Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,2,Mod(361,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("3528.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.s (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: | \(28.1712218331\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.361 |
Dual form | 3528.2.s.bi.3313.2 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.41421 | + | 2.44949i | 0.632456 | + | 1.09545i | 0.987048 | + | 0.160424i | \(0.0512862\pi\) |
−0.354593 | + | 0.935021i | \(0.615380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | − | 2.44949i | 0.342997 | − | 0.594089i | −0.641991 | − | 0.766712i | \(-0.721891\pi\) |
0.984988 | + | 0.172624i | \(0.0552245\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | − | 4.89898i | −0.648886 | − | 1.12390i | −0.983389 | − | 0.181509i | \(-0.941902\pi\) |
0.334504 | − | 0.942394i | \(-0.391431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | + | 2.59808i | −0.300000 | + | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | − | 4.89898i | 0.508001 | − | 0.879883i | −0.491957 | − | 0.870620i | \(-0.663718\pi\) |
0.999957 | − | 0.00926296i | \(-0.00294853\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | − | 9.79796i | −0.825137 | − | 1.42918i | −0.901815 | − | 0.432123i | \(-0.857765\pi\) |
0.0766776 | − | 0.997056i | \(-0.475569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.65685 | + | 9.79796i | −0.736460 | + | 1.27559i | 0.217620 | + | 0.976034i | \(0.430171\pi\) |
−0.954080 | + | 0.299552i | \(0.903163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.82843 | − | 4.89898i | −0.362143 | − | 0.627250i | 0.626170 | − | 0.779686i | \(-0.284621\pi\) |
−0.988313 | + | 0.152436i | \(0.951288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | + | 13.8564i | 0.992278 | + | 1.71868i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3137 | −1.24184 | −0.620920 | − | 0.783874i | \(-0.713241\pi\) | ||||
−0.620920 | + | 0.783874i | \(0.713241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264 | + | 7.34847i | 0.449719 | + | 0.778936i | 0.998367 | − | 0.0571170i | \(-0.0181908\pi\) |
−0.548648 | + | 0.836053i | \(0.684857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.00000 | − | 13.8564i | 0.820783 | − | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3137 | −1.14873 | −0.574367 | − | 0.818598i | \(-0.694752\pi\) | ||||
−0.574367 | + | 0.818598i | \(0.694752\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264 | − | 7.34847i | 0.422159 | − | 0.731200i | −0.573992 | − | 0.818861i | \(-0.694606\pi\) |
0.996150 | + | 0.0876610i | \(0.0279392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.48528 | + | 14.6969i | 0.836080 | + | 1.44813i | 0.893148 | + | 0.449762i | \(0.148491\pi\) |
−0.0570688 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | + | 15.5885i | 0.870063 | + | 1.50699i | 0.861931 | + | 0.507026i | \(0.169255\pi\) |
0.00813215 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | + | 12.1244i | −0.670478 | + | 1.16130i | 0.307290 | + | 0.951616i | \(0.400578\pi\) |
−0.977769 | + | 0.209687i | \(0.932756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.48528 | + | 14.6969i | −0.791257 | + | 1.37050i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | + | 9.79796i | 0.494242 | + | 0.856052i | 0.999978 | − | 0.00663646i | \(-0.00211246\pi\) |
−0.505736 | + | 0.862688i | \(0.668779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.00000 | − | 6.92820i | 0.341743 | − | 0.591916i | −0.643013 | − | 0.765855i | \(-0.722316\pi\) |
0.984757 | + | 0.173939i | \(0.0556494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3137 | −0.959616 | −0.479808 | − | 0.877373i | \(-0.659294\pi\) | ||||
−0.479808 | + | 0.877373i | \(0.659294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | − | 9.79796i | 0.473050 | − | 0.819346i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.65685 | + | 9.79796i | 0.469776 | + | 0.813676i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0000 | + | 17.3205i | 0.819232 | + | 1.41895i | 0.906249 | + | 0.422744i | \(0.138933\pi\) |
−0.0870170 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.82843 | − | 4.89898i | 0.225733 | − | 0.390981i | −0.730806 | − | 0.682585i | \(-0.760856\pi\) |
0.956539 | + | 0.291604i | \(0.0941890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | + | 3.46410i | 0.156652 | + | 0.271329i | 0.933659 | − | 0.358162i | \(-0.116597\pi\) |
