Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 11x^{4} + 23x^{3} + 9x^{2} - 23x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(4.26681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | 3.93128 | 1.75812 | 0.879062 | − | 0.476708i | \(-0.158170\pi\) | ||||
0.879062 | + | 0.476708i | \(0.158170\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.69846 | −0.813617 | −0.406808 | − | 0.913513i | \(-0.633358\pi\) | ||||
−0.406808 | + | 0.913513i | \(0.633358\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.59242 | −0.441659 | −0.220830 | − | 0.975312i | \(-0.570876\pi\) | ||||
−0.220830 | + | 0.975312i | \(0.570876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.93128 | 1.01505 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.68098 | −0.407698 | −0.203849 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203849 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69846 | −0.619070 | −0.309535 | − | 0.950888i | \(-0.600173\pi\) | ||||
−0.309535 | + | 0.950888i | \(0.600173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.4550 | 2.09100 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.39770 | 0.816633 | 0.408317 | − | 0.912840i | \(-0.366116\pi\) | ||||
0.408317 | + | 0.912840i | \(0.366116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.29927 | 1.49059 | 0.745297 | − | 0.666733i | \(-0.232308\pi\) | ||||
0.745297 | + | 0.666733i | \(0.232308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.69846 | −0.469742 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.93128 | 0.664508 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.24043 | 1.02592 | 0.512960 | − | 0.858412i | \(-0.328549\pi\) | ||||
0.512960 | + | 0.858412i | \(0.328549\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.59242 | −0.254992 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.60466 | 0.406779 | 0.203390 | − | 0.979098i | \(-0.434804\pi\) | ||||
0.203390 | + | 0.979098i | \(0.434804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.2306 | −1.56015 | −0.780073 | − | 0.625689i | \(-0.784818\pi\) | ||||
−0.780073 | + | 0.625689i | \(0.784818\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.93128 | 0.586041 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.07632 | 0.448728 | 0.224364 | − | 0.974505i | \(-0.427970\pi\) | ||||
0.224364 | + | 0.974505i | \(0.427970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.68098 | −0.235385 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.38932 | 0.328198 | 0.164099 | − | 0.986444i | \(-0.447528\pi\) | ||||
0.164099 | + | 0.986444i | \(0.447528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6084 | −1.43044 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.69846 | −0.357420 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.63053 | −0.212276 | −0.106138 | − | 0.994351i | \(-0.533849\pi\) | ||||
−0.106138 | + | 0.994351i | \(0.533849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.29167 | −0.165381 | −0.0826905 | − | 0.996575i | \(-0.526351\pi\) | ||||
−0.0826905 | + | 0.996575i | \(0.526351\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.26027 | −0.776491 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0771 | −1.35329 | −0.676643 | − | 0.736311i | \(-0.736566\pi\) | ||||
−0.676643 | + | 0.736311i | \(0.736566\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.70607 | 0.914542 | 0.457271 | − | 0.889327i | \(-0.348827\pi\) | ||||
0.457271 | + | 0.889327i | \(0.348827\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.36643 | 1.09626 | 0.548129 | − | 0.836394i | \(-0.315340\pi\) | ||||
0.548129 | + | 0.836394i | \(0.315340\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.4550 | 1.20724 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.69846 | −0.307518 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.54355 | 0.848716 | 0.424358 | − | 0.905495i | \(-0.360500\pi\) | ||||
0.424358 | + | 0.905495i | \(0.360500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.16174 | −0.237282 | −0.118641 | − | 0.992937i | \(-0.537854\pi\) | ||||
−0.118641 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.60842 | −0.716784 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.39770 | 0.471483 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.84350 | 0.619410 | 0.309705 | − | 0.950833i | \(-0.399770\pi\) | ||||
0.309705 | + | 0.950833i | \(0.399770\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.59242 | −0.166931 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.29927 | 0.860595 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.6084 | −1.08840 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.64198 | 0.775926 | 0.387963 | − | 0.921675i | \(-0.373179\pi\) | ||||
0.387963 | + | 0.921675i | \(0.373179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.69846 | −0.271206 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.232042 | −0.0230890 | −0.0115445 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115445 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2612 | 1.01106 | 0.505532 | − | 0.862808i | \(-0.331296\pi\) | ||||
0.505532 | + | 0.862808i | \(0.331296\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.93128 | 0.383654 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.8420 | 1.72486 | 0.862428 | − | 0.506180i | \(-0.168943\pi\) | ||||
0.862428 | + | 0.506180i | \(0.168943\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.7741 | 1.89402 | 0.947008 | − | 0.321210i | \(-0.104090\pi\) | ||||
0.947008 | + | 0.321210i | \(0.104090\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.24043 | 0.592315 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.2412 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.93128 | 0.366594 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.59242 | −0.147220 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.68098 | −0.154095 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.71830 | −0.338028 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.60466 | 0.234854 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 21.4451 | 1.91811 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.24804 | 0.820631 | 0.410315 | − | 0.911944i | \(-0.365419\pi\) | ||||
