Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.4 | ||
Root | \(-1.38232 + 0.298668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.c.373.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.75410 | + | 3.03819i | 0.784457 | + | 1.35872i | 0.929323 | + | 0.369268i | \(0.120391\pi\) |
−0.144866 | + | 0.989451i | \(0.546275\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 1.12588 | + | 2.39424i | 0.425543 | + | 0.904938i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.50820 | −1.10939 | ||||||||
\(11\) | −6.40782 | −1.93203 | −0.966015 | − | 0.258485i | \(-0.916777\pi\) | ||||
−0.966015 | + | 0.258485i | \(0.916777\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −0.213022 | + | 3.59925i | −0.0590817 | + | 0.998253i | ||||
\(14\) | −2.63641 | − | 0.222079i | −0.704611 | − | 0.0593532i | ||||
\(15\) | 1.75410 | + | 3.03819i | 0.452906 | + | 0.784457i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.33890 | − | 4.05110i | −0.567267 | − | 0.982536i | −0.996835 | − | 0.0795010i | \(-0.974667\pi\) |
0.429567 | − | 0.903035i | \(-0.358666\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 5.23821 | 1.20173 | 0.600864 | − | 0.799351i | \(-0.294823\pi\) | ||||
0.600864 | + | 0.799351i | \(0.294823\pi\) | |||||||
\(20\) | 1.75410 | − | 3.03819i | 0.392228 | − | 0.679359i | ||||
\(21\) | 1.12588 | + | 2.39424i | 0.245687 | + | 0.522466i | ||||
\(22\) | 3.20391 | − | 5.54934i | 0.683076 | − | 1.18312i | ||||
\(23\) | 1.08480 | − | 1.87894i | 0.226197 | − | 0.391785i | −0.730481 | − | 0.682933i | \(-0.760704\pi\) |
0.956678 | + | 0.291148i | \(0.0940372\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.65372 | + | 6.32843i | −0.730745 | + | 1.26569i | ||||
\(26\) | −3.01053 | − | 1.98411i | −0.590414 | − | 0.389116i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.51053 | − | 2.17216i | 0.285464 | − | 0.410500i | ||||
\(29\) | −1.23033 | − | 2.13099i | −0.228467 | − | 0.395716i | 0.728887 | − | 0.684634i | \(-0.240038\pi\) |
−0.957354 | + | 0.288918i | \(0.906705\pi\) | |||||||
\(30\) | −3.50820 | −0.640506 | ||||||||
\(31\) | 4.46035 | − | 7.72555i | 0.801102 | − | 1.38755i | −0.117790 | − | 0.993039i | \(-0.537581\pi\) |
0.918892 | − | 0.394510i | \(-0.129086\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −6.40782 | −1.11546 | ||||||||
\(34\) | 4.67781 | 0.802237 | ||||||||
\(35\) | −5.29925 | + | 7.62037i | −0.895737 | + | 1.28808i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −1.94981 | + | 3.37717i | −0.320547 | + | 0.555204i | −0.980601 | − | 0.196014i | \(-0.937200\pi\) |
0.660054 | + | 0.751218i | \(0.270533\pi\) | |||||||
\(38\) | −2.61911 | + | 4.53642i | −0.424875 | + | 0.735905i | ||||
\(39\) | −0.213022 | + | 3.59925i | −0.0341108 | + | 0.576342i | ||||
\(40\) | 1.75410 | + | 3.03819i | 0.277347 | + | 0.480380i | ||||
\(41\) | 5.09300 | + | 8.82134i | 0.795393 | + | 1.37766i | 0.922589 | + | 0.385784i | \(0.126069\pi\) |
−0.127196 | + | 0.991878i | \(0.540598\pi\) | |||||||
\(42\) | −2.63641 | − | 0.222079i | −0.406808 | − | 0.0342676i | ||||
\(43\) | −1.19338 | + | 2.06699i | −0.181988 | + | 0.315213i | −0.942558 | − | 0.334044i | \(-0.891587\pi\) |
0.760569 | + | 0.649257i | \(0.224920\pi\) | |||||||
\(44\) | 3.20391 | + | 5.54934i | 0.483008 | + | 0.836594i | ||||
\(45\) | 1.75410 | + | 3.03819i | 0.261486 | + | 0.452906i | ||||
\(46\) | 1.08480 | + | 1.87894i | 0.159946 | + | 0.277034i | ||||
\(47\) | −2.44070 | − | 4.22742i | −0.356013 | − | 0.616632i | 0.631278 | − | 0.775557i | \(-0.282531\pi\) |
−0.987291 | + | 0.158924i | \(0.949197\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −4.46478 | + | 5.39126i | −0.637826 | + | 0.770180i | ||||
\(50\) | −3.65372 | − | 6.32843i | −0.516714 | − | 0.894976i | ||||
\(51\) | −2.33890 | − | 4.05110i | −0.327512 | − | 0.567267i | ||||
\(52\) | 3.22356 | − | 1.61514i | 0.447027 | − | 0.223980i | ||||
\(53\) | −1.05395 | + | 1.82549i | −0.144771 | + | 0.250750i | −0.929287 | − | 0.369358i | \(-0.879578\pi\) |
0.784517 | + | 0.620108i | \(0.212911\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −11.2399 | − | 19.4682i | −1.51559 | − | 2.62509i | ||||
\(56\) | 1.12588 | + | 2.39424i | 0.150452 | + | 0.319944i | ||||
\(57\) | 5.23821 | 0.693818 | ||||||||
\(58\) | 2.46066 | 0.323101 | ||||||||
\(59\) | 5.89729 | + | 10.2144i | 0.767761 | + | 1.32980i | 0.938774 | + | 0.344533i | \(0.111963\pi\) |
−0.171013 | + | 0.985269i | \(0.554704\pi\) | |||||||
\(60\) | 1.75410 | − | 3.03819i | 0.226453 | − | 0.392228i | ||||
\(61\) | 9.35561 | 1.19786 | 0.598932 | − | 0.800800i | \(-0.295592\pi\) | ||||
0.598932 | + | 0.800800i | \(0.295592\pi\) | |||||||
\(62\) | 4.46035 | + | 7.72555i | 0.566464 | + | 0.981145i | ||||
\(63\) | 1.12588 | + | 2.39424i | 0.141848 | + | 0.301646i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.3089 | + | 5.66624i | −1.40269 | + | 0.702811i | ||||
\(66\) | 3.20391 | − | 5.54934i | 0.394374 | − | 0.683076i | ||||
\(67\) | 7.28922 | 0.890520 | 0.445260 | − | 0.895401i | \(-0.353111\pi\) | ||||
0.445260 | + | 0.895401i | \(0.353111\pi\) | |||||||
\(68\) | −2.33890 | + | 4.05110i | −0.283634 | + | 0.491268i | ||||
\(69\) | 1.08480 | − | 1.87894i | 0.130595 | − | 0.226197i | ||||
\(70\) | −3.94981 | − | 8.39947i | −0.472093 | − | 1.00393i | ||||
\(71\) | 2.79339 | − | 4.83829i | 0.331514 | − | 0.574199i | −0.651295 | − | 0.758825i | \(-0.725774\pi\) |
0.982809 | + | 0.184625i | \(0.0591072\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.23175 | − | 7.32961i | 0.495289 | − | 0.857866i | −0.504696 | − | 0.863297i | \(-0.668395\pi\) |
0.999985 | + | 0.00543110i | \(0.00172878\pi\) | |||||||
\(74\) | −1.94981 | − | 3.37717i | −0.226661 | − | 0.392588i | ||||
\(75\) | −3.65372 | + | 6.32843i | −0.421896 | + | 0.730745i | ||||
\(76\) | −2.61911 | − | 4.53642i | −0.300432 | − | 0.520364i | ||||
\(77\) | −7.21444 | − | 15.3419i | −0.822162 | − | 1.74837i | ||||
\(78\) | −3.01053 | − | 1.98411i | −0.340876 | − | 0.224656i | ||||
\(79\) | 0.893764 | + | 1.54804i | 0.100556 | + | 0.174169i | 0.911914 | − | 0.410381i | \(-0.134604\pi\) |
−0.811358 | + | 0.584550i | \(0.801271\pi\) | |||||||
\(80\) | −3.50820 | −0.392228 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.1860 | −1.12486 | ||||||||
\(83\) | −2.59218 | −0.284529 | −0.142264 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142264 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(84\) | 1.51053 | − | 2.17216i | 0.164813 | − | 0.237002i | ||||
\(85\) | 8.20533 | − | 14.2121i | 0.889993 | − | 1.54151i | ||||
\(86\) | −1.19338 | − | 2.06699i | −0.128685 | − | 0.222889i | ||||
\(87\) | −1.23033 | − | 2.13099i | −0.131905 | − | 0.228467i | ||||
\(88\) | −6.40782 | −0.683076 | ||||||||
\(89\) | −3.50376 | + | 6.06869i | −0.371398 | + | 0.643280i | −0.989781 | − | 0.142597i | \(-0.954455\pi\) |
0.618383 | + | 0.785877i | \(0.287788\pi\) | |||||||
\(90\) | −3.50820 | −0.369796 | ||||||||
\(91\) | −8.85732 | + | 3.54230i | −0.928499 | + | 0.371334i | ||||
\(92\) | −2.16961 | −0.226197 | ||||||||
\(93\) | 4.46035 | − | 7.72555i | 0.462516 | − | 0.801102i | ||||
\(94\) | 4.88140 | 0.503478 | ||||||||
\(95\) | 9.18834 | + | 15.9147i | 0.942704 | + | 1.63281i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −4.92513 | + | 8.53057i | −0.500071 | + | 0.866149i | 0.499929 | + | 0.866066i | \(0.333359\pi\) |
−1.00000 | 8.21569e-5i | \(0.999974\pi\) | ||||||||
\(98\) | −2.43658 | − | 6.56225i | −0.246132 | − | 0.662887i | ||||
\(99\) | −6.40782 | −0.644010 | ||||||||
\(100\) | 7.30745 | 0.730745 | ||||||||
\(101\) | 13.8203 | 1.37517 | 0.687586 | − | 0.726103i | \(-0.258670\pi\) | ||||
0.687586 | + | 0.726103i | \(0.258670\pi\) | |||||||
\(102\) | 4.67781 | 0.463172 | ||||||||
\(103\) | −6.56658 | − | 11.3737i | −0.647025 | − | 1.12068i | −0.983830 | − | 0.179105i | \(-0.942680\pi\) |
0.336805 | − | 0.941574i | \(-0.390654\pi\) | |||||||
\(104\) | −0.213022 | + | 3.59925i | −0.0208885 | + | 0.352936i | ||||
\(105\) | −5.29925 | + | 7.62037i | −0.517154 | + | 0.743672i | ||||
\(106\) | −1.05395 | − | 1.82549i | −0.102368 | − | 0.177307i | ||||
\(107\) | 4.88232 | − | 8.45642i | 0.471991 | − | 0.817513i | −0.527495 | − | 0.849558i | \(-0.676869\pi\) |
0.999486 | + | 0.0320452i | \(0.0102020\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 1.14786 | − | 1.98816i | 0.109945 | − | 0.190431i | −0.805803 | − | 0.592184i | \(-0.798266\pi\) |
0.915748 | + | 0.401753i | \(0.131599\pi\) | |||||||
\(110\) | 22.4799 | 2.14337 | ||||||||
\(111\) | −1.94981 | + | 3.37717i | −0.185068 | + | 0.320547i | ||||
\(112\) | −2.63641 | − | 0.222079i | −0.249118 | − | 0.0209845i | ||||
\(113\) | 1.96268 | − | 3.39947i | 0.184634 | − | 0.319795i | −0.758819 | − | 0.651301i | \(-0.774223\pi\) |
0.943453 | + | 0.331506i | \(0.107557\pi\) | |||||||
\(114\) | −2.61911 | + | 4.53642i | −0.245302 | + | 0.424875i | ||||
\(115\) | 7.61142 | 0.709768 | ||||||||
\(116\) | −1.23033 | + | 2.13099i | −0.114233 | + | 0.197858i | ||||
\(117\) | −0.213022 | + | 3.59925i | −0.0196939 | + | 0.332751i | ||||
\(118\) | −11.7946 | −1.08578 | ||||||||
\(119\) | 7.06598 | − | 10.1610i | 0.647738 | − | 0.931453i | ||||
\(120\) | 1.75410 | + | 3.03819i | 0.160127 | + | 0.277347i | ||||
\(121\) | 30.0602 | 2.73274 | ||||||||
\(122\) | −4.67781 | + | 8.10220i | −0.423509 | + | 0.733539i | ||||
\(123\) | 5.09300 | + | 8.82134i | 0.459220 | + | 0.795393i | ||||
\(124\) | −8.92069 | −0.801102 | ||||||||
\(125\) | −8.09497 | −0.724036 | ||||||||
\(126\) | −2.63641 | − | 0.222079i | −0.234870 | − | 0.0197844i | ||||
