Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58579 | 0.709185 | 0.354593 | − | 0.935021i | \(-0.384620\pi\) | ||||
0.354593 | + | 0.935021i | \(0.384620\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.24264 | 0.709185 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.24264 | −0.579047 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | −1.41421 | −0.333333 | ||||||||
\(19\) | −7.24264 | −1.66158 | −0.830788 | − | 0.556589i | \(-0.812110\pi\) | ||||
−0.830788 | + | 0.556589i | \(0.812110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | −5.82843 | −1.21531 | −0.607656 | − | 0.794201i | \(-0.707890\pi\) | ||||
−0.607656 | + | 0.794201i | \(0.707890\pi\) | |||||||
\(24\) | 4.00000 | 0.816497 | ||||||||
\(25\) | −2.48528 | −0.497056 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.171573 | 0.0318603 | 0.0159301 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159301 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(30\) | −3.17157 | −0.579047 | ||||||||
\(31\) | 3.24264 | 0.582395 | 0.291198 | − | 0.956663i | \(-0.405946\pi\) | ||||
0.291198 | + | 0.956663i | \(0.405946\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | 1.04447 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24264 | −0.368688 | −0.184344 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184344 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(38\) | −10.2426 | −1.66158 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.48528 | −0.709185 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.58579 | −0.236395 | ||||||||
\(46\) | −8.24264 | −1.21531 | ||||||||
\(47\) | 1.58579 | 0.231311 | 0.115655 | − | 0.993289i | \(-0.463103\pi\) | ||||
0.115655 | + | 0.993289i | \(0.463103\pi\) | |||||||
\(48\) | 5.65685 | 0.816497 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.51472 | −0.497056 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.171573 | −0.0235673 | −0.0117837 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117837 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(54\) | 8.00000 | 1.08866 | ||||||||
\(55\) | −6.72792 | −0.907193 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.2426 | 1.35667 | ||||||||
\(58\) | 0.242641 | 0.0318603 | ||||||||
\(59\) | 0.343146 | 0.0446738 | 0.0223369 | − | 0.999751i | \(-0.492889\pi\) | ||||
0.0223369 | + | 0.999751i | \(0.492889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 4.58579 | 0.582395 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.48528 | 1.04447 | ||||||||
\(67\) | 14.4853 | 1.76966 | 0.884829 | − | 0.465915i | \(-0.154275\pi\) | ||||
0.884829 | + | 0.465915i | \(0.154275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24264 | 0.992297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.0711 | 1.55125 | 0.775625 | − | 0.631194i | \(-0.217435\pi\) | ||||
0.775625 | + | 0.631194i | \(0.217435\pi\) | |||||||
\(72\) | 2.82843 | 0.333333 | ||||||||
\(73\) | −9.24264 | −1.08177 | −0.540885 | − | 0.841097i | \(-0.681910\pi\) | ||||
−0.540885 | + | 0.841097i | \(0.681910\pi\) | |||||||
\(74\) | −3.17157 | −0.368688 | ||||||||
\(75\) | 3.51472 | 0.405845 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4853 | 1.74223 | 0.871115 | − | 0.491079i | \(-0.163397\pi\) | ||||
0.871115 | + | 0.491079i | \(0.163397\pi\) | |||||||
\(80\) | −6.34315 | −0.709185 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 12.4853 | 1.37877 | ||||||||
\(83\) | 13.2426 | 1.45357 | 0.726784 | − | 0.686866i | \(-0.241014\pi\) | ||||
0.726784 | + | 0.686866i | \(0.241014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.24264 | −0.243249 | ||||||||
\(86\) | −7.07107 | −0.762493 | ||||||||
\(87\) | −0.242641 | −0.0260138 | ||||||||
\(88\) | 12.0000 | 1.27920 | ||||||||
\(89\) | 1.58579 | 0.168093 | 0.0840465 | − | 0.996462i | \(-0.473216\pi\) | ||||
0.0840465 | + | 0.996462i | \(0.473216\pi\) | |||||||
\(90\) | −2.24264 | −0.236395 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.58579 | −0.475524 | ||||||||
\(94\) | 2.24264 | 0.231311 | ||||||||
\(95\) | −11.4853 | −1.17837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7279 | 1.19079 | 0.595395 | − | 0.803433i | \(-0.296996\pi\) | ||||
0.595395 | + | 0.803433i | \(0.296996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2426 | −1.01918 | −0.509590 | − | 0.860417i | \(-0.670203\pi\) | ||||
−0.509590 | + | 0.860417i | \(0.670203\pi\) | |||||||
\(102\) | 2.82843 | 0.280056 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.242641 | −0.0235673 | ||||||||
\(107\) | −20.1421 | −1.94721 | −0.973607 | − | 0.228232i | \(-0.926706\pi\) | ||||
−0.973607 | + | 0.228232i | \(0.926706\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.7279 | −1.60224 | −0.801122 | − | 0.598501i | \(-0.795763\pi\) | ||||
−0.801122 | + | 0.598501i | \(0.795763\pi\) | |||||||
\(110\) | −9.51472 | −0.907193 | ||||||||
\(111\) | 3.17157 | 0.301032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.31371 | 0.217655 | 0.108828 | − | 0.994061i | \(-0.465290\pi\) | ||||
0.108828 | + | 0.994061i | \(0.465290\pi\) | |||||||
\(114\) | 14.4853 | 1.35667 | ||||||||
\(115\) | −9.24264 | −0.861881 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.485281 | 0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.34315 | 0.579047 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −8.48528 | −0.768221 | ||||||||
\(123\) | −12.4853 | −1.12576 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8701 | −1.06169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | 7.07107 | 0.622573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.82843 | 0.247121 | 0.123560 | − | 0.992337i | \(-0.460569\pi\) | ||||
0.123560 | + | 0.992337i | \(0.460569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20.4853 | 1.76966 | ||||||||
\(135\) | 8.97056 | 0.772063 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 4.58579 | 0.391790 | 0.195895 | − | 0.980625i | \(-0.437239\pi\) | ||||
0.195895 | + | 0.980625i | \(0.437239\pi\) | |||||||
\(138\) | 11.6569 | 0.992297 | ||||||||
\(139\) | −6.24264 | −0.529494 | −0.264747 | − | 0.964318i | \(-0.585288\pi\) | ||||