0.410315 | + | 0.911944i | \(0.365419\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.2306 | −0.900750 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.855736 | 0.0747660 | 0.0373830 | − | 0.999301i | \(-0.488098\pi\) | ||||
0.0373830 | + | 0.999301i | \(0.488098\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.69846 | −0.233986 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.93128 | 0.338351 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.46723 | −0.210789 | −0.105395 | − | 0.994430i | \(-0.533611\pi\) | ||||
−0.105395 | + | 0.994430i | \(0.533611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.50523 | −0.127672 | −0.0638358 | − | 0.997960i | \(-0.520333\pi\) | ||||
−0.0638358 | + | 0.997960i | \(0.520333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.07632 | 0.259073 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.29710 | 0.359341 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.2886 | 1.43574 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.63577 | −0.134008 | −0.0670038 | − | 0.997753i | \(-0.521344\pi\) | ||||
−0.0670038 | + | 0.997753i | \(0.521344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.726816 | 0.0591474 | 0.0295737 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295737 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.68098 | −0.135899 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.6268 | 2.62065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.96278 | 0.555690 | 0.277845 | − | 0.960626i | \(-0.410380\pi\) | ||||
0.277845 | + | 0.960626i | \(0.410380\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.38932 | 0.189485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.19708 | −0.328741 | −0.164370 | − | 0.986399i | \(-0.552559\pi\) | ||||
−0.164370 | + | 0.986399i | \(0.552559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6084 | −0.825864 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.29691 | 0.100358 | 0.0501790 | − | 0.998740i | \(-0.484021\pi\) | ||||
0.0501790 | + | 0.998740i | \(0.484021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4642 | −0.804937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.69846 | −0.206357 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9405 | −1.13590 | −0.567952 | − | 0.823062i | \(-0.692264\pi\) | ||||
−0.567952 | + | 0.823062i | \(0.692264\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.4550 | 0.790323 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.63053 | −0.122558 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8474 | −0.960263 | −0.480132 | − | 0.877196i | \(-0.659411\pi\) | ||||
−0.480132 | + | 0.877196i | \(0.659411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.55867 | 0.710490 | 0.355245 | − | 0.934773i | \(-0.384397\pi\) | ||||
0.355245 | + | 0.934773i | \(0.384397\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.29167 | −0.0954827 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5329 | 1.80369 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.53607 | 0.331710 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2222 | −0.884365 | −0.442183 | − | 0.896925i | \(-0.645796\pi\) | ||||
−0.442183 | + | 0.896925i | \(0.645796\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67784 | −0.120774 | −0.0603868 | − | 0.998175i | \(-0.519233\pi\) | ||||
−0.0603868 | + | 0.998175i | \(0.519233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.26027 | −0.448307 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.43525 | −0.672234 | −0.336117 | − | 0.941820i | \(-0.609114\pi\) | ||||
−0.336117 | + | 0.941820i | \(0.609114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.55028 | 0.677001 | 0.338501 | − | 0.940966i | \(-0.390080\pi\) | ||||
0.338501 | + | 0.940966i | \(0.390080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0771 | −0.781320 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.39770 | 0.308658 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2397 | 0.715168 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.28170 | 0.503685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.7063 | −1.63201 | −0.816004 | − | 0.578046i | \(-0.803815\pi\) | ||||
−0.816004 | + | 0.578046i | \(0.803815\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.70607 | 0.528011 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −40.2192 | −2.74293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.29927 | 0.563391 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.36643 | 0.632925 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.67684 | 0.180064 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6313 | 0.711926 | 0.355963 | − | 0.934500i | \(-0.384153\pi\) | ||||
0.355963 | + | 0.934500i | \(0.384153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.4550 | 0.696999 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2230 | −0.811267 | −0.405634 | − | 0.914036i | \(-0.632949\pi\) | ||||
−0.405634 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.6259 | −1.03259 | −0.516294 | − | 0.856411i | \(-0.672689\pi\) | ||||
−0.516294 | + | 0.856411i | \(0.672689\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.69846 | −0.177546 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.3685 | −1.46541 | −0.732705 | − | 0.680546i | \(-0.761742\pi\) | ||||
−0.732705 | + | 0.680546i | \(0.761742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0939 | 0.788919 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.54355 | 0.490006 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4193 | −1.32081 | −0.660406 | − | 0.750909i | \(-0.729616\pi\) | ||||
−0.660406 | + | 0.750909i | \(0.729616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00158 | 0.515427 | 0.257714 | − | 0.966221i | \(-0.417031\pi\) | ||||
0.257714 | + | 0.966221i | \(0.417031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.93128 | 0.251161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.29710 | 0.273418 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.16174 | −0.136995 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −31.4694 | −1.98633 | −0.993166 | − | 0.116707i | \(-0.962766\pi\) | ||||
