Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(3.23048\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.42840 | 0.638798 | 0.319399 | − | 0.947620i | \(-0.396519\pi\) | ||||
0.319399 | + | 0.947620i | \(0.396519\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.28162 | −0.862372 | −0.431186 | − | 0.902263i | \(-0.641905\pi\) | ||||
−0.431186 | + | 0.902263i | \(0.641905\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.42840 | −0.451698 | ||||||||
\(11\) | −0.378203 | −0.114033 | −0.0570163 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570163 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.28162 | 0.609789 | ||||||||
\(15\) | 1.42840 | 0.368810 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.07828 | −0.261521 | −0.130761 | − | 0.991414i | \(-0.541742\pi\) | ||||
−0.130761 | + | 0.991414i | \(0.541742\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.85408 | −1.57243 | −0.786217 | − | 0.617950i | \(-0.787963\pi\) | ||||
−0.786217 | + | 0.617950i | \(0.787963\pi\) | |||||||
\(20\) | 1.42840 | 0.319399 | ||||||||
\(21\) | −2.28162 | −0.497891 | ||||||||
\(22\) | 0.378203 | 0.0806332 | ||||||||
\(23\) | −1.64807 | −0.343647 | −0.171824 | − | 0.985128i | \(-0.554966\pi\) | ||||
−0.171824 | + | 0.985128i | \(0.554966\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.95968 | −0.591937 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.28162 | −0.431186 | ||||||||
\(29\) | −5.09337 | −0.945816 | −0.472908 | − | 0.881112i | \(-0.656796\pi\) | ||||
−0.472908 | + | 0.881112i | \(0.656796\pi\) | |||||||
\(30\) | −1.42840 | −0.260788 | ||||||||
\(31\) | 10.3699 | 1.86248 | 0.931240 | − | 0.364406i | \(-0.118728\pi\) | ||||
0.931240 | + | 0.364406i | \(0.118728\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.378203 | −0.0658367 | ||||||||
\(34\) | 1.07828 | 0.184923 | ||||||||
\(35\) | −3.25906 | −0.550881 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.76199 | 1.60486 | 0.802430 | − | 0.596746i | \(-0.203540\pi\) | ||||
0.802430 | + | 0.596746i | \(0.203540\pi\) | |||||||
\(38\) | 6.85408 | 1.11188 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.42840 | −0.225849 | ||||||||
\(41\) | 0.952622 | 0.148775 | 0.0743873 | − | 0.997229i | \(-0.476300\pi\) | ||||
0.0743873 | + | 0.997229i | \(0.476300\pi\) | |||||||
\(42\) | 2.28162 | 0.352062 | ||||||||
\(43\) | 2.65892 | 0.405482 | 0.202741 | − | 0.979232i | \(-0.435015\pi\) | ||||
0.202741 | + | 0.979232i | \(0.435015\pi\) | |||||||
\(44\) | −0.378203 | −0.0570163 | ||||||||
\(45\) | 1.42840 | 0.212933 | ||||||||
\(46\) | 1.64807 | 0.242995 | ||||||||
\(47\) | 7.38329 | 1.07696 | 0.538482 | − | 0.842637i | \(-0.318998\pi\) | ||||
0.538482 | + | 0.842637i | \(0.318998\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.79420 | −0.256315 | ||||||||
\(50\) | 2.95968 | 0.418563 | ||||||||
\(51\) | −1.07828 | −0.150989 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 7.79122 | 1.07021 | 0.535103 | − | 0.844787i | \(-0.320273\pi\) | ||||
0.535103 | + | 0.844787i | \(0.320273\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.540224 | −0.0728438 | ||||||||
\(56\) | 2.28162 | 0.304894 | ||||||||
\(57\) | −6.85408 | −0.907846 | ||||||||
\(58\) | 5.09337 | 0.668793 | ||||||||
\(59\) | −0.731526 | −0.0952366 | −0.0476183 | − | 0.998866i | \(-0.515163\pi\) | ||||
−0.0476183 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(60\) | 1.42840 | 0.184405 | ||||||||
\(61\) | −4.05568 | −0.519277 | −0.259638 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259638 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(62\) | −10.3699 | −1.31697 | ||||||||
\(63\) | −2.28162 | −0.287457 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.42840 | 0.177171 | ||||||||
\(66\) | 0.378203 | 0.0465536 | ||||||||
\(67\) | −9.03946 | −1.10435 | −0.552173 | − | 0.833730i | \(-0.686201\pi\) | ||||
−0.552173 | + | 0.833730i | \(0.686201\pi\) | |||||||
\(68\) | −1.07828 | −0.130761 | ||||||||
\(69\) | −1.64807 | −0.198405 | ||||||||
\(70\) | 3.25906 | 0.389532 | ||||||||
\(71\) | 3.02171 | 0.358611 | 0.179306 | − | 0.983793i | \(-0.442615\pi\) | ||||
0.179306 | + | 0.983793i | \(0.442615\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.2549 | −1.31728 | −0.658641 | − | 0.752457i | \(-0.728868\pi\) | ||||
−0.658641 | + | 0.752457i | \(0.728868\pi\) | |||||||
\(74\) | −9.76199 | −1.13481 | ||||||||
\(75\) | −2.95968 | −0.341755 | ||||||||
\(76\) | −6.85408 | −0.786217 | ||||||||
\(77\) | 0.862916 | 0.0983384 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 5.25463 | 0.591193 | 0.295596 | − | 0.955313i | \(-0.404482\pi\) | ||||
0.295596 | + | 0.955313i | \(0.404482\pi\) | |||||||
\(80\) | 1.42840 | 0.159700 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.952622 | −0.105200 | ||||||||
\(83\) | −11.2812 | −1.23827 | −0.619136 | − | 0.785284i | \(-0.712517\pi\) | ||||
−0.619136 | + | 0.785284i | \(0.712517\pi\) | |||||||
\(84\) | −2.28162 | −0.248945 | ||||||||
\(85\) | −1.54021 | −0.167059 | ||||||||
\(86\) | −2.65892 | −0.286719 | ||||||||
\(87\) | −5.09337 | −0.546067 | ||||||||
\(88\) | 0.378203 | 0.0403166 | ||||||||
\(89\) | −5.26838 | −0.558447 | −0.279223 | − | 0.960226i | \(-0.590077\pi\) | ||||
−0.279223 | + | 0.960226i | \(0.590077\pi\) | |||||||
\(90\) | −1.42840 | −0.150566 | ||||||||
\(91\) | −2.28162 | −0.239179 | ||||||||
\(92\) | −1.64807 | −0.171824 | ||||||||
\(93\) | 10.3699 | 1.07530 | ||||||||
\(94\) | −7.38329 | −0.761528 | ||||||||
\(95\) | −9.79035 | −1.00447 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.0419 | −1.01960 | −0.509802 | − | 0.860292i | \(-0.670281\pi\) | ||||
−0.509802 | + | 0.860292i | \(0.670281\pi\) | |||||||
\(98\) | 1.79420 | 0.181242 | ||||||||
\(99\) | −0.378203 | −0.0380108 | ||||||||
\(100\) | −2.95968 | −0.295968 | ||||||||
\(101\) | 6.99307 | 0.695836 | 0.347918 | − | 0.937525i | \(-0.386889\pi\) | ||||
0.347918 | + | 0.937525i | \(0.386889\pi\) | |||||||
\(102\) | 1.07828 | 0.106766 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −3.25906 | −0.318052 | ||||||||
\(106\) | −7.79122 | −0.756751 | ||||||||
\(107\) | −10.4990 | −1.01497 | −0.507487 | − | 0.861660i | \(-0.669425\pi\) | ||||
−0.507487 | + | 0.861660i | \(0.669425\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.860752 | 0.0824450 | 0.0412225 | − | 0.999150i | \(-0.486875\pi\) | ||||
0.0412225 | + | 0.999150i | \(0.486875\pi\) | |||||||
\(110\) | 0.540224 | 0.0515083 | ||||||||
\(111\) | 9.76199 | 0.926567 | ||||||||
\(112\) | −2.28162 | −0.215593 | ||||||||
\(113\) | −2.84635 | −0.267762 | −0.133881 | − | 0.990997i | \(-0.542744\pi\) | ||||
−0.133881 | + | 0.990997i | \(0.542744\pi\) | |||||||
\(114\) | 6.85408 | 0.641944 | ||||||||
\(115\) | −2.35410 | −0.219521 | ||||||||
\(116\) | −5.09337 | −0.472908 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0.731526 | 0.0673424 | ||||||||
\(119\) | 2.46023 | 0.225528 | ||||||||
\(120\) | −1.42840 | −0.130394 | ||||||||
\(121\) | −10.8570 | −0.986997 | ||||||||
\(122\) | 4.05568 | 0.367184 | ||||||||
\(123\) | 0.952622 | 0.0858951 | ||||||||