−0.264747 | + | 0.964318i | \(0.585288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.24264 | −0.188864 | ||||||||
\(142\) | 18.4853 | 1.55125 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 0.272078 | 0.0225948 | ||||||||
\(146\) | −13.0711 | −1.08177 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2426 | −1.33065 | −0.665324 | − | 0.746554i | \(-0.731707\pi\) | ||||
−0.665324 | + | 0.746554i | \(0.731707\pi\) | |||||||
\(150\) | 4.97056 | 0.405845 | ||||||||
\(151\) | 9.75736 | 0.794043 | 0.397021 | − | 0.917809i | \(-0.370044\pi\) | ||||
0.397021 | + | 0.917809i | \(0.370044\pi\) | |||||||
\(152\) | 20.4853 | 1.66158 | ||||||||
\(153\) | 1.41421 | 0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.14214 | 0.413026 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75736 | 0.299870 | 0.149935 | − | 0.988696i | \(-0.452094\pi\) | ||||
0.149935 | + | 0.988696i | \(0.452094\pi\) | |||||||
\(158\) | 21.8995 | 1.74223 | ||||||||
\(159\) | 0.242641 | 0.0192427 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.07107 | −0.555556 | ||||||||
\(163\) | −8.48528 | −0.664619 | −0.332309 | − | 0.943170i | \(-0.607828\pi\) | ||||
−0.332309 | + | 0.943170i | \(0.607828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.51472 | 0.740720 | ||||||||
\(166\) | 18.7279 | 1.45357 | ||||||||
\(167\) | 15.3848 | 1.19051 | 0.595255 | − | 0.803537i | \(-0.297051\pi\) | ||||
0.595255 | + | 0.803537i | \(0.297051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.17157 | −0.243249 | ||||||||
\(171\) | 7.24264 | 0.553859 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.7279 | −1.88003 | −0.940015 | − | 0.341134i | \(-0.889189\pi\) | ||||
−0.940015 | + | 0.341134i | \(0.889189\pi\) | |||||||
\(174\) | −0.343146 | −0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.9706 | 1.27920 | ||||||||
\(177\) | −0.485281 | −0.0364760 | ||||||||
\(178\) | 2.24264 | 0.168093 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7279 | 1.39204 | 0.696018 | − | 0.718025i | \(-0.254953\pi\) | ||||
0.696018 | + | 0.718025i | \(0.254953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.48528 | 0.627250 | ||||||||
\(184\) | 16.4853 | 1.21531 | ||||||||
\(185\) | −3.55635 | −0.261468 | ||||||||
\(186\) | −6.48528 | −0.475524 | ||||||||
\(187\) | 6.00000 | 0.438763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2426 | −1.17837 | ||||||||
\(191\) | 15.1716 | 1.09778 | 0.548888 | − | 0.835896i | \(-0.315051\pi\) | ||||
0.548888 | + | 0.835896i | \(0.315051\pi\) | |||||||
\(192\) | −11.3137 | −0.816497 | ||||||||
\(193\) | 14.4853 | 1.04267 | 0.521337 | − | 0.853351i | \(-0.325434\pi\) | ||||
0.521337 | + | 0.853351i | \(0.325434\pi\) | |||||||
\(194\) | 16.5858 | 1.19079 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.3431 | −0.879413 | −0.439706 | − | 0.898142i | \(-0.644917\pi\) | ||||
−0.439706 | + | 0.898142i | \(0.644917\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | 3.75736 | 0.266352 | 0.133176 | − | 0.991092i | \(-0.457482\pi\) | ||||
0.133176 | + | 0.991092i | \(0.457482\pi\) | |||||||
\(200\) | 7.02944 | 0.497056 | ||||||||
\(201\) | −20.4853 | −1.44492 | ||||||||
\(202\) | −14.4853 | −1.01918 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | 0.977802 | ||||||||
\(206\) | 11.3137 | 0.788263 | ||||||||
\(207\) | 5.82843 | 0.405104 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.7279 | 2.12549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9706 | −1.09946 | −0.549729 | − | 0.835343i | \(-0.685269\pi\) | ||||
−0.549729 | + | 0.835343i | \(0.685269\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.4853 | −1.26659 | ||||||||
\(214\) | −28.4853 | −1.94721 | ||||||||
\(215\) | −7.92893 | −0.540749 | ||||||||
\(216\) | −16.0000 | −1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −23.6569 | −1.60224 | ||||||||
\(219\) | 13.0711 | 0.883261 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.48528 | 0.301032 | ||||||||
\(223\) | 0.757359 | 0.0507165 | 0.0253583 | − | 0.999678i | \(-0.491927\pi\) | ||||
0.0253583 | + | 0.999678i | \(0.491927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.48528 | 0.165685 | ||||||||
\(226\) | 3.27208 | 0.217655 | ||||||||
\(227\) | 26.8284 | 1.78067 | 0.890333 | − | 0.455311i | \(-0.150472\pi\) | ||||
0.890333 | + | 0.455311i | \(0.150472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.4558 | 1.94650 | 0.973248 | − | 0.229755i | \(-0.0737925\pi\) | ||||
0.973248 | + | 0.229755i | \(0.0737925\pi\) | |||||||
\(230\) | −13.0711 | −0.861881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.485281 | −0.0318603 | ||||||||
\(233\) | −14.6569 | −0.960202 | −0.480101 | − | 0.877213i | \(-0.659400\pi\) | ||||
−0.480101 | + | 0.877213i | \(0.659400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.51472 | 0.164042 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.8995 | −1.42253 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.51472 | −0.227348 | −0.113674 | − | 0.993518i | \(-0.536262\pi\) | ||||
−0.113674 | + | 0.993518i | \(0.536262\pi\) | |||||||
\(240\) | 8.97056 | 0.579047 | ||||||||
\(241\) | −20.2132 | −1.30205 | −0.651023 | − | 0.759058i | \(-0.725660\pi\) | ||||
−0.651023 | + | 0.759058i | \(0.725660\pi\) | |||||||
\(242\) | 9.89949 | 0.636364 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −17.6569 | −1.12576 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.17157 | −0.582395 | ||||||||
\(249\) | −18.7279 | −1.18683 | ||||||||
\(250\) | −16.7868 | −1.06169 | ||||||||
\(251\) | −16.5858 | −1.04689 | −0.523443 | − | 0.852061i | \(-0.675353\pi\) | ||||
−0.523443 | + | 0.852061i | \(0.675353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.7279 | 1.55463 | ||||||||
\(254\) | 2.82843 | 0.177471 | ||||||||
\(255\) | 3.17157 | 0.198612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.4142 | 1.21103 | 0.605513 | − | 0.795836i | \(-0.292968\pi\) | ||||
0.605513 | + | 0.795836i | \(0.292968\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.171573 | −0.0106201 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | 1.97056 | 0.121510 | 0.0607551 | − | 0.998153i | \(-0.480649\pi\) | ||||
