Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.12745506816.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 8x^{6} + 55x^{4} + 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.4 | ||
Root | \(0.581861 - 1.00781i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.361 |
Dual form | 1764.2.k.m.1549.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.87083 | + | 3.24037i | 0.836660 | + | 1.44914i | 0.892672 | + | 0.450708i | \(0.148828\pi\) |
−0.0560116 | + | 0.998430i | \(0.517838\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64575 | − | 4.58258i | 0.797724 | − | 1.38170i | −0.123371 | − | 0.992361i | \(-0.539370\pi\) |
0.921095 | − | 0.389338i | \(-0.127296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.87083 | − | 3.24037i | 0.453743 | − | 0.785905i | −0.544872 | − | 0.838519i | \(-0.683422\pi\) |
0.998615 | + | 0.0526138i | \(0.0167552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | + | 2.44949i | 0.324443 | + | 0.561951i | 0.981399 | − | 0.191977i | \(-0.0614899\pi\) |
−0.656957 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.64575 | − | 4.58258i | −0.551677 | − | 0.955533i | −0.998154 | − | 0.0607377i | \(-0.980655\pi\) |
0.446476 | − | 0.894795i | \(-0.352679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50000 | + | 7.79423i | −0.900000 | + | 1.55885i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29150 | 0.982607 | 0.491304 | − | 0.870988i | \(-0.336521\pi\) | ||||
0.491304 | + | 0.870988i | \(0.336521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24264 | − | 7.34847i | 0.762001 | − | 1.31982i | −0.179817 | − | 0.983700i | \(-0.557551\pi\) |
0.941818 | − | 0.336124i | \(-0.109116\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.74166 | −0.584349 | −0.292174 | − | 0.956365i | \(-0.594379\pi\) | ||||
−0.292174 | + | 0.956365i | \(0.594379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.74166 | − | 6.48074i | −0.545777 | − | 0.945313i | −0.998558 | − | 0.0536913i | \(-0.982901\pi\) |
0.452781 | − | 0.891622i | \(-0.350432\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.29150 | + | 9.16515i | −0.726844 | + | 1.25893i | 0.231367 | + | 0.972867i | \(0.425680\pi\) |
−0.958211 | + | 0.286064i | \(0.907653\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.7990 | 2.66970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.74166 | + | 6.48074i | −0.487122 | + | 0.843721i | −0.999890 | − | 0.0148066i | \(-0.995287\pi\) |
0.512768 | + | 0.858527i | \(0.328620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.94975 | + | 8.57321i | 0.633750 | + | 1.09769i | 0.986778 | + | 0.162075i | \(0.0518186\pi\) |
−0.353028 | + | 0.935613i | \(0.614848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.93725 | + | 13.7477i | 0.984495 | + | 1.70520i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | + | 10.3923i | −0.733017 | + | 1.26962i | 0.222571 | + | 0.974916i | \(0.428555\pi\) |
−0.955588 | + | 0.294706i | \(0.904778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.8745 | −1.88396 | −0.941979 | − | 0.335673i | \(-0.891036\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.707107 | − | 1.22474i | 0.0827606 | − | 0.143346i | −0.821674 | − | 0.569958i | \(-0.806960\pi\) |
0.904435 | + | 0.426612i | \(0.140293\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9666 | 1.64280 | 0.821401 | − | 0.570352i | \(-0.193193\pi\) | ||||
0.821401 | + | 0.570352i | \(0.193193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0000 | 1.51851 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.87083 | − | 3.24037i | −0.198307 | − | 0.343479i | 0.749672 | − | 0.661809i | \(-0.230211\pi\) |
−0.947980 | + | 0.318331i | \(0.896878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.29150 | + | 9.16515i | −0.542897 | + | 0.940325i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.89949 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332388\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.61249 | + | 9.72111i | −0.558463 | + | 0.967287i | 0.439162 | + | 0.898408i | \(0.355275\pi\) |
−0.997625 | + | 0.0688787i | \(0.978058\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41421 | − | 2.44949i | −0.139347 | − | 0.241355i | 0.787903 | − | 0.615800i | \(-0.211167\pi\) |
−0.927249 | + | 0.374444i | \(0.877834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.64575 | − | 4.58258i | −0.255774 | − | 0.443014i | 0.709331 | − | 0.704875i | \(-0.248997\pi\) |
−0.965106 | + | 0.261861i | \(0.915664\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | + | 13.8564i | −0.766261 | + | 1.32720i | 0.173316 | + | 0.984866i | \(0.444552\pi\) |
