Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(577,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.k (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: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.577 |
Dual form | 2304.2.k.c.1729.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264 | + | 4.24264i | 0.973329 | + | 0.973329i | 0.999653 | − | 0.0263249i | \(-0.00838045\pi\) |
−0.0263249 | + | 0.999653i | \(0.508380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528i | 1.76930i | 0.466252 | + | 0.884652i | \(0.345604\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | − | 6.00000i | −1.11417 | − | 1.11417i | −0.992580 | − | 0.121592i | \(-0.961200\pi\) |
−0.121592 | − | 0.992580i | \(-0.538800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41421 | −0.254000 | −0.127000 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127000 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | − | 5.00000i | 0.821995 | − | 0.821995i | −0.164399 | − | 0.986394i | \(-0.552568\pi\) |
0.986394 | + | 0.164399i | \(0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24264 | + | 4.24264i | −0.646997 | + | 0.646997i | −0.952266 | − | 0.305269i | \(-0.901253\pi\) |
0.305269 | + | 0.952266i | \(0.401253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.48528 | 1.23771 | 0.618853 | − | 0.785507i | \(-0.287598\pi\) | ||||
0.618853 | + | 0.785507i | \(0.287598\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 6.00000i | 0.824163 | − | 0.824163i | −0.162539 | − | 0.986702i | \(-0.551968\pi\) |
0.986702 | + | 0.162539i | \(0.0519683\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 5.00000i | 0.640184 | + | 0.640184i | 0.950601 | − | 0.310416i | \(-0.100468\pi\) |
−0.310416 | + | 0.950601i | \(0.600468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | + | 2.82843i | 0.345547 | + | 0.345547i | 0.858448 | − | 0.512901i | \(-0.171429\pi\) |
−0.512901 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528i | 1.00702i | 0.863990 | + | 0.503509i | \(0.167958\pi\) | ||||
−0.863990 | + | 0.503509i | \(0.832042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.41421 | 0.159111 | 0.0795557 | − | 0.996830i | \(-0.474650\pi\) | ||||
0.0795557 | + | 0.996830i | \(0.474650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41421 | − | 1.41421i | 0.148250 | − | 0.148250i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | −1.21842 | −0.609208 | − | 0.793011i | \(-0.708512\pi\) | ||||
−0.609208 | + | 0.793011i | \(0.708512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | − | 6.00000i | 0.597022 | − | 0.597022i | −0.342497 | − | 0.939519i | \(-0.611273\pi\) |
0.939519 | + | 0.342497i | \(0.111273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89949i | 0.975426i | 0.873004 | + | 0.487713i | \(0.162169\pi\) | ||||
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.48528 | + | 8.48528i | −0.820303 | + | 0.820303i | −0.986151 | − | 0.165848i | \(-0.946964\pi\) |
0.165848 | + | 0.986151i | \(0.446964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0000 | − | 13.0000i | −1.24517 | − | 1.24517i | −0.957826 | − | 0.287348i | \(-0.907226\pi\) |
−0.287348 | − | 0.957826i | \(-0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528i | 0.777844i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000i | 1.00000i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89949 | 0.878438 | 0.439219 | − | 0.898380i | \(-0.355255\pi\) | ||||
0.439219 | + | 0.898380i | \(0.355255\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.48528 | + | 8.48528i | 0.741362 | + | 0.741362i | 0.972840 | − | 0.231478i | \(-0.0743560\pi\) |
−0.231478 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 6.00000i | 0.520266 | − | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000i | 1.53784i | 0.639343 | + | 0.768922i | \(0.279207\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82843 | − | 2.82843i | 0.239904 | − | 0.239904i | −0.576906 | − | 0.816810i | \(-0.695740\pi\) |
