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: | \(8\) |
Coefficient field: | 8.0.3317760000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.7 | ||
Root | \(1.40294 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.c.3025.2 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.80588i | 1.25483i | 0.778685 | + | 0.627415i | \(0.215887\pi\) | ||||
−0.778685 | + | 0.627415i | \(0.784113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.51867i | 1.06092i | 0.847710 | + | 0.530460i | \(0.177981\pi\) | ||||
−0.847710 | + | 0.530460i | \(0.822019\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.87298i | − 1.35152i | −0.737121 | − | 0.675761i | \(-0.763815\pi\) | ||||
0.737121 | − | 0.675761i | \(-0.236185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.87298i | − 1.80619i | −0.429445 | − | 0.903093i | \(-0.641291\pi\) | ||||
0.429445 | − | 0.903093i | \(-0.358709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.356394 | 0.0743133 | 0.0371566 | − | 0.999309i | \(-0.488170\pi\) | ||||
0.0371566 | + | 0.999309i | \(0.488170\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.87298 | −0.574597 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44949i | 0.454859i | 0.973795 | + | 0.227429i | \(0.0730321\pi\) | ||||
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.80588i | 0.474281i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.87298i | 0.965513i | 0.875755 | + | 0.482756i | \(0.160364\pi\) | ||||
−0.875755 | + | 0.482756i | \(0.839636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1544 | 1.58584 | 0.792922 | − | 0.609323i | \(-0.208559\pi\) | ||||
0.792922 | + | 0.609323i | \(0.208559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.87298i | − 1.35312i | −0.736389 | − | 0.676559i | \(-0.763471\pi\) | ||||
0.736389 | − | 0.676559i | \(-0.236529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.34847 | −1.07188 | −0.535942 | − | 0.844255i | \(-0.680044\pi\) | ||||
−0.535942 | + | 0.844255i | \(0.680044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.87298 | −1.33127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 12.9602i | − 1.68728i | −0.536910 | − | 0.843640i | \(-0.680409\pi\) | ||||
0.536910 | − | 0.843640i | \(-0.319591\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.74597i | 0.223548i | 0.993734 | + | 0.111774i | \(0.0356533\pi\) | ||||
−0.993734 | + | 0.111774i | \(0.964347\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.6730 | 1.69593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.6190i | − 1.78599i | −0.450068 | − | 0.892995i | \(-0.648600\pi\) | ||||
0.450068 | − | 0.892995i | \(-0.351400\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.51867 | −0.417589 | −0.208795 | − | 0.977959i | \(-0.566954\pi\) | ||||
−0.208795 | + | 0.977959i | \(0.566954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.87298 | −0.804422 | −0.402211 | − | 0.915547i | \(-0.631758\pi\) | ||||
−0.402211 | + | 0.915547i | \(0.631758\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.51867i | 0.400990i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6190 | 1.19473 | 0.597363 | − | 0.801971i | \(-0.296215\pi\) | ||||
0.597363 | + | 0.801971i | \(0.296215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.9602i | − 1.42257i | −0.702903 | − | 0.711285i | \(-0.748113\pi\) | ||||
0.702903 | − | 0.711285i | \(-0.251887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.87298i | 0.962410i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1544 | 1.07636 | 0.538180 | − | 0.842830i | \(-0.319112\pi\) | ||||
0.538180 | + | 0.842830i | \(0.319112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.87298i | − 0.510827i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.0907 | 2.26646 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74597 | 0.583415 | 0.291707 | − | 0.956508i | \(-0.405777\pi\) | ||||
0.291707 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.8592i | − 1.77706i | −0.458820 | − | 0.888529i | \(-0.651728\pi\) | ||||
0.458820 | − | 0.888529i | \(-0.348272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.74597 | −0.467634 | −0.233817 | − | 0.972281i | \(-0.575122\pi\) | ||||
−0.233817 | + | 0.972281i | \(0.575122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.58785i | 0.443525i | 0.975101 | + | 0.221762i | \(0.0711809\pi\) | ||||
−0.975101 | + | 0.221762i | \(0.928819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.74597i | 0.263016i | 0.991315 | + | 0.131508i | \(0.0419819\pi\) | ||||
−0.991315 | + | 0.131508i | \(0.958018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.13836 | 0.201160 | 0.100580 | − | 0.994929i | \(-0.467930\pi\) | ||||