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.6274 | 1.75096 | 0.875481 | − | 0.483252i | \(-0.160545\pi\) | ||||
0.875481 | + | 0.483252i | \(0.160545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.41421 | − | 2.44949i | −0.107521 | − | 0.186231i | 0.807245 | − | 0.590217i | \(-0.200958\pi\) |
−0.914765 | + | 0.403986i | \(0.867625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0000 | − | 19.0526i | 0.822179 | − | 1.42406i | −0.0818780 | − | 0.996642i | \(-0.526092\pi\) |
0.904057 | − | 0.427413i | \(-0.140575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9706 | −1.26141 | −0.630706 | − | 0.776022i | \(-0.717235\pi\) | ||||
−0.630706 | + | 0.776022i | \(0.717235\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | + | 4.89898i | −0.207950 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.82843 | − | 4.89898i | −0.206835 | − | 0.358249i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | + | 19.0526i | −0.791797 | + | 1.37143i | 0.133056 | + | 0.991109i | \(0.457521\pi\) |
−0.924853 | + | 0.380325i | \(0.875812\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 4.00000 | + | 6.92820i | 0.279372 | + | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3137 | −0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | − | 9.79796i | −0.385794 | − | 0.668215i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | − | 13.8564i | 0.538138 | − | 0.932083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3137 | −0.757622 | −0.378811 | − | 0.925474i | \(-0.623667\pi\) | ||||
−0.378811 | + | 0.925474i | \(0.623667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.48528 | + | 14.6969i | 0.560723 | + | 0.971201i | 0.997434 | + | 0.0715988i | \(0.0228101\pi\) |
−0.436710 | + | 0.899602i | \(0.643857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | + | 6.92820i | 0.262049 | + | 0.453882i | 0.966786 | − | 0.255586i | \(-0.0822686\pi\) |
−0.704737 | + | 0.709468i | \(0.748935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | − | 27.7128i | 1.04372 | − | 1.80778i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65685 | + | 9.79796i | −0.364390 | + | 0.631142i | −0.988678 | − | 0.150052i | \(-0.952056\pi\) |
0.624288 | + | 0.781194i | \(0.285389\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0000 | − | 27.7128i | −1.01806 | − | 1.76332i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.6274 | −1.42823 | −0.714115 | − | 0.700028i | \(-0.753171\pi\) | ||||
−0.714115 | + | 0.700028i | \(0.753171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.7279 | − | 22.0454i | −0.793946 | − | 1.37515i | −0.923506 | − | 0.383583i | \(-0.874690\pi\) |
0.129560 | − | 0.991572i | \(-0.458643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | + | 8.66025i | −0.308313 | + | 0.534014i | −0.977993 | − | 0.208635i | \(-0.933098\pi\) |
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.9411 | 2.08499 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.5563 | + | 26.9444i | −0.948487 | + | 1.64283i | −0.199874 | + | 0.979822i | \(0.564053\pi\) |
−0.748614 | + | 0.663007i | \(0.769280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.48528 | − | 14.6969i | −0.515444 | − | 0.892775i | −0.999839 | − | 0.0179261i | \(-0.994294\pi\) |
0.484395 | − | 0.874849i | \(-0.339040\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1421 | − | 24.4949i | 0.840663 | − | 1.45607i | −0.0486726 | − | 0.998815i | \(-0.515499\pi\) |
0.889335 | − | 0.457256i | \(-0.151168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.50000 | + | 7.79423i | 0.264706 | + | 0.458484i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.7990 | −1.15667 | −0.578335 | − | 0.815800i | \(-0.696297\pi\) | ||||
−0.578335 | + | 0.815800i | \(0.696297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.0000 | −1.86311 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9706 | + | 29.3939i | 0.981433 | + | 1.69989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | − | 13.8564i | 0.458079 | − | 0.793416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9706 | 0.968561 | 0.484281 | − | 0.874913i | \(-0.339081\pi\) | ||||
0.484281 | + | 0.874913i | \(0.339081\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685 | − | 9.79796i | 0.320771 | − | 0.555591i | −0.659877 | − | 0.751374i | \(-0.729391\pi\) |
0.980647 | + | 0.195783i | \(0.0627248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9706 | − | 29.3939i | −0.959233 | − | 1.66144i | −0.724370 | − | 0.689412i | \(-0.757869\pi\) |
−0.234863 | − | 0.972028i | \(-0.575464\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | − | 6.92820i | 0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.48528 | + | 14.6969i | −0.470679 | + | 0.815239i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | + | 17.3205i | 0.549650 | + | 0.952021i | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.9411 | 1.85440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.65685 | − | 9.79796i | −0.306336 | − | 0.530589i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.00000 | + | 1.73205i | −0.0536828 | + | 0.0929814i | −0.891618 | − | 0.452788i | \(-0.850429\pi\) |
0.837935 | + | 0.545770i | \(0.183763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9706 | 0.908413 | 0.454207 | − | 0.890896i | \(-0.349923\pi\) | ||||
0.454207 | + | 0.890896i | \(0.349923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.41421 | − | 2.44949i | 0.0752710 | − | 0.130373i | −0.825933 | − | 0.563768i | \(-0.809351\pi\) |
0.901204 | + | 0.433395i | \(0.142684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.48528 | + | 14.6969i | 0.450352 | + | 0.780033i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | − | 5.19615i | −0.158334 | − | 0.274242i | 0.775934 | − | 0.630814i | \(-0.217279\pi\) |
−0.934268 | + | 0.356572i | \(0.883946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.50000 | + | 11.2583i | −0.342105 | + | 0.592544i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.6274 | 1.16537 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.65685 | + | 9.79796i | 0.289052 | + | 0.500652i | 0.973584 | − | 0.228331i | \(-0.0733267\pi\) |
−0.684532 | + | 0.728983i | \(0.739993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | + | 24.2487i | −0.709828 | + | 1.22946i | 0.255092 | + | 0.966917i | \(0.417894\pi\) |
−0.964921 | + | 0.262542i | \(0.915439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9706 | 0.858238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3137 | − | 19.5959i | 0.569254 | − | 0.985978i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.48528 | − | 14.6969i | −0.425864 | − | 0.737618i | 0.570637 | − | 0.821203i | \(-0.306696\pi\) |
−0.996501 | + | 0.0835845i | \(0.973363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0000 | − | 27.7128i | 0.797017 | − | 1.38047i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.9706 | − | 29.3939i | 0.839140 | − | 1.45343i | −0.0514740 | − | 0.998674i | \(-0.516392\pi\) |
0.890614 | − | 0.454759i | \(-0.150275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | − | 27.7128i | −0.785409 | − | 1.36037i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3137 | −0.552711 | −0.276355 | − | 0.961056i | \(-0.589127\pi\) | ||||
−0.276355 | + | 0.961056i | \(0.589127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24264 | + | 7.34847i | 0.205798 | + | 0.356453i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3137 | −0.543702 | −0.271851 | − | 0.962339i | \(-0.587636\pi\) | ||||
−0.271851 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.9706 | − | 29.3939i | 0.811812 | − | 1.40610i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.9706 | − | 29.3939i | −0.809961 | − | 1.40289i | −0.912890 | − | 0.408205i | \(-0.866155\pi\) |
0.102930 | − | 0.994689i | \(-0.467178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.00000 | − | 1.73205i | −0.0475114 | − | 0.0822922i | 0.841292 | − | 0.540581i | \(-0.181796\pi\) |
−0.888803 | + | 0.458289i | \(0.848462\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | + | 20.7846i | −0.568855 | + | 0.985285i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0000 | −1.51017 | −0.755087 | − | 0.655625i | \(-0.772405\pi\) | ||||
−0.755087 | + | 0.655625i | \(0.772405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.82843 | − | 4.89898i | 0.133185 | − | 0.230684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00000 | − | 5.19615i | −0.140334 | − | 0.243066i | 0.787288 | − | 0.616585i | \(-0.211484\pi\) |
−0.927622 | + | 0.373519i | \(0.878151\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1421 | 0.658665 | 0.329332 | − | 0.944214i | \(-0.393176\pi\) | ||||
0.329332 | + | 0.944214i | \(0.393176\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9706 | 0.778663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | + | 9.79796i | −0.258468 | + | 0.447680i | −0.965832 | − | 0.259170i | \(-0.916551\pi\) |
