Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.7 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.a.1007.7 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.12344 | − | 2.71222i | 0.502418 | − | 1.21294i | −0.445745 | − | 0.895160i | \(-0.647061\pi\) |
0.948163 | − | 0.317784i | \(-0.102939\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.03150 | + | 3.03150i | −1.14580 | + | 1.14580i | −0.158430 | + | 0.987370i | \(0.550643\pi\) |
−0.987370 | + | 0.158430i | \(0.949357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.616847 | − | 1.48920i | 0.185986 | − | 0.449011i | −0.803194 | − | 0.595718i | \(-0.796868\pi\) |
0.989180 | + | 0.146707i | \(0.0468676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35133 | − | 1.38816i | 0.929490 | − | 0.385008i | 0.134005 | − | 0.990981i | \(-0.457216\pi\) |
0.795485 | + | 0.605973i | \(0.207216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.76709 | −1.15619 | −0.578094 | − | 0.815970i | \(-0.696203\pi\) | ||||
−0.578094 | + | 0.815970i | \(0.696203\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13264 | − | 2.73444i | −0.259846 | − | 0.627323i | 0.739082 | − | 0.673615i | \(-0.235259\pi\) |
−0.998928 | + | 0.0462921i | \(0.985259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.11192 | − | 4.11192i | 0.857395 | − | 0.857395i | −0.133636 | − | 0.991031i | \(-0.542665\pi\) |
0.991031 | + | 0.133636i | \(0.0426652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.55851 | − | 2.55851i | −0.511702 | − | 0.511702i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.16664 | − | 3.38273i | 1.51651 | − | 0.628158i | 0.539620 | − | 0.841909i | \(-0.318568\pi\) |
0.976888 | + | 0.213751i | \(0.0685681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.16305i | − | 1.10692i | −0.832877 | − | 0.553458i | \(-0.813308\pi\) | ||
0.832877 | − | 0.553458i | \(-0.186692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.81640 | + | 11.6278i | 0.814121 | + | 1.96546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.38963 | − | 3.88931i | −1.54365 | − | 0.639399i | −0.561493 | − | 0.827482i | \(-0.689773\pi\) |
−0.982153 | + | 0.188083i | \(0.939773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.169917 | + | 0.169917i | 0.0265365 | + | 0.0265365i | 0.720251 | − | 0.693714i | \(-0.244027\pi\) |
−0.693714 | + | 0.720251i | \(0.744027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.57687 | − | 3.13844i | −1.15546 | − | 0.478608i | −0.279100 | − | 0.960262i | \(-0.590036\pi\) |
−0.876361 | + | 0.481654i | \(0.840036\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.44049i | − | 0.355981i | −0.984032 | − | 0.177991i | \(-0.943040\pi\) | ||
0.984032 | − | 0.177991i | \(-0.0569597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11.3800i | − | 1.62572i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.99073 | − | 0.824586i | −0.273447 | − | 0.113266i | 0.241746 | − | 0.970340i | \(-0.422280\pi\) |
−0.515193 | + | 0.857074i | \(0.672280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.34605 | − | 3.34605i | −0.451182 | − | 0.451182i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.21488 | + | 0.503218i | 0.158163 | + | 0.0655134i | 0.460361 | − | 0.887732i | \(-0.347720\pi\) |
−0.302197 | + | 0.953245i | \(0.597720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04489 | + | 2.52258i | 0.133784 | + | 0.322983i | 0.976548 | − | 0.215300i | \(-0.0690731\pi\) |
−0.842764 | + | 0.538283i | \(0.819073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.6491i | − | 1.32085i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.91551 | + | 1.62186i | −0.478355 | + | 0.198141i | −0.608815 | − | 0.793312i | \(-0.708355\pi\) |
0.130459 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.28919 | − | 5.28919i | −0.627711 | − | 0.627711i | 0.319781 | − | 0.947492i | \(-0.396391\pi\) |
−0.947492 | + | 0.319781i | \(0.896391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.57482 | + | 1.57482i | −0.184319 | + | 0.184319i | −0.793235 | − | 0.608916i | \(-0.791605\pi\) |
0.608916 | + | 0.793235i | \(0.291605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.64454 | + | 6.38449i | 0.301373 | + | 0.727580i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7711 | 1.54937 | 0.774684 | − | 0.632348i | \(-0.217909\pi\) | ||||
0.774684 | + | 0.632348i | \(0.217909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.31934 | − | 1.37492i | 0.364345 | − | 0.150917i | −0.192997 | − | 0.981199i | \(-0.561821\pi\) |
0.557343 | + | 0.830282i | \(0.311821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35554 | + | 12.9294i | −0.580890 | + | 1.40239i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.99010 | + | 6.99010i | −0.740949 | + | 0.740949i | −0.972761 | − | 0.231811i | \(-0.925535\pi\) |
0.231811 | + | 0.972761i | \(0.425535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.95133 | + | 14.3678i | −0.623869 | + | 1.50615i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.68886 | −0.891459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5584 | −1.37665 | −0.688323 | − | 0.725404i | \(-0.741653\pi\) | ||||
−0.688323 | + | 0.725404i | \(0.741653\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.10479 | − | 2.66720i | 0.109931 | − | 0.265396i | −0.859335 | − | 0.511413i | \(-0.829122\pi\) |
0.969265 | + | 0.246018i | \(0.0791221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8009 | − | 12.8009i | 1.26131 | − | 1.26131i | 0.310851 | − | 0.950459i | \(-0.399386\pi\) |
0.950459 | − | 0.310851i | \(-0.100614\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.720677 | + | 1.73987i | −0.0696704 | + | 0.168199i | −0.954879 | − | 0.296995i | \(-0.904016\pi\) |
0.885209 | + | 0.465194i | \(0.154016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45017 | − | 1.84332i | 0.426249 | − | 0.176558i | −0.159238 | − | 0.987240i | \(-0.550904\pi\) |
