Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.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: | \(48.0859120972\) |
Analytic rank: | \(1\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-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 | ||||||||
\(3\) | −3.41719 | −1.97291 | −0.986457 | − | 0.164023i | \(-0.947553\pi\) | ||||
−0.986457 | + | 0.164023i | \(0.947553\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0151085 | 0.00675671 | 0.00337836 | − | 0.999994i | \(-0.498925\pi\) | ||||
0.00337836 | + | 0.999994i | \(0.498925\pi\) | |||||||
\(6\) | 3.41719 | 1.39506 | ||||||||
\(7\) | −2.13229 | −0.805929 | −0.402964 | − | 0.915216i | \(-0.632020\pi\) | ||||
−0.402964 | + | 0.915216i | \(0.632020\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 8.67716 | 2.89239 | ||||||||
\(10\) | −0.0151085 | −0.00477772 | ||||||||
\(11\) | 4.39461 | 1.32503 | 0.662513 | − | 0.749050i | \(-0.269490\pi\) | ||||
0.662513 | + | 0.749050i | \(0.269490\pi\) | |||||||
\(12\) | −3.41719 | −0.986457 | ||||||||
\(13\) | −4.28516 | −1.18849 | −0.594245 | − | 0.804284i | \(-0.702549\pi\) | ||||
−0.594245 | + | 0.804284i | \(0.702549\pi\) | |||||||
\(14\) | 2.13229 | 0.569878 | ||||||||
\(15\) | −0.0516285 | −0.0133304 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.201836 | −0.0489524 | −0.0244762 | − | 0.999700i | \(-0.507792\pi\) | ||||
−0.0244762 | + | 0.999700i | \(0.507792\pi\) | |||||||
\(18\) | −8.67716 | −2.04523 | ||||||||
\(19\) | −3.00008 | −0.688266 | −0.344133 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344133 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(20\) | 0.0151085 | 0.00337836 | ||||||||
\(21\) | 7.28642 | 1.59003 | ||||||||
\(22\) | −4.39461 | −0.936935 | ||||||||
\(23\) | 5.10083 | 1.06360 | 0.531799 | − | 0.846871i | \(-0.321516\pi\) | ||||
0.531799 | + | 0.846871i | \(0.321516\pi\) | |||||||
\(24\) | 3.41719 | 0.697530 | ||||||||
\(25\) | −4.99977 | −0.999954 | ||||||||
\(26\) | 4.28516 | 0.840389 | ||||||||
\(27\) | −19.3999 | −3.73351 | ||||||||
\(28\) | −2.13229 | −0.402964 | ||||||||
\(29\) | 2.44671 | 0.454343 | 0.227171 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227171 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(30\) | 0.0516285 | 0.00942602 | ||||||||
\(31\) | 7.95639 | 1.42901 | 0.714505 | − | 0.699631i | \(-0.246652\pi\) | ||||
0.714505 | + | 0.699631i | \(0.246652\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −15.0172 | −2.61416 | ||||||||
\(34\) | 0.201836 | 0.0346145 | ||||||||
\(35\) | −0.0322156 | −0.00544543 | ||||||||
\(36\) | 8.67716 | 1.44619 | ||||||||
\(37\) | 9.17741 | 1.50876 | 0.754379 | − | 0.656440i | \(-0.227938\pi\) | ||||
0.754379 | + | 0.656440i | \(0.227938\pi\) | |||||||
\(38\) | 3.00008 | 0.486677 | ||||||||
\(39\) | 14.6432 | 2.34479 | ||||||||
\(40\) | −0.0151085 | −0.00238886 | ||||||||
\(41\) | −8.64483 | −1.35010 | −0.675048 | − | 0.737774i | \(-0.735877\pi\) | ||||
−0.675048 | + | 0.737774i | \(0.735877\pi\) | |||||||
\(42\) | −7.28642 | −1.12432 | ||||||||
\(43\) | −10.9025 | −1.66261 | −0.831304 | − | 0.555818i | \(-0.812405\pi\) | ||||
−0.831304 | + | 0.555818i | \(0.812405\pi\) | |||||||
\(44\) | 4.39461 | 0.662513 | ||||||||
\(45\) | 0.131099 | 0.0195430 | ||||||||
\(46\) | −5.10083 | −0.752077 | ||||||||
\(47\) | 9.64339 | 1.40663 | 0.703316 | − | 0.710877i | \(-0.251702\pi\) | ||||
0.703316 | + | 0.710877i | \(0.251702\pi\) | |||||||
\(48\) | −3.41719 | −0.493228 | ||||||||
\(49\) | −2.45335 | −0.350479 | ||||||||
\(50\) | 4.99977 | 0.707074 | ||||||||
\(51\) | 0.689710 | 0.0965787 | ||||||||
\(52\) | −4.28516 | −0.594245 | ||||||||
\(53\) | −8.68052 | −1.19236 | −0.596180 | − | 0.802851i | \(-0.703316\pi\) | ||||
−0.596180 | + | 0.802851i | \(0.703316\pi\) | |||||||
\(54\) | 19.3999 | 2.63999 | ||||||||
\(55\) | 0.0663959 | 0.00895282 | ||||||||
\(56\) | 2.13229 | 0.284939 | ||||||||
\(57\) | 10.2518 | 1.35789 | ||||||||
\(58\) | −2.44671 | −0.321269 | ||||||||
\(59\) | −0.684446 | −0.0891073 | −0.0445537 | − | 0.999007i | \(-0.514187\pi\) | ||||
−0.0445537 | + | 0.999007i | \(0.514187\pi\) | |||||||
\(60\) | −0.0516285 | −0.00666521 | ||||||||
\(61\) | −2.90418 | −0.371842 | −0.185921 | − | 0.982565i | \(-0.559527\pi\) | ||||
−0.185921 | + | 0.982565i | \(0.559527\pi\) | |||||||
\(62\) | −7.95639 | −1.01046 | ||||||||
\(63\) | −18.5022 | −2.33106 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0647422 | −0.00803029 | ||||||||
\(66\) | 15.0172 | 1.84849 | ||||||||
\(67\) | −1.50427 | −0.183775 | −0.0918877 | − | 0.995769i | \(-0.529290\pi\) | ||||
−0.0918877 | + | 0.995769i | \(0.529290\pi\) | |||||||
\(68\) | −0.201836 | −0.0244762 | ||||||||
\(69\) | −17.4305 | −2.09839 | ||||||||
\(70\) | 0.0322156 | 0.00385050 | ||||||||
\(71\) | 8.92618 | 1.05934 | 0.529671 | − | 0.848203i | \(-0.322315\pi\) | ||||
0.529671 | + | 0.848203i | \(0.322315\pi\) | |||||||
\(72\) | −8.67716 | −1.02261 | ||||||||
\(73\) | −14.0485 | −1.64425 | −0.822127 | − | 0.569305i | \(-0.807212\pi\) | ||||
−0.822127 | + | 0.569305i | \(0.807212\pi\) | |||||||
\(74\) | −9.17741 | −1.06685 | ||||||||
\(75\) | 17.0851 | 1.97282 | ||||||||
\(76\) | −3.00008 | −0.344133 | ||||||||
\(77\) | −9.37058 | −1.06788 | ||||||||
\(78\) | −14.6432 | −1.65801 | ||||||||
\(79\) | −13.4421 | −1.51235 | −0.756176 | − | 0.654368i | \(-0.772935\pi\) | ||||
−0.756176 | + | 0.654368i | \(0.772935\pi\) | |||||||
\(80\) | 0.0151085 | 0.00168918 | ||||||||
\(81\) | 40.2616 | 4.47351 | ||||||||
\(82\) | 8.64483 | 0.954662 | ||||||||
\(83\) | −11.1809 | −1.22726 | −0.613631 | − | 0.789593i | \(-0.710292\pi\) | ||||
−0.613631 | + | 0.789593i | \(0.710292\pi\) | |||||||
\(84\) | 7.28642 | 0.795014 | ||||||||
\(85\) | −0.00304943 | −0.000330757 0 | ||||||||
\(86\) | 10.9025 | 1.17564 | ||||||||
\(87\) | −8.36087 | −0.896379 | ||||||||
\(88\) | −4.39461 | −0.468468 | ||||||||
\(89\) | 9.74468 | 1.03293 | 0.516467 | − | 0.856307i | \(-0.327247\pi\) | ||||
0.516467 | + | 0.856307i | \(0.327247\pi\) | |||||||
\(90\) | −0.131099 | −0.0138190 | ||||||||
\(91\) | 9.13719 | 0.957838 | ||||||||
\(92\) | 5.10083 | 0.531799 | ||||||||
\(93\) | −27.1884 | −2.81931 | ||||||||
\(94\) | −9.64339 | −0.994640 | ||||||||
\(95\) | −0.0453266 | −0.00465041 | ||||||||
\(96\) | 3.41719 | 0.348765 | ||||||||
\(97\) | −12.7413 | −1.29368 | −0.646840 | − | 0.762625i | \(-0.723910\pi\) | ||||
−0.646840 | + | 0.762625i | \(0.723910\pi\) | |||||||
\(98\) | 2.45335 | 0.247826 | ||||||||
\(99\) | 38.1328 | 3.83249 | ||||||||
\(100\) | −4.99977 | −0.499977 | ||||||||
\(101\) | 14.9315 | 1.48574 | 0.742872 | − | 0.669434i | \(-0.233463\pi\) | ||||
0.742872 | + | 0.669434i | \(0.233463\pi\) | |||||||
\(102\) | −0.689710 | −0.0682915 | ||||||||
\(103\) | 10.9195 | 1.07593 | 0.537966 | − | 0.842967i | \(-0.319193\pi\) | ||||
0.537966 | + | 0.842967i | \(0.319193\pi\) | |||||||
\(104\) | 4.28516 | 0.420195 | ||||||||
\(105\) | 0.110087 | 0.0107434 | ||||||||
\(106\) | 8.68052 | 0.843126 | ||||||||
\(107\) | 19.8606 | 1.92000 | 0.959998 | − | 0.280008i | \(-0.0903372\pi\) | ||||
0.959998 | + | 0.280008i | \(0.0903372\pi\) | |||||||
\(108\) | −19.3999 | −1.86676 | ||||||||
\(109\) | 18.5266 | 1.77453 | 0.887263 | − | 0.461264i | \(-0.152604\pi\) | ||||
