Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(1\) |
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 | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.23607 | 0.299791 | 0.149895 | − | 0.988702i | \(-0.452106\pi\) | ||||
0.149895 | + | 0.988702i | \(0.452106\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.472136 | 0.0984472 | 0.0492236 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492236 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.23607 | −1.34370 | −0.671852 | − | 0.740685i | \(-0.734501\pi\) | ||||
−0.671852 | + | 0.740685i | \(0.734501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | 1.16243 | 0.581215 | − | 0.813750i | \(-0.302578\pi\) | ||||
0.581215 | + | 0.813750i | \(0.302578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.23607 | 0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.23607 | 0.472029 | 0.236015 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236015 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.23607 | 0.444508 | 0.222254 | − | 0.974989i | \(-0.428659\pi\) | ||||
0.222254 | + | 0.974989i | \(0.428659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.52786 | −0.745377 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.52786 | 0.685647 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.52786 | −0.186658 | −0.0933292 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933292 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.23607 | −0.621407 | −0.310703 | − | 0.950507i | \(-0.600565\pi\) | ||||
−0.310703 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.47214 | 0.523424 | 0.261712 | − | 0.965146i | \(-0.415713\pi\) | ||||
0.261712 | + | 0.965146i | \(0.415713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.47214 | −0.509647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.70820 | 0.626557 | 0.313278 | − | 0.949661i | \(-0.398573\pi\) | ||||
0.313278 | + | 0.949661i | \(0.398573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.52786 | −0.165720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9443 | −1.16009 | −0.580045 | − | 0.814584i | \(-0.696965\pi\) | ||||
−0.580045 | + | 0.814584i | \(0.696965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.23607 | −0.126818 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.1803 | −1.80901 | −0.904506 | − | 0.426461i | \(-0.859760\pi\) | ||||
−0.904506 | + | 0.426461i | \(0.859760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.70820 | 0.745180 | 0.372590 | − | 0.927996i | \(-0.378470\pi\) | ||||
0.372590 | + | 0.927996i | \(0.378470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9443 | 1.43140 | 0.715701 | − | 0.698407i | \(-0.246107\pi\) | ||||
0.715701 | + | 0.698407i | \(0.246107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.2361 | −1.43329 | −0.716644 | − | 0.697439i | \(-0.754323\pi\) | ||||
−0.716644 | + | 0.697439i | \(0.754323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.583592 | −0.0544202 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4721 | −0.929252 | −0.464626 | − | 0.885507i | \(-0.653811\pi\) | ||||
−0.464626 | + | 0.885507i | \(0.653811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.76393 | −0.765708 | −0.382854 | − | 0.923809i | \(-0.625059\pi\) | ||||
−0.382854 | + | 0.923809i | \(0.625059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.944272 | 0.0806746 | 0.0403373 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403373 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.52786 | −0.129592 | −0.0647959 | − | 0.997899i | \(-0.520640\pi\) | ||||
−0.0647959 | + | 0.997899i | \(0.520640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.0000 | −1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.94427 | 0.742781 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4721 | −0.857911 | −0.428955 | − | 0.903326i | \(-0.641118\pi\) | ||||
−0.428955 | + | 0.903326i | \(0.641118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3607 | 1.78458 | 0.892288 | − | 0.451466i | \(-0.149099\pi\) | ||||
0.892288 | + | 0.451466i | \(0.149099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.472136 | −0.0372095 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.47214 | 0.191300 | 0.0956498 | − | 0.995415i | \(-0.469507\pi\) | ||||
0.0956498 | + | 0.995415i | \(0.469507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.94427 | −0.527963 | −0.263982 | − | 0.964528i | \(-0.585036\pi\) | ||||
−0.263982 | + | 0.964528i | \(0.585036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.70820 | −0.576138 | −0.288069 | − | 0.957610i | \(-0.593013\pi\) | ||||
−0.288069 | + | 0.957610i | \(0.593013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.47214 | 0.332411 | 0.166206 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166206 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.52786 | 0.406417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.52786 | 0.404237 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.4721 | −1.77074 | −0.885371 | − | 0.464886i | \(-0.846095\pi\) | ||||
−0.885371 | + | 0.464886i | \(0.846095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.472136 | −0.0339851 | −0.0169925 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169925 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.94427 | 0.350490 | 0.175245 | − | 0.984525i | \(-0.443928\pi\) | ||||
0.175245 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.23607 | 0.507872 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.47214 | −0.172661 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.47214 | 0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.47214 | −0.445560 | −0.222780 | − | 0.974869i | \(-0.571513\pi\) | ||||
−0.222780 | + | 0.974869i | \(0.571513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.88854 | −0.674393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.52786 | −0.371844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4164 | −1.56808 | −0.784039 | − | 0.620711i | \(-0.786844\pi\) | ||||
−0.784039 | + | 0.620711i | \(0.786844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.4164 | 1.02322 | 0.511611 | − | 0.859217i | \(-0.329049\pi\) | ||||
0.511611 | + | 0.859217i | \(0.329049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.9443 | 1.51620 | 0.758100 | − | 0.652138i | \(-0.226128\pi\) | ||||
0.758100 | + | 0.652138i | \(0.226128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.47214 | 0.161955 | 0.0809775 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809775 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.05573 | 0.327028 | 0.163514 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163514 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.472136 | 0.0304130 | 0.0152065 | − | 0.999884i | \(-0.495159\pi\) | ||||
0.0152065 | + | 0.999884i | \(0.495159\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.23607 | −0.0789695 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.47214 | −0.284555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.180340 | 0.0113830 | 0.00569148 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569148 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.11146 | 0.132746 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4721 | −0.777990 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | 0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.94427 | −0.181552 | −0.0907758 | − | 0.995871i | \(-0.528935\pi\) | ||||
−0.0907758 | + | 0.995871i | \(0.528935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.5279 | −0.946751 | −0.473375 | − | 0.880861i | \(-0.656965\pi\) | ||||
−0.473375 | + | 0.880861i | \(0.656965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.52786 | −0.335794 | −0.167897 | − | 0.985805i | \(-0.553698\pi\) | ||||
−0.167897 | + | 0.985805i | \(0.553698\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5279 | −0.936365 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.47214 | −0.268705 | −0.134352 | − | 0.990934i | \(-0.542895\pi\) | ||||
−0.134352 | + | 0.990934i | \(0.542895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18034 | −0.487998 | −0.243999 | − | 0.969775i | \(-0.578459\pi\) | ||||
−0.243999 | + | 0.969775i | \(0.578459\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.05573 | −0.419419 | −0.209710 | − | 0.977764i | \(-0.567252\pi\) | ||||
−0.209710 | + | 0.977764i | \(0.567252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4721 | −0.910126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.94427 | −0.287867 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.11146 | −0.122109 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.36068 | 0.249692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5279 | 1.00037 | 0.500184 | − | 0.865919i | \(-0.333266\pi\) | ||||
0.500184 | + | 0.865919i | \(0.333266\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.1803 | 0.917503 | 0.458751 | − | 0.888565i | \(-0.348297\pi\) | ||||
0.458751 | + | 0.888565i | \(0.348297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.52786 | 0.199407 | 0.0997033 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997033 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1246 | −0.737152 | −0.368576 | − | 0.929598i | \(-0.620155\pi\) | ||||
−0.368576 | + | 0.929598i | \(0.620155\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.3607 | −1.81185 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23607 | 0.0687767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.5279 | 0.861331 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23607 | −0.178410 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.88854 | −0.543524 | −0.271762 | − | 0.962365i | \(-0.587606\pi\) | ||||
−0.271762 | + | 0.962365i | \(0.587606\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.88854 | 0.103182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.94427 | 0.160385 | 0.0801924 | − | 0.996779i | \(-0.474447\pi\) | ||||
0.0801924 | + | 0.996779i | \(0.474447\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.9443 | 1.56742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.0000 | −1.61048 | −0.805242 | − | 0.592946i | \(-0.797965\pi\) | ||||
−0.805242 | + | 0.592946i | \(0.797965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.8328 | −1.32927 | −0.664635 | − | 0.747168i | \(-0.731413\pi\) | ||||
−0.664635 | + | 0.747168i | \(0.731413\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.7082 | −1.47476 | −0.737379 | − | 0.675479i | \(-0.763937\pi\) | ||||
−0.737379 | + | 0.675479i | \(0.763937\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.47214 | 0.343505 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.58359 | 0.136357 | 0.0681784 | − | 0.997673i | \(-0.478281\pi\) | ||||
0.0681784 | + | 0.997673i | \(0.478281\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.52786 | −0.289342 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.94427 | 0.258089 | 0.129044 | − | 0.991639i | \(-0.458809\pi\) | ||||
0.129044 | + | 0.991639i | \(0.458809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.23607 | −0.168008 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9443 | −0.773785 | −0.386893 | − | 0.922125i | \(-0.626452\pi\) | ||||
−0.386893 | + | 0.922125i | \(0.626452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.3607 | 1.66666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9443 | −1.07583 | −0.537917 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537917 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.52786 | 0.0780702 | 0.0390351 | − | 0.999238i | \(-0.487572\pi\) | ||||
0.0390351 | + | 0.999238i | \(0.487572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.52786 | 0.281726 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.58359 | 0.232397 | 0.116199 | − | 0.993226i | \(-0.462929\pi\) | ||||
0.116199 | + | 0.993226i | \(0.462929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.583592 | 0.0295135 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.8328 | 0.746320 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8885 | 1.19893 | 0.599466 | − | 0.800400i | \(-0.295380\pi\) | ||||
0.599466 | + | 0.800400i | \(0.295380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.81966 | −0.390495 | −0.195248 | − | 0.980754i | \(-0.562551\pi\) | ||||
−0.195248 | + | 0.980754i | \(0.562551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.9443 | −1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.3607 | 1.10566 | 0.552832 | − | 0.833293i | \(-0.313547\pi\) | ||||
0.552832 | + | 0.833293i | \(0.313547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.05573 | −0.346352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.1246 | −1.03200 | −0.516002 | − | 0.856587i | \(-0.672580\pi\) | ||||
−0.516002 | + | 0.856587i | \(0.672580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.3050 | −1.91561 | −0.957803 | − | 0.287425i | \(-0.907201\pi\) | ||||
−0.957803 | + | 0.287425i | \(0.907201\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.29180 | −0.208183 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.52786 | 0.170725 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0689 | −1.73738 | −0.868688 | − | 0.495359i | \(-0.835037\pi\) | ||||
−0.868688 | + | 0.495359i | \(0.835037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.472136 | −0.0226894 | −0.0113447 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113447 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.472136 | 0.0225853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.4164 | −1.88124 | −0.940621 | − | 0.339458i | \(-0.889756\pi\) | ||||
−0.940621 | + | 0.339458i | \(0.889756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8885 | −0.754887 | −0.377444 | − | 0.926033i | \(-0.623197\pi\) | ||||
−0.377444 | + | 0.926033i | \(0.623197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5279 | 0.641282 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.2361 | 0.719035 | 0.359517 | − | 0.933138i | \(-0.382941\pi\) | ||||
0.359517 | + | 0.933138i | \(0.382941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.94427 | 0.421169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.52786 | −0.259150 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4164 | 1.00182 | 0.500909 | − | 0.865500i | \(-0.332999\pi\) | ||||
0.500909 | + | 0.865500i | \(0.332999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.23607 | −0.243868 | −0.121934 | − | 0.992538i | \(-0.538910\pi\) | ||||
−0.121934 | + | 0.992538i | \(0.538910\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8885 | −1.20314 | −0.601571 | − | 0.798819i | \(-0.705458\pi\) | ||||
−0.601571 | + | 0.798819i | \(0.705458\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.1803 | 1.11893 | 0.559466 | − | 0.828853i | \(-0.311006\pi\) | ||||
0.559466 | + | 0.828853i | \(0.311006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52786 | 0.0705502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.7771 | 1.64503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.47214 | −0.159313 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.1246 | −0.965208 | −0.482604 | − | 0.875839i | \(-0.660309\pi\) | ||||
−0.482604 | + | 0.875839i | \(0.660309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.36068 | −0.198008 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.4164 | 1.06110 | 0.530549 | − | 0.847654i | \(-0.321986\pi\) | ||||
0.530549 | + | 0.847654i | \(0.321986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94427 | −0.402830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.23607 | 0.234870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.8885 | 1.69612 | 0.848062 | − | 0.529897i | \(-0.177769\pi\) | ||||
0.848062 | + | 0.529897i | \(0.177769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.1803 | 1.25650 | 0.628250 | − | 0.778012i | \(-0.283772\pi\) | ||||
0.628250 | + | 0.778012i | \(0.283772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4721 | 0.999997 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5279 | −1.39745 | −0.698724 | − | 0.715391i | \(-0.746248\pi\) | ||||
−0.698724 | + | 0.715391i | \(0.746248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.47214 | −0.197836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.0557 | 0.487174 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4721 | 0.636484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.41641 | 0.0620540 | 0.0310270 | − | 0.999519i | \(-0.490122\pi\) | ||||
0.0310270 | + | 0.999519i | \(0.490122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.5279 | −0.941348 | −0.470674 | − | 0.882307i | \(-0.655989\pi\) | ||||
−0.470674 | + | 0.882307i | \(0.655989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.94427 | −0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.52786 | −0.411925 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.47214 | 0.192629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.8885 | −1.54297 | −0.771485 | − | 0.636248i | \(-0.780485\pi\) | ||||
−0.771485 | + | 0.636248i | \(0.780485\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4721 | −0.791259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8328 | −0.634205 | −0.317103 | − | 0.948391i | \(-0.602710\pi\) | ||||
−0.317103 | + | 0.948391i | \(0.602710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.23607 | −0.308267 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.583592 | −0.0247276 | −0.0123638 | − | 0.999924i | \(-0.503936\pi\) | ||||
−0.0123638 | + | 0.999924i | \(0.503936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.7771 | −1.51321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.4164 | −0.986884 | −0.493442 | − | 0.869779i | \(-0.664261\pi\) | ||||
−0.493442 | + | 0.869779i | \(0.664261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8328 | 0.792303 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.7082 | 1.07774 | 0.538872 | − | 0.842388i | \(-0.318851\pi\) | ||||
0.538872 | + | 0.842388i | \(0.318851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.88854 | 0.246428 | 0.123214 | − | 0.992380i | \(-0.460680\pi\) | ||||
0.123214 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.63932 | −0.0683644 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.4164 | −1.05810 | −0.529049 | − | 0.848591i | \(-0.677451\pi\) | ||||
−0.529049 | + | 0.848591i | \(0.677451\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.70820 | −0.236816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.4721 | 0.599375 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2918 | 0.920081 | 0.460040 | − | 0.887898i | \(-0.347835\pi\) | ||||
0.460040 | + | 0.887898i | \(0.347835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.47214 | 0.266680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.7082 | 1.63062 | 0.815310 | − | 0.579024i | \(-0.196566\pi\) | ||||
0.815310 | + | 0.579024i | \(0.196566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.52786 | 0.0626363 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5967 | −0.882419 | −0.441210 | − | 0.897404i | \(-0.645450\pi\) | ||||
−0.441210 | + | 0.897404i | \(0.645450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5836 | 0.758041 | 0.379020 | − | 0.925388i | \(-0.376261\pi\) | ||||
0.379020 | + | 0.925388i | \(0.376261\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.1246 | −0.452280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4721 | −0.585480 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3607 | 0.418464 | 0.209232 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209232 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −48.9443 | −1.97042 | −0.985211 | − | 0.171345i | \(-0.945189\pi\) | ||||
−0.985211 | + | 0.171345i | \(0.945189\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.58359 | 0.184230 | 0.0921151 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921151 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9443 | 0.438473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.52786 | −0.220410 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.9443 | −0.674541 | −0.337270 | − | 0.941408i | \(-0.609504\pi\) | ||||
−0.337270 | + | 0.941408i | \(0.609504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9443 | 0.513678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.7082 | −1.33139 | −0.665697 | − | 0.746222i | \(-0.731866\pi\) | ||||
−0.665697 | + | 0.746222i | \(0.731866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0557 | 0.593740 | 0.296870 | − | 0.954918i | \(-0.404057\pi\) | ||||
0.296870 | + | 0.954918i | \(0.404057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.65248 | −0.261536 | −0.130768 | − | 0.991413i | \(-0.541744\pi\) | ||||
−0.130768 | + | 0.991413i | \(0.541744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.8885 | 0.702187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.11146 | −0.239160 | −0.119580 | − | 0.992825i | \(-0.538155\pi\) | ||||
−0.119580 | + | 0.992825i | \(0.538155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8328 | 0.423273 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.7082 | −1.70263 | −0.851315 | − | 0.524655i | \(-0.824194\pi\) | ||||
−0.851315 | + | 0.524655i | \(0.824194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4164 | 0.988584 | 0.494292 | − | 0.869296i | \(-0.335427\pi\) | ||||
0.494292 | + | 0.869296i | \(0.335427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.23607 | 0.0479327 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.41641 | −0.132284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.7771 | −0.609068 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.2492 | −1.39730 | −0.698652 | − | 0.715461i | \(-0.746217\pi\) | ||||
−0.698652 | + | 0.715461i | \(0.746217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.41641 | 0.361902 | 0.180951 | − | 0.983492i | \(-0.442082\pi\) | ||||
0.180951 | + | 0.983492i | \(0.442082\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.7639 | −0.717982 | −0.358991 | − | 0.933341i | \(-0.616879\pi\) | ||||
−0.358991 | + | 0.933341i | \(0.616879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.16718 | −0.0445958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.4721 | −0.551344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4721 | 0.854880 | 0.427440 | − | 0.904044i | \(-0.359415\pi\) | ||||
0.427440 | + | 0.904044i | \(0.359415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.88854 | 0.0716366 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.47214 | 0.0936388 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8328 | 0.560228 | 0.280114 | − | 0.959967i | \(-0.409628\pi\) | ||||
0.280114 | + | 0.959967i | \(0.409628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.47214 | −0.168670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.1803 | 0.683742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.2492 | −1.36137 | −0.680684 | − | 0.732577i | \(-0.738317\pi\) | ||||
−0.680684 | + | 0.732577i | \(0.738317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.05573 | 0.114438 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.7214 | 0.924526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.1246 | −1.53369 | −0.766845 | − | 0.641833i | \(-0.778174\pi\) | ||||
−0.766845 | + | 0.641833i | \(0.778174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.94427 | 0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.1246 | 0.933105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.36068 | 0.161729 | 0.0808643 | − | 0.996725i | \(-0.474232\pi\) | ||||
0.0808643 | + | 0.996725i | \(0.474232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5279 | 0.425791 | 0.212896 | − | 0.977075i | \(-0.431711\pi\) | ||||
0.212896 | + | 0.977075i | \(0.431711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.83282 | −0.251690 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.8885 | 0.658041 | 0.329020 | − | 0.944323i | \(-0.393282\pi\) | ||||
0.329020 | + | 0.944323i | \(0.393282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.65248 | 0.170683 | 0.0853414 | − | 0.996352i | \(-0.472802\pi\) | ||||
0.0853414 | + | 0.996352i | \(0.472802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.9443 | 0.474241 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.70820 | −0.281652 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.8328 | 0.687219 | 0.343610 | − | 0.939113i | \(-0.388350\pi\) | ||||
0.343610 | + | 0.939113i | \(0.388350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.7214 | −0.899702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8885 | 0.722861 | 0.361431 | − | 0.932399i | \(-0.382288\pi\) | ||||
0.361431 | + | 0.932399i | \(0.382288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.7639 | 1.40519 | 0.702596 | − | 0.711589i | \(-0.252024\pi\) | ||||
0.702596 | + | 0.711589i | \(0.252024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9443 | −0.541019 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.8885 | −0.645918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.3607 | −0.517859 | −0.258930 | − | 0.965896i | \(-0.583370\pi\) | ||||
−0.258930 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.8885 | 1.14695 | 0.573476 | − | 0.819223i | \(-0.305595\pi\) | ||||
0.573476 | + | 0.819223i | \(0.305595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.4721 | −0.807223 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.00000 | 0.0716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.4164 | −0.837905 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.6393 | −0.986490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5836 | −0.591141 | −0.295571 | − | 0.955321i | \(-0.595510\pi\) | ||||
−0.295571 | + | 0.955321i | \(0.595510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2361 | 0.541732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7771 | 0.560261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0557 | 0.887519 | 0.443760 | − | 0.896146i | \(-0.353644\pi\) | ||||
0.443760 | + | 0.896146i | \(0.353644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | 0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.583592 | 0.0205689 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.83282 | 0.239933 | 0.119966 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119966 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | 0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.3607 | −0.989795 | −0.494897 | − | 0.868951i | \(-0.664794\pi\) | ||||
−0.494897 | + | 0.868951i | \(0.664794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.8328 | −1.49306 | −0.746529 | − | 0.665353i | \(-0.768281\pi\) | ||||
−0.746529 | + | 0.665353i | \(0.768281\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.7639 | 0.930673 | 0.465337 | − | 0.885134i | \(-0.345933\pi\) | ||||
0.465337 | + | 0.885134i | \(0.345933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.4721 | −0.572101 | −0.286050 | − | 0.958215i | \(-0.592343\pi\) | ||||
−0.286050 | + | 0.958215i | \(0.592343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.23607 | 0.0428272 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.05573 | −0.105748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3607 | 0.805541 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.65248 | −0.297654 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00000 | −0.309244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.11146 | −0.0723798 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.7771 | 1.15651 | 0.578253 | − | 0.815858i | \(-0.303735\pi\) | ||||
0.578253 | + | 0.815858i | \(0.303735\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.8328 | −0.984910 | −0.492455 | − | 0.870338i | \(-0.663900\pi\) | ||||
−0.492455 | + | 0.870338i | \(0.663900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.944272 | 0.0322181 | 0.0161091 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161091 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.1803 | 1.16351 | 0.581756 | − | 0.813363i | \(-0.302366\pi\) | ||||
0.581756 | + | 0.813363i | \(0.302366\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.58359 | 0.291851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.6656 | −1.82048 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.83282 | 0.231521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4721 | −0.354023 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.8885 | 1.34694 | 0.673470 | − | 0.739214i | \(-0.264803\pi\) | ||||
0.673470 | + | 0.739214i | \(0.264803\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7082 | −0.394459 | −0.197230 | − | 0.980357i | \(-0.563194\pi\) | ||||
−0.197230 | + | 0.980357i | \(0.563194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.1115 | 0.609499 | 0.304750 | − | 0.952433i | \(-0.401427\pi\) | ||||
0.304750 | + | 0.952433i | \(0.401427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.63932 | 0.122196 | 0.0610982 | − | 0.998132i | \(-0.480540\pi\) | ||||
0.0610982 | + | 0.998132i | \(0.480540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4721 | 0.351224 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.23607 | 0.108291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.52786 | 0.318481 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.8328 | −1.56196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.52786 | −0.183752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5836 | 0.417831 | 0.208916 | − | 0.977934i | \(-0.433007\pi\) | ||||
0.208916 | + | 0.977934i | \(0.433007\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.1246 | 1.16373 | 0.581865 | − | 0.813285i | \(-0.302323\pi\) | ||||
0.581865 | + | 0.813285i | \(0.302323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.5279 | 0.844849 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.76393 | 0.289411 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.8885 | 0.853984 | 0.426992 | − | 0.904255i | \(-0.359573\pi\) | ||||
0.426992 | + | 0.904255i | \(0.359573\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.4164 | 0.770760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.5279 | 0.510553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.0132 | 1.08313 | 0.541563 | − | 0.840660i | \(-0.317833\pi\) | ||||
0.541563 | + | 0.840660i | \(0.317833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.83282 | −0.223457 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3050 | 0.498927 | 0.249464 | − | 0.968384i | \(-0.419746\pi\) | ||||
0.249464 | + | 0.968384i | \(0.419746\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.944272 | 0.0307497 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4721 | 0.925220 | 0.462610 | − | 0.886562i | \(-0.346913\pi\) | ||||
0.462610 | + | 0.886562i | \(0.346913\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.5410 | −1.70197 | −0.850985 | − | 0.525190i | \(-0.823994\pi\) | ||||
−0.850985 | + | 0.525190i | \(0.823994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.2492 | 0.978842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.944272 | −0.0304921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.583592 | 0.0187865 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8328 | 1.12015 | 0.560074 | − | 0.828443i | \(-0.310773\pi\) | ||||
0.560074 | + | 0.828443i | \(0.310773\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.8328 | 0.476008 | 0.238004 | − | 0.971264i | \(-0.423507\pi\) | ||||
0.238004 | + | 0.971264i | \(0.423507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52786 | 0.0489811 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.12461 | 0.163951 | 0.0819754 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819754 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.9443 | −1.56427 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.0557 | −0.607783 | −0.303892 | − | 0.952707i | \(-0.598286\pi\) | ||||
−0.303892 | + | 0.952707i | \(0.598286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.94427 | 0.157538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.77709 | 0.120104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.583592 | −0.0185384 | −0.00926921 | − | 0.999957i | \(-0.502951\pi\) | ||||
−0.00926921 | + | 0.999957i | \(0.502951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.11146 | −0.193746 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3607 | −0.328126 | −0.164063 | − | 0.986450i | \(-0.552460\pi\) | ||||
−0.164063 | + | 0.986450i | \(0.552460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9576.2.a.bq.1.1 | yes | 2 | |
3.2 | odd | 2 | 9576.2.a.be.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9576.2.a.be.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
9576.2.a.bq.1.1 | yes | 2 | 1.1 | even | 1 | trivial |