Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
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: | \( x^{12} - 16x^{10} + 92x^{8} - 228x^{6} + 225x^{4} - 60x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.318530\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.318530 | −0.225235 | −0.112617 | − | 0.993638i | \(-0.535923\pi\) | ||||
−0.112617 | + | 0.993638i | \(0.535923\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.89854 | −0.949269 | ||||||||
\(5\) | 0.278702 | 0.124639 | 0.0623197 | − | 0.998056i | \(-0.480150\pi\) | ||||
0.0623197 | + | 0.998056i | \(0.480150\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.24180 | 0.439043 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0887749 | −0.0280731 | ||||||||
\(11\) | −4.26805 | −1.28687 | −0.643433 | − | 0.765503i | \(-0.722490\pi\) | ||||
−0.643433 | + | 0.765503i | \(0.722490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.40153 | 0.850382 | ||||||||
\(17\) | 6.27885 | 1.52284 | 0.761422 | − | 0.648256i | \(-0.224501\pi\) | ||||
0.761422 | + | 0.648256i | \(0.224501\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.935311 | 0.214575 | 0.107287 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107287 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(20\) | −0.529127 | −0.118316 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.35950 | 0.289847 | ||||||||
\(23\) | 0.554198 | 0.115558 | 0.0577792 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577792 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92233 | −0.984465 | ||||||||
\(26\) | 0.318530 | 0.0624688 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.49614 | −0.834913 | −0.417456 | − | 0.908697i | \(-0.637078\pi\) | ||||
−0.417456 | + | 0.908697i | \(0.637078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.861767 | 0.154778 | 0.0773890 | − | 0.997001i | \(-0.475342\pi\) | ||||
0.0773890 | + | 0.997001i | \(0.475342\pi\) | |||||||
\(32\) | −3.56709 | −0.630578 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.40123 | 0.723557 | 0.361779 | − | 0.932264i | \(-0.382170\pi\) | ||||
0.361779 | + | 0.932264i | \(0.382170\pi\) | |||||||
\(38\) | −0.297924 | −0.0483297 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.346092 | 0.0547220 | ||||||||
\(41\) | −0.979596 | −0.152987 | −0.0764936 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764936 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.71659 | −0.261777 | −0.130889 | − | 0.991397i | \(-0.541783\pi\) | ||||
−0.130889 | + | 0.991397i | \(0.541783\pi\) | |||||||
\(44\) | 8.10306 | 1.22158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.176529 | −0.0260277 | ||||||||
\(47\) | 4.42810 | 0.645905 | 0.322953 | − | 0.946415i | \(-0.395325\pi\) | ||||
0.322953 | + | 0.946415i | \(0.395325\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.56791 | 0.221736 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.89854 | 0.263280 | ||||||||
\(53\) | 9.30603 | 1.27828 | 0.639141 | − | 0.769090i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769090i | \(0.279290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18951 | −0.160394 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.43215 | 0.188051 | ||||||||
\(59\) | −12.5106 | −1.62874 | −0.814372 | − | 0.580343i | \(-0.802919\pi\) | ||||
−0.814372 | + | 0.580343i | \(0.802919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.97463 | 0.252825 | 0.126413 | − | 0.991978i | \(-0.459654\pi\) | ||||
0.126413 | + | 0.991978i | \(0.459654\pi\) | |||||||
\(62\) | −0.274498 | −0.0348613 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.66683 | −0.708354 | ||||||||
\(65\) | −0.278702 | −0.0345687 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97361 | −0.485453 | −0.242727 | − | 0.970095i | \(-0.578042\pi\) | ||||
−0.242727 | + | 0.970095i | \(0.578042\pi\) | |||||||
\(68\) | −11.9206 | −1.44559 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.43794 | −0.289330 | −0.144665 | − | 0.989481i | \(-0.546210\pi\) | ||||
−0.144665 | + | 0.989481i | \(0.546210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.83639 | 0.566057 | 0.283029 | − | 0.959111i | \(-0.408661\pi\) | ||||
0.283029 | + | 0.959111i | \(0.408661\pi\) | |||||||
\(74\) | −1.40192 | −0.162970 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.77572 | −0.203689 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5478 | 1.41174 | 0.705871 | − | 0.708341i | \(-0.250556\pi\) | ||||
0.705871 | + | 0.708341i | \(0.250556\pi\) | |||||||
\(80\) | 0.948013 | 0.105991 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.312030 | 0.0344580 | ||||||||
\(83\) | 11.1808 | 1.22725 | 0.613623 | − | 0.789599i | \(-0.289711\pi\) | ||||
0.613623 | + | 0.789599i | \(0.289711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.74993 | 0.189806 | ||||||||
\(86\) | 0.546784 | 0.0589613 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.30007 | −0.564989 | ||||||||
\(89\) | 12.1828 | 1.29137 | 0.645686 | − | 0.763603i | \(-0.276572\pi\) | ||||
0.645686 | + | 0.763603i | \(0.276572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.05217 | −0.109696 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.41048 | −0.145480 | ||||||||
\(95\) | 0.260673 | 0.0267445 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9099 | −1.31081 | −0.655403 | − | 0.755280i | \(-0.727501\pi\) | ||||
−0.655403 | + | 0.755280i | \(0.727501\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.34523 | 0.934523 | ||||||||
\(101\) | 5.10341 | 0.507809 | 0.253904 | − | 0.967229i | \(-0.418285\pi\) | ||||
0.253904 | + | 0.967229i | \(0.418285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.361087 | −0.0355789 | −0.0177895 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177895 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(104\) | −1.24180 | −0.121769 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.96425 | −0.287913 | ||||||||
\(107\) | −13.2663 | −1.28250 | −0.641252 | − | 0.767330i | \(-0.721585\pi\) | ||||
−0.641252 | + | 0.767330i | \(0.721585\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7826 | −1.32014 | −0.660069 | − | 0.751205i | \(-0.729473\pi\) | ||||