0.585486 | + | 0.810682i | \(0.300904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6612 | 1.28514 | 0.642568 | − | 0.766229i | \(-0.277869\pi\) | ||||
0.642568 | + | 0.766229i | \(0.277869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.53296 | − | 15.7720i | −0.609201 | − | 1.47074i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4514 | − | 14.4514i | 1.32476 | − | 1.32476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.94096 | + | 5.94096i | 0.540087 | + | 0.540087i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.74754 | − | 1.55228i | 0.335190 | − | 0.138840i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2014i | 1.17143i | 0.810515 | + | 0.585717i | \(0.199187\pi\) | ||||
−0.810515 | + | 0.585717i | \(0.800813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.56553 | − | 6.19375i | −0.224152 | − | 0.541150i | 0.771294 | − | 0.636479i | \(-0.219610\pi\) |
−0.995446 | + | 0.0953287i | \(0.969610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7231 | + | 4.85585i | 1.01652 | + | 0.421056i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.77333 | − | 9.77333i | −0.834992 | − | 0.834992i | 0.153203 | − | 0.988195i | \(-0.451041\pi\) |
−0.988195 | + | 0.153203i | \(0.951041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.26616 | + | 3.42396i | 0.701127 | + | 0.290416i | 0.704627 | − | 0.709578i | \(-0.251114\pi\) |
−0.00350050 | + | 0.999994i | \(0.501114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.84708i | − | 0.488957i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 25.9501i | − | 2.15504i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.9803 | + | 7.86190i | 1.55493 | + | 0.644072i | 0.984199 | − | 0.177066i | \(-0.0566607\pi\) |
0.570729 | + | 0.821139i | \(0.306661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83326 | − | 7.83326i | −0.637462 | − | 0.637462i | 0.312467 | − | 0.949929i | \(-0.398845\pi\) |
−0.949929 | + | 0.312467i | \(0.898845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.7156 | − | 6.92381i | −1.34263 | − | 0.556134i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58014 | + | 8.64323i | 0.285727 | + | 0.689805i | 0.999949 | − | 0.0101140i | \(-0.00321944\pi\) |
−0.714222 | + | 0.699919i | \(0.753219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.9306i | 1.96481i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.73693 | − | 1.96210i | 0.371025 | − | 0.153684i | −0.189377 | − | 0.981904i | \(-0.560647\pi\) |
0.560402 | + | 0.828221i | \(0.310647\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.55199 | − | 4.55199i | −0.352244 | − | 0.352244i | 0.508700 | − | 0.860944i | \(-0.330126\pi\) |
−0.860944 | + | 0.508700i | \(0.830126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.111994 | − | 0.111994i | 0.00861490 | − | 0.00861490i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.28444 | + | 10.3436i | 0.325740 | + | 0.786406i | 0.998899 | + | 0.0469083i | \(0.0149368\pi\) |
−0.673159 | + | 0.739498i | \(0.735063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5123 | 1.17262 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.2246 | − | 4.23519i | 0.764226 | − | 0.316553i | 0.0336946 | − | 0.999432i | \(-0.489273\pi\) |
0.730531 | + | 0.682880i | \(0.239273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.33358 | + | 3.21956i | −0.0991246 | + | 0.239308i | −0.965661 | − | 0.259806i | \(-0.916341\pi\) |
0.866536 | + | 0.499114i | \(0.166341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.0974 | + | 21.0974i | −1.55111 | + | 1.55111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.94056 | + | 7.09915i | −0.215035 | + | 0.519141i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.82446 | 0.349085 | 0.174543 | − | 0.984650i | \(-0.444155\pi\) | ||||
0.174543 | + | 0.984650i | \(0.444155\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.222878 | 0.0160431 | 0.00802155 | − | 0.999968i | \(-0.497447\pi\) | ||||
0.00802155 | + | 0.999968i | \(0.497447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.44160 | − | 22.7940i | 0.672686 | − | 1.62401i | −0.104341 | − | 0.994542i | \(-0.533273\pi\) |
0.777028 | − | 0.629467i | \(-0.216727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8710 | + | 14.8710i | −1.05418 | + | 1.05418i | −0.0557310 | + | 0.998446i | \(0.517749\pi\) |
−0.998446 | + | 0.0557310i | \(0.982251\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.5024 | + | 35.0120i | −1.01787 | + | 2.45736i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.651743 | − | 0.269961i | 0.0455197 | − | 0.0188549i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.77079 | −0.330003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.644000 | + | 1.55475i | 0.0443348 | + | 0.107034i | 0.944496 | − | 0.328524i | \(-0.106551\pi\) |
−0.900161 | + | 0.435558i | \(0.856551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.0243 | + | 17.0243i | −1.16105 | + | 1.16105i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.6833 | + | 18.6833i | 1.26830 | + | 1.26830i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.9761 | + | 6.61750i | −1.07467 | + | 0.445141i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4280i | 1.56885i | 0.620221 | + | 0.784427i | \(0.287043\pi\) | ||||
−0.620221 | + | 0.784427i | \(0.712957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.10690 | + | 12.3292i | 0.338957 | + | 0.818315i | 0.997816 | + | 0.0660486i | \(0.0210392\pi\) |
−0.658859 | + | 0.752266i | \(0.728961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.82666 | − | 3.24191i | −0.517200 | − | 0.214231i | 0.108786 | − | 0.994065i | \(-0.465304\pi\) |
−0.625987 | + | 0.779834i | \(0.715304\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.66805 | − | 9.66805i | −0.633375 | − | 0.633375i | 0.315538 | − | 0.948913i | \(-0.397815\pi\) |
−0.948913 | + | 0.315538i | \(0.897815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.61915 | − | 2.74174i | −0.431785 | − | 0.178851i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8579i | 1.67261i | 0.548268 | + | 0.836303i | \(0.315287\pi\) | ||||
−0.548268 | + | 0.836303i | \(0.684713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9358i | 1.60626i | 0.595805 | + | 0.803129i | \(0.296833\pi\) | ||||
−0.595805 | + | 0.803129i | \(0.703167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.8652 | − | 12.7848i | −1.97190 | − | 0.816789i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.59170 | − | 7.59170i | −0.483048 | − | 0.483048i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5486 | + | 4.78358i | 0.728939 | + | 0.301937i | 0.716116 | − | 0.697981i | \(-0.245918\pi\) |
0.0128233 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.58705 | − | 8.65990i | −0.225516 | − | 0.544443i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.0780i | − | 1.06530i | −0.846337 | − | 0.532648i | \(-0.821197\pi\) | ||
0.846337 | − | 0.532648i | \(-0.178803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.2552 | − | 16.6742i | 2.50133 | − | 1.03609i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4595 | − | 10.4595i | −0.644963 | − | 0.644963i | 0.306809 | − | 0.951771i | \(-0.400739\pi\) |
−0.951771 | + | 0.306809i | \(0.900739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.47292 | + | 4.47292i | −0.274770 | + | 0.274770i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.47587 | + | 8.39150i | 0.211928 | + | 0.511639i | 0.993719 | − | 0.111901i | \(-0.0356939\pi\) |
−0.781792 | + | 0.623540i | \(0.785694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.66173 | 0.343925 | 0.171963 | − | 0.985103i | \(-0.444989\pi\) | ||||
0.171963 | + | 0.985103i | \(0.444989\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.38834 | + | 2.23192i | −0.324929 | + | 0.134590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.27625 | + | 12.7380i | −0.317019 | + | 0.765352i | 0.682390 | + | 0.730988i | \(0.260940\pi\) |
−0.999409 | + | 0.0343637i | \(0.989060\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.75892 | − | 5.75892i | 0.343548 | − | 0.343548i | −0.514151 | − | 0.857700i | \(-0.671893\pi\) |
0.857700 | + | 0.514151i | \(0.171893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4136 | + | 25.1407i | −0.619025 | + | 1.49446i | 0.233812 | + | 0.972282i | \(0.424880\pi\) |
−0.852837 | + | 0.522177i | \(0.825120\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.03021 | −0.0608111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.72512 | 0.336772 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.21345 | + | 12.5864i | −0.304573 | + | 0.735304i | 0.695290 | + | 0.718729i | \(0.255276\pi\) |
−0.999863 | + | 0.0165743i | \(0.994724\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.72968 | − | 2.72968i | 0.158928 | − | 0.158928i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.07236 | − | 19.4884i | 0.466837 | − | 1.12704i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.4835 | − | 13.4551i | 1.87232 | − | 0.775539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.01566 | 0.458975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.98052 | + | 21.6809i | 0.512545 | + | 1.23739i | 0.942398 | + | 0.334495i | \(0.108566\pi\) |
−0.429852 | + | 0.902899i | \(0.641434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7177 | − | 12.7177i | 0.721157 | − | 0.721157i | −0.247684 | − | 0.968841i | \(-0.579670\pi\) |
0.968841 | + | 0.247684i | \(0.0796695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1388 | + | 10.1388i | 0.573081 | + | 0.573081i | 0.932988 | − | 0.359907i | \(-0.117192\pi\) |
−0.359907 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.52668 | + | 1.04659i | −0.141913 | + | 0.0587822i | −0.452509 | − | 0.891760i | \(-0.649471\pi\) |
0.310597 | + | 0.950542i | \(0.399471\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.2484i | − | 0.797757i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.39940 | + | 13.0353i | 0.300431 | + | 0.725304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1260 | − | 5.02277i | −0.672631 | − | 0.278613i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.39834 | + | 7.39834i | 0.407884 | + | 0.407884i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.49794 | + | 2.27732i | 0.302194 | + | 0.125173i | 0.528628 | − | 0.848854i | \(-0.322707\pi\) |
−0.226434 | + | 0.974027i | \(0.572707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4418i | 0.679768i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.85273i | − | 0.318818i | −0.987213 | − | 0.159409i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159409i | \(-0.0509589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.17801 | − | 3.80166i | −0.497017 | − | 0.205871i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2780 | + | 13.2780i | 0.716946 | + | 0.716946i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.23994 | − | 2.99888i | −0.388660 | − | 0.160988i | 0.179792 | − | 0.983705i | \(-0.442458\pi\) |
−0.568452 | + | 0.822716i | \(0.692458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.01973 | − | 9.70449i | −0.215171 | − | 0.519469i | 0.779032 | − | 0.626984i | \(-0.215711\pi\) |
−0.994204 | + | 0.107515i | \(0.965711\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.6657i | − | 0.887026i | −0.896268 | − | 0.443513i | \(-0.853732\pi\) | ||
0.896268 | − | 0.443513i | \(-0.146268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.2875 | + | 8.40338i | −1.07675 | + | 0.446005i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.54649 | + | 9.54649i | 0.503845 | + | 0.503845i | 0.912630 | − | 0.408786i | \(-0.134048\pi\) |