\(127\) | 3.51196 | + | 6.08289i | 0.311636 | + | 0.539769i | 0.978717 | − | 0.205216i | \(-0.0657898\pi\) |
−0.667081 | + | 0.744985i | \(0.732457\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.19338 | + | 2.06699i | −0.105071 | + | 0.181988i | ||||
\(130\) | 0.747323 | − | 12.6269i | 0.0655446 | − | 1.10745i | ||||
\(131\) | −4.56251 | − | 7.90250i | −0.398628 | − | 0.690444i | 0.594929 | − | 0.803778i | \(-0.297180\pi\) |
−0.993557 | + | 0.113334i | \(0.963847\pi\) | |||||||
\(132\) | 3.20391 | + | 5.54934i | 0.278865 | + | 0.483008i | ||||
\(133\) | 5.89760 | + | 12.5415i | 0.511387 | + | 1.08749i | ||||
\(134\) | −3.64461 | + | 6.31265i | −0.314846 | + | 0.545330i | ||||
\(135\) | 1.75410 | + | 3.03819i | 0.150969 | + | 0.261486i | ||||
\(136\) | −2.33890 | − | 4.05110i | −0.200559 | − | 0.347379i | ||||
\(137\) | −7.53370 | − | 13.0488i | −0.643648 | − | 1.11483i | −0.984612 | − | 0.174754i | \(-0.944087\pi\) |
0.340964 | − | 0.940076i | \(-0.389246\pi\) | |||||||
\(138\) | 1.08480 | + | 1.87894i | 0.0923447 | + | 0.159946i | ||||
\(139\) | 7.02519 | − | 12.1680i | 0.595869 | − | 1.03208i | −0.397555 | − | 0.917578i | \(-0.630141\pi\) |
0.993424 | − | 0.114497i | \(-0.0365255\pi\) | |||||||
\(140\) | 9.24906 | + | 0.779098i | 0.781688 | + | 0.0658458i | ||||
\(141\) | −2.44070 | − | 4.22742i | −0.205544 | − | 0.356013i | ||||
\(142\) | 2.79339 | + | 4.83829i | 0.234416 | + | 0.406020i | ||||
\(143\) | 1.36501 | − | 23.0634i | 0.114148 | − | 1.92866i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.31624 | − | 7.47595i | 0.358444 | − | 0.620844i | ||||
\(146\) | 4.23175 | + | 7.32961i | 0.350222 | + | 0.606603i | ||||
\(147\) | −4.46478 | + | 5.39126i | −0.368249 | + | 0.444664i | ||||
\(148\) | 3.89962 | 0.320547 | ||||||||
\(149\) | 1.22934 | 0.100711 | 0.0503555 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503555 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(150\) | −3.65372 | − | 6.32843i | −0.298325 | − | 0.516714i | ||||
\(151\) | 8.17245 | − | 14.1551i | 0.665065 | − | 1.15193i | −0.314203 | − | 0.949356i | \(-0.601737\pi\) |
0.979268 | − | 0.202570i | \(-0.0649294\pi\) | |||||||
\(152\) | 5.23821 | 0.424875 | ||||||||
\(153\) | −2.33890 | − | 4.05110i | −0.189089 | − | 0.327512i | ||||
\(154\) | 16.8937 | + | 1.42304i | 1.36133 | + | 0.114672i | ||||
\(155\) | 31.2955 | 2.51372 | ||||||||
\(156\) | 3.22356 | − | 1.61514i | 0.258091 | − | 0.129315i | ||||
\(157\) | −7.98494 | + | 13.8303i | −0.637267 | + | 1.10378i | 0.348763 | + | 0.937211i | \(0.386602\pi\) |
−0.986030 | + | 0.166568i | \(0.946731\pi\) | |||||||
\(158\) | −1.78753 | −0.142208 | ||||||||
\(159\) | −1.05395 | + | 1.82549i | −0.0835834 | + | 0.144771i | ||||
\(160\) | 1.75410 | − | 3.03819i | 0.138674 | − | 0.240190i | ||||
\(161\) | 5.71999 | + | 0.481825i | 0.450798 | + | 0.0379731i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 7.78633 | 0.609872 | 0.304936 | − | 0.952373i | \(-0.401365\pi\) | ||||
0.304936 | + | 0.952373i | \(0.401365\pi\) | |||||||
\(164\) | 5.09300 | − | 8.82134i | 0.397697 | − | 0.688831i | ||||
\(165\) | −11.2399 | − | 19.4682i | −0.875029 | − | 1.51559i | ||||
\(166\) | 1.29609 | − | 2.24489i | 0.100596 | − | 0.174237i | ||||
\(167\) | 3.32333 | + | 5.75618i | 0.257167 | + | 0.445427i | 0.965482 | − | 0.260470i | \(-0.0838776\pi\) |
−0.708315 | + | 0.705897i | \(0.750544\pi\) | |||||||
\(168\) | 1.12588 | + | 2.39424i | 0.0868636 | + | 0.184720i | ||||
\(169\) | −12.9092 | − | 1.53344i | −0.993019 | − | 0.117957i | ||||
\(170\) | 8.20533 | + | 14.2121i | 0.629320 | + | 1.09001i | ||||
\(171\) | 5.23821 | 0.400576 | ||||||||
\(172\) | 2.38675 | 0.181988 | ||||||||
\(173\) | −14.6067 | −1.11053 | −0.555265 | − | 0.831673i | \(-0.687383\pi\) | ||||
−0.555265 | + | 0.831673i | \(0.687383\pi\) | |||||||
\(174\) | 2.46066 | 0.186542 | ||||||||
\(175\) | −19.2655 | − | 1.62283i | −1.45633 | − | 0.122675i | ||||
\(176\) | 3.20391 | − | 5.54934i | 0.241504 | − | 0.418297i | ||||
\(177\) | 5.89729 | + | 10.2144i | 0.443267 | + | 0.767761i | ||||
\(178\) | −3.50376 | − | 6.06869i | −0.262618 | − | 0.454867i | ||||
\(179\) | −14.1285 | −1.05601 | −0.528006 | − | 0.849240i | \(-0.677060\pi\) | ||||
−0.528006 | + | 0.849240i | \(0.677060\pi\) | |||||||
\(180\) | 1.75410 | − | 3.03819i | 0.130743 | − | 0.226453i | ||||
\(181\) | −13.6453 | −1.01425 | −0.507124 | − | 0.861873i | \(-0.669291\pi\) | ||||
−0.507124 | + | 0.861873i | \(0.669291\pi\) | |||||||
\(182\) | 1.36093 | − | 9.44181i | 0.100879 | − | 0.699874i | ||||
\(183\) | 9.35561 | 0.691587 | ||||||||
\(184\) | 1.08480 | − | 1.87894i | 0.0799729 | − | 0.138517i | ||||
\(185\) | −13.6807 | −1.00582 | ||||||||
\(186\) | 4.46035 | + | 7.72555i | 0.327048 | + | 0.566464i | ||||
\(187\) | 14.9873 | + | 25.9587i | 1.09598 | + | 1.89829i | ||||
\(188\) | −2.44070 | + | 4.22742i | −0.178006 | + | 0.308316i | ||||
\(189\) | 1.12588 | + | 2.39424i | 0.0818958 | + | 0.174155i | ||||
\(190\) | −18.3767 | −1.33318 | ||||||||
\(191\) | −2.43145 | −0.175933 | −0.0879666 | − | 0.996123i | \(-0.528037\pi\) | ||||
−0.0879666 | + | 0.996123i | \(0.528037\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.51754 | 0.253198 | 0.126599 | − | 0.991954i | \(-0.459594\pi\) | ||||
0.126599 | + | 0.991954i | \(0.459594\pi\) | |||||||
\(194\) | −4.92513 | − | 8.53057i | −0.353604 | − | 0.612460i | ||||
\(195\) | −11.3089 | + | 5.66624i | −0.809845 | + | 0.405768i | ||||
\(196\) | 6.90136 | + | 1.17099i | 0.492954 | + | 0.0836418i | ||||
\(197\) | 1.15702 | + | 2.00402i | 0.0824345 | + | 0.142781i | 0.904295 | − | 0.426908i | \(-0.140397\pi\) |
−0.821861 | + | 0.569689i | \(0.807064\pi\) | |||||||
\(198\) | 3.20391 | − | 5.54934i | 0.227692 | − | 0.394374i | ||||
\(199\) | −2.84733 | − | 4.93173i | −0.201842 | − | 0.349601i | 0.747280 | − | 0.664509i | \(-0.231359\pi\) |
−0.949122 | + | 0.314909i | \(0.898026\pi\) | |||||||
\(200\) | −3.65372 | + | 6.32843i | −0.258357 | + | 0.447488i | ||||
\(201\) | 7.28922 | 0.514142 | ||||||||
\(202\) | −6.91016 | + | 11.9687i | −0.486197 | + | 0.842118i | ||||
\(203\) | 3.71691 | − | 5.34495i | 0.260876 | − | 0.375142i | ||||
\(204\) | −2.33890 | + | 4.05110i | −0.163756 | + | 0.283634i | ||||
\(205\) | −17.8673 | + | 30.9470i | −1.24790 | + | 2.16143i | ||||
\(206\) | 13.1332 | 0.915031 | ||||||||
\(207\) | 1.08480 | − | 1.87894i | 0.0753991 | − | 0.130595i | ||||
\(208\) | −3.01053 | − | 1.98411i | −0.208743 | − | 0.137573i | ||||
\(209\) | −33.5655 | −2.32178 | ||||||||
\(210\) | −3.94981 | − | 8.39947i | −0.272563 | − | 0.579619i | ||||
\(211\) | 0.291966 | + | 0.505700i | 0.0200998 | + | 0.0348139i | 0.875900 | − | 0.482492i | \(-0.160268\pi\) |
−0.855801 | + | 0.517306i | \(0.826935\pi\) | |||||||
\(212\) | 2.10789 | 0.144771 | ||||||||
\(213\) | 2.79339 | − | 4.83829i | 0.191400 | − | 0.331514i | ||||
\(214\) | 4.88232 | + | 8.45642i | 0.333748 | + | 0.578069i | ||||
\(215\) | −8.37320 | −0.571048 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 23.5186 | + | 1.98110i | 1.59655 | + | 0.134486i | ||||
\(218\) | 1.14786 | + | 1.98816i | 0.0777430 | + | 0.134655i | ||||
\(219\) | 4.23175 | − | 7.32961i | 0.285955 | − | 0.495289i | ||||
\(220\) | −11.2399 | + | 19.4682i | −0.757797 | + | 1.31254i | ||||
\(221\) | 15.0792 | − | 7.55533i | 1.01433 | − | 0.508227i | ||||
\(222\) | −1.94981 | − | 3.37717i | −0.130863 | − | 0.226661i | ||||
\(223\) | −7.25749 | − | 12.5703i | −0.485998 | − | 0.841773i | 0.513873 | − | 0.857866i | \(-0.328210\pi\) |
−0.999870 | + | 0.0160938i | \(0.994877\pi\) | |||||||
\(224\) | 1.51053 | − | 2.17216i | 0.100927 | − | 0.145134i | ||||
\(225\) | −3.65372 | + | 6.32843i | −0.243582 | + | 0.421896i | ||||
\(226\) | 1.96268 | + | 3.39947i | 0.130556 | + | 0.226129i | ||||
\(227\) | −10.1232 | − | 17.5339i | −0.671899 | − | 1.16376i | −0.977365 | − | 0.211560i | \(-0.932146\pi\) |
0.305466 | − | 0.952203i | \(-0.401188\pi\) | |||||||
\(228\) | −2.61911 | − | 4.53642i | −0.173455 | − | 0.300432i | ||||
\(229\) | −0.668929 | − | 1.15862i | −0.0442041 | − | 0.0765637i | 0.843077 | − | 0.537793i | \(-0.180742\pi\) |
−0.887281 | + | 0.461229i | \(0.847409\pi\) | |||||||
\(230\) | −3.80571 | + | 6.59168i | −0.250941 | + | 0.434643i | ||||
\(231\) | −7.21444 | − | 15.3419i | −0.474676 | − | 1.00942i | ||||
\(232\) | −1.23033 | − | 2.13099i | −0.0807752 | − | 0.139907i | ||||
\(233\) | 6.97568 | + | 12.0822i | 0.456992 | + | 0.791534i | 0.998800 | − | 0.0489686i | \(-0.0155934\pi\) |
−0.541808 | + | 0.840502i | \(0.682260\pi\) | |||||||
\(234\) | −3.01053 | − | 1.98411i | −0.196805 | − | 0.129705i | ||||
\(235\) | 8.56246 | − | 14.8306i | 0.558553 | − | 0.967443i | ||||
\(236\) | 5.89729 | − | 10.2144i | 0.383881 | − | 0.664901i | ||||
\(237\) | 0.893764 | + | 1.54804i | 0.0580562 | + | 0.100556i | ||||
\(238\) | 5.26665 | + | 11.1998i | 0.341386 | + | 0.725975i | ||||
\(239\) | 9.05495 | 0.585716 | 0.292858 | − | 0.956156i | \(-0.405394\pi\) | ||||
0.292858 | + | 0.956156i | \(0.405394\pi\) | |||||||
\(240\) | −3.50820 | −0.226453 | ||||||||
\(241\) | −10.0551 | − | 17.4159i | −0.647705 | − | 1.12186i | −0.983670 | − | 0.179983i | \(-0.942396\pi\) |
0.335965 | − | 0.941875i | \(-0.390938\pi\) | |||||||
\(242\) | −15.0301 | + | 26.0329i | −0.966171 | + | 1.67346i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.67781 | − | 8.10220i | −0.299466 | − | 0.518690i | ||||
\(245\) | −24.2113 | − | 4.10805i | −1.54681 | − | 0.262454i | ||||
\(246\) | −10.1860 | −0.649436 | ||||||||
\(247\) | −1.11585 | + | 18.8536i | −0.0710001 | + | 1.19963i | ||||
\(248\) | 4.46035 | − | 7.72555i | 0.283232 | − | 0.490573i | ||||
