Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(1,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.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: | \(1.49320251780\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | −1.93185 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 1.73205 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | −3.73205 | −1.66902 | −0.834512 | − | 0.550990i | \(-0.814250\pi\) | ||||
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | −4.73205 | −1.93185 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −9.46410 | −3.34607 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.1962 | 3.22431 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 9.46410 | 2.73205 | ||||||||
\(13\) | −3.26795 | −0.906366 | −0.453183 | − | 0.891417i | \(-0.649712\pi\) | ||||
−0.453183 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(14\) | 5.46410 | 1.46034 | ||||||||
\(15\) | −6.46410 | −1.66902 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.19615 | −1.42149 | −0.710747 | − | 0.703447i | \(-0.751643\pi\) | ||||
−0.710747 | + | 0.703447i | \(0.751643\pi\) | |||||||
\(20\) | −20.3923 | −4.55986 | ||||||||
\(21\) | −3.46410 | −0.755929 | ||||||||
\(22\) | −2.73205 | −0.582475 | ||||||||
\(23\) | −3.73205 | −0.778186 | −0.389093 | − | 0.921198i | \(-0.627212\pi\) | ||||
−0.389093 | + | 0.921198i | \(0.627212\pi\) | |||||||
\(24\) | −16.3923 | −3.34607 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | 8.92820 | 1.75096 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −10.9282 | −2.06524 | ||||||||
\(29\) | −1.26795 | −0.235452 | −0.117726 | − | 0.993046i | \(-0.537560\pi\) | ||||
−0.117726 | + | 0.993046i | \(0.537560\pi\) | |||||||
\(30\) | 17.6603 | 3.22431 | ||||||||
\(31\) | 2.26795 | 0.407336 | 0.203668 | − | 0.979040i | \(-0.434714\pi\) | ||||
0.203668 | + | 0.979040i | \(0.434714\pi\) | |||||||
\(32\) | −21.8564 | −3.86370 | ||||||||
\(33\) | 1.73205 | 0.301511 | ||||||||
\(34\) | −2.73205 | −0.468543 | ||||||||
\(35\) | 7.46410 | 1.26166 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.73205 | −0.613545 | −0.306773 | − | 0.951783i | \(-0.599249\pi\) | ||||
−0.306773 | + | 0.951783i | \(0.599249\pi\) | |||||||
\(38\) | 16.9282 | 2.74612 | ||||||||
\(39\) | −5.66025 | −0.906366 | ||||||||
\(40\) | 35.3205 | 5.58466 | ||||||||
\(41\) | 9.46410 | 1.47804 | 0.739022 | − | 0.673681i | \(-0.235288\pi\) | ||||
0.739022 | + | 0.673681i | \(0.235288\pi\) | |||||||
\(42\) | 9.46410 | 1.46034 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 5.46410 | 0.823744 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.1962 | 1.50334 | ||||||||
\(47\) | 0.928203 | 0.135392 | 0.0676962 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676962 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(48\) | 25.8564 | 3.73205 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −24.3923 | −3.44959 | ||||||||
\(51\) | 1.73205 | 0.242536 | ||||||||
\(52\) | −17.8564 | −2.47624 | ||||||||
\(53\) | −2.53590 | −0.348332 | −0.174166 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174166 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(54\) | 14.1962 | 1.93185 | ||||||||
\(55\) | −3.73205 | −0.503230 | ||||||||
\(56\) | 18.9282 | 2.52939 | ||||||||
\(57\) | −10.7321 | −1.42149 | ||||||||
\(58\) | 3.46410 | 0.454859 | ||||||||
\(59\) | 3.00000 | 0.390567 | 0.195283 | − | 0.980747i | \(-0.437437\pi\) | ||||
0.195283 | + | 0.980747i | \(0.437437\pi\) | |||||||
\(60\) | −35.3205 | −4.55986 | ||||||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | −6.19615 | −0.786912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | 12.1962 | 1.51275 | ||||||||
\(66\) | −4.73205 | −0.582475 | ||||||||
\(67\) | 1.00000 | 0.122169 | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) | ||||
0.0610847 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(68\) | 5.46410 | 0.662620 | ||||||||
\(69\) | −6.46410 | −0.778186 | ||||||||
\(70\) | −20.3923 | −2.43735 | ||||||||
\(71\) | 0.267949 | 0.0317997 | 0.0158999 | − | 0.999874i | \(-0.494939\pi\) | ||||
0.0158999 | + | 0.999874i | \(0.494939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.80385 | 0.445207 | 0.222603 | − | 0.974909i | \(-0.428545\pi\) | ||||
0.222603 | + | 0.974909i | \(0.428545\pi\) | |||||||
\(74\) | 10.1962 | 1.18528 | ||||||||
\(75\) | 15.4641 | 1.78564 | ||||||||
\(76\) | −33.8564 | −3.88360 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 15.4641 | 1.75096 | ||||||||
\(79\) | 2.19615 | 0.247086 | 0.123543 | − | 0.992339i | \(-0.460574\pi\) | ||||
0.123543 | + | 0.992339i | \(0.460574\pi\) | |||||||
\(80\) | −55.7128 | −6.22888 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −25.8564 | −2.85536 | ||||||||
\(83\) | 15.8564 | 1.74047 | 0.870233 | − | 0.492640i | \(-0.163968\pi\) | ||||
0.870233 | + | 0.492640i | \(0.163968\pi\) | |||||||
\(84\) | −18.9282 | −2.06524 | ||||||||
\(85\) | −3.73205 | −0.404798 | ||||||||
\(86\) | 5.46410 | 0.589209 | ||||||||
\(87\) | −2.19615 | −0.235452 | ||||||||
\(88\) | −9.46410 | −1.00888 | ||||||||
\(89\) | −11.9282 | −1.26439 | −0.632194 | − | 0.774811i | \(-0.717845\pi\) | ||||
−0.632194 | + | 0.774811i | \(0.717845\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.53590 | 0.685148 | ||||||||
\(92\) | −20.3923 | −2.12604 | ||||||||
\(93\) | 3.92820 | 0.407336 | ||||||||
\(94\) | −2.53590 | −0.261558 | ||||||||
\(95\) | 23.1244 | 2.37251 | ||||||||
\(96\) | −37.8564 | −3.86370 | ||||||||
\(97\) | 15.7321 | 1.59735 | 0.798674 | − | 0.601764i | \(-0.205535\pi\) | ||||
0.798674 | + | 0.601764i | \(0.205535\pi\) | |||||||
\(98\) | 8.19615 | 0.827936 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 48.7846 | 4.87846 | ||||||||
\(101\) | 1.66025 | 0.165201 | 0.0826007 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826007 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | −11.8564 | −1.16825 | −0.584123 | − | 0.811665i | \(-0.698562\pi\) | ||||
−0.584123 | + | 0.811665i | \(0.698562\pi\) | |||||||
\(104\) | 30.9282 | 3.03276 | ||||||||
\(105\) | 12.9282 | 1.26166 | ||||||||
\(106\) | 6.92820 | 0.672927 | ||||||||
\(107\) | −11.2679 | −1.08931 | −0.544657 | − | 0.838659i | \(-0.683340\pi\) | ||||
−0.544657 | + | 0.838659i | \(0.683340\pi\) | |||||||
\(108\) | −28.3923 | −2.73205 | ||||||||
\(109\) | −2.19615 | −0.210353 | −0.105177 | − | 0.994454i | \(-0.533541\pi\) | ||||
−0.105177 | + | 0.994454i | \(0.533541\pi\) | |||||||
\(110\) | 10.1962 | 0.972165 | ||||||||
\(111\) | −6.46410 | −0.613545 | ||||||||
\(112\) | −29.8564 | −2.82117 | ||||||||
\(113\) | −6.26795 | −0.589639 | −0.294820 | − | 0.955553i | \(-0.595260\pi\) | ||||
−0.294820 | + | 0.955553i | \(0.595260\pi\) | |||||||
\(114\) | 29.3205 | 2.74612 | ||||||||
\(115\) | 13.9282 | 1.29881 | ||||||||