0.707364 | + | 0.706850i | \(0.249884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65685 | + | 9.79796i | 0.257930 | + | 0.446748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | − | 27.7128i | −0.726523 | − | 1.25837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0000 | + | 20.7846i | −0.543772 | + | 0.941841i | 0.454911 | + | 0.890537i | \(0.349671\pi\) |
−0.998683 | + | 0.0513038i | \(0.983662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 0.0902587 | 0.0451294 | − | 0.998981i | \(-0.485630\pi\) | ||||
0.0451294 | + | 0.998981i | \(0.485630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685 | − | 9.79796i | 0.254772 | − | 0.441278i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0000 | + | 17.3205i | 0.447661 | + | 0.775372i | 0.998233 | − | 0.0594153i | \(-0.0189236\pi\) |
−0.550572 | + | 0.834788i | \(0.685590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.3137 | −0.504453 | −0.252227 | − | 0.967668i | \(-0.581163\pi\) | ||||
−0.252227 | + | 0.967668i | \(0.581163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.41421 | + | 2.44949i | 0.0626839 | + | 0.108572i | 0.895664 | − | 0.444731i | \(-0.146701\pi\) |
−0.832980 | + | 0.553303i | \(0.813367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0000 | + | 41.5692i | −1.05757 | + | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.6274 | −0.995153 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5563 | + | 26.9444i | −0.681536 | + | 1.18046i | 0.292976 | + | 0.956120i | \(0.405354\pi\) |
−0.974512 | + | 0.224335i | \(0.927979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3137 | + | 19.5959i | 0.494714 | + | 0.856870i | 0.999981 | − | 0.00609311i | \(-0.00193951\pi\) |
−0.505268 | + | 0.862963i | \(0.668606\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | − | 13.8564i | −0.348485 | − | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0000 | 0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.4558 | + | 44.0908i | −1.10055 | + | 1.90621i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.5980 | −1.69619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | − | 19.5959i | −0.481980 | − | 0.834814i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | + | 10.3923i | −0.254228 | + | 0.440336i | −0.964686 | − | 0.263404i | \(-0.915155\pi\) |
0.710457 | + | 0.703740i | \(0.248488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.6274 | −0.957038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.9706 | + | 29.3939i | −0.715224 | + | 1.23880i | 0.247649 | + | 0.968850i | \(0.420342\pi\) |
−0.962873 | + | 0.269954i | \(0.912991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3137 | + | 19.5959i | 0.475971 | + | 0.824406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | − | 38.1051i | 0.920671 | − | 1.59465i | 0.122292 | − | 0.992494i | \(-0.460975\pi\) |
0.798379 | − | 0.602155i | \(-0.205691\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.0000 | −0.750652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.0000 | −1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.07107 | + | 12.2474i | 0.290374 | + | 0.502942i | 0.973898 | − | 0.226985i | \(-0.0728870\pi\) |
−0.683524 | + | 0.729928i | \(0.739554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.0000 | + | 19.0526i | −0.449448 | + | 0.778466i | −0.998350 | − | 0.0574201i | \(-0.981713\pi\) |
0.548902 | + | 0.835887i | \(0.315046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6274 | −0.922992 | −0.461496 | − | 0.887142i | \(-0.652687\pi\) | ||||
−0.461496 | + | 0.887142i | \(0.652687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.89949 | + | 17.1464i | −0.402472 | + | 0.697101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.65685 | + | 9.79796i | 0.229605 | + | 0.397687i | 0.957691 | − | 0.287799i | \(-0.0929234\pi\) |
−0.728086 | + | 0.685485i | \(0.759590\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.0000 | − | 55.4256i | −1.29458 | − | 2.24228i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 5.19615i | 0.121169 | − | 0.209871i | −0.799060 | − | 0.601251i | \(-0.794669\pi\) |
0.920229 | + | 0.391381i | \(0.128002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −48.0000 | −1.93241 | −0.966204 | − | 0.257780i | \(-0.917009\pi\) | ||||
−0.966204 | + | 0.257780i | \(0.917009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.65685 | + | 9.79796i | −0.227368 | + | 0.393813i | −0.957027 | − | 0.289998i | \(-0.906345\pi\) |
0.729659 | + | 0.683811i | \(0.239679\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 26.8468i | 0.620000 | + | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65685 | 0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.6274 | − | 39.1918i | −0.897942 | − | 1.55528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.0000 | + | 34.6410i | −0.789953 | + | 1.36824i | 0.136043 | + | 0.990703i | \(0.456562\pi\) |
−0.925995 | + | 0.377535i | \(0.876772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.9706 | −0.669254 | −0.334627 | − | 0.942351i | \(-0.608610\pi\) | ||||
−0.334627 | + | 0.942351i | \(0.608610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3137 | + | 19.5959i | 0.444102 | + | 0.769207i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0000 | − | 17.3205i | −0.391330 | − | 0.677804i | 0.601295 | − | 0.799027i | \(-0.294652\pi\) |
−0.992625 | + | 0.121223i | \(0.961318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | + | 27.7128i | −0.625172 | + | 1.08283i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.00000 | 0.233727 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.82843 | + | 4.89898i | −0.110013 | + | 0.190548i | −0.915775 | − | 0.401691i | \(-0.868423\pi\) |
0.805762 | + | 0.592239i | \(0.201756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.3137 | −0.436761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00000 | −0.231283 | −0.115642 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.24264 | + | 7.34847i | 0.163058 | + | 0.282425i | 0.935964 | − | 0.352096i | \(-0.114531\pi\) |
−0.772906 | + | 0.634521i | \(0.781198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.00000 | − | 12.1244i | 0.267848 | − | 0.463926i | −0.700458 | − | 0.713693i | \(-0.747021\pi\) |
0.968306 | + | 0.249768i | \(0.0803543\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.6274 | 0.864549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.9411 | − | 58.7878i | 1.29305 | − | 2.23964i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.3137 | + | 19.5959i | 0.430394 | + | 0.745464i | 0.996907 | − | 0.0785887i | \(-0.0250414\pi\) |
−0.566513 | + | 0.824053i | \(0.691708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0000 | − | 27.7128i | −0.606915 | − | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | − | 6.92820i | 0.151511 | − | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.00000 | −0.151078 | −0.0755390 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755390 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(702\) | 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 | ||||||||
\(709\) | −19.0000 | − | 32.9090i | −0.713560 | − | 1.23592i | −0.963512 | − | 0.267664i | \(-0.913748\pi\) |
0.249952 | − | 0.968258i | \(-0.419585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.9411 | 1.27111 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | 1.19673 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.65685 | − | 9.79796i | −0.210965 | − | 0.365402i | 0.741052 | − | 0.671448i | \(-0.234327\pi\) |
−0.952017 | + | 0.306046i | \(0.900994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.5980 | −1.46861 | −0.734304 | − | 0.678821i | \(-0.762491\pi\) | ||||
−0.734304 | + | 0.678821i | \(0.762491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.65685 | + | 9.79796i | −0.209226 | + | 0.362391i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.48528 | − | 14.6969i | −0.313411 | − | 0.542844i | 0.665687 | − | 0.746231i | \(-0.268138\pi\) |
−0.979098 | + | 0.203387i | \(0.934805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0000 | − | 31.1769i | 0.662141 | − | 1.14686i | −0.317911 | − | 0.948120i | \(-0.602981\pi\) |
0.980052 | − | 0.198741i | \(-0.0636852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.0000 | −0.953847 | −0.476924 | − | 0.878945i | \(-0.658248\pi\) | ||||
−0.476924 | + | 0.878945i | \(0.658248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.2843 | + | 48.9898i | −1.03626 | + | 1.79485i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | − | 41.5692i | −0.875772 | − | 1.51688i | −0.855938 | − | 0.517079i | \(-0.827019\pi\) |
−0.0198348 | − | 0.999803i | \(-0.506314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6274 | 0.823496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5563 | + | 26.9444i | 0.563917 | + | 0.976733i | 0.997150 | + | 0.0754510i | \(0.0240396\pi\) |