0.100580 | + | 0.994929i | \(0.467930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000i | 0.0932505i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.16228 | 0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.38105 | −0.125550 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.96816i | 0.533809i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.12702 | −0.277478 | −0.138739 | − | 0.990329i | \(-0.544305\pi\) | ||||
−0.138739 | + | 0.990329i | \(0.544305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.87507i | 0.338566i | 0.985567 | + | 0.169283i | \(0.0541452\pi\) | ||||
−0.985567 | + | 0.169283i | \(0.945855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.87298i | − 0.682674i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.3858 | −1.22906 | −0.614531 | − | 0.788892i | \(-0.710655\pi\) | ||||
−0.614531 | + | 0.788892i | \(0.710655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.1464 | 1.43386 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.87298 | −0.570770 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79796i | 0.802680i | 0.915929 | + | 0.401340i | \(0.131455\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.6412i | 1.57762i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8730i | 1.18699i | 0.804836 | + | 0.593497i | \(0.202253\pi\) | ||||
−0.804836 | + | 0.593497i | \(0.797747\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.356394 | 0.0280878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1270i | 1.18484i | 0.805630 | + | 0.592420i | \(0.201827\pi\) | ||||
−0.805630 | + | 0.592420i | \(0.798173\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.2235 | −0.868503 | −0.434252 | − | 0.900792i | \(-0.642987\pi\) | ||||
−0.434252 | + | 0.900792i | \(0.642987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7460 | −0.826613 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.72878i | − 0.663637i | −0.943343 | − | 0.331818i | \(-0.892338\pi\) | ||||
0.943343 | − | 0.331818i | \(-0.107662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.87298 | −0.217177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.87507i | 0.289636i | 0.989458 | + | 0.144818i | \(0.0462597\pi\) | ||||
−0.989458 | + | 0.144818i | \(0.953740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.25403i | − 0.464859i | −0.972613 | − | 0.232429i | \(-0.925333\pi\) | ||||
0.972613 | − | 0.232429i | \(-0.0746674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.4789 | −1.21155 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.1270i | 0.813688i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3301 | 1.39867 | 0.699337 | − | 0.714792i | \(-0.253479\pi\) | ||||
0.699337 | + | 0.714792i | \(0.253479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.4919 | 1.54702 | 0.773512 | − | 0.633782i | \(-0.218498\pi\) | ||||
0.773512 | + | 0.633782i | \(0.218498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.3460i | 1.94833i | 0.225848 | + | 0.974163i | \(0.427485\pi\) | ||||
−0.225848 | + | 0.974163i | \(0.572515\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.87298 | −0.558101 | −0.279050 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279050 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.44949i | 0.171920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.4919i | 1.98996i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.7024 | 1.91622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 20.0000i | − 1.37686i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) | ||||
0.725304 | − | 0.688428i | \(-0.241699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.8966 | 1.69793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.00000 | 0.475191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 15.4097i | − 1.03657i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.6190 | 1.04592 | 0.522961 | − | 0.852357i | \(-0.324827\pi\) | ||||
0.522961 | + | 0.852357i | \(0.324827\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2714i | 0.880851i | 0.897789 | + | 0.440426i | \(0.145172\pi\) | ||||
−0.897789 | + | 0.440426i | \(0.854828\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 0.254033i | − 0.0167870i | −0.999965 | − | 0.00839350i | \(-0.997328\pi\) | ||||
0.999965 | − | 0.00839350i | \(-0.00267176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.712788 | −0.0466963 | −0.0233481 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233481 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 20.6190i | − 1.34503i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2474 | −0.792222 | −0.396111 | − | 0.918203i | \(-0.629640\pi\) | ||||
−0.396111 | + | 0.918203i | \(0.629640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38105 | 0.346624 | 0.173312 | − | 0.984867i | \(-0.444553\pi\) | ||||
