Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(1\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.05896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 | \(0.655434\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.239314 | −0.119657 | ||||||||
\(5\) | 0.326909 | 0.146198 | 0.0730990 | − | 0.997325i | \(-0.476711\pi\) | ||||
0.0730990 | + | 0.997325i | \(0.476711\pi\) | |||||||
\(6\) | −1.32691 | −0.541708 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.97136 | 1.05054 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.433778 | −0.137173 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.239314 | −0.0690839 | ||||||||
\(13\) | 0.0589594 | 0.0163524 | 0.00817619 | − | 0.999967i | \(-0.497397\pi\) | ||||
0.00817619 | + | 0.999967i | \(0.497397\pi\) | |||||||
\(14\) | −1.32691 | −0.354631 | ||||||||
\(15\) | 0.326909 | 0.0844074 | ||||||||
\(16\) | −3.46410 | −0.866025 | ||||||||
\(17\) | −6.28375 | −1.52403 | −0.762016 | − | 0.647558i | \(-0.775790\pi\) | ||||
−0.762016 | + | 0.647558i | \(0.775790\pi\) | |||||||
\(18\) | −1.32691 | −0.312755 | ||||||||
\(19\) | −2.43378 | −0.558347 | −0.279173 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279173 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(20\) | −0.0782337 | −0.0174936 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.93756 | 1.23807 | 0.619034 | − | 0.785364i | \(-0.287524\pi\) | ||||
0.619034 | + | 0.785364i | \(0.287524\pi\) | |||||||
\(24\) | 2.97136 | 0.606527 | ||||||||
\(25\) | −4.89313 | −0.978626 | ||||||||
\(26\) | −0.0782337 | −0.0153429 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.239314 | −0.0452260 | ||||||||
\(29\) | −9.43072 | −1.75124 | −0.875620 | − | 0.483000i | \(-0.839547\pi\) | ||||
−0.875620 | + | 0.483000i | \(0.839547\pi\) | |||||||
\(30\) | −0.433778 | −0.0791966 | ||||||||
\(31\) | 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 | ||||||||
\(36\) | −0.239314 | −0.0398856 | ||||||||
\(37\) | −6.53242 | −1.07392 | −0.536962 | − | 0.843607i | \(-0.680428\pi\) | ||||
−0.536962 | + | 0.843607i | \(0.680428\pi\) | |||||||
\(38\) | 3.22940 | 0.523878 | ||||||||
\(39\) | 0.0589594 | 0.00944105 | ||||||||
\(40\) | 0.971364 | 0.153586 | ||||||||
\(41\) | 0.0782337 | 0.0122180 | 0.00610902 | − | 0.999981i | \(-0.498055\pi\) | ||||
0.00610902 | + | 0.999981i | \(0.498055\pi\) | |||||||
\(42\) | −1.32691 | −0.204746 | ||||||||
\(43\) | −4.92177 | −0.750562 | −0.375281 | − | 0.926911i | \(-0.622454\pi\) | ||||
−0.375281 | + | 0.926911i | \(0.622454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.326909 | 0.0487327 | ||||||||
\(46\) | −7.87861 | −1.16164 | ||||||||
\(47\) | 6.01621 | 0.877555 | 0.438778 | − | 0.898596i | \(-0.355412\pi\) | ||||
0.438778 | + | 0.898596i | \(0.355412\pi\) | |||||||
\(48\) | −3.46410 | −0.500000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.49274 | 0.918212 | ||||||||
\(51\) | −6.28375 | −0.879901 | ||||||||
\(52\) | −0.0141098 | −0.00195667 | ||||||||
\(53\) | −5.94273 | −0.816297 | −0.408148 | − | 0.912916i | \(-0.633825\pi\) | ||||
−0.408148 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(54\) | −1.32691 | −0.180569 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.97136 | 0.397065 | ||||||||
\(57\) | −2.43378 | −0.322362 | ||||||||
\(58\) | 12.5137 | 1.64313 | ||||||||
\(59\) | 1.13719 | 0.148050 | 0.0740250 | − | 0.997256i | \(-0.476416\pi\) | ||||
0.0740250 | + | 0.997256i | \(0.476416\pi\) | |||||||
\(60\) | −0.0782337 | −0.0100999 | ||||||||
\(61\) | −12.2807 | −1.57238 | −0.786190 | − | 0.617984i | \(-0.787950\pi\) | ||||
−0.786190 | + | 0.617984i | \(0.787950\pi\) | |||||||
\(62\) | −2.63509 | −0.334657 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 5.93756 | 0.714799 | ||||||||
\(70\) | −0.433778 | −0.0518464 | ||||||||
\(71\) | −1.65857 | −0.196836 | −0.0984178 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984178 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(72\) | 2.97136 | 0.350179 | ||||||||
\(73\) | −9.40514 | −1.10079 | −0.550394 | − | 0.834905i | \(-0.685523\pi\) | ||||
−0.550394 | + | 0.834905i | \(0.685523\pi\) | |||||||
\(74\) | 8.66793 | 1.00763 | ||||||||
\(75\) | −4.89313 | −0.565010 | ||||||||
\(76\) | 0.582436 | 0.0668100 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0782337 | −0.00885822 | ||||||||
\(79\) | 13.0717 | 1.47068 | 0.735340 | − | 0.677698i | \(-0.237022\pi\) | ||||
0.735340 | + | 0.677698i | \(0.237022\pi\) | |||||||
\(80\) | −1.13244 | −0.126611 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.103809 | −0.0114638 | ||||||||
\(83\) | 7.49443 | 0.822620 | 0.411310 | − | 0.911496i | \(-0.365071\pi\) | ||||
0.411310 | + | 0.911496i | \(0.365071\pi\) | |||||||
\(84\) | −0.239314 | −0.0261113 | ||||||||
\(85\) | −2.05421 | −0.222810 | ||||||||
\(86\) | 6.53073 | 0.704227 | ||||||||
\(87\) | −9.43072 | −1.01108 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6013 | 1.12373 | 0.561867 | − | 0.827227i | \(-0.310083\pi\) | ||||
0.561867 | + | 0.827227i | \(0.310083\pi\) | |||||||
\(90\) | −0.433778 | −0.0457242 | ||||||||
\(91\) | 0.0589594 | 0.00618062 | ||||||||
\(92\) | −1.42094 | −0.148143 | ||||||||
\(93\) | 1.98589 | 0.205927 | ||||||||
\(94\) | −7.98297 | −0.823380 | ||||||||
\(95\) | −0.795623 | −0.0816292 | ||||||||
\(96\) | −1.34618 | −0.137394 | ||||||||
\(97\) | −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 | \(0.638082\pi\) | |||||||
\(102\) | 8.33796 | 0.825581 | ||||||||
\(103\) | −15.9631 | −1.57289 | −0.786447 | − | 0.617657i | \(-0.788082\pi\) | ||||
−0.786447 | + | 0.617657i | \(0.788082\pi\) | |||||||
\(104\) | 0.175190 | 0.0171788 | ||||||||
\(105\) | 0.326909 | 0.0319030 | ||||||||
\(106\) | 7.88546 | 0.765903 | ||||||||
\(107\) | 5.17044 | 0.499845 | 0.249923 | − | 0.968266i | \(-0.419595\pi\) | ||||
0.249923 | + | 0.968266i | \(0.419595\pi\) | |||||||
\(108\) | −0.239314 | −0.0230280 | ||||||||
\(109\) | −3.02444 | −0.289689 | −0.144844 | − | 0.989454i | \(-0.546268\pi\) | ||||
−0.144844 | + | 0.989454i | \(0.546268\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.53242 | −0.620030 | ||||||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | −6.23584 | −0.586618 | −0.293309 | − | 0.956018i | \(-0.594757\pi\) | ||||
−0.293309 | + | 0.956018i | \(0.594757\pi\) | |||||||
\(114\) | 3.22940 | 0.302461 | ||||||||
\(115\) | 1.94104 | 0.181003 | ||||||||