−0.660069 | + | 0.751205i | \(0.729473\pi\) | |||||||
\(110\) | 0.378896 | 0.0361263 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.99313 | −0.281570 | −0.140785 | − | 0.990040i | \(-0.544963\pi\) | ||||
−0.140785 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.154456 | 0.0144031 | ||||||||
\(116\) | 8.53610 | 0.792557 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.98501 | 0.366849 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21625 | 0.656022 | ||||||||
\(122\) | −0.628978 | −0.0569449 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.63610 | −0.146926 | ||||||||
\(125\) | −2.76537 | −0.247342 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.71157 | −0.595556 | −0.297778 | − | 0.954635i | \(-0.596245\pi\) | ||||
−0.297778 | + | 0.954635i | \(0.596245\pi\) | |||||||
\(128\) | 8.93923 | 0.790124 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0887749 | 0.00778607 | ||||||||
\(131\) | −9.52731 | −0.832405 | −0.416203 | − | 0.909272i | \(-0.636639\pi\) | ||||
−0.416203 | + | 0.909272i | \(0.636639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.26571 | 0.109341 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.79708 | 0.668594 | ||||||||
\(137\) | 21.1133 | 1.80383 | 0.901915 | − | 0.431913i | \(-0.142161\pi\) | ||||
0.901915 | + | 0.431913i | \(0.142161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.6811 | −1.24524 | −0.622618 | − | 0.782526i | \(-0.713931\pi\) | ||||
−0.622618 | + | 0.782526i | \(0.713931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.776556 | 0.0651671 | ||||||||
\(143\) | 4.26805 | 0.356912 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.25308 | −0.104063 | ||||||||
\(146\) | −1.54054 | −0.127496 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.35590 | −0.686851 | ||||||||
\(149\) | −13.5524 | −1.11026 | −0.555130 | − | 0.831764i | \(-0.687331\pi\) | ||||
−0.555130 | + | 0.831764i | \(0.687331\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.52294 | −0.693587 | −0.346794 | − | 0.937941i | \(-0.612730\pi\) | ||||
−0.346794 | + | 0.937941i | \(0.612730\pi\) | |||||||
\(152\) | 1.16147 | 0.0942076 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.240176 | 0.0192914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.9303 | −1.11176 | −0.555879 | − | 0.831263i | \(-0.687618\pi\) | ||||
−0.555879 | + | 0.831263i | \(0.687618\pi\) | |||||||
\(158\) | −3.99686 | −0.317973 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.994155 | −0.0785948 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6518 | 1.38260 | 0.691298 | − | 0.722569i | \(-0.257039\pi\) | ||||
0.691298 | + | 0.722569i | \(0.257039\pi\) | |||||||
\(164\) | 1.85980 | 0.145226 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.56140 | −0.276418 | ||||||||
\(167\) | 7.45254 | 0.576695 | 0.288348 | − | 0.957526i | \(-0.406894\pi\) | ||||
0.288348 | + | 0.957526i | \(0.406894\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.557404 | −0.0427509 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.25901 | 0.248497 | ||||||||
\(173\) | −19.1846 | −1.45858 | −0.729290 | − | 0.684205i | \(-0.760149\pi\) | ||||
−0.729290 | + | 0.684205i | \(0.760149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.5179 | −1.09433 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.88058 | −0.290861 | ||||||||
\(179\) | −19.6322 | −1.46738 | −0.733692 | − | 0.679483i | \(-0.762204\pi\) | ||||
−0.733692 | + | 0.679483i | \(0.762204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5654 | −1.00831 | −0.504153 | − | 0.863614i | \(-0.668195\pi\) | ||||
−0.504153 | + | 0.863614i | \(0.668195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.688204 | 0.0507351 | ||||||||
\(185\) | 1.22663 | 0.0901837 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.7984 | −1.95970 | ||||||||
\(188\) | −8.40693 | −0.613138 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0830321 | −0.00602378 | ||||||||
\(191\) | −2.86026 | −0.206961 | −0.103481 | − | 0.994631i | \(-0.532998\pi\) | ||||
−0.103481 | + | 0.994631i | \(0.532998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.318196 | 0.0229043 | 0.0114521 | − | 0.999934i | \(-0.496355\pi\) | ||||
0.0114521 | + | 0.999934i | \(0.496355\pi\) | |||||||
\(194\) | 4.11220 | 0.295239 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.15763 | 0.153725 | 0.0768624 | − | 0.997042i | \(-0.475510\pi\) | ||||
0.0768624 | + | 0.997042i | \(0.475510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7721 | −0.976280 | −0.488140 | − | 0.872765i | \(-0.662325\pi\) | ||||
−0.488140 | + | 0.872765i | \(0.662325\pi\) | |||||||
\(200\) | −6.11255 | −0.432222 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.62559 | −0.114376 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.273015 | −0.0190682 | ||||||||
\(206\) | 0.115017 | 0.00801361 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.40153 | −0.235853 | ||||||||
\(209\) | −3.99195 | −0.276129 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.05624 | −0.348086 | −0.174043 | − | 0.984738i | \(-0.555683\pi\) | ||||
−0.174043 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(212\) | −17.6679 | −1.21343 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.22572 | 0.288864 | ||||||||
\(215\) | −0.478417 | −0.0326277 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.39018 | 0.297340 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.25834 | 0.152257 | ||||||||
\(221\) | −6.27885 | −0.422361 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.9620 | −1.60462 | −0.802309 | − | 0.596910i | \(-0.796395\pi\) | ||||
−0.802309 | + | 0.596910i | \(0.796395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.953402 | 0.0634194 | ||||||||
\(227\) | 18.8419 | 1.25058 | 0.625292 | − | 0.780391i | \(-0.284980\pi\) | ||||
0.625292 | + | 0.780391i | \(0.284980\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9695 | −1.25354 | −0.626768 | − | 0.779206i | \(-0.715623\pi\) | ||||
−0.626768 | + | 0.779206i | \(0.715623\pi\) | |||||||
\(230\) | −0.0491989 | −0.00324408 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.58331 | −0.366562 | ||||||||
\(233\) | 27.3238 | 1.79004 | 0.895022 | − | 0.446022i | \(-0.147160\pi\) | ||||
