Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 1805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.937092 | −0.662624 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(3\) | −1.03012 | −0.594742 | −0.297371 | − | 0.954762i | \(-0.596110\pi\) | ||||
−0.297371 | + | 0.954762i | \(0.596110\pi\) | |||||||
\(4\) | −1.12186 | −0.560930 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.965321 | 0.394091 | ||||||||
\(7\) | −1.65832 | −0.626786 | −0.313393 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313393 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(8\) | 2.92547 | 1.03431 | ||||||||
\(9\) | −1.93884 | −0.646282 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.63847 | 1.39855 | 0.699276 | − | 0.714852i | \(-0.253506\pi\) | ||||
0.699276 | + | 0.714852i | \(0.253506\pi\) | |||||||
\(12\) | 1.15565 | 0.333609 | ||||||||
\(13\) | −5.55629 | −1.54104 | −0.770519 | − | 0.637416i | \(-0.780003\pi\) | ||||
−0.770519 | + | 0.637416i | \(0.780003\pi\) | |||||||
\(14\) | 1.55400 | 0.415324 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.497714 | −0.124428 | ||||||||
\(17\) | 7.23729 | 1.75530 | 0.877651 | − | 0.479301i | \(-0.159110\pi\) | ||||
0.877651 | + | 0.479301i | \(0.159110\pi\) | |||||||
\(18\) | 1.81688 | 0.428242 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.70828 | 0.372776 | ||||||||
\(22\) | −4.34667 | −0.926714 | ||||||||
\(23\) | 4.65440 | 0.970508 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(24\) | −3.01360 | −0.615148 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.20676 | 1.02113 | ||||||||
\(27\) | 5.08762 | 0.979113 | ||||||||
\(28\) | 1.86040 | 0.351583 | ||||||||
\(29\) | 5.69836 | 1.05816 | 0.529079 | − | 0.848573i | \(-0.322537\pi\) | ||||
0.529079 | + | 0.848573i | \(0.322537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.93959 | 1.24639 | 0.623194 | − | 0.782067i | \(-0.285835\pi\) | ||||
0.623194 | + | 0.782067i | \(0.285835\pi\) | |||||||
\(32\) | −5.38453 | −0.951860 | ||||||||
\(33\) | −4.77820 | −0.831778 | ||||||||
\(34\) | −6.78201 | −1.16310 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.17511 | 0.362518 | ||||||||
\(37\) | −0.159177 | −0.0261685 | −0.0130843 | − | 0.999914i | \(-0.504165\pi\) | ||||
−0.0130843 | + | 0.999914i | \(0.504165\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.72367 | 0.916521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.04774 | 1.10067 | 0.550336 | − | 0.834944i | \(-0.314500\pi\) | ||||
0.550336 | + | 0.834944i | \(0.314500\pi\) | |||||||
\(42\) | −1.60081 | −0.247011 | ||||||||
\(43\) | 3.60620 | 0.549940 | 0.274970 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274970 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(44\) | −5.20371 | −0.784489 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.36160 | −0.643082 | ||||||||
\(47\) | −7.34488 | −1.07136 | −0.535681 | − | 0.844421i | \(-0.679945\pi\) | ||||
−0.535681 | + | 0.844421i | \(0.679945\pi\) | |||||||
\(48\) | 0.512707 | 0.0740029 | ||||||||
\(49\) | −4.24997 | −0.607139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.45531 | −1.04395 | ||||||||
\(52\) | 6.23338 | 0.864414 | ||||||||
\(53\) | 0.175188 | 0.0240640 | 0.0120320 | − | 0.999928i | \(-0.496170\pi\) | ||||
0.0120320 | + | 0.999928i | \(0.496170\pi\) | |||||||
\(54\) | −4.76757 | −0.648784 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.85137 | −0.648291 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.33988 | −0.701161 | ||||||||
\(59\) | 1.30720 | 0.170183 | 0.0850915 | − | 0.996373i | \(-0.472882\pi\) | ||||
0.0850915 | + | 0.996373i | \(0.472882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.22814 | 0.797431 | 0.398716 | − | 0.917075i | \(-0.369456\pi\) | ||||
0.398716 | + | 0.917075i | \(0.369456\pi\) | |||||||
\(62\) | −6.50303 | −0.825886 | ||||||||
\(63\) | 3.21523 | 0.405080 | ||||||||
\(64\) | 6.04123 | 0.755154 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.47761 | 0.551156 | ||||||||
\(67\) | −1.45987 | −0.178352 | −0.0891760 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891760 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(68\) | −8.11922 | −0.984600 | ||||||||
\(69\) | −4.79460 | −0.577202 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1796 | −1.20810 | −0.604050 | − | 0.796946i | \(-0.706447\pi\) | ||||
−0.604050 | + | 0.796946i | \(0.706447\pi\) | |||||||
\(72\) | −5.67203 | −0.668455 | ||||||||
\(73\) | 2.72447 | 0.318875 | 0.159437 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159437 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(74\) | 0.149163 | 0.0173399 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.69207 | −0.876593 | ||||||||
\(78\) | −5.36361 | −0.607309 | ||||||||
\(79\) | 2.47593 | 0.278564 | 0.139282 | − | 0.990253i | \(-0.455521\pi\) | ||||
0.139282 | + | 0.990253i | \(0.455521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.575652 | 0.0639614 | ||||||||
\(82\) | −6.60437 | −0.729331 | ||||||||
\(83\) | 5.13444 | 0.563578 | 0.281789 | − | 0.959476i | \(-0.409072\pi\) | ||||
0.281789 | + | 0.959476i | \(0.409072\pi\) | |||||||
\(84\) | −1.91645 | −0.209101 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.37934 | −0.364403 | ||||||||
\(87\) | −5.87001 | −0.629331 | ||||||||
\(88\) | 13.5697 | 1.44653 | ||||||||
\(89\) | −3.66487 | −0.388476 | −0.194238 | − | 0.980954i | \(-0.562223\pi\) | ||||
−0.194238 | + | 0.980954i | \(0.562223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.21412 | 0.965902 | ||||||||
\(92\) | −5.22158 | −0.544387 | ||||||||
\(93\) | −7.14864 | −0.741279 | ||||||||
\(94\) | 6.88283 | 0.709910 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.54674 | 0.566111 | ||||||||
\(97\) | 5.45553 | 0.553925 | 0.276962 | − | 0.960881i | \(-0.410672\pi\) | ||||
0.276962 | + | 0.960881i | \(0.410672\pi\) | |||||||
\(98\) | 3.98261 | 0.402305 | ||||||||
\(99\) | −8.99327 | −0.903858 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.6577 | 1.25949 | 0.629746 | − | 0.776801i | \(-0.283159\pi\) | ||||
0.629746 | + | 0.776801i | \(0.283159\pi\) | |||||||
\(102\) | 6.98631 | 0.691747 | ||||||||
\(103\) | −12.5555 | −1.23713 | −0.618566 | − | 0.785733i | \(-0.712286\pi\) | ||||
−0.618566 | + | 0.785733i | \(0.712286\pi\) | |||||||
\(104\) | −16.2548 | −1.59391 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.164167 | −0.0159454 | ||||||||
\(107\) | −8.39376 | −0.811455 | −0.405728 | − | 0.913994i | \(-0.632982\pi\) | ||||
−0.405728 | + | 0.913994i | \(0.632982\pi\) | |||||||
\(108\) | −5.70760 | −0.549214 | ||||||||
\(109\) | −5.69743 | −0.545715 | −0.272858 | − | 0.962054i | \(-0.587969\pi\) | ||||
−0.272858 | + | 0.962054i | \(0.587969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.163972 | 0.0155635 | ||||||||
\(112\) | 0.825369 | 0.0779901 | ||||||||
