Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [644,2,Mod(1,644)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(644, 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("644.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 644 = 2^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 644.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: | \(5.14236589017\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.6963152.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.76321\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 644.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.76321 | −1.01799 | −0.508995 | − | 0.860769i | \(-0.669983\pi\) | ||||
−0.508995 | + | 0.860769i | \(0.669983\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.11657 | −1.39377 | −0.696885 | − | 0.717183i | \(-0.745431\pi\) | ||||
−0.696885 | + | 0.717183i | \(0.745431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.108911 | 0.0363037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23940 | −1.57974 | −0.789870 | − | 0.613274i | \(-0.789852\pi\) | ||||
−0.789870 | + | 0.613274i | \(0.789852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.34832 | 1.76071 | 0.880353 | − | 0.474319i | \(-0.157306\pi\) | ||||
0.880353 | + | 0.474319i | \(0.157306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.49516 | 1.41884 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.585105 | −0.141909 | −0.0709544 | − | 0.997480i | \(-0.522604\pi\) | ||||
−0.0709544 | + | 0.997480i | \(0.522604\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.48889 | 1.94748 | 0.973742 | − | 0.227653i | \(-0.0731051\pi\) | ||||
0.973742 | + | 0.227653i | \(0.0731051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76321 | 0.384764 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.71298 | 0.942597 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.09760 | 0.981033 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.59780 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.97640 | −1.07339 | −0.536696 | − | 0.843776i | \(-0.680328\pi\) | ||||
−0.536696 | + | 0.843776i | \(0.680328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.23817 | 1.60816 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.11657 | 0.526796 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0153 | 1.64651 | 0.823253 | − | 0.567674i | \(-0.192157\pi\) | ||||
0.823253 | + | 0.567674i | \(0.192157\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.1934 | −1.79238 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.17811 | 0.183989 | 0.0919946 | − | 0.995760i | \(-0.470676\pi\) | ||||
0.0919946 | + | 0.995760i | \(0.470676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.96247 | −0.451772 | −0.225886 | − | 0.974154i | \(-0.572528\pi\) | ||||
−0.225886 | + | 0.974154i | \(0.572528\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.339428 | −0.0505990 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.55043 | −0.372018 | −0.186009 | − | 0.982548i | \(-0.559555\pi\) | ||||
−0.186009 | + | 0.982548i | \(0.559555\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.03166 | 0.144462 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.27107 | 1.13612 | 0.568059 | − | 0.822988i | \(-0.307694\pi\) | ||||
0.568059 | + | 0.822988i | \(0.307694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3289 | 2.20180 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.9677 | −1.98252 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.6004 | 1.90081 | 0.950406 | − | 0.311012i | \(-0.100668\pi\) | ||||
0.950406 | + | 0.311012i | \(0.100668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.15410 | 0.787951 | 0.393976 | − | 0.919121i | \(-0.371099\pi\) | ||||
0.393976 | + | 0.919121i | \(0.371099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.108911 | −0.0137215 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19.7849 | −2.45402 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.52015 | −1.04090 | −0.520451 | − | 0.853892i | \(-0.674236\pi\) | ||||
−0.520451 | + | 0.853892i | \(0.674236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.76321 | 0.212266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.38625 | 0.995265 | 0.497632 | − | 0.867388i | \(-0.334203\pi\) | ||||
0.497632 | + | 0.867388i | \(0.334203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.358396 | −0.0419471 | −0.0209735 | − | 0.999780i | \(-0.506677\pi\) | ||||
−0.0209735 | + | 0.999780i | \(0.506677\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.30998 | −0.959554 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.23940 | 0.597086 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0216 | −1.24002 | −0.620012 | − | 0.784592i | \(-0.712872\pi\) | ||||
−0.620012 | + | 0.784592i | \(0.712872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.31487 | −1.03499 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7446 | −1.17938 | −0.589689 | − | 0.807630i | \(-0.700750\pi\) | ||||
−0.589689 | + | 0.807630i | \(0.700750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82352 | 0.197788 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.81726 | 0.302042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.1369 | 1.92251 | 0.961255 | − | 0.275662i | \(-0.0888970\pi\) | ||||
0.961255 | + | 0.275662i | \(0.0888970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.34832 | −0.665484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5376 | 1.09270 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.4562 | −2.71435 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.38723 | −0.851594 | −0.425797 | − | 0.904819i | \(-0.640006\pi\) | ||||
−0.425797 | + | 0.904819i | \(0.640006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.570629 | −0.0573503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.79708 | 0.676335 | 0.338168 | − | 0.941086i | \(-0.390193\pi\) | ||||
0.338168 | + | 0.941086i | \(0.390193\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.75955 | −0.961637 | −0.480819 | − | 0.876820i | \(-0.659660\pi\) | ||||
−0.480819 | + | 0.876820i | \(0.659660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.49516 | −0.536273 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.96247 | −0.673087 | −0.336544 | − | 0.941668i | \(-0.609258\pi\) | ||||
−0.336544 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.03794 | −0.195199 | −0.0975994 | − | 0.995226i | \(-0.531116\pi\) | ||||