0.816810 | + | 0.576906i | \(0.195740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0000 | − | 12.0000i | 0.983078 | − | 0.983078i | −0.0167809 | − | 0.999859i | \(-0.505342\pi\) |
0.999859 | + | 0.0167809i | \(0.00534177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3848i | 1.49613i | 0.663624 | + | 0.748066i | \(0.269017\pi\) | ||||
−0.663624 | + | 0.748066i | \(0.730983\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | − | 5.00000i | −0.399043 | − | 0.399043i | 0.478852 | − | 0.877896i | \(-0.341053\pi\) |
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.24264 | − | 4.24264i | −0.332309 | − | 0.332309i | 0.521154 | − | 0.853463i | \(-0.325502\pi\) |
−0.853463 | + | 0.521154i | \(0.825502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.9706i | − | 1.31322i | −0.754230 | − | 0.656611i | \(-0.771989\pi\) | ||
0.754230 | − | 0.656611i | \(-0.228011\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0000 | + | 12.0000i | 0.912343 | + | 0.912343i | 0.996456 | − | 0.0841131i | \(-0.0268057\pi\) |
−0.0841131 | + | 0.996456i | \(0.526806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.07107 | 0.534522 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.9706 | + | 16.9706i | 1.26844 | + | 1.26844i | 0.946894 | + | 0.321545i | \(0.104202\pi\) |
0.321545 | + | 0.946894i | \(0.395798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0000 | + | 11.0000i | −0.817624 | + | 0.817624i | −0.985763 | − | 0.168140i | \(-0.946224\pi\) |
0.168140 | + | 0.985763i | \(0.446224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | + | 6.00000i | −0.427482 | + | 0.427482i | −0.887770 | − | 0.460288i | \(-0.847746\pi\) |
0.460288 | + | 0.887770i | \(0.347746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.89949i | − | 0.701757i | −0.936421 | − | 0.350878i | \(-0.885883\pi\) | ||
0.936421 | − | 0.350878i | \(-0.114117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.48528 | + | 8.48528i | −0.595550 | + | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.82843 | − | 2.82843i | −0.194717 | − | 0.194717i | 0.603014 | − | 0.797731i | \(-0.293966\pi\) |
−0.797731 | + | 0.603014i | \(0.793966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000i | 0.135769i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 6.00000i | −0.403604 | − | 0.403604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8701 | −1.79935 | −0.899676 | − | 0.436558i | \(-0.856197\pi\) | ||||
−0.899676 | + | 0.436558i | \(0.856197\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.48528 | − | 8.48528i | −0.563188 | − | 0.563188i | 0.367024 | − | 0.930212i | \(-0.380377\pi\) |
−0.930212 | + | 0.367024i | \(0.880377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | − | 1.00000i | 0.0660819 | − | 0.0660819i | −0.673293 | − | 0.739375i | \(-0.735121\pi\) |
0.739375 | + | 0.673293i | \(0.235121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.48528i | 0.539906i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9706 | − | 16.9706i | 1.07117 | − | 1.07117i | 0.0739073 | − | 0.997265i | \(-0.476453\pi\) |
0.997265 | − | 0.0739073i | \(-0.0235469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.07107 | − | 7.07107i | −0.439375 | − | 0.439375i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | − | 6.00000i | −0.365826 | − | 0.365826i | 0.500126 | − | 0.865953i | \(-0.333287\pi\) |
−0.865953 | + | 0.500126i | \(0.833287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8701 | 1.63224 | 0.816120 | − | 0.577883i | \(-0.196121\pi\) | ||||
0.816120 | + | 0.577883i | \(0.196121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 11.0000i | 0.660926 | − | 0.660926i | −0.294672 | − | 0.955598i | \(-0.595211\pi\) |
0.955598 | + | 0.294672i | \(0.0952105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.82843 | − | 2.82843i | 0.168133 | − | 0.168133i | −0.618026 | − | 0.786158i | \(-0.712067\pi\) |