\(124\) | 10.3699 | 0.931240 | ||||||||
\(125\) | −11.3696 | −1.01693 | ||||||||
\(126\) | 2.28162 | 0.203263 | ||||||||
\(127\) | −1.00129 | −0.0888504 | −0.0444252 | − | 0.999013i | \(-0.514146\pi\) | ||||
−0.0444252 | + | 0.999013i | \(0.514146\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.65892 | 0.234105 | ||||||||
\(130\) | −1.42840 | −0.125279 | ||||||||
\(131\) | −7.05133 | −0.616078 | −0.308039 | − | 0.951374i | \(-0.599673\pi\) | ||||
−0.308039 | + | 0.951374i | \(0.599673\pi\) | |||||||
\(132\) | −0.378203 | −0.0329183 | ||||||||
\(133\) | 15.6384 | 1.35602 | ||||||||
\(134\) | 9.03946 | 0.780890 | ||||||||
\(135\) | 1.42840 | 0.122937 | ||||||||
\(136\) | 1.07828 | 0.0924617 | ||||||||
\(137\) | −6.33167 | −0.540951 | −0.270476 | − | 0.962727i | \(-0.587181\pi\) | ||||
−0.270476 | + | 0.962727i | \(0.587181\pi\) | |||||||
\(138\) | 1.64807 | 0.140293 | ||||||||
\(139\) | −15.7204 | −1.33339 | −0.666693 | − | 0.745332i | \(-0.732291\pi\) | ||||
−0.666693 | + | 0.745332i | \(0.732291\pi\) | |||||||
\(140\) | −3.25906 | −0.275441 | ||||||||
\(141\) | 7.38329 | 0.621785 | ||||||||
\(142\) | −3.02171 | −0.253577 | ||||||||
\(143\) | −0.378203 | −0.0316269 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.27536 | −0.604185 | ||||||||
\(146\) | 11.2549 | 0.931459 | ||||||||
\(147\) | −1.79420 | −0.147984 | ||||||||
\(148\) | 9.76199 | 0.802430 | ||||||||
\(149\) | −10.5290 | −0.862570 | −0.431285 | − | 0.902216i | \(-0.641940\pi\) | ||||
−0.431285 | + | 0.902216i | \(0.641940\pi\) | |||||||
\(150\) | 2.95968 | 0.241657 | ||||||||
\(151\) | −5.65260 | −0.460002 | −0.230001 | − | 0.973190i | \(-0.573873\pi\) | ||||
−0.230001 | + | 0.973190i | \(0.573873\pi\) | |||||||
\(152\) | 6.85408 | 0.555940 | ||||||||
\(153\) | −1.07828 | −0.0871737 | ||||||||
\(154\) | −0.862916 | −0.0695358 | ||||||||
\(155\) | 14.8123 | 1.18975 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 13.3002 | 1.06147 | 0.530736 | − | 0.847537i | \(-0.321916\pi\) | ||||
0.530736 | + | 0.847537i | \(0.321916\pi\) | |||||||
\(158\) | −5.25463 | −0.418036 | ||||||||
\(159\) | 7.79122 | 0.617884 | ||||||||
\(160\) | −1.42840 | −0.112925 | ||||||||
\(161\) | 3.76028 | 0.296352 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −6.40325 | −0.501542 | −0.250771 | − | 0.968046i | \(-0.580684\pi\) | ||||
−0.250771 | + | 0.968046i | \(0.580684\pi\) | |||||||
\(164\) | 0.952622 | 0.0743873 | ||||||||
\(165\) | −0.540224 | −0.0420564 | ||||||||
\(166\) | 11.2812 | 0.875591 | ||||||||
\(167\) | 4.33757 | 0.335651 | 0.167826 | − | 0.985817i | \(-0.446325\pi\) | ||||
0.167826 | + | 0.985817i | \(0.446325\pi\) | |||||||
\(168\) | 2.28162 | 0.176031 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.54021 | 0.118129 | ||||||||
\(171\) | −6.85408 | −0.524145 | ||||||||
\(172\) | 2.65892 | 0.202741 | ||||||||
\(173\) | −9.30906 | −0.707755 | −0.353878 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353878 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(174\) | 5.09337 | 0.386128 | ||||||||
\(175\) | 6.75288 | 0.510470 | ||||||||
\(176\) | −0.378203 | −0.0285081 | ||||||||
\(177\) | −0.731526 | −0.0549849 | ||||||||
\(178\) | 5.26838 | 0.394882 | ||||||||
\(179\) | 6.22986 | 0.465642 | 0.232821 | − | 0.972520i | \(-0.425204\pi\) | ||||
0.232821 | + | 0.972520i | \(0.425204\pi\) | |||||||
\(180\) | 1.42840 | 0.106466 | ||||||||
\(181\) | −5.27430 | −0.392035 | −0.196018 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196018 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(182\) | 2.28162 | 0.169125 | ||||||||
\(183\) | −4.05568 | −0.299805 | ||||||||
\(184\) | 1.64807 | 0.121498 | ||||||||
\(185\) | 13.9440 | 1.02518 | ||||||||
\(186\) | −10.3699 | −0.760354 | ||||||||
\(187\) | 0.407809 | 0.0298219 | ||||||||
\(188\) | 7.38329 | 0.538482 | ||||||||
\(189\) | −2.28162 | −0.165964 | ||||||||
\(190\) | 9.79035 | 0.710266 | ||||||||
\(191\) | −2.75574 | −0.199399 | −0.0996993 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996993 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −6.08283 | −0.437852 | −0.218926 | − | 0.975742i | \(-0.570255\pi\) | ||||
−0.218926 | + | 0.975742i | \(0.570255\pi\) | |||||||
\(194\) | 10.0419 | 0.720969 | ||||||||
\(195\) | 1.42840 | 0.102290 | ||||||||
\(196\) | −1.79420 | −0.128157 | ||||||||
\(197\) | −10.1965 | −0.726468 | −0.363234 | − | 0.931698i | \(-0.618328\pi\) | ||||
−0.363234 | + | 0.931698i | \(0.618328\pi\) | |||||||
\(198\) | 0.378203 | 0.0268777 | ||||||||
\(199\) | 1.25424 | 0.0889107 | 0.0444554 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444554 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(200\) | 2.95968 | 0.209281 | ||||||||
\(201\) | −9.03946 | −0.637594 | ||||||||
\(202\) | −6.99307 | −0.492030 | ||||||||
\(203\) | 11.6211 | 0.815645 | ||||||||
\(204\) | −1.07828 | −0.0754947 | ||||||||
\(205\) | 1.36072 | 0.0950369 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −1.64807 | −0.114549 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 2.59224 | 0.179309 | ||||||||
\(210\) | 3.25906 | 0.224896 | ||||||||
\(211\) | −16.2651 | −1.11973 | −0.559867 | − | 0.828582i | \(-0.689148\pi\) | ||||
−0.559867 | + | 0.828582i | \(0.689148\pi\) | |||||||
\(212\) | 7.79122 | 0.535103 | ||||||||
\(213\) | 3.02171 | 0.207044 | ||||||||
\(214\) | 10.4990 | 0.717695 | ||||||||
\(215\) | 3.79799 | 0.259021 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −23.6601 | −1.60615 | ||||||||
\(218\) | −0.860752 | −0.0582974 | ||||||||
\(219\) | −11.2549 | −0.760533 | ||||||||
\(220\) | −0.540224 | −0.0364219 | ||||||||
\(221\) | −1.07828 | −0.0725329 | ||||||||
\(222\) | −9.76199 | −0.655182 | ||||||||
\(223\) | −21.2527 | −1.42319 | −0.711593 | − | 0.702592i | \(-0.752026\pi\) | ||||
−0.711593 | + | 0.702592i | \(0.752026\pi\) | |||||||
\(224\) | 2.28162 | 0.152447 | ||||||||
\(225\) | −2.95968 | −0.197312 | ||||||||
\(226\) | 2.84635 | 0.189336 | ||||||||
\(227\) | −25.4900 | −1.69183 | −0.845914 | − | 0.533319i | \(-0.820945\pi\) | ||||
−0.845914 | + | 0.533319i | \(0.820945\pi\) | |||||||
\(228\) | −6.85408 | −0.453923 | ||||||||
\(229\) | 25.8974 | 1.71135 | 0.855674 | − | 0.517515i | \(-0.173143\pi\) | ||||
0.855674 | + | 0.517515i | \(0.173143\pi\) | |||||||
\(230\) | 2.35410 | 0.155225 | ||||||||
\(231\) | 0.862916 | 0.0567757 | ||||||||
\(232\) | 5.09337 | 0.334396 | ||||||||
\(233\) | −0.935399 | −0.0612800 | −0.0306400 | − | 0.999530i | \(-0.509755\pi\) | ||||
−0.0306400 | + | 0.999530i | \(0.509755\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 10.5463 | 0.687962 | ||||||||
\(236\) | −0.731526 | −0.0476183 | ||||||||
\(237\) | 5.25463 | 0.341325 | ||||||||
\(238\) | −2.46023 | −0.159473 | ||||||||
\(239\) | −7.83371 | −0.506720 | −0.253360 | − | 0.967372i | \(-0.581536\pi\) | ||||
−0.253360 | + | 0.967372i | \(0.581536\pi\) | |||||||
\(240\) | 1.42840 | 0.0922026 | ||||||||
\(241\) | 23.8091 | 1.53368 | 0.766841 | − | 0.641837i | \(-0.221827\pi\) | ||||
0.766841 | + | 0.641837i | \(0.221827\pi\) | |||||||
