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 | 1.1 | ||
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 | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.41421 | 1.97410 | 0.987048 | − | 0.160424i | \(-0.0512862\pi\) | ||||
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −6.24264 | −1.97410 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.24264 | 1.61184 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.41421 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(18\) | 1.41421 | 0.333333 | ||||||||
\(19\) | 1.24264 | 0.285081 | 0.142541 | − | 0.989789i | \(-0.454473\pi\) | ||||
0.142541 | + | 0.989789i | \(0.454473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | −0.171573 | −0.0357754 | −0.0178877 | − | 0.999840i | \(-0.505694\pi\) | ||||
−0.0178877 | + | 0.999840i | \(0.505694\pi\) | |||||||
\(24\) | 4.00000 | 0.816497 | ||||||||
\(25\) | 14.4853 | 2.89706 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.82843 | 1.08231 | 0.541156 | − | 0.840922i | \(-0.317987\pi\) | ||||
0.541156 | + | 0.840922i | \(0.317987\pi\) | |||||||
\(30\) | −8.82843 | −1.61184 | ||||||||
\(31\) | −5.24264 | −0.941606 | −0.470803 | − | 0.882238i | \(-0.656036\pi\) | ||||
−0.470803 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | 1.04447 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.24264 | 1.02628 | 0.513142 | − | 0.858304i | \(-0.328481\pi\) | ||||
0.513142 | + | 0.858304i | \(0.328481\pi\) | |||||||
\(38\) | −1.75736 | −0.285081 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.4853 | 1.97410 | ||||||||
\(41\) | 3.17157 | 0.495316 | 0.247658 | − | 0.968847i | \(-0.420339\pi\) | ||||
0.247658 | + | 0.968847i | \(0.420339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.41421 | −0.658032 | ||||||||
\(46\) | 0.242641 | 0.0357754 | ||||||||
\(47\) | 4.41421 | 0.643879 | 0.321940 | − | 0.946760i | \(-0.395665\pi\) | ||||
0.321940 | + | 0.946760i | \(0.395665\pi\) | |||||||
\(48\) | −5.65685 | −0.816497 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −20.4853 | −2.89706 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.82843 | −0.800596 | −0.400298 | − | 0.916385i | \(-0.631093\pi\) | ||||
−0.400298 | + | 0.916385i | \(0.631093\pi\) | |||||||
\(54\) | 8.00000 | 1.08866 | ||||||||
\(55\) | 18.7279 | 2.52527 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.75736 | 0.232768 | ||||||||
\(58\) | −8.24264 | −1.08231 | ||||||||
\(59\) | 11.6569 | 1.51759 | 0.758797 | − | 0.651328i | \(-0.225788\pi\) | ||||
0.758797 | + | 0.651328i | \(0.225788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 7.41421 | 0.941606 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.48528 | −1.04447 | ||||||||
\(67\) | −2.48528 | −0.303625 | −0.151813 | − | 0.988409i | \(-0.548511\pi\) | ||||
−0.151813 | + | 0.988409i | \(0.548511\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.242641 | −0.0292105 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.07107 | −0.127112 | −0.0635562 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635562 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −0.757359 | −0.0886422 | −0.0443211 | − | 0.999017i | \(-0.514112\pi\) | ||||
−0.0443211 | + | 0.999017i | \(0.514112\pi\) | |||||||
\(74\) | −8.82843 | −1.02628 | ||||||||
\(75\) | 20.4853 | 2.36544 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.48528 | −0.167107 | −0.0835536 | − | 0.996503i | \(-0.526627\pi\) | ||||
−0.0835536 | + | 0.996503i | \(0.526627\pi\) | |||||||
\(80\) | −17.6569 | −1.97410 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −4.48528 | −0.495316 | ||||||||
\(83\) | 4.75736 | 0.522188 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24264 | 0.677109 | ||||||||
\(86\) | 7.07107 | 0.762493 | ||||||||
\(87\) | 8.24264 | 0.883704 | ||||||||
\(88\) | 12.0000 | 1.27920 | ||||||||
\(89\) | 4.41421 | 0.467906 | 0.233953 | − | 0.972248i | \(-0.424834\pi\) | ||||
0.233953 | + | 0.972248i | \(0.424834\pi\) | |||||||
\(90\) | 6.24264 | 0.658032 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.41421 | −0.768818 | ||||||||
\(94\) | −6.24264 | −0.643879 | ||||||||
\(95\) | 5.48528 | 0.562778 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7279 | −1.39386 | −0.696930 | − | 0.717139i | \(-0.745451\pi\) | ||||
−0.696930 | + | 0.717139i | \(0.745451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.24264 | −0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.75736 | −0.174864 | −0.0874319 | − | 0.996170i | \(-0.527866\pi\) | ||||
−0.0874319 | + | 0.996170i | \(0.527866\pi\) | |||||||
\(102\) | −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 | ||||||||
\(106\) | 8.24264 | 0.800596 | ||||||||
\(107\) | 8.14214 | 0.787130 | 0.393565 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393565 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.72792 | 0.835983 | 0.417992 | − | 0.908451i | \(-0.362734\pi\) | ||||
0.417992 | + | 0.908451i | \(0.362734\pi\) | |||||||
\(110\) | −26.4853 | −2.52527 | ||||||||
\(111\) | 8.82843 | 0.837957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.3137 | −1.91095 | −0.955476 | − | 0.295067i | \(-0.904658\pi\) | ||||
−0.955476 | + | 0.295067i | \(0.904658\pi\) | |||||||
\(114\) | −2.48528 | −0.232768 | ||||||||
\(115\) | −0.757359 | −0.0706241 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.4853 | −1.51759 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 17.6569 | 1.61184 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 8.48528 | 0.768221 | ||||||||
\(123\) | 4.48528 | 0.404424 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.8701 | 3.74497 | ||||||||
\(126\) | 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 | \(-0.539431\pi\) | ||||
−0.123560 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.51472 | 0.303625 | ||||||||
\(135\) | −24.9706 | −2.14912 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 7.41421 | 0.633439 | 0.316720 | − | 0.948519i | \(-0.397419\pi\) | ||||
0.316720 | + | 0.948519i | \(0.397419\pi\) | |||||||
\(138\) | 0.343146 | 0.0292105 | ||||||||
