Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(239,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.g (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: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 437.2 | ||
Root | \(0.500000 - 1.33108i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.437 |
Dual form | 1014.2.g.c.239.2 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.796225 | − | 1.53819i | −0.459701 | − | 0.888074i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.313444 | − | 0.313444i | 0.140176 | − | 0.140176i | −0.633536 | − | 0.773713i | \(-0.718397\pi\) |
0.773713 | + | 0.633536i | \(0.218397\pi\) | |||||||
\(6\) | 1.65068 | + | 0.524648i | 0.673887 | + | 0.214186i | ||||
\(7\) | −0.203775 | + | 0.203775i | −0.0770196 | + | 0.0770196i | −0.744567 | − | 0.667548i | \(-0.767344\pi\) |
0.667548 | + | 0.744567i | \(0.267344\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −1.73205 | + | 2.44949i | −0.577350 | + | 0.816497i | ||||
\(10\) | 0.443277i | 0.140176i | ||||||||
\(11\) | 0.412157 | + | 0.412157i | 0.124270 | + | 0.124270i | 0.766506 | − | 0.642237i | \(-0.221993\pi\) |
−0.642237 | + | 0.766506i | \(0.721993\pi\) | |||||||
\(12\) | −1.53819 | + | 0.796225i | −0.444037 | + | 0.229850i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | − | 0.288181i | − | 0.0770196i | ||||||
\(15\) | −0.731708 | − | 0.232564i | −0.188926 | − | 0.0600478i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.59813 | −1.35775 | −0.678873 | − | 0.734256i | \(-0.737531\pi\) | ||||
−0.678873 | + | 0.734256i | \(0.737531\pi\) | |||||||
\(18\) | −0.507306 | − | 2.95680i | −0.119573 | − | 0.696923i | ||||
\(19\) | 4.97155 | + | 4.97155i | 1.14055 | + | 1.14055i | 0.988349 | + | 0.152203i | \(0.0486368\pi\) |
0.152203 | + | 0.988349i | \(0.451363\pi\) | |||||||
\(20\) | −0.313444 | − | 0.313444i | −0.0700882 | − | 0.0700882i | ||||
\(21\) | 0.475695 | + | 0.151194i | 0.103805 | + | 0.0329931i | ||||
\(22\) | −0.582877 | −0.124270 | ||||||||
\(23\) | −6.65190 | −1.38702 | −0.693509 | − | 0.720448i | \(-0.743936\pi\) | ||||
−0.693509 | + | 0.720448i | \(0.743936\pi\) | |||||||
\(24\) | 0.524648 | − | 1.65068i | 0.107093 | − | 0.336944i | ||||
\(25\) | 4.80351i | 0.960701i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.14688 | + | 0.713876i | 0.990518 | + | 0.137386i | ||||
\(28\) | 0.203775 | + | 0.203775i | 0.0385098 | + | 0.0385098i | ||||
\(29\) | − | 4.13015i | − | 0.766949i | −0.923551 | − | 0.383475i | \(-0.874727\pi\) | ||
0.923551 | − | 0.383475i | \(-0.125273\pi\) | |||||||
\(30\) | 0.681844 | − | 0.352948i | 0.124487 | − | 0.0644392i | ||||
\(31\) | −1.03573 | − | 1.03573i | −0.186022 | − | 0.186022i | 0.607952 | − | 0.793974i | \(-0.291991\pi\) |
−0.793974 | + | 0.607952i | \(0.791991\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.305805 | − | 0.962144i | 0.0532339 | − | 0.167488i | ||||
\(34\) | 3.95848 | − | 3.95848i | 0.678873 | − | 0.678873i | ||||
\(35\) | 0.127744i | 0.0215927i | ||||||||
\(36\) | 2.44949 | + | 1.73205i | 0.408248 | + | 0.288675i | ||||
\(37\) | −4.92046 | + | 4.92046i | −0.808918 | + | 0.808918i | −0.984470 | − | 0.175552i | \(-0.943829\pi\) |
0.175552 | + | 0.984470i | \(0.443829\pi\) | |||||||
\(38\) | −7.03084 | −1.14055 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.443277 | 0.0700882 | ||||||||
\(41\) | 5.39512 | − | 5.39512i | 0.842577 | − | 0.842577i | −0.146617 | − | 0.989193i | \(-0.546838\pi\) |
0.989193 | + | 0.146617i | \(0.0468384\pi\) | |||||||
\(42\) | −0.443277 | + | 0.229457i | −0.0683991 | + | 0.0354060i | ||||
\(43\) | 3.76778i | 0.574581i | 0.957844 | + | 0.287290i | \(0.0927545\pi\) | ||||
−0.957844 | + | 0.287290i | \(0.907246\pi\) | |||||||
\(44\) | 0.412157 | − | 0.412157i | 0.0621349 | − | 0.0621349i | ||||
\(45\) | 0.224877 | + | 1.31068i | 0.0335227 | + | 0.195385i | ||||
\(46\) | 4.70360 | − | 4.70360i | 0.693509 | − | 0.693509i | ||||
\(47\) | 3.71799 | + | 3.71799i | 0.542325 | + | 0.542325i | 0.924210 | − | 0.381885i | \(-0.124725\pi\) |
−0.381885 | + | 0.924210i | \(0.624725\pi\) | |||||||
\(48\) | 0.796225 | + | 1.53819i | 0.114925 | + | 0.222018i | ||||
\(49\) | 6.91695i | 0.988136i | ||||||||
\(50\) | −3.39659 | − | 3.39659i | −0.480351 | − | 0.480351i | ||||
\(51\) | 4.45737 | + | 8.61098i | 0.624157 | + | 1.20578i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.64778i | 0.501062i | 0.968109 | + | 0.250531i | \(0.0806052\pi\) | ||||
−0.968109 | + | 0.250531i | \(0.919395\pi\) | |||||||
\(54\) | −4.14418 | + | 3.13461i | −0.563952 | + | 0.426566i | ||||
\(55\) | 0.258376 | 0.0348394 | ||||||||
\(56\) | −0.288181 | −0.0385098 | ||||||||
\(57\) | 3.68871 | − | 11.6057i | 0.488582 | − | 1.53721i | ||||
\(58\) | 2.92046 | + | 2.92046i | 0.383475 | + | 0.383475i | ||||
\(59\) | 2.40926 | + | 2.40926i | 0.313659 | + | 0.313659i | 0.846325 | − | 0.532666i | \(-0.178810\pi\) |
−0.532666 | + | 0.846325i | \(0.678810\pi\) | |||||||
\(60\) | −0.232564 | + | 0.731708i | −0.0300239 | + | 0.0944632i | ||||
\(61\) | 10.5111 | 1.34581 | 0.672903 | − | 0.739731i | \(-0.265047\pi\) | ||||
0.672903 | + | 0.739731i | \(0.265047\pi\) | |||||||
\(62\) | 1.46474 | 0.186022 | ||||||||
\(63\) | −0.146196 | − | 0.852093i | −0.0184190 | − | 0.107354i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.464102 | + | 0.896575i | 0.0571270 | + | 0.110361i | ||||
\(67\) | 6.26033 | + | 6.26033i | 0.764821 | + | 0.764821i | 0.977190 | − | 0.212369i | \(-0.0681178\pi\) |
−0.212369 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(68\) | 5.59813i | 0.678873i | ||||||||
\(69\) | 5.29641 | + | 10.2319i | 0.637613 | + | 1.23177i | ||||
\(70\) | −0.0903287 | − | 0.0903287i | −0.0107963 | − | 0.0107963i | ||||
\(71\) | −10.8798 | + | 10.8798i | −1.29120 | + | 1.29120i | −0.357149 | + | 0.934047i | \(0.616251\pi\) |
−0.934047 | + | 0.357149i | \(0.883749\pi\) | |||||||
\(72\) | −2.95680 | + | 0.507306i | −0.348462 | + | 0.0597866i | ||||
\(73\) | 3.52053 | − | 3.52053i | 0.412047 | − | 0.412047i | −0.470404 | − | 0.882451i | \(-0.655892\pi\) |
0.882451 | + | 0.470404i | \(0.155892\pi\) | |||||||
\(74\) | − | 6.95858i | − | 0.808918i | ||||||
\(75\) | 7.38870 | − | 3.82467i | 0.853174 | − | 0.441635i | ||||
\(76\) | 4.97155 | − | 4.97155i | 0.570276 | − | 0.570276i | ||||
\(77\) | −0.167974 | −0.0191424 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.10886 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(80\) | −0.313444 | + | 0.313444i | −0.0350441 | + | 0.0350441i | ||||
\(81\) | −3.00000 | − | 8.48528i | −0.333333 | − | 0.942809i | ||||
\(82\) | 7.62986i | 0.842577i | ||||||||
\(83\) | −8.23032 | + | 8.23032i | −0.903395 | + | 0.903395i | −0.995728 | − | 0.0923332i | \(-0.970567\pi\) |
0.0923332 | + | 0.995728i | \(0.470567\pi\) | |||||||
\(84\) | 0.151194 | − | 0.475695i | 0.0164966 | − | 0.0519026i | ||||
\(85\) | −1.75470 | + | 1.75470i | −0.190324 | + | 0.190324i | ||||
\(86\) | −2.66422 | − | 2.66422i | −0.287290 | − | 0.287290i | ||||
\(87\) | −6.35295 | + | 3.28853i | −0.681108 | + | 0.352567i | ||||
\(88\) | 0.582877i | 0.0621349i | ||||||||
\(89\) | 9.95774 | + | 9.95774i | 1.05552 | + | 1.05552i | 0.998365 | + | 0.0571524i | \(0.0182021\pi\) |
0.0571524 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(90\) | −1.08580 | − | 0.767778i | −0.114454 | − | 0.0809309i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.65190i | 0.693509i | ||||||||
\(93\) | −0.768472 | + | 2.41782i | −0.0796869 | + | 0.250716i | ||||
\(94\) | −5.25803 | −0.542325 | ||||||||
\(95\) | 3.11661 | 0.319757 | ||||||||
\(96\) | −1.65068 | − | 0.524648i | −0.168472 | − | 0.0535466i | ||||
\(97\) | −1.89781 | − | 1.89781i | −0.192693 | − | 0.192693i | 0.604166 | − | 0.796859i | \(-0.293506\pi\) |
−0.796859 | + | 0.604166i | \(0.793506\pi\) | |||||||
\(98\) | −4.89102 | − | 4.89102i | −0.494068 | − | 0.494068i | ||||
\(99\) | −1.72345 | + | 0.295697i | −0.173213 | + | 0.0297187i | ||||
\(100\) | 4.80351 | 0.480351 | ||||||||
\(101\) | −14.2406 | −1.41699 | −0.708497 | − | 0.705714i | \(-0.750626\pi\) | ||||
−0.708497 | + | 0.705714i | \(0.750626\pi\) | |||||||
\(102\) | −9.24072 | − | 2.93705i | −0.914968 | − | 0.290811i | ||||
\(103\) | 4.60903i | 0.454141i | 0.973878 | + | 0.227071i | \(0.0729148\pi\) | ||||
−0.973878 | + | 0.227071i | \(0.927085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.196494 | − | 0.101713i | 0.0191759 | − | 0.00992617i | ||||
\(106\) | −2.57937 | − | 2.57937i | −0.250531 | − | 0.250531i | ||||
\(107\) | 13.5120i | 1.30625i | 0.757248 | + | 0.653127i | \(0.226543\pi\) | ||||
−0.757248 | + | 0.653127i | \(0.773457\pi\) | |||||||
\(108\) | 0.713876 | − | 5.14688i | 0.0686928 | − | 0.495259i | ||||
\(109\) | 2.06188 | + | 2.06188i | 0.197492 | + | 0.197492i | 0.798924 | − | 0.601432i | \(-0.205403\pi\) |
−0.601432 | + | 0.798924i | \(0.705403\pi\) | |||||||
\(110\) | −0.182699 | + | 0.182699i | −0.0174197 | + | 0.0174197i | ||||
\(111\) | 11.4864 | + | 3.65080i | 1.09024 | + | 0.346519i | ||||
\(112\) | 0.203775 | − | 0.203775i | 0.0192549 | − | 0.0192549i | ||||
\(113\) | − | 10.4166i | − | 0.979916i | −0.871746 | − | 0.489958i | \(-0.837012\pi\) | ||
0.871746 | − | 0.489958i | \(-0.162988\pi\) | |||||||
\(114\) | 5.59813 | + | 10.8148i | 0.524313 | + | 1.01289i | ||||
\(115\) | −2.08500 | + | 2.08500i | −0.194427 | + | 0.194427i | ||||
\(116\) | −4.13015 | −0.383475 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.40721 | −0.313659 | ||||||||
\(119\) | 1.14076 | − | 1.14076i | 0.104573 | − | 0.104573i | ||||
\(120\) | −0.352948 | − | 0.681844i | −0.0322196 | − | 0.0622435i | ||||
\(121\) | − | 10.6603i | − | 0.969114i | ||||||
\(122\) | −7.43246 | + | 7.43246i | −0.672903 | + | 0.672903i | ||||
\(123\) | −12.5945 | − | 4.00299i | −1.13560 | − | 0.360937i | ||||
\(124\) | −1.03573 | + | 1.03573i | −0.0930111 | + | 0.0930111i | ||||
\(125\) | 3.07285 | + | 3.07285i | 0.274844 | + | 0.274844i | ||||
\(126\) | 0.705897 | + | 0.499144i | 0.0628863 | + | 0.0444673i | ||||
\(127\) | − | 0.241453i | − | 0.0214255i | −0.999943 | − | 0.0107127i | \(-0.996590\pi\) | ||
0.999943 | − | 0.0107127i | \(-0.00341004\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 5.79555 | − | 3.00000i | 0.510270 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.09043i | − | 0.706864i | −0.935460 | − | 0.353432i | \(-0.885015\pi\) | ||
0.935460 | − | 0.353432i | \(-0.114985\pi\) | |||||||
\(132\) | −0.962144 | − | 0.305805i | −0.0837439 | − | 0.0266169i | ||||
\(133\) | −2.02615 | −0.175690 | ||||||||
\(134\) | −8.85344 | −0.764821 | ||||||||
\(135\) | 1.83702 | − | 1.38950i | 0.158105 | − | 0.119589i | ||||
\(136\) | −3.95848 | − | 3.95848i | −0.339437 | − | 0.339437i | ||||
\(137\) | 0.0584822 | + | 0.0584822i | 0.00499647 | + | 0.00499647i | 0.709601 | − | 0.704604i | \(-0.248875\pi\) |
−0.704604 | + | 0.709601i | \(0.748875\pi\) | |||||||
\(138\) | −10.9802 | − | 3.48990i | −0.934693 | − | 0.297080i | ||||
\(139\) | −6.24145 | −0.529393 | −0.264697 | − | 0.964332i | \(-0.585272\pi\) | ||||
−0.264697 | + | 0.964332i | \(0.585272\pi\) | |||||||
\(140\) | 0.127744 | 0.0107963 | ||||||||
\(141\) | 2.75862 | − | 8.67933i | 0.232317 | − | 0.730932i | ||||
\(142\) | − | 15.3864i | − | 1.29120i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.73205 | − | 2.44949i | 0.144338 | − | 0.204124i | ||||
\(145\) | −1.29457 | − | 1.29457i | −0.107508 | − | 0.107508i | ||||
\(146\) | 4.97878i | 0.412047i | ||||||||
\(147\) | 10.6396 | − | 5.50745i | 0.877538 | − | 0.454247i | ||||
\(148\) | 4.92046 | + | 4.92046i | 0.404459 | + | 0.404459i | ||||
\(149\) | 10.2794 | − | 10.2794i | 0.842119 | − | 0.842119i | −0.147015 | − | 0.989134i | \(-0.546967\pi\) |
0.989134 | + | 0.147015i | \(0.0469665\pi\) | |||||||
\(150\) | −2.52015 | + | 7.92905i | −0.205769 | + | 0.647404i | ||||
\(151\) | −6.40358 | + | 6.40358i | −0.521116 | + | 0.521116i | −0.917908 | − | 0.396793i | \(-0.870123\pi\) |
0.396793 | + | 0.917908i | \(0.370123\pi\) | |||||||
\(152\) | 7.03084i | 0.570276i | ||||||||
\(153\) | 9.69625 | − | 13.7126i | 0.783895 | − | 1.10859i | ||||
\(154\) | 0.118776 | − | 0.118776i | 0.00957122 | − | 0.00957122i | ||||
\(155\) | −0.649285 | −0.0521519 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2127 | −0.815065 | −0.407532 | − | 0.913191i | \(-0.633611\pi\) | ||||
−0.407532 | + | 0.913191i | \(0.633611\pi\) | |||||||
\(158\) | −0.784083 | + | 0.784083i | −0.0623783 | + | 0.0623783i | ||||
\(159\) | 5.61098 | − | 2.90446i | 0.444980 | − | 0.230339i | ||||
\(160\) | − | 0.443277i | − | 0.0350441i | ||||||
\(161\) | 1.35549 | − | 1.35549i | 0.106828 | − | 0.106828i | ||||
\(162\) | 8.12132 | + | 3.87868i | 0.638071 | + | 0.304738i | ||||
\(163\) | −9.81476 | + | 9.81476i | −0.768751 | + | 0.768751i | −0.977887 | − | 0.209136i | \(-0.932935\pi\) |
0.209136 | + | 0.977887i | \(0.432935\pi\) | |||||||
\(164\) | −5.39512 | − | 5.39512i | −0.421288 | − | 0.421288i | ||||
\(165\) | −0.205726 | − | 0.397431i | −0.0160157 | − | 0.0309400i | ||||
\(166\) | − | 11.6394i | − | 0.903395i | ||||||
\(167\) | 9.48357 | + | 9.48357i | 0.733861 | + | 0.733861i | 0.971382 | − | 0.237522i | \(-0.0763350\pi\) |
−0.237522 | + | 0.971382i | \(0.576335\pi\) | |||||||
\(168\) | 0.229457 | + | 0.443277i | 0.0177030 | + | 0.0341996i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | − | 2.48152i | − | 0.190324i | ||||||
\(171\) | −20.7888 | + | 3.56679i | −1.58976 | + | 0.272759i | ||||
\(172\) | 3.76778 | 0.287290 | ||||||||
\(173\) | −1.10220 | −0.0837986 | −0.0418993 | − | 0.999122i | \(-0.513341\pi\) | ||||
−0.0418993 | + | 0.999122i | \(0.513341\pi\) | |||||||
\(174\) | 2.16687 | − | 6.81755i | 0.164270 | − | 0.516837i | ||||
\(175\) | −0.978833 | − | 0.978833i | −0.0739928 | − | 0.0739928i | ||||
\(176\) | −0.412157 | − | 0.412157i | −0.0310675 | − | 0.0310675i | ||||
\(177\) | 1.78758 | − | 5.62421i | 0.134363 | − | 0.422741i | ||||
\(178\) | −14.0824 | −1.05552 | ||||||||
\(179\) | −5.59555 | −0.418231 | −0.209115 | − | 0.977891i | \(-0.567058\pi\) | ||||
−0.209115 | + | 0.977891i | \(0.567058\pi\) | |||||||
\(180\) | 1.31068 | − | 0.224877i | 0.0976923 | − | 0.0167613i | ||||
\(181\) | − | 14.4687i | − | 1.07545i | −0.843119 | − | 0.537727i | \(-0.819283\pi\) | ||
0.843119 | − | 0.537727i | \(-0.180717\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.36919 | − | 16.1680i | −0.618668 | − | 1.19518i | ||||
\(184\) | −4.70360 | − | 4.70360i | −0.346754 | − | 0.346754i | ||||
\(185\) | 3.08458i | 0.226783i | ||||||||
\(186\) | −1.16626 | − | 2.25305i | −0.0855145 | − | 0.165201i | ||||
\(187\) | −2.30731 | − | 2.30731i | −0.168727 | − | 0.168727i | ||||
\(188\) | 3.71799 | − | 3.71799i | 0.271162 | − | 0.271162i | ||||
\(189\) | −1.19427 | + | 0.903335i | −0.0868707 | + | 0.0657079i | ||||
\(190\) | −2.20377 | + | 2.20377i | −0.159879 | + | 0.159879i | ||||
\(191\) | 6.67573i | 0.483039i | 0.970396 | + | 0.241520i | \(0.0776458\pi\) | ||||
−0.970396 | + | 0.241520i | \(0.922354\pi\) | |||||||
\(192\) | 1.53819 | − | 0.796225i | 0.111009 | − | 0.0574626i | ||||
\(193\) | −4.30947 | + | 4.30947i | −0.310203 | + | 0.310203i | −0.844988 | − | 0.534785i | \(-0.820392\pi\) |
0.534785 | + | 0.844988i | \(0.320392\pi\) | |||||||
\(194\) | 2.68390 | 0.192693 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.91695 | 0.494068 | ||||||||
\(197\) | 10.4569 | − | 10.4569i | 0.745022 | − | 0.745022i | −0.228518 | − | 0.973540i | \(-0.573388\pi\) |
0.973540 | + | 0.228518i | \(0.0733879\pi\) | |||||||
\(198\) | 1.00957 | − | 1.42775i | 0.0717472 | − | 0.101466i | ||||
\(199\) | − | 15.4803i | − | 1.09737i | −0.836028 | − | 0.548686i | \(-0.815128\pi\) | ||
0.836028 | − | 0.548686i | \(-0.184872\pi\) | |||||||
\(200\) | −3.39659 | + | 3.39659i | −0.240175 | + | 0.240175i | ||||
\(201\) | 4.64494 | − | 14.6142i | 0.327629 | − | 1.03081i | ||||
\(202\) | 10.0696 | − | 10.0696i | 0.708497 | − | 0.708497i | ||||
\(203\) | 0.841620 | + | 0.841620i | 0.0590701 | + | 0.0590701i | ||||
\(204\) | 8.61098 | − | 4.45737i | 0.602889 | − | 0.312078i | ||||
\(205\) | − | 3.38214i | − | 0.236219i | ||||||
\(206\) | −3.25908 | − | 3.25908i | −0.227071 | − | 0.227071i | ||||
\(207\) | 11.5214 | − | 16.2938i | 0.800795 | − | 1.13249i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.09812i | 0.283473i | ||||||||
\(210\) | −0.0670206 | + | 0.210865i | −0.00462486 | + | 0.0145510i | ||||
\(211\) | 18.8144 | 1.29524 | 0.647619 | − | 0.761964i | \(-0.275765\pi\) | ||||
0.647619 | + | 0.761964i | \(0.275765\pi\) | |||||||
\(212\) | 3.64778 | 0.250531 | ||||||||
\(213\) | 25.3980 | + | 8.07243i | 1.74024 | + | 0.553114i | ||||
\(214\) | −9.55443 | − | 9.55443i | −0.653127 | − | 0.653127i | ||||
\(215\) | 1.18099 | + | 1.18099i | 0.0805427 | + | 0.0805427i | ||||
\(216\) | 3.13461 | + | 4.14418i | 0.213283 | + | 0.281976i | ||||
\(217\) | 0.422110 | 0.0286547 | ||||||||
\(218\) | −2.91594 | −0.197492 | ||||||||
\(219\) | −8.21837 | − | 2.61210i | −0.555346 | − | 0.176510i | ||||
\(220\) | − | 0.258376i | − | 0.0174197i | ||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.7036 | + | 5.54059i | −0.718379 | + | 0.371860i | ||||
\(223\) | −5.08804 | − | 5.08804i | −0.340720 | − | 0.340720i | 0.515918 | − | 0.856638i | \(-0.327451\pi\) |
−0.856638 | + | 0.515918i | \(0.827451\pi\) | |||||||
\(224\) | 0.288181i | 0.0192549i | ||||||||
\(225\) | −11.7661 | − | 8.31992i | −0.784409 | − | 0.554661i | ||||
\(226\) | 7.36568 | + | 7.36568i | 0.489958 | + | 0.489958i | ||||
\(227\) | 3.79025 | − | 3.79025i | 0.251568 | − | 0.251568i | −0.570045 | − | 0.821613i | \(-0.693074\pi\) |
0.821613 | + | 0.570045i | \(0.193074\pi\) | |||||||
\(228\) | −11.6057 | − | 3.68871i | −0.768604 | − | 0.244291i | ||||
\(229\) | −8.24846 | + | 8.24846i | −0.545074 | + | 0.545074i | −0.925012 | − | 0.379938i | \(-0.875945\pi\) |
0.379938 | + | 0.925012i | \(0.375945\pi\) | |||||||
\(230\) | − | 2.94863i | − | 0.194427i | ||||||
\(231\) | 0.133745 | + | 0.258376i | 0.00879979 | + | 0.0169999i | ||||
\(232\) | 2.92046 | − | 2.92046i | 0.191737 | − | 0.191737i | ||||
\(233\) | −9.54763 | −0.625486 | −0.312743 | − | 0.949838i | \(-0.601248\pi\) | ||||
−0.312743 | + | 0.949838i | \(0.601248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.33077 | 0.152042 | ||||||||
\(236\) | 2.40926 | − | 2.40926i | 0.156829 | − | 0.156829i | ||||
\(237\) | −0.882903 | − | 1.70564i | −0.0573507 | − | 0.110793i | ||||
\(238\) | 1.61328i | 0.104573i | ||||||||
\(239\) | −20.6375 | + | 20.6375i | −1.33493 | + | 1.33493i | −0.434036 | + | 0.900895i | \(0.642911\pi\) |
−0.900895 | + | 0.434036i | \(0.857089\pi\) | |||||||
\(240\) | 0.731708 | + | 0.232564i | 0.0472316 | + | 0.0150120i | ||||
\(241\) | −7.88702 | + | 7.88702i | −0.508048 | + | 0.508048i | −0.913927 | − | 0.405879i | \(-0.866965\pi\) |
0.405879 | + | 0.913927i | \(0.366965\pi\) | |||||||
\(242\) | 7.53794 | + | 7.53794i | 0.484557 | + | 0.484557i | ||||
\(243\) | −10.6633 | + | 11.3708i | −0.684050 | + | 0.729435i | ||||
\(244\) | − | 10.5111i | − | 0.672903i | ||||||
\(245\) | 2.16808 | + | 2.16808i | 0.138513 | + | 0.138513i | ||||
\(246\) | 11.7362 | − | 6.07508i | 0.748270 | − | 0.387333i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 1.46474i | − | 0.0930111i | ||||||
\(249\) | 19.2130 | + | 6.10660i | 1.21757 | + | 0.386990i | ||||
\(250\) | −4.34567 | −0.274844 | ||||||||
\(251\) | −4.46952 | −0.282113 | −0.141057 | − | 0.990002i | \(-0.545050\pi\) | ||||
−0.141057 | + | 0.990002i | \(0.545050\pi\) | |||||||
\(252\) | −0.852093 | + | 0.146196i | −0.0536768 | + | 0.00920948i | ||||
\(253\) | −2.74162 | − | 2.74162i | −0.172364 | − | 0.172364i | ||||
\(254\) | 0.170733 | + | 0.170733i | 0.0107127 | + | 0.0107127i | ||||
\(255\) | 4.09620 | + | 1.30192i | 0.256514 | + | 0.0815297i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.9483 | 0.745315 | 0.372658 | − | 0.927969i | \(-0.378447\pi\) | ||||
0.372658 | + | 0.927969i | \(0.378447\pi\) | |||||||
\(258\) | −1.97676 | + | 6.21940i | −0.123067 | + | 0.387203i | ||||
\(259\) | − | 2.00533i | − | 0.124605i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1168 | + | 7.15363i | 0.626211 | + | 0.442798i | ||||
\(262\) | 5.72080 | + | 5.72080i | 0.353432 | + | 0.353432i | ||||
\(263\) | − | 2.75121i | − | 0.169647i | −0.996396 | − | 0.0848234i | \(-0.972967\pi\) | ||
0.996396 | − | 0.0848234i | \(-0.0270326\pi\) | |||||||
\(264\) | 0.896575 | − | 0.464102i | 0.0551804 | − | 0.0285635i | ||||
\(265\) | 1.14338 | + | 1.14338i | 0.0702371 | + | 0.0702371i | ||||
\(266\) | 1.43271 | − | 1.43271i | 0.0878449 | − | 0.0878449i | ||||
\(267\) | 7.38828 | − | 23.2455i | 0.452155 | − | 1.42260i | ||||
\(268\) | 6.26033 | − | 6.26033i | 0.382410 | − | 0.382410i | ||||
\(269\) | − | 6.24027i | − | 0.380476i | −0.981738 | − | 0.190238i | \(-0.939074\pi\) | ||
0.981738 | − | 0.190238i | \(-0.0609260\pi\) | |||||||
\(270\) | −0.316445 | + | 2.28149i | −0.0192582 | + | 0.138847i | ||||
\(271\) | 15.8164 | − | 15.8164i | 0.960780 | − | 0.960780i | −0.0384794 | − | 0.999259i | \(-0.512251\pi\) |
0.999259 | + | 0.0384794i | \(0.0122514\pi\) | |||||||
\(272\) | 5.59813 | 0.339437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0827063 | −0.00499647 | ||||||||
\(275\) | −1.97980 | + | 1.97980i | −0.119386 | + | 0.119386i | ||||
\(276\) | 10.2319 | − | 5.29641i | 0.615887 | − | 0.318806i | ||||
\(277\) | 5.59837i | 0.336374i | 0.985755 | + | 0.168187i | \(0.0537912\pi\) | ||||
−0.985755 | + | 0.168187i | \(0.946209\pi\) | |||||||
\(278\) | 4.41337 | − | 4.41337i | 0.264697 | − | 0.264697i | ||||
\(279\) | 4.33094 | − | 0.743071i | 0.259286 | − | 0.0444865i | ||||
\(280\) | −0.0903287 | + | 0.0903287i | −0.00539817 | + | 0.00539817i | ||||
\(281\) | −8.82870 | − | 8.82870i | −0.526676 | − | 0.526676i | 0.392903 | − | 0.919580i | \(-0.371471\pi\) |
−0.919580 | + | 0.392903i | \(0.871471\pi\) | |||||||
\(282\) | 4.18658 | + | 8.08785i | 0.249307 | + | 0.481624i | ||||
\(283\) | − | 6.85872i | − | 0.407709i | −0.979001 | − | 0.203854i | \(-0.934653\pi\) | ||
0.979001 | − | 0.203854i | \(-0.0653469\pi\) | |||||||
\(284\) | 10.8798 | + | 10.8798i | 0.645598 | + | 0.645598i | ||||
\(285\) | −2.48152 | − | 4.79393i | −0.146993 | − | 0.283968i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19878i | 0.129790i | ||||||||
\(288\) | 0.507306 | + | 2.95680i | 0.0298933 | + | 0.174231i | ||||
\(289\) | 14.3391 | 0.843474 | ||||||||
\(290\) | 1.83080 | 0.107508 | ||||||||
\(291\) | −1.40810 | + | 4.43026i | −0.0825445 | + | 0.259707i | ||||
\(292\) | −3.52053 | − | 3.52053i | −0.206023 | − | 0.206023i | ||||
\(293\) | −19.3431 | − | 19.3431i | −1.13004 | − | 1.13004i | −0.990170 | − | 0.139867i | \(-0.955333\pi\) |
−0.139867 | − | 0.990170i | \(-0.544667\pi\) | |||||||
\(294\) | −3.62896 | + | 11.4177i | −0.211645 | + | 0.665892i | ||||
\(295\) | 1.51034 | 0.0879352 | ||||||||
\(296\) | −6.95858 | −0.404459 | ||||||||
\(297\) | 1.82709 | + | 2.41555i | 0.106019 | + | 0.140164i | ||||
\(298\) | 14.5372i | 0.842119i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.82467 | − | 7.38870i | −0.220818 | − | 0.426587i | ||||
\(301\) | −0.767778 | − | 0.767778i | −0.0442540 | − | 0.0442540i | ||||
\(302\) | − | 9.05603i | − | 0.521116i | ||||||
\(303\) | 11.3387 | + | 21.9047i | 0.651393 | + | 1.25839i | ||||
\(304\) | −4.97155 | − | 4.97155i | −0.285138 | − | 0.285138i | ||||
\(305\) | 3.29464 | − | 3.29464i | 0.188650 | − | 0.188650i | ||||
\(306\) | 2.83996 | + | 16.5525i | 0.162350 | + | 0.946245i | ||||
\(307\) | −15.4869 | + | 15.4869i | −0.883883 | + | 0.883883i | −0.993927 | − | 0.110044i | \(-0.964901\pi\) |
0.110044 | + | 0.993927i | \(0.464901\pi\) | |||||||
\(308\) | 0.167974i | 0.00957122i | ||||||||
\(309\) | 7.08956 | − | 3.66983i | 0.403311 | − | 0.208769i | ||||
\(310\) | 0.459114 | − | 0.459114i | 0.0260759 | − | 0.0260759i | ||||
\(311\) | 31.8012 | 1.80328 | 0.901642 | − | 0.432484i | \(-0.142363\pi\) | ||||
0.901642 | + | 0.432484i | \(0.142363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.7424 | −1.34200 | −0.670999 | − | 0.741458i | \(-0.734135\pi\) | ||||
−0.670999 | + | 0.741458i | \(0.734135\pi\) | |||||||
\(314\) | 7.22149 | − | 7.22149i | 0.407532 | − | 0.407532i | ||||
\(315\) | −0.312908 | − | 0.221259i | −0.0176303 | − | 0.0124665i | ||||
\(316\) | − | 1.10886i | − | 0.0623783i | ||||||
\(317\) | 16.8936 | − | 16.8936i | 0.948841 | − | 0.948841i | −0.0499128 | − | 0.998754i | \(-0.515894\pi\) |
0.998754 | + | 0.0499128i | \(0.0158944\pi\) | |||||||
\(318\) | −1.91380 | + | 6.02133i | −0.107321 | + | 0.337659i | ||||
\(319\) | 1.70227 | − | 1.70227i | 0.0953087 | − | 0.0953087i | ||||
\(320\) | 0.313444 | + | 0.313444i | 0.0175221 | + | 0.0175221i | ||||
\(321\) | 20.7840 | − | 10.7586i | 1.16005 | − | 0.600486i | ||||
\(322\) | 1.91695i | 0.106828i | ||||||||
\(323\) | −27.8314 | − | 27.8314i | −1.54858 | − | 1.54858i | ||||
\(324\) | −8.48528 | + | 3.00000i | −0.471405 | + | 0.166667i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.8802i | − | 0.768751i | ||||||
\(327\) | 1.52984 | − | 4.81329i | 0.0846004 | − | 0.266175i | ||||
\(328\) | 7.62986 | 0.421288 | ||||||||
\(329\) | −1.51527 | −0.0835393 | ||||||||
\(330\) | 0.426496 | + | 0.135556i | 0.0234778 | + | 0.00746213i | ||||
\(331\) | −11.6586 | − | 11.6586i | −0.640813 | − | 0.640813i | 0.309942 | − | 0.950755i | \(-0.399690\pi\) |
−0.950755 | + | 0.309942i | \(0.899690\pi\) | |||||||
\(332\) | 8.23032 | + | 8.23032i | 0.451697 | + | 0.451697i | ||||
\(333\) | −3.53013 | − | 20.5751i | −0.193450 | − | 1.12751i | ||||
\(334\) | −13.4118 | −0.733861 | ||||||||
\(335\) | 3.92453 | 0.214420 | ||||||||
\(336\) | −0.475695 | − | 0.151194i | −0.0259513 | − | 0.00824828i | ||||
\(337\) | − | 3.24846i | − | 0.176955i | −0.996078 | − | 0.0884775i | \(-0.971800\pi\) | ||
0.996078 | − | 0.0884775i | \(-0.0282001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0228 | + | 8.29400i | −0.870238 | + | 0.450468i | ||||
\(340\) | 1.75470 | + | 1.75470i | 0.0951620 | + | 0.0951620i | ||||
\(341\) | − | 0.853764i | − | 0.0462339i | ||||||
\(342\) | 12.1778 | − | 17.2220i | 0.658498 | − | 0.931257i | ||||
\(343\) | −2.83592 | − | 2.83592i | −0.153125 | − | 0.153125i | ||||
\(344\) | −2.66422 | + | 2.66422i | −0.143645 | + | 0.143645i | ||||
\(345\) | 4.86725 | + | 1.54699i | 0.262044 | + | 0.0832873i | ||||
\(346\) | 0.779372 | − | 0.779372i | 0.0418993 | − | 0.0418993i | ||||
\(347\) | 8.21818i | 0.441175i | 0.975367 | + | 0.220587i | \(0.0707974\pi\) | ||||
−0.975367 | + | 0.220587i | \(0.929203\pi\) | |||||||
\(348\) | 3.28853 | + | 6.35295i | 0.176284 | + | 0.340554i | ||||
\(349\) | −5.66593 | + | 5.66593i | −0.303290 | + | 0.303290i | −0.842300 | − | 0.539010i | \(-0.818799\pi\) |
0.539010 | + | 0.842300i | \(0.318799\pi\) | |||||||
\(350\) | 1.38428 | 0.0739928 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.582877 | 0.0310675 | ||||||||
\(353\) | −1.97680 | + | 1.97680i | −0.105214 | + | 0.105214i | −0.757754 | − | 0.652540i | \(-0.773703\pi\) |
0.652540 | + | 0.757754i | \(0.273703\pi\) | |||||||
\(354\) | 2.71290 | + | 5.24093i | 0.144189 | + | 0.278552i | ||||
\(355\) | 6.82043i | 0.361991i | ||||||||
\(356\) | 9.95774 | − | 9.95774i | 0.527759 | − | 0.527759i | ||||
\(357\) | −2.66300 | − | 0.846401i | −0.140941 | − | 0.0447963i | ||||
\(358\) | 3.95665 | − | 3.95665i | 0.209115 | − | 0.209115i | ||||
\(359\) | 11.6531 | + | 11.6531i | 0.615028 | + | 0.615028i | 0.944252 | − | 0.329224i | \(-0.106787\pi\) |
−0.329224 | + | 0.944252i | \(0.606787\pi\) | |||||||
\(360\) | −0.767778 | + | 1.08580i | −0.0404655 | + | 0.0572268i | ||||
\(361\) | 30.4327i | 1.60172i | ||||||||
\(362\) | 10.2309 | + | 10.2309i | 0.537727 | + | 0.537727i | ||||
\(363\) | −16.3975 | + | 8.48796i | −0.860645 | + | 0.445503i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.20698i | − | 0.115519i | ||||||
\(366\) | 17.3504 | + | 5.51461i | 0.906922 | + | 0.288253i | ||||
\(367\) | −37.1859 | −1.94109 | −0.970544 | − | 0.240924i | \(-0.922550\pi\) | ||||
−0.970544 | + | 0.240924i | \(0.922550\pi\) | |||||||
\(368\) | 6.65190 | 0.346754 | ||||||||
\(369\) | 3.87067 | + | 22.5599i | 0.201499 | + | 1.17442i | ||||
\(370\) | −2.18112 | − | 2.18112i | −0.113391 | − | 0.113391i | ||||
\(371\) | −0.743327 | − | 0.743327i | −0.0385916 | − | 0.0385916i | ||||
\(372\) | 2.41782 | + | 0.768472i | 0.125358 | + | 0.0398434i | ||||
\(373\) | −7.88823 | −0.408437 | −0.204219 | − | 0.978925i | \(-0.565465\pi\) | ||||
−0.204219 | + | 0.978925i | \(0.565465\pi\) | |||||||
\(374\) | 3.26302 | 0.168727 | ||||||||
\(375\) | 2.27994 | − | 7.17331i | 0.117736 | − | 0.370428i | ||||
\(376\) | 5.25803i | 0.271162i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.205726 | − | 1.48323i | 0.0105814 | − | 0.0762893i | ||||
\(379\) | 1.31661 | + | 1.31661i | 0.0676295 | + | 0.0676295i | 0.740113 | − | 0.672483i | \(-0.234772\pi\) |
−0.672483 | + | 0.740113i | \(0.734772\pi\) | |||||||
\(380\) | − | 3.11661i | − | 0.159879i | ||||||
\(381\) | −0.371400 | + | 0.192251i | −0.0190274 | + | 0.00984931i | ||||
\(382\) | −4.72046 | − | 4.72046i | −0.241520 | − | 0.241520i | ||||
\(383\) | 2.03681 | − | 2.03681i | 0.104076 | − | 0.104076i | −0.653151 | − | 0.757227i | \(-0.726553\pi\) |
0.757227 | + | 0.653151i | \(0.226553\pi\) | |||||||
\(384\) | −0.524648 | + | 1.65068i | −0.0267733 | + | 0.0842359i | ||||
\(385\) | −0.0526505 | + | 0.0526505i | −0.00268332 | + | 0.00268332i | ||||
\(386\) | − | 6.09452i | − | 0.310203i | ||||||
\(387\) | −9.22913 | − | 6.52598i | −0.469143 | − | 0.331734i | ||||
\(388\) | −1.89781 | + | 1.89781i | −0.0963465 | + | 0.0963465i | ||||
\(389\) | −23.4187 | −1.18738 | −0.593688 | − | 0.804695i | \(-0.702329\pi\) | ||||
−0.593688 | + | 0.804695i | \(0.702329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.2382 | 1.88322 | ||||||||
\(392\) | −4.89102 | + | 4.89102i | −0.247034 | + | 0.247034i | ||||
\(393\) | −12.4446 | + | 6.44181i | −0.627748 | + | 0.324946i | ||||
\(394\) | 14.7883i | 0.745022i | ||||||||
\(395\) | 0.347566 | − | 0.347566i | 0.0174879 | − | 0.0174879i | ||||
\(396\) | 0.295697 | + | 1.72345i | 0.0148593 | + | 0.0866066i | ||||
\(397\) | 13.0162 | − | 13.0162i | 0.653266 | − | 0.653266i | −0.300512 | − | 0.953778i | \(-0.597157\pi\) |
0.953778 | + | 0.300512i | \(0.0971575\pi\) | |||||||
\(398\) | 10.9463 | + | 10.9463i | 0.548686 | + | 0.548686i | ||||
\(399\) | 1.61328 | + | 3.11661i | 0.0807648 | + | 0.156026i | ||||
\(400\) | − | 4.80351i | − | 0.240175i | ||||||
\(401\) | −4.79769 | − | 4.79769i | −0.239585 | − | 0.239585i | 0.577093 | − | 0.816678i | \(-0.304187\pi\) |
−0.816678 | + | 0.577093i | \(0.804187\pi\) | |||||||
\(402\) | 7.04933 | + | 13.6183i | 0.351589 | + | 0.679217i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.2406i | 0.708497i | ||||||||
\(405\) | −3.59999 | − | 1.71933i | −0.178885 | − | 0.0854342i | ||||
\(406\) | −1.19023 | −0.0590701 | ||||||||
\(407\) | −4.05600 | −0.201048 | ||||||||
\(408\) | −2.93705 | + | 9.24072i | −0.145405 | + | 0.457484i | ||||
\(409\) | 20.7093 | + | 20.7093i | 1.02401 | + | 1.02401i | 0.999705 | + | 0.0243059i | \(0.00773758\pi\) |
0.0243059 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(410\) | 2.39153 | + | 2.39153i | 0.118109 | + | 0.118109i | ||||
\(411\) | 0.0433917 | − | 0.136522i | 0.00214035 | − | 0.00673412i | ||||
\(412\) | 4.60903 | 0.227071 | ||||||||
\(413\) | −0.981893 | −0.0483158 | ||||||||
\(414\) | 3.37455 | + | 19.6683i | 0.165850 | + | 0.966645i | ||||
\(415\) | 5.15949i | 0.253269i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.96960 | + | 9.60053i | 0.243362 | + | 0.470140i | ||||
\(418\) | −2.89781 | − | 2.89781i | −0.141736 | − | 0.141736i | ||||
\(419\) | 9.24219i | 0.451510i | 0.974184 | + | 0.225755i | \(0.0724850\pi\) | ||||
−0.974184 | + | 0.225755i | \(0.927515\pi\) | |||||||
\(420\) | −0.101713 | − | 0.196494i | −0.00496309 | − | 0.00958795i | ||||
\(421\) | −18.4490 | − | 18.4490i | −0.899149 | − | 0.899149i | 0.0962115 | − | 0.995361i | \(-0.469327\pi\) |
−0.995361 | + | 0.0962115i | \(0.969327\pi\) | |||||||
\(422\) | −13.3038 | + | 13.3038i | −0.647619 | + | 0.647619i | ||||
\(423\) | −15.5469 | + | 2.66743i | −0.755918 | + | 0.129695i | ||||
\(424\) | −2.57937 | + | 2.57937i | −0.125265 | + | 0.125265i | ||||
\(425\) | − | 26.8906i | − | 1.30439i | ||||||
\(426\) | −23.6672 | + | 12.2510i | −1.14668 | + | 0.593564i | ||||
\(427\) | −2.14189 | + | 2.14189i | −0.103653 | + | 0.103653i | ||||
\(428\) | 13.5120 | 0.653127 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.67017 | −0.0805427 | ||||||||
\(431\) | −15.8134 | + | 15.8134i | −0.761705 | + | 0.761705i | −0.976630 | − | 0.214925i | \(-0.931049\pi\) |
0.214925 | + | 0.976630i | \(0.431049\pi\) | |||||||
\(432\) | −5.14688 | − | 0.713876i | −0.247629 | − | 0.0343464i | ||||
\(433\) | − | 3.94803i | − | 0.189730i | −0.995490 | − | 0.0948652i | \(-0.969758\pi\) | ||
0.995490 | − | 0.0948652i | \(-0.0302420\pi\) | |||||||
\(434\) | −0.298477 | + | 0.298477i | −0.0143274 | + | 0.0143274i | ||||
\(435\) | −0.960525 | + | 3.02206i | −0.0460536 | + | 0.144897i | ||||
\(436\) | 2.06188 | − | 2.06188i | 0.0987462 | − | 0.0987462i | ||||
\(437\) | −33.0703 | − | 33.0703i | −1.58197 | − | 1.58197i | ||||
\(438\) | 7.65830 | − | 3.96423i | 0.365928 | − | 0.189418i | ||||
\(439\) | 18.3100i | 0.873889i | 0.899489 | + | 0.436944i | \(0.143939\pi\) | ||||
−0.899489 | + | 0.436944i | \(0.856061\pi\) | |||||||
\(440\) | 0.182699 | + | 0.182699i | 0.00870986 | + | 0.00870986i | ||||
\(441\) | −16.9430 | − | 11.9805i | −0.806810 | − | 0.570501i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.86371i | − | 0.278593i | −0.990251 | − | 0.139297i | \(-0.955516\pi\) | ||
0.990251 | − | 0.139297i | \(-0.0444841\pi\) | |||||||
\(444\) | 3.65080 | − | 11.4864i | 0.173259 | − | 0.545120i | ||||
\(445\) | 6.24239 | 0.295918 | ||||||||
\(446\) | 7.19557 | 0.340720 | ||||||||
\(447\) | −23.9963 | − | 7.62693i | −1.13499 | − | 0.360741i | ||||
\(448\) | −0.203775 | − | 0.203775i | −0.00962745 | − | 0.00962745i | ||||
\(449\) | 20.1557 | + | 20.1557i | 0.951207 | + | 0.951207i | 0.998864 | − | 0.0476571i | \(-0.0151755\pi\) |
−0.0476571 | + | 0.998864i | \(0.515175\pi\) | |||||||
\(450\) | 14.2030 | − | 2.43685i | 0.669535 | − | 0.114874i | ||||
\(451\) | 4.44727 | 0.209414 | ||||||||
\(452\) | −10.4166 | −0.489958 | ||||||||
\(453\) | 14.9486 | + | 4.75122i | 0.702347 | + | 0.223232i | ||||
\(454\) | 5.36023i | 0.251568i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.8148 | − | 5.59813i | 0.506447 | − | 0.262156i | ||||
\(457\) | −13.5552 | − | 13.5552i | −0.634084 | − | 0.634084i | 0.315006 | − | 0.949090i | \(-0.397994\pi\) |
−0.949090 | + | 0.315006i | \(0.897994\pi\) | |||||||
\(458\) | − | 11.6651i | − | 0.545074i | ||||||
\(459\) | −28.8129 | − | 3.99637i | −1.34487 | − | 0.186535i | ||||
\(460\) | 2.08500 | + | 2.08500i | 0.0972136 | + | 0.0972136i | ||||
\(461\) | −20.9657 | + | 20.9657i | −0.976471 | + | 0.976471i | −0.999729 | − | 0.0232588i | \(-0.992596\pi\) |
0.0232588 | + | 0.999729i | \(0.492596\pi\) | |||||||
\(462\) | −0.277272 | − | 0.0881273i | −0.0128998 | − | 0.00410005i | ||||
\(463\) | 18.2554 | − | 18.2554i | 0.848400 | − | 0.848400i | −0.141533 | − | 0.989934i | \(-0.545203\pi\) |
0.989934 | + | 0.141533i | \(0.0452032\pi\) | |||||||
\(464\) | 4.13015i | 0.191737i | ||||||||
\(465\) | 0.516977 | + | 0.998724i | 0.0239743 | + | 0.0463147i | ||||
\(466\) | 6.75120 | − | 6.75120i | 0.312743 | − | 0.312743i | ||||
\(467\) | −32.4456 | −1.50140 | −0.750701 | − | 0.660642i | \(-0.770284\pi\) | ||||
−0.750701 | + | 0.660642i | \(0.770284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.55139 | −0.117812 | ||||||||
\(470\) | −1.64810 | + | 1.64810i | −0.0760212 | + | 0.0760212i | ||||
\(471\) | 8.13164 | + | 15.7091i | 0.374686 | + | 0.723838i | ||||
\(472\) | 3.40721i | 0.156829i | ||||||||
\(473\) | −1.55291 | + | 1.55291i | −0.0714031 | + | 0.0714031i | ||||
\(474\) | 1.83037 | + | 0.581761i | 0.0840719 | + | 0.0267212i | ||||
\(475\) | −23.8809 | + | 23.8809i | −1.09573 | + | 1.09573i | ||||
\(476\) | −1.14076 | − | 1.14076i | −0.0522865 | − | 0.0522865i | ||||
\(477\) | −8.93521 | − | 6.31815i | −0.409115 | − | 0.289288i | ||||
\(478\) | − | 29.1859i | − | 1.33493i | ||||||
\(479\) | −5.86220 | − | 5.86220i | −0.267851 | − | 0.267851i | 0.560383 | − | 0.828234i | \(-0.310654\pi\) |
−0.828234 | + | 0.560383i | \(0.810654\pi\) | |||||||
\(480\) | −0.681844 | + | 0.352948i | −0.0311218 | + | 0.0161098i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 11.1539i | − | 0.508048i | ||||||
\(483\) | −3.16427 | − | 1.00572i | −0.143979 | − | 0.0457620i | ||||
\(484\) | −10.6603 | −0.484557 | ||||||||
\(485\) | −1.18971 | −0.0540220 | ||||||||
\(486\) | −0.500258 | − | 15.5804i | −0.0226921 | − | 0.706743i | ||||
\(487\) | 22.7198 | + | 22.7198i | 1.02953 | + | 1.02953i | 0.999550 | + | 0.0299840i | \(0.00954563\pi\) |
0.0299840 | + | 0.999550i | \(0.490454\pi\) | |||||||
\(488\) | 7.43246 | + | 7.43246i | 0.336451 | + | 0.336451i | ||||
\(489\) | 22.9117 | + | 7.28219i | 1.03610 | + | 0.329312i | ||||
\(490\) | −3.06613 | −0.138513 | ||||||||
\(491\) | 26.4199 | 1.19231 | 0.596157 | − | 0.802868i | \(-0.296694\pi\) | ||||
0.596157 | + | 0.802868i | \(0.296694\pi\) | |||||||
\(492\) | −4.00299 | + | 12.5945i | −0.180469 | + | 0.567802i | ||||
\(493\) | 23.1211i | 1.04132i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.447520 | + | 0.632890i | −0.0201145 | + | 0.0284463i | ||||
\(496\) | 1.03573 | + | 1.03573i | 0.0465055 | + | 0.0465055i | ||||
\(497\) | − | 4.43406i | − | 0.198895i | ||||||
\(498\) | −17.9036 | + | 9.26761i | −0.802281 | + | 0.415291i | ||||
\(499\) | −9.27427 | − | 9.27427i | −0.415173 | − | 0.415173i | 0.468363 | − | 0.883536i | \(-0.344844\pi\) |
−0.883536 | + | 0.468363i | \(0.844844\pi\) | |||||||
\(500\) | 3.07285 | − | 3.07285i | 0.137422 | − | 0.137422i | ||||
\(501\) | 7.03647 | − | 22.1386i | 0.314366 | − | 0.989079i | ||||
\(502\) | 3.16043 | − | 3.16043i | 0.141057 | − | 0.141057i | ||||
\(503\) | 30.5434i | 1.36186i | 0.732348 | + | 0.680931i | \(0.238424\pi\) | ||||
−0.732348 | + | 0.680931i | \(0.761576\pi\) | |||||||
\(504\) | 0.499144 | − | 0.705897i | 0.0222337 | − | 0.0314431i | ||||
\(505\) | −4.46363 | + | 4.46363i | −0.198629 | + | 0.198629i | ||||
\(506\) | 3.87724 | 0.172364 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.241453 | −0.0107127 | ||||||||
\(509\) | −16.8650 | + | 16.8650i | −0.747529 | + | 0.747529i | −0.974014 | − | 0.226486i | \(-0.927276\pi\) |
0.226486 | + | 0.974014i | \(0.427276\pi\) | |||||||
\(510\) | −3.81705 | + | 1.97585i | −0.169022 | + | 0.0874921i | ||||
\(511\) | 1.43479i | 0.0634714i | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 22.0389 | + | 29.1371i | 0.973042 | + | 1.28643i | ||||
\(514\) | −8.44873 | + | 8.44873i | −0.372658 | + | 0.372658i | ||||
\(515\) | 1.44467 | + | 1.44467i | 0.0636599 | + | 0.0636599i | ||||
\(516\) | −3.00000 | − | 5.79555i | −0.132068 | − | 0.255135i | ||||
\(517\) | 3.06479i | 0.134789i | ||||||||
\(518\) | 1.41798 | + | 1.41798i | 0.0623026 | + | 0.0623026i | ||||
\(519\) | 0.877598 | + | 1.69539i | 0.0385223 | + | 0.0744193i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.5422i | 1.86381i | 0.362704 | + | 0.931904i | \(0.381854\pi\) | ||||
−0.362704 | + | 0.931904i | \(0.618146\pi\) | |||||||
\(522\) | −12.2120 | + | 2.09525i | −0.534505 | + | 0.0917065i | ||||
\(523\) | −34.0800 | −1.49021 | −0.745107 | − | 0.666945i | \(-0.767602\pi\) | ||||
−0.745107 | + | 0.666945i | \(0.767602\pi\) | |||||||
\(524\) | −8.09043 | −0.353432 | ||||||||
\(525\) | −0.726259 | + | 2.28500i | −0.0316965 | + | 0.0997257i | ||||
\(526\) | 1.94540 | + | 1.94540i | 0.0848234 | + | 0.0848234i | ||||
\(527\) | 5.79814 | + | 5.79814i | 0.252571 | + | 0.252571i | ||||
\(528\) | −0.305805 | + | 0.962144i | −0.0133085 | + | 0.0418719i | ||||
\(529\) | 21.2478 | 0.923816 | ||||||||
\(530\) | −1.61698 | −0.0702371 | ||||||||
\(531\) | −10.0744 | + | 1.72850i | −0.437192 | + | 0.0750104i | ||||
\(532\) | 2.02615i | 0.0878449i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 11.2127 | + | 21.6613i | 0.485222 | + | 0.937378i | ||||
\(535\) | 4.23526 | + | 4.23526i | 0.183106 | + | 0.183106i | ||||
\(536\) | 8.85344i | 0.382410i | ||||||||
\(537\) | 4.45532 | + | 8.60701i | 0.192261 | + | 0.371420i | ||||
\(538\) | 4.41254 | + | 4.41254i | 0.190238 | + | 0.190238i | ||||
\(539\) | −2.85087 | + | 2.85087i | −0.122796 | + | 0.122796i | ||||
\(540\) | −1.38950 | − | 1.83702i | −0.0597945 | − | 0.0790527i | ||||
\(541\) | 18.5013 | − | 18.5013i | 0.795434 | − | 0.795434i | −0.186938 | − | 0.982372i | \(-0.559856\pi\) |
0.982372 | + | 0.186938i | \(0.0598564\pi\) | |||||||
\(542\) | 22.3678i | 0.960780i | ||||||||
\(543\) | −22.2557 | + | 11.5204i | −0.955082 | + | 0.494387i | ||||
\(544\) | −3.95848 | + | 3.95848i | −0.169718 | + | 0.169718i | ||||
\(545\) | 1.29257 | 0.0553676 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.5058 | 1.68915 | 0.844573 | − | 0.535440i | \(-0.179854\pi\) | ||||
0.844573 | + | 0.535440i | \(0.179854\pi\) | |||||||
\(548\) | 0.0584822 | − | 0.0584822i | 0.00249824 | − | 0.00249824i | ||||
\(549\) | −18.2057 | + | 25.7468i | −0.777001 | + | 1.09885i | ||||
\(550\) | − | 2.79985i | − | 0.119386i | ||||||
\(551\) | 20.5332 | − | 20.5332i | 0.874746 | − | 0.874746i | ||||
\(552\) | −3.48990 | + | 10.9802i | −0.148540 | + | 0.467347i | ||||
\(553\) | −0.225958 | + | 0.225958i | −0.00960870 | + | 0.00960870i | ||||
\(554\) | −3.95865 | − | 3.95865i | −0.168187 | − | 0.168187i | ||||
\(555\) | 4.74466 | − | 2.45602i | 0.201400 | − | 0.104252i | ||||
\(556\) | 6.24145i | 0.264697i | ||||||||
\(557\) | −11.1678 | − | 11.1678i | −0.473193 | − | 0.473193i | 0.429753 | − | 0.902946i | \(-0.358601\pi\) |
−0.902946 | + | 0.429753i | \(0.858601\pi\) | |||||||
\(558\) | −2.53700 | + | 3.58786i | −0.107400 | + | 0.151886i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 0.127744i | − | 0.00539817i | ||||||
\(561\) | −1.71194 | + | 5.38621i | −0.0722781 | + | 0.227406i | ||||
\(562\) | 12.4857 | 0.526676 | ||||||||
\(563\) | 21.3812 | 0.901109 | 0.450555 | − | 0.892749i | \(-0.351226\pi\) | ||||
0.450555 | + | 0.892749i | \(0.351226\pi\) | |||||||
\(564\) | −8.67933 | − | 2.75862i | −0.365466 | − | 0.116159i | ||||
\(565\) | −3.26504 | − | 3.26504i | −0.137361 | − | 0.137361i | ||||
\(566\) | 4.84985 | + | 4.84985i | 0.203854 | + | 0.203854i | ||||
\(567\) | 2.34041 | + | 1.11776i | 0.0982880 | + | 0.0469416i | ||||
\(568\) | −15.3864 | −0.645598 | ||||||||
\(569\) | 29.0407 | 1.21745 | 0.608725 | − | 0.793382i | \(-0.291681\pi\) | ||||
0.608725 | + | 0.793382i | \(0.291681\pi\) | |||||||
\(570\) | 5.14452 | + | 1.63512i | 0.215480 | + | 0.0684877i | ||||
\(571\) | 9.91137i | 0.414778i | 0.978259 | + | 0.207389i | \(0.0664966\pi\) | ||||
−0.978259 | + | 0.207389i | \(0.933503\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.2685 | − | 5.31539i | 0.428974 | − | 0.222054i | ||||
\(574\) | −1.55477 | − | 1.55477i | −0.0648949 | − | 0.0648949i | ||||
\(575\) | − | 31.9524i | − | 1.33251i | ||||||
\(576\) | −2.44949 | − | 1.73205i | −0.102062 | − | 0.0721688i | ||||
\(577\) | −4.91283 | − | 4.91283i | −0.204524 | − | 0.204524i | 0.597411 | − | 0.801935i | \(-0.296196\pi\) |
−0.801935 | + | 0.597411i | \(0.796196\pi\) | |||||||
\(578\) | −10.1392 | + | 10.1392i | −0.421737 | + | 0.421737i | ||||
\(579\) | 10.0601 | + | 3.19747i | 0.418083 | + | 0.132882i | ||||
\(580\) | −1.29457 | + | 1.29457i | −0.0537541 | + | 0.0537541i | ||||
\(581\) | − | 3.35426i | − | 0.139158i | ||||||
\(582\) | −2.13699 | − | 4.12835i | −0.0885811 | − | 0.171126i | ||||
\(583\) | −1.50346 | + | 1.50346i | −0.0622669 | + | 0.0622669i | ||||
\(584\) | 4.97878 | 0.206023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.3553 | 1.13004 | ||||||||
\(587\) | −16.9836 | + | 16.9836i | −0.700989 | + | 0.700989i | −0.964623 | − | 0.263634i | \(-0.915079\pi\) |
0.263634 | + | 0.964623i | \(0.415079\pi\) | |||||||
\(588\) | −5.50745 | − | 10.6396i | −0.227123 | − | 0.438769i | ||||
\(589\) | − | 10.2983i | − | 0.424336i | ||||||
\(590\) | −1.06797 | + | 1.06797i | −0.0439676 | + | 0.0439676i | ||||
\(591\) | −24.4107 | − | 7.75863i | −1.00412 | − | 0.319147i | ||||
\(592\) | 4.92046 | − | 4.92046i | 0.202229 | − | 0.202229i | ||||
\(593\) | 22.0744 | + | 22.0744i | 0.906489 | + | 0.906489i | 0.995987 | − | 0.0894984i | \(-0.0285264\pi\) |
−0.0894984 | + | 0.995987i | \(0.528526\pi\) | |||||||
\(594\) | −3.00000 | − | 0.416102i | −0.123091 | − | 0.0170729i | ||||
\(595\) | − | 0.715128i | − | 0.0293174i | ||||||
\(596\) | −10.2794 | − | 10.2794i | −0.421060 | − | 0.421060i | ||||
\(597\) | −23.8117 | + | 12.3258i | −0.974548 | + | 0.504463i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.2538i | − | 1.44043i | −0.693750 | − | 0.720216i | \(-0.744043\pi\) | ||
0.693750 | − | 0.720216i | \(-0.255957\pi\) | |||||||
\(600\) | 7.92905 | + | 2.52015i | 0.323702 | + | 0.102885i | ||||
\(601\) | 20.1767 | 0.823023 | 0.411512 | − | 0.911405i | \(-0.365001\pi\) | ||||
0.411512 | + | 0.911405i | \(0.365001\pi\) | |||||||
\(602\) | 1.08580 | 0.0442540 | ||||||||
\(603\) | −26.1778 | + | 4.49140i | −1.06604 | + | 0.182904i | ||||
\(604\) | 6.40358 | + | 6.40358i | 0.260558 | + | 0.260558i | ||||
\(605\) | −3.34139 | − | 3.34139i | −0.135847 | − | 0.135847i | ||||
\(606\) | −23.5067 | − | 7.47130i | −0.954894 | − | 0.303501i | ||||
\(607\) | −4.85675 | −0.197129 | −0.0985647 | − | 0.995131i | \(-0.531425\pi\) | ||||
−0.0985647 | + | 0.995131i | \(0.531425\pi\) | |||||||
\(608\) | 7.03084 | 0.285138 | ||||||||
\(609\) | 0.624452 | − | 1.96469i | 0.0253041 | − | 0.0796132i | ||||
\(610\) | 4.65932i | 0.188650i | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −13.7126 | − | 9.69625i | −0.554297 | − | 0.391948i | ||||
\(613\) | −0.643275 | − | 0.643275i | −0.0259816 | − | 0.0259816i | 0.693997 | − | 0.719978i | \(-0.255848\pi\) |
−0.719978 | + | 0.693997i | \(0.755848\pi\) | |||||||
\(614\) | − | 21.9018i | − | 0.883883i | ||||||
\(615\) | −5.20237 | + | 2.69294i | −0.209780 | + | 0.108590i | ||||
\(616\) | −0.118776 | − | 0.118776i | −0.00478561 | − | 0.00478561i | ||||
\(617\) | 31.8135 | − | 31.8135i | 1.28076 | − | 1.28076i | 0.340529 | − | 0.940234i | \(-0.389394\pi\) |
0.940234 | − | 0.340529i | \(-0.110606\pi\) | |||||||
\(618\) | −2.41812 | + | 7.60804i | −0.0972709 | + | 0.306040i | ||||
\(619\) | 11.7433 | − | 11.7433i | 0.472003 | − | 0.472003i | −0.430559 | − | 0.902562i | \(-0.641684\pi\) |
0.902562 | + | 0.430559i | \(0.141684\pi\) | |||||||
\(620\) | 0.649285i | 0.0260759i | ||||||||
\(621\) | −34.2365 | − | 4.74863i | −1.37386 | − | 0.190556i | ||||
\(622\) | −22.4869 | + | 22.4869i | −0.901642 | + | 0.901642i | ||||
\(623\) | −4.05827 | −0.162591 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.0912 | −0.883648 | ||||||||
\(626\) | 16.7884 | − | 16.7884i | 0.670999 | − | 0.670999i | ||||
\(627\) | 6.30368 | − | 3.26302i | 0.251745 | − | 0.130313i | ||||
\(628\) | 10.2127i | 0.407532i | ||||||||
\(629\) | 27.5454 | − | 27.5454i | 1.09831 | − | 1.09831i | ||||
\(630\) | 0.377713 | − | 0.0648053i | 0.0150484 | − | 0.00258190i | ||||
\(631\) | 25.8085 | − | 25.8085i | 1.02742 | − | 1.02742i | 0.0278066 | − | 0.999613i | \(-0.491148\pi\) |
0.999613 | − | 0.0278066i | \(-0.00885225\pi\) | |||||||
\(632\) | 0.784083 | + | 0.784083i | 0.0311891 | + | 0.0311891i | ||||
\(633\) | −14.9805 | − | 28.9401i | −0.595422 | − | 1.15027i | ||||
\(634\) | 23.8912i | 0.948841i | ||||||||
\(635\) | −0.0756820 | − | 0.0756820i | −0.00300335 | − | 0.00300335i | ||||
\(636\) | −2.90446 | − | 5.61098i | −0.115169 | − | 0.222490i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.40737i | 0.0953087i | ||||||||
\(639\) | −7.80560 | − | 45.4944i | −0.308785 | − | 1.79973i | ||||
\(640\) | −0.443277 | −0.0175221 | ||||||||
\(641\) | 0.848907 | 0.0335298 | 0.0167649 | − | 0.999859i | \(-0.494663\pi\) | ||||
0.0167649 | + | 0.999859i | \(0.494663\pi\) | |||||||
\(642\) | −7.08904 | + | 22.3040i | −0.279782 | + | 0.880269i | ||||
\(643\) | 12.2124 | + | 12.2124i | 0.481610 | + | 0.481610i | 0.905645 | − | 0.424036i | \(-0.139387\pi\) |
−0.424036 | + | 0.905645i | \(0.639387\pi\) | |||||||
\(644\) | −1.35549 | − | 1.35549i | −0.0534138 | − | 0.0534138i | ||||
\(645\) | 0.876250 | − | 2.75692i | 0.0345023 | − | 0.108553i | ||||
\(646\) | 39.3595 | 1.54858 | ||||||||
\(647\) | −15.7525 | −0.619293 | −0.309646 | − | 0.950852i | \(-0.600211\pi\) | ||||
−0.309646 | + | 0.950852i | \(0.600211\pi\) | |||||||
\(648\) | 3.87868 | − | 8.12132i | 0.152369 | − | 0.319036i | ||||
\(649\) | 1.98598i | 0.0779567i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.336095 | − | 0.649285i | −0.0131726 | − | 0.0254475i | ||||
\(652\) | 9.81476 | + | 9.81476i | 0.384376 | + | 0.384376i | ||||
\(653\) | 24.6413i | 0.964289i | 0.876092 | + | 0.482145i | \(0.160142\pi\) | ||||
−0.876092 | + | 0.482145i | \(0.839858\pi\) | |||||||
\(654\) | 2.32175 | + | 4.48527i | 0.0907874 | + | 0.175388i | ||||
\(655\) | −2.53590 | − | 2.53590i | −0.0990857 | − | 0.0990857i | ||||
\(656\) | −5.39512 | + | 5.39512i | −0.210644 | + | 0.210644i | ||||
\(657\) | 2.52576 | + | 14.7212i | 0.0985394 | + | 0.574330i | ||||
\(658\) | 1.07145 | − | 1.07145i | 0.0417697 | − | 0.0417697i | ||||
\(659\) | 17.7144i | 0.690056i | 0.938592 | + | 0.345028i | \(0.112131\pi\) | ||||
−0.938592 | + | 0.345028i | \(0.887869\pi\) | |||||||
\(660\) | −0.397431 | + | 0.205726i | −0.0154700 | + | 0.00800786i | ||||
\(661\) | 6.70314 | − | 6.70314i | 0.260722 | − | 0.260722i | −0.564625 | − | 0.825347i | \(-0.690979\pi\) |
0.825347 | + | 0.564625i | \(0.190979\pi\) | |||||||
\(662\) | 16.4877 | 0.640813 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.6394 | −0.451697 | ||||||||
\(665\) | −0.635086 | + | 0.635086i | −0.0246276 | + | 0.0246276i | ||||
\(666\) | 17.0450 | + | 12.0526i | 0.660479 | + | 0.467029i | ||||
\(667\) | 27.4733i | 1.06377i | ||||||||
\(668\) | 9.48357 | − | 9.48357i | 0.366930 | − | 0.366930i | ||||
\(669\) | −3.77514 | + | 11.8776i | −0.145955 | + | 0.459214i | ||||
\(670\) | −2.77506 | + | 2.77506i | −0.107210 | + | 0.107210i | ||||
\(671\) | 4.33221 | + | 4.33221i | 0.167243 | + | 0.167243i | ||||
\(672\) | 0.443277 | − | 0.229457i | 0.0170998 | − | 0.00885150i | ||||
\(673\) | − | 0.173307i | − | 0.00668051i | −0.999994 | − | 0.00334025i | \(-0.998937\pi\) | ||
0.999994 | − | 0.00334025i | \(-0.00106324\pi\) | |||||||
\(674\) | 2.29701 | + | 2.29701i | 0.0884775 | + | 0.0884775i | ||||
\(675\) | −3.42911 | + | 24.7231i | −0.131986 | + | 0.951591i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.12205i | 0.0815568i | 0.999168 | + | 0.0407784i | \(0.0129838\pi\) | ||||
−0.999168 | + | 0.0407784i | \(0.987016\pi\) | |||||||
\(678\) | 5.46507 | − | 17.1946i | 0.209885 | − | 0.660353i | ||||
\(679\) | 0.773450 | 0.0296823 | ||||||||
\(680\) | −2.48152 | −0.0951620 | ||||||||
\(681\) | −8.84802 | − | 2.81223i | −0.339057 | − | 0.107765i | ||||
\(682\) | 0.603702 | + | 0.603702i | 0.0231169 | + | 0.0231169i | ||||
\(683\) | −22.6901 | − | 22.6901i | −0.868214 | − | 0.868214i | 0.124061 | − | 0.992275i | \(-0.460408\pi\) |
−0.992275 | + | 0.124061i | \(0.960408\pi\) | |||||||
\(684\) | 3.56679 | + | 20.7888i | 0.136379 | + | 0.794878i | ||||
\(685\) | 0.0366618 | 0.00140078 | ||||||||
\(686\) | 4.01060 | 0.153125 | ||||||||
\(687\) | 19.2553 | + | 6.12006i | 0.734636 | + | 0.233495i | ||||
\(688\) | − | 3.76778i | − | 0.143645i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.53556 | + | 2.34778i | −0.172666 | + | 0.0893783i | ||||
\(691\) | 21.5583 | + | 21.5583i | 0.820118 | + | 0.820118i | 0.986125 | − | 0.166007i | \(-0.0530874\pi\) |
−0.166007 | + | 0.986125i | \(0.553087\pi\) | |||||||
\(692\) | 1.10220i | 0.0418993i | ||||||||
\(693\) | 0.290940 | − | 0.411451i | 0.0110519 | − | 0.0156297i | ||||
\(694\) | −5.81113 | − | 5.81113i | −0.220587 | − | 0.220587i | ||||
\(695\) | −1.95635 | + | 1.95635i | −0.0742085 | + | 0.0742085i | ||||
\(696\) | −6.81755 | − | 2.16687i | −0.258419 | − | 0.0821351i | ||||
\(697\) | −30.2026 | + | 30.2026i | −1.14401 | + | 1.14401i | ||||
\(698\) | − | 8.01283i | − | 0.303290i | ||||||
\(699\) | 7.60207 | + | 14.6861i | 0.287537 | + | 0.555478i | ||||
\(700\) | −0.978833 | + | 0.978833i | −0.0369964 | + | 0.0369964i | ||||
\(701\) | 1.23549 | 0.0466638 | 0.0233319 | − | 0.999728i | \(-0.492573\pi\) | ||||
0.0233319 | + | 0.999728i | \(0.492573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −48.9246 | −1.84523 | ||||||||
\(704\) | −0.412157 | + | 0.412157i | −0.0155337 | + | 0.0155337i | ||||
\(705\) | −1.85581 | − | 3.58516i | −0.0698940 | − | 0.135025i | ||||
\(706\) | − | 2.79561i | − | 0.105214i | ||||||
\(707\) | 2.90188 | − | 2.90188i | 0.109136 | − | 0.109136i | ||||
\(708\) | −5.62421 | − | 1.78758i | −0.211371 | − | 0.0671815i | ||||
\(709\) | 11.1940 | − | 11.1940i | 0.420399 | − | 0.420399i | −0.464942 | − | 0.885341i | \(-0.653925\pi\) |
0.885341 | + | 0.464942i | \(0.153925\pi\) | |||||||
\(710\) | −4.82277 | − | 4.82277i | −0.180995 | − | 0.180995i | ||||
\(711\) | −1.92060 | + | 2.71614i | −0.0720282 | + | 0.101863i | ||||
\(712\) | 14.0824i | 0.527759i | ||||||||
\(713\) | 6.88956 | + | 6.88956i | 0.258016 | + | 0.258016i | ||||
\(714\) | 2.48152 | − | 1.28453i | 0.0928686 | − | 0.0480723i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.59555i | 0.209115i | ||||||||
\(717\) | 48.1766 | + | 15.3123i | 1.79919 | + | 0.571849i | ||||
\(718\) | −16.4800 | −0.615028 | ||||||||
\(719\) | 3.10067 | 0.115635 | 0.0578176 | − | 0.998327i | \(-0.481586\pi\) | ||||
0.0578176 | + | 0.998327i | \(0.481586\pi\) | |||||||
\(720\) | −0.224877 | − | 1.31068i | −0.00838067 | − | 0.0488461i | ||||
\(721\) | −0.939204 | − | 0.939204i | −0.0349778 | − | 0.0349778i | ||||
\(722\) | −21.5192 | − | 21.5192i | −0.800860 | − | 0.800860i | ||||
\(723\) | 18.4116 | + | 5.85188i | 0.684734 | + | 0.217634i | ||||
\(724\) | −14.4687 | −0.537727 | ||||||||
\(725\) | 19.8392 | 0.736809 | ||||||||
\(726\) | 5.59288 | − | 17.5967i | 0.207571 | − | 0.653074i | ||||
\(727\) | − | 20.0877i | − | 0.745011i | −0.928030 | − | 0.372506i | \(-0.878499\pi\) | ||
0.928030 | − | 0.372506i | \(-0.121501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9808 | + | 7.34847i | 0.962250 | + | 0.272166i | ||||
\(730\) | 1.56057 | + | 1.56057i | 0.0577593 | + | 0.0577593i | ||||
\(731\) | − | 21.0925i | − | 0.780135i | ||||||
\(732\) | −16.1680 | + | 8.36919i | −0.597588 | + | 0.309334i | ||||
\(733\) | 35.4832 | + | 35.4832i | 1.31060 | + | 1.31060i | 0.920972 | + | 0.389628i | \(0.127396\pi\) |
0.389628 | + | 0.920972i | \(0.372604\pi\) | |||||||
\(734\) | 26.2944 | − | 26.2944i | 0.970544 | − | 0.970544i | ||||
\(735\) | 1.60864 | − | 5.06119i | 0.0593354 | − | 0.186685i | ||||
\(736\) | −4.70360 | + | 4.70360i | −0.173377 | + | 0.173377i | ||||
\(737\) | 5.16047i | 0.190088i | ||||||||
\(738\) | −18.6893 | − | 13.2153i | −0.687961 | − | 0.486462i | ||||
\(739\) | 16.4638 | − | 16.4638i | 0.605629 | − | 0.605629i | −0.336172 | − | 0.941801i | \(-0.609132\pi\) |
0.941801 | + | 0.336172i | \(0.109132\pi\) | |||||||
\(740\) | 3.08458 | 0.113391 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.05122 | 0.0385916 | ||||||||
\(743\) | 18.9507 | − | 18.9507i | 0.695235 | − | 0.695235i | −0.268144 | − | 0.963379i | \(-0.586410\pi\) |
0.963379 | + | 0.268144i | \(0.0864102\pi\) | |||||||
\(744\) | −2.25305 | + | 1.16626i | −0.0826007 | + | 0.0427573i | ||||
\(745\) | − | 6.44402i | − | 0.236091i | ||||||
\(746\) | 5.57782 | − | 5.57782i | 0.204219 | − | 0.204219i | ||||
\(747\) | −5.90475 | − | 34.4154i | −0.216044 | − | 1.25919i | ||||
\(748\) | −2.30731 | + | 2.30731i | −0.0843635 | + | 0.0843635i | ||||
\(749\) | −2.75341 | − | 2.75341i | −0.100607 | − | 0.100607i | ||||
\(750\) | 3.46013 | + | 6.68446i | 0.126346 | + | 0.244082i | ||||
\(751\) | − | 17.8164i | − | 0.650131i | −0.945692 | − | 0.325065i | \(-0.894614\pi\) | ||
0.945692 | − | 0.325065i | \(-0.105386\pi\) | |||||||
\(752\) | −3.71799 | − | 3.71799i | −0.135581 | − | 0.135581i | ||||
\(753\) | 3.55874 | + | 6.87496i | 0.129688 | + | 0.250537i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.01433i | 0.146096i | ||||||||
\(756\) | 0.903335 | + | 1.19427i | 0.0328540 | + | 0.0434353i | ||||
\(757\) | 24.7813 | 0.900690 | 0.450345 | − | 0.892855i | \(-0.351301\pi\) | ||||
0.450345 | + | 0.892855i | \(0.351301\pi\) | |||||||
\(758\) | −1.86196 | −0.0676295 | ||||||||
\(759\) | −2.03419 | + | 6.40009i | −0.0738363 | + | 0.232308i | ||||
\(760\) | 2.20377 | + | 2.20377i | 0.0799393 | + | 0.0799393i | ||||
\(761\) | 10.7526 | + | 10.7526i | 0.389781 | + | 0.389781i | 0.874609 | − | 0.484828i | \(-0.161118\pi\) |
−0.484828 | + | 0.874609i | \(0.661118\pi\) | |||||||
\(762\) | 0.126678 | − | 0.398562i | 0.00458905 | − | 0.0144384i | ||||
\(763\) | −0.840319 | −0.0304216 | ||||||||
\(764\) | 6.67573 | 0.241520 | ||||||||
\(765\) | −1.25889 | − | 7.33735i | −0.0455153 | − | 0.265283i | ||||
\(766\) | 2.88048i | 0.104076i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.796225 | − | 1.53819i | −0.0287313 | − | 0.0555046i | ||||
\(769\) | 12.9589 | + | 12.9589i | 0.467311 | + | 0.467311i | 0.901042 | − | 0.433731i | \(-0.142803\pi\) |
−0.433731 | + | 0.901042i | \(0.642803\pi\) | |||||||
\(770\) | − | 0.0744591i | − | 0.00268332i | ||||||
\(771\) | −9.51355 | − | 18.3788i | −0.342622 | − | 0.661895i | ||||
\(772\) | 4.30947 | + | 4.30947i | 0.155101 | + | 0.155101i | ||||
\(773\) | −23.8031 | + | 23.8031i | −0.856138 | + | 0.856138i | −0.990881 | − | 0.134742i | \(-0.956979\pi\) |
0.134742 | + | 0.990881i | \(0.456979\pi\) | |||||||
\(774\) | 11.1406 | − | 1.91142i | 0.400439 | − | 0.0687044i | ||||
\(775\) | 4.97512 | − | 4.97512i | 0.178712 | − | 0.178712i | ||||
\(776\) | − | 2.68390i | − | 0.0963465i | ||||||
\(777\) | −3.08458 | + | 1.59669i | −0.110659 | + | 0.0572811i | ||||
\(778\) | 16.5595 | − | 16.5595i | 0.593688 | − | 0.593688i | ||||
\(779\) | 53.6443 | 1.92201 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.96837 | −0.320914 | ||||||||
\(782\) | −26.3314 | + | 26.3314i | −0.941608 | + | 0.941608i | ||||
\(783\) | 2.94841 | − | 21.2574i | 0.105368 | − | 0.759677i | ||||
\(784\) | − | 6.91695i | − | 0.247034i | ||||||
\(785\) | −3.20112 | + | 3.20112i | −0.114253 | + | 0.114253i | ||||
\(786\) | 4.24463 | − | 13.3547i | 0.151401 | − | 0.476347i | ||||
\(787\) | −6.66227 | + | 6.66227i | −0.237484 | + | 0.237484i | −0.815808 | − | 0.578323i | \(-0.803707\pi\) |
0.578323 | + | 0.815808i | \(0.303707\pi\) | |||||||
\(788\) | −10.4569 | − | 10.4569i | −0.372511 | − | 0.372511i | ||||
\(789\) | −4.23188 | + | 2.19058i | −0.150659 | + | 0.0779868i | ||||
\(790\) | 0.491532i | 0.0174879i | ||||||||
\(791\) | 2.12265 | + | 2.12265i | 0.0754728 | + | 0.0754728i | ||||
\(792\) | −1.42775 | − | 1.00957i | −0.0507330 | − | 0.0358736i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.4077i | 0.653266i | ||||||||
\(795\) | 0.848344 | − | 2.66911i | 0.0300877 | − | 0.0946637i | ||||
\(796\) | −15.4803 | −0.548686 | ||||||||
\(797\) | 46.8501 | 1.65951 | 0.829757 | − | 0.558124i | \(-0.188479\pi\) | ||||
0.829757 | + | 0.558124i | \(0.188479\pi\) | |||||||
\(798\) | −3.34453 | − | 1.06302i | −0.118395 | − | 0.0376304i | ||||
\(799\) | −20.8138 | − | 20.8138i | −0.736339 | − | 0.736339i | ||||
\(800\) | 3.39659 | + | 3.39659i | 0.120088 | + | 0.120088i | ||||
\(801\) | −41.6387 | + | 7.14407i | −1.47123 | + | 0.252423i | ||||
\(802\) | 6.78495 | 0.239585 | ||||||||
\(803\) | 2.90202 | 0.102410 | ||||||||
\(804\) | −14.6142 | − | 4.64494i | −0.515403 | − | 0.163814i | ||||
\(805\) | − | 0.849740i | − | 0.0299494i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.59871 | + | 4.96866i | −0.337891 | + | 0.174905i | ||||
\(808\) | −10.0696 | − | 10.0696i | −0.354248 | − | 0.354248i | ||||
\(809\) | − | 40.6329i | − | 1.42858i | −0.699851 | − | 0.714289i | \(-0.746750\pi\) | ||
0.699851 | − | 0.714289i | \(-0.253250\pi\) | |||||||
\(810\) | 3.76133 | − | 1.32983i | 0.132160 | − | 0.0467255i | ||||
\(811\) | 16.5531 | + | 16.5531i | 0.581257 | + | 0.581257i | 0.935249 | − | 0.353992i | \(-0.115176\pi\) |
−0.353992 | + | 0.935249i | \(0.615176\pi\) | |||||||
\(812\) | 0.841620 | − | 0.841620i | 0.0295351 | − | 0.0295351i | ||||
\(813\) | −36.9221 | − | 11.7352i | −1.29492 | − | 0.411572i | ||||
\(814\) | 2.86802 | − | 2.86802i | 0.100524 | − | 0.100524i | ||||
\(815\) | 6.15276i | 0.215522i | ||||||||
\(816\) | −4.45737 | − | 8.61098i | −0.156039 | − | 0.301445i | ||||
\(817\) | −18.7317 | + | 18.7317i | −0.655340 | + | 0.655340i | ||||
\(818\) | −29.2874 | −1.02401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.38214 | −0.118109 | ||||||||
\(821\) | −2.49011 | + | 2.49011i | −0.0869053 | + | 0.0869053i | −0.749223 | − | 0.662318i | \(-0.769573\pi\) |
0.662318 | + | 0.749223i | \(0.269573\pi\) | |||||||
\(822\) | 0.0658528 | + | 0.127218i | 0.00229688 | + | 0.00443723i | ||||
\(823\) | − | 10.3686i | − | 0.361426i | −0.983536 | − | 0.180713i | \(-0.942160\pi\) | ||
0.983536 | − | 0.180713i | \(-0.0578405\pi\) | |||||||
\(824\) | −3.25908 | + | 3.25908i | −0.113535 | + | 0.113535i | ||||
\(825\) | 4.62166 | + | 1.46894i | 0.160906 | + | 0.0511418i | ||||
\(826\) | 0.694303 | − | 0.694303i | 0.0241579 | − | 0.0241579i | ||||
\(827\) | −5.61338 | − | 5.61338i | −0.195196 | − | 0.195196i | 0.602741 | − | 0.797937i | \(-0.294075\pi\) |
−0.797937 | + | 0.602741i | \(0.794075\pi\) | |||||||
\(828\) | −16.2938 | − | 11.5214i | −0.566247 | − | 0.400397i | ||||
\(829\) | − | 2.03548i | − | 0.0706950i | −0.999375 | − | 0.0353475i | \(-0.988746\pi\) | ||
0.999375 | − | 0.0353475i | \(-0.0112538\pi\) | |||||||
\(830\) | −3.64831 | − | 3.64831i | −0.126635 | − | 0.126635i | ||||
\(831\) | 8.61135 | − | 4.45757i | 0.298725 | − | 0.154631i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 38.7220i | − | 1.34164i | ||||||
\(834\) | −10.3026 | − | 3.27456i | −0.356751 | − | 0.113389i | ||||
\(835\) | 5.94514 | 0.205740 | ||||||||
\(836\) | 4.09812 | 0.141736 | ||||||||
\(837\) | −4.59138 | − | 6.07015i | −0.158701 | − | 0.209815i | ||||
\(838\) | −6.53521 | − | 6.53521i | −0.225755 | − | 0.225755i | ||||
\(839\) | 11.0461 | + | 11.0461i | 0.381354 | + | 0.381354i | 0.871590 | − | 0.490236i | \(-0.163089\pi\) |
−0.490236 | + | 0.871590i | \(0.663089\pi\) | |||||||
\(840\) | 0.210865 | + | 0.0670206i | 0.00727552 | + | 0.00231243i | ||||
\(841\) | 11.9419 | 0.411789 | ||||||||
\(842\) | 26.0908 | 0.899149 | ||||||||
\(843\) | −6.55058 | + | 20.6098i | −0.225614 | + | 0.709841i | ||||
\(844\) | − | 18.8144i | − | 0.647619i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.10718 | − | 12.8795i | 0.313111 | − | 0.442806i | ||||
\(847\) | 2.17229 | + | 2.17229i | 0.0746408 | + | 0.0746408i | ||||
\(848\) | − | 3.64778i | − | 0.125265i | ||||||
\(849\) | −10.5500 | + | 5.46109i | −0.362075 | + | 0.187424i | ||||
\(850\) | 19.0146 | + | 19.0146i | 0.652194 | + | 0.652194i | ||||
\(851\) | 32.7304 | − | 32.7304i | 1.12198 | − | 1.12198i | ||||
\(852\) | 8.07243 | − | 25.3980i | 0.276557 | − | 0.870121i | ||||
\(853\) | 21.4461 | − | 21.4461i | 0.734300 | − | 0.734300i | −0.237168 | − | 0.971469i | \(-0.576219\pi\) |
0.971469 | + | 0.237168i | \(0.0762193\pi\) | |||||||
\(854\) | − | 3.02909i | − | 0.103653i | ||||||
\(855\) | −5.39812 | + | 7.63410i | −0.184612 | + | 0.261081i | ||||
\(856\) | −9.55443 | + | 9.55443i | −0.326564 | + | 0.326564i | ||||
\(857\) | 17.8872 | 0.611017 | 0.305508 | − | 0.952189i | \(-0.401174\pi\) | ||||
0.305508 | + | 0.952189i | \(0.401174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.29875 | −0.0443127 | −0.0221564 | − | 0.999755i | \(-0.507053\pi\) | ||||
−0.0221564 | + | 0.999755i | \(0.507053\pi\) | |||||||
\(860\) | 1.18099 | − | 1.18099i | 0.0402714 | − | 0.0402714i | ||||
\(861\) | 3.38214 | − | 1.75072i | 0.115263 | − | 0.0596645i | ||||
\(862\) | − | 22.3635i | − | 0.761705i | ||||||
\(863\) | 15.1285 | − | 15.1285i | 0.514979 | − | 0.514979i | −0.401069 | − | 0.916048i | \(-0.631361\pi\) |
0.916048 | + | 0.401069i | \(0.131361\pi\) | |||||||
\(864\) | 4.14418 | − | 3.13461i | 0.140988 | − | 0.106642i | ||||
\(865\) | −0.345478 | + | 0.345478i | −0.0117466 | + | 0.0117466i | ||||
\(866\) | 2.79168 | + | 2.79168i | 0.0948652 | + | 0.0948652i | ||||
\(867\) | −11.4171 | − | 22.0562i | −0.387746 | − | 0.749067i | ||||
\(868\) | − | 0.422110i | − | 0.0143274i | ||||||
\(869\) | 0.457024 | + | 0.457024i | 0.0155035 | + | 0.0155035i | ||||
\(870\) | −1.45773 | − | 2.81612i | −0.0494216 | − | 0.0954753i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.91594i | 0.0987462i | ||||||||
\(873\) | 7.93575 | − | 1.36156i | 0.268584 | − | 0.0460818i | ||||
\(874\) | 46.7684 | 1.58197 | ||||||||
\(875\) | −1.25234 | −0.0423368 | ||||||||
\(876\) | −2.61210 | + | 8.21837i | −0.0882548 | + | 0.277673i | ||||
\(877\) | −15.7315 | − | 15.7315i | −0.531215 | − | 0.531215i | 0.389719 | − | 0.920934i | \(-0.372572\pi\) |
−0.920934 | + | 0.389719i | \(0.872572\pi\) | |||||||
\(878\) | −12.9471 | − | 12.9471i | −0.436944 | − | 0.436944i | ||||
\(879\) | −14.3519 | + | 45.1549i | −0.484077 | + | 1.52304i | ||||
\(880\) | −0.258376 | −0.00870986 | ||||||||
\(881\) | 20.5028 | 0.690758 | 0.345379 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345379 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(882\) | 20.4520 | − | 3.50901i | 0.688655 | − | 0.118155i | ||||
\(883\) | − | 27.7709i | − | 0.934566i | −0.884108 | − | 0.467283i | \(-0.845233\pi\) | ||
0.884108 | − | 0.467283i | \(-0.154767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.20257 | − | 2.32318i | −0.0404239 | − | 0.0780929i | ||||
\(886\) | 4.14627 | + | 4.14627i | 0.139297 | + | 0.139297i | ||||
\(887\) | 13.2051i | 0.443385i | 0.975117 | + | 0.221692i | \(0.0711581\pi\) | ||||
−0.975117 | + | 0.221692i | \(0.928842\pi\) | |||||||
\(888\) | 5.54059 | + | 10.7036i | 0.185930 | + | 0.359189i | ||||
\(889\) | 0.0492020 | + | 0.0492020i | 0.00165018 | + | 0.00165018i | ||||
\(890\) | −4.41403 | + | 4.41403i | −0.147959 | + | 0.147959i | ||||
\(891\) | 2.26079 | − | 4.73373i | 0.0757395 | − | 0.158586i | ||||
\(892\) | −5.08804 | + | 5.08804i | −0.170360 | + | 0.170360i | ||||
\(893\) | 36.9684i | 1.23710i | ||||||||
\(894\) | 22.3610 | − | 11.5749i | 0.747864 | − | 0.387123i | ||||
\(895\) | −1.75389 | + | 1.75389i | −0.0586261 | + | 0.0586261i | ||||
\(896\) | 0.288181 | 0.00962745 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.5045 | −0.951207 | ||||||||
\(899\) | −4.27771 | + | 4.27771i | −0.142670 | + | 0.142670i | ||||
\(900\) | −8.31992 | + | 11.7661i | −0.277331 | + | 0.392205i | ||||
\(901\) | − | 20.4208i | − | 0.680315i | ||||||
\(902\) | −3.14469 | + | 3.14469i | −0.104707 | + | 0.104707i | ||||
\(903\) | −0.569664 | + | 1.79231i | −0.0189572 | + | 0.0596444i | ||||
\(904\) | 7.36568 | − | 7.36568i | 0.244979 | − | 0.244979i | ||||
\(905\) | −4.53514 | − | 4.53514i | −0.150753 | − | 0.150753i | ||||
\(906\) | −13.9299 | + | 7.21064i | −0.462789 | + | 0.239557i | ||||
\(907\) | − | 27.9622i | − | 0.928470i | −0.885712 | − | 0.464235i | \(-0.846329\pi\) | ||
0.885712 | − | 0.464235i | \(-0.153671\pi\) | |||||||
\(908\) | −3.79025 | − | 3.79025i | −0.125784 | − | 0.125784i | ||||
\(909\) | 24.6655 | − | 34.8822i | 0.818101 | − | 1.15697i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2713i | 1.10233i | 0.834397 | + | 0.551164i | \(0.185816\pi\) | ||||
−0.834397 | + | 0.551164i | \(0.814184\pi\) | |||||||
\(912\) | −3.68871 | + | 11.6057i | −0.122145 | + | 0.384302i | ||||
\(913\) | −6.78436 | −0.224530 | ||||||||
\(914\) | 19.1699 | 0.634084 | ||||||||
\(915\) | −7.69105 | − | 2.44450i | −0.254258 | − | 0.0808127i | ||||
\(916\) | 8.24846 | + | 8.24846i | 0.272537 | + | 0.272537i | ||||
\(917\) | 1.64863 | + | 1.64863i | 0.0544424 | + | 0.0544424i | ||||
\(918\) | 23.1997 | − | 17.5479i | 0.765703 | − | 0.579168i | ||||
\(919\) | 14.4374 | 0.476244 | 0.238122 | − | 0.971235i | \(-0.423468\pi\) | ||||
0.238122 | + | 0.971235i | \(0.423468\pi\) | |||||||
\(920\) | −2.94863 | −0.0972136 | ||||||||
\(921\) | 36.1528 | + | 11.4907i | 1.19127 | + | 0.378632i | ||||
\(922\) | − | 29.6500i | − | 0.976471i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.258376 | − | 0.133745i | 0.00849995 | − | 0.00439990i | ||||
\(925\) | −23.6354 | − | 23.6354i | −0.777128 | − | 0.777128i | ||||
\(926\) | 25.8170i | 0.848400i | ||||||||
\(927\) | −11.2898 | − | 7.98308i | −0.370805 | − | 0.262199i | ||||
\(928\) | −2.92046 | − | 2.92046i | −0.0958687 | − | 0.0958687i | ||||
\(929\) | 9.95732 | − | 9.95732i | 0.326689 | − | 0.326689i | −0.524637 | − | 0.851326i | \(-0.675799\pi\) |
0.851326 | + | 0.524637i | \(0.175799\pi\) | |||||||
\(930\) | −1.07176 | − | 0.340646i | −0.0351445 | − | 0.0111702i | ||||
\(931\) | −34.3880 | + | 34.3880i | −1.12702 | + | 1.12702i | ||||
\(932\) | 9.54763i | 0.312743i | ||||||||
\(933\) | −25.3210 | − | 48.9163i | −0.828971 | − | 1.60145i | ||||
\(934\) | 22.9425 | − | 22.9425i | 0.750701 | − | 0.750701i | ||||
\(935\) | −1.44642 | −0.0473031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6098 | 0.836635 | 0.418317 | − | 0.908301i | \(-0.362620\pi\) | ||||
0.418317 | + | 0.908301i | \(0.362620\pi\) | |||||||
\(938\) | 1.80411 | − | 1.80411i | 0.0589062 | − | 0.0589062i | ||||
\(939\) | 18.9043 | + | 36.5202i | 0.616918 | + | 1.19179i | ||||
\(940\) | − | 2.33077i | − | 0.0760212i | ||||||
\(941\) | −24.7798 | + | 24.7798i | −0.807800 | + | 0.807800i | −0.984300 | − | 0.176501i | \(-0.943522\pi\) |
0.176501 | + | 0.984300i | \(0.443522\pi\) | |||||||
\(942\) | −16.8580 | − | 5.35809i | −0.549262 | − | 0.174576i | ||||
\(943\) | −35.8878 | + | 35.8878i | −1.16867 | + | 1.16867i | ||||
\(944\) | −2.40926 | − | 2.40926i | −0.0784147 | − | 0.0784147i | ||||
\(945\) | −0.0911934 | + | 0.657483i | −0.00296652 | + | 0.0213879i | ||||
\(946\) | − | 2.19615i | − | 0.0714031i | ||||||
\(947\) | −8.13217 | − | 8.13217i | −0.264260 | − | 0.264260i | 0.562522 | − | 0.826782i | \(-0.309831\pi\) |
−0.826782 | + | 0.562522i | \(0.809831\pi\) | |||||||
\(948\) | −1.70564 | + | 0.882903i | −0.0553965 | + | 0.0286753i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 33.7727i | − | 1.09573i | ||||||
\(951\) | −39.4367 | − | 12.5345i | −1.27882 | − | 0.406458i | ||||
\(952\) | 1.61328 | 0.0522865 | ||||||||
\(953\) | −48.5516 | −1.57274 | −0.786370 | − | 0.617755i | \(-0.788042\pi\) | ||||
−0.786370 | + | 0.617755i | \(0.788042\pi\) | |||||||
\(954\) | 10.7858 | − | 1.85054i | 0.349202 | − | 0.0599135i | ||||
\(955\) | 2.09247 | + | 2.09247i | 0.0677107 | + | 0.0677107i | ||||
\(956\) | 20.6375 | + | 20.6375i | 0.667466 | + | 0.667466i | ||||
\(957\) | −3.97380 | − | 1.26302i | −0.128455 | − | 0.0408277i | ||||
\(958\) | 8.29040 | 0.267851 | ||||||||
\(959\) | −0.0238344 | −0.000769653 | ||||||||
\(960\) | 0.232564 | − | 0.731708i | 0.00750598 | − | 0.0236158i | ||||
\(961\) | − | 28.8545i | − | 0.930792i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.0975 | − | 23.4035i | −1.06655 | − | 0.754167i | ||||
\(964\) | 7.88702 | + | 7.88702i | 0.254024 | + | 0.254024i | ||||
\(965\) | 2.70156i | 0.0869662i | ||||||||
\(966\) | 2.94863 | − | 1.52633i | 0.0948707 | − | 0.0491087i | ||||
\(967\) | 15.4257 | + | 15.4257i | 0.496058 | + | 0.496058i | 0.910209 | − | 0.414150i | \(-0.135921\pi\) |
−0.414150 | + | 0.910209i | \(0.635921\pi\) | |||||||
\(968\) | 7.53794 | − | 7.53794i | 0.242279 | − | 0.242279i | ||||
\(969\) | −20.6499 | + | 64.9700i | −0.663370 | + | 2.08714i | ||||
\(970\) | 0.841253 | − | 0.841253i | 0.0270110 | − | 0.0270110i | ||||
\(971\) | − | 7.66202i | − | 0.245886i | −0.992414 | − | 0.122943i | \(-0.960767\pi\) | ||
0.992414 | − | 0.122943i | \(-0.0392332\pi\) | |||||||
\(972\) | 11.3708 | + | 10.6633i | 0.364717 | + | 0.342025i | ||||
\(973\) | 1.27185 | − | 1.27185i | 0.0407737 | − | 0.0407737i | ||||
\(974\) | −32.1307 | −1.02953 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.5111 | −0.336451 | ||||||||
\(977\) | 14.2640 | − | 14.2640i | 0.456346 | − | 0.456346i | −0.441108 | − | 0.897454i | \(-0.645414\pi\) |
0.897454 | + | 0.441108i | \(0.145414\pi\) | |||||||
\(978\) | −21.3503 | + | 11.0517i | −0.682708 | + | 0.353396i | ||||
\(979\) | 8.20829i | 0.262338i | ||||||||
\(980\) | 2.16808 | − | 2.16808i | 0.0692567 | − | 0.0692567i | ||||
\(981\) | −8.62184 | + | 1.47927i | −0.275274 | + | 0.0472296i | ||||
\(982\) | −18.6817 | + | 18.6817i | −0.596157 | + | 0.596157i | ||||
\(983\) | −0.922992 | − | 0.922992i | −0.0294389 | − | 0.0294389i | 0.692234 | − | 0.721673i | \(-0.256627\pi\) |
−0.721673 | + | 0.692234i | \(0.756627\pi\) | |||||||
\(984\) | −6.07508 | − | 11.7362i | −0.193667 | − | 0.374135i | ||||
\(985\) | − | 6.55530i | − | 0.208869i | ||||||
\(986\) | −16.3491 | − | 16.3491i | −0.520661 | − | 0.520661i | ||||
\(987\) | 1.20649 | + | 2.33077i | 0.0384031 | + | 0.0741891i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 25.0629i | − | 0.796953i | ||||||
\(990\) | −0.131076 | − | 0.763965i | −0.00416586 | − | 0.0242804i | ||||
\(991\) | 20.5965 | 0.654269 | 0.327135 | − | 0.944978i | \(-0.393917\pi\) | ||||
0.327135 | + | 0.944978i | \(0.393917\pi\) | |||||||
\(992\) | −1.46474 | −0.0465055 | ||||||||
\(993\) | −8.65024 | + | 27.2159i | −0.274507 | + | 0.863672i | ||||
\(994\) | 3.13536 | + | 3.13536i | 0.0994475 | + | 0.0994475i | ||||
\(995\) | −4.85222 | − | 4.85222i | −0.153826 | − | 0.153826i | ||||
\(996\) | 6.10660 | − | 19.2130i | 0.193495 | − | 0.608786i | ||||
\(997\) | −32.1789 | −1.01912 | −0.509558 | − | 0.860436i | \(-0.670191\pi\) | ||||
−0.509558 | + | 0.860436i | \(0.670191\pi\) | |||||||
\(998\) | 13.1158 | 0.415173 | ||||||||
\(999\) | −28.8376 | + | 21.8124i | −0.912381 | + | 0.690114i |
(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 | 1014.2.g.c.437.2 | 16 | ||
3.2 | odd | 2 | inner | 1014.2.g.c.437.6 | 16 | ||
13.2 | odd | 12 | 78.2.k.a.71.2 | yes | 16 | ||
13.5 | odd | 4 | inner | 1014.2.g.c.239.6 | 16 | ||
13.8 | odd | 4 | 1014.2.g.d.239.2 | 16 | |||
13.9 | even | 3 | 78.2.k.a.11.3 | yes | 16 | ||
13.12 | even | 2 | 1014.2.g.d.437.6 | 16 | |||
39.2 | even | 12 | 78.2.k.a.71.3 | yes | 16 | ||
39.5 | even | 4 | inner | 1014.2.g.c.239.2 | 16 | ||
39.8 | even | 4 | 1014.2.g.d.239.6 | 16 | |||
39.35 | odd | 6 | 78.2.k.a.11.2 | ✓ | 16 | ||
39.38 | odd | 2 | 1014.2.g.d.437.2 | 16 | |||
52.15 | even | 12 | 624.2.cn.d.305.1 | 16 | |||
52.35 | odd | 6 | 624.2.cn.d.401.3 | 16 | |||
156.35 | even | 6 | 624.2.cn.d.401.1 | 16 | |||
156.119 | odd | 12 | 624.2.cn.d.305.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.k.a.11.2 | ✓ | 16 | 39.35 | odd | 6 | ||
78.2.k.a.11.3 | yes | 16 | 13.9 | even | 3 | ||
78.2.k.a.71.2 | yes | 16 | 13.2 | odd | 12 | ||
78.2.k.a.71.3 | yes | 16 | 39.2 | even | 12 | ||
624.2.cn.d.305.1 | 16 | 52.15 | even | 12 | |||
624.2.cn.d.305.3 | 16 | 156.119 | odd | 12 | |||
624.2.cn.d.401.1 | 16 | 156.35 | even | 6 | |||
624.2.cn.d.401.3 | 16 | 52.35 | odd | 6 | |||
1014.2.g.c.239.2 | 16 | 39.5 | even | 4 | inner | ||
1014.2.g.c.239.6 | 16 | 13.5 | odd | 4 | inner | ||
1014.2.g.c.437.2 | 16 | 1.1 | even | 1 | trivial | ||
1014.2.g.c.437.6 | 16 | 3.2 | odd | 2 | inner | ||
1014.2.g.d.239.2 | 16 | 13.8 | odd | 4 | |||
1014.2.g.d.239.6 | 16 | 39.8 | even | 4 | |||
1014.2.g.d.437.2 | 16 | 39.38 | odd | 2 | |||
1014.2.g.d.437.6 | 16 | 13.12 | even | 2 |