0.786158 | + | 0.618026i | \(0.212067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48528 | 0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | + | 6.00000i | −0.350524 | + | 0.350524i | −0.860304 | − | 0.509781i | \(-0.829727\pi\) |
0.509781 | + | 0.860304i | \(0.329727\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | + | 8.48528i | −0.490716 | + | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 6.00000i | 0.345834 | + | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1421 | + | 14.1421i | 0.807134 | + | 0.807134i | 0.984199 | − | 0.177065i | \(-0.0566602\pi\) |
−0.177065 | + | 0.984199i | \(0.556660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.9706i | 0.962312i | 0.876635 | + | 0.481156i | \(0.159783\pi\) | ||||
−0.876635 | + | 0.481156i | \(0.840217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 6.00000i | 0.336994 | + | 0.336994i | 0.855235 | − | 0.518241i | \(-0.173413\pi\) |
−0.518241 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.4558 | − | 25.4558i | −1.41640 | − | 1.41640i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | + | 5.00000i | −0.277350 | + | 0.277350i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.0000i | − | 0.661581i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7990 | + | 19.7990i | −1.08825 | + | 1.08825i | −0.0925421 | + | 0.995709i | \(0.529499\pi\) |
−0.995709 | + | 0.0925421i | \(0.970501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.0000 | 1.30736 | 0.653682 | − | 0.756770i | \(-0.273224\pi\) | ||||
0.653682 | + | 0.756770i | \(0.273224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.48528 | − | 8.48528i | 0.455514 | − | 0.455514i | −0.441666 | − | 0.897180i | \(-0.645612\pi\) |
0.897180 | + | 0.441666i | \(0.145612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0000 | + | 19.0000i | 1.01705 | + | 1.01705i | 0.999852 | + | 0.0171945i | \(0.00547346\pi\) |
0.0171945 | + | 0.999852i | \(0.494527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 25.4558i | − | 1.34351i | −0.740774 | − | 0.671754i | \(-0.765541\pi\) | ||
0.740774 | − | 0.671754i | \(-0.234459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000i | 0.894737i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.5269 | −1.69789 | −0.848945 | − | 0.528480i | \(-0.822762\pi\) | ||||
−0.848945 | + | 0.528480i | \(0.822762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48528 | − | 8.48528i | −0.440534 | − | 0.440534i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | + | 5.00000i | −0.258890 | + | 0.258890i | −0.824603 | − | 0.565712i | \(-0.808601\pi\) |
0.565712 | + | 0.824603i | \(0.308601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2132 | − | 21.2132i | 1.08965 | − | 1.08965i | 0.0940849 | − | 0.995564i | \(-0.470007\pi\) |
0.995564 | − | 0.0940849i | \(-0.0299925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9411 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0000 | + | 12.0000i | −0.608424 | + | 0.608424i | −0.942534 | − | 0.334110i | \(-0.891564\pi\) |
0.334110 | + | 0.942534i | \(0.391564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 50.9117i | − | 2.57471i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | − | 7.00000i | −0.351320 | − | 0.351320i | 0.509281 | − | 0.860601i | \(-0.329912\pi\) |
−0.860601 | + | 0.509281i | \(0.829912\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.41421 | − | 1.41421i | −0.0704470 | − | 0.0704470i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.0000i | − | 0.593362i | −0.954977 | − | 0.296681i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4558 | − | 25.4558i | −1.24360 | − | 1.24360i | −0.958497 | − | 0.285102i | \(-0.907972\pi\) |
−0.285102 | − | 0.958497i | \(-0.592028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | + | 11.0000i | −0.536107 | + | 0.536107i | −0.922383 | − | 0.386276i | \(-0.873761\pi\) |
0.386276 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 30.0000i | − | 1.45521i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.07107 | − | 7.07107i | 0.342193 | − | 0.342193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.48528 | 0.408722 | 0.204361 | − | 0.978896i | \(-0.434488\pi\) | ||||
0.204361 | + | 0.978896i | \(0.434488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.0000 | + | 36.0000i | −1.72211 | + | 1.72211i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.07107i | − | 0.337484i | −0.985660 | − | 0.168742i | \(-0.946030\pi\) | ||
0.985660 | − | 0.168742i | \(-0.0539704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.48528 | − | 8.48528i | 0.403148 | − | 0.403148i | −0.476193 | − | 0.879341i | \(-0.657984\pi\) |
0.879341 | + | 0.476193i | \(0.157984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 12.0000i | − | 0.561336i | −0.959805 | − | 0.280668i | \(-0.909444\pi\) | ||
0.959805 | − | 0.280668i | \(-0.0905560\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0000 | − | 24.0000i | −1.11779 | − | 1.11779i | −0.992065 | − | 0.125726i | \(-0.959874\pi\) |
−0.125726 | − | 0.992065i | \(-0.540126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.07107 | 0.328620 | 0.164310 | − | 0.986409i | \(-0.447460\pi\) | ||||
0.164310 | + | 0.986409i | \(0.447460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.48528 | − | 8.48528i | −0.392652 | − | 0.392652i | 0.482980 | − | 0.875632i | \(-0.339555\pi\) |
−0.875632 | + | 0.482980i | \(0.839555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | − | 4.00000i | 0.184703 | − | 0.184703i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.2132 | + | 21.2132i | −0.973329 | + | 0.973329i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.48528 | 0.387702 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3848i | 0.833094i | 0.909114 | + | 0.416547i | \(0.136760\pi\) | ||||
−0.909114 | + | 0.416547i | \(0.863240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9706 | − | 16.9706i | 0.765871 | − | 0.765871i | −0.211506 | − | 0.977377i | \(-0.567837\pi\) |
0.977377 | + | 0.211506i | \(0.0678368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000 | + | 36.0000i | 1.62136 | + | 1.62136i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.82843 | + | 2.82843i | 0.126618 | + | 0.126618i | 0.767576 | − | 0.640958i | \(-0.221463\pi\) |
−0.640958 | + | 0.767576i | \(0.721463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.48528i | 0.378340i | 0.981944 | + | 0.189170i | \(0.0605797\pi\) | ||||
−0.981944 | + | 0.189170i | \(0.939420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.0000 | + | 18.0000i | 0.797836 | + | 0.797836i | 0.982754 | − | 0.184918i | \(-0.0592019\pi\) |
−0.184918 | + | 0.982754i | \(0.559202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 30.0000i | − | 1.31432i | −0.753749 | − | 0.657162i | \(-0.771757\pi\) | ||
0.753749 | − | 0.657162i | \(-0.228243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7279 | − | 12.7279i | 0.556553 | − | 0.556553i | −0.371771 | − | 0.928324i | \(-0.621249\pi\) |
0.928324 | + | 0.371771i | \(0.121249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.48528 | 0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | + | 6.00000i | −0.259889 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0000 | − | 25.0000i | −1.07483 | − | 1.07483i | −0.996963 | − | 0.0778705i | \(-0.975188\pi\) |
−0.0778705 | − | 0.996963i | \(-0.524812\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.7279 | − | 12.7279i | −0.544207 | − | 0.544207i | 0.380553 | − | 0.924759i | \(-0.375734\pi\) |
−0.924759 | + | 0.380553i | \(0.875734\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 50.9117i | − | 2.16891i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.0000 | + | 12.0000i | 0.508456 | + | 0.508456i | 0.914052 | − | 0.405596i | \(-0.132936\pi\) |
