Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, 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("546.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.27492 | 1.46459 | 0.732294 | − | 0.680989i | \(-0.238450\pi\) | ||||
0.732294 | + | 0.680989i | \(0.238450\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.27492 | −1.03562 | ||||||||
\(11\) | 5.27492 | 1.59045 | 0.795224 | − | 0.606316i | \(-0.207353\pi\) | ||||
0.795224 | + | 0.606316i | \(0.207353\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.27492 | −0.845580 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.27492 | −1.76443 | −0.882213 | − | 0.470850i | \(-0.843947\pi\) | ||||
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.27492 | 1.21015 | 0.605075 | − | 0.796169i | \(-0.293143\pi\) | ||||
0.605075 | + | 0.796169i | \(0.293143\pi\) | |||||||
\(20\) | 3.27492 | 0.732294 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.27492 | −1.12462 | ||||||||
\(23\) | −5.27492 | −1.09990 | −0.549948 | − | 0.835199i | \(-0.685353\pi\) | ||||
−0.549948 | + | 0.835199i | \(0.685353\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.72508 | 1.14502 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.725083 | 0.134644 | 0.0673222 | − | 0.997731i | \(-0.478554\pi\) | ||||
0.0673222 | + | 0.997731i | \(0.478554\pi\) | |||||||
\(30\) | 3.27492 | 0.597915 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.27492 | −0.918245 | ||||||||
\(34\) | 7.27492 | 1.24764 | ||||||||
\(35\) | 3.27492 | 0.553562 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.27492 | 0.538393 | 0.269197 | − | 0.963085i | \(-0.413242\pi\) | ||||
0.269197 | + | 0.963085i | \(0.413242\pi\) | |||||||
\(38\) | −5.27492 | −0.855705 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −3.27492 | −0.517810 | ||||||||
\(41\) | −8.54983 | −1.33526 | −0.667630 | − | 0.744493i | \(-0.732691\pi\) | ||||
−0.667630 | + | 0.744493i | \(0.732691\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 5.27492 | 0.804417 | 0.402209 | − | 0.915548i | \(-0.368243\pi\) | ||||
0.402209 | + | 0.915548i | \(0.368243\pi\) | |||||||
\(44\) | 5.27492 | 0.795224 | ||||||||
\(45\) | 3.27492 | 0.488196 | ||||||||
\(46\) | 5.27492 | 0.777744 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.72508 | −0.809649 | ||||||||
\(51\) | 7.27492 | 1.01869 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 17.2749 | 2.32935 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −5.27492 | −0.698680 | ||||||||
\(58\) | −0.725083 | −0.0952080 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | −3.27492 | −0.422790 | ||||||||
\(61\) | −4.72508 | −0.604985 | −0.302492 | − | 0.953152i | \(-0.597819\pi\) | ||||
−0.302492 | + | 0.953152i | \(0.597819\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.27492 | −0.406203 | ||||||||
\(66\) | 5.27492 | 0.649297 | ||||||||
\(67\) | −2.54983 | −0.311512 | −0.155756 | − | 0.987796i | \(-0.549781\pi\) | ||||
−0.155756 | + | 0.987796i | \(0.549781\pi\) | |||||||
\(68\) | −7.27492 | −0.882213 | ||||||||
\(69\) | 5.27492 | 0.635025 | ||||||||
\(70\) | −3.27492 | −0.391427 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.82475 | 1.14990 | 0.574950 | − | 0.818188i | \(-0.305021\pi\) | ||||
0.574950 | + | 0.818188i | \(0.305021\pi\) | |||||||
\(74\) | −3.27492 | −0.380701 | ||||||||
\(75\) | −5.72508 | −0.661076 | ||||||||
\(76\) | 5.27492 | 0.605075 | ||||||||
\(77\) | 5.27492 | 0.601133 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −2.54983 | −0.286879 | −0.143439 | − | 0.989659i | \(-0.545816\pi\) | ||||
−0.143439 | + | 0.989659i | \(0.545816\pi\) | |||||||
\(80\) | 3.27492 | 0.366147 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.54983 | 0.944171 | ||||||||
\(83\) | 10.5498 | 1.15799 | 0.578997 | − | 0.815329i | \(-0.303444\pi\) | ||||
0.578997 | + | 0.815329i | \(0.303444\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −23.8248 | −2.58416 | ||||||||
\(86\) | −5.27492 | −0.568809 | ||||||||
\(87\) | −0.725083 | −0.0777370 | ||||||||
\(88\) | −5.27492 | −0.562308 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | −3.27492 | −0.345207 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −5.27492 | −0.549948 | ||||||||
\(93\) | −8.00000 | −0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.2749 | 1.77237 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −15.0997 | −1.53314 | −0.766570 | − | 0.642161i | \(-0.778038\pi\) | ||||
−0.766570 | + | 0.642161i | \(0.778038\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 5.27492 | 0.530149 | ||||||||
\(100\) | 5.72508 | 0.572508 | ||||||||
\(101\) | −12.5498 | −1.24876 | −0.624378 | − | 0.781123i | \(-0.714647\pi\) | ||||
−0.624378 | + | 0.781123i | \(0.714647\pi\) | |||||||
\(102\) | −7.27492 | −0.720324 | ||||||||
\(103\) | 2.72508 | 0.268510 | 0.134255 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134255 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −3.27492 | −0.319599 | ||||||||
\(106\) | −10.0000 | −0.971286 | ||||||||
\(107\) | −14.5498 | −1.40659 | −0.703293 | − | 0.710900i | \(-0.748288\pi\) | ||||
−0.703293 | + | 0.710900i | \(0.748288\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.27492 | −0.696811 | −0.348405 | − | 0.937344i | \(-0.613277\pi\) | ||||
−0.348405 | + | 0.937344i | \(0.613277\pi\) | |||||||
\(110\) | −17.2749 | −1.64710 | ||||||||
\(111\) | −3.27492 | −0.310841 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 5.27492 | 0.494041 | ||||||||
\(115\) | −17.2749 | −1.61089 | ||||||||
\(116\) | 0.725083 | 0.0673222 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −8.00000 | −0.736460 | ||||||||
\(119\) | −7.27492 | −0.666891 | ||||||||
\(120\) | 3.27492 | 0.298958 | ||||||||
\(121\) | 16.8248 | 1.52952 | ||||||||
\(122\) | 4.72508 | 0.427789 | ||||||||
\(123\) | 8.54983 | 0.770913 | ||||||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | 2.37459 | 0.212389 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −5.45017 | −0.483624 | −0.241812 | − | 0.970323i | \(-0.577742\pi\) | ||||
−0.241812 | + | 0.970323i | \(0.577742\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.27492 | −0.464431 | ||||||||
\(130\) | 3.27492 | 0.287229 | ||||||||
\(131\) | −15.8248 | −1.38261 | −0.691307 | − | 0.722561i | \(-0.742965\pi\) | ||||
−0.691307 | + | 0.722561i | \(0.742965\pi\) | |||||||
\(132\) | −5.27492 | −0.459123 | ||||||||
\(133\) | 5.27492 | 0.457393 | ||||||||
\(134\) | 2.54983 | 0.220272 | ||||||||
\(135\) | −3.27492 | −0.281860 | ||||||||
\(136\) | 7.27492 | 0.623819 | ||||||||
