Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1716) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 1.06904 | 0.534522 | − | 0.845154i | \(-0.320491\pi\) | ||||
0.534522 | + | 0.845154i | \(0.320491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.24264 | 0.543920 | 0.271960 | − | 0.962309i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962309i | \(0.412328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | −0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.828427 | −0.172739 | −0.0863695 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863695 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.41421 | −0.634004 | −0.317002 | − | 0.948425i | \(-0.602676\pi\) | ||||
−0.317002 | + | 0.948425i | \(0.602676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.58579 | 0.464421 | 0.232210 | − | 0.972666i | \(-0.425404\pi\) | ||||
0.232210 | + | 0.972666i | \(0.425404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.65685 | −0.280059 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.82843 | −0.793789 | −0.396894 | − | 0.917864i | \(-0.629912\pi\) | ||||
−0.396894 | + | 0.917864i | \(0.629912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.24264 | −1.25699 | −0.628495 | − | 0.777813i | \(-0.716329\pi\) | ||||
−0.628495 | + | 0.777813i | \(0.716329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.585786 | −0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.24264 | −0.314033 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.3137 | −1.82878 | −0.914389 | − | 0.404836i | \(-0.867329\pi\) | ||||
−0.914389 | + | 0.404836i | \(0.867329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.585786 | −0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.82843 | −1.13036 | −0.565182 | − | 0.824966i | \(-0.691194\pi\) | ||||
−0.565182 | + | 0.824966i | \(0.691194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.585786 | 0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.24264 | 0.518321 | 0.259161 | − | 0.965834i | \(-0.416554\pi\) | ||||
0.259161 | + | 0.965834i | \(0.416554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.17157 | 0.613753 | 0.306876 | − | 0.951749i | \(-0.400716\pi\) | ||||
0.306876 | + | 0.951749i | \(0.400716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.65685 | 0.662085 | 0.331042 | − | 0.943616i | \(-0.392600\pi\) | ||||
0.331042 | + | 0.943616i | \(0.392600\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82843 | 0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.07107 | −0.795557 | −0.397779 | − | 0.917481i | \(-0.630219\pi\) | ||||
−0.397779 | + | 0.917481i | \(0.630219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.34315 | 0.696251 | 0.348125 | − | 0.937448i | \(-0.386818\pi\) | ||||
0.348125 | + | 0.937448i | \(0.386818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31371 | −0.142492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41421 | 0.366042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.89949 | 0.837345 | 0.418672 | − | 0.908137i | \(-0.362496\pi\) | ||||
0.418672 | + | 0.908137i | \(0.362496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.58579 | −0.268134 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.17157 | −0.728163 | −0.364081 | − | 0.931367i | \(-0.618617\pi\) | ||||
−0.364081 | + | 0.931367i | \(0.618617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.72792 | 0.669453 | 0.334727 | − | 0.942315i | \(-0.391356\pi\) | ||||
0.334727 | + | 0.942315i | \(0.391356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.65685 | 0.161692 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.82843 | −0.660129 | −0.330064 | − | 0.943958i | \(-0.607070\pi\) | ||||
−0.330064 | + | 0.943958i | \(0.607070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.31371 | 0.700526 | 0.350263 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350263 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.82843 | 0.458294 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9706 | −1.40831 | −0.704156 | − | 0.710045i | \(-0.748674\pi\) | ||||
−0.704156 | + | 0.710045i | \(0.748674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.485281 | 0.0452527 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.34315 | 0.581475 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.65685 | 0.690395 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.07107 | −0.627456 | −0.313728 | − | 0.949513i | \(-0.601578\pi\) | ||||
−0.313728 | + | 0.949513i | \(0.601578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.24264 | 0.725724 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.585786 | 0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.07107 | −0.0915075 | −0.0457537 | − | 0.998953i | \(-0.514569\pi\) | ||||
−0.0457537 | + | 0.998953i | \(0.514569\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.242641 | 0.0205805 | 0.0102903 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102903 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.4853 | −1.18668 | −0.593340 | − | 0.804952i | \(-0.702191\pi\) | ||||
−0.593340 | + | 0.804952i | \(0.702191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.24264 | 0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.51472 | −0.121665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6569 | 1.40917 | 0.704585 | − | 0.709619i | \(-0.251133\pi\) | ||||
