Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,2,Mod(28,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.88259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.6053445140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(1.52045 + 0.553400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.99 |
Dual form | 361.2.e.j.62.1 |
$q$-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 \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.52045 | − | 0.553400i | −1.07512 | − | 0.391313i | −0.257033 | − | 0.966403i | \(-0.582745\pi\) |
−0.818090 | + | 0.575090i | \(0.804967\pi\) | |||||||
\(3\) | 0.0663277 | + | 0.376163i | 0.0382943 | + | 0.217178i | 0.997950 | − | 0.0640004i | \(-0.0203859\pi\) |
−0.959656 | + | 0.281178i | \(0.909275\pi\) | |||||||
\(4\) | 0.473442 | + | 0.397265i | 0.236721 | + | 0.198632i | ||||
\(5\) | 2.47897 | − | 2.08010i | 1.10863 | − | 0.930251i | 0.110655 | − | 0.993859i | \(-0.464705\pi\) |
0.997975 | + | 0.0636079i | \(0.0202607\pi\) | |||||||
\(6\) | 0.107320 | − | 0.608645i | 0.0438134 | − | 0.248478i | ||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | 1.11803 | + | 1.93649i | 0.395285 | + | 0.684653i | ||||
\(9\) | 2.68198 | − | 0.976160i | 0.893993 | − | 0.325387i | ||||
\(10\) | −4.92029 | + | 1.79084i | −1.55593 | + | 0.566314i | ||||
\(11\) | 0.809017 | + | 1.40126i | 0.243928 | + | 0.422495i | 0.961830 | − | 0.273649i | \(-0.0882307\pi\) |
−0.717902 | + | 0.696144i | \(0.754897\pi\) | |||||||
\(12\) | −0.118034 | + | 0.204441i | −0.0340735 | + | 0.0590170i | ||||
\(13\) | −0.173648 | + | 0.984808i | −0.0481613 | + | 0.273137i | −0.999373 | − | 0.0354021i | \(-0.988729\pi\) |
0.951212 | + | 0.308539i | \(0.0998399\pi\) | |||||||
\(14\) | 3.71846 | − | 3.12016i | 0.993800 | − | 0.833897i | ||||
\(15\) | 0.946883 | + | 0.794529i | 0.244484 | + | 0.205147i | ||||
\(16\) | −0.842906 | − | 4.78036i | −0.210726 | − | 1.19509i | ||||
\(17\) | −0.717861 | − | 0.261280i | −0.174107 | − | 0.0633697i | 0.253496 | − | 0.967336i | \(-0.418420\pi\) |
−0.427603 | + | 0.903967i | \(0.640642\pi\) | |||||||
\(18\) | −4.61803 | −1.08848 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | −1.07679 | − | 0.391920i | −0.234975 | − | 0.0855240i | ||||
\(22\) | −0.454617 | − | 2.57826i | −0.0969246 | − | 0.549687i | ||||
\(23\) | 4.12283 | + | 3.45946i | 0.859668 | + | 0.721347i | 0.961897 | − | 0.273413i | \(-0.0881527\pi\) |
−0.102228 | + | 0.994761i | \(0.532597\pi\) | |||||||
\(24\) | −0.654280 | + | 0.549006i | −0.133554 | + | 0.112065i | ||||
\(25\) | 0.950226 | − | 5.38900i | 0.190045 | − | 1.07780i | ||||
\(26\) | 0.809017 | − | 1.40126i | 0.158661 | − | 0.274809i | ||||
\(27\) | 1.11803 | + | 1.93649i | 0.215166 | + | 0.372678i | ||||
\(28\) | −1.74229 | + | 0.634140i | −0.329261 | + | 0.119841i | ||||
\(29\) | 3.39984 | − | 1.23744i | 0.631334 | − | 0.229787i | −0.00647759 | − | 0.999979i | \(-0.502062\pi\) |
0.637812 | + | 0.770192i | \(0.279840\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | 4.42705 | − | 7.66788i | 0.795122 | − | 1.37719i | −0.127640 | − | 0.991821i | \(-0.540740\pi\) |
0.922762 | − | 0.385371i | \(-0.125926\pi\) | |||||||
\(32\) | −0.587272 | + | 3.33059i | −0.103816 | + | 0.588770i | ||||
\(33\) | −0.473442 | + | 0.397265i | −0.0824156 | + | 0.0691549i | ||||
\(34\) | 0.946883 | + | 0.794529i | 0.162389 | + | 0.136261i | ||||
\(35\) | 1.68581 | + | 9.56071i | 0.284954 | + | 1.61606i | ||||
\(36\) | 1.65755 | + | 0.603300i | 0.276259 | + | 0.100550i | ||||
\(37\) | 8.85410 | 1.45561 | 0.727803 | − | 0.685787i | \(-0.240542\pi\) | ||||
0.727803 | + | 0.685787i | \(0.240542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.381966 | −0.0611635 | ||||||||
\(40\) | 6.79968 | + | 2.47488i | 1.07512 | + | 0.391313i | ||||
\(41\) | −0.520945 | − | 2.95442i | −0.0813579 | − | 0.461403i | −0.998083 | − | 0.0618855i | \(-0.980289\pi\) |
0.916725 | − | 0.399518i | \(-0.130822\pi\) | |||||||
\(42\) | 1.42032 | + | 1.19179i | 0.219161 | + | 0.183898i | ||||
\(43\) | −0.111764 | + | 0.0937814i | −0.0170439 | + | 0.0143015i | −0.651270 | − | 0.758846i | \(-0.725763\pi\) |
0.634226 | + | 0.773148i | \(0.281319\pi\) | |||||||
\(44\) | −0.173648 | + | 0.984808i | −0.0261784 | + | 0.148465i | ||||
\(45\) | 4.61803 | − | 7.99867i | 0.688416 | − | 1.19237i | ||||
\(46\) | −4.35410 | − | 7.54153i | −0.641977 | − | 1.11194i | ||||
\(47\) | −2.81908 | + | 1.02606i | −0.411205 | + | 0.149666i | −0.539335 | − | 0.842091i | \(-0.681325\pi\) |
0.128131 | + | 0.991757i | \(0.459102\pi\) | |||||||
\(48\) | 1.74229 | − | 0.634140i | 0.251477 | − | 0.0915303i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | −4.42705 | + | 7.66788i | −0.626080 | + | 1.08440i | ||||
\(51\) | 0.0506699 | − | 0.287363i | 0.00709520 | − | 0.0402389i | ||||
\(52\) | −0.473442 | + | 0.397265i | −0.0656545 | + | 0.0550907i | ||||
\(53\) | −4.84618 | − | 4.06643i | −0.665674 | − | 0.558567i | 0.246108 | − | 0.969243i | \(-0.420848\pi\) |
−0.911781 | + | 0.410676i | \(0.865293\pi\) | |||||||
\(54\) | −0.628265 | − | 3.56307i | −0.0854960 | − | 0.484872i | ||||
\(55\) | 4.92029 | + | 1.79084i | 0.663452 | + | 0.241477i | ||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | −0.306563 | − | 0.111580i | −0.0399112 | − | 0.0145265i | 0.321987 | − | 0.946744i | \(-0.395649\pi\) |
−0.361899 | + | 0.932217i | \(0.617871\pi\) | |||||||
\(60\) | 0.132655 | + | 0.752326i | 0.0171257 | + | 0.0971249i | ||||
\(61\) | −7.84128 | − | 6.57962i | −1.00397 | − | 0.842434i | −0.0164434 | − | 0.999865i | \(-0.505234\pi\) |
−0.987530 | + | 0.157431i | \(0.949679\pi\) | |||||||
\(62\) | −10.9745 | + | 9.20873i | −1.39377 | + | 1.16951i | ||||
\(63\) | −1.48683 | + | 8.43223i | −0.187323 | + | 1.06236i | ||||
\(64\) | −2.11803 | + | 3.66854i | −0.264754 | + | 0.458568i | ||||
\(65\) | 1.61803 | + | 2.80252i | 0.200692 | + | 0.347609i | ||||
\(66\) | 0.939693 | − | 0.342020i | 0.115668 | − | 0.0420998i | ||||
\(67\) | 6.57785 | − | 2.39414i | 0.803612 | − | 0.292491i | 0.0926296 | − | 0.995701i | \(-0.470473\pi\) |
0.710982 | + | 0.703210i | \(0.248251\pi\) | |||||||
\(68\) | −0.236068 | − | 0.408882i | −0.0286274 | − | 0.0495842i | ||||
\(69\) | −1.02786 | + | 1.78031i | −0.123740 | + | 0.214324i | ||||
\(70\) | 2.72770 | − | 15.4696i | 0.326023 | − | 1.84897i | ||||
\(71\) | −5.72399 | + | 4.80300i | −0.679312 | + | 0.570011i | −0.915805 | − | 0.401622i | \(-0.868446\pi\) |
0.236493 | + | 0.971633i | \(0.424002\pi\) | |||||||
\(72\) | 4.88887 | + | 4.10225i | 0.576159 | + | 0.483455i | ||||
\(73\) | −0.470275 | − | 2.66706i | −0.0550415 | − | 0.312156i | 0.944840 | − | 0.327531i | \(-0.106217\pi\) |
−0.999882 | + | 0.0153756i | \(0.995106\pi\) | |||||||
\(74\) | −13.4623 | − | 4.89986i | −1.56496 | − | 0.569597i | ||||
\(75\) | 2.09017 | 0.241352 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | 0.580762 | + | 0.211380i | 0.0657583 | + | 0.0239341i | ||||
\(79\) | 2.32973 | + | 13.2126i | 0.262116 | + | 1.48653i | 0.777125 | + | 0.629347i | \(0.216678\pi\) |
−0.515009 | + | 0.857185i | \(0.672211\pi\) | |||||||
\(80\) | −12.0332 | − | 10.0970i | −1.34535 | − | 1.12888i | ||||
\(81\) | 5.90483 | − | 4.95474i | 0.656092 | − | 0.550526i | ||||
\(82\) | −0.842906 | + | 4.78036i | −0.0930834 | + | 0.527902i | ||||
\(83\) | −4.23607 | + | 7.33708i | −0.464969 | + | 0.805350i | −0.999200 | − | 0.0399887i | \(-0.987268\pi\) |
0.534231 | + | 0.845338i | \(0.320601\pi\) | |||||||
\(84\) | −0.354102 | − | 0.613323i | −0.0386357 | − | 0.0669190i | ||||
\(85\) | −2.32305 | + | 0.845520i | −0.251970 | + | 0.0917096i | ||||
\(86\) | 0.221831 | − | 0.0807400i | 0.0239207 | − | 0.00870642i | ||||
\(87\) | 0.690983 | + | 1.19682i | 0.0740812 | + | 0.128312i | ||||
\(88\) | −1.80902 | + | 3.13331i | −0.192842 | + | 0.334012i | ||||
\(89\) | −1.34819 | + | 7.64598i | −0.142908 | + | 0.810472i | 0.826115 | + | 0.563502i | \(0.190546\pi\) |
−0.969023 | + | 0.246971i | \(0.920565\pi\) | |||||||
\(90\) | −11.4480 | + | 9.60599i | −1.20672 | + | 1.01256i | ||||
\(91\) | −2.29813 | − | 1.92836i | −0.240910 | − | 0.202147i | ||||
\(92\) | 0.577595 | + | 3.27570i | 0.0602185 | + | 0.341516i | ||||
\(93\) | 3.17801 | + | 1.15670i | 0.329544 | + | 0.119944i | ||||
\(94\) | 4.85410 | 0.500662 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.29180 | −0.131843 | ||||||||
\(97\) | −13.0186 | − | 4.73838i | −1.32184 | − | 0.481110i | −0.417791 | − | 0.908543i | \(-0.637196\pi\) |
−0.904047 | + | 0.427433i | \(0.859418\pi\) | |||||||
\(98\) | 0.561937 | + | 3.18690i | 0.0567642 | + | 0.321926i | ||||
\(99\) | 3.53762 | + | 2.96842i | 0.355544 | + | 0.298337i | ||||
\(100\) | 2.59074 | − | 2.17389i | 0.259074 | − | 0.217389i | ||||
\(101\) | −1.59415 | + | 9.04087i | −0.158624 | + | 0.899600i | 0.796774 | + | 0.604278i | \(0.206538\pi\) |
−0.955398 | + | 0.295323i | \(0.904573\pi\) | |||||||
\(102\) | −0.236068 | + | 0.408882i | −0.0233742 | + | 0.0404853i | ||||
\(103\) | −7.16312 | − | 12.4069i | −0.705803 | − | 1.22249i | −0.966401 | − | 0.257039i | \(-0.917253\pi\) |
0.260598 | − | 0.965447i | \(-0.416080\pi\) | |||||||
\(104\) | −2.10122 | + | 0.764780i | −0.206041 | + | 0.0749929i | ||||
\(105\) | −3.48457 | + | 1.26828i | −0.340059 | + | 0.123771i | ||||
\(106\) | 5.11803 | + | 8.86469i | 0.497107 | + | 0.861015i | ||||
\(107\) | −8.20820 | + | 14.2170i | −0.793517 | + | 1.37441i | 0.130260 | + | 0.991480i | \(0.458419\pi\) |
−0.923777 | + | 0.382932i | \(0.874914\pi\) | |||||||
\(108\) | −0.239976 | + | 1.36097i | −0.0230917 | + | 0.130959i | ||||
\(109\) | −2.52166 | + | 2.11593i | −0.241531 | + | 0.202669i | −0.755515 | − | 0.655131i | \(-0.772613\pi\) |
0.513984 | + | 0.857800i | \(0.328169\pi\) | |||||||
\(110\) | −6.49003 | − | 5.44578i | −0.618800 | − | 0.519235i | ||||
\(111\) | 0.587272 | + | 3.33059i | 0.0557414 | + | 0.316125i | ||||
\(112\) | 13.6841 | + | 4.98060i | 1.29303 | + | 0.470623i | ||||
\(113\) | 6.76393 | 0.636297 | 0.318149 | − | 0.948041i | \(-0.396939\pi\) | ||||
0.318149 | + | 0.948041i | \(0.396939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4164 | 1.62409 | ||||||||
\(116\) | 2.10122 | + | 0.764780i | 0.195093 | + | 0.0710081i | ||||
