Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(97,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.x (of order \(4\), degree \(2\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 153.4 | ||
Character | \(\chi\) | \(=\) | 280.153 |
Dual form | 280.2.x.a.97.4 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.03893 | + | 1.03893i | −0.599825 | + | 0.599825i | −0.940266 | − | 0.340441i | \(-0.889424\pi\) |
0.340441 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21973 | + | 1.87411i | 0.545478 | + | 0.838125i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11557 | − | 1.58883i | 0.799609 | − | 0.600520i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.841261i | 0.280420i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34687 | −0.707609 | −0.353804 | − | 0.935319i | \(-0.615112\pi\) | ||||
−0.353804 | + | 0.935319i | \(0.615112\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.96436 | + | 1.96436i | −0.544816 | + | 0.544816i | −0.924937 | − | 0.380121i | \(-0.875882\pi\) |
0.380121 | + | 0.924937i | \(0.375882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.21426 | − | 0.679854i | −0.829919 | − | 0.175537i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.15858 | + | 5.15858i | 1.25114 | + | 1.25114i | 0.955210 | + | 0.295929i | \(0.0956291\pi\) |
0.295929 | + | 0.955210i | \(0.404371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.74821 | −0.859899 | −0.429949 | − | 0.902853i | \(-0.641469\pi\) | ||||
−0.429949 | + | 0.902853i | \(0.641469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.547244 | + | 3.84860i | −0.119419 | + | 0.839833i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.08007 | + | 6.08007i | 1.26778 | + | 1.26778i | 0.947232 | + | 0.320550i | \(0.103868\pi\) |
0.320550 | + | 0.947232i | \(0.396132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.02454 | + | 4.57179i | −0.404908 | + | 0.914357i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.99079 | − | 3.99079i | −0.768028 | − | 0.768028i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.89034i | − | 1.09381i | −0.837195 | − | 0.546905i | \(-0.815806\pi\) | ||
0.837195 | − | 0.546905i | \(-0.184194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.56648i | − | 0.281348i | −0.990056 | − | 0.140674i | \(-0.955073\pi\) | ||
0.990056 | − | 0.140674i | \(-0.0449270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.43823 | − | 2.43823i | 0.424441 | − | 0.424441i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.55804 | + | 2.02686i | 0.939480 | + | 0.342603i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53441 | − | 1.53441i | 0.252256 | − | 0.252256i | −0.569639 | − | 0.821895i | \(-0.692917\pi\) |
0.821895 | + | 0.569639i | \(0.192917\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.08166i | − | 0.653588i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.51977i | − | 1.48674i | −0.668882 | − | 0.743369i | \(-0.733227\pi\) | ||
0.668882 | − | 0.743369i | \(-0.266773\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86313 | + | 1.86313i | 0.284125 | + | 0.284125i | 0.834752 | − | 0.550626i | \(-0.185611\pi\) |
−0.550626 | + | 0.834752i | \(0.685611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.57661 | + | 1.02611i | −0.235027 | + | 0.152963i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.59474 | − | 4.59474i | −0.670212 | − | 0.670212i | 0.287553 | − | 0.957765i | \(-0.407158\pi\) |
−0.957765 | + | 0.287553i | \(0.907158\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.95125 | − | 6.72254i | 0.278750 | − | 0.960364i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.7188 | −1.50093 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.88128 | + | 3.88128i | 0.533135 | + | 0.533135i | 0.921504 | − | 0.388369i | \(-0.126961\pi\) |
−0.388369 | + | 0.921504i | \(0.626961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.86254 | − | 4.39829i | −0.385985 | − | 0.593065i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.89412 | − | 3.89412i | 0.515789 | − | 0.515789i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.62061 | 0.601552 | 0.300776 | − | 0.953695i | \(-0.402754\pi\) | ||||
0.300776 | + | 0.953695i | \(0.402754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.00065i | − | 0.256156i | −0.991764 | − | 0.128078i | \(-0.959119\pi\) | ||
0.991764 | − | 0.128078i | \(-0.0408808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.33662 | + | 1.77974i | 0.168398 | + | 0.224227i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.07740 | − | 1.28544i | −0.753809 | − | 0.159439i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.69156 | − | 2.69156i | 0.328827 | − | 0.328827i | −0.523314 | − | 0.852140i | \(-0.675304\pi\) |
0.852140 | + | 0.523314i | \(0.175304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.6335 | −1.52089 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.392229 | −0.0465491 | −0.0232745 | − | 0.999729i | \(-0.507409\pi\) | ||||
−0.0232745 | + | 0.999729i | \(0.507409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.08543 | − | 7.08543i | 0.829287 | − | 0.829287i | −0.158131 | − | 0.987418i | \(-0.550547\pi\) |
0.987418 | + | 0.158131i | \(0.0505468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.64640 | − | 6.85310i | −0.305580 | − | 0.791328i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.96497 | + | 3.72878i | −0.565811 | + | 0.424934i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.98717i | 0.561100i | 0.959839 | + | 0.280550i | \(0.0905169\pi\) | ||||
−0.959839 | + | 0.280550i | \(0.909483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.76850 | 0.640944 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.36651 | − | 9.36651i | 1.02811 | − | 1.02811i | 0.0285148 | − | 0.999593i | \(-0.490922\pi\) |
0.999593 | − | 0.0285148i | \(-0.00907776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.37567 | + | 15.9598i | −0.366143 | + | 1.73108i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.11964 | + | 6.11964i | 0.656094 | + | 0.656094i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.83200 | 1.04219 | 0.521095 | − | 0.853499i | \(-0.325524\pi\) | ||||
0.521095 | + | 0.853499i | \(0.325524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03471 | + | 7.27677i | −0.108467 | + | 0.762813i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.62746 | + | 1.62746i | 0.168760 | + | 0.168760i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.57179 | − | 7.02454i | −0.469055 | − | 0.720703i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8576 | − | 11.8576i | −1.20396 | − | 1.20396i | −0.972952 | − | 0.231006i | \(-0.925798\pi\) |
−0.231006 | − | 0.972952i | \(-0.574202\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.97433i | − | 0.198428i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.41529i | 0.837353i | 0.908135 | + | 0.418676i | \(0.137506\pi\) | ||||
−0.908135 | + | 0.418676i | \(0.862494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.77874 | + | 8.77874i | −0.864995 | + | 0.864995i | −0.991913 | − | 0.126918i | \(-0.959491\pi\) |
0.126918 | + | 0.991913i | \(0.459491\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.88016 | + | 3.66864i | −0.769025 | + | 0.358022i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3741 | − | 10.3741i | 1.00290 | − | 1.00290i | 0.00290471 | − | 0.999996i | \(-0.499075\pi\) |
0.999996 | − | 0.00290471i | \(-0.000924598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.92724i | − | 0.471944i | −0.971760 | − | 0.235972i | \(-0.924173\pi\) | ||
0.971760 | − | 0.235972i | \(-0.0758273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.18828i | 0.302618i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.79963 | − | 3.79963i | −0.357439 | − | 0.357439i | 0.505429 | − | 0.862868i | \(-0.331334\pi\) |