\(242\) | 10.8570 | 0.697912 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.05568 | −0.259638 | ||||||||
\(245\) | −2.56284 | −0.163734 | ||||||||
\(246\) | −0.952622 | −0.0607370 | ||||||||
\(247\) | −6.85408 | −0.436115 | ||||||||
\(248\) | −10.3699 | −0.658486 | ||||||||
\(249\) | −11.2812 | −0.714917 | ||||||||
\(250\) | 11.3696 | 0.719076 | ||||||||
\(251\) | −7.47104 | −0.471568 | −0.235784 | − | 0.971805i | \(-0.575766\pi\) | ||||
−0.235784 | + | 0.971805i | \(0.575766\pi\) | |||||||
\(252\) | −2.28162 | −0.143729 | ||||||||
\(253\) | 0.623307 | 0.0391870 | ||||||||
\(254\) | 1.00129 | 0.0628267 | ||||||||
\(255\) | −1.54021 | −0.0964517 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.3198 | −1.82892 | −0.914459 | − | 0.404679i | \(-0.867383\pi\) | ||||
−0.914459 | + | 0.404679i | \(0.867383\pi\) | |||||||
\(258\) | −2.65892 | −0.165537 | ||||||||
\(259\) | −22.2732 | −1.38399 | ||||||||
\(260\) | 1.42840 | 0.0885854 | ||||||||
\(261\) | −5.09337 | −0.315272 | ||||||||
\(262\) | 7.05133 | 0.435633 | ||||||||
\(263\) | −25.4645 | −1.57021 | −0.785106 | − | 0.619362i | \(-0.787391\pi\) | ||||
−0.785106 | + | 0.619362i | \(0.787391\pi\) | |||||||
\(264\) | 0.378203 | 0.0232768 | ||||||||
\(265\) | 11.1290 | 0.683646 | ||||||||
\(266\) | −15.6384 | −0.958853 | ||||||||
\(267\) | −5.26838 | −0.322420 | ||||||||
\(268\) | −9.03946 | −0.552173 | ||||||||
\(269\) | −23.3373 | −1.42290 | −0.711451 | − | 0.702736i | \(-0.751961\pi\) | ||||
−0.711451 | + | 0.702736i | \(0.751961\pi\) | |||||||
\(270\) | −1.42840 | −0.0869294 | ||||||||
\(271\) | −6.22070 | −0.377881 | −0.188940 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188940 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(272\) | −1.07828 | −0.0653803 | ||||||||
\(273\) | −2.28162 | −0.138090 | ||||||||
\(274\) | 6.33167 | 0.382510 | ||||||||
\(275\) | 1.11936 | 0.0675001 | ||||||||
\(276\) | −1.64807 | −0.0992024 | ||||||||
\(277\) | 10.9355 | 0.657053 | 0.328526 | − | 0.944495i | \(-0.393448\pi\) | ||||
0.328526 | + | 0.944495i | \(0.393448\pi\) | |||||||
\(278\) | 15.7204 | 0.942846 | ||||||||
\(279\) | 10.3699 | 0.620827 | ||||||||
\(280\) | 3.25906 | 0.194766 | ||||||||
\(281\) | 16.4408 | 0.980778 | 0.490389 | − | 0.871504i | \(-0.336855\pi\) | ||||
0.490389 | + | 0.871504i | \(0.336855\pi\) | |||||||
\(282\) | −7.38329 | −0.439668 | ||||||||
\(283\) | 17.3544 | 1.03161 | 0.515805 | − | 0.856706i | \(-0.327493\pi\) | ||||
0.515805 | + | 0.856706i | \(0.327493\pi\) | |||||||
\(284\) | 3.02171 | 0.179306 | ||||||||
\(285\) | −9.79035 | −0.579930 | ||||||||
\(286\) | 0.378203 | 0.0223636 | ||||||||
\(287\) | −2.17352 | −0.128299 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.8373 | −0.931607 | ||||||||
\(290\) | 7.27536 | 0.427224 | ||||||||
\(291\) | −10.0419 | −0.588669 | ||||||||
\(292\) | −11.2549 | −0.658641 | ||||||||
\(293\) | 9.58413 | 0.559911 | 0.279956 | − | 0.960013i | \(-0.409680\pi\) | ||||
0.279956 | + | 0.960013i | \(0.409680\pi\) | |||||||
\(294\) | 1.79420 | 0.104640 | ||||||||
\(295\) | −1.04491 | −0.0608369 | ||||||||
\(296\) | −9.76199 | −0.567404 | ||||||||
\(297\) | −0.378203 | −0.0219456 | ||||||||
\(298\) | 10.5290 | 0.609929 | ||||||||
\(299\) | −1.64807 | −0.0953106 | ||||||||
\(300\) | −2.95968 | −0.170877 | ||||||||
\(301\) | −6.06665 | −0.349676 | ||||||||
\(302\) | 5.65260 | 0.325271 | ||||||||
\(303\) | 6.99307 | 0.401741 | ||||||||
\(304\) | −6.85408 | −0.393109 | ||||||||
\(305\) | −5.79312 | −0.331713 | ||||||||
\(306\) | 1.07828 | 0.0616411 | ||||||||
\(307\) | −12.5014 | −0.713495 | −0.356747 | − | 0.934201i | \(-0.616114\pi\) | ||||
−0.356747 | + | 0.934201i | \(0.616114\pi\) | |||||||
\(308\) | 0.862916 | 0.0491692 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −14.8123 | −0.841279 | ||||||||
\(311\) | −26.1921 | −1.48522 | −0.742609 | − | 0.669725i | \(-0.766412\pi\) | ||||
−0.742609 | + | 0.669725i | \(0.766412\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 7.61225 | 0.430270 | 0.215135 | − | 0.976584i | \(-0.430981\pi\) | ||||
0.215135 | + | 0.976584i | \(0.430981\pi\) | |||||||
\(314\) | −13.3002 | −0.750574 | ||||||||
\(315\) | −3.25906 | −0.183627 | ||||||||
\(316\) | 5.25463 | 0.295596 | ||||||||
\(317\) | 7.73483 | 0.434431 | 0.217216 | − | 0.976124i | \(-0.430303\pi\) | ||||
0.217216 | + | 0.976124i | \(0.430303\pi\) | |||||||
\(318\) | −7.79122 | −0.436910 | ||||||||
\(319\) | 1.92633 | 0.107854 | ||||||||
\(320\) | 1.42840 | 0.0798498 | ||||||||
\(321\) | −10.4990 | −0.585995 | ||||||||
\(322\) | −3.76028 | −0.209552 | ||||||||
\(323\) | 7.39062 | 0.411225 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.95968 | −0.164174 | ||||||||
\(326\) | 6.40325 | 0.354643 | ||||||||
\(327\) | 0.860752 | 0.0475997 | ||||||||
\(328\) | −0.952622 | −0.0525998 | ||||||||
\(329\) | −16.8459 | −0.928743 | ||||||||
\(330\) | 0.540224 | 0.0297383 | ||||||||
\(331\) | 25.0994 | 1.37959 | 0.689794 | − | 0.724006i | \(-0.257701\pi\) | ||||
0.689794 | + | 0.724006i | \(0.257701\pi\) | |||||||
\(332\) | −11.2812 | −0.619136 | ||||||||
\(333\) | 9.76199 | 0.534954 | ||||||||
\(334\) | −4.33757 | −0.237341 | ||||||||
\(335\) | −12.9119 | −0.705454 | ||||||||
\(336\) | −2.28162 | −0.124473 | ||||||||
\(337\) | −13.9072 | −0.757576 | −0.378788 | − | 0.925483i | \(-0.623659\pi\) | ||||
−0.378788 | + | 0.925483i | \(0.623659\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −2.84635 | −0.154592 | ||||||||
\(340\) | −1.54021 | −0.0835296 | ||||||||
\(341\) | −3.92191 | −0.212383 | ||||||||
\(342\) | 6.85408 | 0.370626 | ||||||||
\(343\) | 20.0650 | 1.08341 | ||||||||
\(344\) | −2.65892 | −0.143359 | ||||||||
\(345\) | −2.35410 | −0.126741 | ||||||||
\(346\) | 9.30906 | 0.500458 | ||||||||
\(347\) | −29.0558 | −1.55980 | −0.779898 | − | 0.625907i | \(-0.784729\pi\) | ||||
−0.779898 | + | 0.625907i | \(0.784729\pi\) | |||||||
\(348\) | −5.09337 | −0.273033 | ||||||||
\(349\) | 23.8454 | 1.27642 | 0.638209 | − | 0.769864i | \(-0.279676\pi\) | ||||
0.638209 | + | 0.769864i | \(0.279676\pi\) | |||||||
\(350\) | −6.75288 | −0.360957 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0.378203 | 0.0201583 | ||||||||
\(353\) | 25.2391 | 1.34334 | 0.671671 | − | 0.740850i | \(-0.265577\pi\) | ||||
0.671671 | + | 0.740850i | \(0.265577\pi\) | |||||||
\(354\) | 0.731526 | 0.0388802 | ||||||||
\(355\) | 4.31620 | 0.229080 | ||||||||
\(356\) | −5.26838 | −0.279223 | ||||||||
\(357\) | 2.46023 | 0.130209 | ||||||||
\(358\) | −6.22986 | −0.329259 | ||||||||
\(359\) | −10.1016 | −0.533144 | −0.266572 | − | 0.963815i | \(-0.585891\pi\) | ||||
−0.266572 | + | 0.963815i | \(0.585891\pi\) | |||||||
\(360\) | −1.42840 | −0.0752831 | ||||||||
\(361\) | 27.9785 | 1.47255 | ||||||||
\(362\) | 5.27430 | 0.277211 | ||||||||
\(363\) | −10.8570 | −0.569843 | ||||||||
\(364\) | −2.28162 | −0.119589 | ||||||||
\(365\) | −16.0764 | −0.841477 | ||||||||
\(366\) | 4.05568 | 0.211994 | ||||||||
\(367\) | 7.36016 | 0.384197 | 0.192099 | − | 0.981376i | \(-0.438471\pi\) | ||||
0.192099 | + | 0.981376i | \(0.438471\pi\) | |||||||
