Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −2.67759 | −1.54591 | −0.772955 | − | 0.634461i | \(-0.781222\pi\) | ||||
−0.772955 | + | 0.634461i | \(0.781222\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.43345 | 1.08827 | 0.544136 | − | 0.838997i | \(-0.316858\pi\) | ||||
0.544136 | + | 0.838997i | \(0.316858\pi\) | |||||||
\(6\) | 2.67759 | 1.09312 | ||||||||
\(7\) | −4.11067 | −1.55369 | −0.776844 | − | 0.629694i | \(-0.783180\pi\) | ||||
−0.776844 | + | 0.629694i | \(0.783180\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.16951 | 1.38984 | ||||||||
\(10\) | −2.43345 | −0.769525 | ||||||||
\(11\) | 1.05949 | 0.319449 | 0.159725 | − | 0.987162i | \(-0.448939\pi\) | ||||
0.159725 | + | 0.987162i | \(0.448939\pi\) | |||||||
\(12\) | −2.67759 | −0.772955 | ||||||||
\(13\) | −4.86114 | −1.34824 | −0.674119 | − | 0.738623i | \(-0.735477\pi\) | ||||
−0.674119 | + | 0.738623i | \(0.735477\pi\) | |||||||
\(14\) | 4.11067 | 1.09862 | ||||||||
\(15\) | −6.51579 | −1.68237 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.22105 | −1.26629 | −0.633145 | − | 0.774033i | \(-0.718236\pi\) | ||||
−0.633145 | + | 0.774033i | \(0.718236\pi\) | |||||||
\(18\) | −4.16951 | −0.982764 | ||||||||
\(19\) | −4.63882 | −1.06422 | −0.532109 | − | 0.846676i | \(-0.678600\pi\) | ||||
−0.532109 | + | 0.846676i | \(0.678600\pi\) | |||||||
\(20\) | 2.43345 | 0.544136 | ||||||||
\(21\) | 11.0067 | 2.40186 | ||||||||
\(22\) | −1.05949 | −0.225885 | ||||||||
\(23\) | −7.57779 | −1.58008 | −0.790039 | − | 0.613057i | \(-0.789940\pi\) | ||||
−0.790039 | + | 0.613057i | \(0.789940\pi\) | |||||||
\(24\) | 2.67759 | 0.546562 | ||||||||
\(25\) | 0.921680 | 0.184336 | ||||||||
\(26\) | 4.86114 | 0.953348 | ||||||||
\(27\) | −3.13148 | −0.602654 | ||||||||
\(28\) | −4.11067 | −0.776844 | ||||||||
\(29\) | 0.794274 | 0.147493 | 0.0737465 | − | 0.997277i | \(-0.476504\pi\) | ||||
0.0737465 | + | 0.997277i | \(0.476504\pi\) | |||||||
\(30\) | 6.51579 | 1.18962 | ||||||||
\(31\) | −5.03209 | −0.903791 | −0.451895 | − | 0.892071i | \(-0.649252\pi\) | ||||
−0.451895 | + | 0.892071i | \(0.649252\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.83689 | −0.493840 | ||||||||
\(34\) | 5.22105 | 0.895402 | ||||||||
\(35\) | −10.0031 | −1.69083 | ||||||||
\(36\) | 4.16951 | 0.694919 | ||||||||
\(37\) | 2.84483 | 0.467687 | 0.233843 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233843 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(38\) | 4.63882 | 0.752516 | ||||||||
\(39\) | 13.0162 | 2.08426 | ||||||||
\(40\) | −2.43345 | −0.384762 | ||||||||
\(41\) | −5.07384 | −0.792401 | −0.396201 | − | 0.918164i | \(-0.629672\pi\) | ||||
−0.396201 | + | 0.918164i | \(0.629672\pi\) | |||||||
\(42\) | −11.0067 | −1.69837 | ||||||||
\(43\) | −0.955623 | −0.145731 | −0.0728656 | − | 0.997342i | \(-0.523214\pi\) | ||||
−0.0728656 | + | 0.997342i | \(0.523214\pi\) | |||||||
\(44\) | 1.05949 | 0.159725 | ||||||||
\(45\) | 10.1463 | 1.51252 | ||||||||
\(46\) | 7.57779 | 1.11728 | ||||||||
\(47\) | 11.0124 | 1.60633 | 0.803164 | − | 0.595758i | \(-0.203148\pi\) | ||||
0.803164 | + | 0.595758i | \(0.203148\pi\) | |||||||
\(48\) | −2.67759 | −0.386477 | ||||||||
\(49\) | 9.89761 | 1.41394 | ||||||||
\(50\) | −0.921680 | −0.130345 | ||||||||
\(51\) | 13.9798 | 1.95757 | ||||||||
\(52\) | −4.86114 | −0.674119 | ||||||||
\(53\) | −6.98643 | −0.959660 | −0.479830 | − | 0.877361i | \(-0.659302\pi\) | ||||
−0.479830 | + | 0.877361i | \(0.659302\pi\) | |||||||
\(54\) | 3.13148 | 0.426140 | ||||||||
\(55\) | 2.57822 | 0.347648 | ||||||||
\(56\) | 4.11067 | 0.549311 | ||||||||
\(57\) | 12.4209 | 1.64518 | ||||||||
\(58\) | −0.794274 | −0.104293 | ||||||||
\(59\) | −4.06419 | −0.529113 | −0.264556 | − | 0.964370i | \(-0.585225\pi\) | ||||
−0.264556 | + | 0.964370i | \(0.585225\pi\) | |||||||
\(60\) | −6.51579 | −0.841185 | ||||||||
\(61\) | 5.19597 | 0.665276 | 0.332638 | − | 0.943055i | \(-0.392061\pi\) | ||||
0.332638 | + | 0.943055i | \(0.392061\pi\) | |||||||
\(62\) | 5.03209 | 0.639076 | ||||||||
\(63\) | −17.1395 | −2.15937 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.8293 | −1.46725 | ||||||||
\(66\) | 2.83689 | 0.349197 | ||||||||
\(67\) | −8.04508 | −0.982863 | −0.491432 | − | 0.870916i | \(-0.663526\pi\) | ||||
−0.491432 | + | 0.870916i | \(0.663526\pi\) | |||||||
\(68\) | −5.22105 | −0.633145 | ||||||||
\(69\) | 20.2902 | 2.44266 | ||||||||
\(70\) | 10.0031 | 1.19560 | ||||||||
\(71\) | −7.05132 | −0.836837 | −0.418419 | − | 0.908254i | \(-0.637415\pi\) | ||||
−0.418419 | + | 0.908254i | \(0.637415\pi\) | |||||||
\(72\) | −4.16951 | −0.491382 | ||||||||
\(73\) | 2.51912 | 0.294841 | 0.147420 | − | 0.989074i | \(-0.452903\pi\) | ||||
0.147420 | + | 0.989074i | \(0.452903\pi\) | |||||||
\(74\) | −2.84483 | −0.330705 | ||||||||
\(75\) | −2.46789 | −0.284967 | ||||||||
\(76\) | −4.63882 | −0.532109 | ||||||||
\(77\) | −4.35523 | −0.496324 | ||||||||
\(78\) | −13.0162 | −1.47379 | ||||||||
\(79\) | 2.83622 | 0.319100 | 0.159550 | − | 0.987190i | \(-0.448996\pi\) | ||||
0.159550 | + | 0.987190i | \(0.448996\pi\) | |||||||
\(80\) | 2.43345 | 0.272068 | ||||||||
\(81\) | −4.12370 | −0.458189 | ||||||||
\(82\) | 5.07384 | 0.560312 | ||||||||
\(83\) | −9.91499 | −1.08831 | −0.544156 | − | 0.838984i | \(-0.683150\pi\) | ||||
−0.544156 | + | 0.838984i | \(0.683150\pi\) | |||||||
\(84\) | 11.0067 | 1.20093 | ||||||||
\(85\) | −12.7052 | −1.37807 | ||||||||
\(86\) | 0.955623 | 0.103047 | ||||||||
\(87\) | −2.12674 | −0.228011 | ||||||||
\(88\) | −1.05949 | −0.112942 | ||||||||
\(89\) | 6.57163 | 0.696591 | 0.348296 | − | 0.937385i | \(-0.386761\pi\) | ||||
0.348296 | + | 0.937385i | \(0.386761\pi\) | |||||||
\(90\) | −10.1463 | −1.06951 | ||||||||
\(91\) | 19.9826 | 2.09474 | ||||||||
\(92\) | −7.57779 | −0.790039 | ||||||||
\(93\) | 13.4739 | 1.39718 | ||||||||
\(94\) | −11.0124 | −1.13585 | ||||||||
\(95\) | −11.2883 | −1.15816 | ||||||||
\(96\) | 2.67759 | 0.273281 | ||||||||
\(97\) | 13.2264 | 1.34293 | 0.671467 | − | 0.741035i | \(-0.265665\pi\) | ||||
0.671467 | + | 0.741035i | \(0.265665\pi\) | |||||||
\(98\) | −9.89761 | −0.999809 | ||||||||
\(99\) | 4.41757 | 0.443983 | ||||||||
\(100\) | 0.921680 | 0.0921680 | ||||||||
\(101\) | −1.97607 | −0.196626 | −0.0983132 | − | 0.995156i | \(-0.531345\pi\) | ||||
−0.0983132 | + | 0.995156i | \(0.531345\pi\) | |||||||
\(102\) | −13.9798 | −1.38421 | ||||||||
\(103\) | −6.94001 | −0.683820 | −0.341910 | − | 0.939733i | \(-0.611074\pi\) | ||||
−0.341910 | + | 0.939733i | \(0.611074\pi\) | |||||||
\(104\) | 4.86114 | 0.476674 | ||||||||
\(105\) | 26.7843 | 2.61388 | ||||||||
\(106\) | 6.98643 | 0.678582 | ||||||||
\(107\) | −12.9585 | −1.25274 | −0.626371 | − | 0.779525i | \(-0.715461\pi\) | ||||
−0.626371 | + | 0.779525i | \(0.715461\pi\) | |||||||
\(108\) | −3.13148 | −0.301327 | ||||||||
\(109\) | 14.4654 | 1.38554 | 0.692768 | − | 0.721160i | \(-0.256391\pi\) | ||||
0.692768 | + | 0.721160i | \(0.256391\pi\) | |||||||
\(110\) | −2.57822 | −0.245824 | ||||||||
\(111\) | −7.61730 | −0.723002 | ||||||||
\(112\) | −4.11067 | −0.388422 | ||||||||
\(113\) | 14.2872 | 1.34403 | 0.672015 | − | 0.740538i | \(-0.265429\pi\) | ||||
