Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(109,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 + 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.109 |
Dual form | 189.2.e.f.163.1 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.730252 | − | 1.26483i | −0.516366 | − | 0.894373i | −0.999819 | − | 0.0190026i | \(-0.993951\pi\) |
0.483453 | − | 0.875370i | \(-0.339382\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0665372 | + | 0.115246i | −0.0332686 | + | 0.0576229i | ||||
\(5\) | −0.296790 | − | 0.514055i | −0.132728 | − | 0.229892i | 0.791999 | − | 0.610522i | \(-0.209040\pi\) |
−0.924727 | + | 0.380630i | \(0.875707\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32383 | − | 1.26483i | 0.878326 | − | 0.478062i | ||||
\(8\) | −2.72665 | −0.964018 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.433463 | + | 0.750780i | −0.137073 | + | 0.237417i | ||||
\(11\) | 2.23025 | − | 3.86291i | 0.672446 | − | 1.16471i | −0.304762 | − | 0.952429i | \(-0.598577\pi\) |
0.977208 | − | 0.212283i | \(-0.0680898\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.51459 | −1.25212 | −0.626061 | − | 0.779774i | \(-0.715334\pi\) | ||||
−0.626061 | + | 0.779774i | \(0.715334\pi\) | |||||||
\(14\) | −3.29679 | − | 2.01561i | −0.881104 | − | 0.538695i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.12422 | + | 3.67926i | 0.531055 | + | 0.919814i | ||||
\(17\) | −0.136673 | + | 0.236725i | −0.0331481 | + | 0.0574142i | −0.882124 | − | 0.471018i | \(-0.843887\pi\) |
0.848975 | + | 0.528432i | \(0.177220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.43346 | − | 2.48283i | −0.328859 | − | 0.569600i | 0.653427 | − | 0.756990i | \(-0.273331\pi\) |
−0.982286 | + | 0.187389i | \(0.939997\pi\) | |||||||
\(20\) | 0.0789903 | 0.0176628 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.51459 | −1.38892 | ||||||||
\(23\) | 2.52704 | + | 4.37697i | 0.526925 | + | 0.912660i | 0.999508 | + | 0.0313742i | \(0.00998836\pi\) |
−0.472583 | + | 0.881286i | \(0.656678\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32383 | − | 4.02499i | 0.464766 | − | 0.804999i | ||||
\(26\) | 3.29679 | + | 5.71021i | 0.646554 | + | 1.11986i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.00885441 | + | 0.351971i | −0.00167333 | + | 0.0665162i | ||||
\(29\) | −0.352336 | −0.0654272 | −0.0327136 | − | 0.999465i | \(-0.510415\pi\) | ||||
−0.0327136 | + | 0.999465i | \(0.510415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.25729 | + | 2.17770i | −0.225817 | + | 0.391126i | −0.956564 | − | 0.291522i | \(-0.905838\pi\) |
0.730747 | + | 0.682648i | \(0.239172\pi\) | |||||||
\(32\) | 0.375780 | − | 0.650870i | 0.0664291 | − | 0.115059i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.399223 | 0.0684663 | ||||||||
\(35\) | −1.33988 | − | 0.819187i | −0.226482 | − | 0.138468i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.32383 | + | 5.75705i | 0.546435 | + | 0.946452i | 0.998515 | + | 0.0544753i | \(0.0173486\pi\) |
−0.452081 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(38\) | −2.09358 | + | 3.62619i | −0.339623 | + | 0.588245i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.809243 | + | 1.40165i | 0.127953 | + | 0.221620i | ||||
\(41\) | 10.8961 | 1.70169 | 0.850843 | − | 0.525420i | \(-0.176092\pi\) | ||||
0.850843 | + | 0.525420i | \(0.176092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.38151 | 0.515676 | 0.257838 | − | 0.966188i | \(-0.416990\pi\) | ||||
0.257838 | + | 0.966188i | \(0.416990\pi\) | |||||||
\(44\) | 0.296790 | + | 0.514055i | 0.0447427 | + | 0.0774967i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.69076 | − | 6.39258i | 0.544172 | − | 0.942534i | ||||
\(47\) | 6.21780 | + | 10.7695i | 0.906959 | + | 1.57090i | 0.818265 | + | 0.574841i | \(0.194936\pi\) |
0.0886938 | + | 0.996059i | \(0.471731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.80039 | − | 5.87852i | 0.542913 | − | 0.839789i | ||||
\(50\) | −6.78794 | −0.959959 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.300388 | − | 0.520288i | 0.0416564 | − | 0.0721509i | ||||
\(53\) | 5.66372 | − | 9.80984i | 0.777971 | − | 1.34749i | −0.155138 | − | 0.987893i | \(-0.549582\pi\) |
0.933109 | − | 0.359593i | \(-0.117084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.64766 | −0.357011 | ||||||||
\(56\) | −6.33628 | + | 3.44877i | −0.846722 | + | 0.460861i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.257295 | + | 0.445647i | 0.0337844 | + | 0.0585163i | ||||
\(59\) | −4.02704 | + | 6.97504i | −0.524276 | + | 0.908073i | 0.475324 | + | 0.879811i | \(0.342331\pi\) |
−0.999601 | + | 0.0282624i | \(0.991003\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.36693 | + | 2.36758i | 0.175017 | + | 0.303138i | 0.940167 | − | 0.340714i | \(-0.110669\pi\) |
−0.765150 | + | 0.643852i | \(0.777335\pi\) | |||||||
\(62\) | 3.67257 | 0.466417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.39922 | 0.924903 | ||||||||
\(65\) | 1.33988 | + | 2.32075i | 0.166192 | + | 0.287853i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.93346 | + | 5.08091i | −0.358380 | + | 0.620732i | −0.987690 | − | 0.156422i | \(-0.950004\pi\) |
0.629311 | + | 0.777154i | \(0.283337\pi\) | |||||||
\(68\) | −0.0181877 | − | 0.0315020i | −0.00220558 | − | 0.00382018i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0576828 | + | 2.29294i | −0.00689442 | + | 0.274059i | ||||
\(71\) | −2.60078 | −0.308655 | −0.154328 | − | 0.988020i | \(-0.549321\pi\) | ||||
−0.154328 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55768 | + | 9.62619i | −0.650478 | + | 1.12666i | 0.332530 | + | 0.943093i | \(0.392098\pi\) |
−0.983007 | + | 0.183567i | \(0.941235\pi\) | |||||||
\(74\) | 4.85447 | − | 8.40819i | 0.564321 | − | 0.977433i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.381515 | 0.0437627 | ||||||||
\(77\) | 0.296790 | − | 11.7977i | 0.0338223 | − | 1.34447i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.58113 | − | 9.66679i | −0.627926 | − | 1.08760i | −0.987967 | − | 0.154663i | \(-0.950571\pi\) |
0.360042 | − | 0.932936i | \(-0.382763\pi\) | |||||||
\(80\) | 1.26089 | − | 2.18393i | 0.140972 | − | 0.244171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.95691 | − | 13.7818i | −0.878693 | − | 1.52194i | ||||
\(83\) | −16.5438 | −1.81591 | −0.907957 | − | 0.419063i | \(-0.862359\pi\) | ||||
−0.907957 | + | 0.419063i | \(0.862359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.162253 | 0.0175988 | ||||||||
\(86\) | −2.46936 | − | 4.27706i | −0.266278 | − | 0.461207i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.08113 | + | 10.5328i | −0.648250 | + | 1.12280i | ||||
\(89\) | −2.68716 | − | 4.65430i | −0.284838 | − | 0.493354i | 0.687732 | − | 0.725965i | \(-0.258607\pi\) |
−0.972570 | + | 0.232611i | \(0.925273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4911 | + | 5.71021i | −1.09977 | + | 0.598592i | ||||
\(92\) | −0.672570 | −0.0701202 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.08113 | − | 15.7290i | 0.936647 | − | 1.62232i | ||||
\(95\) | −0.850874 | + | 1.47376i | −0.0872978 | + | 0.151204i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.26615 | −0.230093 | −0.115046 | − | 0.993360i | \(-0.536702\pi\) | ||||
−0.115046 | + | 0.993360i | \(0.536702\pi\) | |||||||
\(98\) | −10.2106 | − | 0.514055i | −1.03143 | − | 0.0519274i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.309243 | + | 0.535624i | 0.0309243 | + | 0.0535624i | ||||
\(101\) | 4.67830 | − | 8.10306i | 0.465509 | − | 0.806285i | −0.533716 | − | 0.845664i | \(-0.679205\pi\) |
0.999224 | + | 0.0393793i | \(0.0125381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.88151 | + | 13.6512i | 0.776589 | + | 1.34509i | 0.933897 | + | 0.357542i | \(0.116385\pi\) |
−0.157309 | + | 0.987550i | \(0.550282\pi\) | |||||||
\(104\) | 12.3097 | 1.20707 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.5438 | −1.60687 | ||||||||
\(107\) | 0.512453 | + | 0.887595i | 0.0495407 | + | 0.0858070i | 0.889732 | − | 0.456483i | \(-0.150891\pi\) |
−0.840192 | + | 0.542290i | \(0.817558\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.647664 | + | 1.12179i | −0.0620349 | + | 0.107448i | −0.895375 | − | 0.445313i | \(-0.853092\pi\) |
0.833340 | + | 0.552761i | \(0.186426\pi\) | |||||||
\(110\) | 1.93346 | + | 3.34886i | 0.184348 | + | 0.319301i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.58998 | + | 5.86319i | 0.906168 | + | 0.554019i | ||||
\(113\) | −14.2953 | −1.34479 | −0.672396 | − | 0.740192i | \(-0.734735\pi\) | ||||
