Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.05896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32691 | −0.938266 | −0.469133 | − | 0.883128i | \(-0.655434\pi\) | ||||
−0.469133 | + | 0.883128i | \(0.655434\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.239314 | −0.119657 | ||||||||
\(5\) | −0.326909 | −0.146198 | −0.0730990 | − | 0.997325i | \(-0.523289\pi\) | ||||
−0.0730990 | + | 0.997325i | \(0.523289\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.97136 | 1.05054 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.433778 | 0.137173 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0589594 | −0.0163524 | −0.00817619 | − | 0.999967i | \(-0.502603\pi\) | ||||
−0.00817619 | + | 0.999967i | \(0.502603\pi\) | |||||||
\(14\) | 1.32691 | 0.354631 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.46410 | −0.866025 | ||||||||
\(17\) | −6.28375 | −1.52403 | −0.762016 | − | 0.647558i | \(-0.775790\pi\) | ||||
−0.762016 | + | 0.647558i | \(0.775790\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.43378 | 0.558347 | 0.279173 | − | 0.960241i | \(-0.409940\pi\) | ||||
0.279173 | + | 0.960241i | \(0.409940\pi\) | |||||||
\(20\) | 0.0782337 | 0.0174936 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.93756 | −1.23807 | −0.619034 | − | 0.785364i | \(-0.712476\pi\) | ||||
−0.619034 | + | 0.785364i | \(0.712476\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89313 | −0.978626 | ||||||||
\(26\) | 0.0782337 | 0.0153429 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.239314 | 0.0452260 | ||||||||
\(29\) | −9.43072 | −1.75124 | −0.875620 | − | 0.483000i | \(-0.839547\pi\) | ||||
−0.875620 | + | 0.483000i | \(0.839547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.98589 | 0.356676 | 0.178338 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178338 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(32\) | −1.34618 | −0.237974 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.33796 | 1.42995 | ||||||||
\(35\) | 0.326909 | 0.0552576 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.53242 | −1.07392 | −0.536962 | − | 0.843607i | \(-0.680428\pi\) | ||||
−0.536962 | + | 0.843607i | \(0.680428\pi\) | |||||||
\(38\) | −3.22940 | −0.523878 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.971364 | −0.153586 | ||||||||
\(41\) | 0.0782337 | 0.0122180 | 0.00610902 | − | 0.999981i | \(-0.498055\pi\) | ||||
0.00610902 | + | 0.999981i | \(0.498055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.92177 | 0.750562 | 0.375281 | − | 0.926911i | \(-0.377546\pi\) | ||||
0.375281 | + | 0.926911i | \(0.377546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.87861 | 1.16164 | ||||||||
\(47\) | −6.01621 | −0.877555 | −0.438778 | − | 0.898596i | \(-0.644588\pi\) | ||||
−0.438778 | + | 0.898596i | \(0.644588\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.49274 | 0.918212 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0141098 | 0.00195667 | ||||||||
\(53\) | 5.94273 | 0.816297 | 0.408148 | − | 0.912916i | \(-0.366175\pi\) | ||||
0.408148 | + | 0.912916i | \(0.366175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.97136 | −0.397065 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.5137 | 1.64313 | ||||||||
\(59\) | −1.13719 | −0.148050 | −0.0740250 | − | 0.997256i | \(-0.523584\pi\) | ||||
−0.0740250 | + | 0.997256i | \(0.523584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2807 | 1.57238 | 0.786190 | − | 0.617984i | \(-0.212050\pi\) | ||||
0.786190 | + | 0.617984i | \(0.212050\pi\) | |||||||
\(62\) | −2.63509 | −0.334657 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.71446 | 1.08931 | ||||||||
\(65\) | 0.0192743 | 0.00239069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.75721 | 1.06986 | 0.534932 | − | 0.844895i | \(-0.320337\pi\) | ||||
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(68\) | 1.50379 | 0.182361 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.433778 | −0.0518464 | ||||||||
\(71\) | 1.65857 | 0.196836 | 0.0984178 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984178 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.40514 | 1.10079 | 0.550394 | − | 0.834905i | \(-0.314477\pi\) | ||||
0.550394 | + | 0.834905i | \(0.314477\pi\) | |||||||
\(74\) | 8.66793 | 1.00763 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.582436 | −0.0668100 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0717 | −1.47068 | −0.735340 | − | 0.677698i | \(-0.762978\pi\) | ||||
−0.735340 | + | 0.677698i | \(0.762978\pi\) | |||||||
\(80\) | 1.13244 | 0.126611 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.103809 | −0.0114638 | ||||||||
\(83\) | 7.49443 | 0.822620 | 0.411310 | − | 0.911496i | \(-0.365071\pi\) | ||||
0.411310 | + | 0.911496i | \(0.365071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.05421 | 0.222810 | ||||||||
\(86\) | −6.53073 | −0.704227 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6013 | −1.12373 | −0.561867 | − | 0.827227i | \(-0.689917\pi\) | ||||
−0.561867 | + | 0.827227i | \(0.689917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0589594 | 0.00618062 | ||||||||
\(92\) | 1.42094 | 0.148143 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.98297 | 0.823380 | ||||||||
\(95\) | −0.795623 | −0.0816292 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.71278 | −0.681579 | −0.340790 | − | 0.940140i | \(-0.610694\pi\) | ||||
−0.340790 | + | 0.940140i | \(0.610694\pi\) | |||||||
\(98\) | −1.32691 | −0.134038 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.17099 | 0.117099 | ||||||||
\(101\) | −8.44830 | −0.840638 | −0.420319 | − | 0.907376i | \(-0.638082\pi\) | ||||
−0.420319 | + | 0.907376i | \(0.638082\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9631 | −1.57289 | −0.786447 | − | 0.617657i | \(-0.788082\pi\) | ||||
−0.786447 | + | 0.617657i | \(0.788082\pi\) | |||||||
\(104\) | −0.175190 | −0.0171788 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.88546 | −0.765903 | ||||||||
\(107\) | 5.17044 | 0.499845 | 0.249923 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249923 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.02444 | 0.289689 | 0.144844 | − | 0.989454i | \(-0.453732\pi\) | ||||
0.144844 | + | 0.989454i | \(0.453732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.46410 | 0.327327 | ||||||||