−0.862868 | + | 0.505429i | \(0.831334\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.97868 | + | 18.8107i | −0.371013 | + | 1.75411i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.65254 | − | 1.65254i | −0.152777 | − | 0.152777i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.1094 | + | 2.71723i | 1.75176 | + | 0.249088i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.49219 | −0.499290 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.89034 | + | 9.89034i | 0.891782 | + | 0.891782i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0374 | + | 1.78212i | −0.987214 | + | 0.159397i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.777755 | + | 0.777755i | −0.0690146 | + | 0.0690146i | −0.740772 | − | 0.671757i | \(-0.765540\pi\) |
0.671757 | + | 0.740772i | \(0.265540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.87132 | −0.340851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0373i | 0.964336i | 0.876079 | + | 0.482168i | \(0.160151\pi\) | ||||
−0.876079 | + | 0.482168i | \(0.839849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.92959 | + | 5.95526i | −0.687583 | + | 0.516387i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.61149 | − | 12.3468i | 0.224762 | − | 1.06265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.65313 | − | 2.65313i | 0.226672 | − | 0.226672i | −0.584629 | − | 0.811301i | \(-0.698760\pi\) |
0.811301 | + | 0.584629i | \(0.198760\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.15451 | −0.606838 | −0.303419 | − | 0.952857i | \(-0.598128\pi\) | ||||
−0.303419 | + | 0.952857i | \(0.598128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.54720 | 0.804019 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.61011 | − | 4.61011i | 0.385516 | − | 0.385516i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.0391 | − | 7.18460i | 0.916750 | − | 0.596649i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.95702 | + | 9.01144i | 0.408848 | + | 0.743251i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.2552i | − | 1.00399i | −0.864872 | − | 0.501993i | \(-0.832600\pi\) | ||
0.864872 | − | 0.501993i | \(-0.167400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2221 | −1.07600 | −0.537998 | − | 0.842946i | \(-0.680819\pi\) | ||||
−0.537998 | + | 0.842946i | \(0.680819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.33971 | + | 4.33971i | −0.350845 | + | 0.350845i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.93575 | − | 1.91068i | 0.235805 | − | 0.153469i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.35401 | + | 8.35401i | 0.666723 | + | 0.666723i | 0.956956 | − | 0.290233i | \(-0.0937329\pi\) |
−0.290233 | + | 0.956956i | \(0.593733\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.06474 | −0.639576 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.5230 | + | 3.20261i | 1.77506 | + | 0.252401i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.21768 | + | 2.21768i | 0.173702 | + | 0.173702i | 0.788604 | − | 0.614902i | \(-0.210804\pi\) |
−0.614902 | + | 0.788604i | \(0.710804\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.54347 | + | 1.59553i | 0.587258 | + | 0.124212i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1934 | + | 15.1934i | 1.17570 | + | 1.17570i | 0.980829 | + | 0.194871i | \(0.0624288\pi\) |
0.194871 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.28257i | 0.406352i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.15322i | − | 0.241133i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.60458 | + | 4.60458i | −0.350080 | + | 0.350080i | −0.860139 | − | 0.510059i | \(-0.829623\pi\) |
0.510059 | + | 0.860139i | \(0.329623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.98073 | + | 12.8886i | 0.225322 | + | 0.974284i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.80047 | + | 4.80047i | −0.360826 | + | 0.360826i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5721i | 0.864939i | 0.901648 | + | 0.432470i | \(0.142358\pi\) | ||||
−0.901648 | + | 0.432470i | \(0.857642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.28640i | − | 0.392935i | −0.980510 | − | 0.196467i | \(-0.937053\pi\) | ||
0.980510 | − | 0.196467i | \(-0.0629470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.07852 | + | 2.07852i | 0.153649 | + | 0.153649i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.74721 | + | 1.00409i | 0.349022 | + | 0.0738220i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1065 | − | 12.1065i | −0.885317 | − | 0.885317i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.7835 | − | 2.10211i | −1.07534 | − | 0.152906i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6115 | −0.840179 | −0.420089 | − | 0.907483i | \(-0.638001\pi\) | ||||
−0.420089 | + | 0.907483i | \(0.638001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.6369 | − | 17.6369i | −1.26954 | − | 1.26954i | −0.946328 | − | 0.323207i | \(-0.895239\pi\) |
−0.323207 | − | 0.946328i | \(-0.604761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.64945 | − | 4.97850i | 0.547789 | − | 0.356518i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2130 | + | 17.2130i | −1.22637 | + | 1.22637i | −0.261049 | + | 0.965325i | \(0.584069\pi\) |
−0.965325 | + | 0.261049i | \(0.915931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.95883 | −0.493299 | −0.246649 | − | 0.969105i | \(-0.579330\pi\) | ||||
−0.246649 | + | 0.969105i | \(0.579330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.59267i | 0.394477i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.35874 | − | 12.4614i | −0.656855 | − | 0.874620i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.8410 | − | 11.6115i | 1.24607 | − | 0.810982i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.11492 | + | 5.11492i | −0.355512 | + | 0.355512i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.79658 | 0.608472 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.28431 | 0.639159 | 0.319579 | − | 0.947560i | \(-0.396458\pi\) | ||||
0.319579 | + | 0.947560i | \(0.396458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.407498 | − | 0.407498i | 0.0279213 | − | 0.0279213i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.21920 | + | 5.76422i | −0.0831487 | + | 0.393117i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.48887 | − | 3.31400i | −0.168955 | − | 0.224969i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.7225i | 0.994854i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.2666 | −1.36328 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.77582 | + | 4.77582i | −0.319813 | + | 0.319813i | −0.848695 | − | 0.528882i | \(-0.822611\pi\) |
0.528882 | + | 0.848695i | \(0.322611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.84606 | − | 1.70317i | −0.256404 | − | 0.113545i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.49990 | − | 2.49990i | −0.165925 | − | 0.165925i | 0.619261 | − | 0.785185i | \(-0.287432\pi\) |
−0.785185 | + | 0.619261i | \(0.787432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0694 | 1.19406 | 0.597031 | − | 0.802218i | \(-0.296347\pi\) | ||||
0.597031 | + | 0.802218i | \(0.296347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.28431 | − | 9.03217i | 0.0845016 | − | 0.594273i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.14278 | + | 9.14278i | 0.598963 | + | 0.598963i | 0.940037 | − | 0.341073i | \(-0.110790\pi\) |
−0.341073 | + | 0.940037i | \(0.610790\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00671 | − | 14.2153i | 0.196136 | − | 0.927307i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.18130 | − | 5.18130i | −0.336562 | − | 0.336562i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.3719i | − | 0.735590i | −0.929907 | − | 0.367795i | \(-0.880113\pi\) | ||
