Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 197.14 | ||
Character | \(\chi\) | \(=\) | 405.197 |
Dual form | 405.2.r.a.368.14 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{13}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.19031 | − | 0.191628i | 1.54878 | − | 0.135501i | 0.719566 | − | 0.694425i | \(-0.244341\pi\) |
0.829219 | + | 0.558923i | \(0.188785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.79113 | − | 0.492152i | 1.39557 | − | 0.246076i | ||||
\(5\) | 2.15257 | + | 0.605349i | 0.962658 | + | 0.270720i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.000530458 | 0 | 0.000371431i | 0.000200494 | 0 | 0.000140388i | −0.573476 | − | 0.819222i | \(-0.694405\pi\) |
0.573677 | + | 0.819082i | \(0.305517\pi\) | |||||||
\(8\) | 1.77162 | − | 0.474704i | 0.626362 | − | 0.167833i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.83080 | + | 0.913412i | 1.52763 | + | 0.288846i | ||||
\(11\) | −0.925209 | − | 2.54199i | −0.278961 | − | 0.766439i | −0.997481 | − | 0.0709326i | \(-0.977402\pi\) |
0.718520 | − | 0.695506i | \(-0.244820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.277011 | + | 3.16625i | −0.0768289 | + | 0.878159i | 0.855797 | + | 0.517313i | \(0.173068\pi\) |
−0.932625 | + | 0.360846i | \(0.882488\pi\) | |||||||
\(14\) | 0.00109069 | 0.000915200i | 0.000291500 | 0.000244597i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.53710 | + | 0.559459i | −0.384275 | + | 0.139865i | ||||
\(17\) | −6.58840 | − | 1.76536i | −1.59792 | − | 0.428162i | −0.653507 | − | 0.756921i | \(-0.726703\pi\) |
−0.944414 | + | 0.328759i | \(0.893370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.52337 | + | 0.879517i | 0.349485 | + | 0.201775i | 0.664458 | − | 0.747325i | \(-0.268662\pi\) |
−0.314974 | + | 0.949100i | \(0.601996\pi\) | |||||||
\(20\) | 6.30603 | + | 0.630218i | 1.41007 | + | 0.140921i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.51361 | − | 5.39046i | −0.535904 | − | 1.14925i | ||||
\(23\) | 2.93096 | − | 4.18584i | 0.611147 | − | 0.872808i | −0.387652 | − | 0.921806i | \(-0.626714\pi\) |
0.998799 | + | 0.0489979i | \(0.0156028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.26710 | + | 2.60611i | 0.853421 | + | 0.521222i | ||||
\(26\) | 6.98815i | 1.37049i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.00129778 | − | 0.00129778i | 0.000245257 | − | 0.000245257i | ||||
\(29\) | 4.37718 | + | 3.67289i | 0.812822 | + | 0.682038i | 0.951279 | − | 0.308330i | \(-0.0997701\pi\) |
−0.138458 | + | 0.990368i | \(0.544215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.944975 | − | 5.35922i | −0.169723 | − | 0.962544i | −0.944061 | − | 0.329772i | \(-0.893028\pi\) |
0.774338 | − | 0.632772i | \(-0.218083\pi\) | |||||||
\(32\) | −6.58407 | + | 3.07020i | −1.16391 | + | 0.542740i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.7689 | − | 2.60416i | −2.53285 | − | 0.446610i | ||||
\(35\) | 0.00136669 | 0.000478418i | 0.000231013 | 8.08674e-5i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0678960 | + | 0.253391i | −0.0111620 | + | 0.0416573i | −0.971282 | − | 0.237930i | \(-0.923531\pi\) |
0.960120 | + | 0.279587i | \(0.0901977\pi\) | |||||||
\(38\) | 3.50519 | + | 1.63450i | 0.568617 | + | 0.265151i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.10090 | + | 0.0506152i | 0.648408 | + | 0.00800297i | ||||
\(41\) | −7.56097 | − | 9.01082i | −1.18083 | − | 1.40725i | −0.893289 | − | 0.449483i | \(-0.851608\pi\) |
−0.287537 | − | 0.957770i | \(-0.592836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.67622 | + | 7.88368i | −0.560618 | + | 1.20225i | 0.397955 | + | 0.917405i | \(0.369720\pi\) |
−0.958574 | + | 0.284845i | \(0.908058\pi\) | |||||||
\(44\) | −3.83342 | − | 6.63969i | −0.577910 | − | 1.00097i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.61759 | − | 9.72995i | 0.828268 | − | 1.43460i | ||||
\(47\) | 0.403711 | + | 0.576559i | 0.0588873 | + | 0.0840997i | 0.847516 | − | 0.530770i | \(-0.178097\pi\) |
−0.788628 | + | 0.614870i | \(0.789208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.39414 | + | 6.57785i | −0.342020 | + | 0.939693i | ||||
\(50\) | 9.84570 | + | 4.89050i | 1.39239 | + | 0.691622i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.785101 | + | 8.97374i | 0.108874 | + | 1.24443i | ||||
\(53\) | −5.73786 | − | 5.73786i | −0.788156 | − | 0.788156i | 0.193036 | − | 0.981192i | \(-0.438167\pi\) |
−0.981192 | + | 0.193036i | \(0.938167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.452784 | − | 6.03188i | −0.0610534 | − | 0.813339i | ||||
\(56\) | 0.000763450 | 0 | 0.000909845i | 0.000102020 | 0 | 0.000121583i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2912 | + | 7.20599i | 1.35130 | + | 0.946193i | ||||
\(59\) | 2.11198 | + | 0.768697i | 0.274956 | + | 0.100076i | 0.475818 | − | 0.879544i | \(-0.342152\pi\) |
−0.200862 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.14333 | + | 6.48417i | −0.146389 | + | 0.830213i | 0.819852 | + | 0.572575i | \(0.194055\pi\) |
−0.966241 | + | 0.257638i | \(0.917056\pi\) | |||||||
\(62\) | −3.09676 | − | 11.5573i | −0.393290 | − | 1.46778i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.9996 | + | 6.35064i | −1.37495 | + | 0.793830i | ||||
\(65\) | −2.51297 | + | 6.64787i | −0.311695 | + | 0.824567i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.47165 | + | 0.216242i | 0.301960 | + | 0.0264181i | 0.237129 | − | 0.971478i | \(-0.423794\pi\) |
0.0648313 | + | 0.997896i | \(0.479349\pi\) | |||||||
\(68\) | −19.2579 | − | 1.68485i | −2.33536 | − | 0.204318i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.00290181 | − | 0.00130978i | 0.000346832 | − | 0.000156549i | ||||
\(71\) | 10.4316 | − | 6.02267i | 1.23800 | − | 0.714759i | 0.269314 | − | 0.963052i | \(-0.413203\pi\) |
0.968685 | + | 0.248294i | \(0.0798698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.375408 | − | 1.40104i | −0.0439381 | − | 0.163979i | 0.940471 | − | 0.339875i | \(-0.110385\pi\) |
−0.984409 | + | 0.175895i | \(0.943718\pi\) | |||||||
\(74\) | −0.100157 | + | 0.568017i | −0.0116430 | + | 0.0660306i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.68478 | + | 1.70512i | 0.537381 | + | 0.195591i | ||||
\(77\) | −0.00143496 | − | 0.00100477i | −0.000163529 | − | 0.000114504i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.36157 | − | 4.00616i | 0.378206 | − | 0.450729i | −0.543041 | − | 0.839706i | \(-0.682727\pi\) |
0.921247 | + | 0.388978i | \(0.127172\pi\) | |||||||
\(80\) | −3.64738 | + | 0.273791i | −0.407790 | + | 0.0306108i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −18.2876 | − | 18.2876i | −2.01953 | − | 2.01953i | ||||
\(83\) | 1.39592 | + | 15.9554i | 0.153222 | + | 1.75134i | 0.551594 | + | 0.834113i | \(0.314020\pi\) |
−0.398372 | + | 0.917224i | \(0.630425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.1133 | − | 7.78833i | −1.42234 | − | 0.844763i | ||||
\(86\) | −6.54134 | + | 17.9722i | −0.705371 | + | 1.93799i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.84581 | − | 4.06424i | −0.303364 | − | 0.433249i | ||||
\(89\) | −2.99426 | + | 5.18621i | −0.317391 | + | 0.549737i | −0.979943 | − | 0.199279i | \(-0.936140\pi\) |
0.662552 | + | 0.749016i | \(0.269473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.00102910 | + | 0.00178245i | 0.000107879 | + | 0.000186852i | ||||
\(92\) | 6.12062 | − | 13.1257i | 0.638118 | − | 1.36845i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.994737 | + | 1.18548i | 0.102599 | + | 0.122273i | ||||
\(95\) | 2.74674 | + | 2.81539i | 0.281810 | + | 0.288853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.62753 | + | 3.55678i | 0.774459 | + | 0.361136i | 0.769331 | − | 0.638851i | \(-0.220590\pi\) |
0.00512815 | + | 0.999987i | \(0.498368\pi\) | |||||||
\(98\) | −3.98342 | + | 14.8663i | −0.402386 | + | 1.50173i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.1927 | + | 5.17394i | 1.31927 | + | 0.517394i | ||||
\(101\) | −11.3335 | − | 1.99841i | −1.12773 | − | 0.198849i | −0.421496 | − | 0.906830i | \(-0.638495\pi\) |
−0.706231 | + | 0.707981i | \(0.749606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.21507 | − | 2.89813i | 0.612389 | − | 0.285562i | −0.0915740 | − | 0.995798i | \(-0.529190\pi\) |
0.703963 | + | 0.710237i | \(0.251412\pi\) | |||||||
\(104\) | 1.01227 | + | 5.74088i | 0.0992615 | + | 0.562940i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.6672 | − | 11.4682i | −1.32748 | − | 1.11389i | ||||
\(107\) | 9.67551 | − | 9.67551i | 0.935367 | − | 0.935367i | −0.0626673 | − | 0.998034i | \(-0.519961\pi\) |
0.998034 | + | 0.0626673i | \(0.0199607\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.73835i | − | 0.358069i | −0.983843 | − | 0.179034i | \(-0.942703\pi\) | ||
0.983843 | − | 0.179034i | \(-0.0572974\pi\) | |||||||
\(110\) | −2.14761 | − | 13.1249i | −0.204767 | − | 1.25141i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.000607567 | 0 | 0.000867696i | −5.74097e−5 | 0 | 8.19895e-5i | ||||
\(113\) | 0.472320 | + | 1.01289i | 0.0444322 | + | 0.0952851i | 0.927271 | − | 0.374391i | \(-0.122148\pi\) |
−0.882839 | + | 0.469676i | \(0.844371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.84298 | − | 7.23605i | 0.824612 | − | 0.674766i | ||||
\(116\) | 14.0249 | + | 8.09728i | 1.30218 | + | 0.751814i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.77320 | + | 1.27897i | 0.439408 | + | 0.117739i | ||||
\(119\) | −0.00415058 | + | 0.00151069i | −0.000380483 | + | 0.000138484i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.82079 | − | 2.36692i | 0.256435 | − | 0.215175i | ||||
\(122\) | −1.26171 | + | 14.4215i | −0.114230 | + | 1.30566i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.27510 | − | 14.4932i | −0.473718 | − | 1.30153i | ||||
\(125\) | 7.60763 | + | 8.19292i | 0.680447 | + | 0.732797i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0914 | + | 2.70398i | −0.895467 | + | 0.239940i | −0.677068 | − | 0.735920i | \(-0.736750\pi\) |
−0.218398 | + | 0.975860i | \(0.570083\pi\) | |||||||
\(128\) | −10.9739 | + | 7.68398i | −0.969962 | + | 0.679175i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.23027 | + | 15.0425i | −0.371019 | + | 1.31931i | ||||
\(131\) | 14.3376 | − | 2.52811i | 1.25269 | − | 0.220882i | 0.492341 | − | 0.870402i | \(-0.336141\pi\) |
0.760345 | + | 0.649520i | \(0.225030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.00113476 | 9.92788e-5i | 9.83964e−5 | 8.60857e-6i | ||||||
\(134\) | 5.45513 | 0.471251 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.5102 | −1.07274 | ||||||||
\(137\) | 7.28394 | − | 0.637262i | 0.622309 | − | 0.0544450i | 0.228359 | − | 0.973577i | \(-0.426664\pi\) |
0.393950 | + | 0.919132i | \(0.371108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00586 | − | 0.530014i | 0.254953 | − | 0.0449552i | −0.0447106 | − | 0.999000i | \(-0.514237\pi\) |
0.299664 | + | 0.954045i | \(0.403125\pi\) | |||||||
\(140\) | 0.00357917 | − | 0.00200795i | 0.000302495 | − | 0.000169703i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.6943 | − | 15.1905i | 1.82054 | − | 1.27476i | ||||
\(143\) | 8.30486 | − | 2.22528i | 0.694487 | − | 0.186087i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.19880 | + | 10.5559i | 0.597828 | + | 0.876617i | ||||
\(146\) | −1.09074 | − | 2.99678i | −0.0902701 | − | 0.248015i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0647997 | + | 0.740664i | −0.00532650 | + | 0.0608822i | ||||
\(149\) | 7.76525 | − | 6.51582i | 0.636154 | − | 0.533797i | −0.266680 | − | 0.963785i | \(-0.585927\pi\) |
0.902834 | + | 0.429988i | \(0.141482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4779 | − | 6.36142i | 1.42233 | − | 0.517685i | 0.487605 | − | 0.873064i | \(-0.337870\pi\) |
0.934722 | + | 0.355379i | \(0.115648\pi\) | |||||||
\(152\) | 3.11634 | + | 0.835020i | 0.252768 | + | 0.0677291i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.00333555 | − | 0.00192578i | −0.000268786 | − | 0.000155184i | ||||
\(155\) | 1.21008 | − | 12.1081i | 0.0971956 | − | 0.972548i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.136723 | − | 0.293204i | −0.0109117 | − | 0.0234002i | 0.900776 | − | 0.434283i | \(-0.142998\pi\) |
−0.911688 | + | 0.410883i | \(0.865220\pi\) | |||||||
\(158\) | 6.59520 | − | 9.41892i | 0.524686 | − | 0.749329i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0312 | + | 2.62316i | −1.26738 | + | 0.207379i | ||||
\(161\) | − | 0.00330906i | − | 0.000260790i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.86594 | + | 3.86594i | −0.302804 | + | 0.302804i | −0.842110 | − | 0.539306i | \(-0.818687\pi\) |
0.539306 | + | 0.842110i | \(0.318687\pi\) | |||||||
\(164\) | −25.5384 | − | 21.4292i | −1.99421 | − | 1.67334i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.11500 | + | 34.6799i | 0.474616 | + | 2.69168i | ||||
\(167\) | −16.6893 | + | 7.78235i | −1.29146 | + | 0.602217i | −0.942276 | − | 0.334838i | \(-0.891318\pi\) |
−0.349182 | + | 0.937055i | \(0.613541\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.85412 | + | 0.503259i | 0.219548 | + | 0.0387122i | ||||
\(170\) | −30.2147 | − | 14.5460i | −2.31736 | − | 1.11563i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.38085 | + | 23.8136i | −0.486535 | + | 1.81577i | ||||
\(173\) | 2.69896 | + | 1.25855i | 0.205198 | + | 0.0956855i | 0.522501 | − | 0.852639i | \(-0.324999\pi\) |
−0.317302 | + | 0.948324i | \(0.602777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.00323151 | 0.000202501i | 0.000244279 | 1.53077e-5i | ||||||
\(176\) | 2.84428 | + | 3.38968i | 0.214395 | + | 0.255506i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.56454 | + | 11.9332i | −0.417080 | + | 0.894431i | ||||
\(179\) | −8.26245 | − | 14.3110i | −0.617564 | − | 1.06965i | −0.989929 | − | 0.141566i | \(-0.954786\pi\) |
0.372365 | − | 0.928087i | \(-0.378547\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.81540 | − | 8.34051i | 0.357926 | − | 0.619945i | −0.629688 | − | 0.776848i | \(-0.716817\pi\) |
0.987614 | + | 0.156902i | \(0.0501508\pi\) | |||||||
\(182\) | 0.00259561 | + | 0.00370692i | 0.000192400 | + | 0.000274775i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.20550 | − | 8.80705i | 0.236313 | − | 0.649264i | ||||
\(185\) | −0.299541 | + | 0.504341i | −0.0220227 | + | 0.0370799i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.60813 | + | 18.3810i | 0.117598 | + | 1.34415i | ||||
\(188\) | 1.41056 | + | 1.41056i | 0.102876 | + | 0.102876i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.55572 | + | 5.64023i | 0.475602 | + | 0.409185i | ||||
\(191\) | −0.797244 | + | 0.950119i | −0.0576866 | + | 0.0687482i | −0.794116 | − | 0.607766i | \(-0.792066\pi\) |
0.736430 | + | 0.676514i | \(0.236510\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5052 | − | 10.1567i | −1.04411 | − | 0.731093i | −0.0800524 | − | 0.996791i | \(-0.525509\pi\) |
−0.964056 | + | 0.265698i | \(0.914398\pi\) | |||||||
\(194\) | 17.3883 | + | 6.32881i | 1.24840 | + | 0.454382i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.44506 | + | 19.5379i | −0.246076 | + | 1.39557i | ||||
\(197\) | 4.39615 | + | 16.4067i | 0.313213 | + | 1.16893i | 0.925642 | + | 0.378401i | \(0.123526\pi\) |
−0.612429 | + | 0.790526i | \(0.709807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.13371 | − | 5.27335i | 0.647472 | − | 0.373818i | −0.140015 | − | 0.990149i | \(-0.544715\pi\) |
0.787487 | + | 0.616331i | \(0.211382\pi\) | |||||||
\(200\) | 8.79682 | + | 2.59143i | 0.622029 | + | 0.183241i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −25.2069 | − | 2.20532i | −1.77355 | − | 0.155166i | ||||
\(203\) | 0.00368613 | 0.000322495i | 0.000258716 | 2.26347e-5i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.8208 | − | 23.9734i | −0.755759 | − | 1.67438i | ||||
\(206\) | 13.0576 | − | 7.53880i | 0.909765 | − | 0.525253i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.34559 | − | 5.02181i | −0.0932999 | − | 0.348200i | ||||
\(209\) | 0.826290 | − | 4.68612i | 0.0571557 | − | 0.324146i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.169003 | + | 0.0615119i | 0.0116346 | + | 0.00423465i | 0.347831 | − | 0.937557i | \(-0.386918\pi\) |
−0.336196 | + | 0.941792i | \(0.609141\pi\) | |||||||
\(212\) | −18.8390 | − | 13.1912i | −1.29387 | − | 0.905978i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.3383 | − | 23.0465i | 1.32194 | − | 1.57543i | ||||
\(215\) | −12.6857 | + | 14.7448i | −0.865157 | + | 1.00558i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.00249185 | − | 0.00249185i | −0.000169158 | − | 0.000169158i | ||||
\(218\) | −0.716371 | − | 8.18815i | −0.0485187 | − | 0.554572i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.23238 | − | 16.6129i | −0.285347 | − | 1.12004i | ||||
\(221\) | 7.41460 | − | 20.3715i | 0.498760 | − | 1.37033i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5728 | + | 15.0996i | 0.708010 | + | 1.01114i | 0.998526 | + | 0.0542728i | \(0.0172841\pi\) |
−0.290516 | + | 0.956870i | \(0.593827\pi\) | |||||||
\(224\) | −0.00235221 | + | 0.00407414i | −0.000157163 | + | 0.000272215i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.22863 | + | 2.12804i | 0.0817271 | + | 0.141555i | ||||
\(227\) | −6.61613 | + | 14.1883i | −0.439128 | + | 0.941713i | 0.554831 | + | 0.831963i | \(0.312783\pi\) |
−0.993959 | + | 0.109750i | \(0.964995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.54463 | + | 5.41608i | 0.300318 | + | 0.357904i | 0.895008 | − | 0.446050i | \(-0.147170\pi\) |
−0.594690 | + | 0.803955i | \(0.702725\pi\) | |||||||
\(230\) | 17.9823 | − | 17.5438i | 1.18571 | − | 1.15680i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.49823 | + | 4.42910i | 0.623590 | + | 0.290785i | ||||
\(233\) | −0.591957 | + | 2.20921i | −0.0387804 | + | 0.144730i | −0.982601 | − | 0.185726i | \(-0.940536\pi\) |
0.943821 | + | 0.330457i | \(0.107203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.519996 | + | 1.48547i | 0.0339208 | + | 0.0969013i | ||||
\(236\) | 6.27313 | + | 1.10612i | 0.408346 | + | 0.0720024i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.00880157 | + | 0.00410424i | −0.000570521 | + | 0.000266038i | ||||
\(239\) | −1.33675 | − | 7.58107i | −0.0864670 | − | 0.490379i | −0.997030 | − | 0.0770092i | \(-0.975463\pi\) |
