Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \( 2 \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.d.1537.3 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.82843i | 1.26491i | 0.774597 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.24264 | −1.60357 | −0.801784 | − | 0.597614i | \(-0.796115\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.00000i | − 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.24264i | − 1.17670i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||||
0.808608 | − | 0.588348i | \(-0.200222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.24264i | 0.925820i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.65685i | 1.05045i | 0.850963 | + | 0.525226i | \(0.176019\pi\) | ||||
−0.850963 | + | 0.525226i | \(0.823981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.24264 | −0.762001 | −0.381000 | − | 0.924575i | \(-0.624420\pi\) | ||||
−0.381000 | + | 0.924575i | \(0.624420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | −0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 12.0000i | − 2.02837i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24264i | 0.697486i | 0.937218 | + | 0.348743i | \(0.113391\pi\) | ||||
−0.937218 | + | 0.348743i | \(0.886609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000i | 0.914991i | 0.889212 | + | 0.457496i | \(0.151253\pi\) | ||||
−0.889212 | + | 0.457496i | \(0.848747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.82843i | − 0.421637i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000 | 1.57143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 6.00000i | − 0.840168i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.65685i | − 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3137 | 1.52554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.24264i | 0.543214i | 0.962408 | + | 0.271607i | \(0.0875552\pi\) | ||||
−0.962408 | + | 0.271607i | \(0.912445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264 | 0.534522 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843i | 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.82843 | −0.335673 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.0000 | −1.87266 | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000i | 0.346410i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.9706i | 1.93398i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24264 | −0.477334 | −0.238667 | − | 0.971101i | \(-0.576710\pi\) | ||||
−0.238667 | + | 0.971101i | \(0.576710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9706i | 1.84072i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.65685 | 0.606478 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.0000i | 1.88691i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.24264i | 0.439941i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.65685 | −0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | −0.406138 | −0.203069 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203069 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000i | 0.402015i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.3137i | 1.12576i | 0.826540 | + | 0.562878i | \(0.190306\pi\) | ||||
−0.826540 | + | 0.562878i | \(0.809694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3848 | 1.81151 | 0.905753 | − | 0.423806i | \(-0.139306\pi\) | ||||
0.905753 | + | 0.423806i | \(0.139306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.0000 | −1.17108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.89949i | 0.948200i | 0.880471 | + | 0.474100i | \(0.157226\pi\) | ||||
−0.880471 | + | 0.474100i | \(0.842774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.24264 | 0.402694 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 8.00000i | − 0.746004i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.24264i | 0.392232i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.4558 | −2.33353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 10.0000i | − 0.901670i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.24264 | −0.376473 | −0.188237 | − | 0.982124i | \(-0.560277\pi\) | ||||
−0.188237 | + | 0.982124i | \(0.560277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0000i | 1.74741i | 0.486458 | + | 0.873704i | \(0.338289\pi\) | ||||
−0.486458 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 8.48528i | − 0.735767i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.82843 | −0.243432 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0000 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843i | 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.9706 | −1.41915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.0000 | −1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 11.0000i | − 0.907265i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.48528i | − 0.695141i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) | ||||
0.937654 | − | 0.347571i | \(-0.112993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.41421 | 0.115087 | 0.0575435 | − | 0.998343i | \(-0.481673\pi\) | ||||
0.0575435 | + | 0.998343i | \(0.481673\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 12.0000i | − 0.963863i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.07107i | 0.564333i | 0.959366 | + | 0.282166i | \(0.0910530\pi\) | ||||
−0.959366 | + | 0.282166i | \(0.908947\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.65685 | −0.448618 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000i | 0.783260i | 0.920123 | + | 0.391630i | \(0.128089\pi\) | ||||
−0.920123 | + | 0.391630i | \(0.871911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 11.3137i | − 0.880771i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3137 | 0.875481 | 0.437741 | − | 0.899101i | \(-0.355779\pi\) | ||||