\(117\) | 0.495610 | + | 2.81074i | 0.0458191 | + | 0.259853i | ||||
\(118\) | 0.404367 | + | 0.339304i | 0.0372250 | + | 0.0312355i | ||||
\(119\) | 1.75562 | − | 1.47314i | 0.160937 | − | 0.135042i | ||||
\(120\) | −0.479952 | + | 2.72194i | −0.0438134 | + | 0.248478i | ||||
\(121\) | 4.19098 | − | 7.25900i | 0.380998 | − | 0.659909i | ||||
\(122\) | 8.28115 | + | 14.3434i | 0.749740 | + | 1.29859i | ||||
\(123\) | 1.07679 | − | 0.391920i | 0.0970911 | − | 0.0353383i | ||||
\(124\) | 5.14213 | − | 1.87158i | 0.461777 | − | 0.168073i | ||||
\(125\) | −0.763932 | − | 1.32317i | −0.0683282 | − | 0.118348i | ||||
\(126\) | 6.92705 | − | 11.9980i | 0.617111 | − | 1.06887i | ||||
\(127\) | 1.00090 | − | 5.67636i | 0.0888152 | − | 0.503696i | −0.907653 | − | 0.419722i | \(-0.862128\pi\) |
0.996468 | − | 0.0839740i | \(-0.0267613\pi\) | |||||||
\(128\) | 10.4320 | − | 8.75350i | 0.922069 | − | 0.773708i | ||||
\(129\) | −0.0426902 | − | 0.0358213i | −0.00375866 | − | 0.00315389i | ||||
\(130\) | −0.909234 | − | 5.15652i | −0.0797451 | − | 0.452257i | ||||
\(131\) | −14.1801 | − | 5.16114i | −1.23892 | − | 0.450931i | −0.362279 | − | 0.932070i | \(-0.618001\pi\) |
−0.876644 | + | 0.481139i | \(0.840223\pi\) | |||||||
\(132\) | −0.381966 | −0.0332459 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.3262 | −0.978438 | ||||||||
\(135\) | 6.79968 | + | 2.47488i | 0.585223 | + | 0.213004i | ||||
\(136\) | −0.296626 | − | 1.68225i | −0.0254355 | − | 0.144252i | ||||
\(137\) | 5.72399 | + | 4.80300i | 0.489033 | + | 0.410348i | 0.853680 | − | 0.520798i | \(-0.174366\pi\) |
−0.364646 | + | 0.931146i | \(0.618810\pi\) | |||||||
\(138\) | 2.54805 | − | 2.13806i | 0.216904 | − | 0.182004i | ||||
\(139\) | 2.56971 | − | 14.5736i | 0.217960 | − | 1.23611i | −0.657736 | − | 0.753249i | \(-0.728486\pi\) |
0.875696 | − | 0.482864i | \(-0.160403\pi\) | |||||||
\(140\) | −3.00000 | + | 5.19615i | −0.253546 | + | 0.439155i | ||||
\(141\) | −0.572949 | − | 0.992377i | −0.0482510 | − | 0.0835732i | ||||
\(142\) | 11.3610 | − | 4.13508i | 0.953398 | − | 0.347008i | ||||
\(143\) | −1.52045 | + | 0.553400i | −0.127147 | + | 0.0462777i | ||||
\(144\) | −6.92705 | − | 11.9980i | −0.577254 | − | 0.999834i | ||||
\(145\) | 5.85410 | − | 10.1396i | 0.486157 | − | 0.842048i | ||||
\(146\) | −0.760920 | + | 4.31539i | −0.0629742 | + | 0.357145i | ||||
\(147\) | 0.585206 | − | 0.491046i | 0.0482670 | − | 0.0405008i | ||||
\(148\) | 4.19190 | + | 3.51742i | 0.344572 | + | 0.289130i | ||||
\(149\) | −0.331639 | − | 1.88082i | −0.0271689 | − | 0.154082i | 0.968205 | − | 0.250157i | \(-0.0804823\pi\) |
−0.995374 | + | 0.0960748i | \(0.969371\pi\) | |||||||
\(150\) | −3.17801 | − | 1.15670i | −0.259483 | − | 0.0944442i | ||||
\(151\) | −21.0902 | −1.71629 | −0.858147 | − | 0.513404i | \(-0.828384\pi\) | ||||
−0.858147 | + | 0.513404i | \(0.828384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.18034 | −0.176270 | ||||||||
\(154\) | 7.38044 | + | 2.68626i | 0.594733 | + | 0.216465i | ||||
\(155\) | −4.97545 | − | 28.2172i | −0.399638 | − | 2.26646i | ||||
\(156\) | −0.180839 | − | 0.151742i | −0.0144787 | − | 0.0121490i | ||||
\(157\) | −13.6770 | + | 11.4764i | −1.09155 | + | 0.915916i | −0.996828 | − | 0.0795880i | \(-0.974640\pi\) |
−0.0947184 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(158\) | 3.76959 | − | 21.3784i | 0.299892 | − | 1.70077i | ||||
\(159\) | 1.20820 | − | 2.09267i | 0.0958168 | − | 0.165960i | ||||
\(160\) | 5.47214 | + | 9.47802i | 0.432610 | + | 0.749303i | ||||
\(161\) | −15.1722 | + | 5.52222i | −1.19574 | + | 0.435212i | ||||
\(162\) | −11.7200 | + | 4.26572i | −0.920808 | + | 0.335147i | ||||
\(163\) | −0.881966 | − | 1.52761i | −0.0690809 | − | 0.119652i | 0.829416 | − | 0.558631i | \(-0.188673\pi\) |
−0.898497 | + | 0.438980i | \(0.855340\pi\) | |||||||
\(164\) | 0.927051 | − | 1.60570i | 0.0723905 | − | 0.125384i | ||||
\(165\) | −0.347296 | + | 1.96962i | −0.0270370 | + | 0.153334i | ||||
\(166\) | 10.5011 | − | 8.81146i | 0.815043 | − | 0.683902i | ||||
\(167\) | 15.5017 | + | 13.0075i | 1.19956 | + | 1.00655i | 0.999642 | + | 0.0267373i | \(0.00851176\pi\) |
0.199917 | + | 0.979813i | \(0.435933\pi\) | |||||||
\(168\) | −0.444940 | − | 2.52338i | −0.0343278 | − | 0.194683i | ||||
\(169\) | 11.2763 | + | 4.10424i | 0.867409 | + | 0.315711i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0901699 | −0.00687539 | ||||||||
\(173\) | 0.443663 | + | 0.161480i | 0.0337310 | + | 0.0122771i | 0.358831 | − | 0.933403i | \(-0.383176\pi\) |
−0.325100 | + | 0.945680i | \(0.605398\pi\) | |||||||
\(174\) | −0.388289 | − | 2.20210i | −0.0294361 | − | 0.166941i | ||||
\(175\) | 12.5757 | + | 10.5523i | 0.950633 | + | 0.797676i | ||||
\(176\) | 6.01659 | − | 5.04852i | 0.453518 | − | 0.380546i | ||||
\(177\) | 0.0216386 | − | 0.122719i | 0.00162646 | − | 0.00922410i | ||||
\(178\) | 6.28115 | − | 10.8793i | 0.470792 | − | 0.815436i | ||||
\(179\) | −6.11803 | − | 10.5967i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840680i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486416i | \(0.984511\pi\) | |||||||
\(180\) | 5.36396 | − | 1.95232i | 0.399806 | − | 0.145517i | ||||
\(181\) | −11.2763 | + | 4.10424i | −0.838162 | + | 0.305066i | −0.725204 | − | 0.688534i | \(-0.758255\pi\) |
−0.112958 | + | 0.993600i | \(0.536032\pi\) | |||||||
\(182\) | 2.42705 | + | 4.20378i | 0.179905 | + | 0.311605i | ||||
\(183\) | 1.95492 | − | 3.38601i | 0.144511 | − | 0.250301i | ||||
\(184\) | −2.08976 | + | 11.8516i | −0.154059 | + | 0.873712i | ||||
\(185\) | 21.9491 | − | 18.4175i | 1.61373 | − | 1.35408i | ||||
\(186\) | −4.19190 | − | 3.51742i | −0.307365 | − | 0.257910i | ||||
\(187\) | −0.214641 | − | 1.21729i | −0.0156961 | − | 0.0890170i | ||||
\(188\) | −1.74229 | − | 0.634140i | −0.127069 | − | 0.0462494i | ||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2361 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(192\) | −1.52045 | − | 0.553400i | −0.109729 | − | 0.0399382i | ||||
\(193\) | 0.877918 | + | 4.97892i | 0.0631939 | + | 0.358391i | 0.999964 | + | 0.00844596i | \(0.00268847\pi\) |
−0.936770 | + | 0.349945i | \(0.886200\pi\) | |||||||
\(194\) | 17.1720 | + | 14.4090i | 1.23288 | + | 1.03451i | ||||
\(195\) | −0.946883 | + | 0.794529i | −0.0678077 | + | 0.0568974i | ||||
\(196\) | 0.214641 | − | 1.21729i | 0.0153315 | − | 0.0869492i | ||||
\(197\) | −1.50000 | + | 2.59808i | −0.106871 | + | 0.185105i | −0.914501 | − | 0.404584i | \(-0.867416\pi\) |
0.807630 | + | 0.589689i | \(0.200750\pi\) | |||||||
\(198\) | −3.73607 | − | 6.47106i | −0.265511 | − | 0.459878i | ||||
\(199\) | 12.6073 | − | 4.58868i | 0.893708 | − | 0.325283i | 0.145979 | − | 0.989288i | \(-0.453367\pi\) |
0.747728 | + | 0.664005i | \(0.231144\pi\) | |||||||
\(200\) | 11.4981 | − | 4.18498i | 0.813041 | − | 0.295923i | ||||
\(201\) | 1.33688 | + | 2.31555i | 0.0942963 | + | 0.163326i | ||||
\(202\) | 7.42705 | − | 12.8640i | 0.522565 | − | 0.905110i | ||||
\(203\) | −1.88480 | + | 10.6892i | −0.132287 | + | 0.750235i | ||||
\(204\) | 0.138148 | − | 0.115920i | 0.00967232 | − | 0.00811604i | ||||
\(205\) | −7.43692 | − | 6.24031i | −0.519417 | − | 0.435842i | ||||
\(206\) | 4.02522 | + | 22.8282i | 0.280451 | + | 1.59051i | ||||
\(207\) | 14.4343 | + | 5.25366i | 1.00325 | + | 0.365155i | ||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | 3.62167 | + | 1.31818i | 0.249326 | + | 0.0907473i | 0.463660 | − | 0.886013i | \(-0.346536\pi\) |
−0.214334 | + | 0.976760i | \(0.568758\pi\) | |||||||
\(212\) | −0.678935 | − | 3.85043i | −0.0466294 | − | 0.264449i | ||||
\(213\) | −2.18637 | − | 1.83458i | −0.149808 | − | 0.125703i | ||||
\(214\) | 20.3479 | − | 17.0739i | 1.39095 | − | 1.16715i | ||||
\(215\) | −0.0819855 | + | 0.464963i | −0.00559137 | + | 0.0317102i | ||||
\(216\) | −2.50000 | + | 4.33013i | −0.170103 | + | 0.294628i | ||||
\(217\) | 13.2812 | + | 23.0036i | 0.901583 | + | 1.56159i | ||||
\(218\) | 5.00503 | − | 1.82168i | 0.338983 | − | 0.123380i | ||||
\(219\) | 0.972057 | − | 0.353800i | 0.0656856 | − | 0.0239076i | ||||
\(220\) | 1.61803 | + | 2.80252i | 0.109088 | + | 0.188946i | ||||
\(221\) | 0.381966 | − | 0.661585i | 0.0256938 | − | 0.0445030i | ||||
\(222\) | 0.950226 | − | 5.38900i | 0.0637750 | − | 0.361686i | ||||
\(223\) | −8.92631 | + | 7.49007i | −0.597750 | + | 0.501572i | −0.890722 | − | 0.454549i | \(-0.849800\pi\) |
0.292971 | + | 0.956121i | \(0.405356\pi\) | |||||||
\(224\) | −7.77221 | − | 6.52166i | −0.519303 | − | 0.435747i | ||||
\(225\) | −2.71204 | − | 15.3808i | −0.180803 | − | 1.02538i | ||||
\(226\) | −10.2843 | − | 3.74316i | −0.684098 | − | 0.248991i | ||||
\(227\) | 16.4164 | 1.08960 | 0.544798 | − | 0.838568i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838568i | \(0.316606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6180 | −0.899905 | −0.449953 | − | 0.893052i | \(-0.648559\pi\) | ||||
−0.449953 | + | 0.893052i | \(0.648559\pi\) | |||||||
\(230\) | −26.4809 | − | 9.63824i | −1.74610 | − | 0.635527i | ||||
\(231\) | −0.321961 | − | 1.82593i | −0.0211835 | − | 0.120138i | ||||
\(232\) | 6.19743 | + | 5.20026i | 0.406881 | + | 0.341414i | ||||
\(233\) | 3.46855 | − | 2.91045i | 0.227232 | − | 0.190670i | −0.522063 | − | 0.852907i | \(-0.674837\pi\) |
0.749294 | + | 0.662237i | \(0.230393\pi\) | |||||||
\(234\) | 0.801913 | − | 4.54788i | 0.0524227 | − | 0.297304i | ||||
\(235\) | −4.85410 | + | 8.40755i | −0.316647 | + | 0.548448i | ||||
\(236\) | −0.100813 | − | 0.174613i | −0.00656237 | − | 0.0113664i | ||||
\(237\) | −4.81556 | + | 1.75272i | −0.312804 | + | 0.113851i | ||||
\(238\) | −3.48457 | + | 1.26828i | −0.225871 | + | 0.0822104i | ||||
\(239\) | 0.163119 | + | 0.282530i | 0.0105513 | + | 0.0182754i | 0.871253 | − | 0.490834i | \(-0.163308\pi\) |
−0.860702 | + | 0.509110i | \(0.829975\pi\) | |||||||
\(240\) | 3.00000 | − | 5.19615i | 0.193649 | − | 0.335410i | ||||
\(241\) | 0.552260 | − | 3.13202i | 0.0355742 | − | 0.201751i | −0.961841 | − | 0.273610i | \(-0.911782\pi\) |
0.997415 | + | 0.0718591i | \(0.0228932\pi\) | |||||||
\(242\) | −10.3893 | + | 8.71768i | −0.667851 | + | 0.560394i | ||||
\(243\) | 7.39423 | + | 6.20449i | 0.474340 | + | 0.398018i | ||||
