Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(62,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.62");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.u (of order \(6\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 62.11 | ||
Character | \(\chi\) | \(=\) | 273.62 |
Dual form | 273.2.u.c.251.11 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.584057 | − | 1.01162i | −0.412991 | − | 0.715321i | 0.582224 | − | 0.813028i | \(-0.302183\pi\) |
−0.995215 | + | 0.0977069i | \(0.968849\pi\) | |||||||
\(3\) | −0.340045 | − | 1.69834i | −0.196325 | − | 0.980539i | ||||
\(4\) | 0.317754 | − | 0.550366i | 0.158877 | − | 0.275183i | ||||
\(5\) | 3.55045i | 1.58781i | 0.608042 | + | 0.793905i | \(0.291955\pi\) | ||||
−0.608042 | + | 0.793905i | \(0.708045\pi\) | |||||||
\(6\) | −1.51947 | + | 1.33593i | −0.620320 | + | 0.545389i | ||||
\(7\) | −1.36289 | − | 2.26771i | −0.515124 | − | 0.857115i | ||||
\(8\) | −3.07858 | −1.08844 | ||||||||
\(9\) | −2.76874 | + | 1.15503i | −0.922913 | + | 0.385009i | ||||
\(10\) | 3.59170 | − | 2.07367i | 1.13579 | − | 0.655751i | ||||
\(11\) | −2.54090 | − | 4.40096i | −0.766109 | − | 1.32694i | −0.939658 | − | 0.342115i | \(-0.888857\pi\) |
0.173549 | − | 0.984825i | \(-0.444477\pi\) | |||||||
\(12\) | −1.04276 | − | 0.352506i | −0.301019 | − | 0.101760i | ||||
\(13\) | −3.23163 | − | 1.59893i | −0.896293 | − | 0.443462i | ||||
\(14\) | −1.49805 | + | 2.70320i | −0.400371 | + | 0.722460i | ||||
\(15\) | 6.02988 | − | 1.20731i | 1.55691 | − | 0.311727i | ||||
\(16\) | 1.16256 | + | 2.01361i | 0.290639 | + | 0.503402i | ||||
\(17\) | 1.08363 | − | 1.87690i | 0.262818 | − | 0.455215i | −0.704171 | − | 0.710030i | \(-0.748681\pi\) |
0.966990 | + | 0.254815i | \(0.0820146\pi\) | |||||||
\(18\) | 2.78555 | + | 2.12630i | 0.656560 | + | 0.501174i | ||||
\(19\) | −1.43850 | + | 2.49155i | −0.330014 | + | 0.571600i | −0.982514 | − | 0.186188i | \(-0.940387\pi\) |
0.652501 | + | 0.757788i | \(0.273720\pi\) | |||||||
\(20\) | 1.95405 | + | 1.12817i | 0.436938 | + | 0.252266i | ||||
\(21\) | −3.38791 | + | 3.08578i | −0.739303 | + | 0.673373i | ||||
\(22\) | −2.96806 | + | 5.14083i | −0.632792 | + | 1.09603i | ||||
\(23\) | 2.33890 | − | 1.35037i | 0.487695 | − | 0.281571i | −0.235923 | − | 0.971772i | \(-0.575811\pi\) |
0.723618 | + | 0.690201i | \(0.242478\pi\) | |||||||
\(24\) | 1.04685 | + | 5.22848i | 0.213688 | + | 1.06726i | ||||
\(25\) | −7.60570 | −1.52114 | ||||||||
\(26\) | 0.269957 | + | 4.20304i | 0.0529429 | + | 0.824283i | ||||
\(27\) | 2.90313 | + | 4.30951i | 0.558707 | + | 0.829365i | ||||
\(28\) | −1.68114 | + | 0.0295138i | −0.317705 | + | 0.00557758i | ||||
\(29\) | 6.51871 | − | 3.76358i | 1.21049 | − | 0.698879i | 0.247627 | − | 0.968856i | \(-0.420349\pi\) |
0.962867 | + | 0.269977i | \(0.0870160\pi\) | |||||||
\(30\) | −4.74314 | − | 5.39479i | −0.865974 | − | 0.984950i | ||||
\(31\) | 3.58776 | 0.644381 | 0.322190 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322190 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(32\) | −1.72058 | + | 2.98012i | −0.304158 | + | 0.526817i | ||||
\(33\) | −6.61033 | + | 5.81184i | −1.15071 | + | 1.01171i | ||||
\(34\) | −2.53160 | −0.434167 | ||||||||
\(35\) | 8.05141 | − | 4.83888i | 1.36094 | − | 0.817920i | ||||
\(36\) | −0.244091 | + | 1.89083i | −0.0406818 | + | 0.315139i | ||||
\(37\) | 2.53568 | − | 1.46398i | 0.416863 | − | 0.240676i | −0.276871 | − | 0.960907i | \(-0.589297\pi\) |
0.693734 | + | 0.720231i | \(0.255964\pi\) | |||||||
\(38\) | 3.36066 | 0.545171 | ||||||||
\(39\) | −1.61662 | + | 6.03212i | −0.258867 | + | 0.965913i | ||||
\(40\) | − | 10.9303i | − | 1.72824i | ||||||
\(41\) | −5.45458 | + | 3.14920i | −0.851862 | + | 0.491823i | −0.861279 | − | 0.508133i | \(-0.830336\pi\) |
0.00941653 | + | 0.999956i | \(0.497003\pi\) | |||||||
\(42\) | 5.10036 | + | 1.62500i | 0.787003 | + | 0.250742i | ||||
\(43\) | 4.48749 | − | 7.77256i | 0.684336 | − | 1.18530i | −0.289309 | − | 0.957236i | \(-0.593426\pi\) |
0.973645 | − | 0.228069i | \(-0.0732411\pi\) | |||||||
\(44\) | −3.22952 | −0.486869 | ||||||||
\(45\) | −4.10086 | − | 9.83027i | −0.611321 | − | 1.46541i | ||||
\(46\) | −2.73210 | − | 1.57738i | −0.402827 | − | 0.232572i | ||||
\(47\) | − | 10.3146i | − | 1.50454i | −0.658857 | − | 0.752269i | \(-0.728960\pi\) | ||
0.658857 | − | 0.752269i | \(-0.271040\pi\) | |||||||
\(48\) | 3.02448 | − | 2.65914i | 0.436545 | − | 0.383813i | ||||
\(49\) | −3.28506 | + | 6.18130i | −0.469294 | + | 0.883042i | ||||
\(50\) | 4.44217 | + | 7.69406i | 0.628217 | + | 1.08810i | ||||
\(51\) | −3.55610 | − | 1.20214i | −0.497954 | − | 0.168334i | ||||
\(52\) | −1.90686 | + | 1.27051i | −0.264434 | + | 0.176189i | ||||
\(53\) | − | 1.79048i | − | 0.245942i | −0.992410 | − | 0.122971i | \(-0.960758\pi\) | ||
0.992410 | − | 0.122971i | \(-0.0392422\pi\) | |||||||
\(54\) | 2.66398 | − | 5.45385i | 0.362522 | − | 0.742175i | ||||
\(55\) | 15.6254 | − | 9.02133i | 2.10693 | − | 1.21644i | ||||
\(56\) | 4.19576 | + | 6.98133i | 0.560682 | + | 0.932919i | ||||
\(57\) | 4.72066 | + | 1.59582i | 0.625266 | + | 0.211372i | ||||
\(58\) | −7.61460 | − | 4.39629i | −0.999846 | − | 0.577261i | ||||
\(59\) | 4.23466 | + | 2.44488i | 0.551305 | + | 0.318296i | 0.749648 | − | 0.661836i | \(-0.230223\pi\) |
−0.198343 | + | 0.980133i | \(0.563556\pi\) | |||||||
\(60\) | 1.25156 | − | 3.70227i | 0.161575 | − | 0.477961i | ||||
\(61\) | −0.145945 | − | 0.0842615i | −0.0186864 | − | 0.0107886i | 0.490628 | − | 0.871369i | \(-0.336768\pi\) |
−0.509314 | + | 0.860581i | \(0.670101\pi\) | |||||||
\(62\) | −2.09546 | − | 3.62944i | −0.266123 | − | 0.460939i | ||||
\(63\) | 6.39276 | + | 4.70453i | 0.805412 | + | 0.592716i | ||||
\(64\) | 8.66989 | 1.08374 | ||||||||
\(65\) | 5.67691 | − | 11.4737i | 0.704134 | − | 1.42314i | ||||
\(66\) | 9.74017 | + | 3.29267i | 1.19893 | + | 0.405300i | ||||
\(67\) | 3.78238 | − | 2.18376i | 0.462091 | − | 0.266788i | −0.250832 | − | 0.968031i | \(-0.580704\pi\) |
0.712923 | + | 0.701242i | \(0.247371\pi\) | |||||||
\(68\) | −0.688654 | − | 1.19278i | −0.0835116 | − | 0.144646i | ||||
\(69\) | −3.08871 | − | 3.51307i | −0.371838 | − | 0.422924i | ||||
\(70\) | −9.59758 | − | 5.31876i | −1.14713 | − | 0.635713i | ||||
\(71\) | −5.26351 | + | 9.11667i | −0.624664 | + | 1.08195i | 0.363942 | + | 0.931422i | \(0.381431\pi\) |
−0.988606 | + | 0.150528i | \(0.951903\pi\) | |||||||
\(72\) | 8.52377 | − | 3.55584i | 1.00454 | − | 0.419059i | ||||
\(73\) | −10.7603 | −1.25940 | −0.629700 | − | 0.776838i | \(-0.716822\pi\) | ||||
−0.629700 | + | 0.776838i | \(0.716822\pi\) | |||||||
\(74\) | −2.96197 | − | 1.71009i | −0.344322 | − | 0.198794i | ||||
\(75\) | 2.58628 | + | 12.9171i | 0.298638 | + | 1.49154i | ||||
\(76\) | 0.914176 | + | 1.58340i | 0.104863 | + | 0.181628i | ||||
\(77\) | −6.51716 | + | 11.7601i | −0.742699 | + | 1.34018i | ||||
\(78\) | 7.04640 | − | 1.88770i | 0.797848 | − | 0.213740i | ||||
\(79\) | −4.68895 | −0.527548 | −0.263774 | − | 0.964584i | \(-0.584967\pi\) | ||||
−0.263774 | + | 0.964584i | \(0.584967\pi\) | |||||||
\(80\) | −7.14922 | + | 4.12760i | −0.799307 | + | 0.461480i | ||||
\(81\) | 6.33183 | − | 6.39593i | 0.703537 | − | 0.710659i | ||||
\(82\) | 6.37157 | + | 3.67863i | 0.703623 | + | 0.406237i | ||||
\(83\) | − | 0.468856i | − | 0.0514637i | −0.999669 | − | 0.0257318i | \(-0.991808\pi\) | ||
0.999669 | − | 0.0257318i | \(-0.00819160\pi\) | |||||||
\(84\) | 0.621787 | + | 2.84511i | 0.0678425 | + | 0.310427i | ||||
\(85\) | 6.66384 | + | 3.84737i | 0.722795 | + | 0.417306i | ||||
\(86\) | −10.4838 | −1.13050 | ||||||||
\(87\) | −8.60850 | − | 9.79122i | −0.922928 | − | 1.04973i | ||||
\(88\) | 7.82234 | + | 13.5487i | 0.833865 | + | 1.44430i | ||||
\(89\) | 5.64141 | − | 3.25707i | 0.597989 | − | 0.345249i | −0.170261 | − | 0.985399i | \(-0.554461\pi\) |
0.768250 | + | 0.640150i | \(0.221128\pi\) | |||||||
\(90\) | −7.54933 | + | 9.88995i | −0.795769 | + | 1.04249i | ||||
\(91\) | 0.778454 | + | 9.50758i | 0.0816041 | + | 0.996665i | ||||
\(92\) | − | 1.71634i | − | 0.178940i | ||||||
\(93\) | −1.22000 | − | 6.09325i | −0.126508 | − | 0.631840i | ||||
\(94\) | −10.4344 | + | 6.02431i | −1.07623 | + | 0.621360i | ||||
\(95\) | −8.84612 | − | 5.10731i | −0.907593 | − | 0.523999i | ||||
\(96\) | 5.64635 | + | 1.90875i | 0.576278 | + | 0.194811i | ||||
\(97\) | 4.02073 | − | 6.96410i | 0.408243 | − | 0.707098i | −0.586450 | − | 0.809985i | \(-0.699475\pi\) |
0.994693 | + | 0.102888i | \(0.0328083\pi\) | |||||||
\(98\) | 8.17176 | − | 0.287013i | 0.825473 | − | 0.0289927i | ||||
\(99\) | 12.1183 | + | 9.25031i | 1.21794 | + | 0.929692i | ||||
\(100\) | −2.41674 | + | 4.18592i | −0.241674 | + | 0.418592i | ||||
\(101\) | 1.05407 | + | 1.82570i | 0.104883 | + | 0.181663i | 0.913691 | − | 0.406411i | \(-0.133220\pi\) |
−0.808807 | + | 0.588074i | \(0.799886\pi\) | |||||||
\(102\) | 0.860859 | + | 4.29953i | 0.0852378 | + | 0.425717i | ||||
\(103\) | − | 6.48373i | − | 0.638860i | −0.947610 | − | 0.319430i | \(-0.896508\pi\) | ||
0.947610 | − | 0.319430i | \(-0.103492\pi\) | |||||||
\(104\) | 9.94882 | + | 4.92241i | 0.975562 | + | 0.482682i | ||||
\(105\) | −10.9559 | − | 12.0286i | −1.06919 | − | 1.17387i | ||||
\(106\) | −1.81128 | + | 1.04575i | −0.175927 | + | 0.101572i | ||||
\(107\) | −1.45422 | + | 0.839596i | −0.140585 | + | 0.0811668i | −0.568643 | − | 0.822585i | \(-0.692531\pi\) |
0.428058 | + | 0.903751i | \(0.359198\pi\) | |||||||
\(108\) | 3.29429 | − | 0.228419i | 0.316993 | − | 0.0219796i | ||||
\(109\) | − | 10.6995i | − | 1.02483i | −0.858738 | − | 0.512415i | \(-0.828751\pi\) | ||
0.858738 | − | 0.512415i | \(-0.171249\pi\) | |||||||
\(110\) | −18.2523 | − | 10.5380i | −1.74029 | − | 1.00475i | ||||
\(111\) | −3.34858 | − | 3.80864i | −0.317833 | − | 0.361500i | ||||
\(112\) | 2.98185 | − | 5.38067i | 0.281758 | − | 0.508426i | ||||
\(113\) | 3.60061 | + | 2.07881i | 0.338717 | + | 0.195558i | 0.659704 | − | 0.751525i | \(-0.270681\pi\) |
−0.320988 | + | 0.947083i | \(0.604015\pi\) | |||||||
\(114\) | −1.14277 | − | 5.70755i | −0.107031 | − | 0.534561i | ||||
\(115\) | 4.79441 | + | 8.30415i | 0.447081 | + | 0.774366i | ||||
\(116\) | − | 4.78357i | − | 0.444143i | ||||||
\(117\) | 10.7943 | + | 0.694390i | 0.997937 | + | 0.0641964i | ||||
\(118\) | − | 5.71180i | − | 0.525814i | ||||||
\(119\) | −5.73314 | + | 0.100650i | −0.525556 | + | 0.00922658i | ||||
\(120\) | −18.5635 | + | 3.71680i | −1.69460 | + | 0.339296i | ||||
\(121\) | −7.41232 | + | 12.8385i | −0.673847 | + | 1.16714i | ||||
\(122\) | 0.196854i | 0.0178223i | ||||||||
\(123\) | 7.20323 | + | 8.19288i | 0.649493 | + | 0.738727i | ||||
\(124\) | 1.14002 | − | 1.97458i | 0.102377 | − | 0.177323i | ||||
\(125\) | − | 9.25143i | − | 0.827473i | ||||||
\(126\) | 1.02545 | − | 9.21474i | 0.0913542 | − | 0.820914i | ||||
\(127\) | −11.1004 | − | 19.2265i | −0.985001 | − | 1.70607i | −0.641931 | − | 0.766763i | \(-0.721866\pi\) |
−0.343071 | − | 0.939310i | \(-0.611467\pi\) | |||||||
\(128\) | −1.62256 | − | 2.81036i | −0.143415 | − | 0.248403i | ||||
\(129\) | −14.7264 | − | 4.97828i | −1.29659 | − | 0.438313i | ||||
\(130\) | −14.9227 | + | 0.958469i | −1.30881 | + | 0.0840633i | ||||
\(131\) | −4.74553 | −0.414619 | −0.207310 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207310 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(132\) | 1.09818 | + | 5.48483i | 0.0955845 | + | 0.477394i | ||||
\(133\) | 7.61063 | − | 0.133611i | 0.659926 | − | 0.0115856i | ||||
\(134\) | −4.41825 | − | 2.55088i | −0.381679 | − | 0.220362i | ||||
\(135\) | −15.3007 | + | 10.3074i | −1.31687 | + | 0.887120i | ||||
\(136\) | −3.33603 | + | 5.77818i | −0.286062 | + | 0.495475i | ||||
\(137\) | −3.97315 | + | 6.88169i | −0.339449 | + | 0.587943i | −0.984329 | − | 0.176341i | \(-0.943574\pi\) |
0.644880 | + | 0.764284i | \(0.276907\pi\) | |||||||
\(138\) | −1.74990 | + | 5.17643i | −0.148961 | + | 0.440647i | ||||
\(139\) | −1.09322 | − | 0.631171i | −0.0927257 | − | 0.0535352i | 0.452920 | − | 0.891551i | \(-0.350382\pi\) |
−0.545646 | + | 0.838016i | \(0.683716\pi\) | |||||||
\(140\) | −0.104787 | − | 5.96879i | −0.00885614 | − | 0.504455i | ||||
\(141\) | −17.5177 | + | 3.50742i | −1.47526 | + | 0.295378i | ||||
\(142\) | 12.2968 | 1.03192 | ||||||||
\(143\) | 1.17443 | + | 18.2850i | 0.0982106 | + | 1.52907i | ||||
\(144\) | −5.54459 | − | 4.23237i | −0.462049 | − | 0.352698i | ||||
\(145\) | 13.3624 | + | 23.1444i | 1.10969 | + | 1.92203i | ||||
\(146\) | 6.28464 | + | 10.8853i | 0.520121 | + | 0.900876i | ||||
\(147\) | 11.6150 | + | 3.47723i | 0.957991 | + | 0.286797i | ||||
\(148\) | − | 1.86074i | − | 0.152952i | ||||||
\(149\) | 4.39027 | − | 7.60417i | 0.359665 | − | 0.622958i | −0.628240 | − | 0.778020i | \(-0.716224\pi\) |
0.987905 | + | 0.155062i | \(0.0495576\pi\) | |||||||
\(150\) | 11.5566 | − | 10.1607i | 0.943594 | − | 0.829614i | ||||
\(151\) | 15.1199i | 1.23044i | 0.788354 | + | 0.615222i | \(0.210933\pi\) | ||||
−0.788354 | + | 0.615222i | \(0.789067\pi\) | |||||||
\(152\) | 4.42852 | − | 7.67042i | 0.359200 | − | 0.622153i | ||||
\(153\) | −0.832416 | + | 6.44826i | −0.0672969 | + | 0.521311i | ||||
\(154\) | 15.7031 | − | 0.275681i | 1.26539 | − | 0.0222150i | ||||
\(155\) | 12.7382i | 1.02315i | ||||||||
\(156\) | 2.80619 | + | 2.80647i | 0.224675 | + | 0.224697i | ||||
\(157\) | 5.64339i | 0.450391i | 0.974314 | + | 0.225196i | \(0.0723021\pi\) | ||||
−0.974314 | + | 0.225196i | \(0.927698\pi\) | |||||||
\(158\) | 2.73862 | + | 4.74342i | 0.217873 | + | 0.377367i | ||||
\(159\) | −3.04086 | + | 0.608845i | −0.241156 | + | 0.0482846i | ||||
\(160\) | −10.5808 | − | 6.10882i | −0.836485 | − | 0.482945i | ||||
\(161\) | −6.24991 | − | 3.46356i | −0.492562 | − | 0.272967i | ||||
\(162\) | −10.1684 | − | 2.66980i | −0.798904 | − | 0.209759i | ||||
\(163\) | 6.08960 | + | 3.51583i | 0.476974 | + | 0.275381i | 0.719155 | − | 0.694850i | \(-0.244529\pi\) |
−0.242181 | + | 0.970231i | \(0.577863\pi\) | |||||||
\(164\) | 4.00269i | 0.312557i | ||||||||
\(165\) | −20.6347 | − | 23.4696i | −1.60641 | − | 1.82711i | ||||
\(166\) | −0.474303 | + | 0.273839i | −0.0368130 | + | 0.0212540i | ||||
\(167\) | −6.76367 | + | 3.90501i | −0.523388 | + | 0.302178i | −0.738320 | − | 0.674451i | \(-0.764381\pi\) |
0.214931 | + | 0.976629i | \(0.431047\pi\) | |||||||
\(168\) | 10.4299 | − | 9.49981i | 0.804688 | − | 0.732926i | ||||
\(169\) | 7.88687 | + | 10.3343i | 0.606682 | + | 0.794944i | ||||
\(170\) | − | 8.98834i | − | 0.689374i | ||||||
\(171\) | 1.10502 | − | 8.55995i | 0.0845027 | − | 0.654596i | ||||
\(172\) | −2.85184 | − | 4.93952i | −0.217450 | − | 0.376635i | ||||
\(173\) | 0.714366 | − | 1.23732i | 0.0543122 | − | 0.0940715i | −0.837591 | − | 0.546298i | \(-0.816037\pi\) |
0.891903 | + | 0.452226i | \(0.149370\pi\) | |||||||
\(174\) | −4.87710 | + | 14.4271i | −0.369732 | + | 1.09372i | ||||
\(175\) | 10.3657 | + | 17.2476i | 0.783577 | + | 1.30379i | ||||
\(176\) | 5.90788 | − | 10.2327i | 0.445323 | − | 0.771322i | ||||
\(177\) | 2.71227 | − | 8.02327i | 0.203867 | − | 0.603066i | ||||
\(178\) | −6.58982 | − | 3.80463i | −0.493928 | − | 0.285169i | ||||
\(179\) | 8.02921 | − | 4.63566i | 0.600131 | − | 0.346486i | −0.168962 | − | 0.985623i | \(-0.554042\pi\) |
0.769093 | + | 0.639137i | \(0.220708\pi\) | |||||||
\(180\) | −6.71331 | − | 0.866632i | −0.500381 | − | 0.0645949i | ||||
\(181\) | 18.8579i | 1.40169i | 0.713312 | + | 0.700847i | \(0.247194\pi\) | ||||
−0.713312 | + | 0.700847i | \(0.752806\pi\) | |||||||
\(182\) | 9.16336 | − | 6.34047i | 0.679234 | − | 0.469987i | ||||
\(183\) | −0.0934770 | + | 0.276518i | −0.00691002 | + | 0.0204408i | ||||
\(184\) | −7.20048 | + | 4.15720i | −0.530827 | + | 0.306473i | ||||
\(185\) | 5.19778 | + | 9.00281i | 0.382148 | + | 0.661900i | ||||
\(186\) | −5.45148 | + | 4.79298i | −0.399722 | + | 0.351438i | ||||
\(187\) | −11.0136 | −0.805391 | ||||||||
\(188\) | −5.67680 | − | 3.27750i | −0.414023 | − | 0.239036i | ||||
\(189\) | 5.81609 | − | 12.4569i | 0.423058 | − | 0.906103i | ||||
\(190\) | 11.9318i | 0.865627i | ||||||||
\(191\) | −12.6936 | − | 7.32866i | −0.918477 | − | 0.530283i | −0.0353282 | − | 0.999376i | \(-0.511248\pi\) |
−0.883149 | + | 0.469093i | \(0.844581\pi\) | |||||||
\(192\) | −2.94815 | − | 14.7244i | −0.212765 | − | 1.06265i | ||||
\(193\) | 17.8122 | − | 10.2839i | 1.28215 | − | 0.740248i | 0.304907 | − | 0.952382i | \(-0.401375\pi\) |
0.977241 | + | 0.212134i | \(0.0680414\pi\) | |||||||
\(194\) | −9.39334 | −0.674403 | ||||||||
\(195\) | −21.4168 | − | 5.73975i | −1.53369 | − | 0.411032i | ||||
\(196\) | 2.35814 | + | 3.77211i | 0.168438 | + | 0.269437i | ||||
\(197\) | 1.25664 | + | 2.17657i | 0.0895322 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(198\) | 2.27999 | − | 17.6618i | 0.162032 | − | 1.25517i | ||||
\(199\) | 8.53047 | + | 4.92507i | 0.604709 | + | 0.349129i | 0.770892 | − | 0.636966i | \(-0.219811\pi\) |
−0.166183 | + | 0.986095i | \(0.553144\pi\) | |||||||
\(200\) | 23.4147 | 1.65567 | ||||||||
\(201\) | −4.99494 | − | 5.68120i | −0.352316 | − | 0.400721i | ||||
\(202\) | 1.23127 | − | 2.13262i | 0.0866318 | − | 0.150051i | ||||
\(203\) | −17.4190 | − | 9.65322i | −1.22257 | − | 0.677523i | ||||
\(204\) | −1.79158 | + | 1.57517i | −0.125436 | + | 0.110284i | ||||
\(205\) | −11.1811 | − | 19.3662i | −0.780921 | − | 1.35260i | ||||
\(206\) | −6.55905 | + | 3.78687i | −0.456990 | + | 0.263844i | ||||
\(207\) | −4.91610 | + | 6.44030i | −0.341692 | + | 0.447632i | ||||
\(208\) | −0.537345 | − | 8.36608i | −0.0372582 | − | 0.580083i | ||||
\(209\) | 14.6203 | 1.01131 | ||||||||
\(210\) | −5.76947 | + | 18.1086i | −0.398131 | + | 1.24961i | ||||
\(211\) | −4.82479 | − | 8.35678i | −0.332152 | − | 0.575304i | 0.650782 | − | 0.759265i | \(-0.274441\pi\) |
−0.982934 | + | 0.183961i | \(0.941108\pi\) | |||||||
\(212\) | −0.985422 | − | 0.568933i | −0.0676790 | − | 0.0390745i | ||||
\(213\) | 17.2731 | + | 5.83917i | 1.18353 | + | 0.400093i | ||||
\(214\) | 1.69870 | + | 0.980745i | 0.116121 | + | 0.0670423i | ||||
\(215\) | 27.5961 | + | 15.9326i | 1.88204 | + | 1.08660i | ||||
\(216\) | −8.93749 | − | 13.2671i | −0.608119 | − | 0.902715i | ||||
\(217\) | −4.88973 | − | 8.13601i | −0.331936 | − | 0.552309i | ||||
\(218\) | −10.8238 | + | 6.24915i | −0.733083 | + | 0.423246i | ||||
\(219\) | 3.65899 | + | 18.2747i | 0.247252 | + | 1.23489i | ||||
\(220\) | − | 11.4663i | − | 0.773055i | ||||||
\(221\) | −6.50291 | + | 4.33280i | −0.437433 | + | 0.291456i | ||||
\(222\) | −1.89712 | + | 5.61194i | −0.127326 | + | 0.376649i | ||||
\(223\) | −5.03517 | − | 8.72117i | −0.337180 | − | 0.584013i | 0.646721 | − | 0.762727i | \(-0.276140\pi\) |
−0.983901 | + | 0.178714i | \(0.942806\pi\) | |||||||
\(224\) | 9.10303 | − | 0.159811i | 0.608222 | − | 0.0106778i | ||||
\(225\) | 21.0582 | − | 8.78479i | 1.40388 | − | 0.585652i | ||||
\(226\) | − | 4.85658i | − | 0.323055i | ||||||
\(227\) | 8.91928 | + | 5.14955i | 0.591993 | + | 0.341787i | 0.765885 | − | 0.642977i | \(-0.222301\pi\) |
−0.173892 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(228\) | 2.37829 | − | 2.09101i | 0.157506 | − | 0.138481i | ||||
\(229\) | 15.5100 | 1.02493 | 0.512464 | − | 0.858709i | \(-0.328733\pi\) | ||||
0.512464 | + | 0.858709i | \(0.328733\pi\) | |||||||
\(230\) | 5.60042 | − | 9.70020i | 0.369280 | − | 0.639613i | ||||
\(231\) | 22.1887 | + | 7.06942i | 1.45991 | + | 0.465134i | ||||
\(232\) | −20.0683 | + | 11.5865i | −1.31755 | + | 0.760688i | ||||
\(233\) | − | 2.29887i | − | 0.150604i | −0.997161 | − | 0.0753020i | \(-0.976008\pi\) | ||
0.997161 | − | 0.0753020i | \(-0.0239921\pi\) | |||||||
\(234\) | −5.60206 | − | 11.3253i | −0.366218 | − | 0.740358i | ||||
\(235\) | 36.6214 | 2.38892 | ||||||||
\(236\) | 2.69116 | − | 1.55374i | 0.175179 | − | 0.101140i | ||||
\(237\) | 1.59445 | + | 7.96345i | 0.103571 | + | 0.517282i | ||||
\(238\) | 3.45030 | + | 5.74095i | 0.223650 | + | 0.372131i | ||||
\(239\) | 24.3089 | 1.57241 | 0.786205 | − | 0.617965i | \(-0.212043\pi\) | ||||
0.786205 | + | 0.617965i | \(0.212043\pi\) | |||||||
\(240\) | 9.44114 | + | 10.7383i | 0.609423 | + | 0.693151i | ||||
\(241\) | −6.90894 | + | 11.9666i | −0.445044 | + | 0.770839i | −0.998055 | − | 0.0623347i | \(-0.980145\pi\) |
0.553011 | + | 0.833174i | \(0.313479\pi\) | |||||||
\(242\) | 17.3169 | 1.11317 | ||||||||
\(243\) | −13.0156 | − | 8.57872i | −0.834951 | − | 0.550325i | ||||
\(244\) | −0.0927493 | + | 0.0535488i | −0.00593767 | + | 0.00342811i | ||||
\(245\) | −21.9464 | − | 11.6634i | −1.40210 | − | 0.745149i | ||||
\(246\) | 4.08095 | − | 12.0720i | 0.260192 | − | 0.769684i | ||||
\(247\) | 8.63249 | − | 5.75172i | 0.549272 | − | 0.365973i | ||||
\(248\) | −11.0452 | −0.701370 | ||||||||
\(249\) | −0.796279 | + | 0.159432i | −0.0504621 | + | 0.0101036i | ||||
\(250\) | −9.35890 | + | 5.40336i | −0.591909 | + | 0.341739i | ||||
\(251\) | −4.27689 | + | 7.40779i | −0.269955 | + | 0.467576i | −0.968850 | − | 0.247649i | \(-0.920342\pi\) |
0.698895 | + | 0.715224i | \(0.253676\pi\) | |||||||
\(252\) | 4.62054 | − | 2.02347i | 0.291067 | − | 0.127467i | ||||
\(253\) | −11.8858 | − | 6.86228i | −0.747255 | − | 0.431428i | ||||
\(254\) | −12.9665 | + | 22.4587i | −0.813593 | + | 1.40918i | ||||
\(255\) | 4.26815 | − | 12.6258i | 0.267282 | − | 0.790656i | ||||
\(256\) | 6.77455 | − | 11.7339i | 0.423409 | − | 0.733367i | ||||
\(257\) | 0.974388 | + | 1.68769i | 0.0607806 | + | 0.105275i | 0.894815 | − | 0.446438i | \(-0.147308\pi\) |
−0.834034 | + | 0.551713i | \(0.813974\pi\) | |||||||
\(258\) | 3.56497 | + | 17.8051i | 0.221945 | + | 1.10850i | ||||
\(259\) | −6.77574 | − | 3.75496i | −0.421024 | − | 0.233322i | ||||
\(260\) | −4.51090 | − | 6.77021i | −0.279754 | − | 0.419870i | ||||
\(261\) | −13.7016 | + | 17.9496i | −0.848106 | + | 1.11105i | ||||
\(262\) | 2.77166 | + | 4.80066i | 0.171234 | + | 0.296586i | ||||
\(263\) | −6.70957 | + | 3.87377i | −0.413730 | + | 0.238867i | −0.692391 | − | 0.721523i | \(-0.743443\pi\) |
0.278661 | + | 0.960389i | \(0.410109\pi\) | |||||||
\(264\) | 20.3504 | − | 17.8922i | 1.25248 | − | 1.10119i | ||||
\(265\) | 6.35703 | 0.390509 | ||||||||
\(266\) | −4.58021 | − | 7.62101i | −0.280831 | − | 0.467274i | ||||
\(267\) | −7.44996 | − | 8.47351i | −0.455930 | − | 0.518570i | ||||
\(268\) | − | 2.77559i | − | 0.169546i | ||||||
\(269\) | 14.1755 | − | 24.5528i | 0.864298 | − | 1.49701i | −0.00344363 | − | 0.999994i | \(-0.501096\pi\) |
0.867742 | − | 0.497015i | \(-0.165571\pi\) | |||||||
\(270\) | 19.3636 | + | 9.45833i | 1.17843 | + | 0.575616i | ||||
\(271\) | −13.4325 | − | 23.2658i | −0.815969 | − | 1.41330i | −0.908630 | − | 0.417601i | \(-0.862871\pi\) |
0.0926617 | − | 0.995698i | \(-0.470462\pi\) | |||||||
\(272\) | 5.03912 | 0.305541 | ||||||||
\(273\) | 15.8824 | − | 4.55509i | 0.961248 | − | 0.275686i | ||||
\(274\) | 9.28218 | 0.560757 | ||||||||
\(275\) | 19.3253 | + | 33.4724i | 1.16536 | + | 2.01846i | ||||
\(276\) | −2.91493 | + | 0.583631i | −0.175458 | + | 0.0351305i | ||||
\(277\) | −6.79226 | + | 11.7645i | −0.408108 | + | 0.706863i | −0.994678 | − | 0.103035i | \(-0.967145\pi\) |
0.586570 | + | 0.809898i | \(0.300478\pi\) | |||||||
\(278\) | 1.47456i | 0.0884382i | ||||||||
\(279\) | −9.93357 | + | 4.14396i | −0.594707 | + | 0.248092i | ||||
\(280\) | −24.7869 | + | 14.8969i | −1.48130 | + | 0.890257i | ||||
\(281\) | −13.4869 | −0.804561 | −0.402281 | − | 0.915516i | \(-0.631782\pi\) | ||||
−0.402281 | + | 0.915516i | \(0.631782\pi\) | |||||||
\(282\) | 13.7795 | + | 15.6727i | 0.820558 | + | 0.933294i | ||||
\(283\) | −9.37572 | + | 5.41308i | −0.557329 | + | 0.321774i | −0.752073 | − | 0.659080i | \(-0.770946\pi\) |
0.194744 | + | 0.980854i | \(0.437612\pi\) | |||||||
\(284\) | 3.34500 | + | 5.79371i | 0.198489 | + | 0.343794i | ||||
\(285\) | −5.66589 | + | 16.7605i | −0.335618 | + | 0.992804i | ||||
\(286\) | 17.8115 | − | 11.8676i | 1.05321 | − | 0.701743i | ||||
\(287\) | 14.5755 | + | 8.07741i | 0.860364 | + | 0.476794i | ||||
\(288\) | 1.32170 | − | 10.2385i | 0.0778821 | − | 0.603309i | ||||
\(289\) | 6.15150 | + | 10.6547i | 0.361853 | + | 0.626748i | ||||
\(290\) | 15.6088 | − | 27.0353i | 0.916581 | − | 1.58757i | ||||
\(291\) | −13.1947 | − | 4.46047i | −0.773485 | − | 0.261477i | ||||
\(292\) | −3.41913 | + | 5.92211i | −0.200090 | + | 0.346565i | ||||
\(293\) | −23.5405 | − | 13.5911i | −1.37525 | − | 0.794000i | −0.383666 | − | 0.923472i | \(-0.625339\pi\) |
−0.991583 | + | 0.129471i | \(0.958672\pi\) | |||||||
\(294\) | −3.26621 | − | 13.7809i | −0.190489 | − | 0.803716i | ||||
\(295\) | −8.68042 | + | 15.0349i | −0.505394 | + | 0.875368i | ||||
\(296\) | −7.80629 | + | 4.50696i | −0.453731 | + | 0.261962i | ||||
\(297\) | 11.5894 | − | 23.7266i | 0.672487 | − | 1.37676i | ||||
\(298\) | −10.2567 | −0.594154 | ||||||||
\(299\) | −9.71760 | + | 0.624152i | −0.561983 | + | 0.0360956i | ||||
\(300\) | 7.93093 | + | 2.68106i | 0.457893 | + | 0.154791i | ||||
\(301\) | −23.7419 | + | 0.416809i | −1.36846 | + | 0.0240245i | ||||
\(302\) | 15.2956 | − | 8.83091i | 0.880162 | − | 0.508162i | ||||
\(303\) | 2.74223 | − | 2.41098i | 0.157537 | − | 0.138507i | ||||
\(304\) | −6.68933 | −0.383660 | ||||||||
\(305\) | 0.299166 | − | 0.518171i | 0.0171302 | − | 0.0296704i | ||||
\(306\) | 7.00935 | − | 2.92407i | 0.400698 | − | 0.167158i | ||||
\(307\) | 34.4944 | 1.96870 | 0.984350 | − | 0.176225i | \(-0.0563887\pi\) | ||||
0.984350 | + | 0.176225i | \(0.0563887\pi\) | |||||||
\(308\) | 4.40149 | + | 7.32363i | 0.250798 | + | 0.417303i | ||||
\(309\) | −11.0116 | + | 2.20476i | −0.626428 | + | 0.125424i | ||||
\(310\) | 12.8861 | − | 7.43982i | 0.731884 | − | 0.422553i | ||||
\(311\) | −16.5987 | −0.941228 | −0.470614 | − | 0.882339i | \(-0.655968\pi\) | ||||
−0.470614 | + | 0.882339i | \(0.655968\pi\) | |||||||
\(312\) | 4.97690 | − | 18.5704i | 0.281762 | − | 1.05134i | ||||
\(313\) | − | 2.40647i | − | 0.136022i | −0.997685 | − | 0.0680109i | \(-0.978335\pi\) | ||
0.997685 | − | 0.0680109i | \(-0.0216653\pi\) | |||||||
\(314\) | 5.70895 | − | 3.29606i | 0.322175 | − | 0.186008i | ||||
\(315\) | −16.7032 | + | 22.6972i | −0.941120 | + | 1.27884i | ||||
\(316\) | −1.48993 | + | 2.58064i | −0.0838153 | + | 0.145172i | ||||
\(317\) | 14.4082 | 0.809247 | 0.404624 | − | 0.914483i | \(-0.367403\pi\) | ||||
0.404624 | + | 0.914483i | \(0.367403\pi\) | |||||||
\(318\) | 2.39195 | + | 2.72058i | 0.134134 | + | 0.152563i | ||||
\(319\) | −33.1267 | − | 19.1257i | −1.85474 | − | 1.07084i | ||||
\(320\) | 30.7820i | 1.72077i | ||||||||
\(321\) | 1.92042 | + | 2.18427i | 0.107188 | + | 0.121914i | ||||
\(322\) | 0.146511 | + | 8.34543i | 0.00816475 | + | 0.465073i | ||||
\(323\) | 3.11759 | + | 5.39982i | 0.173467 | + | 0.300454i | ||||
\(324\) | −1.50814 | − | 5.51716i | −0.0837855 | − | 0.306509i | ||||
\(325\) | 24.5788 | + | 12.1610i | 1.36339 | + | 0.674569i | ||||
\(326\) | − | 8.21379i | − | 0.454919i | ||||||
\(327\) | −18.1715 | + | 3.63833i | −1.00489 | + | 0.201200i | ||||
\(328\) | 16.7923 | − | 9.69506i | 0.927202 | − | 0.535320i | ||||
\(329\) | −23.3905 | + | 14.0577i | −1.28956 | + | 0.775024i | ||||
\(330\) | −11.6905 | + | 34.5820i | −0.643539 | + | 1.90368i | ||||
\(331\) | 3.78126 | + | 2.18311i | 0.207837 | + | 0.119995i | 0.600306 | − | 0.799771i | \(-0.295046\pi\) |
−0.392469 | + | 0.919765i | \(0.628379\pi\) | |||||||
\(332\) | −0.258043 | − | 0.148981i | −0.0141619 | − | 0.00817639i | ||||
\(333\) | −5.32971 | + | 6.98214i | −0.292066 | + | 0.382619i | ||||
\(334\) | 7.90074 | + | 4.56150i | 0.432309 | + | 0.249594i | ||||
\(335\) | 7.75332 | + | 13.4291i | 0.423609 | + | 0.733712i | ||||
\(336\) | −10.1522 | − | 3.23453i | −0.553848 | − | 0.176458i | ||||
\(337\) | 8.68524 | 0.473115 | 0.236558 | − | 0.971617i | \(-0.423981\pi\) | ||||
0.236558 | + | 0.971617i | \(0.423981\pi\) | |||||||
\(338\) | 5.84794 | − | 14.0143i | 0.318086 | − | 0.762278i | ||||
\(339\) | 2.30617 | − | 6.82196i | 0.125254 | − | 0.370518i | ||||
\(340\) | 4.23492 | − | 2.44503i | 0.229671 | − | 0.132601i | ||||
\(341\) | −9.11613 | − | 15.7896i | −0.493666 | − | 0.855055i | ||||
\(342\) | −9.30478 | + | 3.88165i | −0.503145 | + | 0.209895i | ||||
\(343\) | 18.4946 | − | 0.974866i | 0.998614 | − | 0.0526378i | ||||
\(344\) | −13.8151 | + | 23.9284i | −0.744859 | + | 1.29013i | ||||
\(345\) | 12.4730 | − | 10.9663i | 0.671523 | − | 0.590407i | ||||
\(346\) | −1.66892 | −0.0897218 | ||||||||
\(347\) | 14.4709 | + | 8.35477i | 0.776838 | + | 0.448508i | 0.835309 | − | 0.549781i | \(-0.185289\pi\) |
−0.0584704 | + | 0.998289i | \(0.518622\pi\) | |||||||
\(348\) | −8.12414 | + | 1.62663i | −0.435499 | + | 0.0871964i | ||||
\(349\) | −16.6660 | − | 28.8664i | −0.892111 | − | 1.54518i | −0.837340 | − | 0.546683i | \(-0.815890\pi\) |
−0.0547712 | − | 0.998499i | \(-0.517443\pi\) | |||||||
\(350\) | 11.3937 | − | 20.5597i | 0.609021 | − | 1.09896i | ||||
\(351\) | −2.49125 | − | 18.5686i | −0.132973 | − | 0.991120i | ||||
\(352\) | 17.4872 | 0.932072 | ||||||||
\(353\) | −10.3711 | + | 5.98773i | −0.551996 | + | 0.318695i | −0.749927 | − | 0.661521i | \(-0.769911\pi\) |
0.197931 | + | 0.980216i | \(0.436578\pi\) | |||||||
\(354\) | −9.70059 | + | 1.94227i | −0.515581 | + | 0.103230i | ||||
\(355\) | −32.3683 | − | 18.6878i | −1.71793 | − | 0.991847i | ||||
\(356\) | − | 4.13979i | − | 0.219408i | ||||||
\(357\) | 2.12046 | + | 9.70261i | 0.112227 | + | 0.513517i | ||||
\(358\) | −9.37903 | − | 5.41499i | −0.495697 | − | 0.286191i | ||||
\(359\) | 5.50745 | 0.290672 | 0.145336 | − | 0.989382i | \(-0.453574\pi\) | ||||
0.145336 | + | 0.989382i | \(0.453574\pi\) | |||||||
\(360\) | 12.6248 | + | 30.2632i | 0.665386 | + | 1.59501i | ||||
\(361\) | 5.36146 | + | 9.28632i | 0.282182 | + | 0.488754i | ||||
\(362\) | 19.0769 | − | 11.0141i | 1.00266 | − | 0.578887i | ||||
\(363\) | 24.3247 | + | 8.22299i | 1.27672 | + | 0.431595i | ||||
\(364\) | 5.48000 | + | 2.59264i | 0.287230 | + | 0.135891i | ||||
\(365\) | − | 38.2040i | − | 1.99969i | ||||||
\(366\) | 0.334326 | − | 0.0669393i | 0.0174755 | − | 0.00349897i | ||||
\(367\) | −8.24711 | + | 4.76147i | −0.430496 | + | 0.248547i | −0.699558 | − | 0.714576i | \(-0.746620\pi\) |
0.269062 | + | 0.963123i | \(0.413286\pi\) | |||||||
\(368\) | 5.43821 | + | 3.13975i | 0.283486 | + | 0.163671i | ||||
\(369\) | 11.4649 | − | 15.0195i | 0.596839 | − | 0.781884i | ||||
\(370\) | 6.07160 | − | 10.5163i | 0.315647 | − | 0.546717i | ||||
\(371\) | −4.06031 | + | 2.44023i | −0.210801 | + | 0.126691i | ||||
\(372\) | −3.74118 | − | 1.26471i | −0.193971 | − | 0.0655720i | ||||
\(373\) | −7.40112 | + | 12.8191i | −0.383216 | + | 0.663749i | −0.991520 | − | 0.129955i | \(-0.958517\pi\) |
0.608304 | + | 0.793704i | \(0.291850\pi\) | |||||||
\(374\) | 6.43255 | + | 11.1415i | 0.332619 | + | 0.576113i | ||||
\(375\) | −15.7121 | + | 3.14590i | −0.811369 | + | 0.162454i | ||||
\(376\) | 31.7542i | 1.63760i | ||||||||
\(377\) | −27.0837 | + | 1.73956i | −1.39488 | + | 0.0895920i | ||||
\(378\) | −15.9985 | + | 1.39186i | −0.822874 | + | 0.0715897i | ||||
\(379\) | 9.74185 | − | 5.62446i | 0.500405 | − | 0.288909i | −0.228476 | − | 0.973550i | \(-0.573374\pi\) |
0.728881 | + | 0.684641i | \(0.240041\pi\) | |||||||
\(380\) | −5.62178 | + | 3.24574i | −0.288391 | + | 0.166503i | ||||
\(381\) | −28.8785 | + | 25.3902i | −1.47949 | + | 1.30078i | ||||
\(382\) | 17.1214i | 0.876008i | ||||||||
\(383\) | −10.2167 | − | 5.89859i | −0.522047 | − | 0.301404i | 0.215725 | − | 0.976454i | \(-0.430789\pi\) |
−0.737772 | + | 0.675050i | \(0.764122\pi\) | |||||||
\(384\) | −4.22121 | + | 3.71131i | −0.215413 | + | 0.189392i | ||||
\(385\) | −41.7535 | − | 23.1389i | −2.12796 | − | 1.17927i | ||||
\(386\) | −20.8066 | − | 12.0127i | −1.05903 | − | 0.611431i | ||||
\(387\) | −3.44718 | + | 26.7034i | −0.175230 | + | 1.35741i | ||||
\(388\) | −2.55520 | − | 4.42574i | −0.129721 | − | 0.224683i | ||||
\(389\) | 15.3002i | 0.775749i | 0.921712 | + | 0.387874i | \(0.126791\pi\) | ||||
−0.921712 | + | 0.387874i | \(0.873209\pi\) | |||||||
\(390\) | 6.70219 | + | 25.0179i | 0.339379 | + | 1.26683i | ||||
\(391\) | − | 5.85317i | − | 0.296008i | ||||||
\(392\) | 10.1133 | − | 19.0296i | 0.510798 | − | 0.961139i | ||||
\(393\) | 1.61370 | + | 8.05955i | 0.0814002 | + | 0.406550i | ||||
\(394\) | 1.46791 | − | 2.54249i | 0.0739520 | − | 0.128089i | ||||
\(395\) | − | 16.6479i | − | 0.837647i | ||||||
\(396\) | 8.94170 | − | 3.73018i | 0.449337 | − | 0.187449i | ||||
\(397\) | 10.7610 | − | 18.6387i | 0.540081 | − | 0.935449i | −0.458817 | − | 0.888531i | \(-0.651727\pi\) |
0.998899 | − | 0.0469179i | \(-0.0149399\pi\) | |||||||
\(398\) | − | 11.5061i | − | 0.576748i | ||||||
\(399\) | −2.81487 | − | 12.8800i | −0.140920 | − | 0.644808i | ||||
\(400\) | −8.84206 | − | 15.3149i | −0.442103 | − | 0.765745i | ||||
\(401\) | −6.81360 | − | 11.8015i | −0.340255 | − | 0.589339i | 0.644225 | − | 0.764836i | \(-0.277180\pi\) |
−0.984480 | + | 0.175497i | \(0.943847\pi\) | |||||||
\(402\) | −2.82986 | + | 8.37111i | −0.141141 | + | 0.417513i | ||||
\(403\) | −11.5943 | − | 5.73656i | −0.577554 | − | 0.285758i | ||||
\(404\) | 1.33973 | 0.0666543 | ||||||||
\(405\) | 22.7084 | + | 22.4809i | 1.12839 | + | 1.11708i | ||||
\(406\) | 0.408338 | + | 23.2594i | 0.0202655 | + | 1.15434i | ||||
\(407\) | −12.8858 | − | 7.43963i | −0.638726 | − | 0.368769i | ||||
\(408\) | 10.9477 | + | 3.70089i | 0.541993 | + | 0.183221i | ||||
\(409\) | −12.5613 | + | 21.7568i | −0.621117 | + | 1.07581i | 0.368161 | + | 0.929762i | \(0.379988\pi\) |
−0.989278 | + | 0.146045i | \(0.953346\pi\) | |||||||
\(410\) | −13.0608 | + | 22.6220i | −0.645027 | + | 1.11722i | ||||
\(411\) | 13.0385 | + | 4.40768i | 0.643143 | + | 0.217415i | ||||
\(412\) | −3.56842 | − | 2.06023i | −0.175804 | − | 0.101500i | ||||
\(413\) | −0.227087 | − | 12.9351i | −0.0111742 | − | 0.636494i | ||||
\(414\) | 9.38640 | + | 1.21170i | 0.461316 | + | 0.0595520i | ||||
\(415\) | 1.66465 | 0.0817145 | ||||||||
\(416\) | 10.3253 | − | 6.87959i | 0.506238 | − | 0.337300i | ||||
\(417\) | −0.700201 | + | 2.07129i | −0.0342890 | + | 0.101431i | ||||
\(418\) | −8.53908 | − | 14.7901i | −0.417660 | − | 0.723409i | ||||
\(419\) | −3.24454 | − | 5.61971i | −0.158506 | − | 0.274541i | 0.775824 | − | 0.630949i | \(-0.217334\pi\) |
−0.934330 | + | 0.356408i | \(0.884001\pi\) | |||||||
\(420\) | −10.1014 | + | 2.20762i | −0.492899 | + | 0.107721i | ||||
\(421\) | − | 21.8360i | − | 1.06422i | −0.846674 | − | 0.532111i | \(-0.821399\pi\) | ||
0.846674 | − | 0.532111i | \(-0.178601\pi\) | |||||||
\(422\) | −5.63590 | + | 9.76167i | −0.274352 | + | 0.475191i | ||||
\(423\) | 11.9136 | + | 28.5584i | 0.579260 | + | 1.38856i | ||||
\(424\) | 5.51214i | 0.267693i | ||||||||
\(425\) | −8.24176 | + | 14.2751i | −0.399784 | + | 0.692446i | ||||
\(426\) | −4.18145 | − | 20.8841i | −0.202592 | − | 1.01184i | ||||
\(427\) | 0.00782642 | + | 0.445801i | 0.000378747 | + | 0.0215738i | ||||
\(428\) | 1.06714i | 0.0515822i | ||||||||
\(429\) | 30.6548 | − | 8.21230i | 1.48003 | − | 0.396494i | ||||
\(430\) | − | 37.2222i | − | 1.79502i | ||||||
\(431\) | −13.6869 | − | 23.7064i | −0.659275 | − | 1.14190i | −0.980804 | − | 0.194998i | \(-0.937530\pi\) |
0.321529 | − | 0.946900i | \(-0.395803\pi\) | |||||||
\(432\) | −5.30261 | + | 10.8558i | −0.255122 | + | 0.522300i | ||||
\(433\) | 15.4442 | + | 8.91673i | 0.742203 | + | 0.428511i | 0.822870 | − | 0.568230i | \(-0.192372\pi\) |
−0.0806671 | + | 0.996741i | \(0.525705\pi\) | |||||||
\(434\) | −5.37465 | + | 9.69843i | −0.257991 | + | 0.465539i | ||||
\(435\) | 34.7632 | − | 30.5641i | 1.66677 | − | 1.46543i | ||||
\(436\) | −5.88867 | − | 3.39982i | −0.282016 | − | 0.162822i | ||||
\(437\) | 7.76998i | 0.371689i | ||||||||
\(438\) | 16.3500 | − | 14.3750i | 0.781231 | − | 0.686863i | ||||
\(439\) | 29.6011 | − | 17.0902i | 1.41278 | − | 0.815671i | 0.417133 | − | 0.908845i | \(-0.363035\pi\) |
0.995650 | + | 0.0931745i | \(0.0297015\pi\) | |||||||
\(440\) | −48.1040 | + | 27.7729i | −2.29327 | + | 1.32402i | ||||
\(441\) | 1.95590 | − | 20.9087i | 0.0931383 | − | 0.995653i | ||||
\(442\) | 8.18121 | + | 4.04785i | 0.389140 | + | 0.192536i | ||||
\(443\) | 29.5103i | 1.40208i | 0.713123 | + | 0.701039i | \(0.247280\pi\) | ||||
−0.713123 | + | 0.701039i | \(0.752720\pi\) | |||||||
\(444\) | −3.16017 | + | 0.632734i | −0.149975 | + | 0.0300282i | ||||
\(445\) | 11.5641 | + | 20.0296i | 0.548190 | + | 0.949493i | ||||
\(446\) | −5.88166 | + | 10.1873i | −0.278505 | + | 0.482384i | ||||
\(447\) | −14.4074 | − | 4.87043i | −0.681446 | − | 0.230363i | ||||
\(448\) | −11.8161 | − | 19.6608i | −0.558259 | − | 0.928887i | ||||
\(449\) | −1.47702 | + | 2.55828i | −0.0697051 | + | 0.120733i | −0.898771 | − | 0.438417i | \(-0.855539\pi\) |
0.829066 | + | 0.559150i | \(0.188872\pi\) | |||||||
\(450\) | −21.1860 | − | 16.1720i | −0.998720 | − | 0.762357i | ||||
\(451\) | 27.7191 | + | 16.0036i | 1.30524 | + | 0.753580i | ||||
\(452\) | 2.28822 | − | 1.32110i | 0.107629 | − | 0.0621394i | ||||
\(453\) | 25.6788 | − | 5.14146i | 1.20650 | − | 0.241567i | ||||
\(454\) | − | 12.0305i | − | 0.564620i | ||||||
\(455\) | −33.7562 | + | 2.76386i | −1.58251 | + | 0.129572i | ||||
\(456\) | −14.5329 | − | 4.91286i | −0.680565 | − | 0.230066i | ||||
\(457\) | 3.49027 | − | 2.01511i | 0.163268 | − | 0.0942627i | −0.416140 | − | 0.909301i | \(-0.636617\pi\) |
0.579408 | + | 0.815038i | \(0.303284\pi\) | |||||||
\(458\) | −9.05871 | − | 15.6901i | −0.423286 | − | 0.733152i | ||||
\(459\) | 11.2344 | − | 0.778971i | 0.524378 | − | 0.0363592i | ||||
\(460\) | 6.09377 | 0.284123 | ||||||||
\(461\) | 32.8020 | + | 18.9383i | 1.52774 | + | 0.882043i | 0.999456 | + | 0.0329769i | \(0.0104988\pi\) |
0.528287 | + | 0.849066i | \(0.322835\pi\) | |||||||
\(462\) | −5.80795 | − | 26.5755i | −0.270210 | − | 1.23640i | ||||
\(463\) | 27.4672i | 1.27651i | 0.769825 | + | 0.638255i | \(0.220343\pi\) | ||||
−0.769825 | + | 0.638255i | \(0.779657\pi\) | |||||||
\(464\) | 15.1567 | + | 8.75075i | 0.703634 | + | 0.406243i | ||||
\(465\) | 21.6338 | − | 4.33155i | 1.00324 | − | 0.200871i | ||||
\(466\) | −2.32558 | + | 1.34267i | −0.107730 | + | 0.0621981i | ||||
\(467\) | −23.9875 | −1.11001 | −0.555005 | − | 0.831847i | \(-0.687284\pi\) | ||||
−0.555005 | + | 0.831847i | \(0.687284\pi\) | |||||||
\(468\) | 3.81211 | − | 5.72019i | 0.176215 | − | 0.264416i | ||||
\(469\) | −10.1071 | − | 5.60113i | −0.466702 | − | 0.258636i | ||||
\(470\) | −21.3890 | − | 37.0469i | −0.986602 | − | 1.70884i | ||||
\(471\) | 9.58441 | − | 1.91901i | 0.441626 | − | 0.0884231i | ||||
\(472\) | −13.0367 | − | 7.52675i | −0.600063 | − | 0.346447i | ||||
\(473\) | −45.6090 | −2.09710 | ||||||||
\(474\) | 7.12471 | − | 6.26409i | 0.327249 | − | 0.287719i | ||||
\(475\) | 10.9408 | − | 18.9500i | 0.501997 | − | 0.869485i | ||||
\(476\) | −1.76633 | + | 3.18731i | −0.0809597 | + | 0.146090i | ||||
\(477\) | 2.06806 | + | 4.95738i | 0.0946898 | + | 0.226983i | ||||
\(478\) | −14.1978 | − | 24.5913i | −0.649391 | − | 1.12478i | ||||
\(479\) | −10.7451 | + | 6.20368i | −0.490956 | + | 0.283453i | −0.724971 | − | 0.688780i | \(-0.758147\pi\) |
0.234015 | + | 0.972233i | \(0.424813\pi\) | |||||||
\(480\) | −6.77693 | + | 20.0471i | −0.309323 | + | 0.915020i | ||||
\(481\) | −10.5352 | + | 0.676664i | −0.480363 | + | 0.0308532i | ||||
\(482\) | 16.1409 | 0.735197 | ||||||||
\(483\) | −3.75706 | + | 11.7923i | −0.170952 | + | 0.536566i | ||||
\(484\) | 4.71059 | + | 8.15897i | 0.214118 | + | 0.370862i | ||||
\(485\) | 24.7257 | + | 14.2754i | 1.12274 | + | 0.648212i | ||||
\(486\) | −1.07652 | + | 18.1773i | −0.0488320 | + | 0.824537i | ||||
\(487\) | −27.6788 | − | 15.9804i | −1.25425 | − | 0.724140i | −0.282297 | − | 0.959327i | \(-0.591096\pi\) |
−0.971950 | + | 0.235187i | \(0.924430\pi\) | |||||||
\(488\) | 0.449303 | + | 0.259405i | 0.0203390 | + | 0.0117427i | ||||
\(489\) | 3.90035 | − | 11.5378i | 0.176380 | − | 0.521756i | ||||
\(490\) | 1.01903 | + | 29.0135i | 0.0460349 | + | 1.31069i | ||||
\(491\) | 25.3216 | − | 14.6195i | 1.14275 | − | 0.659767i | 0.195640 | − | 0.980676i | \(-0.437322\pi\) |
0.947110 | + | 0.320909i | \(0.103988\pi\) | |||||||
\(492\) | 6.79794 | − | 1.36109i | 0.306475 | − | 0.0613628i | ||||
\(493\) | − | 16.3133i | − | 0.734713i | ||||||
