Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.a.2591.7 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − 2.66390i | − 1.19133i | −0.803232 | − | 0.595667i | \(-0.796888\pi\) | ||||
0.803232 | − | 0.595667i | \(-0.203112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.164525 | −0.0496061 | −0.0248030 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248030 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56048 | 0.987499 | 0.493749 | − | 0.869604i | \(-0.335626\pi\) | ||||
0.493749 | + | 0.869604i | \(0.335626\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.41421i | − 0.828068i | −0.910261 | − | 0.414034i | \(-0.864119\pi\) | ||||
0.910261 | − | 0.414034i | \(-0.135881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.89898i | 0.894487i | 0.894412 | + | 0.447244i | \(0.147594\pi\) | ||||
−0.894412 | + | 0.447244i | \(0.852406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.29958 | −1.10504 | −0.552519 | − | 0.833500i | \(-0.686333\pi\) | ||||
−0.552519 | + | 0.833500i | \(0.686333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.09638 | −0.419275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.84304i | 1.45642i | 0.685356 | + | 0.728208i | \(0.259646\pi\) | ||||
−0.685356 | + | 0.728208i | \(0.740354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.72741i | − 1.56749i | −0.621084 | − | 0.783744i | \(-0.713307\pi\) | ||||
0.621084 | − | 0.783744i | \(-0.286693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.66390 | −0.450282 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.82843 | 1.28699 | 0.643493 | − | 0.765452i | \(-0.277485\pi\) | ||||
0.643493 | + | 0.765452i | \(0.277485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 1.62863i | − 0.254349i | −0.991880 | − | 0.127174i | \(-0.959409\pi\) | ||||
0.991880 | − | 0.127174i | \(-0.0405908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.2173i | − 1.71063i | −0.518111 | − | 0.855314i | \(-0.673364\pi\) | ||||
0.518111 | − | 0.855314i | \(-0.326636\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.585786 | 0.0854457 | 0.0427229 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427229 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14.2268i | − 1.95420i | −0.212783 | − | 0.977100i | \(-0.568253\pi\) | ||||
0.212783 | − | 0.977100i | \(-0.431747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.438278i | 0.0590973i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.98539 | −0.909420 | −0.454710 | − | 0.890640i | \(-0.650257\pi\) | ||||
−0.454710 | + | 0.890640i | \(0.650257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 9.48477i | − 1.17644i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.83183i | − 0.834640i | −0.908759 | − | 0.417320i | \(-0.862969\pi\) | ||||
0.908759 | − | 0.417320i | \(-0.137031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2144 | 1.21223 | 0.606114 | − | 0.795378i | \(-0.292728\pi\) | ||||
0.606114 | + | 0.795378i | \(0.292728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.48993 | 0.642547 | 0.321274 | − | 0.946986i | \(-0.395889\pi\) | ||||
0.321274 | + | 0.946986i | \(0.395889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.164525i | 0.0187493i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.09513i | 1.02328i | 0.859199 | + | 0.511641i | \(0.170962\pi\) | ||||
−0.859199 | + | 0.511641i | \(0.829038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.95492 | −0.214580 | −0.107290 | − | 0.994228i | \(-0.534217\pi\) | ||||
−0.107290 | + | 0.994228i | \(0.534217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.09513 | −0.986506 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.05745i | 0.642089i | 0.947064 | + | 0.321044i | \(0.104034\pi\) | ||||
−0.947064 | + | 0.321044i | \(0.895966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.56048i | − 0.373240i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3865 | 1.06563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.72865 | 0.480122 | 0.240061 | − | 0.970758i | \(-0.422833\pi\) | ||||
0.240061 | + | 0.970758i | \(0.422833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.6563i | − 1.06035i | −0.847890 | − | 0.530173i | \(-0.822127\pi\) | ||||
0.847890 | − | 0.530173i | \(-0.177873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.58630i | 0.648968i | 0.945891 | + | 0.324484i | \(0.105191\pi\) | ||||
−0.945891 | + | 0.324484i | \(0.894809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1416 | −1.46380 | −0.731898 | − | 0.681414i | \(-0.761365\pi\) | ||||
−0.731898 | + | 0.681414i | \(0.761365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1163 | −1.44788 | −0.723940 | − | 0.689863i | \(-0.757671\pi\) | ||||
−0.723940 | + | 0.689863i | \(0.757671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5.69818i | − 0.536040i | −0.963413 | − | 0.268020i | \(-0.913631\pi\) | ||||
