Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5600,2,Mod(1,5600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5600.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: | \(44.7162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5600.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.47214 | −0.745377 | −0.372689 | − | 0.927957i | \(-0.621564\pi\) | ||||
−0.372689 | + | 0.927957i | \(0.621564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.23607 | −0.742405 | −0.371202 | − | 0.928552i | \(-0.621054\pi\) | ||||
−0.371202 | + | 0.928552i | \(0.621054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.9443 | 2.71325 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.472136 | 0.0737352 | 0.0368676 | − | 0.999320i | \(-0.488262\pi\) | ||||
0.0368676 | + | 0.999320i | \(0.488262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.52786 | 0.222862 | 0.111431 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111431 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.4721 | −2.02650 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4721 | 1.38707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.76393 | 0.620211 | 0.310106 | − | 0.950702i | \(-0.399636\pi\) | ||||
0.310106 | + | 0.950702i | \(0.399636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.76393 | 0.866033 | 0.433016 | − | 0.901386i | \(-0.357449\pi\) | ||||
0.433016 | + | 0.901386i | \(0.357449\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.9443 | −1.55831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9443 | −1.53620 | −0.768101 | − | 0.640328i | \(-0.778798\pi\) | ||||
−0.768101 | + | 0.640328i | \(0.778798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9443 | −1.74909 | −0.874547 | − | 0.484940i | \(-0.838841\pi\) | ||||
−0.874547 | + | 0.484940i | \(0.838841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.47214 | −0.281726 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427 | 0.556274 | 0.278137 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278137 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.76393 | −0.522909 | −0.261455 | − | 0.965216i | \(-0.584202\pi\) | ||||
−0.261455 | + | 0.965216i | \(0.584202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.4721 | −1.55158 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23607 | −0.548889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.9443 | 2.17182 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52786 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.4721 | −1.85652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7082 | 1.16501 | 0.582505 | − | 0.812827i | \(-0.302073\pi\) | ||||
0.582505 | + | 0.812827i | \(0.302073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4721 | −1.42598 | −0.712991 | − | 0.701173i | \(-0.752660\pi\) | ||||
−0.712991 | + | 0.701173i | \(0.752660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.94427 | −0.864675 | −0.432338 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.472136 | −0.0452224 | −0.0226112 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226112 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.4721 | 1.37363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.52786 | 0.331874 | 0.165937 | − | 0.986136i | \(-0.446935\pi\) | ||||
0.165937 | + | 0.986136i | \(0.446935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −39.1246 | −3.61707 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.47214 | 0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.88854 | −0.444413 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.52786 | −0.137763 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.94427 | −0.793676 | −0.396838 | − | 0.917889i | \(-0.629892\pi\) | ||||
−0.396838 | + | 0.917889i | \(0.629892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.70820 | 0.149246 | 0.0746232 | − | 0.997212i | \(-0.476225\pi\) | ||||
0.0746232 | + | 0.997212i | \(0.476225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23607 | −0.280603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.94427 | 0.251546 | 0.125773 | − | 0.992059i | \(-0.459859\pi\) | ||||
0.125773 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23607 | 0.274480 | 0.137240 | − | 0.990538i | \(-0.456177\pi\) | ||||
0.137240 | + | 0.990538i | \(0.456177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.94427 | −0.416383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.9443 | 1.08245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.23607 | −0.266906 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.9443 | −1.22428 | −0.612141 | − | 0.790748i | \(-0.709692\pi\) | ||||
−0.612141 | + | 0.790748i | \(0.709692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.4164 | 2.70156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.23607 | −0.417884 | −0.208942 | − | 0.977928i | \(-0.567002\pi\) | ||||
