2796 | −0.914880 | −0.457440 | − | 0.889240i | \(-0.651234\pi\) | ||||
−0.457440 | + | 0.889240i | \(0.651234\pi\) | |||||||
\(542\) | 25.0006 | 1.07387 | ||||||||
\(543\) | −13.6802 | −0.587073 | ||||||||
\(544\) | 6.76353 | 0.289984 | ||||||||
\(545\) | −30.3679 | −1.30082 | ||||||||
\(546\) | 8.25456 | 0.353263 | ||||||||
\(547\) | 12.0951 | 0.517148 | 0.258574 | − | 0.965991i | \(-0.416747\pi\) | ||||
0.258574 | + | 0.965991i | \(0.416747\pi\) | |||||||
\(548\) | 18.5007 | 0.790310 | ||||||||
\(549\) | −2.19824 | −0.0938186 | ||||||||
\(550\) | 3.32923 | 0.141959 | ||||||||
\(551\) | 2.88565 | 0.122933 | ||||||||
\(552\) | 3.81454 | 0.162358 | ||||||||
\(553\) | −9.53492 | −0.405466 | ||||||||
\(554\) | −18.4958 | −0.785810 | ||||||||
\(555\) | −12.9538 | −0.549857 | ||||||||
\(556\) | 20.6993 | 0.877848 | ||||||||
\(557\) | 37.4678 | 1.58756 | 0.793781 | − | 0.608204i | \(-0.208110\pi\) | ||||
0.793781 | + | 0.608204i | \(0.208110\pi\) | |||||||
\(558\) | 4.78519 | 0.202573 | ||||||||
\(559\) | −26.1567 | −1.10631 | ||||||||
\(560\) | 3.07192 | 0.129812 | ||||||||
\(561\) | −13.6369 | −0.575751 | ||||||||
\(562\) | 26.7049 | 1.12648 | ||||||||
\(563\) | −14.7701 | −0.622487 | −0.311243 | − | 0.950330i | \(-0.600745\pi\) | ||||
−0.311243 | + | 0.950330i | \(0.600745\pi\) | |||||||
\(564\) | −0.326577 | −0.0137514 | ||||||||
\(565\) | −18.4204 | −0.774950 | ||||||||
\(566\) | 0.720726 | 0.0302944 | ||||||||
\(567\) | 1.67867 | 0.0704975 | ||||||||
\(568\) | −5.02747 | −0.210948 | ||||||||
\(569\) | −31.5765 | −1.32376 | −0.661879 | − | 0.749611i | \(-0.730241\pi\) | ||||
−0.661879 | + | 0.749611i | \(0.730241\pi\) | |||||||
\(570\) | −1.82997 | −0.0766491 | ||||||||
\(571\) | 28.1232 | 1.17692 | 0.588459 | − | 0.808527i | \(-0.299735\pi\) | ||||
0.588459 | + | 0.808527i | \(0.299735\pi\) | |||||||
\(572\) | −9.91450 | −0.414546 | ||||||||
\(573\) | 3.79372 | 0.158485 | ||||||||
\(574\) | 15.4916 | 0.646605 | ||||||||
\(575\) | 6.29859 | 0.262669 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −0.531062 | −0.0221084 | −0.0110542 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110542 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(578\) | −28.7454 | −1.19565 | ||||||||
\(579\) | −12.1220 | −0.503772 | ||||||||
\(580\) | 5.28066 | 0.219267 | ||||||||
\(581\) | 6.09807 | 0.252991 | ||||||||
\(582\) | −14.3188 | −0.593535 | ||||||||
\(583\) | −2.01624 | −0.0835042 | ||||||||
\(584\) | 14.3454 | 0.593617 | ||||||||
\(585\) | −8.99856 | −0.372045 | ||||||||
\(586\) | −9.39722 | −0.388196 | ||||||||
\(587\) | −35.1264 | −1.44982 | −0.724910 | − | 0.688844i | \(-0.758119\pi\) | ||||
−0.724910 | + | 0.688844i | \(0.758119\pi\) | |||||||
\(588\) | −4.18206 | −0.172465 | ||||||||
\(589\) | −4.78519 | −0.197170 | ||||||||
\(590\) | 3.54330 | 0.145875 | ||||||||
\(591\) | −15.7107 | −0.646253 | ||||||||
\(592\) | −7.07868 | −0.290932 | ||||||||
\(593\) | −11.4375 | −0.469681 | −0.234840 | − | 0.972034i | \(-0.575457\pi\) | ||||
−0.234840 | + | 0.972034i | \(0.575457\pi\) | |||||||
\(594\) | −2.01624 | −0.0827274 | ||||||||
\(595\) | −20.7770 | −0.851775 | ||||||||
\(596\) | 9.67726 | 0.396396 | ||||||||
\(597\) | −9.53375 | −0.390190 | ||||||||
