Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 124 x^{16} + 364 x^{15} - 1554 x^{14} - 2310 x^{13} + 10113 x^{12} + 8368 x^{11} - 36567 x^{10} - 18074 x^{9} + 72868 x^{8} + 23819 x^{7} + \cdots + 139 \) |
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 | 1.19 | ||
Root | \(3.30281\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.30281 | 1.90688 | 0.953440 | − | 0.301582i | \(-0.0975149\pi\) | ||||
0.953440 | + | 0.301582i | \(0.0975149\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36124 | −0.608765 | −0.304382 | − | 0.952550i | \(-0.598450\pi\) | ||||
−0.304382 | + | 0.952550i | \(0.598450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46762 | 0.932672 | 0.466336 | − | 0.884608i | \(-0.345574\pi\) | ||||
0.466336 | + | 0.884608i | \(0.345574\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.90858 | 2.63619 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61612 | −0.487278 | −0.243639 | − | 0.969866i | \(-0.578341\pi\) | ||||
−0.243639 | + | 0.969866i | \(0.578341\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.79921 | 1.05371 | 0.526856 | − | 0.849954i | \(-0.323371\pi\) | ||||
0.526856 | + | 0.849954i | \(0.323371\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.49592 | −1.16084 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.80568 | 1.40808 | 0.704042 | − | 0.710158i | \(-0.251377\pi\) | ||||
0.704042 | + | 0.710158i | \(0.251377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.15008 | 1.77849 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.190450 | 0.0397115 | 0.0198557 | − | 0.999803i | \(-0.493679\pi\) | ||||
0.0198557 | + | 0.999803i | \(0.493679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.14703 | −0.629405 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.2121 | 3.12002 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.449717 | −0.0835104 | −0.0417552 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417552 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.15951 | 0.567465 | 0.283733 | − | 0.958903i | \(-0.408427\pi\) | ||||
0.283733 | + | 0.958903i | \(0.408427\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.33773 | −0.929180 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.35902 | −0.567778 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75573 | 0.617439 | 0.308719 | − | 0.951153i | \(-0.400100\pi\) | ||||
0.308719 | + | 0.951153i | \(0.400100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.5481 | 2.00930 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.76176 | −0.899836 | −0.449918 | − | 0.893070i | \(-0.648547\pi\) | ||||
−0.449918 | + | 0.893070i | \(0.648547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1067 | −1.69376 | −0.846878 | − | 0.531788i | \(-0.821520\pi\) | ||||
−0.846878 | + | 0.531788i | \(0.821520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.7655 | −1.60482 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.59038 | −0.523710 | −0.261855 | − | 0.965107i | \(-0.584334\pi\) | ||||
−0.261855 | + | 0.965107i | \(0.584334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.910860 | −0.130123 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.1751 | 2.68505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.19992 | 0.296638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.30281 | −0.437468 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.88021 | 1.02592 | 0.512958 | − | 0.858414i | \(-0.328550\pi\) | ||||
0.512958 | + | 0.858414i | \(0.328550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.92689 | −0.374750 | −0.187375 | − | 0.982288i | \(-0.559998\pi\) | ||||
−0.187375 | + | 0.982288i | \(0.559998\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.5153 | 2.45870 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.17164 | −0.641463 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.20479 | 1.00237 | 0.501187 | − | 0.865339i | \(-0.332897\pi\) | ||||
0.501187 | + | 0.865339i | \(0.332897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.629019 | 0.0757250 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.88321 | −0.342174 | −0.171087 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171087 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.34889 | −0.274917 | −0.137458 | − | 0.990508i | \(-0.543893\pi\) | ||||
−0.137458 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.3940 | −1.20020 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.98796 | −0.454470 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.56433 | −0.513527 | −0.256764 | − | 0.966474i | \(-0.582656\pi\) | ||||
−0.256764 | + | 0.966474i | \(0.582656\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8198 | 3.31332 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.53645 | −0.388176 | −0.194088 | − | 0.980984i | \(-0.562175\pi\) | ||||
−0.194088 | + | 0.980984i | \(0.562175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.90292 | −0.857192 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.48533 | −0.159244 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.05543 | 0.853874 | 0.426937 | − | 0.904281i | \(-0.359593\pi\) | ||||
0.426937 | + | 0.904281i | \(0.359593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.37501 | 0.982768 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.4353 | 1.08209 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36124 | 0.139660 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.69548 | −0.375219 | −0.187610 | − | 0.982244i | \(-0.560074\pi\) | ||||
−0.187610 | + | 0.982244i | \(0.560074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.7812 | −1.28456 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2888 | −1.12328 | −0.561641 | − | 0.827381i | \(-0.689830\pi\) | ||||
−0.561641 | + | 0.827381i | \(0.689830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4463 | 1.42343 | 0.711716 | − | 0.702468i | \(-0.247918\pi\) | ||||
0.711716 | + | 0.702468i | \(0.247918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.0942 | −1.08268 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.4687 | 1.68877 | 0.844384 | − | 0.535739i | \(-0.179967\pi\) | ||||
0.844384 | + | 0.535739i | \(0.179967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2491 | 1.26903 | 0.634517 | − | 0.772909i | \(-0.281199\pi\) | ||||
