Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + 5778 x^{8} - 5124 x^{7} - 9405 x^{6} + 8288 x^{5} + 6405 x^{4} - 6032 x^{3} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.50224\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50224 | −1.76935 | −0.884675 | − | 0.466208i | \(-0.845620\pi\) | ||||
−0.884675 | + | 0.466208i | \(0.845620\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.26120 | 2.13060 | ||||||||
\(5\) | −0.499377 | −0.223328 | −0.111664 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111664 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.377265 | 0.142593 | 0.0712963 | − | 0.997455i | \(-0.477286\pi\) | ||||
0.0712963 | + | 0.997455i | \(0.477286\pi\) | |||||||
\(8\) | −5.65806 | −2.00043 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.24956 | 0.395146 | ||||||||
\(11\) | −0.280990 | −0.0847216 | −0.0423608 | − | 0.999102i | \(-0.513488\pi\) | ||||
−0.0423608 | + | 0.999102i | \(0.513488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81091 | 0.779606 | 0.389803 | − | 0.920898i | \(-0.372543\pi\) | ||||
0.389803 | + | 0.920898i | \(0.372543\pi\) | |||||||
\(14\) | −0.944007 | −0.252296 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.63543 | 1.40886 | ||||||||
\(17\) | −3.47193 | −0.842067 | −0.421033 | − | 0.907045i | \(-0.638333\pi\) | ||||
−0.421033 | + | 0.907045i | \(0.638333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.13228 | −0.718593 | −0.359297 | − | 0.933223i | \(-0.616983\pi\) | ||||
−0.359297 | + | 0.933223i | \(0.616983\pi\) | |||||||
\(20\) | −2.12795 | −0.475823 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.703104 | 0.149902 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75062 | −0.950124 | ||||||||
\(26\) | −7.03357 | −1.37940 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.60760 | 0.303808 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.49306 | −1.52540 | −0.762700 | − | 0.646753i | \(-0.776127\pi\) | ||||
−0.762700 | + | 0.646753i | \(0.776127\pi\) | |||||||
\(32\) | −2.78506 | −0.492334 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.68760 | 1.48991 | ||||||||
\(35\) | −0.188397 | −0.0318450 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.30358 | −0.543106 | −0.271553 | − | 0.962424i | \(-0.587537\pi\) | ||||
−0.271553 | + | 0.962424i | \(0.587537\pi\) | |||||||
\(38\) | 7.83770 | 1.27144 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.82551 | 0.446752 | ||||||||
\(41\) | 3.07528 | 0.480278 | 0.240139 | − | 0.970739i | \(-0.422807\pi\) | ||||
0.240139 | + | 0.970739i | \(0.422807\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.93400 | 1.05743 | 0.528713 | − | 0.848801i | \(-0.322675\pi\) | ||||
0.528713 | + | 0.848801i | \(0.322675\pi\) | |||||||
\(44\) | −1.19735 | −0.180508 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.50224 | −0.368935 | ||||||||
\(47\) | −1.62857 | −0.237551 | −0.118776 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118776 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85767 | −0.979667 | ||||||||
\(50\) | 11.8872 | 1.68110 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.9779 | 1.66103 | ||||||||
\(53\) | −5.80717 | −0.797676 | −0.398838 | − | 0.917021i | \(-0.630586\pi\) | ||||
−0.398838 | + | 0.917021i | \(0.630586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.140320 | 0.0189207 | ||||||||
\(56\) | −2.13459 | −0.285246 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.50224 | −0.328560 | ||||||||
\(59\) | −4.19192 | −0.545742 | −0.272871 | − | 0.962051i | \(-0.587973\pi\) | ||||
−0.272871 | + | 0.962051i | \(0.587973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5885 | 1.86786 | 0.933932 | − | 0.357451i | \(-0.116354\pi\) | ||||
0.933932 | + | 0.357451i | \(0.116354\pi\) | |||||||
\(62\) | 21.2517 | 2.69897 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.30197 | −0.537746 | ||||||||
\(65\) | −1.40370 | −0.174108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.61416 | 0.808048 | 0.404024 | − | 0.914748i | \(-0.367611\pi\) | ||||
0.404024 | + | 0.914748i | \(0.367611\pi\) | |||||||
\(68\) | −14.7946 | −1.79411 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.471415 | 0.0563449 | ||||||||
\(71\) | 8.99710 | 1.06776 | 0.533880 | − | 0.845561i | \(-0.320734\pi\) | ||||
0.533880 | + | 0.845561i | \(0.320734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65881 | −0.428231 | −0.214115 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214115 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(74\) | 8.26635 | 0.960944 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.3473 | −1.53104 | ||||||||
\(77\) | −0.106008 | −0.0120807 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1301 | 1.13973 | 0.569865 | − | 0.821738i | \(-0.306995\pi\) | ||||
0.569865 | + | 0.821738i | \(0.306995\pi\) | |||||||
\(80\) | −2.81420 | −0.314638 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.69509 | −0.849780 | ||||||||
\(83\) | −14.4012 | −1.58073 | −0.790367 | − | 0.612633i | \(-0.790110\pi\) | ||||
−0.790367 | + | 0.612633i | \(0.790110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73380 | 0.188057 | ||||||||
\(86\) | −17.3505 | −1.87096 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.58986 | 0.169480 | ||||||||
\(89\) | 15.5648 | 1.64987 | 0.824933 | − | 0.565230i | \(-0.191213\pi\) | ||||
0.824933 | + | 0.565230i | \(0.191213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06046 | 0.111166 | ||||||||
\(92\) | 4.26120 | 0.444261 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.07507 | 0.420311 | ||||||||
\(95\) | 1.56419 | 0.160482 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.680933 | 0.0691383 | 0.0345691 | − | 0.999402i | \(-0.488994\pi\) | ||||
0.0345691 | + | 0.999402i | \(0.488994\pi\) | |||||||
\(98\) | 17.1595 | 1.73337 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −20.2434 | −2.02434 | ||||||||
\(101\) | 3.18551 | 0.316970 | 0.158485 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158485 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4798 | −1.03261 | −0.516305 | − | 0.856405i | \(-0.672693\pi\) | ||||
−0.516305 | + | 0.856405i | \(0.672693\pi\) | |||||||
\(104\) | −15.9043 | −1.55955 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.5309 | 1.41137 | ||||||||
\(107\) | −6.58541 | −0.636636 | −0.318318 | − | 0.947984i | \(-0.603118\pi\) | ||||
−0.318318 | + | 0.947984i | \(0.603118\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.159462 | 0.0152737 | 0.00763685 | − | 0.999971i | \(-0.497569\pi\) | ||||
0.00763685 | + | 0.999971i | \(0.497569\pi\) | |||||||
\(110\) | −0.351114 | −0.0334774 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.12605 | 0.200893 | ||||||||
\(113\) | 15.4677 | 1.45508 | 0.727538 | − | 0.686067i | \(-0.240664\pi\) | ||||
0.727538 | + | 0.686067i | \(0.240664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.499377 | −0.0465672 | ||||||||
\(116\) | 4.26120 | 0.395643 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4892 | 0.965609 | ||||||||
\(119\) | −1.30984 | −0.120073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9210 | −0.992822 | ||||||||
\(122\) | −36.5039 | −3.30491 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −36.1906 | −3.25002 | ||||||||
\(125\) | 4.86924 | 0.435518 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3000 | 0.913977 | 0.456989 | − | 0.889473i | \(-0.348928\pi\) | ||||
0.456989 | + | 0.889473i | \(0.348928\pi\) | |||||||
\(128\) | 16.3347 | 1.44379 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.51240 | 0.308058 | ||||||||
\(131\) | 5.86940 | 0.512812 | 0.256406 | − | 0.966569i | \(-0.417462\pi\) | ||||
0.256406 | + | 0.966569i | \(0.417462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.18170 | −0.102466 | ||||||||
\(134\) | −16.5502 | −1.42972 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.6444 | 1.68449 | ||||||||
\(137\) | 8.10245 | 0.692239 | 0.346119 | − | 0.938190i | \(-0.387499\pi\) | ||||
0.346119 | + | 0.938190i | \(0.387499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.897029 | −0.0760850 | −0.0380425 | − | 0.999276i | \(-0.512112\pi\) | ||||
−0.0380425 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(140\) | −0.802799 | −0.0678489 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.5129 | −1.88924 | ||||||||
\(143\) | −0.789837 | −0.0660495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.499377 | −0.0414710 | ||||||||
\(146\) | 9.15521 | 0.757690 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.0772 | −1.15714 | ||||||||
\(149\) | 8.58730 | 0.703499 | 0.351749 | − | 0.936094i | \(-0.385587\pi\) | ||||
0.351749 | + | 0.936094i | \(0.385587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.7857 | −1.61013 | −0.805067 | − | 0.593183i | \(-0.797871\pi\) | ||||
−0.805067 | + | 0.593183i | \(0.797871\pi\) | |||||||
\(152\) | 17.7226 | 1.43749 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.265256 | 0.0213750 | ||||||||
\(155\) | 4.24124 | 0.340665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.76040 | −0.140495 | −0.0702476 | − | 0.997530i | \(-0.522379\pi\) | ||||
−0.0702476 | + | 0.997530i | \(0.522379\pi\) | |||||||
\(158\) | −25.3480 | −2.01658 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.39080 | 0.109952 | ||||||||
\(161\) | 0.377265 | 0.0297326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4964 | 1.29210 | 0.646048 | − | 0.763296i | \(-0.276420\pi\) | ||||
0.646048 | + | 0.763296i | \(0.276420\pi\) | |||||||
\(164\) | 13.1044 | 1.02328 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36.0352 | 2.79687 | ||||||||
\(167\) | 21.1152 | 1.63394 | 0.816970 | − | 0.576680i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.09878 | −0.392214 | ||||||||
\(170\) | −4.33839 | −0.332739 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 29.5472 | 2.25295 | ||||||||
\(173\) | 1.30202 | 0.0989910 | 0.0494955 | − | 0.998774i | \(-0.484239\pi\) | ||||
0.0494955 | + | 0.998774i | \(0.484239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.79224 | −0.135481 | ||||||||
\(176\) | −1.58350 | −0.119361 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −38.9469 | −2.91919 | ||||||||
\(179\) | −5.51022 | −0.411853 | −0.205927 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205927 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.29654 | 0.245030 | 0.122515 | − | 0.992467i | \(-0.460904\pi\) | ||||
0.122515 | + | 0.992467i | \(0.460904\pi\) | |||||||
\(182\) | −2.65352 | −0.196692 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.65806 | −0.417118 | ||||||||
\(185\) | 1.64973 | 0.121291 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.975578 | 0.0713413 | ||||||||
\(188\) | −6.93966 | −0.506127 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.91397 | −0.283949 | ||||||||
\(191\) | 22.1285 | 1.60116 | 0.800581 | − | 0.599225i | \(-0.204524\pi\) | ||||
0.800581 | + | 0.599225i | \(0.204524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7430 | 1.34915 | 0.674574 | − | 0.738207i | \(-0.264327\pi\) | ||||
0.674574 | + | 0.738207i | \(0.264327\pi\) | |||||||
\(194\) | −1.70386 | −0.122330 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.2219 | −2.08728 | ||||||||
\(197\) | −16.3147 | −1.16237 | −0.581186 | − | 0.813771i | \(-0.697411\pi\) | ||||
−0.581186 | + | 0.813771i | \(0.697411\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9140 | 0.915453 | 0.457726 | − | 0.889093i | \(-0.348664\pi\) | ||||
0.457726 | + | 0.889093i | \(0.348664\pi\) | |||||||
\(200\) | 26.8793 | 1.90066 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.97091 | −0.560831 | ||||||||
\(203\) | 0.377265 | 0.0264788 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.53572 | −0.107260 | ||||||||
\(206\) | 26.2231 | 1.82705 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.8407 | 1.09835 | ||||||||
\(209\) | 0.880138 | 0.0608804 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4592 | 0.995414 | 0.497707 | − | 0.867345i | \(-0.334176\pi\) | ||||
0.497707 | + | 0.867345i | \(0.334176\pi\) | |||||||
\(212\) | −24.7455 | −1.69953 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.4783 | 1.12643 | ||||||||
\(215\) | −3.46268 | −0.236153 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.20413 | −0.217511 | ||||||||
\(218\) | −0.399012 | −0.0270245 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.597931 | 0.0403125 | ||||||||
\(221\) | −9.75929 | −0.656481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.78586 | 0.521380 | 0.260690 | − | 0.965423i | \(-0.416050\pi\) | ||||
0.260690 | + | 0.965423i | \(0.416050\pi\) | |||||||
\(224\) | −1.05071 | −0.0702032 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −38.7038 | −2.57454 | ||||||||
\(227\) | 19.0309 | 1.26313 | 0.631563 | − | 0.775325i | \(-0.282414\pi\) | ||||
0.631563 | + | 0.775325i | \(0.282414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.2950 | −1.93587 | −0.967935 | − | 0.251201i | \(-0.919175\pi\) | ||||
−0.967935 | + | 0.251201i | \(0.919175\pi\) | |||||||
\(230\) | 1.24956 | 0.0823936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.65806 | −0.371470 | ||||||||
\(233\) | 13.0823 | 0.857053 | 0.428526 | − | 0.903529i | \(-0.359033\pi\) | ||||
0.428526 | + | 0.903529i | \(0.359033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.813270 | 0.0530519 | ||||||||
\(236\) | −17.8626 | −1.16276 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.27753 | 0.212450 | ||||||||
\(239\) | −25.0289 | −1.61899 | −0.809494 | − | 0.587128i | \(-0.800258\pi\) | ||||
−0.809494 | + | 0.587128i | \(0.800258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.924120 | −0.0595278 | −0.0297639 | − | 0.999557i | \(-0.509476\pi\) | ||||
−0.0297639 | + | 0.999557i | \(0.509476\pi\) | |||||||
\(242\) | 27.3271 | 1.75665 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 62.1645 | 3.97967 | ||||||||
\(245\) | 3.42456 | 0.218787 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.80455 | −0.560220 | ||||||||
\(248\) | 48.0543 | 3.05145 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1840 | −0.770584 | ||||||||
\(251\) | 0.948617 | 0.0598762 | 0.0299381 | − | 0.999552i | \(-0.490469\pi\) | ||||
0.0299381 | + | 0.999552i | \(0.490469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.280990 | −0.0176657 | ||||||||
\(254\) | −25.7731 | −1.61715 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.2693 | −2.01683 | ||||||||
\(257\) | −11.2748 | −0.703302 | −0.351651 | − | 0.936131i | \(-0.614380\pi\) | ||||
−0.351651 | + | 0.936131i | \(0.614380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24633 | −0.0774429 | ||||||||
\(260\) | −5.98147 | −0.370955 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.6866 | −0.907343 | ||||||||
\(263\) | −18.0974 | −1.11593 | −0.557965 | − | 0.829864i | \(-0.688418\pi\) | ||||
−0.557965 | + | 0.829864i | \(0.688418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.89997 | 0.178144 | ||||||||
\(266\) | 2.95689 | 0.181298 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 28.1842 | 1.72163 | ||||||||
\(269\) | 16.1467 | 0.984479 | 0.492240 | − | 0.870460i | \(-0.336178\pi\) | ||||
0.492240 | + | 0.870460i | \(0.336178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1429 | 0.737631 | 0.368815 | − | 0.929503i | \(-0.379763\pi\) | ||||
0.368815 | + | 0.929503i | \(0.379763\pi\) | |||||||
\(272\) | −19.5658 | −1.18635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2743 | −1.22481 | ||||||||
\(275\) | 1.33488 | 0.0804961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.34216 | 0.200811 | 0.100405 | − | 0.994947i | \(-0.467986\pi\) | ||||
0.100405 | + | 0.994947i | \(0.467986\pi\) | |||||||
\(278\) | 2.24458 | 0.134621 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.06596 | 0.0637036 | ||||||||
\(281\) | 0.0599960 | 0.00357906 | 0.00178953 | − | 0.999998i | \(-0.499430\pi\) | ||||
0.00178953 | + | 0.999998i | \(0.499430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3954 | 0.855718 | 0.427859 | − | 0.903845i | \(-0.359268\pi\) | ||||
0.427859 | + | 0.903845i | \(0.359268\pi\) | |||||||
\(284\) | 38.3384 | 2.27497 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.97636 | 0.116865 | ||||||||
\(287\) | 1.16019 | 0.0684841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.94570 | −0.290923 | ||||||||
\(290\) | 1.24956 | 0.0733767 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.5909 | −0.912389 | ||||||||
\(293\) | −11.9152 | −0.696091 | −0.348046 | − | 0.937478i | \(-0.613155\pi\) | ||||
−0.348046 | + | 0.937478i | \(0.613155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09335 | 0.121880 | ||||||||
\(296\) | 18.6919 | 1.08644 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.4875 | −1.24474 | ||||||||
\(299\) | 2.81091 | 0.162559 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.61595 | 0.150781 | ||||||||
\(302\) | 49.5085 | 2.84889 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17.6517 | −1.01240 | ||||||||
\(305\) | −7.28515 | −0.417147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.76417 | 0.214832 | 0.107416 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107416 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(308\) | −0.451720 | −0.0257391 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.6126 | −0.602755 | ||||||||
\(311\) | −21.5328 | −1.22101 | −0.610506 | − | 0.792011i | \(-0.709034\pi\) | ||||
−0.610506 | + | 0.792011i | \(0.709034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.37433 | 0.473345 | 0.236673 | − | 0.971589i | \(-0.423943\pi\) | ||||
0.236673 | + | 0.971589i | \(0.423943\pi\) | |||||||
\(314\) | 4.40494 | 0.248585 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43.1666 | 2.42831 | ||||||||
\(317\) | −29.4201 | −1.65240 | −0.826200 | − | 0.563377i | \(-0.809502\pi\) | ||||
−0.826200 | + | 0.563377i | \(0.809502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.280990 | −0.0157324 | ||||||||
\(320\) | 2.14830 | 0.120094 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.944007 | −0.0526074 | ||||||||
\(323\) | 10.8750 | 0.605104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.3536 | −0.740723 | ||||||||
\(326\) | −41.2779 | −2.28617 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.4001 | −0.960762 | ||||||||
\(329\) | −0.614402 | −0.0338731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.34926 | −0.458917 | −0.229458 | − | 0.973318i | \(-0.573695\pi\) | ||||
−0.229458 | + | 0.973318i | \(0.573695\pi\) | |||||||
\(332\) | −61.3663 | −3.36791 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −52.8352 | −2.89101 | ||||||||
\(335\) | −3.30296 | −0.180460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0675 | 1.20209 | 0.601047 | − | 0.799214i | \(-0.294751\pi\) | ||||
0.601047 | + | 0.799214i | \(0.294751\pi\) | |||||||
\(338\) | 12.7584 | 0.693964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.38808 | 0.400675 | ||||||||
\(341\) | 2.38647 | 0.129234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.22801 | −0.282286 | ||||||||
\(344\) | −39.2330 | −2.11530 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.25797 | −0.175150 | ||||||||
\(347\) | −32.3908 | −1.73883 | −0.869414 | − | 0.494084i | \(-0.835504\pi\) | ||||
−0.869414 | + | 0.494084i | \(0.835504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8925 | −0.904233 | −0.452117 | − | 0.891959i | \(-0.649331\pi\) | ||||
−0.452117 | + | 0.891959i | \(0.649331\pi\) | |||||||
\(350\) | 4.48462 | 0.239713 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.782574 | 0.0417113 | ||||||||
\(353\) | 31.9878 | 1.70254 | 0.851269 | − | 0.524730i | \(-0.175834\pi\) | ||||
0.851269 | + | 0.524730i | \(0.175834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.49295 | −0.238461 | ||||||||
\(356\) | 66.3248 | 3.51521 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.7879 | 0.728713 | ||||||||
\(359\) | −5.58652 | −0.294845 | −0.147423 | − | 0.989074i | \(-0.547098\pi\) | ||||
−0.147423 | + | 0.989074i | \(0.547098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.18885 | −0.483624 | ||||||||
\(362\) | −8.24872 | −0.433543 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.51882 | 0.236851 | ||||||||
\(365\) | 1.82712 | 0.0956360 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.70892 | 0.141404 | 0.0707022 | − | 0.997497i | \(-0.477476\pi\) | ||||
0.0707022 | + | 0.997497i | \(0.477476\pi\) | |||||||
\(368\) | 5.63543 | 0.293767 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.12803 | −0.214606 | ||||||||
\(371\) | −2.19084 | −0.113743 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1027 | 1.29977 | 0.649883 | − | 0.760034i | \(-0.274818\pi\) | ||||
0.649883 | + | 0.760034i | \(0.274818\pi\) | |||||||
\(374\) | −2.44113 | −0.126228 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.21455 | 0.475204 | ||||||||
\(377\) | 2.81091 | 0.144769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.8338 | −1.32700 | −0.663498 | − | 0.748178i | \(-0.730929\pi\) | ||||
−0.663498 | + | 0.748178i | \(0.730929\pi\) | |||||||
\(380\) | 6.66531 | 0.341923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −55.3708 | −2.83302 | ||||||||
\(383\) | −18.0940 | −0.924561 | −0.462281 | − | 0.886734i | \(-0.652969\pi\) | ||||
−0.462281 | + | 0.886734i | \(0.652969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0529378 | 0.00269796 | ||||||||
\(386\) | −46.8994 | −2.38711 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.90159 | 0.147306 | ||||||||
\(389\) | 0.751401 | 0.0380976 | 0.0190488 | − | 0.999819i | \(-0.493936\pi\) | ||||
0.0190488 | + | 0.999819i | \(0.493936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.47193 | −0.175583 | ||||||||
\(392\) | 38.8011 | 1.95975 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 40.8232 | 2.05664 | ||||||||
\(395\) | −5.05876 | −0.254534 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.7706 | 1.84546 | 0.922731 | − | 0.385445i | \(-0.125952\pi\) | ||||
0.922731 | + | 0.385445i | \(0.125952\pi\) | |||||||
\(398\) | −32.3140 | −1.61976 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.7718 | −1.33859 | ||||||||
\(401\) | −27.6609 | −1.38132 | −0.690659 | − | 0.723181i | \(-0.742679\pi\) | ||||
−0.690659 | + | 0.723181i | \(0.742679\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.8732 | −1.18921 | ||||||||
\(404\) | 13.5741 | 0.675337 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.944007 | −0.0468503 | ||||||||
\(407\) | 0.928273 | 0.0460128 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6783 | 0.824691 | 0.412345 | − | 0.911028i | \(-0.364710\pi\) | ||||
0.412345 | + | 0.911028i | \(0.364710\pi\) | |||||||
\(410\) | 3.84275 | 0.189780 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −44.6567 | −2.20008 | ||||||||
\(413\) | −1.58147 | −0.0778188 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.19162 | 0.353023 | ||||||||
\(416\) | −7.82856 | −0.383827 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.20232 | −0.107719 | ||||||||
\(419\) | −4.12698 | −0.201616 | −0.100808 | − | 0.994906i | \(-0.532143\pi\) | ||||
−0.100808 | + | 0.994906i | \(0.532143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9526 | 0.533795 | 0.266897 | − | 0.963725i | \(-0.414002\pi\) | ||||
0.266897 | + | 0.963725i | \(0.414002\pi\) | |||||||
\(422\) | −36.1804 | −1.76124 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.8573 | 1.59569 | ||||||||
\(425\) | 16.4938 | 0.800068 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.50372 | 0.266344 | ||||||||
\(428\) | −28.0618 | −1.35642 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.66446 | 0.417837 | ||||||||
\(431\) | 20.7355 | 0.998793 | 0.499396 | − | 0.866374i | \(-0.333555\pi\) | ||||
0.499396 | + | 0.866374i | \(0.333555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.2333 | 1.11652 | 0.558261 | − | 0.829665i | \(-0.311469\pi\) | ||||
0.558261 | + | 0.829665i | \(0.311469\pi\) | |||||||
\(434\) | 8.01751 | 0.384853 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.679500 | 0.0325422 | ||||||||
\(437\) | −3.13228 | −0.149837 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.90645 | 0.425082 | 0.212541 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212541 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(440\) | −0.793939 | −0.0378496 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.4201 | 1.16154 | ||||||||
\(443\) | 6.58936 | 0.313070 | 0.156535 | − | 0.987672i | \(-0.449968\pi\) | ||||
0.156535 | + | 0.987672i | \(0.449968\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.77271 | −0.368462 | ||||||||
\(446\) | −19.4821 | −0.922504 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.62298 | −0.0766786 | ||||||||
\(449\) | 2.64648 | 0.124895 | 0.0624477 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624477 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.864123 | −0.0406899 | ||||||||
\(452\) | 65.9109 | 3.10019 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −47.6199 | −2.23491 | ||||||||
\(455\) | −0.529568 | −0.0248265 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1702 | 1.31775 | 0.658873 | − | 0.752255i | \(-0.271034\pi\) | ||||
0.658873 | + | 0.752255i | \(0.271034\pi\) | |||||||
\(458\) | 73.3032 | 3.42523 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.12795 | −0.0992160 | ||||||||
\(461\) | 9.37170 | 0.436484 | 0.218242 | − | 0.975895i | \(-0.429968\pi\) | ||||
0.218242 | + | 0.975895i | \(0.429968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.05249 | −0.420705 | −0.210353 | − | 0.977626i | \(-0.567461\pi\) | ||||
−0.210353 | + | 0.977626i | \(0.567461\pi\) | |||||||
\(464\) | 5.63543 | 0.261618 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −32.7351 | −1.51643 | ||||||||
\(467\) | 24.7217 | 1.14398 | 0.571992 | − | 0.820259i | \(-0.306171\pi\) | ||||
0.571992 | + | 0.820259i | \(0.306171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.49529 | 0.115222 | ||||||||
\(470\) | −2.03500 | −0.0938674 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.7182 | 1.09172 | ||||||||
\(473\) | −1.94838 | −0.0895868 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8803 | 0.682753 | ||||||||
\(476\) | −5.58148 | −0.255827 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 62.6284 | 2.86456 | ||||||||
\(479\) | −6.57206 | −0.300285 | −0.150143 | − | 0.988664i | \(-0.547973\pi\) | ||||
−0.150143 | + | 0.988664i | \(0.547973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.28608 | −0.423409 | ||||||||
\(482\) | 2.31237 | 0.105326 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.5368 | −2.11531 | ||||||||
\(485\) | −0.340042 | −0.0154405 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.76562 | −0.0800077 | −0.0400038 | − | 0.999200i | \(-0.512737\pi\) | ||||
−0.0400038 | + | 0.999200i | \(0.512737\pi\) | |||||||
\(488\) | −82.5426 | −3.73653 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.56908 | −0.387111 | ||||||||
\(491\) | −0.943575 | −0.0425829 | −0.0212915 | − | 0.999773i | \(-0.506778\pi\) | ||||
−0.0212915 | + | 0.999773i | \(0.506778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.47193 | −0.156368 | ||||||||
\(494\) | 22.0311 | 0.991225 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −47.8621 | −2.14907 | ||||||||
\(497\) | 3.39429 | 0.152255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7953 | −0.796626 | −0.398313 | − | 0.917250i | \(-0.630404\pi\) | ||||
−0.398313 | + | 0.917250i | \(0.630404\pi\) | |||||||
\(500\) | 20.7488 | 0.927914 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.37367 | −0.105942 | ||||||||
\(503\) | 0.846449 | 0.0377413 | 0.0188706 | − | 0.999822i | \(-0.493993\pi\) | ||||
0.0188706 | + | 0.999822i | \(0.493993\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59077 | −0.0707884 | ||||||||
\(506\) | 0.703104 | 0.0312568 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 43.8904 | 1.94732 | ||||||||
\(509\) | 15.7969 | 0.700184 | 0.350092 | − | 0.936715i | \(-0.386150\pi\) | ||||
0.350092 | + | 0.936715i | \(0.386150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.38034 | −0.0610626 | ||||||||
\(512\) | 48.0762 | 2.12469 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.2122 | 1.24439 | ||||||||
\(515\) | 5.23340 | 0.230611 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.457611 | 0.0201257 | ||||||||
\(518\) | 3.11860 | 0.137024 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.94225 | 0.348291 | ||||||||
\(521\) | 31.9344 | 1.39907 | 0.699536 | − | 0.714597i | \(-0.253390\pi\) | ||||
0.699536 | + | 0.714597i | \(0.253390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.79011 | 0.296911 | 0.148455 | − | 0.988919i | \(-0.452570\pi\) | ||||
0.148455 | + | 0.988919i | \(0.452570\pi\) | |||||||
\(524\) | 25.0107 | 1.09260 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.2839 | 1.97447 | ||||||||
\(527\) | 29.4873 | 1.28449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −7.25641 | −0.315198 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.03545 | −0.218314 | ||||||||
\(533\) | 8.64434 | 0.374428 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.28860 | 0.142179 | ||||||||
\(536\) | −37.4233 | −1.61644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −40.4028 | −1.74189 | ||||||||
\(539\) | 1.92694 | 0.0829990 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3565 | 0.617236 | 0.308618 | − | 0.951186i | \(-0.400134\pi\) | ||||
0.308618 | + | 0.951186i | \(0.400134\pi\) | |||||||
\(542\) | −30.3845 | −1.30513 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.66954 | 0.414578 | ||||||||
\(545\) | −0.0796317 | −0.00341105 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5383 | 1.22021 | 0.610104 | − | 0.792321i | \(-0.291128\pi\) | ||||
0.610104 | + | 0.792321i | \(0.291128\pi\) | |||||||
\(548\) | 34.5261 | 1.47488 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.34018 | −0.142426 | ||||||||
\(551\) | −3.13228 | −0.133439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.82175 | 0.162517 | ||||||||
\(554\) | −8.36288 | −0.355305 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.82242 | −0.162107 | ||||||||
\(557\) | −21.9328 | −0.929324 | −0.464662 | − | 0.885488i | \(-0.653824\pi\) | ||||
−0.464662 | + | 0.885488i | \(0.653824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4909 | 0.824375 | ||||||||
\(560\) | −1.06170 | −0.0448650 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.150124 | −0.00633261 | ||||||||
\(563\) | 15.4453 | 0.650941 | 0.325471 | − | 0.945552i | \(-0.394477\pi\) | ||||
0.325471 | + | 0.945552i | \(0.394477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.72421 | −0.324960 | ||||||||
\(566\) | −36.0208 | −1.51407 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −50.9062 | −2.13598 | ||||||||
\(569\) | −21.7539 | −0.911970 | −0.455985 | − | 0.889987i | \(-0.650713\pi\) | ||||
−0.455985 | + | 0.889987i | \(0.650713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6666 | −0.655626 | −0.327813 | − | 0.944743i | \(-0.606312\pi\) | ||||
−0.327813 | + | 0.944743i | \(0.606312\pi\) | |||||||
\(572\) | −3.36566 | −0.140725 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.90308 | −0.121172 | ||||||||
\(575\) | −4.75062 | −0.198115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.7042 | 0.945186 | 0.472593 | − | 0.881281i | \(-0.343318\pi\) | ||||
0.472593 | + | 0.881281i | \(0.343318\pi\) | |||||||
\(578\) | 12.3753 | 0.514745 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.12795 | −0.0883581 | ||||||||
\(581\) | −5.43306 | −0.225401 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.63176 | 0.0675804 | ||||||||
\(584\) | 20.7018 | 0.856645 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.8146 | 1.23163 | ||||||||
\(587\) | −0.863910 | −0.0356574 | −0.0178287 | − | 0.999841i | \(-0.505675\pi\) | ||||
−0.0178287 | + | 0.999841i | \(0.505675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.6026 | 1.09614 | ||||||||
\(590\) | −5.23806 | −0.215648 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.6171 | −0.765158 | ||||||||
\(593\) | 31.8728 | 1.30886 | 0.654429 | − | 0.756123i | \(-0.272909\pi\) | ||||
0.654429 | + | 0.756123i | \(0.272909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.654103 | 0.0268156 | ||||||||
\(596\) | 36.5922 | 1.49887 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.03357 | −0.287624 | ||||||||
\(599\) | −20.4372 | −0.835042 | −0.417521 | − | 0.908667i | \(-0.637101\pi\) | ||||
−0.417521 | + | 0.908667i | \(0.637101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.55415 | −0.226559 | −0.113279 | − | 0.993563i | \(-0.536135\pi\) | ||||
−0.113279 | + | 0.993563i | \(0.536135\pi\) | |||||||
\(602\) | −6.54574 | −0.266785 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −84.3107 | −3.43055 | ||||||||
\(605\) | 5.45372 | 0.221725 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.04486 | 0.326531 | 0.163265 | − | 0.986582i | \(-0.447797\pi\) | ||||
0.163265 | + | 0.986582i | \(0.447797\pi\) | |||||||
\(608\) | 8.72358 | 0.353788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.2292 | 0.738079 | ||||||||
\(611\) | −4.57776 | −0.185196 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.92270 | 0.118047 | 0.0590234 | − | 0.998257i | \(-0.481201\pi\) | ||||