\(139\) | 2.24264 | 0.190218 | 0.0951092 | − | 0.995467i | \(-0.469680\pi\) | ||||
0.0951092 | + | 0.995467i | \(0.469680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.24264 | 0.525725 | ||||||||
\(142\) | 1.51472 | 0.127112 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 25.7279 | 2.13659 | ||||||||
\(146\) | 1.07107 | 0.0886422 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.75736 | −0.635508 | −0.317754 | − | 0.948173i | \(-0.602929\pi\) | ||||
−0.317754 | + | 0.948173i | \(0.602929\pi\) | |||||||
\(150\) | −28.9706 | −2.36544 | ||||||||
\(151\) | 18.2426 | 1.48457 | 0.742283 | − | 0.670087i | \(-0.233743\pi\) | ||||
0.742283 | + | 0.670087i | \(0.233743\pi\) | |||||||
\(152\) | 3.51472 | 0.285081 | ||||||||
\(153\) | −1.41421 | −0.114332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.1421 | −1.85882 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2426 | 0.977069 | 0.488535 | − | 0.872545i | \(-0.337532\pi\) | ||||
0.488535 | + | 0.872545i | \(0.337532\pi\) | |||||||
\(158\) | 2.10051 | 0.167107 | ||||||||
\(159\) | −8.24264 | −0.653684 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.07107 | 0.555556 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26.4853 | 2.06188 | ||||||||
\(166\) | −6.72792 | −0.522188 | ||||||||
\(167\) | −21.3848 | −1.65480 | −0.827402 | − | 0.561610i | \(-0.810182\pi\) | ||||
−0.827402 | + | 0.561610i | \(0.810182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.82843 | −0.677109 | ||||||||
\(171\) | −1.24264 | −0.0950271 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.727922 | 0.0553429 | 0.0276714 | − | 0.999617i | \(-0.491191\pi\) | ||||
0.0276714 | + | 0.999617i | \(0.491191\pi\) | |||||||
\(174\) | −11.6569 | −0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9706 | −1.27920 | ||||||||
\(177\) | 16.4853 | 1.23911 | ||||||||
\(178\) | −6.24264 | −0.467906 | ||||||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.72792 | −0.500083 | −0.250041 | − | 0.968235i | \(-0.580444\pi\) | ||||
−0.250041 | + | 0.968235i | \(0.580444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.48528 | −0.627250 | ||||||||
\(184\) | −0.485281 | −0.0357754 | ||||||||
\(185\) | 27.5563 | 2.02598 | ||||||||
\(186\) | 10.4853 | 0.768818 | ||||||||
\(187\) | 6.00000 | 0.438763 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.75736 | −0.562778 | ||||||||
\(191\) | 20.8284 | 1.50709 | 0.753546 | − | 0.657395i | \(-0.228342\pi\) | ||||
0.753546 | + | 0.657395i | \(0.228342\pi\) | |||||||
\(192\) | 11.3137 | 0.816497 | ||||||||
\(193\) | −2.48528 | −0.178894 | −0.0894472 | − | 0.995992i | \(-0.528510\pi\) | ||||
−0.0894472 | + | 0.995992i | \(0.528510\pi\) | |||||||
\(194\) | 19.4142 | 1.39386 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.6569 | −1.68548 | −0.842741 | − | 0.538320i | \(-0.819059\pi\) | ||||
−0.842741 | + | 0.538320i | \(0.819059\pi\) | |||||||
\(198\) | 6.00000 | 0.426401 | ||||||||
\(199\) | 12.2426 | 0.867858 | 0.433929 | − | 0.900947i | \(-0.357127\pi\) | ||||
0.433929 | + | 0.900947i | \(0.357127\pi\) | |||||||
\(200\) | 40.9706 | 2.89706 | ||||||||
\(201\) | −3.51472 | −0.247909 | ||||||||
\(202\) | 2.48528 | 0.174864 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.0000 | 0.977802 | ||||||||
\(206\) | −11.3137 | −0.788263 | ||||||||
\(207\) | 0.171573 | 0.0119251 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.27208 | 0.364677 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9706 | 1.23714 | 0.618572 | − | 0.785728i | \(-0.287711\pi\) | ||||
0.618572 | + | 0.785728i | \(0.287711\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.51472 | −0.103787 | ||||||||
\(214\) | −11.5147 | −0.787130 | ||||||||
\(215\) | −22.0711 | −1.50523 | ||||||||
\(216\) | −16.0000 | −1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.3431 | −0.835983 | ||||||||
\(219\) | −1.07107 | −0.0723761 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12.4853 | −0.837957 | ||||||||
\(223\) | 9.24264 | 0.618933 | 0.309466 | − | 0.950910i | \(-0.399850\pi\) | ||||
0.309466 | + | 0.950910i | \(0.399850\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.4853 | −0.965685 | ||||||||
\(226\) | 28.7279 | 1.91095 | ||||||||
\(227\) | 21.1716 | 1.40521 | 0.702603 | − | 0.711582i | \(-0.252021\pi\) | ||||
0.702603 | + | 0.711582i | \(0.252021\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.4558 | −1.41784 | −0.708921 | − | 0.705288i | \(-0.750818\pi\) | ||||
−0.708921 | + | 0.705288i | \(0.750818\pi\) | |||||||
\(230\) | 1.07107 | 0.0706241 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.4853 | 1.08231 | ||||||||
\(233\) | −3.34315 | −0.219017 | −0.109508 | − | 0.993986i | \(-0.534928\pi\) | ||||
−0.109508 | + | 0.993986i | \(0.534928\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.4853 | 1.27108 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.10051 | −0.136442 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4853 | −1.32508 | −0.662541 | − | 0.749025i | \(-0.730522\pi\) | ||||
−0.662541 | + | 0.749025i | \(0.730522\pi\) | |||||||
\(240\) | −24.9706 | −1.61184 | ||||||||
\(241\) | 22.2132 | 1.43088 | 0.715439 | − | 0.698675i | \(-0.246227\pi\) | ||||
0.715439 | + | 0.698675i | \(0.246227\pi\) | |||||||
\(242\) | −9.89949 | −0.636364 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.34315 | −0.404424 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −14.8284 | −0.941606 | ||||||||
\(249\) | 6.72792 | 0.426365 | ||||||||
\(250\) | −59.2132 | −3.74497 | ||||||||
\(251\) | −19.4142 | −1.22541 | −0.612707 | − | 0.790310i | \(-0.709919\pi\) | ||||
−0.612707 | + | 0.790310i | \(0.709919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.727922 | −0.0457641 | ||||||||
\(254\) | −2.82843 | −0.177471 | ||||||||
\(255\) | 8.82843 | 0.552858 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5858 | 1.03459 | 0.517296 | − | 0.855806i | \(-0.326938\pi\) | ||||
0.517296 | + | 0.855806i | \(0.326938\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.82843 | −0.360771 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | −31.9706 | −1.97139 | −0.985695 | − | 0.168541i | \(-0.946095\pi\) | ||||