\(598\) | −18.7573 | −0.767044 | ||||||||
\(599\) | −19.3478 | −0.790530 | −0.395265 | − | 0.918567i | \(-0.629347\pi\) | ||||
−0.395265 | + | 0.918567i | \(0.629347\pi\) | |||||||
\(600\) | 1.65120 | 0.0674101 | ||||||||
\(601\) | 9.78644 | 0.399197 | 0.199599 | − | 0.979878i | \(-0.436036\pi\) | ||||
0.199599 | + | 0.979878i | \(0.436036\pi\) | |||||||
\(602\) | −8.92937 | −0.363934 | ||||||||
\(603\) | 1.21471 | 0.0494670 | ||||||||
\(604\) | 15.6367 | 0.636246 | ||||||||
\(605\) | −12.6904 | −0.515939 | ||||||||
\(606\) | −11.7632 | −0.477848 | ||||||||
\(607\) | −41.3958 | −1.68021 | −0.840103 | − | 0.542427i | \(-0.817505\pi\) | ||||
−0.840103 | + | 0.542427i | \(0.817505\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 4.84406 | 0.196291 | ||||||||
\(610\) | 4.02272 | 0.162875 | ||||||||
\(611\) | 1.60589 | 0.0649672 | ||||||||
\(612\) | −6.76353 | −0.273400 | ||||||||
\(613\) | −41.7485 | −1.68621 | −0.843103 | − | 0.537753i | \(-0.819273\pi\) | ||||
−0.843103 | + | 0.537753i | \(0.819273\pi\) | |||||||
\(614\) | 20.7864 | 0.838870 | ||||||||
\(615\) | −16.8878 | −0.680983 | ||||||||
\(616\) | −3.38461 | −0.136370 | ||||||||
\(617\) | −27.7405 | −1.11679 | −0.558395 | − | 0.829576i | \(-0.688582\pi\) | ||||
−0.558395 | + | 0.829576i | \(0.688582\pi\) | |||||||
\(618\) | −0.462585 | −0.0186079 | ||||||||
\(619\) | −6.81231 | −0.273810 | −0.136905 | − | 0.990584i | \(-0.543716\pi\) | ||||
−0.136905 | + | 0.990584i | \(0.543716\pi\) | |||||||
\(620\) | −8.75676 | −0.351680 | ||||||||
\(621\) | −3.81454 | −0.153072 | ||||||||
\(622\) | −20.5249 | −0.822975 | ||||||||
\(623\) | −20.0927 | −0.804999 | ||||||||
\(624\) | −4.91732 | −0.196850 | ||||||||
\(625\) | −14.0175 | −0.560700 | ||||||||
\(626\) | 24.1449 | 0.965024 | ||||||||
\(627\) | 2.01624 | 0.0805209 | ||||||||
\(628\) | −13.0127 | −0.519264 | ||||||||
\(629\) | 47.8769 | 1.90898 | ||||||||
\(630\) | −3.07192 | −0.122388 | ||||||||
\(631\) | 21.5675 | 0.858590 | 0.429295 | − | 0.903164i | \(-0.358762\pi\) | ||||
0.429295 | + | 0.903164i | \(0.358762\pi\) | |||||||
\(632\) | 5.68004 | 0.225940 | ||||||||
\(633\) | −5.22430 | −0.207647 | ||||||||
\(634\) | −13.5367 | −0.537613 | ||||||||
\(635\) | −22.8340 | −0.906139 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 20.5646 | 0.814797 | ||||||||
\(638\) | −5.81817 | −0.230343 | ||||||||
\(639\) | 5.02747 | 0.198883 | ||||||||
\(640\) | −1.82997 | −0.0723360 | ||||||||
\(641\) | −10.7407 | −0.424231 | −0.212115 | − | 0.977245i | \(-0.568035\pi\) | ||||
−0.212115 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(642\) | 16.0364 | 0.632908 | ||||||||
\(643\) | −35.4056 | −1.39626 | −0.698131 | − | 0.715970i | \(-0.745985\pi\) | ||||
−0.698131 | + | 0.715970i | \(0.745985\pi\) | |||||||
\(644\) | −6.40336 | −0.252328 | ||||||||
\(645\) | 9.73418 | 0.383283 | ||||||||
\(646\) | 6.76353 | 0.266108 | ||||||||
\(647\) | 29.3106 | 1.15232 | 0.576160 | − | 0.817337i | \(-0.304550\pi\) | ||||
0.576160 | + | 0.817337i | \(0.304550\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −3.90396 | −0.153244 | ||||||||
\(650\) | −8.11950 | −0.318473 | ||||||||
\(651\) | −8.03276 | −0.314829 | ||||||||
\(652\) | 14.4971 | 0.567752 | ||||||||