0.0607551 | + | 0.998153i | \(0.480649\pi\) | |||||||
\(264\) | −16.9706 | −1.04447 | ||||||||
\(265\) | −0.272078 | −0.0167136 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.24264 | −0.137247 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.17157 | −0.559201 | −0.279600 | − | 0.960116i | \(-0.590202\pi\) | ||||
−0.279600 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(270\) | 12.6863 | 0.772063 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 5.65685 | 0.342997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.48528 | 0.391790 | ||||||||
\(275\) | 10.5442 | 0.635837 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.48528 | −0.449747 | −0.224873 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224873 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(278\) | −8.82843 | −0.529494 | ||||||||
\(279\) | −3.24264 | −0.194132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.5563 | −0.928014 | −0.464007 | − | 0.885832i | \(-0.653589\pi\) | ||||
−0.464007 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(282\) | −3.17157 | −0.188864 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.2426 | 0.962131 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 0.384776 | 0.0225948 | ||||||||
\(291\) | −16.5858 | −0.972276 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3848 | 0.898788 | 0.449394 | − | 0.893334i | \(-0.351640\pi\) | ||||
0.449394 | + | 0.893334i | \(0.351640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.544156 | 0.0316820 | ||||||||
\(296\) | 6.34315 | 0.368688 | ||||||||
\(297\) | −24.0000 | −1.39262 | ||||||||
\(298\) | −22.9706 | −1.33065 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.7990 | 0.794043 | ||||||||
\(303\) | 14.4853 | 0.832158 | ||||||||
\(304\) | 28.9706 | 1.66158 | ||||||||
\(305\) | −9.51472 | −0.544811 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 13.2426 | 0.755797 | 0.377899 | − | 0.925847i | \(-0.376647\pi\) | ||||
0.377899 | + | 0.925847i | \(0.376647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3137 | −0.643614 | ||||||||
\(310\) | 7.27208 | 0.413026 | ||||||||
\(311\) | 7.41421 | 0.420421 | 0.210211 | − | 0.977656i | \(-0.432585\pi\) | ||||
0.210211 | + | 0.977656i | \(0.432585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2132 | −1.31209 | −0.656044 | − | 0.754723i | \(-0.727771\pi\) | ||||
−0.656044 | + | 0.754723i | \(0.727771\pi\) | |||||||
\(314\) | 5.31371 | 0.299870 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.3137 | 0.635441 | 0.317721 | − | 0.948184i | \(-0.397083\pi\) | ||||
0.317721 | + | 0.948184i | \(0.397083\pi\) | |||||||
\(318\) | 0.343146 | 0.0192427 | ||||||||
\(319\) | −0.727922 | −0.0407558 | ||||||||
\(320\) | 12.6863 | 0.709185 | ||||||||
\(321\) | 28.4853 | 1.58989 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.2426 | 0.569916 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 23.6569 | 1.30823 | ||||||||
\(328\) | −24.9706 | −1.37877 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13.4558 | 0.740720 | ||||||||
\(331\) | 18.0000 | 0.989369 | 0.494685 | − | 0.869072i | \(-0.335284\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.24264 | 0.122896 | ||||||||
\(334\) | 21.7574 | 1.19051 | ||||||||
\(335\) | 22.9706 | 1.25502 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.27208 | −0.177715 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.7574 | −0.745003 | ||||||||
\(342\) | 10.2426 | 0.553859 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.1421 | 0.762493 | ||||||||
\(345\) | 13.0711 | 0.703723 | ||||||||
\(346\) | −34.9706 | −1.88003 | ||||||||
\(347\) | −5.65685 | −0.303676 | −0.151838 | − | 0.988405i | \(-0.548519\pi\) | ||||
−0.151838 | + | 0.988405i | \(0.548519\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7279 | −1.37718 | −0.688592 | − | 0.725149i | \(-0.741771\pi\) | ||||
−0.688592 | + | 0.725149i | \(0.741771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.48528 | −0.451626 | −0.225813 | − | 0.974171i | \(-0.572504\pi\) | ||||
−0.225813 | + | 0.974171i | \(0.572504\pi\) | |||||||
\(354\) | −0.686292 | −0.0364760 | ||||||||
\(355\) | 20.7279 | 1.10012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.7279 | −0.672692 | ||||||||
\(359\) | 27.8995 | 1.47248 | 0.736240 | − | 0.676721i | \(-0.236600\pi\) | ||||
0.736240 | + | 0.676721i | \(0.236600\pi\) | |||||||
\(360\) | 4.48528 | 0.236395 | ||||||||
\(361\) | 33.4558 | 1.76083 | ||||||||
\(362\) | 26.4853 | 1.39204 | ||||||||
\(363\) | −9.89949 | −0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6569 | −0.767175 | ||||||||
\(366\) | 12.0000 | 0.627250 | ||||||||
\(367\) | −10.2426 | −0.534661 | −0.267331 | − | 0.963605i | \(-0.586142\pi\) | ||||
−0.267331 | + | 0.963605i | \(0.586142\pi\) | |||||||
\(368\) | 23.3137 | 1.21531 | ||||||||
\(369\) | −8.82843 | −0.459590 | ||||||||
\(370\) | −5.02944 | −0.261468 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.48528 | 0.439351 | 0.219676 | − | 0.975573i | \(-0.429500\pi\) | ||||
0.219676 | + | 0.975573i | \(0.429500\pi\) | |||||||
\(374\) | 8.48528 | 0.438763 | ||||||||
\(375\) | 16.7868 | 0.866866 | ||||||||
\(376\) | −4.48528 | −0.231311 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.7574 | −1.22033 | −0.610167 | − | 0.792273i | \(-0.708898\pi\) | ||||
−0.610167 | + | 0.792273i | \(0.708898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.82843 | −0.144905 | ||||||||
\(382\) | 21.4558 | 1.09778 | ||||||||
\(383\) | −20.4853 | −1.04675 | −0.523374 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523374 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(384\) | −16.0000 | −0.816497 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.4853 | 1.04267 | ||||||||
\(387\) | 5.00000 | 0.254164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.6569 | 1.50366 | 0.751831 | − | 0.659356i | \(-0.229171\pi\) | ||||
