Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.776244 | 0.548887 | 0.274444 | − | 0.961603i | \(-0.411506\pi\) | ||||
0.274444 | + | 0.961603i | \(0.411506\pi\) | |||||||
\(3\) | 3.01008 | 1.73787 | 0.868936 | − | 0.494925i | \(-0.164804\pi\) | ||||
0.868936 | + | 0.494925i | \(0.164804\pi\) | |||||||
\(4\) | −1.39745 | −0.698723 | ||||||||
\(5\) | 0.0164567 | 0.00735967 | 0.00367983 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367983 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(6\) | 2.33656 | 0.953896 | ||||||||
\(7\) | 0.793722 | 0.299999 | 0.149999 | − | 0.988686i | \(-0.452073\pi\) | ||||
0.149999 | + | 0.988686i | \(0.452073\pi\) | |||||||
\(8\) | −2.63725 | −0.932407 | ||||||||
\(9\) | 6.06060 | 2.02020 | ||||||||
\(10\) | 0.0127744 | 0.00403963 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −4.20643 | −1.21429 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.616122 | 0.164665 | ||||||||
\(15\) | 0.0495361 | 0.0127902 | ||||||||
\(16\) | 0.747743 | 0.186936 | ||||||||
\(17\) | 3.12834 | 0.758734 | 0.379367 | − | 0.925246i | \(-0.376142\pi\) | ||||
0.379367 | + | 0.925246i | \(0.376142\pi\) | |||||||
\(18\) | 4.70450 | 1.10886 | ||||||||
\(19\) | 1.22596 | 0.281254 | 0.140627 | − | 0.990063i | \(-0.455088\pi\) | ||||
0.140627 | + | 0.990063i | \(0.455088\pi\) | |||||||
\(20\) | −0.0229974 | −0.00514237 | ||||||||
\(21\) | 2.38917 | 0.521359 | ||||||||
\(22\) | 0.776244 | 0.165496 | ||||||||
\(23\) | 4.26925 | 0.890201 | 0.445100 | − | 0.895481i | \(-0.353168\pi\) | ||||
0.445100 | + | 0.895481i | \(0.353168\pi\) | |||||||
\(24\) | −7.93833 | −1.62040 | ||||||||
\(25\) | −4.99973 | −0.999946 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.21265 | 1.77298 | ||||||||
\(28\) | −1.10918 | −0.209616 | ||||||||
\(29\) | 8.01948 | 1.48918 | 0.744590 | − | 0.667522i | \(-0.232645\pi\) | ||||
0.744590 | + | 0.667522i | \(0.232645\pi\) | |||||||
\(30\) | 0.0384521 | 0.00702036 | ||||||||
\(31\) | 2.49364 | 0.447870 | 0.223935 | − | 0.974604i | \(-0.428110\pi\) | ||||
0.223935 | + | 0.974604i | \(0.428110\pi\) | |||||||
\(32\) | 5.85492 | 1.03501 | ||||||||
\(33\) | 3.01008 | 0.523988 | ||||||||
\(34\) | 2.42836 | 0.416460 | ||||||||
\(35\) | 0.0130621 | 0.00220789 | ||||||||
\(36\) | −8.46935 | −1.41156 | ||||||||
\(37\) | −8.88674 | −1.46097 | −0.730486 | − | 0.682928i | \(-0.760706\pi\) | ||||
−0.730486 | + | 0.682928i | \(0.760706\pi\) | |||||||
\(38\) | 0.951641 | 0.154377 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0434004 | −0.00686221 | ||||||||
\(41\) | −8.43142 | −1.31677 | −0.658384 | − | 0.752683i | \(-0.728760\pi\) | ||||
−0.658384 | + | 0.752683i | \(0.728760\pi\) | |||||||
\(42\) | 1.85458 | 0.286167 | ||||||||
\(43\) | 11.8954 | 1.81404 | 0.907018 | − | 0.421092i | \(-0.138353\pi\) | ||||
0.907018 | + | 0.421092i | \(0.138353\pi\) | |||||||
\(44\) | −1.39745 | −0.210673 | ||||||||
\(45\) | 0.0997375 | 0.0148680 | ||||||||
\(46\) | 3.31398 | 0.488620 | ||||||||
\(47\) | 12.2753 | 1.79054 | 0.895268 | − | 0.445528i | \(-0.146984\pi\) | ||||
0.895268 | + | 0.445528i | \(0.146984\pi\) | |||||||
\(48\) | 2.25077 | 0.324871 | ||||||||
\(49\) | −6.37001 | −0.910001 | ||||||||
\(50\) | −3.88101 | −0.548858 | ||||||||
\(51\) | 9.41657 | 1.31858 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.56675 | 0.627292 | 0.313646 | − | 0.949540i | \(-0.398450\pi\) | ||||
0.313646 | + | 0.949540i | \(0.398450\pi\) | |||||||
\(54\) | 7.15126 | 0.973164 | ||||||||
\(55\) | 0.0164567 | 0.00221902 | ||||||||
\(56\) | −2.09324 | −0.279721 | ||||||||
\(57\) | 3.69023 | 0.488783 | ||||||||
\(58\) | 6.22507 | 0.817392 | ||||||||
\(59\) | 0.265214 | 0.0345279 | 0.0172639 | − | 0.999851i | \(-0.494504\pi\) | ||||
0.0172639 | + | 0.999851i | \(0.494504\pi\) | |||||||
\(60\) | −0.0692239 | −0.00893677 | ||||||||
\(61\) | −4.49240 | −0.575192 | −0.287596 | − | 0.957752i | \(-0.592856\pi\) | ||||
−0.287596 | + | 0.957752i | \(0.592856\pi\) | |||||||
\(62\) | 1.93567 | 0.245830 | ||||||||
\(63\) | 4.81043 | 0.606057 | ||||||||
\(64\) | 3.04936 | 0.381170 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.33656 | 0.287610 | ||||||||
\(67\) | 5.31411 | 0.649221 | 0.324611 | − | 0.945848i | \(-0.394767\pi\) | ||||
0.324611 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(68\) | −4.37169 | −0.530145 | ||||||||
\(69\) | 12.8508 | 1.54706 | ||||||||
\(70\) | 0.0101393 | 0.00121188 | ||||||||
\(71\) | −13.1162 | −1.55661 | −0.778304 | − | 0.627888i | \(-0.783920\pi\) | ||||
−0.778304 | + | 0.627888i | \(0.783920\pi\) | |||||||
\(72\) | −15.9833 | −1.88365 | ||||||||
\(73\) | −11.5434 | −1.35106 | −0.675529 | − | 0.737333i | \(-0.736085\pi\) | ||||
−0.675529 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(74\) | −6.89828 | −0.801909 | ||||||||
\(75\) | −15.0496 | −1.73778 | ||||||||
\(76\) | −1.71321 | −0.196518 | ||||||||
\(77\) | 0.793722 | 0.0904530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.35606 | −1.05264 | −0.526320 | − | 0.850287i | \(-0.676428\pi\) | ||||
−0.526320 | + | 0.850287i | \(0.676428\pi\) | |||||||
\(80\) | 0.0123054 | 0.00137579 | ||||||||
\(81\) | 9.54904 | 1.06100 | ||||||||
\(82\) | −6.54484 | −0.722757 | ||||||||
\(83\) | −4.81647 | −0.528677 | −0.264338 | − | 0.964430i | \(-0.585154\pi\) | ||||
−0.264338 | + | 0.964430i | \(0.585154\pi\) | |||||||
\(84\) | −3.33873 | −0.364285 | ||||||||
\(85\) | 0.0514822 | 0.00558403 | ||||||||
\(86\) | 9.23375 | 0.995701 | ||||||||
\(87\) | 24.1393 | 2.58800 | ||||||||
\(88\) | −2.63725 | −0.281131 | ||||||||
\(89\) | −1.66164 | −0.176134 | −0.0880668 | − | 0.996115i | \(-0.528069\pi\) | ||||
−0.0880668 | + | 0.996115i | \(0.528069\pi\) | |||||||
\(90\) | 0.0774207 | 0.00816085 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.96605 | −0.622003 | ||||||||
\(93\) | 7.50605 | 0.778341 | ||||||||
\(94\) | 9.52863 | 0.982803 | ||||||||
\(95\) | 0.0201752 | 0.00206993 | ||||||||
\(96\) | 17.6238 | 1.79872 | ||||||||
\(97\) | 8.35282 | 0.848101 | 0.424050 | − | 0.905639i | \(-0.360608\pi\) | ||||
0.424050 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(98\) | −4.94468 | −0.499488 | ||||||||
\(99\) | 6.06060 | 0.609113 | ||||||||
\(100\) | 6.98685 | 0.698685 | ||||||||
\(101\) | 5.67235 | 0.564420 | 0.282210 | − | 0.959353i | \(-0.408933\pi\) | ||||
0.282210 | + | 0.959353i | \(0.408933\pi\) | |||||||
\(102\) | 7.30955 | 0.723754 | ||||||||
\(103\) | 16.9225 | 1.66743 | 0.833714 | − | 0.552197i | \(-0.186210\pi\) | ||||
0.833714 | + | 0.552197i | \(0.186210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0393178 | 0.00383703 | ||||||||
\(106\) | 3.54491 | 0.344312 | ||||||||
\(107\) | 4.36032 | 0.421528 | 0.210764 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210764 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(108\) | −12.8742 | −1.23882 | ||||||||
\(109\) | −17.4935 | −1.67557 | −0.837787 | − | 0.545997i | \(-0.816151\pi\) | ||||
−0.837787 | + | 0.545997i | \(0.816151\pi\) | |||||||
\(110\) | 0.0127744 | 0.00121799 | ||||||||
\(111\) | −26.7498 | −2.53898 | ||||||||
\(112\) | 0.593500 | 0.0560805 | ||||||||