−0.985695 | + | 0.168541i | \(0.946095\pi\) | |||||||
\(264\) | 16.9706 | 1.04447 | ||||||||
\(265\) | −25.7279 | −1.58045 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.24264 | 0.382043 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8284 | −0.904105 | −0.452053 | − | 0.891991i | \(-0.649308\pi\) | ||||
−0.452053 | + | 0.891991i | \(0.649308\pi\) | |||||||
\(270\) | 35.3137 | 2.14912 | ||||||||
\(271\) | 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 | ||||||||
\(274\) | −10.4853 | −0.633439 | ||||||||
\(275\) | 61.4558 | 3.70593 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.48528 | 0.569915 | 0.284958 | − | 0.958540i | \(-0.408020\pi\) | ||||
0.284958 | + | 0.958540i | \(0.408020\pi\) | |||||||
\(278\) | −3.17157 | −0.190218 | ||||||||
\(279\) | 5.24264 | 0.313869 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.5563 | 0.928014 | 0.464007 | − | 0.885832i | \(-0.346411\pi\) | ||||
0.464007 | + | 0.885832i | \(0.346411\pi\) | |||||||
\(282\) | −8.82843 | −0.525725 | ||||||||
\(283\) | −8.48528 | −0.504398 | −0.252199 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252199 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.75736 | 0.459506 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | −36.3848 | −2.13659 | ||||||||
\(291\) | −19.4142 | −1.13808 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3848 | −1.24931 | −0.624656 | − | 0.780900i | \(-0.714761\pi\) | ||||
−0.624656 | + | 0.780900i | \(0.714761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 51.4558 | 2.99588 | ||||||||
\(296\) | 17.6569 | 1.02628 | ||||||||
\(297\) | −24.0000 | −1.39262 | ||||||||
\(298\) | 10.9706 | 0.635508 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.7990 | −1.48457 | ||||||||
\(303\) | −2.48528 | −0.142776 | ||||||||
\(304\) | −4.97056 | −0.285081 | ||||||||
\(305\) | −26.4853 | −1.51654 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 4.75736 | 0.271517 | 0.135758 | − | 0.990742i | \(-0.456653\pi\) | ||||
0.135758 | + | 0.990742i | \(0.456653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.3137 | 0.643614 | ||||||||
\(310\) | 32.7279 | 1.85882 | ||||||||
\(311\) | 4.58579 | 0.260036 | 0.130018 | − | 0.991512i | \(-0.458496\pi\) | ||||
0.130018 | + | 0.991512i | \(0.458496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.2132 | 1.08599 | 0.542997 | − | 0.839734i | \(-0.317289\pi\) | ||||
0.542997 | + | 0.839734i | \(0.317289\pi\) | |||||||
\(314\) | −17.3137 | −0.977069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3137 | −0.635441 | −0.317721 | − | 0.948184i | \(-0.602917\pi\) | ||||
−0.317721 | + | 0.948184i | \(0.602917\pi\) | |||||||
\(318\) | 11.6569 | 0.653684 | ||||||||
\(319\) | 24.7279 | 1.38450 | ||||||||
\(320\) | 35.3137 | 1.97410 | ||||||||
\(321\) | 11.5147 | 0.642689 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75736 | 0.0977821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 12.3431 | 0.682578 | ||||||||
\(328\) | 8.97056 | 0.495316 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −37.4558 | −2.06188 | ||||||||
\(331\) | 18.0000 | 0.989369 | 0.494685 | − | 0.869072i | \(-0.335284\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.24264 | −0.342095 | ||||||||
\(334\) | 30.2426 | 1.65480 | ||||||||
\(335\) | −10.9706 | −0.599386 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.7279 | −1.56029 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.2426 | −1.20451 | ||||||||
\(342\) | 1.75736 | 0.0950271 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.1421 | −0.762493 | ||||||||
\(345\) | −1.07107 | −0.0576644 | ||||||||
\(346\) | −1.02944 | −0.0553429 | ||||||||
\(347\) | 5.65685 | 0.303676 | 0.151838 | − | 0.988405i | \(-0.451481\pi\) | ||||
0.151838 | + | 0.988405i | \(0.451481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.272078 | −0.0145640 | −0.00728200 | − | 0.999973i | \(-0.502318\pi\) | ||||
−0.00728200 | + | 0.999973i | \(0.502318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.48528 | 0.451626 | 0.225813 | − | 0.974171i | \(-0.427496\pi\) | ||||
0.225813 | + | 0.974171i | \(0.427496\pi\) | |||||||
\(354\) | −23.3137 | −1.23911 | ||||||||
\(355\) | −4.72792 | −0.250932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7279 | 0.672692 | ||||||||
\(359\) | 8.10051 | 0.427528 | 0.213764 | − | 0.976885i | \(-0.431428\pi\) | ||||
0.213764 | + | 0.976885i | \(0.431428\pi\) | |||||||
\(360\) | −12.4853 | −0.658032 | ||||||||
\(361\) | −17.4558 | −0.918729 | ||||||||
\(362\) | 9.51472 | 0.500083 | ||||||||
\(363\) | 9.89949 | 0.519589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.34315 | −0.174988 | ||||||||
\(366\) | 12.0000 | 0.627250 | ||||||||
\(367\) | −1.75736 | −0.0917334 | −0.0458667 | − | 0.998948i | \(-0.514605\pi\) | ||||
−0.0458667 | + | 0.998948i | \(0.514605\pi\) | |||||||
\(368\) | 0.686292 | 0.0357754 | ||||||||
\(369\) | −3.17157 | −0.165105 | ||||||||
\(370\) | −38.9706 | −2.02598 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.48528 | −0.439351 | −0.219676 | − | 0.975573i | \(-0.570500\pi\) | ||||
−0.219676 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(374\) | −8.48528 | −0.438763 | ||||||||
\(375\) | 59.2132 | 3.05776 | ||||||||
\(376\) | 12.4853 | 0.643879 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.2426 | −1.65619 | −0.828097 | − | 0.560585i | \(-0.810576\pi\) | ||||
−0.828097 | + | 0.560585i | \(0.810576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.82843 | 0.144905 | ||||||||
\(382\) | −29.4558 | −1.50709 | ||||||||
\(383\) | −3.51472 | −0.179594 | −0.0897969 | − | 0.995960i | \(-0.528622\pi\) | ||||
−0.0897969 | + | 0.995960i | \(0.528622\pi\) | |||||||
\(384\) | −16.0000 | −0.816497 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.51472 | 0.178894 | ||||||||
\(387\) | 5.00000 | 0.254164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3431 | 0.930034 | 0.465017 | − | 0.885302i | \(-0.346048\pi\) | ||||