0.887263 | + | 0.461264i | \(0.152604\pi\) | |||||||
\(110\) | −0.0663959 | −0.00633060 | ||||||||
\(111\) | −31.3609 | −2.97665 | ||||||||
\(112\) | −2.13229 | −0.201482 | ||||||||
\(113\) | 6.74409 | 0.634430 | 0.317215 | − | 0.948354i | \(-0.397252\pi\) | ||||
0.317215 | + | 0.948354i | \(0.397252\pi\) | |||||||
\(114\) | −10.2518 | −0.960172 | ||||||||
\(115\) | 0.0770658 | 0.00718642 | ||||||||
\(116\) | 2.44671 | 0.227171 | ||||||||
\(117\) | −37.1830 | −3.43757 | ||||||||
\(118\) | 0.684446 | 0.0630084 | ||||||||
\(119\) | 0.430372 | 0.0394521 | ||||||||
\(120\) | 0.0516285 | 0.00471301 | ||||||||
\(121\) | 8.31264 | 0.755695 | ||||||||
\(122\) | 2.90418 | 0.262932 | ||||||||
\(123\) | 29.5410 | 2.66362 | ||||||||
\(124\) | 7.95639 | 0.714505 | ||||||||
\(125\) | −0.151081 | −0.0135131 | ||||||||
\(126\) | 18.5022 | 1.64831 | ||||||||
\(127\) | 15.2060 | 1.34932 | 0.674659 | − | 0.738130i | \(-0.264291\pi\) | ||||
0.674659 | + | 0.738130i | \(0.264291\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 37.2557 | 3.28018 | ||||||||
\(130\) | 0.0647422 | 0.00567827 | ||||||||
\(131\) | 2.06243 | 0.180196 | 0.0900978 | − | 0.995933i | \(-0.471282\pi\) | ||||
0.0900978 | + | 0.995933i | \(0.471282\pi\) | |||||||
\(132\) | −15.0172 | −1.30708 | ||||||||
\(133\) | 6.39703 | 0.554693 | ||||||||
\(134\) | 1.50427 | 0.129949 | ||||||||
\(135\) | −0.293103 | −0.0252263 | ||||||||
\(136\) | 0.201836 | 0.0173073 | ||||||||
\(137\) | 11.7016 | 0.999736 | 0.499868 | − | 0.866102i | \(-0.333382\pi\) | ||||
0.499868 | + | 0.866102i | \(0.333382\pi\) | |||||||
\(138\) | 17.4305 | 1.48378 | ||||||||
\(139\) | −7.67261 | −0.650782 | −0.325391 | − | 0.945580i | \(-0.605496\pi\) | ||||
−0.325391 | + | 0.945580i | \(0.605496\pi\) | |||||||
\(140\) | −0.0322156 | −0.00272272 | ||||||||
\(141\) | −32.9533 | −2.77516 | ||||||||
\(142\) | −8.92618 | −0.749068 | ||||||||
\(143\) | −18.8316 | −1.57478 | ||||||||
\(144\) | 8.67716 | 0.723096 | ||||||||
\(145\) | 0.0369661 | 0.00306987 | ||||||||
\(146\) | 14.0485 | 1.16266 | ||||||||
\(147\) | 8.38356 | 0.691465 | ||||||||
\(148\) | 9.17741 | 0.754379 | ||||||||
\(149\) | 0.471765 | 0.0386485 | 0.0193242 | − | 0.999813i | \(-0.493849\pi\) | ||||
0.0193242 | + | 0.999813i | \(0.493849\pi\) | |||||||
\(150\) | −17.0851 | −1.39500 | ||||||||
\(151\) | 11.8515 | 0.964463 | 0.482232 | − | 0.876044i | \(-0.339826\pi\) | ||||
0.482232 | + | 0.876044i | \(0.339826\pi\) | |||||||
\(152\) | 3.00008 | 0.243339 | ||||||||
\(153\) | −1.75136 | −0.141589 | ||||||||
\(154\) | 9.37058 | 0.755103 | ||||||||
\(155\) | 0.120209 | 0.00965541 | ||||||||
\(156\) | 14.6432 | 1.17239 | ||||||||
\(157\) | 12.1497 | 0.969651 | 0.484825 | − | 0.874611i | \(-0.338883\pi\) | ||||
0.484825 | + | 0.874611i | \(0.338883\pi\) | |||||||
\(158\) | 13.4421 | 1.06939 | ||||||||
\(159\) | 29.6629 | 2.35242 | ||||||||
\(160\) | −0.0151085 | −0.00119443 | ||||||||
\(161\) | −10.8764 | −0.857184 | ||||||||
\(162\) | −40.2616 | −3.16325 | ||||||||
\(163\) | 0.240334 | 0.0188244 | 0.00941222 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941222 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(164\) | −8.64483 | −0.675048 | ||||||||
\(165\) | −0.226887 | −0.0176631 | ||||||||
\(166\) | 11.1809 | 0.867805 | ||||||||
\(167\) | 10.1834 | 0.788012 | 0.394006 | − | 0.919108i | \(-0.371089\pi\) | ||||
0.394006 | + | 0.919108i | \(0.371089\pi\) | |||||||
\(168\) | −7.28642 | −0.562160 | ||||||||
\(169\) | 5.36260 | 0.412508 | ||||||||
\(170\) | 0.00304943 | 0.000233881 0 | ||||||||
\(171\) | −26.0322 | −1.99073 | ||||||||
\(172\) | −10.9025 | −0.831304 | ||||||||
\(173\) | −4.33021 | −0.329220 | −0.164610 | − | 0.986359i | \(-0.552637\pi\) | ||||
−0.164610 | + | 0.986359i | \(0.552637\pi\) | |||||||
\(174\) | 8.36087 | 0.633836 | ||||||||
\(175\) | 10.6609 | 0.805892 | ||||||||
\(176\) | 4.39461 | 0.331257 | ||||||||
\(177\) | 2.33888 | 0.175801 | ||||||||
\(178\) | −9.74468 | −0.730395 | ||||||||
\(179\) | −2.46791 | −0.184460 | −0.0922302 | − | 0.995738i | \(-0.529400\pi\) | ||||
−0.0922302 | + | 0.995738i | \(0.529400\pi\) | |||||||
\(180\) | 0.131099 | 0.00977151 | ||||||||
\(181\) | −16.4091 | −1.21968 | −0.609841 | − | 0.792524i | \(-0.708767\pi\) | ||||
−0.609841 | + | 0.792524i | \(0.708767\pi\) | |||||||
\(182\) | −9.13719 | −0.677294 | ||||||||
\(183\) | 9.92411 | 0.733611 | ||||||||
\(184\) | −5.10083 | −0.376038 | ||||||||
\(185\) | 0.138657 | 0.0101942 | ||||||||
\(186\) | 27.1884 | 1.99355 | ||||||||
\(187\) | −0.886990 | −0.0648632 | ||||||||
\(188\) | 9.64339 | 0.703316 | ||||||||
\(189\) | 41.3662 | 3.00894 | ||||||||
\(190\) | 0.0453266 | 0.00328834 | ||||||||
\(191\) | 5.07962 | 0.367548 | 0.183774 | − | 0.982968i | \(-0.441168\pi\) | ||||
0.183774 | + | 0.982968i | \(0.441168\pi\) | |||||||
\(192\) | −3.41719 | −0.246614 | ||||||||
\(193\) | −13.7083 | −0.986742 | −0.493371 | − | 0.869819i | \(-0.664236\pi\) | ||||
−0.493371 | + | 0.869819i | \(0.664236\pi\) | |||||||
\(194\) | 12.7413 | 0.914770 | ||||||||
\(195\) | 0.221236 | 0.0158431 | ||||||||
\(196\) | −2.45335 | −0.175239 | ||||||||
\(197\) | −22.5171 | −1.60428 | −0.802140 | − | 0.597136i | \(-0.796305\pi\) | ||||
−0.802140 | + | 0.597136i | \(0.796305\pi\) | |||||||
\(198\) | −38.1328 | −2.70998 | ||||||||
\(199\) | −7.47856 | −0.530141 | −0.265070 | − | 0.964229i | \(-0.585395\pi\) | ||||
−0.265070 | + | 0.964229i | \(0.585395\pi\) | |||||||
\(200\) | 4.99977 | 0.353537 | ||||||||
\(201\) | 5.14036 | 0.362573 | ||||||||
\(202\) | −14.9315 | −1.05058 | ||||||||
\(203\) | −5.21709 | −0.366168 | ||||||||
\(204\) | 0.689710 | 0.0482894 | ||||||||
\(205\) | −0.130610 | −0.00912221 | ||||||||
\(206\) | −10.9195 | −0.760799 | ||||||||
\(207\) | 44.2607 | 3.07633 | ||||||||
\(208\) | −4.28516 | −0.297122 | ||||||||
\(209\) | −13.1842 | −0.911970 | ||||||||
\(210\) | −0.110087 | −0.00759670 | ||||||||
\(211\) | 0.0379606 | 0.00261331 | 0.00130666 | − | 0.999999i | \(-0.499584\pi\) | ||||
0.00130666 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(212\) | −8.68052 | −0.596180 | ||||||||
\(213\) | −30.5024 | −2.08999 | ||||||||
\(214\) | −19.8606 | −1.35764 | ||||||||
\(215\) | −0.164719 | −0.0112338 | ||||||||
\(216\) | 19.3999 | 1.32000 | ||||||||
\(217\) | −16.9653 | −1.15168 | ||||||||
\(218\) | −18.5266 | −1.25478 | ||||||||
\(219\) | 48.0064 | 3.24397 | ||||||||
\(220\) | 0.0663959 | 0.00447641 | ||||||||
\(221\) | 0.864899 | 0.0581794 | ||||||||
\(222\) | 31.3609 | 2.10481 | ||||||||
\(223\) | 8.87363 | 0.594222 | 0.297111 | − | 0.954843i | \(-0.403977\pi\) | ||||
0.297111 | + | 0.954843i | \(0.403977\pi\) | |||||||
\(224\) | 2.13229 | 0.142469 | ||||||||
\(225\) | −43.3838 | −2.89225 | ||||||||
\(226\) | −6.74409 | −0.448610 | ||||||||
\(227\) | 7.00388 | 0.464864 | 0.232432 | − | 0.972613i | \(-0.425332\pi\) | ||||
0.232432 | + | 0.972613i | \(0.425332\pi\) | |||||||
\(228\) | 10.2518 | 0.678944 | ||||||||
\(229\) | −21.6430 | −1.43021 | −0.715106 | − | 0.699016i | \(-0.753622\pi\) | ||||
−0.715106 | + | 0.699016i | \(0.753622\pi\) | |||||||
\(230\) | −0.0770658 | −0.00508157 | ||||||||
\(231\) | 32.0210 | 2.10683 | ||||||||
\(232\) | −2.44671 | −0.160634 | ||||||||
\(233\) | 5.77415 | 0.378277 | 0.189139 | − | 0.981950i | \(-0.439430\pi\) | ||||
