Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,2,Mod(37,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.f (of order \(5\), degree \(4\), 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: | \(0.790518980011\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(1.73855 - 1.26313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.91 |
Dual form | 99.2.f.c.37.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73855 | − | 1.26313i | 1.22934 | − | 0.893166i | 0.232497 | − | 0.972597i | \(-0.425310\pi\) |
0.996840 | + | 0.0794309i | \(0.0253103\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.809017 | − | 2.48990i | 0.404508 | − | 1.24495i | ||||
\(5\) | −1.73855 | − | 1.26313i | −0.777501 | − | 0.564888i | 0.126727 | − | 0.991938i | \(-0.459553\pi\) |
−0.904228 | + | 0.427050i | \(0.859553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30902 | + | 4.02874i | −0.494762 | + | 1.52272i | 0.322566 | + | 0.946547i | \(0.395455\pi\) |
−0.817327 | + | 0.576173i | \(0.804545\pi\) | |||||||
\(8\) | −0.410415 | − | 1.26313i | −0.145104 | − | 0.446583i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.61803 | −1.46035 | ||||||||
\(11\) | 3.22344 | − | 0.780656i | 0.971904 | − | 0.235377i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.190983 | + | 0.138757i | −0.0529692 | + | 0.0384843i | −0.613955 | − | 0.789341i | \(-0.710422\pi\) |
0.560986 | + | 0.827826i | \(0.310422\pi\) | |||||||
\(14\) | 2.81303 | + | 8.65761i | 0.751813 | + | 2.31384i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.92705 | + | 1.40008i | 0.481763 | + | 0.350021i | ||||
\(17\) | −4.96199 | − | 3.60510i | −1.20346 | − | 0.874364i | −0.208838 | − | 0.977950i | \(-0.566968\pi\) |
−0.994620 | + | 0.103586i | \(0.966968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.736068 | − | 2.26538i | −0.168866 | − | 0.519715i | 0.830435 | − | 0.557116i | \(-0.188092\pi\) |
−0.999300 | + | 0.0374011i | \(0.988092\pi\) | |||||||
\(20\) | −4.55157 | + | 3.30691i | −1.01776 | + | 0.739448i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.61803 | − | 5.42882i | 0.984568 | − | 1.15743i | ||||
\(23\) | −3.98439 | −0.830803 | −0.415402 | − | 0.909638i | \(-0.636359\pi\) | ||||
−0.415402 | + | 0.909638i | \(0.636359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.118034 | − | 0.363271i | −0.0236068 | − | 0.0726543i | ||||
\(26\) | −0.156765 | + | 0.482472i | −0.0307441 | + | 0.0946205i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.97214 | + | 6.51864i | 1.69557 | + | 1.23191i | ||||
\(29\) | −2.14896 | + | 6.61382i | −0.399052 | + | 1.22816i | 0.526709 | + | 0.850046i | \(0.323426\pi\) |
−0.925761 | + | 0.378110i | \(0.876574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73607 | − | 2.71441i | 0.671018 | − | 0.487523i | −0.199348 | − | 0.979929i | \(-0.563882\pi\) |
0.870366 | + | 0.492406i | \(0.163882\pi\) | |||||||
\(32\) | 7.77501 | 1.37444 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.1803 | −2.26041 | ||||||||
\(35\) | 7.36460 | − | 5.35069i | 1.24484 | − | 0.904432i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.545085 | − | 1.67760i | 0.0896114 | − | 0.275796i | −0.896201 | − | 0.443649i | \(-0.853684\pi\) |
0.985812 | + | 0.167854i | \(0.0536836\pi\) | |||||||
\(38\) | −4.14116 | − | 3.00873i | −0.671784 | − | 0.488080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.881966 | + | 2.71441i | −0.139451 | + | 0.429186i | ||||
\(41\) | 0.917716 | + | 2.82444i | 0.143323 | + | 0.441103i | 0.996792 | − | 0.0800413i | \(-0.0255052\pi\) |
−0.853468 | + | 0.521145i | \(0.825505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.70820 | 0.412997 | 0.206499 | − | 0.978447i | \(-0.433793\pi\) | ||||
0.206499 | + | 0.978447i | \(0.433793\pi\) | |||||||
\(44\) | 0.664066 | − | 8.65761i | 0.100112 | − | 1.30518i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.92705 | + | 5.03280i | −1.02134 | + | 0.742045i | ||||
\(47\) | −1.07448 | − | 3.30691i | −0.156729 | − | 0.482363i | 0.841603 | − | 0.540097i | \(-0.181612\pi\) |
−0.998332 | + | 0.0577343i | \(0.981612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.85410 | − | 6.43288i | −1.26487 | − | 0.918983i | ||||
\(50\) | −0.664066 | − | 0.482472i | −0.0939130 | − | 0.0682318i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.190983 | + | 0.587785i | 0.0264846 | + | 0.0815111i | ||||
\(53\) | −1.48490 | + | 1.07884i | −0.203966 | + | 0.148190i | −0.685079 | − | 0.728468i | \(-0.740233\pi\) |
0.481113 | + | 0.876658i | \(0.340233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.59017 | − | 2.71441i | −0.888618 | − | 0.366011i | ||||
\(56\) | 5.62605 | 0.751813 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.61803 | + | 14.2128i | 0.606378 | + | 1.86624i | ||||
\(59\) | 2.30573 | − | 7.09629i | 0.300180 | − | 0.923859i | −0.681252 | − | 0.732049i | \(-0.738564\pi\) |
0.981432 | − | 0.191810i | \(-0.0614357\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.16312 | + | 6.65740i | 1.17322 | + | 0.852392i | 0.991391 | − | 0.130938i | \(-0.0417990\pi\) |
0.181827 | + | 0.983331i | \(0.441799\pi\) | |||||||
\(62\) | 3.06668 | − | 9.43826i | 0.389468 | − | 1.19866i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.66312 | − | 7.02067i | 1.20789 | − | 0.877583i | ||||
\(65\) | 0.507301 | 0.0629229 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.85410 | −0.348684 | −0.174342 | − | 0.984685i | \(-0.555780\pi\) | ||||
−0.174342 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(68\) | −12.9907 | + | 9.43826i | −1.57535 | + | 1.14456i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.04508 | − | 18.6049i | 0.722526 | − | 2.22371i | ||||
\(71\) | 8.69273 | + | 6.31564i | 1.03164 | + | 0.749528i | 0.968636 | − | 0.248485i | \(-0.0799327\pi\) |
0.0630016 | + | 0.998013i | \(0.479933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.763932 | − | 2.35114i | 0.0894115 | − | 0.275180i | −0.896346 | − | 0.443356i | \(-0.853788\pi\) |
0.985757 | + | 0.168176i | \(0.0537877\pi\) | |||||||
\(74\) | −1.17137 | − | 3.60510i | −0.136169 | − | 0.419084i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.23607 | −0.715326 | ||||||||
\(77\) | −1.07448 | + | 14.0083i | −0.122448 | + | 1.59639i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.66312 | − | 5.56758i | 0.862168 | − | 0.626402i | −0.0663057 | − | 0.997799i | \(-0.521121\pi\) |
0.928474 | + | 0.371397i | \(0.121121\pi\) | |||||||
\(80\) | −1.58178 | − | 4.86822i | −0.176849 | − | 0.544284i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.16312 | + | 3.75123i | 0.570171 | + | 0.414254i | ||||
\(83\) | 6.70053 | + | 4.86822i | 0.735479 | + | 0.534357i | 0.891292 | − | 0.453430i | \(-0.149800\pi\) |
−0.155813 | + | 0.987787i | \(0.549800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.07295 | + | 12.5352i | 0.441773 | + | 1.35964i | ||||
\(86\) | 4.70834 | − | 3.42081i | 0.507713 | − | 0.368875i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.30902 | − | 3.75123i | −0.246142 | − | 0.399882i | ||||
\(89\) | −8.90937 | −0.944392 | −0.472196 | − | 0.881494i | \(-0.656538\pi\) | ||||
−0.472196 | + | 0.881494i | \(0.656538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.309017 | − | 0.951057i | −0.0323938 | − | 0.0996978i | ||||
\(92\) | −3.22344 | + | 9.92073i | −0.336067 | + | 1.03431i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.04508 | − | 4.39201i | −0.623503 | − | 0.453001i | ||||
\(95\) | −1.58178 | + | 4.86822i | −0.162287 | + | 0.499469i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.54508 | + | 6.93491i | −0.969157 | + | 0.704133i | −0.955259 | − | 0.295770i | \(-0.904424\pi\) |
−0.0138974 | + | 0.999903i | \(0.504424\pi\) | |||||||
\(98\) | −23.5188 | −2.37576 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −0.253650 | + | 0.184288i | −0.0252392 | + | 0.0183373i | −0.600333 | − | 0.799750i | \(-0.704965\pi\) |
0.575094 | + | 0.818087i | \(0.304965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.38197 | + | 10.4086i | −0.333235 | + | 1.02559i | 0.634350 | + | 0.773046i | \(0.281268\pi\) |
−0.967585 | + | 0.252546i | \(0.918732\pi\) | |||||||
\(104\) | 0.253650 | + | 0.184288i | 0.0248725 | + | 0.0180709i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.21885 | + | 3.75123i | −0.118385 | + | 0.364351i | ||||
\(107\) | 3.38021 | + | 10.4032i | 0.326777 | + | 1.00572i | 0.970632 | + | 0.240569i | \(0.0773339\pi\) |
−0.643855 | + | 0.765147i | \(0.722666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7082 | −1.31301 | −0.656504 | − | 0.754323i | \(-0.727965\pi\) | ||||
−0.656504 | + | 0.754323i | \(0.727965\pi\) | |||||||
\(110\) | −14.8860 | + | 3.60510i | −1.41932 | + | 0.343732i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.16312 | + | 5.93085i | −0.771342 | + | 0.560413i | ||||