−0.993166 | + | 0.116707i | \(0.962766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.69846 | −0.169651 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.60842 | −0.413835 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.89989 | −0.430403 | −0.215202 | − | 0.976570i | \(-0.569041\pi\) | ||||
−0.215202 | + | 0.976570i | \(0.569041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.24043 | 0.387761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.39770 | 0.272211 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.80925 | −0.234888 | −0.117444 | − | 0.993079i | \(-0.537470\pi\) | ||||
−0.117444 | + | 0.993079i | \(0.537470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.39308 | 0.577012 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.84350 | 0.357616 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.8222 | 1.08664 | 0.543320 | − | 0.839526i | \(-0.317167\pi\) | ||||
0.543320 | + | 0.839526i | \(0.317167\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6062 | −1.73770 | −0.868851 | − | 0.495074i | \(-0.835141\pi\) | ||||
−0.868851 | + | 0.495074i | \(0.835141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.59242 | −0.0963779 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.2124 | −1.70127 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.806180 | −0.0484387 | −0.0242193 | − | 0.999707i | \(-0.507710\pi\) | ||||
−0.0242193 | + | 0.999707i | \(0.507710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.29927 | 0.496865 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.1136 | 1.08057 | 0.540285 | − | 0.841482i | \(-0.318317\pi\) | ||||
0.540285 | + | 0.841482i | \(0.318317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.23431 | 0.192260 | 0.0961298 | − | 0.995369i | \(-0.469354\pi\) | ||||
0.0961298 | + | 0.995369i | \(0.469354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.6084 | −0.628389 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.60466 | 0.153748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1743 | −0.833782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.64198 | 0.447981 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.6703 | 0.798629 | 0.399315 | − | 0.916814i | \(-0.369248\pi\) | ||||
0.399315 | + | 0.916814i | \(0.369248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.41006 | −0.373208 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.69846 | −0.156581 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.59242 | −0.0920923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.2306 | −0.589680 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.232042 | −0.0133304 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.07791 | −0.290760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.8940 | −0.907118 | −0.453559 | − | 0.891226i | \(-0.649846\pi\) | ||||
−0.453559 | + | 0.891226i | \(0.649846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2612 | 0.583738 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9375 | 0.733620 | 0.366810 | − | 0.930296i | \(-0.380450\pi\) | ||||
0.366810 | + | 0.930296i | \(0.380450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.9670 | −0.789464 | −0.394732 | − | 0.918796i | \(-0.629163\pi\) | ||||
−0.394732 | + | 0.918796i | \(0.629163\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.93128 | 0.221503 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.0258 | 1.85491 | 0.927457 | − | 0.373930i | \(-0.121990\pi\) | ||||
0.927457 | + | 0.373930i | \(0.121990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.8670 | −0.664426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.8420 | 0.995846 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.53607 | 0.252394 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6488 | −0.923508 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7741 | 1.09351 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.07632 | 0.169603 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.51818 | 0.523166 | 0.261583 | − | 0.965181i | \(-0.415755\pi\) | ||||
0.261583 | + | 0.965181i | \(0.415755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.24043 | 0.341973 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.5473 | −2.37925 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.2420 | −1.26607 | −0.633037 | − | 0.774121i | \(-0.718192\pi\) | ||||
−0.633037 | + | 0.774121i | \(0.718192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.2412 | 0.664851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.3953 | −1.21277 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.93128 | 0.211653 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.2712 | 1.35663 | 0.678314 | − | 0.734772i | \(-0.262711\pi\) | ||||
0.678314 | + | 0.734772i | \(0.262711\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.31241 | −0.177309 | −0.0886546 | − | 0.996062i | \(-0.528257\pi\) | ||||
−0.0886546 | + | 0.996062i | \(0.528257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.59242 | −0.0849973 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.7291 | −1.47587 | −0.737936 | − | 0.674871i | \(-0.764199\pi\) | ||||
−0.737936 | + | 0.674871i | \(0.764199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.2947 | 1.60788 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.68098 | −0.0889670 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2809 | −0.753717 | −0.376858 | − | 0.926271i | \(-0.622996\pi\) | ||||
−0.376858 | + | 0.926271i | \(0.622996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7183 | −0.616753 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.71830 | −0.195160 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.8221 | 1.92736 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.9110 | 1.87454 | 0.937269 | − | 0.348607i | \(-0.113345\pi\) | ||||