\(116\) | −6.92820 | −0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.19615 | −0.754517 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 61.1769 | 5.58466 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.00000 | −0.724286 | ||||||||
\(123\) | 16.3923 | 1.47804 | ||||||||
\(124\) | 12.3923 | 1.11286 | ||||||||
\(125\) | −14.6603 | −1.31125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −37.8564 | −3.34607 | ||||||||
\(129\) | −3.46410 | −0.304997 | ||||||||
\(130\) | −33.3205 | −2.92240 | ||||||||
\(131\) | −8.92820 | −0.780061 | −0.390030 | − | 0.920802i | \(-0.627535\pi\) | ||||
−0.390030 | + | 0.920802i | \(0.627535\pi\) | |||||||
\(132\) | 9.46410 | 0.823744 | ||||||||
\(133\) | 12.3923 | 1.07455 | ||||||||
\(134\) | −2.73205 | −0.236013 | ||||||||
\(135\) | 19.3923 | 1.66902 | ||||||||
\(136\) | −9.46410 | −0.811540 | ||||||||
\(137\) | −19.3923 | −1.65680 | −0.828398 | − | 0.560140i | \(-0.810747\pi\) | ||||
−0.828398 | + | 0.560140i | \(0.810747\pi\) | |||||||
\(138\) | 17.6603 | 1.50334 | ||||||||
\(139\) | 15.6603 | 1.32829 | 0.664143 | − | 0.747606i | \(-0.268797\pi\) | ||||
0.664143 | + | 0.747606i | \(0.268797\pi\) | |||||||
\(140\) | 40.7846 | 3.44693 | ||||||||
\(141\) | 1.60770 | 0.135392 | ||||||||
\(142\) | −0.732051 | −0.0614323 | ||||||||
\(143\) | −3.26795 | −0.273280 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.73205 | 0.392975 | ||||||||
\(146\) | −10.3923 | −0.860073 | ||||||||
\(147\) | −5.19615 | −0.428571 | ||||||||
\(148\) | −20.3923 | −1.67624 | ||||||||
\(149\) | −19.1244 | −1.56673 | −0.783364 | − | 0.621563i | \(-0.786498\pi\) | ||||
−0.783364 | + | 0.621563i | \(0.786498\pi\) | |||||||
\(150\) | −42.2487 | −3.44959 | ||||||||
\(151\) | −12.1962 | −0.992509 | −0.496254 | − | 0.868177i | \(-0.665292\pi\) | ||||
−0.496254 | + | 0.868177i | \(0.665292\pi\) | |||||||
\(152\) | 58.6410 | 4.75641 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.46410 | 0.440310 | ||||||||
\(155\) | −8.46410 | −0.679853 | ||||||||
\(156\) | −30.9282 | −2.47624 | ||||||||
\(157\) | −19.7846 | −1.57898 | −0.789492 | − | 0.613761i | \(-0.789656\pi\) | ||||
−0.789492 | + | 0.613761i | \(0.789656\pi\) | |||||||
\(158\) | −6.00000 | −0.477334 | ||||||||
\(159\) | −4.39230 | −0.348332 | ||||||||
\(160\) | 81.5692 | 6.44861 | ||||||||
\(161\) | 7.46410 | 0.588254 | ||||||||
\(162\) | 24.5885 | 1.93185 | ||||||||
\(163\) | −2.53590 | −0.198627 | −0.0993134 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993134 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(164\) | 51.7128 | 4.03809 | ||||||||
\(165\) | −6.46410 | −0.503230 | ||||||||
\(166\) | −43.3205 | −3.36232 | ||||||||
\(167\) | 18.7321 | 1.44953 | 0.724765 | − | 0.688996i | \(-0.241948\pi\) | ||||
0.724765 | + | 0.688996i | \(0.241948\pi\) | |||||||
\(168\) | 32.7846 | 2.52939 | ||||||||
\(169\) | −2.32051 | −0.178501 | ||||||||
\(170\) | 10.1962 | 0.782009 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.9282 | −0.833268 | ||||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | −17.8564 | −1.34982 | ||||||||
\(176\) | 14.9282 | 1.12526 | ||||||||
\(177\) | 5.19615 | 0.390567 | ||||||||
\(178\) | 32.5885 | 2.44261 | ||||||||
\(179\) | −3.00000 | −0.224231 | −0.112115 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6603 | 0.941029 | 0.470515 | − | 0.882392i | \(-0.344068\pi\) | ||||
0.470515 | + | 0.882392i | \(0.344068\pi\) | |||||||
\(182\) | −17.8564 | −1.32360 | ||||||||
\(183\) | 5.07180 | 0.374918 | ||||||||
\(184\) | 35.3205 | 2.60386 | ||||||||
\(185\) | 13.9282 | 1.02402 | ||||||||
\(186\) | −10.7321 | −0.786912 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 5.07180 | 0.369899 | ||||||||
\(189\) | 10.3923 | 0.755929 | ||||||||
\(190\) | −63.1769 | −4.58334 | ||||||||
\(191\) | 26.4641 | 1.91488 | 0.957438 | − | 0.288640i | \(-0.0932032\pi\) | ||||
0.957438 | + | 0.288640i | \(0.0932032\pi\) | |||||||
\(192\) | 51.7128 | 3.73205 | ||||||||
\(193\) | −24.1962 | −1.74168 | −0.870839 | − | 0.491569i | \(-0.836424\pi\) | ||||
−0.870839 | + | 0.491569i | \(0.836424\pi\) | |||||||
\(194\) | −42.9808 | −3.08584 | ||||||||
\(195\) | 21.1244 | 1.51275 | ||||||||
\(196\) | −16.3923 | −1.17088 | ||||||||
\(197\) | −21.1244 | −1.50505 | −0.752524 | − | 0.658565i | \(-0.771164\pi\) | ||||
−0.752524 | + | 0.658565i | \(0.771164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7846 | −1.18983 | −0.594915 | − | 0.803789i | \(-0.702814\pi\) | ||||
−0.594915 | + | 0.803789i | \(0.702814\pi\) | |||||||
\(200\) | −84.4974 | −5.97487 | ||||||||
\(201\) | 1.73205 | 0.122169 | ||||||||
\(202\) | −4.53590 | −0.319145 | ||||||||
\(203\) | 2.53590 | 0.177985 | ||||||||
\(204\) | 9.46410 | 0.662620 | ||||||||
\(205\) | −35.3205 | −2.46689 | ||||||||
\(206\) | 32.3923 | 2.25688 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −48.7846 | −3.38260 | ||||||||
\(209\) | −6.19615 | −0.428597 | ||||||||
\(210\) | −35.3205 | −2.43735 | ||||||||
\(211\) | −1.46410 | −0.100793 | −0.0503965 | − | 0.998729i | \(-0.516048\pi\) | ||||
−0.0503965 | + | 0.998729i | \(0.516048\pi\) | |||||||
\(212\) | −13.8564 | −0.951662 | ||||||||
\(213\) | 0.464102 | 0.0317997 | ||||||||
\(214\) | 30.7846 | 2.10439 | ||||||||
\(215\) | 7.46410 | 0.509048 | ||||||||
\(216\) | 49.1769 | 3.34607 | ||||||||
\(217\) | −4.53590 | −0.307917 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 6.58846 | 0.445207 | ||||||||
\(220\) | −20.3923 | −1.37485 | ||||||||
\(221\) | −3.26795 | −0.219826 | ||||||||
\(222\) | 17.6603 | 1.18528 | ||||||||
\(223\) | 20.3205 | 1.36076 | 0.680381 | − | 0.732859i | \(-0.261814\pi\) | ||||
0.680381 | + | 0.732859i | \(0.261814\pi\) | |||||||
\(224\) | 43.7128 | 2.92069 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.1244 | 1.13910 | ||||||||
\(227\) | 16.7321 | 1.11055 | 0.555273 | − | 0.831668i | \(-0.312614\pi\) | ||||
0.555273 | + | 0.831668i | \(0.312614\pi\) | |||||||
\(228\) | −58.6410 | −3.88360 | ||||||||
\(229\) | −12.4641 | −0.823651 | −0.411826 | − | 0.911263i | \(-0.635109\pi\) | ||||
−0.411826 | + | 0.911263i | \(0.635109\pi\) | |||||||
\(230\) | −38.0526 | −2.50911 | ||||||||
\(231\) | −3.46410 | −0.227921 | ||||||||
\(232\) | 12.0000 | 0.787839 | ||||||||
\(233\) | −5.07180 | −0.332264 | −0.166132 | − | 0.986103i | \(-0.553128\pi\) | ||||
−0.166132 | + | 0.986103i | \(0.553128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.46410 | −0.225973 | ||||||||
\(236\) | 16.3923 | 1.06705 | ||||||||
\(237\) | 3.80385 | 0.247086 | ||||||||
\(238\) | 5.46410 | 0.354185 | ||||||||
\(239\) | 4.19615 | 0.271427 | 0.135713 | − | 0.990748i | \(-0.456667\pi\) | ||||
0.135713 | + | 0.990748i | \(0.456667\pi\) | |||||||
\(240\) | −96.4974 | −6.22888 | ||||||||
\(241\) | 18.9282 | 1.21927 | 0.609636 | − | 0.792681i | \(-0.291315\pi\) | ||||
0.609636 | + | 0.792681i | \(0.291315\pi\) | |||||||
\(242\) | −2.73205 | −0.175623 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.0000 | 1.02430 | ||||||||
\(245\) | 11.1962 | 0.715296 | ||||||||