\(113\) | −5.52917 | − | 17.0170i | −0.520140 | − | 1.60083i | −0.773730 | − | 0.633515i | \(-0.781611\pi\) |
0.253590 | − | 0.967312i | \(-0.418389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.92705 | + | 5.03280i | 0.645951 | + | 0.469311i | ||||
\(116\) | 14.7292 | + | 10.7014i | 1.36757 | + | 0.993599i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.95492 | − | 15.2497i | −0.456137 | − | 1.40385i | ||||
\(119\) | 21.0193 | − | 15.2714i | 1.92684 | − | 1.39993i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.78115 | − | 5.03280i | 0.889196 | − | 0.457527i | ||||
\(122\) | 24.3396 | 2.20361 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.73607 | − | 11.4984i | −0.335509 | − | 1.03259i | ||||
\(125\) | −3.57398 | + | 10.9996i | −0.319666 | + | 0.983832i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.23607 | + | 1.62460i | 0.198419 | + | 0.144160i | 0.682558 | − | 0.730831i | \(-0.260867\pi\) |
−0.484139 | + | 0.874991i | \(0.660867\pi\) | |||||||
\(128\) | 3.12656 | − | 9.62255i | 0.276351 | − | 0.850521i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.881966 | − | 0.640786i | 0.0773535 | − | 0.0562006i | ||||
\(131\) | −2.46249 | −0.215149 | −0.107574 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107574 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0902 | 0.874929 | ||||||||
\(134\) | −4.96199 | + | 3.60510i | −0.428650 | + | 0.311433i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.51722 | + | 7.74721i | −0.215850 | + | 0.664318i | ||||
\(137\) | 0.253650 | + | 0.184288i | 0.0216708 | + | 0.0157448i | 0.598568 | − | 0.801072i | \(-0.295737\pi\) |
−0.576897 | + | 0.816817i | \(0.695737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.51722 | + | 10.8249i | −0.298327 | + | 0.918155i | 0.683757 | + | 0.729710i | \(0.260345\pi\) |
−0.982084 | + | 0.188446i | \(0.939655\pi\) | |||||||
\(140\) | −7.36460 | − | 22.6659i | −0.622422 | − | 1.91562i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 23.0902 | 1.93768 | ||||||||
\(143\) | −0.507301 | + | 0.596368i | −0.0424226 | + | 0.0498708i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0902 | − | 8.78402i | 1.00403 | − | 0.729473i | ||||
\(146\) | −1.64166 | − | 5.05251i | −0.135865 | − | 0.418149i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.73607 | − | 2.71441i | −0.307103 | − | 0.223123i | ||||
\(149\) | −3.73074 | − | 2.71054i | −0.305634 | − | 0.222056i | 0.424387 | − | 0.905481i | \(-0.360490\pi\) |
−0.730021 | + | 0.683425i | \(0.760490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.09017 | − | 12.5882i | −0.332853 | − | 1.02442i | −0.967770 | − | 0.251836i | \(-0.918966\pi\) |
0.634917 | − | 0.772581i | \(-0.281034\pi\) | |||||||
\(152\) | −2.55938 | + | 1.85950i | −0.207593 | + | 0.150825i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.8262 | + | 25.7113i | 1.27531 | + | 2.07187i | ||||
\(155\) | −9.92398 | −0.797113 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.38197 | − | 19.6417i | −0.509336 | − | 1.56758i | −0.793356 | − | 0.608758i | \(-0.791668\pi\) |
0.284020 | − | 0.958818i | \(-0.408332\pi\) | |||||||
\(158\) | 6.29012 | − | 19.3590i | 0.500415 | − | 1.54012i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.5172 | − | 9.82084i | −1.06863 | − | 0.776405i | ||||
\(161\) | 5.21564 | − | 16.0521i | 0.411050 | − | 1.26508i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.11803 | + | 0.812299i | −0.0875712 | + | 0.0636242i | −0.630709 | − | 0.776019i | \(-0.717236\pi\) |
0.543138 | + | 0.839643i | \(0.317236\pi\) | |||||||
\(164\) | 7.77501 | 0.607127 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7984 | 1.38142 | ||||||||
\(167\) | −8.69273 | + | 6.31564i | −0.672664 | + | 0.488719i | −0.870916 | − | 0.491432i | \(-0.836474\pi\) |
0.198252 | + | 0.980151i | \(0.436474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | + | 12.3107i | −0.307692 | + | 0.946980i | ||||
\(170\) | 22.9146 | + | 16.6485i | 1.75747 | + | 1.27688i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.19098 | − | 6.74315i | 0.167061 | − | 0.514161i | ||||
\(173\) | 4.14116 | + | 12.7452i | 0.314846 | + | 0.968998i | 0.975818 | + | 0.218586i | \(0.0701445\pi\) |
−0.660971 | + | 0.750411i | \(0.729855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.61803 | 0.122312 | ||||||||
\(176\) | 7.30472 | + | 3.00873i | 0.550614 | + | 0.226791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.4894 | + | 11.2537i | −1.16098 | + | 0.843499i | ||||
\(179\) | −0.604187 | − | 1.85950i | −0.0451590 | − | 0.138985i | 0.925935 | − | 0.377684i | \(-0.123279\pi\) |
−0.971094 | + | 0.238698i | \(0.923279\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89919 | − | 7.19218i | −0.735801 | − | 0.534591i | 0.155592 | − | 0.987821i | \(-0.450271\pi\) |
−0.891393 | + | 0.453231i | \(0.850271\pi\) | |||||||
\(182\) | −1.73855 | − | 1.26313i | −0.128870 | − | 0.0936293i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.63525 | + | 5.03280i | 0.120553 | + | 0.371023i | ||||
\(185\) | −3.06668 | + | 2.22807i | −0.225467 | + | 0.163811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.8090 | − | 7.74721i | −1.37545 | − | 0.566532i | ||||
\(188\) | −9.10315 | −0.663915 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.39919 | + | 10.4616i | 0.246603 | + | 0.758966i | ||||
\(191\) | 3.06668 | − | 9.43826i | 0.221897 | − | 0.682929i | −0.776695 | − | 0.629877i | \(-0.783105\pi\) |
0.998592 | − | 0.0530515i | \(-0.0168948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.97214 | − | 4.33901i | −0.429884 | − | 0.312329i | 0.351719 | − | 0.936106i | \(-0.385597\pi\) |
−0.781602 | + | 0.623777i | \(0.785597\pi\) | |||||||
\(194\) | −7.83489 | + | 24.1133i | −0.562513 | + | 1.73124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.1803 | + | 16.8415i | −1.65574 | + | 1.20296i | ||||
\(197\) | 2.46249 | 0.175445 | 0.0877226 | − | 0.996145i | \(-0.472041\pi\) | ||||
0.0877226 | + | 0.996145i | \(0.472041\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.416408 | 0.0295184 | 0.0147592 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147592 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(200\) | −0.410415 | + | 0.298184i | −0.0290207 | + | 0.0210848i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.208204 | + | 0.640786i | −0.0146492 | + | 0.0450855i | ||||
\(203\) | −23.8323 | − | 17.3152i | −1.67270 | − | 1.21529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.97214 | − | 6.06961i | 0.137740 | − | 0.423920i | ||||
\(206\) | 7.26771 | + | 22.3677i | 0.506366 | + | 1.55843i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.562306 | −0.0389889 | ||||||||
\(209\) | −4.14116 | − | 6.72772i | −0.286450 | − | 0.465366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5902 | − | 10.6004i | 1.00443 | − | 0.729760i | 0.0413955 | − | 0.999143i | \(-0.486820\pi\) |
0.963033 | + | 0.269383i | \(0.0868196\pi\) | |||||||
\(212\) | 1.48490 | + | 4.57004i | 0.101983 | + | 0.313872i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.0172 | + | 13.8168i | 1.29999 | + | 0.944498i | ||||
\(215\) | −4.70834 | − | 3.42081i | −0.321106 | − | 0.233297i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.04508 | + | 18.6049i | 0.410367 | + | 1.26298i | ||||
\(218\) | −23.8323 | + | 17.3152i | −1.61413 | + | 1.17273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0902 | + | 14.2128i | −0.815119 | + | 0.958230i | ||||
\(221\) | 1.44789 | 0.0973955 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.982779 | + | 3.02468i | 0.0658118 | + | 0.202548i | 0.978555 | − | 0.205986i | \(-0.0660402\pi\) |
−0.912743 | + | 0.408534i | \(0.866040\pi\) | |||||||
\(224\) | −10.1776 | + | 31.3235i | −0.680021 | + | 2.09289i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.1074 | − | 22.6008i | −2.06923 | − | 1.50339i | ||||
\(227\) | −3.38021 | + | 10.4032i | −0.224352 | + | 0.690485i | 0.774005 | + | 0.633180i | \(0.218251\pi\) |
−0.998357 | + | 0.0573050i | \(0.981749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9443 | − | 10.8576i | 0.987545 | − | 0.717494i | 0.0281631 | − | 0.999603i | \(-0.491034\pi\) |
0.959382 | + | 0.282110i | \(0.0910342\pi\) | |||||||
\(230\) | 18.4001 | 1.21326 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.23607 | 0.606378 | ||||||||
\(233\) | 18.6167 | − | 13.5258i | 1.21962 | − | 0.886106i | 0.223552 | − | 0.974692i | \(-0.428235\pi\) |
0.996069 | + | 0.0885854i | \(0.0282346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.30902 | + | 7.10642i | −0.150624 | + | 0.463572i | ||||
\(236\) | −15.8037 | − | 11.4820i | −1.02873 | − | 0.747417i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.2533 | − | 53.1002i | 1.11836 | − | 3.44197i | ||||