\(244\) | −1.09854 | − | 6.23013i | −0.0703268 | − | 0.398843i | ||||
\(245\) | −6.08182 | − | 2.21360i | −0.388553 | − | 0.141422i | ||||
\(246\) | −1.85410 | −0.118213 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.7984 | 1.25720 | ||||||||
\(249\) | −3.04091 | − | 1.10680i | −0.192710 | − | 0.0701406i | ||||
\(250\) | 0.429282 | + | 2.43458i | 0.0271502 | + | 0.153976i | ||||
\(251\) | −19.4274 | − | 16.3015i | −1.22625 | − | 1.02894i | −0.998474 | − | 0.0552293i | \(-0.982411\pi\) |
−0.227773 | − | 0.973714i | \(-0.573145\pi\) | |||||||
\(252\) | −4.05375 | + | 3.40150i | −0.255362 | + | 0.214274i | ||||
\(253\) | −1.51216 | + | 8.57591i | −0.0950689 | + | 0.539163i | ||||
\(254\) | −4.66312 | + | 8.07676i | −0.292590 | + | 0.506781i | ||||
\(255\) | −0.472136 | − | 0.817763i | −0.0295663 | − | 0.0512103i | ||||
\(256\) | −12.7444 | + | 4.63858i | −0.796525 | + | 0.289911i | ||||
\(257\) | −19.1328 | + | 6.96376i | −1.19347 | + | 0.434388i | −0.860941 | − | 0.508705i | \(-0.830124\pi\) |
−0.332529 | + | 0.943093i | \(0.607902\pi\) | |||||||
\(258\) | 0.0450850 | + | 0.0780895i | 0.00280687 | + | 0.00486164i | ||||
\(259\) | −13.2812 | + | 23.0036i | −0.825251 | + | 1.42938i | ||||
\(260\) | −0.347296 | + | 1.96962i | −0.0215384 | + | 0.122150i | ||||
\(261\) | 7.91036 | − | 6.63758i | 0.489639 | − | 0.410856i | ||||
\(262\) | 18.7041 | + | 15.6946i | 1.15554 | + | 0.969613i | ||||
\(263\) | −2.59505 | − | 14.7172i | −0.160017 | − | 0.907504i | −0.954054 | − | 0.299634i | \(-0.903135\pi\) |
0.794037 | − | 0.607870i | \(-0.207976\pi\) | |||||||
\(264\) | −1.29862 | − | 0.472660i | −0.0799247 | − | 0.0290902i | ||||
\(265\) | −20.4721 | −1.25759 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.96556 | −0.181489 | ||||||||
\(268\) | 4.06533 | + | 1.47966i | 0.248330 | + | 0.0903847i | ||||
\(269\) | 5.26610 | + | 29.8655i | 0.321080 | + | 1.82093i | 0.535903 | + | 0.844280i | \(0.319971\pi\) |
−0.214823 | + | 0.976653i | \(0.568918\pi\) | |||||||
\(270\) | −8.96900 | − | 7.52589i | −0.545836 | − | 0.458011i | ||||
\(271\) | 0.877809 | − | 0.736569i | 0.0533231 | − | 0.0447434i | −0.615737 | − | 0.787952i | \(-0.711141\pi\) |
0.669060 | + | 0.743209i | \(0.266697\pi\) | |||||||
\(272\) | −0.643923 | + | 3.65187i | −0.0390436 | + | 0.221427i | ||||
\(273\) | 0.572949 | − | 0.992377i | 0.0346765 | − | 0.0600614i | ||||
\(274\) | −6.04508 | − | 10.4704i | −0.365197 | − | 0.632540i | ||||
\(275\) | 8.32013 | − | 3.02828i | 0.501723 | − | 0.182612i | ||||
\(276\) | −1.19389 | + | 0.434540i | −0.0718637 | + | 0.0261562i | ||||
\(277\) | −5.70820 | − | 9.88690i | −0.342973 | − | 0.594046i | 0.642011 | − | 0.766696i | \(-0.278101\pi\) |
−0.984983 | + | 0.172650i | \(0.944767\pi\) | |||||||
\(278\) | −11.9721 | + | 20.7363i | −0.718041 | + | 1.24368i | ||||
\(279\) | 4.38818 | − | 24.8866i | 0.262713 | − | 1.48992i | ||||
\(280\) | −16.6294 | + | 13.9538i | −0.993800 | + | 0.833897i | ||||
\(281\) | −22.6033 | − | 18.9665i | −1.34840 | − | 1.13144i | −0.979381 | − | 0.202024i | \(-0.935248\pi\) |
−0.369022 | − | 0.929421i | \(-0.620307\pi\) | |||||||
\(282\) | 0.321961 | + | 1.82593i | 0.0191725 | + | 0.108733i | ||||
\(283\) | −24.4644 | − | 8.90430i | −1.45426 | − | 0.529306i | −0.510479 | − | 0.859890i | \(-0.670532\pi\) |
−0.943777 | + | 0.330584i | \(0.892754\pi\) | |||||||
\(284\) | −4.61803 | −0.274030 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.61803 | 0.154808 | ||||||||
\(287\) | 8.45723 | + | 3.07818i | 0.499215 | + | 0.181699i | ||||
\(288\) | 1.67613 | + | 9.50583i | 0.0987672 | + | 0.560137i | ||||
\(289\) | −12.5757 | − | 10.5523i | −0.739747 | − | 0.620721i | ||||
\(290\) | −14.5122 | + | 12.1771i | −0.852183 | + | 0.715066i | ||||
\(291\) | 0.918911 | − | 5.21140i | 0.0538675 | − | 0.305498i | ||||
\(292\) | 0.836881 | − | 1.44952i | 0.0489748 | − | 0.0848268i | ||||
\(293\) | 5.07295 | + | 8.78661i | 0.296365 | + | 0.513319i | 0.975301 | − | 0.220878i | \(-0.0708922\pi\) |
−0.678937 | + | 0.734197i | \(0.737559\pi\) | |||||||
\(294\) | −1.16152 | + | 0.422760i | −0.0677415 | + | 0.0246559i | ||||
\(295\) | −0.992060 | + | 0.361080i | −0.0577600 | + | 0.0210229i | ||||
\(296\) | 9.89919 | + | 17.1459i | 0.575379 | + | 0.996585i | ||||
\(297\) | −1.80902 | + | 3.13331i | −0.104970 | + | 0.181813i | ||||
\(298\) | −0.536602 | + | 3.04322i | −0.0310845 | + | 0.176289i | ||||
\(299\) | −4.12283 | + | 3.45946i | −0.238429 | + | 0.200066i | ||||
\(300\) | 0.989573 | + | 0.830351i | 0.0571330 | + | 0.0479403i | ||||
\(301\) | −0.0760048 | − | 0.431045i | −0.00438084 | − | 0.0248450i | ||||
\(302\) | 32.0666 | + | 11.6713i | 1.84523 | + | 0.671608i | ||||
\(303\) | −3.50658 | −0.201448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.1246 | −1.89671 | ||||||||
\(306\) | 3.31511 | + | 1.20660i | 0.189512 | + | 0.0689768i | ||||
\(307\) | −3.00867 | − | 17.0630i | −0.171714 | − | 0.973838i | −0.941869 | − | 0.335981i | \(-0.890932\pi\) |
0.770155 | − | 0.637857i | \(-0.220179\pi\) | |||||||
\(308\) | −2.29813 | − | 1.92836i | −0.130948 | − | 0.109879i | ||||
\(309\) | 4.19190 | − | 3.51742i | 0.238469 | − | 0.200099i | ||||
\(310\) | −8.05045 | + | 45.6564i | −0.457235 | + | 2.59311i | ||||
\(311\) | −6.32624 | + | 10.9574i | −0.358728 | + | 0.621335i | −0.987749 | − | 0.156053i | \(-0.950123\pi\) |
0.629021 | + | 0.777389i | \(0.283456\pi\) | |||||||
\(312\) | −0.427051 | − | 0.739674i | −0.0241770 | − | 0.0418758i | ||||
\(313\) | 10.6432 | − | 3.87380i | 0.601588 | − | 0.218960i | −0.0232304 | − | 0.999730i | \(-0.507395\pi\) |
0.624819 | + | 0.780770i | \(0.285173\pi\) | |||||||
\(314\) | 27.1464 | − | 9.88046i | 1.53196 | − | 0.557587i | ||||
\(315\) | 13.8541 | + | 23.9960i | 0.780590 | + | 1.35202i | ||||
\(316\) | −4.14590 | + | 7.18091i | −0.233225 | + | 0.403958i | ||||
\(317\) | 3.12567 | − | 17.7265i | 0.175555 | − | 0.995622i | −0.761946 | − | 0.647640i | \(-0.775756\pi\) |
0.937501 | − | 0.347982i | \(-0.113133\pi\) | |||||||
\(318\) | −2.99510 | + | 2.51319i | −0.167957 | + | 0.140933i | ||||
\(319\) | 4.48450 | + | 3.76294i | 0.251084 | + | 0.210684i | ||||
\(320\) | 2.38040 | + | 13.4999i | 0.133069 | + | 0.754670i | ||||
\(321\) | −5.89235 | − | 2.14464i | −0.328879 | − | 0.119702i | ||||
\(322\) | 26.1246 | 1.45587 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.76393 | 0.264663 | ||||||||
\(325\) | 5.14213 | + | 1.87158i | 0.285234 | + | 0.103817i | ||||
\(326\) | 0.495610 | + | 2.81074i | 0.0274493 | + | 0.155673i | ||||
\(327\) | −0.963189 | − | 0.808212i | −0.0532645 | − | 0.0446942i | ||||
\(328\) | 5.13878 | − | 4.31195i | 0.283742 | − | 0.238088i | ||||
\(329\) | 1.56283 | − | 8.86327i | 0.0861618 | − | 0.488648i | ||||
\(330\) | 1.61803 | − | 2.80252i | 0.0890698 | − | 0.154273i | ||||
\(331\) | −5.47214 | − | 9.47802i | −0.300776 | − | 0.520959i | 0.675536 | − | 0.737327i | \(-0.263912\pi\) |
−0.976312 | + | 0.216368i | \(0.930579\pi\) | |||||||
\(332\) | −4.92029 | + | 1.79084i | −0.270036 | + | 0.0982852i | ||||
\(333\) | 23.7465 | − | 8.64302i | 1.30130 | − | 0.473635i | ||||
\(334\) | −16.3713 | − | 28.3560i | −0.895799 | − | 1.55157i | ||||
\(335\) | 11.3262 | − | 19.6176i | 0.618818 | − | 1.07183i | ||||
\(336\) | −0.965884 | + | 5.47780i | −0.0526933 | + | 0.298839i | ||||
\(337\) | −13.1182 | + | 11.0075i | −0.714595 | + | 0.599616i | −0.925884 | − | 0.377807i | \(-0.876678\pi\) |
0.211290 | + | 0.977424i | \(0.432234\pi\) | |||||||
\(338\) | −14.8738 | − | 12.4806i | −0.809030 | − | 0.678857i | ||||
\(339\) | 0.448636 | + | 2.54434i | 0.0243666 | + | 0.138190i | ||||
\(340\) | −1.43572 | − | 0.522560i | −0.0778630 | − | 0.0283398i | ||||
\(341\) | 14.3262 | 0.775809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | −0.306563 | − | 0.111580i | −0.0165288 | − | 0.00601599i | ||||
\(345\) | 1.15519 | + | 6.55141i | 0.0621934 | + | 0.352716i | ||||
\(346\) | −0.585206 | − | 0.491046i | −0.0314609 | − | 0.0263988i | ||||
\(347\) | −19.4701 | + | 16.3374i | −1.04521 | + | 0.877035i | −0.992582 | − | 0.121579i | \(-0.961204\pi\) |
−0.0526279 | + | 0.998614i | \(0.516760\pi\) | |||||||
\(348\) | −0.148313 | + | 0.841126i | −0.00795042 | + | 0.0450891i | ||||
\(349\) | 10.4894 | − | 18.1681i | 0.561482 | − | 0.972516i | −0.435885 | − | 0.900002i | \(-0.643565\pi\) |
0.997367 | − | 0.0725137i | \(-0.0231021\pi\) | |||||||
\(350\) | −13.2812 | − | 23.0036i | −0.709907 | − | 1.22960i | ||||
\(351\) | −2.10122 | + | 0.764780i | −0.112155 | + | 0.0408210i | ||||
\(352\) | −5.14213 | + | 1.87158i | −0.274076 | + | 0.0997556i | ||||
\(353\) | −12.2254 | − | 21.1751i | −0.650694 | − | 1.12703i | −0.982955 | − | 0.183847i | \(-0.941145\pi\) |
0.332261 | − | 0.943187i | \(-0.392188\pi\) | |||||||
\(354\) | −0.100813 | + | 0.174613i | −0.00535815 | + | 0.00928059i | ||||
\(355\) | −4.19887 | + | 23.8130i | −0.222853 | + | 1.26386i | ||||
\(356\) | −3.67577 | + | 3.08434i | −0.194815 | + | 0.163469i | ||||
\(357\) | 0.670586 | + | 0.562689i | 0.0354912 | + | 0.0297806i | ||||
\(358\) | 3.43795 | + | 19.4976i | 0.181701 | + | 1.03048i | ||||
\(359\) | −6.61021 | − | 2.40592i | −0.348874 | − | 0.126980i | 0.161639 | − | 0.986850i | \(-0.448322\pi\) |
−0.510512 | + | 0.859870i | \(0.670544\pi\) | |||||||
\(360\) | 20.6525 | 1.08848 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 19.4164 | 1.02050 | ||||||||
\(363\) | 3.00854 | + | 1.09502i | 0.157908 | + | 0.0574737i | ||||
\(364\) | −0.321961 | − | 1.82593i | −0.0168754 | − | 0.0957049i | ||||
\(365\) | −6.71356 | − | 5.63335i | −0.351404 | − | 0.294863i | ||||
\(366\) | −4.84618 | + | 4.06643i | −0.253314 | + | 0.212556i | ||||
\(367\) | −2.76869 | + | 15.7020i | −0.144525 | + | 0.819640i | 0.823223 | + | 0.567718i | \(0.192174\pi\) |
−0.967748 | + | 0.251922i | \(0.918937\pi\) | |||||||
\(368\) | 13.0623 | − | 22.6246i | 0.680920 | − | 1.17939i | ||||
\(369\) | −4.28115 | − | 7.41517i | −0.222868 | − | 0.386019i | ||||
\(370\) | −43.5648 | + | 15.8563i | −2.26483 | + | 0.824329i | ||||
\(371\) | 17.8342 | − | 6.49110i | 0.925903 | − | 0.337001i | ||||
\(372\) | 1.04508 | + | 1.81014i | 0.0541851 | + | 0.0938514i | ||||
\(373\) | 2.73607 | − | 4.73901i | 0.141668 | − | 0.245377i | −0.786457 | − | 0.617645i | \(-0.788087\pi\) |
