Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1248,2,Mod(1,1248)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1248, 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("1248.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.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: | \(9.96533017226\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1248.1 |
$q$-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 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.23607 | 1.97905 | 0.989524 | − | 0.144370i | \(-0.0461154\pi\) | ||||
0.989524 | + | 0.144370i | \(0.0461154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23607 | −0.319151 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.23607 | −1.14260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.23607 | 1.65885 | 0.829423 | − | 0.558620i | \(-0.188669\pi\) | ||||
0.829423 | + | 0.558620i | \(0.188669\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.47214 | −0.778499 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.47214 | 1.09399 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.23607 | −1.44243 | −0.721216 | − | 0.692711i | \(-0.756416\pi\) | ||||
−0.721216 | + | 0.692711i | \(0.756416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.23607 | 0.184262 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.472136 | −0.0688681 | −0.0344341 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344341 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.4164 | 2.91663 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.472136 | 0.0648529 | 0.0324264 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324264 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.52786 | 0.745377 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.23607 | 0.163721 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.94427 | −0.904067 | −0.452034 | − | 0.892001i | \(-0.649301\pi\) | ||||
−0.452034 | + | 0.892001i | \(0.649301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.52786 | 0.451697 | 0.225848 | − | 0.974162i | \(-0.427485\pi\) | ||||
0.225848 | + | 0.974162i | \(0.427485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.23607 | 0.659683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23607 | −0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.70820 | −0.941707 | −0.470853 | − | 0.882211i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882211i | \(0.656054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.47214 | 0.297610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.47214 | −0.523424 | −0.261712 | − | 0.965146i | \(-0.584287\pi\) | ||||
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.47214 | 0.400928 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.4164 | 2.66855 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.94427 | −0.323176 | −0.161588 | − | 0.986858i | \(-0.551662\pi\) | ||||
−0.161588 | + | 0.986858i | \(0.551662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.52786 | 0.599581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.47214 | 0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7082 | −1.66507 | −0.832533 | − | 0.553975i | \(-0.813110\pi\) | ||||
−0.832533 | + | 0.553975i | \(0.813110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23607 | −0.548889 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.23607 | −0.957736 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.52786 | −0.156756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4721 | 1.67249 | 0.836246 | − | 0.548354i | \(-0.184746\pi\) | ||||
0.836246 | + | 0.548354i | \(0.184746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214 | 0.449467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4164 | −1.12489 | −0.562446 | − | 0.826834i | \(-0.690140\pi\) | ||||
−0.562446 | + | 0.826834i | \(0.690140\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.47214 | −0.631616 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.47214 | 0.625685 | 0.312842 | − | 0.949805i | \(-0.398719\pi\) | ||||
0.312842 | + | 0.949805i | \(0.398719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.47214 | 0.424476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.94427 | −0.653262 | −0.326631 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326631 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.05573 | −0.284948 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.4164 | 2.14658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.23607 | 0.832788 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4164 | 1.01304 | 0.506521 | − | 0.862228i | \(-0.330931\pi\) | ||||
0.506521 | + | 0.862228i | \(0.330931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.47214 | −0.569840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.52786 | −0.832453 | −0.416227 | − | 0.909261i | \(-0.636648\pi\) | ||||
−0.416227 | + | 0.909261i | \(0.636648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.47214 | −0.561205 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.23607 | −0.106384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.65248 | 0.739231 | 0.369615 | − | 0.929185i | \(-0.379489\pi\) | ||||
0.369615 | + | 0.929185i | \(0.379489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9443 | −1.43719 | −0.718597 | − | 0.695427i | \(-0.755215\pi\) | ||||
−0.718597 | + | 0.695427i | \(0.755215\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.472136 | 0.0397610 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.47214 | −0.373979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4721 | −0.869664 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.4164 | −1.68392 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.1803 | −0.834006 | −0.417003 | − | 0.908905i | \(-0.636920\pi\) | ||||
−0.417003 | + | 0.908905i | \(0.636920\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1803 | −1.15398 | −0.576990 | − | 0.816751i | \(-0.695773\pi\) | ||||
−0.576990 | + | 0.816751i | \(0.695773\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.47214 | 0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4164 | 0.916988 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.52786 | −0.281554 | −0.140777 | − | 0.990041i | \(-0.544960\pi\) | ||||
−0.140777 | + | 0.990041i | \(0.544960\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.472136 | −0.0374428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.9443 | −1.02015 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.76393 | −0.529792 | −0.264896 | − | 0.964277i | \(-0.585338\pi\) | ||||
−0.264896 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.52786 | −0.430344 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4721 | 0.965123 | 0.482561 | − | 0.875862i | \(-0.339707\pi\) | ||||
0.482561 | + | 0.875862i | \(0.339707\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.23607 | −0.0945245 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9443 | −0.832078 | −0.416039 | − | 0.909347i | \(-0.636582\pi\) | ||||
−0.416039 | + | 0.909347i | \(0.636582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.1803 | −1.37430 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.94427 | 0.521963 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.52786 | −0.413172 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.4164 | 1.88919 | 0.944593 | − | 0.328243i | \(-0.106456\pi\) | ||||
0.944593 | + | 0.328243i | \(0.106456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.52786 | −0.260787 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.52786 | −0.406417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.0000 | 1.46254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.23607 | −0.380868 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.41641 | 0.247203 | 0.123601 | − | 0.992332i | \(-0.460556\pi\) | ||||
0.123601 | + | 0.992332i | \(0.460556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23607 | 0.0885167 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6525 | −1.18644 | −0.593220 | − | 0.805040i | \(-0.702144\pi\) | ||||
−0.593220 | + | 0.805040i | \(0.702144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.52786 | 0.108307 | 0.0541537 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541537 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.70820 | 0.543695 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −44.3607 | −3.11351 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4164 | −0.797357 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.47214 | −0.171825 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.52786 | −0.382370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.94427 | 0.615749 | 0.307875 | − | 0.951427i | \(-0.400382\pi\) | ||||
0.307875 | + | 0.951427i | \(0.400382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0000 | −0.685189 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48.3607 | 3.28294 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.47214 | 0.302199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.47214 | −0.300828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.18034 | 0.413866 | 0.206933 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206933 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47214 | −0.231476 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.41641 | −0.0940103 | −0.0470051 | − | 0.998895i | \(-0.514968\pi\) | ||||
−0.0470051 | + | 0.998895i | \(0.514968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.4164 | −1.54069 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.4721 | −1.86527 | −0.932636 | − | 0.360819i | \(-0.882497\pi\) | ||||
−0.932636 | + | 0.360819i | \(0.882497\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.583592 | −0.0380694 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.94427 | −0.580993 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8885 | −1.54522 | −0.772611 | − | 0.634880i | \(-0.781050\pi\) | ||||
−0.772611 | + | 0.634880i | \(0.781050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.41641 | −0.0912389 | −0.0456194 | − | 0.998959i | \(-0.514526\pi\) | ||||
−0.0456194 | + | 0.998959i | \(0.514526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.2361 | 1.61227 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.23607 | 0.0786491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.94427 | 0.186586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0000 | −1.00991 | −0.504956 | − | 0.863145i | \(-0.668491\pi\) | ||||
−0.504956 | + | 0.863145i | \(0.668491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.0557 | −0.695068 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52786 | −0.346168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.41641 | −0.0883531 | −0.0441765 | − | 0.999024i | \(-0.514066\pi\) | ||||
−0.0441765 | + | 0.999024i | \(0.514066\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.4164 | −1.45502 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.0000 | 1.72655 | 0.863277 | − | 0.504730i | \(-0.168408\pi\) | ||||
0.863277 | + | 0.504730i | \(0.168408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.583592 | 0.0358498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.7082 | 0.961326 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.4164 | 1.06190 | 0.530949 | − | 0.847404i | \(-0.321836\pi\) | ||||
0.530949 | + | 0.847404i | \(0.321836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6525 | −0.768583 | −0.384292 | − | 0.923212i | \(-0.625554\pi\) | ||||
−0.384292 | + | 0.923212i | \(0.625554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.23607 | 0.316901 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5279 | −0.936365 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05573 | 0.0634326 | 0.0317163 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317163 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.23607 | 0.552949 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.29180 | −0.256027 | −0.128014 | − | 0.991772i | \(-0.540860\pi\) | ||||
−0.128014 | + | 0.991772i | \(0.540860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.4721 | 1.81138 | 0.905690 | − | 0.423940i | \(-0.139353\pi\) | ||||
0.905690 | + | 0.423940i | \(0.139353\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.52786 | 0.0905029 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −48.3607 | −2.85464 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4721 | −0.965614 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.5967 | 1.96274 | 0.981371 | − | 0.192120i | \(-0.0615362\pi\) | ||||
0.981371 | + | 0.192120i | \(0.0615362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.58359 | −0.499756 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.47214 | −0.259500 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.47214 | 0.142967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.8885 | 1.95330 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0000 | −0.574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.36068 | 0.249692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.29180 | −0.473238 | −0.236619 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236619 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.4164 | 0.649457 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.4721 | −1.50110 | −0.750549 | − | 0.660815i | \(-0.770211\pi\) | ||||
−0.750549 | + | 0.660815i | \(0.770211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.88854 | −0.219793 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.47214 | 0.364664 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.6525 | −0.935296 | −0.467648 | − | 0.883915i | \(-0.654899\pi\) | ||||
−0.467648 | + | 0.883915i | \(0.654899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.8885 | −2.12135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.47214 | −0.361239 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52786 | −0.307579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.47214 | 0.192599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.9443 | −0.826420 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.47214 | −0.136293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.2361 | 0.727520 | 0.363760 | − | 0.931493i | \(-0.381493\pi\) | ||||
0.363760 | + | 0.931493i | \(0.381493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.47214 | −0.245072 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.52786 | −0.520563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.9443 | −1.24985 | −0.624927 | − | 0.780683i | \(-0.714871\pi\) | ||||
−0.624927 | + | 0.780683i | \(0.714871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.94427 | 0.377161 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.3050 | 2.23679 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 70.2492 | 3.79310 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.05573 | 0.164515 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0000 | 1.07366 | 0.536828 | − | 0.843692i | \(-0.319622\pi\) | ||||
0.536828 | + | 0.843692i | \(0.319622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3607 | 0.554594 | 0.277297 | − | 0.960784i | \(-0.410561\pi\) | ||||
0.277297 | + | 0.960784i | \(0.410561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2918 | −0.654226 | −0.327113 | − | 0.944985i | \(-0.606076\pi\) | ||||
−0.327113 | + | 0.944985i | \(0.606076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.3607 | 0.656037 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.4164 | −1.23933 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4164 | 0.919203 | 0.459601 | − | 0.888125i | \(-0.347992\pi\) | ||||
0.459601 | + | 0.888125i | \(0.347992\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.52786 | −0.289342 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0557 | 0.785903 | 0.392951 | − | 0.919559i | \(-0.371454\pi\) | ||||
0.392951 | + | 0.919559i | \(0.371454\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.23607 | −0.480810 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.47214 | 0.128347 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9443 | −0.566673 | −0.283336 | − | 0.959021i | \(-0.591441\pi\) | ||||
−0.283336 | + | 0.959021i | \(0.591441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4721 | 0.540779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.47214 | 0.436337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.0689 | −1.64727 | −0.823634 | − | 0.567122i | \(-0.808057\pi\) | ||||
−0.823634 | + | 0.567122i | \(0.808057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4164 | −0.584880 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.41641 | 0.276766 | 0.138383 | − | 0.990379i | \(-0.455810\pi\) | ||||
0.138383 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.9443 | 1.47514 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.47214 | 0.328997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.88854 | −0.197157 | −0.0985785 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985785 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0557 | −0.559112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.52786 | 0.480617 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0557 | 0.556274 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.52786 | 0.177058 | 0.0885292 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885292 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.47214 | 0.324012 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.29180 | 0.414073 | 0.207036 | − | 0.978333i | \(-0.433618\pi\) | ||||
0.207036 | + | 0.978333i | \(0.433618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.23607 | −0.460081 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.23607 | 0.0614207 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3607 | −1.10566 | −0.552832 | − | 0.833293i | \(-0.686453\pi\) | ||||
−0.552832 | + | 0.833293i | \(0.686453\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.65248 | −0.426795 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.3607 | −1.78919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.63932 | −0.178647 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9443 | 0.829765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4721 | 0.707010 | 0.353505 | − | 0.935433i | \(-0.384990\pi\) | ||||
0.353505 | + | 0.935433i | \(0.384990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9443 | −0.533391 | −0.266696 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266696 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.472136 | −0.0229560 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.5279 | −0.753212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4721 | 0.893929 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.47214 | 0.215917 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.4721 | −0.600762 | −0.300381 | − | 0.953819i | \(-0.597114\pi\) | ||||
−0.300381 | + | 0.953819i | \(0.597114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.41641 | 0.0680682 | 0.0340341 | − | 0.999421i | \(-0.489165\pi\) | ||||
0.0340341 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4721 | 0.502100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.05573 | 0.146175 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4164 | −0.926695 | −0.463347 | − | 0.886177i | \(-0.653352\pi\) | ||||
−0.463347 | + | 0.886177i | \(0.653352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.4164 | 0.972210 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.52786 | 0.452682 | 0.226341 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226341 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4164 | −0.920426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1803 | 0.481514 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.6525 | −1.72974 | −0.864869 | − | 0.501998i | \(-0.832598\pi\) | ||||
−0.864869 | + | 0.501998i | \(0.832598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.3050 | −1.94497 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.1803 | 0.666250 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.47214 | −0.303418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5279 | 1.28770 | 0.643850 | − | 0.765152i | \(-0.277336\pi\) | ||||
0.643850 | + | 0.765152i | \(0.277336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.23607 | 0.0575694 | 0.0287847 | − | 0.999586i | \(-0.490836\pi\) | ||||
0.0287847 | + | 0.999586i | \(0.490836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8197 | −0.642254 | −0.321127 | − | 0.947036i | \(-0.604062\pi\) | ||||
−0.321127 | + | 0.947036i | \(0.604062\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.4164 | −0.529423 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.9443 | 1.70958 | 0.854789 | − | 0.518976i | \(-0.173687\pi\) | ||||
0.854789 | + | 0.518976i | \(0.173687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.3607 | −1.86368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.52786 | 0.162555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.9443 | 1.33086 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.29180 | 0.196921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.472136 | 0.0216176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.47214 | 0.203912 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.9443 | 0.588985 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.3607 | 0.924531 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6525 | −0.754596 | −0.377298 | − | 0.926092i | \(-0.623147\pi\) | ||||
−0.377298 | + | 0.926092i | \(0.623147\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.76393 | 0.305876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.88854 | −0.446264 | −0.223132 | − | 0.974788i | \(-0.571628\pi\) | ||||
−0.223132 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.8885 | −1.70641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.52786 | 0.248459 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 52.3607 | 2.34870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2361 | 1.30879 | 0.654393 | − | 0.756155i | \(-0.272924\pi\) | ||||
0.654393 | + | 0.756155i | \(0.272924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4721 | −0.557214 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.9443 | −1.11221 | −0.556105 | − | 0.831112i | \(-0.687705\pi\) | ||||
−0.556105 | + | 0.831112i | \(0.687705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.3607 | 0.550043 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.1803 | 1.69231 | 0.846157 | − | 0.532934i | \(-0.178911\pi\) | ||||
0.846157 | + | 0.532934i | \(0.178911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4164 | −1.03588 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.23607 | 0.0545737 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.1115 | −0.621825 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.11146 | −0.0928617 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9443 | 0.480400 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.111456 | −0.00488298 | −0.00244149 | − | 0.999997i | \(-0.500777\pi\) | ||||
−0.00244149 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.11146 | 0.0923275 | 0.0461638 | − | 0.998934i | \(-0.485300\pi\) | ||||
0.0461638 | + | 0.998934i | \(0.485300\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.1803 | 0.793455 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 41.3050 | 1.79927 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.94427 | −0.301356 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.23607 | 0.400059 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.52786 | 0.238545 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 91.3050 | 3.93278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7771 | 1.62416 | 0.812082 | − | 0.583543i | \(-0.198334\pi\) | ||||
0.812082 | + | 0.583543i | \(0.198334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.4164 | −1.09072 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.4721 | 0.791259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.7771 | −1.70075 | −0.850373 | − | 0.526181i | \(-0.823624\pi\) | ||||
−0.850373 | + | 0.526181i | \(0.823624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.52786 | 0.150566 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4721 | 0.446128 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.8328 | 1.99153 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.52786 | 0.234645 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.0689 | −1.18932 | −0.594658 | − | 0.803978i | \(-0.702713\pi\) | ||||
−0.594658 | + | 0.803978i | \(0.702713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.47214 | −0.273742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0000 | −0.844401 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.47214 | −0.104188 | −0.0520941 | − | 0.998642i | \(-0.516590\pi\) | ||||
−0.0520941 | + | 0.998642i | \(0.516590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.58359 | −0.361114 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.23607 | 0.219894 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.41641 | −0.394756 | −0.197378 | − | 0.980327i | \(-0.563243\pi\) | ||||
−0.197378 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.4164 | 0.477762 | 0.238881 | − | 0.971049i | \(-0.423219\pi\) | ||||
0.238881 | + | 0.971049i | \(0.423219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.41641 | −0.142722 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.58359 | 0.357961 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.8328 | 1.03380 | 0.516902 | − | 0.856045i | \(-0.327085\pi\) | ||||
0.516902 | + | 0.856045i | \(0.327085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4164 | −0.639580 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.11146 | 0.0874476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.23607 | −0.0511051 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9443 | 0.947011 | 0.473506 | − | 0.880791i | \(-0.342988\pi\) | ||||
0.473506 | + | 0.880791i | \(0.342988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.4164 | −0.470405 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.6525 | 0.684991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.65248 | −0.191054 | −0.0955271 | − | 0.995427i | \(-0.530454\pi\) | ||||
−0.0955271 | + | 0.995427i | \(0.530454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.9443 | 1.18660 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.52786 | −0.0625313 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8885 | −1.46392 | −0.731962 | − | 0.681345i | \(-0.761395\pi\) | ||||
−0.731962 | + | 0.681345i | \(0.761395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.70820 | −0.313902 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.1246 | 0.452280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9443 | −0.687747 | −0.343873 | − | 0.939016i | \(-0.611739\pi\) | ||||
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44.3607 | 1.79759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.472136 | 0.0191006 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.472136 | 0.0190694 | 0.00953470 | − | 0.999955i | \(-0.496965\pi\) | ||||
0.00953470 | + | 0.999955i | \(0.496965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.4164 | 0.460354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.0689 | −1.61311 | −0.806556 | − | 0.591157i | \(-0.798671\pi\) | ||||
−0.806556 | + | 0.591157i | \(0.798671\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.59675 | 0.385726 | 0.192863 | − | 0.981226i | \(-0.438223\pi\) | ||||
0.192863 | + | 0.981226i | \(0.438223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.47214 | 0.0992034 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −82.2492 | −3.29525 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.52786 | 0.220762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0000 | −0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7082 | 0.466096 | 0.233048 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233048 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.94427 | −0.355503 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.1115 | 0.559996 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.4164 | −0.808928 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.0000 | 0.395594 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.47214 | 0.176639 | 0.0883194 | − | 0.996092i | \(-0.471850\pi\) | ||||
0.0883194 | + | 0.996092i | \(0.471850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.1803 | 1.66343 | 0.831715 | − | 0.555203i | \(-0.187359\pi\) | ||||
0.831715 | + | 0.555203i | \(0.187359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0000 | 0.629025 | 0.314512 | − | 0.949253i | \(-0.398159\pi\) | ||||
0.314512 | + | 0.949253i | \(0.398159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.0557 | −1.21904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.3607 | −1.89540 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.4721 | 0.801137 | 0.400568 | − | 0.916267i | \(-0.368813\pi\) | ||||
0.400568 | + | 0.916267i | \(0.368813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7771 | −0.460169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.47214 | −0.174475 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8328 | −0.421987 | −0.210993 | − | 0.977488i | \(-0.567670\pi\) | ||||
−0.210993 | + | 0.977488i | \(0.567670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.4721 | −1.10744 | −0.553719 | − | 0.832704i | \(-0.686792\pi\) | ||||
−0.553719 | + | 0.832704i | \(0.686792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.47214 | 0.173683 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.9443 | 0.810965 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.18034 | −0.238946 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.7771 | 0.609068 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4721 | −1.71427 | −0.857137 | − | 0.515088i | \(-0.827759\pi\) | ||||
−0.857137 | + | 0.515088i | \(0.827759\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.47214 | 0.133643 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.41641 | −0.0544370 | −0.0272185 | − | 0.999630i | \(-0.508665\pi\) | ||||
−0.0272185 | + | 0.999630i | \(0.508665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 86.2492 | 3.30994 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41641 | 0.0542769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.4164 | −1.12559 | −0.562794 | − | 0.826597i | \(-0.690273\pi\) | ||||
−0.562794 | + | 0.826597i | \(0.690273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6950 | 0.408637 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.472136 | −0.0179869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.12461 | 0.271033 | 0.135517 | − | 0.990775i | \(-0.456731\pi\) | ||||
0.135517 | + | 0.990775i | \(0.456731\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.4164 | 0.889516 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9443 | −0.794462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.3050 | −1.56454 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.4721 | 1.07692 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.8885 | −1.05334 | −0.526668 | − | 0.850071i | \(-0.676559\pi\) | ||||
−0.526668 | + | 0.850071i | \(0.676559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.52786 | 0.208487 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.583592 | 0.0219794 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 52.3607 | 1.96923 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.8885 | −1.49805 | −0.749023 | − | 0.662544i | \(-0.769477\pi\) | ||||
−0.749023 | + | 0.662544i | \(0.769477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.94427 | 0.335436 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8328 | −0.855096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.52786 | −0.206730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.8885 | 0.892134 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.47214 | −0.0921951 | −0.0460976 | − | 0.998937i | \(-0.514679\pi\) | ||||
−0.0460976 | + | 0.998937i | \(0.514679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.7771 | −2.22622 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.41641 | 0.0526768 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.4164 | 1.09250 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3607 | 0.606784 | 0.303392 | − | 0.952866i | \(-0.401881\pi\) | ||||
0.303392 | + | 0.952866i | \(0.401881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.9443 | 1.07054 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.8885 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.2361 | −0.930846 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.4721 | −1.26980 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2361 | −0.486897 | −0.243448 | − | 0.969914i | \(-0.578279\pi\) | ||||
−0.243448 | + | 0.969914i | \(0.578279\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23607 | −0.0454081 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0557 | 0.772460 | 0.386230 | − | 0.922403i | \(-0.373777\pi\) | ||||
0.386230 | + | 0.922403i | \(0.373777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.5836 | −0.461027 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.94427 | −0.107725 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.8885 | 1.23826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.5279 | −0.931525 | −0.465762 | − | 0.884910i | \(-0.654220\pi\) | ||||
−0.465762 | + | 0.884910i | \(0.654220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0000 | 0.583072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.5279 | −0.637904 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.41641 | 0.196863 | 0.0984313 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984313 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.0557 | 0.401298 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.81966 | 0.0659626 | 0.0329813 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329813 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 78.2492 | 2.83281 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.52786 | 0.199860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.94427 | 0.250743 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9443 | 0.538904 | 0.269452 | − | 0.963014i | \(-0.413157\pi\) | ||||