0.189139 | + | 0.981950i | \(0.439430\pi\) | |||||||
\(234\) | 37.1830 | 2.43073 | ||||||||
\(235\) | 0.145697 | 0.00950422 | ||||||||
\(236\) | −0.684446 | −0.0445537 | ||||||||
\(237\) | 45.9341 | 2.98374 | ||||||||
\(238\) | −0.430372 | −0.0278969 | ||||||||
\(239\) | −25.4396 | −1.64555 | −0.822775 | − | 0.568367i | \(-0.807576\pi\) | ||||
−0.822775 | + | 0.568367i | \(0.807576\pi\) | |||||||
\(240\) | −0.0516285 | −0.00333260 | ||||||||
\(241\) | −20.3513 | −1.31094 | −0.655471 | − | 0.755220i | \(-0.727530\pi\) | ||||
−0.655471 | + | 0.755220i | \(0.727530\pi\) | |||||||
\(242\) | −8.31264 | −0.534357 | ||||||||
\(243\) | −79.3816 | −5.09233 | ||||||||
\(244\) | −2.90418 | −0.185921 | ||||||||
\(245\) | −0.0370664 | −0.00236809 | ||||||||
\(246\) | −29.5410 | −1.88346 | ||||||||
\(247\) | 12.8558 | 0.817997 | ||||||||
\(248\) | −7.95639 | −0.505231 | ||||||||
\(249\) | 38.2071 | 2.42128 | ||||||||
\(250\) | 0.151081 | 0.00955522 | ||||||||
\(251\) | 4.01409 | 0.253367 | 0.126684 | − | 0.991943i | \(-0.459567\pi\) | ||||
0.126684 | + | 0.991943i | \(0.459567\pi\) | |||||||
\(252\) | −18.5022 | −1.16553 | ||||||||
\(253\) | 22.4162 | 1.40929 | ||||||||
\(254\) | −15.2060 | −0.954112 | ||||||||
\(255\) | 0.0104205 | 0.000652555 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.8011 | 1.54705 | 0.773526 | − | 0.633764i | \(-0.218491\pi\) | ||||
0.773526 | + | 0.633764i | \(0.218491\pi\) | |||||||
\(258\) | −37.2557 | −2.31944 | ||||||||
\(259\) | −19.5689 | −1.21595 | ||||||||
\(260\) | −0.0647422 | −0.00401514 | ||||||||
\(261\) | 21.2305 | 1.31413 | ||||||||
\(262\) | −2.06243 | −0.127417 | ||||||||
\(263\) | 18.2121 | 1.12301 | 0.561503 | − | 0.827475i | \(-0.310223\pi\) | ||||
0.561503 | + | 0.827475i | \(0.310223\pi\) | |||||||
\(264\) | 15.0172 | 0.924246 | ||||||||
\(265\) | −0.131149 | −0.00805644 | ||||||||
\(266\) | −6.39703 | −0.392227 | ||||||||
\(267\) | −33.2994 | −2.03789 | ||||||||
\(268\) | −1.50427 | −0.0918877 | ||||||||
\(269\) | −0.860887 | −0.0524892 | −0.0262446 | − | 0.999656i | \(-0.508355\pi\) | ||||
−0.0262446 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(270\) | 0.293103 | 0.0178377 | ||||||||
\(271\) | 32.2518 | 1.95916 | 0.979578 | − | 0.201064i | \(-0.0644400\pi\) | ||||
0.979578 | + | 0.201064i | \(0.0644400\pi\) | |||||||
\(272\) | −0.201836 | −0.0122381 | ||||||||
\(273\) | −31.2235 | −1.88973 | ||||||||
\(274\) | −11.7016 | −0.706920 | ||||||||
\(275\) | −21.9721 | −1.32497 | ||||||||
\(276\) | −17.4305 | −1.04919 | ||||||||
\(277\) | 2.83466 | 0.170318 | 0.0851590 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851590 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(278\) | 7.67261 | 0.460172 | ||||||||
\(279\) | 69.0388 | 4.13325 | ||||||||
\(280\) | 0.0322156 | 0.00192525 | ||||||||
\(281\) | 8.89513 | 0.530639 | 0.265320 | − | 0.964161i | \(-0.414523\pi\) | ||||
0.265320 | + | 0.964161i | \(0.414523\pi\) | |||||||
\(282\) | 32.9533 | 1.96234 | ||||||||
\(283\) | 25.2588 | 1.50148 | 0.750740 | − | 0.660598i | \(-0.229697\pi\) | ||||
0.750740 | + | 0.660598i | \(0.229697\pi\) | |||||||
\(284\) | 8.92618 | 0.529671 | ||||||||
\(285\) | 0.154890 | 0.00917486 | ||||||||
\(286\) | 18.8316 | 1.11354 | ||||||||
\(287\) | 18.4333 | 1.08808 | ||||||||
\(288\) | −8.67716 | −0.511306 | ||||||||
\(289\) | −16.9593 | −0.997604 | ||||||||
\(290\) | −0.0369661 | −0.00217072 | ||||||||
\(291\) | 43.5393 | 2.55232 | ||||||||
\(292\) | −14.0485 | −0.822127 | ||||||||
\(293\) | −20.9972 | −1.22667 | −0.613335 | − | 0.789823i | \(-0.710173\pi\) | ||||
−0.613335 | + | 0.789823i | \(0.710173\pi\) | |||||||
\(294\) | −8.38356 | −0.488939 | ||||||||
\(295\) | −0.0103409 | −0.000602073 0 | ||||||||
\(296\) | −9.17741 | −0.533426 | ||||||||
\(297\) | −85.2551 | −4.94700 | ||||||||
\(298\) | −0.471765 | −0.0273286 | ||||||||
\(299\) | −21.8579 | −1.26407 | ||||||||
\(300\) | 17.0851 | 0.986411 | ||||||||
\(301\) | 23.2472 | 1.33994 | ||||||||
\(302\) | −11.8515 | −0.681978 | ||||||||
\(303\) | −51.0238 | −2.93124 | ||||||||
\(304\) | −3.00008 | −0.172066 | ||||||||
\(305\) | −0.0438777 | −0.00251243 | ||||||||
\(306\) | 1.75136 | 0.100119 | ||||||||
\(307\) | 12.8942 | 0.735909 | 0.367955 | − | 0.929844i | \(-0.380058\pi\) | ||||
0.367955 | + | 0.929844i | \(0.380058\pi\) | |||||||
\(308\) | −9.37058 | −0.533938 | ||||||||
\(309\) | −37.3140 | −2.12272 | ||||||||
\(310\) | −0.120209 | −0.00682740 | ||||||||
\(311\) | −17.6739 | −1.00219 | −0.501097 | − | 0.865391i | \(-0.667070\pi\) | ||||
−0.501097 | + | 0.865391i | \(0.667070\pi\) | |||||||
\(312\) | −14.6432 | −0.829007 | ||||||||
\(313\) | −14.7044 | −0.831140 | −0.415570 | − | 0.909561i | \(-0.636418\pi\) | ||||
−0.415570 | + | 0.909561i | \(0.636418\pi\) | |||||||
\(314\) | −12.1497 | −0.685647 | ||||||||
\(315\) | −0.279540 | −0.0157503 | ||||||||
\(316\) | −13.4421 | −0.756176 | ||||||||
\(317\) | 13.0243 | 0.731518 | 0.365759 | − | 0.930709i | \(-0.380809\pi\) | ||||
0.365759 | + | 0.930709i | \(0.380809\pi\) | |||||||
\(318\) | −29.6629 | −1.66341 | ||||||||
\(319\) | 10.7524 | 0.602016 | ||||||||
\(320\) | 0.0151085 | 0.000844589 0 | ||||||||
\(321\) | −67.8673 | −3.78798 | ||||||||
\(322\) | 10.8764 | 0.606120 | ||||||||
\(323\) | 0.605523 | 0.0336922 | ||||||||
\(324\) | 40.2616 | 2.23675 | ||||||||
\(325\) | 21.4248 | 1.18844 | ||||||||
\(326\) | −0.240334 | −0.0133109 | ||||||||
\(327\) | −63.3088 | −3.50098 | ||||||||
\(328\) | 8.64483 | 0.477331 | ||||||||
\(329\) | −20.5625 | −1.13365 | ||||||||
\(330\) | 0.226887 | 0.0124897 | ||||||||
\(331\) | −23.3022 | −1.28080 | −0.640402 | − | 0.768040i | \(-0.721232\pi\) | ||||
−0.640402 | + | 0.768040i | \(0.721232\pi\) | |||||||
\(332\) | −11.1809 | −0.613631 | ||||||||
\(333\) | 79.6338 | 4.36391 | ||||||||
\(334\) | −10.1834 | −0.557209 | ||||||||
\(335\) | −0.0227272 | −0.00124172 | ||||||||
\(336\) | 7.28642 | 0.397507 | ||||||||
\(337\) | −30.1845 | −1.64426 | −0.822128 | − | 0.569302i | \(-0.807213\pi\) | ||||
−0.822128 | + | 0.569302i | \(0.807213\pi\) | |||||||
\(338\) | −5.36260 | −0.291687 | ||||||||
\(339\) | −23.0458 | −1.25168 | ||||||||
\(340\) | −0.00304943 | −0.000165379 0 | ||||||||
\(341\) | 34.9653 | 1.89347 | ||||||||
\(342\) | 26.0322 | 1.40766 | ||||||||
\(343\) | 20.1573 | 1.08839 | ||||||||
\(344\) | 10.9025 | 0.587821 | ||||||||
\(345\) | −0.263348 | −0.0141782 | ||||||||
\(346\) | 4.33021 | 0.232793 | ||||||||
\(347\) | −27.2728 | −1.46408 | −0.732040 | − | 0.681261i | \(-0.761432\pi\) | ||||
−0.732040 | + | 0.681261i | \(0.761432\pi\) | |||||||
\(348\) | −8.36087 | −0.448189 | ||||||||
\(349\) | −36.6309 | −1.96081 | −0.980404 | − | 0.196998i | \(-0.936881\pi\) | ||||
−0.980404 | + | 0.196998i | \(0.936881\pi\) | |||||||
\(350\) | −10.6609 | −0.569852 | ||||||||
\(351\) | 83.1317 | 4.43724 | ||||||||
\(352\) | −4.39461 | −0.234234 | ||||||||
\(353\) | 10.2633 | 0.546258 | 0.273129 | − | 0.961977i | \(-0.411941\pi\) | ||||
0.273129 | + | 0.961977i | \(0.411941\pi\) | |||||||
\(354\) | −2.33888 | −0.124310 | ||||||||
\(355\) | 0.134861 | 0.00715767 | ||||||||
\(356\) | 9.74468 | 0.516467 | ||||||||
\(357\) | −1.47066 | −0.0778356 | ||||||||
\(358\) | 2.46791 | 0.130433 | ||||||||