\(239\) | −3.53697 | − | 10.8857i | −0.228788 | − | 0.704136i | −0.997885 | − | 0.0650043i | \(-0.979294\pi\) |
0.769097 | − | 0.639132i | \(-0.220706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 10.6479 | − | 21.1046i | 0.684474 | − | 1.35665i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.9894 | − | 17.4293i | 1.53576 | − | 1.11580i | ||||
\(245\) | 7.26771 | + | 22.3677i | 0.464317 | + | 1.42902i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.454915 | + | 0.330515i | 0.0289456 | + | 0.0210302i | ||||
\(248\) | −4.96199 | − | 3.60510i | −0.315087 | − | 0.228924i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.68034 | + | 23.6377i | 0.485747 | + | 1.49498i | ||||
\(251\) | −18.3631 | + | 13.3415i | −1.15907 | + | 0.842111i | −0.989660 | − | 0.143436i | \(-0.954185\pi\) |
−0.169406 | + | 0.985546i | \(0.554185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8435 | + | 3.11044i | −0.807461 | + | 0.195552i | ||||
\(254\) | 5.93958 | 0.372683 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.663119 | + | 2.04087i | 0.0414449 | + | 0.127554i | ||||
\(257\) | 3.82763 | − | 11.7802i | 0.238761 | − | 0.734831i | −0.757839 | − | 0.652441i | \(-0.773745\pi\) |
0.996600 | − | 0.0823893i | \(-0.0262551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.04508 | + | 4.39201i | 0.375623 | + | 0.272906i | ||||
\(260\) | 0.410415 | − | 1.26313i | 0.0254529 | − | 0.0783359i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.28115 | + | 3.11044i | −0.264491 | + | 0.192164i | ||||
\(263\) | 6.44688 | 0.397532 | 0.198766 | − | 0.980047i | \(-0.436307\pi\) | ||||
0.198766 | + | 0.980047i | \(0.436307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94427 | 0.242295 | ||||||||
\(266\) | 17.5422 | − | 12.7452i | 1.07558 | − | 0.781457i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.30902 | + | 7.10642i | −0.141046 | + | 0.434094i | ||||
\(269\) | 16.3709 | + | 11.8941i | 0.998149 | + | 0.725198i | 0.961690 | − | 0.274138i | \(-0.0883924\pi\) |
0.0364584 | + | 0.999335i | \(0.488392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.298374 | + | 0.918300i | −0.0181249 | + | 0.0557828i | −0.959710 | − | 0.280993i | \(-0.909336\pi\) |
0.941585 | + | 0.336775i | \(0.109336\pi\) | |||||||
\(272\) | −4.51457 | − | 13.8944i | −0.273736 | − | 0.842472i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.673762 | 0.0407035 | ||||||||
\(275\) | −0.664066 | − | 1.07884i | −0.0400447 | − | 0.0650565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6803 | + | 11.3924i | −0.942140 | + | 0.684505i | −0.948935 | − | 0.315472i | \(-0.897837\pi\) |
0.00679460 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(278\) | 7.55837 | + | 23.2623i | 0.453321 | + | 1.39518i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.78115 | − | 7.10642i | −0.584536 | − | 0.424690i | ||||
\(281\) | −13.4011 | − | 9.73645i | −0.799441 | − | 0.580828i | 0.111309 | − | 0.993786i | \(-0.464496\pi\) |
−0.910750 | + | 0.412958i | \(0.864496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.38197 | − | 10.4086i | −0.201037 | − | 0.618728i | −0.999853 | − | 0.0171527i | \(-0.994540\pi\) |
0.798816 | − | 0.601576i | \(-0.205460\pi\) | |||||||
\(284\) | 22.7579 | − | 16.5346i | 1.35043 | − | 0.981145i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.128677 | + | 1.67760i | −0.00760884 | + | 0.0991985i | ||||
\(287\) | −12.5802 | −0.742588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.37132 | + | 19.6089i | 0.374784 | + | 1.15347i | ||||
\(290\) | 9.92398 | − | 30.5429i | 0.582756 | − | 1.79354i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.23607 | − | 3.80423i | −0.306418 | − | 0.222625i | ||||
\(293\) | 1.54477 | − | 4.75433i | 0.0902467 | − | 0.277751i | −0.895739 | − | 0.444580i | \(-0.853353\pi\) |
0.985986 | + | 0.166829i | \(0.0533529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9721 | + | 9.42481i | −0.755267 | + | 0.548734i | ||||
\(296\) | −2.34273 | −0.136169 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.90983 | −0.574061 | ||||||||
\(299\) | 0.760951 | − | 0.552864i | 0.0440070 | − | 0.0319729i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.54508 | + | 10.9106i | −0.204335 | + | 0.628879i | ||||
\(302\) | −23.0115 | − | 16.7188i | −1.32416 | − | 0.962061i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.75329 | − | 5.39607i | 0.100558 | − | 0.309486i | ||||
\(305\) | −7.52136 | − | 23.1484i | −0.430672 | − | 1.32547i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.2705 | 0.985680 | 0.492840 | − | 0.870120i | \(-0.335959\pi\) | ||||
0.492840 | + | 0.870120i | \(0.335959\pi\) | |||||||
\(308\) | 34.0100 | + | 14.0083i | 1.93790 | + | 0.798197i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.2533 | + | 12.5352i | −0.979921 | + | 0.711954i | ||||
\(311\) | 8.88650 | + | 27.3498i | 0.503907 | + | 1.55087i | 0.802600 | + | 0.596518i | \(0.203449\pi\) |
−0.298693 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.6074 | − | 18.6049i | −1.44742 | − | 1.05161i | −0.986427 | − | 0.164203i | \(-0.947495\pi\) |
−0.460989 | − | 0.887406i | \(-0.652505\pi\) | |||||||
\(314\) | −35.9053 | − | 26.0867i | −2.02625 | − | 1.47216i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.66312 | − | 23.5847i | −0.431084 | − | 1.32674i | ||||
\(317\) | −0.253650 | + | 0.184288i | −0.0142464 | + | 0.0103506i | −0.594886 | − | 0.803810i | \(-0.702803\pi\) |
0.580639 | + | 0.814161i | \(0.302803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.76393 | + | 22.9969i | −0.0987612 | + | 1.28758i | ||||
\(320\) | −25.6678 | −1.43487 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.2082 | − | 34.4953i | −0.624609 | − | 1.92235i | ||||
\(323\) | −4.51457 | + | 13.8944i | −0.251197 | + | 0.773105i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0729490 | + | 0.0530006i | 0.00404648 | + | 0.00293994i | ||||
\(326\) | −0.917716 | + | 2.82444i | −0.0508276 | + | 0.156431i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.19098 | − | 2.31838i | 0.176193 | − | 0.128011i | ||||
\(329\) | 14.7292 | 0.812047 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.29180 | 0.400793 | 0.200397 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200397 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(332\) | 17.5422 | − | 12.7452i | 0.962755 | − | 0.699482i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.13525 | + | 21.9601i | −0.390424 | + | 1.20160i | ||||
\(335\) | 4.96199 | + | 3.60510i | 0.271102 | + | 0.196967i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.23607 | + | 25.3480i | −0.448647 | + | 1.38079i | 0.429787 | + | 0.902930i | \(0.358589\pi\) |
−0.878434 | + | 0.477864i | \(0.841411\pi\) | |||||||
\(338\) | 8.59584 | + | 26.4553i | 0.467552 | + | 1.43898i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 34.5066 | 1.87138 | ||||||||
\(341\) | 9.92398 | − | 11.6663i | 0.537413 | − | 0.631767i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5172 | − | 9.82084i | 0.729861 | − | 0.530275i | ||||
\(344\) | −1.11149 | − | 3.42081i | −0.0599274 | − | 0.184438i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.2984 | + | 16.9273i | 1.25253 | + | 0.910015i | ||||
\(347\) | 20.3553 | + | 14.7890i | 1.09273 | + | 0.793913i | 0.979858 | − | 0.199697i | \(-0.0639958\pi\) |
0.112869 | + | 0.993610i | \(0.463996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.83688 | + | 8.73102i | 0.151855 | + | 0.467361i | 0.997829 | − | 0.0658634i | \(-0.0209802\pi\) |
−0.845974 | + | 0.533224i | \(0.820980\pi\) | |||||||
\(350\) | 2.81303 | − | 2.04378i | 0.150363 | − | 0.109245i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.0623 | − | 6.06961i | 1.33583 | − | 0.323511i | ||||
\(353\) | 33.7563 | 1.79667 | 0.898334 | − | 0.439314i | \(-0.144778\pi\) | ||||
0.898334 | + | 0.439314i | \(0.144778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.13525 | − | 21.9601i | −0.378700 | − | 1.16552i | ||||
\(356\) | −7.20783 | + | 22.1834i | −0.382014 | + | 1.17572i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.39919 | − | 2.46965i | −0.179653 | − | 0.130525i | ||||
\(359\) | −0.627058 | + | 1.92989i | −0.0330949 | + | 0.101856i | −0.966239 | − | 0.257646i | \(-0.917053\pi\) |
0.933145 | + | 0.359501i | \(0.117053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.7812 | − | 7.83297i | 0.567429 | − | 0.412261i | ||||
\(362\) | −26.2948 | −1.38203 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.61803 | −0.137222 | ||||||||
\(365\) | −4.29792 | + | 3.12262i | −0.224964 | + | 0.163446i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.11803 | − | 21.9071i | 0.371558 | − | 1.14354i | −0.574213 | − | 0.818706i | \(-0.694692\pi\) |
0.945771 | − | 0.324833i | \(-0.105308\pi\) | |||||||