\(113\) | −12.6186 | −1.18706 | −0.593529 | − | 0.804813i | \(-0.702266\pi\) | ||||
−0.593529 | + | 0.804813i | \(0.702266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.39275 | −0.593552 | ||||||||
\(117\) | 10.7728 | 0.995945 | ||||||||
\(118\) | −1.22497 | −0.112767 | ||||||||
\(119\) | −12.0018 | −1.10020 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5154 | 0.955947 | ||||||||
\(122\) | −5.83634 | −0.528397 | ||||||||
\(123\) | −7.26004 | −0.654616 | ||||||||
\(124\) | −7.78524 | −0.699136 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.01296 | −0.268416 | ||||||||
\(127\) | −2.29831 | −0.203942 | −0.101971 | − | 0.994787i | \(-0.532515\pi\) | ||||
−0.101971 | + | 0.994787i | \(0.532515\pi\) | |||||||
\(128\) | 5.10788 | 0.451477 | ||||||||
\(129\) | −3.71483 | −0.327073 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12308 | −0.185494 | −0.0927472 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927472 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(132\) | 5.36047 | 0.466569 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.36804 | 0.118180 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.1725 | 1.81552 | ||||||||
\(137\) | −0.0104664 | −0.000894205 0 | −0.000447103 | − | 1.00000i | \(-0.500142\pi\) | ||||
−0.000447103 | 1.00000i | \(0.500142\pi\) | ||||||||
\(138\) | 4.49298 | 0.382468 | ||||||||
\(139\) | 18.2404 | 1.54713 | 0.773564 | − | 0.633719i | \(-0.218472\pi\) | ||||
0.773564 | + | 0.633719i | \(0.218472\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.56614 | 0.637184 | ||||||||
\(142\) | 9.53925 | 0.800516 | ||||||||
\(143\) | −25.7727 | −2.15522 | ||||||||
\(144\) | 0.964990 | 0.0804158 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.55307 | −0.211294 | ||||||||
\(147\) | 4.37800 | 0.361091 | ||||||||
\(148\) | 0.178574 | 0.0146787 | ||||||||
\(149\) | 4.58418 | 0.375550 | 0.187775 | − | 0.982212i | \(-0.439872\pi\) | ||||
0.187775 | + | 0.982212i | \(0.439872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1633 | 1.72224 | 0.861122 | − | 0.508398i | \(-0.169762\pi\) | ||||
0.861122 | + | 0.508398i | \(0.169762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.0320 | −1.13442 | ||||||||
\(154\) | 7.20818 | 0.580852 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.42115 | −0.514104 | ||||||||
\(157\) | 6.03786 | 0.481874 | 0.240937 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(158\) | −2.32017 | −0.184583 | ||||||||
\(159\) | −0.180466 | −0.0143119 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.71848 | −0.608301 | ||||||||
\(162\) | −0.539439 | −0.0423823 | ||||||||
\(163\) | 0.710826 | 0.0556762 | 0.0278381 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278381 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(164\) | −7.90657 | −0.617399 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.81144 | −0.373440 | ||||||||
\(167\) | −18.9237 | −1.46436 | −0.732181 | − | 0.681111i | \(-0.761497\pi\) | ||||
−0.732181 | + | 0.681111i | \(0.761497\pi\) | |||||||
\(168\) | 4.99751 | 0.385566 | ||||||||
\(169\) | 17.8724 | 1.37480 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.04565 | −0.308478 | ||||||||
\(173\) | 8.75776 | 0.665840 | 0.332920 | − | 0.942955i | \(-0.391966\pi\) | ||||
0.332920 | + | 0.942955i | \(0.391966\pi\) | |||||||
\(174\) | 5.50074 | 0.417010 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.30863 | −0.174020 | ||||||||
\(177\) | −1.34658 | −0.101215 | ||||||||
\(178\) | 3.43432 | 0.257413 | ||||||||
\(179\) | 7.40606 | 0.553555 | 0.276778 | − | 0.960934i | \(-0.410733\pi\) | ||||
0.276778 | + | 0.960934i | \(0.410733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4532 | −1.37161 | −0.685807 | − | 0.727783i | \(-0.740551\pi\) | ||||
−0.685807 | + | 0.727783i | \(0.740551\pi\) | |||||||
\(182\) | −8.63448 | −0.640030 | ||||||||
\(183\) | −6.41575 | −0.474266 | ||||||||
\(184\) | 13.6163 | 1.00381 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.69893 | 0.491189 | ||||||||
\(187\) | 33.5700 | 2.45488 | ||||||||
\(188\) | 8.23993 | 0.600958 | ||||||||
\(189\) | −8.43691 | −0.613695 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.89265 | 0.354020 | 0.177010 | − | 0.984209i | \(-0.443358\pi\) | ||||
0.177010 | + | 0.984209i | \(0.443358\pi\) | |||||||
\(192\) | −6.22321 | −0.449122 | ||||||||
\(193\) | −9.38838 | −0.675790 | −0.337895 | − | 0.941184i | \(-0.609715\pi\) | ||||
−0.337895 | + | 0.941184i | \(0.609715\pi\) | |||||||
\(194\) | −5.11233 | −0.367044 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.76787 | 0.340562 | ||||||||
\(197\) | −5.93272 | −0.422689 | −0.211344 | − | 0.977412i | \(-0.567784\pi\) | ||||
−0.211344 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(198\) | 8.42752 | 0.598918 | ||||||||
\(199\) | 6.01622 | 0.426478 | 0.213239 | − | 0.977000i | \(-0.431599\pi\) | ||||
0.213239 | + | 0.977000i | \(0.431599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.50385 | 0.106074 | ||||||||
\(202\) | −11.8615 | −0.834570 | ||||||||
\(203\) | −9.44970 | −0.663239 | ||||||||
\(204\) | 8.36380 | 0.585583 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.7657 | 0.819753 | ||||||||
\(207\) | −9.02415 | −0.627222 | ||||||||
\(208\) | 2.76545 | 0.191749 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.67907 | −0.115592 | −0.0577959 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577959 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(212\) | −0.196537 | −0.0134982 | ||||||||
\(213\) | 10.4863 | 0.718509 | ||||||||
\(214\) | 7.86572 | 0.537690 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.8837 | 1.01271 | ||||||||
\(217\) | −11.5081 | −0.781219 | ||||||||
\(218\) | 5.33902 | 0.361604 | ||||||||
\(219\) | −2.80654 | −0.189648 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40.2125 | −2.70499 | ||||||||
\(222\) | −0.153657 | −0.0103128 | ||||||||
\(223\) | 20.3605 | 1.36344 | 0.681719 | − | 0.731614i | \(-0.261233\pi\) | ||||
0.681719 | + | 0.731614i | \(0.261233\pi\) | |||||||
\(224\) | 8.92928 | 0.596613 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8248 | 0.786573 | ||||||||
\(227\) | −17.9725 | −1.19287 | −0.596437 | − | 0.802660i | \(-0.703417\pi\) | ||||
−0.596437 | + | 0.802660i | \(0.703417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.44953 | −0.161870 | −0.0809348 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809348 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.92379 | 0.521347 | ||||||||
\(232\) | 16.6704 | 1.09446 | ||||||||
\(233\) | −21.4829 | −1.40739 | −0.703695 | − | 0.710502i | \(-0.748468\pi\) | ||||
−0.703695 | + | 0.710502i | \(0.748468\pi\) | |||||||
\(234\) | −10.0951 | −0.659937 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.46649 | −0.0954607 | ||||||||
\(237\) | −2.55051 | −0.165674 | ||||||||
