Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.7 | ||
Root | \(1.41323 - 0.0526497i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.143 |
Dual form | 1600.2.j.d.1007.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.28110i | 0.739642i | 0.929103 | + | 0.369821i | \(0.120581\pi\) | ||||
−0.929103 | + | 0.369821i | \(0.879419\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.13975 | + | 1.13975i | −0.430785 | + | 0.430785i | −0.888895 | − | 0.458111i | \(-0.848526\pi\) |
0.458111 | + | 0.888895i | \(0.348526\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.35879 | 0.452930 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.32204 | − | 2.32204i | 0.700120 | − | 0.700120i | −0.264316 | − | 0.964436i | \(-0.585146\pi\) |
0.964436 | + | 0.264316i | \(0.0851462\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.36502 | −0.378589 | −0.189294 | − | 0.981920i | \(-0.560620\pi\) | ||||
−0.189294 | + | 0.981920i | \(0.560620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.25380 | + | 5.25380i | −1.27423 | + | 1.27423i | −0.330389 | + | 0.943845i | \(0.607180\pi\) |
−0.943845 | + | 0.330389i | \(0.892820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.69752 | + | 3.69752i | −0.848269 | + | 0.848269i | −0.989917 | − | 0.141648i | \(-0.954760\pi\) |
0.141648 | + | 0.989917i | \(0.454760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46013 | − | 1.46013i | −0.318626 | − | 0.318626i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.911118 | − | 0.911118i | −0.189981 | − | 0.189981i | 0.605707 | − | 0.795688i | \(-0.292890\pi\) |
−0.795688 | + | 0.605707i | \(0.792890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.58403i | 1.07465i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.37343 | + | 2.37343i | 0.440736 | + | 0.440736i | 0.892259 | − | 0.451524i | \(-0.149119\pi\) |
−0.451524 | + | 0.892259i | \(0.649119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.242577i | − | 0.0435681i | −0.999763 | − | 0.0217841i | \(-0.993065\pi\) | ||
0.999763 | − | 0.0217841i | \(-0.00693463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.97475 | + | 2.97475i | 0.517838 | + | 0.517838i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34494 | 0.549905 | 0.274953 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274953 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.74872i | − | 0.280020i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66956i | 0.416915i | 0.978031 | + | 0.208457i | \(0.0668442\pi\) | ||||
−0.978031 | + | 0.208457i | \(0.933156\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.04874 | 1.37992 | 0.689960 | − | 0.723847i | \(-0.257628\pi\) | ||||
0.689960 | + | 0.723847i | \(0.257628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.87820 | − | 7.87820i | −1.14915 | − | 1.14915i | −0.986719 | − | 0.162435i | \(-0.948065\pi\) |
−0.162435 | − | 0.986719i | \(-0.551935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.40194i | 0.628849i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.73063 | − | 6.73063i | −0.942476 | − | 0.942476i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.80113i | 0.796846i | 0.917202 | + | 0.398423i | \(0.130442\pi\) | ||||
−0.917202 | + | 0.398423i | \(0.869558\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.73688 | − | 4.73688i | −0.627415 | − | 0.627415i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.91474 | + | 5.91474i | 0.770033 | + | 0.770033i | 0.978112 | − | 0.208079i | \(-0.0667210\pi\) |
−0.208079 | + | 0.978112i | \(0.566721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.67404 | + | 6.67404i | −0.854523 | + | 0.854523i | −0.990686 | − | 0.136163i | \(-0.956523\pi\) |
0.136163 | + | 0.990686i | \(0.456523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.54868 | + | 1.54868i | −0.195116 | + | 0.195116i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.54673 | −0.555471 | −0.277736 | − | 0.960658i | \(-0.589584\pi\) | ||||
−0.277736 | + | 0.960658i | \(0.589584\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.16723 | − | 1.16723i | 0.140518 | − | 0.140518i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.4389 | −1.83226 | −0.916128 | − | 0.400885i | \(-0.868703\pi\) | ||||
−0.916128 | + | 0.400885i | \(0.868703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.49307 | + | 1.49307i | −0.174750 | + | 0.174750i | −0.789063 | − | 0.614313i | \(-0.789433\pi\) |
0.614313 | + | 0.789063i | \(0.289433\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.29308i | 0.603202i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3024 | −1.15911 | −0.579556 | − | 0.814932i | \(-0.696774\pi\) | ||||
−0.579556 | + | 0.814932i | \(0.696774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.07731 | −0.341924 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.26589i | 0.358478i | 0.983806 | + | 0.179239i | \(0.0573636\pi\) | ||||
−0.983806 | + | 0.179239i | \(0.942636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.04060 | + | 3.04060i | −0.325986 | + | 0.325986i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.77206 | −1.03584 | −0.517918 | − | 0.855430i | \(-0.673293\pi\) | ||||
−0.517918 | + | 0.855430i | \(0.673293\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.55578 | − | 1.55578i | 0.163090 | − | 0.163090i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.310765 | 0.0322248 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63587 | − | 1.63587i | 0.166097 | − | 0.166097i | −0.619164 | − | 0.785262i | \(-0.712528\pi\) |
0.785262 | + | 0.619164i | \(0.212528\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.15516 | − | 3.15516i | 0.317106 | − | 0.317106i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.63953 | − | 6.63953i | −0.660658 | − | 0.660658i | 0.294877 | − | 0.955535i | \(-0.404721\pi\) |
−0.955535 | + | 0.294877i | \(0.904721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.62219 | + | 1.62219i | 0.159839 | + | 0.159839i | 0.782496 | − | 0.622656i | \(-0.213946\pi\) |
−0.622656 | + | 0.782496i | \(0.713946\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.65206i | − | 0.353058i | −0.984295 | − | 0.176529i | \(-0.943513\pi\) | ||
0.984295 | − | 0.176529i | \(-0.0564869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.20757 | − | 5.20757i | −0.498795 | − | 0.498795i | 0.412268 | − | 0.911063i | \(-0.364737\pi\) |
−0.911063 | + | 0.412268i | \(0.864737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.28519i | 0.406733i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.27905 | + | 4.27905i | 0.402539 | + | 0.402539i | 0.879127 | − | 0.476588i | \(-0.158127\pi\) |