−0.433232 | + | 0.901282i | \(0.642627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.0000 | + | 55.4256i | −1.15545 | + | 2.00130i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.9411 | −1.22395 | −0.611974 | − | 0.790878i | \(-0.709624\pi\) | ||||
−0.611974 | + | 0.790878i | \(0.709624\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.5563 | − | 26.9444i | 0.559523 | − | 0.969122i | −0.438013 | − | 0.898969i | \(-0.644318\pi\) |
0.997536 | − | 0.0701537i | \(-0.0223490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.48528 | + | 14.6969i | 0.304800 | + | 0.527930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | − | 13.8564i | −0.286630 | − | 0.496457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.0000 | 0.571064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.9706 | − | 29.3939i | 0.604935 | − | 1.04778i | −0.387126 | − | 0.922027i | \(-0.626532\pi\) |
0.992062 | − | 0.125752i | \(-0.0401343\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0000 | − | 27.7128i | −0.568177 | − | 0.984111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4558 | 0.901692 | 0.450846 | − | 0.892602i | \(-0.351122\pi\) | ||||
0.450846 | + | 0.892602i | \(0.351122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.6274 | −0.794556 | −0.397278 | − | 0.917698i | \(-0.630045\pi\) | ||||
−0.397278 | + | 0.917698i | \(0.630045\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65685 | + | 9.79796i | −0.198151 | + | 0.343208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.3137 | + | 19.5959i | 0.395817 | + | 0.685574i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | + | 27.7128i | −0.557725 | + | 0.966008i | 0.439961 | + | 0.898017i | \(0.354992\pi\) |
−0.997686 | + | 0.0679910i | \(0.978341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.0000 | −1.73867 | −0.869335 | − | 0.494223i | \(-0.835453\pi\) | ||||
−0.869335 | + | 0.494223i | \(0.835453\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.82843 | − | 4.89898i | 0.0982353 | − | 0.170149i | −0.812719 | − | 0.582656i | \(-0.802014\pi\) |
0.910954 | + | 0.412507i | \(0.135347\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000 | + | 55.4256i | 1.10741 | + | 1.91808i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.2548 | −1.56237 | −0.781185 | − | 0.624299i | \(-0.785385\pi\) | ||||
−0.781185 | + | 0.624299i | \(0.785385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.8701 | + | 46.5403i | 0.924358 | + | 1.60104i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9706 | 0.581061 | 0.290531 | − | 0.956866i | \(-0.406168\pi\) | ||||
0.290531 | + | 0.956866i | \(0.406168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.07107 | + | 12.2474i | −0.241543 | + | 0.418365i | −0.961154 | − | 0.276013i | \(-0.910987\pi\) |
0.719611 | + | 0.694377i | \(0.244320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.4558 | − | 44.0908i | −0.868542 | − | 1.50436i | −0.863486 | − | 0.504372i | \(-0.831724\pi\) |
−0.00505571 | − | 0.999987i | \(-0.501609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.00000 | − | 15.5885i | −0.306364 | − | 0.530637i | 0.671200 | − | 0.741276i | \(-0.265779\pi\) |
−0.977564 | + | 0.210639i | \(0.932446\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00000 | − | 6.92820i | 0.136004 | − | 0.235566i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.9411 | − | 58.7878i | 1.15005 | − | 1.99195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | + | 39.8372i | 0.776655 | + | 1.34521i | 0.933860 | + | 0.357640i | \(0.116418\pi\) |
−0.157205 | + | 0.987566i | \(0.550248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.48528 | 0.285876 | 0.142938 | − | 0.989732i | \(-0.454345\pi\) | ||||
0.142938 | + | 0.989732i | \(0.454345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6274 | + | 39.1918i | 0.759754 | + | 1.31593i | 0.942976 | + | 0.332861i | \(0.108014\pi\) |
−0.183221 | + | 0.983072i | \(0.558653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.0000 | + | 55.4256i | −1.07084 | + | 1.85475i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.2254 | 2.07997 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.3137 | − | 19.5959i | 0.377333 | − | 0.653560i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.9706 | − | 29.3939i | −0.565371 | − | 0.979252i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.0000 | − | 41.5692i | −0.797787 | − | 1.38181i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | + | 17.3205i | −0.332045 | + | 0.575118i | −0.982913 | − | 0.184073i | \(-0.941072\pi\) |