\(368\) | −7.67813 | − | 5.57849i | −0.400250 | − | 0.290799i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.51722 | + | 7.74721i | −0.130864 | + | 0.402758i | ||||
\(371\) | −2.40261 | − | 7.39448i | −0.124737 | − | 0.383902i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4164 | −0.746453 | −0.373227 | − | 0.927740i | \(-0.621749\pi\) | ||||
−0.373227 | + | 0.927740i | \(0.621749\pi\) | |||||||
\(374\) | −42.4861 | + | 10.2893i | −2.19690 | + | 0.532048i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.73607 | + | 2.71441i | −0.192673 | + | 0.139985i | ||||
\(377\) | −0.507301 | − | 1.56131i | −0.0261273 | − | 0.0804116i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.04508 | − | 3.66547i | −0.259149 | − | 0.188282i | 0.450623 | − | 0.892714i | \(-0.351202\pi\) |
−0.709772 | + | 0.704432i | \(0.751202\pi\) | |||||||
\(380\) | 10.8417 | + | 7.87695i | 0.556167 | + | 0.404079i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.59017 | − | 20.2825i | −0.337182 | − | 1.03774i | ||||
\(383\) | −27.5631 | + | 20.0258i | −1.40841 | + | 1.02327i | −0.414856 | + | 0.909887i | \(0.636168\pi\) |
−0.993552 | + | 0.113381i | \(0.963832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.5623 | − | 22.9969i | 0.996987 | − | 1.17203i | ||||
\(386\) | −15.8636 | −0.807434 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.54508 | + | 29.3768i | 0.484578 | + | 1.49138i | ||||
\(389\) | −6.89431 | + | 21.2185i | −0.349555 | + | 1.07582i | 0.609545 | + | 0.792752i | \(0.291352\pi\) |
−0.959100 | + | 0.283068i | \(0.908648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.7705 | + | 14.3641i | 0.999838 | + | 0.726425i | ||||
\(392\) | −4.49169 | + | 13.8240i | −0.226865 | + | 0.698218i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.28115 | − | 3.11044i | 0.215681 | − | 0.156702i | ||||
\(395\) | −20.3553 | −1.02418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4164 | 1.22542 | 0.612712 | − | 0.790306i | \(-0.290078\pi\) | ||||
0.612712 | + | 0.790306i | \(0.290078\pi\) | |||||||
\(398\) | 0.723944 | − | 0.525976i | 0.0362880 | − | 0.0263648i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.281153 | − | 0.865300i | 0.0140576 | − | 0.0432650i | ||||
\(401\) | −15.3933 | − | 11.1839i | −0.768703 | − | 0.558495i | 0.132864 | − | 0.991134i | \(-0.457583\pi\) |
−0.901567 | + | 0.432639i | \(0.857583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.336881 | + | 1.03681i | −0.0167812 | + | 0.0516473i | ||||
\(404\) | 0.253650 | + | 0.780656i | 0.0126196 | + | 0.0388391i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −63.3050 | −3.14177 | ||||||||
\(407\) | 0.447422 | − | 5.83317i | 0.0221779 | − | 0.289139i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.09017 | − | 2.97168i | 0.202246 | − | 0.146940i | −0.482053 | − | 0.876142i | \(-0.660109\pi\) |
0.684298 | + | 0.729202i | \(0.260109\pi\) | |||||||
\(410\) | −4.23804 | − | 13.0434i | −0.209302 | − | 0.644165i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 23.1803 | + | 16.8415i | 1.14201 | + | 0.829721i | ||||
\(413\) | 25.5709 | + | 18.5783i | 1.25826 | + | 0.914180i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.50000 | − | 16.9273i | −0.269984 | − | 0.830926i | ||||
\(416\) | −1.48490 | + | 1.07884i | −0.0728030 | + | 0.0528945i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.6976 | − | 6.46564i | −0.767793 | − | 0.316245i | ||||
\(419\) | 35.2782 | 1.72345 | 0.861727 | − | 0.507372i | \(-0.169383\pi\) | ||||
0.861727 | + | 0.507372i | \(0.169383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.02786 | − | 27.7849i | −0.439991 | − | 1.35415i | −0.887884 | − | 0.460067i | \(-0.847826\pi\) |
0.447893 | − | 0.894087i | \(-0.352174\pi\) | |||||||
\(422\) | 11.9761 | − | 36.8585i | 0.582985 | − | 1.79424i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.97214 | + | 1.43284i | 0.0957754 | + | 0.0695849i | ||||
\(425\) | −0.723944 | + | 2.22807i | −0.0351165 | + | 0.108077i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.8156 | + | 28.2012i | −1.87842 | + | 1.36475i | ||||
\(428\) | 28.6376 | 1.38425 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.5066 | −0.603121 | ||||||||
\(431\) | −28.7943 | + | 20.9203i | −1.38697 | + | 1.00770i | −0.390785 | + | 0.920482i | \(0.627796\pi\) |
−0.996190 | + | 0.0872135i | \(0.972204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.819660 | + | 2.52265i | −0.0393904 | + | 0.121231i | −0.968818 | − | 0.247773i | \(-0.920301\pi\) |
0.929428 | + | 0.369004i | \(0.120301\pi\) | |||||||
\(434\) | 34.0100 | + | 24.7097i | 1.63253 | + | 1.18610i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.0902 | + | 34.1320i | −0.531123 | + | 1.63463i | ||||
\(437\) | 2.93278 | + | 9.02618i | 0.140294 | + | 0.431781i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0000 | −1.19318 | −0.596592 | − | 0.802544i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802544i | \(0.703479\pi\) | |||||||
\(440\) | −0.723944 | + | 9.43826i | −0.0345127 | + | 0.449951i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.51722 | − | 1.82887i | 0.119732 | − | 0.0869904i | ||||
\(443\) | −6.76041 | − | 20.8064i | −0.321197 | − | 0.988542i | −0.973128 | − | 0.230264i | \(-0.926041\pi\) |
0.651931 | − | 0.758278i | \(-0.273959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.4894 | + | 11.2537i | 0.734266 | + | 0.533475i | ||||
\(446\) | 5.52917 | + | 4.01718i | 0.261814 | + | 0.190219i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.6353 | + | 48.1204i | 0.738696 | + | 2.27347i | ||||
\(449\) | 23.8323 | − | 17.3152i | 1.12472 | − | 0.817155i | 0.139800 | − | 0.990180i | \(-0.455354\pi\) |
0.984918 | + | 0.173024i | \(0.0553539\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.16312 | + | 8.38800i | 0.243122 | + | 0.394975i | ||||
\(452\) | −46.8439 | −2.20335 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.26393 | + | 22.3561i | 0.340913 | + | 1.04922i | ||||
\(455\) | −0.664066 | + | 2.04378i | −0.0311319 | + | 0.0958140i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.3885 | − | 20.6255i | −1.32796 | − | 0.964819i | −0.999796 | − | 0.0201987i | \(-0.993570\pi\) |
−0.328164 | − | 0.944621i | \(-0.606430\pi\) | |||||||
\(458\) | 12.2667 | − | 37.7530i | 0.573186 | − | 1.76408i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.1353 | − | 13.1760i | 0.845561 | − | 0.614336i | ||||
\(461\) | −1.52190 | −0.0708821 | −0.0354410 | − | 0.999372i | \(-0.511284\pi\) | ||||
−0.0354410 | + | 0.999372i | \(0.511284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5623 | −1.00209 | −0.501043 | − | 0.865423i | \(-0.667050\pi\) | ||||
−0.501043 | + | 0.865423i | \(0.667050\pi\) | |||||||
\(464\) | −13.4011 | + | 9.73645i | −0.622129 | + | 0.452003i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.2812 | − | 47.0306i | 0.707886 | − | 2.17865i | ||||
\(467\) | 17.1318 | + | 12.4470i | 0.792766 | + | 0.575978i | 0.908783 | − | 0.417269i | \(-0.137013\pi\) |
−0.116017 | + | 0.993247i | \(0.537013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.73607 | − | 11.4984i | 0.172516 | − | 0.530948i | ||||
\(470\) | 4.96199 | + | 15.2714i | 0.228879 | + | 0.704418i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.90983 | −0.456137 | ||||||||
\(473\) | 8.72974 | − | 2.11418i | 0.401394 | − | 0.0972099i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.736068 | + | 0.534785i | −0.0337731 | + | 0.0245376i | ||||
\(476\) | −21.0193 | − | 64.6908i | −0.963419 | − | 2.96510i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.8992 | − | 14.4576i | −0.910168 | − | 0.661275i | ||||
\(479\) | −29.8089 | − | 21.6575i | −1.36200 | − | 0.989555i | −0.998315 | − | 0.0580346i | \(-0.981517\pi\) |
−0.363690 | − | 0.931520i | \(-0.618483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.128677 | + | 0.396027i | 0.00586717 | + | 0.0180573i | ||||
\(482\) | 24.3396 | − | 17.6838i | 1.10864 | − | 0.805474i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.61803 | − | 28.4257i | −0.209911 | − | 1.29208i | ||||
\(485\) | 25.3542 | 1.15128 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.83688 | + | 17.9641i | 0.264494 | + | 0.814030i | 0.991809 | + | 0.127726i | \(0.0407679\pi\) |
−0.727315 | + | 0.686304i | \(0.759232\pi\) | |||||||
\(488\) | 4.64846 | − | 14.3065i | 0.210426 | − | 0.647624i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 40.8885 | + | 29.7073i | 1.84716 | + | 1.34204i | ||||
\(491\) | 5.99946 | − | 18.4644i | 0.270752 | − | 0.833289i | −0.719560 | − | 0.694430i | \(-0.755657\pi\) |
0.990312 | − | 0.138859i | \(-0.0443434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.5066 | − | 25.0705i | 1.55410 | − | 1.12912i | ||||
\(494\) | 1.20837 | 0.0543673 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.0000 | 0.493915 | ||||||||