−0.476588 | + | 0.879127i | \(0.658127\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.85478 | −0.171474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 11.9760i | − | 1.09784i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.216302i | 0.0196639i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41996 | −0.308367 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.29257 | + | 7.29257i | 0.647111 | + | 0.647111i | 0.952294 | − | 0.305183i | \(-0.0987175\pi\) |
−0.305183 | + | 0.952294i | \(0.598718\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5923i | 1.02065i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.9793 | + | 11.9793i | 1.04664 | + | 1.04664i | 0.998858 | + | 0.0477778i | \(0.0152139\pi\) |
0.0477778 | + | 0.998858i | \(0.484786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.42848i | − | 0.730842i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.92762 | − | 4.92762i | −0.420995 | − | 0.420995i | 0.464551 | − | 0.885546i | \(-0.346216\pi\) |
−0.885546 | + | 0.464551i | \(0.846216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3015 | + | 10.3015i | 0.873761 | + | 0.873761i | 0.992880 | − | 0.119119i | \(-0.0380071\pi\) |
−0.119119 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0927 | − | 10.0927i | 0.849962 | − | 0.849962i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.16963 | + | 3.16963i | −0.265058 | + | 0.265058i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.63931 | −0.465123 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.2040 | − | 15.2040i | 1.24556 | − | 1.24556i | 0.287896 | − | 0.957662i | \(-0.407044\pi\) |
0.957662 | − | 0.287896i | \(-0.0929557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7055 | 0.871204 | 0.435602 | − | 0.900139i | \(-0.356536\pi\) | ||||
0.435602 | + | 0.900139i | \(0.356536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.13882 | + | 7.13882i | −0.577139 | + | 0.577139i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.34588i | 0.187222i | 0.995609 | + | 0.0936108i | \(0.0298409\pi\) | ||||
−0.995609 | + | 0.0936108i | \(0.970159\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.43180 | −0.589380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07689 | 0.163682 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.73625i | − | 0.214319i | −0.994242 | − | 0.107160i | \(-0.965824\pi\) | ||
0.994242 | − | 0.107160i | \(-0.0341756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1328 | − | 10.1328i | 0.784097 | − | 0.784097i | −0.196423 | − | 0.980519i | \(-0.562932\pi\) |
0.980519 | + | 0.196423i | \(0.0629325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1367 | −0.856670 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.02415 | + | 5.02415i | −0.384207 | + | 0.384207i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.79590 | 0.668740 | 0.334370 | − | 0.942442i | \(-0.391477\pi\) | ||||
0.334370 | + | 0.942442i | \(0.391477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.57735 | + | 7.57735i | −0.569549 | + | 0.569549i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.62071 | − | 6.62071i | 0.494855 | − | 0.494855i | −0.414977 | − | 0.909832i | \(-0.636210\pi\) |
0.909832 | + | 0.414977i | \(0.136210\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.84339 | − | 5.84339i | −0.434336 | − | 0.434336i | 0.455765 | − | 0.890100i | \(-0.349366\pi\) |
−0.890100 | + | 0.455765i | \(0.849366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.55009 | − | 8.55009i | −0.632041 | − | 0.632041i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.3990i | 1.78423i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.36440 | − | 6.36440i | −0.462942 | − | 0.462942i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.83906i | − | 0.133070i | −0.997784 | − | 0.0665349i | \(-0.978806\pi\) | ||
0.997784 | − | 0.0665349i | \(-0.0211944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.18343 | − | 6.18343i | −0.445093 | − | 0.445093i | 0.448626 | − | 0.893719i | \(-0.351913\pi\) |
−0.893719 | + | 0.448626i | \(0.851913\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.55669 | −0.395898 | −0.197949 | − | 0.980212i | \(-0.563428\pi\) | ||||
−0.197949 | + | 0.980212i | \(0.563428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.96413i | 0.493674i | 0.969057 | + | 0.246837i | \(0.0793912\pi\) | ||||
−0.969057 | + | 0.246837i | \(0.920609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.82480i | − | 0.410850i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.41024 | −0.379724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.23802 | − | 1.23802i | −0.0860483 | − | 0.0860483i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.1715i | 1.18778i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.43389 | − | 5.43389i | −0.374084 | − | 0.374084i | 0.494878 | − | 0.868962i | \(-0.335213\pi\) |
−0.868962 | + | 0.494878i | \(0.835213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 19.7787i | − | 1.35521i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.276477 | + | 0.276477i | 0.0187685 | + | 0.0187685i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.91276 | − | 1.91276i | −0.129253 | − | 0.129253i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.17155 | − | 7.17155i | 0.482411 | − | 0.482411i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.61776 | + | 8.61776i | −0.577088 | + | 0.577088i | −0.934100 | − | 0.357012i | \(-0.883796\pi\) |
0.357012 | + | 0.934100i | \(0.383796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.01977 | 0.399546 | 0.199773 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199773 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.568504 | − | 0.568504i | 0.0375678 | − | 0.0375678i | −0.688073 | − | 0.725641i | \(-0.741543\pi\) |
0.725641 | + | 0.688073i | \(0.241543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.78094 | −0.446153 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.6979 | − | 12.6979i | 0.831869 | − | 0.831869i | −0.155904 | − | 0.987772i | \(-0.549829\pi\) |
0.987772 | + | 0.155904i | \(0.0498289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.1984i | − | 0.857327i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.78306 | 0.115336 | 0.0576682 | − | 0.998336i | \(-0.481633\pi\) | ||||
0.0576682 | + | 0.998336i | \(0.481633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4440 | 0.672754 | 0.336377 | − | 0.941727i | \(-0.390798\pi\) | ||||
