Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(257,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.e (of order \(4\), degree \(2\), 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: | \(8.17668116698\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.257 |
Dual form | 1024.2.e.h.769.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.00000i | −0.577350 | − | 0.577350i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 1.41421i | −0.632456 | + | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) |
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 3.00000i | 0.904534 | − | 0.904534i | −0.0912903 | − | 0.995824i | \(-0.529099\pi\) |
0.995824 | + | 0.0912903i | \(0.0290991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | − | 4.24264i | −1.17670 | − | 1.17670i | −0.980581 | − | 0.196116i | \(-0.937167\pi\) |
−0.196116 | − | 0.980581i | \(-0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 3.00000i | 0.688247 | + | 0.688247i | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | − | 2.82843i | 0.617213 | − | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528i | 1.76930i | 0.466252 | + | 0.884652i | \(0.345604\pi\) | ||||
−0.466252 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421 | + | 1.41421i | 0.262613 | + | 0.262613i | 0.826115 | − | 0.563502i | \(-0.190546\pi\) |
−0.563502 | + | 0.826115i | \(0.690546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | − | 4.00000i | −0.676123 | − | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.24264 | + | 4.24264i | −0.697486 | + | 0.697486i | −0.963868 | − | 0.266382i | \(-0.914172\pi\) |
0.266382 | + | 0.963868i | \(0.414172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.48528i | 1.35873i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | + | 1.41421i | 0.210819 | + | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.41421 | + | 1.41421i | −0.194257 | + | 0.194257i | −0.797533 | − | 0.603276i | \(-0.793862\pi\) |
0.603276 | + | 0.797533i | \(0.293862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.48528i | 1.14416i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | + | 1.00000i | −0.130189 | + | 0.130189i | −0.769199 | − | 0.639010i | \(-0.779344\pi\) |
0.639010 | + | 0.769199i | \(0.279344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.24264 | + | 4.24264i | 0.543214 | + | 0.543214i | 0.924470 | − | 0.381255i | \(-0.124508\pi\) |
−0.381255 | + | 0.924470i | \(0.624508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00000 | + | 9.00000i | 1.09952 | + | 1.09952i | 0.994466 | + | 0.105059i | \(0.0335031\pi\) |
0.105059 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.48528 | − | 8.48528i | 1.02151 | − | 1.02151i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528i | 1.00702i | 0.863990 | + | 0.503509i | \(0.167958\pi\) | ||||
−0.863990 | + | 0.503509i | \(0.832042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.0000i | − | 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | − | 1.00000i | 0.115470 | − | 0.115470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.48528 | + | 8.48528i | 0.966988 | + | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.65685 | 0.636446 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00000 | − | 3.00000i | −0.329293 | − | 0.329293i | 0.523025 | − | 0.852318i | \(-0.324804\pi\) |
−0.852318 | + | 0.523025i | \(0.824804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.82843i | − | 0.303239i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | − | 12.0000i | 1.25794 | − | 1.25794i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.65685 | − | 5.65685i | −0.586588 | − | 0.586588i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.48528 | −0.870572 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.00000 | − | 3.00000i | −0.301511 | − | 0.301511i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.07107 | − | 7.07107i | 0.703598 | − | 0.703598i | −0.261583 | − | 0.965181i | \(-0.584245\pi\) |
0.965181 | + | 0.261583i | \(0.0842446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.82843i | − | 0.278693i | −0.990244 | − | 0.139347i | \(-0.955500\pi\) | ||
0.990244 | − | 0.139347i | \(-0.0445002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000i | 0.780720i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.00000 | + | 5.00000i | −0.483368 | + | 0.483368i | −0.906206 | − | 0.422837i | \(-0.861034\pi\) |
0.422837 | + | 0.906206i | \(0.361034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.24264 | + | 4.24264i | 0.406371 | + | 0.406371i | 0.880471 | − | 0.474100i | \(-0.157226\pi\) |
−0.474100 | + | 0.880471i | \(0.657226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.48528 | 0.805387 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0000 | − | 12.0000i | −1.11901 | − | 1.11901i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24264 | + | 4.24264i | −0.392232 | + | 0.392232i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7.00000i | − | 0.636364i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | − | 6.00000i | 0.541002 | − | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.48528 | − | 8.48528i | −0.758947 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | + | 1.00000i | 0.0873704 | + | 0.0873704i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48528 | + | 8.48528i | −0.735767 | + | 0.735767i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 11.3137i | − | 0.973729i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | + | 3.00000i | −0.254457 | + | 0.254457i | −0.822795 | − | 0.568338i | \(-0.807586\pi\) |
0.568338 | + | 0.822795i | \(0.307586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.4558 | −2.12872 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | −0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | + | 1.00000i | 0.0824786 | + | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5563 | + | 15.5563i | −1.27443 | + | 1.27443i | −0.330684 | + | 0.943741i | \(0.607280\pi\) |
−0.943741 | + | 0.330684i | \(0.892720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.1421i | − | 1.15087i | −0.817847 | − | 0.575435i | \(-0.804833\pi\) | ||