\(113\) | 6.23584 | 0.586618 | 0.293309 | − | 0.956018i | \(-0.405243\pi\) | ||||
0.293309 | + | 0.956018i | \(0.405243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.94104 | 0.181003 | ||||||||
\(116\) | 2.25690 | 0.209548 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.50895 | 0.138910 | ||||||||
\(119\) | 6.28375 | 0.576030 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.2953 | −1.47531 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.475251 | −0.0426788 | ||||||||
\(125\) | 3.23415 | 0.289271 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.40039 | 0.656679 | 0.328339 | − | 0.944560i | \(-0.393511\pi\) | ||||
0.328339 | + | 0.944560i | \(0.393511\pi\) | |||||||
\(128\) | −8.87093 | −0.784087 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0255753 | −0.00224310 | ||||||||
\(131\) | −10.9479 | −0.956522 | −0.478261 | − | 0.878218i | \(-0.658733\pi\) | ||||
−0.478261 | + | 0.878218i | \(0.658733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43378 | −0.211035 | ||||||||
\(134\) | −11.6200 | −1.00382 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −18.6713 | −1.60105 | ||||||||
\(137\) | −4.96620 | −0.424291 | −0.212146 | − | 0.977238i | \(-0.568045\pi\) | ||||
−0.212146 | + | 0.977238i | \(0.568045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.19560 | −0.525504 | −0.262752 | − | 0.964863i | \(-0.584630\pi\) | ||||
−0.262752 | + | 0.964863i | \(0.584630\pi\) | |||||||
\(140\) | −0.0782337 | −0.00661195 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.20077 | −0.184684 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.08298 | 0.256028 | ||||||||
\(146\) | −12.4798 | −1.03283 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.56330 | 0.128502 | ||||||||
\(149\) | 20.3158 | 1.66433 | 0.832166 | − | 0.554527i | \(-0.187101\pi\) | ||||
0.832166 | + | 0.554527i | \(0.187101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.49959 | 0.773066 | 0.386533 | − | 0.922276i | \(-0.373673\pi\) | ||||
0.386533 | + | 0.922276i | \(0.373673\pi\) | |||||||
\(152\) | 7.23164 | 0.586564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.649205 | −0.0521454 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4500 | −1.39266 | −0.696330 | − | 0.717721i | \(-0.745185\pi\) | ||||
−0.696330 | + | 0.717721i | \(0.745185\pi\) | |||||||
\(158\) | 17.3449 | 1.37989 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.440079 | 0.0347913 | ||||||||
\(161\) | 5.93756 | 0.467946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.35304 | −0.575934 | −0.287967 | − | 0.957640i | \(-0.592979\pi\) | ||||
−0.287967 | + | 0.957640i | \(0.592979\pi\) | |||||||
\(164\) | −0.0187224 | −0.00146197 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.94442 | −0.771836 | ||||||||
\(167\) | 4.74141 | 0.366901 | 0.183451 | − | 0.983029i | \(-0.441273\pi\) | ||||
0.183451 | + | 0.983029i | \(0.441273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9965 | −0.999733 | ||||||||
\(170\) | −2.72575 | −0.209055 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.17785 | −0.0898099 | ||||||||
\(173\) | 8.04791 | 0.611871 | 0.305936 | − | 0.952052i | \(-0.401031\pi\) | ||||
0.305936 | + | 0.952052i | \(0.401031\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.89313 | 0.369886 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.0669 | 1.05436 | ||||||||
\(179\) | 10.5393 | 0.787742 | 0.393871 | − | 0.919166i | \(-0.371136\pi\) | ||||
0.393871 | + | 0.919166i | \(0.371136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.5389 | −1.74963 | −0.874815 | − | 0.484457i | \(-0.839017\pi\) | ||||
−0.874815 | + | 0.484457i | \(0.839017\pi\) | |||||||
\(182\) | −0.0782337 | −0.00579907 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.6427 | −1.30063 | ||||||||
\(185\) | 2.13550 | 0.157005 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.43976 | 0.105005 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.05572 | 0.0765899 | ||||||||
\(191\) | −17.9188 | −1.29656 | −0.648281 | − | 0.761401i | \(-0.724512\pi\) | ||||
−0.648281 | + | 0.761401i | \(0.724512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1962 | 0.805917 | 0.402958 | − | 0.915218i | \(-0.367982\pi\) | ||||
0.402958 | + | 0.915218i | \(0.367982\pi\) | |||||||
\(194\) | 8.90724 | 0.639503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.239314 | −0.0170938 | ||||||||
\(197\) | −5.32512 | −0.379399 | −0.189700 | − | 0.981842i | \(-0.560751\pi\) | ||||
−0.189700 | + | 0.981842i | \(0.560751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.05938 | 0.642202 | 0.321101 | − | 0.947045i | \(-0.395947\pi\) | ||||
0.321101 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(200\) | −14.5393 | −1.02808 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.2101 | 0.788742 | ||||||||
\(203\) | 9.43072 | 0.661907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0255753 | −0.00178625 | ||||||||
\(206\) | 21.1816 | 1.47579 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.204241 | 0.0141616 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.8370 | 1.91638 | 0.958189 | − | 0.286136i | \(-0.0923710\pi\) | ||||
0.958189 | + | 0.286136i | \(0.0923710\pi\) | |||||||
\(212\) | −1.42218 | −0.0976755 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.86070 | −0.468988 | ||||||||
\(215\) | −1.60897 | −0.109731 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.98589 | −0.134811 | ||||||||
\(218\) | −4.01315 | −0.271805 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.370486 | 0.0249216 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3064 | 1.29285 | 0.646426 | − | 0.762977i | \(-0.276263\pi\) | ||||
0.646426 | + | 0.762977i | \(0.276263\pi\) | |||||||
\(224\) | 1.34618 | 0.0899456 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.27439 | −0.550404 | ||||||||
\(227\) | −1.31586 | −0.0873366 | −0.0436683 | − | 0.999046i | \(-0.513904\pi\) | ||||
−0.0436683 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.440079 | −0.0290812 | −0.0145406 | − | 0.999894i | \(-0.504629\pi\) | ||||
−0.0145406 | + | 0.999894i | \(0.504629\pi\) | |||||||
\(230\) | −2.57558 | −0.169829 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −28.0221 | −1.83974 | ||||||||
\(233\) | 5.29786 | 0.347074 | 0.173537 | − | 0.984827i | \(-0.444480\pi\) | ||||
0.173537 | + | 0.984827i | \(0.444480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.96675 | 0.128297 | ||||||||