\(368\) | −1.64807 | −0.0859118 | ||||||||
\(369\) | 0.952622 | 0.0495915 | ||||||||
\(370\) | −13.9440 | −0.724913 | ||||||||
\(371\) | −17.7766 | −0.922916 | ||||||||
\(372\) | 10.3699 | 0.537652 | ||||||||
\(373\) | −11.0954 | −0.574496 | −0.287248 | − | 0.957856i | \(-0.592740\pi\) | ||||
−0.287248 | + | 0.957856i | \(0.592740\pi\) | |||||||
\(374\) | −0.407809 | −0.0210873 | ||||||||
\(375\) | −11.3696 | −0.587123 | ||||||||
\(376\) | −7.38329 | −0.380764 | ||||||||
\(377\) | −5.09337 | −0.262322 | ||||||||
\(378\) | 2.28162 | 0.117354 | ||||||||
\(379\) | 2.69689 | 0.138530 | 0.0692649 | − | 0.997598i | \(-0.477935\pi\) | ||||
0.0692649 | + | 0.997598i | \(0.477935\pi\) | |||||||
\(380\) | −9.79035 | −0.502234 | ||||||||
\(381\) | −1.00129 | −0.0512978 | ||||||||
\(382\) | 2.75574 | 0.140996 | ||||||||
\(383\) | −3.30815 | −0.169038 | −0.0845192 | − | 0.996422i | \(-0.526935\pi\) | ||||
−0.0845192 | + | 0.996422i | \(0.526935\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 1.23259 | 0.0628184 | ||||||||
\(386\) | 6.08283 | 0.309608 | ||||||||
\(387\) | 2.65892 | 0.135161 | ||||||||
\(388\) | −10.0419 | −0.509802 | ||||||||
\(389\) | 23.1855 | 1.17555 | 0.587776 | − | 0.809024i | \(-0.300004\pi\) | ||||
0.587776 | + | 0.809024i | \(0.300004\pi\) | |||||||
\(390\) | −1.42840 | −0.0723296 | ||||||||
\(391\) | 1.77708 | 0.0898711 | ||||||||
\(392\) | 1.79420 | 0.0906210 | ||||||||
\(393\) | −7.05133 | −0.355693 | ||||||||
\(394\) | 10.1965 | 0.513691 | ||||||||
\(395\) | 7.50570 | 0.377653 | ||||||||
\(396\) | −0.378203 | −0.0190054 | ||||||||
\(397\) | 32.2041 | 1.61628 | 0.808138 | − | 0.588994i | \(-0.200476\pi\) | ||||
0.808138 | + | 0.588994i | \(0.200476\pi\) | |||||||
\(398\) | −1.25424 | −0.0628694 | ||||||||
\(399\) | 15.6384 | 0.782900 | ||||||||
\(400\) | −2.95968 | −0.147984 | ||||||||
\(401\) | −0.522173 | −0.0260761 | −0.0130380 | − | 0.999915i | \(-0.504150\pi\) | ||||
−0.0130380 | + | 0.999915i | \(0.504150\pi\) | |||||||
\(402\) | 9.03946 | 0.450847 | ||||||||
\(403\) | 10.3699 | 0.516559 | ||||||||
\(404\) | 6.99307 | 0.347918 | ||||||||
\(405\) | 1.42840 | 0.0709776 | ||||||||
\(406\) | −11.6211 | −0.576748 | ||||||||
\(407\) | −3.69201 | −0.183006 | ||||||||
\(408\) | 1.07828 | 0.0533828 | ||||||||
\(409\) | 28.7704 | 1.42260 | 0.711302 | − | 0.702887i | \(-0.248106\pi\) | ||||
0.711302 | + | 0.702887i | \(0.248106\pi\) | |||||||
\(410\) | −1.36072 | −0.0672013 | ||||||||
\(411\) | −6.33167 | −0.312318 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 1.66907 | 0.0821293 | ||||||||
\(414\) | 1.64807 | 0.0809984 | ||||||||
\(415\) | −16.1140 | −0.791006 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −15.7204 | −0.769831 | ||||||||
\(418\) | −2.59224 | −0.126790 | ||||||||
\(419\) | −37.5198 | −1.83296 | −0.916482 | − | 0.400075i | \(-0.868984\pi\) | ||||
−0.916482 | + | 0.400075i | \(0.868984\pi\) | |||||||
\(420\) | −3.25906 | −0.159026 | ||||||||
\(421\) | 2.98562 | 0.145510 | 0.0727552 | − | 0.997350i | \(-0.476821\pi\) | ||||
0.0727552 | + | 0.997350i | \(0.476821\pi\) | |||||||
\(422\) | 16.2651 | 0.791772 | ||||||||
\(423\) | 7.38329 | 0.358988 | ||||||||
\(424\) | −7.79122 | −0.378375 | ||||||||
\(425\) | 3.19137 | 0.154804 | ||||||||
\(426\) | −3.02171 | −0.146403 | ||||||||
\(427\) | 9.25353 | 0.447810 | ||||||||
\(428\) | −10.4990 | −0.507487 | ||||||||
\(429\) | −0.378203 | −0.0182598 | ||||||||
\(430\) | −3.79799 | −0.183156 | ||||||||
\(431\) | −11.3097 | −0.544770 | −0.272385 | − | 0.962188i | \(-0.587812\pi\) | ||||
−0.272385 | + | 0.962188i | \(0.587812\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −2.35879 | −0.113356 | −0.0566781 | − | 0.998393i | \(-0.518051\pi\) | ||||
−0.0566781 | + | 0.998393i | \(0.518051\pi\) | |||||||
\(434\) | 23.6601 | 1.13572 | ||||||||
\(435\) | −7.27536 | −0.348827 | ||||||||
\(436\) | 0.860752 | 0.0412225 | ||||||||
\(437\) | 11.2960 | 0.540363 | ||||||||
\(438\) | 11.2549 | 0.537778 | ||||||||
\(439\) | 26.2481 | 1.25275 | 0.626376 | − | 0.779521i | \(-0.284538\pi\) | ||||
0.626376 | + | 0.779521i | \(0.284538\pi\) | |||||||
\(440\) | 0.540224 | 0.0257542 | ||||||||
\(441\) | −1.79420 | −0.0854383 | ||||||||
\(442\) | 1.07828 | 0.0512885 | ||||||||
\(443\) | 6.78372 | 0.322304 | 0.161152 | − | 0.986930i | \(-0.448479\pi\) | ||||
0.161152 | + | 0.986930i | \(0.448479\pi\) | |||||||
\(444\) | 9.76199 | 0.463283 | ||||||||
\(445\) | −7.52533 | −0.356735 | ||||||||
\(446\) | 21.2527 | 1.00634 | ||||||||
\(447\) | −10.5290 | −0.498005 | ||||||||
\(448\) | −2.28162 | −0.107796 | ||||||||
\(449\) | 37.5659 | 1.77284 | 0.886422 | − | 0.462879i | \(-0.153183\pi\) | ||||
0.886422 | + | 0.462879i | \(0.153183\pi\) | |||||||
\(450\) | 2.95968 | 0.139521 | ||||||||
\(451\) | −0.360285 | −0.0169651 | ||||||||
\(452\) | −2.84635 | −0.133881 | ||||||||
\(453\) | −5.65260 | −0.265582 | ||||||||
\(454\) | 25.4900 | 1.19630 | ||||||||
\(455\) | −3.25906 | −0.152787 | ||||||||
\(456\) | 6.85408 | 0.320972 | ||||||||
\(457\) | −7.90872 | −0.369954 | −0.184977 | − | 0.982743i | \(-0.559221\pi\) | ||||
−0.184977 | + | 0.982743i | \(0.559221\pi\) | |||||||
\(458\) | −25.8974 | −1.21011 | ||||||||
\(459\) | −1.07828 | −0.0503298 | ||||||||
\(460\) | −2.35410 | −0.109761 | ||||||||
\(461\) | 0.520571 | 0.0242454 | 0.0121227 | − | 0.999927i | \(-0.496141\pi\) | ||||
0.0121227 | + | 0.999927i | \(0.496141\pi\) | |||||||
\(462\) | −0.862916 | −0.0401465 | ||||||||
\(463\) | −9.28449 | −0.431487 | −0.215744 | − | 0.976450i | \(-0.569218\pi\) | ||||
−0.215744 | + | 0.976450i | \(0.569218\pi\) | |||||||
\(464\) | −5.09337 | −0.236454 | ||||||||
\(465\) | 14.8123 | 0.686902 | ||||||||
\(466\) | 0.935399 | 0.0433315 | ||||||||
\(467\) | −0.410904 | −0.0190144 | −0.00950719 | − | 0.999955i | \(-0.503026\pi\) | ||||
−0.00950719 | + | 0.999955i | \(0.503026\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 20.6246 | 0.952357 | ||||||||
\(470\) | −10.5463 | −0.486463 | ||||||||
\(471\) | 13.3002 | 0.612841 | ||||||||
\(472\) | 0.731526 | 0.0336712 | ||||||||
\(473\) | −1.00561 | −0.0462381 | ||||||||
\(474\) | −5.25463 | −0.241353 | ||||||||
\(475\) | 20.2859 | 0.930782 | ||||||||
\(476\) | 2.46023 | 0.112764 | ||||||||
\(477\) | 7.79122 | 0.356736 | ||||||||
\(478\) | 7.83371 | 0.358305 | ||||||||
\(479\) | −35.7133 | −1.63178 | −0.815890 | − | 0.578207i | \(-0.803753\pi\) | ||||
−0.815890 | + | 0.578207i | \(0.803753\pi\) | |||||||
\(480\) | −1.42840 | −0.0651971 | ||||||||
\(481\) | 9.76199 | 0.445108 | ||||||||
\(482\) | −23.8091 | −1.08448 | ||||||||
\(483\) | 3.76028 | 0.171099 | ||||||||
\(484\) | −10.8570 | −0.493498 | ||||||||
\(485\) | −14.3439 | −0.651322 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 9.35930 | 0.424110 | 0.212055 | − | 0.977258i | \(-0.431984\pi\) | ||||
0.212055 | + | 0.977258i | \(0.431984\pi\) | |||||||
\(488\) | 4.05568 | 0.183592 | ||||||||
\(489\) | −6.40325 | −0.289565 | ||||||||
\(490\) | 2.56284 | 0.115777 | ||||||||
\(491\) | −24.5502 | −1.10793 | −0.553967 | − | 0.832539i | \(-0.686887\pi\) | ||||
