Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [740,2,Mod(1,740)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(740, 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("740.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 740 = 2^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 740.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: | \(5.90892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.286164.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 11x^{2} - 3x + 12 \) |
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 | 1.3 | ||
Root | \(-1.51951\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 740.1 |
$q$-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 | ||||||||
\(3\) | 2.51951 | 1.45464 | 0.727320 | − | 0.686299i | \(-0.240766\pi\) | ||||
0.727320 | + | 0.686299i | \(0.240766\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.519509 | 0.196356 | 0.0981780 | − | 0.995169i | \(-0.468699\pi\) | ||||
0.0981780 | + | 0.995169i | \(0.468699\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.34793 | 1.11598 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.16241 | 1.85804 | 0.929019 | − | 0.370033i | \(-0.120654\pi\) | ||||
0.929019 | + | 0.370033i | \(0.120654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.51034 | −1.80564 | −0.902822 | − | 0.430015i | \(-0.858508\pi\) | ||||
−0.902822 | + | 0.430015i | \(0.858508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.51951 | 0.650535 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.51034 | −0.608847 | −0.304423 | − | 0.952537i | \(-0.598464\pi\) | ||||
−0.304423 | + | 0.952537i | \(0.598464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.68192 | 1.53294 | 0.766469 | − | 0.642281i | \(-0.222012\pi\) | ||||
0.766469 | + | 0.642281i | \(0.222012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30891 | 0.285627 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.03902 | −0.633679 | −0.316840 | − | 0.948479i | \(-0.602622\pi\) | ||||
−0.316840 | + | 0.948479i | \(0.602622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.876607 | 0.168703 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.03902 | −0.564332 | −0.282166 | − | 0.959366i | \(-0.591053\pi\) | ||||
−0.282166 | + | 0.959366i | \(0.591053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.33876 | −0.779264 | −0.389632 | − | 0.920971i | \(-0.627398\pi\) | ||||
−0.389632 | + | 0.920971i | \(0.627398\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.5263 | 2.70277 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.519509 | 0.0878131 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.4029 | −2.62656 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1624 | 1.89945 | 0.949725 | − | 0.313086i | \(-0.101363\pi\) | ||||
0.949725 | + | 0.313086i | \(0.101363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34316 | −0.357329 | −0.178665 | − | 0.983910i | \(-0.557178\pi\) | ||||
−0.178665 | + | 0.983910i | \(0.557178\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.34793 | 0.499080 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.54019 | 1.39158 | 0.695790 | − | 0.718245i | \(-0.255055\pi\) | ||||
0.695790 | + | 0.718245i | \(0.255055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73011 | −0.961444 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.32482 | −0.885653 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.20143 | −1.26391 | −0.631957 | − | 0.775004i | \(-0.717748\pi\) | ||||
−0.631957 | + | 0.775004i | \(0.717748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.16241 | 0.830939 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.8352 | 2.22987 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.37778 | −1.22088 | −0.610441 | − | 0.792062i | \(-0.709008\pi\) | ||||
−0.610441 | + | 0.792062i | \(0.709008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.73928 | 0.219129 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.51034 | −0.807508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.357097 | 0.0436264 | 0.0218132 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218132 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.65684 | −0.921775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87661 | −0.341390 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2404 | −1.19855 | −0.599277 | − | 0.800542i | \(-0.704545\pi\) | ||||
−0.599277 | + | 0.800542i | \(0.704545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.51951 | 0.290928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.20143 | 0.364837 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.681922 | 0.0767222 | 0.0383611 | − | 0.999264i | \(-0.487786\pi\) | ||||
0.0383611 | + | 0.999264i | \(0.487786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.83516 | −0.870574 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.17635 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.51034 | −0.272285 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.65684 | −0.820899 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0207 | −1.16819 | −0.584095 | − | 0.811685i | \(-0.698550\pi\) | ||||
−0.584095 | + | 0.811685i | \(0.698550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.38218 | −0.354549 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.9315 | −1.13355 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.68192 | 0.685551 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.34316 | 0.644051 | 0.322025 | − | 0.946731i | \(-0.395636\pi\) | ||||
0.322025 | + | 0.946731i | \(0.395636\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.6313 | 2.07352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.4466 | 1.93501 | 0.967507 | − | 0.252845i | \(-0.0813664\pi\) | ||||
0.967507 | + | 0.252845i | \(0.0813664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | 0.197066 | 0.0985329 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985329 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30891 | 0.127736 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0251 | −1.45253 | −0.726265 | − | 0.687415i | \(-0.758745\pi\) | ||||
−0.726265 | + | 0.687415i | \(0.758745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.7070 | 1.50446 | 0.752229 | − | 0.658902i | \(-0.228979\pi\) | ||||
