Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.16 | ||
Root | \(0.725842 + 1.21374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.e.3025.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.06888i | 1.37244i | 0.727392 | + | 0.686222i | \(0.240732\pi\) | ||||
−0.727392 | + | 0.686222i | \(0.759268\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.80820i | 1.75124i | 0.483001 | + | 0.875620i | \(0.339547\pi\) | ||||
−0.483001 | + | 0.875620i | \(0.660453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.52392i | 0.977359i | 0.872463 | + | 0.488680i | \(0.162521\pi\) | ||||
−0.872463 | + | 0.488680i | \(0.837479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.79736 | 1.64860 | 0.824301 | − | 0.566151i | \(-0.191568\pi\) | ||||
0.824301 | + | 0.566151i | \(0.191568\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.28617i | 1.21273i | 0.795186 | + | 0.606365i | \(0.207373\pi\) | ||||
−0.795186 | + | 0.606365i | \(0.792627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65085 | −1.17828 | −0.589141 | − | 0.808030i | \(-0.700534\pi\) | ||||
−0.589141 | + | 0.808030i | \(0.700534\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41801 | −0.883601 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.21394i | 0.225422i | 0.993628 | + | 0.112711i | \(0.0359534\pi\) | ||||
−0.993628 | + | 0.112711i | \(0.964047\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.107385 | −0.0192868 | −0.00964342 | − | 0.999954i | \(-0.503070\pi\) | ||||
−0.00964342 | + | 0.999954i | \(0.503070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.06888i | 0.518735i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.90235i | 0.805942i | 0.915213 | + | 0.402971i | \(0.132022\pi\) | ||||
−0.915213 | + | 0.402971i | \(0.867978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6855 | 1.82497 | 0.912485 | − | 0.409111i | \(-0.134161\pi\) | ||||
0.912485 | + | 0.409111i | \(0.134161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.85684i | − 0.283165i | −0.989926 | − | 0.141583i | \(-0.954781\pi\) | ||||
0.989926 | − | 0.141583i | \(-0.0452191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.76459 | 0.986717 | 0.493359 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493359 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4861i | 1.57773i | 0.614566 | + | 0.788865i | \(0.289331\pi\) | ||||
−0.614566 | + | 0.788865i | \(0.710669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.8247 | −2.40348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.85494i | 1.02263i | 0.859394 | + | 0.511313i | \(0.170841\pi\) | ||||
−0.859394 | + | 0.511313i | \(0.829159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 12.0556i | − 1.54356i | −0.635890 | − | 0.771779i | \(-0.719367\pi\) | ||||
0.635890 | − | 0.771779i | \(-0.280633\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.8145 | −1.34137 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.66942i | − 0.814800i | −0.913250 | − | 0.407400i | \(-0.866436\pi\) | ||||
0.913250 | − | 0.407400i | \(-0.133564\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.98478 | 0.235550 | 0.117775 | − | 0.993040i | \(-0.462424\pi\) | ||||
0.117775 | + | 0.993040i | \(0.462424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.52879 | −0.764137 | −0.382068 | − | 0.924134i | \(-0.624788\pi\) | ||||
−0.382068 | + | 0.924134i | \(0.624788\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.80820i | 0.661906i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.30741 | −0.259604 | −0.129802 | − | 0.991540i | \(-0.541434\pi\) | ||||
−0.129802 | + | 0.991540i | \(0.541434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.5795i | − 1.38078i | −0.723436 | − | 0.690391i | \(-0.757438\pi\) | ||||
0.723436 | − | 0.690391i | \(-0.242562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.8603i | 2.26261i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.79151 | 0.825898 | 0.412949 | − | 0.910754i | \(-0.364499\pi\) | ||||
0.412949 | + | 0.910754i | \(0.364499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.52392i | 0.369407i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.2226 | −1.66440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05981 | 0.412212 | 0.206106 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206106 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.3336i | − 1.02823i | −0.857721 | − | 0.514116i | \(-0.828120\pi\) | ||||
0.857721 | − | 0.514116i | \(-0.171880\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94679 | −0.881554 | −0.440777 | − | 0.897617i | \(-0.645297\pi\) | ||||
−0.440777 | + | 0.897617i | \(0.645297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 17.8845i | − 1.72896i | −0.502669 | − | 0.864479i | \(-0.667649\pi\) | ||||
0.502669 | − | 0.864479i | \(-0.332351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9610i | 1.14566i | 0.819676 | + | 0.572828i | \(0.194154\pi\) | ||||