−0.405596 | + | 0.914052i | \(0.632936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.48528 | −0.358889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000i | 0.754599i | 0.926091 | + | 0.377300i | \(0.123147\pi\) | ||||
−0.926091 | + | 0.377300i | \(0.876853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.82843 | + | 2.82843i | −0.118366 | + | 0.118366i | −0.763809 | − | 0.645443i | \(-0.776673\pi\) |
0.645443 | + | 0.763809i | \(0.276673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −42.4264 | −1.76930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0000 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | − | 12.0000i | 0.497844 | − | 0.497844i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | − | 6.00000i | −0.247226 | − | 0.247226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.4558i | − | 1.04010i | −0.854137 | − | 0.520049i | \(-0.825914\pi\) | ||
0.854137 | − | 0.520049i | \(-0.174086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.0000i | − | 0.489490i | −0.969587 | − | 0.244745i | \(-0.921296\pi\) | ||
0.969587 | − | 0.244745i | \(-0.0787043\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0416 | −0.975820 | −0.487910 | − | 0.872894i | \(-0.662241\pi\) | ||||
−0.487910 | + | 0.872894i | \(0.662241\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | + | 8.48528i | 0.343278 | + | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | + | 19.0000i | −0.767403 | + | 0.767403i | −0.977649 | − | 0.210246i | \(-0.932574\pi\) |
0.210246 | + | 0.977649i | \(0.432574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7990 | + | 19.7990i | −0.795789 | + | 0.795789i | −0.982428 | − | 0.186640i | \(-0.940240\pi\) |
0.186640 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.48528 | 0.339956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.0000 | + | 30.0000i | −1.19618 | + | 1.19618i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.3848i | − | 0.731886i | −0.930637 | − | 0.365943i | \(-0.880746\pi\) | ||
0.930637 | − | 0.365943i | \(-0.119254\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.00000 | + | 5.00000i | 0.198107 | + | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.0000 | 1.65890 | 0.829450 | − | 0.558581i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558581i | \(0.188654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.7279 | − | 12.7279i | −0.501940 | − | 0.501940i | 0.410100 | − | 0.912040i | \(-0.365494\pi\) |
−0.912040 | + | 0.410100i | \(0.865494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8.48528i | − | 0.333591i | −0.985992 | − | 0.166795i | \(-0.946658\pi\) | ||
0.985992 | − | 0.166795i | \(-0.0533419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000 | + | 12.0000i | 0.469596 | + | 0.469596i | 0.901784 | − | 0.432187i | \(-0.142258\pi\) |
−0.432187 | + | 0.901784i | \(0.642258\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | + | 7.00000i | −0.272268 | + | 0.272268i | −0.830013 | − | 0.557744i | \(-0.811667\pi\) |
0.557744 | + | 0.830013i | \(0.311667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.9117 | − | 50.9117i | 1.97131 | − | 1.97131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | −0.925132 | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||||
−0.462566 | + | 0.886585i | \(0.653071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.9706i | 0.651270i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.4558 | + | 25.4558i | −0.974041 | + | 0.974041i | −0.999671 | − | 0.0256307i | \(-0.991841\pi\) |
0.0256307 | + | 0.999671i | \(0.491841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.6985 | − | 29.6985i | −1.12978 | − | 1.12978i | −0.990212 | − | 0.139572i | \(-0.955427\pi\) |
−0.139572 | − | 0.990212i | \(-0.544573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.0000i | − | 1.36360i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | + | 18.0000i | 0.679851 | + | 0.679851i | 0.959966 | − | 0.280116i | \(-0.0903728\pi\) |
−0.280116 | + | 0.959966i | \(0.590373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.4264 | 1.60014 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.48528 | − | 8.48528i | −0.319122 | − | 0.319122i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00000 | + | 1.00000i | −0.0375558 | + | 0.0375558i | −0.725635 | − | 0.688080i | \(-0.758454\pi\) |
0.688080 | + | 0.725635i | \(0.258454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.48528 | −0.316448 | −0.158224 | − | 0.987403i | \(-0.550577\pi\) | ||||
−0.158224 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | 0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.0000 | − | 30.0000i | 1.11417 | − | 1.11417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.5269i | 1.20636i | 0.797606 | + | 0.603178i | \(0.206099\pi\) | ||||
−0.797606 | + | 0.603178i | \(0.793901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4558 | − | 25.4558i | 0.941518 | − | 0.941518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.0000 | − | 35.0000i | −1.29275 | − | 1.29275i | −0.933076 | − | 0.359678i | \(-0.882887\pi\) |
−0.359678 | − | 0.933076i | \(-0.617113\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.1421 | − | 14.1421i | −0.520227 | − | 0.520227i | 0.397413 | − | 0.917640i | \(-0.369908\pi\) |
−0.917640 | + | 0.397413i | \(0.869908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.9706i | − | 0.622590i | −0.950313 | − | 0.311295i | \(-0.899237\pi\) | ||
0.950313 | − | 0.311295i | \(-0.100763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | + | 12.0000i | 0.438470 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.4975 | 1.80619 | 0.903094 | − | 0.429442i | \(-0.141290\pi\) | ||||
0.903094 | + | 0.429442i | \(0.141290\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | − | 1.00000i | 0.0363456 | − | 0.0363456i | −0.688700 | − | 0.725046i | \(-0.741818\pi\) |
0.725046 | + | 0.688700i | \(0.241818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.00000i | − | 0.217500i | −0.994069 | − | 0.108750i | \(-0.965315\pi\) | ||
0.994069 | − | 0.108750i | \(-0.0346848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3848 | + | 18.3848i | −0.665574 | + | 0.665574i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0000 | − | 18.0000i | 0.647415 | − | 0.647415i | −0.304953 | − | 0.952368i | \(-0.598641\pi\) |
0.952368 | + | 0.304953i | \(0.0986406\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.07107i | − | 0.254000i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.4558 | + | 25.4558i | −0.912050 | + | 0.912050i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7279 | + | 12.7279i | 0.453701 | + | 0.453701i | 0.896581 | − | 0.442880i | \(-0.146043\pi\) |
−0.442880 | + | 0.896581i | \(0.646043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.48528i | 0.301702i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000i | 0.355110i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0000 | − | 12.0000i | −0.425062 | − | 0.425062i | 0.461880 | − | 0.886942i | \(-0.347175\pi\) |
−0.886942 | + | 0.461880i | \(0.847175\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.9117 | −1.80113 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000i | 0.632846i | 0.948618 | + | 0.316423i | \(0.102482\pi\) | ||||
−0.948618 | + | 0.316423i | \(0.897518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24264 | − | 4.24264i | 0.148979 | − | 0.148979i | −0.628683 | − | 0.777662i | \(-0.716406\pi\) |
0.777662 | + | 0.628683i | \(0.216406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | + | 6.00000i | −0.209401 | + | 0.209401i | −0.804013 | − | 0.594612i | \(-0.797306\pi\) |
0.594612 | + | 0.804013i | \(0.297306\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.5269i | 1.13382i | 0.823781 | + | 0.566908i | \(0.191861\pi\) | ||||
−0.823781 | + | 0.566908i | \(0.808139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.48528 | + | 8.48528i | −0.295062 | + | 0.295062i | −0.839076 | − | 0.544014i | \(-0.816904\pi\) |
0.544014 | + | 0.839076i | \(0.316904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | − | 11.0000i | −0.382046 | − | 0.382046i | 0.489793 | − | 0.871839i | \(-0.337072\pi\) |
−0.871839 | + | 0.489793i | \(0.837072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.0000 | −1.03944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4558i | 0.878833i | 0.898283 | + | 0.439417i | \(0.144815\pi\) | ||||
−0.898283 | + | 0.439417i | \(0.855185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000i | 1.48276i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.5563 | 0.534522 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.4264 | + | 42.4264i | 1.45436 | + | 1.45436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0000 | − | 31.0000i | 1.06142 | − | 1.06142i | 0.0634337 | − | 0.997986i | \(-0.479795\pi\) |
0.997986 | − | 0.0634337i | \(-0.0202051\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.24264 | + | 4.24264i | −0.144757 | + | 0.144757i | −0.775771 | − | 0.631014i | \(-0.782639\pi\) |
0.631014 | + | 0.775771i | \(0.282639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685i | 0.191675i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | − | 5.00000i | −0.168838 | − | 0.168838i | 0.617630 | − | 0.786468i | \(-0.288093\pi\) |
−0.786468 | + | 0.617630i | \(0.788093\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2132 | + | 21.2132i | 0.713881 | + | 0.713881i | 0.967345 | − | 0.253464i | \(-0.0815699\pi\) |
−0.253464 | + | 0.967345i | \(0.581570\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 16.9706i | − | 0.569816i | −0.958555 | − | 0.284908i | \(-0.908037\pi\) | ||
0.958555 | − | 0.284908i | \(-0.0919630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.0000i | − | 0.469545i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0000 | + | 36.0000i | 1.20469 | + | 1.20469i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.48528 | + | 8.48528i | 0.283000 | + | 0.283000i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | + | 36.0000i | −1.19933 | + | 1.19933i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.24264 | − | 4.24264i | 0.140875 | − | 0.140875i | −0.633153 | − | 0.774027i | \(-0.718239\pi\) |
0.774027 | + | 0.633153i | \(0.218239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9706 | −0.562260 | −0.281130 | − | 0.959670i | \(-0.590709\pi\) | ||||
−0.281130 | + | 0.959670i | \(0.590709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000 | − | 12.0000i | 0.396275 | − | 0.396275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.41421i | − | 0.0466506i | −0.999728 | − | 0.0233253i | \(-0.992575\pi\) | ||
0.999728 | − | 0.0233253i | \(-0.00742535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.48528 | + | 8.48528i | −0.279296 | + | 0.279296i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.0000 | + | 25.0000i | 0.821995 | + | 0.821995i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2132 | + | 21.2132i | 0.695235 | + | 0.695235i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | \(0.0104006\pi\) | ||||
−0.999466 | + | 0.0326686i | \(0.989599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.0000 | − | 36.0000i | −1.17357 | − | 1.17357i | −0.981353 | − | 0.192213i | \(-0.938433\pi\) |
−0.192213 | − | 0.981353i | \(-0.561567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.9117 | −1.65791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9706 | + | 16.9706i | 0.551469 | + | 0.551469i | 0.926865 | − | 0.375396i | \(-0.122493\pi\) |
−0.375396 | + | 0.926865i | \(0.622493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.4558 | 0.822012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.0122i | − | 1.31886i | −0.751765 | − | 0.659432i | \(-0.770797\pi\) | ||