0.634517 | + | 0.772909i | \(0.281199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.4045 | 1.17738 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9483 | −1.12400 | −0.562002 | − | 0.827136i | \(-0.689969\pi\) | ||||
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.259248 | −0.0241750 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.0464 | 2.77779 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.3262 | 1.31328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.38816 | −0.762560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.0300 | −1.71588 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0901 | 0.991925 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1382 | 1.78698 | 0.893488 | − | 0.449086i | \(-0.148250\pi\) | ||||
0.893488 | + | 0.449086i | \(0.148250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −36.6833 | −3.22979 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3360 | −1.51465 | −0.757326 | − | 0.653037i | \(-0.773495\pi\) | ||||
−0.757326 | + | 0.653037i | \(0.773495\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.46762 | −0.213970 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.0686 | −1.89936 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.76509 | −0.407109 | −0.203555 | − | 0.979064i | \(-0.565249\pi\) | ||||
−0.203555 | + | 0.979064i | \(0.565249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.585771 | −0.0496844 | −0.0248422 | − | 0.999691i | \(-0.507908\pi\) | ||||
−0.0248422 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8583 | −0.998653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.13997 | −0.513450 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.612173 | 0.0508382 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00840 | −0.248129 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8537 | −1.54455 | −0.772277 | − | 0.635286i | \(-0.780882\pi\) | ||||
−0.772277 | + | 0.635286i | \(0.780882\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.325422 | −0.0264824 | −0.0132412 | − | 0.999912i | \(-0.504215\pi\) | ||||
−0.0132412 | + | 0.999912i | \(0.504215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 45.9147 | 3.71198 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.30085 | −0.345453 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.24083 | 0.178837 | 0.0894187 | − | 0.995994i | \(-0.471499\pi\) | ||||
0.0894187 | + | 0.995994i | \(0.471499\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.30281 | −0.261930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.469957 | 0.0370378 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.83476 | −0.222036 | −0.111018 | − | 0.993818i | \(-0.535411\pi\) | ||||
−0.111018 | + | 0.993818i | \(0.535411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.26593 | 0.565652 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.36625 | −0.337871 | −0.168935 | − | 0.985627i | \(-0.554033\pi\) | ||||
−0.168935 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.43402 | 0.110309 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.90858 | −0.604784 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.20871 | 0.319982 | 0.159991 | − | 0.987118i | \(-0.448853\pi\) | ||||
0.159991 | + | 0.987118i | \(0.448853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.76566 | −0.587029 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.0269 | 1.95630 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8986 | −1.03883 | −0.519416 | − | 0.854521i | \(-0.673851\pi\) | ||||
−0.519416 | + | 0.854521i | \(0.673851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9446 | 1.18515 | 0.592577 | − | 0.805514i | \(-0.298110\pi\) | ||||
0.592577 | + | 0.805514i | \(0.298110\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.66699 | −0.714604 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.11245 | −0.375875 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.38266 | −0.686128 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 40.0053 | 2.90996 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5324 | 1.05152 | 0.525762 | − | 0.850631i | \(-0.323780\pi\) | ||||
0.525762 | + | 0.850631i | \(0.323780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1303 | 1.44901 | 0.724506 | − | 0.689268i | \(-0.242068\pi\) | ||||
0.724506 | + | 0.689268i | \(0.242068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.0810 | −1.22319 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3371 | 1.44896 | 0.724479 | − | 0.689297i | \(-0.242081\pi\) | ||||
0.724479 | + | 0.689297i | \(0.242081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3629 | −1.65615 | −0.828075 | − | 0.560617i | \(-0.810564\pi\) | ||||
−0.828075 | + | 0.560617i | \(0.810564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.0989 | 1.91141 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.10973 | −0.0778878 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.84314 | 0.547788 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50619 | 0.104687 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.61612 | 0.111789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3865 | 0.715039 | 0.357519 | − | 0.933906i | \(-0.383623\pi\) | ||||
0.357519 | + | 0.933906i | \(0.383623\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.52272 | −0.652486 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.1189 | 1.03110 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.79647 | 0.529259 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.75795 | −0.524234 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.0570 | 1.48372 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.50818 | 0.234925 | 0.117462 | − | 0.993077i | \(-0.462524\pi\) | ||||
0.117462 | + | 0.993077i | \(0.462524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.8885 | −1.65923 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.3856 | −1.81764 | −0.908821 | − | 0.417185i | \(-0.863017\pi\) | ||||
−0.908821 | + | 0.417185i | \(0.863017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5269 | 1.35646 | 0.678228 | − | 0.734852i | \(-0.262748\pi\) | ||||
0.678228 | + | 0.734852i | \(0.262748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1715 | −0.866620 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.24612 | −0.474709 | −0.237355 | − | 0.971423i | \(-0.576280\pi\) | ||||