0.817847 | − | 0.575435i | \(-0.195167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | + | 8.00000i | −0.642575 | + | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.24264 | + | 4.24264i | 0.338600 | + | 0.338600i | 0.855840 | − | 0.517241i | \(-0.173041\pi\) |
−0.517241 | + | 0.855840i | \(0.673041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82843 | 0.224309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.0000 | + | 15.0000i | 1.17489 | + | 1.17489i | 0.981029 | + | 0.193862i | \(0.0621013\pi\) |
0.193862 | + | 0.981029i | \(0.437899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.48528 | − | 8.48528i | 0.660578 | − | 0.660578i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.48528i | − | 0.656611i | −0.944572 | − | 0.328305i | \(-0.893522\pi\) | ||
0.944572 | − | 0.328305i | \(-0.106478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000i | 1.76923i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | − | 3.00000i | 0.229416 | − | 0.229416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.89949 | − | 9.89949i | −0.752645 | − | 0.752645i | 0.222327 | − | 0.974972i | \(-0.428635\pi\) |
−0.974972 | + | 0.222327i | \(0.928635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82843 | −0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | 0.150329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0000 | + | 13.0000i | 0.971666 | + | 0.971666i | 0.999609 | − | 0.0279439i | \(-0.00889597\pi\) |
−0.0279439 | + | 0.999609i | \(0.508896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.7279 | − | 12.7279i | 0.946059 | − | 0.946059i | −0.0525588 | − | 0.998618i | \(-0.516738\pi\) |
0.998618 | + | 0.0525588i | \(0.0167377\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.48528i | − | 0.627250i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 12.0000i | − | 0.882258i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.3137 | − | 11.3137i | −0.822951 | − | 0.822951i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.0000 | 1.72756 | 0.863779 | − | 0.503871i | \(-0.168091\pi\) | ||||
0.863779 | + | 0.503871i | \(0.168091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | − | 12.0000i | −0.859338 | − | 0.859338i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.07107 | + | 7.07107i | −0.503793 | + | 0.503793i | −0.912614 | − | 0.408822i | \(-0.865940\pi\) |
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.7990i | − | 1.40351i | −0.712417 | − | 0.701757i | \(-0.752399\pi\) | ||
0.712417 | − | 0.701757i | \(-0.247601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 18.0000i | − | 1.26962i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00000 | + | 4.00000i | −0.280745 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.48528 | − | 8.48528i | −0.592638 | − | 0.592638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.48528 | 0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.0000 | 1.24509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | − | 3.00000i | −0.206529 | − | 0.206529i | 0.596262 | − | 0.802790i | \(-0.296652\pi\) |
−0.802790 | + | 0.596262i | \(0.796652\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.48528 | − | 8.48528i | 0.581402 | − | 0.581402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.48528i | − | 0.578691i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | + | 12.0000i | −0.810885 | + | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.65685 | −0.378811 | −0.189405 | − | 0.981899i | \(-0.560656\pi\) | ||||
−0.189405 | + | 0.981899i | \(0.560656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00000 | − | 9.00000i | −0.597351 | − | 0.597351i | 0.342256 | − | 0.939607i | \(-0.388809\pi\) |
−0.939607 | + | 0.342256i | \(0.888809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7279 | + | 12.7279i | −0.841085 | + | 0.841085i | −0.989000 | − | 0.147915i | \(-0.952744\pi\) |
0.147915 | + | 0.989000i | \(0.452744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16.9706i | − | 1.11658i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 12.0000i | − | 0.786146i | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||
0.919507 | − | 0.393073i | \(-0.128588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65685 | − | 5.65685i | −0.367452 | − | 0.367452i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9706 | −1.09773 | −0.548867 | − | 0.835910i | \(-0.684941\pi\) | ||||
−0.548867 | + | 0.835910i | \(0.684941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421 | − | 1.41421i | 0.0903508 | − | 0.0903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 25.4558i | − | 1.61972i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000i | 0.380235i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.00000 | + | 9.00000i | −0.568075 | + | 0.568075i | −0.931589 | − | 0.363514i | \(-0.881577\pi\) |
0.363514 | + | 0.931589i | \(0.381577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.4558 | + | 25.4558i | 1.60040 | + | 1.60040i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0000 | − | 12.0000i | −0.745644 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.41421 | − | 1.41421i | 0.0875376 | − | 0.0875376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.48528i | 0.523225i | 0.965173 | + | 0.261612i | \(0.0842542\pi\) | ||||
−0.965173 | + | 0.261612i | \(0.915746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.00000i | − | 0.245718i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000 | − | 12.0000i | 0.734388 | − | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.89949 | + | 9.89949i | 0.603583 | + | 0.603583i | 0.941261 | − | 0.337679i | \(-0.109642\pi\) |
−0.337679 | + | 0.941261i | \(0.609642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.6274 | 1.37452 | 0.687259 | − | 0.726413i | \(-0.258814\pi\) | ||||
0.687259 | + | 0.726413i | \(0.258814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.0000 | −1.45255 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 3.00000i | 0.180907 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24264 | − | 4.24264i | 0.254916 | − | 0.254916i | −0.568067 | − | 0.822982i | \(-0.692309\pi\) |
0.822982 | + | 0.568067i | \(0.192309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.65685i | − | 0.338667i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.0000i | − | 0.715860i | −0.933748 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00000 | − | 9.00000i | 0.534994 | − | 0.534994i | −0.387060 | − | 0.922055i | \(-0.626509\pi\) |