0.895022 | + | 0.446022i | \(0.147160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.23412 | 0.0805052 | ||||||||
\(236\) | 23.7519 | 1.54612 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.8749 | 1.54434 | 0.772170 | − | 0.635416i | \(-0.219171\pi\) | ||||
0.772170 | + | 0.635416i | \(0.219171\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3941 | −1.05603 | −0.528017 | − | 0.849234i | \(-0.677064\pi\) | ||||
−0.528017 | + | 0.849234i | \(0.677064\pi\) | |||||||
\(242\) | −2.29859 | −0.147759 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.74891 | −0.239999 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.935311 | −0.0595124 | ||||||||
\(248\) | 1.07014 | 0.0679541 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.880853 | 0.0557100 | ||||||||
\(251\) | −7.88947 | −0.497979 | −0.248989 | − | 0.968506i | \(-0.580098\pi\) | ||||
−0.248989 | + | 0.968506i | \(0.580098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.36535 | −0.148708 | ||||||||
\(254\) | 2.13783 | 0.134140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.48625 | 0.530391 | ||||||||
\(257\) | 21.0559 | 1.31343 | 0.656715 | − | 0.754139i | \(-0.271946\pi\) | ||||
0.656715 | + | 0.754139i | \(0.271946\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.529127 | 0.0328150 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.03473 | 0.187486 | ||||||||
\(263\) | 9.45167 | 0.582815 | 0.291408 | − | 0.956599i | \(-0.405876\pi\) | ||||
0.291408 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.59361 | 0.159324 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.54405 | 0.460826 | ||||||||
\(269\) | 13.4282 | 0.818731 | 0.409365 | − | 0.912371i | \(-0.365750\pi\) | ||||
0.409365 | + | 0.912371i | \(0.365750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.94268 | −0.543229 | −0.271615 | − | 0.962406i | \(-0.587558\pi\) | ||||
−0.271615 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(272\) | 21.3577 | 1.29500 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.72521 | −0.406285 | ||||||||
\(275\) | 21.0087 | 1.26687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.08015 | −0.365321 | −0.182661 | − | 0.983176i | \(-0.558471\pi\) | ||||
−0.182661 | + | 0.983176i | \(0.558471\pi\) | |||||||
\(278\) | 4.67637 | 0.280470 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7806 | −1.00105 | −0.500523 | − | 0.865723i | \(-0.666859\pi\) | ||||
−0.500523 | + | 0.865723i | \(0.666859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.49011 | 0.266909 | 0.133455 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133455 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(284\) | 4.62852 | 0.274652 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.35950 | −0.0803890 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.4239 | 1.31906 | ||||||||
\(290\) | 0.399144 | 0.0234386 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.18208 | −0.537341 | ||||||||
\(293\) | 7.74333 | 0.452370 | 0.226185 | − | 0.974084i | \(-0.427375\pi\) | ||||
0.226185 | + | 0.974084i | \(0.427375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.48674 | −0.203006 | ||||||||
\(296\) | 5.46545 | 0.317673 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.31686 | 0.250069 | ||||||||
\(299\) | −0.554198 | −0.0320501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.71481 | 0.156220 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.18148 | 0.182471 | ||||||||
\(305\) | 0.550333 | 0.0315120 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.02736 | −0.401073 | −0.200536 | − | 0.979686i | \(-0.564268\pi\) | ||||
−0.200536 | + | 0.979686i | \(0.564268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0765033 | −0.00434509 | ||||||||
\(311\) | −33.4422 | −1.89633 | −0.948165 | − | 0.317777i | \(-0.897064\pi\) | ||||
−0.948165 | + | 0.317777i | \(0.897064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.8389 | −0.725700 | −0.362850 | − | 0.931848i | \(-0.618196\pi\) | ||||
−0.362850 | + | 0.931848i | \(0.618196\pi\) | |||||||
\(314\) | 4.43721 | 0.250406 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.8225 | −1.34012 | ||||||||
\(317\) | 3.14685 | 0.176745 | 0.0883723 | − | 0.996088i | \(-0.471833\pi\) | ||||
0.0883723 | + | 0.996088i | \(0.471833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1898 | 1.07442 | ||||||||
\(320\) | −1.57936 | −0.0882888 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.87267 | 0.326764 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.92233 | 0.273041 | ||||||||
\(326\) | −5.62263 | −0.311409 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.21646 | −0.0671679 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.26160 | 0.344169 | 0.172084 | − | 0.985082i | \(-0.444950\pi\) | ||||
0.172084 | + | 0.985082i | \(0.444950\pi\) | |||||||
\(332\) | −21.2271 | −1.16499 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.37386 | −0.129892 | ||||||||
\(335\) | −1.10745 | −0.0605066 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8596 | −0.863929 | −0.431964 | − | 0.901891i | \(-0.642179\pi\) | ||||
−0.431964 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(338\) | −0.318530 | −0.0173257 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.32231 | −0.180177 | ||||||||
\(341\) | −3.67806 | −0.199178 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.13166 | −0.114931 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.11087 | 0.328522 | ||||||||
\(347\) | −13.1466 | −0.705747 | −0.352873 | − | 0.935671i | \(-0.614795\pi\) | ||||
−0.352873 | + | 0.935671i | \(0.614795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.8740 | −1.59912 | −0.799559 | − | 0.600588i | \(-0.794933\pi\) | ||||
−0.799559 | + | 0.600588i | \(0.794933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.2245 | 0.811469 | ||||||||
\(353\) | 0.661559 | 0.0352112 | 0.0176056 | − | 0.999845i | \(-0.494396\pi\) | ||||
0.0176056 | + | 0.999845i | \(0.494396\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.679458 | −0.0360619 | ||||||||
\(356\) | −23.1295 | −1.22586 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.25345 | 0.330505 | ||||||||