\(116\) | 2.25690 | 0.209548 | ||||||||
\(117\) | 0.0589594 | 0.00545080 | ||||||||
\(118\) | −1.50895 | −0.138910 | ||||||||
\(119\) | −6.28375 | −0.576030 | ||||||||
\(120\) | 0.971364 | 0.0886730 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.2953 | 1.47531 | ||||||||
\(123\) | 0.0782337 | 0.00705409 | ||||||||
\(124\) | −0.475251 | −0.0426788 | ||||||||
\(125\) | −3.23415 | −0.289271 | ||||||||
\(126\) | −1.32691 | −0.118210 | ||||||||
\(127\) | −7.40039 | −0.656679 | −0.328339 | − | 0.944560i | \(-0.606489\pi\) | ||||
−0.328339 | + | 0.944560i | \(0.606489\pi\) | |||||||
\(128\) | −8.87093 | −0.784087 | ||||||||
\(129\) | −4.92177 | −0.433337 | ||||||||
\(130\) | −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 | ||||||||
\(135\) | 0.326909 | 0.0281358 | ||||||||
\(136\) | −18.6713 | −1.60105 | ||||||||
\(137\) | 4.96620 | 0.424291 | 0.212146 | − | 0.977238i | \(-0.431955\pi\) | ||||
0.212146 | + | 0.977238i | \(0.431955\pi\) | |||||||
\(138\) | −7.87861 | −0.670671 | ||||||||
\(139\) | 6.19560 | 0.525504 | 0.262752 | − | 0.964863i | \(-0.415370\pi\) | ||||
0.262752 | + | 0.964863i | \(0.415370\pi\) | |||||||
\(140\) | −0.0782337 | −0.00661195 | ||||||||
\(141\) | 6.01621 | 0.506657 | ||||||||
\(142\) | 2.20077 | 0.184684 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.46410 | −0.288675 | ||||||||
\(145\) | −3.08298 | −0.256028 | ||||||||
\(146\) | 12.4798 | 1.03283 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 1.56330 | 0.128502 | ||||||||
\(149\) | 20.3158 | 1.66433 | 0.832166 | − | 0.554527i | \(-0.187101\pi\) | ||||
0.832166 | + | 0.554527i | \(0.187101\pi\) | |||||||
\(150\) | 6.49274 | 0.530130 | ||||||||
\(151\) | −9.49959 | −0.773066 | −0.386533 | − | 0.922276i | \(-0.626327\pi\) | ||||
−0.386533 | + | 0.922276i | \(0.626327\pi\) | |||||||
\(152\) | −7.23164 | −0.586564 | ||||||||
\(153\) | −6.28375 | −0.508011 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.649205 | 0.0521454 | ||||||||
\(156\) | −0.0141098 | −0.00112969 | ||||||||
\(157\) | −17.4500 | −1.39266 | −0.696330 | − | 0.717721i | \(-0.745185\pi\) | ||||
−0.696330 | + | 0.717721i | \(0.745185\pi\) | |||||||
\(158\) | −17.3449 | −1.37989 | ||||||||
\(159\) | −5.94273 | −0.471289 | ||||||||
\(160\) | −0.440079 | −0.0347913 | ||||||||
\(161\) | 5.93756 | 0.467946 | ||||||||
\(162\) | −1.32691 | −0.104252 | ||||||||
\(163\) | −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 | \(0.441273\pi\) | |||||||
\(168\) | 2.97136 | 0.229246 | ||||||||
\(169\) | −12.9965 | −0.999733 | ||||||||
\(170\) | 2.72575 | 0.209055 | ||||||||
\(171\) | −2.43378 | −0.186116 | ||||||||
\(172\) | 1.17785 | 0.0898099 | ||||||||
\(173\) | 8.04791 | 0.611871 | 0.305936 | − | 0.952052i | \(-0.401031\pi\) | ||||
0.305936 | + | 0.952052i | \(0.401031\pi\) | |||||||
\(174\) | 12.5137 | 0.948661 | ||||||||
\(175\) | −4.89313 | −0.369886 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.13719 | 0.0854767 | ||||||||
\(178\) | −14.0669 | −1.05436 | ||||||||
\(179\) | −10.5393 | −0.787742 | −0.393871 | − | 0.919166i | \(-0.628864\pi\) | ||||
−0.393871 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(180\) | −0.0782337 | −0.00583119 | ||||||||
\(181\) | −23.5389 | −1.74963 | −0.874815 | − | 0.484457i | \(-0.839017\pi\) | ||||
−0.874815 | + | 0.484457i | \(0.839017\pi\) | |||||||
\(182\) | −0.0782337 | −0.00579907 | ||||||||
\(183\) | −12.2807 | −0.907815 | ||||||||
\(184\) | 17.6427 | 1.30063 | ||||||||
\(185\) | −2.13550 | −0.157005 | ||||||||
\(186\) | −2.63509 | −0.193215 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.43976 | −0.105005 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 1.05572 | 0.0765899 | ||||||||
\(191\) | 17.9188 | 1.29656 | 0.648281 | − | 0.761401i | \(-0.275488\pi\) | ||||
0.648281 | + | 0.761401i | \(0.275488\pi\) | |||||||
\(192\) | 8.71446 | 0.628912 | ||||||||
\(193\) | −11.1962 | −0.805917 | −0.402958 | − | 0.915218i | \(-0.632018\pi\) | ||||
−0.402958 | + | 0.915218i | \(0.632018\pi\) | |||||||
\(194\) | 8.90724 | 0.639503 | ||||||||
\(195\) | 0.0192743 | 0.00138026 | ||||||||
\(196\) | −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 | ||||||||
\(201\) | 8.75721 | 0.617686 | ||||||||
\(202\) | 11.2101 | 0.788742 | ||||||||
\(203\) | −9.43072 | −0.661907 | ||||||||
\(204\) | 1.50379 | 0.105286 | ||||||||
\(205\) | 0.0255753 | 0.00178625 | ||||||||
\(206\) | 21.1816 | 1.47579 | ||||||||
\(207\) | 5.93756 | 0.412689 | ||||||||
\(208\) | −0.204241 | −0.0141616 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.433778 | −0.0299335 | ||||||||
\(211\) | −27.8370 | −1.91638 | −0.958189 | − | 0.286136i | \(-0.907629\pi\) | ||||
−0.958189 | + | 0.286136i | \(0.907629\pi\) | |||||||
\(212\) | 1.42218 | 0.0976755 | ||||||||
\(213\) | −1.65857 | −0.113643 | ||||||||
\(214\) | −6.86070 | −0.468988 | ||||||||
\(215\) | −1.60897 | −0.109731 | ||||||||
\(216\) | 2.97136 | 0.202176 | ||||||||
\(217\) | 1.98589 | 0.134811 | ||||||||
\(218\) | 4.01315 | 0.271805 | ||||||||
\(219\) | −9.40514 | −0.635541 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.370486 | −0.0249216 | ||||||||
\(222\) | 8.66793 | 0.581753 | ||||||||
\(223\) | 19.3064 | 1.29285 | 0.646426 | − | 0.762977i | \(-0.276263\pi\) | ||||
0.646426 | + | 0.762977i | \(0.276263\pi\) | |||||||
\(224\) | −1.34618 | −0.0899456 | ||||||||
\(225\) | −4.89313 | −0.326209 | ||||||||
\(226\) | 8.27439 | 0.550404 | ||||||||
\(227\) | −1.31586 | −0.0873366 | −0.0436683 | − | 0.999046i | \(-0.513904\pi\) | ||||
−0.0436683 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(228\) | 0.582436 | 0.0385728 | ||||||||
\(229\) | −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 | \(0.444480\pi\) | |||||||
\(234\) | −0.0782337 | −0.00511430 | ||||||||
\(235\) | 1.96675 | 0.128297 | ||||||||
\(236\) | −0.272146 | −0.0177152 | ||||||||
\(237\) | 13.0717 | 0.849098 | ||||||||
\(238\) | 8.33796 | 0.540470 | ||||||||
\(239\) | −24.3293 | −1.57373 | −0.786866 | − | 0.617123i | \(-0.788298\pi\) | ||||
−0.786866 | + | 0.617123i | \(0.788298\pi\) | |||||||
\(240\) | −1.13244 | −0.0730990 | ||||||||
\(241\) | 26.5165 | 1.70808 | 0.854040 | − | 0.520208i | \(-0.174145\pi\) | ||||
0.854040 | + | 0.520208i | \(0.174145\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.93894 | 0.188146 | ||||||||
\(245\) | 0.326909 | 0.0208854 | ||||||||
\(246\) | −0.103809 | −0.00661862 | ||||||||