−0.819676 | + | 0.572828i | \(0.805846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3192 | 1.25297 | 0.626484 | − | 0.779434i | \(-0.284493\pi\) | ||||
0.626484 | + | 0.779434i | \(0.284493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 17.3417i | − 1.61713i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.79736 | 0.623113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −22.7352 | −2.06684 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.78606i | 0.159750i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.42140 | 0.658543 | 0.329271 | − | 0.944235i | \(-0.393197\pi\) | ||||
0.329271 | + | 0.944235i | \(0.393197\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 4.82695i | − 0.421733i | −0.977515 | − | 0.210866i | \(-0.932372\pi\) | ||||
0.977515 | − | 0.210866i | \(-0.0676285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.28617i | 0.458369i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.8496 | 1.26868 | 0.634342 | − | 0.773052i | \(-0.281271\pi\) | ||||
0.634342 | + | 0.773052i | \(0.281271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.99694i | − 0.423835i | −0.977288 | − | 0.211918i | \(-0.932029\pi\) | ||||
0.977288 | − | 0.211918i | \(-0.0679708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.4676 | −1.71159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.72542 | −0.309379 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 9.54688i | − 0.782111i | −0.920367 | − | 0.391055i | \(-0.872110\pi\) | ||||
0.920367 | − | 0.391055i | \(-0.127890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4778 | 0.934052 | 0.467026 | − | 0.884244i | \(-0.345325\pi\) | ||||
0.467026 | + | 0.884244i | \(0.345325\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.329550i | − 0.0264701i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.38325i | − 0.110396i | −0.998475 | − | 0.0551979i | \(-0.982421\pi\) | ||||
0.998475 | − | 0.0551979i | \(-0.0175790\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65085 | −0.445349 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.0101i | − 0.784050i | −0.919955 | − | 0.392025i | \(-0.871775\pi\) | ||||
0.919955 | − | 0.392025i | \(-0.128225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.63373 | 0.126422 | 0.0632110 | − | 0.998000i | \(-0.479866\pi\) | ||||
0.0632110 | + | 0.998000i | \(0.479866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.581993 | 0.0447687 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.93513i | 0.299182i | 0.988748 | + | 0.149591i | \(0.0477957\pi\) | ||||
−0.988748 | + | 0.149591i | \(0.952204\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.41801 | −0.333970 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.199235i | 0.0148915i | 0.999972 | + | 0.00744577i | \(0.00237008\pi\) | ||||
−0.999972 | + | 0.00744577i | \(0.997630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 7.14783i | − 0.531294i | −0.964070 | − | 0.265647i | \(-0.914414\pi\) | ||||
0.964070 | − | 0.265647i | \(-0.0855855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0447 | −1.10611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.4805i | 2.88710i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8761 | −1.29347 | −0.646733 | − | 0.762717i | \(-0.723865\pi\) | ||||
−0.646733 | + | 0.762717i | \(0.723865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.2993 | −1.02928 | −0.514642 | − | 0.857405i | \(-0.672075\pi\) | ||||
−0.514642 | + | 0.857405i | \(0.672075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.13436i | − 0.294561i | −0.989095 | − | 0.147280i | \(-0.952948\pi\) | ||||
0.989095 | − | 0.147280i | \(-0.0470520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.5173 | −1.02910 | −0.514550 | − | 0.857460i | \(-0.672041\pi\) | ||||
−0.514550 | + | 0.857460i | \(0.672041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.21394i | 0.0852015i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 35.8614i | 2.50467i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30.7031 | −2.12378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9076i | 0.957439i | 0.877968 | + | 0.478719i | \(0.158899\pi\) | ||||
−0.877968 | + | 0.478719i | \(0.841101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.69841 | 0.388628 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.107385 | −0.00728974 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.9534i | 1.61128i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1591 | 0.814231 | 0.407115 | − | 0.913377i | \(-0.366535\pi\) | ||||
0.407115 | + | 0.913377i | \(0.366535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 24.4059i | − 1.61987i | −0.586517 | − | 0.809937i | \(-0.699501\pi\) | ||||
0.586517 | − | 0.809937i | \(-0.300499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.95033i | 0.128881i | 0.997922 | + | 0.0644407i | \(0.0205263\pi\) | ||||
−0.997922 | + | 0.0644407i | \(0.979474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.3094 | −1.06847 | −0.534233 | − | 0.845337i | \(-0.679400\pi\) | ||||