−0.553967 | + | 0.832539i | \(0.686887\pi\) | |||||||
\(492\) | 0.952622 | 0.0429475 | ||||||||
\(493\) | 5.49208 | 0.247351 | ||||||||
\(494\) | 6.85408 | 0.308380 | ||||||||
\(495\) | −0.540224 | −0.0242813 | ||||||||
\(496\) | 10.3699 | 0.465620 | ||||||||
\(497\) | −6.89441 | −0.309256 | ||||||||
\(498\) | 11.2812 | 0.505523 | ||||||||
\(499\) | 0.932509 | 0.0417448 | 0.0208724 | − | 0.999782i | \(-0.493356\pi\) | ||||
0.0208724 | + | 0.999782i | \(0.493356\pi\) | |||||||
\(500\) | −11.3696 | −0.508463 | ||||||||
\(501\) | 4.33757 | 0.193788 | ||||||||
\(502\) | 7.47104 | 0.333449 | ||||||||
\(503\) | −34.4919 | −1.53792 | −0.768958 | − | 0.639299i | \(-0.779225\pi\) | ||||
−0.768958 | + | 0.639299i | \(0.779225\pi\) | |||||||
\(504\) | 2.28162 | 0.101631 | ||||||||
\(505\) | 9.98887 | 0.444499 | ||||||||
\(506\) | −0.623307 | −0.0277094 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −1.00129 | −0.0444252 | ||||||||
\(509\) | −24.9502 | −1.10590 | −0.552948 | − | 0.833215i | \(-0.686497\pi\) | ||||
−0.552948 | + | 0.833215i | \(0.686497\pi\) | |||||||
\(510\) | 1.54021 | 0.0682017 | ||||||||
\(511\) | 25.6793 | 1.13599 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.85408 | −0.302615 | ||||||||
\(514\) | 29.3198 | 1.29324 | ||||||||
\(515\) | −1.42840 | −0.0629426 | ||||||||
\(516\) | 2.65892 | 0.117053 | ||||||||
\(517\) | −2.79238 | −0.122809 | ||||||||
\(518\) | 22.2732 | 0.978626 | ||||||||
\(519\) | −9.30906 | −0.408623 | ||||||||
\(520\) | −1.42840 | −0.0626393 | ||||||||
\(521\) | 0.944534 | 0.0413808 | 0.0206904 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206904 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(522\) | 5.09337 | 0.222931 | ||||||||
\(523\) | 37.5492 | 1.64191 | 0.820955 | − | 0.570993i | \(-0.193442\pi\) | ||||
0.820955 | + | 0.570993i | \(0.193442\pi\) | |||||||
\(524\) | −7.05133 | −0.308039 | ||||||||
\(525\) | 6.75288 | 0.294720 | ||||||||
\(526\) | 25.4645 | 1.11031 | ||||||||
\(527\) | −11.1816 | −0.487078 | ||||||||
\(528\) | −0.378203 | −0.0164592 | ||||||||
\(529\) | −20.2839 | −0.881907 | ||||||||
\(530\) | −11.1290 | −0.483411 | ||||||||
\(531\) | −0.731526 | −0.0317455 | ||||||||
\(532\) | 15.6384 | 0.678012 | ||||||||
\(533\) | 0.952622 | 0.0412626 | ||||||||
\(534\) | 5.26838 | 0.227985 | ||||||||
\(535\) | −14.9967 | −0.648363 | ||||||||
\(536\) | 9.03946 | 0.390445 | ||||||||
\(537\) | 6.22986 | 0.268839 | ||||||||
\(538\) | 23.3373 | 1.00614 | ||||||||
\(539\) | 0.678574 | 0.0292282 | ||||||||
\(540\) | 1.42840 | 0.0614684 | ||||||||
\(541\) | −8.92867 | −0.383874 | −0.191937 | − | 0.981407i | \(-0.561477\pi\) | ||||
−0.191937 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(542\) | 6.22070 | 0.267202 | ||||||||
\(543\) | −5.27430 | −0.226342 | ||||||||
\(544\) | 1.07828 | 0.0462309 | ||||||||
\(545\) | 1.22949 | 0.0526657 | ||||||||
\(546\) | 2.28162 | 0.0976444 | ||||||||
\(547\) | 1.16295 | 0.0497243 | 0.0248622 | − | 0.999691i | \(-0.492085\pi\) | ||||
0.0248622 | + | 0.999691i | \(0.492085\pi\) | |||||||
\(548\) | −6.33167 | −0.270476 | ||||||||
\(549\) | −4.05568 | −0.173092 | ||||||||
\(550\) | −1.11936 | −0.0477297 | ||||||||
\(551\) | 34.9104 | 1.48723 | ||||||||
\(552\) | 1.64807 | 0.0701467 | ||||||||
\(553\) | −11.9891 | −0.509828 | ||||||||
\(554\) | −10.9355 | −0.464606 | ||||||||
\(555\) | 13.9440 | 0.591889 | ||||||||
\(556\) | −15.7204 | −0.666693 | ||||||||
\(557\) | 39.8724 | 1.68945 | 0.844723 | − | 0.535203i | \(-0.179765\pi\) | ||||
0.844723 | + | 0.535203i | \(0.179765\pi\) | |||||||
\(558\) | −10.3699 | −0.438991 | ||||||||
\(559\) | 2.65892 | 0.112460 | ||||||||
\(560\) | −3.25906 | −0.137720 | ||||||||
\(561\) | 0.407809 | 0.0172177 | ||||||||
\(562\) | −16.4408 | −0.693515 | ||||||||
\(563\) | 20.4700 | 0.862707 | 0.431353 | − | 0.902183i | \(-0.358036\pi\) | ||||
0.431353 | + | 0.902183i | \(0.358036\pi\) | |||||||
\(564\) | 7.38329 | 0.310893 | ||||||||
\(565\) | −4.06571 | −0.171046 | ||||||||
\(566\) | −17.3544 | −0.729458 | ||||||||
\(567\) | −2.28162 | −0.0958191 | ||||||||
\(568\) | −3.02171 | −0.126788 | ||||||||
\(569\) | 44.0758 | 1.84775 | 0.923876 | − | 0.382692i | \(-0.125003\pi\) | ||||
0.923876 | + | 0.382692i | \(0.125003\pi\) | |||||||
\(570\) | 9.79035 | 0.410072 | ||||||||
\(571\) | −21.6029 | −0.904053 | −0.452026 | − | 0.892005i | \(-0.649299\pi\) | ||||
−0.452026 | + | 0.892005i | \(0.649299\pi\) | |||||||
\(572\) | −0.378203 | −0.0158135 | ||||||||
\(573\) | −2.75574 | −0.115123 | ||||||||
\(574\) | 2.17352 | 0.0907211 | ||||||||
\(575\) | 4.87778 | 0.203418 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.4529 | −0.643314 | −0.321657 | − | 0.946856i | \(-0.604240\pi\) | ||||
−0.321657 | + | 0.946856i | \(0.604240\pi\) | |||||||
\(578\) | 15.8373 | 0.658745 | ||||||||
\(579\) | −6.08283 | −0.252794 | ||||||||
\(580\) | −7.27536 | −0.302093 | ||||||||
\(581\) | 25.7394 | 1.06785 | ||||||||
\(582\) | 10.0419 | 0.416252 | ||||||||
\(583\) | −2.94666 | −0.122038 | ||||||||
\(584\) | 11.2549 | 0.465730 | ||||||||
\(585\) | 1.42840 | 0.0590569 | ||||||||
\(586\) | −9.58413 | −0.395917 | ||||||||
\(587\) | 36.1032 | 1.49014 | 0.745068 | − | 0.666988i | \(-0.232417\pi\) | ||||
0.745068 | + | 0.666988i | \(0.232417\pi\) | |||||||
\(588\) | −1.79420 | −0.0739918 | ||||||||
\(589\) | −71.0758 | −2.92863 | ||||||||
\(590\) | 1.04491 | 0.0430182 | ||||||||
\(591\) | −10.1965 | −0.419427 | ||||||||
\(592\) | 9.76199 | 0.401215 | ||||||||
\(593\) | −1.69894 | −0.0697669 | −0.0348835 | − | 0.999391i | \(-0.511106\pi\) | ||||
−0.0348835 | + | 0.999391i | \(0.511106\pi\) | |||||||
\(594\) | 0.378203 | 0.0155179 | ||||||||
\(595\) | 3.51418 | 0.144067 | ||||||||
\(596\) | −10.5290 | −0.431285 | ||||||||
\(597\) | 1.25424 | 0.0513326 | ||||||||
\(598\) | 1.64807 | 0.0673948 | ||||||||
\(599\) | −20.6681 | −0.844477 | −0.422238 | − | 0.906485i | \(-0.638755\pi\) | ||||
−0.422238 | + | 0.906485i | \(0.638755\pi\) | |||||||
\(600\) | 2.95968 | 0.120829 | ||||||||
\(601\) | 2.38180 | 0.0971556 | 0.0485778 | − | 0.998819i | \(-0.484531\pi\) | ||||
0.0485778 | + | 0.998819i | \(0.484531\pi\) | |||||||
\(602\) | 6.06665 | 0.247258 | ||||||||
\(603\) | −9.03946 | −0.368115 | ||||||||
\(604\) | −5.65260 | −0.230001 | ||||||||
\(605\) | −15.5080 | −0.630492 | ||||||||
\(606\) | −6.99307 | −0.284074 | ||||||||
\(607\) | 1.91188 | 0.0776006 | 0.0388003 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388003 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(608\) | 6.85408 | 0.277970 | ||||||||
\(609\) | 11.6211 | 0.470913 | ||||||||
\(610\) | 5.79312 | 0.234557 | ||||||||
\(611\) | 7.38329 | 0.298696 | ||||||||
\(612\) | −1.07828 | −0.0435869 | ||||||||
\(613\) | 3.62282 | 0.146324 | 0.0731621 | − | 0.997320i | \(-0.476691\pi\) | ||||
0.0731621 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(614\) | 12.5014 | 0.504517 | ||||||||
\(615\) | 1.36072 | 0.0548696 | ||||||||
\(616\) | −0.862916 | −0.0347679 | ||||||||
