Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.82093 | −1.05131 | −0.525657 | − | 0.850696i | \(-0.676181\pi\) | ||||
−0.525657 | + | 0.850696i | \(0.676181\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.80048 | −1.69962 | −0.849812 | − | 0.527086i | \(-0.823285\pi\) | ||||
−0.849812 | + | 0.527086i | \(0.823285\pi\) | |||||||
\(6\) | 1.82093 | 0.743392 | ||||||||
\(7\) | −3.54475 | −1.33979 | −0.669894 | − | 0.742457i | \(-0.733661\pi\) | ||||
−0.669894 | + | 0.742457i | \(0.733661\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.315788 | 0.105263 | ||||||||
\(10\) | 3.80048 | 1.20182 | ||||||||
\(11\) | −4.23704 | −1.27752 | −0.638758 | − | 0.769408i | \(-0.720551\pi\) | ||||
−0.638758 | + | 0.769408i | \(0.720551\pi\) | |||||||
\(12\) | −1.82093 | −0.525657 | ||||||||
\(13\) | 1.93193 | 0.535821 | 0.267911 | − | 0.963444i | \(-0.413667\pi\) | ||||
0.267911 | + | 0.963444i | \(0.413667\pi\) | |||||||
\(14\) | 3.54475 | 0.947373 | ||||||||
\(15\) | 6.92040 | 1.78684 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.25106 | −1.75864 | −0.879320 | − | 0.476232i | \(-0.842002\pi\) | ||||
−0.879320 | + | 0.476232i | \(0.842002\pi\) | |||||||
\(18\) | −0.315788 | −0.0744321 | ||||||||
\(19\) | 1.65314 | 0.379256 | 0.189628 | − | 0.981856i | \(-0.439272\pi\) | ||||
0.189628 | + | 0.981856i | \(0.439272\pi\) | |||||||
\(20\) | −3.80048 | −0.849812 | ||||||||
\(21\) | 6.45474 | 1.40854 | ||||||||
\(22\) | 4.23704 | 0.903340 | ||||||||
\(23\) | 2.77810 | 0.579274 | 0.289637 | − | 0.957137i | \(-0.406465\pi\) | ||||
0.289637 | + | 0.957137i | \(0.406465\pi\) | |||||||
\(24\) | 1.82093 | 0.371696 | ||||||||
\(25\) | 9.44361 | 1.88872 | ||||||||
\(26\) | −1.93193 | −0.378883 | ||||||||
\(27\) | 4.88776 | 0.940650 | ||||||||
\(28\) | −3.54475 | −0.669894 | ||||||||
\(29\) | 6.62357 | 1.22997 | 0.614983 | − | 0.788540i | \(-0.289163\pi\) | ||||
0.614983 | + | 0.788540i | \(0.289163\pi\) | |||||||
\(30\) | −6.92040 | −1.26349 | ||||||||
\(31\) | −9.37689 | −1.68414 | −0.842069 | − | 0.539369i | \(-0.818663\pi\) | ||||
−0.842069 | + | 0.539369i | \(0.818663\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.71535 | 1.34307 | ||||||||
\(34\) | 7.25106 | 1.24355 | ||||||||
\(35\) | 13.4717 | 2.27714 | ||||||||
\(36\) | 0.315788 | 0.0526314 | ||||||||
\(37\) | −1.32098 | −0.217168 | −0.108584 | − | 0.994087i | \(-0.534632\pi\) | ||||
−0.108584 | + | 0.994087i | \(0.534632\pi\) | |||||||
\(38\) | −1.65314 | −0.268174 | ||||||||
\(39\) | −3.51791 | −0.563317 | ||||||||
\(40\) | 3.80048 | 0.600908 | ||||||||
\(41\) | 7.72437 | 1.20634 | 0.603172 | − | 0.797611i | \(-0.293903\pi\) | ||||
0.603172 | + | 0.797611i | \(0.293903\pi\) | |||||||
\(42\) | −6.45474 | −0.995988 | ||||||||
\(43\) | 12.2401 | 1.86659 | 0.933297 | − | 0.359106i | \(-0.116918\pi\) | ||||
0.933297 | + | 0.359106i | \(0.116918\pi\) | |||||||
\(44\) | −4.23704 | −0.638758 | ||||||||
\(45\) | −1.20015 | −0.178907 | ||||||||
\(46\) | −2.77810 | −0.409609 | ||||||||
\(47\) | 2.77894 | 0.405350 | 0.202675 | − | 0.979246i | \(-0.435036\pi\) | ||||
0.202675 | + | 0.979246i | \(0.435036\pi\) | |||||||
\(48\) | −1.82093 | −0.262829 | ||||||||
\(49\) | 5.56523 | 0.795033 | ||||||||
\(50\) | −9.44361 | −1.33553 | ||||||||
\(51\) | 13.2037 | 1.84888 | ||||||||
\(52\) | 1.93193 | 0.267911 | ||||||||
\(53\) | −8.53389 | −1.17222 | −0.586110 | − | 0.810231i | \(-0.699341\pi\) | ||||
−0.586110 | + | 0.810231i | \(0.699341\pi\) | |||||||
\(54\) | −4.88776 | −0.665140 | ||||||||
\(55\) | 16.1028 | 2.17130 | ||||||||
\(56\) | 3.54475 | 0.473687 | ||||||||
\(57\) | −3.01025 | −0.398717 | ||||||||
\(58\) | −6.62357 | −0.869718 | ||||||||
\(59\) | −10.9129 | −1.42073 | −0.710367 | − | 0.703831i | \(-0.751471\pi\) | ||||
−0.710367 | + | 0.703831i | \(0.751471\pi\) | |||||||
\(60\) | 6.92040 | 0.893420 | ||||||||
\(61\) | −12.6169 | −1.61543 | −0.807716 | − | 0.589572i | \(-0.799296\pi\) | ||||
−0.807716 | + | 0.589572i | \(0.799296\pi\) | |||||||
\(62\) | 9.37689 | 1.19087 | ||||||||
\(63\) | −1.11939 | −0.141030 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.34226 | −0.910695 | ||||||||
\(66\) | −7.71535 | −0.949694 | ||||||||
\(67\) | 11.2323 | 1.37224 | 0.686119 | − | 0.727489i | \(-0.259313\pi\) | ||||
0.686119 | + | 0.727489i | \(0.259313\pi\) | |||||||
\(68\) | −7.25106 | −0.879320 | ||||||||
\(69\) | −5.05873 | −0.609000 | ||||||||
\(70\) | −13.4717 | −1.61018 | ||||||||
\(71\) | −2.85150 | −0.338410 | −0.169205 | − | 0.985581i | \(-0.554120\pi\) | ||||
−0.169205 | + | 0.985581i | \(0.554120\pi\) | |||||||
\(72\) | −0.315788 | −0.0372160 | ||||||||
\(73\) | 5.54156 | 0.648590 | 0.324295 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324295 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(74\) | 1.32098 | 0.153561 | ||||||||
\(75\) | −17.1962 | −1.98564 | ||||||||
\(76\) | 1.65314 | 0.189628 | ||||||||
\(77\) | 15.0192 | 1.71160 | ||||||||
\(78\) | 3.51791 | 0.398325 | ||||||||
\(79\) | 11.7255 | 1.31923 | 0.659613 | − | 0.751605i | \(-0.270720\pi\) | ||||
0.659613 | + | 0.751605i | \(0.270720\pi\) | |||||||
\(80\) | −3.80048 | −0.424906 | ||||||||
\(81\) | −9.84764 | −1.09418 | ||||||||
\(82\) | −7.72437 | −0.853014 | ||||||||
\(83\) | 9.05386 | 0.993790 | 0.496895 | − | 0.867811i | \(-0.334473\pi\) | ||||
0.496895 | + | 0.867811i | \(0.334473\pi\) | |||||||
\(84\) | 6.45474 | 0.704270 | ||||||||
\(85\) | 27.5575 | 2.98903 | ||||||||
\(86\) | −12.2401 | −1.31988 | ||||||||
\(87\) | −12.0611 | −1.29308 | ||||||||
\(88\) | 4.23704 | 0.451670 | ||||||||
\(89\) | −1.09101 | −0.115646 | −0.0578232 | − | 0.998327i | \(-0.518416\pi\) | ||||
−0.0578232 | + | 0.998327i | \(0.518416\pi\) | |||||||
\(90\) | 1.20015 | 0.126507 | ||||||||
\(91\) | −6.84821 | −0.717887 | ||||||||
\(92\) | 2.77810 | 0.289637 | ||||||||
\(93\) | 17.0747 | 1.77056 | ||||||||
\(94\) | −2.77894 | −0.286626 | ||||||||
\(95\) | −6.28271 | −0.644592 | ||||||||
\(96\) | 1.82093 | 0.185848 | ||||||||
\(97\) | −3.33585 | −0.338704 | −0.169352 | − | 0.985556i | \(-0.554167\pi\) | ||||
−0.169352 | + | 0.985556i | \(0.554167\pi\) | |||||||
\(98\) | −5.56523 | −0.562173 | ||||||||
\(99\) | −1.33801 | −0.134475 | ||||||||
\(100\) | 9.44361 | 0.944361 | ||||||||
\(101\) | 17.3615 | 1.72753 | 0.863765 | − | 0.503894i | \(-0.168100\pi\) | ||||
0.863765 | + | 0.503894i | \(0.168100\pi\) | |||||||
\(102\) | −13.2037 | −1.30736 | ||||||||
\(103\) | 5.49812 | 0.541746 | 0.270873 | − | 0.962615i | \(-0.412688\pi\) | ||||
0.270873 | + | 0.962615i | \(0.412688\pi\) | |||||||
\(104\) | −1.93193 | −0.189441 | ||||||||
\(105\) | −24.5311 | −2.39399 | ||||||||
\(106\) | 8.53389 | 0.828885 | ||||||||
\(107\) | −10.1626 | −0.982460 | −0.491230 | − | 0.871030i | \(-0.663453\pi\) | ||||
−0.491230 | + | 0.871030i | \(0.663453\pi\) | |||||||
\(108\) | 4.88776 | 0.470325 | ||||||||
\(109\) | −6.14727 | −0.588802 | −0.294401 | − | 0.955682i | \(-0.595120\pi\) | ||||
−0.294401 | + | 0.955682i | \(0.595120\pi\) | |||||||
\(110\) | −16.1028 | −1.53534 | ||||||||
\(111\) | 2.40541 | 0.228312 | ||||||||
\(112\) | −3.54475 | −0.334947 | ||||||||