−0.0975994 | + | 0.995226i | \(0.531116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.6591 | −1.67613 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.20815 | 0.301797 | 0.150898 | − | 0.988549i | \(-0.451783\pi\) | ||||
0.150898 | + | 0.988549i | \(0.451783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.11657 | 0.290621 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.691401 | 0.0639201 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.585105 | 0.0536365 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4514 | 1.49558 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.07725 | −0.187299 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.894506 | 0.0800070 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.83720 | 0.429232 | 0.214616 | − | 0.976698i | \(-0.431150\pi\) | ||||
0.214616 | + | 0.976698i | \(0.431150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.22346 | 0.459900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.9917 | 1.22246 | 0.611231 | − | 0.791453i | \(-0.290675\pi\) | ||||
0.611231 | + | 0.791453i | \(0.290675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48889 | −0.736080 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.8870 | −1.36734 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.65910 | 0.312618 | 0.156309 | − | 0.987708i | \(-0.450040\pi\) | ||||
0.156309 | + | 0.987708i | \(0.450040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4852 | 1.39826 | 0.699130 | − | 0.714995i | \(-0.253571\pi\) | ||||
0.699130 | + | 0.714995i | \(0.253571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.49694 | 0.378711 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −33.2614 | −2.78146 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.97965 | 0.413537 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.76321 | −0.145427 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7596 | −1.29107 | −0.645536 | − | 0.763729i | \(-0.723366\pi\) | ||||
−0.645536 | + | 0.763729i | \(0.723366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.13049 | 0.498892 | 0.249446 | − | 0.968389i | \(-0.419751\pi\) | ||||
0.249446 | + | 0.968389i | \(0.419751\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0637243 | −0.00515181 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.6258 | 1.49606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.65811 | 0.291949 | 0.145974 | − | 0.989288i | \(-0.453368\pi\) | ||||
0.145974 | + | 0.989288i | \(0.453368\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.5836 | −1.15656 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9381 | −1.40502 | −0.702509 | − | 0.711675i | \(-0.747937\pi\) | ||||
−0.702509 | + | 0.711675i | \(0.747937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.7914 | −2.24141 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.419935 | 0.0324956 | 0.0162478 | − | 0.999868i | \(-0.494828\pi\) | ||||
0.0162478 | + | 0.999868i | \(0.494828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.3011 | 2.10009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.924533 | 0.0707008 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.48889 | 0.189227 | 0.0946134 | − | 0.995514i | \(-0.469839\pi\) | ||||
0.0946134 | + | 0.995514i | \(0.469839\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.71298 | −0.356268 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.7436 | −1.93501 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.64201 | −0.197473 | −0.0987365 | − | 0.995114i | \(-0.531480\pi\) | ||||
−0.0987365 | + | 0.995114i | \(0.531480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.38950 | 0.103281 | 0.0516405 | − | 0.998666i | \(-0.483555\pi\) | ||||
0.0516405 | + | 0.998666i | \(0.483555\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8510 | −0.802127 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.2134 | −2.29485 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.06560 | 0.224179 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.09760 | −0.370796 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0682 | 0.945578 | 0.472789 | − | 0.881176i | \(-0.343247\pi\) | ||||
0.472789 | + | 0.881176i | \(0.343247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5964 | 1.55454 | 0.777270 | − | 0.629167i | \(-0.216604\pi\) | ||||
0.777270 | + | 0.629167i | \(0.216604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 34.8850 | 2.49817 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2410 | 0.729643 | 0.364822 | − | 0.931077i | \(-0.381130\pi\) | ||||
0.364822 | + | 0.931077i | \(0.381130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6744 | −1.53646 | −0.768229 | − | 0.640175i | \(-0.778862\pi\) | ||||
−0.768229 | + | 0.640175i | \(0.778862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.0228 | 1.05963 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.59780 | 0.112144 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.67164 | −0.256439 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.108911 | −0.00756983 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −44.4767 | −3.07652 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8499 | 1.09115 | 0.545577 | − | 0.838061i | \(-0.316311\pi\) | ||||
0.545577 | + | 0.838061i | \(0.316311\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7867 | −1.01317 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.23273 | 0.629667 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.97640 | 0.405704 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.631927 | 0.0427017 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.71443 | −0.249860 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.04860 | 0.0702197 | 0.0351098 | − | 0.999383i | \(-0.488822\pi\) | ||||
0.0351098 | + | 0.999383i | \(0.488822\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.513296 | 0.0342197 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.9455 | 1.85481 | 0.927403 | − | 0.374063i | \(-0.122036\pi\) | ||||
0.927403 | + | 0.374063i | \(0.122036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.8239 | −1.17783 | −0.588917 | − | 0.808193i | \(-0.700446\pi\) | ||||
−0.588917 | + | 0.808193i | \(0.700446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.23817 | −0.607827 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.53528 | 0.624677 | 0.312339 | − | 0.949971i | \(-0.398888\pi\) | ||||