0.173312 | + | 0.984867i | \(0.444553\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.80588i | 0.179261i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38.3649 | −2.44110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.13836i | 0.134972i | 0.997720 | + | 0.0674862i | \(0.0214979\pi\) | ||||
−0.997720 | + | 0.0674862i | \(0.978502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.25403i | 0.0788404i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.3913 | 1.70862 | 0.854312 | − | 0.519761i | \(-0.173979\pi\) | ||||
0.854312 | + | 0.519761i | \(0.173979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.87298i | 0.364929i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.356394 | −0.0219762 | −0.0109881 | − | 0.999940i | \(-0.503498\pi\) | ||||
−0.0109881 | + | 0.999940i | \(0.503498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.9045i | 1.09166i | 0.837897 | + | 0.545828i | \(0.183785\pi\) | ||||
−0.837897 | + | 0.545828i | \(0.816215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.25403 | 0.258414 | 0.129207 | − | 0.991618i | \(-0.458757\pi\) | ||||
0.129207 | + | 0.991618i | \(0.458757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 10.1091i | − 0.609601i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87298i | 0.112537i | 0.998416 | + | 0.0562683i | \(0.0179202\pi\) | ||||
−0.998416 | + | 0.0562683i | \(0.982080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0454 | 1.31512 | 0.657559 | − | 0.753403i | \(-0.271589\pi\) | ||||
0.657559 | + | 0.753403i | \(0.271589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4919i | 1.15868i | 0.815088 | + | 0.579338i | \(0.196689\pi\) | ||||
−0.815088 | + | 0.579338i | \(0.803311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1544 | 0.599393 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 31.8434i | − 1.86031i | −0.367168 | − | 0.930155i | \(-0.619673\pi\) | ||||
0.367168 | − | 0.930155i | \(-0.380327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.3649 | 2.11725 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.73670i | − 0.100436i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.87298i | − 0.511430i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.89898 | −0.280515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.38105i | − 0.364186i | −0.983281 | − | 0.182093i | \(-0.941713\pi\) | ||||
0.983281 | − | 0.182093i | \(-0.0582872\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9124 | 0.618786 | 0.309393 | − | 0.950934i | \(-0.399874\pi\) | ||||
0.309393 | + | 0.950934i | \(0.399874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.87298 | −0.275437 | −0.137719 | − | 0.990471i | \(-0.543977\pi\) | ||||
−0.137719 | + | 0.990471i | \(0.543977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.02391i | − 0.0575087i | −0.999587 | − | 0.0287544i | \(-0.990846\pi\) | ||||
0.999587 | − | 0.0287544i | \(-0.00915406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.61895 | −0.482569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 24.8966i | − 1.38528i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000i | 0.776580i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.34847 | −0.405134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000i | 0.549650i | 0.961494 | + | 0.274825i | \(0.0886199\pi\) | ||||
−0.961494 | + | 0.274825i | \(0.911380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 41.0191 | 2.24111 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7460 | −1.02116 | −0.510579 | − | 0.859831i | \(-0.670569\pi\) | ||||
−0.510579 | + | 0.859831i | \(0.670569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.6307i | 1.33383i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.63312i | − 0.248719i | −0.992237 | − | 0.124359i | \(-0.960312\pi\) | ||||
0.992237 | − | 0.124359i | \(-0.0396876\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.49193i | − 0.401034i | −0.979690 | − | 0.200517i | \(-0.935738\pi\) | ||||
0.979690 | − | 0.200517i | \(-0.0642622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.82980 | −0.203840 | −0.101920 | − | 0.994793i | \(-0.532499\pi\) | ||||
−0.101920 | + | 0.994793i | \(0.532499\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9.87298i | − 0.524004i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.0723 | −1.79827 | −0.899133 | − | 0.437676i | \(-0.855802\pi\) | ||||
−0.899133 | + | 0.437676i | \(0.855802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −42.9839 | −2.26231 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 19.2848i | − 1.00941i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.1270 | −0.737424 | −0.368712 | − | 0.929544i | \(-0.620201\pi\) | ||||
−0.368712 | + | 0.929544i | \(0.620201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.2379i | 0.944323i | 0.881512 | + | 0.472161i | \(0.156526\pi\) | ||||