\(653\) | 1.99591 | 0.0781059 | 0.0390529 | − | 0.999237i | \(-0.487566\pi\) | ||||
0.0390529 | + | 0.999237i | \(0.487566\pi\) | |||||||
\(654\) | 16.5947 | 0.648905 | ||||||||
\(655\) | 2.16981 | 0.0847815 | ||||||||
\(656\) | −9.22847 | −0.360311 | ||||||||
\(657\) | −14.3454 | −0.559667 | ||||||||
\(658\) | 0.548216 | 0.0213717 | ||||||||
\(659\) | −0.418966 | −0.0163206 | −0.00816031 | − | 0.999967i | \(-0.502598\pi\) | ||||
−0.00816031 | + | 0.999967i | \(0.502598\pi\) | |||||||
\(660\) | 3.68966 | 0.143620 | ||||||||
\(661\) | −18.6749 | −0.726368 | −0.363184 | − | 0.931717i | \(-0.618310\pi\) | ||||
−0.363184 | + | 0.931717i | \(0.618310\pi\) | |||||||
\(662\) | −19.8754 | −0.772478 | ||||||||
\(663\) | 33.2585 | 1.29165 | ||||||||
\(664\) | −3.63268 | −0.140975 | ||||||||
\(665\) | 3.07192 | 0.119124 | ||||||||
\(666\) | 7.07868 | 0.274293 | ||||||||
\(667\) | −11.0074 | −0.426209 | ||||||||
\(668\) | 13.7105 | 0.530474 | ||||||||
\(669\) | 8.03389 | 0.310608 | ||||||||
\(670\) | −2.22289 | −0.0858778 | ||||||||
\(671\) | −4.43218 | −0.171103 | ||||||||
\(672\) | −1.67867 | −0.0647561 | ||||||||
\(673\) | 2.96407 | 0.114256 | 0.0571282 | − | 0.998367i | \(-0.481806\pi\) | ||||
0.0571282 | + | 0.998367i | \(0.481806\pi\) | |||||||
\(674\) | 24.2650 | 0.934652 | ||||||||
\(675\) | −1.65120 | −0.0635549 | ||||||||
\(676\) | 11.1800 | 0.430002 | ||||||||
\(677\) | −39.6440 | −1.52364 | −0.761822 | − | 0.647786i | \(-0.775695\pi\) | ||||
−0.761822 | + | 0.647786i | \(0.775695\pi\) | |||||||
\(678\) | 10.0659 | 0.386580 | ||||||||
\(679\) | 24.0366 | 0.922441 | ||||||||
\(680\) | 12.3771 | 0.474639 | ||||||||
\(681\) | 23.5491 | 0.902403 | ||||||||
\(682\) | 9.64810 | 0.369445 | ||||||||
\(683\) | −38.9148 | −1.48904 | −0.744518 | − | 0.667603i | \(-0.767320\pi\) | ||||
−0.744518 | + | 0.667603i | \(0.767320\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 33.8557 | 1.29356 | ||||||||
\(686\) | 18.7710 | 0.716680 | ||||||||
\(687\) | 13.4028 | 0.511348 | ||||||||
\(688\) | 5.31931 | 0.202797 | ||||||||
\(689\) | 4.91732 | 0.187335 | ||||||||
\(690\) | 6.98050 | 0.265743 | ||||||||
\(691\) | −43.8421 | −1.66783 | −0.833916 | − | 0.551892i | \(-0.813906\pi\) | ||||
−0.833916 | + | 0.551892i | \(0.813906\pi\) | |||||||
\(692\) | 16.9629 | 0.644832 | ||||||||
\(693\) | 3.38461 | 0.128571 | ||||||||
\(694\) | −26.6638 | −1.01214 | ||||||||
\(695\) | 37.8792 | 1.43684 | ||||||||
\(696\) | −2.88565 | −0.109380 | ||||||||
\(697\) | 62.4171 | 2.36421 | ||||||||
\(698\) | −12.8924 | −0.487983 | ||||||||
\(699\) | 1.75466 | 0.0663673 | ||||||||
\(700\) | −2.77183 | −0.104765 | ||||||||
\(701\) | 45.6227 | 1.72315 | 0.861573 | − | 0.507634i | \(-0.169480\pi\) | ||||
0.861573 | + | 0.507634i | \(0.169480\pi\) | |||||||
\(702\) | 4.91732 | 0.185592 | ||||||||
\(703\) | −7.07868 | −0.266977 | ||||||||
\(704\) | 2.01624 | 0.0759900 | ||||||||
\(705\) | −0.597627 | −0.0225079 | ||||||||
\(706\) | −6.26395 | −0.235747 | ||||||||
\(707\) | 19.7465 | 0.742645 | ||||||||
\(708\) | −1.93626 | −0.0727690 | ||||||||
\(709\) | −12.8780 | −0.483645 | −0.241822 | − | 0.970321i | \(-0.577745\pi\) | ||||
−0.241822 | + | 0.970321i | \(0.577745\pi\) | |||||||