0.0590234 | + | 0.998257i | \(0.481201\pi\) | |||||||
\(614\) | −9.41884 | −0.380114 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.599798 | 0.0241665 | ||||||||
\(617\) | 32.7544 | 1.31864 | 0.659322 | − | 0.751861i | \(-0.270843\pi\) | ||||
0.659322 | + | 0.751861i | \(0.270843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.77841 | 0.312641 | 0.156320 | − | 0.987706i | \(-0.450037\pi\) | ||||
0.156320 | + | 0.987706i | \(0.450037\pi\) | |||||||
\(620\) | 18.0728 | 0.725820 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 53.8802 | 2.16040 | ||||||||
\(623\) | 5.87205 | 0.235259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.3215 | 0.852861 | ||||||||
\(626\) | −20.9546 | −0.837513 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.50142 | −0.299339 | ||||||||
\(629\) | 11.4698 | 0.457331 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0815 | 1.79467 | 0.897333 | − | 0.441354i | \(-0.145502\pi\) | ||||
0.897333 | + | 0.441354i | \(0.145502\pi\) | |||||||
\(632\) | −57.3170 | −2.27995 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 73.6162 | 2.92367 | ||||||||
\(635\) | −5.14359 | −0.204117 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.2763 | −0.763755 | ||||||||
\(638\) | 0.703104 | 0.0278362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.15716 | −0.322440 | ||||||||
\(641\) | −25.1043 | −0.991561 | −0.495780 | − | 0.868448i | \(-0.665118\pi\) | ||||
−0.495780 | + | 0.868448i | \(0.665118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.8245 | 1.49165 | 0.745826 | − | 0.666140i | \(-0.232055\pi\) | ||||
0.745826 | + | 0.666140i | \(0.232055\pi\) | |||||||
\(644\) | 1.60760 | 0.0633483 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.2120 | −1.07064 | ||||||||
\(647\) | −6.99373 | −0.274952 | −0.137476 | − | 0.990505i | \(-0.543899\pi\) | ||||
−0.137476 | + | 0.990505i | \(0.543899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.17789 | 0.0462362 | ||||||||
\(650\) | 33.4138 | 1.31060 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 70.2944 | 2.75294 | ||||||||
\(653\) | 34.0332 | 1.33182 | 0.665911 | − | 0.746031i | \(-0.268043\pi\) | ||||
0.665911 | + | 0.746031i | \(0.268043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.93104 | −0.114525 | ||||||||
\(656\) | 17.3305 | 0.676643 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.53738 | 0.0599333 | ||||||||
\(659\) | −27.9925 | −1.09043 | −0.545217 | − | 0.838295i | \(-0.683553\pi\) | ||||
−0.545217 | + | 0.838295i | \(0.683553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.9800 | −1.08829 | −0.544147 | − | 0.838990i | \(-0.683147\pi\) | ||||
−0.544147 | + | 0.838990i | \(0.683147\pi\) | |||||||
\(662\) | 20.8918 | 0.811984 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 81.4828 | 3.16215 | ||||||||
\(665\) | 0.590113 | 0.0228836 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 89.9759 | 3.48127 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.26479 | 0.319297 | ||||||||
\(671\) | −4.09922 | −0.158249 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.9531 | 1.92555 | 0.962776 | − | 0.270300i | \(-0.0871228\pi\) | ||||
0.962776 | + | 0.270300i | \(0.0871228\pi\) | |||||||
\(674\) | −55.2182 | −2.12692 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.7269 | −0.835651 | ||||||||
\(677\) | −13.7220 | −0.527380 | −0.263690 | − | 0.964607i | \(-0.584940\pi\) | ||||
−0.263690 | + | 0.964607i | \(0.584940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.256892 | 0.00985861 | ||||||||
\(680\) | −9.80997 | −0.376195 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.97151 | −0.228661 | ||||||||
\(683\) | 51.7531 | 1.98028 | 0.990138 | − | 0.140095i | \(-0.0447408\pi\) | ||||
0.990138 | + | 0.140095i | \(0.0447408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.04618 | −0.154596 | ||||||||
\(686\) | 13.0817 | 0.499463 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.0761 | 1.48976 | ||||||||
\(689\) | −16.3234 | −0.621873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.2514 | −0.922566 | −0.461283 | − | 0.887253i | \(-0.652611\pi\) | ||||
−0.461283 | + | 0.887253i | \(0.652611\pi\) | |||||||
\(692\) | 5.54818 | 0.210910 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 81.0495 | 3.07660 | ||||||||
\(695\) | 0.447956 | 0.0169919 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.6772 | −0.404426 | ||||||||
\(698\) | 42.2690 | 1.59991 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.63710 | −0.288655 | ||||||||
\(701\) | 3.36677 | 0.127161 | 0.0635807 | − | 0.997977i | \(-0.479748\pi\) | ||||
0.0635807 | + | 0.997977i | \(0.479748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3477 | 0.390272 | ||||||||
\(704\) | 1.20881 | 0.0455587 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −80.0410 | −3.01238 | ||||||||
\(707\) | 1.20178 | 0.0451976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.4206 | 0.579133 | 0.289566 | − | 0.957158i | \(-0.406489\pi\) | ||||
0.289566 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(710\) | 11.2424 | 0.421921 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −88.0667 | −3.30044 | ||||||||
\(713\) | −8.49306 | −0.318068 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.394427 | 0.0147507 | ||||||||
\(716\) | −23.4802 | −0.877495 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.9788 | 0.521685 | ||||||||
\(719\) | 29.3650 | 1.09513 | 0.547565 | − | 0.836763i | \(-0.315555\pi\) | ||||
0.547565 | + | 0.836763i | \(0.315555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.95368 | −0.147243 | ||||||||
\(722\) | 22.9927 | 0.855700 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0472 | 0.522060 | ||||||||
\(725\) | −4.75062 | −0.176434 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1116 | 0.708811 | 0.354405 | − | 0.935092i | \(-0.384683\pi\) | ||||
0.354405 | + | 0.935092i | \(0.384683\pi\) | |||||||
\(728\) | −6.00014 | −0.222380 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.57190 | −0.169214 | ||||||||
\(731\) | −24.0744 | −0.890423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.6961 | −1.31846 | −0.659232 | − | 0.751939i | \(-0.729119\pi\) | ||||
−0.659232 | + | 0.751939i | \(0.729119\pi\) | |||||||
\(734\) | −6.77836 | −0.250194 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.78506 | −0.102659 | ||||||||
\(737\) | −1.85851 | −0.0684591 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4540 | 0.642057 | 0.321028 | − | 0.947070i | \(-0.395972\pi\) | ||||
0.321028 | + | 0.947070i | \(0.395972\pi\) | |||||||
\(740\) | 7.02985 | 0.258422 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.48200 | 0.201251 | ||||||||
\(743\) | −22.3796 | −0.821028 | −0.410514 | − | 0.911854i | \(-0.634651\pi\) | ||||
−0.410514 | + | 0.911854i | \(0.634651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.28830 | −0.157111 | ||||||||
\(746\) | −62.8129 | −2.29974 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.15713 | 0.152000 | ||||||||
\(749\) | −2.48444 | −0.0907796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.1094 | 0.733804 | 0.366902 | − | 0.930260i | \(-0.380418\pi\) | ||||
0.366902 | + | 0.930260i | \(0.380418\pi\) | |||||||
\(752\) | −9.17768 | −0.334676 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.03357 | −0.256148 | ||||||||
\(755\) | 9.88051 | 0.359589 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.1745 | 1.35113 | 0.675565 | − | 0.737300i | \(-0.263900\pi\) | ||||
0.675565 | + | 0.737300i | \(0.263900\pi\) | |||||||
\(758\) | 64.6424 | 2.34792 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.85027 | −0.321033 | ||||||||
\(761\) | 51.3836 | 1.86265 | 0.931327 | − | 0.364184i | \(-0.118652\pi\) | ||||
0.931327 | + | 0.364184i | \(0.118652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0601594 | 0.00217792 | ||||||||
\(764\) | 94.2940 | 3.41144 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.2756 | 1.63587 | ||||||||
\(767\) | −11.7831 | −0.425464 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3771 | −1.16755 | −0.583775 | − | 0.811916i | \(-0.698425\pi\) | ||||
−0.583775 | + | 0.811916i | \(0.698425\pi\) | |||||||
\(770\) | −0.132463 | −0.00477363 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 79.8675 | 2.87449 | ||||||||
\(773\) | 13.8667 | 0.498751 | 0.249375 | − | 0.968407i | \(-0.419775\pi\) | ||||
0.249375 | + | 0.968407i | \(0.419775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.3473 | 1.44932 | ||||||||
\(776\) | −3.85276 | −0.138306 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.88019 | −0.0674079 | ||||||||
\(779\) | −9.63262 | −0.345125 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.52809 | −0.0904623 | ||||||||
\(782\) | 8.68760 | 0.310668 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −38.6459 | −1.38021 | ||||||||
\(785\) | 0.879103 | 0.0313765 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.4534 | 1.08555 | 0.542773 | − | 0.839879i | \(-0.317374\pi\) | ||||
0.542773 | + | 0.839879i | \(0.317374\pi\) | |||||||
\(788\) | −69.5201 | −2.47655 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.6582 | 0.450360 | ||||||||
\(791\) | 5.83541 | 0.207483 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.0069 | 1.45620 | ||||||||
\(794\) | −92.0087 | −3.26527 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.0293 | 1.95046 | ||||||||
\(797\) | 24.1771 | 0.856395 | 0.428198 | − | 0.903685i | \(-0.359149\pi\) | ||||
0.428198 | + | 0.903685i | \(0.359149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.65428 | 0.200034 | ||||||||
\(800\) | 13.2308 | 0.467779 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 69.2141 | 2.44404 | ||||||||
\(803\) | 1.02809 | 0.0362804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.188397 | −0.00664014 | ||||||||
\(806\) | 59.7366 | 2.10413 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.0238 | −0.634076 | ||||||||
\(809\) | −28.4412 | −0.999941 | −0.499970 | − | 0.866042i | \(-0.666656\pi\) | ||||
−0.499970 | + | 0.866042i | \(0.666656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.10171 | −0.214260 | −0.107130 | − | 0.994245i | \(-0.534166\pi\) | ||||
−0.107130 | + | 0.994245i | \(0.534166\pi\) | |||||||
\(812\) | 1.60760 | 0.0564157 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.32276 | −0.0814128 | ||||||||
\(815\) | −8.23792 | −0.288562 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.7192 | −0.759859 | ||||||||
\(818\) | −41.7332 | −1.45917 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.54403 | −0.228527 | ||||||||
\(821\) | 34.8159 | 1.21508 | 0.607542 | − | 0.794288i | \(-0.292156\pi\) | ||||
0.607542 | + | 0.794288i | \(0.292156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.6531 | 0.998783 | 0.499392 | − | 0.866376i | \(-0.333557\pi\) | ||||
0.499392 | + | 0.866376i | \(0.333557\pi\) | |||||||
\(824\) | 59.2957 | 2.06566 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.95720 | 0.137689 | ||||||||
\(827\) | −35.5993 | −1.23791 | −0.618954 | − | 0.785427i | \(-0.712443\pi\) | ||||
−0.618954 | + | 0.785427i | \(0.712443\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.0733 | −1.11395 | −0.556976 | − | 0.830529i | \(-0.688038\pi\) | ||||
−0.556976 | + | 0.830529i | \(0.688038\pi\) | |||||||
\(830\) | −17.9951 | −0.624621 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.0924 | −0.419230 | ||||||||
\(833\) | 23.8094 | 0.824945 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5444 | −0.364905 | ||||||||
\(836\) | 3.75044 | 0.129712 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.3267 | 0.356729 | ||||||||
\(839\) | 1.42992 | 0.0493662 | 0.0246831 | − | 0.999695i | \(-0.492142\pi\) | ||||
0.0246831 | + | 0.999695i | \(0.492142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −27.4059 | −0.944470 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 61.6136 | 2.12083 | ||||||||
\(845\) | 2.54622 | 0.0875925 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.12013 | −0.141569 | ||||||||
\(848\) | −32.7259 | −1.12381 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −41.2715 | −1.41560 | ||||||||
\(851\) | −3.30358 | −0.113245 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.61657 | −0.0553503 | −0.0276752 | − | 0.999617i | \(-0.508810\pi\) | ||||
−0.0276752 | + | 0.999617i | \(0.508810\pi\) | |||||||
\(854\) | −13.7716 | −0.471255 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 37.2607 | 1.27354 | ||||||||
\(857\) | 29.6871 | 1.01409 | 0.507046 | − | 0.861919i | \(-0.330737\pi\) | ||||
0.507046 | + | 0.861919i | \(0.330737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.4766 | 1.10809 | 0.554044 | − | 0.832487i | \(-0.313084\pi\) | ||||
0.554044 | + | 0.832487i | \(0.313084\pi\) | |||||||
\(860\) | −14.7552 | −0.503147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −51.8851 | −1.76721 | ||||||||
\(863\) | 1.28776 | 0.0438357 | 0.0219179 | − | 0.999760i | \(-0.493023\pi\) | ||||
0.0219179 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.650201 | −0.0221075 | ||||||||
\(866\) | −58.1353 | −1.97552 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.6535 | −0.463428 | ||||||||
\(869\) | −2.84647 | −0.0965598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5918 | 0.629959 | ||||||||
\(872\) | −0.902247 | −0.0305539 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.83770 | 0.265114 | ||||||||
