Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(1,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.1 |
$q$-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 | ||||||||
\(5\) | 0.267949 | 0.119831 | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) | ||||
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.732051 | 0.276689 | 0.138345 | − | 0.990384i | \(-0.455822\pi\) | ||||
0.138345 | + | 0.990384i | \(0.455822\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.267949 | 0.0847330 | ||||||||
\(11\) | 4.73205 | 1.42677 | 0.713384 | − | 0.700774i | \(-0.247162\pi\) | ||||
0.713384 | + | 0.700774i | \(0.247162\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.732051 | 0.195649 | ||||||||
\(15\) | 0.267949 | 0.0691842 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.26795 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | 0.267949 | 0.0599153 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | 4.73205 | 1.00888 | ||||||||
\(23\) | −6.19615 | −1.29199 | −0.645994 | − | 0.763343i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763343i | \(0.723557\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.92820 | −0.985641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.732051 | 0.138345 | ||||||||
\(29\) | 2.46410 | 0.457572 | 0.228786 | − | 0.973477i | \(-0.426524\pi\) | ||||
0.228786 | + | 0.973477i | \(0.426524\pi\) | |||||||
\(30\) | 0.267949 | 0.0489206 | ||||||||
\(31\) | −5.46410 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.73205 | 0.823744 | ||||||||
\(34\) | −2.26795 | −0.388950 | ||||||||
\(35\) | 0.196152 | 0.0331558 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.4641 | 1.72029 | 0.860144 | − | 0.510052i | \(-0.170374\pi\) | ||||
0.860144 | + | 0.510052i | \(0.170374\pi\) | |||||||
\(38\) | 1.26795 | 0.205689 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.267949 | 0.0423665 | ||||||||
\(41\) | 11.3923 | 1.77918 | 0.889590 | − | 0.456761i | \(-0.150990\pi\) | ||||
0.889590 | + | 0.456761i | \(0.150990\pi\) | |||||||
\(42\) | 0.732051 | 0.112958 | ||||||||
\(43\) | 7.66025 | 1.16818 | 0.584089 | − | 0.811690i | \(-0.301452\pi\) | ||||
0.584089 | + | 0.811690i | \(0.301452\pi\) | |||||||
\(44\) | 4.73205 | 0.713384 | ||||||||
\(45\) | 0.267949 | 0.0399435 | ||||||||
\(46\) | −6.19615 | −0.913573 | ||||||||
\(47\) | −8.19615 | −1.19553 | −0.597766 | − | 0.801671i | \(-0.703945\pi\) | ||||
−0.597766 | + | 0.801671i | \(0.703945\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.46410 | −0.923443 | ||||||||
\(50\) | −4.92820 | −0.696953 | ||||||||
\(51\) | −2.26795 | −0.317576 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.464102 | 0.0637493 | 0.0318746 | − | 0.999492i | \(-0.489852\pi\) | ||||
0.0318746 | + | 0.999492i | \(0.489852\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.26795 | 0.170970 | ||||||||
\(56\) | 0.732051 | 0.0978244 | ||||||||
\(57\) | 1.26795 | 0.167944 | ||||||||
\(58\) | 2.46410 | 0.323552 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0.267949 | 0.0345921 | ||||||||
\(61\) | 1.19615 | 0.153152 | 0.0765758 | − | 0.997064i | \(-0.475601\pi\) | ||||
0.0765758 | + | 0.997064i | \(0.475601\pi\) | |||||||
\(62\) | −5.46410 | −0.693942 | ||||||||
\(63\) | 0.732051 | 0.0922297 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.73205 | 0.582475 | ||||||||
\(67\) | −11.1244 | −1.35906 | −0.679528 | − | 0.733649i | \(-0.737815\pi\) | ||||
−0.679528 | + | 0.733649i | \(0.737815\pi\) | |||||||
\(68\) | −2.26795 | −0.275029 | ||||||||
\(69\) | −6.19615 | −0.745929 | ||||||||
\(70\) | 0.196152 | 0.0234447 | ||||||||
\(71\) | 1.26795 | 0.150478 | 0.0752389 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752389 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −9.73205 | −1.13905 | −0.569525 | − | 0.821974i | \(-0.692873\pi\) | ||||
−0.569525 | + | 0.821974i | \(0.692873\pi\) | |||||||
\(74\) | 10.4641 | 1.21643 | ||||||||
\(75\) | −4.92820 | −0.569060 | ||||||||
\(76\) | 1.26795 | 0.145444 | ||||||||
\(77\) | 3.46410 | 0.394771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.46410 | −1.06479 | −0.532397 | − | 0.846495i | \(-0.678709\pi\) | ||||
−0.532397 | + | 0.846495i | \(0.678709\pi\) | |||||||
\(80\) | 0.267949 | 0.0299576 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.3923 | 1.25807 | ||||||||
\(83\) | 10.1962 | 1.11917 | 0.559587 | − | 0.828772i | \(-0.310960\pi\) | ||||
0.559587 | + | 0.828772i | \(0.310960\pi\) | |||||||
\(84\) | 0.732051 | 0.0798733 | ||||||||
\(85\) | −0.607695 | −0.0659138 | ||||||||
\(86\) | 7.66025 | 0.826026 | ||||||||
\(87\) | 2.46410 | 0.264179 | ||||||||
\(88\) | 4.73205 | 0.504438 | ||||||||
\(89\) | −2.53590 | −0.268805 | −0.134402 | − | 0.990927i | \(-0.542911\pi\) | ||||
−0.134402 | + | 0.990927i | \(0.542911\pi\) | |||||||
\(90\) | 0.267949 | 0.0282443 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.19615 | −0.645994 | ||||||||
\(93\) | −5.46410 | −0.566601 | ||||||||
\(94\) | −8.19615 | −0.845369 | ||||||||
\(95\) | 0.339746 | 0.0348572 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −6.46410 | −0.652973 | ||||||||
\(99\) | 4.73205 | 0.475589 | ||||||||
\(100\) | −4.92820 | −0.492820 | ||||||||
\(101\) | −11.9282 | −1.18690 | −0.593450 | − | 0.804871i | \(-0.702235\pi\) | ||||
−0.593450 | + | 0.804871i | \(0.702235\pi\) | |||||||
\(102\) | −2.26795 | −0.224560 | ||||||||
\(103\) | −18.7321 | −1.84572 | −0.922862 | − | 0.385131i | \(-0.874156\pi\) | ||||
−0.922862 | + | 0.385131i | \(0.874156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.196152 | 0.0191425 | ||||||||
\(106\) | 0.464102 | 0.0450775 | ||||||||
\(107\) | −0.196152 | −0.0189628 | −0.00948139 | − | 0.999955i | \(-0.503018\pi\) | ||||
−0.00948139 | + | 0.999955i | \(0.503018\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −5.46410 | −0.523366 | −0.261683 | − | 0.965154i | \(-0.584277\pi\) | ||||
−0.261683 | + | 0.965154i | \(0.584277\pi\) | |||||||
\(110\) | 1.26795 | 0.120894 | ||||||||
\(111\) | 10.4641 | 0.993209 | ||||||||
\(112\) | 0.732051 | 0.0691723 | ||||||||
\(113\) | −18.6603 | −1.75541 | −0.877705 | − | 0.479202i | \(-0.840926\pi\) | ||||
−0.877705 | + | 0.479202i | \(0.840926\pi\) | |||||||
\(114\) | 1.26795 | 0.118754 | ||||||||
\(115\) | −1.66025 | −0.154819 | ||||||||
\(116\) | 2.46410 | 0.228786 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | −1.66025 | −0.152195 | ||||||||
\(120\) | 0.267949 | 0.0244603 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 1.19615 | 0.108295 | ||||||||
\(123\) | 11.3923 | 1.02721 | ||||||||
\(124\) | −5.46410 | −0.490691 | ||||||||
\(125\) | −2.66025 | −0.237940 | ||||||||
\(126\) | 0.732051 | 0.0652163 | ||||||||
\(127\) | 17.8564 | 1.58450 | 0.792250 | − | 0.610197i | \(-0.208910\pi\) | ||||
