Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(244,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.244");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.c (of order \(3\), degree \(2\), not 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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{36})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{6} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 244.4 | ||
Root | \(-0.342020 - 0.939693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.244 |
Dual form | 729.2.c.c.487.4 |
$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.342020 | + | 0.592396i | 0.241845 | + | 0.418887i | 0.961240 | − | 0.275714i | \(-0.0889142\pi\) |
−0.719395 | + | 0.694601i | \(0.755581\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.766044 | − | 1.32683i | 0.383022 | − | 0.663414i | ||||
\(5\) | 0.524005 | − | 0.907604i | 0.234342 | − | 0.405893i | −0.724739 | − | 0.689023i | \(-0.758040\pi\) |
0.959081 | + | 0.283131i | \(0.0913730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0603074 | + | 0.104455i | 0.0227940 | + | 0.0394804i | 0.877197 | − | 0.480130i | \(-0.159410\pi\) |
−0.854403 | + | 0.519610i | \(0.826077\pi\) | |||||||
\(8\) | 2.41609 | 0.854217 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.716881 | 0.226698 | ||||||||
\(11\) | −2.71686 | − | 4.70574i | −0.819164 | − | 1.41883i | −0.906299 | − | 0.422637i | \(-0.861105\pi\) |
0.0871355 | − | 0.996196i | \(-0.472229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28699 | − | 3.96118i | 0.634297 | − | 1.09863i | −0.352367 | − | 0.935862i | \(-0.614623\pi\) |
0.986664 | − | 0.162772i | \(-0.0520435\pi\) | |||||||
\(14\) | −0.0412527 | + | 0.0714517i | −0.0110252 | + | 0.0190963i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.705737 | − | 1.22237i | −0.176434 | − | 0.305593i | ||||
\(17\) | −4.77833 | −1.15892 | −0.579458 | − | 0.815002i | \(-0.696736\pi\) | ||||
−0.579458 | + | 0.815002i | \(0.696736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.588526 | −0.135017 | −0.0675085 | − | 0.997719i | \(-0.521505\pi\) | ||||
−0.0675085 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(20\) | −0.802823 | − | 1.39053i | −0.179517 | − | 0.310932i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.85844 | − | 3.21891i | 0.396221 | − | 0.686275i | ||||
\(23\) | −3.89798 | + | 6.75150i | −0.812785 | + | 1.40778i | 0.0981231 | + | 0.995174i | \(0.468716\pi\) |
−0.910908 | + | 0.412610i | \(0.864617\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.95084 | + | 3.37895i | 0.390167 | + | 0.675790i | ||||
\(26\) | 3.12879 | 0.613605 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.184793 | 0.0349225 | ||||||||
\(29\) | 2.53487 | + | 4.39053i | 0.470714 | + | 0.815301i | 0.999439 | − | 0.0334924i | \(-0.0106630\pi\) |
−0.528725 | + | 0.848793i | \(0.677330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.37939 | − | 7.58532i | 0.786561 | − | 1.36236i | −0.141501 | − | 0.989938i | \(-0.545193\pi\) |
0.928062 | − | 0.372425i | \(-0.121474\pi\) | |||||||
\(32\) | 2.89884 | − | 5.02094i | 0.512448 | − | 0.887586i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.63429 | − | 2.83067i | −0.280278 | − | 0.485455i | ||||
\(35\) | 0.126406 | 0.0213664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.18479 | −0.359178 | −0.179589 | − | 0.983742i | \(-0.557477\pi\) | ||||
−0.179589 | + | 0.983742i | \(0.557477\pi\) | |||||||
\(38\) | −0.201288 | − | 0.348641i | −0.0326532 | − | 0.0565570i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.26604 | − | 2.19285i | 0.200179 | − | 0.346721i | ||||
\(41\) | 3.77920 | − | 6.54576i | 0.590211 | − | 1.02228i | −0.403992 | − | 0.914762i | \(-0.632378\pi\) |
0.994204 | − | 0.107514i | \(-0.0342889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.652704 | + | 1.13052i | 0.0995364 | + | 0.172402i | 0.911493 | − | 0.411316i | \(-0.134931\pi\) |
−0.811956 | + | 0.583718i | \(0.801597\pi\) | |||||||
\(44\) | −8.32494 | −1.25503 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.33275 | −0.786271 | ||||||||
\(47\) | 1.20805 | + | 2.09240i | 0.176212 | + | 0.305207i | 0.940580 | − | 0.339572i | \(-0.110282\pi\) |
−0.764368 | + | 0.644780i | \(0.776949\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.49273 | − | 6.04958i | 0.498961 | − | 0.864226i | ||||
\(50\) | −1.33445 | + | 2.31134i | −0.188720 | + | 0.326872i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.50387 | − | 6.06888i | −0.485899 | − | 0.841602i | ||||
\(53\) | 3.04628 | 0.418439 | 0.209219 | − | 0.977869i | \(-0.432908\pi\) | ||||
0.209219 | + | 0.977869i | \(0.432908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.69459 | −0.767859 | ||||||||
\(56\) | 0.145708 | + | 0.252374i | 0.0194711 | + | 0.0337249i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.73396 | + | 3.00330i | −0.227680 | + | 0.394352i | ||||
\(59\) | −0.0219501 | + | 0.0380187i | −0.00285766 | + | 0.00494961i | −0.867451 | − | 0.497523i | \(-0.834243\pi\) |
0.864593 | + | 0.502473i | \(0.167576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.10607 | + | 8.84397i | 0.653765 | + | 1.13235i | 0.982202 | + | 0.187828i | \(0.0601448\pi\) |
−0.328437 | + | 0.944526i | \(0.606522\pi\) | |||||||
\(62\) | 5.99135 | 0.760902 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.14290 | 0.142863 | ||||||||
\(65\) | −2.39679 | − | 4.15136i | −0.297285 | − | 0.514913i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.929892 | − | 1.61062i | 0.113604 | − | 0.196769i | −0.803617 | − | 0.595147i | \(-0.797094\pi\) |
0.917221 | + | 0.398379i | \(0.130427\pi\) | |||||||
\(68\) | −3.66041 | + | 6.34002i | −0.443890 | + | 0.768841i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0432332 | + | 0.0748822i | 0.00516736 | + | 0.00895013i | ||||
\(71\) | 6.51038 | 0.772640 | 0.386320 | − | 0.922365i | \(-0.373746\pi\) | ||||
0.386320 | + | 0.922365i | \(0.373746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2344 | 1.43193 | 0.715965 | − | 0.698136i | \(-0.245987\pi\) | ||||
0.715965 | + | 0.698136i | \(0.245987\pi\) | |||||||
\(74\) | −0.747243 | − | 1.29426i | −0.0868652 | − | 0.150455i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.450837 | + | 0.780873i | −0.0517145 | + | 0.0895722i | ||||
\(77\) | 0.327693 | − | 0.567581i | 0.0373441 | − | 0.0646819i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.351167 | − | 0.608239i | −0.0395093 | − | 0.0684322i | 0.845595 | − | 0.533826i | \(-0.179246\pi\) |
−0.885104 | + | 0.465394i | \(0.845913\pi\) | |||||||
\(80\) | −1.47924 | −0.165384 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.17024 | 0.570958 | ||||||||
\(83\) | 3.38830 | + | 5.86871i | 0.371914 | + | 0.644174i | 0.989860 | − | 0.142046i | \(-0.0453682\pi\) |
−0.617946 | + | 0.786221i | \(0.712035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.50387 | + | 4.33683i | −0.271583 | + | 0.470395i | ||||
\(86\) | −0.446476 | + | 0.773318i | −0.0481447 | + | 0.0833891i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.56418 | − | 11.3695i | −0.699744 | − | 1.21199i | ||||
\(89\) | −6.85565 | −0.726697 | −0.363349 | − | 0.931653i | \(-0.618367\pi\) | ||||
−0.363349 | + | 0.931653i | \(0.618367\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.551689 | 0.0578327 | ||||||||
\(92\) | 5.97205 | + | 10.3439i | 0.622629 | + | 1.07843i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.826352 | + | 1.43128i | −0.0852317 | + | 0.147626i | ||||
\(95\) | −0.308391 | + | 0.534148i | −0.0316402 | + | 0.0548025i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.51367 | + | 7.81791i | 0.458294 | + | 0.793788i | 0.998871 | − | 0.0475063i | \(-0.0151274\pi\) |
−0.540577 | + | 0.841294i | \(0.681794\pi\) | |||||||
\(98\) | 4.77833 | 0.482684 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.97771 | 0.597771 | ||||||||
\(101\) | 6.49605 | + | 11.2515i | 0.646382 | + | 1.11957i | 0.983981 | + | 0.178276i | \(0.0570519\pi\) |
−0.337599 | + | 0.941290i | \(0.609615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.53596 | + | 7.85651i | −0.446941 | + | 0.774125i | −0.998185 | − | 0.0602191i | \(-0.980820\pi\) |
0.551244 | + | 0.834344i | \(0.314153\pi\) | |||||||
\(104\) | 5.52557 | − | 9.57057i | 0.541827 | − | 0.938472i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.04189 | + | 1.80460i | 0.101197 | + | 0.175279i | ||||
\(107\) | −11.3865 | −1.10077 | −0.550386 | − | 0.834911i | \(-0.685519\pi\) | ||||