0.312339 | + | 0.949971i | \(0.398888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.94858 | 0.518508 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.4334 | 1.26233 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6190 | 0.880939 | 0.440469 | − | 0.897768i | \(-0.354812\pi\) | ||||
0.440469 | + | 0.897768i | \(0.354812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1115 | 1.03783 | 0.518917 | − | 0.854824i | \(-0.326335\pi\) | ||||
0.518917 | + | 0.854824i | \(0.326335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.13128 | 0.0725718 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.11657 | −0.199110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 53.8901 | 3.42895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.9451 | 1.20060 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7822 | 1.12240 | 0.561201 | − | 0.827680i | \(-0.310340\pi\) | ||||
0.561201 | + | 0.827680i | \(0.310340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.23940 | 0.329399 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.21525 | −0.201347 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.3733 | −0.709447 | −0.354724 | − | 0.934971i | \(-0.615425\pi\) | ||||
−0.354724 | + | 0.934971i | \(0.615425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0153 | −0.622321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.174018 | −0.0107714 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.22726 | 0.507315 | 0.253657 | − | 0.967294i | \(-0.418366\pi\) | ||||
0.253657 | + | 0.967294i | \(0.418366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.7773 | −1.58349 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.9792 | −1.95710 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.31078 | 0.201862 | 0.100931 | − | 0.994893i | \(-0.467818\pi\) | ||||
0.100931 | + | 0.994893i | \(0.467818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.3447 | 1.47883 | 0.739416 | − | 0.673248i | \(-0.235102\pi\) | ||||
0.739416 | + | 0.673248i | \(0.235102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.1934 | 0.677456 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.6932 | −1.48906 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1492 | −0.850144 | −0.425072 | − | 0.905160i | \(-0.639751\pi\) | ||||
−0.425072 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.650895 | −0.0389681 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2231 | 0.609856 | 0.304928 | − | 0.952375i | \(-0.401368\pi\) | ||||
0.304928 | + | 0.952375i | \(0.401368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.80480 | 0.345060 | 0.172530 | − | 0.985004i | \(-0.444806\pi\) | ||||
0.172530 | + | 0.985004i | \(0.444806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 46.6478 | 2.76318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.17811 | −0.0695414 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6577 | −0.979862 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.7885 | 0.866914 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.1117 | −1.81757 | −0.908783 | − | 0.417269i | \(-0.862987\pi\) | ||||
−0.908783 | + | 0.417269i | \(0.862987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.5032 | −2.64930 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.7084 | −1.54978 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.34832 | −0.367133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.96247 | 0.170754 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9847 | −0.688502 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.1797 | −1.09822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.55784 | −0.260130 | −0.130065 | − | 0.991505i | \(-0.541519\pi\) | ||||
−0.130065 | + | 0.991505i | \(0.541519\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2081 | 0.978937 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.08872 | 0.0617358 | 0.0308679 | − | 0.999523i | \(-0.490173\pi\) | ||||
0.0308679 | + | 0.999523i | \(0.490173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9086 | 0.955731 | 0.477866 | − | 0.878433i | \(-0.341411\pi\) | ||||
0.477866 | + | 0.878433i | \(0.341411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.339428 | 0.0191246 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.26439 | −0.239512 | −0.119756 | − | 0.992803i | \(-0.538211\pi\) | ||||
−0.119756 | + | 0.992803i | \(0.538211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.37152 | 0.468715 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2763 | 0.685196 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.96689 | −0.276365 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.9195 | 1.65964 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.59331 | 0.198710 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.55043 | 0.140610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.9450 | 0.931380 | 0.465690 | − | 0.884948i | \(-0.345806\pi\) | ||||
0.465690 | + | 0.884948i | \(0.345806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.09078 | 0.0597742 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.5536 | 1.45078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7547 | 0.585847 | 0.292924 | − | 0.956136i | \(-0.405372\pi\) | ||||
0.292924 | + | 0.956136i | \(0.405372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.65663 | −0.307226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.3128 | 1.69568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.49516 | −0.295850 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.2105 | 1.62178 | 0.810892 | − | 0.585195i | \(-0.198982\pi\) | ||||
0.810892 | + | 0.585195i | \(0.198982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2309 | −1.08294 | −0.541469 | − | 0.840721i | \(-0.682132\pi\) | ||||
−0.541469 | + | 0.840721i | \(0.682132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.3612 | 1.72731 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0953 | 0.750218 | 0.375109 | − | 0.926981i | \(-0.377605\pi\) | ||||
0.375109 | + | 0.926981i | \(0.377605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.1363 | −1.38717 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.03166 | −0.0546014 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0086 | −0.844903 | −0.422452 | − | 0.906385i | \(-0.638830\pi\) | ||||