\(359\) | 20.1126 | 1.06150 | 0.530751 | − | 0.847528i | \(-0.321910\pi\) | ||||
0.530751 | + | 0.847528i | \(0.321910\pi\) | |||||||
\(360\) | −0.131099 | −0.00690950 | ||||||||
\(361\) | −9.99952 | −0.526291 | ||||||||
\(362\) | 16.4091 | 0.862445 | ||||||||
\(363\) | −28.4058 | −1.49092 | ||||||||
\(364\) | 9.13719 | 0.478919 | ||||||||
\(365\) | −0.212251 | −0.0111098 | ||||||||
\(366\) | −9.92411 | −0.518741 | ||||||||
\(367\) | 1.99567 | 0.104173 | 0.0520867 | − | 0.998643i | \(-0.483413\pi\) | ||||
0.0520867 | + | 0.998643i | \(0.483413\pi\) | |||||||
\(368\) | 5.10083 | 0.265899 | ||||||||
\(369\) | −75.0126 | −3.90500 | ||||||||
\(370\) | −0.138657 | −0.00720842 | ||||||||
\(371\) | 18.5093 | 0.960958 | ||||||||
\(372\) | −27.1884 | −1.40966 | ||||||||
\(373\) | 4.12517 | 0.213593 | 0.106796 | − | 0.994281i | \(-0.465941\pi\) | ||||
0.106796 | + | 0.994281i | \(0.465941\pi\) | |||||||
\(374\) | 0.886990 | 0.0458652 | ||||||||
\(375\) | 0.516273 | 0.0266602 | ||||||||
\(376\) | −9.64339 | −0.497320 | ||||||||
\(377\) | −10.4846 | −0.539982 | ||||||||
\(378\) | −41.3662 | −2.12765 | ||||||||
\(379\) | 12.0298 | 0.617931 | 0.308965 | − | 0.951073i | \(-0.400017\pi\) | ||||
0.308965 | + | 0.951073i | \(0.400017\pi\) | |||||||
\(380\) | −0.0453266 | −0.00232521 | ||||||||
\(381\) | −51.9619 | −2.66209 | ||||||||
\(382\) | −5.07962 | −0.259896 | ||||||||
\(383\) | −1.87726 | −0.0959235 | −0.0479618 | − | 0.998849i | \(-0.515273\pi\) | ||||
−0.0479618 | + | 0.998849i | \(0.515273\pi\) | |||||||
\(384\) | 3.41719 | 0.174383 | ||||||||
\(385\) | −0.141575 | −0.00721534 | ||||||||
\(386\) | 13.7083 | 0.697732 | ||||||||
\(387\) | −94.6023 | −4.80890 | ||||||||
\(388\) | −12.7413 | −0.646840 | ||||||||
\(389\) | −17.4199 | −0.883226 | −0.441613 | − | 0.897206i | \(-0.645594\pi\) | ||||
−0.441613 | + | 0.897206i | \(0.645594\pi\) | |||||||
\(390\) | −0.221236 | −0.0112027 | ||||||||
\(391\) | −1.02953 | −0.0520656 | ||||||||
\(392\) | 2.45335 | 0.123913 | ||||||||
\(393\) | −7.04771 | −0.355510 | ||||||||
\(394\) | 22.5171 | 1.13440 | ||||||||
\(395\) | −0.203089 | −0.0102185 | ||||||||
\(396\) | 38.1328 | 1.91624 | ||||||||
\(397\) | −10.1319 | −0.508505 | −0.254252 | − | 0.967138i | \(-0.581829\pi\) | ||||
−0.254252 | + | 0.967138i | \(0.581829\pi\) | |||||||
\(398\) | 7.47856 | 0.374866 | ||||||||
\(399\) | −21.8598 | −1.09436 | ||||||||
\(400\) | −4.99977 | −0.249989 | ||||||||
\(401\) | 20.8919 | 1.04329 | 0.521646 | − | 0.853162i | \(-0.325318\pi\) | ||||
0.521646 | + | 0.853162i | \(0.325318\pi\) | |||||||
\(402\) | −5.14036 | −0.256378 | ||||||||
\(403\) | −34.0944 | −1.69836 | ||||||||
\(404\) | 14.9315 | 0.742872 | ||||||||
\(405\) | 0.608291 | 0.0302262 | ||||||||
\(406\) | 5.21709 | 0.258920 | ||||||||
\(407\) | 40.3312 | 1.99914 | ||||||||
\(408\) | −0.689710 | −0.0341457 | ||||||||
\(409\) | 28.2601 | 1.39737 | 0.698686 | − | 0.715428i | \(-0.253768\pi\) | ||||
0.698686 | + | 0.715428i | \(0.253768\pi\) | |||||||
\(410\) | 0.130610 | 0.00645038 | ||||||||
\(411\) | −39.9866 | −1.97239 | ||||||||
\(412\) | 10.9195 | 0.537966 | ||||||||
\(413\) | 1.45944 | 0.0718141 | ||||||||
\(414\) | −44.2607 | −2.17530 | ||||||||
\(415\) | −0.168926 | −0.00829225 | ||||||||
\(416\) | 4.28516 | 0.210097 | ||||||||
\(417\) | 26.2187 | 1.28394 | ||||||||
\(418\) | 13.1842 | 0.644860 | ||||||||
\(419\) | −5.87543 | −0.287033 | −0.143517 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143517 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(420\) | 0.110087 | 0.00537168 | ||||||||
\(421\) | 11.5769 | 0.564225 | 0.282112 | − | 0.959381i | \(-0.408965\pi\) | ||||
0.282112 | + | 0.959381i | \(0.408965\pi\) | |||||||
\(422\) | −0.0379606 | −0.00184789 | ||||||||
\(423\) | 83.6772 | 4.06853 | ||||||||
\(424\) | 8.68052 | 0.421563 | ||||||||
\(425\) | 1.00913 | 0.0489501 | ||||||||
\(426\) | 30.5024 | 1.47785 | ||||||||
\(427\) | 6.19254 | 0.299678 | ||||||||
\(428\) | 19.8606 | 0.959998 | ||||||||
\(429\) | 64.3512 | 3.10690 | ||||||||
\(430\) | 0.164719 | 0.00794347 | ||||||||
\(431\) | −0.0977132 | −0.00470668 | −0.00235334 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235334 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(432\) | −19.3999 | −0.933378 | ||||||||
\(433\) | −14.0181 | −0.673667 | −0.336833 | − | 0.941564i | \(-0.609356\pi\) | ||||
−0.336833 | + | 0.941564i | \(0.609356\pi\) | |||||||
\(434\) | 16.9653 | 0.814360 | ||||||||
\(435\) | −0.126320 | −0.00605658 | ||||||||
\(436\) | 18.5266 | 0.887263 | ||||||||
\(437\) | −15.3029 | −0.732037 | ||||||||
\(438\) | −48.0064 | −2.29383 | ||||||||
\(439\) | 19.7608 | 0.943131 | 0.471566 | − | 0.881831i | \(-0.343689\pi\) | ||||
0.471566 | + | 0.881831i | \(0.343689\pi\) | |||||||
\(440\) | −0.0663959 | −0.00316530 | ||||||||
\(441\) | −21.2881 | −1.01372 | ||||||||
\(442\) | −0.864899 | −0.0411390 | ||||||||
\(443\) | −36.5124 | −1.73476 | −0.867379 | − | 0.497648i | \(-0.834197\pi\) | ||||
−0.867379 | + | 0.497648i | \(0.834197\pi\) | |||||||
\(444\) | −31.3609 | −1.48832 | ||||||||
\(445\) | 0.147227 | 0.00697924 | ||||||||
\(446\) | −8.87363 | −0.420179 | ||||||||
\(447\) | −1.61211 | −0.0762501 | ||||||||
\(448\) | −2.13229 | −0.100741 | ||||||||
\(449\) | −27.9839 | −1.32064 | −0.660320 | − | 0.750984i | \(-0.729579\pi\) | ||||
−0.660320 | + | 0.750984i | \(0.729579\pi\) | |||||||
\(450\) | 43.3838 | 2.04513 | ||||||||
\(451\) | −37.9907 | −1.78891 | ||||||||
\(452\) | 6.74409 | 0.317215 | ||||||||
\(453\) | −40.4988 | −1.90280 | ||||||||
\(454\) | −7.00388 | −0.328708 | ||||||||
\(455\) | 0.138049 | 0.00647184 | ||||||||
\(456\) | −10.2518 | −0.480086 | ||||||||
\(457\) | −16.3647 | −0.765510 | −0.382755 | − | 0.923850i | \(-0.625025\pi\) | ||||
−0.382755 | + | 0.923850i | \(0.625025\pi\) | |||||||
\(458\) | 21.6430 | 1.01131 | ||||||||
\(459\) | 3.91559 | 0.182764 | ||||||||
\(460\) | 0.0770658 | 0.00359321 | ||||||||
\(461\) | −25.6050 | −1.19254 | −0.596272 | − | 0.802782i | \(-0.703352\pi\) | ||||
−0.596272 | + | 0.802782i | \(0.703352\pi\) | |||||||
\(462\) | −32.0210 | −1.48975 | ||||||||
\(463\) | 31.2481 | 1.45222 | 0.726111 | − | 0.687578i | \(-0.241326\pi\) | ||||
0.726111 | + | 0.687578i | \(0.241326\pi\) | |||||||
\(464\) | 2.44671 | 0.113586 | ||||||||
\(465\) | −0.410776 | −0.0190493 | ||||||||
\(466\) | −5.77415 | −0.267482 | ||||||||
\(467\) | −5.33209 | −0.246740 | −0.123370 | − | 0.992361i | \(-0.539370\pi\) | ||||
−0.123370 | + | 0.992361i | \(0.539370\pi\) | |||||||
\(468\) | −37.1830 | −1.71879 | ||||||||
\(469\) | 3.20753 | 0.148110 | ||||||||
\(470\) | −0.145697 | −0.00672050 | ||||||||
\(471\) | −41.5177 | −1.91304 | ||||||||
\(472\) | 0.684446 | 0.0315042 | ||||||||
\(473\) | −47.9121 | −2.20300 | ||||||||
\(474\) | −45.9341 | −2.10982 | ||||||||
\(475\) | 14.9997 | 0.688234 | ||||||||
\(476\) | 0.430372 | 0.0197261 | ||||||||
\(477\) | −75.3222 | −3.44877 | ||||||||
\(478\) | 25.4396 | 1.16358 | ||||||||
\(479\) | −41.1818 | −1.88164 | −0.940822 | − | 0.338901i | \(-0.889945\pi\) | ||||
−0.940822 | + | 0.338901i | \(0.889945\pi\) | |||||||
\(480\) | 0.0516285 | 0.00235651 | ||||||||
\(481\) | −39.3267 | −1.79314 | ||||||||
\(482\) | 20.3513 | 0.926976 | ||||||||
\(483\) | 37.1668 | 1.69115 | ||||||||
\(484\) | 8.31264 | 0.377847 | ||||||||