\(236\) | 0.272146 | 0.0177152 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.33796 | −0.540470 | ||||||||
\(239\) | −24.3293 | −1.57373 | −0.786866 | − | 0.617123i | \(-0.788298\pi\) | ||||
−0.786866 | + | 0.617123i | \(0.788298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.5165 | −1.70808 | −0.854040 | − | 0.520208i | \(-0.825855\pi\) | ||||
−0.854040 | + | 0.520208i | \(0.825855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.93894 | −0.188146 | ||||||||
\(245\) | −0.326909 | −0.0208854 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.143494 | −0.00913030 | ||||||||
\(248\) | 5.90080 | 0.374701 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.29142 | −0.271413 | ||||||||
\(251\) | 19.1828 | 1.21081 | 0.605403 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605403 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.81965 | −0.616139 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.65801 | −0.353626 | ||||||||
\(257\) | −12.2417 | −0.763618 | −0.381809 | − | 0.924241i | \(-0.624699\pi\) | ||||
−0.381809 | + | 0.924241i | \(0.624699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.53242 | 0.405905 | ||||||||
\(260\) | −0.00461261 | −0.000286062 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.5269 | 0.897472 | ||||||||
\(263\) | 18.2025 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310338\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.94273 | −0.119341 | ||||||||
\(266\) | 3.22940 | 0.198007 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.09572 | −0.128016 | ||||||||
\(269\) | −9.40683 | −0.573545 | −0.286772 | − | 0.957999i | \(-0.592582\pi\) | ||||
−0.286772 | + | 0.957999i | \(0.592582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5252 | −0.882341 | −0.441170 | − | 0.897423i | \(-0.645437\pi\) | ||||
−0.441170 | + | 0.897423i | \(0.645437\pi\) | |||||||
\(272\) | 21.7675 | 1.31985 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.58969 | 0.398098 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.26447 | 0.496564 | 0.248282 | − | 0.968688i | \(-0.420134\pi\) | ||||
0.248282 | + | 0.968688i | \(0.420134\pi\) | |||||||
\(278\) | 8.22100 | 0.493063 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.971364 | 0.0580501 | ||||||||
\(281\) | 24.0080 | 1.43220 | 0.716098 | − | 0.697999i | \(-0.245926\pi\) | ||||
0.716098 | + | 0.697999i | \(0.245926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0512 | 0.954142 | 0.477071 | − | 0.878865i | \(-0.341698\pi\) | ||||
0.477071 | + | 0.878865i | \(0.341698\pi\) | |||||||
\(284\) | −0.396917 | −0.0235527 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0782337 | −0.00461799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.4855 | 1.32268 | ||||||||
\(290\) | −4.09084 | −0.240222 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.25078 | −0.131717 | ||||||||
\(293\) | −7.60088 | −0.444048 | −0.222024 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222024 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.371758 | 0.0216446 | ||||||||
\(296\) | −19.4102 | −1.12820 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.9572 | −1.56159 | ||||||||
\(299\) | 0.350075 | 0.0202454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.92177 | −0.283686 | ||||||||
\(302\) | −12.6051 | −0.725341 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.43085 | −0.483543 | ||||||||
\(305\) | −4.01466 | −0.229879 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7345 | 1.12631 | 0.563153 | − | 0.826353i | \(-0.309588\pi\) | ||||
0.563153 | + | 0.826353i | \(0.309588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.861435 | 0.0489262 | ||||||||
\(311\) | 30.3127 | 1.71888 | 0.859438 | − | 0.511240i | \(-0.170814\pi\) | ||||
0.859438 | + | 0.511240i | \(0.170814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7850 | −1.11832 | −0.559158 | − | 0.829061i | \(-0.688875\pi\) | ||||
−0.559158 | + | 0.829061i | \(0.688875\pi\) | |||||||
\(314\) | 23.1545 | 1.30669 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.12824 | 0.175977 | ||||||||
\(317\) | 18.9639 | 1.06512 | 0.532558 | − | 0.846393i | \(-0.321231\pi\) | ||||
0.532558 | + | 0.846393i | \(0.321231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.84883 | −0.159255 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.87861 | −0.439057 | ||||||||
\(323\) | −15.2932 | −0.850939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.288496 | 0.0160029 | ||||||||
\(326\) | 9.75681 | 0.540380 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.232461 | 0.0128355 | ||||||||
\(329\) | 6.01621 | 0.331685 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.98895 | −0.219253 | −0.109626 | − | 0.993973i | \(-0.534965\pi\) | ||||
−0.109626 | + | 0.993973i | \(0.534965\pi\) | |||||||
\(332\) | −1.79352 | −0.0984321 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.29142 | −0.344251 | ||||||||
\(335\) | −2.86281 | −0.156412 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.5690 | 1.50178 | 0.750891 | − | 0.660426i | \(-0.229624\pi\) | ||||
0.750891 | + | 0.660426i | \(0.229624\pi\) | |||||||
\(338\) | 17.2452 | 0.938015 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.491601 | −0.0266608 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 14.6244 | 0.788493 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.6788 | −0.574098 | ||||||||
\(347\) | 32.5280 | 1.74619 | 0.873097 | − | 0.487547i | \(-0.162108\pi\) | ||||
0.873097 | + | 0.487547i | \(0.162108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.7099 | 1.53680 | 0.768402 | − | 0.639968i | \(-0.221052\pi\) | ||||
0.768402 | + | 0.639968i | \(0.221052\pi\) | |||||||
\(350\) | −6.49274 | −0.347051 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.421356 | 0.0224265 | 0.0112133 | − | 0.999937i | \(-0.496431\pi\) | ||||
0.0112133 | + | 0.999937i | \(0.496431\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.542199 | −0.0287770 | ||||||||
\(356\) | 2.53703 | 0.134463 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.9847 | −0.739112 | ||||||||
\(359\) | −8.17340 | −0.431376 | −0.215688 | − | 0.976462i | \(-0.569199\pi\) | ||||
−0.215688 | + | 0.976462i | \(0.569199\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0767 | −0.688249 | ||||||||
\(362\) | 31.2339 | 1.64162 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0141098 | −0.000739554 0 | ||||||||