\(710\) | −9.20012 | −0.345274 | ||||||||
\(711\) | −5.68004 | −0.213018 | ||||||||
\(712\) | 11.9694 | 0.448574 | ||||||||
\(713\) | 18.2533 | 0.683592 | ||||||||
\(714\) | 11.3537 | 0.424903 | ||||||||
\(715\) | −18.1433 | −0.678519 | ||||||||
\(716\) | 15.6436 | 0.584630 | ||||||||
\(717\) | −7.06655 | −0.263905 | ||||||||
\(718\) | −8.33428 | −0.311032 | ||||||||
\(719\) | −13.4057 | −0.499947 | −0.249974 | − | 0.968253i | \(-0.580422\pi\) | ||||
−0.249974 | + | 0.968253i | \(0.580422\pi\) | |||||||
\(720\) | 1.82997 | 0.0681990 | ||||||||
\(721\) | 0.776528 | 0.0289194 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 22.3701 | 0.831951 | ||||||||
\(724\) | −13.6802 | −0.508421 | ||||||||
\(725\) | −4.76480 | −0.176960 | ||||||||
\(726\) | 6.93477 | 0.257373 | ||||||||
\(727\) | −2.26162 | −0.0838789 | −0.0419395 | − | 0.999120i | \(-0.513354\pi\) | ||||
−0.0419395 | + | 0.999120i | \(0.513354\pi\) | |||||||
\(728\) | 8.25456 | 0.305934 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 26.2517 | 0.971618 | ||||||||
\(731\) | −35.9773 | −1.33067 | ||||||||
\(732\) | −2.19824 | −0.0812493 | ||||||||
\(733\) | 25.3470 | 0.936214 | 0.468107 | − | 0.883672i | \(-0.344936\pi\) | ||||
0.468107 | + | 0.883672i | \(0.344936\pi\) | |||||||
\(734\) | 9.60416 | 0.354496 | ||||||||
\(735\) | −7.65306 | −0.282287 | ||||||||
\(736\) | 3.81454 | 0.140606 | ||||||||
\(737\) | 2.44916 | 0.0902158 | ||||||||
\(738\) | 9.22847 | 0.339705 | ||||||||
\(739\) | −38.5157 | −1.41682 | −0.708412 | − | 0.705799i | \(-0.750588\pi\) | ||||
−0.708412 | + | 0.705799i | \(0.750588\pi\) | |||||||
\(740\) | −12.9538 | −0.476190 | ||||||||
\(741\) | −4.91732 | −0.180642 | ||||||||
\(742\) | 1.67867 | 0.0616259 | ||||||||
\(743\) | −38.5507 | −1.41429 | −0.707144 | − | 0.707070i | \(-0.750017\pi\) | ||||
−0.707144 | + | 0.707070i | \(0.750017\pi\) | |||||||
\(744\) | 4.78519 | 0.175434 | ||||||||
\(745\) | 17.7091 | 0.648811 | ||||||||
\(746\) | 14.6242 | 0.535431 | ||||||||
\(747\) | 3.63268 | 0.132913 | ||||||||
\(748\) | −13.6369 | −0.498615 | ||||||||
\(749\) | −26.9199 | −0.983632 | ||||||||
\(750\) | 12.1715 | 0.444441 | ||||||||
\(751\) | 14.7174 | 0.537044 | 0.268522 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268522 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(752\) | −0.326577 | −0.0119091 | ||||||||
\(753\) | 19.4392 | 0.708404 | ||||||||
\(754\) | 14.1897 | 0.516757 | ||||||||
\(755\) | 28.6146 | 1.04139 | ||||||||
\(756\) | 1.67867 | 0.0610527 | ||||||||
\(757\) | 37.2544 | 1.35403 | 0.677017 | − | 0.735967i | \(-0.263272\pi\) | ||||
0.677017 | + | 0.735967i | \(0.263272\pi\) | |||||||
\(758\) | −29.1960 | −1.06045 | ||||||||
\(759\) | −7.69104 | −0.279167 | ||||||||
\(760\) | −1.82997 | −0.0663800 | ||||||||
\(761\) | 5.30595 | 0.192341 | 0.0961703 | − | 0.995365i | \(-0.469341\pi\) | ||||
0.0961703 | + | 0.995365i | \(0.469341\pi\) | |||||||
\(762\) | 12.4778 | 0.452022 | ||||||||
\(763\) | −27.8571 | −1.00849 | ||||||||
\(764\) | 3.79372 | 0.137252 | ||||||||
\(765\) | −12.3771 | −0.447494 | ||||||||
\(766\) | −13.4192 | −0.484855 | ||||||||
\(767\) | 9.52120 | 0.343791 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −28.1883 | −1.01649 | −0.508247 | − | 0.861211i | \(-0.669706\pi\) | ||||
