Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(141,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.b (of order \(2\), degree \(1\), 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: | \(12\) |
Coefficient field: | 12.0.8272021826830336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 141.9 | ||
Root | \(-0.722588 + 1.21568i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.141 |
Dual form | 280.2.b.d.141.10 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21568 | − | 0.722588i | 0.859612 | − | 0.510947i | ||||
\(3\) | 1.52755i | 0.881933i | 0.897524 | + | 0.440967i | \(0.145364\pi\) | ||||
−0.897524 | + | 0.440967i | \(0.854636\pi\) | |||||||
\(4\) | 0.955734 | − | 1.75686i | 0.477867 | − | 0.878432i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.10379 | + | 1.85701i | 0.450621 | + | 0.758121i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.107626 | − | 2.82638i | −0.0380516 | − | 0.999276i | ||||
\(9\) | 0.666582 | 0.222194 | ||||||||
\(10\) | 0.722588 | + | 1.21568i | 0.228502 | + | 0.384430i | ||||
\(11\) | 1.22377i | 0.368980i | 0.982834 | + | 0.184490i | \(0.0590634\pi\) | ||||
−0.982834 | + | 0.184490i | \(0.940937\pi\) | |||||||
\(12\) | 2.68370 | + | 1.45993i | 0.774718 | + | 0.421447i | ||||
\(13\) | 1.21525i | 0.337050i | 0.985697 | + | 0.168525i | \(0.0539004\pi\) | ||||
−0.985697 | + | 0.168525i | \(0.946100\pi\) | |||||||
\(14\) | 1.21568 | − | 0.722588i | 0.324903 | − | 0.193120i | ||||
\(15\) | −1.52755 | −0.394412 | ||||||||
\(16\) | −2.17314 | − | 3.35819i | −0.543286 | − | 0.839548i | ||||
\(17\) | 2.59497 | 0.629372 | 0.314686 | − | 0.949196i | \(-0.398101\pi\) | ||||
0.314686 | + | 0.949196i | \(0.398101\pi\) | |||||||
\(18\) | 0.810347 | − | 0.481664i | 0.191001 | − | 0.113529i | ||||
\(19\) | − | 0.616085i | − | 0.141340i | −0.997500 | − | 0.0706698i | \(-0.977486\pi\) | ||
0.997500 | − | 0.0706698i | \(-0.0225137\pi\) | |||||||
\(20\) | 1.75686 | + | 0.955734i | 0.392847 | + | 0.213709i | ||||
\(21\) | 1.52755i | 0.333339i | ||||||||
\(22\) | 0.884280 | + | 1.48771i | 0.188529 | + | 0.317180i | ||||
\(23\) | −8.36914 | −1.74509 | −0.872543 | − | 0.488537i | \(-0.837531\pi\) | ||||
−0.872543 | + | 0.488537i | \(0.837531\pi\) | |||||||
\(24\) | 4.31744 | − | 0.164405i | 0.881294 | − | 0.0335589i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.878126 | + | 1.47735i | 0.172215 | + | 0.289733i | ||||
\(27\) | 5.60090i | 1.07789i | ||||||||
\(28\) | 0.955734 | − | 1.75686i | 0.180617 | − | 0.332016i | ||||
\(29\) | − | 9.00634i | − | 1.67244i | −0.548398 | − | 0.836218i | \(-0.684762\pi\) | ||
0.548398 | − | 0.836218i | \(-0.315238\pi\) | |||||||
\(30\) | −1.85701 | + | 1.10379i | −0.339042 | + | 0.201524i | ||||
\(31\) | −1.50644 | −0.270564 | −0.135282 | − | 0.990807i | \(-0.543194\pi\) | ||||
−0.135282 | + | 0.990807i | \(0.543194\pi\) | |||||||
\(32\) | −5.06843 | − | 2.51218i | −0.895980 | − | 0.444095i | ||||
\(33\) | −1.86937 | −0.325416 | ||||||||
\(34\) | 3.15464 | − | 1.87509i | 0.541016 | − | 0.321576i | ||||
\(35\) | 1.00000i | 0.169031i | ||||||||
\(36\) | 0.637075 | − | 1.17109i | 0.106179 | − | 0.195182i | ||||
\(37\) | − | 4.36914i | − | 0.718282i | −0.933283 | − | 0.359141i | \(-0.883070\pi\) | ||
0.933283 | − | 0.359141i | \(-0.116930\pi\) | |||||||
\(38\) | −0.445175 | − | 0.748959i | −0.0722170 | − | 0.121497i | ||||
\(39\) | −1.85636 | −0.297256 | ||||||||
\(40\) | 2.82638 | − | 0.107626i | 0.446890 | − | 0.0170172i | ||||
\(41\) | −4.58844 | −0.716593 | −0.358297 | − | 0.933608i | \(-0.616642\pi\) | ||||
−0.358297 | + | 0.933608i | \(0.616642\pi\) | |||||||
\(42\) | 1.10379 | + | 1.85701i | 0.170319 | + | 0.286543i | ||||
\(43\) | − | 0.301914i | − | 0.0460415i | −0.999735 | − | 0.0230208i | \(-0.992672\pi\) | ||
0.999735 | − | 0.0230208i | \(-0.00732838\pi\) | |||||||
\(44\) | 2.15000 | + | 1.16960i | 0.324124 | + | 0.176323i | ||||
\(45\) | 0.666582i | 0.0993681i | ||||||||
\(46\) | −10.1742 | + | 6.04744i | −1.50010 | + | 0.891646i | ||||
\(47\) | −10.6855 | −1.55864 | −0.779322 | − | 0.626624i | \(-0.784436\pi\) | ||||
−0.779322 | + | 0.626624i | \(0.784436\pi\) | |||||||
\(48\) | 5.12981 | − | 3.31959i | 0.740425 | − | 0.479142i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.21568 | + | 0.722588i | −0.171922 | + | 0.102189i | ||||
\(51\) | 3.96395i | 0.555064i | ||||||||
\(52\) | 2.13503 | + | 1.16146i | 0.296076 | + | 0.161065i | ||||
\(53\) | 4.62460i | 0.635238i | 0.948218 | + | 0.317619i | \(0.102883\pi\) | ||||
−0.948218 | + | 0.317619i | \(0.897117\pi\) | |||||||
\(54\) | 4.04714 | + | 6.80887i | 0.550746 | + | 0.926570i | ||||
\(55\) | −1.22377 | −0.165013 | ||||||||
\(56\) | −0.107626 | − | 2.82638i | −0.0143821 | − | 0.377691i | ||||
\(57\) | 0.941102 | 0.124652 | ||||||||
\(58\) | −6.50787 | − | 10.9488i | −0.854525 | − | 1.43765i | ||||
\(59\) | − | 5.34775i | − | 0.696218i | −0.937454 | − | 0.348109i | \(-0.886824\pi\) | ||
0.937454 | − | 0.348109i | \(-0.113176\pi\) | |||||||
\(60\) | −1.45993 | + | 2.68370i | −0.188477 | + | 0.346465i | ||||
\(61\) | − | 3.54867i | − | 0.454361i | −0.973853 | − | 0.227180i | \(-0.927049\pi\) | ||
0.973853 | − | 0.227180i | \(-0.0729507\pi\) | |||||||
\(62\) | −1.83134 | + | 1.08853i | −0.232580 | + | 0.138244i | ||||
\(63\) | 0.666582 | 0.0839814 | ||||||||
\(64\) | −7.97683 | + | 0.608384i | −0.997104 | + | 0.0760480i | ||||
\(65\) | −1.21525 | −0.150733 | ||||||||
\(66\) | −2.27255 | + | 1.35079i | −0.279732 | + | 0.166270i | ||||
\(67\) | 9.16229i | 1.11935i | 0.828712 | + | 0.559676i | \(0.189074\pi\) | ||||
−0.828712 | + | 0.559676i | \(0.810926\pi\) | |||||||
\(68\) | 2.48010 | − | 4.55901i | 0.300756 | − | 0.552861i | ||||
\(69\) | − | 12.7843i | − | 1.53905i | ||||||
\(70\) | 0.722588 | + | 1.21568i | 0.0863657 | + | 0.145301i | ||||
\(71\) | 13.3881 | 1.58887 | 0.794436 | − | 0.607347i | \(-0.207766\pi\) | ||||
0.794436 | + | 0.607347i | \(0.207766\pi\) | |||||||
\(72\) | −0.0717416 | − | 1.88401i | −0.00845482 | − | 0.222033i | ||||
\(73\) | 15.3881 | 1.80104 | 0.900519 | − | 0.434816i | \(-0.143187\pi\) | ||||
0.900519 | + | 0.434816i | \(0.143187\pi\) | |||||||
\(74\) | −3.15709 | − | 5.31145i | −0.367004 | − | 0.617444i | ||||
\(75\) | − | 1.52755i | − | 0.176387i | ||||||
\(76\) | −1.08238 | − | 0.588813i | −0.124157 | − | 0.0675415i | ||||
\(77\) | 1.22377i | 0.139461i | ||||||||
\(78\) | −2.25673 | + | 1.34138i | −0.255525 | + | 0.151882i | ||||
\(79\) | −6.69217 | −0.752928 | −0.376464 | − | 0.926431i | \(-0.622860\pi\) | ||||
−0.376464 | + | 0.926431i | \(0.622860\pi\) | |||||||
\(80\) | 3.35819 | − | 2.17314i | 0.375457 | − | 0.242965i | ||||
\(81\) | −6.55592 | −0.728436 | ||||||||
\(82\) | −5.57805 | + | 3.31555i | −0.615993 | + | 0.366141i | ||||
\(83\) | 9.02746i | 0.990892i | 0.868639 | + | 0.495446i | \(0.164995\pi\) | ||||
−0.868639 | + | 0.495446i | \(0.835005\pi\) | |||||||
\(84\) | 2.68370 | + | 1.45993i | 0.292816 | + | 0.159292i | ||||
\(85\) | 2.59497i | 0.281464i | ||||||||
\(86\) | −0.218160 | − | 0.367030i | −0.0235248 | − | 0.0395779i | ||||
\(87\) | 13.7577 | 1.47498 | ||||||||
\(88\) | 3.45883 | − | 0.131709i | 0.368713 | − | 0.0140403i | ||||
\(89\) | −12.5124 | −1.32631 | −0.663154 | − | 0.748483i | \(-0.730783\pi\) | ||||
−0.663154 | + | 0.748483i | \(0.730783\pi\) | |||||||
\(90\) | 0.481664 | + | 0.810347i | 0.0507718 | + | 0.0854181i | ||||
\(91\) | 1.21525i | 0.127393i | ||||||||
\(92\) | −7.99867 | + | 14.7034i | −0.833919 | + | 1.53294i | ||||
\(93\) | − | 2.30116i | − | 0.238619i | ||||||
\(94\) | −12.9901 | + | 7.72123i | −1.33983 | + | 0.796384i | ||||
\(95\) | 0.616085 | 0.0632090 | ||||||||
\(96\) | 3.83749 | − | 7.74229i | 0.391662 | − | 0.790194i | ||||
\(97\) | 2.91526 | 0.296000 | 0.148000 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148000 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(98\) | 1.21568 | − | 0.722588i | 0.122802 | − | 0.0729924i | ||||
\(99\) | 0.815742i | 0.0819852i | ||||||||
\(100\) | −0.955734 | + | 1.75686i | −0.0955734 | + | 0.175686i | ||||
\(101\) | 12.0587i | 1.19989i | 0.800043 | + | 0.599943i | \(0.204810\pi\) | ||||
−0.800043 | + | 0.599943i | \(0.795190\pi\) | |||||||
\(102\) | 2.86430 | + | 4.81888i | 0.283608 | + | 0.477140i | ||||
\(103\) | 1.23059 | 0.121254 | 0.0606269 | − | 0.998160i | \(-0.480690\pi\) | ||||
0.0606269 | + | 0.998160i | \(0.480690\pi\) | |||||||
\(104\) | 3.43476 | − | 0.130793i | 0.336806 | − | 0.0128253i | ||||
\(105\) | −1.52755 | −0.149074 | ||||||||
\(106\) | 3.34168 | + | 5.62202i | 0.324573 | + | 0.546058i | ||||
\(107\) | 10.9852i | 1.06198i | 0.847378 | + | 0.530991i | \(0.178180\pi\) | ||||
−0.847378 | + | 0.530991i | \(0.821820\pi\) | |||||||
\(108\) | 9.84002 | + | 5.35297i | 0.946856 | + | 0.515090i | ||||
\(109\) | − | 11.1496i | − | 1.06793i | −0.845505 | − | 0.533967i | \(-0.820700\pi\) | ||
0.845505 | − | 0.533967i | \(-0.179300\pi\) | |||||||
\(110\) | −1.48771 | + | 0.884280i | −0.141847 | + | 0.0843128i | ||||
\(111\) | 6.67409 | 0.633477 | ||||||||
\(112\) | −2.17314 | − | 3.35819i | −0.205343 | − | 0.317319i | ||||
\(113\) | 15.7046 | 1.47736 | 0.738681 | − | 0.674055i | \(-0.235449\pi\) | ||||
0.738681 | + | 0.674055i | \(0.235449\pi\) | |||||||
\(114\) | 1.14408 | − | 0.680029i | 0.107152 | − | 0.0636906i | ||||
\(115\) | − | 8.36914i | − | 0.780426i | ||||||
\(116\) | −15.8229 | − | 8.60767i | −1.46912 | − | 0.799202i | ||||
\(117\) | 0.810065i | 0.0748905i | ||||||||
\(118\) | −3.86422 | − | 6.50113i | −0.355730 | − | 0.598477i | ||||
\(119\) | 2.59497 | 0.237880 | ||||||||
\(120\) | 0.164405 | + | 4.31744i | 0.0150080 | + | 0.394127i | ||||
\(121\) | 9.50239 | 0.863854 | ||||||||
\(122\) | −2.56423 | − | 4.31403i | −0.232154 | − | 0.390574i | ||||
\(123\) | − | 7.00908i | − | 0.631987i | ||||||
\(124\) | −1.43975 | + | 2.64660i | −0.129294 | + | 0.237672i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0.810347 | − | 0.481664i | 0.0721915 | − | 0.0429100i | ||||
\(127\) | 8.55227 | 0.758891 | 0.379446 | − | 0.925214i | \(-0.376115\pi\) | ||||
0.379446 | + | 0.925214i | \(0.376115\pi\) | |||||||
\(128\) | −9.25763 | + | 6.50356i | −0.818267 | + | 0.574839i | ||||
\(129\) | 0.461190 | 0.0406055 | ||||||||
\(130\) | −1.47735 | + | 0.878126i | −0.129572 | + | 0.0770168i | ||||
\(131\) | − | 10.9491i | − | 0.956624i | −0.878190 | − | 0.478312i | \(-0.841249\pi\) | ||
0.878190 | − | 0.478312i | \(-0.158751\pi\) | |||||||
\(132\) | −1.78662 | + | 3.28423i | −0.155506 | + | 0.285856i | ||||
\(133\) | − | 0.616085i | − | 0.0534213i | ||||||
\(134\) | 6.62056 | + | 11.1384i | 0.571929 | + | 0.962208i | ||||
\(135\) | −5.60090 | −0.482049 | ||||||||
\(136\) | −0.279286 | − | 7.33436i | −0.0239486 | − | 0.628916i | ||||
\(137\) | −12.9668 | −1.10783 | −0.553916 | − | 0.832572i | \(-0.686867\pi\) | ||||
−0.553916 | + | 0.832572i | \(0.686867\pi\) | |||||||
\(138\) | −9.23778 | − | 15.5416i | −0.786372 | − | 1.32299i | ||||
\(139\) | − | 10.5377i | − | 0.893795i | −0.894585 | − | 0.446897i | \(-0.852529\pi\) | ||
0.894585 | − | 0.446897i | \(-0.147471\pi\) | |||||||
\(140\) | 1.75686 | + | 0.955734i | 0.148482 | + | 0.0807743i | ||||
\(141\) | − | 16.3227i | − | 1.37462i | ||||||
\(142\) | 16.2756 | − | 9.67406i | 1.36581 | − | 0.811829i | ||||
\(143\) | −1.48719 | −0.124365 | ||||||||
\(144\) | −1.44858 | − | 2.23851i | −0.120715 | − | 0.186542i | ||||
\(145\) | 9.00634 | 0.747936 | ||||||||
\(146\) | 18.7069 | − | 11.1192i | 1.54819 | − | 0.920235i | ||||
\(147\) | 1.52755i | 0.125990i | ||||||||
\(148\) | −7.67598 | − | 4.17573i | −0.630962 | − | 0.343243i | ||||
\(149\) | 4.27806i | 0.350472i | 0.984526 | + | 0.175236i | \(0.0560689\pi\) | ||||
−0.984526 | + | 0.175236i | \(0.943931\pi\) | |||||||
\(150\) | −1.10379 | − | 1.85701i | −0.0901242 | − | 0.151624i | ||||
\(151\) | 18.3166 | 1.49058 | 0.745291 | − | 0.666739i | \(-0.232311\pi\) | ||||
0.745291 | + | 0.666739i | \(0.232311\pi\) | |||||||
\(152\) | −1.74129 | + | 0.0663068i | −0.141237 | + | 0.00537819i | ||||
\(153\) | 1.72976 | 0.139843 | ||||||||
\(154\) | 0.884280 | + | 1.48771i | 0.0712573 | + | 0.119883i | ||||
\(155\) | − | 1.50644i | − | 0.121000i | ||||||
\(156\) | −1.77419 | + | 3.26138i | −0.142049 | + | 0.261119i | ||||
\(157\) | − | 6.32577i | − | 0.504852i | −0.967616 | − | 0.252426i | \(-0.918772\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812283\pi\) | |||||||
\(158\) | −8.13551 | + | 4.83568i | −0.647226 | + | 0.384706i | ||||
\(159\) | −7.06432 | −0.560237 | ||||||||
\(160\) | 2.51218 | − | 5.06843i | 0.198605 | − | 0.400694i | ||||
\(161\) | −8.36914 | −0.659580 | ||||||||
\(162\) | −7.96988 | + | 4.73723i | −0.626173 | + | 0.372192i | ||||
\(163\) | − | 2.52500i | − | 0.197774i | −0.995099 | − | 0.0988868i | \(-0.968472\pi\) | ||
0.995099 | − | 0.0988868i | \(-0.0315282\pi\) | |||||||
\(164\) | −4.38532 | + | 8.06126i | −0.342436 | + | 0.629479i | ||||
\(165\) | − | 1.86937i | − | 0.145530i | ||||||
\(166\) | 6.52313 | + | 10.9745i | 0.506293 | + | 0.851783i | ||||
\(167\) | −5.19991 | −0.402381 | −0.201191 | − | 0.979552i | \(-0.564481\pi\) | ||||
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(168\) | 4.31744 | − | 0.164405i | 0.333098 | − | 0.0126841i | ||||
\(169\) | 11.5232 | 0.886397 | ||||||||
\(170\) | 1.87509 | + | 3.15464i | 0.143813 | + | 0.241950i | ||||
\(171\) | − | 0.410671i | − | 0.0314048i | ||||||
\(172\) | −0.530423 | − | 0.288550i | −0.0404444 | − | 0.0220017i | ||||
\(173\) | 22.4890i | 1.70981i | 0.518787 | + | 0.854903i | \(0.326384\pi\) | ||||
−0.518787 | + | 0.854903i | \(0.673616\pi\) | |||||||
\(174\) | 16.7249 | − | 9.94112i | 1.26791 | − | 0.753634i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 4.10965 | − | 2.65943i | 0.309776 | − | 0.200462i | ||||
\(177\) | 8.16897 | 0.614017 | ||||||||
\(178\) | −15.2110 | + | 9.04128i | −1.14011 | + | 0.677673i | ||||
\(179\) | − | 18.5336i | − | 1.38526i | −0.721291 | − | 0.692632i | \(-0.756451\pi\) | ||
0.721291 | − | 0.692632i | \(-0.243549\pi\) | |||||||
\(180\) | 1.17109 | + | 0.637075i | 0.0872882 | + | 0.0474848i | ||||
\(181\) | 6.92786i | 0.514944i | 0.966286 | + | 0.257472i | \(0.0828895\pi\) | ||||
−0.966286 | + | 0.257472i | \(0.917111\pi\) | |||||||
\(182\) | 0.878126 | + | 1.47735i | 0.0650910 | + | 0.109509i | ||||
\(183\) | 5.42078 | 0.400716 | ||||||||
\(184\) | 0.900737 | + | 23.6544i | 0.0664032 | + | 1.74382i | ||||
\(185\) | 4.36914 | 0.321225 | ||||||||
\(186\) | −1.66279 | − | 2.79746i | −0.121922 | − | 0.205120i | ||||
\(187\) | 3.17564i | 0.232226i | ||||||||
\(188\) | −10.2125 | + | 18.7730i | −0.744824 | + | 1.36916i | ||||
\(189\) | 5.60090i | 0.407405i | ||||||||
\(190\) | 0.748959 | − | 0.445175i | 0.0543352 | − | 0.0322964i | ||||
\(191\) | −2.49777 | −0.180732 | −0.0903660 | − | 0.995909i | \(-0.528804\pi\) | ||||
−0.0903660 | + | 0.995909i | \(0.528804\pi\) | |||||||
\(192\) | −0.929339 | − | 12.1850i | −0.0670692 | − | 0.879379i | ||||
\(193\) | 7.13085 | 0.513290 | 0.256645 | − | 0.966506i | \(-0.417383\pi\) | ||||
0.256645 | + | 0.966506i | \(0.417383\pi\) | |||||||
\(194\) | 3.54401 | − | 2.10653i | 0.254445 | − | 0.151240i | ||||
\(195\) | − | 1.85636i | − | 0.132937i | ||||||
\(196\) | 0.955734 | − | 1.75686i | 0.0682667 | − | 0.125490i | ||||
\(197\) | 9.55907i | 0.681056i | 0.940234 | + | 0.340528i | \(0.110606\pi\) | ||||
−0.940234 | + | 0.340528i | \(0.889394\pi\) | |||||||
\(198\) | 0.589445 | + | 0.991678i | 0.0418900 | + | 0.0704755i | ||||
\(199\) | −1.51023 | −0.107057 | −0.0535286 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535286 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(200\) | 0.107626 | + | 2.82638i | 0.00761031 | + | 0.199855i | ||||
\(201\) | −13.9959 | −0.987193 | ||||||||
\(202\) | 8.71347 | + | 14.6595i | 0.613078 | + | 1.03144i | ||||
\(203\) | − | 9.00634i | − | 0.632121i | ||||||
\(204\) | 6.96412 | + | 3.78848i | 0.487586 | + | 0.265247i | ||||
\(205\) | − | 4.58844i | − | 0.320470i | ||||||
\(206\) | 1.49600 | − | 0.889211i | 0.104231 | − | 0.0619543i | ||||
\(207\) | −5.57871 | −0.387747 | ||||||||
\(208\) | 4.08105 | − | 2.64092i | 0.282970 | − | 0.183115i | ||||
\(209\) | 0.753946 | 0.0521515 | ||||||||
\(210\) | −1.85701 | + | 1.10379i | −0.128146 | + | 0.0761688i | ||||
\(211\) | 3.63666i | 0.250358i | 0.992134 | + | 0.125179i | \(0.0399505\pi\) | ||||
−0.992134 | + | 0.125179i | \(0.960050\pi\) | |||||||
\(212\) | 8.12480 | + | 4.41989i | 0.558013 | + | 0.303559i | ||||
\(213\) | 20.4510i | 1.40128i | ||||||||
\(214\) | 7.93779 | + | 13.3545i | 0.542616 | + | 0.912893i | ||||
\(215\) | 0.301914 | 0.0205904 | ||||||||
\(216\) | 15.8303 | − | 0.602803i | 1.07711 | − | 0.0410155i | ||||
\(217\) | −1.50644 | −0.102264 | ||||||||
\(218\) | −8.05654 | − | 13.5543i | −0.545658 | − | 0.918010i | ||||
\(219\) | 23.5061i | 1.58840i | ||||||||
\(220\) | −1.16960 | + | 2.15000i | −0.0788543 | + | 0.144953i | ||||
\(221\) | 3.15354i | 0.212130i | ||||||||
\(222\) | 8.11353 | − | 4.82262i | 0.544544 | − | 0.323673i | ||||
\(223\) | −11.1788 | −0.748585 | −0.374292 | − | 0.927311i | \(-0.622114\pi\) | ||||
−0.374292 | + | 0.927311i | \(0.622114\pi\) | |||||||
\(224\) | −5.06843 | − | 2.51218i | −0.338648 | − | 0.167852i | ||||
\(225\) | −0.666582 | −0.0444388 | ||||||||
\(226\) | 19.0917 | − | 11.3479i | 1.26996 | − | 0.754853i | ||||
\(227\) | − | 28.6749i | − | 1.90322i | −0.307311 | − | 0.951609i | \(-0.599429\pi\) | ||
0.307311 | − | 0.951609i | \(-0.400571\pi\) | |||||||
\(228\) | 0.899444 | − | 1.65339i | 0.0595671 | − | 0.109498i | ||||
\(229\) | 25.7972i | 1.70473i | 0.522951 | + | 0.852363i | \(0.324831\pi\) | ||||
−0.522951 | + | 0.852363i | \(0.675169\pi\) | |||||||
\(230\) | −6.04744 | − | 10.1742i | −0.398756 | − | 0.670864i | ||||
\(231\) | −1.86937 | −0.122996 | ||||||||
\(232\) | −25.4553 | + | 0.969317i | −1.67122 | + | 0.0636388i | ||||
\(233\) | 1.67971 | 0.110041 | 0.0550207 | − | 0.998485i | \(-0.482478\pi\) | ||||
0.0550207 | + | 0.998485i | \(0.482478\pi\) | |||||||
\(234\) | 0.585343 | + | 0.984776i | 0.0382651 | + | 0.0643768i | ||||
\(235\) | − | 10.6855i | − | 0.697047i | ||||||
\(236\) | −9.39527 | − | 5.11103i | −0.611580 | − | 0.332699i | ||||
\(237\) | − | 10.2226i | − | 0.664032i | ||||||
\(238\) | 3.15464 | − | 1.87509i | 0.204485 | − | 0.121544i | ||||
\(239\) | 7.35061 | 0.475471 | 0.237736 | − | 0.971330i | \(-0.423595\pi\) | ||||
0.237736 | + | 0.971330i | \(0.423595\pi\) | |||||||
\(240\) | 3.31959 | + | 5.12981i | 0.214279 | + | 0.331128i | ||||
\(241\) | −9.47954 | −0.610631 | −0.305315 | − | 0.952251i | \(-0.598762\pi\) | ||||
−0.305315 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(242\) | 11.5518 | − | 6.86631i | 0.742579 | − | 0.441383i | ||||
\(243\) | 6.78817i | 0.435462i | ||||||||
\(244\) | −6.23453 | − | 3.39159i | −0.399125 | − | 0.217124i | ||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | −5.06467 | − | 8.52077i | −0.322912 | − | 0.543264i | ||||
\(247\) | 0.748699 | 0.0476385 | ||||||||
\(248\) | 0.162132 | + | 4.25776i | 0.0102954 | + | 0.270368i | ||||
\(249\) | −13.7899 | −0.873901 | ||||||||
\(250\) | −0.722588 | − | 1.21568i | −0.0457005 | − | 0.0768861i | ||||
\(251\) | 26.4286i | 1.66816i | 0.551645 | + | 0.834079i | \(0.314000\pi\) | ||||
−0.551645 | + | 0.834079i | \(0.686000\pi\) | |||||||
\(252\) | 0.637075 | − | 1.17109i | 0.0401319 | − | 0.0737720i | ||||
\(253\) | − | 10.2419i | − | 0.643902i | ||||||
\(254\) | 10.3968 | − | 6.17977i | 0.652352 | − | 0.387753i | ||||
\(255\) | −3.96395 | −0.248232 | ||||||||
\(256\) | −6.55488 | + | 14.5957i | −0.409680 | + | 0.912229i | ||||
\(257\) | −30.0639 | −1.87533 | −0.937666 | − | 0.347538i | \(-0.887018\pi\) | ||||
−0.937666 | + | 0.347538i | \(0.887018\pi\) | |||||||
\(258\) | 0.560658 | − | 0.333250i | 0.0349050 | − | 0.0207473i | ||||
\(259\) | − | 4.36914i | − | 0.271485i | ||||||
\(260\) | −1.16146 | + | 2.13503i | −0.0720306 | + | 0.132409i | ||||
\(261\) | − | 6.00346i | − | 0.371605i | ||||||
\(262\) | −7.91165 | − | 13.3105i | −0.488784 | − | 0.822326i | ||||
\(263\) | −10.0971 | −0.622617 | −0.311308 | − | 0.950309i | \(-0.600767\pi\) | ||||
−0.311308 | + | 0.950309i | \(0.600767\pi\) | |||||||
\(264\) | 0.201193 | + | 5.28355i | 0.0123826 | + | 0.325180i | ||||
\(265\) | −4.62460 | −0.284087 | ||||||||
\(266\) | −0.445175 | − | 0.748959i | −0.0272955 | − | 0.0459216i | ||||
\(267\) | − | 19.1133i | − | 1.16972i | ||||||
\(268\) | 16.0969 | + | 8.75671i | 0.983274 | + | 0.534901i | ||||
\(269\) | − | 3.89504i | − | 0.237484i | −0.992925 | − | 0.118742i | \(-0.962114\pi\) | ||
0.992925 | − | 0.118742i | \(-0.0378862\pi\) | |||||||
\(270\) | −6.80887 | + | 4.04714i | −0.414375 | + | 0.246301i | ||||
\(271\) | 4.59538 | 0.279149 | 0.139575 | − | 0.990212i | \(-0.455426\pi\) | ||||
0.139575 | + | 0.990212i | \(0.455426\pi\) | |||||||
\(272\) | −5.63924 | − | 8.71439i | −0.341929 | − | 0.528388i | ||||
\(273\) | −1.85636 | −0.112352 | ||||||||
\(274\) | −15.7635 | + | 9.36968i | −0.952306 | + | 0.566043i | ||||
\(275\) | − | 1.22377i | − | 0.0737960i | ||||||
\(276\) | −22.4603 | − | 12.2184i | −1.35195 | − | 0.735461i | ||||
\(277\) | 23.8524i | 1.43315i | 0.697509 | + | 0.716576i | \(0.254292\pi\) | ||||
−0.697509 | + | 0.716576i | \(0.745708\pi\) | |||||||
\(278\) | −7.61440 | − | 12.8104i | −0.456681 | − | 0.768317i | ||||
\(279\) | −1.00416 | −0.0601176 | ||||||||
\(280\) | 2.82638 | − | 0.107626i | 0.168908 | − | 0.00643189i | ||||
\(281\) | −18.5743 | −1.10805 | −0.554026 | − | 0.832499i | \(-0.686909\pi\) | ||||
−0.554026 | + | 0.832499i | \(0.686909\pi\) | |||||||
\(282\) | −11.7946 | − | 19.8431i | −0.702357 | − | 1.18164i | ||||
\(283\) | − | 26.2412i | − | 1.55988i | −0.625855 | − | 0.779939i | \(-0.715250\pi\) | ||
0.625855 | − | 0.779939i | \(-0.284750\pi\) | |||||||
\(284\) | 12.7954 | − | 23.5210i | 0.759270 | − | 1.39572i | ||||
\(285\) | 0.941102i | 0.0557461i | ||||||||
\(286\) | −1.80794 | + | 1.07462i | −0.106906 | + | 0.0635438i | ||||
\(287\) | −4.58844 | −0.270847 | ||||||||
\(288\) | −3.37852 | − | 1.67457i | −0.199081 | − | 0.0986753i | ||||
\(289\) | −10.2661 | −0.603891 | ||||||||
\(290\) | 10.9488 | − | 6.50787i | 0.642935 | − | 0.382155i | ||||
\(291\) | 4.45321i | 0.261052i | ||||||||
\(292\) | 14.7069 | − | 27.0348i | 0.860657 | − | 1.58209i | ||||
\(293\) | 32.6791i | 1.90913i | 0.297995 | + | 0.954567i | \(0.403682\pi\) | ||||
−0.297995 | + | 0.954567i | \(0.596318\pi\) | |||||||
\(294\) | 1.10379 | + | 1.85701i | 0.0643744 | + | 0.108303i | ||||
\(295\) | 5.34775 | 0.311358 | ||||||||
\(296\) | −12.3488 | + | 0.470233i | −0.717762 | + | 0.0273317i | ||||
\(297\) | −6.85421 | −0.397721 | ||||||||
\(298\) | 3.09127 | + | 5.20073i | 0.179073 | + | 0.301270i | ||||
\(299\) | − | 10.1706i | − | 0.588182i | ||||||
\(300\) | −2.68370 | − | 1.45993i | −0.154944 | − | 0.0842894i | ||||
\(301\) | − | 0.301914i | − | 0.0174021i | ||||||
\(302\) | 22.2670 | − | 13.2353i | 1.28132 | − | 0.761608i | ||||
\(303\) | −18.4203 | −1.05822 | ||||||||
\(304\) | −2.06893 | + | 1.33884i | −0.118661 | + | 0.0767878i | ||||
\(305\) | 3.54867 | 0.203196 | ||||||||
\(306\) | 2.10282 | − | 1.24990i | 0.120210 | − | 0.0714521i | ||||
\(307\) | 14.6454i | 0.835857i | 0.908480 | + | 0.417928i | \(0.137244\pi\) | ||||
−0.908480 | + | 0.417928i | \(0.862756\pi\) | |||||||
\(308\) | 2.15000 | + | 1.16960i | 0.122507 | + | 0.0666440i | ||||
\(309\) | 1.87979i | 0.106938i | ||||||||
\(310\) | −1.08853 | − | 1.83134i | −0.0618245 | − | 0.104013i | ||||
\(311\) | −7.95771 | −0.451240 | −0.225620 | − | 0.974215i | \(-0.572441\pi\) | ||||
−0.225620 | + | 0.974215i | \(0.572441\pi\) | |||||||
\(312\) | 0.199793 | + | 5.24678i | 0.0113110 | + | 0.297041i | ||||
\(313\) | 22.7593 | 1.28643 | 0.643215 | − | 0.765685i | \(-0.277600\pi\) | ||||
0.643215 | + | 0.765685i | \(0.277600\pi\) | |||||||
\(314\) | −4.57092 | − | 7.69009i | −0.257952 | − | 0.433977i | ||||
\(315\) | 0.666582i | 0.0375576i | ||||||||
\(316\) | −6.39593 | + | 11.7572i | −0.359799 | + | 0.661396i | ||||
\(317\) | − | 24.6960i | − | 1.38707i | −0.720424 | − | 0.693534i | \(-0.756053\pi\) | ||
0.720424 | − | 0.693534i | \(-0.243947\pi\) | |||||||
\(318\) | −8.58793 | + | 5.10459i | −0.481587 | + | 0.286251i | ||||
\(319\) | 11.0217 | 0.617096 | ||||||||
\(320\) | −0.608384 | − | 7.97683i | −0.0340097 | − | 0.445919i | ||||
\(321\) | −16.7805 | −0.936597 | ||||||||
\(322\) | −10.1742 | + | 6.04744i | −0.566984 | + | 0.337010i | ||||
\(323\) | − | 1.59872i | − | 0.0889552i | ||||||
\(324\) | −6.26572 | + | 11.5179i | −0.348096 | + | 0.639882i | ||||
\(325\) | − | 1.21525i | − | 0.0674101i | ||||||
\(326\) | −1.82454 | − | 3.06959i | −0.101052 | − | 0.170009i | ||||
\(327\) | 17.0316 | 0.941847 | ||||||||
\(328\) | 0.493835 | + | 12.9687i | 0.0272675 | + | 0.716074i | ||||
\(329\) | −10.6855 | −0.589112 | ||||||||
\(330\) | −1.35079 | − | 2.27255i | −0.0743583 | − | 0.125100i | ||||
\(331\) | 21.9090i | 1.20423i | 0.798411 | + | 0.602113i | \(0.205674\pi\) | ||||
−0.798411 | + | 0.602113i | \(0.794326\pi\) | |||||||
\(332\) | 15.8600 | + | 8.62785i | 0.870432 | + | 0.473515i | ||||
\(333\) | − | 2.91239i | − | 0.159598i | ||||||
\(334\) | −6.32141 | + | 3.75739i | −0.345892 | + | 0.205595i | ||||
\(335\) | −9.16229 | −0.500589 | ||||||||
\(336\) | 5.12981 | − | 3.31959i | 0.279854 | − | 0.181099i | ||||
\(337\) | −8.11255 | −0.441919 | −0.220959 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220959 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(338\) | 14.0084 | − | 8.32650i | 0.761958 | − | 0.452902i | ||||
\(339\) | 23.9896i | 1.30293i | ||||||||
\(340\) | 4.55901 | + | 2.48010i | 0.247247 | + | 0.134502i | ||||
\(341\) | − | 1.84353i | − | 0.0998327i | ||||||
\(342\) | −0.296746 | − | 0.499243i | −0.0160462 | − | 0.0269959i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.853325 | + | 0.0324939i | −0.0460082 | + | 0.00175195i | ||||
\(345\) | 12.7843 | 0.688284 | ||||||||
\(346\) | 16.2503 | + | 27.3393i | 0.873620 | + | 1.46977i | ||||
\(347\) | − | 16.4019i | − | 0.880502i | −0.897875 | − | 0.440251i | \(-0.854889\pi\) | ||
0.897875 | − | 0.440251i | \(-0.145111\pi\) | |||||||
\(348\) | 13.1487 | − | 24.1703i | 0.704842 | − | 1.29567i | ||||
\(349\) | − | 6.10529i | − | 0.326809i | −0.986559 | − | 0.163404i | \(-0.947752\pi\) | ||
0.986559 | − | 0.163404i | \(-0.0522476\pi\) | |||||||
\(350\) | −1.21568 | + | 0.722588i | −0.0649806 | + | 0.0386239i | ||||
\(351\) | −6.80650 | −0.363304 | ||||||||
\(352\) | 3.07433 | − | 6.20258i | 0.163862 | − | 0.330599i | ||||
\(353\) | −32.8495 | −1.74840 | −0.874202 | − | 0.485562i | \(-0.838615\pi\) | ||||
−0.874202 | + | 0.485562i | \(0.838615\pi\) | |||||||
\(354\) | 9.93082 | − | 5.90280i | 0.527817 | − | 0.313730i | ||||
\(355\) | 13.3881i | 0.710565i | ||||||||
\(356\) | −11.9585 | + | 21.9825i | −0.633799 | + | 1.16507i | ||||
\(357\) | 3.96395i | 0.209795i | ||||||||
\(358\) | −13.3921 | − | 22.5308i | −0.707796 | − | 1.19079i | ||||
\(359\) | 5.79226 | 0.305704 | 0.152852 | − | 0.988249i | \(-0.451154\pi\) | ||||
0.152852 | + | 0.988249i | \(0.451154\pi\) | |||||||
\(360\) | 1.88401 | − | 0.0717416i | 0.0992962 | − | 0.00378111i | ||||
\(361\) | 18.6204 | 0.980023 | ||||||||
\(362\) | 5.00599 | + | 8.42203i | 0.263109 | + | 0.442652i | ||||
\(363\) | 14.5154i | 0.761861i | ||||||||
\(364\) | 2.13503 | + | 1.16146i | 0.111906 | + | 0.0608769i | ||||
\(365\) | 15.3881i | 0.805449i | ||||||||
\(366\) | 6.58991 | − | 3.91699i | 0.344460 | − | 0.204744i | ||||
\(367\) | 34.3223 | 1.79161 | 0.895806 | − | 0.444446i | \(-0.146599\pi\) | ||||
0.895806 | + | 0.444446i | \(0.146599\pi\) | |||||||
\(368\) | 18.1873 | + | 28.1052i | 0.948081 | + | 1.46508i | ||||
\(369\) | −3.05857 | −0.159223 | ||||||||
\(370\) | 5.31145 | − | 3.15709i | 0.276129 | − | 0.164129i | ||||
\(371\) | 4.62460i | 0.240097i | ||||||||
\(372\) | −4.04283 | − | 2.19930i | −0.209611 | − | 0.114028i | ||||
\(373\) | − | 25.7019i | − | 1.33079i | −0.746489 | − | 0.665397i | \(-0.768262\pi\) | ||
0.746489 | − | 0.665397i | \(-0.231738\pi\) | |||||||
\(374\) | 2.29468 | + | 3.86055i | 0.118655 | + | 0.199624i | ||||
\(375\) | 1.52755 | 0.0788825 | ||||||||
\(376\) | 1.15004 | + | 30.2013i | 0.0593088 | + | 1.55751i | ||||
\(377\) | 10.9450 | 0.563695 | ||||||||
\(378\) | 4.04714 | + | 6.80887i | 0.208162 | + | 0.350211i | ||||
\(379\) | 21.1070i | 1.08419i | 0.840316 | + | 0.542097i | \(0.182369\pi\) | ||||
−0.840316 | + | 0.542097i | \(0.817631\pi\) | |||||||
\(380\) | 0.588813 | − | 1.08238i | 0.0302055 | − | 0.0555248i | ||||
\(381\) | 13.0640i | 0.669291i | ||||||||
\(382\) | −3.03647 | + | 1.80485i | −0.155359 | + | 0.0923444i | ||||
\(383\) | 16.1690 | 0.826196 | 0.413098 | − | 0.910687i | \(-0.364447\pi\) | ||||
0.413098 | + | 0.910687i | \(0.364447\pi\) | |||||||
\(384\) | −9.93453 | − | 14.1415i | −0.506969 | − | 0.721656i | ||||
\(385\) | −1.22377 | −0.0623690 | ||||||||
\(386\) | 8.66880 | − | 5.15266i | 0.441230 | − | 0.262264i | ||||
\(387\) | − | 0.201251i | − | 0.0102301i | ||||||
\(388\) | 2.78621 | − | 5.12172i | 0.141449 | − | 0.260016i | ||||
\(389\) | 15.6258i | 0.792258i | 0.918195 | + | 0.396129i | \(0.129647\pi\) | ||||
−0.918195 | + | 0.396129i | \(0.870353\pi\) | |||||||
\(390\) | −1.34138 | − | 2.25673i | −0.0679236 | − | 0.114274i | ||||
\(391\) | −21.7176 | −1.09831 | ||||||||
\(392\) | −0.107626 | − | 2.82638i | −0.00543594 | − | 0.142754i | ||||
\(393\) | 16.7253 | 0.843678 | ||||||||
\(394\) | 6.90727 | + | 11.6207i | 0.347983 | + | 0.585444i | ||||
\(395\) | − | 6.69217i | − | 0.336720i | ||||||
\(396\) | 1.43315 | + | 0.779632i | 0.0720184 | + | 0.0391780i | ||||
\(397\) | − | 25.6663i | − | 1.28815i | −0.764961 | − | 0.644076i | \(-0.777242\pi\) | ||
0.764961 | − | 0.644076i | \(-0.222758\pi\) | |||||||
\(398\) | −1.83595 | + | 1.09127i | −0.0920277 | + | 0.0547005i | ||||
\(399\) | 0.941102 | 0.0471140 | ||||||||
\(400\) | 2.17314 | + | 3.35819i | 0.108657 | + | 0.167910i | ||||
\(401\) | 4.29958 | 0.214711 | 0.107355 | − | 0.994221i | \(-0.465762\pi\) | ||||
0.107355 | + | 0.994221i | \(0.465762\pi\) | |||||||
\(402\) | −17.0144 | + | 10.1132i | −0.848604 | + | 0.504403i | ||||
\(403\) | − | 1.83070i | − | 0.0911936i | ||||||
\(404\) | 21.1855 | + | 11.5249i | 1.05402 | + | 0.573386i | ||||
\(405\) | − | 6.55592i | − | 0.325766i | ||||||
\(406\) | −6.50787 | − | 10.9488i | −0.322980 | − | 0.543379i | ||||
\(407\) | 5.34682 | 0.265032 | ||||||||
\(408\) | 11.2036 | − | 0.426624i | 0.554662 | − | 0.0211211i | ||||
\(409\) | −18.1383 | −0.896881 | −0.448440 | − | 0.893813i | \(-0.648020\pi\) | ||||
−0.448440 | + | 0.893813i | \(0.648020\pi\) | |||||||
\(410\) | −3.31555 | − | 5.57805i | −0.163743 | − | 0.275480i | ||||
\(411\) | − | 19.8075i | − | 0.977034i | ||||||
\(412\) | 1.17612 | − | 2.16198i | 0.0579432 | − | 0.106513i | ||||
\(413\) | − | 5.34775i | − | 0.263146i | ||||||
\(414\) | −6.78191 | + | 4.03111i | −0.333313 | + | 0.198118i | ||||
\(415\) | −9.02746 | −0.443140 | ||||||||
\(416\) | 3.05293 | − | 6.15942i | 0.149682 | − | 0.301990i | ||||
\(417\) | 16.0969 | 0.788267 | ||||||||
\(418\) | 0.916553 | − | 0.544792i | 0.0448301 | − | 0.0266466i | ||||
\(419\) | − | 33.4913i | − | 1.63616i | −0.575107 | − | 0.818078i | \(-0.695040\pi\) | ||
0.575107 | − | 0.818078i | \(-0.304960\pi\) | |||||||
\(420\) | −1.45993 | + | 2.68370i | −0.0712375 | + | 0.130951i | ||||
\(421\) | − | 24.4624i | − | 1.19222i | −0.802901 | − | 0.596112i | \(-0.796711\pi\) | ||
0.802901 | − | 0.596112i | \(-0.203289\pi\) | |||||||
\(422\) | 2.62780 | + | 4.42099i | 0.127919 | + | 0.215211i | ||||
\(423\) | −7.12277 | −0.346321 | ||||||||
\(424\) | 13.0709 | − | 0.497728i | 0.634778 | − | 0.0241718i | ||||
\(425\) | −2.59497 | −0.125874 | ||||||||
\(426\) | 14.7776 | + | 24.8618i | 0.715979 | + | 1.20456i | ||||
\(427\) | − | 3.54867i | − | 0.171732i | ||||||
\(428\) | 19.2995 | + | 10.4990i | 0.932879 | + | 0.507486i | ||||
\(429\) | − | 2.27176i | − | 0.109682i | ||||||
\(430\) | 0.367030 | − | 0.218160i | 0.0176998 | − | 0.0105206i | ||||
\(431\) | 40.9753 | 1.97371 | 0.986856 | − | 0.161602i | \(-0.0516662\pi\) | ||||
0.986856 | + | 0.161602i | \(0.0516662\pi\) | |||||||
\(432\) | 18.8089 | − | 12.1716i | 0.904943 | − | 0.585605i | ||||
\(433\) | 16.8063 | 0.807657 | 0.403828 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403828 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(434\) | −1.83134 | + | 1.08853i | −0.0879070 | + | 0.0522512i | ||||
\(435\) | 13.7577i | 0.659629i | ||||||||
\(436\) | −19.5883 | − | 10.6560i | −0.938108 | − | 0.510331i | ||||
\(437\) | 5.15610i | 0.246650i | ||||||||
\(438\) | 16.9852 | + | 28.5758i | 0.811585 | + | 1.36540i | ||||
\(439\) | 11.0244 | 0.526167 | 0.263084 | − | 0.964773i | \(-0.415261\pi\) | ||||
0.263084 | + | 0.964773i | \(0.415261\pi\) | |||||||
\(440\) | 0.131709 | + | 3.45883i | 0.00627900 | + | 0.164893i | ||||
\(441\) | 0.666582 | 0.0317420 | ||||||||
\(442\) | 2.27871 | + | 3.83368i | 0.108387 | + | 0.182350i | ||||
\(443\) | − | 16.7121i | − | 0.794015i | −0.917815 | − | 0.397008i | \(-0.870049\pi\) | ||
0.917815 | − | 0.397008i | \(-0.129951\pi\) | |||||||
\(444\) | 6.37865 | − | 11.7255i | 0.302718 | − | 0.556466i | ||||
\(445\) | − | 12.5124i | − | 0.593143i | ||||||
\(446\) | −13.5897 | + | 8.07763i | −0.643493 | + | 0.382487i | ||||
\(447\) | −6.53496 | −0.309093 | ||||||||
\(448\) | −7.97683 | + | 0.608384i | −0.376870 | + | 0.0287434i | ||||
\(449\) | 31.8563 | 1.50339 | 0.751696 | − | 0.659509i | \(-0.229236\pi\) | ||||
0.751696 | + | 0.659509i | \(0.229236\pi\) | |||||||
\(450\) | −0.810347 | + | 0.481664i | −0.0382001 | + | 0.0227058i | ||||
\(451\) | − | 5.61519i | − | 0.264409i | ||||||
\(452\) | 15.0094 | − | 27.5908i | 0.705983 | − | 1.29776i | ||||
\(453\) | 27.9795i | 1.31459i | ||||||||
\(454\) | −20.7201 | − | 34.8593i | −0.972443 | − | 1.63603i | ||||
\(455\) | −1.21525 | −0.0569719 | ||||||||
\(456\) | −0.101287 | − | 2.65991i | −0.00474320 | − | 0.124562i | ||||
\(457\) | −7.35361 | −0.343987 | −0.171994 | − | 0.985098i | \(-0.555021\pi\) | ||||
−0.171994 | + | 0.985098i | \(0.555021\pi\) | |||||||
\(458\) | 18.6407 | + | 31.3610i | 0.871024 | + | 1.46540i | ||||
\(459\) | 14.5341i | 0.678396i | ||||||||
\(460\) | −14.7034 | − | 7.99867i | −0.685551 | − | 0.372940i | ||||
\(461\) | − | 25.7173i | − | 1.19777i | −0.800833 | − | 0.598887i | \(-0.795610\pi\) | ||
0.800833 | − | 0.598887i | \(-0.204390\pi\) | |||||||
\(462\) | −2.27255 | + | 1.35079i | −0.105729 | + | 0.0628442i | ||||
\(463\) | −26.1530 | −1.21543 | −0.607716 | − | 0.794154i | \(-0.707914\pi\) | ||||
−0.607716 | + | 0.794154i | \(0.707914\pi\) | |||||||
\(464\) | −30.2450 | + | 19.5721i | −1.40409 | + | 0.908611i | ||||
\(465\) | 2.30116 | 0.106714 | ||||||||
\(466\) | 2.04198 | − | 1.21374i | 0.0945929 | − | 0.0562252i | ||||
\(467\) | − | 7.89518i | − | 0.365345i | −0.983174 | − | 0.182673i | \(-0.941525\pi\) | ||
0.983174 | − | 0.182673i | \(-0.0584748\pi\) | |||||||
\(468\) | 1.42317 | + | 0.774207i | 0.0657862 | + | 0.0357877i | ||||
\(469\) | 9.16229i | 0.423075i | ||||||||
\(470\) | −7.72123 | − | 12.9901i | −0.356154 | − | 0.599190i | ||||
\(471\) | 9.66295 | 0.445245 | ||||||||
\(472\) | −15.1148 | + | 0.575557i | −0.695713 | + | 0.0264922i | ||||
\(473\) | 0.369474 | 0.0169884 | ||||||||
\(474\) | −7.38676 | − | 12.4274i | −0.339285 | − | 0.570810i | ||||
\(475\) | 0.616085i | 0.0282679i | ||||||||
\(476\) | 2.48010 | − | 4.55901i | 0.113675 | − | 0.208962i | ||||
\(477\) | 3.08268i | 0.141146i | ||||||||
\(478\) | 8.93595 | − | 5.31146i | 0.408721 | − | 0.242940i | ||||
\(479\) | 24.6752 | 1.12744 | 0.563720 | − | 0.825966i | \(-0.309370\pi\) | ||||
0.563720 | + | 0.825966i | \(0.309370\pi\) | |||||||
\(480\) | 7.74229 | + | 3.83749i | 0.353386 | + | 0.175157i | ||||
\(481\) | 5.30960 | 0.242097 | ||||||||
\(482\) | −11.5240 | + | 6.84980i | −0.524906 | + | 0.312000i | ||||
\(483\) | − | 12.7843i | − | 0.581706i | ||||||
\(484\) | 9.08176 | − | 16.6944i | 0.412807 | − | 0.758837i | ||||
\(485\) | 2.91526i | 0.132375i | ||||||||
\(486\) | 4.90505 | + | 8.25222i | 0.222498 | + | 0.374328i | ||||
\(487\) | −14.2369 | −0.645138 | −0.322569 | − | 0.946546i | \(-0.604546\pi\) | ||||
−0.322569 | + | 0.946546i | \(0.604546\pi\) | |||||||
\(488\) | −10.0299 | + | 0.381929i | −0.454032 | + | 0.0172891i | ||||
\(489\) | 3.85708 | 0.174423 | ||||||||
\(490\) | 0.722588 | + | 1.21568i | 0.0326432 | + | 0.0549186i | ||||
\(491\) | 14.6003i | 0.658902i | 0.944173 | + | 0.329451i | \(0.106864\pi\) | ||||
−0.944173 | + | 0.329451i | \(0.893136\pi\) | |||||||
\(492\) | −12.3140 | − | 6.69882i | −0.555158 | − | 0.302006i | ||||
\(493\) | − | 23.3712i | − | 1.05258i | ||||||
\(494\) | 0.910174 | − | 0.541000i | 0.0409507 | − | 0.0243408i | ||||
\(495\) | −0.815742 | −0.0366649 | ||||||||
\(496\) | 3.27370 | + | 5.05890i | 0.146994 | + | 0.227151i | ||||
\(497\) | 13.3881 | 0.600537 | ||||||||
\(498\) | −16.7641 | + | 9.96443i | −0.751216 | + | 0.446517i | ||||
\(499\) | 22.9361i | 1.02676i | 0.858161 | + | 0.513381i | \(0.171607\pi\) | ||||
−0.858161 | + | 0.513381i | \(0.828393\pi\) | |||||||
\(500\) | −1.75686 | − | 0.955734i | −0.0785694 | − | 0.0427417i | ||||
\(501\) | − | 7.94314i | − | 0.354873i | ||||||
\(502\) | 19.0970 | + | 32.1286i | 0.852340 | + | 1.43397i | ||||
\(503\) | −11.5344 | −0.514293 | −0.257147 | − | 0.966372i | \(-0.582782\pi\) | ||||
−0.257147 | + | 0.966372i | \(0.582782\pi\) | |||||||
\(504\) | −0.0717416 | − | 1.88401i | −0.00319562 | − | 0.0839206i | ||||
\(505\) | −12.0587 | −0.536605 | ||||||||
\(506\) | −7.40066 | − | 12.4508i | −0.329000 | − | 0.553506i | ||||
\(507\) | 17.6022i | 0.781743i | ||||||||
\(508\) | 8.17370 | − | 15.0252i | 0.362649 | − | 0.666635i | ||||
\(509\) | 10.7973i | 0.478582i | 0.970948 | + | 0.239291i | \(0.0769151\pi\) | ||||
−0.970948 | + | 0.239291i | \(0.923085\pi\) | |||||||
\(510\) | −4.81888 | + | 2.86430i | −0.213383 | + | 0.126833i | ||||
\(511\) | 15.3881 | 0.680729 | ||||||||
\(512\) | 2.57804 | + | 22.4801i | 0.113934 | + | 0.993488i | ||||
\(513\) | 3.45063 | 0.152349 | ||||||||
\(514\) | −36.5479 | + | 21.7238i | −1.61206 | + | 0.958195i | ||||
\(515\) | 1.23059i | 0.0542264i | ||||||||
\(516\) | 0.440775 | − | 0.810249i | 0.0194040 | − | 0.0356692i | ||||
\(517\) | − | 13.0766i | − | 0.575109i | ||||||
\(518\) | −3.15709 | − | 5.31145i | −0.138714 | − | 0.233372i | ||||
\(519\) | −34.3531 | −1.50794 | ||||||||
\(520\) | 0.130793 | + | 3.43476i | 0.00573564 | + | 0.150624i | ||||
\(521\) | 44.2258 | 1.93757 | 0.968784 | − | 0.247904i | \(-0.0797419\pi\) | ||||
0.968784 | + | 0.247904i | \(0.0797419\pi\) | |||||||
\(522\) | −4.33803 | − | 7.29826i | −0.189870 | − | 0.319436i | ||||
\(523\) | − | 11.9059i | − | 0.520608i | −0.965527 | − | 0.260304i | \(-0.916177\pi\) | ||
0.965527 | − | 0.260304i | \(-0.0838228\pi\) | |||||||
\(524\) | −19.2360 | − | 10.4644i | −0.840329 | − | 0.457139i | ||||
\(525\) | − | 1.52755i | − | 0.0666679i | ||||||
\(526\) | −12.2749 | + | 7.29608i | −0.535209 | + | 0.318124i | ||||
\(527\) | −3.90915 | −0.170285 | ||||||||
\(528\) | 4.06242 | + | 6.27771i | 0.176794 | + | 0.273202i | ||||
\(529\) | 47.0425 | 2.04532 | ||||||||
\(530\) | −5.62202 | + | 3.34168i | −0.244205 | + | 0.145153i | ||||
\(531\) | − | 3.56471i | − | 0.154695i | ||||||
\(532\) | −1.08238 | − | 0.588813i | −0.0469270 | − | 0.0255283i | ||||
\(533\) | − | 5.57611i | − | 0.241528i | ||||||
\(534\) | −13.8110 | − | 23.2356i | −0.597662 | − | 1.00550i | ||||
\(535\) | −10.9852 | −0.474933 | ||||||||
\(536\) | 25.8961 | − | 0.986101i | 1.11854 | − | 0.0425931i | ||||
\(537\) | 28.3110 | 1.22171 | ||||||||
\(538\) | −2.81450 | − | 4.73510i | −0.121342 | − | 0.204145i | ||||
\(539\) | 1.22377i | 0.0527115i | ||||||||
\(540\) | −5.35297 | + | 9.84002i | −0.230355 | + | 0.423447i | ||||
\(541\) | − | 24.9088i | − | 1.07091i | −0.844563 | − | 0.535457i | \(-0.820140\pi\) | ||
0.844563 | − | 0.535457i | \(-0.179860\pi\) | |||||||
\(542\) | 5.58649 | − | 3.32056i | 0.239960 | − | 0.142630i | ||||
\(543\) | −10.5827 | −0.454146 | ||||||||
\(544\) | −13.1524 | − | 6.51903i | −0.563905 | − | 0.279501i | ||||
\(545\) | 11.1496 | 0.477595 | ||||||||
\(546\) | −2.25673 | + | 1.34138i | −0.0965793 | + | 0.0574060i | ||||
\(547\) | − | 22.2892i | − | 0.953016i | −0.879170 | − | 0.476508i | \(-0.841902\pi\) | ||
0.879170 | − | 0.476508i | \(-0.158098\pi\) | |||||||
\(548\) | −12.3929 | + | 22.7810i | −0.529397 | + | 0.973156i | ||||
\(549\) | − | 2.36548i | − | 0.100956i | ||||||
\(550\) | −0.884280 | − | 1.48771i | −0.0377058 | − | 0.0634360i | ||||
\(551\) | −5.54867 | −0.236381 | ||||||||
\(552\) | −36.1333 | + | 1.37592i | −1.53793 | + | 0.0585632i | ||||
\(553\) | −6.69217 | −0.284580 | ||||||||
\(554\) | 17.2355 | + | 28.9968i | 0.732265 | + | 1.23196i | ||||
\(555\) | 6.67409i | 0.283299i | ||||||||
\(556\) | −18.5133 | − | 10.0712i | −0.785138 | − | 0.427115i | ||||
\(557\) | 36.4724i | 1.54538i | 0.634781 | + | 0.772692i | \(0.281090\pi\) | ||||
−0.634781 | + | 0.772692i | \(0.718910\pi\) | |||||||
\(558\) | −1.22074 | + | 0.725595i | −0.0516779 | + | 0.0307169i | ||||
\(559\) | 0.366902 | 0.0155183 | ||||||||
\(560\) | 3.35819 | − | 2.17314i | 0.141909 | − | 0.0918321i | ||||
\(561\) | −4.85096 | −0.204808 | ||||||||
\(562\) | −22.5804 | + | 13.4216i | −0.952495 | + | 0.566156i | ||||
\(563\) | 36.8169i | 1.55165i | 0.630951 | + | 0.775823i | \(0.282665\pi\) | ||||
−0.630951 | + | 0.775823i | \(0.717335\pi\) | |||||||
\(564\) | −28.6768 | − | 15.6002i | −1.20751 | − | 0.656885i | ||||
\(565\) | 15.7046i | 0.660697i | ||||||||
\(566\) | −18.9616 | − | 31.9008i | −0.797015 | − | 1.34089i | ||||
\(567\) | −6.55592 | −0.275323 | ||||||||
\(568\) | −1.44091 | − | 37.8398i | −0.0604591 | − | 1.58772i | ||||
\(569\) | −5.01521 | −0.210248 | −0.105124 | − | 0.994459i | \(-0.533524\pi\) | ||||
−0.105124 | + | 0.994459i | \(0.533524\pi\) | |||||||
\(570\) | 0.680029 | + | 1.14408i | 0.0284833 | + | 0.0479200i | ||||
\(571\) | 14.0744i | 0.588995i | 0.955652 | + | 0.294498i | \(0.0951523\pi\) | ||||
−0.955652 | + | 0.294498i | \(0.904848\pi\) | |||||||
\(572\) | −1.42136 | + | 2.61279i | −0.0594299 | + | 0.109246i | ||||
\(573\) | − | 3.81547i | − | 0.159394i | ||||||
\(574\) | −5.57805 | + | 3.31555i | −0.232823 | + | 0.138388i | ||||
\(575\) | 8.36914 | 0.349017 | ||||||||
\(576\) | −5.31721 | + | 0.405538i | −0.221550 | + | 0.0168974i | ||||
\(577\) | −44.3287 | −1.84543 | −0.922714 | − | 0.385485i | \(-0.874034\pi\) | ||||
−0.922714 | + | 0.385485i | \(0.874034\pi\) | |||||||
\(578\) | −12.4803 | + | 7.41819i | −0.519112 | + | 0.308556i | ||||
\(579\) | 10.8927i | 0.452687i | ||||||||
\(580\) | 8.60767 | − | 15.8229i | 0.357414 | − | 0.657011i | ||||
\(581\) | 9.02746i | 0.374522i | ||||||||
\(582\) | 3.21784 | + | 5.41366i | 0.133384 | + | 0.224404i | ||||
\(583\) | −5.65944 | −0.234390 | ||||||||
\(584\) | −1.65616 | − | 43.4925i | −0.0685323 | − | 1.79973i | ||||
\(585\) | −0.810065 | −0.0334921 | ||||||||
\(586\) | 23.6135 | + | 39.7272i | 0.975466 | + | 1.64112i | ||||
\(587\) | − | 7.17908i | − | 0.296313i | −0.988964 | − | 0.148156i | \(-0.952666\pi\) | ||
0.988964 | − | 0.148156i | \(-0.0473339\pi\) | |||||||
\(588\) | 2.68370 | + | 1.45993i | 0.110674 | + | 0.0602067i | ||||
\(589\) | 0.928092i | 0.0382414i | ||||||||
\(590\) | 6.50113 | − | 3.86422i | 0.267647 | − | 0.159087i | ||||
\(591\) | −14.6020 | −0.600646 | ||||||||
\(592\) | −14.6724 | + | 9.49477i | −0.603032 | + | 0.390233i | ||||
\(593\) | −13.2728 | −0.545051 | −0.272525 | − | 0.962149i | \(-0.587859\pi\) | ||||
−0.272525 | + | 0.962149i | \(0.587859\pi\) | |||||||
\(594\) | −8.33249 | + | 4.95276i | −0.341886 | + | 0.203214i | ||||
\(595\) | 2.59497i | 0.106383i | ||||||||
\(596\) | 7.51597 | + | 4.08869i | 0.307866 | + | 0.167479i | ||||
\(597\) | − | 2.30695i | − | 0.0944173i | ||||||
\(598\) | −7.34916 | − | 12.3642i | −0.300529 | − | 0.505608i | ||||
\(599\) | −9.23655 | −0.377395 | −0.188698 | − | 0.982035i | \(-0.560427\pi\) | ||||
−0.188698 | + | 0.982035i | \(0.560427\pi\) | |||||||
\(600\) | −4.31744 | + | 0.164405i | −0.176259 | + | 0.00671179i | ||||
\(601\) | −22.0644 | −0.900027 | −0.450014 | − | 0.893022i | \(-0.648581\pi\) | ||||
−0.450014 | + | 0.893022i | \(0.648581\pi\) | |||||||
\(602\) | −0.218160 | − | 0.367030i | −0.00889152 | − | 0.0149590i | ||||
\(603\) | 6.10741i | 0.248713i | ||||||||
\(604\) | 17.5058 | − | 32.1797i | 0.712300 | − | 1.30938i | ||||
\(605\) | 9.50239i | 0.386327i | ||||||||
\(606\) | −22.3931 | + | 13.3103i | −0.909659 | + | 0.540694i | ||||
\(607\) | 12.1921 | 0.494864 | 0.247432 | − | 0.968905i | \(-0.420413\pi\) | ||||
0.247432 | + | 0.968905i | \(0.420413\pi\) | |||||||
\(608\) | −1.54772 | + | 3.12258i | −0.0627682 | + | 0.126637i | ||||
\(609\) | 13.7577 | 0.557489 | ||||||||
\(610\) | 4.31403 | − | 2.56423i | 0.174670 | − | 0.103822i | ||||
\(611\) | − | 12.9856i | − | 0.525341i | ||||||
\(612\) | 1.65319 | − | 3.03895i | 0.0668262 | − | 0.122842i | ||||
\(613\) | − | 13.6108i | − | 0.549737i | −0.961482 | − | 0.274868i | \(-0.911366\pi\) | ||
0.961482 | − | 0.274868i | \(-0.0886343\pi\) | |||||||
\(614\) | 10.5826 | + | 17.8040i | 0.427078 | + | 0.718513i | ||||
\(615\) | 7.00908 | 0.282633 | ||||||||
\(616\) | 3.45883 | − | 0.131709i | 0.139360 | − | 0.00530672i | ||||
\(617\) | 8.92315 | 0.359233 | 0.179616 | − | 0.983737i | \(-0.442514\pi\) | ||||
0.179616 | + | 0.983737i | \(0.442514\pi\) | |||||||
\(618\) | 1.35832 | + | 2.28522i | 0.0546395 | + | 0.0919251i | ||||
\(619\) | − | 18.4729i | − | 0.742487i | −0.928536 | − | 0.371243i | \(-0.878932\pi\) | ||
0.928536 | − | 0.371243i | \(-0.121068\pi\) | |||||||
\(620\) | −2.64660 | − | 1.43975i | −0.106290 | − | 0.0578218i | ||||
\(621\) | − | 46.8747i | − | 1.88102i | ||||||
\(622\) | −9.67400 | + | 5.75015i | −0.387892 | + | 0.230560i | ||||
\(623\) | −12.5124 | −0.501297 | ||||||||
\(624\) | 4.03414 | + | 6.23402i | 0.161495 | + | 0.249560i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 27.6679 | − | 16.4456i | 1.10583 | − | 0.657297i | ||||
\(627\) | 1.15169i | 0.0459941i | ||||||||
\(628\) | −11.1135 | − | 6.04576i | −0.443478 | − | 0.241252i | ||||
\(629\) | − | 11.3378i | − | 0.452067i | ||||||
\(630\) | 0.481664 | + | 0.810347i | 0.0191899 | + | 0.0322850i | ||||
\(631\) | −31.4140 | −1.25057 | −0.625286 | − | 0.780396i | \(-0.715018\pi\) | ||||
−0.625286 | + | 0.780396i | \(0.715018\pi\) | |||||||
\(632\) | 0.720252 | + | 18.9146i | 0.0286501 | + | 0.752383i | ||||
\(633\) | −5.55518 | −0.220799 | ||||||||
\(634\) | −17.8451 | − | 30.0224i | −0.708718 | − | 1.19234i | ||||
\(635\) | 8.55227i | 0.339387i | ||||||||
\(636\) | −6.75162 | + | 12.4111i | −0.267719 | + | 0.492131i | ||||
\(637\) | 1.21525i | 0.0481500i | ||||||||
\(638\) | 13.3988 | − | 7.96413i | 0.530463 | − | 0.315303i | ||||
\(639\) | 8.92425 | 0.353038 | ||||||||
\(640\) | −6.50356 | − | 9.25763i | −0.257076 | − | 0.365940i | ||||
\(641\) | −1.35417 | −0.0534864 | −0.0267432 | − | 0.999642i | \(-0.508514\pi\) | ||||
−0.0267432 | + | 0.999642i | \(0.508514\pi\) | |||||||
\(642\) | −20.3997 | + | 12.1254i | −0.805110 | + | 0.478551i | ||||
\(643\) | − | 1.55217i | − | 0.0612116i | −0.999532 | − | 0.0306058i | \(-0.990256\pi\) | ||
0.999532 | − | 0.0306058i | \(-0.00974365\pi\) | |||||||
\(644\) | −7.99867 | + | 14.7034i | −0.315192 | + | 0.579397i | ||||
\(645\) | 0.461190i | 0.0181594i | ||||||||
\(646\) | −1.15522 | − | 1.94353i | −0.0454514 | − | 0.0764670i | ||||
\(647\) | 14.9269 | 0.586837 | 0.293418 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293418 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(648\) | 0.705588 | + | 18.5295i | 0.0277181 | + | 0.727908i | ||||
\(649\) | 6.54441 | 0.256891 | ||||||||
\(650\) | −0.878126 | − | 1.47735i | −0.0344429 | − | 0.0579465i | ||||
\(651\) | − | 2.30116i | − | 0.0901896i | ||||||
\(652\) | −4.43609 | − | 2.41323i | −0.173731 | − | 0.0945095i | ||||
\(653\) | − | 43.8373i | − | 1.71549i | −0.514078 | − | 0.857744i | \(-0.671866\pi\) | ||
0.514078 | − | 0.857744i | \(-0.328134\pi\) | |||||||
\(654\) | 20.7048 | − | 12.3068i | 0.809624 | − | 0.481234i | ||||
\(655\) | 10.9491 | 0.427815 | ||||||||
\(656\) | 9.97134 | + | 15.4088i | 0.389315 | + | 0.601614i | ||||
\(657\) | 10.2574 | 0.400180 | ||||||||
\(658\) | −12.9901 | + | 7.72123i | −0.506408 | + | 0.301005i | ||||
\(659\) | 21.8689i | 0.851893i | 0.904748 | + | 0.425946i | \(0.140059\pi\) | ||||
−0.904748 | + | 0.425946i | \(0.859941\pi\) | |||||||
\(660\) | −3.28423 | − | 1.78662i | −0.127839 | − | 0.0695442i | ||||
\(661\) | 13.0207i | 0.506446i | 0.967408 | + | 0.253223i | \(0.0814906\pi\) | ||||
−0.967408 | + | 0.253223i | \(0.918509\pi\) | |||||||
\(662\) | 15.8311 | + | 26.6342i | 0.615295 | + | 1.03517i | ||||
\(663\) | −4.81720 | −0.187085 | ||||||||
\(664\) | 25.5150 | − | 0.971590i | 0.990175 | − | 0.0377050i | ||||
\(665\) | 0.616085 | 0.0238907 | ||||||||
\(666\) | −2.10446 | − | 3.54052i | −0.0815460 | − | 0.137192i | ||||
\(667\) | 75.3753i | 2.91854i | ||||||||
\(668\) | −4.96973 | + | 9.13554i | −0.192285 | + | 0.353465i | ||||
\(669\) | − | 17.0761i | − | 0.660202i | ||||||
\(670\) | −11.1384 | + | 6.62056i | −0.430313 | + | 0.255774i | ||||
\(671\) | 4.34275 | 0.167650 | ||||||||
\(672\) | 3.83749 | − | 7.74229i | 0.148034 | − | 0.298665i | ||||
\(673\) | −23.1308 | −0.891629 | −0.445814 | − | 0.895125i | \(-0.647086\pi\) | ||||
−0.445814 | + | 0.895125i | \(0.647086\pi\) | |||||||
\(674\) | −9.86223 | + | 5.86203i | −0.379879 | + | 0.225797i | ||||
\(675\) | − | 5.60090i | − | 0.215579i | ||||||
\(676\) | 11.0131 | − | 20.2446i | 0.423580 | − | 0.778640i | ||||
\(677\) | − | 23.4736i | − | 0.902162i | −0.892483 | − | 0.451081i | \(-0.851039\pi\) | ||
0.892483 | − | 0.451081i | \(-0.148961\pi\) | |||||||
\(678\) | 17.3346 | + | 29.1635i | 0.665730 | + | 1.12002i | ||||
\(679\) | 2.91526 | 0.111877 | ||||||||
\(680\) | 7.33436 | − | 0.279286i | 0.281260 | − | 0.0107101i | ||||
\(681\) | 43.8024 | 1.67851 | ||||||||
\(682\) | −1.33211 | − | 2.24113i | −0.0510092 | − | 0.0858174i | ||||
\(683\) | − | 33.0062i | − | 1.26295i | −0.775397 | − | 0.631475i | \(-0.782450\pi\) | ||
0.775397 | − | 0.631475i | \(-0.217550\pi\) | |||||||
\(684\) | −0.721493 | − | 0.392492i | −0.0275870 | − | 0.0150073i | ||||
\(685\) | − | 12.9668i | − | 0.495438i | ||||||
\(686\) | 1.21568 | − | 0.722588i | 0.0464147 | − | 0.0275885i | ||||
\(687\) | −39.4066 | −1.50345 | ||||||||
\(688\) | −1.01389 | + | 0.656104i | −0.0386540 | + | 0.0250137i | ||||
\(689\) | −5.62006 | −0.214107 | ||||||||
\(690\) | 15.5416 | − | 9.23778i | 0.591657 | − | 0.351676i | ||||
\(691\) | − | 25.0583i | − | 0.953263i | −0.879103 | − | 0.476631i | \(-0.841858\pi\) | ||
0.879103 | − | 0.476631i | \(-0.158142\pi\) | |||||||
\(692\) | 39.5101 | + | 21.4935i | 1.50195 | + | 0.817060i | ||||
\(693\) | 0.815742i | 0.0309875i | ||||||||
\(694\) | −11.8518 | − | 19.9394i | −0.449890 | − | 0.756891i | ||||
\(695\) | 10.5377 | 0.399717 | ||||||||
\(696\) | −1.48068 | − | 38.8844i | −0.0561251 | − | 1.47391i | ||||
\(697\) | −11.9068 | −0.451004 | ||||||||
\(698\) | −4.41161 | − | 7.42206i | −0.166982 | − | 0.280929i | ||||
\(699\) | 2.56584i | 0.0970491i | ||||||||
\(700\) | −0.955734 | + | 1.75686i | −0.0361234 | + | 0.0664032i | ||||
\(701\) | 2.91899i | 0.110249i | 0.998479 | + | 0.0551244i | \(0.0175555\pi\) | ||||
−0.998479 | + | 0.0551244i | \(0.982444\pi\) | |||||||
\(702\) | −8.27450 | + | 4.91830i | −0.312301 | + | 0.185629i | ||||
\(703\) | −2.69176 | −0.101522 | ||||||||
\(704\) | −0.744521 | − | 9.76180i | −0.0280602 | − | 0.367912i | ||||
\(705\) | 16.3227 | 0.614749 | ||||||||
\(706\) | −39.9344 | + | 23.7367i | −1.50295 | + | 0.893341i | ||||
\(707\) | 12.0587i | 0.453514i | ||||||||
\(708\) | 7.80736 | − | 14.3518i | 0.293419 | − | 0.539373i | ||||
\(709\) | 27.0827i | 1.01711i | 0.861029 | + | 0.508556i | \(0.169821\pi\) | ||||
−0.861029 | + | 0.508556i | \(0.830179\pi\) | |||||||
\(710\) | 9.67406 | + | 16.2756i | 0.363061 | + | 0.610811i | ||||
\(711\) | −4.46088 | −0.167296 | ||||||||
\(712\) | 1.34666 | + | 35.3647i | 0.0504681 | + | 1.32535i | ||||
\(713\) | 12.6076 | 0.472157 | ||||||||
\(714\) | 2.86430 | + | 4.81888i | 0.107194 | + | 0.180342i | ||||
\(715\) | − | 1.48719i | − | 0.0556177i | ||||||
\(716\) | −32.5610 | − | 17.7132i | −1.21686 | − | 0.661972i | ||||
\(717\) | 11.2284i | 0.419334i | ||||||||
\(718\) | 7.04150 | − | 4.18541i | 0.262787 | − | 0.156198i | ||||
\(719\) | 33.3718 | 1.24456 | 0.622280 | − | 0.782795i | \(-0.286207\pi\) | ||||
0.622280 | + | 0.782795i | \(0.286207\pi\) | |||||||
\(720\) | 2.23851 | − | 1.44858i | 0.0834243 | − | 0.0539853i | ||||
\(721\) | 1.23059 | 0.0458296 | ||||||||
\(722\) | 22.6364 | − | 13.4549i | 0.842440 | − | 0.500740i | ||||
\(723\) | − | 14.4805i | − | 0.538536i | ||||||
\(724\) | 12.1713 | + | 6.62119i | 0.452343 | + | 0.246075i | ||||
\(725\) | 9.00634i | 0.334487i | ||||||||
\(726\) | 10.4887 | + | 17.6460i | 0.389270 | + | 0.654905i | ||||
\(727\) | −24.7727 | −0.918768 | −0.459384 | − | 0.888238i | \(-0.651930\pi\) | ||||
−0.459384 | + | 0.888238i | \(0.651930\pi\) | |||||||
\(728\) | 3.43476 | − | 0.130793i | 0.127301 | − | 0.00484750i | ||||
\(729\) | −30.0371 | −1.11248 | ||||||||
\(730\) | 11.1192 | + | 18.7069i | 0.411541 | + | 0.692374i | ||||
\(731\) | − | 0.783458i | − | 0.0289772i | ||||||
\(732\) | 5.18083 | − | 9.52358i | 0.191489 | − | 0.352002i | ||||
\(733\) | − | 9.77137i | − | 0.360914i | −0.983583 | − | 0.180457i | \(-0.942242\pi\) | ||
0.983583 | − | 0.180457i | \(-0.0577576\pi\) | |||||||
\(734\) | 41.7248 | − | 24.8009i | 1.54009 | − | 0.915418i | ||||
\(735\) | −1.52755 | −0.0563446 | ||||||||
\(736\) | 42.4184 | + | 21.0248i | 1.56356 | + | 0.774984i | ||||
\(737\) | −11.2125 | −0.413019 | ||||||||
\(738\) | −3.71823 | + | 2.21008i | −0.136870 | + | 0.0813543i | ||||
\(739\) | 8.19838i | 0.301582i | 0.988566 | + | 0.150791i | \(0.0481821\pi\) | ||||
−0.988566 | + | 0.150791i | \(0.951818\pi\) | |||||||
\(740\) | 4.17573 | − | 7.67598i | 0.153503 | − | 0.282175i | ||||
\(741\) | 1.14368i | 0.0420140i | ||||||||
\(742\) | 3.34168 | + | 5.62202i | 0.122677 | + | 0.206391i | ||||
\(743\) | 16.1936 | 0.594085 | 0.297043 | − | 0.954864i | \(-0.404000\pi\) | ||||
0.297043 | + | 0.954864i | \(0.404000\pi\) | |||||||
\(744\) | −6.50395 | + | 0.247665i | −0.238446 | + | 0.00907983i | ||||
\(745\) | −4.27806 | −0.156736 | ||||||||
\(746\) | −18.5719 | − | 31.2452i | −0.679965 | − | 1.14397i | ||||
\(747\) | 6.01754i | 0.220170i | ||||||||
\(748\) | 5.57917 | + | 3.03507i | 0.203995 | + | 0.110973i | ||||
\(749\) | 10.9852i | 0.401391i | ||||||||
\(750\) | 1.85701 | − | 1.10379i | 0.0678084 | − | 0.0403047i | ||||
\(751\) | −27.1393 | −0.990328 | −0.495164 | − | 0.868800i | \(-0.664892\pi\) | ||||
−0.495164 | + | 0.868800i | \(0.664892\pi\) | |||||||
\(752\) | 23.2212 | + | 35.8840i | 0.846790 | + | 1.30856i | ||||
\(753\) | −40.3711 | −1.47120 | ||||||||
\(754\) | 13.3055 | − | 7.90870i | 0.484559 | − | 0.288018i | ||||
\(755\) | 18.3166i | 0.666609i | ||||||||
\(756\) | 9.84002 | + | 5.35297i | 0.357878 | + | 0.194686i | ||||
\(757\) | 41.8750i | 1.52197i | 0.648768 | + | 0.760986i | \(0.275285\pi\) | ||||
−0.648768 | + | 0.760986i | \(0.724715\pi\) | |||||||
\(758\) | 15.2517 | + | 25.6593i | 0.553965 | + | 0.931986i | ||||
\(759\) | 15.6450 | 0.567879 | ||||||||
\(760\) | −0.0663068 | − | 1.74129i | −0.00240520 | − | 0.0631632i | ||||
\(761\) | −22.8830 | −0.829509 | −0.414754 | − | 0.909933i | \(-0.636132\pi\) | ||||
−0.414754 | + | 0.909933i | \(0.636132\pi\) | |||||||
\(762\) | 9.43992 | + | 15.8816i | 0.341972 | + | 0.575331i | ||||
\(763\) | − | 11.1496i | − | 0.403641i | ||||||
\(764\) | −2.38720 | + | 4.38824i | −0.0863658 | + | 0.158761i | ||||
\(765\) | 1.72976i | 0.0625395i | ||||||||
\(766\) | 19.6562 | − | 11.6835i | 0.710208 | − | 0.422142i | ||||
\(767\) | 6.49886 | 0.234660 | ||||||||
\(768\) | −22.2957 | − | 10.0129i | −0.804525 | − | 0.361311i | ||||
\(769\) | 19.1315 | 0.689899 | 0.344949 | − | 0.938621i | \(-0.387896\pi\) | ||||
0.344949 | + | 0.938621i | \(0.387896\pi\) | |||||||
\(770\) | −1.48771 | + | 0.884280i | −0.0536132 | + | 0.0318673i | ||||
\(771\) | − | 45.9241i | − | 1.65392i | ||||||
\(772\) | 6.81519 | − | 12.5279i | 0.245284 | − | 0.450890i | ||||
\(773\) | − | 31.7796i | − | 1.14303i | −0.820590 | − | 0.571517i | \(-0.806355\pi\) | ||
0.820590 | − | 0.571517i | \(-0.193645\pi\) | |||||||
\(774\) | −0.145421 | − | 0.244655i | −0.00522706 | − | 0.00879396i | ||||
\(775\) | 1.50644 | 0.0541128 | ||||||||
\(776\) | −0.313758 | − | 8.23963i | −0.0112633 | − | 0.295785i | ||||
\(777\) | 6.67409 | 0.239432 | ||||||||
\(778\) | 11.2910 | + | 18.9959i | 0.404802 | + | 0.681035i | ||||
\(779\) | 2.82687i | 0.101283i | ||||||||
\(780\) | −3.26138 | − | 1.77419i | −0.116776 | − | 0.0635261i | ||||
\(781\) | 16.3839i | 0.586263i | ||||||||
\(782\) | −26.4016 | + | 15.6929i | −0.944119 | + | 0.561177i | ||||
\(783\) | 50.4436 | 1.80271 | ||||||||
\(784\) | −2.17314 | − | 3.35819i | −0.0776123 | − | 0.119935i | ||||
\(785\) | 6.32577 | 0.225776 | ||||||||
\(786\) | 20.3325 | − | 12.0855i | 0.725236 | − | 0.431074i | ||||
\(787\) | 48.3246i | 1.72259i | 0.508109 | + | 0.861293i | \(0.330345\pi\) | ||||
−0.508109 | + | 0.861293i | \(0.669655\pi\) | |||||||
\(788\) | 16.7940 | + | 9.13593i | 0.598261 | + | 0.325454i | ||||
\(789\) | − | 15.4239i | − | 0.549107i | ||||||
\(790\) | −4.83568 | − | 8.13551i | −0.172046 | − | 0.289448i | ||||
\(791\) | 15.7046 | 0.558391 | ||||||||
\(792\) | 2.30560 | − | 0.0877951i | 0.0819258 | − | 0.00311966i | ||||
\(793\) | 4.31253 | 0.153142 | ||||||||
\(794\) | −18.5461 | − | 31.2018i | −0.658177 | − | 1.10731i | ||||
\(795\) | − | 7.06432i | − | 0.250546i | ||||||
\(796\) | −1.44338 | + | 2.65326i | −0.0511591 | + | 0.0940425i | ||||
\(797\) | − | 4.83126i | − | 0.171132i | −0.996332 | − | 0.0855661i | \(-0.972730\pi\) | ||
0.996332 | − | 0.0855661i | \(-0.0272699\pi\) | |||||||
\(798\) | 1.14408 | − | 0.680029i | 0.0404998 | − | 0.0240728i | ||||
\(799\) | −27.7286 | −0.980967 | ||||||||
\(800\) | 5.06843 | + | 2.51218i | 0.179196 | + | 0.0888190i | ||||
\(801\) | −8.34051 | −0.294698 | ||||||||
\(802\) | 5.22690 | − | 3.10683i | 0.184568 | − | 0.109706i | ||||
\(803\) | 18.8315i | 0.664548i | ||||||||
\(804\) | −13.3763 | + | 24.5889i | −0.471747 | + | 0.867182i | ||||
\(805\) | − | 8.36914i | − | 0.294973i | ||||||
\(806\) | −1.32284 | − | 2.22554i | −0.0465951 | − | 0.0783912i | ||||
\(807\) | 5.94987 | 0.209445 | ||||||||
\(808\) | 34.0825 | − | 1.29783i | 1.19902 | − | 0.0456575i | ||||
\(809\) | −26.9745 | −0.948374 | −0.474187 | − | 0.880424i | \(-0.657258\pi\) | ||||
−0.474187 | + | 0.880424i | \(0.657258\pi\) | |||||||
\(810\) | −4.73723 | − | 7.96988i | −0.166449 | − | 0.280033i | ||||
\(811\) | 8.63552i | 0.303234i | 0.988439 | + | 0.151617i | \(0.0484481\pi\) | ||||
−0.988439 | + | 0.151617i | \(0.951552\pi\) | |||||||
\(812\) | −15.8229 | − | 8.60767i | −0.555276 | − | 0.302070i | ||||
\(813\) | 7.01968i | 0.246191i | ||||||||
\(814\) | 6.49999 | − | 3.86354i | 0.227825 | − | 0.135417i | ||||
\(815\) | 2.52500 | 0.0884470 | ||||||||
\(816\) | 13.3117 | − | 8.61424i | 0.466003 | − | 0.301559i | ||||
\(817\) | −0.186005 | −0.00650749 | ||||||||
\(818\) | −22.0503 | + | 13.1065i | −0.770970 | + | 0.458258i | ||||
\(819\) | 0.810065i | 0.0283060i | ||||||||
\(820\) | −8.06126 | − | 4.38532i | −0.281511 | − | 0.153142i | ||||
\(821\) | 49.4882i | 1.72715i | 0.504221 | + | 0.863575i | \(0.331780\pi\) | ||||
−0.504221 | + | 0.863575i | \(0.668220\pi\) | |||||||
\(822\) | −14.3127 | − | 24.0795i | −0.499212 | − | 0.839871i | ||||
\(823\) | −10.1490 | −0.353773 | −0.176886 | − | 0.984231i | \(-0.556602\pi\) | ||||
−0.176886 | + | 0.984231i | \(0.556602\pi\) | |||||||
\(824\) | −0.132444 | − | 3.47812i | −0.00461390 | − | 0.121166i | ||||
\(825\) | 1.86937 | 0.0650832 | ||||||||
\(826\) | −3.86422 | − | 6.50113i | −0.134453 | − | 0.226203i | ||||
\(827\) | − | 23.3610i | − | 0.812341i | −0.913797 | − | 0.406170i | \(-0.866864\pi\) | ||
0.913797 | − | 0.406170i | \(-0.133136\pi\) | |||||||
\(828\) | −5.33177 | + | 9.80104i | −0.185292 | + | 0.340610i | ||||
\(829\) | − | 7.55731i | − | 0.262476i | −0.991351 | − | 0.131238i | \(-0.958105\pi\) | ||
0.991351 | − | 0.131238i | \(-0.0418952\pi\) | |||||||
\(830\) | −10.9745 | + | 6.52313i | −0.380929 | + | 0.226421i | ||||
\(831\) | −36.4358 | −1.26395 | ||||||||
\(832\) | −0.739340 | − | 9.69386i | −0.0256320 | − | 0.336074i | ||||
\(833\) | 2.59497 | 0.0899103 | ||||||||
\(834\) | 19.5686 | − | 11.6314i | 0.677604 | − | 0.402763i | ||||
\(835\) | − | 5.19991i | − | 0.179950i | ||||||
\(836\) | 0.720572 | − | 1.32458i | 0.0249215 | − | 0.0458116i | ||||
\(837\) | − | 8.43739i | − | 0.291639i | ||||||
\(838\) | −24.2004 | − | 40.7145i | −0.835989 | − | 1.40646i | ||||
\(839\) | 5.56944 | 0.192279 | 0.0961393 | − | 0.995368i | \(-0.469351\pi\) | ||||
0.0961393 | + | 0.995368i | \(0.469351\pi\) | |||||||
\(840\) | 0.164405 | + | 4.31744i | 0.00567249 | + | 0.148966i | ||||
\(841\) | −52.1142 | −1.79704 | ||||||||
\(842\) | −17.6762 | − | 29.7383i | −0.609163 | − | 1.02485i | ||||
\(843\) | − | 28.3733i | − | 0.977228i | ||||||
\(844\) | 6.38911 | + | 3.47568i | 0.219922 | + | 0.119638i | ||||
\(845\) | 11.5232i | 0.396409i | ||||||||
\(846\) | −8.65898 | + | 5.14683i | −0.297702 | + | 0.176952i | ||||
\(847\) | 9.50239 | 0.326506 | ||||||||
\(848\) | 15.5303 | − | 10.0499i | 0.533312 | − | 0.345116i | ||||
\(849\) | 40.0848 | 1.37571 | ||||||||
\(850\) | −3.15464 | + | 1.87509i | −0.108203 | + | 0.0643151i | ||||
\(851\) | 36.5659i | 1.25346i | ||||||||
\(852\) | 35.9296 | + | 19.5457i | 1.23093 | + | 0.669625i | ||||
\(853\) | 8.90694i | 0.304968i | 0.988306 | + | 0.152484i | \(0.0487272\pi\) | ||||
−0.988306 | + | 0.152484i | \(0.951273\pi\) | |||||||
\(854\) | −2.56423 | − | 4.31403i | −0.0877460 | − | 0.147623i | ||||
\(855\) | 0.410671 | 0.0140447 | ||||||||
\(856\) | 31.0484 | − | 1.18230i | 1.06121 | − | 0.0404101i | ||||
\(857\) | −25.2236 | −0.861622 | −0.430811 | − | 0.902442i | \(-0.641773\pi\) | ||||
−0.430811 | + | 0.902442i | \(0.641773\pi\) | |||||||
\(858\) | −1.64154 | − | 2.76172i | −0.0560414 | − | 0.0942836i | ||||
\(859\) | − | 29.6267i | − | 1.01085i | −0.862871 | − | 0.505424i | \(-0.831336\pi\) | ||
0.862871 | − | 0.505424i | \(-0.168664\pi\) | |||||||
\(860\) | 0.288550 | − | 0.530423i | 0.00983947 | − | 0.0180873i | ||||
\(861\) | − | 7.00908i | − | 0.238869i | ||||||
\(862\) | 49.8127 | − | 29.6083i | 1.69663 | − | 1.00846i | ||||
\(863\) | 49.8219 | 1.69596 | 0.847978 | − | 0.530031i | \(-0.177820\pi\) | ||||
0.847978 | + | 0.530031i | \(0.177820\pi\) | |||||||
\(864\) | 14.0705 | − | 28.3877i | 0.478687 | − | 0.965770i | ||||
\(865\) | −22.4890 | −0.764649 | ||||||||
\(866\) | 20.4310 | − | 12.1440i | 0.694272 | − | 0.412670i | ||||
\(867\) | − | 15.6821i | − | 0.532591i | ||||||
\(868\) | −1.43975 | + | 2.64660i | −0.0488684 | + | 0.0898316i | ||||
\(869\) | − | 8.18967i | − | 0.277816i | ||||||
\(870\) | 9.94112 | + | 16.7249i | 0.337035 | + | 0.567026i | ||||
\(871\) | −11.1345 | −0.377278 | ||||||||
\(872\) | −31.5129 | + | 1.19998i | −1.06716 | + | 0.0406366i | ||||
\(873\) | 1.94326 | 0.0657693 | ||||||||
\(874\) | 3.72573 | + | 6.26814i | 0.126025 | + | 0.212023i | ||||
\(875\) | − | 1.00000i | − | 0.0338062i | ||||||
\(876\) | 41.2970 | + | 22.4656i | 1.39530 | + | 0.759042i | ||||
\(877\) | 5.95625i | 0.201128i | 0.994931 | + | 0.100564i | \(0.0320648\pi\) | ||||
−0.994931 | + | 0.100564i | \(0.967935\pi\) | |||||||
\(878\) | 13.4021 | − | 7.96611i | 0.452300 | − | 0.268843i | ||||
\(879\) | −49.9191 | −1.68373 | ||||||||
\(880\) | 2.65943 | + | 4.10965i | 0.0896493 | + | 0.138536i | ||||
\(881\) | 23.9797 | 0.807895 | 0.403948 | − | 0.914782i | \(-0.367638\pi\) | ||||
0.403948 | + | 0.914782i | \(0.367638\pi\) | |||||||
\(882\) | 0.810347 | − | 0.481664i | 0.0272858 | − | 0.0162185i | ||||
\(883\) | 34.2431i | 1.15237i | 0.817319 | + | 0.576186i | \(0.195459\pi\) | ||||
−0.817319 | + | 0.576186i | \(0.804541\pi\) | |||||||
\(884\) | 5.54034 | + | 3.01395i | 0.186342 | + | 0.101370i | ||||
\(885\) | 8.16897i | 0.274597i | ||||||||
\(886\) | −12.0759 | − | 20.3165i | −0.405699 | − | 0.682545i | ||||
\(887\) | −46.8360 | −1.57260 | −0.786300 | − | 0.617845i | \(-0.788006\pi\) | ||||
−0.786300 | + | 0.617845i | \(0.788006\pi\) | |||||||
\(888\) | −0.718306 | − | 18.8635i | −0.0241048 | − | 0.633018i | ||||
\(889\) | 8.55227 | 0.286834 | ||||||||
\(890\) | −9.04128 | − | 15.2110i | −0.303064 | − | 0.509873i | ||||
\(891\) | − | 8.02294i | − | 0.268778i | ||||||
\(892\) | −10.6839 | + | 19.6396i | −0.357724 | + | 0.657581i | ||||
\(893\) | 6.58319i | 0.220298i | ||||||||
\(894\) | −7.94439 | + | 4.72208i | −0.265700 | + | 0.157930i | ||||
\(895\) | 18.5336 | 0.619509 | ||||||||
\(896\) | −9.25763 | + | 6.50356i | −0.309276 | + | 0.217269i | ||||
\(897\) | 15.5361 | 0.518737 | ||||||||
\(898\) | 38.7270 | − | 23.0190i | 1.29234 | − | 0.768154i | ||||
\(899\) | 13.5675i | 0.452501i | ||||||||
\(900\) | −0.637075 | + | 1.17109i | −0.0212358 | + | 0.0390365i | ||||
\(901\) | 12.0007i | 0.399801i | ||||||||
\(902\) | −4.05746 | − | 6.82624i | −0.135099 | − | 0.227289i | ||||
\(903\) | 0.461190 | 0.0153475 | ||||||||
\(904\) | −1.69022 | − | 44.3871i | −0.0562159 | − | 1.47629i | ||||
\(905\) | −6.92786 | −0.230290 | ||||||||
\(906\) | 20.2177 | + | 34.0141i | 0.671687 | + | 1.13004i | ||||
\(907\) | 11.4406i | 0.379879i | 0.981796 | + | 0.189939i | \(0.0608292\pi\) | ||||
−0.981796 | + | 0.189939i | \(0.939171\pi\) | |||||||
\(908\) | −50.3779 | − | 27.4056i | −1.67185 | − | 0.909485i | ||||
\(909\) | 8.03811i | 0.266607i | ||||||||
\(910\) | −1.47735 | + | 0.878126i | −0.0489738 | + | 0.0291096i | ||||
\(911\) | 35.7370 | 1.18402 | 0.592010 | − | 0.805930i | \(-0.298334\pi\) | ||||
0.592010 | + | 0.805930i | \(0.298334\pi\) | |||||||
\(912\) | −2.04515 | − | 3.16040i | −0.0677217 | − | 0.104651i | ||||
\(913\) | −11.0475 | −0.365620 | ||||||||
\(914\) | −8.93960 | + | 5.31363i | −0.295696 | + | 0.175759i | ||||
\(915\) | 5.42078i | 0.179206i | ||||||||
\(916\) | 45.3221 | + | 24.6552i | 1.49749 | + | 0.814632i | ||||
\(917\) | − | 10.9491i | − | 0.361570i | ||||||
\(918\) | 10.5022 | + | 17.6688i | 0.346624 | + | 0.583158i | ||||
\(919\) | 4.15619 | 0.137100 | 0.0685500 | − | 0.997648i | \(-0.478163\pi\) | ||||
0.0685500 | + | 0.997648i | \(0.478163\pi\) | |||||||
\(920\) | −23.6544 | + | 0.900737i | −0.779861 | + | 0.0296964i | ||||
\(921\) | −22.3716 | −0.737170 | ||||||||
\(922\) | −18.5830 | − | 31.2639i | −0.611999 | − | 1.02962i | ||||
\(923\) | 16.2699i | 0.535530i | ||||||||
\(924\) | −1.78662 | + | 3.28423i | −0.0587756 | + | 0.108043i | ||||
\(925\) | 4.36914i | 0.143656i | ||||||||
\(926\) | −31.7936 | + | 18.8978i | −1.04480 | + | 0.621021i | ||||
\(927\) | 0.820290 | 0.0269419 | ||||||||
\(928\) | −22.6256 | + | 45.6480i | −0.742721 | + | 1.49847i | ||||
\(929\) | −24.1240 | −0.791483 | −0.395742 | − | 0.918362i | \(-0.629512\pi\) | ||||
−0.395742 | + | 0.918362i | \(0.629512\pi\) | |||||||
\(930\) | 2.79746 | − | 1.66279i | 0.0917325 | − | 0.0545250i | ||||
\(931\) | − | 0.616085i | − | 0.0201914i | ||||||
\(932\) | 1.60535 | − | 2.95102i | 0.0525851 | − | 0.0966638i | ||||
\(933\) | − | 12.1558i | − | 0.397964i | ||||||
\(934\) | −5.70496 | − | 9.59797i | −0.186672 | − | 0.314055i | ||||
\(935\) | −3.17564 | −0.103855 | ||||||||
\(936\) | 2.28955 | − | 0.0871841i | 0.0748363 | − | 0.00284970i | ||||
\(937\) | 21.6990 | 0.708875 | 0.354438 | − | 0.935080i | \(-0.384672\pi\) | ||||
0.354438 | + | 0.935080i | \(0.384672\pi\) | |||||||
\(938\) | 6.62056 | + | 11.1384i | 0.216169 | + | 0.363681i | ||||
\(939\) | 34.7660i | 1.13455i | ||||||||
\(940\) | −18.7730 | − | 10.2125i | −0.612308 | − | 0.333096i | ||||
\(941\) | 51.1661i | 1.66797i | 0.551789 | + | 0.833984i | \(0.313945\pi\) | ||||
−0.551789 | + | 0.833984i | \(0.686055\pi\) | |||||||
\(942\) | 11.7470 | − | 6.98233i | 0.382738 | − | 0.227497i | ||||
\(943\) | 38.4013 | 1.25052 | ||||||||
\(944\) | −17.9588 | + | 11.6214i | −0.584508 | + | 0.378245i | ||||
\(945\) | −5.60090 | −0.182197 | ||||||||
\(946\) | 0.449160 | − | 0.266977i | 0.0146034 | − | 0.00868017i | ||||
\(947\) | − | 23.5083i | − | 0.763916i | −0.924180 | − | 0.381958i | \(-0.875250\pi\) | ||
0.924180 | − | 0.381958i | \(-0.124750\pi\) | |||||||
\(948\) | −17.9598 | − | 9.77013i | −0.583307 | − | 0.317319i | ||||
\(949\) | 18.7004i | 0.607040i | ||||||||
\(950\) | 0.445175 | + | 0.748959i | 0.0144434 | + | 0.0242995i | ||||
\(951\) | 37.7245 | 1.22330 | ||||||||
\(952\) | −0.279286 | − | 7.33436i | −0.00905171 | − | 0.237708i | ||||
\(953\) | 22.8816 | 0.741208 | 0.370604 | − | 0.928791i | \(-0.379151\pi\) | ||||
0.370604 | + | 0.928791i | \(0.379151\pi\) | |||||||
\(954\) | 2.22750 | + | 3.74753i | 0.0721181 | + | 0.121331i | ||||
\(955\) | − | 2.49777i | − | 0.0808258i | ||||||
\(956\) | 7.02523 | − | 12.9140i | 0.227212 | − | 0.417669i | ||||
\(957\) | 16.8362i | 0.544237i | ||||||||
\(958\) | 29.9971 | − | 17.8300i | 0.969161 | − | 0.576061i | ||||
\(959\) | −12.9668 | −0.418721 | ||||||||
\(960\) | 12.1850 | − | 0.929339i | 0.393270 | − | 0.0299943i | ||||
\(961\) | −28.7307 | −0.926795 | ||||||||
\(962\) | 6.45476 | − | 3.83665i | 0.208110 | − | 0.123699i | ||||
\(963\) | 7.32255i | 0.235966i | ||||||||
\(964\) | −9.05992 | + | 16.6543i | −0.291800 | + | 0.536398i | ||||
\(965\) | 7.13085i | 0.229550i | ||||||||
\(966\) | −9.23778 | − | 15.5416i | −0.297221 | − | 0.500042i | ||||
\(967\) | −16.0161 | −0.515043 | −0.257522 | − | 0.966273i | \(-0.582906\pi\) | ||||
−0.257522 | + | 0.966273i | \(0.582906\pi\) | |||||||
\(968\) | −1.02270 | − | 26.8574i | −0.0328710 | − | 0.863228i | ||||
\(969\) | 2.44213 | 0.0784525 | ||||||||
\(970\) | 2.10653 | + | 3.54401i | 0.0676366 | + | 0.113791i | ||||
\(971\) | − | 56.1089i | − | 1.80062i | −0.435248 | − | 0.900311i | \(-0.643339\pi\) | ||
0.435248 | − | 0.900311i | \(-0.356661\pi\) | |||||||
\(972\) | 11.9259 | + | 6.48769i | 0.382523 | + | 0.208093i | ||||
\(973\) | − | 10.5377i | − | 0.337823i | ||||||
\(974\) | −17.3075 | + | 10.2874i | −0.554568 | + | 0.329631i | ||||
\(975\) | 1.85636 | 0.0594512 | ||||||||
\(976\) | −11.9171 | + | 7.71177i | −0.381457 | + | 0.246848i | ||||
\(977\) | 31.2207 | 0.998839 | 0.499420 | − | 0.866360i | \(-0.333547\pi\) | ||||
0.499420 | + | 0.866360i | \(0.333547\pi\) | |||||||
\(978\) | 4.68896 | − | 2.78708i | 0.149936 | − | 0.0891209i | ||||
\(979\) | − | 15.3122i | − | 0.489382i | ||||||
\(980\) | 1.75686 | + | 0.955734i | 0.0561210 | + | 0.0305298i | ||||
\(981\) | − | 7.43210i | − | 0.237289i | ||||||
\(982\) | 10.5500 | + | 17.7492i | 0.336664 | + | 0.566400i | ||||
\(983\) | −1.55847 | −0.0497074 | −0.0248537 | − | 0.999691i | \(-0.507912\pi\) | ||||
−0.0248537 | + | 0.999691i | \(0.507912\pi\) | |||||||
\(984\) | −19.8103 | + | 0.754360i | −0.631530 | + | 0.0240481i | ||||
\(985\) | −9.55907 | −0.304577 | ||||||||
\(986\) | −16.8877 | − | 28.4117i | −0.537814 | − | 0.904814i | ||||
\(987\) | − | 16.3227i | − | 0.519557i | ||||||
\(988\) | 0.715557 | − | 1.31536i | 0.0227649 | − | 0.0418472i | ||||
\(989\) | 2.52676i | 0.0803464i | ||||||||
\(990\) | −0.991678 | + | 0.589445i | −0.0315176 | + | 0.0187338i | ||||
\(991\) | −23.8733 | −0.758360 | −0.379180 | − | 0.925323i | \(-0.623794\pi\) | ||||
−0.379180 | + | 0.925323i | \(0.623794\pi\) | |||||||
\(992\) | 7.63526 | + | 3.78444i | 0.242420 | + | 0.120156i | ||||
\(993\) | −33.4671 | −1.06205 | ||||||||
\(994\) | 16.2756 | − | 9.67406i | 0.516229 | − | 0.306843i | ||||
\(995\) | − | 1.51023i | − | 0.0478774i | ||||||
\(996\) | −13.1795 | + | 24.2270i | −0.417608 | + | 0.767662i | ||||
\(997\) | 16.1965i | 0.512949i | 0.966551 | + | 0.256474i | \(0.0825609\pi\) | ||||
−0.966551 | + | 0.256474i | \(0.917439\pi\) | |||||||
\(998\) | 16.5734 | + | 27.8829i | 0.524620 | + | 0.882617i | ||||
\(999\) | 24.4711 | 0.774231 |
(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.b.d.141.9 | ✓ | 12 | |
4.3 | odd | 2 | 1120.2.b.d.561.4 | 12 | |||
8.3 | odd | 2 | 1120.2.b.d.561.9 | 12 | |||
8.5 | even | 2 | inner | 280.2.b.d.141.10 | yes | 12 | |
16.3 | odd | 4 | 8960.2.a.cg.1.5 | 6 | |||
16.5 | even | 4 | 8960.2.a.ca.1.5 | 6 | |||
16.11 | odd | 4 | 8960.2.a.cd.1.2 | 6 | |||
16.13 | even | 4 | 8960.2.a.cf.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.b.d.141.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
280.2.b.d.141.10 | yes | 12 | 8.5 | even | 2 | inner | |
1120.2.b.d.561.4 | 12 | 4.3 | odd | 2 | |||
1120.2.b.d.561.9 | 12 | 8.3 | odd | 2 | |||
8960.2.a.ca.1.5 | 6 | 16.5 | even | 4 | |||
8960.2.a.cd.1.2 | 6 | 16.11 | odd | 4 | |||
8960.2.a.cf.1.2 | 6 | 16.13 | even | 4 | |||
8960.2.a.cg.1.5 | 6 | 16.3 | odd | 4 |