0.792250 | + | 0.610197i | \(0.208910\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.66025 | 0.674448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4641 | 1.17636 | 0.588182 | − | 0.808729i | \(-0.299844\pi\) | ||||
0.588182 | + | 0.808729i | \(0.299844\pi\) | |||||||
\(132\) | 4.73205 | 0.411872 | ||||||||
\(133\) | 0.928203 | 0.0804854 | ||||||||
\(134\) | −11.1244 | −0.960998 | ||||||||
\(135\) | 0.267949 | 0.0230614 | ||||||||
\(136\) | −2.26795 | −0.194475 | ||||||||
\(137\) | −1.92820 | −0.164738 | −0.0823688 | − | 0.996602i | \(-0.526249\pi\) | ||||
−0.0823688 | + | 0.996602i | \(0.526249\pi\) | |||||||
\(138\) | −6.19615 | −0.527452 | ||||||||
\(139\) | −9.85641 | −0.836009 | −0.418005 | − | 0.908445i | \(-0.637270\pi\) | ||||
−0.418005 | + | 0.908445i | \(0.637270\pi\) | |||||||
\(140\) | 0.196152 | 0.0165779 | ||||||||
\(141\) | −8.19615 | −0.690241 | ||||||||
\(142\) | 1.26795 | 0.106404 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.660254 | 0.0548311 | ||||||||
\(146\) | −9.73205 | −0.805430 | ||||||||
\(147\) | −6.46410 | −0.533150 | ||||||||
\(148\) | 10.4641 | 0.860144 | ||||||||
\(149\) | 2.80385 | 0.229700 | 0.114850 | − | 0.993383i | \(-0.463361\pi\) | ||||
0.114850 | + | 0.993383i | \(0.463361\pi\) | |||||||
\(150\) | −4.92820 | −0.402386 | ||||||||
\(151\) | 3.26795 | 0.265942 | 0.132971 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132971 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(152\) | 1.26795 | 0.102844 | ||||||||
\(153\) | −2.26795 | −0.183353 | ||||||||
\(154\) | 3.46410 | 0.279145 | ||||||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.5885 | −1.88256 | −0.941282 | − | 0.337622i | \(-0.890378\pi\) | ||||
−0.941282 | + | 0.337622i | \(0.890378\pi\) | |||||||
\(158\) | −9.46410 | −0.752923 | ||||||||
\(159\) | 0.464102 | 0.0368057 | ||||||||
\(160\) | 0.267949 | 0.0211832 | ||||||||
\(161\) | −4.53590 | −0.357479 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.53590 | −0.511931 | −0.255966 | − | 0.966686i | \(-0.582393\pi\) | ||||
−0.255966 | + | 0.966686i | \(0.582393\pi\) | |||||||
\(164\) | 11.3923 | 0.889590 | ||||||||
\(165\) | 1.26795 | 0.0987097 | ||||||||
\(166\) | 10.1962 | 0.791375 | ||||||||
\(167\) | −2.53590 | −0.196234 | −0.0981169 | − | 0.995175i | \(-0.531282\pi\) | ||||
−0.0981169 | + | 0.995175i | \(0.531282\pi\) | |||||||
\(168\) | 0.732051 | 0.0564789 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.607695 | −0.0466081 | ||||||||
\(171\) | 1.26795 | 0.0969625 | ||||||||
\(172\) | 7.66025 | 0.584089 | ||||||||
\(173\) | −16.3923 | −1.24628 | −0.623142 | − | 0.782109i | \(-0.714144\pi\) | ||||
−0.623142 | + | 0.782109i | \(0.714144\pi\) | |||||||
\(174\) | 2.46410 | 0.186803 | ||||||||
\(175\) | −3.60770 | −0.272716 | ||||||||
\(176\) | 4.73205 | 0.356692 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | −2.53590 | −0.190074 | ||||||||
\(179\) | 22.0526 | 1.64829 | 0.824143 | − | 0.566382i | \(-0.191657\pi\) | ||||
0.824143 | + | 0.566382i | \(0.191657\pi\) | |||||||
\(180\) | 0.267949 | 0.0199718 | ||||||||
\(181\) | 8.80385 | 0.654385 | 0.327192 | − | 0.944958i | \(-0.393897\pi\) | ||||
0.327192 | + | 0.944958i | \(0.393897\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19615 | 0.0884221 | ||||||||
\(184\) | −6.19615 | −0.456786 | ||||||||
\(185\) | 2.80385 | 0.206143 | ||||||||
\(186\) | −5.46410 | −0.400647 | ||||||||
\(187\) | −10.7321 | −0.784805 | ||||||||
\(188\) | −8.19615 | −0.597766 | ||||||||
\(189\) | 0.732051 | 0.0532489 | ||||||||
\(190\) | 0.339746 | 0.0246478 | ||||||||
\(191\) | 6.92820 | 0.501307 | 0.250654 | − | 0.968077i | \(-0.419354\pi\) | ||||
0.250654 | + | 0.968077i | \(0.419354\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.26795 | −0.595140 | −0.297570 | − | 0.954700i | \(-0.596176\pi\) | ||||
−0.297570 | + | 0.954700i | \(0.596176\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | 9.85641 | 0.702240 | 0.351120 | − | 0.936330i | \(-0.385801\pi\) | ||||
0.351120 | + | 0.936330i | \(0.385801\pi\) | |||||||
\(198\) | 4.73205 | 0.336292 | ||||||||
\(199\) | −3.80385 | −0.269648 | −0.134824 | − | 0.990870i | \(-0.543047\pi\) | ||||
−0.134824 | + | 0.990870i | \(0.543047\pi\) | |||||||
\(200\) | −4.92820 | −0.348477 | ||||||||
\(201\) | −11.1244 | −0.784652 | ||||||||
\(202\) | −11.9282 | −0.839265 | ||||||||
\(203\) | 1.80385 | 0.126605 | ||||||||
\(204\) | −2.26795 | −0.158788 | ||||||||
\(205\) | 3.05256 | 0.213200 | ||||||||
\(206\) | −18.7321 | −1.30512 | ||||||||
\(207\) | −6.19615 | −0.430662 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0.196152 | 0.0135358 | ||||||||
\(211\) | −4.39230 | −0.302379 | −0.151189 | − | 0.988505i | \(-0.548310\pi\) | ||||
−0.151189 | + | 0.988505i | \(0.548310\pi\) | |||||||
\(212\) | 0.464102 | 0.0318746 | ||||||||
\(213\) | 1.26795 | 0.0868784 | ||||||||
\(214\) | −0.196152 | −0.0134087 | ||||||||
\(215\) | 2.05256 | 0.139983 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | −5.46410 | −0.370076 | ||||||||
\(219\) | −9.73205 | −0.657631 | ||||||||
\(220\) | 1.26795 | 0.0854851 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.4641 | 0.702305 | ||||||||
\(223\) | −13.0718 | −0.875352 | −0.437676 | − | 0.899133i | \(-0.644198\pi\) | ||||
−0.437676 | + | 0.899133i | \(0.644198\pi\) | |||||||
\(224\) | 0.732051 | 0.0489122 | ||||||||
\(225\) | −4.92820 | −0.328547 | ||||||||
\(226\) | −18.6603 | −1.24126 | ||||||||
\(227\) | −1.80385 | −0.119726 | −0.0598628 | − | 0.998207i | \(-0.519066\pi\) | ||||
−0.0598628 | + | 0.998207i | \(0.519066\pi\) | |||||||
\(228\) | 1.26795 | 0.0839720 | ||||||||
\(229\) | 15.8564 | 1.04782 | 0.523910 | − | 0.851773i | \(-0.324473\pi\) | ||||
0.523910 | + | 0.851773i | \(0.324473\pi\) | |||||||
\(230\) | −1.66025 | −0.109474 | ||||||||
\(231\) | 3.46410 | 0.227921 | ||||||||
\(232\) | 2.46410 | 0.161776 | ||||||||
\(233\) | 19.8564 | 1.30084 | 0.650418 | − | 0.759576i | \(-0.274594\pi\) | ||||
0.650418 | + | 0.759576i | \(0.274594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.19615 | −0.143261 | ||||||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | −9.46410 | −0.614759 | ||||||||
\(238\) | −1.66025 | −0.107618 | ||||||||
\(239\) | −9.66025 | −0.624870 | −0.312435 | − | 0.949939i | \(-0.601145\pi\) | ||||
−0.312435 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(240\) | 0.267949 | 0.0172960 | ||||||||
\(241\) | −17.5885 | −1.13297 | −0.566486 | − | 0.824071i | \(-0.691698\pi\) | ||||
−0.566486 | + | 0.824071i | \(0.691698\pi\) | |||||||
\(242\) | 11.3923 | 0.732325 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.19615 | 0.0765758 | ||||||||
\(245\) | −1.73205 | −0.110657 | ||||||||
\(246\) | 11.3923 | 0.726347 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.46410 | −0.346971 | ||||||||
\(249\) | 10.1962 | 0.646155 | ||||||||