0.751831 | + | 0.659356i | \(0.229171\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.24264 | 0.416848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −17.4558 | −0.879413 | ||||||||
\(395\) | 24.5563 | 1.23556 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2132 | −0.914094 | −0.457047 | − | 0.889442i | \(-0.651093\pi\) | ||||
−0.457047 | + | 0.889442i | \(0.651093\pi\) | |||||||
\(398\) | 5.31371 | 0.266352 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.94113 | 0.497056 | ||||||||
\(401\) | −6.34315 | −0.316762 | −0.158381 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158381 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(402\) | −28.9706 | −1.44492 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.92893 | −0.393992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.51472 | 0.471627 | ||||||||
\(408\) | −5.65685 | −0.280056 | ||||||||
\(409\) | 3.24264 | 0.160338 | 0.0801691 | − | 0.996781i | \(-0.474454\pi\) | ||||
0.0801691 | + | 0.996781i | \(0.474454\pi\) | |||||||
\(410\) | 19.7990 | 0.977802 | ||||||||
\(411\) | −6.48528 | −0.319895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.24264 | 0.405104 | ||||||||
\(415\) | 21.0000 | 1.03085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.82843 | 0.432330 | ||||||||
\(418\) | 43.4558 | 2.12549 | ||||||||
\(419\) | 20.8701 | 1.01957 | 0.509785 | − | 0.860302i | \(-0.329725\pi\) | ||||
0.509785 | + | 0.860302i | \(0.329725\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.72792 | −0.327899 | −0.163949 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163949 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(422\) | −22.5858 | −1.09946 | ||||||||
\(423\) | −1.58579 | −0.0771036 | ||||||||
\(424\) | 0.485281 | 0.0235673 | ||||||||
\(425\) | 3.51472 | 0.170489 | ||||||||
\(426\) | −26.1421 | −1.26659 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.2132 | −0.540749 | ||||||||
\(431\) | 12.3431 | 0.594548 | 0.297274 | − | 0.954792i | \(-0.403922\pi\) | ||||
0.297274 | + | 0.954792i | \(0.403922\pi\) | |||||||
\(432\) | −22.6274 | −1.08866 | ||||||||
\(433\) | 24.9706 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.384776 | −0.0184486 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 42.2132 | 2.01933 | ||||||||
\(438\) | 18.4853 | 0.883261 | ||||||||
\(439\) | 34.4853 | 1.64589 | 0.822946 | − | 0.568119i | \(-0.192329\pi\) | ||||
0.822946 | + | 0.568119i | \(0.192329\pi\) | |||||||
\(440\) | 19.0294 | 0.907193 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.68629 | −0.175141 | −0.0875705 | − | 0.996158i | \(-0.527910\pi\) | ||||
−0.0875705 | + | 0.996158i | \(0.527910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.51472 | 0.119209 | ||||||||
\(446\) | 1.07107 | 0.0507165 | ||||||||
\(447\) | 22.9706 | 1.08647 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1716 | −0.999148 | −0.499574 | − | 0.866271i | \(-0.666510\pi\) | ||||
−0.499574 | + | 0.866271i | \(0.666510\pi\) | |||||||
\(450\) | 3.51472 | 0.165685 | ||||||||
\(451\) | −37.4558 | −1.76373 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.7990 | −0.648333 | ||||||||
\(454\) | 37.9411 | 1.78067 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.9706 | −1.35667 | ||||||||
\(457\) | 7.21320 | 0.337419 | 0.168710 | − | 0.985666i | \(-0.446040\pi\) | ||||
0.168710 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(458\) | 41.6569 | 1.94650 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.82843 | 0.411181 | 0.205590 | − | 0.978638i | \(-0.434089\pi\) | ||||
0.205590 | + | 0.978638i | \(0.434089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.24264 | 0.197172 | 0.0985861 | − | 0.995129i | \(-0.468568\pi\) | ||||
0.0985861 | + | 0.995129i | \(0.468568\pi\) | |||||||
\(464\) | −0.686292 | −0.0318603 | ||||||||
\(465\) | −7.27208 | −0.337235 | ||||||||
\(466\) | −20.7279 | −0.960202 | ||||||||
\(467\) | 3.89949 | 0.180447 | 0.0902236 | − | 0.995922i | \(-0.471242\pi\) | ||||
0.0902236 | + | 0.995922i | \(0.471242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.55635 | 0.164042 | ||||||||
\(471\) | −5.31371 | −0.244843 | ||||||||
\(472\) | −0.970563 | −0.0446738 | ||||||||
\(473\) | 21.2132 | 0.975384 | ||||||||
\(474\) | −30.9706 | −1.42253 | ||||||||
\(475\) | 18.0000 | 0.825897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.171573 | 0.00785578 | ||||||||
\(478\) | −4.97056 | −0.227348 | ||||||||
\(479\) | −6.21320 | −0.283889 | −0.141944 | − | 0.989875i | \(-0.545335\pi\) | ||||
−0.141944 | + | 0.989875i | \(0.545335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.5858 | −1.30205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.5980 | 0.844491 | ||||||||
\(486\) | −14.0000 | −0.635053 | ||||||||
\(487\) | 11.4558 | 0.519114 | 0.259557 | − | 0.965728i | \(-0.416423\pi\) | ||||
0.259557 | + | 0.965728i | \(0.416423\pi\) | |||||||
\(488\) | 16.9706 | 0.768221 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6274 | 0.750385 | 0.375192 | − | 0.926947i | \(-0.377577\pi\) | ||||
0.375192 | + | 0.926947i | \(0.377577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.242641 | −0.0109280 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.72792 | 0.302398 | ||||||||
\(496\) | −12.9706 | −0.582395 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.4853 | −1.18683 | ||||||||
\(499\) | 13.2721 | 0.594140 | 0.297070 | − | 0.954856i | \(-0.403991\pi\) | ||||
0.297070 | + | 0.954856i | \(0.403991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.7574 | −0.972047 | ||||||||
\(502\) | −23.4558 | −1.04689 | ||||||||
\(503\) | 28.6274 | 1.27643 | 0.638217 | − | 0.769857i | \(-0.279672\pi\) | ||||
0.638217 | + | 0.769857i | \(0.279672\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2426 | −0.722788 | ||||||||
\(506\) | 34.9706 | 1.55463 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.10051 | −0.226076 | −0.113038 | − | 0.993591i | \(-0.536058\pi\) | ||||
−0.113038 | + | 0.993591i | \(0.536058\pi\) | |||||||
\(510\) | 4.48528 | 0.198612 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −40.9706 | −1.80889 | ||||||||
\(514\) | 27.4558 | 1.21103 | ||||||||
