Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(151,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.226 |
Dual form | 525.2.i.d.151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | −0.633316 | − | 0.773893i | \(-0.718307\pi\) |
0.986869 | + | 0.161521i | \(0.0516399\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.242536 | + | 0.420084i | 0.961436 | − | 0.275029i | \(-0.0886875\pi\) |
−0.718900 | + | 0.695113i | \(0.755354\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.73205i | 0.208514 | − | 0.361158i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.951247 | + | 0.308431i | \(0.0998038\pi\) | |||||||
\(24\) | 1.50000 | + | 2.59808i | 0.306186 | + | 0.530330i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.50000 | − | 2.59808i | 0.294174 | − | 0.509525i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 2.50000 | + | 4.33013i | 0.441942 | + | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | 1.50000 | + | 2.59808i | 0.240192 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0.500000 | − | 2.59808i | 0.0771517 | − | 0.400892i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | − | 1.73205i | −0.147442 | − | 0.255377i | ||||
\(47\) | −5.00000 | + | 8.66025i | −0.729325 | + | 1.26323i | 0.227844 | + | 0.973698i | \(0.426832\pi\) |
−0.957169 | + | 0.289530i | \(0.906501\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 1.50000 | + | 2.59808i | 0.208013 | + | 0.360288i | ||||
\(53\) | −7.00000 | − | 12.1244i | −0.961524 | − | 1.66541i | −0.718677 | − | 0.695344i | \(-0.755252\pi\) |
−0.242846 | − | 0.970065i | \(-0.578081\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 7.79423i | 0.200446 | − | 1.04155i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −4.00000 | + | 6.92820i | −0.525226 | + | 0.909718i | ||||
\(59\) | −5.00000 | − | 8.66025i | −0.650945 | − | 1.12747i | −0.982894 | − | 0.184172i | \(-0.941040\pi\) |
0.331949 | − | 0.943297i | \(-0.392294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | −1.50000 | + | 2.59808i | −0.176777 | + | 0.306186i | ||||
\(73\) | −5.50000 | − | 9.52628i | −0.643726 | − | 1.11497i | −0.984594 | − | 0.174855i | \(-0.944054\pi\) |
0.340868 | − | 0.940111i | \(-0.389279\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | 3.50000 | − | 6.06218i | 0.393781 | − | 0.682048i | −0.599164 | − | 0.800626i | \(-0.704500\pi\) |
0.992945 | + | 0.118578i | \(0.0378336\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0000 | −1.53670 | −0.768350 | − | 0.640030i | \(-0.778922\pi\) | ||||
−0.768350 | + | 0.640030i | \(0.778922\pi\) | |||||||
\(84\) | 2.00000 | + | 1.73205i | 0.218218 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | −4.00000 | − | 6.92820i | −0.428845 | − | 0.742781i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50000 | − | 7.79423i | 0.157243 | − | 0.817057i | ||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | 5.00000 | + | 8.66025i | 0.515711 | + | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.50000 | + | 4.33013i | −0.255155 | + | 0.441942i | ||||
\(97\) | −9.00000 | −0.913812 | −0.456906 | − | 0.889515i | \(-0.651042\pi\) | ||||
−0.456906 | + | 0.889515i | \(0.651042\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | + | 13.8564i | 0.796030 | + | 1.37876i | 0.922183 | + | 0.386753i | \(0.126403\pi\) |
−0.126153 | + | 0.992011i | \(0.540263\pi\) | |||||||
\(102\) | 1.00000 | + | 1.73205i | 0.0990148 | + | 0.171499i | ||||
\(103\) | −6.50000 | + | 11.2583i | −0.640464 | + | 1.10932i | 0.344865 | + | 0.938652i | \(0.387925\pi\) |
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 9.00000 | 0.882523 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.0000 | −1.35980 | ||||||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 7.50000 | + | 12.9904i | 0.718370 | + | 1.24425i | 0.961645 | + | 0.274296i | \(0.0884447\pi\) |
−0.243276 | + | 0.969957i | \(0.578222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.00000 | 0.664411 | ||||||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.00000 | − | 6.92820i | −0.371391 | − | 0.643268i | ||||
\(117\) | −1.50000 | + | 2.59808i | −0.138675 | + | 0.240192i | ||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | 5.00000 | − | 1.73205i | 0.458349 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | ||||
\(122\) | 3.50000 | + | 6.06218i | 0.316875 | + | 0.548844i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | −1.50000 | + | 2.59808i | −0.132583 | + | 0.229640i | ||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00000 | + | 12.1244i | −0.611593 | + | 1.05931i | 0.379379 | + | 0.925241i | \(0.376138\pi\) |
−0.990972 | + | 0.134069i | \(0.957196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 1.73205i | 0.173422 | + | 0.150188i | ||||
\(134\) | −5.00000 | −0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | + | 5.19615i | 0.257248 | + | 0.445566i | ||||
\(137\) | −5.00000 | − | 8.66025i | −0.427179 | − | 0.739895i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
−0.996621 | + | 0.0821359i | \(0.973826\pi\) | |||||||
\(138\) | 1.00000 | − | 1.73205i | 0.0851257 | − | 0.147442i | ||||
\(139\) | 3.00000 | 0.254457 | 0.127228 | − | 0.991873i | \(-0.459392\pi\) | ||||
0.127228 | + | 0.991873i | \(0.459392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | −0.842152 | ||||||||
\(142\) | −6.00000 | + | 10.3923i | −0.503509 | + | 0.872103i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | −1.00000 | − | 6.92820i | −0.0824786 | − | 0.571429i | ||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | 2.00000 | − | 3.46410i | 0.163846 | − | 0.283790i | −0.772399 | − | 0.635138i | \(-0.780943\pi\) |
0.936245 | + | 0.351348i | \(0.114277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | + | 0.866025i | 0.0406894 | + | 0.0704761i | 0.885653 | − | 0.464348i | \(-0.153711\pi\) |
−0.844963 | + | 0.534824i | \(0.820378\pi\) | |||||||
\(152\) | −1.50000 | + | 2.59808i | −0.121666 | + | 0.210732i | ||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.50000 | + | 2.59808i | −0.120096 | + | 0.208013i | ||||
\(157\) | 3.50000 | + | 6.06218i | 0.279330 | + | 0.483814i | 0.971219 | − | 0.238190i | \(-0.0765542\pi\) |
−0.691888 | + | 0.722005i | \(0.743221\pi\) | |||||||
\(158\) | −3.50000 | − | 6.06218i | −0.278445 | − | 0.482281i | ||||
\(159\) | 7.00000 | − | 12.1244i | 0.555136 | − | 0.961524i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | − | 3.46410i | −0.315244 | − | 0.273009i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.50000 | + | 7.79423i | −0.352467 | + | 0.610491i | −0.986681 | − | 0.162667i | \(-0.947991\pi\) |