\(365\) | −3.07462 | −0.160933 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9415 | −0.571139 | −0.285570 | − | 0.958358i | \(-0.592183\pi\) | ||||
−0.285570 | + | 0.958358i | \(0.592183\pi\) | |||||||
\(368\) | 20.5683 | 1.07220 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.83362 | −0.147313 | ||||||||
\(371\) | −5.94273 | −0.308531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.2953 | 0.791963 | 0.395982 | − | 0.918258i | \(-0.370404\pi\) | ||||
0.395982 | + | 0.918258i | \(0.370404\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.8764 | −0.921903 | ||||||||
\(377\) | 0.556029 | 0.0286370 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1698 | 1.65245 | 0.826226 | − | 0.563339i | \(-0.190484\pi\) | ||||
0.826226 | + | 0.563339i | \(0.190484\pi\) | |||||||
\(380\) | 0.190403 | 0.00976749 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.7767 | 1.21652 | ||||||||
\(383\) | 20.5485 | 1.04998 | 0.524991 | − | 0.851108i | \(-0.324069\pi\) | ||||
0.524991 | + | 0.851108i | \(0.324069\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.8563 | −0.756164 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.60646 | 0.0815556 | ||||||||
\(389\) | −16.9025 | −0.856992 | −0.428496 | − | 0.903544i | \(-0.640956\pi\) | ||||
−0.428496 | + | 0.903544i | \(0.640956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.3102 | 1.88686 | ||||||||
\(392\) | 2.97136 | 0.150077 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.06595 | 0.355977 | ||||||||
\(395\) | 4.27325 | 0.215011 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7606 | 0.891378 | 0.445689 | − | 0.895188i | \(-0.352959\pi\) | ||||
0.445689 | + | 0.895188i | \(0.352959\pi\) | |||||||
\(398\) | −12.0210 | −0.602556 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.9503 | 0.847515 | ||||||||
\(401\) | −8.19963 | −0.409470 | −0.204735 | − | 0.978817i | \(-0.565633\pi\) | ||||
−0.204735 | + | 0.978817i | \(0.565633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.117087 | −0.00583251 | ||||||||
\(404\) | 2.02179 | 0.100588 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.5137 | −0.621044 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.5772 | −1.80862 | −0.904312 | − | 0.426871i | \(-0.859616\pi\) | ||||
−0.904312 | + | 0.426871i | \(0.859616\pi\) | |||||||
\(410\) | 0.0339360 | 0.00167598 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.82020 | 0.188208 | ||||||||
\(413\) | 1.13719 | 0.0559576 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.44999 | −0.120265 | ||||||||
\(416\) | 0.0793701 | 0.00389144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8296 | 0.675618 | 0.337809 | − | 0.941215i | \(-0.390314\pi\) | ||||
0.337809 | + | 0.941215i | \(0.390314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.8503 | −1.50355 | −0.751775 | − | 0.659419i | \(-0.770802\pi\) | ||||
−0.751775 | + | 0.659419i | \(0.770802\pi\) | |||||||
\(422\) | −36.9371 | −1.79807 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.6580 | 0.857549 | ||||||||
\(425\) | 30.7472 | 1.49146 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2807 | −0.594304 | ||||||||
\(428\) | −1.23736 | −0.0598099 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.13495 | 0.102957 | ||||||||
\(431\) | 3.61107 | 0.173939 | 0.0869696 | − | 0.996211i | \(-0.472282\pi\) | ||||
0.0869696 | + | 0.996211i | \(0.472282\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.0051 | 1.82641 | 0.913203 | − | 0.407504i | \(-0.133601\pi\) | ||||
0.913203 | + | 0.407504i | \(0.133601\pi\) | |||||||
\(434\) | 2.63509 | 0.126489 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.723790 | −0.0346632 | ||||||||
\(437\) | −14.4507 | −0.691271 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.8855 | −1.23545 | −0.617723 | − | 0.786396i | \(-0.711945\pi\) | ||||
−0.617723 | + | 0.786396i | \(0.711945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.491601 | −0.0233831 | ||||||||
\(443\) | −14.8247 | −0.704342 | −0.352171 | − | 0.935936i | \(-0.614556\pi\) | ||||
−0.352171 | + | 0.935936i | \(0.614556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.46565 | 0.164288 | ||||||||
\(446\) | −25.6178 | −1.21304 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.71446 | −0.411720 | ||||||||
\(449\) | −37.8071 | −1.78423 | −0.892114 | − | 0.451810i | \(-0.850779\pi\) | ||||
−0.892114 | + | 0.451810i | \(0.850779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.49232 | −0.0701929 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.74602 | 0.0819450 | ||||||||
\(455\) | −0.0192743 | −0.000903594 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.5114 | −1.09982 | −0.549908 | − | 0.835226i | \(-0.685337\pi\) | ||||
−0.549908 | + | 0.835226i | \(0.685337\pi\) | |||||||
\(458\) | 0.583944 | 0.0272859 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.464518 | −0.0216582 | ||||||||
\(461\) | 40.9211 | 1.90589 | 0.952943 | − | 0.303149i | \(-0.0980380\pi\) | ||||
0.952943 | + | 0.303149i | \(0.0980380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0607472 | 0.00282316 | 0.00141158 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00141158 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(464\) | 32.6690 | 1.51662 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.02977 | −0.325648 | ||||||||
\(467\) | 37.4362 | 1.73234 | 0.866170 | − | 0.499749i | \(-0.166575\pi\) | ||||
0.866170 | + | 0.499749i | \(0.166575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.75721 | −0.404370 | ||||||||
\(470\) | −2.60970 | −0.120376 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.37902 | −0.155532 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.9088 | −0.546413 | ||||||||
\(476\) | −1.50379 | −0.0689259 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.2828 | 1.47658 | ||||||||
\(479\) | −31.3978 | −1.43460 | −0.717300 | − | 0.696764i | \(-0.754622\pi\) | ||||
−0.717300 | + | 0.696764i | \(0.754622\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.385147 | 0.0175612 | ||||||||
\(482\) | 35.1850 | 1.60263 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.19446 | 0.0996455 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3881 | −0.923873 | −0.461937 | − | 0.886913i | \(-0.652845\pi\) | ||||
−0.461937 | + | 0.886913i | \(0.652845\pi\) | |||||||