\(359\) | −13.2792 | −0.700851 | −0.350425 | − | 0.936591i | \(-0.613963\pi\) | ||||
−0.350425 | + | 0.936591i | \(0.613963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1252 | −0.953958 | ||||||||
\(362\) | 4.32097 | 0.227105 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.34791 | 0.0705530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.0453 | −1.88155 | −0.940776 | − | 0.339029i | \(-0.889902\pi\) | ||||
−0.940776 | + | 0.339029i | \(0.889902\pi\) | |||||||
\(368\) | 1.88512 | 0.0982687 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.390718 | −0.0203125 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.95464 | −0.308320 | −0.154160 | − | 0.988046i | \(-0.549267\pi\) | ||||
−0.154160 | + | 0.988046i | \(0.549267\pi\) | |||||||
\(374\) | 8.53610 | 0.441391 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.49882 | 0.283580 | ||||||||
\(377\) | 4.49614 | 0.231563 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7760 | −0.964457 | −0.482229 | − | 0.876045i | \(-0.660173\pi\) | ||||
−0.482229 | + | 0.876045i | \(0.660173\pi\) | |||||||
\(380\) | −0.494898 | −0.0253877 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.911079 | 0.0466149 | ||||||||
\(383\) | −11.2426 | −0.574473 | −0.287236 | − | 0.957860i | \(-0.592736\pi\) | ||||
−0.287236 | + | 0.957860i | \(0.592736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.101355 | −0.00515883 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.5100 | 1.24431 | ||||||||
\(389\) | 10.2488 | 0.519632 | 0.259816 | − | 0.965658i | \(-0.416338\pi\) | ||||
0.259816 | + | 0.965658i | \(0.416338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.47973 | 0.175977 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.687269 | −0.0346241 | ||||||||
\(395\) | 3.49711 | 0.175958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.24651 | 0.213126 | 0.106563 | − | 0.994306i | \(-0.466015\pi\) | ||||
0.106563 | + | 0.994306i | \(0.466015\pi\) | |||||||
\(398\) | 4.38683 | 0.219892 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.7434 | −0.837171 | ||||||||
\(401\) | 16.0419 | 0.801092 | 0.400546 | − | 0.916277i | \(-0.368820\pi\) | ||||
0.400546 | + | 0.916277i | \(0.368820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.861767 | −0.0429277 | ||||||||
\(404\) | −9.68903 | −0.482047 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.7847 | −0.931121 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4352 | −0.515986 | −0.257993 | − | 0.966147i | \(-0.583061\pi\) | ||||
−0.257993 | + | 0.966147i | \(0.583061\pi\) | |||||||
\(410\) | 0.0869635 | 0.00429482 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.685537 | 0.0337740 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.11610 | 0.152963 | ||||||||
\(416\) | 3.56709 | 0.174891 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.27156 | 0.0621938 | ||||||||
\(419\) | −26.0460 | −1.27243 | −0.636215 | − | 0.771512i | \(-0.719501\pi\) | ||||
−0.636215 | + | 0.771512i | \(0.719501\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4906 | 0.949912 | 0.474956 | − | 0.880009i | \(-0.342464\pi\) | ||||
0.474956 | + | 0.880009i | \(0.342464\pi\) | |||||||
\(422\) | 1.61056 | 0.0784009 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5562 | 0.561220 | ||||||||
\(425\) | −30.9065 | −1.49919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 25.1866 | 1.21744 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.152390 | 0.00734889 | ||||||||
\(431\) | −3.84680 | −0.185294 | −0.0926468 | − | 0.995699i | \(-0.529533\pi\) | ||||
−0.0926468 | + | 0.995699i | \(0.529533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.34412 | −0.0645943 | −0.0322972 | − | 0.999478i | \(-0.510282\pi\) | ||||
−0.0322972 | + | 0.999478i | \(0.510282\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.1669 | 1.25317 | ||||||||
\(437\) | 0.518348 | 0.0247959 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.1985 | −1.72766 | −0.863831 | − | 0.503781i | \(-0.831942\pi\) | ||||
−0.863831 | + | 0.503781i | \(0.831942\pi\) | |||||||
\(440\) | −1.47714 | −0.0704198 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −11.1890 | −0.531608 | −0.265804 | − | 0.964027i | \(-0.585637\pi\) | ||||
−0.265804 | + | 0.964027i | \(0.585637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.39536 | 0.160956 | ||||||||
\(446\) | 7.63262 | 0.361415 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3847 | 0.490082 | 0.245041 | − | 0.969513i | \(-0.421199\pi\) | ||||
0.245041 | + | 0.969513i | \(0.421199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.18096 | 0.196874 | ||||||||
\(452\) | 5.68258 | 0.267286 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.00172 | −0.281675 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.0132 | −1.26363 | −0.631813 | − | 0.775121i | \(-0.717689\pi\) | ||||
−0.631813 | + | 0.775121i | \(0.717689\pi\) | |||||||
\(458\) | 6.04233 | 0.282340 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.293241 | −0.0136724 | ||||||||
\(461\) | −17.3981 | −0.810309 | −0.405154 | − | 0.914248i | \(-0.632782\pi\) | ||||
−0.405154 | + | 0.914248i | \(0.632782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.57924 | 0.259289 | 0.129645 | − | 0.991561i | \(-0.458616\pi\) | ||||
0.129645 | + | 0.991561i | \(0.458616\pi\) | |||||||
\(464\) | −15.2937 | −0.709994 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.70345 | −0.403180 | ||||||||
\(467\) | 1.10964 | 0.0513479 | 0.0256740 | − | 0.999670i | \(-0.491827\pi\) | ||||
0.0256740 | + | 0.999670i | \(0.491827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.393104 | −0.0181326 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.5357 | −0.715088 | ||||||||
\(473\) | 7.32648 | 0.336872 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.60390 | −0.211242 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.60487 | −0.347839 | ||||||||
\(479\) | −28.7672 | −1.31441 | −0.657204 | − | 0.753713i | \(-0.728261\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.40123 | −0.200679 | ||||||||
\(482\) | 5.22200 | 0.237856 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.7003 | −0.622742 | ||||||||