\(494\) | −10.8604 | − | 5.37344i | −0.488633 | − | 0.241763i | ||||
\(495\) | −32.8428 | + | 43.0255i | −1.47617 | + | 1.93385i | ||||
\(496\) | 4.17097 | + | 7.22434i | 0.187282 | + | 0.324382i | ||||
\(497\) | 27.8476 | − | 0.488888i | 1.24913 | − | 0.0219296i | ||||
\(498\) | 0.626357 | + | 0.712412i | 0.0280677 | + | 0.0319239i | ||||
\(499\) | − | 14.0573i | − | 0.629292i | −0.949209 | − | 0.314646i | \(-0.898114\pi\) | ||
0.949209 | − | 0.314646i | \(-0.101886\pi\) | |||||||
\(500\) | −5.09167 | − | 2.93968i | −0.227706 | − | 0.131466i | ||||
\(501\) | 8.93199 | + | 10.1592i | 0.399052 | + | 0.453878i | ||||
\(502\) | 9.99180 | 0.445956 | ||||||||
\(503\) | 9.67979 | − | 16.7659i | 0.431600 | − | 0.747554i | −0.565411 | − | 0.824809i | \(-0.691282\pi\) |
0.997011 | + | 0.0772557i | \(0.0246158\pi\) | |||||||
\(504\) | −19.6806 | − | 14.4833i | −0.876643 | − | 0.645136i | ||||
\(505\) | −6.48204 | + | 3.74241i | −0.288447 | + | 0.166535i | ||||
\(506\) | 16.0319i | 0.712703i | ||||||||
\(507\) | 14.8693 | − | 16.9087i | 0.660367 | − | 0.750943i | ||||
\(508\) | −14.1088 | −0.625976 | ||||||||
\(509\) | 28.3202 | − | 16.3507i | 1.25527 | − | 0.724732i | 0.283121 | − | 0.959084i | \(-0.408630\pi\) |
0.972152 | + | 0.234352i | \(0.0752968\pi\) | |||||||
\(510\) | −15.2653 | + | 3.05644i | −0.675958 | + | 0.135341i | ||||
\(511\) | 14.6651 | + | 24.4013i | 0.648748 | + | 1.07945i | ||||
\(512\) | −22.3171 | −0.986288 | ||||||||
\(513\) | −14.9135 | + | 1.03407i | −0.658446 | + | 0.0456553i | ||||
\(514\) | 1.13820 | − | 1.97141i | 0.0502037 | − | 0.0869554i | ||||
\(515\) | 23.0202 | 1.01439 | ||||||||
\(516\) | −7.41926 | + | 6.52306i | −0.326615 | + | 0.287162i | ||||
\(517\) | −45.3941 | + | 26.2083i | −1.99643 | + | 1.15264i | ||||
\(518\) | 0.158838 | + | 9.04756i | 0.00697893 | + | 0.397527i | ||||
\(519\) | −2.34431 | − | 0.792495i | −0.102904 | − | 0.0347866i | ||||
\(520\) | −17.4768 | + | 35.3228i | −0.766408 | + | 1.54901i | ||||
\(521\) | −13.9767 | −0.612330 | −0.306165 | − | 0.951978i | \(-0.599046\pi\) | ||||
−0.306165 | + | 0.951978i | \(0.599046\pi\) | |||||||
\(522\) | 26.1607 | + | 3.37712i | 1.14502 | + | 0.147813i | ||||
\(523\) | 9.57398 | − | 5.52754i | 0.418641 | − | 0.241702i | −0.275855 | − | 0.961199i | \(-0.588961\pi\) |
0.694496 | + | 0.719497i | \(0.255628\pi\) | |||||||
\(524\) | −1.50791 | + | 2.61178i | −0.0658735 | + | 0.114096i | ||||
\(525\) | 25.7675 | − | 23.4695i | 1.12458 | − | 1.02429i | ||||
\(526\) | 7.83754 | + | 4.52501i | 0.341733 | + | 0.197300i | ||||
\(527\) | 3.88780 | − | 6.73386i | 0.169355 | − | 0.293332i | ||||
\(528\) | −19.3876 | − | 6.55401i | −0.843739 | − | 0.285227i | ||||
\(529\) | −7.85303 | + | 13.6018i | −0.341436 | + | 0.591385i | ||||
\(530\) | −3.71287 | − | 6.43088i | −0.161277 | − | 0.279339i | ||||
\(531\) | −14.5486 | − | 1.87810i | −0.631353 | − | 0.0815024i | ||||
\(532\) | 2.34477 | − | 4.23109i | 0.101659 | − | 0.183441i | ||||
\(533\) | 22.6625 | − | 1.45559i | 0.981623 | − | 0.0630487i | ||||
\(534\) | −4.22074 | + | 12.4855i | −0.182649 | + | 0.540301i | ||||
\(535\) | −2.98095 | − | 5.16315i | −0.128878 | − | 0.223222i | ||||
\(536\) | −11.6443 | + | 6.72286i | −0.502958 | + | 0.290383i | ||||
\(537\) | −10.6032 | − | 12.0600i | −0.457564 | − | 0.520428i | ||||
\(538\) | −33.1173 | −1.42779 | ||||||||
\(539\) | 35.5506 | − | 1.24863i | 1.53127 | − | 0.0537822i | ||||
\(540\) | 0.810990 | + | 11.6962i | 0.0348995 | + | 0.503324i | ||||
\(541\) | − | 20.4903i | − | 0.880947i | −0.897766 | − | 0.440473i | \(-0.854811\pi\) | ||
0.897766 | − | 0.440473i | \(-0.145189\pi\) | |||||||
\(542\) | −15.6907 | + | 27.1772i | −0.673975 | + | 1.16736i | ||||
\(543\) | 32.0271 | − | 6.41252i | 1.37441 | − | 0.275187i | ||||
\(544\) | 3.72893 | + | 6.45869i | 0.159877 | + | 0.276914i | ||||
\(545\) | 37.9882 | 1.62724 | ||||||||
\(546\) | −13.8842 | − | 13.4065i | −0.594191 | − | 0.573745i | ||||
\(547\) | 26.2483 | 1.12230 | 0.561148 | − | 0.827715i | \(-0.310360\pi\) | ||||
0.561148 | + | 0.827715i | \(0.310360\pi\) | |||||||
\(548\) | 2.52497 | + | 4.37337i | 0.107861 | + | 0.186821i | ||||
\(549\) | 0.501408 | + | 0.0647276i | 0.0213996 | + | 0.00276251i | ||||
\(550\) | 22.5742 | − | 39.0996i | 0.962566 | − | 1.66721i | ||||
\(551\) | 21.6556i | 0.922558i | ||||||||
\(552\) | 9.50884 | + | 10.8153i | 0.404723 | + | 0.460328i | ||||
\(553\) | 6.39053 | + | 10.6332i | 0.271753 | + | 0.452170i | ||||
\(554\) | 15.8683 | 0.674179 | ||||||||
\(555\) | 13.5224 | − | 11.8890i | 0.573993 | − | 0.504659i | ||||
\(556\) | −0.694750 | + | 0.401114i | −0.0294640 | + | 0.0170110i | ||||
\(557\) | 19.9909 | + | 34.6252i | 0.847041 | + | 1.46712i | 0.883837 | + | 0.467795i | \(0.154952\pi\) |
−0.0367957 | + | 0.999323i | \(0.511715\pi\) | |||||||
\(558\) | 9.99387 | + | 7.62866i | 0.423074 | + | 0.322947i | ||||
\(559\) | −26.9297 | + | 17.9429i | −1.13900 | + | 0.758903i | ||||
\(560\) | 19.1038 | + | 10.5869i | 0.807284 | + | 0.447378i | ||||
\(561\) | 3.74510 | + | 18.7048i | 0.158118 | + | 0.789717i | ||||
\(562\) | 7.87713 | + | 13.6436i | 0.332277 | + | 0.575520i | ||||
\(563\) | 21.4554 | − | 37.1618i | 0.904237 | − | 1.56618i | 0.0822995 | − | 0.996608i | \(-0.473774\pi\) |
0.821938 | − | 0.569577i | \(-0.192893\pi\) | |||||||
\(564\) | −3.63595 | + | 10.7556i | −0.153101 | + | 0.452895i | ||||
\(565\) | −7.38072 | + | 12.7838i | −0.310509 | + | 0.537818i | ||||
\(566\) | 10.9519 | + | 6.32309i | 0.460344 | + | 0.265780i | ||||
\(567\) | −23.1337 | − | 5.64182i | −0.971526 | − | 0.236934i | ||||
\(568\) | 16.2041 | − | 28.0663i | 0.679909 | − | 1.17764i | ||||
\(569\) | 23.9412 | − | 13.8224i | 1.00367 | − | 0.579467i | 0.0943349 | − | 0.995541i | \(-0.469928\pi\) |
0.909331 | + | 0.416074i | \(0.136594\pi\) | |||||||
\(570\) | 20.2644 | − | 4.05737i | 0.848781 | − | 0.169944i | ||||
\(571\) | 11.8871 | 0.497458 | 0.248729 | − | 0.968573i | \(-0.419987\pi\) | ||||
0.248729 | + | 0.968573i | \(0.419987\pi\) | |||||||
\(572\) | 10.4366 | + | 5.16376i | 0.436377 | + | 0.215908i | ||||
\(573\) | −8.13018 | + | 24.0502i | −0.339643 | + | 1.00471i | ||||
\(574\) | −0.341680 | − | 19.4625i | −0.0142615 | − | 0.812348i | ||||
\(575\) | −17.7890 | + | 10.2705i | −0.741852 | + | 0.428309i | ||||
\(576\) | −24.0047 | + | 10.0139i | −1.00019 | + | 0.417248i | ||||
\(577\) | −26.4428 | −1.10083 | −0.550414 | − | 0.834892i | \(-0.685530\pi\) | ||||
−0.550414 | + | 0.834892i | \(0.685530\pi\) | |||||||
\(578\) | 7.18566 | − | 12.4459i | 0.298884 | − | 0.517682i | ||||
\(579\) | −23.5224 | − | 26.7542i | −0.977559 | − | 1.11187i | ||||
\(580\) | 16.9838 | 0.705215 | ||||||||
\(581\) | −1.06323 | + | 0.639000i | −0.0441103 | + | 0.0265102i | ||||
\(582\) | 3.19416 | + | 15.9531i | 0.132402 | + | 0.661278i | ||||
\(583\) | −7.87985 | + | 4.54944i | −0.326350 | + | 0.188418i | ||||
\(584\) | 33.1265 | 1.37078 | ||||||||
\(585\) | −2.46540 | + | 38.3248i | −0.101932 | + | 1.58453i | ||||
\(586\) | 31.7519i | 1.31166i | ||||||||
\(587\) | −7.27507 | + | 4.20026i | −0.300274 | + | 0.173363i | −0.642566 | − | 0.766230i | \(-0.722130\pi\) |
0.342292 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(588\) | 5.60447 | − | 5.28761i | 0.231125 | − | 0.218057i | ||||
\(589\) | −5.16098 | + | 8.93908i | −0.212654 | + | 0.368328i | ||||
\(590\) | 20.2795 | 0.834892 | ||||||||
\(591\) | 3.26925 | − | 2.87435i | 0.134479 | − | 0.118235i | ||||
\(592\) | 5.89575 | + | 3.40391i | 0.242314 | + | 0.139900i | ||||
\(593\) | 23.8760i | 0.980468i | 0.871591 | + | 0.490234i | \(0.163089\pi\) | ||||
−0.871591 | + | 0.490234i | \(0.836911\pi\) | |||||||
\(594\) | −30.7711 | + | 2.13360i | −1.26255 | + | 0.0875428i | ||||
\(595\) | −0.357353 | − | 20.3552i | −0.0146501 | − | 0.834483i | ||||
\(596\) | −2.79005 | − | 4.83251i | −0.114285 | − | 0.197947i | ||||
\(597\) | 5.46371 | − | 16.1624i | 0.223615 | − | 0.661483i | ||||
\(598\) | 6.30704 | + | 9.46595i | 0.257914 | + | 0.387091i | ||||
\(599\) | − | 38.5869i | − | 1.57662i | −0.615279 | − | 0.788310i | \(-0.710956\pi\) | ||
0.615279 | − | 0.788310i | \(-0.289044\pi\) | |||||||
\(600\) | −7.96206 | − | 39.7663i | −0.325050 | − | 1.62345i | ||||
\(601\) | 2.90334 | − | 1.67625i | 0.118430 | − | 0.0683755i | −0.439615 | − | 0.898186i | \(-0.644885\pi\) |
0.558045 | + | 0.829811i | \(0.311552\pi\) | |||||||
\(602\) | 14.2883 | + | 23.7743i | 0.582347 | + | 0.968967i | ||||
\(603\) | −7.95011 | + | 10.4150i | −0.323754 | + | 0.424131i | ||||
\(604\) | 8.32150 | + | 4.80442i | 0.338597 | + | 0.195489i | ||||
\(605\) | −45.5825 | − | 26.3171i | −1.85319 | − | 1.06994i | ||||
\(606\) | −4.04061 | − | 1.36593i | −0.164139 | − | 0.0554872i | ||||
\(607\) | 13.3140 | + | 7.68682i | 0.540397 | + | 0.311998i | 0.745240 | − | 0.666797i | \(-0.232335\pi\) |
−0.204843 | + | 0.978795i | \(0.565668\pi\) | |||||||
\(608\) | −4.95008 | − | 8.57380i | −0.200752 | − | 0.347713i | ||||
\(609\) | −10.4712 | + | 32.8660i | −0.424316 | + | 1.33180i | ||||
\(610\) | −0.698921 | −0.0282985 | ||||||||
\(611\) | −16.4923 | + | 33.3329i | −0.667205 | + | 1.34851i | ||||
\(612\) | 3.28440 | + | 2.50709i | 0.132764 | + | 0.101343i | ||||
\(613\) | −22.6306 | + | 13.0658i | −0.914043 | + | 0.527723i | −0.881730 | − | 0.471755i | \(-0.843621\pi\) |
−0.0323129 | + | 0.999478i | \(0.510287\pi\) | |||||||
\(614\) | −20.1467 | − | 34.8951i | −0.813055 | − | 1.40825i | ||||
\(615\) | −29.0884 | + | 25.5747i | −1.17296 | + | 1.03127i | ||||
\(616\) | 20.0636 | − | 36.2042i | 0.808384 | − | 1.45871i | ||||
\(617\) | 4.95040 | − | 8.57435i | 0.199296 | − | 0.345190i | −0.749005 | − | 0.662565i | \(-0.769468\pi\) |
0.948300 | + | 0.317375i | \(0.102801\pi\) | |||||||
\(618\) | 8.66177 | + | 9.85181i | 0.348428 | + | 0.396298i | ||||
\(619\) | −5.81010 | −0.233528 | −0.116764 | − | 0.993160i | \(-0.537252\pi\) | ||||
−0.116764 | + | 0.993160i | \(0.537252\pi\) | |||||||
\(620\) | 7.01065 | + | 4.04760i | 0.281555 | + | 0.162556i | ||||
\(621\) | 12.6095 | + | 6.15923i | 0.506003 | + | 0.247161i | ||||
\(622\) | 9.69462 | + | 16.7916i | 0.388719 | + | 0.673281i | ||||
\(623\) | −15.0747 | − | 8.35408i | −0.603957 | − | 0.334699i | ||||
\(624\) | −14.0258 | + | 3.75744i | −0.561479 | + | 0.150418i | ||||
\(625\) | −5.18178 | −0.207271 | ||||||||
\(626\) | −2.43443 | + | 1.40552i | −0.0972993 | + | 0.0561758i | ||||
\(627\) | −4.97155 | − | 24.8303i | −0.198545 | − | 0.991625i | ||||
\(628\) | 3.10593 | + | 1.79321i | 0.123940 | + | 0.0715568i | ||||
\(629\) | − | 6.34562i | − | 0.253017i | ||||||
\(630\) | 32.7165 | + | 3.64081i | 1.30346 | + | 0.145053i | ||||
\(631\) | 30.6338 | + | 17.6864i | 1.21951 | + | 0.704086i | 0.964814 | − | 0.262934i | \(-0.0846901\pi\) |
0.254700 | + | 0.967020i | \(0.418023\pi\) | |||||||
\(632\) | 14.4353 | 0.574205 | ||||||||
\(633\) | −12.5520 | + | 11.0358i | −0.498898 | + | 0.438635i | ||||
\(634\) | −8.41524 | − | 14.5756i | −0.334212 | − | 0.578872i | ||||
\(635\) | 68.2626 | − | 39.4114i | 2.70892 | − | 1.56400i | ||||
\(636\) | −0.631157 | + | 1.86705i | −0.0250270 | + | 0.0740332i | ||||
\(637\) | 20.4995 | − | 14.7231i | 0.812220 | − | 0.583351i | ||||
\(638\) | 44.6821i | 1.76898i | ||||||||
\(639\) | 4.04330 | − | 31.3212i | 0.159950 | − | 1.23905i | ||||
\(640\) | 9.97803 | − | 5.76082i | 0.394416 | − | 0.227716i | ||||
\(641\) | −1.24524 | − | 0.718939i | −0.0491840 | − | 0.0283964i | 0.475206 | − | 0.879874i | \(-0.342373\pi\) |
−0.524390 | + | 0.851478i | \(0.675707\pi\) | |||||||
\(642\) | 1.08801 | − | 3.21847i | 0.0429402 | − | 0.127023i | ||||
\(643\) | 15.9331 | − | 27.5969i | 0.628339 | − | 1.08831i | −0.359546 | − | 0.933127i | \(-0.617069\pi\) |
0.987885 | − | 0.155187i | \(-0.0495981\pi\) | |||||||
\(644\) | −3.89216 | + | 2.33918i | −0.153373 | + | 0.0921765i | ||||
\(645\) | 17.6751 | − | 52.2855i | 0.695958 | − | 2.05874i | ||||
\(646\) | 3.64170 | − | 6.30761i | 0.143281 | − | 0.248170i | ||||
\(647\) | 4.68755 | + | 8.11907i | 0.184287 | + | 0.319194i | 0.943336 | − | 0.331839i | \(-0.107669\pi\) |
−0.759049 | + | 0.651033i | \(0.774336\pi\) | |||||||
\(648\) | −19.4930 | + | 19.6904i | −0.765758 | + | 0.773510i | ||||
\(649\) | − | 24.8487i | − | 0.975399i | ||||||
\(650\) | −2.05321 | − | 31.9671i | −0.0805337 | − | 1.25385i | ||||
\(651\) | −12.1550 | + | 11.0710i | −0.476393 | + | 0.433908i | ||||
\(652\) | 3.86999 | − | 2.23434i | 0.151560 | − | 0.0875034i | ||||
\(653\) | 0.786151 | − | 0.453885i | 0.0307645 | − | 0.0177619i | −0.484539 | − | 0.874770i | \(-0.661013\pi\) |
0.515303 | + | 0.857008i | \(0.327679\pi\) | |||||||
\(654\) | 14.2938 | + | 16.2576i | 0.558931 | + | 0.635723i | ||||
\(655\) | − | 16.8488i | − | 0.658337i | ||||||
\(656\) | −12.6825 | − | 7.32226i | −0.495169 | − | 0.285886i | ||||
\(657\) | 29.7925 | − | 12.4284i | 1.16232 | − | 0.484880i | ||||
\(658\) | 27.8824 | + | 15.4518i | 1.08697 | + | 0.602373i | ||||
\(659\) | 23.6999 | + | 13.6832i | 0.923218 | + | 0.533020i | 0.884660 | − | 0.466236i | \(-0.154390\pi\) |
0.0385576 | + | 0.999256i | \(0.487724\pi\) | |||||||
\(660\) | −19.4736 | + | 3.89904i | −0.758010 | + | 0.151770i | ||||
\(661\) | −16.8620 | − | 29.2058i | −0.655854 | − | 1.13597i | −0.981679 | − | 0.190543i | \(-0.938975\pi\) |
0.325825 | − | 0.945430i | \(-0.394358\pi\) | |||||||
\(662\) | − | 5.10025i | − | 0.198227i | ||||||
\(663\) | 9.56987 | + | 9.57082i | 0.371663 | + | 0.371700i | ||||
\(664\) | 1.44341i | 0.0560151i | ||||||||
\(665\) | 0.474380 | + | 27.0212i | 0.0183957 | + | 1.04784i | ||||
\(666\) | 10.1761 | + | 1.31365i | 0.394316 | + | 0.0509029i | ||||
\(667\) | 10.1644 | − | 17.6053i | 0.393567 | − | 0.681679i | ||||
\(668\) | 4.96333i | 0.192037i | ||||||||
\(669\) | −13.0994 | + | 11.5170i | −0.506451 | + | 0.445275i | ||||
\(670\) | 9.05676 | − | 15.6868i | 0.349893 | − | 0.606033i | ||||
\(671\) | 0.856399i | 0.0330609i | ||||||||
\(672\) | −3.36685 | − | 15.4057i | −0.129879 | − | 0.594289i | ||||
\(673\) | 6.43713 | + | 11.1494i | 0.248133 | + | 0.429779i | 0.963008 | − | 0.269473i | \(-0.0868496\pi\) |
−0.714875 | + | 0.699253i | \(0.753516\pi\) | |||||||
\(674\) | −5.07268 | − | 8.78613i | −0.195392 | − | 0.338429i | ||||
\(675\) | −22.0803 | − | 32.7768i | −0.849872 | − | 1.26158i | ||||
\(676\) | 8.19372 | − | 1.05691i | 0.315143 | − | 0.0406504i | ||||
\(677\) | 10.4739 | 0.402543 | 0.201271 | − | 0.979536i | \(-0.435493\pi\) | ||||
0.201271 | + | 0.979536i | \(0.435493\pi\) | |||||||
\(678\) | −8.24815 | + | 1.65146i | −0.316768 | + | 0.0634238i | ||||
\(679\) | −21.2724 | + | 0.373455i | −0.816360 | + | 0.0143319i | ||||
\(680\) | −20.5151 | − | 11.8444i | −0.786719 | − | 0.454213i | ||||
\(681\) | 5.71274 | − | 16.8991i | 0.218913 | − | 0.647574i | ||||
\(682\) | −10.6487 | + | 18.4441i | −0.407759 | + | 0.706260i | ||||
\(683\) | 13.4691 | − | 23.3292i | 0.515382 | − | 0.892668i | −0.484458 | − | 0.874814i | \(-0.660983\pi\) |
0.999841 | − | 0.0178539i | \(-0.00568339\pi\) | |||||||
\(684\) | −4.35998 | − | 3.32812i | −0.166708 | − | 0.127254i | ||||
\(685\) | −24.4331 | − | 14.1065i | −0.933541 | − | 0.538980i | ||||
\(686\) | −11.7881 | − | 18.1401i | −0.450071 | − | 0.692591i | ||||
\(687\) | −5.27409 | − | 26.3412i | −0.201219 | − | 1.00498i | ||||
\(688\) | 20.8679 | 0.795579 | ||||||||
\(689\) | −2.86285 | + | 5.78618i | −0.109066 | + | 0.220436i | ||||
\(690\) | −18.3787 | − | 6.21292i | −0.699664 | − | 0.236522i | ||||
\(691\) | −1.32650 | − | 2.29757i | −0.0504625 | − | 0.0874036i | 0.839691 | − | 0.543065i | \(-0.182736\pi\) |
−0.890153 | + | 0.455661i | \(0.849403\pi\) | |||||||
\(692\) | −0.453985 | − | 0.786325i | −0.0172579 | − | 0.0298916i | ||||
\(693\) | 4.46114 | − | 40.0880i | 0.169465 | − | 1.52282i | ||||
\(694\) | − | 19.5187i | − | 0.740918i | ||||||
\(695\) | 2.24094 | − | 3.88142i | 0.0850037 | − | 0.147231i | ||||
\(696\) | 26.5019 | + | 30.1430i | 1.00455 | + | 1.14257i | ||||
\(697\) | 13.6503i | 0.517041i | ||||||||
\(698\) | −19.4678 | + | 33.7192i | −0.736868 | + | 1.27629i | ||||
\(699\) | −3.90427 | + | 0.781719i | −0.147673 | + | 0.0295673i | ||||
\(700\) | 12.7862 | − | 0.224473i | 0.483274 | − | 0.00848429i | ||||
\(701\) | − | 10.5490i | − | 0.398429i | −0.979956 | − | 0.199215i | \(-0.936161\pi\) | ||
0.979956 | − | 0.199215i | \(-0.0638391\pi\) | |||||||
\(702\) | −17.3293 | + | 13.3653i | −0.654052 | + | 0.504442i | ||||
\(703\) | 8.42370i | 0.317706i | ||||||||
\(704\) | −22.0293 | − | 38.1559i | −0.830260 | − | 1.43805i | ||||
\(705\) | −12.4529 | − | 62.1958i | −0.469005 | − | 2.34243i | ||||
\(706\) | 12.1146 | + | 6.99436i | 0.455939 | + | 0.263236i | ||||
\(707\) | 2.70358 | − | 4.87854i | 0.101679 | − | 0.183477i | ||||
\(708\) | −3.55390 | − | 4.04217i | −0.133564 | − | 0.151914i | ||||
\(709\) | 22.0271 | + | 12.7174i | 0.827245 | + | 0.477610i | 0.852909 | − | 0.522060i | \(-0.174836\pi\) |
−0.0256633 | + | 0.999671i | \(0.508170\pi\) | |||||||
\(710\) | 43.6591i | 1.63850i | ||||||||
\(711\) | 12.9825 | − | 5.41586i | 0.486881 | − | 0.203111i | ||||
\(712\) | −17.3675 | + | 10.0271i | −0.650875 | + | 0.375783i | ||||
\(713\) | 8.39141 | − | 4.84478i | 0.314261 | − | 0.181439i | ||||
\(714\) | 8.57685 | − | 7.81198i | 0.320981 | − | 0.292356i | ||||
\(715\) | −64.9200 | + | 4.16975i | −2.42787 | + | 0.155940i | ||||
\(716\) | − | 5.89200i | − | 0.220194i | ||||||
\(717\) | −8.26611 | − | 41.2848i | −0.308704 | − | 1.54181i | ||||
\(718\) | −3.21667 | − | 5.57143i | −0.120045 | − | 0.207924i | ||||
\(719\) | −1.57349 | + | 2.72536i | −0.0586811 | + | 0.101639i | −0.893874 | − | 0.448319i | \(-0.852023\pi\) |
0.835192 | + | 0.549958i | \(0.185356\pi\) | |||||||
\(720\) | 15.0268 | − | 19.6858i | 0.560017 | − | 0.733646i | ||||
\(721\) | −14.7032 | + | 8.83661i | −0.547577 | + | 0.329093i | ||||
\(722\) | 6.26280 | − | 10.8475i | 0.233077 | − | 0.403702i | ||||
\(723\) | 22.6728 | + | 7.66456i | 0.843211 | + | 0.285048i | ||||
\(724\) | 10.3787 | + | 5.99216i | 0.385722 | + | 0.222697i | ||||
\(725\) | −49.5794 | + | 28.6247i | −1.84133 | + | 1.06309i | ||||
\(726\) | −5.88852 | − | 29.4100i | −0.218543 | − | 1.09151i | ||||
\(727\) | 23.8257i | 0.883647i | 0.897102 | + | 0.441824i | \(0.145668\pi\) | ||||
−0.897102 | + | 0.441824i | \(0.854332\pi\) | |||||||
\(728\) | −2.39653 | − | 29.2698i | −0.0888213 | − | 1.08481i | ||||
\(729\) | −10.1437 | + | 25.0221i | −0.375693 | + | 0.926744i | ||||
\(730\) | −38.6478 | + | 22.3133i | −1.43042 | + | 0.825853i | ||||
\(731\) | −9.72554 | − | 16.8451i | −0.359712 | − | 0.623040i | ||||
\(732\) | 0.122483 | + | 0.139311i | 0.00452711 | + | 0.00514909i | ||||
\(733\) | −23.3759 | −0.863407 | −0.431704 | − | 0.902016i | \(-0.642087\pi\) | ||||
−0.431704 | + | 0.902016i | \(0.642087\pi\) | |||||||
\(734\) | 9.63357 | + | 5.56195i | 0.355582 | + | 0.205295i | ||||
\(735\) | −12.3457 | + | 41.2386i | −0.455380 | + | 1.52111i | ||||
\(736\) | 9.29362i | 0.342567i | ||||||||
\(737\) | −19.2213 | − | 11.0974i | −0.708024 | − | 0.408778i | ||||
\(738\) | −21.8901 | − | 2.82583i | −0.805787 | − | 0.104020i | ||||
\(739\) | −8.74351 | + | 5.04807i | −0.321635 | + | 0.185696i | −0.652121 | − | 0.758115i | \(-0.726121\pi\) |
0.330486 | + | 0.943811i | \(0.392787\pi\) | |||||||
\(740\) | 6.60646 | 0.242858 | ||||||||
\(741\) | −12.7038 | − | 12.7051i | −0.466686 | − | 0.466733i | ||||
\(742\) | 4.84004 | + | 2.68224i | 0.177683 | + | 0.0984680i | ||||
\(743\) | 5.58427 | + | 9.67223i | 0.204867 | + | 0.354840i | 0.950090 | − | 0.311975i | \(-0.100991\pi\) |
−0.745223 | + | 0.666815i | \(0.767657\pi\) | |||||||
\(744\) | 3.75586 | + | 18.7585i | 0.137697 | + | 0.687721i | ||||
\(745\) | 26.9982 | + | 15.5874i | 0.989139 | + | 0.571080i | ||||
\(746\) | 17.2907 | 0.633058 | ||||||||
\(747\) | 0.541541 | + | 1.29814i | 0.0198140 | + | 0.0474965i | ||||
\(748\) | −3.49960 | + | 6.06148i | −0.127958 | + | 0.221630i | ||||
\(749\) | 3.88591 | + | 2.15348i | 0.141988 | + | 0.0786866i | ||||
\(750\) | 12.3592 | + | 14.0572i | 0.451295 | + | 0.513298i | ||||
\(751\) | 19.1851 | + | 33.2296i | 0.700074 | + | 1.21256i | 0.968440 | + | 0.249247i | \(0.0801832\pi\) |
−0.268366 | + | 0.963317i | \(0.586483\pi\) | |||||||
\(752\) | 20.7695 | − | 11.9913i | 0.757387 | − | 0.437278i | ||||
\(753\) | 14.0353 | + | 4.74465i | 0.511475 | + | 0.172905i | ||||
\(754\) | 17.5782 | + | 26.3824i | 0.640161 | + | 0.960789i | ||||
\(755\) | −53.6826 | −1.95371 | ||||||||
\(756\) | −5.00774 | − | 7.15919i | −0.182130 | − | 0.260377i | ||||
\(757\) | −0.537117 | − | 0.930315i | −0.0195219 | − | 0.0338129i | 0.856099 | − | 0.516811i | \(-0.172881\pi\) |
−0.875621 | + | 0.482998i | \(0.839548\pi\) | |||||||
\(758\) | −11.3796 | − | 6.57001i | −0.413326 | − | 0.238634i | ||||
\(759\) | −7.61279 | + | 22.5197i | −0.276327 | + | 0.817412i | ||||
\(760\) | 27.2335 | + | 15.7232i | 0.987861 | + | 0.570342i | ||||
\(761\) | 19.3646 | + | 11.1801i | 0.701965 | + | 0.405280i | 0.808079 | − | 0.589074i | \(-0.200508\pi\) |
−0.106114 | + | 0.994354i | \(0.533841\pi\) | |||||||
\(762\) | 42.5518 | + | 14.3847i | 1.54149 | + | 0.521101i | ||||
\(763\) | −24.2635 | + | 14.5823i | −0.878398 | + | 0.527915i | ||||
\(764\) | −8.06689 | + | 4.65742i | −0.291850 | + | 0.168500i | ||||
\(765\) | −22.8942 | − | 2.95545i | −0.827743 | − | 0.106855i | ||||
\(766\) | 13.7805i | 0.497908i | ||||||||
\(767\) | −9.77566 | − | 14.6718i | −0.352979 | − | 0.529770i | ||||
\(768\) | −22.2318 | − | 7.51547i | −0.802220 | − | 0.271191i | ||||
\(769\) | 27.4733 | + | 47.5851i | 0.990711 | + | 1.71596i | 0.613121 | + | 0.789989i | \(0.289914\pi\) |
0.377590 | + | 0.925973i | \(0.376753\pi\) | |||||||
\(770\) | 0.978791 | + | 55.7530i | 0.0352732 | + | 2.00920i | ||||
\(771\) | 2.53494 | − | 2.22873i | 0.0912936 | − | 0.0802659i | ||||
\(772\) | − | 13.0709i | − | 0.470433i | ||||||
\(773\) | 32.8675 | + | 18.9761i | 1.18216 | + | 0.682521i | 0.956514 | − | 0.291687i | \(-0.0942167\pi\) |
0.225648 | + | 0.974209i | \(0.427550\pi\) | |||||||
\(774\) | 29.0269 | − | 12.1091i | 1.04335 | − | 0.435252i | ||||
\(775\) | −27.2874 | −0.980194 | ||||||||
\(776\) | −12.3781 | + | 21.4395i | −0.444348 | + | 0.769634i | ||||
\(777\) | −4.07315 | + | 12.7844i | −0.146124 | + | 0.458637i | ||||
\(778\) | 15.4779 | − | 8.93617i | 0.554910 | − | 0.320377i | ||||
\(779\) | − | 18.1205i | − | 0.649233i | ||||||
\(780\) | −9.96422 | + | 9.96323i | −0.356776 | + | 0.356741i | ||||
\(781\) | 53.4961 | 1.91424 | ||||||||
\(782\) | −5.92117 | + | 3.41859i | −0.211741 | + | 0.122249i | ||||
\(783\) | 35.1438 | + | 17.1663i | 1.25594 | + | 0.613473i | ||||
\(784\) | −16.2658 | + | 0.571295i | −0.580920 | + | 0.0204034i | ||||
\(785\) | −20.0366 | −0.715136 | ||||||||
\(786\) | 7.21068 | − | 6.33968i | 0.257197 | − | 0.226129i | ||||
\(787\) | −11.9389 | + | 20.6788i | −0.425576 | + | 0.737120i | −0.996474 | − | 0.0839014i | \(-0.973262\pi\) |
0.570898 | + | 0.821021i | \(0.306595\pi\) | |||||||
\(788\) | 1.59722 | 0.0568985 | ||||||||
\(789\) | 8.86055 | + | 10.0779i | 0.315444 | + | 0.358782i | ||||
\(790\) | −16.8413 | + | 9.72333i | −0.599186 | + | 0.345940i | ||||
\(791\) | −0.193085 | − | 10.9984i | −0.00686533 | − | 0.391056i | ||||
\(792\) | −37.3071 | − | 28.4778i | −1.32565 | − | 1.01191i | ||||
\(793\) | 0.336913 | + | 0.505658i | 0.0119641 | + | 0.0179564i | ||||
\(794\) | −25.1403 | −0.892195 | ||||||||
\(795\) | −2.16167 | − | 10.7964i | −0.0766667 | − | 0.382909i | ||||
\(796\) | 5.42118 | − | 3.12992i | 0.192149 | − | 0.110937i | ||||
\(797\) | −6.27271 | + | 10.8646i | −0.222191 | + | 0.384845i | −0.955473 | − | 0.295079i | \(-0.904654\pi\) |
0.733282 | + | 0.679924i | \(0.237987\pi\) | |||||||
\(798\) | −11.3856 | + | 10.3703i | −0.403046 | + | 0.367103i | ||||
\(799\) | −19.3594 | − | 11.1772i | −0.684888 | − | 0.395420i | ||||
\(800\) | 13.0862 | − | 22.6659i | 0.462667 | − | 0.801362i | ||||
\(801\) | −11.8576 | + | 15.5340i | −0.418968 | + | 0.548866i | ||||
\(802\) | −7.95907 | + | 13.7855i | −0.281045 | + | 0.486783i | ||||
\(803\) | 27.3409 | + | 47.3558i | 0.964838 | + | 1.67115i | ||||
\(804\) | −4.71390 | + | 0.943825i | −0.166246 | + | 0.0332861i | ||||
\(805\) | 12.2972 | − | 22.1900i | 0.433419 | − | 0.782095i | ||||
\(806\) | 0.968541 | + | 15.0795i | 0.0341154 | + | 0.531152i | ||||
\(807\) | −46.5194 | − | 15.7259i | −1.63756 | − | 0.553578i | ||||
\(808\) | −3.24502 | − | 5.62054i | −0.114159 | − | 0.197730i | ||||
\(809\) | −16.5215 | + | 9.53870i | −0.580866 | + | 0.335363i | −0.761477 | − | 0.648192i | \(-0.775526\pi\) |
0.180612 | + | 0.983554i | \(0.442192\pi\) | |||||||
\(810\) | 9.47898 | − | 36.1024i | 0.333057 | − | 1.26851i | ||||
\(811\) | −10.1759 | −0.357324 | −0.178662 | − | 0.983910i | \(-0.557177\pi\) | ||||
−0.178662 | + | 0.983910i | \(0.557177\pi\) | |||||||
\(812\) | −10.8478 | + | 6.51948i | −0.380682 | + | 0.228789i | ||||
\(813\) | −34.9457 | + | 30.7245i | −1.22560 | + | 1.07755i | ||||
\(814\) | 17.3807i | 0.609192i | ||||||||
\(815\) | −12.4828 | + | 21.6208i | −0.437253 | + | 0.757344i | ||||
\(816\) | −1.71353 | − | 8.55815i | −0.0599854 | − | 0.299595i | ||||
\(817\) | 12.9105 | + | 22.3616i | 0.451680 | + | 0.782333i | ||||
\(818\) | 29.3461 | 1.02606 | ||||||||
\(819\) | −13.1368 | − | 25.4249i | −0.459038 | − | 0.888417i | ||||
\(820\) | −14.2113 | −0.496282 | ||||||||
\(821\) | −6.84141 | − | 11.8497i | −0.238767 | − | 0.413556i | 0.721594 | − | 0.692317i | \(-0.243410\pi\) |
−0.960361 | + | 0.278760i | \(0.910077\pi\) | |||||||
\(822\) | −3.15636 | − | 15.7643i | −0.110091 | − | 0.549844i | ||||
\(823\) | −6.07866 | + | 10.5285i | −0.211889 | + | 0.367002i | −0.952306 | − | 0.305146i | \(-0.901295\pi\) |
0.740417 | + | 0.672148i | \(0.234628\pi\) | |||||||
\(824\) | 19.9606i | 0.695362i | ||||||||
\(825\) | 50.2762 | − | 44.2031i | 1.75039 | − | 1.53896i | ||||
\(826\) | −12.9527 | + | 7.78456i | −0.450683 | + | 0.270859i | ||||
\(827\) | −1.41387 | −0.0491652 | −0.0245826 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245826 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(828\) | 1.98241 | + | 4.75208i | 0.0688936 | + | 0.165146i | ||||
\(829\) | 29.3186 | − | 16.9271i | 1.01828 | − | 0.587903i | 0.104673 | − | 0.994507i | \(-0.466620\pi\) |
0.913605 | + | 0.406604i | \(0.133287\pi\) | |||||||
\(830\) | −0.972252 | − | 1.68399i | −0.0337474 | − | 0.0584521i | ||||
\(831\) | 22.2899 | + | 7.53512i | 0.773228 | + | 0.261390i | ||||
\(832\) | −28.0179 | − | 13.8625i | −0.971345 | − | 0.480596i | ||||
\(833\) | 8.04189 | + | 12.8639i | 0.278635 | + | 0.445709i | ||||
\(834\) | 2.50431 | − | 0.501417i | 0.0867171 | − | 0.0173626i | ||||
\(835\) | −13.8645 | − | 24.0141i | −0.479802 | − | 0.831042i | ||||
\(836\) | 4.64565 | − | 8.04651i | 0.160673 | − | 0.278294i | ||||
\(837\) | 10.4157 | + | 15.4615i | 0.360020 | + | 0.534427i | ||||
\(838\) | −3.79000 | + | 6.56447i | −0.130923 | + | 0.226766i | ||||
\(839\) | −41.7382 | − | 24.0976i | −1.44096 | − | 0.831940i | −0.443048 | − | 0.896498i | \(-0.646103\pi\) |
−0.997914 | + | 0.0645579i | \(0.979436\pi\) | |||||||
\(840\) | 33.7286 | + | 37.0310i | 1.16375 | + | 1.27769i | ||||
\(841\) | 13.8290 | − | 23.9526i | 0.476863 | − | 0.825951i | ||||
\(842\) | −22.0897 | + | 12.7535i | −0.761261 | + | 0.439514i | ||||
\(843\) | 4.58615 | + | 22.9054i | 0.157956 | + | 0.788904i | ||||
\(844\) | −6.13238 | −0.211085 | ||||||||
\(845\) | −36.6913 | + | 28.0020i | −1.26222 | + | 0.963297i | ||||
\(846\) | 21.9319 | − | 28.7318i | 0.754035 | − | 0.987818i | ||||
\(847\) | 39.2163 | − | 0.688475i | 1.34749 | − | 0.0236563i | ||||
\(848\) | 3.60533 | − | 2.08154i | 0.123808 | − | 0.0714804i | ||||
\(849\) | 12.3814 | + | 14.0825i | 0.424930 | + | 0.483310i | ||||
\(850\) | 19.2546 | 0.660429 | ||||||||
\(851\) | 3.95380 | − | 6.84819i | 0.135535 | − | 0.234753i | ||||
\(852\) | 8.70226 | − | 7.65108i | 0.298135 | − | 0.262122i | ||||
\(853\) | 20.7351 | 0.709956 | 0.354978 | − | 0.934875i | \(-0.384488\pi\) | ||||
0.354978 | + | 0.934875i | \(0.384488\pi\) | |||||||
\(854\) | 0.446409 | − | 0.268291i | 0.0152758 | − | 0.00918072i | ||||
\(855\) | 30.3917 | + | 3.92331i | 1.03937 | + | 0.134174i | ||||
\(856\) | 4.47694 | − | 2.58476i | 0.153019 | − | 0.0883453i | ||||
\(857\) | −10.5052 | −0.358851 | −0.179426 | − | 0.983772i | \(-0.557424\pi\) | ||||
−0.179426 | + | 0.983772i | \(0.557424\pi\) | |||||||
\(858\) | −26.2119 | − | 26.2145i | −0.894859 | − | 0.894948i | ||||
\(859\) | − | 12.9974i | − | 0.443464i | −0.975108 | − | 0.221732i | \(-0.928829\pi\) | ||
0.975108 | − | 0.221732i | \(-0.0711711\pi\) | |||||||
\(860\) | 17.5375 | − | 10.1253i | 0.598025 | − | 0.345270i | ||||
\(861\) | 8.76189 | − | 27.5009i | 0.298604 | − | 0.937227i | ||||
\(862\) | −15.9879 | + | 27.6918i | −0.544549 | + | 0.943187i | ||||
\(863\) | −54.6116 | −1.85900 | −0.929500 | − | 0.368822i | \(-0.879761\pi\) | ||||
−0.929500 | + | 0.368822i | \(0.879761\pi\) | |||||||
\(864\) | −17.8379 | + | 1.23684i | −0.606858 | + | 0.0420783i | ||||
\(865\) | 4.39304 | + | 2.53632i | 0.149368 | + | 0.0862375i | ||||
\(866\) | − | 20.8315i | − | 0.707884i | ||||||
\(867\) | 16.0036 | − | 14.0704i | 0.543510 | − | 0.477857i | ||||
\(868\) | −6.03151 | + | 0.105888i | −0.204723 | + | 0.00359409i | ||||
\(869\) | 11.9141 | + | 20.6359i | 0.404160 | + | 0.700025i | ||||
\(870\) | −51.2228 | − | 17.3159i | −1.73662 | − | 0.587065i | ||||
\(871\) | −15.7149 | + | 1.00935i | −0.532479 | + | 0.0342006i | ||||
\(872\) | 32.9394i | 1.11547i | ||||||||
\(873\) | −3.08862 | + | 23.9258i | −0.104534 | + | 0.809767i | ||||
\(874\) | 7.86024 | − | 4.53811i | 0.265877 | − | 0.153504i | ||||
\(875\) | −20.9796 | + | 12.6087i | −0.709240 | + | 0.426251i | ||||
\(876\) | 11.2204 | + | 3.79308i | 0.379104 | + | 0.128156i | ||||
\(877\) | −25.9547 | − | 14.9849i | −0.876427 | − | 0.506005i | −0.00694821 | − | 0.999976i | \(-0.502212\pi\) |
−0.869479 | + | 0.493971i | \(0.835545\pi\) | |||||||
\(878\) | −34.5775 | − | 19.9633i | −1.16693 | − | 0.673729i | ||||
\(879\) | −15.0775 | + | 44.6014i | −0.508552 | + | 1.50437i | ||||
\(880\) | 36.3308 | + | 20.9756i | 1.22471 | + | 0.707088i | ||||
\(881\) | −24.5095 | − | 42.4518i | −0.825747 | − | 1.43024i | −0.901347 | − | 0.433098i | \(-0.857420\pi\) |
0.0755992 | − | 0.997138i | \(-0.475913\pi\) | |||||||
\(882\) | −22.2940 | + | 10.2333i | −0.750677 | + | 0.344572i | ||||
\(883\) | −23.5583 | −0.792800 | −0.396400 | − | 0.918078i | \(-0.629741\pi\) | ||||
−0.396400 | + | 0.918078i | \(0.629741\pi\) | |||||||
\(884\) | 0.318303 | + | 4.95575i | 0.0107057 | + | 0.166680i | ||||
\(885\) | 28.4862 | + | 9.62979i | 0.957554 | + | 0.323702i | ||||
\(886\) | 29.8531 | − | 17.2357i | 1.00294 | − | 0.579045i | ||||
\(887\) | −23.4791 | − | 40.6669i | −0.788350 | − | 1.36546i | −0.926977 | − | 0.375117i | \(-0.877602\pi\) |
0.138627 | − | 0.990345i | \(-0.455731\pi\) | |||||||
\(888\) | 10.3089 | + | 11.7252i | 0.345943 | + | 0.393471i | ||||
\(889\) | −28.4715 | + | 51.3761i | −0.954903 | + | 1.72310i | ||||
\(890\) | 13.5082 | − | 23.3968i | 0.452795 | − | 0.784264i | ||||
\(891\) | −44.2368 | − | 11.6147i | −1.48199 | − | 0.389109i | ||||
\(892\) | −6.39978 | −0.214281 | ||||||||
\(893\) | 25.6993 | + | 14.8375i | 0.859994 | + | 0.496518i | ||||
\(894\) | 3.48773 | + | 17.4194i | 0.116647 | + | 0.582591i | ||||
\(895\) | 16.4587 | + | 28.5073i | 0.550154 | + | 0.952894i | ||||
\(896\) | −4.16171 | + | 7.50971i | −0.139033 | + | 0.250882i | ||||
\(897\) | 4.36444 | + | 16.2916i | 0.145725 | + | 0.543960i | ||||
\(898\) | 3.45067 | 0.115150 | ||||||||
\(899\) | 23.3876 | − | 13.5028i | 0.780018 | − | 0.450344i | ||||
\(900\) | 1.85648 | − | 14.3811i | 0.0618827 | − | 0.479371i | ||||
\(901\) | −3.36056 | − | 1.94022i | −0.111956 | − | 0.0646381i | ||||
\(902\) | − | 37.3881i | − | 1.24489i | ||||||
\(903\) | 8.78120 | + | 40.1802i | 0.292220 | + | 1.33711i | ||||
\(904\) | −11.0848 | − | 6.39978i | −0.368673 | − | 0.212854i | ||||
\(905\) | −66.9539 | −2.22562 | ||||||||
\(906\) | −20.1991 | − | 22.9742i | −0.671070 | − | 0.763268i | ||||
\(907\) | −20.1500 | − | 34.9009i | −0.669071 | − | 1.15887i | −0.978164 | − | 0.207834i | \(-0.933359\pi\) |
0.309093 | − | 0.951032i | \(-0.399975\pi\) | |||||||
\(908\) | 5.66827 | − | 3.27258i | 0.188108 | − | 0.108604i | ||||
\(909\) | −5.02716 | − | 3.83740i | −0.166740 | − | 0.127279i | ||||
\(910\) | 22.5115 | + | 32.5341i | 0.746250 | + | 1.07849i | ||||
\(911\) | 11.3974i | 0.377612i | 0.982014 | + | 0.188806i | \(0.0604617\pi\) | ||||
−0.982014 | + | 0.188806i | \(0.939538\pi\) | |||||||
\(912\) | 2.27467 | + | 11.3608i | 0.0753220 | + | 0.376193i | ||||
\(913\) | −2.06342 | + | 1.19132i | −0.0682892 | + | 0.0394268i | ||||
\(914\) | −4.07703 | − | 2.35387i | −0.134856 | − | 0.0778593i | ||||
\(915\) | −0.981763 | − | 0.331886i | −0.0324561 | − | 0.0109718i | ||||
\(916\) | 4.92835 | − | 8.53616i | 0.162837 | − | 0.282043i | ||||
\(917\) | 6.46765 | + | 10.7615i | 0.213581 | + | 0.355377i | ||||
\(918\) | −7.34957 | − | 10.9100i | −0.242572 | − | 0.360083i | ||||
\(919\) | 10.8590 | − | 18.8083i | 0.358205 | − | 0.620430i | −0.629456 | − | 0.777036i | \(-0.716722\pi\) |
0.987661 | + | 0.156606i | \(0.0500554\pi\) | |||||||
\(920\) | −14.7599 | − | 25.5650i | −0.486621 | − | 0.842852i | ||||
\(921\) | −11.7296 | − | 58.5833i | −0.386505 | − | 1.93039i | ||||
\(922\) | − | 44.2441i | − | 1.45710i | ||||||
\(923\) | 31.5866 | − | 21.0457i | 1.03969 | − | 0.692729i | ||||
\(924\) | 10.9413 | − | 9.96560i | 0.359943 | − | 0.327844i | ||||
\(925\) | −19.2856 | + | 11.1346i | −0.634108 | + | 0.366102i | ||||
\(926\) | 27.7863 | − | 16.0424i | 0.913115 | − | 0.527187i | ||||
\(927\) | 7.48887 | + | 17.9517i | 0.245967 | + | 0.589613i | ||||
\(928\) | 25.9021i | 0.850277i | ||||||||
\(929\) | −13.4799 | − | 7.78265i | −0.442263 | − | 0.255340i | 0.262294 | − | 0.964988i | \(-0.415521\pi\) |
−0.704557 | + | 0.709647i | \(0.748854\pi\) | |||||||
\(930\) | −17.0172 | − | 19.3552i | −0.558017 | − | 0.634683i | ||||
\(931\) | −10.6755 | − | 17.0766i | −0.349874 | − | 0.559664i | ||||
\(932\) | −1.26522 | − | 0.730475i | −0.0414437 | − | 0.0239275i | ||||
\(933\) | 5.64432 | + | 28.1904i | 0.184787 | + | 0.922911i | ||||
\(934\) | 14.0101 | + | 24.2662i | 0.458424 | + | 0.794014i | ||||
\(935\) | − | 39.1031i | − | 1.27881i | ||||||
\(936\) | −33.2312 | − | 2.13773i | −1.08620 | − | 0.0698740i | ||||
\(937\) | − | 25.7421i | − | 0.840957i | −0.907302 | − | 0.420479i | \(-0.861862\pi\) | ||
0.907302 | − | 0.420479i | \(-0.138138\pi\) | |||||||
\(938\) | 0.236932 | + | 13.4959i | 0.00773610 | + | 0.440656i | ||||
\(939\) | −4.08701 | + | 0.818309i | −0.133375 | + | 0.0267045i | ||||
\(940\) | 11.6366 | − | 20.1552i | 0.379544 | − | 0.657390i | ||||
\(941\) | − | 52.3679i | − | 1.70714i | −0.520975 | − | 0.853572i | \(-0.674431\pi\) | ||
0.520975 | − | 0.853572i | \(-0.325569\pi\) | |||||||
\(942\) | −7.53914 | − | 8.57494i | −0.245639 | − | 0.279387i | ||||
\(943\) | −8.50515 | + | 14.7313i | −0.276966 | + | 0.479719i | ||||
\(944\) | 11.3692i | 0.370037i | ||||||||
\(945\) | 44.2274 | + | 20.6497i | 1.43872 | + | 0.671736i | ||||
\(946\) | 26.6383 | + | 46.1389i | 0.866085 | + | 1.50010i | ||||
\(947\) | −22.3864 | − | 38.7745i | −0.727462 | − | 1.26000i | −0.957953 | − | 0.286926i | \(-0.907367\pi\) |
0.230491 | − | 0.973074i | \(-0.425967\pi\) | |||||||
\(948\) | 4.88946 | + | 1.65288i | 0.158802 | + | 0.0536832i | ||||
\(949\) | 34.7734 | + | 17.2050i | 1.12879 | + | 0.558496i | ||||
\(950\) | −25.5602 | −0.829281 | ||||||||
\(951\) | −4.89945 | − | 24.4701i | −0.158876 | − | 0.793498i | ||||
\(952\) | 17.6499 | − | 0.309859i | 0.572037 | − | 0.0100426i | ||||
\(953\) | 27.2295 | + | 15.7209i | 0.882048 | + | 0.509251i | 0.871333 | − | 0.490692i | \(-0.163256\pi\) |
0.0107152 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(954\) | 3.80711 | − | 4.98748i | 0.123260 | − | 0.161476i | ||||
\(955\) | 26.0200 | − | 45.0680i | 0.841989 | − | 1.45837i | ||||
\(956\) | 7.72424 | − | 13.3788i | 0.249820 | − | 0.432701i | ||||
\(957\) | −21.2175 | + | 62.7642i | −0.685863 | + | 2.02888i | ||||
\(958\) | 12.5515 | + | 7.24661i | 0.405520 | + | 0.234127i | ||||
\(959\) | 21.0207 | − | 0.369036i | 0.678793 | − | 0.0119168i | ||||
\(960\) | 52.2784 | − | 10.4673i | 1.68728 | − | 0.337830i | ||||
\(961\) | −18.1280 | −0.584774 | ||||||||
\(962\) | 6.83767 | + | 10.2623i | 0.220455 | + | 0.330871i | ||||
\(963\) | 3.05661 | − | 4.00429i | 0.0984979 | − | 0.129036i | ||||
\(964\) | 4.39069 | + | 7.60490i | 0.141415 | + | 0.244937i | ||||
\(965\) | 36.5123 | + | 63.2412i | 1.17537 | + | 2.03581i | ||||
\(966\) | 14.1236 | − | 3.08665i | 0.454419 | − | 0.0993113i | ||||
\(967\) | − | 15.6510i | − | 0.503302i | −0.967818 | − | 0.251651i | \(-0.919026\pi\) | ||
0.967818 | − | 0.251651i | \(-0.0809735\pi\) | |||||||
\(968\) | 22.8194 | − | 39.5243i | 0.733443 | − | 1.27036i | ||||
\(969\) | 8.11063 | − | 7.13092i | 0.260551 | − | 0.229078i | ||||
\(970\) | − | 33.3506i | − | 1.07082i | ||||||
\(971\) | −15.8546 | + | 27.4610i | −0.508800 | + | 0.881267i | 0.491148 | + | 0.871076i | \(0.336577\pi\) |
−0.999948 | + | 0.0101910i | \(0.996756\pi\) | |||||||
\(972\) | −8.85719 | + | 4.43742i | −0.284094 | + | 0.142330i | ||||
\(973\) | 0.0586247 | + | 3.33933i | 0.00187942 | + | 0.107054i | ||||
\(974\) | 37.3338i | 1.19625i | ||||||||
\(975\) | 12.2956 | − | 45.8786i | 0.393773 | − | 1.46929i | ||||
\(976\) | − | 0.391835i | − | 0.0125423i | ||||||
\(977\) | 15.0361 | + | 26.0433i | 0.481047 | + | 0.833198i | 0.999763 | − | 0.0217482i | \(-0.00692321\pi\) |
−0.518716 | + | 0.854946i | \(0.673590\pi\) | |||||||
\(978\) | −13.9498 | + | 2.79306i | −0.446066 | + | 0.0893121i | ||||
\(979\) | −28.6685 | − | 16.5518i | −0.916249 | − | 0.528997i | ||||
\(980\) | −13.3927 | + | 8.37245i | −0.427814 | + | 0.267448i | ||||
\(981\) | 12.3583 | + | 29.6242i | 0.394569 | + | 0.945829i | ||||
\(982\) | −29.5786 | − | 17.0772i | −0.943891 | − | 0.544955i | ||||
\(983\) | 2.46092i | 0.0784910i | 0.999230 | + | 0.0392455i | \(0.0124954\pi\) | ||||
−0.999230 | + | 0.0392455i | \(0.987505\pi\) | |||||||
\(984\) | −22.1757 | − | 25.2224i | −0.706935 | − | 0.804061i | ||||
\(985\) | −7.72782 | + | 4.46166i | −0.246229 | + | 0.142160i | ||||
\(986\) | −16.5028 | + | 9.52789i | −0.525556 | + | 0.303430i | ||||
\(987\) | 31.8286 | + | 34.9449i | 1.01311 | + | 1.11231i | ||||
\(988\) | −0.422541 | − | 6.57866i | −0.0134428 | − | 0.209295i | ||||
\(989\) | − | 24.2390i | − | 0.770755i | ||||||
\(990\) | 62.7074 | + | 8.09499i | 1.99297 | + | 0.257276i | ||||
\(991\) | 13.9551 | + | 24.1710i | 0.443299 | + | 0.767817i | 0.997932 | − | 0.0642786i | \(-0.0204746\pi\) |
−0.554633 | + | 0.832095i | \(0.687141\pi\) | |||||||
\(992\) | −6.17301 | + | 10.6920i | −0.195993 | + | 0.339470i | ||||
\(993\) | 2.42187 | − | 7.16423i | 0.0768558 | − | 0.227350i | ||||
\(994\) | −16.7592 | − | 27.8856i | −0.531568 | − | 0.884476i | ||||
\(995\) | −17.4862 | + | 30.2870i | −0.554350 | + | 0.960163i | ||||
\(996\) | −0.165275 | + | 0.488905i | −0.00523693 | + | 0.0154915i | ||||
\(997\) | 21.3078 | + | 12.3020i | 0.674823 | + | 0.389609i | 0.797902 | − | 0.602788i | \(-0.205943\pi\) |
−0.123078 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(998\) | −14.2206 | + | 8.21029i | −0.450146 | + | 0.259892i | ||||
\(999\) | 13.6704 | + | 6.67743i | 0.432513 | + | 0.211265i |
(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 | 273.2.u.c.62.11 | ✓ | 64 | |
3.2 | odd | 2 | inner | 273.2.u.c.62.22 | yes | 64 | |
7.6 | odd | 2 | inner | 273.2.u.c.62.12 | yes | 64 | |
13.4 | even | 6 | inner | 273.2.u.c.251.21 | yes | 64 | |
21.20 | even | 2 | inner | 273.2.u.c.62.21 | yes | 64 | |
39.17 | odd | 6 | inner | 273.2.u.c.251.12 | yes | 64 | |
91.69 | odd | 6 | inner | 273.2.u.c.251.22 | yes | 64 | |
273.251 | even | 6 | inner | 273.2.u.c.251.11 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.u.c.62.11 | ✓ | 64 | 1.1 | even | 1 | trivial | |
273.2.u.c.62.12 | yes | 64 | 7.6 | odd | 2 | inner | |
273.2.u.c.62.21 | yes | 64 | 21.20 | even | 2 | inner | |
273.2.u.c.62.22 | yes | 64 | 3.2 | odd | 2 | inner | |
273.2.u.c.251.11 | yes | 64 | 273.251 | even | 6 | inner | |
273.2.u.c.251.12 | yes | 64 | 39.17 | odd | 6 | inner | |
273.2.u.c.251.21 | yes | 64 | 13.4 | even | 6 | inner | |
273.2.u.c.251.22 | yes | 64 | 91.69 | odd | 6 | inner |