\(113\) | 1.17709 | 0.110731 | 0.0553655 | − | 0.998466i | \(-0.482368\pi\) | ||||
0.0553655 | + | 0.998466i | \(0.482368\pi\) | |||||||
\(114\) | 2.86452 | 0.268287 | ||||||||
\(115\) | 0.0702579 | 0.00655158 | ||||||||
\(116\) | −11.2068 | −1.04052 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.205870 | 0.0189519 | ||||||||
\(119\) | 2.48303 | 0.227619 | ||||||||
\(120\) | −0.130639 | −0.0119256 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.48720 | −0.315716 | ||||||||
\(123\) | −25.3793 | −2.28837 | ||||||||
\(124\) | −3.48472 | −0.312937 | ||||||||
\(125\) | −0.164563 | −0.0147189 | ||||||||
\(126\) | 3.73406 | 0.332657 | ||||||||
\(127\) | −0.134766 | −0.0119585 | −0.00597926 | − | 0.999982i | \(-0.501903\pi\) | ||||
−0.00597926 | + | 0.999982i | \(0.501903\pi\) | |||||||
\(128\) | −9.34280 | −0.825795 | ||||||||
\(129\) | 35.8062 | 3.15256 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.2414 | −1.85587 | −0.927933 | − | 0.372746i | \(-0.878416\pi\) | ||||
−0.927933 | + | 0.372746i | \(0.878416\pi\) | |||||||
\(132\) | −4.20643 | −0.366122 | ||||||||
\(133\) | 0.973068 | 0.0843757 | ||||||||
\(134\) | 4.12504 | 0.356349 | ||||||||
\(135\) | 0.151610 | 0.0130485 | ||||||||
\(136\) | −8.25021 | −0.707450 | ||||||||
\(137\) | 10.7421 | 0.917763 | 0.458882 | − | 0.888497i | \(-0.348250\pi\) | ||||
0.458882 | + | 0.888497i | \(0.348250\pi\) | |||||||
\(138\) | 9.97536 | 0.849159 | ||||||||
\(139\) | −13.7985 | −1.17037 | −0.585186 | − | 0.810899i | \(-0.698979\pi\) | ||||
−0.585186 | + | 0.810899i | \(0.698979\pi\) | |||||||
\(140\) | −0.0182535 | −0.00154270 | ||||||||
\(141\) | 36.9497 | 3.11172 | ||||||||
\(142\) | −10.1814 | −0.854402 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.53177 | 0.377648 | ||||||||
\(145\) | 0.131974 | 0.0109599 | ||||||||
\(146\) | −8.96053 | −0.741579 | ||||||||
\(147\) | −19.1742 | −1.58146 | ||||||||
\(148\) | 12.4187 | 1.02081 | ||||||||
\(149\) | −12.7827 | −1.04720 | −0.523600 | − | 0.851964i | \(-0.675411\pi\) | ||||
−0.523600 | + | 0.851964i | \(0.675411\pi\) | |||||||
\(150\) | −11.6822 | −0.953844 | ||||||||
\(151\) | 8.66190 | 0.704895 | 0.352448 | − | 0.935832i | \(-0.385349\pi\) | ||||
0.352448 | + | 0.935832i | \(0.385349\pi\) | |||||||
\(152\) | −3.23315 | −0.262243 | ||||||||
\(153\) | 18.9596 | 1.53279 | ||||||||
\(154\) | 0.616122 | 0.0496485 | ||||||||
\(155\) | 0.0410371 | 0.00329618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.07034 | −0.404657 | −0.202328 | − | 0.979318i | \(-0.564851\pi\) | ||||
−0.202328 | + | 0.979318i | \(0.564851\pi\) | |||||||
\(158\) | −7.26259 | −0.577780 | ||||||||
\(159\) | 13.7463 | 1.09015 | ||||||||
\(160\) | 0.0963528 | 0.00761736 | ||||||||
\(161\) | 3.38860 | 0.267059 | ||||||||
\(162\) | 7.41239 | 0.582372 | ||||||||
\(163\) | 18.7754 | 1.47060 | 0.735300 | − | 0.677741i | \(-0.237041\pi\) | ||||
0.735300 | + | 0.677741i | \(0.237041\pi\) | |||||||
\(164\) | 11.7825 | 0.920055 | ||||||||
\(165\) | 0.0495361 | 0.00385638 | ||||||||
\(166\) | −3.73876 | −0.290184 | ||||||||
\(167\) | −15.4424 | −1.19497 | −0.597483 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597483 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(168\) | −6.30082 | −0.486119 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.0399628 | 0.00306500 | ||||||||
\(171\) | 7.43003 | 0.568188 | ||||||||
\(172\) | −16.6232 | −1.26751 | ||||||||
\(173\) | −7.64125 | −0.580953 | −0.290477 | − | 0.956882i | \(-0.593814\pi\) | ||||
−0.290477 | + | 0.956882i | \(0.593814\pi\) | |||||||
\(174\) | 18.7380 | 1.42052 | ||||||||
\(175\) | −3.96839 | −0.299982 | ||||||||
\(176\) | 0.747743 | 0.0563633 | ||||||||
\(177\) | 0.798315 | 0.0600050 | ||||||||
\(178\) | −1.28984 | −0.0966776 | ||||||||
\(179\) | −21.6699 | −1.61968 | −0.809841 | − | 0.586649i | \(-0.800447\pi\) | ||||
−0.809841 | + | 0.586649i | \(0.800447\pi\) | |||||||
\(180\) | −0.139378 | −0.0103886 | ||||||||
\(181\) | −11.9637 | −0.889252 | −0.444626 | − | 0.895716i | \(-0.646663\pi\) | ||||
−0.444626 | + | 0.895716i | \(0.646663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.5225 | −0.999611 | ||||||||
\(184\) | −11.2591 | −0.830030 | ||||||||
\(185\) | −0.146247 | −0.0107523 | ||||||||
\(186\) | 5.82653 | 0.427222 | ||||||||
\(187\) | 3.12834 | 0.228767 | ||||||||
\(188\) | −17.1541 | −1.25109 | ||||||||
\(189\) | 7.31228 | 0.531890 | ||||||||
\(190\) | 0.0156609 | 0.00113616 | ||||||||
\(191\) | −11.5803 | −0.837924 | −0.418962 | − | 0.908004i | \(-0.637606\pi\) | ||||
−0.418962 | + | 0.908004i | \(0.637606\pi\) | |||||||
\(192\) | 9.17884 | 0.662425 | ||||||||
\(193\) | −23.4115 | −1.68519 | −0.842597 | − | 0.538545i | \(-0.818974\pi\) | ||||
−0.842597 | + | 0.538545i | \(0.818974\pi\) | |||||||
\(194\) | 6.48383 | 0.465512 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.90173 | 0.635838 | ||||||||
\(197\) | 6.57290 | 0.468300 | 0.234150 | − | 0.972200i | \(-0.424769\pi\) | ||||
0.234150 | + | 0.972200i | \(0.424769\pi\) | |||||||
\(198\) | 4.70450 | 0.334334 | ||||||||
\(199\) | 19.8590 | 1.40777 | 0.703884 | − | 0.710315i | \(-0.251448\pi\) | ||||
0.703884 | + | 0.710315i | \(0.251448\pi\) | |||||||
\(200\) | 13.1855 | 0.932357 | ||||||||
\(201\) | 15.9959 | 1.12826 | ||||||||
\(202\) | 4.40313 | 0.309803 | ||||||||
\(203\) | 6.36523 | 0.446752 | ||||||||
\(204\) | −13.1591 | −0.921324 | ||||||||
\(205\) | −0.138754 | −0.00969097 | ||||||||
\(206\) | 13.1360 | 0.915230 | ||||||||
\(207\) | 25.8742 | 1.79838 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.22596 | 0.0848012 | ||||||||
\(210\) | 0.0305202 | 0.00210610 | ||||||||
\(211\) | 7.79372 | 0.536542 | 0.268271 | − | 0.963343i | \(-0.413548\pi\) | ||||
0.268271 | + | 0.963343i | \(0.413548\pi\) | |||||||
\(212\) | −6.38179 | −0.438303 | ||||||||
\(213\) | −39.4809 | −2.70518 | ||||||||
\(214\) | 3.38467 | 0.231372 | ||||||||
\(215\) | 0.195760 | 0.0133507 | ||||||||
\(216\) | −24.2960 | −1.65314 | ||||||||
\(217\) | 1.97925 | 0.134360 | ||||||||
\(218\) | −13.5792 | −0.919702 | ||||||||
\(219\) | −34.7467 | −2.34797 | ||||||||
\(220\) | −0.0229974 | −0.00155048 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −20.7644 | −1.39361 | ||||||||
\(223\) | 4.38266 | 0.293485 | 0.146742 | − | 0.989175i | \(-0.453121\pi\) | ||||
0.146742 | + | 0.989175i | \(0.453121\pi\) | |||||||
\(224\) | 4.64718 | 0.310503 | ||||||||
\(225\) | −30.3013 | −2.02009 | ||||||||
\(226\) | 0.913707 | 0.0607789 | ||||||||
\(227\) | 21.0447 | 1.39679 | 0.698393 | − | 0.715714i | \(-0.253899\pi\) | ||||
0.698393 | + | 0.715714i | \(0.253899\pi\) | |||||||
\(228\) | −5.15689 | −0.341524 | ||||||||
\(229\) | −12.8810 | −0.851197 | −0.425599 | − | 0.904912i | \(-0.639936\pi\) | ||||
−0.425599 | + | 0.904912i | \(0.639936\pi\) | |||||||
\(230\) | 0.0545373 | 0.00359608 | ||||||||
\(231\) | 2.38917 | 0.157196 | ||||||||
\(232\) | −21.1493 | −1.38852 | ||||||||
\(233\) | −13.8170 | −0.905185 | −0.452592 | − | 0.891717i | \(-0.649501\pi\) | ||||
−0.452592 | + | 0.891717i | \(0.649501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.202011 | 0.0131778 | ||||||||
\(236\) | −0.370621 | −0.0241254 | ||||||||