−0.881512 | + | 0.472161i | \(0.843474\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.9363 | 0.614752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.12702i | 0.0578910i | 0.999581 | + | 0.0289455i | \(0.00921492\pi\) | ||||
−0.999581 | + | 0.0289455i | \(0.990785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.4312 | 1.86155 | 0.930774 | − | 0.365595i | \(-0.119134\pi\) | ||||
0.930774 | + | 0.365595i | \(0.119134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.87298 | −0.503174 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9.08517i | − 0.460636i | −0.973115 | − | 0.230318i | \(-0.926023\pi\) | ||||
0.973115 | − | 0.230318i | \(-0.0739767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.12702 | 0.0569957 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.7955i | 1.49918i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000i | 0.501886i | 0.968002 | + | 0.250943i | \(0.0807406\pi\) | ||||
−0.968002 | + | 0.250943i | \(0.919259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.4232 | 1.06982 | 0.534911 | − | 0.844909i | \(-0.320345\pi\) | ||||
0.534911 | + | 0.844909i | \(0.320345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 34.1109i | − 1.69918i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.6651 | −1.02433 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.3649 | 1.30366 | 0.651831 | − | 0.758365i | \(-0.274001\pi\) | ||||
0.651831 | + | 0.758365i | \(0.274001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 12.9602i | − 0.637732i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.3649 | 1.78508 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.17571i | 0.448263i | 0.974559 | + | 0.224131i | \(0.0719545\pi\) | ||||
−0.974559 | + | 0.224131i | \(0.928046\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 35.1109i | − 1.71120i | −0.517638 | − | 0.855600i | \(-0.673189\pi\) | ||||
0.517638 | − | 0.855600i | \(-0.326811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.08517 | −0.440696 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.74597i | 0.0844933i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.6278 | 0.656426 | 0.328213 | − | 0.944604i | \(-0.393554\pi\) | ||||
0.328213 | + | 0.944604i | \(0.393554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.87298 | 0.138067 | 0.0690334 | − | 0.997614i | \(-0.478009\pi\) | ||||
0.0690334 | + | 0.997614i | \(0.478009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.80588i | − 0.134224i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2540 | −0.489398 | −0.244699 | − | 0.969599i | \(-0.578689\pi\) | ||||
−0.244699 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.758056i | 0.0360163i | 0.999838 | + | 0.0180082i | \(0.00573249\pi\) | ||||
−0.999838 | + | 0.0180082i | \(0.994268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.4919i | 1.35065i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0110 | −1.22754 | −0.613768 | − | 0.789487i | \(-0.710347\pi\) | ||||
−0.613768 | + | 0.789487i | \(0.710347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.7298i | 1.68245i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6730 | 0.641001 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.7460 | 1.15757 | 0.578784 | − | 0.815481i | \(-0.303528\pi\) | ||||
0.578784 | + | 0.815481i | \(0.303528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.3994i | 1.97474i | 0.158444 | + | 0.987368i | \(0.449352\pi\) | ||||
−0.158444 | + | 0.987368i | \(0.550648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4919 | −1.46355 | −0.731777 | − | 0.681544i | \(-0.761309\pi\) | ||||
−0.731777 | + | 0.681544i | \(0.761309\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.8966i | 1.15208i | 0.817423 | + | 0.576038i | \(0.195402\pi\) | ||||
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 14.6190i | − 0.675040i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.2211 | 1.43555 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.6190i | 1.03783i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.61177 | 0.256408 | 0.128204 | − | 0.991748i | \(-0.459079\pi\) | ||||
0.128204 | + | 0.991748i | \(0.459079\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.6190 | 1.30491 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.1225i | 0.732086i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.1109 | 1.27383 | 0.636913 | − | 0.770936i | \(-0.280211\pi\) | ||||
0.636913 | + | 0.770936i | \(0.280211\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 40.3516i | − 1.82104i | −0.413465 | − | 0.910520i | \(-0.635682\pi\) | ||||
0.413465 | − | 0.910520i | \(-0.364318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.74597i | 0.348861i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.51867 | −0.157834 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.36492i | 0.195401i | 0.995216 | + | 0.0977003i | \(0.0311486\pi\) | ||||