−0.208942 | + | 0.977928i | \(0.567002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.3607 | −2.56637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.4164 | 1.83411 | 0.917057 | − | 0.398755i | \(-0.130558\pi\) | ||||
0.917057 | + | 0.398755i | \(0.130558\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.41641 | −0.264370 | −0.132185 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132185 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.1803 | −1.84912 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.70820 | 0.586044 | 0.293022 | − | 0.956106i | \(-0.405339\pi\) | ||||
0.293022 | + | 0.956106i | \(0.405339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.4164 | −1.15877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.9443 | 1.86442 | 0.932211 | − | 0.361915i | \(-0.117877\pi\) | ||||
0.932211 | + | 0.361915i | \(0.117877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1803 | 0.756699 | 0.378349 | − | 0.925663i | \(-0.376492\pi\) | ||||
0.378349 | + | 0.925663i | \(0.376492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.8885 | −1.61805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0557 | −0.808475 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.4721 | −1.05269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9443 | 0.936615 | 0.468307 | − | 0.883566i | \(-0.344864\pi\) | ||||
0.468307 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.47214 | 0.609838 | 0.304919 | − | 0.952378i | \(-0.401371\pi\) | ||||
0.304919 | + | 0.952378i | \(0.401371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.94427 | 0.494759 | 0.247379 | − | 0.968919i | \(-0.420431\pi\) | ||||
0.247379 | + | 0.968919i | \(0.420431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4164 | 0.809288 | 0.404644 | − | 0.914474i | \(-0.367395\pi\) | ||||
0.404644 | + | 0.914474i | \(0.367395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9443 | −0.913019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29.8885 | 2.07740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.8885 | 2.87016 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 48.3607 | 3.26791 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.4164 | −1.57516 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.94427 | −0.331093 | −0.165546 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165546 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7639 | −0.847172 | −0.423586 | − | 0.905856i | \(-0.639229\pi\) | ||||
−0.423586 | + | 0.905856i | \(0.639229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.5967 | −1.69148 | −0.845740 | − | 0.533595i | \(-0.820841\pi\) | ||||
−0.845740 | + | 0.533595i | \(0.820841\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8885 | −1.30294 | −0.651471 | − | 0.758674i | \(-0.725848\pi\) | ||||
−0.651471 | + | 0.758674i | \(0.725848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.8885 | −1.41585 | −0.707926 | − | 0.706287i | \(-0.750369\pi\) | ||||
−0.707926 | + | 0.706287i | \(0.750369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.52786 | 0.227250 | 0.113625 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113625 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9443 | 1.07814 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.4164 | 0.976975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.7082 | −1.11773 | −0.558866 | − | 0.829258i | \(-0.688763\pi\) | ||||
−0.558866 | + | 0.829258i | \(0.688763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.88854 | −0.621687 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.47214 | −0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33.4164 | 2.06842 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.9443 | 1.78478 | 0.892390 | − | 0.451265i | \(-0.149027\pi\) | ||||
0.892390 | + | 0.451265i | \(0.149027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4164 | 1.18826 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1803 | 1.10847 | 0.554237 | − | 0.832359i | \(-0.313010\pi\) | ||||
0.554237 | + | 0.832359i | \(0.313010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.9443 | 1.02551 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.8885 | 1.67566 | 0.837830 | − | 0.545931i | \(-0.183824\pi\) | ||||
0.837830 | + | 0.545931i | \(0.183824\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −48.3607 | −2.89528 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1803 | 0.961821 | 0.480911 | − | 0.876770i | \(-0.340306\pi\) | ||||
0.480911 | + | 0.876770i | \(0.340306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.472136 | 0.0278693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4164 | 0.669242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2361 | 1.00694 | 0.503471 | − | 0.864012i | \(-0.332056\pi\) | ||||
0.503471 | + | 0.864012i | \(0.332056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.7771 | 2.07600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.9443 | −1.21124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47214 | −0.142492 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.8885 | −2.17664 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1803 | 1.38004 | 0.690022 | − | 0.723788i | \(-0.257601\pi\) | ||||
0.690022 | + | 0.723788i | \(0.257601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 46.8328 | 2.66423 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.472136 | −0.0266867 | −0.0133434 | − | 0.999911i | \(-0.504247\pi\) | ||||
−0.0133434 | + | 0.999911i | \(0.504247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.9443 | −1.51334 | −0.756671 | − | 0.653796i | \(-0.773175\pi\) | ||||
−0.756671 | + | 0.653796i | \(0.773175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0557 | −0.619002 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.9443 | 1.61551 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4721 | −0.805251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52786 | 0.0844911 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.52786 | 0.0842339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5279 | −0.743559 | −0.371779 | − | 0.928321i | \(-0.621252\pi\) | ||||
−0.371779 | + | 0.928321i | \(0.621252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −33.4164 | −1.83121 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.3607 | 1.87175 | 0.935873 | − | 0.352338i | \(-0.114613\pi\) | ||||
0.935873 | + | 0.352338i | \(0.114613\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4164 | −0.620054 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.47214 | −0.132711 | −0.0663556 | − | 0.997796i | \(-0.521137\pi\) | ||||
−0.0663556 | + | 0.997796i | \(0.521137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.65248 | −0.249041 | −0.124521 | − | 0.992217i | \(-0.539739\pi\) | ||||
−0.124521 | + | 0.992217i | \(0.539739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75.7771 | 4.04468 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.8885 | −1.05856 | −0.529280 | − | 0.848447i | \(-0.677538\pi\) | ||||
−0.529280 | + | 0.848447i | \(0.677538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.4721 | −0.765947 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.944272 | −0.0498368 | −0.0249184 | − | 0.999689i | \(-0.507933\pi\) | ||||
−0.0249184 | + | 0.999689i | \(0.507933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.8197 | 0.830317 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.8328 | 1.60946 | 0.804730 | − | 0.593641i | \(-0.202310\pi\) | ||||
0.804730 | + | 0.593641i | \(0.202310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52786 | 0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0000 | 0.519174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.9443 | 0.773785 | 0.386893 | − | 0.922125i | \(-0.373548\pi\) | ||||
0.386893 | + | 0.922125i | \(0.373548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.4164 | −1.20601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.4164 | 1.61375 | 0.806876 | − | 0.590721i | \(-0.201156\pi\) | ||||
0.806876 | + | 0.590721i | \(0.201156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.9443 | 1.48286 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4164 | 0.583351 | 0.291676 | − | 0.956517i | \(-0.405787\pi\) | ||||
0.291676 | + | 0.956517i | \(0.405787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.4721 | −0.938991 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.47214 | 0.226746 | 0.113373 | − | 0.993552i | \(-0.463834\pi\) | ||||
0.113373 | + | 0.993552i | \(0.463834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8885 | 0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.52786 | −0.278844 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7639 | 0.540226 | 0.270113 | − | 0.962829i | \(-0.412939\pi\) | ||||
0.270113 | + | 0.962829i | \(0.412939\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.4721 | 0.524263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.4721 | −1.62158 | −0.810791 | − | 0.585336i | \(-0.800962\pi\) | ||||
−0.810791 | + | 0.585336i | \(0.800962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.8885 | 1.68811 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0557 | 0.548012 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.41641 | 0.267824 | 0.133912 | − | 0.990993i | \(-0.457246\pi\) | ||||
0.133912 | + | 0.990993i | \(0.457246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.52786 | −0.469975 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76393 | 0.234418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.4721 | −0.512823 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.180340 | 0.00881018 | 0.00440509 | − | 0.999990i | \(-0.498598\pi\) | ||||
0.00440509 | + | 0.999990i | \(0.498598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.4164 | 0.555085 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.76393 | 0.327330 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −41.8885 | −2.02240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.0000 | 1.34871 | 0.674356 | − | 0.738406i | \(-0.264421\pi\) | ||||