−0.534233 | + | 0.845337i | \(0.679400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.7597i | 1.35421i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65345 | 0.106953 | 0.0534764 | − | 0.998569i | \(-0.482970\pi\) | ||||
0.0534764 | + | 0.998569i | \(0.482970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.63938 | 0.234433 | 0.117217 | − | 0.993106i | \(-0.462603\pi\) | ||||
0.117217 | + | 0.993106i | \(0.462603\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.06888i | 0.196063i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.6280 | −1.18527 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.2386i | 1.59305i | 0.604607 | + | 0.796524i | \(0.293330\pi\) | ||||
−0.604607 | + | 0.796524i | \(0.706670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 32.8213i | − 2.06346i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.2051 | 0.886087 | 0.443044 | − | 0.896500i | \(-0.353899\pi\) | ||||
0.443044 | + | 0.896500i | \(0.353899\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.90235i | 0.304617i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3785 | −1.00994 | −0.504971 | − | 0.863137i | \(-0.668497\pi\) | ||||
−0.504971 | + | 0.863137i | \(0.668497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.2493 | −2.16535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.73448i | 0.288666i | 0.989529 | + | 0.144333i | \(0.0461037\pi\) | ||||
−0.989529 | + | 0.144333i | \(0.953896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3680 | −1.23727 | −0.618634 | − | 0.785679i | \(-0.712314\pi\) | ||||
−0.618634 | + | 0.785679i | \(0.712314\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 25.6607i | − 1.54740i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 29.0135i | − 1.74325i | −0.490170 | − | 0.871627i | \(-0.663065\pi\) | ||||
0.490170 | − | 0.871627i | \(-0.336935\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5849 | 0.989373 | 0.494687 | − | 0.869071i | \(-0.335283\pi\) | ||||
0.494687 | + | 0.869071i | \(0.335283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8603i | 1.29946i | 0.760165 | + | 0.649730i | \(0.225118\pi\) | ||||
−0.760165 | + | 0.649730i | \(0.774882\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6855 | 0.689774 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.2041 | 1.71789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.59022i | − 0.209743i | −0.994486 | − | 0.104872i | \(-0.966557\pi\) | ||||
0.994486 | − | 0.104872i | \(-0.0334431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.1059 | −1.40350 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 19.9131i | − 1.15161i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.85684i | − 0.107026i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.9971 | 2.11845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1418i | 0.978333i | 0.872191 | + | 0.489166i | \(0.162699\pi\) | ||||
−0.872191 | + | 0.489166i | \(0.837301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2814 | 1.20676 | 0.603379 | − | 0.797454i | \(-0.293820\pi\) | ||||
0.603379 | + | 0.797454i | \(0.293820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.14361 | −0.403781 | −0.201890 | − | 0.979408i | \(-0.564708\pi\) | ||||
−0.201890 | + | 0.979408i | \(0.564708\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 31.4066i | − 1.76397i | −0.471277 | − | 0.881986i | \(-0.656207\pi\) | ||||
0.471277 | − | 0.881986i | \(-0.343793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.05078 | −0.394768 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.9320i | 1.99931i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 15.5687i | − 0.863596i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.76459 | 0.372944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 11.6712i | − 0.641506i | −0.947163 | − | 0.320753i | \(-0.896064\pi\) | ||||
0.947163 | − | 0.320753i | \(-0.103936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.4676 | 1.11827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4008 | 1.11130 | 0.555652 | − | 0.831415i | \(-0.312469\pi\) | ||||
0.555652 | + | 0.831415i | \(0.312469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 0.623712i | − 0.0337759i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5903i | 0.675881i | 0.941167 | + | 0.337940i | \(0.109730\pi\) | ||||
−0.941167 | + | 0.337940i | \(0.890270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8022i | 0.685286i | 0.939466 | + | 0.342643i | \(0.111322\pi\) | ||||
−0.939466 | + | 0.342643i | \(0.888678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.2495 | −0.918099 | −0.459050 | − | 0.888411i | \(-0.651810\pi\) | ||||
−0.459050 | + | 0.888411i | \(0.651810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.09103i | 0.323278i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.52892 | 0.0806935 | 0.0403468 | − | 0.999186i | \(-0.487154\pi\) | ||||
0.0403468 | + | 0.999186i | \(0.487154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.94358 | −0.470715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 20.0360i | − 1.04873i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.04525 | 0.211160 | 0.105580 | − | 0.994411i | \(-0.466330\pi\) | ||||
