Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(1297,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, 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("2016.1297");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.cr (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1297.4 | ||
Root | \(1.40126 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.1297 |
Dual form | 2016.2.cr.a.1873.4 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 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 | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 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 | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46410 | + | 6.00000i | −0.722315 | + | 1.25109i | 0.237754 | + | 0.971325i | \(0.423589\pi\) |
−0.960070 | + | 0.279761i | \(0.909745\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 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 | 0.817625 | − | 0.575751i | \(-0.195290\pi\) |
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 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 | \(0.886374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73205 | − | 3.00000i | 0.252646 | − | 0.437595i | −0.711608 | − | 0.702577i | \(-0.752033\pi\) |
0.964253 | + | 0.264982i | \(0.0853660\pi\) | |||||||
\(48\) | 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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | 0.00474543 | − | 0.999989i | \(-0.498489\pi\) |
−0.863643 | + | 0.504104i | \(0.831823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 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 | \(0.176447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923 | 1.23334 | 0.616670 | − | 0.787222i | \(-0.288481\pi\) | ||||
0.616670 | + | 0.787222i | \(0.288481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.93649 | − | 5.59017i | −0.220684 | − | 0.637059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50000 | + | 11.2583i | −0.731307 | + | 1.26666i | 0.225018 | + | 0.974355i | \(0.427756\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 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 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 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 | 0 | ||||||||
\(99\) | 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 | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | −0.785588 | − | 0.618750i | \(-0.787640\pi\) |
0.143059 | + | 0.989714i | \(0.454306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −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 | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.66025 | − | 3.00000i | 0.793884 | − | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | + | 5.19615i | −0.272727 | + | 0.472377i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 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 | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 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 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | − | 4.33013i | 0.207614 | − | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 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 | 0.687741 | − | 0.725956i | \(-0.258602\pi\) |
−0.972567 | + | 0.232623i | \(0.925269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 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 | \(0.121197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 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 | \(0.874178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.3923 | −0.804181 | −0.402090 | − | 0.915600i | \(-0.631716\pi\) | ||||
−0.402090 | + | 0.915600i | \(0.631716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 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 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.331814\pi\) | ||||
−0.504127 | + | 0.863630i | \(0.668186\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.66025 | − | 15.0000i | −0.636715 | − | 1.10282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.70820 | + | 3.87298i | 0.490552 | + | 0.283221i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.46410 | + | 6.00000i | −0.250654 | + | 0.434145i | −0.963706 | − | 0.266966i | \(-0.913979\pi\) |
0.713052 | + | 0.701111i | \(0.247312\pi\) | |||||||
\(192\) | 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 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 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 | 0.972257 | − | 0.233915i | \(-0.0751537\pi\) |
−0.688705 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.80948 | − | 1.11803i | −0.407745 | − | 0.0784706i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.1246 | + | 11.6190i | 1.40556 | + | 0.811503i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 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 | \(-0.295104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.50000 | + | 0.866025i | −0.169711 | + | 0.0587896i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.00000 | 0.468755 | 0.234377 | − | 0.972146i | \(-0.424695\pi\) | ||||
0.234377 | + | 0.972146i | \(0.424695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −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 | 0.261702 | − | 0.965149i | \(-0.415716\pi\) |
−0.704992 | + | 0.709215i | \(0.749050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −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 | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | − | 19.9186i | −0.740780 | − | 1.28307i | −0.952141 | − | 0.305661i | \(-0.901123\pi\) |
0.211360 | − | 0.977408i | \(-0.432211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.68246 | − | 12.2984i | −0.618590 | − | 0.785714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 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 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.46410 | + | 6.00000i | 0.213606 | + | 0.369976i | 0.952840 | − | 0.303472i | \(-0.0981459\pi\) |
−0.739235 | + | 0.673448i | \(0.764813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.0000 | 1.53574 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −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 | −0.880812 | − | 0.473466i | \(-0.843003\pi\) |
0.850439 | + | 0.526073i | \(0.176336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 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 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(0.485645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 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 | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.66025 | − | 15.0000i | −0.495885 | − | 0.858898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1244 | − | 21.0000i | −0.687509 | − | 1.19080i | −0.972641 | − | 0.232313i | \(-0.925371\pi\) |
0.285132 | − | 0.958488i | \(-0.407963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.5000 | + | 19.9186i | −0.650018 | + | 1.12586i | 0.333099 | + | 0.942892i | \(0.391906\pi\) |
−0.983118 | + | 0.182973i | \(0.941428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 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 | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.8328i | 1.49302i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −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 | \(0.806659\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.3205 | 0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −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 | 0 | ||||||||
\(347\) | −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 | \(-0.786341\pi\) | ||
0.783058 | − | 0.621948i | \(-0.213659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −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 | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.66025 | + | 15.0000i | −0.457071 | + | 0.791670i | −0.998805 | − | 0.0488803i | \(-0.984435\pi\) |
0.541734 | + | 0.840550i | \(0.317768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.5000 | + | 35.5070i | 1.07895 | + | 1.86879i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.3607i | 1.17041i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50000 | + | 4.33013i | 0.130499 | + | 0.226031i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.793370 | + | 0.608740i | \(0.791675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −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 | \(0.730935\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.2379i | − | 1.19365i | −0.802371 | − | 0.596825i | \(-0.796429\pi\) | ||
0.802371 | − | 0.596825i | \(-0.203571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.46410 | + | 6.00000i | −0.177007 | + | 0.306586i | −0.940854 | − | 0.338812i | \(-0.889975\pi\) |
0.763847 | + | 0.645398i | \(0.223308\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | − | 12.9904i | 0.127412 | − | 0.662051i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −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 | \(0.950188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 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 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −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 | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −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 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.191615\pi\) | ||||
−0.824218 | + | 0.566273i | \(0.808385\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.4164 | + | 15.4919i | −0.649265 | + | 0.749707i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.1244 | − | 21.0000i | −0.584010 | − | 1.01153i | −0.994998 | − | 0.0998939i | \(-0.968150\pi\) |
0.410988 | − | 0.911641i | \(-0.365184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −46.4758 | + | 26.8328i | −2.22324 | + | 1.28359i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.50000 | + | 6.06218i | −0.167046 | + | 0.289332i | −0.937380 | − | 0.348309i | \(-0.886756\pi\) |
0.770334 | + | 0.637641i | \(0.220089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 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 | \(0.203977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 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 | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.92820 | − | 12.0000i | −0.316558 | − | 0.548294i | 0.663210 | − | 0.748434i | \(-0.269194\pi\) |
−0.979767 | + | 0.200140i | \(0.935860\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.93649 | − | 1.11803i | −0.0879316 | − | 0.0507673i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.500000 | − | 0.866025i | −0.0226572 | − | 0.0392434i | 0.854475 | − | 0.519493i | \(-0.173879\pi\) |
−0.877132 | + | 0.480250i | \(0.840546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 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 | \(0.422728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1769 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.4919 | − | 8.94427i | 0.682656 | − | 0.394132i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.74597i | − | 0.340667i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 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 | \(0.429767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.73205 | − | 3.00000i | 0.0754493 | − | 0.130682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5000 | − | 21.6506i | −0.543478 | − | 0.941332i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5000 | + | 21.6506i | 0.540422 | + | 0.936039i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −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 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.3205 | −0.741929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2379i | 0.993581i | 0.867871 | + | 0.496790i | \(0.165488\pi\) | ||||
−0.867871 | + | 0.496790i | \(0.834512\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 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 | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −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 | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 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 | \(-0.426465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.0474 | − | 5.59017i | −1.20509 | − | 0.231919i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5000 | − | 21.6506i | 0.517697 | − | 0.896678i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 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 | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 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 | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.73205 | − | 3.00000i | −0.0707697 | − | 0.122577i | 0.828469 | − | 0.560035i | \(-0.189212\pi\) |
−0.899239 | + | 0.437458i | \(0.855879\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.6190 | + | 6.70820i | −0.472377 | + | 0.272727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5000 | − | 25.1147i | 0.588537 | − | 1.01938i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 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 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −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 | \(0.283580\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.7128 | + | 24.0000i | 1.11029 | + | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 26.8328i | − | 1.06989i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0000 | −0.437903 | −0.218952 | − | 0.975736i | \(-0.570264\pi\) | ||||
−0.218952 | + | 0.975736i | \(0.570264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.68246 | − | 5.59017i | −0.384237 | − | 0.221839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 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 | \(-0.151508\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.5167 | − | 39.0000i | −0.885221 | − | 1.53325i | −0.845460 | − | 0.534039i | \(-0.820674\pi\) |
−0.0397614 | − | 0.999209i | \(-0.512660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.50000 | − | 4.33013i | 0.0981336 | − | 0.169972i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 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 | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 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 | −0.215848 | − | 0.976427i | \(-0.569252\pi\) |
0.737686 | + | 0.675144i | \(0.235918\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 43.3013 | − | 15.0000i | 1.67915 | − | 0.581675i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4164 | + | 7.74597i | 0.519485 | + | 0.299925i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3205 | −0.668651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | −0.269830 | −0.134915 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134915 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −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 | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 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 | \(0.930272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 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 | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −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 | \(0.572710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.92820 | 0.259463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.2487 | + | 42.0000i | −0.904324 | + | 1.56634i | −0.0825027 | + | 0.996591i | \(0.526291\pi\) |
−0.821822 | + | 0.569745i | \(0.807042\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | − | 13.8564i | −0.595871 | − | 0.516040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.0000 | −1.07555 | −0.537775 | − | 0.843088i | \(-0.680735\pi\) | ||||
−0.537775 | + | 0.843088i | \(0.680735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 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 | \(0.574306\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 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 | \(0.425307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.3923 | −0.381257 | −0.190628 | − | 0.981662i | \(-0.561053\pi\) | ||||
−0.190628 | + | 0.981662i | \(0.561053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0000 | + | 43.3013i | 0.915929 | + | 1.58644i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.3649 | − | 22.3607i | 0.707579 | − | 0.817041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.5000 | + | 37.2391i | −0.784546 | + | 1.35887i | 0.144724 | + | 0.989472i | \(0.453771\pi\) |
−0.929270 | + | 0.369402i | \(0.879563\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 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 | \(-0.138776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 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 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 69.7137 | + | 40.2492i | 2.49775 | + | 1.44208i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1246 | − | 11.6190i | 0.720115 | − | 0.415759i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 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 | \(0.575848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.19615 | + | 27.0000i | −0.184754 | + | 0.960009i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 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 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 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 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 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 | \(-0.133772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.3205 | − | 30.0000i | −0.606711 | − | 1.05085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 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 | 0.985997 | − | 0.166762i | \(-0.0533313\pi\) |
−0.637419 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 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 | −0.611949 | − | 0.790898i | \(-0.709614\pi\) |
0.378963 | + | 0.925412i | \(0.376281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 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 | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.1769 | 1.07635 | 0.538173 | − | 0.842834i | \(-0.319115\pi\) | ||||
0.538173 | + | 0.842834i | \(0.319115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.0000 | 0.827586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.1744 | + | 14.5344i | 0.866025 | + | 0.500000i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.0000 | + | 10.3923i | 0.412325 | + | 0.357084i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 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 | \(-0.130235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 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 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.8564 | + | 24.0000i | −0.471678 | + | 0.816970i | −0.999475 | − | 0.0324008i | \(-0.989685\pi\) |
0.527797 | + | 0.849370i | \(0.323018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.00000 | − | 8.66025i | −0.170005 | − | 0.294457i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.0689i | 0.986094i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −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 | \(0.841901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 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 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.8564 | + | 24.0000i | −0.465253 | + | 0.805841i | −0.999213 | − | 0.0396684i | \(-0.987370\pi\) |
0.533960 | + | 0.845510i | \(0.320703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | + | 12.9904i | −0.0838473 | + | 0.435683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.2379 | − | 13.4164i | 0.777627 | − | 0.448963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.93649 | + | 1.11803i | −0.0645856 | + | 0.0372885i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.5410 | + | 19.3649i | 1.11741 | + | 0.645139i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −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 | \(0.416133\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923 | 0.344312 | 0.172156 | − | 0.985070i | \(-0.444927\pi\) | ||||
0.172156 | + | 0.985070i | \(0.444927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.5000 | − | 21.6506i | −0.413690 | − | 0.716531i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.3649 | − | 22.3607i | 0.639486 | − | 0.738415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 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 | \(0.473974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −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 | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 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 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 38.0132i | − | 1.22369i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0000 | 0.610999 | 0.305499 | − | 0.952192i | \(-0.401177\pi\) | ||||
0.305499 | + | 0.952192i | \(0.401177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 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 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.0526 | + | 33.0000i | 0.607682 | + | 1.05254i | 0.991621 | + | 0.129178i | \(0.0412339\pi\) |
−0.383939 | + | 0.923358i | \(0.625433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.00000 | + | 8.66025i | −0.159313 | + | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.500000 | − | 0.866025i | −0.0158830 | − | 0.0275102i | 0.857975 | − | 0.513692i | \(-0.171723\pi\) |
−0.873858 | + | 0.486182i | \(0.838389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 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 | \(0.372475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2016.2.cr.a.1297.4 | 8 | ||
3.2 | odd | 2 | inner | 2016.2.cr.a.1297.1 | 8 | ||
4.3 | odd | 2 | 504.2.cj.a.37.4 | yes | 8 | ||
7.4 | even | 3 | inner | 2016.2.cr.a.1873.2 | 8 | ||
8.3 | odd | 2 | 504.2.cj.a.37.2 | yes | 8 | ||
8.5 | even | 2 | inner | 2016.2.cr.a.1297.2 | 8 | ||
12.11 | even | 2 | 504.2.cj.a.37.1 | ✓ | 8 | ||
21.11 | odd | 6 | inner | 2016.2.cr.a.1873.3 | 8 | ||
24.5 | odd | 2 | inner | 2016.2.cr.a.1297.3 | 8 | ||
24.11 | even | 2 | 504.2.cj.a.37.3 | yes | 8 | ||
28.11 | odd | 6 | 504.2.cj.a.109.2 | yes | 8 | ||
56.11 | odd | 6 | 504.2.cj.a.109.4 | yes | 8 | ||
56.53 | even | 6 | inner | 2016.2.cr.a.1873.4 | 8 | ||
84.11 | even | 6 | 504.2.cj.a.109.3 | yes | 8 | ||
168.11 | even | 6 | 504.2.cj.a.109.1 | yes | 8 | ||
168.53 | odd | 6 | inner | 2016.2.cr.a.1873.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cj.a.37.1 | ✓ | 8 | 12.11 | even | 2 | ||
504.2.cj.a.37.2 | yes | 8 | 8.3 | odd | 2 | ||
504.2.cj.a.37.3 | yes | 8 | 24.11 | even | 2 | ||
504.2.cj.a.37.4 | yes | 8 | 4.3 | odd | 2 | ||
504.2.cj.a.109.1 | yes | 8 | 168.11 | even | 6 | ||
504.2.cj.a.109.2 | yes | 8 | 28.11 | odd | 6 | ||
504.2.cj.a.109.3 | yes | 8 | 84.11 | even | 6 | ||
504.2.cj.a.109.4 | yes | 8 | 56.11 | odd | 6 | ||
2016.2.cr.a.1297.1 | 8 | 3.2 | odd | 2 | inner | ||
2016.2.cr.a.1297.2 | 8 | 8.5 | even | 2 | inner | ||
2016.2.cr.a.1297.3 | 8 | 24.5 | odd | 2 | inner | ||
2016.2.cr.a.1297.4 | 8 | 1.1 | even | 1 | trivial | ||
2016.2.cr.a.1873.1 | 8 | 168.53 | odd | 6 | inner | ||
2016.2.cr.a.1873.2 | 8 | 7.4 | even | 3 | inner | ||
2016.2.cr.a.1873.3 | 8 | 21.11 | odd | 6 | inner | ||
2016.2.cr.a.1873.4 | 8 | 56.53 | even | 6 | inner |