0.929907 | − | 0.367795i | \(-0.119887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.6361i | − | 1.26488i | −0.774611 | − | 0.632438i | \(-0.782054\pi\) | ||
0.774611 | − | 0.632438i | \(-0.217946\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.97932 | − | 5.97932i | 0.383574 | − | 0.383574i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.9787 | − | 4.54280i | 0.956957 | − | 0.290229i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.36284 | − | 7.36284i | 0.468486 | − | 0.468486i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.4622i | 1.23337i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.2420i | − | 1.65638i | −0.560447 | − | 0.828190i | \(-0.689371\pi\) | ||
0.560447 | − | 0.828190i | \(-0.310629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.2691 | − | 14.2691i | −0.897094 | − | 0.897094i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.0740 | − | 20.0881i | −0.818723 | − | 1.25797i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.93157 | + | 1.93157i | 0.120488 | + | 0.120488i | 0.764780 | − | 0.644292i | \(-0.222848\pi\) |
−0.644292 | + | 0.764780i | \(0.722848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.808236 | − | 5.68406i | 0.0502213 | − | 0.353191i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.95532 | 0.306726 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.64248 | + | 2.64248i | 0.162942 | + | 0.162942i | 0.783869 | − | 0.620927i | \(-0.213243\pi\) |
−0.620927 | + | 0.783869i | \(0.713243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53984 | + | 12.0080i | −0.156021 | + | 0.737648i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.2147 | + | 10.2147i | −0.625131 | + | 0.625131i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.17948 | −0.0719143 | −0.0359572 | − | 0.999353i | \(-0.511448\pi\) | ||||
−0.0359572 | + | 0.999353i | \(0.511448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.7880i | − | 0.898306i | −0.893455 | − | 0.449153i | \(-0.851726\pi\) | ||
0.893455 | − | 0.449153i | \(-0.148274\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.48505 | − | 8.63502i | −0.392493 | − | 0.522615i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.75134 | − | 10.7294i | 0.286517 | − | 0.647007i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6478 | − | 11.6478i | 0.699848 | − | 0.699848i | −0.264529 | − | 0.964378i | \(-0.585217\pi\) |
0.964378 | + | 0.264529i | \(0.0852166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.31782 | 0.0788957 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.2153 | 1.20594 | 0.602971 | − | 0.797763i | \(-0.293983\pi\) | ||||
0.602971 | + | 0.797763i | \(0.293983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.53654 | + | 5.53654i | −0.329113 | + | 0.329113i | −0.852249 | − | 0.523136i | \(-0.824762\pi\) |
0.523136 | + | 0.852249i | \(0.324762\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0477 | + | 2.54823i | 0.713647 | + | 0.150944i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.1253 | − | 20.1397i | −0.892816 | − | 1.18881i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.2218i | 2.13070i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.6384 | 1.44433 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.12050 | − | 1.12050i | 0.0654601 | − | 0.0654601i | −0.673619 | − | 0.739079i | \(-0.735261\pi\) |
0.739079 | + | 0.673619i | \(0.235261\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.63587 | + | 8.65950i | 0.328133 | + | 0.504176i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.36588 | + | 9.36588i | 0.543463 | + | 0.543463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8869 | −1.38141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.90179 | + | 0.981388i | 0.397812 | + | 0.0565662i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.74288 | − | 8.74288i | −0.502265 | − | 0.502265i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.74942 | − | 2.44024i | 0.214691 | − | 0.139728i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.43044 | + | 9.43044i | 0.538224 | + | 0.538224i | 0.923007 | − | 0.384783i | \(-0.125724\pi\) |
−0.384783 | + | 0.923007i | \(0.625724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18.2409i | − | 1.03769i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.6035i | − | 0.828090i | −0.910256 | − | 0.414045i | \(-0.864116\pi\) | ||
0.910256 | − | 0.414045i | \(-0.135884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.05535 | − | 7.05535i | 0.398792 | − | 0.398792i | −0.479015 | − | 0.877807i | \(-0.659006\pi\) |
0.877807 | + | 0.479015i | \(0.159006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.70512 | + | 4.67576i | −0.0960727 | + | 0.263449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2538 | + | 11.2538i | −0.632075 | + | 0.632075i | −0.948588 | − | 0.316513i | \(-0.897488\pi\) |
0.316513 | + | 0.948588i | \(0.397488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8239i | 0.773989i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5558i | 1.20313i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.3354 | − | 19.3354i | −1.07585 | − | 1.07585i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00371 | − | 12.9576i | −0.277556 | − | 0.718757i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.11904 | + | 5.11904i | 0.283084 | + | 0.283084i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.0207 | − | 2.42023i | −0.938383 | − | 0.133432i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.6643 | −1.85036 | −0.925179 | − | 0.379531i | \(-0.876085\pi\) | ||||
−0.925179 | + | 0.379531i | \(0.876085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.29084 | + | 1.29084i | 0.0707376 | + | 0.0707376i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.32724 | + | 1.76131i | 0.454965 | + | 0.0962304i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8298 | − | 12.8298i | 0.698885 | − | 0.698885i | −0.265285 | − | 0.964170i | \(-0.585466\pi\) |
0.964170 | + | 0.265285i | \(0.0854661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.89507 | 0.428802 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.67633i | 0.199085i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.55296 | − | 17.3222i | −0.353826 | − | 0.935311i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.4094 | − | 23.6765i | −0.829614 | − | 1.27470i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.6439 | + | 20.6439i | −1.10822 | + | 1.10822i | −0.114837 | + | 0.993384i | \(0.536635\pi\) |
−0.993384 | + | 0.114837i | \(0.963365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3356 | 1.57030 | 0.785150 | − | 0.619306i | \(-0.212586\pi\) | ||||
0.785150 | + | 0.619306i | \(0.212586\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.6787 | 0.836867 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.5837 | + | 16.5837i | −0.882662 | + | 0.882662i | −0.993805 | − | 0.111142i | \(-0.964549\pi\) |
0.111142 | + | 0.993805i | \(0.464549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.478412 | − | 0.735079i | −0.0253915 | − | 0.0390140i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.6763 | + | 17.0303i | −1.20016 | + | 0.901338i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.4050i | 1.60472i | 0.596843 | + | 0.802358i | \(0.296421\pi\) | ||||
−0.596843 | + | 0.802358i | \(0.703579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.95092 | −0.260575 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.70598 | − | 5.70598i | 0.299486 | − | 0.299486i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.9211 | + | 4.63657i | 1.14740 | + | 0.242689i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6007 | − | 13.6007i | −0.709950 | − | 0.709950i | 0.256574 | − | 0.966525i | \(-0.417406\pi\) |