−0.508247 | + | 0.861211i | \(0.669706\pi\) | |||||||
\(770\) | −6.19373 | −0.223207 | ||||||||
\(771\) | −16.8818 | −0.607983 | ||||||||
\(772\) | −12.1220 | −0.436280 | ||||||||
\(773\) | −49.9900 | −1.79802 | −0.899008 | − | 0.437932i | \(-0.855711\pi\) | ||||
−0.899008 | + | 0.437932i | \(0.855711\pi\) | |||||||
\(774\) | −5.31931 | −0.191199 | ||||||||
\(775\) | 7.90133 | 0.283824 | ||||||||
\(776\) | −14.3188 | −0.514016 | ||||||||
\(777\) | −11.8828 | −0.426292 | ||||||||
\(778\) | −17.8705 | −0.640690 | ||||||||
\(779\) | −9.22847 | −0.330644 | ||||||||
\(780\) | −8.99856 | −0.322200 | ||||||||
\(781\) | 10.1366 | 0.362716 | ||||||||
\(782\) | −25.7998 | −0.922598 | ||||||||
\(783\) | 2.88565 | 0.103125 | ||||||||
\(784\) | −4.18206 | −0.149359 | ||||||||
\(785\) | −23.8129 | −0.849918 | ||||||||
\(786\) | −1.18571 | −0.0422928 | ||||||||
\(787\) | −26.3721 | −0.940065 | −0.470032 | − | 0.882649i | \(-0.655758\pi\) | ||||
−0.470032 | + | 0.882649i | \(0.655758\pi\) | |||||||
\(788\) | −15.7107 | −0.559671 | ||||||||
\(789\) | −11.3054 | −0.402483 | ||||||||
\(790\) | 10.3943 | 0.369813 | ||||||||
\(791\) | −16.8974 | −0.600801 | ||||||||
\(792\) | −2.01624 | −0.0716440 | ||||||||
\(793\) | 10.8095 | 0.383855 | ||||||||
\(794\) | 6.69808 | 0.237706 | ||||||||
\(795\) | −1.82997 | −0.0649024 | ||||||||
\(796\) | −9.53375 | −0.337915 | ||||||||
\(797\) | −15.8357 | −0.560929 | −0.280464 | − | 0.959864i | \(-0.590488\pi\) | ||||
−0.280464 | + | 0.959864i | \(0.590488\pi\) | |||||||
\(798\) | −1.67867 | −0.0594243 | ||||||||
\(799\) | 2.20882 | 0.0781423 | ||||||||
\(800\) | 1.65120 | 0.0583789 | ||||||||
\(801\) | −11.9694 | −0.422919 | ||||||||
\(802\) | 16.2790 | 0.574833 | ||||||||
\(803\) | −28.9238 | −1.02070 | ||||||||
\(804\) | 1.21471 | 0.0428396 | ||||||||
\(805\) | −11.7180 | −0.413004 | ||||||||
\(806\) | −23.5303 | −0.828820 | ||||||||
\(807\) | 22.7265 | 0.800012 | ||||||||
\(808\) | −11.7632 | −0.413828 | ||||||||
\(809\) | 25.9199 | 0.911295 | 0.455648 | − | 0.890160i | \(-0.349408\pi\) | ||||
0.455648 | + | 0.890160i | \(0.349408\pi\) | |||||||
\(810\) | −1.82997 | −0.0642986 | ||||||||
\(811\) | 26.0318 | 0.914100 | 0.457050 | − | 0.889441i | \(-0.348906\pi\) | ||||
0.457050 | + | 0.889441i | \(0.348906\pi\) | |||||||
\(812\) | 4.84406 | 0.169993 | ||||||||
\(813\) | −25.0006 | −0.876809 | ||||||||
\(814\) | 14.2723 | 0.500245 | ||||||||
\(815\) | 26.5293 | 0.929282 | ||||||||
\(816\) | −6.76353 | −0.236771 | ||||||||
\(817\) | 5.31931 | 0.186099 | ||||||||
\(818\) | 36.0746 | 1.26132 | ||||||||
\(819\) | −8.25456 | −0.288438 | ||||||||
\(820\) | −16.8878 | −0.589749 | ||||||||
\(821\) | 45.8717 | 1.60093 | 0.800466 | − | 0.599378i | \(-0.204585\pi\) | ||||
0.800466 | + | 0.599378i | \(0.204585\pi\) | |||||||
\(822\) | −18.5007 | −0.645285 | ||||||||
\(823\) | −29.3130 | −1.02179 | −0.510893 | − | 0.859644i | \(-0.670685\pi\) | ||||
−0.510893 | + | 0.859644i | \(0.670685\pi\) | |||||||
\(824\) | −0.462585 | −0.0161149 | ||||||||
\(825\) | −3.32923 | −0.115909 | ||||||||
\(826\) | 3.25034 | 0.113094 | ||||||||
\(827\) | 24.2294 | 0.842540 | 0.421270 | − | 0.906935i | \(-0.361584\pi\) | ||||