\(113\) | −8.41808 | −0.791906 | −0.395953 | − | 0.918271i | \(-0.629586\pi\) | ||||
−0.395953 | + | 0.918271i | \(0.629586\pi\) | |||||||
\(114\) | 3.01025 | 0.281936 | ||||||||
\(115\) | −10.5581 | −0.984548 | ||||||||
\(116\) | 6.62357 | 0.614983 | ||||||||
\(117\) | 0.610082 | 0.0564021 | ||||||||
\(118\) | 10.9129 | 1.00461 | ||||||||
\(119\) | 25.7032 | 2.35620 | ||||||||
\(120\) | −6.92040 | −0.631743 | ||||||||
\(121\) | 6.95249 | 0.632045 | ||||||||
\(122\) | 12.6169 | 1.14228 | ||||||||
\(123\) | −14.0655 | −1.26825 | ||||||||
\(124\) | −9.37689 | −0.842069 | ||||||||
\(125\) | −16.8878 | −1.51049 | ||||||||
\(126\) | 1.11939 | 0.0997232 | ||||||||
\(127\) | 10.0912 | 0.895445 | 0.447722 | − | 0.894173i | \(-0.352235\pi\) | ||||
0.447722 | + | 0.894173i | \(0.352235\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −22.2883 | −1.96238 | ||||||||
\(130\) | 7.34226 | 0.643959 | ||||||||
\(131\) | −20.2477 | −1.76905 | −0.884525 | − | 0.466493i | \(-0.845517\pi\) | ||||
−0.884525 | + | 0.466493i | \(0.845517\pi\) | |||||||
\(132\) | 7.71535 | 0.671535 | ||||||||
\(133\) | −5.85995 | −0.508122 | ||||||||
\(134\) | −11.2323 | −0.970319 | ||||||||
\(135\) | −18.5758 | −1.59875 | ||||||||
\(136\) | 7.25106 | 0.621773 | ||||||||
\(137\) | 5.37282 | 0.459031 | 0.229515 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229515 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(138\) | 5.05873 | 0.430628 | ||||||||
\(139\) | 1.01967 | 0.0864874 | 0.0432437 | − | 0.999065i | \(-0.486231\pi\) | ||||
0.0432437 | + | 0.999065i | \(0.486231\pi\) | |||||||
\(140\) | 13.4717 | 1.13857 | ||||||||
\(141\) | −5.06026 | −0.426150 | ||||||||
\(142\) | 2.85150 | 0.239292 | ||||||||
\(143\) | −8.18567 | −0.684520 | ||||||||
\(144\) | 0.315788 | 0.0263157 | ||||||||
\(145\) | −25.1727 | −2.09048 | ||||||||
\(146\) | −5.54156 | −0.458623 | ||||||||
\(147\) | −10.1339 | −0.835829 | ||||||||
\(148\) | −1.32098 | −0.108584 | ||||||||
\(149\) | −5.09976 | −0.417789 | −0.208895 | − | 0.977938i | \(-0.566987\pi\) | ||||
−0.208895 | + | 0.977938i | \(0.566987\pi\) | |||||||
\(150\) | 17.1962 | 1.40406 | ||||||||
\(151\) | −10.3479 | −0.842104 | −0.421052 | − | 0.907037i | \(-0.638339\pi\) | ||||
−0.421052 | + | 0.907037i | \(0.638339\pi\) | |||||||
\(152\) | −1.65314 | −0.134087 | ||||||||
\(153\) | −2.28980 | −0.185119 | ||||||||
\(154\) | −15.0192 | −1.21028 | ||||||||
\(155\) | 35.6366 | 2.86240 | ||||||||
\(156\) | −3.51791 | −0.281659 | ||||||||
\(157\) | 8.43226 | 0.672968 | 0.336484 | − | 0.941689i | \(-0.390762\pi\) | ||||
0.336484 | + | 0.941689i | \(0.390762\pi\) | |||||||
\(158\) | −11.7255 | −0.932834 | ||||||||
\(159\) | 15.5396 | 1.23237 | ||||||||
\(160\) | 3.80048 | 0.300454 | ||||||||
\(161\) | −9.84767 | −0.776105 | ||||||||
\(162\) | 9.84764 | 0.773704 | ||||||||
\(163\) | 22.8876 | 1.79270 | 0.896349 | − | 0.443349i | \(-0.146210\pi\) | ||||
0.896349 | + | 0.443349i | \(0.146210\pi\) | |||||||
\(164\) | 7.72437 | 0.603172 | ||||||||
\(165\) | −29.3220 | −2.28272 | ||||||||
\(166\) | −9.05386 | −0.702716 | ||||||||
\(167\) | −3.29537 | −0.255004 | −0.127502 | − | 0.991838i | \(-0.540696\pi\) | ||||
−0.127502 | + | 0.991838i | \(0.540696\pi\) | |||||||
\(168\) | −6.45474 | −0.497994 | ||||||||
\(169\) | −9.26764 | −0.712895 | ||||||||
\(170\) | −27.5575 | −2.11356 | ||||||||
\(171\) | 0.522042 | 0.0399215 | ||||||||
\(172\) | 12.2401 | 0.933297 | ||||||||
\(173\) | −8.41833 | −0.640034 | −0.320017 | − | 0.947412i | \(-0.603689\pi\) | ||||
−0.320017 | + | 0.947412i | \(0.603689\pi\) | |||||||
\(174\) | 12.0611 | 0.914347 | ||||||||
\(175\) | −33.4752 | −2.53049 | ||||||||
\(176\) | −4.23704 | −0.319379 | ||||||||
\(177\) | 19.8716 | 1.49364 | ||||||||
\(178\) | 1.09101 | 0.0817743 | ||||||||
\(179\) | 18.2974 | 1.36761 | 0.683807 | − | 0.729663i | \(-0.260323\pi\) | ||||
0.683807 | + | 0.729663i | \(0.260323\pi\) | |||||||
\(180\) | −1.20015 | −0.0894536 | ||||||||
\(181\) | −5.28677 | −0.392962 | −0.196481 | − | 0.980508i | \(-0.562951\pi\) | ||||
−0.196481 | + | 0.980508i | \(0.562951\pi\) | |||||||
\(182\) | 6.84821 | 0.507623 | ||||||||
\(183\) | 22.9745 | 1.69833 | ||||||||
\(184\) | −2.77810 | −0.204804 | ||||||||
\(185\) | 5.02035 | 0.369104 | ||||||||
\(186\) | −17.0747 | −1.25198 | ||||||||
\(187\) | 30.7230 | 2.24669 | ||||||||
\(188\) | 2.77894 | 0.202675 | ||||||||
\(189\) | −17.3259 | −1.26027 | ||||||||
\(190\) | 6.28271 | 0.455795 | ||||||||
\(191\) | −14.4080 | −1.04252 | −0.521262 | − | 0.853397i | \(-0.674539\pi\) | ||||
−0.521262 | + | 0.853397i | \(0.674539\pi\) | |||||||
\(192\) | −1.82093 | −0.131414 | ||||||||
\(193\) | 19.9624 | 1.43692 | 0.718461 | − | 0.695567i | \(-0.244847\pi\) | ||||
0.718461 | + | 0.695567i | \(0.244847\pi\) | |||||||
\(194\) | 3.33585 | 0.239500 | ||||||||
\(195\) | 13.3697 | 0.957427 | ||||||||
\(196\) | 5.56523 | 0.397516 | ||||||||
\(197\) | −6.27526 | −0.447093 | −0.223547 | − | 0.974693i | \(-0.571764\pi\) | ||||
−0.223547 | + | 0.974693i | \(0.571764\pi\) | |||||||
\(198\) | 1.33801 | 0.0950881 | ||||||||
\(199\) | 8.50276 | 0.602745 | 0.301372 | − | 0.953506i | \(-0.402555\pi\) | ||||
0.301372 | + | 0.953506i | \(0.402555\pi\) | |||||||
\(200\) | −9.44361 | −0.667764 | ||||||||
\(201\) | −20.4532 | −1.44266 | ||||||||
\(202\) | −17.3615 | −1.22155 | ||||||||
\(203\) | −23.4789 | −1.64789 | ||||||||
\(204\) | 13.2037 | 0.924442 | ||||||||
\(205\) | −29.3563 | −2.05033 | ||||||||
\(206\) | −5.49812 | −0.383072 | ||||||||
\(207\) | 0.877292 | 0.0609760 | ||||||||
\(208\) | 1.93193 | 0.133955 | ||||||||
\(209\) | −7.00441 | −0.484505 | ||||||||
\(210\) | 24.5311 | 1.69280 | ||||||||
\(211\) | 3.50204 | 0.241090 | 0.120545 | − | 0.992708i | \(-0.461536\pi\) | ||||
0.120545 | + | 0.992708i | \(0.461536\pi\) | |||||||
\(212\) | −8.53389 | −0.586110 | ||||||||
\(213\) | 5.19238 | 0.355776 | ||||||||
\(214\) | 10.1626 | 0.694704 | ||||||||
\(215\) | −46.5181 | −3.17251 | ||||||||
\(216\) | −4.88776 | −0.332570 | ||||||||
\(217\) | 33.2387 | 2.25639 | ||||||||
\(218\) | 6.14727 | 0.416346 | ||||||||
\(219\) | −10.0908 | −0.681873 | ||||||||
\(220\) | 16.1028 | 1.08565 | ||||||||
\(221\) | −14.0085 | −0.942317 | ||||||||
\(222\) | −2.40541 | −0.161441 | ||||||||
\(223\) | 8.62891 | 0.577834 | 0.288917 | − | 0.957354i | \(-0.406705\pi\) | ||||
0.288917 | + | 0.957354i | \(0.406705\pi\) | |||||||
\(224\) | 3.54475 | 0.236843 | ||||||||
\(225\) | 2.98218 | 0.198812 | ||||||||
\(226\) | 8.41808 | 0.559962 | ||||||||
\(227\) | −18.6343 | −1.23680 | −0.618401 | − | 0.785863i | \(-0.712219\pi\) | ||||
−0.618401 | + | 0.785863i | \(0.712219\pi\) | |||||||
\(228\) | −3.01025 | −0.199359 | ||||||||
\(229\) | 4.45951 | 0.294693 | 0.147346 | − | 0.989085i | \(-0.452927\pi\) | ||||
0.147346 | + | 0.989085i | \(0.452927\pi\) | |||||||
\(230\) | 10.5581 | 0.696181 | ||||||||
\(231\) | −27.3490 | −1.79943 | ||||||||
\(232\) | −6.62357 | −0.434859 | ||||||||
\(233\) | 27.1983 | 1.78182 | 0.890910 | − | 0.454180i | \(-0.150068\pi\) | ||||
0.890910 | + | 0.454180i | \(0.150068\pi\) | |||||||
\(234\) | −0.610082 | −0.0398823 | ||||||||
\(235\) | −10.5613 | −0.688943 | ||||||||
\(236\) | −10.9129 | −0.710367 | ||||||||
\(237\) | −21.3514 | −1.38692 | ||||||||
\(238\) | −25.7032 | −1.66609 | ||||||||
\(239\) | 28.7485 | 1.85959 | 0.929794 | − | 0.368080i | \(-0.119985\pi\) | ||||
0.929794 | + | 0.368080i | \(0.119985\pi\) | |||||||
\(240\) | 6.92040 | 0.446710 | ||||||||
\(241\) | −12.7200 | −0.819366 | −0.409683 | − | 0.912228i | \(-0.634361\pi\) | ||||
−0.409683 | + | 0.912228i | \(0.634361\pi\) | |||||||
\(242\) | −6.95249 | −0.446923 | ||||||||
\(243\) | 3.26859 | 0.209680 | ||||||||
\(244\) | −12.6169 | −0.807716 | ||||||||
\(245\) | −21.1505 | −1.35126 | ||||||||
\(246\) | 14.0655 | 0.896786 | ||||||||
\(247\) | 3.19375 | 0.203213 | ||||||||
\(248\) | 9.37689 | 0.595433 | ||||||||
\(249\) | −16.4864 | −1.04479 | ||||||||
\(250\) | 16.8878 | 1.06808 | ||||||||
\(251\) | 5.69500 | 0.359465 | 0.179733 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179733 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(252\) | −1.11939 | −0.0705149 | ||||||||
\(253\) | −11.7709 | −0.740032 | ||||||||
\(254\) | −10.0912 | −0.633175 | ||||||||
\(255\) | −50.1802 | −3.14241 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.3344 | −1.08129 | −0.540645 | − | 0.841251i | \(-0.681820\pi\) | ||||
−0.540645 | + | 0.841251i | \(0.681820\pi\) | |||||||
\(258\) | 22.2883 | 1.38761 | ||||||||
\(259\) | 4.68254 | 0.290959 | ||||||||
\(260\) | −7.34226 | −0.455348 | ||||||||
\(261\) | 2.09165 | 0.129470 | ||||||||
\(262\) | 20.2477 | 1.25091 | ||||||||
\(263\) | 0.573248 | 0.0353480 | 0.0176740 | − | 0.999844i | \(-0.494374\pi\) | ||||
0.0176740 | + | 0.999844i | \(0.494374\pi\) | |||||||
\(264\) | −7.71535 | −0.474847 | ||||||||
\(265\) | 32.4329 | 1.99233 | ||||||||
\(266\) | 5.85995 | 0.359297 | ||||||||
\(267\) | 1.98665 | 0.121581 | ||||||||
\(268\) | 11.2323 | 0.686119 | ||||||||
\(269\) | −11.7841 | −0.718490 | −0.359245 | − | 0.933243i | \(-0.616966\pi\) | ||||
−0.359245 | + | 0.933243i | \(0.616966\pi\) | |||||||
\(270\) | 18.5758 | 1.13049 | ||||||||
\(271\) | 1.72211 | 0.104611 | 0.0523054 | − | 0.998631i | \(-0.483343\pi\) | ||||
0.0523054 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(272\) | −7.25106 | −0.439660 | ||||||||
\(273\) | 12.4701 | 0.754725 | ||||||||
\(274\) | −5.37282 | −0.324584 | ||||||||
\(275\) | −40.0129 | −2.41287 | ||||||||
\(276\) | −5.05873 | −0.304500 | ||||||||
\(277\) | −0.604596 | −0.0363266 | −0.0181633 | − | 0.999835i | \(-0.505782\pi\) | ||||
−0.0181633 | + | 0.999835i | \(0.505782\pi\) | |||||||
\(278\) | −1.01967 | −0.0611558 | ||||||||
\(279\) | −2.96111 | −0.177277 | ||||||||
\(280\) | −13.4717 | −0.805089 | ||||||||
\(281\) | 3.80725 | 0.227121 | 0.113561 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113561 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(282\) | 5.06026 | 0.301334 | ||||||||
\(283\) | −0.610355 | −0.0362818 | −0.0181409 | − | 0.999835i | \(-0.505775\pi\) | ||||
−0.0181409 | + | 0.999835i | \(0.505775\pi\) | |||||||
\(284\) | −2.85150 | −0.169205 | ||||||||
\(285\) | 11.4404 | 0.677669 | ||||||||
\(286\) | 8.18567 | 0.484029 | ||||||||
\(287\) | −27.3809 | −1.61625 | ||||||||
\(288\) | −0.315788 | −0.0186080 | ||||||||
\(289\) | 35.5778 | 2.09281 | ||||||||
\(290\) | 25.1727 | 1.47819 | ||||||||
\(291\) | 6.07435 | 0.356084 | ||||||||
\(292\) | 5.54156 | 0.324295 | ||||||||
\(293\) | −2.88815 | −0.168728 | −0.0843638 | − | 0.996435i | \(-0.526886\pi\) | ||||
−0.0843638 | + | 0.996435i | \(0.526886\pi\) | |||||||
\(294\) | 10.1339 | 0.591021 | ||||||||
\(295\) | 41.4741 | 2.41472 | ||||||||
\(296\) | 1.32098 | 0.0767804 | ||||||||
\(297\) | −20.7096 | −1.20170 | ||||||||
\(298\) | 5.09976 | 0.295421 | ||||||||
\(299\) | 5.36710 | 0.310388 | ||||||||
\(300\) | −17.1962 | −0.992821 | ||||||||
\(301\) | −43.3879 | −2.50084 | ||||||||
\(302\) | 10.3479 | 0.595457 | ||||||||
\(303\) | −31.6140 | −1.81618 | ||||||||
\(304\) | 1.65314 | 0.0948139 | ||||||||
\(305\) | 47.9503 | 2.74563 | ||||||||
\(306\) | 2.28980 | 0.130899 | ||||||||
\(307\) | −21.8437 | −1.24668 | −0.623342 | − | 0.781949i | \(-0.714226\pi\) | ||||
−0.623342 | + | 0.781949i | \(0.714226\pi\) | |||||||
\(308\) | 15.0192 | 0.855800 | ||||||||
\(309\) | −10.0117 | −0.569546 | ||||||||
\(310\) | −35.6366 | −2.02402 | ||||||||
\(311\) | 19.5894 | 1.11081 | 0.555407 | − | 0.831579i | \(-0.312563\pi\) | ||||
0.555407 | + | 0.831579i | \(0.312563\pi\) | |||||||
\(312\) | 3.51791 | 0.199163 | ||||||||
\(313\) | 25.3964 | 1.43549 | 0.717745 | − | 0.696306i | \(-0.245174\pi\) | ||||
0.717745 | + | 0.696306i | \(0.245174\pi\) | |||||||
\(314\) | −8.43226 | −0.475860 | ||||||||
\(315\) | 4.25421 | 0.239698 | ||||||||
\(316\) | 11.7255 | 0.659613 | ||||||||
\(317\) | −5.85823 | −0.329031 | −0.164516 | − | 0.986374i | \(-0.552606\pi\) | ||||
−0.164516 | + | 0.986374i | \(0.552606\pi\) | |||||||
\(318\) | −15.5396 | −0.871419 | ||||||||
\(319\) | −28.0643 | −1.57130 | ||||||||
\(320\) | −3.80048 | −0.212453 | ||||||||
\(321\) | 18.5055 | 1.03287 | ||||||||
\(322\) | 9.84767 | 0.548789 | ||||||||
\(323\) | −11.9870 | −0.666974 | ||||||||
\(324\) | −9.84764 | −0.547091 | ||||||||
\(325\) | 18.2444 | 1.01202 | ||||||||
\(326\) | −22.8876 | −1.26763 | ||||||||
\(327\) | 11.1938 | 0.619016 | ||||||||
\(328\) | −7.72437 | −0.426507 | ||||||||
\(329\) | −9.85064 | −0.543083 | ||||||||
\(330\) | 29.3220 | 1.61412 | ||||||||
\(331\) | −32.5253 | −1.78775 | −0.893875 | − | 0.448316i | \(-0.852024\pi\) | ||||
−0.893875 | + | 0.448316i | \(0.852024\pi\) | |||||||
\(332\) | 9.05386 | 0.496895 | ||||||||
\(333\) | −0.417150 | −0.0228597 | ||||||||
\(334\) | 3.29537 | 0.180315 | ||||||||
\(335\) | −42.6879 | −2.33229 | ||||||||
\(336\) | 6.45474 | 0.352135 | ||||||||
\(337\) | −34.0500 | −1.85482 | −0.927412 | − | 0.374042i | \(-0.877972\pi\) | ||||
−0.927412 | + | 0.374042i | \(0.877972\pi\) | |||||||
\(338\) | 9.26764 | 0.504093 | ||||||||
\(339\) | 15.3287 | 0.832542 | ||||||||
\(340\) | 27.5575 | 1.49451 | ||||||||
\(341\) | 39.7302 | 2.15151 | ||||||||
\(342\) | −0.522042 | −0.0282288 | ||||||||
\(343\) | 5.08590 | 0.274613 | ||||||||
\(344\) | −12.2401 | −0.659940 | ||||||||
\(345\) | 19.2256 | 1.03507 | ||||||||
\(346\) | 8.41833 | 0.452572 | ||||||||
\(347\) | −6.91669 | −0.371307 | −0.185654 | − | 0.982615i | \(-0.559440\pi\) | ||||
−0.185654 | + | 0.982615i | \(0.559440\pi\) | |||||||
\(348\) | −12.0611 | −0.646541 | ||||||||
\(349\) | −6.42314 | −0.343823 | −0.171911 | − | 0.985112i | \(-0.554994\pi\) | ||||
−0.171911 | + | 0.985112i | \(0.554994\pi\) | |||||||
\(350\) | 33.4752 | 1.78933 | ||||||||
\(351\) | 9.44282 | 0.504021 | ||||||||
\(352\) | 4.23704 | 0.225835 | ||||||||
\(353\) | 4.64082 | 0.247006 | 0.123503 | − | 0.992344i | \(-0.460587\pi\) | ||||
0.123503 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(354\) | −19.8716 | −1.05616 | ||||||||
\(355\) | 10.8370 | 0.575170 | ||||||||
\(356\) | −1.09101 | −0.0578232 | ||||||||
\(357\) | −46.8037 | −2.47711 | ||||||||
\(358\) | −18.2974 | −0.967049 | ||||||||
\(359\) | −13.8789 | −0.732501 | −0.366251 | − | 0.930516i | \(-0.619359\pi\) | ||||
−0.366251 | + | 0.930516i | \(0.619359\pi\) | |||||||
\(360\) | 1.20015 | 0.0632533 | ||||||||
\(361\) | −16.2671 | −0.856165 | ||||||||
\(362\) | 5.28677 | 0.277866 | ||||||||
\(363\) | −12.6600 | −0.664478 | ||||||||
\(364\) | −6.84821 | −0.358944 | ||||||||
\(365\) | −21.0606 | −1.10236 | ||||||||
\(366\) | −22.9745 | −1.20090 | ||||||||
\(367\) | 17.2289 | 0.899343 | 0.449672 | − | 0.893194i | \(-0.351541\pi\) | ||||
0.449672 | + | 0.893194i | \(0.351541\pi\) | |||||||
\(368\) | 2.77810 | 0.144819 | ||||||||
\(369\) | 2.43927 | 0.126983 | ||||||||
\(370\) | −5.02035 | −0.260996 | ||||||||
\(371\) | 30.2505 | 1.57053 | ||||||||
\(372\) | 17.0747 | 0.885280 | ||||||||
\(373\) | 5.54848 | 0.287289 | 0.143645 | − | 0.989629i | \(-0.454118\pi\) | ||||
0.143645 | + | 0.989629i | \(0.454118\pi\) | |||||||
\(374\) | −30.7230 | −1.58865 | ||||||||
\(375\) | 30.7516 | 1.58800 | ||||||||
\(376\) | −2.77894 | −0.143313 | ||||||||
\(377\) | 12.7963 | 0.659042 | ||||||||
\(378\) | 17.3259 | 0.891147 | ||||||||
\(379\) | 26.7795 | 1.37557 | 0.687785 | − | 0.725915i | \(-0.258583\pi\) | ||||
0.687785 | + | 0.725915i | \(0.258583\pi\) | |||||||
\(380\) | −6.28271 | −0.322296 | ||||||||
\(381\) | −18.3753 | −0.941394 | ||||||||
\(382\) | 14.4080 | 0.737176 | ||||||||
\(383\) | 19.7557 | 1.00947 | 0.504736 | − | 0.863274i | \(-0.331590\pi\) | ||||
0.504736 | + | 0.863274i | \(0.331590\pi\) | |||||||
\(384\) | 1.82093 | 0.0929240 | ||||||||
\(385\) | −57.0802 | −2.90908 | ||||||||
\(386\) | −19.9624 | −1.01606 | ||||||||
\(387\) | 3.86527 | 0.196483 | ||||||||
\(388\) | −3.33585 | −0.169352 | ||||||||
\(389\) | 5.74262 | 0.291162 | 0.145581 | − | 0.989346i | \(-0.453495\pi\) | ||||
0.145581 | + | 0.989346i | \(0.453495\pi\) | |||||||
\(390\) | −13.3697 | −0.677003 | ||||||||
\(391\) | −20.1442 | −1.01873 | ||||||||
\(392\) | −5.56523 | −0.281086 | ||||||||
\(393\) | 36.8697 | 1.85983 | ||||||||
\(394\) | 6.27526 | 0.316143 | ||||||||
\(395\) | −44.5626 | −2.24219 | ||||||||
\(396\) | −1.33801 | −0.0672374 | ||||||||
\(397\) | −3.86966 | −0.194213 | −0.0971063 | − | 0.995274i | \(-0.530959\pi\) | ||||
−0.0971063 | + | 0.995274i | \(0.530959\pi\) | |||||||
\(398\) | −8.50276 | −0.426205 | ||||||||
\(399\) | 10.6706 | 0.534197 | ||||||||
\(400\) | 9.44361 | 0.472181 | ||||||||
\(401\) | −13.3000 | −0.664170 | −0.332085 | − | 0.943250i | \(-0.607752\pi\) | ||||
−0.332085 | + | 0.943250i | \(0.607752\pi\) | |||||||
\(402\) | 20.4532 | 1.02011 | ||||||||
\(403\) | −18.1155 | −0.902398 | ||||||||
\(404\) | 17.3615 | 0.863765 | ||||||||
\(405\) | 37.4257 | 1.85970 | ||||||||
\(406\) | 23.4789 | 1.16524 | ||||||||
\(407\) | 5.59704 | 0.277435 | ||||||||
\(408\) | −13.2037 | −0.653679 | ||||||||
\(409\) | 13.1153 | 0.648509 | 0.324255 | − | 0.945970i | \(-0.394887\pi\) | ||||
0.324255 | + | 0.945970i | \(0.394887\pi\) | |||||||
\(410\) | 29.3563 | 1.44980 | ||||||||
\(411\) | −9.78353 | −0.482586 | ||||||||
\(412\) | 5.49812 | 0.270873 | ||||||||
\(413\) | 38.6834 | 1.90348 | ||||||||
\(414\) | −0.877292 | −0.0431166 | ||||||||
\(415\) | −34.4090 | −1.68907 | ||||||||
\(416\) | −1.93193 | −0.0947207 | ||||||||
\(417\) | −1.85675 | −0.0909254 | ||||||||
\(418\) | 7.00441 | 0.342597 | ||||||||
\(419\) | 35.9124 | 1.75443 | 0.877217 | − | 0.480094i | \(-0.159398\pi\) | ||||
0.877217 | + | 0.480094i | \(0.159398\pi\) | |||||||
\(420\) | −24.5311 | −1.19699 | ||||||||
\(421\) | −4.37921 | −0.213429 | −0.106715 | − | 0.994290i | \(-0.534033\pi\) | ||||
−0.106715 | + | 0.994290i | \(0.534033\pi\) | |||||||
\(422\) | −3.50204 | −0.170477 | ||||||||
\(423\) | 0.877557 | 0.0426683 | ||||||||
\(424\) | 8.53389 | 0.414443 | ||||||||
\(425\) | −68.4762 | −3.32158 | ||||||||
\(426\) | −5.19238 | −0.251571 | ||||||||
\(427\) | 44.7238 | 2.16434 | ||||||||
\(428\) | −10.1626 | −0.491230 | ||||||||
\(429\) | 14.9055 | 0.719646 | ||||||||
\(430\) | 46.5181 | 2.24330 | ||||||||
\(431\) | −6.34634 | −0.305693 | −0.152846 | − | 0.988250i | \(-0.548844\pi\) | ||||
−0.152846 | + | 0.988250i | \(0.548844\pi\) | |||||||
\(432\) | 4.88776 | 0.235163 | ||||||||
\(433\) | −12.1995 | −0.586272 | −0.293136 | − | 0.956071i | \(-0.594699\pi\) | ||||
−0.293136 | + | 0.956071i | \(0.594699\pi\) | |||||||
\(434\) | −33.2387 | −1.59551 | ||||||||
\(435\) | 45.8378 | 2.19775 | ||||||||
\(436\) | −6.14727 | −0.294401 | ||||||||
\(437\) | 4.59258 | 0.219693 | ||||||||
\(438\) | 10.0908 | 0.482157 | ||||||||
\(439\) | −32.3638 | −1.54464 | −0.772320 | − | 0.635233i | \(-0.780904\pi\) | ||||
−0.772320 | + | 0.635233i | \(0.780904\pi\) | |||||||
\(440\) | −16.1028 | −0.767669 | ||||||||
\(441\) | 1.75743 | 0.0836874 | ||||||||
\(442\) | 14.0085 | 0.666319 | ||||||||
\(443\) | 11.8677 | 0.563852 | 0.281926 | − | 0.959436i | \(-0.409027\pi\) | ||||
0.281926 | + | 0.959436i | \(0.409027\pi\) | |||||||
\(444\) | 2.40541 | 0.114156 | ||||||||
\(445\) | 4.14634 | 0.196555 | ||||||||
\(446\) | −8.62891 | −0.408591 | ||||||||
\(447\) | 9.28632 | 0.439228 | ||||||||
\(448\) | −3.54475 | −0.167474 | ||||||||
\(449\) | −1.98188 | −0.0935308 | −0.0467654 | − | 0.998906i | \(-0.514891\pi\) | ||||
−0.0467654 | + | 0.998906i | \(0.514891\pi\) | |||||||
\(450\) | −2.98218 | −0.140581 | ||||||||
\(451\) | −32.7285 | −1.54112 | ||||||||
\(452\) | −8.41808 | −0.395953 | ||||||||
\(453\) | 18.8429 | 0.885316 | ||||||||
\(454\) | 18.6343 | 0.874551 | ||||||||
\(455\) | 26.0264 | 1.22014 | ||||||||
\(456\) | 3.01025 | 0.140968 | ||||||||
\(457\) | 24.4134 | 1.14201 | 0.571006 | − | 0.820946i | \(-0.306553\pi\) | ||||
0.571006 | + | 0.820946i | \(0.306553\pi\) | |||||||
\(458\) | −4.45951 | −0.208379 | ||||||||
\(459\) | −35.4414 | −1.65427 | ||||||||
\(460\) | −10.5581 | −0.492274 | ||||||||
\(461\) | −39.3419 | −1.83234 | −0.916168 | − | 0.400793i | \(-0.868735\pi\) | ||||
−0.916168 | + | 0.400793i | \(0.868735\pi\) | |||||||
\(462\) | 27.3490 | 1.27239 | ||||||||
\(463\) | 10.7789 | 0.500938 | 0.250469 | − | 0.968125i | \(-0.419415\pi\) | ||||
0.250469 | + | 0.968125i | \(0.419415\pi\) | |||||||
\(464\) | 6.62357 | 0.307492 | ||||||||
\(465\) | −64.8918 | −3.00929 | ||||||||
\(466\) | −27.1983 | −1.25994 | ||||||||
\(467\) | −4.75747 | −0.220150 | −0.110075 | − | 0.993923i | \(-0.535109\pi\) | ||||
−0.110075 | + | 0.993923i | \(0.535109\pi\) | |||||||
\(468\) | 0.610082 | 0.0282010 | ||||||||
\(469\) | −39.8155 | −1.83851 | ||||||||
\(470\) | 10.5613 | 0.487156 | ||||||||
\(471\) | −15.3546 | −0.707501 | ||||||||
\(472\) | 10.9129 | 0.502306 | ||||||||
\(473\) | −51.8616 | −2.38460 | ||||||||
\(474\) | 21.3514 | 0.980702 | ||||||||
\(475\) | 15.6116 | 0.716309 | ||||||||
\(476\) | 25.7032 | 1.17810 | ||||||||
\(477\) | −2.69491 | −0.123391 | ||||||||
\(478\) | −28.7485 | −1.31493 | ||||||||
\(479\) | −20.4210 | −0.933061 | −0.466530 | − | 0.884505i | \(-0.654496\pi\) | ||||
−0.466530 | + | 0.884505i | \(0.654496\pi\) | |||||||
\(480\) | −6.92040 | −0.315872 | ||||||||
\(481\) | −2.55204 | −0.116363 | ||||||||
\(482\) | 12.7200 | 0.579379 | ||||||||
\(483\) | 17.9319 | 0.815930 | ||||||||
\(484\) | 6.95249 | 0.316022 | ||||||||
\(485\) | 12.6778 | 0.575669 | ||||||||
\(486\) | −3.26859 | −0.148266 | ||||||||
\(487\) | 35.8756 | 1.62568 | 0.812840 | − | 0.582487i | \(-0.197920\pi\) | ||||
0.812840 | + | 0.582487i | \(0.197920\pi\) | |||||||
\(488\) | 12.6169 | 0.571141 | ||||||||
\(489\) | −41.6768 | −1.88469 | ||||||||
\(490\) | 21.1505 | 0.955483 | ||||||||
\(491\) | 9.30422 | 0.419893 | 0.209947 | − | 0.977713i | \(-0.432671\pi\) | ||||
0.209947 | + | 0.977713i | \(0.432671\pi\) | |||||||
\(492\) | −14.0655 | −0.634124 | ||||||||
\(493\) | −48.0279 | −2.16307 | ||||||||
\(494\) | −3.19375 | −0.143694 | ||||||||
\(495\) | 5.08507 | 0.228557 | ||||||||
\(496\) | −9.37689 | −0.421035 | ||||||||
\(497\) | 10.1078 | 0.453398 | ||||||||
\(498\) | 16.4864 | 0.738775 | ||||||||
\(499\) | −21.5100 | −0.962919 | −0.481459 | − | 0.876468i | \(-0.659893\pi\) | ||||
−0.481459 | + | 0.876468i | \(0.659893\pi\) | |||||||
\(500\) | −16.8878 | −0.755247 | ||||||||
\(501\) | 6.00065 | 0.268089 | ||||||||
\(502\) | −5.69500 | −0.254180 | ||||||||
\(503\) | −35.4074 | −1.57874 | −0.789370 | − | 0.613918i | \(-0.789593\pi\) | ||||
−0.789370 | + | 0.613918i | \(0.789593\pi\) | |||||||
\(504\) | 1.11939 | 0.0498616 | ||||||||
\(505\) | −65.9818 | −2.93615 | ||||||||
\(506\) | 11.7709 | 0.523281 | ||||||||
\(507\) | 16.8757 | 0.749477 | ||||||||
\(508\) | 10.0912 | 0.447722 | ||||||||
\(509\) | 3.08047 | 0.136539 | 0.0682697 | − | 0.997667i | \(-0.478252\pi\) | ||||
0.0682697 | + | 0.997667i | \(0.478252\pi\) | |||||||
\(510\) | 50.1802 | 2.22202 | ||||||||
\(511\) | −19.6434 | −0.868974 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.08014 | 0.356747 | ||||||||
\(514\) | 17.3344 | 0.764588 | ||||||||
\(515\) | −20.8955 | −0.920765 | ||||||||
\(516\) | −22.2883 | −0.981189 | ||||||||
\(517\) | −11.7745 | −0.517841 | ||||||||
\(518\) | −4.68254 | −0.205739 | ||||||||
\(519\) | 15.3292 | 0.672877 | ||||||||
\(520\) | 7.34226 | 0.321979 | ||||||||
\(521\) | 18.2326 | 0.798786 | 0.399393 | − | 0.916780i | \(-0.369221\pi\) | ||||
0.399393 | + | 0.916780i | \(0.369221\pi\) | |||||||
\(522\) | −2.09165 | −0.0915489 | ||||||||
\(523\) | −2.60504 | −0.113911 | −0.0569553 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569553 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(524\) | −20.2477 | −0.884525 | ||||||||
\(525\) | 60.9560 | 2.66034 | ||||||||
\(526\) | −0.573248 | −0.0249948 | ||||||||
\(527\) | 67.9924 | 2.96179 | ||||||||
\(528\) | 7.71535 | 0.335768 | ||||||||
\(529\) | −15.2822 | −0.664441 | ||||||||
\(530\) | −32.4329 | −1.40879 | ||||||||
\(531\) | −3.44616 | −0.149551 | ||||||||
\(532\) | −5.85995 | −0.254061 | ||||||||
\(533\) | 14.9230 | 0.646385 | ||||||||
\(534\) | −1.98665 | −0.0859706 | ||||||||
\(535\) | 38.6229 | 1.66981 | ||||||||
\(536\) | −11.2323 | −0.485160 | ||||||||
\(537\) | −33.3184 | −1.43779 | ||||||||
\(538\) | 11.7841 | 0.508050 | ||||||||
\(539\) | −23.5801 | −1.01567 | ||||||||
\(540\) | −18.5758 | −0.799376 | ||||||||
\(541\) | −30.9651 | −1.33129 | −0.665647 | − | 0.746267i | \(-0.731844\pi\) | ||||
−0.665647 | + | 0.746267i | \(0.731844\pi\) | |||||||
\(542\) | −1.72211 | −0.0739710 | ||||||||
\(543\) | 9.62683 | 0.413127 | ||||||||
\(544\) | 7.25106 | 0.310887 | ||||||||
\(545\) | 23.3626 | 1.00074 | ||||||||
\(546\) | −12.4701 | −0.533672 | ||||||||
\(547\) | −15.4319 | −0.659821 | −0.329910 | − | 0.944012i | \(-0.607019\pi\) | ||||
−0.329910 | + | 0.944012i | \(0.607019\pi\) | |||||||
\(548\) | 5.37282 | 0.229515 | ||||||||
\(549\) | −3.98428 | −0.170045 | ||||||||
\(550\) | 40.0129 | 1.70616 | ||||||||
\(551\) | 10.9497 | 0.466472 | ||||||||
\(552\) | 5.05873 | 0.215314 | ||||||||
\(553\) | −41.5641 | −1.76748 | ||||||||
\(554\) | 0.604596 | 0.0256868 | ||||||||
\(555\) | −9.14171 | −0.388044 | ||||||||
\(556\) | 1.01967 | 0.0432437 | ||||||||
\(557\) | −20.9715 | −0.888592 | −0.444296 | − | 0.895880i | \(-0.646546\pi\) | ||||
−0.444296 | + | 0.895880i | \(0.646546\pi\) | |||||||
\(558\) | 2.96111 | 0.125354 | ||||||||
\(559\) | 23.6470 | 1.00016 | ||||||||
\(560\) | 13.4717 | 0.569284 | ||||||||
\(561\) | −55.9445 | −2.36198 | ||||||||
\(562\) | −3.80725 | −0.160599 | ||||||||
\(563\) | 1.78839 | 0.0753716 | 0.0376858 | − | 0.999290i | \(-0.488001\pi\) | ||||
0.0376858 | + | 0.999290i | \(0.488001\pi\) | |||||||
\(564\) | −5.06026 | −0.213075 | ||||||||
\(565\) | 31.9927 | 1.34594 | ||||||||
\(566\) | 0.610355 | 0.0256551 | ||||||||
\(567\) | 34.9074 | 1.46597 | ||||||||
\(568\) | 2.85150 | 0.119646 | ||||||||
\(569\) | 16.6280 | 0.697081 | 0.348540 | − | 0.937294i | \(-0.386677\pi\) | ||||
0.348540 | + | 0.937294i | \(0.386677\pi\) | |||||||
\(570\) | −11.4404 | −0.479185 | ||||||||
\(571\) | 17.3291 | 0.725201 | 0.362601 | − | 0.931945i | \(-0.381889\pi\) | ||||
0.362601 | + | 0.931945i | \(0.381889\pi\) | |||||||
\(572\) | −8.18567 | −0.342260 | ||||||||
\(573\) | 26.2359 | 1.09602 | ||||||||
\(574\) | 27.3809 | 1.14286 | ||||||||
\(575\) | 26.2353 | 1.09409 | ||||||||
\(576\) | 0.315788 | 0.0131579 | ||||||||
\(577\) | −12.6121 | −0.525049 | −0.262524 | − | 0.964925i | \(-0.584555\pi\) | ||||
−0.262524 | + | 0.964925i | \(0.584555\pi\) | |||||||
\(578\) | −35.5778 | −1.47984 | ||||||||
\(579\) | −36.3501 | −1.51066 | ||||||||
\(580\) | −25.1727 | −1.04524 | ||||||||
\(581\) | −32.0936 | −1.33147 | ||||||||
\(582\) | −6.07435 | −0.251790 | ||||||||
\(583\) | 36.1584 | 1.49753 | ||||||||
\(584\) | −5.54156 | −0.229311 | ||||||||
\(585\) | −2.31860 | −0.0958623 | ||||||||
\(586\) | 2.88815 | 0.119308 | ||||||||
\(587\) | 29.9048 | 1.23430 | 0.617151 | − | 0.786845i | \(-0.288287\pi\) | ||||
0.617151 | + | 0.786845i | \(0.288287\pi\) | |||||||
\(588\) | −10.1339 | −0.417915 | ||||||||
\(589\) | −15.5013 | −0.638719 | ||||||||
\(590\) | −41.4741 | −1.70746 | ||||||||
\(591\) | 11.4268 | 0.470036 | ||||||||
\(592\) | −1.32098 | −0.0542920 | ||||||||
\(593\) | −28.4837 | −1.16968 | −0.584842 | − | 0.811147i | \(-0.698844\pi\) | ||||
−0.584842 | + | 0.811147i | \(0.698844\pi\) | |||||||
\(594\) | 20.7096 | 0.849727 | ||||||||
\(595\) | −97.6842 | −4.00466 | ||||||||
\(596\) | −5.09976 | −0.208895 | ||||||||
\(597\) | −15.4829 | −0.633675 | ||||||||
\(598\) | −5.36710 | −0.219477 | ||||||||
\(599\) | 13.6918 | 0.559430 | 0.279715 | − | 0.960083i | \(-0.409760\pi\) | ||||
0.279715 | + | 0.960083i | \(0.409760\pi\) | |||||||
\(600\) | 17.1962 | 0.702030 | ||||||||
\(601\) | 33.9178 | 1.38353 | 0.691767 | − | 0.722121i | \(-0.256833\pi\) | ||||
0.691767 | + | 0.722121i | \(0.256833\pi\) | |||||||
\(602\) | 43.3879 | 1.76836 | ||||||||
\(603\) | 3.54702 | 0.144446 | ||||||||
\(604\) | −10.3479 | −0.421052 | ||||||||
\(605\) | −26.4228 | −1.07424 | ||||||||
\(606\) | 31.6140 | 1.28423 | ||||||||
\(607\) | 23.3715 | 0.948620 | 0.474310 | − | 0.880358i | \(-0.342698\pi\) | ||||
0.474310 | + | 0.880358i | \(0.342698\pi\) | |||||||
\(608\) | −1.65314 | −0.0670436 | ||||||||
\(609\) | 42.7534 | 1.73246 | ||||||||
\(610\) | −47.9503 | −1.94145 | ||||||||
\(611\) | 5.36872 | 0.217195 | ||||||||
\(612\) | −2.28980 | −0.0925597 | ||||||||
\(613\) | −7.62645 | −0.308029 | −0.154015 | − | 0.988069i | \(-0.549220\pi\) | ||||
−0.154015 | + | 0.988069i | \(0.549220\pi\) | |||||||
\(614\) | 21.8437 | 0.881539 | ||||||||
\(615\) | 53.4558 | 2.15554 | ||||||||
\(616\) | −15.0192 | −0.605142 | ||||||||
\(617\) | 27.2887 | 1.09860 | 0.549301 | − | 0.835625i | \(-0.314894\pi\) | ||||
0.549301 | + | 0.835625i | \(0.314894\pi\) | |||||||
\(618\) | 10.0117 | 0.402730 | ||||||||
\(619\) | 34.6326 | 1.39200 | 0.696001 | − | 0.718041i | \(-0.254961\pi\) | ||||
0.696001 | + | 0.718041i | \(0.254961\pi\) | |||||||
\(620\) | 35.6366 | 1.43120 | ||||||||
\(621\) | 13.5787 | 0.544895 | ||||||||
\(622\) | −19.5894 | −0.785464 | ||||||||
\(623\) | 3.86734 | 0.154942 | ||||||||
\(624\) | −3.51791 | −0.140829 | ||||||||
\(625\) | 16.9637 | 0.678550 | ||||||||
\(626\) | −25.3964 | −1.01504 | ||||||||
\(627\) | 12.7545 | 0.509367 | ||||||||
\(628\) | 8.43226 | 0.336484 | ||||||||
\(629\) | 9.57850 | 0.381920 | ||||||||
\(630\) | −4.25421 | −0.169492 | ||||||||
\(631\) | −26.4862 | −1.05440 | −0.527199 | − | 0.849742i | \(-0.676758\pi\) | ||||
−0.527199 | + | 0.849742i | \(0.676758\pi\) | |||||||
\(632\) | −11.7255 | −0.466417 | ||||||||
\(633\) | −6.37697 | −0.253462 | ||||||||
\(634\) | 5.85823 | 0.232660 | ||||||||
\(635\) | −38.3512 | −1.52192 | ||||||||
\(636\) | 15.5396 | 0.616186 | ||||||||
\(637\) | 10.7516 | 0.425995 | ||||||||
\(638\) | 28.0643 | 1.11108 | ||||||||
\(639\) | −0.900469 | −0.0356220 | ||||||||
\(640\) | 3.80048 | 0.150227 | ||||||||
\(641\) | 21.7321 | 0.858365 | 0.429183 | − | 0.903218i | \(-0.358802\pi\) | ||||
0.429183 | + | 0.903218i | \(0.358802\pi\) | |||||||
\(642\) | −18.5055 | −0.730353 | ||||||||
\(643\) | 37.2441 | 1.46876 | 0.734382 | − | 0.678737i | \(-0.237472\pi\) | ||||
0.734382 | + | 0.678737i | \(0.237472\pi\) | |||||||
\(644\) | −9.84767 | −0.388052 | ||||||||
\(645\) | 84.7062 | 3.33530 | ||||||||
\(646\) | 11.9870 | 0.471622 | ||||||||
\(647\) | 34.3429 | 1.35016 | 0.675079 | − | 0.737745i | \(-0.264109\pi\) | ||||
0.675079 | + | 0.737745i | \(0.264109\pi\) | |||||||
\(648\) | 9.84764 | 0.386852 | ||||||||
\(649\) | 46.2383 | 1.81501 | ||||||||
\(650\) | −18.2444 | −0.715605 | ||||||||
\(651\) | −60.5254 | −2.37218 | ||||||||
\(652\) | 22.8876 | 0.896349 | ||||||||
\(653\) | 28.8878 | 1.13047 | 0.565234 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565234 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(654\) | −11.1938 | −0.437711 | ||||||||
\(655\) | 76.9509 | 3.00672 | ||||||||
\(656\) | 7.72437 | 0.301586 | ||||||||
\(657\) | 1.74996 | 0.0682725 | ||||||||
\(658\) | 9.85064 | 0.384018 | ||||||||
\(659\) | −39.0221 | −1.52008 | −0.760042 | − | 0.649874i | \(-0.774822\pi\) | ||||
−0.760042 | + | 0.649874i | \(0.774822\pi\) | |||||||
\(660\) | −29.3220 | −1.14136 | ||||||||
\(661\) | −2.31263 | −0.0899511 | −0.0449755 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449755 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(662\) | 32.5253 | 1.26413 | ||||||||
\(663\) | 25.5086 | 0.990672 | ||||||||
\(664\) | −9.05386 | −0.351358 | ||||||||
\(665\) | 22.2706 | 0.863617 | ||||||||
\(666\) | 0.417150 | 0.0161642 | ||||||||
\(667\) | 18.4010 | 0.712488 | ||||||||
\(668\) | −3.29537 | −0.127502 | ||||||||
\(669\) | −15.7126 | −0.607486 | ||||||||
\(670\) | 42.6879 | 1.64918 | ||||||||
\(671\) | 53.4584 | 2.06374 | ||||||||
\(672\) | −6.45474 | −0.248997 | ||||||||
\(673\) | −38.9917 | −1.50302 | −0.751509 | − | 0.659723i | \(-0.770674\pi\) | ||||
−0.751509 | + | 0.659723i | \(0.770674\pi\) | |||||||
\(674\) | 34.0500 | 1.31156 | ||||||||
\(675\) | 46.1581 | 1.77663 | ||||||||
\(676\) | −9.26764 | −0.356448 | ||||||||
\(677\) | 5.38730 | 0.207051 | 0.103525 | − | 0.994627i | \(-0.466988\pi\) | ||||
0.103525 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(678\) | −15.3287 | −0.588696 | ||||||||
\(679\) | 11.8247 | 0.453792 | ||||||||
\(680\) | −27.5575 | −1.05678 | ||||||||
\(681\) | 33.9318 | 1.30027 | ||||||||
\(682\) | −39.7302 | −1.52135 | ||||||||
\(683\) | 29.7789 | 1.13946 | 0.569729 | − | 0.821833i | \(-0.307048\pi\) | ||||
0.569729 | + | 0.821833i | \(0.307048\pi\) | |||||||
\(684\) | 0.522042 | 0.0199608 | ||||||||
\(685\) | −20.4193 | −0.780180 | ||||||||
\(686\) | −5.08590 | −0.194181 | ||||||||
\(687\) | −8.12045 | −0.309815 | ||||||||
\(688\) | 12.2401 | 0.466648 | ||||||||
\(689\) | −16.4869 | −0.628101 | ||||||||
\(690\) | −19.2256 | −0.731905 | ||||||||
\(691\) | −2.89807 | −0.110248 | −0.0551238 | − | 0.998480i | \(-0.517555\pi\) | ||||
−0.0551238 | + | 0.998480i | \(0.517555\pi\) | |||||||
\(692\) | −8.41833 | −0.320017 | ||||||||
\(693\) | 4.74290 | 0.180168 | ||||||||
\(694\) | 6.91669 | 0.262554 | ||||||||
\(695\) | −3.87523 | −0.146996 | ||||||||
\(696\) | 12.0611 | 0.457174 | ||||||||
\(697\) | −56.0099 | −2.12152 | ||||||||
\(698\) | 6.42314 | 0.243119 | ||||||||
\(699\) | −49.5262 | −1.87325 | ||||||||
\(700\) | −33.4752 | −1.26524 | ||||||||
\(701\) | 40.7677 | 1.53977 | 0.769887 | − | 0.638181i | \(-0.220313\pi\) | ||||
0.769887 | + | 0.638181i | \(0.220313\pi\) | |||||||
\(702\) | −9.44282 | −0.356396 | ||||||||
\(703\) | −2.18376 | −0.0823621 | ||||||||
\(704\) | −4.23704 | −0.159689 | ||||||||
\(705\) | 19.2314 | 0.724296 | ||||||||
\(706\) | −4.64082 | −0.174660 | ||||||||
\(707\) | −61.5420 | −2.31453 | ||||||||
\(708\) | 19.8716 | 0.746820 | ||||||||
\(709\) | −12.9280 | −0.485522 | −0.242761 | − | 0.970086i | \(-0.578053\pi\) | ||||
−0.242761 | + | 0.970086i | \(0.578053\pi\) | |||||||
\(710\) | −10.8370 | −0.406707 | ||||||||
\(711\) | 3.70279 | 0.138866 | ||||||||
\(712\) | 1.09101 | 0.0408872 | ||||||||
\(713\) | −26.0499 | −0.975578 | ||||||||
\(714\) | 46.8037 | 1.75158 | ||||||||
\(715\) | 31.1094 | 1.16343 | ||||||||
\(716\) | 18.2974 | 0.683807 | ||||||||
\(717\) | −52.3491 | −1.95501 | ||||||||
\(718\) | 13.8789 | 0.517957 | ||||||||
\(719\) | 18.6463 | 0.695391 | 0.347696 | − | 0.937607i | \(-0.386964\pi\) | ||||
0.347696 | + | 0.937607i | \(0.386964\pi\) | |||||||
\(720\) | −1.20015 | −0.0447268 | ||||||||
\(721\) | −19.4894 | −0.725825 | ||||||||
\(722\) | 16.2671 | 0.605400 | ||||||||
\(723\) | 23.1622 | 0.861412 | ||||||||
\(724\) | −5.28677 | −0.196481 | ||||||||
\(725\) | 62.5504 | 2.32307 | ||||||||
\(726\) | 12.6600 | 0.469857 | ||||||||
\(727\) | 19.3731 | 0.718509 | 0.359254 | − | 0.933240i | \(-0.383031\pi\) | ||||
0.359254 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(728\) | 6.84821 | 0.253811 | ||||||||
\(729\) | 23.5911 | 0.873743 | ||||||||
\(730\) | 21.0606 | 0.779486 | ||||||||
\(731\) | −88.7534 | −3.28266 | ||||||||
\(732\) | 22.9745 | 0.849164 | ||||||||
\(733\) | −31.7529 | −1.17282 | −0.586410 | − | 0.810014i | \(-0.699459\pi\) | ||||
−0.586410 | + | 0.810014i | \(0.699459\pi\) | |||||||
\(734\) | −17.2289 | −0.635932 | ||||||||
\(735\) | 38.5136 | 1.42060 | ||||||||
\(736\) | −2.77810 | −0.102402 | ||||||||
\(737\) | −47.5915 | −1.75306 | ||||||||
\(738\) | −2.43927 | −0.0897907 | ||||||||
\(739\) | −8.70497 | −0.320218 | −0.160109 | − | 0.987099i | \(-0.551185\pi\) | ||||
−0.160109 | + | 0.987099i | \(0.551185\pi\) | |||||||
\(740\) | 5.02035 | 0.184552 | ||||||||
\(741\) | −5.81559 | −0.213641 | ||||||||
\(742\) | −30.2505 | −1.11053 | ||||||||
