Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(1,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3312.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.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: | \(26.4464531494\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.1 |
$q$-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 | ||||||||
\(5\) | 3.64575 | 1.63043 | 0.815215 | − | 0.579159i | \(-0.196619\pi\) | ||||
0.815215 | + | 0.579159i | \(0.196619\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.64575 | 1.09924 | 0.549618 | − | 0.835416i | \(-0.314773\pi\) | ||||
0.549618 | + | 0.835416i | \(0.314773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.29150 | −1.46760 | −0.733799 | − | 0.679366i | \(-0.762255\pi\) | ||||
−0.733799 | + | 0.679366i | \(0.762255\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.29150 | −1.76845 | −0.884225 | − | 0.467062i | \(-0.845312\pi\) | ||||
−0.884225 | + | 0.467062i | \(0.845312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.64575 | −1.29522 | −0.647612 | − | 0.761970i | \(-0.724232\pi\) | ||||
−0.647612 | + | 0.761970i | \(0.724232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.29150 | 1.65830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.29150 | 0.239826 | 0.119913 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119913 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.29150 | −1.66880 | −0.834402 | − | 0.551157i | \(-0.814187\pi\) | ||||
−0.834402 | + | 0.551157i | \(0.814187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.29150 | −1.23249 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.93725 | −1.46928 | −0.734638 | − | 0.678460i | \(-0.762648\pi\) | ||||
−0.734638 | + | 0.678460i | \(0.762648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64575 | −0.860969 | −0.430485 | − | 0.902598i | \(-0.641657\pi\) | ||||
−0.430485 | + | 0.902598i | \(0.641657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.64575 | −0.500782 | −0.250391 | − | 0.968145i | \(-0.580559\pi\) | ||||
−0.250391 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2915 | 1.79223 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.64575 | 0.722864 | 0.361432 | − | 0.932398i | \(-0.382288\pi\) | ||||
0.361432 | + | 0.932398i | \(0.382288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −19.2915 | −2.39282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.937254 | −0.114504 | −0.0572519 | − | 0.998360i | \(-0.518234\pi\) | ||||
−0.0572519 | + | 0.998360i | \(0.518234\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29150 | 0.385241 | 0.192621 | − | 0.981273i | \(-0.438301\pi\) | ||||
0.192621 | + | 0.981273i | \(0.438301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.29150 | −0.830944 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5830 | 1.41570 | 0.707849 | − | 0.706363i | \(-0.249666\pi\) | ||||
0.707849 | + | 0.706363i | \(0.249666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.35425 | −0.916998 | −0.458499 | − | 0.888695i | \(-0.651613\pi\) | ||||
−0.458499 | + | 0.888695i | \(0.651613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.5830 | −2.88333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5830 | 1.10940 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.5830 | −2.11177 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.29150 | 0.943409 | 0.471705 | − | 0.881757i | \(-0.343639\pi\) | ||||
0.471705 | + | 0.881757i | \(0.343639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.29150 | 0.128509 | 0.0642547 | − | 0.997934i | \(-0.479533\pi\) | ||||
0.0642547 | + | 0.997934i | \(0.479533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2915 | 1.70378 | 0.851891 | − | 0.523719i | \(-0.175456\pi\) | ||||
0.851891 | + | 0.523719i | \(0.175456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.35425 | −0.807636 | −0.403818 | − | 0.914839i | \(-0.632317\pi\) | ||||
−0.403818 | + | 0.914839i | \(0.632317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.22876 | 0.788172 | 0.394086 | − | 0.919074i | \(-0.371061\pi\) | ||||
0.394086 | + | 0.919074i | \(0.371061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.5830 | 1.37185 | 0.685927 | − | 0.727670i | \(-0.259397\pi\) | ||||
0.685927 | + | 0.727670i | \(0.259397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.64575 | 0.339968 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.5830 | 1.33682 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.29150 | 0.208318 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5830 | −0.939090 | −0.469545 | − | 0.882909i | \(-0.655582\pi\) | ||||
−0.469545 | + | 0.882909i | \(0.655582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.87451 | 0.862740 | 0.431370 | − | 0.902175i | \(-0.358030\pi\) | ||||
0.431370 | + | 0.902175i | \(0.358030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2915 | 0.979097 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.87451 | 0.843636 | 0.421818 | − | 0.906680i | \(-0.361392\pi\) | ||||