0.672015 | + | 0.740538i | \(0.265429\pi\) | |||||||
\(114\) | −12.4209 | −1.16332 | ||||||||
\(115\) | −18.4402 | −1.71955 | ||||||||
\(116\) | 0.794274 | 0.0737465 | ||||||||
\(117\) | −20.2686 | −1.87383 | ||||||||
\(118\) | 4.06419 | 0.374139 | ||||||||
\(119\) | 21.4620 | 1.96742 | ||||||||
\(120\) | 6.51579 | 0.594808 | ||||||||
\(121\) | −9.87747 | −0.897952 | ||||||||
\(122\) | −5.19597 | −0.470421 | ||||||||
\(123\) | 13.5857 | 1.22498 | ||||||||
\(124\) | −5.03209 | −0.451895 | ||||||||
\(125\) | −9.92439 | −0.887664 | ||||||||
\(126\) | 17.1395 | 1.52691 | ||||||||
\(127\) | 12.7024 | 1.12715 | 0.563576 | − | 0.826064i | \(-0.309425\pi\) | ||||
0.563576 | + | 0.826064i | \(0.309425\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.55877 | 0.225287 | ||||||||
\(130\) | 11.8293 | 1.03750 | ||||||||
\(131\) | 2.68811 | 0.234862 | 0.117431 | − | 0.993081i | \(-0.462534\pi\) | ||||
0.117431 | + | 0.993081i | \(0.462534\pi\) | |||||||
\(132\) | −2.83689 | −0.246920 | ||||||||
\(133\) | 19.0687 | 1.65346 | ||||||||
\(134\) | 8.04508 | 0.694989 | ||||||||
\(135\) | −7.62030 | −0.655851 | ||||||||
\(136\) | 5.22105 | 0.447701 | ||||||||
\(137\) | 1.54509 | 0.132006 | 0.0660031 | − | 0.997819i | \(-0.478975\pi\) | ||||
0.0660031 | + | 0.997819i | \(0.478975\pi\) | |||||||
\(138\) | −20.2902 | −1.72722 | ||||||||
\(139\) | −4.95650 | −0.420404 | −0.210202 | − | 0.977658i | \(-0.567412\pi\) | ||||
−0.210202 | + | 0.977658i | \(0.567412\pi\) | |||||||
\(140\) | −10.0031 | −0.845417 | ||||||||
\(141\) | −29.4868 | −2.48324 | ||||||||
\(142\) | 7.05132 | 0.591733 | ||||||||
\(143\) | −5.15035 | −0.430694 | ||||||||
\(144\) | 4.16951 | 0.347459 | ||||||||
\(145\) | 1.93283 | 0.160512 | ||||||||
\(146\) | −2.51912 | −0.208484 | ||||||||
\(147\) | −26.5018 | −2.18583 | ||||||||
\(148\) | 2.84483 | 0.233843 | ||||||||
\(149\) | −4.48625 | −0.367528 | −0.183764 | − | 0.982970i | \(-0.558828\pi\) | ||||
−0.183764 | + | 0.982970i | \(0.558828\pi\) | |||||||
\(150\) | 2.46789 | 0.201502 | ||||||||
\(151\) | −18.6905 | −1.52101 | −0.760507 | − | 0.649330i | \(-0.775050\pi\) | ||||
−0.760507 | + | 0.649330i | \(0.775050\pi\) | |||||||
\(152\) | 4.63882 | 0.376258 | ||||||||
\(153\) | −21.7692 | −1.75994 | ||||||||
\(154\) | 4.35523 | 0.350954 | ||||||||
\(155\) | −12.2453 | −0.983570 | ||||||||
\(156\) | 13.0162 | 1.04213 | ||||||||
\(157\) | −4.68508 | −0.373910 | −0.186955 | − | 0.982368i | \(-0.559862\pi\) | ||||
−0.186955 | + | 0.982368i | \(0.559862\pi\) | |||||||
\(158\) | −2.83622 | −0.225638 | ||||||||
\(159\) | 18.7068 | 1.48355 | ||||||||
\(160\) | −2.43345 | −0.192381 | ||||||||
\(161\) | 31.1498 | 2.45495 | ||||||||
\(162\) | 4.12370 | 0.323989 | ||||||||
\(163\) | −2.98365 | −0.233698 | −0.116849 | − | 0.993150i | \(-0.537279\pi\) | ||||
−0.116849 | + | 0.993150i | \(0.537279\pi\) | |||||||
\(164\) | −5.07384 | −0.396201 | ||||||||
\(165\) | −6.90344 | −0.537432 | ||||||||
\(166\) | 9.91499 | 0.769552 | ||||||||
\(167\) | −14.9757 | −1.15885 | −0.579427 | − | 0.815024i | \(-0.696724\pi\) | ||||
−0.579427 | + | 0.815024i | \(0.696724\pi\) | |||||||
\(168\) | −11.0067 | −0.849186 | ||||||||
\(169\) | 10.6307 | 0.817747 | ||||||||
\(170\) | 12.7052 | 0.974441 | ||||||||
\(171\) | −19.3416 | −1.47909 | ||||||||
\(172\) | −0.955623 | −0.0728656 | ||||||||
\(173\) | −3.82867 | −0.291089 | −0.145544 | − | 0.989352i | \(-0.546493\pi\) | ||||
−0.145544 | + | 0.989352i | \(0.546493\pi\) | |||||||
\(174\) | 2.12674 | 0.161228 | ||||||||
\(175\) | −3.78872 | −0.286401 | ||||||||
\(176\) | 1.05949 | 0.0798623 | ||||||||
\(177\) | 10.8823 | 0.817960 | ||||||||
\(178\) | −6.57163 | −0.492564 | ||||||||
\(179\) | 6.70714 | 0.501315 | 0.250657 | − | 0.968076i | \(-0.419353\pi\) | ||||
0.250657 | + | 0.968076i | \(0.419353\pi\) | |||||||
\(180\) | 10.1463 | 0.756261 | ||||||||
\(181\) | 15.0132 | 1.11592 | 0.557962 | − | 0.829866i | \(-0.311583\pi\) | ||||
0.557962 | + | 0.829866i | \(0.311583\pi\) | |||||||
\(182\) | −19.9826 | −1.48121 | ||||||||
\(183\) | −13.9127 | −1.02846 | ||||||||
\(184\) | 7.57779 | 0.558642 | ||||||||
\(185\) | 6.92275 | 0.508971 | ||||||||
\(186\) | −13.4739 | −0.987955 | ||||||||
\(187\) | −5.53167 | −0.404515 | ||||||||
\(188\) | 11.0124 | 0.803164 | ||||||||
\(189\) | 12.8725 | 0.936335 | ||||||||
\(190\) | 11.2883 | 0.818942 | ||||||||
\(191\) | −17.7619 | −1.28520 | −0.642602 | − | 0.766200i | \(-0.722145\pi\) | ||||
−0.642602 | + | 0.766200i | \(0.722145\pi\) | |||||||
\(192\) | −2.67759 | −0.193239 | ||||||||
\(193\) | −14.1089 | −1.01558 | −0.507790 | − | 0.861481i | \(-0.669537\pi\) | ||||
−0.507790 | + | 0.861481i | \(0.669537\pi\) | |||||||
\(194\) | −13.2264 | −0.949597 | ||||||||
\(195\) | 31.6742 | 2.26824 | ||||||||
\(196\) | 9.89761 | 0.706972 | ||||||||
\(197\) | −20.3268 | −1.44823 | −0.724113 | − | 0.689681i | \(-0.757751\pi\) | ||||
−0.724113 | + | 0.689681i | \(0.757751\pi\) | |||||||
\(198\) | −4.41757 | −0.313943 | ||||||||
\(199\) | −6.28032 | −0.445200 | −0.222600 | − | 0.974910i | \(-0.571454\pi\) | ||||
−0.222600 | + | 0.974910i | \(0.571454\pi\) | |||||||
\(200\) | −0.921680 | −0.0651726 | ||||||||
\(201\) | 21.5415 | 1.51942 | ||||||||
\(202\) | 1.97607 | 0.139036 | ||||||||
\(203\) | −3.26500 | −0.229158 | ||||||||
\(204\) | 13.9798 | 0.978785 | ||||||||
\(205\) | −12.3469 | −0.862348 | ||||||||
\(206\) | 6.94001 | 0.483534 | ||||||||
\(207\) | −31.5957 | −2.19605 | ||||||||
\(208\) | −4.86114 | −0.337060 | ||||||||
\(209\) | −4.91480 | −0.339964 | ||||||||
\(210\) | −26.7843 | −1.84829 | ||||||||
\(211\) | −7.77030 | −0.534929 | −0.267465 | − | 0.963568i | \(-0.586186\pi\) | ||||
−0.267465 | + | 0.963568i | \(0.586186\pi\) | |||||||
\(212\) | −6.98643 | −0.479830 | ||||||||
\(213\) | 18.8806 | 1.29367 | ||||||||
\(214\) | 12.9585 | 0.885823 | ||||||||
\(215\) | −2.32546 | −0.158595 | ||||||||
\(216\) | 3.13148 | 0.213070 | ||||||||
\(217\) | 20.6853 | 1.40421 | ||||||||
\(218\) | −14.4654 | −0.979722 | ||||||||
\(219\) | −6.74518 | −0.455797 | ||||||||
\(220\) | 2.57822 | 0.173824 | ||||||||
\(221\) | 25.3803 | 1.70726 | ||||||||
\(222\) | 7.61730 | 0.511239 | ||||||||
\(223\) | 22.9131 | 1.53437 | 0.767187 | − | 0.641424i | \(-0.221656\pi\) | ||||
0.767187 | + | 0.641424i | \(0.221656\pi\) | |||||||
\(224\) | 4.11067 | 0.274656 | ||||||||
\(225\) | 3.84296 | 0.256197 | ||||||||
\(226\) | −14.2872 | −0.950373 | ||||||||
\(227\) | 0.0390277 | 0.00259036 | 0.00129518 | − | 0.999999i | \(-0.499588\pi\) | ||||
0.00129518 | + | 0.999999i | \(0.499588\pi\) | |||||||
\(228\) | 12.4209 | 0.822592 | ||||||||
\(229\) | 9.09822 | 0.601227 | 0.300614 | − | 0.953746i | \(-0.402809\pi\) | ||||
0.300614 | + | 0.953746i | \(0.402809\pi\) | |||||||
\(230\) | 18.4402 | 1.21591 | ||||||||
\(231\) | 11.6615 | 0.767273 | ||||||||
\(232\) | −0.794274 | −0.0521466 | ||||||||
\(233\) | 8.16189 | 0.534703 | 0.267352 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267352 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(234\) | 20.2686 | 1.32500 | ||||||||
\(235\) | 26.7982 | 1.74812 | ||||||||
\(236\) | −4.06419 | −0.264556 | ||||||||