0.704585 | + | 0.709619i | \(0.251133\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.34315 | −0.184666 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7279 | −0.996928 | −0.498464 | − | 0.866910i | \(-0.666102\pi\) | ||||
−0.498464 | + | 0.866910i | \(0.666102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.585786 | 0.0456034 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.100505 | 0.00764126 | 0.00382063 | − | 0.999993i | \(-0.498784\pi\) | ||||
0.00382063 | + | 0.999993i | \(0.498784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.1716 | −0.995677 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.82843 | −0.212598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.828427 | 0.0619196 | 0.0309598 | − | 0.999521i | \(-0.490144\pi\) | ||||
0.0309598 | + | 0.999521i | \(0.490144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.97056 | −0.666777 | −0.333388 | − | 0.942790i | \(-0.608192\pi\) | ||||
−0.333388 | + | 0.942790i | \(0.608192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.82843 | 0.652616 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.82843 | 0.207950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24264 | 0.163998 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6569 | 0.988175 | 0.494088 | − | 0.869412i | \(-0.335502\pi\) | ||||
0.494088 | + | 0.869412i | \(0.335502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.65685 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.585786 | −0.0419490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1421 | 1.15008 | 0.575040 | − | 0.818125i | \(-0.304987\pi\) | ||||
0.575040 | + | 0.818125i | \(0.304987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4853 | −0.885058 | −0.442529 | − | 0.896754i | \(-0.645919\pi\) | ||||
−0.442529 | + | 0.896754i | \(0.645919\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.24264 | −0.299253 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.65685 | −0.677778 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.48528 | 0.313266 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.828427 | −0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4142 | −0.923473 | −0.461736 | − | 0.887017i | \(-0.652773\pi\) | ||||
−0.461736 | + | 0.887017i | \(0.652773\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.17157 | −0.354350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.82843 | 0.329296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.31371 | 0.496487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.65685 | −0.382255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24264 | −0.150856 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.10051 | 0.140660 | 0.0703301 | − | 0.997524i | \(-0.477595\pi\) | ||||
0.0703301 | + | 0.997524i | \(0.477595\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1421 | 1.07139 | 0.535696 | − | 0.844411i | \(-0.320049\pi\) | ||||
0.535696 | + | 0.844411i | \(0.320049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3137 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.82843 | −0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4142 | 0.747770 | 0.373885 | − | 0.927475i | \(-0.378025\pi\) | ||||
0.373885 | + | 0.927475i | \(0.378025\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.68629 | −0.305700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.07107 | 0.459315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.14214 | 0.526671 | 0.263335 | − | 0.964704i | \(-0.415177\pi\) | ||||
0.263335 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6569 | −0.750884 | −0.375442 | − | 0.926846i | \(-0.622509\pi\) | ||||
−0.375442 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.585786 | −0.0374245 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.34315 | −0.401981 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3431 | −0.905331 | −0.452666 | − | 0.891680i | \(-0.649527\pi\) | ||||
−0.452666 | + | 0.891680i | \(0.649527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.828427 | −0.0520828 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.31371 | 0.0822676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.82843 | 0.301189 | 0.150595 | − | 0.988596i | \(-0.451881\pi\) | ||||
0.150595 | + | 0.988596i | \(0.451881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6569 | −0.848596 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.41421 | −0.211335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528 | 0.523225 | 0.261612 | − | 0.965173i | \(-0.415746\pi\) | ||||
0.261612 | + | 0.965173i | \(0.415746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.79899 | 0.479088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.89949 | −0.483441 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.17157 | −0.193374 | −0.0966871 | − | 0.995315i | \(-0.530825\pi\) | ||||
−0.0966871 | + | 0.995315i | \(0.530825\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.65685 | 0.586612 | 0.293306 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293306 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | 0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.65685 | −0.280819 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9706 | −1.13983 | −0.569915 | − | 0.821703i | \(-0.693024\pi\) | ||||
