Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | −2.70156 | −1.20818 | −0.604088 | − | 0.796918i | \(-0.706462\pi\) | ||||
−0.604088 | + | 0.796918i | \(0.706462\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.70156 | 0.854309 | ||||||||
\(11\) | 0.701562 | 0.211529 | 0.105764 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.70156 | 0.697540 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.70156 | −0.655225 | −0.327613 | − | 0.944812i | \(-0.606244\pi\) | ||||
−0.327613 | + | 0.944812i | \(0.606244\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.701562 | 0.160949 | 0.0804747 | − | 0.996757i | \(-0.474356\pi\) | ||||
0.0804747 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(20\) | −2.70156 | −0.604088 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −0.701562 | −0.149574 | ||||||||
\(23\) | 4.70156 | 0.980343 | 0.490172 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490172 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.29844 | 0.459688 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.70156 | 0.501667 | 0.250834 | − | 0.968030i | \(-0.419295\pi\) | ||||
0.250834 | + | 0.968030i | \(0.419295\pi\) | |||||||
\(30\) | −2.70156 | −0.493236 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.701562 | −0.122126 | ||||||||
\(34\) | 2.70156 | 0.463314 | ||||||||
\(35\) | 2.70156 | 0.456647 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.7016 | −1.75933 | −0.879663 | − | 0.475598i | \(-0.842232\pi\) | ||||
−0.879663 | + | 0.475598i | \(0.842232\pi\) | |||||||
\(38\) | −0.701562 | −0.113808 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.70156 | 0.427154 | ||||||||
\(41\) | −3.40312 | −0.531479 | −0.265739 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265739 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −10.1047 | −1.54095 | −0.770475 | − | 0.637470i | \(-0.779981\pi\) | ||||
−0.770475 | + | 0.637470i | \(0.779981\pi\) | |||||||
\(44\) | 0.701562 | 0.105764 | ||||||||
\(45\) | −2.70156 | −0.402725 | ||||||||
\(46\) | −4.70156 | −0.693208 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.29844 | −0.325048 | ||||||||
\(51\) | 2.70156 | 0.378294 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.89531 | −0.255564 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −0.701562 | −0.0929242 | ||||||||
\(58\) | −2.70156 | −0.354732 | ||||||||
\(59\) | 14.8062 | 1.92761 | 0.963805 | − | 0.266609i | \(-0.0859033\pi\) | ||||
0.963805 | + | 0.266609i | \(0.0859033\pi\) | |||||||
\(60\) | 2.70156 | 0.348770 | ||||||||
\(61\) | 1.29844 | 0.166248 | 0.0831240 | − | 0.996539i | \(-0.473510\pi\) | ||||
0.0831240 | + | 0.996539i | \(0.473510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.701562 | 0.0863563 | ||||||||
\(67\) | −5.40312 | −0.660097 | −0.330048 | − | 0.943964i | \(-0.607065\pi\) | ||||
−0.330048 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(68\) | −2.70156 | −0.327613 | ||||||||
\(69\) | −4.70156 | −0.566002 | ||||||||
\(70\) | −2.70156 | −0.322898 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.29844 | 0.151971 | 0.0759853 | − | 0.997109i | \(-0.475790\pi\) | ||||
0.0759853 | + | 0.997109i | \(0.475790\pi\) | |||||||
\(74\) | 10.7016 | 1.24403 | ||||||||
\(75\) | −2.29844 | −0.265401 | ||||||||
\(76\) | 0.701562 | 0.0804747 | ||||||||
\(77\) | −0.701562 | −0.0799504 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.40312 | 1.05793 | 0.528967 | − | 0.848642i | \(-0.322579\pi\) | ||||
0.528967 | + | 0.848642i | \(0.322579\pi\) | |||||||
\(80\) | −2.70156 | −0.302044 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.40312 | 0.375812 | ||||||||
\(83\) | 13.4031 | 1.47118 | 0.735592 | − | 0.677425i | \(-0.236904\pi\) | ||||
0.735592 | + | 0.677425i | \(0.236904\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 7.29844 | 0.791627 | ||||||||
\(86\) | 10.1047 | 1.08962 | ||||||||
\(87\) | −2.70156 | −0.289638 | ||||||||
\(88\) | −0.701562 | −0.0747868 | ||||||||
\(89\) | 8.80625 | 0.933460 | 0.466730 | − | 0.884400i | \(-0.345432\pi\) | ||||
0.466730 | + | 0.884400i | \(0.345432\pi\) | |||||||
\(90\) | 2.70156 | 0.284770 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.70156 | 0.490172 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −1.89531 | −0.194455 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.80625 | 0.894139 | 0.447070 | − | 0.894499i | \(-0.352468\pi\) | ||||
0.447070 | + | 0.894499i | \(0.352468\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0.701562 | 0.0705096 | ||||||||
\(100\) | 2.29844 | 0.229844 | ||||||||
\(101\) | −3.40312 | −0.338624 | −0.169312 | − | 0.985563i | \(-0.554154\pi\) | ||||
−0.169312 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(102\) | −2.70156 | −0.267495 | ||||||||
\(103\) | −3.29844 | −0.325005 | −0.162502 | − | 0.986708i | \(-0.551957\pi\) | ||||
−0.162502 | + | 0.986708i | \(0.551957\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.70156 | −0.263645 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −5.40312 | −0.522340 | −0.261170 | − | 0.965293i | \(-0.584108\pi\) | ||||
−0.261170 | + | 0.965293i | \(0.584108\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.29844 | −0.890629 | −0.445314 | − | 0.895374i | \(-0.646908\pi\) | ||||
−0.445314 | + | 0.895374i | \(0.646908\pi\) | |||||||
\(110\) | 1.89531 | 0.180711 | ||||||||
\(111\) | 10.7016 | 1.01575 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 4.80625 | 0.452134 | 0.226067 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226067 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(114\) | 0.701562 | 0.0657073 | ||||||||
\(115\) | −12.7016 | −1.18443 | ||||||||
\(116\) | 2.70156 | 0.250834 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.8062 | −1.36303 | ||||||||
\(119\) | 2.70156 | 0.247652 | ||||||||
\(120\) | −2.70156 | −0.246618 | ||||||||
\(121\) | −10.5078 | −0.955256 | ||||||||
\(122\) | −1.29844 | −0.117555 | ||||||||
\(123\) | 3.40312 | 0.306849 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.29844 | 0.652792 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −6.59688 | −0.585378 | −0.292689 | − | 0.956208i | \(-0.594550\pi\) | ||||
−0.292689 | + | 0.956208i | \(0.594550\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.1047 | 0.889668 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.29844 | −0.637667 | −0.318834 | − | 0.947811i | \(-0.603291\pi\) | ||||
−0.318834 | + | 0.947811i | \(0.603291\pi\) | |||||||
\(132\) | −0.701562 | −0.0610631 | ||||||||
\(133\) | −0.701562 | −0.0608332 | ||||||||
\(134\) | 5.40312 | 0.466759 | ||||||||
\(135\) | 2.70156 | 0.232513 | ||||||||
\(136\) | 2.70156 | 0.231657 | ||||||||
\(137\) | 18.7016 | 1.59778 | 0.798891 | − | 0.601476i | \(-0.205420\pi\) | ||||
0.798891 | + | 0.601476i | \(0.205420\pi\) | |||||||
\(138\) | 4.70156 | 0.400224 | ||||||||
\(139\) | 6.80625 | 0.577298 | 0.288649 | − | 0.957435i | \(-0.406794\pi\) | ||||
0.288649 | + | 0.957435i | \(0.406794\pi\) | |||||||
\(140\) | 2.70156 | 0.228324 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −7.29844 | −0.606102 | ||||||||
\(146\) | −1.29844 | −0.107459 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −10.7016 | −0.879663 | ||||||||
\(149\) | −15.4031 | −1.26187 | −0.630937 | − | 0.775834i | \(-0.717329\pi\) | ||||
−0.630937 | + | 0.775834i | \(0.717329\pi\) | |||||||
\(150\) | 2.29844 | 0.187667 | ||||||||
\(151\) | 4.70156 | 0.382608 | 0.191304 | − | 0.981531i | \(-0.438728\pi\) | ||||
0.191304 | + | 0.981531i | \(0.438728\pi\) | |||||||
\(152\) | −0.701562 | −0.0569042 | ||||||||
\(153\) | −2.70156 | −0.218408 | ||||||||
\(154\) | 0.701562 | 0.0565335 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1047 | 1.60453 | 0.802264 | − | 0.596969i | \(-0.203628\pi\) | ||||
0.802264 | + | 0.596969i | \(0.203628\pi\) | |||||||
\(158\) | −9.40312 | −0.748072 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 2.70156 | 0.213577 | ||||||||
\(161\) | −4.70156 | −0.370535 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.40312 | −0.423205 | −0.211603 | − | 0.977356i | \(-0.567868\pi\) | ||||
−0.211603 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(164\) | −3.40312 | −0.265739 | ||||||||
\(165\) | 1.89531 | 0.147550 | ||||||||
\(166\) | −13.4031 | −1.04028 | ||||||||
\(167\) | −3.29844 | −0.255241 | −0.127620 | − | 0.991823i | \(-0.540734\pi\) | ||||
−0.127620 | + | 0.991823i | \(0.540734\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −7.29844 | −0.559765 | ||||||||
\(171\) | 0.701562 | 0.0536498 | ||||||||
\(172\) | −10.1047 | −0.770475 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 2.70156 | 0.204805 | ||||||||
\(175\) | −2.29844 | −0.173746 | ||||||||
\(176\) | 0.701562 | 0.0528822 | ||||||||
\(177\) | −14.8062 | −1.11291 | ||||||||
\(178\) | −8.80625 | −0.660056 | ||||||||
\(179\) | 14.8062 | 1.10667 | 0.553335 | − | 0.832958i | \(-0.313355\pi\) | ||||
0.553335 | + | 0.832958i | \(0.313355\pi\) | |||||||
\(180\) | −2.70156 | −0.201363 | ||||||||
\(181\) | 8.80625 | 0.654563 | 0.327282 | − | 0.944927i | \(-0.393867\pi\) | ||||
0.327282 | + | 0.944927i | \(0.393867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.29844 | −0.0959833 | ||||||||
\(184\) | −4.70156 | −0.346604 | ||||||||
\(185\) | 28.9109 | 2.12557 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.89531 | −0.138599 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.89531 | 0.137501 | ||||||||
\(191\) | 12.7016 | 0.919053 | 0.459526 | − | 0.888164i | \(-0.348019\pi\) | ||||
0.459526 | + | 0.888164i | \(0.348019\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −11.4031 | −0.820815 | −0.410407 | − | 0.911902i | \(-0.634614\pi\) | ||||
−0.410407 | + | 0.911902i | \(0.634614\pi\) | |||||||
\(194\) | −8.80625 | −0.632252 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.40312 | 0.242463 | 0.121231 | − | 0.992624i | \(-0.461316\pi\) | ||||
0.121231 | + | 0.992624i | \(0.461316\pi\) | |||||||
\(198\) | −0.701562 | −0.0498578 | ||||||||
\(199\) | 22.1047 | 1.56696 | 0.783480 | − | 0.621417i | \(-0.213443\pi\) | ||||
0.783480 | + | 0.621417i | \(0.213443\pi\) | |||||||
\(200\) | −2.29844 | −0.162524 | ||||||||
\(201\) | 5.40312 | 0.381107 | ||||||||
\(202\) | 3.40312 | 0.239443 | ||||||||
\(203\) | −2.70156 | −0.189612 | ||||||||
\(204\) | 2.70156 | 0.189147 | ||||||||
\(205\) | 9.19375 | 0.642119 | ||||||||
\(206\) | 3.29844 | 0.229813 | ||||||||
\(207\) | 4.70156 | 0.326781 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.492189 | 0.0340455 | ||||||||
\(210\) | 2.70156 | 0.186425 | ||||||||
\(211\) | −24.7016 | −1.70053 | −0.850263 | − | 0.526358i | \(-0.823557\pi\) | ||||
−0.850263 | + | 0.526358i | \(0.823557\pi\) | |||||||
\(212\) | −2.00000 | −0.137361 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 5.40312 | 0.369350 | ||||||||
\(215\) | 27.2984 | 1.86174 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9.29844 | 0.629770 | ||||||||
\(219\) | −1.29844 | −0.0877403 | ||||||||
\(220\) | −1.89531 | −0.127782 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.7016 | −0.718242 | ||||||||
\(223\) | −9.40312 | −0.629680 | −0.314840 | − | 0.949145i | \(-0.601951\pi\) | ||||
−0.314840 | + | 0.949145i | \(0.601951\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 2.29844 | 0.153229 | ||||||||
\(226\) | −4.80625 | −0.319707 | ||||||||
\(227\) | −21.4031 | −1.42058 | −0.710288 | − | 0.703912i | \(-0.751435\pi\) | ||||
−0.710288 | + | 0.703912i | \(0.751435\pi\) | |||||||
\(228\) | −0.701562 | −0.0464621 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 12.7016 | 0.837516 | ||||||||
\(231\) | 0.701562 | 0.0461594 | ||||||||
\(232\) | −2.70156 | −0.177366 | ||||||||
\(233\) | −18.2094 | −1.19294 | −0.596468 | − | 0.802637i | \(-0.703430\pi\) | ||||
−0.596468 | + | 0.802637i | \(0.703430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.6125 | −1.40984 | ||||||||
\(236\) | 14.8062 | 0.963805 | ||||||||
\(237\) | −9.40312 | −0.610799 | ||||||||
\(238\) | −2.70156 | −0.175116 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 2.70156 | 0.174385 | ||||||||
\(241\) | 24.8062 | 1.59791 | 0.798955 | − | 0.601390i | \(-0.205386\pi\) | ||||
0.798955 | + | 0.601390i | \(0.205386\pi\) | |||||||
\(242\) | 10.5078 | 0.675468 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.29844 | 0.0831240 | ||||||||
\(245\) | −2.70156 | −0.172596 | ||||||||
\(246\) | −3.40312 | −0.216975 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.4031 | −0.849388 | ||||||||
\(250\) | −7.29844 | −0.461594 | ||||||||
\(251\) | 3.50781 | 0.221411 | 0.110706 | − | 0.993853i | \(-0.464689\pi\) | ||||
0.110706 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 3.29844 | 0.207371 | ||||||||
\(254\) | 6.59688 | 0.413925 | ||||||||
\(255\) | −7.29844 | −0.457046 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.00000 | −0.374270 | −0.187135 | − | 0.982334i | \(-0.559920\pi\) | ||||
−0.187135 | + | 0.982334i | \(0.559920\pi\) | |||||||
\(258\) | −10.1047 | −0.629090 | ||||||||
\(259\) | 10.7016 | 0.664963 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.70156 | 0.167222 | ||||||||
\(262\) | 7.29844 | 0.450899 | ||||||||
\(263\) | −26.8062 | −1.65294 | −0.826472 | − | 0.562978i | \(-0.809656\pi\) | ||||
−0.826472 | + | 0.562978i | \(0.809656\pi\) | |||||||
\(264\) | 0.701562 | 0.0431782 | ||||||||
\(265\) | 5.40312 | 0.331911 | ||||||||
\(266\) | 0.701562 | 0.0430155 | ||||||||
\(267\) | −8.80625 | −0.538934 | ||||||||
\(268\) | −5.40312 | −0.330048 | ||||||||
\(269\) | −4.80625 | −0.293042 | −0.146521 | − | 0.989208i | \(-0.546808\pi\) | ||||
−0.146521 | + | 0.989208i | \(0.546808\pi\) | |||||||
\(270\) | −2.70156 | −0.164412 | ||||||||
\(271\) | −12.2094 | −0.741667 | −0.370833 | − | 0.928699i | \(-0.620928\pi\) | ||||
−0.370833 | + | 0.928699i | \(0.620928\pi\) | |||||||
\(272\) | −2.70156 | −0.163806 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.7016 | −1.12980 | ||||||||
\(275\) | 1.61250 | 0.0972372 | ||||||||
\(276\) | −4.70156 | −0.283001 | ||||||||
\(277\) | 27.6125 | 1.65907 | 0.829537 | − | 0.558452i | \(-0.188604\pi\) | ||||
0.829537 | + | 0.558452i | \(0.188604\pi\) | |||||||
\(278\) | −6.80625 | −0.408212 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.70156 | −0.161449 | ||||||||
\(281\) | −12.8062 | −0.763957 | −0.381978 | − | 0.924171i | \(-0.624757\pi\) | ||||
−0.381978 | + | 0.924171i | \(0.624757\pi\) | |||||||
\(282\) | 8.00000 | 0.476393 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 1.89531 | 0.112269 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.40312 | 0.200880 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.70156 | −0.570680 | ||||||||
\(290\) | 7.29844 | 0.428579 | ||||||||
\(291\) | −8.80625 | −0.516231 | ||||||||
\(292\) | 1.29844 | 0.0759853 | ||||||||
\(293\) | 12.8062 | 0.748149 | 0.374075 | − | 0.927399i | \(-0.377960\pi\) | ||||
0.374075 | + | 0.927399i | \(0.377960\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −40.0000 | −2.32889 | ||||||||
\(296\) | 10.7016 | 0.622016 | ||||||||
\(297\) | −0.701562 | −0.0407088 | ||||||||
\(298\) | 15.4031 | 0.892279 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.29844 | −0.132700 | ||||||||
\(301\) | 10.1047 | 0.582424 | ||||||||
\(302\) | −4.70156 | −0.270544 | ||||||||
\(303\) | 3.40312 | 0.195504 | ||||||||
\(304\) | 0.701562 | 0.0402373 | ||||||||
\(305\) | −3.50781 | −0.200857 | ||||||||
\(306\) | 2.70156 | 0.154438 | ||||||||
\(307\) | 6.80625 | 0.388453 | 0.194227 | − | 0.980957i | \(-0.437780\pi\) | ||||
0.194227 | + | 0.980957i | \(0.437780\pi\) | |||||||
\(308\) | −0.701562 | −0.0399752 | ||||||||
\(309\) | 3.29844 | 0.187642 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5969 | 0.827713 | 0.413856 | − | 0.910342i | \(-0.364182\pi\) | ||||
0.413856 | + | 0.910342i | \(0.364182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.2094 | 1.25535 | 0.627674 | − | 0.778476i | \(-0.284007\pi\) | ||||
0.627674 | + | 0.778476i | \(0.284007\pi\) | |||||||
\(314\) | −20.1047 | −1.13457 | ||||||||
\(315\) | 2.70156 | 0.152216 | ||||||||
\(316\) | 9.40312 | 0.528967 | ||||||||
\(317\) | −7.40312 | −0.415801 | −0.207900 | − | 0.978150i | \(-0.566663\pi\) | ||||
−0.207900 | + | 0.978150i | \(0.566663\pi\) | |||||||
\(318\) | −2.00000 | −0.112154 | ||||||||
\(319\) | 1.89531 | 0.106117 | ||||||||
\(320\) | −2.70156 | −0.151022 | ||||||||
\(321\) | 5.40312 | 0.301573 | ||||||||
\(322\) | 4.70156 | 0.262008 | ||||||||
\(323\) | −1.89531 | −0.105458 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.40312 | 0.299251 | ||||||||
\(327\) | 9.29844 | 0.514205 | ||||||||
\(328\) | 3.40312 | 0.187906 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | −1.89531 | −0.104334 | ||||||||
\(331\) | −32.2094 | −1.77039 | −0.885194 | − | 0.465223i | \(-0.845974\pi\) | ||||
−0.885194 | + | 0.465223i | \(0.845974\pi\) | |||||||
\(332\) | 13.4031 | 0.735592 | ||||||||
\(333\) | −10.7016 | −0.586442 | ||||||||
\(334\) | 3.29844 | 0.180482 | ||||||||
\(335\) | 14.5969 | 0.797513 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −29.5078 | −1.60739 | −0.803696 | − | 0.595040i | \(-0.797136\pi\) | ||||
−0.803696 | + | 0.595040i | \(0.797136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.80625 | −0.261040 | ||||||||
\(340\) | 7.29844 | 0.395813 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.701562 | −0.0379361 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 10.1047 | 0.544808 | ||||||||
\(345\) | 12.7016 | 0.683829 | ||||||||
\(346\) | 18.0000 | 0.967686 | ||||||||
\(347\) | 4.00000 | 0.214731 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | −2.70156 | −0.144819 | ||||||||
\(349\) | −30.0000 | −1.60586 | −0.802932 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802932 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(350\) | 2.29844 | 0.122857 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.701562 | −0.0373934 | ||||||||
\(353\) | −20.8062 | −1.10740 | −0.553702 | − | 0.832715i | \(-0.686785\pi\) | ||||
−0.553702 | + | 0.832715i | \(0.686785\pi\) | |||||||
\(354\) | 14.8062 | 0.786943 | ||||||||
\(355\) | −21.6125 | −1.14707 | ||||||||
\(356\) | 8.80625 | 0.466730 | ||||||||
\(357\) | −2.70156 | −0.142982 | ||||||||
\(358\) | −14.8062 | −0.782535 | ||||||||
\(359\) | −26.8062 | −1.41478 | −0.707390 | − | 0.706824i | \(-0.750127\pi\) | ||||
−0.707390 | + | 0.706824i | \(0.750127\pi\) | |||||||
\(360\) | 2.70156 | 0.142385 | ||||||||
\(361\) | −18.5078 | −0.974095 | ||||||||
\(362\) | −8.80625 | −0.462846 | ||||||||
\(363\) | 10.5078 | 0.551517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.50781 | −0.183607 | ||||||||
\(366\) | 1.29844 | 0.0678704 | ||||||||
\(367\) | −29.6125 | −1.54576 | −0.772880 | − | 0.634552i | \(-0.781184\pi\) | ||||
−0.772880 | + | 0.634552i | \(0.781184\pi\) | |||||||
\(368\) | 4.70156 | 0.245086 | ||||||||
\(369\) | −3.40312 | −0.177160 | ||||||||
\(370\) | −28.9109 | −1.50301 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4031 | −1.00466 | −0.502328 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502328 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(374\) | 1.89531 | 0.0980043 | ||||||||
\(375\) | −7.29844 | −0.376890 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 17.6125 | 0.904693 | 0.452347 | − | 0.891842i | \(-0.350587\pi\) | ||||
0.452347 | + | 0.891842i | \(0.350587\pi\) | |||||||
\(380\) | −1.89531 | −0.0972275 | ||||||||
\(381\) | 6.59688 | 0.337968 | ||||||||
\(382\) | −12.7016 | −0.649868 | ||||||||
\(383\) | −16.9109 | −0.864108 | −0.432054 | − | 0.901848i | \(-0.642211\pi\) | ||||
−0.432054 | + | 0.901848i | \(0.642211\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.89531 | 0.0965941 | ||||||||
\(386\) | 11.4031 | 0.580404 | ||||||||
\(387\) | −10.1047 | −0.513650 | ||||||||
\(388\) | 8.80625 | 0.447070 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7016 | −0.642346 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 7.29844 | 0.368157 | ||||||||
\(394\) | −3.40312 | −0.171447 | ||||||||
\(395\) | −25.4031 | −1.27817 | ||||||||
\(396\) | 0.701562 | 0.0352548 | ||||||||
\(397\) | −0.806248 | −0.0404645 | −0.0202322 | − | 0.999795i | \(-0.506441\pi\) | ||||
−0.0202322 | + | 0.999795i | \(0.506441\pi\) | |||||||
\(398\) | −22.1047 | −1.10801 | ||||||||
\(399\) | 0.701562 | 0.0351220 | ||||||||
\(400\) | 2.29844 | 0.114922 | ||||||||
\(401\) | −4.80625 | −0.240013 | −0.120006 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120006 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(402\) | −5.40312 | −0.269483 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.40312 | −0.169312 | ||||||||
\(405\) | −2.70156 | −0.134242 | ||||||||
\(406\) | 2.70156 | 0.134076 | ||||||||
\(407\) | −7.50781 | −0.372148 | ||||||||
\(408\) | −2.70156 | −0.133747 | ||||||||
\(409\) | −5.29844 | −0.261991 | −0.130995 | − | 0.991383i | \(-0.541817\pi\) | ||||
−0.130995 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(410\) | −9.19375 | −0.454047 | ||||||||
\(411\) | −18.7016 | −0.922480 | ||||||||
\(412\) | −3.29844 | −0.162502 | ||||||||
\(413\) | −14.8062 | −0.728568 | ||||||||
\(414\) | −4.70156 | −0.231069 | ||||||||
\(415\) | −36.2094 | −1.77745 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.80625 | −0.333303 | ||||||||
\(418\) | −0.492189 | −0.0240738 | ||||||||
\(419\) | 34.1047 | 1.66612 | 0.833061 | − | 0.553180i | \(-0.186586\pi\) | ||||
0.833061 | + | 0.553180i | \(0.186586\pi\) | |||||||
\(420\) | −2.70156 | −0.131823 | ||||||||
\(421\) | −19.6125 | −0.955855 | −0.477927 | − | 0.878399i | \(-0.658612\pi\) | ||||
−0.477927 | + | 0.878399i | \(0.658612\pi\) | |||||||
\(422\) | 24.7016 | 1.20245 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | 2.00000 | 0.0971286 | ||||||||
\(425\) | −6.20937 | −0.301199 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | −1.29844 | −0.0628358 | ||||||||
\(428\) | −5.40312 | −0.261170 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27.2984 | −1.31645 | ||||||||
\(431\) | 12.2094 | 0.588105 | 0.294052 | − | 0.955789i | \(-0.404996\pi\) | ||||
0.294052 | + | 0.955789i | \(0.404996\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.2094 | 0.682859 | 0.341429 | − | 0.939907i | \(-0.389089\pi\) | ||||
0.341429 | + | 0.939907i | \(0.389089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.29844 | 0.349933 | ||||||||
\(436\) | −9.29844 | −0.445314 | ||||||||
\(437\) | 3.29844 | 0.157786 | ||||||||
\(438\) | 1.29844 | 0.0620418 | ||||||||
\(439\) | −0.492189 | −0.0234909 | −0.0117455 | − | 0.999931i | \(-0.503739\pi\) | ||||
−0.0117455 | + | 0.999931i | \(0.503739\pi\) | |||||||
\(440\) | 1.89531 | 0.0903555 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.209373 | 0.00994760 | 0.00497380 | − | 0.999988i | \(-0.498417\pi\) | ||||
0.00497380 | + | 0.999988i | \(0.498417\pi\) | |||||||
\(444\) | 10.7016 | 0.507874 | ||||||||
\(445\) | −23.7906 | −1.12778 | ||||||||
\(446\) | 9.40312 | 0.445251 | ||||||||
\(447\) | 15.4031 | 0.728543 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 7.89531 | 0.372603 | 0.186301 | − | 0.982493i | \(-0.440350\pi\) | ||||
0.186301 | + | 0.982493i | \(0.440350\pi\) | |||||||
\(450\) | −2.29844 | −0.108349 | ||||||||
\(451\) | −2.38750 | −0.112423 | ||||||||
\(452\) | 4.80625 | 0.226067 | ||||||||
\(453\) | −4.70156 | −0.220899 | ||||||||
\(454\) | 21.4031 | 1.00450 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.701562 | 0.0328537 | ||||||||
\(457\) | −0.596876 | −0.0279207 | −0.0139603 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139603 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(458\) | 6.00000 | 0.280362 | ||||||||
\(459\) | 2.70156 | 0.126098 | ||||||||
\(460\) | −12.7016 | −0.592213 | ||||||||
\(461\) | 20.3141 | 0.946120 | 0.473060 | − | 0.881030i | \(-0.343149\pi\) | ||||
0.473060 | + | 0.881030i | \(0.343149\pi\) | |||||||
\(462\) | −0.701562 | −0.0326396 | ||||||||
\(463\) | 34.3141 | 1.59471 | 0.797355 | − | 0.603511i | \(-0.206232\pi\) | ||||
0.797355 | + | 0.603511i | \(0.206232\pi\) | |||||||
\(464\) | 2.70156 | 0.125417 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.2094 | 0.843533 | ||||||||
\(467\) | −4.49219 | −0.207874 | −0.103937 | − | 0.994584i | \(-0.533144\pi\) | ||||
−0.103937 | + | 0.994584i | \(0.533144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.40312 | 0.249493 | ||||||||
\(470\) | 21.6125 | 0.996910 | ||||||||
\(471\) | −20.1047 | −0.926375 | ||||||||
\(472\) | −14.8062 | −0.681513 | ||||||||
\(473\) | −7.08907 | −0.325956 | ||||||||
\(474\) | 9.40312 | 0.431900 | ||||||||
\(475\) | 1.61250 | 0.0739864 | ||||||||
\(476\) | 2.70156 | 0.123826 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | −7.50781 | −0.343041 | −0.171520 | − | 0.985181i | \(-0.554868\pi\) | ||||
−0.171520 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(480\) | −2.70156 | −0.123309 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −24.8062 | −1.12989 | ||||||||
\(483\) | 4.70156 | 0.213928 | ||||||||
\(484\) | −10.5078 | −0.477628 | ||||||||
\(485\) | −23.7906 | −1.08028 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | −1.29844 | −0.0587775 | ||||||||
\(489\) | 5.40312 | 0.244338 | ||||||||
\(490\) | 2.70156 | 0.122044 | ||||||||
\(491\) | 26.5969 | 1.20030 | 0.600150 | − | 0.799887i | \(-0.295108\pi\) | ||||
0.600150 | + | 0.799887i | \(0.295108\pi\) | |||||||
\(492\) | 3.40312 | 0.153425 | ||||||||
\(493\) | −7.29844 | −0.328705 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.89531 | −0.0851880 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 13.4031 | 0.600608 | ||||||||
\(499\) | 1.19375 | 0.0534397 | 0.0267198 | − | 0.999643i | \(-0.491494\pi\) | ||||
0.0267198 | + | 0.999643i | \(0.491494\pi\) | |||||||
\(500\) | 7.29844 | 0.326396 | ||||||||
\(501\) | 3.29844 | 0.147363 | ||||||||
\(502\) | −3.50781 | −0.156561 | ||||||||
\(503\) | −33.4031 | −1.48937 | −0.744686 | − | 0.667415i | \(-0.767401\pi\) | ||||
−0.744686 | + | 0.667415i | \(0.767401\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 9.19375 | 0.409117 | ||||||||
\(506\) | −3.29844 | −0.146633 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.59688 | −0.292689 | ||||||||
\(509\) | −38.9109 | −1.72470 | −0.862348 | − | 0.506315i | \(-0.831007\pi\) | ||||
−0.862348 | + | 0.506315i | \(0.831007\pi\) | |||||||
\(510\) | 7.29844 | 0.323180 | ||||||||
\(511\) | −1.29844 | −0.0574395 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.701562 | −0.0309747 | ||||||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 8.91093 | 0.392663 | ||||||||
\(516\) | 10.1047 | 0.444834 | ||||||||
\(517\) | 5.61250 | 0.246837 | ||||||||
\(518\) | −10.7016 | −0.470200 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.29844 | −0.0568856 | −0.0284428 | − | 0.999595i | \(-0.509055\pi\) | ||||
−0.0284428 | + | 0.999595i | \(0.509055\pi\) | |||||||
\(522\) | −2.70156 | −0.118244 | ||||||||
\(523\) | −33.6125 | −1.46977 | −0.734886 | − | 0.678191i | \(-0.762764\pi\) | ||||
−0.734886 | + | 0.678191i | \(0.762764\pi\) | |||||||
\(524\) | −7.29844 | −0.318834 | ||||||||
\(525\) | 2.29844 | 0.100312 | ||||||||
\(526\) | 26.8062 | 1.16881 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.701562 | −0.0305316 | ||||||||
\(529\) | −0.895314 | −0.0389267 | ||||||||
\(530\) | −5.40312 | −0.234697 | ||||||||
\(531\) | 14.8062 | 0.642536 | ||||||||
\(532\) | −0.701562 | −0.0304166 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 8.80625 | 0.381084 | ||||||||
\(535\) | 14.5969 | 0.631078 | ||||||||
\(536\) | 5.40312 | 0.233379 | ||||||||
\(537\) | −14.8062 | −0.638937 | ||||||||
\(538\) | 4.80625 | 0.207212 | ||||||||
\(539\) | 0.701562 | 0.0302184 | ||||||||
\(540\) | 2.70156 | 0.116257 | ||||||||
\(541\) | 6.70156 | 0.288123 | 0.144061 | − | 0.989569i | \(-0.453984\pi\) | ||||
0.144061 | + | 0.989569i | \(0.453984\pi\) | |||||||
\(542\) | 12.2094 | 0.524437 | ||||||||
\(543\) | −8.80625 | −0.377912 | ||||||||
\(544\) | 2.70156 | 0.115829 | ||||||||
\(545\) | 25.1203 | 1.07604 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.61250 | 0.411001 | 0.205500 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205500 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(548\) | 18.7016 | 0.798891 | ||||||||
\(549\) | 1.29844 | 0.0554160 | ||||||||
\(550\) | −1.61250 | −0.0687571 | ||||||||
\(551\) | 1.89531 | 0.0807431 | ||||||||
\(552\) | 4.70156 | 0.200112 | ||||||||
\(553\) | −9.40312 | −0.399862 | ||||||||
\(554\) | −27.6125 | −1.17314 | ||||||||
\(555\) | −28.9109 | −1.22720 | ||||||||
\(556\) | 6.80625 | 0.288649 | ||||||||
\(557\) | 24.5969 | 1.04220 | 0.521102 | − | 0.853495i | \(-0.325521\pi\) | ||||
0.521102 | + | 0.853495i | \(0.325521\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.70156 | 0.114162 | ||||||||
\(561\) | 1.89531 | 0.0800202 | ||||||||
\(562\) | 12.8062 | 0.540199 | ||||||||
\(563\) | 8.70156 | 0.366727 | 0.183364 | − | 0.983045i | \(-0.441301\pi\) | ||||
0.183364 | + | 0.983045i | \(0.441301\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | −12.9844 | −0.546257 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | 26.0000 | 1.08998 | 0.544988 | − | 0.838444i | \(-0.316534\pi\) | ||||
0.544988 | + | 0.838444i | \(0.316534\pi\) | |||||||
\(570\) | −1.89531 | −0.0793860 | ||||||||
\(571\) | −1.19375 | −0.0499569 | −0.0249785 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249785 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.7016 | −0.530615 | ||||||||
\(574\) | −3.40312 | −0.142044 | ||||||||
\(575\) | 10.8062 | 0.450652 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.80625 | 0.366609 | 0.183304 | − | 0.983056i | \(-0.441321\pi\) | ||||
0.183304 | + | 0.983056i | \(0.441321\pi\) | |||||||
\(578\) | 9.70156 | 0.403532 | ||||||||
\(579\) | 11.4031 | 0.473898 | ||||||||
\(580\) | −7.29844 | −0.303051 | ||||||||
\(581\) | −13.4031 | −0.556055 | ||||||||
\(582\) | 8.80625 | 0.365031 | ||||||||
\(583\) | −1.40312 | −0.0581115 | ||||||||
\(584\) | −1.29844 | −0.0537297 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8062 | −0.529021 | ||||||||
\(587\) | −35.0156 | −1.44525 | −0.722625 | − | 0.691241i | \(-0.757064\pi\) | ||||
−0.722625 | + | 0.691241i | \(0.757064\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 40.0000 | 1.64677 | ||||||||
\(591\) | −3.40312 | −0.139986 | ||||||||
\(592\) | −10.7016 | −0.439831 | ||||||||
\(593\) | 16.8062 | 0.690150 | 0.345075 | − | 0.938575i | \(-0.387853\pi\) | ||||
0.345075 | + | 0.938575i | \(0.387853\pi\) | |||||||
\(594\) | 0.701562 | 0.0287854 | ||||||||
\(595\) | −7.29844 | −0.299207 | ||||||||
\(596\) | −15.4031 | −0.630937 | ||||||||
\(597\) | −22.1047 | −0.904685 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2984 | 0.461642 | 0.230821 | − | 0.972996i | \(-0.425859\pi\) | ||||
0.230821 | + | 0.972996i | \(0.425859\pi\) | |||||||
\(600\) | 2.29844 | 0.0938333 | ||||||||
\(601\) | −15.4031 | −0.628307 | −0.314153 | − | 0.949372i | \(-0.601721\pi\) | ||||
−0.314153 | + | 0.949372i | \(0.601721\pi\) | |||||||
\(602\) | −10.1047 | −0.411836 | ||||||||
\(603\) | −5.40312 | −0.220032 | ||||||||
\(604\) | 4.70156 | 0.191304 | ||||||||
\(605\) | 28.3875 | 1.15412 | ||||||||
\(606\) | −3.40312 | −0.138242 | ||||||||
\(607\) | 7.50781 | 0.304733 | 0.152366 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152366 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(608\) | −0.701562 | −0.0284521 | ||||||||
\(609\) | 2.70156 | 0.109473 | ||||||||
\(610\) | 3.50781 | 0.142027 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.70156 | −0.109204 | ||||||||
\(613\) | −38.9109 | −1.57160 | −0.785799 | − | 0.618482i | \(-0.787748\pi\) | ||||
−0.785799 | + | 0.618482i | \(0.787748\pi\) | |||||||
\(614\) | −6.80625 | −0.274678 | ||||||||
\(615\) | −9.19375 | −0.370728 | ||||||||
\(616\) | 0.701562 | 0.0282667 | ||||||||
\(617\) | 30.9109 | 1.24443 | 0.622214 | − | 0.782847i | \(-0.286233\pi\) | ||||
0.622214 | + | 0.782847i | \(0.286233\pi\) | |||||||
\(618\) | −3.29844 | −0.132683 | ||||||||
\(619\) | −7.29844 | −0.293349 | −0.146674 | − | 0.989185i | \(-0.546857\pi\) | ||||
−0.146674 | + | 0.989185i | \(0.546857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.70156 | −0.188667 | ||||||||
\(622\) | −14.5969 | −0.585281 | ||||||||
\(623\) | −8.80625 | −0.352815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2094 | −1.24837 | ||||||||
\(626\) | −22.2094 | −0.887665 | ||||||||
\(627\) | −0.492189 | −0.0196562 | ||||||||
\(628\) | 20.1047 | 0.802264 | ||||||||
\(629\) | 28.9109 | 1.15275 | ||||||||
\(630\) | −2.70156 | −0.107633 | ||||||||
\(631\) | 7.50781 | 0.298881 | 0.149441 | − | 0.988771i | \(-0.452253\pi\) | ||||
0.149441 | + | 0.988771i | \(0.452253\pi\) | |||||||
\(632\) | −9.40312 | −0.374036 | ||||||||
\(633\) | 24.7016 | 0.981799 | ||||||||
\(634\) | 7.40312 | 0.294016 | ||||||||
\(635\) | 17.8219 | 0.707239 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.89531 | −0.0750362 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 2.70156 | 0.106789 | ||||||||
\(641\) | −48.8062 | −1.92773 | −0.963865 | − | 0.266390i | \(-0.914169\pi\) | ||||
−0.963865 | + | 0.266390i | \(0.914169\pi\) | |||||||
\(642\) | −5.40312 | −0.213244 | ||||||||
\(643\) | −46.3141 | −1.82645 | −0.913224 | − | 0.407458i | \(-0.866415\pi\) | ||||
−0.913224 | + | 0.407458i | \(0.866415\pi\) | |||||||
\(644\) | −4.70156 | −0.185268 | ||||||||
\(645\) | −27.2984 | −1.07487 | ||||||||
\(646\) | 1.89531 | 0.0745701 | ||||||||
\(647\) | −8.00000 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 10.3875 | 0.407745 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.40312 | −0.211603 | ||||||||
\(653\) | −9.50781 | −0.372069 | −0.186035 | − | 0.982543i | \(-0.559564\pi\) | ||||
−0.186035 | + | 0.982543i | \(0.559564\pi\) | |||||||
\(654\) | −9.29844 | −0.363598 | ||||||||
\(655\) | 19.7172 | 0.770414 | ||||||||
\(656\) | −3.40312 | −0.132870 | ||||||||
\(657\) | 1.29844 | 0.0506569 | ||||||||
\(658\) | 8.00000 | 0.311872 | ||||||||
\(659\) | −35.0156 | −1.36401 | −0.682007 | − | 0.731345i | \(-0.738893\pi\) | ||||
−0.682007 | + | 0.731345i | \(0.738893\pi\) | |||||||
\(660\) | 1.89531 | 0.0737750 | ||||||||
\(661\) | 50.4187 | 1.96106 | 0.980531 | − | 0.196365i | \(-0.0629136\pi\) | ||||
0.980531 | + | 0.196365i | \(0.0629136\pi\) | |||||||
\(662\) | 32.2094 | 1.25185 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.4031 | −0.520142 | ||||||||
\(665\) | 1.89531 | 0.0734971 | ||||||||
\(666\) | 10.7016 | 0.414677 | ||||||||
\(667\) | 12.7016 | 0.491806 | ||||||||
\(668\) | −3.29844 | −0.127620 | ||||||||
\(669\) | 9.40312 | 0.363546 | ||||||||
\(670\) | −14.5969 | −0.563927 | ||||||||
\(671\) | 0.910935 | 0.0351662 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 42.9109 | 1.65409 | 0.827047 | − | 0.562132i | \(-0.190019\pi\) | ||||
0.827047 | + | 0.562132i | \(0.190019\pi\) | |||||||
\(674\) | 29.5078 | 1.13660 | ||||||||
\(675\) | −2.29844 | −0.0884669 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 4.80625 | 0.184583 | ||||||||
\(679\) | −8.80625 | −0.337953 | ||||||||
\(680\) | −7.29844 | −0.279882 | ||||||||
\(681\) | 21.4031 | 0.820170 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5078 | −0.440334 | −0.220167 | − | 0.975462i | \(-0.570660\pi\) | ||||
−0.220167 | + | 0.975462i | \(0.570660\pi\) | |||||||
\(684\) | 0.701562 | 0.0268249 | ||||||||
\(685\) | −50.5234 | −1.93040 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | −10.1047 | −0.385238 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −12.7016 | −0.483540 | ||||||||
\(691\) | −49.6125 | −1.88735 | −0.943674 | − | 0.330876i | \(-0.892656\pi\) | ||||
−0.943674 | + | 0.330876i | \(0.892656\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | −0.701562 | −0.0266501 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | −18.3875 | −0.697478 | ||||||||
\(696\) | 2.70156 | 0.102402 | ||||||||
\(697\) | 9.19375 | 0.348238 | ||||||||
\(698\) | 30.0000 | 1.13552 | ||||||||
\(699\) | 18.2094 | 0.688742 | ||||||||
\(700\) | −2.29844 | −0.0868728 | ||||||||
\(701\) | 3.19375 | 0.120626 | 0.0603132 | − | 0.998180i | \(-0.480790\pi\) | ||||
0.0603132 | + | 0.998180i | \(0.480790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.50781 | −0.283162 | ||||||||
\(704\) | 0.701562 | 0.0264411 | ||||||||
\(705\) | 21.6125 | 0.813974 | ||||||||
\(706\) | 20.8062 | 0.783053 | ||||||||
\(707\) | 3.40312 | 0.127988 | ||||||||
\(708\) | −14.8062 | −0.556453 | ||||||||
\(709\) | −51.6125 | −1.93835 | −0.969174 | − | 0.246377i | \(-0.920760\pi\) | ||||
−0.969174 | + | 0.246377i | \(0.920760\pi\) | |||||||
\(710\) | 21.6125 | 0.811103 | ||||||||
\(711\) | 9.40312 | 0.352645 | ||||||||
\(712\) | −8.80625 | −0.330028 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 2.70156 | 0.101103 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.8062 | 0.553335 | ||||||||
\(717\) | 16.0000 | 0.597531 | ||||||||
\(718\) | 26.8062 | 1.00040 | ||||||||
\(719\) | −31.0156 | −1.15669 | −0.578344 | − | 0.815793i | \(-0.696301\pi\) | ||||
−0.578344 | + | 0.815793i | \(0.696301\pi\) | |||||||
\(720\) | −2.70156 | −0.100681 | ||||||||
\(721\) | 3.29844 | 0.122840 | ||||||||
\(722\) | 18.5078 | 0.688789 | ||||||||
\(723\) | −24.8062 | −0.922554 | ||||||||
\(724\) | 8.80625 | 0.327282 | ||||||||
\(725\) | 6.20937 | 0.230610 | ||||||||
\(726\) | −10.5078 | −0.389981 | ||||||||
\(727\) | −22.1047 | −0.819817 | −0.409909 | − | 0.912127i | \(-0.634439\pi\) | ||||
−0.409909 | + | 0.912127i | \(0.634439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.50781 | 0.129830 | ||||||||
\(731\) | 27.2984 | 1.00967 | ||||||||
\(732\) | −1.29844 | −0.0479916 | ||||||||
\(733\) | −20.5969 | −0.760763 | −0.380381 | − | 0.924830i | \(-0.624207\pi\) | ||||
−0.380381 | + | 0.924830i | \(0.624207\pi\) | |||||||
\(734\) | 29.6125 | 1.09302 | ||||||||
\(735\) | 2.70156 | 0.0996486 | ||||||||
\(736\) | −4.70156 | −0.173302 | ||||||||
\(737\) | −3.79063 | −0.139630 | ||||||||
\(738\) | 3.40312 | 0.125271 | ||||||||
\(739\) | −40.2094 | −1.47913 | −0.739563 | − | 0.673088i | \(-0.764968\pi\) | ||||
−0.739563 | + | 0.673088i | \(0.764968\pi\) | |||||||
\(740\) | 28.9109 | 1.06279 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00000 | −0.0734223 | ||||||||
\(743\) | −23.0156 | −0.844361 | −0.422181 | − | 0.906512i | \(-0.638735\pi\) | ||||
−0.422181 | + | 0.906512i | \(0.638735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.6125 | 1.52456 | ||||||||
\(746\) | 19.4031 | 0.710399 | ||||||||
\(747\) | 13.4031 | 0.490395 | ||||||||
\(748\) | −1.89531 | −0.0692995 | ||||||||
\(749\) | 5.40312 | 0.197426 | ||||||||
\(750\) | 7.29844 | 0.266501 | ||||||||
\(751\) | 34.8062 | 1.27010 | 0.635049 | − | 0.772472i | \(-0.280980\pi\) | ||||
0.635049 | + | 0.772472i | \(0.280980\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | −3.50781 | −0.127832 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.7016 | −0.462257 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 30.4187 | 1.10559 | 0.552794 | − | 0.833318i | \(-0.313562\pi\) | ||||
0.552794 | + | 0.833318i | \(0.313562\pi\) | |||||||
\(758\) | −17.6125 | −0.639715 | ||||||||
\(759\) | −3.29844 | −0.119726 | ||||||||
\(760\) | 1.89531 | 0.0687503 | ||||||||
\(761\) | −32.5969 | −1.18164 | −0.590818 | − | 0.806805i | \(-0.701195\pi\) | ||||
−0.590818 | + | 0.806805i | \(0.701195\pi\) | |||||||
\(762\) | −6.59688 | −0.238980 | ||||||||
\(763\) | 9.29844 | 0.336626 | ||||||||
\(764\) | 12.7016 | 0.459526 | ||||||||
\(765\) | 7.29844 | 0.263876 | ||||||||
\(766\) | 16.9109 | 0.611017 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −50.9109 | −1.83590 | −0.917948 | − | 0.396702i | \(-0.870155\pi\) | ||||
−0.917948 | + | 0.396702i | \(0.870155\pi\) | |||||||
\(770\) | −1.89531 | −0.0683024 | ||||||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | −11.4031 | −0.410407 | ||||||||
\(773\) | 28.3141 | 1.01839 | 0.509193 | − | 0.860652i | \(-0.329944\pi\) | ||||
0.509193 | + | 0.860652i | \(0.329944\pi\) | |||||||
\(774\) | 10.1047 | 0.363205 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.80625 | −0.316126 | ||||||||
\(777\) | −10.7016 | −0.383916 | ||||||||
\(778\) | −14.0000 | −0.501924 | ||||||||
\(779\) | −2.38750 | −0.0855412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.61250 | 0.200831 | ||||||||
\(782\) | 12.7016 | 0.454207 | ||||||||
\(783\) | −2.70156 | −0.0965460 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −54.3141 | −1.93855 | ||||||||
\(786\) | −7.29844 | −0.260327 | ||||||||
\(787\) | −20.9109 | −0.745394 | −0.372697 | − | 0.927953i | \(-0.621567\pi\) | ||||
−0.372697 | + | 0.927953i | \(0.621567\pi\) | |||||||
\(788\) | 3.40312 | 0.121231 | ||||||||
\(789\) | 26.8062 | 0.954328 | ||||||||
\(790\) | 25.4031 | 0.903803 | ||||||||
\(791\) | −4.80625 | −0.170891 | ||||||||
\(792\) | −0.701562 | −0.0249289 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.806248 | 0.0286127 | ||||||||
\(795\) | −5.40312 | −0.191629 | ||||||||
\(796\) | 22.1047 | 0.783480 | ||||||||
\(797\) | −40.5969 | −1.43802 | −0.719008 | − | 0.695002i | \(-0.755403\pi\) | ||||
−0.719008 | + | 0.695002i | \(0.755403\pi\) | |||||||
\(798\) | −0.701562 | −0.0248350 | ||||||||
\(799\) | −21.6125 | −0.764595 | ||||||||
\(800\) | −2.29844 | −0.0812621 | ||||||||
\(801\) | 8.80625 | 0.311153 | ||||||||
\(802\) | 4.80625 | 0.169715 | ||||||||
\(803\) | 0.910935 | 0.0321462 | ||||||||
\(804\) | 5.40312 | 0.190553 | ||||||||
\(805\) | 12.7016 | 0.447671 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.80625 | 0.169188 | ||||||||
\(808\) | 3.40312 | 0.119721 | ||||||||
\(809\) | −11.6125 | −0.408274 | −0.204137 | − | 0.978942i | \(-0.565439\pi\) | ||||
−0.204137 | + | 0.978942i | \(0.565439\pi\) | |||||||
\(810\) | 2.70156 | 0.0949232 | ||||||||
\(811\) | 21.8953 | 0.768848 | 0.384424 | − | 0.923157i | \(-0.374400\pi\) | ||||
0.384424 | + | 0.923157i | \(0.374400\pi\) | |||||||
\(812\) | −2.70156 | −0.0948062 | ||||||||
\(813\) | 12.2094 | 0.428201 | ||||||||
\(814\) | 7.50781 | 0.263149 | ||||||||
\(815\) | 14.5969 | 0.511306 | ||||||||
\(816\) | 2.70156 | 0.0945736 | ||||||||
\(817\) | −7.08907 | −0.248015 | ||||||||
\(818\) | 5.29844 | 0.185256 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.19375 | 0.321060 | ||||||||
\(821\) | −28.5969 | −0.998038 | −0.499019 | − | 0.866591i | \(-0.666306\pi\) | ||||
−0.499019 | + | 0.866591i | \(0.666306\pi\) | |||||||
\(822\) | 18.7016 | 0.652292 | ||||||||
\(823\) | 5.19375 | 0.181043 | 0.0905214 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905214 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(824\) | 3.29844 | 0.114907 | ||||||||
\(825\) | −1.61250 | −0.0561399 | ||||||||
\(826\) | 14.8062 | 0.515175 | ||||||||
\(827\) | −52.9109 | −1.83989 | −0.919947 | − | 0.392043i | \(-0.871768\pi\) | ||||
−0.919947 | + | 0.392043i | \(0.871768\pi\) | |||||||
\(828\) | 4.70156 | 0.163391 | ||||||||
\(829\) | −36.3141 | −1.26124 | −0.630620 | − | 0.776092i | \(-0.717199\pi\) | ||||
−0.630620 | + | 0.776092i | \(0.717199\pi\) | |||||||
\(830\) | 36.2094 | 1.25685 | ||||||||
\(831\) | −27.6125 | −0.957867 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.70156 | −0.0936036 | ||||||||
\(834\) | 6.80625 | 0.235681 | ||||||||
\(835\) | 8.91093 | 0.308376 | ||||||||
\(836\) | 0.492189 | 0.0170227 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −34.1047 | −1.17813 | ||||||||
\(839\) | −34.8062 | −1.20165 | −0.600823 | − | 0.799382i | \(-0.705160\pi\) | ||||
−0.600823 | + | 0.799382i | \(0.705160\pi\) | |||||||
\(840\) | 2.70156 | 0.0932127 | ||||||||
\(841\) | −21.7016 | −0.748330 | ||||||||
\(842\) | 19.6125 | 0.675891 | ||||||||
\(843\) | 12.8062 | 0.441071 | ||||||||
\(844\) | −24.7016 | −0.850263 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 10.5078 | 0.361053 | ||||||||
\(848\) | −2.00000 | −0.0686803 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 6.20937 | 0.212980 | ||||||||
\(851\) | −50.3141 | −1.72474 | ||||||||
\(852\) | −8.00000 | −0.274075 | ||||||||
\(853\) | 22.2094 | 0.760434 | 0.380217 | − | 0.924897i | \(-0.375849\pi\) | ||||
0.380217 | + | 0.924897i | \(0.375849\pi\) | |||||||
\(854\) | 1.29844 | 0.0444316 | ||||||||
\(855\) | −1.89531 | −0.0648184 | ||||||||
\(856\) | 5.40312 | 0.184675 | ||||||||
\(857\) | −16.8062 | −0.574091 | −0.287045 | − | 0.957917i | \(-0.592673\pi\) | ||||
−0.287045 | + | 0.957917i | \(0.592673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.8062 | 1.32405 | 0.662026 | − | 0.749481i | \(-0.269697\pi\) | ||||
0.662026 | + | 0.749481i | \(0.269697\pi\) | |||||||
\(860\) | 27.2984 | 0.930869 | ||||||||
\(861\) | −3.40312 | −0.115978 | ||||||||
\(862\) | −12.2094 | −0.415853 | ||||||||
\(863\) | 22.5969 | 0.769207 | 0.384603 | − | 0.923082i | \(-0.374338\pi\) | ||||
0.384603 | + | 0.923082i | \(0.374338\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 48.6281 | 1.65341 | ||||||||
\(866\) | −14.2094 | −0.482854 | ||||||||
\(867\) | 9.70156 | 0.329482 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.59688 | 0.223784 | ||||||||
\(870\) | −7.29844 | −0.247440 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.29844 | 0.314885 | ||||||||
\(873\) | 8.80625 | 0.298046 | ||||||||
\(874\) | −3.29844 | −0.111571 | ||||||||
\(875\) | −7.29844 | −0.246732 | ||||||||
\(876\) | −1.29844 | −0.0438702 | ||||||||
\(877\) | −0.387503 | −0.0130850 | −0.00654252 | − | 0.999979i | \(-0.502083\pi\) | ||||
−0.00654252 | + | 0.999979i | \(0.502083\pi\) | |||||||
\(878\) | 0.492189 | 0.0166106 | ||||||||
\(879\) | −12.8062 | −0.431944 | ||||||||
\(880\) | −1.89531 | −0.0638910 | ||||||||
\(881\) | −8.31406 | −0.280108 | −0.140054 | − | 0.990144i | \(-0.544728\pi\) | ||||