\(249\) | −2.59218 | −0.164273 | ||||||||
\(250\) | 4.04749 | − | 7.01045i | 0.255986 | − | 0.443380i | ||||
\(251\) | 4.09035 | − | 7.08469i | 0.258181 | − | 0.447182i | −0.707574 | − | 0.706639i | \(-0.750210\pi\) |
0.965755 | + | 0.259457i | \(0.0835437\pi\) | |||||||
\(252\) | 1.51053 | − | 2.17216i | 0.0951547 | − | 0.136833i | ||||
\(253\) | −6.95123 | + | 12.0399i | −0.437020 | + | 0.756941i | ||||
\(254\) | −7.02391 | −0.440719 | ||||||||
\(255\) | 8.20533 | − | 14.2121i | 0.513838 | − | 0.889993i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.87696 | + | 8.44715i | −0.304217 | + | 0.526919i | −0.977087 | − | 0.212842i | \(-0.931728\pi\) |
0.672870 | + | 0.739761i | \(0.265061\pi\) | |||||||
\(258\) | −1.19338 | − | 2.06699i | −0.0742964 | − | 0.128685i | ||||
\(259\) | −10.2810 | − | 0.866025i | −0.638832 | − | 0.0538122i | ||||
\(260\) | 10.5615 | + | 6.96065i | 0.654999 | + | 0.431681i | ||||
\(261\) | −1.23033 | − | 2.13099i | −0.0761555 | − | 0.131905i | ||||
\(262\) | 9.12502 | 0.563745 | ||||||||
\(263\) | −2.94716 | −0.181730 | −0.0908648 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908648 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(264\) | −6.40782 | −0.394374 | ||||||||
\(265\) | −7.39490 | −0.454265 | ||||||||
\(266\) | −13.8101 | − | 1.16330i | −0.846751 | − | 0.0713264i | ||||
\(267\) | −3.50376 | + | 6.06869i | −0.214427 | + | 0.371398i | ||||
\(268\) | −3.64461 | − | 6.31265i | −0.222630 | − | 0.385607i | ||||
\(269\) | 11.9676 | + | 20.7285i | 0.729679 | + | 1.26384i | 0.957019 | + | 0.290026i | \(0.0936639\pi\) |
−0.227340 | + | 0.973816i | \(0.573003\pi\) | |||||||
\(270\) | −3.50820 | −0.213502 | ||||||||
\(271\) | −9.68335 | + | 16.7721i | −0.588222 | + | 1.01883i | 0.406244 | + | 0.913765i | \(0.366838\pi\) |
−0.994465 | + | 0.105065i | \(0.966495\pi\) | |||||||
\(272\) | 4.67781 | 0.283634 | ||||||||
\(273\) | −8.85732 | + | 3.54230i | −0.536069 | + | 0.214390i | ||||
\(274\) | 15.0674 | 0.910255 | ||||||||
\(275\) | 23.4124 | − | 40.5515i | 1.41182 | − | 2.44535i | ||||
\(276\) | −2.16961 | −0.130595 | ||||||||
\(277\) | −1.21710 | − | 2.10807i | −0.0731282 | − | 0.126662i | 0.827143 | − | 0.561992i | \(-0.189965\pi\) |
−0.900271 | + | 0.435330i | \(0.856632\pi\) | |||||||
\(278\) | 7.02519 | + | 12.1680i | 0.421343 | + | 0.729787i | ||||
\(279\) | 4.46035 | − | 7.72555i | 0.267034 | − | 0.462516i | ||||
\(280\) | −5.29925 | + | 7.62037i | −0.316691 | + | 0.455404i | ||||
\(281\) | −2.80329 | −0.167230 | −0.0836152 | − | 0.996498i | \(-0.526647\pi\) | ||||
−0.0836152 | + | 0.996498i | \(0.526647\pi\) | |||||||
\(282\) | 4.88140 | 0.290683 | ||||||||
\(283\) | −16.9541 | −1.00782 | −0.503909 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503909 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(284\) | −5.58678 | −0.331514 | ||||||||
\(285\) | 9.18834 | + | 15.9147i | 0.544270 | + | 0.942704i | ||||
\(286\) | 19.2910 | + | 12.7138i | 1.14070 | + | 0.751784i | ||||
\(287\) | −15.3863 | + | 22.1257i | −0.908224 | + | 1.30604i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −2.44094 | + | 4.22782i | −0.143584 | + | 0.248696i | ||||
\(290\) | 4.31624 | + | 7.47595i | 0.253458 | + | 0.439003i | ||||
\(291\) | −4.92513 | + | 8.53057i | −0.288716 | + | 0.500071i | ||||
\(292\) | −8.46350 | −0.495289 | ||||||||
\(293\) | 2.84568 | − | 4.92886i | 0.166246 | − | 0.287947i | −0.770851 | − | 0.637016i | \(-0.780169\pi\) |
0.937097 | + | 0.349069i | \(0.113502\pi\) | |||||||
\(294\) | −2.43658 | − | 6.56225i | −0.142104 | − | 0.382718i | ||||
\(295\) | −20.6888 | + | 35.8341i | −1.20455 | + | 2.08634i | ||||
\(296\) | −1.94981 | + | 3.37717i | −0.113331 | + | 0.196294i | ||||
\(297\) | −6.40782 | −0.371820 | ||||||||
\(298\) | −0.614668 | + | 1.06464i | −0.0356067 | + | 0.0616727i | ||||
\(299\) | 6.53168 | + | 4.30474i | 0.377737 | + | 0.248950i | ||||
\(300\) | 7.30745 | 0.421896 | ||||||||
\(301\) | −6.29247 | − | 0.530048i | −0.362692 | − | 0.0305515i | ||||
\(302\) | 8.17245 | + | 14.1551i | 0.470272 | + | 0.814535i | ||||
\(303\) | 13.8203 | 0.793956 | ||||||||
\(304\) | −2.61911 | + | 4.53642i | −0.150216 | + | 0.260182i | ||||
\(305\) | 16.4107 | + | 28.4241i | 0.939672 | + | 1.62756i | ||||
\(306\) | 4.67781 | 0.267412 | ||||||||
\(307\) | 3.48603 | 0.198958 | 0.0994791 | − | 0.995040i | \(-0.468282\pi\) | ||||
0.0994791 | + | 0.995040i | \(0.468282\pi\) | |||||||
\(308\) | −9.67923 | + | 13.9188i | −0.551525 | + | 0.793099i | ||||
\(309\) | −6.56658 | − | 11.3737i | −0.373560 | − | 0.647025i | ||||
\(310\) | −15.6478 | + | 27.1027i | −0.888734 | + | 1.53933i | ||||
\(311\) | 12.0016 | − | 20.7873i | 0.680546 | − | 1.17874i | −0.294268 | − | 0.955723i | \(-0.595076\pi\) |
0.974814 | − | 0.223018i | \(-0.0715908\pi\) | |||||||
\(312\) | −0.213022 | + | 3.59925i | −0.0120600 | + | 0.203768i | ||||
\(313\) | −8.77758 | − | 15.2032i | −0.496138 | − | 0.859337i | 0.503852 | − | 0.863790i | \(-0.331916\pi\) |
−0.999990 | + | 0.00445337i | \(0.998582\pi\) | |||||||
\(314\) | −7.98494 | − | 13.8303i | −0.450616 | − | 0.780490i | ||||
\(315\) | −5.29925 | + | 7.62037i | −0.298579 | + | 0.429359i | ||||
\(316\) | 0.893764 | − | 1.54804i | 0.0502781 | − | 0.0870843i | ||||
\(317\) | −1.42018 | − | 2.45983i | −0.0797655 | − | 0.138158i | 0.823383 | − | 0.567486i | \(-0.192084\pi\) |
−0.903149 | + | 0.429328i | \(0.858750\pi\) | |||||||
\(318\) | −1.05395 | − | 1.82549i | −0.0591024 | − | 0.102368i | ||||
\(319\) | 7.88374 | + | 13.6550i | 0.441405 | + | 0.764535i | ||||
\(320\) | 1.75410 | + | 3.03819i | 0.0980571 | + | 0.169840i | ||||
\(321\) | 4.88232 | − | 8.45642i | 0.272504 | − | 0.471991i | ||||
\(322\) | −3.27727 | + | 4.71274i | −0.182635 | + | 0.262631i | ||||
\(323\) | −12.2517 | − | 21.2205i | −0.681701 | − | 1.18074i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −21.9993 | − | 14.4988i | −1.22030 | − | 0.804247i | ||||
\(326\) | −3.89316 | + | 6.74316i | −0.215622 | + | 0.373469i | ||||
\(327\) | 1.14786 | − | 1.98816i | 0.0634769 | − | 0.109945i | ||||
\(328\) | 5.09300 | + | 8.82134i | 0.281214 | + | 0.487077i | ||||
\(329\) | 7.37352 | − | 10.6032i | 0.406515 | − | 0.584573i | ||||
\(330\) | 22.4799 | 1.23748 | ||||||||
\(331\) | −18.8749 | −1.03746 | −0.518729 | − | 0.854939i | \(-0.673595\pi\) | ||||
−0.518729 | + | 0.854939i | \(0.673595\pi\) | |||||||
\(332\) | 1.29609 | + | 2.24489i | 0.0711321 | + | 0.123204i | ||||
\(333\) | −1.94981 | + | 3.37717i | −0.106849 | + | 0.185068i | ||||
\(334\) | −6.64666 | −0.363689 | ||||||||
\(335\) | 12.7860 | + | 22.1460i | 0.698575 | + | 1.20997i | ||||
\(336\) | −2.63641 | − | 0.222079i | −0.143828 | − | 0.0121154i | ||||
\(337\) | 10.9560 | 0.596813 | 0.298407 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298407 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(338\) | 7.78262 | − | 10.4130i | 0.423319 | − | 0.566393i | ||||
\(339\) | 1.96268 | − | 3.39947i | 0.106598 | − | 0.184634i | ||||
\(340\) | −16.4107 | −0.889993 | ||||||||
\(341\) | −28.5811 | + | 49.5039i | −1.54775 | + | 2.68079i | ||||
\(342\) | −2.61911 | + | 4.53642i | −0.141625 | + | 0.245302i | ||||
\(343\) | −17.9348 | − | 4.61985i | −0.968388 | − | 0.249449i | ||||
\(344\) | −1.19338 | + | 2.06699i | −0.0643426 | + | 0.111445i | ||||
\(345\) | 7.61142 | 0.409785 | ||||||||
\(346\) | 7.30337 | − | 12.6498i | 0.392632 | − | 0.680058i | ||||
\(347\) | 16.0515 | + | 27.8020i | 0.861688 | + | 1.49249i | 0.870299 | + | 0.492524i | \(0.163926\pi\) |
−0.00861062 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(348\) | −1.23033 | + | 2.13099i | −0.0659526 | + | 0.114233i | ||||
\(349\) | −9.04373 | − | 15.6642i | −0.484100 | − | 0.838485i | 0.515734 | − | 0.856749i | \(-0.327519\pi\) |
−0.999833 | + | 0.0182638i | \(0.994186\pi\) | |||||||
\(350\) | 11.0381 | − | 15.8730i | 0.590013 | − | 0.848445i | ||||
\(351\) | −0.213022 | + | 3.59925i | −0.0113703 | + | 0.192114i | ||||
\(352\) | 3.20391 | + | 5.54934i | 0.170769 | + | 0.295781i | ||||
\(353\) | −27.4645 | −1.46179 | −0.730894 | − | 0.682491i | \(-0.760897\pi\) | ||||
−0.730894 | + | 0.682491i | \(0.760897\pi\) | |||||||
\(354\) | −11.7946 | −0.626875 | ||||||||
\(355\) | 19.5995 | 1.04023 | ||||||||
\(356\) | 7.00752 | 0.371398 | ||||||||
\(357\) | 7.06598 | − | 10.1610i | 0.373971 | − | 0.537775i | ||||
\(358\) | 7.06425 | − | 12.2356i | 0.373357 | − | 0.646673i | ||||
\(359\) | −10.8390 | − | 18.7738i | −0.572063 | − | 0.990842i | −0.996354 | − | 0.0853162i | \(-0.972810\pi\) |
0.424291 | − | 0.905526i | \(-0.360523\pi\) | |||||||
\(360\) | 1.75410 | + | 3.03819i | 0.0924491 | + | 0.160127i | ||||
\(361\) | 8.43886 | 0.444151 | ||||||||
\(362\) | 6.82265 | − | 11.8172i | 0.358591 | − | 0.621097i | ||||
\(363\) | 30.0602 | 1.57775 | ||||||||
\(364\) | 7.49638 | + | 5.89951i | 0.392917 | + | 0.309218i | ||||
\(365\) | 29.6916 | 1.55413 | ||||||||
\(366\) | −4.67781 | + | 8.10220i | −0.244513 | + | 0.423509i | ||||
\(367\) | 15.3217 | 0.799788 | 0.399894 | − | 0.916561i | \(-0.369047\pi\) | ||||
0.399894 | + | 0.916561i | \(0.369047\pi\) | |||||||
\(368\) | 1.08480 | + | 1.87894i | 0.0565494 | + | 0.0979463i | ||||
\(369\) | 5.09300 | + | 8.82134i | 0.265131 | + | 0.459220i | ||||
\(370\) | 6.84033 | − | 11.8478i | 0.355612 | − | 0.615937i | ||||
\(371\) | −5.55728 | − | 0.468119i | −0.288520 | − | 0.0243035i | ||||
\(372\) | −8.92069 | −0.462516 | ||||||||
\(373\) | −33.3585 | −1.72724 | −0.863618 | − | 0.504147i | \(-0.831807\pi\) | ||||
−0.863618 | + | 0.504147i | \(0.831807\pi\) | |||||||
\(374\) | −29.9745 | −1.54995 | ||||||||
\(375\) | −8.09497 | −0.418023 | ||||||||
\(376\) | −2.44070 | − | 4.22742i | −0.125870 | − | 0.218012i | ||||
\(377\) | 7.93208 | − | 3.97432i | 0.408523 | − | 0.204688i | ||||
\(378\) | −2.63641 | − | 0.222079i | −0.135603 | − | 0.0114225i | ||||
\(379\) | 8.43868 | + | 14.6162i | 0.433466 | + | 0.750785i | 0.997169 | − | 0.0751926i | \(-0.0239571\pi\) |
−0.563703 | + | 0.825977i | \(0.690624\pi\) | |||||||
\(380\) | 9.18834 | − | 15.9147i | 0.471352 | − | 0.816405i | ||||
\(381\) | 3.51196 | + | 6.08289i | 0.179923 | + | 0.311636i | ||||
\(382\) | 1.21572 | − | 2.10569i | 0.0622018 | − | 0.107737i | ||||
\(383\) | 21.5866 | 1.10302 | 0.551512 | − | 0.834167i | \(-0.314051\pi\) | ||||
0.551512 | + | 0.834167i | \(0.314051\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 33.9566 | − | 48.8300i | 1.73059 | − | 2.48861i | ||||
\(386\) | −1.75877 | + | 3.04628i | −0.0895191 | + | 0.155052i | ||||
\(387\) | −1.19338 | + | 2.06699i | −0.0606628 | + | 0.105071i | ||||
\(388\) | 9.85026 | 0.500071 | ||||||||
\(389\) | 8.68908 | − | 15.0499i | 0.440554 | − | 0.763062i | −0.557177 | − | 0.830394i | \(-0.688115\pi\) |
0.997731 | + | 0.0673322i | \(0.0214487\pi\) | |||||||
\(390\) | 0.747323 | − | 12.6269i | 0.0378422 | − | 0.639387i | ||||
\(391\) | −10.1490 | −0.513258 | ||||||||
\(392\) | −4.46478 | + | 5.39126i | −0.225506 | + | 0.272300i | ||||
\(393\) | −4.56251 | − | 7.90250i | −0.230148 | − | 0.398628i | ||||
\(394\) | −2.31405 | −0.116580 | ||||||||
\(395\) | −3.13550 | + | 5.43084i | −0.157764 | + | 0.273255i | ||||
\(396\) | 3.20391 | + | 5.54934i | 0.161003 | + | 0.278865i | ||||
\(397\) | 5.87435 | 0.294825 | 0.147413 | − | 0.989075i | \(-0.452905\pi\) | ||||
0.147413 | + | 0.989075i | \(0.452905\pi\) | |||||||
\(398\) | 5.69467 | 0.285448 | ||||||||
\(399\) | 5.89760 | + | 12.5415i | 0.295249 | + | 0.627863i | ||||
\(400\) | −3.65372 | − | 6.32843i | −0.182686 | − | 0.316422i | ||||
\(401\) | 6.98855 | − | 12.1045i | 0.348992 | − | 0.604471i | −0.637079 | − | 0.770799i | \(-0.719857\pi\) |
0.986071 | + | 0.166327i | \(0.0531908\pi\) | |||||||
\(402\) | −3.64461 | + | 6.31265i | −0.181777 | + | 0.314846i | ||||
\(403\) | 26.8560 | + | 17.6996i | 1.33779 | + | 0.881681i | ||||
\(404\) | −6.91016 | − | 11.9687i | −0.343793 | − | 0.595467i | ||||
\(405\) | 1.75410 | + | 3.03819i | 0.0871619 | + | 0.150969i | ||||
\(406\) | 2.77041 | + | 5.89142i | 0.137493 | + | 0.292386i | ||||
\(407\) | 12.4940 | − | 21.6403i | 0.619307 | − | 1.07267i | ||||
\(408\) | −2.33890 | − | 4.05110i | −0.115793 | − | 0.200559i | ||||
\(409\) | 18.7448 | + | 32.4670i | 0.926873 | + | 1.60539i | 0.788521 | + | 0.615008i | \(0.210847\pi\) |
0.138352 | + | 0.990383i | \(0.455819\pi\) | |||||||
\(410\) | −17.8673 | − | 30.9470i | −0.882401 | − | 1.52836i | ||||
\(411\) | −7.53370 | − | 13.0488i | −0.371610 | − | 0.643648i | ||||
\(412\) | −6.56658 | + | 11.3737i | −0.323512 | + | 0.560340i | ||||
\(413\) | −17.8161 | + | 25.6197i | −0.876673 | + | 1.26066i | ||||
\(414\) | 1.08480 | + | 1.87894i | 0.0533152 | + | 0.0923447i | ||||
\(415\) | −4.54694 | − | 7.87553i | −0.223200 | − | 0.386594i | ||||
\(416\) | 3.22356 | − | 1.61514i | 0.158048 | − | 0.0791889i | ||||
\(417\) | 7.02519 | − | 12.1680i | 0.344025 | − | 0.595869i | ||||
\(418\) | 16.7828 | − | 29.0686i | 0.820872 | − | 1.42179i | ||||
\(419\) | −16.9548 | − | 29.3665i | −0.828294 | − | 1.43465i | −0.899375 | − | 0.437177i | \(-0.855978\pi\) |
0.0710814 | − | 0.997471i | \(-0.477355\pi\) | |||||||
\(420\) | 9.24906 | + | 0.779098i | 0.451308 | + | 0.0380161i | ||||
\(421\) | −10.5503 | −0.514192 | −0.257096 | − | 0.966386i | \(-0.582766\pi\) | ||||
−0.257096 | + | 0.966386i | \(0.582766\pi\) | |||||||
\(422\) | −0.583933 | −0.0284254 | ||||||||
\(423\) | −2.44070 | − | 4.22742i | −0.118671 | − | 0.205544i | ||||
\(424\) | −1.05395 | + | 1.82549i | −0.0511842 | + | 0.0886536i | ||||
\(425\) | 34.1828 | 1.65811 | ||||||||
\(426\) | 2.79339 | + | 4.83829i | 0.135340 | + | 0.234416i | ||||
\(427\) | 10.5333 | + | 22.3996i | 0.509742 | + | 1.08399i | ||||
\(428\) | −9.76463 | −0.471991 | ||||||||
\(429\) | 1.36501 | − | 23.0634i | 0.0659032 | − | 1.11351i | ||||
\(430\) | 4.18660 | − | 7.25141i | 0.201896 | − | 0.349694i | ||||
\(431\) | −25.6086 | −1.23352 | −0.616761 | − | 0.787151i | \(-0.711555\pi\) | ||||
−0.616761 | + | 0.787151i | \(0.711555\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 3.68968 | − | 6.39071i | 0.177315 | − | 0.307118i | −0.763645 | − | 0.645636i | \(-0.776592\pi\) |
0.940960 | + | 0.338518i | \(0.109926\pi\) | |||||||
\(434\) | −13.4750 | + | 19.3772i | −0.646821 | + | 0.930135i | ||||
\(435\) | 4.31624 | − | 7.47595i | 0.206948 | − | 0.358444i | ||||
\(436\) | −2.29572 | −0.109945 | ||||||||
\(437\) | 5.68244 | − | 9.84227i | 0.271828 | − | 0.470820i | ||||
\(438\) | 4.23175 | + | 7.32961i | 0.202201 | + | 0.350222i | ||||
\(439\) | 11.5255 | − | 19.9628i | 0.550082 | − | 0.952771i | −0.448186 | − | 0.893941i | \(-0.647930\pi\) |
0.998268 | − | 0.0588301i | \(-0.0187370\pi\) | |||||||
\(440\) | −11.2399 | − | 19.4682i | −0.535844 | − | 0.928108i | ||||
\(441\) | −4.46478 | + | 5.39126i | −0.212609 | + | 0.256727i | ||||
\(442\) | −0.996476 | + | 16.8366i | −0.0473975 | + | 0.800836i | ||||
\(443\) | 9.05605 | + | 15.6855i | 0.430266 | + | 0.745242i | 0.996896 | − | 0.0787300i | \(-0.0250865\pi\) |
−0.566630 | + | 0.823972i | \(0.691753\pi\) | |||||||
\(444\) | 3.89962 | 0.185068 | ||||||||
\(445\) | −24.5837 | −1.16538 | ||||||||
\(446\) | 14.5150 | 0.687304 | ||||||||
\(447\) | 1.22934 | 0.0581456 | ||||||||
\(448\) | 1.12588 | + | 2.39424i | 0.0531929 | + | 0.113117i | ||||
\(449\) | −9.23084 | + | 15.9883i | −0.435630 | + | 0.754534i | −0.997347 | − | 0.0727961i | \(-0.976808\pi\) |
0.561717 | + | 0.827330i | \(0.310141\pi\) | |||||||
\(450\) | −3.65372 | − | 6.32843i | −0.172238 | − | 0.298325i | ||||
\(451\) | −32.6350 | − | 56.5256i | −1.53672 | − | 2.66168i | ||||
\(452\) | −3.92536 | −0.184634 | ||||||||
\(453\) | 8.17245 | − | 14.1551i | 0.383975 | − | 0.665065i | ||||
\(454\) | 20.2464 | 0.950209 | ||||||||
\(455\) | −26.2988 | − | 20.6966i | −1.23291 | − | 0.970274i | ||||
\(456\) | 5.23821 | 0.245302 | ||||||||
\(457\) | 8.90233 | − | 15.4193i | 0.416433 | − | 0.721283i | −0.579145 | − | 0.815225i | \(-0.696613\pi\) |
0.995578 | + | 0.0939414i | \(0.0299466\pi\) | |||||||
\(458\) | 1.33786 | 0.0625140 | ||||||||
\(459\) | −2.33890 | − | 4.05110i | −0.109171 | − | 0.189089i | ||||
\(460\) | −3.80571 | − | 6.59168i | −0.177442 | − | 0.307339i | ||||
\(461\) | −2.51030 | + | 4.34797i | −0.116916 | + | 0.202505i | −0.918544 | − | 0.395318i | \(-0.870634\pi\) |
0.801628 | + | 0.597823i | \(0.203968\pi\) | |||||||
\(462\) | 16.8937 | + | 1.42304i | 0.785965 | + | 0.0662060i | ||||
\(463\) | −25.0075 | −1.16220 | −0.581099 | − | 0.813833i | \(-0.697377\pi\) | ||||
−0.581099 | + | 0.813833i | \(0.697377\pi\) | |||||||
\(464\) | 2.46066 | 0.114233 | ||||||||
\(465\) | 31.2955 | 1.45130 | ||||||||
\(466\) | −13.9514 | −0.646284 | ||||||||
\(467\) | 12.9128 | + | 22.3656i | 0.597532 | + | 1.03496i | 0.993184 | + | 0.116555i | \(0.0371851\pi\) |
−0.395653 | + | 0.918400i | \(0.629482\pi\) | |||||||
\(468\) | 3.22356 | − | 1.61514i | 0.149009 | − | 0.0746601i | ||||
\(469\) | 8.20680 | + | 17.4522i | 0.378955 | + | 0.805866i | ||||
\(470\) | 8.56246 | + | 14.8306i | 0.394957 | + | 0.684085i | ||||
\(471\) | −7.98494 | + | 13.8303i | −0.367926 | + | 0.637267i | ||||
\(472\) | 5.89729 | + | 10.2144i | 0.271445 | + | 0.470156i | ||||
\(473\) | 7.64695 | − | 13.2449i | 0.351607 | − | 0.609001i | ||||
\(474\) | −1.78753 | −0.0821039 | ||||||||
\(475\) | −19.1390 | + | 33.1497i | −0.878156 | + | 1.52101i | ||||
\(476\) | −12.3326 | − | 1.03884i | −0.565265 | − | 0.0476153i | ||||
\(477\) | −1.05395 | + | 1.82549i | −0.0482569 | + | 0.0835834i | ||||
\(478\) | −4.52748 | + | 7.84182i | −0.207082 | + | 0.358677i | ||||
\(479\) | 23.1137 | 1.05609 | 0.528047 | − | 0.849215i | \(-0.322925\pi\) | ||||
0.528047 | + | 0.849215i | \(0.322925\pi\) | |||||||
\(480\) | 1.75410 | − | 3.03819i | 0.0800633 | − | 0.138674i | ||||
\(481\) | −11.7399 | − | 7.73728i | −0.535296 | − | 0.352790i | ||||
\(482\) | 20.1102 | 0.915993 | ||||||||
\(483\) | 5.71999 | + | 0.481825i | 0.260269 | + | 0.0219238i | ||||
\(484\) | −15.0301 | − | 26.0329i | −0.683186 | − | 1.18331i | ||||
\(485\) | −34.5566 | −1.56914 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 8.13701 | + | 14.0937i | 0.368723 | + | 0.638647i | 0.989366 | − | 0.145446i | \(-0.0464617\pi\) |
−0.620643 | + | 0.784093i | \(0.713128\pi\) | |||||||
\(488\) | 9.35561 | 0.423509 | ||||||||
\(489\) | 7.78633 | 0.352110 | ||||||||
\(490\) | 15.6633 | − | 18.9136i | 0.707598 | − | 0.854430i | ||||
\(491\) | −19.0299 | − | 32.9608i | −0.858809 | − | 1.48750i | −0.873065 | − | 0.487603i | \(-0.837871\pi\) |
0.0142561 | − | 0.999898i | \(-0.495462\pi\) | |||||||
\(492\) | 5.09300 | − | 8.82134i | 0.229610 | − | 0.397697i | ||||
\(493\) | −5.75525 | + | 9.96838i | −0.259203 | + | 0.448953i | ||||
\(494\) | −15.7698 | − | 10.3932i | −0.709517 | − | 0.467611i | ||||
\(495\) | −11.2399 | − | 19.4682i | −0.505198 | − | 0.875029i | ||||
\(496\) | 4.46035 | + | 7.72555i | 0.200275 | + | 0.346887i | ||||
\(497\) | 14.7291 | + | 1.24071i | 0.660689 | + | 0.0556533i | ||||
\(498\) | 1.29609 | − | 2.24489i | 0.0580792 | − | 0.100596i | ||||
\(499\) | 17.1178 | + | 29.6489i | 0.766297 | + | 1.32727i | 0.939558 | + | 0.342389i | \(0.111236\pi\) |
−0.173261 | + | 0.984876i | \(0.555430\pi\) | |||||||