\(238\) | 11.2467 | 0.729018 | ||||||||
\(239\) | −1.79620 | −0.116187 | −0.0580933 | − | 0.998311i | \(-0.518502\pi\) | ||||
−0.0580933 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.2978 | −1.11425 | −0.557125 | − | 0.830429i | \(-0.688095\pi\) | ||||
−0.557125 | + | 0.830429i | \(0.688095\pi\) | |||||||
\(242\) | −9.85391 | −0.633433 | ||||||||
\(243\) | −15.8559 | −1.01715 | ||||||||
\(244\) | −6.98709 | −0.447303 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.80332 | 0.433764 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 20.3016 | 1.28915 | ||||||||
\(249\) | −5.28911 | −0.335184 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.50798 | −0.221422 | −0.110711 | − | 0.993853i | \(-0.535313\pi\) | ||||
−0.110711 | + | 0.993853i | \(0.535313\pi\) | |||||||
\(252\) | −3.60703 | −0.227222 | ||||||||
\(253\) | 21.5893 | 1.35731 | ||||||||
\(254\) | 2.15373 | 0.135137 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.8690 | −1.05431 | ||||||||
\(257\) | 0.0821166 | 0.00512229 | 0.00256115 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256115 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(258\) | 3.48114 | 0.216726 | ||||||||
\(259\) | 0.263966 | 0.0164021 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.0482 | −0.683868 | ||||||||
\(262\) | 1.98952 | 0.122913 | ||||||||
\(263\) | 24.2253 | 1.49380 | 0.746898 | − | 0.664939i | \(-0.231542\pi\) | ||||
0.746898 | + | 0.664939i | \(0.231542\pi\) | |||||||
\(264\) | −13.9785 | −0.860316 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.77527 | 0.231043 | ||||||||
\(268\) | 1.63777 | 0.100043 | ||||||||
\(269\) | 14.4267 | 0.879611 | 0.439806 | − | 0.898093i | \(-0.355047\pi\) | ||||
0.439806 | + | 0.898093i | \(0.355047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.8909 | −1.57276 | −0.786382 | − | 0.617741i | \(-0.788048\pi\) | ||||
−0.786382 | + | 0.617741i | \(0.788048\pi\) | |||||||
\(272\) | −3.60210 | −0.218409 | ||||||||
\(273\) | −9.49169 | −0.574463 | ||||||||
\(274\) | 0.00980798 | 0.000592522 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.37887 | 0.323770 | ||||||||
\(277\) | 26.2297 | 1.57599 | 0.787994 | − | 0.615683i | \(-0.211120\pi\) | ||||
0.787994 | + | 0.615683i | \(0.211120\pi\) | |||||||
\(278\) | −17.0929 | −1.02516 | ||||||||
\(279\) | −13.4548 | −0.805517 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6414 | 1.23136 | 0.615682 | − | 0.787994i | \(-0.288880\pi\) | ||||
0.615682 | + | 0.787994i | \(0.288880\pi\) | |||||||
\(282\) | −7.09017 | −0.422213 | ||||||||
\(283\) | −20.8771 | −1.24102 | −0.620508 | − | 0.784200i | \(-0.713073\pi\) | ||||
−0.620508 | + | 0.784200i | \(0.713073\pi\) | |||||||
\(284\) | 11.4201 | 0.677659 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.1514 | 1.42810 | ||||||||
\(287\) | −11.6874 | −0.689886 | ||||||||
\(288\) | 10.4398 | 0.615170 | ||||||||
\(289\) | 35.3784 | 2.08108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.61987 | −0.329443 | ||||||||
\(292\) | −3.05647 | −0.178866 | ||||||||
\(293\) | 6.62626 | 0.387110 | 0.193555 | − | 0.981089i | \(-0.437998\pi\) | ||||
0.193555 | + | 0.981089i | \(0.437998\pi\) | |||||||
\(294\) | −4.10259 | −0.239268 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.465667 | −0.0270663 | ||||||||
\(297\) | 23.5988 | 1.36934 | ||||||||
\(298\) | −4.29580 | −0.248849 | ||||||||
\(299\) | −25.8612 | −1.49559 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.98023 | −0.344695 | ||||||||
\(302\) | −19.8319 | −1.14120 | ||||||||
\(303\) | −13.0390 | −0.749074 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.1493 | 0.751693 | ||||||||
\(307\) | −11.4661 | −0.654405 | −0.327203 | − | 0.944954i | \(-0.606106\pi\) | ||||
−0.327203 | + | 0.944954i | \(0.606106\pi\) | |||||||
\(308\) | 8.62942 | 0.491707 | ||||||||
\(309\) | 12.9337 | 0.735774 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4613 | 1.50048 | 0.750240 | − | 0.661165i | \(-0.229938\pi\) | ||||
0.750240 | + | 0.661165i | \(0.229938\pi\) | |||||||
\(312\) | 16.7444 | 0.947966 | ||||||||
\(313\) | −18.3102 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(314\) | −5.65803 | −0.319301 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.77764 | −0.156255 | ||||||||
\(317\) | −10.5284 | −0.591333 | −0.295666 | − | 0.955291i | \(-0.595542\pi\) | ||||
−0.295666 | + | 0.955291i | \(0.595542\pi\) | |||||||
\(318\) | 0.169113 | 0.00948338 | ||||||||
\(319\) | 26.4317 | 1.47989 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.64661 | 0.482607 | ||||||||
\(322\) | 7.23292 | 0.403075 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.645801 | −0.0358778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.666109 | −0.0368924 | ||||||||
\(327\) | 5.86906 | 0.324560 | ||||||||
\(328\) | 20.6179 | 1.13843 | ||||||||
\(329\) | 12.1802 | 0.671515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.7708 | −1.41649 | −0.708245 | − | 0.705967i | \(-0.750513\pi\) | ||||
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(332\) | −5.76012 | −0.316128 | ||||||||
\(333\) | 0.308619 | 0.0169122 | ||||||||
\(334\) | 17.7333 | 0.970321 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.850233 | −0.0463840 | ||||||||
\(337\) | −16.6242 | −0.905579 | −0.452789 | − | 0.891618i | \(-0.649571\pi\) | ||||
−0.452789 | + | 0.891618i | \(0.649571\pi\) | |||||||
\(338\) | −16.7481 | −0.910976 | ||||||||
\(339\) | 12.9987 | 0.705994 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.1891 | 1.74314 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6561 | 1.00733 | ||||||||
\(344\) | 10.5498 | 0.568808 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.20683 | −0.441202 | ||||||||
\(347\) | −9.54628 | −0.512471 | −0.256236 | − | 0.966614i | \(-0.582482\pi\) | ||||
−0.256236 | + | 0.966614i | \(0.582482\pi\) | |||||||
\(348\) | 6.58533 | 0.353011 | ||||||||
\(349\) | 32.0012 | 1.71298 | 0.856492 | − | 0.516160i | \(-0.172639\pi\) | ||||
0.856492 | + | 0.516160i | \(0.172639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.2683 | −1.50885 | ||||||||
\(352\) | −24.9760 | −1.33123 | ||||||||
\(353\) | −18.7280 | −0.996789 | −0.498394 | − | 0.866950i | \(-0.666077\pi\) | ||||
−0.498394 | + | 0.866950i | \(0.666077\pi\) | |||||||
\(354\) | 1.26187 | 0.0670675 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.11147 | 0.217908 | ||||||||
\(357\) | 12.3633 | 0.654335 | ||||||||
\(358\) | −6.94016 | −0.366799 | ||||||||
\(359\) | −9.87122 | −0.520983 | −0.260492 | − | 0.965476i | \(-0.583885\pi\) | ||||
−0.260492 | + | 0.965476i | \(0.583885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.2923 | 0.908864 | ||||||||
\(363\) | −10.8322 | −0.568542 | ||||||||
\(364\) | −10.3369 | −0.541803 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.01215 | 0.314260 | ||||||||