0.937269 | + | 0.348607i | \(0.113345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.60466 | 0.135593 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.38932 | 0.124047 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.16923 | 0.371208 | 0.185604 | − | 0.982625i | \(-0.440576\pi\) | ||||
0.185604 | + | 0.982625i | \(0.440576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.4451 | 1.10742 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.00301 | −0.360673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8434 | −1.07066 | −0.535328 | − | 0.844644i | \(-0.679812\pi\) | ||||
−0.535328 | + | 0.844644i | \(0.679812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.24804 | 0.473791 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0398 | −0.666304 | −0.333152 | − | 0.942873i | \(-0.608112\pi\) | ||||
−0.333152 | + | 0.942873i | \(0.608112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.6084 | −0.540655 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.2306 | −0.520048 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.35563 | 0.423647 | 0.211824 | − | 0.977308i | \(-0.432060\pi\) | ||||
0.211824 | + | 0.977308i | \(0.432060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.68098 | −0.0850109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.855736 | 0.0431662 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.6558 | 1.49215 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2960 | −0.968439 | −0.484219 | − | 0.874947i | \(-0.660896\pi\) | ||||
−0.484219 | + | 0.874947i | \(0.660896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.69846 | −0.135092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.6589 | 1.33128 | 0.665640 | − | 0.746273i | \(-0.268158\pi\) | ||||
0.665640 | + | 0.746273i | \(0.268158\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2160 | −0.658334 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.93128 | 0.195347 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.8396 | −0.834706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.60910 | −0.227905 | −0.113953 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113953 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.46723 | −0.121699 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.63053 | −0.0802329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.49842 | −0.417171 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.50523 | −0.0737112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7226 | −1.11007 | −0.555037 | − | 0.831826i | \(-0.687296\pi\) | ||||
−0.555037 | + | 0.831826i | \(0.687296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.03667 | 0.391683 | 0.195842 | − | 0.980636i | \(-0.437256\pi\) | ||||
0.195842 | + | 0.980636i | \(0.437256\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.07632 | 0.149576 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.5747 | −0.852496 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.29167 | −0.0625081 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.29710 | 0.207466 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.3215 | −0.786178 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.3297 | −1.74590 | −0.872948 | − | 0.487814i | \(-0.837795\pi\) | ||||
−0.872948 | + | 0.487814i | \(0.837795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.2886 | 0.828926 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.69846 | −0.129085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.7223 | −1.56175 | −0.780875 | − | 0.624687i | \(-0.785227\pi\) | ||||
−0.780875 | + | 0.624687i | \(0.785227\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.8360 | 1.08497 | 0.542486 | − | 0.840065i | \(-0.317483\pi\) | ||||
0.542486 | + | 0.840065i | \(0.317483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9725 | 1.08900 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.63577 | −0.0773693 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8511 | 1.21999 | 0.609995 | − | 0.792405i | \(-0.291171\pi\) | ||||
0.609995 | + | 0.792405i | \(0.291171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.02857 | −0.330963 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.726816 | 0.0341488 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.26027 | −0.293486 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6361 | 1.24598 | 0.622991 | − | 0.782229i | \(-0.285917\pi\) | ||||
0.622991 | + | 0.782229i | \(0.285917\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.68098 | −0.0784615 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.647907 | 0.0301760 | 0.0150880 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150880 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.94371 | 0.369176 | 0.184588 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184588 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.6268 | 1.51303 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.54750 | 0.256707 | 0.128354 | − | 0.991728i | \(-0.459031\pi\) | ||||
0.128354 | + | 0.991728i | \(0.459031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0771 | −0.511494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.96278 | 0.320828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.6068 | 1.26936 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.2124 | −1.29447 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.38932 | 0.109399 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.71594 | −0.0784034 | −0.0392017 | − | 0.999231i | \(-0.512481\pi\) | ||||
−0.0392017 | + | 0.999231i | \(0.512481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.93741 | −0.453107 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.0428 | 1.36417 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7399 | −0.803873 | −0.401936 | − | 0.915668i | \(-0.631663\pi\) | ||||
−0.401936 | + | 0.915668i | \(0.631663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.19708 | −0.189799 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0497 | 0.498666 | 0.249333 | − | 0.968418i | \(-0.419789\pi\) | ||||
0.249333 | + | 0.968418i | \(0.419789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.39246 | −0.332940 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.6084 | −0.476813 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.70607 | 0.345664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0954 | 0.854828 | 0.427414 | − | 0.904056i | \(-0.359425\pi\) | ||||
