Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.3 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.2.c.g.1727.6 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.317837i | − 0.142141i | −0.997471 | − | 0.0710706i | \(-0.977358\pi\) | ||||
0.997471 | − | 0.0710706i | \(-0.0226416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.44949i | − 0.547856i | −0.961750 | − | 0.273928i | \(-0.911677\pi\) | ||||
0.961750 | − | 0.273928i | \(-0.0883229\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09638 | 0.330570 | 0.165285 | − | 0.986246i | \(-0.447146\pi\) | ||||
0.165285 | + | 0.986246i | \(0.447146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.89898 | −0.804032 | −0.402016 | − | 0.915633i | \(-0.631690\pi\) | ||||
−0.402016 | + | 0.915633i | \(0.631690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.46410i | − 0.840168i | −0.907485 | − | 0.420084i | \(-0.862001\pi\) | ||||
0.907485 | − | 0.420084i | \(-0.137999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | 0.979796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 9.12096i | − 1.69372i | −0.531817 | − | 0.846859i | \(-0.678490\pi\) | ||||
0.531817 | − | 0.846859i | \(-0.321510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.44949i | − 1.33797i | −0.743277 | − | 0.668984i | \(-0.766729\pi\) | ||||
0.743277 | − | 0.668984i | \(-0.233271\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.460702 | −0.0778728 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | −0.805387 | −0.402694 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 9.75663i | − 1.52373i | −0.647736 | − | 0.761865i | \(-0.724284\pi\) | ||||
0.647736 | − | 0.761865i | \(-0.275716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.89898i | 1.05208i | 0.850458 | + | 0.526042i | \(0.176325\pi\) | ||||
−0.850458 | + | 0.526042i | \(0.823675\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.12096 | −1.33043 | −0.665214 | − | 0.746653i | \(-0.731660\pi\) | ||||
−0.665214 | + | 0.746653i | \(0.731660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.41761i | − 0.606806i | −0.952862 | − | 0.303403i | \(-0.901877\pi\) | ||||
0.952862 | − | 0.303403i | \(-0.0981228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.348469i | − 0.0469876i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.12096 | −1.18745 | −0.593724 | − | 0.804669i | \(-0.702343\pi\) | ||||
−0.593724 | + | 0.804669i | \(0.702343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.921404i | 0.114286i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.10102i | − 0.623189i | −0.950215 | − | 0.311594i | \(-0.899137\pi\) | ||||
0.950215 | − | 0.311594i | \(-0.100863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.56388 | 0.897667 | 0.448834 | − | 0.893615i | \(-0.351840\pi\) | ||||
0.448834 | + | 0.893615i | \(0.351840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.89898 | 0.222259 | 0.111129 | − | 0.993806i | \(-0.464553\pi\) | ||||
0.111129 | + | 0.993806i | \(0.464553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.58919i | − 0.181105i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000i | 0.225018i | 0.993651 | + | 0.112509i | \(0.0358886\pi\) | ||||
−0.993651 | + | 0.112509i | \(0.964111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8742 | 1.74242 | 0.871209 | − | 0.490912i | \(-0.163336\pi\) | ||||
0.871209 | + | 0.490912i | \(0.163336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.10102 | −0.119422 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 11.9494i | − 1.26663i | −0.773893 | − | 0.633316i | \(-0.781693\pi\) | ||||
0.773893 | − | 0.633316i | \(-0.218307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.20204i | 0.440494i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55708 | 0.159753 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15.7313i | − 1.56533i | −0.622446 | − | 0.782663i | \(-0.713861\pi\) | ||||
0.622446 | − | 0.782663i | \(-0.286139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.0000i | − 0.985329i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||||
0.870219 | − | 0.492665i | \(-0.163977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.66025 | −0.837218 | −0.418609 | − | 0.908166i | \(-0.637482\pi\) | ||||
−0.418609 | + | 0.908166i | \(0.637482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89898 | 0.469237 | 0.234619 | − | 0.972088i | \(-0.424616\pi\) | ||||
0.234619 | + | 0.972088i | \(0.424616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.1421i | − 1.33038i | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||||