−0.237355 | + | 0.971423i | \(0.576280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.88736 | 0.318816 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.0751 | −0.979235 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.604707 | 0.0391152 | 0.0195576 | − | 0.999809i | \(-0.493774\pi\) | ||||
0.0195576 | + | 0.999809i | \(0.493774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0652 | 1.48576 | 0.742880 | − | 0.669425i | \(-0.233459\pi\) | ||||
0.742880 | + | 0.669425i | \(0.233459\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 49.8531 | 3.19808 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23990 | 0.0792142 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.79921 | −0.241738 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.6802 | −0.740204 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.72188 | 0.171803 | 0.0859017 | − | 0.996304i | \(-0.472623\pi\) | ||||
0.0859017 | + | 0.996304i | \(0.472623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.307789 | −0.0193505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.1019 | −1.63456 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9536 | −0.932780 | −0.466390 | − | 0.884579i | \(-0.654446\pi\) | ||||
−0.466390 | + | 0.884579i | \(0.654446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.26771 | 0.575868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.55662 | −0.220150 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.81332 | −0.481790 | −0.240895 | − | 0.970551i | \(-0.577441\pi\) | ||||
−0.240895 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36124 | 0.0836203 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.6056 | 1.62824 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.73144 | 0.410423 | 0.205212 | − | 0.978718i | \(-0.434212\pi\) | ||||
0.205212 | + | 0.978718i | \(0.434212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.275159 | −0.0167147 | −0.00835736 | − | 0.999965i | \(-0.502660\pi\) | ||||
−0.00835736 | + | 0.999965i | \(0.502660\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.9639 | 1.87402 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.08596 | 0.306695 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.8188 | −1.31096 | −0.655482 | − | 0.755211i | \(-0.727535\pi\) | ||||
−0.655482 | + | 0.755211i | \(0.727535\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.9872 | 1.49595 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.59747 | −0.333917 | −0.166959 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166959 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.62668 | −0.0966963 | −0.0483481 | − | 0.998831i | \(-0.515396\pi\) | ||||
−0.0483481 | + | 0.998831i | \(0.515396\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.49592 | 0.266315 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.2178 | −0.839252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7059 | 0.982702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2055 | −0.715498 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.2205 | −1.12287 | −0.561436 | − | 0.827520i | \(-0.689751\pi\) | ||||
−0.561436 | + | 0.827520i | \(0.689751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7269 | −0.624541 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.2007 | −1.52032 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.723559 | 0.0418445 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.4071 | −1.57972 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.2849 | −2.14196 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.98421 | 0.228135 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00548 | −0.114459 | −0.0572294 | − | 0.998361i | \(-0.518227\pi\) | ||||
−0.0572294 | + | 0.998361i | \(0.518227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 47.7133 | 2.71431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.6226 | −1.45293 | −0.726463 | − | 0.687205i | \(-0.758837\pi\) | ||||
−0.726463 | + | 0.687205i | \(0.758837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.1232 | −1.53310 | −0.766548 | − | 0.642187i | \(-0.778027\pi\) | ||||
−0.766548 | + | 0.642187i | \(0.778027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.5651 | −1.49677 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2414 | −0.687543 | −0.343772 | − | 0.939053i | \(-0.611705\pi\) | ||||
−0.343772 | + | 0.939053i | \(0.611705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.726796 | 0.0406928 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 57.6960 | 3.22028 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.80568 | −0.323037 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9562 | −0.663212 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43.7593 | 2.41990 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.85968 | −0.488450 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7150 | 0.698881 | 0.349441 | − | 0.936959i | \(-0.386372\pi\) | ||||
0.349441 | + | 0.936959i | \(0.386372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.7025 | 1.62769 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.1687 | −0.610210 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2102 | −1.04645 | −0.523223 | − | 0.852196i | \(-0.675271\pi\) | ||||
−0.523223 | + | 0.852196i | \(0.675271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.4631 | −2.14334 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.10614 | −0.276513 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.5210 | −1.05403 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.856246 | −0.0460987 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.63724 | 0.195257 | 0.0976286 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976286 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4674 | 0.774421 | 0.387210 | − | 0.921991i | \(-0.373439\pi\) | ||||
0.387210 | + | 0.921991i | \(0.373439\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 61.5933 | 3.28761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8466 | −1.00310 | −0.501552 | − | 0.865127i | \(-0.667237\pi\) | ||||
−0.501552 | + | 0.865127i | \(0.667237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.92474 | 0.208304 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 47.3168 | 2.50427 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0552 | −0.530695 | −0.265348 | − | 0.964153i | \(-0.585487\pi\) | ||||