\(250\) | −2.66025 | −0.168249 | ||||||||
\(251\) | 6.53590 | 0.412542 | 0.206271 | − | 0.978495i | \(-0.433867\pi\) | ||||
0.206271 | + | 0.978495i | \(0.433867\pi\) | |||||||
\(252\) | 0.732051 | 0.0461149 | ||||||||
\(253\) | −29.3205 | −1.84336 | ||||||||
\(254\) | 17.8564 | 1.12041 | ||||||||
\(255\) | −0.607695 | −0.0380553 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.6603 | 1.66302 | 0.831510 | − | 0.555509i | \(-0.187477\pi\) | ||||
0.831510 | + | 0.555509i | \(0.187477\pi\) | |||||||
\(258\) | 7.66025 | 0.476907 | ||||||||
\(259\) | 7.66025 | 0.475985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.46410 | 0.152524 | ||||||||
\(262\) | 13.4641 | 0.831815 | ||||||||
\(263\) | 28.0526 | 1.72979 | 0.864897 | − | 0.501949i | \(-0.167383\pi\) | ||||
0.864897 | + | 0.501949i | \(0.167383\pi\) | |||||||
\(264\) | 4.73205 | 0.291238 | ||||||||
\(265\) | 0.124356 | 0.00763911 | ||||||||
\(266\) | 0.928203 | 0.0569118 | ||||||||
\(267\) | −2.53590 | −0.155194 | ||||||||
\(268\) | −11.1244 | −0.679528 | ||||||||
\(269\) | −1.46410 | −0.0892679 | −0.0446339 | − | 0.999003i | \(-0.514212\pi\) | ||||
−0.0446339 | + | 0.999003i | \(0.514212\pi\) | |||||||
\(270\) | 0.267949 | 0.0163069 | ||||||||
\(271\) | 5.85641 | 0.355751 | 0.177876 | − | 0.984053i | \(-0.443078\pi\) | ||||
0.177876 | + | 0.984053i | \(0.443078\pi\) | |||||||
\(272\) | −2.26795 | −0.137515 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.92820 | −0.116487 | ||||||||
\(275\) | −23.3205 | −1.40628 | ||||||||
\(276\) | −6.19615 | −0.372965 | ||||||||
\(277\) | −2.26795 | −0.136268 | −0.0681339 | − | 0.997676i | \(-0.521705\pi\) | ||||
−0.0681339 | + | 0.997676i | \(0.521705\pi\) | |||||||
\(278\) | −9.85641 | −0.591148 | ||||||||
\(279\) | −5.46410 | −0.327127 | ||||||||
\(280\) | 0.196152 | 0.0117223 | ||||||||
\(281\) | −22.3205 | −1.33153 | −0.665765 | − | 0.746162i | \(-0.731895\pi\) | ||||
−0.665765 | + | 0.746162i | \(0.731895\pi\) | |||||||
\(282\) | −8.19615 | −0.488074 | ||||||||
\(283\) | 8.33975 | 0.495746 | 0.247873 | − | 0.968792i | \(-0.420268\pi\) | ||||
0.247873 | + | 0.968792i | \(0.420268\pi\) | |||||||
\(284\) | 1.26795 | 0.0752389 | ||||||||
\(285\) | 0.339746 | 0.0201248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.33975 | 0.492280 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | 0.660254 | 0.0387715 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | −9.73205 | −0.569525 | ||||||||
\(293\) | −14.5167 | −0.848072 | −0.424036 | − | 0.905645i | \(-0.639387\pi\) | ||||
−0.424036 | + | 0.905645i | \(0.639387\pi\) | |||||||
\(294\) | −6.46410 | −0.376994 | ||||||||
\(295\) | 2.14359 | 0.124805 | ||||||||
\(296\) | 10.4641 | 0.608214 | ||||||||
\(297\) | 4.73205 | 0.274581 | ||||||||
\(298\) | 2.80385 | 0.162423 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.92820 | −0.284530 | ||||||||
\(301\) | 5.60770 | 0.323222 | ||||||||
\(302\) | 3.26795 | 0.188049 | ||||||||
\(303\) | −11.9282 | −0.685257 | ||||||||
\(304\) | 1.26795 | 0.0727219 | ||||||||
\(305\) | 0.320508 | 0.0183522 | ||||||||
\(306\) | −2.26795 | −0.129650 | ||||||||
\(307\) | 8.58846 | 0.490169 | 0.245085 | − | 0.969502i | \(-0.421184\pi\) | ||||
0.245085 | + | 0.969502i | \(0.421184\pi\) | |||||||
\(308\) | 3.46410 | 0.197386 | ||||||||
\(309\) | −18.7321 | −1.06563 | ||||||||
\(310\) | −1.46410 | −0.0831554 | ||||||||
\(311\) | 15.6603 | 0.888012 | 0.444006 | − | 0.896024i | \(-0.353557\pi\) | ||||
0.444006 | + | 0.896024i | \(0.353557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4641 | 0.761036 | 0.380518 | − | 0.924774i | \(-0.375746\pi\) | ||||
0.380518 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(314\) | −23.5885 | −1.33117 | ||||||||
\(315\) | 0.196152 | 0.0110519 | ||||||||
\(316\) | −9.46410 | −0.532397 | ||||||||
\(317\) | 3.33975 | 0.187579 | 0.0937894 | − | 0.995592i | \(-0.470102\pi\) | ||||
0.0937894 | + | 0.995592i | \(0.470102\pi\) | |||||||
\(318\) | 0.464102 | 0.0260255 | ||||||||
\(319\) | 11.6603 | 0.652849 | ||||||||
\(320\) | 0.267949 | 0.0149788 | ||||||||
\(321\) | −0.196152 | −0.0109482 | ||||||||
\(322\) | −4.53590 | −0.252776 | ||||||||
\(323\) | −2.87564 | −0.160005 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.53590 | −0.361990 | ||||||||
\(327\) | −5.46410 | −0.302166 | ||||||||
\(328\) | 11.3923 | 0.629035 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 1.26795 | 0.0697983 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 10.1962 | 0.559587 | ||||||||
\(333\) | 10.4641 | 0.573429 | ||||||||
\(334\) | −2.53590 | −0.138758 | ||||||||
\(335\) | −2.98076 | −0.162856 | ||||||||
\(336\) | 0.732051 | 0.0399366 | ||||||||
\(337\) | 6.85641 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.6603 | −1.01349 | ||||||||
\(340\) | −0.607695 | −0.0329569 | ||||||||
\(341\) | −25.8564 | −1.40020 | ||||||||
\(342\) | 1.26795 | 0.0685628 | ||||||||
\(343\) | −9.85641 | −0.532196 | ||||||||
\(344\) | 7.66025 | 0.413013 | ||||||||
\(345\) | −1.66025 | −0.0893851 | ||||||||
\(346\) | −16.3923 | −0.881256 | ||||||||
\(347\) | 8.87564 | 0.476470 | 0.238235 | − | 0.971208i | \(-0.423431\pi\) | ||||
0.238235 | + | 0.971208i | \(0.423431\pi\) | |||||||
\(348\) | 2.46410 | 0.132090 | ||||||||
\(349\) | −19.3205 | −1.03420 | −0.517102 | − | 0.855924i | \(-0.672989\pi\) | ||||
−0.517102 | + | 0.855924i | \(0.672989\pi\) | |||||||
\(350\) | −3.60770 | −0.192839 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.73205 | 0.252219 | ||||||||
\(353\) | 19.7846 | 1.05303 | 0.526514 | − | 0.850166i | \(-0.323499\pi\) | ||||
0.526514 | + | 0.850166i | \(0.323499\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | 0.339746 | 0.0180318 | ||||||||
\(356\) | −2.53590 | −0.134402 | ||||||||
\(357\) | −1.66025 | −0.0878700 | ||||||||
\(358\) | 22.0526 | 1.16551 | ||||||||
\(359\) | 23.1244 | 1.22046 | 0.610228 | − | 0.792226i | \(-0.291078\pi\) | ||||
0.610228 | + | 0.792226i | \(0.291078\pi\) | |||||||
\(360\) | 0.267949 | 0.0141222 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 8.80385 | 0.462720 | ||||||||
\(363\) | 11.3923 | 0.597941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.60770 | −0.136493 | ||||||||
\(366\) | 1.19615 | 0.0625239 | ||||||||
\(367\) | −14.7321 | −0.769007 | −0.384503 | − | 0.923124i | \(-0.625627\pi\) | ||||
−0.384503 | + | 0.923124i | \(0.625627\pi\) | |||||||
\(368\) | −6.19615 | −0.322997 | ||||||||
\(369\) | 11.3923 | 0.593060 | ||||||||
\(370\) | 2.80385 | 0.145765 | ||||||||
\(371\) | 0.339746 | 0.0176387 | ||||||||
\(372\) | −5.46410 | −0.283300 | ||||||||
\(373\) | −10.2679 | −0.531654 | −0.265827 | − | 0.964021i | \(-0.585645\pi\) | ||||
−0.265827 | + | 0.964021i | \(0.585645\pi\) | |||||||
\(374\) | −10.7321 | −0.554941 | ||||||||