\(137\) | 20.3746 | 1.74072 | 0.870359 | − | 0.492417i | \(-0.163887\pi\) | ||||
0.870359 | + | 0.492417i | \(0.163887\pi\) | |||||||
\(138\) | −5.27492 | −0.449031 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 3.27492 | 0.276781 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.27492 | −0.441111 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.37459 | 0.197199 | ||||||||
\(146\) | −9.82475 | −0.813102 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 3.27492 | 0.269197 | ||||||||
\(149\) | 7.45017 | 0.610341 | 0.305171 | − | 0.952298i | \(-0.401286\pi\) | ||||
0.305171 | + | 0.952298i | \(0.401286\pi\) | |||||||
\(150\) | 5.72508 | 0.467451 | ||||||||
\(151\) | −1.27492 | −0.103751 | −0.0518756 | − | 0.998654i | \(-0.516520\pi\) | ||||
−0.0518756 | + | 0.998654i | \(0.516520\pi\) | |||||||
\(152\) | −5.27492 | −0.427852 | ||||||||
\(153\) | −7.27492 | −0.588142 | ||||||||
\(154\) | −5.27492 | −0.425065 | ||||||||
\(155\) | 26.1993 | 2.10438 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 24.3746 | 1.94530 | 0.972652 | − | 0.232268i | \(-0.0746146\pi\) | ||||
0.972652 | + | 0.232268i | \(0.0746146\pi\) | |||||||
\(158\) | 2.54983 | 0.202854 | ||||||||
\(159\) | −10.0000 | −0.793052 | ||||||||
\(160\) | −3.27492 | −0.258905 | ||||||||
\(161\) | −5.27492 | −0.415722 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.54983 | −0.199718 | −0.0998592 | − | 0.995002i | \(-0.531839\pi\) | ||||
−0.0998592 | + | 0.995002i | \(0.531839\pi\) | |||||||
\(164\) | −8.54983 | −0.667630 | ||||||||
\(165\) | −17.2749 | −1.34485 | ||||||||
\(166\) | −10.5498 | −0.818826 | ||||||||
\(167\) | −9.27492 | −0.717715 | −0.358857 | − | 0.933392i | \(-0.616834\pi\) | ||||
−0.358857 | + | 0.933392i | \(0.616834\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 23.8248 | 1.82728 | ||||||||
\(171\) | 5.27492 | 0.403383 | ||||||||
\(172\) | 5.27492 | 0.402209 | ||||||||
\(173\) | −23.0997 | −1.75624 | −0.878118 | − | 0.478445i | \(-0.841201\pi\) | ||||
−0.878118 | + | 0.478445i | \(0.841201\pi\) | |||||||
\(174\) | 0.725083 | 0.0549684 | ||||||||
\(175\) | 5.72508 | 0.432776 | ||||||||
\(176\) | 5.27492 | 0.397612 | ||||||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 14.0000 | 1.04934 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 3.27492 | 0.244098 | ||||||||
\(181\) | −11.0997 | −0.825032 | −0.412516 | − | 0.910950i | \(-0.635350\pi\) | ||||
−0.412516 | + | 0.910950i | \(0.635350\pi\) | |||||||
\(182\) | 1.00000 | 0.0741249 | ||||||||
\(183\) | 4.72508 | 0.349288 | ||||||||
\(184\) | 5.27492 | 0.388872 | ||||||||
\(185\) | 10.7251 | 0.788524 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | −38.3746 | −2.80623 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −17.2749 | −1.25325 | ||||||||
\(191\) | −5.27492 | −0.381680 | −0.190840 | − | 0.981621i | \(-0.561121\pi\) | ||||
−0.190840 | + | 0.981621i | \(0.561121\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.45017 | −0.248348 | −0.124174 | − | 0.992260i | \(-0.539628\pi\) | ||||
−0.124174 | + | 0.992260i | \(0.539628\pi\) | |||||||
\(194\) | 15.0997 | 1.08409 | ||||||||
\(195\) | 3.27492 | 0.234522 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 12.5498 | 0.894139 | 0.447069 | − | 0.894499i | \(-0.352468\pi\) | ||||
0.447069 | + | 0.894499i | \(0.352468\pi\) | |||||||
\(198\) | −5.27492 | −0.374872 | ||||||||
\(199\) | −15.8248 | −1.12179 | −0.560893 | − | 0.827888i | \(-0.689542\pi\) | ||||
−0.560893 | + | 0.827888i | \(0.689542\pi\) | |||||||
\(200\) | −5.72508 | −0.404824 | ||||||||
\(201\) | 2.54983 | 0.179851 | ||||||||
\(202\) | 12.5498 | 0.883003 | ||||||||
\(203\) | 0.725083 | 0.0508908 | ||||||||
\(204\) | 7.27492 | 0.509346 | ||||||||
\(205\) | −28.0000 | −1.95560 | ||||||||
\(206\) | −2.72508 | −0.189866 | ||||||||
\(207\) | −5.27492 | −0.366632 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 27.8248 | 1.92468 | ||||||||
\(210\) | 3.27492 | 0.225991 | ||||||||
\(211\) | 23.8248 | 1.64016 | 0.820082 | − | 0.572246i | \(-0.193928\pi\) | ||||
0.820082 | + | 0.572246i | \(0.193928\pi\) | |||||||
\(212\) | 10.0000 | 0.686803 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.5498 | 0.994606 | ||||||||
\(215\) | 17.2749 | 1.17814 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.00000 | 0.543075 | ||||||||
\(218\) | 7.27492 | 0.492720 | ||||||||
\(219\) | −9.82475 | −0.663895 | ||||||||
\(220\) | 17.2749 | 1.16467 | ||||||||
\(221\) | 7.27492 | 0.489364 | ||||||||
\(222\) | 3.27492 | 0.219798 | ||||||||
\(223\) | −23.6495 | −1.58369 | −0.791844 | − | 0.610723i | \(-0.790879\pi\) | ||||
−0.791844 | + | 0.610723i | \(0.790879\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 5.72508 | 0.381672 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | −5.45017 | −0.361740 | −0.180870 | − | 0.983507i | \(-0.557891\pi\) | ||||
−0.180870 | + | 0.983507i | \(0.557891\pi\) | |||||||
\(228\) | −5.27492 | −0.349340 | ||||||||
\(229\) | −11.0997 | −0.733487 | −0.366743 | − | 0.930322i | \(-0.619527\pi\) | ||||
−0.366743 | + | 0.930322i | \(0.619527\pi\) | |||||||
\(230\) | 17.2749 | 1.13907 | ||||||||
\(231\) | −5.27492 | −0.347064 | ||||||||
\(232\) | −0.725083 | −0.0476040 | ||||||||
\(233\) | 20.5498 | 1.34626 | 0.673132 | − | 0.739522i | \(-0.264948\pi\) | ||||
0.673132 | + | 0.739522i | \(0.264948\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | 2.54983 | 0.165630 | ||||||||
\(238\) | 7.27492 | 0.471563 | ||||||||
\(239\) | −5.09967 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(240\) | −3.27492 | −0.211395 | ||||||||
\(241\) | −15.0997 | −0.972655 | −0.486328 | − | 0.873777i | \(-0.661664\pi\) | ||||
−0.486328 | + | 0.873777i | \(0.661664\pi\) | |||||||
\(242\) | −16.8248 | −1.08154 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.72508 | −0.302492 | ||||||||
\(245\) | 3.27492 | 0.209227 | ||||||||
\(246\) | −8.54983 | −0.545118 | ||||||||
\(247\) | −5.27492 | −0.335635 | ||||||||
\(248\) | −8.00000 | −0.508001 | ||||||||
\(249\) | −10.5498 | −0.668569 | ||||||||
\(250\) | −2.37459 | −0.150182 | ||||||||
\(251\) | −28.9244 | −1.82569 | −0.912847 | − | 0.408303i | \(-0.866121\pi\) | ||||
−0.912847 | + | 0.408303i | \(0.866121\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −27.8248 | −1.74933 | ||||||||
\(254\) | 5.45017 | 0.341974 | ||||||||
\(255\) | 23.8248 | 1.49196 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 5.27492 | 0.328402 | ||||||||
\(259\) | 3.27492 | 0.203493 | ||||||||
\(260\) | −3.27492 | −0.203102 | ||||||||
\(261\) | 0.725083 | 0.0448815 | ||||||||