−0.265348 | + | 0.964153i | \(0.585487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.7045 | −1.45411 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.19740 | 0.167360 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.2269 | 1.05584 | 0.527918 | − | 0.849295i | \(-0.322973\pi\) | ||||
0.527918 | + | 0.849295i | \(0.322973\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −45.5673 | −2.37214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.46762 | −0.128112 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.58343 | −0.340877 | −0.170438 | − | 0.985368i | \(-0.554518\pi\) | ||||
−0.170438 | + | 0.985368i | \(0.554518\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.6284 | 1.89148 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.70857 | −0.0879960 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.72104 | −0.499336 | −0.249668 | − | 0.968331i | \(-0.580322\pi\) | ||||
−0.249668 | + | 0.968331i | \(0.580322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.5127 | 3.40755 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.3123 | −0.782421 | −0.391210 | − | 0.920301i | \(-0.627943\pi\) | ||||
−0.391210 | + | 0.920301i | \(0.627943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.42857 | 0.276666 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −87.8382 | −4.46506 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.61393 | −0.233935 | −0.116968 | − | 0.993136i | \(-0.537317\pi\) | ||||
−0.116968 | + | 0.993136i | \(0.537317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10569 | 0.0559171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −57.2575 | −2.88826 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.21315 | 0.312617 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0394 | 1.00575 | 0.502875 | − | 0.864359i | \(-0.332275\pi\) | ||||
0.502875 | + | 0.864359i | \(0.332275\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.15008 | −0.408014 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.5669 | −1.42656 | −0.713282 | − | 0.700877i | \(-0.752792\pi\) | ||||
−0.713282 | + | 0.700877i | \(0.752792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0037 | 0.597945 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −40.5920 | −2.01703 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.06970 | −0.300864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36323 | −0.0674073 | −0.0337037 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337037 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.7382 | −0.776309 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.4453 | 0.956843 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.81395 | 0.236308 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.93469 | −0.0947422 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.8248 | −1.35933 | −0.679666 | − | 0.733521i | \(-0.737875\pi\) | ||||
−0.679666 | + | 0.733521i | \(0.737875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.6880 | −1.20322 | −0.601610 | − | 0.798790i | \(-0.705474\pi\) | ||||
−0.601610 | + | 0.798790i | \(0.705474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.3948 | −1.38060 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.2706 | −0.886256 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.22246 | −0.349519 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.2792 | −0.979089 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6653 | −0.658234 | −0.329117 | − | 0.944289i | \(-0.606751\pi\) | ||||
−0.329117 | + | 0.944289i | \(0.606751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.497570 | −0.0239117 | −0.0119558 | − | 0.999929i | \(-0.503806\pi\) | ||||
−0.0119558 | + | 0.999929i | \(0.503806\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.02189 | 0.0969424 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.190450 | −0.00911044 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.9878 | 1.47897 | 0.739484 | − | 0.673174i | \(-0.235069\pi\) | ||||
0.739484 | + | 0.673174i | \(0.235069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.20361 | −0.343029 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.62366 | −0.457234 | −0.228617 | − | 0.973516i | \(-0.573420\pi\) | ||||
−0.228617 | + | 0.973516i | \(0.573420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9654 | −0.519809 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −62.2702 | −2.94528 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.3689 | −1.57477 | −0.787387 | − | 0.616459i | \(-0.788567\pi\) | ||||
−0.787387 | + | 0.616459i | \(0.788567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31168 | 0.438470 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.07481 | −0.0504988 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.7616 | −0.598275 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.12651 | −0.333364 | −0.166682 | − | 0.986011i | \(-0.553305\pi\) | ||||
−0.166682 | + | 0.986011i | \(0.553305\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 94.1223 | 4.39325 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.9427 | 1.02197 | 0.510987 | − | 0.859589i | \(-0.329280\pi\) | ||||
0.510987 | + | 0.859589i | \(0.329280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.3472 | 0.573823 | 0.286911 | − | 0.957957i | \(-0.407371\pi\) | ||||
0.286911 | + | 0.957957i | \(0.407371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.2049 | −0.658737 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4938 | 0.485593 | 0.242797 | − | 0.970077i | \(-0.421935\pi\) | ||||
0.242797 | + | 0.970077i | \(0.421935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.2463 | 0.934887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.40103 | 0.341022 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.9497 | 0.825329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.14703 | 0.144395 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.90858 | −0.362109 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.0827 | 1.74004 | 0.870021 | − | 0.493014i | \(-0.164105\pi\) | ||||
0.870021 | + | 0.493014i | \(0.164105\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2688 | 0.650603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.55218 | 0.0706266 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.03043 | 0.228420 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.50810 | −0.430853 | −0.215427 | − | 0.976520i | \(-0.569114\pi\) | ||||