\(237\) | −7.59426 | −0.493300 | ||||||||
\(238\) | −21.4620 | −1.39118 | ||||||||
\(239\) | 22.4745 | 1.45375 | 0.726876 | − | 0.686768i | \(-0.240971\pi\) | ||||
0.726876 | + | 0.686768i | \(0.240971\pi\) | |||||||
\(240\) | −6.51579 | −0.420593 | ||||||||
\(241\) | 8.44935 | 0.544271 | 0.272135 | − | 0.962259i | \(-0.412270\pi\) | ||||
0.272135 | + | 0.962259i | \(0.412270\pi\) | |||||||
\(242\) | 9.87747 | 0.634948 | ||||||||
\(243\) | 20.4360 | 1.31097 | ||||||||
\(244\) | 5.19597 | 0.332638 | ||||||||
\(245\) | 24.0853 | 1.53876 | ||||||||
\(246\) | −13.5857 | −0.866192 | ||||||||
\(247\) | 22.5500 | 1.43482 | ||||||||
\(248\) | 5.03209 | 0.319538 | ||||||||
\(249\) | 26.5483 | 1.68243 | ||||||||
\(250\) | 9.92439 | 0.627673 | ||||||||
\(251\) | 16.8167 | 1.06146 | 0.530729 | − | 0.847541i | \(-0.321918\pi\) | ||||
0.530729 | + | 0.847541i | \(0.321918\pi\) | |||||||
\(252\) | −17.1395 | −1.07969 | ||||||||
\(253\) | −8.02862 | −0.504755 | ||||||||
\(254\) | −12.7024 | −0.797016 | ||||||||
\(255\) | 34.0193 | 2.13037 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.3936 | 1.39688 | 0.698438 | − | 0.715671i | \(-0.253879\pi\) | ||||
0.698438 | + | 0.715671i | \(0.253879\pi\) | |||||||
\(258\) | −2.55877 | −0.159302 | ||||||||
\(259\) | −11.6941 | −0.726639 | ||||||||
\(260\) | −11.8293 | −0.733625 | ||||||||
\(261\) | 3.31173 | 0.204991 | ||||||||
\(262\) | −2.68811 | −0.166072 | ||||||||
\(263\) | −12.8444 | −0.792018 | −0.396009 | − | 0.918247i | \(-0.629605\pi\) | ||||
−0.396009 | + | 0.918247i | \(0.629605\pi\) | |||||||
\(264\) | 2.83689 | 0.174599 | ||||||||
\(265\) | −17.0011 | −1.04437 | ||||||||
\(266\) | −19.0687 | −1.16917 | ||||||||
\(267\) | −17.5962 | −1.07687 | ||||||||
\(268\) | −8.04508 | −0.491432 | ||||||||
\(269\) | 0.237234 | 0.0144644 | 0.00723221 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723221 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(270\) | 7.62030 | 0.463757 | ||||||||
\(271\) | 2.48344 | 0.150858 | 0.0754291 | − | 0.997151i | \(-0.475967\pi\) | ||||
0.0754291 | + | 0.997151i | \(0.475967\pi\) | |||||||
\(272\) | −5.22105 | −0.316572 | ||||||||
\(273\) | −53.5052 | −3.23828 | ||||||||
\(274\) | −1.54509 | −0.0933425 | ||||||||
\(275\) | 0.976514 | 0.0588860 | ||||||||
\(276\) | 20.2902 | 1.22133 | ||||||||
\(277\) | −18.6309 | −1.11942 | −0.559711 | − | 0.828688i | \(-0.689088\pi\) | ||||
−0.559711 | + | 0.828688i | \(0.689088\pi\) | |||||||
\(278\) | 4.95650 | 0.297271 | ||||||||
\(279\) | −20.9814 | −1.25612 | ||||||||
\(280\) | 10.0031 | 0.597800 | ||||||||
\(281\) | 13.3646 | 0.797263 | 0.398632 | − | 0.917111i | \(-0.369485\pi\) | ||||
0.398632 | + | 0.917111i | \(0.369485\pi\) | |||||||
\(282\) | 29.4868 | 1.75591 | ||||||||
\(283\) | −24.6956 | −1.46800 | −0.734001 | − | 0.679148i | \(-0.762349\pi\) | ||||
−0.734001 | + | 0.679148i | \(0.762349\pi\) | |||||||
\(284\) | −7.05132 | −0.418419 | ||||||||
\(285\) | 30.2256 | 1.79041 | ||||||||
\(286\) | 5.15035 | 0.304546 | ||||||||
\(287\) | 20.8569 | 1.23114 | ||||||||
\(288\) | −4.16951 | −0.245691 | ||||||||
\(289\) | 10.2593 | 0.603490 | ||||||||
\(290\) | −1.93283 | −0.113499 | ||||||||
\(291\) | −35.4148 | −2.07605 | ||||||||
\(292\) | 2.51912 | 0.147420 | ||||||||
\(293\) | 28.5865 | 1.67004 | 0.835021 | − | 0.550217i | \(-0.185455\pi\) | ||||
0.835021 | + | 0.550217i | \(0.185455\pi\) | |||||||
\(294\) | 26.5018 | 1.54562 | ||||||||
\(295\) | −9.89001 | −0.575818 | ||||||||
\(296\) | −2.84483 | −0.165352 | ||||||||
\(297\) | −3.31778 | −0.192517 | ||||||||
\(298\) | 4.48625 | 0.259881 | ||||||||
\(299\) | 36.8367 | 2.13032 | ||||||||
\(300\) | −2.46789 | −0.142483 | ||||||||
\(301\) | 3.92825 | 0.226421 | ||||||||
\(302\) | 18.6905 | 1.07552 | ||||||||
\(303\) | 5.29112 | 0.303967 | ||||||||
\(304\) | −4.63882 | −0.266054 | ||||||||
\(305\) | 12.6441 | 0.724001 | ||||||||
\(306\) | 21.7692 | 1.24446 | ||||||||
\(307\) | −4.44773 | −0.253845 | −0.126923 | − | 0.991913i | \(-0.540510\pi\) | ||||
−0.126923 | + | 0.991913i | \(0.540510\pi\) | |||||||
\(308\) | −4.35523 | −0.248162 | ||||||||
\(309\) | 18.5825 | 1.05712 | ||||||||
\(310\) | 12.2453 | 0.695489 | ||||||||
\(311\) | 31.1713 | 1.76756 | 0.883781 | − | 0.467901i | \(-0.154990\pi\) | ||||
0.883781 | + | 0.467901i | \(0.154990\pi\) | |||||||
\(312\) | −13.0162 | −0.736895 | ||||||||
\(313\) | 16.8653 | 0.953282 | 0.476641 | − | 0.879098i | \(-0.341854\pi\) | ||||
0.476641 | + | 0.879098i | \(0.341854\pi\) | |||||||
\(314\) | 4.68508 | 0.264395 | ||||||||
\(315\) | −41.7081 | −2.34999 | ||||||||
\(316\) | 2.83622 | 0.159550 | ||||||||
\(317\) | −27.4996 | −1.54453 | −0.772267 | − | 0.635298i | \(-0.780877\pi\) | ||||
−0.772267 | + | 0.635298i | \(0.780877\pi\) | |||||||
\(318\) | −18.7068 | −1.04903 | ||||||||
\(319\) | 0.841528 | 0.0471165 | ||||||||
\(320\) | 2.43345 | 0.136034 | ||||||||
\(321\) | 34.6975 | 1.93663 | ||||||||
\(322\) | −31.1498 | −1.73591 | ||||||||
\(323\) | 24.2195 | 1.34761 | ||||||||
\(324\) | −4.12370 | −0.229095 | ||||||||
\(325\) | −4.48042 | −0.248529 | ||||||||
\(326\) | 2.98365 | 0.165249 | ||||||||
\(327\) | −38.7325 | −2.14191 | ||||||||
\(328\) | 5.07384 | 0.280156 | ||||||||
\(329\) | −45.2685 | −2.49573 | ||||||||
\(330\) | 6.90344 | 0.380022 | ||||||||
\(331\) | 14.0627 | 0.772955 | 0.386478 | − | 0.922299i | \(-0.373692\pi\) | ||||
0.386478 | + | 0.922299i | \(0.373692\pi\) | |||||||
\(332\) | −9.91499 | −0.544156 | ||||||||
\(333\) | 11.8615 | 0.650009 | ||||||||
\(334\) | 14.9757 | 0.819434 | ||||||||
\(335\) | −19.5773 | −1.06962 | ||||||||
\(336\) | 11.0067 | 0.600465 | ||||||||
\(337\) | 31.8017 | 1.73235 | 0.866174 | − | 0.499742i | \(-0.166572\pi\) | ||||
0.866174 | + | 0.499742i | \(0.166572\pi\) | |||||||
\(338\) | −10.6307 | −0.578234 | ||||||||
\(339\) | −38.2554 | −2.07775 | ||||||||
\(340\) | −12.7052 | −0.689034 | ||||||||
\(341\) | −5.33147 | −0.288715 | ||||||||
\(342\) | 19.3416 | 1.04587 | ||||||||
\(343\) | −11.9111 | −0.643140 | ||||||||
\(344\) | 0.955623 | 0.0515237 | ||||||||
\(345\) | 49.3753 | 2.65828 | ||||||||
\(346\) | 3.82867 | 0.205831 | ||||||||
\(347\) | 32.8021 | 1.76091 | 0.880454 | − | 0.474131i | \(-0.157238\pi\) | ||||
0.880454 | + | 0.474131i | \(0.157238\pi\) | |||||||
\(348\) | −2.12674 | −0.114005 | ||||||||
\(349\) | 10.3535 | 0.554213 | 0.277106 | − | 0.960839i | \(-0.410625\pi\) | ||||
0.277106 | + | 0.960839i | \(0.410625\pi\) | |||||||
\(350\) | 3.78872 | 0.202516 | ||||||||
\(351\) | 15.2226 | 0.812521 | ||||||||
\(352\) | −1.05949 | −0.0564712 | ||||||||
\(353\) | −8.48982 | −0.451868 | −0.225934 | − | 0.974143i | \(-0.572543\pi\) | ||||
−0.225934 | + | 0.974143i | \(0.572543\pi\) | |||||||
\(354\) | −10.8823 | −0.578385 | ||||||||
\(355\) | −17.1590 | −0.910706 | ||||||||
\(356\) | 6.57163 | 0.348296 | ||||||||
\(357\) | −57.4665 | −3.04145 | ||||||||
\(358\) | −6.70714 | −0.354483 | ||||||||
\(359\) | 3.52096 | 0.185829 | 0.0929146 | − | 0.995674i | \(-0.470382\pi\) | ||||
0.0929146 | + | 0.995674i | \(0.470382\pi\) | |||||||
\(360\) | −10.1463 | −0.534757 | ||||||||
\(361\) | 2.51863 | 0.132560 | ||||||||
\(362\) | −15.0132 | −0.789078 | ||||||||