−0.672396 | + | 0.740192i | \(0.734735\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50000 | − | 2.59808i | 0.139876 | − | 0.242272i | ||||
\(116\) | 0.0234435 | − | 0.0406053i | 0.00217667 | − | 0.00377011i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7630 | 1.08287 | ||||||||
\(119\) | −0.0181877 | + | 0.722977i | −0.00166726 | + | 0.0662752i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.44805 | − | 7.70425i | −0.404368 | − | 0.700387i | ||||
\(122\) | 1.99640 | − | 3.45787i | 0.180746 | − | 0.313061i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.167314 | − | 0.289796i | −0.0150252 | − | 0.0260245i | ||||
\(125\) | −5.72665 | −0.512207 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.3346 | 1.09452 | 0.547261 | − | 0.836962i | \(-0.315671\pi\) | ||||
0.547261 | + | 0.836962i | \(0.315671\pi\) | |||||||
\(128\) | −6.15486 | − | 10.6605i | −0.544018 | − | 0.942267i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.95691 | − | 3.38946i | 0.171632 | − | 0.297275i | ||||
\(131\) | −1.59718 | − | 2.76639i | −0.139546 | − | 0.241701i | 0.787779 | − | 0.615958i | \(-0.211231\pi\) |
−0.927325 | + | 0.374257i | \(0.877898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.47150 | − | 3.95659i | −0.561150 | − | 0.343080i | ||||
\(134\) | 8.56867 | 0.740221 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.372660 | − | 0.645466i | 0.0319553 | − | 0.0553483i | ||||
\(137\) | 5.05408 | − | 8.75393i | 0.431800 | − | 0.747899i | −0.565229 | − | 0.824934i | \(-0.691212\pi\) |
0.997028 | + | 0.0770354i | \(0.0245455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.0761 | 1.53319 | 0.766596 | − | 0.642130i | \(-0.221949\pi\) | ||||
0.766596 | + | 0.642130i | \(0.221949\pi\) | |||||||
\(140\) | 0.183560 | − | 0.0999096i | 0.0155137 | − | 0.00844390i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.89922 | + | 3.28955i | 0.159379 | + | 0.276053i | ||||
\(143\) | −10.0687 | + | 17.4395i | −0.841985 | + | 1.45836i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.104570 | + | 0.181120i | 0.00868405 | + | 0.0150412i | ||||
\(146\) | 16.2340 | 1.34354 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.884634 | −0.0727165 | ||||||||
\(149\) | 7.02704 | + | 12.1712i | 0.575678 | + | 0.997103i | 0.995968 | + | 0.0897132i | \(0.0285950\pi\) |
−0.420290 | + | 0.907390i | \(0.638072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.190757 | + | 0.330401i | −0.0155236 | + | 0.0268877i | −0.873683 | − | 0.486496i | \(-0.838275\pi\) |
0.858159 | + | 0.513384i | \(0.171608\pi\) | |||||||
\(152\) | 3.90856 | + | 6.76982i | 0.317026 | + | 0.549105i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.1388 | + | 8.23988i | −1.21992 | + | 0.663988i | ||||
\(155\) | 1.49261 | 0.119889 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75729 | − | 6.50783i | 0.299865 | − | 0.519381i | −0.676240 | − | 0.736681i | \(-0.736392\pi\) |
0.976105 | + | 0.217300i | \(0.0697251\pi\) | |||||||
\(158\) | −8.15126 | + | 14.1184i | −0.648480 | + | 1.12320i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.446110 | −0.0352681 | ||||||||
\(161\) | 11.4086 | + | 6.97504i | 0.899120 | + | 0.549710i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.59572 | − | 13.1562i | −0.594942 | − | 1.03047i | −0.993555 | − | 0.113351i | \(-0.963842\pi\) |
0.398613 | − | 0.917119i | \(-0.369492\pi\) | |||||||
\(164\) | −0.724997 | + | 1.25573i | −0.0566127 | + | 0.0980561i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0811 | + | 20.9251i | 0.937677 | + | 1.62410i | ||||
\(167\) | −8.95311 | −0.692813 | −0.346406 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346406 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.38151 | 0.567809 | ||||||||
\(170\) | −0.118485 | − | 0.205223i | −0.00908741 | − | 0.0157399i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.224997 | + | 0.389706i | −0.0171558 | + | 0.0297148i | ||||
\(173\) | −5.23025 | − | 9.05906i | −0.397649 | − | 0.688748i | 0.595787 | − | 0.803143i | \(-0.296840\pi\) |
−0.993435 | + | 0.114395i | \(0.963507\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.309243 | − | 12.2927i | 0.0233766 | − | 0.929239i | ||||
\(176\) | 18.9502 | 1.42842 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.92461 | + | 6.79762i | −0.294162 | + | 0.509503i | ||||
\(179\) | −4.48395 | + | 7.76643i | −0.335146 | + | 0.580490i | −0.983513 | − | 0.180838i | \(-0.942119\pi\) |
0.648367 | + | 0.761328i | \(0.275452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.04689 | 0.375132 | 0.187566 | − | 0.982252i | \(-0.439940\pi\) | ||||
0.187566 | + | 0.982252i | \(0.439940\pi\) | |||||||
\(182\) | 14.8837 | + | 9.09967i | 1.10325 | + | 0.674512i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.89037 | − | 11.9345i | −0.507965 | − | 0.879821i | ||||
\(185\) | 1.97296 | − | 3.41726i | 0.145055 | − | 0.251242i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.609631 | + | 1.05591i | 0.0445806 | + | 0.0772159i | ||||
\(188\) | −1.65486 | −0.120693 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.48541 | 0.180311 | ||||||||
\(191\) | 6.06507 | + | 10.5050i | 0.438853 | + | 0.760116i | 0.997601 | − | 0.0692211i | \(-0.0220514\pi\) |
−0.558748 | + | 0.829338i | \(0.688718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.58113 | + | 14.8629i | −0.617683 | + | 1.06986i | 0.372224 | + | 0.928143i | \(0.378595\pi\) |
−0.989907 | + | 0.141716i | \(0.954738\pi\) | |||||||
\(194\) | 1.65486 | + | 2.86630i | 0.118812 | + | 0.205789i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.424608 | + | 0.829120i | 0.0303292 | + | 0.0592228i | ||||
\(197\) | −0.751560 | −0.0535464 | −0.0267732 | − | 0.999642i | \(-0.508523\pi\) | ||||
−0.0267732 | + | 0.999642i | \(0.508523\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.14766 | + | 8.91601i | −0.364908 | + | 0.632040i | −0.988761 | − | 0.149502i | \(-0.952233\pi\) |
0.623853 | + | 0.781542i | \(0.285566\pi\) | |||||||
\(200\) | −6.33628 | + | 10.9748i | −0.448043 | + | 0.776033i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.6654 | −0.961492 | ||||||||
\(203\) | −0.818771 | + | 0.445647i | −0.0574664 | + | 0.0312783i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.23385 | − | 5.60119i | −0.225862 | − | 0.391204i | ||||
\(206\) | 11.5110 | − | 19.9376i | 0.802009 | − | 1.38912i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.58998 | − | 16.6103i | −0.664946 | − | 1.15172i | ||||
\(209\) | −12.7879 | −0.884560 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1154 | −1.10943 | −0.554714 | − | 0.832041i | \(-0.687172\pi\) | ||||
−0.554714 | + | 0.832041i | \(0.687172\pi\) | |||||||
\(212\) | 0.753696 | + | 1.30544i | 0.0517640 | + | 0.0896580i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.748440 | − | 1.29634i | 0.0511623 | − | 0.0886157i | ||||
\(215\) | −1.00360 | − | 1.73828i | −0.0684449 | − | 0.118550i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.167314 | + | 6.65087i | −0.0113580 | + | 0.451491i | ||||
\(218\) | 1.89183 | 0.128131 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.176168 | − | 0.305132i | 0.0118773 | − | 0.0205720i | ||||
\(221\) | 0.617023 | − | 1.06871i | 0.0415054 | − | 0.0718895i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.95311 | −0.465615 | −0.232807 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232807 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(224\) | 0.0500067 | − | 1.98781i | 0.00334121 | − | 0.132816i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4392 | + | 18.0812i | 0.694405 | + | 1.20274i | ||||
\(227\) | −2.64553 | + | 4.58219i | −0.175590 | + | 0.304131i | −0.940365 | − | 0.340166i | \(-0.889517\pi\) |
0.764775 | + | 0.644297i | \(0.222850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.86186 | − | 10.1530i | −0.387363 | − | 0.670932i | 0.604731 | − | 0.796430i | \(-0.293281\pi\) |
−0.992094 | + | 0.125498i | \(0.959947\pi\) | |||||||
\(230\) | −4.38151 | −0.288909 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.960699 | 0.0630730 | ||||||||
\(233\) | −1.93560 | − | 3.35256i | −0.126805 | − | 0.219633i | 0.795632 | − | 0.605780i | \(-0.207139\pi\) |
−0.922437 | + | 0.386147i | \(0.873806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.69076 | − | 6.39258i | 0.240758 | − | 0.417006i | ||||
\(236\) | −0.535897 | − | 0.928200i | −0.0348839 | − | 0.0604207i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.927728 | − | 0.504951i | 0.0601357 | − | 0.0327311i | ||||
\(239\) | 12.3992 | 0.802039 | 0.401020 | − | 0.916069i | \(-0.368656\pi\) | ||||
0.401020 | + | 0.916069i | \(0.368656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.28074 | − | 14.3427i | 0.533409 | − | 0.923892i | −0.465829 | − | 0.884875i | \(-0.654244\pi\) |
0.999239 | − | 0.0390173i | \(-0.0124227\pi\) | |||||||
\(242\) | −6.49640 | + | 11.2521i | −0.417604 | + | 0.723312i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.363806 | −0.0232903 | ||||||||
\(245\) | −4.14980 | − | 0.208922i | −0.265121 | − | 0.0133476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.47150 | + | 11.2090i | 0.411771 | + | 0.713209i | ||||
\(248\) | 3.42821 | − | 5.93783i | 0.217691 | − | 0.377052i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.18190 | + | 7.24327i | 0.264487 | + | 0.458105i | ||||
\(251\) | 1.84922 | 0.116722 | 0.0583608 | − | 0.998296i | \(-0.481413\pi\) | ||||
0.0583608 | + | 0.998296i | \(0.481413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.5438 | 1.41731 | ||||||||
\(254\) | −9.00739 | − | 15.6013i | −0.565174 | − | 0.978910i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.58998 | + | 2.75393i | −0.0993738 | + | 0.172120i | ||||
\(257\) | −13.4210 | − | 23.2459i | −0.837180 | − | 1.45004i | −0.892243 | − | 0.451555i | \(-0.850870\pi\) |
0.0550638 | − | 0.998483i | \(-0.482464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.0057 | + | 9.17431i | 0.932411 | + | 0.570064i | ||||
\(260\) | −0.356609 | −0.0221159 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.33269 | + | 4.04033i | −0.144114 | + | 0.249612i | ||||
\(263\) | −10.1424 | + | 17.5672i | −0.625408 | + | 1.08324i | 0.363054 | + | 0.931768i | \(0.381734\pi\) |
−0.988462 | + | 0.151470i | \(0.951599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.72373 | −0.413035 | ||||||||
\(266\) | −0.278602 | + | 11.0747i | −0.0170822 | + | 0.679032i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.390369 | − | 0.676139i | −0.0238456 | − | 0.0413018i | ||||
\(269\) | 4.36333 | − | 7.55750i | 0.266037 | − | 0.460789i | −0.701798 | − | 0.712376i | \(-0.747619\pi\) |
0.967835 | + | 0.251587i | \(0.0809524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0957 | − | 20.9504i | −0.734762 | − | 1.27265i | −0.954828 | − | 0.297161i | \(-0.903960\pi\) |
0.220065 | − | 0.975485i | \(-0.429373\pi\) | |||||||
\(272\) | −1.16129 | −0.0704138 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7630 | −0.891867 | ||||||||
\(275\) | −10.3655 | − | 17.9535i | −0.625061 | − | 1.08264i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.55768 | − | 6.16209i | 0.213760 | − | 0.370244i | −0.739128 | − | 0.673565i | \(-0.764762\pi\) |
0.952888 | + | 0.303321i | \(0.0980955\pi\) | |||||||
\(278\) | −13.2001 | − | 22.8632i | −0.791689 | − | 1.37125i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.65340 | + | 2.23364i | 0.218332 | + | 0.133485i | ||||
\(281\) | 7.89610 | 0.471042 | 0.235521 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235521 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.10457 | + | 1.91317i | −0.0656599 | + | 0.113726i | −0.896987 | − | 0.442058i | \(-0.854249\pi\) |
0.831327 | + | 0.555784i | \(0.187582\pi\) | |||||||
\(284\) | 0.173048 | − | 0.299729i | 0.0102685 | − | 0.0177856i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.4107 | 1.73909 | ||||||||
\(287\) | 25.3207 | − | 13.7818i | 1.49463 | − | 0.813512i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46264 | + | 14.6577i | 0.497802 | + | 0.862219i | ||||
\(290\) | 0.152725 | − | 0.264527i | 0.00896830 | − | 0.0155336i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.739586 | − | 1.28100i | −0.0432810 | − | 0.0749649i | ||||
\(293\) | −19.1914 | −1.12118 | −0.560588 | − | 0.828095i | \(-0.689425\pi\) | ||||
−0.560588 | + | 0.828095i | \(0.689425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.78074 | 0.278345 | ||||||||
\(296\) | −9.06294 | − | 15.6975i | −0.526773 | − | 0.912397i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.2630 | − | 17.7761i | 0.594521 | − | 1.02974i | ||||
\(299\) | −11.4086 | − | 19.7602i | −0.659774 | − | 1.14276i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.85807 | − | 4.27706i | 0.452932 | − | 0.246525i | ||||
\(302\) | 0.557204 | 0.0320635 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.08998 | − | 10.5482i | 0.349284 | − | 0.604978i | ||||
\(305\) | 0.811379 | − | 1.40535i | 0.0464594 | − | 0.0804701i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.9138 | −0.794103 | −0.397052 | − | 0.917796i | \(-0.629967\pi\) | ||||
−0.397052 | + | 0.917796i | \(0.629967\pi\) | |||||||
\(308\) | 1.33988 | + | 0.819187i | 0.0763469 | + | 0.0466775i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.08998 | − | 1.88790i | −0.0619067 | − | 0.107226i | ||||
\(311\) | −5.32743 | + | 9.22738i | −0.302091 | + | 0.523237i | −0.976609 | − | 0.215021i | \(-0.931018\pi\) |
0.674519 | + | 0.738258i | \(0.264351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.28074 | + | 14.3427i | 0.468055 | + | 0.810695i | 0.999334 | − | 0.0365022i | \(-0.0116216\pi\) |
−0.531279 | + | 0.847197i | \(0.678288\pi\) | |||||||
\(314\) | −10.9751 | −0.619360 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.48541 | 0.0835609 | ||||||||
\(317\) | 13.3186 | + | 23.0685i | 0.748046 | + | 1.29565i | 0.948758 | + | 0.316003i | \(0.102341\pi\) |
−0.200712 | + | 0.979650i | \(0.564326\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.785799 | + | 1.36104i | −0.0439963 | + | 0.0762038i | ||||
\(320\) | −2.19601 | − | 3.80361i | −0.122761 | − | 0.212628i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.491146 | − | 19.5235i | 0.0273705 | − | 1.08800i | ||||
\(323\) | 0.783663 | 0.0436042 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4911 | + | 18.1712i | −0.581944 | + | 1.00796i | ||||
\(326\) | −11.0936 | + | 19.2146i | −0.614417 | + | 1.06420i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.7099 | −1.64045 | ||||||||
\(329\) | 28.0708 | + | 17.1621i | 1.54759 | + | 0.946179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6534 | + | 20.1843i | 0.640529 | + | 1.10943i | 0.985315 | + | 0.170747i | \(0.0546181\pi\) |
−0.344786 | + | 0.938681i | \(0.612049\pi\) | |||||||
\(332\) | 1.10078 | − | 1.90660i | 0.0604130 | − | 0.104638i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.53803 | + | 11.3242i | 0.357745 | + | 0.619633i | ||||
\(335\) | 3.48249 | 0.190269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.2383 | −1.26587 | −0.632936 | − | 0.774204i | \(-0.718150\pi\) | ||||
−0.632936 | + | 0.774204i | \(0.718150\pi\) | |||||||
\(338\) | −5.39037 | − | 9.33639i | −0.293197 | − | 0.507833i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.0107958 | + | 0.0186989i | −0.000585487 | + | 0.00101409i | ||||
\(341\) | 5.60817 | + | 9.71363i | 0.303699 | + | 0.526023i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.39610 | − | 18.4676i | 0.0753825 | − | 0.997155i | ||||
\(344\) | −9.22022 | −0.497121 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.63881 | + | 13.2308i | −0.410665 | + | 0.711293i | ||||
\(347\) | 8.56867 | − | 14.8414i | 0.459990 | − | 0.796727i | −0.538969 | − | 0.842325i | \(-0.681186\pi\) |
0.998960 | + | 0.0455985i | \(0.0145195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5146 | −1.04459 | −0.522296 | − | 0.852764i | \(-0.674924\pi\) | ||||
−0.522296 | + | 0.852764i | \(0.674924\pi\) | |||||||
\(350\) | −15.7740 | + | 8.58561i | −0.843157 | + | 0.458920i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.67617 | − | 2.90321i | −0.0893401 | − | 0.154742i | ||||
\(353\) | 8.03064 | − | 13.9095i | 0.427428 | − | 0.740327i | −0.569216 | − | 0.822188i | \(-0.692753\pi\) |
0.996644 | + | 0.0818613i | \(0.0260865\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.771884 | + | 1.33694i | 0.0409673 | + | 0.0709575i | ||||
\(356\) | 0.715184 | 0.0379047 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.0977 | 0.692233 | ||||||||
\(359\) | 6.93200 | + | 12.0066i | 0.365857 | + | 0.633683i | 0.988913 | − | 0.148494i | \(-0.0474426\pi\) |
−0.623056 | + | 0.782177i | \(0.714109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.39037 | − | 9.33639i | 0.283704 | − | 0.491389i | ||||
\(362\) | −3.68550 | − | 6.38348i | −0.193706 | − | 0.335508i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0399740 | − | 1.58900i | 0.00209521 | − | 0.0832864i | ||||
\(365\) | 6.59785 | 0.345347 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6477 | + | 21.9064i | −0.660203 | + | 1.14350i | 0.320360 | + | 0.947296i | \(0.396196\pi\) |
−0.980562 | + | 0.196209i | \(0.937137\pi\) | |||||||
\(368\) | −10.7360 | + | 18.5953i | −0.559652 | + | 0.969346i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.76303 | −0.299606 | ||||||||
\(371\) | 0.753696 | − | 29.9601i | 0.0391299 | − | 1.55545i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00000 | − | 1.73205i | −0.0517780 | − | 0.0896822i | 0.838975 | − | 0.544170i | \(-0.183156\pi\) |
−0.890753 | + | 0.454488i | \(0.849822\pi\) | |||||||
\(374\) | 0.890369 | − | 1.54216i | 0.0460399 | − | 0.0797434i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.9538 | − | 29.3648i | −0.874325 | − | 1.51437i | ||||
\(377\) | 1.59065 | 0.0819229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8099 | −0.966200 | −0.483100 | − | 0.875565i | \(-0.660489\pi\) | ||||
−0.483100 | + | 0.875565i | \(0.660489\pi\) | |||||||
\(380\) | −0.113230 | − | 0.196119i | −0.00580856 | − | 0.0100607i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.85807 | − | 15.3426i | 0.453218 | − | 0.784997i | ||||
\(383\) | 17.5708 | + | 30.4335i | 0.897826 | + | 1.55508i | 0.830267 | + | 0.557366i | \(0.188188\pi\) |
0.0675593 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.15272 | + | 3.34886i | −0.313572 | + | 0.170673i | ||||
\(386\) | 25.0656 | 1.27580 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.150783 | − | 0.261164i | 0.00765486 | − | 0.0132586i | ||||
\(389\) | −4.18929 | + | 7.25607i | −0.212406 | + | 0.367897i | −0.952467 | − | 0.304642i | \(-0.901463\pi\) |
0.740061 | + | 0.672539i | \(0.234796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.38151 | −0.0698662 | ||||||||
\(392\) | −10.3623 | + | 16.0287i | −0.523377 | + | 0.809572i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.548828 | + | 0.950599i | 0.0276496 | + | 0.0478905i | ||||
\(395\) | −3.31284 | + | 5.73801i | −0.166687 | + | 0.288711i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.62422 | + | 8.00938i | 0.232083 | + | 0.401979i | 0.958421 | − | 0.285358i | \(-0.0921126\pi\) |
−0.726338 | + | 0.687338i | \(0.758779\pi\) | |||||||
\(398\) | 15.0364 | 0.753705 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.7453 | 0.987266 | ||||||||
\(401\) | −0.0737345 | − | 0.127712i | −0.00368212 | − | 0.00637763i | 0.864178 | − | 0.503185i | \(-0.167839\pi\) |
−0.867861 | + | 0.496808i | \(0.834505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.67617 | − | 9.83141i | 0.282750 | − | 0.489738i | ||||
\(404\) | 0.622563 | + | 1.07831i | 0.0309737 | + | 0.0536480i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.16158 | + | 0.710174i | 0.0576482 | + | 0.0352454i | ||||
\(407\) | 29.6519 | 1.46979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.96264 | − | 3.39939i | 0.0970463 | − | 0.168089i | −0.813414 | − | 0.581685i | \(-0.802394\pi\) |
0.910461 | + | 0.413595i | \(0.135727\pi\) | |||||||
\(410\) | −4.72306 | + | 8.18057i | −0.233255 | + | 0.404010i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.09766 | −0.103344 | ||||||||
\(413\) | −0.535897 | + | 21.3024i | −0.0263697 | + | 1.04822i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.91002 | + | 8.50440i | 0.241023 | + | 0.417465i | ||||
\(416\) | −1.69649 | + | 2.93841i | −0.0831774 | + | 0.144067i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.33842 | + | 16.1746i | 0.456757 | + | 0.791126i | ||||
\(419\) | −21.0000 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.6883 | −1.20323 | −0.601617 | − | 0.798784i | \(-0.705477\pi\) | ||||
−0.601617 | + | 0.798784i | \(0.705477\pi\) | |||||||
\(422\) | 11.7683 | + | 20.3833i | 0.572871 | + | 0.992242i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.4430 | + | 26.7480i | −0.749978 | + | 1.29900i | ||||
\(425\) | 0.635211 | + | 1.10022i | 0.0308122 | + | 0.0533684i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.17111 | + | 3.77293i | 0.298641 | + | 0.182585i | ||||
\(428\) | −0.136389 | −0.00659260 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.46576 | + | 2.53877i | −0.0706853 | + | 0.122430i | ||||
\(431\) | −2.73745 | + | 4.74140i | −0.131858 | + | 0.228385i | −0.924393 | − | 0.381442i | \(-0.875428\pi\) |
0.792535 | + | 0.609827i | \(0.208761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.6300 | 1.13558 | 0.567792 | − | 0.823172i | \(-0.307798\pi\) | ||||
0.567792 | + | 0.823172i | \(0.307798\pi\) | |||||||
\(434\) | 8.53443 | − | 4.64519i | 0.409666 | − | 0.222976i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0861875 | − | 0.149281i | −0.00412763 | − | 0.00714927i | ||||
\(437\) | 7.24484 | − | 12.5484i | 0.346568 | − | 0.600273i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.63307 | + | 4.56062i | 0.125670 | + | 0.217666i | 0.921995 | − | 0.387203i | \(-0.126559\pi\) |
−0.796325 | + | 0.604869i | \(0.793225\pi\) | |||||||
\(440\) | 7.21926 | 0.344165 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.80233 | −0.0857281 | ||||||||
\(443\) | 3.01819 | + | 5.22765i | 0.143398 | + | 0.248373i | 0.928774 | − | 0.370646i | \(-0.120864\pi\) |
−0.785376 | + | 0.619019i | \(0.787530\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.59504 | + | 2.76269i | −0.0756122 | + | 0.130964i | ||||
\(446\) | 5.07753 | + | 8.79454i | 0.240428 | + | 0.416433i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.1946 | − | 9.35879i | 0.812366 | − | 0.442161i | ||||
\(449\) | −22.1445 | −1.04507 | −0.522533 | − | 0.852619i | \(-0.675013\pi\) | ||||
−0.522533 | + | 0.852619i | \(0.675013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.3011 | − | 42.0907i | 1.14429 | − | 1.98197i | ||||
\(452\) | 0.951172 | − | 1.64748i | 0.0447393 | − | 0.0774908i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.72761 | 0.362675 | ||||||||
\(455\) | 6.04902 | + | 3.69829i | 0.283583 | + | 0.173379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.66731 | + | 4.61992i | 0.124772 | + | 0.216111i | 0.921644 | − | 0.388037i | \(-0.126847\pi\) |
−0.796872 | + | 0.604148i | \(0.793513\pi\) | |||||||
\(458\) | −8.56128 | + | 14.8286i | −0.400042 | + | 0.692894i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.199612 | + | 0.345738i | 0.00930694 | + | 0.0161201i | ||||
\(461\) | 29.6946 | 1.38301 | 0.691507 | − | 0.722370i | \(-0.256947\pi\) | ||||
0.691507 | + | 0.722370i | \(0.256947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5907 | 0.863981 | 0.431990 | − | 0.901878i | \(-0.357811\pi\) | ||||
0.431990 | + | 0.901878i | \(0.357811\pi\) | |||||||
\(464\) | −0.748440 | − | 1.29634i | −0.0347455 | − | 0.0601809i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.82695 | + | 4.89642i | −0.130956 | + | 0.226822i | ||||
\(467\) | −12.3063 | − | 21.3152i | −0.569468 | − | 0.986348i | −0.996619 | − | 0.0821676i | \(-0.973816\pi\) |
0.427150 | − | 0.904181i | \(-0.359518\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.390369 | + | 15.5175i | −0.0180256 | + | 0.716532i | ||||
\(470\) | −10.7807 | −0.497278 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.9803 | − | 19.0185i | 0.505412 | − | 0.875399i | ||||
\(473\) | 7.54163 | − | 13.0625i | 0.346765 | − | 0.600614i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.3245 | −0.611370 | ||||||||
\(476\) | −0.0821100 | − | 0.0502010i | −0.00376351 | − | 0.00230096i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.05456 | − | 15.6830i | −0.414146 | − | 0.717322i | ||||
\(479\) | 0.178304 | − | 0.308832i | 0.00814693 | − | 0.0141109i | −0.861923 | − | 0.507039i | \(-0.830740\pi\) |
0.870070 | + | 0.492928i | \(0.164073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0057 | − | 25.9907i | −0.684203 | − | 1.18507i | ||||
\(482\) | −24.1881 | −1.10174 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.18384 | 0.0538111 | ||||||||
\(485\) | 0.672570 | + | 1.16492i | 0.0305398 | + | 0.0528965i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.43920 | − | 11.1530i | 0.291788 | − | 0.505391i | −0.682445 | − | 0.730937i | \(-0.739083\pi\) |
0.974233 | + | 0.225546i | \(0.0724165\pi\) | |||||||
\(488\) | −3.72713 | − | 6.45558i | −0.168719 | − | 0.292231i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.76615 | + | 5.40138i | 0.124962 | + | 0.244009i | ||||
\(491\) | 5.55389 | 0.250644 | 0.125322 | − | 0.992116i | \(-0.460004\pi\) | ||||
0.125322 | + | 0.992116i | \(0.460004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0481549 | − | 0.0834068i | 0.00216879 | − | 0.00375645i | ||||
\(494\) | 9.45165 | − | 16.3707i | 0.425250 | − | 0.736554i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.6831 | −0.479685 | ||||||||