−0.408786 | + | 0.912630i | \(0.634048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24075 | − | 7.24075i | 0.381092 | − | 0.381092i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.50205 | + | 6.04049i | 0.130963 | + | 0.316173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.31072 | 0.329417 | 0.164708 | − | 0.986342i | \(-0.447332\pi\) | ||||
0.164708 | + | 0.986342i | \(0.447332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.53463 | − | 3.53516i | 0.443096 | − | 0.183536i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.06259 | + | 7.39375i | −0.158575 | + | 0.382834i | −0.983120 | − | 0.182963i | \(-0.941431\pi\) |
0.824545 | + | 0.565797i | \(0.191431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.6733 | − | 22.6733i | 1.16773 | − | 1.16773i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31838 | − | 20.0823i | 0.427286 | − | 1.03156i | −0.552858 | − | 0.833275i | \(-0.686463\pi\) |
0.980144 | − | 0.198285i | \(-0.0635372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.95308 | −0.406383 | −0.203192 | − | 0.979139i | \(-0.565131\pi\) | ||||
−0.203192 | + | 0.979139i | \(0.565131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2871 | 1.03393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.38215 | − | 5.75102i | 0.120780 | − | 0.291588i | −0.851913 | − | 0.523683i | \(-0.824558\pi\) |
0.972693 | + | 0.232094i | \(0.0745578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.6019 | + | 19.6019i | −0.991310 | + | 0.991310i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.4710 | − | 37.3503i | 0.778430 | − | 1.87930i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3118 | − | 10.4845i | 1.27036 | − | 0.526202i | 0.357288 | − | 0.933994i | \(-0.383701\pi\) |
0.913075 | + | 0.407792i | \(0.133701\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.81017 | 0.0903954 | 0.0451977 | − | 0.998978i | \(-0.485608\pi\) | ||||
0.0451977 | + | 0.998978i | \(0.485608\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.55532 | − | 20.6544i | −0.426171 | − | 1.02887i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.5839 | + | 11.5839i | −0.574194 | + | 0.574194i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4331 | − | 14.4331i | −0.713672 | − | 0.713672i | 0.253630 | − | 0.967301i | \(-0.418376\pi\) |
−0.967301 | + | 0.253630i | \(0.918376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.20841 | + | 2.15739i | −0.256289 | + | 0.106158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 10.5474i | − | 0.517754i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.33902 | − | 3.23269i | −0.0654155 | − | 0.157927i | 0.887791 | − | 0.460247i | \(-0.152239\pi\) |
−0.953207 | + | 0.302320i | \(0.902239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5557 | − | 4.37232i | −0.514454 | − | 0.213094i | 0.110325 | − | 0.993896i | \(-0.464811\pi\) |
−0.624779 | + | 0.780802i | \(0.714811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1966 | + | 12.1966i | 0.591624 | + | 0.591624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8148 | − | 4.47963i | −0.523364 | − | 0.216784i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31967i | 0.159903i | 0.996799 | + | 0.0799513i | \(0.0254765\pi\) | ||||
−0.996799 | + | 0.0799513i | \(0.974524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53298i | 0.217841i | 0.994050 | + | 0.108921i | \(0.0347394\pi\) | ||||
−0.994050 | + | 0.108921i | \(0.965261\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.9011 | − | 6.58646i | −0.760654 | − | 0.315073i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9703 | − | 20.9703i | −1.00086 | − | 1.00086i | −1.00000 | 0.000858061i | \(-0.999727\pi\) | |
−0.000858061 | − | 1.00000i | \(-0.500273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.9708 | − | 13.2427i | −1.51898 | − | 0.629181i | −0.541590 | − | 0.840643i | \(-0.682178\pi\) |
−0.977386 | + | 0.211462i | \(0.932178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.1058 | + | 26.8117i | 0.526464 | + | 1.27100i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0485i | 0.993340i | 0.867940 | + | 0.496670i | \(0.165444\pi\) | ||||
−0.867940 | + | 0.496670i | \(0.834556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.357852 | − | 0.148227i | 0.0168506 | − | 0.00697975i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.2827 | + | 32.2827i | 1.51344 | + | 1.51344i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.62656 | + | 4.62656i | −0.216421 | + | 0.216421i | −0.806988 | − | 0.590567i | \(-0.798904\pi\) |
0.590567 | + | 0.806988i | \(0.298904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.84388 | − | 11.6942i | −0.225602 | − | 0.544652i | 0.770031 | − | 0.638007i | \(-0.220241\pi\) |
−0.995633 | + | 0.0933550i | \(0.970241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2219 | −0.660950 | −0.330475 | − | 0.943815i | \(-0.607209\pi\) | ||||
−0.330475 | + | 0.943815i | \(0.607209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.5241 | + | 14.3003i | −1.59758 | + | 0.661741i | −0.991071 | − | 0.133333i | \(-0.957432\pi\) |
−0.606512 | + | 0.795074i | \(0.707432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95321 | − | 16.7865i | 0.321069 | − | 0.775130i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.34754 | + | 9.34754i | −0.429800 | + | 0.429800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.09821 | + | 9.89396i | −0.188039 | + | 0.453966i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.4016 | 0.612333 | 0.306167 | − | 0.951978i | \(-0.400954\pi\) | ||||
0.306167 | + | 0.951978i | \(0.400954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.8667 | −1.68098 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2320 | + | 36.7734i | −0.691652 | + | 1.66979i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.26750 | + | 1.26750i | −0.0574358 | + | 0.0574358i | −0.735241 | − | 0.677805i | \(-0.762931\pi\) |
