Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4608,2,Mod(2305,4608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4608.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.d (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: | \(36.7950652514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2305.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4608.2305 |
Dual form | 4608.2.d.o.2305.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(3583\) | \(4097\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.585786i | 0.261972i | 0.991384 | + | 0.130986i | \(0.0418142\pi\) | ||||
−0.991384 | + | 0.130986i | \(0.958186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41421 | 1.29045 | 0.645226 | − | 0.763992i | \(-0.276763\pi\) | ||||
0.645226 | + | 0.763992i | \(0.276763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.00000i | − 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685i | 1.29777i | 0.760886 | + | 0.648886i | \(0.224765\pi\) | ||||
−0.760886 | + | 0.648886i | \(0.775235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.17157 | −0.244290 | −0.122145 | − | 0.992512i | \(-0.538977\pi\) | ||||
−0.122145 | + | 0.992512i | \(0.538977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685 | 0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.585786i | − 0.108778i | −0.998520 | − | 0.0543889i | \(-0.982679\pi\) | ||||
0.998520 | − | 0.0543889i | \(-0.0173211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58579 | −0.823632 | −0.411816 | − | 0.911267i | \(-0.635105\pi\) | ||||
−0.411816 | + | 0.911267i | \(0.635105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000i | 0.338062i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.65685i | 1.58758i | 0.608194 | + | 0.793789i | \(0.291894\pi\) | ||||
−0.608194 | + | 0.793789i | \(0.708106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.6569 | −1.82049 | −0.910247 | − | 0.414065i | \(-0.864109\pi\) | ||||
−0.910247 | + | 0.414065i | \(0.864109\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685i | 0.252668i | 0.991988 | + | 0.126334i | \(0.0403211\pi\) | ||||
−0.991988 | + | 0.126334i | \(0.959679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4853 | 1.82117 | 0.910583 | − | 0.413327i | \(-0.135633\pi\) | ||||
0.910583 | + | 0.413327i | \(0.135633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.8995i | 1.63452i | 0.576268 | + | 0.817261i | \(0.304508\pi\) | ||||
−0.576268 | + | 0.817261i | \(0.695492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.17157 | 0.157975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.65685i | − 1.23643i | −0.786008 | − | 0.618217i | \(-0.787855\pi\) | ||||
0.786008 | − | 0.618217i | \(-0.212145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.65685 | −0.205507 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.17157 | −1.08847 | −0.544233 | − | 0.838934i | \(-0.683179\pi\) | ||||
−0.544233 | + | 0.838934i | \(0.683179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.65685 | 0.193920 | 0.0969601 | − | 0.995288i | \(-0.469088\pi\) | ||||
0.0969601 | + | 0.995288i | \(0.469088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.82843i | − 0.778171i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.75736 | −0.647754 | −0.323877 | − | 0.946099i | \(-0.604986\pi\) | ||||
−0.323877 | + | 0.946099i | \(0.604986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.31371i | 1.02231i | 0.859488 | + | 0.511156i | \(0.170783\pi\) | ||||
−0.859488 | + | 0.511156i | \(0.829217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.14214i | − 0.232347i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.65685i | 1.01231i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.31371 | −0.339979 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3137 | 1.35180 | 0.675901 | − | 0.736992i | \(-0.263755\pi\) | ||||
0.675901 | + | 0.736992i | \(0.263755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.5563i | − 1.74692i | −0.486894 | − | 0.873461i | \(-0.661870\pi\) | ||||
0.486894 | − | 0.873461i | \(-0.338130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.07107 | 0.893799 | 0.446899 | − | 0.894584i | \(-0.352528\pi\) | ||||
0.446899 | + | 0.894584i | \(0.352528\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3137i | 1.48043i | 0.672369 | + | 0.740216i | \(0.265277\pi\) | ||||
−0.672369 | + | 0.740216i | \(0.734723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.1716i | − 1.26161i | −0.775942 | − | 0.630804i | \(-0.782725\pi\) | ||||