−0.215427 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.36269 | −0.423396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0069 | −1.12854 | −0.564272 | − | 0.825589i | \(-0.690843\pi\) | ||||
−0.564272 | + | 0.825589i | \(0.690843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.61092 | −0.117590 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.3983 | 0.781994 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.11467 | −0.319137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7494 | −1.10794 | −0.553968 | − | 0.832538i | \(-0.686887\pi\) | ||||
−0.553968 | + | 0.832538i | \(0.686887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.4209 | −0.644279 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.8402 | −0.661690 | −0.330845 | − | 0.943685i | \(-0.607334\pi\) | ||||
−0.330845 | + | 0.943685i | \(0.607334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.3668 | 0.683814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.73631 | 0.210347 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.3200 | 1.47688 | 0.738441 | − | 0.674319i | \(-0.235563\pi\) | ||||
0.738441 | + | 0.674319i | \(0.235563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.79617 | −0.256407 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.2121 | −0.715782 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.6648 | −0.866535 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.80247 | 0.255192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9006 | 0.610168 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5146 | −0.942572 | −0.471286 | − | 0.881980i | \(-0.656210\pi\) | ||||
−0.471286 | + | 0.881980i | \(0.656210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.5273 | 1.68468 | 0.842340 | − | 0.538946i | \(-0.181177\pi\) | ||||
0.842340 | + | 0.538946i | \(0.181177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.6485 | −1.11939 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.3431 | 0.799039 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9637 | −0.998423 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 62.3212 | 2.70451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.8902 | −0.948168 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.7792 | −1.02806 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.9046 | −1.98093 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.47206 | 0.0634060 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5751 | 0.454658 | 0.227329 | − | 0.973818i | \(-0.427001\pi\) | ||||
0.227329 | + | 0.973818i | \(0.427001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 52.6621 | 2.25995 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.0352 | −0.772544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8990 | −1.23563 | −0.617816 | − | 0.786323i | \(-0.711982\pi\) | ||||
−0.617816 | + | 0.786323i | \(0.711982\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.1476 | −0.987914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.449717 | 0.0191586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.2630 | −0.478952 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.8855 | −0.716749 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.8756 | −0.926900 | −0.463450 | − | 0.886123i | \(-0.653389\pi\) | ||||
−0.463450 | + | 0.886123i | \(0.653389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.1967 | −1.78473 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.9892 | −1.30836 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.0135 | 1.13848 | 0.569242 | − | 0.822170i | \(-0.307237\pi\) | ||||
0.569242 | + | 0.822170i | \(0.307237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.2645 | 0.684254 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 73.5840 | 3.09024 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.30868 | 0.222551 | 0.111276 | − | 0.993790i | \(-0.464506\pi\) | ||||
0.111276 | + | 0.993790i | \(0.464506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.7065 | 0.740992 | 0.370496 | − | 0.928834i | \(-0.379188\pi\) | ||||
0.370496 | + | 0.928834i | \(0.379188\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47.9977 | 2.00513 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.599350 | −0.0249946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.79362 | 0.407714 | 0.203857 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203857 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 66.4867 | 2.76309 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.72660 | −0.362041 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.61612 | 0.0669327 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −40.9003 | −1.69102 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.0667 | 1.90137 | 0.950687 | − | 0.310150i | \(-0.100379\pi\) | ||||
0.950687 | + | 0.310150i | \(0.100379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.15951 | −0.130185 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 67.1696 | 2.76299 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.2147 | −1.61036 | −0.805178 | − | 0.593033i | \(-0.797930\pi\) | ||||
−0.805178 | + | 0.593033i | \(0.797930\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5014 | −0.799479 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −77.1632 | −3.15808 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.4553 | −0.468051 | −0.234025 | − | 0.972230i | \(-0.575190\pi\) | ||||
−0.234025 | + | 0.972230i | \(0.575190\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.4147 | −0.465614 | −0.232807 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232807 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 64.8882 | 2.64245 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4183 | 0.464220 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.50158 | −0.385657 | −0.192829 | − | 0.981232i | \(-0.561766\pi\) | ||||
−0.192829 | + | 0.981232i | \(0.561766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.66523 | −0.148523 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.6406 | −0.551840 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1349 | 1.45947 | 0.729737 | − | 0.683727i | \(-0.239642\pi\) | ||||
