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 | 37.2 | ||
Root | \(-0.535233 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.37 |
Dual form | 504.2.cj.a.109.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.535233 | − | 1.30902i | −0.378467 | − | 0.925615i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.42705 | + | 1.40126i | −0.713525 | + | 0.700629i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 2.59808 | + | 1.11803i | 0.918559 | + | 0.395285i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.427051 | + | 3.13331i | −0.135045 | + | 0.990839i | ||||
\(11\) | 1.93649 | − | 1.11803i | 0.583874 | − | 0.337100i | −0.178797 | − | 0.983886i | \(-0.557221\pi\) |
0.762672 | + | 0.646786i | \(0.223887\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 3.66854 | − | 0.736068i | 0.980459 | − | 0.196722i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0729490 | − | 3.99933i | 0.0182373 | − | 0.999834i | ||||
\(17\) | 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 | \(0.0149348\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 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 | ||||||||
\(28\) | −2.92705 | − | 4.40822i | −0.553161 | − | 0.833075i | ||||
\(29\) | 2.23607i | 0.415227i | 0.978211 | + | 0.207614i | \(0.0665697\pi\) | ||||
−0.978211 | + | 0.207614i | \(0.933430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | −5.27424 | + | 2.04508i | −0.932363 | + | 0.361523i | ||||
\(33\) | 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 | 0.936961 | − | 0.349435i | \(-0.113626\pi\) |
0.165861 | + | 0.986149i | \(0.446960\pi\) | |||||||
\(38\) | 1.47935 | − | 10.8541i | 0.239982 | − | 1.76077i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.78115 | − | 5.06980i | −0.597853 | − | 0.801606i | ||||
\(41\) | 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 | \(\pi\) | |||||||||
\(44\) | −1.19682 | + | 4.30902i | −0.180427 | + | 0.649609i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.70820 | − | 1.32317i | −1.43140 | − | 0.195091i | ||||
\(47\) | −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 | −0.985297 | − | 0.170848i | \(-0.945349\pi\) |
−0.344690 | + | 0.938716i | \(0.612016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | −4.20378 | + | 6.19098i | −0.561753 | + | 0.827305i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.92705 | − | 1.19682i | 0.384341 | − | 0.157150i | ||||
\(59\) | 1.93649 | − | 1.11803i | 0.252110 | − | 0.145556i | −0.368620 | − | 0.929580i | \(-0.620170\pi\) |
0.620730 | + | 0.784024i | \(0.286836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.70820 | + | 3.87298i | 0.858898 | + | 0.495885i | 0.863643 | − | 0.504104i | \(-0.168177\pi\) |
−0.00474543 | + | 0.999989i | \(0.501511\pi\) | |||||||
\(62\) | 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 | −0.0307194 | − | 0.999528i | \(-0.509780\pi\) |
0.850257 | + | 0.526368i | \(0.176447\pi\) | |||||||
\(68\) | −6.67550 | − | 1.85410i | −0.809523 | − | 0.224843i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.92705 | − | 2.67617i | −0.947464 | − | 0.319863i | ||||
\(71\) | −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 | \(0.634347\pi\) | |||||||
\(74\) | 1.47935 | − | 10.8541i | 0.171971 | − | 1.26176i | ||||
\(75\) | 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 | \(-0.0944227\pi\) | |||||||
\(80\) | −4.61266 | + | 7.66312i | −0.515711 | + | 0.856763i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.56231 | − | 13.6037i | −0.614254 | − | 1.50228i | ||||
\(83\) | − | 11.1803i | − | 1.22720i | −0.789616 | − | 0.613601i | \(-0.789720\pi\) | ||
0.789616 | − | 0.613601i | \(-0.210280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.74597i | − | 0.840168i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.28115 | − | 0.739674i | 0.669573 | − | 0.0788495i | ||||
\(89\) | −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 | ||||||||
\(94\) | 4.85410 | + | 0.661585i | 0.500662 | + | 0.0682372i | ||||
\(95\) | −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 | \(0.516167\pi\) | |||||||
\(98\) | 0.0780895 | + | 9.89919i | 0.00788823 | + | 0.999969i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.87298 | + | 2.23607i | −0.385376 | + | 0.222497i | −0.680155 | − | 0.733069i | \(-0.738087\pi\) |
0.294779 | + | 0.955566i | \(0.404754\pi\) | |||||||
\(102\) | 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 | 0.888716 | − | 0.458458i | \(-0.151598\pi\) |
0.0473223 | + | 0.998880i | \(0.484931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.70820 | − | 3.87298i | 0.642529 | − | 0.370965i | −0.143059 | − | 0.989714i | \(-0.545694\pi\) |
0.785588 | + | 0.618750i | \(0.212360\pi\) | |||||||
\(110\) | 2.67617 | + | 6.54508i | 0.255162 | + | 0.624049i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.3541 | + | 2.18919i | 0.978371 | + | 0.206859i | ||||
\(113\) | −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 | ||||
\(116\) | −3.13331 | − | 3.19098i | −0.290920 | − | 0.296275i | ||||
\(117\) | 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 | ||||