0.746674 | − | 0.665190i | \(-0.231650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.898979i | − 0.0838303i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.02118 | −0.460291 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.79796 | −0.890724 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.14626i | − 0.281410i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2474i | 1.35299i | 0.736446 | + | 0.676496i | \(0.236502\pi\) | ||||
−0.736446 | + | 0.676496i | \(0.763498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00340 | 0.262408 | 0.131204 | − | 0.991355i | \(-0.458116\pi\) | ||||
0.131204 | + | 0.991355i | \(0.458116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.10102 | 0.615737 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6780i | 0.912286i | 0.889906 | + | 0.456143i | \(0.150769\pi\) | ||||
−0.889906 | + | 0.456143i | \(0.849231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 20.0000i | − 1.69638i | −0.529694 | − | 0.848189i | \(-0.677693\pi\) | ||||
0.529694 | − | 0.848189i | \(-0.322307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.17837 | −0.265789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.89898 | −0.240747 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.78194i | 0.309829i | 0.987928 | + | 0.154914i | \(0.0495101\pi\) | ||||
−0.987928 | + | 0.154914i | \(0.950490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2474i | 1.40358i | 0.712385 | + | 0.701789i | \(0.247615\pi\) | ||||
−0.712385 | + | 0.701789i | \(0.752385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.36773 | −0.190180 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7980 | 1.10120 | 0.550599 | − | 0.834770i | \(-0.314400\pi\) | ||||
0.550599 | + | 0.834770i | \(0.314400\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4.09978i | − 0.323108i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.9774 | 1.77804 | 0.889021 | − | 0.457867i | \(-0.151386\pi\) | ||||
0.889021 | + | 0.457867i | \(0.151386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59592 | −0.353532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.33902i | − 0.405918i | −0.979187 | − | 0.202959i | \(-0.934944\pi\) | ||||
0.979187 | − | 0.202959i | \(-0.0650558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7.10102i | − 0.536787i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.66025 | 0.647298 | 0.323649 | − | 0.946177i | \(-0.395090\pi\) | ||||
0.323649 | + | 0.946177i | \(0.395090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79796 | 0.728277 | 0.364138 | − | 0.931345i | \(-0.381364\pi\) | ||||
0.364138 | + | 0.931345i | \(0.381364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.55708i | 0.114479i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.79796i | − 0.277734i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6062 | −1.27394 | −0.636971 | − | 0.770888i | \(-0.719813\pi\) | ||||
−0.636971 | + | 0.770888i | \(0.719813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.10102 | 0.151235 | 0.0756174 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756174 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.2672i | 0.874003i | 0.899461 | + | 0.437002i | \(0.143960\pi\) | ||||
−0.899461 | + | 0.437002i | \(0.856040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3485i | 1.44246i | 0.692693 | + | 0.721232i | \(0.256424\pi\) | ||||
−0.692693 | + | 0.721232i | \(0.743576\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.2207 | −0.927913 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.10102 | −0.216585 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.37113i | 0.371528i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 28.4949i | − 1.96167i | −0.194841 | − | 0.980835i | \(-0.562419\pi\) | ||||
0.194841 | − | 0.980835i | \(-0.437581\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.19275 | 0.149544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0424i | 0.675522i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.202041i | 0.0135297i | 0.999977 | + | 0.00676483i | \(0.00215333\pi\) | ||||
−0.999977 | + | 0.00676483i | \(0.997847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6637 | 0.774144 | 0.387072 | − | 0.922050i | \(-0.373487\pi\) | ||||
0.387072 | + | 0.922050i | \(0.373487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2207i | 0.866119i | 0.901365 | + | 0.433059i | \(0.142566\pi\) | ||||
−0.901365 | + | 0.433059i | \(0.857434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.89898i | 0.189109i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0703 | −1.36293 | −0.681463 | − | 0.731852i | \(-0.738656\pi\) | ||||
−0.681463 | + | 0.731852i | \(0.738656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7980 | −1.27530 | −0.637649 | − | 0.770327i | \(-0.720093\pi\) | ||||