0.437741 | + | 0.899101i | \(0.355779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.00000i | − 0.152944i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.82843i | 0.215041i | 0.994203 | + | 0.107521i | \(0.0342912\pi\) | ||||
−0.994203 | + | 0.107521i | \(0.965709\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7279 | 0.962140 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41421i | 0.105118i | 0.998618 | + | 0.0525588i | \(0.0167377\pi\) | ||||
−0.998618 | + | 0.0525588i | \(0.983262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.24264 | 0.313625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.0000 | −0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 24.0000i | − 1.75505i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 4.24264i | − 0.308607i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274 | 1.63726 | 0.818631 | − | 0.574320i | \(-0.194733\pi\) | ||||
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | 1.29567 | 0.647834 | − | 0.761781i | \(-0.275675\pi\) | ||||
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 12.0000i | − 0.859338i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.65685i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645872\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.07107 | −0.501255 | −0.250627 | − | 0.968084i | \(-0.580637\pi\) | ||||
−0.250627 | + | 0.968084i | \(0.580637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 24.0000i | − 1.68447i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.2843i | 1.97546i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 12.0000i | − 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.82843i | 0.193801i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.9706 | −1.15738 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | 1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0000i | 1.08118i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 25.4558i | − 1.71235i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2132 | 1.42054 | 0.710271 | − | 0.703929i | \(-0.248573\pi\) | ||||
0.710271 | + | 0.703929i | \(0.248573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5563i | 1.02799i | 0.857792 | + | 0.513996i | \(0.171835\pi\) | ||||
−0.857792 | + | 0.513996i | \(0.828165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.9706 | 1.11658 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.00000i | − 0.521862i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.24264i | 0.275589i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 31.1127i | 1.98772i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.48528 | 0.539906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0000 | 1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.00000i | − 0.252478i | −0.992000 | − | 0.126239i | \(-0.959709\pi\) | ||||
0.992000 | − | 0.126239i | \(-0.0402906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137i | 0.711287i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.9706 | 1.06274 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0000 | −0.873296 | −0.436648 | − | 0.899632i | \(-0.643834\pi\) | ||||
−0.436648 | + | 0.899632i | \(0.643834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 18.0000i | − 1.11847i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 5.65685i | − 0.350150i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.6274 | −1.39527 | −0.697633 | − | 0.716455i | \(-0.745763\pi\) | ||||
−0.697633 | + | 0.716455i | \(0.745763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0000 | 0.982872 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0000i | 0.856786i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.41421 | −0.0859074 | −0.0429537 | − | 0.999077i | \(-0.513677\pi\) | ||||
−0.0429537 | + | 0.999077i | \(0.513677\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.0000 | 1.08941 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000i | 0.723627i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.41421i | − 0.0849719i | −0.999097 | − | 0.0424859i | \(-0.986472\pi\) | ||||
0.999097 | − | 0.0424859i | \(-0.0135278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.24264 | 0.254000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.00000i | − 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.65685i | 0.335083i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.4264 | −2.50435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000i | 0.234484i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.65685i | 0.330477i | 0.986254 | + | 0.165238i | \(0.0528394\pi\) | ||||
−0.986254 | + | 0.165238i | \(0.947161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000i | 0.693978i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 25.4558i | − 1.46725i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.3137 | 0.649956 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.00000i | − 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 18.3848i | − 1.04587i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.2843 | 1.60385 | 0.801927 | − | 0.597422i | \(-0.203808\pi\) | ||||
0.801927 | + | 0.597422i | \(0.203808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0000 | −1.46961 | −0.734803 | − | 0.678280i | \(-0.762726\pi\) | ||||
−0.734803 | + | 0.678280i | \(0.762726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.0000i | 0.676123i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9706i | 0.953162i | 0.879131 | + | 0.476581i | \(0.158124\pi\) | ||||