0.421270 | + | 0.906935i | \(0.361584\pi\) | |||||||
\(828\) | −3.81454 | −0.132564 | ||||||||
\(829\) | 56.8385 | 1.97408 | 0.987042 | − | 0.160465i | \(-0.0512994\pi\) | ||||
0.987042 | + | 0.160465i | \(0.0512994\pi\) | |||||||
\(830\) | −6.64770 | −0.230745 | ||||||||
\(831\) | 18.4958 | 0.641612 | ||||||||
\(832\) | −4.91732 | −0.170477 | ||||||||
\(833\) | 28.2855 | 0.980036 | ||||||||
\(834\) | −20.6993 | −0.716760 | ||||||||
\(835\) | 25.0898 | 0.868268 | ||||||||
\(836\) | 2.01624 | 0.0697332 | ||||||||
\(837\) | −4.78519 | −0.165400 | ||||||||
\(838\) | −13.0160 | −0.449630 | ||||||||
\(839\) | −52.6638 | −1.81816 | −0.909078 | − | 0.416627i | \(-0.863212\pi\) | ||||
−0.909078 | + | 0.416627i | \(0.863212\pi\) | |||||||
\(840\) | −3.07192 | −0.105991 | ||||||||
\(841\) | −20.6730 | −0.712863 | ||||||||
\(842\) | 11.2940 | 0.389218 | ||||||||
\(843\) | −26.7049 | −0.919765 | ||||||||
\(844\) | −5.22430 | −0.179828 | ||||||||
\(845\) | 20.4592 | 0.703816 | ||||||||
\(846\) | 0.326577 | 0.0112280 | ||||||||
\(847\) | −11.6412 | −0.399996 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | −0.720726 | −0.0247353 | ||||||||
\(850\) | −11.1680 | −0.383058 | ||||||||
\(851\) | 27.0019 | 0.925613 | ||||||||
\(852\) | 5.02747 | 0.172238 | ||||||||
\(853\) | −33.1659 | −1.13558 | −0.567789 | − | 0.823174i | \(-0.692201\pi\) | ||||
−0.567789 | + | 0.823174i | \(0.692201\pi\) | |||||||
\(854\) | 3.69012 | 0.126273 | ||||||||
\(855\) | 1.82997 | 0.0625837 | ||||||||
\(856\) | 16.0364 | 0.548114 | ||||||||
\(857\) | −13.4674 | −0.460037 | −0.230019 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230019 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(858\) | 9.91450 | 0.338476 | ||||||||
\(859\) | 54.8632 | 1.87191 | 0.935954 | − | 0.352122i | \(-0.114540\pi\) | ||||
0.935954 | + | 0.352122i | \(0.114540\pi\) | |||||||
\(860\) | 9.73418 | 0.331933 | ||||||||
\(861\) | −15.4916 | −0.527951 | ||||||||
\(862\) | 6.00406 | 0.204499 | ||||||||
\(863\) | 8.17369 | 0.278236 | 0.139118 | − | 0.990276i | \(-0.455573\pi\) | ||||
0.139118 | + | 0.990276i | \(0.455573\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 31.0416 | 1.05545 | ||||||||
\(866\) | 12.1053 | 0.411353 | ||||||||
\(867\) | 28.7454 | 0.976244 | ||||||||
\(868\) | −8.03276 | −0.272650 | ||||||||
\(869\) | −11.4523 | −0.388494 | ||||||||
\(870\) | −5.28066 | −0.179031 | ||||||||
\(871\) | −5.97314 | −0.202392 | ||||||||
\(872\) | 16.5947 | 0.561968 | ||||||||
\(873\) | 14.3188 | 0.484619 | ||||||||
\(874\) | 3.81454 | 0.129029 | ||||||||
\(875\) | −20.4320 | −0.690726 | ||||||||
\(876\) | −14.3454 | −0.484686 | ||||||||
\(877\) | −19.2098 | −0.648668 | −0.324334 | − | 0.945943i | \(-0.605140\pi\) | ||||
−0.324334 | + | 0.945943i | \(0.605140\pi\) | |||||||
\(878\) | −15.4987 | −0.523055 | ||||||||
\(879\) | 9.39722 | 0.316960 | ||||||||
\(880\) | 3.68966 | 0.124379 | ||||||||
\(881\) | 13.5303 | 0.455846 | 0.227923 | − | 0.973679i | \(-0.426807\pi\) | ||||
0.227923 | + | 0.973679i | \(0.426807\pi\) | |||||||
\(882\) | 4.18206 | 0.140817 | ||||||||
\(883\) | −21.3701 | −0.719160 | −0.359580 | − | 0.933114i | \(-0.617080\pi\) | ||||