0.751765 | − | 0.659432i | \(-0.229203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.4264 | − | 42.4264i | 1.36153 | − | 1.36153i | 0.489557 | − | 0.871971i | \(-0.337159\pi\) |
0.871971 | − | 0.489557i | \(-0.162841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | − | 4.00000i | −0.128234 | − | 0.128234i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.00000 | 0.191957 | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) | ||||
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9411i | 1.08255i | 0.840844 | + | 0.541277i | \(0.182059\pi\) | ||||
−0.840844 | + | 0.541277i | \(0.817941\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0000 | − | 36.0000i | −1.14473 | − | 1.14473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.3259 | 1.66219 | 0.831094 | − | 0.556133i | \(-0.187715\pi\) | ||||
0.831094 | + | 0.556133i | \(0.187715\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.0000 | − | 41.0000i | 1.29848 | − | 1.29848i | 0.369089 | − | 0.929394i | \(-0.379670\pi\) |
0.929394 | − | 0.369089i | \(-0.120330\pi\) | |||||||
\(998\) | 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 | 2304.2.k.c.577.1 | 4 | ||
3.2 | odd | 2 | 768.2.j.c.577.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 2304.2.k.c.577.2 | 4 | ||
8.3 | odd | 2 | 2304.2.k.b.577.2 | 4 | |||
8.5 | even | 2 | 2304.2.k.b.577.1 | 4 | |||
12.11 | even | 2 | 768.2.j.c.577.1 | yes | 4 | ||
16.3 | odd | 4 | 2304.2.k.b.1729.1 | 4 | |||
16.5 | even | 4 | inner | 2304.2.k.c.1729.2 | 4 | ||
16.11 | odd | 4 | inner | 2304.2.k.c.1729.1 | 4 | ||
16.13 | even | 4 | 2304.2.k.b.1729.2 | 4 | |||
24.5 | odd | 2 | 768.2.j.b.577.1 | yes | 4 | ||
24.11 | even | 2 | 768.2.j.b.577.2 | yes | 4 | ||
32.5 | even | 8 | 9216.2.a.o.1.2 | 2 | |||
32.11 | odd | 8 | 9216.2.a.o.1.1 | 2 | |||
32.21 | even | 8 | 9216.2.a.n.1.2 | 2 | |||
32.27 | odd | 8 | 9216.2.a.n.1.1 | 2 | |||
48.5 | odd | 4 | 768.2.j.c.193.2 | yes | 4 | ||
48.11 | even | 4 | 768.2.j.c.193.1 | yes | 4 | ||
48.29 | odd | 4 | 768.2.j.b.193.1 | ✓ | 4 | ||
48.35 | even | 4 | 768.2.j.b.193.2 | yes | 4 | ||
96.5 | odd | 8 | 3072.2.a.a.1.2 | 2 | |||
96.11 | even | 8 | 3072.2.a.a.1.1 | 2 | |||
96.29 | odd | 8 | 3072.2.d.a.1537.3 | 4 | |||
96.35 | even | 8 | 3072.2.d.a.1537.2 | 4 | |||
96.53 | odd | 8 | 3072.2.a.g.1.2 | 2 | |||
96.59 | even | 8 | 3072.2.a.g.1.1 | 2 | |||
96.77 | odd | 8 | 3072.2.d.a.1537.1 | 4 | |||
96.83 | even | 8 | 3072.2.d.a.1537.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.b.193.1 | ✓ | 4 | 48.29 | odd | 4 | ||
768.2.j.b.193.2 | yes | 4 | 48.35 | even | 4 | ||
768.2.j.b.577.1 | yes | 4 | 24.5 | odd | 2 | ||
768.2.j.b.577.2 | yes | 4 | 24.11 | even | 2 | ||
768.2.j.c.193.1 | yes | 4 | 48.11 | even | 4 | ||
768.2.j.c.193.2 | yes | 4 | 48.5 | odd | 4 | ||
768.2.j.c.577.1 | yes | 4 | 12.11 | even | 2 | ||
768.2.j.c.577.2 | yes | 4 | 3.2 | odd | 2 | ||
2304.2.k.b.577.1 | 4 | 8.5 | even | 2 | |||
2304.2.k.b.577.2 | 4 | 8.3 | odd | 2 | |||
2304.2.k.b.1729.1 | 4 | 16.3 | odd | 4 | |||
2304.2.k.b.1729.2 | 4 | 16.13 | even | 4 | |||
2304.2.k.c.577.1 | 4 | 1.1 | even | 1 | trivial | ||
2304.2.k.c.577.2 | 4 | 4.3 | odd | 2 | inner | ||
2304.2.k.c.1729.1 | 4 | 16.11 | odd | 4 | inner | ||
2304.2.k.c.1729.2 | 4 | 16.5 | even | 4 | inner | ||
3072.2.a.a.1.1 | 2 | 96.11 | even | 8 | |||
3072.2.a.a.1.2 | 2 | 96.5 | odd | 8 | |||
3072.2.a.g.1.1 | 2 | 96.59 | even | 8 | |||
3072.2.a.g.1.2 | 2 | 96.53 | odd | 8 | |||
3072.2.d.a.1537.1 | 4 | 96.77 | odd | 8 | |||
3072.2.d.a.1537.2 | 4 | 96.35 | even | 8 | |||
3072.2.d.a.1537.3 | 4 | 96.29 | odd | 8 | |||
3072.2.d.a.1537.4 | 4 | 96.83 | even | 8 | |||
9216.2.a.n.1.1 | 2 | 32.27 | odd | 8 | |||
9216.2.a.n.1.2 | 2 | 32.21 | even | 8 | |||
9216.2.a.o.1.1 | 2 | 32.11 | odd | 8 | |||
9216.2.a.o.1.2 | 2 | 32.5 | even | 8 |