Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.3 | ||
Root | \(2.09292i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.737 |
Dual form | 2070.2.j.i.323.3 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.27669 | − | 1.83577i | 0.570954 | − | 0.820982i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.54563 | − | 1.54563i | −0.584193 | − | 0.584193i | 0.351860 | − | 0.936053i | \(-0.385549\pi\) |
−0.936053 | + | 0.351860i | \(0.885549\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.395329 | + | 2.20084i | 0.125014 | + | 0.695968i | ||||
\(11\) | − | 3.67154i | − | 1.10701i | −0.832845 | − | 0.553506i | \(-0.813290\pi\) | ||
0.832845 | − | 0.553506i | \(-0.186710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 2.00000i | 0.554700 | − | 0.554700i | −0.373094 | − | 0.927794i | \(-0.621703\pi\) |
0.927794 | + | 0.373094i | \(0.121703\pi\) | |||||||
\(14\) | 2.18585 | 0.584193 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.367535 | + | 0.367535i | −0.0891404 | + | 0.0891404i | −0.750271 | − | 0.661131i | \(-0.770077\pi\) |
0.661131 | + | 0.750271i | \(0.270077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.79066i | − | 0.640221i | −0.947380 | − | 0.320110i | \(-0.896280\pi\) | ||
0.947380 | − | 0.320110i | \(-0.103720\pi\) | |||||||
\(20\) | −1.83577 | − | 1.27669i | −0.410491 | − | 0.285477i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.59617 | + | 2.59617i | 0.553506 | + | 0.553506i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.74011 | − | 4.68743i | −0.348023 | − | 0.937486i | ||||
\(26\) | 2.82843i | 0.554700i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.54563 | + | 1.54563i | −0.292096 | + | 0.292096i | ||||
\(29\) | −8.41078 | −1.56184 | −0.780921 | − | 0.624630i | \(-0.785250\pi\) | ||||
−0.780921 | + | 0.624630i | \(0.785250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.519773 | −0.0933541 | −0.0466770 | − | 0.998910i | \(-0.514863\pi\) | ||||
−0.0466770 | + | 0.998910i | \(0.514863\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.519773i | − | 0.0891404i | ||||||
\(35\) | −4.81071 | + | 0.864129i | −0.813159 | + | 0.146064i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.14180 | + | 6.14180i | 1.00971 | + | 1.00971i | 0.999952 | + | 0.00975355i | \(0.00310470\pi\) |
0.00975355 | + | 0.999952i | \(0.496895\pi\) | |||||||
\(38\) | 1.97329 | + | 1.97329i | 0.320110 | + | 0.320110i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.20084 | − | 0.395329i | 0.347984 | − | 0.0625069i | ||||
\(41\) | 12.1033i | 1.89022i | 0.326748 | + | 0.945112i | \(0.394047\pi\) | ||||
−0.326748 | + | 0.945112i | \(0.605953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14180 | − | 4.14180i | 0.631619 | − | 0.631619i | −0.316855 | − | 0.948474i | \(-0.602627\pi\) |
0.948474 | + | 0.316855i | \(0.102627\pi\) | |||||||
\(44\) | −3.67154 | −0.553506 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 1.13917 | − | 1.13917i | 0.166165 | − | 0.166165i | −0.619126 | − | 0.785291i | \(-0.712513\pi\) |
0.785291 | + | 0.619126i | \(0.212513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.22206i | − | 0.317438i | ||||||
\(50\) | 4.54496 | + | 2.08407i | 0.642754 | + | 0.294732i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | − | 2.00000i | −0.277350 | − | 0.277350i | ||||
\(53\) | −6.41647 | − | 6.41647i | −0.881370 | − | 0.881370i | 0.112304 | − | 0.993674i | \(-0.464177\pi\) |
−0.993674 | + | 0.112304i | \(0.964177\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.74011 | − | 4.68743i | −0.908837 | − | 0.632053i | ||||
\(56\) | − | 2.18585i | − | 0.292096i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.94732 | − | 5.94732i | 0.780921 | − | 0.780921i | ||||
\(59\) | −8.96086 | −1.16660 | −0.583302 | − | 0.812255i | \(-0.698240\pi\) | ||||
−0.583302 | + | 0.812255i | \(0.698240\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.88191 | 0.240955 | 0.120477 | − | 0.992716i | \(-0.461558\pi\) | ||||
0.120477 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(62\) | 0.367535 | − | 0.367535i | 0.0466770 | − | 0.0466770i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −1.11816 | − | 6.22493i | −0.138690 | − | 0.772107i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.12908 | + | 2.12908i | 0.260109 | + | 0.260109i | 0.825098 | − | 0.564989i | \(-0.191120\pi\) |
−0.564989 | + | 0.825098i | \(0.691120\pi\) | |||||||
\(68\) | 0.367535 | + | 0.367535i | 0.0445702 | + | 0.0445702i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.79066 | − | 4.01272i | 0.333547 | − | 0.479612i | ||||
\(71\) | 13.7211i | 1.62840i | 0.580587 | + | 0.814198i | \(0.302823\pi\) | ||||
−0.580587 | + | 0.814198i | \(0.697177\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.42754 | + | 4.42754i | −0.518205 | + | 0.518205i | −0.917028 | − | 0.398823i | \(-0.869419\pi\) |
0.398823 | + | 0.917028i | \(0.369419\pi\) | |||||||
\(74\) | −8.68582 | −1.00971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.79066 | −0.320110 | ||||||||
\(77\) | −5.67484 | + | 5.67484i | −0.646708 | + | 0.646708i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.23189i | − | 0.926160i | −0.886316 | − | 0.463080i | \(-0.846744\pi\) | ||
0.886316 | − | 0.463080i | \(-0.153256\pi\) | |||||||
\(80\) | −1.27669 | + | 1.83577i | −0.142739 | + | 0.205245i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.55835 | − | 8.55835i | −0.945112 | − | 0.945112i | ||||
\(83\) | −5.86639 | − | 5.86639i | −0.643920 | − | 0.643920i | 0.307597 | − | 0.951517i | \(-0.400475\pi\) |
−0.951517 | + | 0.307597i | \(0.900475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.205481 | + | 1.14394i | 0.0222876 | + | 0.124078i | ||||
\(86\) | 5.85739i | 0.631619i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.59617 | − | 2.59617i | 0.276753 | − | 0.276753i | ||||
\(89\) | −8.50327 | −0.901345 | −0.450672 | − | 0.892689i | \(-0.648816\pi\) | ||||
−0.450672 | + | 0.892689i | \(0.648816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.18252 | −0.648104 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.61103i | 0.166165i | ||||||||
\(95\) | −5.12301 | − | 3.56281i | −0.525610 | − | 0.365537i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.72525 | − | 4.72525i | −0.479777 | − | 0.479777i | 0.425283 | − | 0.905060i | \(-0.360174\pi\) |
−0.905060 | + | 0.425283i | \(0.860174\pi\) | |||||||
\(98\) | 1.57124 | + | 1.57124i | 0.158719 | + | 0.158719i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.68743 | + | 1.74011i | −0.468743 | + | 0.174011i | ||||
\(101\) | 13.3326i | 1.32664i | 0.748336 | + | 0.663320i | \(0.230853\pi\) | ||||
−0.748336 | + | 0.663320i | \(0.769147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.54563 | − | 1.54563i | 0.152295 | − | 0.152295i | −0.626847 | − | 0.779142i | \(-0.715655\pi\) |
0.779142 | + | 0.626847i | \(0.215655\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.07426 | 0.881370 | ||||||||
\(107\) | 8.40178 | − | 8.40178i | 0.812231 | − | 0.812231i | −0.172737 | − | 0.984968i | \(-0.555261\pi\) |
0.984968 | + | 0.172737i | \(0.0552611\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.14008i | − | 0.588113i | −0.955788 | − | 0.294056i | \(-0.904995\pi\) | ||
0.955788 | − | 0.294056i | \(-0.0950054\pi\) | |||||||
\(110\) | 8.08049 | − | 1.45147i | 0.770445 | − | 0.138392i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.54563 | + | 1.54563i | 0.146048 | + | 0.146048i | ||||
\(113\) | 9.75351 | + | 9.75351i | 0.917533 | + | 0.917533i | 0.996849 | − | 0.0793164i | \(-0.0252737\pi\) |
−0.0793164 | + | 0.996849i | \(0.525274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.20084 | + | 0.395329i | −0.205230 | + | 0.0368646i | ||||
\(116\) | 8.41078i | 0.780921i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.33629 | − | 6.33629i | 0.583302 | − | 0.583302i | ||||
\(119\) | 1.13615 | 0.104150 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.48023 | −0.225475 | ||||||||