\(262\) | 15.8248 | 0.977656 | ||||||||
\(263\) | 28.0000 | 1.72655 | 0.863277 | − | 0.504730i | \(-0.168408\pi\) | ||||
0.863277 | + | 0.504730i | \(0.168408\pi\) | |||||||
\(264\) | 5.27492 | 0.324649 | ||||||||
\(265\) | 32.7492 | 2.01177 | ||||||||
\(266\) | −5.27492 | −0.323426 | ||||||||
\(267\) | 14.0000 | 0.856786 | ||||||||
\(268\) | −2.54983 | −0.155756 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 3.27492 | 0.199305 | ||||||||
\(271\) | 13.4502 | 0.817039 | 0.408520 | − | 0.912750i | \(-0.366045\pi\) | ||||
0.408520 | + | 0.912750i | \(0.366045\pi\) | |||||||
\(272\) | −7.27492 | −0.441107 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | −20.3746 | −1.23087 | ||||||||
\(275\) | 30.1993 | 1.82109 | ||||||||
\(276\) | 5.27492 | 0.317513 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | −3.27492 | −0.195714 | ||||||||
\(281\) | −15.0997 | −0.900771 | −0.450385 | − | 0.892834i | \(-0.648713\pi\) | ||||
−0.450385 | + | 0.892834i | \(0.648713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.2749 | −1.02328 | ||||||||
\(286\) | 5.27492 | 0.311912 | ||||||||
\(287\) | −8.54983 | −0.504681 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 35.9244 | 2.11320 | ||||||||
\(290\) | −2.37459 | −0.139440 | ||||||||
\(291\) | 15.0997 | 0.885158 | ||||||||
\(292\) | 9.82475 | 0.574950 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 26.1993 | 1.52538 | ||||||||
\(296\) | −3.27492 | −0.190351 | ||||||||
\(297\) | −5.27492 | −0.306082 | ||||||||
\(298\) | −7.45017 | −0.431577 | ||||||||
\(299\) | 5.27492 | 0.305056 | ||||||||
\(300\) | −5.72508 | −0.330538 | ||||||||
\(301\) | 5.27492 | 0.304041 | ||||||||
\(302\) | 1.27492 | 0.0733632 | ||||||||
\(303\) | 12.5498 | 0.720969 | ||||||||
\(304\) | 5.27492 | 0.302537 | ||||||||
\(305\) | −15.4743 | −0.886053 | ||||||||
\(306\) | 7.27492 | 0.415879 | ||||||||
\(307\) | −9.09967 | −0.519346 | −0.259673 | − | 0.965697i | \(-0.583615\pi\) | ||||
−0.259673 | + | 0.965697i | \(0.583615\pi\) | |||||||
\(308\) | 5.27492 | 0.300566 | ||||||||
\(309\) | −2.72508 | −0.155025 | ||||||||
\(310\) | −26.1993 | −1.48802 | ||||||||
\(311\) | 18.5498 | 1.05186 | 0.525932 | − | 0.850526i | \(-0.323717\pi\) | ||||
0.525932 | + | 0.850526i | \(0.323717\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 17.6495 | 0.997609 | 0.498804 | − | 0.866715i | \(-0.333773\pi\) | ||||
0.498804 | + | 0.866715i | \(0.333773\pi\) | |||||||
\(314\) | −24.3746 | −1.37554 | ||||||||
\(315\) | 3.27492 | 0.184521 | ||||||||
\(316\) | −2.54983 | −0.143439 | ||||||||
\(317\) | −16.5498 | −0.929531 | −0.464766 | − | 0.885434i | \(-0.653861\pi\) | ||||
−0.464766 | + | 0.885434i | \(0.653861\pi\) | |||||||
\(318\) | 10.0000 | 0.560772 | ||||||||
\(319\) | 3.82475 | 0.214145 | ||||||||
\(320\) | 3.27492 | 0.183073 | ||||||||
\(321\) | 14.5498 | 0.812093 | ||||||||
\(322\) | 5.27492 | 0.293960 | ||||||||
\(323\) | −38.3746 | −2.13522 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.72508 | −0.317570 | ||||||||
\(326\) | 2.54983 | 0.141222 | ||||||||
\(327\) | 7.27492 | 0.402304 | ||||||||
\(328\) | 8.54983 | 0.472086 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 17.2749 | 0.950953 | ||||||||
\(331\) | 15.6495 | 0.860174 | 0.430087 | − | 0.902787i | \(-0.358483\pi\) | ||||
0.430087 | + | 0.902787i | \(0.358483\pi\) | |||||||
\(332\) | 10.5498 | 0.578997 | ||||||||
\(333\) | 3.27492 | 0.179464 | ||||||||
\(334\) | 9.27492 | 0.507501 | ||||||||
\(335\) | −8.35050 | −0.456236 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −28.3746 | −1.54566 | −0.772831 | − | 0.634612i | \(-0.781160\pi\) | ||||
−0.772831 | + | 0.634612i | \(0.781160\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | −23.8248 | −1.29208 | ||||||||
\(341\) | 42.1993 | 2.28522 | ||||||||
\(342\) | −5.27492 | −0.285235 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −5.27492 | −0.284404 | ||||||||
\(345\) | 17.2749 | 0.930050 | ||||||||
\(346\) | 23.0997 | 1.24185 | ||||||||
\(347\) | −25.0997 | −1.34742 | −0.673710 | − | 0.738995i | \(-0.735300\pi\) | ||||
−0.673710 | + | 0.738995i | \(0.735300\pi\) | |||||||
\(348\) | −0.725083 | −0.0388685 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −5.72508 | −0.306019 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −5.27492 | −0.281154 | ||||||||
\(353\) | −3.09967 | −0.164979 | −0.0824894 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824894 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(354\) | 8.00000 | 0.425195 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 7.27492 | 0.385029 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −32.0000 | −1.68890 | −0.844448 | − | 0.535638i | \(-0.820071\pi\) | ||||
−0.844448 | + | 0.535638i | \(0.820071\pi\) | |||||||
\(360\) | −3.27492 | −0.172603 | ||||||||
\(361\) | 8.82475 | 0.464461 | ||||||||
\(362\) | 11.0997 | 0.583386 | ||||||||
\(363\) | −16.8248 | −0.883070 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | 32.1752 | 1.68413 | ||||||||
\(366\) | −4.72508 | −0.246984 | ||||||||
\(367\) | −33.0997 | −1.72779 | −0.863894 | − | 0.503673i | \(-0.831982\pi\) | ||||
−0.863894 | + | 0.503673i | \(0.831982\pi\) | |||||||
\(368\) | −5.27492 | −0.274974 | ||||||||
\(369\) | −8.54983 | −0.445087 | ||||||||
\(370\) | −10.7251 | −0.557571 | ||||||||
\(371\) | 10.0000 | 0.519174 | ||||||||
\(372\) | −8.00000 | −0.414781 | ||||||||
\(373\) | 11.4502 | 0.592867 | 0.296434 | − | 0.955053i | \(-0.404203\pi\) | ||||
0.296434 | + | 0.955053i | \(0.404203\pi\) | |||||||
\(374\) | 38.3746 | 1.98430 | ||||||||
\(375\) | −2.37459 | −0.122623 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.725083 | −0.0373437 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −2.90033 | −0.148980 | −0.0744900 | − | 0.997222i | \(-0.523733\pi\) | ||||
−0.0744900 | + | 0.997222i | \(0.523733\pi\) | |||||||
\(380\) | 17.2749 | 0.886185 | ||||||||
\(381\) | 5.45017 | 0.279220 | ||||||||
\(382\) | 5.27492 | 0.269888 | ||||||||
\(383\) | 22.7251 | 1.16120 | 0.580599 | − | 0.814190i | \(-0.302819\pi\) | ||||
0.580599 | + | 0.814190i | \(0.302819\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 17.2749 | 0.880411 | ||||||||
\(386\) | 3.45017 | 0.175609 | ||||||||
\(387\) | 5.27492 | 0.268139 | ||||||||
\(388\) | −15.0997 | −0.766570 | ||||||||
\(389\) | −32.1993 | −1.63257 | −0.816286 | − | 0.577649i | \(-0.803970\pi\) | ||||
−0.816286 | + | 0.577649i | \(0.803970\pi\) | |||||||
\(390\) | −3.27492 | −0.165832 | ||||||||
\(391\) | 38.3746 | 1.94069 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 15.8248 | 0.798253 | ||||||||