0.634214 | + | 0.773158i | \(0.281324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.00000 | + | 12.1244i | −0.543305 | + | 0.941033i | ||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 7.50000 | − | 2.59808i | 0.578638 | − | 0.200446i | ||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 4.00000 | + | 6.92820i | 0.304997 | + | 0.528271i | ||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00000 | − | 8.66025i | 0.375823 | − | 0.650945i | ||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | −6.00000 | − | 5.19615i | −0.444750 | − | 0.385164i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | + | 6.92820i | 0.293294 | + | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −10.0000 | −0.729325 | ||||||||
\(189\) | −0.500000 | + | 2.59808i | −0.0363696 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | − | 6.92820i | 0.289430 | − | 0.501307i | −0.684244 | − | 0.729253i | \(-0.739868\pi\) |
0.973674 | + | 0.227946i | \(0.0732010\pi\) | |||||||
\(192\) | 3.50000 | + | 6.06218i | 0.252591 | + | 0.437500i | ||||
\(193\) | 3.00000 | + | 5.19615i | 0.215945 | + | 0.374027i | 0.953564 | − | 0.301189i | \(-0.0973836\pi\) |
−0.737620 | + | 0.675216i | \(0.764050\pi\) | |||||||
\(194\) | −4.50000 | + | 7.79423i | −0.323081 | + | 0.559593i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | − | 6.92820i | −0.0714286 | − | 0.494872i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.50000 | − | 9.52628i | −0.389885 | − | 0.675300i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.50000 | − | 4.33013i | 0.176336 | − | 0.305424i | ||||
\(202\) | 16.0000 | 1.12576 | ||||||||
\(203\) | −4.00000 | + | 20.7846i | −0.280745 | + | 1.45879i | ||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.50000 | + | 11.2583i | 0.452876 | + | 0.784405i | ||||
\(207\) | 1.00000 | + | 1.73205i | 0.0695048 | + | 0.120386i | ||||
\(208\) | 1.50000 | − | 2.59808i | 0.104006 | − | 0.180144i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 7.00000 | − | 12.1244i | 0.480762 | − | 0.832704i | ||||
\(213\) | −6.00000 | − | 10.3923i | −0.411113 | − | 0.712069i | ||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | 20.0000 | − | 6.92820i | 1.35769 | − | 0.470317i | ||||
\(218\) | 15.0000 | 1.01593 | ||||||||
\(219\) | 5.50000 | − | 9.52628i | 0.371656 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 3.50000 | − | 6.06218i | 0.234905 | − | 0.406867i | ||||
\(223\) | 15.0000 | 1.00447 | 0.502237 | − | 0.864730i | \(-0.332510\pi\) | ||||
0.502237 | + | 0.864730i | \(0.332510\pi\) | |||||||
\(224\) | 12.5000 | − | 4.33013i | 0.835191 | − | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | −0.500000 | − | 0.866025i | −0.0331133 | − | 0.0573539i | ||||
\(229\) | −6.50000 | + | 11.2583i | −0.429532 | + | 0.743971i | −0.996832 | − | 0.0795401i | \(-0.974655\pi\) |
0.567300 | + | 0.823511i | \(0.307988\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.0000 | −1.57568 | ||||||||
\(233\) | 12.0000 | − | 20.7846i | 0.786146 | − | 1.36165i | −0.142166 | − | 0.989843i | \(-0.545407\pi\) |
0.928312 | − | 0.371802i | \(-0.121260\pi\) | |||||||
\(234\) | 1.50000 | + | 2.59808i | 0.0980581 | + | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.00000 | − | 8.66025i | 0.325472 | − | 0.563735i | ||||
\(237\) | 7.00000 | 0.454699 | ||||||||
\(238\) | 1.00000 | − | 5.19615i | 0.0648204 | − | 0.336817i | ||||
\(239\) | −28.0000 | −1.81117 | −0.905585 | − | 0.424165i | \(-0.860568\pi\) | ||||
−0.905585 | + | 0.424165i | \(0.860568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | − | 18.1865i | −0.676364 | − | 1.17150i | −0.976068 | − | 0.217465i | \(-0.930221\pi\) |
0.299704 | − | 0.954032i | \(-0.403112\pi\) | |||||||
\(242\) | −5.50000 | − | 9.52628i | −0.353553 | − | 0.612372i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.50000 | + | 2.59808i | −0.0954427 | + | 0.165312i | ||||
\(248\) | 12.0000 | + | 20.7846i | 0.762001 | + | 1.31982i | ||||
\(249\) | −7.00000 | − | 12.1244i | −0.443607 | − | 0.768350i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −0.500000 | + | 2.59808i | −0.0314970 | + | 0.163663i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.50000 | + | 9.52628i | −0.345101 | + | 0.597732i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | −14.0000 | − | 12.1244i | −0.869918 | − | 0.753371i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 7.00000 | + | 12.1244i | 0.432461 | + | 0.749045i | ||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.50000 | − | 0.866025i | 0.153285 | − | 0.0530994i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 2.50000 | − | 4.33013i | 0.152712 | − | 0.264505i | ||||
\(269\) | 8.00000 | + | 13.8564i | 0.487769 | + | 0.844840i | 0.999901 | − | 0.0140665i | \(-0.00447764\pi\) |
−0.512132 | + | 0.858906i | \(0.671144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | − | 10.3923i | 0.364474 | − | 0.631288i | −0.624218 | − | 0.781251i | \(-0.714582\pi\) |
0.988692 | + | 0.149963i | \(0.0479155\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 7.50000 | − | 2.59808i | 0.453921 | − | 0.157243i | ||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | + | 1.73205i | 0.0601929 | + | 0.104257i | ||||
\(277\) | 2.50000 | + | 4.33013i | 0.150210 | + | 0.260172i | 0.931305 | − | 0.364241i | \(-0.118672\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 1.50000 | − | 2.59808i | 0.0899640 | − | 0.155822i | ||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | −5.00000 | + | 8.66025i | −0.297746 | + | 0.515711i | ||||
\(283\) | −9.50000 | − | 16.4545i | −0.564716 | − | 0.978117i | −0.997076 | − | 0.0764162i | \(-0.975652\pi\) |
0.432360 | − | 0.901701i | \(-0.357681\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.00000 | −0.294628 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | − | 7.79423i | −0.263795 | − | 0.456906i | ||||
\(292\) | 5.50000 | − | 9.52628i | 0.321863 | − | 0.557483i | ||||
\(293\) | 16.0000 | 0.934730 | 0.467365 | − | 0.884064i | \(-0.345203\pi\) | ||||
0.467365 | + | 0.884064i | \(0.345203\pi\) | |||||||
\(294\) | −6.50000 | − | 2.59808i | −0.379088 | − | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.5000 | − | 18.1865i | 0.610300 | − | 1.05707i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.00000 | − | 3.46410i | −0.115857 | − | 0.200670i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 20.7846i | 0.230556 | − | 1.19800i | ||||
\(302\) | 1.00000 | 0.0575435 | ||||||||
\(303\) | −8.00000 | + | 13.8564i | −0.459588 | + | 0.796030i | ||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0000 | −0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | + | 25.9808i | 0.850572 | + | 1.47323i | 0.880693 | + | 0.473688i | \(0.157077\pi\) |
−0.0301210 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(312\) | 4.50000 | + | 7.79423i | 0.254762 | + | 0.441261i | ||||
\(313\) | 7.00000 | − | 12.1244i | 0.395663 | − | 0.685309i | −0.597522 | − | 0.801852i | \(-0.703848\pi\) |
0.993186 | + | 0.116543i | \(0.0371814\pi\) | |||||||
\(314\) | 7.00000 | 0.395033 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | 0.393781 | ||||||||
\(317\) | 7.00000 | − | 12.1244i | 0.393159 | − | 0.680972i | −0.599705 | − | 0.800221i | \(-0.704715\pi\) |
0.992864 | + | 0.119249i | \(0.0380488\pi\) | |||||||
\(318\) | −7.00000 | − | 12.1244i | −0.392541 | − | 0.679900i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | −5.00000 | + | 1.73205i | −0.278639 | + | 0.0965234i | ||||
\(323\) | −2.00000 | −0.111283 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.50000 | + | 7.79423i | 0.249232 | + | 0.431682i | ||||
\(327\) | −7.50000 | + | 12.9904i | −0.414751 | + | 0.718370i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.0000 | + | 17.3205i | 1.10264 | + | 0.954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5000 | + | 18.1865i | −0.577132 | + | 0.999622i | 0.418674 | + | 0.908137i | \(0.362495\pi\) |
−0.995806 | + | 0.0914858i | \(0.970838\pi\) | |||||||
\(332\) | −7.00000 | − | 12.1244i | −0.384175 | − | 0.665410i | ||||
\(333\) | 3.50000 | + | 6.06218i | 0.191799 | + | 0.332205i | ||||
\(334\) | −1.00000 | + | 1.73205i | −0.0547176 | + | 0.0947736i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.500000 | − | 2.59808i | 0.0272772 | − | 0.141737i | ||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 24.0000 | 1.29399 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | − | 15.5885i | −0.483843 | − | 0.838041i | ||||
\(347\) | 5.00000 | + | 8.66025i | 0.268414 | + | 0.464907i | 0.968452 | − | 0.249198i | \(-0.0801671\pi\) |
−0.700038 | + | 0.714105i | \(0.746834\pi\) | |||||||
\(348\) | 4.00000 | − | 6.92820i | 0.214423 | − | 0.371391i | ||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.00000 | −0.160128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | + | 20.7846i | 0.638696 | + | 1.10625i | 0.985719 | + | 0.168397i | \(0.0538590\pi\) |
−0.347024 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(354\) | −5.00000 | − | 8.66025i | −0.265747 | − | 0.460287i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 4.00000 | + | 3.46410i | 0.211702 | + | 0.183340i | ||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 11.0000 | − | 19.0526i | 0.578147 | − | 1.00138i | ||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 7.50000 | − | 2.59808i | 0.393107 | − | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.50000 | + | 6.06218i | −0.182948 | + | 0.316875i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | −1.00000 | − | 1.73205i | −0.0521286 | − | 0.0902894i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.0000 | + | 12.1244i | −1.81711 | + | 0.629465i | ||||
\(372\) | −8.00000 | −0.414781 | ||||||||
\(373\) | 5.50000 | − | 9.52628i | 0.284779 | − | 0.493252i | −0.687776 | − | 0.725923i | \(-0.741413\pi\) |
0.972556 | + | 0.232671i | \(0.0747464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.0000 | + | 25.9808i | −0.773566 | + | 1.33986i | ||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 2.00000 | + | 1.73205i | 0.102869 | + | 0.0890871i | ||||
\(379\) | 35.0000 | 1.79783 | 0.898915 | − | 0.438124i | \(-0.144357\pi\) | ||||
0.898915 | + | 0.438124i | \(0.144357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50000 | − | 9.52628i | −0.281774 | − | 0.488046i | ||||
\(382\) | −4.00000 | − | 6.92820i | −0.204658 | − | 0.354478i | ||||
\(383\) | 5.00000 | − | 8.66025i | 0.255488 | − | 0.442518i | −0.709540 | − | 0.704665i | \(-0.751097\pi\) |
0.965028 | + | 0.262147i | \(0.0844305\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | −4.50000 | − | 7.79423i | −0.228453 | − | 0.395692i | ||||
\(389\) | 18.0000 | + | 31.1769i | 0.912636 | + | 1.58073i | 0.810326 | + | 0.585980i | \(0.199290\pi\) |
0.102311 | + | 0.994753i | \(0.467376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | −19.5000 | − | 7.79423i | −0.984899 | − | 0.393668i | ||||
\(393\) | −14.0000 | −0.706207 | ||||||||
\(394\) | −6.00000 | + | 10.3923i | −0.302276 | + | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00000 | − | 12.1244i | 0.351320 | − | 0.608504i | −0.635161 | − | 0.772380i | \(-0.719066\pi\) |
0.986481 | + | 0.163876i | \(0.0523996\pi\) | |||||||
\(398\) | −11.0000 | −0.551380 | ||||||||
\(399\) | −0.500000 | + | 2.59808i | −0.0250313 | + | 0.130066i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | −2.50000 | − | 4.33013i | −0.124689 | − | 0.215967i | ||||
\(403\) | 12.0000 | + | 20.7846i | 0.597763 | + | 1.03536i | ||||
\(404\) | −8.00000 | + | 13.8564i | −0.398015 | + | 0.689382i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.0000 | + | 13.8564i | 0.794067 | + | 0.687682i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.00000 | + | 5.19615i | −0.148522 | + | 0.257248i | ||||
\(409\) | −2.50000 | − | 4.33013i | −0.123617 | − | 0.214111i | 0.797574 | − | 0.603220i | \(-0.206116\pi\) |
−0.921192 | + | 0.389109i | \(0.872783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.00000 | − | 8.66025i | 0.246632 | − | 0.427179i | ||||
\(412\) | −13.0000 | −0.640464 | ||||||||
\(413\) | −25.0000 | + | 8.66025i | −1.23017 | + | 0.426143i | ||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.50000 | + | 12.9904i | 0.367718 | + | 0.636906i | ||||
\(417\) | 1.50000 | + | 2.59808i | 0.0734553 | + | 0.127228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0000 | −1.70580 | −0.852898 | − | 0.522078i | \(-0.825157\pi\) | ||||
−0.852898 | + | 0.522078i | \(0.825157\pi\) | |||||||
\(422\) | −2.50000 | + | 4.33013i | −0.121698 | + | 0.210787i | ||||
\(423\) | −5.00000 | − | 8.66025i | −0.243108 | − | 0.421076i | ||||
\(424\) | −21.0000 | − | 36.3731i | −1.01985 | − | 1.76643i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 14.0000 | + | 12.1244i | 0.677507 | + | 0.586739i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 0.0481683 | + | 0.0834300i | 0.889104 | − | 0.457705i | \(-0.151328\pi\) |
−0.840936 | + | 0.541135i | \(0.817995\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 4.00000 | − | 20.7846i | 0.192006 | − | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.50000 | + | 12.9904i | −0.359185 | + | 0.622126i | ||||