\(488\) | 36.4904 | 1.65184 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.433778 | 0.0195961 | ||||||||
\(491\) | −11.6120 | −0.524043 | −0.262022 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 59.2602 | 2.66895 | ||||||||
\(494\) | 0.190403 | 0.00856665 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.87933 | −0.308891 | ||||||||
\(497\) | −1.65857 | −0.0743968 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.1606 | 1.70830 | 0.854151 | − | 0.520025i | \(-0.174078\pi\) | ||||
0.854151 | + | 0.520025i | \(0.174078\pi\) | |||||||
\(500\) | −0.773976 | −0.0346133 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.4538 | −1.13606 | ||||||||
\(503\) | 32.5721 | 1.45232 | 0.726160 | − | 0.687526i | \(-0.241303\pi\) | ||||
0.726160 | + | 0.687526i | \(0.241303\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.76182 | 0.122899 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.77102 | −0.0785761 | ||||||||
\(509\) | 23.4898 | 1.04117 | 0.520584 | − | 0.853811i | \(-0.325714\pi\) | ||||
0.520584 | + | 0.853811i | \(0.325714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.40514 | −0.416059 | ||||||||
\(512\) | 25.2495 | 1.11588 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.2436 | 0.716477 | ||||||||
\(515\) | 5.21849 | 0.229954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.66793 | −0.380847 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0572710 | 0.00251150 | ||||||||
\(521\) | 34.5918 | 1.51549 | 0.757747 | − | 0.652548i | \(-0.226300\pi\) | ||||
0.757747 | + | 0.652548i | \(0.226300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.30429 | 0.363121 | 0.181561 | − | 0.983380i | \(-0.441885\pi\) | ||||
0.181561 | + | 0.983380i | \(0.441885\pi\) | |||||||
\(524\) | 2.61998 | 0.114454 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.1530 | −1.05312 | ||||||||
\(527\) | −12.4788 | −0.543586 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.2547 | 0.532812 | ||||||||
\(530\) | 2.57782 | 0.111974 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.582436 | 0.0252518 | ||||||||
\(533\) | −0.00461261 | −0.000199794 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.69026 | −0.0730764 | ||||||||
\(536\) | 26.0209 | 1.12393 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.4820 | 0.538137 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3943 | −1.00580 | −0.502899 | − | 0.864345i | \(-0.667733\pi\) | ||||
−0.502899 | + | 0.864345i | \(0.667733\pi\) | |||||||
\(542\) | 19.2736 | 0.827871 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.45907 | 0.362680 | ||||||||
\(545\) | −0.988715 | −0.0423519 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.1606 | −0.819247 | −0.409623 | − | 0.912255i | \(-0.634340\pi\) | ||||
−0.409623 | + | 0.912255i | \(0.634340\pi\) | |||||||
\(548\) | 1.18848 | 0.0507693 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.9523 | −0.977800 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0717 | 0.555865 | ||||||||
\(554\) | −10.9662 | −0.465909 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.48269 | 0.0628801 | ||||||||
\(557\) | −25.9067 | −1.09770 | −0.548852 | − | 0.835920i | \(-0.684935\pi\) | ||||
−0.548852 | + | 0.835920i | \(0.684935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.290184 | −0.0122735 | ||||||||
\(560\) | −1.13244 | −0.0478545 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.8564 | −1.34378 | ||||||||
\(563\) | 2.58381 | 0.108895 | 0.0544473 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544473 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.03855 | −0.0857624 | ||||||||
\(566\) | −21.2984 | −0.895239 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.92820 | 0.206783 | ||||||||
\(569\) | −25.6769 | −1.07643 | −0.538215 | − | 0.842807i | \(-0.680901\pi\) | ||||
−0.538215 | + | 0.842807i | \(0.680901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.12907 | 0.0472500 | 0.0236250 | − | 0.999721i | \(-0.492479\pi\) | ||||
0.0236250 | + | 0.999721i | \(0.492479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.103809 | 0.00433290 | ||||||||
\(575\) | 29.0533 | 1.21161 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.9141 | −1.41186 | −0.705932 | − | 0.708280i | \(-0.749472\pi\) | ||||
−0.705932 | + | 0.708280i | \(0.749472\pi\) | |||||||
\(578\) | −29.8362 | −1.24102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.737800 | −0.0306355 | ||||||||
\(581\) | −7.49443 | −0.310921 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 27.9461 | 1.15642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0857 | 0.416635 | ||||||||
\(587\) | −42.7729 | −1.76543 | −0.882713 | − | 0.469912i | \(-0.844286\pi\) | ||||
−0.882713 | + | 0.469912i | \(0.844286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.83322 | 0.199149 | ||||||||
\(590\) | −0.493289 | −0.0203084 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.6290 | 0.930045 | ||||||||
\(593\) | 30.9085 | 1.26926 | 0.634630 | − | 0.772816i | \(-0.281152\pi\) | ||||
0.634630 | + | 0.772816i | \(0.281152\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.05421 | −0.0842144 | ||||||||
\(596\) | −4.86184 | −0.199149 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.464518 | −0.0189955 | ||||||||
\(599\) | −10.2428 | −0.418509 | −0.209255 | − | 0.977861i | \(-0.567104\pi\) | ||||
−0.209255 | + | 0.977861i | \(0.567104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5452 | 1.12359 | 0.561795 | − | 0.827276i | \(-0.310111\pi\) | ||||
0.561795 | + | 0.827276i | \(0.310111\pi\) | |||||||
\(602\) | 6.53073 | 0.266173 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.27338 | −0.0925026 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.3982 | −0.706171 | −0.353085 | − | 0.935591i | \(-0.614867\pi\) | ||||
−0.353085 | + | 0.935591i | \(0.614867\pi\) | |||||||
\(608\) | −3.27631 | −0.132872 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.32709 | 0.215688 | ||||||||
\(611\) | 0.354712 | 0.0143501 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.178250 | 0.00719945 | 0.00359973 | − | 0.999994i | \(-0.498854\pi\) | ||||
0.00359973 | + | 0.999994i | \(0.498854\pi\) | |||||||
\(614\) | −26.1858 | −1.05677 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.66139 | 0.147402 | 0.0737010 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737010 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7370 | 0.954070 | 0.477035 | − | 0.878884i | \(-0.341712\pi\) | ||||