−0.550386 | + | 0.834911i | \(0.685519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.89899 | 0.277672 | 0.138836 | − | 0.990315i | \(-0.455664\pi\) | ||||
0.138836 | + | 0.990315i | \(0.455664\pi\) | |||||||
\(110\) | −1.94767 | − | 3.37346i | −0.185703 | − | 0.321646i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0851223 | − | 0.147436i | 0.00804330 | − | 0.0139314i | ||||
\(113\) | −5.79006 | + | 10.0287i | −0.544683 | + | 0.943419i | 0.453943 | + | 0.891031i | \(0.350017\pi\) |
−0.998627 | + | 0.0523888i | \(0.983316\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.08512 | + | 7.07564i | 0.380940 | + | 0.659807i | ||||
\(116\) | 7.76730 | 0.721176 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0300295 | −0.00276444 | ||||||||
\(119\) | −0.288169 | − | 0.499123i | −0.0264164 | − | 0.0457545i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.26264 | + | 16.0434i | −0.842058 | + | 1.45849i | ||||
\(122\) | −3.49276 | + | 6.04963i | −0.316219 | + | 0.547708i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.70961 | − | 11.6214i | −0.602541 | − | 1.04363i | ||||
\(125\) | 9.32905 | 0.834415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4192 | −1.36823 | −0.684117 | − | 0.729372i | \(-0.739812\pi\) | ||||
−0.684117 | + | 0.729372i | \(0.739812\pi\) | |||||||
\(128\) | −5.40679 | − | 9.36484i | −0.477897 | − | 0.827742i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.63950 | − | 2.83970i | 0.143794 | − | 0.249058i | ||||
\(131\) | 6.67804 | − | 11.5667i | 0.583463 | − | 1.01059i | −0.411602 | − | 0.911364i | \(-0.635031\pi\) |
0.995065 | − | 0.0992240i | \(-0.0316360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0354925 | − | 0.0614747i | −0.00307759 | − | 0.00533054i | ||||
\(134\) | 1.27217 | 0.109899 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.5449 | −0.989965 | ||||||||
\(137\) | −9.81180 | − | 16.9945i | −0.838279 | − | 1.45194i | −0.891333 | − | 0.453350i | \(-0.850229\pi\) |
0.0530541 | − | 0.998592i | \(-0.483104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.15317 | + | 14.1217i | −0.691543 | + | 1.19779i | 0.279789 | + | 0.960061i | \(0.409735\pi\) |
−0.971332 | + | 0.237726i | \(0.923598\pi\) | |||||||
\(140\) | 0.0968323 | − | 0.167718i | 0.00818382 | − | 0.0141748i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.22668 | + | 3.85673i | 0.186859 | + | 0.323649i | ||||
\(143\) | −24.8537 | −2.07837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.31315 | 0.441233 | ||||||||
\(146\) | 4.18442 | + | 7.24763i | 0.346305 | + | 0.599818i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.67365 | + | 2.89884i | −0.137573 | + | 0.238283i | ||||
\(149\) | 5.52385 | − | 9.56758i | 0.452531 | − | 0.783807i | −0.546011 | − | 0.837778i | \(-0.683854\pi\) |
0.998543 | + | 0.0539709i | \(0.0171878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.40033 | + | 5.88954i | 0.276715 | + | 0.479284i | 0.970566 | − | 0.240834i | \(-0.0774209\pi\) |
−0.693851 | + | 0.720118i | \(0.744088\pi\) | |||||||
\(152\) | −1.42193 | −0.115334 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.448311 | 0.0361259 | ||||||||
\(155\) | −4.58964 | − | 7.94949i | −0.368649 | − | 0.638519i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.44356 | + | 14.6247i | −0.673870 | + | 1.16718i | 0.302928 | + | 0.953013i | \(0.402036\pi\) |
−0.976798 | + | 0.214163i | \(0.931298\pi\) | |||||||
\(158\) | 0.240212 | − | 0.416060i | 0.0191103 | − | 0.0330999i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.03802 | − | 5.26200i | −0.240176 | − | 0.415998i | ||||
\(161\) | −0.940307 | −0.0741066 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.41147 | 0.658838 | 0.329419 | − | 0.944184i | \(-0.393147\pi\) | ||||
0.329419 | + | 0.944184i | \(0.393147\pi\) | |||||||
\(164\) | −5.79006 | − | 10.0287i | −0.452128 | − | 0.783109i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.31773 | + | 4.01443i | −0.179891 | + | 0.311580i | ||||
\(167\) | −1.31250 | + | 2.27332i | −0.101564 | + | 0.175915i | −0.912329 | − | 0.409457i | \(-0.865718\pi\) |
0.810765 | + | 0.585372i | \(0.199051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.96064 | − | 6.86002i | −0.304664 | − | 0.527694i | ||||
\(170\) | −3.42550 | −0.262724 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 6.55163 | + | 11.3478i | 0.498112 | + | 0.862754i | 0.999998 | − | 0.00217926i | \(-0.000693680\pi\) |
−0.501886 | + | 0.864934i | \(0.667360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.235300 | + | 0.407551i | −0.0177870 | + | 0.0308080i | ||||
\(176\) | −3.83478 | + | 6.64203i | −0.289057 | + | 0.500662i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.34477 | − | 4.06126i | −0.175748 | − | 0.304404i | ||||
\(179\) | 22.0988 | 1.65174 | 0.825872 | − | 0.563857i | \(-0.190683\pi\) | ||||
0.825872 | + | 0.563857i | \(0.190683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.05913 | −0.153054 | −0.0765268 | − | 0.997068i | \(-0.524383\pi\) | ||||
−0.0765268 | + | 0.997068i | \(0.524383\pi\) | |||||||
\(182\) | 0.188689 | + | 0.326819i | 0.0139865 | + | 0.0242254i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.41787 | + | 16.3122i | −0.694295 | + | 1.20255i | ||||
\(185\) | −1.14484 | + | 1.98293i | −0.0841705 | + | 0.145788i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9820 | + | 22.4856i | 0.949341 | + | 1.64431i | ||||
\(188\) | 3.70167 | 0.269972 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.421903 | −0.0306081 | ||||||||
\(191\) | −1.97459 | − | 3.42009i | −0.142876 | − | 0.247469i | 0.785702 | − | 0.618605i | \(-0.212302\pi\) |
−0.928579 | + | 0.371136i | \(0.878968\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.22328 | − | 7.31493i | 0.303998 | − | 0.526540i | −0.673040 | − | 0.739606i | \(-0.735012\pi\) |
0.977038 | + | 0.213066i | \(0.0683450\pi\) | |||||||
\(194\) | −3.08753 | + | 5.34776i | −0.221672 | + | 0.383947i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.35117 | − | 9.26849i | −0.382226 | − | 0.662035i | ||||
\(197\) | 2.29498 | 0.163511 | 0.0817553 | − | 0.996652i | \(-0.473947\pi\) | ||||
0.0817553 | + | 0.996652i | \(0.473947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.5030 | −1.66608 | −0.833042 | − | 0.553210i | \(-0.813403\pi\) | ||||
−0.833042 | + | 0.553210i | \(0.813403\pi\) | |||||||
\(200\) | 4.71340 | + | 8.16385i | 0.333288 | + | 0.577271i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.44356 | + | 7.69648i | −0.312648 | + | 0.541522i | ||||
\(203\) | −0.305743 | + | 0.529563i | −0.0214590 | + | 0.0371680i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.96064 | − | 6.86002i | −0.276623 | − | 0.479125i | ||||
\(206\) | −6.20556 | −0.432362 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.45605 | −0.447647 | ||||||||
\(209\) | 1.59894 | + | 2.76945i | 0.110601 | + | 0.191567i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.833626 | − | 1.44388i | 0.0573892 | − | 0.0994010i | −0.835904 | − | 0.548876i | \(-0.815056\pi\) |
0.893293 | + | 0.449475i | \(0.148389\pi\) | |||||||
\(212\) | 2.33359 | − | 4.04189i | 0.160271 | − | 0.277598i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.89440 | − | 6.74530i | −0.266216 | − | 0.461099i | ||||
\(215\) | 1.36808 | 0.0933023 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.05644 | 0.0717156 | ||||||||
\(218\) | 0.991511 | + | 1.71735i | 0.0671536 | + | 0.116313i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.36231 | + | 7.55574i | −0.294107 | + | 0.509408i | ||||
\(221\) | −10.9280 | + | 18.9278i | −0.735096 | + | 1.27322i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.90033 | + | 8.48762i | 0.328150 | + | 0.568373i | 0.982145 | − | 0.188126i | \(-0.0602414\pi\) |
−0.653995 | + | 0.756499i | \(0.726908\pi\) | |||||||
\(224\) | 0.699287 | 0.0467231 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.92127 | −0.526915 | ||||||||
\(227\) | −7.74038 | − | 13.4067i | −0.513747 | − | 0.889836i | −0.999873 | − | 0.0159469i | \(-0.994924\pi\) |
0.486126 | − | 0.873889i | \(-0.338410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.62701 | − | 9.74627i | 0.371843 | − | 0.644052i | −0.618006 | − | 0.786174i | \(-0.712059\pi\) |
0.989849 | + | 0.142122i | \(0.0453925\pi\) | |||||||
\(230\) | −2.79439 | + | 4.84002i | −0.184257 | + | 0.319142i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.12449 | + | 10.6079i | 0.402092 | + | 0.696444i | ||||
\(233\) | 5.23476 | 0.342940 | 0.171470 | − | 0.985189i | \(-0.445148\pi\) | ||||
0.171470 | + | 0.985189i | \(0.445148\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.53209 | 0.165175 | ||||||||
\(236\) | 0.0336295 | + | 0.0582480i | 0.00218909 | + | 0.00379162i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.197119 | − | 0.341420i | 0.0127773 | − | 0.0221310i | ||||
\(239\) | 5.15490 | − | 8.92855i | 0.333443 | − | 0.577540i | −0.649742 | − | 0.760155i | \(-0.725123\pi\) |
0.983184 | + | 0.182615i | \(0.0584563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.37211 | − | 9.30477i | −0.346048 | − | 0.599373i | 0.639496 | − | 0.768795i | \(-0.279143\pi\) |
−0.985544 | + | 0.169422i | \(0.945810\pi\) | |||||||
\(242\) | −12.6720 | −0.814590 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.6459 | 1.00163 | ||||||||
\(245\) | −3.66041 | − | 6.34002i | −0.233855 | − | 0.405049i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.34595 | + | 2.33126i | −0.0856409 | + | 0.148334i | ||||
\(248\) | 10.5810 | − | 18.3268i | 0.671894 | − | 1.16375i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.19072 | + | 5.52649i | 0.201799 | + | 0.349526i | ||||
\(251\) | 15.0729 | 0.951392 | 0.475696 | − | 0.879610i | \(-0.342196\pi\) | ||||
0.475696 | + | 0.879610i | \(0.342196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.3610 | 2.66321 | ||||||||
\(254\) | −5.27368 | − | 9.13429i | −0.330900 | − | 0.573136i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.84137 | − | 8.38549i | 0.302585 | − | 0.524093i | ||||
\(257\) | 1.66122 | − | 2.87733i | 0.103624 | − | 0.179483i | −0.809551 | − | 0.587050i | \(-0.800289\pi\) |
0.913175 | + | 0.407567i | \(0.133623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.131759 | − | 0.228213i | −0.00818711 | − | 0.0141805i | ||||
\(260\) | −7.34419 | −0.455467 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.13610 | 0.564430 | ||||||||
\(263\) | −4.41934 | − | 7.65451i | −0.272508 | − | 0.471998i | 0.696995 | − | 0.717076i | \(-0.254520\pi\) |
−0.969503 | + | 0.245078i | \(0.921186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.59627 | − | 2.76481i | 0.0980579 | − | 0.169841i | ||||
\(266\) | 0.0242783 | − | 0.0420512i | 0.00148860 | − | 0.00257832i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.42468 | − | 2.46761i | −0.0870261 | − | 0.150734i | ||||
\(269\) | 8.09267 | 0.493419 | 0.246709 | − | 0.969090i | \(-0.420651\pi\) | ||||
0.246709 | + | 0.969090i | \(0.420651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0000 | −1.15417 | −0.577084 | − | 0.816685i | \(-0.695809\pi\) | ||||
−0.577084 | + | 0.816685i | \(0.695809\pi\) | |||||||
\(272\) | 3.37225 | + | 5.84090i | 0.204472 | + | 0.354157i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.71167 | − | 11.6249i | 0.405467 | − | 0.702289i | ||||
\(275\) | 10.6003 | − | 18.3603i | 0.639222 | − | 1.10716i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.11468 | + | 3.66274i | 0.127059 | + | 0.220073i | 0.922536 | − | 0.385911i | \(-0.126113\pi\) |
−0.795477 | + | 0.605984i | \(0.792780\pi\) | |||||||
\(278\) | −11.1542 | −0.668984 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.305407 | 0.0182516 | ||||||||
\(281\) | −3.65106 | − | 6.32383i | −0.217804 | − | 0.377248i | 0.736332 | − | 0.676620i | \(-0.236556\pi\) |
−0.954136 | + | 0.299372i | \(0.903223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.01027 | + | 13.8742i | −0.476161 | + | 0.824735i | −0.999627 | − | 0.0273116i | \(-0.991305\pi\) |
0.523466 | + | 0.852047i | \(0.324639\pi\) | |||||||
\(284\) | 4.98724 | − | 8.63816i | 0.295938 | − | 0.512580i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.50047 | − | 14.7232i | −0.502643 | − | 0.870603i | ||||
\(287\) | 0.911654 | 0.0538132 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.83244 | 0.343085 | ||||||||
\(290\) | 1.81720 | + | 3.14749i | 0.106710 | + | 0.184827i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.37211 | − | 16.2330i | 0.548461 | − | 0.949963i | ||||
\(293\) | −9.00227 | + | 15.5924i | −0.525918 | + | 0.910918i | 0.473626 | + | 0.880726i | \(0.342945\pi\) |
−0.999544 | + | 0.0301913i | \(0.990388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0230039 | + | 0.0398440i | 0.00133934 | + | 0.00231981i | ||||
\(296\) | −5.27866 | −0.306816 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.55707 | 0.437769 | ||||||||
\(299\) | 17.8293 | + | 30.8812i | 1.03109 | + | 1.78591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0787257 | + | 0.136357i | −0.00453767 | + | 0.00785948i | ||||
\(302\) | −2.32596 | + | 4.02869i | −0.133844 | + | 0.231825i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.415345 | + | 0.719398i | 0.0238216 | + | 0.0412603i | ||||
\(305\) | 10.7024 | 0.612819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5107 | −0.771098 | −0.385549 | − | 0.922687i | \(-0.625988\pi\) | ||||
−0.385549 | + | 0.922687i | \(0.625988\pi\) | |||||||
\(308\) | −0.502055 | − | 0.869585i | −0.0286072 | − | 0.0495492i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.13950 | − | 5.43777i | 0.178312 | − | 0.308845i | ||||
\(311\) | −8.21113 | + | 14.2221i | −0.465611 | + | 0.806461i | −0.999229 | − | 0.0392643i | \(-0.987499\pi\) |
0.533618 | + | 0.845725i | \(0.320832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.78240 | + | 16.9436i | 0.552934 | + | 0.957710i | 0.998061 | + | 0.0622425i | \(0.0198252\pi\) |
−0.445127 | + | 0.895467i | \(0.646841\pi\) | |||||||
\(314\) | −11.5515 | −0.651887 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.07604 | −0.0605318 | ||||||||
\(317\) | 12.1893 | + | 21.1125i | 0.684619 | + | 1.18579i | 0.973557 | + | 0.228446i | \(0.0733645\pi\) |
−0.288938 | + | 0.957348i | \(0.593302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7738 | − | 23.8569i | 0.771184 | − | 1.33573i | ||||
\(320\) | 0.598887 | − | 1.03730i | 0.0334788 | − | 0.0579870i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.321604 | − | 0.557035i | −0.0179223 | − | 0.0310423i | ||||
\(323\) | 2.81217 | 0.156473 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.8462 | 0.989927 | ||||||||
\(326\) | 2.87689 | + | 4.98293i | 0.159336 | + | 0.275979i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.13088 | − | 15.8152i | 0.504169 | − | 0.873246i | ||||
\(329\) | −0.145708 | + | 0.252374i | −0.00803315 | + | 0.0139138i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.2494 | − | 24.6807i | −0.783220 | − | 1.35658i | −0.930057 | − | 0.367416i | \(-0.880243\pi\) |
0.146837 | − | 0.989161i | \(-0.453091\pi\) | |||||||
\(332\) | 10.3824 | 0.569806 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.79561 | −0.0982512 | ||||||||
\(335\) | −0.974537 | − | 1.68795i | −0.0532446 | − | 0.0922224i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.72328 | − | 15.1092i | 0.475187 | − | 0.823048i | −0.524409 | − | 0.851467i | \(-0.675714\pi\) |
0.999596 | + | 0.0284181i | \(0.00904699\pi\) | |||||||
\(338\) | 2.70924 | − | 4.69253i | 0.147363 | − | 0.255240i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.83615 | + | 6.64441i | 0.208045 | + | 0.360344i | ||||
\(341\) | −47.5927 | −2.57729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.68685 | 0.0910814 | ||||||||
\(344\) | 1.57699 | + | 2.73143i | 0.0850257 | + | 0.147269i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.48158 | + | 7.76233i | −0.240931 | + | 0.417305i | ||||
\(347\) | −12.5945 | + | 21.8143i | −0.676109 | + | 1.17105i | 0.300035 | + | 0.953928i | \(0.403002\pi\) |
−0.976144 | + | 0.217126i | \(0.930332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.92602 | + | 10.2642i | 0.317213 | + | 0.549428i | 0.979905 | − | 0.199463i | \(-0.0639198\pi\) |
−0.662693 | + | 0.748891i | \(0.730586\pi\) | |||||||
\(350\) | −0.321909 | −0.0172068 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −31.5030 | −1.67912 | ||||||||
\(353\) | 4.19875 | + | 7.27244i | 0.223477 | + | 0.387073i | 0.955861 | − | 0.293818i | \(-0.0949260\pi\) |
−0.732385 | + | 0.680891i | \(0.761593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41147 | − | 5.90885i | 0.181062 | − | 0.313609i | ||||
\(356\) | −5.25173 | + | 9.09627i | −0.278341 | + | 0.482101i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.55825 | + | 13.0913i | 0.399466 | + | 0.691895i | ||||
\(359\) | 2.64025 | 0.139347 | 0.0696735 | − | 0.997570i | \(-0.477804\pi\) | ||||
0.0696735 | + | 0.997570i | \(0.477804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6536 | −0.981770 | ||||||||
\(362\) | −0.704262 | − | 1.21982i | −0.0370152 | − | 0.0641122i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.422618 | − | 0.731997i | 0.0221512 | − | 0.0383671i | ||||
