Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4608,2,Mod(1153,4608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4608, 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("4608.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4608 = 2^{9} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4608.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: | \(36.7950652514\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1536) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1153.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4608.1153 |
Dual form | 4608.2.k.bb.3457.2 |
$q$-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 \(\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(3583\) | \(4097\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.00000i | 0.447214 | − | 0.447214i | −0.447214 | − | 0.894427i | \(-0.647584\pi\) |
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | 3.00000 | + | 3.00000i | 0.832050 | + | 0.832050i | 0.987797 | − | 0.155747i | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685 | + | 5.65685i | 1.29777 | + | 1.29777i | 0.929861 | + | 0.367910i | \(0.119927\pi\) |
0.367910 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | + | 1.00000i | 0.185695 | + | 0.185695i | 0.793832 | − | 0.608137i | \(-0.208083\pi\) |
−0.608137 | + | 0.793832i | \(0.708083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.82843 | − | 2.82843i | −0.478091 | − | 0.478091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000i | 0.624695i | 0.949968 | + | 0.312348i | \(0.101115\pi\) | ||||
−0.949968 | + | 0.312348i | \(0.898885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3137 | −1.65027 | −0.825137 | − | 0.564933i | \(-0.808902\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.00000 | + | 5.00000i | −0.686803 | + | 0.686803i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) |
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.48528 | + | 8.48528i | −1.10469 | + | 1.10469i | −0.110853 | + | 0.993837i | \(0.535358\pi\) |
−0.993837 | + | 0.110853i | \(0.964642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.00000i | −0.128037 | − | 0.128037i | 0.640184 | − | 0.768221i | \(-0.278858\pi\) |
−0.768221 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 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 | ||||||||
\(71\) | 11.3137i | 1.34269i | 0.741145 | + | 0.671345i | \(0.234283\pi\) | ||||
−0.741145 | + | 0.671345i | \(0.765717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3137 | − | 11.3137i | −1.24184 | − | 1.24184i | −0.959237 | − | 0.282604i | \(-0.908802\pi\) |
−0.282604 | − | 0.959237i | \(-0.591198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | − | 4.00000i | 0.433861 | − | 0.433861i | ||||
\(86\) | 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 | ||||||||
\(91\) | 8.48528 | − | 8.48528i | 0.889499 | − | 0.889499i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3137 | 1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0000 | 1.62455 | 0.812277 | − | 0.583272i | \(-0.198228\pi\) | ||||
0.812277 | + | 0.583272i | \(0.198228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.0000 | − | 11.0000i | 1.09454 | − | 1.09454i | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) |
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.7990i | − | 1.95085i | −0.220326 | − | 0.975426i | \(-0.570712\pi\) | ||
0.220326 | − | 0.975426i | \(-0.429288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.48528 | − | 8.48528i | 0.820303 | − | 0.820303i | −0.165848 | − | 0.986151i | \(-0.553036\pi\) |
0.986151 | + | 0.165848i | \(0.0530362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00000 | − | 3.00000i | −0.287348 | − | 0.287348i | 0.548683 | − | 0.836031i | \(-0.315129\pi\) |
−0.836031 | + | 0.548683i | \(0.815129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65685 | + | 5.65685i | 0.527504 | + | 0.527504i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 11.3137i | − | 1.03713i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000i | 1.00000i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.00000 | + | 8.00000i | 0.715542 | + | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.48528 | 0.752947 | 0.376473 | − | 0.926427i | \(-0.377137\pi\) | ||||
0.376473 | + | 0.926427i | \(0.377137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.82843 | + | 2.82843i | 0.247121 | + | 0.247121i | 0.819788 | − | 0.572667i | \(-0.194091\pi\) |
−0.572667 | + | 0.819788i | \(0.694091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000 | − | 16.0000i | 1.38738 | − | 1.38738i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.82843 | + | 2.82843i | −0.239904 | + | 0.239904i | −0.816810 | − | 0.576906i | \(-0.804260\pi\) |