−0.359580 | + | 0.933114i | \(0.617080\pi\) | |||||||
\(884\) | 33.2585 | 1.11860 | ||||||||
\(885\) | −3.54330 | −0.119107 | ||||||||
\(886\) | 15.4339 | 0.518512 | ||||||||
\(887\) | −8.86929 | −0.297802 | −0.148901 | − | 0.988852i | \(-0.547574\pi\) | ||||
−0.148901 | + | 0.988852i | \(0.547574\pi\) | |||||||
\(888\) | 7.07868 | 0.237545 | ||||||||
\(889\) | −20.9461 | −0.702509 | ||||||||
\(890\) | 21.9037 | 0.734215 | ||||||||
\(891\) | 2.01624 | 0.0675466 | ||||||||
\(892\) | 8.03389 | 0.268995 | ||||||||
\(893\) | −0.326577 | −0.0109285 | ||||||||
\(894\) | −9.67726 | −0.323656 | ||||||||
\(895\) | 28.6274 | 0.956908 | ||||||||
\(896\) | −1.67867 | −0.0560805 | ||||||||
\(897\) | 18.7573 | 0.626289 | ||||||||
\(898\) | −23.3945 | −0.780686 | ||||||||
\(899\) | −13.8084 | −0.460535 | ||||||||
\(900\) | −1.65120 | −0.0550402 | ||||||||
\(901\) | 6.76353 | 0.225326 | ||||||||
\(902\) | 18.6068 | 0.619539 | ||||||||
\(903\) | 8.92937 | 0.297151 | ||||||||
\(904\) | 10.0659 | 0.334788 | ||||||||
\(905\) | −25.0344 | −0.832171 | ||||||||
\(906\) | −15.6367 | −0.519493 | ||||||||
\(907\) | −39.8019 | −1.32160 | −0.660800 | − | 0.750562i | \(-0.729783\pi\) | ||||
−0.660800 | + | 0.750562i | \(0.729783\pi\) | |||||||
\(908\) | 23.5491 | 0.781504 | ||||||||
\(909\) | 11.7632 | 0.390161 | ||||||||
\(910\) | 15.1056 | 0.500746 | ||||||||
\(911\) | −37.1868 | −1.23205 | −0.616026 | − | 0.787726i | \(-0.711259\pi\) | ||||
−0.616026 | + | 0.787726i | \(0.711259\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 7.32436 | 0.242401 | ||||||||
\(914\) | 7.37685 | 0.244004 | ||||||||
\(915\) | −4.02272 | −0.132987 | ||||||||
\(916\) | 13.4028 | 0.442840 | ||||||||
\(917\) | 1.99041 | 0.0657292 | ||||||||
\(918\) | 6.76353 | 0.223230 | ||||||||
\(919\) | −28.2951 | −0.933370 | −0.466685 | − | 0.884424i | \(-0.654552\pi\) | ||||
−0.466685 | + | 0.884424i | \(0.654552\pi\) | |||||||
\(920\) | 6.98050 | 0.230140 | ||||||||
\(921\) | −20.7864 | −0.684934 | ||||||||
\(922\) | −19.0342 | −0.626858 | ||||||||
\(923\) | −24.7217 | −0.813723 | ||||||||
\(924\) | 3.38461 | 0.111345 | ||||||||
\(925\) | 11.6883 | 0.384310 | ||||||||
\(926\) | −18.9218 | −0.621810 | ||||||||
\(927\) | 0.462585 | 0.0151933 | ||||||||
\(928\) | −2.88565 | −0.0947261 | ||||||||
\(929\) | −6.76250 | −0.221870 | −0.110935 | − | 0.993828i | \(-0.535385\pi\) | ||||
−0.110935 | + | 0.993828i | \(0.535385\pi\) | |||||||
\(930\) | 8.75676 | 0.287145 | ||||||||
\(931\) | −4.18206 | −0.137062 | ||||||||
\(932\) | 1.75466 | 0.0574757 | ||||||||
\(933\) | 20.5249 | 0.671957 | ||||||||
\(934\) | 6.93699 | 0.226985 | ||||||||
\(935\) | −24.9552 | −0.816121 | ||||||||
\(936\) | 4.91732 | 0.160728 | ||||||||
\(937\) | −7.29075 | −0.238178 | −0.119089 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119089 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(938\) | −2.03910 | −0.0665791 | ||||||||
\(939\) | −24.1449 | −0.787939 | ||||||||
\(940\) | −0.597627 | −0.0194925 | ||||||||
\(941\) | −48.1838 | −1.57075 | −0.785373 | − | 0.619022i | \(-0.787529\pi\) | ||||
−0.785373 | + | 0.619022i | \(0.787529\pi\) | |||||||
\(942\) | 13.0127 | 0.423977 | ||||||||
\(943\) | 35.2024 | 1.14635 | ||||||||