0.421818 | + | 0.906680i | \(0.361392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.2915 | −1.61324 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.70850 | 0.391019 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6458 | −1.28175 | −0.640875 | − | 0.767645i | \(-0.721428\pi\) | ||||
−0.640875 | + | 0.767645i | \(0.721428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.70850 | −0.545930 | −0.272965 | − | 0.962024i | \(-0.588004\pi\) | ||||
−0.272965 | + | 0.962024i | \(0.588004\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.8745 | −2.72087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.64575 | −0.131345 | −0.0656726 | − | 0.997841i | \(-0.520919\pi\) | ||||
−0.0656726 | + | 0.997841i | \(0.520919\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2915 | 0.884419 | 0.442209 | − | 0.896912i | \(-0.354195\pi\) | ||||
0.442209 | + | 0.896912i | \(0.354195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.1660 | 1.79264 | 0.896320 | − | 0.443408i | \(-0.146231\pi\) | ||||
0.896320 | + | 0.443408i | \(0.146231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0000 | 1.15385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.8745 | −1.20692 | −0.603458 | − | 0.797395i | \(-0.706211\pi\) | ||||
−0.603458 | + | 0.797395i | \(0.706211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.5830 | −1.25356 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.70850 | 0.351930 | 0.175965 | − | 0.984396i | \(-0.443696\pi\) | ||||
0.175965 | + | 0.984396i | \(0.443696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3542 | 0.769625 | 0.384813 | − | 0.922995i | \(-0.374266\pi\) | ||||
0.384813 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.5830 | −2.39555 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5830 | −1.94394 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.29150 | −0.527595 | −0.263797 | − | 0.964578i | \(-0.584975\pi\) | ||||
−0.263797 | + | 0.964578i | \(0.584975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.0000 | −1.58359 | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.58301 | −0.181291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.8745 | −1.52778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.5830 | −1.42376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.708497 | −0.0487750 | −0.0243875 | − | 0.999703i | \(-0.507764\pi\) | ||||
−0.0243875 | + | 0.999703i | \(0.507764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.5830 | −1.40375 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.5830 | 1.26150 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 38.5830 | 2.59537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8745 | −0.795176 | −0.397588 | − | 0.917564i | \(-0.630153\pi\) | ||||
−0.397588 | + | 0.917564i | \(0.630153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.9373 | −1.52240 | −0.761200 | − | 0.648518i | \(-0.775389\pi\) | ||||
−0.761200 | + | 0.648518i | \(0.775389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9373 | 1.64790 | 0.823950 | − | 0.566662i | \(-0.191766\pi\) | ||||
0.823950 | + | 0.566662i | \(0.191766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.8745 | 1.42694 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.29150 | −0.340856 | −0.170428 | − | 0.985370i | \(-0.554515\pi\) | ||||
−0.170428 | + | 0.985370i | \(0.554515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.9373 | −0.698756 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.8745 | 1.90087 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3542 | −1.28475 | −0.642374 | − | 0.766391i | \(-0.722051\pi\) | ||||
−0.642374 | + | 0.766391i | \(0.722051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.64575 | 0.229206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.41699 | −0.213146 | −0.106573 | − | 0.994305i | \(-0.533988\pi\) | ||||
−0.106573 | + | 0.994305i | \(0.533988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.8745 | 1.11067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.41699 | −0.580677 | −0.290338 | − | 0.956924i | \(-0.593768\pi\) | ||||
−0.290338 | + | 0.956924i | \(0.593768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2915 | −0.816491 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.5830 | 1.98662 | 0.993310 | − | 0.115474i | \(-0.0368389\pi\) | ||||
0.993310 | + | 0.115474i | \(0.0368389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.2288 | 1.82286 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.29150 | −0.317936 | −0.158968 | − | 0.987284i | \(-0.550817\pi\) | ||||
−0.158968 | + | 0.987284i | \(0.550817\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5203 | −0.922584 | −0.461292 | − | 0.887248i | \(-0.652614\pi\) | ||||