0.576906 | + | 0.816810i | \(0.304260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | − | 9.00000i | 0.737309 | − | 0.737309i | −0.234748 | − | 0.972056i | \(-0.575426\pi\) |
0.972056 | + | 0.234748i | \(0.0754264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.82843i | − | 0.230174i | −0.993355 | − | 0.115087i | \(-0.963285\pi\) | ||
0.993355 | − | 0.115087i | \(-0.0367147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82843 | + | 2.82843i | −0.227185 | + | 0.227185i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0000 | + | 15.0000i | 1.19713 | + | 1.19713i | 0.975022 | + | 0.222108i | \(0.0712939\pi\) |
0.222108 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3137 | − | 11.3137i | −0.886158 | − | 0.886158i | 0.107994 | − | 0.994152i | \(-0.465557\pi\) |
−0.994152 | + | 0.107994i | \(0.965557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137i | 0.875481i | 0.899101 | + | 0.437741i | \(0.144221\pi\) | ||||
−0.899101 | + | 0.437741i | \(0.855779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.00000 | − | 5.00000i | −0.380143 | − | 0.380143i | 0.491011 | − | 0.871154i | \(-0.336628\pi\) |
−0.871154 | + | 0.491011i | \(0.836628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.48528 | 0.641427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.82843 | + | 2.82843i | 0.211407 | + | 0.211407i | 0.804865 | − | 0.593458i | \(-0.202238\pi\) |
−0.593458 | + | 0.804865i | \(0.702238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.00000 | − | 9.00000i | 0.668965 | − | 0.668965i | −0.288512 | − | 0.957476i | \(-0.593160\pi\) |
0.957476 | + | 0.288512i | \(0.0931604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.00000i | − | 0.441129i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | − | 5.00000i | 0.356235 | − | 0.356235i | −0.506188 | − | 0.862423i | \(-0.668946\pi\) |
0.862423 | + | 0.506188i | \(0.168946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.48528i | 0.601506i | 0.953702 | + | 0.300753i | \(0.0972379\pi\) | ||||
−0.953702 | + | 0.300753i | \(0.902762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | − | 2.82843i | 0.198517 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 4.00000i | 0.279372 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.48528 | − | 8.48528i | −0.584151 | − | 0.584151i | 0.351890 | − | 0.936041i | \(-0.385539\pi\) |
−0.936041 | + | 0.351890i | \(0.885539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000i | 0.543075i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | + | 12.0000i | 0.807207 | + | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4558 | −1.70465 | −0.852325 | − | 0.523013i | \(-0.824808\pi\) | ||||
−0.852325 | + | 0.523013i | \(0.824808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.65685 | + | 5.65685i | 0.375459 | + | 0.375459i | 0.869461 | − | 0.494002i | \(-0.164466\pi\) |
−0.494002 | + | 0.869461i | \(0.664466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0000 | − | 17.0000i | 1.12339 | − | 1.12339i | 0.132164 | − | 0.991228i | \(-0.457808\pi\) |
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000i | 0.655122i | 0.944830 | + | 0.327561i | \(0.106227\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3137 | + | 11.3137i | −0.738025 | + | 0.738025i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.65685 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 1.00000i | −0.0638877 | + | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.9411i | 2.15962i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.65685 | − | 5.65685i | 0.357057 | − | 0.357057i | −0.505670 | − | 0.862727i | \(-0.668755\pi\) |
0.862727 | + | 0.505670i | \(0.168755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.48528 | − | 8.48528i | −0.527250 | − | 0.527250i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.2843i | − | 1.74408i | −0.489432 | − | 0.872041i | \(-0.662796\pi\) | ||
0.489432 | − | 0.872041i | \(-0.337204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000i | 0.614295i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | − | 15.0000i | −0.914566 | − | 0.914566i | 0.0820612 | − | 0.996627i | \(-0.473850\pi\) |
−0.996627 | + | 0.0820612i | \(0.973850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.48528 | −0.515444 | −0.257722 | − | 0.966219i | \(-0.582972\pi\) | ||||
−0.257722 | + | 0.966219i | \(0.582972\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.00000i | −0.0600842 | + | 0.0600842i | −0.736510 | − | 0.676426i | \(-0.763528\pi\) |