−0.569915 | + | 0.821703i | \(0.693024\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.58579 | 0.154807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3431 | −0.736330 | −0.368165 | − | 0.929760i | \(-0.620014\pi\) | ||||
−0.368165 | + | 0.929760i | \(0.620014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9289 | −0.768545 | −0.384273 | − | 0.923220i | \(-0.625548\pi\) | ||||
−0.384273 | + | 0.923220i | \(0.625548\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.6569 | −1.27836 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.17157 | 0.420405 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4853 | −1.07992 | −0.539961 | − | 0.841690i | \(-0.681561\pi\) | ||||
−0.539961 | + | 0.841690i | \(0.681561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.65685 | −0.0964658 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.828427 | 0.0479092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3137 | −1.34378 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.72792 | −0.386509 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.17157 | 0.296123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.82843 | 0.160904 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1716 | 1.08712 | 0.543560 | − | 0.839370i | \(-0.317076\pi\) | ||||
0.543560 | + | 0.839370i | \(0.317076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.6274 | 1.27898 | 0.639489 | − | 0.768801i | \(-0.279146\pi\) | ||||
0.639489 | + | 0.768801i | \(0.279146\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.65685 | −0.0933532 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.0711 | −1.18347 | −0.591735 | − | 0.806133i | \(-0.701557\pi\) | ||||
−0.591735 | + | 0.806133i | \(0.701557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.41421 | −0.191159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.82843 | 0.381126 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.65685 | 0.258316 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.31371 | −0.404449 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.443651 | −0.0243853 | −0.0121926 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121926 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.82843 | −0.264596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.48528 | −0.135785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4853 | 1.44275 | 0.721373 | − | 0.692547i | \(-0.243512\pi\) | ||||
0.721373 | + | 0.692547i | \(0.243512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.9706 | 0.813089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.58579 | 0.140028 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.485281 | −0.0261267 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.3431 | 0.769980 | 0.384990 | − | 0.922921i | \(-0.374205\pi\) | ||||
0.384990 | + | 0.922921i | \(0.374205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.9411 | 1.70977 | 0.854885 | − | 0.518818i | \(-0.173628\pi\) | ||||
0.854885 | + | 0.518818i | \(0.173628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7279 | −0.570990 | −0.285495 | − | 0.958380i | \(-0.592158\pi\) | ||||
−0.285495 | + | 0.958380i | \(0.592158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.02944 | −0.160786 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.34315 | −0.335715 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1421 | −0.640837 | −0.320419 | − | 0.947276i | \(-0.603824\pi\) | ||||
−0.320419 | + | 0.947276i | \(0.603824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.31371 | −0.173447 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.3137 | −1.63456 | −0.817281 | − | 0.576239i | \(-0.804520\pi\) | ||||
−0.817281 | + | 0.576239i | \(0.804520\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.65685 | −0.398600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −37.6569 | −1.95505 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.4558 | −1.62872 | −0.814361 | − | 0.580359i | \(-0.802912\pi\) | ||||
−0.814361 | + | 0.580359i | \(0.802912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41421 | 0.175841 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6985 | 1.52551 | 0.762754 | − | 0.646688i | \(-0.223847\pi\) | ||||
0.762754 | + | 0.646688i | \(0.223847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.07107 | 0.362262 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.7990 | −1.01168 | −0.505841 | − | 0.862627i | \(-0.668818\pi\) | ||||
−0.505841 | + | 0.862627i | \(0.668818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.65685 | −0.0844411 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.24264 | −0.418997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.7990 | 1.10525 | 0.552626 | − | 0.833429i | \(-0.313626\pi\) | ||||
0.552626 | + | 0.833429i | \(0.313626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85786 | −0.0939562 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.14214 | 0.208413 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.79899 | 0.0902887 | 0.0451444 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451444 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2132 | 1.15921 | 0.579606 | − | 0.814897i | \(-0.303206\pi\) | ||||
0.579606 | + | 0.814897i | \(0.303206\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.58579 | −0.128807 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.585786 | −0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.82843 | −0.239336 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6569 | 0.675288 | 0.337644 | − | 0.941274i | \(-0.390370\pi\) | ||||
0.337644 | + | 0.941274i | \(0.390370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.07107 | 0.0528319 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.71573 | −0.182398 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.242641 | −0.0118822 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.1716 | −1.13201 | −0.566003 | − | 0.824403i | \(-0.691511\pi\) | ||||
−0.566003 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6863 | −0.715766 | −0.357883 | − | 0.933766i | \(-0.616501\pi\) | ||||
−0.357883 | + | 0.933766i | \(0.616501\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.4437 | −0.506591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.9706 | −1.20841 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.34315 | 0.112865 | 0.0564327 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564327 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.58579 | −0.314322 | −0.157161 | − | 0.987573i | \(-0.550234\pi\) | ||||
−0.157161 | + | 0.987573i | \(0.550234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.686292 | 0.0326067 | 0.0163033 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163033 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.62742 | −0.219361 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.4853 | 0.685130 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4142 | 0.538670 | 0.269335 | − | 0.963047i | \(-0.413196\pi\) | ||||
0.269335 | + | 0.963047i | \(0.413196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.65685 | −0.360547 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65685 | 0.0776745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.68629 | 0.125659 | 0.0628297 | − | 0.998024i | \(-0.479988\pi\) | ||||
0.0628297 | + | 0.998024i | \(0.479988\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.24264 | −0.104678 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.9706 | −1.06985 | −0.534923 | − | 0.844901i | \(-0.679659\pi\) | ||||
−0.534923 | + | 0.844901i | \(0.679659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0711 | −1.25810 | −0.629050 | − | 0.777365i | \(-0.716556\pi\) | ||||
−0.629050 | + | 0.777365i | \(0.716556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.51472 | 0.0702434 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.4558 | −1.27050 | −0.635252 | − | 0.772305i | \(-0.719104\pi\) | ||||
−0.635252 | + | 0.772305i | \(0.719104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | 0.554109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.6569 | −0.813585 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.24264 | −0.378997 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3137 | −0.609593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.14214 | 0.189259 | 0.0946295 | − | 0.995513i | \(-0.469833\pi\) | ||||
0.0946295 | + | 0.995513i | \(0.469833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.82843 | 0.220157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.34315 | 0.106617 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.20101 | 0.190758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.5563 | −0.886183 | −0.443091 | − | 0.896476i | \(-0.646118\pi\) | ||||
−0.443091 | + | 0.896476i | \(0.646118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.7279 | 0.575577 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9706 | 0.585353 | 0.292677 | − | 0.956211i | \(-0.405454\pi\) | ||||
0.292677 | + | 0.956211i | \(0.405454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.65685 | −0.344847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.585786 | −0.0263291 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6274 | 0.656129 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.89949 | 0.443162 | 0.221581 | − | 0.975142i | \(-0.428878\pi\) | ||||
0.221581 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.3137 | −0.505459 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.51472 | 0.335065 | 0.167532 | − | 0.985867i | \(-0.446420\pi\) | ||||
0.167532 | + | 0.985867i | \(0.446420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.94113 | −0.175378 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.5563 | −0.955468 | −0.477734 | − | 0.878504i | \(-0.658542\pi\) | ||||
−0.477734 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0000 | 0.707798 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.65685 | 0.0730097 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.100505 | −0.00441168 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9706 | −0.831115 | −0.415558 | − | 0.909567i | \(-0.636414\pi\) | ||||
−0.415558 | + | 0.909567i | \(0.636414\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8995 | 0.957598 | 0.478799 | − | 0.877925i | \(-0.341072\pi\) | ||||