0.105580 | + | 0.994411i | \(0.466330\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.4861i | 0.596326i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1416i | 1.30178i | 0.759171 | + | 0.650891i | \(0.225605\pi\) | ||||
−0.759171 | + | 0.650891i | \(0.774395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.27781 | −0.220318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10.1885i | − 0.523349i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||||
0.965156 | − | 0.261675i | \(-0.0842747\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.9423 | −1.83657 | −0.918284 | − | 0.395923i | \(-0.870425\pi\) | ||||
−0.918284 | + | 0.395923i | \(0.870425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.8247 | −0.908429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.81471i | − 0.345519i | −0.984964 | − | 0.172760i | \(-0.944732\pi\) | ||||
0.984964 | − | 0.172760i | \(-0.0552684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.4108 | −1.94252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.08116i | − 0.356292i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.1982i | − 0.562021i | −0.959705 | − | 0.281010i | \(-0.909330\pi\) | ||||
0.959705 | − | 0.281010i | \(-0.0906695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.9404 | 1.49515 | 0.747577 | − | 0.664175i | \(-0.231217\pi\) | ||||
0.747577 | + | 0.664175i | \(0.231217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.378415i | − 0.0188502i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.4739 | −1.41140 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0213 | −0.544968 | −0.272484 | − | 0.962160i | \(-0.587845\pi\) | ||||
−0.272484 | + | 0.962160i | \(0.587845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.85494i | 0.386516i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.6050 | 1.89505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 14.0133i | − 0.684594i | −0.939592 | − | 0.342297i | \(-0.888795\pi\) | ||||
0.939592 | − | 0.342297i | \(-0.111205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 19.4716i | − 0.948988i | −0.880259 | − | 0.474494i | \(-0.842631\pi\) | ||||
0.880259 | − | 0.474494i | \(-0.157369\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.0308 | −1.45671 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 12.0556i | − 0.583410i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.2120 | 1.79244 | 0.896219 | − | 0.443612i | \(-0.146303\pi\) | ||||
0.896219 | + | 0.443612i | \(0.146303\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4042 | −1.12474 | −0.562368 | − | 0.826887i | \(-0.690109\pi\) | ||||
−0.562368 | + | 0.826887i | \(0.690109\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 29.8713i | − 1.42894i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.7533 | −1.03823 | −0.519115 | − | 0.854705i | \(-0.673738\pi\) | ||||
−0.519115 | + | 0.854705i | \(0.673738\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 12.8369i | − 0.609901i | −0.952368 | − | 0.304951i | \(-0.901360\pi\) | ||||
0.952368 | − | 0.304951i | \(-0.0986400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.9112i | 1.13350i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.7889 | −0.556353 | −0.278176 | − | 0.960530i | \(-0.589730\pi\) | ||||
−0.278176 | + | 0.960530i | \(0.589730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.8718i | 3.19596i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.8145 | −0.506990 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.5157 | −1.56780 | −0.783900 | − | 0.620888i | \(-0.786772\pi\) | ||||
−0.783900 | + | 0.620888i | \(0.786772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10.0902i | − 0.469946i | −0.972002 | − | 0.234973i | \(-0.924500\pi\) | ||||
0.972002 | − | 0.234973i | \(-0.0755002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6131 | 1.09739 | 0.548697 | − | 0.836021i | \(-0.315124\pi\) | ||||
0.548697 | + | 0.836021i | \(0.315124\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.52944i | 0.117048i | 0.998286 | + | 0.0585242i | \(0.0186395\pi\) | ||||
−0.998286 | + | 0.0585242i | \(0.981361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.66942i | − 0.307965i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7849 | 0.495890 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 23.3543i | − 1.07157i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.1106 | −0.690421 | −0.345210 | − | 0.938525i | \(-0.612192\pi\) | ||||
−0.345210 | + | 0.938525i | \(0.612192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2755 | −0.787695 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.4591i | 0.565737i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.1541 | −1.86487 | −0.932436 | − | 0.361335i | \(-0.882321\pi\) | ||||
−0.932436 | + | 0.361335i | \(0.882321\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.6868i | 1.65565i | 0.560984 | + | 0.827827i | \(0.310423\pi\) | ||||
−0.560984 | + | 0.827827i | \(0.689577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.25156i | 0.371631i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.98478 | 0.0890294 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 20.1824i | − 0.903489i | −0.892147 | − | 0.451744i | \(-0.850802\pi\) | ||||
0.892147 | − | 0.451744i | \(-0.149198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.5011 | 0.468222 | 0.234111 | − | 0.972210i | \(-0.424782\pi\) | ||||
0.234111 | + | 0.972210i | \(0.424782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.7125 | 1.41119 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.5910i | 1.26727i | 0.773630 | + | 0.633637i | \(0.218439\pi\) | ||||
−0.773630 | + | 0.633637i | \(0.781561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.52879 | −0.288816 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 27.4566i | − 1.20988i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.2901i | 1.72798i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8325 | −0.474578 | −0.237289 | − | 0.971439i | \(-0.576259\pi\) | ||||
−0.237289 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.77247i | − 0.0775047i | −0.999249 | − | 0.0387523i | \(-0.987662\pi\) | ||||
0.999249 | − | 0.0387523i | \(-0.0123383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.729932 | −0.0317963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.93205 | 0.388350 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.1788i | 1.78365i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.8853 | 2.37290 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.80820i | 0.250177i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 11.0556i | − 0.475316i | −0.971349 | − | 0.237658i | \(-0.923620\pi\) | ||||
0.971349 | − | 0.237658i | \(-0.0763797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −36.7068 | −1.57235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.55978i | − 0.237719i | −0.992911 | − | 0.118859i | \(-0.962076\pi\) | ||||
0.992911 | − | 0.118859i | \(-0.0379238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.41707 | −0.273376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.30741 | −0.0981211 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.30560i | 0.182434i | 0.995831 | + | 0.0912171i | \(0.0290757\pi\) | ||||
−0.995831 | + | 0.0912171i | \(0.970924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.54335 | 0.276754 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.43447i | 0.102601i | 0.998683 | + | 0.0513003i | \(0.0163366\pi\) | ||||
−0.998683 | + | 0.0513003i | \(0.983663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.8751i | 1.71963i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.9163 | −0.457635 | −0.228818 | − | 0.973469i | \(-0.573486\pi\) | ||||
−0.228818 | + | 0.973469i | \(0.573486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 11.3442i | − 0.474740i | −0.971419 | − | 0.237370i | \(-0.923715\pi\) | ||||
0.971419 | − | 0.237370i | \(-0.0762854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.9655 | 1.04113 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.97962 | 0.332196 | 0.166098 | − | 0.986109i | \(-0.446883\pi\) | ||||
0.166098 | + | 0.986109i | \(0.446883\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12.5795i | − 0.521887i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −66.7133 | −2.76298 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.7410i | 1.72283i | 0.507898 | + | 0.861417i | \(0.330423\pi\) | ||||
−0.507898 | + | 0.861417i | \(0.669577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 0.567653i | − 0.0233897i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.43527 | −0.182135 | −0.0910673 | − | 0.995845i | \(-0.529028\pi\) | ||||
−0.0910673 | + | 0.995845i | \(0.529028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.8603i | 0.855188i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4875 | 0.510224 | 0.255112 | − | 0.966911i | \(-0.417888\pi\) | ||||
0.255112 | + | 0.966911i | \(0.417888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1871 | 1.51690 | 0.758448 | − | 0.651734i | \(-0.225958\pi\) | ||||
0.758448 | + | 0.651734i | \(0.225958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 69.7716i | − 2.83662i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.8403 | 0.886470 | 0.443235 | − | 0.896405i | \(-0.353831\pi\) | ||||
0.443235 | + | 0.896405i | \(0.353831\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.8379i | 0.964377i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 30.7687i | − 1.24274i | −0.783519 | − | 0.621368i | \(-0.786577\pi\) | ||||
0.783519 | − | 0.621368i | \(-0.213423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.0402 | −1.53144 | −0.765721 | − | 0.643173i | \(-0.777617\pi\) | ||||
−0.765721 | + | 0.643173i | \(0.777617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 14.9005i | − 0.598903i | −0.954111 | − | 0.299452i | \(-0.903196\pi\) | ||||