0.775942 | − | 0.630804i | \(-0.217275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.686292i | − 0.0639970i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4853 | −1.14452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.72792 | −0.597007 | −0.298503 | − | 0.954409i | \(-0.596487\pi\) | ||||
−0.298503 | + | 0.954409i | \(0.596487\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.00000i | − 0.349482i | −0.984614 | − | 0.174741i | \(-0.944091\pi\) | ||||
0.984614 | − | 0.174741i | \(-0.0559088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3137i | 1.67471i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.34315 | 0.371060 | 0.185530 | − | 0.982639i | \(-0.440600\pi\) | ||||
0.185530 | + | 0.982639i | \(0.440600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3137i | 1.63817i | 0.573674 | + | 0.819084i | \(0.305518\pi\) | ||||
−0.573674 | + | 0.819084i | \(0.694482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.343146 | 0.0284967 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.2426i | 1.16680i | 0.812184 | + | 0.583401i | \(0.198278\pi\) | ||||
−0.812184 | + | 0.583401i | \(0.801722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.58579 | 0.373186 | 0.186593 | − | 0.982437i | \(-0.440255\pi\) | ||||
0.186593 | + | 0.982437i | \(0.440255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.68629i | − 0.215768i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 20.0000i | − 1.59617i | −0.602542 | − | 0.798087i | \(-0.705846\pi\) | ||||
0.602542 | − | 0.798087i | \(-0.294154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.34315i | − 0.496834i | −0.968653 | − | 0.248417i | \(-0.920090\pi\) | ||||
0.968653 | − | 0.248417i | \(-0.0799102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.6569 | 1.67586 | 0.837929 | − | 0.545779i | \(-0.183766\pi\) | ||||
0.837929 | + | 0.545779i | \(0.183766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18.7279i | − 1.42386i | −0.702252 | − | 0.711929i | \(-0.747822\pi\) | ||||
0.702252 | − | 0.711929i | \(-0.252178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.8995 | 1.20189 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.00000i | − 0.298974i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) | ||||
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.48528i | − 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.65685 | −0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.31371i | 0.534831i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.6569 | −1.55889 | −0.779447 | − | 0.626468i | \(-0.784500\pi\) | ||||
−0.779447 | + | 0.626468i | \(0.784500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.92893i | 0.208678i | 0.994542 | + | 0.104339i | \(0.0332727\pi\) | ||||
−0.994542 | + | 0.104339i | \(0.966727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5563 | −0.960984 | −0.480492 | − | 0.876999i | \(-0.659542\pi\) | ||||
−0.480492 | + | 0.876999i | \(0.659542\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.00000i | − 0.140372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 6.82843i | − 0.476918i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3137 | 0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3137i | 1.32961i | 0.747017 | + | 0.664805i | \(0.231485\pi\) | ||||
−0.747017 | + | 0.664805i | \(0.768515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.970563 | −0.0661918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.6569 | −1.06286 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 10.3431i | − 0.695755i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.89949 | −0.528989 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.3137i | 1.94562i | 0.231606 | + | 0.972810i | \(0.425602\pi\) | ||||
−0.231606 | + | 0.972810i | \(0.574398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4853i | 1.08938i | 0.838638 | + | 0.544689i | \(0.183352\pi\) | ||||
−0.838638 | + | 0.544689i | \(0.816648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.31371 | 0.610161 | 0.305081 | − | 0.952327i | \(-0.401317\pi\) | ||||
0.305081 | + | 0.952327i | \(0.401317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.31371i | 0.477094i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6569 | −1.13738 | −0.568689 | − | 0.822553i | \(-0.692549\pi\) | ||||
−0.568689 | + | 0.822553i | \(0.692549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.72792i | 0.174281i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0000 | −1.01806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0000i | 1.38863i | 0.719672 | + | 0.694314i | \(0.244292\pi\) | ||||
−0.719672 | + | 0.694314i | \(0.755708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.34315i | 0.147312i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.31371 | 0.0819469 | 0.0409734 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409734 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.9706i | 2.04869i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6569 | 0.842118 | 0.421059 | − | 0.907033i | \(-0.361659\pi\) | ||||
0.421059 | + | 0.907033i | \(0.361659\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.97056 | −0.428198 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.24264i | 0.380621i | 0.981724 | + | 0.190310i | \(0.0609494\pi\) | ||||
−0.981724 | + | 0.190310i | \(0.939051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4142 | 1.17933 | 0.589665 | − | 0.807648i | \(-0.299260\pi\) | ||||
0.589665 | + | 0.807648i | \(0.299260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 9.31371i | − 0.561638i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.51472i | 0.451516i | 0.974183 | + | 0.225758i | \(0.0724858\pi\) | ||||
−0.974183 | + | 0.225758i | \(0.927514\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3137i | 0.910305i | 0.890413 | + | 0.455153i | \(0.150415\pi\) | ||||
−0.890413 | + | 0.455153i | \(0.849585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −39.7990 | −2.34926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.8995i | 1.62991i | 0.579527 | + | 0.814953i | \(0.303237\pi\) | ||||
−0.579527 | + | 0.814953i | \(0.696763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.34315 | −0.136423 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.31371i | − 0.191637i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65685i | 0.326056i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.65685 | 0.323911 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000i | 0.913168i | 0.889680 | + | 0.456584i | \(0.150927\pi\) | ||||
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9706 | −0.959233 | −0.479616 | − | 0.877478i | \(-0.659224\pi\) | ||||
−0.479616 | + | 0.877478i | \(0.659224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5.07107i | − 0.284820i | −0.989808 | − | 0.142410i | \(-0.954515\pi\) | ||||
0.989808 | − | 0.142410i | \(-0.0454851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17157 | −0.0655955 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 20.6863i | − 1.15102i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.1716i | 0.730627i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.6274 | 2.35013 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.68629 | −0.256039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9706 | 1.14234 | 0.571170 | − | 0.820832i | \(-0.306490\pi\) | ||||
0.571170 | + | 0.820832i | \(0.306490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.17157i | 0.496669i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 25.3137i | − 1.35891i | −0.733717 | − | 0.679456i | \(-0.762216\pi\) | ||||
0.733717 | − | 0.679456i | \(-0.237784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 0.686292i | − 0.0367363i | −0.999831 | − | 0.0183682i | \(-0.994153\pi\) | ||||
0.999831 | − | 0.0183682i | \(-0.00584710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3137 | 0.708617 | 0.354309 | − | 0.935129i | \(-0.384716\pi\) | ||||
0.354309 | + | 0.935129i | \(0.384716\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.37258i | − 0.285147i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7990 | 0.833839 | 0.416919 | − | 0.908943i | \(-0.363110\pi\) | ||||
0.416919 | + | 0.908943i | \(0.363110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.970563i | 0.0508016i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7279 | 1.18639 | 0.593194 | − | 0.805060i | \(-0.297867\pi\) | ||||
0.593194 | + | 0.805060i | \(0.297867\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.6274i | 2.10927i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2843i | 1.25739i | 0.777651 | + | 0.628696i | \(0.216411\pi\) | ||||
−0.777651 | + | 0.628696i | \(0.783589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65685 | 0.0853323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 18.3431i | − 0.942224i | −0.882073 | − | 0.471112i | \(-0.843853\pi\) | ||||
0.882073 | − | 0.471112i | \(-0.156147\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3137 | −0.986884 | −0.493442 | − | 0.869779i | \(-0.664262\pi\) | ||||
−0.493442 | + | 0.869779i | \(0.664262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 22.2426i | − 1.12775i | −0.825861 | − | 0.563873i | \(-0.809311\pi\) | ||||
0.825861 | − | 0.563873i | \(-0.190689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.28427 | 0.216665 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3.37258i | − 0.169693i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.00000i | − 0.200754i | −0.994949 | − | 0.100377i | \(-0.967995\pi\) | ||||
0.994949 | − | 0.100377i | \(-0.0320049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.6569 | 1.58087 | 0.790434 | − | 0.612547i | \(-0.209855\pi\) | ||||
0.790434 | + | 0.612547i | \(0.209855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 12.9706i | − 0.646110i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.3137 | 0.957345 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.31371 | −0.0649587 | −0.0324794 | − | 0.999472i | \(-0.510340\pi\) | ||||
−0.0324794 | + | 0.999472i | \(0.510340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.6569i | 0.672010i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.45584 | −0.267817 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.31371i | − 0.0641789i | −0.999485 | − | 0.0320894i | \(-0.989784\pi\) | ||||
0.999485 | − | 0.0320894i | \(-0.0102161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 22.1421i | − 1.07914i | −0.841940 | − | 0.539571i | \(-0.818587\pi\) | ||||
0.841940 | − | 0.539571i | \(-0.181413\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.0294 | −0.826049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 32.9706i | − 1.59556i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.1127 | 1.69132 | 0.845660 | − | 0.533723i | \(-0.179207\pi\) | ||||
0.845660 | + | 0.533723i | \(0.179207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6274 | −0.799063 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.62742i | − 0.317032i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.8995 | −0.758841 | −0.379421 | − | 0.925224i | \(-0.623877\pi\) | ||||
−0.379421 | + | 0.925224i | \(0.623877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9411i | 1.32752i | 0.747944 | + | 0.663761i | \(0.231041\pi\) | ||||
−0.747944 | + | 0.663761i | \(0.768959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.17157i | 0.0555379i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.65685 | 0.361349 | 0.180675 | − | 0.983543i | \(-0.442172\pi\) | ||||
0.180675 | + | 0.983543i | \(0.442172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.3137i | 1.09780i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3137 | 0.809901 | 0.404951 | − | 0.914339i | \(-0.367289\pi\) | ||||
0.404951 | + | 0.914339i | \(0.367289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.9289i | 0.509011i | 0.967071 | + | 0.254506i | \(0.0819127\pi\) | ||||
−0.967071 | + | 0.254506i | \(0.918087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.44365 | −0.113566 | −0.0567830 | − | 0.998387i | \(-0.518084\pi\) | ||||
−0.0567830 | + | 0.998387i | \(0.518084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 9.31371i | − 0.430987i | −0.976505 | − | 0.215494i | \(-0.930864\pi\) | ||||
0.976505 | − | 0.215494i | \(-0.0691360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.3137i | 1.26123i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.31371 | 0.152364 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.3431i | 1.20871i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.48528 | −0.204938 | −0.102469 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102469 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.3137 | −1.24540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.79899i | 0.354134i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.55635 | −0.251782 | −0.125891 | − | 0.992044i | \(-0.540179\pi\) | ||||
−0.125891 | + | 0.992044i | \(0.540179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.686292i | 0.0309719i | 0.999880 | + | 0.0154860i | \(0.00492953\pi\) | ||||
−0.999880 | + | 0.0154860i | \(0.995070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.14214i | 0.0964769i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.3137 | −1.40461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 23.3137i | − 1.04366i | −0.853048 | − | 0.521832i | \(-0.825249\pi\) | ||||
0.853048 | − | 0.521832i | \(-0.174751\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.48528 | 0.199989 | 0.0999944 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999944 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2843 | 0.457644 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 23.2132i | − 1.02891i | −0.857518 | − | 0.514454i | \(-0.827995\pi\) | ||||
0.857518 | − | 0.514454i | \(-0.172005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.65685 | 0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.31371i | 0.234150i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 24.9706i | − 1.09820i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9706 | −0.480629 | −0.240315 | − | 0.970695i | \(-0.577251\pi\) | ||||
−0.240315 | + | 0.970695i | \(0.577251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.3431i | 1.15191i | 0.817483 | + | 0.575953i | \(0.195369\pi\) | ||||
−0.817483 | + | 0.575953i | \(0.804631\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.7696 | 0.730493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 32.9706i | − 1.42811i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.97056 | −0.387831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 9.31371i | − 0.401170i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 5.17157i | − 0.222343i | −0.993801 | − | 0.111172i | \(-0.964540\pi\) | ||||
0.993801 | − | 0.111172i | \(-0.0354603\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.71573 | 0.330506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.9706i | − 1.23869i | −0.785118 | − | 0.619346i | \(-0.787398\pi\) | ||||
0.785118 | − | 0.619346i | \(-0.212602\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.31371 | 0.141169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6569 | −0.835894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0711i | 0.553839i | 0.960893 | + | 0.276919i | \(0.0893135\pi\) | ||||
−0.960893 | + | 0.276919i | \(0.910686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.68629 | −0.198209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 28.6274i | − 1.20650i | −0.797551 | − | 0.603251i | \(-0.793872\pi\) | ||||
0.797551 | − | 0.603251i | \(-0.206128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3.51472i | − 0.147865i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9706 | 0.795287 | 0.397644 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397644 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 20.0000i | − 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.45584 | −0.227524 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2843 | 1.17749 | 0.588745 | − | 0.808319i | \(-0.299622\pi\) | ||||
0.588745 | + | 0.808319i | \(0.299622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7990i | 1.31924i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7990 | 0.985653 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.68629i | 0.358522i | 0.983802 | + | 0.179261i | \(0.0573706\pi\) | ||||
−0.983802 | + | 0.179261i | \(0.942629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 25.9411i | − 1.06889i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7.31371i | − 0.299833i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.4853 | −1.16388 | −0.581939 | − | 0.813233i | \(-0.697706\pi\) | ||||
−0.581939 | + | 0.813233i | \(0.697706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.65685 | −0.230748 | −0.115374 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115374 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.10051i | 0.166709i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8995 | 0.645341 | 0.322670 | − | 0.946511i | \(-0.395419\pi\) | ||||
0.322670 | + | 0.946511i | \(0.395419\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.3137i | 1.42864i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 34.6274i | − 1.39859i | −0.714834 | − | 0.699294i | \(-0.753498\pi\) | ||||
0.714834 | − | 0.699294i | \(-0.246502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.9411 | −1.76900 | −0.884502 | − | 0.466537i | \(-0.845501\pi\) | ||||
−0.884502 | + | 0.466537i | \(0.845501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.82843 | 0.273575 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 35.3137i | − 1.40805i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0711 | 1.31654 | 0.658269 | − | 0.752783i | \(-0.271289\pi\) | ||||
0.658269 | + | 0.752783i | \(0.271289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 3.94113i | − 0.156399i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.1716i | 0.521877i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9706 | −1.69724 | −0.848618 | − | 0.529007i | \(-0.822565\pi\) | ||||
−0.848618 | + | 0.529007i | \(0.822565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 24.2843i | − 0.957678i | −0.877903 | − | 0.478839i | \(-0.841058\pi\) | ||||
0.877903 | − | 0.478839i | \(-0.158942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.1716 | 0.675084 | 0.337542 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337542 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 23.4142i | − 0.916269i | −0.888883 | − | 0.458134i | \(-0.848518\pi\) | ||||