0.963413 | − | 0.268020i | \(-0.0863693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1176i | 1.31647i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.41421 | −0.312980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9729 | −0.997539 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 7.73497i | − 0.691837i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.63103i | 0.499673i | 0.968288 | + | 0.249837i | \(0.0803769\pi\) | ||||
−0.968288 | + | 0.249837i | \(0.919623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.71279 | −0.586500 | −0.293250 | − | 0.956036i | \(-0.594737\pi\) | ||||
−0.293250 | + | 0.956036i | \(0.594737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.89898 | 0.338084 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.91484i | 0.761646i | 0.924648 | + | 0.380823i | \(0.124359\pi\) | ||||
−0.924648 | + | 0.380823i | \(0.875641\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.46410i | − 0.802735i | −0.915917 | − | 0.401367i | \(-0.868535\pi\) | ||||
0.915917 | − | 0.401367i | \(-0.131465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.585786 | −0.0489859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.8931 | 1.73508 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0280i | 1.23114i | 0.788082 | + | 0.615570i | \(0.211074\pi\) | ||||
−0.788082 | + | 0.615570i | \(0.788926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.2490 | −1.86740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2173 | 1.37409 | 0.687046 | − | 0.726614i | \(-0.258907\pi\) | ||||
0.687046 | + | 0.726614i | \(0.258907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.29958i | 0.417665i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.3584i | − 1.35962i | −0.733389 | − | 0.679809i | \(-0.762063\pi\) | ||||
0.733389 | − | 0.679809i | \(-0.237937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.18670 | 0.0918296 | 0.0459148 | − | 0.998945i | \(-0.485380\pi\) | ||||
0.0459148 | + | 0.998945i | \(0.485380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.322997 | −0.0248459 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.73497i | 0.588079i | 0.955793 | + | 0.294039i | \(0.0949997\pi\) | ||||
−0.955793 | + | 0.294039i | \(0.905000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.09638i | 0.158471i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8844 | −0.888279 | −0.444140 | − | 0.895958i | \(-0.646491\pi\) | ||||
−0.444140 | + | 0.895958i | \(0.646491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.141105 | 0.0104882 | 0.00524412 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524412 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 20.8542i | − 1.53323i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.561722i | 0.0410772i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5841 | −1.05527 | −0.527633 | − | 0.849473i | \(-0.676920\pi\) | ||||
−0.527633 | + | 0.849473i | \(0.676920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1928 | −1.02162 | −0.510808 | − | 0.859695i | \(-0.670654\pi\) | ||||
−0.510808 | + | 0.859695i | \(0.670654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 24.8824i | − 1.77280i | −0.462923 | − | 0.886399i | \(-0.653199\pi\) | ||||
0.462923 | − | 0.886399i | \(-0.346801\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.4181i | 1.66007i | 0.557713 | + | 0.830034i | \(0.311679\pi\) | ||||
−0.557713 | + | 0.830034i | \(0.688321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.84304 | 0.550473 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.33850 | −0.303014 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 0.641478i | − 0.0443720i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 15.1210i | − 1.04097i | −0.853871 | − | 0.520485i | \(-0.825751\pi\) | ||||
0.853871 | − | 0.520485i | \(-0.174249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.8819 | −2.03793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.72741 | −0.592455 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 12.1562i | − 0.817717i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.01654i | − 0.335932i | −0.985793 | − | 0.167966i | \(-0.946280\pi\) | ||||
0.985793 | − | 0.167966i | \(-0.0537199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6556 | −0.707238 | −0.353619 | − | 0.935390i | \(-0.615049\pi\) | ||||
−0.353619 | + | 0.935390i | \(0.615049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9189 | −1.25020 | −0.625099 | − | 0.780546i | \(-0.714941\pi\) | ||||
−0.625099 | + | 0.780546i | \(0.714941\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.89898i | − 0.582992i | −0.956572 | − | 0.291496i | \(-0.905847\pi\) | ||||
0.956572 | − | 0.291496i | \(-0.0941529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.56048i | − 0.101794i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.11439 | −0.330822 | −0.165411 | − | 0.986225i | \(-0.552895\pi\) | ||||
−0.165411 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.03262 | 0.388595 | 0.194298 | − | 0.980943i | \(-0.437757\pi\) | ||||
0.194298 | + | 0.980943i | \(0.437757\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.66390i | 0.170190i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8822i | 0.883305i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.95867 | 0.502347 | 0.251173 | − | 0.967942i | \(-0.419184\pi\) | ||||
0.251173 | + | 0.967942i | \(0.419184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.871911 | 0.0548166 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 24.3565i | − 1.51932i | −0.650321 | − | 0.759660i | \(-0.725365\pi\) | ||||
0.650321 | − | 0.759660i | \(-0.274635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.82843i | − 0.486435i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9106 | −1.04275 | −0.521377 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521377 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.8988 | −2.32810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.20512i | − 0.256391i | −0.991749 | − | 0.128195i | \(-0.959082\pi\) | ||||
0.991749 | − | 0.128195i | \(-0.0409185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6544i | 1.55839i | 0.626781 | + | 0.779196i | \(0.284372\pi\) | ||||
−0.626781 | + | 0.779196i | \(0.715628\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.344906 | 0.0207986 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0320 | 0.783019 | 0.391510 | − | 0.920174i | \(-0.371953\pi\) | ||||
0.391510 | + | 0.920174i | \(0.371953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 20.1252i | − 1.20057i | −0.799786 | − | 0.600286i | \(-0.795053\pi\) | ||||
0.799786 | − | 0.600286i | \(-0.204947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.70850i | 0.220448i | 0.993907 | + | 0.110224i | \(0.0351568\pi\) | ||||
−0.993907 | + | 0.110224i | \(0.964843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.62863 | −0.0961348 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.34315 | 0.314303 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 32.3696i | − 1.89106i | −0.325542 | − | 0.945528i | \(-0.605547\pi\) | ||||
0.325542 | − | 0.945528i | \(-0.394453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.6084i | 1.08342i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.8690 | −1.09122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2173 | −0.646556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 13.1283i | − 0.751722i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.300573i | − 0.0171546i | −0.999963 | − | 0.00857730i | \(-0.997270\pi\) | ||||
0.999963 | − | 0.00857730i | \(-0.00273027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5140 | 0.652898 | 0.326449 | − | 0.945215i | \(-0.394148\pi\) | ||||
0.326449 | + | 0.945215i | \(0.394148\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.28788 | −0.185842 | −0.0929211 | − | 0.995673i | \(-0.529620\pi\) | ||||
−0.0929211 | + | 0.995673i | \(0.529620\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9267i | 1.23153i | 0.787931 | + | 0.615764i | \(0.211152\pi\) | ||||
−0.787931 | + | 0.615764i | \(0.788848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.29037i | − 0.0722470i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.3119 | 0.740697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.46410 | −0.414034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 0.585786i | − 0.0322955i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.8673i | 1.36683i | 0.730031 | + | 0.683414i | \(0.239506\pi\) | ||||
−0.730031 | + | 0.683414i | \(0.760494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.1993 | −0.994335 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.80725 | −0.152921 | −0.0764603 | − | 0.997073i | \(-0.524362\pi\) | ||||
−0.0764603 | + | 0.997073i | \(0.524362\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43587i | 0.0777569i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.04765 | 0.485703 | 0.242852 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242852 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.7169 | −1.32306 | −0.661532 | − | 0.749917i | \(-0.730093\pi\) | ||||
−0.661532 | + | 0.749917i | \(0.730093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0161i | 0.746003i | 0.927831 | + | 0.373001i | \(0.121671\pi\) | ||||
−0.927831 | + | 0.373001i | \(0.878329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 27.2102i | − 1.44417i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2870 | 1.07071 | 0.535353 | − | 0.844628i | \(-0.320178\pi\) | ||||
0.535353 | + | 0.844628i | \(0.320178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.79796 | 0.199893 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 14.6246i | − 0.765488i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.3887i | 1.48188i | 0.671573 | + | 0.740939i | \(0.265619\pi\) | ||||
−0.671573 | + | 0.740939i | \(0.734381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.2268 | −0.738618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.6522 | 1.53533 | 0.767667 | − | 0.640849i | \(-0.221418\pi\) | ||||
0.767667 | + | 0.640849i | \(0.221418\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.9250i | 1.43821i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.15888i | 0.367727i | 0.982952 | + | 0.183864i | \(0.0588605\pi\) | ||||
−0.982952 | + | 0.183864i | \(0.941140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0413286 | −0.00211179 | −0.00105590 | − | 0.999999i | \(-0.500336\pi\) | ||||
−0.00105590 | + | 0.999999i | \(0.500336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.438278 | 0.0223367 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.2147i | 0.822117i | 0.911609 | + | 0.411058i | \(0.134841\pi\) | ||||
−0.911609 | + | 0.411058i | \(0.865159\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0939i | 0.915047i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.2285 | 1.21907 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5536 | −0.981365 | −0.490682 | − | 0.871338i | \(-0.663252\pi\) | ||||
−0.490682 | + | 0.871338i | \(0.663252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 22.5964i | − 1.12841i | −0.825634 | − | 0.564206i | \(-0.809182\pi\) | ||||
0.825634 | − | 0.564206i | \(-0.190818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 31.0737i | − 1.54789i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.28797 | −0.0638423 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.5298 | 1.36126 | 0.680630 | − | 0.732627i | \(-0.261706\pi\) | ||||
0.680630 | + | 0.732627i | \(0.261706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.98539i | 0.343728i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.20772i | 0.255637i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.1691 | −1.32730 | −0.663648 | − | 0.748045i | \(-0.730993\pi\) | ||||
−0.663648 | + | 0.748045i | \(0.730993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.6264 | −1.24895 | −0.624477 | − | 0.781043i | \(-0.714688\pi\) | ||||
−0.624477 | + | 0.781043i | \(0.714688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.15748i | 0.347189i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.92820i | − 0.238492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.6123 | −0.896521 | −0.448260 | − | 0.893903i | \(-0.647956\pi\) | ||||
−0.448260 | + | 0.893903i | \(0.647956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.5592 | 0.988014 | 0.494007 | − | 0.869458i | \(-0.335532\pi\) | ||||
0.494007 | + | 0.869458i | \(0.335532\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 20.6629i | − 0.988443i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 23.6476i | − 1.12864i | −0.825557 | − | 0.564318i | \(-0.809139\pi\) | ||||
0.825557 | − | 0.564318i | \(-0.190861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.87880 | 0.184287 | 0.0921436 | − | 0.995746i | \(-0.470628\pi\) | ||||
0.0921436 | + | 0.995746i | \(0.470628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1365 | 0.764942 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 22.6536i | − 1.06909i | −0.845140 | − | 0.534545i | \(-0.820483\pi\) | ||||
0.845140 | − | 0.534545i | \(-0.179517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.267949i | 0.0126172i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.48477 | −0.444653 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.57826 | 0.167384 | 0.0836919 | − | 0.996492i | \(-0.473329\pi\) | ||||
0.0836919 | + | 0.996492i | \(0.473329\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.46383i | − 0.347625i | −0.984779 | − | 0.173813i | \(-0.944391\pi\) | ||||
0.984779 | − | 0.173813i | \(-0.0556087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17.7060i | − 0.822868i | −0.911440 | − | 0.411434i | \(-0.865028\pi\) | ||||
0.911440 | − | 0.411434i | \(-0.134972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.59864 | −0.166525 | −0.0832626 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832626 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.83183 | −0.315464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.84553i | 0.0848575i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 8.17373i | − 0.375036i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7287 | −0.490205 | −0.245102 | − | 0.969497i | \(-0.578822\pi\) | ||||
−0.245102 | + | 0.969497i | \(0.578822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.8729 | 1.27090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 12.5967i | − 0.571985i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.41133i | − 0.381154i | −0.981672 | − | 0.190577i | \(-0.938964\pi\) | ||||
0.981672 | − | 0.190577i | \(-0.0610358\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.1908 | 1.85892 | 0.929458 | − | 0.368929i | \(-0.120275\pi\) | ||||
0.929458 | + | 0.368929i | \(0.120275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.7778 | 1.20601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 10.2144i | − 0.458179i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.23997i | 0.189807i | 0.995486 | + | 0.0949036i | \(0.0302543\pi\) | ||||
−0.995486 | + | 0.0949036i | \(0.969746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.5551 | −1.36238 | −0.681192 | − | 0.732104i | \(-0.738538\pi\) | ||||
−0.681192 | + | 0.732104i | \(0.738538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.3874 | −1.26322 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.1136i | 0.714225i | 0.934061 | + | 0.357112i | \(0.116239\pi\) | ||||
−0.934061 | + | 0.357112i | \(0.883761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 5.48993i | − 0.242860i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.5453 | 0.773137 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0963763 | −0.00423863 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6291i | 0.728536i | 0.931294 | + | 0.364268i | \(0.118681\pi\) | ||||
−0.931294 | + | 0.364268i | \(0.881319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17.7812i | − 0.777518i | −0.921339 | − | 0.388759i | \(-0.872904\pi\) | ||||
0.921339 | − | 0.388759i | \(-0.127096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.7972 | −1.29799 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.08552 | 0.221109 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.79869i | − 0.251169i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.3358i | 1.74387i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.164525 | 0.00708658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.3392 | 1.94928 | 0.974642 | − | 0.223769i | \(-0.0718361\pi\) | ||||
0.974642 | + | 0.223769i | \(0.0718361\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.2684i | 1.72491i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 22.3004i | − 0.953495i | −0.879040 | − | 0.476747i | \(-0.841816\pi\) | ||||
0.879040 | − | 0.476747i | \(-0.158184\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.5798 | −1.30275 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.09513 | 0.386764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 40.0247i | − 1.69590i | −0.530074 | − | 0.847951i | \(-0.677836\pi\) | ||||
0.530074 | − | 0.847951i | \(-0.322164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 39.9391i | − 1.68924i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.8844 | 1.00661 | 0.503303 | − | 0.864110i | \(-0.332118\pi\) | ||||
0.503303 | + | 0.864110i | \(0.332118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.1794 | −0.638602 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.4677i | 0.941894i | 0.882162 | + | 0.470947i | \(0.156088\pi\) | ||||
−0.882162 | + | 0.470947i | \(0.843912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 10.3948i | − 0.435009i | −0.976059 | − | 0.217504i | \(-0.930208\pi\) | ||||
0.976059 | − | 0.217504i | \(-0.0697916\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1099 | 0.463315 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.27292 | −0.344406 | −0.172203 | − | 0.985061i | \(-0.555089\pi\) | ||||
−0.172203 | + | 0.985061i | \(0.555089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.95492i | 0.0811037i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34066i | 0.0969401i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.5531 | −1.46743 | −0.733717 | − | 0.679455i | \(-0.762216\pi\) | ||||
−0.733717 | + | 0.679455i | \(0.762216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.0280 | 1.40210 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.7443i | − 0.728669i | −0.931268 | − | 0.364335i | \(-0.881296\pi\) | ||||
0.931268 | − | 0.364335i | \(-0.118704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.09513i | 0.372864i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.9951 | 1.30728 | 0.653641 | − | 0.756804i | \(-0.273241\pi\) | ||||
0.653641 | + | 0.756804i | \(0.273241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.89558 | 0.362858 | 0.181429 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181429 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.2308i | 1.18840i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.7060i | 0.881020i | 0.897748 | + | 0.440510i | \(0.145202\pi\) | ||||
−0.897748 | + | 0.440510i | \(0.854798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.08568 | 0.0843776 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.4771 | −1.55408 | −0.777038 | − | 0.629454i | \(-0.783279\pi\) | ||||
−0.777038 | + | 0.629454i | \(0.783279\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 21.7856i | − 0.877056i | −0.898717 | − | 0.438528i | \(-0.855500\pi\) | ||||
0.898717 | − | 0.438528i | \(-0.144500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 44.1549i | − 1.77474i | −0.461061 | − | 0.887368i | \(-0.652531\pi\) | ||||
0.461061 | − | 0.887368i | \(-0.347469\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.05745 | 0.242687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0871 | −1.24348 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 26.7279i | − 1.06571i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 30.9355i | − 1.23152i | −0.787933 | − | 0.615760i | \(-0.788849\pi\) | ||||
0.787933 | − | 0.615760i | \(-0.211151\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.0005 | 0.595277 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.56048 | −0.141071 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 18.5427i | − 0.732393i | −0.930538 | − | 0.366196i | \(-0.880660\pi\) | ||||
0.930538 | − | 0.366196i | \(-0.119340\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5243i | 0.415039i | 0.978231 | + | 0.207520i | \(0.0665391\pi\) | ||||
−0.978231 | + | 0.207520i | \(0.933461\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.6531 | 0.772643 | 0.386322 | − | 0.922364i | \(-0.373745\pi\) | ||||
0.386322 | + | 0.922364i | \(0.373745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.14927 | 0.0451127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 23.0308i | − 0.901264i | −0.892710 | − | 0.450632i | \(-0.851199\pi\) | ||||
0.892710 | − | 0.450632i | \(-0.148801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8822i | 0.698717i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.4901 | 1.10981 | 0.554907 | − | 0.831912i | \(-0.312754\pi\) | ||||
0.554907 | + | 0.831912i | \(0.312754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.94349 | −0.153384 | −0.0766921 | − | 0.997055i | \(-0.524436\pi\) | ||||
−0.0766921 | + | 0.997055i | \(0.524436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 10.3865i | − 0.402771i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 41.5648i | − 1.60940i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.810811 | −0.0313010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.1588i | 1.50499i | 0.658595 | + | 0.752497i | \(0.271151\pi\) | ||||
−0.658595 | + | 0.752497i | \(0.728849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.72865i | − 0.181469i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.23582 | −0.123815 | −0.0619077 | − | 0.998082i | \(-0.519718\pi\) | ||||
−0.0619077 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.7483 | 0.907374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 50.6542i | − 1.92977i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 7.22219i | − 0.274745i | −0.990519 | − | 0.137373i | \(-0.956134\pi\) | ||||
0.990519 | − | 0.137373i | \(-0.0438657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.2114 | −0.956325 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.56048 | −0.210618 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9289i | 0.563858i | 0.959435 | + | 0.281929i | \(0.0909743\pi\) | ||||
−0.959435 | + | 0.281929i | \(0.909026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.5229i | 1.15119i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6563 | −0.400773 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3317 | −0.613350 | −0.306675 | − | 0.951814i | \(-0.599216\pi\) | ||||
−0.306675 | + | 0.951814i | \(0.599216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.2516i | 1.73213i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.56048i | 0.0583586i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.0552 | 1.71757 | 0.858785 | − | 0.512336i | \(-0.171220\pi\) | ||||
0.858785 | + | 0.512336i | \(0.171220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.58630 | 0.245287 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 16.4420i | − 0.610639i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5984i | 0.949392i | 0.880150 | + | 0.474696i | \(0.157442\pi\) | ||||
−0.880150 | + | 0.474696i | \(0.842558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.2984 | −1.41652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.3584 | 1.52761 | 0.763804 | − | 0.645448i | \(-0.223329\pi\) | ||||
0.763804 | + | 0.645448i | \(0.223329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.12400i | 0.0414032i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0109i | 0.405041i | 0.979278 | + | 0.202521i | \(0.0649133\pi\) | ||||
−0.979278 | + | 0.202521i | \(0.935087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.4506 | 1.00706 | 0.503532 | − | 0.863976i | \(-0.332033\pi\) | ||||
0.503532 | + | 0.863976i | \(0.332033\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.0331 | 1.46670 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1416i | 0.553263i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8414i | 0.979458i | 0.871875 | + | 0.489729i | \(0.162904\pi\) | ||||