0.478799 | + | 0.877925i | \(0.341072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.1716 | 0.574855 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.79899 | 0.252608 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | 0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.65685 | 0.331655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.828427 | −0.0357493 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0000 | 0.773880 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.97056 | 0.384964 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.28427 | −0.183518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.8995 | −1.96252 | −0.981260 | − | 0.192687i | \(-0.938280\pi\) | ||||
−0.981260 | + | 0.192687i | \(0.938280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.82843 | −0.376788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | −0.850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.82843 | −0.120060 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.51472 | 0.403152 | 0.201576 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201576 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.24264 | 0.348627 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.24264 | −0.0946844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.65685 | −0.406988 | −0.203494 | − | 0.979076i | \(-0.565230\pi\) | ||||
−0.203494 | + | 0.979076i | \(0.565230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.76955 | 0.368938 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5563 | −0.736000 | −0.368000 | − | 0.929826i | \(-0.619957\pi\) | ||||
−0.368000 | + | 0.929826i | \(0.619957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0416 | −0.838716 | −0.419358 | − | 0.907821i | \(-0.637745\pi\) | ||||
−0.419358 | + | 0.907821i | \(0.637745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.6569 | −0.570523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.85786 | 0.160884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.97056 | −0.290188 | −0.145094 | − | 0.989418i | \(-0.546349\pi\) | ||||
−0.145094 | + | 0.989418i | \(0.546349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65685 | −0.235091 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.9411 | 0.744323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3137 | −0.551397 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.585786 | 0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.79899 | −0.321899 | −0.160949 | − | 0.986963i | \(-0.551456\pi\) | ||||
−0.160949 | + | 0.986963i | \(0.551456\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.1421 | −0.663999 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.8284 | −1.01958 | −0.509791 | − | 0.860298i | \(-0.670277\pi\) | ||||
−0.509791 | + | 0.860298i | \(0.670277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.71573 | −0.152330 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4853 | 0.510989 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.34315 | 0.0957383 | 0.0478692 | − | 0.998854i | \(-0.484757\pi\) | ||||
0.0478692 | + | 0.998854i | \(0.484757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.2548 | −1.92756 | −0.963782 | − | 0.266690i | \(-0.914070\pi\) | ||||
−0.963782 | + | 0.266690i | \(0.914070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.24264 | 0.172774 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.585786 | −0.0238156 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.2132 | 1.18573 | 0.592864 | − | 0.805303i | \(-0.297997\pi\) | ||||
0.592864 | + | 0.805303i | \(0.297997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.65685 | 0.391315 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.9411 | 1.20931 | 0.604655 | − | 0.796487i | \(-0.293311\pi\) | ||||
0.604655 | + | 0.796487i | \(0.293311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.48528 | −0.180864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.0711 | 1.65346 | 0.826729 | − | 0.562600i | \(-0.190199\pi\) | ||||
0.826729 | + | 0.562600i | \(0.190199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.58579 | −0.264705 | −0.132353 | − | 0.991203i | \(-0.542253\pi\) | ||||
−0.132353 | + | 0.991203i | \(0.542253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.3431 | 0.895159 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8284 | −0.431758 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.9289 | 1.15164 | 0.575821 | − | 0.817576i | \(-0.304682\pi\) | ||||
0.575821 | + | 0.817576i | \(0.304682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.4142 | 0.533167 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.14214 | 0.164376 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.17157 | 0.204584 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.5980 | −1.64302 | −0.821511 | − | 0.570193i | \(-0.806868\pi\) | ||||
−0.821511 | + | 0.570193i | \(0.806868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.5563 | −0.928972 | −0.464486 | − | 0.885581i | \(-0.653761\pi\) | ||||
−0.464486 | + | 0.885581i | \(0.653761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82843 | −0.190119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.3431 | −0.721143 | −0.360572 | − | 0.932731i | \(-0.617418\pi\) | ||||
−0.360572 | + | 0.932731i | \(0.617418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82843 | 0.111025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.31371 | −0.286647 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.1716 | −0.906774 | −0.453387 | − | 0.891314i | \(-0.649784\pi\) | ||||
−0.453387 | + | 0.891314i | \(0.649784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.68629 | 0.183109 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.65685 | 0.220695 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.1127 | −1.21198 | −0.605989 | − | 0.795473i | \(-0.707223\pi\) | ||||
−0.605989 | + | 0.795473i | \(0.707223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.17157 | 0.123360 | 0.0616799 | − | 0.998096i | \(-0.480354\pi\) | ||||
0.0616799 | + | 0.998096i | \(0.480354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.24264 | 0.0870969 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82843 | 0.109517 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.10051 | −0.0812102 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.82843 | −0.340818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.343146 | −0.0132273 | −0.00661365 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661365 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.2426 | −0.854854 | −0.427427 | − | 0.904050i | \(-0.640580\pi\) | ||||
−0.427427 | + | 0.904050i | \(0.640580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.2843 | −0.778439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.1421 | −0.618568 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.17157 | −0.0448290 | −0.0224145 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224145 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.627417 | 0.0239724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.3137 | 0.813169 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.3137 | 0.507212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5563 | 1.50479 | 0.752397 | − | 0.658710i | \(-0.228897\pi\) | ||||
0.752397 | + | 0.658710i | \(0.228897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.82843 | 0.107443 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.142136 | −0.00539151 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.1716 | −0.650420 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.4142 | −0.431725 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7574 | 0.821764 | 0.410882 | − | 0.911689i | \(-0.365221\pi\) | ||||
0.410882 | + | 0.911689i | \(0.365221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.68629 | 0.176496 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.0294 | 0.715676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.37258 | −0.126660 | −0.0633300 | − | 0.997993i | \(-0.520172\pi\) | ||||
−0.0633300 | + | 0.997993i | \(0.520172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.07107 | −0.265186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.14214 | −0.0802236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.585786 | 0.0219072 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.14214 | −0.304074 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.6863 | 0.473119 | 0.236559 | − | 0.971617i | \(-0.423980\pi\) | ||||
0.236559 | + | 0.971617i | \(0.423980\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6569 | 0.433523 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.8995 | 0.590492 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8284 | 0.846659 | 0.423330 | − | 0.905976i | \(-0.360861\pi\) | ||||
0.423330 | + | 0.905976i | \(0.360861\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4853 | −0.683703 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6274 | −1.13125 | −0.565625 | − | 0.824663i | \(-0.691365\pi\) | ||||
−0.565625 | + | 0.824663i | \(0.691365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.585786 | 0.0216071 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.24264 | 0.156280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.8284 | −0.545473 | −0.272736 | − | 0.962089i | \(-0.587929\pi\) | ||||
−0.272736 | + | 0.962089i | \(0.587929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.9411 | 1.53867 | 0.769335 | − | 0.638845i | \(-0.220588\pi\) | ||||
0.769335 | + | 0.638845i | \(0.220588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.48528 | 0.310877 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.34315 | 0.232084 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.3137 | −0.705708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.31371 | −0.120919 | −0.0604595 | − | 0.998171i | \(-0.519257\pi\) | ||||
−0.0604595 | + | 0.998171i | \(0.519257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.3431 | 0.522693 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.02944 | 0.255827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2843 | 1.17339 | 0.586696 | − | 0.809807i | \(-0.300428\pi\) | ||||
0.586696 | + | 0.809807i | \(0.300428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.828427 | 0.0300700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8284 | −0.900030 | −0.450015 | − | 0.893021i | \(-0.648581\pi\) | ||||