−0.939577 | + | 0.342337i | \(0.888782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.89949 | − | 17.1464i | 0.923133 | − | 1.59891i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.50000 | − | 14.7224i | −0.772727 | − | 1.33840i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14.9666 | −1.33866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.93725 | − | 13.7477i | 0.678125 | − | 1.17455i | −0.297419 | − | 0.954747i | \(-0.596126\pi\) |
0.975545 | − | 0.219801i | \(-0.0705407\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.65685 | 0.479808 | 0.239904 | − | 0.970797i | \(-0.422884\pi\) | ||||
0.239904 | + | 0.970797i | \(0.422884\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2250 | − | 19.4422i | 0.938679 | − | 1.62584i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.89949 | + | 17.1464i | 0.822108 | + | 1.42393i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.29150 | − | 9.16515i | −0.433497 | − | 0.750838i | 0.563675 | − | 0.825997i | \(-0.309387\pi\) |
−0.997172 | + | 0.0751583i | \(0.976054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.7490 | 2.55014 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.94975 | + | 8.57321i | −0.395033 | + | 0.684217i | −0.993105 | − | 0.117225i | \(-0.962600\pi\) |
0.598073 | + | 0.801442i | \(0.295933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | + | 17.3205i | 0.783260 | + | 1.35665i | 0.930033 | + | 0.367477i | \(0.119778\pi\) |
−0.146772 | + | 0.989170i | \(0.546888\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.48331 | −0.579076 | −0.289538 | − | 0.957166i | \(-0.593502\pi\) | ||||
−0.289538 | + | 0.957166i | \(0.593502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.61249 | + | 9.72111i | 0.426709 | + | 0.739082i | 0.996578 | − | 0.0826532i | \(-0.0263394\pi\) |
−0.569869 | + | 0.821736i | \(0.693006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.93725 | − | 13.7477i | 0.593258 | − | 1.02755i | −0.400532 | − | 0.916283i | \(-0.631175\pi\) |
0.993790 | − | 0.111271i | \(-0.0354920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.24264 | −0.315353 | −0.157676 | − | 0.987491i | \(-0.550400\pi\) | ||||
−0.157676 | + | 0.987491i | \(0.550400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.48331 | − | 12.9615i | 0.550184 | − | 0.952947i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.89949 | − | 17.1464i | −0.723923 | − | 1.25387i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.64575 | − | 4.58258i | −0.191440 | − | 0.331584i | 0.754288 | − | 0.656544i | \(-0.227982\pi\) |
−0.945728 | + | 0.324960i | \(0.894649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5830 | −0.754008 | −0.377004 | − | 0.926212i | \(-0.623046\pi\) | ||||
−0.377004 | + | 0.926212i | \(0.623046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.00000 | − | 12.1244i | −0.488901 | − | 0.846802i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9666 | 1.03526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.9666 | + | 25.9230i | 1.02072 | + | 1.76793i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.93725 | − | 13.7477i | 0.533917 | − | 0.924772i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2250 | + | 19.4422i | −0.745028 | + | 1.29043i | 0.205154 | + | 0.978730i | \(0.434230\pi\) |
−0.950182 | + | 0.311696i | \(0.899103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.36396 | − | 11.0227i | −0.420542 | − | 0.728401i | 0.575450 | − | 0.817837i | \(-0.304827\pi\) |
−0.995993 | + | 0.0894361i | \(0.971494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.93725 | − | 13.7477i | −0.519987 | − | 0.900644i | −0.999730 | − | 0.0232346i | \(-0.992604\pi\) |
0.479743 | − | 0.877409i | \(-0.340730\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0000 | − | 24.2487i | 0.913259 | − | 1.58181i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.8745 | −1.02684 | −0.513418 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513418 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8492 | + | 25.7196i | −0.956524 | + | 1.65675i | −0.225682 | + | 0.974201i | \(0.572461\pi\) |
−0.730842 | + | 0.682547i | \(0.760872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | + | 10.3923i | 0.381771 | + | 0.661247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.48331 | −0.472343 | −0.236171 | − | 0.971711i | \(-0.575893\pi\) | ||||
−0.236171 | + | 0.971711i | \(0.575893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.0000 | −1.76034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.61249 | − | 9.72111i | −0.350097 | − | 0.606386i | 0.636169 | − | 0.771550i | \(-0.280518\pi\) |