\(497\) | −36.8230 | + | 26.7535i | −1.65174 | + | 1.20006i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.1180 | − | 31.1401i | 0.452945 | − | 1.39402i | −0.420585 | − | 0.907253i | \(-0.638175\pi\) |
0.873530 | − | 0.486770i | \(-0.161825\pi\) | |||||||
\(500\) | 24.4964 | + | 17.7977i | 1.09551 | + | 0.795937i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.0729 | + | 46.3898i | −0.672739 | + | 2.07048i | ||||
\(503\) | −1.83543 | − | 5.64888i | −0.0818379 | − | 0.251871i | 0.901763 | − | 0.432231i | \(-0.142274\pi\) |
−0.983601 | + | 0.180360i | \(0.942274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.673762 | 0.0299820 | ||||||||
\(506\) | −18.4001 | + | 21.6306i | −0.817983 | + | 0.961596i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.85410 | − | 4.25325i | 0.259734 | − | 0.188708i | ||||
\(509\) | −5.05887 | − | 15.5696i | −0.224231 | − | 0.690111i | −0.998369 | − | 0.0570943i | \(-0.981816\pi\) |
0.774138 | − | 0.633017i | \(-0.218184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.47214 | + | 6.15537i | 0.374785 | + | 0.272297i | ||||
\(512\) | 20.1016 | + | 14.6047i | 0.888374 | + | 0.645441i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.22542 | − | 25.3153i | −0.362808 | − | 1.11661i | ||||
\(515\) | 19.0271 | − | 13.8240i | 0.838435 | − | 0.609159i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.04508 | − | 9.82084i | −0.265863 | − | 0.431920i | ||||
\(518\) | 16.0573 | 0.705519 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.208204 | − | 0.640786i | −0.00913035 | − | 0.0281003i | ||||
\(521\) | 8.28232 | − | 25.4903i | 0.362855 | − | 1.11675i | −0.588459 | − | 0.808527i | \(-0.700265\pi\) |
0.951313 | − | 0.308225i | \(-0.0997350\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.2984 | + | 22.0131i | 1.32486 | + | 0.962564i | 0.999858 | + | 0.0168489i | \(0.00536341\pi\) |
0.324997 | + | 0.945715i | \(0.394637\pi\) | |||||||
\(524\) | −1.99220 | + | 6.13135i | −0.0870295 | + | 0.267849i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.2082 | − | 8.14324i | 0.488701 | − | 0.355062i | ||||
\(527\) | −28.3240 | −1.23381 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.12461 | −0.309766 | ||||||||
\(530\) | 6.85730 | − | 4.98212i | 0.297862 | − | 0.216409i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.16312 | − | 25.1235i | 0.353916 | − | 1.08924i | ||||
\(533\) | −0.567180 | − | 0.412080i | −0.0245673 | − | 0.0178492i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.26393 | − | 22.3561i | 0.314047 | − | 0.966538i | ||||
\(536\) | 1.17137 | + | 3.60510i | 0.0505953 | + | 0.155716i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 43.4853 | 1.87478 | ||||||||
\(539\) | −33.5625 | − | 13.8240i | −1.44564 | − | 0.595442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.2533 | + | 22.7068i | −1.34368 | + | 0.976243i | −0.344384 | + | 0.938829i | \(0.611912\pi\) |
−0.999300 | + | 0.0374146i | \(0.988088\pi\) | |||||||
\(542\) | 0.641194 | + | 1.97339i | 0.0275416 | + | 0.0847644i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −38.5795 | − | 28.0297i | −1.65408 | − | 1.20176i | ||||
\(545\) | 23.8323 | + | 17.3152i | 1.02087 | + | 0.741702i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.19098 | + | 19.0539i | 0.264707 | + | 0.814685i | 0.991761 | + | 0.128104i | \(0.0408893\pi\) |
−0.727053 | + | 0.686581i | \(0.759111\pi\) | |||||||
\(548\) | 0.664066 | − | 0.482472i | 0.0283675 | − | 0.0206102i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.51722 | − | 1.03681i | −0.107335 | − | 0.0442099i | ||||
\(551\) | 16.5646 | 0.705677 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3992 | + | 38.1608i | 0.527267 | + | 1.62276i | ||||
\(554\) | −12.8709 | + | 39.6125i | −0.546832 | + | 1.68298i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.1074 | + | 17.5150i | 1.02238 | + | 0.742803i | ||||
\(557\) | −1.67867 | + | 5.16641i | −0.0711274 | + | 0.218908i | −0.980301 | − | 0.197510i | \(-0.936715\pi\) |
0.909173 | + | 0.416418i | \(0.136715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.517221 | + | 0.375783i | −0.0218761 | + | 0.0158939i | ||||
\(560\) | 21.6834 | 0.916290 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.5967 | −1.50156 | ||||||||
\(563\) | 12.6401 | − | 9.18358i | 0.532717 | − | 0.387042i | −0.288656 | − | 0.957433i | \(-0.593208\pi\) |
0.821373 | + | 0.570391i | \(0.193208\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8820 | + | 36.5689i | −0.499878 | + | 1.53847i | ||||
\(566\) | −19.0271 | − | 13.8240i | −0.799770 | − | 0.581067i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.40983 | − | 13.5721i | 0.185032 | − | 0.569471i | ||||
\(569\) | −9.80422 | − | 30.1743i | −0.411014 | − | 1.26497i | −0.915768 | − | 0.401708i | \(-0.868417\pi\) |
0.504754 | − | 0.863263i | \(-0.331583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.9787 | 0.501294 | 0.250647 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250647 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(572\) | 1.07448 | + | 1.74560i | 0.0449263 | + | 0.0729872i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.8713 | + | 15.8904i | −0.912891 | + | 0.663254i | ||||
\(575\) | 0.470294 | + | 1.44742i | 0.0196126 | + | 0.0603614i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.09017 | + | 0.792055i | 0.0453844 | + | 0.0329737i | 0.610246 | − | 0.792212i | \(-0.291071\pi\) |
−0.564862 | + | 0.825186i | \(0.691071\pi\) | |||||||
\(578\) | 35.8454 | + | 26.0432i | 1.49097 | + | 1.08325i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.0902 | − | 37.2097i | −0.502017 | − | 1.54505i | ||||
\(581\) | −28.3839 | + | 20.6221i | −1.17756 | + | 0.855550i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.94427 | + | 4.63677i | −0.163355 | + | 0.192035i | ||||
\(584\) | −3.28332 | −0.135865 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.31966 | − | 10.2169i | −0.137134 | − | 0.422055i | ||||
\(587\) | −11.3490 | + | 34.9286i | −0.468423 | + | 1.44166i | 0.386203 | + | 0.922414i | \(0.373786\pi\) |
−0.854626 | + | 0.519244i | \(0.826214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.89919 | − | 6.46564i | −0.366685 | − | 0.266412i | ||||
\(590\) | −10.6479 | + | 32.7709i | −0.438368 | + | 1.34916i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.39919 | − | 2.46965i | 0.139706 | − | 0.101502i | ||||
\(593\) | −27.3094 | −1.12146 | −0.560732 | − | 0.827997i | \(-0.689480\pi\) | ||||
−0.560732 | + | 0.827997i | \(0.689480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.8328 | −2.28892 | ||||||||
\(596\) | −9.76721 | + | 7.09629i | −0.400081 | + | 0.290676i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.624612 | − | 1.92236i | 0.0255423 | − | 0.0786110i | ||||
\(599\) | 13.9084 | + | 10.1050i | 0.568281 | + | 0.412880i | 0.834480 | − | 0.551038i | \(-0.185768\pi\) |
−0.266200 | + | 0.963918i | \(0.585768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.89261 | + | 8.90254i | −0.117992 | + | 0.363142i | −0.992559 | − | 0.121762i | \(-0.961146\pi\) |
0.874567 | + | 0.484904i | \(0.161146\pi\) | |||||||
\(602\) | 7.61825 | + | 23.4466i | 0.310497 | + | 0.955611i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.6525 | −1.40999 | ||||||||
\(605\) | −23.3621 | − | 3.60510i | −0.949802 | − | 0.146568i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1525 | − | 16.8213i | 0.939730 | − | 0.682754i | −0.00862566 | − | 0.999963i | \(-0.502746\pi\) |
0.948356 | + | 0.317209i | \(0.102746\pi\) | |||||||
\(608\) | −5.72294 | − | 17.6134i | −0.232096 | − | 0.714318i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −42.3156 | − | 30.7441i | −1.71331 | − | 1.24479i | ||||
\(611\) | 0.664066 | + | 0.482472i | 0.0268652 | + | 0.0195187i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.74265 | + | 23.8294i | 0.312723 | + | 0.962461i | 0.976682 | + | 0.214692i | \(0.0688748\pi\) |
−0.663959 | + | 0.747769i | \(0.731125\pi\) | |||||||
\(614\) | 30.0256 | − | 21.8149i | 1.21173 | − | 0.880376i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.1353 | − | 4.39201i | 0.730690 | − | 0.176959i | ||||
\(617\) | −16.8782 | −0.679489 | −0.339745 | − | 0.940518i | \(-0.610341\pi\) | ||||
−0.339745 | + | 0.940518i | \(0.610341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.12868 | + | 6.55139i | 0.0855588 | + | 0.263323i | 0.984678 | − | 0.174380i | \(-0.0557922\pi\) |
−0.899120 | + | 0.437703i | \(0.855792\pi\) | |||||||
\(620\) | −8.02866 | + | 24.7097i | −0.322439 | + | 0.992365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 49.9959 | + | 36.3242i | 2.00465 | + | 1.45647i | ||||
\(623\) | 11.6625 | − | 35.8936i | 0.467249 | − | 1.43804i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5623 | − | 13.4863i | 0.742492 | − | 0.539452i | ||||
\(626\) | −68.0199 | −2.71862 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −54.0689 | −2.15758 | ||||||||
\(629\) | −8.75261 | + | 6.35914i | −0.348989 | + | 0.253556i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.37132 | + | 16.5312i | −0.213829 | + | 0.658098i | 0.785406 | + | 0.618981i | \(0.212454\pi\) |
−0.999235 | + | 0.0391166i | \(0.987546\pi\) | |||||||
\(632\) | −10.1776 | − | 7.39448i | −0.404844 | − | 0.294137i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.208204 | + | 0.640786i | −0.00826883 | + | 0.0254489i | ||||
\(635\) | −1.83543 | − | 5.64888i | −0.0728369 | − | 0.224169i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.58359 | 0.102366 | ||||||||
\(638\) | 25.9813 | + | 42.2092i | 1.02861 | + | 1.67108i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.5902 | + | 12.7800i | −0.695313 | + | 0.505174i | ||||
\(641\) | 6.60365 | + | 20.3239i | 0.260828 | + | 0.802747i | 0.992625 | + | 0.121224i | \(0.0386820\pi\) |
−0.731797 | + | 0.681523i | \(0.761318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.2984 | + | 24.1927i | 1.31316 | + | 0.954066i | 0.999990 | + | 0.00436901i | \(0.00139070\pi\) |
0.313169 | + | 0.949697i | \(0.398609\pi\) | |||||||
\(644\) | −35.7485 | − | 25.9728i | −1.40869 | − | 1.02347i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.70163 | + | 29.8585i | 0.381705 | + | 1.17477i | ||||
\(647\) | −9.45368 | + | 6.86850i | −0.371663 | + | 0.270029i | −0.757900 | − | 0.652371i | \(-0.773775\pi\) |
0.386237 | + | 0.922399i | \(0.373775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.89261 | − | 24.6745i | 0.0742914 | − | 0.968558i | ||||
\(650\) | 0.193772 | 0.00760035 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.11803 | + | 3.44095i | 0.0437856 | + | 0.134758i | ||||
\(653\) | 10.5652 | − | 32.5162i | 0.413447 | − | 1.27246i | −0.500186 | − | 0.865918i | \(-0.666735\pi\) |
0.913633 | − | 0.406541i | \(-0.133265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28115 | + | 3.11044i | 0.167278 | + | 0.121535i | ||||
\(656\) | −2.18597 | + | 6.72772i | −0.0853477 | + | 0.262673i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.6074 | − | 18.6049i | 0.998280 | − | 0.725293i | ||||
\(659\) | 33.7563 | 1.31496 | 0.657480 | − | 0.753472i | \(-0.271623\pi\) | ||||
0.657480 | + | 0.753472i | \(0.271623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.43769 | 0.0948153 | 0.0474077 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474077 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(662\) | 12.6771 | − | 9.21047i | 0.492710 | − | 0.357975i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.39919 | − | 10.4616i | 0.131914 | − | 0.405990i | ||||
\(665\) | −17.5422 | − | 12.7452i | −0.680258 | − | 0.494237i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.56231 | − | 26.3521i | 0.331534 | − | 1.02036i | ||||
\(668\) | 8.69273 | + | 26.7535i | 0.336332 | + | 1.03512i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.1803 | 0.509201 | ||||||||
\(671\) | 34.7339 | + | 14.3065i | 1.34089 | + | 0.552296i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7533 | + | 10.7189i | −0.568697 | + | 0.413183i | −0.834632 | − | 0.550808i | \(-0.814320\pi\) |
0.265934 | + | 0.963991i | \(0.414320\pi\) | |||||||
\(674\) | 17.6990 | + | 54.4719i | 0.681740 | + | 2.09818i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.4164 | + | 19.9192i | 1.05448 | + | 0.766123i | ||||
\(677\) | −6.95418 | − | 5.05251i | −0.267271 | − | 0.194184i | 0.446075 | − | 0.894995i | \(-0.352821\pi\) |
−0.713346 | + | 0.700812i | \(0.752821\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.4443 | − | 47.5326i | −0.592697 | − | 1.82413i | ||||
\(680\) | 14.1620 | − | 10.2893i | 0.543089 | − | 0.394577i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.51722 | − | 32.8177i | 0.0963894 | − | 1.25665i | ||||
\(683\) | 0.940588 | 0.0359906 | 0.0179953 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179953 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.208204 | − | 0.640786i | −0.00795506 | − | 0.0244832i | ||||
\(686\) | 11.0953 | − | 34.1480i | 0.423622 | − | 1.30377i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.21885 | + | 3.79171i | 0.198967 | + | 0.144558i | ||||
\(689\) | 0.133893 | − | 0.412080i | 0.00510092 | − | 0.0156990i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.1803 | + | 19.0211i | −0.995947 | + | 0.723598i | −0.961215 | − | 0.275799i | \(-0.911058\pi\) |
−0.0347317 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(692\) | 35.0845 | 1.33371 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 54.0689 | 2.05243 | ||||||||
\(695\) | 19.7881 | − | 14.3769i | 0.750604 | − | 0.545346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.62868 | − | 17.3233i | 0.213201 | − | 0.656166i | ||||
\(698\) | 15.9604 | + | 11.5959i | 0.604112 | + | 0.438913i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.30902 | − | 4.02874i | 0.0494762 | − | 0.152272i | ||||
\(701\) | −7.23071 | − | 22.2538i | −0.273100 | − | 0.840515i | −0.989716 | − | 0.143047i | \(-0.954310\pi\) |
0.716616 | − | 0.697468i | \(-0.245690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.20163 | −0.158467 | ||||||||
\(704\) | 25.6678 | − | 30.1743i | 0.967391 | − | 1.13724i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 58.6869 | − | 42.6385i | 2.20871 | − | 1.60472i | ||||
\(707\) | −0.410415 | − | 1.26313i | −0.0154352 | − | 0.0475048i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2984 | + | 8.93529i | 0.461875 | + | 0.335572i | 0.794266 | − | 0.607570i | \(-0.207855\pi\) |
−0.332391 | + | 0.943142i | \(0.607855\pi\) | |||||||
\(710\) | −40.1433 | − | 29.1658i | −1.50655 | − | 1.09457i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.65654 | + | 11.2537i | 0.137035 | + | 0.421749i | ||||
\(713\) | −14.8860 | + | 10.8153i | −0.557484 | + | 0.405036i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63525 | − | 0.396027i | 0.0611551 | − | 0.0148106i | ||||
\(716\) | −5.11875 | −0.191297 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.34752 | + | 4.14725i | 0.0502892 | + | 0.154774i | ||||
\(719\) | 4.00726 | − | 12.3331i | 0.149446 | − | 0.459947i | −0.848110 | − | 0.529820i | \(-0.822259\pi\) |
0.997556 | + | 0.0698732i | \(0.0222595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.5066 | − | 27.2501i | −1.39682 | − | 1.01485i | ||||
\(722\) | 8.84950 | − | 27.2359i | 0.329344 | − | 1.01362i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.9164 | + | 18.8294i | −0.963176 | + | 0.699788i | ||||
\(725\) | 2.65626 | 0.0986511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5623 | 0.725526 | 0.362763 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362763 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(728\) | −1.07448 | + | 0.780656i | −0.0398229 | + | 0.0289330i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.52786 | + | 10.8576i | −0.130572 | + | 0.401860i | ||||
\(731\) | −13.4381 | − | 9.76333i | −0.497025 | − | 0.361110i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.52786 | + | 13.9353i | −0.167240 | + | 0.514713i | −0.999194 | − | 0.0401315i | \(-0.987222\pi\) |
0.831954 | + | 0.554845i | \(0.187222\pi\) | |||||||
\(734\) | −15.2964 | − | 47.0774i | −0.564600 | − | 1.73766i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.9787 | −1.14189 | ||||||||
\(737\) | −9.20003 | + | 2.22807i | −0.338888 | + | 0.0820721i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.7533 | + | 10.7189i | −0.542709 | + | 0.394301i | −0.825090 | − | 0.565001i | \(-0.808876\pi\) |
0.282381 | + | 0.959302i | \(0.408876\pi\) | |||||||
\(740\) | 3.06668 | + | 9.43826i | 0.112733 | + | 0.346957i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.5172 | − | 9.82084i | −0.496233 | − | 0.360534i | ||||
\(743\) | 14.6693 | + | 10.6579i | 0.538165 | + | 0.391000i | 0.823403 | − | 0.567457i | \(-0.192073\pi\) |
−0.285238 | + | 0.958457i | \(0.592073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.06231 | + | 9.42481i | 0.112194 | + | 0.345298i | ||||
\(746\) | −25.0636 | + | 18.2098i | −0.917643 | + | 0.666707i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −34.5066 | + | 40.5649i | −1.26169 | + | 1.48320i | ||||
\(749\) | −46.3366 | −1.69310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.465558 | − | 1.43284i | −0.0169885 | − | 0.0522851i | 0.942203 | − | 0.335043i | \(-0.108751\pi\) |
−0.959191 | + | 0.282758i | \(0.908751\pi\) | |||||||
\(752\) | 2.55938 | − | 7.87695i | 0.0933308 | − | 0.287243i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.85410 | − | 2.07363i | −0.103940 | − | 0.0755170i | ||||
\(755\) | −8.78962 | + | 27.0517i | −0.319887 | + | 0.984511i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0795 | − | 24.0337i | 1.20230 | − | 0.873519i | 0.207787 | − | 0.978174i | \(-0.433374\pi\) |
0.994509 | + | 0.104655i | \(0.0333738\pi\) | |||||||
\(758\) | −13.4011 | −0.486749 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.79837 | 0.246603 | ||||||||
\(761\) | 27.0558 | − | 19.6572i | 0.980771 | − | 0.712572i | 0.0228906 | − | 0.999738i | \(-0.492713\pi\) |
0.957881 | + | 0.287166i | \(0.0927131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9443 | − | 55.2268i | 0.649626 | − | 1.99934i | ||||
\(764\) | −21.0193 | − | 15.2714i | −0.760452 | − | 0.552501i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.6246 | + | 69.6314i | −0.817460 | + | 2.51588i | ||||
\(767\) | 0.544308 | + | 1.67521i | 0.0196538 | + | 0.0604882i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.2705 | −0.803095 | −0.401548 | − | 0.915838i | \(-0.631528\pi\) | ||||
−0.401548 | + | 0.915838i | \(0.631528\pi\) | |||||||
\(770\) | 4.96199 | − | 64.6908i | 0.178818 | − | 2.33129i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.6353 | + | 11.3597i | −0.562725 | + | 0.408844i | ||||
\(773\) | 10.4084 | + | 32.0338i | 0.374364 | + | 1.15217i | 0.943907 | + | 0.330213i | \(0.107121\pi\) |
−0.569542 | + | 0.821962i | \(0.692879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.42705 | − | 1.03681i | −0.0512612 | − | 0.0372434i | ||||
\(776\) | 12.6771 | + | 9.21047i | 0.455082 | + | 0.330637i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.8156 | + | 45.5977i | 0.531165 | + | 1.63476i | ||||
\(779\) | 5.72294 | − | 4.15796i | 0.205046 | − | 0.148974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.9508 | + | 13.5721i | 1.17907 | + | 0.485647i | ||||
\(782\) | 52.5157 | 1.87796 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.05573 | − | 24.7930i | −0.287705 | − | 0.885464i | ||||
\(785\) | −13.7146 | + | 42.2092i | −0.489495 | + | 1.50651i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.4721 | − | 16.3270i | −0.801045 | − | 0.581993i | 0.110175 | − | 0.993912i | \(-0.464859\pi\) |
−0.911221 | + | 0.411919i | \(0.864859\pi\) | |||||||
\(788\) | 1.99220 | − | 6.13135i | 0.0709691 | − | 0.218420i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −35.3885 | + | 25.7113i | −1.25907 | + | 0.914766i | ||||
\(791\) | 75.7950 | 2.69496 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67376 | −0.0949481 | ||||||||
\(794\) | 42.4491 | − | 30.8410i | 1.50646 | − | 1.09451i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.336881 | − | 1.03681i | 0.0119404 | − | 0.0367489i | ||||
\(797\) | 3.47709 | + | 2.52626i | 0.123165 | + | 0.0894846i | 0.647662 | − | 0.761927i | \(-0.275747\pi\) |
−0.524497 | + | 0.851412i | \(0.675747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.59017 | + | 20.2825i | −0.233143 | + | 0.717542i | ||||
\(800\) | −0.917716 | − | 2.82444i | −0.0324462 | − | 0.0998590i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −40.8885 | −1.44382 | ||||||||
\(803\) | 0.627058 | − | 8.17513i | 0.0221284 | − | 0.288494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.3435 | + | 21.3193i | −1.03422 | + | 0.751406i | ||||
\(806\) | 0.723944 | + | 2.22807i | 0.0254998 | + | 0.0784805i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.336881 | + | 0.244758i | 0.0118514 | + | 0.00861057i | ||||
\(809\) | −5.72294 | − | 4.15796i | −0.201208 | − | 0.146186i | 0.482619 | − | 0.875830i | \(-0.339686\pi\) |
−0.683827 | + | 0.729644i | \(0.739686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6631 | − | 42.0508i | −0.479777 | − | 1.47660i | −0.839405 | − | 0.543506i | \(-0.817096\pi\) |
0.359628 | − | 0.933096i | \(-0.382904\pi\) | |||||||
\(812\) | −62.3939 | + | 45.3318i | −2.18960 | + | 1.59083i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.59017 | − | 10.7064i | −0.230985 | − | 0.375258i | ||||
\(815\) | 2.96979 | 0.104027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.99342 | − | 6.13512i | −0.0697410 | − | 0.214641i | ||||
\(818\) | 3.35733 | − | 10.3328i | 0.117386 | − | 0.361278i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.5172 | − | 9.82084i | −0.472042 | − | 0.342958i | ||||
\(821\) | −12.2896 | + | 37.8234i | −0.428909 | + | 1.32005i | 0.470292 | + | 0.882511i | \(0.344149\pi\) |
−0.899201 | + | 0.437536i | \(0.855851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.4615 | + | 11.2334i | −0.538954 | + | 0.391573i | −0.823696 | − | 0.567031i | \(-0.808092\pi\) |
0.284743 | + | 0.958604i | \(0.408092\pi\) | |||||||
\(824\) | 14.5354 | 0.506366 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 67.9230 | 2.36334 | ||||||||
\(827\) | 9.41667 | − | 6.84161i | 0.327450 | − | 0.237906i | −0.411898 | − | 0.911230i | \(-0.635134\pi\) |
0.739348 | + | 0.673324i | \(0.235134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.19098 | − | 19.0539i | 0.215022 | − | 0.661769i | −0.784130 | − | 0.620596i | \(-0.786891\pi\) |
0.999152 | − | 0.0411726i | \(-0.0131094\pi\) | |||||||
\(830\) | −30.9433 | − | 22.4816i | −1.07406 | − | 0.780348i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.871323 | + | 2.68166i | −0.0302077 | + | 0.0929697i | ||||
\(833\) | 20.7428 | + | 63.8398i | 0.718695 | + | 2.21192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.0902 | 0.799068 | ||||||||
\(836\) | −20.1016 | + | 4.86822i | −0.695228 | + | 0.168371i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.3328 | − | 44.5609i | 2.11871 | − | 1.53933i | ||||
\(839\) | 4.32079 | + | 13.2980i | 0.149170 | + | 0.459099i | 0.997524 | − | 0.0703313i | \(-0.0224056\pi\) |
−0.848353 | + | 0.529430i | \(0.822406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6631 | − | 11.3799i | −0.540108 | − | 0.392411i | ||||
\(842\) | −50.7912 | − | 36.9020i | −1.75038 | − | 1.27173i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.5902 | − | 44.9039i | −0.502214 | − | 1.54566i | ||||
\(845\) | 22.5042 | − | 16.3503i | 0.774168 | − | 0.562466i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.47214 | + | 45.9937i | 0.256746 | + | 1.58036i | ||||
\(848\) | −4.37194 | −0.150133 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.55573 | + | 4.78804i | 0.0533610 | + | 0.164228i | ||||
\(851\) | −2.17183 | + | 6.68421i | −0.0744495 | + | 0.229132i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.954915 | + | 0.693786i | 0.0326957 | + | 0.0237548i | 0.604013 | − | 0.796974i | \(-0.293567\pi\) |
−0.571317 | + | 0.820729i | \(0.693567\pi\) | |||||||
\(854\) | −31.8610 | + | 98.0581i | −1.09026 | + | 3.35548i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.7533 | − | 8.53926i | 0.401719 | − | 0.291866i | ||||
\(857\) | −13.8344 | −0.472573 | −0.236286 | − | 0.971683i | \(-0.575930\pi\) | ||||
−0.236286 | + | 0.971683i | \(0.575930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4164 | 1.44723 | 0.723615 | − | 0.690204i | \(-0.242479\pi\) | ||||
0.723615 | + | 0.690204i | \(0.242479\pi\) | |||||||
\(860\) | −12.3266 | + | 8.95579i | −0.420333 | + | 0.305390i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.6353 | + | 72.7418i | −0.805020 | + | 2.47760i | ||||
\(863\) | −27.8167 | − | 20.2100i | −0.946893 | − | 0.687958i | 0.00317717 | − | 0.999995i | \(-0.498989\pi\) |
−0.950070 | + | 0.312037i | \(0.898989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.89919 | − | 27.3889i | 0.302581 | − | 0.931250i | ||||
\(866\) | 1.76142 | + | 5.42109i | 0.0598554 | + | 0.184216i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 51.2148 | 1.73834 | ||||||||
\(869\) | 20.3553 | − | 23.9290i | 0.690505 | − | 0.811737i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.545085 | − | 0.396027i | 0.0184695 | − | 0.0134189i | ||||
\(872\) | 5.62605 | + | 17.3152i | 0.190522 | + | 0.586367i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.5000 | + | 11.9880i | 0.558121 | + | 0.405499i | ||||
\(875\) | −39.6360 | − | 28.7973i | −1.33994 | − | 0.973525i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.54508 | + | 10.9106i | 0.119709 | + | 0.368426i | 0.992900 | − | 0.118952i | \(-0.0379533\pi\) |
−0.873191 | + | 0.487378i | \(0.837953\pi\) | |||||||
\(878\) | −43.4637 | + | 31.5782i | −1.46683 | + | 1.06571i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.89919 | − | 14.4576i | −0.299992 | − | 0.487366i | ||||
\(881\) | −34.3376 | −1.15686 | −0.578432 | − | 0.815730i | \(-0.696335\pi\) | ||||
−0.578432 | + | 0.815730i | \(0.696335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.36068 | − | 13.4208i | −0.146749 | − | 0.451646i | 0.850483 | − | 0.526002i | \(-0.176310\pi\) |
−0.997232 | + | 0.0743567i | \(0.976310\pi\) | |||||||
\(884\) | 1.17137 | − | 3.60510i | 0.0393973 | − | 0.121252i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.0344 | − | 27.6336i | −1.27779 | − | 0.928370i | ||||
\(887\) | 17.4823 | − | 53.8051i | 0.587000 | − | 1.80660i | −0.00408722 | − | 0.999992i | \(-0.501301\pi\) |
0.591087 | − | 0.806608i | \(-0.298699\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.47214 | + | 6.88191i | −0.317685 | + | 0.230812i | ||||
\(890\) | 41.1438 | 1.37914 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.32624 | 0.278783 | ||||||||
\(893\) | −6.70053 | + | 4.86822i | −0.224225 | + | 0.162909i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.29837 | + | 3.99598i | −0.0433999 | + | 0.133571i | ||||
\(896\) | 34.6740 | + | 25.1922i | 1.15838 | + | 0.841611i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5623 | − | 60.2066i | 0.652803 | − | 2.00912i | ||||
\(899\) | 9.92398 | + | 30.5429i | 0.330983 | + | 1.01866i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2574 | 0.375037 | ||||||||
\(902\) | 19.5714 | + | 8.06124i | 0.651657 | + | 0.268410i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.2254 | + | 13.9681i | −0.639428 | + | 0.464572i | ||||
\(905\) | 8.12555 | + | 25.0079i | 0.270102 | + | 0.831290i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0172 | + | 21.0822i | 0.963501 | + | 0.700024i | 0.953961 | − | 0.299930i | \(-0.0969633\pi\) |
0.00953981 | + | 0.999954i | \(0.496963\pi\) | |||||||
\(908\) | 23.1683 | + | 16.8327i | 0.768866 | + | 0.558614i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.42705 | + | 4.39201i | 0.0473063 | + | 0.145594i | ||||
\(911\) | 7.71514 | − | 5.60537i | 0.255614 | − | 0.185714i | −0.452597 | − | 0.891715i | \(-0.649502\pi\) |
0.708211 | + | 0.706001i | \(0.249502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.3992 | + | 10.4616i | 0.840590 | + | 0.346229i | ||||
\(914\) | −75.4074 | −2.49426 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.9443 | − | 45.9937i | −0.493773 | − | 1.51968i | ||||
\(917\) | 3.22344 | − | 9.92073i | 0.106447 | − | 0.327611i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.3713 | + | 14.8006i | 0.671988 | + | 0.488228i | 0.870690 | − | 0.491832i | \(-0.163673\pi\) |
−0.198702 | + | 0.980060i | \(0.563673\pi\) | |||||||
\(920\) | 3.51410 | − | 10.8153i | 0.115856 | − | 0.356569i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.64590 | + | 1.92236i | −0.0871380 | + | 0.0633095i | ||||
\(923\) | −2.53650 | −0.0834901 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.673762 | −0.0221532 | ||||||||
\(926\) | −37.4871 | + | 27.2359i | −1.23190 | + | 0.895029i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.7082 | + | 51.4226i | −0.548474 | + | 1.68803i | ||||
\(929\) | 34.0100 | + | 24.7097i | 1.11583 | + | 0.810699i | 0.983572 | − | 0.180517i | \(-0.0577769\pi\) |
0.132259 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.05573 | + | 24.7930i | −0.264016 | + | 0.812557i | ||||
\(932\) | −18.6167 | − | 57.2963i | −0.609810 | − | 1.87680i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.5066 | 1.48902 | ||||||||
\(935\) | 22.9146 | + | 37.2271i | 0.749388 | + | 1.21746i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.75329 | + | 6.35964i | −0.285957 | + | 0.207760i | −0.721512 | − | 0.692402i | \(-0.756552\pi\) |
0.435554 | + | 0.900162i | \(0.356552\pi\) | |||||||
\(938\) | −8.02866 | − | 24.7097i | −0.262145 | − | 0.806800i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.8262 | + | 11.4984i | 0.516195 | + | 0.375038i | ||||
\(941\) | −7.42448 | − | 5.39420i | −0.242031 | − | 0.175846i | 0.460157 | − | 0.887838i | \(-0.347793\pi\) |
−0.702188 | + | 0.711992i | \(0.747793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.65654 | − | 11.2537i | −0.119073 | − | 0.366470i | ||||
\(944\) | 14.3787 | − | 10.4467i | 0.467986 | − | 0.340011i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.5066 | − | 14.7024i | 0.406624 | − | 0.478015i | ||||
\(947\) | 22.3845 | 0.727397 | 0.363699 | − | 0.931517i | \(-0.381514\pi\) | ||||
0.363699 | + | 0.931517i | \(0.381514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.180340 | + | 0.555029i | 0.00585408 | + | 0.0180170i | ||||
\(950\) | −0.604187 | + | 1.85950i | −0.0196024 | + | 0.0603300i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.9164 | − | 20.2825i | −0.904776 | − | 0.657358i | ||||
\(953\) | −5.19277 | + | 15.9817i | −0.168210 | + | 0.517698i | −0.999259 | − | 0.0385025i | \(-0.987741\pi\) |
0.831048 | + | 0.556200i | \(0.187741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.2533 | + | 12.5352i | −0.558303 | + | 0.405631i | ||||
\(956\) | −29.9657 | −0.969160 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −79.1803 | −2.55820 | ||||||||
\(959\) | −1.07448 | + | 0.780656i | −0.0346968 | + | 0.0252087i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.98936 | + | 9.20029i | −0.0964309 | + | 0.296784i | ||||
\(962\) | 0.723944 | + | 0.525976i | 0.0233409 | + | 0.0169582i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.3262 | − | 34.8586i | 0.364794 | − | 1.12272i | ||||
\(965\) | 4.90211 | + | 15.0871i | 0.157804 | + | 0.485672i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.6869 | −0.568773 | −0.284386 | − | 0.958710i | \(-0.591790\pi\) | ||||
−0.284386 | + | 0.958710i | \(0.591790\pi\) | |||||||
\(968\) | −10.3714 | − | 10.2893i | −0.333349 | − | 0.330711i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44.0795 | − | 32.0257i | 1.41531 | − | 1.02828i | ||||
\(971\) | −0.313529 | − | 0.964944i | −0.0100616 | − | 0.0309665i | 0.945900 | − | 0.324459i | \(-0.105182\pi\) |
−0.955961 | + | 0.293493i | \(0.905182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.0066 | − | 28.3399i | −1.25049 | − | 0.908537i | ||||
\(974\) | 32.8386 | + | 23.8586i | 1.05222 | + | 0.764480i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.33688 | + | 25.6583i | 0.266857 | + | 0.821302i | ||||
\(977\) | −2.71614 | + | 1.97339i | −0.0868970 | + | 0.0631344i | −0.630385 | − | 0.776282i | \(-0.717103\pi\) |
0.543488 | + | 0.839417i | \(0.317103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.7188 | + | 6.95515i | −0.917858 | + | 0.222288i | ||||
\(980\) | 61.5731 | 1.96688 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8926 | − | 39.6794i | −0.411420 | − | 1.26622i | ||||
\(983\) | 15.6698 | − | 48.2266i | 0.499789 | − | 1.53819i | −0.309570 | − | 0.950877i | \(-0.600185\pi\) |
0.809359 | − | 0.587314i | \(-0.199815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.28115 | − | 3.11044i | −0.136409 | − | 0.0991068i | ||||
\(986\) | 28.3240 | − | 87.1724i | 0.902021 | − | 2.77614i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.19098 | − | 0.865300i | 0.0378902 | − | 0.0275289i | ||||
\(989\) | −10.7905 | −0.343119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.2705 | −1.85102 | −0.925512 | − | 0.378719i | \(-0.876365\pi\) | ||||
−0.925512 | + | 0.378719i | \(0.876365\pi\) | |||||||
\(992\) | 29.0480 | − | 21.1046i | 0.922274 | − | 0.670072i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.2254 | + | 93.0243i | −0.958692 | + | 2.95055i | ||||
\(995\) | −0.723944 | − | 0.525976i | −0.0229506 | − | 0.0166746i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.9721 | − | 36.8464i | 0.379161 | − | 1.16694i | −0.561467 | − | 0.827499i | \(-0.689763\pi\) |
0.940628 | − | 0.339439i | \(-0.110237\pi\) | |||||||
\(998\) | −21.7433 | − | 66.9189i | −0.688271 | − | 2.11828i | ||||
\(999\) | 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 | 99.2.f.c.91.2 | yes | 8 | |
3.2 | odd | 2 | inner | 99.2.f.c.91.1 | yes | 8 | |
9.2 | odd | 6 | 891.2.n.e.190.2 | 16 | |||
9.4 | even | 3 | 891.2.n.e.784.2 | 16 | |||
9.5 | odd | 6 | 891.2.n.e.784.1 | 16 | |||
9.7 | even | 3 | 891.2.n.e.190.1 | 16 | |||
11.2 | odd | 10 | 1089.2.a.w.1.4 | 4 | |||
11.4 | even | 5 | inner | 99.2.f.c.37.2 | yes | 8 | |
11.9 | even | 5 | 1089.2.a.v.1.1 | 4 | |||
33.2 | even | 10 | 1089.2.a.w.1.1 | 4 | |||
33.20 | odd | 10 | 1089.2.a.v.1.4 | 4 | |||
33.26 | odd | 10 | inner | 99.2.f.c.37.1 | ✓ | 8 | |
99.4 | even | 15 | 891.2.n.e.136.1 | 16 | |||
99.59 | odd | 30 | 891.2.n.e.136.2 | 16 | |||
99.70 | even | 15 | 891.2.n.e.433.2 | 16 | |||
99.92 | odd | 30 | 891.2.n.e.433.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.f.c.37.1 | ✓ | 8 | 33.26 | odd | 10 | inner | |
99.2.f.c.37.2 | yes | 8 | 11.4 | even | 5 | inner | |
99.2.f.c.91.1 | yes | 8 | 3.2 | odd | 2 | inner | |
99.2.f.c.91.2 | yes | 8 | 1.1 | even | 1 | trivial | |
891.2.n.e.136.1 | 16 | 99.4 | even | 15 | |||
891.2.n.e.136.2 | 16 | 99.59 | odd | 30 | |||
891.2.n.e.190.1 | 16 | 9.7 | even | 3 | |||
891.2.n.e.190.2 | 16 | 9.2 | odd | 6 | |||
891.2.n.e.433.1 | 16 | 99.92 | odd | 30 | |||
891.2.n.e.433.2 | 16 | 99.70 | even | 15 | |||
891.2.n.e.784.1 | 16 | 9.5 | odd | 6 | |||
891.2.n.e.784.2 | 16 | 9.4 | even | 3 | |||
1089.2.a.v.1.1 | 4 | 11.9 | even | 5 | |||
1089.2.a.v.1.4 | 4 | 33.20 | odd | 10 | |||
1089.2.a.w.1.1 | 4 | 33.2 | even | 10 | |||
1089.2.a.w.1.4 | 4 | 11.2 | odd | 10 |