Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3905,4032)]
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([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3905");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.k (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: | \(16\) |
Coefficient field: | 16.0.101415451701035401216.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3905.7 | ||
Root | \(0.137538 + 0.752908i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3905 |
Dual form | 4032.2.k.h.3905.8 |
$q$-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 | ||||||||
\(5\) | −0.841723 | −0.376430 | −0.188215 | − | 0.982128i | \(-0.560270\pi\) | ||||
−0.188215 | + | 0.982128i | \(0.560270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.16372 | − | 2.37608i | 0.439846 | − | 0.898073i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.64575i | − | 1.09924i | −0.835416 | − | 0.549618i | \(-0.814773\pi\) | ||
0.835416 | − | 0.549618i | \(-0.185227\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53019i | 1.53380i | 0.641767 | + | 0.766899i | \(0.278201\pi\) | ||||
−0.641767 | + | 0.766899i | \(0.721799\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.841723 | 0.204148 | 0.102074 | − | 0.994777i | \(-0.467452\pi\) | ||||
0.102074 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.06871i | 0.704011i | 0.935998 | + | 0.352005i | \(0.114500\pi\) | ||||
−0.935998 | + | 0.352005i | \(0.885500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.64575i | − | 0.760192i | −0.924947 | − | 0.380096i | \(-0.875891\pi\) | ||
0.924947 | − | 0.380096i | \(-0.124109\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.29150 | −0.858301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.89753i | 1.65223i | 0.563502 | + | 0.826115i | \(0.309454\pi\) | ||||
−0.563502 | + | 0.826115i | \(0.690546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.82087i | 1.40467i | 0.711847 | + | 0.702335i | \(0.247859\pi\) | ||||
−0.711847 | + | 0.702335i | \(0.752141\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.979531 | + | 2.00000i | −0.165571 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.29150 | 0.541120 | 0.270560 | − | 0.962703i | \(-0.412791\pi\) | ||||
0.270560 | + | 0.962703i | \(0.412791\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.66259 | 1.35287 | 0.676435 | − | 0.736502i | \(-0.263524\pi\) | ||||
0.676435 | + | 0.736502i | \(0.263524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.32744 | 0.354932 | 0.177466 | − | 0.984127i | \(-0.443210\pi\) | ||||
0.177466 | + | 0.984127i | \(0.443210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.10132 | 1.32756 | 0.663782 | − | 0.747926i | \(-0.268950\pi\) | ||||
0.663782 | + | 0.747926i | \(0.268950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29150 | − | 5.53019i | −0.613072 | − | 0.790027i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.24264i | − | 0.582772i | −0.956606 | − | 0.291386i | \(-0.905884\pi\) | ||
0.956606 | − | 0.291386i | \(-0.0941163\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.06871i | 0.413785i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0604 | 1.43994 | 0.719969 | − | 0.694006i | \(-0.244156\pi\) | ||||
0.719969 | + | 0.694006i | \(0.244156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.10132i | 1.16530i | 0.812722 | + | 0.582652i | \(0.197985\pi\) | ||||
−0.812722 | + | 0.582652i | \(0.802015\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.65489i | − | 0.577368i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | −1.03664 | −0.518321 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.354249i | 0.0420416i | 0.999779 | + | 0.0210208i | \(0.00669162\pi\) | ||||
−0.999779 | + | 0.0210208i | \(0.993308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.6315i | − | 1.71249i | −0.516571 | − | 0.856244i | \(-0.672792\pi\) | ||
0.516571 | − | 0.856244i | \(-0.327208\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.66259 | − | 4.24264i | −0.987194 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.10132 | 0.998999 | 0.499500 | − | 0.866314i | \(-0.333517\pi\) | ||||
0.499500 | + | 0.866314i | \(0.333517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.708497 | −0.0768473 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.97915 | 0.739788 | 0.369894 | − | 0.929074i | \(-0.379394\pi\) | ||||
0.369894 | + | 0.929074i | \(0.379394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.1402 | + | 6.43560i | 1.37746 | + | 0.674635i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.58301i | − | 0.265011i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.57113i | − | 0.362593i | −0.983428 | − | 0.181297i | \(-0.941971\pi\) | ||
0.983428 | − | 0.181297i | \(-0.0580294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.8000 | −1.47266 | −0.736328 | − | 0.676624i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676624i | \(0.763442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.05034i | 0.497625i | 0.968552 | + | 0.248812i | \(0.0800402\pi\) | ||||
−0.968552 | + | 0.248812i | \(0.919960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.22876i | − | 0.602157i | −0.953599 | − | 0.301078i | \(-0.902653\pi\) | ||
0.953599 | − | 0.301078i | \(-0.0973466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5830 | 1.01367 | 0.506834 | − | 0.862044i | \(-0.330816\pi\) | ||||
0.506834 | + | 0.862044i | \(0.330816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.412247i | − | 0.0387809i | −0.999812 | − | 0.0193905i | \(-0.993827\pi\) | ||
0.999812 | − | 0.0193905i | \(-0.00617256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.06871i | 0.286159i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.979531 | − | 2.00000i | 0.0897935 | − | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.29150 | −0.208318 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.82087 | 0.699520 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7951 | 1.57906 | 0.789528 | − | 0.613715i | \(-0.210325\pi\) | ||||
0.789528 | + | 0.613715i | \(0.210325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.95906 | 0.171164 | 0.0855821 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855821 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.29150 | + | 3.57113i | 0.632253 | + | 0.309656i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.89753i | − | 0.760167i | −0.924952 | − | 0.380084i | \(-0.875895\pi\) | ||
0.924952 | − | 0.380084i | \(-0.124105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8712i | 1.09172i | 0.837876 | + | 0.545861i | \(0.183797\pi\) | ||||
−0.837876 | + | 0.545861i | \(0.816203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.1617 | 1.68601 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.48925i | − | 0.621949i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.89753i | 0.728914i | 0.931220 | + | 0.364457i | \(0.118745\pi\) | ||||
−0.931220 | + | 0.364457i | \(0.881255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2980 | 1.57045 | 0.785225 | − | 0.619211i | \(-0.212547\pi\) | ||||
0.785225 | + | 0.619211i | \(0.212547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.58301i | − | 0.528760i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.95906i | 0.156350i | 0.996940 | + | 0.0781751i | \(0.0249093\pi\) | ||||
−0.996940 | + | 0.0781751i | \(0.975091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.66259 | − | 4.24264i | −0.682708 | − | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0194 | 1.00747 | 0.503737 | − | 0.863857i | \(-0.331958\pi\) | ||||
0.503737 | + | 0.863857i | \(0.331958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.5830 | −1.35254 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0295 | −0.914585 | −0.457292 | − | 0.889316i | \(-0.651181\pi\) | ||||
−0.457292 | + | 0.889316i | \(0.651181\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.99412 | + | 10.1969i | −0.377520 | + | 0.770817i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.9373i | − | 1.41544i | −0.706495 | − | 0.707718i | \(-0.749725\pi\) | ||
0.706495 | − | 0.707718i | \(-0.250275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.53019i | 0.411056i | 0.978651 | + | 0.205528i | \(0.0658911\pi\) | ||||
−0.978651 | + | 0.205528i | \(0.934109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.77053 | −0.203694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.06871i | − | 0.224406i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 25.5203i | − | 1.84658i | −0.384102 | − | 0.923291i | \(-0.625489\pi\) | ||
0.384102 | − | 0.923291i | \(-0.374511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2915 | 1.10071 | 0.550353 | − | 0.834932i | \(-0.314493\pi\) | ||||
0.550353 | + | 0.834932i | \(0.314493\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.06713i | − | 0.361018i | −0.983573 | − | 0.180509i | \(-0.942225\pi\) | ||
0.983573 | − | 0.180509i | \(-0.0577746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.52269i | − | 0.533269i | −0.963798 | − | 0.266635i | \(-0.914088\pi\) | ||
0.963798 | − | 0.266635i | \(-0.0859117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.1412 | + | 10.3542i | 1.48382 | + | 0.726726i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.29150 | −0.509261 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1878 | 0.773874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98233 | 0.480684 | 0.240342 | − | 0.970688i | \(-0.422740\pi\) | ||||
0.240342 | + | 0.970688i | \(0.422740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.95906 | −0.133607 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.5830 | + | 9.10132i | 1.26150 | + | 0.617838i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.65489i | 0.313122i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.75216i | 0.318228i | 0.987260 | + | 0.159114i | \(0.0508637\pi\) | ||||
−0.987260 | + | 0.159114i | \(0.949136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0604 | −0.734103 | −0.367052 | − | 0.930201i | \(-0.619633\pi\) | ||||
−0.367052 | + | 0.930201i | \(0.619633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.53019i | 0.365445i | 0.983165 | + | 0.182723i | \(0.0584910\pi\) | ||||
−0.983165 | + | 0.182723i | \(0.941509\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5524i | 0.887848i | 0.896064 | + | 0.443924i | \(0.146414\pi\) | ||||
−0.896064 | + | 0.443924i | \(0.853586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.66079 | −0.499735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.06275i | 0.327482i | 0.986503 | + | 0.163741i | \(0.0523561\pi\) | ||||
−0.986503 | + | 0.163741i | \(0.947644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.48925i | 0.482425i | 0.970472 | + | 0.241213i | \(0.0775451\pi\) | ||||
−0.970472 | + | 0.241213i | \(0.922455\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.61226 | + | 4.65489i | 0.230779 | + | 0.297390i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.9706 | −1.07981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1617 | 1.27260 | 0.636298 | − | 0.771444i | \(-0.280465\pi\) | ||||
0.636298 | + | 0.771444i | \(0.280465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2915 | −0.835630 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0295 | −0.750379 | −0.375189 | − | 0.926948i | \(-0.622422\pi\) | ||||
−0.375189 | + | 0.926948i | \(0.622422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83039 | − | 7.82087i | 0.238009 | − | 0.485965i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.9373i | 1.90767i | 0.300327 | + | 0.953836i | \(0.402904\pi\) | ||||
−0.300327 | + | 0.953836i | \(0.597096\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.57113i | 0.219373i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.3547 | 1.78979 | 0.894893 | − | 0.446281i | \(-0.147252\pi\) | ||||
0.894893 | + | 0.446281i | \(0.147252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4626i | 1.42525i | 0.701544 | + | 0.712626i | \(0.252494\pi\) | ||||
−0.701544 | + | 0.712626i | \(0.747506\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.6458i | 0.943474i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.87451 | −0.232797 | −0.116398 | − | 0.993203i | \(-0.537135\pi\) | ||||
−0.116398 | + | 0.993203i | \(0.537135\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8681i | 1.54316i | 0.636132 | + | 0.771580i | \(0.280533\pi\) | ||||
−0.636132 | + | 0.771580i | \(0.719467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.4442i | 1.51250i | 0.654281 | + | 0.756251i | \(0.272971\pi\) | ||||
−0.654281 | + | 0.756251i | \(0.727029\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0808 | − | 20.5830i | 0.595054 | − | 1.21498i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2915 | −0.958324 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.97915 | −0.407726 | −0.203863 | − | 0.978999i | \(-0.565350\pi\) | ||||
−0.203863 | + | 0.978999i | \(0.565350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.30978 | −0.542036 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.1617 | 1.16598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.70850 | − | 5.53019i | 0.156115 | − | 0.318755i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 7.66079i | − | 0.438655i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.06871i | 0.175141i | 0.996158 | + | 0.0875703i | \(0.0279103\pi\) | ||||
−0.996158 | + | 0.0875703i | \(0.972090\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0604 | −0.627177 | −0.313588 | − | 0.949559i | \(-0.601531\pi\) | ||||
−0.313588 | + | 0.949559i | \(0.601531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1208i | 1.25034i | 0.780489 | + | 0.625170i | \(0.214970\pi\) | ||||
−0.780489 | + | 0.625170i | \(0.785030\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.89753i | − | 0.499735i | −0.968280 | − | 0.249867i | \(-0.919613\pi\) | ||
0.968280 | − | 0.249867i | \(-0.0803871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.4382 | 1.81619 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.58301i | 0.143722i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 23.7328i | − | 1.31646i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5914 | − | 21.6255i | 0.583923 | − | 1.19225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2980 | 1.06071 | 0.530357 | − | 0.847774i | \(-0.322058\pi\) | ||||
0.530357 | + | 0.847774i | \(0.322058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.14226 | 0.390223 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.41699 | −0.512976 | −0.256488 | − | 0.966547i | \(-0.582565\pi\) | ||||
−0.256488 | + | 0.966547i | \(0.582565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.5129 | 1.54406 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1343 | + | 3.76135i | −0.979159 | + | 0.203094i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.9373i | − | 1.01661i | −0.861179 | − | 0.508303i | \(-0.830273\pi\) | ||
0.861179 | − | 0.508303i | \(-0.169727\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.1617i | − | 1.07923i | −0.841912 | − | 0.539615i | \(-0.818570\pi\) | ||
0.841912 | − | 0.539615i | \(-0.181430\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6209 | 1.20399 | 0.601994 | − | 0.798500i | \(-0.294373\pi\) | ||||
0.601994 | + | 0.798500i | \(0.294373\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.298179i | − | 0.0158257i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.77124i | − | 0.0934827i | −0.998907 | − | 0.0467413i | \(-0.985116\pi\) | ||
0.998907 | − | 0.0467413i | \(-0.0148836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.58301 | 0.504369 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3157i | 0.644632i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.75216i | 0.248061i | 0.992278 | + | 0.124030i | \(0.0395820\pi\) | ||||
−0.992278 | + | 0.124030i | \(0.960418\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0808 | − | 4.93725i | −0.523372 | − | 0.256329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.58301 | −0.444411 | −0.222206 | − | 0.975000i | \(-0.571326\pi\) | ||||
−0.222206 | + | 0.975000i | \(0.571326\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49.2050 | −2.53419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.2980 | −0.991272 | −0.495636 | − | 0.868530i | \(-0.665065\pi\) | ||||
−0.495636 | + | 0.868530i | \(0.665065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0798 | 1.23042 | 0.615211 | − | 0.788363i | \(-0.289071\pi\) | ||||
0.615211 | + | 0.788363i | \(0.289071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.29150 | + | 3.57113i | 0.371609 | + | 0.182002i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 21.2132i | − | 1.07555i | −0.843088 | − | 0.537776i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537776i | \(-0.180735\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.06871i | − | 0.155191i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.14226 | 0.359366 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 35.1402i | − | 1.76364i | −0.471590 | − | 0.881818i | \(-0.656320\pi\) | ||
0.471590 | − | 0.881818i | \(-0.343680\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3828i | 0.868056i | 0.900899 | + | 0.434028i | \(0.142908\pi\) | ||||
−0.900899 | + | 0.434028i | \(0.857092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.2509 | −2.15448 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.0000i | − | 0.594818i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.48925i | 0.370320i | 0.982708 | + | 0.185160i | \(0.0592803\pi\) | ||||
−0.982708 | + | 0.185160i | \(0.940720\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.8712 | − | 26.2803i | 0.633351 | − | 1.29317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.66079 | −0.376053 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.3234 | −1.96993 | −0.984963 | − | 0.172763i | \(-0.944731\pi\) | ||||
−0.984963 | + | 0.172763i | \(0.944731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.29150 | −0.452840 | −0.226420 | − | 0.974030i | \(-0.572702\pi\) | ||||
−0.226420 | + | 0.974030i | \(0.572702\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.61226 | −0.175220 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.6255 | + | 10.5914i | 1.04653 | + | 0.512554i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.52026i | − | 0.0732283i | −0.999329 | − | 0.0366142i | \(-0.988343\pi\) | ||
0.999329 | − | 0.0366142i | \(-0.0116573\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0604i | 0.531528i | 0.964038 | + | 0.265764i | \(0.0856242\pi\) | ||||
−0.964038 | + | 0.265764i | \(0.914376\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.1878 | 0.535183 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.4946i | − | 1.45543i | −0.685881 | − | 0.727713i | \(-0.740583\pi\) | ||
0.685881 | − | 0.727713i | \(-0.259417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.06275i | 0.430584i | 0.976550 | + | 0.215292i | \(0.0690703\pi\) | ||||
−0.976550 | + | 0.215292i | \(0.930930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.87451 | −0.278478 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.1779i | 1.66015i | 0.557655 | + | 0.830073i | \(0.311701\pi\) | ||||
−0.557655 | + | 0.830073i | \(0.688299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 31.5817i | − | 1.48712i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.0604 | − | 5.41699i | −0.518519 | − | 0.253953i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.7490 | 1.29804 | 0.649022 | − | 0.760770i | \(-0.275178\pi\) | ||||
0.649022 | + | 0.760770i | \(0.275178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4331 | −0.532494 | −0.266247 | − | 0.963905i | \(-0.585784\pi\) | ||||
−0.266247 | + | 0.963905i | \(0.585784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7951 | 0.827006 | 0.413503 | − | 0.910503i | \(-0.364305\pi\) | ||||
0.413503 | + | 0.910503i | \(0.364305\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.95906 | −0.0906546 | −0.0453273 | − | 0.998972i | \(-0.514433\pi\) | ||||
−0.0453273 | + | 0.998972i | \(0.514433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.87451 | + | 20.1617i | −0.455962 | + | 0.930981i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.48528i | − | 0.390154i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 13.1694i | − | 0.604253i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.2026i | 0.829969i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.00590i | 0.136491i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.6137 | 1.43255 | 0.716276 | − | 0.697817i | \(-0.245845\pi\) | ||||
0.716276 | + | 0.697817i | \(0.245845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.8118i | − | 1.66129i | −0.556801 | − | 0.830646i | \(-0.687971\pi\) | ||
0.556801 | − | 0.830646i | \(-0.312029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.48925i | 0.337299i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.841723 | + | 0.412247i | 0.0377564 | + | 0.0184918i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.9235 | 1.83199 | 0.915993 | − | 0.401195i | \(-0.131405\pi\) | ||||
0.915993 | + | 0.401195i | \(0.131405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.1402 | −1.56682 | −0.783412 | − | 0.621503i | \(-0.786523\pi\) | ||||
−0.783412 | + | 0.621503i | \(0.786523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4575 | 0.554352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8504 | −0.879852 | −0.439926 | − | 0.898034i | \(-0.644995\pi\) | ||||
−0.439926 | + | 0.898034i | \(0.644995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.7656 | − | 17.0270i | −1.53794 | − | 0.753230i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.25098i | − | 0.187321i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.1811i | − | 1.45930i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.1252 | −1.40743 | −0.703715 | − | 0.710482i | \(-0.748477\pi\) | ||||
−0.703715 | + | 0.710482i | \(0.748477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.3842i | 1.80960i | 0.425834 | + | 0.904801i | \(0.359981\pi\) | ||||
−0.425834 | + | 0.904801i | \(0.640019\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.58301i | 0.286760i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.70850 | 0.422109 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.9058i | 2.07503i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.24289i | 0.226670i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.1617 | + | 15.6458i | −0.868426 | + | 0.673910i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.29150 | 0.399473 | 0.199736 | − | 0.979850i | \(-0.435991\pi\) | ||||
0.199736 | + | 0.979850i | \(0.435991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.90796 | −0.381575 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1048 | −1.15892 | −0.579459 | − | 0.815001i | \(-0.696736\pi\) | ||||
−0.579459 | + | 0.815001i | \(0.696736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.3040 | −1.16319 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.87451 | + | 20.1617i | −0.419907 | + | 0.857363i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 36.0024i | − | 1.52547i | −0.646712 | − | 0.762734i | \(-0.723856\pi\) | ||
0.646712 | − | 0.762734i | \(-0.276144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8712i | 0.544394i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0194 | 0.548704 | 0.274352 | − | 0.961629i | \(-0.411537\pi\) | ||||
0.274352 | + | 0.961629i | \(0.411537\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.346998i | 0.0145983i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 31.3475i | − | 1.31415i | −0.753823 | − | 0.657077i | \(-0.771793\pi\) | ||
0.753823 | − | 0.657077i | \(-0.228207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1461 | −0.675692 | −0.337846 | − | 0.941201i | \(-0.609698\pi\) | ||||
−0.337846 | + | 0.941201i | \(0.609698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6458i | 0.652473i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2630i | 1.21824i | 0.793080 | + | 0.609118i | \(0.208476\pi\) | ||||
−0.793080 | + | 0.609118i | \(0.791524\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5914 | − | 21.6255i | 0.439405 | − | 0.897175i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.4676 | −0.640603 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0194 | 0.537370 | 0.268685 | − | 0.963228i | \(-0.413411\pi\) | ||||
0.268685 | + | 0.963228i | \(0.413411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.5424 | −1.66488 | −0.832439 | − | 0.554117i | \(-0.813056\pi\) | ||||
−0.832439 | + | 0.554117i | \(0.813056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.824494 | + | 1.68345i | −0.0338010 | + | 0.0690145i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.8118i | 1.17722i | 0.808418 | + | 0.588608i | \(0.200324\pi\) | ||||
−0.808418 | + | 0.588608i | \(0.799676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.9785i | − | 0.610986i | −0.952194 | − | 0.305493i | \(-0.901179\pi\) | ||
0.952194 | − | 0.305493i | \(-0.0988213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.92881 | 0.0784173 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.98162i | 0.0804317i | 0.999191 | + | 0.0402158i | \(0.0128046\pi\) | ||||
−0.999191 | + | 0.0402158i | \(0.987195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.3320i | 2.03622i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5830 | 1.31602 | 0.658008 | − | 0.753011i | \(-0.271399\pi\) | ||||
0.658008 | + | 0.753011i | \(0.271399\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5583i | 0.666613i | 0.942819 | + | 0.333306i | \(0.108164\pi\) | ||||
−0.942819 | + | 0.333306i | \(0.891836\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.5129i | − | 1.14603i | −0.819544 | − | 0.573016i | \(-0.805773\pi\) | ||
0.819544 | − | 0.573016i | \(-0.194227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.12179 | − | 16.5830i | 0.325393 | − | 0.664384i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8745 | 0.594980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.77053 | 0.110468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.1048 | −1.07903 | −0.539513 | − | 0.841977i | \(-0.681392\pi\) | ||||
−0.539513 | + | 0.841977i | \(0.681392\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.9785 | −0.594404 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.5830 | − | 23.7328i | 1.21174 | − | 0.940329i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 39.0083i | − | 1.54073i | −0.637601 | − | 0.770367i | \(-0.720073\pi\) | ||
0.637601 | − | 0.770367i | \(-0.279927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 34.3522i | − | 1.35472i | −0.735653 | − | 0.677359i | \(-0.763124\pi\) | ||
0.735653 | − | 0.677359i | \(-0.236876\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.2630 | −1.15045 | −0.575224 | − | 0.817996i | \(-0.695085\pi\) | ||||
−0.575224 | + | 0.817996i | \(0.695085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 40.3234i | − | 1.58283i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5524i | 0.530347i | 0.964201 | + | 0.265174i | \(0.0854292\pi\) | ||||
−0.964201 | + | 0.265174i | \(0.914571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.64899 | −0.0644313 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8118i | 1.12235i | 0.827698 | + | 0.561173i | \(0.189650\pi\) | ||||
−0.827698 | + | 0.561173i | \(0.810350\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.95906i | − | 0.0761987i | −0.999274 | − | 0.0380994i | \(-0.987870\pi\) | ||
0.999274 | − | 0.0380994i | \(-0.0121303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.13742 | − | 3.00590i | −0.237999 | − | 0.116564i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.4382 | 1.25601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.1811 | 1.28094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2915 | −0.589444 | −0.294722 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294722 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.61226 | −0.138830 | −0.0694151 | − | 0.997588i | \(-0.522113\pi\) | ||||
−0.0694151 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.48528 | − | 4.15580i | −0.325635 | − | 0.159485i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 30.2288i | − | 1.15667i | −0.815799 | − | 0.578336i | \(-0.803702\pi\) | ||
0.815799 | − | 0.578336i | \(-0.196298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.48925i | 0.286150i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.4626 | 0.893854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 34.0540i | − | 1.29548i | −0.761863 | − | 0.647738i | \(-0.775715\pi\) | ||
0.761863 | − | 0.647738i | \(-0.224285\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10.8340i | − | 0.410957i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.29150 | 0.276185 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.5289i | 1.26637i | 0.774001 | + | 0.633184i | \(0.218252\pi\) | ||||
−0.774001 | + | 0.633184i | \(0.781748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1007i | 0.380954i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2231 | + | 35.1660i | −0.647742 | + | 1.32255i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.0000 | −1.05156 | −0.525781 | − | 0.850620i | \(-0.676227\pi\) | ||||
−0.525781 | + | 0.850620i | \(0.676227\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.5129 | 1.06782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.9706 | −0.634663 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2026 | −0.678844 | −0.339422 | − | 0.940634i | \(-0.610231\pi\) | ||||
−0.339422 | + | 0.940634i | \(0.610231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | + | 5.87719i | 0.446903 | + | 0.218878i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 38.1838i | − | 1.41811i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.3338i | − | 1.34755i | −0.738938 | − | 0.673773i | \(-0.764672\pi\) | ||
0.738938 | − | 0.673773i | \(-0.235328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.95906 | 0.0724586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7328i | 0.876592i | 0.898831 | + | 0.438296i | \(0.144418\pi\) | ||||
−0.898831 | + | 0.438296i | \(0.855582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.9352i | 1.13951i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.0754 | −1.62134 | −0.810670 | − | 0.585504i | \(-0.800897\pi\) | ||||
−0.810670 | + | 0.585504i | \(0.800897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.2288i | 0.668748i | 0.942440 | + | 0.334374i | \(0.108525\pi\) | ||||
−0.942440 | + | 0.334374i | \(0.891475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.48925i | − | 0.274385i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.8000 | − | 7.24854i | −0.540781 | − | 0.264856i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.2921 | 0.594507 | 0.297254 | − | 0.954799i | \(-0.403929\pi\) | ||||
0.297254 | + | 0.954799i | \(0.403929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.2436 | −0.591164 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.1660 | −1.49620 | −0.748102 | − | 0.663584i | \(-0.769035\pi\) | ||||
−0.748102 | + | 0.663584i | \(0.769035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.8173 | 1.91462 | 0.957312 | − | 0.289055i | \(-0.0933411\pi\) | ||||
0.957312 | + | 0.289055i | \(0.0933411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3157 | − | 25.1461i | 0.445857 | − | 0.910348i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 61.1660i | 2.20858i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.3449i | − | 0.913960i | −0.889477 | − | 0.456980i | \(-0.848931\pi\) | ||
0.889477 | − | 0.456980i | \(-0.151069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.20861 | 0.151373 | 0.0756867 | − | 0.997132i | \(-0.475885\pi\) | ||||
0.0756867 | + | 0.997132i | \(0.475885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 33.5633i | − | 1.20563i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.5830i | 0.952435i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.29150 | 0.0462136 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.64899i | − | 0.0588549i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.7424i | 0.917618i | 0.888535 | + | 0.458809i | \(0.151724\pi\) | ||||
−0.888535 | + | 0.458809i | \(0.848276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.979531 | − | 0.479741i | −0.0348281 | − | 0.0170576i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.3320 | −1.78734 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0295 | 0.426106 | 0.213053 | − | 0.977041i | \(-0.431659\pi\) | ||||
0.213053 | + | 0.977041i | \(0.431659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.66079 | 0.271019 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −53.3428 | −1.88243 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.29150 | + | 3.57113i | 0.256992 | + | 0.125866i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.3475i | 1.10212i | 0.834466 | + | 0.551059i | \(0.185776\pi\) | ||||
−0.834466 | + | 0.551059i | \(0.814224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.2835i | 1.09851i | 0.835654 | + | 0.549256i | \(0.185089\pi\) | ||||
−0.835654 | + | 0.549256i | \(0.814911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.14226 | −0.250182 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.14226i | 0.249876i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5524i | 0.472983i | 0.971634 | + | 0.236491i | \(0.0759975\pi\) | ||||
−0.971634 | + | 0.236491i | \(0.924003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4558 | 0.887335 | 0.443667 | − | 0.896191i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896191i | \(0.353677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.3542i | − | 0.429599i | −0.976658 | − | 0.214800i | \(-0.931090\pi\) | ||
0.976658 | − | 0.214800i | \(-0.0689099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.8751i | 1.07234i | 0.844111 | + | 0.536168i | \(0.180129\pi\) | ||||
−0.844111 | + | 0.536168i | \(0.819871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.61226 | − | 4.65489i | −0.125157 | − | 0.161282i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.9588 | −0.379244 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.3643 | −1.32448 | −0.662242 | − | 0.749290i | \(-0.730395\pi\) | ||||
−0.662242 | + | 0.749290i | \(0.730395\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1660 | −1.72986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.8000 | 0.509136 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.66667 | + | 5.44479i | −0.0916279 | + | 0.187085i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12.0000i | − | 0.411355i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.3040i | 0.934870i | 0.884028 | + | 0.467435i | \(0.154822\pi\) | ||||
−0.884028 | + | 0.467435i | \(0.845178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4331 | 0.390548 | 0.195274 | − | 0.980749i | \(-0.437440\pi\) | ||||
0.195274 | + | 0.980749i | \(0.437440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.4442i | − | 0.868146i | −0.900878 | − | 0.434073i | \(-0.857076\pi\) | ||
0.900878 | − | 0.434073i | \(-0.142924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.64575i | − | 0.124103i | −0.998073 | − | 0.0620514i | \(-0.980236\pi\) | ||
0.998073 | − | 0.0620514i | \(-0.0197643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.1255 | 0.344277 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.9352i | 1.04941i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 46.9252i | − | 1.59000i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.10132 | − | 18.5830i | 0.307681 | − | 0.628220i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.69934 | 0.158325 | 0.0791624 | − | 0.996862i | \(-0.474775\pi\) | ||||
0.0791624 | + | 0.996862i | \(0.474775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6078 | 0.962729 | 0.481364 | − | 0.876521i | \(-0.340141\pi\) | ||||
0.481364 | + | 0.876521i | \(0.340141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.3428 | −1.79108 | −0.895539 | − | 0.444984i | \(-0.853209\pi\) | ||||
−0.895539 | + | 0.444984i | \(0.853209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7085 | − | 42.2825i | 0.694541 | − | 1.41811i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.9293i | 0.934619i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.9399i | 0.532813i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −69.5864 | −2.32084 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.57113i | − | 0.118972i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.65489i | − | 0.154734i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9529 | −0.795343 | −0.397671 | − | 0.917528i | \(-0.630182\pi\) | ||||
−0.397671 | + | 0.917528i | \(0.630182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 23.6458i | − | 0.783419i | −0.920089 | − | 0.391709i | \(-0.871884\pi\) | ||
0.920089 | − | 0.391709i | \(-0.128116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 33.1811i | − | 1.09814i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.27980 | − | 4.65489i | 0.0752858 | − | 0.153718i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.8881 | −1.81059 | −0.905296 | − | 0.424781i | \(-0.860351\pi\) | ||||
−0.905296 | + | 0.424781i | \(0.860351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.95906 | −0.0644833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1255 | −0.464443 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.9964 | 1.47628 | 0.738142 | − | 0.674645i | \(-0.235703\pi\) | ||||
0.738142 | + | 0.674645i | \(0.235703\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9706 | − | 13.1694i | 0.556188 | − | 0.431609i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.58301i | 0.0844733i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.2415i | 1.44531i | 0.691210 | + | 0.722654i | \(0.257078\pi\) | ||||
−0.691210 | + | 0.722654i | \(0.742922\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.0467 | −1.63148 | −0.815739 | − | 0.578421i | \(-0.803669\pi\) | ||||
−0.815739 | + | 0.578421i | \(0.803669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31.5817i | − | 1.02844i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 10.2288i | − | 0.332390i | −0.986093 | − | 0.166195i | \(-0.946852\pi\) | ||
0.986093 | − | 0.166195i | \(-0.0531481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.9150 | 2.62661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.0436i | 0.811242i | 0.914041 | + | 0.405621i | \(0.132945\pi\) | ||||
−0.914041 | + | 0.405621i | \(0.867055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4810i | 0.695108i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.1412 | − | 10.3542i | −0.682686 | − | 0.334356i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1660 | −0.973097 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8712 | −0.414339 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.48528 | 0.272868 | 0.136434 | − | 0.990649i | \(-0.456436\pi\) | ||||
0.136434 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.1811 | 1.06483 | 0.532417 | − | 0.846482i | \(-0.321284\pi\) | ||||
0.532417 | + | 0.846482i | \(0.321284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.5830 | + | 14.9785i | 0.980446 | + | 0.480189i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60.6337i | − | 1.93984i | −0.243415 | − | 0.969922i | \(-0.578268\pi\) | ||
0.243415 | − | 0.969922i | \(-0.421732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 25.4442i | − | 0.813201i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0194 | 0.415256 | 0.207628 | − | 0.978208i | \(-0.433426\pi\) | ||||
0.207628 | + | 0.978208i | \(0.433426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.26512i | 0.135898i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 8.48528i | − | 0.269816i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.8881 | 1.74358 | 0.871789 | − | 0.489881i | \(-0.162960\pi\) | ||||
0.871789 | + | 0.489881i | \(0.162960\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.33202i | 0.200739i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.10132i | 0.288242i | 0.989560 | + | 0.144121i | \(0.0460354\pi\) | ||||
−0.989560 | + | 0.144121i | \(0.953965\pi\) | |||||||
\(998\) | 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.k.h.3905.7 | 16 | ||
3.2 | odd | 2 | inner | 4032.2.k.h.3905.11 | 16 | ||
4.3 | odd | 2 | inner | 4032.2.k.h.3905.6 | 16 | ||
7.6 | odd | 2 | inner | 4032.2.k.h.3905.12 | 16 | ||
8.3 | odd | 2 | 2016.2.k.b.1889.10 | yes | 16 | ||
8.5 | even | 2 | 2016.2.k.b.1889.11 | yes | 16 | ||
12.11 | even | 2 | inner | 4032.2.k.h.3905.10 | 16 | ||
21.20 | even | 2 | inner | 4032.2.k.h.3905.8 | 16 | ||
24.5 | odd | 2 | 2016.2.k.b.1889.7 | yes | 16 | ||
24.11 | even | 2 | 2016.2.k.b.1889.6 | yes | 16 | ||
28.27 | even | 2 | inner | 4032.2.k.h.3905.9 | 16 | ||
56.13 | odd | 2 | 2016.2.k.b.1889.8 | yes | 16 | ||
56.27 | even | 2 | 2016.2.k.b.1889.5 | ✓ | 16 | ||
84.83 | odd | 2 | inner | 4032.2.k.h.3905.5 | 16 | ||
168.83 | odd | 2 | 2016.2.k.b.1889.9 | yes | 16 | ||
168.125 | even | 2 | 2016.2.k.b.1889.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.k.b.1889.5 | ✓ | 16 | 56.27 | even | 2 | ||
2016.2.k.b.1889.6 | yes | 16 | 24.11 | even | 2 | ||
2016.2.k.b.1889.7 | yes | 16 | 24.5 | odd | 2 | ||
2016.2.k.b.1889.8 | yes | 16 | 56.13 | odd | 2 | ||
2016.2.k.b.1889.9 | yes | 16 | 168.83 | odd | 2 | ||
2016.2.k.b.1889.10 | yes | 16 | 8.3 | odd | 2 | ||
2016.2.k.b.1889.11 | yes | 16 | 8.5 | even | 2 | ||
2016.2.k.b.1889.12 | yes | 16 | 168.125 | even | 2 | ||
4032.2.k.h.3905.5 | 16 | 84.83 | odd | 2 | inner | ||
4032.2.k.h.3905.6 | 16 | 4.3 | odd | 2 | inner | ||
4032.2.k.h.3905.7 | 16 | 1.1 | even | 1 | trivial | ||
4032.2.k.h.3905.8 | 16 | 21.20 | even | 2 | inner | ||
4032.2.k.h.3905.9 | 16 | 28.27 | even | 2 | inner | ||
4032.2.k.h.3905.10 | 16 | 12.11 | even | 2 | inner | ||
4032.2.k.h.3905.11 | 16 | 3.2 | odd | 2 | inner | ||
4032.2.k.h.3905.12 | 16 | 7.6 | odd | 2 | inner |