\(363\) | 26.4479 | 1.38815 | ||||||||
\(364\) | 19.9826 | 1.04737 | ||||||||
\(365\) | 6.13015 | 0.320867 | ||||||||
\(366\) | 13.9127 | 0.727229 | ||||||||
\(367\) | −2.87976 | −0.150322 | −0.0751612 | − | 0.997171i | \(-0.523947\pi\) | ||||
−0.0751612 | + | 0.997171i | \(0.523947\pi\) | |||||||
\(368\) | −7.57779 | −0.395019 | ||||||||
\(369\) | −21.1555 | −1.10131 | ||||||||
\(370\) | −6.92275 | −0.359897 | ||||||||
\(371\) | 28.7189 | 1.49101 | ||||||||
\(372\) | 13.4739 | 0.698589 | ||||||||
\(373\) | 4.69567 | 0.243133 | 0.121566 | − | 0.992583i | \(-0.461208\pi\) | ||||
0.121566 | + | 0.992583i | \(0.461208\pi\) | |||||||
\(374\) | 5.53167 | 0.286036 | ||||||||
\(375\) | 26.5735 | 1.37225 | ||||||||
\(376\) | −11.0124 | −0.567923 | ||||||||
\(377\) | −3.86108 | −0.198856 | ||||||||
\(378\) | −12.8725 | −0.662089 | ||||||||
\(379\) | 17.5661 | 0.902310 | 0.451155 | − | 0.892446i | \(-0.351012\pi\) | ||||
0.451155 | + | 0.892446i | \(0.351012\pi\) | |||||||
\(380\) | −11.2883 | −0.579079 | ||||||||
\(381\) | −34.0117 | −1.74247 | ||||||||
\(382\) | 17.7619 | 0.908776 | ||||||||
\(383\) | 29.3181 | 1.49809 | 0.749043 | − | 0.662521i | \(-0.230514\pi\) | ||||
0.749043 | + | 0.662521i | \(0.230514\pi\) | |||||||
\(384\) | 2.67759 | 0.136640 | ||||||||
\(385\) | −10.5982 | −0.540136 | ||||||||
\(386\) | 14.1089 | 0.718123 | ||||||||
\(387\) | −3.98448 | −0.202543 | ||||||||
\(388\) | 13.2264 | 0.671467 | ||||||||
\(389\) | −24.4342 | −1.23886 | −0.619431 | − | 0.785051i | \(-0.712636\pi\) | ||||
−0.619431 | + | 0.785051i | \(0.712636\pi\) | |||||||
\(390\) | −31.6742 | −1.60389 | ||||||||
\(391\) | 39.5640 | 2.00084 | ||||||||
\(392\) | −9.89761 | −0.499905 | ||||||||
\(393\) | −7.19768 | −0.363075 | ||||||||
\(394\) | 20.3268 | 1.02405 | ||||||||
\(395\) | 6.90181 | 0.347268 | ||||||||
\(396\) | 4.41757 | 0.221991 | ||||||||
\(397\) | −17.8022 | −0.893467 | −0.446734 | − | 0.894667i | \(-0.647413\pi\) | ||||
−0.446734 | + | 0.894667i | \(0.647413\pi\) | |||||||
\(398\) | 6.28032 | 0.314804 | ||||||||
\(399\) | −51.0581 | −2.55610 | ||||||||
\(400\) | 0.921680 | 0.0460840 | ||||||||
\(401\) | −27.1614 | −1.35638 | −0.678189 | − | 0.734888i | \(-0.737235\pi\) | ||||
−0.678189 | + | 0.734888i | \(0.737235\pi\) | |||||||
\(402\) | −21.5415 | −1.07439 | ||||||||
\(403\) | 24.4617 | 1.21853 | ||||||||
\(404\) | −1.97607 | −0.0983132 | ||||||||
\(405\) | −10.0348 | −0.498635 | ||||||||
\(406\) | 3.26500 | 0.162039 | ||||||||
\(407\) | 3.01408 | 0.149402 | ||||||||
\(408\) | −13.9798 | −0.692106 | ||||||||
\(409\) | 0.0400064 | 0.00197819 | 0.000989094 | − | 1.00000i | \(-0.499685\pi\) | ||||
0.000989094 | 1.00000i | \(0.499685\pi\) | ||||||||
\(410\) | 12.3469 | 0.609772 | ||||||||
\(411\) | −4.13713 | −0.204070 | ||||||||
\(412\) | −6.94001 | −0.341910 | ||||||||
\(413\) | 16.7065 | 0.822075 | ||||||||
\(414\) | 31.5957 | 1.55284 | ||||||||
\(415\) | −24.1276 | −1.18438 | ||||||||
\(416\) | 4.86114 | 0.238337 | ||||||||
\(417\) | 13.2715 | 0.649907 | ||||||||
\(418\) | 4.91480 | 0.240391 | ||||||||
\(419\) | 3.34725 | 0.163524 | 0.0817619 | − | 0.996652i | \(-0.473945\pi\) | ||||
0.0817619 | + | 0.996652i | \(0.473945\pi\) | |||||||
\(420\) | 26.7843 | 1.30694 | ||||||||
\(421\) | 39.2445 | 1.91266 | 0.956329 | − | 0.292292i | \(-0.0944179\pi\) | ||||
0.956329 | + | 0.292292i | \(0.0944179\pi\) | |||||||
\(422\) | 7.77030 | 0.378252 | ||||||||
\(423\) | 45.9165 | 2.23253 | ||||||||
\(424\) | 6.98643 | 0.339291 | ||||||||
\(425\) | −4.81214 | −0.233423 | ||||||||
\(426\) | −18.8806 | −0.914766 | ||||||||
\(427\) | −21.3589 | −1.03363 | ||||||||
\(428\) | −12.9585 | −0.626371 | ||||||||
\(429\) | 13.7905 | 0.665814 | ||||||||
\(430\) | 2.32546 | 0.112144 | ||||||||
\(431\) | −8.10983 | −0.390637 | −0.195318 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195318 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(432\) | −3.13148 | −0.150663 | ||||||||
\(433\) | −3.52249 | −0.169280 | −0.0846400 | − | 0.996412i | \(-0.526974\pi\) | ||||
−0.0846400 | + | 0.996412i | \(0.526974\pi\) | |||||||
\(434\) | −20.6853 | −0.992925 | ||||||||
\(435\) | −5.17532 | −0.248138 | ||||||||
\(436\) | 14.4654 | 0.692768 | ||||||||
\(437\) | 35.1520 | 1.68155 | ||||||||
\(438\) | 6.74518 | 0.322297 | ||||||||
\(439\) | −20.7205 | −0.988936 | −0.494468 | − | 0.869196i | \(-0.664637\pi\) | ||||
−0.494468 | + | 0.869196i | \(0.664637\pi\) | |||||||
\(440\) | −2.57822 | −0.122912 | ||||||||
\(441\) | 41.2682 | 1.96515 | ||||||||
\(442\) | −25.3803 | −1.20722 | ||||||||
\(443\) | 32.4349 | 1.54103 | 0.770514 | − | 0.637424i | \(-0.220000\pi\) | ||||
0.770514 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(444\) | −7.61730 | −0.361501 | ||||||||
\(445\) | 15.9917 | 0.758081 | ||||||||
\(446\) | −22.9131 | −1.08497 | ||||||||
\(447\) | 12.0123 | 0.568164 | ||||||||
\(448\) | −4.11067 | −0.194211 | ||||||||
\(449\) | −7.36674 | −0.347658 | −0.173829 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173829 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(450\) | −3.84296 | −0.181159 | ||||||||
\(451\) | −5.37570 | −0.253132 | ||||||||
\(452\) | 14.2872 | 0.672015 | ||||||||
\(453\) | 50.0457 | 2.35135 | ||||||||
\(454\) | −0.0390277 | −0.00183166 | ||||||||
\(455\) | 48.6265 | 2.27965 | ||||||||
\(456\) | −12.4209 | −0.581661 | ||||||||
\(457\) | −27.9691 | −1.30834 | −0.654171 | − | 0.756347i | \(-0.726982\pi\) | ||||
−0.654171 | + | 0.756347i | \(0.726982\pi\) | |||||||
\(458\) | −9.09822 | −0.425132 | ||||||||
\(459\) | 16.3496 | 0.763134 | ||||||||
\(460\) | −18.4402 | −0.859777 | ||||||||
\(461\) | 10.2155 | 0.475785 | 0.237893 | − | 0.971291i | \(-0.423543\pi\) | ||||
0.237893 | + | 0.971291i | \(0.423543\pi\) | |||||||
\(462\) | −11.6615 | −0.542544 | ||||||||
\(463\) | −8.00352 | −0.371955 | −0.185978 | − | 0.982554i | \(-0.559545\pi\) | ||||
−0.185978 | + | 0.982554i | \(0.559545\pi\) | |||||||
\(464\) | 0.794274 | 0.0368732 | ||||||||
\(465\) | 32.7881 | 1.52051 | ||||||||
\(466\) | −8.16189 | −0.378092 | ||||||||
\(467\) | 7.17708 | 0.332116 | 0.166058 | − | 0.986116i | \(-0.446896\pi\) | ||||
0.166058 | + | 0.986116i | \(0.446896\pi\) | |||||||
\(468\) | −20.2686 | −0.936916 | ||||||||
\(469\) | 33.0707 | 1.52706 | ||||||||
\(470\) | −26.7982 | −1.23611 | ||||||||
\(471\) | 12.5448 | 0.578032 | ||||||||
\(472\) | 4.06419 | 0.187070 | ||||||||
\(473\) | −1.01248 | −0.0465537 | ||||||||
\(474\) | 7.59426 | 0.348816 | ||||||||
\(475\) | −4.27551 | −0.196174 | ||||||||
\(476\) | 21.4620 | 0.983709 | ||||||||
\(477\) | −29.1300 | −1.33377 | ||||||||
\(478\) | −22.4745 | −1.02796 | ||||||||
\(479\) | 13.6050 | 0.621630 | 0.310815 | − | 0.950470i | \(-0.399398\pi\) | ||||
0.310815 | + | 0.950470i | \(0.399398\pi\) | |||||||
\(480\) | 6.51579 | 0.297404 | ||||||||
\(481\) | −13.8291 | −0.630553 | ||||||||
\(482\) | −8.44935 | −0.384857 | ||||||||
\(483\) | −83.4065 | −3.79513 | ||||||||
\(484\) | −9.87747 | −0.448976 | ||||||||
\(485\) | 32.1857 | 1.46148 | ||||||||
\(486\) | −20.4360 | −0.926998 | ||||||||
\(487\) | −28.4639 | −1.28982 | −0.644911 | − | 0.764257i | \(-0.723106\pi\) | ||||
