Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(37,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(1.40126 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.37 |
Dual form | 504.2.cj.a.109.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40126 | − | 0.190983i | 0.990839 | − | 0.135045i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.92705 | − | 0.535233i | 0.963525 | − | 0.267617i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 2.59808 | − | 1.11803i | 0.918559 | − | 0.395285i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.92705 | + | 1.19682i | 0.925615 | + | 0.378467i | ||||
\(11\) | −1.93649 | + | 1.11803i | −0.583874 | + | 0.337100i | −0.762672 | − | 0.646786i | \(-0.776113\pi\) |
0.178797 | + | 0.983886i | \(0.442779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −0.204441 | + | 3.73607i | −0.0546391 | + | 0.998506i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.42705 | − | 2.06284i | 0.856763 | − | 0.515711i | ||||
\(17\) | 1.73205 | + | 3.00000i | 0.420084 | + | 0.727607i | 0.995947 | − | 0.0899392i | \(-0.0286673\pi\) |
−0.575863 | + | 0.817546i | \(0.695334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.70820 | − | 3.87298i | −1.53897 | − | 0.888523i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
−0.540068 | − | 0.841621i | \(-0.681602\pi\) | |||||||
\(20\) | 4.33013 | + | 1.11803i | 0.968246 | + | 0.250000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.50000 | + | 1.93649i | −0.533002 | + | 0.412861i | ||||
\(23\) | 3.46410 | − | 6.00000i | 0.722315 | − | 1.25109i | −0.237754 | − | 0.971325i | \(-0.576411\pi\) |
0.960070 | − | 0.279761i | \(-0.0902553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.427051 | + | 5.27424i | 0.0807050 | + | 0.996738i | ||||
\(29\) | − | 2.23607i | − | 0.415227i | −0.978211 | − | 0.207614i | \(-0.933430\pi\) | ||
0.978211 | − | 0.207614i | \(-0.0665697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | 4.40822 | − | 3.54508i | 0.779270 | − | 0.626688i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | + | 3.87298i | 0.514496 | + | 0.664211i | ||||
\(35\) | −3.87298 | + | 4.47214i | −0.654654 | + | 0.755929i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.70820 | − | 3.87298i | −1.10282 | − | 0.636715i | −0.165861 | − | 0.986149i | \(-0.553040\pi\) |
−0.936961 | + | 0.349435i | \(0.886374\pi\) | |||||||
\(38\) | −10.1396 | − | 4.14590i | −1.64486 | − | 0.672553i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.28115 | + | 0.739674i | 0.993137 | + | 0.116953i | ||||
\(41\) | 10.3923 | 1.62301 | 0.811503 | − | 0.584349i | \(-0.198650\pi\) | ||||
0.811503 | + | 0.584349i | \(0.198650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −3.13331 | + | 3.19098i | −0.472364 | + | 0.481059i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.70820 | − | 9.06914i | 0.546745 | − | 1.33717i | ||||
\(47\) | −1.73205 | + | 3.00000i | −0.252646 | + | 0.437595i | −0.964253 | − | 0.264982i | \(-0.914634\pi\) |
0.711608 | + | 0.702577i | \(0.247967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.68246 | − | 5.59017i | 1.32999 | − | 0.767869i | 0.344690 | − | 0.938716i | \(-0.387984\pi\) |
0.985297 | + | 0.170848i | \(0.0546505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 1.60570 | + | 7.30902i | 0.214571 | + | 0.976708i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.427051 | − | 3.13331i | −0.0560745 | − | 0.411424i | ||||
\(59\) | −1.93649 | + | 1.11803i | −0.252110 | + | 0.145556i | −0.620730 | − | 0.784024i | \(-0.713164\pi\) |
0.368620 | + | 0.929580i | \(0.379830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.70820 | − | 3.87298i | −0.858898 | − | 0.495885i | 0.00474543 | − | 0.999989i | \(-0.498489\pi\) |
−0.863643 | + | 0.504104i | \(0.831823\pi\) | |||||||
\(62\) | 0.866025 | + | 1.11803i | 0.109985 | + | 0.141990i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.50000 | − | 5.80948i | 0.687500 | − | 0.726184i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70820 | + | 3.87298i | −0.819538 | + | 0.473160i | −0.850257 | − | 0.526368i | \(-0.823553\pi\) |
0.0307194 | + | 0.999528i | \(0.490220\pi\) | |||||||
\(68\) | 4.94345 | + | 4.85410i | 0.599481 | + | 0.588646i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.57295 | + | 7.00629i | −0.546572 | + | 0.837412i | ||||
\(71\) | −10.3923 | −1.23334 | −0.616670 | − | 0.787222i | \(-0.711519\pi\) | ||||
−0.616670 | + | 0.787222i | \(0.711519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | −10.1396 | − | 4.14590i | −1.17870 | − | 0.481951i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.0000 | − | 3.87298i | −1.72062 | − | 0.444262i | ||||
\(77\) | −1.93649 | − | 5.59017i | −0.220684 | − | 0.637059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 8.94278 | − | 0.163119i | 0.999834 | − | 0.0182373i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.5623 | − | 1.98475i | 1.60814 | − | 0.219179i | ||||
\(83\) | 11.1803i | 1.22720i | 0.789616 | + | 0.613601i | \(0.210280\pi\) | ||||
−0.789616 | + | 0.613601i | \(0.789720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.74597i | 0.840168i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.78115 | + | 5.06980i | −0.403072 | + | 0.540443i | ||||
\(89\) | −6.92820 | + | 12.0000i | −0.734388 | + | 1.27200i | 0.220603 | + | 0.975364i | \(0.429197\pi\) |
−0.954991 | + | 0.296634i | \(0.904136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.46410 | − | 13.4164i | 0.361158 | − | 1.39876i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.85410 | + | 4.53457i | −0.191236 | + | 0.467705i | ||||
\(95\) | −8.66025 | − | 15.0000i | −0.888523 | − | 1.53897i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | −9.60437 | − | 2.39919i | −0.970188 | − | 0.242354i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.87298 | − | 2.23607i | 0.385376 | − | 0.222497i | −0.294779 | − | 0.955566i | \(-0.595246\pi\) |
0.680155 | + | 0.733069i | \(0.261913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.5000 | − | 9.68246i | 1.21411 | − | 0.940443i | ||||
\(107\) | −9.68246 | − | 5.59017i | −0.936039 | − | 0.540422i | −0.0473223 | − | 0.998880i | \(-0.515069\pi\) |
−0.888716 | + | 0.458458i | \(0.848402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.70820 | + | 3.87298i | −0.642529 | + | 0.370965i | −0.785588 | − | 0.618750i | \(-0.787640\pi\) |
0.143059 | + | 0.989714i | \(0.454306\pi\) | |||||||
\(110\) | −7.00629 | + | 0.954915i | −0.668024 | + | 0.0910476i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.64590 | + | 9.93516i | 0.344505 | + | 0.938784i | ||||
\(113\) | −10.3923 | −0.977626 | −0.488813 | − | 0.872389i | \(-0.662570\pi\) | ||||
−0.488813 | + | 0.872389i | \(0.662570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.4164 | − | 7.74597i | 1.25109 | − | 0.722315i | ||||
\(116\) | −1.19682 | − | 4.30902i | −0.111122 | − | 0.400082i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.50000 | + | 1.93649i | −0.230144 | + | 0.178269i | ||||
\(119\) | −8.66025 | + | 3.00000i | −0.793884 | + | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | + | 5.19615i | −0.272727 | + | 0.472377i | ||||
\(122\) | −10.1396 | − | 4.14590i | −0.917996 | − | 0.375352i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.42705 | + | 1.40126i | 0.128153 | + | 0.125837i | ||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 6.59741 | − | 9.19098i | 0.583134 | − | 0.812376i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.68246 | − | 5.59017i | −0.845960 | − | 0.488415i | 0.0133255 | − | 0.999911i | \(-0.495758\pi\) |
−0.859286 | + | 0.511496i | \(0.829092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4164 | − | 15.4919i | 1.16335 | − | 1.34332i | ||||