\(247\) | −0.143494 | −0.00913030 | ||||||||
\(248\) | 5.90080 | 0.374701 | ||||||||
\(249\) | 7.49443 | 0.474940 | ||||||||
\(250\) | 4.29142 | 0.271413 | ||||||||
\(251\) | −19.1828 | −1.21081 | −0.605403 | − | 0.795919i | \(-0.706988\pi\) | ||||
−0.605403 | + | 0.795919i | \(0.706988\pi\) | |||||||
\(252\) | −0.239314 | −0.0150753 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.81965 | 0.616139 | ||||||||
\(255\) | −2.05421 | −0.128640 | ||||||||
\(256\) | −5.65801 | −0.353626 | ||||||||
\(257\) | 12.2417 | 0.763618 | 0.381809 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381809 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(258\) | 6.53073 | 0.406586 | ||||||||
\(259\) | −6.53242 | −0.405905 | ||||||||
\(260\) | −0.00461261 | −0.000286062 0 | ||||||||
\(261\) | −9.43072 | −0.583747 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 10.6013 | 0.648789 | ||||||||
\(268\) | −2.09572 | −0.128016 | ||||||||
\(269\) | 9.40683 | 0.573545 | 0.286772 | − | 0.957999i | \(-0.407418\pi\) | ||||
0.286772 | + | 0.957999i | \(0.407418\pi\) | |||||||
\(270\) | −0.433778 | −0.0263989 | ||||||||
\(271\) | 14.5252 | 0.882341 | 0.441170 | − | 0.897423i | \(-0.354563\pi\) | ||||
0.441170 | + | 0.897423i | \(0.354563\pi\) | |||||||
\(272\) | 21.7675 | 1.31985 | ||||||||
\(273\) | 0.0589594 | 0.00356838 | ||||||||
\(274\) | −6.58969 | −0.398098 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.42094 | −0.0855306 | ||||||||
\(277\) | −8.26447 | −0.496564 | −0.248282 | − | 0.968688i | \(-0.579866\pi\) | ||||
−0.248282 | + | 0.968688i | \(0.579866\pi\) | |||||||
\(278\) | −8.22100 | −0.493063 | ||||||||
\(279\) | 1.98589 | 0.118892 | ||||||||
\(280\) | 0.971364 | 0.0580501 | ||||||||
\(281\) | 24.0080 | 1.43220 | 0.716098 | − | 0.697999i | \(-0.245926\pi\) | ||||
0.716098 | + | 0.697999i | \(0.245926\pi\) | |||||||
\(282\) | −7.98297 | −0.475379 | ||||||||
\(283\) | −16.0512 | −0.954142 | −0.477071 | − | 0.878865i | \(-0.658302\pi\) | ||||
−0.477071 | + | 0.878865i | \(0.658302\pi\) | |||||||
\(284\) | 0.396917 | 0.0235527 | ||||||||
\(285\) | −0.795623 | −0.0471286 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0782337 | 0.00461799 | ||||||||
\(288\) | −1.34618 | −0.0793246 | ||||||||
\(289\) | 22.4855 | 1.32268 | ||||||||
\(290\) | 4.09084 | 0.240222 | ||||||||
\(291\) | −6.71278 | −0.393510 | ||||||||
\(292\) | 2.25078 | 0.131717 | ||||||||
\(293\) | −7.60088 | −0.444048 | −0.222024 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222024 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(294\) | −1.32691 | −0.0773869 | ||||||||
\(295\) | 0.371758 | 0.0216446 | ||||||||
\(296\) | −19.4102 | −1.12820 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.9572 | −1.56159 | ||||||||
\(299\) | 0.350075 | 0.0202454 | ||||||||
\(300\) | 1.17099 | 0.0676073 | ||||||||
\(301\) | −4.92177 | −0.283686 | ||||||||
\(302\) | 12.6051 | 0.725341 | ||||||||
\(303\) | −8.44830 | −0.485342 | ||||||||
\(304\) | 8.43085 | 0.483543 | ||||||||
\(305\) | −4.01466 | −0.229879 | ||||||||
\(306\) | 8.33796 | 0.476649 | ||||||||
\(307\) | −19.7345 | −1.12631 | −0.563153 | − | 0.826353i | \(-0.690412\pi\) | ||||
−0.563153 | + | 0.826353i | \(0.690412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.9631 | −0.908111 | ||||||||
\(310\) | −0.861435 | −0.0489262 | ||||||||
\(311\) | −30.3127 | −1.71888 | −0.859438 | − | 0.511240i | \(-0.829186\pi\) | ||||
−0.859438 | + | 0.511240i | \(0.829186\pi\) | |||||||
\(312\) | 0.175190 | 0.00991817 | ||||||||
\(313\) | −19.7850 | −1.11832 | −0.559158 | − | 0.829061i | \(-0.688875\pi\) | ||||
−0.559158 | + | 0.829061i | \(0.688875\pi\) | |||||||
\(314\) | 23.1545 | 1.30669 | ||||||||
\(315\) | 0.326909 | 0.0184192 | ||||||||
\(316\) | −3.12824 | −0.175977 | ||||||||
\(317\) | −18.9639 | −1.06512 | −0.532558 | − | 0.846393i | \(-0.678769\pi\) | ||||
−0.532558 | + | 0.846393i | \(0.678769\pi\) | |||||||
\(318\) | 7.88546 | 0.442195 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.84883 | 0.159255 | ||||||||
\(321\) | 5.17044 | 0.288586 | ||||||||
\(322\) | −7.87861 | −0.439057 | ||||||||
\(323\) | 15.2932 | 0.850939 | ||||||||
\(324\) | −0.239314 | −0.0132952 | ||||||||
\(325\) | −0.288496 | −0.0160029 | ||||||||
\(326\) | 9.75681 | 0.540380 | ||||||||
\(327\) | −3.02444 | −0.167252 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | −6.53242 | −0.357975 | ||||||||
\(334\) | −6.29142 | −0.344251 | ||||||||
\(335\) | 2.86281 | 0.156412 | ||||||||
\(336\) | −3.46410 | −0.188982 | ||||||||
\(337\) | −27.5690 | −1.50178 | −0.750891 | − | 0.660426i | \(-0.770376\pi\) | ||||
−0.750891 | + | 0.660426i | \(0.770376\pi\) | |||||||
\(338\) | 17.2452 | 0.938015 | ||||||||
\(339\) | −6.23584 | −0.338684 | ||||||||
\(340\) | 0.491601 | 0.0266608 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.22940 | 0.174626 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −14.6244 | −0.788493 | ||||||||
\(345\) | 1.94104 | 0.104502 | ||||||||
\(346\) | −10.6788 | −0.574098 | ||||||||
\(347\) | 32.5280 | 1.74619 | 0.873097 | − | 0.487547i | \(-0.162108\pi\) | ||||
0.873097 | + | 0.487547i | \(0.162108\pi\) | |||||||
\(348\) | 2.25690 | 0.120983 | ||||||||
\(349\) | −28.7099 | −1.53680 | −0.768402 | − | 0.639968i | \(-0.778948\pi\) | ||||
−0.768402 | + | 0.639968i | \(0.778948\pi\) | |||||||
\(350\) | 6.49274 | 0.347051 | ||||||||
\(351\) | 0.0589594 | 0.00314702 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.421356 | −0.0224265 | −0.0112133 | − | 0.999937i | \(-0.503569\pi\) | ||||
−0.0112133 | + | 0.999937i | \(0.503569\pi\) | |||||||
\(354\) | −1.50895 | −0.0801999 | ||||||||
\(355\) | −0.542199 | −0.0287770 | ||||||||
\(356\) | −2.53703 | −0.134463 | ||||||||
\(357\) | −6.28375 | −0.332571 | ||||||||
\(358\) | 13.9847 | 0.739112 | ||||||||
\(359\) | −8.17340 | −0.431376 | −0.215688 | − | 0.976462i | \(-0.569199\pi\) | ||||
−0.215688 | + | 0.976462i | \(0.569199\pi\) | |||||||
\(360\) | 0.971364 | 0.0511954 | ||||||||
\(361\) | −13.0767 | −0.688249 | ||||||||
\(362\) | 31.2339 | 1.64162 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0141098 | −0.000739554 0 | ||||||||
\(365\) | −3.07462 | −0.160933 | ||||||||
\(366\) | 16.2953 | 0.851772 | ||||||||
\(367\) | −10.9415 | −0.571139 | −0.285570 | − | 0.958358i | \(-0.592183\pi\) | ||||
−0.285570 | + | 0.958358i | \(0.592183\pi\) | |||||||
\(368\) | −20.5683 | −1.07220 | ||||||||
