Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-0.560392\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 1.40727 | 0.812488 | 0.406244 | − | 0.913765i | \(-0.366838\pi\) | ||||
0.406244 | + | 0.913765i | \(0.366838\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.40727 | −0.574516 | ||||||||
\(7\) | −2.31473 | −0.874884 | −0.437442 | − | 0.899247i | \(-0.644116\pi\) | ||||
−0.437442 | + | 0.899247i | \(0.644116\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.01959 | −0.339863 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.47910 | 1.04899 | 0.524494 | − | 0.851414i | \(-0.324254\pi\) | ||||
0.524494 | + | 0.851414i | \(0.324254\pi\) | |||||||
\(12\) | 1.40727 | 0.406244 | ||||||||
\(13\) | −0.582324 | −0.161508 | −0.0807538 | − | 0.996734i | \(-0.525733\pi\) | ||||
−0.0807538 | + | 0.996734i | \(0.525733\pi\) | |||||||
\(14\) | 2.31473 | 0.618637 | ||||||||
\(15\) | −1.40727 | −0.363356 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.139348 | −0.0337969 | −0.0168984 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168984 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(18\) | 1.01959 | 0.240319 | ||||||||
\(19\) | 1.62864 | 0.373635 | 0.186818 | − | 0.982395i | \(-0.440183\pi\) | ||||
0.186818 | + | 0.982395i | \(0.440183\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.25745 | −0.710833 | ||||||||
\(22\) | −3.47910 | −0.741747 | ||||||||
\(23\) | 3.15142 | 0.657116 | 0.328558 | − | 0.944484i | \(-0.393437\pi\) | ||||
0.328558 | + | 0.944484i | \(0.393437\pi\) | |||||||
\(24\) | −1.40727 | −0.287258 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.582324 | 0.114203 | ||||||||
\(27\) | −5.65665 | −1.08862 | ||||||||
\(28\) | −2.31473 | −0.437442 | ||||||||
\(29\) | −0.911191 | −0.169204 | −0.0846020 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846020 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(30\) | 1.40727 | 0.256931 | ||||||||
\(31\) | 2.01676 | 0.362221 | 0.181110 | − | 0.983463i | \(-0.442031\pi\) | ||||
0.181110 | + | 0.983463i | \(0.442031\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.89604 | 0.852291 | ||||||||
\(34\) | 0.139348 | 0.0238980 | ||||||||
\(35\) | 2.31473 | 0.391260 | ||||||||
\(36\) | −1.01959 | −0.169931 | ||||||||
\(37\) | −9.08644 | −1.49380 | −0.746901 | − | 0.664935i | \(-0.768459\pi\) | ||||
−0.746901 | + | 0.664935i | \(0.768459\pi\) | |||||||
\(38\) | −1.62864 | −0.264200 | ||||||||
\(39\) | −0.819488 | −0.131223 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.4730 | −1.63561 | −0.817804 | − | 0.575496i | \(-0.804809\pi\) | ||||
−0.817804 | + | 0.575496i | \(0.804809\pi\) | |||||||
\(42\) | 3.25745 | 0.502635 | ||||||||
\(43\) | 11.6852 | 1.78197 | 0.890987 | − | 0.454029i | \(-0.150014\pi\) | ||||
0.890987 | + | 0.454029i | \(0.150014\pi\) | |||||||
\(44\) | 3.47910 | 0.524494 | ||||||||
\(45\) | 1.01959 | 0.151991 | ||||||||
\(46\) | −3.15142 | −0.464651 | ||||||||
\(47\) | −0.278443 | −0.0406150 | −0.0203075 | − | 0.999794i | \(-0.506465\pi\) | ||||
−0.0203075 | + | 0.999794i | \(0.506465\pi\) | |||||||
\(48\) | 1.40727 | 0.203122 | ||||||||
\(49\) | −1.64204 | −0.234577 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.196101 | −0.0274596 | ||||||||
\(52\) | −0.582324 | −0.0807538 | ||||||||
\(53\) | −4.00326 | −0.549890 | −0.274945 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274945 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(54\) | 5.65665 | 0.769773 | ||||||||
\(55\) | −3.47910 | −0.469122 | ||||||||
\(56\) | 2.31473 | 0.309318 | ||||||||
\(57\) | 2.29194 | 0.303574 | ||||||||
\(58\) | 0.911191 | 0.119645 | ||||||||
\(59\) | −2.63264 | −0.342740 | −0.171370 | − | 0.985207i | \(-0.554819\pi\) | ||||
−0.171370 | + | 0.985207i | \(0.554819\pi\) | |||||||
\(60\) | −1.40727 | −0.181678 | ||||||||
\(61\) | 6.69819 | 0.857615 | 0.428808 | − | 0.903396i | \(-0.358934\pi\) | ||||
0.428808 | + | 0.903396i | \(0.358934\pi\) | |||||||
\(62\) | −2.01676 | −0.256129 | ||||||||
\(63\) | 2.36007 | 0.297340 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.582324 | 0.0722284 | ||||||||
\(66\) | −4.89604 | −0.602661 | ||||||||
\(67\) | −3.55128 | −0.433858 | −0.216929 | − | 0.976187i | \(-0.569604\pi\) | ||||
−0.216929 | + | 0.976187i | \(0.569604\pi\) | |||||||
\(68\) | −0.139348 | −0.0168984 | ||||||||
\(69\) | 4.43490 | 0.533899 | ||||||||
\(70\) | −2.31473 | −0.276663 | ||||||||
\(71\) | 11.1295 | 1.32083 | 0.660415 | − | 0.750901i | \(-0.270381\pi\) | ||||
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(72\) | 1.01959 | 0.120160 | ||||||||
\(73\) | −13.7611 | −1.61062 | −0.805308 | − | 0.592857i | \(-0.798000\pi\) | ||||
−0.805308 | + | 0.592857i | \(0.798000\pi\) | |||||||
\(74\) | 9.08644 | 1.05628 | ||||||||
\(75\) | 1.40727 | 0.162498 | ||||||||
\(76\) | 1.62864 | 0.186818 | ||||||||
\(77\) | −8.05317 | −0.917744 | ||||||||
\(78\) | 0.819488 | 0.0927888 | ||||||||
\(79\) | 4.01383 | 0.451591 | 0.225796 | − | 0.974175i | \(-0.427502\pi\) | ||||
0.225796 | + | 0.974175i | \(0.427502\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −4.90168 | −0.544631 | ||||||||
\(82\) | 10.4730 | 1.15655 | ||||||||
\(83\) | −1.94410 | −0.213393 | −0.106696 | − | 0.994292i | \(-0.534027\pi\) | ||||
−0.106696 | + | 0.994292i | \(0.534027\pi\) | |||||||
\(84\) | −3.25745 | −0.355417 | ||||||||
\(85\) | 0.139348 | 0.0151144 | ||||||||
\(86\) | −11.6852 | −1.26005 | ||||||||
\(87\) | −1.28229 | −0.137476 | ||||||||
\(88\) | −3.47910 | −0.370874 | ||||||||
\(89\) | −5.16178 | −0.547148 | −0.273574 | − | 0.961851i | \(-0.588206\pi\) | ||||
−0.273574 | + | 0.961851i | \(0.588206\pi\) | |||||||
\(90\) | −1.01959 | −0.107474 | ||||||||
\(91\) | 1.34792 | 0.141301 | ||||||||
\(92\) | 3.15142 | 0.328558 | ||||||||
\(93\) | 2.83813 | 0.294300 | ||||||||
\(94\) | 0.278443 | 0.0287192 | ||||||||
\(95\) | −1.62864 | −0.167095 | ||||||||
\(96\) | −1.40727 | −0.143629 | ||||||||
\(97\) | −3.28753 | −0.333798 | −0.166899 | − | 0.985974i | \(-0.553375\pi\) | ||||
−0.166899 | + | 0.985974i | \(0.553375\pi\) | |||||||
\(98\) | 1.64204 | 0.165871 | ||||||||
\(99\) | −3.54725 | −0.356512 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.53218 | 0.948488 | 0.474244 | − | 0.880394i | \(-0.342722\pi\) | ||||
0.474244 | + | 0.880394i | \(0.342722\pi\) | |||||||
\(102\) | 0.196101 | 0.0194168 | ||||||||
\(103\) | −7.77644 | −0.766235 | −0.383118 | − | 0.923700i | \(-0.625150\pi\) | ||||
−0.383118 | + | 0.923700i | \(0.625150\pi\) | |||||||
\(104\) | 0.582324 | 0.0571016 | ||||||||
\(105\) | 3.25745 | 0.317894 | ||||||||
\(106\) | 4.00326 | 0.388831 | ||||||||
\(107\) | −10.6438 | −1.02897 | −0.514487 | − | 0.857498i | \(-0.672018\pi\) | ||||
−0.514487 | + | 0.857498i | \(0.672018\pi\) | |||||||
\(108\) | −5.65665 | −0.544311 | ||||||||
\(109\) | 3.07843 | 0.294861 | 0.147430 | − | 0.989072i | \(-0.452900\pi\) | ||||
0.147430 | + | 0.989072i | \(0.452900\pi\) | |||||||
\(110\) | 3.47910 | 0.331719 | ||||||||
\(111\) | −12.7871 | −1.21370 | ||||||||
\(112\) | −2.31473 | −0.218721 | ||||||||
\(113\) | −11.0361 | −1.03819 | −0.519097 | − | 0.854715i | \(-0.673732\pi\) | ||||