0.269452 | + | 0.963014i | \(0.413157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41641 | 0.0510107 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.8197 | 0.784799 | 0.392399 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392399 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0689 | −1.15195 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.4164 | 0.840059 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.4164 | 0.409035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.7214 | 1.60026 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.47214 | 0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.36068 | −0.155639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.7639 | 1.23920 | 0.619600 | − | 0.784918i | \(-0.287295\pi\) | ||||
0.619600 | + | 0.784918i | \(0.287295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.0000 | −0.996826 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.3607 | −1.29284 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.52786 | −0.125278 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.583592 | −0.0206979 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.7771 | 1.47982 | 0.739910 | − | 0.672706i | \(-0.234868\pi\) | ||||
0.739910 | + | 0.672706i | \(0.234868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.11146 | −0.0746979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.7082 | −0.555022 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.0000 | −0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.0000 | −0.563926 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.4164 | −0.613087 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0000 | −1.47664 | −0.738321 | − | 0.674450i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.40325 | −0.0843896 | −0.0421948 | − | 0.999109i | \(-0.513435\pi\) | ||||
−0.0421948 | + | 0.999109i | \(0.513435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.6525 | 0.443742 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.36068 | −0.292862 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.23607 | −0.182963 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.12461 | −0.248651 | −0.124325 | − | 0.992242i | \(-0.539677\pi\) | ||||
−0.124325 | + | 0.992242i | \(0.539677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.47214 | 0.225604 | 0.112802 | − | 0.993617i | \(-0.464017\pi\) | ||||
0.112802 | + | 0.993617i | \(0.464017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.5279 | 0.540611 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.4164 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.4721 | 0.572101 | 0.286050 | − | 0.958215i | \(-0.407657\pi\) | ||||
0.286050 | + | 0.958215i | \(0.407657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.05573 | −0.0366228 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 91.3050 | 3.16353 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.4164 | 0.533507 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.23607 | −0.319245 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.88854 | −0.134247 | −0.0671237 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671237 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.29180 | 0.147817 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.23607 | 0.0425220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.1246 | 1.61922 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.4721 | −1.04580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0557 | 0.378985 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.4164 | −1.41807 | −0.709035 | − | 0.705173i | \(-0.750869\pi\) | ||||
−0.709035 | + | 0.705173i | \(0.750869\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.52786 | −0.0522518 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.4721 | 0.562677 | 0.281339 | − | 0.959609i | \(-0.409222\pi\) | ||||
0.281339 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9443 | −0.578131 | −0.289066 | − | 0.957309i | \(-0.593345\pi\) | ||||
−0.289066 | + | 0.957309i | \(0.593345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.3607 | 1.64813 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.3050 | 1.88260 | 0.941301 | − | 0.337568i | \(-0.109604\pi\) | ||||
0.941301 | + | 0.337568i | \(0.109604\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5279 | −0.459961 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.00000 | −0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.0000 | 1.35691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.70820 | 0.261183 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4721 | 0.557497 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −54.8328 | −1.85369 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5279 | 0.389268 | 0.194634 | − | 0.980876i | \(-0.437648\pi\) | ||||
0.194634 | + | 0.980876i | \(0.437648\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.5967 | −1.13319 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5279 | 0.657910 | 0.328955 | − | 0.944346i | \(-0.393303\pi\) | ||||
0.328955 | + | 0.944346i | \(0.393303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4721 | 0.487026 | 0.243513 | − | 0.969898i | \(-0.421700\pi\) | ||||
0.243513 | + | 0.969898i | \(0.421700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.58359 | 0.288534 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5836 | 0.691129 | 0.345565 | − | 0.938395i | \(-0.387687\pi\) | ||||