\(246\) | −44.7846 | −2.85536 | ||||||||
\(247\) | 20.2487 | 1.28839 | ||||||||
\(248\) | −21.4641 | −1.36297 | ||||||||
\(249\) | 27.4641 | 1.74047 | ||||||||
\(250\) | 40.0526 | 2.53315 | ||||||||
\(251\) | −26.3205 | −1.66134 | −0.830668 | − | 0.556768i | \(-0.812041\pi\) | ||||
−0.830668 | + | 0.556768i | \(0.812041\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.73205 | −0.234632 | ||||||||
\(254\) | 10.9282 | 0.685696 | ||||||||
\(255\) | −6.46410 | −0.404798 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | 20.7846 | 1.29651 | 0.648254 | − | 0.761424i | \(-0.275499\pi\) | ||||
0.648254 | + | 0.761424i | \(0.275499\pi\) | |||||||
\(258\) | 9.46410 | 0.589209 | ||||||||
\(259\) | 7.46410 | 0.463797 | ||||||||
\(260\) | 66.6410 | 4.13290 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.3923 | 1.50696 | ||||||||
\(263\) | 11.1244 | 0.685957 | 0.342979 | − | 0.939343i | \(-0.388564\pi\) | ||||
0.342979 | + | 0.939343i | \(0.388564\pi\) | |||||||
\(264\) | −16.3923 | −1.00888 | ||||||||
\(265\) | 9.46410 | 0.581375 | ||||||||
\(266\) | −33.8564 | −2.07587 | ||||||||
\(267\) | −20.6603 | −1.26439 | ||||||||
\(268\) | 5.46410 | 0.333773 | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | −52.9808 | −3.22431 | ||||||||
\(271\) | −9.07180 | −0.551072 | −0.275536 | − | 0.961291i | \(-0.588855\pi\) | ||||
−0.275536 | + | 0.961291i | \(0.588855\pi\) | |||||||
\(272\) | 14.9282 | 0.905155 | ||||||||
\(273\) | 11.3205 | 0.685148 | ||||||||
\(274\) | 52.9808 | 3.20068 | ||||||||
\(275\) | 8.92820 | 0.538391 | ||||||||
\(276\) | −35.3205 | −2.12604 | ||||||||
\(277\) | 18.3923 | 1.10509 | 0.552543 | − | 0.833484i | \(-0.313657\pi\) | ||||
0.552543 | + | 0.833484i | \(0.313657\pi\) | |||||||
\(278\) | −42.7846 | −2.56605 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −70.6410 | −4.22161 | ||||||||
\(281\) | −27.1244 | −1.61810 | −0.809052 | − | 0.587737i | \(-0.800019\pi\) | ||||
−0.809052 | + | 0.587737i | \(0.800019\pi\) | |||||||
\(282\) | −4.39230 | −0.261558 | ||||||||
\(283\) | −2.73205 | −0.162404 | −0.0812018 | − | 0.996698i | \(-0.525876\pi\) | ||||
−0.0812018 | + | 0.996698i | \(0.525876\pi\) | |||||||
\(284\) | 1.46410 | 0.0868784 | ||||||||
\(285\) | 40.0526 | 2.37251 | ||||||||
\(286\) | 8.92820 | 0.527936 | ||||||||
\(287\) | −18.9282 | −1.11730 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −12.9282 | −0.759170 | ||||||||
\(291\) | 27.2487 | 1.59735 | ||||||||
\(292\) | 20.7846 | 1.21633 | ||||||||
\(293\) | −13.8564 | −0.809500 | −0.404750 | − | 0.914427i | \(-0.632641\pi\) | ||||
−0.404750 | + | 0.914427i | \(0.632641\pi\) | |||||||
\(294\) | 14.1962 | 0.827936 | ||||||||
\(295\) | −11.1962 | −0.651865 | ||||||||
\(296\) | 35.3205 | 2.05296 | ||||||||
\(297\) | −5.19615 | −0.301511 | ||||||||
\(298\) | 52.2487 | 3.02669 | ||||||||
\(299\) | 12.1962 | 0.705322 | ||||||||
\(300\) | 84.4974 | 4.87846 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 33.3205 | 1.91738 | ||||||||
\(303\) | 2.87564 | 0.165201 | ||||||||
\(304\) | −92.4974 | −5.30509 | ||||||||
\(305\) | −10.9282 | −0.625747 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.80385 | −0.559535 | −0.279768 | − | 0.960068i | \(-0.590257\pi\) | ||||
−0.279768 | + | 0.960068i | \(0.590257\pi\) | |||||||
\(308\) | −10.9282 | −0.622692 | ||||||||
\(309\) | −20.5359 | −1.16825 | ||||||||
\(310\) | 23.1244 | 1.31338 | ||||||||
\(311\) | −0.392305 | −0.0222456 | −0.0111228 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111228 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(312\) | 53.5692 | 3.03276 | ||||||||
\(313\) | 8.80385 | 0.497623 | 0.248811 | − | 0.968552i | \(-0.419960\pi\) | ||||
0.248811 | + | 0.968552i | \(0.419960\pi\) | |||||||
\(314\) | 54.0526 | 3.05036 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | 25.4449 | 1.42913 | 0.714563 | − | 0.699571i | \(-0.246626\pi\) | ||||
0.714563 | + | 0.699571i | \(0.246626\pi\) | |||||||
\(318\) | 12.0000 | 0.672927 | ||||||||
\(319\) | −1.26795 | −0.0709915 | ||||||||
\(320\) | −111.426 | −6.22888 | ||||||||
\(321\) | −19.5167 | −1.08931 | ||||||||
\(322\) | −20.3923 | −1.13642 | ||||||||
\(323\) | −6.19615 | −0.344763 | ||||||||
\(324\) | −49.1769 | −2.73205 | ||||||||
\(325\) | −29.1769 | −1.61844 | ||||||||
\(326\) | 6.92820 | 0.383718 | ||||||||
\(327\) | −3.80385 | −0.210353 | ||||||||
\(328\) | −89.5692 | −4.94563 | ||||||||
\(329\) | −1.85641 | −0.102347 | ||||||||
\(330\) | 17.6603 | 0.972165 | ||||||||
\(331\) | −30.8564 | −1.69602 | −0.848011 | − | 0.529979i | \(-0.822200\pi\) | ||||
−0.848011 | + | 0.529979i | \(0.822200\pi\) | |||||||
\(332\) | 86.6410 | 4.75504 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −51.1769 | −2.80028 | ||||||||
\(335\) | −3.73205 | −0.203904 | ||||||||
\(336\) | −51.7128 | −2.82117 | ||||||||
\(337\) | −9.60770 | −0.523365 | −0.261682 | − | 0.965154i | \(-0.584277\pi\) | ||||
−0.261682 | + | 0.965154i | \(0.584277\pi\) | |||||||
\(338\) | 6.33975 | 0.344837 | ||||||||
\(339\) | −10.8564 | −0.589639 | ||||||||
\(340\) | −20.3923 | −1.10593 | ||||||||
\(341\) | 2.26795 | 0.122816 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 18.9282 | 1.02054 | ||||||||
\(345\) | 24.1244 | 1.29881 | ||||||||
\(346\) | 38.2487 | 2.05626 | ||||||||
\(347\) | −18.5359 | −0.995059 | −0.497530 | − | 0.867447i | \(-0.665759\pi\) | ||||
−0.497530 | + | 0.867447i | \(0.665759\pi\) | |||||||
\(348\) | −12.0000 | −0.643268 | ||||||||
\(349\) | −15.4641 | −0.827774 | −0.413887 | − | 0.910328i | \(-0.635829\pi\) | ||||
−0.413887 | + | 0.910328i | \(0.635829\pi\) | |||||||
\(350\) | 48.7846 | 2.60765 | ||||||||
\(351\) | 16.9808 | 0.906366 | ||||||||
\(352\) | −21.8564 | −1.16495 | ||||||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | −14.1962 | −0.754517 | ||||||||
\(355\) | −1.00000 | −0.0530745 | ||||||||
\(356\) | −65.1769 | −3.45437 | ||||||||
\(357\) | −3.46410 | −0.183340 | ||||||||
\(358\) | 8.19615 | 0.433180 | ||||||||
\(359\) | 2.19615 | 0.115908 | 0.0579542 | − | 0.998319i | \(-0.481542\pi\) | ||||
0.0579542 | + | 0.998319i | \(0.481542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3923 | 1.02065 | ||||||||
\(362\) | −34.5885 | −1.81793 | ||||||||
\(363\) | 1.73205 | 0.0909091 | ||||||||
\(364\) | 35.7128 | 1.87186 | ||||||||
\(365\) | −14.1962 | −0.743061 | ||||||||
\(366\) | −13.8564 | −0.724286 | ||||||||
\(367\) | 4.12436 | 0.215290 | 0.107645 | − | 0.994189i | \(-0.465669\pi\) | ||||
0.107645 | + | 0.994189i | \(0.465669\pi\) | |||||||
\(368\) | −55.7128 | −2.90423 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −38.0526 | −1.97826 | ||||||||
\(371\) | 5.07180 | 0.263315 | ||||||||
\(372\) | 21.4641 | 1.11286 | ||||||||
\(373\) | 8.19615 | 0.424381 | 0.212190 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212190 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(374\) | −2.73205 | −0.141271 | ||||||||