0.336377 | + | 0.941727i | \(0.390798\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8098i | 0.821747i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.04719 | − | 5.04719i | 0.321145 | − | 0.321145i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.18392 | −0.265145 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.6497 | − | 12.6497i | 0.798445 | − | 0.798445i | −0.184406 | − | 0.982850i | \(-0.559036\pi\) |
0.982850 | + | 0.184406i | \(0.0590360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.23130 | −0.266019 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.13062 | − | 4.13062i | 0.257661 | − | 0.257661i | −0.566441 | − | 0.824102i | \(-0.691680\pi\) |
0.824102 | + | 0.566441i | \(0.191680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.81240 | + | 3.81240i | −0.236891 | + | 0.236891i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.22500 | + | 3.22500i | 0.199623 | + | 0.199623i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.1303 | + | 17.1303i | 1.05630 | + | 1.05630i | 0.998318 | + | 0.0579798i | \(0.0184659\pi\) |
0.0579798 | + | 0.998318i | \(0.481534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.5190i | − | 0.766147i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.8075 | + | 19.8075i | 1.20768 | + | 1.20768i | 0.971775 | + | 0.235910i | \(0.0758070\pi\) |
0.235910 | + | 0.971775i | \(0.424193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9542i | 1.69810i | 0.528316 | + | 0.849048i | \(0.322824\pi\) | ||||
−0.528316 | + | 0.849048i | \(0.677176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.99311 | + | 1.99311i | 0.120628 | + | 0.120628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.0257 | 1.56373 | 0.781866 | − | 0.623447i | \(-0.214268\pi\) | ||||
0.781866 | + | 0.623447i | \(0.214268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.329612i | − | 0.0197333i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1001i | 1.43769i | 0.695170 | + | 0.718846i | \(0.255329\pi\) | ||||
−0.695170 | + | 0.718846i | \(0.744671\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.73708 | 0.281590 | 0.140795 | − | 0.990039i | \(-0.455034\pi\) | ||||
0.140795 | + | 0.990039i | \(0.455034\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.04262 | − | 3.04262i | −0.179600 | − | 0.179600i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 38.2049i | − | 2.24734i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.09571 | + | 2.09571i | 0.122852 | + | 0.122852i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.11001i | 0.181689i | 0.995865 | + | 0.0908445i | \(0.0289566\pi\) | ||||
−0.995865 | + | 0.0908445i | \(0.971043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9663 | + | 12.9663i | 0.752382 | + | 0.752382i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24370 | + | 1.24370i | 0.0719248 | + | 0.0719248i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.3133 | + | 10.3133i | −0.594449 | + | 0.594449i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.50588 | − | 8.50588i | 0.488650 | − | 0.488650i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.5670 | 0.831382 | 0.415691 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415691 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.07819 | + | 2.07819i | −0.118224 | + | 0.118224i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4572 | 0.819791 | 0.409896 | − | 0.912132i | \(-0.365565\pi\) | ||||
0.409896 | + | 0.912132i | \(0.365565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1273 | + | 10.1273i | −0.572429 | + | 0.572429i | −0.932807 | − | 0.360377i | \(-0.882648\pi\) |
0.360377 | + | 0.932807i | \(0.382648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.8750i | − | 0.779295i | −0.920964 | − | 0.389648i | \(-0.872597\pi\) | ||
0.920964 | − | 0.389648i | \(-0.127403\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0224 | 0.617136 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.67864 | 0.261136 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 38.8520i | − | 2.16179i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.67140 | − | 6.67140i | 0.368930 | − | 0.368930i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.9584 | 0.990076 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.69458 | + | 1.69458i | −0.0931425 | + | 0.0931425i | −0.752143 | − | 0.659000i | \(-0.770980\pi\) |
0.659000 | + | 0.752143i | \(0.270980\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.54508 | 0.249069 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.53338 | − | 9.53338i | 0.519316 | − | 0.519316i | −0.398048 | − | 0.917364i | \(-0.630312\pi\) |
0.917364 | + | 0.398048i | \(0.130312\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.48188 | + | 5.48188i | −0.297735 | + | 0.297735i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.563273 | − | 0.563273i | −0.0305029 | − | 0.0305029i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.9954 | − | 12.9954i | −0.701683 | − | 0.701683i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.67273i | 0.358211i | 0.983830 | + | 0.179105i | \(0.0573203\pi\) | ||||
−0.983830 | + | 0.179105i | \(0.942680\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.02618 | − | 2.02618i | −0.108459 | − | 0.108459i | 0.650795 | − | 0.759254i | \(-0.274436\pi\) |
−0.759254 | + | 0.650795i | \(0.774436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7.62233i | − | 0.406850i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36542 | + | 5.36542i | 0.285572 | + | 0.285572i | 0.835327 | − | 0.549754i | \(-0.185279\pi\) |
−0.549754 | + | 0.835327i | \(0.685279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.3425 | 0.812009 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7.76117i | − | 0.409619i | −0.978802 | − | 0.204809i | \(-0.934343\pi\) | ||
0.978802 | − | 0.204809i | \(-0.0656574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 8.34326i | − | 0.439119i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.277104 | −0.0145442 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0536 | − | 18.0536i | −0.942389 | − | 0.942389i | 0.0560392 | − | 0.998429i | \(-0.482153\pi\) |
−0.998429 | + | 0.0560392i | \(0.982153\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.62737i | 0.188833i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.61183 | − | 6.61183i | −0.343269 | − | 0.343269i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.36197i | 0.225854i | 0.993603 | + | 0.112927i | \(0.0360226\pi\) | ||||