−0.637649 | + | 0.770327i | \(0.720093\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.55708i | − 0.0994781i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 14.2020i | − 0.903654i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.10102 | 0.194959 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6637i | 0.727559i | 0.931485 | + | 0.363779i | \(0.118514\pi\) | ||||
−0.931485 | + | 0.363779i | \(0.881486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.10102i | 0.441236i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8844 | 1.53444 | 0.767218 | − | 0.641386i | \(-0.221640\pi\) | ||||
0.767218 | + | 0.641386i | \(0.221640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.40408 | −0.0862521 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3923i | 0.633630i | 0.948487 | + | 0.316815i | \(0.102613\pi\) | ||||
−0.948487 | + | 0.316815i | \(0.897387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5505i | 0.762389i | 0.924495 | + | 0.381195i | \(0.124487\pi\) | ||||
−0.924495 | + | 0.381195i | \(0.875513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.37113 | 0.323891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7980 | 0.829039 | 0.414520 | − | 0.910040i | \(-0.363950\pi\) | ||||
0.414520 | + | 0.910040i | \(0.363950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 0.921404i | − 0.0549663i | −0.999622 | − | 0.0274832i | \(-0.991251\pi\) | ||||
0.999622 | − | 0.0274832i | \(-0.00874927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.10102i | − 0.184337i | −0.995743 | − | 0.0921683i | \(-0.970620\pi\) | ||||
0.995743 | − | 0.0921683i | \(-0.0293798\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1421 | −0.834784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00680i | 0.350921i | 0.984486 | + | 0.175460i | \(0.0561414\pi\) | ||||
−0.984486 | + | 0.175460i | \(0.943859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.89898i | 0.168785i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.19955 | −0.474192 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | 0.576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.27135i | 0.0727972i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000i | 1.02731i | 0.857996 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.09978 | −0.232477 | −0.116238 | − | 0.993221i | \(-0.537084\pi\) | ||||
−0.116238 | + | 0.993221i | \(0.537084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.4949 | 1.66715 | 0.833575 | − | 0.552406i | \(-0.186290\pi\) | ||||
0.833575 | + | 0.552406i | \(0.186290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.5877i | 1.66181i | 0.556413 | + | 0.830906i | \(0.312177\pi\) | ||||
−0.556413 | + | 0.830906i | \(0.687823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 10.0000i | − 0.559893i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.9706 | 0.944267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.2020 | −0.787787 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2207i | 0.728883i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.696938i | 0.0383072i | 0.999817 | + | 0.0191536i | \(0.00609715\pi\) | ||||
−0.999817 | + | 0.0191536i | \(0.993903\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.62129 | −0.0885808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.20204 | 0.228900 | 0.114450 | − | 0.993429i | \(-0.463489\pi\) | ||||
0.114450 | + | 0.993429i | \(0.463489\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.16744i | − 0.442292i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 17.2474i | − 0.931275i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.48188 | 0.294283 | 0.147141 | − | 0.989115i | \(-0.452993\pi\) | ||||
0.147141 | + | 0.989115i | \(0.452993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.8990 | −1.33281 | −0.666406 | − | 0.745589i | \(-0.732168\pi\) | ||||
−0.666406 | + | 0.745589i | \(0.732168\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.1421i | 0.752710i | 0.926476 | + | 0.376355i | \(0.122823\pi\) | ||||
−0.926476 | + | 0.376355i | \(0.877177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.40408i | − 0.127595i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.2911 | 1.80981 | 0.904907 | − | 0.425610i | \(-0.139940\pi\) | ||||
0.904907 | + | 0.425610i | \(0.139940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.603566i | − 0.0315921i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.55051i | 0.446333i | 0.974780 | + | 0.223167i | \(0.0716394\pi\) | ||||
−0.974780 | + | 0.223167i | \(0.928361\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.40329 | −0.332442 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.4949 | −1.78608 | −0.893039 | − | 0.449979i | \(-0.851431\pi\) | ||||
−0.893039 | + | 0.449979i | \(0.851431\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.4415i | 1.36180i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.74983 | 0.191607 | 0.0958037 | − | 0.995400i | \(-0.469458\pi\) | ||||