0.928125 | + | 0.372269i | \(0.121420\pi\) | |||||||
\(374\) | −0.347296 | + | 1.96962i | −0.0179583 | + | 0.101846i | ||||
\(375\) | 0.447058 | − | 0.375126i | 0.0230860 | − | 0.0193714i | ||||
\(376\) | −5.13878 | − | 4.31195i | −0.265012 | − | 0.222372i | ||||
\(377\) | 0.628265 | + | 3.56307i | 0.0323573 | + | 0.183507i | ||||
\(378\) | 10.1995 | + | 3.71232i | 0.524607 | + | 0.190941i | ||||
\(379\) | −15.1246 | −0.776899 | −0.388450 | − | 0.921470i | \(-0.626989\pi\) | ||||
−0.388450 | + | 0.921470i | \(0.626989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.20163 | 0.112793 | ||||||||
\(382\) | −21.6453 | − | 7.87824i | −1.10747 | − | 0.403086i | ||||
\(383\) | 0.0663277 | + | 0.376163i | 0.00338919 | + | 0.0192210i | 0.986455 | − | 0.164029i | \(-0.0524492\pi\) |
−0.983066 | + | 0.183250i | \(0.941338\pi\) | |||||||
\(384\) | 3.98468 | + | 3.34354i | 0.203342 | + | 0.170624i | ||||
\(385\) | −12.0332 | + | 10.0970i | −0.613268 | + | 0.514593i | ||||
\(386\) | 1.42050 | − | 8.05606i | 0.0723016 | − | 0.410043i | ||||
\(387\) | −0.208204 | + | 0.360620i | −0.0105836 | + | 0.0183313i | ||||
\(388\) | −4.28115 | − | 7.41517i | −0.217343 | − | 0.376448i | ||||
\(389\) | −8.71143 | + | 3.17070i | −0.441687 | + | 0.160761i | −0.553284 | − | 0.832993i | \(-0.686626\pi\) |
0.111597 | + | 0.993754i | \(0.464403\pi\) | |||||||
\(390\) | 1.87939 | − | 0.684040i | 0.0951664 | − | 0.0346377i | ||||
\(391\) | −2.05573 | − | 3.56063i | −0.103963 | − | 0.180069i | ||||
\(392\) | 2.23607 | − | 3.87298i | 0.112938 | − | 0.195615i | ||||
\(393\) | 1.00090 | − | 5.67636i | 0.0504885 | − | 0.286335i | ||||
\(394\) | 3.71846 | − | 3.12016i | 0.187333 | − | 0.157191i | ||||
\(395\) | 33.2589 | + | 27.9075i | 1.67344 | + | 1.40418i | ||||
\(396\) | 0.495610 | + | 2.81074i | 0.0249053 | + | 0.141245i | ||||
\(397\) | 10.7803 | + | 3.92370i | 0.541047 | + | 0.196925i | 0.598064 | − | 0.801448i | \(-0.295937\pi\) |
−0.0570173 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(398\) | −21.7082 | −1.08813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | 33.7242 | + | 12.2746i | 1.68411 | + | 0.612965i | 0.993864 | − | 0.110613i | \(-0.0352815\pi\) |
0.690243 | + | 0.723578i | \(0.257504\pi\) | |||||||
\(402\) | −0.751243 | − | 4.26051i | −0.0374686 | − | 0.212495i | ||||
\(403\) | 6.78264 | + | 5.69131i | 0.337867 | + | 0.283504i | ||||
\(404\) | −4.34635 | + | 3.64702i | −0.216239 | + | 0.181446i | ||||
\(405\) | 4.33153 | − | 24.5653i | 0.215235 | − | 1.22066i | ||||
\(406\) | 8.78115 | − | 15.2094i | 0.435801 | − | 0.754830i | ||||
\(407\) | 7.16312 | + | 12.4069i | 0.355063 | + | 0.614987i | ||||
\(408\) | 0.613127 | − | 0.223160i | 0.0303543 | − | 0.0110481i | ||||
\(409\) | 7.79174 | − | 2.83596i | 0.385277 | − | 0.140229i | −0.142118 | − | 0.989850i | \(-0.545391\pi\) |
0.527395 | + | 0.849620i | \(0.323169\pi\) | |||||||
\(410\) | 7.85410 | + | 13.6037i | 0.387886 | + | 0.671839i | ||||
\(411\) | −1.42705 | + | 2.47172i | −0.0703912 | + | 0.121921i | ||||
\(412\) | 1.53750 | − | 8.71959i | 0.0757471 | − | 0.429583i | ||||
\(413\) | 0.749738 | − | 0.629105i | 0.0368922 | − | 0.0309562i | ||||
\(414\) | −19.0393 | − | 15.9759i | −0.935733 | − | 0.785173i | ||||
\(415\) | 4.76081 | + | 26.9999i | 0.233699 | + | 1.32537i | ||||
\(416\) | −3.17801 | − | 1.15670i | −0.155815 | − | 0.0567119i | ||||
\(417\) | 5.65248 | 0.276803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.94427 | −0.436956 | −0.218478 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | −2.15358 | − | 0.783840i | −0.105084 | − | 0.0382475i | ||||
\(421\) | −4.77049 | − | 27.0548i | −0.232499 | − | 1.31857i | −0.847817 | − | 0.530289i | \(-0.822083\pi\) |
0.615317 | − | 0.788279i | \(-0.289028\pi\) | |||||||
\(422\) | −4.77711 | − | 4.00847i | −0.232546 | − | 0.195129i | ||||
\(423\) | −6.55911 | + | 5.50374i | −0.318915 | + | 0.267601i | ||||
\(424\) | 2.45641 | − | 13.9310i | 0.119294 | − | 0.676549i | ||||
\(425\) | −2.09017 | + | 3.62028i | −0.101388 | + | 0.175609i | ||||
\(426\) | 2.30902 | + | 3.99933i | 0.111872 | + | 0.193768i | ||||
\(427\) | 28.8563 | − | 10.5028i | 1.39645 | − | 0.508267i | ||||
\(428\) | −9.53403 | + | 3.47010i | −0.460845 | + | 0.167734i | ||||
\(429\) | −0.309017 | − | 0.535233i | −0.0149195 | − | 0.0258413i | ||||
\(430\) | 0.381966 | − | 0.661585i | 0.0184200 | − | 0.0319044i | ||||
\(431\) | 4.80180 | − | 27.2324i | 0.231295 | − | 1.31174i | −0.618984 | − | 0.785404i | \(-0.712455\pi\) |
0.850278 | − | 0.526333i | \(-0.176434\pi\) | |||||||
\(432\) | 8.31472 | − | 6.97688i | 0.400042 | − | 0.335675i | ||||
\(433\) | −2.63343 | − | 2.20971i | −0.126554 | − | 0.106192i | 0.577314 | − | 0.816522i | \(-0.304101\pi\) |
−0.703868 | + | 0.710331i | \(0.748545\pi\) | |||||||
\(434\) | −7.46318 | − | 42.3258i | −0.358244 | − | 2.03170i | ||||
\(435\) | 4.20243 | + | 1.52956i | 0.201491 | + | 0.0733368i | ||||
\(436\) | −2.03444 | −0.0974321 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.67376 | −0.0799754 | ||||||||
\(439\) | 32.5103 | + | 11.8328i | 1.55163 | + | 0.564748i | 0.968800 | − | 0.247844i | \(-0.0797221\pi\) |
0.582832 | + | 0.812592i | \(0.301944\pi\) | |||||||
\(440\) | 2.03311 | + | 11.5303i | 0.0969246 | + | 0.549687i | ||||
\(441\) | −4.37274 | − | 3.66916i | −0.208226 | − | 0.174722i | ||||
\(442\) | −0.946883 | + | 0.794529i | −0.0450386 | + | 0.0377919i | ||||
\(443\) | −1.31688 | + | 7.46838i | −0.0625667 | + | 0.354833i | 0.937411 | + | 0.348224i | \(0.113215\pi\) |
−0.999978 | + | 0.00660970i | \(0.997896\pi\) | |||||||
\(444\) | −1.04508 | + | 1.81014i | −0.0495975 | + | 0.0859055i | ||||
\(445\) | 12.5623 | + | 21.7586i | 0.595510 | + | 1.03145i | ||||
\(446\) | 17.7171 | − | 6.44848i | 0.838927 | − | 0.305345i | ||||
\(447\) | 0.685497 | − | 0.249500i | 0.0324229 | − | 0.0118010i | ||||
\(448\) | −6.35410 | − | 11.0056i | −0.300203 | − | 0.519967i | ||||
\(449\) | −1.44427 | + | 2.50155i | −0.0681594 | + | 0.118056i | −0.898091 | − | 0.439809i | \(-0.855046\pi\) |
0.829932 | + | 0.557865i | \(0.188379\pi\) | |||||||
\(450\) | −4.38818 | + | 24.8866i | −0.206861 | + | 1.17317i | ||||
\(451\) | 3.71846 | − | 3.12016i | 0.175095 | − | 0.146922i | ||||
\(452\) | 3.20233 | + | 2.68707i | 0.150625 | + | 0.126389i | ||||
\(453\) | −1.39886 | − | 7.93334i | −0.0657243 | − | 0.372741i | ||||
\(454\) | −24.9604 | − | 9.08484i | −1.17145 | − | 0.426373i | ||||
\(455\) | −9.70820 | −0.455128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7082 | 0.921911 | 0.460955 | − | 0.887423i | \(-0.347507\pi\) | ||||
0.460955 | + | 0.887423i | \(0.347507\pi\) | |||||||
\(458\) | 20.7056 | + | 7.53622i | 0.967509 | + | 0.352145i | ||||
\(459\) | −0.296626 | − | 1.68225i | −0.0138453 | − | 0.0785208i | ||||
\(460\) | 8.24565 | + | 6.91892i | 0.384455 | + | 0.322596i | ||||
\(461\) | 16.0442 | − | 13.4627i | 0.747255 | − | 0.627021i | −0.187520 | − | 0.982261i | \(-0.560045\pi\) |
0.934775 | + | 0.355239i | \(0.115601\pi\) | |||||||
\(462\) | −0.520945 | + | 2.95442i | −0.0242365 | + | 0.137452i | ||||
\(463\) | −14.1353 | + | 24.4830i | −0.656921 | + | 1.13782i | 0.324487 | + | 0.945890i | \(0.394808\pi\) |
−0.981409 | + | 0.191931i | \(0.938525\pi\) | |||||||
\(464\) | −8.78115 | − | 15.2094i | −0.407655 | − | 0.706079i | ||||
\(465\) | 10.2843 | − | 3.74316i | 0.476921 | − | 0.173585i | ||||
\(466\) | −6.88441 | + | 2.50572i | −0.318914 | + | 0.116075i | ||||
\(467\) | 7.97214 | + | 13.8081i | 0.368906 | + | 0.638965i | 0.989395 | − | 0.145251i | \(-0.0463989\pi\) |
−0.620488 | + | 0.784216i | \(0.713066\pi\) | |||||||
\(468\) | −0.881966 | + | 1.52761i | −0.0407689 | + | 0.0706138i | ||||
\(469\) | −3.64661 | + | 20.6810i | −0.168385 | + | 0.954958i | ||||
\(470\) | 12.0332 | − | 10.0970i | 0.555049 | − | 0.465742i | ||||
\(471\) | −5.22416 | − | 4.38359i | −0.240717 | − | 0.201985i | ||||
\(472\) | −0.126675 | − | 0.718408i | −0.00583067 | − | 0.0330674i | ||||
\(473\) | −0.221831 | − | 0.0807400i | −0.0101998 | − | 0.00371243i | ||||
\(474\) | 8.29180 | 0.380855 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.41641 | 0.0649209 | ||||||||
\(477\) | −16.9668 | − | 6.17542i | −0.776858 | − | 0.282753i | ||||
\(478\) | −0.0916626 | − | 0.519845i | −0.00419255 | − | 0.0237771i | ||||
\(479\) | 17.6881 | + | 14.8421i | 0.808190 | + | 0.678152i | 0.950175 | − | 0.311717i | \(-0.100904\pi\) |
−0.141985 | + | 0.989869i | \(0.545349\pi\) | |||||||
\(480\) | −3.20233 | + | 2.68707i | −0.146166 | + | 0.122647i | ||||
\(481\) | −1.53750 | + | 8.71959i | −0.0701039 | + | 0.397579i | ||||
\(482\) | −2.57295 | + | 4.45648i | −0.117195 | + | 0.202987i | ||||
\(483\) | −3.08359 | − | 5.34094i | −0.140308 | − | 0.243021i | ||||
\(484\) | 4.86793 | − | 1.77178i | 0.221269 | − | 0.0805355i | ||||
\(485\) | −42.1291 | + | 15.3337i | −1.91298 | + | 0.696269i | ||||
\(486\) | −7.80902 | − | 13.5256i | −0.354224 | − | 0.613534i | ||||
\(487\) | −2.09017 | + | 3.62028i | −0.0947146 | + | 0.164051i | −0.909489 | − | 0.415727i | \(-0.863527\pi\) |
0.814775 | + | 0.579778i | \(0.196861\pi\) | |||||||
\(488\) | 3.97455 | − | 22.5408i | 0.179920 | − | 1.02037i | ||||
\(489\) | 0.516132 | − | 0.433086i | 0.0233403 | − | 0.0195848i | ||||
\(490\) | 8.02212 | + | 6.73136i | 0.362403 | + | 0.304092i | ||||
\(491\) | −3.68391 | − | 20.8925i | −0.166252 | − | 0.942864i | −0.947764 | − | 0.318973i | \(-0.896662\pi\) |
0.781511 | − | 0.623891i | \(-0.214449\pi\) | |||||||
\(492\) | 0.665494 | + | 0.242220i | 0.0300028 | + | 0.0109201i | ||||
\(493\) | −2.76393 | −0.124481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9443 | 0.671695 | ||||||||
\(496\) | −40.3868 | − | 14.6996i | −1.81342 | − | 0.660031i | ||||
\(497\) | −3.89257 | − | 22.0759i | −0.174606 | − | 0.990237i | ||||
\(498\) | 4.01106 | + | 3.36568i | 0.179740 | + | 0.150820i | ||||
\(499\) | 19.2466 | − | 16.1498i | 0.861595 | − | 0.722964i | −0.100716 | − | 0.994915i | \(-0.532113\pi\) |
0.962311 | + | 0.271951i | \(0.0876690\pi\) | |||||||
\(500\) | 0.163971 | − | 0.929926i | 0.00733301 | − | 0.0415876i | ||||
\(501\) | −3.86475 | + | 6.69393i | −0.172664 | + | 0.299063i | ||||