0.910563 | − | 0.413369i | \(-0.135648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.35154 | − | 6.16868i | −0.473555 | − | 0.397359i | 0.374535 | − | 0.927213i | \(-0.377802\pi\) |
−0.848089 | + | 0.529853i | \(0.822247\pi\) | |||||||
\(242\) | 5.72484 | − | 5.72484i | 0.368007 | − | 0.368007i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.6609i | 1.19464i | ||||||||
\(245\) | −9.13545 | + | 12.7100i | −0.583642 | + | 0.812011i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.20676 | + | 4.57972i | −0.204041 | + | 0.291401i | ||||
\(248\) | −4.21818 | − | 9.04592i | −0.267855 | − | 0.574416i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.2331 | + | 16.4872i | 1.15316 | + | 1.04274i | ||||
\(251\) | 4.10987 | + | 2.37283i | 0.259413 | + | 0.149772i | 0.624067 | − | 0.781371i | \(-0.285479\pi\) |
−0.364654 | + | 0.931143i | \(0.618813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.3521 | − | 3.57769i | −0.839440 | − | 0.224927i | ||||
\(254\) | −21.5852 | + | 7.85635i | −1.35437 | + | 0.492951i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.10423 | + | 2.60476i | −0.194015 | + | 0.162798i | ||||
\(257\) | −1.05277 | + | 12.0332i | −0.0656701 | + | 0.750612i | 0.889959 | + | 0.456040i | \(0.150733\pi\) |
−0.955629 | + | 0.294572i | \(0.904823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.81013e−5 | 0 | 0.000159632i | 3.61024e−6 | 0 | 9.91906e-6i | ||||
\(260\) | −3.74226 | + | 19.7919i | −0.232085 | + | 1.22744i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 30.9195 | − | 8.28485i | 1.91021 | − | 0.511840i | ||||
\(263\) | 7.01542 | − | 4.91225i | 0.432589 | − | 0.302902i | −0.336926 | − | 0.941531i | \(-0.609387\pi\) |
0.769515 | + | 0.638629i | \(0.220498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.87774 | − | 15.8246i | −0.545355 | − | 0.972095i | ||||
\(266\) | 0.00246646 | 0.000434903i | 0.000151228 | 2.66656e-5i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00513 | − | 0.612870i | 0.427907 | − | 0.0374370i | ||||
\(269\) | 17.3406 | 1.05728 | 0.528638 | − | 0.848847i | \(-0.322703\pi\) | ||||
0.528638 | + | 0.848847i | \(0.322703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8573 | −0.720278 | −0.360139 | − | 0.932899i | \(-0.617271\pi\) | ||||
−0.360139 | + | 0.932899i | \(0.617271\pi\) | |||||||
\(272\) | 11.1147 | − | 0.972407i | 0.673926 | − | 0.0589609i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.8320 | − | 2.79161i | 0.956446 | − | 0.168647i | ||||
\(275\) | 2.67675 | − | 13.2581i | 0.161414 | − | 0.799495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3872 | + | 11.4745i | −0.984613 | + | 0.689433i | −0.950739 | − | 0.309993i | \(-0.899673\pi\) |
−0.0338740 | + | 0.999426i | \(0.510784\pi\) | |||||||
\(278\) | 6.48220 | − | 1.73690i | 0.388776 | − | 0.104172i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.00219415 | − | 0.00149635i | 0.000131126 | − | 8.94240e-5i | ||||
\(281\) | 2.66069 | + | 7.31019i | 0.158724 | + | 0.436089i | 0.993407 | − | 0.114641i | \(-0.0365716\pi\) |
−0.834683 | + | 0.550730i | \(0.814349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30970 | − | 14.9700i | 0.0778538 | − | 0.889873i | −0.852384 | − | 0.522916i | \(-0.824844\pi\) |
0.930238 | − | 0.366957i | \(-0.119600\pi\) | |||||||
\(284\) | 26.1518 | − | 21.9440i | 1.55182 | − | 1.30213i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.7638 | − | 6.46550i | 1.05040 | − | 0.382313i | ||||
\(287\) | −0.00735767 | − | 0.00197148i | −0.000434310 | − | 0.000116373i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.5680 | + | 14.7617i | 1.50400 | + | 0.868336i | ||||
\(290\) | 17.7904 | + | 21.7412i | 1.04469 | + | 1.27669i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.73734 | − | 3.72573i | −0.101670 | − | 0.218032i | ||||
\(293\) | −12.9347 | + | 18.4726i | −0.755651 | + | 1.07918i | 0.238495 | + | 0.971144i | \(0.423346\pi\) |
−0.994147 | + | 0.108038i | \(0.965543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.08085 | + | 2.93316i | 0.237596 | + | 0.170775i | ||||
\(296\) | 0.481143i | 0.0279659i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.7597 | − | 15.7597i | 0.912936 | − | 0.912936i | ||||
\(299\) | 12.4415 | + | 10.4396i | 0.719510 | + | 0.603740i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.000978160 | 0.00554742i | 5.63802e−5 | 0.000319748i | ||||||
\(302\) | 37.0629 | − | 17.2827i | 2.13273 | − | 0.994510i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.83362 | − | 0.499644i | −0.162519 | − | 0.0286566i | ||||
\(305\) | −6.38629 | + | 13.2655i | −0.365678 | + | 0.759581i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.30818 | + | 4.88220i | −0.0746619 | + | 0.278642i | −0.993156 | − | 0.116792i | \(-0.962739\pi\) |
0.918495 | + | 0.395434i | \(0.129406\pi\) | |||||||
\(308\) | −0.00449965 | − | 0.00209822i | −0.000256392 | − | 0.000119557i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.330192 | − | 26.7525i | 0.0187536 | − | 1.51944i | ||||
\(311\) | −12.6744 | − | 15.1048i | −0.718699 | − | 0.856512i | 0.275805 | − | 0.961214i | \(-0.411056\pi\) |
−0.994504 | + | 0.104702i | \(0.966611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4671 | + | 24.5912i | −0.648157 | + | 1.38998i | 0.257629 | + | 0.966244i | \(0.417059\pi\) |
−0.905787 | + | 0.423734i | \(0.860719\pi\) | |||||||
\(314\) | −0.355652 | − | 0.616007i | −0.0200706 | − | 0.0347633i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.41094 | − | 12.8361i | 0.416898 | − | 0.722089i | ||||
\(317\) | −0.143177 | − | 0.204479i | −0.00804165 | − | 0.0114847i | 0.815111 | − | 0.579305i | \(-0.196676\pi\) |
−0.823153 | + | 0.567820i | \(0.807787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.28664 | − | 14.5249i | 0.295995 | − | 0.813240i | ||||
\(320\) | −27.5218 | + | 7.01157i | −1.53852 | + | 0.391959i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.000634107 | − | 0.00724787i | −3.53374e−5 | − | 0.000403908i | ||||
\(323\) | −8.48389 | − | 8.48389i | −0.472056 | − | 0.472056i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.43362 | + | 12.7888i | −0.523283 | + | 0.709394i | ||||
\(326\) | −7.72680 | + | 9.20844i | −0.427948 | + | 0.510009i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.6726 | − | 12.3745i | −0.975808 | − | 0.683268i | ||||
\(329\) | 0.000428303 | 0 | 0.000155890i | 2.36131e−5 | 0 | 8.59448e-6i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.820786 | − | 4.65491i | 0.0451145 | − | 0.255857i | −0.953906 | − | 0.300105i | \(-0.902978\pi\) |
0.999021 | + | 0.0442484i | \(0.0140893\pi\) | |||||||
\(332\) | 11.7487 | + | 43.8467i | 0.644794 | + | 2.40640i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −35.0635 | + | 20.2439i | −1.91859 | + | 1.10770i | ||||
\(335\) | 5.18950 | + | 1.96169i | 0.283533 | + | 0.107178i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7791 | + | 0.943046i | 0.587173 | + | 0.0513710i | 0.376872 | − | 0.926266i | \(-0.377000\pi\) |
0.210302 | + | 0.977637i | \(0.432555\pi\) | |||||||
\(338\) | 6.34786 | + | 0.555366i | 0.345278 | + | 0.0302079i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −40.4340 | − | 15.2845i | −2.19284 | − | 0.828919i | ||||
\(341\) | −12.7488 | + | 7.36051i | −0.690385 | + | 0.398594i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.00234645 | + | 0.00875706i | 0.000126696 | + | 0.000472837i | ||||
\(344\) | −2.77045 | + | 15.7120i | −0.149373 | + | 0.847134i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.15274 | + | 2.23942i | 0.330774 | + | 0.120392i | ||||
\(347\) | −19.7058 | − | 13.7981i | −1.05786 | − | 0.740723i | −0.0909561 | − | 0.995855i | \(-0.528992\pi\) |
−0.966906 | + | 0.255132i | \(0.917881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.752338 | − | 0.896601i | 0.0402717 | − | 0.0479940i | −0.745533 | − | 0.666469i | \(-0.767805\pi\) |
0.785804 | + | 0.618475i | \(0.212249\pi\) | |||||||
\(350\) | 0.00703921 | − | 0.00106279i | 0.000376262 | − | 5.68084e-5i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.8961 | + | 13.8961i | 0.740662 | + | 0.740662i | ||||
\(353\) | −1.76656 | − | 20.1919i | −0.0940245 | − | 1.07470i | −0.885855 | − | 0.463963i | \(-0.846427\pi\) |
0.791830 | − | 0.610741i | \(-0.209129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.1005 | − | 6.64946i | 1.38527 | − | 0.352917i | ||||
\(356\) | −5.80497 | + | 15.9490i | −0.307663 | + | 0.845296i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.8397 | − | 29.7622i | −1.10141 | − | 1.57298i | ||||
\(359\) | 13.1082 | − | 22.7040i | 0.691823 | − | 1.19827i | −0.279418 | − | 0.960170i | \(-0.590141\pi\) |
0.971240 | − | 0.238102i | \(-0.0765253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.95290 | − | 13.7748i | −0.418574 | − | 0.724991i | ||||
\(362\) | 8.94895 | − | 19.1911i | 0.470347 | − | 1.00866i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.00374959 | + | 0.00446858i | 0.000196532 | + | 0.000234217i | ||||
\(365\) | 0.0400278 | − | 3.24309i | 0.00209515 | − | 0.169751i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0178 | − | 8.86817i | −0.992723 | − | 0.462914i | −0.142761 | − | 0.989757i | \(-0.545598\pi\) |