\(875\) | 1.83699 | 0.0621017 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.5699 | 0.694595 | 0.347297 | − | 0.937755i | \(-0.387099\pi\) | ||||
0.347297 | + | 0.937755i | \(0.387099\pi\) | |||||||
\(878\) | −22.2861 | −0.752119 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.790763 | 0.0266566 | ||||||||
\(881\) | −15.6728 | −0.528030 | −0.264015 | − | 0.964519i | \(-0.585047\pi\) | ||||
−0.264015 | + | 0.964519i | \(0.585047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2059 | −0.814594 | −0.407297 | − | 0.913296i | \(-0.633529\pi\) | ||||
−0.407297 | + | 0.913296i | \(0.633529\pi\) | |||||||
\(884\) | −41.5863 | −1.39870 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.4881 | −0.553930 | ||||||||
\(887\) | 12.4786 | 0.418990 | 0.209495 | − | 0.977810i | \(-0.432818\pi\) | ||||
0.209495 | + | 0.977810i | \(0.432818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.88583 | 0.130326 | ||||||||
\(890\) | 19.4492 | 0.651938 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.1771 | 1.11085 | ||||||||
\(893\) | 5.10113 | 0.170703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.75168 | 0.0919785 | ||||||||
\(896\) | 6.16250 | 0.205875 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.62214 | −0.220984 | ||||||||
\(899\) | −8.49306 | −0.283260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.1621 | 0.671696 | ||||||||
\(902\) | 2.16224 | 0.0719948 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −87.5171 | −2.91078 | ||||||||
\(905\) | −1.64621 | −0.0547220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.8227 | −0.691407 | −0.345704 | − | 0.938344i | \(-0.612360\pi\) | ||||
−0.345704 | + | 0.938344i | \(0.612360\pi\) | |||||||
\(908\) | 81.0945 | 2.69122 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.32511 | 0.0439268 | ||||||||
\(911\) | 46.6670 | 1.54615 | 0.773074 | − | 0.634316i | \(-0.218718\pi\) | ||||
0.773074 | + | 0.634316i | \(0.218718\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.04659 | 0.133922 | ||||||||
\(914\) | −70.4885 | −2.33155 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −124.832 | −4.12457 | ||||||||
\(917\) | 2.21432 | 0.0731232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.68386 | −0.286454 | −0.143227 | − | 0.989690i | \(-0.545748\pi\) | ||||
−0.143227 | + | 0.989690i | \(0.545748\pi\) | |||||||
\(920\) | 2.82551 | 0.0931542 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.4502 | −0.772293 | ||||||||
\(923\) | 25.2900 | 0.832432 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6941 | 0.516018 | ||||||||
\(926\) | 22.6515 | 0.744375 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.78506 | −0.0914241 | ||||||||
\(929\) | 16.0979 | 0.528156 | 0.264078 | − | 0.964501i | \(-0.414932\pi\) | ||||
0.264078 | + | 0.964501i | \(0.414932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.4801 | 0.703982 | ||||||||
\(932\) | 55.7465 | 1.82604 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −61.8596 | −2.02411 | ||||||||
\(935\) | −0.487181 | −0.0159325 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3985 | −1.31976 | −0.659881 | − | 0.751370i | \(-0.729393\pi\) | ||||
−0.659881 | + | 0.751370i | \(0.729393\pi\) | |||||||
\(938\) | −6.24381 | −0.203868 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.46551 | 0.113032 | ||||||||
\(941\) | 1.57266 | 0.0512674 | 0.0256337 | − | 0.999671i | \(-0.491840\pi\) | ||||
0.0256337 | + | 0.999671i | \(0.491840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.07528 | 0.100145 | ||||||||
\(944\) | −23.6233 | −0.768873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.87532 | 0.158510 | ||||||||
\(947\) | 42.5119 | 1.38145 | 0.690725 | − | 0.723118i | \(-0.257292\pi\) | ||||
0.690725 | + | 0.723118i | \(0.257292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2846 | −0.333851 | ||||||||
\(950\) | −37.2340 | −1.20803 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.41114 | 0.240197 | ||||||||
\(953\) | −21.9061 | −0.709608 | −0.354804 | − | 0.934941i | \(-0.615452\pi\) | ||||
−0.354804 | + | 0.934941i | \(0.615452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.0505 | −0.357585 | ||||||||
\(956\) | −106.653 | −3.44942 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.4449 | 0.531310 | ||||||||
\(959\) | 3.05677 | 0.0987082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.1321 | 1.32684 | ||||||||
\(962\) | 23.2360 | 0.749158 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.93786 | −0.126830 | ||||||||
\(965\) | −9.35980 | −0.301303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3109 | 1.03905 | 0.519524 | − | 0.854456i | \(-0.326109\pi\) | ||||
0.519524 | + | 0.854456i | \(0.326109\pi\) | |||||||
\(968\) | 61.7920 | 1.98607 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.850867 | 0.0273197 | ||||||||
\(971\) | 11.7064 | 0.375677 | 0.187839 | − | 0.982200i | \(-0.439852\pi\) | ||||
0.187839 | + | 0.982200i | \(0.439852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.338418 | −0.0108492 | ||||||||
\(974\) | 4.41799 | 0.141562 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 82.2124 | 2.63155 | ||||||||
\(977\) | 5.86810 | 0.187737 | 0.0938685 | − | 0.995585i | \(-0.470077\pi\) | ||||
0.0938685 | + | 0.995585i | \(0.470077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.37355 | −0.139779 | ||||||||
\(980\) | 14.5928 | 0.466148 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.36105 | 0.0753441 | ||||||||
\(983\) | 18.1817 | 0.579907 | 0.289953 | − | 0.957041i | \(-0.406360\pi\) | ||||
0.289953 | + | 0.957041i | \(0.406360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.14717 | 0.259591 | ||||||||
\(986\) | 8.68760 | 0.276670 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.5179 | −1.19360 | ||||||||
\(989\) | 6.93400 | 0.220488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.5666 | 1.44747 | 0.723736 | − | 0.690077i | \(-0.242423\pi\) | ||||
0.723736 | + | 0.690077i | \(0.242423\pi\) | |||||||
\(992\) | 23.6537 | 0.751006 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.49332 | −0.269392 | ||||||||
\(995\) | −6.44898 | −0.204446 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5989 | 0.747384 | 0.373692 | − | 0.927553i | \(-0.378092\pi\) | ||||
0.373692 | + | 0.927553i | \(0.378092\pi\) | |||||||
\(998\) | 44.5280 | 1.40951 | ||||||||
\(999\) | 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 | 6003.2.a.r.1.2 | 16 | ||
3.2 | odd | 2 | 2001.2.a.n.1.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.15 | ✓ | 16 | 3.2 | odd | 2 | ||
6003.2.a.r.1.2 | 16 | 1.1 | even | 1 | trivial |