−0.995216 | + | 0.0977003i | \(0.968851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.34847 | 0.327652 | 0.163826 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163826 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.1109 | 2.22991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 19.2848i | − 0.854783i | −0.904067 | − | 0.427392i | \(-0.859433\pi\) | ||||
0.904067 | − | 0.427392i | \(-0.140567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.87298 | −0.304043 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13.3166i | − 0.586801i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 25.8569i | − 1.13718i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5934 | −0.770779 | −0.385390 | − | 0.922754i | \(-0.625933\pi\) | ||||
−0.385390 | + | 0.922754i | \(0.625933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2540i | 0.841920i | 0.907079 | + | 0.420960i | \(0.138307\pi\) | ||||
−0.907079 | + | 0.420960i | \(0.861693\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.1359 | 0.964257 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8730 | −0.994478 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 49.4820i | − 2.14330i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.8730 | −0.556548 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.51867i | 0.151560i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 38.8569i | − 1.67059i | −0.549805 | − | 0.835293i | \(-0.685298\pi\) | ||||
0.549805 | − | 0.835293i | \(-0.314702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.70486 | −0.330040 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.23790i | 0.309470i | 0.987956 | + | 0.154735i | \(0.0494524\pi\) | ||||
−0.987956 | + | 0.154735i | \(0.950548\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.2848 | 0.821560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6190 | 0.451564 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.7716i | 1.21909i | 0.792750 | + | 0.609546i | \(0.208648\pi\) | ||||
−0.792750 | + | 0.609546i | \(0.791352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −43.2379 | −1.82877 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.34847i | 0.309701i | 0.987938 | + | 0.154851i | \(0.0494896\pi\) | ||||
−0.987938 | + | 0.154851i | \(0.950510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000i | 0.252422i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.4686 | 1.82230 | 0.911148 | − | 0.412078i | \(-0.135197\pi\) | ||||
0.911148 | + | 0.412078i | \(0.135197\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 28.9839i | − 1.21294i | −0.795107 | − | 0.606469i | \(-0.792586\pi\) | ||||
0.795107 | − | 0.606469i | \(-0.207414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.02391 | −0.0427002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.7460 | −1.57139 | −0.785693 | − | 0.618617i | \(-0.787693\pi\) | ||||
−0.785693 | + | 0.618617i | \(0.787693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 12.9602i | − 0.537681i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 6.23402i | − 0.257306i | −0.991690 | − | 0.128653i | \(-0.958935\pi\) | ||||
0.991690 | − | 0.128653i | \(-0.0410653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 55.1109i | − 2.27080i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.65704 | −0.232307 | −0.116153 | − | 0.993231i | \(-0.537056\pi\) | ||||
−0.116153 | + | 0.993231i | \(0.537056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.87298i | 0.363757i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.265858 | −0.0108627 | −0.00543133 | − | 0.999985i | \(-0.501729\pi\) | ||||
−0.00543133 | + | 0.999985i | \(0.501729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1109 | −0.901922 | −0.450961 | − | 0.892544i | \(-0.648919\pi\) | ||||
−0.450961 | + | 0.892544i | \(0.648919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.87507i | − 0.157544i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2379 | 1.26791 | 0.633954 | − | 0.773371i | \(-0.281431\pi\) | ||||
0.633954 | + | 0.773371i | \(0.281431\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.8090i | 1.44868i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.23790i | 0.251946i | 0.992034 | + | 0.125973i | \(0.0402053\pi\) | ||||
−0.992034 | + | 0.125973i | \(0.959795\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.3700 | −1.14213 | −0.571066 | − | 0.820904i | \(-0.693470\pi\) | ||||
−0.571066 | + | 0.820904i | \(0.693470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.4919i | 1.22557i | 0.790248 | + | 0.612787i | \(0.209952\pi\) | ||||