\(497\) | −6.04377 | + | 3.28955i | −0.271100 | + | 0.147557i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0577 | + | 24.3486i | 0.629308 | + | 1.08999i | 0.987691 | + | 0.156419i | \(0.0499951\pi\) |
−0.358382 | + | 0.933575i | \(0.616672\pi\) | |||||||
\(500\) | 0.381036 | − | 0.659973i | 0.0170404 | − | 0.0295149i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.35040 | − | 2.33895i | −0.0602711 | − | 0.104393i | ||||
\(503\) | 16.9430 | 0.755451 | 0.377725 | − | 0.925918i | \(-0.376706\pi\) | ||||
0.377725 | + | 0.925918i | \(0.376706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.55389 | −0.247145 | ||||||||
\(506\) | −16.4626 | − | 28.5141i | −0.731854 | − | 1.26761i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.820712 | + | 1.42151i | −0.0364132 | + | 0.0630695i | ||||
\(509\) | 11.1513 | + | 19.3146i | 0.494271 | + | 0.856102i | 0.999978 | − | 0.00660269i | \(-0.00210172\pi\) |
−0.505707 | + | 0.862705i | \(0.668768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.739586 | + | 29.3992i | −0.0327173 | + | 1.30054i | ||||
\(512\) | −19.9751 | −0.882783 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.6015 | + | 33.9507i | −0.864583 | + | 1.49750i | ||||
\(515\) | 4.67830 | − | 8.10306i | 0.206151 | − | 0.357064i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 55.4690 | 2.43953 | ||||||||
\(518\) | 0.646006 | − | 25.6793i | 0.0283839 | − | 1.12828i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.65340 | − | 6.32787i | −0.160212 | − | 0.277496i | ||||
\(521\) | −6.18044 | + | 10.7048i | −0.270770 | + | 0.468987i | −0.969059 | − | 0.246828i | \(-0.920612\pi\) |
0.698289 | + | 0.715816i | \(0.253945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.09572 | − | 5.36194i | −0.135366 | − | 0.234461i | 0.790371 | − | 0.612628i | \(-0.209888\pi\) |
−0.925737 | + | 0.378167i | \(0.876554\pi\) | |||||||
\(524\) | 0.425087 | 0.0185700 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.6261 | 1.29176 | ||||||||
\(527\) | −0.343677 | − | 0.595265i | −0.0149708 | − | 0.0259302i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.27188 | + | 2.20297i | −0.0552993 | + | 0.0957812i | ||||
\(530\) | 4.91002 | + | 8.50440i | 0.213278 | + | 0.369408i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.886576 | − | 0.482553i | 0.0384379 | − | 0.0209213i | ||||
\(533\) | −49.1914 | −2.13072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.304182 | − | 0.526858i | 0.0131509 | − | 0.0227781i | ||||
\(536\) | 7.99854 | − | 13.8539i | 0.345484 | − | 0.598396i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.7453 | −0.549490 | ||||||||
\(539\) | −14.2324 | − | 27.7912i | −0.613032 | − | 1.19705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4100 | − | 23.2268i | −0.576542 | − | 0.998600i | −0.995872 | − | 0.0907660i | \(-0.971068\pi\) |
0.419330 | − | 0.907834i | \(-0.362265\pi\) | |||||||
\(542\) | −17.6659 | + | 30.5982i | −0.758813 | + | 1.31430i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.102718 | + | 0.177913i | 0.00440400 | + | 0.00762795i | ||||
\(545\) | 0.768879 | 0.0329352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6591 | −0.626779 | −0.313390 | − | 0.949625i | \(-0.601465\pi\) | ||||
−0.313390 | + | 0.949625i | \(0.601465\pi\) | |||||||
\(548\) | 0.672570 | + | 1.16492i | 0.0287307 | + | 0.0497631i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.1388 | + | 26.2212i | −0.645521 | + | 1.11808i | ||||
\(551\) | 0.505061 | + | 0.874792i | 0.0215163 | + | 0.0372674i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1965 | − | 15.4048i | −1.07146 | − | 0.655079i | ||||
\(554\) | −10.3920 | −0.441515 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.20273 | + | 2.08319i | −0.0510072 | + | 0.0883470i | ||||
\(557\) | 11.8399 | − | 20.5073i | 0.501672 | − | 0.868921i | −0.498326 | − | 0.866990i | \(-0.666052\pi\) |
0.999998 | − | 0.00193169i | \(-0.000614877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2661 | −0.645689 | ||||||||
\(560\) | 0.167793 | − | 6.66991i | 0.00709054 | − | 0.281855i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.76615 | − | 9.98726i | −0.243230 | − | 0.421287i | ||||
\(563\) | 8.19289 | − | 14.1905i | 0.345289 | − | 0.598059i | −0.640117 | − | 0.768277i | \(-0.721114\pi\) |
0.985406 | + | 0.170219i | \(0.0544475\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.24271 | + | 7.34858i | 0.178492 | + | 0.309157i | ||||
\(566\) | 3.22646 | 0.135618 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.09142 | 0.297549 | ||||||||
\(569\) | 7.89397 | + | 13.6728i | 0.330932 | + | 0.573192i | 0.982695 | − | 0.185231i | \(-0.0593035\pi\) |
−0.651763 | + | 0.758423i | \(0.725970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.19076 | + | 5.52655i | −0.133529 | + | 0.231279i | −0.925035 | − | 0.379883i | \(-0.875964\pi\) |
0.791506 | + | 0.611162i | \(0.209298\pi\) | |||||||
\(572\) | −1.33988 | − | 2.32075i | −0.0560233 | − | 0.0970353i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −35.9222 | − | 21.9623i | −1.49936 | − | 0.916690i | ||||
\(575\) | 23.4897 | 0.979587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5203 | − | 32.0781i | 0.771011 | − | 1.33543i | −0.165998 | − | 0.986126i | \(-0.553085\pi\) |
0.937009 | − | 0.349304i | \(-0.113582\pi\) | |||||||
\(578\) | 12.3597 | − | 21.4077i | 0.514097 | − | 0.890442i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0278311 | −0.00115563 | ||||||||
\(581\) | −38.4449 | + | 20.9251i | −1.59496 | + | 0.868120i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.2630 | − | 43.7569i | −1.04629 | − | 1.81222i | ||||
\(584\) | 15.1539 | − | 26.2473i | 0.627072 | − | 1.08612i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0146 | + | 24.2740i | 0.578937 | + | 1.00275i | ||||
\(587\) | −12.0938 | −0.499163 | −0.249582 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249582 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.20914 | 0.297047 | ||||||||
\(590\) | −3.49115 | − | 6.04684i | −0.143728 | − | 0.248945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.1211 | + | 24.4585i | −0.580374 | + | 1.00524i | ||||
\(593\) | −8.26449 | − | 14.3145i | −0.339382 | − | 0.587827i | 0.644935 | − | 0.764238i | \(-0.276885\pi\) |
−0.984317 | + | 0.176411i | \(0.943551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.377048 | − | 0.205223i | 0.0154575 | − | 0.00841331i | ||||
\(596\) | −1.87024 | −0.0766080 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.6623 | + | 28.8599i | −0.681370 | + | 1.18017i | ||||
\(599\) | 4.37412 | − | 7.57620i | 0.178722 | − | 0.309555i | −0.762721 | − | 0.646727i | \(-0.776137\pi\) |
0.941443 | + | 0.337172i | \(0.109470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.92393 | −0.241642 | −0.120821 | − | 0.992674i | \(-0.538553\pi\) | ||||
−0.120821 | + | 0.992674i | \(0.538553\pi\) | |||||||
\(602\) | −11.1481 | − | 6.81583i | −0.454364 | − | 0.277792i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0253849 | − | 0.0439680i | −0.00103290 | − | 0.00178903i | ||||
\(605\) | −2.64027 | + | 4.57308i | −0.107342 | + | 0.185922i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.370719 | + | 0.642104i | 0.0150470 | + | 0.0260622i | 0.873451 | − | 0.486912i | \(-0.161877\pi\) |
−0.858404 | + | 0.512974i | \(0.828544\pi\) | |||||||
\(608\) | −2.15467 | −0.0873833 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.37005 | −0.0959603 | ||||||||
\(611\) | −28.0708 | − | 48.6201i | −1.13562 | − | 1.96696i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.25350 | + | 3.90318i | −0.0910181 | + | 0.157648i | −0.907940 | − | 0.419101i | \(-0.862345\pi\) |
0.816922 | + | 0.576749i | \(0.195679\pi\) | |||||||
\(614\) | 10.1606 | + | 17.5987i | 0.410048 | + | 0.710224i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.809243 | + | 32.1681i | −0.0326053 | + | 1.29609i | ||||
\(617\) | −17.2016 | −0.692508 | −0.346254 | − | 0.938141i | \(-0.612547\pi\) | ||||
−0.346254 | + | 0.938141i | \(0.612547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.24271 | + | 3.88448i | −0.0901419 | + | 0.156130i | −0.907571 | − | 0.419899i | \(-0.862065\pi\) |
0.817429 | + | 0.576030i | \(0.195399\pi\) | |||||||
\(620\) | −0.0993140 | + | 0.172017i | −0.00398855 | + | 0.00690837i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.5615 | 0.623958 | ||||||||
\(623\) | −12.1314 | − | 7.41699i | −0.486035 | − | 0.297155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.91955 | − | 17.1812i | −0.396782 | − | 0.687246i | ||||
\(626\) | 12.0941 | − | 20.9475i | 0.483376 | − | 0.837231i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.500000 | + | 0.866025i | 0.0199522 | + | 0.0345582i | ||||
\(629\) | −1.81711 | −0.0724531 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3068 | −0.688973 | −0.344486 | − | 0.938791i | \(-0.611947\pi\) | ||||
−0.344486 | + | 0.938791i | \(0.611947\pi\) | |||||||
\(632\) | 15.2178 | + | 26.3580i | 0.605332 | + | 1.04847i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.4518 | − | 33.6916i | 0.772531 | − | 1.33806i | ||||
\(635\) | −3.66079 | − | 6.34067i | −0.145274 | − | 0.251622i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.1572 | + | 26.5391i | −0.679793 | + | 1.05152i | ||||
\(638\) | 2.29533 | 0.0908729 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.65340 | + | 6.32787i | −0.144413 | + | 0.250131i | ||||
\(641\) | −21.6608 | + | 37.5176i | −0.855550 | + | 1.48186i | 0.0205843 | + | 0.999788i | \(0.493447\pi\) |
−0.876134 | + | 0.482068i | \(0.839886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.9823 | 1.18239 | 0.591193 | − | 0.806530i | \(-0.298657\pi\) | ||||
0.591193 | + | 0.806530i | \(0.298657\pi\) | |||||||
\(644\) | −1.56294 | + | 0.850689i | −0.0615884 | + | 0.0335218i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.572272 | − | 0.991204i | −0.0225157 | − | 0.0389984i | ||||
\(647\) | −7.08472 | + | 12.2711i | −0.278529 | + | 0.482427i | −0.971019 | − | 0.239000i | \(-0.923180\pi\) |
0.692490 | + | 0.721427i | \(0.256514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.9626 | + | 31.1122i | 0.705095 | + | 1.22126i | ||||
\(650\) | 30.6447 | 1.20199 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.02159 | 0.0791716 | ||||||||
\(653\) | 14.1981 | + | 24.5919i | 0.555617 | + | 0.962356i | 0.997855 | + | 0.0654587i | \(0.0208511\pi\) |
−0.442239 | + | 0.896897i | \(0.645816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.948052 | + | 1.64207i | −0.0370435 | + | 0.0641611i | ||||
\(656\) | 23.1457 | + | 40.0896i | 0.903689 | + | 1.56523i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.20847 | − | 48.0376i | 0.0471109 | − | 1.87270i | ||||
\(659\) | 9.39922 | 0.366142 | 0.183071 | − | 0.983100i | \(-0.441396\pi\) | ||||
0.183071 | + | 0.983100i | \(0.441396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.35807 | − | 11.0125i | 0.247300 | − | 0.428337i | −0.715476 | − | 0.698638i | \(-0.753790\pi\) |
0.962776 | + | 0.270301i | \(0.0871232\pi\) | |||||||
\(662\) | 17.0198 | − | 29.4792i | 0.661495 | − | 1.14574i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.1091 | 1.75057 | ||||||||
\(665\) | −0.113230 | + | 4.50098i | −0.00439086 | + | 0.174540i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.890369 | − | 1.54216i | −0.0344752 | − | 0.0597128i | ||||
\(668\) | 0.595715 | − | 1.03181i | 0.0230489 | − | 0.0399219i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.54309 | − | 4.40477i | −0.0982483 | − | 0.170171i | ||||
\(671\) | 12.1944 | 0.470758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7922 | 1.37969 | 0.689844 | − | 0.723958i | \(-0.257679\pi\) | ||||
0.689844 | + | 0.723958i | \(0.257679\pi\) | |||||||
\(674\) | 16.9698 | + | 29.3926i | 0.653654 | + | 1.13216i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.491146 | + | 0.850689i | −0.0188902 | + | 0.0327188i | ||||
\(677\) | 5.44592 | + | 9.43260i | 0.209304 | + | 0.362524i | 0.951495 | − | 0.307663i | \(-0.0995470\pi\) |
−0.742192 | + | 0.670188i | \(0.766214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.26615 | + | 2.86630i | −0.202096 | + | 0.109999i | ||||
\(680\) | −0.442407 | −0.0169655 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.19076 | − | 14.1868i | 0.313640 | − | 0.543241i | ||||
\(683\) | 17.5079 | − | 30.3245i | 0.669920 | − | 1.16034i | −0.308006 | − | 0.951384i | \(-0.599662\pi\) |
0.977926 | − | 0.208951i | \(-0.0670050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | −24.3779 | + | 11.7201i | −0.930753 | + | 0.447477i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.18308 | + | 12.4415i | 0.273852 | + | 0.474326i | ||||
\(689\) | −25.5693 | + | 44.2874i | −0.974115 | + | 1.68722i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.21041 | − | 7.29264i | −0.160171 | − | 0.277425i | 0.774759 | − | 0.632257i | \(-0.217871\pi\) |
−0.934930 | + | 0.354832i | \(0.884538\pi\) | |||||||
\(692\) | 1.39203 | 0.0529169 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.0292 | −0.950095 | ||||||||
\(695\) | −5.36479 | − | 9.29209i | −0.203498 | − | 0.352469i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48920 | + | 2.57938i | −0.0564076 | + | 0.0977009i | ||||
\(698\) | 14.2506 | + | 24.6827i | 0.539392 | + | 0.934255i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.39610 | + | 0.853559i | 0.0527678 | + | 0.0322615i | ||||
\(701\) | −42.7453 | −1.61447 | −0.807234 | − | 0.590231i | \(-0.799037\pi\) | ||||
−0.807234 | + | 0.590231i | \(0.799037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.52918 | − | 16.5050i | 0.359400 | − | 0.622499i | ||||
\(704\) | 16.5021 | − | 28.5825i | 0.621948 | − | 1.07724i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.4576 | −0.882838 | ||||||||
\(707\) | 0.622563 | − | 24.7474i | 0.0234139 | − | 0.930723i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0431 | + | 20.8593i | 0.452288 | + | 0.783386i | 0.998528 | − | 0.0542432i | \(-0.0172746\pi\) |
−0.546240 | + | 0.837629i | \(0.683941\pi\) | |||||||
\(710\) | 1.12734 | − | 1.95261i | 0.0423083 | − | 0.0732801i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.32695 | + | 12.6907i | 0.274589 | + | 0.475602i | ||||
\(713\) | −12.7089 | −0.475954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9531 | 0.447021 | ||||||||
\(716\) | −0.596699 | − | 1.03351i | −0.0222997 | − | 0.0386242i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.1242 | − | 17.5357i | 0.377833 | − | 0.654425i | ||||
\(719\) | 21.0512 | + | 36.4617i | 0.785076 | + | 1.35979i | 0.928954 | + | 0.370196i | \(0.120709\pi\) |
−0.143878 | + | 0.989595i | \(0.545957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.5818 | + | 21.7542i | 1.32514 | + | 0.810170i | ||||
\(722\) | −15.7453 | −0.585980 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.335806 | + | 0.581633i | −0.0124801 | + | 0.0216162i | ||||
\(725\) | −0.818771 | + | 1.41815i | −0.0304084 | + | 0.0526689i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.0698 | 1.33776 | 0.668878 | − | 0.743372i | \(-0.266775\pi\) | ||||
0.668878 | + | 0.743372i | \(0.266775\pi\) | |||||||
\(728\) | 28.6057 | − | 15.5698i | 1.06020 | − | 0.577054i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.81810 | − | 8.34519i | −0.178326 | − | 0.308869i | ||||
\(731\) | −0.462162 | + | 0.800488i | −0.0170937 | + | 0.0296071i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.0665 | − | 29.5601i | −0.630367 | − | 1.09183i | −0.987477 | − | 0.157765i | \(-0.949571\pi\) |
0.357110 | − | 0.934062i | \(-0.383762\pi\) | |||||||
\(734\) | 36.9439 | 1.36363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.79845 | 0.140013 | ||||||||
\(737\) | 13.0847 | + | 22.6634i | 0.481982 | + | 0.834817i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9481 | + | 18.9626i | −0.402731 | + | 0.697550i | −0.994054 | − | 0.108884i | \(-0.965272\pi\) |
0.591324 | + | 0.806434i | \(0.298606\pi\) | |||||||
\(740\) | 0.262550 | + | 0.454751i | 0.00965154 | + | 0.0167170i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −38.4449 | + | 20.9251i | −1.41136 | + | 0.768185i | ||||
\(743\) | 28.2852 | 1.03768 | 0.518842 | − | 0.854870i | \(-0.326363\pi\) | ||||
0.518842 | + | 0.854870i | \(0.326363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.17111 | − | 7.22457i | 0.152818 | − | 0.264688i | ||||
\(746\) | −1.46050 | + | 2.52967i | −0.0534729 | + | 0.0926177i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.162253 | −0.00593254 | ||||||||
\(749\) | 2.31351 | + | 1.41445i | 0.0845340 | + | 0.0516830i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.24844 | + | 12.5547i | 0.264499 | + | 0.458126i | 0.967432 | − | 0.253130i | \(-0.0814600\pi\) |
−0.702933 | + | 0.711256i | \(0.748127\pi\) | |||||||
\(752\) | −26.4159 | + | 45.7538i | −0.963291 | + | 1.66847i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.16158 | − | 2.01191i | −0.0423022 | − | 0.0732696i | ||||
\(755\) | 0.226459 | 0.00824169 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.9646 | −1.41619 | −0.708096 | − | 0.706116i | \(-0.750446\pi\) | ||||
−0.708096 | + | 0.706116i | \(0.750446\pi\) | |||||||
\(758\) | 13.7360 | + | 23.7914i | 0.498914 | + | 0.864144i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.32004 | − | 4.01842i | 0.0841566 | − | 0.145764i | ||||
\(761\) | 0.627819 | + | 1.08741i | 0.0227584 | + | 0.0394187i | 0.877180 | − | 0.480161i | \(-0.159422\pi\) |
−0.854422 | + | 0.519580i | \(0.826088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0861875 | + | 3.42603i | −0.00312020 | + | 0.124031i | ||||
\(764\) | −1.61421 | −0.0584002 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.6623 | − | 44.4483i | 0.927215 | − | 1.60598i | ||||
\(767\) | 18.1804 | − | 31.4894i | 0.656458 | − | 1.13702i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6883 | −0.998466 | −0.499233 | − | 0.866468i | \(-0.666385\pi\) | ||||
−0.499233 | + | 0.866468i | \(0.666385\pi\) | |||||||
\(770\) | 8.72879 | + | 5.33667i | 0.314564 | + | 0.192320i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14193 | − | 1.97788i | −0.0410989 | − | 0.0711854i | ||||
\(773\) | −3.95544 | + | 6.85103i | −0.142267 | + | 0.246414i | −0.928350 | − | 0.371707i | \(-0.878773\pi\) |
0.786083 | + | 0.618121i | \(0.212106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.84348 | + | 10.1212i | 0.209904 | + | 0.363565i | ||||
\(776\) | 6.17900 | 0.221813 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.2370 | 0.438717 | ||||||||
\(779\) | −15.6192 | − | 27.0532i | −0.559614 | − | 0.969281i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.80039 | + | 10.0466i | −0.207554 | + | 0.359494i | ||||
\(782\) | 1.00885 | + | 1.74739i | 0.0360766 | + | 0.0624864i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29.7015 | + | 1.49533i | 1.06077 | + | 0.0534045i | ||||
\(785\) | −4.46050 | −0.159202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.8346 | + | 27.4264i | −0.564444 | + | 0.977645i | 0.432658 | + | 0.901558i | \(0.357576\pi\) |
−0.997101 | + | 0.0760866i | \(0.975757\pi\) | |||||||
\(788\) | 0.0500067 | − | 0.0866142i | 0.00178142 | − | 0.00308550i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.67684 | 0.344287 | ||||||||
\(791\) | −33.2199 | + | 18.0812i | −1.18116 | + | 0.642894i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.17111 | − | 10.6887i | −0.219142 | − | 0.379566i | ||||
\(794\) | 6.75370 | − | 11.6977i | 0.239680 | − | 0.415137i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.685023 | − | 1.18649i | −0.0242800 | − | 0.0420542i | ||||
\(797\) | 33.7922 | 1.19698 | 0.598491 | − | 0.801130i | \(-0.295767\pi\) | ||||
0.598491 | + | 0.801130i | \(0.295767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.39922 | −0.120256 | ||||||||
\(800\) | −1.74650 | − | 3.02502i | −0.0617481 | − | 0.106951i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.107690 | + | 0.186524i | −0.00380265 | + | 0.00658638i | ||||
\(803\) | 24.7901 | + | 42.9377i | 0.874823 | + | 1.51524i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.199612 | − | 7.93474i | 0.00703539 | − | 0.279663i | ||||
\(806\) | −16.5801 | −0.584011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.7561 | + | 22.0942i | −0.448759 | + | 0.777273i | ||||
\(809\) | −18.3801 | + | 31.8352i | −0.646208 | + | 1.11927i | 0.337813 | + | 0.941213i | \(0.390313\pi\) |
−0.984021 | + | 0.178052i | \(0.943020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.54377 | 0.124438 | 0.0622192 | − | 0.998063i | \(-0.480182\pi\) | ||||
0.0622192 | + | 0.998063i | \(0.480182\pi\) | |||||||
\(812\) | 0.00311973 | − | 0.124012i | 0.000109481 | − | 0.00435197i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.6534 | − | 37.5048i | −0.758951 | − | 1.31454i | ||||
\(815\) | −4.50866 | + | 7.80923i | −0.157931 | + | 0.273545i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.84728 | − | 8.39573i | −0.169585 | − | 0.293729i | ||||
\(818\) | −5.73289 | −0.200446 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.860686 | 0.0300565 | ||||||||
\(821\) | −10.4318 | − | 18.0684i | −0.364073 | − | 0.630592i | 0.624554 | − | 0.780981i | \(-0.285281\pi\) |
−0.988627 | + | 0.150389i | \(0.951947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7003 | + | 39.3180i | −0.791282 | + | 1.37054i | 0.133891 | + | 0.990996i | \(0.457253\pi\) |
−0.925173 | + | 0.379545i | \(0.876081\pi\) | |||||||
\(824\) | −21.4902 | − | 37.2221i | −0.748645 | − | 1.29669i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.3353 | − | 14.8783i | 0.951117 | − | 0.517682i | ||||
\(827\) | −5.34221 | −0.185767 | −0.0928835 | − | 0.995677i | \(-0.529608\pi\) | ||||
−0.0928835 | + | 0.995677i | \(0.529608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.45185 | + | 14.6390i | −0.293545 | + | 0.508434i | −0.974645 | − | 0.223755i | \(-0.928168\pi\) |
0.681101 | + | 0.732190i | \(0.261502\pi\) | |||||||
\(830\) | 7.17111 | − | 12.4207i | 0.248913 | − | 0.431130i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −33.4045 | −1.15809 | ||||||||
\(833\) | 0.872181 | + | 1.70308i | 0.0302193 | + | 0.0590083i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.65719 | + | 4.60239i | 0.0919559 | + | 0.159272i | ||||
\(836\) | 0.850874 | − | 1.47376i | 0.0294281 | − | 0.0509709i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.3353 | + | 26.5615i | 0.529749 | + | 0.917553i | ||||
\(839\) | −9.83909 | −0.339683 | −0.169842 | − | 0.985471i | \(-0.554326\pi\) | ||||
−0.169842 | + | 0.985471i | \(0.554326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8759 | −0.995719 | ||||||||
\(842\) | 18.0287 | + | 31.2266i | 0.621310 | + | 1.07614i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.07227 | − | 1.85723i | 0.0369091 | − | 0.0639285i | ||||
\(845\) | −2.19076 | − | 3.79450i | −0.0753643 | − | 0.130535i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0811 | − | 12.2773i | −0.689996 | − | 0.421854i | ||||
\(848\) | 48.1239 | 1.65258 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.927728 | − | 1.60687i | 0.0318208 | − | 0.0551153i | ||||
\(851\) | −16.7989 | + | 29.0966i | −0.575860 | + | 0.997418i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.4868 | −1.89983 | −0.949915 | − | 0.312508i | \(-0.898831\pi\) | ||||
−0.949915 | + | 0.312508i | \(0.898831\pi\) | |||||||
\(854\) | 0.265670 | − | 10.5606i | 0.00909104 | − | 0.361377i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.39728 | − | 2.42016i | −0.0477581 | − | 0.0827195i | ||||
\(857\) | 28.1732 | − | 48.7975i | 0.962380 | − | 1.66689i | 0.245884 | − | 0.969299i | \(-0.420922\pi\) |
0.716496 | − | 0.697591i | \(-0.245745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9626 | − | 38.0404i | −0.749356 | − | 1.29792i | −0.948132 | − | 0.317877i | \(-0.897030\pi\) |
0.198776 | − | 0.980045i | \(-0.436303\pi\) | |||||||
\(860\) | 0.267107 | 0.00910826 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.99612 | 0.272349 | ||||||||
\(863\) | −5.66372 | − | 9.80984i | −0.192795 | − | 0.333931i | 0.753380 | − | 0.657585i | \(-0.228422\pi\) |
−0.946175 | + | 0.323654i | \(0.895089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.10457 | + | 5.37727i | −0.105559 | + | 0.182833i | ||||
\(866\) | −17.2558 | − | 29.8880i | −0.586377 | − | 1.01563i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.755353 | − | 0.461813i | −0.0256384 | − | 0.0156750i | ||||
\(869\) | −49.7893 | −1.68899 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2434 | − | 22.9382i | 0.448735 | − | 0.777231i | ||||
\(872\) | 1.76595 | − | 3.05872i | 0.0598028 | − | 0.103581i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −21.1623 | −0.715824 | ||||||||
\(875\) | −13.3078 | + | 7.24327i | −0.449885 | + | 0.244867i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2307 | + | 40.2368i | 0.784446 | + | 1.35870i | 0.929329 | + | 0.369252i | \(0.120386\pi\) |
−0.144883 | + | 0.989449i | \(0.546281\pi\) | |||||||
\(878\) | 3.84562 | − | 6.66081i | 0.129783 | − | 0.224791i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.62422 | − | 9.74143i | −0.189592 | − | 0.328384i | ||||
\(881\) | 21.6578 | 0.729669 | 0.364835 | − | 0.931072i | \(-0.381126\pi\) | ||||
0.364835 | + | 0.931072i | \(0.381126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4868 | 0.386560 | 0.193280 | − | 0.981144i | \(-0.438087\pi\) | ||||
0.193280 | + | 0.981144i | \(0.438087\pi\) | |||||||
\(884\) | 0.0821100 | + | 0.142219i | 0.00276166 | + | 0.00478333i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.40808 | − | 7.63501i | 0.148092 | − | 0.256503i | ||||
\(887\) | −8.92101 | − | 15.4516i | −0.299538 | − | 0.518815i | 0.676492 | − | 0.736450i | \(-0.263499\pi\) |
−0.976030 | + | 0.217634i | \(0.930166\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.6636 | − | 15.6013i | 0.961346 | − | 0.523249i | ||||
\(890\) | 4.65913 | 0.156174 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.462641 | − | 0.801318i | 0.0154904 | − | 0.0268301i | ||||
\(893\) | 17.8260 | − | 30.8755i | 0.596523 | − | 1.03321i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.32316 | 0.177934 | ||||||||
\(896\) | −27.7867 | − | 16.9884i | −0.928287 | − | 0.567543i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.1711 | + | 28.0092i | 0.539637 | + | 0.934678i | ||||
\(899\) | 0.442991 | − | 0.767282i | 0.0147746 | − | 0.0255903i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.54815 | + | 2.68148i | 0.0515765 | + | 0.0893331i | ||||
\(902\) | −70.9836 | −2.36350 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38.9784 | 1.29640 | ||||||||
\(905\) | −1.49786 | − | 2.59438i | −0.0497907 | − | 0.0862400i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9253 | − | 44.9039i | 0.860835 | − | 1.49101i | −0.0102894 | − | 0.999947i | \(-0.503275\pi\) |
0.871124 | − | 0.491063i | \(-0.163391\pi\) | |||||||
\(908\) | −0.352052 | − | 0.609772i | −0.0116833 | − | 0.0202360i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.260414 | − | 10.3517i | 0.00863265 | − | 0.343155i | ||||
\(911\) | −6.48676 | −0.214916 | −0.107458 | − | 0.994210i | \(-0.534271\pi\) | ||||
−0.107458 | + | 0.994210i | \(0.534271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.8968 | + | 63.9071i | −1.22111 | + | 2.11502i | ||||
\(914\) | 3.89562 | − | 6.74742i | 0.128856 | − | 0.223185i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.56013 | 0.0515481 | ||||||||
\(917\) | −7.21060 | − | 4.40847i | −0.238115 | − | 0.145580i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.84221 | + | 10.1190i | 0.192717 | + | 0.333795i | 0.946150 | − | 0.323730i | \(-0.104937\pi\) |
−0.753433 | + | 0.657525i | \(0.771603\pi\) | |||||||
\(920\) | −4.08998 | + | 7.08405i | −0.134843 | + | 0.233554i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.6845 | − | 37.5587i | −0.714142 | − | 1.23693i | ||||
\(923\) | 11.7414 | 0.386474 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.8961 | 1.01586 | ||||||||
\(926\) | −13.5759 | − | 23.5141i | −0.446131 | − | 0.772721i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.132401 | + | 0.229325i | −0.00434627 | + | 0.00752797i | ||||
\(929\) | −0.730252 | − | 1.26483i | −0.0239588 | − | 0.0414979i | 0.853797 | − | 0.520605i | \(-0.174294\pi\) |
−0.877756 | + | 0.479108i | \(0.840960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0431 | − | 1.00907i | −0.656886 | − | 0.0330710i | ||||
\(932\) | 0.515158 | 0.0168745 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.9734 | + | 31.1309i | −0.588109 | + | 1.01863i | ||||
\(935\) | 0.361864 | − | 0.626767i | 0.0118342 | − | 0.0204975i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.87451 | 0.322586 | 0.161293 | − | 0.986907i | \(-0.448434\pi\) | ||||
0.161293 | + | 0.986907i | \(0.448434\pi\) | |||||||
\(938\) | 19.9122 | − | 10.8380i | 0.650155 | − | 0.353872i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.491146 | + | 0.850689i | 0.0160194 | + | 0.0277464i | ||||
\(941\) | 27.0972 | − | 46.9337i | 0.883343 | − | 1.52999i | 0.0357414 | − | 0.999361i | \(-0.488621\pi\) |
0.847601 | − | 0.530633i | \(-0.178046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5349 | + | 47.6919i | 0.896660 | + | 1.55306i | ||||
\(944\) | −34.2173 | −1.11368 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.0292 | −0.716230 | ||||||||
\(947\) | −27.4451 | − | 47.5364i | −0.891847 | − | 1.54472i | −0.837659 | − | 0.546193i | \(-0.816076\pi\) |
−0.0541875 | − | 0.998531i | \(-0.517257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.0907 | − | 43.4583i | 0.814477 | − | 1.41072i | ||||
\(950\) | 9.73025 | + | 16.8533i | 0.315691 | + | 0.546793i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0495916 | − | 1.97131i | 0.00160727 | − | 0.0638905i | ||||
\(953\) | 27.0406 | 0.875932 | 0.437966 | − | 0.898991i | \(-0.355699\pi\) | ||||
0.437966 | + | 0.898991i | \(0.355699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.60010 | − | 6.23556i | 0.116497 | − | 0.201778i | ||||
\(956\) | −0.825010 | + | 1.42896i | −0.0266827 | + | 0.0462158i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.520829 | −0.0168272 | ||||||||
\(959\) | 0.672570 | − | 26.7352i | 0.0217184 | − | 0.863326i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3384 | + | 21.3708i | 0.398014 | + | 0.689380i | ||||
\(962\) | −21.9159 | + | 37.9595i | −0.706599 | + | 1.22386i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.10195 | + | 1.90864i | 0.0354916 | + | 0.0614732i | ||||
\(965\) | 10.1872 | 0.327936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5146 | −0.434600 | −0.217300 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217300 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(968\) | 12.1283 | + | 21.0068i | 0.389818 | + | 0.675185i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.982291 | − | 1.70138i | 0.0315395 | − | 0.0546280i | ||||
\(971\) | 6.46557 | + | 11.1987i | 0.207490 | + | 0.359383i | 0.950923 | − | 0.309427i | \(-0.100137\pi\) |
−0.743433 | + | 0.668810i | \(0.766804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.0057 | − | 22.8632i | 1.34664 | − | 0.732961i | ||||
\(974\) | −18.8090 | −0.602678 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.80730 | + | 10.0585i | −0.185887 | + | 0.321966i | ||||
\(977\) | −18.2989 | + | 31.6947i | −0.585435 | + | 1.01400i | 0.409387 | + | 0.912361i | \(0.365743\pi\) |
−0.994821 | + | 0.101641i | \(0.967591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9722 | −0.766154 | ||||||||
\(980\) | 0.300194 | − | 0.464346i | 0.00958933 | − | 0.0148330i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.05574 | − | 7.02475i | −0.129424 | − | 0.224169i | ||||
\(983\) | −8.61896 | + | 14.9285i | −0.274902 | + | 0.476145i | −0.970110 | − | 0.242664i | \(-0.921979\pi\) |
0.695208 | + | 0.718808i | \(0.255312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.223055 | + | 0.386343i | 0.00710713 | + | 0.0123099i | ||||
\(986\) | −0.140661 | −0.00447956 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.72238 | −0.0547963 | ||||||||
\(989\) | 8.54523 | + | 14.8008i | 0.271722 | + | 0.470637i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.67111 | − | 13.2867i | 0.243681 | − | 0.422067i | −0.718079 | − | 0.695961i | \(-0.754978\pi\) |
0.961760 | + | 0.273894i | \(0.0883118\pi\) | |||||||
\(992\) | 0.944932 | + | 1.63667i | 0.0300016 | + | 0.0519643i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.57421 | + | 5.24216i | 0.271958 | + | 0.166271i | ||||
\(995\) | 6.11109 | 0.193735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0577 | − | 29.5448i | 0.540222 | − | 0.935692i | −0.458669 | − | 0.888607i | \(-0.651674\pi\) |
0.998891 | − | 0.0470850i | \(-0.0149932\pi\) | |||||||
\(998\) | 20.5313 | − | 35.5613i | 0.649907 | − | 1.12567i | ||||
\(999\) | 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 | 189.2.e.f.109.1 | yes | 6 | |
3.2 | odd | 2 | 189.2.e.e.109.3 | ✓ | 6 | ||
7.2 | even | 3 | inner | 189.2.e.f.163.1 | yes | 6 | |
7.3 | odd | 6 | 1323.2.a.y.1.3 | 3 | |||
7.4 | even | 3 | 1323.2.a.x.1.3 | 3 | |||
9.2 | odd | 6 | 567.2.g.h.109.3 | 6 | |||
9.4 | even | 3 | 567.2.h.h.298.3 | 6 | |||
9.5 | odd | 6 | 567.2.h.i.298.1 | 6 | |||
9.7 | even | 3 | 567.2.g.i.109.1 | 6 | |||
21.2 | odd | 6 | 189.2.e.e.163.3 | yes | 6 | ||
21.11 | odd | 6 | 1323.2.a.ba.1.1 | 3 | |||
21.17 | even | 6 | 1323.2.a.z.1.1 | 3 | |||
63.2 | odd | 6 | 567.2.h.i.352.1 | 6 | |||
63.16 | even | 3 | 567.2.h.h.352.3 | 6 | |||
63.23 | odd | 6 | 567.2.g.h.541.3 | 6 | |||
63.58 | even | 3 | 567.2.g.i.541.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.e.e.109.3 | ✓ | 6 | 3.2 | odd | 2 | ||
189.2.e.e.163.3 | yes | 6 | 21.2 | odd | 6 | ||
189.2.e.f.109.1 | yes | 6 | 1.1 | even | 1 | trivial | |
189.2.e.f.163.1 | yes | 6 | 7.2 | even | 3 | inner | |
567.2.g.h.109.3 | 6 | 9.2 | odd | 6 | |||
567.2.g.h.541.3 | 6 | 63.23 | odd | 6 | |||
567.2.g.i.109.1 | 6 | 9.7 | even | 3 | |||
567.2.g.i.541.1 | 6 | 63.58 | even | 3 | |||
567.2.h.h.298.3 | 6 | 9.4 | even | 3 | |||
567.2.h.h.352.3 | 6 | 63.16 | even | 3 | |||
567.2.h.i.298.1 | 6 | 9.5 | odd | 6 | |||
567.2.h.i.352.1 | 6 | 63.2 | odd | 6 | |||
1323.2.a.x.1.3 | 3 | 7.4 | even | 3 | |||
1323.2.a.y.1.3 | 3 | 7.3 | odd | 6 | |||
1323.2.a.z.1.1 | 3 | 21.17 | even | 6 | |||
1323.2.a.ba.1.1 | 3 | 21.11 | odd | 6 |