−0.461292 | + | 0.887248i | \(0.652614\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.1660 | 2.12741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.77124 | 0.337160 | 0.168580 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168580 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.29150 | −0.306015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.2915 | 0.650831 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.5830 | 1.17858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.87451 | 0.106984 | 0.0534919 | − | 0.998568i | \(-0.482965\pi\) | ||||
0.0534919 | + | 0.998568i | \(0.482965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.1660 | −1.65385 | −0.826926 | − | 0.562310i | \(-0.809913\pi\) | ||||
−0.826926 | + | 0.562310i | \(0.809913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.29150 | −0.299093 | −0.149547 | − | 0.988755i | \(-0.547781\pi\) | ||||
−0.149547 | + | 0.988755i | \(0.547781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.7085 | −0.601449 | −0.300725 | − | 0.953711i | \(-0.597228\pi\) | ||||
−0.300725 | + | 0.953711i | \(0.597228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.70850 | 0.263625 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.1660 | 2.29054 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −43.8745 | −2.43372 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.87451 | −0.322892 | −0.161446 | − | 0.986882i | \(-0.551616\pi\) | ||||
−0.161446 | + | 0.986882i | \(0.551616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.41699 | −0.186690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.1660 | −1.47983 | −0.739913 | − | 0.672702i | \(-0.765134\pi\) | ||||
−0.739913 | + | 0.672702i | \(0.765134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.8745 | −1.83441 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.70850 | 0.252765 | 0.126383 | − | 0.991982i | \(-0.459663\pi\) | ||||
0.126383 | + | 0.991982i | \(0.459663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.5830 | −0.776175 | −0.388088 | − | 0.921623i | \(-0.626864\pi\) | ||||
−0.388088 | + | 0.921623i | \(0.626864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.8745 | −1.16098 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.87451 | 0.521157 | 0.260578 | − | 0.965453i | \(-0.416087\pi\) | ||||
0.260578 | + | 0.965453i | \(0.416087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8745 | 0.677606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.1660 | −1.62685 | −0.813426 | − | 0.581668i | \(-0.802400\pi\) | ||||
−0.813426 | + | 0.581668i | \(0.802400\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.29150 | 0.378556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0627 | −0.572807 | −0.286404 | − | 0.958109i | \(-0.592460\pi\) | ||||
−0.286404 | + | 0.958109i | \(0.592460\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.83399 | −0.351968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.52026 | −0.180824 | −0.0904118 | − | 0.995904i | \(-0.528818\pi\) | ||||
−0.0904118 | + | 0.995904i | \(0.528818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.7490 | −1.62230 | −0.811149 | − | 0.584839i | \(-0.801158\pi\) | ||||
−0.811149 | + | 0.584839i | \(0.801158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.5830 | −1.35480 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.9373 | 1.16296 | 0.581482 | − | 0.813559i | \(-0.302473\pi\) | ||||
0.581482 | + | 0.813559i | \(0.302473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.29150 | −0.368747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 45.8745 | 2.30820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.8745 | 1.09236 | 0.546180 | − | 0.837668i | \(-0.316081\pi\) | ||||
0.546180 | + | 0.837668i | \(0.316081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.1660 | 2.44913 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.5830 | −1.61508 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1660 | −1.34327 | −0.671636 | − | 0.740881i | \(-0.734408\pi\) | ||||
−0.671636 | + | 0.740881i | \(0.734408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.4575 | −1.49510 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.06275 | 0.0519185 | 0.0259593 | − | 0.999663i | \(-0.491736\pi\) | ||||
0.0259593 | + | 0.999663i | \(0.491736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22876 | −0.206097 | −0.103048 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103048 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −60.4575 | −2.93262 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2915 | −0.546434 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.12549 | −0.102381 | −0.0511907 | − | 0.998689i | \(-0.516302\pi\) | ||||
−0.0511907 | + | 0.998689i | \(0.516302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.2915 | −1.40766 | −0.703830 | − | 0.710369i | \(-0.748528\pi\) | ||||