0.674356 | + | 0.738406i | \(0.264421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4164 | 0.836979 | 0.418490 | − | 0.908222i | \(-0.362560\pi\) | ||||
0.418490 | + | 0.908222i | \(0.362560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.9443 | −0.619208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.8885 | 1.03996 | 0.519978 | − | 0.854180i | \(-0.325940\pi\) | ||||
0.519978 | + | 0.854180i | \(0.325940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.3607 | 2.28738 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8885 | 1.31614 | 0.658071 | − | 0.752956i | \(-0.271373\pi\) | ||||
0.658071 | + | 0.752956i | \(0.271373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.16718 | −0.0549606 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.9443 | 1.35992 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4721 | 0.770534 | 0.385267 | − | 0.922805i | \(-0.374109\pi\) | ||||
0.385267 | + | 0.922805i | \(0.374109\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −64.7214 | −3.02093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.29180 | 0.386187 | 0.193094 | − | 0.981180i | \(-0.438148\pi\) | ||||
0.193094 | + | 0.981180i | \(0.438148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7771 | 1.66270 | 0.831351 | − | 0.555748i | \(-0.187568\pi\) | ||||
0.831351 | + | 0.555748i | \(0.187568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.0689 | 1.20632 | 0.603162 | − | 0.797619i | \(-0.293907\pi\) | ||||
0.603162 | + | 0.797619i | \(0.293907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9443 | 0.780751 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.11146 | 0.281005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 74.7214 | 3.42126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.4164 | 1.61822 | 0.809108 | − | 0.587659i | \(-0.199950\pi\) | ||||
0.809108 | + | 0.587659i | \(0.199950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.4164 | 1.06770 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.9443 | −0.588985 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | 0.906287 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −75.7771 | −3.42676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.11146 | −0.0952887 | −0.0476443 | − | 0.998864i | \(-0.515171\pi\) | ||||
−0.0476443 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.9443 | −0.580630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8885 | 0.621737 | 0.310868 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310868 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0557 | 0.493934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9443 | 0.577157 | 0.288578 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −46.6525 | −2.07191 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.875388 | −0.0388009 | −0.0194004 | − | 0.999812i | \(-0.506176\pi\) | ||||
−0.0194004 | + | 0.999812i | \(0.506176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9443 | −0.661096 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46.8328 | 2.06772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.77709 | −0.166116 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.9443 | −1.09493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.4164 | −1.46400 | −0.732000 | − | 0.681305i | \(-0.761413\pi\) | ||||
−0.732000 | + | 0.681305i | \(0.761413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.7082 | −0.774326 | −0.387163 | − | 0.922011i | \(-0.626545\pi\) | ||||
−0.387163 | + | 0.922011i | \(0.626545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.9443 | −1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.5967 | 1.54477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.47214 | −0.107080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −80.7214 | −3.48338 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.47214 | −0.106482 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9443 | −0.986451 | −0.493226 | − | 0.869901i | \(-0.664182\pi\) | ||||
−0.493226 | + | 0.869901i | \(0.664182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.9443 | −1.41377 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4164 | −1.34327 | −0.671634 | − | 0.740883i | \(-0.734407\pi\) | ||||
−0.671634 | + | 0.740883i | \(0.734407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 50.5410 | 2.15704 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.4721 | −0.616534 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427 | 0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.9443 | −1.14167 | −0.570833 | − | 0.821066i | \(-0.693380\pi\) | ||||
−0.570833 | + | 0.821066i | \(0.693380\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9443 | 0.547484 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.7771 | 1.51051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.1803 | −1.69340 | −0.846700 | − | 0.532071i | \(-0.821414\pi\) | ||||
−0.846700 | + | 0.532071i | \(0.821414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.4164 | 1.02539 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.3607 | −0.769720 | −0.384860 | − | 0.922975i | \(-0.625750\pi\) | ||||
−0.384860 | + | 0.922975i | \(0.625750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.52786 | 0.231334 | 0.115667 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115667 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −41.8885 | −1.74992 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.00000 | 0.249783 | 0.124892 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124892 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.4164 | −1.13939 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.76393 | −0.197641 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.7214 | −1.02385 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.70820 | 0.400700 | 0.200350 | − | 0.979724i | \(-0.435792\pi\) | ||||
0.200350 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.9443 | 0.862994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.4721 | −0.924380 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8328 | 0.855501 | 0.427751 | − | 0.903897i | \(-0.359306\pi\) | ||||
0.427751 | + | 0.903897i | \(0.359306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.9443 | −1.51203 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.8885 | 0.730906 | 0.365453 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365453 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.7771 | −1.70412 | −0.852061 | − | 0.523442i | \(-0.824648\pi\) | ||||
−0.852061 | + | 0.523442i | \(0.824648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.8885 | 1.21716 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8885 | −1.05078 | −0.525392 | − | 0.850860i | \(-0.676081\pi\) | ||||
−0.525392 | + | 0.850860i | \(0.676081\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.4721 | −0.586441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.58359 | −0.104350 | −0.0521752 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521752 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3607 | 0.417105 | 0.208553 | − | 0.978011i | \(-0.433125\pi\) | ||||
0.208553 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0689 | −0.404703 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −57.8885 | −2.32299 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.8885 | −1.03389 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0557 | 1.07707 | 0.538536 | − | 0.842603i | \(-0.318978\pi\) | ||||
0.538536 | + | 0.842603i | \(0.318978\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.8328 | −1.54347 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.23607 | −0.207461 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −96.7214 | −3.82624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.4164 | 1.63585 | 0.817925 | − | 0.575325i | \(-0.195124\pi\) | ||||
0.817925 | + | 0.575325i | \(0.195124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2918 | −1.19459 | −0.597296 | − | 0.802021i | \(-0.703758\pi\) | ||||
−0.597296 | + | 0.802021i | \(0.703758\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.3607 | 0.957717 | 0.478859 | − | 0.877892i | \(-0.341051\pi\) | ||||
0.478859 | + | 0.877892i | \(0.341051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7771 | −0.462291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9443 | 0.820871 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.4164 | −0.681557 | −0.340778 | − | 0.940144i | \(-0.610691\pi\) | ||||
−0.340778 | + | 0.940144i | \(0.610691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −111.666 | −4.35649 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.3050 | 0.985741 | 0.492870 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492870 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.65248 | 0.336542 | 0.168271 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168271 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 75.7771 | 2.94294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8885 | 0.692647 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.7214 | −0.645521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9443 | −0.576059 | −0.288030 | − | 0.957621i | \(-0.593000\pi\) | ||||
−0.288030 | + | 0.957621i | \(0.593000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.1803 | −1.62112 | −0.810561 | − | 0.585654i | \(-0.800838\pi\) | ||||
−0.810561 | + | 0.585654i | \(0.800838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.3050 | 1.58281 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.7771 | −1.82814 | −0.914070 | − | 0.405557i | \(-0.867078\pi\) | ||||
−0.914070 | + | 0.405557i | \(0.867078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 82.8328 | 3.16027 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.3607 | −1.99478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.18034 | −0.311195 | −0.155597 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155597 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.4721 | −0.701698 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11146 | 0.0799771 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 64.3607 | 2.43434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5836 | −0.550815 | −0.275407 | − | 0.961328i | \(-0.588813\pi\) | ||||
−0.275407 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.4721 | 0.545827 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.7082 | 0.440332 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3607 | 1.74111 | 0.870556 | − | 0.492069i | \(-0.163759\pi\) | ||||
0.870556 | + | 0.492069i | \(0.163759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.9443 | 1.38552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.8885 | −0.969534 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 70.8328 | 2.64530 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.1935 | 1.76002 | 0.880010 | − | 0.474955i | \(-0.157536\pi\) | ||||
0.880010 | + | 0.474955i | \(0.157536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4721 | −0.538971 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.4164 | −0.424581 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3607 | −1.20019 | −0.600096 | − | 0.799928i | \(-0.704871\pi\) | ||||
−0.600096 | + | 0.799928i | \(0.704871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0557 | −0.408911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.23607 | 0.341142 | 0.170571 | − | 0.985345i | \(-0.445439\pi\) | ||||
0.170571 | + | 0.985345i | \(0.445439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.88854 | −0.364249 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.4164 | −0.861386 | −0.430693 | − | 0.902498i | \(-0.641731\pi\) | ||||
−0.430693 | + | 0.902498i | \(0.641731\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −54.8328 | −2.01433 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.05573 | 0.258850 | 0.129425 | − | 0.991589i | \(-0.458687\pi\) | ||||
0.129425 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.5967 | −1.30242 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.94427 | −0.326817 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0000 | −1.31366 | −0.656829 | − | 0.754039i | \(-0.728103\pi\) | ||||
−0.656829 | + | 0.754039i | \(0.728103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 57.3050 | 2.08831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3050 | 0.847033 | 0.423516 | − | 0.905888i | \(-0.360796\pi\) | ||||
0.423516 | + | 0.905888i | \(0.360796\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.0000 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4721 | −0.452115 | −0.226057 | − | 0.974114i | \(-0.572584\pi\) | ||||
−0.226057 | + | 0.974114i | \(0.572584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.472136 | −0.0170925 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.9443 | −0.900685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.3607 | 0.950590 | 0.475295 | − | 0.879826i | \(-0.342341\pi\) | ||||
0.475295 | + | 0.879826i | \(0.342341\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.3050 | −1.63162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.8197 | −0.640929 | −0.320464 | − | 0.947261i | \(-0.603839\pi\) | ||||
−0.320464 | + | 0.947261i | \(0.603839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.4721 | 0.519185 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.52786 | −0.0547414 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −64.7214 | −2.31295 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7082 | −0.916399 | −0.458199 | − | 0.888850i | \(-0.651505\pi\) | ||||
−0.458199 | + | 0.888850i | \(0.651505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −93.6656 | −3.33458 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.52786 | 0.125436 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.4164 | −1.25767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.8197 | 1.05627 | 0.528133 | − | 0.849161i | \(-0.322892\pi\) | ||||
0.528133 | + | 0.849161i | \(0.322892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.83282 | 0.241728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.8328 | −1.58409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9443 | 1.30374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58.8328 | −2.07101 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.41641 | 0.331063 | 0.165532 | − | 0.986204i | \(-0.447066\pi\) | ||||
0.165532 | + | 0.986204i | \(0.447066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0132 | −0.808101 | −0.404051 | − | 0.914737i | \(-0.632398\pi\) | ||||