−0.966525 | + | 0.256574i | \(0.917406\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.00861 | 0.416911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.3778 | + | 2.04443i | 0.746459 | + | 0.106141i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8626 | + | 13.8626i | 0.717776 | + | 0.717776i | 0.968149 | − | 0.250373i | \(-0.0805533\pi\) |
−0.250373 | + | 0.968149i | \(0.580553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.61556 | − | 13.3185i | 0.496545 | − | 0.687766i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.5708 | + | 11.5708i | 0.595925 | + | 0.595925i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8896i | 0.610727i | 0.952236 | + | 0.305363i | \(0.0987779\pi\) | ||||
−0.952236 | + | 0.305363i | \(0.901222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1.61606i | − | 0.0827934i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.5186 | + | 16.5186i | −0.844059 | + | 0.844059i | −0.989384 | − | 0.145325i | \(-0.953577\pi\) |
0.145325 | + | 0.989384i | \(0.453577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.0440 | − | 4.75679i | −0.664785 | − | 0.242429i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.56738 | + | 1.56738i | −0.0796745 | + | 0.0796745i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9.62098i | − | 0.487803i | −0.969800 | − | 0.243902i | \(-0.921573\pi\) | ||
0.969800 | − | 0.243902i | \(-0.0784274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 62.7290i | 3.17234i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.4670 | − | 11.4670i | −0.578433 | − | 0.578433i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.34648 | + | 6.08297i | −0.470272 | + | 0.306068i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5393 | + | 17.5393i | 0.880270 | + | 0.880270i | 0.993562 | − | 0.113292i | \(-0.0361394\pi\) |
−0.113292 | + | 0.993562i | \(0.536139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.05119 | − | 14.4254i | 0.102688 | − | 0.722171i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.2238 | −0.710302 | −0.355151 | − | 0.934809i | \(-0.615571\pi\) | ||||
−0.355151 | + | 0.934809i | \(0.615571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.07713 | + | 3.07713i | 0.153283 | + | 0.153283i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.03598 | + | 10.8108i | 0.349621 | + | 0.537192i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.60107 | + | 3.60107i | −0.178498 | + | 0.178498i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.2602 | −0.705123 | −0.352562 | − | 0.935789i | \(-0.614689\pi\) | ||||
−0.352562 | + | 0.935789i | \(0.614689\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.51281i | 0.271927i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.77520 | − | 7.34135i | 0.481006 | − | 0.361244i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.9784 | + | 6.12926i | 1.42249 | + | 0.300874i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.43302 | − | 7.43302i | 0.363996 | − | 0.363996i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5802 | 0.663434 | 0.331717 | − | 0.943379i | \(-0.392372\pi\) | ||||
0.331717 | + | 0.943379i | \(0.392372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.7805 | −0.622884 | −0.311442 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311442 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.86537 | − | 3.86537i | 0.187941 | − | 0.187941i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.0277 | + | 13.1402i | −1.65058 | + | 0.637391i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.17868 | − | 4.23250i | −0.153827 | − | 0.204825i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.57913i | 0.462485i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.7947 | 1.82051 | 0.910254 | − | 0.414049i | \(-0.135886\pi\) | ||||
0.910254 | + | 0.414049i | \(0.135886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2122 | + | 14.2122i | −0.682996 | + | 0.682996i | −0.960674 | − | 0.277678i | \(-0.910435\pi\) |
0.277678 | + | 0.960674i | \(0.410435\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00457 | + | 18.9331i | −0.192005 | + | 0.907774i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.7894 | − | 22.7894i | −1.09016 | − | 1.09016i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.7697 | 1.32538 | 0.662688 | − | 0.748896i | \(-0.269416\pi\) | ||||
0.662688 | + | 0.748896i | \(0.269416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.65541 | + | 1.64151i | 0.269305 | + | 0.0781673i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.8951 | + | 11.8951i | 0.565152 | + | 0.565152i | 0.930766 | − | 0.365615i | \(-0.119141\pi\) |
−0.365615 | + | 0.930766i | \(0.619141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.9923 | + | 18.4262i | 0.568491 | + | 0.873485i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7323 | + | 12.7323i | 0.602216 | + | 0.602216i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.92227i | − | 0.185104i | −0.995708 | − | 0.0925518i | \(-0.970498\pi\) | ||
0.995708 | − | 0.0925518i | \(-0.0295024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3417i | 1.05203i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.7367 | − | 13.7367i | 0.645409 | − | 0.645409i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.8995 | + | 6.93651i | −0.698499 | + | 0.325188i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6596 | − | 17.6596i | 0.826083 | − | 0.826083i | −0.160889 | − | 0.986972i | \(-0.551436\pi\) |
0.986972 | + | 0.160889i | \(0.0514362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 41.1736i | − | 1.92182i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.616064i | − | 0.0286930i | −0.999897 | − | 0.0143465i | \(-0.995433\pi\) | ||
0.999897 | − | 0.0143465i | \(-0.00456678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.9726 | − | 11.9726i | −0.556413 | − | 0.556413i | 0.371871 | − | 0.928284i | \(-0.378716\pi\) |
−0.928284 | + | 0.371871i | \(0.878716\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.06498 | + | 5.03508i | −0.0493871 | + | 0.233496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.8767 | + | 12.8767i | 0.595861 | + | 0.595861i | 0.939208 | − | 0.343348i | \(-0.111561\pi\) |
−0.343348 | + | 0.939208i | \(0.611561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.41775 | − | 9.97061i | 0.0654658 | − | 0.460400i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.3584 | −0.799834 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.37254 | − | 4.37254i | −0.201050 | − | 0.201050i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.58841 | − | 17.1360i | 0.348180 | − | 0.786254i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.26517 | + | 3.26517i | −0.149502 | + | 0.149502i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.34016 | −0.381072 | −0.190536 | − | 0.981680i | \(-0.561023\pi\) | ||||
−0.190536 | + | 0.981680i | \(0.561023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.02827i | 0.274866i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.7270 | + | 20.0724i | −1.21612 | + | 0.913328i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.75939 | − | 36.6854i | 0.352336 | − | 1.66580i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.90541 | + | 6.90541i | −0.312914 | + | 0.312914i | −0.846037 | − | 0.533123i | \(-0.821018\pi\) |
0.533123 | + | 0.846037i | \(0.321018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.60801 | −0.208381 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1783 | 1.13628 | 0.568140 | − | 0.822932i | \(-0.307663\pi\) | ||||
0.568140 | + | 0.822932i | \(0.307663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.3858 | − | 30.3858i | 1.36851 | − | 1.36851i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.70011 | − | 2.40814i | 0.166307 | − | 0.108238i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.829788 | + | 0.623185i | −0.0372211 | + | 0.0279537i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.8907i | − | 0.935197i | −0.883941 | − | 0.467599i | \(-0.845119\pi\) | ||
0.883941 | − | 0.467599i | \(-0.154881\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.5696 | −1.41043 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.585795 | − | 0.585795i | 0.0261193 | − | 0.0261193i | −0.693927 | − | 0.720046i | \(-0.744121\pi\) |
0.720046 | + | 0.693927i | \(0.244121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7711 | + | 10.2643i | −0.701807 | + | 0.456757i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.48821 | − | 5.48821i | −0.243740 | − | 0.243740i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.2153 | −1.69386 | −0.846932 | − | 0.531701i | \(-0.821553\pi\) | ||||
−0.846932 | + | 0.531701i | \(0.821553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.73218 | − | 26.2472i | 0.165102 | − | 1.16111i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.9583 | + | 14.9583i | 0.660426 | + | 0.660426i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.1599 | − | 5.74464i | −1.19681 | − | 0.253139i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7833 | + | 10.7833i | 0.474248 | + | 0.474248i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.56765i | − | 0.419973i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.40522i | 0.368239i | 0.982904 | + | 0.184120i | \(0.0589434\pi\) | ||||
−0.982904 | + | 0.184120i | \(0.941057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.1989 | − | 14.1989i | 0.620876 | − | 0.620876i | −0.324879 | − | 0.945755i | \(-0.605324\pi\) |
0.945755 | + | 0.324879i | \(0.105324\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.4870 | − | 10.2935i | −0.719554 | − | 0.449246i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.08081 | − | 8.08081i | 0.352006 | − | 0.352006i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.9344i | 2.21454i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.88713i | 0.168687i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.7003 | + | 18.7003i | 0.809998 | + | 0.809998i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0957 | + | 6.78860i | 1.38762 | + | 0.293497i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0226 | − | 12.0226i | −0.518812 | − | 0.518812i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.57934 | + | 15.7770i | −0.197246 | + | 0.679562i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9363 | −1.67400 | −0.837001 | − | 0.547202i | \(-0.815693\pi\) | ||||
−0.837001 | + | 0.547202i | \(0.815693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.49218 | + | 5.49218i | 0.235692 | + | 0.235692i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.23416 | − | 6.00987i | 0.395548 | − | 0.257435i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.30390 | − | 2.30390i | 0.0985078 | − | 0.0985078i | −0.656135 | − | 0.754643i | \(-0.727810\pi\) |
0.754643 | + | 0.656135i | \(0.227810\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.68306 | 0.0718314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.0783i | 0.940565i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.92375 | + | 10.5507i | 0.336952 | + | 0.448661i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.97518 | + | 3.88883i | −0.253632 | + | 0.165072i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.69913 | − | 7.69913i | 0.326223 | − | 0.326223i | −0.524926 | − | 0.851148i | \(-0.675907\pi\) |
0.851148 | + | 0.524926i | \(0.175907\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.31974 | −0.309592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.1556 | 1.06207 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.8855 | + | 11.8855i | −0.500914 | + | 0.500914i | −0.911722 | − | 0.410808i | \(-0.865247\pi\) |
0.410808 | + | 0.911722i | \(0.365247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.48640 | − | 11.7554i | 0.104604 | − | 0.494554i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.2036 | − | 9.16515i | 0.512505 | − | 0.384900i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.16924i | − | 0.132861i | −0.997791 | − | 0.0664307i | \(-0.978839\pi\) | ||
0.997791 | − | 0.0664307i | \(-0.0211611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.8492 | −1.03991 | −0.519953 | − | 0.854195i | \(-0.674050\pi\) | ||||
−0.519953 | + | 0.854195i | \(0.674050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0635 | − | 12.0635i | 0.503960 | − | 0.503960i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −40.1061 | + | 15.4874i | −1.67254 | + | 0.645870i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2688 | − | 29.2688i | −1.21848 | − | 1.21848i | −0.968166 | − | 0.250309i | \(-0.919468\pi\) |
−0.250309 | − | 0.968166i | \(-0.580532\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.6470 | 1.52300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.93372 | − | 34.6973i | 0.204685 | − | 1.43948i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.10888 | − | 9.10888i | −0.377251 | − | 0.377251i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.08139 | − | 5.11268i | 0.0447100 | − | 0.211383i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.3313 | − | 16.3313i | −0.674065 | − | 0.674065i | 0.284586 | − | 0.958651i | \(-0.408144\pi\) |
−0.958651 | + | 0.284586i | \(0.908144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.87150i | 0.241931i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 35.7661i | − | 1.47122i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.5540 | + | 17.5540i | −0.720858 | + | 0.720858i | −0.968780 | − | 0.247922i | \(-0.920252\pi\) |
0.247922 | + | 0.968780i | \(0.420252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.2159 | + | 39.1273i | 0.746777 | + | 1.60406i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.22972 | − | 7.22972i | 0.295893 | − | 0.295893i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 21.4754i | − | 0.877461i | −0.898619 | − | 0.438731i | \(-0.855428\pi\) | ||
0.898619 | − | 0.438731i | \(-0.144572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.4373i | − | 1.32314i | −0.749882 | − | 0.661572i | \(-0.769890\pi\) | ||
0.749882 | − | 0.661572i | \(-0.230110\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.26431 | + | 2.26431i | 0.0922096 | + | 0.0922096i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.69896 | − | 10.2929i | −0.272351 | − | 0.418467i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.4507 | + | 13.4507i | 0.545947 | + | 0.545947i | 0.925266 | − | 0.379319i | \(-0.123842\pi\) |
−0.379319 | + | 0.925266i | \(0.623842\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.6696 | + | 3.22346i | 0.918617 | + | 0.130621i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0515 | 0.730284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.66986 | − | 1.66986i | −0.0674449 | − | 0.0674449i | 0.672580 | − | 0.740025i | \(-0.265186\pi\) |
−0.740025 | + | 0.672580i | \(0.765186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47205 | + | 30.5990i | −0.260978 | + | 1.23387i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.0944 | + | 16.0944i | −0.647938 | + | 0.647938i | −0.952494 | − | 0.304556i | \(-0.901492\pi\) |
0.304556 | + | 0.952494i | \(0.401492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.973019 | 0.0391089 | 0.0195545 | − | 0.999809i | \(-0.493775\pi\) | ||||
0.0195545 | + | 0.999809i | \(0.493775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 48.5285i | − | 1.94738i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.8003 | − | 15.6213i | 0.833345 | − | 0.625856i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.8025 | − | 18.5115i | −0.672098 | − | 0.740462i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.13900 | + | 9.13900i | −0.364977 | + | 0.364977i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8308 | 0.631213 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4830 | 0.695987 | 0.347994 | − | 0.937497i | \(-0.386863\pi\) | ||||
0.347994 | + | 0.937497i | \(0.386863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.64573 | + | 9.64573i | −0.383383 | + | 0.383383i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.40624 | − | 0.508948i | −0.0954888 | − | 0.0201970i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.37254 | + | 17.0385i | 0.371353 | + | 0.675089i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 0.329967i | − | 0.0130533i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.0710 | −0.990244 | −0.495122 | − | 0.868823i | \(-0.664877\pi\) | ||||
−0.495122 | + | 0.868823i | \(0.664877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.86619 | − | 3.86619i | 0.152468 | − | 0.152468i | −0.626752 | − | 0.779219i | \(-0.715616\pi\) |
0.779219 | + | 0.626752i | \(0.215616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.72195 | − | 7.25527i | −0.185927 | − | 0.285676i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.4727 | − | 24.4727i | −0.962119 | − | 0.962119i | 0.0371889 | − | 0.999308i | \(-0.488160\pi\) |
−0.999308 | + | 0.0371889i | \(0.988160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8440 | −0.425663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.02875 | + | 0.857248i | 0.236285 | + | 0.0335982i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.1478 | + | 23.1478i | 0.905845 | + | 0.905845i | 0.995934 | − | 0.0900885i | \(-0.0287150\pi\) |
−0.0900885 | + | 0.995934i | \(0.528715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6851 | + | 13.4625i | −0.808235 | + | 0.526024i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.96070 | + | 5.96070i | 0.232549 | + | 0.232549i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.1548i | − | 1.40839i | −0.710006 | − | 0.704195i | \(-0.751308\pi\) | ||
0.710006 | − | 0.704195i | \(-0.248692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.4541i | 1.30121i | 0.759415 | + | 0.650606i | \(0.225485\pi\) | ||||
−0.759415 | + | 0.650606i | \(0.774515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.0555 | − | 21.0555i | 0.817729 | − | 0.817729i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.8327 | − | 7.59711i | −0.807858 | − | 0.294603i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.8137 | − | 35.8137i | 1.38671 | − | 1.38671i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9.92347i | − | 0.383663i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.69526i | 0.181259i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.30998 | − | 6.30998i | −0.243232 | − | 0.243232i | 0.574954 | − | 0.818186i | \(-0.305020\pi\) |
−0.818186 | + | 0.574954i | \(0.805020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.3246 | − | 10.1655i | 1.01323 | − | 0.391271i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.88730 | − | 6.88730i | −0.264700 | − | 0.264700i | 0.562260 | − | 0.826960i | \(-0.309932\pi\) |
−0.826960 | + | 0.562260i | \(0.809932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.9253 | − | 6.24588i | −1.68570 | − | 0.239695i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.19444 | 0.199051 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.06740 | + | 1.06740i | 0.0408430 | + | 0.0408430i | 0.727233 | − | 0.686390i | \(-0.240806\pi\) |
−0.686390 | + | 0.727233i | \(0.740806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.20832 | + | 1.73615i | 0.313624 | + | 0.0663350i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7728 | + | 18.7728i | −0.716228 | + | 0.716228i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.2485 | −0.580921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 43.8638i | − | 1.66866i | −0.551267 | − | 0.834329i | \(-0.685855\pi\) | ||
0.551267 | − | 0.834329i | \(-0.314145\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.13687 | − | 4.17683i | −0.119160 | − | 0.158665i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.72654 | − | 13.4083i | −0.331016 | − | 0.508606i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.1085 | − | 49.1085i | 1.86012 | − | 1.86012i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.9974 | −0.718546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.6200 | −1.38312 | −0.691559 | − | 0.722320i | \(-0.743076\pi\) | ||||
−0.691559 | + | 0.722320i | \(0.743076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.75130 | + | 5.75130i | −0.216914 | + | 0.216914i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.6450 | + | 17.8925i | 0.438574 | + | 0.673869i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.3705 | + | 17.8031i | 0.502848 | + | 0.669555i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 30.7975i | − | 1.15662i | −0.815816 | − | 0.578311i | \(-0.803712\pi\) | ||
0.815816 | − | 0.578311i | \(-0.196288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.19551 | −0.157344 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.52431 | − | 9.52431i | 0.356688 | − | 0.356688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.2629 | + | 3.01676i | 0.533402 | + | 0.112821i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.8146 | + | 11.8146i | 0.441225 | + | 0.441225i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.9703 | −1.37876 | −0.689379 | − | 0.724401i | \(-0.742117\pi\) | ||||
−0.689379 | + | 0.724401i | \(0.742117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.62411 | + | 32.5199i | −0.172211 | + | 1.21111i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.4005 | + | 20.4005i | 0.758704 | + | 0.758704i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.9294 | + | 11.9252i | 1.00013 | + | 0.442893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.99011 | − | 4.99011i | −0.185073 | − | 0.185073i | 0.608489 | − | 0.793562i | \(-0.291776\pi\) |
−0.793562 | + | 0.608489i | \(0.791776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7297i | 1.10110i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2222i | 0.710960i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9857 | + | 18.9857i | −0.701252 | + | 0.701252i | −0.964679 | − | 0.263427i | \(-0.915147\pi\) |
0.263427 | + | 0.964679i | \(0.415147\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.8422 | + | 20.2815i | −0.399920 | + | 0.748093i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.31675 | + | 6.31675i | −0.232681 | + | 0.232681i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4.09135i | − | 0.150503i | −0.997165 | − | 0.0752515i | \(-0.976024\pi\) | ||
0.997165 | − | 0.0752515i | \(-0.0239759\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.2989i | 0.562019i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.7330 | + | 37.7330i | 1.38429 | + | 1.38429i | 0.836838 | + | 0.547451i | \(0.184402\pi\) |
0.547451 | + | 0.836838i | \(0.315598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.9676 | − | 14.9480i | 0.841467 | − | 0.547652i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.87968 | + | 7.87968i | 0.288302 | + | 0.288302i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.46444 | − | 38.4297i | 0.199666 | − | 1.40419i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.3975 | −0.780805 | −0.390403 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390403 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.2635 | + | 27.2635i | 0.993538 | + | 0.993538i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1273 | − | 24.7795i | −0.586931 | − | 0.901819i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8160 | − | 24.8160i | 0.901952 | − | 0.901952i | −0.0936529 | − | 0.995605i | \(-0.529854\pi\) |
0.995605 | + | 0.0936529i | \(0.0298544\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.6492 | 1.07620 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4451i | 0.741135i | 0.928806 | + | 0.370567i | \(0.120837\pi\) | ||||
−0.928806 | + | 0.370567i | \(0.879163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.82853 | − | 10.4239i | −0.283412 | − | 0.377371i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.4263 | − | 2.83982i | −0.485430 | − | 0.102674i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.07654 | + | 9.07654i | −0.327735 | + | 0.327735i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.20785 | −0.223861 | −0.111930 | − | 0.993716i | \(-0.535703\pi\) | ||||
−0.111930 | + | 0.993716i | \(0.535703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.01351 | −0.144543 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.7179 | + | 12.7179i | −0.457430 | + | 0.457430i | −0.897811 | − | 0.440381i | \(-0.854843\pi\) |
0.440381 | + | 0.897811i | \(0.354843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.16161 | + | 3.17141i | 0.257253 | + | 0.113920i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.06563 | + | 6.74503i | 0.181728 | + | 0.241976i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.6821i | 1.27844i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.920513 | 0.0329385 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.5071 | + | 23.5071i | −0.840076 | + | 0.840076i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.46670 | + | 25.8459i | −0.195115 | + | 0.922480i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6842 | + | 32.6842i | 1.16506 | + | 1.16506i | 0.983352 | + | 0.181713i | \(0.0581642\pi\) |
0.181713 | + | 0.983352i | \(0.441836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.49068 | −0.195474 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0753 | − | 2.00142i | −0.500461 | − | 0.0711622i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.92999 | + | 3.92999i | 0.139558 | + | 0.139558i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.83677 | − | 15.1142i | −0.348874 | − | 0.536045i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.76878 | − | 8.76878i | −0.310606 | − | 0.310606i | 0.534538 | − | 0.845144i | \(-0.320486\pi\) |
−0.845144 | + | 0.534538i | \(0.820486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 47.4046i | − | 1.67706i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.27127i | 0.292251i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.6286 | + | 16.6286i | −0.586811 | + | 0.586811i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.4698 | + | 46.1167i | 0.756711 | + | 1.62540i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.22540 | − | 1.22540i | 0.0431360 | − | 0.0431360i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.9362i | − | 0.560287i | −0.959958 | − | 0.280144i | \(-0.909618\pi\) | ||
0.959958 | − | 0.280144i | \(-0.0903821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.6560i | − | 1.74366i | −0.489812 | − | 0.871828i | \(-0.662935\pi\) | ||
0.489812 | − | 0.871828i | \(-0.337065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3636 | + | 15.3636i | 0.538826 | + | 0.538826i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.45120 | + | 6.86112i | −0.0508335 | + | 0.240334i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.98342 | − | 6.98342i | −0.244319 | − | 0.244319i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.12166 | − | 0.870459i | −0.213908 | − | 0.0304163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.1755 | −1.05313 | −0.526566 | − | 0.850135i | \(-0.676521\pi\) | ||||
−0.526566 | + | 0.850135i | \(0.676521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.2900 | + | 17.2900i | 0.602693 | + | 0.602693i | 0.941026 | − | 0.338333i | \(-0.109863\pi\) |
−0.338333 | + | 0.941026i | \(0.609863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.21077 | + | 16.0834i | 0.216231 | + | 0.559951i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.93183 | − | 1.93183i | 0.0671761 | − | 0.0671761i | −0.672721 | − | 0.739897i | \(-0.734874\pi\) |
0.739897 | + | 0.672721i | \(0.234874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2032 | 1.08373 | 0.541865 | − | 0.840465i | \(-0.317718\pi\) | ||||
0.541865 | + | 0.840465i | \(0.317718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.2024i | 0.839573i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.7445 | − | 24.6131i | 1.55030 | − | 0.852793i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.94226 | + | 47.0058i | −0.344066 | + | 1.62670i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.25150 | + | 6.25150i | −0.216083 | + | 0.216083i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.79348 | −0.269061 | −0.134530 | − | 0.990909i | \(-0.542953\pi\) | ||||
−0.134530 | + | 0.990909i | \(0.542953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.69616 | −0.196419 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.0022 | + | 21.0022i | −0.723354 | + | 0.723354i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.90010 | + | 6.44329i | −0.340574 | + | 0.221656i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.6191 | + | 8.72614i | −0.399237 | + | 0.299834i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 11.5041i | − | 0.394821i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.6586 | 0.639610 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.5954 | + | 16.5954i | −0.568215 | + | 0.568215i | −0.931628 | − | 0.363413i | \(-0.881611\pi\) |
0.363413 | + | 0.931628i | \(0.381611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.90947 | − | 3.84606i | 0.202100 | − | 0.131533i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.2133 | + | 29.2133i | 0.997909 | + | 0.997909i | 0.999998 | − | 0.00208912i | \(-0.000664987\pi\) |
−0.00208912 | + | 0.999998i | \(0.500665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3754 | 0.626962 | 0.313481 | − | 0.949594i | \(-0.398505\pi\) | ||||
0.313481 | + | 0.949594i | \(0.398505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.6377 | + | 5.20964i | 1.24861 | + | 0.177544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.7261 | − | 31.7261i | −1.07997 | − | 1.07997i | −0.996511 | − | 0.0834585i | \(-0.973403\pi\) |
−0.0834585 | − | 0.996511i | \(-0.526597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2458 | − | 3.01315i | −0.484372 | − | 0.102450i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.6318 | − | 37.6318i | −1.27804 | − | 1.27804i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.7042i | − | 0.397039i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5744i | 0.358300i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.97534 | − | 9.97534i | 0.337614 | − | 0.337614i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.5189 | + | 21.3067i | −0.693665 | + | 0.720298i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.2606 | + | 32.2606i | −1.08936 | + | 1.08936i | −0.0937674 | + | 0.995594i | \(0.529891\pi\) |
−0.995594 | + | 0.0937674i | \(0.970109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.32823i | 0.0785292i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.96766i | 0.335819i | 0.985802 | + | 0.167909i | \(0.0537016\pi\) | ||||
−0.985802 | + | 0.167909i | \(0.946298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.7464 | − | 36.7464i | −1.23662 | − | 1.23662i | −0.961376 | − | 0.275239i | \(-0.911243\pi\) |
−0.275239 | − | 0.961376i | \(-0.588757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.8518 | − | 3.14134i | −0.499239 | − | 0.105595i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.82975 | + | 9.82975i | 0.330051 | + | 0.330051i | 0.852606 | − | 0.522555i | \(-0.175021\pi\) |
−0.522555 | + | 0.852606i | \(0.675021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.409675 | + | 2.88111i | −0.0137401 | + | 0.0966294i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5379 | −0.453538 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.2221 | + | 17.2221i | 0.576314 | + | 0.576314i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.6873 | + | 14.1148i | −0.724928 | + | 0.471805i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.8167 | − | 24.8167i | 0.828607 | − | 0.828607i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.22711 | −0.307741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.0438i | 1.33405i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.19004 | + | 6.15086i | −0.272548 | + | 0.204688i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.90727 | − | 6.44795i | 0.329329 | − | 0.214337i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4096 | − | 10.4096i | 0.345646 | − | 0.345646i | −0.512839 | − | 0.858485i | \(-0.671406\pi\) |
0.858485 | + | 0.512839i | \(0.171406\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.07946 | −0.234811 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.5150 | 0.547167 | 0.273583 | − | 0.961848i | \(-0.411791\pi\) | ||||
0.273583 | + | 0.961848i | \(0.411791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9820 | + | 21.9820i | −0.727498 | + | 0.727498i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.36015 | + | 6.43060i | −0.0449650 | + | 0.212589i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5364 | + | 23.3502i | 0.579104 | + | 0.771092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.9494i | 0.493134i | 0.969126 | + | 0.246567i | \(0.0793026\pi\) | ||||
−0.969126 | + | 0.246567i | \(0.920697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.5951 | −0.645680 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.770480 | − | 0.770480i | 0.0253607 | − | 0.0253607i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.90852 | + | 10.1215i | 0.128511 | + | 0.332792i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.38521 | − | 7.38521i | −0.242562 | − | 0.242562i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.36098 | 0.0774611 | 0.0387306 | − | 0.999250i | \(-0.487669\pi\) | ||||
0.0387306 | + | 0.999250i | \(0.487669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.31371 | + | 25.1975i | −0.239697 | + | 0.825815i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1720 | + | 15.1720i | 0.496709 | + | 0.496709i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.92227 | − | 37.4555i | 0.259086 | − | 1.22493i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.28379 | − | 2.28379i | −0.0746081 | − | 0.0746081i | 0.668818 | − | 0.743426i | \(-0.266801\pi\) |
−0.743426 | + | 0.668818i | \(0.766801\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.6600i | 0.478410i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.1034i | 0.981344i | 0.871344 | + | 0.490672i | \(0.163249\pi\) | ||||
−0.871344 | + | 0.490672i | \(0.836751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.8808 | − | 57.8808i | 1.88486 | − | 1.88486i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.0922 | − | 30.2698i | −0.458419 | − | 0.984676i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.50072 | − | 9.50072i | 0.308732 | − | 0.308732i | −0.535686 | − | 0.844417i | \(-0.679947\pi\) |
0.844417 | + | 0.535686i | \(0.179947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.8367i | 0.903617i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 23.3837i | − | 0.758269i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.9629 | − | 21.9629i | −0.711448 | − | 0.711448i | 0.255390 | − | 0.966838i | \(-0.417796\pi\) |
−0.966838 | + | 0.255390i | \(0.917796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.1628 | − | 21.7612i | −0.458299 | − | 0.704175i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.3620 | − | 14.3620i | −0.464258 | − | 0.464258i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.39751 | − | 9.82823i | 0.0451279 | − | 0.317370i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5461 | 0.920843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.72731 | + | 8.72731i | 0.281234 | + | 0.281234i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5413 | − | 54.5657i | 0.371527 | − | 1.75653i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.6279 | − | 14.6279i | 0.470400 | − | 0.470400i | −0.431644 | − | 0.902044i | \(-0.642066\pi\) |
0.902044 | + | 0.431644i | \(0.142066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.1762 | 1.29065 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.5120i | − | 0.465712i | −0.972511 | − | 0.232856i | \(-0.925193\pi\) | ||
0.972511 | − | 0.232856i | \(-0.0748071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.1359 | + | 11.3673i | −0.485233 | + | 0.364419i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.6605 | + | 8.26348i | 0.597613 | + | 0.264643i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.07281 | − | 3.07281i | 0.0983080 | − | 0.0983080i | −0.656242 | − | 0.754550i | \(-0.727855\pi\) |
0.754550 | + | 0.656242i | \(0.227855\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.0744 | −0.737463 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.14509 | 0.132343 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.2010 | − | 38.2010i | 1.21842 | − | 1.21842i | 0.250238 | − | 0.968184i | \(-0.419491\pi\) |
0.968184 | − | 0.250238i | \(-0.0805088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.2541 | − | 11.2638i | −1.69682 | − | 0.358896i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.1977 | − | 15.1689i | 0.642901 | − | 0.482830i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.6560i | 0.720418i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.3300 | 1.34466 | 0.672328 | − | 0.740253i | \(-0.265294\pi\) | ||||
0.672328 | + | 0.740253i | \(0.265294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.9748 | − | 34.9748i | 1.10989 | − | 1.10989i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.48786 | − | 13.0416i | −0.269083 | − | 0.413446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.3987 | − | 24.3987i | −0.772713 | − | 0.772713i | 0.205867 | − | 0.978580i | \(-0.433999\pi\) |
−0.978580 | + | 0.205867i | \(0.933999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.2470 | −0.387479 |
(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 | 280.2.x.a.153.4 | yes | 24 | |
4.3 | odd | 2 | 560.2.bj.d.433.9 | 24 | |||
5.2 | odd | 4 | inner | 280.2.x.a.97.9 | yes | 24 | |
5.3 | odd | 4 | 1400.2.x.b.657.4 | 24 | |||
5.4 | even | 2 | 1400.2.x.b.993.9 | 24 | |||
7.6 | odd | 2 | inner | 280.2.x.a.153.9 | yes | 24 | |
20.7 | even | 4 | 560.2.bj.d.97.4 | 24 | |||
28.27 | even | 2 | 560.2.bj.d.433.4 | 24 | |||
35.13 | even | 4 | 1400.2.x.b.657.9 | 24 | |||
35.27 | even | 4 | inner | 280.2.x.a.97.4 | ✓ | 24 | |
35.34 | odd | 2 | 1400.2.x.b.993.4 | 24 | |||
140.27 | odd | 4 | 560.2.bj.d.97.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.x.a.97.4 | ✓ | 24 | 35.27 | even | 4 | inner | |
280.2.x.a.97.9 | yes | 24 | 5.2 | odd | 4 | inner | |
280.2.x.a.153.4 | yes | 24 | 1.1 | even | 1 | trivial | |
280.2.x.a.153.9 | yes | 24 | 7.6 | odd | 2 | inner | |
560.2.bj.d.97.4 | 24 | 20.7 | even | 4 | |||
560.2.bj.d.97.9 | 24 | 140.27 | odd | 4 | |||
560.2.bj.d.433.4 | 24 | 28.27 | even | 2 | |||
560.2.bj.d.433.9 | 24 | 4.3 | odd | 2 | |||
1400.2.x.b.657.4 | 24 | 5.3 | odd | 4 | |||
1400.2.x.b.657.9 | 24 | 35.13 | even | 4 | |||
1400.2.x.b.993.4 | 24 | 35.34 | odd | 2 | |||
1400.2.x.b.993.9 | 24 | 5.4 | even | 2 |