\(122\) | −1.33071 | + | 1.33071i | −0.120477 | + | 0.120477i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.519773i | 0.0466770i | ||||||||
\(125\) | −10.8266 | − | 2.78996i | −0.968364 | − | 0.249541i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.18252 | + | 3.18252i | 0.282403 | + | 0.282403i | 0.834067 | − | 0.551664i | \(-0.186007\pi\) |
−0.551664 | + | 0.834067i | \(0.686007\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.19235 | + | 3.61103i | 0.455399 | + | 0.316708i | ||||
\(131\) | − | 20.3105i | − | 1.77454i | −0.461250 | − | 0.887270i | \(-0.652599\pi\) | ||
0.461250 | − | 0.887270i | \(-0.347401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.31332 | + | 4.31332i | −0.374012 | + | 0.374012i | ||||
\(134\) | −3.01098 | −0.260109 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.519773 | −0.0445702 | ||||||||
\(137\) | −5.30731 | + | 5.30731i | −0.453434 | + | 0.453434i | −0.896493 | − | 0.443059i | \(-0.853893\pi\) |
0.443059 | + | 0.896493i | \(0.353893\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.54949i | 0.216245i | 0.994138 | + | 0.108122i | \(0.0344839\pi\) | ||||
−0.994138 | + | 0.108122i | \(0.965516\pi\) | |||||||
\(140\) | 0.864129 | + | 4.81071i | 0.0730322 | + | 0.406580i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.70229 | − | 9.70229i | −0.814198 | − | 0.814198i | ||||
\(143\) | −7.34309 | − | 7.34309i | −0.614060 | − | 0.614060i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7380 | + | 15.4403i | −0.891740 | + | 1.28224i | ||||
\(146\) | − | 6.26149i | − | 0.518205i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.14180 | − | 6.14180i | 0.504853 | − | 0.504853i | ||||
\(149\) | −17.2636 | −1.41429 | −0.707144 | − | 0.707069i | \(-0.750017\pi\) | ||||
−0.707144 | + | 0.707069i | \(0.750017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0297170 | −0.00241833 | −0.00120917 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00120917 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(152\) | 1.97329 | − | 1.97329i | 0.160055 | − | 0.160055i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 8.02544i | − | 0.646708i | ||||||
\(155\) | −0.663591 | + | 0.954185i | −0.0533009 | + | 0.0766420i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9056 | − | 11.9056i | −0.950173 | − | 0.950173i | 0.0486434 | − | 0.998816i | \(-0.484510\pi\) |
−0.998816 | + | 0.0486434i | \(0.984510\pi\) | |||||||
\(158\) | 5.82083 | + | 5.82083i | 0.463080 | + | 0.463080i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.395329 | − | 2.20084i | −0.0312535 | − | 0.173992i | ||||
\(161\) | 2.18585i | 0.172269i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.777937 | − | 0.777937i | 0.0609328 | − | 0.0609328i | −0.675984 | − | 0.736917i | \(-0.736281\pi\) |
0.736917 | + | 0.675984i | \(0.236281\pi\) | |||||||
\(164\) | 12.1033 | 0.945112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.29632 | 0.643920 | ||||||||
\(167\) | 3.10347 | − | 3.10347i | 0.240154 | − | 0.240154i | −0.576760 | − | 0.816914i | \(-0.695683\pi\) |
0.816914 | + | 0.576760i | \(0.195683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | −0.954185 | − | 0.663591i | −0.0731827 | − | 0.0508951i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.14180 | − | 4.14180i | −0.315809 | − | 0.315809i | ||||
\(173\) | 0.771636 | + | 0.771636i | 0.0586664 | + | 0.0586664i | 0.735831 | − | 0.677165i | \(-0.236792\pi\) |
−0.677165 | + | 0.735831i | \(0.736792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.55546 | + | 9.93460i | −0.344360 | + | 0.750985i | ||||
\(176\) | 3.67154i | 0.276753i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.01272 | − | 6.01272i | 0.450672 | − | 0.450672i | ||||
\(179\) | −13.3746 | −0.999664 | −0.499832 | − | 0.866123i | \(-0.666605\pi\) | ||||
−0.499832 | + | 0.866123i | \(0.666605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.01272 | 0.446922 | 0.223461 | − | 0.974713i | \(-0.428264\pi\) | ||||
0.223461 | + | 0.974713i | \(0.428264\pi\) | |||||||
\(182\) | 4.37170 | − | 4.37170i | 0.324052 | − | 0.324052i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 19.1161 | − | 3.43375i | 1.40545 | − | 0.252455i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.34942 | + | 1.34942i | 0.0986795 | + | 0.0986795i | ||||
\(188\) | −1.13917 | − | 1.13917i | −0.0830826 | − | 0.0830826i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.14180 | − | 1.10323i | 0.445573 | − | 0.0800365i | ||||
\(191\) | − | 25.8509i | − | 1.87050i | −0.353983 | − | 0.935252i | \(-0.615173\pi\) | ||
0.353983 | − | 0.935252i | \(-0.384827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.42852 | − | 6.42852i | 0.462735 | − | 0.462735i | −0.436816 | − | 0.899551i | \(-0.643894\pi\) |
0.899551 | + | 0.436816i | \(0.143894\pi\) | |||||||
\(194\) | 6.68252 | 0.479777 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.22206 | −0.158719 | ||||||||
\(197\) | 16.6180 | − | 16.6180i | 1.18398 | − | 1.18398i | 0.205279 | − | 0.978703i | \(-0.434190\pi\) |
0.978703 | − | 0.205279i | \(-0.0658103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.25816i | 0.160077i | 0.996792 | + | 0.0800385i | \(0.0255043\pi\) | ||||
−0.996792 | + | 0.0800385i | \(0.974496\pi\) | |||||||
\(200\) | 2.08407 | − | 4.54496i | 0.147366 | − | 0.321377i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.42754 | − | 9.42754i | −0.663320 | − | 0.663320i | ||||
\(203\) | 12.9999 | + | 12.9999i | 0.912417 | + | 0.912417i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.2190 | + | 15.4522i | 1.55184 | + | 1.07923i | ||||
\(206\) | 2.18585i | 0.152295i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | + | 2.00000i | −0.138675 | + | 0.138675i | ||||
\(209\) | −10.2460 | −0.708732 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4101 | −1.54278 | −0.771389 | − | 0.636364i | \(-0.780437\pi\) | ||||
−0.771389 | + | 0.636364i | \(0.780437\pi\) | |||||||
\(212\) | −6.41647 | + | 6.41647i | −0.440685 | + | 0.440685i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.8819i | 0.812231i | ||||||||
\(215\) | −2.31559 | − | 12.8912i | −0.157922 | − | 0.879173i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.803377 | + | 0.803377i | 0.0545368 | + | 0.0545368i | ||||
\(218\) | 4.34169 | + | 4.34169i | 0.294056 | + | 0.294056i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.68743 | + | 6.74011i | −0.316027 | + | 0.454418i | ||||
\(221\) | 1.47014i | 0.0988924i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9035 | − | 15.9035i | 1.06498 | − | 1.06498i | 0.0672398 | − | 0.997737i | \(-0.478581\pi\) |
0.997737 | − | 0.0672398i | \(-0.0214193\pi\) | |||||||
\(224\) | −2.18585 | −0.146048 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7935 | −0.917533 | ||||||||
\(227\) | 14.9593 | − | 14.9593i | 0.992886 | − | 0.992886i | −0.00708922 | − | 0.999975i | \(-0.502257\pi\) |
0.999975 | + | 0.00708922i | \(0.00225659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.1698i | − | 0.804203i | −0.915595 | − | 0.402101i | \(-0.868280\pi\) | ||
0.915595 | − | 0.402101i | \(-0.131720\pi\) | |||||||
\(230\) | 1.27669 | − | 1.83577i | 0.0841826 | − | 0.121047i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.94732 | − | 5.94732i | −0.390461 | − | 0.390461i | ||||
\(233\) | −12.5213 | − | 12.5213i | −0.820300 | − | 0.820300i | 0.165851 | − | 0.986151i | \(-0.446963\pi\) |
−0.986151 | + | 0.165851i | \(0.946963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.636887 | − | 3.54563i | −0.0415459 | − | 0.231291i | ||||
\(236\) | 8.96086i | 0.583302i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.803377 | + | 0.803377i | −0.0520752 | + | 0.0520752i | ||||
\(239\) | 7.80476 | 0.504848 | 0.252424 | − | 0.967617i | \(-0.418772\pi\) | ||||
0.252424 | + | 0.967617i | \(0.418772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.71212 | 0.496781 | 0.248391 | − | 0.968660i | \(-0.420098\pi\) | ||||
0.248391 | + | 0.968660i | \(0.420098\pi\) | |||||||
\(242\) | 1.75378 | − | 1.75378i | 0.112738 | − | 0.112738i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.88191i | − | 0.120477i | ||||||