\(365\) | 6.41090 | − | 11.1040i | 0.335562 | − | 0.581210i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.59879 | − | 7.96534i | −0.240055 | − | 0.415788i | 0.720675 | − | 0.693273i | \(-0.243832\pi\) |
−0.960730 | + | 0.277486i | \(0.910499\pi\) | |||||||
\(368\) | 11.0038 | 0.573612 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.56624 | −0.0814248 | ||||||||
\(371\) | 0.183713 | + | 0.318201i | 0.00953791 | + | 0.0165201i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3956 | − | 23.2018i | 0.693597 | − | 1.20135i | −0.277054 | − | 0.960854i | \(-0.589358\pi\) |
0.970651 | − | 0.240491i | \(-0.0773084\pi\) | |||||||
\(374\) | −8.88024 | + | 15.3810i | −0.459186 | + | 0.795334i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.91875 | + | 5.05542i | 0.150523 | + | 0.260713i | ||||
\(377\) | 23.1889 | 1.19429 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.1242 | −1.39328 | −0.696639 | − | 0.717422i | \(-0.745322\pi\) | ||||
−0.696639 | + | 0.717422i | \(0.745322\pi\) | |||||||
\(380\) | 0.472482 | + | 0.818363i | 0.0242378 | + | 0.0419811i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.35070 | − | 2.33948i | 0.0691078 | − | 0.119698i | ||||
\(383\) | 17.2134 | − | 29.8145i | 0.879564 | − | 1.52345i | 0.0277437 | − | 0.999615i | \(-0.491168\pi\) |
0.851820 | − | 0.523834i | \(-0.175499\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.343426 | − | 0.594831i | −0.0175026 | − | 0.0303154i | ||||
\(386\) | 5.77778 | 0.294081 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.8307 | 0.702147 | ||||||||
\(389\) | 0.378297 | + | 0.655230i | 0.0191804 | + | 0.0332215i | 0.875456 | − | 0.483297i | \(-0.160561\pi\) |
−0.856276 | + | 0.516519i | \(0.827228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.6258 | − | 32.2609i | 0.941949 | − | 1.63150i | ||||
\(392\) | 8.43874 | − | 14.6163i | 0.426221 | − | 0.738236i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.784930 | + | 1.35954i | 0.0395442 | + | 0.0684925i | ||||
\(395\) | −0.736053 | −0.0370348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00774 | 0.351708 | 0.175854 | − | 0.984416i | \(-0.443731\pi\) | ||||
0.175854 | + | 0.984416i | \(0.443731\pi\) | |||||||
\(398\) | −8.03850 | − | 13.9231i | −0.402933 | − | 0.697901i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.75356 | − | 4.76930i | 0.137678 | − | 0.238465i | ||||
\(401\) | −4.72540 | + | 8.18463i | −0.235975 | + | 0.408721i | −0.959556 | − | 0.281519i | \(-0.909162\pi\) |
0.723580 | + | 0.690240i | \(0.242495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.0312 | − | 34.6951i | −0.997826 | − | 1.72828i | ||||
\(404\) | 19.9051 | 0.990314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.418281 | −0.0207590 | ||||||||
\(407\) | 5.93577 | + | 10.2811i | 0.294225 | + | 0.509613i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.75877 | + | 4.77833i | −0.136412 | + | 0.236273i | −0.926136 | − | 0.377189i | \(-0.876891\pi\) |
0.789724 | + | 0.613463i | \(0.210224\pi\) | |||||||
\(410\) | 2.70924 | − | 4.69253i | 0.133800 | − | 0.231748i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.94949 | + | 12.0369i | 0.342377 | + | 0.593014i | ||||
\(413\) | −0.00529501 | −0.000260550 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.10195 | 0.348621 | ||||||||
\(416\) | −13.2592 | − | 22.9657i | −0.650088 | − | 1.12599i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.09374 | + | 1.89441i | −0.0534966 | + | 0.0926588i | ||||
\(419\) | −0.233189 | + | 0.403895i | −0.0113920 | + | 0.0197316i | −0.871665 | − | 0.490102i | \(-0.836960\pi\) |
0.860273 | + | 0.509833i | \(0.170293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.20708 | + | 2.09073i | 0.0588295 | + | 0.101896i | 0.893940 | − | 0.448186i | \(-0.147930\pi\) |
−0.835111 | + | 0.550082i | \(0.814596\pi\) | |||||||
\(422\) | 1.14047 | 0.0555171 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.36009 | 0.357438 | ||||||||
\(425\) | −9.32174 | − | 16.1457i | −0.452171 | − | 0.783183i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.615867 | + | 1.06671i | −0.0298039 | + | 0.0516219i | ||||
\(428\) | −8.72254 | + | 15.1079i | −0.421620 | + | 0.730267i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.467911 | + | 0.810446i | 0.0225647 | + | 0.0390832i | ||||
\(431\) | −12.0992 | −0.582796 | −0.291398 | − | 0.956602i | \(-0.594120\pi\) | ||||
−0.291398 | + | 0.956602i | \(0.594120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.3509 | 1.60274 | 0.801371 | − | 0.598167i | \(-0.204104\pi\) | ||||
0.801371 | + | 0.598167i | \(0.204104\pi\) | |||||||
\(434\) | 0.361323 | + | 0.625829i | 0.0173440 | + | 0.0300408i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.22075 | − | 3.84645i | 0.106355 | − | 0.184212i | ||||
\(437\) | 2.29406 | − | 3.97343i | 0.109740 | − | 0.190075i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.52229 | + | 7.83283i | 0.215837 | + | 0.373841i | 0.953531 | − | 0.301294i | \(-0.0974187\pi\) |
−0.737694 | + | 0.675135i | \(0.764085\pi\) | |||||||
\(440\) | −13.7587 | −0.655918 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.9504 | −0.711117 | ||||||||
\(443\) | 2.33856 | + | 4.05051i | 0.111108 | + | 0.192445i | 0.916217 | − | 0.400681i | \(-0.131227\pi\) |
−0.805109 | + | 0.593127i | \(0.797893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.59240 | + | 6.22221i | −0.170296 | + | 0.294961i | ||||
\(446\) | −3.35202 | + | 5.80587i | −0.158723 | + | 0.274916i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0689255 | + | 0.119382i | 0.00325642 | + | 0.00564029i | ||||
\(449\) | −26.7069 | −1.26037 | −0.630187 | − | 0.776443i | \(-0.717022\pi\) | ||||
−0.630187 | + | 0.776443i | \(0.717022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.0702 | −1.93392 | ||||||||
\(452\) | 8.87089 | + | 15.3648i | 0.417252 | + | 0.722701i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.29473 | − | 9.17074i | 0.248494 | − | 0.430404i | ||||
\(455\) | 0.289088 | − | 0.500715i | 0.0135527 | − | 0.0234739i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.328878 | + | 0.569633i | 0.0153843 | + | 0.0266463i | 0.873615 | − | 0.486618i | \(-0.161770\pi\) |
−0.858231 | + | 0.513264i | \(0.828436\pi\) | |||||||
\(458\) | 7.69820 | 0.359713 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.5175 | 0.583633 | ||||||||
\(461\) | −10.3519 | − | 17.9299i | −0.482134 | − | 0.835081i | 0.517655 | − | 0.855589i | \(-0.326805\pi\) |
−0.999790 | + | 0.0205082i | \(0.993472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4119 | − | 21.4981i | 0.576832 | − | 0.999102i | −0.419008 | − | 0.907982i | \(-0.637622\pi\) |
0.995840 | − | 0.0911195i | \(-0.0290445\pi\) | |||||||
\(464\) | 3.57791 | − | 6.19712i | 0.166100 | − | 0.287694i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.79039 | + | 3.10105i | 0.0829383 | + | 0.143653i | ||||
\(467\) | 26.6729 | 1.23428 | 0.617138 | − | 0.786855i | \(-0.288292\pi\) | ||||
0.617138 | + | 0.786855i | \(0.288292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.224318 | 0.0103580 | ||||||||
\(470\) | 0.866025 | + | 1.50000i | 0.0399468 | + | 0.0691898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0530334 | + | 0.0918566i | −0.00244106 | + | 0.00422804i | ||||
\(473\) | 3.54661 | − | 6.14290i | 0.163073 | − | 0.282451i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.14812 | − | 1.98860i | −0.0526793 | − | 0.0912432i | ||||
\(476\) | −0.883000 | −0.0404722 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.05232 | 0.322566 | ||||||||
\(479\) | 1.61327 | + | 2.79426i | 0.0737121 | + | 0.127673i | 0.900525 | − | 0.434803i | \(-0.143182\pi\) |
−0.826813 | + | 0.562476i | \(0.809849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.99660 | + | 8.65436i | −0.227825 | + | 0.394605i | ||||
\(482\) | 3.67474 | − | 6.36484i | 0.167380 | − | 0.289910i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.1912 | + | 24.5799i | 0.645054 | + | 1.11727i | ||||
\(485\) | 9.46075 | 0.429590 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.77930 | −0.352514 | −0.176257 | − | 0.984344i | \(-0.556399\pi\) | ||||
−0.176257 | + | 0.984344i | \(0.556399\pi\) | |||||||
\(488\) | 12.3367 | + | 21.3678i | 0.558457 | + | 0.967276i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.50387 | − | 4.33683i | 0.113113 | − | 0.195918i | ||||
\(491\) | −8.52298 | + | 14.7622i | −0.384637 | + | 0.666210i | −0.991719 | − | 0.128429i | \(-0.959007\pi\) |
0.607082 | + | 0.794639i | \(0.292340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.1125 | − | 20.9794i | −0.545518 | − | 0.944865i | ||||