\(375\) | −25.3923 | −1.31125 | ||||||||
\(376\) | −8.78461 | −0.453032 | ||||||||
\(377\) | 4.14359 | 0.213406 | ||||||||
\(378\) | −28.3923 | −1.46034 | ||||||||
\(379\) | −9.73205 | −0.499902 | −0.249951 | − | 0.968259i | \(-0.580414\pi\) | ||||
−0.249951 | + | 0.968259i | \(0.580414\pi\) | |||||||
\(380\) | 126.354 | 6.48181 | ||||||||
\(381\) | −6.92820 | −0.354943 | ||||||||
\(382\) | −72.3013 | −3.69925 | ||||||||
\(383\) | −20.3205 | −1.03833 | −0.519165 | − | 0.854674i | \(-0.673757\pi\) | ||||
−0.519165 | + | 0.854674i | \(0.673757\pi\) | |||||||
\(384\) | −65.5692 | −3.34607 | ||||||||
\(385\) | 7.46410 | 0.380406 | ||||||||
\(386\) | 66.1051 | 3.36466 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 85.9615 | 4.36404 | ||||||||
\(389\) | 9.92820 | 0.503380 | 0.251690 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(390\) | −57.7128 | −2.92240 | ||||||||
\(391\) | −3.73205 | −0.188738 | ||||||||
\(392\) | 28.3923 | 1.43403 | ||||||||
\(393\) | −15.4641 | −0.780061 | ||||||||
\(394\) | 57.7128 | 2.90753 | ||||||||
\(395\) | −8.19615 | −0.412393 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.7128 | 1.39087 | 0.695433 | − | 0.718591i | \(-0.255213\pi\) | ||||
0.695433 | + | 0.718591i | \(0.255213\pi\) | |||||||
\(398\) | 45.8564 | 2.29857 | ||||||||
\(399\) | 21.4641 | 1.07455 | ||||||||
\(400\) | 133.282 | 6.66410 | ||||||||
\(401\) | −28.7846 | −1.43743 | −0.718717 | − | 0.695302i | \(-0.755270\pi\) | ||||
−0.718717 | + | 0.695302i | \(0.755270\pi\) | |||||||
\(402\) | −4.73205 | −0.236013 | ||||||||
\(403\) | −7.41154 | −0.369195 | ||||||||
\(404\) | 9.07180 | 0.451339 | ||||||||
\(405\) | 33.5885 | 1.66902 | ||||||||
\(406\) | −6.92820 | −0.343841 | ||||||||
\(407\) | −3.73205 | −0.184991 | ||||||||
\(408\) | −16.3923 | −0.811540 | ||||||||
\(409\) | −9.66025 | −0.477669 | −0.238834 | − | 0.971060i | \(-0.576765\pi\) | ||||
−0.238834 | + | 0.971060i | \(0.576765\pi\) | |||||||
\(410\) | 96.4974 | 4.76567 | ||||||||
\(411\) | −33.5885 | −1.65680 | ||||||||
\(412\) | −64.7846 | −3.19171 | ||||||||
\(413\) | −6.00000 | −0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −59.1769 | −2.90488 | ||||||||
\(416\) | 71.4256 | 3.50193 | ||||||||
\(417\) | 27.1244 | 1.32829 | ||||||||
\(418\) | 16.9282 | 0.827985 | ||||||||
\(419\) | 21.8564 | 1.06776 | 0.533878 | − | 0.845562i | \(-0.320734\pi\) | ||||
0.533878 | + | 0.845562i | \(0.320734\pi\) | |||||||
\(420\) | 70.6410 | 3.44693 | ||||||||
\(421\) | 17.8564 | 0.870268 | 0.435134 | − | 0.900366i | \(-0.356701\pi\) | ||||
0.435134 | + | 0.900366i | \(0.356701\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.0000 | 1.16554 | ||||||||
\(425\) | 8.92820 | 0.433081 | ||||||||
\(426\) | −1.26795 | −0.0614323 | ||||||||
\(427\) | −5.85641 | −0.283411 | ||||||||
\(428\) | −61.5692 | −2.97606 | ||||||||
\(429\) | −5.66025 | −0.273280 | ||||||||
\(430\) | −20.3923 | −0.983404 | ||||||||
\(431\) | 0.339746 | 0.0163650 | 0.00818249 | − | 0.999967i | \(-0.497395\pi\) | ||||
0.00818249 | + | 0.999967i | \(0.497395\pi\) | |||||||
\(432\) | −77.5692 | −3.73205 | ||||||||
\(433\) | 18.6077 | 0.894229 | 0.447114 | − | 0.894477i | \(-0.352452\pi\) | ||||
0.447114 | + | 0.894477i | \(0.352452\pi\) | |||||||
\(434\) | 12.3923 | 0.594850 | ||||||||
\(435\) | 8.19615 | 0.392975 | ||||||||
\(436\) | −12.0000 | −0.574696 | ||||||||
\(437\) | 23.1244 | 1.10619 | ||||||||
\(438\) | −18.0000 | −0.860073 | ||||||||
\(439\) | −16.1962 | −0.773000 | −0.386500 | − | 0.922289i | \(-0.626316\pi\) | ||||
−0.386500 | + | 0.922289i | \(0.626316\pi\) | |||||||
\(440\) | 35.3205 | 1.68384 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.92820 | 0.424671 | ||||||||
\(443\) | 35.3923 | 1.68154 | 0.840770 | − | 0.541393i | \(-0.182103\pi\) | ||||
0.840770 | + | 0.541393i | \(0.182103\pi\) | |||||||
\(444\) | −35.3205 | −1.67624 | ||||||||
\(445\) | 44.5167 | 2.11029 | ||||||||
\(446\) | −55.5167 | −2.62879 | ||||||||
\(447\) | −33.1244 | −1.56673 | ||||||||
\(448\) | −59.7128 | −2.82117 | ||||||||
\(449\) | 14.5167 | 0.685084 | 0.342542 | − | 0.939503i | \(-0.388712\pi\) | ||||
0.342542 | + | 0.939503i | \(0.388712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.46410 | 0.445647 | ||||||||
\(452\) | −34.2487 | −1.61092 | ||||||||
\(453\) | −21.1244 | −0.992509 | ||||||||
\(454\) | −45.7128 | −2.14541 | ||||||||
\(455\) | −24.3923 | −1.14353 | ||||||||
\(456\) | 101.569 | 4.75641 | ||||||||
\(457\) | −4.73205 | −0.221356 | −0.110678 | − | 0.993856i | \(-0.535302\pi\) | ||||
−0.110678 | + | 0.993856i | \(0.535302\pi\) | |||||||
\(458\) | 34.0526 | 1.59117 | ||||||||
\(459\) | −5.19615 | −0.242536 | ||||||||
\(460\) | 76.1051 | 3.54842 | ||||||||
\(461\) | −13.0718 | −0.608814 | −0.304407 | − | 0.952542i | \(-0.598458\pi\) | ||||
−0.304407 | + | 0.952542i | \(0.598458\pi\) | |||||||
\(462\) | 9.46410 | 0.440310 | ||||||||
\(463\) | 41.9282 | 1.94857 | 0.974284 | − | 0.225322i | \(-0.0723433\pi\) | ||||
0.974284 | + | 0.225322i | \(0.0723433\pi\) | |||||||
\(464\) | −18.9282 | −0.878720 | ||||||||
\(465\) | −14.6603 | −0.679853 | ||||||||
\(466\) | 13.8564 | 0.641886 | ||||||||
\(467\) | −5.78461 | −0.267680 | −0.133840 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133840 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 9.46410 | 0.436546 | ||||||||
\(471\) | −34.2679 | −1.57898 | ||||||||
\(472\) | −28.3923 | −1.30686 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | −10.3923 | −0.477334 | ||||||||
\(475\) | −55.3205 | −2.53828 | ||||||||
\(476\) | −10.9282 | −0.500893 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.4641 | −0.524356 | ||||||||
\(479\) | −8.78461 | −0.401379 | −0.200690 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200690 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(480\) | 141.282 | 6.44861 | ||||||||
\(481\) | 12.1962 | 0.556097 | ||||||||
\(482\) | −51.7128 | −2.35545 | ||||||||
\(483\) | 12.9282 | 0.588254 | ||||||||
\(484\) | 5.46410 | 0.248368 | ||||||||
\(485\) | −58.7128 | −2.66601 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.947441 | 0.0429327 | 0.0214663 | − | 0.999770i | \(-0.493167\pi\) | ||||
0.0214663 | + | 0.999770i | \(0.493167\pi\) | |||||||
\(488\) | −27.7128 | −1.25450 | ||||||||
\(489\) | −4.39230 | −0.198627 | ||||||||
\(490\) | −30.5885 | −1.38185 | ||||||||
\(491\) | −1.12436 | −0.0507415 | −0.0253707 | − | 0.999678i | \(-0.508077\pi\) | ||||
−0.0253707 | + | 0.999678i | \(0.508077\pi\) | |||||||
\(492\) | 89.5692 | 4.03809 | ||||||||
\(493\) | −1.26795 | −0.0571056 | ||||||||
\(494\) | −55.3205 | −2.48899 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.8564 | 1.52020 | ||||||||
\(497\) | −0.535898 | −0.0240383 | ||||||||
\(498\) | −75.0333 | −3.36232 | ||||||||
\(499\) | 6.39230 | 0.286159 | 0.143079 | − | 0.989711i | \(-0.454300\pi\) | ||||
0.143079 | + | 0.989711i | \(0.454300\pi\) | |||||||