\(500\) | 4.04749 | + | 7.01045i | 0.181009 | + | 0.313517i | ||||
\(501\) | 3.32333 | + | 5.75618i | 0.148476 | + | 0.257167i | ||||
\(502\) | 4.09035 | + | 7.08469i | 0.182561 | + | 0.316205i | ||||
\(503\) | −1.12053 | + | 1.94081i | −0.0499619 | + | 0.0865365i | −0.889925 | − | 0.456107i | \(-0.849243\pi\) |
0.839963 | + | 0.542644i | \(0.182577\pi\) | |||||||
\(504\) | 1.12588 | + | 2.39424i | 0.0501507 | + | 0.106648i | ||||
\(505\) | 24.2422 | + | 41.9887i | 1.07876 | + | 1.86847i | ||||
\(506\) | −6.95123 | − | 12.0399i | −0.309020 | − | 0.535238i | ||||
\(507\) | −12.9092 | − | 1.53344i | −0.573320 | − | 0.0681025i | ||||
\(508\) | 3.51196 | − | 6.08289i | 0.155818 | − | 0.269884i | ||||
\(509\) | 12.9164 | − | 22.3718i | 0.572509 | − | 0.991614i | −0.423799 | − | 0.905756i | \(-0.639304\pi\) |
0.996307 | − | 0.0858576i | \(-0.0273630\pi\) | |||||||
\(510\) | 8.20533 | + | 14.2121i | 0.363338 | + | 0.629320i | ||||
\(511\) | 22.3133 | + | 1.87957i | 0.987083 | + | 0.0831472i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.23821 | 0.231273 | ||||||||
\(514\) | −4.87696 | − | 8.44715i | −0.215114 | − | 0.372588i | ||||
\(515\) | 23.0369 | − | 39.9010i | 1.01513 | − | 1.75825i | ||||
\(516\) | 2.38675 | 0.105071 | ||||||||
\(517\) | 15.6396 | + | 27.0885i | 0.687828 | + | 1.19135i | ||||
\(518\) | 5.89051 | − | 8.47062i | 0.258814 | − | 0.372178i | ||||
\(519\) | −14.6067 | −0.641165 | ||||||||
\(520\) | −11.3089 | + | 5.66624i | −0.495927 | + | 0.248481i | ||||
\(521\) | −12.1715 | + | 21.0817i | −0.533245 | + | 0.923607i | 0.466001 | + | 0.884784i | \(0.345694\pi\) |
−0.999246 | + | 0.0388230i | \(0.987639\pi\) | |||||||
\(522\) | 2.46066 | 0.107700 | ||||||||
\(523\) | −4.44354 | + | 7.69644i | −0.194303 | + | 0.336542i | −0.946672 | − | 0.322200i | \(-0.895578\pi\) |
0.752369 | + | 0.658742i | \(0.228911\pi\) | |||||||
\(524\) | −4.56251 | + | 7.90250i | −0.199314 | + | 0.345222i | ||||
\(525\) | −19.2655 | − | 1.62283i | −0.840813 | − | 0.0708262i | ||||
\(526\) | 1.47358 | − | 2.55232i | 0.0642511 | − | 0.111286i | ||||
\(527\) | −41.7293 | −1.81776 | ||||||||
\(528\) | 3.20391 | − | 5.54934i | 0.139432 | − | 0.241504i | ||||
\(529\) | 9.14640 | + | 15.8420i | 0.397669 | + | 0.688784i | ||||
\(530\) | 3.69745 | − | 6.40417i | 0.160607 | − | 0.278180i | ||||
\(531\) | 5.89729 | + | 10.2144i | 0.255920 | + | 0.443267i | ||||
\(532\) | 7.91249 | − | 11.3782i | 0.343050 | − | 0.493310i | ||||
\(533\) | −32.8351 | + | 16.4519i | −1.42225 | + | 0.712609i | ||||
\(534\) | −3.50376 | − | 6.06869i | −0.151622 | − | 0.262618i | ||||
\(535\) | 34.2563 | 1.48103 | ||||||||
\(536\) | 7.28922 | 0.314846 | ||||||||
\(537\) | −14.1285 | −0.609689 | ||||||||
\(538\) | −23.9353 | −1.03192 | ||||||||
\(539\) | 28.6095 | − | 34.5462i | 1.23230 | − | 1.48801i | ||||
\(540\) | 1.75410 | − | 3.03819i | 0.0754844 | − | 0.130743i | ||||
\(541\) | 8.01702 | + | 13.8859i | 0.344679 | + | 0.597001i | 0.985295 | − | 0.170860i | \(-0.0546545\pi\) |
−0.640617 | + | 0.767861i | \(0.721321\pi\) | |||||||
\(542\) | −9.68335 | − | 16.7721i | −0.415936 | − | 0.720422i | ||||
\(543\) | −13.6453 | −0.585576 | ||||||||
\(544\) | −2.33890 | + | 4.05110i | −0.100280 | + | 0.173689i | ||||
\(545\) | 8.05385 | 0.344989 | ||||||||
\(546\) | 1.36093 | − | 9.44181i | 0.0582426 | − | 0.404072i | ||||
\(547\) | −10.3955 | −0.444481 | −0.222240 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222240 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(548\) | −7.53370 | + | 13.0488i | −0.321824 | + | 0.557415i | ||||
\(549\) | 9.35561 | 0.399288 | ||||||||
\(550\) | 23.4124 | + | 40.5515i | 0.998308 | + | 1.72912i | ||||
\(551\) | −6.44473 | − | 11.1626i | −0.274555 | − | 0.475543i | ||||
\(552\) | 1.08480 | − | 1.87894i | 0.0461724 | − | 0.0799729i | ||||
\(553\) | −2.70012 | + | 3.88280i | −0.114821 | + | 0.165113i | ||||
\(554\) | 2.43419 | 0.103419 | ||||||||
\(555\) | −13.6807 | −0.580711 | ||||||||
\(556\) | −14.0504 | −0.595869 | ||||||||
\(557\) | 32.3902 | 1.37242 | 0.686209 | − | 0.727404i | \(-0.259274\pi\) | ||||
0.686209 | + | 0.727404i | \(0.259274\pi\) | |||||||
\(558\) | 4.46035 | + | 7.72555i | 0.188821 | + | 0.327048i | ||||
\(559\) | −7.18540 | − | 4.73558i | −0.303910 | − | 0.200294i | ||||
\(560\) | −3.94981 | − | 8.39947i | −0.166910 | − | 0.354942i | ||||
\(561\) | 14.9873 | + | 25.9587i | 0.632763 | + | 1.09598i | ||||
\(562\) | 1.40165 | − | 2.42772i | 0.0591248 | − | 0.102407i | ||||
\(563\) | 1.21655 | + | 2.10712i | 0.0512713 | + | 0.0888045i | 0.890522 | − | 0.454940i | \(-0.150339\pi\) |
−0.839251 | + | 0.543745i | \(0.817006\pi\) | |||||||
\(564\) | −2.44070 | + | 4.22742i | −0.102772 | + | 0.178006i | ||||
\(565\) | 13.7710 | 0.579348 | ||||||||
\(566\) | 8.47705 | − | 14.6827i | 0.356317 | − | 0.617159i | ||||
\(567\) | 1.12588 | + | 2.39424i | 0.0472826 | + | 0.100549i | ||||
\(568\) | 2.79339 | − | 4.83829i | 0.117208 | − | 0.203010i | ||||
\(569\) | 3.97033 | − | 6.87681i | 0.166445 | − | 0.288291i | −0.770723 | − | 0.637171i | \(-0.780105\pi\) |
0.937167 | + | 0.348880i | \(0.113438\pi\) | |||||||
\(570\) | −18.3767 | −0.769714 | ||||||||
\(571\) | 18.0463 | − | 31.2571i | 0.755214 | − | 1.30807i | −0.190054 | − | 0.981774i | \(-0.560866\pi\) |
0.945268 | − | 0.326295i | \(-0.105800\pi\) | |||||||
\(572\) | −20.6560 | + | 10.3496i | −0.863669 | + | 0.432737i | ||||
\(573\) | −2.43145 | −0.101575 | ||||||||
\(574\) | −11.4682 | − | 24.3878i | −0.478675 | − | 1.01793i | ||||
\(575\) | 7.92715 | + | 13.7302i | 0.330585 | + | 0.572590i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.3980 | + | 28.4021i | −0.682657 | + | 1.18240i | 0.291510 | + | 0.956568i | \(0.405842\pi\) |
−0.974167 | + | 0.225829i | \(0.927491\pi\) | |||||||
\(578\) | −2.44094 | − | 4.22782i | −0.101530 | − | 0.175854i | ||||
\(579\) | 3.51754 | 0.146184 | ||||||||
\(580\) | −8.63248 | −0.358444 | ||||||||
\(581\) | −2.91848 | − | 6.20630i | −0.121079 | − | 0.257481i | ||||
\(582\) | −4.92513 | − | 8.53057i | −0.204153 | − | 0.353604i | ||||
\(583\) | 6.75350 | − | 11.6974i | 0.279701 | − | 0.484457i | ||||
\(584\) | 4.23175 | − | 7.32961i | 0.175111 | − | 0.303301i | ||||
\(585\) | −11.3089 | + | 5.66624i | −0.467564 | + | 0.234270i | ||||
\(586\) | 2.84568 | + | 4.92886i | 0.117554 | + | 0.203609i | ||||
\(587\) | 10.9482 | + | 18.9629i | 0.451881 | + | 0.782681i | 0.998503 | − | 0.0546984i | \(-0.0174197\pi\) |
−0.546622 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(588\) | 6.90136 | + | 1.17099i | 0.284607 | + | 0.0482906i | ||||
\(589\) | 23.3642 | − | 40.4680i | 0.962707 | − | 1.66746i | ||||
\(590\) | −20.6888 | − | 35.8341i | −0.851746 | − | 1.47527i | ||||
\(591\) | 1.15702 | + | 2.00402i | 0.0475936 | + | 0.0824345i | ||||
\(592\) | −1.94981 | − | 3.37717i | −0.0801368 | − | 0.138801i | ||||
\(593\) | 3.25002 | + | 5.62921i | 0.133463 | + | 0.231164i | 0.925009 | − | 0.379945i | \(-0.124057\pi\) |
−0.791547 | + | 0.611109i | \(0.790724\pi\) | |||||||
\(594\) | 3.20391 | − | 5.54934i | 0.131458 | − | 0.227692i | ||||
\(595\) | 43.2653 | + | 3.64447i | 1.77370 | + | 0.149409i | ||||
\(596\) | −0.614668 | − | 1.06464i | −0.0251778 | − | 0.0436092i | ||||
\(597\) | −2.84733 | − | 4.93173i | −0.116534 | − | 0.201842i | ||||
\(598\) | −6.99386 | + | 3.50423i | −0.286000 | + | 0.143299i | ||||
\(599\) | 1.40105 | − | 2.42668i | 0.0572452 | − | 0.0991516i | −0.835983 | − | 0.548756i | \(-0.815102\pi\) |
0.893228 | + | 0.449604i | \(0.148435\pi\) | |||||||
\(600\) | −3.65372 | + | 6.32843i | −0.149163 | + | 0.258357i | ||||
\(601\) | −11.8591 | − | 20.5405i | −0.483741 | − | 0.837864i | 0.516085 | − | 0.856538i | \(-0.327389\pi\) |
−0.999826 | + | 0.0186737i | \(0.994056\pi\) | |||||||
\(602\) | 3.60527 | − | 5.18442i | 0.146940 | − | 0.211301i | ||||
\(603\) | 7.28922 | 0.296840 | ||||||||
\(604\) | −16.3449 | −0.665065 | ||||||||
\(605\) | 52.7285 | + | 91.3284i | 2.14372 | + | 3.71303i | ||||
\(606\) | −6.91016 | + | 11.9687i | −0.280706 | + | 0.486197i | ||||
\(607\) | −11.8430 | −0.480694 | −0.240347 | − | 0.970687i | \(-0.577261\pi\) | ||||
−0.240347 | + | 0.970687i | \(0.577261\pi\) | |||||||
\(608\) | −2.61911 | − | 4.53642i | −0.106219 | − | 0.183976i | ||||
\(609\) | 3.71691 | − | 5.34495i | 0.150617 | − | 0.216589i | ||||
\(610\) | −32.8213 | −1.32890 | ||||||||
\(611\) | 15.7355 | − | 7.88417i | 0.636589 | − | 0.318959i | ||||
\(612\) | −2.33890 | + | 4.05110i | −0.0945446 | + | 0.163756i | ||||
\(613\) | −16.1979 | −0.654227 | −0.327114 | − | 0.944985i | \(-0.606076\pi\) | ||||
−0.327114 | + | 0.944985i | \(0.606076\pi\) | |||||||
\(614\) | −1.74302 | + | 3.01899i | −0.0703424 | + | 0.121837i | ||||
\(615\) | −17.8673 | + | 30.9470i | −0.720477 | + | 1.24790i | ||||
\(616\) | −7.21444 | − | 15.3419i | −0.290678 | − | 0.618142i | ||||
\(617\) | −22.0973 | + | 38.2737i | −0.889606 | + | 1.54084i | −0.0492637 | + | 0.998786i | \(0.515687\pi\) |
−0.840342 | + | 0.542057i | \(0.817646\pi\) | |||||||
\(618\) | 13.1332 | 0.528293 | ||||||||
\(619\) | −17.0272 | + | 29.4920i | −0.684383 | + | 1.18539i | 0.289248 | + | 0.957254i | \(0.406595\pi\) |
−0.973630 | + | 0.228131i | \(0.926738\pi\) | |||||||
\(620\) | −15.6478 | − | 27.1027i | −0.628430 | − | 1.08847i | ||||
\(621\) | 1.08480 | − | 1.87894i | 0.0435317 | − | 0.0753991i | ||||
\(622\) | 12.0016 | + | 20.7873i | 0.481219 | + | 0.833496i | ||||
\(623\) | −18.4747 | − | 1.55622i | −0.740174 | − | 0.0623488i | ||||
\(624\) | −3.01053 | − | 1.98411i | −0.120518 | − | 0.0794279i | ||||
\(625\) | 4.06923 | + | 7.04812i | 0.162769 | + | 0.281925i | ||||
\(626\) | 17.5552 | 0.701646 | ||||||||
\(627\) | −33.5655 | −1.34048 | ||||||||
\(628\) | 15.9699 | 0.637267 | ||||||||
\(629\) | 18.2417 | 0.727344 | ||||||||
\(630\) | −3.94981 | − | 8.39947i | −0.157364 | − | 0.334643i | ||||
\(631\) | −0.712707 | + | 1.23444i | −0.0283724 | + | 0.0491424i | −0.879863 | − | 0.475227i | \(-0.842366\pi\) |
0.851491 | + | 0.524370i | \(0.175699\pi\) | |||||||
\(632\) | 0.893764 | + | 1.54804i | 0.0355520 | + | 0.0615779i | ||||
\(633\) | 0.291966 | + | 0.505700i | 0.0116046 | + | 0.0200998i | ||||
\(634\) | 2.84037 | 0.112805 | ||||||||
\(635\) | −12.3206 | + | 21.3400i | −0.488929 | + | 0.846850i | ||||
\(636\) | 2.10789 | 0.0835834 | ||||||||
\(637\) | −18.4534 | − | 17.2183i | −0.731151 | − | 0.682216i | ||||
\(638\) | −15.7675 | −0.624240 | ||||||||
\(639\) | 2.79339 | − | 4.83829i | 0.110505 | − | 0.191400i | ||||
\(640\) | −3.50820 | −0.138674 | ||||||||
\(641\) | 11.6001 | + | 20.0919i | 0.458175 | + | 0.793582i | 0.998865 | − | 0.0476400i | \(-0.0151700\pi\) |
−0.540690 | + | 0.841222i | \(0.681837\pi\) | |||||||
\(642\) | 4.88232 | + | 8.45642i | 0.192690 | + | 0.333748i | ||||
\(643\) | 3.41821 | − | 5.92052i | 0.134801 | − | 0.233482i | −0.790720 | − | 0.612178i | \(-0.790294\pi\) |
0.925521 | + | 0.378695i | \(0.123627\pi\) | |||||||
\(644\) | −2.44272 | − | 5.19457i | −0.0962567 | − | 0.204695i | ||||
\(645\) | −8.37320 | −0.329695 | ||||||||
\(646\) | 24.5033 | 0.964071 | ||||||||
\(647\) | −42.5965 | −1.67464 | −0.837320 | − | 0.546713i | \(-0.815879\pi\) | ||||
−0.837320 | + | 0.546713i | \(0.815879\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −37.7888 | − | 65.4521i | −1.48334 | − | 2.56922i | ||||
\(650\) | 23.5560 | − | 11.8026i | 0.923941 | − | 0.462935i | ||||
\(651\) | 23.5186 | + | 1.98110i | 0.921768 | + | 0.0776454i | ||||
\(652\) | −3.89316 | − | 6.74316i | −0.152468 | − | 0.264082i | ||||
\(653\) | 19.7223 | − | 34.1601i | 0.771794 | − | 1.33679i | −0.164784 | − | 0.986330i | \(-0.552693\pi\) |
0.936579 | − | 0.350457i | \(-0.113974\pi\) | |||||||
\(654\) | 1.14786 | + | 1.98816i | 0.0448850 | + | 0.0777430i | ||||
\(655\) | 16.0062 | − | 27.7235i | 0.625413 | − | 1.08325i | ||||
\(656\) | −10.1860 | −0.397697 | ||||||||
\(657\) | 4.23175 | − | 7.32961i | 0.165096 | − | 0.285955i | ||||
\(658\) | 5.49588 | + | 11.6873i | 0.214252 | + | 0.455617i | ||||
\(659\) | 0.667872 | − | 1.15679i | 0.0260166 | − | 0.0450621i | −0.852724 | − | 0.522362i | \(-0.825051\pi\) |
0.878741 | + | 0.477300i | \(0.158384\pi\) | |||||||
\(660\) | −11.2399 | + | 19.4682i | −0.437514 | + | 0.757797i | ||||
\(661\) | −12.8932 | −0.501488 | −0.250744 | − | 0.968053i | \(-0.580675\pi\) | ||||
−0.250744 | + | 0.968053i | \(0.580675\pi\) | |||||||
\(662\) | 9.43745 | − | 16.3461i | 0.366797 | − | 0.635311i | ||||
\(663\) | 15.0792 | − | 7.55533i | 0.585626 | − | 0.293425i | ||||
\(664\) | −2.59218 | −0.100596 | ||||||||
\(665\) | −27.7586 | + | 39.9171i | −1.07643 | + | 1.54792i | ||||
\(666\) | −1.94981 | − | 3.37717i | −0.0755537 | − | 0.130863i | ||||
\(667\) | −5.33867 | −0.206714 | ||||||||
\(668\) | 3.32333 | − | 5.75618i | 0.128584 | − | 0.222713i | ||||
\(669\) | −7.25749 | − | 12.5703i | −0.280591 | − | 0.485998i | ||||
\(670\) | −25.5720 | −0.987934 | ||||||||
\(671\) | −59.9491 | −2.31431 | ||||||||
\(672\) | 1.51053 | − | 2.17216i | 0.0582701 | − | 0.0837930i | ||||
\(673\) | −13.8759 | − | 24.0338i | −0.534877 | − | 0.926434i | −0.999169 | − | 0.0407519i | \(-0.987025\pi\) |
0.464292 | − | 0.885682i | \(-0.346309\pi\) | |||||||
\(674\) | −5.47802 | + | 9.48821i | −0.211005 | + | 0.365472i | ||||
\(675\) | −3.65372 | + | 6.32843i | −0.140632 | + | 0.243582i | ||||
\(676\) | 5.12662 | + | 11.9465i | 0.197178 | + | 0.459479i | ||||
\(677\) | −1.50219 | − | 2.60188i | −0.0577340 | − | 0.0999982i | 0.835714 | − | 0.549165i | \(-0.185054\pi\) |
−0.893448 | + | 0.449167i | \(0.851721\pi\) | |||||||
\(678\) | 1.96268 | + | 3.39947i | 0.0753764 | + | 0.130556i | ||||
\(679\) | −25.9694 | − | 2.18754i | −0.996613 | − | 0.0839500i | ||||
\(680\) | 8.20533 | − | 14.2121i | 0.314660 | − | 0.545007i | ||||
\(681\) | −10.1232 | − | 17.5339i | −0.387921 | − | 0.671899i | ||||
\(682\) | −28.5811 | − | 49.5039i | −1.09443 | − | 1.89560i | ||||
\(683\) | 7.43467 | + | 12.8772i | 0.284480 | + | 0.492733i | 0.972483 | − | 0.232974i | \(-0.0748458\pi\) |
−0.688003 | + | 0.725708i | \(0.741513\pi\) | |||||||
\(684\) | −2.61911 | − | 4.53642i | −0.100144 | − | 0.173455i | ||||
\(685\) | 26.4297 | − | 45.7776i | 1.00983 | − | 1.74907i | ||||
\(686\) | 12.9683 | − | 13.2221i | 0.495132 | − | 0.504821i | ||||
\(687\) | −0.668929 | − | 1.15862i | −0.0255212 | − | 0.0442041i | ||||
\(688\) | −1.19338 | − | 2.06699i | −0.0454971 | − | 0.0788033i | ||||
\(689\) | −6.34588 | − | 4.18229i | −0.241759 | − | 0.159333i | ||||
\(690\) | −3.80571 | + | 6.59168i | −0.144881 | + | 0.250941i | ||||
\(691\) | −4.19053 | + | 7.25822i | −0.159415 | + | 0.276116i | −0.934658 | − | 0.355548i | \(-0.884294\pi\) |
0.775243 | + | 0.631664i | \(0.217628\pi\) | |||||||
\(692\) | 7.30337 | + | 12.6498i | 0.277633 | + | 0.480874i | ||||
\(693\) | −7.21444 | − | 15.3419i | −0.274054 | − | 0.582789i | ||||
\(694\) | −32.1029 | −1.21861 | ||||||||
\(695\) | 49.2915 | 1.86973 | ||||||||
\(696\) | −1.23033 | − | 2.13099i | −0.0466356 | − | 0.0807752i | ||||
\(697\) | 23.8241 | − | 41.2645i | 0.902401 | − | 1.56300i | ||||
\(698\) | 18.0875 | 0.684620 | ||||||||
\(699\) | 6.97568 | + | 12.0822i | 0.263845 | + | 0.456992i | ||||
\(700\) | 8.22731 | + | 17.4958i | 0.310963 | + | 0.661279i | ||||
\(701\) | 39.2809 | 1.48362 | 0.741809 | − | 0.670611i | \(-0.233968\pi\) | ||||
0.741809 | + | 0.670611i | \(0.233968\pi\) | |||||||
\(702\) | −3.01053 | − | 1.98411i | −0.113625 | − | 0.0748854i | ||||
\(703\) | −10.2135 | + | 17.6904i | −0.385211 | + | 0.667204i | ||||
\(704\) | −6.40782 | −0.241504 | ||||||||
\(705\) | 8.56246 | − | 14.8306i | 0.322481 | − | 0.558553i | ||||
\(706\) | 13.7323 | − | 23.7850i | 0.516820 | − | 0.895159i | ||||
\(707\) | 15.5600 | + | 33.0892i | 0.585195 | + | 1.24445i | ||||
\(708\) | 5.89729 | − | 10.2144i | 0.221634 | − | 0.383881i | ||||
\(709\) | 19.3204 | 0.725592 | 0.362796 | − | 0.931869i | \(-0.381822\pi\) | ||||
0.362796 | + | 0.931869i | \(0.381822\pi\) | |||||||
\(710\) | −9.79976 | + | 16.9737i | −0.367778 | + | 0.637011i | ||||
\(711\) | 0.893764 | + | 1.54804i | 0.0335188 | + | 0.0580562i | ||||
\(712\) | −3.50376 | + | 6.06869i | −0.131309 | + | 0.227434i | ||||
\(713\) | −9.67721 | − | 16.7614i | −0.362414 | − | 0.627720i | ||||
\(714\) | 5.26665 | + | 11.1998i | 0.197100 | + | 0.419142i | ||||
\(715\) | 72.4652 | − | 36.3083i | 2.71004 | − | 1.35785i | ||||
\(716\) | 7.06425 | + | 12.2356i | 0.264003 | + | 0.457267i | ||||
\(717\) | 9.05495 | 0.338163 | ||||||||
\(718\) | 21.6781 | 0.809019 | ||||||||
\(719\) | −28.4410 | −1.06067 | −0.530335 | − | 0.847788i | \(-0.677934\pi\) | ||||
−0.530335 | + | 0.847788i | \(0.677934\pi\) | |||||||
\(720\) | −3.50820 | −0.130743 | ||||||||
\(721\) | 19.8381 | − | 28.5274i | 0.738809 | − | 1.06241i | ||||
\(722\) | −4.21943 | + | 7.30827i | −0.157031 | + | 0.271986i | ||||
\(723\) | −10.0551 | − | 17.4159i | −0.373953 | − | 0.647705i | ||||
\(724\) | 6.82265 | + | 11.8172i | 0.253562 | + | 0.439182i | ||||
\(725\) | 17.9811 | 0.667803 | ||||||||
\(726\) | −15.0301 | + | 26.0329i | −0.557819 | + | 0.966171i | ||||
\(727\) | −48.4057 | −1.79527 | −0.897634 | − | 0.440741i | \(-0.854716\pi\) | ||||
−0.897634 | + | 0.440741i | \(0.854716\pi\) | |||||||
\(728\) | −8.85732 | + | 3.54230i | −0.328274 | + | 0.131287i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −14.8458 | + | 25.7137i | −0.549468 | + | 0.951707i | ||||
\(731\) | 11.1648 | 0.412944 | ||||||||
\(732\) | −4.67781 | − | 8.10220i | −0.172897 | − | 0.299466i | ||||
\(733\) | −3.69118 | − | 6.39332i | −0.136337 | − | 0.236143i | 0.789770 | − | 0.613403i | \(-0.210200\pi\) |
−0.926107 | + | 0.377260i | \(0.876866\pi\) | |||||||
\(734\) | −7.66086 | + | 13.2690i | −0.282768 | + | 0.489768i | ||||
\(735\) | −24.2113 | − | 4.10805i | −0.893049 | − | 0.151528i | ||||
\(736\) | −2.16961 | −0.0799729 | ||||||||
\(737\) | −46.7080 | −1.72051 | ||||||||
\(738\) | −10.1860 | −0.374952 | ||||||||
\(739\) | 4.82426 | 0.177463 | 0.0887316 | − | 0.996056i | \(-0.471719\pi\) | ||||
0.0887316 | + | 0.996056i | \(0.471719\pi\) | |||||||
\(740\) | 6.84033 | + | 11.8478i | 0.251455 | + | 0.435533i | ||||
\(741\) | −1.11585 | + | 18.8536i | −0.0409920 | + | 0.692606i | ||||
\(742\) | 3.18404 | − | 4.57868i | 0.116890 | − | 0.168089i | ||||
\(743\) | 17.8556 | + | 30.9268i | 0.655059 | + | 1.13460i | 0.981879 | + | 0.189509i | \(0.0606895\pi\) |
−0.326820 | + | 0.945087i | \(0.605977\pi\) | |||||||
\(744\) | 4.46035 | − | 7.72555i | 0.163524 | − | 0.283232i | ||||
\(745\) | 2.15637 | + | 3.73495i | 0.0790035 | + | 0.136838i | ||||
\(746\) | 16.6792 | − | 28.8893i | 0.610670 | − | 1.05771i | ||||
\(747\) | −2.59218 | −0.0948429 | ||||||||
\(748\) | 14.9873 | − | 25.9587i | 0.547989 | − | 0.949145i | ||||
\(749\) | 25.7436 | + | 2.16852i | 0.940651 | + | 0.0792361i | ||||
\(750\) | 4.04749 | − | 7.01045i | 0.147793 | − | 0.255986i | ||||
\(751\) | −6.54845 | + | 11.3422i | −0.238956 | + | 0.413885i | −0.960415 | − | 0.278573i | \(-0.910139\pi\) |
0.721459 | + | 0.692457i | \(0.243472\pi\) | |||||||
\(752\) | 4.88140 | 0.178006 | ||||||||
\(753\) | 4.09035 | − | 7.08469i | 0.149061 | − | 0.258181i | ||||
\(754\) | −0.524175 | + | 8.85654i | −0.0190893 | + | 0.322536i | ||||