0.427414 | + | 0.904056i | \(0.359425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.29691 | 0.0579417 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.59024 | 0.383020 | 0.191510 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.912222 | −0.0405933 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.4642 | −0.464731 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.7427 | −1.89454 | −0.947269 | − | 0.320440i | \(-0.896169\pi\) | ||||
−0.947269 | + | 0.320440i | \(0.896169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.36643 | 0.414347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.69846 | −0.119140 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.3396 | 1.77757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.30134 | −0.365093 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9405 | −0.655814 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2763 | 0.669265 | 0.334633 | − | 0.942349i | \(-0.391388\pi\) | ||||
0.334633 | + | 0.942349i | \(0.391388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.77637 | −0.165129 | −0.0825645 | − | 0.996586i | \(-0.526311\pi\) | ||||
−0.0825645 | + | 0.996586i | \(0.526311\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.4550 | 0.456293 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.9509 | −0.607712 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.63053 | −0.0707588 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.14772 | −0.179658 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 70.1421 | 3.03251 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.8474 | −0.554408 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.69846 | −0.116231 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.2494 | −0.956578 | −0.478289 | − | 0.878203i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878203i | \(0.658743\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.55867 | 0.410202 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 77.7376 | 3.32991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2224 | 1.20670 | 0.603351 | − | 0.797476i | \(-0.293832\pi\) | ||||
0.603351 | + | 0.797476i | \(0.293832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.29167 | −0.0551270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.8670 | −0.505553 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.54355 | 0.320784 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.5329 | 1.04136 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.6304 | −0.789397 | −0.394699 | − | 0.918811i | \(-0.629151\pi\) | ||||
−0.394699 | + | 0.918811i | \(0.629151\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2914 | 0.689052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.53607 | 0.191513 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.4535 | −0.482709 | −0.241354 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241354 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.1237 | 2.02458 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.98194 | −0.125009 | −0.0625046 | − | 0.998045i | \(-0.519909\pi\) | ||||
−0.0625046 | + | 0.998045i | \(0.519909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.6458 | −1.28249 | −0.641243 | − | 0.767338i | \(-0.721581\pi\) | ||||
−0.641243 | + | 0.767338i | \(0.721581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.2222 | −0.510588 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4550 | 0.436003 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0107 | −0.791424 | −0.395712 | − | 0.918375i | \(-0.629502\pi\) | ||||
−0.395712 | + | 0.918375i | \(0.629502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.67784 | −0.0697286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.16174 | −0.0896842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.44748 | −0.267027 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.26027 | −0.258830 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.8626 | −0.778544 | −0.389272 | − | 0.921123i | \(-0.627273\pi\) | ||||
−0.389272 | + | 0.921123i | \(0.627273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.3953 | −0.922781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.43525 | −0.388114 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.7993 | −1.88075 | −0.940376 | − | 0.340137i | \(-0.889526\pi\) | ||||
−0.940376 | + | 0.340137i | \(0.889526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.60842 | −0.270919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.55028 | 0.390867 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.42959 | −0.303565 | −0.151782 | − | 0.988414i | \(-0.548501\pi\) | ||||
−0.151782 | + | 0.988414i | \(0.548501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7887 | −1.09273 | −0.546367 | − | 0.837546i | \(-0.683990\pi\) | ||||
−0.546367 | + | 0.837546i | \(0.683990\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.0771 | −0.451096 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.6177 | −0.594294 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1182 | −0.938339 | −0.469170 | − | 0.883108i | \(-0.655447\pi\) | ||||
−0.469170 | + | 0.883108i | \(0.655447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.39770 | 0.178204 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.89881 | −0.198185 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.5827 | −1.84107 | −0.920533 | − | 0.390665i | \(-0.872245\pi\) | ||||
−0.920533 | + | 0.390665i | \(0.872245\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.2397 | 0.412903 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.3459 | −0.819093 | −0.409547 | − | 0.912289i | \(-0.634313\pi\) | ||||
−0.409547 | + | 0.912289i | \(0.634313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.7563 | 1.35678 | 0.678391 | − | 0.734701i | \(-0.262678\pi\) | ||||