\(500\) | −80.1051 | −3.58241 | ||||||||
\(501\) | 32.4449 | 1.44953 | ||||||||
\(502\) | 71.9090 | 3.20945 | ||||||||
\(503\) | 39.3731 | 1.75556 | 0.877779 | − | 0.479066i | \(-0.159024\pi\) | ||||
0.877779 | + | 0.479066i | \(0.159024\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.19615 | −0.275725 | ||||||||
\(506\) | 10.1962 | 0.453274 | ||||||||
\(507\) | −4.01924 | −0.178501 | ||||||||
\(508\) | −21.8564 | −0.969721 | ||||||||
\(509\) | 3.78461 | 0.167750 | 0.0838749 | − | 0.996476i | \(-0.473270\pi\) | ||||
0.0838749 | + | 0.996476i | \(0.473270\pi\) | |||||||
\(510\) | 17.6603 | 0.782009 | ||||||||
\(511\) | −7.60770 | −0.336545 | ||||||||
\(512\) | −43.7128 | −1.93185 | ||||||||
\(513\) | 32.1962 | 1.42149 | ||||||||
\(514\) | −56.7846 | −2.50466 | ||||||||
\(515\) | 44.2487 | 1.94983 | ||||||||
\(516\) | −18.9282 | −0.833268 | ||||||||
\(517\) | 0.928203 | 0.0408223 | ||||||||
\(518\) | −20.3923 | −0.895986 | ||||||||
\(519\) | −24.2487 | −1.06440 | ||||||||
\(520\) | −115.426 | −5.06175 | ||||||||
\(521\) | 0.947441 | 0.0415081 | 0.0207541 | − | 0.999785i | \(-0.493393\pi\) | ||||
0.0207541 | + | 0.999785i | \(0.493393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.24871 | 0.273237 | 0.136619 | − | 0.990624i | \(-0.456377\pi\) | ||||
0.136619 | + | 0.990624i | \(0.456377\pi\) | |||||||
\(524\) | −48.7846 | −2.13117 | ||||||||
\(525\) | −30.9282 | −1.34982 | ||||||||
\(526\) | −30.3923 | −1.32517 | ||||||||
\(527\) | 2.26795 | 0.0987934 | ||||||||
\(528\) | 25.8564 | 1.12526 | ||||||||
\(529\) | −9.07180 | −0.394426 | ||||||||
\(530\) | −25.8564 | −1.12313 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 67.7128 | 2.93572 | ||||||||
\(533\) | −30.9282 | −1.33965 | ||||||||
\(534\) | 56.4449 | 2.44261 | ||||||||
\(535\) | 42.0526 | 1.81809 | ||||||||
\(536\) | −9.46410 | −0.408787 | ||||||||
\(537\) | −5.19615 | −0.224231 | ||||||||
\(538\) | 38.2487 | 1.64902 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 105.962 | 4.55986 | ||||||||
\(541\) | 6.33975 | 0.272567 | 0.136283 | − | 0.990670i | \(-0.456484\pi\) | ||||
0.136283 | + | 0.990670i | \(0.456484\pi\) | |||||||
\(542\) | 24.7846 | 1.06459 | ||||||||
\(543\) | 21.9282 | 0.941029 | ||||||||
\(544\) | −21.8564 | −0.937086 | ||||||||
\(545\) | 8.19615 | 0.351085 | ||||||||
\(546\) | −30.9282 | −1.32360 | ||||||||
\(547\) | 38.7321 | 1.65606 | 0.828031 | − | 0.560682i | \(-0.189461\pi\) | ||||
0.828031 | + | 0.560682i | \(0.189461\pi\) | |||||||
\(548\) | −105.962 | −4.52645 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.3923 | −1.04009 | ||||||||
\(551\) | 7.85641 | 0.334694 | ||||||||
\(552\) | 61.1769 | 2.60386 | ||||||||
\(553\) | −4.39230 | −0.186780 | ||||||||
\(554\) | −50.2487 | −2.13486 | ||||||||
\(555\) | 24.1244 | 1.02402 | ||||||||
\(556\) | 85.5692 | 3.62894 | ||||||||
\(557\) | −12.9282 | −0.547786 | −0.273893 | − | 0.961760i | \(-0.588311\pi\) | ||||
−0.273893 | + | 0.961760i | \(0.588311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.53590 | 0.276439 | ||||||||
\(560\) | 111.426 | 4.70859 | ||||||||
\(561\) | 1.73205 | 0.0731272 | ||||||||
\(562\) | 74.1051 | 3.12594 | ||||||||
\(563\) | −11.2679 | −0.474887 | −0.237444 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237444 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(564\) | 8.78461 | 0.369899 | ||||||||
\(565\) | 23.3923 | 0.984122 | ||||||||
\(566\) | 7.46410 | 0.313740 | ||||||||
\(567\) | 18.0000 | 0.755929 | ||||||||
\(568\) | −2.53590 | −0.106404 | ||||||||
\(569\) | 4.00000 | 0.167689 | 0.0838444 | − | 0.996479i | \(-0.473280\pi\) | ||||
0.0838444 | + | 0.996479i | \(0.473280\pi\) | |||||||
\(570\) | −109.426 | −4.58334 | ||||||||
\(571\) | 8.98076 | 0.375833 | 0.187917 | − | 0.982185i | \(-0.439827\pi\) | ||||
0.187917 | + | 0.982185i | \(0.439827\pi\) | |||||||
\(572\) | −17.8564 | −0.746614 | ||||||||
\(573\) | 45.8372 | 1.91488 | ||||||||
\(574\) | 51.7128 | 2.15845 | ||||||||
\(575\) | −33.3205 | −1.38956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.39230 | −0.141223 | −0.0706117 | − | 0.997504i | \(-0.522495\pi\) | ||||
−0.0706117 | + | 0.997504i | \(0.522495\pi\) | |||||||
\(578\) | −2.73205 | −0.113638 | ||||||||
\(579\) | −41.9090 | −1.74168 | ||||||||
\(580\) | 25.8564 | 1.07363 | ||||||||
\(581\) | −31.7128 | −1.31567 | ||||||||
\(582\) | −74.4449 | −3.08584 | ||||||||
\(583\) | −2.53590 | −0.105026 | ||||||||
\(584\) | −36.0000 | −1.48969 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 37.8564 | 1.56383 | ||||||||
\(587\) | −44.9282 | −1.85439 | −0.927193 | − | 0.374585i | \(-0.877785\pi\) | ||||
−0.927193 | + | 0.374585i | \(0.877785\pi\) | |||||||
\(588\) | −28.3923 | −1.17088 | ||||||||
\(589\) | −14.0526 | −0.579026 | ||||||||
\(590\) | 30.5885 | 1.25931 | ||||||||
\(591\) | −36.5885 | −1.50505 | ||||||||
\(592\) | −55.7128 | −2.28978 | ||||||||
\(593\) | 2.87564 | 0.118089 | 0.0590443 | − | 0.998255i | \(-0.481195\pi\) | ||||
0.0590443 | + | 0.998255i | \(0.481195\pi\) | |||||||
\(594\) | 14.1962 | 0.582475 | ||||||||
\(595\) | 7.46410 | 0.305998 | ||||||||
\(596\) | −104.497 | −4.28038 | ||||||||
\(597\) | −29.0718 | −1.18983 | ||||||||
\(598\) | −33.3205 | −1.36258 | ||||||||
\(599\) | 12.2487 | 0.500469 | 0.250234 | − | 0.968185i | \(-0.419492\pi\) | ||||
0.250234 | + | 0.968185i | \(0.419492\pi\) | |||||||
\(600\) | −146.354 | −5.97487 | ||||||||
\(601\) | −16.5359 | −0.674513 | −0.337257 | − | 0.941413i | \(-0.609499\pi\) | ||||
−0.337257 | + | 0.941413i | \(0.609499\pi\) | |||||||
\(602\) | −10.9282 | −0.445400 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −66.6410 | −2.71158 | ||||||||
\(605\) | −3.73205 | −0.151729 | ||||||||
\(606\) | −7.85641 | −0.319145 | ||||||||
\(607\) | 22.7846 | 0.924799 | 0.462399 | − | 0.886672i | \(-0.346989\pi\) | ||||
0.462399 | + | 0.886672i | \(0.346989\pi\) | |||||||
\(608\) | 135.426 | 5.49223 | ||||||||
\(609\) | 4.39230 | 0.177985 | ||||||||
\(610\) | 29.8564 | 1.20885 | ||||||||
\(611\) | −3.03332 | −0.122715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.6410 | −1.23758 | −0.618789 | − | 0.785557i | \(-0.712377\pi\) | ||||
−0.618789 | + | 0.785557i | \(0.712377\pi\) | |||||||
\(614\) | 26.7846 | 1.08094 | ||||||||
\(615\) | −61.1769 | −2.46689 | ||||||||
\(616\) | 18.9282 | 0.762639 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 56.1051 | 2.25688 | ||||||||
\(619\) | −13.0526 | −0.524627 | −0.262313 | − | 0.964983i | \(-0.584485\pi\) | ||||
−0.262313 | + | 0.964983i | \(0.584485\pi\) | |||||||
\(620\) | −46.2487 | −1.85739 | ||||||||
\(621\) | 19.3923 | 0.778186 | ||||||||
\(622\) | 1.07180 | 0.0429751 | ||||||||
\(623\) | 23.8564 | 0.955787 | ||||||||
\(624\) | −84.4974 | −3.38260 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | −24.0526 | −0.961334 | ||||||||
\(627\) | −10.7321 | −0.428597 | ||||||||
\(628\) | −108.105 | −4.31386 | ||||||||