0.922055 | + | 0.387060i | \(0.126509\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.48528 | + | 8.48528i | 0.502625 | + | 0.502625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.9706 | −1.00174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.00000 | + | 8.00000i | 0.468968 | + | 0.468968i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.07107 | + | 7.07107i | −0.413096 | + | 0.413096i | −0.882816 | − | 0.469720i | \(-0.844355\pi\) |
0.469720 | + | 0.882816i | \(0.344355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.82843i | − | 0.164677i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.0000i | 1.39262i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.0000 | − | 36.0000i | 2.08193 | − | 2.08193i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.48528 | − | 8.48528i | −0.489083 | − | 0.489083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.1421 | −0.812444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.00000 | + | 3.00000i | 0.171219 | + | 0.171219i | 0.787515 | − | 0.616296i | \(-0.211367\pi\) |
−0.616296 | + | 0.787515i | \(0.711367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82843 | + | 2.82843i | −0.160904 | + | 0.160904i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.48528i | − | 0.481156i | −0.970630 | − | 0.240578i | \(-0.922663\pi\) | ||
0.970630 | − | 0.240578i | \(-0.0773370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.00000i | − | 0.339140i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||
0.985518 | − | 0.169570i | \(-0.0542379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | + | 4.00000i | −0.225374 | + | 0.225374i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.07107 | + | 7.07107i | 0.397151 | + | 0.397151i | 0.877227 | − | 0.480076i | \(-0.159391\pi\) |
−0.480076 | + | 0.877227i | \(0.659391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.48528 | 0.475085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0000 | 0.558146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.24264 | − | 4.24264i | 0.235339 | − | 0.235339i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.48528i | − | 0.469237i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.0000 | + | 21.0000i | −1.15426 | + | 1.15426i | −0.168576 | + | 0.985689i | \(0.553917\pi\) |
−0.985689 | + | 0.168576i | \(0.946083\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.24264 | + | 4.24264i | 0.232495 | + | 0.232495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.4558 | −1.39080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | + | 6.00000i | 0.325875 | + | 0.325875i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706 | − | 16.9706i | 0.919007 | − | 0.919007i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.0000i | 1.29212i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0000 | − | 15.0000i | 0.805242 | − | 0.805242i | −0.178667 | − | 0.983910i | \(-0.557179\pi\) |
0.983910 | + | 0.178667i | \(0.0571786\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.24264 | − | 4.24264i | −0.227103 | − | 0.227103i | 0.584378 | − | 0.811481i | \(-0.301338\pi\) |
−0.811481 | + | 0.584378i | \(0.801338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.9411 | 1.81164 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | − | 12.0000i | −0.636894 | − | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.48528i | 0.447836i | 0.974608 | + | 0.223918i | \(0.0718848\pi\) | ||||
−0.974608 | + | 0.223918i | \(0.928115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | + | 7.00000i | −0.367405 | + | 0.367405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9706 | + | 16.9706i | 0.888280 | + | 0.888280i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3137 | 0.590571 | 0.295285 | − | 0.955409i | \(-0.404585\pi\) | ||||
0.295285 | + | 0.955409i | \(0.404585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | − | 4.00000i | −0.207670 | − | 0.207670i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24264 | − | 4.24264i | 0.219676 | − | 0.219676i | −0.588686 | − | 0.808362i | \(-0.700355\pi\) |
0.808362 | + | 0.588686i | \(0.200355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.9706i | 0.876356i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.00000 | + | 9.00000i | −0.462299 | + | 0.462299i | −0.899408 | − | 0.437109i | \(-0.856002\pi\) |
0.437109 | + | 0.899408i | \(0.356002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.65685 | − | 5.65685i | −0.289809 | − | 0.289809i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.9411 | −1.73431 | −0.867155 | − | 0.498038i | \(-0.834054\pi\) | ||||
−0.867155 | + | 0.498038i | \(0.834054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | −1.22315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.00000 | + | 3.00000i | 0.152499 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3848 | − | 18.3848i | 0.932145 | − | 0.932145i | −0.0656946 | − | 0.997840i | \(-0.520926\pi\) |
0.997840 | + | 0.0656946i | \(0.0209263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.00000i | − | 0.100887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | + | 8.00000i | −0.402524 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7279 | − | 12.7279i | −0.638796 | − | 0.638796i | 0.311462 | − | 0.950258i | \(-0.399181\pi\) |
−0.950258 | + | 0.311462i | \(0.899181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.9706 | 0.849591 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0000 | − | 24.0000i | −1.19553 | − | 1.19553i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.07107 | + | 7.07107i | −0.351364 | + | 0.351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4558i | 1.26180i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.0000i | − | 1.08783i | −0.839140 | − | 0.543915i | \(-0.816941\pi\) | ||
0.839140 | − | 0.543915i | \(-0.183059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 6.00000i | −0.295958 | + | 0.295958i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.82843 | − | 2.82843i | −0.139178 | − | 0.139178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.48528 | 0.416526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.00000 | + | 9.00000i | 0.439679 | + | 0.439679i | 0.891904 | − | 0.452225i | \(-0.149370\pi\) |