−0.422452 | + | 0.906385i | \(0.638830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.0612 | 2.79270 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.0072 | −1.52248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.11696 | 0.0584646 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.8277 | −1.50479 | −0.752397 | − | 0.658710i | \(-0.771102\pi\) | ||||
−0.752397 | + | 0.658710i | \(0.771102\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.128309 | 0.00667948 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.27107 | −0.429412 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.6273 | −0.964484 | −0.482242 | − | 0.876038i | \(-0.660177\pi\) | ||||
−0.482242 | + | 0.876038i | \(0.660177\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.57720 | −0.0814464 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.1433 | −0.522409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8138 | 0.760936 | 0.380468 | − | 0.924794i | \(-0.375763\pi\) | ||||
0.380468 | + | 0.924794i | \(0.375763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.52901 | −0.436954 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.611968 | 0.0312701 | 0.0156351 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156351 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3289 | −0.832200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.322645 | −0.0164010 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4514 | 0.580607 | 0.290303 | − | 0.956935i | \(-0.406244\pi\) | ||||
0.290303 | + | 0.956935i | \(0.406244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.585105 | 0.0295900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.6703 | −1.24445 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.3495 | 1.72831 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9228 | 0.799140 | 0.399570 | − | 0.916703i | \(-0.369159\pi\) | ||||
0.399570 | + | 0.916703i | \(0.369159\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.9677 | 0.749322 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.1157 | −1.75359 | −0.876797 | − | 0.480861i | \(-0.840324\pi\) | ||||
−0.876797 | + | 0.480861i | \(0.840324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.9400 | −1.88993 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.0304 | 1.44253 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −52.4743 | −2.60105 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6726 | 1.21998 | 0.609991 | − | 0.792408i | \(-0.291173\pi\) | ||||
0.609991 | + | 0.792408i | \(0.291173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.45176 | −0.318242 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.6004 | −0.718439 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.4864 | 1.64378 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.0669 | −1.42341 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0411 | 1.12563 | 0.562816 | − | 0.826582i | \(-0.309718\pi\) | ||||
0.562816 | + | 0.826582i | \(0.309718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8048 | 0.575331 | 0.287665 | − | 0.957731i | \(-0.407121\pi\) | ||||
0.287665 | + | 0.957731i | \(0.407121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.277770 | −0.0135056 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.75759 | −0.133763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.15410 | −0.297818 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 58.6468 | 2.83150 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.56873 | −0.171899 | −0.0859497 | − | 0.996299i | \(-0.527392\pi\) | ||||
−0.0859497 | + | 0.996299i | \(0.527392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.0992 | −1.97510 | −0.987550 | − | 0.157305i | \(-0.949719\pi\) | ||||
−0.987550 | + | 0.157305i | \(0.949719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.78017 | −0.420977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.48889 | −0.406079 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.6361 | 1.50991 | 0.754954 | − | 0.655778i | \(-0.227659\pi\) | ||||
0.754954 | + | 0.655778i | \(0.227659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.108911 | 0.00518624 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.30070 | 0.156821 | 0.0784106 | − | 0.996921i | \(-0.475015\pi\) | ||||
0.0784106 | + | 0.996921i | \(0.475015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −56.5249 | −2.67954 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.7874 | 1.31430 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8820 | −0.938289 | −0.469145 | − | 0.883121i | \(-0.655438\pi\) | ||||
−0.469145 | + | 0.883121i | \(0.655438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.17257 | −0.290655 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.8093 | −0.507868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7849 | 0.927532 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2707 | 0.714332 | 0.357166 | − | 0.934041i | \(-0.383743\pi\) | ||||
0.357166 | + | 0.934041i | \(0.383743\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.98263 | −0.139217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.68922 | −0.404697 | −0.202349 | − | 0.979314i | \(-0.564857\pi\) | ||||
−0.202349 | + | 0.979314i | \(0.564857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.57355 | 0.398447 | 0.199223 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199223 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32.8413 | −1.52298 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.1327 | 1.39437 | 0.697187 | − | 0.716889i | \(-0.254435\pi\) | ||||
0.697187 | + | 0.716889i | \(0.254435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.52015 | 0.393424 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.45001 | −0.297201 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5216 | 0.713683 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.0080 | 1.83569 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.900810 | 0.0412452 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.74988 | 0.217027 | 0.108514 | − | 0.994095i | \(-0.465391\pi\) | ||||
0.108514 | + | 0.994095i | \(0.465391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 63.5803 | 2.89901 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.76321 | −0.0802289 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.1394 | 1.18693 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.9728 | −0.859741 | −0.429870 | − | 0.902891i | \(-0.641441\pi\) | ||||