\(743\) | 16.4876 | 0.604872 | 0.302436 | − | 0.953170i | \(-0.402200\pi\) | ||||
0.302436 | + | 0.953170i | \(0.402200\pi\) | |||||||
\(744\) | −17.0747 | −0.625988 | ||||||||
\(745\) | 19.3815 | 0.710084 | ||||||||
\(746\) | −5.54848 | −0.203144 | ||||||||
\(747\) | 2.85910 | 0.104609 | ||||||||
\(748\) | 30.7230 | 1.12334 | ||||||||
\(749\) | 36.0240 | 1.31629 | ||||||||
\(750\) | −30.7516 | −1.12289 | ||||||||
\(751\) | −12.5440 | −0.457735 | −0.228868 | − | 0.973458i | \(-0.573502\pi\) | ||||
−0.228868 | + | 0.973458i | \(0.573502\pi\) | |||||||
\(752\) | 2.77894 | 0.101338 | ||||||||
\(753\) | −10.3702 | −0.377911 | ||||||||
\(754\) | −12.7963 | −0.466013 | ||||||||
\(755\) | 39.3271 | 1.43126 | ||||||||
\(756\) | −17.3259 | −0.630136 | ||||||||
\(757\) | 16.3930 | 0.595815 | 0.297908 | − | 0.954595i | \(-0.403711\pi\) | ||||
0.297908 | + | 0.954595i | \(0.403711\pi\) | |||||||
\(758\) | −26.7795 | −0.972674 | ||||||||
\(759\) | 21.4340 | 0.778006 | ||||||||
\(760\) | 6.28271 | 0.227898 | ||||||||
\(761\) | 17.2389 | 0.624911 | 0.312455 | − | 0.949932i | \(-0.398849\pi\) | ||||
0.312455 | + | 0.949932i | \(0.398849\pi\) | |||||||
\(762\) | 18.3753 | 0.665666 | ||||||||
\(763\) | 21.7905 | 0.788870 | ||||||||
\(764\) | −14.4080 | −0.521262 | ||||||||
\(765\) | 8.70233 | 0.314633 | ||||||||
\(766\) | −19.7557 | −0.713804 | ||||||||
\(767\) | −21.0829 | −0.761260 | ||||||||
\(768\) | −1.82093 | −0.0657072 | ||||||||
\(769\) | −1.92188 | −0.0693049 | −0.0346524 | − | 0.999399i | \(-0.511032\pi\) | ||||
−0.0346524 | + | 0.999399i | \(0.511032\pi\) | |||||||
\(770\) | 57.0802 | 2.05703 | ||||||||
\(771\) | 31.5648 | 1.13678 | ||||||||
\(772\) | 19.9624 | 0.718461 | ||||||||
\(773\) | 0.651155 | 0.0234204 | 0.0117102 | − | 0.999931i | \(-0.496272\pi\) | ||||
0.0117102 | + | 0.999931i | \(0.496272\pi\) | |||||||
\(774\) | −3.86527 | −0.138934 | ||||||||
\(775\) | −88.5517 | −3.18087 | ||||||||
\(776\) | 3.33585 | 0.119750 | ||||||||
\(777\) | −8.52658 | −0.305889 | ||||||||
\(778\) | −5.74262 | −0.205883 | ||||||||
\(779\) | 12.7694 | 0.457513 | ||||||||
\(780\) | 13.3697 | 0.478714 | ||||||||
\(781\) | 12.0819 | 0.432324 | ||||||||
\(782\) | 20.1442 | 0.720354 | ||||||||
\(783\) | 32.3745 | 1.15697 | ||||||||
\(784\) | 5.56523 | 0.198758 | ||||||||
\(785\) | −32.0466 | −1.14379 | ||||||||
\(786\) | −36.8697 | −1.31510 | ||||||||
\(787\) | 20.8161 | 0.742015 | 0.371007 | − | 0.928630i | \(-0.379012\pi\) | ||||
0.371007 | + | 0.928630i | \(0.379012\pi\) | |||||||
\(788\) | −6.27526 | −0.223547 | ||||||||
\(789\) | −1.04384 | −0.0371618 | ||||||||
\(790\) | 44.5626 | 1.58547 | ||||||||
\(791\) | 29.8399 | 1.06099 | ||||||||
\(792\) | 1.33801 | 0.0475440 | ||||||||
\(793\) | −24.3750 | −0.865583 | ||||||||
\(794\) | 3.86966 | 0.137329 | ||||||||
\(795\) | −59.0580 | −2.09457 | ||||||||
\(796\) | 8.50276 | 0.301372 | ||||||||
\(797\) | −12.8114 | −0.453801 | −0.226901 | − | 0.973918i | \(-0.572859\pi\) | ||||
−0.226901 | + | 0.973918i | \(0.572859\pi\) | |||||||
\(798\) | −10.6706 | −0.377734 | ||||||||
\(799\) | −20.1503 | −0.712865 | ||||||||
\(800\) | −9.44361 | −0.333882 | ||||||||
\(801\) | −0.344527 | −0.0121733 | ||||||||
\(802\) | 13.3000 | 0.469639 | ||||||||
\(803\) | −23.4798 | −0.828584 | ||||||||
\(804\) | −20.4532 | −0.721328 | ||||||||
\(805\) | 37.4258 | 1.31909 | ||||||||
\(806\) | 18.1155 | 0.638092 | ||||||||
\(807\) | 21.4581 | 0.755360 | ||||||||
\(808\) | −17.3615 | −0.610774 | ||||||||
\(809\) | 12.4630 | 0.438174 | 0.219087 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219087 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(810\) | −37.4257 | −1.31501 | ||||||||
\(811\) | −32.9912 | −1.15848 | −0.579238 | − | 0.815158i | \(-0.696650\pi\) | ||||
−0.579238 | + | 0.815158i | \(0.696650\pi\) | |||||||
\(812\) | −23.4789 | −0.823947 | ||||||||
\(813\) | −3.13584 | −0.109979 | ||||||||
\(814\) | −5.59704 | −0.196176 | ||||||||
\(815\) | −86.9839 | −3.04691 | ||||||||
\(816\) | 13.2037 | 0.462221 | ||||||||
\(817\) | 20.2345 | 0.707916 | ||||||||
\(818\) | −13.1153 | −0.458565 | ||||||||
\(819\) | −2.16259 | −0.0755668 | ||||||||
\(820\) | −29.3563 | −1.02517 | ||||||||
\(821\) | 21.2066 | 0.740116 | 0.370058 | − | 0.929009i | \(-0.379338\pi\) | ||||
0.370058 | + | 0.929009i | \(0.379338\pi\) | |||||||
\(822\) | 9.78353 | 0.341240 | ||||||||
\(823\) | −3.53700 | −0.123292 | −0.0616461 | − | 0.998098i | \(-0.519635\pi\) | ||||
−0.0616461 | + | 0.998098i | \(0.519635\pi\) | |||||||
\(824\) | −5.49812 | −0.191536 | ||||||||
\(825\) | 72.8608 | 2.53669 | ||||||||
\(826\) | −38.6834 | −1.34597 | ||||||||
\(827\) | −47.9059 | −1.66585 | −0.832925 | − | 0.553386i | \(-0.813335\pi\) | ||||
−0.832925 | + | 0.553386i | \(0.813335\pi\) | |||||||
\(828\) | 0.877292 | 0.0304880 | ||||||||
\(829\) | 32.5398 | 1.13015 | 0.565077 | − | 0.825038i | \(-0.308846\pi\) | ||||
0.565077 | + | 0.825038i | \(0.308846\pi\) | |||||||
\(830\) | 34.4090 | 1.19435 | ||||||||
\(831\) | 1.10093 | 0.0381907 | ||||||||
\(832\) | 1.93193 | 0.0669777 | ||||||||
\(833\) | −40.3538 | −1.39818 | ||||||||
\(834\) | 1.85675 | 0.0642940 | ||||||||
\(835\) | 12.5240 | 0.433410 | ||||||||
\(836\) | −7.00441 | −0.242252 | ||||||||
\(837\) | −45.8320 | −1.58419 | ||||||||
\(838\) | −35.9124 | −1.24057 | ||||||||
\(839\) | −32.9144 | −1.13633 | −0.568165 | − | 0.822914i | \(-0.692347\pi\) | ||||
−0.568165 | + | 0.822914i | \(0.692347\pi\) | |||||||
\(840\) | 24.5311 | 0.846402 | ||||||||
\(841\) | 14.8717 | 0.512818 | ||||||||
\(842\) | 4.37921 | 0.150917 | ||||||||
\(843\) | −6.93274 | −0.238776 | ||||||||
\(844\) | 3.50204 | 0.120545 | ||||||||
\(845\) | 35.2214 | 1.21165 | ||||||||
\(846\) | −0.877557 | −0.0301710 | ||||||||
\(847\) | −24.6448 | −0.846806 | ||||||||
\(848\) | −8.53389 | −0.293055 | ||||||||
\(849\) | 1.11141 | 0.0381436 | ||||||||
\(850\) | 68.4762 | 2.34871 | ||||||||
\(851\) | −3.66982 | −0.125800 | ||||||||
\(852\) | 5.19238 | 0.177888 | ||||||||
\(853\) | 3.99008 | 0.136618 | 0.0683088 | − | 0.997664i | \(-0.478240\pi\) | ||||
0.0683088 | + | 0.997664i | \(0.478240\pi\) | |||||||
\(854\) | −44.7238 | −1.53042 | ||||||||
\(855\) | −1.98401 | −0.0678516 | ||||||||
\(856\) | 10.1626 | 0.347352 | ||||||||
\(857\) | 24.7741 | 0.846269 | 0.423134 | − | 0.906067i | \(-0.360930\pi\) | ||||
0.423134 | + | 0.906067i | \(0.360930\pi\) | |||||||
\(858\) | −14.9055 | −0.508867 | ||||||||
\(859\) | 45.9502 | 1.56780 | 0.783900 | − | 0.620887i | \(-0.213227\pi\) | ||||
0.783900 | + | 0.620887i | \(0.213227\pi\) | |||||||
\(860\) | −46.5181 | −1.58625 | ||||||||
\(861\) | 49.8588 | 1.69918 | ||||||||
\(862\) | 6.34634 | 0.216157 | ||||||||
\(863\) | 17.8391 | 0.607251 | 0.303626 | − | 0.952791i | \(-0.401803\pi\) | ||||
0.303626 | + | 0.952791i | \(0.401803\pi\) | |||||||
\(864\) | −4.88776 | −0.166285 | ||||||||
\(865\) | 31.9937 | 1.08782 | ||||||||
\(866\) | 12.1995 | 0.414557 | ||||||||
\(867\) | −64.7848 | −2.20021 | ||||||||
\(868\) | 33.2387 | 1.12819 | ||||||||
\(869\) | −49.6816 | −1.68533 | ||||||||
\(870\) | −45.8378 | −1.55405 | ||||||||
\(871\) | 21.7000 | 0.735275 | ||||||||