−0.993603 | + | 0.112927i | \(0.963977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.23979 | − | 3.23979i | −0.166858 | − | 0.166858i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.93072 | − | 5.93072i | −0.304641 | − | 0.304641i | 0.538186 | − | 0.842826i | \(-0.319110\pi\) |
−0.842826 | + | 0.538186i | \(0.819110\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.34249 | + | 9.34249i | −0.478630 | + | 0.478630i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3340 | − | 19.3340i | 0.987922 | − | 0.987922i | −0.0120057 | − | 0.999928i | \(-0.503822\pi\) |
0.999928 | + | 0.0120057i | \(0.00382161\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.2954 | 0.625008 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.28607 | + | 6.28607i | −0.318716 | + | 0.318716i | −0.848274 | − | 0.529558i | \(-0.822358\pi\) |
0.529558 | + | 0.848274i | \(0.322358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.57367 | 0.484161 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3466 | + | 15.3466i | −0.774135 | + | 0.774135i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.58413i | 0.330448i | 0.986256 | + | 0.165224i | \(0.0528347\pi\) | ||||
−0.986256 | + | 0.165224i | \(0.947165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7977 | 0.540561 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.7951 | 0.988522 | 0.494261 | − | 0.869313i | \(-0.335439\pi\) | ||||
0.494261 | + | 0.869313i | \(0.335439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.331123i | 0.0164944i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.76707 | − | 7.76707i | 0.385000 | − | 0.385000i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.76937 | −0.285277 | −0.142638 | − | 0.989775i | \(-0.545559\pi\) | ||||
−0.142638 | + | 0.989775i | \(0.545559\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.31276 | − | 6.31276i | 0.311385 | − | 0.311385i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4826 | −0.663437 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.1972 | + | 13.1972i | −0.646270 | + | 0.646270i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.68932 | − | 8.68932i | 0.424501 | − | 0.424501i | −0.462249 | − | 0.886750i | \(-0.652957\pi\) |
0.886750 | + | 0.462249i | \(0.152957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1193 | + | 20.1193i | 0.980555 | + | 0.980555i | 0.999815 | − | 0.0192594i | \(-0.00613083\pi\) |
−0.0192594 | + | 0.999815i | \(0.506131\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7048 | − | 10.7048i | −0.520487 | − | 0.520487i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 15.2135i | − | 0.736231i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.06060 | − | 4.06060i | −0.196048 | − | 0.196048i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.6247i | − | 1.61965i | −0.586675 | − | 0.809823i | \(-0.699563\pi\) | ||
0.586675 | − | 0.809823i | \(-0.300437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.46558 | − | 7.46558i | −0.358773 | − | 0.358773i | 0.504588 | − | 0.863361i | \(-0.331645\pi\) |
−0.863361 | + | 0.504588i | \(0.831645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.73775 | 0.322310 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.91929i | − | 0.377967i | −0.981980 | − | 0.188984i | \(-0.939481\pi\) | ||
0.981980 | − | 0.188984i | \(-0.0605193\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.98132i | 0.284825i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6463 | 0.505823 | 0.252911 | − | 0.967489i | \(-0.418612\pi\) | ||||
0.252911 | + | 0.967489i | \(0.418612\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.4778 | + | 19.4778i | 0.921266 | + | 0.921266i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.08115i | 0.286987i | 0.989651 | + | 0.143494i | \(0.0458336\pi\) | ||||
−0.989651 | + | 0.143494i | \(0.954166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.19880 | + | 6.19880i | 0.291890 | + | 0.291890i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.7148i | 0.644379i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.313815 | + | 0.313815i | 0.0146796 | + | 0.0146796i | 0.714409 | − | 0.699729i | \(-0.246696\pi\) |
−0.699729 | + | 0.714409i | \(0.746696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −29.3374 | − | 29.3374i | −1.36935 | − | 1.36935i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.90949 | − | 9.90949i | 0.461531 | − | 0.461531i | −0.437626 | − | 0.899157i | \(-0.644181\pi\) |
0.899157 | + | 0.437626i | \(0.144181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3430 | + | 17.3430i | −0.805999 | + | 0.805999i | −0.984026 | − | 0.178027i | \(-0.943029\pi\) |
0.178027 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.52267 | 0.0704606 | 0.0352303 | − | 0.999379i | \(-0.488784\pi\) | ||||
0.0352303 | + | 0.999379i | \(0.488784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.18213 | − | 5.18213i | 0.239289 | − | 0.239289i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00530 | −0.138477 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.0115 | − | 21.0115i | 0.966110 | − | 0.966110i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.88252i | 0.360916i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.507657 | 0.0231955 | 0.0115977 | − | 0.999933i | \(-0.496308\pi\) | ||||
0.0115977 | + | 0.999933i | \(0.496308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.56592 | −0.208188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.66070i | 0.121066i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.9809 | + | 25.9809i | −1.17730 | + | 1.17730i | −0.196876 | + | 0.980428i | \(0.563080\pi\) |
−0.980428 | + | 0.196876i | \(0.936920\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.50539 | 0.158519 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.28208 | − | 3.28208i | 0.148118 | − | 0.148118i | −0.629159 | − | 0.777277i | \(-0.716600\pi\) |
0.777277 | + | 0.629159i | \(0.216600\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.9391 | −1.12320 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.5964 | − | 17.5964i | 0.789308 | − | 0.789308i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.73907 | + | 6.73907i | −0.301682 | + | 0.301682i | −0.841672 | − | 0.539990i | \(-0.818428\pi\) |
0.539990 | + | 0.841672i | \(0.318428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9810 | + | 12.9810i | 0.579950 | + | 0.579950i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.12090 | − | 6.12090i | −0.272918 | − | 0.272918i | 0.557356 | − | 0.830274i | \(-0.311816\pi\) |
−0.830274 | + | 0.557356i | \(0.811816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 14.2672i | − | 0.633629i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.8727 | − | 13.8727i | −0.614894 | − | 0.614894i | 0.329323 | − | 0.944217i | \(-0.393180\pi\) |