0.0958037 | + | 0.995400i | \(0.469458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.505103 | −0.0257424 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.0662i | 1.62582i | 0.582388 | + | 0.812911i | \(0.302118\pi\) | ||||
−0.582388 | + | 0.812911i | \(0.697882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.79796i | − 0.495504i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.635674 | 0.0319843 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.69694 | −0.436487 | −0.218243 | − | 0.975894i | \(-0.570033\pi\) | ||||
−0.218243 | + | 0.975894i | \(0.570033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.5959i | 1.07577i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.37113 | −0.266237 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | −0.346128 | −0.173064 | − | 0.984911i | \(-0.555367\pi\) | ||||
−0.173064 | + | 0.984911i | \(0.555367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.2207i | 0.650550i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 5.04541i | − 0.247669i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0915 | 1.27465 | 0.637327 | − | 0.770593i | \(-0.280040\pi\) | ||||
0.637327 | + | 0.770593i | \(0.280040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7980 | 1.45226 | 0.726132 | − | 0.687556i | \(-0.241316\pi\) | ||||
0.726132 | + | 0.687556i | \(0.241316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 16.9706i | − 0.823193i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.79796i | 0.280583i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3629 | −1.31802 | −0.659011 | − | 0.752133i | \(-0.729025\pi\) | ||||
−0.659011 | + | 0.752133i | \(0.729025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3939 | 1.55675 | 0.778375 | − | 0.627799i | \(-0.216044\pi\) | ||||
0.778375 | + | 0.627799i | \(0.216044\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8564i | 0.662842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 19.2474i | − 0.918631i | −0.888273 | − | 0.459315i | \(-0.848095\pi\) | ||||
0.888273 | − | 0.459315i | \(-0.151905\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.6342 | −1.36045 | −0.680226 | − | 0.733002i | \(-0.738119\pi\) | ||||
−0.680226 | + | 0.733002i | \(0.738119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.79796 | −0.180041 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3417i | 1.05437i | 0.849751 | + | 0.527185i | \(0.176752\pi\) | ||||
−0.849751 | + | 0.527185i | \(0.823248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 10.6969i | − 0.503699i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.33557 | 0.0626123 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0000 | 1.16945 | 0.584725 | − | 0.811231i | \(-0.301202\pi\) | ||||
0.584725 | + | 0.811231i | \(0.301202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.87492i | 0.0873235i | 0.999046 | + | 0.0436618i | \(0.0139024\pi\) | ||||
−0.999046 | + | 0.0436618i | \(0.986098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 27.0454i | − 1.25691i | −0.777847 | − | 0.628453i | \(-0.783688\pi\) | ||||
0.777847 | − | 0.628453i | \(-0.216312\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.174973 | 0.00809677 | 0.00404838 | − | 0.999992i | \(-0.498711\pi\) | ||||
0.00404838 | + | 0.999992i | \(0.498711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.39388 | −0.341418 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.56388i | 0.347787i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0000i | 1.10120i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.0915 | 1.19215 | 0.596076 | − | 0.802928i | \(-0.296726\pi\) | ||||
0.596076 | + | 0.802928i | \(0.296726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2020 | 0.647557 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.58919i | 0.0721612i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.79796i | 0.172102i | 0.996291 | + | 0.0860510i | \(0.0274248\pi\) | ||||
−0.996291 | + | 0.0860510i | \(0.972575\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3171 | −0.646122 | −0.323061 | − | 0.946378i | \(-0.604712\pi\) | ||||
−0.323061 | + | 0.946378i | \(0.604712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.5959 | −1.42301 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 10.9638i | − 0.491792i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8990i | 0.666970i | 0.942755 | + | 0.333485i | \(0.108225\pi\) | ||||
−0.942755 | + | 0.333485i | \(0.891775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.1127 | −1.38725 | −0.693623 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 26.6951i | − 1.18324i | −0.806217 | − | 0.591619i | \(-0.798489\pi\) | ||||