\(485\) | −0.192501 | −0.00874103 | ||||||||
\(486\) | 79.3816 | 3.60082 | ||||||||
\(487\) | −31.9269 | −1.44674 | −0.723372 | − | 0.690459i | \(-0.757409\pi\) | ||||
−0.723372 | + | 0.690459i | \(0.757409\pi\) | |||||||
\(488\) | 2.90418 | 0.131466 | ||||||||
\(489\) | −0.821268 | −0.0371390 | ||||||||
\(490\) | 0.0370664 | 0.00167449 | ||||||||
\(491\) | −30.6498 | −1.38321 | −0.691603 | − | 0.722278i | \(-0.743095\pi\) | ||||
−0.691603 | + | 0.722278i | \(0.743095\pi\) | |||||||
\(492\) | 29.5410 | 1.33181 | ||||||||
\(493\) | −0.493834 | −0.0222412 | ||||||||
\(494\) | −12.8558 | −0.578411 | ||||||||
\(495\) | 0.576128 | 0.0258950 | ||||||||
\(496\) | 7.95639 | 0.357252 | ||||||||
\(497\) | −19.0332 | −0.853754 | ||||||||
\(498\) | −38.2071 | −1.71210 | ||||||||
\(499\) | 16.2059 | 0.725478 | 0.362739 | − | 0.931891i | \(-0.381842\pi\) | ||||
0.362739 | + | 0.931891i | \(0.381842\pi\) | |||||||
\(500\) | −0.151081 | −0.00675656 | ||||||||
\(501\) | −34.7984 | −1.55468 | ||||||||
\(502\) | −4.01409 | −0.179158 | ||||||||
\(503\) | −28.7110 | −1.28016 | −0.640079 | − | 0.768309i | \(-0.721099\pi\) | ||||
−0.640079 | + | 0.768309i | \(0.721099\pi\) | |||||||
\(504\) | 18.5022 | 0.824153 | ||||||||
\(505\) | 0.225593 | 0.0100387 | ||||||||
\(506\) | −22.4162 | −0.996522 | ||||||||
\(507\) | −18.3250 | −0.813842 | ||||||||
\(508\) | 15.2060 | 0.674659 | ||||||||
\(509\) | −16.5987 | −0.735724 | −0.367862 | − | 0.929880i | \(-0.619910\pi\) | ||||
−0.367862 | + | 0.929880i | \(0.619910\pi\) | |||||||
\(510\) | −0.0104205 | −0.000461426 0 | ||||||||
\(511\) | 29.9554 | 1.32515 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 58.2013 | 2.56965 | ||||||||
\(514\) | −24.8011 | −1.09393 | ||||||||
\(515\) | 0.164977 | 0.00726977 | ||||||||
\(516\) | 37.2557 | 1.64009 | ||||||||
\(517\) | 42.3790 | 1.86383 | ||||||||
\(518\) | 19.5689 | 0.859807 | ||||||||
\(519\) | 14.7971 | 0.649522 | ||||||||
\(520\) | 0.0647422 | 0.00283914 | ||||||||
\(521\) | 2.74625 | 0.120315 | 0.0601577 | − | 0.998189i | \(-0.480840\pi\) | ||||
0.0601577 | + | 0.998189i | \(0.480840\pi\) | |||||||
\(522\) | −21.2305 | −0.929234 | ||||||||
\(523\) | 12.4005 | 0.542235 | 0.271117 | − | 0.962546i | \(-0.412607\pi\) | ||||
0.271117 | + | 0.962546i | \(0.412607\pi\) | |||||||
\(524\) | 2.06243 | 0.0900978 | ||||||||
\(525\) | −36.4304 | −1.58995 | ||||||||
\(526\) | −18.2121 | −0.794085 | ||||||||
\(527\) | −1.60588 | −0.0699534 | ||||||||
\(528\) | −15.0172 | −0.653540 | ||||||||
\(529\) | 3.01850 | 0.131239 | ||||||||
\(530\) | 0.131149 | 0.00569676 | ||||||||
\(531\) | −5.93905 | −0.257733 | ||||||||
\(532\) | 6.39703 | 0.277346 | ||||||||
\(533\) | 37.0445 | 1.60458 | ||||||||
\(534\) | 33.2994 | 1.44101 | ||||||||
\(535\) | 0.300063 | 0.0129729 | ||||||||
\(536\) | 1.50427 | 0.0649744 | ||||||||
\(537\) | 8.43331 | 0.363924 | ||||||||
\(538\) | 0.860887 | 0.0371155 | ||||||||
\(539\) | −10.7815 | −0.464394 | ||||||||
\(540\) | −0.293103 | −0.0126131 | ||||||||
\(541\) | −6.70042 | −0.288073 | −0.144037 | − | 0.989572i | \(-0.546008\pi\) | ||||
−0.144037 | + | 0.989572i | \(0.546008\pi\) | |||||||
\(542\) | −32.2518 | −1.38533 | ||||||||
\(543\) | 56.0731 | 2.40633 | ||||||||
\(544\) | 0.201836 | 0.00865364 | ||||||||
\(545\) | 0.279909 | 0.0119900 | ||||||||
\(546\) | 31.2235 | 1.33624 | ||||||||
\(547\) | 7.44833 | 0.318468 | 0.159234 | − | 0.987241i | \(-0.449098\pi\) | ||||
0.159234 | + | 0.987241i | \(0.449098\pi\) | |||||||
\(548\) | 11.7016 | 0.499868 | ||||||||
\(549\) | −25.2000 | −1.07551 | ||||||||
\(550\) | 21.9721 | 0.936892 | ||||||||
\(551\) | −7.34033 | −0.312709 | ||||||||
\(552\) | 17.4305 | 0.741891 | ||||||||
\(553\) | 28.6624 | 1.21885 | ||||||||
\(554\) | −2.83466 | −0.120433 | ||||||||
\(555\) | −0.473816 | −0.0201124 | ||||||||
\(556\) | −7.67261 | −0.325391 | ||||||||
\(557\) | −36.4674 | −1.54517 | −0.772587 | − | 0.634909i | \(-0.781038\pi\) | ||||
−0.772587 | + | 0.634909i | \(0.781038\pi\) | |||||||
\(558\) | −69.0388 | −2.92265 | ||||||||
\(559\) | 46.7188 | 1.97599 | ||||||||
\(560\) | −0.0322156 | −0.00136136 | ||||||||
\(561\) | 3.03101 | 0.127969 | ||||||||
\(562\) | −8.89513 | −0.375218 | ||||||||
\(563\) | 33.4738 | 1.41075 | 0.705375 | − | 0.708834i | \(-0.250778\pi\) | ||||
0.705375 | + | 0.708834i | \(0.250778\pi\) | |||||||
\(564\) | −32.9533 | −1.38758 | ||||||||
\(565\) | 0.101893 | 0.00428666 | ||||||||
\(566\) | −25.2588 | −1.06171 | ||||||||
\(567\) | −85.8493 | −3.60533 | ||||||||
\(568\) | −8.92618 | −0.374534 | ||||||||
\(569\) | −11.3960 | −0.477744 | −0.238872 | − | 0.971051i | \(-0.576778\pi\) | ||||
−0.238872 | + | 0.971051i | \(0.576778\pi\) | |||||||
\(570\) | −0.154890 | −0.00648761 | ||||||||
\(571\) | −26.7603 | −1.11988 | −0.559942 | − | 0.828532i | \(-0.689177\pi\) | ||||
−0.559942 | + | 0.828532i | \(0.689177\pi\) | |||||||
\(572\) | −18.8316 | −0.787390 | ||||||||
\(573\) | −17.3580 | −0.725141 | ||||||||
\(574\) | −18.4333 | −0.769389 | ||||||||
\(575\) | −25.5030 | −1.06355 | ||||||||
\(576\) | 8.67716 | 0.361548 | ||||||||
\(577\) | 15.3467 | 0.638890 | 0.319445 | − | 0.947605i | \(-0.396504\pi\) | ||||
0.319445 | + | 0.947605i | \(0.396504\pi\) | |||||||
\(578\) | 16.9593 | 0.705412 | ||||||||
\(579\) | 46.8437 | 1.94676 | ||||||||
\(580\) | 0.0369661 | 0.00153493 | ||||||||
\(581\) | 23.8408 | 0.989085 | ||||||||
\(582\) | −43.5393 | −1.80476 | ||||||||
\(583\) | −38.1475 | −1.57991 | ||||||||
\(584\) | 14.0485 | 0.581331 | ||||||||
\(585\) | −0.561779 | −0.0232267 | ||||||||
\(586\) | 20.9972 | 0.867387 | ||||||||
\(587\) | −34.4797 | −1.42313 | −0.711565 | − | 0.702620i | \(-0.752013\pi\) | ||||
−0.711565 | + | 0.702620i | \(0.752013\pi\) | |||||||
\(588\) | 8.38356 | 0.345732 | ||||||||
\(589\) | −23.8698 | −0.983538 | ||||||||
\(590\) | 0.0103409 | 0.000425730 0 | ||||||||
\(591\) | 76.9453 | 3.16511 | ||||||||
\(592\) | 9.17741 | 0.377189 | ||||||||
\(593\) | 7.71039 | 0.316628 | 0.158314 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158314 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(594\) | 85.2551 | 3.49806 | ||||||||
\(595\) | 0.00650226 | 0.000266567 0 | ||||||||
\(596\) | 0.471765 | 0.0193242 | ||||||||
\(597\) | 25.5556 | 1.04592 | ||||||||
\(598\) | 21.8579 | 0.893836 | ||||||||
\(599\) | −8.13716 | −0.332475 | −0.166238 | − | 0.986086i | \(-0.553162\pi\) | ||||
−0.166238 | + | 0.986086i | \(0.553162\pi\) | |||||||
\(600\) | −17.0851 | −0.697498 | ||||||||
\(601\) | 28.9741 | 1.18188 | 0.590939 | − | 0.806716i | \(-0.298757\pi\) | ||||
0.590939 | + | 0.806716i | \(0.298757\pi\) | |||||||
\(602\) | −23.2472 | −0.947483 | ||||||||
\(603\) | −13.0528 | −0.531549 | ||||||||
\(604\) | 11.8515 | 0.482232 | ||||||||
\(605\) | 0.125591 | 0.00510601 | ||||||||
\(606\) | 51.0238 | 2.07270 | ||||||||
\(607\) | −19.8981 | −0.807639 | −0.403820 | − | 0.914839i | \(-0.632318\pi\) | ||||
−0.403820 | + | 0.914839i | \(0.632318\pi\) | |||||||
\(608\) | 3.00008 | 0.121669 | ||||||||
\(609\) | 17.8278 | 0.722417 | ||||||||
\(610\) | 0.0438777 | 0.00177655 | ||||||||
\(611\) | −41.3235 | −1.67177 | ||||||||
\(612\) | −1.75136 | −0.0707946 | ||||||||
\(613\) | 27.7242 | 1.11977 | 0.559884 | − | 0.828571i | \(-0.310846\pi\) | ||||
