Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(289,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.k (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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.767178 - 1.18804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.865 |
Dual form | 1152.2.k.d.289.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.37608 | − | 2.37608i | −1.06261 | − | 1.06261i | −0.997904 | − | 0.0647108i | \(-0.979388\pi\) |
−0.0647108 | − | 0.997904i | \(-0.520612\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.64575i | 1.37796i | 0.724778 | + | 0.688982i | \(0.241942\pi\) | ||||
−0.724778 | + | 0.688982i | \(0.758058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.841723 | + | 0.841723i | 0.253789 | + | 0.253789i | 0.822522 | − | 0.568733i | \(-0.192566\pi\) |
−0.568733 | + | 0.822522i | \(0.692566\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64575 | − | 2.64575i | 0.733799 | − | 0.733799i | −0.237571 | − | 0.971370i | \(-0.576351\pi\) |
0.971370 | + | 0.237571i | \(0.0763512\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.06871 | −0.744272 | −0.372136 | − | 0.928178i | \(-0.621375\pi\) | ||||
−0.372136 | + | 0.928178i | \(0.621375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.64575 | − | 1.64575i | 0.377561 | − | 0.377561i | −0.492660 | − | 0.870222i | \(-0.663976\pi\) |
0.870222 | + | 0.492660i | \(0.163976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.82087i | − | 1.63076i | −0.578923 | − | 0.815382i | \(-0.696527\pi\) | ||
0.578923 | − | 0.815382i | \(-0.303473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.29150i | 1.25830i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.692633 | + | 0.692633i | −0.128619 | + | 0.128619i | −0.768486 | − | 0.639867i | \(-0.778989\pi\) |
0.639867 | + | 0.768486i | \(0.278989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.354249 | 0.0636249 | 0.0318125 | − | 0.999494i | \(-0.489872\pi\) | ||||
0.0318125 | + | 0.999494i | \(0.489872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.66259 | − | 8.66259i | 1.46425 | − | 1.46425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.64575 | − | 4.64575i | −0.763757 | − | 0.763757i | 0.213242 | − | 0.976999i | \(-0.431598\pi\) |
−0.976999 | + | 0.213242i | \(0.931598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.43560i | − | 1.00507i | −0.864556 | − | 0.502536i | \(-0.832400\pi\) | ||
0.864556 | − | 0.502536i | \(-0.167600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64575 | − | 5.64575i | −0.860969 | − | 0.860969i | 0.130482 | − | 0.991451i | \(-0.458348\pi\) |
−0.991451 | + | 0.130482i | \(0.958348\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1878 | 1.63190 | 0.815951 | − | 0.578121i | \(-0.196214\pi\) | ||||
0.815951 | + | 0.578121i | \(0.196214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29150 | −0.898786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.44479 | − | 5.44479i | −0.747900 | − | 0.747900i | 0.226185 | − | 0.974084i | \(-0.427375\pi\) |
−0.974084 | + | 0.226185i | \(0.927375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.82087 | − | 7.82087i | −1.01819 | − | 1.01819i | −0.999831 | − | 0.0183591i | \(-0.994156\pi\) |
−0.0183591 | − | 0.999831i | \(-0.505844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.64575 | + | 4.64575i | −0.594828 | + | 0.594828i | −0.938932 | − | 0.344104i | \(-0.888183\pi\) |
0.344104 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.5730 | −1.55949 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | − | 4.00000i | 0.488678 | − | 0.488678i | −0.419211 | − | 0.907889i | \(-0.637693\pi\) |
0.907889 | + | 0.419211i | \(0.137693\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36689i | 0.399577i | 0.979839 | + | 0.199788i | \(0.0640254\pi\) | ||||
−0.979839 | + | 0.199788i | \(0.935975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.29150i | − | 0.853406i | −0.904392 | − | 0.426703i | \(-0.859675\pi\) | ||
0.904392 | − | 0.426703i | \(-0.140325\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.06871 | + | 3.06871i | −0.349712 | + | 0.349712i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.35425 | −0.489891 | −0.244946 | − | 0.969537i | \(-0.578770\pi\) | ||||
−0.244946 | + | 0.969537i | \(0.578770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.841723 | + | 0.841723i | −0.0923911 | + | 0.0923911i | −0.751792 | − | 0.659401i | \(-0.770810\pi\) |
0.659401 | + | 0.751792i | \(0.270810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.29150 | + | 7.29150i | 0.790875 | + | 0.790875i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.50432i | − | 1.00746i | −0.863862 | − | 0.503728i | \(-0.831961\pi\) | ||
0.863862 | − | 0.503728i | \(-0.168039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.64575 | + | 9.64575i | 1.01115 | + | 1.01115i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.82087 | −0.802404 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5830 | 1.07454 | 0.537271 | − | 0.843410i | \(-0.319455\pi\) | ||||
0.537271 | + | 0.843410i | \(0.319455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.37608 | − | 2.37608i | −0.236429 | − | 0.236429i | 0.578941 | − | 0.815370i | \(-0.303466\pi\) |
−0.815370 | + | 0.578941i | \(0.803466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.06275i | 0.104715i | 0.998628 | + | 0.0523577i | \(0.0166736\pi\) | ||||
−0.998628 | + | 0.0523577i | \(0.983326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.50432 | + | 9.50432i | 0.918817 | + | 0.918817i | 0.996943 | − | 0.0781266i | \(-0.0248938\pi\) |
−0.0781266 | + | 0.996943i | \(0.524894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35425 | − | 1.35425i | 0.129713 | − | 0.129713i | −0.639269 | − | 0.768983i | \(-0.720763\pi\) |
0.768983 | + | 0.639269i | \(0.220763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.5830 | + | 18.5830i | −1.73287 | + | 1.73287i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 11.1878i | − | 1.02558i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.58301i | − | 0.871182i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.06871 | − | 3.06871i | 0.274474 | − | 0.274474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9373 | 1.32547 | 0.662733 | − | 0.748855i | \(-0.269396\pi\) | ||||
0.662733 | + | 0.748855i | \(0.269396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.68345 | − | 1.68345i | 0.147083 | − | 0.147083i | −0.629730 | − | 0.776814i | \(-0.716835\pi\) |
0.776814 | + | 0.629730i | \(0.216835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9399i | 1.36184i | 0.732358 | + | 0.680920i | \(0.238420\pi\) | ||||
−0.732358 | + | 0.680920i | \(0.761580\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.58301 | + | 6.58301i | 0.558363 | + | 0.558363i | 0.928841 | − | 0.370478i | \(-0.120806\pi\) |
−0.370478 | + | 0.928841i | \(0.620806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.45398 | 0.372460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.29150 | 0.273344 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.76135 | + | 3.76135i | 0.308141 | + | 0.308141i | 0.844188 | − | 0.536047i | \(-0.180083\pi\) |
−0.536047 | + | 0.844188i | \(0.680083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.6458i | − | 1.27323i | −0.771180 | − | 0.636617i | \(-0.780333\pi\) | ||
0.771180 | − | 0.636617i | \(-0.219667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.841723 | − | 0.841723i | −0.0676088 | − | 0.0676088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.35425 | − | 1.35425i | 0.108081 | − | 0.108081i | −0.650998 | − | 0.759079i | \(-0.725650\pi\) |
0.759079 | + | 0.650998i | \(0.225650\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.5129 | 2.24714 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.35425 | − | 6.35425i | 0.497703 | − | 0.497703i | −0.413019 | − | 0.910722i | \(-0.635526\pi\) |
0.910722 | + | 0.413019i | \(0.135526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.45398i | 0.344659i | 0.985039 | + | 0.172330i | \(0.0551294\pi\) | ||||
−0.985039 | + | 0.172330i | \(0.944871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.44479 | − | 5.44479i | 0.413960 | − | 0.413960i | −0.469156 | − | 0.883115i | \(-0.655442\pi\) |
0.883115 | + | 0.469156i | \(0.155442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.9373 | −1.73389 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.50432 | + | 9.50432i | −0.710386 | + | 0.710386i | −0.966616 | − | 0.256230i | \(-0.917520\pi\) |
0.256230 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.64575 | − | 4.64575i | −0.345316 | − | 0.345316i | 0.513045 | − | 0.858361i | \(-0.328517\pi\) |
−0.858361 | + | 0.513045i | \(0.828517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0773i | 1.62316i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58301 | − | 2.58301i | −0.188888 | − | 0.188888i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1878 | −0.809518 | −0.404759 | − | 0.914423i | \(-0.632645\pi\) | ||||
−0.404759 | + | 0.914423i | \(0.632645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8745 | −1.43060 | −0.715299 | − | 0.698818i | \(-0.753710\pi\) | ||||
−0.715299 | + | 0.698818i | \(0.753710\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.81168 | + | 8.81168i | 0.627806 | + | 0.627806i | 0.947516 | − | 0.319709i | \(-0.103585\pi\) |
−0.319709 | + | 0.947516i | \(0.603585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.35425i | 0.592217i | 0.955154 | + | 0.296108i | \(0.0956890\pi\) | ||||