\(485\) | −3.59803 | −0.163378 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.05808 | −0.365147 | −0.182573 | − | 0.983192i | \(-0.558443\pi\) | ||||
−0.182573 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(488\) | 2.45209 | 0.111001 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.6810 | −1.52000 | −0.760001 | − | 0.649922i | \(-0.774802\pi\) | ||||
−0.760001 | + | 0.649922i | \(0.774802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.2306 | −1.27144 | ||||||||
\(494\) | 0.297924 | 0.0134042 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.93132 | 0.131620 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.98394 | 0.223112 | 0.111556 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111556 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(500\) | 5.25017 | 0.234795 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.51303 | 0.112162 | ||||||||
\(503\) | 10.4861 | 0.467554 | 0.233777 | − | 0.972290i | \(-0.424891\pi\) | ||||
0.233777 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.42233 | 0.0632929 | ||||||||
\(506\) | 0.753433 | 0.0334942 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.7422 | 0.565343 | ||||||||
\(509\) | −27.7170 | −1.22854 | −0.614268 | − | 0.789097i | \(-0.710549\pi\) | ||||
−0.614268 | + | 0.789097i | \(0.710549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.5816 | −0.909586 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.70692 | −0.295830 | ||||||||
\(515\) | −0.100636 | −0.00443454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.8994 | −0.831193 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.346092 | −0.0151772 | ||||||||
\(521\) | 4.84437 | 0.212236 | 0.106118 | − | 0.994354i | \(-0.466158\pi\) | ||||
0.106118 | + | 0.994354i | \(0.466158\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8799 | 1.17538 | 0.587688 | − | 0.809088i | \(-0.300038\pi\) | ||||
0.587688 | + | 0.809088i | \(0.300038\pi\) | |||||||
\(524\) | 18.0880 | 0.790177 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.01064 | −0.131270 | ||||||||
\(527\) | 5.41091 | 0.235703 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6929 | −0.986646 | ||||||||
\(530\) | −0.826142 | −0.0358853 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.979596 | 0.0424310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.69735 | −0.159851 | ||||||||
\(536\) | −4.93443 | −0.213135 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.27727 | −0.184406 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9541 | 0.599933 | 0.299966 | − | 0.953950i | \(-0.403025\pi\) | ||||
0.299966 | + | 0.953950i | \(0.403025\pi\) | |||||||
\(542\) | 2.84851 | 0.122354 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −22.3972 | −0.960272 | ||||||||
\(545\) | −3.84125 | −0.164541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.2066 | 1.67635 | 0.838177 | − | 0.545399i | \(-0.183622\pi\) | ||||
0.838177 | + | 0.545399i | \(0.183622\pi\) | |||||||
\(548\) | −40.0844 | −1.71232 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.69190 | −0.285344 | ||||||||
\(551\) | −4.20529 | −0.179151 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.93671 | 0.0822829 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.8727 | 1.18206 | ||||||||
\(557\) | 7.47685 | 0.316804 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.71659 | 0.0726039 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.34512 | 0.225470 | ||||||||
\(563\) | 18.2725 | 0.770096 | 0.385048 | − | 0.922897i | \(-0.374185\pi\) | ||||
0.385048 | + | 0.922897i | \(0.374185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.834192 | −0.0350947 | ||||||||
\(566\) | −1.43023 | −0.0601172 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.02743 | −0.127028 | ||||||||
\(569\) | −26.0547 | −1.09227 | −0.546136 | − | 0.837697i | \(-0.683902\pi\) | ||||
−0.546136 | + | 0.837697i | \(0.683902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.26065 | −0.0946052 | −0.0473026 | − | 0.998881i | \(-0.515063\pi\) | ||||
−0.0473026 | + | 0.998881i | \(0.515063\pi\) | |||||||
\(572\) | −8.10306 | −0.338806 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.72794 | −0.113763 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8836 | 1.49385 | 0.746927 | − | 0.664906i | \(-0.231529\pi\) | ||||
0.746927 | + | 0.664906i | \(0.231529\pi\) | |||||||
\(578\) | −7.14269 | −0.297097 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.37903 | 0.0987838 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.7186 | −1.64498 | ||||||||
\(584\) | 6.00584 | 0.248523 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.46648 | −0.101889 | ||||||||
\(587\) | −21.2452 | −0.876885 | −0.438443 | − | 0.898759i | \(-0.644470\pi\) | ||||
−0.438443 | + | 0.898759i | \(0.644470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.806020 | 0.0332115 | ||||||||
\(590\) | 1.11063 | 0.0457239 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14.9709 | 0.615300 | ||||||||
\(593\) | 19.0481 | 0.782214 | 0.391107 | − | 0.920345i | \(-0.372092\pi\) | ||||
0.391107 | + | 0.920345i | \(0.372092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25.7298 | 1.05394 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.176529 | 0.00721879 | ||||||||
\(599\) | 21.9481 | 0.896776 | 0.448388 | − | 0.893839i | \(-0.351998\pi\) | ||||
0.448388 | + | 0.893839i | \(0.351998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1249 | 0.453794 | 0.226897 | − | 0.973919i | \(-0.427142\pi\) | ||||
0.226897 | + | 0.973919i | \(0.427142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.1811 | 0.658401 | ||||||||
\(605\) | 2.01118 | 0.0817662 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.29441 | −0.336660 | −0.168330 | − | 0.985731i | \(-0.553837\pi\) | ||||
−0.168330 | + | 0.985731i | \(0.553837\pi\) | |||||||
\(608\) | −3.33634 | −0.135306 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.175297 | −0.00709758 | ||||||||
\(611\) | −4.42810 | −0.179142 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.9909 | −1.00937 | −0.504686 | − | 0.863303i | \(-0.668392\pi\) | ||||
−0.504686 | + | 0.863303i | \(0.668392\pi\) | |||||||
\(614\) | 2.23842 | 0.0903354 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.5367 | 1.18910 | 0.594551 | − | 0.804058i | \(-0.297330\pi\) | ||||