−0.450015 | + | 0.893021i | \(0.648581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.6863 | 0.748894 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.31371 | −0.0474972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.82843 | −0.102129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0000 | −0.649097 | −0.324548 | − | 0.945869i | \(-0.605212\pi\) | ||||
−0.324548 | + | 0.945869i | \(0.605212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.82843 | −0.173892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.41421 | −0.266671 | −0.133335 | − | 0.991071i | \(-0.542569\pi\) | ||||
−0.133335 | + | 0.991071i | \(0.542569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0416 | −0.432548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.6569 | 0.489937 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.17157 | 0.185053 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.41421 | 0.122014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.3431 | −0.369163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.7990 | −0.848342 | −0.424171 | − | 0.905582i | \(-0.639435\pi\) | ||||
−0.424171 | + | 0.905582i | \(0.639435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.48528 | −0.302084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.3431 | −1.50555 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.82843 | 0.313507 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.79899 | −0.276602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.4853 | 0.796470 | 0.398235 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398235 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.9411 | 0.634711 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.89949 | 0.279115 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.65685 | 0.199626 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.37258 | 0.0483772 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.17157 | 0.111645 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.3848 | 0.576058 | 0.288029 | − | 0.957622i | \(-0.407000\pi\) | ||||
0.288029 | + | 0.957622i | \(0.407000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.2843 | 1.41457 | 0.707286 | − | 0.706927i | \(-0.249919\pi\) | ||||
0.707286 | + | 0.706927i | \(0.249919\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.65685 | −0.338681 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.45584 | 0.261167 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.62742 | 0.161498 | 0.0807490 | − | 0.996734i | \(-0.474269\pi\) | ||||
0.0807490 | + | 0.996734i | \(0.474269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.4558 | 1.72392 | 0.861961 | − | 0.506974i | \(-0.169236\pi\) | ||||
0.861961 | + | 0.506974i | \(0.169236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.65685 | 0.162131 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.7696 | 1.06996 | 0.534981 | − | 0.844864i | \(-0.320319\pi\) | ||||
0.534981 | + | 0.844864i | \(0.320319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6863 | −0.649002 | −0.324501 | − | 0.945885i | \(-0.605196\pi\) | ||||
−0.324501 | + | 0.945885i | \(0.605196\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.9706 | 0.658082 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.24264 | 0.0777029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.62742 | −0.229351 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.58579 | −0.0893779 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.3431 | 1.04756 | 0.523781 | − | 0.851853i | \(-0.324521\pi\) | ||||
0.523781 | + | 0.851853i | \(0.324521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.3431 | −0.598040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.3431 | 0.425121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.585786 | −0.0201517 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.82843 | 0.0971859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.9289 | 0.443720 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.31371 | 0.181938 | 0.0909690 | − | 0.995854i | \(-0.471004\pi\) | ||||
0.0909690 | + | 0.995854i | \(0.471004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.9289 | 0.373325 | 0.186663 | − | 0.982424i | \(-0.440233\pi\) | ||||
0.186663 | + | 0.982424i | \(0.440233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.1716 | 0.585887 | 0.292943 | − | 0.956130i | \(-0.405365\pi\) | ||||
0.292943 | + | 0.956130i | \(0.405365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.7696 | 1.79630 | 0.898148 | − | 0.439693i | \(-0.144913\pi\) | ||||
0.898148 | + | 0.439693i | \(0.144913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0588745 | −0.00200179 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.07107 | −0.239870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.24264 | −0.143756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.17157 | −0.242721 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0000 | 0.540899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.3431 | 0.551869 | 0.275934 | − | 0.961176i | \(-0.411013\pi\) | ||||
0.275934 | + | 0.961176i | \(0.411013\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.4853 | 0.623493 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.9706 | 1.58248 | 0.791239 | − | 0.611507i | \(-0.209436\pi\) | ||||
0.791239 | + | 0.611507i | \(0.209436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.1716 | 0.981702 | 0.490851 | − | 0.871244i | \(-0.336686\pi\) | ||||