0.559884 | + | 0.828571i | \(0.310846\pi\) | |||||||
\(614\) | −12.8942 | −0.520366 | ||||||||
\(615\) | 0.446319 | 0.0179973 | ||||||||
\(616\) | 9.37058 | 0.377551 | ||||||||
\(617\) | −25.8137 | −1.03922 | −0.519611 | − | 0.854403i | \(-0.673923\pi\) | ||||
−0.519611 | + | 0.854403i | \(0.673923\pi\) | |||||||
\(618\) | 37.3140 | 1.50099 | ||||||||
\(619\) | 3.12351 | 0.125544 | 0.0627722 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627722 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(620\) | 0.120209 | 0.00482770 | ||||||||
\(621\) | −98.9557 | −3.97095 | ||||||||
\(622\) | 17.6739 | 0.708658 | ||||||||
\(623\) | −20.7785 | −0.832471 | ||||||||
\(624\) | 14.6432 | 0.586197 | ||||||||
\(625\) | 24.9966 | 0.999863 | ||||||||
\(626\) | 14.7044 | 0.587704 | ||||||||
\(627\) | 45.0528 | 1.79924 | ||||||||
\(628\) | 12.1497 | 0.484825 | ||||||||
\(629\) | −1.85233 | −0.0738572 | ||||||||
\(630\) | 0.279540 | 0.0111371 | ||||||||
\(631\) | 41.2627 | 1.64264 | 0.821321 | − | 0.570466i | \(-0.193237\pi\) | ||||
0.821321 | + | 0.570466i | \(0.193237\pi\) | |||||||
\(632\) | 13.4421 | 0.534697 | ||||||||
\(633\) | −0.129718 | −0.00515584 | ||||||||
\(634\) | −13.0243 | −0.517262 | ||||||||
\(635\) | 0.229740 | 0.00911695 | ||||||||
\(636\) | 29.6629 | 1.17621 | ||||||||
\(637\) | 10.5130 | 0.416541 | ||||||||
\(638\) | −10.7524 | −0.425690 | ||||||||
\(639\) | 77.4538 | 3.06403 | ||||||||
\(640\) | −0.0151085 | −0.000597215 0 | ||||||||
\(641\) | 36.8893 | 1.45704 | 0.728521 | − | 0.685024i | \(-0.240208\pi\) | ||||
0.728521 | + | 0.685024i | \(0.240208\pi\) | |||||||
\(642\) | 67.8673 | 2.67851 | ||||||||
\(643\) | −36.2804 | −1.43076 | −0.715379 | − | 0.698736i | \(-0.753746\pi\) | ||||
−0.715379 | + | 0.698736i | \(0.753746\pi\) | |||||||
\(644\) | −10.8764 | −0.428592 | ||||||||
\(645\) | 0.562877 | 0.0221632 | ||||||||
\(646\) | −0.605523 | −0.0238240 | ||||||||
\(647\) | −49.1923 | −1.93395 | −0.966974 | − | 0.254875i | \(-0.917966\pi\) | ||||
−0.966974 | + | 0.254875i | \(0.917966\pi\) | |||||||
\(648\) | −40.2616 | −1.58162 | ||||||||
\(649\) | −3.00788 | −0.118070 | ||||||||
\(650\) | −21.4248 | −0.840351 | ||||||||
\(651\) | 57.9736 | 2.27216 | ||||||||
\(652\) | 0.240334 | 0.00941222 | ||||||||
\(653\) | 38.4746 | 1.50563 | 0.752814 | − | 0.658234i | \(-0.228696\pi\) | ||||
0.752814 | + | 0.658234i | \(0.228696\pi\) | |||||||
\(654\) | 63.3088 | 2.47557 | ||||||||
\(655\) | 0.0311602 | 0.00121753 | ||||||||
\(656\) | −8.64483 | −0.337524 | ||||||||
\(657\) | −121.901 | −4.75581 | ||||||||
\(658\) | 20.5625 | 0.801609 | ||||||||
\(659\) | −18.2495 | −0.710898 | −0.355449 | − | 0.934696i | \(-0.615672\pi\) | ||||
−0.355449 | + | 0.934696i | \(0.615672\pi\) | |||||||
\(660\) | −0.226887 | −0.00883157 | ||||||||
\(661\) | 14.9245 | 0.580495 | 0.290247 | − | 0.956952i | \(-0.406262\pi\) | ||||
0.290247 | + | 0.956952i | \(0.406262\pi\) | |||||||
\(662\) | 23.3022 | 0.905666 | ||||||||
\(663\) | −2.95552 | −0.114783 | ||||||||
\(664\) | 11.1809 | 0.433902 | ||||||||
\(665\) | 0.0966494 | 0.00374790 | ||||||||
\(666\) | −79.6338 | −3.08575 | ||||||||
\(667\) | 12.4803 | 0.483238 | ||||||||
\(668\) | 10.1834 | 0.394006 | ||||||||
\(669\) | −30.3228 | −1.17235 | ||||||||
\(670\) | 0.0227272 | 0.000878027 0 | ||||||||
\(671\) | −12.7627 | −0.492700 | ||||||||
\(672\) | −7.28642 | −0.281080 | ||||||||
\(673\) | −8.51382 | −0.328184 | −0.164092 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164092 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(674\) | 30.1845 | 1.16267 | ||||||||
\(675\) | 96.9951 | 3.73334 | ||||||||
\(676\) | 5.36260 | 0.206254 | ||||||||
\(677\) | 36.0674 | 1.38618 | 0.693090 | − | 0.720851i | \(-0.256249\pi\) | ||||
0.693090 | + | 0.720851i | \(0.256249\pi\) | |||||||
\(678\) | 23.0458 | 0.885068 | ||||||||
\(679\) | 27.1681 | 1.04261 | ||||||||
\(680\) | 0.00304943 | 0.000116940 0 | ||||||||
\(681\) | −23.9336 | −0.917136 | ||||||||
\(682\) | −34.9653 | −1.33889 | ||||||||
\(683\) | −31.0840 | −1.18940 | −0.594699 | − | 0.803949i | \(-0.702729\pi\) | ||||
−0.594699 | + | 0.803949i | \(0.702729\pi\) | |||||||
\(684\) | −26.0322 | −0.995365 | ||||||||
\(685\) | 0.176793 | 0.00675493 | ||||||||
\(686\) | −20.1573 | −0.769608 | ||||||||
\(687\) | 73.9583 | 2.82169 | ||||||||
\(688\) | −10.9025 | −0.415652 | ||||||||
\(689\) | 37.1974 | 1.41711 | ||||||||
\(690\) | 0.263348 | 0.0100255 | ||||||||
\(691\) | 16.2062 | 0.616514 | 0.308257 | − | 0.951303i | \(-0.400254\pi\) | ||||
0.308257 | + | 0.951303i | \(0.400254\pi\) | |||||||
\(692\) | −4.33021 | −0.164610 | ||||||||
\(693\) | −81.3100 | −3.08871 | ||||||||
\(694\) | 27.2728 | 1.03526 | ||||||||
\(695\) | −0.115921 | −0.00439715 | ||||||||
\(696\) | 8.36087 | 0.316918 | ||||||||
\(697\) | 1.74484 | 0.0660904 | ||||||||
\(698\) | 36.6309 | 1.38650 | ||||||||
\(699\) | −19.7313 | −0.746308 | ||||||||
\(700\) | 10.6609 | 0.402946 | ||||||||
\(701\) | −3.50227 | −0.132279 | −0.0661395 | − | 0.997810i | \(-0.521068\pi\) | ||||
−0.0661395 | + | 0.997810i | \(0.521068\pi\) | |||||||
\(702\) | −83.1317 | −3.13760 | ||||||||
\(703\) | −27.5330 | −1.03843 | ||||||||
\(704\) | 4.39461 | 0.165628 | ||||||||
\(705\) | −0.497873 | −0.0187510 | ||||||||
\(706\) | −10.2633 | −0.386263 | ||||||||
\(707\) | −31.8383 | −1.19740 | ||||||||
\(708\) | 2.33888 | 0.0879005 | ||||||||
\(709\) | −17.9428 | −0.673855 | −0.336927 | − | 0.941531i | \(-0.609388\pi\) | ||||
−0.336927 | + | 0.941531i | \(0.609388\pi\) | |||||||
\(710\) | −0.134861 | −0.00506124 | ||||||||
\(711\) | −116.639 | −4.37431 | ||||||||
\(712\) | −9.74468 | −0.365197 | ||||||||
\(713\) | 40.5842 | 1.51989 | ||||||||
\(714\) | 1.47066 | 0.0550381 | ||||||||
\(715\) | −0.284517 | −0.0106403 | ||||||||
\(716\) | −2.46791 | −0.0922302 | ||||||||
\(717\) | 86.9318 | 3.24653 | ||||||||
\(718\) | −20.1126 | −0.750595 | ||||||||
\(719\) | −11.1111 | −0.414374 | −0.207187 | − | 0.978301i | \(-0.566431\pi\) | ||||
−0.207187 | + | 0.978301i | \(0.566431\pi\) | |||||||
\(720\) | 0.131099 | 0.00488576 | ||||||||
\(721\) | −23.2835 | −0.867124 | ||||||||
\(722\) | 9.99952 | 0.372144 | ||||||||
\(723\) | 69.5442 | 2.58638 | ||||||||
\(724\) | −16.4091 | −0.609841 | ||||||||
\(725\) | −12.2330 | −0.454322 | ||||||||
\(726\) | 28.4058 | 1.05424 | ||||||||
\(727\) | 19.2480 | 0.713870 | 0.356935 | − | 0.934129i | \(-0.383822\pi\) | ||||
0.356935 | + | 0.934129i | \(0.383822\pi\) | |||||||
\(728\) | −9.13719 | −0.338647 | ||||||||
\(729\) | 150.477 | 5.57322 | ||||||||
\(730\) | 0.212251 | 0.00785578 | ||||||||
\(731\) | 2.20050 | 0.0813886 | ||||||||
\(732\) | 9.92411 | 0.366806 | ||||||||
\(733\) | −14.0340 | −0.518358 | −0.259179 | − | 0.965829i | \(-0.583452\pi\) | ||||
−0.259179 | + | 0.965829i | \(0.583452\pi\) | |||||||
\(734\) | −1.99567 | −0.0736617 | ||||||||
\(735\) | 0.126663 | 0.00467203 | ||||||||
\(736\) | −5.10083 | −0.188019 | ||||||||
\(737\) | −6.61067 | −0.243507 | ||||||||
\(738\) | 75.0126 | 2.76125 | ||||||||
\(739\) | 7.19844 | 0.264799 | 0.132400 | − | 0.991196i | \(-0.457732\pi\) | ||||
0.132400 | + | 0.991196i | \(0.457732\pi\) | |||||||
\(740\) | 0.138657 | 0.00509712 | ||||||||
\(741\) | −43.9307 | −1.61384 | ||||||||
\(742\) | −18.5093 | −0.679500 | ||||||||
