Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (of order \(3\), 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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1153.4 | ||
Root | \(1.19051 - 1.25805i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.1153 |
Dual form | 3456.2.i.i.2305.4 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.268104 | + | 0.464369i | 0.119900 | + | 0.207672i | 0.919728 | − | 0.392557i | \(-0.128409\pi\) |
−0.799828 | + | 0.600229i | \(0.795076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35014 | + | 4.07056i | −0.888270 | + | 1.53853i | −0.0463510 | + | 0.998925i | \(0.514759\pi\) |
−0.841919 | + | 0.539604i | \(0.818574\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59922 | − | 4.50198i | 0.783695 | − | 1.35740i | −0.146081 | − | 0.989273i | \(-0.546666\pi\) |
0.929776 | − | 0.368126i | \(-0.120001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.778295 | + | 1.34805i | 0.215860 | + | 0.373881i | 0.953538 | − | 0.301272i | \(-0.0974111\pi\) |
−0.737678 | + | 0.675153i | \(0.764078\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.695781 | −0.168752 | −0.0843759 | − | 0.996434i | \(-0.526890\pi\) | ||||
−0.0843759 | + | 0.996434i | \(0.526890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.80593 | 1.33197 | 0.665986 | − | 0.745965i | \(-0.268011\pi\) | ||||
0.665986 | + | 0.745965i | \(0.268011\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.42809 | + | 7.66967i | 0.923320 | + | 1.59924i | 0.794241 | + | 0.607603i | \(0.207869\pi\) |
0.129079 | + | 0.991634i | \(0.458798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35624 | − | 4.08113i | 0.471248 | − | 0.816226i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.92199 | − | 3.32898i | 0.356904 | − | 0.618176i | −0.630538 | − | 0.776159i | \(-0.717166\pi\) |
0.987442 | + | 0.157982i | \(0.0504989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.77035 | − | 4.79840i | −0.497570 | − | 0.861817i | 0.502426 | − | 0.864620i | \(-0.332441\pi\) |
−0.999996 | + | 0.00280317i | \(0.999108\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.52033 | −0.426013 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.09280 | −0.672852 | −0.336426 | − | 0.941710i | \(-0.609218\pi\) | ||||
−0.336426 | + | 0.941710i | \(0.609218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.01019 | − | 1.74970i | −0.157765 | − | 0.273258i | 0.776297 | − | 0.630367i | \(-0.217096\pi\) |
−0.934063 | + | 0.357109i | \(0.883762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.71522 | + | 6.43494i | −0.566565 | + | 0.981319i | 0.430337 | + | 0.902668i | \(0.358395\pi\) |
−0.996902 | + | 0.0786512i | \(0.974939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.186066 | + | 0.322275i | −0.0271404 | + | 0.0470086i | −0.879277 | − | 0.476311i | \(-0.841973\pi\) |
0.852136 | + | 0.523320i | \(0.175307\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.54633 | − | 13.0706i | −1.07805 | − | 1.86723i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.30777 | 0.729078 | 0.364539 | − | 0.931188i | \(-0.381227\pi\) | ||||
0.364539 | + | 0.931188i | \(0.381227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.78744 | 0.375859 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.57152 | + | 4.45401i | 0.334784 | + | 0.579862i | 0.983443 | − | 0.181216i | \(-0.0580034\pi\) |
−0.648660 | + | 0.761079i | \(0.724670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.921988 | − | 1.59693i | 0.118049 | − | 0.204466i | −0.800946 | − | 0.598737i | \(-0.795670\pi\) |
0.918994 | + | 0.394271i | \(0.129003\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.417328 | + | 0.722833i | −0.0517631 | + | 0.0896564i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.79316 | + | 10.0340i | 0.707747 | + | 1.22585i | 0.965691 | + | 0.259694i | \(0.0836218\pi\) |
−0.257944 | + | 0.966160i | \(0.583045\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6289 | 1.26142 | 0.630708 | − | 0.776021i | \(-0.282765\pi\) | ||||
0.630708 | + | 0.776021i | \(0.282765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.40840 | 0.515964 | 0.257982 | − | 0.966150i | \(-0.416943\pi\) | ||||
0.257982 | + | 0.966150i | \(0.416943\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.2171 | + | 21.1606i | 1.39227 | + | 2.41147i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.32244 | + | 5.75464i | −0.373804 | + | 0.647448i | −0.990147 | − | 0.140030i | \(-0.955280\pi\) |
0.616343 | + | 0.787478i | \(0.288613\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.28055 | + | 9.14617i | −0.579615 | + | 1.00392i | 0.415908 | + | 0.909407i | \(0.363464\pi\) |
−0.995523 | + | 0.0945164i | \(0.969870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.186541 | − | 0.323099i | −0.0202333 | − | 0.0350450i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.30777 | 0.774622 | 0.387311 | − | 0.921949i | \(-0.373404\pi\) | ||||
0.387311 | + | 0.921949i | \(0.373404\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.31642 | −0.766969 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55659 | + | 2.69609i | 0.159703 | + | 0.276613i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.81612 | + | 13.5379i | −0.793607 | + | 1.37457i | 0.130113 | + | 0.991499i | \(0.458466\pi\) |
−0.923720 | + | 0.383068i | \(0.874867\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.43218 | + | 7.67676i | −0.441018 | + | 0.763866i | −0.997765 | − | 0.0668159i | \(-0.978716\pi\) |
0.556747 | + | 0.830682i | \(0.312049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.64986 | − | 2.85764i | −0.162565 | − | 0.281571i | 0.773223 | − | 0.634135i | \(-0.218644\pi\) |
−0.935788 | + | 0.352563i | \(0.885310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.12139 | 0.688451 | 0.344226 | − | 0.938887i | \(-0.388142\pi\) | ||||
0.344226 | + | 0.938887i | \(0.388142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.98862 | −0.286258 | −0.143129 | − | 0.989704i | \(-0.545716\pi\) | ||||
−0.143129 | + | 0.989704i | \(0.545716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.40833 | − | 5.90340i | −0.320629 | − | 0.555345i | 0.659989 | − | 0.751275i | \(-0.270561\pi\) |
−0.980618 | + | 0.195930i | \(0.937227\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.37437 | + | 4.11253i | −0.221411 | + | 0.383496i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.63518 | − | 2.83222i | 0.149897 | − | 0.259629i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.01190 | − | 13.8770i | −0.728355 | − | 1.26155i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.20790 | 0.465809 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7567 | 1.57565 | 0.787826 | − | 0.615899i | \(-0.211207\pi\) | ||||
0.787826 | + | 0.615899i | \(0.211207\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.51253 | + | 6.08389i | 0.306892 | + | 0.531552i | 0.977681 | − | 0.210096i | \(-0.0673778\pi\) |
−0.670789 | + | 0.741648i | \(0.734044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.6448 | + | 23.6334i | −1.18315 | + | 2.04928i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.71048 | + | 9.89083i | −0.487879 | + | 0.845031i | −0.999903 | − | 0.0139402i | \(-0.995563\pi\) |
0.512024 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.10659 | + | 5.38078i | 0.263498 | + | 0.456392i | 0.967169 | − | 0.254134i | \(-0.0817905\pi\) |
−0.703671 | + | 0.710526i | \(0.748457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.09185 | 0.676674 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.06117 | 0.171171 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.47858 | − | 9.48918i | −0.448823 | − | 0.777384i | 0.549487 | − | 0.835502i | \(-0.314823\pi\) |
−0.998310 | + | 0.0581186i | \(0.981490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.28439 | + | 12.6169i | −0.592796 | + | 1.02675i | 0.401058 | + | 0.916053i | \(0.368642\pi\) |
−0.993854 | + | 0.110700i | \(0.964691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.48548 | − | 2.57293i | 0.119317 | − | 0.206663i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.66049 | + | 13.2684i | 0.611373 | + | 1.05893i | 0.991009 | + | 0.133794i | \(0.0427159\pi\) |
−0.379636 | + | 0.925136i | \(0.623951\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −41.6265 | −3.28063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0724 | −0.867258 | −0.433629 | − | 0.901091i | \(-0.642767\pi\) | ||||
−0.433629 | + | 0.901091i | \(0.642767\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.15607 | − | 7.19852i | −0.321606 | − | 0.557039i | 0.659213 | − | 0.751956i | \(-0.270889\pi\) |
−0.980820 | + | 0.194917i | \(0.937556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.28851 | − | 9.15997i | 0.406809 | − | 0.704613i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0396656 | − | 0.0687029i | 0.00301572 | − | 0.00522338i | −0.864514 | − | 0.502609i | \(-0.832373\pi\) |
0.867529 | + | 0.497386i | \(0.165707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0750 | + | 19.1825i | 0.837191 | + | 1.45006i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8011 | 1.55475 | 0.777375 | − | 0.629038i | \(-0.216551\pi\) | ||||
0.777375 | + | 0.629038i | \(0.216551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.13118 | 0.381397 | 0.190699 | − | 0.981649i | \(-0.438925\pi\) | ||||
0.190699 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.09729 | − | 1.90057i | −0.0806747 | − | 0.139733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.80849 | + | 3.13240i | −0.132250 | + | 0.229063i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89085 | + | 17.1315i | −0.715677 | + | 1.23959i | 0.247021 | + | 0.969010i | \(0.420548\pi\) |
−0.962698 | + | 0.270579i | \(0.912785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.79574 | + | 3.11031i | 0.129260 | + | 0.223885i | 0.923390 | − | 0.383863i | \(-0.125407\pi\) |
−0.794130 | + | 0.607748i | \(0.792073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.71261 | 0.122019 | 0.0610093 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610093 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.1299 | −1.28520 | −0.642598 | − | 0.766203i | \(-0.722144\pi\) | ||||
−0.642598 | + | 0.766203i | \(0.722144\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.03389 | + | 15.6472i | 0.634055 | + | 1.09822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.541672 | − | 0.938204i | 0.0378320 | − | 0.0655270i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0909 | − | 26.1382i | 1.04386 | − | 1.80802i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.734306 | + | 1.27186i | 0.0505517 | + | 0.0875581i | 0.890194 | − | 0.455582i | \(-0.150569\pi\) |
−0.839642 | + | 0.543140i | \(0.817235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.98425 | −0.271724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.0429 | 1.76791 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.541523 | − | 0.937946i | −0.0364268 | − | 0.0630931i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.57845 | + | 16.5904i | −0.641420 | + | 1.11097i | 0.343696 | + | 0.939081i | \(0.388321\pi\) |
−0.985116 | + | 0.171891i | \(0.945012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.92737 | − | 10.2665i | 0.393414 | − | 0.681412i | −0.599484 | − | 0.800387i | \(-0.704627\pi\) |
0.992897 | + | 0.118975i | \(0.0379607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.57219 | + | 2.72311i | 0.103893 | + | 0.179948i | 0.913285 | − | 0.407320i | \(-0.133537\pi\) |
−0.809392 | + | 0.587268i | \(0.800203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.82935 | 0.185357 | 0.0926783 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926783 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.199539 | −0.0130165 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.58766 | + | 2.74991i | 0.102697 | + | 0.177877i | 0.912795 | − | 0.408418i | \(-0.133919\pi\) |
−0.810098 | + | 0.586295i | \(0.800586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.63053 | − | 11.4844i | 0.427110 | − | 0.739776i | −0.569505 | − | 0.821988i | \(-0.692865\pi\) |
0.996615 | + | 0.0822117i | \(0.0261984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.04640 | − | 7.00857i | 0.258515 | − | 0.447761i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.51873 | + | 7.82666i | 0.287520 | + | 0.497999i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.06394 | 0.193394 | 0.0966970 | − | 0.995314i | \(-0.469172\pi\) | ||||
0.0966970 | + | 0.995314i | \(0.469172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 46.0383 | 2.89440 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.14120 | − | 14.1010i | −0.507834 | − | 0.879595i | −0.999959 | − | 0.00907003i | \(-0.997113\pi\) |
0.492125 | − | 0.870525i | \(-0.336220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.61866 | − | 16.6600i | 0.597674 | − | 1.03520i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0730 | − | 19.1790i | 0.682789 | − | 1.18262i | −0.291337 | − | 0.956620i | \(-0.594100\pi\) |
0.974126 | − | 0.226005i | \(-0.0725664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.42303 | + | 2.46476i | 0.0874162 | + | 0.151409i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.7805 | 1.93769 | 0.968845 | − | 0.247667i | \(-0.0796639\pi\) | ||||
0.968845 | + | 0.247667i | \(0.0796639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.794033 | −0.0482341 | −0.0241170 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241170 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.2488 | − | 21.2155i | −0.738629 | − | 1.27934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6085 | + | 21.8385i | −0.757569 | + | 1.31215i | 0.186519 | + | 0.982451i | \(0.440280\pi\) |
−0.944087 | + | 0.329696i | \(0.893054\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.06672 | − | 8.77581i | 0.302255 | − | 0.523521i | −0.674391 | − | 0.738374i | \(-0.735594\pi\) |
0.976646 | + | 0.214853i | \(0.0689273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6766 | + | 20.2245i | 0.694102 | + | 1.20222i | 0.970482 | + | 0.241172i | \(0.0775319\pi\) |
−0.276380 | + | 0.961048i | \(0.589135\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.49637 | 0.560553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5159 | −0.971523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1967 | − | 22.8573i | −0.770959 | − | 1.33534i | −0.937038 | − | 0.349228i | \(-0.886444\pi\) |
0.166079 | − | 0.986112i | \(-0.446889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.37887 | + | 2.38827i | −0.0802809 | + | 0.139051i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.89272 | + | 11.9385i | −0.398616 | + | 0.690424i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.4626 | − | 30.2461i | −1.00653 | − | 1.74335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.988754 | 0.0566159 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6724 | −1.23691 | −0.618454 | − | 0.785821i | \(-0.712241\pi\) | ||||
−0.618454 | + | 0.785821i | \(0.712241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5448 | + | 25.1924i | 0.824761 | + | 1.42853i | 0.902102 | + | 0.431523i | \(0.142024\pi\) |
−0.0773408 | + | 0.997005i | \(0.524643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.52393 | − | 6.10363i | 0.199185 | − | 0.344998i | −0.749080 | − | 0.662480i | \(-0.769504\pi\) |
0.948264 | + | 0.317482i | \(0.102837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.444372 | − | 0.769675i | 0.0249584 | − | 0.0432292i | −0.853276 | − | 0.521459i | \(-0.825388\pi\) |
0.878235 | + | 0.478230i | \(0.158721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.99135 | − | 17.3055i | −0.559408 | − | 0.968923i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.03966 | −0.224772 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.33540 | 0.406895 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.874561 | − | 1.51478i | −0.0482161 | − | 0.0835127i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4513 | − | 19.8342i | 0.629420 | − | 1.09019i | −0.358249 | − | 0.933626i | \(-0.616626\pi\) |
0.987668 | − | 0.156561i | \(-0.0500407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.10634 | + | 5.38033i | −0.169717 | + | 0.293959i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.415255 | + | 0.719243i | 0.0226204 | + | 0.0391796i | 0.877114 | − | 0.480282i | \(-0.159466\pi\) |
−0.854494 | + | 0.519462i | \(0.826132\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.8031 | −1.55977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.0378 | 2.05385 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.53131 | + | 14.7767i | 0.457985 | + | 0.793253i | 0.998854 | − | 0.0478537i | \(-0.0152381\pi\) |
−0.540870 | + | 0.841106i | \(0.681905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.9443 | + | 18.9561i | −0.585836 | + | 1.01470i | 0.408935 | + | 0.912564i | \(0.365900\pi\) |
−0.994771 | + | 0.102134i | \(0.967433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.53407 | + | 16.5135i | −0.507447 | + | 0.878924i | 0.492516 | + | 0.870304i | \(0.336077\pi\) |
−0.999963 | + | 0.00862082i | \(0.997256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.84964 | + | 4.93572i | 0.151243 | + | 0.261961i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1482 | −0.693938 | −0.346969 | − | 0.937877i | \(-0.612789\pi\) | ||||
−0.346969 | + | 0.937877i | \(0.612789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7088 | 0.774147 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.18191 | + | 2.04712i | 0.0618638 | + | 0.107151i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.79061 | − | 13.4937i | 0.406666 | − | 0.704367i | −0.587848 | − | 0.808972i | \(-0.700025\pi\) |
0.994514 | + | 0.104605i | \(0.0333578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4740 | + | 21.6056i | −0.647618 | + | 1.12171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.92199 | − | 17.1854i | −0.513741 | − | 0.889826i | −0.999873 | − | 0.0159402i | \(-0.994926\pi\) |
0.486132 | − | 0.873885i | \(-0.338407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.98350 | 0.308166 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0470 | −0.772914 | −0.386457 | − | 0.922307i | \(-0.626301\pi\) | ||||
−0.386457 | + | 0.922307i | \(0.626301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4288 | − | 28.4556i | −0.839474 | − | 1.45401i | −0.890335 | − | 0.455305i | \(-0.849530\pi\) |
0.0508616 | − | 0.998706i | \(-0.483803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.55089 | + | 11.3465i | −0.333864 | + | 0.578270i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.87559 | + | 3.24862i | −0.0950962 | + | 0.164711i | −0.909649 | − | 0.415378i | \(-0.863649\pi\) |
0.814553 | + | 0.580090i | \(0.196983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.08098 | − | 5.33641i | −0.155812 | − | 0.269874i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.56304 | −0.179276 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.5495 | 1.18192 | 0.590958 | − | 0.806702i | \(-0.298750\pi\) | ||||
0.590958 | + | 0.806702i | \(0.298750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.28105 | − | 12.6111i | −0.363598 | − | 0.629771i | 0.624952 | − | 0.780663i | \(-0.285119\pi\) |
−0.988550 | + | 0.150893i | \(0.951785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.31231 | − | 7.46914i | 0.214811 | − | 0.372064i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6381 | + | 18.4257i | −0.527310 | + | 0.913328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.23655 | + | 5.60586i | 0.160037 | + | 0.277192i | 0.934882 | − | 0.354959i | \(-0.115505\pi\) |
−0.774845 | + | 0.632152i | \(0.782172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.1738 | −1.18951 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.66294 | −0.277983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.4378 | + | 23.2750i | 0.656481 | + | 1.13706i | 0.981520 | + | 0.191357i | \(0.0612890\pi\) |
−0.325040 | + | 0.945700i | \(0.605378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.85521 | − | 6.67742i | 0.187892 | − | 0.325438i | −0.756656 | − | 0.653814i | \(-0.773168\pi\) |
0.944547 | + | 0.328376i | \(0.106501\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.63943 | + | 2.83957i | −0.0795239 | + | 0.137740i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.33361 | + | 7.50603i | 0.209718 | + | 0.363242i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.45993 | 0.166659 | 0.0833294 | − | 0.996522i | \(-0.473445\pi\) | ||||
0.0833294 | + | 0.996522i | \(0.473445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7863 | −0.614471 | −0.307236 | − | 0.951633i | \(-0.599404\pi\) | ||||
−0.307236 | + | 0.951633i | \(0.599404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.7092 | + | 44.5296i | 1.22984 | + | 2.13014i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.76458 | − | 4.78840i | 0.131946 | − | 0.228538i | −0.792480 | − | 0.609897i | \(-0.791211\pi\) |
0.924427 | + | 0.381359i | \(0.124544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.2718 | − | 22.9874i | 0.630563 | − | 1.09217i | −0.356874 | − | 0.934152i | \(-0.616158\pi\) |
0.987437 | − | 0.158014i | \(-0.0505091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.95924 | + | 3.39350i | 0.0928769 | + | 0.160867i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9625 | 1.41402 | 0.707010 | − | 0.707204i | \(-0.250044\pi\) | ||||
0.707010 | + | 0.707204i | \(0.250044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5028 | −0.494560 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.96156 | − | 3.39752i | −0.0919593 | − | 0.159278i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.3904 | + | 21.4608i | −0.579597 | + | 1.00389i | 0.415928 | + | 0.909398i | \(0.363457\pi\) |
−0.995525 | + | 0.0944945i | \(0.969877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.30632 | + | 9.19081i | −0.247140 | + | 0.428059i | −0.962731 | − | 0.270461i | \(-0.912824\pi\) |
0.715591 | + | 0.698519i | \(0.246157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.31762 | − | 9.21040i | −0.247131 | − | 0.428043i | 0.715598 | − | 0.698513i | \(-0.246154\pi\) |
−0.962729 | + | 0.270469i | \(0.912821\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.3831 | 1.26714 | 0.633569 | − | 0.773686i | \(-0.281589\pi\) | ||||
0.633569 | + | 0.773686i | \(0.281589\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.4590 | −2.51468 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.3133 | + | 33.4517i | 0.888028 | + | 1.53811i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.6802 | − | 23.6947i | 0.627689 | − | 1.08719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.3026 | − | 35.1651i | 0.927649 | − | 1.60674i | 0.140404 | − | 0.990094i | \(-0.455160\pi\) |
0.787245 | − | 0.616641i | \(-0.211507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.18541 | − | 5.51728i | −0.145242 | − | 0.251566i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.38212 | −0.380613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.99658 | 0.226417 | 0.113208 | − | 0.993571i | \(-0.463887\pi\) | ||||
0.113208 | + | 0.993571i | \(0.463887\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.2049 | − | 33.2639i | −0.866705 | − | 1.50118i | −0.865344 | − | 0.501178i | \(-0.832900\pi\) |
−0.00136059 | − | 0.999999i | \(-0.500433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.33728 | + | 2.31624i | −0.0602282 | + | 0.104318i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.9794 | + | 43.2655i | −1.12048 | + | 1.94072i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3616 | + | 19.6788i | 0.508614 | + | 0.880945i | 0.999950 | + | 0.00997497i | \(0.00317518\pi\) |
−0.491337 | + | 0.870970i | \(0.663491\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.2323 | −1.79387 | −0.896935 | − | 0.442161i | \(-0.854212\pi\) | ||||
−0.896935 | + | 0.442161i | \(0.854212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.75313 | −0.211512 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.30968 | + | 7.46459i | 0.191023 | + | 0.330862i | 0.945590 | − | 0.325362i | \(-0.105486\pi\) |
−0.754566 | + | 0.656224i | \(0.772153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3604 | + | 17.9447i | −0.458315 | + | 0.793825i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.884666 | − | 1.53229i | 0.0389830 | − | 0.0675206i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.967251 | + | 1.67533i | 0.0425396 | + | 0.0736808i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.5770 | 0.901496 | 0.450748 | − | 0.892651i | \(-0.351157\pi\) | ||||
0.450748 | + | 0.892651i | \(0.351157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.6990 | −0.686470 | −0.343235 | − | 0.939250i | \(-0.611523\pi\) | ||||
−0.343235 | + | 0.939250i | \(0.611523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.92756 | + | 3.33863i | 0.0839659 | + | 0.145433i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.7159 | + | 48.0054i | −1.20504 | + | 2.08719i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.57245 | − | 2.72357i | 0.0681106 | − | 0.117971i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.90927 | + | 3.30696i | 0.0825450 | + | 0.142972i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −78.4584 | −3.37944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.79886 | −0.206319 | −0.103160 | − | 0.994665i | \(-0.532895\pi\) | ||||
−0.103160 | + | 0.994665i | \(0.532895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.801260 | − | 1.38782i | −0.0343222 | − | 0.0594478i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.26596 | + | 14.3171i | −0.353427 | + | 0.612153i | −0.986847 | − | 0.161654i | \(-0.948317\pi\) |
0.633421 | + | 0.773808i | \(0.281650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.1589 | − | 19.3278i | 0.475386 | − | 0.823393i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6164 | − | 27.0484i | −0.664078 | − | 1.15022i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2466 | 0.603649 | 0.301825 | − | 0.953363i | \(-0.402404\pi\) | ||||
0.301825 | + | 0.953363i | \(0.402404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.5661 | −0.489196 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4981 | − | 23.3794i | −0.568876 | − | 0.985322i | −0.996677 | − | 0.0814497i | \(-0.974045\pi\) |
0.427801 | − | 0.903873i | \(-0.359288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.82757 | − | 3.16545i | 0.0768865 | − | 0.133171i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.82124 | + | 8.35063i | −0.202117 | + | 0.350076i | −0.949210 | − | 0.314643i | \(-0.898115\pi\) |
0.747094 | + | 0.664719i | \(0.231449\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0536 | − | 26.0736i | −0.629973 | − | 1.09115i | −0.987557 | − | 0.157264i | \(-0.949733\pi\) |
0.357584 | − | 0.933881i | \(-0.383601\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.7346 | 1.74045 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9642 | 0.622968 | 0.311484 | − | 0.950251i | \(-0.399174\pi\) | ||||
0.311484 | + | 0.950251i | \(0.399174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.8201 | − | 42.9896i | −1.02971 | − | 1.78351i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.7961 | − | 23.8955i | 0.571375 | − | 0.989650i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0511 | − | 20.8731i | 0.497401 | − | 0.861523i | −0.502595 | − | 0.864522i | \(-0.667621\pi\) |
0.999996 | + | 0.00299890i | \(0.000954581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0845 | − | 27.8591i | −0.662749 | − | 1.14792i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.62882 | −0.231148 | −0.115574 | − | 0.993299i | \(-0.536871\pi\) | ||||
−0.115574 | + | 0.993299i | \(0.536871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.75360 | 0.0718904 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.75087 | + | 16.8890i | 0.398410 | + | 0.690066i | 0.993530 | − | 0.113571i | \(-0.0362289\pi\) |
−0.595120 | + | 0.803637i | \(0.702896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.36834 | + | 2.37003i | −0.0558158 | + | 0.0966757i | −0.892583 | − | 0.450883i | \(-0.851109\pi\) |
0.836767 | + | 0.547558i | \(0.184443\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.29604 | − | 7.44096i | 0.174659 | − | 0.302518i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.6876 | − | 41.0282i | −0.961452 | − | 1.66528i | −0.718860 | − | 0.695155i | \(-0.755336\pi\) |
−0.242592 | − | 0.970128i | \(-0.577998\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.579256 | −0.0234342 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1963 | 0.936891 | 0.468446 | − | 0.883492i | \(-0.344814\pi\) | ||||
0.468446 | + | 0.883492i | \(0.344814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.8253 | + | 34.3384i | 0.798137 | + | 1.38241i | 0.920828 | + | 0.389969i | \(0.127514\pi\) |
−0.122691 | + | 0.992445i | \(0.539152\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.813544 | + | 1.40910i | −0.0326991 | + | 0.0566365i | −0.881912 | − | 0.471414i | \(-0.843744\pi\) |
0.849213 | + | 0.528051i | \(0.177077\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1743 | + | 29.7467i | −0.688074 | + | 1.19178i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.3849 | − | 17.9873i | −0.415398 | − | 0.719490i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.84769 | 0.113545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.9685 | 1.23283 | 0.616417 | − | 0.787420i | \(-0.288583\pi\) | ||||
0.616417 | + | 0.787420i | \(0.288583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.76063 | + | 8.24566i | 0.188920 | + | 0.327219i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.7466 | − | 20.3456i | 0.465415 | − | 0.806123i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1499 | − | 27.9725i | 0.637883 | − | 1.10485i | −0.348014 | − | 0.937489i | \(-0.613144\pi\) |
0.985897 | − | 0.167356i | \(-0.0535230\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.28376 | + | 5.68763i | 0.129499 | + | 0.224298i | 0.923482 | − | 0.383641i | \(-0.125330\pi\) |
−0.793984 | + | 0.607939i | \(0.791997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.0823 | −1.57580 | −0.787899 | − | 0.615805i | \(-0.788831\pi\) | ||||
−0.787899 | + | 0.615805i | \(0.788831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.7358 | 1.04947 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.62772 | + | 2.81929i | 0.0636976 | + | 0.110327i | 0.896116 | − | 0.443821i | \(-0.146377\pi\) |
−0.832418 | + | 0.554148i | \(0.813044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.88345 | + | 3.26223i | −0.0735924 | + | 0.127466i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.58278 | + | 13.1338i | −0.295383 | + | 0.511619i | −0.975074 | − | 0.221880i | \(-0.928781\pi\) |
0.679691 | + | 0.733499i | \(0.262114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1447 | − | 17.5711i | −0.394582 | − | 0.683435i | 0.598466 | − | 0.801148i | \(-0.295777\pi\) |
−0.993048 | + | 0.117713i | \(0.962444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.6328 | −0.567437 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.0429 | 1.31815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.79290 | − | 8.30155i | −0.185028 | − | 0.320478i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6256 | − | 20.1361i | 0.448134 | − | 0.776191i | −0.550130 | − | 0.835079i | \(-0.685422\pi\) |
0.998265 | + | 0.0588875i | \(0.0187553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6380 | − | 27.0859i | 0.601018 | − | 1.04099i | −0.391649 | − | 0.920115i | \(-0.628095\pi\) |
0.992667 | − | 0.120879i | \(-0.0385714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.7380 | − | 63.6320i | −1.40987 | − | 2.44197i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.1812 | −0.925269 | −0.462635 | − | 0.886549i | \(-0.653096\pi\) | ||||
−0.462635 | + | 0.886549i | \(0.653096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.12400 | −0.233986 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.13101 | + | 7.15512i | 0.157379 | + | 0.272588i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.03942 | − | 15.6567i | 0.343876 | − | 0.595610i | −0.641273 | − | 0.767313i | \(-0.721593\pi\) |
0.985149 | + | 0.171702i | \(0.0549268\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.66578 | + | 2.88521i | −0.0631866 | + | 0.109442i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.702872 | + | 1.21741i | 0.0266232 | + | 0.0461127i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.2240 | 0.650541 | 0.325271 | − | 0.945621i | \(-0.394545\pi\) | ||||
0.325271 | + | 0.945621i | \(0.394545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.7625 | −0.896219 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.8325 | − | 36.0830i | −0.783487 | − | 1.35704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.3258 | − | 23.0809i | 0.500459 | − | 0.866821i | −0.499541 | − | 0.866290i | \(-0.666498\pi\) |
1.00000 | 0.000530358i | \(-0.000168818\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.5347 | − | 42.4954i | 0.918833 | − | 1.59147i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.16945 | + | 3.75760i | 0.0811330 | + | 0.140526i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.4273 | −0.388875 | −0.194437 | − | 0.980915i | \(-0.562288\pi\) | ||||
−0.194437 | + | 0.980915i | \(0.562288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5096 | 0.577608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.05733 | − | 15.6878i | −0.336381 | − | 0.582629i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5682 | + | 18.3047i | −0.391954 | + | 0.678884i | −0.992707 | − | 0.120550i | \(-0.961534\pi\) |
0.600753 | + | 0.799434i | \(0.294867\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.58498 | − | 4.47731i | 0.0956088 | − | 0.165599i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6473 | − | 27.1020i | −0.577948 | − | 1.00103i | −0.995714 | − | 0.0924806i | \(-0.970520\pi\) |
0.417767 | − | 0.908554i | \(-0.362813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.2308 | 2.21863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.0455 | 1.14203 | 0.571014 | − | 0.820940i | \(-0.306550\pi\) | ||||
0.571014 | + | 0.820940i | \(0.306550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.93131 | − | 15.4695i | −0.327658 | − | 0.567520i | 0.654389 | − | 0.756158i | \(-0.272926\pi\) |
−0.982047 | + | 0.188638i | \(0.939593\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.93765 | − | 5.08817i | 0.107627 | − | 0.186416i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.7363 | + | 28.9881i | −0.611530 | + | 1.05920i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.70046 | − | 8.14144i | −0.171522 | − | 0.297085i | 0.767430 | − | 0.641133i | \(-0.221535\pi\) |
−0.938952 | + | 0.344047i | \(0.888202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.81189 | −0.284304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.7959 | 1.80986 | 0.904931 | − | 0.425558i | \(-0.139922\pi\) | ||||
0.904931 | + | 0.425558i | \(0.139922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.42633 | − | 9.39868i | −0.196704 | − | 0.340702i | 0.750754 | − | 0.660582i | \(-0.229691\pi\) |
−0.947458 | + | 0.319880i | \(0.896357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.02368 | − | 12.1654i | 0.254274 | − | 0.440416i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00281 | + | 6.93307i | −0.144533 | + | 0.250338i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.93798 | + | 5.08873i | 0.105946 | + | 0.183504i | 0.914124 | − | 0.405434i | \(-0.132880\pi\) |
−0.808178 | + | 0.588938i | \(0.799546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.2781 | −0.945159 | −0.472579 | − | 0.881288i | \(-0.656677\pi\) | ||||
−0.472579 | + | 0.881288i | \(0.656677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.1105 | −0.937917 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.86510 | − | 10.1587i | −0.210139 | − | 0.363971i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.6268 | − | 47.8510i | 0.988564 | − | 1.71224i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10761 | + | 7.11459i | −0.146607 | + | 0.253930i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.3824 | − | 28.3752i | −0.583970 | − | 1.01146i | −0.995003 | − | 0.0998447i | \(-0.968165\pi\) |
0.411034 | − | 0.911620i | \(-0.365168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.0402 | 1.13922 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.87032 | 0.101928 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.8586 | − | 46.5205i | −0.951382 | − | 1.64784i | −0.742440 | − | 0.669913i | \(-0.766331\pi\) |
−0.208942 | − | 0.977928i | \(-0.567002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.129461 | − | 0.224233i | 0.00458000 | − | 0.00793279i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.4584 | − | 19.8465i | 0.404358 | − | 0.700368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1602 | − | 19.3301i | −0.393346 | − | 0.681296i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.82729 | 0.204877 | 0.102438 | − | 0.994739i | \(-0.467336\pi\) | ||||
0.102438 | + | 0.994739i | \(0.467336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.5700 | 0.897883 | 0.448942 | − | 0.893561i | \(-0.351801\pi\) | ||||
0.448942 | + | 0.893561i | \(0.351801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.96855 | − | 5.14169i | −0.103984 | − | 0.180105i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.5703 | + | 37.3608i | −0.754648 | + | 1.30709i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.62309 | + | 11.4715i | −0.231147 | + | 0.400359i | −0.958146 | − | 0.286280i | \(-0.907581\pi\) |
0.726999 | + | 0.686639i | \(0.240915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.17425 | + | 8.96206i | 0.180363 | + | 0.312398i | 0.942004 | − | 0.335601i | \(-0.108939\pi\) |
−0.761641 | + | 0.647999i | \(0.775606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.2799 | 1.08771 | 0.543854 | − | 0.839180i | \(-0.316965\pi\) | ||||
0.543854 | + | 0.839180i | \(0.316965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3415 | −0.602297 | −0.301148 | − | 0.953577i | \(-0.597370\pi\) | ||||
−0.301148 | + | 0.953577i | \(0.597370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.25060 | + | 9.09430i | 0.181922 | + | 0.315099i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.22852 | − | 3.85990i | 0.0771209 | − | 0.133577i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.3050 | − | 19.5809i | 0.390293 | − | 0.676008i | −0.602195 | − | 0.798349i | \(-0.705707\pi\) |
0.992488 | + | 0.122341i | \(0.0390402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.11192 | + | 12.3182i | 0.245239 | + | 0.424766i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.67148 | 0.195105 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 75.3164 | 2.58790 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.1233 | − | 31.3904i | −0.621258 | − | 1.07605i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.98508 | + | 6.90236i | −0.136447 | + | 0.236332i | −0.926149 | − | 0.377157i | \(-0.876902\pi\) |
0.789703 | + | 0.613490i | \(0.210235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.886072 | − | 1.53472i | 0.0302676 | − | 0.0524251i | −0.850495 | − | 0.525983i | \(-0.823697\pi\) |
0.880762 | + | 0.473558i | \(0.157031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.441545 | − | 0.764779i | −0.0150653 | − | 0.0260939i | 0.858394 | − | 0.512990i | \(-0.171462\pi\) |
−0.873460 | + | 0.486896i | \(0.838129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.3624 | −1.71436 | −0.857178 | − | 0.515021i | \(-0.827784\pi\) | ||||
−0.857178 | + | 0.515021i | \(0.827784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0425380 | 0.00144633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.2715 | + | 29.9152i | 0.585896 | + | 1.01480i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.01758 | + | 15.6189i | −0.305549 | + | 0.529226i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.2393 | + | 21.1991i | −0.413764 | + | 0.716661i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.6437 | + | 34.0238i | 0.663319 | + | 1.14890i | 0.979738 | + | 0.200283i | \(0.0641862\pi\) |
−0.316419 | + | 0.948620i | \(0.602480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7416 | −1.06940 | −0.534701 | − | 0.845041i | \(-0.679576\pi\) | ||||
−0.534701 | + | 0.845041i | \(0.679576\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5613 | −0.994818 | −0.497409 | − | 0.867516i | \(-0.665715\pi\) | ||||
−0.497409 | + | 0.867516i | \(0.665715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.39404 | + | 4.14660i | 0.0803839 | + | 0.139229i | 0.903415 | − | 0.428767i | \(-0.141052\pi\) |
−0.823031 | + | 0.567997i | \(0.807719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.7307 | + | 72.2797i | −1.39960 | + | 2.42418i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.08028 | + | 1.87111i | −0.0361503 | + | 0.0626141i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.57686 | + | 9.65941i | 0.186414 | + | 0.322878i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.2984 | −0.710340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.69305 | −0.123033 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.37569 | + | 2.38276i | 0.0457294 | + | 0.0792057i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.27487 | − | 12.6004i | 0.241558 | − | 0.418391i | −0.719600 | − | 0.694389i | \(-0.755675\pi\) |
0.961158 | + | 0.275998i | \(0.0890083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.3323 | + | 42.1448i | −0.806166 | + | 1.39632i | 0.109336 | + | 0.994005i | \(0.465128\pi\) |
−0.915501 | + | 0.402315i | \(0.868206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.4506 | + | 47.5459i | 0.908483 | + | 1.57354i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.0198 | −1.09041 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.6958 | 0.880612 | 0.440306 | − | 0.897848i | \(-0.354870\pi\) | ||||
0.440306 | + | 0.897848i | \(0.354870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.27240 | + | 14.3282i | 0.272289 | + | 0.471619i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.64362 | + | 16.7032i | −0.317080 | + | 0.549199i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.27705 | − | 9.14012i | 0.173134 | − | 0.299878i | −0.766380 | − | 0.642388i | \(-0.777944\pi\) |
0.939514 | + | 0.342510i | \(0.111277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.8135 | − | 75.8871i | −1.43593 | − | 2.48710i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.93945 | −0.0634268 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.1990 | −0.561866 | −0.280933 | − | 0.959727i | \(-0.590644\pi\) | ||||
−0.280933 | + | 0.959727i | \(0.590644\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.3051 | − | 33.4373i | −0.629327 | − | 1.09003i | −0.987687 | − | 0.156443i | \(-0.949997\pi\) |
0.358360 | − | 0.933583i | \(-0.383336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.94643 | − | 15.4957i | 0.291336 | − | 0.504609i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.2306 | + | 26.3802i | −0.494929 | + | 0.857243i | −0.999983 | − | 0.00584526i | \(-0.998139\pi\) |
0.505054 | + | 0.863088i | \(0.331473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.43103 | + | 5.94272i | 0.111376 | + | 0.192909i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.78951 | −0.252327 | −0.126163 | − | 0.992009i | \(-0.540266\pi\) | ||||
−0.126163 | + | 0.992009i | \(0.540266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.6071 | −0.343238 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.8409 | − | 46.4897i | −0.866736 | − | 1.50123i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.150268 | − | 0.260272i | 0.00484736 | − | 0.00839587i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.962887 | + | 1.66777i | −0.0309964 | + | 0.0536874i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.3058 | − | 33.4386i | −0.620832 | − | 1.07531i | −0.989331 | − | 0.145685i | \(-0.953462\pi\) |
0.368499 | − | 0.929628i | \(-0.379872\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7257 | 0.504661 | 0.252331 | − | 0.967641i | \(-0.418803\pi\) | ||||
0.252331 | + | 0.967641i | \(0.418803\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.2037 | −0.936229 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.58188 | + | 16.5963i | 0.306551 | + | 0.530963i | 0.977606 | − | 0.210446i | \(-0.0674915\pi\) |
−0.671054 | + | 0.741408i | \(0.734158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.9945 | − | 32.8995i | 0.607067 | − | 1.05147i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.5590 | + | 33.8772i | −0.623835 | + | 1.08051i | 0.364930 | + | 0.931035i | \(0.381093\pi\) |
−0.988765 | + | 0.149479i | \(0.952240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.459158 | + | 0.795285i | 0.0146300 | + | 0.0253399i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65.8052 | −2.09248 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5470 | 0.875060 | 0.437530 | − | 0.899204i | \(-0.355853\pi\) | ||||
0.437530 | + | 0.899204i | \(0.355853\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.86070 | − | 8.41898i | −0.154095 | − | 0.266900i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.6863 | + | 27.1695i | −0.496791 | + | 0.860467i | −0.999993 | − | 0.00370166i | \(-0.998822\pi\) |
0.503202 | + | 0.864169i | \(0.332155\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3456.2.i.i.1153.4 | 12 | ||
3.2 | odd | 2 | 1152.2.i.l.385.2 | yes | 12 | ||
4.3 | odd | 2 | 3456.2.i.j.1153.4 | 12 | |||
8.3 | odd | 2 | 3456.2.i.l.1153.3 | 12 | |||
8.5 | even | 2 | 3456.2.i.k.1153.3 | 12 | |||
9.4 | even | 3 | inner | 3456.2.i.i.2305.4 | 12 | ||
9.5 | odd | 6 | 1152.2.i.l.769.2 | yes | 12 | ||
12.11 | even | 2 | 1152.2.i.j.385.5 | yes | 12 | ||
24.5 | odd | 2 | 1152.2.i.i.385.5 | ✓ | 12 | ||
24.11 | even | 2 | 1152.2.i.k.385.2 | yes | 12 | ||
36.23 | even | 6 | 1152.2.i.j.769.5 | yes | 12 | ||
36.31 | odd | 6 | 3456.2.i.j.2305.4 | 12 | |||
72.5 | odd | 6 | 1152.2.i.i.769.5 | yes | 12 | ||
72.13 | even | 6 | 3456.2.i.k.2305.3 | 12 | |||
72.59 | even | 6 | 1152.2.i.k.769.2 | yes | 12 | ||
72.67 | odd | 6 | 3456.2.i.l.2305.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.i.385.5 | ✓ | 12 | 24.5 | odd | 2 | ||
1152.2.i.i.769.5 | yes | 12 | 72.5 | odd | 6 | ||
1152.2.i.j.385.5 | yes | 12 | 12.11 | even | 2 | ||
1152.2.i.j.769.5 | yes | 12 | 36.23 | even | 6 | ||
1152.2.i.k.385.2 | yes | 12 | 24.11 | even | 2 | ||
1152.2.i.k.769.2 | yes | 12 | 72.59 | even | 6 | ||
1152.2.i.l.385.2 | yes | 12 | 3.2 | odd | 2 | ||
1152.2.i.l.769.2 | yes | 12 | 9.5 | odd | 6 | ||
3456.2.i.i.1153.4 | 12 | 1.1 | even | 1 | trivial | ||
3456.2.i.i.2305.4 | 12 | 9.4 | even | 3 | inner | ||
3456.2.i.j.1153.4 | 12 | 4.3 | odd | 2 | |||
3456.2.i.j.2305.4 | 12 | 36.31 | odd | 6 | |||
3456.2.i.k.1153.3 | 12 | 8.5 | even | 2 | |||
3456.2.i.k.2305.3 | 12 | 72.13 | even | 6 | |||
3456.2.i.l.1153.3 | 12 | 8.3 | odd | 2 | |||
3456.2.i.l.2305.3 | 12 | 72.67 | odd | 6 |