0.490851 | + | 0.871244i | \(0.336686\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.65685 | 0.0556945 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.48528 | 0.284908 | 0.142454 | − | 0.989801i | \(-0.454501\pi\) | ||||
0.142454 | + | 0.989801i | \(0.454501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | −0.670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.485281 | −0.0162212 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.828427 | −0.0276604 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.82843 | −0.294445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8579 | −0.994710 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.3137 | 0.775832 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.25483 | 0.174677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3137 | 0.375666 | 0.187833 | − | 0.982201i | \(-0.439854\pi\) | ||||
0.187833 | + | 0.982201i | \(0.439854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.72792 | 0.223151 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2843 | 0.406996 | 0.203498 | − | 0.979075i | \(-0.434769\pi\) | ||||
0.203498 | + | 0.979075i | \(0.434769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.34315 | 0.209927 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.17157 | −0.170967 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.6274 | −0.747223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.5858 | 1.27283 | 0.636414 | − | 0.771348i | \(-0.280417\pi\) | ||||
0.636414 | + | 0.771348i | \(0.280417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.0000 | 0.922631 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.17157 | −0.170224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4853 | 0.739311 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.82843 | −0.0928977 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.0711 | −1.08503 | −0.542513 | − | 0.840047i | \(-0.682527\pi\) | ||||
−0.542513 | + | 0.840047i | \(0.682527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.1716 | −0.627649 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.31371 | −0.0429629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2843 | −1.12002 | −0.560009 | − | 0.828486i | \(-0.689202\pi\) | ||||
−0.560009 | + | 0.828486i | \(0.689202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.6274 | −0.738418 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.34315 | 0.206561 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.65685 | 0.0538975 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.6274 | −1.12524 | −0.562620 | − | 0.826716i | \(-0.690207\pi\) | ||||
−0.562620 | + | 0.826716i | \(0.690207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.65685 | −0.183629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.0711 | 0.683276 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.5858 | 1.05556 | 0.527779 | − | 0.849382i | \(-0.323025\pi\) | ||||
0.527779 | + | 0.849382i | \(0.323025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.41421 | 0.110366 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.02944 | −0.0978256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3137 | −0.784313 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.82843 | −0.220043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.31371 | −0.106672 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.4264 | 1.23571 | 0.617855 | − | 0.786292i | \(-0.288002\pi\) | ||||
0.617855 | + | 0.786292i | \(0.288002\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8284 | 1.18188 | 0.590940 | − | 0.806715i | \(-0.298757\pi\) | ||||
0.590940 | + | 0.806715i | \(0.298757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.686292 | 0.0220015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.65685 | −0.149139 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.5563 | −0.561677 | −0.280839 | − | 0.959755i | \(-0.590613\pi\) | ||||
−0.280839 | + | 0.959755i | \(0.590613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.89949 | 0.252469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.31371 | 0.233509 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.5980 | 1.64572 | 0.822860 | − | 0.568244i | \(-0.192377\pi\) | ||||
0.822860 | + | 0.568244i | \(0.192377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.45584 | −0.301288 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6274 | −0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.82843 | 0.217131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.443651 | 0.0140788 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.31371 | 0.231860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1421 | −1.01795 | −0.508976 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508976 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.82843 | 0.152765 |
(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 | 6864.2.a.bb.1.2 | 2 | ||
4.3 | odd | 2 | 1716.2.a.e.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 5148.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1716.2.a.e.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5148.2.a.j.1.1 | 2 | 12.11 | even | 2 | |||
6864.2.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial |