Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 80 x^{9} + 347 x^{8} - 697 x^{7} - 1714 x^{6} + 2146 x^{5} + 3304 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.12492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.12492 | −1.39751 | −0.698754 | − | 0.715362i | \(-0.746262\pi\) | ||||
−0.698754 | + | 0.715362i | \(0.746262\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.33538 | 1.63862 | 0.819310 | − | 0.573351i | \(-0.194357\pi\) | ||||
0.819310 | + | 0.573351i | \(0.194357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.88477 | −1.17130 | −0.585652 | − | 0.810563i | \(-0.699161\pi\) | ||||
−0.585652 | + | 0.810563i | \(0.699161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.76924 | −1.60010 | −0.800050 | − | 0.599933i | \(-0.795194\pi\) | ||||
−0.800050 | + | 0.599933i | \(0.795194\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12492 | 0.806851 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.77786 | 0.431194 | 0.215597 | − | 0.976482i | \(-0.430830\pi\) | ||||
0.215597 | + | 0.976482i | \(0.430830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.14116 | 0.261799 | 0.130900 | − | 0.991396i | \(-0.458213\pi\) | ||||
0.130900 | + | 0.991396i | \(0.458213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.33538 | −0.946058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.76514 | 0.953028 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.76454 | 1.03534 | 0.517671 | − | 0.855580i | \(-0.326799\pi\) | ||||
0.517671 | + | 0.855580i | \(0.326799\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.88477 | 0.676252 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.5477 | −2.28998 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.00519 | 1.48044 | 0.740222 | − | 0.672362i | \(-0.234720\pi\) | ||||
0.740222 | + | 0.672362i | \(0.234720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.76924 | 0.923818 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.21895 | −0.190368 | −0.0951839 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951839 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.15921 | 0.939271 | 0.469636 | − | 0.882860i | \(-0.344385\pi\) | ||||
0.469636 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.12492 | −0.465836 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.33639 | −0.194932 | −0.0974661 | − | 0.995239i | \(-0.531074\pi\) | ||||
−0.0974661 | + | 0.995239i | \(0.531074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7955 | 1.68508 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.77786 | −0.248950 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.98281 | −0.821802 | −0.410901 | − | 0.911680i | \(-0.634786\pi\) | ||||
−0.410901 | + | 0.911680i | \(0.634786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.1396 | 1.63691 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.14116 | −0.151150 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.53101 | −0.980454 | −0.490227 | − | 0.871595i | \(-0.663086\pi\) | ||||
−0.490227 | + | 0.871595i | \(0.663086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.35532 | 0.301568 | 0.150784 | − | 0.988567i | \(-0.451820\pi\) | ||||
0.150784 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.33538 | 0.546207 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.0284 | 2.23615 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.03611 | −0.370920 | −0.185460 | − | 0.982652i | \(-0.559377\pi\) | ||||
−0.185460 | + | 0.982652i | \(0.559377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.64492 | 0.788607 | 0.394304 | − | 0.918980i | \(-0.370986\pi\) | ||||
0.394304 | + | 0.918980i | \(0.370986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.08303 | 0.243800 | 0.121900 | − | 0.992542i | \(-0.461101\pi\) | ||||
0.121900 | + | 0.992542i | \(0.461101\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.76514 | −0.550231 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.8420 | −1.91932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0123 | −1.46400 | −0.732001 | − | 0.681304i | \(-0.761413\pi\) | ||||
−0.732001 | + | 0.681304i | \(0.761413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3584 | −1.57604 | −0.788019 | − | 0.615651i | \(-0.788893\pi\) | ||||
−0.788019 | + | 0.615651i | \(0.788893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.55566 | −0.602596 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.89965 | −0.519362 | −0.259681 | − | 0.965694i | \(-0.583617\pi\) | ||||
−0.259681 | + | 0.965694i | \(0.583617\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.0119 | −2.62196 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.76454 | −0.597755 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.56603 | −0.365866 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.62077 | 0.773772 | 0.386886 | − | 0.922128i | \(-0.373551\pi\) | ||||
0.386886 | + | 0.922128i | \(0.373551\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.88477 | −0.390435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.8588 | 1.67752 | 0.838758 | − | 0.544504i | \(-0.183282\pi\) | ||||
0.838758 | + | 0.544504i | \(0.183282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.87256 | −0.184509 | −0.0922543 | − | 0.995735i | \(-0.529407\pi\) | ||||
−0.0922543 | + | 0.995735i | \(0.529407\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.5477 | 1.32212 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8890 | 1.24603 | 0.623015 | − | 0.782210i | \(-0.285907\pi\) | ||||
0.623015 | + | 0.782210i | \(0.285907\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.163721 | 0.0156817 | 0.00784083 | − | 0.999969i | \(-0.497504\pi\) | ||||
0.00784083 | + | 0.999969i | \(0.497504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00519 | −0.854735 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58635 | −0.149231 | −0.0746155 | − | 0.997212i | \(-0.523773\pi\) | ||||
−0.0746155 | + | 0.997212i | \(0.523773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12492 | −0.291401 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.76924 | −0.533367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.70769 | 0.706563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.09147 | 0.371952 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.21895 | 0.109909 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.733922 | 0.0656440 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0449 | −1.68996 | −0.844981 | − | 0.534796i | \(-0.820388\pi\) | ||||
−0.844981 | + | 0.534796i | \(0.820388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.15921 | −0.542289 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9702 | 1.22058 | 0.610292 | − | 0.792176i | \(-0.291052\pi\) | ||||
0.610292 | + | 0.792176i | \(0.291052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.94735 | 0.428990 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.12492 | 0.268950 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.51252 | 0.556402 | 0.278201 | − | 0.960523i | \(-0.410262\pi\) | ||||
0.278201 | + | 0.960523i | \(0.410262\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.91579 | 0.671409 | 0.335704 | − | 0.941967i | \(-0.391026\pi\) | ||||
0.335704 | + | 0.941967i | \(0.391026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.33639 | 0.112544 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.4122 | 1.87420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.12492 | 0.259511 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.7955 | −0.972879 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3544 | −1.42173 | −0.710865 | − | 0.703328i | \(-0.751696\pi\) | ||||
−0.710865 | + | 0.703328i | \(0.751696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.6742 | −1.68244 | −0.841220 | − | 0.540693i | \(-0.818162\pi\) | ||||
−0.841220 | + | 0.540693i | \(0.818162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.77786 | 0.143731 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.0137 | −1.44690 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.53395 | 0.122422 | 0.0612112 | − | 0.998125i | \(-0.480504\pi\) | ||||
0.0612112 | + | 0.998125i | \(0.480504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.98281 | 0.474468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33538 | 0.341676 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.92716 | 0.307599 | 0.153800 | − | 0.988102i | \(-0.450849\pi\) | ||||
0.153800 | + | 0.988102i | \(0.450849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.1396 | −0.945068 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.2364 | 1.48855 | 0.744277 | − | 0.667871i | \(-0.232794\pi\) | ||||
0.744277 | + | 0.667871i | \(0.232794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.2842 | 1.56032 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14116 | 0.0872664 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6806 | −1.26820 | −0.634102 | − | 0.773249i | \(-0.718630\pi\) | ||||
−0.634102 | + | 0.773249i | \(0.718630\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.6587 | 1.56165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.53101 | 0.566066 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.82298 | −0.734204 | −0.367102 | − | 0.930181i | \(-0.619650\pi\) | ||||
−0.367102 | + | 0.930181i | \(0.619650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3057 | 1.13766 | 0.568831 | − | 0.822454i | \(-0.307396\pi\) | ||||
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.35532 | −0.174110 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.1405 | −2.06893 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.90657 | −0.505059 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.33538 | −0.315353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6137 | −1.12977 | −0.564884 | − | 0.825171i | \(-0.691079\pi\) | ||||
−0.564884 | + | 0.825171i | \(0.691079\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.76207 | −0.342781 | −0.171391 | − | 0.985203i | \(-0.554826\pi\) | ||||
−0.171391 | + | 0.985203i | \(0.554826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.0284 | −1.29104 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.66400 | −0.546037 | −0.273019 | − | 0.962009i | \(-0.588022\pi\) | ||||
−0.273019 | + | 0.962009i | \(0.588022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.8524 | 1.90351 | 0.951757 | − | 0.306853i | \(-0.0992761\pi\) | ||||
0.951757 | + | 0.306853i | \(0.0992761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.03611 | 0.214151 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.33538 | −0.304284 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.80912 | 0.266040 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.43314 | −0.306646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9556 | −1.02959 | −0.514793 | − | 0.857314i | \(-0.672131\pi\) | ||||
−0.514793 | + | 0.857314i | \(0.672131\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.64492 | −0.455303 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.2471 | −1.31264 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.9915 | 1.69653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.08303 | −0.140758 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2569 | −0.689953 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.6301 | −1.71632 | −0.858160 | − | 0.513383i | \(-0.828392\pi\) | ||||
−0.858160 | + | 0.513383i | \(0.828392\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.76514 | 0.317676 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.3625 | −1.41788 | −0.708939 | − | 0.705270i | \(-0.750826\pi\) | ||||
−0.708939 | + | 0.705270i | \(0.750826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.1208 | −1.66003 | −0.830015 | − | 0.557741i | \(-0.811668\pi\) | ||||
−0.830015 | + | 0.557741i | \(0.811668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.8420 | 1.10812 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.74498 | −0.376366 | −0.188183 | − | 0.982134i | \(-0.560260\pi\) | ||||
−0.188183 | + | 0.982134i | \(0.560260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.17611 | 0.272419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.0123 | 0.845241 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.74972 | 0.630657 | 0.315328 | − | 0.948983i | \(-0.397885\pi\) | ||||
0.315328 | + | 0.948983i | \(0.397885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.660892 | −0.0425718 | −0.0212859 | − | 0.999773i | \(-0.506776\pi\) | ||||
−0.0212859 | + | 0.999773i | \(0.506776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36.8601 | −2.35491 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.58361 | −0.418905 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.3584 | 0.909926 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.07690 | 0.194212 | 0.0971062 | − | 0.995274i | \(-0.469041\pi\) | ||||
0.0971062 | + | 0.995274i | \(0.469041\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.88477 | −0.244234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.55566 | 0.347909 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.30458 | 0.0813772 | 0.0406886 | − | 0.999172i | \(-0.487045\pi\) | ||||
0.0406886 | + | 0.999172i | \(0.487045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.0409 | 2.42589 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.7719 | 0.910874 | 0.455437 | − | 0.890268i | \(-0.349483\pi\) | ||||
0.455437 | + | 0.890268i | \(0.349483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.6958 | 1.14847 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.89965 | 0.299854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.6664 | 0.833253 | 0.416627 | − | 0.909078i | \(-0.363212\pi\) | ||||
0.416627 | + | 0.909078i | \(0.363212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00165 | 0.182337 | 0.0911687 | − | 0.995835i | \(-0.470940\pi\) | ||||
0.0911687 | + | 0.995835i | \(0.470940\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.0119 | 1.51379 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.5115 | −1.11628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1613 | 1.09121 | 0.545603 | − | 0.838044i | \(-0.316301\pi\) | ||||
0.545603 | + | 0.838044i | \(0.316301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.76454 | 0.345114 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.73451 | 0.222782 | 0.111391 | − | 0.993777i | \(-0.464469\pi\) | ||||
0.111391 | + | 0.993777i | \(0.464469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.6268 | −1.40447 | −0.702235 | − | 0.711945i | \(-0.747814\pi\) | ||||
−0.702235 | + | 0.711945i | \(0.747814\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.56603 | 0.211233 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.28461 | −0.311941 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8392 | −0.814072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.62077 | −0.446737 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.17862 | −0.419379 | −0.209690 | − | 0.977768i | \(-0.567245\pi\) | ||||
−0.209690 | + | 0.977768i | \(0.567245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.5338 | 1.37019 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.88477 | 0.225417 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.76924 | −0.333644 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.7025 | 1.53911 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8588 | −0.968514 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.36019 | −0.421443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3673 | 0.591690 | 0.295845 | − | 0.955236i | \(-0.404399\pi\) | ||||
0.295845 | + | 0.955236i | \(0.404399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.87256 | 0.106526 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.7060 | −1.68447 | −0.842236 | − | 0.539109i | \(-0.818761\pi\) | ||||
−0.842236 | + | 0.539109i | \(0.818761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6960 | 0.604571 | 0.302286 | − | 0.953217i | \(-0.402250\pi\) | ||||
0.302286 | + | 0.953217i | \(0.402250\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.5477 | −0.763328 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5388 | 0.648083 | 0.324041 | − | 0.946043i | \(-0.394958\pi\) | ||||
0.324041 | + | 0.946043i | \(0.394958\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.88477 | 0.217506 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8890 | −0.719396 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.02881 | 0.112886 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.4913 | −1.52494 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.163721 | −0.00905381 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.79375 | −0.319420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4593 | 0.684827 | 0.342414 | − | 0.939549i | \(-0.388756\pi\) | ||||
0.342414 | + | 0.939549i | \(0.388756\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.00519 | 0.493481 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.48761 | 0.518363 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0473 | −0.928623 | −0.464312 | − | 0.885672i | \(-0.653698\pi\) | ||||
−0.464312 | + | 0.885672i | \(0.653698\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.58635 | 0.0861585 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.3939 | −1.21270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.7905 | 1.12258 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.12492 | 0.168240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.8400 | −1.22612 | −0.613059 | − | 0.790037i | \(-0.710061\pi\) | ||||
−0.613059 | + | 0.790037i | \(0.710061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.40175 | −0.0750337 | −0.0375169 | − | 0.999296i | \(-0.511945\pi\) | ||||
−0.0375169 | + | 0.999296i | \(0.511945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.76924 | 0.307939 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.34698 | 0.0716923 | 0.0358462 | − | 0.999357i | \(-0.488587\pi\) | ||||
0.0358462 | + | 0.999357i | \(0.488587\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.7649 | −1.10208 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.70769 | −0.407934 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.1026 | −0.533195 | −0.266597 | − | 0.963808i | \(-0.585899\pi\) | ||||
−0.266597 | + | 0.963808i | \(0.585899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6978 | −0.931461 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.09147 | −0.214747 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.50930 | −0.340712 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.38990 | 0.124752 | 0.0623758 | − | 0.998053i | \(-0.480132\pi\) | ||||
0.0623758 | + | 0.998053i | \(0.480132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.21895 | −0.0634559 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.9378 | −1.34662 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.2159 | −1.82341 | −0.911705 | − | 0.410845i | \(-0.865234\pi\) | ||||
−0.911705 | + | 0.410845i | \(0.865234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.733922 | −0.0378996 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.76924 | 0.297131 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.92302 | 0.509711 | 0.254856 | − | 0.966979i | \(-0.417972\pi\) | ||||
0.254856 | + | 0.966979i | \(0.417972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.0449 | 0.975700 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.2260 | −1.18680 | −0.593398 | − | 0.804909i | \(-0.702214\pi\) | ||||
−0.593398 | + | 0.804909i | \(0.702214\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52.6299 | 2.68227 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.15921 | 0.313090 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.3840 | −1.89545 | −0.947723 | − | 0.319094i | \(-0.896622\pi\) | ||||
−0.947723 | + | 0.319094i | \(0.896622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.77786 | 0.0899101 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.9702 | −0.704705 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.6625 | 2.04595 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5902 | 0.933016 | 0.466508 | − | 0.884517i | \(-0.345512\pi\) | ||||
0.466508 | + | 0.884517i | \(0.345512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.94735 | −0.247677 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.2176 | −0.610119 | −0.305059 | − | 0.952333i | \(-0.598676\pi\) | ||||
−0.305059 | + | 0.952333i | \(0.598676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.2570 | −1.65665 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.12492 | −0.155279 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.9831 | −1.73405 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.97213 | −0.0975158 | −0.0487579 | − | 0.998811i | \(-0.515526\pi\) | ||||
−0.0487579 | + | 0.998811i | \(0.515526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.51252 | −0.321239 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.6498 | −1.60659 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.8688 | 2.20252 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.91579 | −0.387638 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3906 | 0.654174 | 0.327087 | − | 0.944994i | \(-0.393933\pi\) | ||||
0.327087 | + | 0.944994i | \(0.393933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.8993 | −1.26226 | −0.631128 | − | 0.775678i | \(-0.717408\pi\) | ||||
−0.631128 | + | 0.775678i | \(0.717408\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.33639 | −0.0649774 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.47173 | 0.410939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2112 | 0.494155 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.4122 | −1.08207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.1828 | −0.827667 | −0.413834 | − | 0.910353i | \(-0.635810\pi\) | ||||
−0.413834 | + | 0.910353i | \(0.635810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.495336 | −0.0238043 | −0.0119022 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119022 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.12492 | −0.149829 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.14116 | 0.0545889 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.2342 | −1.06118 | −0.530589 | − | 0.847629i | \(-0.678029\pi\) | ||||
−0.530589 | + | 0.847629i | \(0.678029\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.7955 | 0.561692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.4641 | −0.829745 | −0.414873 | − | 0.909880i | \(-0.636174\pi\) | ||||
−0.414873 | + | 0.909880i | \(0.636174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.3110 | 0.725813 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.3544 | 0.820836 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.9362 | −1.55436 | −0.777178 | − | 0.629280i | \(-0.783350\pi\) | ||||
−0.777178 | + | 0.629280i | \(0.783350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.73534 | 0.222978 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.6742 | 0.971357 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 78.1602 | 3.66421 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8131 | 0.599370 | 0.299685 | − | 0.954038i | \(-0.403118\pi\) | ||||
0.299685 | + | 0.954038i | \(0.403118\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.77786 | −0.0829832 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7073 | 0.498688 | 0.249344 | − | 0.968415i | \(-0.419785\pi\) | ||||
0.249344 | + | 0.968415i | \(0.419785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9367 | −1.57717 | −0.788587 | − | 0.614923i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614923i | \(0.789187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.0137 | 0.835367 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.4185 | −0.991129 | −0.495565 | − | 0.868571i | \(-0.665039\pi\) | ||||
−0.495565 | + | 0.868571i | \(0.665039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.1627 | −0.607797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.53395 | −0.0706807 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.9272 | −1.10017 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.43777 | 0.249502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.98281 | −0.273934 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9177 | 0.864373 | 0.432186 | − | 0.901784i | \(-0.357742\pi\) | ||||
0.432186 | + | 0.901784i | \(0.357742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.9531 | −2.36886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.33538 | −0.197267 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.8143 | −1.08135 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4226 | 1.33327 | 0.666634 | − | 0.745386i | \(-0.267735\pi\) | ||||
0.666634 | + | 0.745386i | \(0.267735\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.92716 | −0.177592 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.0670 | 1.62768 | 0.813841 | − | 0.581088i | \(-0.197373\pi\) | ||||
0.813841 | + | 0.581088i | \(0.197373\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.77786 | −0.0800706 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.1396 | 0.545635 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.8083 | 1.29223 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9469 | 0.758649 | 0.379325 | − | 0.925264i | \(-0.376156\pi\) | ||||
0.379325 | + | 0.925264i | \(0.376156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.2364 | −0.859417 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.80429 | 0.392564 | 0.196282 | − | 0.980547i | \(-0.437113\pi\) | ||||
0.196282 | + | 0.980547i | \(0.437113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.6825 | −2.34434 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.2842 | −0.900852 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2927 | 1.16540 | 0.582701 | − | 0.812687i | \(-0.301996\pi\) | ||||
0.582701 | + | 0.812687i | \(0.301996\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.03072 | 0.399495 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.14116 | −0.0503833 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.85160 | 0.257852 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.19157 | 0.228325 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6806 | 0.732198 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.01412 | −0.351105 | −0.175552 | − | 0.984470i | \(-0.556171\pi\) | ||||
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.7616 | −1.65120 | −0.825599 | − | 0.564258i | \(-0.809162\pi\) | ||||
−0.825599 | + | 0.564258i | \(0.809162\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.6587 | −0.901619 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2485 | 0.446433 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.53101 | −0.326818 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.03241 | 0.304608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.2772 | −1.74134 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.82298 | 0.423893 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −45.8230 | −1.97374 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.1345 | −1.38157 | −0.690785 | − | 0.723060i | \(-0.742735\pi\) | ||||
−0.690785 | + | 0.723060i | \(0.742735\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.3057 | −0.656830 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.511616 | −0.0219152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.9345 | 0.724069 | 0.362034 | − | 0.932165i | \(-0.382082\pi\) | ||||
0.362034 | + | 0.932165i | \(0.382082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.35532 | 0.100523 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.14116 | −0.0486149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.4134 | −2.39894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.1405 | 1.19450 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.86058 | 0.163578 | 0.0817890 | − | 0.996650i | \(-0.473937\pi\) | ||||
0.0817890 | + | 0.996650i | \(0.473937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.5340 | −1.50293 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.90657 | 0.291596 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.7287 | −1.37935 | −0.689676 | − | 0.724118i | \(-0.742247\pi\) | ||||
−0.689676 | + | 0.724118i | \(0.742247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.95721 | 0.208551 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.33538 | 0.182069 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.1935 | −1.14001 | −0.570005 | − | 0.821641i | \(-0.693059\pi\) | ||||
−0.570005 | + | 0.821641i | \(0.693059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.01198 | −0.377140 | −0.188570 | − | 0.982060i | \(-0.560385\pi\) | ||||
−0.188570 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6137 | 0.652271 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.76514 | 0.198720 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5121 | −0.687408 | −0.343704 | − | 0.939078i | \(-0.611682\pi\) | ||||
−0.343704 | + | 0.939078i | \(0.611682\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.76207 | 0.197905 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62.2491 | −2.58253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.2419 | 0.962579 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.0284 | 0.745384 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.61443 | 0.0666346 | 0.0333173 | − | 0.999445i | \(-0.489393\pi\) | ||||
0.0333173 | + | 0.999445i | \(0.489393\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.57824 | 0.271052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.66400 | 0.315255 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.2398 | −0.461562 | −0.230781 | − | 0.973006i | \(-0.574128\pi\) | ||||
−0.230781 | + | 0.973006i | \(0.574128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.0859 | −0.987427 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.8524 | −1.09899 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3436 | 0.545204 | 0.272602 | − | 0.962127i | \(-0.412116\pi\) | ||||
0.272602 | + | 0.962127i | \(0.412116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.6297 | −1.29020 | −0.645101 | − | 0.764097i | \(-0.723185\pi\) | ||||
−0.645101 | + | 0.764097i | \(0.723185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.03611 | −0.123640 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.7855 | −0.519806 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1421 | −1.14225 | −0.571127 | − | 0.820862i | \(-0.693493\pi\) | ||||
−0.571127 | + | 0.820862i | \(0.693493\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.33538 | 0.175679 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.70995 | 0.311911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.5963 | 1.11460 | 0.557301 | − | 0.830310i | \(-0.311837\pi\) | ||||
0.557301 | + | 0.830310i | \(0.311837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.80912 | −0.153599 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.9733 | −1.20668 | −0.603341 | − | 0.797484i | \(-0.706164\pi\) | ||||
−0.603341 | + | 0.797484i | \(0.706164\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8123 | 0.957097 | 0.478548 | − | 0.878061i | \(-0.341163\pi\) | ||||
0.478548 | + | 0.878061i | \(0.341163\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.2419 | −0.851038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.1191 | −1.04477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.43314 | 0.177042 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0099 | 0.638358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7203 | 0.426769 | 0.213384 | − | 0.976968i | \(-0.431551\pi\) | ||||
0.213384 | + | 0.976968i | \(0.431551\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.9556 | 0.594432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 59.5138 | 2.36173 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −68.0513 | −2.69629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.64492 | 0.262869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.7824 | −1.09734 | −0.548670 | − | 0.836039i | \(-0.684866\pi\) | ||||
−0.548670 | + | 0.836039i | \(0.684866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.7862 | −0.583109 | −0.291555 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291555 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.2471 | 0.757853 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.4419 | −0.842969 | −0.421485 | − | 0.906836i | \(-0.638491\pi\) | ||||
−0.421485 | + | 0.906836i | \(0.638491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.2563 | 1.14841 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.9915 | −0.979493 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.45978 | 0.0571255 | 0.0285627 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285627 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.6559 | −1.70578 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.08303 | 0.0812666 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.9684 | −1.82963 | −0.914815 | − | 0.403872i | \(-0.867664\pi\) | ||||
−0.914815 | + | 0.403872i | \(0.867664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.829538 | −0.0322653 | −0.0161326 | − | 0.999870i | \(-0.505135\pi\) | ||||
−0.0161326 | + | 0.999870i | \(0.505135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.2569 | 0.398345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.4601 | −0.599516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.6301 | 0.990917 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.14988 | −0.353227 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.40741 | −0.131346 | −0.0656729 | − | 0.997841i | \(-0.520919\pi\) | ||||
−0.0656729 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.76514 | −0.183410 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.8238 | 1.87645 | 0.938225 | − | 0.346027i | \(-0.112469\pi\) | ||||
0.938225 | + | 0.346027i | \(0.112469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.0389 | 1.26792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.3625 | 0.818612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.0929 | −1.57238 | −0.786188 | − | 0.617987i | \(-0.787948\pi\) | ||||
−0.786188 | + | 0.617987i | \(0.787948\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.3511 | −0.777577 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.1208 | 0.958419 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.5163 | 1.31497 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.2118 | 1.30148 | 0.650739 | − | 0.759301i | \(-0.274459\pi\) | ||||
0.650739 | + | 0.759301i | \(0.274459\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8420 | −0.639774 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.7362 | −0.938299 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.16712 | −0.0820854 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.74498 | 0.217295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.58511 | −0.135408 | −0.0677038 | − | 0.997705i | \(-0.521567\pi\) | ||||
−0.0677038 | + | 0.997705i | \(0.521567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2763 | 0.387579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.17611 | −0.157281 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 73.0894 | 2.74881 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.14577 | 0.305921 | 0.152960 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152960 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.0123 | −0.488000 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.76454 | 0.215884 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −70.0364 | −2.61921 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.74972 | −0.364110 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.60257 | 0.0597658 | 0.0298829 | − | 0.999553i | \(-0.490487\pi\) | ||||
0.0298829 | + | 0.999553i | \(0.490487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.11825 | −0.302339 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.660892 | 0.0245788 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.76514 | −0.176973 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.45074 | 0.313421 | 0.156710 | − | 0.987645i | \(-0.449911\pi\) | ||||
0.156710 | + | 0.987645i | \(0.449911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9502 | 0.405008 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1821 | 0.745442 | 0.372721 | − | 0.927943i | \(-0.378425\pi\) | ||||
0.372721 | + | 0.927943i | \(0.378425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.8601 | 1.35961 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7946 | 0.434460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0703 | 0.444015 | 0.222007 | − | 0.975045i | \(-0.428739\pi\) | ||||
0.222007 | + | 0.975045i | \(0.428739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.58361 | 0.241855 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.2302 | −0.998980 | −0.499490 | − | 0.866320i | \(-0.666479\pi\) | ||||
−0.499490 | + | 0.866320i | \(0.666479\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.2312 | 1.98688 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.3584 | −0.525346 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 55.8789 | 2.04177 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.2040 | 1.28461 | 0.642306 | − | 0.766448i | \(-0.277978\pi\) | ||||
0.642306 | + | 0.766448i | \(0.277978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.07690 | −0.112129 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 64.6052 | 2.35122 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0464 | −1.01936 | −0.509682 | − | 0.860363i | \(-0.670237\pi\) | ||||
−0.509682 | + | 0.860363i | \(0.670237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.88477 | 0.141008 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7067 | 0.786866 | 0.393433 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393433 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.709794 | 0.0256963 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.55566 | −0.200865 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.4483 | 1.56883 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.4309 | 0.844941 | 0.422471 | − | 0.906377i | \(-0.361163\pi\) | ||||
0.422471 | + | 0.906377i | \(0.361163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.30458 | −0.0469831 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.0981 | −0.902717 | −0.451358 | − | 0.892343i | \(-0.649060\pi\) | ||||
−0.451358 | + | 0.892343i | \(0.649060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.4688 | 0.986710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.0409 | −1.40059 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.39101 | −0.0498381 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.8140 | −0.923698 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.79347 | −0.171086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.9599 | −1.60265 | −0.801325 | − | 0.598230i | \(-0.795871\pi\) | ||||
−0.801325 | + | 0.598230i | \(0.795871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.7719 | −0.525894 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.87742 | −0.244533 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.5884 | −0.482538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.6958 | −0.663072 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.0899 | −0.853310 | −0.426655 | − | 0.904415i | \(-0.640308\pi\) | ||||
−0.426655 | + | 0.904415i | \(0.640308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.37591 | −0.0840535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.89965 | −0.173121 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.09209 | −0.285564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5477 | −0.477495 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.6664 | −0.481079 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.4644 | −1.73908 | −0.869538 | − | 0.493866i | \(-0.835583\pi\) | ||||
−0.869538 | + | 0.493866i | \(0.835583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.55785 | 0.335622 | 0.167811 | − | 0.985819i | \(-0.446330\pi\) | ||||
0.167811 | + | 0.985819i | \(0.446330\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.00165 | −0.105273 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.2721 | −0.429872 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.02863 | 0.245901 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.0119 | −0.873986 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.1610 | −0.633824 | −0.316912 | − | 0.948455i | \(-0.602646\pi\) | ||||
−0.316912 | + | 0.948455i | \(0.602646\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.5039 | 1.51645 | 0.758226 | − | 0.651992i | \(-0.226067\pi\) | ||||
0.758226 | + | 0.651992i | \(0.226067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.5115 | 0.644487 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.09541 | −0.107638 | −0.0538190 | − | 0.998551i | \(-0.517139\pi\) | ||||
−0.0538190 | + | 0.998551i | \(0.517139\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.8485 | −1.38399 | −0.691997 | − | 0.721900i | \(-0.743269\pi\) | ||||
−0.691997 | + | 0.721900i | \(0.743269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.1613 | −0.630009 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.9708 | 0.726594 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −60.1121 | −2.08027 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.76454 | −0.199252 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.0042 | 0.932289 | 0.466144 | − | 0.884709i | \(-0.345643\pi\) | ||||
0.466144 | + | 0.884709i | \(0.345643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.73451 | −0.128623 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −63.3865 | −2.18056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7381 | 0.609488 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.6268 | 0.810871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00519 | 0.308694 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.2754 | 0.659978 | 0.329989 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329989 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.56603 | −0.121955 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5762 | 0.737030 | 0.368515 | − | 0.929622i | \(-0.379866\pi\) | ||||
0.368515 | + | 0.929622i | \(0.379866\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.2042 | −0.621121 | −0.310560 | − | 0.950554i | \(-0.600517\pi\) | ||||
−0.310560 | + | 0.950554i | \(0.600517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.28461 | 0.180099 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0426 | 0.886500 | 0.443250 | − | 0.896398i | \(-0.353825\pi\) | ||||
0.443250 | + | 0.896398i | \(0.353825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52.1256 | 1.77233 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.8392 | 0.470005 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.5500 | 1.71479 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5161 | 0.593509 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.62077 | 0.257924 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.18183 | 0.107566 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.1393 | −1.08527 | −0.542633 | − | 0.839970i | \(-0.682573\pi\) | ||||
−0.542633 | + | 0.839970i | \(0.682573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.17862 | 0.242129 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.44207 | 0.0485846 | 0.0242923 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242923 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.05643 | −0.203815 | −0.101908 | − | 0.994794i | \(-0.532495\pi\) | ||||
−0.101908 | + | 0.994794i | \(0.532495\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.5338 | −0.791081 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.2715 | 1.78868 | 0.894340 | − | 0.447388i | \(-0.147646\pi\) | ||||
0.894340 | + | 0.447388i | \(0.147646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.5669 | −2.76921 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.88477 | −0.130145 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.52503 | −0.0510331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.6961 | 1.02606 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.76924 | 0.192629 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.76454 | −0.192258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.6366 | −0.354356 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.7025 | −0.888605 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.8291 | −1.58989 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7289 | 0.887517 | 0.443759 | − | 0.896146i | \(-0.353645\pi\) | ||||
0.443759 | + | 0.896146i | \(0.353645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.8588 | 0.559172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.93260 | 0.329082 | 0.164541 | − | 0.986370i | \(-0.447386\pi\) | ||||
0.164541 | + | 0.986370i | \(0.447386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.7791 | 1.84602 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.36019 | 0.243320 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 60.5663 | 2.00007 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.8801 | 1.41448 | 0.707242 | − | 0.706971i | \(-0.249939\pi\) | ||||
0.707242 | + | 0.706971i | \(0.249939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3673 | −0.341613 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.3362 | −1.26185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.9110 | 1.41090 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.87256 | −0.0615028 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.6843 | 1.82694 | 0.913472 | − | 0.406903i | \(-0.133391\pi\) | ||||
0.913472 | + | 0.406903i | \(0.133391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4606 | 0.441152 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.7060 | 0.972530 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.5825 | 0.705823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.2344 | 1.80443 | 0.902215 | − | 0.431286i | \(-0.141940\pi\) | ||||
0.902215 | + | 0.431286i | \(0.141940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6960 | −0.349049 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.1855 | 0.429835 | 0.214918 | − | 0.976632i | \(-0.431052\pi\) | ||||
0.214918 | + | 0.976632i | \(0.431052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.21895 | −0.0396944 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5477 | 0.440708 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.4167 | 0.403488 | 0.201744 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201744 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0175 | −0.390104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.5388 | −0.374171 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.96101 | −0.322669 | −0.161334 | − | 0.986900i | \(-0.551580\pi\) | ||||
−0.161334 | + | 0.986900i | \(0.551580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.7916 | 1.57886 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.88477 | −0.125577 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.2343 | 0.911732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.22992 | 0.0719328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.8890 | 0.415343 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.8811 | 0.479040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.7790 | −1.37568 | −0.687839 | − | 0.725863i | \(-0.741441\pi\) | ||||
−0.687839 | + | 0.725863i | \(0.741441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.02881 | −0.0651748 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.09189 | −0.259681 | −0.129841 | − | 0.991535i | \(-0.541447\pi\) | ||||
−0.129841 | + | 0.991535i | \(0.541447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.3180 | 1.10018 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.4913 | 0.880425 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6916 | 0.470025 | 0.235013 | − | 0.971992i | \(-0.424487\pi\) | ||||
0.235013 | + | 0.971992i | \(0.424487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.0341 | 0.608331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.163721 | 0.00522722 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.8602 | 1.46271 | 0.731357 | − | 0.681995i | \(-0.238887\pi\) | ||||
0.731357 | + | 0.681995i | \(0.238887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9494 | 0.763091 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.79375 | 0.184417 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.15921 | 0.195852 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0647 | −0.415012 | −0.207506 | − | 0.978234i | \(-0.566535\pi\) | ||||
−0.207506 | + | 0.978234i | \(0.566535\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.4593 | −0.395385 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −83.9116 | −2.66018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.55526 | −0.270948 | −0.135474 | − | 0.990781i | \(-0.543256\pi\) | ||||
−0.135474 | + | 0.990781i | \(0.543256\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.00519 | −0.284912 |
(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 | 8004.2.a.g.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.g.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial |