Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.4 | ||
Character | \(\chi\) | \(=\) | 105.43 |
Dual form | 105.3.l.a.22.4 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.01289 | + | 1.01289i | −0.506444 | + | 0.506444i | −0.913433 | − | 0.406989i | \(-0.866579\pi\) |
0.406989 | + | 0.913433i | \(0.366579\pi\) | |||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.94811i | 0.487029i | ||||||||
\(5\) | 3.97454 | + | 3.03365i | 0.794909 | + | 0.606729i | ||||
\(6\) | −2.48106 | −0.413510 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −6.02478 | − | 6.02478i | −0.753097 | − | 0.753097i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −7.09851 | + | 0.953024i | −0.709851 | + | 0.0953024i | ||||
\(11\) | −10.7111 | −0.973734 | −0.486867 | − | 0.873476i | \(-0.661860\pi\) | ||||
−0.486867 | + | 0.873476i | \(0.661860\pi\) | |||||||
\(12\) | −2.38594 | + | 2.38594i | −0.198829 | + | 0.198829i | ||||
\(13\) | 15.5836 | + | 15.5836i | 1.19874 | + | 1.19874i | 0.974545 | + | 0.224192i | \(0.0719741\pi\) |
0.224192 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(14\) | 3.78988i | 0.270706i | ||||||||
\(15\) | 1.15236 | + | 8.58324i | 0.0768239 | + | 0.572216i | ||||
\(16\) | 4.41239 | 0.275774 | ||||||||
\(17\) | −13.8771 | + | 13.8771i | −0.816298 | + | 0.816298i | −0.985569 | − | 0.169271i | \(-0.945859\pi\) |
0.169271 | + | 0.985569i | \(0.445859\pi\) | |||||||
\(18\) | −3.03866 | − | 3.03866i | −0.168815 | − | 0.168815i | ||||
\(19\) | − | 33.1159i | − | 1.74294i | −0.490446 | − | 0.871472i | \(-0.663166\pi\) | ||
0.490446 | − | 0.871472i | \(-0.336834\pi\) | |||||||
\(20\) | −5.90989 | + | 7.74287i | −0.295494 | + | 0.387143i | ||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | 10.8491 | − | 10.8491i | 0.493142 | − | 0.493142i | ||||
\(23\) | 8.39058 | + | 8.39058i | 0.364808 | + | 0.364808i | 0.865579 | − | 0.500772i | \(-0.166950\pi\) |
−0.500772 | + | 0.865579i | \(0.666950\pi\) | |||||||
\(24\) | − | 14.7576i | − | 0.614901i | ||||||
\(25\) | 6.59399 | + | 24.1147i | 0.263759 | + | 0.964588i | ||||
\(26\) | −31.5688 | −1.21419 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 3.64459 | + | 3.64459i | 0.130164 | + | 0.130164i | ||||
\(29\) | − | 42.0711i | − | 1.45073i | −0.688366 | − | 0.725364i | \(-0.741672\pi\) | ||
0.688366 | − | 0.725364i | \(-0.258328\pi\) | |||||||
\(30\) | −9.86108 | − | 7.52666i | −0.328703 | − | 0.250889i | ||||
\(31\) | 44.7239 | 1.44270 | 0.721352 | − | 0.692568i | \(-0.243521\pi\) | ||||
0.721352 | + | 0.692568i | \(0.243521\pi\) | |||||||
\(32\) | 19.6298 | − | 19.6298i | 0.613433 | − | 0.613433i | ||||
\(33\) | −13.1183 | − | 13.1183i | −0.397525 | − | 0.397525i | ||||
\(34\) | − | 28.1118i | − | 0.826819i | ||||||
\(35\) | 13.1111 | − | 1.76026i | 0.374603 | − | 0.0502931i | ||||
\(36\) | −5.84434 | −0.162343 | ||||||||
\(37\) | 21.6841 | − | 21.6841i | 0.586056 | − | 0.586056i | −0.350505 | − | 0.936561i | \(-0.613990\pi\) |
0.936561 | + | 0.350505i | \(0.113990\pi\) | |||||||
\(38\) | 33.5427 | + | 33.5427i | 0.882703 | + | 0.882703i | ||||
\(39\) | 38.1718i | 0.978764i | ||||||||
\(40\) | −5.66870 | − | 42.2228i | −0.141717 | − | 1.05557i | ||||
\(41\) | −22.6096 | −0.551454 | −0.275727 | − | 0.961236i | \(-0.588919\pi\) | ||||
−0.275727 | + | 0.961236i | \(0.588919\pi\) | |||||||
\(42\) | −4.64164 | + | 4.64164i | −0.110515 | + | 0.110515i | ||||
\(43\) | 9.41107 | + | 9.41107i | 0.218862 | + | 0.218862i | 0.808019 | − | 0.589157i | \(-0.200540\pi\) |
−0.589157 | + | 0.808019i | \(0.700540\pi\) | |||||||
\(44\) | − | 20.8664i | − | 0.474237i | ||||||
\(45\) | −9.10094 | + | 11.9236i | −0.202243 | + | 0.264970i | ||||
\(46\) | −16.9974 | −0.369510 | ||||||||
\(47\) | 46.0043 | − | 46.0043i | 0.978816 | − | 0.978816i | −0.0209647 | − | 0.999780i | \(-0.506674\pi\) |
0.999780 | + | 0.0209647i | \(0.00667376\pi\) | |||||||
\(48\) | 5.40405 | + | 5.40405i | 0.112584 | + | 0.112584i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | −31.1045 | − | 17.7465i | −0.622090 | − | 0.354931i | ||||
\(51\) | −33.9917 | −0.666505 | ||||||||
\(52\) | −30.3586 | + | 30.3586i | −0.583819 | + | 0.583819i | ||||
\(53\) | 51.4312 | + | 51.4312i | 0.970400 | + | 0.970400i | 0.999574 | − | 0.0291746i | \(-0.00928789\pi\) |
−0.0291746 | + | 0.999574i | \(0.509288\pi\) | |||||||
\(54\) | − | 7.44318i | − | 0.137837i | ||||||
\(55\) | −42.5716 | − | 32.4936i | −0.774030 | − | 0.590793i | ||||
\(56\) | −22.5426 | −0.402547 | ||||||||
\(57\) | 40.5586 | − | 40.5586i | 0.711554 | − | 0.711554i | ||||
\(58\) | 42.6133 | + | 42.6133i | 0.734712 | + | 0.734712i | ||||
\(59\) | 5.55721i | 0.0941900i | 0.998890 | + | 0.0470950i | \(0.0149964\pi\) | ||||
−0.998890 | + | 0.0470950i | \(0.985004\pi\) | |||||||
\(60\) | −16.7211 | + | 2.24493i | −0.278686 | + | 0.0374155i | ||||
\(61\) | −49.2291 | −0.807034 | −0.403517 | − | 0.914972i | \(-0.632212\pi\) | ||||
−0.403517 | + | 0.914972i | \(0.632212\pi\) | |||||||
\(62\) | −45.3003 | + | 45.3003i | −0.730649 | + | 0.730649i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 57.4152i | 0.897113i | ||||||||
\(65\) | 14.6625 | + | 109.213i | 0.225578 | + | 1.68019i | ||||
\(66\) | 26.5748 | 0.402649 | ||||||||
\(67\) | −38.8463 | + | 38.8463i | −0.579796 | + | 0.579796i | −0.934847 | − | 0.355051i | \(-0.884463\pi\) |
0.355051 | + | 0.934847i | \(0.384463\pi\) | |||||||
\(68\) | −27.0341 | − | 27.0341i | −0.397561 | − | 0.397561i | ||||
\(69\) | 20.5526i | 0.297864i | ||||||||
\(70\) | −11.4972 | + | 15.0630i | −0.164245 | + | 0.215186i | ||||
\(71\) | 23.5507 | 0.331699 | 0.165850 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165850 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(72\) | 18.0743 | − | 18.0743i | 0.251032 | − | 0.251032i | ||||
\(73\) | −60.1053 | − | 60.1053i | −0.823360 | − | 0.823360i | 0.163228 | − | 0.986588i | \(-0.447809\pi\) |
−0.986588 | + | 0.163228i | \(0.947809\pi\) | |||||||
\(74\) | 43.9271i | 0.593609i | ||||||||
\(75\) | −21.4584 | + | 37.6103i | −0.286112 | + | 0.501471i | ||||
\(76\) | 64.5136 | 0.848863 | ||||||||
\(77\) | −20.0386 | + | 20.0386i | −0.260241 | + | 0.260241i | ||||
\(78\) | −38.6638 | − | 38.6638i | −0.495689 | − | 0.495689i | ||||
\(79\) | 8.04945i | 0.101892i | 0.998701 | + | 0.0509459i | \(0.0162236\pi\) | ||||
−0.998701 | + | 0.0509459i | \(0.983776\pi\) | |||||||
\(80\) | 17.5372 | + | 13.3856i | 0.219215 | + | 0.167320i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 22.9010 | − | 22.9010i | 0.279280 | − | 0.279280i | ||||
\(83\) | −5.76487 | − | 5.76487i | −0.0694562 | − | 0.0694562i | 0.671525 | − | 0.740982i | \(-0.265639\pi\) |
−0.740982 | + | 0.671525i | \(0.765639\pi\) | |||||||
\(84\) | 8.92738i | 0.106278i | ||||||||
\(85\) | −97.2531 | + | 13.0569i | −1.14415 | + | 0.153611i | ||||
\(86\) | −19.0647 | −0.221683 | ||||||||
\(87\) | 51.5264 | − | 51.5264i | 0.592257 | − | 0.592257i | ||||
\(88\) | 64.5318 | + | 64.5318i | 0.733316 | + | 0.733316i | ||||
\(89\) | − | 62.2564i | − | 0.699510i | −0.936841 | − | 0.349755i | \(-0.886265\pi\) | ||
0.936841 | − | 0.349755i | \(-0.113735\pi\) | |||||||
\(90\) | −2.85907 | − | 21.2955i | −0.0317675 | − | 0.236617i | ||||
\(91\) | 58.3084 | 0.640752 | ||||||||
\(92\) | −16.3458 | + | 16.3458i | −0.177672 | + | 0.177672i | ||||
\(93\) | 54.7753 | + | 54.7753i | 0.588982 | + | 0.588982i | ||||
\(94\) | 93.1945i | 0.991431i | ||||||||
\(95\) | 100.462 | − | 131.621i | 1.05749 | − | 1.38548i | ||||
\(96\) | 48.0831 | 0.500866 | ||||||||
\(97\) | 21.9918 | − | 21.9918i | 0.226719 | − | 0.226719i | −0.584601 | − | 0.811321i | \(-0.698749\pi\) |
0.811321 | + | 0.584601i | \(0.198749\pi\) | |||||||
\(98\) | 7.09022 | + | 7.09022i | 0.0723492 | + | 0.0723492i | ||||
\(99\) | − | 32.1332i | − | 0.324578i | ||||||
\(100\) | −46.9782 | + | 12.8458i | −0.469782 | + | 0.128458i | ||||
\(101\) | −85.1311 | −0.842882 | −0.421441 | − | 0.906856i | \(-0.638476\pi\) | ||||
−0.421441 | + | 0.906856i | \(0.638476\pi\) | |||||||
\(102\) | 34.4298 | − | 34.4298i | 0.337547 | − | 0.337547i | ||||
\(103\) | −80.6390 | − | 80.6390i | −0.782903 | − | 0.782903i | 0.197417 | − | 0.980320i | \(-0.436745\pi\) |
−0.980320 | + | 0.197417i | \(0.936745\pi\) | |||||||
\(104\) | − | 187.775i | − | 1.80553i | ||||||
\(105\) | 18.2136 | + | 13.9019i | 0.173463 | + | 0.132399i | ||||
\(106\) | −104.188 | −0.982906 | ||||||||
\(107\) | 32.1195 | − | 32.1195i | 0.300183 | − | 0.300183i | −0.540903 | − | 0.841085i | \(-0.681917\pi\) |
0.841085 | + | 0.540903i | \(0.181917\pi\) | |||||||
\(108\) | −7.15783 | − | 7.15783i | −0.0662762 | − | 0.0662762i | ||||
\(109\) | 59.1909i | 0.543036i | 0.962433 | + | 0.271518i | \(0.0875257\pi\) | ||||
−0.962433 | + | 0.271518i | \(0.912474\pi\) | |||||||
\(110\) | 76.0327 | − | 10.2079i | 0.691207 | − | 0.0927992i | ||||
\(111\) | 53.1149 | 0.478512 | ||||||||
\(112\) | 8.25483 | − | 8.25483i | 0.0737038 | − | 0.0737038i | ||||
\(113\) | −23.2737 | − | 23.2737i | −0.205962 | − | 0.205962i | 0.596587 | − | 0.802549i | \(-0.296523\pi\) |
−0.802549 | + | 0.596587i | \(0.796523\pi\) | |||||||
\(114\) | 82.1626i | 0.720724i | ||||||||
\(115\) | 7.89467 | + | 58.8028i | 0.0686493 | + | 0.511328i | ||||
\(116\) | 81.9593 | 0.706546 | ||||||||
\(117\) | −46.7507 | + | 46.7507i | −0.399579 | + | 0.399579i | ||||
\(118\) | −5.62883 | − | 5.62883i | −0.0477020 | − | 0.0477020i | ||||
\(119\) | 51.9232i | 0.436330i | ||||||||
\(120\) | 44.7694 | − | 58.6548i | 0.373078 | − | 0.488790i | ||||
\(121\) | −6.27280 | −0.0518413 | ||||||||
\(122\) | 49.8635 | − | 49.8635i | 0.408718 | − | 0.408718i | ||||
\(123\) | −27.6910 | − | 27.6910i | −0.225130 | − | 0.225130i | ||||
\(124\) | 87.1272i | 0.702639i | ||||||||
\(125\) | −46.9474 | + | 115.849i | −0.375579 | + | 0.926790i | ||||
\(126\) | −11.3696 | −0.0902353 | ||||||||
\(127\) | 4.63998 | − | 4.63998i | 0.0365353 | − | 0.0365353i | −0.688603 | − | 0.725138i | \(-0.741776\pi\) |
0.725138 | + | 0.688603i | \(0.241776\pi\) | |||||||
\(128\) | 20.3642 | + | 20.3642i | 0.159095 | + | 0.159095i | ||||
\(129\) | 23.0523i | 0.178700i | ||||||||
\(130\) | −125.472 | − | 95.7687i | −0.965167 | − | 0.736682i | ||||
\(131\) | −51.2674 | −0.391354 | −0.195677 | − | 0.980668i | \(-0.562690\pi\) | ||||
−0.195677 | + | 0.980668i | \(0.562690\pi\) | |||||||
\(132\) | 25.5560 | − | 25.5560i | 0.193606 | − | 0.193606i | ||||
\(133\) | −61.9542 | − | 61.9542i | −0.465821 | − | 0.465821i | ||||
\(134\) | − | 78.6939i | − | 0.587268i | ||||||
\(135\) | −25.7497 | + | 3.45708i | −0.190739 | + | 0.0256080i | ||||
\(136\) | 167.212 | 1.22950 | ||||||||
\(137\) | −34.4467 | + | 34.4467i | −0.251436 | + | 0.251436i | −0.821559 | − | 0.570123i | \(-0.806895\pi\) |
0.570123 | + | 0.821559i | \(0.306895\pi\) | |||||||
\(138\) | −20.8175 | − | 20.8175i | −0.150852 | − | 0.150852i | ||||
\(139\) | − | 207.019i | − | 1.48935i | −0.667430 | − | 0.744673i | \(-0.732606\pi\) | ||
0.667430 | − | 0.744673i | \(-0.267394\pi\) | |||||||
\(140\) | 3.42918 | + | 25.5420i | 0.0244942 | + | 0.182443i | ||||
\(141\) | 112.687 | 0.799200 | ||||||||
\(142\) | −23.8542 | + | 23.8542i | −0.167987 | + | 0.167987i | ||||
\(143\) | −166.917 | − | 166.917i | −1.16725 | − | 1.16725i | ||||
\(144\) | 13.2372i | 0.0919248i | ||||||||
\(145\) | 127.629 | − | 167.213i | 0.880199 | − | 1.15320i | ||||
\(146\) | 121.760 | 0.833972 | ||||||||
\(147\) | 8.57321 | − | 8.57321i | 0.0583212 | − | 0.0583212i | ||||
\(148\) | 42.2430 | + | 42.2430i | 0.285426 | + | 0.285426i | ||||
\(149\) | − | 63.0323i | − | 0.423036i | −0.977374 | − | 0.211518i | \(-0.932159\pi\) | ||
0.977374 | − | 0.211518i | \(-0.0678406\pi\) | |||||||
\(150\) | −16.3601 | − | 59.8300i | −0.109067 | − | 0.398867i | ||||
\(151\) | −31.5113 | −0.208684 | −0.104342 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104342 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(152\) | −199.516 | + | 199.516i | −1.31261 | + | 1.31261i | ||||
\(153\) | −41.6312 | − | 41.6312i | −0.272099 | − | 0.272099i | ||||
\(154\) | − | 40.5937i | − | 0.263596i | ||||||
\(155\) | 177.757 | + | 135.676i | 1.14682 | + | 0.875331i | ||||
\(156\) | −74.3631 | −0.476686 | ||||||||
\(157\) | −163.580 | + | 163.580i | −1.04191 | + | 1.04191i | −0.0428304 | + | 0.999082i | \(0.513637\pi\) |
−0.999082 | + | 0.0428304i | \(0.986363\pi\) | |||||||
\(158\) | −8.15319 | − | 8.15319i | −0.0516025 | − | 0.0516025i | ||||
\(159\) | 125.980i | 0.792328i | ||||||||
\(160\) | 137.570 | − | 18.4697i | 0.859810 | − | 0.115435i | ||||
\(161\) | 31.3947 | 0.194998 | ||||||||
\(162\) | 9.11599 | − | 9.11599i | 0.0562716 | − | 0.0562716i | ||||
\(163\) | −80.5107 | − | 80.5107i | −0.493931 | − | 0.493931i | 0.415612 | − | 0.909542i | \(-0.363568\pi\) |
−0.909542 | + | 0.415612i | \(0.863568\pi\) | |||||||
\(164\) | − | 44.0461i | − | 0.268574i | ||||||
\(165\) | −12.3430 | − | 91.9358i | −0.0748061 | − | 0.557187i | ||||
\(166\) | 11.6783 | 0.0703514 | ||||||||
\(167\) | −124.516 | + | 124.516i | −0.745606 | + | 0.745606i | −0.973651 | − | 0.228044i | \(-0.926767\pi\) |
0.228044 | + | 0.973651i | \(0.426767\pi\) | |||||||
\(168\) | −27.6090 | − | 27.6090i | −0.164339 | − | 0.164339i | ||||
\(169\) | 316.696i | 1.87394i | ||||||||
\(170\) | 85.2814 | − | 111.732i | 0.501655 | − | 0.657245i | ||||
\(171\) | 99.3478 | 0.580981 | ||||||||
\(172\) | −18.3338 | + | 18.3338i | −0.106592 | + | 0.106592i | ||||
\(173\) | 161.634 | + | 161.634i | 0.934299 | + | 0.934299i | 0.997971 | − | 0.0636715i | \(-0.0202810\pi\) |
−0.0636715 | + | 0.997971i | \(0.520281\pi\) | |||||||
\(174\) | 104.381i | 0.599890i | ||||||||
\(175\) | 57.4507 | + | 32.7783i | 0.328290 | + | 0.187304i | ||||
\(176\) | −47.2615 | −0.268531 | ||||||||
\(177\) | −6.80616 | + | 6.80616i | −0.0384529 | + | 0.0384529i | ||||
\(178\) | 63.0587 | + | 63.0587i | 0.354263 | + | 0.354263i | ||||
\(179\) | − | 2.98679i | − | 0.0166860i | −0.999965 | − | 0.00834298i | \(-0.997344\pi\) | ||
0.999965 | − | 0.00834298i | \(-0.00265568\pi\) | |||||||
\(180\) | −23.2286 | − | 17.7297i | −0.129048 | − | 0.0984982i | ||||
\(181\) | −91.6182 | −0.506178 | −0.253089 | − | 0.967443i | \(-0.581447\pi\) | ||||
−0.253089 | + | 0.967443i | \(0.581447\pi\) | |||||||
\(182\) | −59.0599 | + | 59.0599i | −0.324505 | + | 0.324505i | ||||
\(183\) | −60.2930 | − | 60.2930i | −0.329470 | − | 0.329470i | ||||
\(184\) | − | 101.103i | − | 0.549471i | ||||||
\(185\) | 151.966 | − | 20.4025i | 0.821438 | − | 0.110284i | ||||
\(186\) | −110.963 | −0.596573 | ||||||||
\(187\) | 148.638 | − | 148.638i | 0.794858 | − | 0.794858i | ||||
\(188\) | 89.6217 | + | 89.6217i | 0.476711 | + | 0.476711i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 31.5603 | + | 235.074i | 0.166107 | + | 1.23723i | ||||
\(191\) | −238.486 | −1.24862 | −0.624308 | − | 0.781178i | \(-0.714619\pi\) | ||||
−0.624308 | + | 0.781178i | \(0.714619\pi\) | |||||||
\(192\) | −70.3190 | + | 70.3190i | −0.366245 | + | 0.366245i | ||||
\(193\) | −69.3305 | − | 69.3305i | −0.359226 | − | 0.359226i | 0.504302 | − | 0.863527i | \(-0.331750\pi\) |
−0.863527 | + | 0.504302i | \(0.831750\pi\) | |||||||
\(194\) | 44.5504i | 0.229641i | ||||||||
\(195\) | −115.800 | + | 151.716i | −0.593845 | + | 0.778028i | ||||
\(196\) | 13.6368 | 0.0695755 | ||||||||
\(197\) | 63.9728 | − | 63.9728i | 0.324735 | − | 0.324735i | −0.525845 | − | 0.850580i | \(-0.676251\pi\) |
0.850580 | + | 0.525845i | \(0.176251\pi\) | |||||||
\(198\) | 32.5474 | + | 32.5474i | 0.164381 | + | 0.164381i | ||||
\(199\) | − | 50.4616i | − | 0.253576i | −0.991930 | − | 0.126788i | \(-0.959533\pi\) | ||
0.991930 | − | 0.126788i | \(-0.0404668\pi\) | |||||||
\(200\) | 105.558 | − | 185.013i | 0.527792 | − | 0.925065i | ||||
\(201\) | −95.1536 | −0.473401 | ||||||||
\(202\) | 86.2283 | − | 86.2283i | 0.426873 | − | 0.426873i | ||||
\(203\) | −78.7078 | − | 78.7078i | −0.387723 | − | 0.387723i | ||||
\(204\) | − | 66.2198i | − | 0.324607i | ||||||
\(205\) | −89.8628 | − | 68.5895i | −0.438355 | − | 0.334583i | ||||
\(206\) | 163.357 | 0.792993 | ||||||||
\(207\) | −25.1717 | + | 25.1717i | −0.121603 | + | 0.121603i | ||||
\(208\) | 68.7608 | + | 68.7608i | 0.330581 | + | 0.330581i | ||||
\(209\) | 354.707i | 1.69716i | ||||||||
\(210\) | −32.5295 | + | 4.36730i | −0.154902 | + | 0.0207967i | ||||
\(211\) | 213.312 | 1.01096 | 0.505478 | − | 0.862840i | \(-0.331316\pi\) | ||||
0.505478 | + | 0.862840i | \(0.331316\pi\) | |||||||
\(212\) | −100.194 | + | 100.194i | −0.472612 | + | 0.472612i | ||||
\(213\) | 28.8436 | + | 28.8436i | 0.135416 | + | 0.135416i | ||||
\(214\) | 65.0670i | 0.304051i | ||||||||
\(215\) | 8.85485 | + | 65.9545i | 0.0411853 | + | 0.306765i | ||||
\(216\) | 44.2729 | 0.204967 | ||||||||
\(217\) | 83.6707 | − | 83.6707i | 0.385579 | − | 0.385579i | ||||
\(218\) | −59.9538 | − | 59.9538i | −0.275017 | − | 0.275017i | ||||
\(219\) | − | 147.227i | − | 0.672271i | ||||||
\(220\) | 63.3013 | − | 82.9344i | 0.287733 | − | 0.376975i | ||||
\(221\) | −432.509 | −1.95705 | ||||||||
\(222\) | −53.7994 | + | 53.7994i | −0.242340 | + | 0.242340i | ||||
\(223\) | −120.538 | − | 120.538i | −0.540530 | − | 0.540530i | 0.383154 | − | 0.923684i | \(-0.374838\pi\) |
−0.923684 | + | 0.383154i | \(0.874838\pi\) | |||||||
\(224\) | − | 73.4482i | − | 0.327894i | ||||||
\(225\) | −72.3441 | + | 19.7820i | −0.321529 | + | 0.0879198i | ||||
\(226\) | 47.1473 | 0.208616 | ||||||||
\(227\) | −106.933 | + | 106.933i | −0.471069 | + | 0.471069i | −0.902260 | − | 0.431191i | \(-0.858093\pi\) |
0.431191 | + | 0.902260i | \(0.358093\pi\) | |||||||
\(228\) | 79.0127 | + | 79.0127i | 0.346547 | + | 0.346547i | ||||
\(229\) | 409.120i | 1.78655i | 0.449508 | + | 0.893276i | \(0.351599\pi\) | ||||
−0.449508 | + | 0.893276i | \(0.648401\pi\) | |||||||
\(230\) | −67.5571 | − | 51.5642i | −0.293726 | − | 0.224192i | ||||
\(231\) | −49.0843 | −0.212486 | ||||||||
\(232\) | −253.469 | + | 253.469i | −1.09254 | + | 1.09254i | ||||
\(233\) | 248.686 | + | 248.686i | 1.06732 | + | 1.06732i | 0.997564 | + | 0.0697560i | \(0.0222221\pi\) |
0.0697560 | + | 0.997564i | \(0.477778\pi\) | |||||||
\(234\) | − | 94.7065i | − | 0.404729i | ||||||
\(235\) | 322.407 | − | 43.2854i | 1.37194 | − | 0.184193i | ||||
\(236\) | −10.8261 | −0.0458732 | ||||||||
\(237\) | −9.85852 | + | 9.85852i | −0.0415971 | + | 0.0415971i | ||||
\(238\) | −52.5924 | − | 52.5924i | −0.220977 | − | 0.220977i | ||||
\(239\) | − | 375.543i | − | 1.57131i | −0.618665 | − | 0.785655i | \(-0.712326\pi\) | ||
0.618665 | − | 0.785655i | \(-0.287674\pi\) | |||||||
\(240\) | 5.08466 | + | 37.8726i | 0.0211861 | + | 0.157803i | ||||