0.650868 | + | 0.759191i | \(0.274405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.0000 | 1.52405 | 0.762024 | − | 0.647549i | \(-0.224206\pi\) | ||||
0.762024 | + | 0.647549i | \(0.224206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3137 | + | 19.5959i | −0.374429 | + | 0.648530i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | − | 13.8564i | −0.263896 | − | 0.457081i | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.9411 | 1.11719 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.3848 | − | 31.8434i | −0.603185 | − | 1.04475i | −0.992336 | − | 0.123573i | \(-0.960565\pi\) |
0.389151 | − | 0.921174i | \(-0.372769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | − | 13.8564i | 0.261628 | − | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.2548 | 1.47841 | 0.739205 | − | 0.673480i | \(-0.235201\pi\) | ||||
0.739205 | + | 0.673480i | \(0.235201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.89949 | + | 17.1464i | −0.322714 | + | 0.558958i | −0.981047 | − | 0.193769i | \(-0.937929\pi\) |
0.658333 | + | 0.752727i | \(0.271262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.48528 | + | 14.6969i | 0.276319 | + | 0.478598i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.0000 | + | 36.3731i | 0.682408 | + | 1.18197i | 0.974244 | + | 0.225497i | \(0.0724007\pi\) |
−0.291835 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.4558 | + | 44.0908i | −0.823732 | + | 1.42675i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | − | 0.866025i | −0.0161290 | − | 0.0279363i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −62.2254 | −2.00311 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3137 | − | 19.5959i | −0.363074 | − | 0.628863i | 0.625391 | − | 0.780312i | \(-0.284940\pi\) |
−0.988465 | + | 0.151449i | \(0.951606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.9706 | 0.542382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.3137 | + | 19.5959i | −0.360851 | + | 0.625013i | −0.988101 | − | 0.153805i | \(-0.950847\pi\) |
0.627250 | + | 0.778818i | \(0.284180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.65685 | − | 9.79796i | −0.180242 | − | 0.312189i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0000 | + | 48.4974i | −0.889449 | + | 1.54057i | −0.0489218 | + | 0.998803i | \(0.515578\pi\) |
−0.840528 | + | 0.541769i | \(0.817755\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7990 | − | 34.2929i | 0.627040 | − | 1.08607i | −0.361102 | − | 0.932526i | \(-0.617599\pi\) |
0.988143 | − | 0.153539i | \(-0.0490672\pi\) | |||||||
\(998\) | 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 | 3528.2.s.bi.361.2 | 4 | ||
3.2 | odd | 2 | 3528.2.s.bf.361.1 | 4 | |||
7.2 | even | 3 | inner | 3528.2.s.bi.3313.2 | 4 | ||
7.3 | odd | 6 | 3528.2.a.bf.1.2 | yes | 2 | ||
7.4 | even | 3 | 3528.2.a.bf.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 3528.2.s.bi.3313.1 | 4 | ||
7.6 | odd | 2 | inner | 3528.2.s.bi.361.1 | 4 | ||
21.2 | odd | 6 | 3528.2.s.bf.3313.1 | 4 | |||
21.5 | even | 6 | 3528.2.s.bf.3313.2 | 4 | |||
21.11 | odd | 6 | 3528.2.a.bi.1.2 | yes | 2 | ||
21.17 | even | 6 | 3528.2.a.bi.1.1 | yes | 2 | ||
21.20 | even | 2 | 3528.2.s.bf.361.2 | 4 | |||
28.3 | even | 6 | 7056.2.a.cq.1.2 | 2 | |||
28.11 | odd | 6 | 7056.2.a.cq.1.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.ck.1.2 | 2 | |||
84.59 | odd | 6 | 7056.2.a.ck.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3528.2.a.bf.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
3528.2.a.bf.1.2 | yes | 2 | 7.3 | odd | 6 | ||
3528.2.a.bi.1.1 | yes | 2 | 21.17 | even | 6 | ||
3528.2.a.bi.1.2 | yes | 2 | 21.11 | odd | 6 | ||
3528.2.s.bf.361.1 | 4 | 3.2 | odd | 2 | |||
3528.2.s.bf.361.2 | 4 | 21.20 | even | 2 | |||
3528.2.s.bf.3313.1 | 4 | 21.2 | odd | 6 | |||
3528.2.s.bf.3313.2 | 4 | 21.5 | even | 6 | |||
3528.2.s.bi.361.1 | 4 | 7.6 | odd | 2 | inner | ||
3528.2.s.bi.361.2 | 4 | 1.1 | even | 1 | trivial | ||
3528.2.s.bi.3313.1 | 4 | 7.5 | odd | 6 | inner | ||
3528.2.s.bi.3313.2 | 4 | 7.2 | even | 3 | inner | ||
7056.2.a.ck.1.1 | 2 | 84.59 | odd | 6 | |||
7056.2.a.ck.1.2 | 2 | 84.11 | even | 6 | |||
7056.2.a.cq.1.1 | 2 | 28.11 | odd | 6 | |||
7056.2.a.cq.1.2 | 2 | 28.3 | even | 6 |