\(134\) | −8.66025 | + | 6.70820i | −0.748132 | + | 0.579501i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.85410 | + | 5.85774i | 0.673484 | + | 0.502297i | ||||
\(137\) | 1.73205 | + | 3.00000i | 0.147979 | + | 0.256307i | 0.930480 | − | 0.366342i | \(-0.119390\pi\) |
−0.782501 | + | 0.622649i | \(0.786057\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −5.06980 | + | 10.6910i | −0.428476 | + | 0.903553i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.5623 | + | 1.98475i | −1.22204 | + | 0.166557i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | − | 4.33013i | 0.207614 | − | 0.359597i | ||||
\(146\) | 8.66025 | + | 11.1803i | 0.716728 | + | 0.925292i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.0000 | − | 3.87298i | −1.23299 | − | 0.318357i | ||||
\(149\) | 19.3649 | + | 11.1803i | 1.58644 | + | 0.915929i | 0.993888 | + | 0.110394i | \(0.0352112\pi\) |
0.592548 | + | 0.805535i | \(0.298122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50000 | + | 6.06218i | 0.284826 | + | 0.493333i | 0.972567 | − | 0.232623i | \(-0.0747309\pi\) |
−0.687741 | + | 0.725956i | \(0.741398\pi\) | |||||||
\(152\) | −21.7586 | − | 2.56231i | −1.76485 | − | 0.207830i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.78115 | − | 7.46344i | −0.304694 | − | 0.601421i | ||||
\(155\) | 2.23607i | 0.179605i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164 | − | 7.74597i | 1.07075 | − | 0.618195i | 0.142361 | − | 0.989815i | \(-0.454531\pi\) |
0.928385 | + | 0.371619i | \(0.121197\pi\) | |||||||
\(158\) | 6.95803 | − | 17.0172i | 0.553551 | − | 1.35382i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.5000 | − | 1.93649i | 0.988212 | − | 0.153093i | ||||
\(161\) | 13.8564 | + | 12.0000i | 1.09204 | + | 0.945732i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4164 | + | 7.74597i | 1.05085 | + | 0.606711i | 0.922888 | − | 0.385068i | \(-0.125822\pi\) |
0.127966 | + | 0.991779i | \(0.459155\pi\) | |||||||
\(164\) | 20.0265 | − | 5.56231i | 1.56381 | − | 0.434343i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.13525 | + | 15.6665i | 0.165728 | + | 1.21596i | ||||
\(167\) | 10.3923 | 0.804181 | 0.402090 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402090 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 1.47935 | + | 10.8541i | 0.113461 | + | 0.832472i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.87298 | − | 2.23607i | −0.294457 | − | 0.170005i | 0.345493 | − | 0.938421i | \(-0.387712\pi\) |
−0.639950 | + | 0.768416i | \(0.721045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.33013 | + | 7.82624i | −0.326396 | + | 0.589925i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.41641 | + | 18.1383i | −0.555883 | + | 1.35952i | ||||
\(179\) | −7.74597 | + | 4.47214i | −0.578961 | + | 0.334263i | −0.760720 | − | 0.649080i | \(-0.775154\pi\) |
0.181760 | + | 0.983343i | \(0.441821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.2379i | 1.72726i | 0.504127 | + | 0.863630i | \(0.331814\pi\) | ||||
−0.504127 | + | 0.863630i | \(0.668186\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.29180 | − | 19.4614i | 0.168953 | − | 1.43472i | ||||
\(185\) | −8.66025 | − | 15.0000i | −0.636715 | − | 1.10282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.70820 | − | 3.87298i | −0.490552 | − | 0.283221i | ||||
\(188\) | −1.73205 | + | 6.70820i | −0.126323 | + | 0.489246i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.0000 | − | 19.3649i | −1.08821 | − | 1.40488i | ||||
\(191\) | 3.46410 | − | 6.00000i | 0.250654 | − | 0.434145i | −0.713052 | − | 0.701111i | \(-0.752688\pi\) |
0.963706 | + | 0.266966i | \(0.0860212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | − | 14.7224i | −0.611843 | − | 1.05974i | −0.990930 | − | 0.134382i | \(-0.957095\pi\) |
0.379086 | − | 0.925361i | \(-0.376238\pi\) | |||||||
\(194\) | −1.40126 | + | 0.190983i | −0.100605 | + | 0.0137118i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.9164 | − | 1.52761i | −0.994029 | − | 0.109115i | ||||
\(197\) | 4.47214i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509280\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | − | 6.92820i | −0.283552 | − | 0.491127i | 0.688705 | − | 0.725042i | \(-0.258180\pi\) |
−0.972257 | + | 0.233915i | \(0.924846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.00000 | − | 3.87298i | 0.351799 | − | 0.272502i | ||||
\(203\) | 5.80948 | + | 1.11803i | 0.407745 | + | 0.0784706i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.1246 | + | 11.6190i | 1.40556 | + | 0.811503i | ||||
\(206\) | −4.28187 | + | 10.4721i | −0.298332 | + | 0.729628i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.3205 | 1.19808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2379i | 1.59976i | 0.600158 | + | 0.799882i | \(0.295104\pi\) | ||||
−0.600158 | + | 0.799882i | \(0.704896\pi\) | |||||||
\(212\) | 15.6665 | − | 15.9549i | 1.07598 | − | 1.09579i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.6353 | − | 5.98409i | −1.00045 | − | 0.409064i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.50000 | + | 0.866025i | −0.169711 | + | 0.0587896i | ||||
\(218\) | −8.66025 | + | 6.70820i | −0.586546 | + | 0.454337i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.63525 | + | 2.67617i | −0.649609 | + | 0.180427i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00000 | −0.468755 | −0.234377 | − | 0.972146i | \(-0.575305\pi\) | ||||
−0.234377 | + | 0.972146i | \(0.575305\pi\) | |||||||
\(224\) | 7.00629 | + | 13.2254i | 0.468128 | + | 0.883661i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.5623 | + | 1.98475i | −0.968670 | + | 0.132024i | ||||
\(227\) | 21.3014 | − | 12.2984i | 1.41382 | − | 0.816272i | 0.418078 | − | 0.908411i | \(-0.362704\pi\) |
0.995746 | + | 0.0921394i | \(0.0293705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.70820 | − | 3.87298i | −0.443291 | − | 0.255934i | 0.261702 | − | 0.965149i | \(-0.415716\pi\) |
−0.704992 | + | 0.709215i | \(0.749050\pi\) | |||||||
\(230\) | 17.3205 | − | 13.4164i | 1.14208 | − | 0.884652i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.50000 | − | 5.80948i | −0.164133 | − | 0.381411i | ||||
\(233\) | −1.73205 | + | 3.00000i | −0.113470 | + | 0.196537i | −0.917167 | − | 0.398502i | \(-0.869530\pi\) |
0.803697 | + | 0.595039i | \(0.202863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70820 | + | 3.87298i | −0.437595 | + | 0.252646i | ||||
\(236\) | −3.13331 | + | 3.19098i | −0.203961 | + | 0.207715i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.5623 | + | 5.85774i | −0.749473 | + | 0.379701i | ||||
\(239\) | 20.7846 | 1.34444 | 0.672222 | − | 0.740349i | \(-0.265340\pi\) | ||||
0.672222 | + | 0.740349i | \(0.265340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | − | 19.9186i | −0.740780 | − | 1.28307i | −0.952141 | − | 0.305661i | \(-0.901123\pi\) |
0.211360 | − | 0.977408i | \(-0.432211\pi\) | |||||||
\(242\) | −3.21140 | + | 7.85410i | −0.206437 | + | 0.504881i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.0000 | − | 3.87298i | −0.960277 | − | 0.247942i | ||||
\(245\) | −9.68246 | − | 12.2984i | −0.618590 | − | 0.785714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.26728 | + | 1.69098i | 0.143973 | + | 0.107378i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.13525 | − | 15.6665i | −0.135045 | − | 0.990839i | ||||
\(251\) | 24.5967i | 1.55253i | 0.630405 | + | 0.776266i | \(0.282889\pi\) | ||||
−0.630405 | + | 0.776266i | \(0.717111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4919i | 0.973970i | ||||||||