\(437\) | 1.00000 | + | 1.73205i | 0.0478365 | + | 0.0828552i | ||||
\(438\) | −5.50000 | − | 9.52628i | −0.262800 | − | 0.455183i | ||||
\(439\) | 5.50000 | − | 9.52628i | 0.262501 | − | 0.454665i | −0.704405 | − | 0.709798i | \(-0.748786\pi\) |
0.966906 | + | 0.255134i | \(0.0821195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | 3.00000 | − | 5.19615i | 0.142534 | − | 0.246877i | −0.785916 | − | 0.618333i | \(-0.787808\pi\) |
0.928450 | + | 0.371457i | \(0.121142\pi\) | |||||||
\(444\) | 3.50000 | + | 6.06218i | 0.166103 | + | 0.287698i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.50000 | − | 12.9904i | 0.355135 | − | 0.615112i | ||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 3.50000 | − | 18.1865i | 0.165359 | − | 0.859233i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | −0.500000 | + | 0.866025i | −0.0234920 | + | 0.0406894i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −1.50000 | + | 2.59808i | −0.0701670 | + | 0.121533i | −0.898974 | − | 0.438001i | \(-0.855687\pi\) |
0.828807 | + | 0.559534i | \(0.189020\pi\) | |||||||
\(458\) | 6.50000 | + | 11.2583i | 0.303725 | + | 0.526067i | ||||
\(459\) | −1.00000 | − | 1.73205i | −0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.00000 | −0.0931493 | −0.0465746 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465746 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.0000 | −1.53364 | −0.766820 | − | 0.641862i | \(-0.778162\pi\) | ||||
−0.766820 | + | 0.641862i | \(0.778162\pi\) | |||||||
\(464\) | −4.00000 | + | 6.92820i | −0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | − | 20.7846i | −0.555889 | − | 0.962828i | ||||
\(467\) | −1.00000 | + | 1.73205i | −0.0462745 | + | 0.0801498i | −0.888235 | − | 0.459390i | \(-0.848068\pi\) |
0.841960 | + | 0.539539i | \(0.181402\pi\) | |||||||
\(468\) | −3.00000 | −0.138675 | ||||||||
\(469\) | −12.5000 | + | 4.33013i | −0.577196 | + | 0.199947i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | + | 6.06218i | −0.161271 | + | 0.279330i | ||||
\(472\) | −15.0000 | − | 25.9808i | −0.690431 | − | 1.19586i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.50000 | − | 6.06218i | 0.160760 | − | 0.278445i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | + | 3.46410i | 0.183340 | + | 0.158777i | ||||
\(477\) | 14.0000 | 0.641016 | ||||||||
\(478\) | −14.0000 | + | 24.2487i | −0.640345 | + | 1.10911i | ||||
\(479\) | −1.00000 | − | 1.73205i | −0.0456912 | − | 0.0791394i | 0.842275 | − | 0.539048i | \(-0.181216\pi\) |
−0.887967 | + | 0.459908i | \(0.847882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 18.1865i | 0.478759 | − | 0.829235i | ||||
\(482\) | −21.0000 | −0.956524 | ||||||||
\(483\) | 1.00000 | − | 5.19615i | 0.0455016 | − | 0.236433i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.00000 | + | 6.92820i | 0.181257 | + | 0.313947i | 0.942309 | − | 0.334744i | \(-0.108650\pi\) |
−0.761052 | + | 0.648691i | \(0.775317\pi\) | |||||||
\(488\) | −10.5000 | + | 18.1865i | −0.475313 | + | 0.823266i | ||||
\(489\) | −9.00000 | −0.406994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00000 | −0.270776 | −0.135388 | − | 0.990793i | \(-0.543228\pi\) | ||||
−0.135388 | + | 0.990793i | \(0.543228\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | − | 13.8564i | −0.360302 | − | 0.624061i | ||||
\(494\) | 1.50000 | + | 2.59808i | 0.0674882 | + | 0.116893i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −6.00000 | + | 31.1769i | −0.269137 | + | 1.39848i | ||||
\(498\) | −14.0000 | −0.627355 | ||||||||
\(499\) | 9.50000 | − | 16.4545i | 0.425278 | − | 0.736604i | −0.571168 | − | 0.820833i | \(-0.693510\pi\) |
0.996446 | + | 0.0842294i | \(0.0268429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | − | 1.73205i | −0.0446767 | − | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.0000 | −1.78351 | −0.891756 | − | 0.452517i | \(-0.850526\pi\) | ||||
−0.891756 | + | 0.452517i | \(0.850526\pi\) | |||||||
\(504\) | 6.00000 | + | 5.19615i | 0.267261 | + | 0.231455i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.00000 | − | 3.46410i | −0.0888231 | − | 0.153846i | ||||
\(508\) | −5.50000 | − | 9.52628i | −0.244023 | − | 0.422660i | ||||
\(509\) | 4.00000 | − | 6.92820i | 0.177297 | − | 0.307087i | −0.763657 | − | 0.645622i | \(-0.776598\pi\) |
0.940954 | + | 0.338535i | \(0.109931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5000 | + | 9.52628i | −1.21653 | + | 0.421418i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −17.5000 | + | 6.06218i | −0.768906 | + | 0.266357i | ||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0000 | − | 29.4449i | −0.744784 | − | 1.29000i | −0.950296 | − | 0.311348i | \(-0.899219\pi\) |
0.205512 | − | 0.978655i | \(-0.434114\pi\) | |||||||
\(522\) | −4.00000 | − | 6.92820i | −0.175075 | − | 0.303239i | ||||
\(523\) | −8.00000 | + | 13.8564i | −0.349816 | + | 0.605898i | −0.986216 | − | 0.165460i | \(-0.947089\pi\) |
0.636401 | + | 0.771358i | \(0.280422\pi\) | |||||||
\(524\) | −14.0000 | −0.611593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | −8.00000 | + | 13.8564i | −0.348485 | + | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | −0.500000 | + | 2.59808i | −0.0216777 | + | 0.112641i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.50000 | − | 12.9904i | −0.323951 | − | 0.561099i | ||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 16.0000 | 0.689809 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.50000 | − | 2.59808i | 0.0644900 | − | 0.111700i | −0.831978 | − | 0.554809i | \(-0.812791\pi\) |
0.896468 | + | 0.443109i | \(0.146125\pi\) | |||||||
\(542\) | −6.00000 | − | 10.3923i | −0.257722 | − | 0.446388i | ||||
\(543\) | 11.0000 | + | 19.0526i | 0.472055 | + | 0.817624i | ||||
\(544\) | −5.00000 | + | 8.66025i | −0.214373 | + | 0.371305i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.50000 | − | 7.79423i | 0.0641941 | − | 0.333562i | ||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 5.00000 | − | 8.66025i | 0.213589 | − | 0.369948i | ||||
\(549\) | −3.50000 | − | 6.06218i | −0.149376 | − | 0.258727i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 6.00000 | 0.255377 | ||||||||
\(553\) | −14.0000 | − | 12.1244i | −0.595341 | − | 0.515580i | ||||
\(554\) | 5.00000 | 0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.50000 | + | 2.59808i | 0.0636142 | + | 0.110183i | ||||
\(557\) | −2.00000 | − | 3.46410i | −0.0847427 | − | 0.146779i | 0.820539 | − | 0.571591i | \(-0.193674\pi\) |
−0.905282 | + | 0.424812i | \(0.860340\pi\) | |||||||
\(558\) | −4.00000 | + | 6.92820i | −0.169334 | + | 0.293294i | ||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.00000 | − | 5.19615i | 0.126547 | − | 0.219186i | ||||
\(563\) | 14.0000 | + | 24.2487i | 0.590030 | + | 1.02196i | 0.994228 | + | 0.107290i | \(0.0342173\pi\) |
−0.404198 | + | 0.914671i | \(0.632449\pi\) | |||||||
\(564\) | −5.00000 | − | 8.66025i | −0.210538 | − | 0.364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.0000 | −0.798630 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | −36.0000 | −1.51053 | ||||||||
\(569\) | −6.00000 | + | 10.3923i | −0.251533 | + | 0.435668i | −0.963948 | − | 0.266090i | \(-0.914268\pi\) |
0.712415 | + | 0.701758i | \(0.247601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50000 | + | 2.59808i | 0.0627730 | + | 0.108726i | 0.895704 | − | 0.444651i | \(-0.146672\pi\) |
−0.832931 | + | 0.553377i | \(0.813339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.50000 | + | 6.06218i | −0.145833 | + | 0.252591i | ||||
\(577\) | −1.00000 | − | 1.73205i | −0.0416305 | − | 0.0721062i | 0.844459 | − | 0.535620i | \(-0.179922\pi\) |
−0.886090 | + | 0.463513i | \(0.846589\pi\) | |||||||
\(578\) | −6.50000 | − | 11.2583i | −0.270364 | − | 0.468285i | ||||
\(579\) | −3.00000 | + | 5.19615i | −0.124676 | + | 0.215945i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.00000 | + | 36.3731i | −0.290409 | + | 1.50901i | ||||
\(582\) | −9.00000 | −0.373062 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −16.5000 | − | 28.5788i | −0.682775 | − | 1.18260i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.00000 | − | 13.8564i | 0.330477 | − | 0.572403i | ||||
\(587\) | 6.00000 | 0.247647 | 0.123823 | − | 0.992304i | \(-0.460484\pi\) | ||||
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(588\) | 5.50000 | − | 4.33013i | 0.226816 | − | 0.178571i | ||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | − | 10.3923i | −0.246807 | − | 0.427482i | ||||
\(592\) | −3.50000 | − | 6.06218i | −0.143849 | − | 0.249154i | ||||
\(593\) | 21.0000 | − | 36.3731i | 0.862367 | − | 1.49366i | −0.00727173 | − | 0.999974i | \(-0.502315\pi\) |
0.869638 | − | 0.493689i | \(-0.164352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 5.50000 | − | 9.52628i | 0.225100 | − | 0.389885i | ||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −13.0000 | − | 22.5167i | −0.531166 | − | 0.920006i | −0.999338 | − | 0.0363689i | \(-0.988421\pi\) |
0.468173 | − | 0.883637i | \(-0.344912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.0000 | −1.83559 | −0.917794 | − | 0.397057i | \(-0.870032\pi\) | ||||
−0.917794 | + | 0.397057i | \(0.870032\pi\) | |||||||
\(602\) | −16.0000 | − | 13.8564i | −0.652111 | − | 0.564745i | ||||
\(603\) | 5.00000 | 0.203616 | ||||||||
\(604\) | −0.500000 | + | 0.866025i | −0.0203447 | + | 0.0352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.00000 | + | 13.8564i | 0.324978 | + | 0.562878i | ||||
\(607\) | −21.5000 | + | 37.2391i | −0.872658 | + | 1.51149i | −0.0134214 | + | 0.999910i | \(0.504272\pi\) |
−0.859237 | + | 0.511578i | \(0.829061\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | −20.0000 | + | 6.92820i | −0.810441 | + | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | + | 25.9808i | −0.606835 | + | 1.05107i | ||||
\(612\) | −1.00000 | − | 1.73205i | −0.0404226 | − | 0.0700140i | ||||
\(613\) | 3.00000 | + | 5.19615i | 0.121169 | + | 0.209871i | 0.920229 | − | 0.391381i | \(-0.128002\pi\) |
−0.799060 | + | 0.601251i | \(0.794669\pi\) | |||||||
\(614\) | 6.00000 | − | 10.3923i | 0.242140 | − | 0.419399i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0000 | 0.966204 | 0.483102 | − | 0.875564i | \(-0.339510\pi\) | ||||
0.483102 | + | 0.875564i | \(0.339510\pi\) | |||||||
\(618\) | −6.50000 | + | 11.2583i | −0.261468 | + | 0.452876i | ||||
\(619\) | 6.00000 | + | 10.3923i | 0.241160 | + | 0.417702i | 0.961045 | − | 0.276392i | \(-0.0891387\pi\) |
−0.719885 | + | 0.694094i | \(0.755805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | + | 1.73205i | −0.0401286 | + | 0.0695048i | ||||
\(622\) | 30.0000 | 1.20289 | ||||||||
\(623\) | −12.0000 | − | 10.3923i | −0.480770 | − | 0.416359i | ||||
\(624\) | 3.00000 | 0.120096 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.00000 | − | 12.1244i | −0.279776 | − | 0.484587i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.50000 | + | 6.06218i | −0.139665 | + | 0.241907i | ||||
\(629\) | 14.0000 | 0.558217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0000 | 1.79142 | 0.895711 | − | 0.444637i | \(-0.146667\pi\) | ||||
0.895711 | + | 0.444637i | \(0.146667\pi\) | |||||||
\(632\) | 10.5000 | − | 18.1865i | 0.417668 | − | 0.723421i | ||||
\(633\) | −2.50000 | − | 4.33013i | −0.0993661 | − | 0.172107i | ||||
\(634\) | −7.00000 | − | 12.1244i | −0.278006 | − | 0.481520i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.0000 | 0.555136 | ||||||||
\(637\) | −19.5000 | − | 7.79423i | −0.772618 | − | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | − | 10.3923i | 0.237356 | − | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.0000 | − | 20.7846i | −0.473972 | − | 0.820943i | 0.525584 | − | 0.850741i | \(-0.323847\pi\) |
−0.999556 | + | 0.0297987i | \(0.990513\pi\) | |||||||
\(642\) | 3.00000 | − | 5.19615i | 0.118401 | − | 0.205076i | ||||
\(643\) | 29.0000 | 1.14365 | 0.571824 | − | 0.820376i | \(-0.306236\pi\) | ||||
0.571824 | + | 0.820376i | \(0.306236\pi\) | |||||||
\(644\) | 1.00000 | − | 5.19615i | 0.0394055 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00000 | + | 1.73205i | −0.0393445 | + | 0.0681466i | ||||
\(647\) | 6.00000 | + | 10.3923i | 0.235884 | + | 0.408564i | 0.959529 | − | 0.281609i | \(-0.0908680\pi\) |
−0.723645 | + | 0.690172i | \(0.757535\pi\) | |||||||
\(648\) | −1.50000 | − | 2.59808i | −0.0589256 | − | 0.102062i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | + | 13.8564i | 0.627089 | + | 0.543075i | ||||
\(652\) | −9.00000 | −0.352467 | ||||||||
\(653\) | 22.0000 | − | 38.1051i | 0.860927 | − | 1.49117i | −0.0101092 | − | 0.999949i | \(-0.503218\pi\) |
0.871036 | − | 0.491220i | \(-0.163449\pi\) | |||||||
\(654\) | 7.50000 | + | 12.9904i | 0.293273 | + | 0.507964i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 25.0000 | − | 8.66025i | 0.974601 | − | 0.337612i | ||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.50000 | − | 9.52628i | −0.213925 | − | 0.370529i | 0.739014 | − | 0.673690i | \(-0.235292\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | 10.5000 | + | 18.1865i | 0.408094 | + | 0.706840i | ||||
