Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(127,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 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("1440.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.x (of order \(4\), degree \(2\), 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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.127 |
Dual form | 1440.2.x.b.703.1 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.00000i | −0.377964 | + | 0.377964i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) |
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.00000i | 1.80907i | 0.426401 | + | 0.904534i | \(0.359781\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.00000i | −0.242536 | − | 0.242536i | 0.575363 | − | 0.817898i | \(-0.304861\pi\) |
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | − | 5.00000i | −1.04257 | − | 1.04257i | −0.999053 | − | 0.0435195i | \(-0.986143\pi\) |
−0.0435195 | − | 0.999053i | \(-0.513857\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.00000i | − | 1.48556i | −0.669534 | − | 0.742781i | \(-0.733506\pi\) | ||
0.669534 | − | 0.742781i | \(-0.266494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | − | 3.00000i | −0.169031 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 5.00000i | −0.821995 | − | 0.821995i | 0.164399 | − | 0.986394i | \(-0.447432\pi\) |
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | + | 3.00000i | 0.457496 | + | 0.457496i | 0.897833 | − | 0.440337i | \(-0.145141\pi\) |
−0.440337 | + | 0.897833i | \(0.645141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.00000 | + | 7.00000i | −1.02105 | + | 1.02105i | −0.0212814 | + | 0.999774i | \(0.506775\pi\) |
−0.999774 | + | 0.0212814i | \(0.993225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | − | 6.00000i | −1.61808 | − | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | − | 3.00000i | −0.124035 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | + | 7.00000i | −0.855186 | + | 0.855186i | −0.990766 | − | 0.135580i | \(-0.956710\pi\) |
0.135580 | + | 0.990766i | \(0.456710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | − | 9.00000i | 1.05337 | − | 1.05337i | 0.0548772 | − | 0.998493i | \(-0.482523\pi\) |
0.998493 | − | 0.0548772i | \(-0.0174767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | − | 6.00000i | −0.683763 | − | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00000 | + | 5.00000i | 0.548821 | + | 0.548821i | 0.926100 | − | 0.377279i | \(-0.123140\pi\) |
−0.377279 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | − | 1.00000i | 0.325396 | − | 0.108465i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.00000i | − | 0.209657i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 8.00000i | −0.410391 | + | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | − | 3.00000i | −0.304604 | − | 0.304604i | 0.538208 | − | 0.842812i | \(-0.319101\pi\) |
−0.842812 | + | 0.538208i | \(0.819101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | − | 3.00000i | −0.295599 | − | 0.295599i | 0.543688 | − | 0.839287i | \(-0.317027\pi\) |
−0.839287 | + | 0.543688i | \(0.817027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | − | 3.00000i | 0.290021 | − | 0.290021i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) |
0.837088 | + | 0.547068i | \(0.184256\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | − | 3.00000i | 0.282216 | − | 0.282216i | −0.551776 | − | 0.833992i | \(-0.686050\pi\) |
0.833992 | + | 0.551776i | \(0.186050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.0000 | − | 5.00000i | 1.39876 | − | 0.466252i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25.0000 | −2.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | + | 5.00000i | −0.443678 | + | 0.443678i | −0.893246 | − | 0.449568i | \(-0.851578\pi\) |
0.449568 | + | 0.893246i | \(0.351578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.00000i | − | 0.174741i | −0.996176 | − | 0.0873704i | \(-0.972154\pi\) | ||
0.996176 | − | 0.0873704i | \(-0.0278464\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 4.00000i | −0.346844 | + | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0000 | − | 13.0000i | −1.11066 | − | 1.11066i | −0.993061 | − | 0.117604i | \(-0.962479\pi\) |
−0.117604 | − | 0.993061i | \(-0.537521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.00000 | − | 6.00000i | −0.501745 | − | 0.501745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | + | 8.00000i | 1.32873 | + | 0.664364i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0000i | 0.983078i | 0.870855 | + | 0.491539i | \(0.163566\pi\) | ||||