\(629\) | −3.73205 | −0.148807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.3923 | 1.88666 | 0.943329 | − | 0.331859i | \(-0.107676\pi\) | ||||
0.943329 | + | 0.331859i | \(0.107676\pi\) | |||||||
\(632\) | −20.7846 | −0.826767 | ||||||||
\(633\) | −2.53590 | −0.100793 | ||||||||
\(634\) | −69.5167 | −2.76086 | ||||||||
\(635\) | 14.9282 | 0.592408 | ||||||||
\(636\) | −24.0000 | −0.951662 | ||||||||
\(637\) | 9.80385 | 0.388443 | ||||||||
\(638\) | 3.46410 | 0.137145 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 141.282 | 5.58466 | ||||||||
\(641\) | −39.8372 | −1.57347 | −0.786737 | − | 0.617289i | \(-0.788231\pi\) | ||||
−0.786737 | + | 0.617289i | \(0.788231\pi\) | |||||||
\(642\) | 53.3205 | 2.10439 | ||||||||
\(643\) | −23.9808 | −0.945709 | −0.472854 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472854 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(644\) | 40.7846 | 1.60714 | ||||||||
\(645\) | 12.9282 | 0.509048 | ||||||||
\(646\) | 16.9282 | 0.666031 | ||||||||
\(647\) | 29.2487 | 1.14989 | 0.574943 | − | 0.818194i | \(-0.305024\pi\) | ||||
0.574943 | + | 0.818194i | \(0.305024\pi\) | |||||||
\(648\) | 85.1769 | 3.34607 | ||||||||
\(649\) | 3.00000 | 0.117760 | ||||||||
\(650\) | 79.7128 | 3.12659 | ||||||||
\(651\) | −7.85641 | −0.307917 | ||||||||
\(652\) | −13.8564 | −0.542659 | ||||||||
\(653\) | 42.3731 | 1.65819 | 0.829093 | − | 0.559111i | \(-0.188857\pi\) | ||||
0.829093 | + | 0.559111i | \(0.188857\pi\) | |||||||
\(654\) | 10.3923 | 0.406371 | ||||||||
\(655\) | 33.3205 | 1.30194 | ||||||||
\(656\) | 141.282 | 5.51614 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.07180 | 0.197719 | ||||||||
\(659\) | −35.1244 | −1.36825 | −0.684125 | − | 0.729364i | \(-0.739816\pi\) | ||||
−0.684125 | + | 0.729364i | \(0.739816\pi\) | |||||||
\(660\) | −35.3205 | −1.37485 | ||||||||
\(661\) | −34.4641 | −1.34050 | −0.670249 | − | 0.742136i | \(-0.733813\pi\) | ||||
−0.670249 | + | 0.742136i | \(0.733813\pi\) | |||||||
\(662\) | 84.3013 | 3.27646 | ||||||||
\(663\) | −5.66025 | −0.219826 | ||||||||
\(664\) | −150.067 | −5.82372 | ||||||||
\(665\) | −46.2487 | −1.79345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.73205 | 0.183226 | ||||||||
\(668\) | 102.354 | 3.96019 | ||||||||
\(669\) | 35.1962 | 1.36076 | ||||||||
\(670\) | 10.1962 | 0.393912 | ||||||||
\(671\) | 2.92820 | 0.113042 | ||||||||
\(672\) | 75.7128 | 2.92069 | ||||||||
\(673\) | 10.1962 | 0.393033 | 0.196516 | − | 0.980501i | \(-0.437037\pi\) | ||||
0.196516 | + | 0.980501i | \(0.437037\pi\) | |||||||
\(674\) | 26.2487 | 1.01106 | ||||||||
\(675\) | −46.3923 | −1.78564 | ||||||||
\(676\) | −12.6795 | −0.487673 | ||||||||
\(677\) | −28.0526 | −1.07815 | −0.539074 | − | 0.842259i | \(-0.681226\pi\) | ||||
−0.539074 | + | 0.842259i | \(0.681226\pi\) | |||||||
\(678\) | 29.6603 | 1.13910 | ||||||||
\(679\) | −31.4641 | −1.20748 | ||||||||
\(680\) | 35.3205 | 1.35448 | ||||||||
\(681\) | 28.9808 | 1.11055 | ||||||||
\(682\) | −6.19615 | −0.237263 | ||||||||
\(683\) | −1.46410 | −0.0560223 | −0.0280111 | − | 0.999608i | \(-0.508917\pi\) | ||||
−0.0280111 | + | 0.999608i | \(0.508917\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 72.3731 | 2.76523 | ||||||||
\(686\) | −54.6410 | −2.08620 | ||||||||
\(687\) | −21.5885 | −0.823651 | ||||||||
\(688\) | −29.8564 | −1.13826 | ||||||||
\(689\) | 8.28719 | 0.315717 | ||||||||
\(690\) | −65.9090 | −2.50911 | ||||||||
\(691\) | −24.5167 | −0.932658 | −0.466329 | − | 0.884611i | \(-0.654424\pi\) | ||||
−0.466329 | + | 0.884611i | \(0.654424\pi\) | |||||||
\(692\) | −76.4974 | −2.90800 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50.6410 | 1.92231 | ||||||||
\(695\) | −58.4449 | −2.21694 | ||||||||
\(696\) | 20.7846 | 0.787839 | ||||||||
\(697\) | 9.46410 | 0.358478 | ||||||||
\(698\) | 42.2487 | 1.59914 | ||||||||
\(699\) | −8.78461 | −0.332264 | ||||||||
\(700\) | −97.5692 | −3.68777 | ||||||||
\(701\) | 28.6410 | 1.08176 | 0.540878 | − | 0.841101i | \(-0.318092\pi\) | ||||
0.540878 | + | 0.841101i | \(0.318092\pi\) | |||||||
\(702\) | −46.3923 | −1.75096 | ||||||||
\(703\) | 23.1244 | 0.872152 | ||||||||
\(704\) | 29.8564 | 1.12526 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | −57.3731 | −2.15926 | ||||||||
\(707\) | −3.32051 | −0.124881 | ||||||||
\(708\) | 28.3923 | 1.06705 | ||||||||
\(709\) | 17.3397 | 0.651208 | 0.325604 | − | 0.945506i | \(-0.394432\pi\) | ||||
0.325604 | + | 0.945506i | \(0.394432\pi\) | |||||||
\(710\) | 2.73205 | 0.102532 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 112.890 | 4.23072 | ||||||||
\(713\) | −8.46410 | −0.316983 | ||||||||
\(714\) | 9.46410 | 0.354185 | ||||||||
\(715\) | 12.1962 | 0.456110 | ||||||||
\(716\) | −16.3923 | −0.612609 | ||||||||
\(717\) | 7.26795 | 0.271427 | ||||||||
\(718\) | −6.00000 | −0.223918 | ||||||||
\(719\) | 28.3731 | 1.05814 | 0.529068 | − | 0.848579i | \(-0.322541\pi\) | ||||
0.529068 | + | 0.848579i | \(0.322541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7128 | 0.883111 | ||||||||
\(722\) | −52.9808 | −1.97174 | ||||||||
\(723\) | 32.7846 | 1.21927 | ||||||||
\(724\) | 69.1769 | 2.57094 | ||||||||
\(725\) | −11.3205 | −0.420433 | ||||||||
\(726\) | −4.73205 | −0.175623 | ||||||||
\(727\) | −23.9282 | −0.887448 | −0.443724 | − | 0.896164i | \(-0.646343\pi\) | ||||
−0.443724 | + | 0.896164i | \(0.646343\pi\) | |||||||
\(728\) | −61.8564 | −2.29255 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 38.7846 | 1.43548 | ||||||||
\(731\) | −2.00000 | −0.0739727 | ||||||||
\(732\) | 27.7128 | 1.02430 | ||||||||
\(733\) | 20.3923 | 0.753207 | 0.376603 | − | 0.926375i | \(-0.377092\pi\) | ||||
0.376603 | + | 0.926375i | \(0.377092\pi\) | |||||||
\(734\) | −11.2679 | −0.415908 | ||||||||
\(735\) | 19.3923 | 0.715296 | ||||||||
\(736\) | 81.5692 | 3.00668 | ||||||||
\(737\) | 1.00000 | 0.0368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0526 | 0.958359 | 0.479179 | − | 0.877717i | \(-0.340934\pi\) | ||||
0.479179 | + | 0.877717i | \(0.340934\pi\) | |||||||
\(740\) | 76.1051 | 2.79768 | ||||||||
\(741\) | 35.0718 | 1.28839 | ||||||||
\(742\) | −13.8564 | −0.508685 | ||||||||
\(743\) | 4.39230 | 0.161138 | 0.0805690 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805690 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(744\) | −37.1769 | −1.36297 | ||||||||
\(745\) | 71.3731 | 2.61491 | ||||||||
\(746\) | −22.3923 | −0.819841 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.46410 | 0.199787 | ||||||||
\(749\) | 22.5359 | 0.823444 | ||||||||
\(750\) | 69.3731 | 2.53315 | ||||||||
\(751\) | 33.0526 | 1.20611 | 0.603053 | − | 0.797701i | \(-0.293951\pi\) | ||||
0.603053 | + | 0.797701i | \(0.293951\pi\) | |||||||
\(752\) | 13.8564 | 0.505291 | ||||||||
\(753\) | −45.5885 | −1.66134 | ||||||||
\(754\) | −11.3205 | −0.412269 | ||||||||
