Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(863,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.863");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.f (of order \(2\), degree \(1\), 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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
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: | \( 2^{16}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.3 | ||
Root | \(1.40126 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.863 |
Dual form | 1728.4.f.e.863.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.4919 | −1.38564 | −0.692820 | − | 0.721110i | \(-0.743632\pi\) | ||||
−0.692820 | + | 0.721110i | \(0.743632\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.0000i | 0.701934i | 0.936388 | + | 0.350967i | \(0.114147\pi\) | ||||
−0.936388 | + | 0.350967i | \(0.885853\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 15.4919i | − 0.424636i | −0.977201 | − | 0.212318i | \(-0.931899\pi\) | ||||
0.977201 | − | 0.212318i | \(-0.0681012\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 22.5167i | − 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) | ||||
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.8328i | 0.382818i | 0.981510 | + | 0.191409i | \(0.0613058\pi\) | ||||
−0.981510 | + | 0.191409i | \(0.938694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −81.4064 | −0.982942 | −0.491471 | − | 0.870894i | \(-0.663541\pi\) | ||||
−0.491471 | + | 0.870894i | \(0.663541\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −26.8328 | −0.243262 | −0.121631 | − | 0.992575i | \(-0.538812\pi\) | ||||
−0.121631 | + | 0.992575i | \(0.538812\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 115.000 | 0.920000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −185.903 | −1.19039 | −0.595196 | − | 0.803581i | \(-0.702926\pi\) | ||||
−0.595196 | + | 0.803581i | \(0.702926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 172.000i | − 0.996520i | −0.867028 | − | 0.498260i | \(-0.833973\pi\) | ||||
0.867028 | − | 0.498260i | \(-0.166027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 201.395i | − 0.972628i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.9090i | 0.146222i | 0.997324 | + | 0.0731108i | \(0.0232927\pi\) | ||||
−0.997324 | + | 0.0731108i | \(0.976707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 268.328i | 1.02209i | 0.859553 | + | 0.511047i | \(0.170742\pi\) | ||||
−0.859553 | + | 0.511047i | \(0.829258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 197.454 | 0.700266 | 0.350133 | − | 0.936700i | \(-0.386136\pi\) | ||||
0.350133 | + | 0.936700i | \(0.386136\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −295.161 | −0.916035 | −0.458018 | − | 0.888943i | \(-0.651440\pi\) | ||||
−0.458018 | + | 0.888943i | \(0.651440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 174.000 | 0.507289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −526.726 | −1.36512 | −0.682560 | − | 0.730830i | \(-0.739133\pi\) | ||||
−0.682560 | + | 0.730830i | \(0.739133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 240.000i | 0.588393i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 697.137i | − 1.53830i | −0.639070 | − | 0.769148i | \(-0.720681\pi\) | ||||
0.639070 | − | 0.769148i | \(-0.279319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 469.386i | − 0.985224i | −0.870249 | − | 0.492612i | \(-0.836042\pi\) | ||||
0.870249 | − | 0.492612i | \(-0.163958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 348.827i | 0.665640i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19.0526 | 0.0347409 | 0.0173705 | − | 0.999849i | \(-0.494471\pi\) | ||||
0.0173705 | + | 0.999849i | \(0.494471\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −590.322 | −0.986737 | −0.493368 | − | 0.869820i | \(-0.664235\pi\) | ||||
−0.493368 | + | 0.869820i | \(0.664235\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 391.000 | 0.626892 | 0.313446 | − | 0.949606i | \(-0.398517\pi\) | ||||
0.313446 | + | 0.949606i | \(0.398517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 201.395 | 0.298066 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 413.000i | 0.588179i | 0.955778 | + | 0.294089i | \(0.0950164\pi\) | ||||
−0.955778 | + | 0.294089i | \(0.904984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 123.935i | − 0.163900i | −0.996636 | − | 0.0819499i | \(-0.973885\pi\) | ||||
0.996636 | − | 0.0819499i | \(-0.0261148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 415.692i | − 0.530449i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1314.81i | − 1.56595i | −0.622054 | − | 0.782974i | \(-0.713702\pi\) | ||||
0.622054 | − | 0.782974i | \(-0.286298\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 292.717 | 0.337198 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1261.14 | 1.36200 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −427.000 | −0.446962 | −0.223481 | − | 0.974708i | \(-0.571742\pi\) | ||||
−0.223481 | + | 0.974708i | \(0.571742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 30.9839 | 0.0305249 | 0.0152624 | − | 0.999884i | \(-0.495142\pi\) | ||||
0.0152624 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1151.00i | 1.10108i | 0.834808 | + | 0.550541i | \(0.185578\pi\) | ||||
−0.834808 | + | 0.550541i | \(0.814422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 945.008i | 0.853807i | 0.904297 | + | 0.426904i | \(0.140396\pi\) | ||||
−0.904297 | + | 0.426904i | \(0.859604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1143.15i | 1.00453i | 0.864712 | + | 0.502267i | \(0.167501\pi\) | ||||
−0.864712 | + | 0.502267i | \(0.832499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2280.79i | 1.89875i | 0.314147 | + | 0.949374i | \(0.398282\pi\) | ||||
−0.314147 | + | 0.949374i | \(0.601718\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 415.692 | 0.337074 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −348.827 | −0.268713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1091.00 | 0.819684 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 154.919 | 0.110851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2260.00i | 1.57908i | 0.613702 | + | 0.789538i | \(0.289680\pi\) | ||||
−0.613702 | + | 0.789538i | \(0.710320\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 495.742i | 0.330635i | 0.986240 | + | 0.165317i | \(0.0528649\pi\) | ||||
−0.986240 | + | 0.165317i | \(0.947135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1058.28i | − 0.689961i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2924.78i | − 1.82395i | −0.410251 | − | 0.911973i | \(-0.634559\pi\) | ||||
0.410251 | − | 0.911973i | \(-0.365441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2939.29 | 1.79358 | 0.896789 | − | 0.442458i | \(-0.145894\pi\) | ||||
0.896789 | + | 0.442458i | \(0.145894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −348.827 | −0.203988 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2880.00 | 1.64946 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2943.47 | 1.61838 | 0.809189 | − | 0.587549i | \(-0.199907\pi\) | ||||
0.809189 | + | 0.587549i | \(0.199907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1039.00i | 0.559951i | 0.960007 | + | 0.279976i | \(0.0903264\pi\) | ||||
−0.960007 | + | 0.279976i | \(0.909674\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2664.61i | 1.38082i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 852.169i | − 0.433188i | −0.976262 | − | 0.216594i | \(-0.930505\pi\) | ||||
0.976262 | − | 0.216594i | \(-0.0694948\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 348.827i | − 0.170754i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −635.663 | −0.305454 | −0.152727 | − | 0.988268i | \(-0.548805\pi\) | ||||
−0.152727 | + | 0.988268i | \(0.548805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3944.42 | 1.82772 | 0.913858 | − | 0.406033i | \(-0.133088\pi\) | ||||
0.913858 | + | 0.406033i | \(0.133088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1690.00 | 0.769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 898.532 | 0.394879 | 0.197440 | − | 0.980315i | \(-0.436737\pi\) | ||||
0.197440 | + | 0.980315i | \(0.436737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1495.00i | 0.645779i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2943.47i | 1.22908i | 0.788886 | + | 0.614539i | \(0.210658\pi\) | ||||
−0.788886 | + | 0.614539i | \(0.789342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3448.51i | − 1.41617i | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
0.706129 | − | 0.708083i | \(-0.250440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 509.823i | − 0.202611i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 415.692 | 0.162558 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −402.492 | −0.152478 | −0.0762390 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762390 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1751.00 | 0.653056 | 0.326528 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326528 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 108.444 | 0.0392197 | 0.0196099 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196099 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 743.000i | 0.264673i | 0.991205 | + | 0.132336i | \(0.0422479\pi\) | ||||
−0.991205 | + | 0.132336i | \(0.957752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2416.74i | − 0.835576i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 4156.92i | − 1.41625i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1261.14i | 0.417393i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 781.155 | 0.254867 | 0.127433 | − | 0.991847i | \(-0.459326\pi\) | ||||
0.127433 | + | 0.991847i | \(0.459326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3058.94 | −0.970316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2236.00 | 0.699491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 604.185 | 0.183900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4660.00i | 1.39936i | 0.714458 | + | 0.699679i | \(0.246673\pi\) | ||||
−0.714458 | + | 0.699679i | \(0.753327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2881.50i | − 0.842519i | −0.906940 | − | 0.421260i | \(-0.861588\pi\) | ||||