−0.429870 | + | 0.902891i | \(0.641441\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.6286 | 1.43029 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.18017 | 0.278907 | 0.139453 | − | 0.990229i | \(-0.455465\pi\) | ||||
0.139453 | + | 0.990229i | \(0.455465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.934881 | 0.0421049 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.77840 | 0.0799332 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.38625 | −0.376175 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9756 | −0.938997 | −0.469498 | − | 0.882933i | \(-0.655565\pi\) | ||||
−0.469498 | + | 0.882933i | \(0.655565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.740435 | −0.0330802 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.42597 | −0.152756 | −0.0763782 | − | 0.997079i | \(-0.524336\pi\) | ||||
−0.0763782 | + | 0.997079i | \(0.524336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.1836 | −0.942656 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −48.1376 | −2.13787 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.6250 | −1.57905 | −0.789526 | − | 0.613718i | \(-0.789673\pi\) | ||||
−0.789526 | + | 0.613718i | \(0.789673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.358396 | 0.0158545 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 43.2729 | 1.91055 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.4163 | 1.34030 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3627 | 0.587692 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.38844 | −0.192631 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.6482 | −1.25510 | −0.627551 | − | 0.778576i | \(-0.715942\pi\) | ||||
−0.627551 | + | 0.778576i | \(0.715942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7717 | −0.645921 | −0.322961 | − | 0.946412i | \(-0.604678\pi\) | ||||
−0.322961 | + | 0.946412i | \(0.604678\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.30998 | 0.362677 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.49682 | 0.152324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.59015 | 0.0690064 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.47899 | 0.323951 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.6990 | 0.938129 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.65842 | 0.201025 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.23940 | −0.225677 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3001 | −0.528824 | −0.264412 | − | 0.964410i | \(-0.585178\pi\) | ||||
−0.264412 | + | 0.964410i | \(0.585178\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.44999 | −0.105139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.35136 | 0.272062 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4059 | −0.872495 | −0.436247 | − | 0.899827i | \(-0.643693\pi\) | ||||
−0.436247 | + | 0.899827i | \(0.643693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.670249 | 0.0286055 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.5635 | −0.577827 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0216 | 0.468685 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.0357 | 2.33614 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.9455 | 0.590889 | 0.295444 | − | 0.955360i | \(-0.404532\pi\) | ||||
0.295444 | + | 0.955360i | \(0.404532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.8067 | −0.795438 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.40530 | −0.228212 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.3868 | −0.943492 | −0.471746 | − | 0.881734i | \(-0.656376\pi\) | ||||
−0.471746 | + | 0.881734i | \(0.656376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.99840 | −0.420636 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.31487 | 0.391188 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0581 | −0.966645 | −0.483322 | − | 0.875442i | \(-0.660570\pi\) | ||||
−0.483322 | + | 0.875442i | \(0.660570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.606257 | 0.0253711 | 0.0126855 | − | 0.999920i | \(-0.495962\pi\) | ||||
0.0126855 | + | 0.999920i | \(0.495962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.0419 | −0.962589 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.71298 | −0.196545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.57828 | 0.232227 | 0.116113 | − | 0.993236i | \(-0.462956\pi\) | ||||
0.116113 | + | 0.993236i | \(0.462956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.0789 | −1.58251 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.7446 | 0.445763 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.3355 | −1.79477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.15480 | −0.0890899 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.5804 | −0.643071 | −0.321536 | − | 0.946898i | \(-0.604199\pi\) | ||||
−0.321536 | + | 0.946898i | \(0.604199\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.7330 | −2.09042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.0571 | −0.742769 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4788 | −0.512443 | −0.256222 | − | 0.966618i | \(-0.582478\pi\) | ||||
−0.256222 | + | 0.966618i | \(0.582478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.82352 | −0.0747569 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.2165 | 1.56410 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6897 | −1.04965 | −0.524827 | − | 0.851209i | \(-0.675870\pi\) | ||||
−0.524827 | + | 0.851209i | \(0.675870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1712 | 0.578055 | 0.289028 | − | 0.957321i | \(-0.406668\pi\) | ||||
0.289028 | + | 0.957321i | \(0.406668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.927938 | −0.0377885 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −51.2717 | −2.08449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.6010 | −1.56677 | −0.783383 | − | 0.621539i | \(-0.786508\pi\) | ||||
−0.783383 | + | 0.621539i | \(0.786508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.81726 | −0.114161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.1909 | −0.655015 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.40423 | −0.0971058 | −0.0485529 | − | 0.998821i | \(-0.515461\pi\) | ||||
−0.0485529 | + | 0.998821i | \(0.515461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.47388 | 0.261052 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5675 | 0.989051 | 0.494526 | − | 0.869163i | \(-0.335342\pi\) | ||||