0.465017 | + | 0.885302i | \(0.346048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.242641 | −0.0122709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 33.4558 | 1.68548 | ||||||||
\(395\) | −6.55635 | −0.329886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2132 | 1.21523 | 0.607613 | − | 0.794233i | \(-0.292127\pi\) | ||||
0.607613 | + | 0.794233i | \(0.292127\pi\) | |||||||
\(398\) | −17.3137 | −0.867858 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −57.9411 | −2.89706 | ||||||||
\(401\) | −17.6569 | −0.881741 | −0.440871 | − | 0.897571i | \(-0.645330\pi\) | ||||
−0.440871 | + | 0.897571i | \(0.645330\pi\) | |||||||
\(402\) | 4.97056 | 0.247909 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.0711 | −1.09672 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.4853 | 1.31283 | ||||||||
\(408\) | 5.65685 | 0.280056 | ||||||||
\(409\) | −5.24264 | −0.259232 | −0.129616 | − | 0.991564i | \(-0.541374\pi\) | ||||
−0.129616 | + | 0.991564i | \(0.541374\pi\) | |||||||
\(410\) | −19.7990 | −0.977802 | ||||||||
\(411\) | 10.4853 | 0.517201 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.242641 | −0.0119251 | ||||||||
\(415\) | 21.0000 | 1.03085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.17157 | 0.155313 | ||||||||
\(418\) | −7.45584 | −0.364677 | ||||||||
\(419\) | −32.8701 | −1.60581 | −0.802904 | − | 0.596109i | \(-0.796713\pi\) | ||||
−0.802904 | + | 0.596109i | \(0.796713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7279 | 0.912743 | 0.456372 | − | 0.889789i | \(-0.349149\pi\) | ||||
0.456372 | + | 0.889789i | \(0.349149\pi\) | |||||||
\(422\) | −25.4142 | −1.23714 | ||||||||
\(423\) | −4.41421 | −0.214626 | ||||||||
\(424\) | −16.4853 | −0.800596 | ||||||||
\(425\) | 20.4853 | 0.993682 | ||||||||
\(426\) | 2.14214 | 0.103787 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.2132 | 1.50523 | ||||||||
\(431\) | 23.6569 | 1.13951 | 0.569755 | − | 0.821814i | \(-0.307038\pi\) | ||||
0.569755 | + | 0.821814i | \(0.307038\pi\) | |||||||
\(432\) | 22.6274 | 1.08866 | ||||||||
\(433\) | −8.97056 | −0.431098 | −0.215549 | − | 0.976493i | \(-0.569154\pi\) | ||||
−0.215549 | + | 0.976493i | \(0.569154\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 36.3848 | 1.74452 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.213203 | −0.0101989 | ||||||||
\(438\) | 1.51472 | 0.0723761 | ||||||||
\(439\) | 17.5147 | 0.835932 | 0.417966 | − | 0.908463i | \(-0.362743\pi\) | ||||
0.417966 | + | 0.908463i | \(0.362743\pi\) | |||||||
\(440\) | 52.9706 | 2.52527 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.3137 | −1.25020 | −0.625101 | − | 0.780544i | \(-0.714942\pi\) | ||||
−0.625101 | + | 0.780544i | \(0.714942\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.4853 | 0.923691 | ||||||||
\(446\) | −13.0711 | −0.618933 | ||||||||
\(447\) | −10.9706 | −0.518890 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.8284 | −1.26611 | −0.633056 | − | 0.774106i | \(-0.718200\pi\) | ||||
−0.633056 | + | 0.774106i | \(0.718200\pi\) | |||||||
\(450\) | 20.4853 | 0.965685 | ||||||||
\(451\) | 13.4558 | 0.633611 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.7990 | 1.21214 | ||||||||
\(454\) | −29.9411 | −1.40521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.97056 | 0.232768 | ||||||||
\(457\) | −35.2132 | −1.64720 | −0.823602 | − | 0.567168i | \(-0.808039\pi\) | ||||
−0.823602 | + | 0.567168i | \(0.808039\pi\) | |||||||
\(458\) | 30.3431 | 1.41784 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.17157 | 0.147715 | 0.0738574 | − | 0.997269i | \(-0.476469\pi\) | ||||
0.0738574 | + | 0.997269i | \(0.476469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24264 | −0.197172 | −0.0985861 | − | 0.995129i | \(-0.531432\pi\) | ||||
−0.0985861 | + | 0.995129i | \(0.531432\pi\) | |||||||
\(464\) | −23.3137 | −1.08231 | ||||||||
\(465\) | −32.7279 | −1.51772 | ||||||||
\(466\) | 4.72792 | 0.219017 | ||||||||
\(467\) | −15.8995 | −0.735741 | −0.367870 | − | 0.929877i | \(-0.619913\pi\) | ||||
−0.367870 | + | 0.929877i | \(0.619913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −27.5563 | −1.27108 | ||||||||
\(471\) | 17.3137 | 0.797774 | ||||||||
\(472\) | 32.9706 | 1.51759 | ||||||||
\(473\) | −21.2132 | −0.975384 | ||||||||
\(474\) | 2.97056 | 0.136442 | ||||||||
\(475\) | 18.0000 | 0.825897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.82843 | 0.266865 | ||||||||
\(478\) | 28.9706 | 1.32508 | ||||||||
\(479\) | 36.2132 | 1.65462 | 0.827312 | − | 0.561743i | \(-0.189869\pi\) | ||||
0.827312 | + | 0.561743i | \(0.189869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −31.4142 | −1.43088 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −60.5980 | −2.75161 | ||||||||
\(486\) | −14.0000 | −0.635053 | ||||||||
\(487\) | −39.4558 | −1.78791 | −0.893957 | − | 0.448152i | \(-0.852082\pi\) | ||||
−0.893957 | + | 0.448152i | \(0.852082\pi\) | |||||||
\(488\) | −16.9706 | −0.768221 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6274 | −1.29194 | −0.645969 | − | 0.763364i | \(-0.723546\pi\) | ||||
−0.645969 | + | 0.763364i | \(0.723546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.24264 | 0.371230 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.7279 | −0.841757 | ||||||||
\(496\) | 20.9706 | 0.941606 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.51472 | −0.426365 | ||||||||
\(499\) | 38.7279 | 1.73370 | 0.866850 | − | 0.498569i | \(-0.166141\pi\) | ||||
0.866850 | + | 0.498569i | \(0.166141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.2426 | −1.35114 | ||||||||
\(502\) | 27.4558 | 1.22541 | ||||||||
\(503\) | −16.6274 | −0.741380 | −0.370690 | − | 0.928757i | \(-0.620879\pi\) | ||||
−0.370690 | + | 0.928757i | \(0.620879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.75736 | −0.345198 | ||||||||
\(506\) | 1.02944 | 0.0457641 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.8995 | −1.10365 | −0.551825 | − | 0.833960i | \(-0.686069\pi\) | ||||
−0.551825 | + | 0.833960i | \(0.686069\pi\) | |||||||