0.729737 | + | 0.683727i | \(0.239642\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25.9044 | 1.04457 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.1518 | −1.73722 | −0.868612 | − | 0.495493i | \(-0.834988\pi\) | ||||
−0.868612 | + | 0.495493i | \(0.834988\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.7775 | −1.71937 | −0.859687 | − | 0.510821i | \(-0.829341\pi\) | ||||
−0.859687 | + | 0.510821i | \(0.829341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.08759 | 0.123901 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.8777 | 0.796385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.638911 | 0.0255564 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.33773 | 0.213169 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.8046 | 0.869406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6862 | −0.783693 | −0.391847 | − | 0.920031i | \(-0.628164\pi\) | ||||
−0.391847 | + | 0.920031i | \(0.628164\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.3048 | 1.36349 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.4129 | −1.08785 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.46055 | −0.137112 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.8021 | −0.902038 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.89125 | 0.193193 | 0.0965963 | − | 0.995324i | \(-0.469204\pi\) | ||||
0.0965963 | + | 0.995324i | \(0.469204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.4838 | 1.87258 | 0.936290 | − | 0.351228i | \(-0.114236\pi\) | ||||
0.936290 | + | 0.351228i | \(0.114236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.9348 | 1.96618 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.60803 | 0.377731 | 0.188865 | − | 0.982003i | \(-0.439519\pi\) | ||||
0.188865 | + | 0.982003i | \(0.439519\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.7353 | −0.499906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.7503 | 1.00923 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.3300 | 1.57823 | 0.789117 | − | 0.614243i | \(-0.210539\pi\) | ||||
0.789117 | + | 0.614243i | \(0.210539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.5984 | 0.922067 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.5764 | −0.724734 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6104 | 0.608095 | 0.304047 | − | 0.952657i | \(-0.401662\pi\) | ||||
0.304047 | + | 0.952657i | \(0.401662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.80323 | 0.109033 | 0.0545164 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545164 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 72.8502 | 2.82927 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.35902 | 0.130257 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0856485 | −0.00331632 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5869 | 0.447974 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.73021 | 0.182608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.27073 | −0.357360 | −0.178680 | − | 0.983907i | \(-0.557183\pi\) | ||||
−0.178680 | + | 0.983907i | \(0.557183\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −51.0199 | −1.96376 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.03024 | −0.0780285 | −0.0390143 | − | 0.999239i | \(-0.512422\pi\) | ||||
−0.0390143 | + | 0.999239i | \(0.512422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.11903 | −0.349956 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −90.4494 | −3.46603 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0043 | −0.918498 | −0.459249 | − | 0.888308i | \(-0.651881\pi\) | ||||
−0.459249 | + | 0.888308i | \(0.651881\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.48643 | 0.247834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.7965 | 2.58660 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.79921 | −0.144739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7232 | 1.39702 | 0.698508 | − | 0.715602i | \(-0.253847\pi\) | ||||
0.698508 | + | 0.715602i | \(0.253847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.5391 | −1.19807 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.797374 | 0.0302461 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.4509 | −1.26704 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.9326 | −0.905213 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.5117 | −1.64341 | −0.821707 | − | 0.569910i | \(-0.806978\pi\) | ||||
−0.821707 | + | 0.569910i | \(0.806978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.75573 | −0.141650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.1420 | 0.607945 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.8566 | −1.04765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1065 | 0.942894 | 0.471447 | − | 0.881894i | \(-0.343732\pi\) | ||||
0.471447 | + | 0.881894i | \(0.343732\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.0973 | −1.35376 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.601728 | 0.0225349 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.35798 | 0.312571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.99723 | 0.0745881 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.3607 | 1.43061 | 0.715307 | − | 0.698811i | \(-0.246287\pi\) | ||||
0.715307 | + | 0.698811i | \(0.246287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.6478 | 1.32759 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.1800 | 2.83316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.41527 | 0.0525619 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.2956 | −0.715632 | −0.357816 | − | 0.933792i | \(-0.616479\pi\) | ||||
−0.357816 | + | 0.933792i | \(0.616479\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 75.1958 | 2.78503 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.4819 | −2.38495 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.02369 | 0.259426 | 0.129713 | − | 0.991552i | \(-0.458594\pi\) | ||||
0.129713 | + | 0.991552i | \(0.458594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.09515 | 0.151052 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.2599 | −0.488435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5531 | 1.38141 | 0.690706 | − | 0.723136i | \(-0.257300\pi\) | ||||
0.690706 | + | 0.723136i | \(0.257300\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.5481 | −0.460966 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1947 | 0.594127 | 0.297063 | − | 0.954858i | \(-0.403993\pi\) | ||||