−0.944217 | + | 0.329323i | \(0.893180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.40344i | − | 0.150559i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.6471 | − | 20.6471i | −0.911590 | − | 0.911590i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.5869 | −1.60909 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.2684i | 0.494628i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.87686i | − | 0.257470i | −0.991679 | − | 0.128735i | \(-0.958908\pi\) | ||
0.991679 | − | 0.128735i | \(-0.0410917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0176 | −1.13767 | −0.568834 | − | 0.822452i | \(-0.692605\pi\) | ||||
−0.568834 | + | 0.822452i | \(0.692605\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.27445 | + | 1.27445i | 0.0555160 | + | 0.0555160i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.3397i | − | 0.927814i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.03690 | + | 8.03690i | 0.348772 | + | 0.348772i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.64400i | − | 0.157839i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.48177 | + | 8.48177i | 0.366016 | + | 0.366016i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.2215 | + | 10.2215i | 0.440270 | + | 0.440270i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.57691 | + | 6.57691i | −0.282764 | + | 0.282764i | −0.834210 | − | 0.551447i | \(-0.814076\pi\) |
0.551447 | + | 0.834210i | \(0.314076\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.48594 | − | 7.48594i | 0.321253 | − | 0.321253i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6170 | −0.453951 | −0.226976 | − | 0.973900i | \(-0.572884\pi\) | ||||
−0.226976 | + | 0.973900i | \(0.572884\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.06863 | + | 9.06863i | −0.387040 | + | 0.387040i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.5516 | −0.747724 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7422 | − | 11.7422i | 0.499328 | − | 0.499328i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9610i | 0.888146i | 0.895991 | + | 0.444073i | \(0.146467\pi\) | ||||
−0.895991 | + | 0.444073i | \(0.853533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.3517 | −0.522422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.2575 | −1.31969 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5598i | 0.697911i | 0.937139 | + | 0.348955i | \(0.113464\pi\) | ||||
−0.937139 | + | 0.348955i | \(0.886536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.50736 | − | 3.50736i | 0.147295 | − | 0.147295i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.6751 | 1.66327 | 0.831634 | − | 0.555325i | \(-0.187406\pi\) | ||||
0.831634 | + | 0.555325i | \(0.187406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0292 | + | 24.0292i | −1.00559 | + | 1.00559i | −0.00560819 | + | 0.999984i | \(0.501785\pi\) |
−0.999984 | + | 0.00560819i | \(0.998215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.35602 | 0.0984240 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7705 | − | 28.7705i | 1.19773 | − | 1.19773i | 0.222888 | − | 0.974844i | \(-0.428451\pi\) |
0.974844 | − | 0.222888i | \(-0.0715485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.92157 | − | 7.92157i | 0.329209 | − | 0.329209i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.72230 | − | 3.72230i | −0.154427 | − | 0.154427i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4704 | + | 13.4704i | 0.557888 | + | 0.557888i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.4854i | − | 1.38209i | −0.722811 | − | 0.691046i | \(-0.757150\pi\) | ||
0.722811 | − | 0.691046i | \(-0.242850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.896933 | + | 0.896933i | 0.0369575 | + | 0.0369575i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 7.11866i | − | 0.292822i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.5298 | − | 11.5298i | −0.473472 | − | 0.473472i | 0.429564 | − | 0.903036i | \(-0.358667\pi\) |
−0.903036 | + | 0.429564i | \(0.858667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.92172 | −0.365142 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.0148i | 0.817781i | 0.912583 | + | 0.408891i | \(0.134084\pi\) | ||||
−0.912583 | + | 0.408891i | \(0.865916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.5924i | − | 1.12552i | −0.826621 | − | 0.562759i | \(-0.809740\pi\) | ||
0.826621 | − | 0.562759i | \(-0.190260\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.17806 | −0.251590 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4850 | + | 30.4850i | 1.23735 | + | 1.23735i | 0.961081 | + | 0.276265i | \(0.0890968\pi\) |
0.276265 | + | 0.961081i | \(0.410903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 6.93104i | − | 0.280860i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.7539 | + | 10.7539i | 0.435057 | + | 0.435057i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2657i | 0.818523i | 0.912417 | + | 0.409261i | \(0.134214\pi\) | ||||
−0.912417 | + | 0.409261i | \(0.865786\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.61302 | + | 1.61302i | 0.0649378 | + | 0.0649378i | 0.738830 | − | 0.673892i | \(-0.235379\pi\) |
−0.673892 | + | 0.738830i | \(0.735379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.46756 | − | 2.46756i | −0.0991797 | − | 0.0991797i | 0.655776 | − | 0.754956i | \(-0.272342\pi\) |
−0.754956 | + | 0.655776i | \(0.772342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.08771 | − | 5.08771i | 0.204163 | − | 0.204163i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.1377 | − | 11.1377i | 0.446222 | − | 0.446222i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.9984 | −0.878531 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.5737 | + | 17.5737i | −0.700708 | + | 0.700708i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.9602 | 1.19270 | 0.596348 | − | 0.802726i | \(-0.296618\pi\) | ||||
0.596348 | + | 0.802726i | \(0.296618\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.96133 | − | 6.96133i | 0.276688 | − | 0.276688i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.00875i | − | 0.238075i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.9782 | −0.829885 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.3386 | −1.47478 | −0.737392 | − | 0.675465i | \(-0.763943\pi\) | ||||
−0.737392 | + | 0.675465i | \(0.763943\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5635i | 0.968691i | 0.874877 | + | 0.484345i | \(0.160942\pi\) | ||||