0.906940 | − | 0.421260i | \(-0.138412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 935.307i | 0.269899i | 0.990852 | + | 0.134949i | \(0.0430872\pi\) | ||||
−0.990852 | + | 0.134949i | \(0.956913\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3810.26i | − 1.07132i | −0.844433 | − | 0.535662i | \(-0.820062\pi\) | ||||
0.844433 | − | 0.535662i | \(-0.179938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4572.61 | 1.26930 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 751.319 | 0.203342 | 0.101671 | − | 0.994818i | \(-0.467581\pi\) | ||||
0.101671 | + | 0.994818i | \(0.467581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6751.00 | 1.80444 | 0.902220 | − | 0.431276i | \(-0.141936\pi\) | ||||
0.902220 | + | 0.431276i | \(0.141936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2695.60 | −0.702920 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1833.00i | 0.472190i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2695.60i | − 0.677867i | −0.940810 | − | 0.338933i | \(-0.889934\pi\) | ||||
0.940810 | − | 0.338933i | \(-0.110066\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 415.692i | 0.103298i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5420.23i | 1.31558i | 0.753200 | + | 0.657791i | \(0.228509\pi\) | ||||
−0.753200 | + | 0.657791i | \(0.771491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −427.817 | −0.102638 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 107.331 | 0.0251647 | 0.0125824 | − | 0.999921i | \(-0.495995\pi\) | ||||
0.0125824 | + | 0.999921i | \(0.495995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8160.00 | 1.89157 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2370.27 | −0.537240 | −0.268620 | − | 0.963246i | \(-0.586568\pi\) | ||||
−0.268620 | + | 0.963246i | \(0.586568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0000i | 0.00694877i | 0.999994 | + | 0.00347438i | \(0.00110593\pi\) | ||||
−0.999994 | + | 0.00347438i | \(0.998894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1781.57i | − 0.390665i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6630.29i | − 1.43818i | −0.694918 | − | 0.719089i | \(-0.744559\pi\) | ||||
0.694918 | − | 0.719089i | \(-0.255441\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 321.994i | − 0.0683578i | −0.999416 | − | 0.0341789i | \(-0.989118\pi\) | ||||
0.999416 | − | 0.0341789i | \(-0.0108816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2296.70 | 0.482419 | 0.241210 | − | 0.970473i | \(-0.422456\pi\) | ||||
0.241210 | + | 0.970473i | \(0.422456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3488.27 | −0.717442 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4193.00 | 0.853450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3764.54 | −0.750603 | −0.375302 | − | 0.926903i | \(-0.622461\pi\) | ||||
−0.375302 | + | 0.926903i | \(0.622461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10800.0i | 2.13153i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 604.185i | 0.116859i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2566.90i | 0.491540i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7271.69i | 1.36517i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7970.90 | 1.48183 | 0.740917 | − | 0.671596i | \(-0.234391\pi\) | ||||
0.740917 | + | 0.671596i | \(0.234391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5178.73 | −0.944241 | −0.472121 | − | 0.881534i | \(-0.656511\pi\) | ||||
−0.472121 | + | 0.881534i | \(0.656511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4811.00 | −0.868798 | −0.434399 | − | 0.900721i | \(-0.643039\pi\) | ||||
−0.434399 | + | 0.900721i | \(0.643039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3470.19 | −0.614844 | −0.307422 | − | 0.951573i | \(-0.599466\pi\) | ||||
−0.307422 | + | 0.951573i | \(0.599466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2880.00i | 0.505483i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2184.36i | − 0.376289i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 2589.42i | − 0.441954i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3837.09i | − 0.642996i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9406.77 | −1.56206 | −0.781031 | − | 0.624492i | \(-0.785306\pi\) | ||||
−0.781031 | + | 0.624492i | \(0.785306\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −295.161 | −0.0481384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 413.000 | 0.0667583 | 0.0333791 | − | 0.999443i | \(-0.489373\pi\) | ||||
0.0333791 | + | 0.999443i | \(0.489373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2664.61 | −0.423158 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6721.00i | 1.05802i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1425.26i | − 0.220495i | −0.993904 | − | 0.110248i | \(-0.964836\pi\) | ||||
0.993904 | − | 0.110248i | \(-0.0351644\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1945.09i | 0.298334i | 0.988812 | + | 0.149167i | \(0.0476591\pi\) | ||||
−0.988812 | + | 0.149167i | \(0.952341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4400.58i | 0.663511i | 0.943365 | + | 0.331755i | \(0.107641\pi\) | ||||
−0.943365 | + | 0.331755i | \(0.892359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9145.23 | 1.36726 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9042.66 | 1.32940 | 0.664698 | − | 0.747112i | \(-0.268560\pi\) | ||||
0.664698 | + | 0.747112i | \(0.268560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −232.000 | −0.0338242 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6057.35 | −0.868647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3983.00i | 0.566515i | 0.959044 | + | 0.283257i | \(0.0914151\pi\) | ||||
−0.959044 | + | 0.283257i | \(0.908585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6847.43i | − 0.958224i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6576.60i | − 0.912931i | −0.889741 | − | 0.456466i | \(-0.849115\pi\) | ||||
0.889741 | − | 0.456466i | \(-0.150885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4185.92i | 0.571846i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6212.87 | 0.842041 | 0.421020 | − | 0.907051i | \(-0.361672\pi\) | ||||
0.421020 | + | 0.907051i | \(0.361672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9069.49 | −1.21000 | −0.604999 | − | 0.796226i | \(-0.706827\pi\) | ||||
−0.604999 | + | 0.796226i | \(0.706827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3120.00 | −0.413013 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3082.89 | 0.401823 | 0.200911 | − | 0.979609i | \(-0.435610\pi\) | ||||
0.200911 | + | 0.979609i | \(0.435610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 720.000i | − 0.0931252i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6398.17i | − 0.815005i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 852.169i | − 0.107731i | −0.998548 | − | 0.0538654i | \(-0.982846\pi\) | ||||
0.998548 | − | 0.0538654i | \(-0.0171542\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 12879.8i | − 1.60395i | −0.597357 | − | 0.801975i | \(-0.703783\pi\) | ||||
0.597357 | − | 0.801975i | \(-0.296217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3872.87 | −0.478713 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 509.823 | 0.0620909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14143.0 | 1.70984 | 0.854922 | − | 0.518756i | \(-0.173605\pi\) | ||||
0.854922 | + | 0.518756i | \(0.173605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9062.78 | 1.07978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1920.00i | 0.227106i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15011.7i | 1.75028i | 0.483867 | + | 0.875142i | \(0.339232\pi\) | ||||
−0.483867 | + | 0.875142i | \(0.660768\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 13283.1i | − 1.53772i | −0.639419 | − | 0.768858i | \(-0.720825\pi\) | ||||
0.639419 | − | 0.768858i | \(-0.279175\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3085.77i | 0.352193i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6102.01 | 0.691563 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14570.2 | 1.62836 | 0.814180 | − | 0.580613i | \(-0.197187\pi\) | ||||
0.814180 | + | 0.580613i | \(0.197187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2350.00 | 0.260817 | 0.130409 | − | 0.991460i | \(-0.458371\pi\) | ||||
0.130409 | + | 0.991460i | \(0.458371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2184.36 | 0.239113 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1484.00i | 0.161338i | 0.996741 | + | 0.0806691i | \(0.0257057\pi\) | ||||
−0.996741 | + | 0.0806691i | \(0.974294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13849.8i | 1.48538i | 0.669635 | + | 0.742690i | \(0.266450\pi\) | ||||
−0.669635 | + | 0.742690i | \(0.733550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20368.9i | 2.16984i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 6627.71i | − 0.696616i | −0.937380 | − | 0.348308i | \(-0.886756\pi\) | ||||
0.937380 | − | 0.348308i | \(-0.113244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4156.92 | 0.434017 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4534.75 | −0.467236 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1430.00 | −0.146373 | −0.0731866 | − | 0.997318i | \(-0.523317\pi\) | ||||
−0.0731866 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14856.8 | 1.50097 | 0.750486 | − | 0.660886i | \(-0.229819\pi\) | ||||
0.750486 | + | 0.660886i | \(0.229819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1499.00i | − 0.150463i | −0.997166 | − | 0.0752316i | \(-0.976030\pi\) | ||||
0.997166 | − | 0.0752316i | \(-0.0239696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6429.15i | 0.637057i | 0.947913 | + | 0.318529i | \(0.103189\pi\) | ||||
−0.947913 | + | 0.318529i | \(0.896811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 247.683i | 0.0243858i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3058.94i | − 0.297358i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9361.73 | −0.904307 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1019.65 | 0.0972628 | 0.0486314 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486314 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 741.000 | 0.0702426 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6615.06 | 0.619328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 15227.0i | − 1.41684i | −0.705791 | − | 0.708420i | \(-0.749408\pi\) | ||||
