Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, 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("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(4.02446026187\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.7 | ||
Root | \(1.40961 + 0.114062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.f.253.8 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.74586 | − | 0.678435i | 0.970807 | − | 0.239863i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | 0 | ||||||||
\(13\) | 0.456247i | 0.126540i | 0.997996 | + | 0.0632701i | \(0.0201530\pi\) | ||||
−0.997996 | + | 0.0632701i | \(0.979847\pi\) | |||||||
\(14\) | 1.40961 | − | 0.114062i | 0.376733 | − | 0.0304843i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.79319 | − | 1.26952i | 0.948298 | − | 0.317381i | ||||
\(17\) | −0.415006 | −0.100654 | −0.0503268 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503268 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.63843i | − | 1.75237i | −0.481970 | − | 0.876187i | \(-0.660079\pi\) | ||
0.481970 | − | 0.876187i | \(-0.339921\pi\) | |||||||
\(20\) | 0.362965 | + | 2.22812i | 0.0811615 | + | 0.498224i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.543753 | + | 6.71984i | 0.115928 | + | 1.43267i | ||||
\(23\) | −1.58499 | −0.330494 | −0.165247 | − | 0.986252i | \(-0.552842\pi\) | ||||
−0.165247 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.72593 | 0.745186 | ||||||||
\(26\) | 0.0520404 | + | 0.643129i | 0.0102060 | + | 0.126128i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.97398 | − | 0.321565i | 0.373047 | − | 0.0607700i | ||||
\(29\) | − | 6.72593i | − | 1.24897i | −0.781035 | − | 0.624487i | \(-0.785308\pi\) | ||
0.781035 | − | 0.624487i | \(-0.214692\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.584994 | + | 0.0473363i | −0.100326 | + | 0.00811811i | ||||
\(35\) | 1.12875i | 0.190793i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.89592i | 0.969283i | 0.874713 | + | 0.484642i | \(0.161050\pi\) | ||||
−0.874713 | + | 0.484642i | \(0.838950\pi\) | |||||||
\(38\) | −0.871253 | − | 10.7672i | −0.141336 | − | 1.74667i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.765782 | + | 3.09938i | 0.121081 | + | 0.490054i | ||||
\(41\) | 0.415006 | 0.0648130 | 0.0324065 | − | 0.999475i | \(-0.489683\pi\) | ||||
0.0324065 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.43967i | 1.43954i | 0.694214 | + | 0.719768i | \(0.255752\pi\) | ||||
−0.694214 | + | 0.719768i | \(0.744248\pi\) | |||||||
\(44\) | 1.53295 | + | 9.41030i | 0.231102 | + | 1.41866i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.23422 | + | 0.180787i | −0.329417 | + | 0.0266557i | ||||
\(47\) | −11.2769 | −1.64490 | −0.822449 | − | 0.568839i | \(-0.807393\pi\) | ||||
−0.822449 | + | 0.568839i | \(0.807393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.25209 | − | 0.424987i | 0.742758 | − | 0.0601022i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | 0 | ||||||||
\(55\) | −5.38093 | −0.725565 | ||||||||
\(56\) | 2.74586 | − | 0.678435i | 0.366930 | − | 0.0906597i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.767172 | − | 9.48091i | −0.100735 | − | 1.24490i | ||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.80125i | − | 0.230626i | −0.993329 | − | 0.115313i | \(-0.963213\pi\) | ||
0.993329 | − | 0.115313i | \(-0.0367871\pi\) | |||||||
\(62\) | −8.31092 | + | 0.672500i | −1.05549 | + | 0.0854075i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.07945 | − | 3.72577i | 0.884931 | − | 0.465721i | ||||
\(65\) | −0.514988 | −0.0638764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.09467i | − | 0.988922i | −0.869200 | − | 0.494461i | \(-0.835366\pi\) | ||
0.869200 | − | 0.494461i | \(-0.164634\pi\) | |||||||
\(68\) | −0.819213 | + | 0.133451i | −0.0993441 | + | 0.0161833i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.128747 | + | 1.59109i | 0.0153882 | + | 0.190171i | ||||
\(71\) | −10.2068 | −1.21133 | −0.605665 | − | 0.795720i | \(-0.707093\pi\) | ||||
−0.605665 | + | 0.795720i | \(0.707093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −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 | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.45625 | − | 15.0781i | −0.281751 | − | 1.72958i | ||||
\(77\) | 4.76717i | 0.543270i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | 0 | ||||||||
\(85\) | − | 0.468436i | − | 0.0508090i | ||||||
\(86\) | 1.07671 | + | 13.3062i | 0.116104 | + | 1.43485i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.23422 | + | 13.0900i | 0.344769 | + | 1.39540i | ||||
\(89\) | −4.92999 | −0.522578 | −0.261289 | − | 0.965261i | \(-0.584148\pi\) | ||||
−0.261289 | + | 0.965261i | \(0.584148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.456247i | 0.0478277i | ||||||||
\(92\) | −3.12875 | + | 0.509678i | −0.326194 | + | 0.0531376i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.8959 | + | 1.28626i | −1.63954 | + | 0.132667i | ||||
\(95\) | 8.62185 | 0.884583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | 0 | ||||||||
\(103\) | −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 | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −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 | 0 | ||||||||
\(109\) | 7.27685i | 0.696996i | 0.937310 | + | 0.348498i | \(0.113308\pi\) | ||||
−0.937310 | + | 0.348498i | \(0.886692\pi\) | |||||||
\(110\) | −7.58499 | + | 0.613759i | −0.723201 | + | 0.0585196i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.79319 | − | 1.26952i | 0.358423 | − | 0.119959i | ||||
\(113\) | 3.34500 | 0.314671 | 0.157336 | − | 0.987545i | \(-0.449710\pi\) | ||||
0.157336 | + | 0.987545i | \(0.449710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.78906i | − | 0.166830i | ||||||
\(116\) | −2.16282 | − | 13.2769i | −0.200813 | − | 1.23272i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.456247 | − | 5.63843i | −0.0420010 | − | 0.519059i | ||||
\(119\) | −0.415006 | −0.0380435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.7259 | −1.06599 | ||||||||
\(122\) | −0.205454 | − | 2.53905i | −0.0186009 | − | 0.229875i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.6384 | + | 1.89592i | −1.04516 | + | 0.170259i | ||||
\(125\) | 9.84937i | 0.880954i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.725930 | + | 0.0587405i | −0.0636683 | + | 0.00515188i | ||||
\(131\) | 6.25749i | 0.546720i | 0.961912 | + | 0.273360i | \(0.0881350\pi\) | ||||
−0.961912 | + | 0.273360i | \(0.911865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 7.63843i | − | 0.662335i | ||||||
\(134\) | −0.923293 | − | 11.4103i | −0.0797604 | − | 0.985700i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.13955 | + | 0.281554i | −0.0977152 | + | 0.0241431i | ||||
\(137\) | 12.9618 | 1.10740 | 0.553702 | − | 0.832715i | \(-0.313215\pi\) | ||||