0.888883 | − | 0.458134i | \(-0.151482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.34315 | 0.0915543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 16.6863i | − 0.650006i | −0.945713 | − | 0.325003i | \(-0.894635\pi\) | ||||
0.945713 | − | 0.325003i | \(-0.105365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 16.6863i | − 0.649022i | −0.945882 | − | 0.324511i | \(-0.894800\pi\) | ||||
0.945882 | − | 0.324511i | \(-0.105200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | −0.438727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.686292i | 0.0265733i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.3137 | −0.745597 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6274 | 1.41188 | 0.705942 | − | 0.708270i | \(-0.250524\pi\) | ||||
0.705942 | + | 0.708270i | \(0.250524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.21320i | 0.277226i | 0.990347 | + | 0.138613i | \(0.0442644\pi\) | ||||
−0.990347 | + | 0.138613i | \(0.955736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.4558 | 1.74444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.3137i | 0.968602i | 0.874901 | + | 0.484301i | \(0.160926\pi\) | ||||
−0.874901 | + | 0.484301i | \(0.839074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.54416i | 0.0972072i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.6569 | −1.28222 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6569i | 0.671698i | 0.941916 | + | 0.335849i | \(0.109023\pi\) | ||||
−0.941916 | + | 0.335849i | \(0.890977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3137 | −0.429153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.6274 | 1.61463 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 7.41421i | − 0.280031i | −0.990149 | − | 0.140015i | \(-0.955285\pi\) | ||||
0.990149 | − | 0.140015i | \(-0.0447152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.6274 | −2.06031 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 59.9411i | − 2.25432i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 31.1127i | − 1.16846i | −0.811587 | − | 0.584231i | \(-0.801396\pi\) | ||||
0.811587 | − | 0.584231i | \(-0.198604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.37258 | 0.201205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.31371i | 0.123926i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.1716 | 0.938741 | 0.469371 | − | 0.883001i | \(-0.344481\pi\) | ||||
0.469371 | + | 0.883001i | \(0.344481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.9706 | 1.15340 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.72792i | − 0.101312i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7574 | −0.510232 | −0.255116 | − | 0.966910i | \(-0.582114\pi\) | ||||
−0.255116 | + | 0.966910i | \(0.582114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 6.05887i | − 0.224096i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.4853i | 1.49536i | 0.664060 | + | 0.747679i | \(0.268832\pi\) | ||||
−0.664060 | + | 0.747679i | \(0.731168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 34.6274i | − 1.27379i | −0.770951 | − | 0.636895i | \(-0.780218\pi\) | ||||
0.770951 | − | 0.636895i | \(-0.219782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0000 | −1.46746 | −0.733729 | − | 0.679442i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.34315 | −0.305669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.2843i | 1.91043i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.7279 | −1.12128 | −0.560639 | − | 0.828060i | \(-0.689444\pi\) | ||||
−0.560639 | + | 0.828060i | \(0.689444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.68629i | 0.0977642i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 15.5147i | − 0.563892i | −0.959430 | − | 0.281946i | \(-0.909020\pi\) | ||||
0.959430 | − | 0.281946i | \(-0.0909799\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3431 | 0.882438 | 0.441219 | − | 0.897399i | \(-0.354546\pi\) | ||||
0.441219 | + | 0.897399i | \(0.354546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 44.9706i | − 1.62804i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3137 | −0.408514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6569 | −0.492479 | −0.246239 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246239 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7279i | 0.673597i | 0.941577 | + | 0.336798i | \(0.109344\pi\) | ||||
−0.941577 | + | 0.336798i | \(0.890656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3553 | −0.767106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 65.9411i | − 2.36259i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.3431i | 0.656369i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.7157 | 0.418152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 10.3431i | − 0.368693i | −0.982861 | − | 0.184347i | \(-0.940983\pi\) | ||||