\(369\) | 0.0782337 | 0.00407268 | ||||||||
\(370\) | 2.83362 | 0.147313 | ||||||||
\(371\) | −5.94273 | −0.308531 | ||||||||
\(372\) | −0.475251 | −0.0246406 | ||||||||
\(373\) | −15.2953 | −0.791963 | −0.395982 | − | 0.918258i | \(-0.629596\pi\) | ||||
−0.395982 | + | 0.918258i | \(0.629596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.23415 | −0.167011 | ||||||||
\(376\) | 17.8764 | 0.921903 | ||||||||
\(377\) | −0.556029 | −0.0286370 | ||||||||
\(378\) | −1.32691 | −0.0682488 | ||||||||
\(379\) | 32.1698 | 1.65245 | 0.826226 | − | 0.563339i | \(-0.190484\pi\) | ||||
0.826226 | + | 0.563339i | \(0.190484\pi\) | |||||||
\(380\) | 0.190403 | 0.00976749 | ||||||||
\(381\) | −7.40039 | −0.379134 | ||||||||
\(382\) | −23.7767 | −1.21652 | ||||||||
\(383\) | −20.5485 | −1.04998 | −0.524991 | − | 0.851108i | \(-0.675931\pi\) | ||||
−0.524991 | + | 0.851108i | \(0.675931\pi\) | |||||||
\(384\) | −8.87093 | −0.452693 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8563 | 0.756164 | ||||||||
\(387\) | −4.92177 | −0.250187 | ||||||||
\(388\) | 1.60646 | 0.0815556 | ||||||||
\(389\) | 16.9025 | 0.856992 | 0.428496 | − | 0.903544i | \(-0.359044\pi\) | ||||
0.428496 | + | 0.903544i | \(0.359044\pi\) | |||||||
\(390\) | −0.0255753 | −0.00129505 | ||||||||
\(391\) | −37.3102 | −1.88686 | ||||||||
\(392\) | 2.97136 | 0.150077 | ||||||||
\(393\) | −10.9479 | −0.552248 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | −2.43378 | −0.121841 | ||||||||
\(400\) | 16.9503 | 0.847515 | ||||||||
\(401\) | 8.19963 | 0.409470 | 0.204735 | − | 0.978817i | \(-0.434367\pi\) | ||||
0.204735 | + | 0.978817i | \(0.434367\pi\) | |||||||
\(402\) | −11.6200 | −0.579554 | ||||||||
\(403\) | 0.117087 | 0.00583251 | ||||||||
\(404\) | 2.02179 | 0.100588 | ||||||||
\(405\) | 0.326909 | 0.0162442 | ||||||||
\(406\) | 12.5137 | 0.621044 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.6713 | −0.924367 | ||||||||
\(409\) | 36.5772 | 1.80862 | 0.904312 | − | 0.426871i | \(-0.140384\pi\) | ||||
0.904312 | + | 0.426871i | \(0.140384\pi\) | |||||||
\(410\) | −0.0339360 | −0.00167598 | ||||||||
\(411\) | 4.96620 | 0.244965 | ||||||||
\(412\) | 3.82020 | 0.188208 | ||||||||
\(413\) | 1.13719 | 0.0559576 | ||||||||
\(414\) | −7.87861 | −0.387212 | ||||||||
\(415\) | 2.44999 | 0.120265 | ||||||||
\(416\) | −0.0793701 | −0.00389144 | ||||||||
\(417\) | 6.19560 | 0.303400 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8296 | −0.675618 | −0.337809 | − | 0.941215i | \(-0.609686\pi\) | ||||
−0.337809 | + | 0.941215i | \(0.609686\pi\) | |||||||
\(420\) | −0.0782337 | −0.00381741 | ||||||||
\(421\) | −30.8503 | −1.50355 | −0.751775 | − | 0.659419i | \(-0.770802\pi\) | ||||
−0.751775 | + | 0.659419i | \(0.770802\pi\) | |||||||
\(422\) | 36.9371 | 1.79807 | ||||||||
\(423\) | 6.01621 | 0.292518 | ||||||||
\(424\) | −17.6580 | −0.857549 | ||||||||
\(425\) | 30.7472 | 1.49146 | ||||||||
\(426\) | 2.20077 | 0.106627 | ||||||||
\(427\) | −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 | \(0.472282\pi\) | |||||||
\(432\) | −3.46410 | −0.166667 | ||||||||
\(433\) | 38.0051 | 1.82641 | 0.913203 | − | 0.407504i | \(-0.133601\pi\) | ||||
0.913203 | + | 0.407504i | \(0.133601\pi\) | |||||||
\(434\) | −2.63509 | −0.126489 | ||||||||
\(435\) | −3.08298 | −0.147818 | ||||||||
\(436\) | 0.723790 | 0.0346632 | ||||||||
\(437\) | −14.4507 | −0.691271 | ||||||||
\(438\) | 12.4798 | 0.596306 | ||||||||
\(439\) | 25.8855 | 1.23545 | 0.617723 | − | 0.786396i | \(-0.288055\pi\) | ||||
0.617723 | + | 0.786396i | \(0.288055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.491601 | 0.0233831 | ||||||||
\(443\) | 14.8247 | 0.704342 | 0.352171 | − | 0.935936i | \(-0.385444\pi\) | ||||
0.352171 | + | 0.935936i | \(0.385444\pi\) | |||||||
\(444\) | 1.56330 | 0.0741908 | ||||||||
\(445\) | 3.46565 | 0.164288 | ||||||||
\(446\) | −25.6178 | −1.21304 | ||||||||
\(447\) | 20.3158 | 0.960902 | ||||||||
\(448\) | 8.71446 | 0.411720 | ||||||||
\(449\) | 37.8071 | 1.78423 | 0.892114 | − | 0.451810i | \(-0.149221\pi\) | ||||
0.892114 | + | 0.451810i | \(0.149221\pi\) | |||||||
\(450\) | 6.49274 | 0.306071 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.49232 | 0.0701929 | ||||||||
\(453\) | −9.49959 | −0.446330 | ||||||||
\(454\) | 1.74602 | 0.0819450 | ||||||||
\(455\) | 0.0192743 | 0.000903594 0 | ||||||||
\(456\) | −7.23164 | −0.338653 | ||||||||
\(457\) | 23.5114 | 1.09982 | 0.549908 | − | 0.835226i | \(-0.314663\pi\) | ||||
0.549908 | + | 0.835226i | \(0.314663\pi\) | |||||||
\(458\) | 0.583944 | 0.0272859 | ||||||||
\(459\) | −6.28375 | −0.293300 | ||||||||
\(460\) | −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 | ||||||||
\(465\) | 0.649205 | 0.0301061 | ||||||||
\(466\) | −7.02977 | −0.325648 | ||||||||
\(467\) | −37.4362 | −1.73234 | −0.866170 | − | 0.499749i | \(-0.833425\pi\) | ||||
−0.866170 | + | 0.499749i | \(0.833425\pi\) | |||||||
\(468\) | −0.0141098 | −0.000652225 0 | ||||||||
\(469\) | 8.75721 | 0.404370 | ||||||||
\(470\) | −2.60970 | −0.120376 | ||||||||
\(471\) | −17.4500 | −0.804053 | ||||||||
\(472\) | 3.37902 | 0.155532 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −17.3449 | −0.796680 | ||||||||
\(475\) | 11.9088 | 0.546413 | ||||||||
\(476\) | 1.50379 | 0.0689259 | ||||||||
\(477\) | −5.94273 | −0.272099 | ||||||||
\(478\) | 32.2828 | 1.47658 | ||||||||
\(479\) | −31.3978 | −1.43460 | −0.717300 | − | 0.696764i | \(-0.754622\pi\) | ||||
−0.717300 | + | 0.696764i | \(0.754622\pi\) | |||||||
\(480\) | −0.440079 | −0.0200868 | ||||||||
\(481\) | −0.385147 | −0.0175612 | ||||||||
\(482\) | −35.1850 | −1.60263 | ||||||||
\(483\) | 5.93756 | 0.270169 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.19446 | −0.0996455 | ||||||||
\(486\) | −1.32691 | −0.0601898 | ||||||||
\(487\) | −20.3881 | −0.923873 | −0.461937 | − | 0.886913i | \(-0.652845\pi\) | ||||
−0.461937 | + | 0.886913i | \(0.652845\pi\) | |||||||
\(488\) | −36.4904 | −1.65184 | ||||||||
\(489\) | −7.35304 | −0.332516 | ||||||||
\(490\) | −0.433778 | −0.0195961 | ||||||||
\(491\) | −11.6120 | −0.524043 | −0.262022 | − | 0.965062i | \(-0.584389\pi\) | ||||
−0.262022 | + | 0.965062i | \(0.584389\pi\) | |||||||
\(492\) | −0.0187224 | −0.000844071 0 | ||||||||
\(493\) | 59.2602 | 2.66895 | ||||||||
\(494\) | 0.190403 | 0.00856665 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.87933 | −0.308891 | ||||||||