0.553702 | + | 0.832715i | \(0.313215\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3644i | 1.55764i | 0.627245 | + | 0.778822i | \(0.284183\pi\) | ||||
−0.627245 | + | 0.778822i | \(0.715817\pi\) | |||||||
\(140\) | 0.362965 | + | 2.22812i | 0.0306762 | + | 0.188311i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.3876 | + | 1.16421i | −1.20738 | + | 0.0976985i | ||||
\(143\) | −2.17501 | −0.181883 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.59187 | 0.630471 | ||||||||
\(146\) | −4.71513 | + | 0.381537i | −0.390227 | + | 0.0315762i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | 0 | ||||||||
\(151\) | 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 | 0 | ||||||||
\(154\) | 0.543753 | + | 6.71984i | 0.0438168 | + | 0.541500i | ||||
\(155\) | − | 6.65500i | − | 0.534543i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.7824i | − | 1.73843i | −0.494437 | − | 0.869214i | \(-0.664626\pi\) | ||
0.494437 | − | 0.869214i | \(-0.335374\pi\) | |||||||
\(158\) | −6.80841 | + | 0.550920i | −0.541648 | + | 0.0438288i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.50829 | + | 5.87186i | 0.198298 | + | 0.464211i | ||||
\(161\) | −1.58499 | −0.124915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.60966i | 0.361056i | 0.983570 | + | 0.180528i | \(0.0577807\pi\) | ||||
−0.983570 | + | 0.180528i | \(0.942219\pi\) | |||||||
\(164\) | 0.819213 | − | 0.133451i | 0.0639698 | − | 0.0104208i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.631258 | − | 7.80125i | −0.0489951 | − | 0.605494i | ||||
\(167\) | 22.9618 | 1.77684 | 0.888420 | − | 0.459032i | \(-0.151804\pi\) | ||||
0.888420 | + | 0.459032i | \(0.151804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7918 | 0.983988 | ||||||||
\(170\) | −0.0534307 | − | 0.660311i | −0.00409795 | − | 0.0506435i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.03546 | + | 18.6337i | 0.231452 | + | 1.42081i | ||||
\(173\) | − | 0.216252i | − | 0.0164413i | −0.999966 | − | 0.00822067i | \(-0.997383\pi\) | ||
0.999966 | − | 0.00822067i | \(-0.00261675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.72593 | 0.281654 | ||||||||
\(176\) | 6.05204 | + | 18.0828i | 0.456190 | + | 1.36304i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −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 | 0 | ||||||||
\(181\) | − | 7.73310i | − | 0.574797i | −0.957811 | − | 0.287398i | \(-0.907210\pi\) | ||
0.957811 | − | 0.287398i | \(-0.0927903\pi\) | |||||||
\(182\) | 0.0520404 | + | 0.643129i | 0.00385749 | + | 0.0476719i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.35217 | + | 1.07532i | −0.320846 | + | 0.0792734i | ||||
\(185\) | −6.65500 | −0.489285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.97840i | − | 0.144675i | ||||||
\(188\) | −22.2603 | + | 3.62624i | −1.62350 | + | 0.264470i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.1534 | − | 0.983424i | 0.881701 | − | 0.0713451i | ||||
\(191\) | −10.2068 | −0.738541 | −0.369271 | − | 0.929322i | \(-0.620392\pi\) | ||||
−0.369271 | + | 0.929322i | \(0.620392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 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 | 0 | ||||||||
\(196\) | 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 | 0 | ||||||||
\(199\) | 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 | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.87125 | + | 23.1254i | 0.131661 | + | 1.62710i | ||||
\(203\) | − | 6.72593i | − | 0.472068i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.468436i | 0.0327170i | ||||||||
\(206\) | −24.2068 | + | 1.95876i | −1.68657 | + | 0.136473i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.579217 | + | 1.73063i | 0.0401615 | + | 0.119998i | ||||
\(209\) | 36.4137 | 2.51879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.1628i | − | 0.699637i | −0.936817 | − | 0.349819i | \(-0.886243\pi\) | ||
0.936817 | − | 0.349819i | \(-0.113757\pi\) | |||||||
\(212\) | −2.45625 | − | 15.0781i | −0.168696 | − | 1.03557i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.45625 | − | 17.9967i | −0.0995470 | − | 1.23023i | ||||
\(215\) | −10.6550 | −0.726665 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.89592 | −0.400241 | ||||||||
\(218\) | 0.830011 | + | 10.2575i | 0.0562154 | + | 0.694725i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.6218 | + | 1.73032i | −0.716125 | + | 0.116658i | ||||
\(221\) | − | 0.189345i | − | 0.0127367i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 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 | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.71513 | − | 0.381537i | 0.313646 | − | 0.0253795i | ||||
\(227\) | 7.91752i | 0.525504i | 0.964863 | + | 0.262752i | \(0.0846301\pi\) | ||||
−0.964863 | + | 0.262752i | \(0.915370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1606i | 0.869676i | 0.900509 | + | 0.434838i | \(0.143194\pi\) | ||||
−0.900509 | + | 0.434838i | \(0.856806\pi\) | |||||||
\(230\) | −0.204063 | − | 2.52187i | −0.0134555 | − | 0.166287i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.56311 | − | 18.4684i | −0.299583 | − | 1.21251i | ||||
\(233\) | −17.2769 | −1.13184 | −0.565922 | − | 0.824459i | \(-0.691480\pi\) | ||||
−0.565922 | + | 0.824459i | \(0.691480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.7287i | − | 0.830330i | ||||||
\(236\) | −1.28626 | − | 7.89592i | −0.0837283 | − | 0.513981i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.584994 | + | 0.0473363i | −0.0379196 | + | 0.00306836i | ||||
\(239\) | 10.5219 | 0.680603 | 0.340301 | − | 0.940316i | \(-0.389471\pi\) | ||||
0.340301 | + | 0.940316i | \(0.389471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −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 | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.579217 | − | 3.55562i | −0.0370806 | − | 0.227626i | ||||
\(245\) | 1.12875i | 0.0721130i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.48501 | 0.221746 | ||||||||
\(248\) | −16.1893 | + | 4.00000i | −1.02802 | + | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.12344 | + | 13.8837i | 0.0710524 | + | 0.878084i | ||||
\(251\) | − | 19.8743i | − | 1.25446i | −0.778836 | − | 0.627228i | \(-0.784189\pi\) | ||
0.778836 | − | 0.627228i | \(-0.215811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.55594i | − | 0.475038i | ||||||
\(254\) | −14.7259 | + | 1.19159i | −0.923987 | + | 0.0747668i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.7766 | − | 9.63110i | 0.798539 | − | 0.601944i | ||||
\(257\) | 14.7550 | 0.920391 | 0.460195 | − | 0.887818i | \(-0.347779\pi\) | ||||
0.460195 | + | 0.887818i | \(0.347779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.89592i | 0.366355i | ||||||||