0.806217 | − | 0.591619i | \(-0.201511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2.75255i | − 0.121766i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.17837 | −0.140056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 21.7060i | − 0.950958i | −0.879727 | − | 0.475479i | \(-0.842275\pi\) | ||||
0.879727 | − | 0.475479i | \(-0.157725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.3939i | 1.19785i | 0.800805 | + | 0.598925i | \(0.204405\pi\) | ||||
−0.800805 | + | 0.598925i | \(0.795595\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.8058 | −1.12412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.2843i | 1.22513i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.75255i | 0.119003i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.37113 | 0.231351 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.55708i | − 0.0666979i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 23.7980i | − 1.01753i | −0.860906 | − | 0.508764i | \(-0.830103\pi\) | ||||
0.860906 | − | 0.508764i | \(-0.169897\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.6834 | 1.90358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.89898 | 0.123277 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 12.5529i | − 0.531886i | −0.963989 | − | 0.265943i | \(-0.914317\pi\) | ||||
0.963989 | − | 0.265943i | \(-0.0856832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 20.0000i | − 0.845910i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.8024 | 0.961006 | 0.480503 | − | 0.876993i | \(-0.340454\pi\) | ||||
0.480503 | + | 0.876993i | \(0.340454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.49490 | −0.189102 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.19955i | 0.343743i | 0.985119 | + | 0.171872i | \(0.0549814\pi\) | ||||
−0.985119 | + | 0.171872i | \(0.945019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 19.7980i | − 0.828519i | −0.910159 | − | 0.414259i | \(-0.864041\pi\) | ||||
0.910159 | − | 0.414259i | \(-0.135959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8564 | 0.577852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.79796 | −0.158111 | −0.0790556 | − | 0.996870i | \(-0.525190\pi\) | ||||
−0.0790556 | + | 0.996870i | \(0.525190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 23.0095i | − 0.954594i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.84337i | − 0.200592i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.0881 | −0.952949 | −0.476474 | − | 0.879188i | \(-0.658085\pi\) | ||||
−0.476474 | + | 0.879188i | \(0.658085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.4949 | 1.50375 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.13534i | 0.334078i | 0.985950 | + | 0.167039i | \(0.0534206\pi\) | ||||
−0.985950 | + | 0.167039i | \(0.946579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.59592i | 0.0654263i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.5201 | −1.04272 | −0.521361 | − | 0.853336i | \(-0.674575\pi\) | ||||
−0.521361 | + | 0.853336i | \(0.674575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3031 | 0.420271 | 0.210135 | − | 0.977672i | \(-0.432610\pi\) | ||||
0.210135 | + | 0.977672i | \(0.432610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.11416i | 0.126608i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7980i | 0.965929i | 0.875640 | + | 0.482965i | \(0.160440\pi\) | ||||
−0.875640 | + | 0.482965i | \(0.839560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.4415 | 1.06971 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.9985i | 1.12718i | 0.826055 | + | 0.563589i | \(0.190580\pi\) | ||||
−0.826055 | + | 0.563589i | \(0.809420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 21.5959i | − 0.868013i | −0.900910 | − | 0.434007i | \(-0.857099\pi\) | ||||
0.900910 | − | 0.434007i | \(-0.142901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.3205 | −0.693932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4949 | 0.939796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9706i | 0.676661i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.7423i | 1.82097i | 0.413538 | + | 0.910487i | \(0.364293\pi\) | ||||
−0.413538 | + | 0.910487i | \(0.635707\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.84621 | 0.192316 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.2020 | −0.562705 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 48.7832i | − 1.92682i | −0.268034 | − | 0.963409i | \(-0.586374\pi\) | ||||
0.268034 | − | 0.963409i | \(-0.413626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.3939i | 1.47467i | 0.675527 | + | 0.737335i | \(0.263916\pi\) | ||||
−0.675527 | + | 0.737335i | \(0.736084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.5597i | 0.726299i | 0.931731 | + | 0.363150i | \(0.118299\pi\) | ||||
−0.931731 | + | 0.363150i | \(0.881701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 0.954592i | − 0.0372990i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.8236 | −1.08385 | −0.541926 | − | 0.840426i | \(-0.682305\pi\) | ||||
−0.541926 | + | 0.840426i | \(0.682305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.49490 | 0.174831 | 0.0874156 | − | 0.996172i | \(-0.472139\pi\) | ||||
0.0874156 | + | 0.996172i | \(0.472139\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2.25697i | − 0.0875215i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 25.7980i | − 0.998901i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.38551 | −0.169301 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.5959 | −1.41067 | −0.705334 | − | 0.708875i | \(-0.749203\pi\) | ||||
−0.705334 | + | 0.708875i | \(0.749203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 10.9638i | − 0.421372i | −0.977554 | − | 0.210686i | \(-0.932430\pi\) | ||||
0.977554 | − | 0.210686i | \(-0.0675697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.24745i | 0.278132i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3923 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.39388 | 0.129673 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.8066i | 0.487891i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 4.00000i | − 0.152167i | −0.997101 | − | 0.0760836i | \(-0.975758\pi\) | ||||
0.997101 | − | 0.0760836i | \(-0.0242416\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.35674 | −0.241125 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.7980 | −1.28019 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 38.7087i | − 1.46201i | −0.682374 | − | 0.731003i | \(-0.739052\pi\) | ||||
0.682374 | − | 0.731003i | \(-0.260948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 24.0000i | − 0.905177i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.8024 | −0.857572 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.0000 | 1.50223 | 0.751116 | − | 0.660171i | \(-0.229516\pi\) | ||||
0.751116 | + | 0.660171i | \(0.229516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 21.0703i | − 0.789090i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.01021i | 0.0377795i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.92820 | −0.258378 | −0.129189 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4949 | −0.539818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 44.6834i | − 1.65950i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.24745i | − 0.268793i | −0.990928 | − | 0.134396i | \(-0.957090\pi\) | ||||
0.990928 | − | 0.134396i | \(-0.0429096\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8988 | 0.883928 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.49490 | −0.166023 | −0.0830114 | − | 0.996549i | \(-0.526454\pi\) | ||||
−0.0830114 | + | 0.996549i | \(0.526454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 5.59264i | − 0.206007i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 19.3939i | − 0.713415i | −0.934216 | − | 0.356708i | \(-0.883899\pi\) | ||||
0.934216 | − | 0.356708i | \(-0.116101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4626 | 1.15425 | 0.577126 | − | 0.816655i | \(-0.304174\pi\) | ||||
0.577126 | + | 0.816655i | \(0.304174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.20204 | 0.0440394 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5529i | 0.458675i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.7423i | 1.74214i | 0.491156 | + | 0.871071i | \(0.336574\pi\) | ||||
−0.491156 | + | 0.871071i | \(0.663426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.48188 | 0.199506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3939 | 1.43179 | 0.715897 | − | 0.698205i | \(-0.246018\pi\) | ||||
0.715897 | + | 0.698205i | \(0.246018\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 52.8829i | − 1.91700i | −0.285085 | − | 0.958502i | \(-0.592022\pi\) | ||||
0.285085 | − | 0.958502i | \(-0.407978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.10102i | − 0.257074i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.4415 | 0.954746 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4949 | 0.414517 | 0.207258 | − | 0.978286i | \(-0.433546\pi\) | ||||
0.207258 | + | 0.978286i | \(0.433546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 34.2911i | − 1.23336i | −0.787212 | − | 0.616682i | \(-0.788476\pi\) | ||||
0.787212 | − | 0.616682i | \(-0.211524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 36.4949i | − 1.31094i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.7975 | 1.71252 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.29286 | 0.296742 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.38551i | − 0.156525i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 35.1918i | − 1.25445i | −0.778837 | − | 0.627227i | \(-0.784190\pi\) | ||||