0.705791 | − | 0.708420i | \(-0.250592\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4260.28i | 0.391576i | 0.980646 | + | 0.195788i | \(0.0627264\pi\) | ||||
−0.980646 | + | 0.195788i | \(0.937274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4988.31i | − 0.455704i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 7674.19i | − 0.692624i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1402.96 | 0.125862 | 0.0629310 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629310 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3032.11 | −0.268777 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −480.000 | −0.0422965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1595.67 | −0.138952 | −0.0694762 | − | 0.997584i | \(-0.522133\pi\) | ||||
−0.0694762 | + | 0.997584i | \(0.522133\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5083.00i | 0.440037i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 17831.2i | − 1.52570i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4572.61i | 0.388981i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10974.6i | 0.922854i | 0.887178 | + | 0.461427i | \(0.152662\pi\) | ||||
−0.887178 | + | 0.461427i | \(0.847338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13116.8 | −1.09667 | −0.548335 | − | 0.836259i | \(-0.684738\pi\) | ||||
−0.548335 | + | 0.836259i | \(0.684738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4615.24 | 0.381486 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11447.0 | −0.940824 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6041.85 | 0.490998 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 14640.0i | − 1.18307i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2695.60i | − 0.215413i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11741.6i | 0.933105i | 0.884494 | + | 0.466552i | \(0.154504\pi\) | ||||
−0.884494 | + | 0.466552i | \(0.845496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 17709.7i | − 1.39192i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20630.5 | −1.61260 | −0.806302 | − | 0.591504i | \(-0.798534\pi\) | ||||
−0.806302 | + | 0.591504i | \(0.798534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15133.7 | 1.17009 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5369.00 | −0.412863 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2029.44 | 0.154381 | 0.0771905 | − | 0.997016i | \(-0.475405\pi\) | ||||
0.0771905 | + | 0.997016i | \(0.475405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 4446.00i | − 0.336397i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21038.0i | 1.57486i | 0.616402 | + | 0.787432i | \(0.288590\pi\) | ||||
−0.616402 | + | 0.787432i | \(0.711410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 35333.8i | − 2.63098i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17307.2i | 1.27514i | 0.770393 | + | 0.637570i | \(0.220060\pi\) | ||||
−0.770393 | + | 0.637570i | \(0.779940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3119.42 | 0.228623 | 0.114312 | − | 0.993445i | \(-0.463534\pi\) | ||||
0.114312 | + | 0.993445i | \(0.463534\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3085.77 | −0.223801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14077.0 | 1.01566 | 0.507828 | − | 0.861459i | \(-0.330449\pi\) | ||||
0.507828 | + | 0.861459i | \(0.330449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1611.16 | 0.115047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8160.00i | 0.579679i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24461.8i | 1.72001i | 0.510287 | + | 0.860004i | \(0.329539\pi\) | ||||
−0.510287 | + | 0.860004i | \(0.670461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14001.9i | 0.979522i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 3434.60i | − 0.237845i | −0.992904 | − | 0.118923i | \(-0.962056\pi\) | ||||
0.992904 | − | 0.118923i | \(-0.0379440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5404.00 | 0.372340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19105.0 | −1.30318 | −0.651592 | − | 0.758569i | \(-0.725899\pi\) | ||||
−0.651592 | + | 0.758569i | \(0.725899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10342.0 | −0.701928 | −0.350964 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350964 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16901.7 | −1.13579 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20627.0i | − 1.37928i | −0.724151 | − | 0.689641i | \(-0.757768\pi\) | ||||
0.724151 | − | 0.689641i | \(-0.242232\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6646.04i | 0.440049i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20148.9i | 1.32758i | 0.747918 | + | 0.663791i | \(0.231054\pi\) | ||||
−0.747918 | + | 0.663791i | \(0.768946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3783.43i | 0.246864i | 0.992353 | + | 0.123432i | \(0.0393901\pi\) | ||||
−0.992353 | + | 0.123432i | \(0.960610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16667.5 | −1.08227 | −0.541134 | − | 0.840936i | \(-0.682005\pi\) | ||||
−0.541134 | + | 0.840936i | \(0.682005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17092.5 | 1.09919 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16775.0 | −1.07360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −883.040 | −0.0559763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 13289.0i | − 0.838394i | −0.907895 | − | 0.419197i | \(-0.862312\pi\) | ||||
0.907895 | − | 0.419197i | \(-0.137688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 35011.8i | − 2.18803i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3917.90i | − 0.243694i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 17226.7i | − 1.06149i | −0.847533 | − | 0.530743i | \(-0.821913\pi\) | ||||
0.847533 | − | 0.530743i | \(-0.178087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25450.8 | 1.56093 | 0.780466 | − | 0.625198i | \(-0.214982\pi\) | ||||
0.780466 | + | 0.625198i | \(0.214982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15831.4 | 0.961971 | 0.480985 | − | 0.876729i | \(-0.340279\pi\) | ||||
0.480985 | + | 0.876729i | \(0.340279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10800.0 | −0.653216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5701.03 | −0.341652 | −0.170826 | − | 0.985301i | \(-0.554644\pi\) | ||||
−0.170826 | + | 0.985301i | \(0.554644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7680.00i | − 0.458141i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 25499.7i | − 1.50733i | −0.657261 | − | 0.753663i | \(-0.728285\pi\) | ||||
0.657261 | − | 0.753663i | \(-0.271715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4851.47i | 0.285477i | 0.989760 | + | 0.142739i | \(0.0455908\pi\) | ||||
−0.989760 | + | 0.142739i | \(0.954409\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16394.9i | 0.956038i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4988.31 | 0.289577 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7271.69 | −0.418362 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30659.0 | −1.75604 | −0.878022 | − | 0.478620i | \(-0.841137\pi\) | ||||
−0.878022 | + | 0.478620i | \(0.841137\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8690.97 | −0.493384 | −0.246692 | − | 0.969094i | \(-0.579344\pi\) | ||||
−0.246692 | + | 0.969094i | \(0.579344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 5551.00i | − 0.313738i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 11433.0i | − 0.640517i | −0.947330 | − | 0.320259i | \(-0.896230\pi\) | ||||
0.947330 | − | 0.320259i | \(-0.103770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45310.4i | 2.52733i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11860.1i | 0.655782i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18030.6 | −0.992646 | −0.496323 | − | 0.868138i | \(-0.665317\pi\) | ||||
−0.496323 | + | 0.868138i | \(0.665317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45535.3 | −2.48525 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7200.00 | −0.391276 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6336.20 | −0.341391 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2679.00i | − 0.143727i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 402.790i | 0.0214264i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 18728.7i | − 0.992059i | −0.868306 | − | 0.496029i | \(-0.834791\pi\) | ||||
0.868306 | − | 0.496029i | \(-0.165209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4615.24i | 0.242416i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5404.00 | 0.282655 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22861.6 | −1.18580 | −0.592901 | − | 0.805275i | \(-0.702018\pi\) | ||||
−0.592901 | + | 0.805275i | \(0.702018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14963.0 | −0.772887 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21378.9 | −1.09516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1180.00i | 0.0601978i | 0.999547 | + | 0.0300989i | \(0.00958222\pi\) | ||||
−0.999547 | + | 0.0300989i | \(0.990418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5298.24i | 0.268075i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39220.6i | 1.97632i | 0.153419 | + | 0.988161i | \(0.450972\pi\) | ||||
−0.153419 | + | 0.988161i | \(0.549028\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 295.161i | − 0.0147522i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28526.9 | −1.42000 | −0.709999 | − | 0.704203i | \(-0.751305\pi\) | ||||
−0.709999 | + | 0.704203i | \(0.751305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37324.4 | 1.84294 | 0.921468 | − | 0.388455i | \(-0.126991\pi\) | ||||
0.921468 | + | 0.388455i | \(0.126991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45600.0 | −2.24249 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12285.1 | −0.599316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 31819.0i | − 1.54606i | −0.634369 | − | 0.773030i | \(-0.718740\pi\) | ||||
0.634369 | − | 0.773030i | \(-0.281260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 16096.1i | − 0.775891i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 28248.0i | − 1.35626i | −0.734940 | − | 0.678132i | \(-0.762790\pi\) | ||||
0.734940 | − | 0.678132i | \(-0.237210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17951.2i | 0.855097i | 0.903992 | + | 0.427548i | \(0.140623\pi\) | ||||
−0.903992 | + | 0.427548i | \(0.859377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14861.0 | −0.705117 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15697.2 | −0.738974 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15503.0 | 0.726986 | 0.363493 | − | 0.931597i | \(-0.381584\pi\) | ||||
0.363493 | + | 0.931597i | \(0.381584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4275.77 | −0.198951 | −0.0994753 | − | 0.995040i | \(-0.531716\pi\) | ||||
−0.0994753 | + | 0.995040i | \(0.531716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 19780.0i | − 0.916798i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 21843.6i | − 1.00466i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9145.23i | 0.419004i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13201.7i | 0.600243i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3864.21 | −0.175024 | −0.0875121 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875121 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29650.3 | −1.33280 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10569.0 | −0.473287 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27296.8 | 1.21318 | 0.606588 | − | 0.795016i | \(-0.292538\pi\) | ||||
0.606588 | + | 0.795016i | \(0.292538\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 7920.00i | − 0.350675i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 6057.35i | − 0.266201i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5404.00i | 0.236604i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 10464.8i | − 0.454787i | −0.973803 | − | 0.227394i | \(-0.926980\pi\) | ||||
0.973803 | − | 0.227394i | \(-0.0730204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10340.3 | 0.447717 | 0.223859 | − | 0.974622i | \(-0.428135\pi\) | ||||
0.223859 | + | 0.974622i | \(0.428135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9847.64 | 0.423249 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16074.0 | −0.688321 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6088.33 | 0.258811 | 0.129406 | − | 0.991592i | \(-0.458693\pi\) | ||||
0.129406 | + | 0.991592i | \(0.458693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5719.00i | 0.242226i | 0.992639 | + | 0.121113i | \(0.0386463\pi\) | ||||
−0.992639 | + | 0.121113i | \(0.961354\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14268.1i | 0.599939i | 0.953949 | + | 0.299969i | \(0.0969765\pi\) | ||||
−0.953949 | + | 0.299969i | \(0.903024\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33381.8i | 1.39855i | 0.714853 | + | 0.699275i | \(0.246494\pi\) | ||||
−0.714853 | + | 0.699275i | \(0.753506\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4668.91i | 0.194199i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61106.8 | −2.53256 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43308.2 | 1.78208 | 0.891039 | − | 0.453926i | \(-0.149977\pi\) | ||||
0.891039 | + | 0.453926i | \(0.149977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10171.0 | 0.417032 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26181.4 | −1.06588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14183.0i | 0.575364i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 883.040i | − 0.0355702i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 29855.4i | − 1.19839i | −0.800603 | − | 0.599196i | \(-0.795487\pi\) | ||||
0.800603 | − | 0.599196i | \(-0.204513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 27101.1i | − 1.08023i | −0.841591 | − | 0.540115i | \(-0.818381\pi\) | ||||
0.841591 | − | 0.540115i | \(-0.181619\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12171.1 | 0.483438 | 0.241719 | − | 0.970346i | \(-0.422289\pi\) | ||||
0.241719 | + | 0.970346i | \(0.422289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7379.02 | −0.291060 | −0.145530 | − | 0.989354i | \(-0.546489\pi\) | ||||
−0.145530 | + | 0.989354i | \(0.546489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13920.0 | −0.547161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6398.17 | 0.249762 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 429.000i | − 0.0166890i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2013.95i | 0.0778103i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38276.6i | 1.47378i | 0.676010 | + | 0.736892i | \(0.263707\pi\) | ||||
−0.676010 | + | 0.736892i | \(0.736293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 46340.3i | − 1.77213i | −0.463564 | − | 0.886063i | \(-0.653430\pi\) | ||||
0.463564 | − | 0.886063i | \(-0.346570\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24347.4 | 0.927924 | 0.463962 | − | 0.885855i | \(-0.346427\pi\) | ||||
0.463962 | + | 0.885855i | \(0.346427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5044.57 | 0.190958 | 0.0954792 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954792 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29380.0 | −1.10841 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24028.0 | 0.900410 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 45600.0i | − 1.70306i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31975.4i | 1.18625i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 14133.5i | − 0.522593i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53424.1i | 1.96230i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14738.0 | −0.539546 | −0.269773 | − | 0.962924i | \(-0.586949\pi\) | ||||
−0.269773 | + | 0.962924i | \(0.586949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16690.0 | −0.606987 | −0.303493 | − | 0.952834i | \(-0.598153\pi\) | ||||
−0.303493 | + | 0.952834i | \(0.598153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1920.00 | −0.0695977 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6444.64 | −0.232084 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 45476.0i | − 1.63233i | −0.577816 | − | 0.816167i | \(-0.696095\pi\) | ||||
0.577816 | − | 0.816167i | \(-0.303905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13292.1i | 0.474013i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3784.53i | 0.134524i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8371.84i | − 0.295663i | −0.989013 | − | 0.147832i | \(-0.952771\pi\) | ||||
0.989013 | − | 0.147832i | \(-0.0472294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14164.7 | −0.498636 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6439.88 | −0.225248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10453.0 | 0.364445 | 0.182222 | − | 0.983257i | \(-0.441671\pi\) | ||||
0.182222 | + | 0.983257i | \(0.441671\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32703.5 | 1.13295 | 0.566473 | − | 0.824080i | \(-0.308307\pi\) | ||||
0.566473 | + | 0.824080i | \(0.308307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 7200.00i | − 0.248637i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1192.88i | − 0.0409328i | −0.999791 | − | 0.0204664i | \(-0.993485\pi\) | ||||
0.999791 | − | 0.0204664i | \(-0.00651511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 8804.01i | − 0.301149i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 24444.7i | − 0.830893i | −0.909618 | − | 0.415447i | \(-0.863625\pi\) | ||||
0.909618 | − | 0.415447i | \(-0.136375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6235.38 | 0.211280 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38022.1 | 1.28029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 207.000 | 0.00694841 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27126.4 | −0.904900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 45643.0i | − 1.51787i | −0.651167 | − | 0.758935i | \(-0.725720\pi\) | ||||
0.651167 | − | 0.758935i | \(-0.274280\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15972.2i | 0.527880i | 0.964539 | + | 0.263940i | \(0.0850221\pi\) | ||||
−0.964539 | + | 0.263940i | \(0.914978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38210.8i | 1.25897i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11377.1i | 0.372555i | 0.982497 | + | 0.186277i | \(0.0596423\pi\) | ||||
−0.982497 | + | 0.186277i | \(0.940358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20368.9 | −0.664958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18434.1 | −0.598126 | −0.299063 | − | 0.954233i | \(-0.596674\pi\) | ||||
−0.299063 | + | 0.954233i | \(0.596674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1680.00 | −0.0543444 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5298.24 | −0.170348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 40081.0i | − 1.28478i | −0.766379 | − | 0.642389i | \(-0.777943\pi\) | ||||
0.766379 | − | 0.642389i | \(-0.222057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 11510.5i | − 0.366741i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31821.2i | − 1.01082i | −0.862879 | − | 0.505411i | \(-0.831341\pi\) | ||||
0.862879 | − | 0.505411i | \(-0.168659\pi\) | |||||||
\(998\) | 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 | 1728.4.f.e.863.3 | yes | 8 | |
3.2 | odd | 2 | inner | 1728.4.f.e.863.7 | yes | 8 | |
4.3 | odd | 2 | inner | 1728.4.f.e.863.1 | ✓ | 8 | |
8.3 | odd | 2 | inner | 1728.4.f.e.863.6 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.f.e.863.8 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.f.e.863.5 | yes | 8 | |
24.5 | odd | 2 | inner | 1728.4.f.e.863.4 | yes | 8 | |
24.11 | even | 2 | inner | 1728.4.f.e.863.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.f.e.863.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
1728.4.f.e.863.2 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.f.e.863.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.f.e.863.4 | yes | 8 | 24.5 | odd | 2 | inner | |
1728.4.f.e.863.5 | yes | 8 | 12.11 | even | 2 | inner | |
1728.4.f.e.863.6 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.4.f.e.863.7 | yes | 8 | 3.2 | odd | 2 | inner | |
1728.4.f.e.863.8 | yes | 8 | 8.5 | even | 2 | inner |