\(755\) | 45.5167 | 1.65652 | ||||||||
\(756\) | 56.7846 | 2.06524 | ||||||||
\(757\) | −43.5692 | −1.58355 | −0.791775 | − | 0.610813i | \(-0.790843\pi\) | ||||
−0.791775 | + | 0.610813i | \(0.790843\pi\) | |||||||
\(758\) | 26.5885 | 0.965736 | ||||||||
\(759\) | −6.46410 | −0.234632 | ||||||||
\(760\) | −218.851 | −7.93857 | ||||||||
\(761\) | 3.94744 | 0.143095 | 0.0715473 | − | 0.997437i | \(-0.477206\pi\) | ||||
0.0715473 | + | 0.997437i | \(0.477206\pi\) | |||||||
\(762\) | 18.9282 | 0.685696 | ||||||||
\(763\) | 4.39230 | 0.159012 | ||||||||
\(764\) | 144.603 | 5.23154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 55.5167 | 2.00590 | ||||||||
\(767\) | −9.80385 | −0.353996 | ||||||||
\(768\) | 75.7128 | 2.73205 | ||||||||
\(769\) | 33.5692 | 1.21054 | 0.605269 | − | 0.796021i | \(-0.293066\pi\) | ||||
0.605269 | + | 0.796021i | \(0.293066\pi\) | |||||||
\(770\) | −20.3923 | −0.734888 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | −132.210 | −4.75835 | ||||||||
\(773\) | −43.3205 | −1.55813 | −0.779065 | − | 0.626943i | \(-0.784306\pi\) | ||||
−0.779065 | + | 0.626943i | \(0.784306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.2487 | 0.727355 | ||||||||
\(776\) | −148.890 | −5.34483 | ||||||||
\(777\) | 12.9282 | 0.463797 | ||||||||
\(778\) | −27.1244 | −0.972455 | ||||||||
\(779\) | −58.6410 | −2.10103 | ||||||||
\(780\) | 115.426 | 4.13290 | ||||||||
\(781\) | 0.267949 | 0.00958798 | ||||||||
\(782\) | 10.1962 | 0.364614 | ||||||||
\(783\) | 6.58846 | 0.235452 | ||||||||
\(784\) | −44.7846 | −1.59945 | ||||||||
\(785\) | 73.8372 | 2.63536 | ||||||||
\(786\) | 42.2487 | 1.50696 | ||||||||
\(787\) | 7.12436 | 0.253956 | 0.126978 | − | 0.991906i | \(-0.459472\pi\) | ||||
0.126978 | + | 0.991906i | \(0.459472\pi\) | |||||||
\(788\) | −115.426 | −4.11187 | ||||||||
\(789\) | 19.2679 | 0.685957 | ||||||||
\(790\) | 22.3923 | 0.796682 | ||||||||
\(791\) | 12.5359 | 0.445725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.56922 | −0.339813 | ||||||||
\(794\) | −75.7128 | −2.68695 | ||||||||
\(795\) | 16.3923 | 0.581375 | ||||||||
\(796\) | −91.7128 | −3.25067 | ||||||||
\(797\) | 5.39230 | 0.191005 | 0.0955026 | − | 0.995429i | \(-0.469554\pi\) | ||||
0.0955026 | + | 0.995429i | \(0.469554\pi\) | |||||||
\(798\) | −58.6410 | −2.07587 | ||||||||
\(799\) | 0.928203 | 0.0328375 | ||||||||
\(800\) | −195.138 | −6.89919 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 78.6410 | 2.77691 | ||||||||
\(803\) | 3.80385 | 0.134235 | ||||||||
\(804\) | 9.46410 | 0.333773 | ||||||||
\(805\) | −27.8564 | −0.981809 | ||||||||
\(806\) | 20.2487 | 0.713230 | ||||||||
\(807\) | −24.2487 | −0.853595 | ||||||||
\(808\) | −15.7128 | −0.552775 | ||||||||
\(809\) | 31.9090 | 1.12186 | 0.560930 | − | 0.827863i | \(-0.310444\pi\) | ||||
0.560930 | + | 0.827863i | \(0.310444\pi\) | |||||||
\(810\) | −91.7654 | −3.22431 | ||||||||
\(811\) | −0.732051 | −0.0257058 | −0.0128529 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128529 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(812\) | 13.8564 | 0.486265 | ||||||||
\(813\) | −15.7128 | −0.551072 | ||||||||
\(814\) | 10.1962 | 0.357375 | ||||||||
\(815\) | 9.46410 | 0.331513 | ||||||||
\(816\) | 25.8564 | 0.905155 | ||||||||
\(817\) | 12.3923 | 0.433552 | ||||||||
\(818\) | 26.3923 | 0.922785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −192.995 | −6.73967 | ||||||||
\(821\) | −4.05256 | −0.141435 | −0.0707176 | − | 0.997496i | \(-0.522529\pi\) | ||||
−0.0707176 | + | 0.997496i | \(0.522529\pi\) | |||||||
\(822\) | 91.7654 | 3.20068 | ||||||||
\(823\) | 39.7321 | 1.38497 | 0.692486 | − | 0.721431i | \(-0.256515\pi\) | ||||
0.692486 | + | 0.721431i | \(0.256515\pi\) | |||||||
\(824\) | 112.210 | 3.90903 | ||||||||
\(825\) | 15.4641 | 0.538391 | ||||||||
\(826\) | 16.3923 | 0.570361 | ||||||||
\(827\) | −29.6603 | −1.03139 | −0.515694 | − | 0.856773i | \(-0.672466\pi\) | ||||
−0.515694 | + | 0.856773i | \(0.672466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.9282 | −0.483746 | −0.241873 | − | 0.970308i | \(-0.577762\pi\) | ||||
−0.241873 | + | 0.970308i | \(0.577762\pi\) | |||||||
\(830\) | 161.674 | 5.61180 | ||||||||
\(831\) | 31.8564 | 1.10509 | ||||||||
\(832\) | −97.5692 | −3.38260 | ||||||||
\(833\) | −3.00000 | −0.103944 | ||||||||
\(834\) | −74.1051 | −2.56605 | ||||||||
\(835\) | −69.9090 | −2.41930 | ||||||||
\(836\) | −33.8564 | −1.17095 | ||||||||
\(837\) | −11.7846 | −0.407336 | ||||||||
\(838\) | −59.7128 | −2.06274 | ||||||||
\(839\) | −5.48334 | −0.189306 | −0.0946530 | − | 0.995510i | \(-0.530174\pi\) | ||||
−0.0946530 | + | 0.995510i | \(0.530174\pi\) | |||||||
\(840\) | −122.354 | −4.22161 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | −48.7846 | −1.68123 | ||||||||
\(843\) | −46.9808 | −1.61810 | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 8.66025 | 0.297922 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −37.8564 | −1.29999 | ||||||||
\(849\) | −4.73205 | −0.162404 | ||||||||
\(850\) | −24.3923 | −0.836649 | ||||||||
\(851\) | 13.9282 | 0.477453 | ||||||||
\(852\) | 2.53590 | 0.0868784 | ||||||||
\(853\) | −13.1244 | −0.449369 | −0.224685 | − | 0.974432i | \(-0.572135\pi\) | ||||
−0.224685 | + | 0.974432i | \(0.572135\pi\) | |||||||
\(854\) | 16.0000 | 0.547509 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 106.641 | 3.64491 | ||||||||
\(857\) | −10.4449 | −0.356790 | −0.178395 | − | 0.983959i | \(-0.557090\pi\) | ||||
−0.178395 | + | 0.983959i | \(0.557090\pi\) | |||||||
\(858\) | 15.4641 | 0.527936 | ||||||||
\(859\) | 17.1436 | 0.584932 | 0.292466 | − | 0.956276i | \(-0.405524\pi\) | ||||
0.292466 | + | 0.956276i | \(0.405524\pi\) | |||||||
\(860\) | 40.7846 | 1.39074 | ||||||||
\(861\) | −32.7846 | −1.11730 | ||||||||
\(862\) | −0.928203 | −0.0316147 | ||||||||
\(863\) | −36.6410 | −1.24727 | −0.623637 | − | 0.781714i | \(-0.714346\pi\) | ||||
−0.623637 | + | 0.781714i | \(0.714346\pi\) | |||||||
\(864\) | 113.569 | 3.86370 | ||||||||
\(865\) | 52.2487 | 1.77651 | ||||||||
\(866\) | −50.8372 | −1.72752 | ||||||||
\(867\) | 1.73205 | 0.0588235 | ||||||||
\(868\) | −24.7846 | −0.841244 | ||||||||
\(869\) | 2.19615 | 0.0744994 | ||||||||
\(870\) | −22.3923 | −0.759170 | ||||||||
\(871\) | −3.26795 | −0.110730 | ||||||||
\(872\) | 20.7846 | 0.703856 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −63.1769 | −2.13699 | ||||||||
\(875\) | 29.3205 | 0.991214 | ||||||||
\(876\) | 36.0000 | 1.21633 | ||||||||
\(877\) | 12.5885 | 0.425082 | 0.212541 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212541 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(878\) | 44.2487 | 1.49332 | ||||||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | −55.7128 | −1.87808 | ||||||||
\(881\) | 22.9090 | 0.771823 | 0.385911 | − | 0.922536i | \(-0.373887\pi\) | ||||