\(944\) | −1.93626 | −0.0630198 | ||||||||
\(945\) | 3.07192 | 0.0999295 | ||||||||
\(946\) | −10.7250 | −0.348700 | ||||||||
\(947\) | 55.7561 | 1.81183 | 0.905915 | − | 0.423460i | \(-0.139185\pi\) | ||||
0.905915 | + | 0.423460i | \(0.139185\pi\) | |||||||
\(948\) | −5.68004 | −0.184479 | ||||||||
\(949\) | 70.5409 | 2.28986 | ||||||||
\(950\) | 1.65120 | 0.0535722 | ||||||||
\(951\) | 13.5367 | 0.438959 | ||||||||
\(952\) | 11.3537 | 0.367977 | ||||||||
\(953\) | −41.9583 | −1.35916 | −0.679582 | − | 0.733600i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733600i | \(0.737839\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 6.94240 | 0.224651 | ||||||||
\(956\) | −7.06655 | −0.228549 | ||||||||
\(957\) | 5.81817 | 0.188075 | ||||||||
\(958\) | 36.7045 | 1.18587 | ||||||||
\(959\) | 31.0565 | 1.00287 | ||||||||
\(960\) | 1.82997 | 0.0590621 | ||||||||
\(961\) | −8.10197 | −0.261354 | ||||||||
\(962\) | −34.8081 | −1.12226 | ||||||||
\(963\) | −16.0364 | −0.516767 | ||||||||
\(964\) | 22.3701 | 0.720491 | ||||||||
\(965\) | −22.1829 | −0.714092 | ||||||||
\(966\) | 6.40336 | 0.206025 | ||||||||
\(967\) | −9.67191 | −0.311028 | −0.155514 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155514 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(968\) | 6.93477 | 0.222892 | ||||||||
\(969\) | −6.76353 | −0.217276 | ||||||||
\(970\) | −26.2031 | −0.841330 | ||||||||
\(971\) | −14.9967 | −0.481267 | −0.240634 | − | 0.970616i | \(-0.577355\pi\) | ||||
−0.240634 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 34.7474 | 1.11395 | ||||||||
\(974\) | 22.6007 | 0.724174 | ||||||||
\(975\) | 8.11950 | 0.260032 | ||||||||
\(976\) | −2.19824 | −0.0703640 | ||||||||
\(977\) | 43.2068 | 1.38231 | 0.691154 | − | 0.722708i | \(-0.257103\pi\) | ||||
0.691154 | + | 0.722708i | \(0.257103\pi\) | |||||||
\(978\) | −14.4971 | −0.463567 | ||||||||
\(979\) | −24.1333 | −0.771303 | ||||||||
\(980\) | −7.65306 | −0.244468 | ||||||||
\(981\) | −16.5947 | −0.529828 | ||||||||
\(982\) | 20.2104 | 0.644938 | ||||||||
\(983\) | −40.9851 | −1.30722 | −0.653611 | − | 0.756831i | \(-0.726747\pi\) | ||||
−0.653611 | + | 0.756831i | \(0.726747\pi\) | |||||||
\(984\) | 9.22847 | 0.294193 | ||||||||
\(985\) | −28.7502 | −0.916056 | ||||||||
\(986\) | 19.5172 | 0.621554 | ||||||||
\(987\) | −0.548216 | −0.0174499 | ||||||||
\(988\) | −4.91732 | −0.156441 | ||||||||
\(989\) | −20.2907 | −0.645207 | ||||||||
\(990\) | −3.68966 | −0.117265 | ||||||||
\(991\) | 1.62421 | 0.0515946 | 0.0257973 | − | 0.999667i | \(-0.491788\pi\) | ||||
0.0257973 | + | 0.999667i | \(0.491788\pi\) | |||||||
\(992\) | 4.78519 | 0.151930 | ||||||||
\(993\) | 19.8754 | 0.630725 | ||||||||
\(994\) | −8.43946 | −0.267683 | ||||||||
\(995\) | −17.4465 | −0.553091 | ||||||||
\(996\) | 3.63268 | 0.115106 | ||||||||
\(997\) | −15.8446 | −0.501804 | −0.250902 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250902 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(998\) | 16.5662 | 0.524394 | ||||||||
\(999\) | −7.07868 | −0.223959 |
(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.v.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.v.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial |