Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(575,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.5 | ||
Root | \(-1.16947 - 0.795191i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.h.575.8 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 0.665647i | − 0.297686i | −0.988861 | − | 0.148843i | \(-0.952445\pi\) | ||||
0.988861 | − | 0.148843i | \(-0.0475550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.07986 | −0.627102 | −0.313551 | − | 0.949571i | \(-0.601519\pi\) | ||||
−0.313551 | + | 0.949571i | \(0.601519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.55691 | −1.54121 | −0.770605 | − | 0.637313i | \(-0.780046\pi\) | ||||
−0.770605 | + | 0.637313i | \(0.780046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.16278i | − 0.524551i | −0.964993 | − | 0.262276i | \(-0.915527\pi\) | ||||
0.964993 | − | 0.262276i | \(-0.0844730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.49828i | − 1.03198i | −0.856596 | − | 0.515988i | \(-0.827425\pi\) | ||||
0.856596 | − | 0.515988i | \(-0.172575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.28167 | 0.892790 | 0.446395 | − | 0.894836i | \(-0.352708\pi\) | ||||
0.446395 | + | 0.894836i | \(0.352708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.55691 | 0.911383 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.41421i | − 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61555i | 1.18819i | 0.804396 | + | 0.594094i | \(0.202489\pi\) | ||||
−0.804396 | + | 0.594094i | \(0.797511\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.665647 | −0.112515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43965 | 0.894273 | 0.447136 | − | 0.894466i | \(-0.352444\pi\) | ||||
0.447136 | + | 0.894466i | \(0.352444\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 5.69588i | − 0.889548i | −0.895643 | − | 0.444774i | \(-0.853284\pi\) | ||||
0.895643 | − | 0.444774i | \(-0.146716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.11727i | 0.322880i | 0.986883 | + | 0.161440i | \(0.0516138\pi\) | ||||
−0.986883 | + | 0.161440i | \(0.948386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5213 | −1.53468 | −0.767341 | − | 0.641239i | \(-0.778421\pi\) | ||||
−0.767341 | + | 0.641239i | \(0.778421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6042i | 1.45659i | 0.685261 | + | 0.728297i | \(0.259688\pi\) | ||||
−0.685261 | + | 0.728297i | \(0.740312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38445i | 0.186680i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.5155 | −1.75957 | −0.879785 | − | 0.475371i | \(-0.842314\pi\) | ||||
−0.879785 | + | 0.475371i | \(0.842314\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.615547 | 0.0788128 | 0.0394064 | − | 0.999223i | \(-0.487453\pi\) | ||||
0.0394064 | + | 0.999223i | \(0.487453\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.69894i | 0.458797i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0552i | 1.71712i | 0.512717 | + | 0.858558i | \(0.328639\pi\) | ||||
−0.512717 | + | 0.858558i | \(0.671361\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.5954 | −1.85083 | −0.925415 | − | 0.378954i | \(-0.876284\pi\) | ||||
−0.925415 | + | 0.378954i | \(0.876284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9379 | −1.39723 | −0.698614 | − | 0.715498i | \(-0.746200\pi\) | ||||
−0.698614 | + | 0.715498i | \(0.746200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.07986i | 0.237022i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 0.824101i | − 0.0927186i | −0.998925 | − | 0.0463593i | \(-0.985238\pi\) | ||||
0.998925 | − | 0.0463593i | \(-0.0147619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.36153 | 0.698269 | 0.349134 | − | 0.937073i | \(-0.386476\pi\) | ||||
0.349134 | + | 0.937073i | \(0.386476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.43965 | −0.156152 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6840i | 1.34450i | 0.740322 | + | 0.672252i | \(0.234673\pi\) | ||||
−0.740322 | + | 0.672252i | \(0.765327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.55691i | 0.582523i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.99427 | −0.307205 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.824101 | 0.0836747 | 0.0418374 | − | 0.999124i | \(-0.486679\pi\) | ||||
0.0418374 | + | 0.999124i | \(0.486679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.8801i | − 1.77914i | −0.456802 | − | 0.889569i | \(-0.651005\pi\) | ||||
0.456802 | − | 0.889569i | \(-0.348995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4983i | 1.23149i | 0.787945 | + | 0.615746i | \(0.211145\pi\) | ||||
−0.787945 | + | 0.615746i | \(0.788855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3936 | −1.29481 | −0.647403 | − | 0.762148i | \(-0.724145\pi\) | ||||
−0.647403 | + | 0.762148i | \(0.724145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.11727 | 0.585928 | 0.292964 | − | 0.956123i | \(-0.405358\pi\) | ||||
0.292964 | + | 0.956123i | \(0.405358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 3.61602i | − 0.340167i | −0.985430 | − | 0.170083i | \(-0.945596\pi\) | ||||
0.985430 | − | 0.170083i | \(-0.0544037\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.85008i | − 0.265771i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.16278 | −0.198262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.67418 | −0.606744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.36153i | − 0.568993i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.17246i | − 0.725189i | −0.931947 | − | 0.362594i | \(-0.881891\pi\) | ||||
0.931947 | − | 0.362594i | \(-0.118109\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.99427 | −0.261610 | −0.130805 | − | 0.991408i | \(-0.541756\pi\) | ||||
−0.130805 | + | 0.991408i | \(0.541756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.49828 | −0.390050 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7700i | 0.920144i | 0.887882 | + | 0.460072i | \(0.152176\pi\) | ||||
−0.887882 | + | 0.460072i | \(0.847824\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000i | 1.35710i | 0.734553 | + | 0.678551i | \(0.237392\pi\) | ||||
−0.734553 | + | 0.678551i | \(0.762608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5576 | 0.966496 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.941367 | −0.0781763 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.57967i | − 0.211335i | −0.994402 | − | 0.105667i | \(-0.966302\pi\) | ||||
0.994402 | − | 0.105667i | \(-0.0336979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 5.23109i | − 0.425700i | −0.977085 | − | 0.212850i | \(-0.931725\pi\) | ||||
0.977085 | − | 0.212850i | \(-0.0682746\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.40362 | 0.353707 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.61211 | 0.447895 | 0.223948 | − | 0.974601i | \(-0.428106\pi\) | ||||
0.223948 | + | 0.974601i | \(0.428106\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4.28167i | − 0.337443i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.17246i | − 0.640117i | −0.947398 | − | 0.320058i | \(-0.896297\pi\) | ||||
0.947398 | − | 0.320058i | \(-0.103703\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.5098 | −1.27757 | −0.638783 | − | 0.769387i | \(-0.720562\pi\) | ||||
−0.638783 | + | 0.769387i | \(0.720562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.8793 | 1.37533 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.19875i | 0.319225i | 0.987180 | + | 0.159613i | \(0.0510245\pi\) | ||||
−0.987180 | + | 0.159613i | \(0.948976\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.55691i | − 0.344470i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.07986 | −0.155456 | −0.0777280 | − | 0.996975i | \(-0.524767\pi\) | ||||
−0.0777280 | + | 0.996975i | \(0.524767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4396 | 0.850302 | 0.425151 | − | 0.905122i | \(-0.360221\pi\) | ||||
0.425151 | + | 0.905122i | \(0.360221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 3.62088i | − 0.266213i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.49828i | 0.328947i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.44139 | −0.610798 | −0.305399 | − | 0.952225i | \(-0.598790\pi\) | ||||
−0.305399 | + | 0.952225i | \(0.598790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.67418 | 0.696363 | 0.348181 | − | 0.937427i | \(-0.386799\pi\) | ||||
0.348181 | + | 0.937427i | \(0.386799\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.4326i | 0.957033i | 0.878079 | + | 0.478516i | \(0.158825\pi\) | ||||
−0.878079 | + | 0.478516i | \(0.841175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.1138i | 1.92205i | 0.276464 | + | 0.961024i | \(0.410837\pi\) | ||||
−0.276464 | + | 0.961024i | \(0.589163\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.41421 | −0.0992583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.79145 | −0.264806 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.35580i | 0.647154i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1138i | 0.765108i | 0.923933 | + | 0.382554i | \(0.124955\pi\) | ||||
−0.923933 | + | 0.382554i | \(0.875045\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.40935 | 0.0961170 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.61555 | 0.449093 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0184i | 0.808444i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.87930i | 0.460672i | 0.973111 | + | 0.230336i | \(0.0739825\pi\) | ||||
−0.973111 | + | 0.230336i | \(0.926018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.19608 | −0.344876 | −0.172438 | − | 0.985020i | \(-0.555164\pi\) | ||||
−0.172438 | + | 0.985020i | \(0.555164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.55691 | −0.367211 | −0.183606 | − | 0.983000i | \(-0.558777\pi\) | ||||
−0.183606 | + | 0.983000i | \(0.558777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 24.1197i | − 1.58013i | −0.613021 | − | 0.790067i | \(-0.710046\pi\) | ||||
0.613021 | − | 0.790067i | \(-0.289954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00344i | 0.456854i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.44139 | 0.546028 | 0.273014 | − | 0.962010i | \(-0.411979\pi\) | ||||
0.273014 | + | 0.962010i | \(0.411979\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8207 | −1.66326 | −0.831628 | − | 0.555334i | \(-0.812591\pi\) | ||||
−0.831628 | + | 0.555334i | \(0.812591\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.665647i | 0.0425266i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.9966i | 1.59049i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8770 | −1.25463 | −0.627314 | − | 0.778766i | \(-0.715846\pi\) | ||||
−0.627314 | + | 0.778766i | \(0.715846\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.90528 | −0.559870 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 21.3352i | − 1.33085i | −0.746465 | − | 0.665425i | \(-0.768250\pi\) | ||||
0.746465 | − | 0.665425i | \(-0.231750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 5.43965i | − 0.338003i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.7551 | −1.21815 | −0.609076 | − | 0.793112i | \(-0.708459\pi\) | ||||
−0.609076 | + | 0.793112i | \(0.708459\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.05863 | 0.433608 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 2.62356i | − 0.159961i | −0.996796 | − | 0.0799806i | \(-0.974514\pi\) | ||||
0.996796 | − | 0.0799806i | \(-0.0254858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.732814i | 0.0445153i | 0.999752 | + | 0.0222576i | \(0.00708541\pi\) | ||||
−0.999752 | + | 0.0222576i | \(0.992915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.47775 | −0.571530 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4396 | −0.687342 | −0.343671 | − | 0.939090i | \(-0.611670\pi\) | ||||
−0.343671 | + | 0.939090i | \(0.611670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.875377i | 0.0522206i | 0.999659 | + | 0.0261103i | \(0.00831212\pi\) | ||||
−0.999659 | + | 0.0261103i | \(0.991688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 22.4914i | − 1.33698i | −0.743723 | − | 0.668488i | \(-0.766942\pi\) | ||||
0.743723 | − | 0.668488i | \(-0.233058\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.69588 | −0.336217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.3224 | 0.724846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2416i | 1.41621i | 0.706106 | + | 0.708106i | \(0.250450\pi\) | ||||
−0.706106 | + | 0.708106i | \(0.749550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.99656i | 0.523800i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.7929 | −1.37598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.11727 | 0.122037 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 0.409737i | − 0.0234615i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.61211i | 0.434446i | 0.976122 | + | 0.217223i | \(0.0696999\pi\) | ||||
−0.976122 | + | 0.217223i | \(0.930300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5155 | −0.766395 | −0.383197 | − | 0.923666i | \(-0.625177\pi\) | ||||
−0.383197 | + | 0.923666i | \(0.625177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.64820 | −0.432302 | −0.216151 | − | 0.976360i | \(-0.569350\pi\) | ||||
−0.216151 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 29.7765i | − 1.67242i | −0.548411 | − | 0.836209i | \(-0.684767\pi\) | ||||
0.548411 | − | 0.836209i | \(-0.315233\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.94137i | 0.164685i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.72879 | −0.541325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.3224 | −1.40463 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5213i | 0.580055i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1138i | 0.610871i | 0.952213 | + | 0.305436i | \(0.0988021\pi\) | ||||
−0.952213 | + | 0.305436i | \(0.901198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.35580 | 0.511162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.88273 | −0.320453 | −0.160226 | − | 0.987080i | \(-0.551222\pi\) | ||||
−0.160226 | + | 0.987080i | \(0.551222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 13.7594i | − 0.745114i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6432 | 0.571357 | 0.285678 | − | 0.958326i | \(-0.407781\pi\) | ||||
0.285678 | + | 0.958326i | \(0.407781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.49828 | −0.133730 | −0.0668650 | − | 0.997762i | \(-0.521300\pi\) | ||||
−0.0668650 | + | 0.997762i | \(0.521300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 0.126811i | − 0.00674945i | −0.999994 | − | 0.00337472i | \(-0.998926\pi\) | ||||
0.999994 | − | 0.00337472i | \(-0.00107421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3810i | 0.550967i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.7551 | −1.04263 | −0.521317 | − | 0.853363i | \(-0.674559\pi\) | ||||
−0.521317 | + | 0.853363i | \(0.674559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.23453 | −0.0649754 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.94645i | 0.415936i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 28.7620i | − 1.50137i | −0.660663 | − | 0.750683i | \(-0.729725\pi\) | ||||
0.660663 | − | 0.750683i | \(-0.270275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6042 | 0.550541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.879296 | 0.0455282 | 0.0227641 | − | 0.999741i | \(-0.492753\pi\) | ||||
0.0227641 | + | 0.999741i | \(0.492753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.85866i | 0.404742i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8793i | 1.17523i | 0.809140 | + | 0.587615i | \(0.199933\pi\) | ||||
−0.809140 | + | 0.587615i | \(0.800067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.3562 | 1.65333 | 0.826663 | − | 0.562698i | \(-0.190237\pi\) | ||||
0.826663 | + | 0.562698i | \(0.190237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.38445 | 0.0705582 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 16.3391i | − 0.828424i | −0.910180 | − | 0.414212i | \(-0.864057\pi\) | ||||
0.910180 | − | 0.414212i | \(-0.135943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.26031i | − 0.468314i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.548560 | −0.0276010 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.85008 | 0.243419 | 0.121709 | − | 0.992566i | \(-0.461162\pi\) | ||||
0.121709 | + | 0.992566i | \(0.461162\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.8305i | 1.04022i | 0.854098 | + | 0.520112i | \(0.174110\pi\) | ||||
−0.854098 | + | 0.520112i | \(0.825890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 36.7620i | − 1.83125i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3137 | −0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9345 | 0.639569 | 0.319785 | − | 0.947490i | \(-0.396389\pi\) | ||||
0.319785 | + | 0.947490i | \(0.396389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.5155i | 0.665055i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 4.23453i | − 0.207865i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5519 | 0.710906 | 0.355453 | − | 0.934694i | \(-0.384327\pi\) | ||||
0.355453 | + | 0.934694i | \(0.384327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9018 | 1.45733 | 0.728663 | − | 0.684872i | \(-0.240142\pi\) | ||||
0.728663 | + | 0.684872i | \(0.240142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 9.85560i | − 0.478067i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.615547i | − 0.0297884i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.86658 | 0.282583 | 0.141292 | − | 0.989968i | \(-0.454874\pi\) | ||||
0.141292 | + | 0.989968i | \(0.454874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1104 | 1.25479 | 0.627393 | − | 0.778703i | \(-0.284122\pi\) | ||||
0.627393 | + | 0.778703i | \(0.284122\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 19.2602i | − 0.921338i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 25.9931i | − 1.24058i | −0.784371 | − | 0.620292i | \(-0.787014\pi\) | ||||
0.784371 | − | 0.620292i | \(-0.212986\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.23385 | 0.438713 | 0.219357 | − | 0.975645i | \(-0.429604\pi\) | ||||
0.219357 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.44309 | 0.400241 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.4755i | 1.57981i | 0.613232 | + | 0.789903i | \(0.289869\pi\) | ||||
−0.613232 | + | 0.789903i | \(0.710131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8466i | 0.557837i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.69894 | 0.173409 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.2277 | −1.41399 | −0.706995 | − | 0.707218i | \(-0.749950\pi\) | ||||
−0.706995 | + | 0.707218i | \(0.749950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.4822i | 0.488206i | 0.969749 | + | 0.244103i | \(0.0784935\pi\) | ||||
−0.969749 | + | 0.244103i | \(0.921507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 9.82066i | − 0.456405i | −0.973614 | − | 0.228202i | \(-0.926715\pi\) | ||||
0.973614 | − | 0.228202i | \(-0.0732848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4620 | 0.993141 | 0.496571 | − | 0.867996i | \(-0.334592\pi\) | ||||
0.496571 | + | 0.867996i | \(0.334592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0552 | 0.649009 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.40362i | − 0.202479i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 20.4983i | − 0.940526i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.56334 | −0.391269 | −0.195634 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195634 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.2277 | −1.37826 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.548560i | − 0.0249088i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.46563i | 0.428929i | 0.976732 | + | 0.214464i | \(0.0688005\pi\) | ||||
−0.976732 | + | 0.214464i | \(0.931199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.6260 | −0.885709 | −0.442854 | − | 0.896593i | \(-0.646034\pi\) | ||||
−0.442854 | + | 0.896593i | \(0.646034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.05863 | −0.137754 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5954i | 0.699548i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.11727i | 0.0947819i | 0.998876 | + | 0.0473909i | \(0.0150907\pi\) | ||||
−0.998876 | + | 0.0473909i | \(0.984909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.03062 | 0.179717 | 0.0898583 | − | 0.995955i | \(-0.471359\pi\) | ||||
0.0898583 | + | 0.995955i | \(0.471359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.9018 | −0.529625 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 13.6423i | − 0.604686i | −0.953199 | − | 0.302343i | \(-0.902231\pi\) | ||||
0.953199 | − | 0.302343i | \(-0.0977687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9379i | 0.528103i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.31944 | 0.366598 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8827 | 0.962402 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 24.4585i | − 1.07155i | −0.844362 | − | 0.535774i | \(-0.820020\pi\) | ||||
0.844362 | − | 0.535774i | \(-0.179980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000i | 0.699631i | 0.936819 | + | 0.349816i | \(0.113756\pi\) | ||||
−0.936819 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.3080 | 0.623265 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.66730 | −0.202926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.6515i | 1.37098i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.91539i | 0.385446i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.07986 | 0.0895859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.20512 | −0.309772 | −0.154886 | − | 0.987932i | \(-0.549501\pi\) | ||||
−0.154886 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 4.07194i | − 0.174423i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 39.0518i | − 1.66973i | −0.550453 | − | 0.834866i | \(-0.685545\pi\) | ||||
0.550453 | − | 0.834866i | \(-0.314455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.36153 | −0.271010 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.824101 | −0.0350443 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.99874i | 0.169432i | 0.996405 | + | 0.0847161i | \(0.0269983\pi\) | ||||
−0.996405 | + | 0.0847161i | \(0.973002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 11.7655i | − 0.497626i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.1372 | 1.64944 | 0.824718 | − | 0.565544i | \(-0.191334\pi\) | ||||
0.824718 | + | 0.565544i | \(0.191334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.40699 | −0.101263 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 32.7708i | − 1.37382i | −0.726741 | − | 0.686912i | \(-0.758966\pi\) | ||||
0.726741 | − | 0.686912i | \(-0.241034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8172i | 0.787476i | 0.919223 | + | 0.393738i | \(0.128818\pi\) | ||||
−0.919223 | + | 0.393738i | \(0.871182\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.5112 | 0.813673 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.00344 | −0.208296 | −0.104148 | − | 0.994562i | \(-0.533212\pi\) | ||||
−0.104148 | + | 0.994562i | \(0.533212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.36153i | − 0.263921i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 22.0552i | − 0.913433i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.8292 | −1.02481 | −0.512406 | − | 0.858743i | \(-0.671246\pi\) | ||||
−0.512406 | + | 0.858743i | \(0.671246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.7586 | 1.22618 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 16.1391i | − 0.662752i | −0.943499 | − | 0.331376i | \(-0.892487\pi\) | ||||
0.943499 | − | 0.331376i | \(-0.107513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.43965i | 0.0590198i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.03204 | −0.287321 | −0.143661 | − | 0.989627i | \(-0.545887\pi\) | ||||
−0.143661 | + | 0.989627i | \(0.545887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.99656 | −0.122232 | −0.0611162 | − | 0.998131i | \(-0.519466\pi\) | ||||
−0.0611162 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.44265i | 0.180619i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 9.46563i | − 0.384198i | −0.981376 | − | 0.192099i | \(-0.938471\pi\) | ||||
0.981376 | − | 0.192099i | \(-0.0615295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.4657 | 2.36527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.2311 | −0.453620 | −0.226810 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226810 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.6352i | 1.51514i | 0.652756 | + | 0.757568i | \(0.273613\pi\) | ||||
−0.652756 | + | 0.757568i | \(0.726387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.3346i | 1.74177i | 0.491491 | + | 0.870883i | \(0.336452\pi\) | ||||
−0.491491 | + | 0.870883i | \(0.663548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.6840 | 0.508175 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.5500 | 0.742002 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 11.7648i | − 0.469092i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2897i | 0.728103i | 0.931379 | + | 0.364051i | \(0.118607\pi\) | ||||
−0.931379 | + | 0.364051i | \(0.881393\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.43997 | −0.215879 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.55691 | 0.220173 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2251i | 0.561856i | 0.959729 | + | 0.280928i | \(0.0906422\pi\) | ||||
−0.959729 | + | 0.280928i | \(0.909358\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 38.4914i | − 1.51795i | −0.651118 | − | 0.758976i | \(-0.725700\pi\) | ||||
0.651118 | − | 0.758976i | \(-0.274300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.792458 | −0.0311547 | −0.0155774 | − | 0.999879i | \(-0.504959\pi\) | ||||
−0.0155774 | + | 0.999879i | \(0.504959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.1104 | 1.10343 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 7.85380i | − 0.307343i | −0.988122 | − | 0.153672i | \(-0.950890\pi\) | ||||
0.988122 | − | 0.153672i | \(-0.0491098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.99312i | 0.0778778i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.3936 | 0.521739 | 0.260870 | − | 0.965374i | \(-0.415991\pi\) | ||||
0.260870 | + | 0.965374i | \(0.415991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2603 | −1.37147 | −0.685734 | − | 0.727853i | \(-0.740518\pi\) | ||||
−0.685734 | + | 0.727853i | \(0.740518\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.99427i | 0.116113i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.05520i | − 0.234458i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.28025 | −0.0494236 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.1364 | 1.54714 | 0.773572 | − | 0.633709i | \(-0.218468\pi\) | ||||
0.773572 | + | 0.633709i | \(0.218468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.2478i | 0.778184i | 0.921199 | + | 0.389092i | \(0.127211\pi\) | ||||
−0.921199 | + | 0.389092i | \(0.872789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 0.824101i | − 0.0316261i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.6685 | −1.55614 | −0.778068 | − | 0.628179i | \(-0.783800\pi\) | ||||
−0.778068 | + | 0.628179i | \(0.783800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.16902 | 0.273914 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 58.9265i | − 2.24492i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 35.1138i | − 1.33579i | −0.744254 | − | 0.667896i | \(-0.767195\pi\) | ||||
0.744254 | − | 0.667896i | \(-0.232805\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.6504 | 0.403991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3189 | −0.466613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 6.73939i | − 0.254543i | −0.991868 | − | 0.127272i | \(-0.959378\pi\) | ||||
0.991868 | − | 0.127272i | \(-0.0406220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 24.4691i | − 0.922868i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.8801 | −0.672451 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1104 | −0.905485 | −0.452742 | − | 0.891641i | \(-0.649554\pi\) | ||||
−0.452742 | + | 0.891641i | \(0.649554\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.3256i | 1.06080i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 7.69328i | − 0.287713i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1267 | −0.638717 | −0.319359 | − | 0.947634i | \(-0.603467\pi\) | ||||
−0.319359 | + | 0.947634i | \(0.603467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.4983 | 0.465460 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 6.44445i | − 0.239341i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.72594i | 0.101099i | 0.998722 | + | 0.0505497i | \(0.0160973\pi\) | ||||
−0.998722 | + | 0.0505497i | \(0.983903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.57918 | 0.169367 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.5535 | −1.71949 | −0.859746 | − | 0.510722i | \(-0.829378\pi\) | ||||
−0.859746 | + | 0.510722i | \(0.829378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 29.2328i | − 1.07681i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 18.2897i | − 0.672799i | −0.941719 | − | 0.336399i | \(-0.890791\pi\) | ||||
0.941719 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3012 | 1.36845 | 0.684225 | − | 0.729271i | \(-0.260141\pi\) | ||||
0.684225 | + | 0.729271i | \(0.260141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.71715 | −0.0629114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.3936i | 0.489390i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 12.2345i | − 0.446444i | −0.974768 | − | 0.223222i | \(-0.928342\pi\) | ||||
0.974768 | − | 0.223222i | \(-0.0716576\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.48206 | −0.126725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.87586 | −0.140870 | −0.0704352 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704352 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.0219i | 1.19704i | 0.801107 | + | 0.598521i | \(0.204245\pi\) | ||||
−0.801107 | + | 0.598521i | \(0.795755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6.11727i | − 0.221460i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 75.1046 | 2.71187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.3415 | −0.841715 | −0.420858 | − | 0.907127i | \(-0.638271\pi\) | ||||
−0.420858 | + | 0.907127i | \(0.638271\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 31.7783i | − 1.14299i | −0.820606 | − | 0.571494i | \(-0.806364\pi\) | ||||
0.820606 | − | 0.571494i | \(-0.193636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.1465i | 1.08289i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.6217 | −0.917992 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.4362 | 1.16066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3.73568i | − 0.133332i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.64820i | − 0.0587520i | −0.999568 | − | 0.0293760i | \(-0.990648\pi\) | ||||
0.999568 | − | 0.0293760i | \(-0.00935202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.61602 | −0.128571 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.42054 | −0.121467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.8376i | 0.738107i | 0.929408 | + | 0.369053i | \(0.120318\pi\) | ||||
−0.929408 | + | 0.369053i | \(0.879682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7552i | 0.805019i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.8292 | 0.876204 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.85008 | −0.100452 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.0262i | 0.950190i | 0.879935 | + | 0.475095i | \(0.157586\pi\) | ||||
−0.879935 | + | 0.475095i | \(0.842414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.65164i | 0.303800i | 0.988396 | + | 0.151900i | \(0.0485392\pi\) | ||||
−0.988396 | + | 0.151900i | \(0.951461\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.43997 | −0.190554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.52406 | 0.333205 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2456i | 0.671675i | 0.941920 | + | 0.335837i | \(0.109019\pi\) | ||||
−0.941920 | + | 0.335837i | \(0.890981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.4036i | 0.746081i | 0.927815 | + | 0.373041i | \(0.121685\pi\) | ||||
−0.927815 | + | 0.373041i | \(0.878315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.4303 | 1.30158 | 0.650790 | − | 0.759258i | \(-0.274438\pi\) | ||||
0.650790 | + | 0.759258i | \(0.274438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.0157 | −1.70238 | −0.851192 | − | 0.524854i | \(-0.824120\pi\) | ||||
−0.851192 | + | 0.524854i | \(0.824120\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.16278i | 0.0749359i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9897i | 0.380314i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9612 | 0.551043 | 0.275521 | − | 0.961295i | \(-0.411150\pi\) | ||||
0.275521 | + | 0.961295i | \(0.411150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 11.9013i | − 0.409417i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.67418i | 0.229328i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.2908 | 0.798398 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.50172 | −0.188375 | −0.0941876 | − | 0.995554i | \(-0.530025\pi\) | ||||
−0.0941876 | + | 0.995554i | \(0.530025\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38.6007i | − 1.31857i | −0.751892 | − | 0.659287i | \(-0.770858\pi\) | ||||
0.751892 | − | 0.659287i | \(-0.229142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 6.14648i | − 0.209715i | −0.994487 | − | 0.104858i | \(-0.966561\pi\) | ||||
0.994487 | − | 0.104858i | \(-0.0334387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.9631 | 1.42844 | 0.714220 | − | 0.699922i | \(-0.246782\pi\) | ||||
0.714220 | + | 0.699922i | \(0.246782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.79488 | 0.0950289 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.71401i | 0.0581439i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 78.1035i | − 2.64644i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.36153 | −0.215059 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8759 | −1.54912 | −0.774559 | − | 0.632502i | \(-0.782028\pi\) | ||||
−0.774559 | + | 0.632502i | \(0.782028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3323i | 1.32514i | 0.749000 | + | 0.662570i | \(0.230534\pi\) | ||||
−0.749000 | + | 0.662570i | \(0.769466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 34.1173i | − 1.14814i | −0.818807 | − | 0.574069i | \(-0.805364\pi\) | ||||
0.818807 | − | 0.574069i | \(-0.194636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.9674 | −1.20767 | −0.603833 | − | 0.797111i | \(-0.706361\pi\) | ||||
−0.603833 | + | 0.797111i | \(0.706361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.17246 | −0.274096 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.3275i | 1.58376i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.38445i | 0.0462771i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.35580 | 0.312033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9345 | 0.764059 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 7.61477i | − 0.253123i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24.3449i | − 0.808360i | −0.914679 | − | 0.404180i | \(-0.867557\pi\) | ||||
0.914679 | − | 0.404180i | \(-0.132443\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.4242 | 0.577289 | 0.288645 | − | 0.957436i | \(-0.406795\pi\) | ||||
0.288645 | + | 0.957436i | \(0.406795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.2311 | −0.437885 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.99427i | 0.0988794i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 7.22422i | − 0.238305i | −0.992876 | − | 0.119152i | \(-0.961982\pi\) | ||||
0.992876 | − | 0.119152i | \(-0.0380177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 86.6622 | 2.85252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.7880 | 0.815025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 36.7208i | − 1.20477i | −0.798206 | − | 0.602385i | \(-0.794217\pi\) | ||||
0.798206 | − | 0.602385i | \(-0.205783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.49828i | 0.147425i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.99427 | 0.0979230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.6448 | −0.674435 | −0.337218 | − | 0.941427i | \(-0.609486\pi\) | ||||
−0.337218 | + | 0.941427i | \(0.609486\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 39.9687i | − 1.30294i | −0.758674 | − | 0.651471i | \(-0.774152\pi\) | ||||
0.758674 | − | 0.651471i | \(-0.225848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 24.3879i | − 0.794179i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.1439 | 0.524607 | 0.262304 | − | 0.964985i | \(-0.415518\pi\) | ||||
0.262304 | + | 0.964985i | \(0.415518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.3380 | 2.15342 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 23.2394i | − 0.752800i | −0.926457 | − | 0.376400i | \(-0.877162\pi\) | ||||
0.926457 | − | 0.376400i | \(-0.122838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.61899i | 0.181826i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.7700 | 0.347782 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7655 | −0.411789 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 6.43959i | − 0.207298i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16.0483i | − 0.516079i | −0.966134 | − | 0.258040i | \(-0.916924\pi\) | ||||
0.966134 | − | 0.258040i | \(-0.0830765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.8134 | 0.924665 | 0.462333 | − | 0.886707i | \(-0.347013\pi\) | ||||
0.462333 | + | 0.886707i | \(0.347013\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0000 | 0.512936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.3043i | 1.12948i | 0.825267 | + | 0.564742i | \(0.191024\pi\) | ||||
−0.825267 | + | 0.564742i | \(0.808976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 26.3810i | − 0.843141i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.2774 | 0.327797 | 0.163898 | − | 0.986477i | \(-0.447593\pi\) | ||||
0.163898 | + | 0.986477i | \(0.447593\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.94137 | 0.284896 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.06543i | 0.288264i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 57.2173i | − 1.81757i | −0.417266 | − | 0.908784i | \(-0.637012\pi\) | ||||
0.417266 | − | 0.908784i | \(-0.362988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0482 | 0.572168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.73625 | −0.181669 | −0.0908345 | − | 0.995866i | \(-0.528953\pi\) | ||||
−0.0908345 | + | 0.995866i | \(0.528953\pi\) | |||||||
\(998\) | 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 | 4032.2.h.h.575.5 | 12 | ||
3.2 | odd | 2 | inner | 4032.2.h.h.575.7 | 12 | ||
4.3 | odd | 2 | inner | 4032.2.h.h.575.6 | 12 | ||
8.3 | odd | 2 | 252.2.e.a.71.10 | yes | 12 | ||
8.5 | even | 2 | 252.2.e.a.71.4 | yes | 12 | ||
12.11 | even | 2 | inner | 4032.2.h.h.575.8 | 12 | ||
24.5 | odd | 2 | 252.2.e.a.71.9 | yes | 12 | ||
24.11 | even | 2 | 252.2.e.a.71.3 | ✓ | 12 | ||
56.13 | odd | 2 | 1764.2.e.g.1079.4 | 12 | |||
56.27 | even | 2 | 1764.2.e.g.1079.10 | 12 | |||
168.83 | odd | 2 | 1764.2.e.g.1079.3 | 12 | |||
168.125 | even | 2 | 1764.2.e.g.1079.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.e.a.71.3 | ✓ | 12 | 24.11 | even | 2 | ||
252.2.e.a.71.4 | yes | 12 | 8.5 | even | 2 | ||
252.2.e.a.71.9 | yes | 12 | 24.5 | odd | 2 | ||
252.2.e.a.71.10 | yes | 12 | 8.3 | odd | 2 | ||
1764.2.e.g.1079.3 | 12 | 168.83 | odd | 2 | |||
1764.2.e.g.1079.4 | 12 | 56.13 | odd | 2 | |||
1764.2.e.g.1079.9 | 12 | 168.125 | even | 2 | |||
1764.2.e.g.1079.10 | 12 | 56.27 | even | 2 | |||
4032.2.h.h.575.5 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.h.h.575.6 | 12 | 4.3 | odd | 2 | inner | ||
4032.2.h.h.575.7 | 12 | 3.2 | odd | 2 | inner | ||
4032.2.h.h.575.8 | 12 | 12.11 | even | 2 | inner |