\(254\) | 7.00629 | − | 0.954915i | 0.439614 | − | 0.0599167i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.48936 | − | 14.1389i | 0.468085 | − | 0.883684i | ||||
\(257\) | 3.46410 | − | 6.00000i | 0.216085 | − | 0.374270i | −0.737523 | − | 0.675322i | \(-0.764005\pi\) |
0.953608 | + | 0.301052i | \(0.0973379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.4164 | − | 15.4919i | 0.833655 | − | 0.962622i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.6353 | − | 5.98409i | −0.904169 | − | 0.369698i | ||||
\(263\) | −3.46410 | − | 6.00000i | −0.213606 | − | 0.369976i | 0.739235 | − | 0.673448i | \(-0.235187\pi\) |
−0.952840 | + | 0.303472i | \(0.901854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.0000 | 1.53574 | ||||||||
\(266\) | 15.8412 | − | 24.2705i | 0.971284 | − | 1.48812i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.8541 | + | 11.0539i | −0.663020 | + | 0.675224i | ||||
\(269\) | −25.1744 | + | 14.5344i | −1.53491 | + | 0.886181i | −0.535785 | + | 0.844355i | \(0.679984\pi\) |
−0.999125 | + | 0.0418260i | \(0.986682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 12.1244 | + | 6.70820i | 0.735147 | + | 0.406745i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | + | 3.87298i | 0.181237 | + | 0.233975i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4164 | − | 7.74597i | 0.806114 | − | 0.465410i | −0.0394907 | − | 0.999220i | \(-0.512574\pi\) |
0.845605 | + | 0.533810i | \(0.179240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.06231 | + | 15.9491i | −0.302531 | + | 0.953140i | ||||
\(281\) | 10.3923 | 0.619953 | 0.309976 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309976 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4164 | − | 7.74597i | 0.797523 | − | 0.460450i | −0.0450815 | − | 0.998983i | \(-0.514355\pi\) |
0.842604 | + | 0.538533i | \(0.181021\pi\) | |||||||
\(284\) | −20.0265 | + | 5.56231i | −1.18835 | + | 0.330062i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.19615 | + | 27.0000i | −0.306719 | + | 1.59376i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.50000 | − | 4.33013i | 0.147059 | − | 0.254713i | ||||
\(290\) | 2.67617 | − | 6.54508i | 0.157150 | − | 0.384341i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.2705 | + | 14.0126i | 0.835118 | + | 0.820025i | ||||
\(293\) | 11.1803i | 0.653162i | 0.945169 | + | 0.326581i | \(0.105897\pi\) | ||||
−0.945169 | + | 0.326581i | \(0.894103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.00000 | −0.291111 | ||||||||
\(296\) | −21.7586 | − | 2.56231i | −1.26469 | − | 0.148931i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 29.2705 | + | 11.9682i | 1.69560 | + | 0.693298i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.06218 | + | 7.82624i | 0.348839 | + | 0.450349i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.9787 | + | 0.565061i | −1.77675 | + | 0.0324085i | ||||
\(305\) | −8.66025 | − | 15.0000i | −0.495885 | − | 0.858898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −6.72376 | − | 9.73607i | −0.383122 | − | 0.554764i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.427051 | + | 3.13331i | 0.0242549 | + | 0.177960i | ||||
\(311\) | 12.1244 | + | 21.0000i | 0.687509 | + | 1.19080i | 0.972641 | + | 0.232313i | \(0.0746292\pi\) |
−0.285132 | + | 0.958488i | \(0.592037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5000 | + | 19.9186i | −0.650018 | + | 1.12586i | 0.333099 | + | 0.942892i | \(0.391906\pi\) |
−0.983118 | + | 0.182973i | \(0.941428\pi\) | |||||||
\(314\) | 17.3205 | − | 13.4164i | 0.977453 | − | 0.757132i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.50000 | − | 25.1744i | 0.365654 | − | 1.41617i | ||||
\(317\) | 1.93649 | + | 1.11803i | 0.108764 | + | 0.0627950i | 0.553395 | − | 0.832919i | \(-0.313332\pi\) |
−0.444631 | + | 0.895714i | \(0.646665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | 17.1459 | − | 5.10081i | 0.958485 | − | 0.285144i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.7082 | + | 14.1688i | 1.20975 | + | 0.789594i | ||||
\(323\) | − | 26.8328i | − | 1.49302i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.2792 | + | 8.29180i | 1.12316 | + | 0.459240i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 27.0000 | − | 11.6190i | 1.49083 | − | 0.641549i | ||||
\(329\) | −6.92820 | − | 6.00000i | −0.381964 | − | 0.330791i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.4164 | + | 7.74597i | 0.737432 | + | 0.425757i | 0.821135 | − | 0.570734i | \(-0.193341\pi\) |
−0.0837026 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(332\) | 5.98409 | + | 21.5451i | 0.328420 | + | 1.18244i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.5623 | − | 1.98475i | 0.796814 | − | 0.108601i | ||||
\(335\) | −17.3205 | −0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | 18.2164 | − | 2.48278i | 0.990839 | − | 0.135045i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.14590 | + | 14.9269i | 0.224843 | + | 0.809523i | ||||
\(341\) | −1.93649 | − | 1.11803i | −0.104867 | − | 0.0605449i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.85410 | − | 2.39364i | −0.314718 | − | 0.128683i | ||||
\(347\) | 15.4919 | − | 8.94427i | 0.831651 | − | 0.480154i | −0.0227669 | − | 0.999741i | \(-0.507248\pi\) |
0.854417 | + | 0.519587i | \(0.173914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.2379i | − | 1.24390i | −0.783058 | − | 0.621948i | \(-0.786341\pi\) | ||
0.783058 | − | 0.621948i | \(-0.213659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.57295 | + | 11.7936i | −0.243739 | + | 0.628599i | ||||
\(353\) | −13.8564 | − | 24.0000i | −0.737502 | − | 1.27739i | −0.953617 | − | 0.301023i | \(-0.902672\pi\) |
0.216115 | − | 0.976368i | \(-0.430661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.1246 | − | 11.6190i | −1.06810 | − | 0.616670i | ||||
\(356\) | −6.92820 | + | 26.8328i | −0.367194 | + | 1.42214i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0000 | + | 7.74597i | −0.528516 | + | 0.409387i | ||||
\(359\) | 8.66025 | − | 15.0000i | 0.457071 | − | 0.791670i | −0.541734 | − | 0.840550i | \(-0.682232\pi\) |
0.998805 | + | 0.0488803i | \(0.0155653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.5000 | + | 35.5070i | 1.07895 | + | 1.86879i | ||||
\(362\) | 4.43804 | + | 32.5623i | 0.233258 | + | 1.71144i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.3607i | 1.17041i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50000 | − | 4.33013i | −0.130499 | − | 0.226031i | 0.793370 | − | 0.608740i | \(-0.208325\pi\) |
−0.923869 | + | 0.382709i | \(0.874991\pi\) | |||||||
\(368\) | −0.505406 | − | 27.7082i | −0.0263461 | − | 1.44439i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.0000 | − | 19.3649i | −0.779813 | − | 1.00673i | ||||
\(371\) | 9.68246 | + | 27.9508i | 0.502688 | + | 1.45114i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.70820 | − | 3.87298i | −0.347338 | − | 0.200535i | 0.316174 | − | 0.948701i | \(-0.397602\pi\) |
−0.663512 | + | 0.748166i | \(0.730935\pi\) | |||||||
\(374\) | −10.1396 | − | 4.14590i | −0.524306 | − | 0.214379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.14590 | + | 9.73072i | −0.0590952 | + | 0.501824i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.2379i | 1.19365i | 0.802371 | + | 0.596825i | \(0.203571\pi\) | ||||
−0.802371 | + | 0.596825i | \(0.796429\pi\) | |||||||
\(380\) | −24.7172 | − | 24.2705i | −1.26797 | − | 1.24505i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.70820 | − | 9.06914i | 0.189728 | − | 0.464017i | ||||
\(383\) | 3.46410 | − | 6.00000i | 0.177007 | − | 0.306586i | −0.763847 | − | 0.645398i | \(-0.776692\pi\) |