−0.790248 | + | 0.612787i | \(0.790048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.1544 | 0.406826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1109 | −1.24444 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.5720i | 0.740514i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.12702 | 0.0448658 | 0.0224329 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224329 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.77405i | − 0.348187i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.87298i | − 0.193075i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.8195 | −1.21730 | −0.608648 | − | 0.793441i | \(-0.708288\pi\) | ||||
−0.608648 | + | 0.793441i | \(0.708288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 31.6190i | − 1.24693i | −0.781851 | − | 0.623465i | \(-0.785724\pi\) | ||||
0.781851 | − | 0.623465i | \(-0.214276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5242 | −0.649632 | −0.324816 | − | 0.945777i | \(-0.605302\pi\) | ||||
−0.324816 | + | 0.945777i | \(0.605302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.6028 | 1.79007 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2848i | 0.754672i | 0.926076 | + | 0.377336i | \(0.123160\pi\) | ||||
−0.926076 | + | 0.377336i | \(0.876840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8730 | −0.424843 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.8752i | 1.00795i | 0.863717 | + | 0.503977i | \(0.168131\pi\) | ||||
−0.863717 | + | 0.503977i | \(0.831869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 23.8569i | − 0.927924i | −0.885855 | − | 0.463962i | \(-0.846427\pi\) | ||||
0.885855 | − | 0.463962i | \(-0.153573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.0907 | 0.856640 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.872983i | 0.0338021i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.14348 | −0.237167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.49193 | −0.0575098 | −0.0287549 | − | 0.999586i | \(-0.509154\pi\) | ||||
−0.0287549 | + | 0.999586i | \(0.509154\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.5560i | 0.405701i | 0.979210 | + | 0.202850i | \(0.0650205\pi\) | ||||
−0.979210 | + | 0.202850i | \(0.934980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.74597 | 0.220510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6038i | 0.482273i | 0.970491 | + | 0.241136i | \(0.0775201\pi\) | ||||
−0.970491 | + | 0.241136i | \(0.922480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 40.3649i | − 1.54226i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.0000i | − 0.836919i | −0.908235 | − | 0.418460i | \(-0.862570\pi\) | ||||
0.908235 | − | 0.418460i | \(-0.137430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.2824 | −1.49007 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.1109 | 1.21629 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 14.4763i | − 0.546764i | −0.961906 | − | 0.273382i | \(-0.911858\pi\) | ||||
0.961906 | − | 0.273382i | \(-0.0881423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.2379 | 1.74390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17.8592i | − 0.671665i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 36.7460i | − 1.38002i | −0.723798 | − | 0.690012i | \(-0.757605\pi\) | ||||
0.723798 | − | 0.690012i | \(-0.242395\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.49476 | 0.0934294 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.1109i | 1.79925i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.43901 | −0.277428 | −0.138714 | − | 0.990332i | \(-0.544297\pi\) | ||||
−0.138714 | + | 0.990332i | \(0.544297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.74597 | −0.176749 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 7.03734i | − 0.261360i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.4919 | 1.01962 | 0.509810 | − | 0.860287i | \(-0.329716\pi\) | ||||
0.509810 | + | 0.860287i | \(0.329716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 28.0588i | − 1.03779i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.3649i | 1.12155i | 0.827967 | + | 0.560777i | \(0.189497\pi\) | ||||
−0.827967 | + | 0.560777i | \(0.810503\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.4393 | 1.89479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 15.7460i | − 0.579225i | −0.957144 | − | 0.289612i | \(-0.906474\pi\) | ||||
0.957144 | − | 0.289612i | \(-0.0935264\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.7532 | −1.49509 | −0.747545 | − | 0.664211i | \(-0.768768\pi\) | ||||
−0.747545 | + | 0.664211i | \(0.768768\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.4919 | −1.00723 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58785i | 0.167637i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.3488 | −1.80076 | −0.900381 | − | 0.435102i | \(-0.856712\pi\) | ||||
−0.900381 | + | 0.435102i | \(0.856712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.6706i | 1.22540i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2540i | 0.372689i | 0.982484 | + | 0.186345i | \(0.0596641\pi\) | ||||
−0.982484 | + | 0.186345i | \(0.940336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.39630 | −0.340616 | −0.170308 | − | 0.985391i | \(-0.554476\pi\) | ||||
−0.170308 | + | 0.985391i | \(0.554476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.74597i | 0.0994107i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63.1550 | −2.28040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.3649 | 1.81621 | 0.908103 | − | 0.418748i | \(-0.137531\pi\) | ||||
0.908103 | + | 0.418748i | \(0.137531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.1361i | 1.58746i | 0.608267 | + | 0.793732i | \(0.291865\pi\) | ||||
−0.608267 | + | 0.793732i | \(0.708135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.1109 | −0.722404 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 79.9451i | − 2.86433i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 12.3810i | − 0.443029i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41.7319 | −1.48947 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7460i | 0.703868i | 0.936025 | + | 0.351934i | \(0.114476\pi\) | ||||
−0.936025 | + | 0.351934i | \(0.885524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.13836 | 0.0760315 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.50807 | 0.302130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.8169i | − 1.02075i | −0.859953 | − | 0.510373i | \(-0.829507\pi\) | ||||
0.859953 | − | 0.510373i | \(-0.170493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.2379 | −0.822098 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 24.1838i | − 0.853427i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00000i | 0.0352454i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3858 | 0.505778 | 0.252889 | − | 0.967495i | \(-0.418619\pi\) | ||||
0.252889 | + | 0.967495i | \(0.418619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.9839i | 0.701728i | 0.936426 | + | 0.350864i | \(0.114112\pi\) | ||||
−0.936426 | + | 0.350864i | \(0.885888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.4446 | −1.48677 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.8569 | −2.44398 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 22.1359i | − 0.772550i | −0.922384 | − | 0.386275i | \(-0.873762\pi\) | ||||
0.922384 | − | 0.386275i | \(-0.126238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.50807 | 0.226857 | 0.113428 | − | 0.993546i | \(-0.463817\pi\) | ||||
0.113428 | + | 0.993546i | \(0.463817\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.69143i | 0.0588169i | 0.999567 | + | 0.0294085i | \(0.00936235\pi\) | ||||
−0.999567 | + | 0.0294085i | \(0.990638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 36.3649i | − 1.26301i | −0.775374 | − | 0.631503i | \(-0.782438\pi\) | ||||
0.775374 | − | 0.631503i | \(-0.217562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16228 | 0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 31.4919i | − 1.08982i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0508 | −0.450563 | −0.225281 | − | 0.974294i | \(-0.572330\pi\) | ||||
−0.225281 | + | 0.974294i | \(0.572330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | 0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 30.1519i | − 1.03726i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.38105 | −0.0474534 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.09310i | 0.0717504i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 41.2379i | − 1.41196i | −0.708232 | − | 0.705979i | \(-0.750507\pi\) | ||||
0.708232 | − | 0.705979i | \(-0.249493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.1227 | −1.30225 | −0.651123 | − | 0.758973i | \(-0.725702\pi\) | ||||
−0.651123 | + | 0.758973i | \(0.725702\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1270i | 0.823203i | 0.911364 | + | 0.411602i | \(0.135030\pi\) | ||||
−0.911364 | + | 0.411602i | \(0.864970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.6252 | 0.395726 | 0.197863 | − | 0.980230i | \(-0.436600\pi\) | ||||
0.197863 | + | 0.980230i | \(0.436600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.4919 | 0.832751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.3646i | 1.26751i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −71.2379 | −2.41380 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.96816i | 0.201761i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 17.4919i | − 0.590661i | −0.955395 | − | 0.295330i | \(-0.904570\pi\) | ||||
0.955395 | − | 0.295330i | \(-0.0954297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.6119 | 0.930269 | 0.465134 | − | 0.885240i | \(-0.346006\pi\) | ||||
0.465134 | + | 0.885240i | \(0.346006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 31.2379i | − 1.05124i | −0.850720 | − | 0.525620i | \(-0.823834\pi\) | ||||