−0.519097 | + | 0.854715i | \(0.673732\pi\) | |||||||
\(114\) | −2.29194 | −0.214660 | ||||||||
\(115\) | −3.15142 | −0.293871 | ||||||||
\(116\) | −0.911191 | −0.0846020 | ||||||||
\(117\) | 0.593731 | 0.0548904 | ||||||||
\(118\) | 2.63264 | 0.242354 | ||||||||
\(119\) | 0.322553 | 0.0295684 | ||||||||
\(120\) | 1.40727 | 0.128466 | ||||||||
\(121\) | 1.10415 | 0.100378 | ||||||||
\(122\) | −6.69819 | −0.606426 | ||||||||
\(123\) | −14.7384 | −1.32891 | ||||||||
\(124\) | 2.01676 | 0.181110 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.36007 | −0.210251 | ||||||||
\(127\) | −2.27475 | −0.201851 | −0.100926 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100926 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 16.4442 | 1.44783 | ||||||||
\(130\) | −0.582324 | −0.0510732 | ||||||||
\(131\) | 5.08920 | 0.444645 | 0.222323 | − | 0.974973i | \(-0.428636\pi\) | ||||
0.222323 | + | 0.974973i | \(0.428636\pi\) | |||||||
\(132\) | 4.89604 | 0.426146 | ||||||||
\(133\) | −3.76985 | −0.326888 | ||||||||
\(134\) | 3.55128 | 0.306784 | ||||||||
\(135\) | 5.65665 | 0.486847 | ||||||||
\(136\) | 0.139348 | 0.0119490 | ||||||||
\(137\) | −3.92866 | −0.335648 | −0.167824 | − | 0.985817i | \(-0.553674\pi\) | ||||
−0.167824 | + | 0.985817i | \(0.553674\pi\) | |||||||
\(138\) | −4.43490 | −0.377524 | ||||||||
\(139\) | −17.1248 | −1.45251 | −0.726255 | − | 0.687426i | \(-0.758741\pi\) | ||||
−0.726255 | + | 0.687426i | \(0.758741\pi\) | |||||||
\(140\) | 2.31473 | 0.195630 | ||||||||
\(141\) | −0.391844 | −0.0329992 | ||||||||
\(142\) | −11.1295 | −0.933967 | ||||||||
\(143\) | −2.02597 | −0.169420 | ||||||||
\(144\) | −1.01959 | −0.0849657 | ||||||||
\(145\) | 0.911191 | 0.0756703 | ||||||||
\(146\) | 13.7611 | 1.13888 | ||||||||
\(147\) | −2.31080 | −0.190591 | ||||||||
\(148\) | −9.08644 | −0.746901 | ||||||||
\(149\) | −17.2232 | −1.41098 | −0.705488 | − | 0.708722i | \(-0.749272\pi\) | ||||
−0.705488 | + | 0.708722i | \(0.749272\pi\) | |||||||
\(150\) | −1.40727 | −0.114903 | ||||||||
\(151\) | −12.1174 | −0.986097 | −0.493048 | − | 0.870002i | \(-0.664117\pi\) | ||||
−0.493048 | + | 0.870002i | \(0.664117\pi\) | |||||||
\(152\) | −1.62864 | −0.132100 | ||||||||
\(153\) | 0.142078 | 0.0114863 | ||||||||
\(154\) | 8.05317 | 0.648943 | ||||||||
\(155\) | −2.01676 | −0.161990 | ||||||||
\(156\) | −0.819488 | −0.0656116 | ||||||||
\(157\) | −1.41886 | −0.113237 | −0.0566187 | − | 0.998396i | \(-0.518032\pi\) | ||||
−0.0566187 | + | 0.998396i | \(0.518032\pi\) | |||||||
\(158\) | −4.01383 | −0.319323 | ||||||||
\(159\) | −5.63368 | −0.446780 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −7.29467 | −0.574900 | ||||||||
\(162\) | 4.90168 | 0.385112 | ||||||||
\(163\) | 12.3056 | 0.963846 | 0.481923 | − | 0.876213i | \(-0.339938\pi\) | ||||
0.481923 | + | 0.876213i | \(0.339938\pi\) | |||||||
\(164\) | −10.4730 | −0.817804 | ||||||||
\(165\) | −4.89604 | −0.381156 | ||||||||
\(166\) | 1.94410 | 0.150891 | ||||||||
\(167\) | −14.7121 | −1.13846 | −0.569228 | − | 0.822180i | \(-0.692758\pi\) | ||||
−0.569228 | + | 0.822180i | \(0.692758\pi\) | |||||||
\(168\) | 3.25745 | 0.251318 | ||||||||
\(169\) | −12.6609 | −0.973915 | ||||||||
\(170\) | −0.139348 | −0.0106875 | ||||||||
\(171\) | −1.66054 | −0.126985 | ||||||||
\(172\) | 11.6852 | 0.890987 | ||||||||
\(173\) | 4.30633 | 0.327404 | 0.163702 | − | 0.986510i | \(-0.447656\pi\) | ||||
0.163702 | + | 0.986510i | \(0.447656\pi\) | |||||||
\(174\) | 1.28229 | 0.0972104 | ||||||||
\(175\) | −2.31473 | −0.174977 | ||||||||
\(176\) | 3.47910 | 0.262247 | ||||||||
\(177\) | −3.70483 | −0.278472 | ||||||||
\(178\) | 5.16178 | 0.386892 | ||||||||
\(179\) | −0.127338 | −0.00951766 | −0.00475883 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00475883 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(180\) | 1.01959 | 0.0759956 | ||||||||
\(181\) | −20.3487 | −1.51251 | −0.756254 | − | 0.654278i | \(-0.772973\pi\) | ||||
−0.756254 | + | 0.654278i | \(0.772973\pi\) | |||||||
\(182\) | −1.34792 | −0.0999146 | ||||||||
\(183\) | 9.42617 | 0.696802 | ||||||||
\(184\) | −3.15142 | −0.232326 | ||||||||
\(185\) | 9.08644 | 0.668049 | ||||||||
\(186\) | −2.83813 | −0.208102 | ||||||||
\(187\) | −0.484806 | −0.0354525 | ||||||||
\(188\) | −0.278443 | −0.0203075 | ||||||||
\(189\) | 13.0936 | 0.952419 | ||||||||
\(190\) | 1.62864 | 0.118154 | ||||||||
\(191\) | −5.25976 | −0.380583 | −0.190291 | − | 0.981728i | \(-0.560943\pi\) | ||||
−0.190291 | + | 0.981728i | \(0.560943\pi\) | |||||||
\(192\) | 1.40727 | 0.101561 | ||||||||
\(193\) | −25.9563 | −1.86837 | −0.934187 | − | 0.356784i | \(-0.883873\pi\) | ||||
−0.934187 | + | 0.356784i | \(0.883873\pi\) | |||||||
\(194\) | 3.28753 | 0.236031 | ||||||||
\(195\) | 0.819488 | 0.0586848 | ||||||||
\(196\) | −1.64204 | −0.117289 | ||||||||
\(197\) | 1.98558 | 0.141467 | 0.0707334 | − | 0.997495i | \(-0.477466\pi\) | ||||
0.0707334 | + | 0.997495i | \(0.477466\pi\) | |||||||
\(198\) | 3.54725 | 0.252092 | ||||||||
\(199\) | 18.6861 | 1.32462 | 0.662311 | − | 0.749229i | \(-0.269576\pi\) | ||||
0.662311 | + | 0.749229i | \(0.269576\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.99762 | −0.352505 | ||||||||
\(202\) | −9.53218 | −0.670682 | ||||||||
\(203\) | 2.10916 | 0.148034 | ||||||||
\(204\) | −0.196101 | −0.0137298 | ||||||||
\(205\) | 10.4730 | 0.731466 | ||||||||
\(206\) | 7.77644 | 0.541810 | ||||||||
\(207\) | −3.21315 | −0.223329 | ||||||||
\(208\) | −0.582324 | −0.0403769 | ||||||||
\(209\) | 5.66620 | 0.391939 | ||||||||
\(210\) | −3.25745 | −0.224785 | ||||||||
\(211\) | −17.0537 | −1.17403 | −0.587014 | − | 0.809577i | \(-0.699697\pi\) | ||||
−0.587014 | + | 0.809577i | \(0.699697\pi\) | |||||||
\(212\) | −4.00326 | −0.274945 | ||||||||
\(213\) | 15.6622 | 1.07316 | ||||||||
\(214\) | 10.6438 | 0.727594 | ||||||||
\(215\) | −11.6852 | −0.796923 | ||||||||
\(216\) | 5.65665 | 0.384886 | ||||||||
\(217\) | −4.66825 | −0.316901 | ||||||||
\(218\) | −3.07843 | −0.208498 | ||||||||
\(219\) | −19.3656 | −1.30861 | ||||||||
\(220\) | −3.47910 | −0.234561 | ||||||||
\(221\) | 0.0811457 | 0.00545845 | ||||||||
\(222\) | 12.7871 | 0.858213 | ||||||||
\(223\) | 9.44253 | 0.632318 | 0.316159 | − | 0.948706i | \(-0.397607\pi\) | ||||
0.316159 | + | 0.948706i | \(0.397607\pi\) | |||||||
\(224\) | 2.31473 | 0.154659 | ||||||||
\(225\) | −1.01959 | −0.0679725 | ||||||||
\(226\) | 11.0361 | 0.734114 | ||||||||
\(227\) | −28.2941 | −1.87795 | −0.938974 | − | 0.343988i | \(-0.888222\pi\) | ||||
−0.938974 | + | 0.343988i | \(0.888222\pi\) | |||||||
\(228\) | 2.29194 | 0.151787 | ||||||||
\(229\) | −14.5510 | −0.961559 | −0.480780 | − | 0.876841i | \(-0.659646\pi\) | ||||
−0.480780 | + | 0.876841i | \(0.659646\pi\) | |||||||
\(230\) | 3.15142 | 0.207798 | ||||||||
\(231\) | −11.3330 | −0.745656 | ||||||||
\(232\) | 0.911191 | 0.0598226 | ||||||||
\(233\) | 5.80631 | 0.380384 | 0.190192 | − | 0.981747i | \(-0.439089\pi\) | ||||
0.190192 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(234\) | −0.593731 | −0.0388134 | ||||||||
\(235\) | 0.278443 | 0.0181636 | ||||||||
\(236\) | −2.63264 | −0.171370 | ||||||||
\(237\) | 5.64855 | 0.366913 | ||||||||
\(238\) | −0.322553 | −0.0209080 | ||||||||
\(239\) | 21.6434 | 1.40000 | 0.699998 | − | 0.714145i | \(-0.253184\pi\) | ||||
0.699998 | + | 0.714145i | \(0.253184\pi\) | |||||||
\(240\) | −1.40727 | −0.0908390 | ||||||||
\(241\) | −7.24006 | −0.466373 | −0.233187 | − | 0.972432i | \(-0.574915\pi\) | ||||
−0.233187 | + | 0.972432i | \(0.574915\pi\) | |||||||
\(242\) | −1.10415 | −0.0709777 | ||||||||
\(243\) | 10.0720 | 0.646117 | ||||||||
\(244\) | 6.69819 | 0.428808 | ||||||||
\(245\) | 1.64204 | 0.104906 | ||||||||
\(246\) | 14.7384 | 0.939684 | ||||||||
\(247\) | −0.948396 | −0.0603450 | ||||||||
\(248\) | −2.01676 | −0.128064 | ||||||||
\(249\) | −2.73588 | −0.173379 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 15.1467 | 0.956051 | 0.478025 | − | 0.878346i | \(-0.341353\pi\) | ||||
0.478025 | + | 0.878346i | \(0.341353\pi\) | |||||||
\(252\) | 2.36007 | 0.148670 | ||||||||
\(253\) | 10.9641 | 0.689307 | ||||||||
\(254\) | 2.27475 | 0.142730 | ||||||||
\(255\) | 0.196101 | 0.0122803 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.3434 | 1.64325 | 0.821627 | − | 0.570026i | \(-0.193067\pi\) | ||||
0.821627 | + | 0.570026i | \(0.193067\pi\) | |||||||
\(258\) | −16.4442 | −1.02377 | ||||||||
\(259\) | 21.0326 | 1.30690 | ||||||||
\(260\) | 0.582324 | 0.0361142 | ||||||||
\(261\) | 0.929039 | 0.0575061 | ||||||||
\(262\) | −5.08920 | −0.314412 | ||||||||
\(263\) | −20.9665 | −1.29285 | −0.646424 | − | 0.762978i | \(-0.723736\pi\) | ||||
−0.646424 | + | 0.762978i | \(0.723736\pi\) | |||||||
\(264\) | −4.89604 | −0.301330 | ||||||||
\(265\) | 4.00326 | 0.245918 | ||||||||
\(266\) | 3.76985 | 0.231145 | ||||||||
\(267\) | −7.26403 | −0.444551 | ||||||||
\(268\) | −3.55128 | −0.216929 | ||||||||
\(269\) | 7.00564 | 0.427142 | 0.213571 | − | 0.976928i | \(-0.431491\pi\) | ||||
0.213571 | + | 0.976928i | \(0.431491\pi\) | |||||||
\(270\) | −5.65665 | −0.344253 | ||||||||
\(271\) | 18.4642 | 1.12162 | 0.560809 | − | 0.827945i | \(-0.310490\pi\) | ||||
0.560809 | + | 0.827945i | \(0.310490\pi\) | |||||||
\(272\) | −0.139348 | −0.00844922 | ||||||||
\(273\) | 1.89689 | 0.114805 | ||||||||
\(274\) | 3.92866 | 0.237339 | ||||||||
\(275\) | 3.47910 | 0.209798 | ||||||||
\(276\) | 4.43490 | 0.266949 | ||||||||
\(277\) | −32.0109 | −1.92335 | −0.961674 | − | 0.274195i | \(-0.911588\pi\) | ||||
−0.961674 | + | 0.274195i | \(0.911588\pi\) | |||||||
\(278\) | 17.1248 | 1.02708 | ||||||||
\(279\) | −2.05626 | −0.123105 | ||||||||
\(280\) | −2.31473 | −0.138331 | ||||||||
\(281\) | −11.3622 | −0.677811 | −0.338905 | − | 0.940820i | \(-0.610057\pi\) | ||||
−0.338905 | + | 0.940820i | \(0.610057\pi\) | |||||||
\(282\) | 0.391844 | 0.0233340 | ||||||||
\(283\) | 21.2582 | 1.26367 | 0.631834 | − | 0.775104i | \(-0.282302\pi\) | ||||
0.631834 | + | 0.775104i | \(0.282302\pi\) | |||||||
\(284\) | 11.1295 | 0.660415 | ||||||||
\(285\) | −2.29194 | −0.135763 | ||||||||
\(286\) | 2.02597 | 0.119798 | ||||||||
\(287\) | 24.2421 | 1.43097 | ||||||||
\(288\) | 1.01959 | 0.0600798 | ||||||||
\(289\) | −16.9806 | −0.998858 | ||||||||
\(290\) | −0.911191 | −0.0535070 | ||||||||
\(291\) | −4.62644 | −0.271207 | ||||||||
\(292\) | −13.7611 | −0.805308 | ||||||||
\(293\) | 20.4238 | 1.19317 | 0.596586 | − | 0.802549i | \(-0.296523\pi\) | ||||
0.596586 | + | 0.802549i | \(0.296523\pi\) | |||||||
\(294\) | 2.31080 | 0.134769 | ||||||||
\(295\) | 2.63264 | 0.153278 | ||||||||
\(296\) | 9.08644 | 0.528139 | ||||||||
\(297\) | −19.6801 | −1.14195 | ||||||||
\(298\) | 17.2232 | 0.997711 | ||||||||
\(299\) | −1.83515 | −0.106129 | ||||||||
\(300\) | 1.40727 | 0.0812488 | ||||||||
\(301\) | −27.0480 | −1.55902 | ||||||||
\(302\) | 12.1174 | 0.697276 | ||||||||
\(303\) | 13.4144 | 0.770635 | ||||||||
\(304\) | 1.62864 | 0.0934089 | ||||||||
\(305\) | −6.69819 | −0.383537 | ||||||||
\(306\) | −0.142078 | −0.00812203 | ||||||||
\(307\) | −20.7595 | −1.18481 | −0.592405 | − | 0.805640i | \(-0.701821\pi\) | ||||
−0.592405 | + | 0.805640i | \(0.701821\pi\) | |||||||
\(308\) | −8.05317 | −0.458872 | ||||||||
\(309\) | −10.9436 | −0.622557 | ||||||||
\(310\) | 2.01676 | 0.114544 | ||||||||
\(311\) | 20.4833 | 1.16150 | 0.580752 | − | 0.814080i | \(-0.302759\pi\) | ||||
0.580752 | + | 0.814080i | \(0.302759\pi\) | |||||||
\(312\) | 0.819488 | 0.0463944 | ||||||||
\(313\) | 19.4038 | 1.09677 | 0.548383 | − | 0.836227i | \(-0.315244\pi\) | ||||
0.548383 | + | 0.836227i | \(0.315244\pi\) | |||||||
\(314\) | 1.41886 | 0.0800709 | ||||||||
\(315\) | −2.36007 | −0.132975 | ||||||||
\(316\) | 4.01383 | 0.225796 | ||||||||
\(317\) | 13.3472 | 0.749652 | 0.374826 | − | 0.927095i | \(-0.377702\pi\) | ||||
0.374826 | + | 0.927095i | \(0.377702\pi\) | |||||||
\(318\) | 5.63368 | 0.315921 | ||||||||
\(319\) | −3.17013 | −0.177493 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −14.9787 | −0.836029 | ||||||||
\(322\) | 7.29467 | 0.406516 | ||||||||
\(323\) | −0.226948 | −0.0126277 | ||||||||
\(324\) | −4.90168 | −0.272315 | ||||||||
\(325\) | −0.582324 | −0.0323015 | ||||||||
\(326\) | −12.3056 | −0.681542 | ||||||||
\(327\) | 4.33219 | 0.239571 | ||||||||
\(328\) | 10.4730 | 0.578275 | ||||||||
\(329\) | 0.644519 | 0.0355335 | ||||||||
\(330\) | 4.89604 | 0.269518 | ||||||||
\(331\) | −15.3821 | −0.845477 | −0.422738 | − | 0.906252i | \(-0.638931\pi\) | ||||
−0.422738 | + | 0.906252i | \(0.638931\pi\) | |||||||
\(332\) | −1.94410 | −0.106696 | ||||||||
\(333\) | 9.26443 | 0.507687 | ||||||||
\(334\) | 14.7121 | 0.805010 | ||||||||
\(335\) | 3.55128 | 0.194027 | ||||||||
\(336\) | −3.25745 | −0.177708 | ||||||||
\(337\) | 6.72138 | 0.366137 | 0.183068 | − | 0.983100i | \(-0.441397\pi\) | ||||
0.183068 | + | 0.983100i | \(0.441397\pi\) | |||||||
\(338\) | 12.6609 | 0.688662 | ||||||||
\(339\) | −15.5309 | −0.843520 | ||||||||
\(340\) | 0.139348 | 0.00755721 | ||||||||
\(341\) | 7.01652 | 0.379966 | ||||||||
\(342\) | 1.66054 | 0.0897918 | ||||||||
\(343\) | 20.0040 | 1.08011 | ||||||||
\(344\) | −11.6852 | −0.630023 | ||||||||
\(345\) | −4.43490 | −0.238767 | ||||||||
\(346\) | −4.30633 | −0.231510 | ||||||||
\(347\) | −17.7250 | −0.951527 | −0.475763 | − | 0.879573i | \(-0.657828\pi\) | ||||
−0.475763 | + | 0.879573i | \(0.657828\pi\) | |||||||
\(348\) | −1.28229 | −0.0687381 | ||||||||
\(349\) | 32.0292 | 1.71448 | 0.857242 | − | 0.514913i | \(-0.172176\pi\) | ||||
0.857242 | + | 0.514913i | \(0.172176\pi\) | |||||||
\(350\) | 2.31473 | 0.123727 | ||||||||
\(351\) | 3.29400 | 0.175821 | ||||||||
\(352\) | −3.47910 | −0.185437 | ||||||||
\(353\) | −19.3684 | −1.03087 | −0.515437 | − | 0.856928i | \(-0.672370\pi\) | ||||
−0.515437 | + | 0.856928i | \(0.672370\pi\) | |||||||
\(354\) | 3.70483 | 0.196910 | ||||||||
\(355\) | −11.1295 | −0.590693 | ||||||||
\(356\) | −5.16178 | −0.273574 | ||||||||
\(357\) | 0.453919 | 0.0240239 | ||||||||
\(358\) | 0.127338 | 0.00673000 | ||||||||
\(359\) | 27.2501 | 1.43821 | 0.719103 | − | 0.694904i | \(-0.244553\pi\) | ||||
0.719103 | + | 0.694904i | \(0.244553\pi\) | |||||||
\(360\) | −1.01959 | −0.0537370 | ||||||||
\(361\) | −16.3475 | −0.860397 | ||||||||
\(362\) | 20.3487 | 1.06951 | ||||||||
\(363\) | 1.55384 | 0.0815557 | ||||||||
\(364\) | 1.34792 | 0.0706503 | ||||||||
\(365\) | 13.7611 | 0.720289 | ||||||||
\(366\) | −9.42617 | −0.492714 | ||||||||
\(367\) | −11.7183 | −0.611689 | −0.305845 | − | 0.952081i | \(-0.598939\pi\) | ||||
−0.305845 | + | 0.952081i | \(0.598939\pi\) | |||||||
\(368\) | 3.15142 | 0.164279 | ||||||||
\(369\) | 10.6781 | 0.555882 | ||||||||
\(370\) | −9.08644 | −0.472382 | ||||||||
\(371\) | 9.26646 | 0.481091 | ||||||||
\(372\) | 2.83813 | 0.147150 | ||||||||
\(373\) | −9.29599 | −0.481328 | −0.240664 | − | 0.970608i | \(-0.577365\pi\) | ||||
−0.240664 | + | 0.970608i | \(0.577365\pi\) | |||||||
\(374\) | 0.484806 | 0.0250687 | ||||||||
\(375\) | −1.40727 | −0.0726712 | ||||||||
\(376\) | 0.278443 | 0.0143596 | ||||||||
\(377\) | 0.530609 | 0.0273277 | ||||||||
\(378\) | −13.0936 | −0.673462 | ||||||||
\(379\) | 10.2709 | 0.527582 | 0.263791 | − | 0.964580i | \(-0.415027\pi\) | ||||
0.263791 | + | 0.964580i | \(0.415027\pi\) | |||||||
\(380\) | −1.62864 | −0.0835474 | ||||||||
\(381\) | −3.20119 | −0.164002 | ||||||||
\(382\) | 5.25976 | 0.269112 | ||||||||
\(383\) | −30.2413 | −1.54526 | −0.772630 | − | 0.634857i | \(-0.781059\pi\) | ||||
−0.772630 | + | 0.634857i | \(0.781059\pi\) | |||||||
\(384\) | −1.40727 | −0.0718145 | ||||||||
\(385\) | 8.05317 | 0.410428 | ||||||||
\(386\) | 25.9563 | 1.32114 | ||||||||
\(387\) | −11.9141 | −0.605626 | ||||||||
\(388\) | −3.28753 | −0.166899 | ||||||||
\(389\) | 24.9976 | 1.26743 | 0.633714 | − | 0.773567i | \(-0.281529\pi\) | ||||
0.633714 | + | 0.773567i | \(0.281529\pi\) | |||||||
\(390\) | −0.819488 | −0.0414964 | ||||||||
\(391\) | −0.439144 | −0.0222085 | ||||||||
\(392\) | 1.64204 | 0.0829356 | ||||||||
\(393\) | 7.16188 | 0.361269 | ||||||||
\(394\) | −1.98558 | −0.100032 | ||||||||
\(395\) | −4.01383 | −0.201958 | ||||||||
\(396\) | −3.54725 | −0.178256 | ||||||||
\(397\) | −5.29439 | −0.265718 | −0.132859 | − | 0.991135i | \(-0.542416\pi\) | ||||
−0.132859 | + | 0.991135i | \(0.542416\pi\) | |||||||
\(398\) | −18.6861 | −0.936649 | ||||||||
\(399\) | −5.30521 | −0.265593 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 4.99762 | 0.249259 | ||||||||
\(403\) | −1.17441 | −0.0585015 | ||||||||
\(404\) | 9.53218 | 0.474244 | ||||||||
\(405\) | 4.90168 | 0.243566 | ||||||||
\(406\) | −2.10916 | −0.104676 | ||||||||
\(407\) | −31.6127 | −1.56698 | ||||||||
\(408\) | 0.196101 | 0.00970842 | ||||||||
\(409\) | −9.22127 | −0.455962 | −0.227981 | − | 0.973666i | \(-0.573212\pi\) | ||||
−0.227981 | + | 0.973666i | \(0.573212\pi\) | |||||||
\(410\) | −10.4730 | −0.517225 | ||||||||
\(411\) | −5.52869 | −0.272710 | ||||||||
\(412\) | −7.77644 | −0.383118 | ||||||||
\(413\) | 6.09383 | 0.299858 | ||||||||
\(414\) | 3.21315 | 0.157918 | ||||||||
\(415\) | 1.94410 | 0.0954322 | ||||||||
\(416\) | 0.582324 | 0.0285508 | ||||||||
\(417\) | −24.0993 | −1.18015 | ||||||||
\(418\) | −5.66620 | −0.277143 | ||||||||
\(419\) | −4.10376 | −0.200482 | −0.100241 | − | 0.994963i | \(-0.531961\pi\) | ||||
−0.100241 | + | 0.994963i | \(0.531961\pi\) | |||||||
\(420\) | 3.25745 | 0.158947 | ||||||||
\(421\) | 10.7992 | 0.526321 | 0.263161 | − | 0.964752i | \(-0.415235\pi\) | ||||
0.263161 | + | 0.964752i | \(0.415235\pi\) | |||||||
\(422\) | 17.0537 | 0.830163 | ||||||||
\(423\) | 0.283897 | 0.0138035 | ||||||||
\(424\) | 4.00326 | 0.194416 | ||||||||
\(425\) | −0.139348 | −0.00675937 | ||||||||
\(426\) | −15.6622 | −0.758838 | ||||||||
\(427\) | −15.5045 | −0.750314 | ||||||||
\(428\) | −10.6438 | −0.514487 | ||||||||
\(429\) | −2.85108 | −0.137652 | ||||||||
\(430\) | 11.6852 | 0.563510 | ||||||||
\(431\) | 5.24419 | 0.252604 | 0.126302 | − | 0.991992i | \(-0.459689\pi\) | ||||
0.126302 | + | 0.991992i | \(0.459689\pi\) | |||||||
\(432\) | −5.65665 | −0.272156 | ||||||||
\(433\) | −29.1625 | −1.40146 | −0.700729 | − | 0.713427i | \(-0.747142\pi\) | ||||
−0.700729 | + | 0.713427i | \(0.747142\pi\) | |||||||
\(434\) | 4.66825 | 0.224083 | ||||||||
\(435\) | 1.28229 | 0.0614812 | ||||||||
\(436\) | 3.07843 | 0.147430 | ||||||||
\(437\) | 5.13252 | 0.245522 | ||||||||
\(438\) | 19.3656 | 0.925325 | ||||||||
\(439\) | −30.0804 | −1.43566 | −0.717830 | − | 0.696219i | \(-0.754864\pi\) | ||||
−0.717830 | + | 0.696219i | \(0.754864\pi\) | |||||||
\(440\) | 3.47910 | 0.165860 | ||||||||
\(441\) | 1.67421 | 0.0797241 | ||||||||
\(442\) | −0.0811457 | −0.00385971 | ||||||||
\(443\) | 2.12105 | 0.100774 | 0.0503872 | − | 0.998730i | \(-0.483954\pi\) | ||||
0.0503872 | + | 0.998730i | \(0.483954\pi\) | |||||||
\(444\) | −12.7871 | −0.606848 | ||||||||
\(445\) | 5.16178 | 0.244692 | ||||||||
\(446\) | −9.44253 | −0.447117 | ||||||||
\(447\) | −24.2377 | −1.14640 | ||||||||
\(448\) | −2.31473 | −0.109361 | ||||||||
\(449\) | −4.81533 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(450\) | 1.01959 | 0.0480638 | ||||||||
\(451\) | −36.4367 | −1.71574 | ||||||||
\(452\) | −11.0361 | −0.519097 | ||||||||
\(453\) | −17.0524 | −0.801192 | ||||||||
\(454\) | 28.2941 | 1.32791 | ||||||||
\(455\) | −1.34792 | −0.0631915 | ||||||||
\(456\) | −2.29194 | −0.107330 | ||||||||
\(457\) | −8.69990 | −0.406964 | −0.203482 | − | 0.979079i | \(-0.565226\pi\) | ||||
−0.203482 | + | 0.979079i | \(0.565226\pi\) | |||||||
\(458\) | 14.5510 | 0.679925 | ||||||||
\(459\) | 0.788243 | 0.0367920 | ||||||||
\(460\) | −3.15142 | −0.146936 | ||||||||
\(461\) | 19.0132 | 0.885532 | 0.442766 | − | 0.896637i | \(-0.353997\pi\) | ||||
0.442766 | + | 0.896637i | \(0.353997\pi\) | |||||||
\(462\) | 11.3330 | 0.527259 | ||||||||
\(463\) | −27.2544 | −1.26662 | −0.633311 | − | 0.773898i | \(-0.718304\pi\) | ||||
−0.633311 | + | 0.773898i | \(0.718304\pi\) | |||||||
\(464\) | −0.911191 | −0.0423010 | ||||||||
\(465\) | −2.83813 | −0.131615 | ||||||||
\(466\) | −5.80631 | −0.268972 | ||||||||
\(467\) | 17.2210 | 0.796893 | 0.398447 | − | 0.917192i | \(-0.369549\pi\) | ||||
0.398447 | + | 0.917192i | \(0.369549\pi\) | |||||||
\(468\) | 0.593731 | 0.0274452 | ||||||||
\(469\) | 8.22025 | 0.379576 | ||||||||
\(470\) | −0.278443 | −0.0128436 | ||||||||
\(471\) | −1.99672 | −0.0920040 | ||||||||
\(472\) | 2.63264 | 0.121177 | ||||||||
\(473\) | 40.6540 | 1.86927 | ||||||||
\(474\) | −5.64855 | −0.259446 | ||||||||
\(475\) | 1.62864 | 0.0747271 | ||||||||
\(476\) | 0.322553 | 0.0147842 | ||||||||
\(477\) | 4.08168 | 0.186887 | ||||||||
\(478\) | −21.6434 | −0.989947 | ||||||||
\(479\) | 37.8840 | 1.73096 | 0.865482 | − | 0.500940i | \(-0.167012\pi\) | ||||
0.865482 | + | 0.500940i | \(0.167012\pi\) | |||||||
\(480\) | 1.40727 | 0.0642328 | ||||||||
\(481\) | 5.29126 | 0.241260 | ||||||||
\(482\) | 7.24006 | 0.329776 | ||||||||
\(483\) | −10.2656 | −0.467100 | ||||||||
\(484\) | 1.10415 | 0.0501888 | ||||||||
\(485\) | 3.28753 | 0.149279 | ||||||||
\(486\) | −10.0720 | −0.456873 | ||||||||
\(487\) | 14.9895 | 0.679241 | 0.339621 | − | 0.940563i | \(-0.389701\pi\) | ||||
0.339621 | + | 0.940563i | \(0.389701\pi\) | |||||||
\(488\) | −6.69819 | −0.303213 | ||||||||
\(489\) | 17.3173 | 0.783114 | ||||||||
\(490\) | −1.64204 | −0.0741799 | ||||||||
\(491\) | 16.8228 | 0.759203 | 0.379601 | − | 0.925150i | \(-0.376061\pi\) | ||||
0.379601 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(492\) | −14.7384 | −0.664457 | ||||||||
\(493\) | 0.126973 | 0.00571856 | ||||||||
\(494\) | 0.948396 | 0.0426704 | ||||||||
\(495\) | 3.54725 | 0.159437 | ||||||||
\(496\) | 2.01676 | 0.0905552 | ||||||||
\(497\) | −25.7618 | −1.15557 | ||||||||
\(498\) | 2.73588 | 0.122598 | ||||||||
\(499\) | 5.83436 | 0.261182 | 0.130591 | − | 0.991436i | \(-0.458313\pi\) | ||||
0.130591 | + | 0.991436i | \(0.458313\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −20.7039 | −0.924983 | ||||||||
\(502\) | −15.1467 | −0.676030 | ||||||||
\(503\) | 30.0823 | 1.34130 | 0.670651 | − | 0.741773i | \(-0.266015\pi\) | ||||
0.670651 | + | 0.741773i | \(0.266015\pi\) | |||||||
\(504\) | −2.36007 | −0.105126 | ||||||||
\(505\) | −9.53218 | −0.424177 | ||||||||
\(506\) | −10.9641 | −0.487414 | ||||||||
\(507\) | −17.8173 | −0.791295 | ||||||||
\(508\) | −2.27475 | −0.100926 | ||||||||
\(509\) | −3.74020 | −0.165781 | −0.0828906 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828906 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(510\) | −0.196101 | −0.00868348 | ||||||||
\(511\) | 31.8532 | 1.40910 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.21264 | −0.406748 | ||||||||
\(514\) | −26.3434 | −1.16196 | ||||||||
\(515\) | 7.77644 | 0.342671 | ||||||||
\(516\) | 16.4442 | 0.723917 | ||||||||
\(517\) | −0.968730 | −0.0426047 | ||||||||
\(518\) | −21.0326 | −0.924121 | ||||||||
\(519\) | 6.06018 | 0.266012 | ||||||||
\(520\) | −0.582324 | −0.0255366 | ||||||||
\(521\) | −9.55314 | −0.418531 | −0.209265 | − | 0.977859i | \(-0.567107\pi\) | ||||
−0.209265 | + | 0.977859i | \(0.567107\pi\) | |||||||
\(522\) | −0.929039 | −0.0406629 | ||||||||
\(523\) | −18.6976 | −0.817589 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(524\) | 5.08920 | 0.222323 | ||||||||
\(525\) | −3.25745 | −0.142167 | ||||||||
\(526\) | 20.9665 | 0.914182 | ||||||||
\(527\) | −0.281032 | −0.0122419 | ||||||||
\(528\) | 4.89604 | 0.213073 | ||||||||
\(529\) | −13.0686 | −0.568199 | ||||||||
\(530\) | −4.00326 | −0.173891 | ||||||||
\(531\) | 2.68420 | 0.116485 | ||||||||
\(532\) | −3.76985 | −0.163444 | ||||||||
\(533\) | 6.09869 | 0.264163 | ||||||||
\(534\) | 7.26403 | 0.314345 | ||||||||
\(535\) | 10.6438 | 0.460171 | ||||||||
\(536\) | 3.55128 | 0.153392 | ||||||||
\(537\) | −0.179198 | −0.00773299 | ||||||||
\(538\) | −7.00564 | −0.302035 | ||||||||
\(539\) | −5.71283 | −0.246069 | ||||||||
\(540\) | 5.65665 | 0.243423 | ||||||||
\(541\) | −17.8749 | −0.768500 | −0.384250 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384250 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(542\) | −18.4642 | −0.793103 | ||||||||
\(543\) | −28.6362 | −1.22890 | ||||||||
\(544\) | 0.139348 | 0.00597450 | ||||||||
\(545\) | −3.07843 | −0.131866 | ||||||||
\(546\) | −1.89689 | −0.0811794 | ||||||||
\(547\) | −12.0523 | −0.515317 | −0.257659 | − | 0.966236i | \(-0.582951\pi\) | ||||
−0.257659 | + | 0.966236i | \(0.582951\pi\) | |||||||
\(548\) | −3.92866 | −0.167824 | ||||||||
\(549\) | −6.82939 | −0.291471 | ||||||||
\(550\) | −3.47910 | −0.148349 | ||||||||
\(551\) | −1.48400 | −0.0632206 | ||||||||
\(552\) | −4.43490 | −0.188762 | ||||||||
\(553\) | −9.29092 | −0.395090 | ||||||||
\(554\) | 32.0109 | 1.36001 | ||||||||
\(555\) | 12.7871 | 0.542782 | ||||||||
\(556\) | −17.1248 | −0.726255 | ||||||||
\(557\) | −30.6283 | −1.29776 | −0.648882 | − | 0.760889i | \(-0.724763\pi\) | ||||
−0.648882 | + | 0.760889i | \(0.724763\pi\) | |||||||
\(558\) | 2.05626 | 0.0870486 | ||||||||
\(559\) | −6.80457 | −0.287802 | ||||||||
\(560\) | 2.31473 | 0.0978150 | ||||||||
\(561\) | −0.682254 | −0.0288048 | ||||||||
\(562\) | 11.3622 | 0.479285 | ||||||||
\(563\) | 3.75483 | 0.158247 | 0.0791236 | − | 0.996865i | \(-0.474788\pi\) | ||||
0.0791236 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(564\) | −0.391844 | −0.0164996 | ||||||||
\(565\) | 11.0361 | 0.464294 | ||||||||
\(566\) | −21.2582 | −0.893548 | ||||||||
\(567\) | 11.3460 | 0.476489 | ||||||||
\(568\) | −11.1295 | −0.466984 | ||||||||
\(569\) | −0.517257 | −0.0216845 | −0.0108423 | − | 0.999941i | \(-0.503451\pi\) | ||||
−0.0108423 | + | 0.999941i | \(0.503451\pi\) | |||||||
\(570\) | 2.29194 | 0.0959987 | ||||||||
\(571\) | −1.99557 | −0.0835120 | −0.0417560 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417560 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(572\) | −2.02597 | −0.0847099 | ||||||||
\(573\) | −7.40190 | −0.309219 | ||||||||
\(574\) | −24.2421 | −1.01185 | ||||||||
\(575\) | 3.15142 | 0.131423 | ||||||||
\(576\) | −1.01959 | −0.0424828 | ||||||||
\(577\) | −1.09999 | −0.0457934 | −0.0228967 | − | 0.999738i | \(-0.507289\pi\) | ||||
−0.0228967 | + | 0.999738i | \(0.507289\pi\) | |||||||
\(578\) | 16.9806 | 0.706299 | ||||||||
\(579\) | −36.5275 | −1.51803 | ||||||||
\(580\) | 0.911191 | 0.0378352 | ||||||||
\(581\) | 4.50006 | 0.186694 | ||||||||
\(582\) | 4.62644 | 0.191772 | ||||||||
\(583\) | −13.9278 | −0.576829 | ||||||||
\(584\) | 13.7611 | 0.569439 | ||||||||
\(585\) | −0.593731 | −0.0245477 | ||||||||
\(586\) | −20.4238 | −0.843700 | ||||||||
\(587\) | 43.8254 | 1.80887 | 0.904433 | − | 0.426616i | \(-0.140294\pi\) | ||||
0.904433 | + | 0.426616i | \(0.140294\pi\) | |||||||
\(588\) | −2.31080 | −0.0952957 | ||||||||
\(589\) | 3.28458 | 0.135339 | ||||||||
\(590\) | −2.63264 | −0.108384 | ||||||||
\(591\) | 2.79425 | 0.114940 | ||||||||
\(592\) | −9.08644 | −0.373451 | ||||||||
\(593\) | −6.60596 | −0.271274 | −0.135637 | − | 0.990759i | \(-0.543308\pi\) | ||||
−0.135637 | + | 0.990759i | \(0.543308\pi\) | |||||||
\(594\) | 19.6801 | 0.807483 | ||||||||
\(595\) | −0.322553 | −0.0132234 | ||||||||
\(596\) | −17.2232 | −0.705488 | ||||||||
\(597\) | 26.2964 | 1.07624 | ||||||||
\(598\) | 1.83515 | 0.0750447 | ||||||||
\(599\) | −21.6376 | −0.884087 | −0.442044 | − | 0.896994i | \(-0.645746\pi\) | ||||
−0.442044 | + | 0.896994i | \(0.645746\pi\) | |||||||
\(600\) | −1.40727 | −0.0574516 | ||||||||
\(601\) | 21.8802 | 0.892512 | 0.446256 | − | 0.894905i | \(-0.352757\pi\) | ||||
0.446256 | + | 0.894905i | \(0.352757\pi\) | |||||||
\(602\) | 27.0480 | 1.10239 | ||||||||
\(603\) | 3.62085 | 0.147452 | ||||||||
\(604\) | −12.1174 | −0.493048 | ||||||||
\(605\) | −1.10415 | −0.0448902 | ||||||||
\(606\) | −13.4144 | −0.544921 | ||||||||
\(607\) | 10.1609 | 0.412419 | 0.206210 | − | 0.978508i | \(-0.433887\pi\) | ||||
0.206210 | + | 0.978508i | \(0.433887\pi\) | |||||||
\(608\) | −1.62864 | −0.0660500 | ||||||||
\(609\) | 2.96816 | 0.120276 | ||||||||
\(610\) | 6.69819 | 0.271202 | ||||||||
\(611\) | 0.162144 | 0.00655964 | ||||||||
\(612\) | 0.142078 | 0.00574315 | ||||||||
\(613\) | −7.86797 | −0.317784 | −0.158892 | − | 0.987296i | \(-0.550792\pi\) | ||||
−0.158892 | + | 0.987296i | \(0.550792\pi\) | |||||||
\(614\) | 20.7595 | 0.837787 | ||||||||
\(615\) | 14.7384 | 0.594308 | ||||||||
\(616\) | 8.05317 | 0.324471 | ||||||||
\(617\) | −16.2628 | −0.654715 | −0.327358 | − | 0.944900i | \(-0.606158\pi\) | ||||
−0.327358 | + | 0.944900i | \(0.606158\pi\) | |||||||
\(618\) | 10.9436 | 0.440215 | ||||||||
\(619\) | −17.9336 | −0.720814 | −0.360407 | − | 0.932795i | \(-0.617362\pi\) | ||||
−0.360407 | + | 0.932795i | \(0.617362\pi\) | |||||||
\(620\) | −2.01676 | −0.0809951 | ||||||||
\(621\) | −17.8265 | −0.715351 | ||||||||
\(622\) | −20.4833 | −0.821307 | ||||||||
\(623\) | 11.9481 | 0.478691 | ||||||||
\(624\) | −0.819488 | −0.0328058 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.4038 | −0.775531 | ||||||||
\(627\) | 7.97388 | 0.318446 | ||||||||
\(628\) | −1.41886 | −0.0566187 | ||||||||
\(629\) | 1.26618 | 0.0504858 | ||||||||
\(630\) | 2.36007 | 0.0940273 | ||||||||
\(631\) | −18.5889 | −0.740013 | −0.370006 | − | 0.929029i | \(-0.620645\pi\) | ||||
−0.370006 | + | 0.929029i | \(0.620645\pi\) | |||||||
\(632\) | −4.01383 | −0.159662 | ||||||||
\(633\) | −23.9992 | −0.953884 | ||||||||
\(634\) | −13.3472 | −0.530084 | ||||||||
\(635\) | 2.27475 | 0.0902706 | ||||||||
\(636\) | −5.63368 | −0.223390 | ||||||||
\(637\) | 0.956201 | 0.0378861 | ||||||||
\(638\) | 3.17013 | 0.125507 | ||||||||
\(639\) | −11.3475 | −0.448900 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −12.9876 | −0.512981 | −0.256490 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256490 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(642\) | 14.9787 | 0.591162 | ||||||||
\(643\) | 45.4288 | 1.79154 | 0.895769 | − | 0.444520i | \(-0.146626\pi\) | ||||
0.895769 | + | 0.444520i | \(0.146626\pi\) | |||||||
\(644\) | −7.29467 | −0.287450 | ||||||||
\(645\) | −16.4442 | −0.647491 | ||||||||
\(646\) | 0.226948 | 0.00892914 | ||||||||
\(647\) | −44.9252 | −1.76619 | −0.883097 | − | 0.469191i | \(-0.844546\pi\) | ||||
−0.883097 | + | 0.469191i | \(0.844546\pi\) | |||||||
\(648\) | 4.90168 | 0.192556 | ||||||||
\(649\) | −9.15921 | −0.359530 | ||||||||
\(650\) | 0.582324 | 0.0228406 | ||||||||
\(651\) | −6.56949 | −0.257479 | ||||||||
\(652\) | 12.3056 | 0.481923 | ||||||||
\(653\) | 6.82076 | 0.266917 | 0.133459 | − | 0.991054i | \(-0.457392\pi\) | ||||
0.133459 | + | 0.991054i | \(0.457392\pi\) | |||||||
\(654\) | −4.33219 | −0.169402 | ||||||||
\(655\) | −5.08920 | −0.198851 | ||||||||
\(656\) | −10.4730 | −0.408902 | ||||||||
\(657\) | 14.0307 | 0.547388 | ||||||||
\(658\) | −0.644519 | −0.0251259 | ||||||||
\(659\) | 29.0943 | 1.13335 | 0.566676 | − | 0.823941i | \(-0.308229\pi\) | ||||
0.566676 | + | 0.823941i | \(0.308229\pi\) | |||||||
\(660\) | −4.89604 | −0.190578 | ||||||||
\(661\) | 13.2971 | 0.517195 | 0.258598 | − | 0.965985i | \(-0.416740\pi\) | ||||
0.258598 | + | 0.965985i | \(0.416740\pi\) | |||||||
\(662\) | 15.3821 | 0.597842 | ||||||||
\(663\) | 0.114194 | 0.00443493 | ||||||||
\(664\) | 1.94410 | 0.0754457 | ||||||||
\(665\) | 3.76985 | 0.146189 | ||||||||
\(666\) | −9.26443 | −0.358989 | ||||||||
\(667\) | −2.87154 | −0.111187 | ||||||||
\(668\) | −14.7121 | −0.569228 | ||||||||
\(669\) | 13.2882 | 0.513751 | ||||||||
\(670\) | −3.55128 | −0.137198 | ||||||||
\(671\) | 23.3037 | 0.899629 | ||||||||
\(672\) | 3.25745 | 0.125659 | ||||||||
\(673\) | 42.0441 | 1.62068 | 0.810341 | − | 0.585958i | \(-0.199282\pi\) | ||||
0.810341 | + | 0.585958i | \(0.199282\pi\) | |||||||
\(674\) | −6.72138 | −0.258898 | ||||||||
\(675\) | −5.65665 | −0.217725 | ||||||||
\(676\) | −12.6609 | −0.486958 | ||||||||
\(677\) | 34.3850 | 1.32152 | 0.660761 | − | 0.750597i | \(-0.270234\pi\) | ||||
0.660761 | + | 0.750597i | \(0.270234\pi\) | |||||||
\(678\) | 15.5309 | 0.596459 | ||||||||
\(679\) | 7.60973 | 0.292035 | ||||||||
\(680\) | −0.139348 | −0.00534375 | ||||||||
\(681\) | −39.8175 | −1.52581 | ||||||||
\(682\) | −7.01652 | −0.268676 | ||||||||
\(683\) | −23.0199 | −0.880834 | −0.440417 | − | 0.897793i | \(-0.645169\pi\) | ||||
−0.440417 | + | 0.897793i | \(0.645169\pi\) | |||||||
\(684\) | −1.66054 | −0.0634924 | ||||||||
\(685\) | 3.92866 | 0.150106 | ||||||||
\(686\) | −20.0040 | −0.763755 | ||||||||
\(687\) | −20.4772 | −0.781256 | ||||||||
\(688\) | 11.6852 | 0.445494 | ||||||||
\(689\) | 2.33120 | 0.0888115 | ||||||||
\(690\) | 4.43490 | 0.168834 | ||||||||
\(691\) | −40.1220 | −1.52631 | −0.763157 | − | 0.646213i | \(-0.776352\pi\) | ||||
−0.763157 | + | 0.646213i | \(0.776352\pi\) | |||||||
\(692\) | 4.30633 | 0.163702 | ||||||||
\(693\) | 8.21091 | 0.311907 | ||||||||
\(694\) | 17.7250 | 0.672831 | ||||||||
\(695\) | 17.1248 | 0.649582 | ||||||||
\(696\) | 1.28229 | 0.0486052 | ||||||||
\(697\) | 1.45939 | 0.0552785 | ||||||||
\(698\) | −32.0292 | −1.21232 | ||||||||
\(699\) | 8.17106 | 0.309058 | ||||||||
\(700\) | −2.31473 | −0.0874884 | ||||||||
\(701\) | 31.6800 | 1.19654 | 0.598269 | − | 0.801295i | \(-0.295855\pi\) | ||||
0.598269 | + | 0.801295i | \(0.295855\pi\) | |||||||
\(702\) | −3.29400 | −0.124324 | ||||||||
\(703\) | −14.7985 | −0.558137 | ||||||||
\(704\) | 3.47910 | 0.131124 | ||||||||
\(705\) | 0.391844 | 0.0147577 | ||||||||
\(706\) | 19.3684 | 0.728938 | ||||||||
\(707\) | −22.0644 | −0.829817 | ||||||||
\(708\) | −3.70483 | −0.139236 | ||||||||
\(709\) | −2.44345 | −0.0917656 | −0.0458828 | − | 0.998947i | \(-0.514610\pi\) | ||||
−0.0458828 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(710\) | 11.1295 | 0.417683 | ||||||||
\(711\) | −4.09245 | −0.153479 | ||||||||
\(712\) | 5.16178 | 0.193446 | ||||||||
\(713\) | 6.35565 | 0.238021 | ||||||||
\(714\) | −0.453919 | −0.0169875 | ||||||||
\(715\) | 2.02597 | 0.0757668 | ||||||||
\(716\) | −0.127338 | −0.00475883 | ||||||||
\(717\) | 30.4582 | 1.13748 | ||||||||
\(718\) | −27.2501 | −1.01697 | ||||||||
\(719\) | −6.45604 | −0.240770 | −0.120385 | − | 0.992727i | \(-0.538413\pi\) | ||||
−0.120385 | + | 0.992727i | \(0.538413\pi\) | |||||||
\(720\) | 1.01959 | 0.0379978 | ||||||||
\(721\) | 18.0003 | 0.670367 | ||||||||
\(722\) | 16.3475 | 0.608392 | ||||||||
\(723\) | −10.1887 | −0.378923 | ||||||||
\(724\) | −20.3487 | −0.756254 | ||||||||
\(725\) | −0.911191 | −0.0338408 | ||||||||
\(726\) | −1.55384 | −0.0576686 | ||||||||
\(727\) | −27.4239 | −1.01710 | −0.508549 | − | 0.861033i | \(-0.669818\pi\) | ||||
−0.508549 | + | 0.861033i | \(0.669818\pi\) | |||||||
\(728\) | −1.34792 | −0.0499573 | ||||||||
\(729\) | 28.8790 | 1.06959 | ||||||||
\(730\) | −13.7611 | −0.509321 | ||||||||
\(731\) | −1.62831 | −0.0602251 | ||||||||
\(732\) | 9.42617 | 0.348401 | ||||||||
\(733\) | −22.7244 | −0.839346 | −0.419673 | − | 0.907675i | \(-0.637855\pi\) | ||||
−0.419673 | + | 0.907675i | \(0.637855\pi\) | |||||||
\(734\) | 11.7183 | 0.432530 | ||||||||
\(735\) | 2.31080 | 0.0852351 | ||||||||
\(736\) | −3.15142 | −0.116163 | ||||||||
\(737\) | −12.3553 | −0.455113 | ||||||||
\(738\) | −10.6781 | −0.393068 | ||||||||
\(739\) | −10.8263 | −0.398250 | −0.199125 | − | 0.979974i | \(-0.563810\pi\) | ||||
−0.199125 | + | 0.979974i | \(0.563810\pi\) | |||||||
\(740\) | 9.08644 | 0.334024 | ||||||||
\(741\) | −1.33465 | −0.0490296 | ||||||||
\(742\) | −9.26646 | −0.340182 | ||||||||
\(743\) | 28.6781 | 1.05210 | 0.526050 | − | 0.850454i | \(-0.323673\pi\) | ||||