−0.703830 | + | 0.710369i | \(0.748528\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.64575 | −0.270073 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.7490 | 1.70621 | 0.853104 | − | 0.521741i | \(-0.174717\pi\) | ||||
0.853104 | + | 0.521741i | \(0.174717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1660 | −0.815582 | −0.407791 | − | 0.913075i | \(-0.633701\pi\) | ||||
−0.407791 | + | 0.913075i | \(0.633701\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.5830 | −1.53769 | −0.768844 | − | 0.639437i | \(-0.779168\pi\) | ||||
−0.768844 | + | 0.639437i | \(0.779168\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.8745 | −1.03003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 38.5830 | 1.80880 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.8745 | −1.49103 | −0.745513 | − | 0.666491i | \(-0.767796\pi\) | ||||
−0.745513 | + | 0.666491i | \(0.767796\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.7490 | 1.75815 | 0.879073 | − | 0.476686i | \(-0.158162\pi\) | ||||
0.879073 | + | 0.476686i | \(0.158162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.1660 | 0.983668 | 0.491834 | − | 0.870689i | \(-0.336327\pi\) | ||||
0.491834 | + | 0.870689i | \(0.336327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.35425 | 0.386589 | 0.193294 | − | 0.981141i | \(-0.438083\pi\) | ||||
0.193294 | + | 0.981141i | \(0.438083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.87451 | 0.0865567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.5830 | −0.946408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −46.8118 | −2.14787 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.4170 | 0.978567 | 0.489284 | − | 0.872125i | \(-0.337258\pi\) | ||||
0.489284 | + | 0.872125i | \(0.337258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.2915 | 2.15631 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.8745 | 1.53816 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1660 | 0.959123 | 0.479562 | − | 0.877508i | \(-0.340796\pi\) | ||||
0.479562 | + | 0.877508i | \(0.340796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.87451 | 0.445630 | 0.222815 | − | 0.974861i | \(-0.428475\pi\) | ||||
0.222815 | + | 0.974861i | \(0.428475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.41699 | −0.424120 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.0405 | 1.92676 | 0.963379 | − | 0.268143i | \(-0.0864100\pi\) | ||||
0.963379 | + | 0.268143i | \(0.0864100\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.8745 | −1.51039 | −0.755195 | − | 0.655500i | \(-0.772458\pi\) | ||||
−0.755195 | + | 0.655500i | \(0.772458\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.70850 | 0.209525 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.87451 | −0.171735 | −0.0858673 | − | 0.996307i | \(-0.527366\pi\) | ||||
−0.0858673 | + | 0.996307i | \(0.527366\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.58301 | −0.291215 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 63.0405 | 2.77790 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8745 | 0.962040 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.4575 | −1.07150 | −0.535752 | − | 0.844376i | \(-0.679972\pi\) | ||||
−0.535752 | + | 0.844376i | \(0.679972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9373 | 0.915522 | 0.457761 | − | 0.889075i | \(-0.348652\pi\) | ||||
0.457761 | + | 0.889075i | \(0.348652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 67.7490 | 2.95119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.7490 | 1.37520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.4575 | −1.31679 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9373 | −0.471101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.583005 | −0.0250654 | −0.0125327 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125327 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.0000 | 1.28506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.2915 | −1.16690 | −0.583450 | − | 0.812149i | \(-0.698298\pi\) | ||||
−0.583450 | + | 0.812149i | \(0.698298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.29150 | −0.310628 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1660 | −1.07017 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1033 | −0.682317 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8745 | 1.26356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3948 | −0.985972 | −0.492986 | − | 0.870037i | \(-0.664095\pi\) | ||||
−0.492986 | + | 0.870037i | \(0.664095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 53.1660 | 2.23671 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.2915 | 0.808742 | 0.404371 | − | 0.914595i | \(-0.367490\pi\) | ||||
0.404371 | + | 0.914595i | \(0.367490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.06275 | −0.128172 | −0.0640860 | − | 0.997944i | \(-0.520413\pi\) | ||||