0.752229 | + | 0.658902i | \(0.228979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.51951 | 0.239141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.18552 | −0.205596 | −0.102798 | − | 0.994702i | \(-0.532780\pi\) | ||||
−0.102798 | + | 0.994702i | \(0.532780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.03902 | −0.283390 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −21.7961 | −2.01505 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.30414 | −0.119551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.9753 | 2.45230 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.6433 | 2.76301 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.17635 | 0.193119 | 0.0965597 | − | 0.995327i | \(-0.469216\pi\) | ||||
0.0965597 | + | 0.995327i | \(0.469216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.90362 | −0.519785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7416 | −1.11324 | −0.556620 | − | 0.830767i | \(-0.687902\pi\) | ||||
−0.556620 | + | 0.830767i | \(0.687902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.47132 | 0.301002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.876607 | 0.0754463 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.26513 | −0.364394 | −0.182197 | − | 0.983262i | \(-0.558321\pi\) | ||||
−0.182197 | + | 0.983262i | \(0.558321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6290 | −0.986356 | −0.493178 | − | 0.869928i | \(-0.664165\pi\) | ||||
−0.493178 | + | 0.869928i | \(0.664165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.0366 | 2.02425 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −40.1194 | −3.35495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.03902 | −0.252377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.9566 | −1.39855 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3591 | −1.42211 | −0.711056 | − | 0.703136i | \(-0.751783\pi\) | ||||
−0.711056 | + | 0.703136i | \(0.751783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.343164 | 0.0279263 | 0.0139631 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139631 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.40444 | −0.679458 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.33876 | −0.348497 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.16241 | −0.332197 | −0.166098 | − | 0.986109i | \(-0.553117\pi\) | ||||
−0.166098 | + | 0.986109i | \(0.553117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.1831 | −1.83854 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.57880 | −0.124427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.3455 | 1.51526 | 0.757628 | − | 0.652686i | \(-0.226358\pi\) | ||||
0.757628 | + | 0.652686i | \(0.226358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.5263 | 1.20872 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.979321 | −0.0757821 | −0.0378911 | − | 0.999282i | \(-0.512064\pi\) | ||||
−0.0378911 | + | 0.999282i | \(0.512064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.3845 | 2.26035 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.3706 | 1.71072 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.9363 | −1.74381 | −0.871907 | − | 0.489671i | \(-0.837117\pi\) | ||||
−0.871907 | + | 0.489671i | \(0.837117\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.519509 | 0.0392712 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.6274 | −1.77594 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7600 | −1.25270 | −0.626349 | − | 0.779543i | \(-0.715452\pi\) | ||||
−0.626349 | + | 0.779543i | \(0.715452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4466 | −0.850822 | −0.425411 | − | 0.905000i | \(-0.639871\pi\) | ||||
−0.425411 | + | 0.905000i | \(0.639871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.03902 | 0.372495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.4697 | −1.13126 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.455405 | 0.0331259 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4351 | −0.755060 | −0.377530 | − | 0.925997i | \(-0.623226\pi\) | ||||
−0.377530 | + | 0.925997i | \(0.623226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4029 | 1.46863 | 0.734315 | − | 0.678809i | \(-0.237503\pi\) | ||||
0.734315 | + | 0.678809i | \(0.237503\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.4029 | −1.17463 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1051 | −0.791202 | −0.395601 | − | 0.918422i | \(-0.629464\pi\) | ||||
−0.395601 | + | 0.918422i | \(0.629464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.622223 | −0.0441083 | −0.0220541 | − | 0.999757i | \(-0.507021\pi\) | ||||
−0.0220541 | + | 0.999757i | \(0.507021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.899710 | 0.0634606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.57880 | −0.110810 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.1624 | 0.849460 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1744 | −0.707171 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 41.1768 | 2.84826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3001 | −1.25983 | −0.629917 | − | 0.776662i | \(-0.716911\pi\) | ||||
−0.629917 | + | 0.776662i | \(0.716911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.24764 | −0.496600 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.34316 | −0.159802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.25403 | −0.153013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −25.8009 | −1.74346 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3432 | 1.09936 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.784636 | −0.0525431 | −0.0262715 | − | 0.999655i | \(-0.508363\pi\) | ||||
−0.0262715 | + | 0.999655i | \(0.508363\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.34793 | 0.223195 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.32482 | 0.419793 | 0.209897 | − | 0.977724i | \(-0.432687\pi\) | ||||
0.209897 | + | 0.977724i | \(0.432687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.08437 | 0.137739 | 0.0688697 | − | 0.997626i | \(-0.478061\pi\) | ||||
0.0688697 | + | 0.997626i | \(0.478061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.06604 | 0.530706 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.4626 | 1.73362 | 0.866810 | − | 0.498639i | \(-0.166167\pi\) | ||||
0.866810 | + | 0.498639i | \(0.166167\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.54019 | 0.622333 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.71811 | 0.111603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.6636 | 1.20725 | 0.603623 | − | 0.797270i | \(-0.293723\pi\) | ||||
0.603623 | + | 0.797270i | \(0.293723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0596981 | −0.00384549 | −0.00192274 | − | 0.999998i | \(-0.500612\pi\) | ||||
−0.00192274 | + | 0.999998i | \(0.500612\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3706 | −1.43507 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.73011 | −0.429971 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.5016 | −2.76794 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5614 | 0.986161 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.05295 | 0.192701 | 0.0963503 | − | 0.995347i | \(-0.469283\pi\) | ||||
0.0963503 | + | 0.995347i | \(0.469283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.7277 | −1.17740 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.32482 | −0.396076 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.9132 | −1.30453 | −0.652265 | − | 0.757991i | \(-0.726181\pi\) | ||||
−0.652265 | + | 0.757991i | \(0.726181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.519509 | 0.0322807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.1744 | −0.629780 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.91122 | −0.487827 | −0.243913 | − | 0.969797i | \(-0.578431\pi\) | ||||
−0.243913 | + | 0.969797i | \(0.578431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.20143 | −0.565239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.7667 | −1.69929 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.606717 | −0.0369922 | −0.0184961 | − | 0.999829i | \(-0.505888\pi\) | ||||
−0.0184961 | + | 0.999829i | \(0.505888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5931 | 1.25094 | 0.625472 | − | 0.780247i | \(-0.284906\pi\) | ||||
0.625472 | + | 0.780247i | \(0.284906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.52144 | −0.515741 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.16241 | 0.371607 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2842 | 1.27885 | 0.639423 | − | 0.768855i | \(-0.279173\pi\) | ||||
0.639423 | + | 0.768855i | \(0.279173\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5258 | −0.869640 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3432 | −0.617021 | −0.308511 | − | 0.951221i | \(-0.599831\pi\) | ||||
−0.308511 | + | 0.951221i | \(0.599831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.67518 | 0.0995789 | 0.0497894 | − | 0.998760i | \(-0.484145\pi\) | ||||
0.0497894 | + | 0.998760i | \(0.484145\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.8352 | 0.997229 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.31849 | 0.372969 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6982 | −0.629306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.9817 | 0.936862 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.96332 | 0.582063 | 0.291032 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291032 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.37778 | −0.545995 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.40201 | 0.313456 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.7850 | 1.14420 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.21730 | −0.0701637 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 48.9960 | 2.81475 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2265 | 1.49683 | 0.748413 | − | 0.663233i | \(-0.230816\pi\) | ||||
0.748413 | + | 0.663233i | \(0.230816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.03902 | 0.286660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.74881 | 0.0991658 | 0.0495829 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495829 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.7762 | −1.23087 | −0.615433 | − | 0.788189i | \(-0.711019\pi\) | ||||
−0.615433 | + | 0.788189i | \(0.711019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.73928 | 0.0979973 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.42120 | 0.248319 | 0.124160 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124160 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.7277 | −1.04855 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.8558 | −2.11291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.7739 | −0.933324 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.51034 | −0.361129 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.5740 | 2.18844 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.95622 | 0.273245 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.4168 | 1.78179 | 0.890894 | − | 0.454211i | \(-0.150079\pi\) | ||||
0.890894 | + | 0.454211i | \(0.150079\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.34793 | 0.183465 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.357097 | 0.0195103 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.8789 | 1.62761 | 0.813805 | − | 0.581138i | \(-0.197392\pi\) | ||||
0.813805 | + | 0.581138i | \(0.197392\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.50643 | −0.299068 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.7372 | −1.44790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.13292 | −0.385142 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.65684 | −0.412230 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.88294 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.5494 | 1.68880 | 0.844399 | − | 0.535714i | \(-0.179958\pi\) | ||||
0.844399 | + | 0.535714i | \(0.179958\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.70701 | −0.304617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.68633 | −0.142979 | −0.0714894 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714894 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.87661 | −0.152674 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.28581 | −0.173903 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9570 | 1.15885 | 0.579423 | − | 0.815027i | \(-0.303278\pi\) | ||||
0.579423 | + | 0.815027i | \(0.303278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.6481 | 1.34990 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 67.9646 | 3.56722 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2404 | −0.536010 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.3499 | −1.32325 | −0.661627 | − | 0.749833i | \(-0.730134\pi\) | ||||
−0.661627 | + | 0.749833i | \(0.730134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40.7189 | 2.11974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.78023 | −0.248177 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6322 | 1.22363 | 0.611813 | − | 0.791002i | \(-0.290440\pi\) | ||||
0.611813 | + | 0.791002i | \(0.290440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.51951 | 0.130107 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7850 | 1.01898 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8216 | −0.966800 | −0.483400 | − | 0.875400i | \(-0.660598\pi\) | ||||
−0.483400 | + | 0.875400i | \(0.660598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.48332 | 0.280919 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.0485 | 0.564554 | 0.282277 | − | 0.959333i | \(-0.408910\pi\) | ||||
0.282277 | + | 0.959333i | \(0.408910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.20143 | 0.163160 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.84474 | −0.398771 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.4235 | 1.49183 | 0.745916 | − | 0.666040i | \(-0.232012\pi\) | ||||
0.745916 | + | 0.666040i | \(0.232012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.62897 | 0.385814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.1026 | −1.61936 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.681922 | 0.0343112 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2014 | 0.863315 | 0.431658 | − | 0.902038i | \(-0.357929\pi\) | ||||
0.431658 | + | 0.902038i | \(0.357929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.74603 | 0.437849 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6496 | 0.931319 | 0.465660 | − | 0.884964i | \(-0.345817\pi\) | ||||
0.465660 | + | 0.884964i | \(0.345817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2468 | 1.40707 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.83516 | −0.389332 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.16241 | 0.305459 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0390 | 0.545844 | 0.272922 | − | 0.962036i | \(-0.412010\pi\) | ||||
0.272922 | + | 0.962036i | \(0.412010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7460 | −0.530062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.87184 | −0.239728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.17635 | 0.303185 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.2993 | −1.43479 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.95698 | −0.486430 | −0.243215 | − | 0.969972i | \(-0.578202\pi\) | ||||
−0.243215 | + | 0.969972i | \(0.578202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8153 | 1.11195 | 0.555974 | − | 0.831200i | \(-0.312346\pi\) | ||||
0.555974 | + | 0.831200i | \(0.312346\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.9399 | 1.55297 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.51034 | −0.121769 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.03902 | 0.0502816 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −101.081 | −4.88025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.67239 | 0.417735 | 0.208867 | − | 0.977944i | \(-0.433022\pi\) | ||||
0.208867 | + | 0.977944i | \(0.433022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.38852 | −0.258956 | −0.129478 | − | 0.991582i | \(-0.541330\pi\) | ||||
−0.129478 | + | 0.991582i | \(0.541330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.65684 | −0.367117 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.3065 | −0.971391 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.603884 | 0.0288218 | 0.0144109 | − | 0.999896i | \(-0.495413\pi\) | ||||
0.0144109 | + | 0.999896i | \(0.495413\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.5319 | −1.07295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.2655 | 1.29542 | 0.647712 | − | 0.761885i | \(-0.275726\pi\) | ||||
0.647712 | + | 0.761885i | \(0.275726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0207 | −0.522430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.7364 | −2.06866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.28581 | 0.438224 | 0.219112 | − | 0.975700i | \(-0.429684\pi\) | ||||
0.219112 | + | 0.975700i | \(0.429684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74.9498 | 3.52925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.864604 | 0.0406227 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.38218 | −0.158559 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2651 | 0.573738 | 0.286869 | − | 0.957970i | \(-0.407385\pi\) | ||||
0.286869 | + | 0.957970i | \(0.407385\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.20058 | −0.102714 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.81291 | 0.0844357 | 0.0422178 | − | 0.999108i | \(-0.486558\pi\) | ||||
0.0422178 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7349 | −1.10305 | −0.551527 | − | 0.834157i | \(-0.685954\pi\) | ||||
−0.551527 | + | 0.834157i | \(0.685954\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.9315 | −0.506938 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.185515 | 0.00856630 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4872 | −0.483226 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.4395 | −0.663931 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.68192 | 0.306588 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.8057 | −1.41050 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.62456 | −0.439758 | −0.219879 | − | 0.975527i | \(-0.570566\pi\) | ||||
−0.219879 | + | 0.975527i | \(0.570566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.51034 | −0.296846 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.97780 | −0.180996 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.34316 | 0.288028 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.7165 | −1.43721 | −0.718607 | − | 0.695417i | \(-0.755220\pi\) | ||||
−0.718607 | + | 0.695417i | \(0.755220\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.7412 | 2.20415 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.02068 | −0.226580 | −0.113290 | − | 0.993562i | \(-0.536139\pi\) | ||||
−0.113290 | + | 0.993562i | \(0.536139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.62897 | 0.343591 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.6313 | 0.927308 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.49442 | −0.0670341 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.8794 | 1.56141 | 0.780707 | − | 0.624897i | \(-0.214859\pi\) | ||||
0.780707 | + | 0.624897i | \(0.214859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.46741 | −0.110236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2158 | 0.901377 | 0.450688 | − | 0.892681i | \(-0.351179\pi\) | ||||
0.450688 | + | 0.892681i | \(0.351179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.4466 | 0.865364 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 74.0346 | 3.28799 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.18075 | 0.185309 | 0.0926543 | − | 0.995698i | \(-0.470465\pi\) | ||||
0.0926543 | + | 0.995698i | \(0.470465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.32001 | −0.235343 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.85742 | 0.258611 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | 0.0881305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 58.7906 | 2.58561 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −57.7882 | −2.53662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.26036 | −0.274271 | −0.137136 | − | 0.990552i | \(-0.543790\pi\) | ||||
−0.137136 | + | 0.990552i | \(0.543790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.3432 | 1.32681 | 0.663407 | − | 0.748259i | \(-0.269110\pi\) | ||||
0.663407 | + | 0.748259i | \(0.269110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30891 | 0.0571255 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.8918 | 0.474452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.7644 | −0.598451 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.3961 | −1.36248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −79.1814 | −3.42973 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0251 | −0.649591 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −42.2269 | −1.82222 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −41.4737 | −1.78640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0502 | −0.690051 | −0.345025 | − | 0.938593i | \(-0.612130\pi\) | ||||
−0.345025 | + | 0.938593i | \(0.612130\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.8399 | −1.23764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.7070 | 0.672814 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0804 | 0.901332 | 0.450666 | − | 0.892693i | \(-0.351187\pi\) | ||||
0.450666 | + | 0.892693i | \(0.351187\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.69586 | 0.285772 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.3065 | −0.865085 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.354265 | 0.0150649 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.51951 | 0.106947 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.959408 | 0.0406514 | 0.0203257 | − | 0.999793i | \(-0.493530\pi\) | ||||
0.0203257 | + | 0.999793i | \(0.493530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2548 | 0.645209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.9762 | −1.64558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.3957 | −1.74462 | −0.872310 | − | 0.488954i | \(-0.837379\pi\) | ||||
−0.872310 | + | 0.488954i | \(0.837379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.18552 | −0.0919453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.07044 | −0.170942 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.4626 | −1.10937 | −0.554684 | − | 0.832061i | \(-0.687161\pi\) | ||||
−0.554684 | + | 0.832061i | \(0.687161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.4482 | 0.730185 | 0.365093 | − | 0.930971i | \(-0.381037\pi\) | ||||
0.365093 | + | 0.930971i | \(0.381037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.2914 | −1.09834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.03902 | −0.126736 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.2954 | 1.26121 | 0.630607 | − | 0.776103i | \(-0.282806\pi\) | ||||
0.630607 | + | 0.776103i | \(0.282806\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.4052 | 2.13633 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.20867 | 0.133118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −56.7030 | −2.34840 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.7961 | −0.901160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.2858 | 0.878559 | 0.439280 | − | 0.898350i | \(-0.355234\pi\) | ||||
0.439280 | + | 0.898350i | \(0.355234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.9912 | −1.19456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.9793 | −1.15091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.5629 | −0.721223 | −0.360612 | − | 0.932716i | \(-0.617432\pi\) | ||||
−0.360612 | + | 0.932716i | \(0.617432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.30414 | −0.0534647 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.56770 | −0.0641616 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.8901 | −0.526675 | −0.263338 | − | 0.964704i | \(-0.584823\pi\) | ||||
−0.263338 | + | 0.964704i | \(0.584823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.8424 | −0.564641 | −0.282321 | − | 0.959320i | \(-0.591104\pi\) | ||||
−0.282321 | + | 0.959320i | \(0.591104\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.19554 | 0.0486860 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.9753 | 1.09670 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.7460 | 1.00441 | 0.502205 | − | 0.864749i | \(-0.332522\pi\) | ||||
0.502205 | + | 0.864749i | \(0.332522\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.97780 | −0.161189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.1099 | −2.51270 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9753 | −0.483679 | −0.241839 | − | 0.970316i | \(-0.577751\pi\) | ||||
−0.241839 | + | 0.970316i | \(0.577751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.6433 | 1.23566 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.5167 | −1.02726 | −0.513632 | − | 0.858010i | \(-0.671700\pi\) | ||||
−0.513632 | + | 0.858010i | \(0.671700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.0660 | −0.967296 | −0.483648 | − | 0.875263i | \(-0.660688\pi\) | ||||
−0.483648 | + | 0.875263i | \(0.660688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.66402 | −0.106904 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.72535 | −0.229381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 103.745 | 4.14318 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.51034 | −0.100094 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5545 | −0.977500 | −0.488750 | − | 0.872424i | \(-0.662547\pi\) | ||||
−0.488750 | + | 0.872424i | \(0.662547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.1074 | −1.83260 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.17635 | 0.0863656 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.8153 | 1.73603 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.63067 | −0.380983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.20300 | −0.205506 | −0.102753 | − | 0.994707i | \(-0.532765\pi\) | ||||
−0.102753 | + | 0.994707i | \(0.532765\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0875650 | −0.00345323 | −0.00172661 | − | 0.999999i | \(-0.500550\pi\) | ||||
−0.00172661 | + | 0.999999i | \(0.500550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.90362 | −0.232455 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.81606 | −0.228653 | −0.114326 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114326 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.7897 | −2.26845 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.67904 | −0.222579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5716 | 0.491965 | 0.245983 | − | 0.969274i | \(-0.420889\pi\) | ||||
0.245983 | + | 0.969274i | \(0.420889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.7416 | −0.497856 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.2843 | −1.33756 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.7730 | 0.848157 | 0.424079 | − | 0.905625i | \(-0.360598\pi\) | ||||
0.424079 | + | 0.905625i | \(0.360598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.29462 | −0.361519 | −0.180759 | − | 0.983527i | \(-0.557856\pi\) | ||||
−0.180759 | + | 0.983527i | \(0.557856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.1768 | 1.59917 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.47132 | 0.134612 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.23563 | 0.357605 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.97690 | −0.0764312 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.3248 | 0.475795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2221 | 1.31917 | 0.659583 | − | 0.751632i | \(-0.270733\pi\) | ||||
0.659583 | + | 0.751632i | \(0.270733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.876607 | 0.0337406 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.4761 | 0.594794 | 0.297397 | − | 0.954754i | \(-0.403881\pi\) | ||||
0.297397 | + | 0.954754i | \(0.403881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.29533 | 0.126463 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9355 | 0.610648 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3750 | 0.473516 | 0.236758 | − | 0.971569i | \(-0.423915\pi\) | ||||
0.236758 | + | 0.971569i | \(0.423915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.26513 | −0.162962 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.25160 | 0.200361 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.9044 | 2.28218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.69819 | 0.0646024 | 0.0323012 | − | 0.999478i | \(-0.489716\pi\) | ||||
0.0323012 | + | 0.999478i | \(0.489716\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.7182 | 0.407149 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.6290 | −0.441112 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.5318 | −1.15647 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 66.6727 | 2.52179 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3869 | 1.26100 | 0.630502 | − | 0.776187i | \(-0.282849\pi\) | ||||
0.630502 | + | 0.776187i | \(0.282849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.68192 | 0.252013 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.0366 | 0.905271 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1027 | 0.379952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.9403 | −0.748874 | −0.374437 | − | 0.927252i | \(-0.622164\pi\) | ||||
−0.374437 | + | 0.927252i | \(0.622164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28302 | 0.0856201 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.1856 | 0.493803 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.1194 | −1.50038 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 47.0231 | 1.75611 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.8694 | 1.63605 | 0.818027 | − | 0.575180i | \(-0.195068\pi\) | ||||
0.818027 | + | 0.575180i | \(0.195068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.03902 | 0.0386951 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.150410 | −0.00559380 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.03902 | −0.112866 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.4052 | −1.53563 | −0.767817 | − | 0.640669i | \(-0.778657\pi\) | ||||
−0.767817 | + | 0.640669i | \(0.778657\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.8574 | −1.21694 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.88214 | 0.217559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6919 | 0.948950 | 0.474475 | − | 0.880269i | \(-0.342638\pi\) | ||||
0.474475 | + | 0.880269i | \(0.342638\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.9566 | −0.625453 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.20058 | 0.0810594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.4195 | −1.70757 | −0.853785 | − | 0.520625i | \(-0.825699\pi\) | ||||
−0.853785 | + | 0.520625i | \(0.825699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −109.603 | −4.02635 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.86501 | 0.361912 | 0.180956 | − | 0.983491i | \(-0.442081\pi\) | ||||
0.180956 | + | 0.983491i | \(0.442081\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.3591 | −0.635987 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.6780 | 0.756567 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.80567 | −0.285213 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.5860 | 1.37153 | 0.685765 | − | 0.727823i | \(-0.259468\pi\) | ||||
0.685765 | + | 0.727823i | \(0.259468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.69194 | 0.280310 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.343164 | 0.0124890 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.1672 | 1.71432 | 0.857161 | − | 0.515049i | \(-0.172226\pi\) | ||||
0.857161 | + | 0.515049i | \(0.172226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −47.1846 | −1.71269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0167 | −1.08810 | −0.544052 | − | 0.839052i | \(-0.683111\pi\) | ||||
−0.544052 | + | 0.839052i | \(0.683111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.15994 | 0.295410 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.40444 | −0.303863 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 61.0525 | 2.20448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3662 | −1.16715 | −0.583577 | − | 0.812058i | \(-0.698347\pi\) | ||||
−0.583577 | + | 0.812058i | \(0.698347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.6910 | −1.89762 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.6338 | −1.46150 | −0.730748 | − | 0.682648i | \(-0.760828\pi\) | ||||
−0.730748 | + | 0.682648i | \(0.760828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.33876 | −0.155853 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.30891 | 0.0469568 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 81.2683 | 2.91174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7268 | −0.634316 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.66402 | −0.0952044 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.16241 | −0.148563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7089 | −0.488671 | −0.244335 | − | 0.969691i | \(-0.578570\pi\) | ||||
−0.244335 | + | 0.969691i | \(0.578570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.9324 | −0.709612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13540 | −0.0403700 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0207 | −0.462378 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.1831 | −0.822220 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.3321 | 0.649355 | 0.324677 | − | 0.945825i | \(-0.394744\pi\) | ||||
0.324677 | + | 0.945825i | \(0.394744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.9491 | −0.847259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.8964 | −1.30367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −63.1059 | −2.22696 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.57880 | −0.0556453 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.52863 | −0.0538103 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.3248 | 0.644267 | 0.322133 | − | 0.946694i | \(-0.395600\pi\) | ||||
0.322133 | + | 0.946694i | \(0.395600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.45775 | −0.332106 | −0.166053 | − | 0.986117i | \(-0.553102\pi\) | ||||
−0.166053 | + | 0.986117i | \(0.553102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.8846 | 1.81967 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.3455 | 0.677643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.6568 | −0.547763 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.3233 | −0.395668 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.4689 | −1.13317 | −0.566586 | − | 0.824003i | \(-0.691736\pi\) | ||||
−0.566586 | + | 0.824003i | \(0.691736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.0370 | 1.11674 | 0.558369 | − | 0.829593i | \(-0.311427\pi\) | ||||
0.558369 | + | 0.829593i | \(0.311427\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.5263 | 0.540555 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.20543 | 0.0766903 | 0.0383451 | − | 0.999265i | \(-0.487791\pi\) | ||||
0.0383451 | + | 0.999265i | \(0.487791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.9745 | 0.936862 | 0.468431 | − | 0.883500i | \(-0.344819\pi\) | ||||
0.468431 | + | 0.883500i | \(0.344819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.6258 | 1.86026 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.8949 | 0.585372 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.979321 | −0.0338908 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.80338 | −0.131464 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.8424 | −0.719560 | −0.359780 | − | 0.933037i | \(-0.617148\pi\) | ||||
−0.359780 | + | 0.933037i | \(0.617148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7644 | −0.681530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.0597 | −0.897544 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.3845 | 1.01086 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0139 | 0.481524 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.22062 | 0.144851 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.03902 | −0.104176 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.7093 | −1.66778 | −0.833888 | − | 0.551933i | \(-0.813890\pi\) | ||||
−0.833888 | + | 0.551933i | \(0.813890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.3706 | 0.765058 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.4212 | −0.970850 | −0.485425 | − | 0.874278i | \(-0.661335\pi\) | ||||
−0.485425 | + | 0.874278i | \(0.661335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2926 | 0.555895 | 0.277947 | − | 0.960596i | \(-0.410346\pi\) | ||||
0.277947 | + | 0.960596i | \(0.410346\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.9195 | 0.542535 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.1333 | 0.957670 | 0.478835 | − | 0.877905i | \(-0.341059\pi\) | ||||
0.478835 | + | 0.877905i | \(0.341059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.9363 | −0.779858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.9542 | −0.915413 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.20228 | 0.142553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.32482 | −0.0787737 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2365 | 0.718745 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.519509 | 0.0175626 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0899 | −0.847226 | −0.423613 | − | 0.905843i | \(-0.639238\pi\) | ||||
−0.423613 | + | 0.905843i | \(0.639238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.1027 | 0.846692 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2197 | 0.984436 | 0.492218 | − | 0.870472i | \(-0.336186\pi\) | ||||
0.492218 | + | 0.870472i | \(0.336186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9745 | 0.907763 | 0.453882 | − | 0.891062i | \(-0.350039\pi\) | ||||
0.453882 | + | 0.891062i | \(0.350039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.6274 | −0.794226 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.2839 | −1.05041 | −0.525205 | − | 0.850976i | \(-0.676011\pi\) | ||||
−0.525205 | + | 0.850976i | \(0.676011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13063 | 0.0379202 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48.2835 | −1.61756 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 63.7468 | 2.13321 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.7600 | −0.560224 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 49.8486 | 1.66440 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.1856 | 0.439763 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.0987 | 0.769530 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.06699 | −0.102063 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.4466 | −0.380499 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4697 | 0.580073 | 0.290037 | − | 0.957016i | \(-0.406332\pi\) | ||||
0.290037 | + | 0.957016i | \(0.406332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 65.1060 | 2.15943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6659 | −1.24793 | −0.623964 | − | 0.781453i | \(-0.714479\pi\) | ||||
−0.623964 | + | 0.781453i | \(0.714479\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.0612 | 1.25964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.03902 | 0.166585 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.61939 | −0.218592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.6119 | −1.43862 | −0.719312 | − | 0.694687i | \(-0.755543\pi\) | ||||
−0.719312 | + | 0.694687i | \(0.755543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.0780 | 2.17734 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.7277 | 0.616429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.69586 | 0.219921 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.8367 | 0.749249 | 0.374625 | − | 0.927177i | \(-0.377772\pi\) | ||||
0.374625 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.9701 | −1.47383 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.40614 | 0.144250 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.4697 | −0.505915 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.2309 | −0.464904 | −0.232452 | − | 0.972608i | \(-0.574675\pi\) | ||||
−0.232452 | + | 0.972608i | \(0.574675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.8654 | −1.79047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4140 | 0.535080 | 0.267540 | − | 0.963547i | \(-0.413789\pi\) | ||||
0.267540 | + | 0.963547i | \(0.413789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.9618 | −1.20364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.455405 | 0.0148143 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.9506 | −1.10325 | −0.551624 | − | 0.834093i | \(-0.685992\pi\) | ||||
−0.551624 | + | 0.834093i | \(0.685992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.6688 | 2.16416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.1393 | 0.361215 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.5358 | −1.34548 | −0.672738 | − | 0.739881i | \(-0.734882\pi\) | ||||
−0.672738 | + | 0.739881i | \(0.734882\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.4351 | −0.337673 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.1846 | −1.52526 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.21577 | −0.0715510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1752 | −0.392748 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.3029 | −1.62099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.4029 | 0.656791 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.2341 | −0.522054 | −0.261027 | − | 0.965332i | \(-0.584061\pi\) | ||||
−0.261027 | + | 0.965332i | \(0.584061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.2620 | −1.35765 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.7277 | 0.986098 | 0.493049 | − | 0.870001i | \(-0.335882\pi\) | ||||
0.493049 | + | 0.870001i | \(0.335882\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.04136 | −0.193677 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.4029 | −0.525312 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.8654 | −0.667544 | −0.333772 | − | 0.942654i | \(-0.608322\pi\) | ||||
−0.333772 | + | 0.942654i | \(0.608322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.9140 | −2.17054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52.5859 | 1.67894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.2360 | −0.645430 | −0.322715 | − | 0.946496i | \(-0.604595\pi\) | ||||
−0.322715 | + | 0.946496i | \(0.604595\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.1051 | −0.353836 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.4872 | 0.397473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.12092 | 0.226432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.33642 | −0.296581 | −0.148291 | − | 0.988944i | \(-0.547377\pi\) | ||||
−0.148291 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 81.6744 | 2.59186 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.622223 | −0.0197258 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.9506 | −0.441821 | −0.220911 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220911 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.876607 | 0.0277346 |
(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 | 740.2.a.f.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 6660.2.a.r.1.3 | 4 | |||
4.3 | odd | 2 | 2960.2.a.v.1.2 | 4 | |||
5.2 | odd | 4 | 3700.2.d.i.149.3 | 8 | |||
5.3 | odd | 4 | 3700.2.d.i.149.6 | 8 | |||
5.4 | even | 2 | 3700.2.a.j.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
740.2.a.f.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2960.2.a.v.1.2 | 4 | 4.3 | odd | 2 | |||
3700.2.a.j.1.2 | 4 | 5.4 | even | 2 | |||
3700.2.d.i.149.3 | 8 | 5.2 | odd | 4 | |||
3700.2.d.i.149.6 | 8 | 5.3 | odd | 4 | |||
6660.2.a.r.1.3 | 4 | 3.2 | odd | 2 |