0.477035 | + | 0.878884i | \(0.341712\pi\) | |||||||
\(620\) | 0.155364 | 0.00623955 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −40.2222 | −1.61276 | ||||||||
\(623\) | 10.6013 | 0.424732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4084 | 0.936335 | ||||||||
\(626\) | 26.2529 | 1.04928 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.17602 | 0.166641 | ||||||||
\(629\) | 41.0481 | 1.63669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0214 | 0.637801 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(632\) | −38.8408 | −1.54500 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.1633 | −0.999363 | ||||||||
\(635\) | −2.41925 | −0.0960051 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0589594 | −0.00233606 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.89998 | 0.114632 | ||||||||
\(641\) | 26.3387 | 1.04032 | 0.520158 | − | 0.854070i | \(-0.325873\pi\) | ||||
0.520158 | + | 0.854070i | \(0.325873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9889 | 1.30095 | 0.650477 | − | 0.759526i | \(-0.274569\pi\) | ||||
0.650477 | + | 0.759526i | \(0.274569\pi\) | |||||||
\(644\) | −1.42094 | −0.0559929 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.2927 | 0.798407 | ||||||||
\(647\) | 15.1898 | 0.597171 | 0.298585 | − | 0.954383i | \(-0.403485\pi\) | ||||
0.298585 | + | 0.954383i | \(0.403485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.382808 | −0.0150150 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.75968 | 0.0689145 | ||||||||
\(653\) | −34.1357 | −1.33583 | −0.667916 | − | 0.744236i | \(-0.732814\pi\) | ||||
−0.667916 | + | 0.744236i | \(0.732814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.57896 | 0.139842 | ||||||||
\(656\) | −0.271009 | −0.0105811 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.98297 | −0.311208 | ||||||||
\(659\) | 11.4960 | 0.447820 | 0.223910 | − | 0.974610i | \(-0.428118\pi\) | ||||
0.223910 | + | 0.974610i | \(0.428118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.84312 | 0.343957 | 0.171979 | − | 0.985101i | \(-0.444984\pi\) | ||||
0.171979 | + | 0.985101i | \(0.444984\pi\) | |||||||
\(662\) | 5.29297 | 0.205717 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.2687 | 0.864192 | ||||||||
\(665\) | 0.795623 | 0.0308529 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.9955 | 2.16815 | ||||||||
\(668\) | −1.13468 | −0.0439023 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.79868 | 0.146756 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.96022 | −0.268297 | −0.134148 | − | 0.990961i | \(-0.542830\pi\) | ||||
−0.134148 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(674\) | −36.5816 | −1.40907 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.11025 | 0.119625 | ||||||||
\(677\) | 24.6140 | 0.945993 | 0.472996 | − | 0.881064i | \(-0.343172\pi\) | ||||
0.472996 | + | 0.881064i | \(0.343172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.71278 | 0.257613 | ||||||||
\(680\) | 6.10381 | 0.234070 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.65760 | 0.101690 | 0.0508451 | − | 0.998707i | \(-0.483809\pi\) | ||||
0.0508451 | + | 0.998707i | \(0.483809\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.62349 | 0.0620305 | ||||||||
\(686\) | 1.32691 | 0.0506616 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.0495 | −0.650006 | ||||||||
\(689\) | −0.350380 | −0.0133484 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.06065 | 0.230558 | 0.115279 | − | 0.993333i | \(-0.463224\pi\) | ||||
0.115279 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(692\) | −1.92597 | −0.0732146 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.1617 | −1.63839 | ||||||||
\(695\) | 2.02539 | 0.0768276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.491601 | −0.0186207 | ||||||||
\(698\) | −38.0953 | −1.44193 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.17099 | −0.0442594 | ||||||||
\(701\) | 29.2016 | 1.10293 | 0.551465 | − | 0.834198i | \(-0.314069\pi\) | ||||
0.551465 | + | 0.834198i | \(0.314069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8985 | −0.599622 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.559101 | −0.0210421 | ||||||||
\(707\) | 8.44830 | 0.317731 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.34783 | 0.200842 | 0.100421 | − | 0.994945i | \(-0.467981\pi\) | ||||
0.100421 | + | 0.994945i | \(0.467981\pi\) | |||||||
\(710\) | 0.719449 | 0.0270004 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.5003 | −1.18052 | ||||||||
\(713\) | −11.7914 | −0.441590 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.52219 | −0.0942588 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.8454 | 0.404745 | ||||||||
\(719\) | −39.3239 | −1.46653 | −0.733267 | − | 0.679941i | \(-0.762005\pi\) | ||||
−0.733267 | + | 0.679941i | \(0.762005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9631 | 0.594498 | ||||||||
\(722\) | 17.3516 | 0.645760 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.63317 | 0.209355 | ||||||||
\(725\) | 46.1457 | 1.71381 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.52389 | −0.130694 | −0.0653470 | − | 0.997863i | \(-0.520815\pi\) | ||||
−0.0653470 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(728\) | 0.175190 | 0.00649296 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.07974 | 0.150998 | ||||||||
\(731\) | −30.9271 | −1.14388 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.58578 | 0.132444 | 0.0662218 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662218 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(734\) | 14.5183 | 0.535881 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.99305 | 0.294628 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4213 | −0.751208 | −0.375604 | − | 0.926780i | \(-0.622565\pi\) | ||||
−0.375604 | + | 0.926780i | \(0.622565\pi\) | |||||||
\(740\) | −0.511055 | −0.0187868 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.88546 | 0.289484 | ||||||||
\(743\) | −26.7582 | −0.981662 | −0.490831 | − | 0.871255i | \(-0.663307\pi\) | ||||
−0.490831 | + | 0.871255i | \(0.663307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.64140 | −0.243322 | ||||||||