\(617\) | 15.5713 | 0.626876 | 0.313438 | − | 0.949609i | \(-0.398519\pi\) | ||||
0.313438 | + | 0.949609i | \(0.398519\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 3.00732 | 0.120874 | 0.0604371 | − | 0.998172i | \(-0.480751\pi\) | ||||
0.0604371 | + | 0.998172i | \(0.480751\pi\) | |||||||
\(620\) | 14.8123 | 0.594874 | ||||||||
\(621\) | −1.64807 | −0.0661350 | ||||||||
\(622\) | 26.1921 | 1.05021 | ||||||||
\(623\) | 12.0204 | 0.481589 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −1.44184 | −0.0576737 | ||||||||
\(626\) | −7.61225 | −0.304247 | ||||||||
\(627\) | 2.59224 | 0.103524 | ||||||||
\(628\) | 13.3002 | 0.530736 | ||||||||
\(629\) | −10.5262 | −0.419705 | ||||||||
\(630\) | 3.25906 | 0.129844 | ||||||||
\(631\) | −7.36563 | −0.293221 | −0.146610 | − | 0.989194i | \(-0.546836\pi\) | ||||
−0.146610 | + | 0.989194i | \(0.546836\pi\) | |||||||
\(632\) | −5.25463 | −0.209018 | ||||||||
\(633\) | −16.2651 | −0.646479 | ||||||||
\(634\) | −7.73483 | −0.307189 | ||||||||
\(635\) | −1.43024 | −0.0567575 | ||||||||
\(636\) | 7.79122 | 0.308942 | ||||||||
\(637\) | −1.79420 | −0.0710890 | ||||||||
\(638\) | −1.92633 | −0.0762641 | ||||||||
\(639\) | 3.02171 | 0.119537 | ||||||||
\(640\) | −1.42840 | −0.0564623 | ||||||||
\(641\) | −38.7570 | −1.53081 | −0.765405 | − | 0.643549i | \(-0.777461\pi\) | ||||
−0.765405 | + | 0.643549i | \(0.777461\pi\) | |||||||
\(642\) | 10.4990 | 0.414361 | ||||||||
\(643\) | 8.06468 | 0.318040 | 0.159020 | − | 0.987275i | \(-0.449167\pi\) | ||||
0.159020 | + | 0.987275i | \(0.449167\pi\) | |||||||
\(644\) | 3.76028 | 0.148176 | ||||||||
\(645\) | 3.79799 | 0.149546 | ||||||||
\(646\) | −7.39062 | −0.290780 | ||||||||
\(647\) | −19.2342 | −0.756176 | −0.378088 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378088 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.276665 | 0.0108601 | ||||||||
\(650\) | 2.95968 | 0.116088 | ||||||||
\(651\) | −23.6601 | −0.927311 | ||||||||
\(652\) | −6.40325 | −0.250771 | ||||||||
\(653\) | −44.8678 | −1.75581 | −0.877906 | − | 0.478834i | \(-0.841060\pi\) | ||||
−0.877906 | + | 0.478834i | \(0.841060\pi\) | |||||||
\(654\) | −0.860752 | −0.0336580 | ||||||||
\(655\) | −10.0721 | −0.393549 | ||||||||
\(656\) | 0.952622 | 0.0371936 | ||||||||
\(657\) | −11.2549 | −0.439094 | ||||||||
\(658\) | 16.8459 | 0.656720 | ||||||||
\(659\) | −7.62830 | −0.297156 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(660\) | −0.540224 | −0.0210282 | ||||||||
\(661\) | 35.8892 | 1.39593 | 0.697963 | − | 0.716133i | \(-0.254090\pi\) | ||||
0.697963 | + | 0.716133i | \(0.254090\pi\) | |||||||
\(662\) | −25.0994 | −0.975516 | ||||||||
\(663\) | −1.07828 | −0.0418769 | ||||||||
\(664\) | 11.2812 | 0.437795 | ||||||||
\(665\) | 22.3379 | 0.866225 | ||||||||
\(666\) | −9.76199 | −0.378269 | ||||||||
\(667\) | 8.39426 | 0.325027 | ||||||||
\(668\) | 4.33757 | 0.167826 | ||||||||
\(669\) | −21.2527 | −0.821677 | ||||||||
\(670\) | 12.9119 | 0.498831 | ||||||||
\(671\) | 1.53387 | 0.0592144 | ||||||||
\(672\) | 2.28162 | 0.0880154 | ||||||||
\(673\) | 43.3613 | 1.67145 | 0.835727 | − | 0.549145i | \(-0.185047\pi\) | ||||
0.835727 | + | 0.549145i | \(0.185047\pi\) | |||||||
\(674\) | 13.9072 | 0.535687 | ||||||||
\(675\) | −2.95968 | −0.113918 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 31.0734 | 1.19425 | 0.597125 | − | 0.802148i | \(-0.296310\pi\) | ||||
0.597125 | + | 0.802148i | \(0.296310\pi\) | |||||||
\(678\) | 2.84635 | 0.109313 | ||||||||
\(679\) | 22.9119 | 0.879278 | ||||||||
\(680\) | 1.54021 | 0.0590644 | ||||||||
\(681\) | −25.4900 | −0.976778 | ||||||||
\(682\) | 3.92191 | 0.150178 | ||||||||
\(683\) | 15.9518 | 0.610379 | 0.305190 | − | 0.952292i | \(-0.401280\pi\) | ||||
0.305190 | + | 0.952292i | \(0.401280\pi\) | |||||||
\(684\) | −6.85408 | −0.262072 | ||||||||
\(685\) | −9.04413 | −0.345559 | ||||||||
\(686\) | −20.0650 | −0.766087 | ||||||||
\(687\) | 25.8974 | 0.988047 | ||||||||
\(688\) | 2.65892 | 0.101370 | ||||||||
\(689\) | 7.79122 | 0.296822 | ||||||||
\(690\) | 2.35410 | 0.0896192 | ||||||||
\(691\) | −21.3599 | −0.812568 | −0.406284 | − | 0.913747i | \(-0.633176\pi\) | ||||
−0.406284 | + | 0.913747i | \(0.633176\pi\) | |||||||
\(692\) | −9.30906 | −0.353878 | ||||||||
\(693\) | 0.862916 | 0.0327795 | ||||||||
\(694\) | 29.0558 | 1.10294 | ||||||||
\(695\) | −22.4549 | −0.851765 | ||||||||
\(696\) | 5.09337 | 0.193064 | ||||||||
\(697\) | −1.02719 | −0.0389077 | ||||||||
\(698\) | −23.8454 | −0.902563 | ||||||||
\(699\) | −0.935399 | −0.0353801 | ||||||||
\(700\) | 6.75288 | 0.255235 | ||||||||
\(701\) | 23.2980 | 0.879954 | 0.439977 | − | 0.898009i | \(-0.354987\pi\) | ||||
0.439977 | + | 0.898009i | \(0.354987\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −66.9095 | −2.52354 | ||||||||
\(704\) | −0.378203 | −0.0142541 | ||||||||
\(705\) | 10.5463 | 0.397195 | ||||||||
\(706\) | −25.2391 | −0.949886 | ||||||||
\(707\) | −15.9555 | −0.600069 | ||||||||
\(708\) | −0.731526 | −0.0274924 | ||||||||
\(709\) | −18.2292 | −0.684612 | −0.342306 | − | 0.939589i | \(-0.611208\pi\) | ||||
−0.342306 | + | 0.939589i | \(0.611208\pi\) | |||||||
\(710\) | −4.31620 | −0.161984 | ||||||||
\(711\) | 5.25463 | 0.197064 | ||||||||
\(712\) | 5.26838 | 0.197441 | ||||||||
\(713\) | −17.0903 | −0.640036 | ||||||||
\(714\) | −2.46023 | −0.0920716 | ||||||||
\(715\) | −0.540224 | −0.0202032 | ||||||||
\(716\) | 6.22986 | 0.232821 | ||||||||
\(717\) | −7.83371 | −0.292555 | ||||||||
\(718\) | 10.1016 | 0.376989 | ||||||||
\(719\) | −17.6809 | −0.659388 | −0.329694 | − | 0.944088i | \(-0.606946\pi\) | ||||
−0.329694 | + | 0.944088i | \(0.606946\pi\) | |||||||
\(720\) | 1.42840 | 0.0532332 | ||||||||
\(721\) | 2.28162 | 0.0849720 | ||||||||
\(722\) | −27.9785 | −1.04125 | ||||||||
\(723\) | 23.8091 | 0.885472 | ||||||||
\(724\) | −5.27430 | −0.196018 | ||||||||
\(725\) | 15.0748 | 0.559863 | ||||||||
\(726\) | 10.8570 | 0.402940 | ||||||||
\(727\) | 21.3312 | 0.791129 | 0.395564 | − | 0.918438i | \(-0.370549\pi\) | ||||
0.395564 | + | 0.918438i | \(0.370549\pi\) | |||||||
\(728\) | 2.28162 | 0.0845625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.0764 | 0.595014 | ||||||||
\(731\) | −2.86706 | −0.106042 | ||||||||
\(732\) | −4.05568 | −0.149902 | ||||||||
\(733\) | −24.7459 | −0.914010 | −0.457005 | − | 0.889464i | \(-0.651078\pi\) | ||||
−0.457005 | + | 0.889464i | \(0.651078\pi\) | |||||||
\(734\) | −7.36016 | −0.271669 | ||||||||
\(735\) | −2.56284 | −0.0945316 | ||||||||
\(736\) | 1.64807 | 0.0607488 | ||||||||
\(737\) | 3.41875 | 0.125931 | ||||||||
\(738\) | −0.952622 | −0.0350665 | ||||||||
\(739\) | −41.3679 | −1.52174 | −0.760871 | − | 0.648903i | \(-0.775228\pi\) | ||||
−0.760871 | + | 0.648903i | \(0.775228\pi\) | |||||||
\(740\) | 13.9440 | 0.512591 | ||||||||
\(741\) | −6.85408 | −0.251791 | ||||||||
\(742\) | 17.7766 | 0.652600 | ||||||||
\(743\) | −11.8013 | −0.432949 | −0.216475 | − | 0.976288i | \(-0.569456\pi\) | ||||
−0.216475 | + | 0.976288i | \(0.569456\pi\) | |||||||
\(744\) | −10.3699 | −0.380177 | ||||||||