0.676426 | + | 0.736510i | \(0.263528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.0000i | − | 1.31241i | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||
0.754583 | − | 0.656205i | \(-0.227839\pi\) | |||||||
\(282\) | 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 | ||||||||
\(287\) | 11.3137 | 0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0000 | − | 13.0000i | 0.759468 | − | 0.759468i | −0.216757 | − | 0.976226i | \(-0.569548\pi\) |
0.976226 | + | 0.216757i | \(0.0695481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.9706i | 0.988064i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9706 | + | 16.9706i | −0.981433 | + | 0.981433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82843 | + | 2.82843i | 0.161427 | + | 0.161427i | 0.783199 | − | 0.621772i | \(-0.213587\pi\) |
−0.621772 | + | 0.783199i | \(0.713587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 28.2843i | − | 1.60385i | −0.597422 | − | 0.801927i | \(-0.703808\pi\) | ||
0.597422 | − | 0.801927i | \(-0.296192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0000i | 0.904373i | 0.891923 | + | 0.452187i | \(0.149356\pi\) | ||||
−0.891923 | + | 0.452187i | \(0.850644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0000 | − | 15.0000i | −0.842484 | − | 0.842484i | 0.146697 | − | 0.989181i | \(-0.453136\pi\) |
−0.989181 | + | 0.146697i | \(0.953136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.6274 | + | 22.6274i | 1.25902 | + | 1.25902i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.00000 | + | 9.00000i | −0.499230 | + | 0.499230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.0000i | 1.76422i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82843 | − | 2.82843i | 0.155464 | − | 0.155464i | −0.625089 | − | 0.780553i | \(-0.714937\pi\) |
0.780553 | + | 0.625089i | \(0.214937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.65685 | 0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | 22.6274 | − | 22.6274i | 1.21470 | − | 1.21470i | 0.245241 | − | 0.969462i | \(-0.421133\pi\) |
0.969462 | − | 0.245241i | \(-0.0788672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.00000 | + | 9.00000i | 0.481759 | + | 0.481759i | 0.905693 | − | 0.423934i | \(-0.139351\pi\) |
−0.423934 | + | 0.905693i | \(0.639351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3137 | + | 11.3137i | 0.600469 | + | 0.600469i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137i | 0.597115i | 0.954392 | + | 0.298557i | \(0.0965054\pi\) | ||||
−0.954392 | + | 0.298557i | \(0.903495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.0000i | 2.36842i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | + | 14.0000i | 0.732793 | + | 0.732793i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.82843 | 0.147643 | 0.0738213 | − | 0.997271i | \(-0.476481\pi\) | ||||
0.0738213 | + | 0.997271i | \(0.476481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.1421 | + | 14.1421i | 0.734223 | + | 0.734223i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | − | 3.00000i | 0.155334 | − | 0.155334i | −0.625161 | − | 0.780496i | \(-0.714967\pi\) |
0.780496 | + | 0.625161i | \(0.214967\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3137 | + | 11.3137i | −0.581146 | + | 0.581146i | −0.935218 | − | 0.354072i | \(-0.884797\pi\) |
0.354072 | + | 0.935218i | \(0.384797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.00000 | − | 7.00000i | 0.354914 | − | 0.354914i | −0.507020 | − | 0.861934i | \(-0.669253\pi\) |
0.861934 | + | 0.507020i | \(0.169253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6274i | 1.14432i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.48528 | − | 8.48528i | 0.426941 | − | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0000 | − | 15.0000i | −0.752828 | − | 0.752828i | 0.222178 | − | 0.975006i | \(-0.428683\pi\) |
−0.975006 | + | 0.222178i | \(0.928683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.0000 | −0.998752 | −0.499376 | − | 0.866385i | \(-0.666437\pi\) | ||||
−0.499376 | + | 0.866385i | \(0.666437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.48528 | − | 8.48528i | −0.422682 | − | 0.422682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.0000i | − | 1.58230i | −0.611623 | − | 0.791149i | \(-0.709483\pi\) | ||
0.611623 | − | 0.791149i | \(-0.290517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | + | 24.0000i | 1.18096 | + | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6274 | −1.11074 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.65685 | + | 5.65685i | 0.276355 | + | 0.276355i | 0.831652 | − | 0.555297i | \(-0.187395\pi\) |
−0.555297 | + | 0.831652i | \(0.687395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.00000 | − | 9.00000i | 0.438633 | − | 0.438633i | −0.452919 | − | 0.891552i | \(-0.649617\pi\) |
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000i | 0.582086i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.82843 | + | 2.82843i | −0.136877 | + | 0.136877i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3137 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.00000 | −0.384455 | −0.192228 | − | 0.981350i | \(-0.561571\pi\) | ||||
−0.192228 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.0000 | + | 32.0000i | −1.53077 | + | 1.53077i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.82843i | 0.134993i | 0.997719 | + | 0.0674967i | \(0.0215012\pi\) | ||||
−0.997719 | + | 0.0674967i | \(0.978499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9706 | + | 16.9706i | −0.806296 | + | 0.806296i | −0.984071 | − | 0.177775i | \(-0.943110\pi\) |
0.177775 | + | 0.984071i | \(0.443110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 6.00000i | 0.284427 | + | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 16.9706i | − | 0.795592i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.0000 | − | 11.0000i | −0.512321 | − | 0.512321i | 0.402916 | − | 0.915237i | \(-0.367997\pi\) |
−0.915237 | + | 0.402916i | \(0.867997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.1127 | −1.44593 | −0.722965 | − | 0.690885i | \(-0.757221\pi\) | ||||
−0.722965 | + | 0.690885i | \(0.757221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.65685 | + | 5.65685i | 0.261768 | + | 0.261768i | 0.825772 | − | 0.564004i | \(-0.190740\pi\) |
−0.564004 | + | 0.825772i | \(0.690740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | − | 8.00000i | 0.369406 | − | 0.369406i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9706 | + | 16.9706i | −0.778663 | + | 0.778663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.2843 | 1.29234 | 0.646171 | − | 0.763193i | \(-0.276369\pi\) | ||||
0.646171 | + | 0.763193i | \(0.276369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0000 | − | 16.0000i | 0.726523 | − | 0.726523i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82843i | 0.128168i | 0.997944 | + | 0.0640841i | \(0.0204126\pi\) | ||||
−0.997944 | + | 0.0640841i | \(0.979587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.48528 | − | 8.48528i | 0.382935 | − | 0.382935i | −0.489223 | − | 0.872159i | \(-0.662720\pi\) |
0.872159 | + | 0.489223i | \(0.162720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | + | 4.00000i | 0.180151 | + | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7990 | − | 19.7990i | −0.886325 | − | 0.886325i | 0.107843 | − | 0.994168i | \(-0.465605\pi\) |
−0.994168 | + | 0.107843i | \(0.965605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.3137i | 0.504453i | 0.967668 | + | 0.252227i | \(0.0811629\pi\) | ||||
−0.967668 | + | 0.252227i | \(0.918837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 22.0000i | − | 0.978987i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.0000 | + | 23.0000i | 1.01946 | + | 1.01946i | 0.999807 | + | 0.0196502i | \(0.00625524\pi\) |
0.0196502 | + | 0.999807i | \(0.493745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.5980 | 1.75171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7990 | − | 19.7990i | −0.872448 | − | 0.872448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.0000i | − | 0.525730i | −0.964833 | − | 0.262865i | \(-0.915333\pi\) | ||
0.964833 | − | 0.262865i | \(-0.0846673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.65685 | − | 5.65685i | 0.247357 | − | 0.247357i | −0.572528 | − | 0.819885i | \(-0.694037\pi\) |
0.819885 | + | 0.572528i | \(0.194037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.3137 | −0.492833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | + | 12.0000i | −0.519778 | + | 0.519778i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.9706i | − | 0.733701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.00000 | + | 3.00000i | 0.128980 | + | 0.128980i | 0.768650 | − | 0.639670i | \(-0.220929\pi\) |
−0.639670 | + | 0.768650i | \(0.720929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.65685 | − | 5.65685i | −0.241870 | − | 0.241870i | 0.575754 | − | 0.817623i | \(-0.304709\pi\) |
−0.817623 | + | 0.575754i | \(0.804709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3137i | 0.481980i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 24.0000i | − | 1.02058i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0000 | − | 21.0000i | −0.889799 | − | 0.889799i | 0.104705 | − | 0.994503i | \(-0.466610\pi\) |
