Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25624 | 0.888293 | 0.444146 | − | 0.895954i | \(-0.353507\pi\) | ||||
0.444146 | + | 0.895954i | \(0.353507\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.421872 | −0.210936 | ||||||||
\(5\) | 0.726022 | 0.324687 | 0.162343 | − | 0.986734i | \(-0.448095\pi\) | ||||
0.162343 | + | 0.986734i | \(0.448095\pi\) | |||||||
\(6\) | −1.25624 | −0.512856 | ||||||||
\(7\) | 0.867951 | 0.328055 | 0.164027 | − | 0.986456i | \(-0.447551\pi\) | ||||
0.164027 | + | 0.986456i | \(0.447551\pi\) | |||||||
\(8\) | −3.04244 | −1.07567 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.912055 | 0.288417 | ||||||||
\(11\) | 3.59453 | 1.08379 | 0.541896 | − | 0.840446i | \(-0.317707\pi\) | ||||
0.541896 | + | 0.840446i | \(0.317707\pi\) | |||||||
\(12\) | 0.421872 | 0.121784 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.09035 | 0.291409 | ||||||||
\(15\) | −0.726022 | −0.187458 | ||||||||
\(16\) | −2.97828 | −0.744570 | ||||||||
\(17\) | −0.939676 | −0.227905 | −0.113952 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113952 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(18\) | 1.25624 | 0.296098 | ||||||||
\(19\) | −5.25134 | −1.20474 | −0.602370 | − | 0.798217i | \(-0.705777\pi\) | ||||
−0.602370 | + | 0.798217i | \(0.705777\pi\) | |||||||
\(20\) | −0.306288 | −0.0684881 | ||||||||
\(21\) | −0.867951 | −0.189402 | ||||||||
\(22\) | 4.51558 | 0.962724 | ||||||||
\(23\) | 1.49063 | 0.310817 | 0.155408 | − | 0.987850i | \(-0.450331\pi\) | ||||
0.155408 | + | 0.987850i | \(0.450331\pi\) | |||||||
\(24\) | 3.04244 | 0.621036 | ||||||||
\(25\) | −4.47289 | −0.894578 | ||||||||
\(26\) | −1.25624 | −0.246368 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.366164 | −0.0691985 | ||||||||
\(29\) | 4.96362 | 0.921722 | 0.460861 | − | 0.887472i | \(-0.347541\pi\) | ||||
0.460861 | + | 0.887472i | \(0.347541\pi\) | |||||||
\(30\) | −0.912055 | −0.166518 | ||||||||
\(31\) | −7.44554 | −1.33726 | −0.668629 | − | 0.743596i | \(-0.733119\pi\) | ||||
−0.668629 | + | 0.743596i | \(0.733119\pi\) | |||||||
\(32\) | 2.34346 | 0.414269 | ||||||||
\(33\) | −3.59453 | −0.625727 | ||||||||
\(34\) | −1.18045 | −0.202446 | ||||||||
\(35\) | 0.630151 | 0.106515 | ||||||||
\(36\) | −0.421872 | −0.0703120 | ||||||||
\(37\) | −4.77506 | −0.785014 | −0.392507 | − | 0.919749i | \(-0.628392\pi\) | ||||
−0.392507 | + | 0.919749i | \(0.628392\pi\) | |||||||
\(38\) | −6.59692 | −1.07016 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.20888 | −0.349254 | ||||||||
\(41\) | −3.53461 | −0.552013 | −0.276006 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276006 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(42\) | −1.09035 | −0.168245 | ||||||||
\(43\) | −2.89646 | −0.441706 | −0.220853 | − | 0.975307i | \(-0.570884\pi\) | ||||
−0.220853 | + | 0.975307i | \(0.570884\pi\) | |||||||
\(44\) | −1.51643 | −0.228611 | ||||||||
\(45\) | 0.726022 | 0.108229 | ||||||||
\(46\) | 1.87258 | 0.276096 | ||||||||
\(47\) | 6.80278 | 0.992287 | 0.496144 | − | 0.868240i | \(-0.334749\pi\) | ||||
0.496144 | + | 0.868240i | \(0.334749\pi\) | |||||||
\(48\) | 2.97828 | 0.429878 | ||||||||
\(49\) | −6.24666 | −0.892380 | ||||||||
\(50\) | −5.61901 | −0.794648 | ||||||||
\(51\) | 0.939676 | 0.131581 | ||||||||
\(52\) | 0.421872 | 0.0585031 | ||||||||
\(53\) | 5.61780 | 0.771664 | 0.385832 | − | 0.922569i | \(-0.373914\pi\) | ||||
0.385832 | + | 0.922569i | \(0.373914\pi\) | |||||||
\(54\) | −1.25624 | −0.170952 | ||||||||
\(55\) | 2.60971 | 0.351893 | ||||||||
\(56\) | −2.64069 | −0.352877 | ||||||||
\(57\) | 5.25134 | 0.695557 | ||||||||
\(58\) | 6.23548 | 0.818759 | ||||||||
\(59\) | 4.52457 | 0.589049 | 0.294524 | − | 0.955644i | \(-0.404839\pi\) | ||||
0.294524 | + | 0.955644i | \(0.404839\pi\) | |||||||
\(60\) | 0.306288 | 0.0395416 | ||||||||
\(61\) | 12.6769 | 1.62311 | 0.811556 | − | 0.584275i | \(-0.198621\pi\) | ||||
0.811556 | + | 0.584275i | \(0.198621\pi\) | |||||||
\(62\) | −9.35335 | −1.18788 | ||||||||
\(63\) | 0.867951 | 0.109352 | ||||||||
\(64\) | 8.90050 | 1.11256 | ||||||||
\(65\) | −0.726022 | −0.0900519 | ||||||||
\(66\) | −4.51558 | −0.555829 | ||||||||
\(67\) | −4.89316 | −0.597795 | −0.298897 | − | 0.954285i | \(-0.596619\pi\) | ||||
−0.298897 | + | 0.954285i | \(0.596619\pi\) | |||||||
\(68\) | 0.396423 | 0.0480733 | ||||||||
\(69\) | −1.49063 | −0.179450 | ||||||||
\(70\) | 0.791619 | 0.0946165 | ||||||||
\(71\) | 6.74725 | 0.800751 | 0.400375 | − | 0.916351i | \(-0.368880\pi\) | ||||
0.400375 | + | 0.916351i | \(0.368880\pi\) | |||||||
\(72\) | −3.04244 | −0.358555 | ||||||||
\(73\) | 4.99757 | 0.584921 | 0.292461 | − | 0.956278i | \(-0.405526\pi\) | ||||
0.292461 | + | 0.956278i | \(0.405526\pi\) | |||||||
\(74\) | −5.99859 | −0.697323 | ||||||||
\(75\) | 4.47289 | 0.516485 | ||||||||
\(76\) | 2.21539 | 0.254123 | ||||||||
\(77\) | 3.11988 | 0.355543 | ||||||||
\(78\) | 1.25624 | 0.142241 | ||||||||
\(79\) | −10.8189 | −1.21722 | −0.608609 | − | 0.793470i | \(-0.708272\pi\) | ||||
−0.608609 | + | 0.793470i | \(0.708272\pi\) | |||||||
\(80\) | −2.16230 | −0.241752 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.44030 | −0.490349 | ||||||||
\(83\) | −11.5859 | −1.27171 | −0.635857 | − | 0.771807i | \(-0.719353\pi\) | ||||
−0.635857 | + | 0.771807i | \(0.719353\pi\) | |||||||
\(84\) | 0.366164 | 0.0399518 | ||||||||
\(85\) | −0.682225 | −0.0739977 | ||||||||
\(86\) | −3.63864 | −0.392365 | ||||||||
\(87\) | −4.96362 | −0.532156 | ||||||||
\(88\) | −10.9361 | −1.16580 | ||||||||
\(89\) | −6.84189 | −0.725238 | −0.362619 | − | 0.931937i | \(-0.618117\pi\) | ||||
−0.362619 | + | 0.931937i | \(0.618117\pi\) | |||||||
\(90\) | 0.912055 | 0.0961390 | ||||||||
\(91\) | −0.867951 | −0.0909860 | ||||||||
\(92\) | −0.628853 | −0.0655624 | ||||||||
\(93\) | 7.44554 | 0.772066 | ||||||||
\(94\) | 8.54589 | 0.881442 | ||||||||
\(95\) | −3.81259 | −0.391163 | ||||||||
\(96\) | −2.34346 | −0.239178 | ||||||||
\(97\) | −4.46972 | −0.453832 | −0.226916 | − | 0.973914i | \(-0.572864\pi\) | ||||
−0.226916 | + | 0.973914i | \(0.572864\pi\) | |||||||
\(98\) | −7.84728 | −0.792695 | ||||||||
\(99\) | 3.59453 | 0.361264 | ||||||||
\(100\) | 1.88699 | 0.188699 | ||||||||
\(101\) | −18.9754 | −1.88813 | −0.944063 | − | 0.329765i | \(-0.893030\pi\) | ||||
−0.944063 | + | 0.329765i | \(0.893030\pi\) | |||||||
\(102\) | 1.18045 | 0.116882 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 3.04244 | 0.298336 | ||||||||
\(105\) | −0.630151 | −0.0614965 | ||||||||
\(106\) | 7.05728 | 0.685464 | ||||||||
\(107\) | −12.5998 | −1.21807 | −0.609034 | − | 0.793144i | \(-0.708443\pi\) | ||||
−0.609034 | + | 0.793144i | \(0.708443\pi\) | |||||||
\(108\) | 0.421872 | 0.0405946 | ||||||||
\(109\) | −19.1826 | −1.83736 | −0.918681 | − | 0.395001i | \(-0.870744\pi\) | ||||
−0.918681 | + | 0.395001i | \(0.870744\pi\) | |||||||
\(110\) | 3.27841 | 0.312584 | ||||||||
\(111\) | 4.77506 | 0.453228 | ||||||||
\(112\) | −2.58500 | −0.244260 | ||||||||
\(113\) | −17.7441 | −1.66922 | −0.834610 | − | 0.550841i | \(-0.814307\pi\) | ||||
−0.834610 | + | 0.550841i | \(0.814307\pi\) | |||||||