−0.879131 | + | 0.476581i | \(0.841876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.6274 | 1.26689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7279i | 0.706018i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.89949 | 0.547443 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.00000i | − 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4.24264i | − 0.232495i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | −0.430706 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 24.0000i | − 1.28839i | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||||
0.764862 | − | 0.644194i | \(-0.222807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 4.24264i | − 0.227103i | −0.993532 | − | 0.113552i | \(-0.963777\pi\) | ||||
0.993532 | − | 0.113552i | \(-0.0362227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.00000i | − 0.424596i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.4558i | 1.34727i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.82843 | −0.149279 | −0.0746393 | − | 0.997211i | \(-0.523781\pi\) | ||||
−0.0746393 | + | 0.997211i | \(0.523781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 45.2548i | − 2.36875i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3848 | 0.959678 | 0.479839 | − | 0.877357i | \(-0.340695\pi\) | ||||
0.479839 | + | 0.877357i | \(0.340695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000i | 1.24602i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 18.3848i | − 0.951928i | −0.879465 | − | 0.475964i | \(-0.842099\pi\) | ||||
0.879465 | − | 0.475964i | \(-0.157901\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.0000i | 1.95193i | 0.217930 | + | 0.975964i | \(0.430070\pi\) | ||||
−0.217930 | + | 0.975964i | \(0.569930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.24264i | 0.217357i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.0000 | −2.44631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6.00000i | − 0.304997i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.82843i | − 0.143407i | −0.997426 | − | 0.0717035i | \(-0.977156\pi\) | ||||
0.997426 | − | 0.0717035i | \(-0.0228435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9706 | −0.858238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.0000i | − 0.603786i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 32.5269i | − 1.63248i | −0.577714 | − | 0.816239i | \(-0.696055\pi\) | ||||
0.577714 | − | 0.816239i | \(-0.303945\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.48528 | −0.424795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000i | 0.896644i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.82843i | 0.140546i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9706 | 0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.0000 | 1.38451 | 0.692255 | − | 0.721653i | \(-0.256617\pi\) | ||||
0.692255 | + | 0.721653i | \(0.256617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0000i | 0.493264i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.2548 | −2.22147 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.0000i | 0.781651i | 0.920465 | + | 0.390826i | \(0.127810\pi\) | ||||
−0.920465 | + | 0.390826i | \(0.872190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 35.3553i | − 1.72311i | −0.507661 | − | 0.861557i | \(-0.669490\pi\) | ||||
0.507661 | − | 0.861557i | \(-0.330510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0000 | −0.873128 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 18.0000i | − 0.871081i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.9706i | 0.819346i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.7696 | −1.77113 | −0.885564 | − | 0.464518i | \(-0.846227\pi\) | ||||
−0.885564 | + | 0.464518i | \(0.846227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.00000 | 0.384455 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0000i | 0.767141i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.65685i | − 0.270604i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.41421 | −0.0674967 | −0.0337484 | − | 0.999430i | \(-0.510744\pi\) | ||||
−0.0337484 | + | 0.999430i | \(0.510744\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | −0.523810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000i | 1.14027i | 0.821549 | + | 0.570137i | \(0.193110\pi\) | ||||
−0.821549 | + | 0.570137i | \(0.806890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 39.5980i | − 1.87712i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.48528 | −0.401340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 40.0000i | − 1.88353i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.41421i | − 0.0664455i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50.9117 | −2.38678 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0000 | −0.561336 | −0.280668 | − | 0.959805i | \(-0.590556\pi\) | ||||
−0.280668 | + | 0.959805i | \(0.590556\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.00000i | 0.280056i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.48528i | − 0.395199i | −0.980283 | − | 0.197599i | \(-0.936685\pi\) | ||||
0.980283 | − | 0.197599i | \(-0.0633145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7279 | 0.591517 | 0.295758 | − | 0.955263i | \(-0.404428\pi\) | ||||
0.295758 | + | 0.955263i | \(0.404428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.0000 | −0.556487 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 24.0000i | − 1.11059i | −0.831654 | − | 0.555294i | \(-0.812606\pi\) | ||||
0.831654 | − | 0.555294i | \(-0.187394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 16.9706i | − 0.783628i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.07107 | 0.325818 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0000 | 1.10352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6.00000i | − 0.275299i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.65685i | 0.259010i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4558 | −1.16311 | −0.581554 | − | 0.813508i | \(-0.697555\pi\) | ||||