\(515\) | 12.6863 | 0.559025 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.72792 | −0.295894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.9706 | 1.53504 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.34315 | 0.277898 | 0.138949 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138949 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(522\) | −0.242641 | −0.0106201 | ||||||||
\(523\) | −30.9706 | −1.35425 | −0.677124 | − | 0.735869i | \(-0.736774\pi\) | ||||
−0.677124 | + | 0.735869i | \(0.736774\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.78680 | 0.121510 | ||||||||
\(527\) | −4.58579 | −0.199760 | ||||||||
\(528\) | −24.0000 | −1.04447 | ||||||||
\(529\) | 10.9706 | 0.476981 | ||||||||
\(530\) | −0.384776 | −0.0167136 | ||||||||
\(531\) | −0.343146 | −0.0148913 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.17157 | −0.137247 | ||||||||
\(535\) | −31.9411 | −1.38094 | ||||||||
\(536\) | −40.9706 | −1.76966 | ||||||||
\(537\) | 12.7279 | 0.549250 | ||||||||
\(538\) | −12.9706 | −0.559201 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.21320 | 0.310120 | 0.155060 | − | 0.987905i | \(-0.450443\pi\) | ||||
0.155060 | + | 0.987905i | \(0.450443\pi\) | |||||||
\(542\) | 28.2843 | 1.21491 | ||||||||
\(543\) | −26.4853 | −1.13659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5269 | −1.13629 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4853 | 1.51724 | 0.758621 | − | 0.651533i | \(-0.225874\pi\) | ||||
0.758621 | + | 0.651533i | \(0.225874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 14.9117 | 0.635837 | ||||||||
\(551\) | −1.24264 | −0.0529383 | ||||||||
\(552\) | −23.3137 | −0.992297 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.5858 | −0.449747 | ||||||||
\(555\) | 5.02944 | 0.213488 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | −0.508456 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(558\) | −4.58579 | −0.194132 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.48528 | −0.358249 | ||||||||
\(562\) | −22.0000 | −0.928014 | ||||||||
\(563\) | 6.34315 | 0.267332 | 0.133666 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133666 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.66905 | 0.154358 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.9706 | −1.55125 | ||||||||
\(569\) | 5.14214 | 0.215570 | 0.107785 | − | 0.994174i | \(-0.465624\pi\) | ||||
0.107785 | + | 0.994174i | \(0.465624\pi\) | |||||||
\(570\) | 22.9706 | 0.962131 | ||||||||
\(571\) | 42.4558 | 1.77672 | 0.888361 | − | 0.459146i | \(-0.151844\pi\) | ||||
0.888361 | + | 0.459146i | \(0.151844\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.4558 | −0.896331 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.4853 | 0.604078 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | −6.97056 | −0.290188 | −0.145094 | − | 0.989418i | \(-0.546349\pi\) | ||||
−0.145094 | + | 0.989418i | \(0.546349\pi\) | |||||||
\(578\) | −21.2132 | −0.882353 | ||||||||
\(579\) | −20.4853 | −0.851339 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.4558 | −0.972276 | ||||||||
\(583\) | 0.727922 | 0.0301475 | ||||||||
\(584\) | 26.1421 | 1.08177 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.7574 | 0.898788 | ||||||||
\(587\) | −6.55635 | −0.270609 | −0.135305 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135305 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4853 | −0.967694 | ||||||||
\(590\) | 0.769553 | 0.0316820 | ||||||||
\(591\) | 17.4558 | 0.718037 | ||||||||
\(592\) | 8.97056 | 0.368688 | ||||||||
\(593\) | −0.556349 | −0.0228465 | −0.0114233 | − | 0.999935i | \(-0.503636\pi\) | ||||
−0.0114233 | + | 0.999935i | \(0.503636\pi\) | |||||||
\(594\) | −33.9411 | −1.39262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.31371 | −0.217476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.7990 | −1.17669 | −0.588347 | − | 0.808608i | \(-0.700221\pi\) | ||||
−0.588347 | + | 0.808608i | \(0.700221\pi\) | |||||||
\(600\) | −9.94113 | −0.405845 | ||||||||
\(601\) | 38.9706 | 1.58964 | 0.794821 | − | 0.606844i | \(-0.207565\pi\) | ||||
0.794821 | + | 0.606844i | \(0.207565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.4853 | −0.589886 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1005 | 0.451300 | ||||||||
\(606\) | 20.4853 | 0.832158 | ||||||||
\(607\) | 26.7279 | 1.08485 | 0.542426 | − | 0.840103i | \(-0.317506\pi\) | ||||
0.542426 | + | 0.840103i | \(0.317506\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.4558 | −0.544811 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0000 | 0.646234 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(614\) | 18.7279 | 0.755797 | ||||||||
\(615\) | −19.7990 | −0.798372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.3431 | −0.496916 | −0.248458 | − | 0.968643i | \(-0.579924\pi\) | ||||
−0.248458 | + | 0.968643i | \(0.579924\pi\) | |||||||
\(618\) | −16.0000 | −0.643614 | ||||||||
\(619\) | 0.970563 | 0.0390102 | 0.0195051 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195051 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.9706 | −1.32306 | ||||||||
\(622\) | 10.4853 | 0.420421 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.39697 | −0.255879 | ||||||||
\(626\) | −32.8284 | −1.31209 | ||||||||
\(627\) | −43.4558 | −1.73546 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.17157 | 0.126459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | −43.7990 | −1.74223 | ||||||||
\(633\) | 22.5858 | 0.897704 | ||||||||
\(634\) | 16.0000 | 0.635441 | ||||||||
\(635\) | 3.17157 | 0.125860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.02944 | −0.0407558 | ||||||||
\(639\) | −13.0711 | −0.517083 | ||||||||
\(640\) | 17.9411 | 0.709185 | ||||||||
\(641\) | 15.3431 | 0.606018 | 0.303009 | − | 0.952988i | \(-0.402009\pi\) | ||||
0.303009 | + | 0.952988i | \(0.402009\pi\) | |||||||
\(642\) | 40.2843 | 1.58989 | ||||||||
\(643\) | −12.4853 | −0.492371 | −0.246186 | − | 0.969223i | \(-0.579177\pi\) | ||||
−0.246186 | + | 0.969223i | \(0.579177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.2132 | 0.441519 | ||||||||