\(502\) | 20.5172 | + | 35.5369i | 0.915728 | + | 1.58609i | ||||
\(503\) | −33.6718 | + | 12.2555i | −1.50135 | + | 0.546448i | −0.956410 | − | 0.292026i | \(-0.905671\pi\) |
−0.544942 | + | 0.838474i | \(0.683448\pi\) | |||||||
\(504\) | −17.9913 | + | 6.54828i | −0.801394 | + | 0.291684i | ||||
\(505\) | 14.8541 | + | 25.7281i | 0.660999 | + | 1.14488i | ||||
\(506\) | 7.04508 | − | 12.2024i | 0.313192 | − | 0.542465i | ||||
\(507\) | −0.795932 | + | 4.51396i | −0.0353486 | + | 0.200472i | ||||
\(508\) | 2.72888 | − | 2.28981i | 0.121075 | − | 0.101594i | ||||
\(509\) | 1.55847 | + | 1.30771i | 0.0690781 | + | 0.0579634i | 0.676673 | − | 0.736284i | \(-0.263421\pi\) |
−0.607595 | + | 0.794247i | \(0.707866\pi\) | |||||||
\(510\) | 0.265311 | + | 1.50465i | 0.0117482 | + | 0.0666271i | ||||
\(511\) | 7.63464 | + | 2.77878i | 0.337736 | + | 0.122926i | ||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.9443 | 1.45311 | ||||||||
\(515\) | −43.5648 | − | 15.8563i | −1.91969 | − | 0.698711i | ||||
\(516\) | −0.00598077 | − | 0.0339186i | −0.000263289 | − | 0.00149318i | ||||
\(517\) | −3.71846 | − | 3.12016i | −0.163538 | − | 0.137224i | ||||
\(518\) | 32.9236 | − | 27.6262i | 1.44658 | − | 1.21382i | ||||
\(519\) | −0.0313157 | + | 0.177600i | −0.00137461 | + | 0.00779578i | ||||
\(520\) | −3.61803 | + | 6.26662i | −0.158661 | + | 0.274809i | ||||
\(521\) | −3.13525 | − | 5.43042i | −0.137358 | − | 0.237911i | 0.789138 | − | 0.614216i | \(-0.210528\pi\) |
−0.926496 | + | 0.376305i | \(0.877194\pi\) | |||||||
\(522\) | −15.7006 | + | 5.71454i | −0.687196 | + | 0.250119i | ||||
\(523\) | 4.15007 | − | 1.51050i | 0.181470 | − | 0.0660496i | −0.249687 | − | 0.968327i | \(-0.580328\pi\) |
0.431157 | + | 0.902277i | \(0.358106\pi\) | |||||||
\(524\) | −4.66312 | − | 8.07676i | −0.203709 | − | 0.352835i | ||||
\(525\) | −3.13525 | + | 5.43042i | −0.136834 | + | 0.237003i | ||||
\(526\) | −4.19887 | + | 23.8130i | −0.183080 | + | 1.03830i | ||||
\(527\) | −5.18147 | + | 4.34777i | −0.225708 | + | 0.189392i | ||||
\(528\) | 2.29813 | + | 1.92836i | 0.100013 | + | 0.0839212i | ||||
\(529\) | 1.03591 | + | 5.87493i | 0.0450395 | + | 0.255432i | ||||
\(530\) | 31.1270 | + | 11.3293i | 1.35207 | + | 0.492113i | ||||
\(531\) | −0.931116 | −0.0404070 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 4.50900 | + | 1.64114i | 0.195123 | + | 0.0710191i | ||||
\(535\) | 9.22499 | + | 52.3175i | 0.398831 | + | 2.26188i | ||||
\(536\) | 11.9905 | + | 10.0612i | 0.517910 | + | 0.434578i | ||||
\(537\) | 3.58031 | − | 3.00424i | 0.154502 | − | 0.129642i | ||||
\(538\) | 8.52072 | − | 48.3234i | 0.367354 | − | 2.08337i | ||||
\(539\) | 1.61803 | − | 2.80252i | 0.0696937 | − | 0.120713i | ||||
\(540\) | 2.23607 | + | 3.87298i | 0.0962250 | + | 0.166667i | ||||
\(541\) | 28.0337 | − | 10.2034i | 1.20526 | − | 0.438679i | 0.340204 | − | 0.940352i | \(-0.389504\pi\) |
0.865058 | + | 0.501672i | \(0.167282\pi\) | |||||||
\(542\) | −1.74229 | + | 0.634140i | −0.0748376 | + | 0.0272387i | ||||
\(543\) | −2.29180 | − | 3.96951i | −0.0983504 | − | 0.170348i | ||||
\(544\) | 1.29180 | − | 2.23746i | 0.0553853 | − | 0.0959302i | ||||
\(545\) | −1.84978 | + | 10.4906i | −0.0792360 | + | 0.449370i | ||||
\(546\) | −1.42032 | + | 1.19179i | −0.0607843 | + | 0.0510041i | ||||
\(547\) | −20.6242 | − | 17.3058i | −0.881827 | − | 0.739941i | 0.0847267 | − | 0.996404i | \(-0.472998\pi\) |
−0.966554 | + | 0.256463i | \(0.917443\pi\) | |||||||
\(548\) | 0.801913 | + | 4.54788i | 0.0342560 | + | 0.194276i | ||||
\(549\) | −27.4529 | − | 9.99204i | −1.17166 | − | 0.426450i | ||||
\(550\) | −14.3262 | −0.610873 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −4.59675 | −0.195651 | ||||||||
\(553\) | −37.8219 | − | 13.7660i | −1.60835 | − | 0.585392i | ||||
\(554\) | 3.20765 | + | 18.1915i | 0.136280 | + | 0.772883i | ||||
\(555\) | 8.38380 | + | 7.03484i | 0.355872 | + | 0.298612i | ||||
\(556\) | 7.00616 | − | 5.87887i | 0.297128 | − | 0.249320i | ||||
\(557\) | −0.142332 | + | 0.807208i | −0.00603082 | + | 0.0342025i | −0.987675 | − | 0.156521i | \(-0.949972\pi\) |
0.981644 | + | 0.190723i | \(0.0610833\pi\) | |||||||
\(558\) | −20.4443 | + | 35.4105i | −0.865475 | + | 1.49905i | ||||
\(559\) | −0.0729490 | − | 0.126351i | −0.00308541 | − | 0.00534409i | ||||
\(560\) | 44.2826 | − | 16.1176i | 1.87128 | − | 0.681091i | ||||
\(561\) | 0.443663 | − | 0.161480i | 0.0187315 | − | 0.00681769i | ||||
\(562\) | 23.8713 | + | 41.3463i | 1.00695 | + | 1.74409i | ||||
\(563\) | 16.4164 | − | 28.4341i | 0.691869 | − | 1.19835i | −0.279356 | − | 0.960188i | \(-0.590121\pi\) |
0.971225 | − | 0.238165i | \(-0.0765458\pi\) | |||||||
\(564\) | 0.122978 | − | 0.697445i | 0.00517832 | − | 0.0293677i | ||||
\(565\) | 16.7676 | − | 14.0697i | 0.705418 | − | 0.591916i | ||||
\(566\) | 32.2693 | + | 27.0772i | 1.35638 | + | 1.13814i | ||||
\(567\) | 4.01555 | + | 22.7733i | 0.168637 | + | 0.956389i | ||||
\(568\) | −15.7006 | − | 5.71454i | −0.658782 | − | 0.239777i | ||||
\(569\) | 16.9098 | 0.708897 | 0.354448 | − | 0.935076i | \(-0.384669\pi\) | ||||
0.354448 | + | 0.935076i | \(0.384669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67376 | 0.279288 | 0.139644 | − | 0.990202i | \(-0.455404\pi\) | ||||
0.139644 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(572\) | −0.939693 | − | 0.342020i | −0.0392905 | − | 0.0143006i | ||||
\(573\) | 0.944246 | + | 5.35508i | 0.0394464 | + | 0.223712i | ||||
\(574\) | −11.1554 | − | 9.36047i | −0.465616 | − | 0.390698i | ||||
\(575\) | 22.5607 | − | 18.9306i | 0.940845 | − | 0.789462i | ||||
\(576\) | −2.09944 | + | 11.9065i | −0.0874765 | + | 0.496104i | ||||
\(577\) | 6.06231 | − | 10.5002i | 0.252377 | − | 0.437130i | −0.711803 | − | 0.702379i | \(-0.752121\pi\) |
0.964180 | + | 0.265250i | \(0.0854543\pi\) | |||||||
\(578\) | 13.2812 | + | 23.0036i | 0.552423 | + | 0.956825i | ||||
\(579\) | −1.81466 | + | 0.660481i | −0.0754145 | + | 0.0274486i | ||||
\(580\) | 6.79968 | − | 2.47488i | 0.282341 | − | 0.102764i | ||||
\(581\) | −12.7082 | − | 22.0113i | −0.527225 | − | 0.913181i | ||||
\(582\) | −4.28115 | + | 7.41517i | −0.177459 | + | 0.307369i | ||||
\(583\) | 1.77747 | − | 10.0806i | 0.0736155 | − | 0.417494i | ||||
\(584\) | 4.63896 | − | 3.89255i | 0.191961 | − | 0.161075i | ||||
\(585\) | 7.07524 | + | 5.93683i | 0.292525 | + | 0.245458i | ||||
\(586\) | −2.85068 | − | 16.1670i | −0.117760 | − | 0.667853i | ||||
\(587\) | 1.99648 | + | 0.726660i | 0.0824036 | + | 0.0299925i | 0.382893 | − | 0.923793i | \(-0.374928\pi\) |
−0.300489 | + | 0.953785i | \(0.597150\pi\) | |||||||
\(588\) | 0.472136 | 0.0194706 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.70820 | 0.0703256 | ||||||||
\(591\) | −1.07679 | − | 0.391920i | −0.0442933 | − | 0.0161214i | ||||
\(592\) | −7.46318 | − | 42.3258i | −0.306735 | − | 1.73958i | ||||
\(593\) | 0.542516 | + | 0.455225i | 0.0222784 | + | 0.0186938i | 0.653859 | − | 0.756617i | \(-0.273149\pi\) |
−0.631580 | + | 0.775310i | \(0.717593\pi\) | |||||||
\(594\) | 4.48450 | − | 3.76294i | 0.184001 | − | 0.154395i | ||||
\(595\) | 1.28785 | − | 7.30374i | 0.0527965 | − | 0.299424i | ||||
\(596\) | 0.590170 | − | 1.02220i | 0.0241743 | − | 0.0418711i | ||||
\(597\) | 2.56231 | + | 4.43804i | 0.104868 | + | 0.181637i | ||||
\(598\) | 8.18303 | − | 2.97838i | 0.334629 | − | 0.121795i | ||||
\(599\) | −26.7027 | + | 9.71898i | −1.09104 | + | 0.397107i | −0.824007 | − | 0.566580i | \(-0.808266\pi\) |
−0.267035 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(600\) | 2.33688 | + | 4.04760i | 0.0954028 | + | 0.165242i | ||||
\(601\) | −10.1459 | + | 17.5732i | −0.413860 | + | 0.716826i | −0.995308 | − | 0.0967572i | \(-0.969153\pi\) |
0.581448 | + | 0.813583i | \(0.302486\pi\) | |||||||
\(602\) | −0.122978 | + | 0.697445i | −0.00501222 | + | 0.0284257i | ||||
\(603\) | 15.3046 | − | 12.8421i | 0.623251 | − | 0.522970i | ||||
\(604\) | −9.98496 | − | 8.37838i | −0.406282 | − | 0.340911i | ||||
\(605\) | −4.71014 | − | 26.7125i | −0.191494 | − | 1.08602i | ||||
\(606\) | 5.33159 | + | 1.94054i | 0.216581 | + | 0.0788291i | ||||
\(607\) | −6.27051 | −0.254512 | −0.127256 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127256 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.14590 | −0.168000 | ||||||||
\(610\) | 50.3645 | + | 18.3312i | 2.03920 | + | 0.742207i | ||||
\(611\) | −0.520945 | − | 2.95442i | −0.0210752 | − | 0.119523i | ||||
\(612\) | −1.03226 | − | 0.866172i | −0.0417268 | − | 0.0350129i | ||||
\(613\) | −15.2782 | + | 12.8199i | −0.617081 | + | 0.517792i | −0.896884 | − | 0.442265i | \(-0.854175\pi\) |
0.279804 | + | 0.960057i | \(0.409731\pi\) | |||||||
\(614\) | −4.86813 | + | 27.6085i | −0.196462 | + | 1.11419i | ||||
\(615\) | 1.85410 | − | 3.21140i | 0.0747646 | − | 0.129496i | ||||
\(616\) | −5.42705 | − | 9.39993i | −0.218662 | − | 0.378734i | ||||
\(617\) | −7.21098 | + | 2.62458i | −0.290303 | + | 0.105662i | −0.483067 | − | 0.875584i | \(-0.660477\pi\) |
0.192764 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(618\) | −8.32013 | + | 3.02828i | −0.334685 | + | 0.121815i | ||||
\(619\) | −5.06231 | − | 8.76817i | −0.203471 | − | 0.352423i | 0.746173 | − | 0.665752i | \(-0.231889\pi\) |
−0.949645 | + | 0.313329i | \(0.898556\pi\) | |||||||
\(620\) | 8.85410 | − | 15.3358i | 0.355589 | − | 0.615899i | ||||
\(621\) | −2.08976 | + | 11.8516i | −0.0838591 | + | 0.475589i | ||||
\(622\) | 15.6826 | − | 13.1592i | 0.628814 | − | 0.527637i | ||||
\(623\) | −17.8426 | − | 14.9717i | −0.714847 | − | 0.599828i | ||||
\(624\) | 0.321961 | + | 1.82593i | 0.0128888 | + | 0.0730959i | ||||
\(625\) | 21.0645 | + | 7.66686i | 0.842581 | + | 0.306675i | ||||
\(626\) | −18.3262 | −0.732464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0344 | −0.440322 | ||||||||
\(629\) | −6.35602 | − | 2.31340i | −0.253431 | − | 0.0922413i | ||||
\(630\) | −7.78514 | − | 44.1517i | −0.310167 | − | 1.75905i | ||||
\(631\) | 22.4916 | + | 18.8727i | 0.895376 | + | 0.751310i | 0.969281 | − | 0.245956i | \(-0.0791018\pi\) |
−0.0739052 | + | 0.997265i | \(0.523546\pi\) | |||||||
\(632\) | −22.9813 | + | 19.2836i | −0.914148 | + | 0.767062i | ||||