−0.994503 | + | 0.104705i | \(0.966610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.65685 | − | 5.65685i | −0.238408 | − | 0.238408i | 0.577783 | − | 0.816191i | \(-0.303918\pi\) |
−0.816191 | + | 0.577783i | \(0.803918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | + | 18.0000i | −0.757266 | + | 0.757266i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 20.0000i | − | 0.838444i | −0.907884 | − | 0.419222i | \(-0.862303\pi\) | ||
0.907884 | − | 0.419222i | \(-0.137697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1421 | − | 14.1421i | 0.591830 | − | 0.591830i | −0.346296 | − | 0.938125i | \(-0.612561\pi\) |
0.938125 | + | 0.346296i | \(0.112561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9706 | −0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.0000 | + | 32.0000i | −1.32758 | + | 1.32758i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.82843 | + | 2.82843i | −0.116742 | + | 0.116742i | −0.763064 | − | 0.646323i | \(-0.776306\pi\) |
0.646323 | + | 0.763064i | \(0.276306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | − | 16.0000i | −0.659269 | − | 0.659269i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3137 | − | 11.3137i | −0.463817 | − | 0.463817i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.5980i | 1.61793i | 0.587857 | + | 0.808965i | \(0.299972\pi\) | ||||
−0.587857 | + | 0.808965i | \(0.700028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.0000i | − | 0.571072i | −0.958368 | − | 0.285536i | \(-0.907828\pi\) | ||
0.958368 | − | 0.285536i | \(-0.0921716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | + | 11.0000i | 0.447214 | + | 0.447214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.4264 | 1.72203 | 0.861017 | − | 0.508576i | \(-0.169828\pi\) | ||||
0.861017 | + | 0.508576i | \(0.169828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.9411 | − | 33.9411i | −1.37311 | − | 1.37311i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 11.0000i | −0.444286 | + | 0.444286i | −0.893449 | − | 0.449164i | \(-0.851722\pi\) |
0.449164 | + | 0.893449i | \(0.351722\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1127 | − | 31.1127i | 1.25052 | − | 1.25052i | 0.295040 | − | 0.955485i | \(-0.404667\pi\) |
0.955485 | − | 0.295040i | \(-0.0953330\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9706 | 0.679911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | − | 12.0000i | 0.478471 | − | 0.478471i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.48528i | 0.337794i | 0.985634 | + | 0.168897i | \(0.0540205\pi\) | ||||
−0.985634 | + | 0.168897i | \(0.945980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.48528 | − | 8.48528i | 0.336728 | − | 0.336728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | − | 3.00000i | −0.118864 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3137 | + | 11.3137i | 0.446169 | + | 0.446169i | 0.894079 | − | 0.447910i | \(-0.147831\pi\) |
−0.447910 | + | 0.894079i | \(0.647831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 39.5980i | − | 1.55676i | −0.627795 | − | 0.778379i | \(-0.716042\pi\) | ||
0.627795 | − | 0.778379i | \(-0.283958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.00000 | − | 3.00000i | −0.117399 | − | 0.117399i | 0.645967 | − | 0.763366i | \(-0.276455\pi\) |
−0.763366 | + | 0.645967i | \(0.776455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.65685 | 0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1421 | + | 14.1421i | 0.550899 | + | 0.550899i | 0.926700 | − | 0.375801i | \(-0.122632\pi\) |
−0.375801 | + | 0.926700i | \(0.622632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | + | 19.0000i | −0.739014 | + | 0.739014i | −0.972387 | − | 0.233373i | \(-0.925024\pi\) |
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 32.0000i | − | 1.24091i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.65685 | + | 5.65685i | −0.219034 | + | 0.219034i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.00000 | −0.308377 | −0.154189 | − | 0.988041i | \(-0.549276\pi\) | ||||
−0.154189 | + | 0.988041i | \(0.549276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.0000 | − | 23.0000i | 0.883962 | − | 0.883962i | −0.109973 | − | 0.993935i | \(-0.535076\pi\) |
0.993935 | + | 0.109973i | \(0.0350764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 45.2548i | − | 1.73672i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.6274 | + | 22.6274i | −0.865814 | + | 0.865814i | −0.992006 | − | 0.126192i | \(-0.959725\pi\) |
0.126192 | + | 0.992006i | \(0.459725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | + | 12.0000i | 0.458496 | + | 0.458496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.0000 | −1.14291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2843 | + | 28.2843i | 1.07598 | + | 1.07598i | 0.996865 | + | 0.0791192i | \(0.0252108\pi\) |