0.940854 | + | 0.338812i | \(0.110025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | − | 12.9904i | 0.127412 | − | 0.662051i | ||||
\(386\) | −14.7224 | − | 19.0066i | −0.749352 | − | 0.967409i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.92705 | + | 0.535233i | −0.0978312 | + | 0.0271723i | ||||
\(389\) | 3.87298 | − | 2.23607i | 0.196368 | − | 0.113373i | −0.398592 | − | 0.917128i | \(-0.630501\pi\) |
0.594960 | + | 0.803755i | \(0.297168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −19.7922 | + | 0.517221i | −0.999659 | + | 0.0261236i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.854102 | + | 6.26662i | 0.0430290 | + | 0.315708i | ||||
\(395\) | 25.1744 | − | 14.5344i | 1.26666 | − | 0.731307i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8328 | − | 15.4919i | −1.34670 | − | 0.777518i | −0.358920 | − | 0.933368i | \(-0.616855\pi\) |
−0.987781 | + | 0.155851i | \(0.950188\pi\) | |||||||
\(398\) | −6.92820 | − | 8.94427i | −0.347279 | − | 0.448336i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.3205 | + | 30.0000i | −0.864945 | + | 1.49813i | 0.00215698 | + | 0.999998i | \(0.499313\pi\) |
−0.867102 | + | 0.498131i | \(0.834020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.26662 | − | 6.38197i | 0.311776 | − | 0.317515i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.35410 | + | 0.457144i | 0.414607 | + | 0.0226877i | ||||
\(407\) | 17.3205 | 0.858546 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 30.4188 | + | 12.4377i | 1.50228 | + | 0.614254i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | + | 15.4919i | −0.197066 | + | 0.763233i | ||||
\(413\) | −1.93649 | − | 5.59017i | −0.0952885 | − | 0.275074i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5000 | + | 21.6506i | −0.613601 | + | 1.06279i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 24.2705 | − | 3.30792i | 1.18711 | − | 0.161796i | ||||
\(419\) | − | 35.7771i | − | 1.74783i | −0.486083 | − | 0.873913i | \(-0.661575\pi\) | ||
0.486083 | − | 0.873913i | \(-0.338425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2379i | 1.13255i | 0.824218 | + | 0.566273i | \(0.191615\pi\) | ||||
−0.824218 | + | 0.566273i | \(0.808385\pi\) | |||||||
\(422\) | 4.43804 | + | 32.5623i | 0.216041 | + | 1.58511i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.9058 | − | 25.3490i | 0.918145 | − | 1.23106i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.4164 | − | 15.4919i | 0.649265 | − | 0.749707i | ||||
\(428\) | −21.6506 | − | 5.59017i | −1.04652 | − | 0.270211i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1244 | + | 21.0000i | 0.584010 | + | 1.01153i | 0.994998 | + | 0.0998939i | \(0.0318503\pi\) |
−0.410988 | + | 0.911641i | \(0.634816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | −3.33775 | + | 1.69098i | −0.160217 | + | 0.0811698i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.8541 | + | 11.0539i | −0.519817 | + | 0.529385i | ||||
\(437\) | −46.4758 | + | 26.8328i | −2.22324 | + | 1.28359i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50000 | − | 6.06218i | 0.167046 | − | 0.289332i | −0.770334 | − | 0.637641i | \(-0.779911\pi\) |
0.937380 | + | 0.348309i | \(0.113244\pi\) | |||||||
\(440\) | −12.9904 | + | 5.59017i | −0.619292 | + | 0.266501i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3014 | − | 12.2984i | −1.01206 | − | 0.584313i | −0.100266 | − | 0.994961i | \(-0.531969\pi\) |
−0.911794 | + | 0.410647i | \(0.865303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.8328 | + | 15.4919i | −1.27200 | + | 0.734388i | ||||
\(446\) | −9.80881 | + | 1.33688i | −0.464461 | + | 0.0633032i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.3435 | + | 17.1942i | 0.583174 | + | 0.812348i | ||||
\(449\) | −20.7846 | −0.980886 | −0.490443 | − | 0.871473i | \(-0.663165\pi\) | ||||
−0.490443 | + | 0.871473i | \(0.663165\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.1246 | + | 11.6190i | −0.947631 | + | 0.547115i | ||||
\(452\) | −20.0265 | + | 5.56231i | −0.941967 | + | 0.261629i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.5000 | − | 21.3014i | 1.29064 | − | 0.999725i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | + | 4.33013i | −0.116945 | + | 0.202555i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) |
0.801611 | + | 0.597847i | \(0.203977\pi\) | |||||||
\(458\) | −10.1396 | − | 4.14590i | −0.473792 | − | 0.193725i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21.7082 | − | 22.1078i | 1.01215 | − | 1.03078i | ||||
\(461\) | − | 22.3607i | − | 1.04144i | −0.853727 | − | 0.520720i | \(-0.825663\pi\) | ||
0.853727 | − | 0.520720i | \(-0.174337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −4.61266 | − | 7.66312i | −0.214137 | − | 0.355751i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.85410 | + | 4.53457i | −0.0858896 | + | 0.210060i | ||||
\(467\) | 7.74597 | + | 4.47214i | 0.358441 | + | 0.206946i | 0.668397 | − | 0.743805i | \(-0.266981\pi\) |
−0.309956 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.70820 | − | 19.3649i | −0.309756 | − | 0.894189i | ||||
\(470\) | −8.66025 | + | 6.70820i | −0.399468 | + | 0.309426i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.78115 | + | 5.06980i | −0.174042 | + | 0.233357i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.0831 | + | 10.4164i | −0.691331 | + | 0.477435i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 29.1246 | − | 3.96951i | 1.33213 | − | 0.181561i | ||||
\(479\) | 6.92820 | + | 12.0000i | 0.316558 | + | 0.548294i | 0.979767 | − | 0.200140i | \(-0.0641396\pi\) |
−0.663210 | + | 0.748434i | \(0.730806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19.9186 | − | 25.7148i | −0.907267 | − | 1.17128i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.00000 | + | 11.6190i | −0.136364 | + | 0.528134i | ||||
\(485\) | −1.93649 | − | 1.11803i | −0.0879316 | − | 0.0507673i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.500000 | + | 0.866025i | 0.0226572 | + | 0.0392434i | 0.877132 | − | 0.480250i | \(-0.159454\pi\) |
−0.854475 | + | 0.519493i | \(0.826121\pi\) | |||||||
\(488\) | −21.7586 | − | 2.56231i | −0.984963 | − | 0.115990i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.9164 | − | 15.3840i | −0.719030 | − | 0.694979i | ||||
\(491\) | − | 29.0689i | − | 1.31186i | −0.754822 | − | 0.655930i | \(-0.772277\pi\) | ||
0.754822 | − | 0.655930i | \(-0.227723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.70820 | − | 3.87298i | 0.302122 | − | 0.174430i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.50000 | + | 1.93649i | 0.157155 | + | 0.0869510i | ||||
\(497\) | 5.19615 | − | 27.0000i | 0.233079 | − | 1.21112i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8328 | − | 15.4919i | −1.20120 | − | 0.693514i | −0.240379 | − | 0.970679i | \(-0.577272\pi\) |
−0.960822 | + | 0.277165i | \(0.910605\pi\) | |||||||
\(500\) | −5.98409 | − | 21.5451i | −0.267617 | − | 0.963525i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.69756 | + | 34.4664i | 0.209662 | + | 1.53831i | ||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 2.95870 | + | 21.7082i | 0.131530 | + | 0.965047i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.63525 | − | 2.67617i | 0.427495 | − | 0.118736i | ||||
\(509\) | 25.1744 | + | 14.5344i | 1.11584 | + | 0.644228i | 0.940334 | − | 0.340251i | \(-0.110512\pi\) |
0.175501 | + | 0.984479i | \(0.443846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0000 | + | 8.66025i | −1.10593 | + | 0.383107i | ||||
\(512\) | 7.79423 | − | 21.2426i | 0.344459 | − | 0.938801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.70820 | − | 9.06914i | 0.163562 | − | 0.400022i | ||||