0.678391 | + | 0.734701i | \(0.262678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.84350 | 0.234115 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.0319 | 1.28128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.28170 | 0.290803 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.4901 | −0.418266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.54510 | −0.141128 | −0.0705642 | − | 0.997507i | \(-0.522480\pi\) | ||||
−0.0705642 | + | 0.997507i | \(0.522480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.7063 | −0.942240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.3567 | 1.44277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.59242 | −0.0630941 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.70607 | 0.304847 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.3914 | 0.884407 | 0.442204 | − | 0.896915i | \(-0.354197\pi\) | ||||
0.442204 | + | 0.896915i | \(0.354197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.35721 | 0.0929594 | 0.0464797 | − | 0.998919i | \(-0.485200\pi\) | ||||
0.0464797 | + | 0.998919i | \(0.485200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.2192 | −1.58363 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4923 | 0.491123 | 0.245561 | − | 0.969381i | \(-0.421028\pi\) | ||||
0.245561 | + | 0.969381i | \(0.421028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.39991 | 0.172712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.29927 | 0.325274 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.2732 | −1.57601 | −0.788007 | − | 0.615666i | \(-0.788887\pi\) | ||||
−0.788007 | + | 0.615666i | \(0.788887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.36414 | 0.131448 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.36643 | 0.365419 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.5709 | 1.26878 | 0.634391 | − | 0.773013i | \(-0.281251\pi\) | ||||
0.634391 | + | 0.773013i | \(0.281251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.7307 | −1.31197 | −0.655985 | − | 0.754774i | \(-0.727747\pi\) | ||||
−0.655985 | + | 0.754774i | \(0.727747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.67684 | 0.103960 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.6084 | −0.411377 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.39770 | 0.170280 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.6313 | 0.411031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.48551 | 0.134557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.9469 | 0.537613 | 0.268806 | − | 0.963194i | \(-0.413371\pi\) | ||||
0.268806 | + | 0.963194i | \(0.413371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.4550 | 0.402413 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.23877 | −0.0476100 | −0.0238050 | − | 0.999717i | \(-0.507578\pi\) | ||||
−0.0238050 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.64198 | 0.293272 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2230 | −0.468385 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.9616 | 1.60562 | 0.802808 | − | 0.596237i | \(-0.203338\pi\) | ||||
0.802808 | + | 0.596237i | \(0.203338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.69937 | −0.370594 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.6259 | −0.596165 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.80481 | −0.144952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8108 | −0.715597 | −0.357799 | − | 0.933799i | \(-0.616473\pi\) | ||||
−0.357799 | + | 0.933799i | \(0.616473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.69846 | −0.102506 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.91747 | −0.224462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.37839 | −0.165843 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.3685 | −0.846055 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0550 | 0.984085 | 0.492042 | − | 0.870571i | \(-0.336251\pi\) | ||||
0.492042 | + | 0.870571i | \(0.336251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.8396 | −0.635116 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.0939 | 0.455483 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.232042 | −0.00872683 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.1870 | 1.65948 | 0.829739 | − | 0.558151i | \(-0.188489\pi\) | ||||
0.829739 | + | 0.558151i | \(0.188489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.54355 | 0.282905 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.29927 | 0.310810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8931 | 0.631766 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.4193 | −0.762571 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.8677 | 1.26305 | 0.631526 | − | 0.775354i | \(-0.282429\pi\) | ||||
0.631526 | + | 0.775354i | \(0.282429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2612 | 0.382146 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.00158 | 0.297582 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.9780 | 1.70758 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.8066 | 1.51343 | 0.756717 | − | 0.653743i | \(-0.226802\pi\) | ||||
0.756717 | + | 0.653743i | \(0.226802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.1974 | 0.636068 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0460 | 0.481863 | 0.240932 | − | 0.970542i | \(-0.422547\pi\) | ||||
0.240932 | + | 0.970542i | \(0.422547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.93128 | 0.145008 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.8912 | 1.10106 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.5452 | 1.71219 | 0.856096 | − | 0.516816i | \(-0.172883\pi\) | ||||
0.856096 | + | 0.516816i | \(0.172883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.29710 | 0.157858 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.36944 | 0.0502398 | 0.0251199 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251199 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.43068 | −0.235602 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.16174 | −0.0790940 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.8420 | 0.651934 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5582 | −0.385276 | −0.192638 | − | 0.981270i | \(-0.561704\pi\) | ||||