\(122\) | 1.47935 | − | 10.8541i | 0.133934 | − | 0.982684i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.92705 | − | 0.535233i | −0.173054 | − | 0.0480654i | ||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 4.66092 | − | 10.3090i | 0.411971 | − | 0.911197i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.68246 | + | 5.59017i | 0.845960 | + | 0.488415i | 0.859286 | − | 0.511496i | \(-0.170908\pi\) |
−0.0133255 | + | 0.999911i | \(0.504242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.4164 | + | 15.4919i | −1.16335 | + | 1.34332i | ||||
\(134\) | −8.66025 | − | 6.70820i | −0.748132 | − | 0.579501i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.14590 | + | 9.73072i | 0.0982599 | + | 0.834402i | ||||
\(137\) | 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 | \(\pi\) | |||||||||
\(140\) | 0.739674 | + | 11.8090i | 0.0625139 | + | 0.998044i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.56231 | + | 13.6037i | 0.466778 | + | 1.14160i | ||||
\(143\) | 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 | \(-0.964789\pi\) |
−0.592548 | − | 0.805535i | \(-0.701878\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50000 | + | 6.06218i | 0.284826 | + | 0.493333i | 0.972567 | − | 0.232623i | \(-0.0747309\pi\) |
−0.687741 | + | 0.725956i | \(0.741398\pi\) | |||||||
\(152\) | 13.0983 | + | 17.5623i | 1.06241 | + | 1.42449i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.28115 | − | 5.52694i | 0.506150 | − | 0.445374i | ||||
\(155\) | − | 2.23607i | − | 0.179605i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4164 | + | 7.74597i | −1.07075 | + | 0.618195i | −0.928385 | − | 0.371619i | \(-0.878803\pi\) |
−0.142361 | + | 0.989815i | \(0.545469\pi\) | |||||||
\(158\) | −18.2164 | − | 2.48278i | −1.44922 | − | 0.197519i | ||||
\(159\) | 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 | −0.127966 | − | 0.991779i | \(-0.540845\pi\) |
−0.922888 | + | 0.385068i | \(0.874178\pi\) | |||||||
\(164\) | −14.8303 | + | 14.5623i | −1.15806 | + | 1.13713i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.6353 | + | 5.98409i | −1.13592 | + | 0.464455i | ||||
\(167\) | 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 | ||||||||
\(170\) | −10.1396 | + | 4.14590i | −0.777672 | + | 0.317976i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.87298 | + | 2.23607i | 0.294457 | + | 0.170005i | 0.639950 | − | 0.768416i | \(-0.278955\pi\) |
−0.345493 | + | 0.938421i | \(0.612288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.33013 | − | 7.82624i | −0.326396 | − | 0.589925i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.4164 | + | 2.64634i | 1.45532 | + | 0.198351i | ||||
\(179\) | 7.74597 | − | 4.47214i | 0.578961 | − | 0.334263i | −0.181760 | − | 0.983343i | \(-0.558179\pi\) |
0.760720 | + | 0.649080i | \(0.224846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.2379i | − | 1.72726i | −0.504127 | − | 0.863630i | \(-0.668186\pi\) | ||
0.504127 | − | 0.863630i | \(-0.331814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.7082 | − | 11.7155i | 1.15802 | − | 0.863676i | ||||
\(185\) | −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 | \(-0.376238\pi\) | |||||||
\(194\) | 0.535233 | + | 1.30902i | 0.0384275 | + | 0.0939819i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.9164 | − | 5.40059i | 0.922601 | − | 0.385757i | ||||
\(197\) | − | 4.47214i | − | 0.318626i | −0.987228 | − | 0.159313i | \(-0.949072\pi\) | ||
0.987228 | − | 0.159313i | \(-0.0509280\pi\) | |||||||
\(198\) | 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 | ||||
\(206\) | 11.2101 | + | 1.52786i | 0.781042 | + | 0.106451i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.3205 | 1.19808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 23.2379i | − | 1.59976i | −0.600158 | − | 0.799882i | \(-0.704896\pi\) | ||
0.600158 | − | 0.799882i | \(-0.295104\pi\) | |||||||
\(212\) | 5.98409 | − | 21.5451i | 0.410989 | − | 1.47972i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.13525 | − | 15.6665i | 0.145963 | − | 1.07094i | ||||
\(215\) | 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 | ||||||||
\(220\) | 7.13525 | − | 7.00629i | 0.481059 | − | 0.472364i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00000 | −0.468755 | −0.234377 | − | 0.972146i | \(-0.575305\pi\) | ||||
−0.234377 | + | 0.972146i | \(0.575305\pi\) | |||||||
\(224\) | −2.67617 | − | 14.7254i | −0.178809 | − | 0.983884i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.56231 | + | 13.6037i | 0.369999 | + | 0.904905i | ||||
\(227\) | −21.3014 | + | 12.2984i | −1.41382 | + | 0.816272i | −0.995746 | − | 0.0921394i | \(-0.970629\pi\) |
−0.418078 | + | 0.908411i | \(0.637296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.70820 | + | 3.87298i | 0.443291 | + | 0.255934i | 0.704992 | − | 0.709215i | \(-0.250950\pi\) |
−0.261702 | + | 0.965149i | \(0.584284\pi\) | |||||||
\(230\) | 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 | ||||
\(236\) | −1.19682 | + | 4.30902i | −0.0779062 | + | 0.280493i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.56231 | + | 9.73072i | 0.555012 | + | 0.630749i | ||||
\(239\) | 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 | \(-0.432211\pi\) | |||||||
\(242\) | 8.40755 | + | 1.14590i | 0.540458 | + | 0.0736611i | ||||
\(243\) | 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 | ||||||||
\(248\) | 0.330792 | + | 2.80902i | 0.0210053 | + | 0.178373i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.6353 | − | 5.98409i | 0.925615 | − | 0.378467i | ||||
\(251\) | − | 24.5967i | − | 1.55253i | −0.630405 | − | 0.776266i | \(-0.717111\pi\) | ||
0.630405 | − | 0.776266i | \(-0.282889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.4919i | − | 0.973970i | ||||||
\(254\) | −2.67617 | − | 6.54508i | −0.167918 | − | 0.410675i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9894 | − | 0.583495i | −0.999335 | − | 0.0364684i | ||||
\(257\) | 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 | ||||||||
\(262\) | 2.13525 | − | 15.6665i | 0.131916 | − | 0.967882i | ||||
\(263\) | −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 | ||||||||
\(266\) | 27.4601 | + | 9.27051i | 1.68369 | + | 0.568411i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.14590 | + | 14.9269i | −0.253251 | + | 0.911804i | ||||
\(269\) | 25.1744 | − | 14.5344i | 1.53491 | − | 0.886181i | 0.535785 | − | 0.844355i | \(-0.320016\pi\) |
0.999125 | − | 0.0418260i | \(-0.0133175\pi\) | |||||||
\(270\) | 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 | −0.845605 | − | 0.533810i | \(-0.820760\pi\) |
0.0394907 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.0623 | − | 7.28882i | 0.900145 | − | 0.435590i | ||||
\(281\) | 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 | −0.842604 | − | 0.538533i | \(-0.818979\pi\) |
0.0450815 | + | 0.998983i | \(0.485645\pi\) | |||||||
\(284\) | 14.8303 | − | 14.5623i | 0.880019 | − | 0.864114i | ||||
\(285\) | 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 | ||||
\(290\) | −7.00629 | − | 0.954915i | −0.411424 | − | 0.0560745i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.2705 | − | 5.35233i | −1.12772 | − | 0.313222i | ||||
\(293\) | − | 11.1803i | − | 0.653162i | −0.945169 | − | 0.326581i | \(-0.894103\pi\) | ||
0.945169 | − | 0.326581i | \(-0.105897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.00000 | −0.291111 | ||||||||
\(296\) | 13.0983 | + | 17.5623i | 0.761323 | + | 1.02079i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.27051 | + | 31.3331i | −0.247384 | + | 1.81508i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.06218 | − | 7.82624i | 0.348839 | − | 0.450349i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.9787 | − | 26.5458i | 0.916442 | − | 1.52251i | ||||
\(305\) | −8.66025 | − | 15.0000i | −0.495885 | − | 0.858898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −10.5967 | − | 5.26393i | −0.603806 | − | 0.299940i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.92705 | + | 1.19682i | −0.166245 | + | 0.0679747i | ||||
\(311\) | 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 | 0.444631 | − | 0.895714i | \(-0.353335\pi\) |
−0.553395 | + | 0.832919i | \(0.686668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | −4.15551 | − | 17.3992i | −0.232300 | − | 0.972644i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.29180 | − | 24.5611i | 0.462084 | − | 1.36873i | ||||
\(323\) | 26.8328i | 1.49302i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.95870 | + | 21.7082i | −0.163867 | + | 1.20231i | ||||
\(327\) | 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 | 0.0837026 | − | 0.996491i | \(-0.473325\pi\) |
−0.821135 | + | 0.570734i | \(0.806659\pi\) | |||||||
\(332\) | 15.6665 | + | 15.9549i | 0.859813 | + | 0.875640i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.56231 | − | 13.6037i | −0.304356 | − | 0.744362i | ||||
\(335\) | −17.3205 | −0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | −6.95803 | − | 17.0172i | −0.378467 | − | 0.925615i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.8541 | + | 11.0539i | 0.588646 | + | 0.599481i | ||||
\(341\) | 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 | ||||||||
\(346\) | 0.854102 | − | 6.26662i | 0.0459168 | − | 0.336896i | ||||
\(347\) | −15.4919 | + | 8.94427i | −0.831651 | + | 0.480154i | −0.854417 | − | 0.519587i | \(-0.826086\pi\) |
0.0227669 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2379i | 1.24390i | 0.783058 | + | 0.621948i | \(0.213659\pi\) | ||||
−0.783058 | + | 0.621948i | \(0.786341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.92705 | + | 9.85707i | −0.422513 | + | 0.525384i | ||||
\(353\) | −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 | ||||
\(362\) | −30.4188 | + | 12.4377i | −1.59878 | + | 0.653711i | ||||
\(363\) | 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 | \(0.874991\pi\) | |||||||
\(368\) | −23.7433 | − | 14.2918i | −1.23771 | − | 0.745011i | ||||
\(369\) | 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 | 0.663512 | − | 0.748166i | \(-0.269065\pi\) |
−0.316174 | + | 0.948701i | \(0.602398\pi\) | |||||||
\(374\) | 1.47935 | − | 10.8541i | 0.0764953 | − | 0.561252i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.85410 | + | 5.85774i | −0.405044 | + | 0.302090i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.2379i | − | 1.19365i | −0.802371 | − | 0.596825i | \(-0.796429\pi\) | ||
0.802371 | − | 0.596825i | \(-0.203571\pi\) | |||||||
\(380\) | 33.3775 | + | 9.27051i | 1.71223 | + | 0.475567i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.70820 | − | 1.32317i | −0.496715 | − | 0.0676992i | ||||
\(383\) | 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 | ||||||||
\(388\) | 1.42705 | − | 1.40126i | 0.0724475 | − | 0.0711381i | ||||
\(389\) | −3.87298 | + | 2.23607i | −0.196368 | + | 0.113373i | −0.594960 | − | 0.803755i | \(-0.702832\pi\) |
0.398592 | + | 0.917128i | \(0.369499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −13.9828 | − | 14.0172i | −0.706236 | − | 0.707977i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.85410 | + | 2.39364i | −0.294925 | + | 0.120590i | ||||
\(395\) | −25.1744 | + | 14.5344i | −1.26666 | + | 0.731307i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.8328 | + | 15.4919i | 1.34670 | + | 0.777518i | 0.987781 | − | 0.155851i | \(-0.0498118\pi\) |
0.358920 | + | 0.933368i | \(0.383145\pi\) | |||||||
\(398\) | −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 | ||||||||
\(404\) | 2.39364 | − | 8.61803i | 0.119088 | − | 0.428763i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.64590 | + | 8.20311i | 0.0816845 | + | 0.407114i | ||||
\(407\) | 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 | \(0.777967\pi\) | |||||||
\(410\) | −4.43804 | + | 32.5623i | −0.219179 | + | 1.60814i | ||||
\(411\) | 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 | ||||||||
\(418\) | −9.27051 | − | 22.6728i | −0.453435 | − | 1.10896i | ||||
\(419\) | 35.7771i | 1.74783i | 0.486083 | + | 0.873913i | \(0.338425\pi\) | ||||
−0.486083 | + | 0.873913i | \(0.661575\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.2379i | − | 1.13255i | −0.824218 | − | 0.566273i | \(-0.808385\pi\) | ||
0.824218 | − | 0.566273i | \(-0.191615\pi\) | |||||||
\(422\) | −30.4188 | + | 12.4377i | −1.48076 | + | 0.605457i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −31.4058 | + | 3.69837i | −1.52520 | + | 0.179609i | ||||
\(425\) | 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 | \(0.677293\pi\) | |||||||
\(434\) | 2.47172 | + | 2.80902i | 0.118647 | + | 0.134837i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.14590 | + | 14.9269i | −0.198553 | + | 0.714868i | ||||
\(437\) | 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 | 0.911794 | − | 0.410647i | \(-0.134697\pi\) |
0.100266 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.8328 | − | 15.4919i | 1.27200 | − | 0.734388i | ||||
\(446\) | 3.74663 | + | 9.16312i | 0.177408 | + | 0.433886i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.8435 | + | 11.3847i | −0.843024 | + | 0.537876i | ||||
\(449\) | −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 | ||||
\(452\) | 14.8303 | − | 14.5623i | 0.697561 | − | 0.684953i | ||||
\(453\) | 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 | \(0.203977\pi\) | |||||||
\(458\) | 1.47935 | − | 10.8541i | 0.0691254 | − | 0.507179i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.29180 | − | 29.8537i | 0.386607 | − | 1.39194i | ||||
\(461\) | 22.3607i | 1.04144i | 0.853727 | + | 0.520720i | \(0.174337\pi\) | ||||
−0.853727 | + | 0.520720i | \(0.825663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 8.94278 | + | 0.163119i | 0.415158 | + | 0.00757261i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.85410 | + | 0.661585i | 0.224862 | + | 0.0306473i | ||||
\(467\) | −7.74597 | − | 4.47214i | −0.358441 | − | 0.206946i | 0.309956 | − | 0.950751i | \(-0.399686\pi\) |
−0.668397 | + | 0.743805i | \(0.733019\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.70820 | + | 19.3649i | 0.309756 | + | 0.894189i | ||||
\(470\) | −8.66025 | − | 6.70820i | −0.399468 | − | 0.309426i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.28115 | − | 0.739674i | 0.289113 | − | 0.0340463i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.15485 | − | 16.4164i | 0.373777 | − | 0.752445i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.1246 | − | 27.2074i | −0.508828 | − | 1.24444i | ||||
\(479\) | 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 | \(0.826121\pi\) | |||||||
\(488\) | 13.0983 | + | 17.5623i | 0.592932 | + | 0.795008i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.9164 | − | 19.2570i | 0.493153 | − | 0.869943i | ||||
\(491\) | 29.0689i | 1.31186i | 0.754822 | + | 0.655930i | \(0.227723\pi\) | ||||
−0.754822 | + | 0.655930i | \(0.772277\pi\) | |||||||
\(492\) | 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 | 0.960822 | − | 0.277165i | \(-0.0893948\pi\) |
0.240379 | + | 0.970679i | \(0.422728\pi\) | |||||||
\(500\) | −15.6665 | − | 15.9549i | −0.700629 | − | 0.713525i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −32.1976 | + | 13.1650i | −1.43705 | + | 0.587582i | ||||
\(503\) | −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 | ||||||||
\(506\) | −20.2792 | + | 8.29180i | −0.901521 | + | 0.368615i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.13525 | + | 7.00629i | −0.316576 | + | 0.310854i | ||||
\(509\) | −25.1744 | − | 14.5344i | −1.11584 | − | 0.644228i | −0.175501 | − | 0.984479i | \(-0.556154\pi\) |
−0.940334 | + | 0.340251i | \(0.889488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0000 | + | 8.66025i | −1.10593 | + | 0.383107i | ||||
\(512\) | 7.79423 | + | 21.2426i | 0.344459 | + | 0.938801i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.70820 | − | 1.32317i | −0.428211 | − | 0.0583625i | ||||
\(515\) | 15.4919 | − | 8.94427i | 0.682656 | − | 0.394132i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.74597i | 0.340667i | ||||||||
\(518\) | 27.4601 | + | 9.27051i | 1.20653 | + | 0.407323i | ||||
\(519\) | 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 | 0.954459 | − | 0.298342i | \(-0.0964335\pi\) |
0.218858 | + | 0.975757i | \(0.429767\pi\) | |||||||
\(524\) | −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 | ||||
\(530\) | −13.3808 | − | 32.7254i | −0.581226 | − | 1.42150i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.56231 | − | 40.9076i | −0.111090 | − | 1.77357i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5000 | − | 21.6506i | −0.540422 | − | 0.936039i | ||||
\(536\) | 21.7586 | − | 2.56231i | 0.939826 | − | 0.110675i | ||||
\(537\) | 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 | 0.183051 | − | 0.983103i | \(-0.441403\pi\) |
−0.759867 | + | 0.650078i | \(0.774736\pi\) | |||||||
\(542\) | −1.40126 | − | 0.190983i | −0.0601892 | − | 0.00820342i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.2705 | − | 12.2805i | −0.654718 | − | 0.526524i | ||||
\(545\) | −17.3205 | −0.741929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2379i | 0.993581i | 0.867871 | + | 0.496790i | \(0.165488\pi\) | ||||
−0.867871 | + | 0.496790i | \(0.834512\pi\) | |||||||
\(548\) | −6.67550 | − | 1.85410i | −0.285163 | − | 0.0792033i | ||||
\(549\) | 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 | −0.184527 | − | 0.982827i | \(-0.559075\pi\) |
0.758890 | + | 0.651219i | \(0.225742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −17.6030 | − | 15.8156i | −0.743864 | − | 0.668331i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.56231 | − | 13.6037i | −0.234632 | − | 0.573838i | ||||
\(563\) | −32.9204 | + | 19.0066i | −1.38743 | + | 0.801032i | −0.993025 | − | 0.117906i | \(-0.962382\pi\) |
−0.394403 | + | 0.918938i | \(0.629049\pi\) | |||||||
\(564\) | 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 | −0.353024 | − | 0.935614i | \(-0.614847\pi\) |
0.633754 | + | 0.773535i | \(0.281513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 38.1246 | − | 7.64944i | 1.59129 | − | 0.319282i | ||||
\(575\) | 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 | \(-0.426465\pi\) | |||||||
\(578\) | −7.00629 | − | 0.954915i | −0.291423 | − | 0.0397192i | ||||
\(579\) | 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 | ||||
\(584\) | 3.30792 | + | 28.0902i | 0.136883 | + | 1.16238i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6353 | + | 5.98409i | −0.604577 | + | 0.247200i | ||||
\(587\) | − | 38.0132i | − | 1.56897i | −0.620147 | − | 0.784485i | \(-0.712927\pi\) | ||
0.620147 | − | 0.784485i | \(-0.287073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.74597i | 0.319167i | ||||||||
\(590\) | 2.67617 | + | 6.54508i | 0.110176 | + | 0.269457i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.9787 | − | 26.5458i | 0.656721 | − | 1.09103i | ||||
\(593\) | 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 | ||||||||
\(604\) | −13.4894 | − | 3.74663i | −0.548874 | − | 0.152448i | ||||
\(605\) | 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 | 0.151857 | − | 0.988402i | \(-0.451475\pi\) |
0.931910 | + | 0.362689i | \(0.118141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.21885 | + | 16.6888i | −0.0491087 | + | 0.672409i | ||||
\(617\) | −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 | −0.359092 | − | 0.933302i | \(-0.616914\pi\) |
0.628717 | + | 0.777634i | \(0.283580\pi\) | |||||||
\(620\) | 3.13331 | + | 3.19098i | 0.125837 | + | 0.128153i | ||||
\(621\) | 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 | ||||
\(626\) | 32.2289 | + | 4.39261i | 1.28813 | + | 0.175564i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.29180 | − | 29.8537i | 0.330879 | − | 1.19129i | ||||
\(629\) | 26.8328i | 1.06989i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0000 | 0.437903 | 0.218952 | − | 0.975736i | \(-0.429736\pi\) | ||||
0.218952 | + | 0.975736i | \(0.429736\pi\) | |||||||
\(632\) | 29.4747 | − | 21.9828i | 1.17244 | − | 0.874428i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.427051 | + | 3.13331i | −0.0169604 | + | 0.124440i | ||||
\(635\) | −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 | ||||||||
\(640\) | −20.5517 | + | 14.7523i | −0.812376 | + | 0.583134i | ||||
\(641\) | 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 | \(-0.848492\pi\) | ||
0.888846 | − | 0.458207i | \(-0.151508\pi\) | |||||||
\(644\) | −36.5889 | + | 2.29180i | −1.44180 | + | 0.0903094i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35.1246 | − | 14.3618i | 1.38196 | − | 0.565058i | ||||