−0.452225 | + | 0.891904i | \(0.649370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.24264 | − | 4.24264i | 0.206774 | − | 0.206774i | −0.596121 | − | 0.802895i | \(-0.703292\pi\) |
0.802895 | + | 0.596121i | \(0.203292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0000 | + | 12.0000i | −0.580721 | + | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.4558 | + | 25.4558i | 1.22902 | + | 1.22902i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9706 | 0.817443 | 0.408722 | − | 0.912659i | \(-0.365975\pi\) | ||||
0.408722 | + | 0.912659i | \(0.365975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00000 | + | 4.00000i | 0.191785 | + | 0.191785i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.4558 | + | 25.4558i | −1.21772 | + | 1.21772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.82843i | 0.134993i | 0.997719 | + | 0.0674967i | \(0.0215012\pi\) | ||||
−0.997719 | + | 0.0674967i | \(0.978499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000i | 0.0476190i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.00000 | − | 9.00000i | 0.427603 | − | 0.427603i | −0.460208 | − | 0.887811i | \(-0.652225\pi\) |
0.887811 | + | 0.460208i | \(0.152225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9706 | − | 16.9706i | −0.804482 | − | 0.804482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.1127 | 1.47158 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0000 | + | 18.0000i | 0.847587 | + | 0.847587i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1421 | + | 14.1421i | −0.664455 | + | 0.664455i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.9411i | 1.59118i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.0000i | − | 0.467780i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) | ||
0.972263 | − | 0.233890i | \(-0.0751456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.3848 | − | 18.3848i | −0.856264 | − | 0.856264i | 0.134631 | − | 0.990896i | \(-0.457015\pi\) |
−0.990896 | + | 0.134631i | \(0.957015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.65685 | −0.262896 | −0.131448 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131448 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.0000 | 0.741982 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | + | 3.00000i | 0.138823 | + | 0.138823i | 0.773103 | − | 0.634280i | \(-0.218703\pi\) |
−0.634280 | + | 0.773103i | \(0.718703\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.4558 | + | 25.4558i | −1.17544 | + | 1.17544i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.48528i | − | 0.390981i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.0000i | 0.827641i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.00000 | + | 3.00000i | −0.137649 | + | 0.137649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.41421 | + | 1.41421i | 0.0647524 | + | 0.0647524i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9706 | −0.775405 | −0.387702 | − | 0.921785i | \(-0.626731\pi\) | ||||
−0.387702 | + | 0.921785i | \(0.626731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.0000 | 1.64146 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.0000 | + | 24.0000i | 1.09204 | + | 1.09204i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3137 | − | 11.3137i | 0.513729 | − | 0.513729i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.7696i | 1.66619i | 0.553132 | + | 0.833094i | \(0.313433\pi\) | ||||
−0.553132 | + | 0.833094i | \(0.686567\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 30.0000i | − | 1.35665i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0000 | + | 19.0000i | −0.857458 | + | 0.857458i | −0.991038 | − | 0.133580i | \(-0.957353\pi\) |
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.48528 | 0.381385 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | −1.07655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00000 | − | 3.00000i | −0.134298 | − | 0.134298i | 0.636762 | − | 0.771060i | \(-0.280273\pi\) |
−0.771060 | + | 0.636762i | \(0.780273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.48528 | + | 8.48528i | −0.379094 | + | 0.379094i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.4264i | 1.89170i | 0.324604 | + | 0.945850i | \(0.394769\pi\) | ||||
−0.324604 | + | 0.945850i | \(0.605231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000i | 0.889988i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.0000 | − | 23.0000i | 1.02147 | − | 1.02147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.0416 | − | 24.0416i | −1.06563 | − | 1.06563i | −0.997690 | − | 0.0679369i | \(-0.978358\pi\) |
−0.0679369 | − | 0.997690i | \(-0.521642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.9411 | 1.50147 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0000 | −1.05963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | + | 4.00000i | 0.176261 | + | 0.176261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.7990i | 0.869079i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.0000i | 1.84005i | 0.391856 | + | 0.920027i | \(0.371833\pi\) | ||||
−0.391856 | + | 0.920027i | \(0.628167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.00000 | − | 3.00000i | 0.131181 | − | 0.131181i | −0.638468 | − | 0.769649i | \(-0.720431\pi\) |
0.769649 | + | 0.638468i | \(0.220431\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82843 | + | 2.82843i | 0.123443 | + | 0.123443i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00000 | + | 1.00000i | 0.0433963 | + | 0.0433963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4558 | − | 25.4558i | 1.10262 | − | 1.10262i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.1421i | − | 0.611418i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 26.0000i | − | 1.12198i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.00000 | + | 3.00000i | −0.129219 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6985 | − | 29.6985i | −1.27684 | − | 1.27684i | −0.942428 | − | 0.334410i | \(-0.891463\pi\) |