\(633\) | −0.255634 | + | 1.44977i | −0.0101605 | + | 0.0576232i | ||||
\(634\) | −14.5623 | + | 25.2227i | −0.578343 | + | 1.00172i | ||||
\(635\) | −9.32624 | − | 16.1535i | −0.370100 | − | 0.641033i | ||||
\(636\) | 1.40336 | − | 0.510780i | 0.0556468 | − | 0.0202538i | ||||
\(637\) | 1.87939 | − | 0.684040i | 0.0744640 | − | 0.0271027i | ||||
\(638\) | −4.73607 | − | 8.20311i | −0.187503 | − | 0.324764i | ||||
\(639\) | −10.6631 | + | 18.4691i | −0.421826 | + | 0.730625i | ||||
\(640\) | 7.65248 | − | 43.3994i | 0.302491 | − | 1.71551i | ||||
\(641\) | −30.2638 | + | 25.3943i | −1.19535 | + | 1.00302i | −0.195597 | + | 0.980684i | \(0.562665\pi\) |
−0.999751 | + | 0.0223318i | \(0.992891\pi\) | |||||||
\(642\) | 7.77221 | + | 6.52166i | 0.306745 | + | 0.257389i | ||||
\(643\) | −4.21823 | − | 23.9227i | −0.166351 | − | 0.943421i | −0.947661 | − | 0.319278i | \(-0.896559\pi\) |
0.781310 | − | 0.624143i | \(-0.214552\pi\) | |||||||
\(644\) | −9.37692 | − | 3.41292i | −0.369503 | − | 0.134488i | ||||
\(645\) | −0.180340 | −0.00710088 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.47214 | 0.293760 | 0.146880 | − | 0.989154i | \(-0.453077\pi\) | ||||
0.146880 | + | 0.989154i | \(0.453077\pi\) | |||||||
\(648\) | 16.1966 | + | 5.89508i | 0.636263 | + | 0.231581i | ||||
\(649\) | −0.0916626 | − | 0.519845i | −0.00359807 | − | 0.0204057i | ||||
\(650\) | −6.78264 | − | 5.69131i | −0.266037 | − | 0.223231i | ||||
\(651\) | −7.77221 | + | 6.52166i | −0.304617 | + | 0.255604i | ||||
\(652\) | 0.189306 | − | 1.07361i | 0.00741380 | − | 0.0420457i | ||||
\(653\) | 11.7812 | − | 20.4056i | 0.461032 | − | 0.798531i | −0.537981 | − | 0.842957i | \(-0.680813\pi\) |
0.999013 | + | 0.0444262i | \(0.0141459\pi\) | |||||||
\(654\) | 1.01722 | + | 1.76188i | 0.0397765 | + | 0.0688949i | ||||
\(655\) | −45.8878 | + | 16.7018i | −1.79299 | + | 0.652594i | ||||
\(656\) | −13.6841 | + | 4.98060i | −0.534274 | + | 0.194460i | ||||
\(657\) | −3.86475 | − | 6.69393i | −0.150778 | − | 0.261155i | ||||
\(658\) | −7.28115 | + | 12.6113i | −0.283849 | + | 0.491641i | ||||
\(659\) | −4.47614 | + | 25.3855i | −0.174366 | + | 0.988878i | 0.764507 | + | 0.644615i | \(0.222982\pi\) |
−0.938873 | + | 0.344263i | \(0.888129\pi\) | |||||||
\(660\) | −0.946883 | + | 0.794529i | −0.0368574 | + | 0.0309270i | ||||
\(661\) | 4.14921 | + | 3.48160i | 0.161386 | + | 0.135419i | 0.719904 | − | 0.694073i | \(-0.244186\pi\) |
−0.558519 | + | 0.829492i | \(0.688630\pi\) | |||||||
\(662\) | 3.07500 | + | 17.4392i | 0.119513 | + | 0.677793i | ||||
\(663\) | 0.274199 | + | 0.0998001i | 0.0106490 | + | 0.00387592i | ||||
\(664\) | −18.9443 | −0.735180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −40.8885 | −1.58440 | ||||||||
\(667\) | 18.2978 | + | 6.65986i | 0.708495 | + | 0.257871i | ||||
\(668\) | 2.17174 | + | 12.3166i | 0.0840273 | + | 0.476543i | ||||
\(669\) | −3.40955 | − | 2.86095i | −0.131821 | − | 0.110611i | ||||
\(670\) | −28.0774 | + | 23.5598i | −1.08473 | + | 0.910193i | ||||
\(671\) | 2.87601 | − | 16.3107i | 0.111027 | − | 0.629667i | ||||
\(672\) | 1.93769 | − | 3.35618i | 0.0747482 | − | 0.129468i | ||||
\(673\) | −17.0623 | − | 29.5528i | −0.657704 | − | 1.13918i | −0.981209 | − | 0.192950i | \(-0.938195\pi\) |
0.323505 | − | 0.946226i | \(-0.395139\pi\) | |||||||
\(674\) | 26.0372 | − | 9.47676i | 1.00292 | − | 0.365031i | ||||
\(675\) | 11.4981 | − | 4.18498i | 0.442564 | − | 0.161080i | ||||
\(676\) | 3.70820 | + | 6.42280i | 0.142623 | + | 0.247031i | ||||
\(677\) | 15.3713 | − | 26.6239i | 0.590768 | − | 1.02324i | −0.403361 | − | 0.915041i | \(-0.632158\pi\) |
0.994129 | − | 0.108199i | \(-0.0345085\pi\) | |||||||
\(678\) | 0.725908 | − | 4.11683i | 0.0278783 | − | 0.158106i | ||||
\(679\) | 31.8386 | − | 26.7157i | 1.22185 | − | 1.02526i | ||||
\(680\) | −4.23459 | − | 3.55324i | −0.162389 | − | 0.136261i | ||||
\(681\) | 1.08886 | + | 6.17525i | 0.0417253 | + | 0.236636i | ||||
\(682\) | −21.7824 | − | 7.92814i | −0.834091 | − | 0.303584i | ||||
\(683\) | 9.65248 | 0.369342 | 0.184671 | − | 0.982800i | \(-0.440878\pi\) | ||||
0.184671 | + | 0.982800i | \(0.440878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1803 | 0.923883 | ||||||||
\(686\) | 22.8068 | + | 8.30100i | 0.870768 | + | 0.316934i | ||||
\(687\) | −0.903253 | − | 5.12260i | −0.0344612 | − | 0.195439i | ||||
\(688\) | 0.542516 | + | 0.455225i | 0.0206832 | + | 0.0173553i | ||||
\(689\) | 4.84618 | − | 4.06643i | 0.184625 | − | 0.154919i | ||||
\(690\) | 1.86914 | − | 10.6004i | 0.0711568 | − | 0.403550i | ||||
\(691\) | 19.5902 | − | 33.9312i | 0.745245 | − | 1.29080i | −0.204835 | − | 0.978797i | \(-0.565666\pi\) |
0.950080 | − | 0.312006i | \(-0.101001\pi\) | |||||||
\(692\) | 0.145898 | + | 0.252703i | 0.00554621 | + | 0.00960632i | ||||
\(693\) | −13.0186 | + | 4.73838i | −0.494536 | + | 0.179996i | ||||
\(694\) | 38.6445 | − | 14.0654i | 1.46692 | − | 0.533917i | ||||
\(695\) | −23.9443 | − | 41.4727i | −0.908258 | − | 1.57315i | ||||
\(696\) | −1.54508 | + | 2.67617i | −0.0585663 | + | 0.101440i | ||||
\(697\) | −0.397966 | + | 2.25698i | −0.0150740 | + | 0.0854892i | ||||
\(698\) | −26.0028 | + | 21.8190i | −0.984221 | + | 0.825860i | ||||
\(699\) | 1.32487 | + | 1.11169i | 0.0501110 | + | 0.0420482i | ||||
\(700\) | 1.76182 | + | 9.99176i | 0.0665904 | + | 0.377653i | ||||
\(701\) | 37.2411 | + | 13.5547i | 1.40658 | + | 0.511953i | 0.930124 | − | 0.367246i | \(-0.119699\pi\) |
0.476455 | + | 0.879199i | \(0.341922\pi\) | |||||||
\(702\) | 3.61803 | 0.136554 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.85410 | −0.258324 | ||||||||
\(705\) | −3.48457 | − | 1.26828i | −0.131237 | − | 0.0477662i | ||||
\(706\) | 6.86992 | + | 38.9613i | 0.258553 | + | 1.46633i | ||||
\(707\) | −21.0976 | − | 17.7030i | −0.793459 | − | 0.665791i | ||||
\(708\) | 0.0589964 | − | 0.0495039i | 0.00221722 | − | 0.00186047i | ||||
\(709\) | 2.87971 | − | 16.3317i | 0.108150 | − | 0.613348i | −0.881766 | − | 0.471688i | \(-0.843645\pi\) |
0.989915 | − | 0.141660i | \(-0.0452440\pi\) | |||||||
\(710\) | 19.5623 | − | 33.8829i | 0.734160 | − | 1.27160i | ||||
\(711\) | 19.1459 | + | 33.1617i | 0.718027 | + | 1.24366i | ||||
\(712\) | −16.3137 | + | 5.93770i | −0.611382 | + | 0.222525i | ||||
\(713\) | 44.7787 | − | 16.2981i | 1.67697 | − | 0.610369i | ||||
\(714\) | −0.708204 | − | 1.22665i | −0.0265039 | − | 0.0459060i | ||||
\(715\) | −2.61803 | + | 4.53457i | −0.0979089 | + | 0.169583i | ||||
\(716\) | 1.31318 | − | 7.44742i | 0.0490759 | − | 0.278323i | ||||
\(717\) | −0.0954582 | + | 0.0800989i | −0.00356495 | + | 0.00299135i | ||||
\(718\) | 8.71909 | + | 7.31619i | 0.325394 | + | 0.273038i | ||||
\(719\) | 8.16745 | + | 46.3199i | 0.304594 | + | 1.72744i | 0.625408 | + | 0.780298i | \(0.284933\pi\) |
−0.320814 | + | 0.947142i | \(0.603956\pi\) | |||||||
\(720\) | −42.1291 | − | 15.3337i | −1.57006 | − | 0.571454i | ||||
\(721\) | 42.9787 | 1.60061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.21478 | 0.0451782 | ||||||||
\(724\) | −6.96914 | − | 2.53656i | −0.259006 | − | 0.0942705i | ||||
\(725\) | −3.43795 | − | 19.4976i | −0.127682 | − | 0.724122i | ||||
\(726\) | −3.96837 | − | 3.32986i | −0.147280 | − | 0.123583i | ||||
\(727\) | −12.3095 | + | 10.3289i | −0.456533 | + | 0.383077i | −0.841854 | − | 0.539706i | \(-0.818535\pi\) |
0.385320 | + | 0.922783i | \(0.374091\pi\) | |||||||
\(728\) | 1.16487 | − | 6.60629i | 0.0431729 | − | 0.244845i | ||||
\(729\) | 9.71885 | − | 16.8335i | 0.359957 | − | 0.623464i | ||||
\(730\) | 7.09017 | + | 12.2805i | 0.262419 | + | 0.454523i | ||||
\(731\) | 0.104735 | − | 0.0381203i | 0.00387375 | − | 0.00140993i | ||||
\(732\) | 2.27068 | − | 0.826460i | 0.0839268 | − | 0.0305468i | ||||
\(733\) | 26.4787 | + | 45.8625i | 0.978014 | + | 1.69397i | 0.669609 | + | 0.742714i | \(0.266462\pi\) |
0.308405 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(734\) | 12.8992 | − | 22.3420i | 0.476118 | − | 0.824660i | ||||
\(735\) | 0.429282 | − | 2.43458i | 0.0158343 | − | 0.0898008i | ||||
\(736\) | −13.9433 | + | 11.6998i | −0.513955 | + | 0.431260i | ||||
\(737\) | 8.67640 | + | 7.28037i | 0.319599 | + | 0.268176i | ||||
\(738\) | 2.40574 | + | 13.6436i | 0.0885565 | + | 0.502229i | ||||
\(739\) | 23.4923 | + | 8.55050i | 0.864179 | + | 0.314535i | 0.735807 | − | 0.677191i | \(-0.236803\pi\) |
0.128371 | + | 0.991726i | \(0.459025\pi\) | |||||||
\(740\) | 17.7082 | 0.650967 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.7082 | −1.12733 | ||||||||
\(743\) | 3.15801 | + | 1.14942i | 0.115856 | + | 0.0421681i | 0.399298 | − | 0.916821i | \(-0.369254\pi\) |
−0.283442 | + | 0.958989i | \(0.591476\pi\) | |||||||
\(744\) | 1.31318 | + | 7.44742i | 0.0481435 | + | 0.273036i | ||||
\(745\) | −4.73442 | − | 3.97265i | −0.173456 | − | 0.145546i | ||||
\(746\) | −6.78264 | + | 5.69131i | −0.248330 | + | 0.208374i | ||||
\(747\) | −4.19887 | + | 23.8130i | −0.153629 | + | 0.871272i | ||||
\(748\) | 0.381966 | − | 0.661585i | 0.0139661 | − | 0.0241899i | ||||
\(749\) | −24.6246 | − | 42.6511i | −0.899764 | − | 1.55844i | ||||
\(750\) | −0.887325 | + | 0.322960i | −0.0324005 | + | 0.0117928i | ||||
\(751\) | 16.1119 | − | 5.86424i | 0.587931 | − | 0.213989i | −0.0308884 | − | 0.999523i | \(-0.509834\pi\) |
0.618819 | + | 0.785534i | \(0.287611\pi\) | |||||||
\(752\) | 7.28115 | + | 12.6113i | 0.265516 | + | 0.459888i | ||||
\(753\) | 4.84346 | − | 8.38912i | 0.176505 | − | 0.305716i | ||||
\(754\) | 1.01655 | − | 5.76517i | 0.0370207 | − | 0.209955i | ||||
\(755\) | −52.2819 | + | 43.8698i | −1.90273 | + | 1.59658i | ||||
\(756\) | −3.17594 | − | 2.66493i | −0.115508 | − | 0.0969226i | ||||
\(757\) | 4.64381 | + | 26.3364i | 0.168782 | + | 0.957211i | 0.945079 | + | 0.326843i | \(0.105985\pi\) |
−0.776296 | + | 0.630368i | \(0.782904\pi\) | |||||||
\(758\) | 22.9963 | + | 8.36996i | 0.835263 | + | 0.304011i | ||||
\(759\) | −3.32624 | −0.120735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.88854 | 0.177210 | 0.0886048 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886048 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(762\) | −3.34747 | − | 1.21838i | −0.121266 | − | 0.0441373i | ||||
\(763\) | −1.71484 | − | 9.72536i | −0.0620815 | − | 0.352082i | ||||
\(764\) | 6.73995 | + | 5.65549i | 0.243843 | + | 0.204608i | ||||
\(765\) | −5.40500 | + | 4.53533i | −0.195418 | + | 0.163975i | ||||
\(766\) | 0.107320 | − | 0.608645i | 0.00387765 | − | 0.0219912i | ||||
\(767\) | 0.163119 | − | 0.282530i | 0.00588988 | − | 0.0102016i | ||||
\(768\) | −2.59017 | − | 4.48631i | −0.0934647 | − | 0.161886i | ||||
\(769\) | −34.4221 | + | 12.5286i | −1.24129 | + | 0.451793i | −0.877450 | − | 0.479668i | \(-0.840757\pi\) |
−0.363841 | + | 0.931461i | \(0.618535\pi\) | |||||||
\(770\) | 23.8836 | − | 8.69292i | 0.860706 | − | 0.313271i | ||||
\(771\) | −3.88854 | − | 6.73516i | −0.140042 | − | 0.242561i | ||||
\(772\) | −1.56231 | + | 2.70599i | −0.0562286 | + | 0.0973908i | ||||
\(773\) | −6.23796 | + | 35.3772i | −0.224364 | + | 1.27243i | 0.639534 | + | 0.768763i | \(0.279127\pi\) |
−0.863898 | + | 0.503668i | \(0.831984\pi\) | |||||||
\(774\) | 0.516132 | − | 0.433086i | 0.0185520 | − | 0.0155670i | ||||
\(775\) | −37.1155 | − | 31.1436i | −1.33323 | − | 1.11871i | ||||
\(776\) | −5.37940 | − | 30.5081i | −0.193109 | − | 1.09518i | ||||
\(777\) | −9.53403 | − | 3.47010i | −0.342031 | − | 0.124489i | ||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.763932 | −0.0273532 | ||||||||
\(781\) | −11.3610 | − | 4.13508i | −0.406530 | − | 0.147965i | ||||
\(782\) | 1.15519 | + | 6.55141i | 0.0413095 | + | 0.234278i | ||||
\(783\) | 6.19743 | + | 5.20026i | 0.221478 | + | 0.185842i | ||||
\(784\) | −7.43692 | + | 6.24031i | −0.265604 | + | 0.222868i | ||||
\(785\) | −10.0329 | + | 56.8993i | −0.358089 | + | 2.03082i | ||||
\(786\) | −4.66312 | + | 8.07676i | −0.166328 | + | 0.288088i | ||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | −1.74229 | + | 0.634140i | −0.0620664 | + | 0.0225903i | ||||
\(789\) | 5.36396 | − | 1.95232i | 0.190962 | − | 0.0695045i | ||||
\(790\) | −35.1246 | − | 60.8376i | −1.24968 | − | 2.16451i | ||||
\(791\) | −10.1459 | + | 17.5732i | −0.360747 | + | 0.624831i | ||||
\(792\) | −1.79313 | + | 10.1694i | −0.0637162 | + | 0.361352i | ||||
\(793\) | 7.84128 | − | 6.57962i | 0.278452 | − | 0.233649i | ||||
\(794\) | −14.2196 | − | 11.9316i | −0.504633 | − | 0.423437i | ||||
\(795\) | −1.35787 | − | 7.70086i | −0.0481587 | − | 0.273121i | ||||
\(796\) | 7.79174 | + | 2.83596i | 0.276171 | + | 0.100518i | ||||
\(797\) | −20.2918 | −0.718772 | −0.359386 | − | 0.933189i | \(-0.617014\pi\) | ||||
−0.359386 | + | 0.933189i | \(0.617014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.29180 | 0.0810779 | ||||||||
\(800\) | 17.3905 | + | 6.32962i | 0.614847 | + | 0.223786i | ||||
\(801\) | 3.84788 | + | 21.8224i | 0.135958 | + | 0.771057i | ||||
\(802\) | −44.4833 | − | 37.3260i | −1.57076 | − | 1.31803i | ||||
\(803\) | 3.35678 | − | 2.81667i | 0.118458 | − | 0.0993982i | ||||
\(804\) | −0.286949 | + | 1.62737i | −0.0101199 | + | 0.0573930i | ||||
\(805\) | −26.1246 | + | 45.2492i | −0.920772 | + | 1.59482i | ||||
\(806\) | −7.16312 | − | 12.4069i | −0.252310 | − | 0.437014i | ||||
\(807\) | −10.8850 | + | 3.96182i | −0.383171 | + | 0.139463i | ||||
\(808\) | −19.2899 | + | 7.02094i | −0.678616 | + | 0.246996i | ||||
\(809\) | 12.3992 | + | 21.4760i | 0.435932 | + | 0.755057i | 0.997371 | − | 0.0724614i | \(-0.0230854\pi\) |
−0.561439 | + | 0.827518i | \(0.689752\pi\) | |||||||
\(810\) | −20.1803 | + | 34.9534i | −0.709065 | + | 1.22814i | ||||
\(811\) | 3.99021 | − | 22.6296i | 0.140115 | − | 0.794633i | −0.831045 | − | 0.556205i | \(-0.812257\pi\) |
0.971160 | − | 0.238428i | \(-0.0766321\pi\) | |||||||
\(812\) | −5.13878 | + | 4.31195i | −0.180336 | + | 0.151320i | ||||
\(813\) | 0.335293 | + | 0.281344i | 0.0117592 | + | 0.00986718i | ||||
\(814\) | −4.02522 | − | 22.8282i | −0.141084 | − | 0.800127i | ||||
\(815\) | −5.36396 | − | 1.95232i | −0.187891 | − | 0.0683868i | ||||
\(816\) | −1.41641 | −0.0495842 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13.4164 | −0.469094 | ||||||||
\(819\) | −8.04594 | − | 2.92848i | −0.281148 | − | 0.102329i | ||||
\(820\) | −1.04189 | − | 5.90885i | −0.0363843 | − | 0.206346i | ||||
\(821\) | 39.8708 | + | 33.4556i | 1.39150 | + | 1.16761i | 0.964728 | + | 0.263247i | \(0.0847935\pi\) |
0.426771 | + | 0.904360i | \(0.359651\pi\) | |||||||
\(822\) | 3.53762 | − | 2.96842i | 0.123389 | − | 0.103535i | ||||
\(823\) | −4.44483 | + | 25.2079i | −0.154937 | + | 0.878691i | 0.803906 | + | 0.594756i | \(0.202751\pi\) |
−0.958843 | + | 0.283935i | \(0.908360\pi\) | |||||||
\(824\) | 16.0172 | − | 27.7426i | 0.557986 | − | 0.966461i | ||||
\(825\) | 1.69098 | + | 2.92887i | 0.0588725 | + | 0.101970i | ||||
\(826\) | −1.48809 | + | 0.541620i | −0.0517773 | + | 0.0188454i | ||||
\(827\) | −30.6309 | + | 11.1487i | −1.06514 | + | 0.387680i | −0.814358 | − | 0.580363i | \(-0.802911\pi\) |
−0.250784 | + | 0.968043i | \(0.580688\pi\) | |||||||
\(828\) | 4.74671 | + | 8.22154i | 0.164960 | + | 0.285718i | ||||
\(829\) | −2.33688 | + | 4.04760i | −0.0811632 | + | 0.140579i | −0.903750 | − | 0.428061i | \(-0.859197\pi\) |
0.822587 | + | 0.568640i | \(0.192530\pi\) | |||||||
\(830\) | 7.70315 | − | 43.6867i | 0.267380 | − | 1.51639i | ||||
\(831\) | 3.34047 | − | 2.80299i | 0.115880 | − | 0.0972347i | ||||
\(832\) | −3.24502 | − | 2.72289i | −0.112501 | − | 0.0943993i | ||||
\(833\) | 0.265311 | + | 1.50465i | 0.00919247 | + | 0.0521331i | ||||
\(834\) | −8.59433 | − | 3.12808i | −0.297597 | − | 0.108317i | ||||
\(835\) | 65.4853 | 2.26621 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7984 | 0.684332 | ||||||||
\(838\) | 13.5994 | + | 4.94976i | 0.469782 | + | 0.170987i | ||||
\(839\) | 2.63973 | + | 14.9707i | 0.0911338 | + | 0.516845i | 0.995864 | + | 0.0908597i | \(0.0289615\pi\) |
−0.904730 | + | 0.425986i | \(0.859927\pi\) | |||||||
\(840\) | −6.35188 | − | 5.32986i | −0.219161 | − | 0.183898i | ||||
\(841\) | −12.1876 | + | 10.2266i | −0.420263 | + | 0.352643i | ||||
\(842\) | −7.71881 | + | 43.7755i | −0.266008 | + | 1.50860i | ||||
\(843\) | 5.63525 | − | 9.76055i | 0.194088 | − | 0.336171i | ||||
\(844\) | 1.19098 | + | 2.06284i | 0.0409953 | + | 0.0710060i | ||||
\(845\) | 36.4909 | − | 13.2816i | 1.25533 | − | 0.456901i | ||||
\(846\) | 13.0186 | − | 4.73838i | 0.447589 | − | 0.162909i | ||||
\(847\) | 12.5729 | + | 21.7770i | 0.432012 | + | 0.748266i | ||||
\(848\) | −15.3541 | + | 26.5941i | −0.527262 | + | 0.913245i | ||||
\(849\) | 1.72680 | − | 9.79320i | 0.0592638 | − | 0.336102i | ||||
\(850\) | 5.18147 | − | 4.34777i | 0.177723 | − | 0.149127i | ||||
\(851\) | 36.5039 | + | 30.6304i | 1.25134 | + | 1.05000i | ||||
\(852\) | −0.306304 | − | 1.73713i | −0.0104938 | − | 0.0595132i | ||||
\(853\) | −28.8563 | − | 10.5028i | −0.988020 | − | 0.359610i | −0.203067 | − | 0.979165i | \(-0.565091\pi\) |
−0.784953 | + | 0.619555i | \(0.787313\pi\) | |||||||
\(854\) | −49.6869 | −1.70025 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | 9.97769 | + | 3.63158i | 0.340831 | + | 0.124052i | 0.506764 | − | 0.862085i | \(-0.330841\pi\) |
−0.165933 | + | 0.986137i | \(0.553064\pi\) | |||||||
\(858\) | 0.173648 | + | 0.984808i | 0.00592825 | + | 0.0336208i | ||||
\(859\) | −37.1846 | − | 31.2016i | −1.26872 | − | 1.06458i | −0.994696 | − | 0.102861i | \(-0.967200\pi\) |
−0.274026 | − | 0.961722i | \(-0.588355\pi\) | |||||||
\(860\) | −0.223529 | + | 0.187563i | −0.00762227 | + | 0.00639584i | ||||
\(861\) | −0.596949 | + | 3.38547i | −0.0203440 | + | 0.115376i | ||||
\(862\) | −22.3713 | + | 38.7483i | −0.761970 | + | 1.31977i | ||||
\(863\) | 13.5279 | + | 23.4309i | 0.460494 | + | 0.797599i | 0.998986 | − | 0.0450321i | \(-0.0143390\pi\) |
−0.538492 | + | 0.842631i | \(0.681006\pi\) | |||||||
\(864\) | −7.10624 | + | 2.58646i | −0.241759 | + | 0.0879932i | ||||
\(865\) | 1.43572 | − | 0.522560i | 0.0488160 | − | 0.0177676i | ||||
\(866\) | 2.78115 | + | 4.81710i | 0.0945074 | + | 0.163692i | ||||
\(867\) | 3.13525 | − | 5.43042i | 0.106479 | − | 0.184427i | ||||
\(868\) | −2.85068 | + | 16.1670i | −0.0967584 | + | 0.548744i | ||||
\(869\) | −16.6294 | + | 13.9538i | −0.564115 | + | 0.473349i | ||||
\(870\) | −5.54315 | − | 4.65125i | −0.187930 | − | 0.157692i | ||||
\(871\) | 1.21554 | + | 6.89365i | 0.0411869 | + | 0.233583i | ||||
\(872\) | −6.91678 | − | 2.51750i | −0.234232 | − | 0.0852533i | ||||
\(873\) | −39.5410 | −1.33826 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.58359 | 0.154954 | ||||||||
\(876\) | 0.600764 | + | 0.218660i | 0.0202980 | + | 0.00738785i | ||||
\(877\) | 2.05246 | + | 11.6401i | 0.0693067 | + | 0.393058i | 0.999652 | + | 0.0263737i | \(0.00839598\pi\) |
−0.930345 | + | 0.366684i | \(0.880493\pi\) | |||||||
\(878\) | −42.8822 | − | 35.9824i | −1.44720 | − | 1.21435i | ||||
\(879\) | −2.96872 | + | 2.49105i | −0.100132 | + | 0.0840211i | ||||
\(880\) | 4.41351 | − | 25.0303i | 0.148779 | − | 0.843770i | ||||
\(881\) | −16.2254 | + | 28.1033i | −0.546648 | + | 0.946823i | 0.451853 | + | 0.892093i | \(0.350763\pi\) |
−0.998501 | + | 0.0547303i | \(0.982570\pi\) | |||||||
\(882\) | 4.61803 | + | 7.99867i | 0.155497 | + | 0.269329i | ||||
\(883\) | 47.8520 | − | 17.4167i | 1.61035 | − | 0.586118i | 0.628838 | − | 0.777536i | \(-0.283531\pi\) |
0.981509 | + | 0.191418i | \(0.0613087\pi\) | |||||||
\(884\) | 0.443663 | − | 0.161480i | 0.0149220 | − | 0.00543116i | ||||
\(885\) | −0.201626 | − | 0.349227i | −0.00677759 | − | 0.0117391i | ||||
\(886\) | 6.13525 | − | 10.6266i | 0.206118 | − | 0.357007i | ||||
\(887\) | 4.74885 | − | 26.9321i | 0.159451 | − | 0.904290i | −0.795153 | − | 0.606410i | \(-0.792609\pi\) |
0.954603 | − | 0.297880i | \(-0.0962797\pi\) | |||||||
\(888\) | −5.79306 | + | 4.86096i | −0.194402 | + | 0.163123i | ||||
\(889\) | 13.2463 | + | 11.1150i | 0.444266 | + | 0.372784i | ||||
\(890\) | −7.05923 | − | 40.0349i | −0.236626 | − | 1.34197i | ||||
\(891\) | 11.7200 | + | 4.26572i | 0.392634 | + | 0.142907i | ||||
\(892\) | −7.20163 | −0.241128 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.18034 | −0.0394765 | ||||||||
\(895\) | −37.2088 | − | 13.5429i | −1.24375 | − | 0.452689i | ||||
\(896\) | 7.09424 | + | 40.2334i | 0.237002 | + | 1.34410i | ||||