−0.581554 | + | 0.813508i | \(0.697555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 12.0000i | − 0.546019i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 11.3137i | − 0.513729i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.8406 | 1.98661 | 0.993304 | − | 0.115529i | \(-0.0368564\pi\) | ||||
0.993304 | + | 0.115529i | \(0.0368564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0000 | 0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8.00000i | − 0.361035i | −0.983572 | − | 0.180517i | \(-0.942223\pi\) | ||||
0.983572 | − | 0.180517i | \(-0.0577772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.9411i | 1.52863i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.3137 | −0.508513 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 11.3137i | − 0.505459i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1421 | 0.630567 | 0.315283 | − | 0.948998i | \(-0.397900\pi\) | ||||
0.315283 | + | 0.948998i | \(0.397900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | −1.42398 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000i | 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6274i | 1.00294i | 0.865174 | + | 0.501471i | \(0.167208\pi\) | ||||
−0.865174 | + | 0.501471i | \(0.832792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 67.8823 | 3.00293 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 52.0000i | 2.29139i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137i | 0.497576i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82843 | 0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0000i | 0.961993i | 0.876723 | + | 0.480996i | \(0.159725\pi\) | ||||
−0.876723 | + | 0.480996i | \(0.840275\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 12.7279i | − 0.555492i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.4558 | −1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 42.4264i | − 1.83769i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3137 | 0.489134 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 44.0000i | − 1.89521i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.0122i | 1.76325i | 0.471949 | + | 0.881626i | \(0.343551\pi\) | ||||
−0.471949 | + | 0.881626i | \(0.656449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41421 | 0.0606897 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.0000 | −1.19939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 34.0000i | − 1.45374i | −0.686778 | − | 0.726868i | \(-0.740975\pi\) | ||||
0.686778 | − | 0.726868i | \(-0.259025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 4.24264i | − 0.181071i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3137 | −0.481980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | 0.765438 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.0000i | 0.509372i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.7990i | 0.838910i | 0.907776 | + | 0.419455i | \(0.137779\pi\) | ||||
−0.907776 | + | 0.419455i | \(0.862221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.4558 | 1.07667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.00000i | − 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 16.9706i | − 0.713957i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.24264 | −0.178174 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000i | 0.836974i | 0.908223 | + | 0.418487i | \(0.137439\pi\) | ||||
−0.908223 | + | 0.418487i | \(0.862561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 22.6274i | − 0.945274i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.00000 | 0.166522 | 0.0832611 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832611 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 18.0000i | − 0.748054i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 67.8823i | − 2.81623i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6274 | −0.937132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.0000 | −0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0000i | 0.990586i | 0.868726 | + | 0.495293i | \(0.164939\pi\) | ||||
−0.868726 | + | 0.495293i | \(0.835061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8.48528i | − 0.349630i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.65685 | 0.232692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 72.0000i | − 2.95171i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.07107i | 0.289400i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.0833 | −1.96463 | −0.982314 | − | 0.187239i | \(-0.940046\pi\) | ||||
−0.982314 | + | 0.187239i | \(0.940046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.00000i | − 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 14.1421i | − 0.574960i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.24264 | −0.172203 | −0.0861017 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861017 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | −0.972529 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 18.3848i | − 0.742554i | −0.928522 | − | 0.371277i | \(-0.878920\pi\) | ||||
0.928522 | − | 0.371277i | \(-0.121080\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.2843 | 1.14053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0000 | −0.885687 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0000i | 1.44696i | 0.690344 | + | 0.723481i | \(0.257459\pi\) | ||||
−0.690344 | + | 0.723481i | \(0.742541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.82843i | − 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 59.3970 | 2.37969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.00000i | − 0.319489i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.4558i | 1.01499i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3553 | −1.40747 | −0.703737 | − | 0.710461i | \(-0.748487\pi\) | ||||
−0.703737 | + | 0.710461i | \(0.748487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 12.0000i | − 0.476205i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 46.6690i | − 1.84909i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.82843 | 0.111891 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.9706i | 0.668215i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.1421 | −0.555985 | −0.277992 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277992 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 18.0000i | − 0.705476i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.48528i | 0.332055i | 0.986121 | + | 0.166027i | \(0.0530940\pi\) | ||||
−0.986121 | + | 0.166027i | \(0.946906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.5685 | −2.21032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0000 | 0.624219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7279i | 0.495059i | 0.968880 | + | 0.247529i | \(0.0796187\pi\) | ||||
−0.968880 | + | 0.247529i | \(0.920381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.4558 | −0.988623 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16.0000i | − 0.619522i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 21.2132i | − 0.820150i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9706 | 0.655141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.00000i | − 0.115470i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 36.7696i | − 1.41317i | −0.707629 | − | 0.706584i | \(-0.750235\pi\) | ||||
0.707629 | − | 0.706584i | \(-0.249765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.9706 | 0.651270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 24.0000i | − 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 28.2843i | − 1.08069i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.5563 | 0.593512 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.0000i | − 0.836919i | −0.908235 | − | 0.418460i | \(-0.862570\pi\) | ||||
0.908235 | − | 0.418460i | \(-0.137430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 16.9706i | − 0.644658i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.9411 | −1.28746 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 60.0000 | 2.27266 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0000i | 0.680823i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.65685i | − 0.213656i | −0.994277 | − | 0.106828i | \(-0.965931\pi\) | ||||
0.994277 | − | 0.106828i | \(-0.0340695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.48528 | −0.320028 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 48.0000i | − 1.80523i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.3848i | 0.690455i | 0.938519 | + | 0.345227i | \(0.112198\pi\) | ||||
−0.938519 | + | 0.345227i | \(0.887802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.24264 | 0.159111 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 48.0000i | − 1.79510i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11.3137i | − 0.422518i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.48528 | 0.316448 | 0.158224 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158224 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −78.0000 | −2.90487 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 18.0000i | − 0.669427i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 16.9706i | − 0.630271i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8701 | 0.996555 | 0.498278 | − | 0.867018i | \(-0.333966\pi\) | ||||
0.498278 | + | 0.867018i | \(0.333966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.0000i | 1.33151i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 35.3553i | − 1.30588i | −0.757410 | − | 0.652940i | \(-0.773536\pi\) | ||||
0.757410 | − | 0.652940i | \(-0.226464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.1127 | 1.14761 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000 | 0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.0000i | 1.32428i | 0.749380 | + | 0.662141i | \(0.230352\pi\) | ||||
−0.749380 | + | 0.662141i | \(0.769648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 8.48528i | − 0.311715i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6274 | 0.830119 | 0.415060 | − | 0.909794i | \(-0.363761\pi\) | ||||
0.415060 | + | 0.909794i | \(0.363761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.0000 | 0.879292 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 16.0000i | − 0.585409i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706i | 0.620091i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7279 | −0.464448 | −0.232224 | − | 0.972662i | \(-0.574600\pi\) | ||||
−0.232224 | + | 0.972662i | \(0.574600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.00000i | 0.145575i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 38.1838i | − 1.38781i | −0.720065 | − | 0.693906i | \(-0.755888\pi\) | ||||
0.720065 | − | 0.693906i | \(-0.244112\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3137 | 0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0000 | 1.23250 | 0.616250 | − | 0.787551i | \(-0.288651\pi\) | ||||
0.616250 | + | 0.787551i | \(0.288651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 42.0000i | − 1.52050i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 16.9706i | − 0.613572i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 14.0000i | 0.504198i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.65685i | − 0.203463i | −0.994812 | − | 0.101731i | \(-0.967562\pi\) | ||||
0.994812 | − | 0.101731i | \(-0.0324382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.7279 | 0.457200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.0000 | −0.645746 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.0000i | 0.716574i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3137i | 0.404836i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.65685 | −0.202159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0000i | 1.35455i | 0.735728 | + | 0.677277i | \(0.236840\pi\) | ||||