0.677805 | + | 0.735241i | \(0.262931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.81902 | − | 21.2910i | 0.397997 | − | 0.960849i | −0.590144 | − | 0.807298i | \(-0.700929\pi\) |
0.988141 | − | 0.153551i | \(-0.0490710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.9311 | + | 16.1258i | −1.75337 | + | 0.726269i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.0684 | 1.43846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.76574 | + | 6.67709i | 0.123812 | + | 0.298908i | 0.973617 | − | 0.228189i | \(-0.0732805\pi\) |
−0.849805 | + | 0.527097i | \(0.823281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.1789 | − | 17.1789i | 0.765968 | − | 0.765968i | −0.211426 | − | 0.977394i | \(-0.567811\pi\) |
0.977394 | + | 0.211426i | \(0.0678108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.99287 | − | 5.99287i | −0.266679 | − | 0.266679i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.432418 | + | 0.179113i | −0.0191666 | + | 0.00793905i | −0.392246 | − | 0.919860i | \(-0.628302\pi\) |
0.373080 | + | 0.927799i | \(0.378302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.54815i | − | 0.422385i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.3379 | − | 49.0999i | −0.896193 | − | 2.16360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.63437 | − | 1.50541i | −0.159839 | − | 0.0662077i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.6495 | + | 20.6495i | 0.904670 | + | 0.904670i | 0.995836 | − | 0.0911655i | \(-0.0290592\pi\) |
−0.0911655 | + | 0.995836i | \(0.529059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.6453 | + | 16.8358i | 1.77729 | + | 0.736180i | 0.993321 | + | 0.115386i | \(0.0368104\pi\) |
0.783974 | + | 0.620794i | \(0.213190\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.3798i | 1.27980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10.8158i | − | 0.470252i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.805318 | + | 0.333574i | 0.0348822 | + | 0.0144487i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.90927 | + | 3.90927i | 0.169013 | + | 0.169013i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.9471 | − | 7.01973i | −0.729964 | − | 0.302361i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.26862 | − | 17.5480i | −0.312502 | − | 0.754447i | −0.999611 | − | 0.0278925i | \(-0.991120\pi\) |
0.687109 | − | 0.726555i | \(-0.258880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 14.1407i | − | 0.605721i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.22407 | − | 2.16388i | 0.223365 | − | 0.0925208i | −0.268195 | − | 0.963365i | \(-0.586427\pi\) |
0.491560 | + | 0.870844i | \(0.336427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.4998 | − | 18.4998i | −0.788116 | − | 0.788116i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.7471 | + | 41.7471i | −1.77527 | + | 1.77527i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.20051 | − | 17.3836i | −0.305095 | − | 0.736565i | −0.999850 | − | 0.0173184i | \(-0.994487\pi\) |
0.694755 | − | 0.719247i | \(-0.255513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.7492 | −1.25826 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.4445 | − | 17.9953i | 1.83097 | − | 0.758411i | 0.864007 | − | 0.503479i | \(-0.167947\pi\) |
0.966959 | − | 0.254932i | \(-0.0820530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3475 | − | 37.0522i | 0.645675 | − | 1.55880i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.66061 | − | 5.66061i | 0.237305 | − | 0.237305i | −0.578428 | − | 0.815733i | \(-0.696334\pi\) |
0.815733 | + | 0.578428i | \(0.196334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7365 | − | 33.1629i | 0.574856 | − | 1.38783i | −0.322522 | − | 0.946562i | \(-0.604531\pi\) |
0.897378 | − | 0.441263i | \(-0.145469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.0408 | −0.877461 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.38583 | 0.182584 | 0.0912922 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912922 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.89454 | + | 14.2307i | −0.244547 | + | 0.590388i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.45595 | + | 2.45595i | −0.101715 | + | 0.101715i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.24918 | + | 10.2584i | −0.175382 | + | 0.423411i | −0.986988 | − | 0.160795i | \(-0.948594\pi\) |
0.811605 | + | 0.584206i | \(0.198594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8525 | + | 6.98052i | −0.694394 | + | 0.287627i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.76763 | −0.236848 | −0.118424 | − | 0.992963i | \(-0.537784\pi\) | ||||
−0.118424 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9602 | − | 55.4309i | −0.941277 | − | 2.27244i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4401 | + | 13.4401i | −0.549149 | + | 0.549149i | −0.926195 | − | 0.377045i | \(-0.876940\pi\) |
0.377045 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.58677 | + | 8.58677i | 0.350262 | + | 0.350262i | 0.860207 | − | 0.509945i | \(-0.170334\pi\) |
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.7875 | − | 9.43890i | 0.926444 | − | 0.383746i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.3743i | − | 0.542847i | −0.962460 | − | 0.271424i | \(-0.912506\pi\) | ||
0.962460 | − | 0.271424i | \(-0.0874944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.38780 | − | 8.17886i | −0.137056 | − | 0.330881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6749 | − | 4.42168i | −0.431154 | − | 0.178590i | 0.156542 | − | 0.987671i | \(-0.449965\pi\) |
−0.587697 | + | 0.809081i | \(0.699965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.8713 | + | 14.8713i | 0.598695 | + | 0.598695i | 0.939965 | − | 0.341270i | \(-0.110857\pi\) |
−0.341270 | + | 0.939965i | \(0.610857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.25062 | + | 2.58909i | 0.251234 | + | 0.104064i | 0.504746 | − | 0.863268i | \(-0.331586\pi\) |