\(245\) | −4.07920 | − | 2.83689i | −0.260610 | − | 0.181242i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.58131 | − | 5.58131i | −0.355131 | − | 0.355131i | ||||
\(248\) | −0.367535 | − | 0.367535i | −0.0233385 | − | 0.0233385i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.62839 | − | 5.68279i | 0.608953 | − | 0.359411i | ||||
\(251\) | − | 16.9296i | − | 1.06859i | −0.845299 | − | 0.534293i | \(-0.820578\pi\) | ||
0.845299 | − | 0.534293i | \(-0.179422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.59617 | + | 2.59617i | −0.163220 | + | 0.163220i | ||||
\(254\) | −4.50076 | −0.282403 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.290594 | + | 0.290594i | −0.0181268 | + | 0.0181268i | −0.716112 | − | 0.697985i | \(-0.754080\pi\) |
0.697985 | + | 0.716112i | \(0.254080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 18.9859i | − | 1.17973i | ||||||
\(260\) | −6.22493 | + | 1.11816i | −0.386054 | + | 0.0693452i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.3617 | + | 14.3617i | 0.887270 | + | 0.887270i | ||||
\(263\) | 12.7404 | + | 12.7404i | 0.785610 | + | 0.785610i | 0.980771 | − | 0.195161i | \(-0.0625231\pi\) |
−0.195161 | + | 0.980771i | \(0.562523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.9710 | + | 3.58731i | −1.22681 | + | 0.220367i | ||||
\(266\) | − | 6.09996i | − | 0.374012i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.12908 | − | 2.12908i | 0.130054 | − | 0.130054i | ||||
\(269\) | 17.2551 | 1.05206 | 0.526031 | − | 0.850465i | \(-0.323679\pi\) | ||||
0.526031 | + | 0.850465i | \(0.323679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1231 | −0.614933 | −0.307467 | − | 0.951559i | \(-0.599481\pi\) | ||||
−0.307467 | + | 0.951559i | \(0.599481\pi\) | |||||||
\(272\) | 0.367535 | − | 0.367535i | 0.0222851 | − | 0.0222851i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 7.50567i | − | 0.453434i | ||||||
\(275\) | −17.2101 | + | 6.38890i | −1.03781 | + | 0.385265i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.5057 | − | 17.5057i | −1.05181 | − | 1.05181i | −0.998582 | − | 0.0532313i | \(-0.983048\pi\) |
−0.0532313 | − | 0.998582i | \(-0.516952\pi\) | |||||||
\(278\) | −1.80276 | − | 1.80276i | −0.108122 | − | 0.108122i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.01272 | − | 2.79066i | −0.239806 | − | 0.166774i | ||||
\(281\) | 18.8238i | 1.12293i | 0.827499 | + | 0.561467i | \(0.189763\pi\) | ||||
−0.827499 | + | 0.561467i | \(0.810237\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.35114 | − | 7.35114i | 0.436980 | − | 0.436980i | −0.454014 | − | 0.890994i | \(-0.650008\pi\) |
0.890994 | + | 0.454014i | \(0.150008\pi\) | |||||||
\(284\) | 13.7211 | 0.814198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.3847 | 0.614060 | ||||||||
\(287\) | 18.7073 | − | 18.7073i | 1.10425 | − | 1.10425i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7298i | 0.984108i | ||||||||
\(290\) | −3.32502 | − | 18.5108i | −0.195252 | − | 1.08699i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.42754 | + | 4.42754i | 0.259102 | + | 0.259102i | ||||
\(293\) | 11.4152 | + | 11.4152i | 0.666883 | + | 0.666883i | 0.956993 | − | 0.290110i | \(-0.0936920\pi\) |
−0.290110 | + | 0.956993i | \(0.593692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4403 | + | 16.4501i | −0.666078 | + | 0.957761i | ||||
\(296\) | 8.68582i | 0.504853i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.2072 | − | 12.2072i | 0.707144 | − | 0.707144i | ||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.8034 | −0.737974 | ||||||||
\(302\) | 0.0210131 | − | 0.0210131i | 0.00120917 | − | 0.00120917i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.79066i | 0.160055i | ||||||||
\(305\) | 2.40263 | − | 3.45477i | 0.137574 | − | 0.197819i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.29343 | − | 5.29343i | −0.302112 | − | 0.302112i | 0.539728 | − | 0.841840i | \(-0.318527\pi\) |
−0.841840 | + | 0.539728i | \(0.818527\pi\) | |||||||
\(308\) | 5.67484 | + | 5.67484i | 0.323354 | + | 0.323354i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.205481 | − | 1.14394i | −0.0116706 | − | 0.0649715i | ||||
\(311\) | 30.1680i | 1.71067i | 0.518074 | + | 0.855336i | \(0.326649\pi\) | ||||
−0.518074 | + | 0.855336i | \(0.673351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6892 | − | 11.6892i | 0.660710 | − | 0.660710i | −0.294837 | − | 0.955547i | \(-0.595265\pi\) |
0.955547 | + | 0.294837i | \(0.0952655\pi\) | |||||||
\(314\) | 16.8371 | 0.950173 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.23189 | −0.463080 | ||||||||
\(317\) | −4.00114 | + | 4.00114i | −0.224726 | + | 0.224726i | −0.810485 | − | 0.585759i | \(-0.800797\pi\) |
0.585759 | + | 0.810485i | \(0.300797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.8805i | 1.72898i | ||||||||
\(320\) | 1.83577 | + | 1.27669i | 0.102623 | + | 0.0713693i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.54563 | − | 1.54563i | −0.0861345 | − | 0.0861345i | ||||
\(323\) | 1.02567 | + | 1.02567i | 0.0570695 | + | 0.0570695i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.8551 | − | 5.89463i | −0.713072 | − | 0.326976i | ||||
\(326\) | 1.10017i | 0.0609328i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.55835 | + | 8.55835i | −0.472556 | + | 0.472556i | ||||
\(329\) | −3.52147 | −0.194145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.1308 | 0.666769 | 0.333385 | − | 0.942791i | \(-0.391809\pi\) | ||||
0.333385 | + | 0.942791i | \(0.391809\pi\) | |||||||
\(332\) | −5.86639 | + | 5.86639i | −0.321960 | + | 0.321960i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.38897i | 0.240154i | ||||||||
\(335\) | 6.62669 | − | 1.19033i | 0.362055 | − | 0.0650344i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4573 | + | 11.4573i | 0.624117 | + | 0.624117i | 0.946581 | − | 0.322465i | \(-0.104511\pi\) |
−0.322465 | + | 0.946581i | \(0.604511\pi\) | |||||||
\(338\) | −3.53553 | − | 3.53553i | −0.192308 | − | 0.192308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.14394 | − | 0.205481i | 0.0620389 | − | 0.0111438i | ||||
\(341\) | 1.90837i | 0.103344i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2539 | + | 14.2539i | −0.769638 | + | 0.769638i | ||||
\(344\) | 5.85739 | 0.315809 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.09126 | −0.0586664 | ||||||||
\(347\) | 12.6914 | − | 12.6914i | 0.681308 | − | 0.681308i | −0.278987 | − | 0.960295i | \(-0.589999\pi\) |
0.960295 | + | 0.278987i | \(0.0899987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.8946i | − | 0.743763i | −0.928280 | − | 0.371881i | \(-0.878713\pi\) | ||
0.928280 | − | 0.371881i | \(-0.121287\pi\) | |||||||
\(350\) | −3.80363 | − | 10.2460i | −0.203312 | − | 0.547673i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.59617 | − | 2.59617i | −0.138376 | − | 0.138376i | ||||
\(353\) | −17.4292 | − | 17.4292i | −0.927664 | − | 0.927664i | 0.0698910 | − | 0.997555i | \(-0.477735\pi\) |
−0.997555 | + | 0.0698910i | \(0.977735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.1888 | + | 17.5176i | 1.33688 | + | 0.929740i | ||||
\(356\) | 8.50327i | 0.450672i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.45726 | − | 9.45726i | 0.499832 | − | 0.499832i | ||||
\(359\) | 9.98653 | 0.527069 | 0.263534 | − | 0.964650i | \(-0.415112\pi\) | ||||
0.263534 | + | 0.964650i | \(0.415112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2122 | 0.590118 | ||||||||
\(362\) | −4.25163 | + | 4.25163i | −0.223461 | + | 0.223461i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.18252i | 0.324052i | ||||||||
\(365\) | 2.47535 | + | 13.7806i | 0.129566 | + | 0.721308i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.4360 | + | 25.4360i | 1.32775 | + | 1.32775i | 0.907331 | + | 0.420416i | \(0.138116\pi\) |
0.420416 | + | 0.907331i | \(0.361884\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.0891 | + | 15.9452i | −0.576496 | + | 0.828950i | ||||
\(371\) | 19.8350i | 1.02978i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.82420 | + | 7.82420i | −0.405122 | + | 0.405122i | −0.880034 | − | 0.474912i | \(-0.842480\pi\) |
0.474912 | + | 0.880034i | \(0.342480\pi\) | |||||||
\(374\) | −1.90837 | −0.0986795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.61103 | 0.0830826 | ||||||||
\(377\) | −16.8216 | + | 16.8216i | −0.866354 | + | 0.866354i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0679i | 0.825351i | 0.910878 | + | 0.412676i | \(0.135406\pi\) | ||||
−0.910878 | + | 0.412676i | \(0.864594\pi\) | |||||||
\(380\) | −3.56281 | + | 5.12301i | −0.182768 | + | 0.262805i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.2793 | + | 18.2793i | 0.935252 | + | 0.935252i | ||||
\(383\) | 2.58830 | + | 2.58830i | 0.132256 | + | 0.132256i | 0.770136 | − | 0.637880i | \(-0.220188\pi\) |
−0.637880 | + | 0.770136i | \(0.720188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.17269 | + | 17.6627i | 0.161695 | + | 0.900177i | ||||
\(386\) | 9.09129i | 0.462735i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.72525 | + | 4.72525i | −0.239888 | + | 0.239888i | ||||
\(389\) | −32.5550 | −1.65060 | −0.825302 | − | 0.564692i | \(-0.808995\pi\) | ||||
−0.825302 | + | 0.564692i | \(0.808995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.519773 | 0.0262861 | ||||||||
\(392\) | 1.57124 | − | 1.57124i | 0.0793594 | − | 0.0793594i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.5014i | 1.18398i | ||||||||
\(395\) | −15.1119 | − | 10.5096i | −0.760361 | − | 0.528795i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3847 | + | 14.3847i | 0.721947 | + | 0.721947i | 0.969002 | − | 0.247055i | \(-0.0794627\pi\) |
−0.247055 | + | 0.969002i | \(0.579463\pi\) | |||||||
\(398\) | −1.59676 | − | 1.59676i | −0.0800385 | − | 0.0800385i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.74011 | + | 4.68743i | 0.0870057 | + | 0.234372i | ||||
\(401\) | − | 14.1912i | − | 0.708676i | −0.935117 | − | 0.354338i | \(-0.884706\pi\) | ||
0.935117 | − | 0.354338i | \(-0.115294\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.03955 | + | 1.03955i | −0.0517835 | + | 0.0517835i | ||||
\(404\) | 13.3326 | 0.663320 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.3847 | −0.912417 | ||||||||
\(407\) | 22.5499 | − | 22.5499i | 1.11776 | − | 1.11776i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2135i | 1.24673i | 0.781932 | + | 0.623364i | \(0.214234\pi\) | ||||
−0.781932 | + | 0.623364i | \(0.785766\pi\) | |||||||
\(410\) | −26.6375 | + | 4.78479i | −1.31553 | + | 0.236304i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.54563 | − | 1.54563i | −0.0761477 | − | 0.0761477i | ||||
\(413\) | 13.8502 | + | 13.8502i | 0.681522 | + | 0.681522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2589 | + | 3.27977i | −0.896295 | + | 0.160998i | ||||
\(416\) | − | 2.82843i | − | 0.138675i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.24503 | − | 7.24503i | 0.354366 | − | 0.354366i | ||||
\(419\) | −14.4111 | −0.704030 | −0.352015 | − | 0.935994i | \(-0.614503\pi\) | ||||
−0.352015 | + | 0.935994i | \(0.614503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9943 | −0.925727 | −0.462864 | − | 0.886430i | \(-0.653178\pi\) | ||||
−0.462864 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(422\) | 15.8464 | − | 15.8464i | 0.771389 | − | 0.771389i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 9.07426i | − | 0.440685i | ||||||
\(425\) | 2.36235 | + | 1.08324i | 0.114591 | + | 0.0525450i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.90874 | − | 2.90874i | −0.140764 | − | 0.140764i | ||||
\(428\) | −8.40178 | − | 8.40178i | −0.406115 | − | 0.406115i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.7528 | + | 7.47809i | 0.518548 | + | 0.360625i | ||||
\(431\) | − | 26.8501i | − | 1.29332i | −0.762777 | − | 0.646662i | \(-0.776164\pi\) | ||
0.762777 | − | 0.646662i | \(-0.223836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.24075 | + | 7.24075i | −0.347968 | + | 0.347968i | −0.859352 | − | 0.511384i | \(-0.829133\pi\) |
0.511384 | + | 0.859352i | \(0.329133\pi\) | |||||||
\(434\) | −1.13615 | −0.0545368 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.14008 | −0.294056 | ||||||||
\(437\) | −1.97329 | + | 1.97329i | −0.0943954 | + | 0.0943954i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.8089i | − | 1.70907i | −0.519396 | − | 0.854533i | \(-0.673843\pi\) | ||
0.519396 | − | 0.854533i | \(-0.326157\pi\) | |||||||
\(440\) | −1.45147 | − | 8.08049i | −0.0691959 | − | 0.385222i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.03955 | − | 1.03955i | −0.0494462 | − | 0.0494462i | ||||
\(443\) | 14.3582 | + | 14.3582i | 0.682180 | + | 0.682180i | 0.960491 | − | 0.278311i | \(-0.0897746\pi\) |
−0.278311 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8561 | + | 15.6101i | −0.514627 | + | 0.739988i | ||||
\(446\) | 22.4909i | 1.06498i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.54563 | − | 1.54563i | 0.0730241 | − | 0.0730241i | ||||
\(449\) | 3.66008 | 0.172730 | 0.0863649 | − | 0.996264i | \(-0.472475\pi\) | ||||
0.0863649 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.4379 | 2.09250 | ||||||||
\(452\) | 9.75351 | − | 9.75351i | 0.458767 | − | 0.458767i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.1557i | 0.992886i | ||||||||
\(455\) | −7.89317 | + | 11.3497i | −0.370038 | + | 0.532081i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.27047 | + | 7.27047i | 0.340098 | + | 0.340098i | 0.856404 | − | 0.516306i | \(-0.172693\pi\) |
−0.516306 | + | 0.856404i | \(0.672693\pi\) | |||||||
\(458\) | 8.60535 | + | 8.60535i | 0.402101 | + | 0.402101i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.395329 | + | 2.20084i | 0.0184323 | + | 0.102615i | ||||
\(461\) | 0.0264291i | 0.00123093i | 1.00000 | 0.000615464i | \(0.000195908\pi\) | |||||
−1.00000 | 0.000615464i | \(0.999804\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00983 | + | 8.00983i | −0.372248 | + | 0.372248i | −0.868296 | − | 0.496047i | \(-0.834784\pi\) |
0.496047 | + | 0.868296i | \(0.334784\pi\) | |||||||
\(464\) | 8.41078 | 0.390461 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.7078 | 0.820300 | ||||||||
\(467\) | −1.97632 | + | 1.97632i | −0.0914531 | + | 0.0914531i | −0.751353 | − | 0.659900i | \(-0.770599\pi\) |
0.659900 | + | 0.751353i | \(0.270599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.58154i | − | 0.303907i | ||||||
\(470\) | 2.95749 | + | 2.05679i | 0.136419 | + | 0.0948727i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.33629 | − | 6.33629i | −0.291651 | − | 0.291651i | ||||
\(473\) | −15.2068 | − | 15.2068i | −0.699210 | − | 0.699210i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.0810 | + | 4.85606i | −0.600198 | + | 0.222811i | ||||
\(476\) | − | 1.13615i | − | 0.0520752i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.51880 | + | 5.51880i | −0.252424 | + | 0.252424i | ||||
\(479\) | 23.5725 | 1.07706 | 0.538528 | − | 0.842608i | \(-0.318981\pi\) | ||||
0.538528 | + | 0.842608i | \(0.318981\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5672 | 1.12017 | ||||||||
\(482\) | −5.45329 | + | 5.45329i | −0.248391 | + | 0.248391i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.48023i | 0.112738i | ||||||||
\(485\) | −14.7072 | + | 2.64179i | −0.667819 | + | 0.119958i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.72428 | − | 7.72428i | −0.350021 | − | 0.350021i | 0.510097 | − | 0.860117i | \(-0.329610\pi\) |
−0.860117 | + | 0.510097i | \(0.829610\pi\) | |||||||
\(488\) | 1.33071 | + | 1.33071i | 0.0602386 | + | 0.0602386i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.89041 | − | 0.878445i | 0.220926 | − | 0.0396841i | ||||
\(491\) | 23.5772i | 1.06402i | 0.846737 | + | 0.532012i | \(0.178564\pi\) | ||||
−0.846737 | + | 0.532012i | \(0.821436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.09126 | − | 3.09126i | 0.139223 | − | 0.139223i | ||||
\(494\) | 7.89317 | 0.355131 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.519773 | 0.0233385 | ||||||||