0.297063 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.6644 | 0.940270 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.9683 | −1.02331 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.1062 | 1.57507 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.79622 | 0.211507 | 0.105754 | − | 0.994392i | \(-0.466275\pi\) | ||||
0.105754 | + | 0.994392i | \(0.466275\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.98986 | 0.327609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.442977 | 0.0161216 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6846 | −0.751796 | −0.375898 | − | 0.926661i | \(-0.622666\pi\) | ||||
−0.375898 | + | 0.926661i | \(0.622666\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.01657 | −0.0368991 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 53.1447 | 1.92649 | 0.963247 | − | 0.268617i | \(-0.0865664\pi\) | ||||
0.963247 | + | 0.268617i | \(0.0865664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.6937 | 1.18359 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −62.5009 | −2.25972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.9386 | 1.08102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.8739 | 1.25758 | 0.628792 | − | 0.777574i | \(-0.283550\pi\) | ||||
0.628792 | + | 0.777574i | \(0.283550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.3890 | −1.77870 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.6436 | 1.28201 | 0.641006 | − | 0.767536i | \(-0.278518\pi\) | ||||
0.641006 | + | 0.767536i | \(0.278518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.94307 | −0.357166 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.6095 | 1.09811 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.76176 | 0.206436 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.65961 | 0.166734 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.29087 | −0.260554 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.05030 | −0.108870 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.5134 | −0.695579 | −0.347789 | − | 0.937573i | \(-0.613068\pi\) | ||||
−0.347789 | + | 0.937573i | \(0.613068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.8059 | −0.918716 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.4839 | −1.04833 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1199 | −0.394879 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.49592 | 0.159454 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.2396 | −0.964878 | −0.482439 | − | 0.875930i | \(-0.660249\pi\) | ||||
−0.482439 | + | 0.875930i | \(0.660249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.8446 | −0.737428 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 63.7070 | 2.25098 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.79608 | 0.133961 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.639724 | −0.0225473 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.2327 | 0.782628 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.1297 | 0.813198 | 0.406599 | − | 0.913607i | \(-0.366715\pi\) | ||||
0.406599 | + | 0.913607i | \(0.366715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0645 | −0.564102 | −0.282051 | − | 0.959399i | \(-0.591015\pi\) | ||||
−0.282051 | + | 0.959399i | \(0.591015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.908799 | −0.0318730 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.85879 | 0.135168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1067 | 0.388574 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 74.1430 | 2.59076 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.205065 | 0.00715682 | 0.00357841 | − | 0.999994i | \(-0.498861\pi\) | ||||
0.00357841 | + | 0.999994i | \(0.498861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.6080 | −0.718351 | −0.359175 | − | 0.933270i | \(-0.616942\pi\) | ||||
−0.359175 | + | 0.933270i | \(0.616942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.7980 | 0.584831 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.897926 | 0.0312239 | 0.0156120 | − | 0.999878i | \(-0.495030\pi\) | ||||
0.0156120 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.5387 | −0.643874 | −0.321937 | − | 0.946761i | \(-0.604334\pi\) | ||||
−0.321937 | + | 0.946761i | \(0.604334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −72.0634 | −2.49985 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.28816 | −0.183224 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.94351 | 0.205684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.2224 | 1.77050 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.3721 | 1.46285 | 0.731423 | − | 0.681924i | \(-0.238857\pi\) | ||||
0.731423 | + | 0.681924i | \(0.238857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7978 | −0.993026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.4874 | −0.636740 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.95205 | −0.0671525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6988 | −0.711219 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.37263 | −0.184388 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.715278 | 0.0245194 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0764 | −0.653165 | −0.326582 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326582 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.7655 | 0.368171 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.07869 | −0.105166 | −0.0525831 | − | 0.998617i | \(-0.516745\pi\) | ||||
−0.0525831 | + | 0.998617i | \(0.516745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2804 | 0.930794 | 0.465397 | − | 0.885102i | \(-0.345911\pi\) | ||||
0.465397 | + | 0.885102i | \(0.345911\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.9588 | −1.60035 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4081 | 0.592579 | 0.296290 | − | 0.955098i | \(-0.404251\pi\) | ||||
0.296290 | + | 0.955098i | \(0.404251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.72906 | −0.194794 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 55.1766 | 1.87389 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.37649 | 0.250230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1717 | 1.05621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.2260 | −0.989150 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.3660 | 0.925140 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.2110 | −0.783781 | −0.391890 | − | 0.920012i | \(-0.628179\pi\) | ||||