−0.140054 | + | 0.990144i | \(0.544728\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 13.8953 | 0.467615 | 0.233807 | − | 0.972283i | \(-0.424882\pi\) | ||||
0.233807 | + | 0.972283i | \(0.424882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.0000 | 1.34459 | ||||||||
\(886\) | −0.209373 | −0.00703401 | ||||||||
\(887\) | −8.00000 | −0.268614 | −0.134307 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134307 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(888\) | −10.7016 | −0.359121 | ||||||||
\(889\) | 6.59688 | 0.221252 | ||||||||
\(890\) | 23.7906 | 0.797464 | ||||||||
\(891\) | 0.701562 | 0.0235032 | ||||||||
\(892\) | −9.40312 | −0.314840 | ||||||||
\(893\) | 5.61250 | 0.187815 | ||||||||
\(894\) | −15.4031 | −0.515158 | ||||||||
\(895\) | −40.0000 | −1.33705 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.89531 | −0.263470 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.29844 | 0.0766146 | ||||||||
\(901\) | 5.40312 | 0.180004 | ||||||||
\(902\) | 2.38750 | 0.0794952 | ||||||||
\(903\) | −10.1047 | −0.336263 | ||||||||
\(904\) | −4.80625 | −0.159853 | ||||||||
\(905\) | −23.7906 | −0.790827 | ||||||||
\(906\) | 4.70156 | 0.156199 | ||||||||
\(907\) | −25.6125 | −0.850449 | −0.425225 | − | 0.905088i | \(-0.639805\pi\) | ||||
−0.425225 | + | 0.905088i | \(0.639805\pi\) | |||||||
\(908\) | −21.4031 | −0.710288 | ||||||||
\(909\) | −3.40312 | −0.112875 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9109 | 1.35544 | 0.677720 | − | 0.735320i | \(-0.262968\pi\) | ||||
0.677720 | + | 0.735320i | \(0.262968\pi\) | |||||||
\(912\) | −0.701562 | −0.0232310 | ||||||||
\(913\) | 9.40312 | 0.311198 | ||||||||
\(914\) | 0.596876 | 0.0197429 | ||||||||
\(915\) | 3.50781 | 0.115965 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | 7.29844 | 0.241016 | ||||||||
\(918\) | −2.70156 | −0.0891648 | ||||||||
\(919\) | −14.5969 | −0.481507 | −0.240753 | − | 0.970586i | \(-0.577394\pi\) | ||||
−0.240753 | + | 0.970586i | \(0.577394\pi\) | |||||||
\(920\) | 12.7016 | 0.418758 | ||||||||
\(921\) | −6.80625 | −0.224274 | ||||||||
\(922\) | −20.3141 | −0.669008 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.701562 | 0.0230797 | ||||||||
\(925\) | −24.5969 | −0.808740 | ||||||||
\(926\) | −34.3141 | −1.12763 | ||||||||
\(927\) | −3.29844 | −0.108335 | ||||||||
\(928\) | −2.70156 | −0.0886831 | ||||||||
\(929\) | −33.0156 | −1.08321 | −0.541604 | − | 0.840634i | \(-0.682183\pi\) | ||||
−0.541604 | + | 0.840634i | \(0.682183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.701562 | 0.0229928 | ||||||||
\(932\) | −18.2094 | −0.596468 | ||||||||
\(933\) | −14.5969 | −0.477880 | ||||||||
\(934\) | 4.49219 | 0.146989 | ||||||||
\(935\) | 5.12031 | 0.167452 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.8062 | 0.941059 | 0.470530 | − | 0.882384i | \(-0.344063\pi\) | ||||
0.470530 | + | 0.882384i | \(0.344063\pi\) | |||||||
\(938\) | −5.40312 | −0.176418 | ||||||||
\(939\) | −22.2094 | −0.724775 | ||||||||
\(940\) | −21.6125 | −0.704922 | ||||||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 20.1047 | 0.655046 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 14.8062 | 0.481902 | ||||||||
\(945\) | −2.70156 | −0.0878818 | ||||||||
\(946\) | 7.08907 | 0.230485 | ||||||||
\(947\) | −4.49219 | −0.145977 | −0.0729883 | − | 0.997333i | \(-0.523254\pi\) | ||||
−0.0729883 | + | 0.997333i | \(0.523254\pi\) | |||||||
\(948\) | −9.40312 | −0.305399 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.61250 | −0.0523163 | ||||||||
\(951\) | 7.40312 | 0.240063 | ||||||||
\(952\) | −2.70156 | −0.0875581 | ||||||||
\(953\) | −39.8219 | −1.28996 | −0.644978 | − | 0.764201i | \(-0.723134\pi\) | ||||
−0.644978 | + | 0.764201i | \(0.723134\pi\) | |||||||
\(954\) | 2.00000 | 0.0647524 | ||||||||
\(955\) | −34.3141 | −1.11038 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | −1.89531 | −0.0612668 | ||||||||
\(958\) | 7.50781 | 0.242566 | ||||||||
\(959\) | −18.7016 | −0.603905 | ||||||||
\(960\) | 2.70156 | 0.0871925 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.40312 | −0.174113 | ||||||||
\(964\) | 24.8062 | 0.798955 | ||||||||
\(965\) | 30.8062 | 0.991688 | ||||||||
\(966\) | −4.70156 | −0.151270 | ||||||||
\(967\) | 51.7172 | 1.66311 | 0.831556 | − | 0.555441i | \(-0.187450\pi\) | ||||
0.831556 | + | 0.555441i | \(0.187450\pi\) | |||||||
\(968\) | 10.5078 | 0.337734 | ||||||||
\(969\) | 1.89531 | 0.0608862 | ||||||||
\(970\) | 23.7906 | 0.763871 | ||||||||
\(971\) | 54.8062 | 1.75882 | 0.879408 | − | 0.476069i | \(-0.157939\pi\) | ||||
0.879408 | + | 0.476069i | \(0.157939\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.80625 | −0.218198 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.29844 | 0.0415620 | ||||||||
\(977\) | 41.7172 | 1.33465 | 0.667325 | − | 0.744766i | \(-0.267439\pi\) | ||||
0.667325 | + | 0.744766i | \(0.267439\pi\) | |||||||
\(978\) | −5.40312 | −0.172773 | ||||||||
\(979\) | 6.17813 | 0.197454 | ||||||||
\(980\) | −2.70156 | −0.0862982 | ||||||||
\(981\) | −9.29844 | −0.296876 | ||||||||
\(982\) | −26.5969 | −0.848740 | ||||||||
\(983\) | 38.1047 | 1.21535 | 0.607675 | − | 0.794186i | \(-0.292102\pi\) | ||||
0.607675 | + | 0.794186i | \(0.292102\pi\) | |||||||
\(984\) | −3.40312 | −0.108488 | ||||||||
\(985\) | −9.19375 | −0.292937 | ||||||||
\(986\) | 7.29844 | 0.232430 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.5078 | −1.51066 | ||||||||
\(990\) | 1.89531 | 0.0602370 | ||||||||
\(991\) | −38.5969 | −1.22607 | −0.613035 | − | 0.790056i | \(-0.710052\pi\) | ||||
−0.613035 | + | 0.790056i | \(0.710052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.2094 | 1.02213 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −59.7172 | −1.89316 | ||||||||
\(996\) | −13.4031 | −0.424694 | ||||||||
\(997\) | −12.8062 | −0.405578 | −0.202789 | − | 0.979222i | \(-0.565001\pi\) | ||||
−0.202789 | + | 0.979222i | \(0.565001\pi\) | |||||||
\(998\) | −1.19375 | −0.0377875 | ||||||||
\(999\) | 10.7016 | 0.338582 |
(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 | 7098.2.a.bh.1.1 | 2 | ||
13.12 | even | 2 | 546.2.a.i.1.2 | ✓ | 2 | ||
39.38 | odd | 2 | 1638.2.a.w.1.1 | 2 | |||
52.51 | odd | 2 | 4368.2.a.bg.1.2 | 2 | |||
91.90 | odd | 2 | 3822.2.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.a.i.1.2 | ✓ | 2 | 13.12 | even | 2 | ||
1638.2.a.w.1.1 | 2 | 39.38 | odd | 2 | |||
3822.2.a.bt.1.1 | 2 | 91.90 | odd | 2 | |||
4368.2.a.bg.1.2 | 2 | 52.51 | odd | 2 | |||
7098.2.a.bh.1.1 | 2 | 1.1 | even | 1 | trivial |