\(663\) | −3.00000 | + | 5.19615i | −0.116510 | + | 0.201802i | ||||
\(664\) | −42.0000 | −1.62992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | −1.00000 | − | 1.73205i | −0.0386912 | − | 0.0670151i | ||||
\(669\) | 7.50000 | + | 12.9904i | 0.289967 | + | 0.502237i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.0000 | + | 8.66025i | 0.385758 | + | 0.334077i | ||||
\(673\) | 1.00000 | 0.0385472 | 0.0192736 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192736 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(674\) | 1.00000 | − | 1.73205i | 0.0385186 | − | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.00000 | − | 3.46410i | −0.0769231 | − | 0.133235i | ||||
\(677\) | −7.00000 | + | 12.1244i | −0.269032 | + | 0.465977i | −0.968612 | − | 0.248577i | \(-0.920037\pi\) |
0.699580 | + | 0.714554i | \(0.253370\pi\) | |||||||
\(678\) | 6.00000 | 0.230429 | ||||||||
\(679\) | −4.50000 | + | 23.3827i | −0.172694 | + | 0.897345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | + | 17.3205i | −0.383201 | + | 0.663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | −13.0000 | −0.495981 | ||||||||
\(688\) | 4.00000 | − | 6.92820i | 0.152499 | − | 0.264135i | ||||
\(689\) | −21.0000 | − | 36.3731i | −0.800036 | − | 1.38570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.50000 | − | 12.9904i | 0.285313 | − | 0.494177i | −0.687372 | − | 0.726306i | \(-0.741236\pi\) |
0.972685 | + | 0.232128i | \(0.0745690\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0000 | 0.379595 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | − | 20.7846i | −0.454859 | − | 0.787839i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −11.0000 | + | 19.0526i | −0.416356 | + | 0.721150i | ||||
\(699\) | 24.0000 | 0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | −1.50000 | + | 2.59808i | −0.0566139 | + | 0.0980581i | ||||
\(703\) | 3.50000 | + | 6.06218i | 0.132005 | + | 0.228639i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 40.0000 | − | 13.8564i | 1.50435 | − | 0.521124i | ||||
\(708\) | 10.0000 | 0.375823 | ||||||||
\(709\) | −0.500000 | + | 0.866025i | −0.0187779 | + | 0.0325243i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.856484 | + | 0.516174i | \(0.172644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.50000 | + | 6.06218i | 0.131260 | + | 0.227349i | ||||
\(712\) | 9.00000 | − | 15.5885i | 0.337289 | − | 0.584202i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 5.00000 | − | 1.73205i | 0.187120 | − | 0.0648204i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | −14.0000 | − | 24.2487i | −0.522840 | − | 0.905585i | ||||
\(718\) | 15.0000 | + | 25.9808i | 0.559795 | + | 0.969593i | ||||
\(719\) | 2.00000 | − | 3.46410i | 0.0745874 | − | 0.129189i | −0.826319 | − | 0.563202i | \(-0.809569\pi\) |
0.900907 | + | 0.434013i | \(0.142903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.0000 | + | 22.5167i | 0.968291 | + | 0.838564i | ||||
\(722\) | 18.0000 | 0.669891 | ||||||||
\(723\) | 10.5000 | − | 18.1865i | 0.390499 | − | 0.676364i | ||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.50000 | − | 9.52628i | 0.204124 | − | 0.353553i | ||||
\(727\) | −43.0000 | −1.59478 | −0.797391 | − | 0.603463i | \(-0.793787\pi\) | ||||
−0.797391 | + | 0.603463i | \(0.793787\pi\) | |||||||
\(728\) | 4.50000 | − | 23.3827i | 0.166781 | − | 0.866620i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | + | 13.8564i | 0.295891 | + | 0.512498i | ||||
\(732\) | −3.50000 | − | 6.06218i | −0.129364 | − | 0.224065i | ||||
\(733\) | −15.5000 | + | 26.8468i | −0.572506 | + | 0.991609i | 0.423802 | + | 0.905755i | \(0.360695\pi\) |
−0.996308 | + | 0.0858539i | \(0.972638\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.0000 | 0.368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5000 | + | 42.4352i | 0.901247 | + | 1.56101i | 0.825877 | + | 0.563850i | \(0.190680\pi\) |
0.0753699 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | −7.00000 | + | 36.3731i | −0.256978 | + | 1.33530i | ||||
\(743\) | −6.00000 | −0.220119 | −0.110059 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110059 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(744\) | −12.0000 | + | 20.7846i | −0.439941 | + | 0.762001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.50000 | − | 9.52628i | −0.201369 | − | 0.348782i | ||||
\(747\) | 7.00000 | − | 12.1244i | 0.256117 | − | 0.443607i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | − | 10.3923i | −0.438470 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | + | 19.9186i | −0.419641 | + | 0.726839i | −0.995903 | − | 0.0904254i | \(-0.971177\pi\) |
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(752\) | 5.00000 | + | 8.66025i | 0.182331 | + | 0.315807i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.0000 | + | 20.7846i | −0.437014 | + | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.50000 | + | 0.866025i | −0.0909241 | + | 0.0314970i | ||||
\(757\) | 43.0000 | 1.56286 | 0.781431 | − | 0.623992i | \(-0.214490\pi\) | ||||
0.781431 | + | 0.623992i | \(0.214490\pi\) | |||||||
\(758\) | 17.5000 | − | 30.3109i | 0.635629 | − | 1.10094i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | −11.0000 | −0.398488 | ||||||||
\(763\) | 37.5000 | − | 12.9904i | 1.35759 | − | 0.470283i | ||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.00000 | − | 8.66025i | −0.180657 | − | 0.312908i | ||||
\(767\) | −15.0000 | − | 25.9808i | −0.541619 | − | 0.938111i | ||||
\(768\) | −8.50000 | + | 14.7224i | −0.306717 | + | 0.531250i | ||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.00000 | + | 5.19615i | −0.107972 | + | 0.187014i | ||||
\(773\) | 24.0000 | + | 41.5692i | 0.863220 | + | 1.49514i | 0.868804 | + | 0.495156i | \(0.164889\pi\) |
−0.00558380 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(774\) | 4.00000 | + | 6.92820i | 0.143777 | + | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −27.0000 | −0.969244 | ||||||||
\(777\) | 3.50000 | − | 18.1865i | 0.125562 | − | 0.652438i | ||||
\(778\) | 36.0000 | 1.29066 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.00000 | − | 3.46410i | 0.0715199 | − | 0.123876i | ||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | −5.50000 | + | 4.33013i | −0.196429 | + | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.00000 | + | 12.1244i | −0.249682 | + | 0.432461i | ||||
\(787\) | −8.50000 | − | 14.7224i | −0.302992 | − | 0.524798i | 0.673820 | − | 0.738896i | \(-0.264652\pi\) |
−0.976812 | + | 0.214097i | \(0.931319\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | −8.00000 | + | 13.8564i | −0.284808 | + | 0.493301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00000 | − | 15.5885i | 0.106668 | − | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5000 | + | 18.1865i | −0.372866 | + | 0.645823i | ||||
\(794\) | −7.00000 | − | 12.1244i | −0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.50000 | − | 9.52628i | 0.194942 | − | 0.337650i | ||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 2.00000 | + | 1.73205i | 0.0707992 | + | 0.0613139i | ||||
\(799\) | −20.0000 | −0.707549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | −6.00000 | − | 10.3923i | −0.211867 | − | 0.366965i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.00000 | 0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | −8.00000 | + | 13.8564i | −0.281613 | + | 0.487769i | ||||
\(808\) | 24.0000 | + | 41.5692i | 0.844317 | + | 1.46240i | ||||
\(809\) | 3.00000 | + | 5.19615i | 0.105474 | + | 0.182687i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.00000 | 0.105344 | 0.0526721 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526721 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(812\) | −20.0000 | + | 6.92820i | −0.701862 | + | 0.243132i | ||||
\(813\) | 12.0000 | 0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | + | 1.73205i | 0.0350070 | + | 0.0606339i | ||||
\(817\) | −4.00000 | + | 6.92820i | −0.139942 | + | 0.242387i | ||||
\(818\) | −5.00000 | −0.174821 | ||||||||
\(819\) | 6.00000 | + | 5.19615i | 0.209657 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0000 | − | 41.5692i | 0.837606 | − | 1.45078i | −0.0542853 | − | 0.998525i | \(-0.517288\pi\) |
0.891891 | − | 0.452250i | \(-0.149379\pi\) | |||||||
\(822\) | −5.00000 | − | 8.66025i | −0.174395 | − | 0.302061i | ||||
\(823\) | 2.50000 | + | 4.33013i | 0.0871445 | + | 0.150939i | 0.906303 | − | 0.422628i | \(-0.138892\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | −19.5000 | + | 33.7750i | −0.679315 | + | 1.17661i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.00000 | + | 25.9808i | −0.173972 | + | 0.903986i | ||||
\(827\) | 24.0000 | 0.834562 | 0.417281 | − | 0.908778i | \(-0.362983\pi\) | ||||
0.417281 | + | 0.908778i | \(0.362983\pi\) | |||||||
\(828\) | −1.00000 | + | 1.73205i | −0.0347524 | + | 0.0601929i | ||||
\(829\) | 7.50000 | + | 12.9904i | 0.260486 | + | 0.451175i | 0.966371 | − | 0.257152i | \(-0.0827840\pi\) |
−0.705885 | + | 0.708326i | \(0.749451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.50000 | + | 4.33013i | −0.0867240 | + | 0.150210i | ||||
\(832\) | 21.0000 | 0.728044 | ||||||||
\(833\) | −2.00000 | − | 13.8564i | −0.0692959 | − | 0.480096i | ||||
\(834\) | 3.00000 | 0.103882 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | − | 6.92820i | −0.138260 | − | 0.239474i | ||||
\(838\) | 12.0000 | − | 20.7846i | 0.414533 | − | 0.717992i | ||||
\(839\) | −42.0000 | −1.45000 | −0.725001 | − | 0.688748i | \(-0.758161\pi\) | ||||
−0.725001 | + | 0.688748i | \(0.758161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −17.5000 | + | 30.3109i | −0.603090 | + | 1.04458i | ||||
\(843\) | 3.00000 | + | 5.19615i | 0.103325 | + | 0.178965i | ||||
\(844\) | −2.50000 | − | 4.33013i | −0.0860535 | − | 0.149049i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.0000 | −0.343807 | ||||||||
\(847\) | −22.0000 | − | 19.0526i | −0.755929 | − | 0.654654i | ||||
\(848\) | −14.0000 | −0.480762 | ||||||||
\(849\) | 9.50000 | − | 16.4545i | 0.326039 | − | 0.564716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.00000 | − | 12.1244i | −0.239957 | − | 0.415618i | ||||
\(852\) | 6.00000 | − | 10.3923i | 0.205557 | − | 0.356034i | ||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | 17.5000 | − | 6.06218i | 0.598838 | − | 0.207443i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0000 | − | 45.0333i | 0.887109 | − | 1.53652i | 0.0438309 | − | 0.999039i | \(-0.486044\pi\) |
0.843278 | − | 0.537478i | \(-0.180623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00000 | 0.0681203 | ||||||||
\(863\) | 3.00000 | − | 5.19615i | 0.102121 | − | 0.176879i | −0.810437 | − | 0.585826i | \(-0.800770\pi\) |
0.912558 | + | 0.408946i | \(0.134104\pi\) | |||||||
\(864\) | −2.50000 | − | 4.33013i | −0.0850517 | − | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.00000 | − | 1.73205i | 0.0339814 | − | 0.0588575i | ||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 16.0000 | + | 13.8564i | 0.543075 | + | 0.470317i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.50000 | − | 12.9904i | −0.254128 | − | 0.440162i | ||||
\(872\) | 22.5000 | + | 38.9711i | 0.761946 | + | 1.31973i | ||||
\(873\) | 4.50000 | − | 7.79423i | 0.152302 | − | 0.263795i | ||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000 | 0.371656 | ||||||||
\(877\) | 11.5000 | − | 19.9186i | 0.388327 | − | 0.672603i | −0.603897 | − | 0.797062i | \(-0.706386\pi\) |
0.992225 | + | 0.124459i | \(0.0397196\pi\) | |||||||
\(878\) | −5.50000 | − | 9.52628i | −0.185616 | − | 0.321496i | ||||
\(879\) | 8.00000 | + | 13.8564i | 0.269833 | + | 0.467365i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | −1.00000 | − | 6.92820i | −0.0336718 | − | 0.233285i | ||||
\(883\) | −31.0000 | −1.04323 | −0.521617 | − | 0.853180i | \(-0.674671\pi\) | ||||
−0.521617 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | − | 5.19615i | −0.100787 | − | 0.174568i | ||||
\(887\) | 29.0000 | − | 50.2295i | 0.973725 | − | 1.68654i | 0.289644 | − | 0.957135i | \(-0.406463\pi\) |
0.684081 | − | 0.729406i | \(-0.260204\pi\) | |||||||
\(888\) | 21.0000 | 0.704714 | ||||||||
\(889\) | −5.50000 | + | 28.5788i | −0.184464 | + | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.50000 | + | 12.9904i | 0.251119 | + | 0.434950i | ||||
\(893\) | −5.00000 | − | 8.66025i | −0.167319 | − | 0.289804i | ||||
\(894\) | 2.00000 | − | 3.46410i | 0.0668900 | − | 0.115857i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.00000 | + | 5.19615i | 0.200446 | + | 0.173591i | ||||
\(897\) | 6.00000 | 0.200334 | ||||||||
\(898\) | 3.00000 | − | 5.19615i | 0.100111 | − | 0.173398i | ||||
\(899\) | −32.0000 | − | 55.4256i | −1.06726 | − | 1.84855i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.0000 | − | 24.2487i | 0.466408 | − | 0.807842i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000 | − | 6.92820i | 0.665558 | − | 0.230556i | ||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.500000 | + | 0.866025i | 0.0166114 | + | 0.0287718i | ||||
\(907\) | 0.500000 | + | 0.866025i | 0.0166022 | + | 0.0287559i | 0.874207 | − | 0.485553i | \(-0.161382\pi\) |