\(394\) | −12.5498 | −0.632252 | ||||||||
\(395\) | −8.35050 | −0.420159 | ||||||||
\(396\) | 5.27492 | 0.265075 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 15.8248 | 0.793223 | ||||||||
\(399\) | −5.27492 | −0.264076 | ||||||||
\(400\) | 5.72508 | 0.286254 | ||||||||
\(401\) | 27.0997 | 1.35329 | 0.676646 | − | 0.736308i | \(-0.263433\pi\) | ||||
0.676646 | + | 0.736308i | \(0.263433\pi\) | |||||||
\(402\) | −2.54983 | −0.127174 | ||||||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | −12.5498 | −0.624378 | ||||||||
\(405\) | 3.27492 | 0.162732 | ||||||||
\(406\) | −0.725083 | −0.0359853 | ||||||||
\(407\) | 17.2749 | 0.856286 | ||||||||
\(408\) | −7.27492 | −0.360162 | ||||||||
\(409\) | −29.8248 | −1.47474 | −0.737370 | − | 0.675490i | \(-0.763932\pi\) | ||||
−0.737370 | + | 0.675490i | \(0.763932\pi\) | |||||||
\(410\) | 28.0000 | 1.38282 | ||||||||
\(411\) | −20.3746 | −1.00500 | ||||||||
\(412\) | 2.72508 | 0.134255 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 5.27492 | 0.259248 | ||||||||
\(415\) | 34.5498 | 1.69598 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | −27.8248 | −1.36095 | ||||||||
\(419\) | −5.27492 | −0.257697 | −0.128848 | − | 0.991664i | \(-0.541128\pi\) | ||||
−0.128848 | + | 0.991664i | \(0.541128\pi\) | |||||||
\(420\) | −3.27492 | −0.159800 | ||||||||
\(421\) | −27.0997 | −1.32076 | −0.660379 | − | 0.750933i | \(-0.729604\pi\) | ||||
−0.660379 | + | 0.750933i | \(0.729604\pi\) | |||||||
\(422\) | −23.8248 | −1.15977 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0000 | −0.485643 | ||||||||
\(425\) | −41.6495 | −2.02030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.72508 | −0.228663 | ||||||||
\(428\) | −14.5498 | −0.703293 | ||||||||
\(429\) | 5.27492 | 0.254675 | ||||||||
\(430\) | −17.2749 | −0.833070 | ||||||||
\(431\) | −26.5498 | −1.27886 | −0.639430 | − | 0.768849i | \(-0.720830\pi\) | ||||
−0.639430 | + | 0.768849i | \(0.720830\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −21.6495 | −1.04041 | −0.520204 | − | 0.854042i | \(-0.674144\pi\) | ||||
−0.520204 | + | 0.854042i | \(0.674144\pi\) | |||||||
\(434\) | −8.00000 | −0.384012 | ||||||||
\(435\) | −2.37459 | −0.113853 | ||||||||
\(436\) | −7.27492 | −0.348405 | ||||||||
\(437\) | −27.8248 | −1.33104 | ||||||||
\(438\) | 9.82475 | 0.469445 | ||||||||
\(439\) | 7.82475 | 0.373455 | 0.186728 | − | 0.982412i | \(-0.440212\pi\) | ||||
0.186728 | + | 0.982412i | \(0.440212\pi\) | |||||||
\(440\) | −17.2749 | −0.823549 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.27492 | −0.346033 | ||||||||
\(443\) | 22.5498 | 1.07137 | 0.535687 | − | 0.844416i | \(-0.320053\pi\) | ||||
0.535687 | + | 0.844416i | \(0.320053\pi\) | |||||||
\(444\) | −3.27492 | −0.155421 | ||||||||
\(445\) | −45.8488 | −2.17344 | ||||||||
\(446\) | 23.6495 | 1.11984 | ||||||||
\(447\) | −7.45017 | −0.352381 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 7.27492 | 0.343325 | 0.171662 | − | 0.985156i | \(-0.445086\pi\) | ||||
0.171662 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(450\) | −5.72508 | −0.269883 | ||||||||
\(451\) | −45.0997 | −2.12366 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 1.27492 | 0.0599008 | ||||||||
\(454\) | 5.45017 | 0.255789 | ||||||||
\(455\) | −3.27492 | −0.153530 | ||||||||
\(456\) | 5.27492 | 0.247021 | ||||||||
\(457\) | −3.45017 | −0.161392 | −0.0806960 | − | 0.996739i | \(-0.525714\pi\) | ||||
−0.0806960 | + | 0.996739i | \(0.525714\pi\) | |||||||
\(458\) | 11.0997 | 0.518653 | ||||||||
\(459\) | 7.27492 | 0.339564 | ||||||||
\(460\) | −17.2749 | −0.805447 | ||||||||
\(461\) | 34.9244 | 1.62659 | 0.813296 | − | 0.581850i | \(-0.197671\pi\) | ||||
0.813296 | + | 0.581850i | \(0.197671\pi\) | |||||||
\(462\) | 5.27492 | 0.245411 | ||||||||
\(463\) | 22.7251 | 1.05612 | 0.528062 | − | 0.849206i | \(-0.322919\pi\) | ||||
0.528062 | + | 0.849206i | \(0.322919\pi\) | |||||||
\(464\) | 0.725083 | 0.0336611 | ||||||||
\(465\) | −26.1993 | −1.21497 | ||||||||
\(466\) | −20.5498 | −0.951953 | ||||||||
\(467\) | −18.7251 | −0.866493 | −0.433247 | − | 0.901275i | \(-0.642632\pi\) | ||||
−0.433247 | + | 0.901275i | \(0.642632\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −2.54983 | −0.117740 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.3746 | −1.12312 | ||||||||
\(472\) | −8.00000 | −0.368230 | ||||||||
\(473\) | 27.8248 | 1.27938 | ||||||||
\(474\) | −2.54983 | −0.117118 | ||||||||
\(475\) | 30.1993 | 1.38564 | ||||||||
\(476\) | −7.27492 | −0.333445 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | 5.09967 | 0.233253 | ||||||||
\(479\) | 14.3746 | 0.656792 | 0.328396 | − | 0.944540i | \(-0.393492\pi\) | ||||
0.328396 | + | 0.944540i | \(0.393492\pi\) | |||||||
\(480\) | 3.27492 | 0.149479 | ||||||||
\(481\) | −3.27492 | −0.149323 | ||||||||
\(482\) | 15.0997 | 0.687771 | ||||||||
\(483\) | 5.27492 | 0.240017 | ||||||||
\(484\) | 16.8248 | 0.764761 | ||||||||
\(485\) | −49.4502 | −2.24542 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 42.1993 | 1.91223 | 0.956117 | − | 0.292984i | \(-0.0946484\pi\) | ||||
0.956117 | + | 0.292984i | \(0.0946484\pi\) | |||||||
\(488\) | 4.72508 | 0.213894 | ||||||||
\(489\) | 2.54983 | 0.115307 | ||||||||
\(490\) | −3.27492 | −0.147946 | ||||||||
\(491\) | −6.54983 | −0.295590 | −0.147795 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147795 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(492\) | 8.54983 | 0.385456 | ||||||||
\(493\) | −5.27492 | −0.237570 | ||||||||
\(494\) | 5.27492 | 0.237330 | ||||||||
\(495\) | 17.2749 | 0.776450 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.5498 | 0.472749 | ||||||||
\(499\) | −5.09967 | −0.228293 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(500\) | 2.37459 | 0.106195 | ||||||||
\(501\) | 9.27492 | 0.414373 | ||||||||
\(502\) | 28.9244 | 1.29096 | ||||||||
\(503\) | −18.5498 | −0.827096 | −0.413548 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413548 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −41.0997 | −1.82891 | ||||||||
\(506\) | 27.8248 | 1.23696 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −5.45017 | −0.241812 | ||||||||
\(509\) | 42.9244 | 1.90259 | 0.951296 | − | 0.308280i | \(-0.0997533\pi\) | ||||
0.951296 | + | 0.308280i | \(0.0997533\pi\) | |||||||
\(510\) | −23.8248 | −1.05498 | ||||||||
\(511\) | 9.82475 | 0.434621 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.27492 | −0.232893 | ||||||||
\(514\) | 14.0000 | 0.617514 | ||||||||