\(755\) | 57.3411 | 2.08686 | ||||||||
\(756\) | 1.51053 | − | 2.17216i | 0.0549376 | − | 0.0790008i | ||||
\(757\) | −22.0344 | − | 38.1646i | −0.800852 | − | 1.38712i | −0.919056 | − | 0.394127i | \(-0.871047\pi\) |
0.118204 | − | 0.992989i | \(-0.462286\pi\) | |||||||
\(758\) | −16.8774 | −0.613013 | ||||||||
\(759\) | −6.95123 | + | 12.0399i | −0.252314 | + | 0.437020i | ||||
\(760\) | 9.18834 | + | 15.9147i | 0.333296 | + | 0.577286i | ||||
\(761\) | −8.61142 | −0.312164 | −0.156082 | − | 0.987744i | \(-0.549886\pi\) | ||||
−0.156082 | + | 0.987744i | \(0.549886\pi\) | |||||||
\(762\) | −7.02391 | −0.254449 | ||||||||
\(763\) | 6.05248 | + | 0.509833i | 0.219115 | + | 0.0184572i | ||||
\(764\) | 1.21572 | + | 2.10569i | 0.0439833 | + | 0.0761814i | ||||
\(765\) | 8.20533 | − | 14.2121i | 0.296664 | − | 0.513838i | ||||
\(766\) | −10.7933 | + | 18.6945i | −0.389978 | + | 0.675461i | ||||
\(767\) | −38.0205 | + | 19.0499i | −1.37284 | + | 0.687853i | ||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −3.20391 | − | 5.54934i | −0.115536 | − | 0.200114i | 0.802458 | − | 0.596709i | \(-0.203525\pi\) |
−0.917994 | + | 0.396595i | \(0.870192\pi\) | |||||||
\(770\) | 25.3097 | + | 53.8223i | 0.912098 | + | 1.93962i | ||||
\(771\) | −4.87696 | + | 8.44715i | −0.175640 | + | 0.304217i | ||||
\(772\) | −1.75877 | − | 3.04628i | −0.0632996 | − | 0.109638i | ||||
\(773\) | −6.29082 | − | 10.8960i | −0.226265 | − | 0.391902i | 0.730433 | − | 0.682984i | \(-0.239318\pi\) |
−0.956698 | + | 0.291082i | \(0.905985\pi\) | |||||||
\(774\) | −1.19338 | − | 2.06699i | −0.0428951 | − | 0.0742964i | ||||
\(775\) | 32.5937 | + | 56.4540i | 1.17080 | + | 2.02789i | ||||
\(776\) | −4.92513 | + | 8.53057i | −0.176802 | + | 0.306230i | ||||
\(777\) | −10.2810 | − | 0.866025i | −0.368830 | − | 0.0310685i | ||||
\(778\) | 8.68908 | + | 15.0499i | 0.311519 | + | 0.539566i | ||||
\(779\) | 26.6782 | + | 46.2080i | 0.955846 | + | 1.65557i | ||||
\(780\) | 10.5615 | + | 6.96065i | 0.378164 | + | 0.249231i | ||||
\(781\) | −17.8995 | + | 31.0029i | −0.640496 | + | 1.10937i | ||||
\(782\) | 5.07451 | − | 8.78930i | 0.181464 | − | 0.314305i | ||||
\(783\) | −1.23033 | − | 2.13099i | −0.0439684 | − | 0.0761555i | ||||
\(784\) | −2.43658 | − | 6.56225i | −0.0870206 | − | 0.234366i | ||||
\(785\) | −56.0255 | −1.99963 | ||||||||
\(786\) | 9.12502 | 0.325479 | ||||||||
\(787\) | 9.60693 | + | 16.6397i | 0.342450 | + | 0.593141i | 0.984887 | − | 0.173198i | \(-0.0554099\pi\) |
−0.642437 | + | 0.766338i | \(0.722077\pi\) | |||||||
\(788\) | 1.15702 | − | 2.00402i | 0.0412172 | − | 0.0713904i | ||||
\(789\) | −2.94716 | −0.104922 | ||||||||
\(790\) | −3.13550 | − | 5.43084i | −0.111556 | − | 0.193221i | ||||
\(791\) | 10.3489 | + | 0.871742i | 0.367964 | + | 0.0309956i | ||||
\(792\) | −6.40782 | −0.227692 | ||||||||
\(793\) | −1.99295 | + | 33.6732i | −0.0707718 | + | 1.19577i | ||||
\(794\) | −2.93718 | + | 5.08734i | −0.104237 | + | 0.180543i | ||||
\(795\) | −7.39490 | −0.262270 | ||||||||
\(796\) | −2.84733 | + | 4.93173i | −0.100921 | + | 0.174800i | ||||
\(797\) | −8.43333 | + | 14.6070i | −0.298724 | + | 0.517405i | −0.975844 | − | 0.218467i | \(-0.929894\pi\) |
0.677120 | + | 0.735872i | \(0.263228\pi\) | |||||||
\(798\) | −13.8101 | − | 1.16330i | −0.488872 | − | 0.0411803i | ||||
\(799\) | −11.4171 | + | 19.7750i | −0.403909 | + | 0.699591i | ||||
\(800\) | 7.30745 | 0.258357 | ||||||||
\(801\) | −3.50376 | + | 6.06869i | −0.123799 | + | 0.214427i | ||||
\(802\) | 6.98855 | + | 12.1045i | 0.246774 | + | 0.427426i | ||||
\(803\) | −27.1163 | + | 46.9668i | −0.956914 | + | 1.65742i | ||||
\(804\) | −3.64461 | − | 6.31265i | −0.128536 | − | 0.222630i | ||||
\(805\) | 8.56955 | + | 18.2236i | 0.302037 | + | 0.642296i | ||||
\(806\) | −28.7563 | + | 14.4082i | −1.01290 | + | 0.507507i | ||||
\(807\) | 11.9676 | + | 20.7285i | 0.421280 | + | 0.729679i | ||||
\(808\) | 13.8203 | 0.486197 | ||||||||
\(809\) | 8.76049 | 0.308002 | 0.154001 | − | 0.988071i | \(-0.450784\pi\) | ||||
0.154001 | + | 0.988071i | \(0.450784\pi\) | |||||||
\(810\) | −3.50820 | −0.123265 | ||||||||
\(811\) | −32.7259 | −1.14916 | −0.574581 | − | 0.818448i | \(-0.694835\pi\) | ||||
−0.574581 | + | 0.818448i | \(0.694835\pi\) | |||||||
\(812\) | −6.48732 | − | 0.546462i | −0.227660 | − | 0.0191770i | ||||
\(813\) | −9.68335 | + | 16.7721i | −0.339610 | + | 0.588222i | ||||
\(814\) | 12.4940 | + | 21.6403i | 0.437916 | + | 0.758493i | ||||
\(815\) | 13.6580 | + | 23.6563i | 0.478418 | + | 0.828645i | ||||
\(816\) | 4.67781 | 0.163756 | ||||||||
\(817\) | −6.25116 | + | 10.8273i | −0.218701 | + | 0.378800i | ||||
\(818\) | −37.4897 | −1.31080 | ||||||||
\(819\) | −8.85732 | + | 3.54230i | −0.309500 | + | 0.123778i | ||||
\(820\) | 35.7345 | 1.24790 | ||||||||
\(821\) | −7.34756 | + | 12.7263i | −0.256432 | + | 0.444152i | −0.965283 | − | 0.261205i | \(-0.915880\pi\) |
0.708852 | + | 0.705357i | \(0.249213\pi\) | |||||||
\(822\) | 15.0674 | 0.525536 | ||||||||
\(823\) | −20.6994 | − | 35.8525i | −0.721537 | − | 1.24974i | −0.960384 | − | 0.278682i | \(-0.910103\pi\) |
0.238846 | − | 0.971057i | \(-0.423231\pi\) | |||||||
\(824\) | −6.56658 | − | 11.3737i | −0.228758 | − | 0.396220i | ||||
\(825\) | 23.4124 | − | 40.5515i | 0.815115 | − | 1.41182i | ||||
\(826\) | −13.2793 | − | 28.2391i | −0.462046 | − | 0.982563i | ||||
\(827\) | 37.8157 | 1.31498 | 0.657491 | − | 0.753462i | \(-0.271618\pi\) | ||||
0.657491 | + | 0.753462i | \(0.271618\pi\) | |||||||
\(828\) | −2.16961 | −0.0753991 | ||||||||
\(829\) | 34.4239 | 1.19559 | 0.597796 | − | 0.801648i | \(-0.296043\pi\) | ||||
0.597796 | + | 0.801648i | \(0.296043\pi\) | |||||||
\(830\) | 9.09387 | 0.315653 | ||||||||
\(831\) | −1.21710 | − | 2.10807i | −0.0422206 | − | 0.0731282i | ||||
\(832\) | −0.213022 | + | 3.59925i | −0.00738521 | + | 0.124782i | ||||
\(833\) | 32.2832 | + | 5.47764i | 1.11855 | + | 0.189789i | ||||
\(834\) | 7.02519 | + | 12.1680i | 0.243262 | + | 0.421343i | ||||
\(835\) | −11.6589 | + | 20.1938i | −0.403473 | + | 0.698836i | ||||
\(836\) | 16.7828 | + | 29.0686i | 0.580444 | + | 1.00536i | ||||
\(837\) | 4.46035 | − | 7.72555i | 0.154172 | − | 0.267034i | ||||
\(838\) | 33.9095 | 1.17138 | ||||||||
\(839\) | −0.709771 | + | 1.22936i | −0.0245040 | + | 0.0424422i | −0.878017 | − | 0.478629i | \(-0.841134\pi\) |
0.853513 | + | 0.521071i | \(0.174467\pi\) | |||||||
\(840\) | −5.29925 | + | 7.62037i | −0.182841 | + | 0.262928i | ||||
\(841\) | 11.4726 | − | 19.8711i | 0.395606 | − | 0.685210i | ||||
\(842\) | 5.27517 | − | 9.13685i | 0.181794 | − | 0.314877i | ||||
\(843\) | −2.80329 | −0.0965505 | ||||||||
\(844\) | 0.291966 | − | 0.505700i | 0.0100499 | − | 0.0174069i | ||||
\(845\) | −17.9852 | − | 41.9105i | −0.618710 | − | 1.44177i | ||||
\(846\) | 4.88140 | 0.167826 | ||||||||
\(847\) | 33.8442 | + | 71.9713i | 1.16290 | + | 2.47296i | ||||
\(848\) | −1.05395 | − | 1.82549i | −0.0361927 | − | 0.0626875i | ||||
\(849\) | −16.9541 | −0.581864 | ||||||||
\(850\) | −17.0914 | + | 29.6032i | −0.586230 | + | 1.01538i | ||||
\(851\) | 4.23033 | + | 7.32715i | 0.145014 | + | 0.251171i | ||||
\(852\) | −5.58678 | −0.191400 | ||||||||
\(853\) | 36.8892 | 1.26306 | 0.631531 | − | 0.775351i | \(-0.282427\pi\) | ||||
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(854\) | −24.6653 | − | 2.07769i | −0.844028 | − | 0.0710970i | ||||
\(855\) | 9.18834 | + | 15.9147i | 0.314235 | + | 0.544270i | ||||
\(856\) | 4.88232 | − | 8.45642i | 0.166874 | − | 0.289034i | ||||
\(857\) | 13.9245 | − | 24.1180i | 0.475653 | − | 0.823855i | −0.523958 | − | 0.851744i | \(-0.675545\pi\) |
0.999611 | + | 0.0278890i | \(0.00887851\pi\) | |||||||
\(858\) | 19.2910 | + | 12.7138i | 0.658583 | + | 0.434043i | ||||
\(859\) | −25.2862 | − | 43.7970i | −0.862754 | − | 1.49433i | −0.869260 | − | 0.494355i | \(-0.835404\pi\) |
0.00650572 | − | 0.999979i | \(-0.497929\pi\) | |||||||
\(860\) | 4.18660 | + | 7.25141i | 0.142762 | + | 0.247271i | ||||
\(861\) | −15.3863 | + | 22.1257i | −0.524364 | + | 0.754040i | ||||
\(862\) | 12.8043 | − | 22.1777i | 0.436116 | − | 0.755375i | ||||
\(863\) | 14.5501 | + | 25.2016i | 0.495293 | + | 0.857872i | 0.999985 | − | 0.00542701i | \(-0.00172748\pi\) |
−0.504693 | + | 0.863299i | \(0.668394\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −25.6217 | − | 44.3780i | −0.871163 | − | 1.50890i | ||||
\(866\) | 3.68968 | + | 6.39071i | 0.125380 | + | 0.217165i | ||||
\(867\) | −2.44094 | + | 4.22782i | −0.0828985 | + | 0.143584i | ||||
\(868\) | −10.0436 | − | 21.3583i | −0.340903 | − | 0.724948i | ||||
\(869\) | −5.72708 | − | 9.91959i | −0.194278 | − | 0.336499i | ||||
\(870\) | 4.31624 | + | 7.47595i | 0.146334 | + | 0.253458i | ||||
\(871\) | −1.55277 | + | 26.2358i | −0.0526135 | + | 0.888965i | ||||
\(872\) | 1.14786 | − | 1.98816i | 0.0388715 | − | 0.0673275i | ||||
\(873\) | −4.92513 | + | 8.53057i | −0.166690 | + | 0.288716i | ||||
\(874\) | 5.68244 | + | 9.84227i | 0.192211 | + | 0.332920i | ||||
\(875\) | −9.11398 | − | 19.3813i | −0.308109 | − | 0.655208i | ||||
\(876\) | −8.46350 | −0.285955 | ||||||||
\(877\) | 1.11266 | 0.0375720 | 0.0187860 | − | 0.999824i | \(-0.494020\pi\) | ||||
0.0187860 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(878\) | 11.5255 | + | 19.9628i | 0.388967 | + | 0.673711i | ||||
\(879\) | 2.84568 | − | 4.92886i | 0.0959823 | − | 0.166246i | ||||
\(880\) | 22.4799 | 0.757797 | ||||||||
\(881\) | −8.14254 | − | 14.1033i | −0.274329 | − | 0.475152i | 0.695636 | − | 0.718394i | \(-0.255122\pi\) |
−0.969966 | + | 0.243242i | \(0.921789\pi\) | |||||||