−0.870855 | + | 0.491539i | \(0.836434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0000i | 1.46482i | 0.680864 | + | 0.732410i | \(0.261604\pi\) | ||||
−0.680864 | + | 0.732410i | \(0.738396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | − | 2.00000i | −0.321288 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | + | 3.00000i | 0.239426 | + | 0.239426i | 0.816612 | − | 0.577186i | \(-0.195849\pi\) |
−0.577186 | + | 0.816612i | \(0.695849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.0000 | 0.788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | − | 1.00000i | −0.0783260 | − | 0.0783260i | 0.666858 | − | 0.745184i | \(-0.267639\pi\) |
−0.745184 | + | 0.666858i | \(0.767639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.00000 | − | 5.00000i | 0.386912 | − | 0.386912i | −0.486673 | − | 0.873584i | \(-0.661790\pi\) |
0.873584 | + | 0.486673i | \(0.161790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.00000 | + | 7.00000i | −0.532200 | + | 0.532200i | −0.921227 | − | 0.389026i | \(-0.872811\pi\) |
0.389026 | + | 0.921227i | \(0.372811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | + | 1.00000i | 0.529150 | + | 0.0755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.0000 | − | 5.00000i | 1.10282 | − | 0.367607i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | − | 6.00000i | 0.438763 | − | 0.438763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.0000i | − | 0.723575i | −0.932261 | − | 0.361787i | \(-0.882167\pi\) | ||
0.932261 | − | 0.361787i | \(-0.117833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.00000i | 0.0719816 | − | 0.0719816i | −0.670199 | − | 0.742181i | \(-0.733791\pi\) |
0.742181 | + | 0.670199i | \(0.233791\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.00000 | + | 1.00000i | 0.0712470 | + | 0.0712470i | 0.741832 | − | 0.670585i | \(-0.233957\pi\) |
−0.670585 | + | 0.741832i | \(0.733957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | + | 8.00000i | 0.561490 | + | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 12.0000i | 0.419058 | − | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000i | 1.66011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000i | 0.688428i | 0.938891 | + | 0.344214i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344214i | \(0.888145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.00000 | + | 3.00000i | −0.613795 | + | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | − | 2.00000i | −0.135769 | − | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0000 | − | 19.0000i | −1.27233 | − | 1.27233i | −0.944860 | − | 0.327474i | \(-0.893803\pi\) |
−0.327474 | − | 0.944860i | \(-0.606197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.0000 | + | 13.0000i | −0.862840 | + | 0.862840i | −0.991667 | − | 0.128827i | \(-0.958879\pi\) |
0.128827 | + | 0.991667i | \(0.458879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0000i | 1.05731i | 0.848837 | + | 0.528655i | \(0.177303\pi\) | ||||
−0.848837 | + | 0.528655i | \(0.822697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.0000 | + | 13.0000i | −0.851658 | + | 0.851658i | −0.990337 | − | 0.138679i | \(-0.955714\pi\) |
0.138679 | + | 0.990337i | \(0.455714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.00000 | − | 21.0000i | −0.456630 | − | 1.36989i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0000 | − | 5.00000i | −0.638877 | − | 0.319438i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | + | 4.00000i | −0.254514 | + | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 18.0000i | − | 1.13615i | −0.822977 | − | 0.568075i | \(-0.807688\pi\) | ||
0.822977 | − | 0.568075i | \(-0.192312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | − | 30.0000i | 1.88608 | − | 1.88608i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0000 | + | 11.0000i | 0.686161 | + | 0.686161i | 0.961381 | − | 0.275220i | \(-0.0887507\pi\) |
−0.275220 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000 | 0.621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | − | 9.00000i | −0.554964 | − | 0.554964i | 0.372906 | − | 0.927869i | \(-0.378362\pi\) |
−0.927869 | + | 0.372906i | \(0.878362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.00000 | + | 3.00000i | 0.0614295 | + | 0.184289i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.00000i | 0.243884i | 0.992537 | + | 0.121942i | \(0.0389122\pi\) | ||||
−0.992537 | + | 0.121942i | \(0.961088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.0000i | − | 1.33640i | −0.743980 | − | 0.668202i | \(-0.767064\pi\) | ||