−0.192638 | + | 0.981270i | \(0.561704\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.4694 | −1.14681 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.85732 | 0.103988 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.1021 | −1.23946 | −0.619731 | − | 0.784814i | \(-0.712758\pi\) | ||||
−0.619731 | + | 0.784814i | \(0.712758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.69846 | −0.0979480 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4495 | 0.741293 | 0.370646 | − | 0.928774i | \(-0.379136\pi\) | ||||
0.370646 | + | 0.928774i | \(0.379136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.7741 | 0.715871 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.60842 | −0.238928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.59649 | 0.0937538 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.6421 | −1.93438 | −0.967192 | − | 0.254046i | \(-0.918238\pi\) | ||||
−0.967192 | + | 0.254046i | \(0.918238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.89989 | −0.248493 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.609681 | −0.0219287 | −0.0109644 | − | 0.999940i | \(-0.503490\pi\) | ||||
−0.0109644 | + | 0.999940i | \(0.503490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 86.7688 | 3.11683 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.24043 | 0.223874 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.02857 | −0.251825 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7945 | −0.744087 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.39770 | 0.157161 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.3727 | 0.976972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.68256 | −0.238208 | −0.119104 | − | 0.992882i | \(-0.538002\pi\) | ||||
−0.119104 | + | 0.992882i | \(0.538002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.80925 | −0.135613 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.2412 | 0.435247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.05688 | 0.0730420 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.39308 | 0.333138 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.15012 | 0.217848 | 0.108924 | − | 0.994050i | \(-0.465259\pi\) | ||||
0.108924 | + | 0.994050i | \(0.465259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.17125 | −0.182946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.84350 | 0.206470 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.2750 | −0.891934 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.93128 | 0.138560 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.8222 | 0.627371 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.64664 | 0.0578928 | 0.0289464 | − | 0.999581i | \(-0.490785\pi\) | ||||
0.0289464 | + | 0.999581i | \(0.490785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.6438 | 1.88369 | 0.941844 | − | 0.336050i | \(-0.109091\pi\) | ||||
0.941844 | + | 0.336050i | \(0.109091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.6062 | −1.00326 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4999 | −0.577967 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.6068 | 0.965839 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.59242 | −0.0556438 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1819 | −0.599652 | −0.299826 | − | 0.953994i | \(-0.596929\pi\) | ||||
−0.299826 | + | 0.953994i | \(0.596929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0941 | 1.39759 | 0.698797 | − | 0.715320i | \(-0.253719\pi\) | ||||
0.698797 | + | 0.715320i | \(0.253719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.2124 | −0.982230 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.90076 | 0.344283 | 0.172142 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172142 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.3433 | −1.50538 | −0.752688 | − | 0.658377i | \(-0.771243\pi\) | ||||
−0.752688 | + | 0.658377i | \(0.771243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.806180 | −0.0279661 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.68098 | −0.0582426 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.09852 | 0.176442 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.29927 | 0.286865 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0056 | −0.483527 | −0.241763 | − | 0.970335i | \(-0.577726\pi\) | ||||
−0.241763 | + | 0.970335i | \(0.577726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.66020 | −0.333110 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.1136 | 0.623867 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −41.1377 | −1.41518 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.71830 | −0.127762 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.23431 | 0.111001 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.24043 | 0.213919 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.58205 | −0.191126 | −0.0955628 | − | 0.995423i | \(-0.530465\pi\) | ||||
−0.0955628 | + | 0.995423i | \(0.530465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.6084 | −0.362800 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.5663 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4543 | 0.459055 | 0.229527 | − | 0.973302i | \(-0.426282\pi\) | ||||
0.229527 | + | 0.973302i | \(0.426282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.60466 | 0.0887665 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.98498 | 0.339893 | 0.169946 | − | 0.985453i | \(-0.445641\pi\) | ||||
0.169946 | + | 0.985453i | \(0.445641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.7352 | −1.99706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.1743 | −0.481384 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.3560 | −0.690529 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.6395 | 0.597691 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.64198 | 0.258642 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.4451 | 0.724977 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.8448 | −1.88575 | −0.942873 | − | 0.333152i | \(-0.891888\pi\) | ||||