\(367\) | 34.1527 | 1.78276 | 0.891379 | − | 0.453258i | \(-0.149738\pi\) | ||||
0.891379 | + | 0.453258i | \(0.149738\pi\) | |||||||
\(368\) | −2.31656 | −0.120759 | ||||||||
\(369\) | −13.6645 | −0.711344 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.290518 | −0.0150830 | ||||||||
\(372\) | 8.01977 | 0.415806 | ||||||||
\(373\) | 9.81800 | 0.508357 | 0.254178 | − | 0.967157i | \(-0.418195\pi\) | ||||
0.254178 | + | 0.967157i | \(0.418195\pi\) | |||||||
\(374\) | −31.4581 | −1.62666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.4872 | −1.10812 | ||||||||
\(377\) | −31.6617 | −1.63066 | ||||||||
\(378\) | 7.90616 | 0.406649 | ||||||||
\(379\) | 6.07203 | 0.311899 | 0.155950 | − | 0.987765i | \(-0.450156\pi\) | ||||
0.155950 | + | 0.987765i | \(0.450156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.36754 | 0.121293 | ||||||||
\(382\) | −4.58486 | −0.234582 | ||||||||
\(383\) | −26.4785 | −1.35299 | −0.676494 | − | 0.736448i | \(-0.736501\pi\) | ||||
−0.676494 | + | 0.736448i | \(0.736501\pi\) | |||||||
\(384\) | −5.26175 | −0.268513 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.79777 | 0.447795 | ||||||||
\(387\) | −6.99186 | −0.355416 | ||||||||
\(388\) | −6.12033 | −0.310713 | ||||||||
\(389\) | 31.4368 | 1.59391 | 0.796954 | − | 0.604040i | \(-0.206443\pi\) | ||||
0.796954 | + | 0.604040i | \(0.206443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.6852 | 1.70353 | ||||||||
\(392\) | −12.4332 | −0.627969 | ||||||||
\(393\) | 2.18704 | 0.110321 | ||||||||
\(394\) | 5.55950 | 0.280084 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.0892 | 0.507001 | ||||||||
\(397\) | 14.6216 | 0.733839 | 0.366919 | − | 0.930253i | \(-0.380413\pi\) | ||||
0.366919 | + | 0.930253i | \(0.380413\pi\) | |||||||
\(398\) | −5.63775 | −0.282595 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.2233 | 1.40940 | 0.704701 | − | 0.709504i | \(-0.251081\pi\) | ||||
0.704701 | + | 0.709504i | \(0.251081\pi\) | |||||||
\(402\) | −1.40925 | −0.0702868 | ||||||||
\(403\) | −38.5584 | −1.92073 | ||||||||
\(404\) | −14.2002 | −0.706487 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.85524 | 0.439478 | ||||||||
\(407\) | −0.738337 | −0.0365980 | ||||||||
\(408\) | −21.8103 | −1.07977 | ||||||||
\(409\) | −13.1999 | −0.652692 | −0.326346 | − | 0.945250i | \(-0.605817\pi\) | ||||
−0.326346 | + | 0.945250i | \(0.605817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0107817 | 0.000531822 0 | ||||||||
\(412\) | 14.0855 | 0.693943 | ||||||||
\(413\) | −2.16776 | −0.106668 | ||||||||
\(414\) | 8.45646 | 0.415612 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 29.9181 | 1.46685 | ||||||||
\(417\) | −18.7898 | −0.920142 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6114 | 0.616109 | 0.308054 | − | 0.951369i | \(-0.400322\pi\) | ||||
0.308054 | + | 0.951369i | \(0.400322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.35565 | 0.309755 | 0.154878 | − | 0.987934i | \(-0.450502\pi\) | ||||
0.154878 | + | 0.987934i | \(0.450502\pi\) | |||||||
\(422\) | 1.57344 | 0.0765938 | ||||||||
\(423\) | 14.2406 | 0.692401 | ||||||||
\(424\) | 0.512508 | 0.0248896 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.82661 | −0.476101 | ||||||||
\(427\) | −10.3283 | −0.499819 | ||||||||
\(428\) | 9.41662 | 0.455169 | ||||||||
\(429\) | 26.5491 | 1.28180 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4091 | −1.27208 | −0.636041 | − | 0.771656i | \(-0.719429\pi\) | ||||
−0.636041 | + | 0.771656i | \(0.719429\pi\) | |||||||
\(432\) | −2.53218 | −0.121830 | ||||||||
\(433\) | 16.0552 | 0.771566 | 0.385783 | − | 0.922590i | \(-0.373931\pi\) | ||||
0.385783 | + | 0.922590i | \(0.373931\pi\) | |||||||
\(434\) | 10.7841 | 0.517654 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.39172 | 0.306108 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.62998 | 0.125665 | ||||||||
\(439\) | −25.1024 | −1.19807 | −0.599036 | − | 0.800722i | \(-0.704449\pi\) | ||||
−0.599036 | + | 0.800722i | \(0.704449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.24004 | 0.392383 | ||||||||
\(442\) | 37.6828 | 1.79239 | ||||||||
\(443\) | −37.7165 | −1.79197 | −0.895983 | − | 0.444088i | \(-0.853528\pi\) | ||||
−0.895983 | + | 0.444088i | \(0.853528\pi\) | |||||||
\(444\) | −0.183953 | −0.00873004 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.0796 | −0.903446 | ||||||||
\(447\) | −4.72227 | −0.223356 | ||||||||
\(448\) | −10.0183 | −0.473320 | ||||||||
\(449\) | 33.7311 | 1.59187 | 0.795934 | − | 0.605384i | \(-0.206980\pi\) | ||||
0.795934 | + | 0.605384i | \(0.206980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.6907 | 1.53935 | ||||||||
\(452\) | 14.1563 | 0.665856 | ||||||||
\(453\) | −21.8008 | −1.02429 | ||||||||
\(454\) | 16.8418 | 0.790427 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.84620 | −0.367030 | −0.183515 | − | 0.983017i | \(-0.558748\pi\) | ||||
−0.183515 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(458\) | 2.29543 | 0.107259 | ||||||||
\(459\) | 36.8206 | 1.71864 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.23991 | −0.150898 | −0.0754489 | − | 0.997150i | \(-0.524039\pi\) | ||||
−0.0754489 | + | 0.997150i | \(0.524039\pi\) | |||||||
\(462\) | −7.42532 | −0.345457 | ||||||||
\(463\) | 14.0731 | 0.654031 | 0.327015 | − | 0.945019i | \(-0.393957\pi\) | ||||
0.327015 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(464\) | −2.83615 | −0.131665 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.1314 | 0.932570 | ||||||||
\(467\) | −16.9146 | −0.782717 | −0.391358 | − | 0.920238i | \(-0.627995\pi\) | ||||
−0.391358 | + | 0.920238i | \(0.627995\pi\) | |||||||
\(468\) | −12.0856 | −0.558655 | ||||||||
\(469\) | 2.42094 | 0.111789 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.21974 | −0.286591 | ||||||||
\(472\) | 3.82417 | 0.176022 | ||||||||
\(473\) | 16.7272 | 0.769120 | ||||||||
\(474\) | 2.39006 | 0.109779 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.4643 | 0.617134 | ||||||||
\(477\) | −0.339663 | −0.0155521 | ||||||||
\(478\) | 1.68321 | 0.0769880 | ||||||||
\(479\) | −6.92210 | −0.316279 | −0.158139 | − | 0.987417i | \(-0.550550\pi\) | ||||
−0.158139 | + | 0.987417i | \(0.550550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.884433 | 0.0403267 | ||||||||
\(482\) | 16.2096 | 0.738328 | ||||||||
\(483\) | 7.95099 | 0.361783 | ||||||||
\(484\) | −11.7968 | −0.536219 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.8584 | 0.673990 | ||||||||
\(487\) | 41.6119 | 1.88562 | 0.942808 | − | 0.333337i | \(-0.108175\pi\) | ||||
0.942808 | + | 0.333337i | \(0.108175\pi\) | |||||||
\(488\) | 18.2202 | 0.824791 | ||||||||
\(489\) | −0.732239 | −0.0331130 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.77453 | −0.0800832 | −0.0400416 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400416 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(492\) | 8.14474 | 0.367193 | ||||||||