\(646\) | 14.4853 | 0.569916 | ||||||||
\(647\) | −14.5269 | −0.571112 | −0.285556 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285556 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(648\) | 14.1421 | 0.555556 | ||||||||
\(649\) | −1.45584 | −0.0571469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.3137 | 0.677538 | 0.338769 | − | 0.940870i | \(-0.389990\pi\) | ||||
0.338769 | + | 0.940870i | \(0.389990\pi\) | |||||||
\(654\) | 33.4558 | 1.30823 | ||||||||
\(655\) | 4.48528 | 0.175254 | ||||||||
\(656\) | −35.3137 | −1.37877 | ||||||||
\(657\) | 9.24264 | 0.360590 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.3431 | −0.597684 | −0.298842 | − | 0.954303i | \(-0.596600\pi\) | ||||
−0.298842 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7574 | −0.418413 | −0.209206 | − | 0.977872i | \(-0.567088\pi\) | ||||
−0.209206 | + | 0.977872i | \(0.567088\pi\) | |||||||
\(662\) | 25.4558 | 0.989369 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.4558 | −1.45357 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.17157 | 0.122896 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.07107 | −0.0414099 | ||||||||
\(670\) | 32.4853 | 1.25502 | ||||||||
\(671\) | 25.4558 | 0.982712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9411 | −1.03850 | −0.519252 | − | 0.854621i | \(-0.673789\pi\) | ||||
−0.519252 | + | 0.854621i | \(0.673789\pi\) | |||||||
\(674\) | −46.6690 | −1.79762 | ||||||||
\(675\) | −14.0589 | −0.541126 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.3553 | 1.58941 | 0.794707 | − | 0.606993i | \(-0.207624\pi\) | ||||
0.794707 | + | 0.606993i | \(0.207624\pi\) | |||||||
\(678\) | −4.62742 | −0.177715 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.34315 | 0.243249 | ||||||||
\(681\) | −37.9411 | −1.45391 | ||||||||
\(682\) | −19.4558 | −0.745003 | ||||||||
\(683\) | 21.1716 | 0.810108 | 0.405054 | − | 0.914293i | \(-0.367253\pi\) | ||||
0.405054 | + | 0.914293i | \(0.367253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.27208 | 0.277852 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.6569 | −1.58931 | ||||||||
\(688\) | 20.0000 | 0.762493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.4853 | 0.703723 | ||||||||
\(691\) | 28.6985 | 1.09174 | 0.545871 | − | 0.837869i | \(-0.316199\pi\) | ||||
0.545871 | + | 0.837869i | \(0.316199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | −0.303676 | ||||||||
\(695\) | −9.89949 | −0.375509 | ||||||||
\(696\) | 0.686292 | 0.0260138 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | −36.3848 | −1.37718 | ||||||||
\(699\) | 20.7279 | 0.784002 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7990 | −0.407872 | −0.203936 | − | 0.978984i | \(-0.565373\pi\) | ||||
−0.203936 | + | 0.978984i | \(0.565373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.2426 | 0.612603 | ||||||||
\(704\) | −33.9411 | −1.27920 | ||||||||
\(705\) | −3.55635 | −0.133940 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.727922 | −0.0273377 | −0.0136688 | − | 0.999907i | \(-0.504351\pi\) | ||||
−0.0136688 | + | 0.999907i | \(0.504351\pi\) | |||||||
\(710\) | 29.3137 | 1.10012 | ||||||||
\(711\) | −15.4853 | −0.580743 | ||||||||
\(712\) | −4.48528 | −0.168093 | ||||||||
\(713\) | −18.8995 | −0.707792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.97056 | 0.185629 | ||||||||
\(718\) | 39.4558 | 1.47248 | ||||||||
\(719\) | 1.75736 | 0.0655384 | 0.0327692 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327692 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(720\) | 6.34315 | 0.236395 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 47.3137 | 1.76083 | ||||||||
\(723\) | 28.5858 | 1.06312 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.426407 | −0.0158364 | ||||||||
\(726\) | −14.0000 | −0.519589 | ||||||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −20.7279 | −0.767175 | ||||||||
\(731\) | 7.07107 | 0.261533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.6985 | −0.616773 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(734\) | −14.4853 | −0.534661 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −61.4558 | −2.26376 | ||||||||
\(738\) | −12.4853 | −0.459590 | ||||||||
\(739\) | 17.6985 | 0.651049 | 0.325525 | − | 0.945534i | \(-0.394459\pi\) | ||||
0.325525 | + | 0.945534i | \(0.394459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.6569 | 1.08800 | 0.544002 | − | 0.839084i | \(-0.316908\pi\) | ||||
0.544002 | + | 0.839084i | \(0.316908\pi\) | |||||||
\(744\) | 12.9706 | 0.475524 | ||||||||
\(745\) | −25.7574 | −0.943677 | ||||||||
\(746\) | 12.0000 | 0.439351 | ||||||||
\(747\) | −13.2426 | −0.484523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 23.7401 | 0.866866 | ||||||||
\(751\) | 15.4853 | 0.565066 | 0.282533 | − | 0.959258i | \(-0.408825\pi\) | ||||
0.282533 | + | 0.959258i | \(0.408825\pi\) | |||||||
\(752\) | −6.34315 | −0.231311 | ||||||||
\(753\) | 23.4558 | 0.854778 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4731 | 0.563123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.4853 | 0.780896 | 0.390448 | − | 0.920625i | \(-0.372320\pi\) | ||||
0.390448 | + | 0.920625i | \(0.372320\pi\) | |||||||
\(758\) | −33.5980 | −1.22033 | ||||||||
\(759\) | −34.9706 | −1.26935 | ||||||||
\(760\) | 32.4853 | 1.17837 | ||||||||
\(761\) | 34.7574 | 1.25995 | 0.629977 | − | 0.776614i | \(-0.283064\pi\) | ||||
0.629977 | + | 0.776614i | \(0.283064\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.24264 | 0.0810828 | ||||||||
\(766\) | −28.9706 | −1.04675 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.2132 | 1.88286 | 0.941428 | − | 0.337214i | \(-0.109484\pi\) | ||||
0.941428 | + | 0.337214i | \(0.109484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.4558 | −0.988798 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.8284 | −1.18076 | −0.590378 | − | 0.807127i | \(-0.701021\pi\) | ||||
−0.590378 | + | 0.807127i | \(0.701021\pi\) | |||||||
\(774\) | 7.07107 | 0.254164 | ||||||||