−0.404051 | + | 0.914737i | \(0.632398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −77.6656 | −2.72385 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | 0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −39.1246 | −1.36712 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8885 | 1.39212 | 0.696060 | − | 0.717984i | \(-0.254935\pi\) | ||||
0.696060 | + | 0.717984i | \(0.254935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.7771 | 1.80484 | 0.902418 | − | 0.430862i | \(-0.141790\pi\) | ||||
0.902418 | + | 0.430862i | \(0.141790\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.9443 | 1.14558 | 0.572792 | − | 0.819701i | \(-0.305860\pi\) | ||||
0.572792 | + | 0.819701i | \(0.305860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.76393 | 0.234921 | 0.117461 | − | 0.993078i | \(-0.462525\pi\) | ||||
0.117461 | + | 0.993078i | \(0.462525\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −90.2492 | −3.13071 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.47214 | 0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 93.6656 | 3.23756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.4721 | 1.05201 | 0.526007 | − | 0.850480i | \(-0.323688\pi\) | ||||
0.526007 | + | 0.850480i | \(0.323688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −84.1378 | −2.89786 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.88854 | −0.167972 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.3607 | −1.79701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.8885 | −0.613211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.291796 | −0.00999091 | −0.00499545 | − | 0.999988i | \(-0.501590\pi\) | ||||
−0.00499545 | + | 0.999988i | \(0.501590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.4721 | 1.24586 | 0.622932 | − | 0.782276i | \(-0.285941\pi\) | ||||
0.622932 | + | 0.782276i | \(0.285941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.1803 | 1.91685 | 0.958424 | − | 0.285347i | \(-0.0921089\pi\) | ||||
0.958424 | + | 0.285347i | \(0.0921089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.52786 | −0.0520695 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.05573 | −0.104018 | −0.0520091 | − | 0.998647i | \(-0.516562\pi\) | ||||
−0.0520091 | + | 0.998647i | \(0.516562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.70820 | −0.329708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2229 | −0.414634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.9443 | −0.709670 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.3607 | −0.892174 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4164 | 0.453040 | 0.226520 | − | 0.974007i | \(-0.427265\pi\) | ||||
0.226520 | + | 0.974007i | \(0.427265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −55.7771 | −1.88131 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.8328 | −0.971402 | −0.485701 | − | 0.874125i | \(-0.661436\pi\) | ||||
−0.485701 | + | 0.874125i | \(0.661436\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.9443 | 1.37788 | 0.688942 | − | 0.724816i | \(-0.258075\pi\) | ||||
0.688942 | + | 0.724816i | \(0.258075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.3050 | 0.983964 | 0.491982 | − | 0.870605i | \(-0.336273\pi\) | ||||
0.491982 | + | 0.870605i | \(0.336273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.94427 | −0.299981 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −60.3607 | −2.02216 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.94427 | −0.165454 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 67.7771 | 2.26301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.9443 | −0.965346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7214 | 1.48988 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.9443 | −0.562625 | −0.281313 | − | 0.959616i | \(-0.590770\pi\) | ||||
−0.281313 | + | 0.959616i | \(0.590770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 87.4853 | 2.90170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8328 | −0.623959 | −0.311980 | − | 0.950089i | \(-0.600992\pi\) | ||||
−0.311980 | + | 0.950089i | \(0.600992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7771 | 0.389765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.70820 | 0.0564099 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.7771 | −1.18018 | −0.590089 | − | 0.807338i | \(-0.700907\pi\) | ||||
−0.590089 | + | 0.807338i | \(0.700907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.2492 | −2.57840 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.7771 | 2.23091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −108.138 | −3.55171 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3050 | 0.502139 | 0.251070 | − | 0.967969i | \(-0.419218\pi\) | ||||
0.251070 | + | 0.967969i | \(0.419218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.23607 | −0.106058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.8885 | 0.847553 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9443 | 0.880231 | 0.440115 | − | 0.897941i | \(-0.354937\pi\) | ||||