\(114\) | 6.59692 | 0.617859 | ||||||||
\(115\) | 1.08223 | 0.100918 | ||||||||
\(116\) | −2.09401 | −0.194424 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 5.68393 | 0.523248 | ||||||||
\(119\) | −0.815593 | −0.0747652 | ||||||||
\(120\) | 2.20888 | 0.201642 | ||||||||
\(121\) | 1.92065 | 0.174604 | ||||||||
\(122\) | 15.9252 | 1.44180 | ||||||||
\(123\) | 3.53461 | 0.318705 | ||||||||
\(124\) | 3.14106 | 0.282076 | ||||||||
\(125\) | −6.87753 | −0.615145 | ||||||||
\(126\) | 1.09035 | 0.0971362 | ||||||||
\(127\) | −15.4264 | −1.36887 | −0.684437 | − | 0.729072i | \(-0.739952\pi\) | ||||
−0.684437 | + | 0.729072i | \(0.739952\pi\) | |||||||
\(128\) | 6.49421 | 0.574012 | ||||||||
\(129\) | 2.89646 | 0.255019 | ||||||||
\(130\) | −0.912055 | −0.0799925 | ||||||||
\(131\) | 11.5715 | 1.01101 | 0.505504 | − | 0.862824i | \(-0.331307\pi\) | ||||
0.505504 | + | 0.862824i | \(0.331307\pi\) | |||||||
\(132\) | 1.51643 | 0.131988 | ||||||||
\(133\) | −4.55791 | −0.395221 | ||||||||
\(134\) | −6.14696 | −0.531017 | ||||||||
\(135\) | −0.726022 | −0.0624860 | ||||||||
\(136\) | 2.85891 | 0.245149 | ||||||||
\(137\) | −3.27157 | −0.279509 | −0.139754 | − | 0.990186i | \(-0.544631\pi\) | ||||
−0.139754 | + | 0.990186i | \(0.544631\pi\) | |||||||
\(138\) | −1.87258 | −0.159404 | ||||||||
\(139\) | −21.1187 | −1.79126 | −0.895632 | − | 0.444796i | \(-0.853276\pi\) | ||||
−0.895632 | + | 0.444796i | \(0.853276\pi\) | |||||||
\(140\) | −0.265843 | −0.0224678 | ||||||||
\(141\) | −6.80278 | −0.572897 | ||||||||
\(142\) | 8.47613 | 0.711301 | ||||||||
\(143\) | −3.59453 | −0.300590 | ||||||||
\(144\) | −2.97828 | −0.248190 | ||||||||
\(145\) | 3.60370 | 0.299271 | ||||||||
\(146\) | 6.27813 | 0.519582 | ||||||||
\(147\) | 6.24666 | 0.515216 | ||||||||
\(148\) | 2.01446 | 0.165588 | ||||||||
\(149\) | −3.53031 | −0.289215 | −0.144607 | − | 0.989489i | \(-0.546192\pi\) | ||||
−0.144607 | + | 0.989489i | \(0.546192\pi\) | |||||||
\(150\) | 5.61901 | 0.458790 | ||||||||
\(151\) | 11.1317 | 0.905882 | 0.452941 | − | 0.891540i | \(-0.350375\pi\) | ||||
0.452941 | + | 0.891540i | \(0.350375\pi\) | |||||||
\(152\) | 15.9769 | 1.29590 | ||||||||
\(153\) | −0.939676 | −0.0759683 | ||||||||
\(154\) | 3.91930 | 0.315826 | ||||||||
\(155\) | −5.40562 | −0.434190 | ||||||||
\(156\) | −0.421872 | −0.0337768 | ||||||||
\(157\) | 4.76685 | 0.380436 | 0.190218 | − | 0.981742i | \(-0.439080\pi\) | ||||
0.190218 | + | 0.981742i | \(0.439080\pi\) | |||||||
\(158\) | −13.5911 | −1.08125 | ||||||||
\(159\) | −5.61780 | −0.445521 | ||||||||
\(160\) | 1.70140 | 0.134508 | ||||||||
\(161\) | 1.29379 | 0.101965 | ||||||||
\(162\) | 1.25624 | 0.0986992 | ||||||||
\(163\) | −16.2779 | −1.27499 | −0.637494 | − | 0.770456i | \(-0.720029\pi\) | ||||
−0.637494 | + | 0.770456i | \(0.720029\pi\) | |||||||
\(164\) | 1.49115 | 0.116439 | ||||||||
\(165\) | −2.60971 | −0.203165 | ||||||||
\(166\) | −14.5546 | −1.12965 | ||||||||
\(167\) | 6.63100 | 0.513122 | 0.256561 | − | 0.966528i | \(-0.417411\pi\) | ||||
0.256561 | + | 0.966528i | \(0.417411\pi\) | |||||||
\(168\) | 2.64069 | 0.203734 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.857036 | −0.0657316 | ||||||||
\(171\) | −5.25134 | −0.401580 | ||||||||
\(172\) | 1.22194 | 0.0931717 | ||||||||
\(173\) | 15.4319 | 1.17326 | 0.586632 | − | 0.809854i | \(-0.300453\pi\) | ||||
0.586632 | + | 0.809854i | \(0.300453\pi\) | |||||||
\(174\) | −6.23548 | −0.472711 | ||||||||
\(175\) | −3.88225 | −0.293471 | ||||||||
\(176\) | −10.7055 | −0.806959 | ||||||||
\(177\) | −4.52457 | −0.340087 | ||||||||
\(178\) | −8.59502 | −0.644224 | ||||||||
\(179\) | −18.3875 | −1.37435 | −0.687174 | − | 0.726493i | \(-0.741149\pi\) | ||||
−0.687174 | + | 0.726493i | \(0.741149\pi\) | |||||||
\(180\) | −0.306288 | −0.0228294 | ||||||||
\(181\) | 14.2111 | 1.05630 | 0.528150 | − | 0.849151i | \(-0.322886\pi\) | ||||
0.528150 | + | 0.849151i | \(0.322886\pi\) | |||||||
\(182\) | −1.09035 | −0.0808222 | ||||||||
\(183\) | −12.6769 | −0.937104 | ||||||||
\(184\) | −4.53514 | −0.334335 | ||||||||
\(185\) | −3.46679 | −0.254884 | ||||||||
\(186\) | 9.35335 | 0.685821 | ||||||||
\(187\) | −3.37769 | −0.247001 | ||||||||
\(188\) | −2.86990 | −0.209309 | ||||||||
\(189\) | −0.867951 | −0.0631341 | ||||||||
\(190\) | −4.78951 | −0.347468 | ||||||||
\(191\) | −2.61191 | −0.188991 | −0.0944955 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944955 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(192\) | −8.90050 | −0.642338 | ||||||||
\(193\) | 13.2196 | 0.951570 | 0.475785 | − | 0.879562i | \(-0.342164\pi\) | ||||
0.475785 | + | 0.879562i | \(0.342164\pi\) | |||||||
\(194\) | −5.61503 | −0.403135 | ||||||||
\(195\) | 0.726022 | 0.0519915 | ||||||||
\(196\) | 2.63529 | 0.188235 | ||||||||
\(197\) | −5.50978 | −0.392556 | −0.196278 | − | 0.980548i | \(-0.562885\pi\) | ||||
−0.196278 | + | 0.980548i | \(0.562885\pi\) | |||||||
\(198\) | 4.51558 | 0.320908 | ||||||||
\(199\) | 8.20184 | 0.581413 | 0.290707 | − | 0.956812i | \(-0.406110\pi\) | ||||
0.290707 | + | 0.956812i | \(0.406110\pi\) | |||||||
\(200\) | 13.6085 | 0.962267 | ||||||||
\(201\) | 4.89316 | 0.345137 | ||||||||
\(202\) | −23.8376 | −1.67721 | ||||||||
\(203\) | 4.30818 | 0.302375 | ||||||||
\(204\) | −0.396423 | −0.0277551 | ||||||||
\(205\) | −2.56620 | −0.179231 | ||||||||
\(206\) | −1.25624 | −0.0875261 | ||||||||
\(207\) | 1.49063 | 0.103606 | ||||||||
\(208\) | 2.97828 | 0.206507 | ||||||||
\(209\) | −18.8761 | −1.30569 | ||||||||
\(210\) | −0.791619 | −0.0546269 | ||||||||
\(211\) | −4.45695 | −0.306829 | −0.153415 | − | 0.988162i | \(-0.549027\pi\) | ||||
−0.153415 | + | 0.988162i | \(0.549027\pi\) | |||||||
\(212\) | −2.36999 | −0.162772 | ||||||||
\(213\) | −6.74725 | −0.462314 | ||||||||
\(214\) | −15.8283 | −1.08200 | ||||||||
\(215\) | −2.10289 | −0.143416 | ||||||||
\(216\) | 3.04244 | 0.207012 | ||||||||
\(217\) | −6.46236 | −0.438694 | ||||||||
\(218\) | −24.0979 | −1.63212 | ||||||||
\(219\) | −4.99757 | −0.337705 | ||||||||
\(220\) | −1.10096 | −0.0742268 | ||||||||
\(221\) | 0.939676 | 0.0632094 | ||||||||
\(222\) | 5.99859 | 0.402599 | ||||||||
\(223\) | 17.3716 | 1.16329 | 0.581643 | − | 0.813444i | \(-0.302410\pi\) | ||||
0.581643 | + | 0.813444i | \(0.302410\pi\) | |||||||
\(224\) | 2.03401 | 0.135903 | ||||||||
\(225\) | −4.47289 | −0.298193 | ||||||||
\(226\) | −22.2907 | −1.48276 | ||||||||
\(227\) | 0.396107 | 0.0262906 | 0.0131453 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131453 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(228\) | −2.21539 | −0.146718 | ||||||||
\(229\) | −13.0026 | −0.859235 | −0.429618 | − | 0.903011i | \(-0.641352\pi\) | ||||
−0.429618 | + | 0.903011i | \(0.641352\pi\) | |||||||
\(230\) | 1.35953 | 0.0896449 | ||||||||
\(231\) | −3.11988 | −0.205273 | ||||||||
\(232\) | −15.1015 | −0.991465 | ||||||||
\(233\) | 0.00103394 | 6.77358e−5 0 | 3.38679e−5 | − | 1.00000i | \(-0.499989\pi\) | ||||
3.38679e−5 | 1.00000i | \(0.499989\pi\) | ||||||||
\(234\) | −1.25624 | −0.0821227 | ||||||||
\(235\) | 4.93897 | 0.322183 | ||||||||
\(236\) | −1.90879 | −0.124252 | ||||||||
\(237\) | 10.8189 | 0.702762 | ||||||||
\(238\) | −1.02458 | −0.0664134 | ||||||||
\(239\) | 20.8018 | 1.34556 | 0.672778 | − | 0.739844i | \(-0.265101\pi\) | ||||
0.672778 | + | 0.739844i | \(0.265101\pi\) | |||||||
\(240\) | 2.16230 | 0.139576 | ||||||||
\(241\) | −13.7419 | −0.885196 | −0.442598 | − | 0.896720i | \(-0.645943\pi\) | ||||
−0.442598 | + | 0.896720i | \(0.645943\pi\) | |||||||
\(242\) | 2.41279 | 0.155100 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.34803 | −0.342373 | ||||||||
\(245\) | −4.53521 | −0.289744 | ||||||||
\(246\) | 4.44030 | 0.283103 | ||||||||
\(247\) | 5.25134 | 0.334135 | ||||||||
\(248\) | 22.6526 | 1.43844 | ||||||||
\(249\) | 11.5859 | 0.734224 | ||||||||
\(250\) | −8.63980 | −0.546429 | ||||||||
\(251\) | −1.28495 | −0.0811051 | −0.0405525 | − | 0.999177i | \(-0.512912\pi\) | ||||
−0.0405525 | + | 0.999177i | \(0.512912\pi\) | |||||||
\(252\) | −0.366164 | −0.0230662 | ||||||||
\(253\) | 5.35810 | 0.336861 | ||||||||
\(254\) | −19.3792 | −1.21596 | ||||||||
\(255\) | 0.682225 | 0.0427226 | ||||||||
\(256\) | −9.64275 | −0.602672 | ||||||||
\(257\) | 13.6547 | 0.851757 | 0.425878 | − | 0.904780i | \(-0.359965\pi\) | ||||
0.425878 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(258\) | 3.63864 | 0.226532 | ||||||||
\(259\) | −4.14451 | −0.257528 | ||||||||
\(260\) | 0.306288 | 0.0189952 | ||||||||
\(261\) | 4.96362 | 0.307241 | ||||||||
\(262\) | 14.5366 | 0.898071 | ||||||||
\(263\) | −22.7598 | −1.40343 | −0.701714 | − | 0.712459i | \(-0.747581\pi\) | ||||
−0.701714 | + | 0.712459i | \(0.747581\pi\) | |||||||
\(264\) | 10.9361 | 0.673074 | ||||||||
\(265\) | 4.07865 | 0.250549 | ||||||||
\(266\) | −5.72581 | −0.351072 | ||||||||
\(267\) | 6.84189 | 0.418717 | ||||||||
\(268\) | 2.06429 | 0.126096 | ||||||||
\(269\) | 1.40354 | 0.0855756 | 0.0427878 | − | 0.999084i | \(-0.486376\pi\) | ||||
0.0427878 | + | 0.999084i | \(0.486376\pi\) | |||||||
\(270\) | −0.912055 | −0.0555059 | ||||||||
\(271\) | 0.793915 | 0.0482269 | 0.0241135 | − | 0.999709i | \(-0.492324\pi\) | ||||
0.0241135 | + | 0.999709i | \(0.492324\pi\) | |||||||
\(272\) | 2.79862 | 0.169691 | ||||||||
\(273\) | 0.867951 | 0.0525308 | ||||||||
\(274\) | −4.10986 | −0.248286 | ||||||||
\(275\) | −16.0779 | −0.969537 | ||||||||
\(276\) | 0.628853 | 0.0378525 | ||||||||
\(277\) | 9.18431 | 0.551832 | 0.275916 | − | 0.961182i | \(-0.411019\pi\) | ||||
0.275916 | + | 0.961182i | \(0.411019\pi\) | |||||||
\(278\) | −26.5301 | −1.59117 | ||||||||
\(279\) | −7.44554 | −0.445753 | ||||||||
\(280\) | −1.91720 | −0.114575 | ||||||||
\(281\) | 25.3899 | 1.51464 | 0.757319 | − | 0.653046i | \(-0.226509\pi\) | ||||
0.757319 | + | 0.653046i | \(0.226509\pi\) | |||||||
\(282\) | −8.54589 | −0.508901 | ||||||||
\(283\) | 1.44014 | 0.0856073 | 0.0428036 | − | 0.999084i | \(-0.486371\pi\) | ||||
0.0428036 | + | 0.999084i | \(0.486371\pi\) | |||||||
\(284\) | −2.84647 | −0.168907 | ||||||||
\(285\) | 3.81259 | 0.225838 | ||||||||
\(286\) | −4.51558 | −0.267012 | ||||||||
\(287\) | −3.06786 | −0.181090 | ||||||||
\(288\) | 2.34346 | 0.138090 | ||||||||
\(289\) | −16.1170 | −0.948059 | ||||||||
\(290\) | 4.52710 | 0.265840 | ||||||||
\(291\) | 4.46972 | 0.262020 | ||||||||
\(292\) | −2.10833 | −0.123381 | ||||||||
\(293\) | −23.1478 | −1.35231 | −0.676155 | − | 0.736759i | \(-0.736355\pi\) | ||||
−0.676155 | + | 0.736759i | \(0.736355\pi\) | |||||||
\(294\) | 7.84728 | 0.457663 | ||||||||
\(295\) | 3.28494 | 0.191256 | ||||||||
\(296\) | 14.5278 | 0.844413 | ||||||||
\(297\) | −3.59453 | −0.208576 | ||||||||
\(298\) | −4.43491 | −0.256907 | ||||||||
\(299\) | −1.49063 | −0.0862051 | ||||||||
\(300\) | −1.88699 | −0.108945 | ||||||||
\(301\) | −2.51399 | −0.144904 | ||||||||
\(302\) | 13.9840 | 0.804689 | ||||||||
\(303\) | 18.9754 | 1.09011 | ||||||||
\(304\) | 15.6400 | 0.897014 | ||||||||
\(305\) | 9.20371 | 0.527003 | ||||||||
\(306\) | −1.18045 | −0.0674821 | ||||||||
\(307\) | 19.2794 | 1.10033 | 0.550167 | − | 0.835054i | \(-0.314564\pi\) | ||||
0.550167 | + | 0.835054i | \(0.314564\pi\) | |||||||
\(308\) | −1.31619 | −0.0749967 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −6.79074 | −0.385688 | ||||||||
\(311\) | 23.7591 | 1.34726 | 0.673628 | − | 0.739071i | \(-0.264735\pi\) | ||||
0.673628 | + | 0.739071i | \(0.264735\pi\) | |||||||
\(312\) | −3.04244 | −0.172244 | ||||||||
\(313\) | −13.7303 | −0.776085 | −0.388042 | − | 0.921642i | \(-0.626849\pi\) | ||||
−0.388042 | + | 0.921642i | \(0.626849\pi\) | |||||||
\(314\) | 5.98829 | 0.337939 | ||||||||
\(315\) | 0.630151 | 0.0355050 | ||||||||
\(316\) | 4.56418 | 0.256755 | ||||||||
\(317\) | −7.62491 | −0.428258 | −0.214129 | − | 0.976805i | \(-0.568691\pi\) | ||||
−0.214129 | + | 0.976805i | \(0.568691\pi\) | |||||||
\(318\) | −7.05728 | −0.395753 | ||||||||
\(319\) | 17.8419 | 0.998955 | ||||||||
\(320\) | 6.46196 | 0.361234 | ||||||||
\(321\) | 12.5998 | 0.703252 | ||||||||
\(322\) | 1.62530 | 0.0905747 | ||||||||
\(323\) | 4.93456 | 0.274566 | ||||||||
\(324\) | −0.421872 | −0.0234373 | ||||||||
\(325\) | 4.47289 | 0.248111 | ||||||||
\(326\) | −20.4489 | −1.13256 | ||||||||
\(327\) | 19.1826 | 1.06080 | ||||||||
\(328\) | 10.7538 | 0.593781 | ||||||||
\(329\) | 5.90448 | 0.325524 | ||||||||
\(330\) | −3.27841 | −0.180470 | ||||||||
\(331\) | −28.2691 | −1.55381 | −0.776904 | − | 0.629619i | \(-0.783211\pi\) | ||||
−0.776904 | + | 0.629619i | \(0.783211\pi\) | |||||||
\(332\) | 4.88775 | 0.268250 | ||||||||
\(333\) | −4.77506 | −0.261671 | ||||||||
\(334\) | 8.33010 | 0.455803 | ||||||||
\(335\) | −3.55254 | −0.194096 | ||||||||
\(336\) | 2.58500 | 0.141023 | ||||||||
\(337\) | 20.2030 | 1.10053 | 0.550264 | − | 0.834991i | \(-0.314527\pi\) | ||||
0.550264 | + | 0.834991i | \(0.314527\pi\) | |||||||
\(338\) | 1.25624 | 0.0683302 | ||||||||
\(339\) | 17.7441 | 0.963725 | ||||||||
\(340\) | 0.287812 | 0.0156088 | ||||||||
\(341\) | −26.7632 | −1.44931 | ||||||||
\(342\) | −6.59692 | −0.356721 | ||||||||
\(343\) | −11.4975 | −0.620804 | ||||||||
\(344\) | 8.81232 | 0.475128 | ||||||||
\(345\) | −1.08223 | −0.0582651 | ||||||||
\(346\) | 19.3861 | 1.04220 | ||||||||
\(347\) | −10.3588 | −0.556088 | −0.278044 | − | 0.960568i | \(-0.589686\pi\) | ||||
−0.278044 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(348\) | 2.09401 | 0.112251 | ||||||||
\(349\) | 25.8477 | 1.38359 | 0.691797 | − | 0.722092i | \(-0.256819\pi\) | ||||
0.691797 | + | 0.722092i | \(0.256819\pi\) | |||||||
\(350\) | −4.87702 | −0.260688 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 8.42364 | 0.448982 | ||||||||
\(353\) | −4.88716 | −0.260117 | −0.130059 | − | 0.991506i | \(-0.541517\pi\) | ||||
−0.130059 | + | 0.991506i | \(0.541517\pi\) | |||||||
\(354\) | −5.68393 | −0.302097 | ||||||||
\(355\) | 4.89865 | 0.259993 | ||||||||
\(356\) | 2.88640 | 0.152979 | ||||||||
\(357\) | 0.815593 | 0.0431657 | ||||||||
\(358\) | −23.0991 | −1.22082 | ||||||||
\(359\) | −31.5578 | −1.66556 | −0.832778 | − | 0.553608i | \(-0.813251\pi\) | ||||
−0.832778 | + | 0.553608i | \(0.813251\pi\) | |||||||
\(360\) | −2.20888 | −0.116418 | ||||||||
\(361\) | 8.57660 | 0.451400 | ||||||||
\(362\) | 17.8525 | 0.938304 | ||||||||
\(363\) | −1.92065 | −0.100808 | ||||||||
\(364\) | 0.366164 | 0.0191922 | ||||||||
\(365\) | 3.62835 | 0.189916 | ||||||||
\(366\) | −15.9252 | −0.832423 | ||||||||
\(367\) | 23.6613 | 1.23511 | 0.617554 | − | 0.786529i | \(-0.288124\pi\) | ||||
0.617554 | + | 0.786529i | \(0.288124\pi\) | |||||||
\(368\) | −4.43950 | −0.231425 | ||||||||
\(369\) | −3.53461 | −0.184004 | ||||||||
\(370\) | −4.35511 | −0.226411 | ||||||||
\(371\) | 4.87598 | 0.253148 | ||||||||
\(372\) | −3.14106 | −0.162856 | ||||||||
\(373\) | 17.2299 | 0.892131 | 0.446066 | − | 0.895000i | \(-0.352825\pi\) | ||||
0.446066 | + | 0.895000i | \(0.352825\pi\) | |||||||
\(374\) | −4.24318 | −0.219410 | ||||||||
\(375\) | 6.87753 | 0.355154 | ||||||||
\(376\) | −20.6971 | −1.06737 | ||||||||
\(377\) | −4.96362 | −0.255640 | ||||||||
\(378\) | −1.09035 | −0.0560816 | ||||||||
\(379\) | −5.53919 | −0.284529 | −0.142265 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142265 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(380\) | 1.60842 | 0.0825104 | ||||||||
\(381\) | 15.4264 | 0.790320 | ||||||||
\(382\) | −3.28117 | −0.167879 | ||||||||
\(383\) | 29.7856 | 1.52198 | 0.760988 | − | 0.648766i | \(-0.224715\pi\) | ||||
0.760988 | + | 0.648766i | \(0.224715\pi\) | |||||||
\(384\) | −6.49421 | −0.331406 | ||||||||
\(385\) | 2.26510 | 0.115440 | ||||||||
\(386\) | 16.6070 | 0.845273 | ||||||||
\(387\) | −2.89646 | −0.147235 | ||||||||
\(388\) | 1.88565 | 0.0957294 | ||||||||
\(389\) | 6.13688 | 0.311152 | 0.155576 | − | 0.987824i | \(-0.450277\pi\) | ||||
0.155576 | + | 0.987824i | \(0.450277\pi\) | |||||||
\(390\) | 0.912055 | 0.0461837 | ||||||||
\(391\) | −1.40070 | −0.0708367 | ||||||||
\(392\) | 19.0051 | 0.959903 | ||||||||
\(393\) | −11.5715 | −0.583706 | ||||||||
\(394\) | −6.92159 | −0.348705 | ||||||||
\(395\) | −7.85474 | −0.395215 | ||||||||
\(396\) | −1.51643 | −0.0762035 | ||||||||
\(397\) | −11.6171 | −0.583046 | −0.291523 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291523 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(398\) | 10.3034 | 0.516465 | ||||||||
\(399\) | 4.55791 | 0.228181 | ||||||||
\(400\) | 13.3215 | 0.666076 | ||||||||
\(401\) | 35.9050 | 1.79301 | 0.896505 | − | 0.443034i | \(-0.146098\pi\) | ||||
0.896505 | + | 0.443034i | \(0.146098\pi\) | |||||||
\(402\) | 6.14696 | 0.306583 | ||||||||
\(403\) | 7.44554 | 0.370889 | ||||||||
\(404\) | 8.00520 | 0.398274 | ||||||||
\(405\) | 0.726022 | 0.0360763 | ||||||||
\(406\) | 5.41209 | 0.268598 | ||||||||
\(407\) | −17.1641 | −0.850792 | ||||||||
\(408\) | −2.85891 | −0.141537 | ||||||||
\(409\) | −13.5194 | −0.668491 | −0.334245 | − | 0.942486i | \(-0.608481\pi\) | ||||
−0.334245 | + | 0.942486i | \(0.608481\pi\) | |||||||
\(410\) | −3.22375 | −0.159210 | ||||||||
\(411\) | 3.27157 | 0.161375 | ||||||||
\(412\) | 0.421872 | 0.0207841 | ||||||||
\(413\) | 3.92710 | 0.193240 | ||||||||
\(414\) | 1.87258 | 0.0920321 | ||||||||
\(415\) | −8.41159 | −0.412909 | ||||||||
\(416\) | −2.34346 | −0.114898 | ||||||||
\(417\) | 21.1187 | 1.03419 | ||||||||
\(418\) | −23.7128 | −1.15983 | ||||||||
\(419\) | 26.8040 | 1.30946 | 0.654730 | − | 0.755863i | \(-0.272782\pi\) | ||||
0.654730 | + | 0.755863i | \(0.272782\pi\) | |||||||
\(420\) | 0.265843 | 0.0129718 | ||||||||
\(421\) | 32.0554 | 1.56228 | 0.781142 | − | 0.624354i | \(-0.214638\pi\) | ||||
0.781142 | + | 0.624354i | \(0.214638\pi\) | |||||||
\(422\) | −5.59898 | −0.272554 | ||||||||
\(423\) | 6.80278 | 0.330762 | ||||||||
\(424\) | −17.0918 | −0.830053 | ||||||||
\(425\) | 4.20307 | 0.203879 | ||||||||
\(426\) | −8.47613 | −0.410670 | ||||||||
\(427\) | 11.0029 | 0.532469 | ||||||||
\(428\) | 5.31550 | 0.256934 | ||||||||
\(429\) | 3.59453 | 0.173546 | ||||||||
\(430\) | −2.64173 | −0.127396 | ||||||||
\(431\) | −14.1512 | −0.681640 | −0.340820 | − | 0.940129i | \(-0.610705\pi\) | ||||
−0.340820 | + | 0.940129i | \(0.610705\pi\) | |||||||
\(432\) | 2.97828 | 0.143293 | ||||||||
\(433\) | −18.9607 | −0.911193 | −0.455597 | − | 0.890186i | \(-0.650574\pi\) | ||||
−0.455597 | + | 0.890186i | \(0.650574\pi\) | |||||||
\(434\) | −8.11825 | −0.389688 | ||||||||
\(435\) | −3.60370 | −0.172784 | ||||||||
\(436\) | 8.09260 | 0.387565 | ||||||||
\(437\) | −7.82778 | −0.374454 | ||||||||
\(438\) | −6.27813 | −0.299981 | ||||||||
\(439\) | −11.8097 | −0.563645 | −0.281822 | − | 0.959467i | \(-0.590939\pi\) | ||||
−0.281822 | + | 0.959467i | \(0.590939\pi\) | |||||||
\(440\) | −7.93988 | −0.378519 | ||||||||
\(441\) | −6.24666 | −0.297460 | ||||||||
\(442\) | 1.18045 | 0.0561485 | ||||||||
\(443\) | −28.3908 | −1.34889 | −0.674443 | − | 0.738327i | \(-0.735616\pi\) | ||||
−0.674443 | + | 0.738327i | \(0.735616\pi\) | |||||||
\(444\) | −2.01446 | −0.0956021 | ||||||||
\(445\) | −4.96736 | −0.235475 | ||||||||
\(446\) | 21.8228 | 1.03334 | ||||||||
\(447\) | 3.53031 | 0.166978 | ||||||||
\(448\) | 7.72520 | 0.364981 | ||||||||
\(449\) | −7.86773 | −0.371301 | −0.185651 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185651 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(450\) | −5.61901 | −0.264883 | ||||||||
\(451\) | −12.7052 | −0.598267 | ||||||||
\(452\) | 7.48572 | 0.352098 | ||||||||
\(453\) | −11.1317 | −0.523011 | ||||||||
\(454\) | 0.497604 | 0.0233537 | ||||||||
\(455\) | −0.630151 | −0.0295420 | ||||||||
\(456\) | −15.9769 | −0.748187 | ||||||||
\(457\) | 10.3630 | 0.484761 | 0.242381 | − | 0.970181i | \(-0.422072\pi\) | ||||
0.242381 | + | 0.970181i | \(0.422072\pi\) | |||||||
\(458\) | −16.3343 | −0.763252 | ||||||||
\(459\) | 0.939676 | 0.0438603 | ||||||||
\(460\) | −0.456561 | −0.0212873 | ||||||||
\(461\) | 26.2629 | 1.22319 | 0.611593 | − | 0.791173i | \(-0.290529\pi\) | ||||
0.611593 | + | 0.791173i | \(0.290529\pi\) | |||||||
\(462\) | −3.91930 | −0.182342 | ||||||||
\(463\) | −19.4088 | −0.902005 | −0.451002 | − | 0.892523i | \(-0.648933\pi\) | ||||
−0.451002 | + | 0.892523i | \(0.648933\pi\) | |||||||
\(464\) | −14.7831 | −0.686287 | ||||||||
\(465\) | 5.40562 | 0.250680 | ||||||||
\(466\) | 0.00129887 | 6.01692e−5 0 | ||||||||
\(467\) | 5.99903 | 0.277602 | 0.138801 | − | 0.990320i | \(-0.455675\pi\) | ||||
0.138801 | + | 0.990320i | \(0.455675\pi\) | |||||||
\(468\) | 0.421872 | 0.0195010 | ||||||||
\(469\) | −4.24702 | −0.196109 | ||||||||
\(470\) | 6.20451 | 0.286192 | ||||||||
\(471\) | −4.76685 | −0.219645 | ||||||||
\(472\) | −13.7657 | −0.633619 | ||||||||
\(473\) | −10.4114 | −0.478718 | ||||||||
\(474\) | 13.5911 | 0.624258 | ||||||||
\(475\) | 23.4887 | 1.07773 | ||||||||
\(476\) | 0.344075 | 0.0157707 | ||||||||
\(477\) | 5.61780 | 0.257221 | ||||||||
\(478\) | 26.1320 | 1.19525 | ||||||||
\(479\) | 20.2738 | 0.926334 | 0.463167 | − | 0.886271i | \(-0.346713\pi\) | ||||
0.463167 | + | 0.886271i | \(0.346713\pi\) | |||||||
\(480\) | −1.70140 | −0.0776581 | ||||||||
\(481\) | 4.77506 | 0.217724 | ||||||||
\(482\) | −17.2631 | −0.786313 | ||||||||
\(483\) | −1.29379 | −0.0588695 | ||||||||
\(484\) | −0.810268 | −0.0368303 | ||||||||
\(485\) | −3.24512 | −0.147353 | ||||||||
\(486\) | −1.25624 | −0.0569840 | ||||||||
\(487\) | −17.7279 | −0.803328 | −0.401664 | − | 0.915787i | \(-0.631568\pi\) | ||||
−0.401664 | + | 0.915787i | \(0.631568\pi\) | |||||||
\(488\) | −38.5688 | −1.74593 | ||||||||
\(489\) | 16.2779 | 0.736114 | ||||||||
\(490\) | −5.69730 | −0.257378 | ||||||||
\(491\) | −12.9916 | −0.586303 | −0.293152 | − | 0.956066i | \(-0.594704\pi\) | ||||
−0.293152 | + | 0.956066i | \(0.594704\pi\) | |||||||
\(492\) | −1.49115 | −0.0672263 | ||||||||
\(493\) | −4.66420 | −0.210065 | ||||||||
\(494\) | 6.59692 | 0.296810 | ||||||||
\(495\) | 2.60971 | 0.117298 | ||||||||
\(496\) | 22.1749 | 0.995683 | ||||||||
\(497\) | 5.85628 | 0.262690 | ||||||||
\(498\) | 14.5546 | 0.652206 | ||||||||
\(499\) | −16.3797 | −0.733254 | −0.366627 | − | 0.930368i | \(-0.619488\pi\) | ||||
−0.366627 | + | 0.930368i | \(0.619488\pi\) | |||||||
\(500\) | 2.90143 | 0.129756 | ||||||||
\(501\) | −6.63100 | −0.296251 | ||||||||
\(502\) | −1.61420 | −0.0720451 | ||||||||
\(503\) | 22.5897 | 1.00723 | 0.503613 | − | 0.863930i | \(-0.332004\pi\) | ||||
0.503613 | + | 0.863930i | \(0.332004\pi\) | |||||||
\(504\) | −2.64069 | −0.117626 | ||||||||
\(505\) | −13.7766 | −0.613050 | ||||||||
\(506\) | 6.73103 | 0.299231 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.50798 | 0.288745 | ||||||||
\(509\) | 38.1459 | 1.69079 | 0.845393 | − | 0.534145i | \(-0.179367\pi\) | ||||
0.845393 | + | 0.534145i | \(0.179367\pi\) | |||||||
\(510\) | 0.857036 | 0.0379502 | ||||||||
\(511\) | 4.33765 | 0.191886 | ||||||||
\(512\) | −25.1020 | −1.10936 | ||||||||
\(513\) | 5.25134 | 0.231852 | ||||||||
\(514\) | 17.1535 | 0.756609 | ||||||||
\(515\) | −0.726022 | −0.0319923 | ||||||||
\(516\) | −1.22194 | −0.0537927 | ||||||||
\(517\) | 24.4528 | 1.07543 | ||||||||
\(518\) | −5.20649 | −0.228760 | ||||||||
\(519\) | −15.4319 | −0.677384 | ||||||||
\(520\) | 2.20888 | 0.0968658 | ||||||||
\(521\) | 11.6402 | 0.509965 | 0.254983 | − | 0.966946i | \(-0.417930\pi\) | ||||
0.254983 | + | 0.966946i | \(0.417930\pi\) | |||||||
\(522\) | 6.23548 | 0.272920 | ||||||||
\(523\) | −2.03449 | −0.0889620 | −0.0444810 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444810 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(524\) | −4.88170 | −0.213258 | ||||||||
\(525\) | 3.88225 | 0.169435 | ||||||||
\(526\) | −28.5916 | −1.24665 | ||||||||
\(527\) | 6.99639 | 0.304768 | ||||||||
\(528\) | 10.7055 | 0.465898 | ||||||||
\(529\) | −20.7780 | −0.903393 | ||||||||
\(530\) | 5.12374 | 0.222561 | ||||||||
\(531\) | 4.52457 | 0.196350 | ||||||||
\(532\) | 1.92285 | 0.0833662 | ||||||||
\(533\) | 3.53461 | 0.153101 | ||||||||
\(534\) | 8.59502 | 0.371943 | ||||||||
\(535\) | −9.14772 | −0.395491 | ||||||||
\(536\) | 14.8872 | 0.643027 | ||||||||
\(537\) | 18.3875 | 0.793480 | ||||||||
\(538\) | 1.76318 | 0.0760162 | ||||||||
\(539\) | −22.4538 | −0.967154 | ||||||||
\(540\) | 0.306288 | 0.0131805 | ||||||||
\(541\) | 19.4194 | 0.834907 | 0.417454 | − | 0.908698i | \(-0.362923\pi\) | ||||
0.417454 | + | 0.908698i | \(0.362923\pi\) | |||||||
\(542\) | 0.997344 | 0.0428396 | ||||||||
\(543\) | −14.2111 | −0.609855 | ||||||||
\(544\) | −2.20209 | −0.0944140 | ||||||||
\(545\) | −13.9270 | −0.596567 | ||||||||
\(546\) | 1.09035 | 0.0466627 | ||||||||
\(547\) | −4.06957 | −0.174002 | −0.0870011 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0870011 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(548\) | 1.38018 | 0.0589584 | ||||||||
\(549\) | 12.6769 | 0.541037 | ||||||||
\(550\) | −20.1977 | −0.861232 | ||||||||
\(551\) | −26.0657 | −1.11044 | ||||||||
\(552\) | 4.53514 | 0.193028 | ||||||||
\(553\) | −9.39026 | −0.399314 | ||||||||
\(554\) | 11.5377 | 0.490188 | ||||||||
\(555\) | 3.46679 | 0.147157 | ||||||||
\(556\) | 8.90938 | 0.377842 | ||||||||
\(557\) | −28.7020 | −1.21614 | −0.608071 | − | 0.793883i | \(-0.708056\pi\) | ||||
−0.608071 | + | 0.793883i | \(0.708056\pi\) | |||||||
\(558\) | −9.35335 | −0.395959 | ||||||||
\(559\) | 2.89646 | 0.122507 | ||||||||
\(560\) | −1.87677 | −0.0793079 | ||||||||
\(561\) | 3.37769 | 0.142606 | ||||||||
\(562\) | 31.8958 | 1.34544 | ||||||||
\(563\) | 5.74931 | 0.242305 | 0.121152 | − | 0.992634i | \(-0.461341\pi\) | ||||
0.121152 | + | 0.992634i | \(0.461341\pi\) | |||||||
\(564\) | 2.86990 | 0.120845 | ||||||||
\(565\) | −12.8826 | −0.541974 | ||||||||
\(566\) | 1.80915 | 0.0760443 | ||||||||
\(567\) | 0.867951 | 0.0364505 | ||||||||
\(568\) | −20.5281 | −0.861340 | ||||||||
\(569\) | 24.9949 | 1.04784 | 0.523920 | − | 0.851768i | \(-0.324469\pi\) | ||||
0.523920 | + | 0.851768i | \(0.324469\pi\) | |||||||
\(570\) | 4.78951 | 0.200611 | ||||||||
\(571\) | 18.6578 | 0.780803 | 0.390402 | − | 0.920645i | \(-0.372336\pi\) | ||||
0.390402 | + | 0.920645i | \(0.372336\pi\) | |||||||
\(572\) | 1.51643 | 0.0634052 | ||||||||
\(573\) | 2.61191 | 0.109114 | ||||||||
\(574\) | −3.85396 | −0.160861 | ||||||||
\(575\) | −6.66741 | −0.278050 | ||||||||
\(576\) | 8.90050 | 0.370854 | ||||||||
\(577\) | −14.9335 | −0.621691 | −0.310845 | − | 0.950460i | \(-0.600612\pi\) | ||||
−0.310845 | + | 0.950460i | \(0.600612\pi\) | |||||||
\(578\) | −20.2468 | −0.842154 | ||||||||
\(579\) | −13.2196 | −0.549389 | ||||||||
\(580\) | −1.52030 | −0.0631270 | ||||||||
\(581\) | −10.0560 | −0.417192 | ||||||||
\(582\) | 5.61503 | 0.232750 | ||||||||
\(583\) | 20.1934 | 0.836324 | ||||||||
\(584\) | −15.2048 | −0.629180 | ||||||||
\(585\) | −0.726022 | −0.0300173 | ||||||||
\(586\) | −29.0791 | −1.20125 | ||||||||
\(587\) | −12.8503 | −0.530388 | −0.265194 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265194 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(588\) | −2.63529 | −0.108678 | ||||||||
\(589\) | 39.0991 | 1.61105 | ||||||||
\(590\) | 4.12665 | 0.169892 | ||||||||
\(591\) | 5.50978 | 0.226642 | ||||||||
\(592\) | 14.2215 | 0.584498 | ||||||||
\(593\) | −30.4911 | −1.25212 | −0.626059 | − | 0.779775i | \(-0.715333\pi\) | ||||
−0.626059 | + | 0.779775i | \(0.715333\pi\) | |||||||
\(594\) | −4.51558 | −0.185276 | ||||||||
\(595\) | −0.592138 | −0.0242753 | ||||||||
\(596\) | 1.48934 | 0.0610057 | ||||||||
\(597\) | −8.20184 | −0.335679 | ||||||||
\(598\) | −1.87258 | −0.0765754 | ||||||||
\(599\) | −40.7333 | −1.66432 | −0.832158 | − | 0.554539i | \(-0.812895\pi\) | ||||
−0.832158 | + | 0.554539i | \(0.812895\pi\) | |||||||
\(600\) | −13.6085 | −0.555565 | ||||||||
\(601\) | 12.5484 | 0.511861 | 0.255930 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255930 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(602\) | −3.15816 | −0.128717 | ||||||||
\(603\) | −4.89316 | −0.199265 | ||||||||
\(604\) | −4.69614 | −0.191083 | ||||||||
\(605\) | 1.39443 | 0.0566918 | ||||||||
\(606\) | 23.8376 | 0.968337 | ||||||||
\(607\) | 4.28572 | 0.173952 | 0.0869760 | − | 0.996210i | \(-0.472280\pi\) | ||||
0.0869760 | + | 0.996210i | \(0.472280\pi\) | |||||||
\(608\) | −12.3063 | −0.499087 | ||||||||
\(609\) | −4.30818 | −0.174576 | ||||||||
\(610\) | 11.5620 | 0.468133 | ||||||||
\(611\) | −6.80278 | −0.275211 | ||||||||
\(612\) | 0.396423 | 0.0160244 | ||||||||
\(613\) | 43.6881 | 1.76454 | 0.882272 | − | 0.470740i | \(-0.156013\pi\) | ||||
0.882272 | + | 0.470740i | \(0.156013\pi\) | |||||||
\(614\) | 24.2195 | 0.977420 | ||||||||
\(615\) | 2.56620 | 0.103479 | ||||||||
\(616\) | −9.49204 | −0.382445 | ||||||||
\(617\) | −4.52035 | −0.181982 | −0.0909911 | − | 0.995852i | \(-0.529003\pi\) | ||||
−0.0909911 | + | 0.995852i | \(0.529003\pi\) | |||||||
\(618\) | 1.25624 | 0.0505332 | ||||||||
\(619\) | 24.1932 | 0.972407 | 0.486204 | − | 0.873846i | \(-0.338381\pi\) | ||||
0.486204 | + | 0.873846i | \(0.338381\pi\) | |||||||
\(620\) | 2.28048 | 0.0915863 | ||||||||
\(621\) | −1.49063 | −0.0598167 | ||||||||
\(622\) | 29.8470 | 1.19676 | ||||||||
\(623\) | −5.93842 | −0.237918 | ||||||||
\(624\) | −2.97828 | −0.119227 | ||||||||
\(625\) | 17.3712 | 0.694849 | ||||||||
\(626\) | −17.2485 | −0.689390 | ||||||||
\(627\) | 18.8761 | 0.753839 | ||||||||
\(628\) | −2.01100 | −0.0802476 | ||||||||
\(629\) | 4.48700 | 0.178909 | ||||||||
\(630\) | 0.791619 | 0.0315388 | ||||||||
\(631\) | 21.0860 | 0.839418 | 0.419709 | − | 0.907659i | \(-0.362132\pi\) | ||||
0.419709 | + | 0.907659i | \(0.362132\pi\) | |||||||
\(632\) | 32.9158 | 1.30932 | ||||||||
\(633\) | 4.45695 | 0.177148 | ||||||||
\(634\) | −9.57869 | −0.380418 | ||||||||
\(635\) | −11.1999 | −0.444456 | ||||||||
\(636\) | 2.36999 | 0.0939763 | ||||||||
\(637\) | 6.24666 | 0.247502 | ||||||||
\(638\) | 22.4136 | 0.887364 | ||||||||
\(639\) | 6.74725 | 0.266917 | ||||||||
\(640\) | 4.71494 | 0.186374 | ||||||||
\(641\) | 1.57660 | 0.0622721 | 0.0311360 | − | 0.999515i | \(-0.490087\pi\) | ||||
0.0311360 | + | 0.999515i | \(0.490087\pi\) | |||||||
\(642\) | 15.8283 | 0.624694 | ||||||||
\(643\) | −34.3478 | −1.35455 | −0.677273 | − | 0.735732i | \(-0.736839\pi\) | ||||
−0.677273 | + | 0.735732i | \(0.736839\pi\) | |||||||
\(644\) | −0.545813 | −0.0215081 | ||||||||
\(645\) | 2.10289 | 0.0828014 | ||||||||
\(646\) | 6.19897 | 0.243895 | ||||||||
\(647\) | −39.0306 | −1.53445 | −0.767226 | − | 0.641377i | \(-0.778364\pi\) | ||||
−0.767226 | + | 0.641377i | \(0.778364\pi\) | |||||||
\(648\) | −3.04244 | −0.119518 | ||||||||
\(649\) | 16.2637 | 0.638406 | ||||||||
\(650\) | 5.61901 | 0.220396 | ||||||||
\(651\) | 6.46236 | 0.253280 | ||||||||
\(652\) | 6.86721 | 0.268941 | ||||||||
\(653\) | 15.8978 | 0.622129 | 0.311064 | − | 0.950389i | \(-0.399314\pi\) | ||||
0.311064 | + | 0.950389i | \(0.399314\pi\) | |||||||
\(654\) | 24.0979 | 0.942302 | ||||||||
\(655\) | 8.40117 | 0.328261 | ||||||||
\(656\) | 10.5270 | 0.411012 | ||||||||
\(657\) | 4.99757 | 0.194974 | ||||||||
\(658\) | 7.41742 | 0.289161 | ||||||||
\(659\) | 24.1342 | 0.940133 | 0.470067 | − | 0.882631i | \(-0.344230\pi\) | ||||
0.470067 | + | 0.882631i | \(0.344230\pi\) | |||||||
\(660\) | 1.10096 | 0.0428549 | ||||||||
\(661\) | −33.0940 | −1.28721 | −0.643605 | − | 0.765358i | \(-0.722562\pi\) | ||||
−0.643605 | + | 0.765358i | \(0.722562\pi\) | |||||||
\(662\) | −35.5126 | −1.38024 | ||||||||
\(663\) | −0.939676 | −0.0364940 | ||||||||
\(664\) | 35.2493 | 1.36794 | ||||||||
\(665\) | −3.30914 | −0.128323 | ||||||||
\(666\) | −5.99859 | −0.232441 | ||||||||
\(667\) | 7.39890 | 0.286487 | ||||||||
\(668\) | −2.79743 | −0.108236 | ||||||||
\(669\) | −17.3716 | −0.671624 | ||||||||
\(670\) | −4.46283 | −0.172414 | ||||||||
\(671\) | 45.5675 | 1.75912 | ||||||||
\(672\) | −2.03401 | −0.0784636 | ||||||||
\(673\) | 32.7435 | 1.26217 | 0.631085 | − | 0.775713i | \(-0.282610\pi\) | ||||
0.631085 | + | 0.775713i | \(0.282610\pi\) | |||||||
\(674\) | 25.3797 | 0.977591 | ||||||||
\(675\) | 4.47289 | 0.172162 | ||||||||
\(676\) | −0.421872 | −0.0162258 | ||||||||
\(677\) | 11.4719 | 0.440900 | 0.220450 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220450 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(678\) | 22.2907 | 0.856070 | ||||||||
\(679\) | −3.87950 | −0.148882 | ||||||||
\(680\) | 2.07563 | 0.0795968 | ||||||||
\(681\) | −0.396107 | −0.0151789 | ||||||||
\(682\) | −33.6209 | −1.28741 | ||||||||
\(683\) | 6.59279 | 0.252266 | 0.126133 | − | 0.992013i | \(-0.459743\pi\) | ||||
0.126133 | + | 0.992013i | \(0.459743\pi\) | |||||||
\(684\) | 2.21539 | 0.0847077 | ||||||||
\(685\) | −2.37523 | −0.0907528 | ||||||||
\(686\) | −14.4435 | −0.551456 | ||||||||
\(687\) | 13.0026 | 0.496080 | ||||||||
\(688\) | 8.62648 | 0.328881 | ||||||||
\(689\) | −5.61780 | −0.214021 | ||||||||
\(690\) | −1.35953 | −0.0517565 | ||||||||
\(691\) | −32.3009 | −1.22878 | −0.614392 | − | 0.789001i | \(-0.710599\pi\) | ||||
−0.614392 | + | 0.789001i | \(0.710599\pi\) | |||||||
\(692\) | −6.51027 | −0.247483 | ||||||||
\(693\) | 3.11988 | 0.118514 | ||||||||
\(694\) | −13.0131 | −0.493969 | ||||||||
\(695\) | −15.3326 | −0.581600 | ||||||||
\(696\) | 15.1015 | 0.572422 | ||||||||
\(697\) | 3.32138 | 0.125806 | ||||||||
\(698\) | 32.4708 | 1.22904 | ||||||||
\(699\) | −0.00103394 | −3.91073e−5 0 | ||||||||
\(700\) | 1.63781 | 0.0619035 | ||||||||
\(701\) | −17.9660 | −0.678567 | −0.339284 | − | 0.940684i | \(-0.610185\pi\) | ||||
−0.339284 | + | 0.940684i | \(0.610185\pi\) | |||||||
\(702\) | 1.25624 | 0.0474136 | ||||||||
\(703\) | 25.0754 | 0.945738 | ||||||||
\(704\) | 31.9931 | 1.20579 | ||||||||
\(705\) | −4.93897 | −0.186012 | ||||||||
\(706\) | −6.13943 | −0.231060 | ||||||||
\(707\) | −16.4697 | −0.619408 | ||||||||
\(708\) | 1.90879 | 0.0717366 | ||||||||
\(709\) | 36.4287 | 1.36811 | 0.684053 | − | 0.729432i | \(-0.260215\pi\) | ||||
0.684053 | + | 0.729432i | \(0.260215\pi\) | |||||||
\(710\) | 6.15386 | 0.230950 | ||||||||
\(711\) | −10.8189 | −0.405740 | ||||||||
\(712\) | 20.8160 | 0.780114 | ||||||||
\(713\) | −11.0985 | −0.415642 | ||||||||
\(714\) | 1.02458 | 0.0383438 | ||||||||
\(715\) | −2.60971 | −0.0975975 | ||||||||
\(716\) | 7.75717 | 0.289899 | ||||||||
\(717\) | −20.8018 | −0.776858 | ||||||||
\(718\) | −39.6440 | −1.47950 | ||||||||
\(719\) | 41.0784 | 1.53197 | 0.765983 | − | 0.642861i | \(-0.222253\pi\) | ||||
0.765983 | + | 0.642861i | \(0.222253\pi\) | |||||||
\(720\) | −2.16230 | −0.0805841 | ||||||||
\(721\) | −0.867951 | −0.0323242 | ||||||||
\(722\) | 10.7742 | 0.400975 | ||||||||
\(723\) | 13.7419 | 0.511068 | ||||||||
\(724\) | −5.99525 | −0.222812 | ||||||||
\(725\) | −22.2018 | −0.824553 | ||||||||
\(726\) | −2.41279 | −0.0895470 | ||||||||
\(727\) | −13.0105 | −0.482534 | −0.241267 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(728\) | 2.64069 | 0.0978705 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.55806 | 0.168701 | ||||||||
\(731\) | 2.72174 | 0.100667 | ||||||||
\(732\) | 5.34803 | 0.197669 | ||||||||
\(733\) | −5.62091 | −0.207613 | −0.103807 | − | 0.994598i | \(-0.533102\pi\) | ||||
−0.103807 | + | 0.994598i | \(0.533102\pi\) | |||||||
\(734\) | 29.7241 | 1.09714 | ||||||||
\(735\) | 4.53521 | 0.167284 | ||||||||
\(736\) | 3.49322 | 0.128762 | ||||||||
\(737\) | −17.5886 | −0.647885 | ||||||||
\(738\) | −4.44030 | −0.163450 | ||||||||
\(739\) | −10.6423 | −0.391483 | −0.195742 | − | 0.980655i | \(-0.562711\pi\) | ||||
−0.195742 | + | 0.980655i | \(0.562711\pi\) | |||||||
\(740\) | 1.46254 | 0.0537641 | ||||||||
\(741\) | −5.25134 | −0.192913 | ||||||||
\(742\) | 6.12538 | 0.224870 | ||||||||
\(743\) | 7.80516 | 0.286344 | 0.143172 | − | 0.989698i | \(-0.454270\pi\) | ||||
0.143172 | + | 0.989698i | \(0.454270\pi\) | |||||||
\(744\) | −22.6526 | −0.830485 | ||||||||
\(745\) | −2.56309 | −0.0939042 | ||||||||
\(746\) | 21.6448 | 0.792474 | ||||||||
\(747\) | −11.5859 | −0.423905 | ||||||||
\(748\) | 1.42495 | 0.0521015 | ||||||||
\(749\) | −10.9360 | −0.399593 | ||||||||
\(750\) | 8.63980 | 0.315481 | ||||||||
\(751\) | −4.12697 | −0.150595 | −0.0752977 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0752977 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(752\) | −20.2606 | −0.738827 | ||||||||
\(753\) | 1.28495 | 0.0468260 | ||||||||
\(754\) | −6.23548 | −0.227083 | ||||||||
\(755\) | 8.08184 | 0.294128 | ||||||||
\(756\) | 0.366164 | 0.0133173 | ||||||||
\(757\) | 5.01666 | 0.182334 | 0.0911668 | − | 0.995836i | \(-0.470940\pi\) | ||||
0.0911668 | + | 0.995836i | \(0.470940\pi\) | |||||||
\(758\) | −6.95853 | −0.252745 | ||||||||
\(759\) | −5.35810 | −0.194487 | ||||||||
\(760\) | 11.5996 | 0.420761 | ||||||||
\(761\) | −18.4794 | −0.669878 | −0.334939 | − | 0.942240i | \(-0.608716\pi\) | ||||
−0.334939 | + | 0.942240i | \(0.608716\pi\) | |||||||
\(762\) | 19.3792 | 0.702036 | ||||||||
\(763\) | −16.6496 | −0.602755 | ||||||||
\(764\) | 1.10189 | 0.0398650 | ||||||||
\(765\) | −0.682225 | −0.0246659 | ||||||||
\(766\) | 37.4178 | 1.35196 | ||||||||
\(767\) | −4.52457 | −0.163373 | ||||||||
\(768\) | 9.64275 | 0.347953 | ||||||||
\(769\) | 30.3155 | 1.09321 | 0.546603 | − | 0.837392i | \(-0.315921\pi\) | ||||
0.546603 | + | 0.837392i | \(0.315921\pi\) | |||||||
\(770\) | 2.84550 | 0.102545 | ||||||||
\(771\) | −13.6547 | −0.491762 | ||||||||
\(772\) | −5.57699 | −0.200720 | ||||||||
\(773\) | −36.0205 | −1.29557 | −0.647783 | − | 0.761825i | \(-0.724304\pi\) | ||||
−0.647783 | + | 0.761825i | \(0.724304\pi\) | |||||||
\(774\) | −3.63864 | −0.130788 | ||||||||
\(775\) | 33.3031 | 1.19628 | ||||||||
\(776\) | 13.5989 | 0.488171 | ||||||||
\(777\) | 4.14451 | 0.148684 | ||||||||
\(778\) | 7.70937 | 0.276394 | ||||||||
\(779\) | 18.5614 | 0.665032 | ||||||||
\(780\) | −0.306288 | −0.0109669 | ||||||||
\(781\) | 24.2532 | 0.867847 | ||||||||
\(782\) | −1.75962 | −0.0629237 | ||||||||
\(783\) | −4.96362 | −0.177385 | ||||||||
\(784\) | 18.6043 | 0.664440 | ||||||||
\(785\) | 3.46084 | 0.123523 | ||||||||
\(786\) | −14.5366 | −0.518502 | ||||||||
\(787\) | 36.7209 | 1.30896 | 0.654479 | − | 0.756080i | \(-0.272888\pi\) | ||||
0.654479 | + | 0.756080i | \(0.272888\pi\) | |||||||
\(788\) | 2.32442 | 0.0828041 | ||||||||
\(789\) | 22.7598 | 0.810269 | ||||||||
\(790\) | −9.86741 | −0.351067 | ||||||||
\(791\) | −15.4010 | −0.547595 | ||||||||
\(792\) | −10.9361 | −0.388599 | ||||||||
\(793\) | −12.6769 | −0.450170 | ||||||||
\(794\) | −14.5938 | −0.517916 | ||||||||
\(795\) | −4.07865 | −0.144655 | ||||||||
\(796\) | −3.46012 | −0.122641 | ||||||||
\(797\) | −4.15280 | −0.147100 | −0.0735499 | − | 0.997292i | \(-0.523433\pi\) | ||||
−0.0735499 | + | 0.997292i | \(0.523433\pi\) | |||||||
\(798\) | 5.72581 | 0.202691 | ||||||||
\(799\) | −6.39241 | −0.226147 | ||||||||
\(800\) | −10.4820 | −0.370596 | ||||||||
\(801\) | −6.84189 | −0.241746 | ||||||||
\(802\) | 45.1051 | 1.59272 | ||||||||
\(803\) | 17.9639 | 0.633933 | ||||||||
\(804\) | −2.06429 | −0.0728017 | ||||||||
\(805\) | 0.939319 | 0.0331067 | ||||||||
\(806\) | 9.35335 | 0.329458 | ||||||||
\(807\) | −1.40354 | −0.0494071 | ||||||||
\(808\) | 57.7316 | 2.03099 | ||||||||
\(809\) | −0.877993 | −0.0308686 | −0.0154343 | − | 0.999881i | \(-0.504913\pi\) | ||||
−0.0154343 | + | 0.999881i | \(0.504913\pi\) | |||||||
\(810\) | 0.912055 | 0.0320463 | ||||||||
\(811\) | 12.3049 | 0.432082 | 0.216041 | − | 0.976384i | \(-0.430685\pi\) | ||||
0.216041 | + | 0.976384i | \(0.430685\pi\) | |||||||
\(812\) | −1.81750 | −0.0637818 | ||||||||
\(813\) | −0.793915 | −0.0278438 | ||||||||
\(814\) | −21.5621 | −0.755752 | ||||||||
\(815\) | −11.8181 | −0.413972 | ||||||||
\(816\) | −2.79862 | −0.0979712 | ||||||||
\(817\) | 15.2103 | 0.532142 | ||||||||
\(818\) | −16.9835 | −0.593816 | ||||||||
\(819\) | −0.867951 | −0.0303287 | ||||||||
\(820\) | 1.08261 | 0.0378063 | ||||||||
\(821\) | −4.13970 | −0.144477 | −0.0722383 | − | 0.997387i | \(-0.523014\pi\) | ||||
−0.0722383 | + | 0.997387i | \(0.523014\pi\) | |||||||
\(822\) | 4.10986 | 0.143348 | ||||||||
\(823\) | 29.6230 | 1.03259 | 0.516296 | − | 0.856410i | \(-0.327310\pi\) | ||||
0.516296 | + | 0.856410i | \(0.327310\pi\) | |||||||
\(824\) | 3.04244 | 0.105988 | ||||||||
\(825\) | 16.0779 | 0.559762 | ||||||||
\(826\) | 4.93337 | 0.171654 | ||||||||
\(827\) | 0.901506 | 0.0313484 | 0.0156742 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156742 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(828\) | −0.628853 | −0.0218541 | ||||||||
\(829\) | 19.8674 | 0.690022 | 0.345011 | − | 0.938599i | \(-0.387875\pi\) | ||||
0.345011 | + | 0.938599i | \(0.387875\pi\) | |||||||
\(830\) | −10.5669 | −0.366784 | ||||||||
\(831\) | −9.18431 | −0.318600 | ||||||||
\(832\) | −8.90050 | −0.308569 | ||||||||
\(833\) | 5.86984 | 0.203378 | ||||||||
\(834\) | 26.5301 | 0.918661 | ||||||||
\(835\) | 4.81425 | 0.166604 | ||||||||
\(836\) | 7.96330 | 0.275416 | ||||||||
\(837\) | 7.44554 | 0.257355 | ||||||||
\(838\) | 33.6721 | 1.16318 | ||||||||
\(839\) | 22.3484 | 0.771553 | 0.385777 | − | 0.922592i | \(-0.373934\pi\) | ||||
0.385777 | + | 0.922592i | \(0.373934\pi\) | |||||||
\(840\) | 1.91720 | 0.0661496 | ||||||||
\(841\) | −4.36243 | −0.150429 | ||||||||
\(842\) | 40.2691 | 1.38777 | ||||||||
\(843\) | −25.3899 | −0.874476 | ||||||||
\(844\) | 1.88026 | 0.0647213 | ||||||||
\(845\) | 0.726022 | 0.0249759 | ||||||||
\(846\) | 8.54589 | 0.293814 | ||||||||
\(847\) | 1.66703 | 0.0572798 | ||||||||
\(848\) | −16.7314 | −0.574558 | ||||||||
\(849\) | −1.44014 | −0.0494254 | ||||||||
\(850\) | 5.28005 | 0.181104 | ||||||||
\(851\) | −7.11782 | −0.243996 | ||||||||
\(852\) | 2.84647 | 0.0975186 | ||||||||
\(853\) | −36.4578 | −1.24829 | −0.624146 | − | 0.781308i | \(-0.714553\pi\) | ||||
−0.624146 | + | 0.781308i | \(0.714553\pi\) | |||||||
\(854\) | 13.8223 | 0.472989 | ||||||||
\(855\) | −3.81259 | −0.130388 | ||||||||
\(856\) | 38.3341 | 1.31023 | ||||||||
\(857\) | 16.9812 | 0.580067 | 0.290033 | − | 0.957017i | \(-0.406334\pi\) | ||||
0.290033 | + | 0.957017i | \(0.406334\pi\) | |||||||
\(858\) | 4.51558 | 0.154159 | ||||||||
\(859\) | 5.55249 | 0.189448 | 0.0947242 | − | 0.995504i | \(-0.469803\pi\) | ||||
0.0947242 | + | 0.995504i | \(0.469803\pi\) | |||||||
\(860\) | 0.887152 | 0.0302516 | ||||||||
\(861\) | 3.06786 | 0.104553 | ||||||||
\(862\) | −17.7773 | −0.605496 | ||||||||
\(863\) | −4.97423 | −0.169325 | −0.0846624 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846624 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(864\) | −2.34346 | −0.0797262 | ||||||||
\(865\) | 11.2039 | 0.380943 | ||||||||
\(866\) | −23.8191 | −0.809406 | ||||||||
\(867\) | 16.1170 | 0.547362 | ||||||||
\(868\) | 2.72629 | 0.0925362 | ||||||||
\(869\) | −38.8888 | −1.31921 | ||||||||
\(870\) | −4.52710 | −0.153483 | ||||||||
\(871\) | 4.89316 | 0.165798 | ||||||||
\(872\) | 58.3620 | 1.97639 | ||||||||
\(873\) | −4.46972 | −0.151277 | ||||||||
\(874\) | −9.83354 | −0.332624 | ||||||||
\(875\) | −5.96936 | −0.201801 | ||||||||
\(876\) | 2.10833 | 0.0712340 | ||||||||
\(877\) | 23.2188 | 0.784042 | 0.392021 | − | 0.919956i | \(-0.371776\pi\) | ||||
0.392021 | + | 0.919956i | \(0.371776\pi\) | |||||||
\(878\) | −14.8357 | −0.500682 | ||||||||
\(879\) | 23.1478 | 0.780756 | ||||||||
\(880\) | −7.77244 | −0.262009 | ||||||||
\(881\) | −47.4334 | −1.59807 | −0.799035 | − | 0.601284i | \(-0.794656\pi\) | ||||
−0.799035 | + | 0.601284i | \(0.794656\pi\) | |||||||
\(882\) | −7.84728 | −0.264232 | ||||||||
\(883\) | −2.67783 | −0.0901163 | −0.0450582 | − | 0.998984i | \(-0.514347\pi\) | ||||
−0.0450582 | + | 0.998984i | \(0.514347\pi\) | |||||||
\(884\) | −0.396423 | −0.0133331 | ||||||||
\(885\) | −3.28494 | −0.110422 | ||||||||
\(886\) | −35.6655 | −1.19821 | ||||||||
\(887\) | −44.5623 | −1.49626 | −0.748128 | − | 0.663554i | \(-0.769047\pi\) | ||||
−0.748128 | + | 0.663554i | \(0.769047\pi\) | |||||||
\(888\) | −14.5278 | −0.487522 | ||||||||
\(889\) | −13.3894 | −0.449066 | ||||||||
\(890\) | −6.24017 | −0.209171 | ||||||||
\(891\) | 3.59453 | 0.120421 | ||||||||
\(892\) | −7.32858 | −0.245379 | ||||||||
\(893\) | −35.7237 | −1.19545 | ||||||||
\(894\) | 4.43491 | 0.148325 | ||||||||
\(895\) | −13.3497 | −0.446233 | ||||||||
\(896\) | 5.63665 | 0.188307 | ||||||||
\(897\) | 1.49063 | 0.0497705 | ||||||||
\(898\) | −9.88373 | −0.329824 | ||||||||
\(899\) | −36.9569 | −1.23258 | ||||||||
\(900\) | 1.88699 | 0.0628996 | ||||||||
\(901\) | −5.27891 | −0.175866 | ||||||||
\(902\) | −15.9608 | −0.531436 | ||||||||
\(903\) | 2.51399 | 0.0836602 | ||||||||
\(904\) | 53.9853 | 1.79552 | ||||||||
\(905\) | 10.3175 | 0.342967 | ||||||||
\(906\) | −13.9840 | −0.464587 | ||||||||
\(907\) | 49.7051 | 1.65043 | 0.825215 | − | 0.564819i | \(-0.191054\pi\) | ||||
0.825215 | + | 0.564819i | \(0.191054\pi\) | |||||||
\(908\) | −0.167106 | −0.00554562 | ||||||||
\(909\) | −18.9754 | −0.629375 | ||||||||
\(910\) | −0.791619 | −0.0262419 | ||||||||
\(911\) | −52.5608 | −1.74142 | −0.870708 | − | 0.491799i | \(-0.836339\pi\) | ||||
−0.870708 | + | 0.491799i | \(0.836339\pi\) | |||||||
\(912\) | −15.6400 | −0.517891 | ||||||||
\(913\) | −41.6457 | −1.37827 | ||||||||
\(914\) | 13.0184 | 0.430610 | ||||||||
\(915\) | −9.20371 | −0.304265 | ||||||||
\(916\) | 5.48542 | 0.181243 | ||||||||
\(917\) | 10.0435 | 0.331666 | ||||||||
\(918\) | 1.18045 | 0.0389608 | ||||||||
\(919\) | −46.7884 | −1.54341 | −0.771703 | − | 0.635983i | \(-0.780595\pi\) | ||||
−0.771703 | + | 0.635983i | \(0.780595\pi\) | |||||||
\(920\) | −3.29261 | −0.108554 | ||||||||
\(921\) | −19.2794 | −0.635279 | ||||||||
\(922\) | 32.9924 | 1.08655 | ||||||||
\(923\) | −6.74725 | −0.222088 | ||||||||
\(924\) | 1.31619 | 0.0432994 | ||||||||
\(925\) | 21.3583 | 0.702257 | ||||||||
\(926\) | −24.3821 | −0.801244 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 11.6321 | 0.381841 | ||||||||
\(929\) | −34.9058 | −1.14522 | −0.572611 | − | 0.819827i | \(-0.694069\pi\) | ||||
−0.572611 | + | 0.819827i | \(0.694069\pi\) | |||||||
\(930\) | 6.79074 | 0.222677 | ||||||||
\(931\) | 32.8034 | 1.07509 | ||||||||
\(932\) | −0.000436191 0 | −1.42879e−5 0 | ||||||||
\(933\) | −23.7591 | −0.777838 | ||||||||
\(934\) | 7.53619 | 0.246592 | ||||||||
\(935\) | −2.45228 | −0.0801981 | ||||||||
\(936\) | 3.04244 | 0.0994453 | ||||||||
\(937\) | 19.7797 | 0.646174 | 0.323087 | − | 0.946369i | \(-0.395279\pi\) | ||||
0.323087 | + | 0.946369i | \(0.395279\pi\) | |||||||
\(938\) | −5.33526 | −0.174202 | ||||||||
\(939\) | 13.7303 | 0.448073 | ||||||||
\(940\) | −2.08361 | −0.0679599 | ||||||||
\(941\) | 46.7587 | 1.52429 | 0.762145 | − | 0.647406i | \(-0.224146\pi\) | ||||
0.762145 | + | 0.647406i | \(0.224146\pi\) | |||||||
\(942\) | −5.98829 | −0.195109 | ||||||||
\(943\) | −5.26877 | −0.171575 | ||||||||
\(944\) | −13.4754 | −0.438588 | ||||||||
\(945\) | −0.630151 | −0.0204988 | ||||||||
\(946\) | −13.0792 | −0.425241 | ||||||||
\(947\) | 24.7249 | 0.803451 | 0.401726 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401726 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(948\) | −4.56418 | −0.148238 | ||||||||
\(949\) | −4.99757 | −0.162228 | ||||||||
\(950\) | 29.5073 | 0.957344 | ||||||||
\(951\) | 7.62491 | 0.247255 | ||||||||
\(952\) | 2.48139 | 0.0804224 | ||||||||
\(953\) | −56.7166 | −1.83723 | −0.918615 | − | 0.395154i | \(-0.870691\pi\) | ||||
−0.918615 | + | 0.395154i | \(0.870691\pi\) | |||||||
\(954\) | 7.05728 | 0.228488 | ||||||||
\(955\) | −1.89630 | −0.0613629 | ||||||||
\(956\) | −8.77569 | −0.283826 | ||||||||
\(957\) | −17.8419 | −0.576747 | ||||||||
\(958\) | 25.4687 | 0.822855 | ||||||||
\(959\) | −2.83956 | −0.0916942 | ||||||||
\(960\) | −6.46196 | −0.208559 | ||||||||
\(961\) | 24.4360 | 0.788259 | ||||||||
\(962\) | 5.99859 | 0.193402 | ||||||||
\(963\) | −12.5998 | −0.406023 | ||||||||
\(964\) | 5.79734 | 0.186720 | ||||||||
\(965\) | 9.59775 | 0.308962 | ||||||||
\(966\) | −1.62530 | −0.0522933 | ||||||||
\(967\) | −22.6203 | −0.727421 | −0.363710 | − | 0.931512i | \(-0.618490\pi\) | ||||
−0.363710 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(968\) | −5.84346 | −0.187816 | ||||||||
\(969\) | −4.93456 | −0.158521 | ||||||||
\(970\) | −4.07663 | −0.130893 | ||||||||
\(971\) | 44.5180 | 1.42865 | 0.714325 | − | 0.699814i | \(-0.246734\pi\) | ||||
0.714325 | + | 0.699814i | \(0.246734\pi\) | |||||||
\(972\) | 0.421872 | 0.0135315 | ||||||||
\(973\) | −18.3300 | −0.587632 | ||||||||
\(974\) | −22.2704 | −0.713590 | ||||||||
\(975\) | −4.47289 | −0.143247 | ||||||||
\(976\) | −37.7554 | −1.20852 | ||||||||
\(977\) | 12.1739 | 0.389477 | 0.194738 | − | 0.980855i | \(-0.437614\pi\) | ||||
0.194738 | + | 0.980855i | \(0.437614\pi\) | |||||||
\(978\) | 20.4489 | 0.653885 | ||||||||
\(979\) | −24.5934 | −0.786007 | ||||||||
\(980\) | 1.91328 | 0.0611174 | ||||||||
\(981\) | −19.1826 | −0.612454 | ||||||||
\(982\) | −16.3205 | −0.520809 | ||||||||
\(983\) | −15.6174 | −0.498118 | −0.249059 | − | 0.968488i | \(-0.580121\pi\) | ||||
−0.249059 | + | 0.968488i | \(0.580121\pi\) | |||||||
\(984\) | −10.7538 | −0.342820 | ||||||||
\(985\) | −4.00022 | −0.127458 | ||||||||
\(986\) | −5.85933 | −0.186599 | ||||||||
\(987\) | −5.90448 | −0.187942 | ||||||||
\(988\) | −2.21539 | −0.0704810 | ||||||||
\(989\) | −4.31754 | −0.137290 | ||||||||
\(990\) | 3.27841 | 0.104195 | ||||||||
\(991\) | 53.0460 | 1.68506 | 0.842531 | − | 0.538647i | \(-0.181064\pi\) | ||||
0.842531 | + | 0.538647i | \(0.181064\pi\) | |||||||
\(992\) | −17.4483 | −0.553985 | ||||||||
\(993\) | 28.2691 | 0.897092 | ||||||||
\(994\) | 7.35687 | 0.233346 | ||||||||
\(995\) | 5.95472 | 0.188777 | ||||||||
\(996\) | −4.88775 | −0.154874 | ||||||||
\(997\) | −57.2409 | −1.81284 | −0.906418 | − | 0.422381i | \(-0.861194\pi\) | ||||
−0.906418 | + | 0.422381i | \(0.861194\pi\) | |||||||
\(998\) | −20.5767 | −0.651345 | ||||||||
\(999\) | 4.77506 | 0.151076 |
(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 | 4017.2.a.i.1.18 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.i.1.18 | ✓ | 25 | 1.1 | even | 1 | trivial |