Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(85,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, 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("168.85");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.c (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: | \(1.34148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.386672896.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 \) |
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 | 85.1 | ||
Root | \(1.40961 - 0.114062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.85 |
Dual form | 168.2.c.b.85.2 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40961 | − | 0.114062i | −0.996742 | − | 0.0806539i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.97398 | + | 0.321565i | 0.986990 | + | 0.160782i | ||||
\(5\) | 1.12875i | 0.504791i | 0.967624 | + | 0.252395i | \(0.0812184\pi\) | ||||
−0.967624 | + | 0.252395i | \(0.918782\pi\) | |||||||
\(6\) | 0.114062 | − | 1.40961i | 0.0465656 | − | 0.575469i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.74586 | − | 0.678435i | −0.970807 | − | 0.239863i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.128747 | − | 1.59109i | 0.0407134 | − | 0.503146i | ||||
\(11\) | 4.76717i | 1.43736i | 0.695343 | + | 0.718678i | \(0.255253\pi\) | ||||
−0.695343 | + | 0.718678i | \(0.744747\pi\) | |||||||
\(12\) | −0.321565 | + | 1.97398i | −0.0928277 | + | 0.569839i | ||||
\(13\) | − | 0.456247i | − | 0.126540i | −0.997996 | − | 0.0632701i | \(-0.979847\pi\) | ||
0.997996 | − | 0.0632701i | \(-0.0201530\pi\) | |||||||
\(14\) | −1.40961 | − | 0.114062i | −0.376733 | − | 0.0304843i | ||||
\(15\) | −1.12875 | −0.291441 | ||||||||
\(16\) | 3.79319 | + | 1.26952i | 0.948298 | + | 0.317381i | ||||
\(17\) | 0.415006 | 0.100654 | 0.0503268 | − | 0.998733i | \(-0.483974\pi\) | ||||
0.0503268 | + | 0.998733i | \(0.483974\pi\) | |||||||
\(18\) | 1.40961 | + | 0.114062i | 0.332247 | + | 0.0268846i | ||||
\(19\) | 7.63843i | 1.75237i | 0.481970 | + | 0.876187i | \(0.339921\pi\) | ||||
−0.481970 | + | 0.876187i | \(0.660079\pi\) | |||||||
\(20\) | −0.362965 | + | 2.22812i | −0.0811615 | + | 0.498224i | ||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0.543753 | − | 6.71984i | 0.115928 | − | 1.43267i | ||||
\(23\) | 1.58499 | 0.330494 | 0.165247 | − | 0.986252i | \(-0.447158\pi\) | ||||
0.165247 | + | 0.986252i | \(0.447158\pi\) | |||||||
\(24\) | 0.678435 | − | 2.74586i | 0.138485 | − | 0.560496i | ||||
\(25\) | 3.72593 | 0.745186 | ||||||||
\(26\) | −0.0520404 | + | 0.643129i | −0.0102060 | + | 0.126128i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.97398 | + | 0.321565i | 0.373047 | + | 0.0607700i | ||||
\(29\) | − | 6.72593i | − | 1.24897i | −0.781035 | − | 0.624487i | \(-0.785308\pi\) | ||
0.781035 | − | 0.624487i | \(-0.214692\pi\) | |||||||
\(30\) | 1.59109 | + | 0.128747i | 0.290492 | + | 0.0235059i | ||||
\(31\) | −5.89592 | −1.05894 | −0.529469 | − | 0.848329i | \(-0.677609\pi\) | ||||
−0.529469 | + | 0.848329i | \(0.677609\pi\) | |||||||
\(32\) | −5.20210 | − | 2.22219i | −0.919611 | − | 0.392831i | ||||
\(33\) | −4.76717 | −0.829858 | ||||||||
\(34\) | −0.584994 | − | 0.0473363i | −0.100326 | − | 0.00811811i | ||||
\(35\) | 1.12875i | 0.190793i | ||||||||
\(36\) | −1.97398 | − | 0.321565i | −0.328997 | − | 0.0535941i | ||||
\(37\) | − | 5.89592i | − | 0.969283i | −0.874713 | − | 0.484642i | \(-0.838950\pi\) | ||
0.874713 | − | 0.484642i | \(-0.161050\pi\) | |||||||
\(38\) | 0.871253 | − | 10.7672i | 0.141336 | − | 1.74667i | ||||
\(39\) | 0.456247 | 0.0730581 | ||||||||
\(40\) | 0.765782 | − | 3.09938i | 0.121081 | − | 0.490054i | ||||
\(41\) | −0.415006 | −0.0648130 | −0.0324065 | − | 0.999475i | \(-0.510317\pi\) | ||||
−0.0324065 | + | 0.999475i | \(0.510317\pi\) | |||||||
\(42\) | 0.114062 | − | 1.40961i | 0.0176001 | − | 0.217507i | ||||
\(43\) | − | 9.43967i | − | 1.43954i | −0.694214 | − | 0.719768i | \(-0.744248\pi\) | ||
0.694214 | − | 0.719768i | \(-0.255752\pi\) | |||||||
\(44\) | −1.53295 | + | 9.41030i | −0.231102 | + | 1.41866i | ||||
\(45\) | − | 1.12875i | − | 0.168264i | ||||||
\(46\) | −2.23422 | − | 0.180787i | −0.329417 | − | 0.0266557i | ||||
\(47\) | 11.2769 | 1.64490 | 0.822449 | − | 0.568839i | \(-0.192607\pi\) | ||||
0.822449 | + | 0.568839i | \(0.192607\pi\) | |||||||
\(48\) | −1.26952 | + | 3.79319i | −0.183240 | + | 0.547500i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −5.25209 | − | 0.424987i | −0.742758 | − | 0.0601022i | ||||
\(51\) | 0.415006i | 0.0581124i | ||||||||
\(52\) | 0.146713 | − | 0.900623i | 0.0203454 | − | 0.124894i | ||||
\(53\) | − | 7.63843i | − | 1.04922i | −0.851343 | − | 0.524609i | \(-0.824211\pi\) | ||
0.851343 | − | 0.524609i | \(-0.175789\pi\) | |||||||
\(54\) | −0.114062 | + | 1.40961i | −0.0155219 | + | 0.191823i | ||||
\(55\) | −5.38093 | −0.725565 | ||||||||
\(56\) | −2.74586 | − | 0.678435i | −0.366930 | − | 0.0906597i | ||||
\(57\) | −7.63843 | −1.01173 | ||||||||
\(58\) | −0.767172 | + | 9.48091i | −0.100735 | + | 1.24490i | ||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | −2.22812 | − | 0.362965i | −0.287650 | − | 0.0468586i | ||||
\(61\) | 1.80125i | 0.230626i | 0.993329 | + | 0.115313i | \(0.0367871\pi\) | ||||
−0.993329 | + | 0.115313i | \(0.963213\pi\) | |||||||
\(62\) | 8.31092 | + | 0.672500i | 1.05549 | + | 0.0854075i | ||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 7.07945 | + | 3.72577i | 0.884931 | + | 0.465721i | ||||
\(65\) | 0.514988 | 0.0638764 | ||||||||
\(66\) | 6.71984 | + | 0.543753i | 0.827155 | + | 0.0669313i | ||||
\(67\) | 8.09467i | 0.988922i | 0.869200 | + | 0.494461i | \(0.164634\pi\) | ||||
−0.869200 | + | 0.494461i | \(0.835366\pi\) | |||||||
\(68\) | 0.819213 | + | 0.133451i | 0.0993441 | + | 0.0161833i | ||||
\(69\) | 1.58499i | 0.190811i | ||||||||
\(70\) | 0.128747 | − | 1.59109i | 0.0153882 | − | 0.190171i | ||||
\(71\) | 10.2068 | 1.21133 | 0.605665 | − | 0.795720i | \(-0.292907\pi\) | ||||
0.605665 | + | 0.795720i | \(0.292907\pi\) | |||||||
\(72\) | 2.74586 | + | 0.678435i | 0.323602 | + | 0.0799544i | ||||
\(73\) | −3.34500 | −0.391503 | −0.195751 | − | 0.980654i | \(-0.562715\pi\) | ||||
−0.195751 | + | 0.980654i | \(0.562715\pi\) | |||||||
\(74\) | −0.672500 | + | 8.31092i | −0.0781765 | + | 0.966125i | ||||
\(75\) | 3.72593i | 0.430233i | ||||||||
\(76\) | −2.45625 | + | 15.0781i | −0.281751 | + | 1.72958i | ||||
\(77\) | 4.76717i | 0.543270i | ||||||||
\(78\) | −0.643129 | − | 0.0520404i | −0.0728201 | − | 0.00589242i | ||||
\(79\) | −4.83001 | −0.543419 | −0.271709 | − | 0.962379i | \(-0.587589\pi\) | ||||
−0.271709 | + | 0.962379i | \(0.587589\pi\) | |||||||
\(80\) | −1.43297 | + | 4.28155i | −0.160211 | + | 0.478692i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.584994 | + | 0.0473363i | 0.0646018 | + | 0.00522742i | ||||
\(83\) | − | 5.53434i | − | 0.607473i | −0.952756 | − | 0.303737i | \(-0.901766\pi\) | ||
0.952756 | − | 0.303737i | \(-0.0982343\pi\) | |||||||
\(84\) | −0.321565 | + | 1.97398i | −0.0350856 | + | 0.215379i | ||||
\(85\) | 0.468436i | 0.0508090i | ||||||||
\(86\) | −1.07671 | + | 13.3062i | −0.116104 | + | 1.43485i | ||||
\(87\) | 6.72593 | 0.721095 | ||||||||
\(88\) | 3.23422 | − | 13.0900i | 0.344769 | − | 1.39540i | ||||
\(89\) | 4.92999 | 0.522578 | 0.261289 | − | 0.965261i | \(-0.415852\pi\) | ||||
0.261289 | + | 0.965261i | \(0.415852\pi\) | |||||||
\(90\) | −0.128747 | + | 1.59109i | −0.0135711 | + | 0.167715i | ||||
\(91\) | − | 0.456247i | − | 0.0478277i | ||||||
\(92\) | 3.12875 | + | 0.509678i | 0.326194 | + | 0.0531376i | ||||
\(93\) | − | 5.89592i | − | 0.611378i | ||||||
\(94\) | −15.8959 | − | 1.28626i | −1.63954 | − | 0.132667i | ||||
\(95\) | −8.62185 | −0.884583 | ||||||||
\(96\) | 2.22219 | − | 5.20210i | 0.226801 | − | 0.530937i | ||||
\(97\) | 16.4468 | 1.66992 | 0.834962 | − | 0.550308i | \(-0.185490\pi\) | ||||
0.834962 | + | 0.550308i | \(0.185490\pi\) | |||||||
\(98\) | −1.40961 | − | 0.114062i | −0.142392 | − | 0.0115220i | ||||
\(99\) | − | 4.76717i | − | 0.479119i | ||||||
\(100\) | 7.35491 | + | 1.19813i | 0.735491 | + | 0.119813i | ||||
\(101\) | 16.4056i | 1.63242i | 0.577757 | + | 0.816209i | \(0.303928\pi\) | ||||
−0.577757 | + | 0.816209i | \(0.696072\pi\) | |||||||
\(102\) | 0.0473363 | − | 0.584994i | 0.00468699 | − | 0.0579231i | ||||
\(103\) | −17.1728 | −1.69208 | −0.846042 | − | 0.533117i | \(-0.821021\pi\) | ||||
−0.846042 | + | 0.533117i | \(0.821021\pi\) | |||||||
\(104\) | −0.309534 | + | 1.25279i | −0.0303523 | + | 0.122846i | ||||
\(105\) | −1.12875 | −0.110154 | ||||||||
\(106\) | −0.871253 | + | 10.7672i | −0.0846236 | + | 1.04580i | ||||
\(107\) | − | 12.7672i | − | 1.23425i | −0.786865 | − | 0.617125i | \(-0.788297\pi\) | ||
0.786865 | − | 0.617125i | \(-0.211703\pi\) | |||||||
\(108\) | 0.321565 | − | 1.97398i | 0.0309426 | − | 0.189946i | ||||
\(109\) | − | 7.27685i | − | 0.696996i | −0.937310 | − | 0.348498i | \(-0.886692\pi\) | ||
0.937310 | − | 0.348498i | \(-0.113308\pi\) | |||||||
\(110\) | 7.58499 | + | 0.613759i | 0.723201 | + | 0.0585196i | ||||
\(111\) | 5.89592 | 0.559616 | ||||||||
\(112\) | 3.79319 | + | 1.26952i | 0.358423 | + | 0.119959i | ||||
\(113\) | −3.34500 | −0.314671 | −0.157336 | − | 0.987545i | \(-0.550290\pi\) | ||||
−0.157336 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(114\) | 10.7672 | + | 0.871253i | 1.00844 | + | 0.0816003i | ||||
\(115\) | 1.78906i | 0.166830i | ||||||||
\(116\) | 2.16282 | − | 13.2769i | 0.200813 | − | 1.23272i | ||||
\(117\) | 0.456247i | 0.0421801i | ||||||||
\(118\) | −0.456247 | + | 5.63843i | −0.0420010 | + | 0.519059i | ||||
\(119\) | 0.415006 | 0.0380435 | ||||||||
\(120\) | 3.09938 | + | 0.765782i | 0.282933 | + | 0.0699060i | ||||
\(121\) | −11.7259 | −1.06599 | ||||||||
\(122\) | 0.205454 | − | 2.53905i | 0.0186009 | − | 0.229875i | ||||
\(123\) | − | 0.415006i | − | 0.0374198i | ||||||
\(124\) | −11.6384 | − | 1.89592i | −1.04516 | − | 0.170259i | ||||
\(125\) | 9.84937i | 0.880954i | ||||||||
\(126\) | 1.40961 | + | 0.114062i | 0.125578 | + | 0.0101614i | ||||
\(127\) | −10.4468 | −0.927007 | −0.463504 | − | 0.886095i | \(-0.653408\pi\) | ||||
−0.463504 | + | 0.886095i | \(0.653408\pi\) | |||||||
\(128\) | −9.55427 | − | 6.05937i | −0.844486 | − | 0.535577i | ||||
\(129\) | 9.43967 | 0.831117 | ||||||||
\(130\) | −0.725930 | − | 0.0587405i | −0.0636683 | − | 0.00515188i | ||||
\(131\) | 6.25749i | 0.546720i | 0.961912 | + | 0.273360i | \(0.0881350\pi\) | ||||
−0.961912 | + | 0.273360i | \(0.911865\pi\) | |||||||
\(132\) | −9.41030 | − | 1.53295i | −0.819062 | − | 0.133427i | ||||
\(133\) | 7.63843i | 0.662335i | ||||||||
\(134\) | 0.923293 | − | 11.4103i | 0.0797604 | − | 0.985700i | ||||
\(135\) | 1.12875 | 0.0971471 | ||||||||
\(136\) | −1.13955 | − | 0.281554i | −0.0977152 | − | 0.0241431i | ||||
\(137\) | −12.9618 | −1.10740 | −0.553702 | − | 0.832715i | \(-0.686785\pi\) | ||||
−0.553702 | + | 0.832715i | \(0.686785\pi\) | |||||||
\(138\) | 0.180787 | − | 2.23422i | 0.0153896 | − | 0.190189i | ||||
\(139\) | − | 18.3644i | − | 1.55764i | −0.627245 | − | 0.778822i | \(-0.715817\pi\) | ||
0.627245 | − | 0.778822i | \(-0.284183\pi\) | |||||||
\(140\) | −0.362965 | + | 2.22812i | −0.0306762 | + | 0.188311i | ||||
\(141\) | 11.2769i | 0.949682i | ||||||||
\(142\) | −14.3876 | − | 1.16421i | −1.20738 | − | 0.0976985i | ||||
\(143\) | 2.17501 | 0.181883 | ||||||||
\(144\) | −3.79319 | − | 1.26952i | −0.316099 | − | 0.105794i | ||||
\(145\) | 7.59187 | 0.630471 | ||||||||
\(146\) | 4.71513 | + | 0.381537i | 0.390227 | + | 0.0315762i | ||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 1.89592 | − | 11.6384i | 0.155844 | − | 0.956673i | ||||
\(149\) | − | 15.6384i | − | 1.28115i | −0.767896 | − | 0.640575i | \(-0.778696\pi\) | ||
0.767896 | − | 0.640575i | \(-0.221304\pi\) | |||||||
\(150\) | 0.424987 | − | 5.25209i | 0.0347000 | − | 0.428832i | ||||
\(151\) | 15.2769 | 1.24321 | 0.621606 | − | 0.783330i | \(-0.286480\pi\) | ||||
0.621606 | + | 0.783330i | \(0.286480\pi\) | |||||||
\(152\) | 5.18218 | − | 20.9740i | 0.420330 | − | 1.70122i | ||||
\(153\) | −0.415006 | −0.0335512 | ||||||||
\(154\) | 0.543753 | − | 6.71984i | 0.0438168 | − | 0.541500i | ||||
\(155\) | − | 6.65500i | − | 0.534543i | ||||||
\(156\) | 0.900623 | + | 0.146713i | 0.0721076 | + | 0.0117464i | ||||
\(157\) | 21.7824i | 1.73843i | 0.494437 | + | 0.869214i | \(0.335374\pi\) | ||||
−0.494437 | + | 0.869214i | \(0.664626\pi\) | |||||||
\(158\) | 6.80841 | + | 0.550920i | 0.541648 | + | 0.0438288i | ||||
\(159\) | 7.63843 | 0.605767 | ||||||||
\(160\) | 2.50829 | − | 5.87186i | 0.198298 | − | 0.464211i | ||||
\(161\) | 1.58499 | 0.124915 | ||||||||
\(162\) | −1.40961 | − | 0.114062i | −0.110749 | − | 0.00896155i | ||||
\(163\) | − | 4.60966i | − | 0.361056i | −0.983570 | − | 0.180528i | \(-0.942219\pi\) | ||
0.983570 | − | 0.180528i | \(-0.0577807\pi\) | |||||||
\(164\) | −0.819213 | − | 0.133451i | −0.0639698 | − | 0.0104208i | ||||
\(165\) | − | 5.38093i | − | 0.418905i | ||||||
\(166\) | −0.631258 | + | 7.80125i | −0.0489951 | + | 0.605494i | ||||
\(167\) | −22.9618 | −1.77684 | −0.888420 | − | 0.459032i | \(-0.848196\pi\) | ||||
−0.888420 | + | 0.459032i | \(0.848196\pi\) | |||||||
\(168\) | 0.678435 | − | 2.74586i | 0.0523424 | − | 0.211847i | ||||
\(169\) | 12.7918 | 0.983988 | ||||||||
\(170\) | 0.0534307 | − | 0.660311i | 0.00409795 | − | 0.0506435i | ||||
\(171\) | − | 7.63843i | − | 0.584125i | ||||||
\(172\) | 3.03546 | − | 18.6337i | 0.231452 | − | 1.42081i | ||||
\(173\) | − | 0.216252i | − | 0.0164413i | −0.999966 | − | 0.00822067i | \(-0.997383\pi\) | ||
0.999966 | − | 0.00822067i | \(-0.00261675\pi\) | |||||||
\(174\) | −9.48091 | − | 0.767172i | −0.718746 | − | 0.0581592i | ||||
\(175\) | 3.72593 | 0.281654 | ||||||||
\(176\) | −6.05204 | + | 18.0828i | −0.456190 | + | 1.36304i | ||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −6.94935 | − | 0.562324i | −0.520876 | − | 0.0421480i | ||||
\(179\) | 22.6165i | 1.69044i | 0.534419 | + | 0.845220i | \(0.320530\pi\) | ||||
−0.534419 | + | 0.845220i | \(0.679470\pi\) | |||||||
\(180\) | 0.362965 | − | 2.22812i | 0.0270538 | − | 0.166075i | ||||
\(181\) | 7.73310i | 0.574797i | 0.957811 | + | 0.287398i | \(0.0927903\pi\) | ||||
−0.957811 | + | 0.287398i | \(0.907210\pi\) | |||||||
\(182\) | −0.0520404 | + | 0.643129i | −0.00385749 | + | 0.0476719i | ||||
\(183\) | −1.80125 | −0.133152 | ||||||||
\(184\) | −4.35217 | − | 1.07532i | −0.320846 | − | 0.0792734i | ||||
\(185\) | 6.65500 | 0.489285 | ||||||||
\(186\) | −0.672500 | + | 8.31092i | −0.0493101 | + | 0.609387i | ||||
\(187\) | 1.97840i | 0.144675i | ||||||||
\(188\) | 22.2603 | + | 3.62624i | 1.62350 | + | 0.264470i | ||||
\(189\) | − | 1.00000i | − | 0.0727393i | ||||||
\(190\) | 12.1534 | + | 0.983424i | 0.881701 | + | 0.0713451i | ||||
\(191\) | 10.2068 | 0.738541 | 0.369271 | − | 0.929322i | \(-0.379608\pi\) | ||||
0.369271 | + | 0.929322i | \(0.379608\pi\) | |||||||
\(192\) | −3.72577 | + | 7.07945i | −0.268884 | + | 0.510915i | ||||
\(193\) | 5.96407 | 0.429303 | 0.214651 | − | 0.976691i | \(-0.431138\pi\) | ||||
0.214651 | + | 0.976691i | \(0.431138\pi\) | |||||||
\(194\) | −23.1836 | − | 1.87596i | −1.66448 | − | 0.134686i | ||||
\(195\) | 0.514988i | 0.0368791i | ||||||||
\(196\) | 1.97398 | + | 0.321565i | 0.140999 | + | 0.0229689i | ||||
\(197\) | 18.8084i | 1.34004i | 0.742341 | + | 0.670022i | \(0.233715\pi\) | ||||
−0.742341 | + | 0.670022i | \(0.766285\pi\) | |||||||
\(198\) | −0.543753 | + | 6.71984i | −0.0386428 | + | 0.477558i | ||||
\(199\) | 3.27685 | 0.232290 | 0.116145 | − | 0.993232i | \(-0.462946\pi\) | ||||
0.116145 | + | 0.993232i | \(0.462946\pi\) | |||||||
\(200\) | −10.2309 | − | 2.52780i | −0.723432 | − | 0.178743i | ||||
\(201\) | −8.09467 | −0.570954 | ||||||||
\(202\) | 1.87125 | − | 23.1254i | 0.131661 | − | 1.62710i | ||||
\(203\) | − | 6.72593i | − | 0.472068i | ||||||
\(204\) | −0.133451 | + | 0.819213i | −0.00934345 | + | 0.0573564i | ||||
\(205\) | − | 0.468436i | − | 0.0327170i | ||||||
\(206\) | 24.2068 | + | 1.95876i | 1.68657 | + | 0.136473i | ||||
\(207\) | −1.58499 | −0.110165 | ||||||||
\(208\) | 0.579217 | − | 1.73063i | 0.0401615 | − | 0.119998i | ||||
\(209\) | −36.4137 | −2.51879 | ||||||||
\(210\) | 1.59109 | + | 0.128747i | 0.109796 | + | 0.00888439i | ||||
\(211\) | 10.1628i | 0.699637i | 0.936817 | + | 0.349819i | \(0.113757\pi\) | ||||
−0.936817 | + | 0.349819i | \(0.886243\pi\) | |||||||
\(212\) | 2.45625 | − | 15.0781i | 0.168696 | − | 1.03557i | ||||
\(213\) | 10.2068i | 0.699361i | ||||||||
\(214\) | −1.45625 | + | 17.9967i | −0.0995470 | + | 1.23023i | ||||
\(215\) | 10.6550 | 0.726665 | ||||||||
\(216\) | −0.678435 | + | 2.74586i | −0.0461617 | + | 0.186832i | ||||
\(217\) | −5.89592 | −0.400241 | ||||||||
\(218\) | −0.830011 | + | 10.2575i | −0.0562154 | + | 0.694725i | ||||
\(219\) | − | 3.34500i | − | 0.226034i | ||||||
\(220\) | −10.6218 | − | 1.73032i | −0.716125 | − | 0.116658i | ||||
\(221\) | − | 0.189345i | − | 0.0127367i | ||||||
\(222\) | −8.31092 | − | 0.672500i | −0.557793 | − | 0.0451352i | ||||
\(223\) | 21.9668 | 1.47101 | 0.735504 | − | 0.677520i | \(-0.236945\pi\) | ||||
0.735504 | + | 0.677520i | \(0.236945\pi\) | |||||||
\(224\) | −5.20210 | − | 2.22219i | −0.347580 | − | 0.148476i | ||||
\(225\) | −3.72593 | −0.248395 | ||||||||
\(226\) | 4.71513 | + | 0.381537i | 0.313646 | + | 0.0253795i | ||||
\(227\) | 7.91752i | 0.525504i | 0.964863 | + | 0.262752i | \(0.0846301\pi\) | ||||
−0.964863 | + | 0.262752i | \(0.915370\pi\) | |||||||
\(228\) | −15.0781 | − | 2.45625i | −0.998571 | − | 0.162669i | ||||
\(229\) | − | 13.1606i | − | 0.869676i | −0.900509 | − | 0.434838i | \(-0.856806\pi\) | ||
0.900509 | − | 0.434838i | \(-0.143194\pi\) | |||||||
\(230\) | 0.204063 | − | 2.52187i | 0.0134555 | − | 0.166287i | ||||
\(231\) | −4.76717 | −0.313657 | ||||||||
\(232\) | −4.56311 | + | 18.4684i | −0.299583 | + | 1.21251i | ||||
\(233\) | 17.2769 | 1.13184 | 0.565922 | − | 0.824459i | \(-0.308520\pi\) | ||||
0.565922 | + | 0.824459i | \(0.308520\pi\) | |||||||
\(234\) | 0.0520404 | − | 0.643129i | 0.00340199 | − | 0.0420427i | ||||
\(235\) | 12.7287i | 0.830330i | ||||||||
\(236\) | 1.28626 | − | 7.89592i | 0.0837283 | − | 0.513981i | ||||
\(237\) | − | 4.83001i | − | 0.313743i | ||||||
\(238\) | −0.584994 | − | 0.0473363i | −0.0379196 | − | 0.00306836i | ||||
\(239\) | −10.5219 | −0.680603 | −0.340301 | − | 0.940316i | \(-0.610529\pi\) | ||||
−0.340301 | + | 0.940316i | \(0.610529\pi\) | |||||||
\(240\) | −4.28155 | − | 1.43297i | −0.276373 | − | 0.0924979i | ||||
\(241\) | −6.10686 | −0.393378 | −0.196689 | − | 0.980466i | \(-0.563019\pi\) | ||||
−0.196689 | + | 0.980466i | \(0.563019\pi\) | |||||||
\(242\) | 16.5289 | + | 1.33748i | 1.06252 | + | 0.0859766i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.579217 | + | 3.55562i | −0.0370806 | + | 0.227626i | ||||
\(245\) | 1.12875i | 0.0721130i | ||||||||
\(246\) | −0.0473363 | + | 0.584994i | −0.00301805 | + | 0.0372979i | ||||
\(247\) | 3.48501 | 0.221746 | ||||||||
\(248\) | 16.1893 | + | 4.00000i | 1.02802 | + | 0.254000i | ||||
\(249\) | 5.53434 | 0.350725 | ||||||||
\(250\) | 1.12344 | − | 13.8837i | 0.0710524 | − | 0.878084i | ||||
\(251\) | − | 19.8743i | − | 1.25446i | −0.778836 | − | 0.627228i | \(-0.784189\pi\) | ||
0.778836 | − | 0.627228i | \(-0.215811\pi\) | |||||||
\(252\) | −1.97398 | − | 0.321565i | −0.124349 | − | 0.0202567i | ||||
\(253\) | 7.55594i | 0.475038i | ||||||||
\(254\) | 14.7259 | + | 1.19159i | 0.923987 | + | 0.0747668i | ||||
\(255\) | −0.468436 | −0.0293346 | ||||||||
\(256\) | 12.7766 | + | 9.63110i | 0.798539 | + | 0.601944i | ||||
\(257\) | −14.7550 | −0.920391 | −0.460195 | − | 0.887818i | \(-0.652221\pi\) | ||||
−0.460195 | + | 0.887818i | \(0.652221\pi\) | |||||||
\(258\) | −13.3062 | − | 1.07671i | −0.828409 | − | 0.0670328i | ||||
\(259\) | − | 5.89592i | − | 0.366355i | ||||||
\(260\) | 1.01658 | + | 0.165602i | 0.0630454 | + | 0.0102702i | ||||
\(261\) | 6.72593i | 0.416325i | ||||||||
\(262\) | 0.713741 | − | 8.82060i | 0.0440951 | − | 0.544939i | ||||
\(263\) | −15.7600 | −0.971804 | −0.485902 | − | 0.874013i | \(-0.661509\pi\) | ||||
−0.485902 | + | 0.874013i | \(0.661509\pi\) | |||||||
\(264\) | 13.0900 | + | 3.23422i | 0.805632 | + | 0.199052i | ||||
\(265\) | 8.62185 | 0.529636 | ||||||||
\(266\) | 0.871253 | − | 10.7672i | 0.0534199 | − | 0.660178i | ||||
\(267\) | 4.92999i | 0.301711i | ||||||||
\(268\) | −2.60296 | + | 15.9787i | −0.159001 | + | 0.976056i | ||||
\(269\) | − | 21.8331i | − | 1.33119i | −0.746315 | − | 0.665593i | \(-0.768179\pi\) | ||
0.746315 | − | 0.665593i | \(-0.231821\pi\) | |||||||
\(270\) | −1.59109 | − | 0.128747i | −0.0968306 | − | 0.00783529i | ||||
\(271\) | −18.8328 | −1.14401 | −0.572005 | − | 0.820250i | \(-0.693834\pi\) | ||||
−0.572005 | + | 0.820250i | \(0.693834\pi\) | |||||||
\(272\) | 1.57420 | + | 0.526860i | 0.0954496 | + | 0.0319456i | ||||
\(273\) | 0.456247 | 0.0276134 | ||||||||
\(274\) | 18.2711 | + | 1.47845i | 1.10380 | + | 0.0893164i | ||||
\(275\) | 17.7622i | 1.07110i | ||||||||
\(276\) | −0.509678 | + | 3.12875i | −0.0306790 | + | 0.188328i | ||||
\(277\) | − | 24.4684i | − | 1.47017i | −0.677977 | − | 0.735083i | \(-0.737143\pi\) | ||
0.677977 | − | 0.735083i | \(-0.262857\pi\) | |||||||
\(278\) | −2.09467 | + | 25.8865i | −0.125630 | + | 1.55257i | ||||
\(279\) | 5.89592 | 0.352979 | ||||||||
\(280\) | 0.765782 | − | 3.09938i | 0.0457642 | − | 0.185223i | ||||
\(281\) | 14.5150 | 0.865892 | 0.432946 | − | 0.901420i | \(-0.357474\pi\) | ||||
0.432946 | + | 0.901420i | \(0.357474\pi\) | |||||||
\(282\) | 1.28626 | − | 15.8959i | 0.0765956 | − | 0.946588i | ||||
\(283\) | − | 16.5509i | − | 0.983850i | −0.870638 | − | 0.491925i | \(-0.836293\pi\) | ||
0.870638 | − | 0.491925i | \(-0.163707\pi\) | |||||||
\(284\) | 20.1481 | + | 3.28216i | 1.19557 | + | 0.194760i | ||||
\(285\) | − | 8.62185i | − | 0.510714i | ||||||
\(286\) | −3.06591 | − | 0.248086i | −0.181291 | − | 0.0146696i | ||||
\(287\) | −0.415006 | −0.0244970 | ||||||||
\(288\) | 5.20210 | + | 2.22219i | 0.306537 | + | 0.130944i | ||||
\(289\) | −16.8278 | −0.989869 | ||||||||
\(290\) | −10.7016 | − | 0.865943i | −0.628417 | − | 0.0508499i | ||||
\(291\) | 16.4468i | 0.964131i | ||||||||
\(292\) | −6.60296 | − | 1.07563i | −0.386409 | − | 0.0629467i | ||||
\(293\) | 9.44377i | 0.551711i | 0.961199 | + | 0.275855i | \(0.0889611\pi\) | ||||
−0.961199 | + | 0.275855i | \(0.911039\pi\) | |||||||
\(294\) | 0.114062 | − | 1.40961i | 0.00665222 | − | 0.0822099i | ||||
\(295\) | 4.51499 | 0.262873 | ||||||||
\(296\) | −4.00000 | + | 16.1893i | −0.232495 | + | 0.940987i | ||||
\(297\) | 4.76717 | 0.276619 | ||||||||
\(298\) | −1.78375 | + | 22.0440i | −0.103330 | + | 1.27698i | ||||
\(299\) | − | 0.723150i | − | 0.0418208i | ||||||
\(300\) | −1.19813 | + | 7.35491i | −0.0691739 | + | 0.424636i | ||||
\(301\) | − | 9.43967i | − | 0.544094i | ||||||
\(302\) | −21.5343 | − | 1.74251i | −1.23916 | − | 0.100270i | ||||
\(303\) | −16.4056 | −0.942477 | ||||||||
\(304\) | −9.69717 | + | 28.9740i | −0.556171 | + | 1.66177i | ||||
\(305\) | −2.03315 | −0.116418 | ||||||||
\(306\) | 0.584994 | + | 0.0473363i | 0.0334419 | + | 0.00270604i | ||||
\(307\) | 0.361575i | 0.0206362i | 0.999947 | + | 0.0103181i | \(0.00328441\pi\) | ||||
−0.999947 | + | 0.0103181i | \(0.996716\pi\) | |||||||
\(308\) | −1.53295 | + | 9.41030i | −0.0873482 | + | 0.536202i | ||||
\(309\) | − | 17.1728i | − | 0.976925i | ||||||
\(310\) | −0.759082 | + | 9.38093i | −0.0431130 | + | 0.532801i | ||||
\(311\) | −11.2769 | −0.639452 | −0.319726 | − | 0.947510i | \(-0.603591\pi\) | ||||
−0.319726 | + | 0.947510i | \(0.603591\pi\) | |||||||
\(312\) | −1.25279 | − | 0.309534i | −0.0709253 | − | 0.0175239i | ||||
\(313\) | 25.5837 | 1.44607 | 0.723037 | − | 0.690809i | \(-0.242745\pi\) | ||||
0.723037 | + | 0.690809i | \(0.242745\pi\) | |||||||
\(314\) | 2.48454 | − | 30.7047i | 0.140211 | − | 1.73276i | ||||
\(315\) | − | 1.12875i | − | 0.0635977i | ||||||
\(316\) | −9.53434 | − | 1.55316i | −0.536349 | − | 0.0873721i | ||||
\(317\) | 0.361575i | 0.0203081i | 0.999948 | + | 0.0101540i | \(0.00323218\pi\) | ||||
−0.999948 | + | 0.0101540i | \(0.996768\pi\) | |||||||
\(318\) | −10.7672 | − | 0.871253i | −0.603793 | − | 0.0488574i | ||||
\(319\) | 32.0637 | 1.79522 | ||||||||
\(320\) | −4.20545 | + | 7.99091i | −0.235092 | + | 0.446705i | ||||
\(321\) | 12.7672 | 0.712594 | ||||||||
\(322\) | −2.23422 | − | 0.180787i | −0.124508 | − | 0.0100749i | ||||
\(323\) | 3.16999i | 0.176383i | ||||||||
\(324\) | 1.97398 | + | 0.321565i | 0.109666 | + | 0.0178647i | ||||
\(325\) | − | 1.69995i | − | 0.0942960i | ||||||
\(326\) | −0.525786 | + | 6.49781i | −0.0291206 | + | 0.359880i | ||||
\(327\) | 7.27685 | 0.402411 | ||||||||
\(328\) | 1.13955 | + | 0.281554i | 0.0629209 | + | 0.0155462i | ||||
\(329\) | 11.2769 | 0.621713 | ||||||||
\(330\) | −0.613759 | + | 7.58499i | −0.0337863 | + | 0.417540i | ||||
\(331\) | 7.80403i | 0.428948i | 0.976730 | + | 0.214474i | \(0.0688037\pi\) | ||||
−0.976730 | + | 0.214474i | \(0.931196\pi\) | |||||||
\(332\) | 1.77965 | − | 10.9247i | 0.0976710 | − | 0.599570i | ||||
\(333\) | 5.89592i | 0.323094i | ||||||||
\(334\) | 32.3671 | + | 2.61907i | 1.77105 | + | 0.143309i | ||||
\(335\) | −9.13684 | −0.499199 | ||||||||
\(336\) | −1.26952 | + | 3.79319i | −0.0692582 | + | 0.206936i | ||||
\(337\) | 8.76186 | 0.477289 | 0.238645 | − | 0.971107i | \(-0.423297\pi\) | ||||
0.238645 | + | 0.971107i | \(0.423297\pi\) | |||||||
\(338\) | −18.0315 | − | 1.45906i | −0.980782 | − | 0.0793625i | ||||
\(339\) | − | 3.34500i | − | 0.181675i | ||||||
\(340\) | −0.150633 | + | 0.924684i | −0.00816920 | + | 0.0501480i | ||||
\(341\) | − | 28.1069i | − | 1.52207i | ||||||
\(342\) | −0.871253 | + | 10.7672i | −0.0471120 | + | 0.582222i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.40421 | + | 25.9200i | −0.345292 | + | 1.39751i | ||||
\(345\) | −1.78906 | −0.0963196 | ||||||||
\(346\) | −0.0246661 | + | 0.304830i | −0.00132606 | + | 0.0163878i | ||||
\(347\) | 2.07717i | 0.111509i | 0.998445 | + | 0.0557543i | \(0.0177563\pi\) | ||||
−0.998445 | + | 0.0557543i | \(0.982244\pi\) | |||||||
\(348\) | 13.2769 | + | 2.16282i | 0.711714 | + | 0.115939i | ||||
\(349\) | − | 18.7381i | − | 1.00303i | −0.865149 | − | 0.501514i | \(-0.832776\pi\) | ||
0.865149 | − | 0.501514i | \(-0.167224\pi\) | |||||||
\(350\) | −5.25209 | − | 0.424987i | −0.280736 | − | 0.0227165i | ||||
\(351\) | −0.456247 | −0.0243527 | ||||||||
\(352\) | 10.5936 | − | 24.7993i | 0.564638 | − | 1.32181i | ||||
\(353\) | −13.2450 | −0.704961 | −0.352481 | − | 0.935819i | \(-0.614662\pi\) | ||||
−0.352481 | + | 0.935819i | \(0.614662\pi\) | |||||||
\(354\) | −5.63843 | − | 0.456247i | −0.299679 | − | 0.0242493i | ||||
\(355\) | 11.5209i | 0.611468i | ||||||||
\(356\) | 9.73171 | + | 1.58531i | 0.515779 | + | 0.0840213i | ||||
\(357\) | 0.415006i | 0.0219644i | ||||||||
\(358\) | 2.57968 | − | 31.8804i | 0.136341 | − | 1.68493i | ||||
\(359\) | −5.69186 | −0.300405 | −0.150202 | − | 0.988655i | \(-0.547993\pi\) | ||||
−0.150202 | + | 0.988655i | \(0.547993\pi\) | |||||||
\(360\) | −0.765782 | + | 3.09938i | −0.0403602 | + | 0.163351i | ||||
\(361\) | −39.3455 | −2.07082 | ||||||||
\(362\) | 0.882052 | − | 10.9006i | 0.0463596 | − | 0.572924i | ||||
\(363\) | − | 11.7259i | − | 0.615452i | ||||||
\(364\) | 0.146713 | − | 0.900623i | 0.00768985 | − | 0.0472055i | ||||
\(365\) | − | 3.77566i | − | 0.197627i | ||||||
\(366\) | 2.53905 | + | 0.205454i | 0.132718 | + | 0.0107392i | ||||
\(367\) | 11.2769 | 0.588647 | 0.294323 | − | 0.955706i | \(-0.404906\pi\) | ||||
0.294323 | + | 0.955706i | \(0.404906\pi\) | |||||||
\(368\) | 6.01219 | + | 2.01219i | 0.313407 | + | 0.104893i | ||||
\(369\) | 0.415006 | 0.0216043 | ||||||||
\(370\) | −9.38093 | − | 0.759082i | −0.487691 | − | 0.0394628i | ||||
\(371\) | − | 7.63843i | − | 0.396567i | ||||||
\(372\) | 1.89592 | − | 11.6384i | 0.0982988 | − | 0.603424i | ||||
\(373\) | − | 7.08751i | − | 0.366977i | −0.983022 | − | 0.183489i | \(-0.941261\pi\) | ||
0.983022 | − | 0.183489i | \(-0.0587390\pi\) | |||||||
\(374\) | 0.225660 | − | 2.78877i | 0.0116686 | − | 0.144204i | ||||
\(375\) | −9.84937 | −0.508619 | ||||||||
\(376\) | −30.9646 | − | 7.65061i | −1.59688 | − | 0.394550i | ||||
\(377\) | −3.06869 | −0.158046 | ||||||||
\(378\) | −0.114062 | + | 1.40961i | −0.00586671 | + | 0.0725023i | ||||
\(379\) | − | 6.67781i | − | 0.343016i | −0.985183 | − | 0.171508i | \(-0.945136\pi\) | ||
0.985183 | − | 0.171508i | \(-0.0548639\pi\) | |||||||
\(380\) | −17.0194 | − | 2.77248i | −0.873075 | − | 0.142225i | ||||
\(381\) | − | 10.4468i | − | 0.535208i | ||||||
\(382\) | −14.3876 | − | 1.16421i | −0.736135 | − | 0.0595662i | ||||
\(383\) | −18.6550 | −0.953226 | −0.476613 | − | 0.879113i | \(-0.658136\pi\) | ||||
−0.476613 | + | 0.879113i | \(0.658136\pi\) | |||||||
\(384\) | 6.05937 | − | 9.55427i | 0.309216 | − | 0.487564i | ||||
\(385\) | −5.38093 | −0.274238 | ||||||||
\(386\) | −8.40699 | − | 0.680273i | −0.427904 | − | 0.0346250i | ||||
\(387\) | 9.43967i | 0.479845i | ||||||||
\(388\) | 32.4657 | + | 5.28872i | 1.64820 | + | 0.268494i | ||||
\(389\) | − | 20.3428i | − | 1.03142i | −0.856764 | − | 0.515709i | \(-0.827528\pi\) | ||
0.856764 | − | 0.515709i | \(-0.172472\pi\) | |||||||
\(390\) | 0.0587405 | − | 0.725930i | 0.00297444 | − | 0.0367589i | ||||
\(391\) | 0.657782 | 0.0332654 | ||||||||
\(392\) | −2.74586 | − | 0.678435i | −0.138687 | − | 0.0342662i | ||||
\(393\) | −6.25749 | −0.315649 | ||||||||
\(394\) | 2.14532 | − | 26.5125i | 0.108080 | − | 1.33568i | ||||
\(395\) | − | 5.45186i | − | 0.274313i | ||||||
\(396\) | 1.53295 | − | 9.41030i | 0.0770338 | − | 0.472885i | ||||
\(397\) | − | 10.9031i | − | 0.547210i | −0.961842 | − | 0.273605i | \(-0.911784\pi\) | ||
0.961842 | − | 0.273605i | \(-0.0882161\pi\) | |||||||
\(398\) | −4.61907 | − | 0.373764i | −0.231533 | − | 0.0187351i | ||||
\(399\) | −7.63843 | −0.382400 | ||||||||
\(400\) | 14.1332 | + | 4.73016i | 0.706659 | + | 0.236508i | ||||
\(401\) | 29.1756 | 1.45696 | 0.728479 | − | 0.685068i | \(-0.240228\pi\) | ||||
0.728479 | + | 0.685068i | \(0.240228\pi\) | |||||||
\(402\) | 11.4103 | + | 0.923293i | 0.569094 | + | 0.0460497i | ||||
\(403\) | 2.69000i | 0.133998i | ||||||||
\(404\) | −5.27546 | + | 32.3843i | −0.262464 | + | 1.61118i | ||||
\(405\) | 1.12875i | 0.0560879i | ||||||||
\(406\) | −0.767172 | + | 9.48091i | −0.0380741 | + | 0.470530i | ||||
\(407\) | 28.1069 | 1.39321 | ||||||||
\(408\) | 0.281554 | − | 1.13955i | 0.0139390 | − | 0.0564159i | ||||
\(409\) | −31.7237 | −1.56864 | −0.784318 | − | 0.620359i | \(-0.786987\pi\) | ||||
−0.784318 | + | 0.620359i | \(0.786987\pi\) | |||||||
\(410\) | −0.0534307 | + | 0.660311i | −0.00263875 | + | 0.0326104i | ||||
\(411\) | − | 12.9618i | − | 0.639360i | ||||||
\(412\) | −33.8987 | − | 5.52216i | −1.67007 | − | 0.272057i | ||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 2.23422 | + | 0.180787i | 0.109806 | + | 0.00888522i | ||||
\(415\) | 6.24687 | 0.306647 | ||||||||
\(416\) | −1.01387 | + | 2.37345i | −0.0497089 | + | 0.116368i | ||||
\(417\) | 18.3644 | 0.899306 | ||||||||
\(418\) | 51.3290 | + | 4.15341i | 2.51058 | + | 0.203150i | ||||
\(419\) | 19.2769i | 0.941736i | 0.882204 | + | 0.470868i | \(0.156059\pi\) | ||||
−0.882204 | + | 0.470868i | \(0.843941\pi\) | |||||||
\(420\) | −2.22812 | − | 0.362965i | −0.108721 | − | 0.0177109i | ||||
\(421\) | 19.3234i | 0.941765i | 0.882196 | + | 0.470882i | \(0.156064\pi\) | ||||
−0.882196 | + | 0.470882i | \(0.843936\pi\) | |||||||
\(422\) | 1.15919 | − | 14.3256i | 0.0564285 | − | 0.697358i | ||||
\(423\) | −11.2769 | −0.548299 | ||||||||
\(424\) | −5.18218 | + | 20.9740i | −0.251669 | + | 1.01859i | ||||
\(425\) | 1.54628 | 0.0750057 | ||||||||
\(426\) | 1.16421 | − | 14.3876i | 0.0564062 | − | 0.697083i | ||||
\(427\) | 1.80125i | 0.0871684i | ||||||||
\(428\) | 4.10547 | − | 25.2021i | 0.198445 | − | 1.21819i | ||||
\(429\) | 2.17501i | 0.105010i | ||||||||
\(430\) | −15.0194 | − | 1.21533i | −0.724298 | − | 0.0586084i | ||||
\(431\) | 14.4150 | 0.694346 | 0.347173 | − | 0.937801i | \(-0.387142\pi\) | ||||
0.347173 | + | 0.937801i | \(0.387142\pi\) | |||||||
\(432\) | 1.26952 | − | 3.79319i | 0.0610800 | − | 0.182500i | ||||
\(433\) | −9.27685 | −0.445817 | −0.222908 | − | 0.974839i | \(-0.571555\pi\) | ||||
−0.222908 | + | 0.974839i | \(0.571555\pi\) | |||||||
\(434\) | 8.31092 | + | 0.672500i | 0.398937 | + | 0.0322810i | ||||
\(435\) | 7.59187i | 0.364002i | ||||||||
\(436\) | 2.33998 | − | 14.3644i | 0.112065 | − | 0.687928i | ||||
\(437\) | 12.1069i | 0.579150i | ||||||||
\(438\) | −0.381537 | + | 4.71513i | −0.0182305 | + | 0.225298i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 14.7753 | + | 3.65061i | 0.704383 | + | 0.174036i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | −0.0215971 | + | 0.266902i | −0.00102727 | + | 0.0126952i | ||||
\(443\) | 15.6465i | 0.743388i | 0.928355 | + | 0.371694i | \(0.121223\pi\) | ||||
−0.928355 | + | 0.371694i | \(0.878777\pi\) | |||||||
\(444\) | 11.6384 | + | 1.89592i | 0.552335 | + | 0.0899763i | ||||
\(445\) | 5.56472i | 0.263793i | ||||||||
\(446\) | −30.9646 | − | 2.50558i | −1.46622 | − | 0.118643i | ||||
\(447\) | 15.6384 | 0.739672 | ||||||||
\(448\) | 7.07945 | + | 3.72577i | 0.334473 | + | 0.176026i | ||||
\(449\) | −12.6550 | −0.597226 | −0.298613 | − | 0.954374i | \(-0.596524\pi\) | ||||
−0.298613 | + | 0.954374i | \(0.596524\pi\) | |||||||
\(450\) | 5.25209 | + | 0.424987i | 0.247586 | + | 0.0200341i | ||||
\(451\) | − | 1.97840i | − | 0.0931594i | ||||||
\(452\) | −6.60296 | − | 1.07563i | −0.310577 | − | 0.0505935i | ||||
\(453\) | 15.2769i | 0.717769i | ||||||||
\(454\) | 0.903087 | − | 11.1606i | 0.0423840 | − | 0.523792i | ||||
\(455\) | 0.514988 | 0.0241430 | ||||||||
\(456\) | 20.9740 | + | 5.18218i | 0.982198 | + | 0.242678i | ||||
\(457\) | −23.9237 | −1.11910 | −0.559551 | − | 0.828796i | \(-0.689026\pi\) | ||||
−0.559551 | + | 0.828796i | \(0.689026\pi\) | |||||||
\(458\) | −1.50112 | + | 18.5512i | −0.0701427 | + | 0.866842i | ||||
\(459\) | − | 0.415006i | − | 0.0193708i | ||||||
\(460\) | −0.575298 | + | 3.53156i | −0.0268234 | + | 0.164660i | ||||
\(461\) | 6.74558i | 0.314173i | 0.987585 | + | 0.157086i | \(0.0502101\pi\) | ||||
−0.987585 | + | 0.157086i | \(0.949790\pi\) | |||||||
\(462\) | 6.71984 | + | 0.543753i | 0.312635 | + | 0.0252977i | ||||
\(463\) | −11.1700 | −0.519113 | −0.259557 | − | 0.965728i | \(-0.583576\pi\) | ||||
−0.259557 | + | 0.965728i | \(0.583576\pi\) | |||||||
\(464\) | 8.53873 | − | 25.5127i | 0.396401 | − | 1.18440i | ||||
\(465\) | 6.65500 | 0.308618 | ||||||||
\(466\) | −24.3536 | − | 1.97063i | −1.12816 | − | 0.0912877i | ||||
\(467\) | 3.70935i | 0.171648i | 0.996310 | + | 0.0858242i | \(0.0273523\pi\) | ||||
−0.996310 | + | 0.0858242i | \(0.972648\pi\) | |||||||
\(468\) | −0.146713 | + | 0.900623i | −0.00678181 | + | 0.0416313i | ||||
\(469\) | 8.09467i | 0.373777i | ||||||||
\(470\) | 1.45186 | − | 17.9425i | 0.0669693 | − | 0.827624i | ||||
\(471\) | −21.7824 | −1.00368 | ||||||||
\(472\) | −2.71374 | + | 10.9834i | −0.124910 | + | 0.505553i | ||||
\(473\) | 45.0005 | 2.06913 | ||||||||
\(474\) | −0.550920 | + | 6.80841i | −0.0253046 | + | 0.312721i | ||||
\(475\) | 28.4602i | 1.30585i | ||||||||
\(476\) | 0.819213 | + | 0.133451i | 0.0375485 | + | 0.00611672i | ||||
\(477\) | 7.63843i | 0.349739i | ||||||||
\(478\) | 14.8317 | + | 1.20014i | 0.678386 | + | 0.0548933i | ||||
\(479\) | −2.17501 | −0.0993788 | −0.0496894 | − | 0.998765i | \(-0.515823\pi\) | ||||
−0.0496894 | + | 0.998765i | \(0.515823\pi\) | |||||||
\(480\) | 5.87186 | + | 2.50829i | 0.268012 | + | 0.114487i | ||||
\(481\) | −2.69000 | −0.122653 | ||||||||
\(482\) | 8.60827 | + | 0.696560i | 0.392096 | + | 0.0317274i | ||||
\(483\) | 1.58499i | 0.0721197i | ||||||||
\(484\) | −23.1467 | − | 3.77064i | −1.05212 | − | 0.171393i | ||||
\(485\) | 18.5643i | 0.842962i | ||||||||
\(486\) | 0.114062 | − | 1.40961i | 0.00517395 | − | 0.0639410i | ||||
\(487\) | −4.51499 | −0.204594 | −0.102297 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102297 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(488\) | 1.22203 | − | 4.94596i | 0.0553187 | − | 0.223893i | ||||
\(489\) | 4.60966 | 0.208456 | ||||||||
\(490\) | 0.128747 | − | 1.59109i | 0.00581620 | − | 0.0718781i | ||||
\(491\) | − | 1.91221i | − | 0.0862967i | −0.999069 | − | 0.0431483i | \(-0.986261\pi\) | ||
0.999069 | − | 0.0431483i | \(-0.0137388\pi\) | |||||||
\(492\) | 0.133451 | − | 0.819213i | 0.00601644 | − | 0.0369330i | ||||
\(493\) | − | 2.79130i | − | 0.125714i | ||||||
\(494\) | −4.91249 | − | 0.397507i | −0.221024 | − | 0.0178847i | ||||
\(495\) | 5.38093 | 0.241855 | ||||||||
\(496\) | −22.3644 | − | 7.48501i | −1.00419 | − | 0.336087i | ||||
\(497\) | 10.2068 | 0.457840 | ||||||||
\(498\) | −7.80125 | − | 0.631258i | −0.349582 | − | 0.0282873i | ||||
\(499\) | 27.4065i | 1.22688i | 0.789740 | + | 0.613442i | \(0.210216\pi\) | ||||
−0.789740 | + | 0.613442i | \(0.789784\pi\) | |||||||
\(500\) | −3.16721 | + | 19.4425i | −0.141642 | + | 0.869493i | ||||
\(501\) | − | 22.9618i | − | 1.02586i | ||||||
\(502\) | −2.26690 | + | 28.0150i | −0.101177 | + | 1.25037i | ||||
\(503\) | 17.1368 | 0.764094 | 0.382047 | − | 0.924143i | \(-0.375219\pi\) | ||||
0.382047 | + | 0.924143i | \(0.375219\pi\) | |||||||
\(504\) | 2.74586 | + | 0.678435i | 0.122310 | + | 0.0302199i | ||||
\(505\) | −18.5178 | −0.824030 | ||||||||
\(506\) | 0.861845 | − | 10.6509i | 0.0383137 | − | 0.473490i | ||||
\(507\) | 12.7918i | 0.568105i | ||||||||
\(508\) | −20.6218 | − | 3.35933i | −0.914947 | − | 0.149046i | ||||
\(509\) | 21.6437i | 0.959342i | 0.877449 | + | 0.479671i | \(0.159244\pi\) | ||||
−0.877449 | + | 0.479671i | \(0.840756\pi\) | |||||||
\(510\) | 0.660311 | + | 0.0534307i | 0.0292390 | + | 0.00236595i | ||||
\(511\) | −3.34500 | −0.147974 | ||||||||
\(512\) | −16.9115 | − | 15.0334i | −0.747388 | − | 0.664388i | ||||
\(513\) | 7.63843 | 0.337245 | ||||||||
\(514\) | 20.7987 | + | 1.68298i | 0.917392 | + | 0.0742331i | ||||
\(515\) | − | 19.3837i | − | 0.854148i | ||||||
\(516\) | 18.6337 | + | 3.03546i | 0.820304 | + | 0.133629i | ||||
\(517\) | 53.7587i | 2.36430i | ||||||||
\(518\) | −0.672500 | + | 8.31092i | −0.0295479 | + | 0.365161i | ||||
\(519\) | 0.216252 | 0.00949241 | ||||||||
\(520\) | −1.41408 | − | 0.349386i | −0.0620116 | − | 0.0153216i | ||||
\(521\) | 28.3137 | 1.24045 | 0.620223 | − | 0.784426i | \(-0.287042\pi\) | ||||
0.620223 | + | 0.784426i | \(0.287042\pi\) | |||||||
\(522\) | 0.767172 | − | 9.48091i | 0.0335782 | − | 0.414968i | ||||
\(523\) | − | 15.0687i | − | 0.658908i | −0.944172 | − | 0.329454i | \(-0.893135\pi\) | ||
0.944172 | − | 0.329454i | \(-0.106865\pi\) | |||||||
\(524\) | −2.01219 | + | 12.3522i | −0.0879029 | + | 0.539607i | ||||
\(525\) | 3.72593i | 0.162613i | ||||||||
\(526\) | 22.2154 | + | 1.79762i | 0.968638 | + | 0.0783798i | ||||
\(527\) | −2.44684 | −0.106586 | ||||||||
\(528\) | −18.0828 | − | 6.05204i | −0.786953 | − | 0.263381i | ||||
\(529\) | −20.4878 | −0.890774 | ||||||||
\(530\) | −12.1534 | − | 0.983424i | −0.527911 | − | 0.0427172i | ||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | −2.45625 | + | 15.0781i | −0.106492 | + | 0.653718i | ||||
\(533\) | 0.189345i | 0.00820145i | ||||||||
\(534\) | 0.562324 | − | 6.94935i | 0.0243342 | − | 0.300728i | ||||
\(535\) | 14.4109 | 0.623038 | ||||||||
\(536\) | 5.49171 | − | 22.2268i | 0.237206 | − | 0.960052i | ||||
\(537\) | −22.6165 | −0.975976 | ||||||||
\(538\) | −2.49032 | + | 30.7760i | −0.107365 | + | 1.32685i | ||||
\(539\) | 4.76717i | 0.205337i | ||||||||
\(540\) | 2.22812 | + | 0.362965i | 0.0958832 | + | 0.0156195i | ||||
\(541\) | 46.2990i | 1.99055i | 0.0971017 | + | 0.995274i | \(0.469043\pi\) | ||||
−0.0971017 | + | 0.995274i | \(0.530957\pi\) | |||||||
\(542\) | 26.5468 | + | 2.14810i | 1.14028 | + | 0.0922689i | ||||
\(543\) | −7.73310 | −0.331859 | ||||||||
\(544\) | −2.15890 | − | 0.922220i | −0.0925622 | − | 0.0395399i | ||||
\(545\) | 8.21372 | 0.351837 | ||||||||
\(546\) | −0.643129 | − | 0.0520404i | −0.0275234 | − | 0.00222713i | ||||
\(547\) | 2.03714i | 0.0871020i | 0.999051 | + | 0.0435510i | \(0.0138671\pi\) | ||||
−0.999051 | + | 0.0435510i | \(0.986133\pi\) | |||||||
\(548\) | −25.5864 | − | 4.16807i | −1.09300 | − | 0.178051i | ||||
\(549\) | − | 1.80125i | − | 0.0768753i | ||||||
\(550\) | 2.02598 | − | 25.0376i | 0.0863882 | − | 1.06761i | ||||
\(551\) | 51.3755 | 2.18867 | ||||||||
\(552\) | 1.07532 | − | 4.35217i | 0.0457685 | − | 0.185241i | ||||
\(553\) | −4.83001 | −0.205393 | ||||||||
\(554\) | −2.79092 | + | 34.4909i | −0.118575 | + | 1.46538i | ||||
\(555\) | 6.65500i | 0.282489i | ||||||||
\(556\) | 5.90533 | − | 36.2509i | 0.250442 | − | 1.53738i | ||||
\(557\) | 11.1234i | 0.471315i | 0.971836 | + | 0.235658i | \(0.0757244\pi\) | ||||
−0.971836 | + | 0.235658i | \(0.924276\pi\) | |||||||
\(558\) | −8.31092 | − | 0.672500i | −0.351829 | − | 0.0284692i | ||||
\(559\) | −4.30683 | −0.182159 | ||||||||
\(560\) | −1.43297 | + | 4.28155i | −0.0605541 | + | 0.180929i | ||||
\(561\) | −1.97840 | −0.0835282 | ||||||||
\(562\) | −20.4604 | − | 1.65561i | −0.863071 | − | 0.0698375i | ||||
\(563\) | − | 37.2437i | − | 1.56963i | −0.619727 | − | 0.784817i | \(-0.712757\pi\) | ||
0.619727 | − | 0.784817i | \(-0.287243\pi\) | |||||||
\(564\) | −3.62624 | + | 22.2603i | −0.152692 | + | 0.937327i | ||||
\(565\) | − | 3.77566i | − | 0.158843i | ||||||
\(566\) | −1.88783 | + | 23.3303i | −0.0793514 | + | 0.980645i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −28.0265 | − | 6.92468i | −1.17597 | − | 0.290553i | ||||
\(569\) | 22.9369 | 0.961564 | 0.480782 | − | 0.876840i | \(-0.340353\pi\) | ||||
0.480782 | + | 0.876840i | \(0.340353\pi\) | |||||||
\(570\) | −0.983424 | + | 12.1534i | −0.0411911 | + | 0.509050i | ||||
\(571\) | − | 35.1634i | − | 1.47154i | −0.677231 | − | 0.735770i | \(-0.736820\pi\) | ||
0.677231 | − | 0.735770i | \(-0.263180\pi\) | |||||||
\(572\) | 4.29343 | + | 0.699406i | 0.179517 | + | 0.0292436i | ||||
\(573\) | 10.2068i | 0.426397i | ||||||||
\(574\) | 0.584994 | + | 0.0473363i | 0.0244172 | + | 0.00197578i | ||||
\(575\) | 5.90558 | 0.246280 | ||||||||
\(576\) | −7.07945 | − | 3.72577i | −0.294977 | − | 0.155240i | ||||
\(577\) | 13.7918 | 0.574162 | 0.287081 | − | 0.957906i | \(-0.407315\pi\) | ||||
0.287081 | + | 0.957906i | \(0.407315\pi\) | |||||||
\(578\) | 23.7205 | + | 1.91941i | 0.986644 | + | 0.0798368i | ||||
\(579\) | 5.96407i | 0.247858i | ||||||||
\(580\) | 14.9862 | + | 2.44128i | 0.622268 | + | 0.101369i | ||||
\(581\) | − | 5.53434i | − | 0.229603i | ||||||
\(582\) | 1.87596 | − | 23.1836i | 0.0777609 | − | 0.960990i | ||||
\(583\) | 36.4137 | 1.50810 | ||||||||
\(584\) | 9.18489 | + | 2.26937i | 0.380073 | + | 0.0939070i | ||||
\(585\) | −0.514988 | −0.0212921 | ||||||||
\(586\) | 1.07717 | − | 13.3120i | 0.0444976 | − | 0.549914i | ||||
\(587\) | 26.9862i | 1.11384i | 0.830566 | + | 0.556920i | \(0.188017\pi\) | ||||
−0.830566 | + | 0.556920i | \(0.811983\pi\) | |||||||
\(588\) | −0.321565 | + | 1.97398i | −0.0132611 | + | 0.0814056i | ||||
\(589\) | − | 45.0355i | − | 1.85566i | ||||||
\(590\) | −6.36436 | − | 0.514988i | −0.262016 | − | 0.0212017i | ||||
\(591\) | −18.8084 | −0.773675 | ||||||||
\(592\) | 7.48501 | − | 22.3644i | 0.307632 | − | 0.919169i | ||||
\(593\) | −31.8337 | −1.30725 | −0.653627 | − | 0.756817i | \(-0.726753\pi\) | ||||
−0.653627 | + | 0.756817i | \(0.726753\pi\) | |||||||
\(594\) | −6.71984 | − | 0.543753i | −0.275718 | − | 0.0223104i | ||||
\(595\) | 0.468436i | 0.0192040i | ||||||||
\(596\) | 5.02876 | − | 30.8699i | 0.205986 | − | 1.26448i | ||||
\(597\) | 3.27685i | 0.134113i | ||||||||
\(598\) | −0.0824838 | + | 1.01936i | −0.00337301 | + | 0.0416846i | ||||
\(599\) | −34.9006 | −1.42600 | −0.712999 | − | 0.701165i | \(-0.752664\pi\) | ||||
−0.712999 | + | 0.701165i | \(0.752664\pi\) | |||||||
\(600\) | 2.52780 | − | 10.2309i | 0.103197 | − | 0.417673i | ||||
\(601\) | −0.175010 | −0.00713881 | −0.00356941 | − | 0.999994i | \(-0.501136\pi\) | ||||
−0.00356941 | + | 0.999994i | \(0.501136\pi\) | |||||||
\(602\) | −1.07671 | + | 13.3062i | −0.0438833 | + | 0.542321i | ||||
\(603\) | − | 8.09467i | − | 0.329641i | ||||||
\(604\) | 30.1562 | + | 4.91249i | 1.22704 | + | 0.199887i | ||||
\(605\) | − | 13.2356i | − | 0.538104i | ||||||
\(606\) | 23.1254 | + | 1.87125i | 0.939407 | + | 0.0760145i | ||||
\(607\) | −32.1705 | −1.30576 | −0.652881 | − | 0.757461i | \(-0.726440\pi\) | ||||
−0.652881 | + | 0.757461i | \(0.726440\pi\) | |||||||
\(608\) | 16.9740 | − | 39.7359i | 0.688387 | − | 1.61150i | ||||
\(609\) | 6.72593 | 0.272548 | ||||||||
\(610\) | 2.86594 | + | 0.231905i | 0.116039 | + | 0.00938956i | ||||
\(611\) | − | 5.14503i | − | 0.208146i | ||||||
\(612\) | −0.819213 | − | 0.133451i | −0.0331147 | − | 0.00539444i | ||||
\(613\) | 8.37869i | 0.338412i | 0.985581 | + | 0.169206i | \(0.0541203\pi\) | ||||
−0.985581 | + | 0.169206i | \(0.945880\pi\) | |||||||
\(614\) | 0.0412419 | − | 0.509678i | 0.00166439 | − | 0.0205689i | ||||
\(615\) | 0.468436 | 0.0188892 | ||||||||
\(616\) | 3.23422 | − | 13.0900i | 0.130310 | − | 0.527410i | ||||
\(617\) | 28.9618 | 1.16596 | 0.582980 | − | 0.812487i | \(-0.301887\pi\) | ||||
0.582980 | + | 0.812487i | \(0.301887\pi\) | |||||||
\(618\) | −1.95876 | + | 24.2068i | −0.0787928 | + | 0.973742i | ||||
\(619\) | − | 6.85497i | − | 0.275524i | −0.990465 | − | 0.137762i | \(-0.956009\pi\) | ||
0.990465 | − | 0.137762i | \(-0.0439910\pi\) | |||||||
\(620\) | 2.14001 | − | 13.1368i | 0.0859450 | − | 0.527588i | ||||
\(621\) | − | 1.58499i | − | 0.0636036i | ||||||
\(622\) | 15.8959 | + | 1.28626i | 0.637368 | + | 0.0515743i | ||||
\(623\) | 4.92999 | 0.197516 | ||||||||
\(624\) | 1.73063 | + | 0.579217i | 0.0692808 | + | 0.0231872i | ||||
\(625\) | 7.51221 | 0.300488 | ||||||||
\(626\) | −36.0629 | − | 2.91812i | −1.44136 | − | 0.116632i | ||||
\(627\) | − | 36.4137i | − | 1.45422i | ||||||
\(628\) | −7.00446 | + | 42.9981i | −0.279508 | + | 1.71581i | ||||
\(629\) | − | 2.44684i | − | 0.0975619i | ||||||
\(630\) | −0.128747 | + | 1.59109i | −0.00512940 | + | 0.0633905i | ||||
\(631\) | −40.2055 | −1.60056 | −0.800278 | − | 0.599629i | \(-0.795315\pi\) | ||||
−0.800278 | + | 0.599629i | \(0.795315\pi\) | |||||||
\(632\) | 13.2625 | + | 3.27685i | 0.527555 | + | 0.130346i | ||||
\(633\) | −10.1628 | −0.403936 | ||||||||
\(634\) | 0.0412419 | − | 0.509678i | 0.00163793 | − | 0.0202419i | ||||
\(635\) | − | 11.7918i | − | 0.467945i | ||||||
\(636\) | 15.0781 | + | 2.45625i | 0.597885 | + | 0.0973965i | ||||
\(637\) | − | 0.456247i | − | 0.0180772i | ||||||
\(638\) | −45.1971 | − | 3.65724i | −1.78937 | − | 0.144792i | ||||
\(639\) | −10.2068 | −0.403777 | ||||||||
\(640\) | 6.83949 | − | 10.7844i | 0.270355 | − | 0.426289i | ||||
\(641\) | −24.0737 | −0.950854 | −0.475427 | − | 0.879755i | \(-0.657706\pi\) | ||||
−0.475427 | + | 0.879755i | \(0.657706\pi\) | |||||||
\(642\) | −17.9967 | − | 1.45625i | −0.710273 | − | 0.0574735i | ||||
\(643\) | − | 23.7559i | − | 0.936841i | −0.883506 | − | 0.468421i | \(-0.844823\pi\) | ||
0.883506 | − | 0.468421i | \(-0.155177\pi\) | |||||||
\(644\) | 3.12875 | + | 0.509678i | 0.123290 | + | 0.0200841i | ||||
\(645\) | 10.6550i | 0.419540i | ||||||||
\(646\) | 0.361575 | − | 4.46844i | 0.0142260 | − | 0.175808i | ||||
\(647\) | −32.6218 | −1.28250 | −0.641249 | − | 0.767333i | \(-0.721583\pi\) | ||||
−0.641249 | + | 0.767333i | \(0.721583\pi\) | |||||||
\(648\) | −2.74586 | − | 0.678435i | −0.107867 | − | 0.0266515i | ||||
\(649\) | 19.0687 | 0.748512 | ||||||||
\(650\) | −0.193899 | + | 2.39625i | −0.00760535 | + | 0.0939888i | ||||
\(651\) | − | 5.89592i | − | 0.231079i | ||||||
\(652\) | 1.48230 | − | 9.09938i | 0.0580515 | − | 0.356359i | ||||
\(653\) | 14.4109i | 0.563942i | 0.959423 | + | 0.281971i | \(0.0909883\pi\) | ||||
−0.959423 | + | 0.281971i | \(0.909012\pi\) | |||||||
\(654\) | −10.2575 | − | 0.830011i | −0.401100 | − | 0.0324560i | ||||
\(655\) | −7.06313 | −0.275979 | ||||||||
\(656\) | −1.57420 | − | 0.526860i | −0.0614620 | − | 0.0205704i | ||||
\(657\) | 3.34500 | 0.130501 | ||||||||
\(658\) | −15.8959 | − | 1.28626i | −0.619687 | − | 0.0501436i | ||||
\(659\) | − | 23.3315i | − | 0.908866i | −0.890781 | − | 0.454433i | \(-0.849842\pi\) | ||
0.890781 | − | 0.454433i | \(-0.150158\pi\) | |||||||
\(660\) | 1.73032 | − | 10.6218i | 0.0673525 | − | 0.413455i | ||||
\(661\) | − | 44.1468i | − | 1.71711i | −0.512721 | − | 0.858555i | \(-0.671362\pi\) | ||
0.512721 | − | 0.858555i | \(-0.328638\pi\) | |||||||
\(662\) | 0.890142 | − | 11.0006i | 0.0345963 | − | 0.427551i | ||||
\(663\) | 0.189345 | 0.00735356 | ||||||||
\(664\) | −3.75469 | + | 15.1965i | −0.145710 | + | 0.589739i | ||||
\(665\) | −8.62185 | −0.334341 | ||||||||
\(666\) | 0.672500 | − | 8.31092i | 0.0260588 | − | 0.322042i | ||||
\(667\) | − | 10.6606i | − | 0.412779i | ||||||
\(668\) | −45.3262 | − | 7.38371i | −1.75372 | − | 0.285684i | ||||
\(669\) | 21.9668i | 0.849287i | ||||||||
\(670\) | 12.8793 | + | 1.04216i | 0.497572 | + | 0.0402623i | ||||
\(671\) | −8.58685 | −0.331492 | ||||||||
\(672\) | 2.22219 | − | 5.20210i | 0.0857228 | − | 0.200675i | ||||
\(673\) | 11.6960 | 0.450846 | 0.225423 | − | 0.974261i | \(-0.427624\pi\) | ||||
0.225423 | + | 0.974261i | \(0.427624\pi\) | |||||||
\(674\) | −12.3508 | − | 0.999394i | −0.475734 | − | 0.0384952i | ||||
\(675\) | − | 3.72593i | − | 0.143411i | ||||||
\(676\) | 25.2508 | + | 4.11340i | 0.971186 | + | 0.158208i | ||||
\(677\) | − | 0.648756i | − | 0.0249337i | −0.999922 | − | 0.0124669i | \(-0.996032\pi\) | ||
0.999922 | − | 0.0124669i | \(-0.00396843\pi\) | |||||||
\(678\) | −0.381537 | + | 4.71513i | −0.0146528 | + | 0.181084i | ||||
\(679\) | 16.4468 | 0.631172 | ||||||||
\(680\) | 0.317804 | − | 1.28626i | 0.0121872 | − | 0.0493258i | ||||
\(681\) | −7.91752 | −0.303400 | ||||||||
\(682\) | −3.20592 | + | 39.6196i | −0.122761 | + | 1.51711i | ||||
\(683\) | − | 22.4909i | − | 0.860589i | −0.902689 | − | 0.430294i | \(-0.858410\pi\) | ||
0.902689 | − | 0.430294i | \(-0.141590\pi\) | |||||||
\(684\) | 2.45625 | − | 15.0781i | 0.0939170 | − | 0.576525i | ||||
\(685\) | − | 14.6306i | − | 0.559007i | ||||||
\(686\) | −1.40961 | − | 0.114062i | −0.0538190 | − | 0.00435490i | ||||
\(687\) | 13.1606 | 0.502107 | ||||||||
\(688\) | 11.9839 | − | 35.8065i | 0.456882 | − | 1.36511i | ||||
\(689\) | −3.48501 | −0.132768 | ||||||||
\(690\) | 2.52187 | + | 0.204063i | 0.0960058 | + | 0.00776856i | ||||
\(691\) | − | 45.2681i | − | 1.72208i | −0.508538 | − | 0.861039i | \(-0.669814\pi\) | ||
0.508538 | − | 0.861039i | \(-0.330186\pi\) | |||||||
\(692\) | 0.0695390 | − | 0.426877i | 0.00264348 | − | 0.0162274i | ||||
\(693\) | − | 4.76717i | − | 0.181090i | ||||||
\(694\) | 0.236926 | − | 2.92800i | 0.00899360 | − | 0.111145i | ||||
\(695\) | 20.7287 | 0.786285 | ||||||||
\(696\) | −18.4684 | − | 4.56311i | −0.700044 | − | 0.172964i | ||||
\(697\) | −0.172230 | −0.00652366 | ||||||||
\(698\) | −2.13730 | + | 26.4134i | −0.0808982 | + | 0.999761i | ||||
\(699\) | 17.2769i | 0.653470i | ||||||||
\(700\) | 7.35491 | + | 1.19813i | 0.277990 | + | 0.0452850i | ||||
\(701\) | 1.03091i | 0.0389370i | 0.999810 | + | 0.0194685i | \(0.00619740\pi\) | ||||
−0.999810 | + | 0.0194685i | \(0.993803\pi\) | |||||||
\(702\) | 0.643129 | + | 0.0520404i | 0.0242734 | + | 0.00196414i | ||||
\(703\) | 45.0355 | 1.69855 | ||||||||
\(704\) | −17.7614 | + | 33.7490i | −0.669408 | + | 1.27196i | ||||
\(705\) | −12.7287 | −0.479391 | ||||||||
\(706\) | 18.6703 | + | 1.51075i | 0.702664 | + | 0.0568579i | ||||
\(707\) | 16.4056i | 0.616996i | ||||||||
\(708\) | 7.89592 | + | 1.28626i | 0.296747 | + | 0.0483406i | ||||
\(709\) | 10.5481i | 0.396144i | 0.980188 | + | 0.198072i | \(0.0634679\pi\) | ||||
−0.980188 | + | 0.198072i | \(0.936532\pi\) | |||||||
\(710\) | 1.31410 | − | 16.2400i | 0.0493173 | − | 0.609476i | ||||
\(711\) | 4.83001 | 0.181140 | ||||||||
\(712\) | −13.5371 | − | 3.34468i | −0.507322 | − | 0.125347i | ||||
\(713\) | −9.34500 | −0.349973 | ||||||||
\(714\) | 0.0473363 | − | 0.584994i | 0.00177152 | − | 0.0218929i | ||||
\(715\) | 2.45504i | 0.0918131i | ||||||||
\(716\) | −7.27268 | + | 44.6446i | −0.271793 | + | 1.66845i | ||||
\(717\) | − | 10.5219i | − | 0.392946i | ||||||
\(718\) | 8.02328 | + | 0.649224i | 0.299426 | + | 0.0242288i | ||||
\(719\) | −7.00502 | −0.261243 | −0.130622 | − | 0.991432i | \(-0.541697\pi\) | ||||
−0.130622 | + | 0.991432i | \(0.541697\pi\) | |||||||
\(720\) | 1.43297 | − | 4.28155i | 0.0534037 | − | 0.159564i | ||||
\(721\) | −17.1728 | −0.639547 | ||||||||
\(722\) | 55.4617 | + | 4.48783i | 2.06407 | + | 0.167020i | ||||
\(723\) | − | 6.10686i | − | 0.227117i | ||||||
\(724\) | −2.48669 | + | 15.2650i | −0.0924171 | + | 0.567318i | ||||
\(725\) | − | 25.0603i | − | 0.930718i | ||||||
\(726\) | −1.33748 | + | 16.5289i | −0.0496386 | + | 0.613447i | ||||
\(727\) | −17.8028 | −0.660270 | −0.330135 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330135 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(728\) | −0.309534 | + | 1.25279i | −0.0114721 | + | 0.0464315i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −0.430659 | + | 5.32219i | −0.0159394 | + | 0.196983i | ||||
\(731\) | − | 3.91752i | − | 0.144895i | ||||||
\(732\) | −3.55562 | − | 0.579217i | −0.131420 | − | 0.0214085i | ||||
\(733\) | 34.3300i | 1.26801i | 0.773330 | + | 0.634004i | \(0.218590\pi\) | ||||
−0.773330 | + | 0.634004i | \(0.781410\pi\) | |||||||
\(734\) | −15.8959 | − | 1.28626i | −0.586729 | − | 0.0474767i | ||||
\(735\) | −1.12875 | −0.0416345 | ||||||||
\(736\) | −8.24531 | − | 3.52216i | −0.303926 | − | 0.129828i | ||||
\(737\) | −38.5887 | −1.42143 | ||||||||
\(738\) | −0.584994 | − | 0.0473363i | −0.0215339 | − | 0.00174247i | ||||
\(739\) | − | 0.0946726i | − | 0.00348259i | −0.999998 | − | 0.00174129i | \(-0.999446\pi\) | ||
0.999998 | − | 0.00174129i | \(-0.000554271\pi\) | |||||||
\(740\) | 13.1368 | + | 2.14001i | 0.482920 | + | 0.0786684i | ||||
\(741\) | 3.48501i | 0.128025i | ||||||||
\(742\) | −0.871253 | + | 10.7672i | −0.0319847 | + | 0.395275i | ||||
\(743\) | −13.2755 | −0.487032 | −0.243516 | − | 0.969897i | \(-0.578301\pi\) | ||||
−0.243516 | + | 0.969897i | \(0.578301\pi\) | |||||||
\(744\) | −4.00000 | + | 16.1893i | −0.146647 | + | 0.593530i | ||||
\(745\) | 17.6518 | 0.646713 | ||||||||
\(746\) | −0.808414 | + | 9.99059i | −0.0295981 | + | 0.365782i | ||||
\(747\) | 5.53434i | 0.202491i | ||||||||
\(748\) | −0.636184 | + | 3.90533i | −0.0232612 | + | 0.142793i | ||||
\(749\) | − | 12.7672i | − | 0.466502i | ||||||
\(750\) | 13.8837 | + | 1.12344i | 0.506962 | + | 0.0410221i | ||||
\(751\) | 15.4187 | 0.562637 | 0.281318 | − | 0.959615i | \(-0.409228\pi\) | ||||
0.281318 | + | 0.959615i | \(0.409228\pi\) | |||||||
\(752\) | 42.7753 | + | 14.3162i | 1.55985 | + | 0.522059i | ||||
\(753\) | 19.8743 | 0.724261 | ||||||||
\(754\) | 4.32564 | + | 0.350020i | 0.157531 | + | 0.0127470i | ||||
\(755\) | 17.2437i | 0.627562i | ||||||||
\(756\) | 0.321565 | − | 1.97398i | 0.0116952 | − | 0.0717930i | ||||
\(757\) | 9.96685i | 0.362251i | 0.983460 | + | 0.181126i | \(0.0579741\pi\) | ||||
−0.983460 | + | 0.181126i | \(0.942026\pi\) | |||||||
\(758\) | −0.761683 | + | 9.41308i | −0.0276656 | + | 0.341899i | ||||
\(759\) | −7.55594 | −0.274263 | ||||||||
\(760\) | 23.6744 | + | 5.84937i | 0.858759 | + | 0.212179i | ||||
\(761\) | 23.4837 | 0.851283 | 0.425642 | − | 0.904892i | \(-0.360048\pi\) | ||||
0.425642 | + | 0.904892i | \(0.360048\pi\) | |||||||
\(762\) | −1.19159 | + | 14.7259i | −0.0431666 | + | 0.533464i | ||||
\(763\) | − | 7.27685i | − | 0.263440i | ||||||
\(764\) | 20.1481 | + | 3.28216i | 0.728933 | + | 0.118744i | ||||
\(765\) | − | 0.468436i | − | 0.0169363i | ||||||
\(766\) | 26.2962 | + | 2.12782i | 0.950121 | + | 0.0768814i | ||||
\(767\) | −1.82499 | −0.0658966 | ||||||||
\(768\) | −9.63110 | + | 12.7766i | −0.347532 | + | 0.461036i | ||||
\(769\) | 22.9369 | 0.827125 | 0.413562 | − | 0.910476i | \(-0.364284\pi\) | ||||
0.413562 | + | 0.910476i | \(0.364284\pi\) | |||||||
\(770\) | 7.58499 | + | 0.613759i | 0.273344 | + | 0.0221183i | ||||
\(771\) | − | 14.7550i | − | 0.531388i | ||||||
\(772\) | 11.7729 | + | 1.91783i | 0.423718 | + | 0.0690243i | ||||
\(773\) | 35.0956i | 1.26230i | 0.775660 | + | 0.631150i | \(0.217417\pi\) | ||||
−0.775660 | + | 0.631150i | \(0.782583\pi\) | |||||||
\(774\) | 1.07671 | − | 13.3062i | 0.0387014 | − | 0.478282i | ||||
\(775\) | −21.9678 | −0.789106 | ||||||||
\(776\) | −45.1607 | − | 11.1581i | −1.62117 | − | 0.400553i | ||||
\(777\) | 5.89592 | 0.211515 | ||||||||
\(778\) | −2.32033 | + | 28.6753i | −0.0831880 | + | 1.02806i | ||||
\(779\) | − | 3.16999i | − | 0.113577i | ||||||
\(780\) | −0.165602 | + | 1.01658i | −0.00592950 | + | 0.0363993i | ||||
\(781\) | 48.6578i | 1.74111i | ||||||||
\(782\) | −0.927213 | − | 0.0750278i | −0.0331571 | − | 0.00268299i | ||||
\(783\) | −6.72593 | −0.240365 | ||||||||
\(784\) | 3.79319 | + | 1.26952i | 0.135471 | + | 0.0453402i | ||||
\(785\) | −24.5869 | −0.877542 | ||||||||
\(786\) | 8.82060 | + | 0.713741i | 0.314620 | + | 0.0254583i | ||||
\(787\) | 17.9480i | 0.639778i | 0.947455 | + | 0.319889i | \(0.103646\pi\) | ||||
−0.947455 | + | 0.319889i | \(0.896354\pi\) | |||||||
\(788\) | −6.04812 | + | 37.1274i | −0.215455 | + | 1.32261i | ||||
\(789\) | − | 15.7600i | − | 0.561071i | ||||||
\(790\) | −0.621849 | + | 7.68498i | −0.0221244 | + | 0.273419i | ||||
\(791\) | −3.34500 | −0.118934 | ||||||||
\(792\) | −3.23422 | + | 13.0900i | −0.114923 | + | 0.465132i | ||||
\(793\) | 0.821814 | 0.0291835 | ||||||||
\(794\) | −1.24363 | + | 15.3691i | −0.0441346 | + | 0.545428i | ||||
\(795\) | 8.62185i | 0.305785i | ||||||||
\(796\) | 6.46844 | + | 1.05372i | 0.229268 | + | 0.0373481i | ||||
\(797\) | − | 34.4199i | − | 1.21922i | −0.792703 | − | 0.609608i | \(-0.791327\pi\) | ||
0.792703 | − | 0.609608i | \(-0.208673\pi\) | |||||||
\(798\) | 10.7672 | + | 0.871253i | 0.381154 | + | 0.0308420i | ||||
\(799\) | 4.67996 | 0.165565 | ||||||||
\(800\) | −19.3827 | − | 8.27972i | −0.685281 | − | 0.292732i | ||||
\(801\) | −4.92999 | −0.174193 | ||||||||
\(802\) | −41.1260 | − | 3.32782i | −1.45221 | − | 0.117509i | ||||
\(803\) | − | 15.9462i | − | 0.562729i | ||||||
\(804\) | −15.9787 | − | 2.60296i | −0.563526 | − | 0.0917993i | ||||
\(805\) | 1.78906i | 0.0630560i | ||||||||
\(806\) | 0.306826 | − | 3.79184i | 0.0108075 | − | 0.133562i | ||||
\(807\) | 21.8331 | 0.768561 | ||||||||
\(808\) | 11.1301 | − | 45.0474i | 0.391557 | − | 1.58476i | ||||
\(809\) | 1.89314 | 0.0665592 | 0.0332796 | − | 0.999446i | \(-0.489405\pi\) | ||||
0.0332796 | + | 0.999446i | \(0.489405\pi\) | |||||||
\(810\) | 0.128747 | − | 1.59109i | 0.00452371 | − | 0.0559052i | ||||
\(811\) | 10.3400i | 0.363086i | 0.983383 | + | 0.181543i | \(0.0581091\pi\) | ||||
−0.983383 | + | 0.181543i | \(0.941891\pi\) | |||||||
\(812\) | 2.16282 | − | 13.2769i | 0.0759002 | − | 0.465926i | ||||
\(813\) | − | 18.8328i | − | 0.660495i | ||||||
\(814\) | −39.6196 | − | 3.20592i | −1.38867 | − | 0.112367i | ||||
\(815\) | 5.20314 | 0.182258 | ||||||||
\(816\) | −0.526860 | + | 1.57420i | −0.0184438 | + | 0.0551079i | ||||
\(817\) | 72.1042 | 2.52261 | ||||||||
\(818\) | 44.7179 | + | 3.61846i | 1.56353 | + | 0.126517i | ||||
\(819\) | 0.456247i | 0.0159426i | ||||||||
\(820\) | 0.150633 | − | 0.924684i | 0.00526032 | − | 0.0322914i | ||||
\(821\) | 2.40029i | 0.0837706i | 0.999122 | + | 0.0418853i | \(0.0133364\pi\) | ||||
−0.999122 | + | 0.0418853i | \(0.986664\pi\) | |||||||
\(822\) | −1.47845 | + | 18.2711i | −0.0515669 | + | 0.637277i | ||||
\(823\) | 25.8655 | 0.901616 | 0.450808 | − | 0.892621i | \(-0.351136\pi\) | ||||
0.450808 | + | 0.892621i | \(0.351136\pi\) | |||||||
\(824\) | 47.1540 | + | 11.6506i | 1.64269 | + | 0.405868i | ||||
\(825\) | −17.7622 | −0.618399 | ||||||||
\(826\) | −0.456247 | + | 5.63843i | −0.0158749 | + | 0.196186i | ||||
\(827\) | 17.0928i | 0.594375i | 0.954819 | + | 0.297188i | \(0.0960487\pi\) | ||||
−0.954819 | + | 0.297188i | \(0.903951\pi\) | |||||||
\(828\) | −3.12875 | − | 0.509678i | −0.108731 | − | 0.0177125i | ||||
\(829\) | − | 41.8893i | − | 1.45488i | −0.686174 | − | 0.727438i | \(-0.740711\pi\) | ||
0.686174 | − | 0.727438i | \(-0.259289\pi\) | |||||||
\(830\) | −8.80563 | − | 0.712530i | −0.305648 | − | 0.0247323i | ||||
\(831\) | 24.4684 | 0.848801 | ||||||||
\(832\) | 1.69987 | − | 3.22998i | 0.0589325 | − | 0.111979i | ||||
\(833\) | 0.415006 | 0.0143791 | ||||||||
\(834\) | −25.8865 | − | 2.09467i | −0.896377 | − | 0.0725326i | ||||
\(835\) | − | 25.9181i | − | 0.896933i | ||||||
\(836\) | −71.8799 | − | 11.7094i | −2.48602 | − | 0.404976i | ||||
\(837\) | 5.89592i | 0.203793i | ||||||||
\(838\) | 2.19875 | − | 27.1728i | 0.0759547 | − | 0.938668i | ||||
\(839\) | −24.5500 | −0.847560 | −0.423780 | − | 0.905765i | \(-0.639297\pi\) | ||||
−0.423780 | + | 0.905765i | \(0.639297\pi\) | |||||||
\(840\) | 3.09938 | + | 0.765782i | 0.106939 | + | 0.0264220i | ||||
\(841\) | −16.2381 | −0.559936 | ||||||||
\(842\) | 2.20406 | − | 27.2384i | 0.0759570 | − | 0.938697i | ||||
\(843\) | 14.5150i | 0.499923i | ||||||||
\(844\) | −3.26800 | + | 20.0612i | −0.112489 | + | 0.690535i | ||||
\(845\) | 14.4387i | 0.496708i | ||||||||
\(846\) | 15.8959 | + | 1.28626i | 0.546513 | + | 0.0442225i | ||||
\(847\) | −11.7259 | −0.402908 | ||||||||
\(848\) | 9.69717 | − | 28.9740i | 0.333002 | − | 0.994972i | ||||
\(849\) | 16.5509 | 0.568026 | ||||||||
\(850\) | −2.17965 | − | 0.176372i | −0.0747613 | − | 0.00604950i | ||||
\(851\) | − | 9.34500i | − | 0.320342i | ||||||
\(852\) | −3.28216 | + | 20.1481i | −0.112445 | + | 0.690263i | ||||
\(853\) | − | 38.7193i | − | 1.32572i | −0.748742 | − | 0.662862i | \(-0.769342\pi\) | ||
0.748742 | − | 0.662862i | \(-0.230658\pi\) | |||||||
\(854\) | 0.205454 | − | 2.53905i | 0.00703048 | − | 0.0868844i | ||||
\(855\) | 8.62185 | 0.294861 | ||||||||
\(856\) | −8.66170 | + | 35.0568i | −0.296051 | + | 1.19822i | ||||
\(857\) | −45.2074 | −1.54425 | −0.772127 | − | 0.635468i | \(-0.780807\pi\) | ||||
−0.772127 | + | 0.635468i | \(0.780807\pi\) | |||||||
\(858\) | 0.248086 | − | 3.06591i | 0.00846951 | − | 0.104668i | ||||
\(859\) | 57.1890i | 1.95126i | 0.219418 | + | 0.975631i | \(0.429584\pi\) | ||||
−0.219418 | + | 0.975631i | \(0.570416\pi\) | |||||||
\(860\) | 21.0328 | + | 3.42627i | 0.717211 | + | 0.116835i | ||||
\(861\) | − | 0.415006i | − | 0.0141434i | ||||||
\(862\) | −20.3195 | − | 1.64420i | −0.692084 | − | 0.0560018i | ||||
\(863\) | −45.1106 | −1.53558 | −0.767791 | − | 0.640701i | \(-0.778644\pi\) | ||||
−0.767791 | + | 0.640701i | \(0.778644\pi\) | |||||||
\(864\) | −2.22219 | + | 5.20210i | −0.0756004 | + | 0.176979i | ||||
\(865\) | 0.244094 | 0.00829944 | ||||||||
\(866\) | 13.0767 | + | 1.05813i | 0.444365 | + | 0.0359569i | ||||
\(867\) | − | 16.8278i | − | 0.571501i | ||||||
\(868\) | −11.6384 | − | 1.89592i | −0.395034 | − | 0.0643517i | ||||
\(869\) | − | 23.0255i | − | 0.781086i | ||||||
\(870\) | 0.865943 | − | 10.7016i | 0.0293582 | − | 0.362817i | ||||
\(871\) | 3.69317 | 0.125138 | ||||||||
\(872\) | −4.93687 | + | 19.9812i | −0.167184 | + | 0.676648i | ||||
\(873\) | −16.4468 | −0.556641 | ||||||||
\(874\) | 1.38093 | − | 17.0659i | 0.0467107 | − | 0.577263i | ||||
\(875\) | 9.84937i | 0.332969i | ||||||||
\(876\) | 1.07563 | − | 6.60296i | 0.0363423 | − | 0.223093i | ||||
\(877\) | − | 17.6600i | − | 0.596337i | −0.954513 | − | 0.298168i | \(-0.903624\pi\) | ||
0.954513 | − | 0.298168i | \(-0.0963757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.44377 | −0.318530 | ||||||||
\(880\) | −20.4109 | − | 6.83122i | −0.688052 | − | 0.230280i | ||||
\(881\) | 6.78998 | 0.228760 | 0.114380 | − | 0.993437i | \(-0.463512\pi\) | ||||
0.114380 | + | 0.993437i | \(0.463512\pi\) | |||||||
\(882\) | 1.40961 | + | 0.114062i | 0.0474639 | + | 0.00384066i | ||||
\(883\) | 28.6015i | 0.962516i | 0.876579 | + | 0.481258i | \(0.159820\pi\) | ||||
−0.876579 | + | 0.481258i | \(0.840180\pi\) | |||||||
\(884\) | 0.0608867 | − | 0.373764i | 0.00204784 | − | 0.0125710i | ||||
\(885\) | 4.51499i | 0.151770i | ||||||||
\(886\) | 1.78467 | − | 22.0554i | 0.0599572 | − | 0.740967i | ||||
\(887\) | 23.5919 | 0.792138 | 0.396069 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396069 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(888\) | −16.1893 | − | 4.00000i | −0.543279 | − | 0.134231i | ||||
\(889\) | −10.4468 | −0.350376 | ||||||||
\(890\) | 0.634722 | − | 7.84406i | 0.0212759 | − | 0.262933i | ||||
\(891\) | 4.76717i | 0.159706i | ||||||||
\(892\) | 43.3621 | + | 7.06376i | 1.45187 | + | 0.236512i | ||||
\(893\) | 86.1374i | 2.88248i | ||||||||
\(894\) | −22.0440 | − | 1.78375i | −0.737262 | − | 0.0596575i | ||||
\(895\) | −25.5284 | −0.853319 | ||||||||
\(896\) | −9.55427 | − | 6.05937i | −0.319186 | − | 0.202429i | ||||
\(897\) | 0.723150 | 0.0241453 | ||||||||
\(898\) | 17.8386 | + | 1.44345i | 0.595281 | + | 0.0481687i | ||||
\(899\) | 39.6555i | 1.32259i | ||||||||
\(900\) | −7.35491 | − | 1.19813i | −0.245164 | − | 0.0399376i | ||||
\(901\) | − | 3.16999i | − | 0.105608i | ||||||
\(902\) | −0.225660 | + | 2.78877i | −0.00751367 | + | 0.0928559i | ||||
\(903\) | 9.43967 | 0.314133 | ||||||||
\(904\) | 9.18489 | + | 2.26937i | 0.305485 | + | 0.0754780i | ||||
\(905\) | −8.72871 | −0.290152 | ||||||||
\(906\) | 1.74251 | − | 21.5343i | 0.0578909 | − | 0.715431i | ||||
\(907\) | 2.02096i | 0.0671050i | 0.999437 | + | 0.0335525i | \(0.0106821\pi\) | ||||
−0.999437 | + | 0.0335525i | \(0.989318\pi\) | |||||||
\(908\) | −2.54599 | + | 15.6290i | −0.0844918 | + | 0.518667i | ||||
\(909\) | − | 16.4056i | − | 0.544139i | ||||||
\(910\) | −0.725930 | − | 0.0587405i | −0.0240644 | − | 0.00194723i | ||||
\(911\) | 52.5524 | 1.74114 | 0.870569 | − | 0.492046i | \(-0.163751\pi\) | ||||
0.870569 | + | 0.492046i | \(0.163751\pi\) | |||||||
\(912\) | −28.9740 | − | 9.69717i | −0.959426 | − | 0.321105i | ||||
\(913\) | 26.3832 | 0.873156 | ||||||||
\(914\) | 33.7229 | + | 2.72878i | 1.11546 | + | 0.0902599i | ||||
\(915\) | − | 2.03315i | − | 0.0672139i | ||||||
\(916\) | 4.23198 | − | 25.9787i | 0.139828 | − | 0.858361i | ||||
\(917\) | 6.25749i | 0.206641i | ||||||||
\(918\) | −0.0473363 | + | 0.584994i | −0.00156233 | + | 0.0193077i | ||||
\(919\) | 21.5237 | 0.710002 | 0.355001 | − | 0.934866i | \(-0.384480\pi\) | ||||
0.355001 | + | 0.934866i | \(0.384480\pi\) | |||||||
\(920\) | 1.21376 | − | 4.91249i | 0.0400165 | − | 0.161960i | ||||
\(921\) | −0.361575 | −0.0119143 | ||||||||
\(922\) | 0.769413 | − | 9.50861i | 0.0253393 | − | 0.313149i | ||||
\(923\) | − | 4.65685i | − | 0.153282i | ||||||
\(924\) | −9.41030 | − | 1.53295i | −0.309576 | − | 0.0504305i | ||||
\(925\) | − | 21.9678i | − | 0.722296i | ||||||
\(926\) | 15.7453 | + | 1.27407i | 0.517422 | + | 0.0418685i | ||||
\(927\) | 17.1728 | 0.564028 | ||||||||
\(928\) | −14.9463 | + | 34.9890i | −0.490636 | + | 1.14857i | ||||
\(929\) | −15.7500 | −0.516739 | −0.258370 | − | 0.966046i | \(-0.583185\pi\) | ||||
−0.258370 | + | 0.966046i | \(0.583185\pi\) | |||||||
\(930\) | −9.38093 | − | 0.759082i | −0.307613 | − | 0.0248913i | ||||
\(931\) | 7.63843i | 0.250339i | ||||||||
\(932\) | 34.1042 | + | 5.55562i | 1.11712 | + | 0.181981i | ||||
\(933\) | − | 11.2769i | − | 0.369188i | ||||||
\(934\) | 0.423096 | − | 5.22873i | 0.0138441 | − | 0.171089i | ||||
\(935\) | −2.23312 | −0.0730307 | ||||||||
\(936\) | 0.309534 | − | 1.25279i | 0.0101174 | − | 0.0409487i | ||||
\(937\) | 17.0687 | 0.557610 | 0.278805 | − | 0.960348i | \(-0.410062\pi\) | ||||
0.278805 | + | 0.960348i | \(0.410062\pi\) | |||||||
\(938\) | 0.923293 | − | 11.4103i | 0.0301466 | − | 0.372560i | ||||
\(939\) | 25.5837i | 0.834892i | ||||||||
\(940\) | −4.09310 | + | 25.1262i | −0.133502 | + | 0.819527i | ||||
\(941\) | − | 26.5456i | − | 0.865362i | −0.901547 | − | 0.432681i | \(-0.857568\pi\) | ||
0.901547 | − | 0.432681i | \(-0.142432\pi\) | |||||||
\(942\) | 30.7047 | + | 2.48454i | 1.00041 | + | 0.0809508i | ||||
\(943\) | −0.657782 | −0.0214203 | ||||||||
\(944\) | 5.07810 | − | 15.1728i | 0.165278 | − | 0.493832i | ||||
\(945\) | 1.12875 | 0.0367181 | ||||||||
\(946\) | −63.4330 | − | 5.13285i | −2.06239 | − | 0.166883i | ||||
\(947\) | − | 20.3265i | − | 0.660522i | −0.943890 | − | 0.330261i | \(-0.892863\pi\) | ||
0.943890 | − | 0.330261i | \(-0.107137\pi\) | |||||||
\(948\) | 1.55316 | − | 9.53434i | 0.0504443 | − | 0.309661i | ||||
\(949\) | 1.52615i | 0.0495408i | ||||||||
\(950\) | 3.24623 | − | 40.1177i | 0.105322 | − | 1.30159i | ||||
\(951\) | −0.361575 | −0.0117249 | ||||||||
\(952\) | −1.13955 | − | 0.281554i | −0.0369329 | − | 0.00912523i | ||||
\(953\) | −38.6855 | −1.25315 | −0.626573 | − | 0.779362i | \(-0.715543\pi\) | ||||
−0.626573 | + | 0.779362i | \(0.715543\pi\) | |||||||
\(954\) | 0.871253 | − | 10.7672i | 0.0282079 | − | 0.348600i | ||||
\(955\) | 11.5209i | 0.372809i | ||||||||
\(956\) | −20.7700 | − | 3.38346i | −0.671748 | − | 0.109429i | ||||
\(957\) | 32.0637i | 1.03647i | ||||||||
\(958\) | 3.06591 | + | 0.248086i | 0.0990550 | + | 0.00801529i | ||||
\(959\) | −12.9618 | −0.418559 | ||||||||
\(960\) | −7.99091 | − | 4.20545i | −0.257905 | − | 0.135730i | ||||
\(961\) | 3.76186 | 0.121350 | ||||||||
\(962\) | 3.79184 | + | 0.306826i | 0.122254 | + | 0.00989247i | ||||
\(963\) | 12.7672i | 0.411416i | ||||||||
\(964\) | −12.0548 | − | 1.96375i | −0.388260 | − | 0.0632482i | ||||
\(965\) | 6.73192i | 0.216708i | ||||||||
\(966\) | 0.180787 | − | 2.23422i | 0.00581674 | − | 0.0718848i | ||||
\(967\) | −26.6606 | −0.857346 | −0.428673 | − | 0.903460i | \(-0.641019\pi\) | ||||
−0.428673 | + | 0.903460i | \(0.641019\pi\) | |||||||
\(968\) | 32.1977 | + | 7.95529i | 1.03487 | + | 0.255693i | ||||
\(969\) | −3.16999 | −0.101835 | ||||||||
\(970\) | 2.11748 | − | 26.1684i | 0.0679882 | − | 0.840216i | ||||
\(971\) | − | 3.27685i | − | 0.105159i | −0.998617 | − | 0.0525796i | \(-0.983256\pi\) | ||
0.998617 | − | 0.0525796i | \(-0.0167443\pi\) | |||||||
\(972\) | −0.321565 | + | 1.97398i | −0.0103142 | + | 0.0633154i | ||||
\(973\) | − | 18.3644i | − | 0.588734i | ||||||
\(974\) | 6.36436 | + | 0.514988i | 0.203927 | + | 0.0165013i | ||||
\(975\) | 1.69995 | 0.0544418 | ||||||||
\(976\) | −2.28673 | + | 6.83247i | −0.0731963 | + | 0.218702i | ||||
\(977\) | 12.0387 | 0.385153 | 0.192576 | − | 0.981282i | \(-0.438316\pi\) | ||||
0.192576 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(978\) | −6.49781 | − | 0.525786i | −0.207777 | − | 0.0168128i | ||||
\(979\) | 23.5021i | 0.751131i | ||||||||
\(980\) | −0.362965 | + | 2.22812i | −0.0115945 | + | 0.0711748i | ||||
\(981\) | 7.27685i | 0.232332i | ||||||||
\(982\) | −0.218110 | + | 2.69546i | −0.00696016 | + | 0.0860155i | ||||
\(983\) | 4.42188 | 0.141036 | 0.0705181 | − | 0.997510i | \(-0.477535\pi\) | ||||
0.0705181 | + | 0.997510i | \(0.477535\pi\) | |||||||
\(984\) | −0.281554 | + | 1.13955i | −0.00897563 | + | 0.0363274i | ||||
\(985\) | −21.2299 | −0.676442 | ||||||||
\(986\) | −0.318381 | + | 3.93463i | −0.0101393 | + | 0.125304i | ||||
\(987\) | 11.2769i | 0.358946i | ||||||||
\(988\) | 6.87934 | + | 1.12066i | 0.218861 | + | 0.0356528i | ||||
\(989\) | − | 14.9618i | − | 0.475758i | ||||||
\(990\) | −7.58499 | − | 0.613759i | −0.241067 | − | 0.0195065i | ||||
\(991\) | −9.10184 | −0.289129 | −0.144565 | − | 0.989495i | \(-0.546178\pi\) | ||||
−0.144565 | + | 0.989495i | \(0.546178\pi\) | |||||||
\(992\) | 30.6712 | + | 13.1018i | 0.973811 | + | 0.415984i | ||||
\(993\) | −7.80403 | −0.247653 | ||||||||
\(994\) | −14.3876 | − | 1.16421i | −0.456348 | − | 0.0369266i | ||||
\(995\) | 3.69873i | 0.117258i | ||||||||
\(996\) | 10.9247 | + | 1.77965i | 0.346162 | + | 0.0563904i | ||||
\(997\) | 42.8556i | 1.35725i | 0.734485 | + | 0.678625i | \(0.237424\pi\) | ||||
−0.734485 | + | 0.678625i | \(0.762576\pi\) | |||||||
\(998\) | 3.12604 | − | 38.6324i | 0.0989530 | − | 1.22289i | ||||
\(999\) | −5.89592 | −0.186539 |
(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 | 168.2.c.b.85.1 | ✓ | 8 | |
3.2 | odd | 2 | 504.2.c.f.253.8 | 8 | |||
4.3 | odd | 2 | 672.2.c.b.337.3 | 8 | |||
7.6 | odd | 2 | 1176.2.c.c.589.1 | 8 | |||
8.3 | odd | 2 | 672.2.c.b.337.6 | 8 | |||
8.5 | even | 2 | inner | 168.2.c.b.85.2 | yes | 8 | |
12.11 | even | 2 | 2016.2.c.e.1009.3 | 8 | |||
16.3 | odd | 4 | 5376.2.a.bq.1.3 | 4 | |||
16.5 | even | 4 | 5376.2.a.bp.1.2 | 4 | |||
16.11 | odd | 4 | 5376.2.a.bl.1.2 | 4 | |||
16.13 | even | 4 | 5376.2.a.bm.1.3 | 4 | |||
24.5 | odd | 2 | 504.2.c.f.253.7 | 8 | |||
24.11 | even | 2 | 2016.2.c.e.1009.6 | 8 | |||
28.27 | even | 2 | 4704.2.c.c.2353.6 | 8 | |||
56.13 | odd | 2 | 1176.2.c.c.589.2 | 8 | |||
56.27 | even | 2 | 4704.2.c.c.2353.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
168.2.c.b.85.2 | yes | 8 | 8.5 | even | 2 | inner | |
504.2.c.f.253.7 | 8 | 24.5 | odd | 2 | |||
504.2.c.f.253.8 | 8 | 3.2 | odd | 2 | |||
672.2.c.b.337.3 | 8 | 4.3 | odd | 2 | |||
672.2.c.b.337.6 | 8 | 8.3 | odd | 2 | |||
1176.2.c.c.589.1 | 8 | 7.6 | odd | 2 | |||
1176.2.c.c.589.2 | 8 | 56.13 | odd | 2 | |||
2016.2.c.e.1009.3 | 8 | 12.11 | even | 2 | |||
2016.2.c.e.1009.6 | 8 | 24.11 | even | 2 | |||
4704.2.c.c.2353.3 | 8 | 56.27 | even | 2 | |||
4704.2.c.c.2353.6 | 8 | 28.27 | even | 2 | |||
5376.2.a.bl.1.2 | 4 | 16.11 | odd | 4 | |||
5376.2.a.bm.1.3 | 4 | 16.13 | even | 4 | |||
5376.2.a.bp.1.2 | 4 | 16.5 | even | 4 | |||
5376.2.a.bq.1.3 | 4 | 16.3 | odd | 4 |