\(494\) | −1.84137 | −0.0828472 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.3628 | −0.555105 | ||||||||
\(497\) | 0.392624 | + | 0.680045i | 0.0176116 | + | 0.0305042i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.96538 | + | 6.86825i | −0.177515 | + | 0.307465i | −0.941029 | − | 0.338327i | \(-0.890139\pi\) |
0.763514 | + | 0.645792i | \(0.223472\pi\) | |||||||
\(500\) | 7.14647 | − | 12.3780i | 0.319600 | − | 0.553563i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.15523 | + | 8.92912i | 0.230089 | + | 0.398526i | ||||
\(503\) | 24.9496 | 1.11245 | 0.556224 | − | 0.831032i | \(-0.312250\pi\) | ||||
0.556224 | + | 0.831032i | \(0.312250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6159 | 0.605898 | ||||||||
\(506\) | 14.4883 | + | 25.0945i | 0.644085 | + | 1.11559i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.8118 | + | 20.4586i | −0.524064 | + | 0.907706i | ||||
\(509\) | 20.2345 | − | 35.0472i | 0.896878 | − | 1.55344i | 0.0654147 | − | 0.997858i | \(-0.479163\pi\) |
0.831463 | − | 0.555580i | \(-0.187504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.737826 | + | 1.27795i | 0.0326395 | + | 0.0565333i | ||||
\(512\) | −15.0038 | −0.663080 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.27269 | 0.100244 | ||||||||
\(515\) | 4.75373 | + | 8.23371i | 0.209475 | + | 0.362820i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.56418 | − | 11.3695i | 0.288692 | − | 0.500030i | ||||
\(518\) | 0.0901285 | − | 0.156107i | 0.00396002 | − | 0.00685896i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.79086 | − | 10.0301i | −0.253946 | − | 0.439847i | ||||
\(521\) | 25.3674 | 1.11137 | 0.555684 | − | 0.831394i | \(-0.312457\pi\) | ||||
0.555684 | + | 0.831394i | \(0.312457\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7219 | 0.556291 | 0.278146 | − | 0.960539i | \(-0.410280\pi\) | ||||
0.278146 | + | 0.960539i | \(0.410280\pi\) | |||||||
\(524\) | −10.2314 | − | 17.7212i | −0.446959 | − | 0.774155i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.02300 | − | 5.23600i | 0.131809 | − | 0.228300i | ||||
\(527\) | −20.9262 | + | 36.2452i | −0.911557 | + | 1.57886i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8885 | − | 32.7158i | −0.821238 | − | 1.42243i | ||||
\(530\) | 2.18382 | 0.0948591 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.108755 | −0.00471514 | ||||||||
\(533\) | −17.2860 | − | 29.9402i | −0.748738 | − | 1.29685i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.96657 | + | 10.3344i | −0.257957 | + | 0.446795i | ||||
\(536\) | 2.24670 | − | 3.89141i | 0.0970429 | − | 0.168083i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.76786 | + | 4.79407i | 0.119331 | + | 0.206687i | ||||
\(539\) | −37.9570 | −1.63492 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.09327 | 0.0899969 | 0.0449984 | − | 0.998987i | \(-0.485672\pi\) | ||||
0.0449984 | + | 0.998987i | \(0.485672\pi\) | |||||||
\(542\) | −6.49838 | − | 11.2555i | −0.279129 | − | 0.483466i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.8516 | + | 23.9917i | −0.593884 | + | 1.02864i | ||||
\(545\) | 1.51908 | − | 2.63113i | 0.0650704 | − | 0.112705i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.72550 | − | 2.98865i | −0.0737770 | − | 0.127786i | 0.826777 | − | 0.562530i | \(-0.190172\pi\) |
−0.900554 | + | 0.434745i | \(0.856839\pi\) | |||||||
\(548\) | −30.0651 | −1.28432 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.5021 | 0.618370 | ||||||||
\(551\) | −1.49184 | − | 2.58394i | −0.0635545 | − | 0.110080i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0423559 | − | 0.0733626i | 0.00180116 | − | 0.00311969i | ||||
\(554\) | −1.44653 | + | 2.50546i | −0.0614572 | + | 0.106447i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.4914 | + | 21.6357i | 0.529753 | + | 0.917558i | ||||
\(557\) | −11.1003 | −0.470337 | −0.235168 | − | 0.971955i | \(-0.575564\pi\) | ||||
−0.235168 | + | 0.971955i | \(0.575564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.97090 | 0.252542 | ||||||||
\(560\) | −0.0892091 | − | 0.154515i | −0.00376977 | − | 0.00652944i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.49747 | − | 4.32575i | 0.105350 | − | 0.182471i | ||||
\(563\) | −12.1553 | + | 21.0537i | −0.512286 | + | 0.887306i | 0.487612 | + | 0.873060i | \(0.337868\pi\) |
−0.999899 | + | 0.0142457i | \(0.995465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.06805 | + | 10.5102i | 0.255285 | + | 0.442166i | ||||
\(566\) | −10.9587 | −0.460628 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.7297 | 0.660002 | ||||||||
\(569\) | −21.3820 | − | 37.0347i | −0.896379 | − | 1.55257i | −0.832088 | − | 0.554643i | \(-0.812855\pi\) |
−0.0642907 | − | 0.997931i | \(-0.520478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.01414 | + | 15.6129i | −0.377230 | + | 0.653381i | −0.990658 | − | 0.136369i | \(-0.956457\pi\) |
0.613428 | + | 0.789751i | \(0.289790\pi\) | |||||||
\(572\) | −19.0390 | + | 32.9766i | −0.796062 | + | 1.37882i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.311804 | + | 0.540060i | 0.0130144 | + | 0.0225417i | ||||
\(575\) | −30.4173 | −1.26849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.2763 | 1.05227 | 0.526133 | − | 0.850402i | \(-0.323641\pi\) | ||||
0.526133 | + | 0.850402i | \(0.323641\pi\) | |||||||
\(578\) | 1.99481 | + | 3.45512i | 0.0829733 | + | 0.143714i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.07011 | − | 7.04963i | 0.169002 | − | 0.292720i | ||||
\(581\) | −0.408679 | + | 0.707853i | −0.0169549 | + | 0.0293667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.27631 | − | 14.3350i | −0.342770 | − | 0.593695i | ||||
\(584\) | 29.5595 | 1.22318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.3158 | −0.508763 | ||||||||
\(587\) | −14.2827 | − | 24.7383i | −0.589508 | − | 1.02106i | −0.994297 | − | 0.106648i | \(-0.965988\pi\) |
0.404788 | − | 0.914410i | \(-0.367345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.57738 | + | 4.46416i | −0.106199 | + | 0.183942i | ||||
\(590\) | −0.0157356 | + | 0.0272549i | −0.000647825 | + | 0.00112207i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.54189 | + | 2.67063i | 0.0633713 | + | 0.109762i | ||||
\(593\) | 20.6009 | 0.845977 | 0.422989 | − | 0.906135i | \(-0.360981\pi\) | ||||
0.422989 | + | 0.906135i | \(0.360981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.604007 | −0.0247619 | ||||||||
\(596\) | −8.46302 | − | 14.6584i | −0.346659 | − | 0.600431i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.1959 | + | 21.1240i | −0.498729 | + | 0.863824i | ||||
\(599\) | 7.23740 | − | 12.5355i | 0.295712 | − | 0.512189i | −0.679438 | − | 0.733733i | \(-0.737776\pi\) |
0.975150 | + | 0.221544i | \(0.0711097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.67752 | + | 11.5658i | 0.272382 | + | 0.471779i | 0.969471 | − | 0.245205i | \(-0.0788553\pi\) |
−0.697090 | + | 0.716984i | \(0.745522\pi\) | |||||||
\(602\) | −0.107703 | −0.00438965 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4192 | 0.423952 | ||||||||
\(605\) | 9.70735 | + | 16.8136i | 0.394660 | + | 0.683571i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6065 | + | 27.0313i | −0.633450 | + | 1.09717i | 0.353392 | + | 0.935475i | \(0.385028\pi\) |
−0.986841 | + | 0.161692i | \(0.948305\pi\) | |||||||
\(608\) | −1.70604 | + | 2.95496i | −0.0691892 | + | 0.119839i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.66044 | + | 6.34008i | 0.148207 | + | 0.256702i | ||||
\(611\) | 11.0511 | 0.447082 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0651 | 1.21432 | 0.607159 | − | 0.794580i | \(-0.292309\pi\) | ||||
0.607159 | + | 0.794580i | \(0.292309\pi\) | |||||||
\(614\) | −4.62094 | − | 8.00371i | −0.186486 | − | 0.323003i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.791737 | − | 1.37133i | 0.0319000 | − | 0.0552524i | ||||
\(617\) | 21.0768 | − | 36.5061i | 0.848521 | − | 1.46968i | −0.0340062 | − | 0.999422i | \(-0.510827\pi\) |
0.882528 | − | 0.470261i | \(-0.155840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.80541 | − | 10.0553i | −0.233339 | − | 0.404155i | 0.725450 | − | 0.688275i | \(-0.241632\pi\) |
−0.958789 | + | 0.284120i | \(0.908299\pi\) | |||||||
\(620\) | −14.0635 | −0.564803 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.2335 | −0.450422 | ||||||||
\(623\) | −0.413446 | − | 0.716110i | −0.0165644 | − | 0.0286903i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.86571 | + | 8.42767i | −0.194629 | + | 0.337107i | ||||
\(626\) | −6.69156 | + | 11.5901i | −0.267448 | + | 0.463234i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.9363 | + | 22.4063i | 0.516214 | + | 0.894109i | ||||
\(629\) | 10.4397 | 0.416257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.3105 | −1.16683 | −0.583415 | − | 0.812174i | \(-0.698284\pi\) | ||||
−0.583415 | + | 0.812174i | \(0.698284\pi\) | |||||||
\(632\) | −0.848451 | − | 1.46956i | −0.0337496 | − | 0.0584560i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.33796 | + | 14.4418i | −0.331143 | + | 0.573556i | ||||
\(635\) | −8.07975 | + | 13.9945i | −0.320635 | + | 0.555356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9757 | − | 27.6706i | −0.632978 | − | 1.09635i | ||||
\(638\) | 18.8436 | 0.746027 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.3327 | −0.447966 | ||||||||
\(641\) | 15.5489 | + | 26.9315i | 0.614146 | + | 1.06373i | 0.990534 | + | 0.137270i | \(0.0438327\pi\) |
−0.376388 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.0360 | + | 36.4354i | −0.829577 | + | 1.43687i | 0.0687930 | + | 0.997631i | \(0.478085\pi\) |
−0.898370 | + | 0.439239i | \(0.855248\pi\) | |||||||
\(644\) | −0.720317 | + | 1.24763i | −0.0283845 | + | 0.0491634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.961819 | + | 1.66592i | 0.0378423 | + | 0.0655447i | ||||
\(647\) | 4.66717 | 0.183485 | 0.0917427 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917427 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.238541 | 0.00936356 | ||||||||
\(650\) | 6.10375 | + | 10.5720i | 0.239409 | + | 0.414668i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.44356 | − | 11.1606i | 0.252349 | − | 0.437082i | ||||
\(653\) | −1.56206 | + | 2.70557i | −0.0611283 | + | 0.105877i | −0.894970 | − | 0.446126i | \(-0.852803\pi\) |
0.833842 | + | 0.552004i | \(0.186137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.99866 | − | 12.1220i | −0.273460 | − | 0.473647i | ||||
\(656\) | −10.6685 | −0.416534 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.199340 | −0.00777110 | ||||||||
\(659\) | 18.7146 | + | 32.4146i | 0.729017 | + | 1.26269i | 0.957299 | + | 0.289100i | \(0.0933559\pi\) |
−0.228282 | + | 0.973595i | \(0.573311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2502 | + | 22.9499i | −0.515371 | + | 0.892649i | 0.484470 | + | 0.874808i | \(0.339013\pi\) |
−0.999841 | + | 0.0178410i | \(0.994321\pi\) | |||||||
\(662\) | 9.74719 | − | 16.8826i | 0.378835 | − | 0.656162i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.18644 | + | 14.1793i | 0.317696 | + | 0.550265i | ||||
\(665\) | −0.0743929 | −0.00288483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −39.5235 | −1.53036 | ||||||||
\(668\) | 2.01087 | + | 3.48293i | 0.0778028 | + | 0.134758i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.666623 | − | 1.15462i | 0.0257539 | − | 0.0446070i | ||||
\(671\) | 27.7449 | − | 48.0556i | 1.07108 | − | 1.85517i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.860500 | − | 1.49043i | −0.0331698 | − | 0.0574519i | 0.848964 | − | 0.528451i | \(-0.177227\pi\) |
−0.882134 | + | 0.470999i | \(0.843894\pi\) | |||||||
\(674\) | 11.9341 | 0.459686 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1361 | −0.466773 | ||||||||
\(677\) | −14.1396 | − | 24.4905i | −0.543429 | − | 0.941247i | −0.998704 | − | 0.0508957i | \(-0.983792\pi\) |
0.455275 | − | 0.890351i | \(-0.349541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.544415 | + | 0.942955i | −0.0208927 | + | 0.0361873i | ||||
\(680\) | −6.04958 | + | 10.4782i | −0.231991 | + | 0.401820i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.2777 | − | 28.1937i | −0.623304 | − | 1.07959i | ||||
\(683\) | −24.7139 | −0.945651 | −0.472825 | − | 0.881156i | \(-0.656766\pi\) | ||||
−0.472825 | + | 0.881156i | \(0.656766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.5657 | −0.785777 | ||||||||
\(686\) | 0.576937 | + | 0.999285i | 0.0220276 | + | 0.0381529i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.921274 | − | 1.59569i | 0.0351233 | − | 0.0608353i | ||||
\(689\) | 6.96681 | − | 12.0669i | 0.265414 | − | 0.459711i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.8862 | + | 37.9081i | 0.832592 | + | 1.44209i | 0.895976 | + | 0.444103i | \(0.146477\pi\) |
−0.0633838 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(692\) | 20.0754 | 0.763151 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.2303 | −0.654053 | ||||||||
\(695\) | 8.54461 | + | 14.7997i | 0.324115 | + | 0.561384i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0582 | + | 31.2778i | −0.684005 | + | 1.18473i | ||||
\(698\) | −4.05364 | + | 7.02111i | −0.153432 | + | 0.265753i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.360500 | + | 0.624404i | 0.0136256 | + | 0.0236003i | ||||
\(701\) | −14.6504 | −0.553338 | −0.276669 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276669 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.28581 | 0.0484951 | ||||||||
\(704\) | −3.10511 | − | 5.37820i | −0.117028 | − | 0.202699i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.87211 | + | 4.97464i | −0.108093 | + | 0.187223i | ||||
\(707\) | −0.783520 | + | 1.35710i | −0.0294673 | + | 0.0510389i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.53684 | − | 4.39393i | −0.0952729 | − | 0.165018i | 0.814450 | − | 0.580234i | \(-0.197039\pi\) |
−0.909722 | + | 0.415217i | \(0.863706\pi\) | |||||||
\(710\) | 4.66717 | 0.175156 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.5639 | −0.620757 | ||||||||
\(713\) | 34.1415 | + | 59.1348i | 1.27861 | + | 2.21462i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0235 | + | 22.5573i | −0.487050 | + | 0.843596i | ||||
\(716\) | 16.9287 | − | 29.3214i | 0.632655 | − | 1.09579i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.903018 | + | 1.56407i | 0.0337003 | + | 0.0583707i | ||||
\(719\) | −5.33717 | −0.199043 | −0.0995213 | − | 0.995035i | \(-0.531731\pi\) | ||||
−0.0995213 | + | 0.995035i | \(0.531731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.09421 | −0.0407504 | ||||||||
\(722\) | −6.37992 | − | 11.0503i | −0.237436 | − | 0.411251i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.57738 | + | 2.73210i | −0.0586229 | + | 0.101538i | ||||
\(725\) | −9.89025 | + | 17.1304i | −0.367315 | + | 0.636208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5599 | − | 32.1467i | −0.688348 | − | 1.19225i | −0.972372 | − | 0.233437i | \(-0.925003\pi\) |
0.284023 | − | 0.958817i | \(-0.408331\pi\) | |||||||
\(728\) | 1.33293 | 0.0494017 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.77063 | 0.324616 | ||||||||
\(731\) | −3.11883 | − | 5.40198i | −0.115354 | − | 0.199799i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9731 | + | 25.9342i | −0.553045 | + | 0.957902i | 0.445008 | + | 0.895527i | \(0.353201\pi\) |
−0.998053 | + | 0.0623753i | \(0.980132\pi\) | |||||||
\(734\) | 3.14576 | − | 5.44862i | 0.116112 | − | 0.201112i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.5993 | + | 39.1431i | 0.833020 | + | 1.44283i | ||||
\(737\) | −10.1055 | −0.372243 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.6100 | −1.05244 | −0.526218 | − | 0.850350i | \(-0.676390\pi\) | ||||
−0.526218 | + | 0.850350i | \(0.676390\pi\) | |||||||
\(740\) | 1.75400 | + | 3.03802i | 0.0644784 | + | 0.111680i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.125667 | + | 0.217662i | −0.00461339 | + | 0.00799062i | ||||
\(743\) | −24.8218 | + | 42.9926i | −0.910624 | + | 1.57725i | −0.0974381 | + | 0.995242i | \(0.531065\pi\) |
−0.813185 | + | 0.582005i | \(0.802269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.78905 | − | 10.0269i | −0.212094 | − | 0.367358i | ||||
\(746\) | 18.3262 | 0.670971 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 39.7793 | 1.45448 | ||||||||
\(749\) | −0.686688 | − | 1.18938i | −0.0250910 | − | 0.0434589i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8118 | − | 27.3868i | 0.576981 | − | 0.999360i | −0.418842 | − | 0.908059i | \(-0.637564\pi\) |
0.995823 | − | 0.0913013i | \(-0.0291026\pi\) | |||||||
\(752\) | 1.70513 | − | 2.95336i | 0.0621795 | − | 0.107698i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.93107 | + | 13.7370i | 0.288833 | + | 0.500273i | ||||
\(755\) | 7.12716 | 0.259384 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.04189 | 0.110559 | 0.0552797 | − | 0.998471i | \(-0.482395\pi\) | ||||
0.0552797 | + | 0.998471i | \(0.482395\pi\) | |||||||
\(758\) | −9.27704 | − | 16.0683i | −0.336957 | − | 0.583627i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.745100 | + | 1.29055i | −0.0270276 | + | 0.0468132i | ||||
\(761\) | −18.9642 | + | 32.8469i | −0.687450 | + | 1.19070i | 0.285210 | + | 0.958465i | \(0.407937\pi\) |
−0.972660 | + | 0.232234i | \(0.925397\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.174830 | + | 0.302815i | 0.00632928 | + | 0.0109626i | ||||
\(764\) | −6.05050 | −0.218899 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.5493 | 0.850872 | ||||||||
\(767\) | 0.100399 | + | 0.173897i | 0.00362521 | + | 0.00627904i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1939 | − | 17.6563i | 0.367601 | − | 0.636703i | −0.621589 | − | 0.783343i | \(-0.713513\pi\) |
0.989190 | + | 0.146640i | \(0.0468460\pi\) | |||||||
\(770\) | 0.234917 | − | 0.406889i | 0.00846583 | − | 0.0146632i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.47044 | − | 11.2071i | −0.232876 | − | 0.403353i | ||||
\(773\) | 24.4664 | 0.879994 | 0.439997 | − | 0.897999i | \(-0.354979\pi\) | ||||
0.439997 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.1739 | 1.22756 | ||||||||
\(776\) | 10.9054 | + | 18.8888i | 0.391482 | + | 0.678068i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.258770 | + | 0.448204i | −0.00927737 | + | 0.0160689i | ||||
\(779\) | −2.22415 | + | 3.85235i | −0.0796886 | + | 0.138025i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.6878 | − | 30.6361i | −0.632919 | − | 1.09625i | ||||
\(782\) | 25.4816 | 0.911221 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.85978 | −0.352135 | ||||||||
\(785\) | 8.84894 | + | 15.3268i | 0.315832 | + | 0.547038i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.7875 | + | 32.5408i | −0.669700 | + | 1.15996i | 0.308287 | + | 0.951293i | \(0.400244\pi\) |
−0.977988 | + | 0.208662i | \(0.933089\pi\) | |||||||
\(788\) | 1.75806 | − | 3.04504i | 0.0626282 | − | 0.108475i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.251745 | − | 0.436035i | −0.00895668 | − | 0.0155134i | ||||
\(791\) | −1.39673 | −0.0496622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.7101 | 1.65872 | ||||||||
\(794\) | 2.39679 | + | 4.15136i | 0.0850588 | + | 0.147326i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0043 | + | 31.1844i | −0.638147 | + | 1.10530i | ||||
\(797\) | −1.15247 | + | 1.99613i | −0.0408224 | + | 0.0707065i | −0.885715 | − | 0.464230i | \(-0.846331\pi\) |
0.844892 | + | 0.534936i | \(0.179664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.77244 | − | 9.99816i | −0.204214 | − | 0.353710i | ||||
\(800\) | 22.6207 | 0.799762 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.46473 | −0.228277 | ||||||||
\(803\) | −33.2392 | − | 57.5720i | −1.17299 | − | 2.03167i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.492726 | + | 0.853427i | −0.0173663 | + | 0.0300793i | ||||
\(806\) | 13.7022 | − | 23.7328i | 0.482638 | − | 0.835953i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.6951 | + | 27.1846i | 0.552150 | + | 0.956352i | ||||
\(809\) | −28.8614 | −1.01471 | −0.507356 | − | 0.861736i | \(-0.669377\pi\) | ||||
−0.507356 | + | 0.861736i | \(0.669377\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.8631 | −1.82116 | −0.910580 | − | 0.413334i | \(-0.864364\pi\) | ||||
−0.910580 | + | 0.413334i | \(0.864364\pi\) | |||||||
\(812\) | 0.468426 | + | 0.811337i | 0.0164385 | + | 0.0284723i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.06031 | + | 7.03266i | −0.142314 | + | 0.246495i | ||||
\(815\) | 4.40766 | − | 7.63429i | 0.154393 | − | 0.267417i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.384133 | − | 0.665338i | −0.0134391 | − | 0.0232772i | ||||
\(818\) | −3.77422 | −0.131963 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.1361 | −0.423811 | ||||||||
\(821\) | −9.22054 | − | 15.9704i | −0.321799 | − | 0.557372i | 0.659060 | − | 0.752090i | \(-0.270954\pi\) |
−0.980859 | + | 0.194718i | \(0.937621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3833 | − | 30.1087i | 0.605942 | − | 1.04952i | −0.385960 | − | 0.922516i | \(-0.626130\pi\) |
0.991902 | − | 0.127007i | \(-0.0405371\pi\) | |||||||
\(824\) | −10.9593 | + | 18.9820i | −0.381785 | + | 0.661271i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.00181100 | − | 0.00313674i | −6.30127e−5 | − | 0.000109141i | ||||
\(827\) | −32.7773 | −1.13978 | −0.569889 | − | 0.821722i | \(-0.693014\pi\) | ||||
−0.569889 | + | 0.821722i | \(0.693014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.35267 | 0.185906 | 0.0929530 | − | 0.995670i | \(-0.470369\pi\) | ||||
0.0929530 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(830\) | 2.42901 | + | 4.20717i | 0.0843121 | + | 0.146033i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.61381 | − | 4.52725i | 0.0906175 | − | 0.156954i | ||||
\(833\) | −16.6894 | + | 28.9069i | −0.578253 | + | 1.00156i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37551 | + | 2.38246i | 0.0476017 | + | 0.0824485i | ||||
\(836\) | 4.89944 | 0.169451 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.319022 | −0.0110204 | ||||||||
\(839\) | −2.71919 | − | 4.70977i | −0.0938768 | − | 0.162599i | 0.815263 | − | 0.579092i | \(-0.196593\pi\) |
−0.909139 | + | 0.416492i | \(0.863259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.64883 | − | 2.85586i | 0.0568563 | − | 0.0984780i | ||||
\(842\) | −0.825692 | + | 1.43014i | −0.0284552 | + | 0.0492859i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.27719 | − | 2.21216i | −0.0439627 | − | 0.0761455i | ||||
\(845\) | −8.30158 | −0.285583 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.23442 | −0.0767757 | ||||||||
\(848\) | −2.14987 | − | 3.72369i | −0.0738269 | − | 0.127872i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.37645 | − | 11.0443i | 0.218710 | − | 0.378817i | ||||
\(851\) | 8.51627 | − | 14.7506i | 0.291934 | − | 0.505645i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5586 | + | 40.8046i | 0.806629 | + | 1.39712i | 0.915185 | + | 0.403033i | \(0.132044\pi\) |
−0.108556 | + | 0.994090i | \(0.534623\pi\) | |||||||
\(854\) | −0.842556 | −0.0288317 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.5107 | −0.940298 | ||||||||
\(857\) | 23.4780 | + | 40.6651i | 0.801993 | + | 1.38909i | 0.918302 | + | 0.395880i | \(0.129560\pi\) |
−0.116309 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.58172 | + | 6.20372i | −0.122207 | + | 0.211668i | −0.920638 | − | 0.390418i | \(-0.872330\pi\) |
0.798431 | + | 0.602086i | \(0.205664\pi\) | |||||||
\(860\) | 1.04801 | − | 1.81521i | 0.0357369 | − | 0.0618981i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.13816 | − | 7.16750i | −0.140946 | − | 0.244126i | ||||
\(863\) | −35.4309 | −1.20608 | −0.603041 | − | 0.797710i | \(-0.706045\pi\) | ||||
−0.603041 | + | 0.797710i | \(0.706045\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7324 | 0.466914 | ||||||||
\(866\) | 11.4067 | + | 19.7570i | 0.387615 | + | 0.671369i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.809278 | − | 1.40171i | 0.0274687 | − | 0.0475771i | ||||
\(869\) | −1.90814 | + | 3.30500i | −0.0647292 | + | 0.112114i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.25331 | − | 7.36694i | −0.144118 | − | 0.249619i | ||||
\(872\) | 7.00421 | 0.237193 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.13846 | 0.106160 | ||||||||
\(875\) | 0.562610 | + | 0.974470i | 0.0190197 | + | 0.0329431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.08647 | + | 7.07797i | −0.137990 | + | 0.239006i | −0.926736 | − | 0.375714i | \(-0.877398\pi\) |
0.788746 | + | 0.614720i | \(0.210731\pi\) | |||||||
\(878\) | −3.09343 | + | 5.35797i | −0.104398 | + | 0.180823i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.01889 | + | 6.96091i | 0.135477 | + | 0.234652i | ||||
\(881\) | −33.2307 | −1.11957 | −0.559785 | − | 0.828638i | \(-0.689116\pi\) | ||||
−0.559785 | + | 0.828638i | \(0.689116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0479 | 1.11215 | 0.556075 | − | 0.831132i | \(-0.312307\pi\) | ||||
0.556075 | + | 0.831132i | \(0.312307\pi\) | |||||||
\(884\) | 16.7427 | + | 28.9991i | 0.563116 | + | 0.975346i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.59967 | + | 2.77071i | −0.0537420 | + | 0.0930838i | ||||
\(887\) | 24.8736 | − | 43.0823i | 0.835174 | − | 1.44656i | −0.0587148 | − | 0.998275i | \(-0.518700\pi\) |
0.893889 | − | 0.448289i | \(-0.147966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.929892 | − | 1.61062i | −0.0311876 | − | 0.0540185i | ||||
\(890\) | −4.91469 | −0.164741 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.0155 | 0.502756 | ||||||||
\(893\) | −0.710966 | − | 1.23143i | −0.0237916 | − | 0.0412082i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.5799 | − | 20.0570i | 0.387074 | − | 0.670431i | ||||
\(896\) | 0.652139 | − | 1.12954i | 0.0217864 | − | 0.0377352i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.13429 | − | 15.8210i | −0.304815 | − | 0.527955i | ||||
\(899\) | 44.4047 | 1.48098 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.5561 | −0.484935 | ||||||||
\(902\) | −14.0468 | − | 24.3298i | −0.467708 | − | 0.810094i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.9893 | + | 24.2302i | −0.465278 | + | 0.805885i | ||||
\(905\) | −1.07899 | + | 1.86887i | −0.0358669 | + | 0.0621233i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2743 | − | 29.9199i | −0.573582 | − | 0.993473i | −0.996194 | − | 0.0871627i | \(-0.972220\pi\) |
0.422612 | − | 0.906311i | \(-0.361113\pi\) | |||||||
\(908\) | −23.7179 | −0.787106 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.395496 | 0.0131106 | ||||||||
\(911\) | 6.81845 | + | 11.8099i | 0.225905 | + | 0.391280i | 0.956591 | − | 0.291435i | \(-0.0941326\pi\) |
−0.730685 | + | 0.682714i | \(0.760799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.4111 | − | 31.8889i | 0.609317 | − | 1.05537i | ||||
\(914\) | −0.224966 | + | 0.389652i | −0.00744121 | + | 0.0128886i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.62108 | − | 14.9322i | −0.284849 | − | 0.493372i | ||||
\(917\) | 1.61094 | 0.0531979 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.7701 | 1.08099 | 0.540493 | − | 0.841348i | \(-0.318238\pi\) | ||||
0.540493 | + | 0.841348i | \(0.318238\pi\) | |||||||
\(920\) | 9.87003 | + | 17.0954i | 0.325405 | + | 0.563618i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.08109 | − | 12.2648i | 0.233203 | − | 0.403920i | ||||
\(923\) | 14.8892 | − | 25.7888i | 0.490083 | − | 0.848849i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.26217 | − | 7.38230i | −0.140139 | − | 0.242729i | ||||
\(926\) | 16.9805 | 0.558015 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.3928 | 0.964866 | ||||||||
\(929\) | −2.76573 | − | 4.79039i | −0.0907408 | − | 0.157168i | 0.817082 | − | 0.576521i | \(-0.195590\pi\) |
−0.907823 | + | 0.419353i | \(0.862257\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.05556 | + | 3.56033i | −0.0673682 | + | 0.116685i | ||||
\(932\) | 4.01006 | − | 6.94562i | 0.131354 | − | 0.227511i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.12267 | + | 15.8009i | 0.298503 | + | 0.517022i | ||||
\(935\) | 27.2106 | 0.889883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.994014 | −0.0324730 | −0.0162365 | − | 0.999868i | \(-0.505168\pi\) | ||||
−0.0162365 | + | 0.999868i | \(0.505168\pi\) | |||||||
\(938\) | 0.0767211 | + | 0.132885i | 0.00250503 | + | 0.00433884i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.93969 | − | 3.35965i | 0.0632658 | − | 0.109580i | ||||
\(941\) | −5.72859 | + | 9.92221i | −0.186747 | + | 0.323455i | −0.944164 | − | 0.329477i | \(-0.893128\pi\) |
0.757417 | + | 0.652931i | \(0.226461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.4624 | + | 51.0305i | 0.959429 | + | 1.66178i | ||||
\(944\) | 0.0619640 | 0.00201676 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.85204 | 0.157754 | ||||||||
\(947\) | 22.8425 | + | 39.5644i | 0.742282 | + | 1.28567i | 0.951454 | + | 0.307791i | \(0.0995898\pi\) |
−0.209172 | + | 0.977879i | \(0.567077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.9800 | − | 48.4628i | 0.908269 | − | 1.57317i | ||||
\(950\) | 0.785359 | − | 1.36028i | 0.0254804 | − | 0.0441334i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.696242 | − | 1.20593i | −0.0225653 | − | 0.0390843i | ||||
\(953\) | −14.5053 | −0.469873 | −0.234936 | − | 0.972011i | \(-0.575488\pi\) | ||||
−0.234936 | + | 0.972011i | \(0.575488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.13878 | −0.133928 | ||||||||
\(956\) | −7.89776 | − | 13.6793i | −0.255432 | − | 0.442421i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.10354 | + | 1.91139i | −0.0356538 | + | 0.0617542i | ||||
\(959\) | 1.18345 | − | 2.04979i | 0.0382155 | − | 0.0661912i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8580 | − | 39.5913i | −0.737356 | − | 1.27714i | ||||
\(962\) | −6.83575 | −0.220393 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.4611 | −0.530176 | ||||||||
\(965\) | −4.42604 | − | 7.66613i | −0.142479 | − | 0.246781i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5184 | − | 21.6825i | 0.402565 | − | 0.697263i | −0.591470 | − | 0.806327i | \(-0.701452\pi\) |
0.994035 | + | 0.109064i | \(0.0347853\pi\) | |||||||
\(968\) | −22.3794 | + | 38.7622i | −0.719301 | + | 1.24587i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.23577 | + | 5.60451i | 0.103894 | + | 0.179950i | ||||
\(971\) | 27.0907 | 0.869383 | 0.434692 | − | 0.900579i | \(-0.356857\pi\) | ||||
0.434692 | + | 0.900579i | \(0.356857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.96679 | −0.0630522 | ||||||||
\(974\) | −2.66068 | − | 4.60843i | −0.0852536 | − | 0.147664i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.20708 | − | 12.4830i | 0.230693 | − | 0.399572i | ||||
\(977\) | 1.23670 | − | 2.14203i | 0.0395655 | − | 0.0685295i | −0.845565 | − | 0.533873i | \(-0.820736\pi\) |
0.885130 | + | 0.465344i | \(0.154069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.6258 | + | 32.2609i | 0.595284 | + | 1.03106i | ||||
\(980\) | −11.2162 | −0.358287 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.6601 | −0.372089 | ||||||||
\(983\) | −9.55401 | − | 16.5480i | −0.304726 | − | 0.527800i | 0.672475 | − | 0.740120i | \(-0.265231\pi\) |
−0.977200 | + | 0.212320i | \(0.931898\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.20258 | − | 2.08293i | 0.0383174 | − | 0.0663678i | ||||
\(986\) | 8.28541 | − | 14.3508i | 0.263861 | − | 0.457021i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.06212 | + | 3.57169i | 0.0656047 | + | 0.113631i | ||||
\(989\) | −10.1769 | −0.323607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.3164 | −1.21716 | −0.608581 | − | 0.793492i | \(-0.708261\pi\) | ||||
−0.608581 | + | 0.793492i | \(0.708261\pi\) | |||||||
\(992\) | −25.3903 | − | 43.9773i | −0.806143 | − | 1.39628i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.268571 | + | 0.465178i | −0.00851854 | + | 0.0147546i | ||||
\(995\) | −12.3157 | + | 21.3314i | −0.390434 | + | 0.676251i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6873 | − | 35.8315i | −0.655174 | − | 1.13479i | −0.981850 | − | 0.189658i | \(-0.939262\pi\) |
0.326676 | − | 0.945136i | \(-0.394071\pi\) | |||||||
\(998\) | −5.42497 | −0.171724 | ||||||||
\(999\) | 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 | 729.2.c.c.244.4 | 12 | ||
3.2 | odd | 2 | inner | 729.2.c.c.244.3 | 12 | ||
9.2 | odd | 6 | inner | 729.2.c.c.487.3 | 12 | ||
9.4 | even | 3 | 729.2.a.c.1.3 | ✓ | 6 | ||
9.5 | odd | 6 | 729.2.a.c.1.4 | yes | 6 | ||
9.7 | even | 3 | inner | 729.2.c.c.487.4 | 12 | ||
27.2 | odd | 18 | 729.2.e.q.82.2 | 12 | |||
27.4 | even | 9 | 729.2.e.q.649.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.m.163.1 | 12 | |||
27.7 | even | 9 | 729.2.e.m.568.2 | 12 | |||
27.11 | odd | 18 | 729.2.e.r.325.2 | 12 | |||
27.13 | even | 9 | 729.2.e.r.406.1 | 12 | |||
27.14 | odd | 18 | 729.2.e.r.406.2 | 12 | |||
27.16 | even | 9 | 729.2.e.r.325.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.m.568.1 | 12 | |||
27.22 | even | 9 | 729.2.e.m.163.2 | 12 | |||
27.23 | odd | 18 | 729.2.e.q.649.2 | 12 | |||
27.25 | even | 9 | 729.2.e.q.82.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.c.1.3 | ✓ | 6 | 9.4 | even | 3 | ||
729.2.a.c.1.4 | yes | 6 | 9.5 | odd | 6 | ||
729.2.c.c.244.3 | 12 | 3.2 | odd | 2 | inner | ||
729.2.c.c.244.4 | 12 | 1.1 | even | 1 | trivial | ||
729.2.c.c.487.3 | 12 | 9.2 | odd | 6 | inner | ||
729.2.c.c.487.4 | 12 | 9.7 | even | 3 | inner | ||
729.2.e.m.163.1 | 12 | 27.5 | odd | 18 | |||
729.2.e.m.163.2 | 12 | 27.22 | even | 9 | |||
729.2.e.m.568.1 | 12 | 27.20 | odd | 18 | |||
729.2.e.m.568.2 | 12 | 27.7 | even | 9 | |||
729.2.e.q.82.1 | 12 | 27.25 | even | 9 | |||
729.2.e.q.82.2 | 12 | 27.2 | odd | 18 | |||
729.2.e.q.649.1 | 12 | 27.4 | even | 9 | |||
729.2.e.q.649.2 | 12 | 27.23 | odd | 18 | |||
729.2.e.r.325.1 | 12 | 27.16 | even | 9 | |||
729.2.e.r.325.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.r.406.1 | 12 | 27.13 | even | 9 | |||
729.2.e.r.406.2 | 12 | 27.14 | odd | 18 |