−0.874877 | + | 0.484345i | \(0.839058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.1347 | + | 23.1347i | −0.909519 | + | 0.909519i | −0.996233 | − | 0.0867142i | \(-0.972363\pi\) |
0.0867142 | + | 0.996233i | \(0.472363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.4685 | 1.07823 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.354194 | + | 0.354194i | −0.0138820 | + | 0.0138820i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 50.8060 | 1.98819 | 0.994097 | − | 0.108496i | \(-0.0346033\pi\) | ||||
0.994097 | + | 0.108496i | \(0.0346033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.02877 | + | 2.02877i | −0.0791497 | + | 0.0791497i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.97780 | + | 9.97780i | −0.388680 | + | 0.388680i | −0.874216 | − | 0.485537i | \(-0.838624\pi\) |
0.485537 | + | 0.874216i | \(0.338624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.09643 | − | 5.09643i | −0.198228 | − | 0.198228i | 0.601012 | − | 0.799240i | \(-0.294764\pi\) |
−0.799240 | + | 0.601012i | \(0.794764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.18745 | + | 9.18745i | 0.356811 | + | 0.356811i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.32496i | − | 0.167463i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.0402 | − | 11.0402i | −0.426838 | − | 0.426838i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9947i | 1.19654i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.6322 | + | 31.6322i | 1.21933 | + | 1.21933i | 0.967867 | + | 0.251464i | \(0.0809121\pi\) |
0.251464 | + | 0.967867i | \(0.419088\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.6600 | −0.986196 | −0.493098 | − | 0.869974i | \(-0.664136\pi\) | ||||
−0.493098 | + | 0.869974i | \(0.664136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.72896i | 0.143104i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.71190i | 0.295521i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3536 | 0.472698 | 0.236349 | − | 0.971668i | \(-0.424049\pi\) | ||||
0.236349 | + | 0.971668i | \(0.424049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.728309 | + | 0.728309i | 0.0277867 | + | 0.0277867i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.91866i | − | 0.301677i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.5426 | − | 22.5426i | −0.857561 | − | 0.857561i | 0.133489 | − | 0.991050i | \(-0.457382\pi\) |
−0.991050 | + | 0.133489i | \(0.957382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.19219i | 0.273209i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0253 | − | 14.0253i | −0.531247 | − | 0.531247i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.2673 | + | 16.2673i | 0.615285 | + | 0.615285i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9530 | − | 26.9530i | 1.01800 | − | 1.01800i | 0.0181663 | − | 0.999835i | \(-0.494217\pi\) |
0.999835 | − | 0.0181663i | \(-0.00578284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.3680 | + | 12.3680i | −0.466467 | + | 0.466467i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.1348 | 0.569203 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.78615 | + | 7.78615i | −0.292415 | + | 0.292415i | −0.838034 | − | 0.545619i | \(-0.816295\pi\) |
0.545619 | + | 0.838034i | \(0.316295\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.9988 | −0.524997 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.221016 | + | 0.221016i | −0.00827713 | + | 0.00827713i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.28427i | 0.0853076i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.6777 | 0.771150 | 0.385575 | − | 0.922677i | \(-0.374003\pi\) | ||||
0.385575 | + | 0.922677i | \(0.374003\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.69779 | −0.137713 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.3797i | 0.497597i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.4994 | − | 20.4994i | 0.760280 | − | 0.760280i | −0.216093 | − | 0.976373i | \(-0.569331\pi\) |
0.976373 | + | 0.216093i | \(0.0693315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.6425 | −0.949722 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.5403 | + | 47.5403i | −1.75834 | + | 1.75834i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7306 | −0.396344 | −0.198172 | − | 0.980167i | \(-0.563500\pi\) | ||||
−0.198172 | + | 0.980167i | \(0.563500\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5577 | + | 10.5577i | −0.388897 | + | 0.388897i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.93837 | − | 2.93837i | 0.108090 | − | 0.108090i | −0.650994 | − | 0.759083i | \(-0.725648\pi\) |
0.759083 | + | 0.650994i | \(0.225648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.46594 | + | 6.46594i | 0.237532 | + | 0.237532i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.223404 | − | 0.223404i | −0.00819590 | − | 0.00819590i | 0.702997 | − | 0.711193i | \(-0.251845\pi\) |
−0.711193 | + | 0.702997i | \(0.751845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.43766i | 0.162366i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.16243 | + | 4.16243i | 0.152092 | + | 0.152092i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 39.9939i | − | 1.45940i | −0.683769 | − | 0.729699i | \(-0.739660\pi\) | ||
0.683769 | − | 0.729699i | \(-0.260340\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.2055 | + | 16.2055i | 0.590563 | + | 0.590563i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.9120 | −1.19621 | −0.598103 | − | 0.801419i | \(-0.704079\pi\) | ||||
−0.598103 | + | 0.801419i | \(0.704079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.42070i | − | 0.196759i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 33.9591i | − | 1.23102i | −0.788130 | − | 0.615509i | \(-0.788951\pi\) | ||
0.788130 | − | 0.615509i | \(-0.211049\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.8707 | 0.429747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.07375 | − | 8.07375i | −0.291526 | − | 0.291526i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.2535i | 1.45158i | 0.687917 | + | 0.725789i | \(0.258525\pi\) | ||||
−0.687917 | + | 0.725789i | \(0.741475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.29172 | + | 5.29172i | 0.190577 | + | 0.190577i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.47175i | − | 0.340675i | −0.985386 | − | 0.170338i | \(-0.945514\pi\) | ||