0.743980 | − | 0.668202i | \(-0.232936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.0000 | − | 18.0000i | 1.44725 | − | 1.08544i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 9.00000i | −0.540758 | − | 0.540758i | 0.382993 | − | 0.923751i | \(-0.374893\pi\) |
−0.923751 | + | 0.382993i | \(0.874893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0000 | + | 15.0000i | 0.891657 | + | 0.891657i | 0.994679 | − | 0.103022i | \(-0.0328511\pi\) |
−0.103022 | + | 0.994679i | \(0.532851\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | − | 6.00000i | 0.354169 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0000i | − | 0.882353i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.0000 | − | 17.0000i | 0.993151 | − | 0.993151i | −0.00682610 | − | 0.999977i | \(-0.502173\pi\) |
0.999977 | + | 0.00682610i | \(0.00217283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | − | 8.00000i | 0.232889 | − | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0000 | 0.578315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | + | 4.00000i | −0.114520 | + | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.00000 | + | 7.00000i | −0.399511 | + | 0.399511i | −0.878061 | − | 0.478549i | \(-0.841163\pi\) |
0.478549 | + | 0.878061i | \(0.341163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.0000i | 1.24751i | 0.781622 | + | 0.623753i | \(0.214393\pi\) | ||||
−0.781622 | + | 0.623753i | \(0.785607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | + | 15.0000i | −0.847850 | + | 0.847850i | −0.989865 | − | 0.142014i | \(-0.954642\pi\) |
0.142014 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.0000 | + | 25.0000i | 1.40414 | + | 1.40414i | 0.786318 | + | 0.617822i | \(0.211985\pi\) |
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.0000 | 2.68748 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | − | 4.00000i | −0.222566 | − | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00000 | + | 1.00000i | 0.388290 | + | 0.0554700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 14.0000i | − | 0.771845i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0000i | 0.989369i | 0.869072 | + | 0.494685i | \(0.164716\pi\) | ||||
−0.869072 | + | 0.494685i | \(0.835284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | − | 21.0000i | −0.382451 | − | 1.14735i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.00000i | 0.0544735 | + | 0.0544735i | 0.733819 | − | 0.679345i | \(-0.237736\pi\) |
−0.679345 | + | 0.733819i | \(0.737736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | + | 9.00000i | −0.483145 | + | 0.483145i | −0.906135 | − | 0.422989i | \(-0.860981\pi\) |
0.422989 | + | 0.906135i | \(0.360981\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.0000i | 1.71292i | 0.516213 | + | 0.856460i | \(0.327341\pi\) | ||||
−0.516213 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | − | 15.0000i | 0.798369 | − | 0.798369i | −0.184469 | − | 0.982838i | \(-0.559057\pi\) |
0.982838 | + | 0.184469i | \(0.0590565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | − | 6.00000i | −0.636894 | − | 0.318447i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | + | 27.0000i | 0.471082 | + | 1.41324i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0000 | + | 13.0000i | −0.678594 | + | 0.678594i | −0.959682 | − | 0.281088i | \(-0.909305\pi\) |
0.281088 | + | 0.959682i | \(0.409305\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000i | 0.103835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.0000 | + | 21.0000i | −1.08734 | + | 1.08734i | −0.0915371 | + | 0.995802i | \(0.529178\pi\) |
−0.995802 | + | 0.0915371i | \(0.970822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | + | 8.00000i | 0.412021 | + | 0.412021i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.0000 | − | 13.0000i | −0.664269 | − | 0.664269i | 0.292114 | − | 0.956383i | \(-0.405641\pi\) |
−0.956383 | + | 0.292114i | \(0.905641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | − | 6.00000i | 0.917365 | − | 0.305788i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000i | 0.608424i | 0.952604 | + | 0.304212i | \(0.0983931\pi\) | ||||
−0.952604 | + | 0.304212i | \(0.901607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000i | 0.505722i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | − | 16.0000i | 0.402524 | − | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0000 | + | 19.0000i | 0.953583 | + | 0.953583i | 0.998969 | − | 0.0453868i | \(-0.0144520\pi\) |
−0.0453868 | + | 0.998969i | \(0.514452\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | − | 2.00000i | −0.0996271 | − | 0.0996271i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.0000 | − | 30.0000i | 1.48704 | − | 1.48704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0000i | 0.988936i | 0.869196 | + | 0.494468i | \(0.164637\pi\) | ||||