\(882\) | −2.43658 | − | 6.56225i | −0.0820438 | − | 0.220962i | ||||
\(883\) | −37.0876 | −1.24810 | −0.624048 | − | 0.781386i | \(-0.714513\pi\) | ||||
−0.624048 | + | 0.781386i | \(0.714513\pi\) | |||||||
\(884\) | −14.0827 | − | 9.28128i | −0.473652 | − | 0.312163i | ||||
\(885\) | −20.6888 | + | 35.8341i | −0.695448 | + | 1.20455i | ||||
\(886\) | −18.1121 | −0.608488 | ||||||||
\(887\) | 10.8028 | − | 18.7110i | 0.362722 | − | 0.628252i | −0.625686 | − | 0.780075i | \(-0.715181\pi\) |
0.988408 | + | 0.151823i | \(0.0485143\pi\) | |||||||
\(888\) | −1.94981 | + | 3.37717i | −0.0654314 | + | 0.113331i | ||||
\(889\) | −10.6099 | + | 15.2571i | −0.355843 | + | 0.511706i | ||||
\(890\) | 12.2919 | − | 21.2902i | 0.412025 | − | 0.713647i | ||||
\(891\) | −6.40782 | −0.214670 | ||||||||
\(892\) | −7.25749 | + | 12.5703i | −0.242999 | + | 0.420886i | ||||
\(893\) | −12.7849 | − | 22.1441i | −0.427831 | − | 0.741024i | ||||
\(894\) | −0.614668 | + | 1.06464i | −0.0205576 | + | 0.0356067i | ||||
\(895\) | −24.7828 | − | 42.9250i | −0.828396 | − | 1.43482i | ||||
\(896\) | −2.63641 | − | 0.222079i | −0.0880764 | − | 0.00741914i | ||||
\(897\) | 6.53168 | + | 4.30474i | 0.218086 | + | 0.143731i | ||||
\(898\) | −9.23084 | − | 15.9883i | −0.308037 | − | 0.533536i | ||||
\(899\) | −21.9508 | −0.732100 | ||||||||
\(900\) | 7.30745 | 0.243582 | ||||||||
\(901\) | 9.86031 | 0.328495 | ||||||||
\(902\) | 65.2701 | 2.17326 | ||||||||
\(903\) | −6.29247 | − | 0.530048i | −0.209400 | − | 0.0176389i | ||||
\(904\) | 1.96268 | − | 3.39947i | 0.0652778 | − | 0.113065i | ||||
\(905\) | −23.9352 | − | 41.4570i | −0.795633 | − | 1.37808i | ||||
\(906\) | 8.17245 | + | 14.1551i | 0.271512 | + | 0.470272i | ||||
\(907\) | −29.0539 | −0.964720 | −0.482360 | − | 0.875973i | \(-0.660220\pi\) | ||||
−0.482360 | + | 0.875973i | \(0.660220\pi\) | |||||||
\(908\) | −10.1232 | + | 17.5339i | −0.335950 | + | 0.581882i | ||||
\(909\) | 13.8203 | 0.458391 | ||||||||
\(910\) | 31.0732 | − | 12.4271i | 1.03007 | − | 0.411954i | ||||
\(911\) | −22.2791 | −0.738141 | −0.369071 | − | 0.929401i | \(-0.620324\pi\) | ||||
−0.369071 | + | 0.929401i | \(0.620324\pi\) | |||||||
\(912\) | −2.61911 | + | 4.53642i | −0.0867273 | + | 0.150216i | ||||
\(913\) | 16.6102 | 0.549718 | ||||||||
\(914\) | 8.90233 | + | 15.4193i | 0.294463 | + | 0.510024i | ||||
\(915\) | 16.4107 | + | 28.4241i | 0.542520 | + | 0.939672i | ||||
\(916\) | −0.668929 | + | 1.15862i | −0.0221020 | + | 0.0382819i | ||||
\(917\) | 13.7836 | − | 19.8210i | 0.455176 | − | 0.654548i | ||||
\(918\) | 4.67781 | 0.154391 | ||||||||
\(919\) | −35.1435 | −1.15928 | −0.579639 | − | 0.814873i | \(-0.696806\pi\) | ||||
−0.579639 | + | 0.814873i | \(0.696806\pi\) | |||||||
\(920\) | 7.61142 | 0.250941 | ||||||||
\(921\) | 3.48603 | 0.114869 | ||||||||
\(922\) | −2.51030 | − | 4.34797i | −0.0826723 | − | 0.143193i | ||||
\(923\) | 16.8192 | + | 11.0848i | 0.553610 | + | 0.364860i | ||||
\(924\) | −9.67923 | + | 13.9188i | −0.318423 | + | 0.457896i | ||||
\(925\) | −14.2481 | − | 24.6785i | −0.468476 | − | 0.811425i | ||||
\(926\) | 12.5038 | − | 21.6571i | 0.410899 | − | 0.711698i | ||||
\(927\) | −6.56658 | − | 11.3737i | −0.215675 | − | 0.373560i | ||||
\(928\) | −1.23033 | + | 2.13099i | −0.0403876 | + | 0.0699533i | ||||
\(929\) | −36.7445 | −1.20555 | −0.602774 | − | 0.797912i | \(-0.705938\pi\) | ||||
−0.602774 | + | 0.797912i | \(0.705938\pi\) | |||||||
\(930\) | −15.6478 | + | 27.1027i | −0.513111 | + | 0.888734i | ||||
\(931\) | −23.3875 | + | 28.2406i | −0.766494 | + | 0.925547i | ||||
\(932\) | 6.97568 | − | 12.0822i | 0.228496 | − | 0.395767i | ||||
\(933\) | 12.0016 | − | 20.7873i | 0.392914 | − | 0.680546i | ||||
\(934\) | −25.8255 | −0.845037 | ||||||||
\(935\) | −52.5783 | + | 91.0683i | −1.71949 | + | 2.97825i | ||||
\(936\) | −0.213022 | + | 3.59925i | −0.00696285 | + | 0.117645i | ||||
\(937\) | 18.5284 | 0.605295 | 0.302647 | − | 0.953103i | \(-0.402130\pi\) | ||||
0.302647 | + | 0.953103i | \(0.402130\pi\) | |||||||
\(938\) | −19.2174 | − | 1.61878i | −0.627471 | − | 0.0528552i | ||||
\(939\) | −8.77758 | − | 15.2032i | −0.286446 | − | 0.496138i | ||||
\(940\) | −17.1249 | −0.558553 | ||||||||
\(941\) | 22.5985 | − | 39.1417i | 0.736689 | − | 1.27598i | −0.217290 | − | 0.976107i | \(-0.569722\pi\) |
0.953979 | − | 0.299875i | \(-0.0969450\pi\) | |||||||
\(942\) | −7.98494 | − | 13.8303i | −0.260163 | − | 0.450616i | ||||
\(943\) | 22.0996 | 0.719664 | ||||||||
\(944\) | −11.7946 | −0.383881 | ||||||||
\(945\) | −5.29925 | + | 7.62037i | −0.172385 | + | 0.247891i | ||||
\(946\) | 7.64695 | + | 13.2449i | 0.248624 | + | 0.430629i | ||||
\(947\) | −14.4333 | + | 24.9993i | −0.469020 | + | 0.812367i | −0.999373 | − | 0.0354104i | \(-0.988726\pi\) |
0.530353 | + | 0.847777i | \(0.322059\pi\) | |||||||
\(948\) | 0.893764 | − | 1.54804i | 0.0290281 | − | 0.0502781i | ||||
\(949\) | 25.4797 | + | 16.7925i | 0.827105 | + | 0.545108i | ||||
\(950\) | −19.1390 | − | 33.1497i | −0.620950 | − | 1.07552i | ||||
\(951\) | −1.42018 | − | 2.45983i | −0.0460526 | − | 0.0797655i | ||||
\(952\) | 7.06598 | − | 10.1610i | 0.229010 | − | 0.329318i | ||||
\(953\) | 8.36687 | − | 14.4919i | 0.271030 | − | 0.469437i | −0.698096 | − | 0.716004i | \(-0.745969\pi\) |
0.969126 | + | 0.246567i | \(0.0793025\pi\) | |||||||
\(954\) | −1.05395 | − | 1.82549i | −0.0341228 | − | 0.0591024i | ||||
\(955\) | −4.26500 | − | 7.38719i | −0.138012 | − | 0.239044i | ||||
\(956\) | −4.52748 | − | 7.84182i | −0.146429 | − | 0.253623i | ||||
\(957\) | 7.88374 | + | 13.6550i | 0.254845 | + | 0.441405i | ||||
\(958\) | −11.5569 | + | 20.0171i | −0.373386 | + | 0.646723i | ||||
\(959\) | 22.7598 | − | 32.7288i | 0.734953 | − | 1.05687i | ||||
\(960\) | 1.75410 | + | 3.03819i | 0.0566133 | + | 0.0980571i | ||||
\(961\) | −24.2894 | − | 42.0704i | −0.783528 | − | 1.35711i | ||||
\(962\) | 12.5707 | − | 6.29845i | 0.405294 | − | 0.203070i | ||||
\(963\) | 4.88232 | − | 8.45642i | 0.157330 | − | 0.272504i | ||||
\(964\) | −10.0551 | + | 17.4159i | −0.323852 | + | 0.560929i | ||||
\(965\) | 6.17012 | + | 10.6870i | 0.198623 | + | 0.344025i | ||||
\(966\) | −3.27727 | + | 4.71274i | −0.105444 | + | 0.151630i | ||||
\(967\) | −3.01759 | −0.0970392 | −0.0485196 | − | 0.998822i | \(-0.515450\pi\) | ||||
−0.0485196 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(968\) | 30.0602 | 0.966171 | ||||||||
\(969\) | −12.2517 | − | 21.2205i | −0.393580 | − | 0.681701i | ||||
\(970\) | 17.2783 | − | 29.9269i | 0.554774 | − | 0.960896i | ||||
\(971\) | 25.6802 | 0.824116 | 0.412058 | − | 0.911158i | \(-0.364810\pi\) | ||||
0.412058 | + | 0.911158i | \(0.364810\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 37.0426 | + | 3.12030i | 1.18753 | + | 0.100032i | ||||
\(974\) | −16.2740 | −0.521453 | ||||||||
\(975\) | −21.9993 | − | 14.4988i | −0.704542 | − | 0.464332i | ||||
\(976\) | −4.67781 | + | 8.10220i | −0.149733 | + | 0.259345i | ||||
\(977\) | −40.6502 | −1.30052 | −0.650258 | − | 0.759713i | \(-0.725339\pi\) | ||||
−0.650258 | + | 0.759713i | \(0.725339\pi\) | |||||||
\(978\) | −3.89316 | + | 6.74316i | −0.124490 | + | 0.215622i | ||||
\(979\) | 22.4515 | − | 38.8871i | 0.717552 | − | 1.24284i | ||||
\(980\) | 8.54799 | + | 23.0217i | 0.273056 | + | 0.735400i | ||||
\(981\) | 1.14786 | − | 1.98816i | 0.0366484 | − | 0.0634769i | ||||
\(982\) | 38.0599 | 1.21454 | ||||||||
\(983\) | −2.39794 | + | 4.15335i | −0.0764823 | + | 0.132471i | −0.901730 | − | 0.432300i | \(-0.857702\pi\) |
0.825248 | + | 0.564771i | \(0.191036\pi\) | |||||||
\(984\) | 5.09300 | + | 8.82134i | 0.162359 | + | 0.281214i | ||||
\(985\) | −4.05906 | + | 7.03051i | −0.129333 | + | 0.224011i | ||||
\(986\) | −5.75525 | − | 9.96838i | −0.183284 | − | 0.317458i | ||||
\(987\) | 7.37352 | − | 10.6032i | 0.234702 | − | 0.337503i | ||||
\(988\) | 16.8857 | − | 8.46047i | 0.537205 | − | 0.269163i | ||||
\(989\) | 2.58916 | + | 4.48456i | 0.0823306 | + | 0.142601i | ||||
\(990\) | 22.4799 | 0.714458 | ||||||||
\(991\) | −39.1431 | −1.24342 | −0.621710 | − | 0.783247i | \(-0.713562\pi\) | ||||
−0.621710 | + | 0.783247i | \(0.713562\pi\) | |||||||
\(992\) | −8.92069 | −0.283232 | ||||||||
\(993\) | −18.8749 | −0.598977 | ||||||||
\(994\) | −8.43901 | + | 12.1354i | −0.267669 | + | 0.384911i | ||||
\(995\) | 9.98901 | − | 17.3015i | 0.316673 | − | 0.548494i | ||||
\(996\) | 1.29609 | + | 2.24489i | 0.0410682 | + | 0.0711321i | ||||
\(997\) | 28.7246 | + | 49.7524i | 0.909716 | + | 1.57567i | 0.814459 | + | 0.580221i | \(0.197034\pi\) |
0.0952567 | + | 0.995453i | \(0.469633\pi\) | |||||||
\(998\) | −34.2356 | −1.08371 | ||||||||
\(999\) | −1.94981 | + | 3.37717i | −0.0616893 | + | 0.106849i |
(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 | 546.2.k.c.445.4 | yes | 8 | |
3.2 | odd | 2 | 1638.2.p.h.991.1 | 8 | |||
7.2 | even | 3 | 546.2.j.c.289.4 | ✓ | 8 | ||
13.9 | even | 3 | 546.2.j.c.529.4 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.m.h.289.1 | 8 | |||
39.35 | odd | 6 | 1638.2.m.h.1621.1 | 8 | |||
91.9 | even | 3 | inner | 546.2.k.c.373.4 | yes | 8 | |
273.191 | odd | 6 | 1638.2.p.h.919.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.c.289.4 | ✓ | 8 | 7.2 | even | 3 | ||
546.2.j.c.529.4 | yes | 8 | 13.9 | even | 3 | ||
546.2.k.c.373.4 | yes | 8 | 91.9 | even | 3 | inner | |
546.2.k.c.445.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1638.2.m.h.289.1 | 8 | 21.2 | odd | 6 | |||
1638.2.m.h.1621.1 | 8 | 39.35 | odd | 6 | |||
1638.2.p.h.919.1 | 8 | 273.191 | odd | 6 | |||
1638.2.p.h.991.1 | 8 | 3.2 | odd | 2 |