\(775\) | −8.05887 | −0.289483 | ||||||||
\(776\) | −33.1716 | −1.19079 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.9411 | 1.50366 | ||||||||
\(779\) | −63.9411 | −2.29093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.4558 | −1.98437 | ||||||||
\(782\) | 11.6569 | 0.416848 | ||||||||
\(783\) | 0.970563 | 0.0346851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.95837 | 0.212663 | ||||||||
\(786\) | −5.65685 | −0.201773 | ||||||||
\(787\) | −24.7574 | −0.882505 | −0.441252 | − | 0.897383i | \(-0.645466\pi\) | ||||
−0.441252 | + | 0.897383i | \(0.645466\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.78680 | −0.0992126 | ||||||||
\(790\) | 34.7279 | 1.23556 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25.7574 | −0.914094 | ||||||||
\(795\) | 0.384776 | 0.0136466 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.3431 | 0.862278 | 0.431139 | − | 0.902285i | \(-0.358112\pi\) | ||||
0.431139 | + | 0.902285i | \(0.358112\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.24264 | −0.0793389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.58579 | −0.0560310 | ||||||||
\(802\) | −8.97056 | −0.316762 | ||||||||
\(803\) | 39.2132 | 1.38380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.9706 | 0.456585 | ||||||||
\(808\) | 28.9706 | 1.01918 | ||||||||
\(809\) | 17.4853 | 0.614750 | 0.307375 | − | 0.951589i | \(-0.400549\pi\) | ||||
0.307375 | + | 0.951589i | \(0.400549\pi\) | |||||||
\(810\) | −11.2132 | −0.393992 | ||||||||
\(811\) | −21.9411 | −0.770457 | −0.385229 | − | 0.922821i | \(-0.625877\pi\) | ||||
−0.385229 | + | 0.922821i | \(0.625877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.2843 | −0.991973 | ||||||||
\(814\) | 13.4558 | 0.471627 | ||||||||
\(815\) | −13.4558 | −0.471338 | ||||||||
\(816\) | −8.00000 | −0.280056 | ||||||||
\(817\) | 36.2132 | 1.26694 | ||||||||
\(818\) | 4.58579 | 0.160338 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.1421 | 0.702965 | 0.351483 | − | 0.936194i | \(-0.385678\pi\) | ||||
0.351483 | + | 0.936194i | \(0.385678\pi\) | |||||||
\(822\) | −9.17157 | −0.319895 | ||||||||
\(823\) | 10.4853 | 0.365494 | 0.182747 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182747 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(824\) | −22.6274 | −0.788263 | ||||||||
\(825\) | −14.9117 | −0.519158 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.4558 | 1.71975 | 0.859874 | − | 0.510506i | \(-0.170542\pi\) | ||||
0.859874 | + | 0.510506i | \(0.170542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.7279 | −1.76185 | −0.880927 | − | 0.473253i | \(-0.843080\pi\) | ||||
−0.880927 | + | 0.473253i | \(0.843080\pi\) | |||||||
\(830\) | 29.6985 | 1.03085 | ||||||||
\(831\) | 10.5858 | 0.367217 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.4853 | 0.432330 | ||||||||
\(835\) | 24.3970 | 0.844292 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.3431 | 0.634032 | ||||||||
\(838\) | 29.5147 | 1.01957 | ||||||||
\(839\) | −33.1716 | −1.14521 | −0.572605 | − | 0.819831i | \(-0.694067\pi\) | ||||
−0.572605 | + | 0.819831i | \(0.694067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9706 | −0.998985 | ||||||||
\(842\) | −9.51472 | −0.327899 | ||||||||
\(843\) | 22.0000 | 0.757720 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.24264 | −0.0771036 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.686292 | 0.0235673 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 4.97056 | 0.170489 | ||||||||
\(851\) | 13.0711 | 0.448070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.7279 | 1.36026 | 0.680129 | − | 0.733092i | \(-0.261924\pi\) | ||||
0.680129 | + | 0.733092i | \(0.261924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4853 | 0.392788 | ||||||||
\(856\) | 56.9706 | 1.94721 | ||||||||
\(857\) | 54.7696 | 1.87089 | 0.935446 | − | 0.353469i | \(-0.114998\pi\) | ||||
0.935446 | + | 0.353469i | \(0.114998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.9706 | −1.05670 | −0.528351 | − | 0.849026i | \(-0.677189\pi\) | ||||
−0.528351 | + | 0.849026i | \(0.677189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.4558 | 0.594548 | ||||||||
\(863\) | −28.2843 | −0.962808 | −0.481404 | − | 0.876499i | \(-0.659873\pi\) | ||||
−0.481404 | + | 0.876499i | \(0.659873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.2132 | −1.33329 | ||||||||
\(866\) | 35.3137 | 1.20001 | ||||||||
\(867\) | 21.2132 | 0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.6985 | −2.22867 | ||||||||
\(870\) | −0.544156 | −0.0184486 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 47.3137 | 1.60224 | ||||||||
\(873\) | −11.7279 | −0.396930 | ||||||||
\(874\) | 59.6985 | 2.01933 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2426 | 0.345869 | 0.172935 | − | 0.984933i | \(-0.444675\pi\) | ||||
0.172935 | + | 0.984933i | \(0.444675\pi\) | |||||||
\(878\) | 48.7696 | 1.64589 | ||||||||
\(879\) | −21.7574 | −0.733858 | ||||||||
\(880\) | 26.9117 | 0.907193 | ||||||||
\(881\) | −13.1127 | −0.441778 | −0.220889 | − | 0.975299i | \(-0.570896\pi\) | ||||
−0.220889 | + | 0.975299i | \(0.570896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.769553 | −0.0258682 | ||||||||
\(886\) | −5.21320 | −0.175141 | ||||||||
\(887\) | −19.1127 | −0.641742 | −0.320871 | − | 0.947123i | \(-0.603976\pi\) | ||||
−0.320871 | + | 0.947123i | \(0.603976\pi\) | |||||||
\(888\) | −8.97056 | −0.301032 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.55635 | 0.119209 | ||||||||
\(891\) | 21.2132 | 0.710669 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.4853 | −0.384340 | ||||||||
\(894\) | 32.4853 | 1.08647 | ||||||||
\(895\) | −14.2721 | −0.477063 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.9411 | −0.999148 | ||||||||
\(899\) | 0.556349 | 0.0185553 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.242641 | 0.00808353 | ||||||||
\(902\) | −52.9706 | −1.76373 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.54416 | −0.217655 | ||||||||
\(905\) | 29.6985 | 0.987211 | ||||||||
\(906\) | −19.5147 | −0.648333 | ||||||||