0.594551 | + | 0.804058i | \(0.297330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2203 | −0.973494 | −0.486747 | − | 0.873543i | \(-0.661817\pi\) | ||||
−0.486747 | + | 0.873543i | \(0.661817\pi\) | |||||||
\(620\) | −0.455984 | −0.0183128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.6523 | 0.427119 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8409 | 0.953636 | ||||||||
\(626\) | 4.08958 | 0.163453 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.4472 | 1.05536 | ||||||||
\(629\) | 27.6346 | 1.10187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9592 | 0.913992 | 0.456996 | − | 0.889469i | \(-0.348925\pi\) | ||||
0.456996 | + | 0.889469i | \(0.348925\pi\) | |||||||
\(632\) | 15.5819 | 0.619815 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.00236 | −0.0398090 | ||||||||
\(635\) | −1.87053 | −0.0742296 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.11251 | −0.241996 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.49138 | 0.0984805 | ||||||||
\(641\) | −40.5768 | −1.60269 | −0.801344 | − | 0.598204i | \(-0.795881\pi\) | ||||
−0.801344 | + | 0.598204i | \(0.795881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.87685 | 0.389505 | 0.194752 | − | 0.980852i | \(-0.437610\pi\) | ||||
0.194752 | + | 0.980852i | \(0.437610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.87062 | −0.0735986 | ||||||||
\(647\) | −44.6596 | −1.75575 | −0.877876 | − | 0.478888i | \(-0.841040\pi\) | ||||
−0.877876 | + | 0.478888i | \(0.841040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.3960 | 2.09597 | ||||||||
\(650\) | −1.56791 | −0.0614984 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.5127 | −1.31246 | ||||||||
\(653\) | 0.169205 | 0.00662149 | 0.00331074 | − | 0.999995i | \(-0.498946\pi\) | ||||
0.00331074 | + | 0.999995i | \(0.498946\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.65528 | −0.103750 | ||||||||
\(656\) | −3.33212 | −0.130097 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3418 | 1.29881 | 0.649405 | − | 0.760443i | \(-0.275018\pi\) | ||||
0.649405 | + | 0.760443i | \(0.275018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.0200 | 1.43991 | 0.719956 | − | 0.694019i | \(-0.244162\pi\) | ||||
0.719956 | + | 0.694019i | \(0.244162\pi\) | |||||||
\(662\) | −1.99451 | −0.0775187 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.8843 | 0.538814 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.49175 | −0.0964811 | ||||||||
\(668\) | −14.1489 | −0.547439 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.352756 | 0.0136282 | ||||||||
\(671\) | −8.42781 | −0.325352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6406 | 1.25820 | 0.629102 | − | 0.777323i | \(-0.283423\pi\) | ||||
0.629102 | + | 0.777323i | \(0.283423\pi\) | |||||||
\(674\) | 5.05176 | 0.194587 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.89854 | −0.0730207 | ||||||||
\(677\) | 34.7106 | 1.33404 | 0.667018 | − | 0.745042i | \(-0.267571\pi\) | ||||
0.667018 | + | 0.745042i | \(0.267571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.17306 | 0.0833331 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.17157 | 0.0448618 | ||||||||
\(683\) | −25.9340 | −0.992337 | −0.496169 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496169 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.88432 | 0.224828 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.83902 | −0.222611 | ||||||||
\(689\) | −9.30603 | −0.354531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3626 | 1.45938 | 0.729691 | − | 0.683777i | \(-0.239664\pi\) | ||||
0.729691 | + | 0.683777i | \(0.239664\pi\) | |||||||
\(692\) | 36.4227 | 1.38458 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.18759 | 0.158959 | ||||||||
\(695\) | −4.09165 | −0.155205 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.15073 | −0.232976 | ||||||||
\(698\) | 9.51575 | 0.360176 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.2477 | −0.991363 | −0.495682 | − | 0.868504i | \(-0.665082\pi\) | ||||
−0.495682 | + | 0.868504i | \(0.665082\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.11652 | 0.155257 | ||||||||
\(704\) | 24.1863 | 0.911556 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.210726 | −0.00793078 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.9709 | 1.31336 | 0.656679 | − | 0.754170i | \(-0.271961\pi\) | ||||
0.656679 | + | 0.754170i | \(0.271961\pi\) | |||||||
\(710\) | 0.216428 | 0.00812238 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.1286 | 0.566967 | ||||||||
\(713\) | 0.477590 | 0.0178859 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.18951 | 0.0444853 | ||||||||
\(716\) | 37.2726 | 1.39294 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.22983 | 0.157856 | ||||||||
\(719\) | 14.2166 | 0.530190 | 0.265095 | − | 0.964222i | \(-0.414597\pi\) | ||||
0.265095 | + | 0.964222i | \(0.414597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.77341 | 0.214864 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25.7544 | 0.957154 | ||||||||
\(725\) | 22.1315 | 0.821942 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.566912 | −0.0210256 | −0.0105128 | − | 0.999945i | \(-0.503346\pi\) | ||||
−0.0105128 | + | 0.999945i | \(0.503346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.429350 | −0.0158910 | ||||||||
\(731\) | −10.7782 | −0.398646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.2007 | −1.04162 | −0.520809 | − | 0.853673i | \(-0.674370\pi\) | ||||
−0.520809 | + | 0.853673i | \(0.674370\pi\) | |||||||
\(734\) | 11.4815 | 0.423790 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.97687 | −0.0728686 | ||||||||
\(737\) | 16.9595 | 0.624713 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.6598 | −1.64284 | −0.821419 | − | 0.570325i | \(-0.806817\pi\) | ||||
−0.821419 | + | 0.570325i | \(0.806817\pi\) | |||||||
\(740\) | −2.32881 | −0.0856086 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.31876 | −0.121754 | −0.0608768 | − | 0.998145i | \(-0.519390\pi\) | ||||
−0.0608768 | + | 0.998145i | \(0.519390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.77709 | −0.138382 | ||||||||