−0.391890 | + | 0.920012i | \(0.628179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −63.4817 | −2.14118 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.0262 | 0.977918 | 0.488959 | − | 0.872307i | \(-0.337377\pi\) | ||||
0.488959 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.6123 | 1.13114 | 0.565572 | − | 0.824699i | \(-0.308655\pi\) | ||||
0.565572 | + | 0.824699i | \(0.308655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.4288 | −1.19093 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.0131 | −1.64570 | −0.822849 | − | 0.568259i | \(-0.807617\pi\) | ||||
−0.822849 | + | 0.568259i | \(0.807617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.6934 | 1.66666 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48.1924 | −1.61451 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.59038 | 0.120147 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.9194 | 0.632405 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.38978 | 0.0797924 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.42089 | −0.0473893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.80568 | −0.193415 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −90.5205 | −3.01233 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.7045 | −0.721481 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.7290 | −1.91686 | −0.958431 | − | 0.285326i | \(-0.907898\pi\) | ||||
−0.958431 | + | 0.285326i | \(0.907898\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −89.2787 | −2.96119 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3471 | 0.574734 | 0.287367 | − | 0.957821i | \(-0.407220\pi\) | ||||
0.287367 | + | 0.957821i | \(0.407220\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.71532 | 0.189149 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.1591 | 0.435026 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.7786 | −1.41267 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.3392 | −0.934825 | −0.467412 | − | 0.884039i | \(-0.654814\pi\) | ||||
−0.467412 | + | 0.884039i | \(0.654814\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.62373 | −0.218259 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9539 | −0.360553 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8194 | −0.388619 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 114.249 | 3.75244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.1079 | −0.922191 | −0.461095 | − | 0.887351i | \(-0.652543\pi\) | ||||
−0.461095 | + | 0.887351i | \(0.652543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.910860 | 0.0298522 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −84.6268 | −2.77056 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7720 | 0.417691 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.6376 | −0.902881 | −0.451440 | − | 0.892301i | \(-0.649090\pi\) | ||||
−0.451440 | + | 0.892301i | \(0.649090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −89.5830 | −2.92343 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.41271 | −0.111251 | −0.0556256 | − | 0.998452i | \(-0.517715\pi\) | ||||
−0.0556256 | + | 0.998452i | \(0.517715\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.09732 | −0.0357338 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −54.4568 | −1.77148 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.42927 | 0.176428 | 0.0882138 | − | 0.996102i | \(-0.471884\pi\) | ||||
0.0882138 | + | 0.996102i | \(0.471884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.92394 | −0.289683 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.4309 | −1.31106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.4941 | 1.08498 | 0.542491 | − | 0.840062i | \(-0.317481\pi\) | ||||
0.542491 | + | 0.840062i | \(0.317481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.7820 | −0.640131 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.40047 | 0.0775962 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.7584 | −0.379700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.0175 | −0.677983 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 138.153 | 4.45192 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.4022 | −0.882108 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.4322 | −1.81474 | −0.907369 | − | 0.420335i | \(-0.861912\pi\) | ||||
−0.907369 | + | 0.420335i | \(0.861912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.1751 | −0.615992 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.6433 | 1.11176 | 0.555878 | − | 0.831264i | \(-0.312382\pi\) | ||||
0.555878 | + | 0.831264i | \(0.312382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.44546 | −0.0463393 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39.4892 | −1.26467 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.9373 | −1.11774 | −0.558871 | − | 0.829255i | \(-0.688765\pi\) | ||||
−0.558871 | + | 0.829255i | \(0.688765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0185 | −0.416074 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 104.782 | 3.34542 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.37952 | 0.0758948 | 0.0379474 | − | 0.999280i | \(-0.487918\pi\) | ||||
0.0379474 | + | 0.999280i | \(0.487918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.6836 | −0.882074 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −29.2619 | −0.931415 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.11527 | −0.0672615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.64207 | −0.179226 | −0.0896132 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896132 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.9954 | 1.33268 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.8025 | 1.00821 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.2183 | −1.71711 | −0.858556 | − | 0.512720i | \(-0.828638\pi\) | ||||
−0.858556 | + | 0.512720i | \(0.828638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 60.8884 | 1.92642 |
(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 | 4028.2.a.f.1.19 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.f.1.19 | ✓ | 19 | 1.1 | even | 1 | trivial |