Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.803961\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.803961 | 0.568486 | 0.284243 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284243 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.35365 | −0.676824 | ||||||||
\(5\) | −0.343335 | −0.153544 | −0.0767720 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767720 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.69620 | −0.953251 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.276028 | −0.0872876 | ||||||||
\(11\) | −4.04620 | −1.21997 | −0.609987 | − | 0.792411i | \(-0.708825\pi\) | ||||
−0.609987 | + | 0.792411i | \(0.708825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07964 | −1.40884 | −0.704419 | − | 0.709784i | \(-0.748792\pi\) | ||||
−0.704419 | + | 0.709784i | \(0.748792\pi\) | |||||||
\(14\) | 0.803961 | 0.214867 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.539656 | 0.134914 | ||||||||
\(17\) | 3.48245 | 0.844617 | 0.422309 | − | 0.906452i | \(-0.361220\pi\) | ||||
0.422309 | + | 0.906452i | \(0.361220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.23803 | −0.513439 | −0.256720 | − | 0.966486i | \(-0.582642\pi\) | ||||
−0.256720 | + | 0.966486i | \(0.582642\pi\) | |||||||
\(20\) | 0.464755 | 0.103922 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.25298 | −0.693538 | ||||||||
\(23\) | 2.35865 | 0.491813 | 0.245906 | − | 0.969294i | \(-0.420914\pi\) | ||||
0.245906 | + | 0.969294i | \(0.420914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88212 | −0.976424 | ||||||||
\(26\) | −4.08383 | −0.800905 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.35365 | −0.255815 | ||||||||
\(29\) | −9.24369 | −1.71651 | −0.858255 | − | 0.513223i | \(-0.828451\pi\) | ||||
−0.858255 | + | 0.513223i | \(0.828451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.54357 | 0.995654 | 0.497827 | − | 0.867276i | \(-0.334131\pi\) | ||||
0.497827 | + | 0.867276i | \(0.334131\pi\) | |||||||
\(32\) | 5.82626 | 1.02995 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.79975 | 0.480153 | ||||||||
\(35\) | −0.343335 | −0.0580342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.87348 | 0.965594 | 0.482797 | − | 0.875732i | \(-0.339621\pi\) | ||||
0.482797 | + | 0.875732i | \(0.339621\pi\) | |||||||
\(38\) | −1.79929 | −0.291883 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.925700 | 0.146366 | ||||||||
\(41\) | 1.66919 | 0.260683 | 0.130342 | − | 0.991469i | \(-0.458393\pi\) | ||||
0.130342 | + | 0.991469i | \(0.458393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3740 | −1.58203 | −0.791013 | − | 0.611799i | \(-0.790446\pi\) | ||||
−0.791013 | + | 0.611799i | \(0.790446\pi\) | |||||||
\(44\) | 5.47712 | 0.825707 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.89626 | 0.279589 | ||||||||
\(47\) | 11.9067 | 1.73677 | 0.868387 | − | 0.495887i | \(-0.165157\pi\) | ||||
0.868387 | + | 0.495887i | \(0.165157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.92503 | −0.555083 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.87604 | 0.953535 | ||||||||
\(53\) | −12.9408 | −1.77756 | −0.888779 | − | 0.458336i | \(-0.848445\pi\) | ||||
−0.888779 | + | 0.458336i | \(0.848445\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38920 | 0.187320 | ||||||||
\(56\) | −2.69620 | −0.360295 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.43157 | −0.975812 | ||||||||
\(59\) | −7.20507 | −0.938020 | −0.469010 | − | 0.883193i | \(-0.655389\pi\) | ||||
−0.469010 | + | 0.883193i | \(0.655389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3500 | −1.32519 | −0.662593 | − | 0.748980i | \(-0.730544\pi\) | ||||
−0.662593 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(62\) | 4.45681 | 0.566015 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.60477 | 0.450597 | ||||||||
\(65\) | 1.74402 | 0.216319 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.97489 | −0.607779 | −0.303890 | − | 0.952707i | \(-0.598285\pi\) | ||||
−0.303890 | + | 0.952707i | \(0.598285\pi\) | |||||||
\(68\) | −4.71400 | −0.571657 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.276028 | −0.0329916 | ||||||||
\(71\) | −8.55324 | −1.01508 | −0.507541 | − | 0.861628i | \(-0.669445\pi\) | ||||
−0.507541 | + | 0.861628i | \(0.669445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9142 | 1.27741 | 0.638703 | − | 0.769454i | \(-0.279471\pi\) | ||||
0.638703 | + | 0.769454i | \(0.279471\pi\) | |||||||
\(74\) | 4.72205 | 0.548927 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.02950 | 0.347508 | ||||||||
\(77\) | −4.04620 | −0.461107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8472 | 1.78295 | 0.891474 | − | 0.453072i | \(-0.149672\pi\) | ||||
0.891474 | + | 0.453072i | \(0.149672\pi\) | |||||||
\(80\) | −0.185283 | −0.0207153 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.34196 | 0.148195 | ||||||||
\(83\) | 11.6255 | 1.27606 | 0.638031 | − | 0.770010i | \(-0.279749\pi\) | ||||
0.638031 | + | 0.770010i | \(0.279749\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19565 | −0.129686 | ||||||||
\(86\) | −8.34032 | −0.899360 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.9094 | 1.16294 | ||||||||
\(89\) | 0.366424 | 0.0388408 | 0.0194204 | − | 0.999811i | \(-0.493818\pi\) | ||||
0.0194204 | + | 0.999811i | \(0.493818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.07964 | −0.532491 | ||||||||
\(92\) | −3.19278 | −0.332871 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.57253 | 0.987332 | ||||||||
\(95\) | 0.768394 | 0.0788356 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.75160 | −0.787056 | −0.393528 | − | 0.919313i | \(-0.628746\pi\) | ||||
−0.393528 | + | 0.919313i | \(0.628746\pi\) | |||||||
\(98\) | 0.803961 | 0.0812123 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.60867 | 0.660867 | ||||||||
\(101\) | 13.1619 | 1.30966 | 0.654831 | − | 0.755776i | \(-0.272740\pi\) | ||||
0.654831 | + | 0.755776i | \(0.272740\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2020 | −1.00523 | −0.502616 | − | 0.864510i | \(-0.667629\pi\) | ||||
−0.502616 | + | 0.864510i | \(0.667629\pi\) | |||||||
\(104\) | 13.6957 | 1.34298 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4039 | −1.01052 | ||||||||
\(107\) | 5.75880 | 0.556724 | 0.278362 | − | 0.960476i | \(-0.410208\pi\) | ||||
0.278362 | + | 0.960476i | \(0.410208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3606 | 0.992362 | 0.496181 | − | 0.868219i | \(-0.334735\pi\) | ||||
0.496181 | + | 0.868219i | \(0.334735\pi\) | |||||||
\(110\) | 1.11686 | 0.106489 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.539656 | 0.0509927 | ||||||||