\(746\) | 1.89673 | 0.0694443 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 50.8779 | 1.86028 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.1595 | −1.21001 | −0.605004 | − | 0.796223i | \(-0.706828\pi\) | ||||
−0.605004 | + | 0.796223i | \(0.706828\pi\) | |||||||
\(752\) | 15.0623 | 0.549266 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.43215 | −0.0521560 | ||||||||
\(755\) | −2.37536 | −0.0864482 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8780 | 0.686133 | 0.343067 | − | 0.939311i | \(-0.388534\pi\) | ||||
0.343067 | + | 0.939311i | \(0.388534\pi\) | |||||||
\(758\) | 5.98071 | 0.217229 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.323704 | 0.0117420 | ||||||||
\(761\) | 28.3937 | 1.02927 | 0.514635 | − | 0.857409i | \(-0.327927\pi\) | ||||
0.514635 | + | 0.857409i | \(0.327927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.43032 | 0.196462 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.58112 | 0.129391 | ||||||||
\(767\) | 12.5106 | 0.451732 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.8171 | −1.32766 | −0.663830 | − | 0.747884i | \(-0.731070\pi\) | ||||
−0.663830 | + | 0.747884i | \(0.731070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.604108 | −0.0217423 | ||||||||
\(773\) | −14.3835 | −0.517337 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.24190 | −0.152373 | ||||||||
\(776\) | −16.0316 | −0.575500 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.26453 | −0.117039 | ||||||||
\(779\) | −0.916226 | −0.0328272 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4052 | 0.372329 | ||||||||
\(782\) | −1.10840 | −0.0396362 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.88240 | −0.138569 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1507 | −1.32428 | −0.662140 | − | 0.749380i | \(-0.730352\pi\) | ||||
−0.662140 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(788\) | −4.09634 | −0.145926 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.11393 | −0.0396319 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.97463 | −0.0701211 | ||||||||
\(794\) | −1.35264 | −0.0480034 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.1469 | 0.926753 | ||||||||
\(797\) | −23.7554 | −0.841460 | −0.420730 | − | 0.907186i | \(-0.638226\pi\) | ||||
−0.420730 | + | 0.907186i | \(0.638226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.8034 | 0.983613 | ||||||||
\(800\) | 17.5584 | 0.620782 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.10981 | −0.180434 | ||||||||
\(803\) | −20.6420 | −0.728439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.274498 | 0.00966879 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.33742 | 0.222950 | ||||||||
\(809\) | −45.9182 | −1.61440 | −0.807200 | − | 0.590279i | \(-0.799018\pi\) | ||||
−0.807200 | + | 0.590279i | \(0.799018\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.21250 | 0.323495 | 0.161747 | − | 0.986832i | \(-0.448287\pi\) | ||||
0.161747 | + | 0.986832i | \(0.448287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.98347 | 0.209721 | ||||||||
\(815\) | 4.91960 | 0.172326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.60554 | −0.0561708 | ||||||||
\(818\) | 3.32391 | 0.116218 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.518330 | 0.0181009 | ||||||||
\(821\) | 9.22432 | 0.321931 | 0.160965 | − | 0.986960i | \(-0.448539\pi\) | ||||
0.160965 | + | 0.986960i | \(0.448539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.3510 | 1.12768 | 0.563842 | − | 0.825883i | \(-0.309323\pi\) | ||||
0.563842 | + | 0.825883i | \(0.309323\pi\) | |||||||
\(824\) | −0.448398 | −0.0156207 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.5118 | 0.887133 | 0.443566 | − | 0.896242i | \(-0.353713\pi\) | ||||
0.443566 | + | 0.896242i | \(0.353713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.2508 | 1.29377 | 0.646887 | − | 0.762586i | \(-0.276071\pi\) | ||||
0.646887 | + | 0.762586i | \(0.276071\pi\) | |||||||
\(830\) | −0.992570 | −0.0344526 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.66683 | 0.196462 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.07704 | 0.0718789 | ||||||||
\(836\) | 7.57888 | 0.262121 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.29642 | 0.286595 | ||||||||
\(839\) | 24.1576 | 0.834012 | 0.417006 | − | 0.908904i | \(-0.363079\pi\) | ||||
0.417006 | + | 0.908904i | \(0.363079\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.78471 | −0.302921 | ||||||||
\(842\) | −6.20833 | −0.213953 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.59946 | 0.330427 | ||||||||
\(845\) | 0.278702 | 0.00958764 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 31.6547 | 1.08703 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.84465 | 0.337669 | ||||||||
\(851\) | 2.43915 | 0.0836131 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.3757 | 1.34820 | 0.674100 | − | 0.738640i | \(-0.264532\pi\) | ||||
0.674100 | + | 0.738640i | \(0.264532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.4741 | −0.563074 | ||||||||
\(857\) | 50.6221 | 1.72922 | 0.864610 | − | 0.502444i | \(-0.167566\pi\) | ||||
0.864610 | + | 0.502444i | \(0.167566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7350 | −0.570991 | −0.285496 | − | 0.958380i | \(-0.592158\pi\) | ||||
−0.285496 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(860\) | 0.908292 | 0.0309725 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.22532 | 0.0417345 | ||||||||
\(863\) | −19.8012 | −0.674040 | −0.337020 | − | 0.941497i | \(-0.609419\pi\) | ||||
−0.337020 | + | 0.941497i | \(0.609419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.34679 | −0.181796 | ||||||||
\(866\) | 0.428142 | 0.0145489 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.5548 | −1.81672 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.97361 | 0.134641 | ||||||||
\(872\) | −17.1153 | −0.579597 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.165109 | −0.00558490 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7398 | −0.700333 | −0.350167 | − | 0.936687i | \(-0.613875\pi\) | ||||
−0.350167 | + | 0.936687i | \(0.613875\pi\) | |||||||