−0.986266 | + | 0.165164i | \(0.947185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.93725 | + | 13.7477i | −0.489432 | + | 0.847721i | −0.999926 | − | 0.0121601i | \(-0.996129\pi\) |
0.510494 | + | 0.859881i | \(0.329463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.5980 | −2.43248 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.87083 | + | 3.24037i | −0.114066 | + | 0.197569i | −0.917406 | − | 0.397952i | \(-0.869721\pi\) |
0.803340 | + | 0.595521i | \(0.203054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.89949 | + | 17.1464i | 0.601351 | + | 1.04157i | 0.992617 | + | 0.121293i | \(0.0387042\pi\) |
−0.391265 | + | 0.920278i | \(0.627962\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.8118 | + | 41.2432i | 1.43590 | + | 2.48706i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.29150 | −0.315665 | −0.157832 | − | 0.987466i | \(-0.550451\pi\) | ||||
−0.157832 | + | 0.987466i | \(0.550451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5563 | − | 26.9444i | 0.924729 | − | 1.60168i | 0.132733 | − | 0.991152i | \(-0.457625\pi\) |
0.791996 | − | 0.610526i | \(-0.209042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.50000 | + | 2.59808i | 0.0882353 | + | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1916 | 1.53013 | 0.765065 | − | 0.643953i | \(-0.222707\pi\) | ||||
0.765065 | + | 0.643953i | \(0.222707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.0000 | −1.63022 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.2250 | − | 19.4422i | −0.649157 | − | 1.12437i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.5203 | + | 32.0780i | −1.06047 | + | 1.83678i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1421 | −0.807134 | −0.403567 | − | 0.914950i | \(-0.632230\pi\) | ||||
−0.403567 | + | 0.914950i | \(0.632230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.74166 | − | 6.48074i | 0.212170 | − | 0.367489i | −0.740223 | − | 0.672361i | \(-0.765280\pi\) |
0.952393 | + | 0.304872i | \(0.0986136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.36396 | − | 11.0227i | −0.359712 | − | 0.623040i | 0.628200 | − | 0.778052i | \(-0.283792\pi\) |
−0.987913 | + | 0.155012i | \(0.950459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.29150 | − | 9.16515i | −0.297200 | − | 0.514766i | 0.678294 | − | 0.734791i | \(-0.262720\pi\) |
−0.975494 | + | 0.220024i | \(0.929386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0000 | − | 24.2487i | 0.783850 | − | 1.35767i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5830 | 0.588854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.0919 | + | 33.0681i | −1.05903 | + | 1.83429i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −44.8999 | −2.45314 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.4499 | − | 38.8844i | −1.21573 | − | 2.10571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.93725 | + | 13.7477i | −0.426094 | + | 0.738017i | −0.996522 | − | 0.0833311i | \(-0.973444\pi\) |
0.570428 | + | 0.821348i | \(0.306777\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6985 | −1.58972 | −0.794862 | − | 0.606791i | \(-0.792457\pi\) | ||||
−0.794862 | + | 0.606791i | \(0.792457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.35414 | + | 16.2019i | −0.497871 | + | 0.862338i | −0.999997 | − | 0.00245682i | \(-0.999218\pi\) |
0.502126 | + | 0.864794i | \(0.332551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.6985 | − | 51.4393i | −1.57623 | − | 2.73011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.64575 | + | 4.58258i | 0.139637 | + | 0.241859i | 0.927359 | − | 0.374172i | \(-0.122073\pi\) |
−0.787722 | + | 0.616031i | \(0.788740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.29150 | 0.276970 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.65685 | + | 9.79796i | −0.295285 | + | 0.511449i | −0.975051 | − | 0.221980i | \(-0.928748\pi\) |
0.679766 | + | 0.733429i | \(0.262081\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.4499 | 1.15623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.48331 | − | 12.9615i | −0.382380 | − | 0.662301i | 0.609022 | − | 0.793153i | \(-0.291562\pi\) |
−0.991402 | + | 0.130852i | \(0.958229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.64575 | + | 4.58258i | −0.134145 | + | 0.232346i | −0.925270 | − | 0.379308i | \(-0.876162\pi\) |