\(497\) | −1.65857 | −0.0743968 | ||||||||
\(498\) | −9.94442 | −0.445620 | ||||||||
\(499\) | 38.1606 | 1.70830 | 0.854151 | − | 0.520025i | \(-0.174078\pi\) | ||||
0.854151 | + | 0.520025i | \(0.174078\pi\) | |||||||
\(500\) | 0.773976 | 0.0346133 | ||||||||
\(501\) | 4.74141 | 0.211831 | ||||||||
\(502\) | 25.4538 | 1.13606 | ||||||||
\(503\) | 32.5721 | 1.45232 | 0.726160 | − | 0.687526i | \(-0.241303\pi\) | ||||
0.726160 | + | 0.687526i | \(0.241303\pi\) | |||||||
\(504\) | 2.97136 | 0.132355 | ||||||||
\(505\) | −2.76182 | −0.122899 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9965 | −0.577196 | ||||||||
\(508\) | 1.77102 | 0.0785761 | ||||||||
\(509\) | −23.4898 | −1.04117 | −0.520584 | − | 0.853811i | \(-0.674286\pi\) | ||||
−0.520584 | + | 0.853811i | \(0.674286\pi\) | |||||||
\(510\) | 2.72575 | 0.120698 | ||||||||
\(511\) | −9.40514 | −0.416059 | ||||||||
\(512\) | 25.2495 | 1.11588 | ||||||||
\(513\) | −2.43378 | −0.107454 | ||||||||
\(514\) | −16.2436 | −0.716477 | ||||||||
\(515\) | −5.21849 | −0.229954 | ||||||||
\(516\) | 1.17785 | 0.0518518 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 8.66793 | 0.380847 | ||||||||
\(519\) | 8.04791 | 0.353264 | ||||||||
\(520\) | 0.0572710 | 0.00251150 | ||||||||
\(521\) | −34.5918 | −1.51549 | −0.757747 | − | 0.652548i | \(-0.773700\pi\) | ||||
−0.757747 | + | 0.652548i | \(0.773700\pi\) | |||||||
\(522\) | 12.5137 | 0.547710 | ||||||||
\(523\) | −8.30429 | −0.363121 | −0.181561 | − | 0.983380i | \(-0.558115\pi\) | ||||
−0.181561 | + | 0.983380i | \(0.558115\pi\) | |||||||
\(524\) | 2.61998 | 0.114454 | ||||||||
\(525\) | −4.89313 | −0.213554 | ||||||||
\(526\) | −24.1530 | −1.05312 | ||||||||
\(527\) | −12.4788 | −0.543586 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.2547 | 0.532812 | ||||||||
\(530\) | 2.57782 | 0.111974 | ||||||||
\(531\) | 1.13719 | 0.0493500 | ||||||||
\(532\) | 0.582436 | 0.0252518 | ||||||||
\(533\) | 0.00461261 | 0.000199794 0 | ||||||||
\(534\) | −14.0669 | −0.608736 | ||||||||
\(535\) | 1.69026 | 0.0730764 | ||||||||
\(536\) | 26.0209 | 1.12393 | ||||||||
\(537\) | −10.5393 | −0.454803 | ||||||||
\(538\) | −12.4820 | −0.538137 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.0782337 | −0.00336664 | ||||||||
\(541\) | 23.3943 | 1.00580 | 0.502899 | − | 0.864345i | \(-0.332267\pi\) | ||||
0.502899 | + | 0.864345i | \(0.332267\pi\) | |||||||
\(542\) | −19.2736 | −0.827871 | ||||||||
\(543\) | −23.5389 | −1.01015 | ||||||||
\(544\) | 8.45907 | 0.362680 | ||||||||
\(545\) | −0.988715 | −0.0423519 | ||||||||
\(546\) | −0.0782337 | −0.00334809 | ||||||||
\(547\) | 19.1606 | 0.819247 | 0.409623 | − | 0.912255i | \(-0.365660\pi\) | ||||
0.409623 | + | 0.912255i | \(0.365660\pi\) | |||||||
\(548\) | −1.18848 | −0.0507693 | ||||||||
\(549\) | −12.2807 | −0.524127 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.9523 | 0.977800 | ||||||||
\(552\) | 17.6427 | 0.750922 | ||||||||
\(553\) | 13.0717 | 0.555865 | ||||||||
\(554\) | 10.9662 | 0.465909 | ||||||||
\(555\) | −2.13550 | −0.0906471 | ||||||||
\(556\) | −1.48269 | −0.0628801 | ||||||||
\(557\) | −25.9067 | −1.09770 | −0.548852 | − | 0.835920i | \(-0.684935\pi\) | ||||
−0.548852 | + | 0.835920i | \(0.684935\pi\) | |||||||
\(558\) | −2.63509 | −0.111552 | ||||||||
\(559\) | −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 | \(0.482660\pi\) | |||||||
\(564\) | −1.43976 | −0.0606249 | ||||||||
\(565\) | −2.03855 | −0.0857624 | ||||||||
\(566\) | 21.2984 | 0.895239 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.92820 | −0.206783 | ||||||||
\(569\) | −25.6769 | −1.07643 | −0.538215 | − | 0.842807i | \(-0.680901\pi\) | ||||
−0.538215 | + | 0.842807i | \(0.680901\pi\) | |||||||
\(570\) | 1.05572 | 0.0442192 | ||||||||
\(571\) | −1.12907 | −0.0472500 | −0.0236250 | − | 0.999721i | \(-0.507521\pi\) | ||||
−0.0236250 | + | 0.999721i | \(0.507521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.9188 | 0.748570 | ||||||||
\(574\) | −0.103809 | −0.00433290 | ||||||||
\(575\) | −29.0533 | −1.21161 | ||||||||
\(576\) | 8.71446 | 0.363103 | ||||||||
\(577\) | −33.9141 | −1.41186 | −0.705932 | − | 0.708280i | \(-0.749472\pi\) | ||||
−0.705932 | + | 0.708280i | \(0.749472\pi\) | |||||||
\(578\) | −29.8362 | −1.24102 | ||||||||
\(579\) | −11.1962 | −0.465296 | ||||||||
\(580\) | 0.737800 | 0.0306355 | ||||||||
\(581\) | 7.49443 | 0.310921 | ||||||||
\(582\) | 8.90724 | 0.369217 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.9461 | −1.15642 | ||||||||
\(585\) | 0.0192743 | 0.000796895 0 | ||||||||
\(586\) | 10.0857 | 0.416635 | ||||||||
\(587\) | 42.7729 | 1.76543 | 0.882713 | − | 0.469912i | \(-0.155714\pi\) | ||||
0.882713 | + | 0.469912i | \(0.155714\pi\) | |||||||
\(588\) | −0.239314 | −0.00986913 | ||||||||
\(589\) | −4.83322 | −0.199149 | ||||||||
\(590\) | −0.493289 | −0.0203084 | ||||||||
\(591\) | −5.32512 | −0.219046 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 9.05938 | 0.370776 | ||||||||
\(598\) | −0.464518 | −0.0189955 | ||||||||
\(599\) | 10.2428 | 0.418509 | 0.209255 | − | 0.977861i | \(-0.432896\pi\) | ||||
0.209255 | + | 0.977861i | \(0.432896\pi\) | |||||||
\(600\) | −14.5393 | −0.593563 | ||||||||
\(601\) | −27.5452 | −1.12359 | −0.561795 | − | 0.827276i | \(-0.689889\pi\) | ||||
−0.561795 | + | 0.827276i | \(0.689889\pi\) | |||||||
\(602\) | 6.53073 | 0.266173 | ||||||||
\(603\) | 8.75721 | 0.356621 | ||||||||
\(604\) | 2.27338 | 0.0925026 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.2101 | 0.455380 | ||||||||
\(607\) | 17.3982 | 0.706171 | 0.353085 | − | 0.935591i | \(-0.385133\pi\) | ||||
0.353085 | + | 0.935591i | \(0.385133\pi\) | |||||||
\(608\) | 3.27631 | 0.132872 | ||||||||
\(609\) | −9.43072 | −0.382152 | ||||||||
\(610\) | 5.32709 | 0.215688 | ||||||||
\(611\) | 0.354712 | 0.0143501 | ||||||||
\(612\) | 1.50379 | 0.0607870 | ||||||||
\(613\) | −0.178250 | −0.00719945 | −0.00359973 | − | 0.999994i | \(-0.501146\pi\) | ||||
−0.00359973 | + | 0.999994i | \(0.501146\pi\) | |||||||
\(614\) | 26.1858 | 1.05677 | ||||||||
\(615\) | 0.0255753 | 0.00103129 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.66139 | −0.147402 | −0.0737010 | − | 0.997280i | \(-0.523481\pi\) | ||||
−0.0737010 | + | 0.997280i | \(0.523481\pi\) | |||||||
\(618\) | 21.1816 | 0.852050 | ||||||||
\(619\) | 23.7370 | 0.954070 | 0.477035 | − | 0.878884i | \(-0.341712\pi\) | ||||