\(237\) | −28.1625 | −1.82935 | ||||||||
\(238\) | 1.92744 | 0.124937 | ||||||||
\(239\) | 3.95240 | 0.255659 | 0.127830 | − | 0.991796i | \(-0.459199\pi\) | ||||
0.127830 | + | 0.991796i | \(0.459199\pi\) | |||||||
\(240\) | 0.0370403 | 0.00239094 | ||||||||
\(241\) | 5.51486 | 0.355243 | 0.177622 | − | 0.984099i | \(-0.443160\pi\) | ||||
0.177622 | + | 0.984099i | \(0.443160\pi\) | |||||||
\(242\) | 0.776244 | 0.0498989 | ||||||||
\(243\) | 1.10546 | 0.0709152 | ||||||||
\(244\) | 6.27788 | 0.401900 | ||||||||
\(245\) | −0.104829 | −0.00669730 | ||||||||
\(246\) | −19.7005 | −1.25606 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.57633 | −0.417598 | ||||||||
\(249\) | −14.4980 | −0.918772 | ||||||||
\(250\) | −0.127741 | −0.00807904 | ||||||||
\(251\) | −6.96137 | −0.439398 | −0.219699 | − | 0.975568i | \(-0.570508\pi\) | ||||
−0.219699 | + | 0.975568i | \(0.570508\pi\) | |||||||
\(252\) | −6.72231 | −0.423466 | ||||||||
\(253\) | 4.26925 | 0.268406 | ||||||||
\(254\) | −0.104611 | −0.00656388 | ||||||||
\(255\) | 0.154966 | 0.00970433 | ||||||||
\(256\) | −13.3510 | −0.834439 | ||||||||
\(257\) | 13.5802 | 0.847108 | 0.423554 | − | 0.905871i | \(-0.360782\pi\) | ||||
0.423554 | + | 0.905871i | \(0.360782\pi\) | |||||||
\(258\) | 27.7944 | 1.73040 | ||||||||
\(259\) | −7.05360 | −0.438289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 48.6028 | 3.00844 | ||||||||
\(262\) | −16.4885 | −1.01866 | ||||||||
\(263\) | −10.5992 | −0.653575 | −0.326788 | − | 0.945098i | \(-0.605966\pi\) | ||||
−0.326788 | + | 0.945098i | \(0.605966\pi\) | |||||||
\(264\) | −7.93833 | −0.488570 | ||||||||
\(265\) | 0.0751537 | 0.00461666 | ||||||||
\(266\) | 0.755338 | 0.0463128 | ||||||||
\(267\) | −5.00168 | −0.306098 | ||||||||
\(268\) | −7.42617 | −0.453626 | ||||||||
\(269\) | 0.00954813 | 0.000582160 0 | 0.000291080 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000291080 | 1.00000i | \(0.499907\pi\) | ||||||||
\(270\) | 0.117686 | 0.00716216 | ||||||||
\(271\) | −3.75212 | −0.227925 | −0.113963 | − | 0.993485i | \(-0.536354\pi\) | ||||
−0.113963 | + | 0.993485i | \(0.536354\pi\) | |||||||
\(272\) | 2.33920 | 0.141835 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.33852 | 0.503749 | ||||||||
\(275\) | −4.99973 | −0.301495 | ||||||||
\(276\) | −17.9583 | −1.08096 | ||||||||
\(277\) | 13.1876 | 0.792368 | 0.396184 | − | 0.918171i | \(-0.370334\pi\) | ||||
0.396184 | + | 0.918171i | \(0.370334\pi\) | |||||||
\(278\) | −10.7110 | −0.642403 | ||||||||
\(279\) | 15.1129 | 0.904787 | ||||||||
\(280\) | −0.0344478 | −0.00205865 | ||||||||
\(281\) | −24.7282 | −1.47516 | −0.737579 | − | 0.675261i | \(-0.764031\pi\) | ||||
−0.737579 | + | 0.675261i | \(0.764031\pi\) | |||||||
\(282\) | 28.6820 | 1.70799 | ||||||||
\(283\) | −23.1300 | −1.37493 | −0.687467 | − | 0.726216i | \(-0.741277\pi\) | ||||
−0.687467 | + | 0.726216i | \(0.741277\pi\) | |||||||
\(284\) | 18.3292 | 1.08764 | ||||||||
\(285\) | 0.0607291 | 0.00359728 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.69220 | −0.395028 | ||||||||
\(288\) | 35.4843 | 2.09093 | ||||||||
\(289\) | −7.21348 | −0.424322 | ||||||||
\(290\) | 0.102444 | 0.00601573 | ||||||||
\(291\) | 25.1427 | 1.47389 | ||||||||
\(292\) | 16.1313 | 0.944015 | ||||||||
\(293\) | 10.9621 | 0.640411 | 0.320206 | − | 0.947348i | \(-0.396248\pi\) | ||||
0.320206 | + | 0.947348i | \(0.396248\pi\) | |||||||
\(294\) | −14.8839 | −0.868046 | ||||||||
\(295\) | 0.00436454 | 0.000254114 0 | ||||||||
\(296\) | 23.4365 | 1.36222 | ||||||||
\(297\) | 9.21265 | 0.534572 | ||||||||
\(298\) | −9.92249 | −0.574795 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 21.0310 | 1.21422 | ||||||||
\(301\) | 9.44166 | 0.544208 | ||||||||
\(302\) | 6.72375 | 0.386908 | ||||||||
\(303\) | 17.0742 | 0.980889 | ||||||||
\(304\) | 0.916701 | 0.0525764 | ||||||||
\(305\) | −0.0739301 | −0.00423322 | ||||||||
\(306\) | 14.7173 | 0.841331 | ||||||||
\(307\) | −19.6256 | −1.12009 | −0.560046 | − | 0.828462i | \(-0.689216\pi\) | ||||
−0.560046 | + | 0.828462i | \(0.689216\pi\) | |||||||
\(308\) | −1.10918 | −0.0632015 | ||||||||
\(309\) | 50.9382 | 2.89777 | ||||||||
\(310\) | 0.0318548 | 0.00180923 | ||||||||
\(311\) | 14.9752 | 0.849167 | 0.424583 | − | 0.905389i | \(-0.360421\pi\) | ||||
0.424583 | + | 0.905389i | \(0.360421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5917 | 0.655201 | 0.327600 | − | 0.944816i | \(-0.393760\pi\) | ||||
0.327600 | + | 0.944816i | \(0.393760\pi\) | |||||||
\(314\) | −3.93582 | −0.222111 | ||||||||
\(315\) | 0.0791638 | 0.00446038 | ||||||||
\(316\) | 13.0746 | 0.735503 | ||||||||
\(317\) | 5.55127 | 0.311791 | 0.155895 | − | 0.987774i | \(-0.450174\pi\) | ||||
0.155895 | + | 0.987774i | \(0.450174\pi\) | |||||||
\(318\) | 10.6705 | 0.598371 | ||||||||
\(319\) | 8.01948 | 0.449004 | ||||||||
\(320\) | 0.0501825 | 0.00280529 | ||||||||
\(321\) | 13.1249 | 0.732562 | ||||||||
\(322\) | 2.63038 | 0.146585 | ||||||||
\(323\) | 3.83521 | 0.213397 | ||||||||
\(324\) | −13.3443 | −0.741348 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.5743 | 0.807194 | ||||||||
\(327\) | −52.6569 | −2.91193 | ||||||||
\(328\) | 22.2357 | 1.22776 | ||||||||
\(329\) | 9.74317 | 0.537158 | ||||||||
\(330\) | 0.0384521 | 0.00211672 | ||||||||
\(331\) | 7.04341 | 0.387141 | 0.193570 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193570 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(332\) | 6.73076 | 0.369398 | ||||||||
\(333\) | −53.8590 | −2.95145 | ||||||||
\(334\) | −11.9870 | −0.655901 | ||||||||
\(335\) | 0.0874527 | 0.00477805 | ||||||||
\(336\) | 1.78648 | 0.0974607 | ||||||||
\(337\) | −16.3751 | −0.892009 | −0.446004 | − | 0.895031i | \(-0.647153\pi\) | ||||
−0.446004 | + | 0.895031i | \(0.647153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.54313 | 0.192436 | ||||||||
\(340\) | −0.0719436 | −0.00390169 | ||||||||
\(341\) | 2.49364 | 0.135038 | ||||||||
\(342\) | 5.76751 | 0.311871 | ||||||||
\(343\) | −10.6121 | −0.572997 | ||||||||
\(344\) | −31.3712 | −1.69142 | ||||||||
\(345\) | 0.211482 | 0.0113858 | ||||||||
\(346\) | −5.93147 | −0.318878 | ||||||||
\(347\) | 11.2716 | 0.605091 | 0.302545 | − | 0.953135i | \(-0.402164\pi\) | ||||
0.302545 | + | 0.953135i | \(0.402164\pi\) | |||||||
\(348\) | −33.7333 | −1.80830 | ||||||||
\(349\) | 22.7506 | 1.21781 | 0.608907 | − | 0.793242i | \(-0.291608\pi\) | ||||
0.608907 | + | 0.793242i | \(0.291608\pi\) | |||||||
\(350\) | −3.08044 | −0.164657 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.85492 | 0.312069 | ||||||||
\(353\) | 3.24835 | 0.172892 | 0.0864462 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864462 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(354\) | 0.619687 | 0.0329360 | ||||||||
\(355\) | −0.215850 | −0.0114561 | ||||||||
\(356\) | 2.32205 | 0.123069 | ||||||||
\(357\) | 7.47413 | 0.395573 | ||||||||
\(358\) | −16.8211 | −0.889023 | ||||||||
\(359\) | 31.4679 | 1.66081 | 0.830405 | − | 0.557160i | \(-0.188109\pi\) | ||||
0.830405 | + | 0.557160i | \(0.188109\pi\) | |||||||
\(360\) | −0.263032 | −0.0138630 | ||||||||