\(241\) | −109.153 | −0.452919 | −0.226459 | − | 0.974021i | \(-0.572715\pi\) | ||||
−0.226459 | + | 0.974021i | \(0.572715\pi\) | |||||||
\(242\) | 6.35364 | − | 6.35364i | 0.0262547 | − | 0.0262547i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 95.9039i | − | 0.393049i | ||||||
\(245\) | 21.2355 | − | 27.8218i | 0.0866756 | − | 0.113558i | ||||
\(246\) | 56.0958 | 0.228032 | ||||||||
\(247\) | 516.065 | − | 516.065i | 2.08933 | − | 2.08933i | ||||
\(248\) | −269.451 | − | 269.451i | −1.08650 | − | 1.08650i | ||||
\(249\) | − | 14.1210i | − | 0.0567108i | ||||||
\(250\) | −69.7894 | − | 164.894i | −0.279158 | − | 0.659577i | ||||
\(251\) | 93.2026 | 0.371325 | 0.185663 | − | 0.982614i | \(-0.440557\pi\) | ||||
0.185663 | + | 0.982614i | \(0.440557\pi\) | |||||||
\(252\) | −10.9338 | + | 10.9338i | −0.0433880 | + | 0.0433880i | ||||
\(253\) | −89.8722 | − | 89.8722i | −0.355226 | − | 0.355226i | ||||
\(254\) | 9.39956i | 0.0370061i | ||||||||
\(255\) | −135.102 | − | 103.119i | −0.529810 | − | 0.404388i | ||||
\(256\) | −270.914 | −1.05826 | ||||||||
\(257\) | 136.298 | − | 136.298i | 0.530344 | − | 0.530344i | −0.390331 | − | 0.920675i | \(-0.627639\pi\) |
0.920675 | + | 0.390331i | \(0.127639\pi\) | |||||||
\(258\) | −23.3494 | − | 23.3494i | −0.0905016 | − | 0.0905016i | ||||
\(259\) | − | 81.1343i | − | 0.313260i | ||||||
\(260\) | −212.759 | + | 28.5643i | −0.818303 | + | 0.109863i | ||||
\(261\) | 126.213 | 0.483576 | ||||||||
\(262\) | 51.9282 | − | 51.9282i | 0.198199 | − | 0.198199i | ||||
\(263\) | −32.1577 | − | 32.1577i | −0.122272 | − | 0.122272i | 0.643323 | − | 0.765595i | \(-0.277555\pi\) |
−0.765595 | + | 0.643323i | \(0.777555\pi\) | |||||||
\(264\) | 158.070i | 0.598750i | ||||||||
\(265\) | 48.3915 | + | 360.439i | 0.182609 | + | 1.36015i | ||||
\(266\) | 125.505 | 0.471825 | ||||||||
\(267\) | 76.2482 | − | 76.2482i | 0.285574 | − | 0.285574i | ||||
\(268\) | −75.6770 | − | 75.6770i | −0.282377 | − | 0.282377i | ||||
\(269\) | − | 148.213i | − | 0.550979i | −0.961304 | − | 0.275489i | \(-0.911160\pi\) | ||
0.961304 | − | 0.275489i | \(-0.0888399\pi\) | |||||||
\(270\) | 22.5800 | − | 29.5832i | 0.0836295 | − | 0.109568i | ||||
\(271\) | 287.937 | 1.06250 | 0.531250 | − | 0.847215i | \(-0.321723\pi\) | ||||
0.531250 | + | 0.847215i | \(0.321723\pi\) | |||||||
\(272\) | −61.2311 | + | 61.2311i | −0.225114 | + | 0.225114i | ||||
\(273\) | 71.4129 | + | 71.4129i | 0.261586 | + | 0.261586i | ||||
\(274\) | − | 69.7814i | − | 0.254677i | ||||||
\(275\) | −70.6287 | − | 258.295i | −0.256832 | − | 0.939253i | ||||
\(276\) | −40.0389 | −0.145068 | ||||||||
\(277\) | 230.005 | − | 230.005i | 0.830342 | − | 0.830342i | −0.157222 | − | 0.987563i | \(-0.550254\pi\) |
0.987563 | + | 0.157222i | \(0.0502537\pi\) | |||||||
\(278\) | 209.687 | + | 209.687i | 0.754270 | + | 0.754270i | ||||
\(279\) | 134.172i | 0.480902i | ||||||||
\(280\) | −89.5967 | − | 68.3864i | −0.319988 | − | 0.244237i | ||||
\(281\) | 204.481 | 0.727689 | 0.363845 | − | 0.931460i | \(-0.381464\pi\) | ||||
0.363845 | + | 0.931460i | \(0.381464\pi\) | |||||||
\(282\) | −114.139 | + | 114.139i | −0.404750 | + | 0.404750i | ||||
\(283\) | −81.5319 | − | 81.5319i | −0.288099 | − | 0.288099i | 0.548229 | − | 0.836328i | \(-0.315302\pi\) |
−0.836328 | + | 0.548229i | \(0.815302\pi\) | |||||||
\(284\) | 45.8794i | 0.161547i | ||||||||
\(285\) | 284.242 | − | 38.1614i | 0.997340 | − | 0.133900i | ||||
\(286\) | 338.136 | 1.18229 | ||||||||
\(287\) | −42.2987 | + | 42.2987i | −0.147382 | + | 0.147382i | ||||
\(288\) | 58.8895 | + | 58.8895i | 0.204478 | + | 0.204478i | ||||
\(289\) | − | 96.1461i | − | 0.332686i | ||||||
\(290\) | 40.0948 | + | 298.642i | 0.138258 | + | 1.02980i | ||||
\(291\) | 53.8686 | 0.185115 | ||||||||
\(292\) | 117.092 | − | 117.092i | 0.401000 | − | 0.401000i | ||||
\(293\) | −92.3268 | − | 92.3268i | −0.315108 | − | 0.315108i | 0.531776 | − | 0.846885i | \(-0.321525\pi\) |
−0.846885 | + | 0.531776i | \(0.821525\pi\) | |||||||
\(294\) | 17.3674i | 0.0590728i | ||||||||
\(295\) | −16.8586 | + | 22.0874i | −0.0571478 | + | 0.0748724i | ||||
\(296\) | −261.283 | −0.882713 | ||||||||
\(297\) | 39.3550 | − | 39.3550i | 0.132508 | − | 0.132508i | ||||
\(298\) | 63.8447 | + | 63.8447i | 0.214244 | + | 0.214244i | ||||
\(299\) | 261.510i | 0.874617i | ||||||||
\(300\) | −73.2692 | − | 41.8035i | −0.244231 | − | 0.139345i | ||||
\(301\) | 35.2130 | 0.116987 | ||||||||
\(302\) | 31.9174 | − | 31.9174i | 0.105687 | − | 0.105687i | ||||
\(303\) | −104.264 | − | 104.264i | −0.344105 | − | 0.344105i | ||||
\(304\) | − | 146.120i | − | 0.480659i | ||||||
\(305\) | −195.663 | − | 149.344i | −0.641518 | − | 0.489651i | ||||
\(306\) | 84.3355 | 0.275606 | ||||||||
\(307\) | −323.348 | + | 323.348i | −1.05325 | + | 1.05325i | −0.0547502 | + | 0.998500i | \(0.517436\pi\) |
−0.998500 | + | 0.0547502i | \(0.982564\pi\) | |||||||
\(308\) | −39.0375 | − | 39.0375i | −0.126745 | − | 0.126745i | ||||
\(309\) | − | 197.524i | − | 0.639238i | ||||||
\(310\) | −317.473 | + | 42.6229i | −1.02411 | + | 0.137493i | ||||
\(311\) | 237.025 | 0.762138 | 0.381069 | − | 0.924547i | \(-0.375556\pi\) | ||||
0.381069 | + | 0.924547i | \(0.375556\pi\) | |||||||
\(312\) | 229.977 | − | 229.977i | 0.737104 | − | 0.737104i | ||||
\(313\) | 92.0773 | + | 92.0773i | 0.294177 | + | 0.294177i | 0.838728 | − | 0.544551i | \(-0.183300\pi\) |
−0.544551 | + | 0.838728i | \(0.683300\pi\) | |||||||
\(314\) | − | 331.377i | − | 1.05534i | ||||||
\(315\) | 5.28077 | + | 39.3334i | 0.0167644 | + | 0.124868i | ||||
\(316\) | −15.6812 | −0.0496242 | ||||||||
\(317\) | 211.432 | − | 211.432i | 0.666979 | − | 0.666979i | −0.290036 | − | 0.957016i | \(-0.593667\pi\) |
0.957016 | + | 0.290036i | \(0.0936674\pi\) | |||||||
\(318\) | −127.604 | − | 127.604i | −0.401270 | − | 0.401270i | ||||
\(319\) | 450.627i | 1.41262i | ||||||||
\(320\) | −174.178 | + | 228.199i | −0.544305 | + | 0.713123i | ||||
\(321\) | 78.6765 | 0.245098 | ||||||||
\(322\) | −31.7993 | + | 31.7993i | −0.0987556 | + | 0.0987556i | ||||
\(323\) | 459.552 | + | 459.552i | 1.42276 | + | 1.42276i | ||||
\(324\) | − | 17.5330i | − | 0.0541143i | ||||||
\(325\) | −273.036 | + | 478.551i | −0.840109 | + | 1.47247i | ||||
\(326\) | 163.097 | 0.500296 | ||||||||
\(327\) | −72.4938 | + | 72.4938i | −0.221694 | + | 0.221694i | ||||
\(328\) | 136.218 | + | 136.218i | 0.415298 | + | 0.415298i | ||||
\(329\) | − | 172.132i | − | 0.523199i | ||||||
\(330\) | 105.623 | + | 80.6186i | 0.320069 | + | 0.244299i | ||||
\(331\) | −31.3695 | −0.0947718 | −0.0473859 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473859 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(332\) | 11.2306 | − | 11.2306i | 0.0338272 | − | 0.0338272i | ||||
\(333\) | 65.0522 | + | 65.0522i | 0.195352 | + | 0.195352i | ||||
\(334\) | − | 252.242i | − | 0.755216i | ||||||
\(335\) | −272.242 | + | 36.5504i | −0.812663 | + | 0.109106i | ||||
\(336\) | 20.2201 | 0.0601789 | ||||||||
\(337\) | −236.725 | + | 236.725i | −0.702449 | + | 0.702449i | −0.964936 | − | 0.262486i | \(-0.915458\pi\) |
0.262486 | + | 0.964936i | \(0.415458\pi\) | |||||||
\(338\) | −320.777 | − | 320.777i | −0.949046 | − | 0.949046i | ||||
\(339\) | − | 57.0086i | − | 0.168167i | ||||||
\(340\) | −25.4363 | − | 189.460i | −0.0748127 | − | 0.557236i | ||||
\(341\) | −479.041 | −1.40481 | ||||||||
\(342\) | −100.628 | + | 100.628i | −0.294234 | + | 0.294234i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 113.399i | − | 0.329649i | ||||||
\(345\) | −62.3494 | + | 81.6874i | −0.180723 | + | 0.236775i | ||||
\(346\) | −327.434 | −0.946341 | ||||||||
\(347\) | −11.7481 | + | 11.7481i | −0.0338562 | + | 0.0338562i | −0.723832 | − | 0.689976i | \(-0.757621\pi\) |
0.689976 | + | 0.723832i | \(0.257621\pi\) | |||||||
\(348\) | 100.379 | + | 100.379i | 0.288446 | + | 0.288446i | ||||
\(349\) | − | 384.239i | − | 1.10097i | −0.834845 | − | 0.550486i | \(-0.814443\pi\) | ||
0.834845 | − | 0.550486i | \(-0.185557\pi\) | |||||||
\(350\) | −91.3919 | + | 24.9904i | −0.261120 | + | 0.0714012i | ||||
\(351\) | −114.515 | −0.326255 | ||||||||
\(352\) | −210.257 | + | 210.257i | −0.597320 | + | 0.597320i | ||||
\(353\) | 244.010 | + | 244.010i | 0.691247 | + | 0.691247i | 0.962506 | − | 0.271259i | \(-0.0874400\pi\) |
−0.271259 | + | 0.962506i | \(0.587440\pi\) | |||||||
\(354\) | − | 13.7878i | − | 0.0389485i | ||||||
\(355\) | 93.6031 | + | 71.4444i | 0.263671 | + | 0.201252i | ||||
\(356\) | 121.283 | 0.340681 | ||||||||
\(357\) | −63.5927 | + | 63.5927i | −0.178131 | + | 0.178131i | ||||
\(358\) | 3.02528 | + | 3.02528i | 0.00845050 | + | 0.00845050i | ||||
\(359\) | 545.782i | 1.52029i | 0.649756 | + | 0.760143i | \(0.274871\pi\) | ||||
−0.649756 | + | 0.760143i | \(0.725129\pi\) | |||||||
\(360\) | 126.668 | − | 17.0061i | 0.351856 | − | 0.0472391i | ||||
\(361\) | −735.664 | −2.03785 | ||||||||
\(362\) | 92.7990 | − | 92.7990i | 0.256351 | − | 0.256351i | ||||
\(363\) | −7.68258 | − | 7.68258i | −0.0211641 | − | 0.0211641i | ||||
\(364\) | 113.591i | 0.312064i | ||||||||
\(365\) | −56.5529 | − | 421.229i | −0.154939 | − | 1.15405i | ||||
\(366\) | 122.140 | 0.333716 | ||||||||
\(367\) | −88.6633 | + | 88.6633i | −0.241589 | + | 0.241589i | −0.817507 | − | 0.575918i | \(-0.804645\pi\) |
0.575918 | + | 0.817507i | \(0.304645\pi\) | |||||||
\(368\) | 37.0225 | + | 37.0225i | 0.100605 | + | 0.100605i | ||||
\(369\) | − | 67.8288i | − | 0.183818i | ||||||
\(370\) | −133.259 | + | 174.590i | −0.360160 | + | 0.471865i | ||||
\(371\) | 192.438 | 0.518700 | ||||||||
\(372\) | −106.709 | + | 106.709i | −0.286851 | + | 0.286851i | ||||
\(373\) | 397.173 | + | 397.173i | 1.06481 | + | 1.06481i | 0.997749 | + | 0.0670567i | \(0.0213608\pi\) |
0.0670567 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(374\) | 301.108i | 0.805102i | ||||||||
\(375\) | −199.384 | + | 84.3866i | −0.531690 | + | 0.225031i | ||||
\(376\) | −554.332 | −1.47429 | ||||||||
\(377\) | 655.618 | − | 655.618i | 1.73904 | − | 1.73904i | ||||
\(378\) | −13.9249 | − | 13.9249i | −0.0368384 | − | 0.0368384i | ||||
\(379\) | 371.866i | 0.981177i | 0.871391 | + | 0.490589i | \(0.163218\pi\) | ||||
−0.871391 | + | 0.490589i | \(0.836782\pi\) | |||||||
\(380\) | 256.412 | + | 195.711i | 0.674769 | + | 0.515030i | ||||
\(381\) | 11.3656 | 0.0298309 | ||||||||
\(382\) | 241.559 | − | 241.559i | 0.632355 | − | 0.632355i | ||||
\(383\) | −40.1675 | − | 40.1675i | −0.104876 | − | 0.104876i | 0.652722 | − | 0.757598i | \(-0.273627\pi\) |
−0.757598 | + | 0.652722i | \(0.773627\pi\) | |||||||
\(384\) | 49.8818i | 0.129900i | ||||||||
\(385\) | −140.434 | + | 18.8543i | −0.364764 | + | 0.0489721i | ||||
\(386\) | 140.448 | 0.363855 | ||||||||
\(387\) | −28.2332 | + | 28.2332i | −0.0729540 | + | 0.0729540i | ||||
\(388\) | 42.8425 | + | 42.8425i | 0.110419 | + | 0.110419i | ||||
\(389\) | 344.589i | 0.885833i | 0.896563 | + | 0.442917i | \(0.146056\pi\) | ||||
−0.896563 | + | 0.442917i | \(0.853944\pi\) | |||||||
\(390\) | −36.3786 | − | 270.963i | −0.0932786 | − | 0.694777i | ||||
\(391\) | −232.873 | −0.595584 | ||||||||
\(392\) | −42.1734 | + | 42.1734i | −0.107585 | + | 0.107585i | ||||
\(393\) | −62.7895 | − | 62.7895i | −0.159770 | − | 0.159770i | ||||
\(394\) | 129.595i | 0.328920i | ||||||||
\(395\) | −24.4192 | + | 31.9929i | −0.0618207 | + | 0.0809946i | ||||
\(396\) | 62.5992 | 0.158079 | ||||||||
\(397\) | −215.178 | + | 215.178i | −0.542009 | + | 0.542009i | −0.924117 | − | 0.382108i | \(-0.875198\pi\) |
0.382108 | + | 0.924117i | \(0.375198\pi\) | |||||||
\(398\) | 51.1120 | + | 51.1120i | 0.128422 | + | 0.128422i | ||||
\(399\) | − | 151.756i | − | 0.380341i | ||||||
\(400\) | 29.0952 | + | 106.404i | 0.0727381 | + | 0.266009i | ||||
\(401\) | 280.987 | 0.700716 | 0.350358 | − | 0.936616i | \(-0.386060\pi\) | ||||
0.350358 | + | 0.936616i | \(0.386060\pi\) | |||||||
\(402\) | 96.3800 | − | 96.3800i | 0.239751 | − | 0.239751i | ||||
\(403\) | 696.958 | + | 696.958i | 1.72942 | + | 1.72942i | ||||
\(404\) | − | 165.845i | − | 0.410508i | ||||||
\(405\) | −35.7709 | − | 27.3028i | −0.0883232 | − | 0.0674144i | ||||
\(406\) | 159.444 | 0.392720 | ||||||||
\(407\) | −232.260 | + | 232.260i | −0.570663 | + | 0.570663i | ||||
\(408\) | 204.793 | + | 204.793i | 0.501943 | + | 0.501943i | ||||
\(409\) | − | 497.992i | − | 1.21758i | −0.793330 | − | 0.608792i | \(-0.791654\pi\) | ||
0.793330 | − | 0.608792i | \(-0.208346\pi\) | |||||||
\(410\) | 160.495 | − | 21.5475i | 0.391450 | − | 0.0525548i | ||||
\(411\) | −84.3770 | −0.205297 | ||||||||
\(412\) | 157.094 | − | 157.094i | 0.381296 | − | 0.381296i | ||||
\(413\) | 10.3966 | + | 10.3966i | 0.0251733 | + | 0.0251733i | ||||
\(414\) | − | 50.9923i | − | 0.123170i | ||||||
\(415\) | −5.42415 | − | 40.4013i | −0.0130702 | − | 0.0973525i | ||||
\(416\) | 611.806 | 1.47069 | ||||||||
\(417\) | 253.545 | − | 253.545i | 0.608023 | − | 0.608023i | ||||
\(418\) | −359.279 | − | 359.279i | −0.859519 | − | 0.859519i | ||||
\(419\) | 151.915i | 0.362565i | 0.983431 | + | 0.181283i | \(0.0580249\pi\) | ||||
−0.983431 | + | 0.181283i | \(0.941975\pi\) | |||||||
\(420\) | −27.0825 | + | 35.4823i | −0.0644822 | + | 0.0844816i | ||||
\(421\) | 157.507 | 0.374126 | 0.187063 | − | 0.982348i | \(-0.440103\pi\) | ||||
0.187063 | + | 0.982348i | \(0.440103\pi\) | |||||||
\(422\) | −216.061 | + | 216.061i | −0.511993 | + | 0.511993i | ||||
\(423\) | 138.013 | + | 138.013i | 0.326272 | + | 0.326272i | ||||
\(424\) | − | 619.723i | − | 1.46161i | ||||||
\(425\) | −426.147 | − | 243.136i | −1.00270 | − | 0.572085i | ||||
\(426\) | −58.4306 | −0.137161 | ||||||||
\(427\) | −92.0991 | + | 92.0991i | −0.215689 | + | 0.215689i | ||||
\(428\) | 62.5725 | + | 62.5725i | 0.146198 | + | 0.146198i | ||||
\(429\) | − | 408.861i | − | 0.953057i | ||||||
\(430\) | −75.7735 | − | 57.8356i | −0.176218 | − | 0.134501i | ||||
\(431\) | −608.684 | −1.41226 | −0.706130 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706130 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(432\) | −16.2122 | + | 16.2122i | −0.0375281 | + | 0.0375281i | ||||
\(433\) | −556.887 | − | 556.887i | −1.28611 | − | 1.28611i | −0.937128 | − | 0.348985i | \(-0.886526\pi\) |
−0.348985 | − | 0.937128i | \(-0.613474\pi\) | |||||||
\(434\) | 169.498i | 0.390549i | ||||||||
\(435\) | 361.106 | − | 48.4810i | 0.830130 | − | 0.111451i | ||||
\(436\) | −115.311 | −0.264474 | ||||||||
\(437\) | 277.862 | − | 277.862i | 0.635839 | − | 0.635839i | ||||
\(438\) | 149.125 | + | 149.125i | 0.340468 | + | 0.340468i | ||||
\(439\) | − | 450.053i | − | 1.02518i | −0.858634 | − | 0.512588i | \(-0.828687\pi\) | ||
0.858634 | − | 0.512588i | \(-0.171313\pi\) | |||||||
\(440\) | 60.7178 | + | 452.251i | 0.137995 | + | 1.02784i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | 438.083 | − | 438.083i | 0.991138 | − | 0.991138i | ||||
\(443\) | −191.060 | − | 191.060i | −0.431287 | − | 0.431287i | 0.457779 | − | 0.889066i | \(-0.348645\pi\) |
−0.889066 | + | 0.457779i | \(0.848645\pi\) | |||||||
\(444\) | 103.474i | 0.233049i | ||||||||
\(445\) | 188.864 | − | 247.441i | 0.424413 | − | 0.556046i | ||||
\(446\) | 244.183 | 0.547497 | ||||||||
\(447\) | 77.1985 | − | 77.1985i | 0.172704 | − | 0.172704i | ||||
\(448\) | 107.414 | + | 107.414i | 0.239764 | + | 0.239764i | ||||
\(449\) | − | 400.837i | − | 0.892733i | −0.894850 | − | 0.446367i | \(-0.852718\pi\) | ||
0.894850 | − | 0.446367i | \(-0.147282\pi\) | |||||||
\(450\) | 53.2396 | − | 93.3134i | 0.118310 | − | 0.207363i | ||||
\(451\) | 242.173 | 0.536969 | ||||||||
\(452\) | 45.3398 | − | 45.3398i | 0.100309 | − | 0.100309i | ||||
\(453\) | −38.5933 | − | 38.5933i | −0.0851950 | − | 0.0851950i | ||||
\(454\) | − | 216.622i | − | 0.477140i | ||||||
\(455\) | 231.749 | + | 176.887i | 0.509339 | + | 0.388763i | ||||
\(456\) | −488.712 | −1.07174 | ||||||||
\(457\) | −209.145 | + | 209.145i | −0.457647 | + | 0.457647i | −0.897882 | − | 0.440235i | \(-0.854895\pi\) |
0.440235 | + | 0.897882i | \(0.354895\pi\) | |||||||
\(458\) | −414.393 | − | 414.393i | −0.904789 | − | 0.904789i | ||||
\(459\) | − | 101.975i | − | 0.222168i | ||||||
\(460\) | −114.555 | + | 15.3797i | −0.249032 | + | 0.0334342i | ||||
\(461\) | 167.687 | 0.363747 | 0.181873 | − | 0.983322i | \(-0.441784\pi\) | ||||
0.181873 | + | 0.983322i | \(0.441784\pi\) | |||||||
\(462\) | 49.7169 | − | 49.7169i | 0.107612 | − | 0.107612i | ||||
\(463\) | −462.257 | − | 462.257i | −0.998395 | − | 0.998395i | 0.00160374 | − | 0.999999i | \(-0.499490\pi\) |
−0.999999 | + | 0.00160374i | \(0.999490\pi\) | |||||||
\(464\) | − | 185.634i | − | 0.400073i | ||||||
\(465\) | 51.5379 | + | 383.876i | 0.110834 | + | 0.825539i | ||||
\(466\) | −503.781 | −1.08108 | ||||||||
\(467\) | 453.333 | − | 453.333i | 0.970734 | − | 0.970734i | −0.0288502 | − | 0.999584i | \(-0.509185\pi\) |
0.999584 | + | 0.0288502i | \(0.00918458\pi\) | |||||||
\(468\) | −91.0758 | − | 91.0758i | −0.194606 | − | 0.194606i | ||||
\(469\) | 145.350i | 0.309914i | ||||||||
\(470\) | −282.719 | + | 370.406i | −0.601530 | + | 0.788097i | ||||
\(471\) | −400.688 | −0.850718 | ||||||||
\(472\) | 33.4809 | − | 33.4809i | 0.0709342 | − | 0.0709342i | ||||
\(473\) | −100.803 | − | 100.803i | −0.213113 | − | 0.213113i | ||||
\(474\) | − | 19.9712i | − | 0.0421332i | ||||||
\(475\) | 798.581 | − | 218.366i | 1.68122 | − | 0.459718i | ||||
\(476\) | −101.152 | −0.212505 | ||||||||
\(477\) | −154.294 | + | 154.294i | −0.323467 | + | 0.323467i | ||||
\(478\) | 380.383 | + | 380.383i | 0.795781 | + | 0.795781i | ||||
\(479\) | − | 508.689i | − | 1.06198i | −0.847378 | − | 0.530991i | \(-0.821820\pi\) | ||
0.847378 | − | 0.530991i | \(-0.178180\pi\) | |||||||
\(480\) | 191.108 | + | 145.867i | 0.398142 | + | 0.303890i | ||||
\(481\) | 675.830 | 1.40505 | ||||||||
\(482\) | 110.560 | − | 110.560i | 0.229378 | − | 0.229378i | ||||
\(483\) | 38.4505 | + | 38.4505i | 0.0796076 | + | 0.0796076i | ||||
\(484\) | − | 12.2201i | − | 0.0252482i | ||||||
\(485\) | 154.122 | − | 20.6920i | 0.317778 | − | 0.0426639i | ||||
\(486\) | 22.3295 | 0.0459455 | ||||||||
\(487\) | −417.605 | + | 417.605i | −0.857505 | + | 0.857505i | −0.991044 | − | 0.133538i | \(-0.957366\pi\) |
0.133538 | + | 0.991044i | \(0.457366\pi\) | |||||||
\(488\) | 296.594 | + | 296.594i | 0.607775 | + | 0.607775i | ||||
\(489\) | − | 197.210i | − | 0.403293i | ||||||
\(490\) | 6.67117 | + | 49.6896i | 0.0136146 | + | 0.101407i | ||||
\(491\) | −269.127 | −0.548120 | −0.274060 | − | 0.961713i | \(-0.588367\pi\) | ||||
−0.274060 | + | 0.961713i | \(0.588367\pi\) | |||||||
\(492\) | 53.9452 | − | 53.9452i | 0.109645 | − | 0.109645i | ||||
\(493\) | 583.824 | + | 583.824i | 1.18423 | + | 1.18423i | ||||
\(494\) | 1045.43i | 2.11626i | ||||||||
\(495\) | 97.4809 | − | 127.715i | 0.196931 | − | 0.258010i | ||||
\(496\) | 197.339 | 0.397861 | ||||||||
\(497\) | 44.0593 | − | 44.0593i | 0.0886504 | − | 0.0886504i | ||||
\(498\) | 14.3030 | + | 14.3030i | 0.0287208 | + | 0.0287208i | ||||
\(499\) | 605.561i | 1.21355i | 0.794874 | + | 0.606774i | \(0.207537\pi\) | ||||
−0.794874 | + | 0.606774i | \(0.792463\pi\) | |||||||
\(500\) | −225.687 | − | 91.4589i | −0.451373 | − | 0.182918i | ||||
\(501\) | −305.001 | −0.608785 | ||||||||
\(502\) | −94.4038 | + | 94.4038i | −0.188055 | + | 0.188055i | ||||
\(503\) | −279.566 | − | 279.566i | −0.555798 | − | 0.555798i | 0.372310 | − | 0.928108i | \(-0.378566\pi\) |
−0.928108 | + | 0.372310i | \(0.878566\pi\) | |||||||
\(504\) | − | 67.6279i | − | 0.134182i | ||||||
\(505\) | −338.357 | − | 258.258i | −0.670014 | − | 0.511401i | ||||
\(506\) | 182.061 | 0.359804 | ||||||||
\(507\) | −387.871 | + | 387.871i | −0.765032 | + | 0.765032i | ||||
\(508\) | 9.03921 | + | 9.03921i | 0.0177937 | + | 0.0177937i | ||||
\(509\) | − | 476.825i | − | 0.936788i | −0.883520 | − | 0.468394i | \(-0.844833\pi\) | ||
0.883520 | − | 0.468394i | \(-0.155167\pi\) | |||||||
\(510\) | 241.291 | − | 32.3949i | 0.473119 | − | 0.0635195i | ||||
\(511\) | −224.893 | −0.440104 | ||||||||
\(512\) | 192.949 | − | 192.949i | 0.376854 | − | 0.376854i | ||||
\(513\) | 121.676 | + | 121.676i | 0.237185 | + | 0.237185i | ||||
\(514\) | 276.110i | 0.537179i | ||||||||
\(515\) | −75.8730 | − | 565.133i | −0.147326 | − | 1.09735i | ||||
\(516\) | −44.9085 | −0.0870321 | ||||||||
\(517\) | −492.756 | + | 492.756i | −0.953106 | + | 0.953106i | ||||
\(518\) | 82.1800 | + | 82.1800i | 0.158649 | + | 0.158649i | ||||
\(519\) | 395.920i | 0.762852i | ||||||||
\(520\) | 569.643 | − | 746.320i | 1.09547 | − | 1.43523i | ||||
\(521\) | −331.427 | −0.636137 | −0.318068 | − | 0.948068i | \(-0.603034\pi\) | ||||
−0.318068 | + | 0.948068i | \(0.603034\pi\) | |||||||
\(522\) | −127.840 | + | 127.840i | −0.244904 | + | 0.244904i | ||||
\(523\) | −103.667 | − | 103.667i | −0.198216 | − | 0.198216i | 0.601019 | − | 0.799235i | \(-0.294762\pi\) |
−0.799235 | + | 0.601019i | \(0.794762\pi\) | |||||||
\(524\) | − | 99.8748i | − | 0.190601i | ||||||
\(525\) | 30.2174 | + | 110.507i | 0.0575570 | + | 0.210490i | ||||
\(526\) | 65.1442 | 0.123848 | ||||||||
\(527\) | −620.636 | + | 620.636i | −1.17768 | + | 1.17768i | ||||
\(528\) | −57.8832 | − | 57.8832i | −0.109627 | − | 0.109627i | ||||
\(529\) | − | 388.196i | − | 0.733831i | ||||||
\(530\) | −414.100 | − | 316.070i | −0.781321 | − | 0.596358i | ||||
\(531\) | −16.6716 | −0.0313967 | ||||||||
\(532\) | 120.694 | − | 120.694i | 0.226868 | − | 0.226868i | ||||
\(533\) | −352.338 | − | 352.338i | −0.661048 | − | 0.661048i | ||||
\(534\) | 154.462i | 0.289254i | ||||||||
\(535\) | 225.100 | − | 30.2212i | 0.420747 | − | 0.0564882i | ||||
\(536\) | 468.080 | 0.873284 | ||||||||
\(537\) | 3.65805 | − | 3.65805i | 0.00681201 | − | 0.00681201i | ||||
\(538\) | 150.123 | + | 150.123i | 0.279040 | + | 0.279040i | ||||
\(539\) | 74.9775i | 0.139105i | ||||||||
\(540\) | −6.73478 | − | 50.1634i | −0.0124718 | − | 0.0928952i | ||||
\(541\) | 533.708 | 0.986521 | 0.493260 | − | 0.869882i | \(-0.335805\pi\) | ||||
0.493260 | + | 0.869882i | \(0.335805\pi\) | |||||||
\(542\) | −291.648 | + | 291.648i | −0.538096 | + | 0.538096i | ||||
\(543\) | −112.209 | − | 112.209i | −0.206646 | − | 0.206646i | ||||
\(544\) | 544.809i | 1.00149i | ||||||||
\(545\) | −179.564 | + | 235.257i | −0.329476 | + | 0.431664i | ||||
\(546\) | −144.667 | −0.264957 | ||||||||
\(547\) | 160.272 | − | 160.272i | 0.293001 | − | 0.293001i | −0.545263 | − | 0.838265i | \(-0.683570\pi\) |
0.838265 | + | 0.545263i | \(0.183570\pi\) | |||||||
\(548\) | −67.1062 | − | 67.1062i | −0.122457 | − | 0.122457i | ||||
\(549\) | − | 147.687i | − | 0.269011i | ||||||
\(550\) | 333.163 | + | 190.085i | 0.605750 | + | 0.345608i | ||||
\(551\) | −1393.22 | −2.52854 | ||||||||
\(552\) | 123.825 | − | 123.825i | 0.224321 | − | 0.224321i | ||||
\(553\) | 15.0591 | + | 15.0591i | 0.0272317 | + | 0.0272317i | ||||
\(554\) | 465.938i | 0.841044i | ||||||||
\(555\) | 211.107 | + | 161.132i | 0.380374 | + | 0.290327i | ||||
\(556\) | 403.297 | 0.725354 | ||||||||
\(557\) | 47.4479 | − | 47.4479i | 0.0851847 | − | 0.0851847i | −0.663231 | − | 0.748415i | \(-0.730815\pi\) |
0.748415 | + | 0.663231i | \(0.230815\pi\) | |||||||
\(558\) | −135.901 | − | 135.901i | −0.243550 | − | 0.243550i | ||||
\(559\) | 293.316i | 0.524716i | ||||||||
\(560\) | 57.8514 | − | 7.76694i | 0.103306 | − | 0.0138695i | ||||
\(561\) | 364.088 | 0.648999 | ||||||||
\(562\) | −207.116 | + | 207.116i | −0.368534 | + | 0.368534i | ||||
\(563\) | −13.3672 | − | 13.3672i | −0.0237428 | − | 0.0237428i | 0.695136 | − | 0.718879i | \(-0.255344\pi\) |
−0.718879 | + | 0.695136i | \(0.755344\pi\) | |||||||
\(564\) | 219.527i | 0.389233i | ||||||||
\(565\) | −21.8981 | − | 163.106i | −0.0387578 | − | 0.288684i | ||||
\(566\) | 165.165 | 0.291812 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | −141.887 | − | 141.887i | −0.249802 | − | 0.249802i | ||||
\(569\) | 510.404i | 0.897020i | 0.893778 | + | 0.448510i | \(0.148045\pi\) | ||||
−0.893778 | + | 0.448510i | \(0.851955\pi\) | |||||||
\(570\) | −249.252 | + | 326.559i | −0.437284 | + | 0.572910i | ||||
\(571\) | 957.728 | 1.67728 | 0.838641 | − | 0.544685i | \(-0.183351\pi\) | ||||
0.838641 | + | 0.544685i | \(0.183351\pi\) | |||||||
\(572\) | 325.173 | − | 325.173i | 0.568485 | − | 0.568485i | ||||
\(573\) | −292.084 | − | 292.084i | −0.509746 | − | 0.509746i | ||||
\(574\) | − | 85.6877i | − | 0.149282i | ||||||
\(575\) | −147.009 | + | 257.664i | −0.255668 | + | 0.448111i | ||||
\(576\) | −172.246 | −0.299038 | ||||||||
\(577\) | −53.6149 | + | 53.6149i | −0.0929202 | + | 0.0929202i | −0.752039 | − | 0.659119i | \(-0.770929\pi\) |
0.659119 | + | 0.752039i | \(0.270929\pi\) | |||||||
\(578\) | 97.3853 | + | 97.3853i | 0.168487 | + | 0.168487i | ||||
\(579\) | − | 169.824i | − | 0.293306i | ||||||
\(580\) | 325.751 | + | 248.636i | 0.561639 | + | 0.428682i | ||||
\(581\) | −21.5702 | −0.0371259 | ||||||||
\(582\) | −54.5629 | + | 54.5629i | −0.0937506 | + | 0.0937506i | ||||
\(583\) | −550.883 | − | 550.883i | −0.944912 | − | 0.944912i | ||||
\(584\) | 724.242i | 1.24014i | ||||||||
\(585\) | −327.638 | + | 43.9876i | −0.560065 | + | 0.0751925i | ||||
\(586\) | 187.033 | 0.319170 | ||||||||
\(587\) | −263.340 | + | 263.340i | −0.448620 | + | 0.448620i | −0.894896 | − | 0.446275i | \(-0.852750\pi\) |
0.446275 | + | 0.894896i | \(0.352750\pi\) | |||||||
\(588\) | 16.7016 | + | 16.7016i | 0.0284041 | + | 0.0284041i | ||||
\(589\) | − | 1481.07i | − | 2.51455i | ||||||
\(590\) | −5.29615 | − | 39.4479i | −0.00897653 | − | 0.0668609i | ||||
\(591\) | 156.701 | 0.265145 | ||||||||
\(592\) | 95.6785 | − | 95.6785i | 0.161619 | − | 0.161619i | ||||
\(593\) | 530.088 | + | 530.088i | 0.893908 | + | 0.893908i | 0.994888 | − | 0.100980i | \(-0.0321978\pi\) |
−0.100980 | + | 0.994888i | \(0.532198\pi\) | |||||||
\(594\) | 79.7245i | 0.134216i | ||||||||
\(595\) | −157.517 | + | 206.371i | −0.264734 | + | 0.346842i | ||||
\(596\) | 122.794 | 0.206030 | ||||||||
\(597\) | 61.8026 | − | 61.8026i | 0.103522 | − | 0.103522i | ||||
\(598\) | −264.881 | − | 264.881i | −0.442945 | − | 0.442945i | ||||
\(599\) | 837.821i | 1.39870i | 0.714780 | + | 0.699349i | \(0.246527\pi\) | ||||
−0.714780 | + | 0.699349i | \(0.753473\pi\) | |||||||
\(600\) | 355.876 | − | 97.3116i | 0.593127 | − | 0.162186i | ||||
\(601\) | −744.532 | −1.23882 | −0.619411 | − | 0.785067i | \(-0.712629\pi\) | ||||
−0.619411 | + | 0.785067i | \(0.712629\pi\) | |||||||
\(602\) | −35.6668 | + | 35.6668i | −0.0592472 | + | 0.0592472i | ||||
\(603\) | −116.539 | − | 116.539i | −0.193265 | − | 0.193265i | ||||
\(604\) | − | 61.3877i | − | 0.101635i | ||||||
\(605\) | −24.9315 | − | 19.0294i | −0.0412091 | − | 0.0314536i | ||||
\(606\) | 211.215 | 0.348540 | ||||||||
\(607\) | −394.249 | + | 394.249i | −0.649504 | + | 0.649504i | −0.952873 | − | 0.303369i | \(-0.901888\pi\) |
0.303369 | + | 0.952873i | \(0.401888\pi\) | |||||||
\(608\) | −650.060 | − | 650.060i | −1.06918 | − | 1.06918i | ||||
\(609\) | − | 192.794i | − | 0.316575i | ||||||
\(610\) | 349.453 | − | 46.9165i | 0.572874 | − | 0.0769123i | ||||
\(611\) | 1433.82 | 2.34668 | ||||||||
\(612\) | 81.1024 | − | 81.1024i | 0.132520 | − | 0.132520i | ||||
\(613\) | 679.539 | + | 679.539i | 1.10855 | + | 1.10855i | 0.993342 | + | 0.115204i | \(0.0367522\pi\) |
0.115204 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(614\) | − | 655.030i | − | 1.06682i | ||||||
\(615\) | −26.0544 | − | 194.064i | −0.0423648 | − | 0.315551i | ||||
\(616\) | 241.456 | 0.391974 | ||||||||
\(617\) | −215.402 | + | 215.402i | −0.349111 | + | 0.349111i | −0.859778 | − | 0.510667i | \(-0.829398\pi\) |
0.510667 | + | 0.859778i | \(0.329398\pi\) | |||||||
\(618\) | 200.070 | + | 200.070i | 0.323738 | + | 0.323738i | ||||
\(619\) | − | 407.617i | − | 0.658508i | −0.944241 | − | 0.329254i | \(-0.893203\pi\) | ||
0.944241 | − | 0.329254i | \(-0.106797\pi\) | |||||||
\(620\) | −264.313 | + | 346.291i | −0.426311 | + | 0.558533i | ||||
\(621\) | −61.6579 | −0.0992881 | ||||||||
\(622\) | −240.080 | + | 240.080i | −0.385980 | + | 0.385980i | ||||
\(623\) | −116.471 | − | 116.471i | −0.186952 | − | 0.186952i | ||||
\(624\) | 168.429i | 0.269918i | ||||||||
\(625\) | −538.039 | + | 318.024i | −0.860862 | + | 0.508839i | ||||
\(626\) | −186.528 | −0.297968 | ||||||||
\(627\) | −434.426 | + | 434.426i | −0.692864 | + | 0.692864i | ||||
\(628\) | −318.673 | − | 318.673i | −0.507441 | − | 0.507441i | ||||
\(629\) | 601.822i | 0.956792i | ||||||||
\(630\) | −45.1891 | − | 34.4915i | −0.0717288 | − | 0.0547484i | ||||
\(631\) | 1160.78 | 1.83959 | 0.919795 | − | 0.392399i | \(-0.128355\pi\) | ||||
0.919795 | + | 0.392399i | \(0.128355\pi\) | |||||||
\(632\) | 48.4961 | − | 48.4961i | 0.0767344 | − | 0.0767344i | ||||
\(633\) | 261.252 | + | 261.252i | 0.412721 | + | 0.412721i | ||||
\(634\) | 428.315i | 0.675576i | ||||||||
\(635\) | 32.5178 | − | 4.36574i | 0.0512092 | − | 0.00687518i | ||||
\(636\) | −245.424 | −0.385886 | ||||||||
\(637\) | 109.085 | − | 109.085i | 0.171248 | − | 0.171248i | ||||
\(638\) | −456.435 | − | 456.435i | −0.715415 | − | 0.715415i | ||||
\(639\) | 70.6520i | 0.110566i | ||||||||
\(640\) | 19.1606 | + | 142.716i | 0.0299384 | + | 0.222993i | ||||
\(641\) | 1053.98 | 1.64428 | 0.822139 | − | 0.569288i | \(-0.192781\pi\) | ||||
0.822139 | + | 0.569288i | \(0.192781\pi\) | |||||||
\(642\) | −79.6905 | + | 79.6905i | −0.124128 | + | 0.124128i | ||||
\(643\) | 391.465 | + | 391.465i | 0.608810 | + | 0.608810i | 0.942635 | − | 0.333825i | \(-0.108340\pi\) |
−0.333825 | + | 0.942635i | \(0.608340\pi\) | |||||||
\(644\) | 61.1604i | 0.0949696i | ||||||||
\(645\) | −69.9325 | + | 91.6224i | −0.108423 | + | 0.142050i | ||||
\(646\) | −930.950 | −1.44110 | ||||||||
\(647\) | 93.4553 | − | 93.4553i | 0.144444 | − | 0.144444i | −0.631187 | − | 0.775631i | \(-0.717432\pi\) |
0.775631 | + | 0.631187i | \(0.217432\pi\) | |||||||
\(648\) | 54.2230 | + | 54.2230i | 0.0836774 | + | 0.0836774i | ||||
\(649\) | − | 59.5237i | − | 0.0917160i | ||||||
\(650\) | −208.165 | − | 761.274i | −0.320253 | − | 1.17119i | ||||
\(651\) | 204.950 | 0.314824 | ||||||||
\(652\) | 156.844 | − | 156.844i | 0.240558 | − | 0.240558i | ||||
\(653\) | −774.653 | − | 774.653i | −1.18630 | − | 1.18630i | −0.978083 | − | 0.208217i | \(-0.933234\pi\) |
−0.208217 | − | 0.978083i | \(-0.566766\pi\) | |||||||
\(654\) | − | 146.856i | − | 0.224551i | ||||||
\(655\) | −203.765 | − | 155.527i | −0.311091 | − | 0.237446i | ||||
\(656\) | −99.7624 | −0.152077 | ||||||||
\(657\) | 180.316 | − | 180.316i | 0.274453 | − | 0.274453i | ||||
\(658\) | 174.351 | + | 174.351i | 0.264971 | + | 0.264971i | ||||
\(659\) | 1143.20i | 1.73476i | 0.497650 | + | 0.867378i | \(0.334196\pi\) | ||||
−0.497650 | + | 0.867378i | \(0.665804\pi\) | |||||||
\(660\) | 179.101 | − | 24.0456i | 0.271366 | − | 0.0364327i | ||||
\(661\) | −27.1447 | −0.0410661 | −0.0205330 | − | 0.999789i | \(-0.506536\pi\) | ||||
−0.0205330 | + | 0.999789i | \(0.506536\pi\) | |||||||
\(662\) | 31.7738 | − | 31.7738i | 0.0479966 | − | 0.0479966i | ||||
\(663\) | −529.713 | − | 529.713i | −0.798964 | − | 0.798964i | ||||
\(664\) | 69.4641i | 0.104615i | ||||||||
\(665\) | −58.2926 | − | 434.187i | −0.0876580 | − | 0.652913i | ||||
\(666\) | −131.781 | −0.197870 | ||||||||
\(667\) | 353.001 | − | 353.001i | 0.529237 | − | 0.529237i | ||||
\(668\) | −242.572 | − | 242.572i | −0.363132 | − | 0.363132i | ||||
\(669\) | − | 295.257i | − | 0.441341i | ||||||
\(670\) | 238.729 | − | 312.772i | 0.356313 | − | 0.466824i | ||||
\(671\) | 527.296 | 0.785837 | ||||||||
\(672\) | 89.9552 | − | 89.9552i | 0.133862 | − | 0.133862i | ||||
\(673\) | −121.151 | − | 121.151i | −0.180016 | − | 0.180016i | 0.611347 | − | 0.791363i | \(-0.290628\pi\) |
−0.791363 | + | 0.611347i | \(0.790628\pi\) | |||||||
\(674\) | − | 479.553i | − | 0.711503i | ||||||
\(675\) | −112.831 | − | 64.3753i | −0.167157 | − | 0.0953708i | ||||
\(676\) | −616.960 | −0.912662 | ||||||||
\(677\) | 344.602 | − | 344.602i | 0.509013 | − | 0.509013i | −0.405210 | − | 0.914224i | \(-0.632802\pi\) |
0.914224 | + | 0.405210i | \(0.132802\pi\) | |||||||
\(678\) | 57.7434 | + | 57.7434i | 0.0851672 | + | 0.0851672i | ||||
\(679\) | − | 82.2857i | − | 0.121187i | ||||||
\(680\) | 664.593 | + | 507.263i | 0.977343 | + | 0.745976i | ||||
\(681\) | −261.931 | −0.384626 | ||||||||
\(682\) | 485.215 | − | 485.215i | 0.711458 | − | 0.711458i | ||||
\(683\) | −436.309 | − | 436.309i | −0.638813 | − | 0.638813i | 0.311449 | − | 0.950263i | \(-0.399186\pi\) |
−0.950263 | + | 0.311449i | \(0.899186\pi\) | |||||||
\(684\) | 193.541i | 0.282954i | ||||||||
\(685\) | −241.409 | + | 32.4109i | −0.352422 | + | 0.0473151i | ||||
\(686\) | 26.5292 | 0.0386723 | ||||||||
\(687\) | −501.068 | + | 501.068i | −0.729357 | + | 0.729357i | ||||
\(688\) | 41.5253 | + | 41.5253i | 0.0603565 | + | 0.0603565i | ||||
\(689\) | 1602.96i | 2.32651i | ||||||||
\(690\) | −19.5872 | − | 145.893i | −0.0283872 | − | 0.211439i | ||||
\(691\) | −250.866 | −0.363048 | −0.181524 | − | 0.983387i | \(-0.558103\pi\) | ||||
−0.181524 | + | 0.983387i | \(0.558103\pi\) | |||||||
\(692\) | −314.881 | + | 314.881i | −0.455031 | + | 0.455031i | ||||
\(693\) | −60.1158 | − | 60.1158i | −0.0867472 | − | 0.0867472i | ||||
\(694\) | − | 23.7990i | − | 0.0342926i | ||||||
\(695\) | 628.022 | − | 822.806i | 0.903629 | − | 1.18389i | ||||
\(696\) | −620.869 | −0.892054 | ||||||||
\(697\) | 313.755 | − | 313.755i | 0.450151 | − | 0.450151i | ||||
\(698\) | 389.191 | + | 389.191i | 0.557580 | + | 0.557580i | ||||
\(699\) | 609.153i | 0.871463i | ||||||||
\(700\) | −63.8558 | + | 111.921i | −0.0912226 | + | 0.159887i | ||||
\(701\) | 73.4709 | 0.104809 | 0.0524044 | − | 0.998626i | \(-0.483312\pi\) | ||||
0.0524044 | + | 0.998626i | \(0.483312\pi\) | |||||||
\(702\) | 115.991 | − | 115.991i | 0.165230 | − | 0.165230i | ||||
\(703\) | −718.088 | − | 718.088i | −1.02146 | − | 1.02146i | ||||
\(704\) | − | 614.979i | − | 0.873550i | ||||||
\(705\) | 447.880 | + | 341.853i | 0.635291 | + | 0.484898i | ||||
\(706\) | −494.310 | −0.700156 | ||||||||
\(707\) | −159.266 | + | 159.266i | −0.225270 | + | 0.225270i | ||||
\(708\) | −13.2592 | − | 13.2592i | −0.0187277 | − | 0.0187277i | ||||
\(709\) | 1378.34i | 1.94407i | 0.234842 | + | 0.972033i | \(0.424543\pi\) | ||||
−0.234842 | + | 0.972033i | \(0.575457\pi\) | |||||||
\(710\) | −167.175 | + | 22.4443i | −0.235457 | + | 0.0316118i | ||||
\(711\) | −24.1483 | −0.0339639 | ||||||||
\(712\) | −375.081 | + | 375.081i | −0.526799 | + | 0.526799i | ||||
\(713\) | 375.259 | + | 375.259i | 0.526310 | + | 0.526310i | ||||
\(714\) | − | 128.825i | − | 0.180427i | ||||||
\(715\) | −157.052 | − | 1169.79i | −0.219653 | − | 1.63606i | ||||
\(716\) | 5.81860 | 0.00812654 | ||||||||
\(717\) | 459.945 | − | 459.945i | 0.641485 | − | 0.641485i | ||||
\(718\) | −552.817 | − | 552.817i | −0.769940 | − | 0.769940i | ||||
\(719\) | − | 1115.67i | − | 1.55170i | −0.630920 | − | 0.775848i | \(-0.717323\pi\) | ||
0.630920 | − | 0.775848i | \(-0.282677\pi\) | |||||||
\(720\) | −40.1569 | + | 52.6117i | −0.0557735 | + | 0.0730718i | ||||
\(721\) | −301.724 | −0.418479 | ||||||||
\(722\) | 745.146 | − | 745.146i | 1.03206 | − | 1.03206i | ||||
\(723\) | −133.685 | − | 133.685i | −0.184903 | − | 0.184903i | ||||
\(724\) | − | 178.483i | − | 0.246523i | ||||||
\(725\) | 1014.53 | − | 277.416i | 1.39935 | − | 0.382643i | ||||
\(726\) | 15.5632 | 0.0214369 | ||||||||
\(727\) | −458.699 | + | 458.699i | −0.630948 | + | 0.630948i | −0.948306 | − | 0.317358i | \(-0.897204\pi\) |
0.317358 | + | 0.948306i | \(0.397204\pi\) | |||||||
\(728\) | −351.295 | − | 351.295i | −0.482548 | − | 0.482548i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 483.940 | + | 369.376i | 0.662931 | + | 0.505995i | ||||
\(731\) | −261.196 | −0.357313 | ||||||||
\(732\) | 117.458 | − | 117.458i | 0.160461 | − | 0.160461i | ||||
\(733\) | 460.978 | + | 460.978i | 0.628892 | + | 0.628892i | 0.947789 | − | 0.318897i | \(-0.103312\pi\) |
−0.318897 | + | 0.947789i | \(0.603312\pi\) | |||||||
\(734\) | − | 179.612i | − | 0.244703i | ||||||
\(735\) | 60.0827 | − | 8.06651i | 0.0817452 | − | 0.0109748i | ||||
\(736\) | 329.412 | 0.447570 | ||||||||
\(737\) | 416.086 | − | 416.086i | 0.564567 | − | 0.564567i | ||||
\(738\) | 68.7030 | + | 68.7030i | 0.0930935 | + | 0.0930935i | ||||
\(739\) | − | 999.301i | − | 1.35223i | −0.736794 | − | 0.676117i | \(-0.763661\pi\) | ||
0.736794 | − | 0.676117i | \(-0.236339\pi\) | |||||||
\(740\) | 39.7464 | + | 296.047i | 0.0537113 | + | 0.400064i | ||||
\(741\) | 1264.09 | 1.70593 | ||||||||
\(742\) | −194.918 | + | 194.918i | −0.262693 | + | 0.262693i | ||||
\(743\) | 698.589 | + | 698.589i | 0.940228 | + | 0.940228i | 0.998312 | − | 0.0580840i | \(-0.0184991\pi\) |
−0.0580840 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(744\) | − | 660.018i | − | 0.887121i | ||||||
\(745\) | 191.218 | − | 250.525i | 0.256668 | − | 0.336275i | ||||
\(746\) | −804.583 | −1.07853 | ||||||||
\(747\) | 17.2946 | − | 17.2946i | 0.0231521 | − | 0.0231521i | ||||
\(748\) | 289.565 | + | 289.565i | 0.387118 | + | 0.387118i | ||||
\(749\) | − | 120.180i | − | 0.160454i | ||||||
\(750\) | 116.479 | − | 287.428i | 0.155306 | − | 0.383237i | ||||
\(751\) | 89.3571 | 0.118984 | 0.0594921 | − | 0.998229i | \(-0.481052\pi\) | ||||
0.0594921 | + | 0.998229i | \(0.481052\pi\) | |||||||
\(752\) | 202.989 | − | 202.989i | 0.269932 | − | 0.269932i | ||||
\(753\) | 114.149 | + | 114.149i | 0.151593 | + | 0.151593i | ||||
\(754\) | 1328.14i | 1.76145i | ||||||||
\(755\) | −125.243 | − | 95.5942i | −0.165885 | − | 0.126615i | ||||
\(756\) | −26.7821 | −0.0354261 | ||||||||
\(757\) | −171.328 | + | 171.328i | −0.226325 | + | 0.226325i | −0.811156 | − | 0.584830i | \(-0.801161\pi\) |
0.584830 | + | 0.811156i | \(0.301161\pi\) | |||||||
\(758\) | −376.659 | − | 376.659i | −0.496912 | − | 0.496912i | ||||
\(759\) | − | 220.141i | − | 0.290041i | ||||||
\(760\) | −1398.25 | + | 187.724i | −1.83980 | + | 0.247005i | ||||
\(761\) | 734.145 | 0.964711 | 0.482356 | − | 0.875975i | \(-0.339781\pi\) | ||||
0.482356 | + | 0.875975i | \(0.339781\pi\) | |||||||
\(762\) | −11.5121 | + | 11.5121i | −0.0151077 | + | 0.0151077i | ||||
\(763\) | 110.736 | + | 110.736i | 0.145133 | + | 0.145133i | ||||
\(764\) | − | 464.598i | − | 0.608112i | ||||||
\(765\) | −39.1707 | − | 291.759i | −0.0512035 | − | 0.381385i | ||||
\(766\) | 81.3703 | 0.106228 | ||||||||
\(767\) | −86.6012 | + | 86.6012i | −0.112909 | + | 0.112909i | ||||
\(768\) | −331.801 | − | 331.801i | −0.432032 | − | 0.432032i | ||||
\(769\) | − | 703.817i | − | 0.915237i | −0.889149 | − | 0.457618i | \(-0.848703\pi\) | ||
0.889149 | − | 0.457618i | \(-0.151297\pi\) | |||||||
\(770\) | 123.147 | − | 161.341i | 0.159931 | − | 0.209534i | ||||
\(771\) | 333.861 | 0.433024 | ||||||||
\(772\) | 135.064 | − | 135.064i | 0.174953 | − | 0.174953i | ||||
\(773\) | 851.260 | + | 851.260i | 1.10124 | + | 1.10124i | 0.994261 | + | 0.106980i | \(0.0341182\pi\) |
0.106980 | + | 0.994261i | \(0.465882\pi\) | |||||||
\(774\) | − | 57.1941i | − | 0.0738942i | ||||||
\(775\) | 294.908 | + | 1078.50i | 0.380527 | + | 1.39162i | ||||
\(776\) | −264.991 | −0.341483 | ||||||||
\(777\) | 99.3688 | − | 99.3688i | 0.127888 | − | 0.127888i | ||||
\(778\) | −349.030 | − | 349.030i | −0.448625 | − | 0.448625i | ||||
\(779\) | 748.738i | 0.961152i | ||||||||
\(780\) | −295.559 | − | 225.591i | −0.378922 | − | 0.289219i | ||||
\(781\) | −252.253 | −0.322987 | ||||||||
\(782\) | 235.875 | − | 235.875i | 0.301630 | − | 0.301630i | ||||
\(783\) | 154.579 | + | 154.579i | 0.197419 | + | 0.197419i | ||||
\(784\) | − | 30.8867i | − | 0.0393963i | ||||||
\(785\) | −1146.40 | + | 153.912i | −1.46038 | + | 0.196067i | ||||
\(786\) | 127.198 | 0.161829 | ||||||||
\(787\) | 1.19018 | − | 1.19018i | 0.00151230 | − | 0.00151230i | −0.706350 | − | 0.707863i | \(-0.749660\pi\) |
0.707863 | + | 0.706350i | \(0.249660\pi\) | |||||||
\(788\) | 124.626 | + | 124.626i | 0.158155 | + | 0.158155i | ||||
\(789\) | − | 78.7698i | − | 0.0998350i | ||||||
\(790\) | −7.67132 | − | 57.1391i | −0.00971053 | − | 0.0723280i | ||||
\(791\) | −87.0821 | −0.110091 | ||||||||
\(792\) | −193.596 | + | 193.596i | −0.244439 | + | 0.244439i | ||||
\(793\) | −767.165 | − | 767.165i | −0.967421 | − | 0.967421i | ||||
\(794\) | − | 435.902i | − | 0.548995i | ||||||
\(795\) | −382.179 | + | 500.714i | −0.480729 | + | 0.629828i | ||||
\(796\) | 98.3050 | 0.123499 | ||||||||
\(797\) | 247.627 | − | 247.627i | 0.310699 | − | 0.310699i | −0.534482 | − | 0.845180i | \(-0.679493\pi\) |
0.845180 | + | 0.534482i | \(0.179493\pi\) | |||||||
\(798\) | 153.712 | + | 153.712i | 0.192622 | + | 0.192622i | ||||
\(799\) | 1276.81i | 1.59801i | ||||||||
\(800\) | 602.807 | + | 343.929i | 0.753509 | + | 0.429911i | ||||
\(801\) | 186.769 | 0.233170 | ||||||||
\(802\) | −284.609 | + | 284.609i | −0.354874 | + | 0.354874i | ||||
\(803\) | 643.792 | + | 643.792i | 0.801734 | + | 0.801734i | ||||
\(804\) | − | 185.370i | − | 0.230560i | ||||||
\(805\) | 124.779 | + | 95.2403i | 0.155006 | + | 0.118311i | ||||
\(806\) | −1411.88 | −1.75171 | ||||||||
\(807\) | 181.523 | − | 181.523i | 0.224936 | − | 0.224936i | ||||
\(808\) | 512.896 | + | 512.896i | 0.634772 | + | 0.634772i | ||||
\(809\) | − | 915.271i | − | 1.13136i | −0.824624 | − | 0.565681i | \(-0.808614\pi\) | ||
0.824624 | − | 0.565681i | \(-0.191386\pi\) | |||||||
\(810\) | 63.8866 | − | 8.57721i | 0.0788724 | − | 0.0105892i | ||||
\(811\) | 1327.40 | 1.63674 | 0.818372 | − | 0.574689i | \(-0.194877\pi\) | ||||
0.818372 | + | 0.574689i | \(0.194877\pi\) | |||||||
\(812\) | 153.332 | − | 153.332i | 0.188832 | − | 0.188832i | ||||
\(813\) | 352.650 | + | 352.650i | 0.433763 | + | 0.433763i | ||||
\(814\) | − | 470.506i | − | 0.578017i | ||||||
\(815\) | −75.7523 | − | 564.234i | −0.0929476 | − | 0.692312i | ||||
\(816\) | −149.985 | −0.183805 | ||||||||
\(817\) | 311.656 | − | 311.656i | 0.381464 | − | 0.381464i | ||||
\(818\) | 504.410 | + | 504.410i | 0.616639 | + | 0.616639i | ||||
\(819\) | 174.925i | 0.213584i | ||||||||
\(820\) | 133.620 | − | 175.063i | 0.162952 | − | 0.213492i | ||||
\(821\) | −1338.19 | −1.62995 | −0.814976 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814976 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(822\) | 85.4644 | − | 85.4644i | 0.103971 | − | 0.103971i | ||||
\(823\) | −230.713 | − | 230.713i | −0.280332 | − | 0.280332i | 0.552909 | − | 0.833241i | \(-0.313518\pi\) |
−0.833241 | + | 0.552909i | \(0.813518\pi\) | |||||||
\(824\) | 971.664i | 1.17920i | ||||||||
\(825\) | 229.843 | − | 402.847i | 0.278597 | − | 0.488300i | ||||
\(826\) | −21.0612 | −0.0254978 | ||||||||
\(827\) | −314.066 | + | 314.066i | −0.379765 | + | 0.379765i | −0.871017 | − | 0.491252i | \(-0.836539\pi\) |
0.491252 | + | 0.871017i | \(0.336539\pi\) | |||||||
\(828\) | −49.0374 | − | 49.0374i | −0.0592240 | − | 0.0592240i | ||||
\(829\) | − | 1137.91i | − | 1.37263i | −0.727304 | − | 0.686316i | \(-0.759227\pi\) | ||
0.727304 | − | 0.686316i | \(-0.240773\pi\) | |||||||
\(830\) | 46.4160 | + | 35.4279i | 0.0559229 | + | 0.0426842i | ||||
\(831\) | 563.394 | 0.677971 | ||||||||
\(832\) | −894.735 | + | 894.735i | −1.07540 | + | 1.07540i | ||||
\(833\) | 97.1395 | + | 97.1395i | 0.116614 | + | 0.116614i | ||||
\(834\) | 513.626i | 0.615859i | ||||||||
\(835\) | −872.634 | + | 117.157i | −1.04507 | + | 0.140308i | ||||
\(836\) | −691.010 | −0.826567 | ||||||||
\(837\) | −164.326 | + | 164.326i | −0.196327 | + | 0.196327i | ||||
\(838\) | −153.873 | − | 153.873i | −0.183619 | − | 0.183619i | ||||
\(839\) | − | 569.389i | − | 0.678652i | −0.940669 | − | 0.339326i | \(-0.889801\pi\) | ||
0.940669 | − | 0.339326i | \(-0.110199\pi\) | |||||||
\(840\) | −25.9772 | − | 193.489i | −0.0309253 | − | 0.230344i | ||||
\(841\) | −928.977 | −1.10461 | ||||||||
\(842\) | −159.537 | + | 159.537i | −0.189474 | + | 0.189474i | ||||
\(843\) | 250.437 | + | 250.437i | 0.297078 | + | 0.297078i | ||||
\(844\) | 415.556i | 0.492365i | ||||||||
\(845\) | −960.743 | + | 1258.72i | −1.13697 | + | 1.48961i | ||||
\(846\) | −279.583 | −0.330477 | ||||||||
\(847\) | −11.7353 | + | 11.7353i | −0.0138552 | + | 0.0138552i | ||||
\(848\) | 226.934 | + | 226.934i | 0.267611 | + | 0.267611i | ||||
\(849\) | − | 199.712i | − | 0.235231i | ||||||
\(850\) | 677.909 | − | 185.369i | 0.797540 | − | 0.218081i | ||||
\(851\) | 363.884 | 0.427595 | ||||||||
\(852\) | −56.1905 | + | 56.1905i | −0.0659513 | + | 0.0659513i | ||||
\(853\) | 247.880 | + | 247.880i | 0.290598 | + | 0.290598i | 0.837316 | − | 0.546719i | \(-0.184123\pi\) |
−0.546719 | + | 0.837316i | \(0.684123\pi\) | |||||||
\(854\) | − | 186.572i | − | 0.218469i | ||||||
\(855\) | 394.862 | + | 301.386i | 0.461827 | + | 0.352498i | ||||
\(856\) | −387.026 | −0.452133 | ||||||||
\(857\) | −1054.40 | + | 1054.40i | −1.23034 | + | 1.23034i | −0.266504 | + | 0.963834i | \(0.585869\pi\) |
−0.963834 | + | 0.266504i | \(0.914131\pi\) | |||||||
\(858\) | 414.131 | + | 414.131i | 0.482670 | + | 0.482670i | ||||
\(859\) | 1669.66i | 1.94373i | 0.235543 | + | 0.971864i | \(0.424313\pi\) | ||||
−0.235543 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(860\) | −128.487 | + | 17.2503i | −0.149403 | + | 0.0200584i | ||||
\(861\) | −103.610 | −0.120337 | ||||||||
\(862\) | 616.529 | − | 616.529i | 0.715230 | − | 0.715230i | ||||
\(863\) | 679.080 | + | 679.080i | 0.786883 | + | 0.786883i | 0.980982 | − | 0.194099i | \(-0.0621784\pi\) |
−0.194099 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(864\) | 144.249i | 0.166955i | ||||||||
\(865\) | 152.081 | + | 1132.76i | 0.175816 | + | 1.30955i | ||||
\(866\) | 1128.13 | 1.30269 | ||||||||
\(867\) | 117.754 | − | 117.754i | 0.135818 | − | 0.135818i | ||||
\(868\) | 163.000 | + | 163.000i | 0.187788 | + | 0.187788i | ||||
\(869\) | − | 86.2183i | − | 0.0992155i | ||||||
\(870\) | −316.655 | + | 414.866i | −0.363971 | + | 0.476858i | ||||
\(871\) | −1210.73 | −1.39004 | ||||||||
\(872\) | 356.612 | − | 356.612i | 0.408959 | − | 0.408959i | ||||
\(873\) | 65.9753 | + | 65.9753i | 0.0755731 | + | 0.0755731i | ||||
\(874\) | 562.886i | 0.644034i | ||||||||
\(875\) | 128.903 | + | 304.564i | 0.147317 | + | 0.348073i | ||||
\(876\) | 286.816 | 0.327415 | ||||||||
\(877\) | −342.730 | + | 342.730i | −0.390798 | + | 0.390798i | −0.874972 | − | 0.484174i | \(-0.839120\pi\) |
0.484174 | + | 0.874972i | \(0.339120\pi\) | |||||||
\(878\) | 455.853 | + | 455.853i | 0.519195 | + | 0.519195i | ||||
\(879\) | − | 226.153i | − | 0.257285i | ||||||
\(880\) | −187.843 | − | 143.375i | −0.213458 | − | 0.162926i | ||||
\(881\) | −342.159 | −0.388376 | −0.194188 | − | 0.980964i | \(-0.562207\pi\) | ||||
−0.194188 | + | 0.980964i | \(0.562207\pi\) | |||||||
\(882\) | −21.2707 | + | 21.2707i | −0.0241164 | + | 0.0241164i | ||||
\(883\) | 249.947 | + | 249.947i | 0.283066 | + | 0.283066i | 0.834330 | − | 0.551265i | \(-0.185855\pi\) |
−0.551265 | + | 0.834330i | \(0.685855\pi\) | |||||||
\(884\) | − | 842.577i | − | 0.953141i | ||||||
\(885\) | −47.6989 | + | 6.40390i | −0.0538971 | + | 0.00723605i | ||||
\(886\) | 387.045 | 0.436846 | ||||||||
\(887\) | −420.721 | + | 420.721i | −0.474319 | + | 0.474319i | −0.903309 | − | 0.428990i | \(-0.858869\pi\) |
0.428990 | + | 0.903309i | \(0.358869\pi\) | |||||||
\(888\) | −320.005 | − | 320.005i | −0.360366 | − | 0.360366i | ||||
\(889\) | − | 17.3612i | − | 0.0195289i | ||||||
\(890\) | 59.3318 | + | 441.928i | 0.0666649 | + | 0.496548i | ||||
\(891\) | 96.3997 | 0.108193 | ||||||||
\(892\) | 234.822 | − | 234.822i | 0.263254 | − | 0.263254i | ||||
\(893\) | −1523.48 | − | 1523.48i | −1.70602 | − | 1.70602i | ||||
\(894\) | 156.387i | 0.174929i | ||||||||
\(895\) | 9.06085 | − | 11.8711i | 0.0101239 | − | 0.0132638i | ||||
\(896\) | 76.1957 | 0.0850398 | ||||||||
\(897\) | −320.284 | + | 320.284i | −0.357061 | + | 0.357061i | ||||
\(898\) | 406.003 | + | 406.003i | 0.452120 | + | 0.452120i | ||||
\(899\) | − | 1881.58i | − | 2.09297i | ||||||
\(900\) | −38.5375 | − | 140.935i | −0.0428195 | − | 0.156594i | ||||
\(901\) | −1427.43 | −1.58427 | ||||||||
\(902\) | −245.294 | + | 245.294i | −0.271945 | + | 0.271945i | ||||
\(903\) | 43.1269 | + | 43.1269i | 0.0477596 | + | 0.0477596i | ||||
\(904\) | 280.437i | 0.310218i | ||||||||
\(905\) | −364.141 | − | 277.937i | −0.402365 | − | 0.307113i | ||||
\(906\) | 78.1814 | 0.0862930 | ||||||||
\(907\) | 345.420 | − | 345.420i | 0.380838 | − | 0.380838i | −0.490566 | − | 0.871404i | \(-0.663210\pi\) |
0.871404 | + | 0.490566i | \(0.163210\pi\) | |||||||
\(908\) | −208.317 | − | 208.317i | −0.229424 | − | 0.229424i | ||||
\(909\) | − | 255.393i | − | 0.280961i | ||||||
\(910\) | −413.903 | + | 55.5693i | −0.454838 | + | 0.0610652i | ||||
\(911\) | −463.217 | −0.508470 | −0.254235 | − | 0.967142i | \(-0.581824\pi\) | ||||
−0.254235 | + | 0.967142i | \(0.581824\pi\) | |||||||
\(912\) | 178.960 | − | 178.960i | 0.196228 | − | 0.196228i | ||||
\(913\) | 61.7479 | + | 61.7479i | 0.0676319 | + | 0.0676319i | ||||
\(914\) | − | 423.681i | − | 0.463545i | ||||||
\(915\) | −56.7296 | − | 422.545i | −0.0619995 | − | 0.461798i | ||||
\(916\) | −797.014 | −0.870102 | ||||||||
\(917\) | −95.9126 | + | 95.9126i | −0.104594 | + | 0.104594i | ||||
\(918\) | 103.290 | + | 103.290i | 0.112516 | + | 0.112516i | ||||
\(919\) | − | 1410.00i | − | 1.53427i | −0.641484 | − | 0.767136i | \(-0.721681\pi\) | ||
0.641484 | − | 0.767136i | \(-0.278319\pi\) | |||||||
\(920\) | 306.710 | − | 401.837i | 0.333380 | − | 0.436779i | ||||
\(921\) | −792.037 | −0.859975 | ||||||||
\(922\) | −169.848 | + | 169.848i | −0.184217 | + | 0.184217i | ||||
\(923\) | 367.004 | + | 367.004i | 0.397620 | + | 0.397620i | ||||
\(924\) | − | 95.6219i | − | 0.103487i | ||||||
\(925\) | 665.889 | + | 379.920i | 0.719880 | + | 0.410725i | ||||
\(926\) | 936.429 | 1.01126 | ||||||||
\(927\) | 241.917 | − | 241.917i | 0.260968 | − | 0.260968i | ||||
\(928\) | −825.849 | − | 825.849i | −0.889924 | − | 0.889924i | ||||
\(929\) | − | 1434.86i | − | 1.54452i | −0.635306 | − | 0.772261i | \(-0.719126\pi\) | ||
0.635306 | − | 0.772261i | \(-0.280874\pi\) | |||||||
\(930\) | −441.025 | − | 336.621i | −0.474221 | − | 0.361958i | ||||
\(931\) | −231.811 | −0.248992 | ||||||||
\(932\) | −484.468 | + | 484.468i | −0.519815 | + | 0.519815i | ||||
\(933\) | 290.295 | + | 290.295i | 0.311142 | + | 0.311142i | ||||
\(934\) | 918.350i | 0.983245i | ||||||||
\(935\) | 1041.69 | − | 139.853i | 1.11410 | − | 0.149576i | ||||
\(936\) | 563.325 | 0.601843 | ||||||||
\(937\) | 1033.63 | − | 1033.63i | 1.10313 | − | 1.10313i | 0.109099 | − | 0.994031i | \(-0.465203\pi\) |
0.994031 | − | 0.109099i | \(-0.0347966\pi\) | |||||||
\(938\) | −147.223 | − | 147.223i | −0.156954 | − | 0.156954i | ||||
\(939\) | 225.542i | 0.240194i | ||||||||
\(940\) | 84.3248 | + | 628.086i | 0.0897073 | + | 0.668176i | ||||
\(941\) | 1768.12 | 1.87898 | 0.939490 | − | 0.342576i | \(-0.111300\pi\) | ||||
0.939490 | + | 0.342576i | \(0.111300\pi\) | |||||||
\(942\) | 405.852 | − | 405.852i | 0.430841 | − | 0.430841i | ||||
\(943\) | −189.708 | − | 189.708i | −0.201175 | − | 0.201175i | ||||
\(944\) | 24.5206i | 0.0259752i | ||||||||
\(945\) | −41.7057 | + | 54.6409i | −0.0441331 | + | 0.0578211i | ||||
\(946\) | 204.204 | 0.215860 | ||||||||
\(947\) | −725.819 | + | 725.819i | −0.766441 | + | 0.766441i | −0.977478 | − | 0.211037i | \(-0.932316\pi\) |
0.211037 | + | 0.977478i | \(0.432316\pi\) | |||||||
\(948\) | −19.2055 | − | 19.2055i | −0.0202590 | − | 0.0202590i | ||||
\(949\) | − | 1873.31i | − | 1.97398i | ||||||
\(950\) | −587.693 | + | 1030.05i | −0.618624 | + | 1.08427i | ||||
\(951\) | 517.902 | 0.544586 | ||||||||
\(952\) | 312.826 | − | 312.826i | 0.328599 | − | 0.328599i | ||||
\(953\) | 1147.42 | + | 1147.42i | 1.20401 | + | 1.20401i | 0.972935 | + | 0.231078i | \(0.0742253\pi\) |
0.231078 | + | 0.972935i | \(0.425775\pi\) | |||||||
\(954\) | − | 312.564i | − | 0.327635i | ||||||
\(955\) | −947.872 | − | 723.481i | −0.992536 | − | 0.757572i | ||||
\(956\) | 731.601 | 0.765273 | ||||||||
\(957\) | −551.903 | + | 551.903i | −0.576701 | + | 0.576701i | ||||
\(958\) | 515.245 | + | 515.245i | 0.537834 | + | 0.537834i | ||||
\(959\) | 128.888i | 0.134398i | ||||||||
\(960\) | −492.809 | + | 66.1630i | −0.513343 | + | 0.0689198i | ||||
\(961\) | 1039.22 | 1.08140 | ||||||||
\(962\) | −684.541 | + | 684.541i | −0.711581 | + | 0.711581i | ||||
\(963\) | 96.3586 | + | 96.3586i | 0.100061 | + | 0.100061i | ||||
\(964\) | − | 212.643i | − | 0.220584i | ||||||
\(965\) | −65.2329 | − | 485.882i | −0.0675989 | − | 0.503504i | ||||
\(966\) | −77.8921 | −0.0806336 | ||||||||
\(967\) | 901.652 | − | 901.652i | 0.932422 | − | 0.932422i | −0.0654346 | − | 0.997857i | \(-0.520843\pi\) |
0.997857 | + | 0.0654346i | \(0.0208434\pi\) | |||||||
\(968\) | 37.7922 | + | 37.7922i | 0.0390415 | + | 0.0390415i | ||||
\(969\) | 1125.67i | 1.16168i | ||||||||
\(970\) | −135.150 | + | 177.067i | −0.139330 | + | 0.182544i | ||||
\(971\) | −370.815 | −0.381890 | −0.190945 | − | 0.981601i | \(-0.561155\pi\) | ||||
−0.190945 | + | 0.981601i | \(0.561155\pi\) | |||||||
\(972\) | 21.4735 | − | 21.4735i | 0.0220921 | − | 0.0220921i | ||||
\(973\) | −387.297 | − | 387.297i | −0.398044 | − | 0.398044i | ||||
\(974\) | − | 845.975i | − | 0.868557i | ||||||
\(975\) | −920.502 | + | 251.704i | −0.944105 | + | 0.258158i | ||||
\(976\) | −217.218 | −0.222559 | ||||||||
\(977\) | −1001.38 | + | 1001.38i | −1.02496 | + | 1.02496i | −0.0252758 | + | 0.999681i | \(0.508046\pi\) |
−0.999681 | + | 0.0252758i | \(0.991954\pi\) | |||||||
\(978\) | 199.752 | + | 199.752i | 0.204245 | + | 0.204245i | ||||
\(979\) | 666.833i | 0.681137i | ||||||||
\(980\) | 54.2001 | + | 41.3692i | 0.0553062 | + | 0.0422135i | ||||
\(981\) | −177.573 | −0.181012 | ||||||||
\(982\) | 272.596 | − | 272.596i | 0.277592 | − | 0.277592i | ||||
\(983\) | −757.649 | − | 757.649i | −0.770751 | − | 0.770751i | 0.207486 | − | 0.978238i | \(-0.433472\pi\) |
−0.978238 | + | 0.207486i | \(0.933472\pi\) | |||||||
\(984\) | 333.664i | 0.339089i | ||||||||
\(985\) | 448.333 | − | 60.1918i | 0.455161 | − | 0.0611084i | ||||
\(986\) | −1182.70 | −1.19949 | ||||||||
\(987\) | 210.818 | − | 210.818i | 0.213595 | − | 0.213595i | ||||
\(988\) | 1005.35 | + | 1005.35i | 1.01756 | + | 1.01756i | ||||
\(989\) | 157.929i | 0.159685i | ||||||||
\(990\) | 30.6237 | + | 228.098i | 0.0309331 | + | 0.230402i | ||||
\(991\) | 1515.68 | 1.52945 | 0.764724 | − | 0.644357i | \(-0.222875\pi\) | ||||
0.764724 | + | 0.644357i | \(0.222875\pi\) | |||||||
\(992\) | 877.922 | − | 877.922i | 0.885002 | − | 0.885002i | ||||
\(993\) | −38.4196 | − | 38.4196i | −0.0386904 | − | 0.0386904i | ||||
\(994\) | 89.2542i | 0.0897930i | ||||||||
\(995\) | 153.083 | − | 200.562i | 0.153852 | − | 0.201570i | ||||
\(996\) | 27.5093 | 0.0276198 | ||||||||
\(997\) | 53.4759 | − | 53.4759i | 0.0536368 | − | 0.0536368i | −0.679780 | − | 0.733416i | \(-0.737925\pi\) |
0.733416 | + | 0.679780i | \(0.237925\pi\) | |||||||
\(998\) | −613.365 | − | 613.365i | −0.614594 | − | 0.614594i | ||||
\(999\) | 159.345i | 0.159504i |
(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 | 105.3.l.a.43.4 | yes | 24 | |
3.2 | odd | 2 | 315.3.o.b.253.9 | 24 | |||
5.2 | odd | 4 | inner | 105.3.l.a.22.4 | ✓ | 24 | |
5.3 | odd | 4 | 525.3.l.e.232.9 | 24 | |||
5.4 | even | 2 | 525.3.l.e.43.9 | 24 | |||
15.2 | even | 4 | 315.3.o.b.127.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.4 | ✓ | 24 | 5.2 | odd | 4 | inner | |
105.3.l.a.43.4 | yes | 24 | 1.1 | even | 1 | trivial | |
315.3.o.b.127.9 | 24 | 15.2 | even | 4 | |||
315.3.o.b.253.9 | 24 | 3.2 | odd | 2 | |||
525.3.l.e.43.9 | 24 | 5.4 | even | 2 | |||
525.3.l.e.232.9 | 24 | 5.3 | odd | 4 |