\(510\) | −12.4853 | −0.552858 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −7.02944 | −0.310357 | ||||||||
\(514\) | −23.4558 | −1.03459 | ||||||||
\(515\) | 35.3137 | 1.55611 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.7279 | 0.823653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.02944 | 0.0451873 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6569 | 0.773561 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(522\) | 8.24264 | 0.360771 | ||||||||
\(523\) | 2.97056 | 0.129894 | 0.0649468 | − | 0.997889i | \(-0.479312\pi\) | ||||
0.0649468 | + | 0.997889i | \(0.479312\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.2132 | 1.97139 | ||||||||
\(527\) | −7.41421 | −0.322968 | ||||||||
\(528\) | −24.0000 | −1.04447 | ||||||||
\(529\) | −22.9706 | −0.998720 | ||||||||
\(530\) | 36.3848 | 1.58045 | ||||||||
\(531\) | −11.6569 | −0.505864 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.82843 | −0.382043 | ||||||||
\(535\) | 35.9411 | 1.55387 | ||||||||
\(536\) | −7.02944 | −0.303625 | ||||||||
\(537\) | −12.7279 | −0.549250 | ||||||||
\(538\) | 20.9706 | 0.904105 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.2132 | −1.51393 | −0.756967 | − | 0.653453i | \(-0.773320\pi\) | ||||
−0.756967 | + | 0.653453i | \(0.773320\pi\) | |||||||
\(542\) | −28.2843 | −1.21491 | ||||||||
\(543\) | −9.51472 | −0.408316 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.5269 | 1.65031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5147 | 0.791632 | 0.395816 | − | 0.918330i | \(-0.370462\pi\) | ||||
0.395816 | + | 0.918330i | \(0.370462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −86.9117 | −3.70593 | ||||||||
\(551\) | 7.24264 | 0.308547 | ||||||||
\(552\) | −0.686292 | −0.0292105 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.4142 | −0.569915 | ||||||||
\(555\) | 38.9706 | 1.65421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | −0.508456 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(558\) | −7.41421 | −0.313869 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.48528 | 0.358249 | ||||||||
\(562\) | −22.0000 | −0.928014 | ||||||||
\(563\) | 17.6569 | 0.744148 | 0.372074 | − | 0.928203i | \(-0.378647\pi\) | ||||
0.372074 | + | 0.928203i | \(0.378647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −89.6690 | −3.77241 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.02944 | −0.127112 | ||||||||
\(569\) | −23.1421 | −0.970169 | −0.485084 | − | 0.874467i | \(-0.661211\pi\) | ||||
−0.485084 | + | 0.874467i | \(0.661211\pi\) | |||||||
\(570\) | −10.9706 | −0.459506 | ||||||||
\(571\) | −8.45584 | −0.353866 | −0.176933 | − | 0.984223i | \(-0.556618\pi\) | ||||
−0.176933 | + | 0.984223i | \(0.556618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.4558 | 1.23054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.48528 | −0.103643 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 26.9706 | 1.12280 | 0.561400 | − | 0.827545i | \(-0.310263\pi\) | ||||
0.561400 | + | 0.827545i | \(0.310263\pi\) | |||||||
\(578\) | 21.2132 | 0.882353 | ||||||||
\(579\) | −3.51472 | −0.146067 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 27.4558 | 1.13808 | ||||||||
\(583\) | −24.7279 | −1.02413 | ||||||||
\(584\) | −2.14214 | −0.0886422 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.2426 | 1.24931 | ||||||||
\(587\) | 24.5563 | 1.01355 | 0.506775 | − | 0.862079i | \(-0.330838\pi\) | ||||
0.506775 | + | 0.862079i | \(0.330838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51472 | −0.268434 | ||||||||
\(590\) | −72.7696 | −2.99588 | ||||||||
\(591\) | −33.4558 | −1.37619 | ||||||||
\(592\) | −24.9706 | −1.02628 | ||||||||
\(593\) | 30.5563 | 1.25480 | 0.627399 | − | 0.778698i | \(-0.284119\pi\) | ||||
0.627399 | + | 0.778698i | \(0.284119\pi\) | |||||||
\(594\) | 33.9411 | 1.39262 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.3137 | 0.708603 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.7990 | 0.441235 | 0.220617 | − | 0.975360i | \(-0.429193\pi\) | ||||
0.220617 | + | 0.975360i | \(0.429193\pi\) | |||||||
\(600\) | 57.9411 | 2.36544 | ||||||||
\(601\) | 5.02944 | 0.205155 | 0.102578 | − | 0.994725i | \(-0.467291\pi\) | ||||
0.102578 | + | 0.994725i | \(0.467291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.48528 | 0.101208 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.8995 | 1.25624 | ||||||||
\(606\) | 3.51472 | 0.142776 | ||||||||
\(607\) | 1.27208 | 0.0516321 | 0.0258160 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258160 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.4558 | 1.51654 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0000 | 0.646234 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(614\) | −6.72792 | −0.271517 | ||||||||
\(615\) | 19.7990 | 0.798372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.6569 | −0.952389 | −0.476195 | − | 0.879340i | \(-0.657984\pi\) | ||||
−0.476195 | + | 0.879340i | \(0.657984\pi\) | |||||||
\(618\) | −16.0000 | −0.643614 | ||||||||
\(619\) | −32.9706 | −1.32520 | −0.662599 | − | 0.748974i | \(-0.730547\pi\) | ||||
−0.662599 | + | 0.748974i | \(0.730547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.970563 | 0.0389473 | ||||||||
\(622\) | −6.48528 | −0.260036 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 112.397 | 4.49588 | ||||||||
\(626\) | −27.1716 | −1.08599 | ||||||||
\(627\) | 7.45584 | 0.297758 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.82843 | 0.352012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | −4.20101 | −0.167107 | ||||||||
\(633\) | 25.4142 | 1.01012 | ||||||||
\(634\) | 16.0000 | 0.635441 | ||||||||
\(635\) | 8.82843 | 0.350345 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −34.9706 | −1.38450 | ||||||||
\(639\) | 1.07107 | 0.0423708 | ||||||||
\(640\) | −49.9411 | −1.97410 | ||||||||
\(641\) | 26.6569 | 1.05288 | 0.526441 | − | 0.850212i | \(-0.323526\pi\) | ||||
0.526441 | + | 0.850212i | \(0.323526\pi\) | |||||||
\(642\) | −16.2843 | −0.642689 | ||||||||