−0.644911 | + | 0.764257i | \(0.723106\pi\) | |||||||
\(488\) | −5.19597 | −0.235211 | ||||||||
\(489\) | 7.98902 | 0.361276 | ||||||||
\(490\) | −24.0853 | −1.08806 | ||||||||
\(491\) | −42.5299 | −1.91935 | −0.959673 | − | 0.281117i | \(-0.909295\pi\) | ||||
−0.959673 | + | 0.281117i | \(0.909295\pi\) | |||||||
\(492\) | 13.5857 | 0.612490 | ||||||||
\(493\) | −4.14694 | −0.186769 | ||||||||
\(494\) | −22.5500 | −1.01457 | ||||||||
\(495\) | 10.7499 | 0.483174 | ||||||||
\(496\) | −5.03209 | −0.225948 | ||||||||
\(497\) | 28.9856 | 1.30018 | ||||||||
\(498\) | −26.5483 | −1.18966 | ||||||||
\(499\) | 28.8151 | 1.28994 | 0.644970 | − | 0.764208i | \(-0.276870\pi\) | ||||
0.644970 | + | 0.764208i | \(0.276870\pi\) | |||||||
\(500\) | −9.92439 | −0.443832 | ||||||||
\(501\) | 40.0989 | 1.79148 | ||||||||
\(502\) | −16.8167 | −0.750565 | ||||||||
\(503\) | −1.20412 | −0.0536888 | −0.0268444 | − | 0.999640i | \(-0.508546\pi\) | ||||
−0.0268444 | + | 0.999640i | \(0.508546\pi\) | |||||||
\(504\) | 17.1395 | 0.763454 | ||||||||
\(505\) | −4.80867 | −0.213983 | ||||||||
\(506\) | 8.02862 | 0.356915 | ||||||||
\(507\) | −28.4647 | −1.26416 | ||||||||
\(508\) | 12.7024 | 0.563576 | ||||||||
\(509\) | 8.30873 | 0.368278 | 0.184139 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184139 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(510\) | −34.0193 | −1.50640 | ||||||||
\(511\) | −10.3553 | −0.458090 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.5264 | 0.641355 | ||||||||
\(514\) | −22.3936 | −0.987740 | ||||||||
\(515\) | −16.8882 | −0.744182 | ||||||||
\(516\) | 2.55877 | 0.112644 | ||||||||
\(517\) | 11.6676 | 0.513140 | ||||||||
\(518\) | 11.6941 | 0.513811 | ||||||||
\(519\) | 10.2516 | 0.449997 | ||||||||
\(520\) | 11.8293 | 0.518751 | ||||||||
\(521\) | −5.14716 | −0.225501 | −0.112751 | − | 0.993623i | \(-0.535966\pi\) | ||||
−0.112751 | + | 0.993623i | \(0.535966\pi\) | |||||||
\(522\) | −3.31173 | −0.144951 | ||||||||
\(523\) | 38.8548 | 1.69900 | 0.849500 | − | 0.527588i | \(-0.176904\pi\) | ||||
0.849500 | + | 0.527588i | \(0.176904\pi\) | |||||||
\(524\) | 2.68811 | 0.117431 | ||||||||
\(525\) | 10.1447 | 0.442750 | ||||||||
\(526\) | 12.8444 | 0.560041 | ||||||||
\(527\) | 26.2728 | 1.14446 | ||||||||
\(528\) | −2.83689 | −0.123460 | ||||||||
\(529\) | 34.4229 | 1.49665 | ||||||||
\(530\) | 17.0011 | 0.738482 | ||||||||
\(531\) | −16.9457 | −0.735380 | ||||||||
\(532\) | 19.0687 | 0.826731 | ||||||||
\(533\) | 24.6647 | 1.06835 | ||||||||
\(534\) | 17.5962 | 0.761460 | ||||||||
\(535\) | −31.5338 | −1.36332 | ||||||||
\(536\) | 8.04508 | 0.347495 | ||||||||
\(537\) | −17.9590 | −0.774988 | ||||||||
\(538\) | −0.237234 | −0.0102279 | ||||||||
\(539\) | 10.4865 | 0.451683 | ||||||||
\(540\) | −7.62030 | −0.327926 | ||||||||
\(541\) | −20.1648 | −0.866951 | −0.433475 | − | 0.901165i | \(-0.642713\pi\) | ||||
−0.433475 | + | 0.901165i | \(0.642713\pi\) | |||||||
\(542\) | −2.48344 | −0.106673 | ||||||||
\(543\) | −40.1993 | −1.72512 | ||||||||
\(544\) | 5.22105 | 0.223851 | ||||||||
\(545\) | 35.2009 | 1.50784 | ||||||||
\(546\) | 53.5052 | 2.28981 | ||||||||
\(547\) | −30.3506 | −1.29770 | −0.648850 | − | 0.760917i | \(-0.724750\pi\) | ||||
−0.648850 | + | 0.760917i | \(0.724750\pi\) | |||||||
\(548\) | 1.54509 | 0.0660031 | ||||||||
\(549\) | 21.6647 | 0.924626 | ||||||||
\(550\) | −0.976514 | −0.0416387 | ||||||||
\(551\) | −3.68449 | −0.156965 | ||||||||
\(552\) | −20.2902 | −0.863610 | ||||||||
\(553\) | −11.6588 | −0.495782 | ||||||||
\(554\) | 18.6309 | 0.791551 | ||||||||
\(555\) | −18.5363 | −0.786823 | ||||||||
\(556\) | −4.95650 | −0.210202 | ||||||||
\(557\) | 33.6954 | 1.42772 | 0.713860 | − | 0.700288i | \(-0.246945\pi\) | ||||
0.713860 | + | 0.700288i | \(0.246945\pi\) | |||||||
\(558\) | 20.9814 | 0.888212 | ||||||||
\(559\) | 4.64542 | 0.196480 | ||||||||
\(560\) | −10.0031 | −0.422709 | ||||||||
\(561\) | 14.8116 | 0.625344 | ||||||||
\(562\) | −13.3646 | −0.563750 | ||||||||
\(563\) | −23.5299 | −0.991669 | −0.495834 | − | 0.868417i | \(-0.665138\pi\) | ||||
−0.495834 | + | 0.868417i | \(0.665138\pi\) | |||||||
\(564\) | −29.4868 | −1.24162 | ||||||||
\(565\) | 34.7673 | 1.46267 | ||||||||
\(566\) | 24.6956 | 1.03803 | ||||||||
\(567\) | 16.9512 | 0.711883 | ||||||||
\(568\) | 7.05132 | 0.295867 | ||||||||
\(569\) | −42.2987 | −1.77325 | −0.886627 | − | 0.462486i | \(-0.846958\pi\) | ||||
−0.886627 | + | 0.462486i | \(0.846958\pi\) | |||||||
\(570\) | −30.2256 | −1.26601 | ||||||||
\(571\) | 3.36129 | 0.140666 | 0.0703329 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703329 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(572\) | −5.15035 | −0.215347 | ||||||||
\(573\) | 47.5591 | 1.98681 | ||||||||
\(574\) | −20.8569 | −0.870550 | ||||||||
\(575\) | −6.98430 | −0.291265 | ||||||||
\(576\) | 4.16951 | 0.173730 | ||||||||
\(577\) | −18.3257 | −0.762908 | −0.381454 | − | 0.924388i | \(-0.624576\pi\) | ||||
−0.381454 | + | 0.924388i | \(0.624576\pi\) | |||||||
\(578\) | −10.2593 | −0.426732 | ||||||||
\(579\) | 37.7779 | 1.56999 | ||||||||
\(580\) | 1.93283 | 0.0802562 | ||||||||
\(581\) | 40.7572 | 1.69090 | ||||||||
\(582\) | 35.4148 | 1.46799 | ||||||||
\(583\) | −7.40208 | −0.306563 | ||||||||
\(584\) | −2.51912 | −0.104242 | ||||||||
\(585\) | −49.3226 | −2.03924 | ||||||||
\(586\) | −28.5865 | −1.18090 | ||||||||
\(587\) | 34.2116 | 1.41206 | 0.706032 | − | 0.708180i | \(-0.250484\pi\) | ||||
0.706032 | + | 0.708180i | \(0.250484\pi\) | |||||||
\(588\) | −26.5018 | −1.09292 | ||||||||
\(589\) | 23.3430 | 0.961830 | ||||||||
\(590\) | 9.89001 | 0.407165 | ||||||||
\(591\) | 54.4270 | 2.23883 | ||||||||
\(592\) | 2.84483 | 0.116922 | ||||||||
\(593\) | −22.1432 | −0.909310 | −0.454655 | − | 0.890668i | \(-0.650237\pi\) | ||||
−0.454655 | + | 0.890668i | \(0.650237\pi\) | |||||||
\(594\) | 3.31778 | 0.136130 | ||||||||
\(595\) | 52.2267 | 2.14109 | ||||||||
\(596\) | −4.48625 | −0.183764 | ||||||||
\(597\) | 16.8162 | 0.688240 | ||||||||
\(598\) | −36.8367 | −1.50636 | ||||||||
\(599\) | −19.8175 | −0.809722 | −0.404861 | − | 0.914378i | \(-0.632680\pi\) | ||||
−0.404861 | + | 0.914378i | \(0.632680\pi\) | |||||||
\(600\) | 2.46789 | 0.100751 | ||||||||
\(601\) | −1.11887 | −0.0456396 | −0.0228198 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228198 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(602\) | −3.92825 | −0.160104 | ||||||||
\(603\) | −33.5441 | −1.36602 | ||||||||
\(604\) | −18.6905 | −0.760507 | ||||||||
\(605\) | −24.0363 | −0.977216 | ||||||||
\(606\) | −5.29112 | −0.214937 | ||||||||
\(607\) | 23.9587 | 0.972453 | 0.486226 | − | 0.873833i | \(-0.338373\pi\) | ||||
0.486226 | + | 0.873833i | \(0.338373\pi\) | |||||||
\(608\) | 4.63882 | 0.188129 | ||||||||
\(609\) | 8.74234 | 0.354257 | ||||||||
\(610\) | −12.6441 | −0.511946 | ||||||||
\(611\) | −53.5330 | −2.16571 | ||||||||
\(612\) | −21.7692 | −0.879969 | ||||||||
\(613\) | −27.2649 | −1.10122 | −0.550609 | − | 0.834763i | \(-0.685605\pi\) | ||||
−0.550609 | + | 0.834763i | \(0.685605\pi\) | |||||||
\(614\) | 4.44773 | 0.179496 | ||||||||
\(615\) | 33.0601 | 1.33311 | ||||||||
\(616\) | 4.35523 | 0.175477 | ||||||||
\(617\) | −6.90660 | −0.278049 | −0.139025 | − | 0.990289i | \(-0.544397\pi\) | ||||
−0.139025 | + | 0.990289i | \(0.544397\pi\) | |||||||
\(618\) | −18.5825 | −0.747500 | ||||||||
\(619\) | −18.2143 | −0.732096 | −0.366048 | − | 0.930596i | \(-0.619289\pi\) | ||||
−0.366048 | + | 0.930596i | \(0.619289\pi\) | |||||||
\(620\) | −12.2453 | −0.491785 | ||||||||
\(621\) | 23.7297 | 0.952240 | ||||||||
\(622\) | −31.1713 | −1.24985 | ||||||||
\(623\) | −27.0138 | −1.08229 | ||||||||
\(624\) | 13.0162 | 0.521064 | ||||||||
\(625\) | −28.7589 | −1.15036 | ||||||||
\(626\) | −16.8653 | −0.674072 | ||||||||
\(627\) | 13.1598 | 0.525553 | ||||||||
\(628\) | −4.68508 | −0.186955 | ||||||||
\(629\) | −14.8530 | −0.592227 | ||||||||
\(630\) | 41.7081 | 1.66169 | ||||||||
\(631\) | −28.9573 | −1.15277 | −0.576386 | − | 0.817178i | \(-0.695537\pi\) | ||||
−0.576386 | + | 0.817178i | \(0.695537\pi\) | |||||||
\(632\) | −2.83622 | −0.112819 | ||||||||
\(633\) | 20.8057 | 0.826953 | ||||||||
\(634\) | 27.4996 | 1.09215 | ||||||||
\(635\) | 30.9105 | 1.22665 | ||||||||
\(636\) | 18.7068 | 0.741774 | ||||||||
\(637\) | −48.1137 | −1.90633 | ||||||||
\(638\) | −0.841528 | −0.0333164 | ||||||||
\(639\) | −29.4005 | −1.16307 | ||||||||
\(640\) | −2.43345 | −0.0961906 | ||||||||
\(641\) | −20.2384 | −0.799368 | −0.399684 | − | 0.916653i | \(-0.630880\pi\) | ||||
−0.399684 | + | 0.916653i | \(0.630880\pi\) | |||||||
\(642\) | −34.6975 | −1.36940 | ||||||||
\(643\) | −29.6131 | −1.16783 | −0.583914 | − | 0.811816i | \(-0.698479\pi\) | ||||
−0.583914 | + | 0.811816i | \(0.698479\pi\) | |||||||
\(644\) | 31.1498 | 1.22747 | ||||||||
\(645\) | 6.22664 | 0.245174 | ||||||||
\(646\) | −24.2195 | −0.952903 | ||||||||
\(647\) | 32.4517 | 1.27581 | 0.637905 | − | 0.770115i | \(-0.279801\pi\) | ||||
0.637905 | + | 0.770115i | \(0.279801\pi\) | |||||||
\(648\) | 4.12370 | 0.161994 | ||||||||
\(649\) | −4.30598 | −0.169025 | ||||||||
\(650\) | 4.48042 | 0.175737 | ||||||||
\(651\) | −55.3868 | −2.17078 | ||||||||
\(652\) | −2.98365 | −0.116849 | ||||||||
\(653\) | −8.07390 | −0.315956 | −0.157978 | − | 0.987443i | \(-0.550498\pi\) | ||||
−0.157978 | + | 0.987443i | \(0.550498\pi\) | |||||||
\(654\) | 38.7325 | 1.51456 | ||||||||
\(655\) | 6.54139 | 0.255593 | ||||||||
\(656\) | −5.07384 | −0.198100 | ||||||||
\(657\) | 10.5035 | 0.409780 | ||||||||
\(658\) | 45.2685 | 1.76475 | ||||||||
\(659\) | −4.36527 | −0.170047 | −0.0850234 | − | 0.996379i | \(-0.527097\pi\) | ||||
−0.0850234 | + | 0.996379i | \(0.527097\pi\) | |||||||
\(660\) | −6.90344 | −0.268716 | ||||||||
\(661\) | −42.6328 | −1.65822 | −0.829112 | − | 0.559082i | \(-0.811154\pi\) | ||||
−0.829112 | + | 0.559082i | \(0.811154\pi\) | |||||||
\(662\) | −14.0627 | −0.546562 | ||||||||
\(663\) | −67.9580 | −2.63927 | ||||||||
\(664\) | 9.91499 | 0.384776 | ||||||||
\(665\) | 46.4026 | 1.79942 | ||||||||
\(666\) | −11.8615 | −0.459626 | ||||||||
\(667\) | −6.01884 | −0.233050 | ||||||||
\(668\) | −14.9757 | −0.579427 | ||||||||
\(669\) | −61.3519 | −2.37200 | ||||||||
\(670\) | 19.5773 | 0.756338 | ||||||||
\(671\) | 5.50510 | 0.212522 | ||||||||
\(672\) | −11.0067 | −0.424593 | ||||||||
\(673\) | −5.20170 | −0.200511 | −0.100255 | − | 0.994962i | \(-0.531966\pi\) | ||||
−0.100255 | + | 0.994962i | \(0.531966\pi\) | |||||||
\(674\) | −31.8017 | −1.22496 | ||||||||
\(675\) | −2.88622 | −0.111091 | ||||||||
\(676\) | 10.6307 | 0.408873 | ||||||||
\(677\) | −5.41537 | −0.208130 | −0.104065 | − | 0.994571i | \(-0.533185\pi\) | ||||
−0.104065 | + | 0.994571i | \(0.533185\pi\) | |||||||
\(678\) | 38.2554 | 1.46919 | ||||||||
\(679\) | −54.3692 | −2.08650 | ||||||||
\(680\) | 12.7052 | 0.487221 | ||||||||
\(681\) | −0.104500 | −0.00400446 | ||||||||
\(682\) | 5.33147 | 0.204153 | ||||||||
\(683\) | −0.760953 | −0.0291171 | −0.0145585 | − | 0.999894i | \(-0.504634\pi\) | ||||
−0.0145585 | + | 0.999894i | \(0.504634\pi\) | |||||||
\(684\) | −19.3416 | −0.739545 | ||||||||
\(685\) | 3.75991 | 0.143659 | ||||||||
\(686\) | 11.9111 | 0.454768 | ||||||||
\(687\) | −24.3613 | −0.929443 | ||||||||
\(688\) | −0.955623 | −0.0364328 | ||||||||
\(689\) | 33.9620 | 1.29385 | ||||||||
\(690\) | −49.3753 | −1.87969 | ||||||||
\(691\) | 43.8137 | 1.66675 | 0.833375 | − | 0.552708i | \(-0.186405\pi\) | ||||
0.833375 | + | 0.552708i | \(0.186405\pi\) | |||||||
\(692\) | −3.82867 | −0.145544 | ||||||||
\(693\) | −18.1592 | −0.689810 | ||||||||
\(694\) | −32.8021 | −1.24515 | ||||||||
\(695\) | −12.0614 | −0.457514 | ||||||||
\(696\) | 2.12674 | 0.0806140 | ||||||||
\(697\) | 26.4908 | 1.00341 | ||||||||
\(698\) | −10.3535 | −0.391888 | ||||||||
\(699\) | −21.8542 | −0.826603 | ||||||||
\(700\) | −3.78872 | −0.143200 | ||||||||
\(701\) | 42.7844 | 1.61595 | 0.807973 | − | 0.589220i | \(-0.200565\pi\) | ||||
0.807973 | + | 0.589220i | \(0.200565\pi\) | |||||||
\(702\) | −15.2226 | −0.574539 | ||||||||
\(703\) | −13.1966 | −0.497721 | ||||||||
\(704\) | 1.05949 | 0.0399312 | ||||||||
\(705\) | −71.7547 | −2.70244 | ||||||||
\(706\) | 8.48982 | 0.319519 | ||||||||
\(707\) | 8.12298 | 0.305496 | ||||||||
\(708\) | 10.8823 | 0.408980 | ||||||||
\(709\) | −3.38059 | −0.126961 | −0.0634803 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634803 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(710\) | 17.1590 | 0.643967 | ||||||||
\(711\) | 11.8257 | 0.443497 | ||||||||
\(712\) | −6.57163 | −0.246282 | ||||||||
\(713\) | 38.1321 | 1.42806 | ||||||||
\(714\) | 57.4665 | 2.15063 | ||||||||
\(715\) | −12.5331 | −0.468712 | ||||||||
\(716\) | 6.70714 | 0.250657 | ||||||||
\(717\) | −60.1775 | −2.24737 | ||||||||
\(718\) | −3.52096 | −0.131401 | ||||||||
\(719\) | −21.5712 | −0.804471 | −0.402236 | − | 0.915536i | \(-0.631767\pi\) | ||||
−0.402236 | + | 0.915536i | \(0.631767\pi\) | |||||||
\(720\) | 10.1463 | 0.378130 | ||||||||
\(721\) | 28.5281 | 1.06244 | ||||||||
\(722\) | −2.51863 | −0.0937338 | ||||||||
\(723\) | −22.6239 | −0.841393 | ||||||||
\(724\) | 15.0132 | 0.557962 | ||||||||
\(725\) | 0.732066 | 0.0271883 | ||||||||
\(726\) | −26.4479 | −0.981573 | ||||||||
\(727\) | 33.7621 | 1.25217 | 0.626083 | − | 0.779756i | \(-0.284657\pi\) | ||||
0.626083 | + | 0.779756i | \(0.284657\pi\) | |||||||
\(728\) | −19.9826 | −0.740603 | ||||||||
\(729\) | −42.3483 | −1.56846 | ||||||||
\(730\) | −6.13015 | −0.226887 | ||||||||
\(731\) | 4.98935 | 0.184538 | ||||||||
\(732\) | −13.9127 | −0.514228 | ||||||||
\(733\) | 37.5615 | 1.38736 | 0.693682 | − | 0.720281i | \(-0.255987\pi\) | ||||
0.693682 | + | 0.720281i | \(0.255987\pi\) | |||||||
\(734\) | 2.87976 | 0.106294 | ||||||||
\(735\) | −64.4908 | −2.37878 | ||||||||
\(736\) | 7.57779 | 0.279321 | ||||||||
\(737\) | −8.52371 | −0.313975 | ||||||||
\(738\) | 21.1555 | 0.778743 | ||||||||
\(739\) | −44.8819 | −1.65101 | −0.825504 | − | 0.564397i | \(-0.809109\pi\) | ||||
−0.825504 | + | 0.564397i | \(0.809109\pi\) | |||||||
\(740\) | 6.92275 | 0.254485 | ||||||||
\(741\) | −60.3796 | −2.21810 | ||||||||
\(742\) | −28.7189 | −1.05430 | ||||||||
\(743\) | −11.8117 | −0.433331 | −0.216665 | − | 0.976246i | \(-0.569518\pi\) | ||||