0.494526 | + | 0.869163i | \(0.335342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.0657 | 1.24864 | 0.624318 | − | 0.781171i | \(-0.285377\pi\) | ||||
0.624318 | + | 0.781171i | \(0.285377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.09760 | −0.204560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.1369 | −0.726640 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.3527 | −1.05411 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 78.4218 | 3.13187 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.86001 | −0.233654 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9461 | −0.634805 | −0.317402 | − | 0.948291i | \(-0.602811\pi\) | ||||
−0.317402 | + | 0.948291i | \(0.602811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.9468 | −1.11078 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.0755 | −0.598252 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.34832 | 0.251529 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.913355 | 0.0361317 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.1109 | −1.34730 | −0.673650 | − | 0.739051i | \(-0.735274\pi\) | ||||
−0.673650 | + | 0.739051i | \(0.735274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.7215 | 0.896050 | 0.448025 | − | 0.894021i | \(-0.352128\pi\) | ||||
0.448025 | + | 0.894021i | \(0.352128\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.2792 | −0.640995 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.53740 | −0.178384 | −0.0891918 | − | 0.996014i | \(-0.528428\pi\) | ||||
−0.0891918 | + | 0.996014i | \(0.528428\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −76.4975 | −3.00279 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5376 | −0.413003 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.9525 | −1.52433 | −0.762164 | − | 0.647384i | \(-0.775863\pi\) | ||||
−0.762164 | + | 0.647384i | \(0.775863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.6061 | −1.70383 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.0390332 | −0.00152283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.8983 | −0.580357 | −0.290179 | − | 0.956973i | \(-0.593715\pi\) | ||||
−0.290179 | + | 0.956973i | \(0.593715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2118 | 0.669461 | 0.334731 | − | 0.942314i | \(-0.391355\pi\) | ||||
0.334731 | + | 0.942314i | \(0.391355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.54932 | 0.254355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.4562 | 1.02593 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.59780 | 0.0618671 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.84891 | −0.0714829 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.2438 | −1.24476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7685 | 0.762018 | 0.381009 | − | 0.924571i | \(-0.375577\pi\) | ||||
0.381009 | + | 0.924571i | \(0.375577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.0249 | 0.924719 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0117 | −1.38404 | −0.692020 | − | 0.721878i | \(-0.743279\pi\) | ||||
−0.692020 | + | 0.721878i | \(0.743279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.38723 | 0.321872 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.2738 | −1.88817 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.0796 | 0.423949 | 0.211975 | − | 0.977275i | \(-0.432011\pi\) | ||||
0.211975 | + | 0.977275i | \(0.432011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4038 | −0.435718 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.4272 | 1.19902 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 52.5073 | 2.00037 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5328 | −0.628936 | −0.314468 | − | 0.949268i | \(-0.601826\pi\) | ||||
−0.314468 | + | 0.949268i | \(0.601826\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.570629 | 0.0216764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.3773 | −1.94885 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.689315 | −0.0261097 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.8127 | −0.635915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.2642 | 0.652058 | 0.326029 | − | 0.945360i | \(-0.394289\pi\) | ||||
0.326029 | + | 0.945360i | \(0.394289\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 85.0189 | 3.20655 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.0150 | −0.527836 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.79708 | −0.255631 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.98260 | −0.149570 | −0.0747849 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747849 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.20037 | −0.0450174 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.97640 | 0.223818 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 103.661 | 3.87671 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0131 | −0.896787 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.33439 | −0.273527 | −0.136763 | − | 0.990604i | \(-0.543670\pi\) | ||||
−0.136763 | + | 0.990604i | \(0.543670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.75955 | 0.363465 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.4080 | −1.05651 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.53041 | −0.279672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.06498 | 0.150762 | 0.0753809 | − | 0.997155i | \(-0.475983\pi\) | ||||
0.0753809 | + | 0.997155i | \(0.475983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9499 | 0.961108 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.73335 | 0.0641104 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2247 | 0.636207 | 0.318104 | − | 0.948056i | \(-0.396954\pi\) | ||||
0.318104 | + | 0.948056i | \(0.396954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.49516 | 0.202692 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 44.6405 | 1.64435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0829 | 0.481262 | 0.240631 | − | 0.970617i | \(-0.422646\pi\) | ||||
0.240631 | + | 0.970617i | \(0.422646\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −95.0197 | −3.49063 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.58553 | −0.351659 | −0.175830 | − | 0.984421i | \(-0.556261\pi\) | ||||