\(643\) | 4.48528 | 0.176882 | 0.0884411 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884411 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.2132 | −1.22902 | ||||||||
\(646\) | −2.48528 | −0.0977821 | ||||||||
\(647\) | 50.5269 | 1.98642 | 0.993209 | − | 0.116344i | \(-0.0371176\pi\) | ||||
0.993209 | + | 0.116344i | \(0.0371176\pi\) | |||||||
\(648\) | −14.1421 | −0.555556 | ||||||||
\(649\) | 49.4558 | 1.94131 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.31371 | −0.207941 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(654\) | −17.4558 | −0.682578 | ||||||||
\(655\) | −12.4853 | −0.487840 | ||||||||
\(656\) | −12.6863 | −0.495316 | ||||||||
\(657\) | 0.757359 | 0.0295474 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.6569 | −1.03840 | −0.519202 | − | 0.854652i | \(-0.673771\pi\) | ||||
−0.519202 | + | 0.854652i | \(0.673771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.2426 | −0.748452 | −0.374226 | − | 0.927338i | \(-0.622092\pi\) | ||||
−0.374226 | + | 0.927338i | \(0.622092\pi\) | |||||||
\(662\) | −25.4558 | −0.989369 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.4558 | 0.522188 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.82843 | 0.342095 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.0711 | 0.505357 | ||||||||
\(670\) | 15.5147 | 0.599386 | ||||||||
\(671\) | −25.4558 | −0.982712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.9411 | 1.57816 | 0.789082 | − | 0.614288i | \(-0.210557\pi\) | ||||
0.789082 | + | 0.614288i | \(0.210557\pi\) | |||||||
\(674\) | 46.6690 | 1.79762 | ||||||||
\(675\) | −81.9411 | −3.15392 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.3553 | −1.12822 | −0.564109 | − | 0.825701i | \(-0.690780\pi\) | ||||
−0.564109 | + | 0.825701i | \(0.690780\pi\) | |||||||
\(678\) | 40.6274 | 1.56029 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.6569 | 0.677109 | ||||||||
\(681\) | 29.9411 | 1.14735 | ||||||||
\(682\) | 31.4558 | 1.20451 | ||||||||
\(683\) | 26.8284 | 1.02656 | 0.513281 | − | 0.858221i | \(-0.328430\pi\) | ||||
0.513281 | + | 0.858221i | \(0.328430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.7279 | 1.25047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.3431 | −1.15766 | ||||||||
\(688\) | 20.0000 | 0.762493 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.51472 | 0.0576644 | ||||||||
\(691\) | −30.6985 | −1.16783 | −0.583913 | − | 0.811816i | \(-0.698479\pi\) | ||||
−0.583913 | + | 0.811816i | \(0.698479\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | −0.303676 | ||||||||
\(695\) | 9.89949 | 0.375509 | ||||||||
\(696\) | 23.3137 | 0.883704 | ||||||||
\(697\) | 4.48528 | 0.169892 | ||||||||
\(698\) | 0.384776 | 0.0145640 | ||||||||
\(699\) | −4.72792 | −0.178826 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.7990 | 1.08772 | 0.543861 | − | 0.839175i | \(-0.316962\pi\) | ||||
0.543861 | + | 0.839175i | \(0.316962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.75736 | 0.292574 | ||||||||
\(704\) | 33.9411 | 1.27920 | ||||||||
\(705\) | 27.5563 | 1.03783 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7279 | 0.928677 | 0.464338 | − | 0.885658i | \(-0.346292\pi\) | ||||
0.464338 | + | 0.885658i | \(0.346292\pi\) | |||||||
\(710\) | 6.68629 | 0.250932 | ||||||||
\(711\) | 1.48528 | 0.0557024 | ||||||||
\(712\) | 12.4853 | 0.467906 | ||||||||
\(713\) | 0.899495 | 0.0336864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.9706 | −1.08193 | ||||||||
\(718\) | −11.4558 | −0.427528 | ||||||||
\(719\) | 10.2426 | 0.381986 | 0.190993 | − | 0.981591i | \(-0.438829\pi\) | ||||
0.190993 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(720\) | 17.6569 | 0.658032 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 24.6863 | 0.918729 | ||||||||
\(723\) | 31.4142 | 1.16831 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 84.4264 | 3.13552 | ||||||||
\(726\) | −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 | ||||||||
\(730\) | 4.72792 | 0.174988 | ||||||||
\(731\) | −7.07107 | −0.261533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.6985 | 1.57710 | 0.788552 | − | 0.614968i | \(-0.210831\pi\) | ||||
0.788552 | + | 0.614968i | \(0.210831\pi\) | |||||||
\(734\) | 2.48528 | 0.0917334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5442 | −0.388399 | ||||||||
\(738\) | 4.48528 | 0.165105 | ||||||||
\(739\) | −41.6985 | −1.53390 | −0.766952 | − | 0.641705i | \(-0.778227\pi\) | ||||
−0.766952 | + | 0.641705i | \(0.778227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3431 | 0.672945 | 0.336472 | − | 0.941693i | \(-0.390766\pi\) | ||||
0.336472 | + | 0.941693i | \(0.390766\pi\) | |||||||
\(744\) | −20.9706 | −0.768818 | ||||||||
\(745\) | −34.2426 | −1.25455 | ||||||||
\(746\) | 12.0000 | 0.439351 | ||||||||
\(747\) | −4.75736 | −0.174063 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −83.7401 | −3.05776 | ||||||||
\(751\) | −1.48528 | −0.0541987 | −0.0270993 | − | 0.999633i | \(-0.508627\pi\) | ||||
−0.0270993 | + | 0.999633i | \(0.508627\pi\) | |||||||
\(752\) | −17.6569 | −0.643879 | ||||||||
\(753\) | −27.4558 | −1.00055 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 80.5269 | 2.93067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51472 | 0.164090 | 0.0820451 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820451 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(758\) | 45.5980 | 1.65619 | ||||||||
\(759\) | −1.02944 | −0.0373662 | ||||||||
\(760\) | 15.5147 | 0.562778 | ||||||||
\(761\) | 43.2426 | 1.56754 | 0.783772 | − | 0.621048i | \(-0.213293\pi\) | ||||
0.783772 | + | 0.621048i | \(0.213293\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.24264 | −0.225703 | ||||||||
\(766\) | 4.97056 | 0.179594 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.78680 | 0.352921 | 0.176460 | − | 0.984308i | \(-0.443535\pi\) | ||||
0.176460 | + | 0.984308i | \(0.443535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.4558 | 0.844742 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.1716 | −0.977294 | −0.488647 | − | 0.872482i | \(-0.662509\pi\) | ||||