0.982861 | − | 0.184347i | \(-0.0590169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.4853 | −0.728373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.3137 | 0.969938 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 32.5858i | − 1.15425i | −0.816657 | − | 0.577124i | \(-0.804175\pi\) | ||||
0.816657 | − | 0.577124i | \(-0.195825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.6569 | −1.61522 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.31371i | − 0.116938i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.34315i | − 0.0825850i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.9706 | −1.37013 | −0.685066 | − | 0.728481i | \(-0.740227\pi\) | ||||
−0.685066 | + | 0.728481i | \(0.740227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 29.6569i | − 1.04139i | −0.853742 | − | 0.520697i | \(-0.825672\pi\) | ||||
0.853742 | − | 0.520697i | \(-0.174328\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.71573 | 0.130156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 44.8701i | − 1.56598i | −0.622037 | − | 0.782988i | \(-0.713695\pi\) | ||||
0.622037 | − | 0.782988i | \(-0.286305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.21320 | −0.112005 | −0.0560026 | − | 0.998431i | \(-0.517836\pi\) | ||||
−0.0560026 | + | 0.998431i | \(0.517836\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 37.9411i | − 1.31934i | −0.751554 | − | 0.659671i | \(-0.770696\pi\) | ||||
0.751554 | − | 0.659671i | \(-0.229304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7696i | 0.721356i | 0.932690 | + | 0.360678i | \(0.117455\pi\) | ||||
−0.932690 | + | 0.360678i | \(0.882545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.0294 | −0.590035 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6863i | 0.439027i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.5147 | −0.397532 | −0.198766 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6569 | 0.988167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.92893i | 0.100758i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.8995 | 0.821196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 11.3137i | − 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6274i | 0.363876i | 0.983310 | + | 0.181938i | \(0.0582370\pi\) | ||||
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.5980 | −1.28432 | −0.642161 | − | 0.766570i | \(-0.721962\pi\) | ||||
−0.642161 | + | 0.766570i | \(0.721962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0294i | 0.376320i | 0.982138 | + | 0.188160i | \(0.0602523\pi\) | ||||
−0.982138 | + | 0.188160i | \(0.939748\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.9706 | 1.66698 | 0.833489 | − | 0.552537i | \(-0.186340\pi\) | ||||
0.833489 | + | 0.552537i | \(0.186340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9706 | 0.373010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5147i | 0.390610i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6274 | −0.766701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.3137i | 0.652923i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 0.686292i | − 0.0231744i | −0.999933 | − | 0.0115872i | \(-0.996312\pi\) | ||||
0.999933 | − | 0.0115872i | \(-0.00368841\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.6863 | −0.764321 | −0.382160 | − | 0.924096i | \(-0.624820\pi\) | ||||
−0.382160 | + | 0.924096i | \(0.624820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 41.6569i | − 1.40186i | −0.713228 | − | 0.700932i | \(-0.752767\pi\) | ||||
0.713228 | − | 0.700932i | \(-0.247233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3431 | 0.615903 | 0.307951 | − | 0.951402i | \(-0.400357\pi\) | ||||
0.307951 | + | 0.951402i | \(0.400357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.9706 | −0.770408 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.6274i | 2.36346i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.34315 | 0.0783227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.68629i | 0.0895928i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 43.5147i | − 1.44969i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.97056 | 0.165227 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 27.5980i | − 0.916376i | −0.888855 | − | 0.458188i | \(-0.848499\pi\) | ||||
0.888855 | − | 0.458188i | \(-0.151501\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.3137 | 1.70010 | 0.850050 | − | 0.526703i | \(-0.176572\pi\) | ||||