0.850720 | − | 0.525620i | \(-0.176166\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.86458 | 0.297643 | 0.148822 | − | 0.988864i | \(-0.452452\pi\) | ||||
0.148822 | + | 0.988864i | \(0.452452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.12702 | −0.104877 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.8544i | 1.93602i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.8730 | −0.363444 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.1464i | 0.571865i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.5481 | 0.583318 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000i | 0.265636i | 0.991140 | + | 0.132818i | \(0.0424025\pi\) | ||||
−0.991140 | + | 0.132818i | \(0.957597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5615 | −0.780628 | −0.390314 | − | 0.920682i | \(-0.627634\pi\) | ||||
−0.390314 | + | 0.920682i | \(0.627634\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.6028 | 1.50923 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.87507i | 0.127966i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.4919 | 1.50064 | 0.750320 | − | 0.661075i | \(-0.229899\pi\) | ||||
0.750320 | + | 0.661075i | \(0.229899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.1464i | 0.564382i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 16.8730i | − 0.554780i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8219 | 0.355054 | 0.177527 | − | 0.984116i | \(-0.443190\pi\) | ||||
0.177527 | + | 0.984116i | \(0.443190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.87298i | − 0.258027i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.2211 | −1.02104 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.5081 | 0.343284 | 0.171642 | − | 0.985159i | \(-0.445093\pi\) | ||||
0.171642 | + | 0.985159i | \(0.445093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 39.9499i | − 1.30233i | −0.758937 | − | 0.651165i | \(-0.774281\pi\) | ||||
0.758937 | − | 0.651165i | \(-0.225719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.61895 | 0.117849 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 49.4367i | − 1.60648i | −0.595657 | − | 0.803239i | \(-0.703108\pi\) | ||||
0.595657 | − | 0.803239i | \(-0.296892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.4919i | 1.08719i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.2848 | −0.624696 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.2379i | 1.75510i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.3858 | −0.464542 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.3039i | 1.94125i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2379 | 0.682965 | 0.341482 | − | 0.939888i | \(-0.389071\pi\) | ||||
0.341482 | + | 0.939888i | \(0.389071\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.1574i | 1.38499i | 0.721424 | + | 0.692494i | \(0.243488\pi\) | ||||
−0.721424 | + | 0.692494i | \(0.756512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000i | 0.448819i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.46292 | −0.270753 | −0.135376 | − | 0.990794i | \(-0.543224\pi\) | ||||
−0.135376 | + | 0.990794i | \(0.543224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.7298i | 1.14193i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.57737 | 0.305471 | 0.152735 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −76.7298 | −2.44482 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.16228i | − 0.100555i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.6190 | −1.29030 | −0.645152 | − | 0.764054i | \(-0.723206\pi\) | ||||
−0.645152 | + | 0.764054i | \(0.723206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 22.0907i | − 0.700321i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0000i | 0.570066i | 0.958518 | + | 0.285033i | \(0.0920045\pi\) | ||||
−0.958518 | + | 0.285033i | \(0.907995\pi\) | |||||||
\(998\) | 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.c.3025.7 | 8 | ||
3.2 | odd | 2 | inner | 6048.2.c.c.3025.1 | 8 | ||
4.3 | odd | 2 | 1512.2.c.c.757.3 | ✓ | 8 | ||
8.3 | odd | 2 | 1512.2.c.c.757.4 | yes | 8 | ||
8.5 | even | 2 | inner | 6048.2.c.c.3025.2 | 8 | ||
12.11 | even | 2 | 1512.2.c.c.757.6 | yes | 8 | ||
24.5 | odd | 2 | inner | 6048.2.c.c.3025.8 | 8 | ||
24.11 | even | 2 | 1512.2.c.c.757.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.c.757.3 | ✓ | 8 | 4.3 | odd | 2 | ||
1512.2.c.c.757.4 | yes | 8 | 8.3 | odd | 2 | ||
1512.2.c.c.757.5 | yes | 8 | 24.11 | even | 2 | ||
1512.2.c.c.757.6 | yes | 8 | 12.11 | even | 2 | ||
6048.2.c.c.3025.1 | 8 | 3.2 | odd | 2 | inner | ||
6048.2.c.c.3025.2 | 8 | 8.5 | even | 2 | inner | ||
6048.2.c.c.3025.7 | 8 | 1.1 | even | 1 | trivial | ||
6048.2.c.c.3025.8 | 8 | 24.5 | odd | 2 | inner |