\(872\) | 6.14727 | 0.208173 | ||||||||
\(873\) | −1.05342 | −0.0356529 | ||||||||
\(874\) | −4.59258 | −0.155346 | ||||||||
\(875\) | 59.8631 | 2.02374 | ||||||||
\(876\) | −10.0908 | −0.340936 | ||||||||
\(877\) | 15.4239 | 0.520829 | 0.260414 | − | 0.965497i | \(-0.416141\pi\) | ||||
0.260414 | + | 0.965497i | \(0.416141\pi\) | |||||||
\(878\) | 32.3638 | 1.09223 | ||||||||
\(879\) | 5.25912 | 0.177386 | ||||||||
\(880\) | 16.1028 | 0.542824 | ||||||||
\(881\) | −10.0524 | −0.338673 | −0.169336 | − | 0.985558i | \(-0.554162\pi\) | ||||
−0.169336 | + | 0.985558i | \(0.554162\pi\) | |||||||
\(882\) | −1.75743 | −0.0591759 | ||||||||
\(883\) | 38.3801 | 1.29159 | 0.645797 | − | 0.763510i | \(-0.276525\pi\) | ||||
0.645797 | + | 0.763510i | \(0.276525\pi\) | |||||||
\(884\) | −14.0085 | −0.471158 | ||||||||
\(885\) | −75.5215 | −2.53863 | ||||||||
\(886\) | −11.8677 | −0.398704 | ||||||||
\(887\) | 4.83508 | 0.162346 | 0.0811730 | − | 0.996700i | \(-0.474133\pi\) | ||||
0.0811730 | + | 0.996700i | \(0.474133\pi\) | |||||||
\(888\) | −2.40541 | −0.0807204 | ||||||||
\(889\) | −35.7706 | −1.19971 | ||||||||
\(890\) | −4.14634 | −0.138986 | ||||||||
\(891\) | 41.7248 | 1.39783 | ||||||||
\(892\) | 8.62891 | 0.288917 | ||||||||
\(893\) | 4.59397 | 0.153731 | ||||||||
\(894\) | −9.28632 | −0.310581 | ||||||||
\(895\) | −69.5389 | −2.32443 | ||||||||
\(896\) | 3.54475 | 0.118422 | ||||||||
\(897\) | −9.77312 | −0.326315 | ||||||||
\(898\) | 1.98188 | 0.0661363 | ||||||||
\(899\) | −62.1085 | −2.07143 | ||||||||
\(900\) | 2.98218 | 0.0994061 | ||||||||
\(901\) | 61.8798 | 2.06151 | ||||||||
\(902\) | 32.7285 | 1.08974 | ||||||||
\(903\) | 79.0064 | 2.62917 | ||||||||
\(904\) | 8.41808 | 0.279981 | ||||||||
\(905\) | 20.0922 | 0.667888 | ||||||||
\(906\) | −18.8429 | −0.626013 | ||||||||
\(907\) | −33.0893 | −1.09871 | −0.549356 | − | 0.835588i | \(-0.685127\pi\) | ||||
−0.549356 | + | 0.835588i | \(0.685127\pi\) | |||||||
\(908\) | −18.6343 | −0.618401 | ||||||||
\(909\) | 5.48255 | 0.181845 | ||||||||
\(910\) | −26.0264 | −0.862768 | ||||||||
\(911\) | −27.4193 | −0.908441 | −0.454220 | − | 0.890889i | \(-0.650082\pi\) | ||||
−0.454220 | + | 0.890889i | \(0.650082\pi\) | |||||||
\(912\) | −3.01025 | −0.0996793 | ||||||||
\(913\) | −38.3615 | −1.26958 | ||||||||
\(914\) | −24.4134 | −0.807524 | ||||||||
\(915\) | −87.3142 | −2.88652 | ||||||||
\(916\) | 4.45951 | 0.147346 | ||||||||
\(917\) | 71.7730 | 2.37015 | ||||||||
\(918\) | 35.4414 | 1.16974 | ||||||||
\(919\) | 47.5869 | 1.56975 | 0.784874 | − | 0.619655i | \(-0.212728\pi\) | ||||
0.784874 | + | 0.619655i | \(0.212728\pi\) | |||||||
\(920\) | 10.5581 | 0.348090 | ||||||||
\(921\) | 39.7758 | 1.31066 | ||||||||
\(922\) | 39.3419 | 1.29566 | ||||||||
\(923\) | −5.50889 | −0.181327 | ||||||||
\(924\) | −27.3490 | −0.899715 | ||||||||
\(925\) | −12.4748 | −0.410170 | ||||||||
\(926\) | −10.7789 | −0.354216 | ||||||||
\(927\) | 1.73624 | 0.0570257 | ||||||||
\(928\) | −6.62357 | −0.217429 | ||||||||
\(929\) | 0.714612 | 0.0234457 | 0.0117228 | − | 0.999931i | \(-0.496268\pi\) | ||||
0.0117228 | + | 0.999931i | \(0.496268\pi\) | |||||||
\(930\) | 64.8918 | 2.12789 | ||||||||
\(931\) | 9.20009 | 0.301521 | ||||||||
\(932\) | 27.1983 | 0.890910 | ||||||||
\(933\) | −35.6710 | −1.16781 | ||||||||
\(934\) | 4.75747 | 0.155669 | ||||||||
\(935\) | −116.762 | −3.81853 | ||||||||
\(936\) | −0.610082 | −0.0199411 | ||||||||
\(937\) | 33.9434 | 1.10888 | 0.554442 | − | 0.832223i | \(-0.312932\pi\) | ||||
0.554442 | + | 0.832223i | \(0.312932\pi\) | |||||||
\(938\) | 39.8155 | 1.30002 | ||||||||
\(939\) | −46.2451 | −1.50915 | ||||||||
\(940\) | −10.5613 | −0.344471 | ||||||||
\(941\) | −35.6616 | −1.16254 | −0.581268 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581268 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(942\) | 15.3546 | 0.500279 | ||||||||
\(943\) | 21.4591 | 0.698804 | ||||||||
\(944\) | −10.9129 | −0.355184 | ||||||||
\(945\) | 65.8466 | 2.14199 | ||||||||
\(946\) | 51.8616 | 1.68617 | ||||||||
\(947\) | 2.03154 | 0.0660163 | 0.0330082 | − | 0.999455i | \(-0.489491\pi\) | ||||
0.0330082 | + | 0.999455i | \(0.489491\pi\) | |||||||
\(948\) | −21.3514 | −0.693461 | ||||||||
\(949\) | 10.7059 | 0.347529 | ||||||||
\(950\) | −15.6116 | −0.506507 | ||||||||
\(951\) | 10.6674 | 0.345915 | ||||||||
\(952\) | −25.7032 | −0.833044 | ||||||||
\(953\) | 29.6684 | 0.961052 | 0.480526 | − | 0.876980i | \(-0.340446\pi\) | ||||
0.480526 | + | 0.876980i | \(0.340446\pi\) | |||||||
\(954\) | 2.69491 | 0.0872508 | ||||||||
\(955\) | 54.7571 | 1.77190 | ||||||||
\(956\) | 28.7485 | 0.929794 | ||||||||
\(957\) | 51.1032 | 1.65193 | ||||||||
\(958\) | 20.4210 | 0.659774 | ||||||||
\(959\) | −19.0453 | −0.615004 | ||||||||
\(960\) | 6.92040 | 0.223355 | ||||||||
\(961\) | 56.9260 | 1.83632 | ||||||||
\(962\) | 2.55204 | 0.0822812 | ||||||||
\(963\) | −3.20925 | −0.103417 | ||||||||
\(964\) | −12.7200 | −0.409683 | ||||||||
\(965\) | −75.8664 | −2.44223 | ||||||||
\(966\) | −17.9319 | −0.576950 | ||||||||
\(967\) | −13.9503 | −0.448611 | −0.224306 | − | 0.974519i | \(-0.572011\pi\) | ||||
−0.224306 | + | 0.974519i | \(0.572011\pi\) | |||||||
\(968\) | −6.95249 | −0.223462 | ||||||||
\(969\) | 21.8275 | 0.701200 | ||||||||
\(970\) | −12.6778 | −0.407060 | ||||||||
\(971\) | −19.6661 | −0.631115 | −0.315558 | − | 0.948906i | \(-0.602192\pi\) | ||||
−0.315558 | + | 0.948906i | \(0.602192\pi\) | |||||||
\(972\) | 3.26859 | 0.104840 | ||||||||
\(973\) | −3.61447 | −0.115875 | ||||||||
\(974\) | −35.8756 | −1.14953 | ||||||||
\(975\) | −33.2218 | −1.06395 | ||||||||
\(976\) | −12.6169 | −0.403858 | ||||||||
\(977\) | −2.46901 | −0.0789905 | −0.0394953 | − | 0.999220i | \(-0.512575\pi\) | ||||
−0.0394953 | + | 0.999220i | \(0.512575\pi\) | |||||||
\(978\) | 41.6768 | 1.33268 | ||||||||
\(979\) | 4.62263 | 0.147740 | ||||||||
\(980\) | −21.1505 | −0.675628 | ||||||||
\(981\) | −1.94124 | −0.0619790 | ||||||||
\(982\) | −9.30422 | −0.296909 | ||||||||
\(983\) | −15.8743 | −0.506311 | −0.253155 | − | 0.967426i | \(-0.581468\pi\) | ||||
−0.253155 | + | 0.967426i | \(0.581468\pi\) | |||||||
\(984\) | 14.0655 | 0.448393 | ||||||||
\(985\) | 23.8490 | 0.759891 | ||||||||
\(986\) | 48.0279 | 1.52952 | ||||||||
\(987\) | 17.9373 | 0.570951 | ||||||||
\(988\) | 3.19375 | 0.101607 | ||||||||
\(989\) | 34.0042 | 1.08127 | ||||||||
\(990\) | −5.08507 | −0.161614 | ||||||||
\(991\) | 56.4317 | 1.79261 | 0.896305 | − | 0.443437i | \(-0.146241\pi\) | ||||
0.896305 | + | 0.443437i | \(0.146241\pi\) | |||||||
\(992\) | 9.37689 | 0.297717 | ||||||||
\(993\) | 59.2263 | 1.87949 | ||||||||
\(994\) | −10.1078 | −0.320601 | ||||||||
\(995\) | −32.3145 | −1.02444 | ||||||||
\(996\) | −16.4864 | −0.522393 | ||||||||
\(997\) | −35.6360 | −1.12860 | −0.564302 | − | 0.825568i | \(-0.690855\pi\) | ||||
−0.564302 | + | 0.825568i | \(0.690855\pi\) | |||||||
\(998\) | 21.5100 | 0.680886 | ||||||||
\(999\) | −6.45664 | −0.204279 |
(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 | 4006.2.a.g.1.11 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.11 | ✓ | 40 | 1.1 | even | 1 | trivial |