\(647\) | 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 | −0.441997 | − | 0.897016i | \(-0.645730\pi\) |
−0.997838 | + | 0.0657275i | \(0.979063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5000 | − | 21.6506i | −0.488415 | − | 0.845960i | ||||
\(656\) | 0.758108 | − | 41.5623i | 0.0295992 | − | 1.62274i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.14590 | + | 12.2805i | −0.161624 | + | 0.478745i | ||||
\(659\) | − | 17.8885i | − | 0.696839i | −0.937339 | − | 0.348419i | \(-0.886719\pi\) | ||
0.937339 | − | 0.348419i | \(-0.113281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4164 | + | 7.74597i | −0.521838 | + | 0.301283i | −0.737686 | − | 0.675144i | \(-0.764082\pi\) |
0.215848 | + | 0.976427i | \(0.430748\pi\) | |||||||
\(662\) | −2.95870 | + | 21.7082i | −0.114993 | + | 0.843713i | ||||
\(663\) | 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 | ||||
\(668\) | −14.8303 | + | 14.5623i | −0.573803 | + | 0.563433i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.27051 | + | 22.6728i | 0.358151 | + | 0.875928i | ||||
\(671\) | 17.3205 | 0.668651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | −0.269830 | −0.134915 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134915 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(674\) | 10.1694 | + | 24.8713i | 0.391712 | + | 0.958008i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.5517 | + | 18.2164i | −0.713525 | + | 0.700629i | ||||
\(677\) | 21.3014 | + | 12.2984i | 0.818680 | + | 0.472665i | 0.849961 | − | 0.526846i | \(-0.176625\pi\) |
−0.0312813 | + | 0.999511i | \(0.509959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.500000 | − | 2.59808i | 0.0191882 | − | 0.0997050i | ||||
\(680\) | 8.66025 | − | 20.1246i | 0.332106 | − | 0.771744i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.427051 | − | 3.13331i | 0.0163526 | − | 0.119981i | ||||
\(683\) | −9.68246 | + | 5.59017i | −0.370489 | + | 0.213902i | −0.673672 | − | 0.739030i | \(-0.735284\pi\) |
0.303183 | + | 0.952932i | \(0.401951\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.74597i | − | 0.295958i | ||||||
\(686\) | −25.7579 | − | 4.74671i | −0.983441 | − | 0.181230i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.5410 | − | 19.3649i | −1.27596 | − | 0.736676i | −0.299857 | − | 0.953984i | \(-0.596939\pi\) |
−0.976103 | + | 0.217308i | \(0.930272\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 30.4188 | − | 12.4377i | 1.15137 | − | 0.470774i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.5967i | − | 0.929006i | −0.885571 | − | 0.464503i | \(-0.846233\pi\) | ||
0.885571 | − | 0.464503i | \(-0.153767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0000 | + | 51.9615i | 1.13147 | + | 1.95977i | ||||
\(704\) | 17.1459 | + | 5.10081i | 0.646210 | + | 0.192244i | ||||
\(705\) | 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 | 0.226444 | − | 0.974024i | \(-0.427290\pi\) |
−0.730308 | + | 0.683118i | \(0.760623\pi\) | |||||||
\(710\) | 4.43804 | − | 32.5623i | 0.166557 | − | 1.22204i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.4164 | + | 23.4309i | −1.17738 | + | 0.878112i | ||||
\(713\) | 6.92820 | 0.259463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.78727 | + | 17.2361i | −0.178909 | + | 0.644142i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.2705 | − | 3.30792i | −0.905767 | − | 0.123451i | ||||
\(719\) | 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 | ||||||||
\(724\) | 32.5623 | + | 33.1617i | 1.21017 | + | 1.23244i | ||||
\(725\) | 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 | ||||||||
\(730\) | −29.2705 | + | 11.9682i | −1.08335 | + | 0.442962i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.4164 | − | 7.74597i | −0.495546 | − | 0.286104i | 0.231326 | − | 0.972876i | \(-0.425694\pi\) |
−0.726872 | + | 0.686772i | \(0.759027\pi\) | |||||||
\(734\) | −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 | −0.726038 | − | 0.687655i | \(-0.758640\pi\) |
0.232507 | + | 0.972595i | \(0.425307\pi\) | |||||||
\(740\) | 33.3775 | + | 9.27051i | 1.22698 | + | 0.340791i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.4058 | + | 27.6347i | −1.15294 | + | 1.01450i | ||||
\(743\) | 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 | ||||
\(746\) | 1.47935 | − | 10.8541i | 0.0541628 | − | 0.397397i | ||||
\(747\) | 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 | \(-0.120437\pi\) | |||||||
\(752\) | 11.8717 | + | 7.14590i | 0.432915 | + | 0.260584i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 15.6525i | − | 0.569652i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.2379i | 0.844596i | 0.906457 | + | 0.422298i | \(0.138776\pi\) | ||||
−0.906457 | + | 0.422298i | \(0.861224\pi\) | |||||||
\(758\) | −30.4188 | + | 12.4377i | −1.10486 | + | 0.451757i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.72949 | − | 48.6536i | −0.207830 | − | 1.76485i | ||||
\(761\) | 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 | ||||||||
\(766\) | −9.70820 | − | 1.32317i | −0.350772 | − | 0.0478080i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | −18.3427 | + | 3.68034i | −0.661025 | + | 0.132630i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.7599 | + | 9.09896i | 1.17905 | + | 0.327479i | ||||
\(773\) | −3.87298 | + | 2.23607i | −0.139302 | + | 0.0804258i | −0.568031 | − | 0.823007i | \(-0.692295\pi\) |
0.428730 | + | 0.903433i | \(0.358961\pi\) | |||||||
\(774\) | 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 | ||||
\(782\) | −12.8456 | − | 31.4164i | −0.459358 | − | 1.12345i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.8647 | + | 25.8061i | −0.388027 | + | 0.921648i | ||||
\(785\) | 34.6410 | 1.23639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.5410 | + | 19.3649i | −1.19561 | + | 0.690285i | −0.959573 | − | 0.281460i | \(-0.909181\pi\) |
−0.236035 | + | 0.971745i | \(0.575848\pi\) | |||||||
\(788\) | 6.26662 | + | 6.38197i | 0.223239 | + | 0.227348i | ||||
\(789\) | 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 | ||||||||
\(794\) | 5.91739 | − | 43.4164i | 0.210000 | − | 1.54079i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.4164 | + | 4.28187i | 0.546420 | + | 0.151767i | ||||
\(797\) | 15.6525i | 0.554439i | 0.960807 | + | 0.277220i | \(0.0894129\pi\) | ||||
−0.960807 | + | 0.277220i | \(0.910587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 48.5410 | + | 6.61585i | 1.71404 | + | 0.233614i | ||||
\(803\) | 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 | ||||||||
\(808\) | −12.5623 | + | 1.47935i | −0.441940 | + | 0.0520433i | ||||
\(809\) | 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 | \(-0.866228\pi\) | ||
0.912983 | − | 0.407997i | \(-0.133772\pi\) | |||||||
\(812\) | 9.85707 | − | 6.54508i | 0.345915 | − | 0.229687i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.27051 | − | 22.6728i | −0.324931 | − | 0.794683i | ||||
\(815\) | 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 | 0.244443 | − | 0.969664i | \(-0.421395\pi\) |
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0000 | − | 17.3205i | −0.348578 | − | 0.603755i | 0.637419 | − | 0.770517i | \(-0.280002\pi\) |
−0.985997 | + | 0.166762i | \(0.946669\pi\) | |||||||
\(824\) | −18.1383 | + | 13.5279i | −0.631877 | + | 0.471265i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.28115 | − | 5.52694i | 0.218549 | − | 0.192307i | ||||
\(827\) | − | 24.5967i | − | 0.855313i | −0.903941 | − | 0.427656i | \(-0.859339\pi\) | ||
0.903941 | − | 0.427656i | \(-0.140661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.70820 | − | 3.87298i | 0.232986 | − | 0.134514i | −0.378963 | − | 0.925412i | \(-0.623719\pi\) |
0.611949 | + | 0.790898i | \(0.290386\pi\) | |||||||
\(830\) | 35.0315 | + | 4.77458i | 1.21596 | + | 0.165728i | ||||
\(831\) | 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 | ||||
\(836\) | −24.7172 | + | 24.2705i | −0.854864 | + | 0.839413i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 46.8328 | − | 19.1491i | 1.61781 | − | 0.661494i | ||||
\(839\) | −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 | ||||||||
\(842\) | −30.4188 | + | 12.4377i | −1.04830 | + | 0.428631i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 32.5623 | + | 33.1617i | 1.12084 | + | 1.14147i | ||||
\(845\) | −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 | \(0.130235\pi\) | ||||
−0.917461 | + | 0.397825i | \(0.869765\pi\) | |||||||
\(854\) | 27.4601 | + | 9.27051i | 0.939666 | + | 0.317230i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9058 | + | 25.3490i | 0.646186 | + | 0.866411i | ||||
\(857\) | 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 | 0.253341 | − | 0.967377i | \(-0.418471\pi\) |
−0.711103 | + | 0.703088i | \(0.751804\pi\) | |||||||
\(860\) | 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 | ||||
\(866\) | 11.7751 | + | 28.7984i | 0.400135 | + | 0.978609i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.35410 | − | 4.73901i | 0.0799034 | − | 0.160852i | ||||
\(869\) | − | 29.0689i | − | 0.986094i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 21.7586 | − | 2.56231i | 0.736838 | − | 0.0867706i | ||||
\(873\) | 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 | 0.879168 | − | 0.476512i | \(-0.158099\pi\) |
0.0269120 | + | 0.999638i | \(0.491433\pi\) | |||||||
\(878\) | −9.80881 | − | 1.33688i | −0.331031 | − | 0.0451175i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.364745 | + | 19.9967i | −0.0122956 | + | 0.674088i | ||||
\(881\) | 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 | \(-0.872126\pi\) | ||
0.920387 | − | 0.391009i | \(-0.127874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.69756 | − | 34.4664i | 0.157818 | − | 1.15792i | ||||
\(887\) | 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 | ||||||||
\(892\) | 9.98936 | − | 9.80881i | 0.334468 | − | 0.328423i | ||||
\(893\) | −23.2379 | + | 13.4164i | −0.777627 | + | 0.448963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 24.4532 | + | 17.2639i | 0.816922 | + | 0.576747i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.1246 | + | 27.2074i | 0.371233 | + | 0.907923i | ||||
\(899\) | −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 | −0.705921 | − | 0.708290i | \(-0.749467\pi\) |