\(361\) | −17.4970 | −0.920896 | ||||||||
\(362\) | −9.28672 | −0.488099 | ||||||||
\(363\) | 3.01008 | 0.157988 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.189967 | −0.00994334 | ||||||||
\(366\) | −10.4967 | −0.548674 | ||||||||
\(367\) | 23.1155 | 1.20662 | 0.603310 | − | 0.797507i | \(-0.293848\pi\) | ||||
0.603310 | + | 0.797507i | \(0.293848\pi\) | |||||||
\(368\) | 3.19231 | 0.166410 | ||||||||
\(369\) | −51.0995 | −2.66013 | ||||||||
\(370\) | −0.113523 | −0.00590178 | ||||||||
\(371\) | 3.62473 | 0.188187 | ||||||||
\(372\) | −10.4893 | −0.543845 | ||||||||
\(373\) | −7.74228 | −0.400880 | −0.200440 | − | 0.979706i | \(-0.564237\pi\) | ||||
−0.200440 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(374\) | 2.42836 | 0.125567 | ||||||||
\(375\) | −0.495347 | −0.0255796 | ||||||||
\(376\) | −32.3730 | −1.66951 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.67611 | 0.291948 | ||||||||
\(379\) | −10.4868 | −0.538670 | −0.269335 | − | 0.963047i | \(-0.586804\pi\) | ||||
−0.269335 | + | 0.963047i | \(0.586804\pi\) | |||||||
\(380\) | −0.0281938 | −0.00144631 | ||||||||
\(381\) | −0.405656 | −0.0207824 | ||||||||
\(382\) | −8.98917 | −0.459926 | ||||||||
\(383\) | 9.84176 | 0.502891 | 0.251445 | − | 0.967872i | \(-0.419094\pi\) | ||||
0.251445 | + | 0.967872i | \(0.419094\pi\) | |||||||
\(384\) | −28.1226 | −1.43513 | ||||||||
\(385\) | 0.0130621 | 0.000665704 0 | ||||||||
\(386\) | −18.1730 | −0.924981 | ||||||||
\(387\) | 72.0934 | 3.66471 | ||||||||
\(388\) | −11.6726 | −0.592587 | ||||||||
\(389\) | −24.0364 | −1.21869 | −0.609347 | − | 0.792904i | \(-0.708568\pi\) | ||||
−0.609347 | + | 0.792904i | \(0.708568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.3557 | 0.675426 | ||||||||
\(392\) | 16.7993 | 0.848492 | ||||||||
\(393\) | −63.9383 | −3.22526 | ||||||||
\(394\) | 5.10218 | 0.257044 | ||||||||
\(395\) | −0.153970 | −0.00774707 | ||||||||
\(396\) | −8.46935 | −0.425601 | ||||||||
\(397\) | 10.7120 | 0.537619 | 0.268809 | − | 0.963193i | \(-0.413370\pi\) | ||||
0.268809 | + | 0.963193i | \(0.413370\pi\) | |||||||
\(398\) | 15.4154 | 0.772706 | ||||||||
\(399\) | 2.92901 | 0.146634 | ||||||||
\(400\) | −3.73851 | −0.186926 | ||||||||
\(401\) | 10.8191 | 0.540281 | 0.270140 | − | 0.962821i | \(-0.412930\pi\) | ||||
0.270140 | + | 0.962821i | \(0.412930\pi\) | |||||||
\(402\) | 12.4167 | 0.619290 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.92679 | −0.394373 | ||||||||
\(405\) | 0.157146 | 0.00780864 | ||||||||
\(406\) | 4.94097 | 0.245216 | ||||||||
\(407\) | −8.88674 | −0.440499 | ||||||||
\(408\) | −24.8338 | −1.22946 | ||||||||
\(409\) | 29.7938 | 1.47321 | 0.736604 | − | 0.676324i | \(-0.236428\pi\) | ||||
0.736604 | + | 0.676324i | \(0.236428\pi\) | |||||||
\(410\) | −0.107707 | −0.00531925 | ||||||||
\(411\) | 32.3347 | 1.59495 | ||||||||
\(412\) | −23.6483 | −1.16507 | ||||||||
\(413\) | 0.210506 | 0.0103583 | ||||||||
\(414\) | 20.0847 | 0.987110 | ||||||||
\(415\) | −0.0792634 | −0.00389088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.5346 | −2.03396 | ||||||||
\(418\) | 0.951641 | 0.0465463 | ||||||||
\(419\) | 0.335538 | 0.0163921 | 0.00819605 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819605 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(420\) | −0.0549445 | −0.00268102 | ||||||||
\(421\) | 34.9448 | 1.70311 | 0.851554 | − | 0.524267i | \(-0.175661\pi\) | ||||
0.851554 | + | 0.524267i | \(0.175661\pi\) | |||||||
\(422\) | 6.04983 | 0.294501 | ||||||||
\(423\) | 74.3956 | 3.61724 | ||||||||
\(424\) | −12.0437 | −0.584891 | ||||||||
\(425\) | −15.6409 | −0.758693 | ||||||||
\(426\) | −30.6468 | −1.48484 | ||||||||
\(427\) | −3.56571 | −0.172557 | ||||||||
\(428\) | −6.09331 | −0.294531 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.151957 | 0.00732803 | ||||||||
\(431\) | 15.8744 | 0.764641 | 0.382320 | − | 0.924030i | \(-0.375125\pi\) | ||||
0.382320 | + | 0.924030i | \(0.375125\pi\) | |||||||
\(432\) | 6.88870 | 0.331433 | ||||||||
\(433\) | −9.59664 | −0.461185 | −0.230593 | − | 0.973050i | \(-0.574066\pi\) | ||||
−0.230593 | + | 0.973050i | \(0.574066\pi\) | |||||||
\(434\) | 1.53638 | 0.0737488 | ||||||||
\(435\) | 0.397253 | 0.0190468 | ||||||||
\(436\) | 24.4462 | 1.17076 | ||||||||
\(437\) | 5.23392 | 0.250372 | ||||||||
\(438\) | −26.9719 | −1.28877 | ||||||||
\(439\) | 7.77923 | 0.371283 | 0.185641 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185641 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(440\) | −0.0434004 | −0.00206903 | ||||||||
\(441\) | −38.6060 | −1.83838 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.0476 | −1.09503 | −0.547513 | − | 0.836797i | \(-0.684425\pi\) | ||||
−0.547513 | + | 0.836797i | \(0.684425\pi\) | |||||||
\(444\) | 37.3814 | 1.77404 | ||||||||
\(445\) | −0.0273452 | −0.00129629 | ||||||||
\(446\) | 3.40201 | 0.161090 | ||||||||
\(447\) | −38.4770 | −1.81990 | ||||||||
\(448\) | 2.42035 | 0.114351 | ||||||||
\(449\) | 29.1978 | 1.37793 | 0.688964 | − | 0.724796i | \(-0.258066\pi\) | ||||
0.688964 | + | 0.724796i | \(0.258066\pi\) | |||||||
\(450\) | −23.5212 | −1.10880 | ||||||||
\(451\) | −8.43142 | −0.397020 | ||||||||
\(452\) | −1.64491 | −0.0773703 | ||||||||
\(453\) | 26.0730 | 1.22502 | ||||||||
\(454\) | 16.3358 | 0.766679 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.73204 | −0.455745 | ||||||||
\(457\) | −31.1916 | −1.45908 | −0.729541 | − | 0.683937i | \(-0.760266\pi\) | ||||
−0.729541 | + | 0.683937i | \(0.760266\pi\) | |||||||
\(458\) | −9.99876 | −0.467211 | ||||||||
\(459\) | 28.8203 | 1.34522 | ||||||||
\(460\) | −0.0981816 | −0.00457774 | ||||||||
\(461\) | −37.6692 | −1.75443 | −0.877215 | − | 0.480097i | \(-0.840601\pi\) | ||||
−0.877215 | + | 0.480097i | \(0.840601\pi\) | |||||||
\(462\) | 1.85458 | 0.0862827 | ||||||||
\(463\) | −0.988906 | −0.0459584 | −0.0229792 | − | 0.999736i | \(-0.507315\pi\) | ||||
−0.0229792 | + | 0.999736i | \(0.507315\pi\) | |||||||
\(464\) | 5.99651 | 0.278381 | ||||||||
\(465\) | 0.123525 | 0.00572833 | ||||||||
\(466\) | −10.7254 | −0.496845 | ||||||||
\(467\) | 11.5156 | 0.532878 | 0.266439 | − | 0.963852i | \(-0.414153\pi\) | ||||
0.266439 | + | 0.963852i | \(0.414153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.21792 | 0.194765 | ||||||||
\(470\) | 0.156810 | 0.00723310 | ||||||||
\(471\) | −15.2621 | −0.703242 | ||||||||
\(472\) | −0.699434 | −0.0321940 | ||||||||
\(473\) | 11.8954 | 0.546952 | ||||||||
\(474\) | −21.8610 | −1.00411 | ||||||||
\(475\) | −6.12945 | −0.281238 | ||||||||
\(476\) | −3.46990 | −0.159043 | ||||||||
\(477\) | 27.6772 | 1.26725 | ||||||||
\(478\) | 3.06803 | 0.140328 | ||||||||
\(479\) | −9.11697 | −0.416565 | −0.208283 | − | 0.978069i | \(-0.566787\pi\) | ||||
−0.208283 | + | 0.978069i | \(0.566787\pi\) | |||||||
\(480\) | 0.290030 | 0.0132380 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4.28088 | 0.194989 | ||||||||
\(483\) | 10.2000 | 0.464114 | ||||||||
\(484\) | −1.39745 | −0.0635202 | ||||||||
\(485\) | 0.137460 | 0.00624174 | ||||||||
\(486\) | 0.858106 | 0.0389245 | ||||||||
\(487\) | 18.6189 | 0.843704 | 0.421852 | − | 0.906665i | \(-0.361380\pi\) | ||||