0.526050 | + | 0.850454i | \(0.323673\pi\) | |||||||
\(744\) | −2.83813 | −0.104051 | ||||||||
\(745\) | 17.2232 | 0.631008 | ||||||||
\(746\) | 9.29599 | 0.340350 | ||||||||
\(747\) | 1.98218 | 0.0725242 | ||||||||
\(748\) | −0.484806 | −0.0177263 | ||||||||
\(749\) | 24.6375 | 0.900233 | ||||||||
\(750\) | 1.40727 | 0.0513863 | ||||||||
\(751\) | 25.4867 | 0.930022 | 0.465011 | − | 0.885305i | \(-0.346050\pi\) | ||||
0.465011 | + | 0.885305i | \(0.346050\pi\) | |||||||
\(752\) | −0.278443 | −0.0101538 | ||||||||
\(753\) | 21.3155 | 0.776780 | ||||||||
\(754\) | −0.530609 | −0.0193236 | ||||||||
\(755\) | 12.1174 | 0.440996 | ||||||||
\(756\) | 13.0936 | 0.476210 | ||||||||
\(757\) | −16.2588 | −0.590935 | −0.295467 | − | 0.955353i | \(-0.595475\pi\) | ||||
−0.295467 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(758\) | −10.2709 | −0.373057 | ||||||||
\(759\) | 15.4295 | 0.560054 | ||||||||
\(760\) | 1.62864 | 0.0590770 | ||||||||
\(761\) | 41.5505 | 1.50621 | 0.753103 | − | 0.657903i | \(-0.228556\pi\) | ||||
0.753103 | + | 0.657903i | \(0.228556\pi\) | |||||||
\(762\) | 3.20119 | 0.115967 | ||||||||
\(763\) | −7.12573 | −0.257969 | ||||||||
\(764\) | −5.25976 | −0.190291 | ||||||||
\(765\) | −0.142078 | −0.00513683 | ||||||||
\(766\) | 30.2413 | 1.09266 | ||||||||
\(767\) | 1.53305 | 0.0553551 | ||||||||
\(768\) | 1.40727 | 0.0507805 | ||||||||
\(769\) | 17.6390 | 0.636080 | 0.318040 | − | 0.948077i | \(-0.396975\pi\) | ||||
0.318040 | + | 0.948077i | \(0.396975\pi\) | |||||||
\(770\) | −8.05317 | −0.290216 | ||||||||
\(771\) | 37.0722 | 1.33512 | ||||||||
\(772\) | −25.9563 | −0.934187 | ||||||||
\(773\) | 18.9896 | 0.683007 | 0.341504 | − | 0.939880i | \(-0.389064\pi\) | ||||
0.341504 | + | 0.939880i | \(0.389064\pi\) | |||||||
\(774\) | 11.9141 | 0.428242 | ||||||||
\(775\) | 2.01676 | 0.0724442 | ||||||||
\(776\) | 3.28753 | 0.118015 | ||||||||
\(777\) | 29.5986 | 1.06184 | ||||||||
\(778\) | −24.9976 | −0.896207 | ||||||||
\(779\) | −17.0567 | −0.611121 | ||||||||
\(780\) | 0.819488 | 0.0293424 | ||||||||
\(781\) | 38.7207 | 1.38554 | ||||||||
\(782\) | 0.439144 | 0.0157038 | ||||||||
\(783\) | 5.15429 | 0.184199 | ||||||||
\(784\) | −1.64204 | −0.0586444 | ||||||||
\(785\) | 1.41886 | 0.0506413 | ||||||||
\(786\) | −7.16188 | −0.255456 | ||||||||
\(787\) | 20.7331 | 0.739057 | 0.369528 | − | 0.929219i | \(-0.379519\pi\) | ||||
0.369528 | + | 0.929219i | \(0.379519\pi\) | |||||||
\(788\) | 1.98558 | 0.0707334 | ||||||||
\(789\) | −29.5055 | −1.05042 | ||||||||
\(790\) | 4.01383 | 0.142806 | ||||||||
\(791\) | 25.5457 | 0.908299 | ||||||||
\(792\) | 3.54725 | 0.126046 | ||||||||
\(793\) | −3.90052 | −0.138511 | ||||||||
\(794\) | 5.29439 | 0.187891 | ||||||||
\(795\) | 5.63368 | 0.199806 | ||||||||
\(796\) | 18.6861 | 0.662311 | ||||||||
\(797\) | 40.1774 | 1.42316 | 0.711578 | − | 0.702607i | \(-0.247981\pi\) | ||||
0.711578 | + | 0.702607i | \(0.247981\pi\) | |||||||
\(798\) | 5.30521 | 0.187802 | ||||||||
\(799\) | 0.0388004 | 0.00137266 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 5.26289 | 0.185955 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −47.8763 | −1.68952 | ||||||||
\(804\) | −4.99762 | −0.176252 | ||||||||
\(805\) | 7.29467 | 0.257103 | ||||||||
\(806\) | 1.17441 | 0.0413668 | ||||||||
\(807\) | 9.85884 | 0.347048 | ||||||||
\(808\) | −9.53218 | −0.335341 | ||||||||
\(809\) | 7.41283 | 0.260621 | 0.130311 | − | 0.991473i | \(-0.458403\pi\) | ||||
0.130311 | + | 0.991473i | \(0.458403\pi\) | |||||||
\(810\) | −4.90168 | −0.172227 | ||||||||
\(811\) | 27.0990 | 0.951575 | 0.475788 | − | 0.879560i | \(-0.342163\pi\) | ||||
0.475788 | + | 0.879560i | \(0.342163\pi\) | |||||||
\(812\) | 2.10916 | 0.0740169 | ||||||||
\(813\) | 25.9841 | 0.911301 | ||||||||
\(814\) | 31.6127 | 1.10802 | ||||||||
\(815\) | −12.3056 | −0.431045 | ||||||||
\(816\) | −0.196101 | −0.00686489 | ||||||||
\(817\) | 19.0310 | 0.665809 | ||||||||
\(818\) | 9.22127 | 0.322414 | ||||||||
\(819\) | −1.37432 | −0.0480228 | ||||||||
\(820\) | 10.4730 | 0.365733 | ||||||||
\(821\) | 1.85828 | 0.0648546 | 0.0324273 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324273 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(822\) | 5.52869 | 0.192835 | ||||||||
\(823\) | 7.92084 | 0.276103 | 0.138052 | − | 0.990425i | \(-0.455916\pi\) | ||||
0.138052 | + | 0.990425i | \(0.455916\pi\) | |||||||
\(824\) | 7.77644 | 0.270905 | ||||||||
\(825\) | 4.89604 | 0.170458 | ||||||||
\(826\) | −6.09383 | −0.212032 | ||||||||
\(827\) | 48.5583 | 1.68854 | 0.844269 | − | 0.535920i | \(-0.180035\pi\) | ||||
0.844269 | + | 0.535920i | \(0.180035\pi\) | |||||||
\(828\) | −3.21315 | −0.111665 | ||||||||
\(829\) | 22.5846 | 0.784397 | 0.392198 | − | 0.919881i | \(-0.371715\pi\) | ||||
0.392198 | + | 0.919881i | \(0.371715\pi\) | |||||||
\(830\) | −1.94410 | −0.0674807 | ||||||||
\(831\) | −45.0480 | −1.56270 | ||||||||
\(832\) | −0.582324 | −0.0201885 | ||||||||
\(833\) | 0.228815 | 0.00792798 | ||||||||
\(834\) | 24.0993 | 0.834490 | ||||||||
\(835\) | 14.7121 | 0.509133 | ||||||||
\(836\) | 5.66620 | 0.195970 | ||||||||
\(837\) | −11.4081 | −0.394322 | ||||||||
\(838\) | 4.10376 | 0.141762 | ||||||||
\(839\) | 6.52784 | 0.225366 | 0.112683 | − | 0.993631i | \(-0.464056\pi\) | ||||
0.112683 | + | 0.993631i | \(0.464056\pi\) | |||||||
\(840\) | −3.25745 | −0.112393 | ||||||||
\(841\) | −28.1697 | −0.971370 | ||||||||
\(842\) | −10.7992 | −0.372165 | ||||||||
\(843\) | −15.9897 | −0.550713 | ||||||||
\(844\) | −17.0537 | −0.587014 | ||||||||
\(845\) | 12.6609 | 0.435548 | ||||||||
\(846\) | −0.283897 | −0.00976057 | ||||||||
\(847\) | −2.55581 | −0.0878188 | ||||||||
\(848\) | −4.00326 | −0.137473 | ||||||||
\(849\) | 29.9160 | 1.02672 | ||||||||
\(850\) | 0.139348 | 0.00477960 | ||||||||
\(851\) | −28.6352 | −0.981601 | ||||||||
\(852\) | 15.6622 | 0.536579 | ||||||||
\(853\) | −34.4213 | −1.17856 | −0.589282 | − | 0.807927i | \(-0.700589\pi\) | ||||
−0.589282 | + | 0.807927i | \(0.700589\pi\) | |||||||
\(854\) | 15.5045 | 0.530552 | ||||||||
\(855\) | 1.66054 | 0.0567893 | ||||||||
\(856\) | 10.6438 | 0.363797 | ||||||||
\(857\) | −26.6137 | −0.909105 | −0.454552 | − | 0.890720i | \(-0.650201\pi\) | ||||
−0.454552 | + | 0.890720i | \(0.650201\pi\) | |||||||
\(858\) | 2.85108 | 0.0973344 | ||||||||
\(859\) | 56.3500 | 1.92264 | 0.961318 | − | 0.275441i | \(-0.0888240\pi\) | ||||
0.961318 | + | 0.275441i | \(0.0888240\pi\) | |||||||
\(860\) | −11.6852 | −0.398462 | ||||||||
\(861\) | 34.1153 | 1.16265 | ||||||||
\(862\) | −5.24419 | −0.178618 | ||||||||
\(863\) | −30.1071 | −1.02486 | −0.512428 | − | 0.858730i | \(-0.671254\pi\) | ||||
−0.512428 | + | 0.858730i | \(0.671254\pi\) | |||||||
\(864\) | 5.65665 | 0.192443 | ||||||||
\(865\) | −4.30633 | −0.146420 | ||||||||
\(866\) | 29.1625 | 0.990981 | ||||||||
\(867\) | −23.8963 | −0.811560 | ||||||||
\(868\) | −4.66825 | −0.158451 | ||||||||
\(869\) | 13.9645 | 0.473714 | ||||||||
\(870\) | −1.28229 | −0.0434738 | ||||||||
\(871\) | 2.06800 | 0.0700715 | ||||||||
\(872\) | −3.07843 | −0.104249 | ||||||||
\(873\) | 3.35192 | 0.113445 | ||||||||