−0.334410 | − | 0.942428i | \(-0.608537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.4558 | −1.09241 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0000 | − | 15.0000i | −0.641354 | − | 0.641354i | 0.309535 | − | 0.950888i | \(-0.399827\pi\) |
−0.950888 | + | 0.309535i | \(0.899827\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.24264 | − | 4.24264i | 0.181071 | − | 0.181071i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.48528i | 0.361485i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000i | 0.680389i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0000 | + | 12.0000i | −0.509372 | + | 0.509372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421 | + | 1.41421i | 0.0599222 | + | 0.0599222i | 0.736433 | − | 0.676511i | \(-0.236509\pi\) |
−0.676511 | + | 0.736433i | \(0.736509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.4558 | 1.07667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0000 | − | 21.0000i | −0.885044 | − | 0.885044i | 0.108998 | − | 0.994042i | \(-0.465236\pi\) |
−0.994042 | + | 0.108998i | \(0.965236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.48528 | − | 8.48528i | 0.356978 | − | 0.356978i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.1421i | 0.593914i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000i | 0.251533i | 0.992060 | + | 0.125767i | \(0.0401390\pi\) | ||||
−0.992060 | + | 0.125767i | \(0.959861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.00000 | − | 9.00000i | 0.376638 | − | 0.376638i | −0.493250 | − | 0.869888i | \(-0.664191\pi\) |
0.869888 | + | 0.493250i | \(0.164191\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9706 | + | 16.9706i | 0.708955 | + | 0.708955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0000 | −0.749350 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.0000 | − | 24.0000i | −0.997406 | − | 0.997406i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.48528 | − | 8.48528i | 0.352029 | − | 0.352029i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.48528i | 0.351424i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 12.0000i | − | 0.496139i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.0000 | − | 11.0000i | 0.454019 | − | 0.454019i | −0.442667 | − | 0.896686i | \(-0.645968\pi\) |
0.896686 | + | 0.442667i | \(0.145968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9706 | + | 16.9706i | 0.699260 | + | 0.699260i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1421 | 0.581730 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.0000 | 1.23195 | 0.615976 | − | 0.787765i | \(-0.288762\pi\) | ||||
0.615976 | + | 0.787765i | \(0.288762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.7990 | + | 19.7990i | −0.810319 | + | 0.810319i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4558i | 1.04010i | 0.854137 | + | 0.520049i | \(0.174086\pi\) | ||||
−0.854137 | + | 0.520049i | \(0.825914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0000i | 0.489490i | 0.969587 | + | 0.244745i | \(0.0787043\pi\) | ||||
−0.969587 | + | 0.244745i | \(0.921296\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.00000 | − | 9.00000i | 0.366508 | − | 0.366508i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.89949 | + | 9.89949i | 0.402472 | + | 0.402472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6274 | 0.918419 | 0.459209 | − | 0.888328i | \(-0.348133\pi\) | ||||
0.459209 | + | 0.888328i | \(0.348133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.24264 | − | 4.24264i | 0.171359 | − | 0.171359i | −0.616217 | − | 0.787576i | \(-0.711336\pi\) |
0.787576 | + | 0.616217i | \(0.211336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.9706i | 0.684319i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.0000i | − | 1.44931i | −0.689114 | − | 0.724653i | \(-0.742000\pi\) | ||
0.689114 | − | 0.724653i | \(-0.258000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.0000 | − | 27.0000i | 1.08522 | − | 1.08522i | 0.0892087 | − | 0.996013i | \(-0.471566\pi\) |
0.996013 | − | 0.0892087i | \(-0.0284338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.9411 | − | 33.9411i | −1.36201 | − | 1.36201i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.9411 | −1.35982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0000 | 0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.0000 | − | 18.0000i | −0.718851 | − | 0.718851i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1127i | 1.23858i | 0.785164 | + | 0.619288i | \(0.212579\pi\) | ||||
−0.785164 | + | 0.619288i | \(0.787421\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.00000i | 0.238479i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 8.00000i | −0.317470 | + | 0.317470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24264 | + | 4.24264i | 0.168100 | + | 0.168100i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.48528 | 0.335673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.00000 | + | 9.00000i | 0.354925 | + | 0.354925i | 0.861938 | − | 0.507013i | \(-0.169250\pi\) |
−0.507013 | + | 0.861938i | \(0.669250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.48528 | + | 8.48528i | −0.334108 | + | 0.334108i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.4558i | − | 1.00077i | −0.865802 | − | 0.500386i | \(-0.833191\pi\) | ||
0.865802 | − | 0.500386i | \(-0.166809\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000i | 0.235521i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | − | 16.0000i | 0.627089 | − | 0.627089i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.41421 | − | 1.41421i | −0.0553425 | − | 0.0553425i | 0.678894 | − | 0.734236i | \(-0.262460\pi\) |
−0.734236 | + | 0.678894i | \(0.762460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.82843 | −0.110516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.0000 | −0.468165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.0000 | + | 29.0000i | 1.12968 | + | 1.12968i | 0.990229 | + | 0.139451i | \(0.0445336\pi\) |
0.139451 | + | 0.990229i | \(0.455466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7279 | − | 12.7279i | 0.495059 | − | 0.495059i | −0.414837 | − | 0.909896i | \(-0.636161\pi\) |