0.421852 | + | 0.906665i | \(0.361380\pi\) | |||||||
\(488\) | 11.8476 | 0.536314 | ||||||||
\(489\) | 56.5154 | 2.55572 | ||||||||
\(490\) | −0.0813732 | −0.00367607 | ||||||||
\(491\) | −25.0177 | −1.12903 | −0.564517 | − | 0.825421i | \(-0.690938\pi\) | ||||
−0.564517 | + | 0.825421i | \(0.690938\pi\) | |||||||
\(492\) | 35.4662 | 1.59894 | ||||||||
\(493\) | 25.0877 | 1.12989 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0997375 | 0.00448287 | ||||||||
\(496\) | 1.86460 | 0.0837230 | ||||||||
\(497\) | −10.4106 | −0.466980 | ||||||||
\(498\) | −11.2540 | −0.504303 | ||||||||
\(499\) | 6.05960 | 0.271265 | 0.135632 | − | 0.990759i | \(-0.456693\pi\) | ||||
0.135632 | + | 0.990759i | \(0.456693\pi\) | |||||||
\(500\) | 0.229967 | 0.0102845 | ||||||||
\(501\) | −46.4828 | −2.07670 | ||||||||
\(502\) | −5.40372 | −0.241180 | ||||||||
\(503\) | 11.7680 | 0.524707 | 0.262354 | − | 0.964972i | \(-0.415501\pi\) | ||||
0.262354 | + | 0.964972i | \(0.415501\pi\) | |||||||
\(504\) | −12.6863 | −0.565092 | ||||||||
\(505\) | 0.0933482 | 0.00415394 | ||||||||
\(506\) | 3.31398 | 0.147324 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.188328 | 0.00835568 | ||||||||
\(509\) | −2.42538 | −0.107503 | −0.0537515 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537515 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(510\) | 0.120291 | 0.00532659 | ||||||||
\(511\) | −9.16228 | −0.405316 | ||||||||
\(512\) | 8.32195 | 0.367782 | ||||||||
\(513\) | 11.2943 | 0.498656 | ||||||||
\(514\) | 10.5415 | 0.464967 | ||||||||
\(515\) | 0.278489 | 0.0122717 | ||||||||
\(516\) | −50.0372 | −2.20277 | ||||||||
\(517\) | 12.2753 | 0.539867 | ||||||||
\(518\) | −5.47531 | −0.240571 | ||||||||
\(519\) | −23.0008 | −1.00962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.3612 | −1.11109 | −0.555547 | − | 0.831485i | \(-0.687491\pi\) | ||||
−0.555547 | + | 0.831485i | \(0.687491\pi\) | |||||||
\(522\) | 37.7276 | 1.65129 | ||||||||
\(523\) | 8.65849 | 0.378609 | 0.189305 | − | 0.981918i | \(-0.439377\pi\) | ||||
0.189305 | + | 0.981918i | \(0.439377\pi\) | |||||||
\(524\) | 29.6836 | 1.29674 | ||||||||
\(525\) | −11.9452 | −0.521331 | ||||||||
\(526\) | −8.22757 | −0.358739 | ||||||||
\(527\) | 7.80095 | 0.339815 | ||||||||
\(528\) | 2.25077 | 0.0979522 | ||||||||
\(529\) | −4.77347 | −0.207542 | ||||||||
\(530\) | 0.0583376 | 0.00253403 | ||||||||
\(531\) | 1.60735 | 0.0697531 | ||||||||
\(532\) | −1.35981 | −0.0589552 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.88252 | −0.168013 | ||||||||
\(535\) | 0.0717566 | 0.00310231 | ||||||||
\(536\) | −14.0146 | −0.605339 | ||||||||
\(537\) | −65.2281 | −2.81480 | ||||||||
\(538\) | 0.00741168 | 0.000319540 0 | ||||||||
\(539\) | −6.37001 | −0.274376 | ||||||||
\(540\) | −0.211867 | −0.00911729 | ||||||||
\(541\) | 29.9184 | 1.28629 | 0.643146 | − | 0.765744i | \(-0.277629\pi\) | ||||
0.643146 | + | 0.765744i | \(0.277629\pi\) | |||||||
\(542\) | −2.91256 | −0.125105 | ||||||||
\(543\) | −36.0116 | −1.54541 | ||||||||
\(544\) | 18.3162 | 0.785301 | ||||||||
\(545\) | −0.287886 | −0.0123317 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8749 | 1.49114 | 0.745572 | − | 0.666425i | \(-0.232176\pi\) | ||||
0.745572 | + | 0.666425i | \(0.232176\pi\) | |||||||
\(548\) | −15.0116 | −0.641262 | ||||||||
\(549\) | −27.2266 | −1.16200 | ||||||||
\(550\) | −3.88101 | −0.165487 | ||||||||
\(551\) | 9.83153 | 0.418837 | ||||||||
\(552\) | −33.8907 | −1.44249 | ||||||||
\(553\) | −7.42611 | −0.315790 | ||||||||
\(554\) | 10.2368 | 0.434921 | ||||||||
\(555\) | −0.440214 | −0.0186861 | ||||||||
\(556\) | 19.2826 | 0.817766 | ||||||||
\(557\) | 29.4325 | 1.24710 | 0.623548 | − | 0.781785i | \(-0.285691\pi\) | ||||
0.623548 | + | 0.781785i | \(0.285691\pi\) | |||||||
\(558\) | 11.7313 | 0.496626 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.00976706 | 0.000412734 0 | ||||||||
\(561\) | 9.41657 | 0.397568 | ||||||||
\(562\) | −19.1951 | −0.809696 | ||||||||
\(563\) | −31.9030 | −1.34455 | −0.672276 | − | 0.740301i | \(-0.734683\pi\) | ||||
−0.672276 | + | 0.740301i | \(0.734683\pi\) | |||||||
\(564\) | −51.6351 | −2.17423 | ||||||||
\(565\) | 0.0193710 | 0.000814943 0 | ||||||||
\(566\) | −17.9545 | −0.754684 | ||||||||
\(567\) | 7.57928 | 0.318300 | ||||||||
\(568\) | 34.5907 | 1.45139 | ||||||||
\(569\) | 1.00569 | 0.0421605 | 0.0210803 | − | 0.999778i | \(-0.493289\pi\) | ||||
0.0210803 | + | 0.999778i | \(0.493289\pi\) | |||||||
\(570\) | 0.0471406 | 0.00197450 | ||||||||
\(571\) | −24.9551 | −1.04434 | −0.522170 | − | 0.852841i | \(-0.674877\pi\) | ||||
−0.522170 | + | 0.852841i | \(0.674877\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.8578 | −1.45620 | ||||||||
\(574\) | −5.19478 | −0.216826 | ||||||||
\(575\) | −21.3451 | −0.890153 | ||||||||
\(576\) | 18.4810 | 0.770040 | ||||||||
\(577\) | −37.2141 | −1.54924 | −0.774621 | − | 0.632426i | \(-0.782059\pi\) | ||||
−0.774621 | + | 0.632426i | \(0.782059\pi\) | |||||||
\(578\) | −5.59942 | −0.232905 | ||||||||
\(579\) | −70.4704 | −2.92865 | ||||||||
\(580\) | −0.184427 | −0.00765791 | ||||||||
\(581\) | −3.82294 | −0.158602 | ||||||||
\(582\) | 19.5169 | 0.809000 | ||||||||
\(583\) | 4.56675 | 0.189136 | ||||||||
\(584\) | 30.4429 | 1.25974 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.50924 | 0.351514 | ||||||||
\(587\) | −2.81457 | −0.116170 | −0.0580849 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580849 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(588\) | 26.7950 | 1.10501 | ||||||||
\(589\) | 3.05709 | 0.125965 | ||||||||
\(590\) | 0.00338795 | 0.000139480 0 | ||||||||
\(591\) | 19.7850 | 0.813845 | ||||||||
\(592\) | −6.64500 | −0.273108 | ||||||||
\(593\) | −12.7265 | −0.522614 | −0.261307 | − | 0.965256i | \(-0.584154\pi\) | ||||
−0.261307 | + | 0.965256i | \(0.584154\pi\) | |||||||
\(594\) | 7.15126 | 0.293420 | ||||||||
\(595\) | 0.0408626 | 0.00167520 | ||||||||
\(596\) | 17.8631 | 0.731702 | ||||||||
\(597\) | 59.7772 | 2.44652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.9274 | −1.26366 | −0.631830 | − | 0.775107i | \(-0.717696\pi\) | ||||
−0.631830 | + | 0.775107i | \(0.717696\pi\) | |||||||
\(600\) | 39.6895 | 1.62032 | ||||||||
\(601\) | −9.40485 | −0.383632 | −0.191816 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191816 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(602\) | 7.32903 | 0.298709 | ||||||||
\(603\) | 32.2067 | 1.31156 | ||||||||
\(604\) | −12.1045 | −0.492526 | ||||||||
\(605\) | 0.0164567 | 0.000669061 0 | ||||||||
\(606\) | 13.2538 | 0.538398 | ||||||||
\(607\) | 37.6487 | 1.52811 | 0.764056 | − | 0.645150i | \(-0.223205\pi\) | ||||
0.764056 | + | 0.645150i | \(0.223205\pi\) | |||||||
\(608\) | 7.17788 | 0.291102 | ||||||||
\(609\) | 19.1599 | 0.776397 | ||||||||
\(610\) | −0.0573878 | −0.00232356 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −26.4950 | −1.07100 | ||||||||
\(613\) | −8.20597 | −0.331436 | −0.165718 | − | 0.986173i | \(-0.552994\pi\) | ||||
−0.165718 | + | 0.986173i | \(0.552994\pi\) | |||||||
\(614\) | −15.2342 | −0.614804 | ||||||||