−0.0640860 | + | 0.997944i | \(0.520413\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.29150 | 0.345780 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.2915 | 1.63573 | 0.817863 | − | 0.575413i | \(-0.195158\pi\) | ||||
0.817863 | + | 0.575413i | \(0.195158\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.7085 | 0.693185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.2915 | −0.550478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.2915 | −1.29154 | −0.645769 | − | 0.763533i | \(-0.723463\pi\) | ||||
−0.645769 | + | 0.763533i | \(0.723463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.4575 | 2.16147 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 53.1660 | 2.17959 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.41699 | 0.384768 | 0.192384 | − | 0.981320i | \(-0.438378\pi\) | ||||
0.192384 | + | 0.981320i | \(0.438378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4575 | 0.834479 | 0.417240 | − | 0.908796i | \(-0.362998\pi\) | ||||
0.417240 | + | 0.908796i | \(0.362998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.35425 | 0.339649 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.12549 | −0.167449 | −0.0837243 | − | 0.996489i | \(-0.526682\pi\) | ||||
−0.0837243 | + | 0.996489i | \(0.526682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.7490 | −1.28443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9373 | 0.522531 | 0.261265 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261265 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6458 | −0.709243 | −0.354621 | − | 0.935010i | \(-0.615390\pi\) | ||||
−0.354621 | + | 0.935010i | \(0.615390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.29150 | 0.0916601 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 65.1660 | 2.59834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.87451 | 0.313479 | 0.156740 | − | 0.987640i | \(-0.449902\pi\) | ||||
0.156740 | + | 0.987640i | \(0.449902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.5830 | −1.53112 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8745 | 0.628971 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4575 | −0.966014 | −0.483007 | − | 0.875617i | \(-0.660455\pi\) | ||||
−0.483007 | + | 0.875617i | \(0.660455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.6458 | −1.16911 | −0.584557 | − | 0.811353i | \(-0.698732\pi\) | ||||
−0.584557 | + | 0.811353i | \(0.698732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.1660 | −1.14663 | −0.573317 | − | 0.819334i | \(-0.694344\pi\) | ||||
−0.573317 | + | 0.819334i | \(0.694344\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8745 | −0.621217 | −0.310609 | − | 0.950538i | \(-0.600533\pi\) | ||||
−0.310609 | + | 0.950538i | \(0.600533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0000 | 1.40664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9373 | 0.893509 | 0.446754 | − | 0.894657i | \(-0.352580\pi\) | ||||
0.446754 | + | 0.894657i | \(0.352580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3542 | 0.869480 | 0.434740 | − | 0.900556i | \(-0.356840\pi\) | ||||
0.434740 | + | 0.900556i | \(0.356840\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41.1660 | 1.59635 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29150 | 0.0500072 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.5830 | 0.794598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2915 | −0.897821 | −0.448911 | − | 0.893577i | \(-0.648188\pi\) | ||||
−0.448911 | + | 0.893577i | \(0.648188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9373 | 0.881550 | 0.440775 | − | 0.897618i | \(-0.354704\pi\) | ||||
0.440775 | + | 0.897618i | \(0.354704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5830 | −0.713150 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.12549 | −0.0813297 | −0.0406648 | − | 0.999173i | \(-0.512948\pi\) | ||||
−0.0406648 | + | 0.999173i | \(0.512948\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2915 | 0.734948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8745 | 0.527811 | 0.263906 | − | 0.964549i | \(-0.414989\pi\) | ||||
0.263906 | + | 0.964549i | \(0.414989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.5830 | 0.553165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.7490 | 1.65711 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9373 | 1.31956 | 0.659781 | − | 0.751458i | \(-0.270649\pi\) | ||||
0.659781 | + | 0.751458i | \(0.270649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.4575 | 1.90304 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.58301 | −0.0971439 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0627 | −0.866140 | −0.433070 | − | 0.901360i | \(-0.642570\pi\) | ||||
−0.433070 | + | 0.901360i | \(0.642570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.29150 | −0.347970 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −70.3320 | −2.63027 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.7490 | 1.63156 | 0.815781 | − | 0.578360i | \(-0.196307\pi\) | ||||