0.850050 | + | 0.526703i | \(0.176572\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.6274 | 0.616478 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 13.6569i | − 0.450989i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.3553 | 1.76003 | 0.880015 | − | 0.474946i | \(-0.157532\pi\) | ||||
0.880015 | + | 0.474946i | \(0.157532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 25.9411i | − 0.853863i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.9706i | 1.47862i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.5980 | 1.62726 | 0.813628 | − | 0.581385i | \(-0.197489\pi\) | ||||
0.813628 | + | 0.581385i | \(0.197489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.3431i | 0.863362i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.28427 | −0.140111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.62742 | 0.281845 | 0.140923 | − | 0.990021i | \(-0.454993\pi\) | ||||
0.140923 | + | 0.990021i | \(0.454993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 16.3848i | − 0.534128i | −0.963679 | − | 0.267064i | \(-0.913946\pi\) | ||||
0.963679 | − | 0.267064i | \(-0.0860536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6569 | 0.444728 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.6274i | 0.345345i | 0.984979 | + | 0.172672i | \(0.0552402\pi\) | ||||
−0.984979 | + | 0.172672i | \(0.944760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.68629i | 0.152123i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.97056 | −0.0962260 | −0.0481130 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481130 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9.94113i | − 0.321687i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.8284 | 0.478835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.97056 | −0.321631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 12.6863i | − 0.408386i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2426 | 0.329381 | 0.164691 | − | 0.986345i | \(-0.447337\pi\) | ||||
0.164691 | + | 0.986345i | \(0.447337\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 6.68629i | − 0.214573i | −0.994228 | − | 0.107287i | \(-0.965784\pi\) | ||||
0.994228 | − | 0.107287i | \(-0.0342163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 65.9411i | 2.11398i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.2843 | −0.840908 | −0.420454 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420454 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.00000i | − 0.127841i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.2843 | −1.66761 | −0.833805 | − | 0.552060i | \(-0.813842\pi\) | ||||
−0.833805 | + | 0.552060i | \(0.813842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.71573 | −0.0546677 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.94113i | − 0.0617242i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.89949 | 0.250936 | 0.125468 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125468 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 7.94113i | − 0.251751i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9706i | 0.664144i | 0.943254 | + | 0.332072i | \(0.107748\pi\) | ||||
−0.943254 | + | 0.332072i | \(0.892252\pi\) | |||||||
\(998\) | 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 | 4608.2.d.o.2305.3 | 4 | ||
3.2 | odd | 2 | 1536.2.d.f.769.2 | 4 | |||
4.3 | odd | 2 | 4608.2.d.c.2305.3 | 4 | |||
8.3 | odd | 2 | 4608.2.d.c.2305.2 | 4 | |||
8.5 | even | 2 | inner | 4608.2.d.o.2305.2 | 4 | ||
12.11 | even | 2 | 1536.2.d.a.769.4 | 4 | |||
16.3 | odd | 4 | 4608.2.a.r.1.1 | 2 | |||
16.5 | even | 4 | 4608.2.a.a.1.2 | 2 | |||
16.11 | odd | 4 | 4608.2.a.e.1.2 | 2 | |||
16.13 | even | 4 | 4608.2.a.n.1.1 | 2 | |||
24.5 | odd | 2 | 1536.2.d.f.769.3 | 4 | |||
24.11 | even | 2 | 1536.2.d.a.769.1 | 4 | |||
48.5 | odd | 4 | 1536.2.a.e.1.1 | yes | 2 | ||
48.11 | even | 4 | 1536.2.a.l.1.1 | yes | 2 | ||
48.29 | odd | 4 | 1536.2.a.g.1.2 | yes | 2 | ||
48.35 | even | 4 | 1536.2.a.b.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.b.1.2 | ✓ | 2 | 48.35 | even | 4 | ||
1536.2.a.e.1.1 | yes | 2 | 48.5 | odd | 4 | ||
1536.2.a.g.1.2 | yes | 2 | 48.29 | odd | 4 | ||
1536.2.a.l.1.1 | yes | 2 | 48.11 | even | 4 | ||
1536.2.d.a.769.1 | 4 | 24.11 | even | 2 | |||
1536.2.d.a.769.4 | 4 | 12.11 | even | 2 | |||
1536.2.d.f.769.2 | 4 | 3.2 | odd | 2 | |||
1536.2.d.f.769.3 | 4 | 24.5 | odd | 2 | |||
4608.2.a.a.1.2 | 2 | 16.5 | even | 4 | |||
4608.2.a.e.1.2 | 2 | 16.11 | odd | 4 | |||
4608.2.a.n.1.1 | 2 | 16.13 | even | 4 | |||
4608.2.a.r.1.1 | 2 | 16.3 | odd | 4 | |||
4608.2.d.c.2305.2 | 4 | 8.3 | odd | 2 | |||
4608.2.d.c.2305.3 | 4 | 4.3 | odd | 2 | |||
4608.2.d.o.2305.2 | 4 | 8.5 | even | 2 | inner | ||
4608.2.d.o.2305.3 | 4 | 1.1 | even | 1 | trivial |