\(615\) | −0.417660 | −0.0168417 | ||||||||
\(616\) | −2.09324 | −0.0843390 | ||||||||
\(617\) | 19.7324 | 0.794396 | 0.397198 | − | 0.917733i | \(-0.369983\pi\) | ||||
0.397198 | + | 0.917733i | \(0.369983\pi\) | |||||||
\(618\) | 39.5405 | 1.59055 | ||||||||
\(619\) | −36.5226 | −1.46797 | −0.733983 | − | 0.679168i | \(-0.762341\pi\) | ||||
−0.733983 | + | 0.679168i | \(0.762341\pi\) | |||||||
\(620\) | −0.0573470 | −0.00230311 | ||||||||
\(621\) | 39.3311 | 1.57830 | ||||||||
\(622\) | 11.6244 | 0.466097 | ||||||||
\(623\) | −1.31888 | −0.0528399 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9959 | 0.999838 | ||||||||
\(626\) | 8.99798 | 0.359631 | ||||||||
\(627\) | 3.69023 | 0.147374 | ||||||||
\(628\) | 7.08552 | 0.282743 | ||||||||
\(629\) | −27.8008 | −1.10849 | ||||||||
\(630\) | 0.0614504 | 0.00244824 | ||||||||
\(631\) | −5.64926 | −0.224894 | −0.112447 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112447 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(632\) | 24.6742 | 0.981489 | ||||||||
\(633\) | 23.4597 | 0.932441 | ||||||||
\(634\) | 4.30914 | 0.171138 | ||||||||
\(635\) | −0.00221780 | −8.80107e−5 0 | ||||||||
\(636\) | −19.2097 | −0.761714 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.22507 | 0.246453 | ||||||||
\(639\) | −79.4921 | −3.14466 | ||||||||
\(640\) | −0.153752 | −0.00607757 | ||||||||
\(641\) | −22.5700 | −0.891461 | −0.445730 | − | 0.895167i | \(-0.647056\pi\) | ||||
−0.445730 | + | 0.895167i | \(0.647056\pi\) | |||||||
\(642\) | 10.1881 | 0.402094 | ||||||||
\(643\) | −27.0779 | −1.06785 | −0.533924 | − | 0.845532i | \(-0.679283\pi\) | ||||
−0.533924 | + | 0.845532i | \(0.679283\pi\) | |||||||
\(644\) | −4.73538 | −0.186600 | ||||||||
\(645\) | 0.589253 | 0.0232018 | ||||||||
\(646\) | 2.97706 | 0.117131 | ||||||||
\(647\) | 1.96650 | 0.0773110 | 0.0386555 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386555 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(648\) | −25.1832 | −0.989289 | ||||||||
\(649\) | 0.265214 | 0.0104105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.95771 | 0.233501 | ||||||||
\(652\) | −26.2376 | −1.02754 | ||||||||
\(653\) | −7.55567 | −0.295676 | −0.147838 | − | 0.989012i | \(-0.547231\pi\) | ||||
−0.147838 | + | 0.989012i | \(0.547231\pi\) | |||||||
\(654\) | −40.8746 | −1.59832 | ||||||||
\(655\) | −0.349563 | −0.0136586 | ||||||||
\(656\) | −6.30454 | −0.246151 | ||||||||
\(657\) | −69.9602 | −2.72941 | ||||||||
\(658\) | 7.56308 | 0.294839 | ||||||||
\(659\) | 12.1726 | 0.474178 | 0.237089 | − | 0.971488i | \(-0.423807\pi\) | ||||
0.237089 | + | 0.971488i | \(0.423807\pi\) | |||||||
\(660\) | −0.0692239 | −0.00269454 | ||||||||
\(661\) | −12.8925 | −0.501459 | −0.250729 | − | 0.968057i | \(-0.580670\pi\) | ||||
−0.250729 | + | 0.968057i | \(0.580670\pi\) | |||||||
\(662\) | 5.46740 | 0.212497 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.7022 | 0.492942 | ||||||||
\(665\) | 0.0160135 | 0.000620977 0 | ||||||||
\(666\) | −41.8077 | −1.62002 | ||||||||
\(667\) | 34.2372 | 1.32567 | ||||||||
\(668\) | 21.5798 | 0.834949 | ||||||||
\(669\) | 13.1922 | 0.510039 | ||||||||
\(670\) | 0.0678847 | 0.00262261 | ||||||||
\(671\) | −4.49240 | −0.173427 | ||||||||
\(672\) | 13.9884 | 0.539614 | ||||||||
\(673\) | −13.8175 | −0.532625 | −0.266312 | − | 0.963887i | \(-0.585805\pi\) | ||||
−0.266312 | + | 0.963887i | \(0.585805\pi\) | |||||||
\(674\) | −12.7111 | −0.489612 | ||||||||
\(675\) | −46.0607 | −1.77288 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.9663 | −1.11326 | −0.556632 | − | 0.830759i | \(-0.687907\pi\) | ||||
−0.556632 | + | 0.830759i | \(0.687907\pi\) | |||||||
\(678\) | 2.75033 | 0.105626 | ||||||||
\(679\) | 6.62982 | 0.254429 | ||||||||
\(680\) | −0.135771 | −0.00520659 | ||||||||
\(681\) | 63.3463 | 2.42744 | ||||||||
\(682\) | 1.93567 | 0.0741206 | ||||||||
\(683\) | −15.3612 | −0.587782 | −0.293891 | − | 0.955839i | \(-0.594950\pi\) | ||||
−0.293891 | + | 0.955839i | \(0.594950\pi\) | |||||||
\(684\) | −10.3831 | −0.397006 | ||||||||
\(685\) | 0.176780 | 0.00675443 | ||||||||
\(686\) | −8.23755 | −0.314511 | ||||||||
\(687\) | −38.7727 | −1.47927 | ||||||||
\(688\) | 8.89473 | 0.339108 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.164162 | 0.00624953 | ||||||||
\(691\) | 21.8394 | 0.830811 | 0.415406 | − | 0.909636i | \(-0.363640\pi\) | ||||
0.415406 | + | 0.909636i | \(0.363640\pi\) | |||||||
\(692\) | 10.6782 | 0.405925 | ||||||||
\(693\) | 4.81043 | 0.182733 | ||||||||
\(694\) | 8.74950 | 0.332127 | ||||||||
\(695\) | −0.227078 | −0.00861355 | ||||||||
\(696\) | −63.6613 | −2.41307 | ||||||||
\(697\) | −26.3764 | −0.999076 | ||||||||
\(698\) | 17.6600 | 0.668443 | ||||||||
\(699\) | −41.5905 | −1.57310 | ||||||||
\(700\) | 5.54561 | 0.209604 | ||||||||
\(701\) | 9.49260 | 0.358531 | 0.179265 | − | 0.983801i | \(-0.442628\pi\) | ||||
0.179265 | + | 0.983801i | \(0.442628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.8948 | −0.410904 | ||||||||
\(704\) | 3.04936 | 0.114927 | ||||||||
\(705\) | 0.608070 | 0.0229012 | ||||||||
\(706\) | 2.52152 | 0.0948985 | ||||||||
\(707\) | 4.50226 | 0.169325 | ||||||||
\(708\) | −1.11560 | −0.0419269 | ||||||||
\(709\) | 47.6774 | 1.79056 | 0.895281 | − | 0.445501i | \(-0.146974\pi\) | ||||
0.895281 | + | 0.445501i | \(0.146974\pi\) | |||||||
\(710\) | −0.167552 | −0.00628812 | ||||||||
\(711\) | −56.7033 | −2.12654 | ||||||||
\(712\) | 4.38216 | 0.164228 | ||||||||
\(713\) | 10.6460 | 0.398695 | ||||||||
\(714\) | 5.80175 | 0.217125 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.2825 | 1.13171 | ||||||||
\(717\) | 11.8970 | 0.444303 | ||||||||
\(718\) | 24.4267 | 0.911598 | ||||||||
\(719\) | −46.3833 | −1.72981 | −0.864903 | − | 0.501938i | \(-0.832620\pi\) | ||||
−0.864903 | + | 0.501938i | \(0.832620\pi\) | |||||||
\(720\) | 0.0745781 | 0.00277936 | ||||||||
\(721\) | 13.4318 | 0.500226 | ||||||||
\(722\) | −13.5820 | −0.505468 | ||||||||
\(723\) | 16.6002 | 0.617367 | ||||||||
\(724\) | 16.7186 | 0.621340 | ||||||||
\(725\) | −40.0952 | −1.48910 | ||||||||
\(726\) | 2.33656 | 0.0867178 | ||||||||
\(727\) | 40.9805 | 1.51988 | 0.759942 | − | 0.649991i | \(-0.225228\pi\) | ||||
0.759942 | + | 0.649991i | \(0.225228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.3196 | −0.937763 | ||||||||
\(730\) | −0.147461 | −0.00545777 | ||||||||
\(731\) | 37.2130 | 1.37637 | ||||||||
\(732\) | 18.8969 | 0.698450 | ||||||||
\(733\) | −35.5052 | −1.31141 | −0.655707 | − | 0.755015i | \(-0.727629\pi\) | ||||
−0.655707 | + | 0.755015i | \(0.727629\pi\) | |||||||
\(734\) | 17.9433 | 0.662298 | ||||||||
\(735\) | −0.315545 | −0.0116391 | ||||||||
\(736\) | 24.9962 | 0.921371 | ||||||||
\(737\) | 5.31411 | 0.195748 | ||||||||
\(738\) | −39.6657 | −1.46011 | ||||||||
\(739\) | −38.0716 | −1.40049 | −0.700243 | − | 0.713905i | \(-0.746925\pi\) | ||||
−0.700243 | + | 0.713905i | \(0.746925\pi\) | |||||||
\(740\) | 0.204372 | 0.00751285 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.81367 | 0.103293 | ||||||||
\(743\) | −11.3244 | −0.415451 | −0.207726 | − | 0.978187i | \(-0.566606\pi\) | ||||