\(907\) | 1.97056 | 0.0654315 | 0.0327157 | − | 0.999465i | \(-0.489584\pi\) | ||||
0.0327157 | + | 0.999465i | \(0.489584\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2426 | 0.339727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.9706 | −1.45681 | −0.728405 | − | 0.685147i | \(-0.759738\pi\) | ||||
−0.728405 | + | 0.685147i | \(0.759738\pi\) | |||||||
\(912\) | −40.9706 | −1.35667 | ||||||||
\(913\) | −56.1838 | −1.85941 | ||||||||
\(914\) | 10.2010 | 0.337419 | ||||||||
\(915\) | 13.4558 | 0.444836 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −11.3137 | −0.373408 | ||||||||
\(919\) | 24.0000 | 0.791687 | 0.395843 | − | 0.918318i | \(-0.370452\pi\) | ||||
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(920\) | 26.1421 | 0.861881 | ||||||||
\(921\) | −18.7279 | −0.617106 | ||||||||
\(922\) | 12.4853 | 0.411181 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.57359 | 0.183259 | ||||||||
\(926\) | 6.00000 | 0.197172 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8995 | 1.21063 | 0.605317 | − | 0.795985i | \(-0.293047\pi\) | ||||
0.605317 | + | 0.795985i | \(0.293047\pi\) | |||||||
\(930\) | −10.2843 | −0.337235 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.4853 | −0.343273 | ||||||||
\(934\) | 5.51472 | 0.180447 | ||||||||
\(935\) | 9.51472 | 0.311165 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.2132 | −1.47705 | −0.738525 | − | 0.674226i | \(-0.764478\pi\) | ||||
−0.738525 | + | 0.674226i | \(0.764478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.8284 | 1.07132 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.0711 | 1.30628 | 0.653140 | − | 0.757237i | \(-0.273451\pi\) | ||||
0.653140 | + | 0.757237i | \(0.273451\pi\) | |||||||
\(942\) | −7.51472 | −0.244843 | ||||||||
\(943\) | −51.4558 | −1.67563 | ||||||||
\(944\) | −1.37258 | −0.0446738 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −15.1716 | −0.493010 | −0.246505 | − | 0.969142i | \(-0.579282\pi\) | ||||
−0.246505 | + | 0.969142i | \(0.579282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 25.4558 | 0.825897 | ||||||||
\(951\) | −16.0000 | −0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1421 | 0.360929 | 0.180465 | − | 0.983581i | \(-0.442240\pi\) | ||||
0.180465 | + | 0.983581i | \(0.442240\pi\) | |||||||
\(954\) | 0.242641 | 0.00785578 | ||||||||
\(955\) | 24.0589 | 0.778527 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.02944 | 0.0332770 | ||||||||
\(958\) | −8.78680 | −0.283889 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −17.9411 | −0.579047 | ||||||||
\(961\) | −20.4853 | −0.660816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.1421 | 0.649071 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.9706 | 0.739449 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.6985 | −0.569145 | −0.284572 | − | 0.958655i | \(-0.591852\pi\) | ||||
−0.284572 | + | 0.958655i | \(0.591852\pi\) | |||||||
\(968\) | −19.7990 | −0.636364 | ||||||||
\(969\) | −14.4853 | −0.465334 | ||||||||
\(970\) | 26.3015 | 0.844491 | ||||||||
\(971\) | −43.4558 | −1.39456 | −0.697282 | − | 0.716797i | \(-0.745608\pi\) | ||||
−0.697282 | + | 0.716797i | \(0.745608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.2010 | 0.519114 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0000 | 0.768221 | ||||||||
\(977\) | −24.0416 | −0.769160 | −0.384580 | − | 0.923092i | \(-0.625654\pi\) | ||||
−0.384580 | + | 0.923092i | \(0.625654\pi\) | |||||||
\(978\) | 16.9706 | 0.542659 | ||||||||
\(979\) | −6.72792 | −0.215025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.7279 | 0.534081 | ||||||||
\(982\) | 23.5147 | 0.750385 | ||||||||
\(983\) | −15.0416 | −0.479754 | −0.239877 | − | 0.970803i | \(-0.577107\pi\) | ||||
−0.239877 | + | 0.970803i | \(0.577107\pi\) | |||||||
\(984\) | 35.3137 | 1.12576 | ||||||||
\(985\) | −19.5736 | −0.623667 | ||||||||
\(986\) | −0.343146 | −0.0109280 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.1421 | 0.926666 | ||||||||
\(990\) | 9.51472 | 0.302398 | ||||||||
\(991\) | 1.02944 | 0.0327012 | 0.0163506 | − | 0.999866i | \(-0.494795\pi\) | ||||
0.0163506 | + | 0.999866i | \(0.494795\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.4558 | −0.807817 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.95837 | 0.188893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.5147 | 0.364675 | 0.182337 | − | 0.983236i | \(-0.441634\pi\) | ||||
0.182337 | + | 0.983236i | \(0.441634\pi\) | |||||||
\(998\) | 18.7696 | 0.594140 | ||||||||
\(999\) | −12.6863 | −0.401377 |
(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 | 8281.2.a.v.1.2 | 2 | ||
7.6 | odd | 2 | 1183.2.a.d.1.2 | 2 | |||
13.12 | even | 2 | 637.2.a.g.1.1 | 2 | |||
39.38 | odd | 2 | 5733.2.a.s.1.2 | 2 | |||
91.12 | odd | 6 | 637.2.e.f.508.2 | 4 | |||
91.25 | even | 6 | 637.2.e.g.79.2 | 4 | |||
91.34 | even | 4 | 1183.2.c.d.337.4 | 4 | |||
91.38 | odd | 6 | 637.2.e.f.79.2 | 4 | |||
91.51 | even | 6 | 637.2.e.g.508.2 | 4 | |||
91.83 | even | 4 | 1183.2.c.d.337.2 | 4 | |||
91.90 | odd | 2 | 91.2.a.c.1.1 | ✓ | 2 | ||
273.272 | even | 2 | 819.2.a.h.1.2 | 2 | |||
364.363 | even | 2 | 1456.2.a.q.1.1 | 2 | |||
455.454 | odd | 2 | 2275.2.a.j.1.2 | 2 | |||
728.181 | odd | 2 | 5824.2.a.bl.1.1 | 2 | |||
728.363 | even | 2 | 5824.2.a.bk.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.c.1.1 | ✓ | 2 | 91.90 | odd | 2 | ||
637.2.a.g.1.1 | 2 | 13.12 | even | 2 | |||
637.2.e.f.79.2 | 4 | 91.38 | odd | 6 | |||
637.2.e.f.508.2 | 4 | 91.12 | odd | 6 | |||
637.2.e.g.79.2 | 4 | 91.25 | even | 6 | |||
637.2.e.g.508.2 | 4 | 91.51 | even | 6 | |||
819.2.a.h.1.2 | 2 | 273.272 | even | 2 | |||
1183.2.a.d.1.2 | 2 | 7.6 | odd | 2 | |||
1183.2.c.d.337.2 | 4 | 91.83 | even | 4 | |||
1183.2.c.d.337.4 | 4 | 91.34 | even | 4 | |||
1456.2.a.q.1.1 | 2 | 364.363 | even | 2 | |||
2275.2.a.j.1.2 | 2 | 455.454 | odd | 2 | |||
5733.2.a.s.1.2 | 2 | 39.38 | odd | 2 | |||
5824.2.a.bk.1.2 | 2 | 728.363 | even | 2 | |||
5824.2.a.bl.1.1 | 2 | 728.181 | odd | 2 | |||
8281.2.a.v.1.2 | 2 | 1.1 | even | 1 | trivial |