0.0791192 | + | 0.996865i | \(0.474789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.65685i | 0.214577i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000i | 0.606043i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.0000 | − | 33.0000i | −1.24639 | − | 1.24639i | −0.957302 | − | 0.289091i | \(-0.906647\pi\) |
−0.289091 | − | 0.957302i | \(-0.593353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9411 | 1.28011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.1127 | − | 31.1127i | −1.17011 | − | 1.17011i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0000 | + | 25.0000i | −0.938895 | + | 0.938895i | −0.998238 | − | 0.0593429i | \(-0.981099\pi\) |
0.0593429 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.0000i | − | 0.599205i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.9706 | 0.632895 | 0.316448 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316448 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.0000 | −2.08555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 3.00000i | −0.111417 | + | 0.111417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.4264i | − | 1.57351i | −0.617266 | − | 0.786754i | \(-0.711760\pi\) | ||
0.617266 | − | 0.786754i | \(-0.288240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.00000 | − | 3.00000i | −0.110808 | − | 0.110808i | 0.649529 | − | 0.760337i | \(-0.274966\pi\) |
−0.760337 | + | 0.649529i | \(0.774966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4558 | + | 25.4558i | 0.936408 | + | 0.936408i | 0.998096 | − | 0.0616872i | \(-0.0196481\pi\) |
−0.0616872 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.3137i | − | 0.415060i | −0.978229 | − | 0.207530i | \(-0.933458\pi\) | ||
0.978229 | − | 0.207530i | \(-0.0665424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 18.0000i | − | 0.659469i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.0000 | − | 24.0000i | −0.876941 | − | 0.876941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.48528 | −0.309632 | −0.154816 | − | 0.987943i | \(-0.549479\pi\) | ||||
−0.154816 | + | 0.987943i | \(0.549479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.82843 | − | 2.82843i | −0.102937 | − | 0.102937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | + | 15.0000i | −0.545184 | + | 0.545184i | −0.925044 | − | 0.379860i | \(-0.875972\pi\) |
0.379860 | + | 0.925044i | \(0.375972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.0000i | 1.30500i | 0.757789 | + | 0.652499i | \(0.226280\pi\) | ||||
−0.757789 | + | 0.652499i | \(0.773720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.48528 | + | 8.48528i | −0.307188 | + | 0.307188i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.9117 | −1.83831 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0000 | + | 13.0000i | −0.467578 | + | 0.467578i | −0.901129 | − | 0.433551i | \(-0.857260\pi\) |
0.433551 | + | 0.901129i | \(0.357260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.48528i | − | 0.304800i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6274 | + | 22.6274i | −0.810711 | + | 0.810711i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.6274 | + | 22.6274i | 0.806580 | + | 0.806580i | 0.984115 | − | 0.177534i | \(-0.0568121\pi\) |
−0.177534 | + | 0.984115i | \(0.556812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.9117i | 1.81021i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.00000i | − | 0.213066i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.0000 | + | 35.0000i | 1.23976 | + | 1.23976i | 0.960097 | + | 0.279666i | \(0.0902238\pi\) |
0.279666 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.2548 | −1.60100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | − | 16.0000i | 0.563926 | − | 0.563926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.00000i | − | 0.140633i | −0.997525 | − | 0.0703163i | \(-0.977599\pi\) | ||
0.997525 | − | 0.0703163i | \(-0.0224008\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2843 | − | 28.2843i | 0.993195 | − | 0.993195i | −0.00678191 | − | 0.999977i | \(-0.502159\pi\) |
0.999977 | + | 0.00678191i | \(0.00215876\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.6274 | −0.792604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | + | 5.00000i | −0.174501 | + | 0.174501i | −0.788954 | − | 0.614453i | \(-0.789377\pi\) |
0.614453 | + | 0.788954i | \(0.289377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.4558i | − | 0.887335i | −0.896191 | − | 0.443667i | \(-0.853677\pi\) | ||