\(743\) | −13.5264 | −0.496236 | −0.248118 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248118 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(744\) | 27.1884 | 0.996777 | ||||||||
\(745\) | 0.00712765 | 0.000261137 0 | ||||||||
\(746\) | −4.12517 | −0.151033 | ||||||||
\(747\) | −97.0183 | −3.54971 | ||||||||
\(748\) | −0.886990 | −0.0324316 | ||||||||
\(749\) | −42.3485 | −1.54738 | ||||||||
\(750\) | −0.516273 | −0.0188516 | ||||||||
\(751\) | 18.6032 | 0.678841 | 0.339421 | − | 0.940635i | \(-0.389769\pi\) | ||||
0.339421 | + | 0.940635i | \(0.389769\pi\) | |||||||
\(752\) | 9.64339 | 0.351658 | ||||||||
\(753\) | −13.7169 | −0.499871 | ||||||||
\(754\) | 10.4846 | 0.381825 | ||||||||
\(755\) | 0.179058 | 0.00651660 | ||||||||
\(756\) | 41.3662 | 1.50447 | ||||||||
\(757\) | −1.02761 | −0.0373492 | −0.0186746 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186746 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(758\) | −12.0298 | −0.436943 | ||||||||
\(759\) | −76.6003 | −2.78042 | ||||||||
\(760\) | 0.0453266 | 0.00164417 | ||||||||
\(761\) | −0.263493 | −0.00955163 | −0.00477581 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477581 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(762\) | 51.9619 | 1.88238 | ||||||||
\(763\) | −39.5040 | −1.43014 | ||||||||
\(764\) | 5.07962 | 0.183774 | ||||||||
\(765\) | −0.0264604 | −0.000956677 0 | ||||||||
\(766\) | 1.87726 | 0.0678282 | ||||||||
\(767\) | 2.93296 | 0.105903 | ||||||||
\(768\) | −3.41719 | −0.123307 | ||||||||
\(769\) | −32.0636 | −1.15624 | −0.578121 | − | 0.815951i | \(-0.696214\pi\) | ||||
−0.578121 | + | 0.815951i | \(0.696214\pi\) | |||||||
\(770\) | 0.141575 | 0.00510201 | ||||||||
\(771\) | −84.7501 | −3.05220 | ||||||||
\(772\) | −13.7083 | −0.493371 | ||||||||
\(773\) | −2.39027 | −0.0859721 | −0.0429861 | − | 0.999076i | \(-0.513687\pi\) | ||||
−0.0429861 | + | 0.999076i | \(0.513687\pi\) | |||||||
\(774\) | 94.6023 | 3.40041 | ||||||||
\(775\) | −39.7801 | −1.42894 | ||||||||
\(776\) | 12.7413 | 0.457385 | ||||||||
\(777\) | 66.8705 | 2.39896 | ||||||||
\(778\) | 17.4199 | 0.624535 | ||||||||
\(779\) | 25.9352 | 0.929224 | ||||||||
\(780\) | 0.221236 | 0.00792153 | ||||||||
\(781\) | 39.2271 | 1.40366 | ||||||||
\(782\) | 1.02953 | 0.0368159 | ||||||||
\(783\) | −47.4660 | −1.69629 | ||||||||
\(784\) | −2.45335 | −0.0876197 | ||||||||
\(785\) | 0.183563 | 0.00655165 | ||||||||
\(786\) | 7.04771 | 0.251384 | ||||||||
\(787\) | −7.23574 | −0.257926 | −0.128963 | − | 0.991649i | \(-0.541165\pi\) | ||||
−0.128963 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(788\) | −22.5171 | −0.802140 | ||||||||
\(789\) | −62.2341 | −2.21559 | ||||||||
\(790\) | 0.203089 | 0.00722559 | ||||||||
\(791\) | −14.3803 | −0.511306 | ||||||||
\(792\) | −38.1328 | −1.35499 | ||||||||
\(793\) | 12.4449 | 0.441930 | ||||||||
\(794\) | 10.1319 | 0.359567 | ||||||||
\(795\) | 0.448162 | 0.0158947 | ||||||||
\(796\) | −7.47856 | −0.265070 | ||||||||
\(797\) | −26.1548 | −0.926450 | −0.463225 | − | 0.886241i | \(-0.653308\pi\) | ||||
−0.463225 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(798\) | 21.8598 | 0.773830 | ||||||||
\(799\) | −1.94638 | −0.0688580 | ||||||||
\(800\) | 4.99977 | 0.176769 | ||||||||
\(801\) | 84.5561 | 2.98764 | ||||||||
\(802\) | −20.8919 | −0.737719 | ||||||||
\(803\) | −61.7378 | −2.17868 | ||||||||
\(804\) | 5.14036 | 0.181286 | ||||||||
\(805\) | −0.164326 | −0.00579175 | ||||||||
\(806\) | 34.0944 | 1.20092 | ||||||||
\(807\) | 2.94181 | 0.103557 | ||||||||
\(808\) | −14.9315 | −0.525290 | ||||||||
\(809\) | −29.8691 | −1.05014 | −0.525071 | − | 0.851059i | \(-0.675961\pi\) | ||||
−0.525071 | + | 0.851059i | \(0.675961\pi\) | |||||||
\(810\) | −0.608291 | −0.0213732 | ||||||||
\(811\) | 11.9348 | 0.419088 | 0.209544 | − | 0.977799i | \(-0.432802\pi\) | ||||
0.209544 | + | 0.977799i | \(0.432802\pi\) | |||||||
\(812\) | −5.21709 | −0.183084 | ||||||||
\(813\) | −110.210 | −3.86524 | ||||||||
\(814\) | −40.3312 | −1.41361 | ||||||||
\(815\) | 0.00363109 | 0.000127191 0 | ||||||||
\(816\) | 0.689710 | 0.0241447 | ||||||||
\(817\) | 32.7082 | 1.14432 | ||||||||
\(818\) | −28.2601 | −0.988092 | ||||||||
\(819\) | 79.2849 | 2.77044 | ||||||||
\(820\) | −0.130610 | −0.00456111 | ||||||||
\(821\) | −11.4622 | −0.400035 | −0.200017 | − | 0.979792i | \(-0.564100\pi\) | ||||
−0.200017 | + | 0.979792i | \(0.564100\pi\) | |||||||
\(822\) | 39.9866 | 1.39469 | ||||||||
\(823\) | 31.6441 | 1.10304 | 0.551521 | − | 0.834161i | \(-0.314048\pi\) | ||||
0.551521 | + | 0.834161i | \(0.314048\pi\) | |||||||
\(824\) | −10.9195 | −0.380399 | ||||||||
\(825\) | 75.0826 | 2.61404 | ||||||||
\(826\) | −1.45944 | −0.0507803 | ||||||||
\(827\) | −42.7597 | −1.48690 | −0.743451 | − | 0.668790i | \(-0.766812\pi\) | ||||
−0.743451 | + | 0.668790i | \(0.766812\pi\) | |||||||
\(828\) | 44.2607 | 1.53817 | ||||||||
\(829\) | 28.6030 | 0.993425 | 0.496712 | − | 0.867915i | \(-0.334540\pi\) | ||||
0.496712 | + | 0.867915i | \(0.334540\pi\) | |||||||
\(830\) | 0.168926 | 0.00586351 | ||||||||
\(831\) | −9.68655 | −0.336023 | ||||||||
\(832\) | −4.28516 | −0.148561 | ||||||||
\(833\) | 0.495174 | 0.0171568 | ||||||||
\(834\) | −26.2187 | −0.907880 | ||||||||
\(835\) | 0.153855 | 0.00532437 | ||||||||
\(836\) | −13.1842 | −0.455985 | ||||||||
\(837\) | −154.353 | −5.33522 | ||||||||
\(838\) | 5.87543 | 0.202963 | ||||||||
\(839\) | 23.9547 | 0.827009 | 0.413504 | − | 0.910502i | \(-0.364305\pi\) | ||||
0.413504 | + | 0.910502i | \(0.364305\pi\) | |||||||
\(840\) | −0.110087 | −0.00379835 | ||||||||
\(841\) | −23.0136 | −0.793573 | ||||||||
\(842\) | −11.5769 | −0.398967 | ||||||||
\(843\) | −30.3963 | −1.04690 | ||||||||
\(844\) | 0.0379606 | 0.00130666 | ||||||||
\(845\) | 0.0810208 | 0.00278720 | ||||||||
\(846\) | −83.6772 | −2.87688 | ||||||||
\(847\) | −17.7249 | −0.609036 | ||||||||
\(848\) | −8.68052 | −0.298090 | ||||||||
\(849\) | −86.3140 | −2.96229 | ||||||||
\(850\) | −1.00913 | −0.0346130 | ||||||||
\(851\) | 46.8124 | 1.60471 | ||||||||
\(852\) | −30.5024 | −1.04500 | ||||||||
\(853\) | −16.7711 | −0.574232 | −0.287116 | − | 0.957896i | \(-0.592697\pi\) | ||||
−0.287116 | + | 0.957896i | \(0.592697\pi\) | |||||||
\(854\) | −6.19254 | −0.211904 | ||||||||
\(855\) | −0.393306 | −0.0134508 | ||||||||
\(856\) | −19.8606 | −0.678821 | ||||||||
\(857\) | −43.0348 | −1.47004 | −0.735020 | − | 0.678045i | \(-0.762827\pi\) | ||||
−0.735020 | + | 0.678045i | \(0.762827\pi\) | |||||||
\(858\) | −64.3512 | −2.19691 | ||||||||
\(859\) | 22.1613 | 0.756135 | 0.378068 | − | 0.925778i | \(-0.376589\pi\) | ||||
0.378068 | + | 0.925778i | \(0.376589\pi\) | |||||||
\(860\) | −0.164719 | −0.00561688 | ||||||||
\(861\) | −62.9899 | −2.14669 | ||||||||
\(862\) | 0.0977132 | 0.00332813 | ||||||||
\(863\) | −28.4901 | −0.969814 | −0.484907 | − | 0.874566i | \(-0.661146\pi\) | ||||
−0.484907 | + | 0.874566i | \(0.661146\pi\) | |||||||
\(864\) | 19.3999 | 0.659998 | ||||||||
\(865\) | −0.0654229 | −0.00222444 | ||||||||
\(866\) | 14.0181 | 0.476354 | ||||||||
\(867\) | 57.9529 | 1.96819 | ||||||||
\(868\) | −16.9653 | −0.575840 | ||||||||
\(869\) | −59.0728 | −2.00391 | ||||||||
\(870\) | 0.126320 | 0.00428265 | ||||||||
