Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(47,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bh (of order \(18\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Character | \(\chi\) | \(=\) | 864.47 |
Dual form | 864.2.bh.b.239.1 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.71829 | − | 0.217923i | −0.992053 | − | 0.125818i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.693543 | − | 3.93328i | −0.310162 | − | 1.75901i | −0.598153 | − | 0.801382i | \(-0.704099\pi\) |
0.287992 | − | 0.957633i | \(-0.407012\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05979 | − | 2.45476i | 0.778528 | − | 0.927814i | −0.220338 | − | 0.975424i | \(-0.570716\pi\) |
0.998866 | + | 0.0476099i | \(0.0151604\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.90502 | + | 0.748909i | 0.968340 | + | 0.249636i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77912 | + | 0.842688i | 1.44096 | + | 0.254080i | 0.838862 | − | 0.544343i | \(-0.183221\pi\) |
0.602096 | + | 0.798423i | \(0.294332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.246151 | − | 0.676295i | 0.0682700 | − | 0.187570i | −0.900866 | − | 0.434098i | \(-0.857067\pi\) |
0.969136 | + | 0.246527i | \(0.0792895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.334553 | + | 6.90964i | 0.0863813 | + | 1.78406i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.707869 | − | 0.408688i | 0.171683 | − | 0.0991214i | −0.411696 | − | 0.911321i | \(-0.635063\pi\) |
0.583379 | + | 0.812200i | \(0.301730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.653550 | − | 1.13198i | 0.149935 | − | 0.259694i | −0.781268 | − | 0.624195i | \(-0.785427\pi\) |
0.931203 | + | 0.364501i | \(0.118760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.07426 | + | 3.76911i | −0.889077 | + | 0.822488i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.96174 | − | 2.48519i | 0.617565 | − | 0.518198i | −0.279472 | − | 0.960154i | \(-0.590160\pi\) |
0.897037 | + | 0.441955i | \(0.145715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.2912 | + | 3.74569i | −2.05824 | + | 0.749138i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.82845 | − | 1.91991i | −0.929236 | − | 0.369487i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.23351 | − | 1.90484i | 0.971838 | − | 0.353720i | 0.193177 | − | 0.981164i | \(-0.438121\pi\) |
0.778662 | + | 0.627444i | \(0.215899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.511632 | − | 0.609740i | −0.0918919 | − | 0.109512i | 0.718139 | − | 0.695900i | \(-0.244994\pi\) |
−0.810031 | + | 0.586387i | \(0.800550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.02826 | − | 2.48946i | −1.39754 | − | 0.433359i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.0838 | − | 6.39925i | −1.87351 | − | 1.08167i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.71792 | + | 1.56919i | −0.446823 | + | 0.257974i | −0.706488 | − | 0.707725i | \(-0.749721\pi\) |
0.259664 | + | 0.965699i | \(0.416388\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.570338 | + | 1.10843i | −0.0913272 | + | 0.177490i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.40768 | − | 9.36253i | 0.532191 | − | 1.46218i | −0.324268 | − | 0.945965i | \(-0.605118\pi\) |
0.856458 | − | 0.516216i | \(-0.172660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.01090 | + | 11.4044i | −0.306660 | + | 1.73915i | 0.308927 | + | 0.951086i | \(0.400030\pi\) |
−0.615587 | + | 0.788069i | \(0.711081\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.930912 | − | 11.9456i | 0.138772 | − | 1.78075i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.89967 | − | 3.27222i | −0.568826 | − | 0.477302i | 0.312430 | − | 0.949941i | \(-0.398857\pi\) |
−0.881256 | + | 0.472639i | \(0.843301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.567588 | − | 3.21895i | −0.0810840 | − | 0.459850i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.30538 | + | 0.547982i | −0.182790 | + | 0.0767329i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.181698 | −0.0249581 | −0.0124790 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124790 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 19.3820i | − | 2.61347i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.36967 | + | 1.80265i | −0.181417 | + | 0.238766i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.908057 | + | 0.160115i | −0.118219 | + | 0.0208452i | −0.232445 | − | 0.972610i | \(-0.574672\pi\) |
0.114226 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.975724 | + | 1.16282i | −0.124929 | + | 0.148884i | −0.824883 | − | 0.565303i | \(-0.808759\pi\) |
0.699954 | + | 0.714187i | \(0.253204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.82213 | − | 5.58854i | 0.985496 | − | 0.704090i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.83077 | − | 0.499141i | −0.351114 | − | 0.0619108i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.95586 | − | 2.16776i | −0.727624 | − | 0.264834i | −0.0484653 | − | 0.998825i | \(-0.515433\pi\) |
−0.679159 | + | 0.733991i | \(0.737655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.63069 | + | 3.62484i | −0.677856 | + | 0.436380i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.91251 | + | 8.50871i | 0.583008 | + | 1.00980i | 0.995121 | + | 0.0986659i | \(0.0314575\pi\) |
−0.412113 | + | 0.911133i | \(0.635209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.606035 | + | 1.04968i | −0.0709311 | + | 0.122856i | −0.899310 | − | 0.437313i | \(-0.855930\pi\) |
0.828379 | + | 0.560169i | \(0.189264\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.4995 | − | 4.19348i | 2.13614 | − | 0.484221i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.9126 | − | 9.99585i | 1.35757 | − | 1.13913i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.336165 | − | 0.923605i | −0.0378215 | − | 0.103914i | 0.919344 | − | 0.393454i | \(-0.128720\pi\) |
−0.957166 | + | 0.289540i | \(0.906498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.87827 | + | 4.35119i | 0.875363 | + | 0.483466i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.517786 | − | 1.42261i | −0.0568344 | − | 0.156151i | 0.908026 | − | 0.418913i | \(-0.137589\pi\) |
−0.964861 | + | 0.262762i | \(0.915367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.09842 | − | 2.50080i | −0.227606 | − | 0.271250i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.40778 | + | 2.13256i | −1.00862 | + | 0.228635i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.93630 | − | 3.42732i | −0.629246 | − | 0.363296i | 0.151214 | − | 0.988501i | \(-0.451682\pi\) |
−0.780460 | + | 0.625206i | \(0.785015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.15312 | − | 1.99727i | −0.120880 | − | 0.209371i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.746255 | + | 1.15920i | 0.0773830 | + | 0.120204i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.90566 | − | 1.78551i | −0.503310 | − | 0.183190i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.47950 | + | 8.39068i | −0.150221 | + | 0.851945i | 0.812805 | + | 0.582536i | \(0.197939\pi\) |
−0.963026 | + | 0.269409i | \(0.913172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.2523 | + | 6.02715i | 1.33191 | + | 0.605751i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0625 | + | 10.9607i | 1.29976 | + | 1.09063i | 0.990186 | + | 0.139756i | \(0.0446317\pi\) |
0.309577 | + | 0.950875i | \(0.399813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4111 | + | 2.01208i | −1.12437 | + | 0.198256i | −0.704757 | − | 0.709448i | \(-0.748944\pi\) |
−0.419610 | + | 0.907705i | \(0.637833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17.6506 | + | 13.4112i | 1.72253 | + | 1.30880i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.92250i | − | 0.669223i | −0.942356 | − | 0.334612i | \(-0.891395\pi\) | ||
0.942356 | − | 0.334612i | \(-0.108605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.45030i | − | 0.330479i | −0.986253 | − | 0.165239i | \(-0.947160\pi\) | ||
0.986253 | − | 0.165239i | \(-0.0528397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.01213 | − | 2.10402i | 0.475730 | − | 0.199705i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4711 | + | 2.55165i | −1.36133 | + | 0.240039i | −0.806160 | − | 0.591698i | \(-0.798458\pi\) |
−0.555170 | + | 0.831737i | \(0.687347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.8290 | − | 9.92574i | −1.10306 | − | 0.925580i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.22156 | − | 1.78030i | 0.112933 | − | 0.164589i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.454829 | − | 2.57946i | 0.0416941 | − | 0.236459i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7932 | + | 4.29239i | 1.07211 | + | 0.390217i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.89569 | + | 15.3449i | −0.711930 | + | 1.38360i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8853 | + | 20.5860i | 1.06306 | + | 1.84127i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.53630 | − | 0.886983i | −0.136325 | − | 0.0787070i | 0.430287 | − | 0.902692i | \(-0.358412\pi\) |
−0.566611 | + | 0.823985i | \(0.691746\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.94059 | − | 19.1578i | 0.523040 | − | 1.68675i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.60193 | + | 1.90910i | 0.139961 | + | 0.166799i | 0.831472 | − | 0.555567i | \(-0.187499\pi\) |
−0.691510 | + | 0.722366i | \(0.743054\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.43257 | − | 3.93596i | −0.124220 | − | 0.341291i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.20281 | + | 20.3232i | −0.361720 | + | 1.74914i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.54495 | + | 15.2346i | 0.473737 | + | 1.30158i | 0.914728 | + | 0.404069i | \(0.132405\pi\) |
−0.440992 | + | 0.897511i | \(0.645373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.802121 | − | 0.673059i | 0.0680350 | − | 0.0570881i | −0.608136 | − | 0.793833i | \(-0.708082\pi\) |
0.676171 | + | 0.736745i | \(0.263638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.98767 | + | 6.47243i | 0.504253 | + | 0.545077i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.74629 | − | 3.02466i | 0.146032 | − | 0.252935i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1219 | − | 19.2638i | −0.923626 | − | 1.59977i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.273795 | + | 5.65477i | 0.0225822 | + | 0.466398i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.8730 | − | 7.59715i | −1.70998 | − | 0.622383i | −0.713085 | − | 0.701078i | \(-0.752703\pi\) |
−0.996899 | + | 0.0786947i | \(0.974925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.72685 | − | 1.00980i | −0.466045 | − | 0.0821762i | −0.0643052 | − | 0.997930i | \(-0.520483\pi\) |
−0.401739 | + | 0.915754i | \(0.631594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.36244 | − | 0.657118i | 0.190992 | − | 0.0531248i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.04344 | + | 2.43527i | −0.164133 | + | 0.195606i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1064 | + | 1.78204i | −0.806582 | + | 0.142222i | −0.561711 | − | 0.827334i | \(-0.689857\pi\) |
−0.244871 | + | 0.969556i | \(0.578746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.312209 | + | 0.0395961i | 0.0247598 | + | 0.00314018i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.3893i | − | 0.976417i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7405 | 0.919590 | 0.459795 | − | 0.888025i | \(-0.347923\pi\) | ||||
0.459795 | + | 0.888025i | \(0.347923\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.22380 | + | 33.3039i | −0.328822 | + | 2.59271i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.71920 | + | 15.4214i | 0.210418 | + | 1.19334i | 0.888683 | + | 0.458523i | \(0.151621\pi\) |
−0.678265 | + | 0.734818i | \(0.737268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.56179 | + | 8.02330i | 0.735523 | + | 0.617177i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.74633 | − | 2.79898i | 0.210017 | − | 0.214043i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.41091 | + | 8.00169i | −0.107270 | + | 0.608357i | 0.883020 | + | 0.469336i | \(0.155507\pi\) |
−0.990289 | + | 0.139021i | \(0.955604\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0029 | + | 32.9778i | −0.907337 | + | 2.49289i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.59519 | − | 0.0772367i | 0.119902 | − | 0.00580547i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3490 | − | 7.70708i | 0.997755 | − | 0.576054i | 0.0901716 | − | 0.995926i | \(-0.471258\pi\) |
0.907583 | + | 0.419872i | \(0.137925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.4342 | + | 7.17888i | 0.924226 | + | 0.533602i | 0.884981 | − | 0.465628i | \(-0.154171\pi\) |
0.0392449 | + | 0.999230i | \(0.487505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.92998 | − | 1.78543i | 0.142668 | − | 0.131983i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.05706 | + | 9.60203i | 0.592367 | + | 0.705955i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.72739 | − | 1.35666i | 0.272573 | − | 0.0992086i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.6585 | + | 7.89809i | −1.06625 | + | 0.574502i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3786 | + | 3.77752i | −0.750972 | + | 0.273332i | −0.689015 | − | 0.724747i | \(-0.741957\pi\) |
−0.0619574 | + | 0.998079i | \(0.519734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.41602 | + | 3.70548i | −0.317872 | + | 0.266726i | −0.787737 | − | 0.616012i | \(-0.788747\pi\) |
0.469865 | + | 0.882738i | \(0.344303\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.75530 | + | 1.47456i | 0.340534 | + | 0.105595i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.38881 | − | 16.2619i | 0.668925 | − | 1.15861i | −0.309280 | − | 0.950971i | \(-0.600088\pi\) |
0.978205 | − | 0.207641i | \(-0.0665785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5780 | − | 6.10722i | 0.749856 | − | 0.432930i | −0.0757858 | − | 0.997124i | \(-0.524147\pi\) |
0.825642 | + | 0.564194i | \(0.190813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.76147 | + | 5.02275i | 0.688521 | + | 0.354277i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.10400 | − | 16.7706i | 0.428417 | − | 1.17707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −39.1888 | − | 6.91004i | −2.73706 | − | 0.482618i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.4651 | − | 5.00146i | 0.727373 | − | 0.347625i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.07730 | − | 4.85914i | 0.282033 | − | 0.336113i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.21591 | + | 18.2383i | 0.221393 | + | 1.25558i | 0.869463 | + | 0.493999i | \(0.164465\pi\) |
−0.648070 | + | 0.761581i | \(0.724424\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.58685 | − | 15.6910i | −0.451324 | − | 1.07513i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 46.2513 | 3.15431 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.55062 | −0.173148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.27009 | − | 1.67159i | 0.0858249 | − | 0.112956i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.102151 | − | 0.579327i | −0.00687142 | − | 0.0389697i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.23856 | − | 8.62658i | 0.484730 | − | 0.577679i | −0.467139 | − | 0.884184i | \(-0.654715\pi\) |
0.951869 | + | 0.306505i | \(0.0991597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −32.7013 | + | 3.17413i | −2.18009 | + | 0.211609i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.98787 | + | 1.58480i | 0.596546 | + | 0.105187i | 0.463765 | − | 0.885958i | \(-0.346498\pi\) |
0.132781 | + | 0.991145i | \(0.457609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.36470 | − | 17.4869i | 0.420591 | − | 1.15557i | −0.530777 | − | 0.847511i | \(-0.678100\pi\) |
0.951369 | − | 0.308054i | \(-0.0996778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.6476 | + | 14.5797i | −1.49010 | + | 0.959274i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.2286 | − | 11.1016i | 1.25971 | − | 0.727291i | 0.286688 | − | 0.958024i | \(-0.407446\pi\) |
0.973017 | + | 0.230732i | \(0.0741122\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1659 | + | 17.6079i | −0.663153 | + | 1.14861i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.376352 | + | 1.66028i | 0.0244467 | + | 0.107847i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4989 | − | 11.3269i | 0.873169 | − | 0.732676i | −0.0915939 | − | 0.995796i | \(-0.529196\pi\) |
0.964763 | + | 0.263121i | \(0.0847517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.85508 | − | 3.22299i | 0.570406 | − | 0.207611i | −0.0406839 | − | 0.999172i | \(-0.512954\pi\) |
0.611090 | + | 0.791561i | \(0.290731\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.5889 | − | 9.19345i | −0.807578 | − | 0.589760i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.2674 | + | 4.46496i | −0.783734 | + | 0.285256i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.604681 | − | 0.720631i | −0.0384749 | − | 0.0458526i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.579686 | + | 2.55728i | 0.0367361 | + | 0.162061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.8008 | + | 15.4735i | 1.69165 | + | 0.976676i | 0.953185 | + | 0.302388i | \(0.0977840\pi\) |
0.738468 | + | 0.674288i | \(0.235549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.2487 | − | 9.38121i | 1.02155 | − | 0.589792i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.06071 | + | 4.75439i | 0.191669 | + | 0.297731i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.14184 | − | 8.63213i | 0.195982 | − | 0.538457i | −0.802308 | − | 0.596911i | \(-0.796395\pi\) |
0.998290 | + | 0.0584533i | \(0.0186169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74635 | + | 9.90406i | −0.108513 | + | 0.615408i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.6300 | − | 1.61418i | 1.02937 | − | 0.0999151i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.59765 | − | 3.01879i | −0.221841 | − | 0.186147i | 0.525093 | − | 0.851045i | \(-0.324030\pi\) |
−0.746934 | + | 0.664898i | \(0.768475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.126015 | + | 0.714667i | 0.00774104 | + | 0.0439016i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.45337 | + | 7.18278i | 0.578537 | + | 0.439579i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.2139 | −1.72023 | −0.860115 | − | 0.510100i | \(-0.829608\pi\) | ||||
−0.860115 | + | 0.510100i | \(0.829608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1576i | 0.920757i | 0.887723 | + | 0.460378i | \(0.152286\pi\) | ||||
−0.887723 | + | 0.460378i | \(0.847714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.54615 | + | 3.68317i | 0.0935770 | + | 0.222916i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −52.3393 | + | 9.22883i | −3.15618 | + | 0.556520i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.43735 | − | 11.2470i | 0.567035 | − | 0.675766i | −0.403984 | − | 0.914766i | \(-0.632375\pi\) |
0.971020 | + | 0.239000i | \(0.0768195\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.02966 | − | 2.15447i | −0.0616443 | − | 0.128985i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.57405 | + | 0.630201i | 0.213210 | + | 0.0375946i | 0.279233 | − | 0.960223i | \(-0.409920\pi\) |
−0.0660229 | + | 0.997818i | \(0.521031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.78947 | + | 2.47116i | 0.403592 | + | 0.146895i | 0.535837 | − | 0.844322i | \(-0.319996\pi\) |
−0.132245 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.04023 | + | 4.13708i | 0.476262 | + | 0.245060i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.9637 | − | 27.6499i | −0.942307 | − | 1.63212i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.16595 | + | 14.1438i | −0.480350 | + | 0.831990i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.37074 | − | 14.0952i | 0.256217 | − | 0.826274i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.40067 | − | 5.37080i | 0.373931 | − | 0.313765i | −0.436383 | − | 0.899761i | \(-0.643741\pi\) |
0.810314 | + | 0.585996i | \(0.199296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.25955 | + | 3.46059i | 0.0733340 | + | 0.201483i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.4579 | − | 13.2444i | −1.24511 | − | 0.768516i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.951687 | − | 2.61474i | −0.0550375 | − | 0.151214i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.8531 | + | 28.4270i | 1.37487 | + | 1.63850i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20.0564 | − | 21.6802i | −1.15221 | − | 1.24550i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.25041 | + | 3.03133i | 0.300638 | + | 0.173573i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2168 | − | 24.6242i | −0.811393 | − | 1.40537i | −0.911889 | − | 0.410437i | \(-0.865376\pi\) |
0.100495 | − | 0.994938i | \(-0.467957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.0460 | − | 0.970593i | 1.14038 | − | 0.0552151i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5053 | − | 3.82361i | −0.595701 | − | 0.216817i | 0.0265343 | − | 0.999648i | \(-0.491553\pi\) |
−0.622235 | + | 0.782831i | \(0.713775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.64149 | + | 9.30937i | −0.0927827 | + | 0.526197i | 0.902622 | + | 0.430435i | \(0.141640\pi\) |
−0.995404 | + | 0.0957617i | \(0.969471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.4063 | − | 26.8907i | −1.54417 | − | 1.51512i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2563 | − | 13.6406i | −0.913043 | − | 0.766134i | 0.0596524 | − | 0.998219i | \(-0.481001\pi\) |
−0.972695 | + | 0.232085i | \(0.925445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.6168 | − | 4.69325i | 1.49025 | − | 0.262772i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.50857 | + | 11.8948i | −0.0842003 | + | 0.663905i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.06839i | − | 0.0594469i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.88189i | 0.437208i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.751900 | + | 5.92860i | −0.0415802 | + | 0.327853i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0650 | + | 2.83270i | −0.885694 | + | 0.156172i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.45482 | + | 6.25534i | 0.409754 | + | 0.343825i | 0.824249 | − | 0.566227i | \(-0.191597\pi\) |
−0.414495 | + | 0.910051i | \(0.636042\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.07079 | + | 2.52306i | −0.497076 | + | 0.138263i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.39574 | + | 24.9295i | −0.240165 | + | 1.36204i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8549 | + | 6.49864i | 0.972617 | + | 0.354004i | 0.778966 | − | 0.627067i | \(-0.215745\pi\) |
0.193652 | + | 0.981070i | \(0.437967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.4216 | − | 1.23087i | 1.38071 | − | 0.0668518i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.93133 | − | 3.34517i | −0.104588 | − | 0.181151i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.3552 | + | 5.97856i | 0.559126 | + | 0.322812i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.1626 | + | 19.6331i | 0.977843 | + | 1.05701i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.03596 | + | 8.38513i | 0.377710 | + | 0.450137i | 0.921090 | − | 0.389350i | \(-0.127300\pi\) |
−0.543380 | + | 0.839487i | \(0.682856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.70795 | − | 23.9249i | −0.466126 | − | 1.28067i | −0.920808 | − | 0.390017i | \(-0.872469\pi\) |
0.454682 | − | 0.890654i | \(-0.349753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.48695 | + | 2.79287i | −0.132744 | + | 0.149072i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.42693 | − | 9.41540i | −0.182397 | − | 0.501131i | 0.814472 | − | 0.580203i | \(-0.197027\pi\) |
−0.996869 | + | 0.0790715i | \(0.974804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.0601 | − | 25.2234i | 1.59542 | − | 1.33872i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.34365 | + | 4.33314i | −0.0711136 | + | 0.229334i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.79690 | + | 4.84437i | −0.147615 | + | 0.255676i | −0.930345 | − | 0.366685i | \(-0.880493\pi\) |
0.782731 | + | 0.622360i | \(0.213826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.64575 | + | 14.9749i | 0.455039 | + | 0.788151i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.3288 | − | 9.94558i | −1.01450 | − | 0.522007i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.54901 | + | 1.65570i | 0.238106 | + | 0.0866635i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.7502 | − | 5.42209i | −1.60515 | − | 0.283031i | −0.701940 | − | 0.712236i | \(-0.747683\pi\) |
−0.903207 | + | 0.429205i | \(0.858794\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.9111 | − | 24.6463i | 0.880355 | − | 1.28303i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.374259 | + | 0.446025i | −0.0194306 | + | 0.0231565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5451 | − | 2.38837i | 0.701340 | − | 0.123665i | 0.188403 | − | 0.982092i | \(-0.439669\pi\) |
0.512936 | + | 0.858427i | \(0.328558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.9362 | − | 37.9627i | −0.822944 | − | 1.96039i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.00827i | − | 0.206437i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.9660 | −1.64199 | −0.820993 | − | 0.570939i | \(-0.806579\pi\) | ||||
−0.820993 | + | 0.570939i | \(0.806579\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.44651 | + | 1.85889i | 0.125338 | + | 0.0952337i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.30024 | − | 7.37403i | −0.0664392 | − | 0.376795i | −0.999839 | − | 0.0179566i | \(-0.994284\pi\) |
0.933400 | − | 0.358839i | \(-0.116827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.5783 | − | 39.9230i | −2.42482 | − | 2.03466i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.3826 | + | 31.6240i | −0.731107 | + | 1.60754i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.61608 | + | 26.1791i | −0.234044 | + | 1.32733i | 0.610572 | + | 0.791960i | \(0.290939\pi\) |
−0.844617 | + | 0.535371i | \(0.820172\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08085 | − | 2.96962i | 0.0546610 | − | 0.150180i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.33654 | − | 3.62949i | −0.117863 | − | 0.183083i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.39965 | + | 1.96279i | −0.171055 | + | 0.0987586i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.7004 | + | 14.8381i | 1.28986 | + | 0.744704i | 0.978630 | − | 0.205629i | \(-0.0659241\pi\) |
0.311235 | + | 0.950333i | \(0.399257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.60383 | + | 7.07529i | 0.0802920 | + | 0.354208i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5172 | − | 18.4927i | −0.774891 | − | 0.923480i | 0.223799 | − | 0.974635i | \(-0.428154\pi\) |
−0.998691 | + | 0.0511557i | \(0.983710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.538303 | + | 0.195926i | −0.0268148 | + | 0.00975977i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.6505 | − | 34.0052i | 0.578919 | − | 1.68973i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.3116 | + | 5.20900i | −0.709400 | + | 0.258200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.17989 | + | 6.02464i | −0.355023 | + | 0.297899i | −0.802803 | − | 0.596244i | \(-0.796659\pi\) |
0.447781 | + | 0.894143i | \(0.352215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.20783 | − | 27.3858i | −0.306210 | − | 1.35084i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.47736 | + | 2.55887i | −0.0726963 | + | 0.125914i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.23640 | + | 3.02323i | −0.257045 | + | 0.148405i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.52495 | + | 0.981708i | −0.0746771 | + | 0.0480745i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.17961 | + | 16.9783i | −0.301894 | + | 0.829446i | 0.692277 | + | 0.721631i | \(0.256607\pi\) |
−0.994171 | + | 0.107814i | \(0.965615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9086 | − | 1.92348i | −0.531653 | − | 0.0937447i | −0.0986239 | − | 0.995125i | \(-0.531444\pi\) |
−0.433029 | + | 0.901380i | \(0.642555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.87804 | − | 12.4264i | −0.431665 | − | 0.604190i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.75400 | + | 6.85735i | −0.279110 | + | 0.332630i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.844667 | + | 4.79035i | 0.0408763 | + | 0.231821i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.65977 | + | 4.81668i | −0.176695 | + | 0.232552i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.5183 | 1.18101 | 0.590503 | − | 0.807036i | \(-0.298930\pi\) | ||||
0.590503 | + | 0.807036i | \(0.298930\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.35856 | −0.401687 | −0.200843 | − | 0.979623i | \(-0.564368\pi\) | ||||
−0.200843 | + | 0.979623i | \(0.564368\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.9127 | + | 35.5244i | 0.715007 | + | 1.70326i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.877549 | − | 4.97683i | −0.0419789 | − | 0.238074i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.95815 | − | 8.29240i | 0.332094 | − | 0.395775i | −0.573997 | − | 0.818858i | \(-0.694608\pi\) |
0.906091 | + | 0.423083i | \(0.139052\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.761848 | − | 9.77619i | 0.0362785 | − | 0.465533i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0932147 | + | 0.0164363i | 0.00442876 | + | 0.000780910i | 0.175862 | − | 0.984415i | \(-0.443729\pi\) |
−0.171433 | + | 0.985196i | \(0.554840\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.36353 | + | 25.7261i | −0.443874 | + | 1.21953i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.2102 | + | 17.6028i | 1.61809 | + | 0.832584i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.5438 | + | 13.0157i | −1.06391 | + | 0.614247i | −0.926511 | − | 0.376269i | \(-0.877207\pi\) |
−0.137397 | + | 0.990516i | \(0.543874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.1754 | − | 41.8730i | 1.13838 | − | 1.97172i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.62032 | + | 2.98314i | 0.452002 | + | 0.140160i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.05607 | + | 5.92075i | −0.330794 | + | 0.277569i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3356 | − | 10.6773i | 1.37226 | − | 0.499463i | 0.452439 | − | 0.891795i | \(-0.350554\pi\) |
0.919823 | + | 0.392333i | \(0.128332\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.20255 | + | 0.614285i | −0.196158 | + | 0.0286724i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.8177 | + | 10.8528i | −1.38875 | + | 0.505464i | −0.924819 | − | 0.380407i | \(-0.875784\pi\) |
−0.463931 | + | 0.885871i | \(0.653562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.54519 | + | 5.41674i | 0.211233 | + | 0.251737i | 0.861249 | − | 0.508183i | \(-0.169683\pi\) |
−0.650017 | + | 0.759920i | \(0.725238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.04191 | − | 3.73918i | 0.187439 | − | 0.173400i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4420 | − | 12.9569i | −1.03849 | − | 0.599572i | −0.119085 | − | 0.992884i | \(-0.537996\pi\) |
−0.919405 | + | 0.393312i | \(0.871329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5892 | + | 10.1551i | −0.812192 | + | 0.468919i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7541 | − | 0.859624i | 0.818066 | − | 0.0396094i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.2207 | + | 52.8084i | −0.883768 | + | 2.42813i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.48576 | + | 14.0974i | −0.114054 | + | 0.646835i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.527835 | − | 0.136075i | −0.0241679 | − | 0.00623045i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.164361 | − | 0.137915i | −0.00750983 | − | 0.00630150i | 0.639025 | − | 0.769186i | \(-0.279338\pi\) |
−0.646535 | + | 0.762884i | \(0.723782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.392217 | + | 2.22437i | 0.0178836 | + | 0.101423i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.69992 | + | 21.2884i | −0.122851 | + | 0.968658i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.0290 | 1.54518 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.392983i | − | 0.0178078i | −0.999960 | − | 0.00890388i | \(-0.997166\pi\) | ||
0.999960 | − | 0.00890388i | \(-0.00283423\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.1736 | − | 2.55854i | −0.912282 | − | 0.115701i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4296 | − | 2.36800i | 0.606070 | − | 0.106866i | 0.137812 | − | 0.990458i | \(-0.455993\pi\) |
0.468258 | + | 0.883592i | \(0.344882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.92615 | − | 3.48725i | 0.131787 | − | 0.157058i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.5154 | − | 56.3052i | 0.652418 | − | 2.53073i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.0056 | + | 5.46713i | 1.39079 | + | 0.245234i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.6543 | + | 8.97345i | 1.10368 | + | 0.401707i | 0.828672 | − | 0.559735i | \(-0.189097\pi\) |
0.275008 | + | 0.961442i | \(0.411319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.31170 | − | 27.0909i | −0.0586023 | − | 1.21033i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.03410 | − | 13.9155i | −0.358223 | − | 0.620460i | 0.629441 | − | 0.777048i | \(-0.283284\pi\) |
−0.987664 | + | 0.156588i | \(0.949950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.0521 | − | 58.9799i | 1.51530 | − | 2.62457i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.6814 | − | 15.8701i | −0.652026 | − | 0.704814i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1393 | − | 11.8643i | 0.626714 | − | 0.525875i | −0.273192 | − | 0.961959i | \(-0.588079\pi\) |
0.899906 | + | 0.436084i | \(0.143635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32842 | + | 3.64980i | 0.0587658 | + | 0.161458i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.32894 | + | 4.21096i | −0.235278 | + | 0.185918i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.8281 | + | 43.4875i | 0.697471 | + | 1.91629i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.8796 | − | 18.9245i | −0.698382 | − | 0.832299i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.16811 | − | 13.4417i | 0.182960 | − | 0.590026i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1275 | + | 12.7753i | 0.969421 | + | 0.559696i | 0.899060 | − | 0.437826i | \(-0.144251\pi\) |
0.0703617 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.67576 | − | 2.90250i | −0.0732759 | − | 0.126918i | 0.827059 | − | 0.562115i | \(-0.190012\pi\) |
−0.900335 | + | 0.435197i | \(0.856679\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.8111 | − | 54.0496i | 1.21378 | − | 2.35892i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.611362 | − | 0.222518i | −0.0266313 | − | 0.00969302i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.39821 | + | 7.92962i | −0.0607915 | + | 0.344766i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.75783 | − | 0.214915i | −0.119680 | − | 0.00932652i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.49302 | − | 4.60919i | −0.237929 | − | 0.199646i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.2281 | + | 4.80105i | −1.17717 | + | 0.207567i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.6170 | + | 10.3339i | −1.06230 | + | 0.445941i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.8621i | − | 0.683227i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.0374i | − | 1.07644i | −0.842804 | − | 0.538221i | \(-0.819097\pi\) | ||
0.842804 | − | 0.538221i | \(-0.180903\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.8010 | − | 15.0451i | −0.849744 | − | 0.645646i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5710 | + | 2.39293i | −0.581317 | + | 0.102502i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.10713 | − | 1.76810i | −0.0900946 | − | 0.0755983i | 0.596628 | − | 0.802518i | \(-0.296507\pi\) |
−0.686723 | + | 0.726920i | \(0.740951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.70535 | + | 2.64729i | −0.158140 | + | 0.112984i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26411 | − | 7.16914i | 0.0538531 | − | 0.305416i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.95966 | − | 1.07723i | −0.125858 | − | 0.0458084i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.7518 | − | 18.2549i | −0.498838 | − | 0.774876i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.8751 | + | 29.2285i | 0.715019 | + | 1.23845i | 0.962952 | + | 0.269673i | \(0.0869155\pi\) |
−0.247933 | + | 0.968777i | \(0.579751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.21775 | + | 4.16717i | 0.305278 | + | 0.176252i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.70036 | + | 1.51884i | −0.282890 | + | 0.0641256i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.43652 | − | 6.47899i | −0.229122 | − | 0.273057i | 0.639219 | − | 0.769025i | \(-0.279258\pi\) |
−0.868341 | + | 0.495968i | \(0.834813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.0727 | + | 55.1493i | 0.844465 | + | 2.32015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9087 | − | 10.3768i | 1.13006 | − | 0.435783i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.75562 | − | 4.82354i | −0.0735996 | − | 0.202213i | 0.897438 | − | 0.441141i | \(-0.145426\pi\) |
−0.971037 | + | 0.238928i | \(0.923204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.13892 | + | 1.79477i | −0.0895112 | + | 0.0751088i | −0.686445 | − | 0.727182i | \(-0.740830\pi\) |
0.596934 | + | 0.802290i | \(0.296385\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.6567 | − | 4.22911i | 0.779395 | − | 0.176674i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1711 | + | 36.6693i | −0.882894 | + | 1.52922i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.57149 | − | 7.91805i | −0.190314 | − | 0.329633i | 0.755041 | − | 0.655678i | \(-0.227617\pi\) |
−0.945354 | + | 0.326045i | \(0.894284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.39549 | − | 5.40472i | 0.348905 | − | 0.224613i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.55869 | − | 1.65923i | −0.189127 | − | 0.0688364i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.868355 | − | 0.153114i | −0.0359636 | − | 0.00634135i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.84963 | − | 3.57000i | −0.324542 | − | 0.147601i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.90264 | − | 2.26748i | 0.0785303 | − | 0.0935887i | −0.725349 | − | 0.688382i | \(-0.758321\pi\) |
0.803879 | + | 0.594793i | \(0.202766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02459 | + | 0.180663i | −0.0422175 | + | 0.00744409i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6765 | + | 25.8966i | −0.809383 | + | 1.06524i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.86981i | − | 0.0767837i | −0.999263 | − | 0.0383919i | \(-0.987776\pi\) | ||
0.999263 | − | 0.0383919i | \(-0.0122235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4612 | −0.428867 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5070 | + | 8.18877i | −0.798368 | + | 0.335144i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.09545 | − | 28.8978i | −0.208195 | − | 1.18073i | −0.892333 | − | 0.451378i | \(-0.850933\pi\) |
0.684138 | − | 0.729352i | \(-0.260179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.02633 | + | 2.53939i | 0.123447 | + | 0.103584i | 0.702421 | − | 0.711762i | \(-0.252102\pi\) |
−0.578974 | + | 0.815346i | \(0.696547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.6784 | − | 10.7578i | −0.638475 | − | 0.438090i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.70404 | − | 49.3630i | 0.353869 | − | 2.00689i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.61399 | − | 20.9193i | 0.309042 | − | 0.849087i | −0.683802 | − | 0.729668i | \(-0.739675\pi\) |
0.992844 | − | 0.119419i | \(-0.0381031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.1431 | + | 27.4865i | −0.573109 | + | 1.11381i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.17289 | + | 1.83187i | −0.128361 | + | 0.0741095i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.5675 | − | 18.8029i | −1.31539 | − | 0.759441i | −0.332407 | − | 0.943136i | \(-0.607861\pi\) |
−0.982983 | + | 0.183695i | \(0.941194\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 65.8317 | + | 20.4136i | 2.65459 | + | 0.823155i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.4585 | + | 21.9980i | 0.743111 | + | 0.885605i | 0.996655 | − | 0.0817186i | \(-0.0260409\pi\) |
−0.253544 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.3178 | + | 8.85094i | −0.977413 | + | 0.355749i | −0.780834 | − | 0.624738i | \(-0.785206\pi\) |
−0.196579 | + | 0.980488i | \(0.562983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.0719 | + | 6.31335i | −0.765331 | + | 0.253346i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.6408 | + | 7.51264i | −0.826956 | + | 0.300988i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.7801 | − | 25.8276i | 1.23121 | − | 1.03310i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.06489 | + | 7.46085i | −0.322081 | + | 0.297958i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.28262 | + | 2.22156i | −0.0511414 | + | 0.0885795i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0456 | − | 6.95454i | 0.479528 | − | 0.276856i | −0.240692 | − | 0.970602i | \(-0.577374\pi\) |
0.720220 | + | 0.693746i | \(0.244041\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.55130 | − | 32.0395i | −0.0616587 | − | 1.27346i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.42326 | + | 6.65785i | −0.0961642 | + | 0.264209i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.31667 | − | 0.408492i | −0.0917899 | − | 0.0161850i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.89868 | + | 28.3970i | 0.312467 | + | 1.12337i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.21478 | − | 1.44771i | 0.0479808 | − | 0.0571813i | −0.741520 | − | 0.670930i | \(-0.765895\pi\) |
0.789501 | + | 0.613749i | \(0.210339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.69381 | − | 15.2774i | −0.106234 | − | 0.602480i | −0.990720 | − | 0.135915i | \(-0.956602\pi\) |
0.884487 | − | 0.466565i | \(-0.154509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.4730 | − | 10.0792i | −3.12925 | − | 0.396869i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.1611 | −1.14644 | −0.573221 | − | 0.819401i | \(-0.694306\pi\) | ||||
−0.573221 | + | 0.819401i | \(0.694306\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.47464 | −0.175645 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.38270 | + | 0.555840i | 0.171772 | + | 0.0217851i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.67688 | − | 9.51004i | −0.0656212 | − | 0.372157i | −0.999879 | − | 0.0155580i | \(-0.995048\pi\) |
0.934258 | − | 0.356599i | \(-0.116064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.39803 | − | 7.62488i | 0.249992 | − | 0.297929i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.54666 | + | 2.59549i | −0.0993547 | + | 0.101260i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.5315 | − | 7.14680i | −1.57888 | − | 0.278400i | −0.685629 | − | 0.727951i | \(-0.740473\pi\) |
−0.893254 | + | 0.449551i | \(0.851584\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8126 | + | 35.2022i | −0.498351 | + | 1.36921i | 0.394516 | + | 0.918889i | \(0.370912\pi\) |
−0.892868 | + | 0.450319i | \(0.851310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0492759 | + | 1.01771i | 0.00191372 | + | 0.0395246i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.4877 | + | 8.36445i | −0.561807 | + | 0.324360i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.7664 | − | 18.6479i | 0.416876 | − | 0.722050i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.3179 | + | 13.2455i | −0.553560 | + | 0.512100i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.64300 | + | 4.73504i | −0.217846 | + | 0.182794i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9812 | − | 4.36081i | 0.461842 | − | 0.168097i | −0.100611 | − | 0.994926i | \(-0.532080\pi\) |
0.562453 | + | 0.826829i | \(0.309858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 56.8819 | + | 1.67231i | 2.18939 | + | 0.0643673i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8147 | − | 7.57594i | 0.799974 | − | 0.291167i | 0.0904985 | − | 0.995897i | \(-0.471154\pi\) |
0.709476 | + | 0.704730i | \(0.248932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5497 | + | 20.9149i | 0.673495 | + | 0.802640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.0984 | − | 4.68181i | −0.578571 | − | 0.179408i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.46338 | + | 5.46368i | 0.362106 | + | 0.209062i | 0.670004 | − | 0.742357i | \(-0.266292\pi\) |
−0.307898 | + | 0.951419i | \(0.599626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.0763 | − | 32.3757i | 2.14256 | − | 1.23701i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7472 | + | 28.6605i | −0.562640 | + | 1.09346i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0447251 | + | 0.122881i | −0.00170389 | + | 0.00468140i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.31599 | − | 18.8059i | 0.126146 | − | 0.715410i | −0.854474 | − | 0.519494i | \(-0.826121\pi\) |
0.980621 | − | 0.195917i | \(-0.0627683\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42.0923 | − | 20.1167i | 1.59895 | − | 0.764170i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.20363 | − | 2.68817i | −0.121521 | − | 0.101968i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.41416 | − | 8.02012i | −0.0535653 | − | 0.303784i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.4595 | + | 14.8854i | −1.34120 | + | 0.563018i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.5901 | −0.890985 | −0.445493 | − | 0.895286i | \(-0.646971\pi\) | ||||
−0.445493 | + | 0.895286i | \(0.646971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.10218i | 0.154717i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.3052 | − | 28.0401i | 0.802399 | − | 1.05605i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 53.8119 | − | 9.48848i | 2.02380 | − | 0.356851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3497 | − | 14.7178i | 0.463804 | − | 0.552740i | −0.482551 | − | 0.875868i | \(-0.660290\pi\) |
0.946355 | + | 0.323128i | \(0.104734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.284869 | − | 2.93485i | −0.0106834 | − | 0.110065i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.03064 | − | 0.534384i | −0.113498 | − | 0.0200128i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.1080 | − | 4.77091i | −0.490210 | − | 0.178422i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.6633 | + | 16.5211i | −0.958414 | + | 0.616993i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.2201 | + | 24.6300i | 0.530321 | + | 0.918542i | 0.999374 | + | 0.0353726i | \(0.0112618\pi\) |
−0.469054 | + | 0.883170i | \(0.655405\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.5653 | + | 32.1560i | −0.691406 | + | 1.19755i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.9179 | + | 3.60829i | −0.591994 | + | 0.134194i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −46.7241 | + | 39.2062i | −1.73529 | + | 1.45608i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.4790 | + | 48.0230i | 0.648259 | + | 1.78108i | 0.624070 | + | 0.781369i | \(0.285478\pi\) |
0.0241888 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.6279 | + | 18.5404i | 0.726958 | + | 0.686681i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.23739 | + | 8.89465i | 0.119739 | + | 0.328980i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4532 | + | 27.9504i | 0.866264 | + | 1.03237i | 0.999149 | + | 0.0412414i | \(0.0131313\pi\) |
−0.132886 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.0519 | − | 4.99874i | 0.813397 | − | 0.184381i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.6370 | − | 15.3789i | −0.981187 | − | 0.566489i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3403 | + | 24.8381i | 0.527516 | + | 0.913684i | 0.999486 | + | 0.0320692i | \(0.0102097\pi\) |
−0.471970 | + | 0.881615i | \(0.656457\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.881973 | + | 1.37002i | 0.0324001 | + | 0.0503291i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.8288 | − | 12.6767i | −1.27775 | − | 0.465061i | −0.388060 | − | 0.921634i | \(-0.626855\pi\) |
−0.889686 | + | 0.456573i | \(0.849077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.4054 | + | 87.3683i | −0.564410 | + | 3.20093i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.438776 | − | 4.52047i | −0.0160540 | − | 0.165395i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9931 | − | 14.2589i | −0.620914 | − | 0.521009i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.3512 | − | 6.23338i | 1.28998 | − | 0.227459i | 0.513770 | − | 0.857928i | \(-0.328248\pi\) |
0.776215 | + | 0.630469i | \(0.217137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.6795 | − | 32.4284i | −1.55533 | − | 1.18176i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.2256i | 0.845267i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.0043i | 1.45398i | 0.686647 | + | 0.726991i | \(0.259082\pi\) | ||||
−0.686647 | + | 0.726991i | \(0.740918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.9644 | + | 12.5786i | −1.08764 | + | 0.456575i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.8212 | − | 8.78482i | 1.80602 | − | 0.318449i | 0.833718 | − | 0.552191i | \(-0.186208\pi\) |
0.972299 | + | 0.233741i | \(0.0750969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.46967 | − | 7.10690i | −0.306623 | − | 0.257287i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.22308 | − | 8.83640i | −0.152686 | − | 0.319481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.115234 | + | 0.653526i | −0.00416087 | + | 0.0235975i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5878 | + | 8.22128i | 0.814536 | + | 0.296467i | 0.715496 | − | 0.698616i | \(-0.246201\pi\) |
0.0990400 | + | 0.995083i | \(0.468423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.27972 | + | 14.1478i | −0.262173 | + | 0.509520i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.65158 | − | 4.59267i | −0.0953707 | − | 0.165187i | 0.814393 | − | 0.580314i | \(-0.197070\pi\) |
−0.909763 | + | 0.415127i | \(0.863737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.54921 | + | 4.35854i | 0.271175 | + | 0.156563i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.15906 | − | 16.6374i | 0.185080 | − | 0.596865i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.37112 | − | 9.97631i | −0.299927 | − | 0.357439i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3073 | + | 44.8039i | 0.583520 | + | 1.60321i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.9269 | − | 0.850441i | −1.03376 | − | 0.0303923i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0185 | + | 38.5155i | 0.500341 | + | 1.37468i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.0660 | + | 17.6764i | −0.750921 | + | 0.630097i | −0.935746 | − | 0.352674i | \(-0.885272\pi\) |
0.184826 | + | 0.982771i | \(0.440828\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.52394 | + | 5.97116i | 0.196657 | + | 0.212579i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.5438 | + | 40.7791i | −0.837122 | + | 1.44994i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.546235 | + | 0.946107i | 0.0193974 | + | 0.0335973i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0607875 | − | 1.25546i | −0.00215591 | − | 0.0445267i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.4946 | + | 9.64326i | 0.938488 | + | 0.341582i | 0.765569 | − | 0.643354i | \(-0.222458\pi\) |
0.172919 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.09777 | − | 0.722548i | −0.144969 | − | 0.0255619i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6783 | − | 14.4022i | −0.518632 | − | 0.508876i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.78087 | + | 4.50587i | −0.133424 | + | 0.159009i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.7307 | + | 8.59254i | −1.71753 | + | 0.302847i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.4795 | + | 6.14846i | 1.70656 | + | 0.216436i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 53.0126i | − | 1.86382i | −0.362683 | − | 0.931912i | \(-0.618139\pi\) | ||
0.362683 | − | 0.931912i | \(-0.381861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1169 | 1.90030 | 0.950150 | − | 0.311792i | \(-0.100929\pi\) | ||||
0.950150 | + | 0.311792i | \(0.100929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.30319 | − | 26.0451i | 0.115848 | − | 0.913440i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.14256 | − | 46.1788i | −0.285222 | − | 1.61757i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5953 | + | 9.72965i | 0.405670 | + | 0.340397i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.85407 | − | 6.66569i | −0.0647866 | − | 0.232918i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.33356 | + | 41.5907i | −0.255943 | + | 1.45152i | 0.537697 | + | 0.843138i | \(0.319294\pi\) |
−0.793640 | + | 0.608387i | \(0.791817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.41874 | − | 9.39291i | 0.119170 | − | 0.327416i | −0.865738 | − | 0.500498i | \(-0.833150\pi\) |
0.984907 | + | 0.173082i | \(0.0553725\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 91.9451 | − | 4.45183i | 3.20112 | − | 0.154993i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9490 | − | 14.4043i | 0.867561 | − | 0.500886i | 0.00102385 | − | 0.999999i | \(-0.499674\pi\) |
0.866537 | + | 0.499113i | \(0.166341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.8979 | − | 14.9522i | −0.899473 | − | 0.519311i | −0.0224435 | − | 0.999748i | \(-0.507145\pi\) |
−0.877029 | + | 0.480437i | \(0.840478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6670 | + | 17.2689i | −0.647553 | + | 0.599053i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.71733 | − | 2.04663i | −0.0595018 | − | 0.0709115i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.7706 | − | 21.3907i | 2.03384 | − | 0.740257i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.29975 | + | 3.92639i | 0.0449258 | + | 0.135716i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4014 | − | 9.24535i | 0.876954 | − | 0.319185i | 0.135974 | − | 0.990712i | \(-0.456584\pi\) |
0.740980 | + | 0.671527i | \(0.234361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.54592 | − | 1.29718i | 0.0533074 | − | 0.0447302i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.00390 | − | 1.86173i | −0.206785 | − | 0.0641215i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.9263 | − | 43.1737i | 0.857492 | − | 1.48522i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.8284 | − | 20.1082i | 1.19672 | − | 0.690926i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.1277 | − | 5.72575i | −0.381903 | − | 0.196507i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.15002 | + | 11.4021i | −0.142261 | + | 0.390858i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.4657 | + | 6.95887i | 1.35128 | + | 0.238267i | 0.801977 | − | 0.597355i | \(-0.203782\pi\) |
0.549304 | + | 0.835623i | \(0.314893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.9138 | − | 8.86085i | −0.441644 | − | 0.303035i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.1106 | + | 25.1586i | −0.721123 | + | 0.859401i | −0.994739 | − | 0.102438i | \(-0.967336\pi\) |
0.273616 | + | 0.961839i | \(0.411780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.44881 | + | 30.9017i | 0.185911 | + | 1.05435i | 0.924779 | + | 0.380504i | \(0.124249\pi\) |
−0.738868 | + | 0.673850i | \(0.764640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.4046 | + | 50.9894i | 0.729468 | + | 1.73771i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.6646 | −0.805553 | −0.402777 | − | 0.915298i | \(-0.631955\pi\) | ||||
−0.402777 | + | 0.915298i | \(0.631955\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.4514 | 1.10338 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.1137 | − | 22.5236i | 0.581212 | − | 0.764942i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.828261 | − | 4.69730i | −0.0280968 | − | 0.159345i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.93208 | + | 3.49432i | −0.0993498 | + | 0.118401i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.5818 | + | 23.2671i | −0.358141 | + | 0.787471i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 75.0151 | + | 13.2272i | 2.53597 | + | 0.447161i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.18418 | + | 19.7384i | −0.242592 | + | 0.666517i | 0.757317 | + | 0.653048i | \(0.226510\pi\) |
−0.999909 | + | 0.0134696i | \(0.995712\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1686 | + | 7.83372i | −0.410437 | + | 0.264225i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.9740 | − | 13.2641i | 0.774014 | − | 0.446877i | −0.0602904 | − | 0.998181i | \(-0.519203\pi\) |
0.834305 | + | 0.551303i | \(0.185869\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5094 | + | 18.2028i | −0.353669 | + | 0.612573i | −0.986889 | − | 0.161399i | \(-0.948399\pi\) |
0.633220 | + | 0.773972i | \(0.281733\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.41013 | − | 6.22078i | −0.0474010 | − | 0.209109i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.1742 | + | 16.9281i | −0.677382 | + | 0.568391i | −0.915240 | − | 0.402909i | \(-0.867999\pi\) |
0.237858 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.34179 | + | 1.94425i | −0.179158 | + | 0.0652082i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.9845 | + | 27.4338i | 1.13852 | + | 0.919066i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.25272 | + | 2.27580i | −0.209239 | + | 0.0761569i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.5722 | − | 47.1603i | −1.32275 | − | 1.57640i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.06546 | + | 4.70027i | 0.0355746 | + | 0.156937i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.83909 | − | 2.21650i | −0.128041 | − | 0.0739244i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.128618 | + | 0.0742576i | −0.00428489 | + | 0.00247388i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.7915 | − | 54.0438i | −1.15779 | − | 1.79847i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.6129 | − | 53.8859i | 0.651954 | − | 1.79123i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.92172 | + | 56.2689i | −0.329445 | + | 1.86838i | 0.146948 | + | 0.989144i | \(0.453055\pi\) |
−0.476393 | + | 0.879233i | \(0.658056\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.7381 | + | 41.6236i | 0.986351 | + | 1.38057i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.5909 | + | 35.7380i | 1.41110 | + | 1.18405i | 0.955911 | + | 0.293658i | \(0.0948726\pi\) |
0.455189 | + | 0.890395i | \(0.349572\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.27575 | − | 7.23514i | −0.0422212 | − | 0.239448i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.36111 | − | 6.35287i | −0.276410 | − | 0.210020i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.98604 | 0.263722 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.1041i | 1.45486i | 0.686182 | + | 0.727430i | \(0.259285\pi\) | ||||
−0.686182 | + | 0.727430i | \(0.740715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.0623 | + | 45.4095i | 0.628124 | + | 1.49629i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.96362 | − | 1.22787i | 0.229210 | − | 0.0404160i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.0929 | − | 26.3294i | 0.726412 | − | 0.865704i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34.6563 | − | 2.70073i | −1.13826 | − | 0.0887035i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.7854 | + | 5.42829i | 1.01004 | + | 0.178096i | 0.654095 | − | 0.756412i | \(-0.273050\pi\) |
0.355940 | + | 0.934509i | \(0.384161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.01474 | − | 1.46125i | −0.131578 | − | 0.0478904i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.2179 | + | 8.85941i | 0.563687 | + | 0.290044i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.92121 | − | 13.7199i | −0.259051 | − | 0.448690i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1116 | − | 17.5138i | 0.330332 | − | 0.572152i | −0.652245 | − | 0.758008i | \(-0.726173\pi\) |
0.982577 | + | 0.185856i | \(0.0595059\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.84928 | − | 15.6384i | 0.158250 | − | 0.510341i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.1063 | + | 14.3539i | −0.557650 | + | 0.467924i | −0.877522 | − | 0.479537i | \(-0.840805\pi\) |
0.319872 | + | 0.947461i | \(0.396360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.1750 | − | 36.1981i | −0.429038 | − | 1.17877i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.2317 | + | 52.1784i | 1.34127 | + | 1.69736i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.78332 | − | 26.8794i | −0.317915 | − | 0.873465i | −0.990995 | − | 0.133895i | \(-0.957251\pi\) |
0.673080 | − | 0.739569i | \(-0.264971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.560719 | + | 0.668239i | 0.0182017 | + | 0.0216920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.9603 | + | 26.9811i | 0.809394 | + | 0.874923i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.8170 | − | 6.82255i | −0.382790 | − | 0.221004i | 0.296241 | − | 0.955113i | \(-0.404267\pi\) |
−0.679032 | + | 0.734109i | \(0.737600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0561 | + | 38.2022i | 0.713717 | + | 1.23619i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −46.7580 | + | 2.26394i | −1.51147 | + | 0.0731829i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.8188 | + | 17.7686i | 1.57644 | + | 0.573778i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.27308 | − | 29.9051i | 0.170099 | − | 0.964681i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.18432 | − | 20.1100i | 0.167062 | − | 0.648035i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.6374 | + | 14.7995i | 0.567767 | + | 0.476413i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2023 | + | 6.20712i | −1.13203 | + | 0.199607i | −0.708117 | − | 0.706095i | \(-0.750455\pi\) |
−0.423913 | + | 0.905703i | \(0.639344\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.232827 | + | 1.83580i | −0.00747949 | + | 0.0589745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.58655i | − | 0.0830062i | −0.999138 | − | 0.0415031i | \(-0.986785\pi\) | ||
0.999138 | − | 0.0415031i | \(-0.0132146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.35538i | − | 0.107569i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.71765 | − | 13.5433i | 0.0550087 | − | 0.433734i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.01215 | − | 1.06011i | 0.192346 | − | 0.0339158i | −0.0766452 | − | 0.997058i | \(-0.524421\pi\) |
0.268991 | + | 0.963143i | \(0.413310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.4821 | − | 21.3820i | −0.814412 | − | 0.683373i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.58396 | − | 10.0232i | 0.0824995 | − | 0.320016i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.84783 | + | 10.4796i | −0.0589367 | + | 0.334247i | −0.999992 | − | 0.00400613i | \(-0.998725\pi\) |
0.941055 | + | 0.338253i | \(0.109836\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.4740 | − | 25.6505i | −2.24549 | − | 0.817291i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.2217 | − | 1.36645i | 0.898305 | − | 0.0434944i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3864 | + | 38.7743i | 0.711845 | + | 1.23295i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.4598 | − | 15.8539i | −0.872288 | − | 0.503616i | −0.00418044 | − | 0.999991i | \(-0.501331\pi\) |
−0.868108 | + | 0.496375i | \(0.834664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.4463 | − | 12.3730i | −0.363239 | − | 0.392647i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.3577 | − | 37.3707i | −0.994106 | − | 1.18473i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.77204 | + | 10.3636i | 0.119462 | + | 0.328218i | 0.984982 | − | 0.172655i | \(-0.0552345\pi\) |
−0.865521 | + | 0.500873i | \(0.833012\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.1361 | − | 2.35860i | 0.510522 | − | 0.0746228i |
(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 | 864.2.bh.b.47.1 | 192 | ||
4.3 | odd | 2 | 216.2.v.b.155.30 | yes | 192 | ||
8.3 | odd | 2 | inner | 864.2.bh.b.47.2 | 192 | ||
8.5 | even | 2 | 216.2.v.b.155.12 | yes | 192 | ||
12.11 | even | 2 | 648.2.v.b.467.3 | 192 | |||
24.5 | odd | 2 | 648.2.v.b.467.21 | 192 | |||
27.23 | odd | 18 | inner | 864.2.bh.b.239.2 | 192 | ||
108.23 | even | 18 | 216.2.v.b.131.12 | ✓ | 192 | ||
108.31 | odd | 18 | 648.2.v.b.179.21 | 192 | |||
216.77 | odd | 18 | 216.2.v.b.131.30 | yes | 192 | ||
216.85 | even | 18 | 648.2.v.b.179.3 | 192 | |||
216.131 | even | 18 | inner | 864.2.bh.b.239.1 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.b.131.12 | ✓ | 192 | 108.23 | even | 18 | ||
216.2.v.b.131.30 | yes | 192 | 216.77 | odd | 18 | ||
216.2.v.b.155.12 | yes | 192 | 8.5 | even | 2 | ||
216.2.v.b.155.30 | yes | 192 | 4.3 | odd | 2 | ||
648.2.v.b.179.3 | 192 | 216.85 | even | 18 | |||
648.2.v.b.179.21 | 192 | 108.31 | odd | 18 | |||
648.2.v.b.467.3 | 192 | 12.11 | even | 2 | |||
648.2.v.b.467.21 | 192 | 24.5 | odd | 2 | |||
864.2.bh.b.47.1 | 192 | 1.1 | even | 1 | trivial | ||
864.2.bh.b.47.2 | 192 | 8.3 | odd | 2 | inner | ||
864.2.bh.b.239.1 | 192 | 216.131 | even | 18 | inner | ||
864.2.bh.b.239.2 | 192 | 27.23 | odd | 18 | inner |