\(745\) | −15.0396 | −0.551008 | ||||||||
\(746\) | 11.0954 | 0.406230 | ||||||||
\(747\) | −11.2812 | −0.412757 | ||||||||
\(748\) | 0.407809 | 0.0149110 | ||||||||
\(749\) | 23.9547 | 0.875284 | ||||||||
\(750\) | 11.3696 | 0.415158 | ||||||||
\(751\) | −40.1233 | −1.46412 | −0.732060 | − | 0.681240i | \(-0.761441\pi\) | ||||
−0.732060 | + | 0.681240i | \(0.761441\pi\) | |||||||
\(752\) | 7.38329 | 0.269241 | ||||||||
\(753\) | −7.47104 | −0.272260 | ||||||||
\(754\) | 5.09337 | 0.185490 | ||||||||
\(755\) | −8.07415 | −0.293848 | ||||||||
\(756\) | −2.28162 | −0.0829818 | ||||||||
\(757\) | −6.41345 | −0.233101 | −0.116550 | − | 0.993185i | \(-0.537184\pi\) | ||||
−0.116550 | + | 0.993185i | \(0.537184\pi\) | |||||||
\(758\) | −2.69689 | −0.0979553 | ||||||||
\(759\) | 0.623307 | 0.0226246 | ||||||||
\(760\) | 9.79035 | 0.355133 | ||||||||
\(761\) | −1.13877 | −0.0412802 | −0.0206401 | − | 0.999787i | \(-0.506570\pi\) | ||||
−0.0206401 | + | 0.999787i | \(0.506570\pi\) | |||||||
\(762\) | 1.00129 | 0.0362730 | ||||||||
\(763\) | −1.96391 | −0.0710983 | ||||||||
\(764\) | −2.75574 | −0.0996993 | ||||||||
\(765\) | −1.54021 | −0.0556864 | ||||||||
\(766\) | 3.30815 | 0.119528 | ||||||||
\(767\) | −0.731526 | −0.0264139 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 20.4055 | 0.735842 | 0.367921 | − | 0.929857i | \(-0.380070\pi\) | ||||
0.367921 | + | 0.929857i | \(0.380070\pi\) | |||||||
\(770\) | −1.23259 | −0.0444193 | ||||||||
\(771\) | −29.3198 | −1.05593 | ||||||||
\(772\) | −6.08283 | −0.218926 | ||||||||
\(773\) | −18.8481 | −0.677921 | −0.338960 | − | 0.940801i | \(-0.610075\pi\) | ||||
−0.338960 | + | 0.940801i | \(0.610075\pi\) | |||||||
\(774\) | −2.65892 | −0.0955730 | ||||||||
\(775\) | −30.6915 | −1.10247 | ||||||||
\(776\) | 10.0419 | 0.360485 | ||||||||
\(777\) | −22.2732 | −0.799045 | ||||||||
\(778\) | −23.1855 | −0.831240 | ||||||||
\(779\) | −6.52935 | −0.233938 | ||||||||
\(780\) | 1.42840 | 0.0511448 | ||||||||
\(781\) | −1.14282 | −0.0408934 | ||||||||
\(782\) | −1.77708 | −0.0635484 | ||||||||
\(783\) | −5.09337 | −0.182022 | ||||||||
\(784\) | −1.79420 | −0.0640787 | ||||||||
\(785\) | 18.9980 | 0.678066 | ||||||||
\(786\) | 7.05133 | 0.251513 | ||||||||
\(787\) | 17.2663 | 0.615476 | 0.307738 | − | 0.951471i | \(-0.400428\pi\) | ||||
0.307738 | + | 0.951471i | \(0.400428\pi\) | |||||||
\(788\) | −10.1965 | −0.363234 | ||||||||
\(789\) | −25.4645 | −0.906562 | ||||||||
\(790\) | −7.50570 | −0.267041 | ||||||||
\(791\) | 6.49428 | 0.230910 | ||||||||
\(792\) | 0.378203 | 0.0134389 | ||||||||
\(793\) | −4.05568 | −0.144021 | ||||||||
\(794\) | −32.2041 | −1.14288 | ||||||||
\(795\) | 11.1290 | 0.394703 | ||||||||
\(796\) | 1.25424 | 0.0444554 | ||||||||
\(797\) | −20.5117 | −0.726561 | −0.363280 | − | 0.931680i | \(-0.618343\pi\) | ||||
−0.363280 | + | 0.931680i | \(0.618343\pi\) | |||||||
\(798\) | −15.6384 | −0.553594 | ||||||||
\(799\) | −7.96125 | −0.281649 | ||||||||
\(800\) | 2.95968 | 0.104641 | ||||||||
\(801\) | −5.26838 | −0.186149 | ||||||||
\(802\) | 0.522173 | 0.0184386 | ||||||||
\(803\) | 4.25662 | 0.150213 | ||||||||
\(804\) | −9.03946 | −0.318797 | ||||||||
\(805\) | 5.37117 | 0.189309 | ||||||||
\(806\) | −10.3699 | −0.365262 | ||||||||
\(807\) | −23.3373 | −0.821512 | ||||||||
\(808\) | −6.99307 | −0.246015 | ||||||||
\(809\) | 1.44475 | 0.0507948 | 0.0253974 | − | 0.999677i | \(-0.491915\pi\) | ||||
0.0253974 | + | 0.999677i | \(0.491915\pi\) | |||||||
\(810\) | −1.42840 | −0.0501887 | ||||||||
\(811\) | 21.9751 | 0.771651 | 0.385825 | − | 0.922572i | \(-0.373917\pi\) | ||||
0.385825 | + | 0.922572i | \(0.373917\pi\) | |||||||
\(812\) | 11.6211 | 0.407822 | ||||||||
\(813\) | −6.22070 | −0.218170 | ||||||||
\(814\) | 3.69201 | 0.129405 | ||||||||
\(815\) | −9.14638 | −0.320384 | ||||||||
\(816\) | −1.07828 | −0.0377473 | ||||||||
\(817\) | −18.2245 | −0.637594 | ||||||||
\(818\) | −28.7704 | −1.00593 | ||||||||
\(819\) | −2.28162 | −0.0797263 | ||||||||
\(820\) | 1.36072 | 0.0475185 | ||||||||
\(821\) | 36.6375 | 1.27866 | 0.639329 | − | 0.768934i | \(-0.279212\pi\) | ||||
0.639329 | + | 0.768934i | \(0.279212\pi\) | |||||||
\(822\) | 6.33167 | 0.220842 | ||||||||
\(823\) | 45.4973 | 1.58594 | 0.792969 | − | 0.609262i | \(-0.208534\pi\) | ||||
0.792969 | + | 0.609262i | \(0.208534\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 1.11936 | 0.0389712 | ||||||||
\(826\) | −1.66907 | −0.0580742 | ||||||||
\(827\) | 26.1671 | 0.909921 | 0.454960 | − | 0.890512i | \(-0.349653\pi\) | ||||
0.454960 | + | 0.890512i | \(0.349653\pi\) | |||||||
\(828\) | −1.64807 | −0.0572746 | ||||||||
\(829\) | −44.0402 | −1.52958 | −0.764790 | − | 0.644279i | \(-0.777158\pi\) | ||||
−0.764790 | + | 0.644279i | \(0.777158\pi\) | |||||||
\(830\) | 16.1140 | 0.559326 | ||||||||
\(831\) | 10.9355 | 0.379350 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 1.93465 | 0.0670318 | ||||||||
\(834\) | 15.7204 | 0.544353 | ||||||||
\(835\) | 6.19576 | 0.214413 | ||||||||
\(836\) | 2.59224 | 0.0896543 | ||||||||
\(837\) | 10.3699 | 0.358434 | ||||||||
\(838\) | 37.5198 | 1.29610 | ||||||||
\(839\) | −3.26703 | −0.112790 | −0.0563952 | − | 0.998409i | \(-0.517961\pi\) | ||||
−0.0563952 | + | 0.998409i | \(0.517961\pi\) | |||||||
\(840\) | 3.25906 | 0.112448 | ||||||||
\(841\) | −3.05754 | −0.105433 | ||||||||
\(842\) | −2.98562 | −0.102891 | ||||||||
\(843\) | 16.4408 | 0.566252 | ||||||||
\(844\) | −16.2651 | −0.559867 | ||||||||
\(845\) | 1.42840 | 0.0491383 | ||||||||
\(846\) | −7.38329 | −0.253843 | ||||||||
\(847\) | 24.7715 | 0.851158 | ||||||||
\(848\) | 7.79122 | 0.267552 | ||||||||
\(849\) | 17.3544 | 0.595600 | ||||||||
\(850\) | −3.19137 | −0.109463 | ||||||||
\(851\) | −16.0885 | −0.551506 | ||||||||
\(852\) | 3.02171 | 0.103522 | ||||||||
\(853\) | 53.1514 | 1.81987 | 0.909935 | − | 0.414751i | \(-0.136131\pi\) | ||||
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(854\) | −9.25353 | −0.316649 | ||||||||
\(855\) | −9.79035 | −0.334823 | ||||||||
\(856\) | 10.4990 | 0.358847 | ||||||||
\(857\) | 25.3084 | 0.864519 | 0.432259 | − | 0.901749i | \(-0.357717\pi\) | ||||
0.432259 | + | 0.901749i | \(0.357717\pi\) | |||||||
\(858\) | 0.378203 | 0.0129116 | ||||||||
\(859\) | −29.3493 | −1.00138 | −0.500692 | − | 0.865625i | \(-0.666921\pi\) | ||||
−0.500692 | + | 0.865625i | \(0.666921\pi\) | |||||||
\(860\) | 3.79799 | 0.129511 | ||||||||
\(861\) | −2.17352 | −0.0740735 | ||||||||
\(862\) | 11.3097 | 0.385210 | ||||||||
\(863\) | −41.2065 | −1.40268 | −0.701342 | − | 0.712825i | \(-0.747415\pi\) | ||||
−0.701342 | + | 0.712825i | \(0.747415\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −13.2970 | −0.452113 | ||||||||
\(866\) | 2.35879 | 0.0801549 | ||||||||
\(867\) | −15.8373 | −0.537863 | ||||||||
\(868\) | −23.6601 | −0.803075 | ||||||||
\(869\) | −1.98732 | −0.0674152 | ||||||||
\(870\) | 7.27536 | 0.246658 | ||||||||
\(871\) | −9.03946 | −0.306290 | ||||||||
\(872\) | −0.860752 | −0.0291487 | ||||||||
\(873\) | −10.0419 | −0.339868 | ||||||||
\(874\) | −11.2960 | −0.382094 | ||||||||
\(875\) | 25.9411 | 0.876969 | ||||||||
\(876\) | −11.2549 | −0.380267 | ||||||||
\(877\) | 23.5574 | 0.795477 | 0.397738 | − | 0.917499i | \(-0.369795\pi\) | ||||
0.397738 | + | 0.917499i | \(0.369795\pi\) | |||||||
\(878\) | −26.2481 | −0.885829 | ||||||||
\(879\) | 9.58413 | 0.323265 | ||||||||
\(880\) | −0.540224 | −0.0182109 | ||||||||
\(881\) | −13.5194 | −0.455481 | −0.227741 | − | 0.973722i | \(-0.573134\pi\) | ||||
−0.227741 | + | 0.973722i | \(0.573134\pi\) | |||||||
\(882\) | 1.79420 | 0.0604140 | ||||||||
\(883\) | 51.2268 | 1.72392 | 0.861959 | − | 0.506978i | \(-0.169237\pi\) | ||||
0.861959 | + | 0.506978i | \(0.169237\pi\) | |||||||
\(884\) | −1.07828 | −0.0362665 | ||||||||
\(885\) | −1.04491 | −0.0351242 | ||||||||
\(886\) | −6.78372 | −0.227903 | ||||||||
\(887\) | 7.59434 | 0.254993 | 0.127496 | − | 0.991839i | \(-0.459306\pi\) | ||||
0.127496 | + | 0.991839i | \(0.459306\pi\) | |||||||
\(888\) | −9.76199 | −0.327591 | ||||||||
\(889\) | 2.28457 | 0.0766221 | ||||||||
\(890\) | 7.52533 | 0.252250 | ||||||||
\(891\) | −0.378203 | −0.0126703 | ||||||||
\(892\) | −21.2527 | −0.711593 | ||||||||
\(893\) | −50.6057 | −1.69345 | ||||||||
\(894\) | 10.5290 | 0.352143 | ||||||||
\(895\) | 8.89871 | 0.297451 | ||||||||
\(896\) | 2.28162 | 0.0762236 | ||||||||
\(897\) | −1.64807 | −0.0550276 | ||||||||
\(898\) | −37.5659 | −1.25359 | ||||||||
\(899\) | −52.8175 | −1.76156 | ||||||||
\(900\) | −2.95968 | −0.0986562 | ||||||||
\(901\) | −8.40112 | −0.279882 | ||||||||
\(902\) | 0.360285 | 0.0119962 | ||||||||
\(903\) | −6.06665 | −0.201886 | ||||||||
\(904\) | 2.84635 | 0.0946681 | ||||||||
\(905\) | −7.53379 | −0.250432 | ||||||||
\(906\) | 5.65260 | 0.187795 | ||||||||
\(907\) | −50.9773 | −1.69267 | −0.846336 | − | 0.532649i | \(-0.821196\pi\) | ||||
−0.846336 | + | 0.532649i | \(0.821196\pi\) | |||||||
\(908\) | −25.4900 | −0.845914 | ||||||||
\(909\) | 6.99307 | 0.231945 | ||||||||
\(910\) | 3.25906 | 0.108037 | ||||||||
\(911\) | −19.8064 | −0.656216 | −0.328108 | − | 0.944640i | \(-0.606411\pi\) | ||||
−0.328108 | + | 0.944640i | \(0.606411\pi\) | |||||||
\(912\) | −6.85408 | −0.226961 | ||||||||
\(913\) | 4.26658 | 0.141203 | ||||||||
\(914\) | 7.90872 | 0.261597 | ||||||||
\(915\) | −5.79312 | −0.191515 | ||||||||
\(916\) | 25.8974 | 0.855674 | ||||||||
\(917\) | 16.0885 | 0.531288 | ||||||||
\(918\) | 1.07828 | 0.0355885 | ||||||||
\(919\) | −54.6613 | −1.80311 | −0.901555 | − | 0.432666i | \(-0.857573\pi\) | ||||
−0.901555 | + | 0.432666i | \(0.857573\pi\) | |||||||
\(920\) | 2.35410 | 0.0776125 | ||||||||
\(921\) | −12.5014 | −0.411936 | ||||||||
\(922\) | −0.520571 | −0.0171441 | ||||||||
\(923\) | 3.02171 | 0.0994609 | ||||||||
\(924\) | 0.862916 | 0.0283879 | ||||||||
\(925\) | −28.8924 | −0.949976 | ||||||||
\(926\) | 9.28449 | 0.305107 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 5.09337 | 0.167198 | ||||||||
\(929\) | −33.8676 | −1.11116 | −0.555580 | − | 0.831463i | \(-0.687504\pi\) | ||||
−0.555580 | + | 0.831463i | \(0.687504\pi\) | |||||||
\(930\) | −14.8123 | −0.485713 | ||||||||
\(931\) | 12.2976 | 0.403039 | ||||||||
\(932\) | −0.935399 | −0.0306400 | ||||||||
\(933\) | −26.1921 | −0.857491 | ||||||||
\(934\) | 0.410904 | 0.0134452 | ||||||||
\(935\) | 0.582512 | 0.0190502 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −26.9085 | −0.879062 | −0.439531 | − | 0.898227i | \(-0.644855\pi\) | ||||
−0.439531 | + | 0.898227i | \(0.644855\pi\) | |||||||
\(938\) | −20.6246 | −0.673418 | ||||||||
\(939\) | 7.61225 | 0.248416 | ||||||||
\(940\) | 10.5463 | 0.343981 | ||||||||
\(941\) | 7.77064 | 0.253316 | 0.126658 | − | 0.991946i | \(-0.459575\pi\) | ||||
0.126658 | + | 0.991946i | \(0.459575\pi\) | |||||||
\(942\) | −13.3002 | −0.433344 | ||||||||
\(943\) | −1.56999 | −0.0511260 | ||||||||
\(944\) | −0.731526 | −0.0238091 | ||||||||
\(945\) | −3.25906 | −0.106017 | ||||||||
\(946\) | 1.00561 | 0.0326953 | ||||||||
\(947\) | −0.0677911 | −0.00220291 | −0.00110146 | − | 0.999999i | \(-0.500351\pi\) | ||||
−0.00110146 | + | 0.999999i | \(0.500351\pi\) | |||||||
\(948\) | 5.25463 | 0.170663 | ||||||||
\(949\) | −11.2549 | −0.365348 | ||||||||
\(950\) | −20.2859 | −0.658162 | ||||||||
\(951\) | 7.73483 | 0.250819 | ||||||||
\(952\) | −2.46023 | −0.0797364 | ||||||||
\(953\) | 1.00211 | 0.0324615 | 0.0162308 | − | 0.999868i | \(-0.494833\pi\) | ||||
0.0162308 | + | 0.999868i | \(0.494833\pi\) | |||||||
\(954\) | −7.79122 | −0.252250 | ||||||||
\(955\) | −3.93629 | −0.127375 | ||||||||
\(956\) | −7.83371 | −0.253360 | ||||||||
\(957\) | 1.92633 | 0.0622694 | ||||||||
\(958\) | 35.7133 | 1.15384 | ||||||||
\(959\) | 14.4465 | 0.466501 | ||||||||
\(960\) | 1.42840 | 0.0461013 | ||||||||
\(961\) | 76.5338 | 2.46883 | ||||||||
\(962\) | −9.76199 | −0.314739 | ||||||||
\(963\) | −10.4990 | −0.338324 | ||||||||
\(964\) | 23.8091 | 0.766841 | ||||||||
\(965\) | −8.68869 | −0.279699 | ||||||||
\(966\) | −3.76028 | −0.120985 | ||||||||
\(967\) | −17.9495 | −0.577218 | −0.288609 | − | 0.957447i | \(-0.593193\pi\) | ||||
−0.288609 | + | 0.957447i | \(0.593193\pi\) | |||||||
\(968\) | 10.8570 | 0.348956 | ||||||||
\(969\) | 7.39062 | 0.237421 | ||||||||
\(970\) | 14.3439 | 0.460554 | ||||||||
\(971\) | −12.1550 | −0.390072 | −0.195036 | − | 0.980796i | \(-0.562482\pi\) | ||||
−0.195036 | + | 0.980796i | \(0.562482\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 35.8680 | 1.14987 | ||||||||
\(974\) | −9.35930 | −0.299891 | ||||||||
\(975\) | −2.95968 | −0.0947858 | ||||||||
\(976\) | −4.05568 | −0.129819 | ||||||||
\(977\) | −9.80531 | −0.313700 | −0.156850 | − | 0.987622i | \(-0.550134\pi\) | ||||
−0.156850 | + | 0.987622i | \(0.550134\pi\) | |||||||
\(978\) | 6.40325 | 0.204753 | ||||||||
\(979\) | 1.99252 | 0.0636811 | ||||||||
\(980\) | −2.56284 | −0.0818668 | ||||||||
\(981\) | 0.860752 | 0.0274817 | ||||||||
\(982\) | 24.5502 | 0.783427 | ||||||||
\(983\) | 27.1478 | 0.865880 | 0.432940 | − | 0.901423i | \(-0.357476\pi\) | ||||
0.432940 | + | 0.901423i | \(0.357476\pi\) | |||||||
\(984\) | −0.952622 | −0.0303685 | ||||||||
\(985\) | −14.5646 | −0.464067 | ||||||||
\(986\) | −5.49208 | −0.174903 | ||||||||
\(987\) | −16.8459 | −0.536210 | ||||||||
\(988\) | −6.85408 | −0.218057 | ||||||||
\(989\) | −4.38210 | −0.139343 | ||||||||
\(990\) | 0.540224 | 0.0171694 | ||||||||
\(991\) | 53.6231 | 1.70339 | 0.851697 | − | 0.524035i | \(-0.175574\pi\) | ||||
0.851697 | + | 0.524035i | \(0.175574\pi\) | |||||||
\(992\) | −10.3699 | −0.329243 | ||||||||
\(993\) | 25.0994 | 0.796505 | ||||||||
\(994\) | 6.89441 | 0.218677 | ||||||||
\(995\) | 1.79155 | 0.0567960 | ||||||||
\(996\) | −11.2812 | −0.357458 | ||||||||
\(997\) | −32.0001 | −1.01345 | −0.506727 | − | 0.862106i | \(-0.669145\pi\) | ||||
−0.506727 | + | 0.862106i | \(0.669145\pi\) | |||||||
\(998\) | −0.932509 | −0.0295181 | ||||||||
\(999\) | 9.76199 | 0.308856 |
(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 | 8034.2.a.w.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |