Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | 10.10.52900342088704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 18x^{8} + 123x^{6} - 390x^{4} + 548x^{2} - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.70641\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.85684 | −1.27762 | −0.638810 | − | 0.769365i | \(-0.720573\pi\) | ||||
−0.638810 | + | 0.769365i | \(0.720573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.48349 | −1.69460 | −0.847301 | − | 0.531113i | \(-0.821774\pi\) | ||||
−0.847301 | + | 0.531113i | \(0.821774\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.85684 | −0.903413 | ||||||||
\(11\) | −0.198365 | −0.0598093 | −0.0299047 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299047 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.70872 | 1.02861 | 0.514307 | − | 0.857606i | \(-0.328049\pi\) | ||||
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(14\) | −4.48349 | −1.19826 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.618594 | 0.150031 | 0.0750156 | − | 0.997182i | \(-0.476099\pi\) | ||||
0.0750156 | + | 0.997182i | \(0.476099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.259187 | 0.0594617 | 0.0297308 | − | 0.999558i | \(-0.490535\pi\) | ||||
0.0297308 | + | 0.999558i | \(0.490535\pi\) | |||||||
\(20\) | −2.85684 | −0.638810 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.198365 | −0.0422916 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.16155 | 0.632310 | ||||||||
\(26\) | 3.70872 | 0.727340 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.48349 | −0.847301 | ||||||||
\(29\) | 7.49661 | 1.39209 | 0.696043 | − | 0.718000i | \(-0.254942\pi\) | ||||
0.696043 | + | 0.718000i | \(0.254942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.80927 | −0.504561 | −0.252280 | − | 0.967654i | \(-0.581181\pi\) | ||||
−0.252280 | + | 0.967654i | \(0.581181\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.618594 | 0.106088 | ||||||||
\(35\) | 12.8086 | 2.16506 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.90747 | −0.971182 | −0.485591 | − | 0.874186i | \(-0.661396\pi\) | ||||
−0.485591 | + | 0.874186i | \(0.661396\pi\) | |||||||
\(38\) | 0.259187 | 0.0420457 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.85684 | −0.451707 | ||||||||
\(41\) | 8.45349 | 1.32021 | 0.660107 | − | 0.751172i | \(-0.270511\pi\) | ||||
0.660107 | + | 0.751172i | \(0.270511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0715 | 1.53589 | 0.767943 | − | 0.640518i | \(-0.221280\pi\) | ||||
0.767943 | + | 0.640518i | \(0.221280\pi\) | |||||||
\(44\) | −0.198365 | −0.0299047 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.81259 | −1.43131 | −0.715657 | − | 0.698452i | \(-0.753872\pi\) | ||||
−0.715657 | + | 0.698452i | \(0.753872\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1017 | 1.87167 | ||||||||
\(50\) | 3.16155 | 0.447111 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.70872 | 0.514307 | ||||||||
\(53\) | 3.93580 | 0.540624 | 0.270312 | − | 0.962773i | \(-0.412873\pi\) | ||||
0.270312 | + | 0.962773i | \(0.412873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.566698 | 0.0764135 | ||||||||
\(56\) | −4.48349 | −0.599132 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.49661 | 0.984353 | ||||||||
\(59\) | −9.81277 | −1.27751 | −0.638757 | − | 0.769409i | \(-0.720551\pi\) | ||||
−0.638757 | + | 0.769409i | \(0.720551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.11918 | 0.655444 | 0.327722 | − | 0.944774i | \(-0.393719\pi\) | ||||
0.327722 | + | 0.944774i | \(0.393719\pi\) | |||||||
\(62\) | −2.80927 | −0.356778 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.5952 | −1.31418 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.35623 | 0.898707 | 0.449353 | − | 0.893354i | \(-0.351654\pi\) | ||||
0.449353 | + | 0.893354i | \(0.351654\pi\) | |||||||
\(68\) | 0.618594 | 0.0750156 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.8086 | 1.53093 | ||||||||
\(71\) | 11.1005 | 1.31739 | 0.658694 | − | 0.752411i | \(-0.271109\pi\) | ||||
0.658694 | + | 0.752411i | \(0.271109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.6323 | −1.82962 | −0.914809 | − | 0.403888i | \(-0.867659\pi\) | ||||
−0.914809 | + | 0.403888i | \(0.867659\pi\) | |||||||
\(74\) | −5.90747 | −0.686729 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.259187 | 0.0297308 | ||||||||
\(77\) | 0.889368 | 0.101353 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9619 | 1.68334 | 0.841670 | − | 0.539992i | \(-0.181573\pi\) | ||||
0.841670 | + | 0.539992i | \(0.181573\pi\) | |||||||
\(80\) | −2.85684 | −0.319405 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.45349 | 0.933532 | ||||||||
\(83\) | −9.62975 | −1.05700 | −0.528501 | − | 0.848933i | \(-0.677246\pi\) | ||||
−0.528501 | + | 0.848933i | \(0.677246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.76723 | −0.191683 | ||||||||
\(86\) | 10.0715 | 1.08604 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.198365 | −0.0211458 | ||||||||
\(89\) | −15.3355 | −1.62556 | −0.812781 | − | 0.582569i | \(-0.802048\pi\) | ||||
−0.812781 | + | 0.582569i | \(0.802048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.6280 | −1.74309 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.81259 | −1.01209 | ||||||||
\(95\) | −0.740458 | −0.0759693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8464 | −1.20282 | −0.601410 | − | 0.798941i | \(-0.705394\pi\) | ||||
−0.601410 | + | 0.798941i | \(0.705394\pi\) | |||||||
\(98\) | 13.1017 | 1.32347 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.16155 | 0.316155 | ||||||||
\(101\) | −18.8858 | −1.87921 | −0.939606 | − | 0.342258i | \(-0.888808\pi\) | ||||
−0.939606 | + | 0.342258i | \(0.888808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33765 | 0.328868 | 0.164434 | − | 0.986388i | \(-0.447420\pi\) | ||||
0.164434 | + | 0.986388i | \(0.447420\pi\) | |||||||
\(104\) | 3.70872 | 0.363670 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.93580 | 0.382279 | ||||||||
\(107\) | −4.94497 | −0.478048 | −0.239024 | − | 0.971014i | \(-0.576827\pi\) | ||||
−0.239024 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.32856 | −0.223036 | −0.111518 | − | 0.993762i | \(-0.535571\pi\) | ||||
−0.111518 | + | 0.993762i | \(0.535571\pi\) | |||||||
\(110\) | 0.566698 | 0.0540325 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.48349 | −0.423650 | ||||||||
\(113\) | −8.00742 | −0.753275 | −0.376637 | − | 0.926361i | \(-0.622920\pi\) | ||||
−0.376637 | + | 0.926361i | \(0.622920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.49661 | 0.696043 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.81277 | −0.903338 | ||||||||
\(119\) | −2.77346 | −0.254243 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9607 | −0.996423 | ||||||||
\(122\) | 5.11918 | 0.463469 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.80927 | −0.252280 | ||||||||
\(125\) | 5.25216 | 0.469767 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.47728 | 0.486030 | 0.243015 | − | 0.970022i | \(-0.421864\pi\) | ||||
0.243015 | + | 0.970022i | \(0.421864\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.5952 | −0.929263 | ||||||||
\(131\) | 5.81959 | 0.508460 | 0.254230 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254230 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.16206 | −0.100764 | ||||||||
\(134\) | 7.35623 | 0.635482 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.618594 | 0.0530440 | ||||||||
\(137\) | −6.21674 | −0.531132 | −0.265566 | − | 0.964093i | \(-0.585559\pi\) | ||||
−0.265566 | + | 0.964093i | \(0.585559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.51441 | 0.298089 | 0.149044 | − | 0.988831i | \(-0.452380\pi\) | ||||
0.149044 | + | 0.988831i | \(0.452380\pi\) | |||||||
\(140\) | 12.8086 | 1.08253 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.1005 | 0.931534 | ||||||||
\(143\) | −0.735680 | −0.0615207 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.4166 | −1.77856 | ||||||||
\(146\) | −15.6323 | −1.29373 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.90747 | −0.485591 | ||||||||
\(149\) | −4.16095 | −0.340879 | −0.170439 | − | 0.985368i | \(-0.554519\pi\) | ||||
−0.170439 | + | 0.985368i | \(0.554519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.91198 | −0.643868 | −0.321934 | − | 0.946762i | \(-0.604333\pi\) | ||||
−0.321934 | + | 0.946762i | \(0.604333\pi\) | |||||||
\(152\) | 0.259187 | 0.0210229 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.889368 | 0.0716673 | ||||||||
\(155\) | 8.02566 | 0.644636 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9469 | −1.43232 | −0.716158 | − | 0.697939i | \(-0.754101\pi\) | ||||
−0.716158 | + | 0.697939i | \(0.754101\pi\) | |||||||
\(158\) | 14.9619 | 1.19030 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.85684 | −0.225853 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.09440 | 0.555676 | 0.277838 | − | 0.960628i | \(-0.410382\pi\) | ||||
0.277838 | + | 0.960628i | \(0.410382\pi\) | |||||||
\(164\) | 8.45349 | 0.660107 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.62975 | −0.747413 | ||||||||
\(167\) | −16.3201 | −1.26289 | −0.631443 | − | 0.775422i | \(-0.717537\pi\) | ||||
−0.631443 | + | 0.775422i | \(0.717537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.754609 | 0.0580469 | ||||||||
\(170\) | −1.76723 | −0.135540 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.0715 | 0.767943 | ||||||||
\(173\) | 15.4737 | 1.17645 | 0.588223 | − | 0.808699i | \(-0.299828\pi\) | ||||
0.588223 | + | 0.808699i | \(0.299828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.1748 | −1.07151 | ||||||||
\(176\) | −0.198365 | −0.0149523 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.3355 | −1.14945 | ||||||||
\(179\) | −4.67890 | −0.349717 | −0.174859 | − | 0.984594i | \(-0.555947\pi\) | ||||
−0.174859 | + | 0.984594i | \(0.555947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.42873 | 0.403514 | 0.201757 | − | 0.979436i | \(-0.435335\pi\) | ||||
0.201757 | + | 0.979436i | \(0.435335\pi\) | |||||||
\(182\) | −16.6280 | −1.23255 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.8767 | 1.24080 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.122707 | −0.00897326 | ||||||||
\(188\) | −9.81259 | −0.715657 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.740458 | −0.0537184 | ||||||||
\(191\) | 5.76873 | 0.417411 | 0.208705 | − | 0.977979i | \(-0.433075\pi\) | ||||
0.208705 | + | 0.977979i | \(0.433075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.78622 | −0.200557 | −0.100278 | − | 0.994959i | \(-0.531973\pi\) | ||||
−0.100278 | + | 0.994959i | \(0.531973\pi\) | |||||||
\(194\) | −11.8464 | −0.850522 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1017 | 0.935837 | ||||||||
\(197\) | −27.7303 | −1.97570 | −0.987852 | − | 0.155400i | \(-0.950333\pi\) | ||||
−0.987852 | + | 0.155400i | \(0.950333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5232 | 1.45485 | 0.727426 | − | 0.686187i | \(-0.240717\pi\) | ||||
0.727426 | + | 0.686187i | \(0.240717\pi\) | |||||||
\(200\) | 3.16155 | 0.223555 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.8858 | −1.32880 | ||||||||
\(203\) | −33.6110 | −2.35903 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.1503 | −1.68673 | ||||||||
\(206\) | 3.33765 | 0.232545 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.70872 | 0.257154 | ||||||||
\(209\) | −0.0514137 | −0.00355636 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0376 | −1.51713 | −0.758566 | − | 0.651596i | \(-0.774100\pi\) | ||||
−0.758566 | + | 0.651596i | \(0.774100\pi\) | |||||||
\(212\) | 3.93580 | 0.270312 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.94497 | −0.338031 | ||||||||
\(215\) | −28.7726 | −1.96228 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.5954 | 0.855029 | ||||||||
\(218\) | −2.32856 | −0.157710 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.566698 | 0.0382068 | ||||||||
\(221\) | 2.29419 | 0.154324 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0615 | 1.07556 | 0.537778 | − | 0.843087i | \(-0.319264\pi\) | ||||
0.537778 | + | 0.843087i | \(0.319264\pi\) | |||||||
\(224\) | −4.48349 | −0.299566 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00742 | −0.532646 | ||||||||
\(227\) | 23.7222 | 1.57450 | 0.787248 | − | 0.616636i | \(-0.211505\pi\) | ||||
0.787248 | + | 0.616636i | \(0.211505\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2142 | 1.26971 | 0.634856 | − | 0.772630i | \(-0.281059\pi\) | ||||
0.634856 | + | 0.772630i | \(0.281059\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.49661 | 0.492177 | ||||||||
\(233\) | −21.4135 | −1.40285 | −0.701423 | − | 0.712745i | \(-0.747452\pi\) | ||||
−0.701423 | + | 0.712745i | \(0.747452\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.0330 | 1.82867 | ||||||||
\(236\) | −9.81277 | −0.638757 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.77346 | −0.179777 | ||||||||
\(239\) | −6.20486 | −0.401359 | −0.200679 | − | 0.979657i | \(-0.564315\pi\) | ||||
−0.200679 | + | 0.979657i | \(0.564315\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.77891 | −0.501083 | −0.250542 | − | 0.968106i | \(-0.580609\pi\) | ||||
−0.250542 | + | 0.968106i | \(0.580609\pi\) | |||||||
\(242\) | −10.9607 | −0.704577 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.11918 | 0.327722 | ||||||||
\(245\) | −37.4296 | −2.39129 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.961253 | 0.0611631 | ||||||||
\(248\) | −2.80927 | −0.178389 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.25216 | 0.332176 | ||||||||
\(251\) | −13.7940 | −0.870669 | −0.435335 | − | 0.900269i | \(-0.643370\pi\) | ||||
−0.435335 | + | 0.900269i | \(0.643370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.47728 | 0.343675 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2445 | −0.763794 | −0.381897 | − | 0.924205i | \(-0.624729\pi\) | ||||
−0.381897 | + | 0.924205i | \(0.624729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.4861 | 1.64577 | ||||||||
\(260\) | −10.5952 | −0.657088 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.81959 | 0.359535 | ||||||||
\(263\) | 13.4719 | 0.830712 | 0.415356 | − | 0.909659i | \(-0.363657\pi\) | ||||
0.415356 | + | 0.909659i | \(0.363657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.2440 | −0.690712 | ||||||||
\(266\) | −1.16206 | −0.0712508 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.35623 | 0.449353 | ||||||||
\(269\) | 10.5981 | 0.646176 | 0.323088 | − | 0.946369i | \(-0.395279\pi\) | ||||
0.323088 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.37018 | −0.386961 | −0.193480 | − | 0.981104i | \(-0.561978\pi\) | ||||
−0.193480 | + | 0.981104i | \(0.561978\pi\) | |||||||
\(272\) | 0.618594 | 0.0375078 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.21674 | −0.375567 | ||||||||
\(275\) | −0.627141 | −0.0378180 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.99485 | −0.240027 | −0.120014 | − | 0.992772i | \(-0.538294\pi\) | ||||
−0.120014 | + | 0.992772i | \(0.538294\pi\) | |||||||
\(278\) | 3.51441 | 0.210780 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.8086 | 0.765463 | ||||||||
\(281\) | −3.63873 | −0.217069 | −0.108534 | − | 0.994093i | \(-0.534616\pi\) | ||||
−0.108534 | + | 0.994093i | \(0.534616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1478 | 0.722113 | 0.361056 | − | 0.932544i | \(-0.382416\pi\) | ||||
0.361056 | + | 0.932544i | \(0.382416\pi\) | |||||||
\(284\) | 11.1005 | 0.658694 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.735680 | −0.0435017 | ||||||||
\(287\) | −37.9012 | −2.23724 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6173 | −0.977491 | ||||||||
\(290\) | −21.4166 | −1.25763 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.6323 | −0.914809 | ||||||||
\(293\) | −15.7068 | −0.917603 | −0.458802 | − | 0.888539i | \(-0.651721\pi\) | ||||
−0.458802 | + | 0.888539i | \(0.651721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.0335 | 1.63218 | ||||||||
\(296\) | −5.90747 | −0.343365 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.16095 | −0.241038 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.1554 | −2.60271 | ||||||||
\(302\) | −7.91198 | −0.455283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.259187 | 0.0148654 | ||||||||
\(305\) | −14.6247 | −0.837408 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.74903 | 0.0998223 | 0.0499112 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499112 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(308\) | 0.889368 | 0.0506765 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.02566 | 0.455827 | ||||||||
\(311\) | −14.3459 | −0.813484 | −0.406742 | − | 0.913543i | \(-0.633335\pi\) | ||||
−0.406742 | + | 0.913543i | \(0.633335\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.21704 | −0.181838 | −0.0909190 | − | 0.995858i | \(-0.528980\pi\) | ||||
−0.0909190 | + | 0.995858i | \(0.528980\pi\) | |||||||
\(314\) | −17.9469 | −1.01280 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.9619 | 0.841670 | ||||||||
\(317\) | −8.57906 | −0.481848 | −0.240924 | − | 0.970544i | \(-0.577450\pi\) | ||||
−0.240924 | + | 0.970544i | \(0.577450\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.48707 | −0.0832597 | ||||||||
\(320\) | −2.85684 | −0.159702 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.160332 | 0.00892110 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7253 | 0.650403 | ||||||||
\(326\) | 7.09440 | 0.392923 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.45349 | 0.466766 | ||||||||
\(329\) | 43.9947 | 2.42551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.4766 | 1.78507 | 0.892537 | − | 0.450974i | \(-0.148923\pi\) | ||||
0.892537 | + | 0.450974i | \(0.148923\pi\) | |||||||
\(332\) | −9.62975 | −0.528501 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.3201 | −0.892995 | ||||||||
\(335\) | −21.0156 | −1.14820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.8665 | 1.08220 | 0.541099 | − | 0.840959i | \(-0.318008\pi\) | ||||
0.541099 | + | 0.840959i | \(0.318008\pi\) | |||||||
\(338\) | 0.754609 | 0.0410453 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.76723 | −0.0958413 | ||||||||
\(341\) | 0.557262 | 0.0301774 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −27.3570 | −1.47714 | ||||||||
\(344\) | 10.0715 | 0.543018 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.4737 | 0.831873 | ||||||||
\(347\) | 18.9201 | 1.01569 | 0.507843 | − | 0.861449i | \(-0.330443\pi\) | ||||
0.507843 | + | 0.861449i | \(0.330443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.333496 | −0.0178516 | −0.00892582 | − | 0.999960i | \(-0.502841\pi\) | ||||
−0.00892582 | + | 0.999960i | \(0.502841\pi\) | |||||||
\(350\) | −14.1748 | −0.757675 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.198365 | −0.0105729 | ||||||||
\(353\) | −7.64132 | −0.406706 | −0.203353 | − | 0.979105i | \(-0.565184\pi\) | ||||
−0.203353 | + | 0.979105i | \(0.565184\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.7124 | −1.68312 | ||||||||
\(356\) | −15.3355 | −0.812781 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.67890 | −0.247287 | ||||||||
\(359\) | −14.5582 | −0.768350 | −0.384175 | − | 0.923260i | \(-0.625514\pi\) | ||||
−0.384175 | + | 0.923260i | \(0.625514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9328 | −0.996464 | ||||||||
\(362\) | 5.42873 | 0.285328 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.6280 | −0.871545 | ||||||||
\(365\) | 44.6589 | 2.33755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3518 | −1.27116 | −0.635578 | − | 0.772037i | \(-0.719238\pi\) | ||||
−0.635578 | + | 0.772037i | \(0.719238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.8767 | 0.877378 | ||||||||
\(371\) | −17.6462 | −0.916143 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4397 | −0.851214 | −0.425607 | − | 0.904908i | \(-0.639939\pi\) | ||||
−0.425607 | + | 0.904908i | \(0.639939\pi\) | |||||||
\(374\) | −0.122707 | −0.00634505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.81259 | −0.506046 | ||||||||
\(377\) | 27.8028 | 1.43192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.37024 | −0.378584 | −0.189292 | − | 0.981921i | \(-0.560619\pi\) | ||||
−0.189292 | + | 0.981921i | \(0.560619\pi\) | |||||||
\(380\) | −0.740458 | −0.0379847 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.76873 | 0.295154 | ||||||||
\(383\) | −23.2014 | −1.18554 | −0.592768 | − | 0.805373i | \(-0.701965\pi\) | ||||
−0.592768 | + | 0.805373i | \(0.701965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.54079 | −0.129490 | ||||||||
\(386\) | −2.78622 | −0.141815 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.8464 | −0.601410 | ||||||||
\(389\) | −20.2192 | −1.02515 | −0.512577 | − | 0.858641i | \(-0.671309\pi\) | ||||
−0.512577 | + | 0.858641i | \(0.671309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 13.1017 | 0.661737 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −27.7303 | −1.39703 | ||||||||
\(395\) | −42.7437 | −2.15067 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2589 | 0.916389 | 0.458195 | − | 0.888852i | \(-0.348496\pi\) | ||||
0.458195 | + | 0.888852i | \(0.348496\pi\) | |||||||
\(398\) | 20.5232 | 1.02874 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.16155 | 0.158078 | ||||||||
\(401\) | −35.9055 | −1.79304 | −0.896519 | − | 0.443006i | \(-0.853912\pi\) | ||||
−0.896519 | + | 0.443006i | \(0.853912\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4188 | −0.518998 | ||||||||
\(404\) | −18.8858 | −0.939606 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.6110 | −1.66809 | ||||||||
\(407\) | 1.17183 | 0.0580857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.2924 | −1.30008 | −0.650038 | − | 0.759901i | \(-0.725247\pi\) | ||||
−0.650038 | + | 0.759901i | \(0.725247\pi\) | |||||||
\(410\) | −24.1503 | −1.19270 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.33765 | 0.164434 | ||||||||
\(413\) | 43.9955 | 2.16488 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.5107 | 1.35045 | ||||||||
\(416\) | 3.70872 | 0.181835 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0514137 | −0.00251473 | ||||||||
\(419\) | −7.27755 | −0.355532 | −0.177766 | − | 0.984073i | \(-0.556887\pi\) | ||||
−0.177766 | + | 0.984073i | \(0.556887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3333 | 1.67330 | 0.836652 | − | 0.547735i | \(-0.184510\pi\) | ||||
0.836652 | + | 0.547735i | \(0.184510\pi\) | |||||||
\(422\) | −22.0376 | −1.07277 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.93580 | 0.191140 | ||||||||
\(425\) | 1.95572 | 0.0948663 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.9518 | −1.11072 | ||||||||
\(428\) | −4.94497 | −0.239024 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −28.7726 | −1.38754 | ||||||||
\(431\) | 18.2265 | 0.877941 | 0.438971 | − | 0.898501i | \(-0.355343\pi\) | ||||
0.438971 | + | 0.898501i | \(0.355343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.14943 | −0.247466 | −0.123733 | − | 0.992316i | \(-0.539487\pi\) | ||||
−0.123733 | + | 0.992316i | \(0.539487\pi\) | |||||||
\(434\) | 12.5954 | 0.604597 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.32856 | −0.111518 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7487 | 0.847097 | 0.423548 | − | 0.905873i | \(-0.360784\pi\) | ||||
0.423548 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(440\) | 0.566698 | 0.0270163 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.29419 | 0.109124 | ||||||||
\(443\) | 3.26754 | 0.155245 | 0.0776227 | − | 0.996983i | \(-0.475267\pi\) | ||||
0.0776227 | + | 0.996983i | \(0.475267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.8112 | 2.07685 | ||||||||
\(446\) | 16.0615 | 0.760533 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.48349 | −0.211825 | ||||||||
\(449\) | 40.2916 | 1.90148 | 0.950738 | − | 0.309995i | \(-0.100327\pi\) | ||||
0.950738 | + | 0.309995i | \(0.100327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67688 | −0.0789610 | ||||||||
\(452\) | −8.00742 | −0.376637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.7222 | 1.11334 | ||||||||
\(455\) | 47.5037 | 2.22701 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9182 | −1.39952 | −0.699758 | − | 0.714380i | \(-0.746709\pi\) | ||||
−0.699758 | + | 0.714380i | \(0.746709\pi\) | |||||||
\(458\) | 19.2142 | 0.897822 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18649 | 0.381283 | 0.190642 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190642 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.92694 | −0.136026 | −0.0680132 | − | 0.997684i | \(-0.521666\pi\) | ||||
−0.0680132 | + | 0.997684i | \(0.521666\pi\) | |||||||
\(464\) | 7.49661 | 0.348021 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.4135 | −0.991963 | ||||||||
\(467\) | −33.2239 | −1.53742 | −0.768709 | − | 0.639598i | \(-0.779101\pi\) | ||||
−0.768709 | + | 0.639598i | \(0.779101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.9816 | −1.52295 | ||||||||
\(470\) | 28.0330 | 1.29307 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.81277 | −0.451669 | ||||||||
\(473\) | −1.99783 | −0.0918603 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.819434 | 0.0375982 | ||||||||
\(476\) | −2.77346 | −0.127122 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.20486 | −0.283803 | ||||||||
\(479\) | −27.5307 | −1.25791 | −0.628955 | − | 0.777442i | \(-0.716517\pi\) | ||||
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.9091 | −0.998971 | ||||||||
\(482\) | −7.77891 | −0.354319 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9607 | −0.498211 | ||||||||
\(485\) | 33.8433 | 1.53675 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.8291 | 0.626657 | 0.313329 | − | 0.949645i | \(-0.398556\pi\) | ||||
0.313329 | + | 0.949645i | \(0.398556\pi\) | |||||||
\(488\) | 5.11918 | 0.231734 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −37.4296 | −1.69089 | ||||||||
\(491\) | 6.40601 | 0.289099 | 0.144550 | − | 0.989498i | \(-0.453827\pi\) | ||||
0.144550 | + | 0.989498i | \(0.453827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.63736 | 0.208856 | ||||||||