−0.488647 | + | 0.872482i | \(0.662509\pi\) | |||||||
\(774\) | −7.07107 | −0.254164 | ||||||||
\(775\) | −75.9411 | −2.72789 | ||||||||
\(776\) | −38.8284 | −1.39386 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.9411 | −0.930034 | ||||||||
\(779\) | 3.94113 | 0.141205 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.54416 | −0.162603 | ||||||||
\(782\) | 0.343146 | 0.0122709 | ||||||||
\(783\) | −32.9706 | −1.17827 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54.0416 | 1.92883 | ||||||||
\(786\) | 5.65685 | 0.201773 | ||||||||
\(787\) | −33.2426 | −1.18497 | −0.592486 | − | 0.805581i | \(-0.701853\pi\) | ||||
−0.592486 | + | 0.805581i | \(0.701853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −45.2132 | −1.60963 | ||||||||
\(790\) | 9.27208 | 0.329886 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −34.2426 | −1.21523 | ||||||||
\(795\) | −36.3848 | −1.29044 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.6569 | 1.26303 | 0.631515 | − | 0.775363i | \(-0.282433\pi\) | ||||
0.631515 | + | 0.775363i | \(0.282433\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.24264 | 0.220849 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.41421 | −0.155969 | ||||||||
\(802\) | 24.9706 | 0.881741 | ||||||||
\(803\) | −3.21320 | −0.113391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.9706 | −0.738199 | ||||||||
\(808\) | −4.97056 | −0.174864 | ||||||||
\(809\) | 0.514719 | 0.0180965 | 0.00904827 | − | 0.999959i | \(-0.497120\pi\) | ||||
0.00904827 | + | 0.999959i | \(0.497120\pi\) | |||||||
\(810\) | 31.2132 | 1.09672 | ||||||||
\(811\) | 45.9411 | 1.61321 | 0.806606 | − | 0.591090i | \(-0.201302\pi\) | ||||
0.806606 | + | 0.591090i | \(0.201302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2843 | 0.991973 | ||||||||
\(814\) | −37.4558 | −1.31283 | ||||||||
\(815\) | 37.4558 | 1.31202 | ||||||||
\(816\) | −8.00000 | −0.280056 | ||||||||
\(817\) | −6.21320 | −0.217372 | ||||||||
\(818\) | 7.41421 | 0.259232 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.14214 | −0.284162 | −0.142081 | − | 0.989855i | \(-0.545379\pi\) | ||||
−0.142081 | + | 0.989855i | \(0.545379\pi\) | |||||||
\(822\) | −14.8284 | −0.517201 | ||||||||
\(823\) | −6.48528 | −0.226063 | −0.113031 | − | 0.993591i | \(-0.536056\pi\) | ||||
−0.113031 | + | 0.993591i | \(0.536056\pi\) | |||||||
\(824\) | 22.6274 | 0.788263 | ||||||||
\(825\) | 86.9117 | 3.02588 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.45584 | −0.0506247 | −0.0253123 | − | 0.999680i | \(-0.508058\pi\) | ||||
−0.0253123 | + | 0.999680i | \(0.508058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.2721 | −0.877736 | −0.438868 | − | 0.898552i | \(-0.644620\pi\) | ||||
−0.438868 | + | 0.898552i | \(0.644620\pi\) | |||||||
\(830\) | −29.6985 | −1.03085 | ||||||||
\(831\) | 13.4142 | 0.465334 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.48528 | −0.155313 | ||||||||
\(835\) | −94.3970 | −3.26674 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.6569 | 1.02509 | ||||||||
\(838\) | 46.4853 | 1.60581 | ||||||||
\(839\) | −38.8284 | −1.34051 | −0.670253 | − | 0.742133i | \(-0.733814\pi\) | ||||
−0.670253 | + | 0.742133i | \(0.733814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.97056 | 0.171399 | ||||||||
\(842\) | −26.4853 | −0.912743 | ||||||||
\(843\) | 22.0000 | 0.757720 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.24264 | 0.214626 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.3137 | 0.800596 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | −28.9706 | −0.993682 | ||||||||
\(851\) | −1.07107 | −0.0367157 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2721 | 0.488667 | 0.244333 | − | 0.969691i | \(-0.421431\pi\) | ||||
0.244333 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48528 | −0.187593 | ||||||||
\(856\) | 23.0294 | 0.787130 | ||||||||
\(857\) | −18.7696 | −0.641156 | −0.320578 | − | 0.947222i | \(-0.603877\pi\) | ||||
−0.320578 | + | 0.947222i | \(0.603877\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.97056 | 0.101354 | 0.0506771 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506771 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.4558 | −1.13951 | ||||||||
\(863\) | 28.2843 | 0.962808 | 0.481404 | − | 0.876499i | \(-0.340127\pi\) | ||||
0.481404 | + | 0.876499i | \(0.340127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.21320 | 0.109252 | ||||||||
\(866\) | 12.6863 | 0.431098 | ||||||||
\(867\) | −21.2132 | −0.720438 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.30152 | −0.213764 | ||||||||
\(870\) | −51.4558 | −1.74452 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 24.6863 | 0.835983 | ||||||||
\(873\) | 13.7279 | 0.464620 | ||||||||
\(874\) | 0.301515 | 0.0101989 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.75736 | 0.0593418 | 0.0296709 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296709 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(878\) | −24.7696 | −0.835932 | ||||||||
\(879\) | −30.2426 | −1.02006 | ||||||||
\(880\) | −74.9117 | −2.52527 | ||||||||
\(881\) | 49.1127 | 1.65465 | 0.827324 | − | 0.561724i | \(-0.189862\pi\) | ||||
0.827324 | + | 0.561724i | \(0.189862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 72.7696 | 2.44612 | ||||||||
\(886\) | 37.2132 | 1.25020 | ||||||||
\(887\) | 43.1127 | 1.44758 | 0.723791 | − | 0.690019i | \(-0.242398\pi\) | ||||
0.723791 | + | 0.690019i | \(0.242398\pi\) | |||||||
\(888\) | 24.9706 | 0.837957 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.5563 | −0.923691 | ||||||||
\(891\) | −21.2132 | −0.710669 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.48528 | 0.183558 | ||||||||
\(894\) | 15.5147 | 0.518890 | ||||||||
\(895\) | −39.7279 | −1.32796 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.9411 | 1.26611 | ||||||||
\(899\) | −30.5563 | −1.01911 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.24264 | −0.274602 | ||||||||
\(902\) | −19.0294 | −0.633611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −57.4558 | −1.91095 | ||||||||