−0.216665 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(744\) | −13.4739 | −0.493977 | ||||||||
\(745\) | −10.9171 | −0.399970 | ||||||||
\(746\) | −4.69567 | −0.171921 | ||||||||
\(747\) | −41.3407 | −1.51258 | ||||||||
\(748\) | −5.53167 | −0.202258 | ||||||||
\(749\) | 53.2680 | 1.94637 | ||||||||
\(750\) | −26.5735 | −0.970327 | ||||||||
\(751\) | 9.97303 | 0.363921 | 0.181960 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181960 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(752\) | 11.0124 | 0.401582 | ||||||||
\(753\) | −45.0282 | −1.64092 | ||||||||
\(754\) | 3.86108 | 0.140612 | ||||||||
\(755\) | −45.4825 | −1.65528 | ||||||||
\(756\) | 12.8725 | 0.468168 | ||||||||
\(757\) | −52.9459 | −1.92435 | −0.962175 | − | 0.272433i | \(-0.912172\pi\) | ||||
−0.962175 | + | 0.272433i | \(0.912172\pi\) | |||||||
\(758\) | −17.5661 | −0.638029 | ||||||||
\(759\) | 21.4974 | 0.780305 | ||||||||
\(760\) | 11.2883 | 0.409471 | ||||||||
\(761\) | 26.3388 | 0.954780 | 0.477390 | − | 0.878692i | \(-0.341583\pi\) | ||||
0.477390 | + | 0.878692i | \(0.341583\pi\) | |||||||
\(762\) | 34.0117 | 1.23212 | ||||||||
\(763\) | −59.4626 | −2.15269 | ||||||||
\(764\) | −17.7619 | −0.642602 | ||||||||
\(765\) | −52.9743 | −1.91529 | ||||||||
\(766\) | −29.3181 | −1.05931 | ||||||||
\(767\) | 19.7566 | 0.713370 | ||||||||
\(768\) | −2.67759 | −0.0966194 | ||||||||
\(769\) | −38.7934 | −1.39892 | −0.699462 | − | 0.714669i | \(-0.746577\pi\) | ||||
−0.699462 | + | 0.714669i | \(0.746577\pi\) | |||||||
\(770\) | 10.5982 | 0.381934 | ||||||||
\(771\) | −59.9610 | −2.15944 | ||||||||
\(772\) | −14.1089 | −0.507790 | ||||||||
\(773\) | 47.7909 | 1.71892 | 0.859459 | − | 0.511204i | \(-0.170800\pi\) | ||||
0.859459 | + | 0.511204i | \(0.170800\pi\) | |||||||
\(774\) | 3.98448 | 0.143219 | ||||||||
\(775\) | −4.63798 | −0.166601 | ||||||||
\(776\) | −13.2264 | −0.474799 | ||||||||
\(777\) | 31.3122 | 1.12332 | ||||||||
\(778\) | 24.4342 | 0.876007 | ||||||||
\(779\) | 23.5366 | 0.843288 | ||||||||
\(780\) | 31.6742 | 1.13412 | ||||||||
\(781\) | −7.47082 | −0.267327 | ||||||||
\(782\) | −39.5640 | −1.41481 | ||||||||
\(783\) | −2.48725 | −0.0888871 | ||||||||
\(784\) | 9.89761 | 0.353486 | ||||||||
\(785\) | −11.4009 | −0.406916 | ||||||||
\(786\) | 7.19768 | 0.256733 | ||||||||
\(787\) | −51.3390 | −1.83004 | −0.915018 | − | 0.403412i | \(-0.867824\pi\) | ||||
−0.915018 | + | 0.403412i | \(0.867824\pi\) | |||||||
\(788\) | −20.3268 | −0.724113 | ||||||||
\(789\) | 34.3920 | 1.22439 | ||||||||
\(790\) | −6.90181 | −0.245555 | ||||||||
\(791\) | −58.7301 | −2.08820 | ||||||||
\(792\) | −4.41757 | −0.156972 | ||||||||
\(793\) | −25.2584 | −0.896951 | ||||||||
\(794\) | 17.8022 | 0.631777 | ||||||||
\(795\) | 45.5221 | 1.61450 | ||||||||
\(796\) | −6.28032 | −0.222600 | ||||||||
\(797\) | −31.6422 | −1.12082 | −0.560412 | − | 0.828214i | \(-0.689357\pi\) | ||||
−0.560412 | + | 0.828214i | \(0.689357\pi\) | |||||||
\(798\) | 51.0581 | 1.80744 | ||||||||
\(799\) | −57.4964 | −2.03408 | ||||||||
\(800\) | −0.921680 | −0.0325863 | ||||||||
\(801\) | 27.4005 | 0.968149 | ||||||||
\(802\) | 27.1614 | 0.959104 | ||||||||
\(803\) | 2.66899 | 0.0941866 | ||||||||
\(804\) | 21.5415 | 0.759709 | ||||||||
\(805\) | 75.8014 | 2.67165 | ||||||||
\(806\) | −24.4617 | −0.861627 | ||||||||
\(807\) | −0.635217 | −0.0223607 | ||||||||
\(808\) | 1.97607 | 0.0695179 | ||||||||
\(809\) | 43.4501 | 1.52763 | 0.763813 | − | 0.645438i | \(-0.223325\pi\) | ||||
0.763813 | + | 0.645438i | \(0.223325\pi\) | |||||||
\(810\) | 10.0348 | 0.352588 | ||||||||
\(811\) | −3.77107 | −0.132420 | −0.0662101 | − | 0.997806i | \(-0.521091\pi\) | ||||
−0.0662101 | + | 0.997806i | \(0.521091\pi\) | |||||||
\(812\) | −3.26500 | −0.114579 | ||||||||
\(813\) | −6.64965 | −0.233213 | ||||||||
\(814\) | −3.01408 | −0.105643 | ||||||||
\(815\) | −7.26057 | −0.254327 | ||||||||
\(816\) | 13.9798 | 0.489393 | ||||||||
\(817\) | 4.43296 | 0.155090 | ||||||||
\(818\) | −0.0400064 | −0.00139879 | ||||||||
\(819\) | 83.3175 | 2.91135 | ||||||||
\(820\) | −12.3469 | −0.431174 | ||||||||
\(821\) | 20.6666 | 0.721270 | 0.360635 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360635 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(822\) | 4.13713 | 0.144299 | ||||||||
\(823\) | 8.43910 | 0.294168 | 0.147084 | − | 0.989124i | \(-0.453011\pi\) | ||||
0.147084 | + | 0.989124i | \(0.453011\pi\) | |||||||
\(824\) | 6.94001 | 0.241767 | ||||||||
\(825\) | −2.61471 | −0.0910325 | ||||||||
\(826\) | −16.7065 | −0.581295 | ||||||||
\(827\) | 15.1689 | 0.527475 | 0.263737 | − | 0.964595i | \(-0.415045\pi\) | ||||
0.263737 | + | 0.964595i | \(0.415045\pi\) | |||||||
\(828\) | −31.5957 | −1.09803 | ||||||||
\(829\) | −9.10167 | −0.316114 | −0.158057 | − | 0.987430i | \(-0.550523\pi\) | ||||
−0.158057 | + | 0.987430i | \(0.550523\pi\) | |||||||
\(830\) | 24.1276 | 0.837482 | ||||||||
\(831\) | 49.8860 | 1.73053 | ||||||||
\(832\) | −4.86114 | −0.168530 | ||||||||
\(833\) | −51.6759 | −1.79046 | ||||||||
\(834\) | −13.2715 | −0.459554 | ||||||||
\(835\) | −36.4426 | −1.26115 | ||||||||
\(836\) | −4.91480 | −0.169982 | ||||||||
\(837\) | 15.7579 | 0.544673 | ||||||||
\(838\) | −3.34725 | −0.115629 | ||||||||
\(839\) | 16.8815 | 0.582816 | 0.291408 | − | 0.956599i | \(-0.405876\pi\) | ||||
0.291408 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(840\) | −26.7843 | −0.924145 | ||||||||
\(841\) | −28.3691 | −0.978246 | ||||||||
\(842\) | −39.2445 | −1.35245 | ||||||||
\(843\) | −35.7849 | −1.23250 | ||||||||
\(844\) | −7.77030 | −0.267465 | ||||||||
\(845\) | 25.8693 | 0.889931 | ||||||||
\(846\) | −45.9165 | −1.57864 | ||||||||
\(847\) | 40.6030 | 1.39514 | ||||||||
\(848\) | −6.98643 | −0.239915 | ||||||||
\(849\) | 66.1249 | 2.26940 | ||||||||
\(850\) | 4.81214 | 0.165055 | ||||||||
\(851\) | −21.5575 | −0.738982 | ||||||||
\(852\) | 18.8806 | 0.646837 | ||||||||
\(853\) | −22.4956 | −0.770236 | −0.385118 | − | 0.922867i | \(-0.625839\pi\) | ||||
−0.385118 | + | 0.922867i | \(0.625839\pi\) | |||||||
\(854\) | 21.3589 | 0.730887 | ||||||||
\(855\) | −47.0668 | −1.60965 | ||||||||
\(856\) | 12.9585 | 0.442911 | ||||||||
\(857\) | 3.62386 | 0.123789 | 0.0618943 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618943 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(858\) | −13.7905 | −0.470801 | ||||||||
\(859\) | 13.7846 | 0.470324 | 0.235162 | − | 0.971956i | \(-0.424438\pi\) | ||||
0.235162 | + | 0.971956i | \(0.424438\pi\) | |||||||
\(860\) | −2.32546 | −0.0792976 | ||||||||
\(861\) | −55.8463 | −1.90324 | ||||||||
\(862\) | 8.10983 | 0.276222 | ||||||||
\(863\) | 13.0348 | 0.443711 | 0.221855 | − | 0.975080i | \(-0.428789\pi\) | ||||
0.221855 | + | 0.975080i | \(0.428789\pi\) | |||||||
\(864\) | 3.13148 | 0.106535 | ||||||||
\(865\) | −9.31688 | −0.316784 | ||||||||
\(866\) | 3.52249 | 0.119699 | ||||||||
\(867\) | −27.4703 | −0.932942 | ||||||||
\(868\) | 20.6853 | 0.702104 | ||||||||
\(869\) | 3.00496 | 0.101936 | ||||||||
\(870\) | 5.17532 | 0.175460 | ||||||||
\(871\) | 39.1083 | 1.32513 | ||||||||
\(872\) | −14.4654 | −0.489861 | ||||||||