\(874\) | −5.13252 | −0.173610 | ||||||||
\(875\) | 2.31473 | 0.0782520 | ||||||||
\(876\) | −19.3656 | −0.654303 | ||||||||
\(877\) | −12.6241 | −0.426286 | −0.213143 | − | 0.977021i | \(-0.568370\pi\) | ||||
−0.213143 | + | 0.977021i | \(0.568370\pi\) | |||||||
\(878\) | 30.0804 | 1.01516 | ||||||||
\(879\) | 28.7419 | 0.969439 | ||||||||
\(880\) | −3.47910 | −0.117281 | ||||||||
\(881\) | −41.3783 | −1.39407 | −0.697036 | − | 0.717036i | \(-0.745498\pi\) | ||||
−0.697036 | + | 0.717036i | \(0.745498\pi\) | |||||||
\(882\) | −1.67421 | −0.0563734 | ||||||||
\(883\) | 32.1412 | 1.08164 | 0.540819 | − | 0.841139i | \(-0.318114\pi\) | ||||
0.540819 | + | 0.841139i | \(0.318114\pi\) | |||||||
\(884\) | 0.0811457 | 0.00272923 | ||||||||
\(885\) | 3.70483 | 0.124537 | ||||||||
\(886\) | −2.12105 | −0.0712582 | ||||||||
\(887\) | −19.6729 | −0.660552 | −0.330276 | − | 0.943884i | \(-0.607142\pi\) | ||||
−0.330276 | + | 0.943884i | \(0.607142\pi\) | |||||||
\(888\) | 12.7871 | 0.429107 | ||||||||
\(889\) | 5.26542 | 0.176596 | ||||||||
\(890\) | −5.16178 | −0.173023 | ||||||||
\(891\) | −17.0534 | −0.571312 | ||||||||
\(892\) | 9.44253 | 0.316159 | ||||||||
\(893\) | −0.453483 | −0.0151752 | ||||||||
\(894\) | 24.2377 | 0.810629 | ||||||||
\(895\) | 0.127338 | 0.00425643 | ||||||||
\(896\) | 2.31473 | 0.0773296 | ||||||||
\(897\) | −2.58255 | −0.0862288 | ||||||||
\(898\) | 4.81533 | 0.160690 | ||||||||
\(899\) | −1.83765 | −0.0612892 | ||||||||
\(900\) | −1.01959 | −0.0339863 | ||||||||
\(901\) | 0.557847 | 0.0185846 | ||||||||
\(902\) | 36.4367 | 1.21321 | ||||||||
\(903\) | −38.0639 | −1.26669 | ||||||||
\(904\) | 11.0361 | 0.367057 | ||||||||
\(905\) | 20.3487 | 0.676414 | ||||||||
\(906\) | 17.0524 | 0.566528 | ||||||||
\(907\) | 32.5781 | 1.08174 | 0.540869 | − | 0.841107i | \(-0.318095\pi\) | ||||
0.540869 | + | 0.841107i | \(0.318095\pi\) | |||||||
\(908\) | −28.2941 | −0.938974 | ||||||||
\(909\) | −9.71890 | −0.322355 | ||||||||
\(910\) | 1.34792 | 0.0446832 | ||||||||
\(911\) | −36.2667 | −1.20157 | −0.600785 | − | 0.799410i | \(-0.705145\pi\) | ||||
−0.600785 | + | 0.799410i | \(0.705145\pi\) | |||||||
\(912\) | 2.29194 | 0.0758936 | ||||||||
\(913\) | −6.76373 | −0.223847 | ||||||||
\(914\) | 8.69990 | 0.287767 | ||||||||
\(915\) | −9.42617 | −0.311620 | ||||||||
\(916\) | −14.5510 | −0.480780 | ||||||||
\(917\) | −11.7801 | −0.389013 | ||||||||
\(918\) | −0.788243 | −0.0260159 | ||||||||
\(919\) | 41.2652 | 1.36121 | 0.680607 | − | 0.732649i | \(-0.261716\pi\) | ||||
0.680607 | + | 0.732649i | \(0.261716\pi\) | |||||||
\(920\) | 3.15142 | 0.103899 | ||||||||
\(921\) | −29.2143 | −0.962644 | ||||||||
\(922\) | −19.0132 | −0.626165 | ||||||||
\(923\) | −6.48098 | −0.213324 | ||||||||
\(924\) | −11.3330 | −0.372828 | ||||||||
\(925\) | −9.08644 | −0.298760 | ||||||||
\(926\) | 27.2544 | 0.895637 | ||||||||
\(927\) | 7.92876 | 0.260415 | ||||||||
\(928\) | 0.911191 | 0.0299113 | ||||||||
\(929\) | 37.5042 | 1.23047 | 0.615236 | − | 0.788343i | \(-0.289061\pi\) | ||||
0.615236 | + | 0.788343i | \(0.289061\pi\) | |||||||
\(930\) | 2.83813 | 0.0930659 | ||||||||
\(931\) | −2.67429 | −0.0876464 | ||||||||
\(932\) | 5.80631 | 0.190192 | ||||||||
\(933\) | 28.8256 | 0.943709 | ||||||||
\(934\) | −17.2210 | −0.563488 | ||||||||
\(935\) | 0.484806 | 0.0158549 | ||||||||
\(936\) | −0.593731 | −0.0194067 | ||||||||
\(937\) | 7.29612 | 0.238354 | 0.119177 | − | 0.992873i | \(-0.461974\pi\) | ||||
0.119177 | + | 0.992873i | \(0.461974\pi\) | |||||||
\(938\) | −8.22025 | −0.268401 | ||||||||
\(939\) | 27.3064 | 0.891110 | ||||||||
\(940\) | 0.278443 | 0.00908180 | ||||||||
\(941\) | 28.6884 | 0.935214 | 0.467607 | − | 0.883936i | \(-0.345116\pi\) | ||||
0.467607 | + | 0.883936i | \(0.345116\pi\) | |||||||
\(942\) | 1.99672 | 0.0650567 | ||||||||
\(943\) | −33.0048 | −1.07478 | ||||||||
\(944\) | −2.63264 | −0.0856850 | ||||||||
\(945\) | −13.0936 | −0.425935 | ||||||||
\(946\) | −40.6540 | −1.32177 | ||||||||
\(947\) | 54.3429 | 1.76591 | 0.882953 | − | 0.469461i | \(-0.155552\pi\) | ||||
0.882953 | + | 0.469461i | \(0.155552\pi\) | |||||||
\(948\) | 5.64855 | 0.183456 | ||||||||
\(949\) | 8.01343 | 0.260127 | ||||||||
\(950\) | −1.62864 | −0.0528400 | ||||||||
\(951\) | 18.7831 | 0.609084 | ||||||||
\(952\) | −0.322553 | −0.0104540 | ||||||||
\(953\) | −13.0826 | −0.423787 | −0.211893 | − | 0.977293i | \(-0.567963\pi\) | ||||
−0.211893 | + | 0.977293i | \(0.567963\pi\) | |||||||
\(954\) | −4.08168 | −0.132149 | ||||||||
\(955\) | 5.25976 | 0.170202 | ||||||||
\(956\) | 21.6434 | 0.699998 | ||||||||
\(957\) | −4.46123 | −0.144211 | ||||||||
\(958\) | −37.8840 | −1.22398 | ||||||||
\(959\) | 9.09377 | 0.293653 | ||||||||
\(960\) | −1.40727 | −0.0454195 | ||||||||
\(961\) | −26.9327 | −0.868796 | ||||||||
\(962\) | −5.29126 | −0.170597 | ||||||||
\(963\) | 10.8523 | 0.349710 | ||||||||
\(964\) | −7.24006 | −0.233187 | ||||||||
\(965\) | 25.9563 | 0.835562 | ||||||||
\(966\) | 10.2656 | 0.330289 | ||||||||
\(967\) | −16.5320 | −0.531634 | −0.265817 | − | 0.964024i | \(-0.585642\pi\) | ||||
−0.265817 | + | 0.964024i | \(0.585642\pi\) | |||||||
\(968\) | −1.10415 | −0.0354888 | ||||||||
\(969\) | −0.319377 | −0.0102599 | ||||||||
\(970\) | −3.28753 | −0.105556 | ||||||||
\(971\) | −34.3647 | −1.10281 | −0.551407 | − | 0.834236i | \(-0.685909\pi\) | ||||
−0.551407 | + | 0.834236i | \(0.685909\pi\) | |||||||
\(972\) | 10.0720 | 0.323058 | ||||||||
\(973\) | 39.6393 | 1.27078 | ||||||||
\(974\) | −14.9895 | −0.480296 | ||||||||
\(975\) | −0.819488 | −0.0262446 | ||||||||
\(976\) | 6.69819 | 0.214404 | ||||||||
\(977\) | −7.12105 | −0.227823 | −0.113911 | − | 0.993491i | \(-0.536338\pi\) | ||||
−0.113911 | + | 0.993491i | \(0.536338\pi\) | |||||||
\(978\) | −17.3173 | −0.553745 | ||||||||
\(979\) | −17.9584 | −0.573952 | ||||||||
\(980\) | 1.64204 | 0.0524531 | ||||||||
\(981\) | −3.13873 | −0.100212 | ||||||||
\(982\) | −16.8228 | −0.536837 | ||||||||
\(983\) | −54.9430 | −1.75241 | −0.876205 | − | 0.481939i | \(-0.839933\pi\) | ||||
−0.876205 | + | 0.481939i | \(0.839933\pi\) | |||||||
\(984\) | 14.7384 | 0.469842 | ||||||||
\(985\) | −1.98558 | −0.0632659 | ||||||||
\(986\) | −0.126973 | −0.00404363 | ||||||||
\(987\) | 0.907012 | 0.0288705 | ||||||||
\(988\) | −0.948396 | −0.0301725 | ||||||||
\(989\) | 36.8249 | 1.17096 | ||||||||
\(990\) | −3.54725 | −0.112739 | ||||||||
\(991\) | −36.7894 | −1.16865 | −0.584327 | − | 0.811518i | \(-0.698641\pi\) | ||||
−0.584327 | + | 0.811518i | \(0.698641\pi\) | |||||||
\(992\) | −2.01676 | −0.0640322 | ||||||||
\(993\) | −21.6468 | −0.686940 | ||||||||
\(994\) | 25.7618 | 0.817113 | ||||||||
\(995\) | −18.6861 | −0.592389 | ||||||||
\(996\) | −2.73588 | −0.0866896 | ||||||||
\(997\) | 26.0627 | 0.825413 | 0.412706 | − | 0.910864i | \(-0.364584\pi\) | ||||
0.412706 | + | 0.910864i | \(0.364584\pi\) | |||||||
\(998\) | −5.83436 | −0.184683 | ||||||||
\(999\) | 51.3988 | 1.62619 |
(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 | 4010.2.a.k.1.12 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.12 | ✓ | 15 | 1.1 | even | 1 | trivial |