0.985386 | − | 0.170338i | \(-0.0544858\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.88405 | − | 4.88405i | −0.175214 | − | 0.175214i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.87073 | − | 9.87073i | −0.353656 | − | 0.353656i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.8496 | + | 35.8496i | −1.28280 | + | 1.28280i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.2533 | + | 13.2533i | −0.473636 | + | 0.473636i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.1367 | −1.71589 | −0.857945 | − | 0.513742i | \(-0.828259\pi\) | ||||
−0.857945 | + | 0.513742i | \(0.828259\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.9455 | + | 21.9455i | −0.781282 | + | 0.781282i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.75409 | −0.346815 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.11021 | − | 9.11021i | 0.323513 | − | 0.323513i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.8962i | − | 1.20066i | −0.799751 | − | 0.600332i | \(-0.795035\pi\) | ||
0.799751 | − | 0.600332i | \(-0.204965\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.7810 | 2.92858 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.2782 | −0.469162 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.93391i | 0.244692i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.3753 | + | 25.3753i | −0.893254 | + | 0.893254i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.5625 | −0.969047 | −0.484523 | − | 0.874778i | \(-0.661007\pi\) | ||||
−0.484523 | + | 0.874778i | \(0.661007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1817 | − | 24.1817i | 0.849133 | − | 0.849133i | −0.140892 | − | 0.990025i | \(-0.544997\pi\) |
0.990025 | + | 0.140892i | \(0.0449970\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −35.8120 | −1.25598 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.4579 | + | 33.4579i | −1.17054 | + | 1.17054i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.11398 | − | 2.11398i | 0.0738686 | − | 0.0738686i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.0575735 | + | 0.0575735i | 0.00200933 | + | 0.00200933i | 0.708111 | − | 0.706101i | \(-0.249548\pi\) |
−0.706101 | + | 0.708111i | \(0.749548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5594 | + | 28.5594i | 0.995518 | + | 0.995518i | 0.999990 | − | 0.00447159i | \(-0.00142335\pi\) |
−0.00447159 | + | 0.999990i | \(0.501423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0863i | 0.802788i | 0.915905 | + | 0.401394i | \(0.131474\pi\) | ||||
−0.915905 | + | 0.401394i | \(0.868526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.3543 | + | 33.3543i | 1.15844 | + | 1.15844i | 0.984811 | + | 0.173631i | \(0.0555499\pi\) |
0.173631 | + | 0.984811i | \(0.444450\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.3414i | 1.15660i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.1269 | − | 23.1269i | −0.801301 | − | 0.801301i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.35456 | 0.0468204 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.4524i | 1.70729i | 0.520859 | + | 0.853643i | \(0.325612\pi\) | ||||
−0.520859 | + | 0.853643i | \(0.674388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 17.7336i | − | 0.611504i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.8746 | −1.06338 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.246530 | − | 0.246530i | −0.00847089 | − | 0.00847089i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.06865i | 0.208276i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.04764 | − | 3.04764i | −0.104472 | − | 0.104472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.3639i | 1.07388i | 0.843621 | + | 0.536939i | \(0.180419\pi\) | ||||
−0.843621 | + | 0.536939i | \(0.819581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1594 | + | 16.1594i | 0.551996 | + | 0.551996i | 0.927016 | − | 0.375021i | \(-0.122364\pi\) |
−0.375021 | + | 0.927016i | \(0.622364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.7369 | − | 30.7369i | −1.04873 | − | 1.04873i | −0.998750 | − | 0.0499792i | \(-0.984085\pi\) |
−0.0499792 | − | 0.998750i | \(-0.515915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.89790 | − | 3.89790i | 0.132840 | − | 0.132840i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9353 | − | 18.9353i | 0.644565 | − | 0.644565i | −0.307109 | − | 0.951674i | \(-0.599362\pi\) |
0.951674 | + | 0.307109i | \(0.0993618\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.9441 | 1.66223 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.9226 | + | 23.9226i | −0.811517 | + | 0.811517i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.20638 | 0.210295 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.22280 | − | 2.22280i | 0.0752305 | − | 0.0752305i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.7461i | 1.67981i | 0.542737 | + | 0.839903i | \(0.317388\pi\) | ||||
−0.542737 | + | 0.839903i | \(0.682612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.98423 | −0.134385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7694 | 0.935574 | 0.467787 | − | 0.883841i | \(-0.345051\pi\) | ||||
0.467787 | + | 0.883841i | \(0.345051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.4602i | − | 1.42890i | −0.699686 | − | 0.714450i | \(-0.746677\pi\) | ||
0.699686 | − | 0.714450i | \(-0.253323\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.1076 | + | 16.1076i | −0.540842 | + | 0.540842i | −0.923776 | − | 0.382934i | \(-0.874914\pi\) |
0.382934 | + | 0.923776i | \(0.374914\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6234 | −0.557531 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.14563 | + | 7.14563i | −0.239388 | + | 0.239388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.2596 | 1.94958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.59329 | + | 1.59329i | −0.0531986 | + | 0.0531986i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.575741 | − | 0.575741i | 0.0192020 | − | 0.0192020i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.4780 | − | 30.4780i | −1.01537 | − | 1.01537i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.2123 | − | 13.2123i | −0.439679 | − | 0.439679i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.20991i | 0.305810i | 0.988241 | + | 0.152905i | \(0.0488628\pi\) | ||||
−0.988241 | + | 0.152905i | \(0.951137\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.02174 | − | 9.02174i | −0.299232 | − | 0.299232i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.8065i | − | 1.51764i | −0.651302 | − | 0.758819i | \(-0.725777\pi\) | ||
0.651302 | − | 0.758819i | \(-0.274223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.58351 | + | 7.58351i | 0.250978 | + | 0.250978i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.3068 | −0.901749 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.52468i | 0.182242i | 0.995840 | + | 0.0911211i | \(0.0290450\pi\) | ||||