0.778837 | − | 0.627227i | \(-0.215810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.4989 | −0.728856 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.5959 | 0.411783 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.24604i | 0.256668i | 0.991731 | + | 0.128334i | \(0.0409629\pi\) | ||||
−0.991731 | + | 0.128334i | \(0.959037\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.5959i | 1.11778i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.08200 | 0.0734720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.30306 | −0.0459269 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 11.9494i | − 0.420118i | −0.977689 | − | 0.210059i | \(-0.932634\pi\) | ||||
0.977689 | − | 0.210059i | \(-0.0673656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 24.4949i | − 0.860132i | −0.902797 | − | 0.430066i | \(-0.858490\pi\) | ||||
0.902797 | − | 0.430066i | \(-0.141510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.90702 | 0.0668001 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33.7980 | −1.18244 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 22.9774i | − 0.801915i | −0.916097 | − | 0.400958i | \(-0.868677\pi\) | ||||
0.916097 | − | 0.400958i | \(-0.131323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6515i | 1.03359i | 0.856110 | + | 0.516794i | \(0.172875\pi\) | ||||
−0.856110 | + | 0.516794i | \(0.827125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6206 | 0.577955 | 0.288978 | − | 0.957336i | \(-0.406685\pi\) | ||||
0.288978 | + | 0.957336i | \(0.406685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5959 | 1.30576 | 0.652880 | − | 0.757461i | \(-0.273561\pi\) | ||||
0.652880 | + | 0.757461i | \(0.273561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 16.9706i | − 0.587995i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 7.30306i | − 0.252733i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.17837 | 0.109730 | 0.0548648 | − | 0.998494i | \(-0.482527\pi\) | ||||
0.0548648 | + | 0.998494i | \(0.482527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −54.1918 | −1.86868 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.46075i | 0.0502515i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.2020i | 0.487988i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8564 | −0.474991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 11.6637i | − 0.398423i | −0.979957 | − | 0.199211i | \(-0.936162\pi\) | ||||
0.979957 | − | 0.199211i | \(-0.0638380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.5959i | 1.35100i | 0.737362 | + | 0.675498i | \(0.236071\pi\) | ||||
−0.737362 | + | 0.675498i | \(0.763929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.92820 | 0.235839 | 0.117919 | − | 0.993023i | \(-0.462378\pi\) | ||||
0.117919 | + | 0.993023i | \(0.462378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.69694 | −0.0576976 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.19275i | 0.0743840i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7878i | 0.501064i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.56048 | −0.154172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2020 | 0.547104 | 0.273552 | − | 0.961857i | \(-0.411801\pi\) | ||||
0.273552 | + | 0.961857i | \(0.411801\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 7.27815i | − 0.245207i | −0.992456 | − | 0.122604i | \(-0.960876\pi\) | ||||
0.992456 | − | 0.122604i | \(-0.0391244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52.8990i | − 1.78019i | −0.455773 | − | 0.890096i | \(-0.650637\pi\) | ||||
0.455773 | − | 0.890096i | \(-0.349363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.3191 | −1.52166 | −0.760832 | − | 0.648948i | \(-0.775209\pi\) | ||||
−0.760832 | + | 0.648948i | \(0.775209\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.1010 | 0.741244 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 44.6834i | − 1.49527i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.75255i | − 0.0920076i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −67.9465 | −2.26614 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3031 | −0.509819 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 3.11416i | − 0.103518i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.49490i | − 0.149251i | −0.997212 | − | 0.0746253i | \(-0.976224\pi\) | ||||
0.997212 | − | 0.0746253i | \(-0.0237761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.921404 | −0.0305275 | −0.0152637 | − | 0.999884i | \(-0.504859\pi\) | ||||