\(515\) | 8.92442 | 0.393257 | ||||||||
\(516\) | −5.27492 | −0.232215 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.27492 | −0.143892 | ||||||||
\(519\) | 23.0997 | 1.01396 | ||||||||
\(520\) | 3.27492 | 0.143615 | ||||||||
\(521\) | 3.27492 | 0.143477 | 0.0717384 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717384 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(522\) | −0.725083 | −0.0317360 | ||||||||
\(523\) | 36.0000 | 1.57417 | 0.787085 | − | 0.616844i | \(-0.211589\pi\) | ||||
0.787085 | + | 0.616844i | \(0.211589\pi\) | |||||||
\(524\) | −15.8248 | −0.691307 | ||||||||
\(525\) | −5.72508 | −0.249863 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | −58.1993 | −2.53520 | ||||||||
\(528\) | −5.27492 | −0.229561 | ||||||||
\(529\) | 4.82475 | 0.209772 | ||||||||
\(530\) | −32.7492 | −1.42253 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 5.27492 | 0.228697 | ||||||||
\(533\) | 8.54983 | 0.370334 | ||||||||
\(534\) | −14.0000 | −0.605839 | ||||||||
\(535\) | −47.6495 | −2.06007 | ||||||||
\(536\) | 2.54983 | 0.110136 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | 5.27492 | 0.227207 | ||||||||
\(540\) | −3.27492 | −0.140930 | ||||||||
\(541\) | −25.4743 | −1.09522 | −0.547612 | − | 0.836732i | \(-0.684463\pi\) | ||||
−0.547612 | + | 0.836732i | \(0.684463\pi\) | |||||||
\(542\) | −13.4502 | −0.577734 | ||||||||
\(543\) | 11.0997 | 0.476332 | ||||||||
\(544\) | 7.27492 | 0.311910 | ||||||||
\(545\) | −23.8248 | −1.02054 | ||||||||
\(546\) | −1.00000 | −0.0427960 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | 20.3746 | 0.870359 | ||||||||
\(549\) | −4.72508 | −0.201662 | ||||||||
\(550\) | −30.1993 | −1.28770 | ||||||||
\(551\) | 3.82475 | 0.162940 | ||||||||
\(552\) | −5.27492 | −0.224515 | ||||||||
\(553\) | −2.54983 | −0.108430 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −10.7251 | −0.455254 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 30.7492 | 1.30288 | 0.651442 | − | 0.758698i | \(-0.274164\pi\) | ||||
0.651442 | + | 0.758698i | \(0.274164\pi\) | |||||||
\(558\) | −8.00000 | −0.338667 | ||||||||
\(559\) | −5.27492 | −0.223105 | ||||||||
\(560\) | 3.27492 | 0.138391 | ||||||||
\(561\) | 38.3746 | 1.62018 | ||||||||
\(562\) | 15.0997 | 0.636941 | ||||||||
\(563\) | 2.37459 | 0.100077 | 0.0500384 | − | 0.998747i | \(-0.484066\pi\) | ||||
0.0500384 | + | 0.998747i | \(0.484066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.6495 | −0.826661 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0997 | −1.13608 | −0.568039 | − | 0.823002i | \(-0.692298\pi\) | ||||
−0.568039 | + | 0.823002i | \(0.692298\pi\) | |||||||
\(570\) | 17.2749 | 0.723567 | ||||||||
\(571\) | −6.90033 | −0.288770 | −0.144385 | − | 0.989522i | \(-0.546120\pi\) | ||||
−0.144385 | + | 0.989522i | \(0.546120\pi\) | |||||||
\(572\) | −5.27492 | −0.220555 | ||||||||
\(573\) | 5.27492 | 0.220363 | ||||||||
\(574\) | 8.54983 | 0.356863 | ||||||||
\(575\) | −30.1993 | −1.25940 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −39.0997 | −1.62774 | −0.813870 | − | 0.581047i | \(-0.802643\pi\) | ||||
−0.813870 | + | 0.581047i | \(0.802643\pi\) | |||||||
\(578\) | −35.9244 | −1.49426 | ||||||||
\(579\) | 3.45017 | 0.143384 | ||||||||
\(580\) | 2.37459 | 0.0985993 | ||||||||
\(581\) | 10.5498 | 0.437681 | ||||||||
\(582\) | −15.0997 | −0.625901 | ||||||||
\(583\) | 52.7492 | 2.18465 | ||||||||
\(584\) | −9.82475 | −0.406551 | ||||||||
\(585\) | −3.27492 | −0.135401 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −28.7492 | −1.18661 | −0.593303 | − | 0.804979i | \(-0.702176\pi\) | ||||
−0.593303 | + | 0.804979i | \(0.702176\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 42.1993 | 1.73879 | ||||||||
\(590\) | −26.1993 | −1.07861 | ||||||||
\(591\) | −12.5498 | −0.516231 | ||||||||
\(592\) | 3.27492 | 0.134598 | ||||||||
\(593\) | 23.0997 | 0.948590 | 0.474295 | − | 0.880366i | \(-0.342703\pi\) | ||||
0.474295 | + | 0.880366i | \(0.342703\pi\) | |||||||
\(594\) | 5.27492 | 0.216432 | ||||||||
\(595\) | −23.8248 | −0.976720 | ||||||||
\(596\) | 7.45017 | 0.305171 | ||||||||
\(597\) | 15.8248 | 0.647664 | ||||||||
\(598\) | −5.27492 | −0.215707 | ||||||||
\(599\) | 29.2749 | 1.19614 | 0.598070 | − | 0.801444i | \(-0.295934\pi\) | ||||
0.598070 | + | 0.801444i | \(0.295934\pi\) | |||||||
\(600\) | 5.72508 | 0.233726 | ||||||||
\(601\) | −21.6495 | −0.883102 | −0.441551 | − | 0.897236i | \(-0.645572\pi\) | ||||
−0.441551 | + | 0.897236i | \(0.645572\pi\) | |||||||
\(602\) | −5.27492 | −0.214990 | ||||||||
\(603\) | −2.54983 | −0.103837 | ||||||||
\(604\) | −1.27492 | −0.0518756 | ||||||||
\(605\) | 55.0997 | 2.24012 | ||||||||
\(606\) | −12.5498 | −0.509802 | ||||||||
\(607\) | 31.8248 | 1.29173 | 0.645863 | − | 0.763453i | \(-0.276498\pi\) | ||||
0.645863 | + | 0.763453i | \(0.276498\pi\) | |||||||
\(608\) | −5.27492 | −0.213926 | ||||||||
\(609\) | −0.725083 | −0.0293818 | ||||||||
\(610\) | 15.4743 | 0.626534 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.27492 | −0.294071 | ||||||||
\(613\) | 8.72508 | 0.352403 | 0.176201 | − | 0.984354i | \(-0.443619\pi\) | ||||
0.176201 | + | 0.984354i | \(0.443619\pi\) | |||||||
\(614\) | 9.09967 | 0.367233 | ||||||||
\(615\) | 28.0000 | 1.12907 | ||||||||
\(616\) | −5.27492 | −0.212532 | ||||||||
\(617\) | 1.82475 | 0.0734617 | 0.0367309 | − | 0.999325i | \(-0.488306\pi\) | ||||
0.0367309 | + | 0.999325i | \(0.488306\pi\) | |||||||
\(618\) | 2.72508 | 0.109619 | ||||||||
\(619\) | 37.2749 | 1.49821 | 0.749103 | − | 0.662454i | \(-0.230485\pi\) | ||||
0.749103 | + | 0.662454i | \(0.230485\pi\) | |||||||
\(620\) | 26.1993 | 1.05219 | ||||||||
\(621\) | 5.27492 | 0.211675 | ||||||||
\(622\) | −18.5498 | −0.743781 | ||||||||
\(623\) | −14.0000 | −0.560898 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −20.8488 | −0.833954 | ||||||||
\(626\) | −17.6495 | −0.705416 | ||||||||
\(627\) | −27.8248 | −1.11121 | ||||||||
\(628\) | 24.3746 | 0.972652 | ||||||||
\(629\) | −23.8248 | −0.949955 | ||||||||
\(630\) | −3.27492 | −0.130476 | ||||||||
\(631\) | 11.8248 | 0.470736 | 0.235368 | − | 0.971906i | \(-0.424370\pi\) | ||||
0.235368 | + | 0.971906i | \(0.424370\pi\) | |||||||
\(632\) | 2.54983 | 0.101427 | ||||||||
\(633\) | −23.8248 | −0.946949 | ||||||||
\(634\) | 16.5498 | 0.657278 | ||||||||
\(635\) | −17.8488 | −0.708310 | ||||||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −3.82475 | −0.151423 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.27492 | −0.129452 | ||||||||