\(497\) | 21.2077 | − | 21.2077i | 0.951297 | − | 0.951297i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.64075i | − | 0.0734500i | −0.999325 | − | 0.0367250i | \(-0.988307\pi\) | ||
0.999325 | − | 0.0367250i | \(-0.0116926\pi\) | |||||||
\(500\) | −2.78996 | + | 10.8266i | −0.124771 | + | 0.484182i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.9710 | + | 11.9710i | 0.534293 | + | 0.534293i | ||||
\(503\) | 3.23088 | + | 3.23088i | 0.144058 | + | 0.144058i | 0.775457 | − | 0.631400i | \(-0.217519\pi\) |
−0.631400 | + | 0.775457i | \(0.717519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4755 | + | 17.0216i | 1.08915 | + | 0.757450i | ||||
\(506\) | − | 3.67154i | − | 0.163220i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.18252 | − | 3.18252i | 0.141201 | − | 0.141201i | ||||
\(509\) | −19.4914 | −0.863942 | −0.431971 | − | 0.901887i | \(-0.642182\pi\) | ||||
−0.431971 | + | 0.901887i | \(0.642182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6867 | 0.605463 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 0.410963i | − | 0.0181268i | ||||||
\(515\) | −0.864129 | − | 4.81071i | −0.0380781 | − | 0.211985i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.18252 | − | 4.18252i | −0.183947 | − | 0.183947i | ||||
\(518\) | 13.4251 | + | 13.4251i | 0.589863 | + | 0.589863i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.61103 | − | 5.19235i | 0.158354 | − | 0.227699i | ||||
\(521\) | 34.3242i | 1.50377i | 0.659294 | + | 0.751886i | \(0.270855\pi\) | ||||
−0.659294 | + | 0.751886i | \(0.729145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6870 | + | 18.6870i | −0.817126 | + | 0.817126i | −0.985691 | − | 0.168565i | \(-0.946087\pi\) |
0.168565 | + | 0.985691i | \(0.446087\pi\) | |||||||
\(524\) | −20.3105 | −0.887270 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0177 | −0.785610 | ||||||||
\(527\) | 0.191035 | − | 0.191035i | 0.00832162 | − | 0.00832162i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 11.5850 | − | 16.6583i | 0.503222 | − | 0.723589i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.31332 | + | 4.31332i | 0.187006 | + | 0.187006i | ||||
\(533\) | 24.2067 | + | 24.2067i | 1.04851 | + | 1.04851i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.69726 | − | 26.1502i | −0.203080 | − | 1.13057i | ||||
\(536\) | 3.01098i | 0.130054i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.2012 | + | 12.2012i | −0.526031 | + | 0.526031i | ||||
\(539\) | −8.15840 | −0.351407 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 7.15810 | − | 7.15810i | 0.307467 | − | 0.307467i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.519773i | 0.0222851i | ||||||||
\(545\) | −11.2718 | − | 7.83899i | −0.482830 | − | 0.335786i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.21862 | − | 1.21862i | −0.0521043 | − | 0.0521043i | 0.680575 | − | 0.732679i | \(-0.261730\pi\) |
−0.732679 | + | 0.680575i | \(0.761730\pi\) | |||||||
\(548\) | 5.30731 | + | 5.30731i | 0.226717 | + | 0.226717i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.65175 | − | 16.6870i | 0.326272 | − | 0.711537i | ||||
\(551\) | 23.4716i | 0.999924i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.7235 | + | 12.7235i | −0.541056 | + | 0.541056i | ||||
\(554\) | 24.7568 | 1.05181 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.54949 | 0.108122 | ||||||||
\(557\) | 32.2385 | − | 32.2385i | 1.36599 | − | 1.36599i | 0.499912 | − | 0.866076i | \(-0.333366\pi\) |
0.866076 | − | 0.499912i | \(-0.166634\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.5672i | − | 0.700718i | ||||||
\(560\) | 4.81071 | − | 0.864129i | 0.203290 | − | 0.0365161i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3104 | − | 13.3104i | −0.561467 | − | 0.561467i | ||||
\(563\) | −2.89500 | − | 2.89500i | −0.122010 | − | 0.122010i | 0.643465 | − | 0.765475i | \(-0.277496\pi\) |
−0.765475 | + | 0.643465i | \(0.777496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.3574 | − | 5.45298i | 1.27715 | − | 0.229409i | ||||
\(566\) | 10.3961i | 0.436980i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.70229 | + | 9.70229i | −0.407099 | + | 0.407099i | ||||
\(569\) | 0.748186 | 0.0313656 | 0.0156828 | − | 0.999877i | \(-0.495008\pi\) | ||||
0.0156828 | + | 0.999877i | \(0.495008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.0121 | −1.71630 | −0.858150 | − | 0.513398i | \(-0.828386\pi\) | ||||
−0.858150 | + | 0.513398i | \(0.828386\pi\) | |||||||
\(572\) | −7.34309 | + | 7.34309i | −0.307030 | + | 0.307030i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 26.4561i | 1.10425i | ||||||||
\(575\) | −2.08407 | + | 4.54496i | −0.0869116 | + | 0.189538i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5803 | + | 18.5803i | 0.773510 | + | 0.773510i | 0.978718 | − | 0.205208i | \(-0.0657872\pi\) |
−0.205208 | + | 0.978718i | \(0.565787\pi\) | |||||||
\(578\) | −11.8298 | − | 11.8298i | −0.492054 | − | 0.492054i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.4403 | + | 10.7380i | 0.641122 | + | 0.445870i | ||||
\(581\) | 18.1345i | 0.752346i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5583 | + | 23.5583i | −0.975687 | + | 0.975687i | ||||
\(584\) | −6.26149 | −0.259102 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.1435 | −0.666883 | ||||||||
\(587\) | 10.8561 | − | 10.8561i | 0.448080 | − | 0.448080i | −0.446636 | − | 0.894716i | \(-0.647378\pi\) |
0.894716 | + | 0.446636i | \(0.147378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.45051i | 0.0597672i | ||||||||
\(590\) | −3.54248 | − | 19.7215i | −0.145842 | − | 0.811920i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.14180 | − | 6.14180i | −0.252426 | − | 0.252426i | ||||
\(593\) | 15.4679 | + | 15.4679i | 0.635192 | + | 0.635192i | 0.949366 | − | 0.314173i | \(-0.101727\pi\) |
−0.314173 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.45051 | − | 2.08571i | 0.0594651 | − | 0.0855056i | ||||
\(596\) | 17.2636i | 0.707144i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.00000 | − | 2.00000i | 0.0817861 | − | 0.0817861i | ||||
\(599\) | 6.03935 | 0.246761 | 0.123381 | − | 0.992359i | \(-0.460626\pi\) | ||||
0.123381 | + | 0.992359i | \(0.460626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.25178 | 0.132643 | 0.0663214 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663214 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(602\) | 9.05335 | − | 9.05335i | 0.368987 | − | 0.368987i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0297170i | 0.00120917i | ||||||||
\(605\) | −3.16649 | + | 4.55313i | −0.128736 | + | 0.185111i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.8937 | − | 28.8937i | −1.17276 | − | 1.17276i | −0.981550 | − | 0.191208i | \(-0.938759\pi\) |
−0.191208 | − | 0.981550i | \(-0.561241\pi\) | |||||||
\(608\) | −1.97329 | − | 1.97329i | −0.0800276 | − | 0.0800276i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.743975 | + | 4.14180i | 0.0301227 | + | 0.167697i | ||||
\(611\) | − | 4.55668i | − | 0.184344i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.4933 | − | 30.4933i | 1.23161 | − | 1.23161i | 0.268268 | − | 0.963344i | \(-0.413549\pi\) |
0.963344 | − | 0.268268i | \(-0.0864511\pi\) | |||||||
\(614\) | 7.48605 | 0.302112 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.02544 | −0.323354 | ||||||||
\(617\) | −3.81450 | + | 3.81450i | −0.153566 | + | 0.153566i | −0.779709 | − | 0.626143i | \(-0.784633\pi\) |
0.626143 | + | 0.779709i | \(0.284633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.28927i | − | 0.0518201i | −0.999664 | − | 0.0259100i | \(-0.991752\pi\) | ||
0.999664 | − | 0.0259100i | \(-0.00824835\pi\) | |||||||
\(620\) | 0.954185 | + | 0.663591i | 0.0383210 | + | 0.0266504i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.3320 | − | 21.3320i | −0.855336 | − | 0.855336i | ||||
\(623\) | 13.1429 | + | 13.1429i | 0.526559 | + | 0.526559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.9440 | + | 16.3133i | −0.757760 | + | 0.652533i | ||||