−0.857605 | + | 0.514309i | \(0.828048\pi\) | |||||||
\(908\) | −10.0000 | + | 17.3205i | −0.331862 | + | 0.574801i | ||||
\(909\) | −16.0000 | −0.530687 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | −0.500000 | + | 0.866025i | −0.0165567 | + | 0.0286770i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.50000 | + | 2.59808i | 0.0496156 | + | 0.0859367i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.0000 | −0.429532 | ||||||||
\(917\) | 28.0000 | + | 24.2487i | 0.924641 | + | 0.800763i | ||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | −12.0000 | + | 20.7846i | −0.395843 | + | 0.685621i | −0.993208 | − | 0.116348i | \(-0.962881\pi\) |
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | −1.00000 | + | 1.73205i | −0.0329332 | + | 0.0570421i | ||||
\(923\) | −36.0000 | −1.18495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.5000 | + | 28.5788i | −0.542224 | + | 0.939159i | ||||
\(927\) | −6.50000 | − | 11.2583i | −0.213488 | − | 0.369772i | ||||
\(928\) | −20.0000 | − | 34.6410i | −0.656532 | − | 1.13715i | ||||
\(929\) | 22.0000 | − | 38.1051i | 0.721797 | − | 1.25019i | −0.238482 | − | 0.971147i | \(-0.576650\pi\) |
0.960279 | − | 0.279042i | \(-0.0900167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50000 | − | 4.33013i | 0.180255 | − | 0.141914i | ||||
\(932\) | 24.0000 | 0.786146 | ||||||||
\(933\) | −15.0000 | + | 25.9808i | −0.491078 | + | 0.850572i | ||||
\(934\) | 1.00000 | + | 1.73205i | 0.0327210 | + | 0.0566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.50000 | + | 7.79423i | −0.147087 | + | 0.254762i | ||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | −2.50000 | + | 12.9904i | −0.0816279 | + | 0.424151i | ||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0000 | − | 36.3731i | −0.684580 | − | 1.18573i | −0.973568 | − | 0.228395i | \(-0.926652\pi\) |
0.288988 | − | 0.957333i | \(-0.406681\pi\) | |||||||
\(942\) | 3.50000 | + | 6.06218i | 0.114036 | + | 0.197516i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −10.0000 | −0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.0000 | + | 19.0526i | −0.357452 | + | 0.619125i | −0.987534 | − | 0.157403i | \(-0.949688\pi\) |
0.630082 | + | 0.776528i | \(0.283021\pi\) | |||||||
\(948\) | 3.50000 | + | 6.06218i | 0.113675 | + | 0.196890i | ||||
\(949\) | −16.5000 | − | 28.5788i | −0.535613 | − | 0.927708i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0000 | 0.453981 | ||||||||
\(952\) | 15.0000 | − | 5.19615i | 0.486153 | − | 0.168408i | ||||
\(953\) | 20.0000 | 0.647864 | 0.323932 | − | 0.946080i | \(-0.394995\pi\) | ||||
0.323932 | + | 0.946080i | \(0.394995\pi\) | |||||||
\(954\) | 7.00000 | − | 12.1244i | 0.226633 | − | 0.392541i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.0000 | − | 24.2487i | −0.452792 | − | 0.784259i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.00000 | −0.0646171 | ||||||||
\(959\) | −25.0000 | + | 8.66025i | −0.807292 | + | 0.279654i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | −10.5000 | − | 18.1865i | −0.338534 | − | 0.586357i | ||||
\(963\) | 3.00000 | + | 5.19615i | 0.0966736 | + | 0.167444i | ||||
\(964\) | 10.5000 | − | 18.1865i | 0.338182 | − | 0.585749i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.00000 | − | 3.46410i | −0.128698 | − | 0.111456i | ||||
\(967\) | 23.0000 | 0.739630 | 0.369815 | − | 0.929105i | \(-0.379421\pi\) | ||||
0.369815 | + | 0.929105i | \(0.379421\pi\) | |||||||
\(968\) | 16.5000 | − | 28.5788i | 0.530330 | − | 0.918559i | ||||
\(969\) | −1.00000 | − | 1.73205i | −0.0321246 | − | 0.0556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00000 | + | 6.92820i | −0.128366 | + | 0.222337i | −0.923044 | − | 0.384695i | \(-0.874307\pi\) |
0.794678 | + | 0.607032i | \(0.207640\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.50000 | − | 7.79423i | 0.0480878 | − | 0.249871i | ||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.50000 | + | 6.06218i | 0.112032 | + | 0.194046i | ||||
\(977\) | −20.0000 | − | 34.6410i | −0.639857 | − | 1.10826i | −0.985464 | − | 0.169885i | \(-0.945660\pi\) |
0.345607 | − | 0.938379i | \(-0.387673\pi\) | |||||||
\(978\) | −4.50000 | + | 7.79423i | −0.143894 | + | 0.249232i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0000 | −0.478913 | ||||||||
\(982\) | −3.00000 | + | 5.19615i | −0.0957338 | + | 0.165816i | ||||
\(983\) | −11.0000 | − | 19.0526i | −0.350846 | − | 0.607682i | 0.635552 | − | 0.772058i | \(-0.280772\pi\) |
−0.986398 | + | 0.164376i | \(0.947439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.0000 | −0.509544 | ||||||||
\(987\) | −5.00000 | + | 25.9808i | −0.159152 | + | 0.826977i | ||||
\(988\) | −3.00000 | −0.0954427 | ||||||||
\(989\) | 8.00000 | − | 13.8564i | 0.254385 | − | 0.440608i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(992\) | −20.0000 | + | 34.6410i | −0.635001 | + | 1.09985i | ||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 24.0000 | + | 20.7846i | 0.761234 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.00000 | − | 12.1244i | 0.221803 | − | 0.384175i | ||||
\(997\) | −18.5000 | − | 32.0429i | −0.585901 | − | 1.01481i | −0.994762 | − | 0.102214i | \(-0.967407\pi\) |
0.408862 | − | 0.912596i | \(-0.365926\pi\) | |||||||
\(998\) | −9.50000 | − | 16.4545i | −0.300717 | − | 0.520858i | ||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(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 | 525.2.i.d.226.1 | yes | 2 | |
5.2 | odd | 4 | 525.2.r.c.499.2 | 4 | |||
5.3 | odd | 4 | 525.2.r.c.499.1 | 4 | |||
5.4 | even | 2 | 525.2.i.b.226.1 | yes | 2 | ||
7.2 | even | 3 | 3675.2.a.e.1.1 | 1 | |||
7.4 | even | 3 | inner | 525.2.i.d.151.1 | yes | 2 | |
7.5 | odd | 6 | 3675.2.a.g.1.1 | 1 | |||
35.4 | even | 6 | 525.2.i.b.151.1 | ✓ | 2 | ||
35.9 | even | 6 | 3675.2.a.m.1.1 | 1 | |||
35.18 | odd | 12 | 525.2.r.c.424.2 | 4 | |||
35.19 | odd | 6 | 3675.2.a.k.1.1 | 1 | |||
35.32 | odd | 12 | 525.2.r.c.424.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.i.b.151.1 | ✓ | 2 | 35.4 | even | 6 | ||
525.2.i.b.226.1 | yes | 2 | 5.4 | even | 2 | ||
525.2.i.d.151.1 | yes | 2 | 7.4 | even | 3 | inner | |
525.2.i.d.226.1 | yes | 2 | 1.1 | even | 1 | trivial | |
525.2.r.c.424.1 | 4 | 35.32 | odd | 12 | |||
525.2.r.c.424.2 | 4 | 35.18 | odd | 12 | |||
525.2.r.c.499.1 | 4 | 5.3 | odd | 4 | |||
525.2.r.c.499.2 | 4 | 5.2 | odd | 4 | |||
3675.2.a.e.1.1 | 1 | 7.2 | even | 3 | |||
3675.2.a.g.1.1 | 1 | 7.5 | odd | 6 | |||
3675.2.a.k.1.1 | 1 | 35.19 | odd | 6 | |||
3675.2.a.m.1.1 | 1 | 35.9 | even | 6 |