−0.175830 | + | 0.984421i | \(0.556261\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.1157 | 1.79946 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.17021 | −0.0428157 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.96247 | 0.254403 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.3151 | 1.43463 | 0.717314 | − | 0.696750i | \(-0.245371\pi\) | ||||
0.717314 | + | 0.696750i | \(0.245371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.3537 | −1.14259 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.1061 | −0.695342 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.7971 | −1.11934 | −0.559670 | − | 0.828716i | \(-0.689072\pi\) | ||||
−0.559670 | + | 0.828716i | \(0.689072\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.23817 | −0.335324 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0651 | 0.691110 | 0.345555 | − | 0.938399i | \(-0.387691\pi\) | ||||
0.345555 | + | 0.938399i | \(0.387691\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03794 | 0.0737782 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.198601 | 0.00718044 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 92.6880 | 3.34677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0861 | 0.507959 | 0.253980 | − | 0.967210i | \(-0.418260\pi\) | ||||
0.253980 | + | 0.967210i | \(0.418260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0535 | 0.722210 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.46538 | −0.196576 | −0.0982879 | − | 0.995158i | \(-0.531337\pi\) | ||||
−0.0982879 | + | 0.995158i | \(0.531337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.1667 | −1.01178 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.6591 | 0.633517 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.0008 | 0.358316 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.9390 | −1.57226 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.14494 | −0.291077 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.4007 | −0.406910 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.3921 | 1.29724 | 0.648618 | − | 0.761114i | \(-0.275347\pi\) | ||||
0.648618 | + | 0.761114i | \(0.275347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.5064 | −0.516441 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.20815 | −0.114069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.0682 | 1.38735 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.4509 | 1.61198 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.5810 | 1.54372 | 0.771858 | − | 0.635794i | \(-0.219327\pi\) | ||||
0.771858 | + | 0.635794i | \(0.219327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.49227 | 0.0527927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.97531 | 0.0697941 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.87778 | 0.0662654 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.11657 | −0.109845 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.83761 | −0.205494 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.11013 | 0.179663 | 0.0898313 | − | 0.995957i | \(-0.471367\pi\) | ||||
0.0898313 | + | 0.995957i | \(0.471367\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.06953 | −0.0726712 | −0.0363356 | − | 0.999340i | \(-0.511569\pi\) | ||||
−0.0363356 | + | 0.999340i | \(0.511569\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.9248 | −1.50544 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55.9052 | 1.95827 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.1481 | −0.879819 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.691401 | −0.0241595 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.87359 | 0.100289 | 0.0501446 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501446 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.81222 | 0.132886 | 0.0664428 | − | 0.997790i | \(-0.478835\pi\) | ||||
0.0664428 | + | 0.997790i | \(0.478835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 43.5394 | 1.51585 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.87210 | −0.238966 | −0.119483 | − | 0.992836i | \(-0.538124\pi\) | ||||
−0.119483 | + | 0.992836i | \(0.538124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.53374 | 0.192195 | 0.0960973 | − | 0.995372i | \(-0.469364\pi\) | ||||
0.0960973 | + | 0.995372i | \(0.469364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9480 | 0.865438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.585105 | −0.0202727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.30876 | −0.0452914 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.4653 | −1.05303 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.16338 | 0.0401642 | 0.0200821 | − | 0.999798i | \(-0.493607\pi\) | ||||
0.0200821 | + | 0.999798i | \(0.493607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4470 | −0.911967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.0254 | −0.620827 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −85.0857 | −2.92704 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4514 | −0.565275 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.2351 | −0.351267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0153 | −0.343320 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.30694 | 0.181706 | 0.0908531 | − | 0.995864i | \(-0.471041\pi\) | ||||
0.0908531 | + | 0.995864i | \(0.471041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.88137 | −0.0985407 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.84412 | −0.0629938 | −0.0314969 | − | 0.999504i | \(-0.510027\pi\) | ||||
−0.0314969 | + | 0.999504i | \(0.510027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1077 | 1.53905 | 0.769527 | − | 0.638615i | \(-0.220492\pi\) | ||||
0.769527 | + | 0.638615i | \(0.220492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.07725 | 0.0707924 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.75173 | 0.0936701 | 0.0468351 | − | 0.998903i | \(-0.485086\pi\) | ||||
0.0468351 | + | 0.998903i | \(0.485086\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.75679 | −0.263739 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.3709 | 0.997490 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.7465 | 1.95892 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.0886 | −1.83272 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.913461 | −0.0309160 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.894506 | −0.0302398 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9340 | 1.11210 | 0.556052 | − | 0.831148i | \(-0.312316\pi\) | ||||