0.815781 | + | 0.578360i | \(0.196307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.5830 | −1.28794 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.7085 | 0.397704 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.3320 | 1.64418 | 0.822092 | − | 0.569355i | \(-0.192807\pi\) | ||||
0.822092 | + | 0.569355i | \(0.192807\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.1660 | 1.52258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.3948 | 1.38121 | 0.690604 | − | 0.723233i | \(-0.257345\pi\) | ||||
0.690604 | + | 0.723233i | \(0.257345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.41699 | −0.125867 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5830 | −0.389302 | −0.194651 | − | 0.980873i | \(-0.562357\pi\) | ||||
−0.194651 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.7490 | 1.60500 | 0.802498 | − | 0.596655i | \(-0.203504\pi\) | ||||
0.802498 | + | 0.596655i | \(0.203504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.0405 | −2.08980 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.7085 | 0.610515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4575 | 0.381600 | 0.190800 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190800 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4575 | −0.890100 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2288 | 1.17137 | 0.585687 | − | 0.810537i | \(-0.300825\pi\) | ||||
0.585687 | + | 0.810537i | \(0.300825\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4575 | −0.595802 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.0405 | −1.76845 | −0.884223 | − | 0.467065i | \(-0.845312\pi\) | ||||
−0.884223 | + | 0.467065i | \(0.845312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.64575 | −0.131129 | −0.0655643 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655643 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −77.0405 | −2.76738 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.8745 | 1.21368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.8745 | −0.782731 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.6458 | 1.76968 | 0.884840 | − | 0.465895i | \(-0.154268\pi\) | ||||
0.884840 | + | 0.465895i | \(0.154268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.1660 | −1.03702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.8745 | −1.06087 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.52026 | −0.0538503 | −0.0269252 | − | 0.999637i | \(-0.508572\pi\) | ||||
−0.0269252 | + | 0.999637i | \(0.508572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.7490 | −1.54773 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.0000 | 0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.29150 | −0.256992 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87451 | 0.0658229 | 0.0329114 | − | 0.999458i | \(-0.489522\pi\) | ||||
0.0329114 | + | 0.999458i | \(0.489522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.1660 | 1.44198 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.8745 | 1.11515 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8745 | 1.39163 | 0.695815 | − | 0.718221i | \(-0.255043\pi\) | ||||
0.695815 | + | 0.718221i | \(0.255043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.70850 | 0.0944123 | 0.0472061 | − | 0.998885i | \(-0.484968\pi\) | ||||
0.0472061 | + | 0.998885i | \(0.484968\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.8118 | 1.14098 | 0.570488 | − | 0.821306i | \(-0.306754\pi\) | ||||
0.570488 | + | 0.821306i | \(0.306754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.5830 | −1.27058 | −0.635290 | − | 0.772274i | \(-0.719119\pi\) | ||||
−0.635290 | + | 0.772274i | \(0.719119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.8745 | 0.757907 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 84.4575 | 2.92277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7490 | −0.681812 | −0.340906 | − | 0.940097i | \(-0.610734\pi\) | ||||
−0.340906 | + | 0.940097i | \(0.610734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3320 | −0.942483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 54.6863 | 1.88126 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.58301 | −0.157474 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.93725 | −0.306365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.1660 | −0.519274 | −0.259637 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259637 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.0000 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.5830 | −1.17996 | −0.589978 | − | 0.807419i | \(-0.700864\pi\) | ||||
−0.589978 | + | 0.807419i | \(0.700864\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.1660 | 1.80979 | 0.904896 | − | 0.425633i | \(-0.139948\pi\) | ||||