0.909896 | + | 0.414837i | \(0.136161\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 24.0000i | − | 0.930680i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | + | 12.0000i | −0.464642 | + | 0.464642i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.65685 | + | 5.65685i | 0.218707 | + | 0.218707i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.4558 | 0.982712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | − | 4.00000i | −0.153960 | − | 0.153960i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8701 | + | 26.8701i | −1.03270 | + | 1.03270i | −0.0332533 | + | 0.999447i | \(0.510587\pi\) |
−0.999447 | + | 0.0332533i | \(0.989413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.6274i | − | 0.868361i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000i | 0.689761i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.0000 | + | 27.0000i | −1.03313 | + | 1.03313i | −0.0336941 | + | 0.999432i | \(0.510727\pi\) |
−0.999432 | + | 0.0336941i | \(0.989273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.48528 | + | 8.48528i | 0.324206 | + | 0.324206i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4558 | 0.971201 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0000 | + | 21.0000i | 0.798878 | + | 0.798878i | 0.982919 | − | 0.184041i | \(-0.0589179\pi\) |
−0.184041 | + | 0.982919i | \(0.558918\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.48528 | − | 8.48528i | 0.322329 | − | 0.322329i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.48528i | − | 0.321865i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0000 | + | 12.0000i | −0.453882 | + | 0.453882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.5269 | + | 32.5269i | 1.22852 | + | 1.22852i | 0.964522 | + | 0.264003i | \(0.0850427\pi\) |
0.264003 | + | 0.964522i | \(0.414957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.4558 | −0.960085 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.0000 | + | 20.0000i | 0.752177 | + | 0.752177i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7279 | − | 12.7279i | 0.478007 | − | 0.478007i | −0.426487 | − | 0.904494i | \(-0.640249\pi\) |
0.904494 | + | 0.426487i | \(0.140249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 5.65685i | − | 0.212149i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.0000 | − | 36.0000i | 1.34632 | − | 1.34632i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9706 | + | 16.9706i | 0.633777 | + | 0.633777i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.9706 | −0.632895 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.41421 | + | 1.41421i | −0.0525226 | + | 0.0525226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.82843i | 0.104901i | 0.998624 | + | 0.0524503i | \(0.0167031\pi\) | ||||
−0.998624 | + | 0.0524503i | \(0.983297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.6985 | + | 29.6985i | 1.09694 | + | 1.09694i | 0.994767 | + | 0.102172i | \(0.0325791\pi\) |
0.102172 | + | 0.994767i | \(0.467421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.82843 | −0.104328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.0000 | 1.98912 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.0000 | − | 33.0000i | −1.21392 | − | 1.21392i | −0.969725 | − | 0.244200i | \(-0.921475\pi\) |
−0.244200 | − | 0.969725i | \(-0.578525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.4558 | + | 25.4558i | −0.935144 | + | 0.935144i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4558i | 0.933884i | 0.884288 | + | 0.466942i | \(0.154644\pi\) | ||||
−0.884288 | + | 0.466942i | \(0.845356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 44.0000i | − | 1.61204i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | + | 3.00000i | −0.109764 | + | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.1421 | − | 14.1421i | −0.516742 | − | 0.516742i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.65685 | 0.206422 | 0.103211 | − | 0.994660i | \(-0.467088\pi\) | ||||
0.103211 | + | 0.994660i | \(0.467088\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.0000 | + | 20.0000i | 0.727875 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.6985 | − | 29.6985i | 1.07941 | − | 1.07941i | 0.0828476 | − | 0.996562i | \(-0.473599\pi\) |
0.996562 | − | 0.0828476i | \(-0.0264015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 50.9117i | − | 1.84798i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000i | 1.52250i | 0.648459 | + | 0.761249i | \(0.275414\pi\) | ||||
−0.648459 | + | 0.761249i | \(0.724586\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.0000 | + | 12.0000i | −0.434429 | + | 0.434429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.48528 | 0.306386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0000 | −0.865462 | −0.432731 | − | 0.901523i | \(-0.642450\pi\) | ||||
−0.432731 | + | 0.901523i | \(0.642450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | − | 6.00000i | −0.216085 | − | 0.216085i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.89949 | + | 9.89949i | −0.356060 | + | 0.356060i | −0.862358 | − | 0.506298i | \(-0.831013\pi\) |
0.506298 | + | 0.862358i | \(0.331013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685i | 0.203200i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000i | 0.860995i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.0000 | + | 18.0000i | −0.644917 | + | 0.644917i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4558 | + | 25.4558i | 0.910882 | + | 0.910882i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.3137 | −0.404319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.0000 | + | 21.0000i | 0.748569 | + | 0.748569i | 0.974210 | − | 0.225641i | \(-0.0724477\pi\) |
−0.225641 | + | 0.974210i | \(0.572448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.48528 | − | 8.48528i | 0.302084 | − | 0.302084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.9706i | − | 0.603404i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 36.0000i | − | 1.27840i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.00000 | + | 4.00000i | −0.141865 | + | 0.141865i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.41421 | − | 1.41421i | −0.0500940 | − | 0.0500940i | 0.681616 | − | 0.731710i | \(-0.261277\pi\) |
−0.731710 | + | 0.681616i | \(0.761277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0000 | 0.423999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.0000 | − | 36.0000i | −1.27041 | − | 1.27041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.9411 | − | 33.9411i | 1.19627 | − | 1.19627i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 19.7990i | − | 0.696957i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42.0000i | − | 1.47664i | −0.674450 | − | 0.738321i | \(-0.735619\pi\) | ||
0.674450 | − | 0.738321i | \(-0.264381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.00000 | − | 3.00000i | 0.105344 | − | 0.105344i | −0.652470 | − | 0.757814i | \(-0.726267\pi\) |
0.757814 | + | 0.652470i | \(0.226267\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.6274 | − | 22.6274i | −0.793578 | − | 0.793578i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.4264 | −1.48613 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0000 | −0.629740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | − | 12.0000i | −0.419314 | − | 0.419314i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8701 | − | 26.8701i | 0.937771 | − | 0.937771i | −0.0604026 | − | 0.998174i | \(-0.519238\pi\) |
0.998174 | + | 0.0604026i | \(0.0192385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.7990i | − | 0.690149i | −0.938575 | − | 0.345075i | \(-0.887854\pi\) | ||
0.938575 | − | 0.345075i | \(-0.112146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.00000i | − | 0.208893i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.0000 | + | 31.0000i | −1.07798 | + | 1.07798i | −0.0812847 | + | 0.996691i | \(0.525902\pi\) |
−0.996691 | + | 0.0812847i | \(0.974098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7279 | − | 12.7279i | −0.442059 | − | 0.442059i | 0.450644 | − | 0.892704i | \(-0.351194\pi\) |
−0.892704 | + | 0.450644i | \(0.851194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.48528 | −0.294351 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 12.0000i | 0.415277 | + | 0.415277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.6274 | + | 22.6274i | −0.782118 | + | 0.782118i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 8.48528i | − | 0.292944i | −0.989215 | − | 0.146472i | \(-0.953208\pi\) | ||
0.989215 | − | 0.146472i | \(-0.0467919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.0000i | − | 0.862069i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.0000 | + | 12.0000i | −0.413302 | + | 0.413302i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.5269 | − | 32.5269i | −1.11896 | − | 1.11896i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.7990 | 0.680301 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.0000 | −0.617758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | − | 36.0000i | −1.23406 | − | 1.23406i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.7279 | + | 12.7279i | −0.435796 | + | 0.435796i | −0.890594 | − | 0.454799i | \(-0.849711\pi\) |
0.454799 | + | 0.890594i | \(0.349711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.48528i | 0.290191i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.0000i | 1.84460i | 0.386469 | + | 0.922302i | \(0.373695\pi\) | ||||
−0.386469 | + | 0.922302i | \(0.626305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0000 | + | 33.0000i | −1.12595 | + | 1.12595i | −0.135116 | + | 0.990830i | \(0.543141\pi\) |
−0.990830 | + | 0.135116i | \(0.956859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.9706 | + | 16.9706i | 0.578355 | + | 0.578355i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.9117 | −1.73305 | −0.866527 | − | 0.499130i | \(-0.833653\pi\) | ||||
−0.866527 | + | 0.499130i | \(0.833653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.0000 | 0.952029 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0000 | + | 17.0000i | 0.577350 | + | 0.577350i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.9706 | − | 16.9706i | 0.575687 | − | 0.575687i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 76.3675i | − | 2.58762i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.00000i | 0.270759i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0000 | − | 24.0000i | 0.811348 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.24264 | + | 4.24264i | 0.143264 | + | 0.143264i | 0.775101 | − | 0.631837i | \(-0.217699\pi\) |
−0.631837 | + | 0.775101i | \(0.717699\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.1421 | 0.477002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0000 | + | 27.0000i | 0.908622 | + | 0.908622i | 0.996161 | − | 0.0875388i | \(-0.0279002\pi\) |
−0.0875388 | + | 0.996161i | \(0.527900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.82843 | + | 2.82843i | −0.0950765 | + | 0.0950765i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 42.4264i | − | 1.42454i | −0.701906 | − | 0.712270i | \(-0.747667\pi\) | ||
0.701906 | − | 0.712270i | \(-0.252333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000i | 0.536623i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.0000 | − | 15.0000i | 0.502519 | − | 0.502519i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.7696 | −1.22907 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −72.0000 | −2.40401 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00000 | + | 8.00000i | 0.266815 | + | 0.266815i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.9706i | 0.564745i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.0000i | 1.19668i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.00000 | + | 3.00000i | −0.0996134 | + | 0.0996134i | −0.755157 | − | 0.655544i | \(-0.772439\pi\) |
0.655544 | + | 0.755157i | \(0.272439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.07107 | − | 7.07107i | −0.234533 | − | 0.234533i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.9411 | 1.12452 | 0.562260 | − | 0.826961i | \(-0.309932\pi\) | ||||
0.562260 | + | 0.826961i | \(0.309932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | −0.595713 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0000 | + | 12.0000i | 0.396708 | + | 0.396708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.82843 | + | 2.82843i | −0.0934029 | + | 0.0934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.82843i | − | 0.0933012i | −0.998911 | − | 0.0466506i | \(-0.985145\pi\) | ||
0.998911 | − | 0.0466506i | \(-0.0148547\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.00000i | − | 0.197707i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | − | 36.0000i | 1.18495 | − | 1.18495i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.24264 | − | 4.24264i | −0.139497 | − | 0.139497i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.82843 | −0.0928977 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0000 | −0.787414 | −0.393707 | − | 0.919236i | \(-0.628808\pi\) | ||||
−0.393707 | + | 0.919236i | \(0.628808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | − | 3.00000i | −0.0983210 | − | 0.0983210i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.48528 | + | 8.48528i | −0.277796 | + | 0.277796i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0000i | 0.653372i | 0.945133 | + | 0.326686i | \(0.105932\pi\) | ||||
−0.945133 | + | 0.326686i | \(0.894068\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00000 | + | 6.00000i | −0.195803 | + | 0.195803i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.5563 | + | 15.5563i | 0.507122 | + | 0.507122i | 0.913642 | − | 0.406520i | \(-0.133258\pi\) |
−0.406520 | + | 0.913642i | \(0.633258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.9117 | −1.65791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.0000 | 1.04096 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.0000 | − | 29.0000i | −0.942373 | − | 0.942373i | 0.0560543 | − | 0.998428i | \(-0.482148\pi\) |
−0.998428 | + | 0.0560543i | \(0.982148\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.9117 | + | 50.9117i | −1.65266 | + | 1.65266i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.1421i | − | 0.458590i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.0000 | − | 24.0000i | 0.776622 | − | 0.776622i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.48528 | − | 8.48528i | −0.274290 | − | 0.274290i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.00000 | + | 5.00000i | 0.161123 | + | 0.161123i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.9411 | + | 33.9411i | −1.09260 | + | 1.09260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1127i | − | 1.00052i | −0.865876 | − | 0.500258i | \(-0.833238\pi\) | ||
0.865876 | − | 0.500258i | \(-0.166762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0000 | − | 21.0000i | 0.673922 | − | 0.673922i | −0.284696 | − | 0.958618i | \(-0.591893\pi\) |
0.958618 | + | 0.284696i | \(0.0918926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.48528 | − | 8.48528i | −0.272026 | − | 0.272026i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.48528 | −0.271746 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.0000 | 1.53566 | 0.767828 | − | 0.640656i | \(-0.221338\pi\) | ||||
0.767828 | + | 0.640656i | \(0.221338\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000 | + | 36.0000i | 1.15056 | + | 1.15056i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.24264 | − | 4.24264i | 0.135457 | − | 0.135457i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.4264i | − | 1.35319i | −0.736354 | − | 0.676596i | \(-0.763454\pi\) | ||
0.736354 | − | 0.676596i | \(-0.236546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 20.0000i | − | 0.637253i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.4558 | − | 25.4558i | −0.809449 | − | 0.809449i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.2548 | 1.43757 | 0.718784 | − | 0.695234i | \(-0.244699\pi\) | ||||
0.718784 | + | 0.695234i | \(0.244699\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.0000 | 1.33283 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.0000 | + | 28.0000i | 0.887660 | + | 0.887660i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7279 | − | 12.7279i | 0.403097 | − | 0.403097i | −0.476226 | − | 0.879323i | \(-0.657995\pi\) |
0.879323 | + | 0.476226i | \(0.157995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 33.9411i | − | 1.07385i |
(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 | 1024.2.e.h.257.1 | 4 | ||
4.3 | odd | 2 | 1024.2.e.n.257.1 | 4 | |||
8.3 | odd | 2 | inner | 1024.2.e.h.257.2 | 4 | ||
8.5 | even | 2 | 1024.2.e.n.257.2 | 4 | |||
16.3 | odd | 4 | inner | 1024.2.e.h.769.2 | 4 | ||
16.5 | even | 4 | inner | 1024.2.e.h.769.1 | 4 | ||
16.11 | odd | 4 | 1024.2.e.n.769.1 | 4 | |||
16.13 | even | 4 | 1024.2.e.n.769.2 | 4 | |||
32.3 | odd | 8 | 512.2.b.e.257.3 | 4 | |||
32.5 | even | 8 | 512.2.a.b.1.2 | yes | 2 | ||
32.11 | odd | 8 | 512.2.a.e.1.2 | yes | 2 | ||
32.13 | even | 8 | 512.2.b.e.257.4 | 4 | |||
32.19 | odd | 8 | 512.2.b.e.257.2 | 4 | |||
32.21 | even | 8 | 512.2.a.e.1.1 | yes | 2 | ||
32.27 | odd | 8 | 512.2.a.b.1.1 | ✓ | 2 | ||
32.29 | even | 8 | 512.2.b.e.257.1 | 4 | |||
96.5 | odd | 8 | 4608.2.a.p.1.1 | 2 | |||
96.11 | even | 8 | 4608.2.a.c.1.2 | 2 | |||
96.29 | odd | 8 | 4608.2.d.j.2305.4 | 4 | |||
96.35 | even | 8 | 4608.2.d.j.2305.3 | 4 | |||
96.53 | odd | 8 | 4608.2.a.c.1.1 | 2 | |||
96.59 | even | 8 | 4608.2.a.p.1.2 | 2 | |||
96.77 | odd | 8 | 4608.2.d.j.2305.2 | 4 | |||
96.83 | even | 8 | 4608.2.d.j.2305.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.a.b.1.1 | ✓ | 2 | 32.27 | odd | 8 | ||
512.2.a.b.1.2 | yes | 2 | 32.5 | even | 8 | ||
512.2.a.e.1.1 | yes | 2 | 32.21 | even | 8 | ||
512.2.a.e.1.2 | yes | 2 | 32.11 | odd | 8 | ||
512.2.b.e.257.1 | 4 | 32.29 | even | 8 | |||
512.2.b.e.257.2 | 4 | 32.19 | odd | 8 | |||
512.2.b.e.257.3 | 4 | 32.3 | odd | 8 | |||
512.2.b.e.257.4 | 4 | 32.13 | even | 8 | |||
1024.2.e.h.257.1 | 4 | 1.1 | even | 1 | trivial | ||
1024.2.e.h.257.2 | 4 | 8.3 | odd | 2 | inner | ||
1024.2.e.h.769.1 | 4 | 16.5 | even | 4 | inner | ||
1024.2.e.h.769.2 | 4 | 16.3 | odd | 4 | inner | ||
1024.2.e.n.257.1 | 4 | 4.3 | odd | 2 | |||
1024.2.e.n.257.2 | 4 | 8.5 | even | 2 | |||
1024.2.e.n.769.1 | 4 | 16.11 | odd | 4 | |||
1024.2.e.n.769.2 | 4 | 16.13 | even | 4 | |||
4608.2.a.c.1.1 | 2 | 96.53 | odd | 8 | |||
4608.2.a.c.1.2 | 2 | 96.11 | even | 8 | |||
4608.2.a.p.1.1 | 2 | 96.5 | odd | 8 | |||
4608.2.a.p.1.2 | 2 | 96.59 | even | 8 | |||
4608.2.d.j.2305.1 | 4 | 96.83 | even | 8 | |||
4608.2.d.j.2305.2 | 4 | 96.77 | odd | 8 | |||
4608.2.d.j.2305.3 | 4 | 96.35 | even | 8 | |||
4608.2.d.j.2305.4 | 4 | 96.29 | odd | 8 |