\(493\) | 41.2407 | 1.85739 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.45393 | −0.155086 | ||||||||
\(497\) | 16.8811 | 0.757221 | ||||||||
\(498\) | 4.95638 | 0.222101 | ||||||||
\(499\) | 27.2650 | 1.22055 | 0.610275 | − | 0.792190i | \(-0.291059\pi\) | ||||
0.610275 | + | 0.792190i | \(0.291059\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.4938 | 0.870918 | ||||||||
\(502\) | 3.28730 | 0.146719 | ||||||||
\(503\) | −0.427240 | −0.0190497 | −0.00952484 | − | 0.999955i | \(-0.503032\pi\) | ||||
−0.00952484 | + | 0.999955i | \(0.503032\pi\) | |||||||
\(504\) | 9.40604 | 0.418978 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.2311 | −0.899384 | ||||||||
\(507\) | −18.4108 | −0.817652 | ||||||||
\(508\) | 2.57838 | 0.114397 | ||||||||
\(509\) | 13.0601 | 0.578878 | 0.289439 | − | 0.957196i | \(-0.406531\pi\) | ||||
0.289439 | + | 0.957196i | \(0.406531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.51804 | −0.199866 | ||||||||
\(512\) | 5.59205 | 0.247136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.0769508 | −0.00339415 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.16752 | 0.183465 | ||||||||
\(517\) | −34.0690 | −1.49835 | ||||||||
\(518\) | −0.247361 | −0.0108684 | ||||||||
\(519\) | −9.02158 | −0.396003 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.51301 | 0.416773 | 0.208386 | − | 0.978047i | \(-0.433179\pi\) | ||||
0.208386 | + | 0.978047i | \(0.433179\pi\) | |||||||
\(522\) | 10.3532 | 0.453147 | ||||||||
\(523\) | −4.22384 | −0.184696 | −0.0923478 | − | 0.995727i | \(-0.529437\pi\) | ||||
−0.0923478 | + | 0.995727i | \(0.529437\pi\) | |||||||
\(524\) | 2.38180 | 0.104049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.7013 | −0.989824 | ||||||||
\(527\) | 50.2238 | 2.18779 | ||||||||
\(528\) | 2.37818 | 0.103497 | ||||||||
\(529\) | −1.33661 | −0.0581133 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.53446 | −0.109986 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −39.1593 | −1.69618 | ||||||||
\(534\) | −3.53778 | −0.153095 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.27082 | −0.184471 | ||||||||
\(537\) | −7.62916 | −0.329223 | ||||||||
\(538\) | −13.5191 | −0.582852 | ||||||||
\(539\) | −19.7134 | −0.849115 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.84642 | −0.122377 | −0.0611887 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611887 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(542\) | 24.2622 | 1.04215 | ||||||||
\(543\) | 19.0091 | 0.815757 | ||||||||
\(544\) | −38.9694 | −1.67080 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.89458 | 0.380653 | ||||||||
\(547\) | 42.2483 | 1.80641 | 0.903203 | − | 0.429213i | \(-0.141209\pi\) | ||||
0.903203 | + | 0.429213i | \(0.141209\pi\) | |||||||
\(548\) | 0.0117418 | 0.000501586 0 | ||||||||
\(549\) | −12.0754 | −0.515365 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −14.0265 | −0.597006 | ||||||||
\(553\) | −4.10588 | −0.174600 | ||||||||
\(554\) | −24.5796 | −1.04429 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.4631 | −0.867829 | ||||||||
\(557\) | 0.534205 | 0.0226350 | 0.0113175 | − | 0.999936i | \(-0.496397\pi\) | ||||
0.0113175 | + | 0.999936i | \(0.496397\pi\) | |||||||
\(558\) | 12.6084 | 0.533755 | ||||||||
\(559\) | −20.0371 | −0.847479 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.5812 | −1.46002 | ||||||||
\(562\) | −19.3429 | −0.815932 | ||||||||
\(563\) | 20.5002 | 0.863980 | 0.431990 | − | 0.901879i | \(-0.357812\pi\) | ||||
0.431990 | + | 0.901879i | \(0.357812\pi\) | |||||||
\(564\) | −8.48815 | −0.357415 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.5638 | 0.822327 | ||||||||
\(567\) | −0.954616 | −0.0400901 | ||||||||
\(568\) | −29.7802 | −1.24955 | ||||||||
\(569\) | 15.6118 | 0.654479 | 0.327239 | − | 0.944941i | \(-0.393882\pi\) | ||||
0.327239 | + | 0.944941i | \(0.393882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.7485 | 1.74712 | 0.873561 | − | 0.486715i | \(-0.161805\pi\) | ||||
0.873561 | + | 0.486715i | \(0.161805\pi\) | |||||||
\(572\) | 28.9134 | 1.20893 | ||||||||
\(573\) | −5.04004 | −0.210551 | ||||||||
\(574\) | 10.9522 | 0.457135 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.7130 | −0.488042 | ||||||||
\(577\) | 16.5613 | 0.689455 | 0.344727 | − | 0.938703i | \(-0.387971\pi\) | ||||
0.344727 | + | 0.938703i | \(0.387971\pi\) | |||||||
\(578\) | −33.1528 | −1.37897 | ||||||||
\(579\) | 9.67119 | 0.401921 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.51455 | −0.353243 | ||||||||
\(582\) | 5.26633 | 0.218296 | ||||||||
\(583\) | 0.812606 | 0.0336547 | ||||||||
\(584\) | 7.97034 | 0.329815 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.20942 | −0.256509 | ||||||||
\(587\) | 10.7958 | 0.445591 | 0.222795 | − | 0.974865i | \(-0.428482\pi\) | ||||
0.222795 | + | 0.974865i | \(0.428482\pi\) | |||||||
\(588\) | −4.91150 | −0.202547 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.11143 | 0.251391 | ||||||||
\(592\) | 0.0792245 | 0.00325611 | ||||||||
\(593\) | −8.68450 | −0.356630 | −0.178315 | − | 0.983973i | \(-0.557065\pi\) | ||||
−0.178315 | + | 0.983973i | \(0.557065\pi\) | |||||||
\(594\) | −22.1142 | −0.907358 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.14280 | −0.210657 | ||||||||
\(597\) | −6.19745 | −0.253645 | ||||||||
\(598\) | 24.2343 | 0.991015 | ||||||||
\(599\) | −3.05376 | −0.124773 | −0.0623865 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623865 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.6668 | −0.598273 | −0.299136 | − | 0.954210i | \(-0.596699\pi\) | ||||
−0.299136 | + | 0.954210i | \(0.596699\pi\) | |||||||
\(602\) | 5.60403 | 0.228403 | ||||||||
\(603\) | 2.83047 | 0.115266 | ||||||||
\(604\) | −23.7422 | −0.966058 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.2188 | 0.496354 | ||||||||
\(607\) | 15.6370 | 0.634687 | 0.317343 | − | 0.948311i | \(-0.397209\pi\) | ||||
0.317343 | + | 0.948311i | \(0.397209\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.73436 | 0.394456 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.8103 | 1.65101 | ||||||||
\(612\) | 15.7419 | 0.636329 | ||||||||
\(613\) | −35.3890 | −1.42935 | −0.714674 | − | 0.699458i | \(-0.753425\pi\) | ||||
−0.714674 | + | 0.699458i | \(0.753425\pi\) | |||||||
\(614\) | 10.7448 | 0.433625 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5029 | −0.906668 | ||||||||
\(617\) | 48.2113 | 1.94091 | 0.970456 | − | 0.241278i | \(-0.0775666\pi\) | ||||
0.970456 | + | 0.241278i | \(0.0775666\pi\) | |||||||
\(618\) | −12.1201 | −0.487542 | ||||||||
\(619\) | −19.3969 | −0.779627 | −0.389814 | − | 0.920894i | \(-0.627461\pi\) | ||||
−0.389814 | + | 0.920894i | \(0.627461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.6798 | 0.950238 | ||||||||