−0.207726 | + | 0.978187i | \(0.566606\pi\) | |||||||
\(744\) | −19.7953 | −0.725731 | ||||||||
\(745\) | −0.210361 | −0.00770704 | ||||||||
\(746\) | −6.00990 | −0.220038 | ||||||||
\(747\) | −29.1907 | −1.06803 | ||||||||
\(748\) | −4.37169 | −0.159845 | ||||||||
\(749\) | 3.46088 | 0.126458 | ||||||||
\(750\) | −0.384510 | −0.0140403 | ||||||||
\(751\) | 1.05097 | 0.0383506 | 0.0191753 | − | 0.999816i | \(-0.493896\pi\) | ||||
0.0191753 | + | 0.999816i | \(0.493896\pi\) | |||||||
\(752\) | 9.17877 | 0.334715 | ||||||||
\(753\) | −20.9543 | −0.763617 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.142546 | 0.00518780 | ||||||||
\(756\) | −10.2185 | −0.371644 | ||||||||
\(757\) | 35.2725 | 1.28200 | 0.641001 | − | 0.767540i | \(-0.278520\pi\) | ||||
0.641001 | + | 0.767540i | \(0.278520\pi\) | |||||||
\(758\) | −8.14031 | −0.295669 | ||||||||
\(759\) | 12.8508 | 0.466455 | ||||||||
\(760\) | −0.0532070 | −0.00193002 | ||||||||
\(761\) | 3.55303 | 0.128797 | 0.0643986 | − | 0.997924i | \(-0.479487\pi\) | ||||
0.0643986 | + | 0.997924i | \(0.479487\pi\) | |||||||
\(762\) | −0.314888 | −0.0114072 | ||||||||
\(763\) | −13.8850 | −0.502670 | ||||||||
\(764\) | 16.1829 | 0.585476 | ||||||||
\(765\) | 0.312013 | 0.0112809 | ||||||||
\(766\) | 7.63961 | 0.276030 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −40.1877 | −1.45015 | ||||||||
\(769\) | −6.79345 | −0.244978 | −0.122489 | − | 0.992470i | \(-0.539088\pi\) | ||||
−0.122489 | + | 0.992470i | \(0.539088\pi\) | |||||||
\(770\) | 0.0101393 | 0.000365396 0 | ||||||||
\(771\) | 40.8774 | 1.47216 | ||||||||
\(772\) | 32.7162 | 1.17748 | ||||||||
\(773\) | 47.9248 | 1.72373 | 0.861867 | − | 0.507135i | \(-0.169295\pi\) | ||||
0.861867 | + | 0.507135i | \(0.169295\pi\) | |||||||
\(774\) | 55.9621 | 2.01151 | ||||||||
\(775\) | −12.4675 | −0.447846 | ||||||||
\(776\) | −22.0285 | −0.790776 | ||||||||
\(777\) | −21.2319 | −0.761691 | ||||||||
\(778\) | −18.6581 | −0.668926 | ||||||||
\(779\) | −10.3366 | −0.370346 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1162 | −0.469335 | ||||||||
\(782\) | 10.3673 | 0.370733 | ||||||||
\(783\) | 73.8806 | 2.64028 | ||||||||
\(784\) | −4.76313 | −0.170112 | ||||||||
\(785\) | −0.0834411 | −0.00297814 | ||||||||
\(786\) | −49.6317 | −1.77030 | ||||||||
\(787\) | 48.8325 | 1.74069 | 0.870345 | − | 0.492442i | \(-0.163896\pi\) | ||||
0.870345 | + | 0.492442i | \(0.163896\pi\) | |||||||
\(788\) | −9.18527 | −0.327212 | ||||||||
\(789\) | −31.9045 | −1.13583 | ||||||||
\(790\) | −0.119518 | −0.00425227 | ||||||||
\(791\) | 0.934279 | 0.0332191 | ||||||||
\(792\) | −15.9833 | −0.567941 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.31511 | 0.295092 | ||||||||
\(795\) | 0.226219 | 0.00802316 | ||||||||
\(796\) | −27.7519 | −0.983639 | ||||||||
\(797\) | −0.103318 | −0.00365971 | −0.00182986 | − | 0.999998i | \(-0.500582\pi\) | ||||
−0.00182986 | + | 0.999998i | \(0.500582\pi\) | |||||||
\(798\) | 2.27363 | 0.0804856 | ||||||||
\(799\) | 38.4013 | 1.35854 | ||||||||
\(800\) | −29.2730 | −1.03496 | ||||||||
\(801\) | −10.0705 | −0.355825 | ||||||||
\(802\) | 8.39827 | 0.296553 | ||||||||
\(803\) | −11.5434 | −0.407359 | ||||||||
\(804\) | −22.3534 | −0.788343 | ||||||||
\(805\) | 0.0557652 | 0.00196547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0287407 | 0.00101172 | ||||||||
\(808\) | −14.9594 | −0.526269 | ||||||||
\(809\) | 26.3906 | 0.927844 | 0.463922 | − | 0.885876i | \(-0.346442\pi\) | ||||
0.463922 | + | 0.885876i | \(0.346442\pi\) | |||||||
\(810\) | 0.121984 | 0.00428606 | ||||||||
\(811\) | 34.1395 | 1.19880 | 0.599399 | − | 0.800450i | \(-0.295406\pi\) | ||||
0.599399 | + | 0.800450i | \(0.295406\pi\) | |||||||
\(812\) | −8.89506 | −0.312155 | ||||||||
\(813\) | −11.2942 | −0.396105 | ||||||||
\(814\) | −6.89828 | −0.241785 | ||||||||
\(815\) | 0.308981 | 0.0108231 | ||||||||
\(816\) | 7.04118 | 0.246490 | ||||||||
\(817\) | 14.5833 | 0.510204 | ||||||||
\(818\) | 23.1272 | 0.808625 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.193900 | 0.00677130 | ||||||||
\(821\) | −10.4146 | −0.363472 | −0.181736 | − | 0.983347i | \(-0.558172\pi\) | ||||
−0.181736 | + | 0.983347i | \(0.558172\pi\) | |||||||
\(822\) | 25.0996 | 0.875451 | ||||||||
\(823\) | 42.5770 | 1.48414 | 0.742070 | − | 0.670322i | \(-0.233844\pi\) | ||||
0.742070 | + | 0.670322i | \(0.233844\pi\) | |||||||
\(824\) | −44.6289 | −1.55472 | ||||||||
\(825\) | −15.0496 | −0.523960 | ||||||||
\(826\) | 0.163404 | 0.00568555 | ||||||||
\(827\) | 26.2465 | 0.912680 | 0.456340 | − | 0.889805i | \(-0.349160\pi\) | ||||
0.456340 | + | 0.889805i | \(0.349160\pi\) | |||||||
\(828\) | −36.1578 | −1.25657 | ||||||||
\(829\) | 28.8072 | 1.00051 | 0.500257 | − | 0.865877i | \(-0.333239\pi\) | ||||
0.500257 | + | 0.865877i | \(0.333239\pi\) | |||||||
\(830\) | −0.0615277 | −0.00213566 | ||||||||
\(831\) | 39.6959 | 1.37703 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.9276 | −0.690449 | ||||||||
\(834\) | −32.2410 | −1.11641 | ||||||||
\(835\) | −0.254130 | −0.00879455 | ||||||||
\(836\) | −1.71321 | −0.0592525 | ||||||||
\(837\) | 22.9730 | 0.794063 | ||||||||
\(838\) | 0.260459 | 0.00899741 | ||||||||
\(839\) | 23.6632 | 0.816944 | 0.408472 | − | 0.912771i | \(-0.366062\pi\) | ||||
0.408472 | + | 0.912771i | \(0.366062\pi\) | |||||||
\(840\) | −0.103691 | −0.00357767 | ||||||||
\(841\) | 35.3120 | 1.21766 | ||||||||
\(842\) | 27.1257 | 0.934814 | ||||||||
\(843\) | −74.4338 | −2.56364 | ||||||||
\(844\) | −10.8913 | −0.374894 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 57.7492 | 1.98546 | ||||||||
\(847\) | 0.793722 | 0.0272726 | ||||||||
\(848\) | 3.41476 | 0.117263 | ||||||||
\(849\) | −69.6231 | −2.38946 | ||||||||
\(850\) | −12.1411 | −0.416437 | ||||||||
\(851\) | −37.9398 | −1.30056 | ||||||||
\(852\) | 55.1724 | 1.89017 | ||||||||
\(853\) | −46.2856 | −1.58479 | −0.792394 | − | 0.610009i | \(-0.791166\pi\) | ||||
−0.792394 | + | 0.610009i | \(0.791166\pi\) | |||||||
\(854\) | −2.76786 | −0.0947143 | ||||||||
\(855\) | 0.122274 | 0.00418168 | ||||||||
\(856\) | −11.4992 | −0.393036 | ||||||||
\(857\) | 4.37312 | 0.149383 | 0.0746915 | − | 0.997207i | \(-0.476203\pi\) | ||||
0.0746915 | + | 0.997207i | \(0.476203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.8769 | 1.25822 | 0.629112 | − | 0.777315i | \(-0.283419\pi\) | ||||
0.629112 | + | 0.777315i | \(0.283419\pi\) | |||||||
\(860\) | −0.273563 | −0.00932843 | ||||||||
\(861\) | −20.1441 | −0.686509 | ||||||||
\(862\) | 12.3224 | 0.419702 | ||||||||
\(863\) | 8.80418 | 0.299698 | 0.149849 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149849 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(864\) | 53.9394 | 1.83505 | ||||||||
\(865\) | −0.125750 | −0.00427562 | ||||||||
\(866\) | −7.44934 | −0.253139 | ||||||||
\(867\) | −21.7132 | −0.737418 | ||||||||
\(868\) | −2.76590 | −0.0938807 | ||||||||
\(869\) | −9.35606 | −0.317383 | ||||||||
\(870\) | 0.308366 | 0.0104546 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 46.1347 | 1.56232 | ||||||||
\(873\) | 50.6231 | 1.71333 | ||||||||