−0.735728 | + | 0.677277i | \(0.763160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6274i | 0.805557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.4558 | 0.905106 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 16.0000i | − 0.567462i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 31.1127i | − 1.10207i | −0.834483 | − | 0.551034i | \(-0.814233\pi\) | ||||
0.834483 | − | 0.551034i | \(-0.185767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9706 | −0.600375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0000 | 0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 64.0000i | 2.25851i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.9411i | 1.19627i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000i | 0.0702295i | 0.999383 | + | 0.0351147i | \(0.0111797\pi\) | ||||
−0.999383 | + | 0.0351147i | \(0.988820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.41421i | 0.0495986i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.2843 | −0.990755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | −0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 18.0000i | − 0.628971i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.2843i | 0.987128i | 0.869710 | + | 0.493564i | \(0.164306\pi\) | ||||
−0.869710 | + | 0.493564i | \(0.835694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.24264 | 0.147889 | 0.0739446 | − | 0.997262i | \(-0.476441\pi\) | ||||
0.0739446 | + | 0.997262i | \(0.476441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 36.0000i | − 1.25184i | −0.779886 | − | 0.625921i | \(-0.784723\pi\) | ||||
0.779886 | − | 0.625921i | \(-0.215277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2132i | 0.736765i | 0.929674 | + | 0.368383i | \(0.120088\pi\) | ||||
−0.929674 | + | 0.368383i | \(0.879912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | −0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 66.0000 | 2.28676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000i | 1.10741i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.24264i | − 0.146647i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1127 | −1.07413 | −0.537065 | − | 0.843541i | \(-0.680467\pi\) | ||||
−0.537065 | + | 0.843541i | \(0.680467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.00000i | 0.206651i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 14.1421i | − 0.486504i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.2132 | 0.728894 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 12.0000i | − 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2132i | 0.726326i | 0.931726 | + | 0.363163i | \(0.118303\pi\) | ||||
−0.931726 | + | 0.363163i | \(0.881697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.65685 | 0.193460 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000i | 0.341196i | 0.985341 | + | 0.170598i | \(0.0545699\pi\) | ||||
−0.985341 | + | 0.170598i | \(0.945430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.4264i | 1.44589i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2843 | −0.962808 | −0.481404 | − | 0.876499i | \(-0.659873\pi\) | ||||
−0.481404 | + | 0.876499i | \(0.659873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | −0.272008 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 19.0000i | − 0.645274i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.9706i | 0.575687i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9706 | 0.575026 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.00000 | 0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 24.0000i | − 0.811348i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5563i | 0.525301i | 0.964891 | + | 0.262650i | \(0.0845966\pi\) | ||||
−0.964891 | + | 0.262650i | \(0.915403\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.65685 | 0.190801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.0000 | 1.95407 | 0.977035 | − | 0.213080i | \(-0.0683494\pi\) | ||||
0.977035 | + | 0.213080i | \(0.0683494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0000i | 1.14419i | 0.820187 | + | 0.572096i | \(0.193869\pi\) | ||||
−0.820187 | + | 0.572096i | \(0.806131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.9706 | −0.569816 | −0.284908 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284908 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.00000i | − 0.134005i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.65685i | − 0.189299i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 24.0000i | − 0.800445i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 33.9411i | − 1.13074i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.4558 | −0.847117 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.00000 | −0.132964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.0000i | 1.92586i | 0.269754 | + | 0.962929i | \(0.413058\pi\) | ||||
−0.269754 | + | 0.962929i | \(0.586942\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 11.3137i | − 0.375252i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6274 | −0.749680 | −0.374840 | − | 0.927090i | \(-0.622302\pi\) | ||||
−0.374840 | + | 0.927090i | \(0.622302\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64.0000 | 2.11809 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000i | 0.396708i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 84.8528i | − 2.80209i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.3848 | −0.606458 | −0.303229 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303229 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | −0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000i | 0.394985i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 12.7279i | − 0.418491i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.3848 | −0.603835 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.0000 | −1.50921 | −0.754606 | − | 0.656179i | \(-0.772172\pi\) | ||||