0.385911 | + | 0.922536i | \(0.373887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.92820 | 0.233153 | 0.116576 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116576 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(884\) | −17.8564 | −0.600576 | ||||||||
\(885\) | −19.3923 | −0.651865 | ||||||||
\(886\) | −96.6936 | −3.24848 | ||||||||
\(887\) | 21.7128 | 0.729045 | 0.364522 | − | 0.931195i | \(-0.381232\pi\) | ||||
0.364522 | + | 0.931195i | \(0.381232\pi\) | |||||||
\(888\) | 61.1769 | 2.05296 | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | −121.622 | −4.07677 | ||||||||
\(891\) | −9.00000 | −0.301511 | ||||||||
\(892\) | 111.033 | 3.71767 | ||||||||
\(893\) | −5.75129 | −0.192460 | ||||||||
\(894\) | 90.4974 | 3.02669 | ||||||||
\(895\) | 11.1962 | 0.374246 | ||||||||
\(896\) | 75.7128 | 2.52939 | ||||||||
\(897\) | 21.1244 | 0.705322 | ||||||||
\(898\) | −39.6603 | −1.32348 | ||||||||
\(899\) | −2.87564 | −0.0959081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.53590 | −0.0844830 | ||||||||
\(902\) | −25.8564 | −0.860924 | ||||||||
\(903\) | 6.92820 | 0.230556 | ||||||||
\(904\) | 59.3205 | 1.97297 | ||||||||
\(905\) | −47.2487 | −1.57060 | ||||||||
\(906\) | 57.7128 | 1.91738 | ||||||||
\(907\) | 1.07180 | 0.0355884 | 0.0177942 | − | 0.999842i | \(-0.494336\pi\) | ||||
0.0177942 | + | 0.999842i | \(0.494336\pi\) | |||||||
\(908\) | 91.4256 | 3.03407 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 66.6410 | 2.20913 | ||||||||
\(911\) | −5.60770 | −0.185791 | −0.0928956 | − | 0.995676i | \(-0.529612\pi\) | ||||
−0.0928956 | + | 0.995676i | \(0.529612\pi\) | |||||||
\(912\) | −160.210 | −5.30509 | ||||||||
\(913\) | 15.8564 | 0.524770 | ||||||||
\(914\) | 12.9282 | 0.427627 | ||||||||
\(915\) | −18.9282 | −0.625747 | ||||||||
\(916\) | −68.1051 | −2.25026 | ||||||||
\(917\) | 17.8564 | 0.589670 | ||||||||
\(918\) | 14.1962 | 0.468543 | ||||||||
\(919\) | −6.67949 | −0.220336 | −0.110168 | − | 0.993913i | \(-0.535139\pi\) | ||||
−0.110168 | + | 0.993913i | \(0.535139\pi\) | |||||||
\(920\) | −131.818 | −4.34591 | ||||||||
\(921\) | −16.9808 | −0.559535 | ||||||||
\(922\) | 35.7128 | 1.17614 | ||||||||
\(923\) | −0.875644 | −0.0288222 | ||||||||
\(924\) | −18.9282 | −0.622692 | ||||||||
\(925\) | −33.3205 | −1.09557 | ||||||||
\(926\) | −114.550 | −3.76435 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 27.7128 | 0.909718 | ||||||||
\(929\) | 45.0333 | 1.47750 | 0.738748 | − | 0.673982i | \(-0.235418\pi\) | ||||
0.738748 | + | 0.673982i | \(0.235418\pi\) | |||||||
\(930\) | 40.0526 | 1.31338 | ||||||||
\(931\) | 18.5885 | 0.609212 | ||||||||
\(932\) | −27.7128 | −0.907763 | ||||||||
\(933\) | −0.679492 | −0.0222456 | ||||||||
\(934\) | 15.8038 | 0.517118 | ||||||||
\(935\) | −3.73205 | −0.122051 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9808 | 0.489400 | 0.244700 | − | 0.969599i | \(-0.421310\pi\) | ||||
0.244700 | + | 0.969599i | \(0.421310\pi\) | |||||||
\(938\) | 5.46410 | 0.178409 | ||||||||
\(939\) | 15.2487 | 0.497623 | ||||||||
\(940\) | −18.9282 | −0.617370 | ||||||||
\(941\) | 24.2487 | 0.790485 | 0.395243 | − | 0.918577i | \(-0.370660\pi\) | ||||
0.395243 | + | 0.918577i | \(0.370660\pi\) | |||||||
\(942\) | 93.6218 | 3.05036 | ||||||||
\(943\) | −35.3205 | −1.15019 | ||||||||
\(944\) | 44.7846 | 1.45761 | ||||||||
\(945\) | −38.7846 | −1.26166 | ||||||||
\(946\) | 5.46410 | 0.177653 | ||||||||
\(947\) | −2.26795 | −0.0736984 | −0.0368492 | − | 0.999321i | \(-0.511732\pi\) | ||||
−0.0368492 | + | 0.999321i | \(0.511732\pi\) | |||||||
\(948\) | 20.7846 | 0.675053 | ||||||||
\(949\) | −12.4308 | −0.403520 | ||||||||
\(950\) | 151.138 | 4.90358 | ||||||||
\(951\) | 44.0718 | 1.42913 | ||||||||
\(952\) | 18.9282 | 0.613467 | ||||||||
\(953\) | −54.7846 | −1.77465 | −0.887324 | − | 0.461147i | \(-0.847438\pi\) | ||||
−0.887324 | + | 0.461147i | \(0.847438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −98.7654 | −3.19597 | ||||||||
\(956\) | 22.9282 | 0.741551 | ||||||||
\(957\) | −2.19615 | −0.0709915 | ||||||||
\(958\) | 24.0000 | 0.775405 | ||||||||
\(959\) | 38.7846 | 1.25242 | ||||||||
\(960\) | −192.995 | −6.22888 | ||||||||
\(961\) | −25.8564 | −0.834078 | ||||||||
\(962\) | −33.3205 | −1.07430 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 103.426 | 3.33112 | ||||||||
\(965\) | 90.3013 | 2.90690 | ||||||||
\(966\) | −35.3205 | −1.13642 | ||||||||
\(967\) | 41.9090 | 1.34770 | 0.673851 | − | 0.738868i | \(-0.264639\pi\) | ||||
0.673851 | + | 0.738868i | \(0.264639\pi\) | |||||||
\(968\) | −9.46410 | −0.304188 | ||||||||
\(969\) | −10.7321 | −0.344763 | ||||||||
\(970\) | 160.406 | 5.15034 | ||||||||
\(971\) | −28.8564 | −0.926046 | −0.463023 | − | 0.886346i | \(-0.653235\pi\) | ||||
−0.463023 | + | 0.886346i | \(0.653235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.3205 | −1.00409 | ||||||||
\(974\) | −2.58846 | −0.0829395 | ||||||||
\(975\) | −50.5359 | −1.61844 | ||||||||
\(976\) | 43.7128 | 1.39921 | ||||||||
\(977\) | −53.7846 | −1.72072 | −0.860361 | − | 0.509685i | \(-0.829762\pi\) | ||||
−0.860361 | + | 0.509685i | \(0.829762\pi\) | |||||||
\(978\) | 12.0000 | 0.383718 | ||||||||
\(979\) | −11.9282 | −0.381227 | ||||||||
\(980\) | 61.1769 | 1.95422 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.07180 | 0.0980250 | ||||||||
\(983\) | 2.66025 | 0.0848489 | 0.0424245 | − | 0.999100i | \(-0.486492\pi\) | ||||
0.0424245 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(984\) | −155.138 | −4.94563 | ||||||||
\(985\) | 78.8372 | 2.51196 | ||||||||
\(986\) | 3.46410 | 0.110319 | ||||||||
\(987\) | −3.21539 | −0.102347 | ||||||||
\(988\) | 110.641 | 3.51996 | ||||||||
\(989\) | 7.46410 | 0.237345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.6410 | −0.719216 | −0.359608 | − | 0.933104i | \(-0.617090\pi\) | ||||
−0.359608 | + | 0.933104i | \(0.617090\pi\) | |||||||
\(992\) | −49.5692 | −1.57382 | ||||||||
\(993\) | −53.4449 | −1.69602 | ||||||||
\(994\) | 1.46410 | 0.0464385 | ||||||||
\(995\) | 62.6410 | 1.98585 | ||||||||
\(996\) | 150.067 | 4.75504 | ||||||||
\(997\) | −61.2295 | −1.93916 | −0.969578 | − | 0.244781i | \(-0.921284\pi\) | ||||
−0.969578 | + | 0.244781i | \(0.921284\pi\) | |||||||
\(998\) | −17.4641 | −0.552816 | ||||||||
\(999\) | 19.3923 | 0.613545 |
(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 | 187.2.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1683.2.a.r.1.2 | 2 | |||
4.3 | odd | 2 | 2992.2.a.j.1.1 | 2 | |||
5.4 | even | 2 | 4675.2.a.v.1.2 | 2 | |||
7.6 | odd | 2 | 9163.2.a.h.1.1 | 2 | |||
11.10 | odd | 2 | 2057.2.a.o.1.2 | 2 | |||
17.16 | even | 2 | 3179.2.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1683.2.a.r.1.2 | 2 | 3.2 | odd | 2 | |||
2057.2.a.o.1.2 | 2 | 11.10 | odd | 2 | |||
2992.2.a.j.1.1 | 2 | 4.3 | odd | 2 | |||
3179.2.a.k.1.1 | 2 | 17.16 | even | 2 | |||
4675.2.a.v.1.2 | 2 | 5.4 | even | 2 | |||
9163.2.a.h.1.1 | 2 | 7.6 | odd | 2 |