\(515\) | −15.4919 | + | 8.94427i | −0.682656 | + | 0.394132i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.74597i | − | 0.340667i | ||||||
\(518\) | 15.8412 | − | 24.2705i | 0.696021 | − | 1.06638i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8564 | − | 24.0000i | −0.607060 | − | 1.05146i | −0.991722 | − | 0.128402i | \(-0.959015\pi\) |
0.384662 | − | 0.923057i | \(-0.374318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.8328 | − | 15.4919i | −1.17332 | − | 0.677415i | −0.218858 | − | 0.975757i | \(-0.570233\pi\) |
−0.954459 | + | 0.298342i | \(0.903566\pi\) | |||||||
\(524\) | −21.6506 | − | 5.59017i | −0.945812 | − | 0.244208i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | − | 7.74597i | −0.261612 | − | 0.337740i | ||||
\(527\) | −1.73205 | + | 3.00000i | −0.0754493 | + | 0.130682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5000 | − | 21.6506i | −0.543478 | − | 0.941332i | ||||
\(530\) | 35.0315 | − | 4.77458i | 1.52167 | − | 0.207394i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.5623 | − | 37.0347i | 0.761423 | − | 1.60566i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5000 | − | 21.6506i | −0.540422 | − | 0.936039i | ||||
\(536\) | −13.0983 | + | 17.5623i | −0.565760 | + | 0.758576i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −32.5000 | + | 25.1744i | −1.40117 | + | 1.08535i | ||||
\(539\) | 15.4919 | − | 2.23607i | 0.667285 | − | 0.0963143i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.4164 | + | 7.74597i | 0.576816 | + | 0.333025i | 0.759867 | − | 0.650078i | \(-0.225264\pi\) |
−0.183051 | + | 0.983103i | \(0.558597\pi\) | |||||||
\(542\) | 0.535233 | − | 1.30902i | 0.0229902 | − | 0.0562271i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.2705 | + | 7.08438i | 0.783342 | + | 0.303740i | ||||
\(545\) | −17.3205 | −0.741929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.2379i | − | 0.993581i | −0.867871 | − | 0.496790i | \(-0.834512\pi\) | ||
0.867871 | − | 0.496790i | \(-0.165488\pi\) | |||||||
\(548\) | 4.94345 | + | 4.85410i | 0.211174 | + | 0.207357i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.66025 | + | 15.0000i | −0.368939 | + | 0.639021i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.0000 | + | 22.5167i | 1.10563 | + | 0.957506i | ||||
\(554\) | 17.3205 | − | 13.4164i | 0.735878 | − | 0.570009i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.5554 | + | 7.82624i | −0.574362 | + | 0.331608i | −0.758890 | − | 0.651219i | \(-0.774258\pi\) |
0.184527 | + | 0.982827i | \(0.440925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.04760 | + | 23.3156i | −0.171042 | + | 0.985264i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.5623 | − | 1.98475i | 0.614274 | − | 0.0837218i | ||||
\(563\) | 32.9204 | − | 19.0066i | 1.38743 | − | 0.801032i | 0.394403 | − | 0.918938i | \(-0.370951\pi\) |
0.993025 | + | 0.117906i | \(0.0376181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1246 | − | 11.6190i | −0.846649 | − | 0.488813i | ||||
\(566\) | 17.3205 | − | 13.4164i | 0.728035 | − | 0.563934i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.0000 | + | 11.6190i | −1.13289 | + | 0.487520i | ||||
\(569\) | −1.73205 | + | 3.00000i | −0.0726113 | + | 0.125767i | −0.900045 | − | 0.435797i | \(-0.856467\pi\) |
0.827434 | + | 0.561563i | \(0.189800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.70820 | + | 3.87298i | −0.280730 | + | 0.162079i | −0.633754 | − | 0.773535i | \(-0.718487\pi\) |
0.353024 | + | 0.935614i | \(0.385153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.12461 | + | 38.8264i | −0.0886796 | + | 1.62058i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5000 | − | 30.3109i | −0.728535 | − | 1.26186i | −0.957503 | − | 0.288425i | \(-0.906868\pi\) |
0.228968 | − | 0.973434i | \(-0.426465\pi\) | |||||||
\(578\) | 2.67617 | − | 6.54508i | 0.111314 | − | 0.272240i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.50000 | − | 9.68246i | 0.103807 | − | 0.402042i | ||||
\(581\) | −29.0474 | − | 5.59017i | −1.20509 | − | 0.231919i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5000 | + | 21.6506i | −0.517697 | + | 0.896678i | ||||
\(584\) | 22.6728 | + | 16.9098i | 0.938209 | + | 0.699734i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.13525 | + | 15.6665i | 0.0882066 | + | 0.647179i | ||||
\(587\) | 38.0132i | 1.56897i | 0.620147 | + | 0.784485i | \(0.287073\pi\) | ||||
−0.620147 | + | 0.784485i | \(0.712927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.74597i | − | 0.319167i | ||||||
\(590\) | −7.00629 | + | 0.954915i | −0.288445 | + | 0.0393132i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.9787 | + | 0.565061i | −1.27322 | + | 0.0232238i | ||||
\(593\) | 3.46410 | − | 6.00000i | 0.142254 | − | 0.246390i | −0.786091 | − | 0.618110i | \(-0.787898\pi\) |
0.928345 | + | 0.371720i | \(0.121232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1246 | − | 3.87298i | −0.825029 | − | 0.158777i | ||||
\(596\) | 43.3013 | + | 11.1803i | 1.77369 | + | 0.457965i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.73205 | + | 3.00000i | 0.0707697 | + | 0.122577i | 0.899239 | − | 0.437458i | \(-0.144121\pi\) |
−0.828469 | + | 0.560035i | \(0.810788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | −0.285536 | −0.142768 | − | 0.989756i | \(-0.545600\pi\) | ||||
−0.142768 | + | 0.989756i | \(0.545600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.98936 | + | 9.80881i | 0.406461 | + | 0.399115i | ||||
\(605\) | −11.6190 | + | 6.70820i | −0.472377 | + | 0.272727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5000 | + | 25.1147i | −0.588537 | + | 1.01938i | 0.405887 | + | 0.913923i | \(0.366962\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | −43.3013 | + | 6.70820i | −1.75610 | + | 0.272054i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.0000 | − | 19.3649i | −0.607332 | − | 0.784063i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.8328 | + | 15.4919i | −1.08377 | + | 0.625713i | −0.931910 | − | 0.362689i | \(-0.881859\pi\) |
−0.151857 | + | 0.988402i | \(0.548525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.2812 | − | 12.3586i | −0.454531 | − | 0.497943i | ||||
\(617\) | −31.1769 | −1.25514 | −0.627568 | − | 0.778562i | \(-0.715949\pi\) | ||||
−0.627568 | + | 0.778562i | \(0.715949\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.70820 | + | 3.87298i | −0.269625 | + | 0.155668i | −0.628717 | − | 0.777634i | \(-0.716420\pi\) |
0.359092 | + | 0.933302i | \(0.383086\pi\) | |||||||
\(620\) | 1.19682 | + | 4.30902i | 0.0480654 | + | 0.173054i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.0000 | + | 27.1109i | 0.842023 | + | 1.08705i | ||||
\(623\) | −27.7128 | − | 24.0000i | −1.11029 | − | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | −12.3104 | + | 30.1074i | −0.492021 | + | 1.20333i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.7082 | − | 22.1078i | 0.866252 | − | 0.882196i | ||||
\(629\) | − | 26.8328i | − | 1.06989i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | 4.30030 | − | 36.5172i | 0.171057 | − | 1.45258i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.92705 | + | 1.19682i | 0.116248 | + | 0.0475317i | ||||
\(635\) | 9.68246 | + | 5.59017i | 0.384237 | + | 0.221839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.33013 | + | 5.59017i | 0.171431 | + | 0.221317i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.0517 | − | 10.4221i | 0.911197 | − | 0.411971i | ||||
\(641\) | 22.5167 | + | 39.0000i | 0.889355 | + | 1.54041i | 0.840640 | + | 0.541595i | \(0.182179\pi\) |
0.0487148 | + | 0.998813i | \(0.484487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2379i | 0.916413i | 0.888846 | + | 0.458207i | \(0.151508\pi\) | ||||
−0.888846 | + | 0.458207i | \(0.848492\pi\) | |||||||
\(644\) | 33.1248 | + | 15.7082i | 1.30530 | + | 0.618990i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.12461 | − | 37.5997i | −0.201625 | − | 1.47934i | ||||
\(647\) | 22.5167 | + | 39.0000i | 0.885221 | + | 1.53325i | 0.845460 | + | 0.534039i | \(0.179326\pi\) |
0.0397614 | + | 0.999209i | \(0.487340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.50000 | − | 4.33013i | 0.0981336 | − | 0.169972i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.0000 | + | 7.74597i | 1.17489 | + | 0.303355i | ||||
\(653\) | 36.7933 | + | 21.2426i | 1.43983 | + | 0.831289i | 0.997838 | − | 0.0657275i | \(-0.0209368\pi\) |
0.441997 | + | 0.897016i | \(0.354270\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5000 | − | 21.6506i | −0.488415 | − | 0.845960i | ||||
\(656\) | 35.6150 | − | 21.4377i | 1.39053 | − | 0.837001i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.8541 | − | 7.08438i | −0.423137 | − | 0.276178i | ||||
\(659\) | 17.8885i | 0.696839i | 0.937339 | + | 0.348419i | \(0.113281\pi\) | ||||
−0.937339 | + | 0.348419i | \(0.886719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4164 | − | 7.74597i | 0.521838 | − | 0.301283i | −0.215848 | − | 0.976427i | \(-0.569252\pi\) |
0.737686 | + | 0.675144i | \(0.235918\pi\) | |||||||
\(662\) | 20.2792 | + | 8.29180i | 0.788174 | + | 0.322270i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.5000 | + | 29.0474i | 0.485094 | + | 1.12726i | ||||
\(665\) | 43.3013 | − | 15.0000i | 1.67915 | − | 0.581675i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.4164 | − | 7.74597i | −0.519485 | − | 0.299925i | ||||
\(668\) | 20.0265 | − | 5.56231i | 0.774849 | − | 0.215212i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.2705 | + | 3.30792i | −0.937652 | + | 0.127796i | ||||
\(671\) | 17.3205 | 0.668651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | −0.269830 | −0.134915 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134915 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(674\) | −26.6239 | + | 3.62868i | −1.02551 | + | 0.139771i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.0517 | − | 6.95803i | 0.963525 | − | 0.267617i | ||||
\(677\) | −21.3014 | − | 12.2984i | −0.818680 | − | 0.472665i | 0.0312813 | − | 0.999511i | \(-0.490041\pi\) |
−0.849961 | + | 0.526846i | \(0.823375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.500000 | − | 2.59808i | 0.0191882 | − | 0.0997050i | ||||
\(680\) | 8.66025 | + | 20.1246i | 0.332106 | + | 0.771744i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.92705 | − | 1.19682i | −0.112083 | − | 0.0458285i | ||||
\(683\) | 9.68246 | − | 5.59017i | 0.370489 | − | 0.213902i | −0.303183 | − | 0.952932i | \(-0.598049\pi\) |
0.673672 | + | 0.739030i | \(0.264716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.74597i | 0.295958i | ||||||||
\(686\) | 11.0355 | − | 23.7533i | 0.421336 | − | 0.906905i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.5410 | + | 19.3649i | 1.27596 | + | 0.736676i | 0.976103 | − | 0.217308i | \(-0.0697276\pi\) |
0.299857 | + | 0.953984i | \(0.403061\pi\) | |||||||
\(692\) | −8.66025 | − | 2.23607i | −0.329213 | − | 0.0850026i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.0000 | − | 15.4919i | 0.759190 | − | 0.588066i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | −4.43804 | − | 32.5623i | −0.167982 | − | 1.23250i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.5967i | 0.929006i | 0.885571 | + | 0.464503i | \(0.153767\pi\) | ||||
−0.885571 | + | 0.464503i | \(0.846233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0000 | + | 51.9615i | 1.13147 | + | 1.95977i | ||||
\(704\) | −4.15551 | + | 17.3992i | −0.156617 | + | 0.655757i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | − | 30.9839i | −0.903252 | − | 1.16609i | ||||
\(707\) | 3.87298 | + | 11.1803i | 0.145659 | + | 0.420480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.4164 | + | 7.74597i | 0.503864 | + | 0.290906i | 0.730308 | − | 0.683118i | \(-0.239377\pi\) |
−0.226444 | + | 0.974024i | \(0.572710\pi\) | |||||||
\(710\) | −30.4188 | − | 12.4377i | −1.14160 | − | 0.466778i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.58359 | + | 38.9229i | −0.171777 | + | 1.45870i | ||||
\(713\) | 6.92820 | 0.259463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.5332 | + | 12.7639i | −0.468389 | + | 0.477011i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.27051 | − | 22.6728i | 0.345972 | − | 0.846143i | ||||
\(719\) | 24.2487 | − | 42.0000i | 0.904324 | − | 1.56634i | 0.0825027 | − | 0.996591i | \(-0.473709\pi\) |
0.821822 | − | 0.569745i | \(-0.192958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | − | 13.8564i | −0.595871 | − | 0.516040i | ||||
\(722\) | 35.5070 | + | 45.8394i | 1.32144 | + | 1.70597i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.4377 | + | 44.7806i | 0.462243 | + | 1.66426i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.0000 | 1.07555 | 0.537775 | − | 0.843088i | \(-0.319265\pi\) | ||||
0.537775 | + | 0.843088i | \(0.319265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.27051 | + | 31.3331i | 0.158059 | + | 1.15969i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4164 | + | 7.74597i | 0.495546 | + | 0.286104i | 0.726872 | − | 0.686772i | \(-0.240973\pi\) |
−0.231326 | + | 0.972876i | \(0.574306\pi\) | |||||||
\(734\) | −4.33013 | − | 5.59017i | −0.159828 | − | 0.206337i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | − | 38.7298i | −0.221163 | − | 1.42760i | ||||
\(737\) | 8.66025 | − | 15.0000i | 0.319005 | − | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4164 | − | 7.74597i | 0.493531 | − | 0.284940i | −0.232507 | − | 0.972595i | \(-0.574693\pi\) |
0.726038 | + | 0.687655i | \(0.241360\pi\) | |||||||
\(740\) | −24.7172 | − | 24.2705i | −0.908624 | − | 0.892202i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.9058 | + | 37.3172i | 0.694052 | + | 1.36996i | ||||
\(743\) | 10.3923 | 0.381257 | 0.190628 | − | 0.981662i | \(-0.438947\pi\) | ||||
0.190628 | + | 0.981662i | \(0.438947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0000 | + | 43.3013i | 0.915929 | + | 1.58644i | ||||
\(746\) | −10.1396 | − | 4.14590i | −0.371237 | − | 0.151792i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.0000 | − | 3.87298i | −0.548454 | − | 0.141610i | ||||
\(749\) | 19.3649 | − | 22.3607i | 0.707579 | − | 0.817041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5000 | − | 37.2391i | 0.784546 | − | 1.35887i | −0.144724 | − | 0.989472i | \(-0.546229\pi\) |
0.929270 | − | 0.369402i | \(-0.120437\pi\) | |||||||
\(752\) | 0.252703 | + | 13.8541i | 0.00921512 | + | 0.505207i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6525i | 0.569652i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 23.2379i | − | 0.844596i | −0.906457 | − | 0.422298i | \(-0.861224\pi\) | ||
0.906457 | − | 0.422298i | \(-0.138776\pi\) | |||||||
\(758\) | 4.43804 | + | 32.5623i | 0.161197 | + | 1.18272i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −39.2705 | − | 29.2887i | −1.42449 | − | 1.06241i | ||||
\(761\) | 3.46410 | − | 6.00000i | 0.125574 | − | 0.217500i | −0.796383 | − | 0.604792i | \(-0.793256\pi\) |
0.921957 | + | 0.387292i | \(0.126590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.70820 | − | 19.3649i | −0.242853 | − | 0.701057i | ||||
\(764\) | 3.46410 | − | 13.4164i | 0.125327 | − | 0.485389i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.70820 | − | 9.06914i | 0.133983 | − | 0.327681i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | 1.02220 | − | 18.6803i | 0.0368377 | − | 0.673193i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.2599 | − | 23.8214i | −0.873132 | − | 0.857351i | ||||
\(773\) | 3.87298 | − | 2.23607i | 0.139302 | − | 0.0804258i | −0.428730 | − | 0.903433i | \(-0.641039\pi\) |
0.568031 | + | 0.823007i | \(0.307705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.59808 | + | 1.11803i | −0.0932655 | + | 0.0401351i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.00000 | − | 3.87298i | 0.179259 | − | 0.138853i | ||||
\(779\) | −69.7137 | − | 40.2492i | −2.49775 | − | 1.44208i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1246 | − | 11.6190i | 0.720115 | − | 0.415759i | ||||
\(782\) | 33.6302 | − | 4.58359i | 1.20261 | − | 0.163909i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.6353 | + | 4.50474i | −0.986973 | + | 0.160884i | ||||
\(785\) | 34.6410 | 1.23639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.5410 | − | 19.3649i | 1.19561 | − | 0.690285i | 0.236035 | − | 0.971745i | \(-0.424152\pi\) |
0.959573 | + | 0.281460i | \(0.0908186\pi\) | |||||||
\(788\) | 2.39364 | + | 8.61803i | 0.0852697 | + | 0.307005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 32.5000 | − | 25.1744i | 1.15630 | − | 0.895665i | ||||
\(791\) | 5.19615 | − | 27.0000i | 0.184754 | − | 0.960009i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −40.5584 | − | 16.5836i | −1.43936 | − | 0.588530i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.4164 | − | 11.2101i | −0.404644 | − | 0.397330i | ||||
\(797\) | − | 15.6525i | − | 0.554439i | −0.960807 | − | 0.277220i | \(-0.910587\pi\) | ||
0.960807 | − | 0.277220i | \(-0.0894129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.5410 | + | 45.3457i | −0.654706 | + | 1.60121i | ||||
\(803\) | −19.3649 | − | 11.1803i | −0.683373 | − | 0.394546i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4164 | + | 38.7298i | 0.472866 | + | 1.36505i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.56231 | − | 10.1396i | 0.266041 | − | 0.356710i | ||||
\(809\) | 17.3205 | + | 30.0000i | 0.608957 | + | 1.05474i | 0.991413 | + | 0.130770i | \(0.0417450\pi\) |
−0.382456 | + | 0.923974i | \(0.624922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.2379i | 0.815993i | 0.912983 | + | 0.407997i | \(0.133772\pi\) | ||||
−0.912983 | + | 0.407997i | \(0.866228\pi\) | |||||||
\(812\) | 11.7936 | − | 0.954915i | 0.413873 | − | 0.0335109i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.2705 | − | 3.30792i | 0.850681 | − | 0.115943i | ||||
\(815\) | 17.3205 | + | 30.0000i | 0.606711 | + | 1.05085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.06218 | + | 7.82624i | 0.211959 | + | 0.273638i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 45.0000 | + | 11.6190i | 1.57147 | + | 0.405751i | ||||
\(821\) | 13.5554 | + | 7.82624i | 0.473088 | + | 0.273138i | 0.717532 | − | 0.696526i | \(-0.245272\pi\) |
−0.244443 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0000 | − | 17.3205i | −0.348578 | − | 0.603755i | 0.637419 | − | 0.770517i | \(-0.280002\pi\) |
−0.985997 | + | 0.166762i | \(0.946669\pi\) | |||||||
\(824\) | −2.64634 | + | 22.4721i | −0.0921896 | + | 0.782854i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.78115 | − | 7.46344i | −0.131563 | − | 0.259686i | ||||
\(827\) | 24.5967i | 0.855313i | 0.903941 | + | 0.427656i | \(0.140661\pi\) | ||||
−0.903941 | + | 0.427656i | \(0.859339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.70820 | + | 3.87298i | −0.232986 | + | 0.134514i | −0.611949 | − | 0.790898i | \(-0.709614\pi\) |
0.378963 | + | 0.925412i | \(0.376281\pi\) | |||||||
\(830\) | −13.3808 | + | 32.7254i | −0.464455 | + | 1.13592i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.46410 | − | 24.0000i | −0.120024 | − | 0.831551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.1246 | + | 11.6190i | 0.696441 | + | 0.402090i | ||||
\(836\) | 33.3775 | − | 9.27051i | 1.15439 | − | 0.320627i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.83282 | − | 50.1329i | −0.236036 | − | 1.73181i | ||||
\(839\) | −31.1769 | −1.07635 | −0.538173 | − | 0.842834i | \(-0.680885\pi\) | ||||
−0.538173 | + | 0.842834i | \(0.680885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.0000 | 0.827586 | ||||||||
\(842\) | 4.43804 | + | 32.5623i | 0.152945 | + | 1.12217i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.4377 | + | 44.7806i | 0.428123 | + | 1.54141i | ||||
\(845\) | 25.1744 | + | 14.5344i | 0.866025 | + | 0.500000i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0000 | − | 10.3923i | −0.412325 | − | 0.357084i | ||||
\(848\) | 21.6506 | − | 39.1312i | 0.743486 | − | 1.34377i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.4758 | + | 26.8328i | −1.59317 | + | 0.919817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.2379i | − | 0.795651i | −0.917461 | − | 0.397825i | \(-0.869765\pi\) | ||
0.917461 | − | 0.397825i | \(-0.130235\pi\) | |||||||
\(854\) | 15.8412 | − | 24.2705i | 0.542073 | − | 0.830520i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.4058 | − | 3.69837i | −1.07343 | − | 0.126408i | ||||
\(857\) | 12.1244 | + | 21.0000i | 0.414160 | + | 0.717346i | 0.995340 | − | 0.0964289i | \(-0.0307420\pi\) |
−0.581180 | + | 0.813775i | \(0.697409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4164 | + | 7.74597i | 0.457762 | + | 0.264289i | 0.711103 | − | 0.703088i | \(-0.248196\pi\) |
−0.253341 | + | 0.967377i | \(0.581529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.0000 | + | 27.1109i | 0.715263 | + | 0.923400i | ||||
\(863\) | 13.8564 | − | 24.0000i | 0.471678 | − | 0.816970i | −0.527797 | − | 0.849370i | \(-0.676982\pi\) |
0.999475 | + | 0.0324008i | \(0.0103153\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00000 | − | 8.66025i | −0.170005 | − | 0.294457i | ||||
\(866\) | −30.8277 | + | 4.20163i | −1.04757 | + | 0.142777i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.35410 | + | 3.00696i | −0.147788 | + | 0.102063i | ||||
\(869\) | 29.0689i | 0.986094i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −13.0983 | + | 17.5623i | −0.443564 | + | 0.594735i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −60.0000 | + | 46.4758i | −2.02953 | + | 1.57207i | ||||
\(875\) | 29.0474 | + | 5.59017i | 0.981981 | + | 0.188982i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8328 | − | 15.4919i | −0.906080 | − | 0.523125i | −0.0269120 | − | 0.999638i | \(-0.508567\pi\) |
−0.879168 | + | 0.476512i | \(0.841901\pi\) | |||||||
\(878\) | 3.74663 | − | 9.16312i | 0.126443 | − | 0.309240i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −17.1353 | + | 10.3142i | −0.577629 | + | 0.347692i | ||||
\(881\) | 10.3923 | 0.350126 | 0.175063 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175063 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.2379i | 0.782018i | 0.920387 | + | 0.391009i | \(0.127874\pi\) | ||||
−0.920387 | + | 0.391009i | \(0.872126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.1976 | − | 13.1650i | −1.08170 | − | 0.442287i | ||||
\(887\) | 13.8564 | − | 24.0000i | 0.465253 | − | 0.805841i | −0.533960 | − | 0.845510i | \(-0.679297\pi\) |
0.999213 | + | 0.0396684i | \(0.0126302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | + | 12.9904i | −0.0838473 | + | 0.435683i | ||||
\(890\) | −34.6410 | + | 26.8328i | −1.16117 | + | 0.899438i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.4894 | + | 3.74663i | −0.451657 | + | 0.125447i | ||||
\(893\) | 23.2379 | − | 13.4164i | 0.777627 | − | 0.448963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 20.5802 | + | 21.7361i | 0.687535 | + | 0.726151i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.1246 | + | 3.96951i | −0.971901 | + | 0.132464i | ||||
\(899\) | 1.93649 | − | 1.11803i | 0.0645856 | − | 0.0372885i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.5410 | + | 19.3649i | 1.11741 | + | 0.645139i | ||||
\(902\) | −25.9808 | + | 20.1246i | −0.865065 | + | 0.670076i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.0000 | + | 11.6190i | −0.898007 | + | 0.386441i | ||||
\(905\) | −25.9808 | + | 45.0000i | −0.863630 | + | 1.49585i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4164 | − | 7.74597i | 0.445485 | − | 0.257201i | −0.260437 | − | 0.965491i | \(-0.583867\pi\) |
0.705921 | + | 0.708290i | \(0.250533\pi\) | |||||||
\(908\) | 34.4664 | − | 35.1008i | 1.14381 | − | 1.16486i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3923 | −0.344312 | −0.172156 | − | 0.985070i | \(-0.555073\pi\) | ||||
−0.172156 | + | 0.985070i | \(0.555073\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5000 | − | 21.6506i | −0.413690 | − | 0.716531i | ||||
\(914\) | −2.67617 | + | 6.54508i | −0.0885197 | + | 0.216492i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.0000 | − | 3.87298i | −0.495614 | − | 0.127967i | ||||
\(917\) | 19.3649 | − | 22.3607i | 0.639486 | − | 0.738415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | + | 6.92820i | −0.131948 | + | 0.228540i | −0.924427 | − | 0.381358i | \(-0.875456\pi\) |
0.792480 | + | 0.609898i | \(0.208790\pi\) | |||||||
\(920\) | 26.1966 | − | 35.1246i | 0.863676 | − | 1.15802i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.27051 | − | 31.3331i | −0.140642 | − | 1.03190i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.2101 | − | 1.52786i | 0.368386 | − | 0.0502087i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.92705 | − | 9.85707i | −0.260218 | − | 0.323574i | ||||
\(929\) | −17.3205 | + | 30.0000i | −0.568267 | + | 0.984268i | 0.428470 | + | 0.903556i | \(0.359053\pi\) |
−0.996737 | + | 0.0807121i | \(0.974281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.5410 | + | 42.6028i | 1.09926 | + | 1.39625i | ||||
\(932\) | −1.73205 | + | 6.70820i | −0.0567352 | + | 0.219735i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.7082 | + | 4.78727i | 0.383104 | + | 0.156644i | ||||
\(935\) | −8.66025 | − | 15.0000i | −0.283221 | − | 0.490552i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.00000 | 0.163343 | 0.0816714 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816714 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(938\) | −13.0983 | − | 25.8541i | −0.427675 | − | 0.844166i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.8541 | + | 11.0539i | −0.354022 | + | 0.360538i | ||||
\(941\) | 9.68246 | − | 5.59017i | 0.315639 | − | 0.182234i | −0.333808 | − | 0.942641i | \(-0.608334\pi\) |
0.649447 | + | 0.760407i | \(0.275000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000 | − | 62.3538i | 1.17232 | − | 2.03052i | ||||
\(944\) | −4.33013 | + | 7.82624i | −0.140934 | + | 0.254722i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.9839 | + | 17.8885i | 1.00684 | + | 0.581300i | 0.910265 | − | 0.414026i | \(-0.135878\pi\) |
0.0965754 | + | 0.995326i | \(0.469211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.1459 | + | 17.4767i | −0.620522 | + | 0.566423i | ||||
\(953\) | −20.7846 | −0.673280 | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.4164 | − | 7.74597i | 0.434145 | − | 0.250654i | ||||
\(956\) | 40.0530 | − | 11.1246i | 1.29541 | − | 0.359796i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | + | 15.4919i | 0.387702 | + | 0.500522i | ||||
\(959\) | −8.66025 | + | 3.00000i | −0.279654 | + | 0.0968751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32.8222 | − | 32.2289i | −1.05713 | − | 1.03802i | ||||
\(965\) | − | 38.0132i | − | 1.22369i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0000 | −0.610999 | −0.305499 | − | 0.952192i | \(-0.598823\pi\) | ||||
−0.305499 | + | 0.952192i | \(0.598823\pi\) | |||||||
\(968\) | −1.98475 | + | 16.8541i | −0.0637924 | + | 0.541711i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.92705 | − | 1.19682i | −0.0939819 | − | 0.0384275i | ||||
\(971\) | −9.68246 | − | 5.59017i | −0.310725 | − | 0.179397i | 0.336526 | − | 0.941674i | \(-0.390748\pi\) |
−0.647251 | + | 0.762277i | \(0.724081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.866025 | + | 1.11803i | 0.0277492 | + | 0.0358241i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30.9787 | + | 0.565061i | −0.991604 | + | 0.0180872i | ||||
\(977\) | 6.92820 | + | 12.0000i | 0.221653 | + | 0.383914i | 0.955310 | − | 0.295606i | \(-0.0955215\pi\) |
−0.733657 | + | 0.679520i | \(0.762188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.9839i | − | 0.990249i | ||||||
\(980\) | −25.2411 | − | 18.5172i | −0.806297 | − | 0.591511i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.55166 | − | 40.7330i | −0.177161 | − | 1.29984i | ||||
\(983\) | −19.0526 | − | 33.0000i | −0.607682 | − | 1.05254i | −0.991621 | − | 0.129178i | \(-0.958766\pi\) |
0.383939 | − | 0.923358i | \(-0.374567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.00000 | + | 8.66025i | −0.159313 | + | 0.275939i | ||||
\(986\) | 8.66025 | − | 6.70820i | 0.275799 | − | 0.213633i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.500000 | + | 0.866025i | 0.0158830 | + | 0.0275102i | 0.873858 | − | 0.486182i | \(-0.161611\pi\) |
−0.857975 | + | 0.513692i | \(0.828277\pi\) | |||||||
\(992\) | 5.27424 | + | 2.04508i | 0.167457 | + | 0.0649315i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.12461 | − | 38.8264i | 0.0673886 | − | 1.23150i | ||||
\(995\) | − | 17.8885i | − | 0.567105i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.70820 | + | 3.87298i | −0.212451 | + | 0.122659i | −0.602450 | − | 0.798157i | \(-0.705809\pi\) |
0.389999 | + | 0.920815i | \(0.372475\pi\) | |||||||
\(998\) | −40.5584 | − | 16.5836i | −1.28385 | − | 0.524944i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.cj.a.37.4 | yes | 8 | |
3.2 | odd | 2 | inner | 504.2.cj.a.37.1 | ✓ | 8 | |
4.3 | odd | 2 | 2016.2.cr.a.1297.4 | 8 | |||
7.4 | even | 3 | inner | 504.2.cj.a.109.2 | yes | 8 | |
8.3 | odd | 2 | 2016.2.cr.a.1297.2 | 8 | |||
8.5 | even | 2 | inner | 504.2.cj.a.37.2 | yes | 8 | |
12.11 | even | 2 | 2016.2.cr.a.1297.1 | 8 | |||
21.11 | odd | 6 | inner | 504.2.cj.a.109.3 | yes | 8 | |
24.5 | odd | 2 | inner | 504.2.cj.a.37.3 | yes | 8 | |
24.11 | even | 2 | 2016.2.cr.a.1297.3 | 8 | |||
28.11 | odd | 6 | 2016.2.cr.a.1873.2 | 8 | |||
56.11 | odd | 6 | 2016.2.cr.a.1873.4 | 8 | |||
56.53 | even | 6 | inner | 504.2.cj.a.109.4 | yes | 8 | |
84.11 | even | 6 | 2016.2.cr.a.1873.3 | 8 | |||
168.11 | even | 6 | 2016.2.cr.a.1873.1 | 8 | |||
168.53 | odd | 6 | inner | 504.2.cj.a.109.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cj.a.37.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
504.2.cj.a.37.2 | yes | 8 | 8.5 | even | 2 | inner | |
504.2.cj.a.37.3 | yes | 8 | 24.5 | odd | 2 | inner | |
504.2.cj.a.37.4 | yes | 8 | 1.1 | even | 1 | trivial | |
504.2.cj.a.109.1 | yes | 8 | 168.53 | odd | 6 | inner | |
504.2.cj.a.109.2 | yes | 8 | 7.4 | even | 3 | inner | |
504.2.cj.a.109.3 | yes | 8 | 21.11 | odd | 6 | inner | |
504.2.cj.a.109.4 | yes | 8 | 56.53 | even | 6 | inner | |
2016.2.cr.a.1297.1 | 8 | 12.11 | even | 2 | |||
2016.2.cr.a.1297.2 | 8 | 8.3 | odd | 2 | |||
2016.2.cr.a.1297.3 | 8 | 24.11 | even | 2 | |||
2016.2.cr.a.1297.4 | 8 | 4.3 | odd | 2 | |||
2016.2.cr.a.1873.1 | 8 | 168.11 | even | 6 | |||
2016.2.cr.a.1873.2 | 8 | 28.11 | odd | 6 | |||
2016.2.cr.a.1873.3 | 8 | 84.11 | even | 6 | |||
2016.2.cr.a.1873.4 | 8 | 56.11 | odd | 6 |