\(622\) | −24.7966 | −0.994254 | ||||||||
\(623\) | 6.07754 | 0.243491 | ||||||||
\(624\) | −2.84875 | −0.114041 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.1584 | 0.685786 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.77363 | −0.270297 | ||||||||
\(629\) | −1.15201 | −0.0459336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5878 | −0.501111 | −0.250556 | − | 0.968102i | \(-0.580613\pi\) | ||||
−0.250556 | + | 0.968102i | \(0.580613\pi\) | |||||||
\(632\) | 7.24325 | 0.288121 | ||||||||
\(633\) | 1.72965 | 0.0687473 | ||||||||
\(634\) | 9.86606 | 0.391831 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.202457 | 0.00802794 | ||||||||
\(637\) | 23.6141 | 0.935625 | ||||||||
\(638\) | −24.7689 | −0.980610 | ||||||||
\(639\) | 19.7367 | 0.780773 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.9593 | −1.49930 | −0.749652 | − | 0.661832i | \(-0.769779\pi\) | ||||
−0.749652 | + | 0.661832i | \(0.769779\pi\) | |||||||
\(642\) | −8.10267 | −0.319787 | ||||||||
\(643\) | 1.82578 | 0.0720018 | 0.0360009 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360009 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(644\) | 8.65905 | 0.341214 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.37469 | 0.171987 | 0.0859933 | − | 0.996296i | \(-0.472594\pi\) | ||||
0.0859933 | + | 0.996296i | \(0.472594\pi\) | |||||||
\(648\) | 1.68405 | 0.0661558 | ||||||||
\(649\) | 6.06341 | 0.238010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.8547 | 0.464624 | ||||||||
\(652\) | −0.797447 | −0.0312304 | ||||||||
\(653\) | 4.65542 | 0.182181 | 0.0910904 | − | 0.995843i | \(-0.470965\pi\) | ||||
0.0910904 | + | 0.995843i | \(0.470965\pi\) | |||||||
\(654\) | −5.49985 | −0.215061 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.50776 | −0.136955 | ||||||||
\(657\) | −5.28231 | −0.206083 | ||||||||
\(658\) | −11.4139 | −0.444962 | ||||||||
\(659\) | −22.1482 | −0.862772 | −0.431386 | − | 0.902168i | \(-0.641975\pi\) | ||||
−0.431386 | + | 0.902168i | \(0.641975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.3989 | 1.45465 | 0.727325 | − | 0.686294i | \(-0.240763\pi\) | ||||
0.727325 | + | 0.686294i | \(0.240763\pi\) | |||||||
\(662\) | 24.1496 | 0.938600 | ||||||||
\(663\) | 41.4239 | 1.60877 | ||||||||
\(664\) | 15.0206 | 0.582914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.289204 | −0.0112064 | ||||||||
\(667\) | 26.5224 | 1.02695 | ||||||||
\(668\) | 21.2297 | 0.821403 | ||||||||
\(669\) | −20.9738 | −0.810894 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.8890 | 1.11525 | ||||||||
\(672\) | −9.19827 | −0.354831 | ||||||||
\(673\) | 3.41423 | 0.131609 | 0.0658044 | − | 0.997833i | \(-0.479039\pi\) | ||||
0.0658044 | + | 0.997833i | \(0.479039\pi\) | |||||||
\(674\) | 15.5784 | 0.600058 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.0503 | −0.771166 | ||||||||
\(677\) | −17.9024 | −0.688046 | −0.344023 | − | 0.938961i | \(-0.611790\pi\) | ||||
−0.344023 | + | 0.938961i | \(0.611790\pi\) | |||||||
\(678\) | −12.1810 | −0.467808 | ||||||||
\(679\) | −9.04701 | −0.347193 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.5139 | 0.709453 | ||||||||
\(682\) | −30.1641 | −1.15504 | ||||||||
\(683\) | 20.3014 | 0.776813 | 0.388407 | − | 0.921488i | \(-0.373026\pi\) | ||||
0.388407 | + | 0.921488i | \(0.373026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.4824 | −0.667483 | ||||||||
\(687\) | 2.52332 | 0.0962707 | ||||||||
\(688\) | −1.79485 | −0.0684282 | ||||||||
\(689\) | −0.973397 | −0.0370835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6152 | 0.746198 | 0.373099 | − | 0.927791i | \(-0.378295\pi\) | ||||
0.373099 | + | 0.927791i | \(0.378295\pi\) | |||||||
\(692\) | −9.82498 | −0.373490 | ||||||||
\(693\) | 14.9137 | 0.566526 | ||||||||
\(694\) | 8.94574 | 0.339576 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.1725 | −0.650923 | ||||||||
\(697\) | 51.0065 | 1.93201 | ||||||||
\(698\) | −29.9881 | −1.13506 | ||||||||
\(699\) | 22.1300 | 0.837035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.53697 | 0.209128 | 0.104564 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104564 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(702\) | 26.4900 | 0.999801 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 28.0221 | 1.05612 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.5498 | 0.660496 | ||||||||
\(707\) | −20.9906 | −0.789433 | ||||||||
\(708\) | 1.51067 | 0.0567745 | ||||||||
\(709\) | −10.8727 | −0.408331 | −0.204166 | − | 0.978936i | \(-0.565448\pi\) | ||||
−0.204166 | + | 0.978936i | \(0.565448\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.80044 | −0.180031 | ||||||||
\(712\) | −10.7215 | −0.401804 | ||||||||
\(713\) | 32.2996 | 1.20963 | ||||||||
\(714\) | −11.5855 | −0.433578 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.30856 | −0.310505 | ||||||||
\(717\) | 1.85031 | 0.0691011 | ||||||||
\(718\) | 9.25024 | 0.345216 | ||||||||
\(719\) | 19.8622 | 0.740733 | 0.370367 | − | 0.928886i | \(-0.379232\pi\) | ||||
0.370367 | + | 0.928886i | \(0.379232\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.8211 | 0.775417 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.8189 | 0.662691 | ||||||||
\(724\) | 20.7019 | 0.769379 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.1507 | 0.376730 | ||||||||
\(727\) | −23.4155 | −0.868434 | −0.434217 | − | 0.900808i | \(-0.642975\pi\) | ||||
−0.434217 | + | 0.900808i | \(0.642975\pi\) | |||||||
\(728\) | 26.9556 | 0.999042 | ||||||||
\(729\) | 14.6065 | 0.540983 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.0991 | 0.965310 | ||||||||
\(732\) | 7.19757 | 0.266030 | ||||||||
\(733\) | 21.7404 | 0.802999 | 0.401499 | − | 0.915859i | \(-0.368489\pi\) | ||||
0.401499 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(734\) | −32.0043 | −1.18130 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.0617 | −0.923788 | ||||||||
\(737\) | −6.77159 | −0.249435 | ||||||||
\(738\) | 12.8049 | 0.471353 | ||||||||
\(739\) | 12.2347 | 0.450060 | 0.225030 | − | 0.974352i | \(-0.427752\pi\) | ||||
0.225030 | + | 0.974352i | \(0.427752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.272242 | 0.00999433 | ||||||||
\(743\) | 50.4338 | 1.85024 | 0.925119 | − | 0.379677i | \(-0.123965\pi\) | ||||
0.925119 | + | 0.379677i | \(0.123965\pi\) | |||||||
\(744\) | −20.9131 | −0.766712 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.20037 | −0.336849 | ||||||||
\(747\) | −9.95489 | −0.364230 | ||||||||
\(748\) | −37.6608 | −1.37701 | ||||||||
\(749\) | 13.9195 | 0.508609 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2970 | 0.813628 | 0.406814 | − | 0.913511i | \(-0.366640\pi\) | ||||
0.406814 | + | 0.913511i | \(0.366640\pi\) | |||||||
\(752\) | 3.65565 | 0.133308 | ||||||||