−0.869196 | + | 0.494468i | \(0.835363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | − | 4.00000i | 0.196827 | − | 0.196827i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0000 | + | 5.00000i | −0.736321 | + | 0.245440i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | + | 7.00000i | −0.0485071 | + | 0.339550i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | + | 2.00000i | −0.0967868 | + | 0.0967868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.0000i | 1.83040i | 0.403005 | + | 0.915198i | \(0.367966\pi\) | ||||
−0.403005 | + | 0.915198i | \(0.632034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.00000 | − | 5.00000i | 0.240285 | − | 0.240285i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) |
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.0000 | − | 20.0000i | −0.956730 | − | 0.956730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.0000 | + | 17.0000i | 0.807694 | + | 0.807694i | 0.984284 | − | 0.176590i | \(-0.0565067\pi\) |
−0.176590 | + | 0.984284i | \(0.556507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.00000i | − | 0.188772i | −0.995536 | − | 0.0943858i | \(-0.969911\pi\) | ||
0.995536 | − | 0.0943858i | \(-0.0300887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.0000i | − | 1.69517i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | + | 2.00000i | 0.187523 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | − | 15.0000i | −0.701670 | − | 0.701670i | 0.263099 | − | 0.964769i | \(-0.415256\pi\) |
−0.964769 | + | 0.263099i | \(0.915256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | + | 17.0000i | 0.790057 | + | 0.790057i | 0.981503 | − | 0.191446i | \(-0.0613177\pi\) |
−0.191446 | + | 0.981503i | \(0.561318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | + | 5.00000i | −0.231372 | + | 0.231372i | −0.813265 | − | 0.581893i | \(-0.802312\pi\) |
0.581893 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.0000i | − | 0.646460i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.0000 | + | 18.0000i | −0.827641 | + | 0.827641i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | − | 16.0000i | −0.550598 | − | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.00000 | − | 3.00000i | 0.408669 | − | 0.136223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0000 | − | 15.0000i | 0.679715 | − | 0.679715i | −0.280221 | − | 0.959936i | \(-0.590408\pi\) |
0.959936 | + | 0.280221i | \(0.0904077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.00000i | − | 0.0902587i | −0.998981 | − | 0.0451294i | \(-0.985630\pi\) | ||
0.998981 | − | 0.0451294i | \(-0.0143700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | + | 8.00000i | −0.360302 | + | 0.360302i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | − | 6.00000i | −0.269137 | − | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0000 | + | 11.0000i | 0.490466 | + | 0.490466i | 0.908453 | − | 0.417987i | \(-0.137264\pi\) |
−0.417987 | + | 0.908453i | \(0.637264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | − | 12.0000i | 0.266996 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000i | 0.796273i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.00000 | − | 3.00000i | 0.396587 | − | 0.132196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.0000 | − | 42.0000i | −1.84716 | − | 1.84716i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0000 | − | 25.0000i | −1.09317 | − | 1.09317i | −0.995188 | − | 0.0979859i | \(-0.968760\pi\) |
−0.0979859 | − | 0.995188i | \(-0.531240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | − | 2.00000i | 0.0871214 | − | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.0000i | 1.17391i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | − | 6.00000i | 0.259889 | − | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 9.00000i | 0.129701 | + | 0.389104i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.0000 | −1.29219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.00000 | − | 4.00000i | −0.342682 | − | 0.171341i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | + | 3.00000i | −0.128271 | + | 0.128271i | −0.768328 | − | 0.640057i | \(-0.778911\pi\) |
0.640057 | + | 0.768328i | \(0.278911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 32.0000i | − | 1.36325i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | − | 8.00000i | 0.340195 | − | 0.340195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | − | 15.0000i | −0.635570 | − | 0.635570i | 0.313889 | − | 0.949460i | \(-0.398368\pi\) |
−0.949460 | + | 0.313889i | \(0.898368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | − | 15.0000i | −0.632175 | − | 0.632175i | 0.316438 | − | 0.948613i | \(-0.397513\pi\) |
−0.948613 | + | 0.316438i | \(0.897513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 9.00000i | 0.126211 | + | 0.378633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0000i | 0.838444i | 0.907884 | + | 0.419222i | \(0.137697\pi\) | ||||
−0.907884 | + | 0.419222i | \(0.862303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0000i | 1.08807i | 0.839064 | + | 0.544033i | \(0.183103\pi\) | ||||
−0.839064 | + | 0.544033i | \(0.816897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.00000 | + | 35.0000i | −0.208514 | + | 1.45960i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | − | 3.00000i | −0.124892 | − | 0.124892i | 0.641898 | − | 0.766790i | \(-0.278147\pi\) |
−0.766790 | + | 0.641898i | \(0.778147\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0000 | −0.414870 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 6.00000i | 0.248495 | + | 0.248495i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.0000 | + | 25.0000i | −1.03186 | + | 1.03186i | −0.0323850 | + | 0.999475i | \(0.510310\pi\) |
−0.999475 | + | 0.0323850i | \(0.989690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.0000 | − | 23.0000i | 0.944497 | − | 0.944497i | −0.0540419 | − | 0.998539i | \(-0.517210\pi\) |
0.998539 | + | 0.0540419i | \(0.0172104\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | + | 4.00000i | −0.0819920 | + | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.0000 | − | 50.0000i | 1.01639 | − | 2.03279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0000 | − | 15.0000i | 0.608831 | − | 0.608831i | −0.333809 | − | 0.942641i | \(-0.608334\pi\) |
0.942641 | + | 0.333809i | \(0.108334\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.0000i | − | 0.566379i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 3.00000i | 0.121169 | − | 0.121169i | −0.643922 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0000 | + | 11.0000i | 0.442843 | + | 0.442843i | 0.892966 | − | 0.450123i | \(-0.148620\pi\) |
−0.450123 | + | 0.892966i | \(0.648620\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0000i | 0.398726i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.0000i | 0.398094i | 0.979990 | + | 0.199047i | \(0.0637846\pi\) | ||||
−0.979990 | + | 0.199047i | \(0.936215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.00000 | − | 15.0000i | −0.198419 | − | 0.595257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.00000 | − | 5.00000i | −0.198107 | − | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0000 | + | 11.0000i | 0.433798 | + | 0.433798i | 0.889918 | − | 0.456120i | \(-0.150761\pi\) |
−0.456120 | + | 0.889918i | \(0.650761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.0000 | + | 31.0000i | −1.21874 | + | 1.21874i | −0.250661 | + | 0.968075i | \(0.580648\pi\) |
−0.968075 | + | 0.250661i | \(0.919352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.00000 | − | 5.00000i | 0.195665 | − | 0.195665i | −0.602474 | − | 0.798139i | \(-0.705818\pi\) |
0.798139 | + | 0.602474i | \(0.205818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | + | 2.00000i | 0.156293 | + | 0.0781465i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −44.0000 | −1.71400 | −0.856998 | − | 0.515319i | \(-0.827673\pi\) | ||||
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.00000 | − | 12.0000i | −0.155113 | − | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.0000 | + | 40.0000i | −1.54881 | + | 1.54881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000i | 0.463255i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0000 | − | 29.0000i | 1.11787 | − | 1.11787i | 0.125814 | − | 0.992054i | \(-0.459846\pi\) |
0.992054 | − | 0.125814i | \(-0.0401543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0000 | − | 15.0000i | −0.576497 | − | 0.576497i | 0.357439 | − | 0.933936i | \(-0.383650\pi\) |
−0.933936 | + | 0.357439i | \(0.883650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000 | 0.230259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0000 | + | 13.0000i | 0.497431 | + | 0.497431i | 0.910637 | − | 0.413206i | \(-0.135591\pi\) |
−0.413206 | + | 0.910637i | \(0.635591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.0000 | − | 13.0000i | 1.49011 | − | 0.496704i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000i | 0.0761939i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000i | 0.380418i | 0.981744 | + | 0.190209i | \(0.0609166\pi\) | ||||
−0.981744 | + | 0.190209i | \(0.939083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | + | 24.0000i | −0.455186 | + | 0.910372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 6.00000i | 0.227266 | + | 0.227266i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | − | 20.0000i | −0.754314 | − | 0.754314i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | − | 6.00000i | 0.225653 | − | 0.225653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 24.0000i | − | 0.901339i | −0.892691 | − | 0.450669i | \(-0.851185\pi\) | ||
0.892691 | − | 0.450669i | \(-0.148815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.0000 | − | 10.0000i | 0.374503 | − | 0.374503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | − | 6.00000i | 0.673162 | − | 0.224387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | 0.596699 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.00000 | 0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.0000 | + | 24.0000i | −1.18845 | + | 0.891338i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0000 | − | 15.0000i | 0.556319 | − | 0.556319i | −0.371938 | − | 0.928257i | \(-0.621307\pi\) |
0.928257 | + | 0.371938i | \(0.121307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.00000i | − | 0.221918i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | + | 9.00000i | −0.332423 | + | 0.332423i | −0.853506 | − | 0.521083i | \(-0.825528\pi\) |
0.521083 | + | 0.853506i | \(0.325528\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.0000 | − | 42.0000i | −1.54709 | − | 1.54709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | − | 9.00000i | −0.330178 | − | 0.330178i | 0.522476 | − | 0.852654i | \(-0.325008\pi\) |
−0.852654 | + | 0.522476i | \(0.825008\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.0000 | − | 12.0000i | −0.879292 | − | 0.439646i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000i | 0.219235i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0000i | 0.948753i | 0.880322 | + | 0.474377i | \(0.157327\pi\) | ||||
−0.880322 | + | 0.474377i | \(0.842673\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.0000 | − | 18.0000i | −1.31017 | − | 0.655087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | − | 1.00000i | −0.0363456 | − | 0.0363456i | 0.688700 | − | 0.725046i | \(-0.258182\pi\) |
−0.725046 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.0000 | −1.81250 | −0.906249 | − | 0.422744i | \(-0.861067\pi\) | ||||
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | − | 4.00000i | −0.144810 | − | 0.144810i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | − | 4.00000i | 0.144432 | − | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.00000i | − | 0.288487i | −0.989542 | − | 0.144244i | \(-0.953925\pi\) | ||
0.989542 | − | 0.144244i | \(-0.0460749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.0000 | + | 35.0000i | −1.25886 | + | 1.25886i | −0.307226 | + | 0.951637i | \(0.599401\pi\) |
−0.951637 | + | 0.307226i | \(0.900599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | − | 6.00000i | 0.287368 | − | 0.215526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.0000 | −0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | + | 3.00000i | −0.321224 | + | 0.107075i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.00000 | − | 9.00000i | 0.320815 | − | 0.320815i | −0.528265 | − | 0.849080i | \(-0.677157\pi\) |
0.849080 | + | 0.528265i | \(0.177157\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000i | 0.213335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | + | 2.00000i | −0.0710221 | + | 0.0710221i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0000 | + | 17.0000i | 0.602171 | + | 0.602171i | 0.940888 | − | 0.338717i | \(-0.109993\pi\) |
−0.338717 | + | 0.940888i | \(0.609993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0000 | 0.495284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.0000 | + | 54.0000i | 1.90562 | + | 1.90562i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.0000 | + | 20.0000i | −0.352454 | + | 0.704907i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.0000i | − | 1.05344i | −0.850038 | − | 0.526721i | \(-0.823421\pi\) | ||
0.850038 | − | 0.526721i | \(-0.176579\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00000 | − | 1.00000i | 0.105085 | − | 0.0350285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | + | 12.0000i | 0.419827 | + | 0.419827i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0000 | 0.767805 | 0.383903 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383903 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | − | 3.00000i | −0.104573 | − | 0.104573i | 0.652884 | − | 0.757458i | \(-0.273559\pi\) |
−0.757458 | + | 0.652884i | \(0.773559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.00000 | − | 7.00000i | 0.243414 | − | 0.243414i | −0.574847 | − | 0.818261i | \(-0.694938\pi\) |
0.818261 | + | 0.574847i | \(0.194938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 36.0000i | − | 1.25033i | −0.780492 | − | 0.625166i | \(-0.785031\pi\) | ||
0.780492 | − | 0.625166i | \(-0.214969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.00000 | − | 5.00000i | 0.173240 | − | 0.173240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.00000 | + | 15.0000i | 0.173032 | + | 0.519096i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0000 | −1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.0000 | − | 11.0000i | −0.756823 | − | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | − | 25.0000i | 0.859010 | − | 0.859010i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.0000i | 1.71398i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0000 | − | 27.0000i | 0.924462 | − | 0.924462i | −0.0728784 | − | 0.997341i | \(-0.523219\pi\) |
0.997341 | + | 0.0728784i | \(0.0232185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.00000 | − | 5.00000i | −0.170797 | − | 0.170797i | 0.616533 | − | 0.787329i | \(-0.288537\pi\) |
−0.787329 | + | 0.616533i | \(0.788537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.0000 | − | 25.0000i | −0.851010 | − | 0.851010i | 0.139248 | − | 0.990258i | \(-0.455532\pi\) |
−0.990258 | + | 0.139248i | \(0.955532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.00000 | − | 21.0000i | −0.238007 | − | 0.714021i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 48.0000i | − | 1.62829i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.0000i | − | 0.474372i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.00000 | + | 13.0000i | −0.304256 | + | 0.439480i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0000 | + | 27.0000i | 0.911725 | + | 0.911725i | 0.996408 | − | 0.0846827i | \(-0.0269877\pi\) |
−0.0846827 | + | 0.996408i | \(0.526988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.0000 | 1.14549 | 0.572745 | − | 0.819734i | \(-0.305879\pi\) | ||||
0.572745 | + | 0.819734i | \(0.305879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0000 | − | 17.0000i | −0.572096 | − | 0.572096i | 0.360618 | − | 0.932714i | \(-0.382566\pi\) |
−0.932714 | + | 0.360618i | \(0.882566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.00000 | + | 7.00000i | −0.235037 | + | 0.235037i | −0.814791 | − | 0.579754i | \(-0.803149\pi\) |
0.579754 | + | 0.814791i | \(0.303149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.0000i | − | 0.335389i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.0000 | + | 28.0000i | −0.936984 | + | 0.936984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 24.0000i | −0.401116 | + | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0000 | 0.533630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | −0.0666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | − | 20.0000i | 0.332411 | − | 0.664822i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0000 | + | 27.0000i | −0.896520 | + | 0.896520i | −0.995127 | − | 0.0986062i | \(-0.968562\pi\) |
0.0986062 | + | 0.995127i | \(0.468562\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.0000i | − | 1.65657i | −0.560304 | − | 0.828287i | \(-0.689316\pi\) | ||
0.560304 | − | 0.828287i | \(-0.310684\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0000 | + | 30.0000i | −0.992855 | + | 0.992855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.00000 | + | 2.00000i | 0.0660458 | + | 0.0660458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | − | 6.00000i | −0.197492 | − | 0.197492i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.00000 | + | 35.0000i | −0.164399 | + | 1.15079i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 12.0000i | − | 0.393707i | −0.980433 | − | 0.196854i | \(-0.936928\pi\) | ||
0.980433 | − | 0.196854i | \(-0.0630724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000i | 0.655474i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.00000 | + | 18.0000i | 0.196221 | + | 0.588663i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.00000 | − | 3.00000i | −0.0980057 | − | 0.0980057i | 0.656404 | − | 0.754410i | \(-0.272077\pi\) |
−0.754410 | + | 0.656404i | \(0.772077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0000 | + | 30.0000i | 0.976934 | + | 0.976934i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.0000 | + | 41.0000i | −1.33232 | + | 1.33232i | −0.429031 | + | 0.903290i | \(0.641145\pi\) |