\(641\) | 15.0997 | 0.596401 | 0.298201 | − | 0.954503i | \(-0.403614\pi\) | ||||
0.298201 | + | 0.954503i | \(0.403614\pi\) | |||||||
\(642\) | −14.5498 | −0.574236 | ||||||||
\(643\) | 28.9244 | 1.14067 | 0.570334 | − | 0.821413i | \(-0.306814\pi\) | ||||
0.570334 | + | 0.821413i | \(0.306814\pi\) | |||||||
\(644\) | −5.27492 | −0.207861 | ||||||||
\(645\) | −17.2749 | −0.680199 | ||||||||
\(646\) | 38.3746 | 1.50983 | ||||||||
\(647\) | 42.1993 | 1.65903 | 0.829514 | − | 0.558487i | \(-0.188618\pi\) | ||||
0.829514 | + | 0.558487i | \(0.188618\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 42.1993 | 1.65647 | ||||||||
\(650\) | 5.72508 | 0.224556 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | −2.54983 | −0.0998592 | ||||||||
\(653\) | 32.3746 | 1.26692 | 0.633458 | − | 0.773777i | \(-0.281635\pi\) | ||||
0.633458 | + | 0.773777i | \(0.281635\pi\) | |||||||
\(654\) | −7.27492 | −0.284472 | ||||||||
\(655\) | −51.8248 | −2.02496 | ||||||||
\(656\) | −8.54983 | −0.333815 | ||||||||
\(657\) | 9.82475 | 0.383300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.5498 | −0.878417 | −0.439208 | − | 0.898385i | \(-0.644741\pi\) | ||||
−0.439208 | + | 0.898385i | \(0.644741\pi\) | |||||||
\(660\) | −17.2749 | −0.672425 | ||||||||
\(661\) | 20.1993 | 0.785663 | 0.392832 | − | 0.919610i | \(-0.371496\pi\) | ||||
0.392832 | + | 0.919610i | \(0.371496\pi\) | |||||||
\(662\) | −15.6495 | −0.608235 | ||||||||
\(663\) | −7.27492 | −0.282534 | ||||||||
\(664\) | −10.5498 | −0.409413 | ||||||||
\(665\) | 17.2749 | 0.669893 | ||||||||
\(666\) | −3.27492 | −0.126900 | ||||||||
\(667\) | −3.82475 | −0.148095 | ||||||||
\(668\) | −9.27492 | −0.358857 | ||||||||
\(669\) | 23.6495 | 0.914343 | ||||||||
\(670\) | 8.35050 | 0.322608 | ||||||||
\(671\) | −24.9244 | −0.962197 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 8.72508 | 0.336327 | 0.168164 | − | 0.985759i | \(-0.446216\pi\) | ||||
0.168164 | + | 0.985759i | \(0.446216\pi\) | |||||||
\(674\) | 28.3746 | 1.09295 | ||||||||
\(675\) | −5.72508 | −0.220359 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −44.1993 | −1.69872 | −0.849359 | − | 0.527815i | \(-0.823011\pi\) | ||||
−0.849359 | + | 0.527815i | \(0.823011\pi\) | |||||||
\(678\) | −6.00000 | −0.230429 | ||||||||
\(679\) | −15.0997 | −0.579472 | ||||||||
\(680\) | 23.8248 | 0.913638 | ||||||||
\(681\) | 5.45017 | 0.208851 | ||||||||
\(682\) | −42.1993 | −1.61590 | ||||||||
\(683\) | −34.3746 | −1.31531 | −0.657653 | − | 0.753321i | \(-0.728451\pi\) | ||||
−0.657653 | + | 0.753321i | \(0.728451\pi\) | |||||||
\(684\) | 5.27492 | 0.201692 | ||||||||
\(685\) | 66.7251 | 2.54943 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 11.0997 | 0.423479 | ||||||||
\(688\) | 5.27492 | 0.201104 | ||||||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | −17.2749 | −0.657645 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −23.0997 | −0.878118 | ||||||||
\(693\) | 5.27492 | 0.200378 | ||||||||
\(694\) | 25.0997 | 0.952770 | ||||||||
\(695\) | 13.0997 | 0.496899 | ||||||||
\(696\) | 0.725083 | 0.0274842 | ||||||||
\(697\) | 62.1993 | 2.35597 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | −20.5498 | −0.777266 | ||||||||
\(700\) | 5.72508 | 0.216388 | ||||||||
\(701\) | 15.0997 | 0.570307 | 0.285153 | − | 0.958482i | \(-0.407955\pi\) | ||||
0.285153 | + | 0.958482i | \(0.407955\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 17.2749 | 0.651536 | ||||||||
\(704\) | 5.27492 | 0.198806 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.09967 | 0.116658 | ||||||||
\(707\) | −12.5498 | −0.471985 | ||||||||
\(708\) | −8.00000 | −0.300658 | ||||||||
\(709\) | 7.09967 | 0.266634 | 0.133317 | − | 0.991073i | \(-0.457437\pi\) | ||||
0.133317 | + | 0.991073i | \(0.457437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.54983 | −0.0956263 | ||||||||
\(712\) | 14.0000 | 0.524672 | ||||||||
\(713\) | −42.1993 | −1.58038 | ||||||||
\(714\) | −7.27492 | −0.272257 | ||||||||
\(715\) | −17.2749 | −0.646045 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | 5.09967 | 0.190451 | ||||||||
\(718\) | 32.0000 | 1.19423 | ||||||||
\(719\) | 15.6495 | 0.583628 | 0.291814 | − | 0.956475i | \(-0.405741\pi\) | ||||
0.291814 | + | 0.956475i | \(0.405741\pi\) | |||||||
\(720\) | 3.27492 | 0.122049 | ||||||||
\(721\) | 2.72508 | 0.101487 | ||||||||
\(722\) | −8.82475 | −0.328423 | ||||||||
\(723\) | 15.0997 | 0.561563 | ||||||||
\(724\) | −11.0997 | −0.412516 | ||||||||
\(725\) | 4.15116 | 0.154170 | ||||||||
\(726\) | 16.8248 | 0.624425 | ||||||||
\(727\) | −2.37459 | −0.0880685 | −0.0440343 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440343 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −32.1752 | −1.19086 | ||||||||
\(731\) | −38.3746 | −1.41934 | ||||||||
\(732\) | 4.72508 | 0.174644 | ||||||||
\(733\) | −0.549834 | −0.0203086 | −0.0101543 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101543 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(734\) | 33.0997 | 1.22173 | ||||||||
\(735\) | −3.27492 | −0.120797 | ||||||||
\(736\) | 5.27492 | 0.194436 | ||||||||
\(737\) | −13.4502 | −0.495443 | ||||||||
\(738\) | 8.54983 | 0.314724 | ||||||||
\(739\) | −7.64950 | −0.281392 | −0.140696 | − | 0.990053i | \(-0.544934\pi\) | ||||
−0.140696 | + | 0.990053i | \(0.544934\pi\) | |||||||
\(740\) | 10.7251 | 0.394262 | ||||||||
\(741\) | 5.27492 | 0.193779 | ||||||||
\(742\) | −10.0000 | −0.367112 | ||||||||
\(743\) | 26.5498 | 0.974019 | 0.487009 | − | 0.873397i | \(-0.338088\pi\) | ||||
0.487009 | + | 0.873397i | \(0.338088\pi\) | |||||||
\(744\) | 8.00000 | 0.293294 | ||||||||
\(745\) | 24.3987 | 0.893898 | ||||||||
\(746\) | −11.4502 | −0.419220 | ||||||||
\(747\) | 10.5498 | 0.385998 | ||||||||
\(748\) | −38.3746 | −1.40311 | ||||||||
\(749\) | −14.5498 | −0.531639 | ||||||||
\(750\) | 2.37459 | 0.0867076 | ||||||||
\(751\) | −50.1993 | −1.83180 | −0.915900 | − | 0.401407i | \(-0.868521\pi\) | ||||
−0.915900 | + | 0.401407i | \(0.868521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.9244 | 1.05406 | ||||||||
\(754\) | 0.725083 | 0.0264060 | ||||||||
\(755\) | −4.17525 | −0.151953 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −4.90033 | −0.178106 | −0.0890528 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890528 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(758\) | 2.90033 | 0.105345 | ||||||||
\(759\) | 27.8248 | 1.00997 | ||||||||
\(760\) | −17.2749 | −0.626627 | ||||||||
\(761\) | 23.4502 | 0.850068 | 0.425034 | − | 0.905177i | \(-0.360262\pi\) | ||||