0.791126 | + | 0.611654i | \(0.209495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7990 | −1.00128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.48331 | + | 12.9615i | −0.376526 | + | 0.652163i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2635 | + | 28.1691i | 0.816239 | + | 1.41377i | 0.908434 | + | 0.418027i | \(0.137278\pi\) |
−0.0921950 | + | 0.995741i | \(0.529388\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.93725 | − | 13.7477i | −0.396368 | − | 0.686529i | 0.596907 | − | 0.802310i | \(-0.296396\pi\) |
−0.993275 | + | 0.115782i | \(0.963063\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | − | 31.1769i | 0.896644 | − | 1.55303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1660 | −1.04916 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6066 | + | 18.3712i | −0.524463 | + | 0.908396i | 0.475132 | + | 0.879915i | \(0.342400\pi\) |
−0.999594 | + | 0.0284813i | \(0.990933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.0000 | + | 48.4974i | 1.37447 | + | 2.38064i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.48331 | 0.365584 | 0.182792 | − | 0.983152i | \(-0.441487\pi\) | ||||
0.182792 | + | 0.983152i | \(0.441487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.8375 | + | 29.1633i | 0.816737 | + | 1.41463i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.93725 | − | 13.7477i | 0.382324 | − | 0.662205i | −0.609070 | − | 0.793117i | \(-0.708457\pi\) |
0.991394 | + | 0.130912i | \(0.0417905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.24264 | 0.203888 | 0.101944 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101944 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.48331 | − | 12.9615i | 0.357975 | − | 0.620032i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.64575 | − | 4.58258i | −0.125703 | − | 0.217725i | 0.796304 | − | 0.604896i | \(-0.206785\pi\) |
−0.922008 | + | 0.387172i | \(0.873452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.00000 | − | 12.1244i | 0.331832 | − | 0.574750i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.89949 | + | 17.1464i | −0.466149 | + | 0.807394i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.00000 | − | 15.5885i | −0.421002 | − | 0.729197i | 0.575036 | − | 0.818128i | \(-0.304988\pi\) |
−0.996038 | + | 0.0889312i | \(0.971655\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.74166 | 0.174266 | 0.0871332 | − | 0.996197i | \(-0.472229\pi\) | ||||
0.0871332 | + | 0.996197i | \(0.472229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7083 | + | 32.4037i | 0.865716 | + | 1.49946i | 0.866334 | + | 0.499465i | \(0.166470\pi\) |
−0.000617928 | 1.00000i | \(0.500197\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.1660 | − | 36.6606i | 0.973214 | − | 1.68566i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4558 | −1.16799 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7083 | − | 32.4037i | 0.854803 | − | 1.48056i | −0.0220238 | − | 0.999757i | \(-0.507011\pi\) |
0.876827 | − | 0.480806i | \(-0.159656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.48528 | − | 14.6969i | −0.386896 | − | 0.670123i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.5203 | + | 32.0780i | 0.840962 | + | 1.45659i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00000 | − | 10.3923i | 0.271886 | − | 0.470920i | −0.697459 | − | 0.716625i | \(-0.745686\pi\) |
0.969345 | + | 0.245705i | \(0.0790193\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8745 | 0.716407 | 0.358203 | − | 0.933644i | \(-0.383389\pi\) | ||||
0.358203 | + | 0.933644i | \(0.383389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.89949 | − | 17.1464i | 0.445851 | − | 0.772236i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | − | 27.7128i | −0.716258 | − | 1.24060i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.246214 | − | 0.969216i | \(-0.420813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9666 | 0.667329 | 0.333665 | − | 0.942692i | \(-0.391715\pi\) | ||||
0.333665 | + | 0.942692i | \(0.391715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.0000 | −1.86898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.5791 | + | 35.6441i | 0.912153 | + | 1.57990i | 0.811017 | + | 0.585023i | \(0.198915\pi\) |
0.101137 | + | 0.994873i | \(0.467752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.29150 | − | 9.16515i | 0.233171 | − | 0.403865i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.5980 | −1.74152 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.35414 | + | 16.2019i | −0.409812 | + | 0.709816i | −0.994868 | − | 0.101177i | \(-0.967739\pi\) |
0.585056 | + | 0.810993i | \(0.301073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.48528 | − | 14.6969i | −0.371035 | − | 0.642652i | 0.618690 | − | 0.785635i | \(-0.287664\pi\) |
−0.989725 | + | 0.142983i | \(0.954331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.8745 | − | 27.4955i | −0.691504 | − | 1.19772i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.50000 | + | 4.33013i | −0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.8745 | −0.687601 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.89949 | − | 17.1464i | 0.427992 | − | 0.741305i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.00000 | − | 8.66025i | −0.214967 | − | 0.372333i | 0.738296 | − | 0.674477i | \(-0.235631\pi\) |
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −59.8665 | −2.56440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.48331 | + | 12.9615i | 0.318800 | + | 0.552178i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.8745 | − | 27.4955i | 0.672624 | − | 1.16502i | −0.304533 | − | 0.952502i | \(-0.598500\pi\) |
0.977157 | − | 0.212518i | \(-0.0681664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.9411 | 1.43556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.74166 | + | 6.48074i | −0.157692 | + | 0.273131i | −0.934036 | − | 0.357179i | \(-0.883739\pi\) |
0.776344 | + | 0.630309i | \(0.217072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.2288 | − | 22.9129i | −0.554578 | − | 0.960558i | −0.997936 | − | 0.0642132i | \(-0.979546\pi\) |
0.443358 | − | 0.896345i | \(-0.353787\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | + | 34.6410i | −0.836974 | + | 1.44968i | 0.0554391 | + | 0.998462i | \(0.482344\pi\) |
−0.892413 | + | 0.451219i | \(0.850989\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 47.6235 | 1.98604 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.6066 | + | 18.3712i | −0.441559 | + | 0.764802i | −0.997805 | − | 0.0662152i | \(-0.978908\pi\) |
0.556247 | + | 0.831017i | \(0.312241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0000 | + | 48.4974i | 1.15964 | + | 2.00856i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4499 | 0.926608 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0958 | − | 22.6826i | −0.537780 | − | 0.931462i | −0.999023 | − | 0.0441886i | \(-0.985930\pi\) |
0.461243 | − | 0.887274i | \(-0.347404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.64575 | + | 4.58258i | −0.108102 | + | 0.187239i | −0.915002 | − | 0.403450i | \(-0.867811\pi\) |
0.806899 | + | 0.590689i | \(0.201144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.24264 | −0.173061 | −0.0865305 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865305 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.8041 | − | 55.0863i | 1.29302 | − | 2.23958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.48528 | + | 14.6969i | 0.344407 | + | 0.596530i | 0.985246 | − | 0.171145i | \(-0.0547467\pi\) |
−0.640839 | + | 0.767675i | \(0.721413\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.8745 | − | 27.4955i | −0.642214 | − | 1.11235i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0000 | − | 20.7846i | 0.484675 | − | 0.839482i | −0.515170 | − | 0.857088i | \(-0.672271\pi\) |
0.999845 | + | 0.0176058i | \(0.00560439\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.4575 | 1.06514 | 0.532570 | − | 0.846386i | \(-0.321226\pi\) | ||||
0.532570 | + | 0.846386i | \(0.321226\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.65685 | − | 9.79796i | 0.227368 | − | 0.393813i | −0.729659 | − | 0.683811i | \(-0.760321\pi\) |
0.957027 | + | 0.289998i | \(0.0936546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.9666 | −0.596759 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.9666 | − | 25.9230i | −0.593933 | − | 1.02872i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.5203 | + | 32.0780i | −0.731506 | + | 1.26701i | 0.224733 | + | 0.974420i | \(0.427849\pi\) |
−0.956239 | + | 0.292586i | \(0.905484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1421 | 0.557711 | 0.278856 | − | 0.960333i | \(-0.410045\pi\) | ||||
0.278856 | + | 0.960333i | \(0.410045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.2250 | + | 19.4422i | −0.441299 | + | 0.764353i | −0.997786 | − | 0.0665037i | \(-0.978816\pi\) |
0.556487 | + | 0.830856i | \(0.312149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.7990 | + | 34.2929i | 0.777178 | + | 1.34611i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.93725 | + | 13.7477i | 0.310609 | + | 0.537990i | 0.978494 | − | 0.206274i | \(-0.0661338\pi\) |
−0.667886 | + | 0.744264i | \(0.732800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.6235 | −1.85515 | −0.927575 | − | 0.373638i | \(-0.878110\pi\) | ||||
−0.927575 | + | 0.373638i | \(0.878110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6066 | + | 18.3712i | −0.412549 | + | 0.714556i | −0.995168 | − | 0.0981898i | \(-0.968695\pi\) |
0.582619 | + | 0.812746i | \(0.302028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0000 | − | 24.2487i | −0.542082 | − | 0.938914i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.3832 | 2.02223 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0000 | 1.38770 | 0.693849 | − | 0.720121i | \(-0.255914\pi\) | ||||
0.693849 | + | 0.720121i | \(0.255914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.8375 | − | 29.1633i | −0.647116 | − | 1.12084i | −0.983808 | − | 0.179223i | \(-0.942642\pi\) |
0.336692 | − | 0.941615i | \(-0.390692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.93725 | − | 13.7477i | 0.303711 | − | 0.526042i | −0.673263 | − | 0.739403i | \(-0.735108\pi\) |
0.976973 | + | 0.213361i | \(0.0684411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.3970 | 2.26944 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.4499 | + | 38.8844i | −0.855275 | + | 1.48138i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.48528 | − | 14.6969i | −0.322795 | − | 0.559098i | 0.658268 | − | 0.752783i | \(-0.271289\pi\) |
−0.981064 | + | 0.193685i | \(0.937956\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5830 | + | 18.3303i | 0.401436 | + | 0.695308i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.00000 | + | 12.1244i | −0.265144 | + | 0.459243i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8745 | 0.599572 | 0.299786 | − | 0.954006i | \(-0.403085\pi\) | ||||
0.299786 | + | 0.954006i | \(0.403085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.65685 | − | 9.79796i | 0.213352 | − | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | + | 6.92820i | 0.150223 | + | 0.260194i | 0.931309 | − | 0.364229i | \(-0.118667\pi\) |
−0.781086 | + | 0.624423i | \(0.785334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.8999 | −1.68151 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.0000 | 3.14142 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9666 | − | 25.9230i | −0.558161 | − | 0.966763i | −0.997650 | − | 0.0685154i | \(-0.978174\pi\) |
0.439489 | − | 0.898248i | \(-0.355160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.8118 | + | 41.2432i | −0.884347 | + | 1.53173i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1421 | 0.524503 | 0.262251 | − | 0.965000i | \(-0.415535\pi\) | ||||
0.262251 | + | 0.965000i | \(0.415535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9666 | − | 25.9230i | 0.553561 | − | 0.958795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.3345 | − | 40.4166i | −0.861880 | − | 1.49282i | −0.870112 | − | 0.492854i | \(-0.835954\pi\) |
0.00823152 | − | 0.999966i | \(-0.497380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.7490 | + | 54.9909i | 1.16949 | + | 2.02562i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.00000 | + | 10.3923i | −0.220714 | + | 0.382287i | −0.955025 | − | 0.296526i | \(-0.904172\pi\) |
0.734311 | + | 0.678813i | \(0.237505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.0405 | −1.35888 | −0.679442 | − | 0.733729i | \(-0.737778\pi\) | ||||
−0.679442 | + | 0.733729i | \(0.737778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.7990 | − | 34.2929i | 0.725379 | − | 1.25639i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.9666 | 0.544691 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5791 | + | 35.6441i | 0.745992 | + | 1.29210i | 0.949730 | + | 0.313071i | \(0.101358\pi\) |
−0.203737 | + | 0.979026i | \(0.565309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8745 | + | 27.4955i | −0.573195 | + | 0.992803i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.24264 | 0.152994 | 0.0764968 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764968 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.3208 | + | 42.1248i | −0.874757 | + | 1.51512i | −0.0177365 | + | 0.999843i | \(0.505646\pi\) |
−0.857021 | + | 0.515282i | \(0.827687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.1838 | + | 66.1362i | 1.37160 | + | 2.37568i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.29150 | − | 9.16515i | −0.189588 | − | 0.328376i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.0000 | + | 72.7461i | −1.50288 | + | 2.60306i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.0405 | −1.32203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7990 | − | 34.2929i | 0.705758 | − | 1.22241i | −0.260660 | − | 0.965431i | \(-0.583940\pi\) |
0.966417 | − | 0.256978i | \(-0.0827266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.0000 | + | 36.3731i | 0.745732 | + | 1.29165i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2250 | 0.397609 | 0.198804 | − | 0.980039i | \(-0.436294\pi\) | ||||
0.198804 | + | 0.980039i | \(0.436294\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.0000 | −0.990569 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.74166 | − | 6.48074i | −0.132040 | − | 0.228700i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.5830 | + | 18.3303i | −0.372079 | + | 0.644459i | −0.989885 | − | 0.141871i | \(-0.954688\pi\) |
0.617806 | + | 0.786330i | \(0.288022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.4166 | + | 64.8074i | −1.31065 | + | 2.27010i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.3137 | + | 19.5959i | 0.395817 | + | 0.685574i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.8745 | + | 27.4955i | 0.554024 | + | 0.959598i | 0.997979 | + | 0.0635487i | \(0.0202418\pi\) |
−0.443955 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | + | 3.46410i | −0.0697156 | + | 0.120751i | −0.898776 | − | 0.438408i | \(-0.855543\pi\) |
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.8745 | −0.552011 | −0.276005 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276005 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.19239 | − | 15.9217i | 0.319265 | − | 0.552983i | −0.661070 | − | 0.750324i | \(-0.729897\pi\) |
0.980335 | + | 0.197341i | \(0.0632307\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | − | 24.2487i | −0.484490 | − | 0.839161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.48331 | 0.258353 | 0.129176 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129176 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | −0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.35414 | + | 16.2019i | 0.321792 | + | 0.557361i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5830 | + | 18.3303i | −0.362781 | + | 0.628355i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.1543 | 1.88845 | 0.944224 | − | 0.329304i | \(-0.106814\pi\) | ||||
0.944224 | + | 0.329304i | \(0.106814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5791 | − | 35.6441i | 0.702969 | − | 1.21758i | −0.264450 | − | 0.964399i | \(-0.585190\pi\) |
0.967419 | − | 0.253179i | \(-0.0814762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.89949 | − | 17.1464i | −0.337766 | − | 0.585029i | 0.646246 | − | 0.763129i | \(-0.276338\pi\) |
−0.984012 | + | 0.178101i | \(0.943005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.64575 | − | 4.58258i | −0.0900624 | − | 0.155993i | 0.817475 | − | 0.575964i | \(-0.195373\pi\) |
−0.907537 | + | 0.419972i | \(0.862040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | + | 36.3731i | −0.714021 | + | 1.23672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.1660 | 0.718008 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.4558 | + | 44.0908i | −0.862538 | + | 1.49396i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.00000 | − | 6.92820i | −0.135070 | − | 0.233949i | 0.790554 | − | 0.612392i | \(-0.209793\pi\) |
−0.925624 | + | 0.378444i | \(0.876459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.1249 | 1.89089 | 0.945447 | − | 0.325775i | \(-0.105625\pi\) | ||||
0.945447 | + | 0.325775i | \(0.105625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7083 | − | 32.4037i | −0.628163 | − | 1.08801i | −0.987920 | − | 0.154964i | \(-0.950474\pi\) |
0.359757 | − | 0.933046i | \(-0.382859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5830 | − | 18.3303i | 0.354147 | − | 0.613400i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59.3970 | 1.98542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.4499 | − | 38.8844i | 0.748748 | − | 1.29687i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7990 | + | 34.2929i | 0.659600 | + | 1.14246i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.93725 | − | 13.7477i | −0.263843 | − | 0.456990i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | + | 13.8564i | −0.265636 | + | 0.460094i | −0.967730 | − | 0.251990i | \(-0.918915\pi\) |
0.702094 | + | 0.712084i | \(0.252248\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.29150 | 0.175315 | 0.0876577 | − | 0.996151i | \(-0.472062\pi\) | ||||