0.556052 | + | 0.831148i | \(0.312316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.8565 | 1.85026 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6201 | 1.36853 | 0.684264 | − | 0.729235i | \(-0.260124\pi\) | ||||
0.684264 | + | 0.729235i | \(0.260124\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.817246 | 0.0275025 | 0.0137513 | − | 0.999905i | \(-0.495623\pi\) | ||||
0.0137513 | + | 0.999905i | \(0.495623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 80.2316 | 2.69696 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.29164 | 0.144099 | 0.0720496 | − | 0.997401i | \(-0.477046\pi\) | ||||
0.0720496 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.83720 | −0.162235 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 48.8044 | 1.63501 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.6503 | −0.724500 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.23399 | 0.275232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.1934 | 0.373737 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.54909 | 0.318480 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.83944 | −0.161225 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.22346 | −0.173826 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.33048 | −0.143950 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.7845 | −1.45384 | −0.726920 | − | 0.686723i | \(-0.759049\pi\) | ||||
−0.726920 | + | 0.686723i | \(0.759049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.740277 | 0.0245534 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.8009 | −1.61684 | −0.808422 | − | 0.588603i | \(-0.799678\pi\) | ||||
−0.808422 | + | 0.588603i | \(0.799678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.2955 | 1.86311 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.8178 | 1.11798 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.9917 | −0.462047 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5677 | 0.348596 | 0.174298 | − | 0.984693i | \(-0.444234\pi\) | ||||
0.174298 | + | 0.984693i | \(0.444234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.03644 | 0.264810 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53.2386 | 1.75237 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.2020 | 1.55199 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.06292 | −0.0349109 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.51933 | 0.181083 | 0.0905417 | − | 0.995893i | \(-0.471140\pi\) | ||||
0.0905417 | + | 0.995893i | \(0.471140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.48889 | 0.278212 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.91965 | −0.0628465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.55415 | −0.312454 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.4761 | −1.68165 | −0.840826 | − | 0.541305i | \(-0.817930\pi\) | ||||
−0.840826 | + | 0.541305i | \(0.817930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.8134 | −0.972925 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0595 | 0.751718 | 0.375859 | − | 0.926677i | \(-0.377348\pi\) | ||||
0.375859 | + | 0.926677i | \(0.377348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.17811 | −0.0383644 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.8870 | 0.516804 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0207 | 0.878054 | 0.439027 | − | 0.898474i | \(-0.355323\pi\) | ||||
0.439027 | + | 0.898474i | \(0.355323\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.27521 | −0.0738564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.51902 | 0.243821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6466 | 0.960348 | 0.480174 | − | 0.877173i | \(-0.340574\pi\) | ||||
0.480174 | + | 0.877173i | \(0.340574\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.7278 | −1.31792 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.7608 | −0.477147 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.65910 | −0.118158 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.71731 | 0.152171 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.758289 | −0.0244355 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −67.3065 | −2.16667 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.6275 | −1.33865 | −0.669324 | − | 0.742970i | \(-0.733416\pi\) | ||||
−0.669324 | + | 0.742970i | \(0.733416\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.75767 | 0.281337 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.4436 | 1.20162 | 0.600811 | − | 0.799391i | \(-0.294845\pi\) | ||||
0.600811 | + | 0.799391i | \(0.294845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.4852 | −0.528492 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −52.7544 | −1.68949 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8568 | 0.827231 | 0.413616 | − | 0.910452i | \(-0.364266\pi\) | ||||
0.413616 | + | 0.910452i | \(0.364266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −95.0266 | −3.03706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.221953 | −0.00708643 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8201 | 1.07869 | 0.539347 | − | 0.842084i | \(-0.318671\pi\) | ||||
0.539347 | + | 0.842084i | \(0.318671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.9168 | −1.01696 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.49694 | −0.143139 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.96247 | 0.0942010 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.9278 | −0.855390 | −0.427695 | − | 0.903923i | \(-0.640674\pi\) | ||||
−0.427695 | + | 0.903923i | \(0.640674\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.8776 | −0.948136 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.5497 | 2.14147 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.87456 | 0.154379 | 0.0771894 | − | 0.997016i | \(-0.475405\pi\) | ||||
0.0771894 | + | 0.997016i | \(0.475405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.0540 | 1.61528 |
(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 | 644.2.a.d.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 5796.2.a.t.1.5 | 5 | |||
4.3 | odd | 2 | 2576.2.a.bb.1.4 | 5 | |||
7.6 | odd | 2 | 4508.2.a.f.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.d.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
2576.2.a.bb.1.4 | 5 | 4.3 | odd | 2 | |||
4508.2.a.f.1.4 | 5 | 7.6 | odd | 2 | |||
5796.2.a.t.1.5 | 5 | 3.2 | odd | 2 |