\(113\) | 12.1901 | 1.14675 | 0.573376 | − | 0.819292i | \(-0.305633\pi\) | ||||
0.573376 | + | 0.819292i | \(0.305633\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.809807 | −0.0755149 | ||||||||
\(116\) | 12.5127 | 1.16178 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.79259 | −0.533251 | ||||||||
\(119\) | 3.48245 | 0.319235 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37170 | 0.488337 | ||||||||
\(122\) | −8.32101 | −0.753349 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.50403 | −0.673882 | ||||||||
\(125\) | 3.39288 | 0.303468 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −8.75443 | −0.773790 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.40212 | 0.122974 | ||||||||
\(131\) | 11.7624 | 1.02768 | 0.513842 | − | 0.857885i | \(-0.328222\pi\) | ||||
0.513842 | + | 0.857885i | \(0.328222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.23803 | −0.194062 | ||||||||
\(134\) | −3.99961 | −0.345514 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.38937 | −0.805132 | ||||||||
\(137\) | 22.2429 | 1.90034 | 0.950169 | − | 0.311737i | \(-0.100911\pi\) | ||||
0.950169 | + | 0.311737i | \(0.100911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.45596 | 0.377950 | 0.188975 | − | 0.981982i | \(-0.439484\pi\) | ||||
0.188975 | + | 0.981982i | \(0.439484\pi\) | |||||||
\(140\) | 0.464755 | 0.0392789 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.87646 | −0.577060 | ||||||||
\(143\) | 20.5532 | 1.71875 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.17368 | 0.263560 | ||||||||
\(146\) | 8.77455 | 0.726187 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.95062 | −0.653537 | ||||||||
\(149\) | 18.9721 | 1.55425 | 0.777126 | − | 0.629345i | \(-0.216677\pi\) | ||||
0.777126 | + | 0.629345i | \(0.216677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7144 | −0.871925 | −0.435962 | − | 0.899965i | \(-0.643592\pi\) | ||||
−0.435962 | + | 0.899965i | \(0.643592\pi\) | |||||||
\(152\) | 6.03418 | 0.489436 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.25298 | −0.262133 | ||||||||
\(155\) | −1.90330 | −0.152877 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4000 | 0.909817 | 0.454909 | − | 0.890538i | \(-0.349672\pi\) | ||||
0.454909 | + | 0.890538i | \(0.349672\pi\) | |||||||
\(158\) | 12.7405 | 1.01358 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00036 | −0.158142 | ||||||||
\(161\) | 2.35865 | 0.185888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.3009 | −1.43344 | −0.716720 | − | 0.697361i | \(-0.754357\pi\) | ||||
−0.716720 | + | 0.697361i | \(0.754357\pi\) | |||||||
\(164\) | −2.25949 | −0.176437 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.34643 | 0.725424 | ||||||||
\(167\) | −13.7796 | −1.06630 | −0.533150 | − | 0.846020i | \(-0.678992\pi\) | ||||
−0.533150 | + | 0.846020i | \(0.678992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8027 | 0.984825 | ||||||||
\(170\) | −0.961252 | −0.0737246 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.0428 | 1.07075 | ||||||||
\(173\) | 23.7433 | 1.80517 | 0.902586 | − | 0.430510i | \(-0.141666\pi\) | ||||
0.902586 | + | 0.430510i | \(0.141666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.88212 | −0.369054 | ||||||||
\(176\) | −2.18356 | −0.164592 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.294590 | 0.0220805 | ||||||||
\(179\) | −6.69909 | −0.500714 | −0.250357 | − | 0.968154i | \(-0.580548\pi\) | ||||
−0.250357 | + | 0.968154i | \(0.580548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.85446 | 0.435159 | 0.217579 | − | 0.976043i | \(-0.430184\pi\) | ||||
0.217579 | + | 0.976043i | \(0.430184\pi\) | |||||||
\(182\) | −4.08383 | −0.302714 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.35940 | −0.468821 | ||||||||
\(185\) | −2.01657 | −0.148261 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0907 | −1.03041 | ||||||||
\(188\) | −16.1175 | −1.17549 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.617759 | 0.0448169 | ||||||||
\(191\) | −6.96386 | −0.503887 | −0.251944 | − | 0.967742i | \(-0.581070\pi\) | ||||
−0.251944 | + | 0.967742i | \(0.581070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.33351 | −0.311933 | −0.155966 | − | 0.987762i | \(-0.549849\pi\) | ||||
−0.155966 | + | 0.987762i | \(0.549849\pi\) | |||||||
\(194\) | −6.23198 | −0.447430 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.35365 | −0.0966891 | ||||||||
\(197\) | −6.88472 | −0.490516 | −0.245258 | − | 0.969458i | \(-0.578873\pi\) | ||||
−0.245258 | + | 0.969458i | \(0.578873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.03022 | −0.427471 | −0.213735 | − | 0.976892i | \(-0.568563\pi\) | ||||
−0.213735 | + | 0.976892i | \(0.568563\pi\) | |||||||
\(200\) | 13.1632 | 0.930777 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5817 | 0.744524 | ||||||||
\(203\) | −9.24369 | −0.648780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.573091 | −0.0400264 | ||||||||
\(206\) | −8.20199 | −0.571460 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.74126 | −0.190072 | ||||||||
\(209\) | 9.05551 | 0.626383 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.7052 | −1.28772 | −0.643858 | − | 0.765145i | \(-0.722667\pi\) | ||||
−0.643858 | + | 0.765145i | \(0.722667\pi\) | |||||||
\(212\) | 17.5173 | 1.20309 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.62985 | 0.316490 | ||||||||
\(215\) | 3.56177 | 0.242911 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.54357 | 0.376322 | ||||||||
\(218\) | 8.32948 | 0.564144 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.88049 | −0.126782 | ||||||||
\(221\) | −17.6896 | −1.18993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.6279 | −0.711696 | −0.355848 | − | 0.934544i | \(-0.615808\pi\) | ||||
−0.355848 | + | 0.934544i | \(0.615808\pi\) | |||||||
\(224\) | 5.82626 | 0.389284 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.80039 | 0.651912 | ||||||||
\(227\) | 2.03230 | 0.134888 | 0.0674442 | − | 0.997723i | \(-0.478516\pi\) | ||||
0.0674442 | + | 0.997723i | \(0.478516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7071 | 0.971873 | 0.485937 | − | 0.873994i | \(-0.338479\pi\) | ||||
0.485937 | + | 0.873994i | \(0.338479\pi\) | |||||||
\(230\) | −0.651053 | −0.0429292 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.9228 | 1.63627 | ||||||||
\(233\) | 18.8646 | 1.23586 | 0.617932 | − | 0.786232i | \(-0.287971\pi\) | ||||
0.617932 | + | 0.786232i | \(0.287971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.08799 | −0.266671 | ||||||||
\(236\) | 9.75313 | 0.634874 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.79975 | 0.181481 | ||||||||
\(239\) | −3.80322 | −0.246010 | −0.123005 | − | 0.992406i | \(-0.539253\pi\) | ||||
−0.123005 | + | 0.992406i | \(0.539253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.5196 | −1.51503 | −0.757515 | − | 0.652818i | \(-0.773587\pi\) | ||||
−0.757515 | + | 0.652818i | \(0.773587\pi\) | |||||||
\(242\) | 4.31864 | 0.277613 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.0103 | 0.896917 | ||||||||
\(245\) | −0.343335 | −0.0219349 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3684 | 0.723353 | ||||||||
\(248\) | −14.9466 | −0.949108 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.72774 | 0.172517 | ||||||||
\(251\) | 24.4633 | 1.54411 | 0.772056 | − | 0.635555i | \(-0.219228\pi\) | ||||
0.772056 | + | 0.635555i | \(0.219228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.54357 | −0.599999 | ||||||||
\(254\) | 0.803961 | 0.0504450 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.2478 | −0.890485 | ||||||||
\(257\) | 1.68358 | 0.105019 | 0.0525096 | − | 0.998620i | \(-0.483278\pi\) | ||||
0.0525096 | + | 0.998620i | \(0.483278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.87348 | 0.364960 | ||||||||
\(260\) | −2.36078 | −0.146410 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.45649 | 0.584224 | ||||||||
\(263\) | 22.2555 | 1.37233 | 0.686166 | − | 0.727445i | \(-0.259292\pi\) | ||||
0.686166 | + | 0.727445i | \(0.259292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.44303 | 0.272933 | ||||||||
\(266\) | −1.79929 | −0.110321 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.73425 | 0.411360 | ||||||||
\(269\) | −10.4180 | −0.635195 | −0.317597 | − | 0.948226i | \(-0.602876\pi\) | ||||
−0.317597 | + | 0.948226i | \(0.602876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90437 | 0.176428 | 0.0882141 | − | 0.996102i | \(-0.471884\pi\) | ||||
0.0882141 | + | 0.996102i | \(0.471884\pi\) | |||||||
\(272\) | 1.87932 | 0.113951 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8824 | 1.08031 | ||||||||
\(275\) | 19.7540 | 1.19121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7288 | 0.945054 | 0.472527 | − | 0.881316i | \(-0.343342\pi\) | ||||
0.472527 | + | 0.881316i | \(0.343342\pi\) | |||||||
\(278\) | 3.58242 | 0.214859 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.925700 | 0.0553211 | ||||||||
\(281\) | 27.1991 | 1.62256 | 0.811280 | − | 0.584657i | \(-0.198771\pi\) | ||||
0.811280 | + | 0.584657i | \(0.198771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1363 | 0.661982 | 0.330991 | − | 0.943634i | \(-0.392617\pi\) | ||||
0.330991 | + | 0.943634i | \(0.392617\pi\) | |||||||
\(284\) | 11.5781 | 0.687032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.5240 | 0.977083 | ||||||||
\(287\) | 1.66919 | 0.0985290 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.87257 | −0.286622 | ||||||||
\(290\) | 2.55152 | 0.149830 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7739 | −0.864578 | ||||||||
\(293\) | −22.3106 | −1.30340 | −0.651700 | − | 0.758477i | \(-0.725944\pi\) | ||||
−0.651700 | + | 0.758477i | \(0.725944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.47375 | 0.144027 | ||||||||
\(296\) | −15.8361 | −0.920454 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2528 | 0.883570 | ||||||||
\(299\) | −11.9811 | −0.692885 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3740 | −0.597950 | ||||||||
\(302\) | −8.61395 | −0.495677 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.20777 | −0.0692702 | ||||||||
\(305\) | 3.55353 | 0.203474 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8361 | 1.18918 | 0.594588 | − | 0.804030i | \(-0.297315\pi\) | ||||
0.594588 | + | 0.804030i | \(0.297315\pi\) | |||||||
\(308\) | 5.47712 | 0.312088 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.53018 | −0.0869083 | ||||||||
\(311\) | −7.05946 | −0.400305 | −0.200153 | − | 0.979765i | \(-0.564144\pi\) | ||||
−0.200153 | + | 0.979765i | \(0.564144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.81011 | 0.497977 | 0.248988 | − | 0.968506i | \(-0.419902\pi\) | ||||
0.248988 | + | 0.968506i | \(0.419902\pi\) | |||||||
\(314\) | 9.16513 | 0.517218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.4515 | −1.20674 | ||||||||
\(317\) | 9.91942 | 0.557130 | 0.278565 | − | 0.960417i | \(-0.410141\pi\) | ||||
0.278565 | + | 0.960417i | \(0.410141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.4018 | 2.09410 | ||||||||
\(320\) | −1.23764 | −0.0691864 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.89626 | 0.105675 | ||||||||
\(323\) | −7.79382 | −0.433660 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.7994 | 1.37562 | ||||||||
\(326\) | −14.7132 | −0.814890 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.50046 | −0.248497 | ||||||||
\(329\) | 11.9067 | 0.656439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.64788 | −0.255471 | −0.127735 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127735 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(332\) | −15.7368 | −0.863669 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.0783 | −0.606177 | ||||||||
\(335\) | 1.70805 | 0.0933209 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.2867 | 1.10509 | 0.552545 | − | 0.833483i | \(-0.313657\pi\) | ||||
0.552545 | + | 0.833483i | \(0.313657\pi\) | |||||||
\(338\) | 10.2929 | 0.559859 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.61848 | 0.0877745 | ||||||||
\(341\) | −22.4304 | −1.21467 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 27.9705 | 1.50807 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.0887 | 1.02621 | ||||||||
\(347\) | 7.49407 | 0.402303 | 0.201151 | − | 0.979560i | \(-0.435532\pi\) | ||||
0.201151 | + | 0.979560i | \(0.435532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.3002 | −1.72899 | −0.864496 | − | 0.502640i | \(-0.832362\pi\) | ||||
−0.864496 | + | 0.502640i | \(0.832362\pi\) | |||||||
\(350\) | −3.92503 | −0.209802 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.5742 | −1.25651 | ||||||||
\(353\) | −20.5000 | −1.09110 | −0.545552 | − | 0.838077i | \(-0.683680\pi\) | ||||
−0.545552 | + | 0.838077i | \(0.683680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.93662 | 0.155860 | ||||||||
\(356\) | −0.496009 | −0.0262884 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.38581 | −0.284649 | ||||||||
\(359\) | 24.6060 | 1.29866 | 0.649328 | − | 0.760508i | \(-0.275050\pi\) | ||||
0.649328 | + | 0.760508i | \(0.275050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9912 | −0.736380 | ||||||||
\(362\) | 4.70675 | 0.247382 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.87604 | 0.360402 | ||||||||
\(365\) | −3.74721 | −0.196138 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.9470 | 0.832429 | 0.416214 | − | 0.909267i | \(-0.363357\pi\) | ||||
0.416214 | + | 0.909267i | \(0.363357\pi\) | |||||||
\(368\) | 1.27286 | 0.0663525 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.62124 | −0.0842845 | ||||||||
\(371\) | −12.9408 | −0.671854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.0230 | −1.45098 | −0.725488 | − | 0.688235i | \(-0.758386\pi\) | ||||
−0.725488 | + | 0.688235i | \(0.758386\pi\) | |||||||
\(374\) | −11.3283 | −0.585774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.1029 | −1.65558 | ||||||||
\(377\) | 46.9546 | 2.41829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1526 | 1.65157 | 0.825783 | − | 0.563987i | \(-0.190733\pi\) | ||||
0.825783 | + | 0.563987i | \(0.190733\pi\) | |||||||
\(380\) | −1.04013 | −0.0533578 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.59867 | −0.286453 | ||||||||
\(383\) | 21.9187 | 1.11999 | 0.559996 | − | 0.828495i | \(-0.310803\pi\) | ||||
0.559996 | + | 0.828495i | \(0.310803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.38920 | 0.0708002 | ||||||||
\(386\) | −3.48397 | −0.177329 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.4929 | 0.532698 | ||||||||
\(389\) | −0.259292 | −0.0131466 | −0.00657331 | − | 0.999978i | \(-0.502092\pi\) | ||||
−0.00657331 | + | 0.999978i | \(0.502092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.21387 | 0.415394 | ||||||||
\(392\) | −2.69620 | −0.136179 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.53504 | −0.278852 | ||||||||
\(395\) | −5.44089 | −0.273761 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.76662 | 0.439984 | 0.219992 | − | 0.975502i | \(-0.429397\pi\) | ||||
0.219992 | + | 0.975502i | \(0.429397\pi\) | |||||||
\(398\) | −4.84805 | −0.243011 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.63467 | −0.131733 | ||||||||
\(401\) | 12.3572 | 0.617091 | 0.308546 | − | 0.951210i | \(-0.400158\pi\) | ||||
0.308546 | + | 0.951210i | \(0.400158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.1593 | −1.40272 | ||||||||
\(404\) | −17.8166 | −0.886410 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.43157 | −0.368822 | ||||||||
\(407\) | −23.7653 | −1.17800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7862 | 0.533346 | 0.266673 | − | 0.963787i | \(-0.414076\pi\) | ||||
0.266673 | + | 0.963787i | \(0.414076\pi\) | |||||||
\(410\) | −0.460742 | −0.0227544 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.8099 | 0.680365 | ||||||||
\(413\) | −7.20507 | −0.354538 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.99143 | −0.195932 | ||||||||
\(416\) | −29.5953 | −1.45103 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.28027 | 0.356090 | ||||||||
\(419\) | 17.4411 | 0.852054 | 0.426027 | − | 0.904710i | \(-0.359913\pi\) | ||||
0.426027 | + | 0.904710i | \(0.359913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.2522 | −1.96177 | −0.980886 | − | 0.194583i | \(-0.937665\pi\) | ||||
−0.980886 | + | 0.194583i | \(0.937665\pi\) | |||||||
\(422\) | −15.0382 | −0.732048 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 34.8910 | 1.69446 | ||||||||
\(425\) | −17.0017 | −0.824705 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3500 | −0.500873 | ||||||||
\(428\) | −7.79538 | −0.376804 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.86352 | 0.138091 | ||||||||
\(431\) | −5.00922 | −0.241286 | −0.120643 | − | 0.992696i | \(-0.538496\pi\) | ||||
−0.120643 | + | 0.992696i | \(0.538496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.9224 | 1.29381 | 0.646904 | − | 0.762571i | \(-0.276063\pi\) | ||||
0.646904 | + | 0.762571i | \(0.276063\pi\) | |||||||
\(434\) | 4.45681 | 0.213934 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0245 | −0.671654 | ||||||||
\(437\) | −5.27873 | −0.252516 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.1663 | −1.43976 | −0.719879 | − | 0.694099i | \(-0.755803\pi\) | ||||
−0.719879 | + | 0.694099i | \(0.755803\pi\) | |||||||
\(440\) | −3.74556 | −0.178563 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.2217 | −0.676458 | ||||||||
\(443\) | −30.6696 | −1.45716 | −0.728579 | − | 0.684962i | \(-0.759819\pi\) | ||||
−0.728579 | + | 0.684962i | \(0.759819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.125806 | −0.00596378 | ||||||||
\(446\) | −8.54440 | −0.404589 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.60477 | 0.170309 | ||||||||
\(449\) | 12.2072 | 0.576093 | 0.288047 | − | 0.957616i | \(-0.406994\pi\) | ||||
0.288047 | + | 0.957616i | \(0.406994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.75386 | −0.318027 | ||||||||
\(452\) | −16.5012 | −0.776149 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.63389 | 0.0766822 | ||||||||
\(455\) | 1.74402 | 0.0817608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.4700 | −1.51888 | −0.759442 | − | 0.650575i | \(-0.774528\pi\) | ||||
−0.759442 | + | 0.650575i | \(0.774528\pi\) | |||||||
\(458\) | 11.8239 | 0.552496 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.09619 | 0.0511103 | ||||||||
\(461\) | 12.1968 | 0.568060 | 0.284030 | − | 0.958815i | \(-0.408329\pi\) | ||||
0.284030 | + | 0.958815i | \(0.408329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.1369 | 1.63295 | 0.816475 | − | 0.577380i | \(-0.195925\pi\) | ||||
0.816475 | + | 0.577380i | \(0.195925\pi\) | |||||||
\(464\) | −4.98842 | −0.231582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.1664 | 0.702571 | ||||||||
\(467\) | 17.0341 | 0.788246 | 0.394123 | − | 0.919058i | \(-0.371048\pi\) | ||||
0.394123 | + | 0.919058i | \(0.371048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.97489 | −0.229719 | ||||||||
\(470\) | −3.28659 | −0.151599 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.4263 | 0.894169 | ||||||||
\(473\) | 41.9754 | 1.93003 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.9263 | 0.501335 | ||||||||
\(476\) | −4.71400 | −0.216066 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.05764 | −0.139853 | ||||||||
\(479\) | −12.1072 | −0.553190 | −0.276595 | − | 0.960987i | \(-0.589206\pi\) | ||||
−0.276595 | + | 0.960987i | \(0.589206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.8352 | −1.36037 | ||||||||
\(482\) | −18.9088 | −0.861273 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.27139 | −0.330518 | ||||||||
\(485\) | 2.66140 | 0.120848 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5980 | 0.706812 | 0.353406 | − | 0.935470i | \(-0.385023\pi\) | ||||