0.477035 | + | 0.878884i | \(0.341712\pi\) | |||||||
\(620\) | −0.155364 | −0.00623955 | ||||||||
\(621\) | 5.93756 | 0.238266 | ||||||||
\(622\) | 40.2222 | 1.61276 | ||||||||
\(623\) | 10.6013 | 0.424732 | ||||||||
\(624\) | −0.204241 | −0.00817619 | ||||||||
\(625\) | 23.4084 | 0.936335 | ||||||||
\(626\) | 26.2529 | 1.04928 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.17602 | 0.166641 | ||||||||
\(629\) | 41.0481 | 1.63669 | ||||||||
\(630\) | −0.433778 | −0.0172821 | ||||||||
\(631\) | 16.0214 | 0.637801 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(632\) | 38.8408 | 1.54500 | ||||||||
\(633\) | −27.8370 | −1.10642 | ||||||||
\(634\) | 25.1633 | 0.999363 | ||||||||
\(635\) | −2.41925 | −0.0960051 | ||||||||
\(636\) | 1.42218 | 0.0563930 | ||||||||
\(637\) | 0.0589594 | 0.00233606 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.65857 | −0.0656118 | ||||||||
\(640\) | −2.89998 | −0.114632 | ||||||||
\(641\) | −26.3387 | −1.04032 | −0.520158 | − | 0.854070i | \(-0.674127\pi\) | ||||
−0.520158 | + | 0.854070i | \(0.674127\pi\) | |||||||
\(642\) | −6.86070 | −0.270770 | ||||||||
\(643\) | 32.9889 | 1.30095 | 0.650477 | − | 0.759526i | \(-0.274569\pi\) | ||||
0.650477 | + | 0.759526i | \(0.274569\pi\) | |||||||
\(644\) | −1.42094 | −0.0559929 | ||||||||
\(645\) | −1.60897 | −0.0633530 | ||||||||
\(646\) | −20.2927 | −0.798407 | ||||||||
\(647\) | −15.1898 | −0.597171 | −0.298585 | − | 0.954383i | \(-0.596515\pi\) | ||||
−0.298585 | + | 0.954383i | \(0.596515\pi\) | |||||||
\(648\) | 2.97136 | 0.116726 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.382808 | 0.0150150 | ||||||||
\(651\) | 1.98589 | 0.0778332 | ||||||||
\(652\) | 1.75968 | 0.0689145 | ||||||||
\(653\) | 34.1357 | 1.33583 | 0.667916 | − | 0.744236i | \(-0.267186\pi\) | ||||
0.667916 | + | 0.744236i | \(0.267186\pi\) | |||||||
\(654\) | 4.01315 | 0.156927 | ||||||||
\(655\) | −3.57896 | −0.139842 | ||||||||
\(656\) | −0.271009 | −0.0105811 | ||||||||
\(657\) | −9.40514 | −0.366930 | ||||||||
\(658\) | −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 | ||||||||
\(663\) | −0.370486 | −0.0143885 | ||||||||
\(664\) | 22.2687 | 0.864192 | ||||||||
\(665\) | −0.795623 | −0.0308529 | ||||||||
\(666\) | 8.66793 | 0.335875 | ||||||||
\(667\) | −55.9955 | −2.16815 | ||||||||
\(668\) | −1.13468 | −0.0439023 | ||||||||
\(669\) | 19.3064 | 0.746428 | ||||||||
\(670\) | −3.79868 | −0.146756 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.34618 | −0.0519301 | ||||||||
\(673\) | 6.96022 | 0.268297 | 0.134148 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134148 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(674\) | 36.5816 | 1.40907 | ||||||||
\(675\) | −4.89313 | −0.188337 | ||||||||
\(676\) | 3.11025 | 0.119625 | ||||||||
\(677\) | 24.6140 | 0.945993 | 0.472996 | − | 0.881064i | \(-0.343172\pi\) | ||||
0.472996 | + | 0.881064i | \(0.343172\pi\) | |||||||
\(678\) | 8.27439 | 0.317776 | ||||||||
\(679\) | −6.71278 | −0.257613 | ||||||||
\(680\) | −6.10381 | −0.234070 | ||||||||
\(681\) | −1.31586 | −0.0504238 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.65760 | −0.101690 | −0.0508451 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508451 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(684\) | 0.582436 | 0.0222700 | ||||||||
\(685\) | 1.62349 | 0.0620305 | ||||||||
\(686\) | −1.32691 | −0.0506616 | ||||||||
\(687\) | −0.440079 | −0.0167900 | ||||||||
\(688\) | 17.0495 | 0.650006 | ||||||||
\(689\) | −0.350380 | −0.0133484 | ||||||||
\(690\) | −2.57558 | −0.0980508 | ||||||||
\(691\) | 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 | ||||||||
\(696\) | −28.0221 | −1.06217 | ||||||||
\(697\) | −0.491601 | −0.0186207 | ||||||||
\(698\) | 38.0953 | 1.44193 | ||||||||
\(699\) | 5.29786 | 0.200383 | ||||||||
\(700\) | 1.17099 | 0.0442594 | ||||||||
\(701\) | 29.2016 | 1.10293 | 0.551465 | − | 0.834198i | \(-0.314069\pi\) | ||||
0.551465 | + | 0.834198i | \(0.314069\pi\) | |||||||
\(702\) | −0.0782337 | −0.00295274 | ||||||||
\(703\) | 15.8985 | 0.599622 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.96675 | 0.0740722 | ||||||||
\(706\) | 0.559101 | 0.0210421 | ||||||||
\(707\) | −8.44830 | −0.317731 | ||||||||
\(708\) | −0.272146 | −0.0102279 | ||||||||
\(709\) | 5.34783 | 0.200842 | 0.100421 | − | 0.994945i | \(-0.467981\pi\) | ||||
0.100421 | + | 0.994945i | \(0.467981\pi\) | |||||||
\(710\) | 0.719449 | 0.0270004 | ||||||||
\(711\) | 13.0717 | 0.490227 | ||||||||
\(712\) | 31.5003 | 1.18052 | ||||||||
\(713\) | 11.7914 | 0.441590 | ||||||||
\(714\) | 8.33796 | 0.312040 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.52219 | 0.0942588 | ||||||||
\(717\) | −24.3293 | −0.908595 | ||||||||
\(718\) | 10.8454 | 0.404745 | ||||||||
\(719\) | 39.3239 | 1.46653 | 0.733267 | − | 0.679941i | \(-0.237995\pi\) | ||||
0.733267 | + | 0.679941i | \(0.237995\pi\) | |||||||
\(720\) | −1.13244 | −0.0422037 | ||||||||
\(721\) | −15.9631 | −0.594498 | ||||||||
\(722\) | 17.3516 | 0.645760 | ||||||||
\(723\) | 26.5165 | 0.986160 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.07974 | 0.150998 | ||||||||
\(731\) | 30.9271 | 1.14388 | ||||||||
\(732\) | 2.93894 | 0.108626 | ||||||||
\(733\) | −3.58578 | −0.132444 | −0.0662218 | − | 0.997805i | \(-0.521095\pi\) | ||||
−0.0662218 | + | 0.997805i | \(0.521095\pi\) | |||||||
\(734\) | 14.5183 | 0.535881 | ||||||||
\(735\) | 0.326909 | 0.0120582 | ||||||||
\(736\) | −7.99305 | −0.294628 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.103809 | −0.00382126 | ||||||||
\(739\) | 20.4213 | 0.751208 | 0.375604 | − | 0.926780i | \(-0.377435\pi\) | ||||
0.375604 | + | 0.926780i | \(0.377435\pi\) | |||||||
\(740\) | 0.511055 | 0.0187868 | ||||||||
\(741\) | −0.143494 | −0.00527138 | ||||||||
\(742\) | 7.88546 | 0.289484 | ||||||||
\(743\) | −26.7582 | −0.981662 | −0.490831 | − | 0.871255i | \(-0.663307\pi\) | ||||
−0.490831 | + | 0.871255i | \(0.663307\pi\) | |||||||
\(744\) | 5.90080 | 0.216334 | ||||||||
\(745\) | 6.64140 | 0.243322 | ||||||||
\(746\) | 20.2955 | 0.743072 | ||||||||
\(747\) | 7.49443 | 0.274207 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.17044 | 0.188924 | ||||||||
\(750\) | 4.29142 | 0.156701 | ||||||||
\(751\) | 40.7545 | 1.48715 | 0.743576 | − | 0.668652i | \(-0.233128\pi\) | ||||
0.743576 | + | 0.668652i | \(0.233128\pi\) | |||||||