\(873\) | 55.1475 | 1.86646 | ||||||||
\(874\) | −35.1520 | −1.18903 | ||||||||
\(875\) | 40.7959 | 1.37915 | ||||||||
\(876\) | −6.74518 | −0.227898 | ||||||||
\(877\) | 19.8386 | 0.669902 | 0.334951 | − | 0.942236i | \(-0.391280\pi\) | ||||
0.334951 | + | 0.942236i | \(0.391280\pi\) | |||||||
\(878\) | 20.7205 | 0.699283 | ||||||||
\(879\) | −76.5431 | −2.58174 | ||||||||
\(880\) | 2.57822 | 0.0869119 | ||||||||
\(881\) | −23.3312 | −0.786047 | −0.393024 | − | 0.919528i | \(-0.628571\pi\) | ||||
−0.393024 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(882\) | −41.2682 | −1.38957 | ||||||||
\(883\) | −27.3927 | −0.921837 | −0.460919 | − | 0.887442i | \(-0.652480\pi\) | ||||
−0.460919 | + | 0.887442i | \(0.652480\pi\) | |||||||
\(884\) | 25.3803 | 0.853630 | ||||||||
\(885\) | 26.4814 | 0.890163 | ||||||||
\(886\) | −32.4349 | −1.08967 | ||||||||
\(887\) | −25.3344 | −0.850647 | −0.425323 | − | 0.905041i | \(-0.639840\pi\) | ||||
−0.425323 | + | 0.905041i | \(0.639840\pi\) | |||||||
\(888\) | 7.61730 | 0.255620 | ||||||||
\(889\) | −52.2152 | −1.75124 | ||||||||
\(890\) | −15.9917 | −0.536044 | ||||||||
\(891\) | −4.36904 | −0.146368 | ||||||||
\(892\) | 22.9131 | 0.767187 | ||||||||
\(893\) | −51.0847 | −1.70948 | ||||||||
\(894\) | −12.0123 | −0.401753 | ||||||||
\(895\) | 16.3215 | 0.545567 | ||||||||
\(896\) | 4.11067 | 0.137328 | ||||||||
\(897\) | −98.6338 | −3.29329 | ||||||||
\(898\) | 7.36674 | 0.245831 | ||||||||
\(899\) | −3.99686 | −0.133303 | ||||||||
\(900\) | 3.84296 | 0.128099 | ||||||||
\(901\) | 36.4765 | 1.21521 | ||||||||
\(902\) | 5.37570 | 0.178991 | ||||||||
\(903\) | −10.5183 | −0.350026 | ||||||||
\(904\) | −14.2872 | −0.475186 | ||||||||
\(905\) | 36.5339 | 1.21443 | ||||||||
\(906\) | −50.0457 | −1.66266 | ||||||||
\(907\) | 37.4225 | 1.24260 | 0.621298 | − | 0.783575i | \(-0.286606\pi\) | ||||
0.621298 | + | 0.783575i | \(0.286606\pi\) | |||||||
\(908\) | 0.0390277 | 0.00129518 | ||||||||
\(909\) | −8.23925 | −0.273279 | ||||||||
\(910\) | −48.6265 | −1.61195 | ||||||||
\(911\) | 37.6270 | 1.24664 | 0.623320 | − | 0.781967i | \(-0.285784\pi\) | ||||
0.623320 | + | 0.781967i | \(0.285784\pi\) | |||||||
\(912\) | 12.4209 | 0.411296 | ||||||||
\(913\) | −10.5049 | −0.347660 | ||||||||
\(914\) | 27.9691 | 0.925137 | ||||||||
\(915\) | −33.8559 | −1.11924 | ||||||||
\(916\) | 9.09822 | 0.300614 | ||||||||
\(917\) | −11.0500 | −0.364902 | ||||||||
\(918\) | −16.3496 | −0.539617 | ||||||||
\(919\) | 40.9577 | 1.35107 | 0.675535 | − | 0.737328i | \(-0.263913\pi\) | ||||
0.675535 | + | 0.737328i | \(0.263913\pi\) | |||||||
\(920\) | 18.4402 | 0.607954 | ||||||||
\(921\) | 11.9092 | 0.392422 | ||||||||
\(922\) | −10.2155 | −0.336431 | ||||||||
\(923\) | 34.2774 | 1.12826 | ||||||||
\(924\) | 11.6615 | 0.383636 | ||||||||
\(925\) | 2.62202 | 0.0862115 | ||||||||
\(926\) | 8.00352 | 0.263012 | ||||||||
\(927\) | −28.9365 | −0.950399 | ||||||||
\(928\) | −0.794274 | −0.0260733 | ||||||||
\(929\) | 30.6539 | 1.00572 | 0.502860 | − | 0.864368i | \(-0.332281\pi\) | ||||
0.502860 | + | 0.864368i | \(0.332281\pi\) | |||||||
\(930\) | −32.7881 | −1.07516 | ||||||||
\(931\) | −45.9132 | −1.50474 | ||||||||
\(932\) | 8.16189 | 0.267352 | ||||||||
\(933\) | −83.4641 | −2.73249 | ||||||||
\(934\) | −7.17708 | −0.234841 | ||||||||
\(935\) | −13.4610 | −0.440223 | ||||||||
\(936\) | 20.2686 | 0.662500 | ||||||||
\(937\) | −21.8677 | −0.714385 | −0.357193 | − | 0.934031i | \(-0.616266\pi\) | ||||
−0.357193 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(938\) | −33.0707 | −1.07980 | ||||||||
\(939\) | −45.1584 | −1.47369 | ||||||||
\(940\) | 26.7982 | 0.874061 | ||||||||
\(941\) | 16.5698 | 0.540162 | 0.270081 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270081 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(942\) | −12.5448 | −0.408730 | ||||||||
\(943\) | 38.4485 | 1.25206 | ||||||||
\(944\) | −4.06419 | −0.132278 | ||||||||
\(945\) | 31.3245 | 1.01899 | ||||||||
\(946\) | 1.01248 | 0.0329184 | ||||||||
\(947\) | −31.6363 | −1.02804 | −0.514021 | − | 0.857778i | \(-0.671845\pi\) | ||||
−0.514021 | + | 0.857778i | \(0.671845\pi\) | |||||||
\(948\) | −7.59426 | −0.246650 | ||||||||
\(949\) | −12.2458 | −0.397515 | ||||||||
\(950\) | 4.27551 | 0.138716 | ||||||||
\(951\) | 73.6329 | 2.38771 | ||||||||
\(952\) | −21.4620 | −0.695588 | ||||||||
\(953\) | −54.9702 | −1.78066 | −0.890330 | − | 0.455316i | \(-0.849526\pi\) | ||||
−0.890330 | + | 0.455316i | \(0.849526\pi\) | |||||||
\(954\) | 29.1300 | 0.943119 | ||||||||
\(955\) | −43.2226 | −1.39865 | ||||||||
\(956\) | 22.4745 | 0.726876 | ||||||||
\(957\) | −2.25327 | −0.0728379 | ||||||||
\(958\) | −13.6050 | −0.439559 | ||||||||
\(959\) | −6.35137 | −0.205096 | ||||||||
\(960\) | −6.51579 | −0.210296 | ||||||||
\(961\) | −5.67804 | −0.183163 | ||||||||
\(962\) | 13.8291 | 0.445869 | ||||||||
\(963\) | −54.0305 | −1.74111 | ||||||||
\(964\) | 8.44935 | 0.272135 | ||||||||
\(965\) | −34.3333 | −1.10523 | ||||||||
\(966\) | 83.4065 | 2.68356 | ||||||||
\(967\) | −12.7845 | −0.411123 | −0.205562 | − | 0.978644i | \(-0.565902\pi\) | ||||
−0.205562 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(968\) | 9.87747 | 0.317474 | ||||||||
\(969\) | −64.8500 | −2.08328 | ||||||||
\(970\) | −32.1857 | −1.03342 | ||||||||
\(971\) | 0.136359 | 0.00437597 | 0.00218799 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218799 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(972\) | 20.4360 | 0.655486 | ||||||||
\(973\) | 20.3745 | 0.653177 | ||||||||
\(974\) | 28.4639 | 0.912042 | ||||||||
\(975\) | 11.9967 | 0.384203 | ||||||||
\(976\) | 5.19597 | 0.166319 | ||||||||
\(977\) | −9.80076 | −0.313554 | −0.156777 | − | 0.987634i | \(-0.550110\pi\) | ||||
−0.156777 | + | 0.987634i | \(0.550110\pi\) | |||||||
\(978\) | −7.98902 | −0.255461 | ||||||||
\(979\) | 6.96260 | 0.222526 | ||||||||
\(980\) | 24.0853 | 0.769378 | ||||||||
\(981\) | 60.3138 | 1.92567 | ||||||||
\(982\) | 42.5299 | 1.35718 | ||||||||
\(983\) | −7.83488 | −0.249894 | −0.124947 | − | 0.992163i | \(-0.539876\pi\) | ||||
−0.124947 | + | 0.992163i | \(0.539876\pi\) | |||||||
\(984\) | −13.5857 | −0.433096 | ||||||||
\(985\) | −49.4643 | −1.57606 | ||||||||
\(986\) | 4.14694 | 0.132065 | ||||||||
\(987\) | 121.211 | 3.85818 | ||||||||
\(988\) | 22.5500 | 0.717410 | ||||||||
\(989\) | 7.24151 | 0.230267 | ||||||||
\(990\) | −10.7499 | −0.341656 | ||||||||
\(991\) | −24.7734 | −0.786952 | −0.393476 | − | 0.919335i | \(-0.628728\pi\) | ||||
−0.393476 | + | 0.919335i | \(0.628728\pi\) | |||||||
\(992\) | 5.03209 | 0.159769 | ||||||||
\(993\) | −37.6542 | −1.19492 | ||||||||
\(994\) | −28.9856 | −0.919368 | ||||||||
\(995\) | −15.2829 | −0.484499 | ||||||||
\(996\) | 26.5483 | 0.841216 | ||||||||
\(997\) | 9.83713 | 0.311545 | 0.155772 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155772 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(998\) | −28.8151 | −0.912125 | ||||||||
\(999\) | −8.90852 | −0.281853 |
(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 | 4006.2.a.h.1.8 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.h.1.8 | ✓ | 42 | 1.1 | even | 1 | trivial |