0.353406 | + | 0.935470i | \(0.385023\pi\) | |||||||
\(488\) | 27.9057 | 1.26323 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.276028 | −0.0124697 | ||||||||
\(491\) | −8.87764 | −0.400642 | −0.200321 | − | 0.979730i | \(-0.564199\pi\) | ||||
−0.200321 | + | 0.979730i | \(0.564199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.1907 | −1.44979 | ||||||||
\(494\) | 9.13973 | 0.411216 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.99162 | 0.134328 | ||||||||
\(497\) | −8.55324 | −0.383665 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.3071 | 0.685241 | 0.342620 | − | 0.939474i | \(-0.388686\pi\) | ||||
0.342620 | + | 0.939474i | \(0.388686\pi\) | |||||||
\(500\) | −4.59276 | −0.205394 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.6676 | 0.877806 | ||||||||
\(503\) | 14.5352 | 0.648091 | 0.324045 | − | 0.946042i | \(-0.394957\pi\) | ||||
0.324045 | + | 0.946042i | \(0.394957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.51895 | −0.201091 | ||||||||
\(506\) | −7.67265 | −0.341091 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.35365 | −0.0600584 | ||||||||
\(509\) | 29.5667 | 1.31052 | 0.655260 | − | 0.755403i | \(-0.272559\pi\) | ||||
0.655260 | + | 0.755403i | \(0.272559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9142 | 0.482814 | ||||||||
\(512\) | 6.05422 | 0.267561 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.35354 | 0.0597019 | ||||||||
\(515\) | 3.50270 | 0.154347 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.1769 | −2.11882 | ||||||||
\(518\) | 4.72205 | 0.207475 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.70222 | −0.206206 | ||||||||
\(521\) | 14.6876 | 0.643478 | 0.321739 | − | 0.946828i | \(-0.395733\pi\) | ||||
0.321739 | + | 0.946828i | \(0.395733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.6693 | 0.728897 | 0.364448 | − | 0.931224i | \(-0.381258\pi\) | ||||
0.364448 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(524\) | −15.9221 | −0.695561 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8925 | 0.780152 | ||||||||
\(527\) | 19.3052 | 0.840946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.4368 | −0.758120 | ||||||||
\(530\) | 3.57202 | 0.155159 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.02950 | 0.131346 | ||||||||
\(533\) | −8.47887 | −0.367261 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.97720 | −0.0854817 | ||||||||
\(536\) | 13.4133 | 0.579366 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.37563 | −0.361099 | ||||||||
\(539\) | −4.04620 | −0.174282 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00282 | −0.387061 | −0.193531 | − | 0.981094i | \(-0.561994\pi\) | ||||
−0.193531 | + | 0.981094i | \(0.561994\pi\) | |||||||
\(542\) | 2.33500 | 0.100297 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.2896 | 0.869911 | ||||||||
\(545\) | −3.55714 | −0.152371 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5632 | 1.47782 | 0.738909 | − | 0.673805i | \(-0.235341\pi\) | ||||
0.738909 | + | 0.673805i | \(0.235341\pi\) | |||||||
\(548\) | −30.1090 | −1.28619 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.8815 | 0.677187 | ||||||||
\(551\) | 20.6877 | 0.881324 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.8472 | 0.673891 | ||||||||
\(554\) | 12.6454 | 0.537250 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.03180 | −0.255805 | ||||||||
\(557\) | −5.54071 | −0.234767 | −0.117384 | − | 0.993087i | \(-0.537451\pi\) | ||||
−0.117384 | + | 0.993087i | \(0.537451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.6964 | 2.22882 | ||||||||
\(560\) | −0.185283 | −0.00782963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.8670 | 0.922403 | ||||||||
\(563\) | 32.8794 | 1.38570 | 0.692852 | − | 0.721080i | \(-0.256354\pi\) | ||||
0.692852 | + | 0.721080i | \(0.256354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.18530 | −0.176077 | ||||||||
\(566\) | 8.95311 | 0.376327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.0612 | 0.967628 | ||||||||
\(569\) | −39.4015 | −1.65180 | −0.825898 | − | 0.563819i | \(-0.809331\pi\) | ||||
−0.825898 | + | 0.563819i | \(0.809331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.97776 | −0.375707 | −0.187854 | − | 0.982197i | \(-0.560153\pi\) | ||||
−0.187854 | + | 0.982197i | \(0.560153\pi\) | |||||||
\(572\) | −27.8218 | −1.16329 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.34196 | 0.0560124 | ||||||||
\(575\) | −11.5152 | −0.480218 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6596 | 1.23474 | 0.617372 | − | 0.786671i | \(-0.288197\pi\) | ||||
0.617372 | + | 0.786671i | \(0.288197\pi\) | |||||||
\(578\) | −3.91736 | −0.162941 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.29605 | −0.178384 | ||||||||
\(581\) | 11.6255 | 0.482306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.3611 | 2.16857 | ||||||||
\(584\) | −29.4268 | −1.21769 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.9369 | −0.740964 | ||||||||
\(587\) | −24.2422 | −1.00058 | −0.500292 | − | 0.865857i | \(-0.666774\pi\) | ||||
−0.500292 | + | 0.865857i | \(0.666774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4067 | −0.511208 | ||||||||
\(590\) | 1.98880 | 0.0818776 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.16966 | 0.130272 | ||||||||
\(593\) | −4.03464 | −0.165683 | −0.0828413 | − | 0.996563i | \(-0.526399\pi\) | ||||
−0.0828413 | + | 0.996563i | \(0.526399\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.19565 | −0.0490167 | ||||||||
\(596\) | −25.6815 | −1.05195 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.63233 | −0.393895 | ||||||||
\(599\) | −13.9844 | −0.571386 | −0.285693 | − | 0.958321i | \(-0.592224\pi\) | ||||
−0.285693 | + | 0.958321i | \(0.592224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.49583 | 0.101807 | 0.0509034 | − | 0.998704i | \(-0.483790\pi\) | ||||
0.0509034 | + | 0.998704i | \(0.483790\pi\) | |||||||
\(602\) | −8.34032 | −0.339926 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.5035 | 0.590139 | ||||||||
\(605\) | −1.84429 | −0.0749812 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.0017 | −1.25832 | −0.629160 | − | 0.777276i | \(-0.716601\pi\) | ||||
−0.629160 | + | 0.777276i | \(0.716601\pi\) | |||||||
\(608\) | −13.0394 | −0.528816 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.85689 | 0.115672 | ||||||||
\(611\) | −60.4818 | −2.44683 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.1533 | 0.652424 | 0.326212 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326212 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(614\) | 16.7514 | 0.676030 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9094 | 0.439550 | ||||||||
\(617\) | 28.2570 | 1.13759 | 0.568793 | − | 0.822481i | \(-0.307411\pi\) | ||||
0.568793 | + | 0.822481i | \(0.307411\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.17631 | 0.328634 | 0.164317 | − | 0.986408i | \(-0.447458\pi\) | ||||
0.164317 | + | 0.986408i | \(0.447458\pi\) | |||||||
\(620\) | 2.57640 | 0.103471 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.67553 | −0.227568 | ||||||||
\(623\) | 0.366424 | 0.0146805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2457 | 0.929828 | ||||||||
\(626\) | 7.08298 | 0.283093 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.4315 | −0.615786 | ||||||||
\(629\) | 20.4541 | 0.815558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.89122 | −0.194716 | −0.0973582 | − | 0.995249i | \(-0.531039\pi\) | ||||
−0.0973582 | + | 0.995249i | \(0.531039\pi\) | |||||||
\(632\) | −42.7272 | −1.69960 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.97483 | 0.316721 | ||||||||
\(635\) | −0.343335 | −0.0136248 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.07964 | −0.201263 | ||||||||
\(638\) | 30.0696 | 1.19047 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00570 | 0.118811 | ||||||||
\(641\) | 25.5390 | 1.00873 | 0.504364 | − | 0.863491i | \(-0.331727\pi\) | ||||
0.504364 | + | 0.863491i | \(0.331727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.19858 | −0.0472675 | −0.0236338 | − | 0.999721i | \(-0.507524\pi\) | ||||
−0.0236338 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(644\) | −3.19278 | −0.125813 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.26592 | −0.246529 | ||||||||
\(647\) | 18.5349 | 0.728684 | 0.364342 | − | 0.931265i | \(-0.381294\pi\) | ||||
0.364342 | + | 0.931265i | \(0.381294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.1531 | 1.14436 | ||||||||
\(650\) | 19.9377 | 0.782023 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.7730 | 0.970186 | ||||||||
\(653\) | 17.4806 | 0.684070 | 0.342035 | − | 0.939687i | \(-0.388884\pi\) | ||||
0.342035 | + | 0.939687i | \(0.388884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.03844 | −0.157795 | ||||||||
\(656\) | 0.900788 | 0.0351699 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.57253 | 0.373176 | ||||||||
\(659\) | −14.2329 | −0.554433 | −0.277217 | − | 0.960807i | \(-0.589412\pi\) | ||||
−0.277217 | + | 0.960807i | \(0.589412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.6188 | 1.61878 | 0.809392 | − | 0.587269i | \(-0.199797\pi\) | ||||
0.809392 | + | 0.587269i | \(0.199797\pi\) | |||||||
\(662\) | −3.73671 | −0.145231 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.3446 | −1.21641 | ||||||||
\(665\) | 0.768394 | 0.0297970 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.8027 | −0.844202 | ||||||||
\(668\) | 18.6528 | 0.721698 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.37321 | 0.0530516 | ||||||||
\(671\) | 41.8782 | 1.61669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.84024 | −0.302219 | −0.151110 | − | 0.988517i | \(-0.548285\pi\) | ||||
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(674\) | 16.3097 | 0.628228 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.3304 | −0.666553 | ||||||||
\(677\) | −10.4000 | −0.399704 | −0.199852 | − | 0.979826i | \(-0.564046\pi\) | ||||
−0.199852 | + | 0.979826i | \(0.564046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.75160 | −0.297479 | ||||||||
\(680\) | 3.22370 | 0.123623 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.0331 | −0.690524 | ||||||||
\(683\) | −30.2573 | −1.15776 | −0.578882 | − | 0.815412i | \(-0.696511\pi\) | ||||
−0.578882 | + | 0.815412i | \(0.696511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.63676 | −0.291786 | ||||||||
\(686\) | 0.803961 | 0.0306954 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.59842 | −0.213438 | ||||||||
\(689\) | 65.7347 | 2.50429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.7198 | −0.902343 | −0.451172 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451172 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(692\) | −32.1401 | −1.22178 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.02494 | 0.228704 | ||||||||
\(695\) | −1.52989 | −0.0580319 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.81286 | 0.220178 | ||||||||
\(698\) | −25.9681 | −0.982907 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.60867 | 0.249784 | ||||||||
\(701\) | 33.5878 | 1.26859 | 0.634297 | − | 0.773090i | \(-0.281290\pi\) | ||||
0.634297 | + | 0.773090i | \(0.281290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.1450 | −0.495774 | ||||||||
\(704\) | −14.5856 | −0.549716 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.4812 | −0.620277 | ||||||||
\(707\) | 13.1619 | 0.495005 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.9016 | −1.04787 | −0.523933 | − | 0.851759i | \(-0.675536\pi\) | ||||
−0.523933 | + | 0.851759i | \(0.675536\pi\) | |||||||
\(710\) | 2.36093 | 0.0886041 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.987952 | −0.0370251 | ||||||||
\(713\) | 13.0753 | 0.489675 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.05664 | −0.263903 | ||||||||
\(716\) | 9.06821 | 0.338895 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.7823 | 0.738268 | ||||||||
\(719\) | 8.25535 | 0.307873 | 0.153936 | − | 0.988081i | \(-0.450805\pi\) | ||||
0.153936 | + | 0.988081i | \(0.450805\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2020 | −0.379942 | ||||||||
\(722\) | −11.2484 | −0.418622 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.92488 | −0.294526 | ||||||||
\(725\) | 45.1288 | 1.67604 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7683 | 0.955694 | 0.477847 | − | 0.878443i | \(-0.341417\pi\) | ||||
0.477847 | + | 0.878443i | \(0.341417\pi\) | |||||||
\(728\) | 13.6957 | 0.507597 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.01261 | −0.111502 | ||||||||
\(731\) | −36.1270 | −1.33621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.2704 | −1.52436 | −0.762179 | − | 0.647366i | \(-0.775870\pi\) | ||||
−0.762179 | + | 0.647366i | \(0.775870\pi\) | |||||||
\(734\) | 12.8208 | 0.473224 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.7421 | 0.506541 | ||||||||
\(737\) | 20.1294 | 0.741475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2673 | −0.451260 | −0.225630 | − | 0.974213i | \(-0.572444\pi\) | ||||
−0.225630 | + | 0.974213i | \(0.572444\pi\) | |||||||
\(740\) | 2.72973 | 0.100347 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.4039 | −0.381939 | ||||||||