\(878\) | 11.5303 | 0.389129 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.04616 | −0.136396 | ||||||||
\(881\) | −1.62325 | −0.0546888 | −0.0273444 | − | 0.999626i | \(-0.508705\pi\) | ||||
−0.0273444 | + | 0.999626i | \(0.508705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8833 | −0.399904 | −0.199952 | − | 0.979806i | \(-0.564079\pi\) | ||||
−0.199952 | + | 0.979806i | \(0.564079\pi\) | |||||||
\(884\) | 11.9206 | 0.400934 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.56404 | 0.119736 | ||||||||
\(887\) | 31.7030 | 1.06448 | 0.532241 | − | 0.846593i | \(-0.321350\pi\) | ||||
0.532241 | + | 0.846593i | \(0.321350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.08152 | −0.0362528 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.4929 | 1.52321 | ||||||||
\(893\) | 4.14165 | 0.138595 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.47155 | −0.182894 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.30782 | −0.110383 | ||||||||
\(899\) | −3.87463 | −0.129226 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.4311 | 1.94662 | ||||||||
\(902\) | −1.33176 | −0.0443428 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.71688 | −0.123621 | ||||||||
\(905\) | −3.78070 | −0.125675 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.45928 | −0.148068 | −0.0740341 | − | 0.997256i | \(-0.523587\pi\) | ||||
−0.0740341 | + | 0.997256i | \(0.523587\pi\) | |||||||
\(908\) | −35.7722 | −1.18714 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.4395 | 1.53861 | 0.769305 | − | 0.638882i | \(-0.220603\pi\) | ||||
0.769305 | + | 0.638882i | \(0.220603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.7200 | −1.57930 | ||||||||
\(914\) | 8.60452 | 0.284612 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.0142 | 1.18994 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.5628 | −0.645317 | −0.322658 | − | 0.946515i | \(-0.604577\pi\) | ||||
−0.322658 | + | 0.946515i | \(0.604577\pi\) | |||||||
\(920\) | 0.191804 | 0.00632358 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.54180 | 0.182509 | ||||||||
\(923\) | 2.43794 | 0.0802457 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.6643 | −0.712317 | ||||||||
\(926\) | −1.77715 | −0.0584009 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.0381 | 0.526478 | ||||||||
\(929\) | 18.1377 | 0.595078 | 0.297539 | − | 0.954710i | \(-0.403834\pi\) | ||||
0.297539 | + | 0.954710i | \(0.403834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −51.8754 | −1.69923 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.353453 | −0.0115653 | ||||||||
\(935\) | −7.46878 | −0.244255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.3697 | 1.31882 | 0.659410 | − | 0.751784i | \(-0.270806\pi\) | ||||
0.659410 | + | 0.751784i | \(0.270806\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.34303 | −0.0764211 | ||||||||
\(941\) | −21.5312 | −0.701898 | −0.350949 | − | 0.936395i | \(-0.614141\pi\) | ||||
−0.350949 | + | 0.936395i | \(0.614141\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.542890 | −0.0176789 | ||||||||
\(944\) | −42.5552 | −1.38505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.33370 | −0.0758752 | ||||||||
\(947\) | −55.9123 | −1.81691 | −0.908454 | − | 0.417986i | \(-0.862736\pi\) | ||||
−0.908454 | + | 0.417986i | \(0.862736\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.83639 | −0.156996 | ||||||||
\(950\) | 1.46648 | 0.0475789 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2497 | 0.688346 | 0.344173 | − | 0.938906i | \(-0.388159\pi\) | ||||
0.344173 | + | 0.938906i | \(0.388159\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.797161 | −0.0257955 | ||||||||
\(956\) | −45.3274 | −1.46599 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.16321 | 0.296050 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2574 | −0.976044 | ||||||||
\(962\) | 1.40192 | 0.0451998 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.1248 | 1.00246 | ||||||||
\(965\) | 0.0886819 | 0.00285477 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.4550 | 1.68684 | 0.843419 | − | 0.537257i | \(-0.180539\pi\) | ||||
0.843419 | + | 0.537257i | \(0.180539\pi\) | |||||||
\(968\) | 8.96114 | 0.288022 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.14608 | 0.0367984 | ||||||||
\(971\) | −16.7283 | −0.536836 | −0.268418 | − | 0.963302i | \(-0.586501\pi\) | ||||
−0.268418 | + | 0.963302i | \(0.586501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.56674 | 0.0822436 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.71675 | 0.214998 | ||||||||
\(977\) | 10.9472 | 0.350232 | 0.175116 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175116 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.9967 | −1.66182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.7284 | 0.342357 | ||||||||
\(983\) | −2.17536 | −0.0693832 | −0.0346916 | − | 0.999398i | \(-0.511045\pi\) | ||||
−0.0346916 | + | 0.999398i | \(0.511045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.601336 | 0.0191601 | ||||||||
\(986\) | 8.99228 | 0.286373 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.77572 | 0.0564933 | ||||||||
\(989\) | −0.951330 | −0.0302505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0099 | 0.762700 | 0.381350 | − | 0.924431i | \(-0.375459\pi\) | ||||
0.381350 | + | 0.924431i | \(0.375459\pi\) | |||||||
\(992\) | −3.07400 | −0.0975996 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.83832 | −0.121683 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5083 | −0.839527 | −0.419763 | − | 0.907634i | \(-0.637887\pi\) | ||||
−0.419763 | + | 0.907634i | \(0.637887\pi\) | |||||||
\(998\) | −1.58753 | −0.0502524 | ||||||||
\(999\) | 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 | 5733.2.a.ca.1.6 | ✓ | 12 | |
3.2 | odd | 2 | inner | 5733.2.a.ca.1.7 | yes | 12 | |
7.6 | odd | 2 | 5733.2.a.cb.1.6 | yes | 12 | ||
21.20 | even | 2 | 5733.2.a.cb.1.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5733.2.a.ca.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
5733.2.a.ca.1.7 | yes | 12 | 3.2 | odd | 2 | inner | |
5733.2.a.cb.1.6 | yes | 12 | 7.6 | odd | 2 | ||
5733.2.a.cb.1.7 | yes | 12 | 21.20 | even | 2 |