0.0876577 | + | 0.996151i | \(0.472062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.5980 | − | 68.5857i | 1.31050 | − | 2.26986i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.00000 | − | 3.46410i | −0.0659739 | − | 0.114270i | 0.831152 | − | 0.556046i | \(-0.187682\pi\) |
−0.897126 | + | 0.441776i | \(0.854349\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67.3498 | −2.21685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.0000 | 1.18367 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.35414 | − | 16.2019i | −0.306899 | − | 0.531566i | 0.670783 | − | 0.741654i | \(-0.265958\pi\) |
−0.977682 | + | 0.210088i | \(0.932625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 37.0405 | − | 64.1561i | 1.21135 | − | 2.09813i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.3553 | 1.15501 | 0.577504 | − | 0.816388i | \(-0.304027\pi\) | ||||
0.577504 | + | 0.816388i | \(0.304027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0958 | − | 22.6826i | 0.426911 | − | 0.739431i | −0.569686 | − | 0.821863i | \(-0.692935\pi\) |
0.996597 | + | 0.0824312i | \(0.0262685\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.89949 | + | 17.1464i | 0.322372 | + | 0.558365i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8118 | − | 41.2432i | −0.773778 | − | 1.34022i | −0.935479 | − | 0.353383i | \(-0.885031\pi\) |
0.161700 | − | 0.986840i | \(-0.448302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.3320 | 1.37127 | 0.685634 | − | 0.727946i | \(-0.259525\pi\) | ||||
0.685634 | + | 0.727946i | \(0.259525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.89949 | − | 17.1464i | 0.320340 | − | 0.554845i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5000 | − | 35.5070i | −0.661290 | − | 1.14539i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.48331 | −0.240896 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.48331 | + | 12.9615i | 0.240151 | + | 0.415954i | 0.960757 | − | 0.277391i | \(-0.0894697\pi\) |
−0.720606 | + | 0.693345i | \(0.756136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.93725 | − | 13.7477i | 0.253935 | − | 0.439829i | −0.710671 | − | 0.703525i | \(-0.751608\pi\) |
0.964606 | + | 0.263696i | \(0.0849417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.7990 | −0.632778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.48331 | + | 12.9615i | −0.238681 | + | 0.413407i | −0.960336 | − | 0.278846i | \(-0.910048\pi\) |
0.721655 | + | 0.692253i | \(0.243382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.7990 | − | 34.2929i | −0.630848 | − | 1.09266i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.1660 | − | 36.6606i | −0.673040 | − | 1.16574i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | + | 38.1051i | −0.698853 | + | 1.21045i | 0.270011 | + | 0.962857i | \(0.412973\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.707107 | − | 1.22474i | 0.0223943 | − | 0.0387881i | −0.854611 | − | 0.519269i | \(-0.826204\pi\) |
0.877005 | + | 0.480481i | \(0.159538\pi\) | |||||||
\(998\) | 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 | 1764.2.k.m.361.4 | 8 | ||
3.2 | odd | 2 | inner | 1764.2.k.m.361.1 | 8 | ||
7.2 | even | 3 | inner | 1764.2.k.m.1549.4 | 8 | ||
7.3 | odd | 6 | 1764.2.a.m.1.3 | yes | 4 | ||
7.4 | even | 3 | 1764.2.a.m.1.1 | ✓ | 4 | ||
7.5 | odd | 6 | inner | 1764.2.k.m.1549.2 | 8 | ||
7.6 | odd | 2 | inner | 1764.2.k.m.361.2 | 8 | ||
21.2 | odd | 6 | inner | 1764.2.k.m.1549.1 | 8 | ||
21.5 | even | 6 | inner | 1764.2.k.m.1549.3 | 8 | ||
21.11 | odd | 6 | 1764.2.a.m.1.4 | yes | 4 | ||
21.17 | even | 6 | 1764.2.a.m.1.2 | yes | 4 | ||
21.20 | even | 2 | inner | 1764.2.k.m.361.3 | 8 | ||
28.3 | even | 6 | 7056.2.a.cy.1.4 | 4 | |||
28.11 | odd | 6 | 7056.2.a.cy.1.2 | 4 | |||
84.11 | even | 6 | 7056.2.a.cy.1.3 | 4 | |||
84.59 | odd | 6 | 7056.2.a.cy.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.a.m.1.1 | ✓ | 4 | 7.4 | even | 3 | ||
1764.2.a.m.1.2 | yes | 4 | 21.17 | even | 6 | ||
1764.2.a.m.1.3 | yes | 4 | 7.3 | odd | 6 | ||
1764.2.a.m.1.4 | yes | 4 | 21.11 | odd | 6 | ||
1764.2.k.m.361.1 | 8 | 3.2 | odd | 2 | inner | ||
1764.2.k.m.361.2 | 8 | 7.6 | odd | 2 | inner | ||
1764.2.k.m.361.3 | 8 | 21.20 | even | 2 | inner | ||
1764.2.k.m.361.4 | 8 | 1.1 | even | 1 | trivial | ||
1764.2.k.m.1549.1 | 8 | 21.2 | odd | 6 | inner | ||
1764.2.k.m.1549.2 | 8 | 7.5 | odd | 6 | inner | ||
1764.2.k.m.1549.3 | 8 | 21.5 | even | 6 | inner | ||
1764.2.k.m.1549.4 | 8 | 7.2 | even | 3 | inner | ||
7056.2.a.cy.1.1 | 4 | 84.59 | odd | 6 | |||
7056.2.a.cy.1.2 | 4 | 28.11 | odd | 6 | |||
7056.2.a.cy.1.3 | 4 | 84.11 | even | 6 | |||
7056.2.a.cy.1.4 | 4 | 28.3 | even | 6 |