0.345565 | + | 0.938395i | \(0.387687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.7771 | 2.00486 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47214 | 0.149822 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.583592 | 0.0195292 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.83282 | −0.228396 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.47214 | −0.0825422 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −78.2492 | −2.60976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11146 | 0.0703428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.8885 | −1.12774 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.4164 | 1.04432 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3050 | −0.441784 | −0.220892 | − | 0.975298i | \(-0.570897\pi\) | ||||
−0.220892 | + | 0.975298i | \(0.570897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.5279 | −1.11083 | −0.555414 | − | 0.831574i | \(-0.687440\pi\) | ||||
−0.555414 | + | 0.831574i | \(0.687440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1672 | −0.435770 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.36068 | −0.144160 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.8885 | −1.64746 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.88854 | −0.194245 | −0.0971226 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971226 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.29180 | 0.273224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.0000 | −0.329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5279 | 0.510553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.4164 | −0.374964 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.6525 | 0.808821 | 0.404411 | − | 0.914577i | \(-0.367477\pi\) | ||||
0.404411 | + | 0.914577i | \(0.367477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.2361 | −0.827079 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.4721 | 0.866659 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.7214 | 0.808475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.1935 | −1.34573 | −0.672866 | − | 0.739764i | \(-0.734937\pi\) | ||||
−0.672866 | + | 0.739764i | \(0.734937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.88854 | 0.126898 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.2361 | −1.47465 | −0.737327 | − | 0.675536i | \(-0.763912\pi\) | ||||
−0.737327 | + | 0.675536i | \(0.763912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.8328 | 0.743539 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.47214 | −0.210539 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.94427 | −0.225659 | −0.112829 | − | 0.993614i | \(-0.535991\pi\) | ||||
−0.112829 | + | 0.993614i | \(0.535991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.47214 | 0.145172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.6525 | 0.539994 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.4164 | 0.434600 | 0.217300 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217300 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.22291 | 0.136650 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.8885 | 1.22476 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.3050 | 1.46297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.3050 | 1.75177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.47214 | 0.208562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.41641 | −0.238743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.70820 | −0.119248 | −0.0596239 | − | 0.998221i | \(-0.518990\pi\) | ||||
−0.0596239 | + | 0.998221i | \(0.518990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.52786 | 0.177581 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.8328 | 0.347642 | 0.173821 | − | 0.984777i | \(-0.444389\pi\) | ||||
0.173821 | + | 0.984777i | \(0.444389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −88.7214 | −2.84428 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.47214 | −0.111197 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.4853 | −1.64716 | −0.823580 | − | 0.567200i | \(-0.808027\pi\) | ||||
−0.823580 | + | 0.567200i | \(0.808027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70.2492 | −2.24517 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.9443 | 0.477134 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.0557 | 0.799154 | 0.399577 | − | 0.916700i | \(-0.369157\pi\) | ||||
0.399577 | + | 0.916700i | \(0.369157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5836 | −0.655848 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47214 | 0.0786890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | −0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0000 | 0.381193 | 0.190596 | − | 0.981669i | \(-0.438958\pi\) | ||||
0.190596 | + | 0.981669i | \(0.438958\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.2361 | −0.420034 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.88854 | 0.0598709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.88854 | 0.249833 | 0.124916 | − | 0.992167i | \(-0.460134\pi\) | ||||
0.124916 | + | 0.992167i | \(0.460134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.47214 | 0.141492 |
(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 | 1248.2.a.k.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3744.2.a.w.1.1 | 2 | |||
4.3 | odd | 2 | 1248.2.a.m.1.2 | yes | 2 | ||
8.3 | odd | 2 | 2496.2.a.bg.1.1 | 2 | |||
8.5 | even | 2 | 2496.2.a.bj.1.1 | 2 | |||
12.11 | even | 2 | 3744.2.a.v.1.1 | 2 | |||
24.5 | odd | 2 | 7488.2.a.ch.1.2 | 2 | |||
24.11 | even | 2 | 7488.2.a.cg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.k.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1248.2.a.m.1.2 | yes | 2 | 4.3 | odd | 2 | ||
2496.2.a.bg.1.1 | 2 | 8.3 | odd | 2 | |||
2496.2.a.bj.1.1 | 2 | 8.5 | even | 2 | |||
3744.2.a.v.1.1 | 2 | 12.11 | even | 2 | |||
3744.2.a.w.1.1 | 2 | 3.2 | odd | 2 | |||
7488.2.a.cg.1.2 | 2 | 24.11 | even | 2 | |||
7488.2.a.ch.1.2 | 2 | 24.5 | odd | 2 |