−0.849963 | + | 0.526843i | \(0.823376\pi\) | |||||||
\(368\) | −2.16337 | + | 8.07380i | −0.112773 | + | 0.420876i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.559443 | + | 1.16207i | −0.0290840 | + | 0.0604129i | ||||
\(371\) | −0.00517492 | 0.000912477i | −0.000268668 | 4.73735e-5i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.52296 | + | 0.710169i | −0.0788560 | + | 0.0367712i | −0.461646 | − | 0.887064i | \(-0.652741\pi\) |
0.382790 | + | 0.923835i | \(0.374963\pi\) | |||||||
\(374\) | 7.04459 | + | 39.9519i | 0.364267 | + | 2.06586i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.988917 | + | 0.829800i | 0.0509995 | + | 0.0427937i | ||||
\(377\) | −12.8418 | + | 12.8418i | −0.661386 | + | 0.661386i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.6637i | − | 0.599126i | −0.954077 | − | 0.299563i | \(-0.903159\pi\) | ||
0.954077 | − | 0.299563i | \(-0.0968408\pi\) | |||||||
\(380\) | 9.05211 | + | 6.50631i | 0.464364 | + | 0.333767i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.56415 | + | 2.23383i | −0.0800286 | + | 0.114293i | ||||
\(383\) | 4.44907 | + | 9.54105i | 0.227337 | + | 0.487525i | 0.986579 | − | 0.163283i | \(-0.0522082\pi\) |
−0.759243 | + | 0.650808i | \(0.774430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.00248061 | − | 0.00303148i | −0.000126424 | − | 0.000154499i | ||||
\(386\) | −33.7173 | − | 19.4667i | −1.71616 | − | 0.990828i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.0399 | + | 6.17353i | 1.16968 | + | 0.313414i | ||||
\(389\) | −36.8621 | + | 13.4167i | −1.86898 | + | 0.680254i | −0.898557 | + | 0.438858i | \(0.855383\pi\) |
−0.970427 | + | 0.241396i | \(0.922395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6998 | + | 22.4038i | −1.35027 | + | 1.13301i | ||||
\(392\) | −1.11898 | + | 12.7900i | −0.0565168 | + | 0.645990i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.7729 | + | 35.0933i | 0.643491 | + | 1.76798i | ||||
\(395\) | 9.66114 | − | 6.58862i | 0.486105 | − | 0.331509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0653 | + | 2.69699i | −0.505162 | + | 0.135358i | −0.502395 | − | 0.864638i | \(-0.667548\pi\) |
−0.00276748 | + | 0.999996i | \(0.500881\pi\) | |||||||
\(398\) | 18.9952 | − | 13.3006i | 0.952141 | − | 0.666697i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.01698 | − | 1.61858i | −0.400849 | − | 0.0809292i | ||||
\(401\) | −26.3401 | + | 4.64448i | −1.31536 | + | 0.231934i | −0.786931 | − | 0.617041i | \(-0.788331\pi\) |
−0.528433 | + | 0.848975i | \(0.677220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2304 | − | 1.50746i | 0.858306 | − | 0.0750921i | ||||
\(404\) | −32.6169 | −1.62275 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.00813559 | 0.000403762 | ||||||||
\(407\) | 0.706936 | − | 0.0618489i | 0.0350415 | − | 0.00306574i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.6400 | + | 5.93165i | −1.66339 | + | 0.293301i | −0.924687 | − | 0.380727i | \(-0.875674\pi\) |
−0.738705 | + | 0.674028i | \(0.764562\pi\) | |||||||
\(410\) | −28.2950 | − | 50.4357i | −1.39739 | − | 2.49084i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.9208 | − | 11.1478i | 0.784359 | − | 0.549214i | ||||
\(413\) | 0.00140583 | 0.000376692i | 6.91766e−5 | 1.85358e-5i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.65380 | + | 35.1902i | −0.326622 | + | 1.72742i | ||||
\(416\) | −7.89716 | − | 21.6973i | −0.387190 | − | 1.06380i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.911843 | − | 10.4224i | 0.0445997 | − | 0.509777i | ||||
\(419\) | −12.2431 | + | 10.2731i | −0.598112 | + | 0.501876i | −0.890838 | − | 0.454321i | \(-0.849882\pi\) |
0.292726 | + | 0.956196i | \(0.405438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9345 | − | 10.8953i | 1.45892 | − | 0.531002i | 0.513850 | − | 0.857880i | \(-0.328219\pi\) |
0.945067 | + | 0.326878i | \(0.105997\pi\) | |||||||
\(422\) | 0.381956 | + | 0.102345i | 0.0185933 | + | 0.00498206i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.8891 | − | 7.44152i | −0.625950 | − | 0.361392i | ||||
\(425\) | −23.5127 | − | 24.7030i | −1.14053 | − | 1.19827i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.00180193 | + | 0.00386425i | 8.72015e−5 | + | 0.000187004i | ||||
\(428\) | 22.2438 | − | 31.7675i | 1.07520 | − | 1.53554i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.9601 | + | 34.7266i | −1.20368 | + | 1.67466i | ||||
\(431\) | 5.93676i | 0.285963i | 0.989725 | + | 0.142982i | \(0.0456690\pi\) | ||||
−0.989725 | + | 0.142982i | \(0.954331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.73933 | + | 7.73933i | −0.371929 | + | 0.371929i | −0.868179 | − | 0.496251i | \(-0.834710\pi\) |
0.496251 | + | 0.868179i | \(0.334710\pi\) | |||||||
\(434\) | −0.00593543 | − | 0.00498042i | −0.000284910 | − | 0.000239068i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.83984 | − | 10.4342i | −0.0881122 | − | 0.499709i | ||||
\(437\) | 8.14644 | − | 3.79875i | 0.389697 | − | 0.181719i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.6483 | − | 5.05146i | −1.36731 | − | 0.241093i | −0.558665 | − | 0.829394i | \(-0.688686\pi\) |
−0.808642 | + | 0.588300i | \(0.799797\pi\) | |||||||
\(440\) | −3.66552 | − | 10.4713i | −0.174747 | − | 0.499198i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.3366 | − | 46.0407i | 0.586791 | − | 2.18993i | ||||
\(443\) | −24.6030 | − | 11.4725i | −1.16892 | − | 0.545077i | −0.261461 | − | 0.965214i | \(-0.584204\pi\) |
−0.907461 | + | 0.420137i | \(0.861982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.58481 | + | 9.35110i | −0.454364 | + | 0.443284i | ||||
\(446\) | 26.0513 | + | 31.0468i | 1.23357 | + | 1.47011i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.00347602 | + | 0.00745435i | −0.000164227 | + | 0.000352185i | ||||
\(449\) | 1.73698 | + | 3.00854i | 0.0819733 | + | 0.141982i | 0.904097 | − | 0.427326i | \(-0.140544\pi\) |
−0.822124 | + | 0.569308i | \(0.807211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.9099 | + | 27.5568i | −0.749169 | + | 1.29760i | ||||
\(452\) | 1.81681 | + | 2.59467i | 0.0854554 | + | 0.122043i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.7725 | + | 32.3447i | −0.552511 | + | 1.51801i | ||||
\(455\) | 0.00113620 | + | 0.00445981i | 5.32659e−5 | + | 0.000209079i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.05624 | − | 23.5029i | −0.0961868 | − | 1.09942i | −0.878890 | − | 0.477025i | \(-0.841715\pi\) |
0.782703 | − | 0.622395i | \(-0.213840\pi\) | |||||||
\(458\) | 10.9920 | + | 10.9920i | 0.513624 | + | 0.513624i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21.1207 | − | 24.5489i | 0.984757 | − | 1.14460i | ||||
\(461\) | −5.14645 | + | 6.13330i | −0.239694 | + | 0.285656i | −0.872459 | − | 0.488688i | \(-0.837476\pi\) |
0.632765 | + | 0.774344i | \(0.281920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.93475 | + | 1.35473i | 0.0899154 | + | 0.0629594i | 0.617670 | − | 0.786438i | \(-0.288077\pi\) |
−0.527754 | + | 0.849397i | \(0.676966\pi\) | |||||||
\(464\) | −8.78299 | − | 3.19675i | −0.407740 | − | 0.148405i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.873225 | + | 4.95230i | −0.0404514 | + | 0.229411i | ||||
\(467\) | −5.32380 | − | 19.8687i | −0.246356 | − | 0.919414i | −0.972697 | − | 0.232079i | \(-0.925447\pi\) |
0.726341 | − | 0.687335i | \(-0.241220\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.00139143 | 0.000803341i | 6.42501e−5 | 3.70948e-5i | ||||||
\(470\) | 1.42361 | + | 3.15399i | 0.0656662 | + | 0.145483i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.10653 | + | 0.359274i | 0.189018 | + | 0.0165369i | ||||
\(473\) | 23.4415 | + | 2.05087i | 1.07784 | + | 0.0942989i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.20825 | + | 7.72306i | 0.193088 | + | 0.354358i | ||||
\(476\) | −0.0108413 | + | 0.00625924i | −0.000496911 | + | 0.000286892i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.38064 | − | 16.3488i | −0.200366 | − | 0.747775i | ||||
\(479\) | −3.74161 | + | 21.2197i | −0.170958 | + | 0.969553i | 0.771748 | + | 0.635929i | \(0.219383\pi\) |
−0.942706 | + | 0.333624i | \(0.891728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.783491 | − | 0.285167i | −0.0357241 | − | 0.0130025i | ||||
\(482\) | −17.2843 | − | 12.1026i | −0.787277 | − | 0.551257i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.70831 | − | 7.99465i | 0.304923 | − | 0.363393i | ||||
\(485\) | 14.2657 | + | 12.2735i | 0.647772 | + | 0.557312i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.20133 | + | 2.20133i | 0.0997518 | + | 0.0997518i | 0.755221 | − | 0.655470i | \(-0.227529\pi\) |
−0.655470 | + | 0.755221i | \(0.727529\pi\) | |||||||
\(488\) | 1.05251 | + | 12.0302i | 0.0476449 | + | 0.544583i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −17.5739 | + | 29.5894i | −0.793908 | + | 1.33671i | ||||
\(491\) | 2.81965 | − | 7.74693i | 0.127249 | − | 0.349614i | −0.859666 | − | 0.510857i | \(-0.829328\pi\) |
0.986915 | + | 0.161243i | \(0.0515503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.3546 | − | 31.9257i | −1.00680 | − | 1.43786i | ||||
\(494\) | −6.14620 | + | 10.6455i | −0.276530 | + | 0.478965i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.45078 | + | 7.70898i | 0.199846 | + | 0.346144i | ||||
\(497\) | 0.00329650 | − | 0.00706937i | 0.000147868 | − | 0.000317105i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9583 | + | 20.2101i | 0.759156 | + | 0.904727i | 0.997794 | − | 0.0663815i | \(-0.0211454\pi\) |
−0.238638 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(500\) | 25.2661 | + | 19.1234i | 1.12993 | + | 0.855225i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.45659 | + | 4.40968i | 0.422068 | + | 0.196814i | ||||
\(503\) | −2.01259 | + | 7.51109i | −0.0897370 | + | 0.334903i | −0.996169 | − | 0.0874487i | \(-0.972129\pi\) |
0.906432 | + | 0.422352i | \(0.138795\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.1865 | − | 11.1624i | −1.03178 | − | 0.496722i | ||||
\(506\) | −29.9309 | − | 5.27762i | −1.33059 | − | 0.234619i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −26.8357 | + | 12.5137i | −1.19064 | + | 0.555204i | ||||
\(509\) | 5.25087 | + | 29.7791i | 0.232741 | + | 1.31994i | 0.847320 | + | 0.531082i | \(0.178215\pi\) |
−0.614580 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.000719528 | 0 | 0.000603755i | −3.18300e−5 | 0 | 2.67086e-5i | ||||
\(512\) | 12.6456 | − | 12.6456i | 0.558861 | − | 0.558861i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.5583i | 1.17144i | ||||||||
\(515\) | 15.1327 | − | 2.47615i | 0.666829 | − | 0.109112i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.09209 | − | 1.55967i | 0.0480300 | − | 0.0685940i | ||||
\(518\) | 0.000157850 | 0 | 0.000338510i | 6.93553e−6 | 0 | 1.48733e-5i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.29625 | + | 12.9704i | −0.0568444 | + | 0.568791i | ||||
\(521\) | −2.44020 | − | 1.40885i | −0.106907 | − | 0.0617227i | 0.445593 | − | 0.895236i | \(-0.352993\pi\) |
−0.552500 | + | 0.833513i | \(0.686326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7481 | + | 3.41584i | 0.557436 | + | 0.149364i | 0.526528 | − | 0.850158i | \(-0.323494\pi\) |
0.0309077 | + | 0.999522i | \(0.490160\pi\) | |||||||
\(524\) | 38.7741 | − | 14.1126i | 1.69385 | − | 0.616512i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.4246 | − | 12.1037i | 0.628944 | − | 0.527747i | ||||
\(527\) | −3.23506 | + | 36.9769i | −0.140921 | + | 1.61074i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.06428 | − | 2.92409i | −0.0462731 | − | 0.127134i | ||||
\(530\) | −22.4774 | − | 32.9595i | −0.976357 | − | 1.43167i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.00311841 | 0.000835576i | 0.000135200 | 3.62268e-5i | ||||||
\(533\) | 30.6249 | − | 21.4438i | 1.32651 | − | 0.928834i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.6843 | − | 14.9701i | 1.15366 | − | 0.647216i | ||||
\(536\) | 4.48148 | − | 0.790206i | 0.193570 | − | 0.0341317i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.9814 | − | 3.32294i | 1.63749 | − | 0.143262i | ||||
\(539\) | 18.9359 | 0.815627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4416 | −0.491911 | −0.245956 | − | 0.969281i | \(-0.579102\pi\) | ||||
−0.245956 | + | 0.969281i | \(0.579102\pi\) | |||||||
\(542\) | −25.9711 | + | 2.27218i | −1.11556 | + | 0.0975985i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 48.7984 | − | 8.60448i | 2.09222 | − | 0.368914i | ||||
\(545\) | 2.26301 | − | 8.04706i | 0.0969366 | − | 0.344698i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2542 | − | 18.3834i | 1.12255 | − | 0.786018i | 0.143503 | − | 0.989650i | \(-0.454163\pi\) |
0.979048 | + | 0.203632i | \(0.0652745\pi\) | |||||||
\(548\) | 20.0168 | − | 5.36349i | 0.855076 | − | 0.229117i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.32229 | − | 29.5524i | 0.141663 | − | 1.26012i | ||||
\(551\) | 3.43769 | + | 9.44496i | 0.146450 | + | 0.402369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.000295160 | − | 0.00337369i | 1.25515e−5 | − | 0.000143464i | ||||
\(554\) | −33.6943 | + | 28.2729i | −1.43153 | + | 1.20120i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.12889 | − | 2.95868i | 0.344742 | − | 0.125476i | ||||
\(557\) | 28.6955 | + | 7.68893i | 1.21587 | + | 0.325791i | 0.809061 | − | 0.587724i | \(-0.199976\pi\) |
0.406806 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.9433 | − | 13.8237i | −1.01269 | − | 0.584679i | ||||
\(560\) | −0.00183309 | + | 0.00149998i | −7.74621e−5 | + | 6.33859e-5i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.22858 | + | 15.5017i | 0.304919 | + | 0.653902i | ||||
\(563\) | −3.43987 | + | 4.91264i | −0.144973 | + | 0.207043i | −0.885071 | − | 0.465456i | \(-0.845890\pi\) |
0.740098 | + | 0.672499i | \(0.234779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.403547 | + | 2.46624i | 0.0169774 | + | 0.103756i | ||||
\(566\) | − | 33.0399i | − | 1.38877i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.6218 | − | 15.6218i | 0.655475 | − | 0.655475i | ||||
\(569\) | 8.00903 | + | 6.72037i | 0.335756 | + | 0.281733i | 0.795040 | − | 0.606557i | \(-0.207450\pi\) |
−0.459284 | + | 0.888289i | \(0.651894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.98699 | − | 11.2688i | −0.0831531 | − | 0.471584i | −0.997740 | − | 0.0671948i | \(-0.978595\pi\) |
0.914587 | − | 0.404390i | \(-0.132516\pi\) | |||||||
\(572\) | 22.0848 | − | 10.2983i | 0.923411 | − | 0.430594i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0164934 | − | 0.00290823i | −0.000688421 | − | 0.000121387i | ||||
\(575\) | 23.4155 | − | 10.2230i | 0.976492 | − | 0.426329i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.8211 | − | 44.1170i | 0.492120 | − | 1.83662i | −0.0534774 | − | 0.998569i | \(-0.517031\pi\) |
0.545597 | − | 0.838047i | \(-0.316303\pi\) | |||||||
\(578\) | 58.8308 | + | 27.4332i | 2.44704 | + | 1.14107i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.2879 | + | 25.9199i | 1.05002 | + | 1.07627i | ||||
\(581\) | 0.00666682 | + | 0.00794521i | 0.000276586 | + | 0.000329623i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.27687 | + | 19.8943i | −0.384209 | + | 0.823938i | ||||
\(584\) | −1.33016 | − | 2.30390i | −0.0550424 | − | 0.0953362i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.7911 | + | 42.9394i | −1.02411 | + | 1.77381i | ||||
\(587\) | −15.9259 | − | 22.7446i | −0.657334 | − | 0.938770i | 0.342666 | − | 0.939457i | \(-0.388670\pi\) |
−1.00000 | 0.000687603i | \(0.999781\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.27398 | − | 8.99519i | 0.134902 | − | 0.370640i | ||||
\(590\) | 9.50041 | + | 5.64253i | 0.391126 | + | 0.232299i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.0373990 | − | 0.427473i | −0.00153709 | − | 0.0175690i | ||||
\(593\) | −12.5526 | − | 12.5526i | −0.515474 | − | 0.515474i | 0.400725 | − | 0.916199i | \(-0.368758\pi\) |
−0.916199 | + | 0.400725i | \(0.868758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.00984889 | 0.000739308i | −0.000403765 | 3.03087e-5i | ||||||
\(596\) | 18.4671 | − | 22.0082i | 0.756441 | − | 0.901491i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.2513 | + | 20.4820i | 1.19617 | + | 0.837570i | ||||
\(599\) | −9.47392 | − | 3.44823i | −0.387094 | − | 0.140891i | 0.141140 | − | 0.989990i | \(-0.454923\pi\) |
−0.528234 | + | 0.849099i | \(0.677146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.977209 | + | 5.54203i | −0.0398612 | + | 0.226064i | −0.998230 | − | 0.0594686i | \(-0.981059\pi\) |
0.958369 | + | 0.285533i | \(0.0921705\pi\) | |||||||
\(602\) | 0.00320552 | + | 0.0119631i | 0.000130647 | + | 0.000487581i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 45.6522 | − | 26.3573i | 1.85756 | − | 1.07246i | ||||
\(605\) | 7.50476 | − | 3.38740i | 0.305112 | − | 0.137717i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1412 | + | 1.06222i | 0.492796 | + | 0.0431140i | 0.330846 | − | 0.943685i | \(-0.392666\pi\) |
0.161950 | + | 0.986799i | \(0.448222\pi\) | |||||||
\(608\) | −12.7303 | − | 1.11375i | −0.516280 | − | 0.0451686i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.4459 | + | 30.2794i | −0.463433 | + | 1.22598i | ||||
\(611\) | −1.93736 | + | 1.11853i | −0.0783771 | + | 0.0452511i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.69311 | + | 21.2470i | 0.229942 | + | 0.858157i | 0.980364 | + | 0.197197i | \(0.0631839\pi\) |
−0.750422 | + | 0.660960i | \(0.770149\pi\) | |||||||
\(614\) | −1.92976 | + | 10.9442i | −0.0778789 | + | 0.441673i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.00301917 | − | 0.00109889i | −0.000121646 | − | 4.42754e-5i | ||||
\(617\) | 5.87642 | + | 4.11472i | 0.236576 | + | 0.165652i | 0.685853 | − | 0.727740i | \(-0.259429\pi\) |
−0.449277 | + | 0.893393i | \(0.648318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.611202 | + | 0.728403i | −0.0245663 | + | 0.0292770i | −0.778188 | − | 0.628032i | \(-0.783861\pi\) |
0.753621 | + | 0.657309i | \(0.228305\pi\) | |||||||
\(620\) | −2.58156 | − | 34.3909i | −0.103678 | − | 1.38117i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.6554 | − | 30.6554i | −1.22917 | − | 1.22917i | ||||
\(623\) | 0.000337988 | 0.00386323i | 1.35412e−5 | 0.000154777i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.4164 | + | 22.2411i | 0.456655 | + | 0.889644i | ||||
\(626\) | −20.4041 | + | 56.0599i | −0.815513 | + | 2.24060i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.525913 | − | 0.751081i | −0.0209862 | − | 0.0299714i | ||||
\(629\) | 0.894651 | − | 1.54958i | 0.0356721 | − | 0.0617859i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0880 | − | 33.0615i | −0.759883 | − | 1.31616i | −0.942910 | − | 0.333048i | \(-0.891923\pi\) |
0.183027 | − | 0.983108i | \(-0.441411\pi\) | |||||||
\(632\) | 4.05368 | − | 8.69315i | 0.161247 | − | 0.345795i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.352787 | − | 0.420435i | −0.0140110 | − | 0.0166976i | ||||
\(635\) | −23.3593 | − | 0.288311i | −0.926985 | − | 0.0114413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.1639 | − | 9.40257i | −0.798922 | − | 0.372543i | ||||
\(638\) | 8.79602 | − | 32.8272i | 0.348238 | − | 1.29964i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.2735 | + | 9.89728i | −1.11761 | + | 0.391224i | ||||
\(641\) | 24.5606 | + | 4.33069i | 0.970084 | + | 0.171052i | 0.636168 | − | 0.771551i | \(-0.280519\pi\) |
0.333916 | + | 0.942603i | \(0.391630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.2010 | − | 18.7461i | 1.58537 | − | 0.739272i | 0.587808 | − | 0.809000i | \(-0.299991\pi\) |
0.997566 | + | 0.0697279i | \(0.0222131\pi\) | |||||||
\(644\) | −0.00162856 | − | 0.00923602i | −6.41742e−5 | − | 0.000363950i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.2081 | − | 16.9566i | −0.795078 | − | 0.667149i | ||||
\(647\) | −4.55768 | + | 4.55768i | −0.179181 | + | 0.179181i | −0.790999 | − | 0.611818i | \(-0.790439\pi\) |
0.611818 | + | 0.790999i | \(0.290439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.07983i | − | 0.238654i | ||||||
\(650\) | −18.2119 | + | 29.8192i | −0.714329 | + | 1.16960i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.88773 | + | 12.6930i | −0.348070 | + | 0.497096i | ||||
\(653\) | 2.85735 | + | 6.12762i | 0.111817 | + | 0.239792i | 0.954251 | − | 0.299008i | \(-0.0966557\pi\) |
−0.842434 | + | 0.538800i | \(0.818878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.3932 | + | 3.23734i | 1.26571 | + | 0.126493i | ||||
\(656\) | 16.6632 | + | 9.62047i | 0.650587 | + | 0.375616i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.000967991 | 0 | 0.000259372i | 3.77362e−5 | 0 | 1.01114e-5i | ||||
\(659\) | 29.5176 | − | 10.7435i | 1.14984 | − | 0.418508i | 0.304383 | − | 0.952550i | \(-0.401550\pi\) |
0.845458 | + | 0.534042i | \(0.179327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6918 | + | 10.6497i | −0.493654 | + | 0.414225i | −0.855334 | − | 0.518078i | \(-0.826648\pi\) |
0.361680 | + | 0.932302i | \(0.382203\pi\) | |||||||
\(662\) | 0.905769 | − | 10.3530i | 0.0352037 | − | 0.402380i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.0472 | + | 27.6043i | 0.389905 | + | 1.07126i | ||||
\(665\) | 0.00250275 | 0.000473223i | 9.70526e−5 | 1.83508e-5i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.2034 | − | 7.55709i | 1.09204 | − | 0.292612i | ||||
\(668\) | −42.7520 | + | 29.9353i | −1.65412 | + | 1.15823i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.7425 | + | 3.30226i | 0.453654 | + | 0.127577i | ||||
\(671\) | 17.5405 | − | 3.09287i | 0.677144 | − | 0.119399i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.80022 | − | 0.682431i | 0.300676 | − | 0.0263058i | 0.0641806 | − | 0.997938i | \(-0.479557\pi\) |
0.236496 | + | 0.971633i | \(0.424001\pi\) | |||||||
\(674\) | 23.7902 | 0.916366 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.21392 | 0.315920 | ||||||||
\(677\) | −30.1802 | + | 2.64043i | −1.15992 | + | 0.101480i | −0.650823 | − | 0.759229i | \(-0.725576\pi\) |
−0.509097 | + | 0.860709i | \(0.670021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.00536718 | 0.000946379i | 0.000205974 | 3.63187e-5i | ||||||
\(680\) | −26.9290 | − | 7.57301i | −1.03268 | − | 0.290412i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.5133 | + | 18.5648i | −1.01525 | + | 0.710885i | ||||
\(683\) | −30.0707 | + | 8.05741i | −1.15062 | + | 0.308308i | −0.783214 | − | 0.621752i | \(-0.786421\pi\) |
−0.367408 | + | 0.930060i | \(0.619755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0650 | + | 3.03758i | 0.613810 | + | 0.116060i | ||||
\(686\) | 0.00681755 | + | 0.0187311i | 0.000260295 | + | 0.000715155i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.24013 | − | 14.1747i | 0.0472793 | − | 0.540405i | ||||
\(689\) | 19.7569 | − | 16.5780i | 0.752679 | − | 0.631573i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.70424 | − | 2.44014i | 0.255041 | − | 0.0928274i | −0.211336 | − | 0.977414i | \(-0.567781\pi\) |
0.466377 | + | 0.884586i | \(0.345559\pi\) | |||||||
\(692\) | 8.15256 | + | 2.18447i | 0.309914 | + | 0.0830411i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.8059 | − | 26.4461i | −1.73877 | − | 1.00388i | ||||
\(695\) | 6.79115 | + | 0.678702i | 0.257603 | + | 0.0257446i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.9074 | + | 72.7146i | 1.28433 | + | 2.75426i | ||||
\(698\) | 1.47604 | − | 2.10801i | 0.0558690 | − | 0.0797892i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.00891991 | − | 0.00215560i | 0.000337141 | − | 8.14741e-5i | ||||
\(701\) | 18.1226i | 0.684482i | 0.939612 | + | 0.342241i | \(0.111186\pi\) | ||||
−0.939612 | + | 0.342241i | \(0.888814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.326292 | + | 0.326292i | −0.0123064 | + | 0.0123064i | ||||
\(704\) | 26.3202 | + | 22.0853i | 0.991981 | + | 0.832371i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.73863 | − | 43.8880i | −0.291247 | − | 1.65175i | ||||
\(707\) | −0.00675423 | + | 0.00314955i | −0.000254019 | + | 0.000118451i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.6080 | − | 3.63375i | −0.773951 | − | 0.136469i | −0.227296 | − | 0.973826i | \(-0.572988\pi\) |
−0.546656 | + | 0.837357i | \(0.684099\pi\) | |||||||
\(710\) | 55.8940 | − | 19.5660i | 2.09766 | − | 0.734298i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.84277 | + | 10.6094i | −0.106537 | + | 0.397603i | ||||
\(713\) | −25.2025 | − | 11.7521i | −0.943842 | − | 0.440121i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.2238 | + | 0.237270i | 0.718931 | + | 0.00887339i | ||||
\(716\) | −30.1048 | − | 35.8774i | −1.12507 | − | 1.34080i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.3603 | − | 52.2408i | 0.909117 | − | 1.94961i | ||||
\(719\) | −4.36807 | − | 7.56572i | −0.162902 | − | 0.282154i | 0.773007 | − | 0.634398i | \(-0.218752\pi\) |
−0.935908 | + | 0.352244i | \(0.885419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.00222038 | − | 0.00384581i | 8.26912e−5 | − | 0.000143225i | ||||
\(722\) | −20.0590 | − | 28.6472i | −0.746518 | − | 1.06614i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.33561 | − | 25.6494i | 0.346955 | − | 0.953252i | ||||
\(725\) | 9.10592 | + | 27.0800i | 0.338186 | + | 1.00573i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.90529 | + | 44.6377i | 0.144839 | + | 1.65552i | 0.626690 | + | 0.779268i | \(0.284409\pi\) |
−0.481851 | + | 0.876253i | \(0.660035\pi\) | |||||||
\(728\) | 0.00266931 | + | 0.00266931i | 9.89311e−5 | + | 9.89311e-5i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.533792 | − | 7.11105i | −0.0197565 | − | 0.263192i | ||||
\(731\) | 38.1379 | − | 45.4510i | 1.41058 | − | 1.68106i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.4458 | − | 12.9159i | −0.681312 | − | 0.477060i | 0.180970 | − | 0.983489i | \(-0.442076\pi\) |
−0.862282 | + | 0.506429i | \(0.830965\pi\) | |||||||
\(734\) | −43.3544 | − | 15.7797i | −1.60024 | − | 0.582440i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.44625 | + | 36.5585i | −0.237612 | + | 1.34756i | ||||
\(737\) | −1.73711 | − | 6.48298i | −0.0639873 | − | 0.238804i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.3820 | + | 16.9637i | −1.08084 | + | 0.624020i | −0.931122 | − | 0.364709i | \(-0.881168\pi\) |
−0.149714 | + | 0.988729i | \(0.547835\pi\) | |||||||
\(740\) | −0.587846 | + | 1.55510i | −0.0216096 | + | 0.0571667i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.0115095 | − | 0.00100695i | −0.000422528 | − | 3.69664e-5i | ||||
\(743\) | −25.4881 | − | 2.22992i | −0.935068 | − | 0.0818078i | −0.390573 | − | 0.920572i | \(-0.627723\pi\) |
−0.544495 | + | 0.838764i | \(0.683279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6596 | − | 9.32506i | 0.756908 | − | 0.341644i | ||||
\(746\) | −3.19968 | + | 1.84733i | −0.117148 | + | 0.0676357i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.5347 | + | 50.5122i | 0.494878 | + | 1.84691i | ||||
\(749\) | 0.00153867 | − | 0.00872624i | 5.62218e−5 | − | 0.000318850i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3171 | − | 6.66687i | −0.668400 | − | 0.243278i | −0.0145411 | − | 0.999894i | \(-0.504629\pi\) |
−0.653859 | + | 0.756617i | \(0.726851\pi\) | |||||||
\(752\) | −0.943105 | − | 0.660369i | −0.0343915 | − | 0.0240812i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.6667 | + | 30.5884i | −0.934726 | + | 1.11396i | ||||
\(755\) | 41.4732 | − | 3.11319i | 1.50936 | − | 0.113301i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3446 | + | 37.3446i | 1.35731 | + | 1.35731i | 0.877215 | + | 0.480097i | \(0.159399\pi\) |
0.480097 | + | 0.877215i | \(0.340601\pi\) | |||||||
\(758\) | −2.23509 | − | 25.5472i | −0.0811822 | − | 0.927917i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.20265 | + | 3.68391i | 0.224994 | + | 0.133630i | ||||
\(761\) | −13.8978 | + | 38.1838i | −0.503793 | + | 1.38416i | 0.383750 | + | 0.923437i | \(0.374632\pi\) |
−0.887543 | + | 0.460724i | \(0.847590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.00138854 | − | 0.00198304i | −5.02685e−5 | − | 7.17908e-5i | ||||
\(764\) | −1.75761 | + | 3.04427i | −0.0635881 | + | 0.110138i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.5732 | + | 20.0453i | 0.418156 | + | 0.724267i | ||||
\(767\) | −3.01892 | + | 6.47410i | −0.109007 | + | 0.233766i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.03060 | + | 1.22823i | 0.0371646 | + | 0.0442910i | 0.784307 | − | 0.620373i | \(-0.213019\pi\) |
−0.747142 | + | 0.664664i | \(0.768575\pi\) | |||||||
\(770\) | −0.00601423 | − | 0.00616454i | −0.000216738 | − | 0.000222155i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −45.4846 | − | 21.2098i | −1.63703 | − | 0.763358i | ||||
\(773\) | 8.72934 | − | 32.5784i | 0.313973 | − | 1.17176i | −0.610970 | − | 0.791654i | \(-0.709220\pi\) |
0.924942 | − | 0.380108i | \(-0.124113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.93442 | − | 25.3311i | 0.356855 | − | 0.909919i | ||||
\(776\) | 15.2015 | + | 2.68044i | 0.545702 | + | 0.0962220i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −78.1685 | + | 36.4506i | −2.80248 | + | 1.30682i | ||||
\(779\) | −3.59298 | − | 20.3768i | −0.128732 | − | 0.730074i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9609 | − | 20.9447i | −0.893172 | − | 0.749460i | ||||
\(782\) | −54.1877 | + | 54.1877i | −1.93775 | + | 1.93775i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 11.4502i | − | 0.408937i | ||||||
\(785\) | −0.116815 | − | 0.713906i | −0.00416932 | − | 0.0254804i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.32801 | + | 1.89659i | −0.0473384 | + | 0.0676063i | −0.842123 | − | 0.539285i | \(-0.818695\pi\) |
0.794785 | + | 0.606891i | \(0.207584\pi\) | |||||||
\(788\) | 20.3448 | + | 43.6296i | 0.724754 | + | 1.55424i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19.8983 | − | 16.2825i | 0.707952 | − | 0.579304i | ||||
\(791\) | 0.000626766 | 0 | 0.000361864i | 2.22852e−5 | 0 | 1.28664e-5i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2138 | − | 5.41626i | −0.717812 | − | 0.192337i | ||||
\(794\) | −21.5293 | + | 7.83603i | −0.764047 | + | 0.278090i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.8981 | − | 19.2138i | 0.811602 | − | 0.681015i | ||||
\(797\) | 1.45181 | − | 16.5943i | 0.0514259 | − | 0.587801i | −0.926141 | − | 0.377177i | \(-0.876895\pi\) |
0.977567 | − | 0.210624i | \(-0.0675495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64198 | − | 4.51129i | −0.0580889 | − | 0.159598i | ||||
\(800\) | −36.0962 | − | 4.05794i | −1.27619 | − | 0.143470i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −56.8031 | + | 15.2204i | −2.00579 | + | 0.537449i | ||||
\(803\) | −3.21410 | + | 2.25054i | −0.113423 | + | 0.0794197i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00200314 | − | 0.00712298i | 7.06013e−5 | − | 0.000251052i | ||||
\(806\) | 37.4510 | − | 6.60363i | 1.31916 | − | 0.232603i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.0273 | + | 1.83965i | −0.739739 | + | 0.0647188i | ||||
\(809\) | −38.2899 | −1.34620 | −0.673100 | − | 0.739551i | \(-0.735038\pi\) | ||||
−0.673100 | + | 0.739551i | \(0.735038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.1974 | 1.69244 | 0.846220 | − | 0.532833i | \(-0.178873\pi\) | ||||
0.846220 | + | 0.532833i | \(0.178873\pi\) | |||||||
\(812\) | 0.0104472 | 0.000914012i | 0.000366625 | 3.20755e-5i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.53656 | − | 0.270937i | 0.0538564 | − | 0.00949633i | ||||
\(815\) | −10.6620 | + | 5.98146i | −0.373472 | + | 0.209522i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5341 | + | 8.77644i | −0.438511 | + | 0.307049i | ||||
\(818\) | −72.5455 | + | 19.4385i | −2.53649 | + | 0.679652i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −42.0009 | − | 61.5875i | −1.46674 | − | 2.15073i | ||||
\(821\) | −5.73809 | − | 15.7653i | −0.200261 | − | 0.550212i | 0.798390 | − | 0.602141i | \(-0.205685\pi\) |
−0.998651 | + | 0.0519288i | \(0.983463\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.01595 | + | 34.4725i | −0.105130 | + | 1.20164i | 0.742056 | + | 0.670338i | \(0.233851\pi\) |
−0.847185 | + | 0.531298i | \(0.821705\pi\) | |||||||
\(824\) | 9.63498 | − | 8.08471i | 0.335651 | − | 0.281644i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.00300703 | − | 0.00109447i | 0.000104628 | − | 3.80815e-5i | ||||
\(827\) | −19.5339 | − | 5.23409i | −0.679261 | − | 0.182007i | −0.0973378 | − | 0.995251i | \(-0.531033\pi\) |
−0.581923 | + | 0.813244i | \(0.697699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.7476 | + | 26.4124i | 1.58888 | + | 0.917340i | 0.993492 | + | 0.113900i | \(0.0363344\pi\) |
0.595387 | + | 0.803439i | \(0.296999\pi\) | |||||||
\(830\) | −7.83048 | + | 78.3526i | −0.271800 | + | 2.71966i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.0607 | − | 36.5867i | −0.591473 | − | 1.26842i | ||||
\(833\) | 27.3858 | − | 39.1110i | 0.948861 | − | 1.35511i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.6359 | + | 6.64919i | −1.40626 | + | 0.230105i | ||||
\(836\) | − | 13.4862i | − | 0.466432i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.8475 | + | 24.8475i | −0.858342 | + | 0.858342i | ||||
\(839\) | 1.94021 | + | 1.62803i | 0.0669835 | + | 0.0562059i | 0.675665 | − | 0.737209i | \(-0.263857\pi\) |
−0.608681 | + | 0.793415i | \(0.708301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.633784 | + | 3.59437i | 0.0218546 | + | 0.123944i | ||||
\(842\) | 63.4780 | − | 29.6003i | 2.18760 | − | 1.02009i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.501982 | + | 0.0885129i | 0.0172789 | + | 0.00304674i | ||||
\(845\) | 5.83905 | + | 2.81104i | 0.200869 | + | 0.0967028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.000617162 | − | 0.00230328i | 2.12059e−5 | − | 7.91417e-5i | ||||
\(848\) | 12.0298 | + | 5.60957i | 0.413104 | + | 0.192634i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −56.2339 | − | 49.6017i | −1.92881 | − | 1.70132i | ||||
\(851\) | 0.861655 | + | 1.02688i | 0.0295371 | + | 0.0352010i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6637 | − | 37.8798i | 0.604792 | − | 1.29698i | −0.330734 | − | 0.943724i | \(-0.607296\pi\) |
0.935526 | − | 0.353257i | \(-0.114926\pi\) | |||||||
\(854\) | 0.00468729 | + | 0.00811862i | 0.000160396 | + | 0.000277813i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.5483 | − | 21.7343i | 0.428893 | − | 0.742864i | ||||
\(857\) | 15.3891 | + | 21.9778i | 0.525680 | + | 0.750749i | 0.990923 | − | 0.134434i | \(-0.0429217\pi\) |
−0.465242 | + | 0.885183i | \(0.654033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.80591 | − | 21.4466i | 0.266334 | − | 0.731747i | −0.732372 | − | 0.680904i | \(-0.761587\pi\) |
0.998707 | − | 0.0508429i | \(-0.0161908\pi\) | |||||||
\(860\) | −28.1508 | + | 47.3979i | −0.959934 | + | 1.61625i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.13765 | + | 13.0034i | 0.0387484 | + | 0.442896i | ||||
\(863\) | 7.93097 | + | 7.93097i | 0.269973 | + | 0.269973i | 0.829089 | − | 0.559116i | \(-0.188859\pi\) |
−0.559116 | + | 0.829089i | \(0.688859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.04784 | + | 4.34292i | 0.171632 | + | 0.147664i | ||||
\(866\) | −15.4685 | + | 18.4346i | −0.525641 | + | 0.626434i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.00818145 | − | 0.00572871i | −0.000277696 | − | 0.000194445i | ||||
\(869\) | −13.2938 | − | 4.83854i | −0.450961 | − | 0.164136i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.36935 | + | 7.76596i | −0.0463986 | + | 0.263139i | ||||
\(872\) | −1.77461 | − | 6.62293i | −0.0600959 | − | 0.224281i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.1153 | − | 9.88153i | 0.578934 | − | 0.334248i | ||||
\(875\) | 0.00707863 | + | 0.00152029i | 0.000239301 | + | 5.13953e-5i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.977840 | + | 0.0855499i | 0.0330193 | + | 0.00288882i | 0.103653 | − | 0.994613i | \(-0.466947\pi\) |
−0.0706341 | + | 0.997502i | \(0.522502\pi\) | |||||||
\(878\) | −63.7167 | − | 5.57448i | −2.15033 | − | 0.188130i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.07056 | + | 9.01829i | 0.137219 | + | 0.304007i | ||||
\(881\) | −22.3414 | + | 12.8988i | −0.752701 | + | 0.434572i | −0.826669 | − | 0.562689i | \(-0.809767\pi\) |
0.0739682 | + | 0.997261i | \(0.476434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.4224 | − | 46.3611i | −0.418048 | − | 1.56018i | −0.778652 | − | 0.627457i | \(-0.784096\pi\) |
0.360604 | − | 0.932719i | \(-0.382571\pi\) | |||||||
\(884\) | 10.6693 | − | 60.5085i | 0.358847 | − | 2.03512i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.0866 | − | 20.4139i | −1.88427 | − | 0.685817i | ||||
\(887\) | 5.46649 | + | 3.82768i | 0.183547 | + | 0.128521i | 0.661739 | − | 0.749734i | \(-0.269819\pi\) |
−0.478192 | + | 0.878255i | \(0.658708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.00434872 | + | 0.00518260i | −0.000145851 | + | 0.000173819i | ||||
\(890\) | −19.2018 | + | 22.3185i | −0.643646 | + | 0.748119i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.9415 | + | 36.9415i | 1.23689 | + | 1.23689i | ||||
\(893\) | 0.107907 | + | 1.23338i | 0.00361097 | + | 0.0412735i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.12235 | − | 35.8070i | −0.304926 | − | 1.19690i | ||||
\(896\) | −0.00296711 | + | 0.00815206i | −9.91241e−5 | + | 0.000272341i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.38105 | + | 6.25679i | 0.146198 | + | 0.208792i | ||||
\(899\) | 15.5475 | − | 26.9291i | 0.518538 | − | 0.898134i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.6739 | + | 47.9327i | 0.921953 | + | 1.59687i | ||||
\(902\) | −29.5671 | + | 63.4068i | −0.984476 | + | 2.11121i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.31760 | + | 1.57025i | 0.0438226 | + | 0.0522258i | ||||
\(905\) | 15.4144 | − | 15.0385i | 0.512392 | − | 0.499898i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07303 | + | 0.500360i | 0.0356292 | + | 0.0166142i | 0.440351 | − | 0.897826i | \(-0.354854\pi\) |
−0.404722 | + | 0.914440i | \(0.632632\pi\) | |||||||
\(908\) | −11.4837 | + | 42.8576i | −0.381099 | + | 1.42228i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.00334326 | + | 0.00955065i | 0.000110828 | + | 0.000316601i | ||||
\(911\) | 27.0446 | + | 4.76870i | 0.896028 | + | 0.157994i | 0.602653 | − | 0.798003i | \(-0.294110\pi\) |
0.293375 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.2670 | − | 18.3105i | 1.29955 | − | 0.605990i | ||||
\(914\) | −9.00761 | − | 51.0847i | −0.297945 | − | 1.68973i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.3502 | + | 12.8803i | 0.507185 | + | 0.425578i | ||||
\(917\) | 0.00666650 | − | 0.00666650i | 0.000220147 | − | 0.000220147i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.2332i | − | 0.700419i | −0.936671 | − | 0.350209i | \(-0.886110\pi\) | ||
0.936671 | − | 0.350209i | \(-0.113890\pi\) | |||||||
\(920\) | 12.2314 | − | 17.0173i | 0.403258 | − | 0.561045i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0970 | + | 14.4200i | −0.332528 | + | 0.474899i | ||||
\(923\) | 16.1796 | + | 34.6972i | 0.532557 | + | 1.14207i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.950085 | + | 0.904303i | −0.0312386 | + | 0.0297333i | ||||
\(926\) | 4.49731 | + | 2.59652i | 0.147791 | + | 0.0853270i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40.0962 | − | 10.7437i | −1.31622 | − | 0.352680i | ||||
\(929\) | 28.3403 | − | 10.3150i | 0.929816 | − | 0.338425i | 0.167679 | − | 0.985842i | \(-0.446373\pi\) |
0.762136 | + | 0.647416i | \(0.224150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.43249 | + | 7.91479i | −0.309137 | + | 0.259397i | ||||
\(932\) | −0.564962 | + | 6.45754i | −0.0185059 | + | 0.211524i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.4682 | − | 42.4985i | −0.506135 | − | 1.39059i | ||||
\(935\) | −7.66529 | + | 40.5397i | −0.250682 | + | 1.32579i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5394 | − | 4.43173i | 0.540320 | − | 0.144778i | 0.0216704 | − | 0.999765i | \(-0.493102\pi\) |
0.518650 | + | 0.854987i | \(0.326435\pi\) | |||||||
\(938\) | 0.00289372 | − | 0.00202620i | 9.44832e−5 | − | 6.61579e-5i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.18245 | + | 3.89022i | 0.0711838 | + | 0.126885i | ||||
\(941\) | 21.0459 | − | 3.71097i | 0.686078 | − | 0.120974i | 0.180266 | − | 0.983618i | \(-0.442304\pi\) |
0.505812 | + | 0.862644i | \(0.331193\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.8787 | + | 5.23871i | −1.94992 | + | 0.170596i | ||||
\(944\) | −3.67638 | −0.119656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 51.7372 | 1.68212 | ||||||||
\(947\) | 28.3818 | − | 2.48308i | 0.922284 | − | 0.0806894i | 0.383886 | − | 0.923380i | \(-0.374585\pi\) |
0.538398 | + | 0.842691i | \(0.319030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.54003 | − | 0.800530i | 0.147376 | − | 0.0259863i | ||||
\(950\) | 10.6973 | + | 16.1095i | 0.347067 | + | 0.522661i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.00663611 | + | 0.00464666i | −0.000215078 | + | 0.000150599i | ||||
\(953\) | −48.9558 | + | 13.1177i | −1.58583 | + | 0.424923i | −0.940726 | − | 0.339169i | \(-0.889854\pi\) |
−0.645108 | + | 0.764091i | \(0.723188\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.29128 | + | 1.56258i | −0.0741440 | + | 0.0505641i | ||||
\(956\) | −7.46208 | − | 20.5019i | −0.241341 | − | 0.663078i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.12901 | + | 47.1948i | −0.133402 | + | 1.52479i | ||||
\(959\) | 0.00362713 | − | 0.00304352i | 0.000117126 | − | 9.82804e-5i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.30221 | − | 0.473965i | 0.0420067 | − | 0.0152892i | ||||
\(962\) | −1.77074 | − | 0.474467i | −0.0570908 | − | 0.0152974i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.5551 | − | 13.5995i | −0.758657 | − | 0.438011i | ||||
\(965\) | −25.0752 | − | 30.6436i | −0.807198 | − | 0.986454i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4321 | − | 48.1057i | −0.721366 | − | 1.54697i | −0.833029 | − | 0.553229i | \(-0.813396\pi\) |
0.111663 | − | 0.993746i | \(-0.464382\pi\) | |||||||
\(968\) | 3.87378 | − | 5.53233i | 0.124508 | − | 0.177816i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33.5983 | + | 24.1492i | 1.07878 | + | 0.775383i | ||||
\(971\) | 12.4548i | 0.399695i | 0.979827 | + | 0.199847i | \(0.0640447\pi\) | ||||
−0.979827 | + | 0.199847i | \(0.935955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.00139762 | − | 0.00139762i | 4.48056e−5 | − | 4.48056e-5i | ||||
\(974\) | 5.24344 | + | 4.39976i | 0.168011 | + | 0.140978i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.87021 | − | 10.6065i | −0.0598639 | − | 0.339505i | ||||
\(977\) | 17.1398 | − | 7.99244i | 0.548352 | − | 0.255701i | −0.128639 | − | 0.991691i | \(-0.541061\pi\) |
0.676992 | + | 0.735991i | \(0.263283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.9536 | + | 2.81305i | 0.509879 | + | 0.0899055i | ||||
\(980\) | −19.2430 | + | 39.9713i | −0.614695 | + | 1.27684i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.69139 | − | 17.5085i | 0.149708 | − | 0.558719i | ||||
\(983\) | −12.0933 | − | 5.63921i | −0.385717 | − | 0.179863i | 0.220080 | − | 0.975482i | \(-0.429368\pi\) |
−0.605798 | + | 0.795619i | \(0.707146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.468739 | + | 37.9777i | −0.0149353 | + | 1.21007i | ||||
\(986\) | −55.0815 | − | 65.6436i | −1.75415 | − | 2.09052i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.69656 | + | 14.3608i | −0.213046 | + | 0.456878i | ||||
\(989\) | 22.2250 | + | 38.4948i | 0.706713 | + | 1.22406i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.99736 | + | 5.19158i | −0.0952142 | + | 0.164916i | −0.909698 | − | 0.415270i | \(-0.863687\pi\) |
0.814484 | + | 0.580186i | \(0.197020\pi\) | |||||||
\(992\) | 22.6757 | + | 32.3842i | 0.719953 | + | 1.02820i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.00586569 | − | 0.0161158i | 0.000186048 | − | 0.000511163i | ||||
\(995\) | 22.8532 | − | 5.82217i | 0.724494 | − | 0.184575i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.98279 | − | 45.5235i | −0.126136 | − | 1.44174i | −0.750634 | − | 0.660718i | \(-0.770252\pi\) |
0.624498 | − | 0.781026i | \(-0.285304\pi\) | |||||||
\(998\) | 41.0167 | + | 41.0167i | 1.29836 | + | 1.29836i | ||||
\(999\) | 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 | 405.2.r.a.197.14 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.92.3 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.278.3 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.443.3 | 192 | |||
15.8 | even | 4 | 135.2.q.a.38.14 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.632.14 | 192 | |||
27.5 | odd | 18 | inner | 405.2.r.a.287.3 | 192 | ||
27.22 | even | 9 | 135.2.q.a.32.14 | ✓ | 192 | ||
135.22 | odd | 36 | 675.2.ba.b.518.14 | 192 | |||
135.49 | even | 18 | 675.2.ba.b.32.3 | 192 | |||
135.103 | odd | 36 | 135.2.q.a.113.3 | yes | 192 | ||
135.113 | even | 36 | inner | 405.2.r.a.368.14 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.14 | ✓ | 192 | 27.22 | even | 9 | ||
135.2.q.a.38.14 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.92.3 | yes | 192 | 3.2 | odd | 2 | ||
135.2.q.a.113.3 | yes | 192 | 135.103 | odd | 36 | ||
405.2.r.a.197.14 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.278.3 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.287.3 | 192 | 27.5 | odd | 18 | inner | ||
405.2.r.a.368.14 | 192 | 135.113 | even | 36 | inner | ||
675.2.ba.b.32.3 | 192 | 135.49 | even | 18 | |||
675.2.ba.b.443.3 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.518.14 | 192 | 135.22 | odd | 36 | |||
675.2.ba.b.632.14 | 192 | 15.14 | odd | 2 |