\(746\) | −20.2955 | −0.743072 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.17044 | −0.188924 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.7545 | 1.48715 | 0.743576 | − | 0.668652i | \(-0.233128\pi\) | ||||
0.743576 | + | 0.668652i | \(0.233128\pi\) | |||||||
\(752\) | 20.8408 | 0.759985 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.737800 | −0.0268691 | ||||||||
\(755\) | −3.10550 | −0.113021 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.4923 | 0.381350 | 0.190675 | − | 0.981653i | \(-0.438932\pi\) | ||||
0.190675 | + | 0.981653i | \(0.438932\pi\) | |||||||
\(758\) | −42.6864 | −1.55044 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.36409 | −0.0857544 | ||||||||
\(761\) | −2.38294 | −0.0863816 | −0.0431908 | − | 0.999067i | \(-0.513752\pi\) | ||||
−0.0431908 | + | 0.999067i | \(0.513752\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.02444 | −0.109492 | ||||||||
\(764\) | 4.28822 | 0.155142 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.2660 | −0.985162 | ||||||||
\(767\) | 0.0670482 | 0.00242097 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.0495 | 0.831186 | 0.415593 | − | 0.909551i | \(-0.363574\pi\) | ||||
0.415593 | + | 0.909551i | \(0.363574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.67939 | −0.0964334 | ||||||||
\(773\) | 30.2708 | 1.08876 | 0.544382 | − | 0.838837i | \(-0.316764\pi\) | ||||
0.544382 | + | 0.838837i | \(0.316764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.71722 | −0.349053 | ||||||||
\(776\) | −19.9461 | −0.716023 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.4281 | 0.804087 | ||||||||
\(779\) | 0.190403 | 0.00682191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −49.5072 | −1.77037 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.46410 | −0.123718 | ||||||||
\(785\) | 5.70455 | 0.203604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.41144 | −0.264189 | −0.132095 | − | 0.991237i | \(-0.542170\pi\) | ||||
−0.132095 | + | 0.991237i | \(0.542170\pi\) | |||||||
\(788\) | 1.27437 | 0.0453977 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.67021 | −0.201737 | ||||||||
\(791\) | −6.23584 | −0.221721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.724062 | −0.0257122 | ||||||||
\(794\) | −23.5667 | −0.836350 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.16803 | −0.0768439 | ||||||||
\(797\) | 33.5597 | 1.18875 | 0.594373 | − | 0.804190i | \(-0.297400\pi\) | ||||
0.594373 | + | 0.804190i | \(0.297400\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.8044 | 1.33742 | ||||||||
\(800\) | 6.58705 | 0.232887 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.8802 | 0.384192 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.94104 | −0.0684127 | ||||||||
\(806\) | 0.155364 | 0.00547245 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.1030 | −0.883120 | ||||||||
\(809\) | −42.2328 | −1.48483 | −0.742413 | − | 0.669942i | \(-0.766319\pi\) | ||||
−0.742413 | + | 0.669942i | \(0.766319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1590 | −0.356730 | −0.178365 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178365 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(812\) | −2.25690 | −0.0792017 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.40377 | 0.0842004 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9785 | 0.419074 | ||||||||
\(818\) | 48.5346 | 1.69697 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.00612051 | 0.000213737 0 | ||||||||
\(821\) | 25.6507 | 0.895214 | 0.447607 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447607 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.8879 | −1.66927 | −0.834634 | − | 0.550805i | \(-0.814321\pi\) | ||||
−0.834634 | + | 0.550805i | \(0.814321\pi\) | |||||||
\(824\) | −47.4323 | −1.65238 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.50895 | −0.0525031 | ||||||||
\(827\) | 13.3901 | 0.465619 | 0.232810 | − | 0.972522i | \(-0.425208\pi\) | ||||
0.232810 | + | 0.972522i | \(0.425208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7867 | −0.687221 | −0.343610 | − | 0.939112i | \(-0.611650\pi\) | ||||
−0.343610 | + | 0.939112i | \(0.611650\pi\) | |||||||
\(830\) | 3.25092 | 0.112841 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.513799 | −0.0178128 | ||||||||
\(833\) | −6.28375 | −0.217719 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.55001 | −0.0536402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.3506 | −0.633910 | ||||||||
\(839\) | −46.1948 | −1.59482 | −0.797410 | − | 0.603437i | \(-0.793797\pi\) | ||||
−0.797410 | + | 0.603437i | \(0.793797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.9384 | 2.06684 | ||||||||
\(842\) | 40.9355 | 1.41073 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.66177 | −0.229308 | ||||||||
\(845\) | 4.24867 | 0.146159 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.5862 | −0.706934 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.7987 | −1.39938 | ||||||||
\(851\) | 38.7867 | 1.32959 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.6343 | −1.28857 | −0.644287 | − | 0.764784i | \(-0.722846\pi\) | ||||
−0.644287 | + | 0.764784i | \(0.722846\pi\) | |||||||
\(854\) | 16.2953 | 0.557615 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.3633 | 0.525106 | ||||||||
\(857\) | 12.9962 | 0.443943 | 0.221972 | − | 0.975053i | \(-0.428751\pi\) | ||||
0.221972 | + | 0.975053i | \(0.428751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0560 | −0.889020 | −0.444510 | − | 0.895774i | \(-0.646622\pi\) | ||||
−0.444510 | + | 0.895774i | \(0.646622\pi\) | |||||||
\(860\) | 0.385048 | 0.0131300 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.79156 | −0.163201 | ||||||||
\(863\) | 19.3134 | 0.657434 | 0.328717 | − | 0.944428i | \(-0.393384\pi\) | ||||
0.328717 | + | 0.944428i | \(0.393384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.63093 | −0.0894543 | ||||||||
\(866\) | −50.4292 | −1.71366 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.475251 | 0.0161311 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.516320 | −0.0174948 | ||||||||
\(872\) | 8.98671 | 0.304328 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.1748 | 0.648596 | ||||||||
\(875\) | −3.23415 | −0.109334 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.9946 | −0.776472 | −0.388236 | − | 0.921560i | \(-0.626916\pi\) | ||||
−0.388236 | + | 0.921560i | \(0.626916\pi\) | |||||||