\(871\) | 6.44602 | 0.218415 | ||||||||
\(872\) | −18.5266 | −0.627390 | ||||||||
\(873\) | −110.558 | −3.74182 | ||||||||
\(874\) | 15.3029 | 0.517629 | ||||||||
\(875\) | 0.322149 | 0.0108906 | ||||||||
\(876\) | 48.0064 | 1.62198 | ||||||||
\(877\) | 40.1545 | 1.35592 | 0.677960 | − | 0.735099i | \(-0.262864\pi\) | ||||
0.677960 | + | 0.735099i | \(0.262864\pi\) | |||||||
\(878\) | −19.7608 | −0.666895 | ||||||||
\(879\) | 71.7514 | 2.42011 | ||||||||
\(880\) | 0.0663959 | 0.00223821 | ||||||||
\(881\) | −35.2639 | −1.18807 | −0.594036 | − | 0.804439i | \(-0.702466\pi\) | ||||
−0.594036 | + | 0.804439i | \(0.702466\pi\) | |||||||
\(882\) | 21.2881 | 0.716809 | ||||||||
\(883\) | −14.2181 | −0.478477 | −0.239239 | − | 0.970961i | \(-0.576898\pi\) | ||||
−0.239239 | + | 0.970961i | \(0.576898\pi\) | |||||||
\(884\) | 0.864899 | 0.0290897 | ||||||||
\(885\) | 0.0353369 | 0.00118784 | ||||||||
\(886\) | 36.5124 | 1.22666 | ||||||||
\(887\) | 43.2231 | 1.45129 | 0.725645 | − | 0.688069i | \(-0.241541\pi\) | ||||
0.725645 | + | 0.688069i | \(0.241541\pi\) | |||||||
\(888\) | 31.3609 | 1.05240 | ||||||||
\(889\) | −32.4236 | −1.08745 | ||||||||
\(890\) | −0.147227 | −0.00493507 | ||||||||
\(891\) | 176.934 | 5.92752 | ||||||||
\(892\) | 8.87363 | 0.297111 | ||||||||
\(893\) | −28.9309 | −0.968137 | ||||||||
\(894\) | 1.61211 | 0.0539170 | ||||||||
\(895\) | −0.0372864 | −0.00124635 | ||||||||
\(896\) | 2.13229 | 0.0712347 | ||||||||
\(897\) | 74.6925 | 2.49391 | ||||||||
\(898\) | 27.9839 | 0.933834 | ||||||||
\(899\) | 19.4670 | 0.649260 | ||||||||
\(900\) | −43.3838 | −1.44613 | ||||||||
\(901\) | 1.75204 | 0.0583689 | ||||||||
\(902\) | 37.9907 | 1.26495 | ||||||||
\(903\) | −79.4398 | −2.64359 | ||||||||
\(904\) | −6.74409 | −0.224305 | ||||||||
\(905\) | −0.247917 | −0.00824104 | ||||||||
\(906\) | 40.4988 | 1.34548 | ||||||||
\(907\) | 12.5178 | 0.415645 | 0.207823 | − | 0.978167i | \(-0.433362\pi\) | ||||
0.207823 | + | 0.978167i | \(0.433362\pi\) | |||||||
\(908\) | 7.00388 | 0.232432 | ||||||||
\(909\) | 129.563 | 4.29734 | ||||||||
\(910\) | −0.138049 | −0.00457628 | ||||||||
\(911\) | −0.164220 | −0.00544087 | −0.00272043 | − | 0.999996i | \(-0.500866\pi\) | ||||
−0.00272043 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(912\) | 10.2518 | 0.339472 | ||||||||
\(913\) | −49.1357 | −1.62615 | ||||||||
\(914\) | 16.3647 | 0.541297 | ||||||||
\(915\) | 0.149938 | 0.00495680 | ||||||||
\(916\) | −21.6430 | −0.715106 | ||||||||
\(917\) | −4.39770 | −0.145225 | ||||||||
\(918\) | −3.91559 | −0.129234 | ||||||||
\(919\) | 22.2274 | 0.733216 | 0.366608 | − | 0.930376i | \(-0.380519\pi\) | ||||
0.366608 | + | 0.930376i | \(0.380519\pi\) | |||||||
\(920\) | −0.0770658 | −0.00254078 | ||||||||
\(921\) | −44.0618 | −1.45188 | ||||||||
\(922\) | 25.6050 | 0.843256 | ||||||||
\(923\) | −38.2501 | −1.25902 | ||||||||
\(924\) | 32.0210 | 1.05341 | ||||||||
\(925\) | −45.8850 | −1.50869 | ||||||||
\(926\) | −31.2481 | −1.02688 | ||||||||
\(927\) | 94.7504 | 3.11201 | ||||||||
\(928\) | −2.44671 | −0.0803172 | ||||||||
\(929\) | −7.94893 | −0.260796 | −0.130398 | − | 0.991462i | \(-0.541626\pi\) | ||||
−0.130398 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(930\) | 0.410776 | 0.0134699 | ||||||||
\(931\) | 7.36025 | 0.241223 | ||||||||
\(932\) | 5.77415 | 0.189139 | ||||||||
\(933\) | 60.3950 | 1.97724 | ||||||||
\(934\) | 5.33209 | 0.174471 | ||||||||
\(935\) | −0.0134011 | −0.000438262 0 | ||||||||
\(936\) | 37.1830 | 1.21536 | ||||||||
\(937\) | 27.9902 | 0.914399 | 0.457200 | − | 0.889364i | \(-0.348852\pi\) | ||||
0.457200 | + | 0.889364i | \(0.348852\pi\) | |||||||
\(938\) | −3.20753 | −0.104729 | ||||||||
\(939\) | 50.2475 | 1.63977 | ||||||||
\(940\) | 0.145697 | 0.00475211 | ||||||||
\(941\) | −39.6684 | −1.29315 | −0.646577 | − | 0.762849i | \(-0.723800\pi\) | ||||
−0.646577 | + | 0.762849i | \(0.723800\pi\) | |||||||
\(942\) | 41.5177 | 1.35272 | ||||||||
\(943\) | −44.0958 | −1.43596 | ||||||||
\(944\) | −0.684446 | −0.0222768 | ||||||||
\(945\) | 0.624979 | 0.0203306 | ||||||||
\(946\) | 47.9121 | 1.55776 | ||||||||
\(947\) | 15.9891 | 0.519577 | 0.259789 | − | 0.965666i | \(-0.416347\pi\) | ||||
0.259789 | + | 0.965666i | \(0.416347\pi\) | |||||||
\(948\) | 45.9341 | 1.49187 | ||||||||
\(949\) | 60.2001 | 1.95418 | ||||||||
\(950\) | −14.9997 | −0.486655 | ||||||||
\(951\) | −44.5065 | −1.44322 | ||||||||
\(952\) | −0.430372 | −0.0139484 | ||||||||
\(953\) | 3.94890 | 0.127917 | 0.0639587 | − | 0.997953i | \(-0.479627\pi\) | ||||
0.0639587 | + | 0.997953i | \(0.479627\pi\) | |||||||
\(954\) | 75.3222 | 2.43865 | ||||||||
\(955\) | 0.0767453 | 0.00248342 | ||||||||
\(956\) | −25.4396 | −0.822775 | ||||||||
\(957\) | −36.7428 | −1.18773 | ||||||||
\(958\) | 41.1818 | 1.33052 | ||||||||
\(959\) | −24.9512 | −0.805716 | ||||||||
\(960\) | −0.0516285 | −0.00166630 | ||||||||
\(961\) | 32.3041 | 1.04207 | ||||||||
\(962\) | 39.3267 | 1.26794 | ||||||||
\(963\) | 172.333 | 5.55337 | ||||||||
\(964\) | −20.3513 | −0.655471 | ||||||||
\(965\) | −0.207111 | −0.00666714 | ||||||||
\(966\) | −37.1668 | −1.19582 | ||||||||
\(967\) | −19.1022 | −0.614285 | −0.307143 | − | 0.951663i | \(-0.599373\pi\) | ||||
−0.307143 | + | 0.951663i | \(0.599373\pi\) | |||||||
\(968\) | −8.31264 | −0.267178 | ||||||||
\(969\) | −2.06919 | −0.0664718 | ||||||||
\(970\) | 0.192501 | 0.00618084 | ||||||||
\(971\) | 47.1302 | 1.51248 | 0.756240 | − | 0.654295i | \(-0.227034\pi\) | ||||
0.756240 | + | 0.654295i | \(0.227034\pi\) | |||||||
\(972\) | −79.3816 | −2.54617 | ||||||||
\(973\) | 16.3602 | 0.524484 | ||||||||
\(974\) | 31.9269 | 1.02300 | ||||||||
\(975\) | −73.2126 | −2.34468 | ||||||||
\(976\) | −2.90418 | −0.0929604 | ||||||||
\(977\) | −29.3203 | −0.938039 | −0.469020 | − | 0.883188i | \(-0.655393\pi\) | ||||
−0.469020 | + | 0.883188i | \(0.655393\pi\) | |||||||
\(978\) | 0.821268 | 0.0262612 | ||||||||
\(979\) | 42.8241 | 1.36867 | ||||||||
\(980\) | −0.0370664 | −0.00118404 | ||||||||
\(981\) | 160.758 | 5.13261 | ||||||||
\(982\) | 30.6498 | 0.978074 | ||||||||
\(983\) | −6.36355 | −0.202966 | −0.101483 | − | 0.994837i | \(-0.532359\pi\) | ||||
−0.101483 | + | 0.994837i | \(0.532359\pi\) | |||||||
\(984\) | −29.5410 | −0.941732 | ||||||||
\(985\) | −0.340200 | −0.0108397 | ||||||||
\(986\) | 0.493834 | 0.0157269 | ||||||||
\(987\) | 70.2658 | 2.23658 | ||||||||
\(988\) | 12.8558 | 0.408998 | ||||||||
\(989\) | −55.6116 | −1.76835 | ||||||||
\(990\) | −0.576128 | −0.0183105 | ||||||||
\(991\) | −62.7090 | −1.99202 | −0.996008 | − | 0.0892633i | \(-0.971549\pi\) | ||||
−0.996008 | + | 0.0892633i | \(0.971549\pi\) | |||||||
\(992\) | −7.95639 | −0.252616 | ||||||||
\(993\) | 79.6279 | 2.52692 | ||||||||
\(994\) | 19.0332 | 0.603695 | ||||||||
\(995\) | −0.112990 | −0.00358201 | ||||||||
\(996\) | 38.2071 | 1.21064 | ||||||||
\(997\) | 7.96510 | 0.252257 | 0.126129 | − | 0.992014i | \(-0.459745\pi\) | ||||
0.126129 | + | 0.992014i | \(0.459745\pi\) | |||||||
\(998\) | −16.2059 | −0.512990 | ||||||||
\(999\) | −178.041 | −5.63296 |
(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 | 6022.2.a.d.1.1 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.d.1.1 | ✓ | 64 | 1.1 | even | 1 | trivial |