−0.903290 | + | 0.429031i | \(0.858855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000i | 0.584305i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00000 | + | 9.00000i | −0.291539 | + | 0.291539i | −0.837688 | − | 0.546149i | \(-0.816093\pi\) |
0.546149 | + | 0.837688i | \(0.316093\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0000 | + | 10.0000i | 0.647185 | + | 0.323592i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.0000 | 0.839584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | + | 3.00000i | 0.0321911 | + | 0.0965734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0000 | + | 37.0000i | −1.18984 | + | 1.18984i | −0.212728 | + | 0.977111i | \(0.568235\pi\) |
−0.977111 | + | 0.212728i | \(0.931765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 26.0000i | − | 0.834380i | −0.908819 | − | 0.417190i | \(-0.863015\pi\) | ||
0.908819 | − | 0.417190i | \(-0.136985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 12.0000i | −0.384702 | + | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0000 | + | 27.0000i | 0.863807 | + | 0.863807i | 0.991778 | − | 0.127971i | \(-0.0408466\pi\) |
−0.127971 | + | 0.991778i | \(0.540847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.0000 | − | 41.0000i | −1.30770 | − | 1.30770i | −0.923074 | − | 0.384623i | \(-0.874331\pi\) |
−0.384623 | − | 0.923074i | \(-0.625669\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.00000 | + | 1.00000i | −0.0955879 | + | 0.0318626i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 30.0000i | − | 0.953945i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.0000i | 1.08005i | 0.841650 | + | 0.540023i | \(0.181584\pi\) | ||||
−0.841650 | + | 0.540023i | \(0.818416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.0000 | + | 27.0000i | 0.855099 | + | 0.855099i | 0.990756 | − | 0.135657i | \(-0.0433146\pi\) |
−0.135657 | + | 0.990756i | \(0.543315\pi\) | |||||||
\(998\) | 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 | 1440.2.x.b.127.1 | 2 | ||
3.2 | odd | 2 | 160.2.n.b.127.1 | yes | 2 | ||
4.3 | odd | 2 | 1440.2.x.e.127.1 | 2 | |||
5.3 | odd | 4 | 1440.2.x.e.703.1 | 2 | |||
12.11 | even | 2 | 160.2.n.e.127.1 | yes | 2 | ||
15.2 | even | 4 | 800.2.n.c.543.1 | 2 | |||
15.8 | even | 4 | 160.2.n.e.63.1 | yes | 2 | ||
15.14 | odd | 2 | 800.2.n.h.607.1 | 2 | |||
20.3 | even | 4 | inner | 1440.2.x.b.703.1 | 2 | ||
24.5 | odd | 2 | 320.2.n.f.127.1 | 2 | |||
24.11 | even | 2 | 320.2.n.c.127.1 | 2 | |||
48.5 | odd | 4 | 1280.2.o.e.127.1 | 2 | |||
48.11 | even | 4 | 1280.2.o.n.127.1 | 2 | |||
48.29 | odd | 4 | 1280.2.o.k.127.1 | 2 | |||
48.35 | even | 4 | 1280.2.o.d.127.1 | 2 | |||
60.23 | odd | 4 | 160.2.n.b.63.1 | ✓ | 2 | ||
60.47 | odd | 4 | 800.2.n.h.543.1 | 2 | |||
60.59 | even | 2 | 800.2.n.c.607.1 | 2 | |||
120.29 | odd | 2 | 1600.2.n.e.1407.1 | 2 | |||
120.53 | even | 4 | 320.2.n.c.63.1 | 2 | |||
120.59 | even | 2 | 1600.2.n.j.1407.1 | 2 | |||
120.77 | even | 4 | 1600.2.n.j.1343.1 | 2 | |||
120.83 | odd | 4 | 320.2.n.f.63.1 | 2 | |||
120.107 | odd | 4 | 1600.2.n.e.1343.1 | 2 | |||
240.53 | even | 4 | 1280.2.o.d.383.1 | 2 | |||
240.83 | odd | 4 | 1280.2.o.e.383.1 | 2 | |||
240.173 | even | 4 | 1280.2.o.n.383.1 | 2 | |||
240.203 | odd | 4 | 1280.2.o.k.383.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.2.n.b.63.1 | ✓ | 2 | 60.23 | odd | 4 | ||
160.2.n.b.127.1 | yes | 2 | 3.2 | odd | 2 | ||
160.2.n.e.63.1 | yes | 2 | 15.8 | even | 4 | ||
160.2.n.e.127.1 | yes | 2 | 12.11 | even | 2 | ||
320.2.n.c.63.1 | 2 | 120.53 | even | 4 | |||
320.2.n.c.127.1 | 2 | 24.11 | even | 2 | |||
320.2.n.f.63.1 | 2 | 120.83 | odd | 4 | |||
320.2.n.f.127.1 | 2 | 24.5 | odd | 2 | |||
800.2.n.c.543.1 | 2 | 15.2 | even | 4 | |||
800.2.n.c.607.1 | 2 | 60.59 | even | 2 | |||
800.2.n.h.543.1 | 2 | 60.47 | odd | 4 | |||
800.2.n.h.607.1 | 2 | 15.14 | odd | 2 | |||
1280.2.o.d.127.1 | 2 | 48.35 | even | 4 | |||
1280.2.o.d.383.1 | 2 | 240.53 | even | 4 | |||
1280.2.o.e.127.1 | 2 | 48.5 | odd | 4 | |||
1280.2.o.e.383.1 | 2 | 240.83 | odd | 4 | |||
1280.2.o.k.127.1 | 2 | 48.29 | odd | 4 | |||
1280.2.o.k.383.1 | 2 | 240.203 | odd | 4 | |||
1280.2.o.n.127.1 | 2 | 48.11 | even | 4 | |||
1280.2.o.n.383.1 | 2 | 240.173 | even | 4 | |||
1440.2.x.b.127.1 | 2 | 1.1 | even | 1 | trivial | ||
1440.2.x.b.703.1 | 2 | 20.3 | even | 4 | inner | ||
1440.2.x.e.127.1 | 2 | 4.3 | odd | 2 | |||
1440.2.x.e.703.1 | 2 | 5.3 | odd | 4 | |||
1600.2.n.e.1343.1 | 2 | 120.107 | odd | 4 | |||
1600.2.n.e.1407.1 | 2 | 120.29 | odd | 2 | |||
1600.2.n.j.1343.1 | 2 | 120.77 | even | 4 | |||
1600.2.n.j.1407.1 | 2 | 120.59 | even | 2 |