\(743\) | −30.3770 | −1.11443 | −0.557213 | − | 0.830370i | \(-0.688129\pi\) | ||||
−0.557213 | + | 0.830370i | \(0.688129\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.51377 | −0.238646 | ||||||||
\(746\) | −22.5294 | −0.824859 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.0738 | 0.697407 | ||||||||
\(749\) | 5.75880 | 0.210422 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9352 | 1.42076 | 0.710382 | − | 0.703816i | \(-0.248522\pi\) | ||||
0.710382 | + | 0.703816i | \(0.248522\pi\) | |||||||
\(752\) | 6.42554 | 0.234315 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.7497 | 1.37476 | ||||||||
\(755\) | 3.67862 | 0.133879 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.998200 | 0.0362802 | 0.0181401 | − | 0.999835i | \(-0.494226\pi\) | ||||
0.0181401 | + | 0.999835i | \(0.494226\pi\) | |||||||
\(758\) | 25.8494 | 0.938892 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.07174 | −0.0751501 | ||||||||
\(761\) | −49.1530 | −1.78180 | −0.890898 | − | 0.454204i | \(-0.849924\pi\) | ||||
−0.890898 | + | 0.454204i | \(0.849924\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3606 | 0.375077 | ||||||||
\(764\) | 9.42662 | 0.341043 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.6218 | 0.636700 | ||||||||
\(767\) | 36.5992 | 1.32152 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.4560 | −1.78343 | −0.891715 | − | 0.452598i | \(-0.850497\pi\) | ||||
−0.891715 | + | 0.452598i | \(0.850497\pi\) | |||||||
\(770\) | 1.11686 | 0.0402489 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.86604 | 0.211124 | ||||||||
\(773\) | 18.8474 | 0.677893 | 0.338946 | − | 0.940806i | \(-0.389929\pi\) | ||||
0.338946 | + | 0.940806i | \(0.389929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.0644 | −0.972181 | ||||||||
\(776\) | 20.8999 | 0.750261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.208460 | −0.00747367 | ||||||||
\(779\) | −3.73569 | −0.133845 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.6081 | 1.23837 | ||||||||
\(782\) | 6.60363 | 0.236145 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.539656 | 0.0192734 | ||||||||
\(785\) | −3.91401 | −0.139697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2531 | 1.14970 | 0.574849 | − | 0.818259i | \(-0.305061\pi\) | ||||
0.574849 | + | 0.818259i | \(0.305061\pi\) | |||||||
\(788\) | 9.31949 | 0.331993 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.37426 | −0.155629 | ||||||||
\(791\) | 12.1901 | 0.433431 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.5744 | 1.86697 | ||||||||
\(794\) | 7.04802 | 0.250125 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.16279 | 0.289322 | ||||||||
\(797\) | −21.3937 | −0.757805 | −0.378902 | − | 0.925437i | \(-0.623698\pi\) | ||||
−0.378902 | + | 0.925437i | \(0.623698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.4645 | 1.46691 | ||||||||
\(800\) | −28.4445 | −1.00567 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.93474 | 0.350808 | ||||||||
\(803\) | −44.1608 | −1.55840 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.809807 | −0.0285420 | ||||||||
\(806\) | −22.6390 | −0.797424 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −35.4872 | −1.24844 | ||||||||
\(809\) | 10.7150 | 0.376721 | 0.188360 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188360 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.31984 | 0.292149 | 0.146075 | − | 0.989274i | \(-0.453336\pi\) | ||||
0.146075 | + | 0.989274i | \(0.453336\pi\) | |||||||
\(812\) | 12.5127 | 0.439110 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.1063 | −0.669677 | ||||||||
\(815\) | 6.28335 | 0.220096 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.2174 | 0.812275 | ||||||||
\(818\) | 8.67172 | 0.303200 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.775763 | 0.0270908 | ||||||||
\(821\) | 5.64944 | 0.197167 | 0.0985834 | − | 0.995129i | \(-0.468569\pi\) | ||||
0.0985834 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.7394 | −0.618356 | −0.309178 | − | 0.951004i | \(-0.600054\pi\) | ||||
−0.309178 | + | 0.951004i | \(0.600054\pi\) | |||||||
\(824\) | 27.5066 | 0.958238 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.79259 | −0.201550 | ||||||||
\(827\) | −19.4735 | −0.677160 | −0.338580 | − | 0.940938i | \(-0.609947\pi\) | ||||
−0.338580 | + | 0.940938i | \(0.609947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.64454 | −0.265506 | −0.132753 | − | 0.991149i | \(-0.542382\pi\) | ||||
−0.132753 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(830\) | −3.20896 | −0.111384 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18.3109 | −0.634818 | ||||||||
\(833\) | 3.48245 | 0.120660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73103 | 0.163724 | ||||||||
\(836\) | −12.2580 | −0.423951 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.0220 | 0.484381 | ||||||||
\(839\) | −36.5165 | −1.26069 | −0.630345 | − | 0.776315i | \(-0.717087\pi\) | ||||
−0.630345 | + | 0.776315i | \(0.717087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.4459 | 1.94641 | ||||||||
\(842\) | −32.3612 | −1.11524 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.3202 | 0.871557 | ||||||||
\(845\) | −4.39562 | −0.151214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.37170 | 0.184574 | ||||||||
\(848\) | −6.98359 | −0.239818 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.6687 | −0.468833 | ||||||||
\(851\) | 13.8535 | 0.474892 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2119 | −0.589325 | −0.294663 | − | 0.955601i | \(-0.595207\pi\) | ||||
−0.294663 | + | 0.955601i | \(0.595207\pi\) | |||||||
\(854\) | −8.32101 | −0.284739 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.5269 | −0.530698 | ||||||||
\(857\) | −36.8613 | −1.25916 | −0.629579 | − | 0.776937i | \(-0.716773\pi\) | ||||
−0.629579 | + | 0.776937i | \(0.716773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.9500 | −1.36308 | −0.681538 | − | 0.731783i | \(-0.738688\pi\) | ||||
−0.681538 | + | 0.731783i | \(0.738688\pi\) | |||||||
\(860\) | −4.82138 | −0.164408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.02722 | −0.137168 | ||||||||
\(863\) | 4.30869 | 0.146670 | 0.0733348 | − | 0.997307i | \(-0.476636\pi\) | ||||
0.0733348 | + | 0.997307i | \(0.476636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.15191 | −0.277173 | ||||||||
\(866\) | 21.6446 | 0.735512 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.50403 | −0.254704 | ||||||||
\(869\) | −64.1208 | −2.17515 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.2706 | 0.856263 | ||||||||
\(872\) | −27.9341 | −0.945970 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.24389 | −0.143552 | ||||||||
\(875\) | 3.39288 | 0.114700 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.7064 | −1.40832 | −0.704162 | − | 0.710039i | \(-0.748677\pi\) | ||||
−0.704162 | + | 0.710039i | \(0.748677\pi\) | |||||||
\(878\) | −24.2525 | −0.818483 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.749691 | 0.0252721 | ||||||||
\(881\) | −14.6304 | −0.492910 | −0.246455 | − | 0.969154i | \(-0.579266\pi\) | ||||
−0.246455 | + | 0.969154i | \(0.579266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.2903 | 0.682821 | 0.341411 | − | 0.939914i | \(-0.389095\pi\) | ||||
0.341411 | + | 0.939914i | \(0.389095\pi\) | |||||||
\(884\) | 23.9454 | 0.805372 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6572 | −0.828374 | ||||||||
\(887\) | 14.1451 | 0.474945 | 0.237473 | − | 0.971394i | \(-0.423681\pi\) | ||||
0.237473 | + | 0.971394i | \(0.423681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −0.101143 | −0.00339033 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.3864 | 0.481692 | ||||||||
\(893\) | −26.6476 | −0.891728 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.30003 | 0.0768816 | ||||||||
\(896\) | −8.75443 | −0.292465 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.81410 | 0.327501 | ||||||||
\(899\) | −51.2430 | −1.70905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.0657 | −1.50136 | ||||||||
\(902\) | −5.42984 | −0.180794 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.8671 | −1.09314 | ||||||||
\(905\) | −2.01004 | −0.0668160 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.2224 | −1.76722 | −0.883611 | − | 0.468223i | \(-0.844895\pi\) | ||||
−0.883611 | + | 0.468223i | \(0.844895\pi\) | |||||||
\(908\) | −2.75102 | −0.0912957 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.40212 | 0.0464799 | ||||||||
\(911\) | −35.5787 | −1.17877 | −0.589387 | − | 0.807851i | \(-0.700631\pi\) | ||||
−0.589387 | + | 0.807851i | \(0.700631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.0390 | −1.55676 | ||||||||
\(914\) | −26.1046 | −0.863464 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.9082 | −0.657787 | ||||||||
\(917\) | 11.7624 | 0.388428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.8133 | 1.84111 | 0.920556 | − | 0.390610i | \(-0.127736\pi\) | ||||
0.920556 | + | 0.390610i | \(0.127736\pi\) | |||||||
\(920\) | 2.18340 | 0.0719847 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.80571 | 0.322934 | ||||||||
\(923\) | 43.4473 | 1.43009 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.6751 | −0.942830 | ||||||||
\(926\) | 28.2487 | 0.928310 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −53.8562 | −1.76792 | ||||||||
\(929\) | −18.8585 | −0.618726 | −0.309363 | − | 0.950944i | \(-0.600116\pi\) | ||||
−0.309363 | + | 0.950944i | \(0.600116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.23803 | −0.0733485 | ||||||||
\(932\) | −25.5361 | −0.836462 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.6948 | 0.448107 | ||||||||
\(935\) | 4.83782 | 0.158213 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.7884 | −1.20183 | −0.600913 | − | 0.799315i | \(-0.705196\pi\) | ||||
−0.600913 | + | 0.799315i | \(0.705196\pi\) | |||||||
\(938\) | −3.99961 | −0.130592 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.53370 | 0.180489 | ||||||||
\(941\) | 16.0773 | 0.524105 | 0.262053 | − | 0.965054i | \(-0.415601\pi\) | ||||
0.262053 | + | 0.965054i | \(0.415601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.93703 | 0.128207 | ||||||||
\(944\) | −3.88826 | −0.126552 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.7466 | 1.09720 | ||||||||
\(947\) | 40.8039 | 1.32595 | 0.662974 | − | 0.748642i | \(-0.269294\pi\) | ||||
0.662974 | + | 0.748642i | \(0.269294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.4400 | −1.79966 | ||||||||
\(950\) | 8.78434 | 0.285002 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.38937 | −0.304311 | ||||||||
\(953\) | −2.02328 | −0.0655406 | −0.0327703 | − | 0.999463i | \(-0.510433\pi\) | ||||
−0.0327703 | + | 0.999463i | \(0.510433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.39094 | 0.0773689 | ||||||||
\(956\) | 5.14823 | 0.166506 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.73368 | −0.314481 | ||||||||
\(959\) | 22.2429 | 0.718260 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.268875 | −0.00867340 | ||||||||
\(962\) | −23.9863 | −0.773349 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.8372 | 1.02541 | ||||||||
\(965\) | 1.48785 | 0.0478954 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.7174 | 1.75959 | 0.879796 | − | 0.475351i | \(-0.157679\pi\) | ||||
0.879796 | + | 0.475351i | \(0.157679\pi\) | |||||||
\(968\) | −14.4832 | −0.465507 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.13966 | 0.0687002 | ||||||||
\(971\) | −13.3453 | −0.428271 | −0.214136 | − | 0.976804i | \(-0.568693\pi\) | ||||
−0.214136 | + | 0.976804i | \(0.568693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.45596 | 0.142852 | ||||||||
\(974\) | 12.5402 | 0.401812 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.58546 | −0.178786 | ||||||||
\(977\) | −30.3067 | −0.969596 | −0.484798 | − | 0.874626i | \(-0.661107\pi\) | ||||
−0.484798 | + | 0.874626i | \(0.661107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.48262 | −0.0473848 | ||||||||
\(980\) | 0.464755 | 0.0148460 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.13727 | −0.227759 | ||||||||
\(983\) | −25.8700 | −0.825124 | −0.412562 | − | 0.910930i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910930i | \(0.635366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.36377 | 0.0753158 | ||||||||
\(986\) | −25.8800 | −0.824188 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.3888 | −0.489582 | ||||||||
\(989\) | −24.4688 | −0.778061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5822 | −0.622050 | −0.311025 | − | 0.950402i | \(-0.600672\pi\) | ||||
−0.311025 | + | 0.950402i | \(0.600672\pi\) | |||||||
\(992\) | 32.2983 | 1.02547 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.87646 | −0.218108 | ||||||||
\(995\) | 2.07038 | 0.0656356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.3683 | −1.62685 | −0.813425 | − | 0.581670i | \(-0.802399\pi\) | ||||
−0.813425 | + | 0.581670i | \(0.802399\pi\) | |||||||
\(998\) | 12.3063 | 0.389550 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.u.1.10 | 18 | ||
3.2 | odd | 2 | 2667.2.a.p.1.9 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.p.1.9 | ✓ | 18 | 3.2 | odd | 2 | ||
8001.2.a.u.1.10 | 18 | 1.1 | even | 1 | trivial |