−0.253513 | + | 0.967332i | \(0.581586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42.3810i | − | 1.69796i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 29.9995i | − | 1.19998i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.7612 | + | 18.5407i | 1.78475 | + | 0.739266i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.78346 | + | 5.78346i | 0.230236 | + | 0.230236i | 0.812791 | − | 0.582555i | \(-0.197947\pi\) |
−0.582555 | + | 0.812791i | \(0.697947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.8052 | + | 14.8310i | 1.42088 | + | 0.588550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7973 | − | 38.1381i | −0.625913 | − | 1.51109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 29.5203i | − | 1.16598i | −0.812479 | − | 0.582990i | \(-0.801883\pi\) | ||
0.812479 | − | 0.582990i | \(-0.198117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0660 | + | 4.16947i | −0.396964 | + | 0.164428i | −0.572230 | − | 0.820093i | \(-0.693921\pi\) |
0.175266 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9256 | + | 31.9256i | 1.25512 | + | 1.25512i | 0.953393 | + | 0.301730i | \(0.0975641\pi\) |
0.301730 | + | 0.953393i | \(0.402436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49878 | − | 1.49878i | 0.0588324 | − | 0.0588324i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.05626 | − | 14.6211i | −0.237000 | − | 0.572168i | 0.759970 | − | 0.649958i | \(-0.225214\pi\) |
−0.996970 | + | 0.0777900i | \(0.975214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.6811 | −0.769002 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2612 | − | 11.7062i | 1.10090 | − | 0.456008i | 0.243106 | − | 0.970000i | \(-0.421834\pi\) |
0.857795 | + | 0.513992i | \(0.171834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.64573 | − | 16.0442i | 0.258489 | − | 0.624047i | −0.740350 | − | 0.672221i | \(-0.765340\pi\) |
0.998839 | + | 0.0481743i | \(0.0153403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.3403 | − | 26.3403i | 1.02143 | − | 1.02143i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.6711 | − | 47.4901i | 0.761666 | − | 1.83883i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.40116 | 0.169905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2884 | 1.32172 | 0.660860 | − | 0.750509i | \(-0.270192\pi\) | ||||
0.660860 | + | 0.750509i | \(0.270192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.6560 | − | 40.2112i | 0.640142 | − | 1.54544i | −0.186345 | − | 0.982484i | \(-0.559664\pi\) |
0.826487 | − | 0.562956i | \(-0.190336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.1023 | − | 41.1023i | 1.57736 | − | 1.57736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.35596 | + | 12.9304i | −0.204940 | + | 0.494769i | −0.992613 | − | 0.121325i | \(-0.961286\pi\) |
0.787673 | + | 0.616094i | \(0.211286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4872 | + | 15.5277i | −1.43231 | + | 0.593284i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.81623 | −0.297775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9998 | + | 48.2837i | 0.760826 | + | 1.83680i | 0.480898 | + | 0.876777i | \(0.340311\pi\) |
0.279929 | + | 0.960021i | \(0.409689\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.5731 | − | 18.5731i | 0.704517 | − | 0.704517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.810008 | − | 0.810008i | −0.0306812 | − | 0.0306812i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.6661 | + | 9.38859i | −0.856085 | + | 0.354602i | −0.767175 | − | 0.641438i | \(-0.778338\pi\) |
−0.0889098 | + | 0.996040i | \(0.528338\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0806i | 1.13451i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.73644 | + | 11.4348i | 0.178132 | + | 0.430049i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.91323 | − | 2.86355i | −0.259632 | − | 0.107543i | 0.249071 | − | 0.968485i | \(-0.419875\pi\) |
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.3420 | − | 25.3420i | −0.949064 | − | 0.949064i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.8586 | − | 6.56884i | −0.593078 | − | 0.245661i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 32.1395i | − | 1.19860i | −0.800525 | − | 0.599300i | \(-0.795446\pi\) | ||
0.800525 | − | 0.599300i | \(-0.204554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.6119i | 2.89042i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.5492 | − | 12.2397i | −1.09743 | − | 0.454570i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0313 | − | 24.0313i | −0.891271 | − | 0.891271i | 0.103372 | − | 0.994643i | \(-0.467037\pi\) |
−0.994643 | + | 0.103372i | \(0.967037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.1196 | + | 14.9612i | 1.33593 | + | 0.553361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28110 | − | 7.92127i | −0.121190 | − | 0.292579i | 0.851629 | − | 0.524145i | \(-0.175615\pi\) |
−0.972819 | + | 0.231566i | \(0.925615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.83141i | 0.251638i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.01435 | + | 1.66280i | −0.147670 | + | 0.0611671i | −0.455295 | − | 0.890341i | \(-0.650466\pi\) |
0.307624 | + | 0.951508i | \(0.400466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6253 | − | 20.6253i | −0.756669 | − | 0.756669i | 0.219046 | − | 0.975715i | \(-0.429706\pi\) |
−0.975715 | + | 0.219046i | \(0.929706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.6465 | − | 42.6465i | 1.56245 | − | 1.56245i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.08968 | − | 7.45915i | −0.112894 | − | 0.272551i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6475 | −0.498004 | −0.249002 | − | 0.968503i | \(-0.580103\pi\) | ||||