\(752\) | −20.8408 | −0.759985 | ||||||||
\(753\) | −19.1828 | −0.699059 | ||||||||
\(754\) | 0.737800 | 0.0268691 | ||||||||
\(755\) | −3.10550 | −0.113021 | ||||||||
\(756\) | −0.239314 | −0.00870375 | ||||||||
\(757\) | 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 | \(0.513752\pi\) | |||||||
\(762\) | 9.81965 | 0.355728 | ||||||||
\(763\) | −3.02444 | −0.109492 | ||||||||
\(764\) | −4.28822 | −0.155142 | ||||||||
\(765\) | −2.05421 | −0.0742701 | ||||||||
\(766\) | 27.2660 | 0.985162 | ||||||||
\(767\) | 0.0670482 | 0.00242097 | ||||||||
\(768\) | −5.65801 | −0.204166 | ||||||||
\(769\) | −23.0495 | −0.831186 | −0.415593 | − | 0.909551i | \(-0.636426\pi\) | ||||
−0.415593 | + | 0.909551i | \(0.636426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.2417 | 0.440875 | ||||||||
\(772\) | 2.67939 | 0.0964334 | ||||||||
\(773\) | −30.2708 | −1.08876 | −0.544382 | − | 0.838837i | \(-0.683236\pi\) | ||||
−0.544382 | + | 0.838837i | \(0.683236\pi\) | |||||||
\(774\) | 6.53073 | 0.234742 | ||||||||
\(775\) | −9.71722 | −0.349053 | ||||||||
\(776\) | −19.9461 | −0.716023 | ||||||||
\(777\) | −6.53242 | −0.234349 | ||||||||
\(778\) | −22.4281 | −0.804087 | ||||||||
\(779\) | −0.190403 | −0.00682191 | ||||||||
\(780\) | −0.00461261 | −0.000165158 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 49.5072 | 1.77037 | ||||||||
\(783\) | −9.43072 | −0.337026 | ||||||||
\(784\) | −3.46410 | −0.123718 | ||||||||
\(785\) | −5.70455 | −0.203604 | ||||||||
\(786\) | 14.5269 | 0.518156 | ||||||||
\(787\) | 7.41144 | 0.264189 | 0.132095 | − | 0.991237i | \(-0.457830\pi\) | ||||
0.132095 | + | 0.991237i | \(0.457830\pi\) | |||||||
\(788\) | 1.27437 | 0.0453977 | ||||||||
\(789\) | 18.2025 | 0.648024 | ||||||||
\(790\) | −5.67021 | −0.201737 | ||||||||
\(791\) | −6.23584 | −0.221721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.724062 | −0.0257122 | ||||||||
\(794\) | −23.5667 | −0.836350 | ||||||||
\(795\) | −1.94273 | −0.0689015 | ||||||||
\(796\) | −2.16803 | −0.0768439 | ||||||||
\(797\) | −33.5597 | −1.18875 | −0.594373 | − | 0.804190i | \(-0.702600\pi\) | ||||
−0.594373 | + | 0.804190i | \(0.702600\pi\) | |||||||
\(798\) | 3.22940 | 0.114320 | ||||||||
\(799\) | −37.8044 | −1.33742 | ||||||||
\(800\) | 6.58705 | 0.232887 | ||||||||
\(801\) | 10.6013 | 0.374578 | ||||||||
\(802\) | −10.8802 | −0.384192 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.09572 | −0.0739104 | ||||||||
\(805\) | 1.94104 | 0.0684127 | ||||||||
\(806\) | −0.155364 | −0.00547245 | ||||||||
\(807\) | 9.40683 | 0.331136 | ||||||||
\(808\) | −25.1030 | −0.883120 | ||||||||
\(809\) | −42.2328 | −1.48483 | −0.742413 | − | 0.669942i | \(-0.766319\pi\) | ||||
−0.742413 | + | 0.669942i | \(0.766319\pi\) | |||||||
\(810\) | −0.433778 | −0.0152414 | ||||||||
\(811\) | 10.1590 | 0.356730 | 0.178365 | − | 0.983964i | \(-0.442919\pi\) | ||||
0.178365 | + | 0.983964i | \(0.442919\pi\) | |||||||
\(812\) | 2.25690 | 0.0792017 | ||||||||
\(813\) | 14.5252 | 0.509420 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.40377 | −0.0842004 | ||||||||
\(816\) | 21.7675 | 0.762016 | ||||||||
\(817\) | 11.9785 | 0.419074 | ||||||||
\(818\) | −48.5346 | −1.69697 | ||||||||
\(819\) | 0.0589594 | 0.00206021 | ||||||||
\(820\) | −0.00612051 | −0.000213737 0 | ||||||||
\(821\) | 25.6507 | 0.895214 | 0.447607 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447607 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(822\) | −6.58969 | −0.229842 | ||||||||
\(823\) | −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 | \(0.425208\pi\) | |||||||
\(828\) | −1.42094 | −0.0493811 | ||||||||
\(829\) | −19.7867 | −0.687221 | −0.343610 | − | 0.939112i | \(-0.611650\pi\) | ||||
−0.343610 | + | 0.939112i | \(0.611650\pi\) | |||||||
\(830\) | −3.25092 | −0.112841 | ||||||||
\(831\) | −8.26447 | −0.286691 | ||||||||
\(832\) | 0.513799 | 0.0178128 | ||||||||
\(833\) | −6.28375 | −0.217719 | ||||||||
\(834\) | −8.22100 | −0.284670 | ||||||||
\(835\) | 1.55001 | 0.0536402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.98589 | 0.0686424 | ||||||||
\(838\) | 18.3506 | 0.633910 | ||||||||
\(839\) | 46.1948 | 1.59482 | 0.797410 | − | 0.603437i | \(-0.206203\pi\) | ||||
0.797410 | + | 0.603437i | \(0.206203\pi\) | |||||||
\(840\) | 0.971364 | 0.0335153 | ||||||||
\(841\) | 59.9384 | 2.06684 | ||||||||
\(842\) | 40.9355 | 1.41073 | ||||||||
\(843\) | 24.0080 | 0.826879 | ||||||||
\(844\) | 6.66177 | 0.229308 | ||||||||
\(845\) | −4.24867 | −0.146159 | ||||||||
\(846\) | −7.98297 | −0.274460 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.5862 | 0.706934 | ||||||||
\(849\) | −16.0512 | −0.550874 | ||||||||
\(850\) | −40.7987 | −1.39938 | ||||||||
\(851\) | −38.7867 | −1.32959 | ||||||||
\(852\) | 0.396917 | 0.0135982 | ||||||||
\(853\) | 37.6343 | 1.28857 | 0.644287 | − | 0.764784i | \(-0.277154\pi\) | ||||
0.644287 | + | 0.764784i | \(0.277154\pi\) | |||||||
\(854\) | 16.2953 | 0.557615 | ||||||||
\(855\) | −0.795623 | −0.0272097 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | 0.0782337 | 0.00266620 | ||||||||
\(862\) | −4.79156 | −0.163201 | ||||||||
\(863\) | −19.3134 | −0.657434 | −0.328717 | − | 0.944428i | \(-0.606616\pi\) | ||||
−0.328717 | + | 0.944428i | \(0.606616\pi\) | |||||||
\(864\) | −1.34618 | −0.0457981 | ||||||||
\(865\) | 2.63093 | 0.0894543 | ||||||||
\(866\) | −50.4292 | −1.71366 | ||||||||
\(867\) | 22.4855 | 0.763647 | ||||||||
\(868\) | −0.475251 | −0.0161311 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.09084 | 0.138692 | ||||||||
\(871\) | 0.516320 | 0.0174948 | ||||||||
\(872\) | −8.98671 | −0.304328 | ||||||||
\(873\) | −6.71278 | −0.227193 | ||||||||
\(874\) | 19.1748 | 0.648596 | ||||||||
\(875\) | −3.23415 | −0.109334 | ||||||||
\(876\) | 2.25078 | 0.0760468 | ||||||||
\(877\) | 22.9946 | 0.776472 | 0.388236 | − | 0.921560i | \(-0.373084\pi\) | ||||
0.388236 | + | 0.921560i | \(0.373084\pi\) | |||||||
\(878\) | −34.3476 | −1.15918 | ||||||||
\(879\) | −7.60088 | −0.256371 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.4759 | −1.70058 | −0.850288 | − | 0.526318i | \(-0.823572\pi\) | ||||
−0.850288 | + | 0.526318i | \(0.823572\pi\) | |||||||
\(882\) | −1.32691 | −0.0446793 | ||||||||
\(883\) | 14.8564 | 0.499958 | 0.249979 | − | 0.968251i | \(-0.419576\pi\) | ||||
0.249979 | + | 0.968251i | \(0.419576\pi\) | |||||||