\(897\) | −1.57478 | − | 1.32140i | −0.0525803 | − | 0.0441201i | ||||
\(898\) | 3.58031 | − | 3.00424i | 0.119476 | − | 0.100253i | ||||
\(899\) | 5.56272 | − | 31.5478i | 0.185527 | − | 1.05218i | ||||
\(900\) | 4.82624 | − | 8.35929i | 0.160875 | − | 0.278643i | ||||
\(901\) | 2.41641 | + | 4.18534i | 0.0805022 | + | 0.139434i | ||||
\(902\) | −7.38044 | + | 2.68626i | −0.245742 | + | 0.0894427i | ||||
\(903\) | 0.157102 | − | 0.0571804i | 0.00522802 | − | 0.00190284i | ||||
\(904\) | 7.56231 | + | 13.0983i | 0.251519 | + | 0.435643i | ||||
\(905\) | −19.4164 | + | 33.6302i | −0.645423 | + | 1.11791i | ||||
\(906\) | −2.26341 | + | 12.8364i | −0.0751967 | + | 0.426461i | ||||
\(907\) | −20.2788 | + | 17.0160i | −0.673348 | + | 0.565006i | −0.914054 | − | 0.405592i | \(-0.867065\pi\) |
0.240707 | + | 0.970598i | \(0.422621\pi\) | |||||||
\(908\) | 7.77221 | + | 6.52166i | 0.257930 | + | 0.216429i | ||||
\(909\) | 4.54986 | + | 25.8036i | 0.150909 | + | 0.855850i | ||||
\(910\) | 14.7609 | + | 5.37252i | 0.489319 | + | 0.178097i | ||||
\(911\) | 3.38197 | 0.112050 | 0.0560248 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560248 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7082 | −0.453675 | ||||||||
\(914\) | −29.9654 | − | 10.9065i | −0.991168 | − | 0.360756i | ||||
\(915\) | −2.19708 | − | 12.4603i | −0.0726332 | − | 0.411923i | ||||
\(916\) | −6.44734 | − | 5.40996i | −0.213026 | − | 0.178750i | ||||
\(917\) | 34.6792 | − | 29.0993i | 1.14521 | − | 0.960944i | ||||
\(918\) | −0.479952 | + | 2.72194i | −0.0158408 | + | 0.0898375i | ||||
\(919\) | −11.6459 | + | 20.1713i | −0.384163 | + | 0.665389i | −0.991653 | − | 0.128938i | \(-0.958843\pi\) |
0.607490 | + | 0.794327i | \(0.292177\pi\) | |||||||
\(920\) | 19.4721 | + | 33.7267i | 0.641977 | + | 1.11194i | ||||
\(921\) | 6.21892 | − | 2.26350i | 0.204920 | − | 0.0745849i | ||||
\(922\) | −31.8448 | + | 11.5906i | −1.04875 | + | 0.381715i | ||||
\(923\) | −3.73607 | − | 6.47106i | −0.122974 | − | 0.212998i | ||||
\(924\) | 0.572949 | − | 0.992377i | 0.0188486 | − | 0.0326468i | ||||
\(925\) | 8.41340 | − | 47.7148i | 0.276631 | − | 1.56885i | ||||
\(926\) | 35.0409 | − | 29.4028i | 1.15152 | − | 0.966236i | ||||
\(927\) | −31.3224 | − | 26.2826i | −1.02876 | − | 0.863235i | ||||
\(928\) | 2.12477 | + | 12.0502i | 0.0697490 | + | 0.395566i | ||||
\(929\) | −15.3940 | − | 5.60296i | −0.505061 | − | 0.183827i | 0.0769078 | − | 0.997038i | \(-0.475495\pi\) |
−0.581969 | + | 0.813211i | \(0.697718\pi\) | |||||||
\(930\) | −17.7082 | −0.580675 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.79837 | 0.0916638 | ||||||||
\(933\) | −4.54136 | − | 1.65292i | −0.148677 | − | 0.0541142i | ||||
\(934\) | −4.47984 | − | 25.4064i | −0.146585 | − | 0.831324i | ||||
\(935\) | −3.06418 | − | 2.57115i | −0.100209 | − | 0.0840856i | ||||
\(936\) | −4.88887 | + | 4.10225i | −0.159798 | + | 0.134086i | ||||
\(937\) | 7.04357 | − | 39.9461i | 0.230103 | − | 1.30498i | −0.622581 | − | 0.782555i | \(-0.713916\pi\) |
0.852685 | − | 0.522426i | \(-0.174973\pi\) | |||||||
\(938\) | 16.9894 | − | 29.4264i | 0.554722 | − | 0.960807i | ||||
\(939\) | 2.16312 | + | 3.74663i | 0.0705907 | + | 0.122267i | ||||
\(940\) | −5.63816 | + | 2.05212i | −0.183896 | + | 0.0669328i | ||||
\(941\) | 10.0424 | − | 3.65514i | 0.327373 | − | 0.119154i | −0.173105 | − | 0.984903i | \(-0.555380\pi\) |
0.500478 | + | 0.865749i | \(0.333158\pi\) | |||||||
\(942\) | 5.51722 | + | 9.55611i | 0.179761 | + | 0.311355i | ||||
\(943\) | 8.07295 | − | 13.9828i | 0.262891 | − | 0.455341i | ||||
\(944\) | −0.274988 | + | 1.55953i | −0.00895009 | + | 0.0507585i | ||||
\(945\) | −16.6294 | + | 13.9538i | −0.540956 | + | 0.453916i | ||||
\(946\) | 0.292603 | + | 0.245523i | 0.00951334 | + | 0.00798264i | ||||
\(947\) | −5.67004 | − | 32.1564i | −0.184252 | − | 1.04494i | −0.926913 | − | 0.375276i | \(-0.877548\pi\) |
0.742661 | − | 0.669667i | \(-0.233563\pi\) | |||||||
\(948\) | −2.97618 | − | 1.08324i | −0.0966618 | − | 0.0351820i | ||||
\(949\) | 2.70820 | 0.0879120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.87539 | 0.222950 | ||||||||
\(952\) | 4.81556 | + | 1.75272i | 0.156073 | + | 0.0568060i | ||||
\(953\) | 3.00269 | + | 17.0291i | 0.0972666 | + | 0.551626i | 0.994029 | + | 0.109114i | \(0.0348015\pi\) |
−0.896763 | + | 0.442512i | \(0.854087\pi\) | |||||||
\(954\) | 22.3798 | + | 18.7789i | 0.724573 | + | 0.607989i | ||||
\(955\) | 35.2908 | − | 29.6125i | 1.14198 | − | 0.958238i | ||||
\(956\) | −0.0350120 | + | 0.198563i | −0.00113237 | + | 0.00642199i | ||||
\(957\) | −1.11803 | + | 1.93649i | −0.0361409 | + | 0.0625979i | ||||
\(958\) | −18.6803 | − | 32.3553i | −0.603534 | − | 1.04535i | ||||
\(959\) | −21.0645 | + | 7.66686i | −0.680209 | + | 0.247576i | ||||
\(960\) | −4.92029 | + | 1.79084i | −0.158802 | + | 0.0577991i | ||||
\(961\) | −23.6976 | − | 41.0454i | −0.764437 | − | 1.32404i | ||||
\(962\) | 7.16312 | − | 12.4069i | 0.230948 | − | 0.400014i | ||||
\(963\) | −8.13613 | + | 46.1423i | −0.262183 | + | 1.48691i | ||||
\(964\) | 1.50570 | − | 1.26344i | 0.0484955 | − | 0.0406925i | ||||
\(965\) | 12.5330 | + | 10.5164i | 0.403452 | + | 0.338536i | ||||
\(966\) | 1.73279 | + | 9.82711i | 0.0557515 | + | 0.316182i | ||||
\(967\) | −6.14655 | − | 2.23716i | −0.197660 | − | 0.0719422i | 0.241293 | − | 0.970452i | \(-0.422428\pi\) |
−0.438953 | + | 0.898510i | \(0.644651\pi\) | |||||||
\(968\) | 18.7426 | 0.602411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.5410 | 2.32915 | ||||||||
\(971\) | −22.0890 | − | 8.03972i | −0.708868 | − | 0.258007i | −0.0376758 | − | 0.999290i | \(-0.511995\pi\) |
−0.671193 | + | 0.741283i | \(0.734218\pi\) | |||||||
\(972\) | 1.03591 | + | 5.87493i | 0.0332268 | + | 0.188438i | ||||
\(973\) | 34.0086 | + | 28.5366i | 1.09027 | + | 0.914842i | ||||
\(974\) | 5.18147 | − | 4.34777i | 0.166025 | − | 0.139312i | ||||
\(975\) | −0.362954 | + | 2.05842i | −0.0116238 | + | 0.0659221i | ||||
\(976\) | −24.8435 | + | 43.0301i | −0.795220 | + | 1.37736i | ||||
\(977\) | −5.31966 | − | 9.21392i | −0.170191 | − | 0.294779i | 0.768296 | − | 0.640095i | \(-0.221105\pi\) |
−0.938487 | + | 0.345316i | \(0.887772\pi\) | |||||||
\(978\) | −1.02442 | + | 0.372860i | −0.0327575 | + | 0.0119228i | ||||
\(979\) | −11.8047 | + | 4.29656i | −0.377280 | + | 0.137319i | ||||
\(980\) | −2.00000 | − | 3.46410i | −0.0638877 | − | 0.110657i | ||||
\(981\) | −4.69756 | + | 8.13641i | −0.149982 | + | 0.259776i | ||||
\(982\) | −5.96069 | + | 33.8047i | −0.190213 | + | 1.07875i | ||||
\(983\) | 24.9869 | − | 20.9665i | 0.796957 | − | 0.668726i | −0.150500 | − | 0.988610i | \(-0.548088\pi\) |
0.947457 | + | 0.319884i | \(0.103644\pi\) | |||||||
\(984\) | 1.96284 | + | 1.64702i | 0.0625731 | + | 0.0525050i | ||||
\(985\) | 1.68581 | + | 9.56071i | 0.0537144 | + | 0.304630i | ||||
\(986\) | 4.20243 | + | 1.52956i | 0.133833 | + | 0.0487111i | ||||
\(987\) | 3.43769 | 0.109423 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.785218 | −0.0249685 | ||||||||
\(990\) | −22.7221 | − | 8.27016i | −0.722155 | − | 0.262843i | ||||
\(991\) | 1.29383 | + | 7.33765i | 0.0410998 | + | 0.233088i | 0.998437 | − | 0.0558838i | \(-0.0177976\pi\) |
−0.957338 | + | 0.288972i | \(0.906687\pi\) | |||||||
\(992\) | 22.9386 | + | 19.2478i | 0.728303 | + | 0.611118i | ||||
\(993\) | 3.20233 | − | 2.68707i | 0.101623 | − | 0.0852716i | ||||
\(994\) | −6.29831 | + | 35.7195i | −0.199770 | + | 1.13295i | ||||
\(995\) | 21.7082 | − | 37.5997i | 0.688196 | − | 1.19199i | ||||
\(996\) | −1.00000 | − | 1.73205i | −0.0316862 | − | 0.0548821i | ||||
\(997\) | −37.3135 | + | 13.5810i | −1.18173 | + | 0.430115i | −0.856813 | − | 0.515628i | \(-0.827559\pi\) |
−0.324918 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(998\) | −38.2008 | + | 13.9040i | −1.20923 | + | 0.440122i | ||||
\(999\) | 9.89919 | + | 17.1459i | 0.313196 | + | 0.542472i |
(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 | 361.2.e.j.99.1 | 12 | ||
19.2 | odd | 18 | 361.2.e.i.54.1 | 12 | |||
19.3 | odd | 18 | 361.2.e.i.245.1 | 12 | |||
19.4 | even | 9 | 361.2.c.d.292.1 | 4 | |||
19.5 | even | 9 | inner | 361.2.e.j.62.1 | 12 | ||
19.6 | even | 9 | 361.2.c.d.68.1 | 4 | |||
19.7 | even | 3 | inner | 361.2.e.j.234.2 | 12 | ||
19.8 | odd | 6 | 361.2.e.i.28.1 | 12 | |||
19.9 | even | 9 | 361.2.a.f.1.2 | yes | 2 | ||
19.10 | odd | 18 | 361.2.a.c.1.1 | ✓ | 2 | ||
19.11 | even | 3 | inner | 361.2.e.j.28.2 | 12 | ||
19.12 | odd | 6 | 361.2.e.i.234.1 | 12 | |||
19.13 | odd | 18 | 361.2.c.g.68.2 | 4 | |||
19.14 | odd | 18 | 361.2.e.i.62.2 | 12 | |||
19.15 | odd | 18 | 361.2.c.g.292.2 | 4 | |||
19.16 | even | 9 | inner | 361.2.e.j.245.2 | 12 | ||
19.17 | even | 9 | inner | 361.2.e.j.54.2 | 12 | ||
19.18 | odd | 2 | 361.2.e.i.99.2 | 12 | |||
57.29 | even | 18 | 3249.2.a.o.1.2 | 2 | |||
57.47 | odd | 18 | 3249.2.a.i.1.1 | 2 | |||
76.47 | odd | 18 | 5776.2.a.s.1.2 | 2 | |||
76.67 | even | 18 | 5776.2.a.bg.1.1 | 2 | |||
95.9 | even | 18 | 9025.2.a.n.1.1 | 2 | |||
95.29 | odd | 18 | 9025.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.1 | ✓ | 2 | 19.10 | odd | 18 | ||
361.2.a.f.1.2 | yes | 2 | 19.9 | even | 9 | ||
361.2.c.d.68.1 | 4 | 19.6 | even | 9 | |||
361.2.c.d.292.1 | 4 | 19.4 | even | 9 | |||
361.2.c.g.68.2 | 4 | 19.13 | odd | 18 | |||
361.2.c.g.292.2 | 4 | 19.15 | odd | 18 | |||
361.2.e.i.28.1 | 12 | 19.8 | odd | 6 | |||
361.2.e.i.54.1 | 12 | 19.2 | odd | 18 | |||
361.2.e.i.62.2 | 12 | 19.14 | odd | 18 | |||
361.2.e.i.99.2 | 12 | 19.18 | odd | 2 | |||
361.2.e.i.234.1 | 12 | 19.12 | odd | 6 | |||
361.2.e.i.245.1 | 12 | 19.3 | odd | 18 | |||
361.2.e.j.28.2 | 12 | 19.11 | even | 3 | inner | ||
361.2.e.j.54.2 | 12 | 19.17 | even | 9 | inner | ||
361.2.e.j.62.1 | 12 | 19.5 | even | 9 | inner | ||
361.2.e.j.99.1 | 12 | 1.1 | even | 1 | trivial | ||
361.2.e.j.234.2 | 12 | 19.7 | even | 3 | inner | ||
361.2.e.j.245.2 | 12 | 19.16 | even | 9 | inner | ||
3249.2.a.i.1.1 | 2 | 57.47 | odd | 18 | |||
3249.2.a.o.1.2 | 2 | 57.29 | even | 18 | |||
5776.2.a.s.1.2 | 2 | 76.47 | odd | 18 | |||
5776.2.a.bg.1.1 | 2 | 76.67 | even | 18 | |||
9025.2.a.n.1.1 | 2 | 95.9 | even | 18 | |||
9025.2.a.s.1.2 | 2 | 95.29 | odd | 18 |