\(626\) | 16.5310i | 0.660710i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.9056 | + | 11.9056i | −0.475086 | + | 0.475086i | ||||
\(629\) | −4.51466 | −0.180011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.0156 | 1.55319 | 0.776593 | − | 0.630002i | \(-0.216946\pi\) | ||||
0.776593 | + | 0.630002i | \(0.216946\pi\) | |||||||
\(632\) | 5.82083 | − | 5.82083i | 0.231540 | − | 0.231540i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 5.65846i | − | 0.224726i | ||||||
\(635\) | 9.90546 | − | 1.77928i | 0.393086 | − | 0.0706085i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.44413 | − | 4.44413i | −0.176083 | − | 0.176083i | ||||
\(638\) | −21.8358 | − | 21.8358i | −0.864489 | − | 0.864489i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.20084 | + | 0.395329i | −0.0869960 | + | 0.0156267i | ||||
\(641\) | 0.282154i | 0.0111444i | 0.999984 | + | 0.00557220i | \(0.00177370\pi\) | ||||
−0.999984 | + | 0.00557220i | \(0.998226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3907 | − | 10.3907i | 0.409769 | − | 0.409769i | −0.471889 | − | 0.881658i | \(-0.656428\pi\) |
0.881658 | + | 0.471889i | \(0.156428\pi\) | |||||||
\(644\) | 2.18585 | 0.0861345 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.45051 | −0.0570695 | ||||||||
\(647\) | −13.6046 | + | 13.6046i | −0.534851 | + | 0.534851i | −0.922012 | − | 0.387161i | \(-0.873456\pi\) |
0.387161 | + | 0.922012i | \(0.373456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.9002i | 1.29145i | ||||||||
\(650\) | 13.2581 | − | 4.92178i | 0.520024 | − | 0.193048i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.777937 | − | 0.777937i | −0.0304664 | − | 0.0304664i | ||||
\(653\) | 18.0017 | + | 18.0017i | 0.704461 | + | 0.704461i | 0.965365 | − | 0.260904i | \(-0.0840207\pi\) |
−0.260904 | + | 0.965365i | \(0.584021\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.2855 | − | 25.9303i | −1.45687 | − | 1.01318i | ||||
\(656\) | − | 12.1033i | − | 0.472556i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.49006 | − | 2.49006i | 0.0970725 | − | 0.0970725i | ||||
\(659\) | −16.0723 | −0.626088 | −0.313044 | − | 0.949739i | \(-0.601349\pi\) | ||||
−0.313044 | + | 0.949739i | \(0.601349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9116 | 0.618891 | 0.309445 | − | 0.950917i | \(-0.399857\pi\) | ||||
0.309445 | + | 0.950917i | \(0.399857\pi\) | |||||||
\(662\) | −8.57777 | + | 8.57777i | −0.333385 | + | 0.333385i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.29632i | − | 0.321960i | ||||||
\(665\) | 2.41149 | + | 13.4251i | 0.0935135 | + | 0.520601i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.94732 | + | 5.94732i | 0.230281 | + | 0.230281i | ||||
\(668\) | −3.10347 | − | 3.10347i | −0.120077 | − | 0.120077i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.84409 | + | 5.52746i | −0.148510 | + | 0.213545i | ||||
\(671\) | − | 6.90953i | − | 0.266740i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.50319 | + | 8.50319i | −0.327774 | + | 0.327774i | −0.851739 | − | 0.523966i | \(-0.824452\pi\) |
0.523966 | + | 0.851739i | \(0.324452\pi\) | |||||||
\(674\) | −16.2030 | −0.624117 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 6.71555 | − | 6.71555i | 0.258100 | − | 0.258100i | −0.566181 | − | 0.824281i | \(-0.691580\pi\) |
0.824281 | + | 0.566181i | \(0.191580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.6070i | 0.560564i | ||||||||
\(680\) | −0.663591 | + | 0.954185i | −0.0254475 | + | 0.0365913i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.34942 | − | 1.34942i | −0.0516720 | − | 0.0516720i | ||||
\(683\) | −22.6129 | − | 22.6129i | −0.865260 | − | 0.865260i | 0.126684 | − | 0.991943i | \(-0.459567\pi\) |
−0.991943 | + | 0.126684i | \(0.959567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.96720 | + | 16.5188i | 0.113371 | + | 0.631151i | ||||
\(686\) | − | 20.1580i | − | 0.769638i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.14180 | + | 4.14180i | −0.157905 | + | 0.157905i | ||||
\(689\) | −25.6659 | −0.977792 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.60120 | −0.175038 | −0.0875190 | − | 0.996163i | \(-0.527894\pi\) | ||||
−0.0875190 | + | 0.996163i | \(0.527894\pi\) | |||||||
\(692\) | 0.771636 | − | 0.771636i | 0.0293332 | − | 0.0293332i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.9483i | 0.681308i | ||||||||
\(695\) | 4.68028 | + | 3.25491i | 0.177533 | + | 0.123466i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.44840 | − | 4.44840i | −0.168495 | − | 0.168495i | ||||
\(698\) | 9.82499 | + | 9.82499i | 0.371881 | + | 0.371881i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.93460 | + | 4.55546i | 0.375492 | + | 0.172180i | ||||
\(701\) | − | 40.2549i | − | 1.52041i | −0.649685 | − | 0.760204i | \(-0.725099\pi\) | ||
0.649685 | − | 0.760204i | \(-0.274901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.1397 | − | 17.1397i | 0.646435 | − | 0.646435i | ||||
\(704\) | 3.67154 | 0.138376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.6486 | 0.927664 | ||||||||
\(707\) | 20.6072 | − | 20.6072i | 0.775013 | − | 0.775013i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 14.5819i | − | 0.547634i | −0.961782 | − | 0.273817i | \(-0.911714\pi\) | ||
0.961782 | − | 0.273817i | \(-0.0882862\pi\) | |||||||
\(710\) | −30.1980 | + | 5.42435i | −1.13331 | + | 0.203572i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.01272 | − | 6.01272i | −0.225336 | − | 0.225336i | ||||
\(713\) | 0.367535 | + | 0.367535i | 0.0137643 | + | 0.0137643i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.8551 | + | 4.10537i | −0.854732 | + | 0.153532i | ||||
\(716\) | 13.3746i | 0.499832i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.06154 | + | 7.06154i | −0.263534 | + | 0.263534i | ||||
\(719\) | 36.4109 | 1.35790 | 0.678949 | − | 0.734185i | \(-0.262436\pi\) | ||||
0.678949 | + | 0.734185i | \(0.262436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.77794 | −0.177940 | ||||||||
\(722\) | −7.92825 | + | 7.92825i | −0.295059 | + | 0.295059i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 6.01272i | − | 0.223461i | ||||||
\(725\) | 14.6357 | + | 39.4249i | 0.543556 | + | 1.46421i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.2118 | − | 29.2118i | −1.08341 | − | 1.08341i | −0.996189 | − | 0.0872170i | \(-0.972203\pi\) |
−0.0872170 | − | 0.996189i | \(-0.527797\pi\) | |||||||
\(728\) | −4.37170 | − | 4.37170i | −0.162026 | − | 0.162026i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.4947 | − | 7.99400i | −0.425437 | − | 0.295871i | ||||
\(731\) | 3.04452i | 0.112606i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.4084 | − | 22.4084i | 0.827673 | − | 0.827673i | −0.159521 | − | 0.987195i | \(-0.550995\pi\) |
0.987195 | + | 0.159521i | \(0.0509950\pi\) | |||||||
\(734\) | −35.9719 | −1.32775 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 7.81702 | − | 7.81702i | 0.287943 | − | 0.287943i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.718504i | 0.0264306i | 0.999913 | + | 0.0132153i | \(0.00420668\pi\) | ||||
−0.999913 | + | 0.0132153i | \(0.995793\pi\) | |||||||
\(740\) | −3.43375 | − | 19.1161i | −0.126227 | − | 0.702723i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.0254 | − | 14.0254i | −0.514890 | − | 0.514890i | ||||
\(743\) | 29.2845 | + | 29.2845i | 1.07435 | + | 1.07435i | 0.997005 | + | 0.0773402i | \(0.0246428\pi\) |
0.0773402 | + | 0.997005i | \(0.475357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0403 | + | 31.6920i | −0.807494 | + | 1.16111i | ||||
\(746\) | − | 11.0651i | − | 0.405122i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.34942 | − | 1.34942i | 0.0493397 | − | 0.0493397i | ||||
\(749\) | −25.9721 | −0.948999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7596 | 0.575074 | 0.287537 | − | 0.957769i | \(-0.407164\pi\) | ||||
0.287537 | + | 0.957769i | \(0.407164\pi\) | |||||||
\(752\) | −1.13917 | + | 1.13917i | −0.0415413 | + | 0.0415413i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 23.7893i | − | 0.866354i | ||||||
\(755\) | −0.0379394 | + | 0.0545535i | −0.00138076 | + | 0.00198541i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.62258 | + | 8.62258i | 0.313393 | + | 0.313393i | 0.846223 | − | 0.532829i | \(-0.178871\pi\) |
−0.532829 | + | 0.846223i | \(0.678871\pi\) | |||||||
\(758\) | −11.3617 | − | 11.3617i | −0.412676 | − | 0.412676i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.10323 | − | 6.14180i | −0.0400182 | − | 0.222787i | ||||
\(761\) | 12.3628i | 0.448152i | 0.974572 | + | 0.224076i | \(0.0719364\pi\) | ||||
−0.974572 | + | 0.224076i | \(0.928064\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.49028 | + | 9.49028i | −0.343571 | + | 0.343571i | ||||
\(764\) | −25.8509 | −0.935252 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.66041 | −0.132256 | ||||||||
\(767\) | −17.9217 | + | 17.9217i | −0.647116 | + | 0.647116i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.7384i | 0.639663i | 0.947474 | + | 0.319831i | \(0.103626\pi\) | ||||
−0.947474 | + | 0.319831i | \(0.896374\pi\) | |||||||
\(770\) | −14.7329 | − | 10.2460i | −0.530936 | − | 0.369241i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.42852 | − | 6.42852i | −0.231367 | − | 0.231367i | ||||
\(773\) | −18.2478 | − | 18.2478i | −0.656327 | − | 0.656327i | 0.298182 | − | 0.954509i | \(-0.403620\pi\) |
−0.954509 | + | 0.298182i | \(0.903620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.904465 | + | 2.43640i | 0.0324893 | + | 0.0875181i | ||||
\(776\) | − | 6.68252i | − | 0.239888i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0199 | − | 23.0199i | 0.825302 | − | 0.825302i | ||||
\(779\) | 33.7763 | 1.21016 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.3776 | 1.80265 | ||||||||
\(782\) | −0.367535 | + | 0.367535i | −0.0131430 | + | 0.0131430i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.22206i | 0.0793594i | ||||||||
\(785\) | −37.0558 | + | 6.65619i | −1.32258 | + | 0.237570i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.3116 | + | 10.3116i | 0.367569 | + | 0.367569i | 0.866590 | − | 0.499021i | \(-0.166307\pi\) |
−0.499021 | + | 0.866590i | \(0.666307\pi\) | |||||||
\(788\) | −16.6180 | − | 16.6180i | −0.591991 | − | 0.591991i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.1171 | − | 3.25430i | 0.644578 | − | 0.115783i | ||||
\(791\) | − | 30.1506i | − | 1.07203i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.76383 | − | 3.76383i | 0.133658 | − | 0.133658i | ||||
\(794\) | −20.3430 | −0.721947 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.25816 | 0.0800385 | ||||||||
\(797\) | −19.8355 | + | 19.8355i | −0.702609 | + | 0.702609i | −0.964970 | − | 0.262361i | \(-0.915499\pi\) |
0.262361 | + | 0.964970i | \(0.415499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.837371i | 0.0296241i | ||||||||
\(800\) | −4.54496 | − | 2.08407i | −0.160689 | − | 0.0736829i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.0347 | + | 10.0347i | 0.354338 | + | 0.354338i | ||||
\(803\) | 16.2559 | + | 16.2559i | 0.573659 | + | 0.573659i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.01272 | + | 2.79066i | 0.141430 | + | 0.0983577i | ||||
\(806\) | − | 1.47014i | − | 0.0517835i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.42754 | + | 9.42754i | −0.331660 | + | 0.331660i | ||||
\(809\) | 31.5588 | 1.10955 | 0.554774 | − | 0.832001i | \(-0.312805\pi\) | ||||
0.554774 | + | 0.832001i | \(0.312805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.7702 | 0.378193 | 0.189097 | − | 0.981958i | \(-0.439444\pi\) | ||||
0.189097 | + | 0.981958i | \(0.439444\pi\) | |||||||
\(812\) | 12.9999 | − | 12.9999i | 0.456208 | − | 0.456208i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 31.8904i | 1.11776i | ||||||||
\(815\) | −0.434929 | − | 2.42130i | −0.0152349 | − | 0.0848145i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.5583 | − | 11.5583i | −0.404375 | − | 0.404375i | ||||
\(818\) | −17.8286 | − | 17.8286i | −0.623364 | − | 0.623364i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.4522 | − | 22.2190i | 0.539615 | − | 0.775919i | ||||
\(821\) | − | 29.6629i | − | 1.03524i | −0.855610 | − | 0.517622i | \(-0.826817\pi\) | ||
0.855610 | − | 0.517622i | \(-0.173183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4671 | − | 17.4671i | 0.608865 | − | 0.608865i | −0.333785 | − | 0.942649i | \(-0.608326\pi\) |
0.942649 | + | 0.333785i | \(0.108326\pi\) | |||||||
\(824\) | 2.18585 | 0.0761477 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.5871 | −0.681522 | ||||||||
\(827\) | −11.0873 | + | 11.0873i | −0.385541 | + | 0.385541i | −0.873094 | − | 0.487552i | \(-0.837890\pi\) |
0.487552 | + | 0.873094i | \(0.337890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.0509i | − | 0.904784i | −0.891819 | − | 0.452392i | \(-0.850571\pi\) | ||
0.891819 | − | 0.452392i | \(-0.149429\pi\) | |||||||
\(830\) | 10.5919 | − | 15.2302i | 0.367649 | − | 0.528646i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | + | 2.00000i | 0.0693375 | + | 0.0693375i | ||||
\(833\) | 0.816687 | + | 0.816687i | 0.0282965 | + | 0.0282965i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.73508 | − | 9.65944i | −0.0600451 | − | 0.334279i | ||||
\(836\) | 10.2460i | 0.354366i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1902 | − | 10.1902i | 0.352015 | − | 0.352015i | ||||
\(839\) | 29.7734 | 1.02789 | 0.513946 | − | 0.857822i | \(-0.328183\pi\) | ||||
0.513946 | + | 0.857822i | \(0.328183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.7412 | 1.43935 | ||||||||
\(842\) | 13.4310 | − | 13.4310i | 0.462864 | − | 0.462864i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.4101i | 0.771389i | ||||||||
\(845\) | 9.17886 | + | 6.38346i | 0.315762 | + | 0.219598i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.83351 | + | 3.83351i | 0.131721 | + | 0.131721i | ||||
\(848\) | 6.41647 | + | 6.41647i | 0.220343 | + | 0.220343i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.43640 | + | 0.904465i | −0.0835679 | + | 0.0310229i | ||||
\(851\) | − | 8.68582i | − | 0.297746i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.27933 | − | 6.27933i | 0.215000 | − | 0.215000i | −0.591387 | − | 0.806388i | \(-0.701420\pi\) |
0.806388 | + | 0.591387i | \(0.201420\pi\) | |||||||
\(854\) | 4.11358 | 0.140764 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.8819 | 0.406115 | ||||||||
\(857\) | 34.1776 | − | 34.1776i | 1.16749 | − | 1.16749i | 0.184689 | − | 0.982797i | \(-0.440872\pi\) |
0.982797 | − | 0.184689i | \(-0.0591278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 50.5764i | − | 1.72564i | −0.505508 | − | 0.862822i | \(-0.668695\pi\) | ||
0.505508 | − | 0.862822i | \(-0.331305\pi\) | |||||||
\(860\) | −12.8912 | + | 2.31559i | −0.439587 | + | 0.0789611i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.9859 | + | 18.9859i | 0.646662 | + | 0.646662i | ||||
\(863\) | −38.9845 | − | 38.9845i | −1.32705 | − | 1.32705i | −0.907932 | − | 0.419117i | \(-0.862340\pi\) |
−0.419117 | − | 0.907932i | \(-0.637660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.40169 | − | 0.431405i | 0.0816599 | − | 0.0146682i | ||||
\(866\) | − | 10.2400i | − | 0.347968i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.803377 | − | 0.803377i | 0.0272684 | − | 0.0272684i | ||||
\(869\) | −30.2237 | −1.02527 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.51633 | 0.288565 | ||||||||
\(872\) | 4.34169 | − | 4.34169i | 0.147028 | − | 0.147028i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.79066i | − | 0.0943954i | ||||||
\(875\) | 12.4217 | + | 21.0462i | 0.419931 | + | 0.711492i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.3345 | + | 30.3345i | 1.02432 | + | 1.02432i | 0.999697 | + | 0.0246260i | \(0.00783948\pi\) |
0.0246260 | + | 0.999697i | \(0.492161\pi\) | |||||||
\(878\) | 25.3207 | + | 25.3207i | 0.854533 | + | 0.854533i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.74011 | + | 4.68743i | 0.227209 | + | 0.158013i | ||||
\(881\) | 8.21130i | 0.276646i | 0.990387 | + | 0.138323i | \(0.0441712\pi\) | ||||
−0.990387 | + | 0.138323i | \(0.955829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.85275 | − | 4.85275i | 0.163308 | − | 0.163308i | −0.620722 | − | 0.784030i | \(-0.713161\pi\) |
0.784030 | + | 0.620722i | \(0.213161\pi\) | |||||||
\(884\) | 1.47014 | 0.0494462 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.3056 | −0.682180 | ||||||||
\(887\) | 27.9893 | − | 27.9893i | 0.939788 | − | 0.939788i | −0.0584995 | − | 0.998287i | \(-0.518632\pi\) |
0.998287 | + | 0.0584995i | \(0.0186316\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.83798i | − | 0.329955i | ||||||
\(890\) | −3.36159 | − | 18.7144i | −0.112681 | − | 0.627307i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.9035 | − | 15.9035i | −0.532488 | − | 0.532488i | ||||
\(893\) | −3.17904 | − | 3.17904i | −0.106382 | − | 0.106382i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.0752 | + | 24.5527i | −0.570762 | + | 0.820706i | ||||
\(896\) | 2.18585i | 0.0730241i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.58807 | + | 2.58807i | −0.0863649 | + | 0.0863649i | ||||
\(899\) | 4.37170 | 0.145804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.71656 | 0.157131 | ||||||||
\(902\) | −31.4223 | + | 31.4223i | −1.04625 | + | 1.04625i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.7935i | 0.458767i | ||||||||
\(905\) | 7.67639 | − | 11.0380i | 0.255172 | − | 0.366915i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.78683 | − | 9.78683i | −0.324966 | − | 0.324966i | 0.525702 | − | 0.850669i | \(-0.323803\pi\) |
−0.850669 | + | 0.525702i | \(0.823803\pi\) | |||||||
\(908\) | −14.9593 | − | 14.9593i | −0.496443 | − | 0.496443i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.44413 | − | 13.6068i | −0.0810220 | − | 0.451059i | ||||
\(911\) | − | 9.22522i | − | 0.305645i | −0.988254 | − | 0.152823i | \(-0.951164\pi\) | ||
0.988254 | − | 0.152823i | \(-0.0488363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.5387 | + | 21.5387i | −0.712827 | + | 0.712827i | ||||
\(914\) | −10.2820 | −0.340098 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.1698 | −0.402101 | ||||||||
\(917\) | −31.3926 | + | 31.3926i | −1.03667 | + | 1.03667i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 6.50784i | − | 0.214674i | −0.994223 | − | 0.107337i | \(-0.965768\pi\) | ||
0.994223 | − | 0.107337i | \(-0.0342323\pi\) | |||||||
\(920\) | −1.83577 | − | 1.27669i | −0.0605236 | − | 0.0420913i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.0186882 | − | 0.0186882i | −0.000615464 | − | 0.000615464i | ||||
\(923\) | 27.4422 | + | 27.4422i | 0.903272 | + | 0.903272i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.1018 | − | 39.4767i | 0.595185 | − | 1.29799i | ||||
\(926\) | − | 11.3276i | − | 0.372248i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.94732 | + | 5.94732i | −0.195230 | + | 0.195230i | ||||
\(929\) | −47.6095 | −1.56202 | −0.781008 | − | 0.624521i | \(-0.785294\pi\) | ||||
−0.781008 | + | 0.624521i | \(0.785294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.20101 | −0.203230 | ||||||||
\(932\) | −12.5213 | + | 12.5213i | −0.410150 | + | 0.410150i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2.79493i | − | 0.0914531i | ||||||
\(935\) | 4.20003 | − | 0.754433i | 0.137356 | − | 0.0246726i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.822065 | − | 0.822065i | −0.0268557 | − | 0.0268557i | 0.693551 | − | 0.720407i | \(-0.256045\pi\) |
−0.720407 | + | 0.693551i | \(0.756045\pi\) | |||||||
\(938\) | 4.65385 | + | 4.65385i | 0.151954 | + | 0.151954i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.54563 | + | 0.636887i | −0.115646 | + | 0.0207730i | ||||
\(941\) | 45.7028i | 1.48987i | 0.667138 | + | 0.744934i | \(0.267519\pi\) | ||||
−0.667138 | + | 0.744934i | \(0.732481\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.55835 | − | 8.55835i | 0.278698 | − | 0.278698i | ||||
\(944\) | 8.96086 | 0.291651 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.5057 | 0.699210 | ||||||||
\(947\) | 3.24399 | − | 3.24399i | 0.105416 | − | 0.105416i | −0.652432 | − | 0.757847i | \(-0.726251\pi\) |
0.757847 | + | 0.652432i | \(0.226251\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.7102i | 0.574897i | ||||||||
\(950\) | 5.81592 | − | 12.6834i | 0.188693 | − | 0.411505i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.803377 | + | 0.803377i | 0.0260376 | + | 0.0260376i | ||||
\(953\) | 3.07943 | + | 3.07943i | 0.0997526 | + | 0.0997526i | 0.755222 | − | 0.655469i | \(-0.227529\pi\) |
−0.655469 | + | 0.755222i | \(0.727529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.4563 | − | 33.0036i | −1.53565 | − | 1.06797i | ||||
\(956\) | − | 7.80476i | − | 0.252424i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.6683 | + | 16.6683i | −0.538528 | + | 0.538528i | ||||
\(959\) | 16.4063 | 0.529786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7298 | −0.991285 | ||||||||
\(962\) | −17.3716 | + | 17.3716i | −0.560084 | + | 0.560084i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 7.71212i | − | 0.248391i | ||||||
\(965\) | −3.59405 | − | 20.0085i | −0.115697 | − | 0.644097i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.6772 | − | 40.6772i | −1.30809 | − | 1.30809i | −0.922793 | − | 0.385296i | \(-0.874099\pi\) |
−0.385296 | − | 0.922793i | \(-0.625901\pi\) | |||||||
\(968\) | −1.75378 | − | 1.75378i | −0.0563688 | − | 0.0563688i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.53152 | − | 12.2676i | 0.273931 | − | 0.393888i | ||||
\(971\) | 32.2259i | 1.03418i | 0.855932 | + | 0.517089i | \(0.172984\pi\) | ||||
−0.855932 | + | 0.517089i | \(0.827016\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.94057 | − | 3.94057i | 0.126329 | − | 0.126329i | ||||
\(974\) | 10.9238 | 0.350021 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.88191 | −0.0602386 | ||||||||
\(977\) | 30.7751 | − | 30.7751i | 0.984582 | − | 0.984582i | −0.0153006 | − | 0.999883i | \(-0.504871\pi\) |
0.999883 | + | 0.0153006i | \(0.00487051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.2201i | 0.997799i | ||||||||
\(980\) | −2.83689 | + | 4.07920i | −0.0906211 | + | 0.130305i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.6716 | − | 16.6716i | −0.532012 | − | 0.532012i | ||||
\(983\) | −3.22950 | − | 3.22950i | −0.103005 | − | 0.103005i | 0.653726 | − | 0.756731i | \(-0.273205\pi\) |
−0.756731 | + | 0.653726i | \(0.773205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.29077 | − | 51.7229i | −0.296029 | − | 1.64803i | ||||
\(986\) | 4.37170i | 0.139223i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.58131 | + | 5.58131i | −0.177565 | + | 0.177565i | ||||
\(989\) | −5.85739 | −0.186254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.33087 | −0.169341 | −0.0846704 | − | 0.996409i | \(-0.526984\pi\) | ||||
−0.0846704 | + | 0.996409i | \(0.526984\pi\) | |||||||
\(992\) | −0.367535 | + | 0.367535i | −0.0116693 | + | 0.0116693i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.9923i | 0.951297i | ||||||||
\(995\) | 4.14547 | + | 2.88298i | 0.131420 | + | 0.0913966i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.6937 | − | 38.6937i | −1.22544 | − | 1.22544i | −0.965670 | − | 0.259773i | \(-0.916352\pi\) |
−0.259773 | − | 0.965670i | \(-0.583648\pi\) | |||||||
\(998\) | 1.16018 | + | 1.16018i | 0.0367250 | + | 0.0367250i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.2.j.i.737.3 | yes | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.i.737.6 | yes | 16 | |
5.3 | odd | 4 | inner | 2070.2.j.i.323.6 | yes | 16 | |
15.8 | even | 4 | inner | 2070.2.j.i.323.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.i.323.3 | ✓ | 16 | 15.8 | even | 4 | inner | |
2070.2.j.i.323.6 | yes | 16 | 5.3 | odd | 4 | inner | |
2070.2.j.i.737.3 | yes | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.i.737.6 | yes | 16 | 3.2 | odd | 2 | inner |