0.954111 | − | 0.299452i | \(-0.0968037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.79151 | 0.312160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.5712 | −1.10285 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.3231i | 1.32868i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8787 | 1.07002 | 0.535011 | − | 0.844845i | \(-0.320307\pi\) | ||||
0.535011 | + | 0.844845i | \(0.320307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.7754i | 0.903813i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.52392i | 0.139623i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.4910 | 0.493365 | 0.246682 | − | 0.969096i | \(-0.420660\pi\) | ||||
0.246682 | + | 0.969096i | \(0.420660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.53414i | − 0.139373i | −0.997569 | − | 0.0696864i | \(-0.977800\pi\) | ||||
0.997569 | − | 0.0696864i | \(-0.0221999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.3282 | 1.11370 | 0.556848 | − | 0.830614i | \(-0.312010\pi\) | ||||
0.556848 | + | 0.830614i | \(0.312010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.6231 | −1.79086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.9962i | 1.17384i | 0.809644 | + | 0.586921i | \(0.199660\pi\) | ||||
−0.809644 | + | 0.586921i | \(0.800340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8133 | 0.578804 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 16.0647i | − 0.625793i | −0.949787 | − | 0.312896i | \(-0.898701\pi\) | ||||
0.949787 | − | 0.312896i | \(-0.101299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 44.3984i | − 1.72690i | −0.504435 | − | 0.863450i | \(-0.668299\pi\) | ||||
0.504435 | − | 0.863450i | \(-0.331701\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.2226 | −0.629086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.85976i | − 0.265611i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.0213 | 2.70314 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.0649 | −1.92986 | −0.964930 | − | 0.262508i | \(-0.915450\pi\) | ||||
−0.964930 | + | 0.262508i | \(0.915450\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 30.1370i | − 1.15826i | −0.815236 | − | 0.579129i | \(-0.803393\pi\) | ||||
0.815236 | − | 0.579129i | \(-0.196607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.05981 | 0.155801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49520i | 0.0572124i | 0.999591 | + | 0.0286062i | \(0.00910688\pi\) | ||||
−0.999591 | + | 0.0286062i | \(0.990893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.5715i | 1.74120i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.4759 | −1.54201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 0.438347i | − 0.0166755i | −0.999965 | − | 0.00833774i | \(-0.997346\pi\) | ||||
0.999965 | − | 0.00833774i | \(-0.00265402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.3350 | 0.581690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 79.4306 | 3.00865 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.1330i | 1.62911i | 0.580084 | + | 0.814556i | \(0.303020\pi\) | ||||
−0.580084 | + | 0.814556i | \(0.696980\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.9147 | −0.977390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 10.3336i | − 0.388635i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8542i | 1.15875i | 0.815060 | + | 0.579376i | \(0.196704\pi\) | ||||
−0.815060 | + | 0.579376i | \(0.803296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.606814 | 0.0227254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 62.8127i | − 2.34906i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.24406 | 0.0836895 | 0.0418447 | − | 0.999124i | \(-0.486677\pi\) | ||||
0.0418447 | + | 0.999124i | \(0.486677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.94679 | −0.333196 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5.36317i | − 0.199183i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9794 | 0.629733 | 0.314866 | − | 0.949136i | \(-0.398040\pi\) | ||||
0.314866 | + | 0.949136i | \(0.398040\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 12.6216i | − 0.466827i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 34.0255i | − 1.25676i | −0.777906 | − | 0.628380i | \(-0.783718\pi\) | ||||
0.777906 | − | 0.628380i | \(-0.216282\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.7374 | 1.42691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.0107994i | 0 0.000397263i | 1.00000 | 0.000198632i | \(6.32264e-5\pi\) | |||||
−1.00000 | 0.000198632i | \(0.999937\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.6360 | 1.67422 | 0.837112 | − | 0.547032i | \(-0.184242\pi\) | ||||
0.837112 | + | 0.547032i | \(0.184242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.2982 | 1.07340 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 17.8845i | − 0.653485i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.95000 | 0.144138 | 0.0720688 | − | 0.997400i | \(-0.477040\pi\) | ||||