−0.871875 | + | 0.489729i | \(0.837096\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9975 | −0.436057 | −0.218028 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218028 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.5682i | 0.818096i | 0.912513 | + | 0.409048i | \(0.134139\pi\) | ||||
−0.912513 | + | 0.409048i | \(0.865861\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.1163i | 0.547247i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.8713 | −0.898051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.549945 | 0.0198315 | 0.00991576 | − | 0.999951i | \(-0.496844\pi\) | ||||
0.00991576 | + | 0.999951i | \(0.496844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5062i | 0.521752i | 0.965372 | + | 0.260876i | \(0.0840114\pi\) | ||||
−0.965372 | + | 0.260876i | \(0.915989\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.2959i | 0.657209i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.34998 | 0.227512 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.68052 | −0.0601338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 45.8653i | − 1.63700i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.63671i | − 0.307865i | −0.988081 | − | 0.153933i | \(-0.950806\pi\) | ||||
0.988081 | − | 0.153933i | \(-0.0491939\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.69818 | −0.202604 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.5468 | 0.623104 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.2737i | 1.81621i | 0.418745 | + | 0.908104i | \(0.362470\pi\) | ||||
−0.418745 | + | 0.908104i | \(0.637530\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 2.00000i | − 0.0707549i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.903228 | −0.0318742 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.1176 | 0.497578 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4293i | 0.823732i | 0.911244 | + | 0.411866i | \(0.135123\pi\) | ||||
−0.911244 | + | 0.411866i | \(0.864877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 51.9554i | − 1.82440i | −0.409745 | − | 0.912200i | \(-0.634382\pi\) | ||||
0.409745 | − | 0.912200i | \(-0.365618\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.2412 | −1.61976 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.7361 | 1.53013 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.94310i | 0.312116i | 0.987748 | + | 0.156058i | \(0.0498787\pi\) | ||||
−0.987748 | + | 0.156058i | \(0.950121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.07180i | 0.107076i | 0.998566 | + | 0.0535381i | \(0.0170498\pi\) | ||||
−0.998566 | + | 0.0535381i | \(0.982950\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.73319 | 0.164589 | 0.0822946 | − | 0.996608i | \(-0.473775\pi\) | ||||
0.0822946 | + | 0.996608i | \(0.473775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7378 | −0.442403 | −0.221201 | − | 0.975228i | \(-0.570998\pi\) | ||||
−0.221201 | + | 0.975228i | \(0.570998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.41421i | 0.118295i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.16125i | − 0.109400i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.3976 | −1.08397 | −0.541983 | − | 0.840389i | \(-0.682326\pi\) | ||||
−0.541983 | + | 0.840389i | \(0.682326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.5133 | −1.12115 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.860432i | 0.0295998i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9729i | 0.377034i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.4874 | −1.42217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.89670 | −0.338857 | −0.169428 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169428 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.24092i | 0.281504i | 0.990045 | + | 0.140752i | \(0.0449521\pi\) | ||||
−0.990045 | + | 0.140752i | \(0.955048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3021i | 0.590342i | 0.955445 | + | 0.295171i | \(0.0953765\pi\) | ||||
−0.955445 | + | 0.295171i | \(0.904623\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.9146 | 0.814063 | 0.407032 | − | 0.913414i | \(-0.366564\pi\) | ||||
0.407032 | + | 0.913414i | \(0.366564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.6052 | 0.700598 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.49637i | − 0.0507610i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 24.3246i | − 0.824207i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.73497 | −0.261490 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1862 | 0.782942 | 0.391471 | − | 0.920190i | \(-0.371966\pi\) | ||||
0.391471 | + | 0.920190i | \(0.371966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.6992i | 1.20274i | 0.798972 | + | 0.601368i | \(0.205377\pi\) | ||||
−0.798972 | + | 0.601368i | \(0.794623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 54.2704i | − 1.82635i | −0.407573 | − | 0.913173i | \(-0.633625\pi\) | ||||
0.407573 | − | 0.913173i | \(-0.366375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8136 | 0.698852 | 0.349426 | − | 0.936964i | \(-0.386377\pi\) | ||||
0.349426 | + | 0.936964i | \(0.386377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.63103 | 0.188859 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.28397i | 0.0764301i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.6588i | 1.05824i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 68.4494 | 2.28291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.5733 | −1.61821 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 0.375889i | − 0.0124950i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 12.1386i | − 0.403056i | −0.979483 | − | 0.201528i | \(-0.935409\pi\) | ||||
0.979483 | − | 0.201528i | \(-0.0645907\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.8093 | 0.921364 | 0.460682 | − | 0.887565i | \(-0.347605\pi\) | ||||
0.460682 | + | 0.887565i | \(0.347605\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.321633 | 0.0106445 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.71279i | 0.221676i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.77101i | 0.0914072i | 0.998955 | + | 0.0457036i | \(0.0145530\pi\) | ||||
−0.998955 | + | 0.0457036i | \(0.985447\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.3682 | 1.19707 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4113 | −0.539601 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.9933i | 1.90270i | 0.308113 | + | 0.951350i | \(0.400303\pi\) | ||||
−0.308113 | + | 0.951350i | \(0.599697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.89898i | − 0.127784i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.49637 | 0.0489366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4813 | −1.19179 | −0.595897 | − | 0.803061i | \(-0.703203\pi\) | ||||
−0.595897 | + | 0.803061i | \(0.703203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 53.8744i | − 1.75625i | −0.478427 | − | 0.878127i | \(-0.658793\pi\) | ||||
0.478427 | − | 0.878127i | \(-0.341207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.63103i | 0.281065i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5198 | −0.829282 | −0.414641 | − | 0.909985i | \(-0.636093\pi\) | ||||
−0.414641 | + | 0.909985i | \(0.636093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5468 | 0.634515 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 40.9794i | − 1.32745i | −0.747975 | − | 0.663727i | \(-0.768974\pi\) | ||||
0.747975 | − | 0.663727i | \(-0.231026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.8505i | 1.25717i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.91484 | 0.287875 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.1676 | −1.45702 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.8081i | 1.21709i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.62129i | 0.180769i | 0.995907 | + | 0.0903843i | \(0.0288095\pi\) | ||||
−0.995907 | + | 0.0903843i | \(0.971190\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.2654 | −1.22799 | −0.613997 | − | 0.789308i | \(-0.710439\pi\) | ||||
−0.613997 | + | 0.789308i | \(0.710439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.46410 | −0.303405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1822i | 0.997608i | 0.866715 | + | 0.498804i | \(0.166227\pi\) | ||||
−0.866715 | + | 0.498804i | \(0.833773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 0.996600i | − 0.0318515i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.5907 | 1.83686 | 0.918429 | − | 0.395585i | \(-0.129458\pi\) | ||||
0.918429 | + | 0.395585i | \(0.129458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66.2843 | −2.11199 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 59.4471i | 1.89031i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3278i | 0.804563i | 0.915516 | + | 0.402281i | \(0.131783\pi\) | ||||
−0.915516 | + | 0.402281i | \(0.868217\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62.3836 | 1.97769 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.3697 | −1.12017 | −0.560084 | − | 0.828436i | \(-0.689231\pi\) | ||||
−0.560084 | + | 0.828436i | \(0.689231\pi\) | |||||||
\(998\) | 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 | 6048.2.h.a.2591.2 | ✓ | 8 | |
3.2 | odd | 2 | 6048.2.h.g.2591.7 | yes | 8 | ||
4.3 | odd | 2 | 6048.2.h.g.2591.2 | yes | 8 | ||
12.11 | even | 2 | inner | 6048.2.h.a.2591.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.a.2591.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.a.2591.7 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.g.2591.2 | yes | 8 | 4.3 | odd | 2 | ||
6048.2.h.g.2591.7 | yes | 8 | 3.2 | odd | 2 |