−0.249002 | + | 0.968503i | \(0.580103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.0458 | + | 12.4454i | −1.09348 | + | 0.452933i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50145 | − | 3.62481i | 0.0545710 | − | 0.131746i | −0.894243 | − | 0.447582i | \(-0.852285\pi\) |
0.948814 | + | 0.315836i | \(0.102285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5824 | − | 10.5824i | 0.383612 | − | 0.383612i | −0.488790 | − | 0.872402i | \(-0.662562\pi\) |
0.872402 | + | 0.488790i | \(0.162562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.90266 | + | 19.0787i | −0.286096 | + | 0.690696i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.76999 | 0.172234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.6343 | −1.53743 | −0.768715 | − | 0.639591i | \(-0.779104\pi\) | ||||
−0.768715 | + | 0.639591i | \(0.779104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5374 | + | 32.6822i | −0.486906 | + | 1.17550i | 0.469362 | + | 0.883006i | \(0.344484\pi\) |
−0.956268 | + | 0.292490i | \(0.905516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.7682 | + | 15.7682i | −0.566411 | + | 0.566411i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.272172 | − | 0.657081i | 0.00975157 | − | 0.0235424i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1393 | + | 4.61404i | −0.398595 | + | 0.165103i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.4645 | 0.980249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1547 | + | 26.9298i | 0.397622 | + | 0.959945i | 0.988228 | + | 0.152985i | \(0.0488887\pi\) |
−0.590606 | + | 0.806960i | \(0.701111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.4139 | + | 41.4139i | −1.47251 | + | 1.47251i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00350 | + | 7.00350i | 0.248702 | + | 0.248702i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.44606 | + | 1.42740i | −0.122066 | + | 0.0505612i | −0.442880 | − | 0.896581i | \(-0.646043\pi\) |
0.320815 | + | 0.947142i | \(0.396043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6340i | 0.411582i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.37380 | + | 3.31665i | 0.0484804 | + | 0.117042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.6174 | + | 28.0080i | 2.38320 | + | 0.987154i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.7746 | − | 27.7746i | −0.976503 | − | 0.976503i | 0.0232274 | − | 0.999730i | \(-0.492606\pi\) |
−0.999730 | + | 0.0232274i | \(0.992606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.7402 | − | 5.69137i | −0.482483 | − | 0.199851i | 0.128165 | − | 0.991753i | \(-0.459091\pi\) |
−0.610649 | + | 0.791902i | \(0.709091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.0519i | − | 0.527246i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.2732i | 0.849212i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.08495 | + | 3.76311i | 0.317067 | + | 0.131333i | 0.535541 | − | 0.844509i | \(-0.320108\pi\) |
−0.218474 | + | 0.975843i | \(0.570108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.7132 | + | 37.7132i | 1.31460 | + | 1.31460i | 0.917985 | + | 0.396615i | \(0.129815\pi\) |
0.396615 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6871 | + | 9.81150i | 0.823680 | + | 0.341179i | 0.754398 | − | 0.656418i | \(-0.227929\pi\) |
0.0692824 | + | 0.997597i | \(0.477929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.99320 | − | 16.8831i | −0.242884 | − | 0.586374i | 0.754683 | − | 0.656090i | \(-0.227791\pi\) |
−0.997567 | + | 0.0697159i | \(0.977791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 54.2495i | 1.87964i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4599 | + | 7.23214i | −0.604225 | + | 0.250278i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.56749 | − | 9.56749i | −0.330306 | − | 0.330306i | 0.522396 | − | 0.852703i | \(-0.325038\pi\) |
−0.852703 | + | 0.522396i | \(0.825038\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.7451 | − | 34.7451i | 1.19811 | − | 1.19811i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.177934 | − | 0.429570i | −0.00612111 | − | 0.0147777i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.0201 | −1.23766 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.6020 | + | 22.6169i | −1.87173 | + | 0.775297i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.73365 | + | 9.01383i | −0.127838 | + | 0.308628i | −0.974820 | − | 0.222994i | \(-0.928417\pi\) |
0.846982 | + | 0.531621i | \(0.178417\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.7027 | + | 19.7027i | −0.673032 | + | 0.673032i | −0.958414 | − | 0.285382i | \(-0.907880\pi\) |
0.285382 | + | 0.958414i | \(0.407880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.30760 | + | 20.0563i | −0.283452 | + | 0.684313i | −0.999911 | − | 0.0133155i | \(-0.995761\pi\) |
0.716460 | + | 0.697629i | \(0.245761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.3303 | 0.998415 | 0.499207 | − | 0.866483i | \(-0.333625\pi\) | ||||
0.499207 | + | 0.866483i | \(0.333625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.8674 | 1.11752 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.49465 | − | 20.5079i | 0.288161 | − | 0.695683i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.8707 | + | 10.8707i | −0.368341 | + | 0.368341i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.65492 | + | 16.0664i | −0.224977 | + | 0.543144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.0165 | − | 17.8180i | 1.45256 | − | 0.601672i | 0.489756 | − | 0.871859i | \(-0.337086\pi\) |
0.962808 | + | 0.270188i | \(0.0870858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.5605 | −1.83819 | −0.919095 | − | 0.394035i | \(-0.871079\pi\) | ||||
−0.919095 | + | 0.394035i | \(0.871079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.61420 | + | 11.1397i | 0.155280 | + | 0.374879i | 0.982306 | − | 0.187285i | \(-0.0599688\pi\) |