−0.995840 | + | 0.0911211i | \(0.970955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6617i | 0.614924i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.0744 | 0.693672 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.20422 | + | 2.20422i | 0.0723961 | + | 0.0723961i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.4288i | − | 1.42485i | −0.701746 | − | 0.712427i | \(-0.747596\pi\) | ||
0.701746 | − | 0.712427i | \(-0.252404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.2763 | − | 16.2763i | −0.533433 | − | 0.533433i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.5210i | 0.606352i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.7275 | + | 20.7275i | 0.677138 | + | 0.677138i | 0.959352 | − | 0.282213i | \(-0.0910686\pi\) |
−0.282213 | + | 0.959352i | \(0.591069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9741 | − | 12.9741i | −0.423392 | − | 0.423392i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3393 | − | 12.3393i | 0.402251 | − | 0.402251i | −0.476775 | − | 0.879026i | \(-0.658194\pi\) |
0.879026 | + | 0.476775i | \(0.158194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.43228 | − | 2.43228i | 0.0792060 | − | 0.0792060i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.3611 | −1.57152 | −0.785762 | − | 0.618529i | \(-0.787729\pi\) | ||||
−0.785762 | + | 0.618529i | \(0.787729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.03807 | − | 2.03807i | 0.0661585 | − | 0.0661585i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.7752 | 0.576399 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0371 | + | 34.0371i | −1.10257 | + | 1.10257i | −0.108471 | + | 0.994100i | \(0.534595\pi\) |
−0.994100 | + | 0.108471i | \(0.965405\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.1208i | 0.456459i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2325 | 0.362716 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9412 | 0.998102 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 4.96238i | − | 0.159911i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.9307 | + | 18.9307i | −0.608770 | + | 0.608770i | −0.942625 | − | 0.333855i | \(-0.891651\pi\) |
0.333855 | + | 0.942625i | \(0.391651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.7732 | 1.59895 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2698 | − | 21.2698i | 0.682580 | − | 0.682580i | −0.278001 | − | 0.960581i | \(-0.589672\pi\) |
0.960581 | + | 0.278001i | \(0.0896719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.4822 | −0.752805 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.13884 | + | 2.13884i | −0.0684275 | + | 0.0684275i | −0.740492 | − | 0.672065i | \(-0.765408\pi\) |
0.672065 | + | 0.740492i | \(0.265408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.6911 | + | 22.6911i | −0.725210 | + | 0.725210i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.07601 | − | 7.07601i | −0.225919 | − | 0.225919i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.18193 | − | 6.18193i | −0.197173 | − | 0.197173i | 0.601614 | − | 0.798787i | \(-0.294525\pi\) |
−0.798787 | + | 0.601614i | \(0.794525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.0064i | 0.732302i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.24447 | − | 8.24447i | −0.262159 | − | 0.262159i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.4847i | 1.38134i | 0.723172 | + | 0.690668i | \(0.242683\pi\) | ||||
−0.723172 | + | 0.690668i | \(0.757317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.17092 | − | 2.17092i | −0.0688921 | − | 0.0688921i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4043 | 1.05793 | 0.528963 | − | 0.848645i | \(-0.322581\pi\) | ||||
0.528963 | + | 0.848645i | \(0.322581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.6783i | 0.590954i |
(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 | 1600.2.j.d.143.7 | 18 | ||
4.3 | odd | 2 | 400.2.j.d.43.8 | 18 | |||
5.2 | odd | 4 | 1600.2.s.d.207.7 | 18 | |||
5.3 | odd | 4 | 320.2.s.b.207.3 | 18 | |||
5.4 | even | 2 | 320.2.j.b.143.3 | 18 | |||
16.3 | odd | 4 | 1600.2.s.d.943.7 | 18 | |||
16.13 | even | 4 | 400.2.s.d.243.6 | 18 | |||
20.3 | even | 4 | 80.2.s.b.27.4 | yes | 18 | ||
20.7 | even | 4 | 400.2.s.d.107.6 | 18 | |||
20.19 | odd | 2 | 80.2.j.b.43.2 | ✓ | 18 | ||
40.3 | even | 4 | 640.2.s.d.287.3 | 18 | |||
40.13 | odd | 4 | 640.2.s.c.287.7 | 18 | |||
40.19 | odd | 2 | 640.2.j.d.543.3 | 18 | |||
40.29 | even | 2 | 640.2.j.c.543.7 | 18 | |||
60.23 | odd | 4 | 720.2.z.g.667.6 | 18 | |||
60.59 | even | 2 | 720.2.bd.g.523.8 | 18 | |||
80.3 | even | 4 | 320.2.j.b.47.7 | 18 | |||
80.13 | odd | 4 | 80.2.j.b.67.2 | yes | 18 | ||
80.19 | odd | 4 | 320.2.s.b.303.3 | 18 | |||
80.29 | even | 4 | 80.2.s.b.3.4 | yes | 18 | ||
80.43 | even | 4 | 640.2.j.c.607.3 | 18 | |||
80.53 | odd | 4 | 640.2.j.d.607.7 | 18 | |||
80.59 | odd | 4 | 640.2.s.c.223.7 | 18 | |||
80.67 | even | 4 | inner | 1600.2.j.d.1007.3 | 18 | ||
80.69 | even | 4 | 640.2.s.d.223.3 | 18 | |||
80.77 | odd | 4 | 400.2.j.d.307.8 | 18 | |||
240.29 | odd | 4 | 720.2.z.g.163.6 | 18 | |||
240.173 | even | 4 | 720.2.bd.g.307.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.2 | ✓ | 18 | 20.19 | odd | 2 | ||
80.2.j.b.67.2 | yes | 18 | 80.13 | odd | 4 | ||
80.2.s.b.3.4 | yes | 18 | 80.29 | even | 4 | ||
80.2.s.b.27.4 | yes | 18 | 20.3 | even | 4 | ||
320.2.j.b.47.7 | 18 | 80.3 | even | 4 | |||
320.2.j.b.143.3 | 18 | 5.4 | even | 2 | |||
320.2.s.b.207.3 | 18 | 5.3 | odd | 4 | |||
320.2.s.b.303.3 | 18 | 80.19 | odd | 4 | |||
400.2.j.d.43.8 | 18 | 4.3 | odd | 2 | |||
400.2.j.d.307.8 | 18 | 80.77 | odd | 4 | |||
400.2.s.d.107.6 | 18 | 20.7 | even | 4 | |||
400.2.s.d.243.6 | 18 | 16.13 | even | 4 | |||
640.2.j.c.543.7 | 18 | 40.29 | even | 2 | |||
640.2.j.c.607.3 | 18 | 80.43 | even | 4 | |||
640.2.j.d.543.3 | 18 | 40.19 | odd | 2 | |||
640.2.j.d.607.7 | 18 | 80.53 | odd | 4 | |||
640.2.s.c.223.7 | 18 | 80.59 | odd | 4 | |||
640.2.s.c.287.7 | 18 | 40.13 | odd | 4 | |||
640.2.s.d.223.3 | 18 | 80.69 | even | 4 | |||
640.2.s.d.287.3 | 18 | 40.3 | even | 4 | |||
720.2.z.g.163.6 | 18 | 240.29 | odd | 4 | |||
720.2.z.g.667.6 | 18 | 60.23 | odd | 4 | |||
720.2.bd.g.307.8 | 18 | 240.173 | even | 4 | |||
720.2.bd.g.523.8 | 18 | 60.59 | even | 2 | |||
1600.2.j.d.143.7 | 18 | 1.1 | even | 1 | trivial | ||
1600.2.j.d.1007.3 | 18 | 80.67 | even | 4 | inner | ||
1600.2.s.d.207.7 | 18 | 5.2 | odd | 4 | |||
1600.2.s.d.943.7 | 18 | 16.3 | odd | 4 |