0.440115 | + | 0.897941i | \(0.354937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.52786 | 0.0498600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.5967 | 0.443241 | 0.221621 | − | 0.975133i | \(-0.428865\pi\) | ||||
0.221621 | + | 0.975133i | \(0.428865\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.88854 | 0.0614994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.4164 | −1.02090 | −0.510448 | − | 0.859909i | \(-0.670520\pi\) | ||||
−0.510448 | + | 0.859909i | \(0.670520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 78.2492 | 2.54008 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 87.1935 | 2.82744 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1115 | −0.521901 | −0.260951 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260951 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.7771 | 1.15651 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.94427 | 0.0950755 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −66.8328 | −2.15366 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.88854 | −0.189363 | −0.0946814 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946814 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46.8328 | 1.50449 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.2361 | −0.874047 | −0.437024 | − | 0.899450i | \(-0.643967\pi\) | ||||
−0.437024 | + | 0.899450i | \(0.643967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.23607 | 0.103744 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.8328 | −1.30636 | −0.653179 | − | 0.757204i | \(-0.726565\pi\) | ||||
−0.653179 | + | 0.757204i | \(0.726565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8328 | 0.474059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.52786 | −0.112636 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.4721 | −0.461589 | −0.230795 | − | 0.973002i | \(-0.574133\pi\) | ||||
−0.230795 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.94427 | −0.157378 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.88854 | −0.314437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.7771 | 1.38922 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.0689 | 1.26899 | 0.634497 | − | 0.772925i | \(-0.281207\pi\) | ||||
0.634497 | + | 0.772925i | \(0.281207\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64.7214 | 2.04769 |
(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 | 5600.2.a.z.1.1 | 2 | ||
4.3 | odd | 2 | 5600.2.a.bk.1.2 | 2 | |||
5.4 | even | 2 | 224.2.a.d.1.2 | yes | 2 | ||
15.14 | odd | 2 | 2016.2.a.o.1.2 | 2 | |||
20.19 | odd | 2 | 224.2.a.c.1.1 | ✓ | 2 | ||
35.4 | even | 6 | 1568.2.i.m.961.1 | 4 | |||
35.9 | even | 6 | 1568.2.i.m.1537.1 | 4 | |||
35.19 | odd | 6 | 1568.2.i.w.1537.2 | 4 | |||
35.24 | odd | 6 | 1568.2.i.w.961.2 | 4 | |||
35.34 | odd | 2 | 1568.2.a.k.1.1 | 2 | |||
40.19 | odd | 2 | 448.2.a.j.1.2 | 2 | |||
40.29 | even | 2 | 448.2.a.i.1.1 | 2 | |||
60.59 | even | 2 | 2016.2.a.r.1.2 | 2 | |||
80.19 | odd | 4 | 1792.2.b.k.897.1 | 4 | |||
80.29 | even | 4 | 1792.2.b.m.897.4 | 4 | |||
80.59 | odd | 4 | 1792.2.b.k.897.4 | 4 | |||
80.69 | even | 4 | 1792.2.b.m.897.1 | 4 | |||
120.29 | odd | 2 | 4032.2.a.bv.1.1 | 2 | |||
120.59 | even | 2 | 4032.2.a.bw.1.1 | 2 | |||
140.19 | even | 6 | 1568.2.i.n.1537.1 | 4 | |||
140.39 | odd | 6 | 1568.2.i.v.961.2 | 4 | |||
140.59 | even | 6 | 1568.2.i.n.961.1 | 4 | |||
140.79 | odd | 6 | 1568.2.i.v.1537.2 | 4 | |||
140.139 | even | 2 | 1568.2.a.v.1.2 | 2 | |||
280.69 | odd | 2 | 3136.2.a.by.1.2 | 2 | |||
280.139 | even | 2 | 3136.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.c.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
224.2.a.d.1.2 | yes | 2 | 5.4 | even | 2 | ||
448.2.a.i.1.1 | 2 | 40.29 | even | 2 | |||
448.2.a.j.1.2 | 2 | 40.19 | odd | 2 | |||
1568.2.a.k.1.1 | 2 | 35.34 | odd | 2 | |||
1568.2.a.v.1.2 | 2 | 140.139 | even | 2 | |||
1568.2.i.m.961.1 | 4 | 35.4 | even | 6 | |||
1568.2.i.m.1537.1 | 4 | 35.9 | even | 6 | |||
1568.2.i.n.961.1 | 4 | 140.59 | even | 6 | |||
1568.2.i.n.1537.1 | 4 | 140.19 | even | 6 | |||
1568.2.i.v.961.2 | 4 | 140.39 | odd | 6 | |||
1568.2.i.v.1537.2 | 4 | 140.79 | odd | 6 | |||
1568.2.i.w.961.2 | 4 | 35.24 | odd | 6 | |||
1568.2.i.w.1537.2 | 4 | 35.19 | odd | 6 | |||
1792.2.b.k.897.1 | 4 | 80.19 | odd | 4 | |||
1792.2.b.k.897.4 | 4 | 80.59 | odd | 4 | |||
1792.2.b.m.897.1 | 4 | 80.69 | even | 4 | |||
1792.2.b.m.897.4 | 4 | 80.29 | even | 4 | |||
2016.2.a.o.1.2 | 2 | 15.14 | odd | 2 | |||
2016.2.a.r.1.2 | 2 | 60.59 | even | 2 | |||
3136.2.a.bf.1.1 | 2 | 280.139 | even | 2 | |||
3136.2.a.by.1.2 | 2 | 280.69 | odd | 2 | |||
4032.2.a.bv.1.1 | 2 | 120.29 | odd | 2 | |||
4032.2.a.bw.1.1 | 2 | 120.59 | even | 2 | |||
5600.2.a.z.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5600.2.a.bk.1.2 | 2 | 4.3 | odd | 2 |