\(753\) | 3.61365 | 0.131689 | ||||||||
\(754\) | 29.6700 | 1.08052 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.46502 | 0.344240 | ||||||||
\(757\) | −32.4795 | −1.18049 | −0.590244 | − | 0.807225i | \(-0.700968\pi\) | ||||
−0.590244 | + | 0.807225i | \(0.700968\pi\) | |||||||
\(758\) | −5.69005 | −0.206672 | ||||||||
\(759\) | −22.2396 | −0.807248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6378 | −1.11062 | −0.555310 | − | 0.831644i | \(-0.687400\pi\) | ||||
−0.555310 | + | 0.831644i | \(0.687400\pi\) | |||||||
\(762\) | −2.21861 | −0.0803716 | ||||||||
\(763\) | 9.44817 | 0.342047 | ||||||||
\(764\) | −5.48887 | −0.198580 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.8128 | 0.896522 | ||||||||
\(767\) | −7.26319 | −0.262259 | ||||||||
\(768\) | 17.3772 | 0.627045 | ||||||||
\(769\) | −46.4253 | −1.67414 | −0.837070 | − | 0.547096i | \(-0.815733\pi\) | ||||
−0.837070 | + | 0.547096i | \(0.815733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0845903 | −0.00304644 | ||||||||
\(772\) | 10.5324 | 0.379071 | ||||||||
\(773\) | 19.6866 | 0.708078 | 0.354039 | − | 0.935231i | \(-0.384808\pi\) | ||||
0.354039 | + | 0.935231i | \(0.384808\pi\) | |||||||
\(774\) | 6.55201 | 0.235507 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.9600 | 0.572930 | ||||||||
\(777\) | −0.271918 | −0.00975500 | ||||||||
\(778\) | −29.4591 | −1.05616 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.2179 | −1.68959 | ||||||||
\(782\) | −31.5661 | −1.12880 | ||||||||
\(783\) | 28.9911 | 1.03606 | ||||||||
\(784\) | 2.11527 | 0.0755454 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.04945 | −0.0731016 | ||||||||
\(787\) | 16.9130 | 0.602882 | 0.301441 | − | 0.953485i | \(-0.402532\pi\) | ||||
0.301441 | + | 0.953485i | \(0.402532\pi\) | |||||||
\(788\) | 6.65567 | 0.237099 | ||||||||
\(789\) | −24.9550 | −0.888423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.9257 | 0.744032 | ||||||||
\(792\) | −26.3095 | −0.934869 | ||||||||
\(793\) | −34.6054 | −1.22887 | ||||||||
\(794\) | −13.7018 | −0.486259 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.74935 | −0.239224 | ||||||||
\(797\) | 25.3986 | 0.899664 | 0.449832 | − | 0.893113i | \(-0.351484\pi\) | ||||
0.449832 | + | 0.893113i | \(0.351484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.1571 | −1.88056 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.10562 | 0.251065 | ||||||||
\(802\) | −26.4478 | −0.933903 | ||||||||
\(803\) | 12.6374 | 0.445963 | ||||||||
\(804\) | −1.68711 | −0.0594998 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 36.1328 | 1.27272 | ||||||||
\(807\) | −14.8613 | −0.523142 | ||||||||
\(808\) | 37.0298 | 1.30270 | ||||||||
\(809\) | 23.9338 | 0.841468 | 0.420734 | − | 0.907184i | \(-0.361773\pi\) | ||||
0.420734 | + | 0.907184i | \(0.361773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.5106 | −1.45763 | −0.728817 | − | 0.684709i | \(-0.759929\pi\) | ||||
−0.728817 | + | 0.684709i | \(0.759929\pi\) | |||||||
\(812\) | 10.6012 | 0.372030 | ||||||||
\(813\) | 26.6709 | 0.935389 | ||||||||
\(814\) | 0.691890 | 0.0242507 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.71061 | 0.129897 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 12.3695 | 0.432489 | ||||||||
\(819\) | −17.8647 | −0.624245 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.396510 | −0.0138383 | −0.00691915 | − | 0.999976i | \(-0.502202\pi\) | ||||
−0.00691915 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(822\) | −0.0101034 | −0.000352398 0 | ||||||||
\(823\) | 47.7970 | 1.66610 | 0.833050 | − | 0.553198i | \(-0.186593\pi\) | ||||
0.833050 | + | 0.553198i | \(0.186593\pi\) | |||||||
\(824\) | −36.7307 | −1.27958 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.03139 | 0.0706810 | ||||||||
\(827\) | −13.1333 | −0.456691 | −0.228346 | − | 0.973580i | \(-0.573332\pi\) | ||||
−0.228346 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(828\) | 10.1238 | 0.351827 | ||||||||
\(829\) | −3.12517 | −0.108542 | −0.0542708 | − | 0.998526i | \(-0.517283\pi\) | ||||
−0.0542708 | + | 0.998526i | \(0.517283\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.0198 | −0.937307 | ||||||||
\(832\) | −33.5669 | −1.16372 | ||||||||
\(833\) | −30.7583 | −1.06571 | ||||||||
\(834\) | 17.6078 | 0.609708 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.3060 | 1.22035 | ||||||||
\(838\) | −11.8181 | −0.408249 | ||||||||
\(839\) | 26.7440 | 0.923304 | 0.461652 | − | 0.887061i | \(-0.347257\pi\) | ||||
0.461652 | + | 0.887061i | \(0.347257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.47126 | 0.119699 | ||||||||
\(842\) | −5.95583 | −0.205251 | ||||||||
\(843\) | −21.2632 | −0.732345 | ||||||||
\(844\) | 1.88368 | 0.0648388 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.3447 | −0.458802 | ||||||||
\(847\) | −17.4379 | −0.599174 | ||||||||
\(848\) | −0.0871936 | −0.00299424 | ||||||||
\(849\) | 21.5060 | 0.738085 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.740872 | −0.0253968 | ||||||||
\(852\) | −11.7641 | −0.403033 | ||||||||
\(853\) | −1.50616 | −0.0515698 | −0.0257849 | − | 0.999668i | \(-0.508209\pi\) | ||||
−0.0257849 | + | 0.999668i | \(0.508209\pi\) | |||||||
\(854\) | 9.67852 | 0.331192 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.5557 | −0.839296 | ||||||||
\(857\) | 11.1639 | 0.381353 | 0.190677 | − | 0.981653i | \(-0.438932\pi\) | ||||
0.190677 | + | 0.981653i | \(0.438932\pi\) | |||||||
\(858\) | −24.8789 | −0.849353 | ||||||||
\(859\) | −15.0137 | −0.512261 | −0.256130 | − | 0.966642i | \(-0.582448\pi\) | ||||
−0.256130 | + | 0.966642i | \(0.582448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0395 | 0.410304 | ||||||||
\(862\) | 24.7477 | 0.842911 | ||||||||
\(863\) | 16.5470 | 0.563267 | 0.281633 | − | 0.959522i | \(-0.409124\pi\) | ||||
0.281633 | + | 0.959522i | \(0.409124\pi\) | |||||||
\(864\) | −27.3945 | −0.931979 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.0452 | −0.511258 | ||||||||
\(867\) | −36.4441 | −1.23771 | ||||||||
\(868\) | 12.9104 | 0.438209 | ||||||||
\(869\) | 11.4845 | 0.389586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.11149 | 0.274847 | ||||||||
\(872\) | −16.6677 | −0.564438 | ||||||||
\(873\) | −10.5774 | −0.357991 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.14854 | 0.106379 | ||||||||
\(877\) | −38.8103 | −1.31053 | −0.655265 | − | 0.755399i | \(-0.727443\pi\) | ||||
−0.655265 | + | 0.755399i | \(0.727443\pi\) | |||||||
\(878\) | 23.5232 | 0.793871 | ||||||||
\(879\) | −6.82587 | −0.230231 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.88434 | −0.231939 | −0.115970 | − | 0.993253i | \(-0.536998\pi\) | ||||
−0.115970 | + | 0.993253i | \(0.536998\pi\) | |||||||
\(882\) | −7.72167 | −0.260002 | ||||||||
\(883\) | 38.0406 | 1.28017 | 0.640083 | − | 0.768306i | \(-0.278900\pi\) | ||||