0.896191 | − | 0.443667i | \(-0.146323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1421 | − | 14.1421i | 0.491770 | − | 0.491770i | −0.417093 | − | 0.908864i | \(-0.636951\pi\) |
0.908864 | + | 0.417093i | \(0.136951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.0000 | − | 37.0000i | −1.28506 | − | 1.28506i | −0.937749 | − | 0.347314i | \(-0.887094\pi\) |
−0.347314 | − | 0.937749i | \(-0.612906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | −0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3137 | + | 11.3137i | 0.391527 | + | 0.391527i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.2548i | 1.56237i | 0.624299 | + | 0.781185i | \(0.285385\pi\) | ||||
−0.624299 | + | 0.781185i | \(0.714615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 27.0000i | − | 0.931034i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.00000 | + | 5.00000i | 0.172005 | + | 0.172005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.1127 | 1.06904 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.9706 | + | 16.9706i | 0.581743 | + | 0.581743i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0000 | − | 11.0000i | 0.376633 | − | 0.376633i | −0.493253 | − | 0.869886i | \(-0.664192\pi\) |
0.869886 | + | 0.493253i | \(0.164192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20.0000i | − | 0.683187i | −0.939848 | − | 0.341593i | \(-0.889033\pi\) | ||
0.939848 | − | 0.341593i | \(-0.110967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.65685 | − | 5.65685i | 0.193009 | − | 0.193009i | −0.603986 | − | 0.796995i | \(-0.706422\pi\) |
0.796995 | + | 0.603986i | \(0.206422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.65685 | 0.192562 | 0.0962808 | − | 0.995354i | \(-0.469305\pi\) | ||||
0.0962808 | + | 0.995354i | \(0.469305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | −0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706i | 0.575026i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6274 | − | 22.6274i | 0.764946 | − | 0.764946i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | − | 23.0000i | −0.776655 | − | 0.776655i | 0.202606 | − | 0.979260i | \(-0.435059\pi\) |
−0.979260 | + | 0.202606i | \(0.935059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9706 | − | 16.9706i | −0.571105 | − | 0.571105i | 0.361332 | − | 0.932437i | \(-0.382322\pi\) |
−0.932437 | + | 0.361332i | \(0.882322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9706i | 0.569816i | 0.958555 | + | 0.284908i | \(0.0919630\pi\) | ||||
−0.958555 | + | 0.284908i | \(0.908037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 24.0000i | − | 0.804934i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −64.0000 | − | 64.0000i | −2.14168 | − | 2.14168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.65685 | 0.189088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.82843 | − | 2.82843i | −0.0943333 | − | 0.0943333i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.0000 | + | 20.0000i | −0.666297 | + | 0.666297i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.0000i | − | 0.598340i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6274 | + | 22.6274i | −0.751331 | + | 0.751331i | −0.974728 | − | 0.223397i | \(-0.928286\pi\) |
0.223397 | + | 0.974728i | \(0.428286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685 | 0.187420 | 0.0937100 | − | 0.995600i | \(-0.470127\pi\) | ||||
0.0937100 | + | 0.995600i | \(0.470127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.00000 | − | 8.00000i | 0.264183 | − | 0.264183i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.82843i | − | 0.0933012i | −0.998911 | − | 0.0466506i | \(-0.985145\pi\) | ||
0.998911 | − | 0.0466506i | \(-0.0148547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9411 | + | 33.9411i | −1.11719 | + | 1.11719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | + | 9.00000i | 0.295918 | + | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.0000 | 0.656179 | 0.328089 | − | 0.944647i | \(-0.393595\pi\) | ||||
0.328089 | + | 0.944647i | \(0.393595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.65685 | − | 5.65685i | −0.185396 | − | 0.185396i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42.0000i | − | 1.37208i | −0.727564 | − | 0.686040i | \(-0.759347\pi\) | ||
0.727564 | − | 0.686040i | \(-0.240653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.0000 | + | 37.0000i | 1.20617 | + | 1.20617i | 0.972259 | + | 0.233906i | \(0.0751509\pi\) |
0.233906 | + | 0.972259i | \(0.424849\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.6274 | −0.736850 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.7696 | − | 36.7696i | −1.19485 | − | 1.19485i | −0.975689 | − | 0.219161i | \(-0.929668\pi\) |