0.0720688 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.2240i | 1.28193i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.6412i | 0.677524i | 0.940872 | + | 0.338762i | \(0.110008\pi\) | ||||
−0.940872 | + | 0.338762i | \(0.889992\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.86842 | −0.176480 | −0.0882401 | − | 0.996099i | \(-0.528124\pi\) | ||||
−0.0882401 | + | 0.996099i | \(0.528124\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.9610i | 0.433017i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.6802 | −0.999473 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.48442 | −0.0535297 | −0.0267649 | − | 0.999642i | \(-0.508521\pi\) | ||||
−0.0267649 | + | 0.999642i | \(0.508521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 14.2868i | − 0.513861i | −0.966430 | − | 0.256931i | \(-0.917289\pi\) | ||||
0.966430 | − | 0.256931i | \(-0.0827112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.474426 | 0.0170419 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 61.7716i | 2.21320i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5280i | 0.412504i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.24504 | 0.151512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 22.3799i | − 0.797758i | −0.917004 | − | 0.398879i | \(-0.869399\pi\) | ||||
0.917004 | − | 0.398879i | \(-0.130601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.3192 | 0.473578 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.4829 | 1.50861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.1872i | 0.821334i | 0.911785 | + | 0.410667i | \(0.134704\pi\) | ||||
−0.911785 | + | 0.410667i | \(0.865296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.9814 | 1.62670 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 37.9205i | − 1.33819i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 17.3417i | − 0.611216i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.8263 | 1.57601 | 0.788004 | − | 0.615670i | \(-0.211114\pi\) | ||||
0.788004 | + | 0.615670i | \(0.211114\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4358i | 0.647370i | 0.946165 | + | 0.323685i | \(0.104922\pi\) | ||||
−0.946165 | + | 0.323685i | \(0.895078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.7197 | 1.07606 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.81556 | 0.343403 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0533i | 0.734764i | 0.930070 | + | 0.367382i | \(0.119746\pi\) | ||||
−0.930070 | + | 0.367382i | \(0.880254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.3206 | 1.12663 | 0.563313 | − | 0.826244i | \(-0.309527\pi\) | ||||
0.563313 | + | 0.826244i | \(0.309527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4599i | 0.433272i | 0.976252 | + | 0.216636i | \(0.0695085\pi\) | ||||
−0.976252 | + | 0.216636i | \(0.930492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.78073i | 0.235504i | 0.993043 | + | 0.117752i | \(0.0375689\pi\) | ||||
−0.993043 | + | 0.117752i | \(0.962431\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.79736 | 0.235515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.01372i | 0.173507i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.6268 | 0.815687 | 0.407843 | − | 0.913052i | \(-0.366281\pi\) | ||||
0.407843 | + | 0.913052i | \(0.366281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.5264 | 0.949185 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.78606i | 0.0614425i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.7352 | −0.781192 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 27.7024i | − 0.949628i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 17.7202i | − 0.606727i | −0.952875 | − | 0.303363i | \(-0.901890\pi\) | ||||
0.952875 | − | 0.303363i | \(-0.0981096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5262 | −0.462046 | −0.231023 | − | 0.972948i | \(-0.574207\pi\) | ||||
−0.231023 | + | 0.972948i | \(0.574207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 27.6249i | − 0.942548i | −0.881987 | − | 0.471274i | \(-0.843794\pi\) | ||||
0.881987 | − | 0.471274i | \(-0.156206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.9545 | 1.36007 | 0.680034 | − | 0.733181i | \(-0.261965\pi\) | ||||
0.680034 | + | 0.733181i | \(0.261965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0764 | −0.410610 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 13.4019i | − 0.454629i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.5025 | 0.796352 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.78606i | 0.0603800i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3922i | 0.384687i | 0.981328 | + | 0.192343i | \(0.0616087\pi\) | ||||
−0.981328 | + | 0.192343i | \(0.938391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.3753 | 1.22551 | 0.612757 | − | 0.790271i | \(-0.290060\pi\) | ||||
0.612757 | + | 0.790271i | \(0.290060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52.0983i | − 1.75325i | −0.481177 | − | 0.876624i | \(-0.659790\pi\) | ||||