0.425034 | + | 0.905177i | \(0.360262\pi\) | |||||||
\(762\) | −5.45017 | −0.197439 | ||||||||
\(763\) | −7.27492 | −0.263370 | ||||||||
\(764\) | −5.27492 | −0.190840 | ||||||||
\(765\) | −23.8248 | −0.861386 | ||||||||
\(766\) | −22.7251 | −0.821091 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 10.1752 | 0.366929 | 0.183464 | − | 0.983026i | \(-0.441269\pi\) | ||||
0.183464 | + | 0.983026i | \(0.441269\pi\) | |||||||
\(770\) | −17.2749 | −0.622545 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | −3.45017 | −0.124174 | ||||||||
\(773\) | 42.9244 | 1.54388 | 0.771942 | − | 0.635693i | \(-0.219286\pi\) | ||||
0.771942 | + | 0.635693i | \(0.219286\pi\) | |||||||
\(774\) | −5.27492 | −0.189603 | ||||||||
\(775\) | 45.8007 | 1.64521 | ||||||||
\(776\) | 15.0997 | 0.542047 | ||||||||
\(777\) | −3.27492 | −0.117487 | ||||||||
\(778\) | 32.1993 | 1.15440 | ||||||||
\(779\) | −45.0997 | −1.61586 | ||||||||
\(780\) | 3.27492 | 0.117261 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −38.3746 | −1.37227 | ||||||||
\(783\) | −0.725083 | −0.0259123 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 79.8248 | 2.84907 | ||||||||
\(786\) | −15.8248 | −0.564450 | ||||||||
\(787\) | −2.72508 | −0.0971387 | −0.0485694 | − | 0.998820i | \(-0.515466\pi\) | ||||
−0.0485694 | + | 0.998820i | \(0.515466\pi\) | |||||||
\(788\) | 12.5498 | 0.447069 | ||||||||
\(789\) | −28.0000 | −0.996826 | ||||||||
\(790\) | 8.35050 | 0.297097 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | −5.27492 | −0.187436 | ||||||||
\(793\) | 4.72508 | 0.167793 | ||||||||
\(794\) | 14.0000 | 0.496841 | ||||||||
\(795\) | −32.7492 | −1.16149 | ||||||||
\(796\) | −15.8248 | −0.560893 | ||||||||
\(797\) | 29.6495 | 1.05024 | 0.525120 | − | 0.851028i | \(-0.324021\pi\) | ||||
0.525120 | + | 0.851028i | \(0.324021\pi\) | |||||||
\(798\) | 5.27492 | 0.186730 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.72508 | −0.202412 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | −27.0997 | −0.956923 | ||||||||
\(803\) | 51.8248 | 1.82886 | ||||||||
\(804\) | 2.54983 | 0.0899257 | ||||||||
\(805\) | −17.2749 | −0.608861 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | 12.5498 | 0.441502 | ||||||||
\(809\) | 4.19934 | 0.147641 | 0.0738204 | − | 0.997272i | \(-0.476481\pi\) | ||||
0.0738204 | + | 0.997272i | \(0.476481\pi\) | |||||||
\(810\) | −3.27492 | −0.115069 | ||||||||
\(811\) | 26.3746 | 0.926137 | 0.463068 | − | 0.886322i | \(-0.346748\pi\) | ||||
0.463068 | + | 0.886322i | \(0.346748\pi\) | |||||||
\(812\) | 0.725083 | 0.0254454 | ||||||||
\(813\) | −13.4502 | −0.471718 | ||||||||
\(814\) | −17.2749 | −0.605486 | ||||||||
\(815\) | −8.35050 | −0.292505 | ||||||||
\(816\) | 7.27492 | 0.254673 | ||||||||
\(817\) | 27.8248 | 0.973465 | ||||||||
\(818\) | 29.8248 | 1.04280 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | −28.0000 | −0.977802 | ||||||||
\(821\) | −13.6495 | −0.476371 | −0.238185 | − | 0.971220i | \(-0.576553\pi\) | ||||
−0.238185 | + | 0.971220i | \(0.576553\pi\) | |||||||
\(822\) | 20.3746 | 0.710645 | ||||||||
\(823\) | 5.09967 | 0.177763 | 0.0888816 | − | 0.996042i | \(-0.471671\pi\) | ||||
0.0888816 | + | 0.996042i | \(0.471671\pi\) | |||||||
\(824\) | −2.72508 | −0.0949328 | ||||||||
\(825\) | −30.1993 | −1.05141 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −18.7251 | −0.651135 | −0.325567 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325567 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(828\) | −5.27492 | −0.183316 | ||||||||
\(829\) | 19.2749 | 0.669446 | 0.334723 | − | 0.942317i | \(-0.391357\pi\) | ||||
0.334723 | + | 0.942317i | \(0.391357\pi\) | |||||||
\(830\) | −34.5498 | −1.19924 | ||||||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −7.27492 | −0.252061 | ||||||||
\(834\) | 4.00000 | 0.138509 | ||||||||
\(835\) | −30.3746 | −1.05116 | ||||||||
\(836\) | 27.8248 | 0.962339 | ||||||||
\(837\) | −8.00000 | −0.276520 | ||||||||
\(838\) | 5.27492 | 0.182219 | ||||||||
\(839\) | 53.0997 | 1.83320 | 0.916602 | − | 0.399801i | \(-0.130921\pi\) | ||||
0.916602 | + | 0.399801i | \(0.130921\pi\) | |||||||
\(840\) | 3.27492 | 0.112995 | ||||||||
\(841\) | −28.4743 | −0.981871 | ||||||||
\(842\) | 27.0997 | 0.933916 | ||||||||
\(843\) | 15.0997 | 0.520060 | ||||||||
\(844\) | 23.8248 | 0.820082 | ||||||||
\(845\) | 3.27492 | 0.112661 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.8248 | 0.578105 | ||||||||
\(848\) | 10.0000 | 0.343401 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 41.6495 | 1.42857 | ||||||||
\(851\) | −17.2749 | −0.592177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6495 | 0.604307 | 0.302154 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302154 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(854\) | 4.72508 | 0.161689 | ||||||||
\(855\) | 17.2749 | 0.590790 | ||||||||
\(856\) | 14.5498 | 0.497303 | ||||||||
\(857\) | −11.0997 | −0.379157 | −0.189579 | − | 0.981866i | \(-0.560712\pi\) | ||||
−0.189579 | + | 0.981866i | \(0.560712\pi\) | |||||||
\(858\) | −5.27492 | −0.180083 | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | 17.2749 | 0.589070 | ||||||||
\(861\) | 8.54983 | 0.291378 | ||||||||
\(862\) | 26.5498 | 0.904291 | ||||||||
\(863\) | −15.6495 | −0.532715 | −0.266358 | − | 0.963874i | \(-0.585820\pi\) | ||||
−0.266358 | + | 0.963874i | \(0.585820\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −75.6495 | −2.57216 | ||||||||
\(866\) | 21.6495 | 0.735680 | ||||||||
\(867\) | −35.9244 | −1.22006 | ||||||||
\(868\) | 8.00000 | 0.271538 | ||||||||
\(869\) | −13.4502 | −0.456266 | ||||||||
\(870\) | 2.37459 | 0.0805060 | ||||||||
\(871\) | 2.54983 | 0.0863978 | ||||||||
\(872\) | 7.27492 | 0.246360 | ||||||||
\(873\) | −15.0997 | −0.511046 | ||||||||
\(874\) | 27.8248 | 0.941186 | ||||||||
\(875\) | 2.37459 | 0.0802757 | ||||||||
\(876\) | −9.82475 | −0.331948 | ||||||||
\(877\) | 20.9003 | 0.705754 | 0.352877 | − | 0.935670i | \(-0.385203\pi\) | ||||
0.352877 | + | 0.935670i | \(0.385203\pi\) | |||||||
\(878\) | −7.82475 | −0.264073 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 17.2749 | 0.582337 | ||||||||
\(881\) | −39.2749 | −1.32321 | −0.661603 | − | 0.749854i | \(-0.730123\pi\) | ||||
−0.661603 | + | 0.749854i | \(0.730123\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −20.9244 | −0.704163 | −0.352081 | − | 0.935969i | \(-0.614526\pi\) | ||||
−0.352081 | + | 0.935969i | \(0.614526\pi\) | |||||||
\(884\) | 7.27492 | 0.244682 | ||||||||