−0.219161 | − | 0.975689i | \(-0.570332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.0000 | + | 42.0000i | −1.36338 | + | 1.36338i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 36.0000i | − | 1.16615i | −0.812417 | − | 0.583077i | \(-0.801849\pi\) | ||
0.812417 | − | 0.583077i | \(-0.198151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.65685 | + | 5.65685i | −0.183052 | + | 0.183052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.9411 | 1.09602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.4264i | 1.36434i | 0.731193 | + | 0.682171i | \(0.238964\pi\) | ||||
−0.731193 | + | 0.682171i | \(0.761036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.9706 | + | 16.9706i | −0.544611 | + | 0.544611i | −0.924877 | − | 0.380266i | \(-0.875832\pi\) |
0.380266 | + | 0.924877i | \(0.375832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | + | 8.00000i | 0.256468 | + | 0.256468i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.0000 | −1.15174 | −0.575871 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575871 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9706i | 0.541277i | 0.962681 | + | 0.270638i | \(0.0872348\pi\) | ||||
−0.962681 | + | 0.270638i | \(0.912765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 10.0000i | − | 0.318626i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4558 | −0.808632 | −0.404316 | − | 0.914619i | \(-0.632490\pi\) | ||||
−0.404316 | + | 0.914619i | \(0.632490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.48528 | + | 8.48528i | 0.269002 | + | 0.269002i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00000 | + | 5.00000i | −0.158352 | + | 0.158352i | −0.781836 | − | 0.623484i | \(-0.785717\pi\) |
0.623484 | + | 0.781836i | \(0.285717\pi\) | |||||||
\(998\) | 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 | 4608.2.k.bb.1153.1 | 4 | ||
3.2 | odd | 2 | 1536.2.j.b.1153.1 | yes | 4 | ||
4.3 | odd | 2 | inner | 4608.2.k.bb.1153.2 | 4 | ||
8.3 | odd | 2 | 4608.2.k.y.1153.2 | 4 | |||
8.5 | even | 2 | 4608.2.k.y.1153.1 | 4 | |||
12.11 | even | 2 | 1536.2.j.b.1153.2 | yes | 4 | ||
16.3 | odd | 4 | 4608.2.k.y.3457.1 | 4 | |||
16.5 | even | 4 | inner | 4608.2.k.bb.3457.2 | 4 | ||
16.11 | odd | 4 | inner | 4608.2.k.bb.3457.1 | 4 | ||
16.13 | even | 4 | 4608.2.k.y.3457.2 | 4 | |||
24.5 | odd | 2 | 1536.2.j.c.1153.2 | yes | 4 | ||
24.11 | even | 2 | 1536.2.j.c.1153.1 | yes | 4 | ||
32.5 | even | 8 | 9216.2.a.i.1.2 | 2 | |||
32.11 | odd | 8 | 9216.2.a.i.1.1 | 2 | |||
32.21 | even | 8 | 9216.2.a.h.1.1 | 2 | |||
32.27 | odd | 8 | 9216.2.a.h.1.2 | 2 | |||
48.5 | odd | 4 | 1536.2.j.b.385.1 | ✓ | 4 | ||
48.11 | even | 4 | 1536.2.j.b.385.2 | yes | 4 | ||
48.29 | odd | 4 | 1536.2.j.c.385.2 | yes | 4 | ||
48.35 | even | 4 | 1536.2.j.c.385.1 | yes | 4 | ||
96.5 | odd | 8 | 3072.2.a.h.1.1 | 2 | |||
96.11 | even | 8 | 3072.2.a.h.1.2 | 2 | |||
96.29 | odd | 8 | 3072.2.d.c.1537.1 | 4 | |||
96.35 | even | 8 | 3072.2.d.c.1537.3 | 4 | |||
96.53 | odd | 8 | 3072.2.a.b.1.2 | 2 | |||
96.59 | even | 8 | 3072.2.a.b.1.1 | 2 | |||
96.77 | odd | 8 | 3072.2.d.c.1537.4 | 4 | |||
96.83 | even | 8 | 3072.2.d.c.1537.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.j.b.385.1 | ✓ | 4 | 48.5 | odd | 4 | ||
1536.2.j.b.385.2 | yes | 4 | 48.11 | even | 4 | ||
1536.2.j.b.1153.1 | yes | 4 | 3.2 | odd | 2 | ||
1536.2.j.b.1153.2 | yes | 4 | 12.11 | even | 2 | ||
1536.2.j.c.385.1 | yes | 4 | 48.35 | even | 4 | ||
1536.2.j.c.385.2 | yes | 4 | 48.29 | odd | 4 | ||
1536.2.j.c.1153.1 | yes | 4 | 24.11 | even | 2 | ||
1536.2.j.c.1153.2 | yes | 4 | 24.5 | odd | 2 | ||
3072.2.a.b.1.1 | 2 | 96.59 | even | 8 | |||
3072.2.a.b.1.2 | 2 | 96.53 | odd | 8 | |||
3072.2.a.h.1.1 | 2 | 96.5 | odd | 8 | |||
3072.2.a.h.1.2 | 2 | 96.11 | even | 8 | |||
3072.2.d.c.1537.1 | 4 | 96.29 | odd | 8 | |||
3072.2.d.c.1537.2 | 4 | 96.83 | even | 8 | |||
3072.2.d.c.1537.3 | 4 | 96.35 | even | 8 | |||
3072.2.d.c.1537.4 | 4 | 96.77 | odd | 8 | |||
4608.2.k.y.1153.1 | 4 | 8.5 | even | 2 | |||
4608.2.k.y.1153.2 | 4 | 8.3 | odd | 2 | |||
4608.2.k.y.3457.1 | 4 | 16.3 | odd | 4 | |||
4608.2.k.y.3457.2 | 4 | 16.13 | even | 4 | |||
4608.2.k.bb.1153.1 | 4 | 1.1 | even | 1 | trivial | ||
4608.2.k.bb.1153.2 | 4 | 4.3 | odd | 2 | inner | ||
4608.2.k.bb.3457.1 | 4 | 16.11 | odd | 4 | inner | ||
4608.2.k.bb.3457.2 | 4 | 16.5 | even | 4 | inner | ||
9216.2.a.h.1.1 | 2 | 32.21 | even | 8 | |||
9216.2.a.h.1.2 | 2 | 32.27 | odd | 8 | |||
9216.2.a.i.1.1 | 2 | 32.11 | odd | 8 | |||
9216.2.a.i.1.2 | 2 | 32.5 | even | 8 |