0.904896 | + | 0.425633i | \(0.139948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.8745 | −1.96779 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.8745 | 1.55619 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95948 | 0.168046 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.0000 | −0.811348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.70850 | −0.0914595 | −0.0457297 | − | 0.998954i | \(-0.514561\pi\) | ||||
−0.0457297 | + | 0.998954i | \(0.514561\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7490 | 1.06965 | 0.534826 | − | 0.844962i | \(-0.320377\pi\) | ||||
0.534826 | + | 0.844962i | \(0.320377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.29150 | −0.110768 | −0.0553839 | − | 0.998465i | \(-0.517638\pi\) | ||||
−0.0553839 | + | 0.998465i | \(0.517638\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.7490 | −1.26749 | −0.633744 | − | 0.773543i | \(-0.718483\pi\) | ||||
−0.633744 | + | 0.773543i | \(0.718483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.1660 | 0.709885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.8745 | −1.13357 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.1660 | 0.573796 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.5830 | 0.885608 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.7490 | 1.25482 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.47974 | 0.281565 | 0.140783 | − | 0.990041i | \(-0.455038\pi\) | ||||
0.140783 | + | 0.990041i | \(0.455038\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.29150 | −0.241578 | −0.120789 | − | 0.992678i | \(-0.538542\pi\) | ||||
−0.120789 | + | 0.992678i | \(0.538542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.4575 | −1.00800 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.7490 | −0.652170 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.7490 | 1.04503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −74.1033 | −2.43650 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9373 | 0.555096 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −96.9150 | −3.16946 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.41699 | −0.242303 | −0.121151 | − | 0.992634i | \(-0.538659\pi\) | ||||
−0.121151 | + | 0.992634i | \(0.538659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8118 | −0.678444 | −0.339222 | − | 0.940706i | \(-0.610164\pi\) | ||||
−0.339222 | + | 0.940706i | \(0.610164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | −0.195387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.8745 | 1.10077 | 0.550387 | − | 0.834910i | \(-0.314480\pi\) | ||||
0.550387 | + | 0.834910i | \(0.314480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4170 | −0.565380 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.0405 | −1.65336 | −0.826682 | − | 0.562669i | \(-0.809775\pi\) | ||||
−0.826682 | + | 0.562669i | \(0.809775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.5830 | −0.860206 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.7490 | −0.637729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.3320 | 1.78490 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −80.2065 | −2.58194 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.87451 | 0.253227 | 0.126614 | − | 0.991952i | \(-0.459589\pi\) | ||||
0.126614 | + | 0.991952i | \(0.459589\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.22876 | 0.199890 | 0.0999452 | − | 0.994993i | \(-0.468133\pi\) | ||||
0.0999452 | + | 0.994993i | \(0.468133\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.87451 | −0.315913 | −0.157957 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157957 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.87451 | 0.314948 | 0.157474 | − | 0.987523i | \(-0.449665\pi\) | ||||
0.157474 | + | 0.987523i | \(0.449665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8745 | 0.696980 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.64575 | −0.179524 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.4575 | −1.22164 | −0.610822 | − | 0.791768i | \(-0.709161\pi\) | ||||
−0.610822 | + | 0.791768i | \(0.709161\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.0405 | −1.61809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.4170 | −0.614942 | −0.307471 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307471 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(998\) | 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 | 3312.2.a.z.1.2 | 2 | ||
3.2 | odd | 2 | 3312.2.a.v.1.1 | 2 | |||
4.3 | odd | 2 | 414.2.a.g.1.2 | yes | 2 | ||
12.11 | even | 2 | 414.2.a.e.1.1 | ✓ | 2 | ||
92.91 | even | 2 | 9522.2.a.bc.1.1 | 2 | |||
276.275 | odd | 2 | 9522.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.a.e.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
414.2.a.g.1.2 | yes | 2 | 4.3 | odd | 2 | ||
3312.2.a.v.1.1 | 2 | 3.2 | odd | 2 | |||
3312.2.a.z.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9522.2.a.bb.1.2 | 2 | 276.275 | odd | 2 | |||
9522.2.a.bc.1.1 | 2 | 92.91 | even | 2 |