\(494\) | 0.961253 | 0.0432488 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.80927 | −0.126140 | ||||||||
\(497\) | −49.7690 | −2.23245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.42182 | 0.197948 | 0.0989738 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989738 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(500\) | 5.25216 | 0.234884 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.7940 | −0.615656 | ||||||||
\(503\) | −24.5192 | −1.09326 | −0.546628 | − | 0.837376i | \(-0.684089\pi\) | ||||
−0.546628 | + | 0.837376i | \(0.684089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.9539 | 2.40092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.47728 | 0.243015 | ||||||||
\(509\) | −4.83296 | −0.214217 | −0.107109 | − | 0.994247i | \(-0.534159\pi\) | ||||
−0.107109 | + | 0.994247i | \(0.534159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 70.0871 | 3.10047 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.2445 | −0.540084 | ||||||||
\(515\) | −9.53513 | −0.420168 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.94647 | 0.0856058 | ||||||||
\(518\) | 26.4861 | 1.16373 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.5952 | −0.464632 | ||||||||
\(521\) | 0.345015 | 0.0151154 | 0.00755769 | − | 0.999971i | \(-0.497594\pi\) | ||||
0.00755769 | + | 0.999971i | \(0.497594\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7245 | −1.43094 | −0.715471 | − | 0.698643i | \(-0.753788\pi\) | ||||
−0.715471 | + | 0.698643i | \(0.753788\pi\) | |||||||
\(524\) | 5.81959 | 0.254230 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.4719 | 0.587402 | ||||||||
\(527\) | −1.73780 | −0.0756998 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −11.2440 | −0.488407 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.16206 | −0.0503819 | ||||||||
\(533\) | 31.3516 | 1.35799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.1270 | 0.610763 | ||||||||
\(536\) | 7.35623 | 0.317741 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.5981 | 0.456915 | ||||||||
\(539\) | −2.59892 | −0.111944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.90403 | −0.253834 | −0.126917 | − | 0.991913i | \(-0.540508\pi\) | ||||
−0.126917 | + | 0.991913i | \(0.540508\pi\) | |||||||
\(542\) | −6.37018 | −0.273623 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.618594 | 0.0265220 | ||||||||
\(545\) | 6.65233 | 0.284954 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7026 | 0.457611 | 0.228806 | − | 0.973472i | \(-0.426518\pi\) | ||||
0.228806 | + | 0.973472i | \(0.426518\pi\) | |||||||
\(548\) | −6.21674 | −0.265566 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.627141 | −0.0267414 | ||||||||
\(551\) | 1.94303 | 0.0827757 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −67.0814 | −2.85259 | ||||||||
\(554\) | −3.99485 | −0.169725 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.51441 | 0.149044 | ||||||||
\(557\) | −35.3336 | −1.49713 | −0.748566 | − | 0.663061i | \(-0.769257\pi\) | ||||
−0.748566 | + | 0.663061i | \(0.769257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.3523 | 1.57983 | ||||||||
\(560\) | 12.8086 | 0.541264 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.63873 | −0.153491 | ||||||||
\(563\) | 12.5021 | 0.526901 | 0.263450 | − | 0.964673i | \(-0.415140\pi\) | ||||
0.263450 | + | 0.964673i | \(0.415140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.8759 | 0.962398 | ||||||||
\(566\) | 12.1478 | 0.510611 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1005 | 0.465767 | ||||||||
\(569\) | −11.1853 | −0.468913 | −0.234457 | − | 0.972127i | \(-0.575331\pi\) | ||||
−0.234457 | + | 0.972127i | \(0.575331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0602 | 0.630251 | 0.315126 | − | 0.949050i | \(-0.397953\pi\) | ||||
0.315126 | + | 0.949050i | \(0.397953\pi\) | |||||||
\(572\) | −0.735680 | −0.0307603 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −37.9012 | −1.58196 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2713 | −1.21858 | −0.609291 | − | 0.792947i | \(-0.708546\pi\) | ||||
−0.609291 | + | 0.792947i | \(0.708546\pi\) | |||||||
\(578\) | −16.6173 | −0.691190 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.4166 | −0.889278 | ||||||||
\(581\) | 43.1749 | 1.79120 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.780726 | −0.0323344 | ||||||||
\(584\) | −15.6323 | −0.646867 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.7068 | −0.648844 | ||||||||
\(587\) | −22.6991 | −0.936894 | −0.468447 | − | 0.883492i | \(-0.655186\pi\) | ||||
−0.468447 | + | 0.883492i | \(0.655186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.728128 | −0.0300020 | ||||||||
\(590\) | 28.0335 | 1.15412 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.90747 | −0.242795 | ||||||||
\(593\) | −8.22045 | −0.337574 | −0.168787 | − | 0.985653i | \(-0.553985\pi\) | ||||
−0.168787 | + | 0.985653i | \(0.553985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.92335 | 0.324826 | ||||||||
\(596\) | −4.16095 | −0.170439 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.8240 | 1.17771 | 0.588857 | − | 0.808237i | \(-0.299578\pi\) | ||||
0.588857 | + | 0.808237i | \(0.299578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.46517 | 0.0597656 | 0.0298828 | − | 0.999553i | \(-0.490487\pi\) | ||||
0.0298828 | + | 0.999553i | \(0.490487\pi\) | |||||||
\(602\) | −45.1554 | −1.84040 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.91198 | −0.321934 | ||||||||
\(605\) | 31.3129 | 1.27305 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.8819 | −0.644626 | −0.322313 | − | 0.946633i | \(-0.604460\pi\) | ||||
−0.322313 | + | 0.946633i | \(0.604460\pi\) | |||||||
\(608\) | 0.259187 | 0.0105114 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.6247 | −0.592137 | ||||||||
\(611\) | −36.3922 | −1.47227 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.7081 | 1.07873 | 0.539364 | − | 0.842073i | \(-0.318665\pi\) | ||||
0.539364 | + | 0.842073i | \(0.318665\pi\) | |||||||
\(614\) | 1.74903 | 0.0705851 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.889368 | 0.0358337 | ||||||||
\(617\) | −40.7125 | −1.63903 | −0.819513 | − | 0.573061i | \(-0.805756\pi\) | ||||
−0.819513 | + | 0.573061i | \(0.805756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7836 | 0.835362 | 0.417681 | − | 0.908594i | \(-0.362843\pi\) | ||||
0.417681 | + | 0.908594i | \(0.362843\pi\) | |||||||
\(620\) | 8.02566 | 0.322318 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.3459 | −0.575220 | ||||||||
\(623\) | 68.7567 | 2.75468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8123 | −1.23249 | ||||||||
\(626\) | −3.21704 | −0.128579 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.9469 | −0.716158 | ||||||||
\(629\) | −3.65433 | −0.145708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.7972 | 0.748305 | 0.374153 | − | 0.927367i | \(-0.377934\pi\) | ||||
0.374153 | + | 0.927367i | \(0.377934\pi\) | |||||||
\(632\) | 14.9619 | 0.595151 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.57906 | −0.340718 | ||||||||
\(635\) | −15.6477 | −0.620962 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.5906 | 1.92523 | ||||||||
\(638\) | −1.48707 | −0.0588735 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.85684 | −0.112927 | ||||||||
\(641\) | −22.2658 | −0.879445 | −0.439722 | − | 0.898134i | \(-0.644923\pi\) | ||||
−0.439722 | + | 0.898134i | \(0.644923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.8885 | 1.02094 | 0.510472 | − | 0.859894i | \(-0.329471\pi\) | ||||
0.510472 | + | 0.859894i | \(0.329471\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.160332 | 0.00630817 | ||||||||
\(647\) | 14.5567 | 0.572283 | 0.286141 | − | 0.958187i | \(-0.407627\pi\) | ||||
0.286141 | + | 0.958187i | \(0.407627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.94651 | 0.0764072 | ||||||||
\(650\) | 11.7253 | 0.459905 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.09440 | 0.277838 | ||||||||
\(653\) | −31.0445 | −1.21486 | −0.607432 | − | 0.794372i | \(-0.707800\pi\) | ||||
−0.607432 | + | 0.794372i | \(0.707800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.6256 | −0.649618 | ||||||||
\(656\) | 8.45349 | 0.330053 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43.9947 | 1.71509 | ||||||||
\(659\) | 32.5712 | 1.26879 | 0.634397 | − | 0.773007i | \(-0.281248\pi\) | ||||
0.634397 | + | 0.773007i | \(0.281248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0721 | −0.702924 | −0.351462 | − | 0.936202i | \(-0.614315\pi\) | ||||
−0.351462 | + | 0.936202i | \(0.614315\pi\) | |||||||
\(662\) | 32.4766 | 1.26224 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.62975 | −0.373707 | ||||||||
\(665\) | 3.31984 | 0.128738 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −16.3201 | −0.631443 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.0156 | −0.811903 | ||||||||
\(671\) | −1.01547 | −0.0392016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5132 | 0.482350 | 0.241175 | − | 0.970482i | \(-0.422467\pi\) | ||||
0.241175 | + | 0.970482i | \(0.422467\pi\) | |||||||
\(674\) | 19.8665 | 0.765230 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.754609 | 0.0290234 | ||||||||
\(677\) | −9.99506 | −0.384141 | −0.192071 | − | 0.981381i | \(-0.561520\pi\) | ||||
−0.192071 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.1133 | 2.03830 | ||||||||
\(680\) | −1.76723 | −0.0677701 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.557262 | 0.0213387 | ||||||||
\(683\) | −42.2674 | −1.61732 | −0.808659 | − | 0.588278i | \(-0.799806\pi\) | ||||
−0.808659 | + | 0.588278i | \(0.799806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.7602 | 0.678584 | ||||||||
\(686\) | −27.3570 | −1.04450 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.0715 | 0.383971 | ||||||||
\(689\) | 14.5968 | 0.556094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.03010 | −0.0391870 | −0.0195935 | − | 0.999808i | \(-0.506237\pi\) | ||||
−0.0195935 | + | 0.999808i | \(0.506237\pi\) | |||||||
\(692\) | 15.4737 | 0.588223 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.9201 | 0.718199 | ||||||||
\(695\) | −10.0401 | −0.380844 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.22928 | 0.198073 | ||||||||
\(698\) | −0.333496 | −0.0126230 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14.1748 | −0.535757 | ||||||||
\(701\) | −6.09647 | −0.230260 | −0.115130 | − | 0.993350i | \(-0.536729\pi\) | ||||
−0.115130 | + | 0.993350i | \(0.536729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53114 | −0.0577481 | ||||||||
\(704\) | −0.198365 | −0.00747616 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.64132 | −0.287585 | ||||||||
\(707\) | 84.6746 | 3.18452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8129 | −0.706532 | −0.353266 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353266 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(710\) | −31.7124 | −1.19015 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.3355 | −0.574723 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.10172 | 0.0786000 | ||||||||
\(716\) | −4.67890 | −0.174859 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.5582 | −0.543306 | ||||||||
\(719\) | 39.0013 | 1.45450 | 0.727252 | − | 0.686371i | \(-0.240797\pi\) | ||||
0.727252 | + | 0.686371i | \(0.240797\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.9643 | −0.557300 | ||||||||
\(722\) | −18.9328 | −0.704607 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.42873 | 0.201757 | ||||||||
\(725\) | 23.7009 | 0.880230 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5647 | 0.577263 | 0.288631 | − | 0.957440i | \(-0.406800\pi\) | ||||
0.288631 | + | 0.957440i | \(0.406800\pi\) | |||||||
\(728\) | −16.6280 | −0.616276 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 44.6589 | 1.65290 | ||||||||
\(731\) | 6.23016 | 0.230431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0598 | 0.962542 | 0.481271 | − | 0.876572i | \(-0.340175\pi\) | ||||
0.481271 | + | 0.876572i | \(0.340175\pi\) | |||||||
\(734\) | −24.3518 | −0.898842 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.45922 | −0.0537510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.92255 | 0.365007 | 0.182503 | − | 0.983205i | \(-0.441580\pi\) | ||||
0.182503 | + | 0.983205i | \(0.441580\pi\) | |||||||
\(740\) | 16.8767 | 0.620400 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.6462 | −0.647811 | ||||||||
\(743\) | 28.1984 | 1.03450 | 0.517249 | − | 0.855835i | \(-0.326956\pi\) | ||||
0.517249 | + | 0.855835i | \(0.326956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8872 | 0.435513 | ||||||||
\(746\) | −16.4397 | −0.601899 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.122707 | −0.00448663 | ||||||||
\(749\) | 22.1707 | 0.810101 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.3162 | −1.36169 | −0.680843 | − | 0.732429i | \(-0.738386\pi\) | ||||
−0.680843 | + | 0.732429i | \(0.738386\pi\) | |||||||
\(752\) | −9.81259 | −0.357828 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.8028 | 1.01252 | ||||||||
\(755\) | 22.6033 | 0.822618 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0571 | 1.20148 | 0.600740 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600740 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(758\) | −7.37024 | −0.267699 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.740458 | −0.0268592 | ||||||||
\(761\) | 3.31453 | 0.120152 | 0.0600759 | − | 0.998194i | \(-0.480866\pi\) | ||||
0.0600759 | + | 0.998194i | \(0.480866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.4401 | 0.377956 | ||||||||
\(764\) | 5.76873 | 0.208705 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.2014 | −0.838301 | ||||||||
\(767\) | −36.3928 | −1.31407 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.88958 | 0.176323 | 0.0881614 | − | 0.996106i | \(-0.471901\pi\) | ||||
0.0881614 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(770\) | −2.54079 | −0.0915636 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.78622 | −0.100278 | ||||||||
\(773\) | 19.5595 | 0.703506 | 0.351753 | − | 0.936093i | \(-0.385586\pi\) | ||||
0.351753 | + | 0.936093i | \(0.385586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.88167 | −0.319039 | ||||||||
\(776\) | −11.8464 | −0.425261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.2192 | −0.724894 | ||||||||
\(779\) | 2.19104 | 0.0785021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.20195 | −0.0787920 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.1017 | 0.467919 | ||||||||
\(785\) | 51.2714 | 1.82995 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3627 | −0.511976 | −0.255988 | − | 0.966680i | \(-0.582401\pi\) | ||||
−0.255988 | + | 0.966680i | \(0.582401\pi\) | |||||||
\(788\) | −27.7303 | −0.987852 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −42.7437 | −1.52075 | ||||||||
\(791\) | 35.9012 | 1.27650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.9856 | 0.674199 | ||||||||
\(794\) | 18.2589 | 0.647985 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5232 | 0.727426 | ||||||||
\(797\) | 34.6629 | 1.22782 | 0.613911 | − | 0.789375i | \(-0.289595\pi\) | ||||
0.613911 | + | 0.789375i | \(0.289595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.07001 | −0.214742 | ||||||||
\(800\) | 3.16155 | 0.111778 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.9055 | −1.26787 | ||||||||
\(803\) | 3.10089 | 0.109428 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.4188 | −0.366987 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.8858 | −0.664402 | ||||||||
\(809\) | 36.5839 | 1.28622 | 0.643111 | − | 0.765773i | \(-0.277643\pi\) | ||||
0.643111 | + | 0.765773i | \(0.277643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.4096 | −1.03271 | −0.516356 | − | 0.856374i | \(-0.672712\pi\) | ||||
−0.516356 | + | 0.856374i | \(0.672712\pi\) | |||||||
\(812\) | −33.6110 | −1.17952 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.17183 | 0.0410728 | ||||||||
\(815\) | −20.2676 | −0.709943 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.61040 | 0.0913263 | ||||||||
\(818\) | −26.2924 | −0.919293 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.1503 | −0.843365 | ||||||||
\(821\) | 0.295199 | 0.0103025 | 0.00515126 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515126 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.2981 | 1.54414 | 0.772068 | − | 0.635540i | \(-0.219223\pi\) | ||||
0.772068 | + | 0.635540i | \(0.219223\pi\) | |||||||
\(824\) | 3.33765 | 0.116272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 43.9955 | 1.53080 | ||||||||
\(827\) | −28.7630 | −1.00019 | −0.500094 | − | 0.865971i | \(-0.666701\pi\) | ||||
−0.500094 | + | 0.865971i | \(0.666701\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.7583 | 0.790428 | 0.395214 | − | 0.918589i | \(-0.370670\pi\) | ||||
0.395214 | + | 0.918589i | \(0.370670\pi\) | |||||||
\(830\) | 27.5107 | 0.954909 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.70872 | 0.128577 | ||||||||
\(833\) | 8.10465 | 0.280809 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.6239 | 1.61349 | ||||||||
\(836\) | −0.0514137 | −0.00177818 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.27755 | −0.251399 | ||||||||
\(839\) | 19.0736 | 0.658494 | 0.329247 | − | 0.944244i | \(-0.393205\pi\) | ||||
0.329247 | + | 0.944244i | \(0.393205\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1992 | 0.937903 | ||||||||
\(842\) | 34.3333 | 1.18320 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.0376 | −0.758566 | ||||||||
\(845\) | −2.15580 | −0.0741618 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.1420 | 1.68854 | ||||||||
\(848\) | 3.93580 | 0.135156 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.95572 | 0.0670806 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.3316 | 0.867336 | 0.433668 | − | 0.901073i | \(-0.357219\pi\) | ||||
0.433668 | + | 0.901073i | \(0.357219\pi\) | |||||||
\(854\) | −22.9518 | −0.785395 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.94497 | −0.169015 | ||||||||
\(857\) | 8.26978 | 0.282490 | 0.141245 | − | 0.989975i | \(-0.454889\pi\) | ||||
0.141245 | + | 0.989975i | \(0.454889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.89082 | 0.0645139 | 0.0322569 | − | 0.999480i | \(-0.489731\pi\) | ||||
0.0322569 | + | 0.999480i | \(0.489731\pi\) | |||||||
\(860\) | −28.7726 | −0.981139 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.2265 | 0.620798 | ||||||||
\(863\) | −8.19194 | −0.278857 | −0.139428 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139428 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.2060 | −1.50305 | ||||||||
\(866\) | −5.14943 | −0.174985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.5954 | 0.427515 | ||||||||
\(869\) | −2.96791 | −0.100679 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.2822 | 0.924422 | ||||||||
\(872\) | −2.32856 | −0.0788550 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.5480 | −0.796068 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.4191 | 1.70253 | 0.851266 | − | 0.524735i | \(-0.175836\pi\) | ||||
0.851266 | + | 0.524735i | \(0.175836\pi\) | |||||||
\(878\) | 17.7487 | 0.598988 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.566698 | 0.0191034 | ||||||||
\(881\) | 2.36032 | 0.0795212 | 0.0397606 | − | 0.999209i | \(-0.487340\pi\) | ||||
0.0397606 | + | 0.999209i | \(0.487340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4264 | −0.754708 | −0.377354 | − | 0.926069i | \(-0.623166\pi\) | ||||
−0.377354 | + | 0.926069i | \(0.623166\pi\) | |||||||
\(884\) | 2.29419 | 0.0771621 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.26754 | 0.109775 | ||||||||
\(887\) | −37.0984 | −1.24564 | −0.622821 | − | 0.782365i | \(-0.714013\pi\) | ||||
−0.622821 | + | 0.782365i | \(0.714013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.5574 | −0.823628 | ||||||||
\(890\) | 43.8112 | 1.46855 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.0615 | 0.537778 | ||||||||
\(893\) | −2.54330 | −0.0851082 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.3669 | 0.446805 | ||||||||
\(896\) | −4.48349 | −0.149783 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.2916 | 1.34455 | ||||||||
\(899\) | −21.0600 | −0.702392 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.43467 | 0.0811105 | ||||||||
\(902\) | −1.67688 | −0.0558339 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.00742 | −0.266323 | ||||||||
\(905\) | −15.5090 | −0.515537 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3091 | 0.408717 | 0.204358 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204358 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(908\) | 23.7222 | 0.787248 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 47.5037 | 1.57473 | ||||||||
\(911\) | −15.7544 | −0.521965 | −0.260983 | − | 0.965343i | \(-0.584047\pi\) | ||||
−0.260983 | + | 0.965343i | \(0.584047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.91020 | 0.0632185 | ||||||||
\(914\) | −29.9182 | −0.989608 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.2142 | 0.634856 | ||||||||
\(917\) | −26.0921 | −0.861636 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.16750 | −0.170460 | −0.0852300 | − | 0.996361i | \(-0.527163\pi\) | ||||
−0.0852300 | + | 0.996361i | \(0.527163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.18649 | 0.269608 | ||||||||
\(923\) | 41.1687 | 1.35508 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.6768 | −0.614088 | ||||||||
\(926\) | −2.92694 | −0.0961852 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.49661 | 0.246088 | ||||||||
\(929\) | −19.1921 | −0.629672 | −0.314836 | − | 0.949146i | \(-0.601949\pi\) | ||||
−0.314836 | + | 0.949146i | \(0.601949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.39580 | 0.111293 | ||||||||
\(932\) | −21.4135 | −0.701423 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.2239 | −1.08712 | ||||||||
\(935\) | 0.350556 | 0.0114644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.05012 | 0.197649 | 0.0988244 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988244 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(938\) | −32.9816 | −1.07689 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.0330 | 0.914336 | ||||||||
\(941\) | −9.68489 | −0.315718 | −0.157859 | − | 0.987462i | \(-0.550459\pi\) | ||||
−0.157859 | + | 0.987462i | \(0.550459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9.81277 | −0.319378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.99783 | −0.0649550 | ||||||||
\(947\) | −23.0242 | −0.748185 | −0.374093 | − | 0.927391i | \(-0.622046\pi\) | ||||
−0.374093 | + | 0.927391i | \(0.622046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.9757 | −1.88197 | ||||||||
\(950\) | 0.819434 | 0.0265860 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.77346 | −0.0898885 | ||||||||
\(953\) | −29.5625 | −0.957624 | −0.478812 | − | 0.877917i | \(-0.658932\pi\) | ||||
−0.478812 | + | 0.877917i | \(0.658932\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.4804 | −0.533292 | ||||||||
\(956\) | −6.20486 | −0.200679 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.5307 | −0.889476 | ||||||||
\(959\) | 27.8727 | 0.900057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1080 | −0.745419 | ||||||||
\(962\) | −21.9091 | −0.706379 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.77891 | −0.250542 | ||||||||
\(965\) | 7.95979 | 0.256235 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.4705 | −1.75165 | −0.875826 | − | 0.482627i | \(-0.839683\pi\) | ||||
−0.875826 | + | 0.482627i | \(0.839683\pi\) | |||||||
\(968\) | −10.9607 | −0.352289 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33.8433 | 1.08664 | ||||||||
\(971\) | −52.6205 | −1.68867 | −0.844336 | − | 0.535813i | \(-0.820005\pi\) | ||||
−0.844336 | + | 0.535813i | \(0.820005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.7569 | −0.505141 | ||||||||
\(974\) | 13.8291 | 0.443114 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.11918 | 0.163861 | ||||||||
\(977\) | −14.1829 | −0.453752 | −0.226876 | − | 0.973924i | \(-0.572851\pi\) | ||||
−0.226876 | + | 0.973924i | \(0.572851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.04203 | 0.0972238 | ||||||||
\(980\) | −37.4296 | −1.19564 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.40601 | 0.204424 | ||||||||
\(983\) | −44.8753 | −1.43130 | −0.715650 | − | 0.698459i | \(-0.753869\pi\) | ||||
−0.715650 | + | 0.698459i | \(0.753869\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 79.2212 | 2.52420 | ||||||||
\(986\) | 4.63736 | 0.147684 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.961253 | 0.0305815 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.31690 | 0.200663 | 0.100331 | − | 0.994954i | \(-0.468010\pi\) | ||||
0.100331 | + | 0.994954i | \(0.468010\pi\) | |||||||
\(992\) | −2.80927 | −0.0891946 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49.7690 | −1.57858 | ||||||||
\(995\) | −58.6316 | −1.85875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.8622 | 1.00909 | 0.504544 | − | 0.863386i | \(-0.331661\pi\) | ||||
0.504544 | + | 0.863386i | \(0.331661\pi\) | |||||||
\(998\) | 4.42182 | 0.139970 | ||||||||
\(999\) | 0 | 0 |
(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 | 9522.2.a.ci.1.3 | 10 | ||
3.2 | odd | 2 | 9522.2.a.ch.1.8 | 10 | |||
23.17 | odd | 22 | 414.2.i.g.289.2 | ✓ | 20 | ||
23.19 | odd | 22 | 414.2.i.g.361.2 | yes | 20 | ||
23.22 | odd | 2 | 9522.2.a.cj.1.8 | 10 | |||
69.17 | even | 22 | 414.2.i.h.289.1 | yes | 20 | ||
69.65 | even | 22 | 414.2.i.h.361.1 | yes | 20 | ||
69.68 | even | 2 | 9522.2.a.cg.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.i.g.289.2 | ✓ | 20 | 23.17 | odd | 22 | ||
414.2.i.g.361.2 | yes | 20 | 23.19 | odd | 22 | ||
414.2.i.h.289.1 | yes | 20 | 69.17 | even | 22 | ||
414.2.i.h.361.1 | yes | 20 | 69.65 | even | 22 | ||
9522.2.a.cg.1.3 | 10 | 69.68 | even | 2 | |||
9522.2.a.ch.1.8 | 10 | 3.2 | odd | 2 | |||
9522.2.a.ci.1.3 | 10 | 1.1 | even | 1 | trivial | ||
9522.2.a.cj.1.8 | 10 | 23.22 | odd | 2 |