\(260\) | −1.01658 | + | 0.165602i | −0.0630454 | + | 0.0102702i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.713741 | + | 8.82060i | 0.0440951 | + | 0.544939i | ||||
\(263\) | 15.7600 | 0.971804 | 0.485902 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485902 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.62185 | 0.529636 | ||||||||
\(266\) | −0.871253 | − | 10.7672i | −0.0534199 | − | 0.660178i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.60296 | − | 15.9787i | −0.159001 | − | 0.976056i | ||||
\(269\) | − | 21.8331i | − | 1.33119i | −0.746315 | − | 0.665593i | \(-0.768179\pi\) | ||
0.746315 | − | 0.665593i | \(-0.231821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −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 | 0 | ||||||||
\(274\) | 18.2711 | − | 1.47845i | 1.10380 | − | 0.0893164i | ||||
\(275\) | 17.7622i | 1.07110i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4684i | 1.47017i | 0.677977 | + | 0.735083i | \(0.262857\pi\) | ||||
−0.677977 | + | 0.735083i | \(0.737143\pi\) | |||||||
\(278\) | 2.09467 | + | 25.8865i | 0.125630 | + | 1.55257i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.765782 | + | 3.09938i | 0.0457642 | + | 0.185223i | ||||
\(281\) | −14.5150 | −0.865892 | −0.432946 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432946 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5509i | 0.983850i | 0.870638 | + | 0.491925i | \(0.163707\pi\) | ||||
−0.870638 | + | 0.491925i | \(0.836293\pi\) | |||||||
\(284\) | −20.1481 | + | 3.28216i | −1.19557 | + | 0.194760i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.06591 | + | 0.248086i | −0.181291 | + | 0.0146696i | ||||
\(287\) | 0.415006 | 0.0244970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8278 | −0.989869 | ||||||||
\(290\) | 10.7016 | − | 0.865943i | 0.628417 | − | 0.0508499i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −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 | 0 | ||||||||
\(295\) | 4.51499 | 0.262873 | ||||||||
\(296\) | 4.00000 | + | 16.1893i | 0.232495 | + | 0.940987i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.78375 | − | 22.0440i | −0.103330 | − | 1.27698i | ||||
\(299\) | − | 0.723150i | − | 0.0418208i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.43967i | 0.544094i | ||||||||
\(302\) | 21.5343 | − | 1.74251i | 1.23916 | − | 0.100270i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.69717 | − | 28.9740i | −0.556171 | − | 1.66177i | ||||
\(305\) | 2.03315 | 0.116418 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.361575i | − | 0.0206362i | −0.999947 | − | 0.0103181i | \(-0.996716\pi\) | ||
0.999947 | − | 0.0103181i | \(-0.00328441\pi\) | |||||||
\(308\) | 1.53295 | + | 9.41030i | 0.0873482 | + | 0.536202i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.759082 | − | 9.38093i | −0.0431130 | − | 0.532801i | ||||
\(311\) | 11.2769 | 0.639452 | 0.319726 | − | 0.947510i | \(-0.396409\pi\) | ||||
0.319726 | + | 0.947510i | \(0.396409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 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 | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.53434 | + | 1.55316i | −0.536349 | + | 0.0873721i | ||||
\(317\) | 0.361575i | 0.0203081i | 0.999948 | + | 0.0101540i | \(0.00323218\pi\) | ||||
−0.999948 | + | 0.0101540i | \(0.996768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.0637 | 1.79522 | ||||||||
\(320\) | 4.20545 | + | 7.99091i | 0.235092 | + | 0.446705i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.23422 | + | 0.180787i | −0.124508 | + | 0.0100749i | ||||
\(323\) | 3.16999i | 0.176383i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.69995i | 0.0942960i | ||||||||
\(326\) | 0.525786 | + | 6.49781i | 0.0291206 | + | 0.359880i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.13955 | − | 0.281554i | 0.0629209 | − | 0.0155462i | ||||
\(329\) | −11.2769 | −0.621713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.80403i | − | 0.428948i | −0.976730 | − | 0.214474i | \(-0.931196\pi\) | ||
0.976730 | − | 0.214474i | \(-0.0688037\pi\) | |||||||
\(332\) | −1.77965 | − | 10.9247i | −0.0976710 | − | 0.599570i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 32.3671 | − | 2.61907i | 1.77105 | − | 0.143309i | ||||
\(335\) | 9.13684 | 0.499199 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.150633 | − | 0.924684i | −0.00816920 | − | 0.0501480i | ||||
\(341\) | − | 28.1069i | − | 1.52207i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.40421 | + | 25.9200i | 0.345292 | + | 1.39751i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0246661 | − | 0.304830i | −0.00132606 | − | 0.0163878i | ||||
\(347\) | 2.07717i | 0.111509i | 0.998445 | + | 0.0557543i | \(0.0177563\pi\) | ||||
−0.998445 | + | 0.0557543i | \(0.982244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.7381i | 1.00303i | 0.865149 | + | 0.501514i | \(0.167224\pi\) | ||||
−0.865149 | + | 0.501514i | \(0.832776\pi\) | |||||||
\(350\) | 5.25209 | − | 0.424987i | 0.280736 | − | 0.0227165i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.5936 | + | 24.7993i | 0.564638 | + | 1.32181i | ||||
\(353\) | 13.2450 | 0.704961 | 0.352481 | − | 0.935819i | \(-0.385338\pi\) | ||||
0.352481 | + | 0.935819i | \(0.385338\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.5209i | − | 0.611468i | ||||||
\(356\) | −9.73171 | + | 1.58531i | −0.515779 | + | 0.0840213i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.57968 | + | 31.8804i | 0.136341 | + | 1.68493i | ||||
\(359\) | 5.69186 | 0.300405 | 0.150202 | − | 0.988655i | \(-0.452007\pi\) | ||||
0.150202 | + | 0.988655i | \(0.452007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.3455 | −2.07082 | ||||||||
\(362\) | −0.882052 | − | 10.9006i | −0.0463596 | − | 0.572924i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.146713 | + | 0.900623i | 0.00768985 | + | 0.0472055i | ||||
\(365\) | − | 3.77566i | − | 0.197627i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 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 | 0 | ||||||||
\(370\) | −9.38093 | + | 0.759082i | −0.487691 | + | 0.0394628i | ||||
\(371\) | − | 7.63843i | − | 0.396567i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.08751i | 0.366977i | 0.983022 | + | 0.183489i | \(0.0587390\pi\) | ||||
−0.983022 | + | 0.183489i | \(0.941261\pi\) | |||||||
\(374\) | −0.225660 | − | 2.78877i | −0.0116686 | − | 0.144204i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.9646 | + | 7.65061i | −1.59688 | + | 0.394550i | ||||
\(377\) | 3.06869 | 0.158046 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.67781i | 0.343016i | 0.985183 | + | 0.171508i | \(0.0548639\pi\) | ||||
−0.985183 | + | 0.171508i | \(0.945136\pi\) | |||||||
\(380\) | 17.0194 | − | 2.77248i | 0.873075 | − | 0.142225i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.3876 | + | 1.16421i | −0.736135 | + | 0.0595662i | ||||