\(905\) | −29.6985 | −0.987211 | ||||||||
\(906\) | −36.4853 | −1.21214 | ||||||||
\(907\) | −31.9706 | −1.06157 | −0.530783 | − | 0.847508i | \(-0.678102\pi\) | ||||
−0.530783 | + | 0.847508i | \(0.678102\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.75736 | 0.0582879 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0294 | −0.332290 | −0.166145 | − | 0.986101i | \(-0.553132\pi\) | ||||
−0.166145 | + | 0.986101i | \(0.553132\pi\) | |||||||
\(912\) | −7.02944 | −0.232768 | ||||||||
\(913\) | 20.1838 | 0.667985 | ||||||||
\(914\) | 49.7990 | 1.64720 | ||||||||
\(915\) | −37.4558 | −1.23825 | ||||||||
\(916\) | 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 | \(0.370452\pi\) | |||||||
\(920\) | −2.14214 | −0.0706241 | ||||||||
\(921\) | 6.72792 | 0.221693 | ||||||||
\(922\) | −4.48528 | −0.147715 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 90.4264 | 2.97320 | ||||||||
\(926\) | 6.00000 | 0.197172 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.1005 | 0.561049 | 0.280525 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280525 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(930\) | 46.2843 | 1.51772 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.48528 | 0.212319 | ||||||||
\(934\) | 22.4853 | 0.735741 | ||||||||
\(935\) | 26.4853 | 0.866161 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.78680 | −0.0910407 | −0.0455203 | − | 0.998963i | \(-0.514495\pi\) | ||||
−0.0455203 | + | 0.998963i | \(0.514495\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.1716 | 0.886711 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.9289 | 0.845259 | 0.422630 | − | 0.906303i | \(-0.361107\pi\) | ||||
0.422630 | + | 0.906303i | \(0.361107\pi\) | |||||||
\(942\) | −24.4853 | −0.797774 | ||||||||
\(943\) | −0.544156 | −0.0177202 | ||||||||
\(944\) | −46.6274 | −1.51759 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −20.8284 | −0.676833 | −0.338416 | − | 0.940996i | \(-0.609891\pi\) | ||||
−0.338416 | + | 0.940996i | \(0.609891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −25.4558 | −0.825897 | ||||||||
\(951\) | −16.0000 | −0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1421 | −0.555288 | −0.277644 | − | 0.960684i | \(-0.589554\pi\) | ||||
−0.277644 | + | 0.960684i | \(0.589554\pi\) | |||||||
\(954\) | −8.24264 | −0.266865 | ||||||||
\(955\) | 91.9411 | 2.97514 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.9706 | 1.13044 | ||||||||
\(958\) | −51.2132 | −1.65462 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 49.9411 | 1.61184 | ||||||||
\(961\) | −3.51472 | −0.113378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.14214 | −0.262377 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.9706 | −0.353155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.6985 | 1.34093 | 0.670466 | − | 0.741940i | \(-0.266094\pi\) | ||||
0.670466 | + | 0.741940i | \(0.266094\pi\) | |||||||
\(968\) | 19.7990 | 0.636364 | ||||||||
\(969\) | 2.48528 | 0.0798387 | ||||||||
\(970\) | 85.6985 | 2.75161 | ||||||||
\(971\) | 7.45584 | 0.239269 | 0.119635 | − | 0.992818i | \(-0.461828\pi\) | ||||
0.119635 | + | 0.992818i | \(0.461828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 55.7990 | 1.78791 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.0000 | 0.768221 | ||||||||
\(977\) | 24.0416 | 0.769160 | 0.384580 | − | 0.923092i | \(-0.374346\pi\) | ||||
0.384580 | + | 0.923092i | \(0.374346\pi\) | |||||||
\(978\) | −16.9706 | −0.542659 | ||||||||
\(979\) | 18.7279 | 0.598547 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.72792 | −0.278661 | ||||||||
\(982\) | 40.4853 | 1.29194 | ||||||||
\(983\) | 33.0416 | 1.05386 | 0.526932 | − | 0.849907i | \(-0.323342\pi\) | ||||
0.526932 | + | 0.849907i | \(0.323342\pi\) | |||||||
\(984\) | 12.6863 | 0.404424 | ||||||||
\(985\) | −104.426 | −3.32730 | ||||||||
\(986\) | −11.6569 | −0.371230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.857864 | 0.0272785 | ||||||||
\(990\) | 26.4853 | 0.841757 | ||||||||
\(991\) | 34.9706 | 1.11088 | 0.555438 | − | 0.831558i | \(-0.312551\pi\) | ||||
0.555438 | + | 0.831558i | \(0.312551\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.4558 | 0.807817 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 54.0416 | 1.71323 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4853 | 0.902138 | 0.451069 | − | 0.892489i | \(-0.351043\pi\) | ||||
0.451069 | + | 0.892489i | \(0.351043\pi\) | |||||||
\(998\) | −54.7696 | −1.73370 | ||||||||
\(999\) | −35.3137 | −1.11728 |
(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.1.1 | 2 | ||
7.6 | odd | 2 | 1183.2.a.d.1.1 | 2 | |||
13.12 | even | 2 | 637.2.a.g.1.2 | 2 | |||
39.38 | odd | 2 | 5733.2.a.s.1.1 | 2 | |||
91.12 | odd | 6 | 637.2.e.f.508.1 | 4 | |||
91.25 | even | 6 | 637.2.e.g.79.1 | 4 | |||
91.34 | even | 4 | 1183.2.c.d.337.1 | 4 | |||
91.38 | odd | 6 | 637.2.e.f.79.1 | 4 | |||
91.51 | even | 6 | 637.2.e.g.508.1 | 4 | |||
91.83 | even | 4 | 1183.2.c.d.337.3 | 4 | |||
91.90 | odd | 2 | 91.2.a.c.1.2 | ✓ | 2 | ||
273.272 | even | 2 | 819.2.a.h.1.1 | 2 | |||
364.363 | even | 2 | 1456.2.a.q.1.2 | 2 | |||
455.454 | odd | 2 | 2275.2.a.j.1.1 | 2 | |||
728.181 | odd | 2 | 5824.2.a.bl.1.2 | 2 | |||
728.363 | even | 2 | 5824.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.c.1.2 | ✓ | 2 | 91.90 | odd | 2 | ||
637.2.a.g.1.2 | 2 | 13.12 | even | 2 | |||
637.2.e.f.79.1 | 4 | 91.38 | odd | 6 | |||
637.2.e.f.508.1 | 4 | 91.12 | odd | 6 | |||
637.2.e.g.79.1 | 4 | 91.25 | even | 6 | |||
637.2.e.g.508.1 | 4 | 91.51 | even | 6 | |||
819.2.a.h.1.1 | 2 | 273.272 | even | 2 | |||
1183.2.a.d.1.1 | 2 | 7.6 | odd | 2 | |||
1183.2.c.d.337.1 | 4 | 91.34 | even | 4 | |||
1183.2.c.d.337.3 | 4 | 91.83 | even | 4 | |||
1456.2.a.q.1.2 | 2 | 364.363 | even | 2 | |||
2275.2.a.j.1.1 | 2 | 455.454 | odd | 2 | |||
5733.2.a.s.1.1 | 2 | 39.38 | odd | 2 | |||
5824.2.a.bk.1.1 | 2 | 728.363 | even | 2 | |||
5824.2.a.bl.1.2 | 2 | 728.181 | odd | 2 | |||
8281.2.a.v.1.1 | 2 | 1.1 | even | 1 | trivial |