\(885\) | −26.1993 | −0.880681 | ||||||||
\(886\) | −22.5498 | −0.757577 | ||||||||
\(887\) | −2.90033 | −0.0973836 | −0.0486918 | − | 0.998814i | \(-0.515505\pi\) | ||||
−0.0486918 | + | 0.998814i | \(0.515505\pi\) | |||||||
\(888\) | 3.27492 | 0.109899 | ||||||||
\(889\) | −5.45017 | −0.182793 | ||||||||
\(890\) | 45.8488 | 1.53686 | ||||||||
\(891\) | 5.27492 | 0.176716 | ||||||||
\(892\) | −23.6495 | −0.791844 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.45017 | 0.249171 | ||||||||
\(895\) | 39.2990 | 1.31362 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −5.27492 | −0.176124 | ||||||||
\(898\) | −7.27492 | −0.242767 | ||||||||
\(899\) | 5.80066 | 0.193463 | ||||||||
\(900\) | 5.72508 | 0.190836 | ||||||||
\(901\) | −72.7492 | −2.42363 | ||||||||
\(902\) | 45.0997 | 1.50165 | ||||||||
\(903\) | −5.27492 | −0.175538 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | −36.3505 | −1.20833 | ||||||||
\(906\) | −1.27492 | −0.0423563 | ||||||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | −5.45017 | −0.180870 | ||||||||
\(909\) | −12.5498 | −0.416252 | ||||||||
\(910\) | 3.27492 | 0.108562 | ||||||||
\(911\) | 15.4743 | 0.512685 | 0.256342 | − | 0.966586i | \(-0.417483\pi\) | ||||
0.256342 | + | 0.966586i | \(0.417483\pi\) | |||||||
\(912\) | −5.27492 | −0.174670 | ||||||||
\(913\) | 55.6495 | 1.84173 | ||||||||
\(914\) | 3.45017 | 0.114121 | ||||||||
\(915\) | 15.4743 | 0.511563 | ||||||||
\(916\) | −11.0997 | −0.366743 | ||||||||
\(917\) | −15.8248 | −0.522579 | ||||||||
\(918\) | −7.27492 | −0.240108 | ||||||||
\(919\) | 2.54983 | 0.0841113 | 0.0420556 | − | 0.999115i | \(-0.486609\pi\) | ||||
0.0420556 | + | 0.999115i | \(0.486609\pi\) | |||||||
\(920\) | 17.2749 | 0.569537 | ||||||||
\(921\) | 9.09967 | 0.299844 | ||||||||
\(922\) | −34.9244 | −1.15017 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5.27492 | −0.173532 | ||||||||
\(925\) | 18.7492 | 0.616469 | ||||||||
\(926\) | −22.7251 | −0.746793 | ||||||||
\(927\) | 2.72508 | 0.0895035 | ||||||||
\(928\) | −0.725083 | −0.0238020 | ||||||||
\(929\) | −0.549834 | −0.0180395 | −0.00901974 | − | 0.999959i | \(-0.502871\pi\) | ||||
−0.00901974 | + | 0.999959i | \(0.502871\pi\) | |||||||
\(930\) | 26.1993 | 0.859110 | ||||||||
\(931\) | 5.27492 | 0.172878 | ||||||||
\(932\) | 20.5498 | 0.673132 | ||||||||
\(933\) | −18.5498 | −0.607294 | ||||||||
\(934\) | 18.7251 | 0.612703 | ||||||||
\(935\) | −125.674 | −4.10997 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 47.0997 | 1.53868 | 0.769340 | − | 0.638840i | \(-0.220585\pi\) | ||||
0.769340 | + | 0.638840i | \(0.220585\pi\) | |||||||
\(938\) | 2.54983 | 0.0832550 | ||||||||
\(939\) | −17.6495 | −0.575970 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.9003 | 0.681331 | 0.340666 | − | 0.940185i | \(-0.389348\pi\) | ||||
0.340666 | + | 0.940185i | \(0.389348\pi\) | |||||||
\(942\) | 24.3746 | 0.794167 | ||||||||
\(943\) | 45.0997 | 1.46865 | ||||||||
\(944\) | 8.00000 | 0.260378 | ||||||||
\(945\) | −3.27492 | −0.106533 | ||||||||
\(946\) | −27.8248 | −0.904661 | ||||||||
\(947\) | −39.8248 | −1.29413 | −0.647065 | − | 0.762435i | \(-0.724004\pi\) | ||||
−0.647065 | + | 0.762435i | \(0.724004\pi\) | |||||||
\(948\) | 2.54983 | 0.0828148 | ||||||||
\(949\) | −9.82475 | −0.318925 | ||||||||
\(950\) | −30.1993 | −0.979796 | ||||||||
\(951\) | 16.5498 | 0.536665 | ||||||||
\(952\) | 7.27492 | 0.235781 | ||||||||
\(953\) | −13.6495 | −0.442151 | −0.221075 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221075 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(954\) | −10.0000 | −0.323762 | ||||||||
\(955\) | −17.2749 | −0.559003 | ||||||||
\(956\) | −5.09967 | −0.164935 | ||||||||
\(957\) | −3.82475 | −0.123637 | ||||||||
\(958\) | −14.3746 | −0.464422 | ||||||||
\(959\) | 20.3746 | 0.657930 | ||||||||
\(960\) | −3.27492 | −0.105697 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 3.27492 | 0.105588 | ||||||||
\(963\) | −14.5498 | −0.468862 | ||||||||
\(964\) | −15.0997 | −0.486328 | ||||||||
\(965\) | −11.2990 | −0.363728 | ||||||||
\(966\) | −5.27492 | −0.169718 | ||||||||
\(967\) | 20.1752 | 0.648792 | 0.324396 | − | 0.945921i | \(-0.394839\pi\) | ||||
0.324396 | + | 0.945921i | \(0.394839\pi\) | |||||||
\(968\) | −16.8248 | −0.540768 | ||||||||
\(969\) | 38.3746 | 1.23277 | ||||||||
\(970\) | 49.4502 | 1.58775 | ||||||||
\(971\) | 1.09967 | 0.0352901 | 0.0176450 | − | 0.999844i | \(-0.494383\pi\) | ||||
0.0176450 | + | 0.999844i | \(0.494383\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 4.00000 | 0.128234 | ||||||||
\(974\) | −42.1993 | −1.35215 | ||||||||
\(975\) | 5.72508 | 0.183349 | ||||||||
\(976\) | −4.72508 | −0.151246 | ||||||||
\(977\) | 38.9244 | 1.24530 | 0.622651 | − | 0.782499i | \(-0.286056\pi\) | ||||
0.622651 | + | 0.782499i | \(0.286056\pi\) | |||||||
\(978\) | −2.54983 | −0.0815347 | ||||||||
\(979\) | −73.8488 | −2.36022 | ||||||||
\(980\) | 3.27492 | 0.104613 | ||||||||
\(981\) | −7.27492 | −0.232270 | ||||||||
\(982\) | 6.54983 | 0.209014 | ||||||||
\(983\) | −22.0241 | −0.702459 | −0.351230 | − | 0.936289i | \(-0.614236\pi\) | ||||
−0.351230 | + | 0.936289i | \(0.614236\pi\) | |||||||
\(984\) | −8.54983 | −0.272559 | ||||||||
\(985\) | 41.0997 | 1.30954 | ||||||||
\(986\) | 5.27492 | 0.167988 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.27492 | −0.167817 | ||||||||
\(989\) | −27.8248 | −0.884776 | ||||||||
\(990\) | −17.2749 | −0.549033 | ||||||||
\(991\) | 28.7492 | 0.913248 | 0.456624 | − | 0.889660i | \(-0.349059\pi\) | ||||
0.456624 | + | 0.889660i | \(0.349059\pi\) | |||||||
\(992\) | −8.00000 | −0.254000 | ||||||||
\(993\) | −15.6495 | −0.496622 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.8248 | −1.64296 | ||||||||
\(996\) | −10.5498 | −0.334284 | ||||||||
\(997\) | −43.0997 | −1.36498 | −0.682490 | − | 0.730895i | \(-0.739103\pi\) | ||||
−0.682490 | + | 0.730895i | \(0.739103\pi\) | |||||||
\(998\) | 5.09967 | 0.161427 | ||||||||
\(999\) | −3.27492 | −0.103614 |
(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 | 546.2.a.h.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.a.y.1.1 | 2 | |||
4.3 | odd | 2 | 4368.2.a.bh.1.2 | 2 | |||
7.6 | odd | 2 | 3822.2.a.bm.1.1 | 2 | |||
13.12 | even | 2 | 7098.2.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.a.h.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1638.2.a.y.1.1 | 2 | 3.2 | odd | 2 | |||
3822.2.a.bm.1.1 | 2 | 7.6 | odd | 2 | |||
4368.2.a.bh.1.2 | 2 | 4.3 | odd | 2 | |||
7098.2.a.bu.1.1 | 2 | 13.12 | even | 2 |