−0.754606 | + | 0.656179i | \(0.772172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0000i | 0.721021i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 28.2843i | − 0.925985i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.8823 | 2.21999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0000i | 0.848478i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 36.7696i | − 1.19865i | −0.800505 | − | 0.599327i | \(-0.795435\pi\) | ||||
0.800505 | − | 0.599327i | \(-0.204565\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.2843 | −0.921063 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.0000 | 0.390360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.8823i | 2.20355i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.9706 | 0.550308 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 64.0000i | 2.07099i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 22.6274i | − 0.731441i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.4264 | 1.37002 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.0000 | −0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.9117i | 1.63891i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.3553 | 1.13695 | 0.568476 | − | 0.822700i | \(-0.307533\pi\) | ||||
0.568476 | + | 0.822700i | \(0.307533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0000 | 0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 32.0000i | − 1.02693i | −0.858111 | − | 0.513464i | \(-0.828362\pi\) | ||||
0.858111 | − | 0.513464i | \(-0.171638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 50.9117i | − 1.63215i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.7279 | 0.407620 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.00000 | 0.0639857 | 0.0319928 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319928 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.0000i | 1.78977i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 9.89949i | − 0.316067i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.6274 | −0.721703 | −0.360851 | − | 0.932623i | \(-0.617514\pi\) | ||||
−0.360851 | + | 0.932623i | \(0.617514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 12.0000i | − 0.381964i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 16.9706i | − 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.6690 | −1.48249 | −0.741246 | − | 0.671234i | \(-0.765765\pi\) | ||||
−0.741246 | + | 0.671234i | \(0.765765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 20.0000i | − 0.634043i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 46.6690i | − 1.47802i | −0.673693 | − | 0.739012i | \(-0.735293\pi\) | ||||
0.673693 | − | 0.739012i | \(-0.264707\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.24264 | −0.134231 |
(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 | 3072.2.d.d.1537.2 | 4 | ||
4.3 | odd | 2 | inner | 3072.2.d.d.1537.4 | 4 | ||
8.3 | odd | 2 | inner | 3072.2.d.d.1537.1 | 4 | ||
8.5 | even | 2 | inner | 3072.2.d.d.1537.3 | 4 | ||
16.3 | odd | 4 | 3072.2.a.d.1.2 | 2 | |||
16.5 | even | 4 | 3072.2.a.d.1.1 | 2 | |||
16.11 | odd | 4 | 3072.2.a.f.1.1 | 2 | |||
16.13 | even | 4 | 3072.2.a.f.1.2 | 2 | |||
32.3 | odd | 8 | 768.2.j.a.193.1 | ✓ | 4 | ||
32.5 | even | 8 | 768.2.j.a.577.2 | yes | 4 | ||
32.11 | odd | 8 | 768.2.j.d.577.2 | yes | 4 | ||
32.13 | even | 8 | 768.2.j.d.193.1 | yes | 4 | ||
32.19 | odd | 8 | 768.2.j.d.193.2 | yes | 4 | ||
32.21 | even | 8 | 768.2.j.d.577.1 | yes | 4 | ||
32.27 | odd | 8 | 768.2.j.a.577.1 | yes | 4 | ||
32.29 | even | 8 | 768.2.j.a.193.2 | yes | 4 | ||
48.5 | odd | 4 | 9216.2.a.e.1.2 | 2 | |||
48.11 | even | 4 | 9216.2.a.q.1.2 | 2 | |||
48.29 | odd | 4 | 9216.2.a.q.1.1 | 2 | |||
48.35 | even | 4 | 9216.2.a.e.1.1 | 2 | |||
96.5 | odd | 8 | 2304.2.k.d.577.1 | 4 | |||
96.11 | even | 8 | 2304.2.k.a.577.2 | 4 | |||
96.29 | odd | 8 | 2304.2.k.d.1729.2 | 4 | |||
96.35 | even | 8 | 2304.2.k.d.1729.1 | 4 | |||
96.53 | odd | 8 | 2304.2.k.a.577.1 | 4 | |||
96.59 | even | 8 | 2304.2.k.d.577.2 | 4 | |||
96.77 | odd | 8 | 2304.2.k.a.1729.2 | 4 | |||
96.83 | even | 8 | 2304.2.k.a.1729.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.a.193.1 | ✓ | 4 | 32.3 | odd | 8 | ||
768.2.j.a.193.2 | yes | 4 | 32.29 | even | 8 | ||
768.2.j.a.577.1 | yes | 4 | 32.27 | odd | 8 | ||
768.2.j.a.577.2 | yes | 4 | 32.5 | even | 8 | ||
768.2.j.d.193.1 | yes | 4 | 32.13 | even | 8 | ||
768.2.j.d.193.2 | yes | 4 | 32.19 | odd | 8 | ||
768.2.j.d.577.1 | yes | 4 | 32.21 | even | 8 | ||
768.2.j.d.577.2 | yes | 4 | 32.11 | odd | 8 | ||
2304.2.k.a.577.1 | 4 | 96.53 | odd | 8 | |||
2304.2.k.a.577.2 | 4 | 96.11 | even | 8 | |||
2304.2.k.a.1729.1 | 4 | 96.83 | even | 8 | |||
2304.2.k.a.1729.2 | 4 | 96.77 | odd | 8 | |||
2304.2.k.d.577.1 | 4 | 96.5 | odd | 8 | |||
2304.2.k.d.577.2 | 4 | 96.59 | even | 8 | |||
2304.2.k.d.1729.1 | 4 | 96.35 | even | 8 | |||
2304.2.k.d.1729.2 | 4 | 96.29 | odd | 8 | |||
3072.2.a.d.1.1 | 2 | 16.5 | even | 4 | |||
3072.2.a.d.1.2 | 2 | 16.3 | odd | 4 | |||
3072.2.a.f.1.1 | 2 | 16.11 | odd | 4 | |||
3072.2.a.f.1.2 | 2 | 16.13 | even | 4 | |||
3072.2.d.d.1537.1 | 4 | 8.3 | odd | 2 | inner | ||
3072.2.d.d.1537.2 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.d.d.1537.3 | 4 | 8.5 | even | 2 | inner | ||
3072.2.d.d.1537.4 | 4 | 4.3 | odd | 2 | inner | ||
9216.2.a.e.1.1 | 2 | 48.35 | even | 4 | |||
9216.2.a.e.1.2 | 2 | 48.5 | odd | 4 | |||
9216.2.a.q.1.1 | 2 | 48.29 | odd | 4 | |||
9216.2.a.q.1.2 | 2 | 48.11 | even | 4 |