−0.0152637 | + | 0.999884i | \(0.504859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4041 | 0.575991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.35340i | − 0.143762i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 2.75255i | − 0.0907983i | −0.998969 | − | 0.0453991i | \(-0.985544\pi\) | ||||
0.998969 | − | 0.0453991i | \(-0.0144560\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.9275 | −0.721753 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0000 | −0.789115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 15.1278i | − 0.496326i | −0.968718 | − | 0.248163i | \(-0.920173\pi\) | ||||
0.968718 | − | 0.248163i | \(-0.0798268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.0000i | 0.786568i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.20713 | −0.0394775 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0000 | −0.490029 | −0.245014 | − | 0.969519i | \(-0.578793\pi\) | ||||
−0.245014 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 41.5371i | − 1.35407i | −0.735950 | − | 0.677036i | \(-0.763264\pi\) | ||||
0.735950 | − | 0.677036i | \(-0.236736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 27.5959i | − 0.898647i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0881 | 0.750263 | 0.375132 | − | 0.926972i | \(-0.377598\pi\) | ||||
0.375132 | + | 0.926972i | \(0.377598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.50510 | −0.178703 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 10.7423i | − 0.347976i | −0.984748 | − | 0.173988i | \(-0.944335\pi\) | ||||
0.984748 | − | 0.173988i | \(-0.0556653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.59592i | 0.181080i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.4777 | 0.499801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4949 | −0.790158 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 0.667783i | − 0.0214967i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.2474i | 1.58369i | 0.610721 | + | 0.791846i | \(0.290880\pi\) | ||||
−0.610721 | + | 0.791846i | \(0.709120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3383 | 0.620595 | 0.310298 | − | 0.950639i | \(-0.399571\pi\) | ||||
0.310298 | + | 0.950639i | \(0.399571\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.9898 | −0.929370 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 31.4626i | − 1.00658i | −0.864118 | − | 0.503290i | \(-0.832123\pi\) | ||||
0.864118 | − | 0.503290i | \(-0.167877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 13.1010i | − 0.418710i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.5330 | −1.67554 | −0.837771 | − | 0.546022i | \(-0.816142\pi\) | ||||
−0.837771 | + | 0.546022i | \(0.816142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.89898 | 0.124232 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.5133i | 0.620486i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 8.75255i | − 0.278034i | −0.990290 | − | 0.139017i | \(-0.955606\pi\) | ||||
0.990290 | − | 0.139017i | \(-0.0443943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.46750 | 0.205034 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.6969 | 1.92229 | 0.961146 | − | 0.276042i | \(-0.0890228\pi\) | ||||
0.961146 | + | 0.276042i | \(0.0890228\pi\) | |||||||
\(998\) | 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 | 1728.2.c.g.1727.3 | 8 | ||
3.2 | odd | 2 | inner | 1728.2.c.g.1727.5 | 8 | ||
4.3 | odd | 2 | inner | 1728.2.c.g.1727.4 | 8 | ||
8.3 | odd | 2 | 864.2.c.a.863.6 | yes | 8 | ||
8.5 | even | 2 | 864.2.c.a.863.5 | yes | 8 | ||
12.11 | even | 2 | inner | 1728.2.c.g.1727.6 | 8 | ||
24.5 | odd | 2 | 864.2.c.a.863.3 | ✓ | 8 | ||
24.11 | even | 2 | 864.2.c.a.863.4 | yes | 8 | ||
72.5 | odd | 6 | 2592.2.s.a.1727.4 | 8 | |||
72.11 | even | 6 | 2592.2.s.h.863.2 | 8 | |||
72.13 | even | 6 | 2592.2.s.h.1727.2 | 8 | |||
72.29 | odd | 6 | 2592.2.s.h.863.1 | 8 | |||
72.43 | odd | 6 | 2592.2.s.a.863.4 | 8 | |||
72.59 | even | 6 | 2592.2.s.a.1727.3 | 8 | |||
72.61 | even | 6 | 2592.2.s.a.863.3 | 8 | |||
72.67 | odd | 6 | 2592.2.s.h.1727.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.a.863.3 | ✓ | 8 | 24.5 | odd | 2 | ||
864.2.c.a.863.4 | yes | 8 | 24.11 | even | 2 | ||
864.2.c.a.863.5 | yes | 8 | 8.5 | even | 2 | ||
864.2.c.a.863.6 | yes | 8 | 8.3 | odd | 2 | ||
1728.2.c.g.1727.3 | 8 | 1.1 | even | 1 | trivial | ||
1728.2.c.g.1727.4 | 8 | 4.3 | odd | 2 | inner | ||
1728.2.c.g.1727.5 | 8 | 3.2 | odd | 2 | inner | ||
1728.2.c.g.1727.6 | 8 | 12.11 | even | 2 | inner | ||
2592.2.s.a.863.3 | 8 | 72.61 | even | 6 | |||
2592.2.s.a.863.4 | 8 | 72.43 | odd | 6 | |||
2592.2.s.a.1727.3 | 8 | 72.59 | even | 6 | |||
2592.2.s.a.1727.4 | 8 | 72.5 | odd | 6 | |||
2592.2.s.h.863.1 | 8 | 72.29 | odd | 6 | |||
2592.2.s.h.863.2 | 8 | 72.11 | even | 6 | |||
2592.2.s.h.1727.1 | 8 | 72.67 | odd | 6 | |||
2592.2.s.h.1727.2 | 8 | 72.13 | even | 6 |