0.481177 | − | 0.876624i | \(-0.340210\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0095 | −1.51127 | −0.755635 | − | 0.654992i | \(-0.772672\pi\) | ||||
−0.755635 | + | 0.654992i | \(0.772672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.42140 | 0.248906 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.7588i | 1.19662i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.611428 | −0.0204378 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 0.130358i | − 0.00434768i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 78.0748i | 2.60105i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.9358 | 0.729171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.96941i | 0.264620i | 0.991208 | + | 0.132310i | \(0.0422394\pi\) | ||||
−0.991208 | + | 0.132310i | \(0.957761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.8457 | 1.58520 | 0.792600 | − | 0.609742i | \(-0.208727\pi\) | ||||
0.792600 | + | 0.609742i | \(0.208727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.0645 | 2.41808 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.82695i | − 0.159400i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.2279 | −1.19505 | −0.597525 | − | 0.801851i | \(-0.703849\pi\) | ||||
−0.597525 | + | 0.801851i | \(0.703849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.99419i | 0.230217i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 21.6586i | − 0.712132i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.44479 | 0.309874 | 0.154937 | − | 0.987924i | \(-0.450483\pi\) | ||||
0.154937 | + | 0.987924i | \(0.450483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.28617i | 0.173247i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −121.161 | −3.96238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2959 | −0.499695 | −0.249847 | − | 0.968285i | \(-0.580380\pi\) | ||||
−0.249847 | + | 0.968285i | \(0.580380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.2847i | 0.954654i | 0.878726 | + | 0.477327i | \(0.158394\pi\) | ||||
−0.878726 | + | 0.477327i | \(0.841606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −66.0330 | −2.15033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23.0133i | − 0.747832i | −0.927463 | − | 0.373916i | \(-0.878015\pi\) | ||||
0.927463 | − | 0.373916i | \(-0.121985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 23.0069i | − 0.746836i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.48602 | −0.145316 | −0.0726582 | − | 0.997357i | \(-0.523148\pi\) | ||||
−0.0726582 | + | 0.997357i | \(0.523148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 54.8594i | − 1.77521i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.8496 | 0.479518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9885 | −0.999628 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 43.8827i | − 1.41263i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4520 | 0.593376 | 0.296688 | − | 0.954974i | \(-0.404118\pi\) | ||||
0.296688 | + | 0.954974i | \(0.404118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.1370i | 0.678317i | 0.940729 | + | 0.339159i | \(0.110142\pi\) | ||||
−0.940729 | + | 0.339159i | \(0.889858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.99694i | − 0.160195i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.4783 | −1.67893 | −0.839465 | − | 0.543414i | \(-0.817131\pi\) | ||||
−0.839465 | + | 0.543414i | \(0.817131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.2547i | 1.44635i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.7453 | −0.948727 | −0.474364 | − | 0.880329i | \(-0.657322\pi\) | ||||
−0.474364 | + | 0.880329i | \(0.657322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6878 | 0.404268 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.4927i | 0.333649i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.11149 | −0.289436 | −0.144718 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144718 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 44.5517i | − 1.41238i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.52824i | − 0.143411i | −0.997426 | − | 0.0717054i | \(-0.977156\pi\) | ||||
0.997426 | − | 0.0717054i | \(-0.0228442\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.e.3025.16 | 20 | ||
3.2 | odd | 2 | inner | 6048.2.c.e.3025.6 | 20 | ||
4.3 | odd | 2 | 1512.2.c.e.757.8 | yes | 20 | ||
8.3 | odd | 2 | 1512.2.c.e.757.7 | ✓ | 20 | ||
8.5 | even | 2 | inner | 6048.2.c.e.3025.5 | 20 | ||
12.11 | even | 2 | 1512.2.c.e.757.13 | yes | 20 | ||
24.5 | odd | 2 | inner | 6048.2.c.e.3025.15 | 20 | ||
24.11 | even | 2 | 1512.2.c.e.757.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.7 | ✓ | 20 | 8.3 | odd | 2 | ||
1512.2.c.e.757.8 | yes | 20 | 4.3 | odd | 2 | ||
1512.2.c.e.757.13 | yes | 20 | 12.11 | even | 2 | ||
1512.2.c.e.757.14 | yes | 20 | 24.11 | even | 2 | ||
6048.2.c.e.3025.5 | 20 | 8.5 | even | 2 | inner | ||
6048.2.c.e.3025.6 | 20 | 3.2 | odd | 2 | inner | ||
6048.2.c.e.3025.15 | 20 | 24.5 | odd | 2 | inner | ||
6048.2.c.e.3025.16 | 20 | 1.1 | even | 1 | trivial |