\(874\) | 4.06280 | 0.137426 | ||||||||
\(875\) | −0.130617 | −0.00441566 | ||||||||
\(876\) | 48.5567 | 1.64058 | ||||||||
\(877\) | 0.0731659 | 0.00247064 | 0.00123532 | − | 0.999999i | \(-0.499607\pi\) | ||||
0.00123532 | + | 0.999999i | \(0.499607\pi\) | |||||||
\(878\) | 6.03858 | 0.203792 | ||||||||
\(879\) | 32.9967 | 1.11295 | ||||||||
\(880\) | 0.0123054 | 0.000414815 0 | ||||||||
\(881\) | 22.5405 | 0.759407 | 0.379704 | − | 0.925108i | \(-0.376026\pi\) | ||||
0.379704 | + | 0.925108i | \(0.376026\pi\) | |||||||
\(882\) | −29.9677 | −1.00907 | ||||||||
\(883\) | −35.3920 | −1.19104 | −0.595518 | − | 0.803342i | \(-0.703053\pi\) | ||||
−0.595518 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0131376 | 0.000441617 0 | ||||||||
\(886\) | −17.8906 | −0.601046 | ||||||||
\(887\) | 25.3897 | 0.852502 | 0.426251 | − | 0.904605i | \(-0.359834\pi\) | ||||
0.426251 | + | 0.904605i | \(0.359834\pi\) | |||||||
\(888\) | 70.5459 | 2.36737 | ||||||||
\(889\) | −0.106966 | −0.00358754 | ||||||||
\(890\) | −0.0212265 | −0.000711515 0 | ||||||||
\(891\) | 9.54904 | 0.319905 | ||||||||
\(892\) | −6.12453 | −0.205064 | ||||||||
\(893\) | 15.0490 | 0.503595 | ||||||||
\(894\) | −29.8675 | −0.998919 | ||||||||
\(895\) | −0.356615 | −0.0119203 | ||||||||
\(896\) | −7.41558 | −0.247737 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6646 | 0.756327 | ||||||||
\(899\) | 19.9977 | 0.666959 | ||||||||
\(900\) | 42.3445 | 1.41148 | ||||||||
\(901\) | 14.2864 | 0.475948 | ||||||||
\(902\) | −6.54484 | −0.217919 | ||||||||
\(903\) | 28.4202 | 0.945764 | ||||||||
\(904\) | −3.10427 | −0.103246 | ||||||||
\(905\) | −0.196882 | −0.00654460 | ||||||||
\(906\) | 20.2390 | 0.672397 | ||||||||
\(907\) | 16.0891 | 0.534228 | 0.267114 | − | 0.963665i | \(-0.413930\pi\) | ||||
0.267114 | + | 0.963665i | \(0.413930\pi\) | |||||||
\(908\) | −29.4088 | −0.975966 | ||||||||
\(909\) | 34.3778 | 1.14024 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6061 | −0.351396 | −0.175698 | − | 0.984444i | \(-0.556218\pi\) | ||||
−0.175698 | + | 0.984444i | \(0.556218\pi\) | |||||||
\(912\) | 2.75934 | 0.0913710 | ||||||||
\(913\) | −4.81647 | −0.159402 | ||||||||
\(914\) | −24.2123 | −0.800872 | ||||||||
\(915\) | −0.222536 | −0.00735680 | ||||||||
\(916\) | 18.0004 | 0.594751 | ||||||||
\(917\) | −16.8597 | −0.556757 | ||||||||
\(918\) | 22.3716 | 0.738373 | ||||||||
\(919\) | −0.0784038 | −0.00258630 | −0.00129315 | − | 0.999999i | \(-0.500412\pi\) | ||||
−0.00129315 | + | 0.999999i | \(0.500412\pi\) | |||||||
\(920\) | −0.185287 | −0.00610874 | ||||||||
\(921\) | −59.0746 | −1.94657 | ||||||||
\(922\) | −29.2405 | −0.962985 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.33873 | −0.109836 | ||||||||
\(925\) | 44.4313 | 1.46089 | ||||||||
\(926\) | −0.767632 | −0.0252260 | ||||||||
\(927\) | 102.561 | 3.36853 | ||||||||
\(928\) | 46.9534 | 1.54132 | ||||||||
\(929\) | −5.70834 | −0.187284 | −0.0936422 | − | 0.995606i | \(-0.529851\pi\) | ||||
−0.0936422 | + | 0.995606i | \(0.529851\pi\) | |||||||
\(930\) | 0.0958855 | 0.00314421 | ||||||||
\(931\) | −7.80935 | −0.255941 | ||||||||
\(932\) | 19.3086 | 0.632473 | ||||||||
\(933\) | 45.0766 | 1.47574 | ||||||||
\(934\) | 8.93891 | 0.292490 | ||||||||
\(935\) | 0.0514822 | 0.00168365 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.6681 | 1.81860 | 0.909299 | − | 0.416143i | \(-0.136619\pi\) | ||||
0.909299 | + | 0.416143i | \(0.136619\pi\) | |||||||
\(938\) | 3.27414 | 0.106904 | ||||||||
\(939\) | 34.8919 | 1.13865 | ||||||||
\(940\) | −0.282299 | −0.00920759 | ||||||||
\(941\) | 17.4945 | 0.570303 | 0.285151 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285151 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(942\) | −11.8471 | −0.386001 | ||||||||
\(943\) | −35.9959 | −1.17219 | ||||||||
\(944\) | 0.198312 | 0.00645450 | ||||||||
\(945\) | 0.120336 | 0.00391453 | ||||||||
\(946\) | 9.23375 | 0.300215 | ||||||||
\(947\) | 38.2431 | 1.24273 | 0.621367 | − | 0.783520i | \(-0.286578\pi\) | ||||
0.621367 | + | 0.783520i | \(0.286578\pi\) | |||||||
\(948\) | 39.3556 | 1.27821 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.75795 | −0.154368 | ||||||||
\(951\) | 16.7098 | 0.541852 | ||||||||
\(952\) | −6.54837 | −0.212234 | ||||||||
\(953\) | −55.0966 | −1.78476 | −0.892378 | − | 0.451289i | \(-0.850964\pi\) | ||||
−0.892378 | + | 0.451289i | \(0.850964\pi\) | |||||||
\(954\) | 21.4843 | 0.695580 | ||||||||
\(955\) | −0.190574 | −0.00616684 | ||||||||
\(956\) | −5.52326 | −0.178635 | ||||||||
\(957\) | 24.1393 | 0.780312 | ||||||||
\(958\) | −7.07700 | −0.228647 | ||||||||
\(959\) | 8.52627 | 0.275328 | ||||||||
\(960\) | 0.151053 | 0.00487523 | ||||||||
\(961\) | −24.7818 | −0.799412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.4262 | 0.851571 | ||||||||
\(964\) | −7.70671 | −0.248216 | ||||||||
\(965\) | −0.385276 | −0.0124025 | ||||||||
\(966\) | 7.91766 | 0.254747 | ||||||||
\(967\) | 25.7894 | 0.829330 | 0.414665 | − | 0.909974i | \(-0.363899\pi\) | ||||
0.414665 | + | 0.909974i | \(0.363899\pi\) | |||||||
\(968\) | −2.63725 | −0.0847643 | ||||||||
\(969\) | 11.5443 | 0.370856 | ||||||||
\(970\) | 0.106703 | 0.00342601 | ||||||||
\(971\) | 42.9387 | 1.37797 | 0.688985 | − | 0.724776i | \(-0.258057\pi\) | ||||
0.688985 | + | 0.724776i | \(0.258057\pi\) | |||||||
\(972\) | −1.54482 | −0.0495501 | ||||||||
\(973\) | −10.9522 | −0.351110 | ||||||||
\(974\) | 14.4528 | 0.463099 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.35916 | −0.107524 | ||||||||
\(977\) | 42.1485 | 1.34845 | 0.674225 | − | 0.738526i | \(-0.264478\pi\) | ||||
0.674225 | + | 0.738526i | \(0.264478\pi\) | |||||||
\(978\) | 43.8698 | 1.40280 | ||||||||
\(979\) | −1.66164 | −0.0531063 | ||||||||
\(980\) | 0.146493 | 0.00467956 | ||||||||
\(981\) | −106.021 | −3.38499 | ||||||||
\(982\) | −19.4199 | −0.619713 | ||||||||
\(983\) | −51.7672 | −1.65112 | −0.825559 | − | 0.564316i | \(-0.809140\pi\) | ||||
−0.825559 | + | 0.564316i | \(0.809140\pi\) | |||||||
\(984\) | 66.9314 | 2.13370 | ||||||||
\(985\) | 0.108168 | 0.00344653 | ||||||||
\(986\) | 19.4741 | 0.620183 | ||||||||
\(987\) | 29.3277 | 0.933512 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.7846 | 1.61486 | ||||||||
\(990\) | 0.0774207 | 0.00246059 | ||||||||
\(991\) | 33.1031 | 1.05155 | 0.525777 | − | 0.850622i | \(-0.323775\pi\) | ||||
0.525777 | + | 0.850622i | \(0.323775\pi\) | |||||||
\(992\) | 14.6001 | 0.463552 | ||||||||
\(993\) | 21.2012 | 0.672801 | ||||||||
\(994\) | −8.08118 | −0.256319 | ||||||||
\(995\) | 0.326814 | 0.0103607 | ||||||||
\(996\) | 20.2601 | 0.641967 | ||||||||
\(997\) | −10.4149 | −0.329842 | −0.164921 | − | 0.986307i | \(-0.552737\pi\) | ||||
−0.164921 | + | 0.986307i | \(0.552737\pi\) | |||||||
\(998\) | 4.70373 | 0.148894 | ||||||||
\(999\) | −81.8704 | −2.59027 |
(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 | 1859.2.a.t.1.13 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.9 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.9 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.13 | yes | 21 | 1.1 | even | 1 | trivial |