\(383\) | 18.6550 | 0.953226 | 0.476613 | − | 0.879113i | \(-0.341864\pi\) | ||||
0.476613 | + | 0.879113i | \(0.341864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.38093 | −0.274238 | ||||||||
\(386\) | 8.40699 | − | 0.680273i | 0.427904 | − | 0.0346250i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | 0 | ||||||||
\(391\) | 0.657782 | 0.0332654 | ||||||||
\(392\) | 2.74586 | − | 0.678435i | 0.138687 | − | 0.0342662i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.14532 | + | 26.5125i | 0.108080 | + | 1.33568i | ||||
\(395\) | − | 5.45186i | − | 0.274313i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9031i | 0.547210i | 0.961842 | + | 0.273605i | \(0.0882161\pi\) | ||||
−0.961842 | + | 0.273605i | \(0.911784\pi\) | |||||||
\(398\) | 4.61907 | − | 0.373764i | 0.231533 | − | 0.0187351i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.1332 | − | 4.73016i | 0.706659 | − | 0.236508i | ||||
\(401\) | −29.1756 | −1.45696 | −0.728479 | − | 0.685068i | \(-0.759772\pi\) | ||||
−0.728479 | + | 0.685068i | \(0.759772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.69000i | − | 0.133998i | ||||||
\(404\) | 5.27546 | + | 32.3843i | 0.262464 | + | 1.61118i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.767172 | − | 9.48091i | −0.0380741 | − | 0.470530i | ||||
\(407\) | −28.1069 | −1.39321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −33.8987 | + | 5.52216i | −1.67007 | + | 0.272057i | ||||
\(413\) | − | 4.00000i | − | 0.196827i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.24687 | 0.306647 | ||||||||
\(416\) | 1.01387 | + | 2.37345i | 0.0497089 | + | 0.116368i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 51.3290 | − | 4.15341i | 2.51058 | − | 0.203150i | ||||
\(419\) | 19.2769i | 0.941736i | 0.882204 | + | 0.470868i | \(0.156059\pi\) | ||||
−0.882204 | + | 0.470868i | \(0.843941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 19.3234i | − | 0.941765i | −0.882196 | − | 0.470882i | \(-0.843936\pi\) | ||
0.882196 | − | 0.470882i | \(-0.156064\pi\) | |||||||
\(422\) | −1.15919 | − | 14.3256i | −0.0564285 | − | 0.697358i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.18218 | − | 20.9740i | −0.251669 | − | 1.01859i | ||||
\(425\) | −1.54628 | −0.0750057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.80125i | − | 0.0871684i | ||||||
\(428\) | −4.10547 | − | 25.2021i | −0.198445 | − | 1.21819i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.0194 | + | 1.21533i | −0.724298 | + | 0.0586084i | ||||
\(431\) | −14.4150 | −0.694346 | −0.347173 | − | 0.937801i | \(-0.612858\pi\) | ||||
−0.347173 | + | 0.937801i | \(0.612858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −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 | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.33998 | + | 14.3644i | 0.112065 | + | 0.687928i | ||||
\(437\) | 12.1069i | 0.579150i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −14.7753 | + | 3.65061i | −0.704383 | + | 0.174036i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0215971 | − | 0.266902i | −0.00102727 | − | 0.0126952i | ||||
\(443\) | 15.6465i | 0.743388i | 0.928355 | + | 0.371694i | \(0.121223\pi\) | ||||
−0.928355 | + | 0.371694i | \(0.878777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.56472i | − | 0.263793i | ||||||
\(446\) | 30.9646 | − | 2.50558i | 1.46622 | − | 0.118643i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.07945 | − | 3.72577i | 0.334473 | − | 0.176026i | ||||
\(449\) | 12.6550 | 0.597226 | 0.298613 | − | 0.954374i | \(-0.403476\pi\) | ||||
0.298613 | + | 0.954374i | \(0.403476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.97840i | 0.0931594i | ||||||||
\(452\) | 6.60296 | − | 1.07563i | 0.310577 | − | 0.0505935i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.903087 | + | 11.1606i | 0.0423840 | + | 0.523792i | ||||
\(455\) | −0.514988 | −0.0241430 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −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 | 0 | ||||||||
\(460\) | −0.575298 | − | 3.53156i | −0.0268234 | − | 0.164660i | ||||
\(461\) | 6.74558i | 0.314173i | 0.987585 | + | 0.157086i | \(0.0502101\pi\) | ||||
−0.987585 | + | 0.157086i | \(0.949790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −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 | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −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 | 0 | ||||||||
\(469\) | − | 8.09467i | − | 0.373777i | ||||||
\(470\) | −1.45186 | − | 17.9425i | −0.0669693 | − | 0.827624i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.71374 | − | 10.9834i | −0.124910 | − | 0.505553i | ||||
\(473\) | −45.0005 | −2.06913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 28.4602i | − | 1.30585i | ||||||
\(476\) | −0.819213 | + | 0.133451i | −0.0375485 | + | 0.00611672i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.8317 | − | 1.20014i | 0.678386 | − | 0.0548933i | ||||
\(479\) | 2.17501 | 0.0993788 | 0.0496894 | − | 0.998765i | \(-0.484177\pi\) | ||||
0.0496894 | + | 0.998765i | \(0.484177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.69000 | −0.122653 | ||||||||
\(482\) | −8.60827 | + | 0.696560i | −0.392096 | + | 0.0317274i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.1467 | + | 3.77064i | −1.05212 | + | 0.171393i | ||||
\(485\) | 18.5643i | 0.842962i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | 0 | ||||||||
\(493\) | 2.79130i | 0.125714i | ||||||||
\(494\) | 4.91249 | − | 0.397507i | 0.221024 | − | 0.0178847i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3644 | + | 7.48501i | −1.00419 | + | 0.336087i | ||||
\(497\) | −10.2068 | −0.457840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 27.4065i | − | 1.22688i | −0.789740 | − | 0.613442i | \(-0.789784\pi\) | ||
0.789740 | − | 0.613442i | \(-0.210216\pi\) | |||||||
\(500\) | 3.16721 | + | 19.4425i | 0.141642 | + | 0.869493i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.26690 | − | 28.0150i | −0.101177 | − | 1.25037i | ||||
\(503\) | −17.1368 | −0.764094 | −0.382047 | − | 0.924143i | \(-0.624781\pi\) | ||||
−0.382047 | + | 0.924143i | \(0.624781\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.5178 | −0.824030 | ||||||||
\(506\) | −0.861845 | − | 10.6509i | −0.0383137 | − | 0.473490i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −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 | 0 | ||||||||
\(511\) | −3.34500 | −0.147974 | ||||||||
\(512\) | 16.9115 | − | 15.0334i | 0.747388 | − | 0.664388i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.7987 | − | 1.68298i | 0.917392 | − | 0.0742331i | ||||
\(515\) | − | 19.3837i | − | 0.854148i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 53.7587i | − | 2.36430i | ||||||
\(518\) | 0.672500 | + | 8.31092i | 0.0295479 | + | 0.365161i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.41408 | + | 0.349386i | −0.0620116 | + | 0.0153216i | ||||
\(521\) | −28.3137 | −1.24045 | −0.620223 | − | 0.784426i | \(-0.712958\pi\) | ||||
−0.620223 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0687i | 0.658908i | 0.944172 | + | 0.329454i | \(0.106865\pi\) | ||||
−0.944172 | + | 0.329454i | \(0.893135\pi\) | |||||||
\(524\) | 2.01219 | + | 12.3522i | 0.0879029 | + | 0.539607i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.2154 | − | 1.79762i | 0.968638 | − | 0.0783798i | ||||
\(527\) | 2.44684 | 0.106586 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4878 | −0.890774 | ||||||||
\(530\) | 12.1534 | − | 0.983424i | 0.527911 | − | 0.0427172i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.45625 | − | 15.0781i | −0.106492 | − | 0.653718i | ||||
\(533\) | 0.189345i | 0.00820145i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.4109 | 0.623038 | ||||||||
\(536\) | −5.49171 | − | 22.2268i | −0.237206 | − | 0.960052i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.49032 | − | 30.7760i | −0.107365 | − | 1.32685i | ||||
\(539\) | 4.76717i | 0.205337i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 46.2990i | − | 1.99055i | −0.0971017 | − | 0.995274i | \(-0.530957\pi\) | ||
0.0971017 | − | 0.995274i | \(-0.469043\pi\) | |||||||
\(542\) | −26.5468 | + | 2.14810i | −1.14028 | + | 0.0922689i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.15890 | + | 0.922220i | −0.0925622 | + | 0.0395399i | ||||
\(545\) | −8.21372 | −0.351837 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.03714i | − | 0.0871020i | −0.999051 | − | 0.0435510i | \(-0.986133\pi\) | ||
0.999051 | − | 0.0435510i | \(-0.0138671\pi\) | |||||||
\(548\) | 25.5864 | − | 4.16807i | 1.09300 | − | 0.178051i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.02598 | + | 25.0376i | 0.0863882 | + | 1.06761i | ||||
\(551\) | −51.3755 | −2.18867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.83001 | −0.205393 | ||||||||
\(554\) | 2.79092 | + | 34.4909i | 0.118575 | + | 1.46538i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.90533 | + | 36.2509i | 0.250442 | + | 1.53738i | ||||
\(557\) | 11.1234i | 0.471315i | 0.971836 | + | 0.235658i | \(0.0757244\pi\) | ||||
−0.971836 | + | 0.235658i | \(0.924276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.30683 | −0.182159 | ||||||||
\(560\) | 1.43297 | + | 4.28155i | 0.0605541 | + | 0.180929i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.4604 | + | 1.65561i | −0.863071 | + | 0.0698375i | ||||
\(563\) | − | 37.2437i | − | 1.56963i | −0.619727 | − | 0.784817i | \(-0.712757\pi\) | ||
0.619727 | − | 0.784817i | \(-0.287243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.77566i | 0.158843i | ||||||||
\(566\) | 1.88783 | + | 23.3303i | 0.0793514 | + | 0.980645i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.0265 | + | 6.92468i | −1.17597 | + | 0.290553i | ||||
\(569\) | −22.9369 | −0.961564 | −0.480782 | − | 0.876840i | \(-0.659647\pi\) | ||||
−0.480782 | + | 0.876840i | \(0.659647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.1634i | 1.47154i | 0.677231 | + | 0.735770i | \(0.263180\pi\) | ||||
−0.677231 | + | 0.735770i | \(0.736820\pi\) | |||||||
\(572\) | −4.29343 | + | 0.699406i | −0.179517 | + | 0.0292436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.584994 | − | 0.0473363i | 0.0244172 | − | 0.00197578i | ||||
\(575\) | −5.90558 | −0.246280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.9862 | − | 2.44128i | 0.622268 | − | 0.101369i | ||||
\(581\) | − | 5.53434i | − | 0.229603i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.4137 | 1.50810 | ||||||||
\(584\) | −9.18489 | + | 2.26937i | −0.380073 | + | 0.0939070i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | 0 | ||||||||
\(589\) | 45.0355i | 1.85566i | ||||||||
\(590\) | 6.36436 | − | 0.514988i | 0.262016 | − | 0.0212017i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.48501 | + | 22.3644i | 0.307632 | + | 0.919169i | ||||
\(593\) | 31.8337 | 1.30725 | 0.653627 | − | 0.756817i | \(-0.273247\pi\) | ||||
0.653627 | + | 0.756817i | \(0.273247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 0.468436i | − | 0.0192040i | ||||||
\(596\) | −5.02876 | − | 30.8699i | −0.205986 | − | 1.26448i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0824838 | − | 1.01936i | −0.00337301 | − | 0.0416846i | ||||
\(599\) | 34.9006 | 1.42600 | 0.712999 | − | 0.701165i | \(-0.247336\pi\) | ||||
0.712999 | + | 0.701165i | \(0.247336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.1562 | − | 4.91249i | 1.22704 | − | 0.199887i | ||||
\(605\) | − | 13.2356i | − | 0.538104i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −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 | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.86594 | − | 0.231905i | 0.116039 | − | 0.00938956i | ||||
\(611\) | − | 5.14503i | − | 0.208146i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.37869i | − | 0.338412i | −0.985581 | − | 0.169206i | \(-0.945880\pi\) | ||
0.985581 | − | 0.169206i | \(-0.0541203\pi\) | |||||||
\(614\) | −0.0412419 | − | 0.509678i | −0.00166439 | − | 0.0205689i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.23422 | + | 13.0900i | 0.130310 | + | 0.527410i | ||||
\(617\) | −28.9618 | −1.16596 | −0.582980 | − | 0.812487i | \(-0.698113\pi\) | ||||
−0.582980 | + | 0.812487i | \(0.698113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.85497i | 0.275524i | 0.990465 | + | 0.137762i | \(0.0439910\pi\) | ||||
−0.990465 | + | 0.137762i | \(0.956009\pi\) | |||||||
\(620\) | −2.14001 | − | 13.1368i | −0.0859450 | − | 0.527588i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.8959 | − | 1.28626i | 0.637368 | − | 0.0515743i | ||||
\(623\) | −4.92999 | −0.197516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.51221 | 0.300488 | ||||||||
\(626\) | 36.0629 | − | 2.91812i | 1.44136 | − | 0.116632i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00446 | − | 42.9981i | −0.279508 | − | 1.71581i | ||||
\(629\) | − | 2.44684i | − | 0.0975619i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0412419 | + | 0.509678i | 0.00163793 | + | 0.0202419i | ||||
\(635\) | − | 11.7918i | − | 0.467945i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.456247i | 0.0180772i | ||||||||
\(638\) | 45.1971 | − | 3.65724i | 1.78937 | − | 0.144792i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.83949 | + | 10.7844i | 0.270355 | + | 0.426289i | ||||
\(641\) | 24.0737 | 0.950854 | 0.475427 | − | 0.879755i | \(-0.342294\pi\) | ||||
0.475427 | + | 0.879755i | \(0.342294\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7559i | 0.936841i | 0.883506 | + | 0.468421i | \(0.155177\pi\) | ||||
−0.883506 | + | 0.468421i | \(0.844823\pi\) | |||||||
\(644\) | −3.12875 | + | 0.509678i | −0.123290 | + | 0.0200841i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.361575 | + | 4.46844i | 0.0142260 | + | 0.175808i | ||||
\(647\) | 32.6218 | 1.28250 | 0.641249 | − | 0.767333i | \(-0.278417\pi\) | ||||
0.641249 | + | 0.767333i | \(0.278417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.0687 | 0.748512 | ||||||||
\(650\) | 0.193899 | + | 2.39625i | 0.00760535 | + | 0.0939888i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.48230 | + | 9.09938i | 0.0580515 | + | 0.356359i | ||||
\(653\) | 14.4109i | 0.563942i | 0.959423 | + | 0.281971i | \(0.0909883\pi\) | ||||
−0.959423 | + | 0.281971i | \(0.909012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.06313 | −0.275979 | ||||||||
\(656\) | 1.57420 | − | 0.526860i | 0.0614620 | − | 0.0205704i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.8959 | + | 1.28626i | −0.619687 | + | 0.0501436i | ||||
\(659\) | − | 23.3315i | − | 0.908866i | −0.890781 | − | 0.454433i | \(-0.849842\pi\) | ||
0.890781 | − | 0.454433i | \(-0.150158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1468i | 1.71711i | 0.512721 | + | 0.858555i | \(0.328638\pi\) | ||||
−0.512721 | + | 0.858555i | \(0.671362\pi\) | |||||||
\(662\) | −0.890142 | − | 11.0006i | −0.0345963 | − | 0.427551i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.75469 | − | 15.1965i | −0.145710 | − | 0.589739i | ||||
\(665\) | 8.62185 | 0.334341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.6606i | 0.412779i | ||||||||
\(668\) | 45.3262 | − | 7.38371i | 1.75372 | − | 0.285684i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.8793 | − | 1.04216i | 0.497572 | − | 0.0402623i | ||||
\(671\) | 8.58685 | 0.331492 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | 0 | ||||||||
\(679\) | 16.4468 | 0.631172 | ||||||||
\(680\) | −0.317804 | − | 1.28626i | −0.0121872 | − | 0.0493258i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.20592 | − | 39.6196i | −0.122761 | − | 1.51711i | ||||
\(683\) | − | 22.4909i | − | 0.860589i | −0.902689 | − | 0.430294i | \(-0.858410\pi\) | ||
0.902689 | − | 0.430294i | \(-0.141590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6306i | 0.559007i | ||||||||
\(686\) | 1.40961 | − | 0.114062i | 0.0538190 | − | 0.00435490i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.9839 | + | 35.8065i | 0.456882 | + | 1.36511i | ||||
\(689\) | 3.48501 | 0.132768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.2681i | 1.72208i | 0.508538 | + | 0.861039i | \(0.330186\pi\) | ||||
−0.508538 | + | 0.861039i | \(0.669814\pi\) | |||||||
\(692\) | −0.0695390 | − | 0.426877i | −0.00264348 | − | 0.0162274i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.236926 | + | 2.92800i | 0.00899360 | + | 0.111145i | ||||
\(695\) | −20.7287 | −0.786285 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.172230 | −0.00652366 | ||||||||
\(698\) | 2.13730 | + | 26.4134i | 0.0808982 | + | 0.999761i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | 0 | ||||||||
\(703\) | 45.0355 | 1.69855 | ||||||||
\(704\) | 17.7614 | + | 33.7490i | 0.669408 | + | 1.27196i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.6703 | − | 1.51075i | 0.702664 | − | 0.0568579i | ||||
\(707\) | 16.4056i | 0.616996i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.5481i | − | 0.396144i | −0.980188 | − | 0.198072i | \(-0.936532\pi\) | ||
0.980188 | − | 0.198072i | \(-0.0634679\pi\) | |||||||
\(710\) | −1.31410 | − | 16.2400i | −0.0493173 | − | 0.609476i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13.5371 | + | 3.34468i | −0.507322 | + | 0.125347i | ||||
\(713\) | 9.34500 | 0.349973 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.45504i | − | 0.0918131i | ||||||
\(716\) | 7.27268 | + | 44.6446i | 0.271793 | + | 1.66845i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.02328 | − | 0.649224i | 0.299426 | − | 0.0242288i | ||||
\(719\) | 7.00502 | 0.261243 | 0.130622 | − | 0.991432i | \(-0.458303\pi\) | ||||
0.130622 | + | 0.991432i | \(0.458303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.1728 | −0.639547 | ||||||||
\(722\) | −55.4617 | + | 4.48783i | −2.06407 | + | 0.167020i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.48669 | − | 15.2650i | −0.0924171 | − | 0.567318i | ||||
\(725\) | − | 25.0603i | − | 0.930718i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.430659 | − | 5.32219i | −0.0159394 | − | 0.196983i | ||||
\(731\) | − | 3.91752i | − | 0.144895i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.3300i | − | 1.26801i | −0.773330 | − | 0.634004i | \(-0.781410\pi\) | ||
0.773330 | − | 0.634004i | \(-0.218590\pi\) | |||||||
\(734\) | 15.8959 | − | 1.28626i | 0.586729 | − | 0.0474767i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.24531 | + | 3.52216i | −0.303926 | + | 0.129828i | ||||
\(737\) | 38.5887 | 1.42143 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.0946726i | 0.00348259i | 0.999998 | + | 0.00174129i | \(0.000554271\pi\) | ||||
−0.999998 | + | 0.00174129i | \(0.999446\pi\) | |||||||
\(740\) | −13.1368 | + | 2.14001i | −0.482920 | + | 0.0786684i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.871253 | − | 10.7672i | −0.0319847 | − | 0.395275i | ||||
\(743\) | 13.2755 | 0.487032 | 0.243516 | − | 0.969897i | \(-0.421699\pi\) | ||||
0.243516 | + | 0.969897i | \(0.421699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6518 | 0.646713 | ||||||||
\(746\) | 0.808414 | + | 9.99059i | 0.0295981 | + | 0.365782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.636184 | − | 3.90533i | −0.0232612 | − | 0.142793i | ||||
\(749\) | − | 12.7672i | − | 0.466502i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.32564 | − | 0.350020i | 0.157531 | − | 0.0127470i | ||||
\(755\) | 17.2437i | 0.627562i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.96685i | − | 0.362251i | −0.983460 | − | 0.181126i | \(-0.942026\pi\) | ||
0.983460 | − | 0.181126i | \(-0.0579741\pi\) | |||||||
\(758\) | 0.761683 | + | 9.41308i | 0.0276656 | + | 0.341899i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23.6744 | − | 5.84937i | 0.858759 | − | 0.212179i | ||||
\(761\) | −23.4837 | −0.851283 | −0.425642 | − | 0.904892i | \(-0.639952\pi\) | ||||
−0.425642 | + | 0.904892i | \(0.639952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.27685i | 0.263440i | ||||||||
\(764\) | −20.1481 | + | 3.28216i | −0.728933 | + | 0.118744i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.2962 | − | 2.12782i | 0.950121 | − | 0.0768814i | ||||
\(767\) | 1.82499 | 0.0658966 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.7729 | − | 1.91783i | 0.423718 | − | 0.0690243i | ||||
\(773\) | 35.0956i | 1.26230i | 0.775660 | + | 0.631150i | \(0.217417\pi\) | ||||
−0.775660 | + | 0.631150i | \(0.782583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.9678 | −0.789106 | ||||||||
\(776\) | 45.1607 | − | 11.1581i | 1.62117 | − | 0.400553i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.32033 | − | 28.6753i | −0.0831880 | − | 1.02806i | ||||
\(779\) | − | 3.16999i | − | 0.113577i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 48.6578i | − | 1.74111i | ||||||
\(782\) | 0.927213 | − | 0.0750278i | 0.0331571 | − | 0.00268299i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.79319 | − | 1.26952i | 0.135471 | − | 0.0453402i | ||||
\(785\) | 24.5869 | 0.877542 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.9480i | − | 0.639778i | −0.947455 | − | 0.319889i | \(-0.896354\pi\) | ||
0.947455 | − | 0.319889i | \(-0.103646\pi\) | |||||||
\(788\) | 6.04812 | + | 37.1274i | 0.215455 | + | 1.32261i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.621849 | − | 7.68498i | −0.0221244 | − | 0.273419i | ||||
\(791\) | 3.34500 | 0.118934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.821814 | 0.0291835 | ||||||||
\(794\) | 1.24363 | + | 15.3691i | 0.0441346 | + | 0.545428i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.46844 | − | 1.05372i | 0.229268 | − | 0.0373481i | ||||
\(797\) | − | 34.4199i | − | 1.21922i | −0.792703 | − | 0.609608i | \(-0.791327\pi\) | ||
0.792703 | − | 0.609608i | \(-0.208673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.67996 | 0.165565 | ||||||||
\(800\) | 19.3827 | − | 8.27972i | 0.685281 | − | 0.292732i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −41.1260 | + | 3.32782i | −1.45221 | + | 0.117509i | ||||
\(803\) | − | 15.9462i | − | 0.562729i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.78906i | − | 0.0630560i | ||||||
\(806\) | −0.306826 | − | 3.79184i | −0.0108075 | − | 0.133562i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.1301 | + | 45.0474i | 0.391557 | + | 1.58476i | ||||
\(809\) | −1.89314 | −0.0665592 | −0.0332796 | − | 0.999446i | \(-0.510595\pi\) | ||||
−0.0332796 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3400i | − | 0.363086i | −0.983383 | − | 0.181543i | \(-0.941891\pi\) | ||
0.983383 | − | 0.181543i | \(-0.0581091\pi\) | |||||||
\(812\) | −2.16282 | − | 13.2769i | −0.0759002 | − | 0.465926i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −39.6196 | + | 3.20592i | −1.38867 | + | 0.112367i | ||||
\(815\) | −5.20314 | −0.182258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.1042 | 2.52261 | ||||||||
\(818\) | −44.7179 | + | 3.61846i | −1.56353 | + | 0.126517i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.150633 | + | 0.924684i | 0.00526032 | + | 0.0322914i | ||||
\(821\) | 2.40029i | 0.0837706i | 0.999122 | + | 0.0418853i | \(0.0133364\pi\) | ||||
−0.999122 | + | 0.0418853i | \(0.986664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.456247 | − | 5.63843i | −0.0158749 | − | 0.196186i | ||||
\(827\) | 17.0928i | 0.594375i | 0.954819 | + | 0.297188i | \(0.0960487\pi\) | ||||
−0.954819 | + | 0.297188i | \(0.903951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.8893i | 1.45488i | 0.686174 | + | 0.727438i | \(0.259289\pi\) | ||||
−0.686174 | + | 0.727438i | \(0.740711\pi\) | |||||||
\(830\) | 8.80563 | − | 0.712530i | 0.305648 | − | 0.0247323i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.69987 | + | 3.22998i | 0.0589325 | + | 0.111979i | ||||
\(833\) | −0.415006 | −0.0143791 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.9181i | 0.896933i | ||||||||
\(836\) | 71.8799 | − | 11.7094i | 2.48602 | − | 0.404976i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.19875 | + | 27.1728i | 0.0759547 | + | 0.938668i | ||||
\(839\) | 24.5500 | 0.847560 | 0.423780 | − | 0.905765i | \(-0.360703\pi\) | ||||
0.423780 | + | 0.905765i | \(0.360703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2381 | −0.559936 | ||||||||
\(842\) | −2.20406 | − | 27.2384i | −0.0759570 | − | 0.938697i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.26800 | − | 20.0612i | −0.112489 | − | 0.690535i | ||||
\(845\) | 14.4387i | 0.496708i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.7259 | −0.402908 | ||||||||
\(848\) | −9.69717 | − | 28.9740i | −0.333002 | − | 0.994972i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.17965 | + | 0.176372i | −0.0747613 | + | 0.00604950i | ||||
\(851\) | − | 9.34500i | − | 0.320342i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.7193i | 1.32572i | 0.748742 | + | 0.662862i | \(0.230658\pi\) | ||||
−0.748742 | + | 0.662862i | \(0.769342\pi\) | |||||||
\(854\) | −0.205454 | − | 2.53905i | −0.00703048 | − | 0.0868844i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.66170 | − | 35.0568i | −0.296051 | − | 1.19822i | ||||
\(857\) | 45.2074 | 1.54425 | 0.772127 | − | 0.635468i | \(-0.219193\pi\) | ||||
0.772127 | + | 0.635468i | \(0.219193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 57.1890i | − | 1.95126i | −0.219418 | − | 0.975631i | \(-0.570416\pi\) | ||
0.219418 | − | 0.975631i | \(-0.429584\pi\) | |||||||
\(860\) | −21.0328 | + | 3.42627i | −0.717211 | + | 0.116835i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.3195 | + | 1.64420i | −0.692084 | + | 0.0560018i | ||||
\(863\) | 45.1106 | 1.53558 | 0.767791 | − | 0.640701i | \(-0.221356\pi\) | ||||
0.767791 | + | 0.640701i | \(0.221356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.244094 | 0.00829944 | ||||||||
\(866\) | −13.0767 | + | 1.05813i | −0.444365 | + | 0.0359569i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6384 | + | 1.89592i | −0.395034 | + | 0.0643517i | ||||
\(869\) | − | 23.0255i | − | 0.781086i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.69317 | 0.125138 | ||||||||
\(872\) | 4.93687 | + | 19.9812i | 0.167184 | + | 0.676648i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.38093 | + | 17.0659i | 0.0467107 | + | 0.577263i | ||||
\(875\) | 9.84937i | 0.332969i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6600i | 0.596337i | 0.954513 | + | 0.298168i | \(0.0963757\pi\) | ||||
−0.954513 | + | 0.298168i | \(0.903624\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −20.4109 | + | 6.83122i | −0.688052 | + | 0.230280i | ||||
\(881\) | −6.78998 | −0.228760 | −0.114380 | − | 0.993437i | \(-0.536488\pi\) | ||||
−0.114380 | + | 0.993437i | \(0.536488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.6015i | − | 0.962516i | −0.876579 | − | 0.481258i | \(-0.840180\pi\) | ||
0.876579 | − | 0.481258i | \(-0.159820\pi\) | |||||||
\(884\) | −0.0608867 | − | 0.373764i | −0.00204784 | − | 0.0125710i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.78467 | + | 22.0554i | 0.0599572 | + | 0.740967i | ||||
\(887\) | −23.5919 | −0.792138 | −0.396069 | − | 0.918221i | \(-0.629626\pi\) | ||||
−0.396069 | + | 0.918221i | \(0.629626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4468 | −0.350376 | ||||||||
\(890\) | −0.634722 | − | 7.84406i | −0.0212759 | − | 0.262933i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.3621 | − | 7.06376i | 1.45187 | − | 0.236512i | ||||
\(893\) | 86.1374i | 2.88248i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.5284 | −0.853319 | ||||||||
\(896\) | 9.55427 | − | 6.05937i | 0.319186 | − | 0.202429i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.8386 | − | 1.44345i | 0.595281 | − | 0.0481687i | ||||
\(899\) | 39.6555i | 1.32259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.16999i | 0.105608i | ||||||||
\(902\) | 0.225660 | + | 2.78877i | 0.00751367 | + | 0.0928559i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.18489 | − | 2.26937i | 0.305485 | − | 0.0754780i | ||||
\(905\) | 8.72871 | 0.290152 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.02096i | − | 0.0671050i | −0.999437 | − | 0.0335525i | \(-0.989318\pi\) | ||
0.999437 | − | 0.0335525i | \(-0.0106821\pi\) | |||||||
\(908\) | 2.54599 | + | 15.6290i | 0.0844918 | + | 0.518667i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.725930 | + | 0.0587405i | −0.0240644 | + | 0.00194723i | ||||
\(911\) | −52.5524 | −1.74114 | −0.870569 | − | 0.492046i | \(-0.836249\pi\) | ||||
−0.870569 | + | 0.492046i | \(0.836249\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.3832 | 0.873156 | ||||||||
\(914\) | −33.7229 | + | 2.72878i | −1.11546 | + | 0.0902599i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.23198 | + | 25.9787i | 0.139828 | + | 0.858361i | ||||
\(917\) | 6.25749i | 0.206641i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | 0 | ||||||||
\(922\) | 0.769413 | + | 9.50861i | 0.0253393 | + | 0.313149i | ||||
\(923\) | − | 4.65685i | − | 0.153282i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.9678i | 0.722296i | ||||||||
\(926\) | −15.7453 | + | 1.27407i | −0.517422 | + | 0.0418685i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.9463 | − | 34.9890i | −0.490636 | − | 1.14857i | ||||
\(929\) | 15.7500 | 0.516739 | 0.258370 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258370 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.63843i | − | 0.250339i | ||||||
\(932\) | −34.1042 | + | 5.55562i | −1.11712 | + | 0.181981i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.423096 | + | 5.22873i | 0.0138441 | + | 0.171089i | ||||
\(935\) | 2.23312 | 0.0730307 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.09310 | − | 25.1262i | −0.133502 | − | 0.819527i | ||||
\(941\) | − | 26.5456i | − | 0.865362i | −0.901547 | − | 0.432681i | \(-0.857568\pi\) | ||
0.901547 | − | 0.432681i | \(-0.142432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.657782 | −0.0214203 | ||||||||
\(944\) | −5.07810 | − | 15.1728i | −0.165278 | − | 0.493832i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −63.4330 | + | 5.13285i | −2.06239 | + | 0.166883i | ||||
\(947\) | − | 20.3265i | − | 0.660522i | −0.943890 | − | 0.330261i | \(-0.892863\pi\) | ||
0.943890 | − | 0.330261i | \(-0.107137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.52615i | − | 0.0495408i | ||||||
\(950\) | −3.24623 | − | 40.1177i | −0.105322 | − | 1.30159i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.13955 | + | 0.281554i | −0.0369329 | + | 0.00912523i | ||||
\(953\) | 38.6855 | 1.25315 | 0.626573 | − | 0.779362i | \(-0.284457\pi\) | ||||
0.626573 | + | 0.779362i | \(0.284457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 11.5209i | − | 0.372809i | ||||||
\(956\) | 20.7700 | − | 3.38346i | 0.671748 | − | 0.109429i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.06591 | − | 0.248086i | 0.0990550 | − | 0.00801529i | ||||
\(959\) | 12.9618 | 0.418559 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.76186 | 0.121350 | ||||||||
\(962\) | −3.79184 | + | 0.306826i | −0.122254 | + | 0.00989247i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.0548 | + | 1.96375i | −0.388260 | + | 0.0632482i | ||||
\(965\) | 6.73192i | 0.216708i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | 0 | ||||||||
\(973\) | 18.3644i | 0.588734i | ||||||||
\(974\) | −6.36436 | + | 0.514988i | −0.203927 | + | 0.0165013i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.28673 | − | 6.83247i | −0.0731963 | − | 0.218702i | ||||
\(977\) | −12.0387 | −0.385153 | −0.192576 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192576 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23.5021i | − | 0.751131i | ||||||
\(980\) | 0.362965 | + | 2.22812i | 0.0115945 | + | 0.0711748i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.218110 | − | 2.69546i | −0.00696016 | − | 0.0860155i | ||||
\(983\) | −4.42188 | −0.141036 | −0.0705181 | − | 0.997510i | \(-0.522465\pi\) | ||||
−0.0705181 | + | 0.997510i | \(0.522465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.2299 | −0.676442 | ||||||||
\(986\) | 0.318381 | + | 3.93463i | 0.0101393 | + | 0.125304i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.87934 | − | 1.12066i | 0.218861 | − | 0.0356528i | ||||
\(989\) | − | 14.9618i | − | 0.475758i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.3876 | + | 1.16421i | −0.456348 | + | 0.0369266i | ||||
\(995\) | 3.69873i | 0.117258i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.8556i | − | 1.35725i | −0.734485 | − | 0.678625i | \(-0.762576\pi\) | ||
0.734485 | − | 0.678625i | \(-0.237424\pi\) | |||||||
\(998\) | −3.12604 | − | 38.6324i | −0.0989530 | − | 1.22289i | ||||
\(999\) | 0 | 0 |
(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 | 504.2.c.f.253.7 | 8 | ||
3.2 | odd | 2 | 168.2.c.b.85.2 | yes | 8 | ||
4.3 | odd | 2 | 2016.2.c.e.1009.6 | 8 | |||
8.3 | odd | 2 | 2016.2.c.e.1009.3 | 8 | |||
8.5 | even | 2 | inner | 504.2.c.f.253.8 | 8 | ||
12.11 | even | 2 | 672.2.c.b.337.6 | 8 | |||
21.20 | even | 2 | 1176.2.c.c.589.2 | 8 | |||
24.5 | odd | 2 | 168.2.c.b.85.1 | ✓ | 8 | ||
24.11 | even | 2 | 672.2.c.b.337.3 | 8 | |||
48.5 | odd | 4 | 5376.2.a.bm.1.3 | 4 | |||
48.11 | even | 4 | 5376.2.a.bq.1.3 | 4 | |||
48.29 | odd | 4 | 5376.2.a.bp.1.2 | 4 | |||
48.35 | even | 4 | 5376.2.a.bl.1.2 | 4 | |||
84.83 | odd | 2 | 4704.2.c.c.2353.3 | 8 | |||
168.83 | odd | 2 | 4704.2.c.c.2353.6 | 8 | |||
168.125 | even | 2 | 1176.2.c.c.589.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.c.b.85.1 | ✓ | 8 | 24.5 | odd | 2 | ||
168.2.c.b.85.2 | yes | 8 | 3.2 | odd | 2 | ||
504.2.c.f.253.7 | 8 | 1.1 | even | 1 | trivial | ||
504.2.c.f.253.8 | 8 | 8.5 | even | 2 | inner | ||
672.2.c.b.337.3 | 8 | 24.11 | even | 2 | |||
672.2.c.b.337.6 | 8 | 12.11 | even | 2 | |||
1176.2.c.c.589.1 | 8 | 168.125 | even | 2 | |||
1176.2.c.c.589.2 | 8 | 21.20 | even | 2 | |||
2016.2.c.e.1009.3 | 8 | 8.3 | odd | 2 | |||
2016.2.c.e.1009.6 | 8 | 4.3 | odd | 2 | |||
4704.2.c.c.2353.3 | 8 | 84.83 | odd | 2 | |||
4704.2.c.c.2353.6 | 8 | 168.83 | odd | 2 | |||
5376.2.a.bl.1.2 | 4 | 48.35 | even | 4 | |||
5376.2.a.bm.1.3 | 4 | 48.5 | odd | 4 | |||
5376.2.a.bp.1.2 | 4 | 48.29 | odd | 4 | |||
5376.2.a.bq.1.3 | 4 | 48.11 | even | 4 |