0.640083 | + | 0.768306i | \(0.278900\pi\) | |||||||
\(884\) | 45.1128 | 1.51731 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.3438 | 1.18740 | ||||||||
\(887\) | 23.7860 | 0.798657 | 0.399329 | − | 0.916808i | \(-0.369243\pi\) | ||||
0.399329 | + | 0.916808i | \(0.369243\pi\) | |||||||
\(888\) | 0.479695 | 0.0160975 | ||||||||
\(889\) | 3.81133 | 0.127828 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.67015 | 0.0894533 | ||||||||
\(892\) | −22.8416 | −0.764793 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 4.42520 | 0.148001 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.47050 | −0.282980 | ||||||||
\(897\) | 26.6402 | 0.889491 | ||||||||
\(898\) | −31.6091 | −1.05481 | ||||||||
\(899\) | 39.5443 | 1.31888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26789 | 0.0422395 | ||||||||
\(902\) | −30.6342 | −1.02001 | ||||||||
\(903\) | 6.16038 | 0.205005 | ||||||||
\(904\) | −36.9153 | −1.22779 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.4294 | 0.678720 | ||||||||
\(907\) | −55.4867 | −1.84241 | −0.921203 | − | 0.389082i | \(-0.872792\pi\) | ||||
−0.921203 | + | 0.389082i | \(0.872792\pi\) | |||||||
\(908\) | 20.1626 | 0.669118 | ||||||||
\(909\) | −24.5414 | −0.813987 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.4481 | −1.87021 | −0.935105 | − | 0.354370i | \(-0.884695\pi\) | ||||
−0.935105 | + | 0.354370i | \(0.884695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.8160 | 0.788193 | ||||||||
\(914\) | 7.35261 | 0.243203 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.74803 | 0.0907974 | ||||||||
\(917\) | 3.52075 | 0.116265 | ||||||||
\(918\) | −34.5043 | −1.13881 | ||||||||
\(919\) | −2.23921 | −0.0738646 | −0.0369323 | − | 0.999318i | \(-0.511759\pi\) | ||||
−0.0369323 | + | 0.999318i | \(0.511759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.8115 | 0.389202 | ||||||||
\(922\) | 3.03610 | 0.0999885 | ||||||||
\(923\) | 56.5611 | 1.86173 | ||||||||
\(924\) | −8.88938 | −0.292439 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.1878 | −0.433376 | ||||||||
\(927\) | 24.3432 | 0.799535 | ||||||||
\(928\) | −30.6830 | −1.00722 | ||||||||
\(929\) | −0.843663 | −0.0276797 | −0.0138399 | − | 0.999904i | \(-0.504406\pi\) | ||||
−0.0138399 | + | 0.999904i | \(0.504406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.1008 | 0.789447 | ||||||||
\(933\) | −27.2584 | −0.892399 | ||||||||
\(934\) | 15.8506 | 0.518647 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.5155 | 1.03012 | ||||||||
\(937\) | 22.1652 | 0.724106 | 0.362053 | − | 0.932158i | \(-0.382076\pi\) | ||||
0.362053 | + | 0.932158i | \(0.382076\pi\) | |||||||
\(938\) | −2.26864 | −0.0740738 | ||||||||
\(939\) | 18.8618 | 0.615531 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.7326 | −1.45824 | −0.729121 | − | 0.684385i | \(-0.760071\pi\) | ||||
−0.729121 | + | 0.684385i | \(0.760071\pi\) | |||||||
\(942\) | 5.82847 | 0.189902 | ||||||||
\(943\) | 32.8029 | 1.06821 | ||||||||
\(944\) | −0.650612 | −0.0211756 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.6750 | −0.509637 | ||||||||
\(947\) | 21.5903 | 0.701589 | 0.350795 | − | 0.936452i | \(-0.385912\pi\) | ||||
0.350795 | + | 0.936452i | \(0.385912\pi\) | |||||||
\(948\) | 2.86132 | 0.0929312 | ||||||||
\(949\) | −15.1379 | −0.491398 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.8455 | 0.351691 | ||||||||
\(952\) | −35.1107 | −1.13795 | ||||||||
\(953\) | 53.5274 | 1.73392 | 0.866962 | − | 0.498374i | \(-0.166070\pi\) | ||||
0.866962 | + | 0.498374i | \(0.166070\pi\) | |||||||
\(954\) | 0.318295 | 0.0103052 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.01509 | 0.0651725 | ||||||||
\(957\) | −27.2279 | −0.880153 | ||||||||
\(958\) | 6.48664 | 0.209574 | ||||||||
\(959\) | 0.0173567 | 0.000560476 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1579 | 0.553482 | ||||||||
\(962\) | −0.828795 | −0.0267214 | ||||||||
\(963\) | 16.2742 | 0.524429 | ||||||||
\(964\) | 19.4057 | 0.625015 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.45081 | −0.239726 | ||||||||
\(967\) | 28.9670 | 0.931515 | 0.465757 | − | 0.884912i | \(-0.345782\pi\) | ||||
0.465757 | + | 0.884912i | \(0.345782\pi\) | |||||||
\(968\) | 30.7625 | 0.988745 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6259 | −0.565642 | −0.282821 | − | 0.959173i | \(-0.591270\pi\) | ||||
−0.282821 | + | 0.959173i | \(0.591270\pi\) | |||||||
\(972\) | 17.7880 | 0.570552 | ||||||||
\(973\) | −30.2484 | −0.969718 | ||||||||
\(974\) | −38.9942 | −1.24945 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.09983 | −0.0992232 | ||||||||
\(977\) | −11.3082 | −0.361782 | −0.180891 | − | 0.983503i | \(-0.557898\pi\) | ||||
−0.180891 | + | 0.983503i | \(0.557898\pi\) | |||||||
\(978\) | 0.686175 | 0.0219415 | ||||||||
\(979\) | −16.9994 | −0.543303 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0464 | 0.352686 | ||||||||
\(982\) | 1.66289 | 0.0530650 | ||||||||
\(983\) | 18.4503 | 0.588474 | 0.294237 | − | 0.955733i | \(-0.404935\pi\) | ||||
0.294237 | + | 0.955733i | \(0.404935\pi\) | |||||||
\(984\) | −21.2390 | −0.677075 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −38.6463 | −1.23075 | ||||||||
\(987\) | −12.5471 | −0.399378 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7847 | 0.533721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.6693 | 0.434218 | 0.217109 | − | 0.976147i | \(-0.430337\pi\) | ||||
0.217109 | + | 0.976147i | \(0.430337\pi\) | |||||||
\(992\) | −37.3665 | −1.18639 | ||||||||
\(993\) | 26.5471 | 0.842446 | ||||||||
\(994\) | −15.8191 | −0.501753 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.93364 | 0.188015 | ||||||||
\(997\) | −43.6905 | −1.38369 | −0.691846 | − | 0.722045i | \(-0.743202\pi\) | ||||
−0.691846 | + | 0.722045i | \(0.743202\pi\) | |||||||
\(998\) | −25.5498 | −0.808765 | ||||||||
\(999\) | −0.809832 | −0.0256219 |
(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 | 9025.2.a.cv.1.15 | 40 | ||
5.2 | odd | 4 | 1805.2.b.m.1084.15 | ✓ | 40 | ||
5.3 | odd | 4 | 1805.2.b.m.1084.26 | yes | 40 | ||
5.4 | even | 2 | inner | 9025.2.a.cv.1.26 | 40 | ||
19.18 | odd | 2 | inner | 9025.2.a.cv.1.25 | 40 | ||
95.18 | even | 4 | 1805.2.b.m.1084.16 | yes | 40 | ||
95.37 | even | 4 | 1805.2.b.m.1084.25 | yes | 40 | ||
95.94 | odd | 2 | inner | 9025.2.a.cv.1.16 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.m.1084.15 | ✓ | 40 | 5.2 | odd | 4 | ||
1805.2.b.m.1084.16 | yes | 40 | 95.18 | even | 4 | ||
1805.2.b.m.1084.25 | yes | 40 | 95.37 | even | 4 | ||
1805.2.b.m.1084.26 | yes | 40 | 5.3 | odd | 4 | ||
9025.2.a.cv.1.15 | 40 | 1.1 | even | 1 | trivial | ||
9025.2.a.cv.1.16 | 40 | 95.94 | odd | 2 | inner | ||
9025.2.a.cv.1.25 | 40 | 19.18 | odd | 2 | inner | ||
9025.2.a.cv.1.26 | 40 | 5.4 | even | 2 | inner |