−0.942873 | + | 0.333152i | \(0.891888\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.6703 | 0.461089 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6444 | −0.459692 | −0.229846 | − | 0.973227i | \(-0.573822\pi\) | ||||
−0.229846 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.6072 | 1.19828 | 0.599138 | − | 0.800646i | \(-0.295510\pi\) | ||||
0.599138 | + | 0.800646i | \(0.295510\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.41006 | −0.215472 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.4118 | 0.685362 | 0.342681 | − | 0.939452i | \(-0.388665\pi\) | ||||
0.342681 | + | 0.939452i | \(0.388665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.24804 | 0.310169 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.69846 | −0.0904019 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.30134 | −0.277794 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.5070 | −1.68826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.59242 | −0.0531695 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.4977 | 1.21727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.01640 | −0.133806 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.2306 | −0.340452 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.5778 | 1.24913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.4107 | −1.54104 | −0.770521 | − | 0.637414i | \(-0.780004\pi\) | ||||
−0.770521 | + | 0.637414i | \(0.780004\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.232042 | −0.00769634 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.2375 | 0.703630 | 0.351815 | − | 0.936070i | \(-0.385565\pi\) | ||||
0.351815 | + | 0.936070i | \(0.385565\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.83338 | 0.193057 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.07791 | −0.167870 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.855736 | 0.0282589 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.0974 | −0.596979 | −0.298490 | − | 0.954413i | \(-0.596483\pi\) | ||||
−0.298490 | + | 0.954413i | \(0.596483\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8940 | −0.523725 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.2713 | −0.403916 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.2436 | 2.14520 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.2612 | 0.337021 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6583 | −0.776204 | −0.388102 | − | 0.921616i | \(-0.626869\pi\) | ||||
−0.388102 | + | 0.921616i | \(0.626869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.69846 | −0.0884385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9375 | 0.423556 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8326 | 0.583187 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.66452 | 0.152383 | 0.0761917 | − | 0.997093i | \(-0.475724\pi\) | ||||
0.0761917 | + | 0.997093i | \(0.475724\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.9670 | −0.455797 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0877 | 0.687439 | 0.343719 | − | 0.939072i | \(-0.388313\pi\) | ||||
0.343719 | + | 0.939072i | \(0.388313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.60466 | 0.0848194 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.93128 | 0.127885 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.95508 | 0.161018 | 0.0805092 | − | 0.996754i | \(-0.474345\pi\) | ||||
0.0805092 | + | 0.996754i | \(0.474345\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9153 | −0.484172 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.0258 | 1.07094 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.8355 | 1.29040 | 0.645199 | − | 0.764015i | \(-0.276775\pi\) | ||||
0.645199 | + | 0.764015i | \(0.276775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.0488 | −1.55482 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.8670 | −0.383607 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.46723 | −0.0796709 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.8779 | 1.22187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.8420 | 0.574952 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.59606 | −0.212335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.3251 | −1.97208 | −0.986041 | − | 0.166504i | \(-0.946752\pi\) | ||||
−0.986041 | + | 0.166504i | \(0.946752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.53607 | 0.145719 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.7183 | 0.953705 | 0.476852 | − | 0.878983i | \(-0.341778\pi\) | ||||
0.476852 | + | 0.878983i | \(0.341778\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.50523 | −0.0482553 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.6488 | −0.533188 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4741 | 0.527054 | 0.263527 | − | 0.964652i | \(-0.415114\pi\) | ||||
0.263527 | + | 0.964652i | \(0.415114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.7685 | −0.503962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.7741 | 0.631339 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.8673 | −1.04830 | −0.524152 | − | 0.851625i | \(-0.675617\pi\) | ||||
−0.524152 | + | 0.851625i | \(0.675617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.0926 | −1.18187 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.07632 | 0.0979205 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.2306 | −0.325313 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.4640 | −1.85717 | −0.928585 | − | 0.371120i | \(-0.878974\pi\) | ||||
−0.928585 | + | 0.371120i | \(0.878974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.51818 | 0.302050 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.5449 | 1.19025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5053 | −1.09279 | −0.546396 | − | 0.837527i | \(-0.684001\pi\) | ||||
−0.546396 | + | 0.837527i | \(0.684001\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.24043 | 0.197438 |
(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 | 7728.2.a.ch.1.6 | 6 | ||
4.3 | odd | 2 | 3864.2.a.w.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.w.1.6 | ✓ | 6 | 4.3 | odd | 2 | ||
7728.2.a.ch.1.6 | 6 | 1.1 | even | 1 | trivial |