\(878\) | 34.3476 | 1.15918 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.4759 | 1.70058 | 0.850288 | − | 0.526318i | \(-0.176428\pi\) | ||||
0.850288 | + | 0.526318i | \(0.176428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.8564 | 0.499958 | 0.249979 | − | 0.968251i | \(-0.419576\pi\) | ||||
0.249979 | + | 0.968251i | \(0.419576\pi\) | |||||||
\(884\) | −0.0886623 | −0.00298204 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.6710 | 0.660860 | ||||||||
\(887\) | 46.0622 | 1.54662 | 0.773309 | − | 0.634029i | \(-0.218600\pi\) | ||||
0.773309 | + | 0.634029i | \(0.218600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.40039 | −0.248201 | ||||||||
\(890\) | −4.59861 | −0.154146 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.62029 | −0.154699 | ||||||||
\(893\) | −14.6421 | −0.489980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.44538 | −0.115166 | ||||||||
\(896\) | 8.87093 | 0.296357 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50.1666 | 1.67408 | ||||||||
\(899\) | −18.7284 | −0.624626 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3426 | −1.24406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.5289 | 0.616264 | ||||||||
\(905\) | 7.69505 | 0.255792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5358 | 0.947516 | 0.473758 | − | 0.880655i | \(-0.342897\pi\) | ||||
0.473758 | + | 0.880655i | \(0.342897\pi\) | |||||||
\(908\) | 0.314903 | 0.0104504 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0255753 | 0.000847812 0 | ||||||||
\(911\) | −31.5458 | −1.04516 | −0.522580 | − | 0.852590i | \(-0.675030\pi\) | ||||
−0.522580 | + | 0.852590i | \(0.675030\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 31.1974 | 1.03192 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.105317 | 0.00347977 | ||||||||
\(917\) | 10.9479 | 0.361531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0921 | −1.32252 | −0.661259 | − | 0.750158i | \(-0.729978\pi\) | ||||
−0.661259 | + | 0.750158i | \(0.729978\pi\) | |||||||
\(920\) | 5.76754 | 0.190150 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −54.2986 | −1.78823 | ||||||||
\(923\) | −0.0977880 | −0.00321873 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.9640 | 1.05097 | ||||||||
\(926\) | −0.0806060 | −0.00264888 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.6955 | 0.416749 | ||||||||
\(929\) | −4.40597 | −0.144555 | −0.0722777 | − | 0.997385i | \(-0.523027\pi\) | ||||
−0.0722777 | + | 0.997385i | \(0.523027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.43378 | 0.0797638 | ||||||||
\(932\) | −1.26785 | −0.0415298 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −49.6744 | −1.62540 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.902908 | 0.0294967 | 0.0147484 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147484 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(938\) | 11.6200 | 0.379407 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.470671 | −0.0153516 | ||||||||
\(941\) | −34.8442 | −1.13589 | −0.567943 | − | 0.823068i | \(-0.692261\pi\) | ||||
−0.567943 | + | 0.823068i | \(0.692261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.464518 | −0.0151268 | ||||||||
\(944\) | 3.93935 | 0.128215 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.9556 | −0.843444 | −0.421722 | − | 0.906725i | \(-0.638574\pi\) | ||||
−0.421722 | + | 0.906725i | \(0.638574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.554521 | −0.0180005 | ||||||||
\(950\) | 15.8019 | 0.512681 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.6713 | 0.605140 | ||||||||
\(953\) | −1.69616 | −0.0549440 | −0.0274720 | − | 0.999623i | \(-0.508746\pi\) | ||||
−0.0274720 | + | 0.999623i | \(0.508746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.85782 | 0.189555 | ||||||||
\(956\) | 5.82234 | 0.188308 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.6620 | 1.34604 | ||||||||
\(959\) | 4.96620 | 0.160367 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0562 | −0.872782 | ||||||||
\(962\) | −0.511055 | −0.0164771 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.34577 | 0.204383 | ||||||||
\(965\) | −3.66012 | −0.117823 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0337 | 0.805028 | 0.402514 | − | 0.915414i | \(-0.368136\pi\) | ||||
0.402514 | + | 0.915414i | \(0.368136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.91185 | −0.0934940 | ||||||||
\(971\) | 57.3356 | 1.83999 | 0.919994 | − | 0.391933i | \(-0.128193\pi\) | ||||
0.919994 | + | 0.391933i | \(0.128193\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.19560 | 0.198622 | ||||||||
\(974\) | 27.0532 | 0.866839 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.5415 | −1.36172 | ||||||||
\(977\) | −19.6196 | −0.627687 | −0.313844 | − | 0.949475i | \(-0.601617\pi\) | ||||
−0.313844 | + | 0.949475i | \(0.601617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.0782337 | 0.00249908 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.4081 | 0.491692 | ||||||||
\(983\) | −32.4742 | −1.03577 | −0.517883 | − | 0.855451i | \(-0.673280\pi\) | ||||
−0.517883 | + | 0.855451i | \(0.673280\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.74083 | 0.0554674 | ||||||||
\(986\) | −78.6329 | −2.50418 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0343401 | 0.00109250 | ||||||||
\(989\) | −29.2233 | −0.929247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.7384 | 0.690543 | 0.345271 | − | 0.938503i | \(-0.387787\pi\) | ||||
0.345271 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(992\) | −2.67337 | −0.0848796 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.20077 | 0.0698040 | ||||||||
\(995\) | −2.96159 | −0.0938886 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.14889 | 0.226408 | 0.113204 | − | 0.993572i | \(-0.463889\pi\) | ||||
0.113204 | + | 0.993572i | \(0.463889\pi\) | |||||||
\(998\) | −50.6356 | −1.60284 | ||||||||
\(999\) | 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 | 7623.2.a.cg.1.2 | 4 | ||
3.2 | odd | 2 | 2541.2.a.bp.1.3 | yes | 4 | ||
11.10 | odd | 2 | 7623.2.a.cn.1.3 | 4 | |||
33.32 | even | 2 | 2541.2.a.bl.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bl.1.2 | ✓ | 4 | 33.32 | even | 2 | ||
2541.2.a.bp.1.3 | yes | 4 | 3.2 | odd | 2 | ||
7623.2.a.cg.1.2 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.cn.1.3 | 4 | 11.10 | odd | 2 |