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2635 | + | 20.2635i | −0.680383 | + | 0.680383i | −0.960086 | − | 0.279704i | \(-0.909764\pi\) |
0.279704 | + | 0.960086i | \(0.409764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0201 | − | 40.0201i | −1.34223 | − | 1.34223i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.67336 | + | 2.76419i | −0.223315 | + | 0.0925003i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.4895i | − | 1.08600i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.8479 | − | 50.3314i | −0.695318 | − | 1.67865i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.48997 | + | 3.93087i | 0.316157 | + | 0.130956i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.23396 | + | 7.23396i | 0.240465 | + | 0.240465i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.3520 | − | 12.9864i | −1.04103 | − | 0.431208i | −0.204347 | − | 0.978899i | \(-0.565507\pi\) |
−0.836681 | + | 0.547691i | \(0.815507\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.6280i | 1.47859i | 0.673380 | + | 0.739296i | \(0.264842\pi\) | ||||
−0.673380 | + | 0.739296i | \(0.735158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.79128i | − | 0.191663i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.5538 | + | 10.9989i | 0.876883 | + | 0.363217i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.85821 | − | 7.85821i | −0.259219 | − | 0.259219i | 0.565518 | − | 0.824736i | \(-0.308676\pi\) |
−0.824736 | + | 0.565518i | \(0.808676\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0680 | − | 10.3835i | −0.825125 | − | 0.341778i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0726 | + | 33.9743i | 0.462705 | + | 1.11707i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.8136i | 0.486018i | 0.970024 | + | 0.243009i | \(0.0781344\pi\) | ||||
−0.970024 | + | 0.243009i | \(0.921866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.1180 | + | 12.8895i | −1.01985 | + | 0.422436i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.9509 | + | 15.9509i | 0.521651 | + | 0.521651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7125 | + | 10.7125i | −0.349961 | + | 0.349961i | −0.860095 | − | 0.510134i | \(-0.829596\pi\) |
0.510134 | + | 0.860095i | \(0.329596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.84380 | + | 4.45134i | 0.0601063 | + | 0.145109i | 0.951079 | − | 0.308947i | \(-0.0999765\pi\) |
−0.890973 | + | 0.454056i | \(0.849977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.39737 | 0.0455046 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.3221 | − | 19.1872i | 1.50527 | − | 0.623501i | 0.530691 | − | 0.847565i | \(-0.321932\pi\) |
0.974574 | + | 0.224064i | \(0.0719324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.09163 | + | 7.46385i | −0.100358 | + | 0.242287i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40430 | − | 2.40430i | 0.0778828 | − | 0.0778828i | −0.667092 | − | 0.744975i | \(-0.732461\pi\) |
0.744975 | + | 0.667092i | \(0.232461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.41999 | − | 13.0850i | 0.175387 | − | 0.423421i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59.2558 | 1.91347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.98312 | −0.225262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.250390 | − | 0.604495i | 0.00806034 | − | 0.0194594i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.6984 | − | 12.6984i | 0.408354 | − | 0.408354i | −0.472811 | − | 0.881164i | \(-0.656761\pi\) |
0.881164 | + | 0.472811i | \(0.156761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.19719 | + | 12.5471i | −0.166786 | + | 0.402657i | −0.985069 | − | 0.172158i | \(-0.944926\pi\) |
0.818283 | + | 0.574815i | \(0.194926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.4386 | + | 14.6792i | −1.13611 | + | 0.470592i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.3021 | −0.649521 | −0.324761 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324761 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.09784 | + | 14.7215i | 0.194888 | + | 0.470501i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.4130 | + | 11.4130i | −0.364017 | + | 0.364017i | −0.865290 | − | 0.501272i | \(-0.832866\pi\) |
0.501272 | + | 0.865290i | \(0.332866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2155 | − | 51.2155i | −1.63186 | − | 1.63186i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.0605 | + | 18.2505i | −1.40104 | + | 0.580331i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.0390i | − | 0.382431i | −0.981548 | − | 0.191216i | \(-0.938757\pi\) | ||
0.981548 | − | 0.191216i | \(-0.0612430\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.6268 | + | 57.0401i | 0.749020 | + | 1.80829i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2248 | + | 7.13474i | 0.545514 | + | 0.225959i | 0.638383 | − | 0.769719i | \(-0.279604\pi\) |
−0.0928685 | + | 0.995678i | \(0.529604\pi\) | |||||||
\(998\) | 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 | 1152.2.w.a.143.7 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.143.2 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.251.4 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.251.5 | yes | 32 | ||
32.13 | even | 8 | 288.2.w.a.179.5 | ✓ | 32 | ||
32.19 | odd | 8 | 1152.2.w.b.1007.2 | 32 | |||
96.77 | odd | 8 | 288.2.w.b.179.4 | yes | 32 | ||
96.83 | even | 8 | inner | 1152.2.w.a.1007.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.5 | ✓ | 32 | 32.13 | even | 8 | ||
288.2.w.a.251.5 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.179.4 | yes | 32 | 96.77 | odd | 8 | ||
288.2.w.b.251.4 | yes | 32 | 4.3 | odd | 2 | ||
1152.2.w.a.143.7 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.a.1007.7 | 32 | 96.83 | even | 8 | inner | ||
1152.2.w.b.143.2 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.1007.2 | 32 | 32.19 | odd | 8 |