\(375\) | −2.66025 | −0.137375 | ||||||||
\(376\) | −8.19615 | −0.422684 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.732051 | 0.0376526 | ||||||||
\(379\) | 1.46410 | 0.0752058 | 0.0376029 | − | 0.999293i | \(-0.488028\pi\) | ||||
0.0376029 | + | 0.999293i | \(0.488028\pi\) | |||||||
\(380\) | 0.339746 | 0.0174286 | ||||||||
\(381\) | 17.8564 | 0.914811 | ||||||||
\(382\) | 6.92820 | 0.354478 | ||||||||
\(383\) | 5.46410 | 0.279203 | 0.139601 | − | 0.990208i | \(-0.455418\pi\) | ||||
0.139601 | + | 0.990208i | \(0.455418\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.928203 | 0.0473056 | ||||||||
\(386\) | −8.26795 | −0.420828 | ||||||||
\(387\) | 7.66025 | 0.389393 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | −29.7846 | −1.51014 | −0.755070 | − | 0.655644i | \(-0.772397\pi\) | ||||
−0.755070 | + | 0.655644i | \(0.772397\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0526 | 0.710668 | ||||||||
\(392\) | −6.46410 | −0.326486 | ||||||||
\(393\) | 13.4641 | 0.679174 | ||||||||
\(394\) | 9.85641 | 0.496559 | ||||||||
\(395\) | −2.53590 | −0.127595 | ||||||||
\(396\) | 4.73205 | 0.237795 | ||||||||
\(397\) | −0.392305 | −0.0196892 | −0.00984461 | − | 0.999952i | \(-0.503134\pi\) | ||||
−0.00984461 | + | 0.999952i | \(0.503134\pi\) | |||||||
\(398\) | −3.80385 | −0.190670 | ||||||||
\(399\) | 0.928203 | 0.0464683 | ||||||||
\(400\) | −4.92820 | −0.246410 | ||||||||
\(401\) | 21.9282 | 1.09504 | 0.547521 | − | 0.836792i | \(-0.315572\pi\) | ||||
0.547521 | + | 0.836792i | \(0.315572\pi\) | |||||||
\(402\) | −11.1244 | −0.554832 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.9282 | −0.593450 | ||||||||
\(405\) | 0.267949 | 0.0133145 | ||||||||
\(406\) | 1.80385 | 0.0895235 | ||||||||
\(407\) | 49.5167 | 2.45445 | ||||||||
\(408\) | −2.26795 | −0.112280 | ||||||||
\(409\) | 14.2679 | 0.705505 | 0.352752 | − | 0.935717i | \(-0.385246\pi\) | ||||
0.352752 | + | 0.935717i | \(0.385246\pi\) | |||||||
\(410\) | 3.05256 | 0.150755 | ||||||||
\(411\) | −1.92820 | −0.0951113 | ||||||||
\(412\) | −18.7321 | −0.922862 | ||||||||
\(413\) | 5.85641 | 0.288175 | ||||||||
\(414\) | −6.19615 | −0.304524 | ||||||||
\(415\) | 2.73205 | 0.134111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.85641 | −0.482670 | ||||||||
\(418\) | 6.00000 | 0.293470 | ||||||||
\(419\) | −10.5359 | −0.514712 | −0.257356 | − | 0.966317i | \(-0.582851\pi\) | ||||
−0.257356 | + | 0.966317i | \(0.582851\pi\) | |||||||
\(420\) | 0.196152 | 0.00957126 | ||||||||
\(421\) | 32.7128 | 1.59432 | 0.797162 | − | 0.603765i | \(-0.206333\pi\) | ||||
0.797162 | + | 0.603765i | \(0.206333\pi\) | |||||||
\(422\) | −4.39230 | −0.213814 | ||||||||
\(423\) | −8.19615 | −0.398511 | ||||||||
\(424\) | 0.464102 | 0.0225388 | ||||||||
\(425\) | 11.1769 | 0.542160 | ||||||||
\(426\) | 1.26795 | 0.0614323 | ||||||||
\(427\) | 0.875644 | 0.0423754 | ||||||||
\(428\) | −0.196152 | −0.00948139 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.05256 | 0.0989832 | ||||||||
\(431\) | −11.1244 | −0.535841 | −0.267921 | − | 0.963441i | \(-0.586337\pi\) | ||||
−0.267921 | + | 0.963441i | \(0.586337\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −14.8564 | −0.713953 | −0.356977 | − | 0.934113i | \(-0.616192\pi\) | ||||
−0.356977 | + | 0.934113i | \(0.616192\pi\) | |||||||
\(434\) | −4.00000 | −0.192006 | ||||||||
\(435\) | 0.660254 | 0.0316568 | ||||||||
\(436\) | −5.46410 | −0.261683 | ||||||||
\(437\) | −7.85641 | −0.375823 | ||||||||
\(438\) | −9.73205 | −0.465015 | ||||||||
\(439\) | −17.6603 | −0.842878 | −0.421439 | − | 0.906857i | \(-0.638475\pi\) | ||||
−0.421439 | + | 0.906857i | \(0.638475\pi\) | |||||||
\(440\) | 1.26795 | 0.0604471 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.3923 | 1.72905 | 0.864525 | − | 0.502589i | \(-0.167619\pi\) | ||||
0.864525 | + | 0.502589i | \(0.167619\pi\) | |||||||
\(444\) | 10.4641 | 0.496604 | ||||||||
\(445\) | −0.679492 | −0.0322110 | ||||||||
\(446\) | −13.0718 | −0.618968 | ||||||||
\(447\) | 2.80385 | 0.132617 | ||||||||
\(448\) | 0.732051 | 0.0345861 | ||||||||
\(449\) | −23.3205 | −1.10056 | −0.550281 | − | 0.834979i | \(-0.685480\pi\) | ||||
−0.550281 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(450\) | −4.92820 | −0.232318 | ||||||||
\(451\) | 53.9090 | 2.53847 | ||||||||
\(452\) | −18.6603 | −0.877705 | ||||||||
\(453\) | 3.26795 | 0.153542 | ||||||||
\(454\) | −1.80385 | −0.0846588 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.26795 | 0.0593772 | ||||||||
\(457\) | 18.6603 | 0.872890 | 0.436445 | − | 0.899731i | \(-0.356237\pi\) | ||||
0.436445 | + | 0.899731i | \(0.356237\pi\) | |||||||
\(458\) | 15.8564 | 0.740921 | ||||||||
\(459\) | −2.26795 | −0.105859 | ||||||||
\(460\) | −1.66025 | −0.0774097 | ||||||||
\(461\) | 25.7321 | 1.19846 | 0.599231 | − | 0.800577i | \(-0.295473\pi\) | ||||
0.599231 | + | 0.800577i | \(0.295473\pi\) | |||||||
\(462\) | 3.46410 | 0.161165 | ||||||||
\(463\) | −28.0526 | −1.30371 | −0.651856 | − | 0.758342i | \(-0.726010\pi\) | ||||
−0.651856 | + | 0.758342i | \(0.726010\pi\) | |||||||
\(464\) | 2.46410 | 0.114393 | ||||||||
\(465\) | −1.46410 | −0.0678961 | ||||||||
\(466\) | 19.8564 | 0.919830 | ||||||||
\(467\) | −12.5885 | −0.582524 | −0.291262 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291262 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.14359 | −0.376036 | ||||||||
\(470\) | −2.19615 | −0.101301 | ||||||||
\(471\) | −23.5885 | −1.08690 | ||||||||
\(472\) | 8.00000 | 0.368230 | ||||||||
\(473\) | 36.2487 | 1.66672 | ||||||||
\(474\) | −9.46410 | −0.434701 | ||||||||
\(475\) | −6.24871 | −0.286711 | ||||||||
\(476\) | −1.66025 | −0.0760976 | ||||||||
\(477\) | 0.464102 | 0.0212498 | ||||||||
\(478\) | −9.66025 | −0.441850 | ||||||||
\(479\) | 26.5359 | 1.21246 | 0.606228 | − | 0.795291i | \(-0.292682\pi\) | ||||
0.606228 | + | 0.795291i | \(0.292682\pi\) | |||||||
\(480\) | 0.267949 | 0.0122302 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.5885 | −0.801132 | ||||||||
\(483\) | −4.53590 | −0.206391 | ||||||||
\(484\) | 11.3923 | 0.517832 | ||||||||
\(485\) | −1.60770 | −0.0730017 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 21.1244 | 0.957236 | 0.478618 | − | 0.878023i | \(-0.341138\pi\) | ||||
0.478618 | + | 0.878023i | \(0.341138\pi\) | |||||||
\(488\) | 1.19615 | 0.0541473 | ||||||||
\(489\) | −6.53590 | −0.295564 | ||||||||
\(490\) | −1.73205 | −0.0782461 | ||||||||
\(491\) | 5.26795 | 0.237739 | 0.118870 | − | 0.992910i | \(-0.462073\pi\) | ||||
0.118870 | + | 0.992910i | \(0.462073\pi\) | |||||||
\(492\) | 11.3923 | 0.513605 | ||||||||
\(493\) | −5.58846 | −0.251691 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.26795 | 0.0569901 | ||||||||
\(496\) | −5.46410 | −0.245345 | ||||||||
\(497\) | 0.928203 | 0.0416356 | ||||||||
\(498\) | 10.1962 | 0.456901 | ||||||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | −2.66025 | −0.118970 | ||||||||
\(501\) | −2.53590 | −0.113296 | ||||||||
\(502\) | 6.53590 | 0.291711 | ||||||||
\(503\) | −10.9808 | −0.489608 | −0.244804 | − | 0.969573i | \(-0.578724\pi\) | ||||
−0.244804 | + | 0.969573i | \(0.578724\pi\) | |||||||
\(504\) | 0.732051 | 0.0326081 | ||||||||
\(505\) | −3.19615 | −0.142227 | ||||||||
\(506\) | −29.3205 | −1.30346 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.8564 | 0.792250 | ||||||||
\(509\) | 10.2679 | 0.455119 | 0.227559 | − | 0.973764i | \(-0.426925\pi\) | ||||
0.227559 | + | 0.973764i | \(0.426925\pi\) | |||||||
\(510\) | −0.607695 | −0.0269092 | ||||||||
\(511\) | −7.12436 | −0.315163 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.26795 | 0.0559813 | ||||||||
\(514\) | 26.6603 | 1.17593 | ||||||||
\(515\) | −5.01924 | −0.221174 | ||||||||
\(516\) | 7.66025 | 0.337224 | ||||||||
\(517\) | −38.7846 | −1.70575 | ||||||||
\(518\) | 7.66025 | 0.336572 | ||||||||
\(519\) | −16.3923 | −0.719542 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4449 | −0.764273 | −0.382137 | − | 0.924106i | \(-0.624812\pi\) | ||||
−0.382137 | + | 0.924106i | \(0.624812\pi\) | |||||||
\(522\) | 2.46410 | 0.107851 | ||||||||
\(523\) | 36.4449 | 1.59362 | 0.796811 | − | 0.604228i | \(-0.206518\pi\) | ||||
0.796811 | + | 0.604228i | \(0.206518\pi\) | |||||||
\(524\) | 13.4641 | 0.588182 | ||||||||
\(525\) | −3.60770 | −0.157453 | ||||||||
\(526\) | 28.0526 | 1.22315 | ||||||||
\(527\) | 12.3923 | 0.539817 | ||||||||
\(528\) | 4.73205 | 0.205936 | ||||||||
\(529\) | 15.3923 | 0.669231 | ||||||||
\(530\) | 0.124356 | 0.00540166 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0.928203 | 0.0402427 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.53590 | −0.109739 | ||||||||
\(535\) | −0.0525589 | −0.00227232 | ||||||||
\(536\) | −11.1244 | −0.480499 | ||||||||
\(537\) | 22.0526 | 0.951638 | ||||||||
\(538\) | −1.46410 | −0.0631219 | ||||||||
\(539\) | −30.5885 | −1.31754 | ||||||||
\(540\) | 0.267949 | 0.0115307 | ||||||||
\(541\) | 40.3205 | 1.73351 | 0.866757 | − | 0.498731i | \(-0.166200\pi\) | ||||
0.866757 | + | 0.498731i | \(0.166200\pi\) | |||||||
\(542\) | 5.85641 | 0.251554 | ||||||||
\(543\) | 8.80385 | 0.377809 | ||||||||
\(544\) | −2.26795 | −0.0972375 | ||||||||
\(545\) | −1.46410 | −0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.19615 | 0.264928 | 0.132464 | − | 0.991188i | \(-0.457711\pi\) | ||||
0.132464 | + | 0.991188i | \(0.457711\pi\) | |||||||
\(548\) | −1.92820 | −0.0823688 | ||||||||
\(549\) | 1.19615 | 0.0510505 | ||||||||
\(550\) | −23.3205 | −0.994390 | ||||||||
\(551\) | 3.12436 | 0.133102 | ||||||||
\(552\) | −6.19615 | −0.263726 | ||||||||
\(553\) | −6.92820 | −0.294617 | ||||||||
\(554\) | −2.26795 | −0.0963559 | ||||||||
\(555\) | 2.80385 | 0.119017 | ||||||||
\(556\) | −9.85641 | −0.418005 | ||||||||
\(557\) | −30.3731 | −1.28695 | −0.643474 | − | 0.765468i | \(-0.722508\pi\) | ||||
−0.643474 | + | 0.765468i | \(0.722508\pi\) | |||||||
\(558\) | −5.46410 | −0.231314 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.196152 | 0.00828895 | ||||||||
\(561\) | −10.7321 | −0.453108 | ||||||||
\(562\) | −22.3205 | −0.941534 | ||||||||
\(563\) | 21.0718 | 0.888070 | 0.444035 | − | 0.896009i | \(-0.353547\pi\) | ||||
0.444035 | + | 0.896009i | \(0.353547\pi\) | |||||||
\(564\) | −8.19615 | −0.345120 | ||||||||
\(565\) | −5.00000 | −0.210352 | ||||||||
\(566\) | 8.33975 | 0.350546 | ||||||||
\(567\) | 0.732051 | 0.0307432 | ||||||||
\(568\) | 1.26795 | 0.0532020 | ||||||||
\(569\) | −38.6410 | −1.61992 | −0.809958 | − | 0.586488i | \(-0.800510\pi\) | ||||
−0.809958 | + | 0.586488i | \(0.800510\pi\) | |||||||
\(570\) | 0.339746 | 0.0142304 | ||||||||
\(571\) | −24.0526 | −1.00657 | −0.503284 | − | 0.864121i | \(-0.667875\pi\) | ||||
−0.503284 | + | 0.864121i | \(0.667875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.92820 | 0.289430 | ||||||||
\(574\) | 8.33975 | 0.348094 | ||||||||
\(575\) | 30.5359 | 1.27343 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 0.267949 | 0.0111549 | 0.00557744 | − | 0.999984i | \(-0.498225\pi\) | ||||
0.00557744 | + | 0.999984i | \(0.498225\pi\) | |||||||
\(578\) | −11.8564 | −0.493161 | ||||||||
\(579\) | −8.26795 | −0.343604 | ||||||||
\(580\) | 0.660254 | 0.0274156 | ||||||||
\(581\) | 7.46410 | 0.309663 | ||||||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | 2.19615 | 0.0909553 | ||||||||
\(584\) | −9.73205 | −0.402715 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5167 | −0.599678 | ||||||||
\(587\) | 16.0000 | 0.660391 | 0.330195 | − | 0.943913i | \(-0.392885\pi\) | ||||
0.330195 | + | 0.943913i | \(0.392885\pi\) | |||||||
\(588\) | −6.46410 | −0.266575 | ||||||||
\(589\) | −6.92820 | −0.285472 | ||||||||
\(590\) | 2.14359 | 0.0882503 | ||||||||
\(591\) | 9.85641 | 0.405438 | ||||||||
\(592\) | 10.4641 | 0.430072 | ||||||||
\(593\) | −36.8564 | −1.51351 | −0.756756 | − | 0.653698i | \(-0.773217\pi\) | ||||
−0.756756 | + | 0.653698i | \(0.773217\pi\) | |||||||
\(594\) | 4.73205 | 0.194158 | ||||||||
\(595\) | −0.444864 | −0.0182376 | ||||||||
\(596\) | 2.80385 | 0.114850 | ||||||||
\(597\) | −3.80385 | −0.155681 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.46410 | −0.386693 | −0.193346 | − | 0.981131i | \(-0.561934\pi\) | ||||
−0.193346 | + | 0.981131i | \(0.561934\pi\) | |||||||
\(600\) | −4.92820 | −0.201193 | ||||||||
\(601\) | −5.92820 | −0.241816 | −0.120908 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120908 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(602\) | 5.60770 | 0.228553 | ||||||||
\(603\) | −11.1244 | −0.453019 | ||||||||
\(604\) | 3.26795 | 0.132971 | ||||||||
\(605\) | 3.05256 | 0.124104 | ||||||||
\(606\) | −11.9282 | −0.484550 | ||||||||
\(607\) | 0.784610 | 0.0318463 | 0.0159232 | − | 0.999873i | \(-0.494931\pi\) | ||||
0.0159232 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(608\) | 1.26795 | 0.0514221 | ||||||||
\(609\) | 1.80385 | 0.0730956 | ||||||||
\(610\) | 0.320508 | 0.0129770 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.26795 | −0.0916764 | ||||||||
\(613\) | 11.3923 | 0.460131 | 0.230065 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230065 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(614\) | 8.58846 | 0.346602 | ||||||||
\(615\) | 3.05256 | 0.123091 | ||||||||
\(616\) | 3.46410 | 0.139573 | ||||||||
\(617\) | 35.2487 | 1.41906 | 0.709530 | − | 0.704675i | \(-0.248907\pi\) | ||||
0.709530 | + | 0.704675i | \(0.248907\pi\) | |||||||
\(618\) | −18.7321 | −0.753514 | ||||||||
\(619\) | 10.5359 | 0.423474 | 0.211737 | − | 0.977327i | \(-0.432088\pi\) | ||||
0.211737 | + | 0.977327i | \(0.432088\pi\) | |||||||
\(620\) | −1.46410 | −0.0587997 | ||||||||
\(621\) | −6.19615 | −0.248643 | ||||||||
\(622\) | 15.6603 | 0.627919 | ||||||||
\(623\) | −1.85641 | −0.0743754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 13.4641 | 0.538134 | ||||||||
\(627\) | 6.00000 | 0.239617 | ||||||||
\(628\) | −23.5885 | −0.941282 | ||||||||
\(629\) | −23.7321 | −0.946259 | ||||||||
\(630\) | 0.196152 | 0.00781490 | ||||||||
\(631\) | 47.7128 | 1.89942 | 0.949709 | − | 0.313135i | \(-0.101379\pi\) | ||||
0.949709 | + | 0.313135i | \(0.101379\pi\) | |||||||
\(632\) | −9.46410 | −0.376462 | ||||||||
\(633\) | −4.39230 | −0.174578 | ||||||||
\(634\) | 3.33975 | 0.132638 | ||||||||
\(635\) | 4.78461 | 0.189871 | ||||||||
\(636\) | 0.464102 | 0.0184028 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.6603 | 0.461634 | ||||||||
\(639\) | 1.26795 | 0.0501593 | ||||||||
\(640\) | 0.267949 | 0.0105916 | ||||||||
\(641\) | 25.9808 | 1.02618 | 0.513089 | − | 0.858335i | \(-0.328501\pi\) | ||||
0.513089 | + | 0.858335i | \(0.328501\pi\) | |||||||
\(642\) | −0.196152 | −0.00774152 | ||||||||
\(643\) | 13.8564 | 0.546443 | 0.273222 | − | 0.961951i | \(-0.411911\pi\) | ||||
0.273222 | + | 0.961951i | \(0.411911\pi\) | |||||||
\(644\) | −4.53590 | −0.178739 | ||||||||
\(645\) | 2.05256 | 0.0808194 | ||||||||
\(646\) | −2.87564 | −0.113141 | ||||||||
\(647\) | 26.2487 | 1.03194 | 0.515972 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515972 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 37.8564 | 1.48599 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | −0.156772 | ||||||||
\(652\) | −6.53590 | −0.255966 | ||||||||
\(653\) | −10.5359 | −0.412302 | −0.206151 | − | 0.978520i | \(-0.566094\pi\) | ||||
−0.206151 | + | 0.978520i | \(0.566094\pi\) | |||||||
\(654\) | −5.46410 | −0.213663 | ||||||||
\(655\) | 3.60770 | 0.140964 | ||||||||
\(656\) | 11.3923 | 0.444795 | ||||||||
\(657\) | −9.73205 | −0.379683 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 38.2487 | 1.48996 | 0.744979 | − | 0.667088i | \(-0.232459\pi\) | ||||
0.744979 | + | 0.667088i | \(0.232459\pi\) | |||||||
\(660\) | 1.26795 | 0.0493549 | ||||||||
\(661\) | −9.39230 | −0.365318 | −0.182659 | − | 0.983176i | \(-0.558470\pi\) | ||||
−0.182659 | + | 0.983176i | \(0.558470\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.1962 | 0.395687 | ||||||||
\(665\) | 0.248711 | 0.00964461 | ||||||||
\(666\) | 10.4641 | 0.405476 | ||||||||
\(667\) | −15.2679 | −0.591177 | ||||||||
\(668\) | −2.53590 | −0.0981169 | ||||||||
\(669\) | −13.0718 | −0.505385 | ||||||||
\(670\) | −2.98076 | −0.115157 | ||||||||
\(671\) | 5.66025 | 0.218512 | ||||||||
\(672\) | 0.732051 | 0.0282395 | ||||||||
\(673\) | 14.0718 | 0.542428 | 0.271214 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271214 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(674\) | 6.85641 | 0.264099 | ||||||||
\(675\) | −4.92820 | −0.189687 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.5359 | −1.48105 | −0.740527 | − | 0.672026i | \(-0.765424\pi\) | ||||
−0.740527 | + | 0.672026i | \(0.765424\pi\) | |||||||
\(678\) | −18.6603 | −0.716643 | ||||||||
\(679\) | −4.39230 | −0.168561 | ||||||||
\(680\) | −0.607695 | −0.0233040 | ||||||||
\(681\) | −1.80385 | −0.0691236 | ||||||||
\(682\) | −25.8564 | −0.990093 | ||||||||
\(683\) | −37.8564 | −1.44854 | −0.724268 | − | 0.689519i | \(-0.757822\pi\) | ||||
−0.724268 | + | 0.689519i | \(0.757822\pi\) | |||||||
\(684\) | 1.26795 | 0.0484812 | ||||||||
\(685\) | −0.516660 | −0.0197406 | ||||||||
\(686\) | −9.85641 | −0.376319 | ||||||||
\(687\) | 15.8564 | 0.604960 | ||||||||
\(688\) | 7.66025 | 0.292044 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.66025 | −0.0632048 | ||||||||
\(691\) | 26.3397 | 1.00201 | 0.501006 | − | 0.865444i | \(-0.332964\pi\) | ||||
0.501006 | + | 0.865444i | \(0.332964\pi\) | |||||||
\(692\) | −16.3923 | −0.623142 | ||||||||
\(693\) | 3.46410 | 0.131590 | ||||||||
\(694\) | 8.87564 | 0.336915 | ||||||||
\(695\) | −2.64102 | −0.100179 | ||||||||
\(696\) | 2.46410 | 0.0934015 | ||||||||
\(697\) | −25.8372 | −0.978653 | ||||||||
\(698\) | −19.3205 | −0.731292 | ||||||||
\(699\) | 19.8564 | 0.751038 | ||||||||
\(700\) | −3.60770 | −0.136358 | ||||||||
\(701\) | 31.3205 | 1.18296 | 0.591480 | − | 0.806320i | \(-0.298544\pi\) | ||||
0.591480 | + | 0.806320i | \(0.298544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2679 | 0.500410 | ||||||||
\(704\) | 4.73205 | 0.178346 | ||||||||
\(705\) | −2.19615 | −0.0827119 | ||||||||
\(706\) | 19.7846 | 0.744604 | ||||||||
\(707\) | −8.73205 | −0.328403 | ||||||||
\(708\) | 8.00000 | 0.300658 | ||||||||
\(709\) | 40.8564 | 1.53439 | 0.767197 | − | 0.641411i | \(-0.221651\pi\) | ||||
0.767197 | + | 0.641411i | \(0.221651\pi\) | |||||||
\(710\) | 0.339746 | 0.0127504 | ||||||||
\(711\) | −9.46410 | −0.354932 | ||||||||
\(712\) | −2.53590 | −0.0950368 | ||||||||
\(713\) | 33.8564 | 1.26793 | ||||||||
\(714\) | −1.66025 | −0.0621334 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.0526 | 0.824143 | ||||||||
\(717\) | −9.66025 | −0.360769 | ||||||||
\(718\) | 23.1244 | 0.862993 | ||||||||
\(719\) | −22.5359 | −0.840447 | −0.420224 | − | 0.907421i | \(-0.638048\pi\) | ||||
−0.420224 | + | 0.907421i | \(0.638048\pi\) | |||||||
\(720\) | 0.267949 | 0.00998588 | ||||||||
\(721\) | −13.7128 | −0.510692 | ||||||||
\(722\) | −17.3923 | −0.647275 | ||||||||
\(723\) | −17.5885 | −0.654122 | ||||||||
\(724\) | 8.80385 | 0.327192 | ||||||||
\(725\) | −12.1436 | −0.451002 | ||||||||
\(726\) | 11.3923 | 0.422808 | ||||||||
\(727\) | 20.9808 | 0.778133 | 0.389067 | − | 0.921210i | \(-0.372798\pi\) | ||||
0.389067 | + | 0.921210i | \(0.372798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.60770 | −0.0965151 | ||||||||
\(731\) | −17.3731 | −0.642566 | ||||||||
\(732\) | 1.19615 | 0.0442111 | ||||||||
\(733\) | 19.0000 | 0.701781 | 0.350891 | − | 0.936416i | \(-0.385879\pi\) | ||||
0.350891 | + | 0.936416i | \(0.385879\pi\) | |||||||
\(734\) | −14.7321 | −0.543770 | ||||||||
\(735\) | −1.73205 | −0.0638877 | ||||||||
\(736\) | −6.19615 | −0.228393 | ||||||||
\(737\) | −52.6410 | −1.93906 | ||||||||
\(738\) | 11.3923 | 0.419357 | ||||||||
\(739\) | −10.9282 | −0.402000 | −0.201000 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.201000 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(740\) | 2.80385 | 0.103071 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.339746 | 0.0124725 | ||||||||
\(743\) | −27.6077 | −1.01283 | −0.506414 | − | 0.862290i | \(-0.669029\pi\) | ||||
−0.506414 | + | 0.862290i | \(0.669029\pi\) | |||||||
\(744\) | −5.46410 | −0.200324 | ||||||||
\(745\) | 0.751289 | 0.0275251 | ||||||||
\(746\) | −10.2679 | −0.375936 | ||||||||
\(747\) | 10.1962 | 0.373058 | ||||||||
\(748\) | −10.7321 | −0.392403 | ||||||||
\(749\) | −0.143594 | −0.00524679 | ||||||||
\(750\) | −2.66025 | −0.0971387 | ||||||||
\(751\) | 15.9090 | 0.580526 | 0.290263 | − | 0.956947i | \(-0.406257\pi\) | ||||
0.290263 | + | 0.956947i | \(0.406257\pi\) | |||||||
\(752\) | −8.19615 | −0.298883 | ||||||||
\(753\) | 6.53590 | 0.238181 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.875644 | 0.0318680 | ||||||||
\(756\) | 0.732051 | 0.0266244 | ||||||||
\(757\) | 7.07180 | 0.257029 | 0.128514 | − | 0.991708i | \(-0.458979\pi\) | ||||
0.128514 | + | 0.991708i | \(0.458979\pi\) | |||||||
\(758\) | 1.46410 | 0.0531786 | ||||||||
\(759\) | −29.3205 | −1.06427 | ||||||||
\(760\) | 0.339746 | 0.0123239 | ||||||||
\(761\) | −23.3205 | −0.845368 | −0.422684 | − | 0.906277i | \(-0.638912\pi\) | ||||
−0.422684 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(762\) | 17.8564 | 0.646869 | ||||||||
\(763\) | −4.00000 | −0.144810 | ||||||||
\(764\) | 6.92820 | 0.250654 | ||||||||
\(765\) | −0.607695 | −0.0219713 | ||||||||
\(766\) | 5.46410 | 0.197426 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −16.1436 | −0.582153 | −0.291076 | − | 0.956700i | \(-0.594013\pi\) | ||||
−0.291076 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(770\) | 0.928203 | 0.0334501 | ||||||||
\(771\) | 26.6603 | 0.960146 | ||||||||
\(772\) | −8.26795 | −0.297570 | ||||||||
\(773\) | −35.0718 | −1.26144 | −0.630722 | − | 0.776009i | \(-0.717241\pi\) | ||||
−0.630722 | + | 0.776009i | \(0.717241\pi\) | |||||||
\(774\) | 7.66025 | 0.275342 | ||||||||
\(775\) | 26.9282 | 0.967290 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 7.66025 | 0.274810 | ||||||||
\(778\) | −29.7846 | −1.06783 | ||||||||
\(779\) | 14.4449 | 0.517541 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 14.0526 | 0.502518 | ||||||||
\(783\) | 2.46410 | 0.0880598 | ||||||||
\(784\) | −6.46410 | −0.230861 | ||||||||
\(785\) | −6.32051 | −0.225589 | ||||||||
\(786\) | 13.4641 | 0.480249 | ||||||||
\(787\) | 39.3205 | 1.40162 | 0.700812 | − | 0.713346i | \(-0.252821\pi\) | ||||
0.700812 | + | 0.713346i | \(0.252821\pi\) | |||||||
\(788\) | 9.85641 | 0.351120 | ||||||||
\(789\) | 28.0526 | 0.998698 | ||||||||
\(790\) | −2.53590 | −0.0902232 | ||||||||
\(791\) | −13.6603 | −0.485703 | ||||||||
\(792\) | 4.73205 | 0.168146 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.392305 | −0.0139224 | ||||||||
\(795\) | 0.124356 | 0.00441044 | ||||||||
\(796\) | −3.80385 | −0.134824 | ||||||||
\(797\) | −34.0000 | −1.20434 | −0.602171 | − | 0.798367i | \(-0.705697\pi\) | ||||
−0.602171 | + | 0.798367i | \(0.705697\pi\) | |||||||
\(798\) | 0.928203 | 0.0328580 | ||||||||
\(799\) | 18.5885 | 0.657612 | ||||||||
\(800\) | −4.92820 | −0.174238 | ||||||||
\(801\) | −2.53590 | −0.0896016 | ||||||||
\(802\) | 21.9282 | 0.774312 | ||||||||
\(803\) | −46.0526 | −1.62516 | ||||||||
\(804\) | −11.1244 | −0.392326 | ||||||||
\(805\) | −1.21539 | −0.0428369 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.46410 | −0.0515388 | ||||||||
\(808\) | −11.9282 | −0.419633 | ||||||||
\(809\) | −22.4115 | −0.787948 | −0.393974 | − | 0.919122i | \(-0.628900\pi\) | ||||
−0.393974 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(810\) | 0.267949 | 0.00941477 | ||||||||
\(811\) | −45.1769 | −1.58638 | −0.793188 | − | 0.608977i | \(-0.791580\pi\) | ||||
−0.793188 | + | 0.608977i | \(0.791580\pi\) | |||||||
\(812\) | 1.80385 | 0.0633026 | ||||||||
\(813\) | 5.85641 | 0.205393 | ||||||||
\(814\) | 49.5167 | 1.73556 | ||||||||
\(815\) | −1.75129 | −0.0613450 | ||||||||
\(816\) | −2.26795 | −0.0793941 | ||||||||
\(817\) | 9.71281 | 0.339808 | ||||||||
\(818\) | 14.2679 | 0.498867 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.05256 | 0.106600 | ||||||||
\(821\) | 12.9282 | 0.451197 | 0.225599 | − | 0.974220i | \(-0.427566\pi\) | ||||
0.225599 | + | 0.974220i | \(0.427566\pi\) | |||||||
\(822\) | −1.92820 | −0.0672538 | ||||||||
\(823\) | −41.5692 | −1.44901 | −0.724506 | − | 0.689269i | \(-0.757932\pi\) | ||||
−0.724506 | + | 0.689269i | \(0.757932\pi\) | |||||||
\(824\) | −18.7321 | −0.652562 | ||||||||
\(825\) | −23.3205 | −0.811916 | ||||||||
\(826\) | 5.85641 | 0.203770 | ||||||||
\(827\) | 33.4641 | 1.16366 | 0.581830 | − | 0.813310i | \(-0.302337\pi\) | ||||
0.581830 | + | 0.813310i | \(0.302337\pi\) | |||||||
\(828\) | −6.19615 | −0.215331 | ||||||||
\(829\) | 12.1244 | 0.421096 | 0.210548 | − | 0.977583i | \(-0.432475\pi\) | ||||
0.210548 | + | 0.977583i | \(0.432475\pi\) | |||||||
\(830\) | 2.73205 | 0.0948309 | ||||||||
\(831\) | −2.26795 | −0.0786743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6603 | 0.507948 | ||||||||
\(834\) | −9.85641 | −0.341299 | ||||||||
\(835\) | −0.679492 | −0.0235148 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | −5.46410 | −0.188867 | ||||||||
\(838\) | −10.5359 | −0.363957 | ||||||||
\(839\) | 14.1436 | 0.488291 | 0.244146 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244146 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(840\) | 0.196152 | 0.00676790 | ||||||||
\(841\) | −22.9282 | −0.790628 | ||||||||
\(842\) | 32.7128 | 1.12736 | ||||||||
\(843\) | −22.3205 | −0.768759 | ||||||||
\(844\) | −4.39230 | −0.151189 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.19615 | −0.281790 | ||||||||
\(847\) | 8.33975 | 0.286557 | ||||||||
\(848\) | 0.464102 | 0.0159373 | ||||||||
\(849\) | 8.33975 | 0.286219 | ||||||||
\(850\) | 11.1769 | 0.383365 | ||||||||
\(851\) | −64.8372 | −2.22259 | ||||||||
\(852\) | 1.26795 | 0.0434392 | ||||||||
\(853\) | 8.17691 | 0.279972 | 0.139986 | − | 0.990153i | \(-0.455294\pi\) | ||||
0.139986 | + | 0.990153i | \(0.455294\pi\) | |||||||
\(854\) | 0.875644 | 0.0299639 | ||||||||
\(855\) | 0.339746 | 0.0116191 | ||||||||
\(856\) | −0.196152 | −0.00670435 | ||||||||
\(857\) | −19.4449 | −0.664224 | −0.332112 | − | 0.943240i | \(-0.607761\pi\) | ||||
−0.332112 | + | 0.943240i | \(0.607761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.8756 | −0.780507 | −0.390253 | − | 0.920707i | \(-0.627613\pi\) | ||||
−0.390253 | + | 0.920707i | \(0.627613\pi\) | |||||||
\(860\) | 2.05256 | 0.0699917 | ||||||||
\(861\) | 8.33975 | 0.284218 | ||||||||
\(862\) | −11.1244 | −0.378897 | ||||||||
\(863\) | 7.12436 | 0.242516 | 0.121258 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121258 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.39230 | −0.149343 | ||||||||
\(866\) | −14.8564 | −0.504841 | ||||||||
\(867\) | −11.8564 | −0.402665 | ||||||||
\(868\) | −4.00000 | −0.135769 | ||||||||
\(869\) | −44.7846 | −1.51921 | ||||||||
\(870\) | 0.660254 | 0.0223847 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.46410 | −0.185038 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | −7.85641 | −0.265747 | ||||||||
\(875\) | −1.94744 | −0.0658355 | ||||||||
\(876\) | −9.73205 | −0.328816 | ||||||||
\(877\) | 10.0718 | 0.340100 | 0.170050 | − | 0.985435i | \(-0.445607\pi\) | ||||
0.170050 | + | 0.985435i | \(0.445607\pi\) | |||||||
\(878\) | −17.6603 | −0.596005 | ||||||||
\(879\) | −14.5167 | −0.489635 | ||||||||
\(880\) | 1.26795 | 0.0427426 | ||||||||
\(881\) | 51.8372 | 1.74644 | 0.873219 | − | 0.487327i | \(-0.162028\pi\) | ||||
0.873219 | + | 0.487327i | \(0.162028\pi\) | |||||||
\(882\) | −6.46410 | −0.217658 | ||||||||
\(883\) | 29.0718 | 0.978344 | 0.489172 | − | 0.872187i | \(-0.337299\pi\) | ||||
0.489172 | + | 0.872187i | \(0.337299\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.14359 | 0.0720561 | ||||||||
\(886\) | 36.3923 | 1.22262 | ||||||||
\(887\) | 10.1436 | 0.340589 | 0.170294 | − | 0.985393i | \(-0.445528\pi\) | ||||
0.170294 | + | 0.985393i | \(0.445528\pi\) | |||||||
\(888\) | 10.4641 | 0.351152 | ||||||||
\(889\) | 13.0718 | 0.438414 | ||||||||
\(890\) | −0.679492 | −0.0227766 | ||||||||
\(891\) | 4.73205 | 0.158530 | ||||||||
\(892\) | −13.0718 | −0.437676 | ||||||||
\(893\) | −10.3923 | −0.347765 | ||||||||
\(894\) | 2.80385 | 0.0937747 | ||||||||
\(895\) | 5.90897 | 0.197515 | ||||||||
\(896\) | 0.732051 | 0.0244561 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.3205 | −0.778215 | ||||||||
\(899\) | −13.4641 | −0.449053 | ||||||||
\(900\) | −4.92820 | −0.164273 | ||||||||
\(901\) | −1.05256 | −0.0350658 | ||||||||
\(902\) | 53.9090 | 1.79497 | ||||||||
\(903\) | 5.60770 | 0.186612 | ||||||||
\(904\) | −18.6603 | −0.620631 | ||||||||
\(905\) | 2.35898 | 0.0784153 | ||||||||
\(906\) | 3.26795 | 0.108570 | ||||||||
\(907\) | 15.6077 | 0.518245 | 0.259123 | − | 0.965844i | \(-0.416567\pi\) | ||||
0.259123 | + | 0.965844i | \(0.416567\pi\) | |||||||
\(908\) | −1.80385 | −0.0598628 | ||||||||
\(909\) | −11.9282 | −0.395634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.46410 | −0.313560 | −0.156780 | − | 0.987634i | \(-0.550111\pi\) | ||||
−0.156780 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(912\) | 1.26795 | 0.0419860 | ||||||||
\(913\) | 48.2487 | 1.59680 | ||||||||
\(914\) | 18.6603 | 0.617226 | ||||||||
\(915\) | 0.320508 | 0.0105957 | ||||||||
\(916\) | 15.8564 | 0.523910 | ||||||||
\(917\) | 9.85641 | 0.325487 | ||||||||
\(918\) | −2.26795 | −0.0748535 | ||||||||
\(919\) | −57.9615 | −1.91197 | −0.955987 | − | 0.293409i | \(-0.905210\pi\) | ||||
−0.955987 | + | 0.293409i | \(0.905210\pi\) | |||||||
\(920\) | −1.66025 | −0.0547370 | ||||||||
\(921\) | 8.58846 | 0.282999 | ||||||||
\(922\) | 25.7321 | 0.847440 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.46410 | 0.113961 | ||||||||
\(925\) | −51.5692 | −1.69559 | ||||||||
\(926\) | −28.0526 | −0.921864 | ||||||||
\(927\) | −18.7321 | −0.615241 | ||||||||
\(928\) | 2.46410 | 0.0808881 | ||||||||
\(929\) | 9.24871 | 0.303440 | 0.151720 | − | 0.988423i | \(-0.451519\pi\) | ||||
0.151720 | + | 0.988423i | \(0.451519\pi\) | |||||||
\(930\) | −1.46410 | −0.0480098 | ||||||||
\(931\) | −8.19615 | −0.268618 | ||||||||
\(932\) | 19.8564 | 0.650418 | ||||||||
\(933\) | 15.6603 | 0.512694 | ||||||||
\(934\) | −12.5885 | −0.411907 | ||||||||
\(935\) | −2.87564 | −0.0940436 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.2487 | 1.41287 | 0.706437 | − | 0.707776i | \(-0.250301\pi\) | ||||
0.706437 | + | 0.707776i | \(0.250301\pi\) | |||||||
\(938\) | −8.14359 | −0.265898 | ||||||||
\(939\) | 13.4641 | 0.439384 | ||||||||
\(940\) | −2.19615 | −0.0716306 | ||||||||
\(941\) | −56.6410 | −1.84644 | −0.923222 | − | 0.384267i | \(-0.874454\pi\) | ||||
−0.923222 | + | 0.384267i | \(0.874454\pi\) | |||||||
\(942\) | −23.5885 | −0.768553 | ||||||||
\(943\) | −70.5885 | −2.29868 | ||||||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | 0.196152 | 0.00638084 | ||||||||
\(946\) | 36.2487 | 1.17855 | ||||||||
\(947\) | 34.9282 | 1.13501 | 0.567507 | − | 0.823369i | \(-0.307908\pi\) | ||||
0.567507 | + | 0.823369i | \(0.307908\pi\) | |||||||
\(948\) | −9.46410 | −0.307380 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.24871 | −0.202735 | ||||||||
\(951\) | 3.33975 | 0.108299 | ||||||||
\(952\) | −1.66025 | −0.0538091 | ||||||||
\(953\) | −41.5692 | −1.34656 | −0.673280 | − | 0.739388i | \(-0.735115\pi\) | ||||
−0.673280 | + | 0.739388i | \(0.735115\pi\) | |||||||
\(954\) | 0.464102 | 0.0150258 | ||||||||
\(955\) | 1.85641 | 0.0600719 | ||||||||
\(956\) | −9.66025 | −0.312435 | ||||||||
\(957\) | 11.6603 | 0.376922 | ||||||||
\(958\) | 26.5359 | 0.857336 | ||||||||
\(959\) | −1.41154 | −0.0455811 | ||||||||
\(960\) | 0.267949 | 0.00864802 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.196152 | −0.00632092 | ||||||||
\(964\) | −17.5885 | −0.566486 | ||||||||
\(965\) | −2.21539 | −0.0713159 | ||||||||
\(966\) | −4.53590 | −0.145940 | ||||||||
\(967\) | −18.8756 | −0.607000 | −0.303500 | − | 0.952831i | \(-0.598155\pi\) | ||||
−0.303500 | + | 0.952831i | \(0.598155\pi\) | |||||||
\(968\) | 11.3923 | 0.366163 | ||||||||
\(969\) | −2.87564 | −0.0923790 | ||||||||
\(970\) | −1.60770 | −0.0516200 | ||||||||
\(971\) | −18.2487 | −0.585629 | −0.292815 | − | 0.956169i | \(-0.594592\pi\) | ||||
−0.292815 | + | 0.956169i | \(0.594592\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −7.21539 | −0.231315 | ||||||||
\(974\) | 21.1244 | 0.676868 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.19615 | 0.0382879 | ||||||||
\(977\) | 32.0718 | 1.02607 | 0.513034 | − | 0.858368i | \(-0.328522\pi\) | ||||
0.513034 | + | 0.858368i | \(0.328522\pi\) | |||||||
\(978\) | −6.53590 | −0.208995 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | −1.73205 | −0.0553283 | ||||||||
\(981\) | −5.46410 | −0.174455 | ||||||||
\(982\) | 5.26795 | 0.168107 | ||||||||
\(983\) | −20.7846 | −0.662926 | −0.331463 | − | 0.943468i | \(-0.607542\pi\) | ||||
−0.331463 | + | 0.943468i | \(0.607542\pi\) | |||||||
\(984\) | 11.3923 | 0.363173 | ||||||||
\(985\) | 2.64102 | 0.0841498 | ||||||||
\(986\) | −5.58846 | −0.177973 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.4641 | −1.50927 | ||||||||
\(990\) | 1.26795 | 0.0402981 | ||||||||
\(991\) | −8.58846 | −0.272821 | −0.136411 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136411 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(992\) | −5.46410 | −0.173485 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0.928203 | 0.0294408 | ||||||||
\(995\) | −1.01924 | −0.0323120 | ||||||||
\(996\) | 10.1962 | 0.323077 | ||||||||
\(997\) | 38.6603 | 1.22438 | 0.612191 | − | 0.790710i | \(-0.290288\pi\) | ||||
0.612191 | + | 0.790710i | \(0.290288\pi\) | |||||||
\(998\) | 32.0000 | 1.01294 | ||||||||
\(999\) | 10.4641 | 0.331070 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))