0.260437 | + | 0.965491i | \(0.416133\pi\) | |||||||
\(908\) | 13.1650 | − | 47.3992i | 0.436896 | − | 1.57300i | ||||
\(909\) | 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 | ||||
\(914\) | 7.00629 | + | 0.954915i | 0.231748 | + | 0.0315858i | ||||
\(915\) | 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 | \(0.208790\pi\) | |||||||
\(920\) | −43.5171 | + | 5.12461i | −1.43472 | + | 0.168953i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.2705 | − | 11.9682i | 0.963973 | − | 0.394151i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.28187 | − | 10.4721i | −0.140711 | − | 0.344136i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.57295 | − | 11.7936i | −0.150114 | − | 0.387143i | ||||
\(929\) | −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 | ||||||||
\(934\) | −1.70820 | + | 12.5332i | −0.0558941 | + | 0.410100i | ||||
\(935\) | −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 | \(0.473974\pi\) | |||||||
\(938\) | 21.7586 | − | 19.1459i | 0.710442 | − | 0.625136i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.14590 | + | 14.9269i | −0.135224 | + | 0.486861i | ||||
\(941\) | −9.68246 | + | 5.59017i | −0.315639 | + | 0.182234i | −0.649447 | − | 0.760407i | \(-0.725000\pi\) |
0.333808 | + | 0.942641i | \(0.391666\pi\) | |||||||
\(942\) | 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 | −0.0965754 | − | 0.995326i | \(-0.530789\pi\) |
−0.910265 | + | 0.414026i | \(0.864122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.8541 | − | 1.88823i | −0.837936 | − | 0.0611979i | ||||
\(953\) | −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 | ||||
\(956\) | −29.6607 | + | 29.1246i | −0.959296 | + | 0.941957i | ||||
\(957\) | 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 | ||||||||
\(964\) | 44.3222 | + | 12.3104i | 1.42752 | + | 0.396490i | ||||
\(965\) | 38.0132i | 1.22369i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0000 | −0.610999 | −0.305499 | − | 0.952192i | \(-0.598823\pi\) | ||||
−0.305499 | + | 0.952192i | \(0.598823\pi\) | |||||||
\(968\) | −13.6037 | + | 10.1459i | −0.437240 | + | 0.326102i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.427051 | − | 3.13331i | 0.0137118 | − | 0.100605i | ||||
\(971\) | 9.68246 | + | 5.59017i | 0.310725 | + | 0.179397i | 0.647251 | − | 0.762277i | \(-0.275919\pi\) |
−0.336526 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.866025 | − | 1.11803i | 0.0277492 | − | 0.0358241i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.9787 | − | 26.5458i | 0.511466 | − | 0.849711i | ||||
\(977\) | 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 | ||||||||
\(980\) | −31.0506 | − | 3.98278i | −0.991874 | − | 0.127225i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38.0517 | − | 15.5586i | 1.21428 | − | 0.496496i | ||||
\(983\) | −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 | \(0.828277\pi\) | |||||||
\(992\) | −4.40822 | − | 3.54508i | −0.139961 | − | 0.112557i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38.1246 | + | 7.64944i | −1.20924 | + | 0.242626i | ||||
\(995\) | 17.8885i | 0.567105i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.70820 | − | 3.87298i | 0.212451 | − | 0.122659i | −0.389999 | − | 0.920815i | \(-0.627525\pi\) |
0.602450 | + | 0.798157i | \(0.294191\pi\) | |||||||
\(998\) | 5.91739 | − | 43.4164i | 0.187312 | − | 1.37432i | ||||
\(999\) | 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.37.2 | yes | 8 | |
3.2 | odd | 2 | inner | 504.2.cj.a.37.3 | yes | 8 | |
4.3 | odd | 2 | 2016.2.cr.a.1297.2 | 8 | |||
7.4 | even | 3 | inner | 504.2.cj.a.109.4 | yes | 8 | |
8.3 | odd | 2 | 2016.2.cr.a.1297.4 | 8 | |||
8.5 | even | 2 | inner | 504.2.cj.a.37.4 | yes | 8 | |
12.11 | even | 2 | 2016.2.cr.a.1297.3 | 8 | |||
21.11 | odd | 6 | inner | 504.2.cj.a.109.1 | yes | 8 | |
24.5 | odd | 2 | inner | 504.2.cj.a.37.1 | ✓ | 8 | |
24.11 | even | 2 | 2016.2.cr.a.1297.1 | 8 | |||
28.11 | odd | 6 | 2016.2.cr.a.1873.4 | 8 | |||
56.11 | odd | 6 | 2016.2.cr.a.1873.2 | 8 | |||
56.53 | even | 6 | inner | 504.2.cj.a.109.2 | yes | 8 | |
84.11 | even | 6 | 2016.2.cr.a.1873.1 | 8 | |||
168.11 | even | 6 | 2016.2.cr.a.1873.3 | 8 | |||
168.53 | odd | 6 | inner | 504.2.cj.a.109.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cj.a.37.1 | ✓ | 8 | 24.5 | odd | 2 | inner | |
504.2.cj.a.37.2 | yes | 8 | 1.1 | even | 1 | trivial | |
504.2.cj.a.37.3 | yes | 8 | 3.2 | odd | 2 | inner | |
504.2.cj.a.37.4 | yes | 8 | 8.5 | even | 2 | inner | |
504.2.cj.a.109.1 | yes | 8 | 21.11 | odd | 6 | inner | |
504.2.cj.a.109.2 | yes | 8 | 56.53 | even | 6 | inner | |
504.2.cj.a.109.3 | yes | 8 | 168.53 | odd | 6 | inner | |
504.2.cj.a.109.4 | yes | 8 | 7.4 | even | 3 | inner | |
2016.2.cr.a.1297.1 | 8 | 24.11 | even | 2 | |||
2016.2.cr.a.1297.2 | 8 | 4.3 | odd | 2 | |||
2016.2.cr.a.1297.3 | 8 | 12.11 | even | 2 | |||
2016.2.cr.a.1297.4 | 8 | 8.3 | odd | 2 | |||
2016.2.cr.a.1873.1 | 8 | 84.11 | even | 6 | |||
2016.2.cr.a.1873.2 | 8 | 56.11 | odd | 6 | |||
2016.2.cr.a.1873.3 | 8 | 168.11 | even | 6 | |||
2016.2.cr.a.1873.4 | 8 | 28.11 | odd | 6 |