\(884\) | 0.0886623 | 0.00298204 | ||||||||
\(885\) | 0.371758 | 0.0124965 | ||||||||
\(886\) | −19.6710 | −0.660860 | ||||||||
\(887\) | 46.0622 | 1.54662 | 0.773309 | − | 0.634029i | \(-0.218600\pi\) | ||||
0.773309 | + | 0.634029i | \(0.218600\pi\) | |||||||
\(888\) | −19.4102 | −0.651364 | ||||||||
\(889\) | −7.40039 | −0.248201 | ||||||||
\(890\) | −4.59861 | −0.154146 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.62029 | −0.154699 | ||||||||
\(893\) | −14.6421 | −0.489980 | ||||||||
\(894\) | −26.9572 | −0.901582 | ||||||||
\(895\) | −3.44538 | −0.115166 | ||||||||
\(896\) | −8.87093 | −0.296357 | ||||||||
\(897\) | 0.350075 | 0.0116887 | ||||||||
\(898\) | −50.1666 | −1.67408 | ||||||||
\(899\) | −18.7284 | −0.624626 | ||||||||
\(900\) | 1.17099 | 0.0390331 | ||||||||
\(901\) | 37.3426 | 1.24406 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.92177 | −0.163786 | ||||||||
\(904\) | −18.5289 | −0.616264 | ||||||||
\(905\) | −7.69505 | −0.255792 | ||||||||
\(906\) | 12.6051 | 0.418776 | ||||||||
\(907\) | 28.5358 | 0.947516 | 0.473758 | − | 0.880655i | \(-0.342897\pi\) | ||||
0.473758 | + | 0.880655i | \(0.342897\pi\) | |||||||
\(908\) | 0.314903 | 0.0104504 | ||||||||
\(909\) | −8.44830 | −0.280213 | ||||||||
\(910\) | −0.0255753 | −0.000847812 0 | ||||||||
\(911\) | 31.5458 | 1.04516 | 0.522580 | − | 0.852590i | \(-0.324970\pi\) | ||||
0.522580 | + | 0.852590i | \(0.324970\pi\) | |||||||
\(912\) | 8.43085 | 0.279173 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −31.1974 | −1.03192 | ||||||||
\(915\) | −4.01466 | −0.132721 | ||||||||
\(916\) | 0.105317 | 0.00347977 | ||||||||
\(917\) | −10.9479 | −0.361531 | ||||||||
\(918\) | 8.33796 | 0.275194 | ||||||||
\(919\) | 40.0921 | 1.32252 | 0.661259 | − | 0.750158i | \(-0.270022\pi\) | ||||
0.661259 | + | 0.750158i | \(0.270022\pi\) | |||||||
\(920\) | 5.76754 | 0.190150 | ||||||||
\(921\) | −19.7345 | −0.650273 | ||||||||
\(922\) | −54.2986 | −1.78823 | ||||||||
\(923\) | −0.0977880 | −0.00321873 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.9640 | 1.05097 | ||||||||
\(926\) | −0.0806060 | −0.00264888 | ||||||||
\(927\) | −15.9631 | −0.524298 | ||||||||
\(928\) | 12.6955 | 0.416749 | ||||||||
\(929\) | 4.40597 | 0.144555 | 0.0722777 | − | 0.997385i | \(-0.476973\pi\) | ||||
0.0722777 | + | 0.997385i | \(0.476973\pi\) | |||||||
\(930\) | −0.861435 | −0.0282476 | ||||||||
\(931\) | −2.43378 | −0.0797638 | ||||||||
\(932\) | −1.26785 | −0.0415298 | ||||||||
\(933\) | −30.3127 | −0.992393 | ||||||||
\(934\) | 49.6744 | 1.62540 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.175190 | 0.00572626 | ||||||||
\(937\) | −0.902908 | −0.0294967 | −0.0147484 | − | 0.999891i | \(-0.504695\pi\) | ||||
−0.0147484 | + | 0.999891i | \(0.504695\pi\) | |||||||
\(938\) | −11.6200 | −0.379407 | ||||||||
\(939\) | −19.7850 | −0.645660 | ||||||||
\(940\) | −0.470671 | −0.0153516 | ||||||||
\(941\) | −34.8442 | −1.13589 | −0.567943 | − | 0.823068i | \(-0.692261\pi\) | ||||
−0.567943 | + | 0.823068i | \(0.692261\pi\) | |||||||
\(942\) | 23.1545 | 0.754416 | ||||||||
\(943\) | 0.464518 | 0.0151268 | ||||||||
\(944\) | −3.93935 | −0.128215 | ||||||||
\(945\) | 0.326909 | 0.0106343 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.9556 | 0.843444 | 0.421722 | − | 0.906725i | \(-0.361426\pi\) | ||||
0.421722 | + | 0.906725i | \(0.361426\pi\) | |||||||
\(948\) | −3.12824 | −0.101600 | ||||||||
\(949\) | −0.554521 | −0.0180005 | ||||||||
\(950\) | −15.8019 | −0.512681 | ||||||||
\(951\) | −18.9639 | −0.614945 | ||||||||
\(952\) | −18.6713 | −0.605140 | ||||||||
\(953\) | −1.69616 | −0.0549440 | −0.0274720 | − | 0.999623i | \(-0.508746\pi\) | ||||
−0.0274720 | + | 0.999623i | \(0.508746\pi\) | |||||||
\(954\) | 7.88546 | 0.255301 | ||||||||
\(955\) | 5.85782 | 0.189555 | ||||||||
\(956\) | 5.82234 | 0.188308 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.6620 | 1.34604 | ||||||||
\(959\) | 4.96620 | 0.160367 | ||||||||
\(960\) | 2.84883 | 0.0919457 | ||||||||
\(961\) | −27.0562 | −0.872782 | ||||||||
\(962\) | 0.511055 | 0.0164771 | ||||||||
\(963\) | 5.17044 | 0.166615 | ||||||||
\(964\) | −6.34577 | −0.204383 | ||||||||
\(965\) | −3.66012 | −0.117823 | ||||||||
\(966\) | −7.87861 | −0.253490 | ||||||||
\(967\) | −25.0337 | −0.805028 | −0.402514 | − | 0.915414i | \(-0.631864\pi\) | ||||
−0.402514 | + | 0.915414i | \(0.631864\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.2932 | 0.491290 | ||||||||
\(970\) | 2.91185 | 0.0934940 | ||||||||
\(971\) | −57.3356 | −1.83999 | −0.919994 | − | 0.391933i | \(-0.871807\pi\) | ||||
−0.919994 | + | 0.391933i | \(0.871807\pi\) | |||||||
\(972\) | −0.239314 | −0.00767599 | ||||||||
\(973\) | 6.19560 | 0.198622 | ||||||||
\(974\) | 27.0532 | 0.866839 | ||||||||
\(975\) | −0.288496 | −0.00923926 | ||||||||
\(976\) | 42.5415 | 1.36172 | ||||||||
\(977\) | 19.6196 | 0.627687 | 0.313844 | − | 0.949475i | \(-0.398383\pi\) | ||||
0.313844 | + | 0.949475i | \(0.398383\pi\) | |||||||
\(978\) | 9.75681 | 0.311988 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0782337 | −0.00249908 | ||||||||
\(981\) | −3.02444 | −0.0965629 | ||||||||
\(982\) | 15.4081 | 0.491692 | ||||||||
\(983\) | 32.4742 | 1.03577 | 0.517883 | − | 0.855451i | \(-0.326720\pi\) | ||||
0.517883 | + | 0.855451i | \(0.326720\pi\) | |||||||
\(984\) | 0.232461 | 0.00741058 | ||||||||
\(985\) | −1.74083 | −0.0554674 | ||||||||
\(986\) | −78.6329 | −2.50418 | ||||||||
\(987\) | 6.01621 | 0.191498 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −3.98895 | −0.126586 | ||||||||
\(994\) | 2.20077 | 0.0698040 | ||||||||
\(995\) | 2.96159 | 0.0938886 | ||||||||
\(996\) | −1.79352 | −0.0568298 | ||||||||
\(997\) | −7.14889 | −0.226408 | −0.113204 | − | 0.993572i | \(-0.536111\pi\) | ||||
−0.113204 | + | 0.993572i | \(0.536111\pi\) | |||||||
\(998\) | −50.6356 | −1.60284 | ||||||||
\(999\) | −6.53242 | −0.206677 |
(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 | 2541.2.a.bl.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 7623.2.a.cn.1.3 | 4 | |||
11.10 | odd | 2 | 2541.2.a.bp.1.3 | yes | 4 | ||
33.32 | even | 2 | 7623.2.a.cg.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bl.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2541.2.a.bp.1.3 | yes | 4 | 11.10 | odd | 2 | ||
7623.2.a.cg.1.2 | 4 | 33.32 | even | 2 | |||
7623.2.a.cn.1.3 | 4 | 3.2 | odd | 2 |