−0.955154 | + | 0.296108i | \(0.904311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.52517 | − | 2.52517i | −0.177232 | − | 0.177232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.2915 | + | 15.2915i | −1.06800 | + | 1.06800i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.77053 | 0.191642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.58301 | − | 6.58301i | 0.453193 | − | 0.453193i | −0.443220 | − | 0.896413i | \(-0.646164\pi\) |
0.896413 | + | 0.443220i | \(0.146164\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.8295i | 1.82976i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.29150i | 0.0876729i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.11905 | + | 8.11905i | −0.546146 | + | 0.546146i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6458 | 1.31558 | 0.657788 | − | 0.753203i | \(-0.271492\pi\) | ||||
0.657788 | + | 0.753203i | \(0.271492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.1669 | + | 18.1669i | −1.20578 | + | 1.20578i | −0.233399 | + | 0.972381i | \(0.574985\pi\) |
−0.972381 | + | 0.233399i | \(0.925015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.06275 | − | 2.06275i | −0.136310 | − | 0.136310i | 0.635659 | − | 0.771970i | \(-0.280728\pi\) |
−0.771970 | + | 0.635659i | \(0.780728\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.7792i | − | 1.42680i | −0.700757 | − | 0.713400i | \(-0.747154\pi\) | ||
0.700757 | − | 0.713400i | \(-0.252846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.5830 | − | 26.5830i | −1.73408 | − | 1.73408i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.4626 | −1.51767 | −0.758835 | − | 0.651283i | \(-0.774231\pi\) | ||||
−0.758835 | + | 0.651283i | \(0.774231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.29150 | 0.598518 | 0.299259 | − | 0.954172i | \(-0.403260\pi\) | ||||
0.299259 | + | 0.954172i | \(0.403260\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.9491 | + | 14.9491i | 0.955063 | + | 0.955063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.70850i | − | 0.554108i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1166 | + | 13.1166i | 0.827911 | + | 0.827911i | 0.987228 | − | 0.159317i | \(-0.0509291\pi\) |
−0.159317 | + | 0.987228i | \(0.550929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.58301 | − | 6.58301i | 0.413870 | − | 0.413870i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.2381 | −1.01290 | −0.506452 | − | 0.862268i | \(-0.669043\pi\) | ||||
−0.506452 | + | 0.862268i | \(0.669043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.9373 | − | 16.9373i | 1.05243 | − | 1.05243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6417i | 0.964511i | 0.876031 | + | 0.482256i | \(0.160182\pi\) | ||||
−0.876031 | + | 0.482256i | \(0.839818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8745i | 1.58946i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.51350 | − | 8.51350i | 0.519077 | − | 0.519077i | −0.398215 | − | 0.917292i | \(-0.630370\pi\) |
0.917292 | + | 0.398215i | \(0.130370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6458 | −0.707429 | −0.353715 | − | 0.935353i | \(-0.615082\pi\) | ||||
−0.353715 | + | 0.935353i | \(0.615082\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.29570 | + | 5.29570i | −0.319343 | + | 0.319343i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.5203 | − | 20.5203i | −1.23294 | − | 1.23294i | −0.962828 | − | 0.270115i | \(-0.912938\pi\) |
−0.270115 | − | 0.962828i | \(-0.587062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.50432i | − | 0.566980i | −0.958975 | − | 0.283490i | \(-0.908508\pi\) | ||
0.958975 | − | 0.283490i | \(-0.0914923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.5830 | + | 18.5830i | 1.10465 | + | 1.10465i | 0.993842 | + | 0.110803i | \(0.0353421\pi\) |
0.110803 | + | 0.993842i | \(0.464658\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.4626 | 1.38495 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.58301 | −0.446059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9491 | + | 14.9491i | 0.873336 | + | 0.873336i | 0.992834 | − | 0.119498i | \(-0.0381286\pi\) |
−0.119498 | + | 0.992834i | \(0.538129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.1660i | 2.16389i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.6921 | − | 20.6921i | −1.19665 | − | 1.19665i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.5830 | − | 20.5830i | 1.18638 | − | 1.18638i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.0773 | 1.26415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | + | 20.0000i | −1.14146 | + | 1.14146i | −0.153277 | + | 0.988183i | \(0.548983\pi\) |
−0.988183 | + | 0.153277i | \(0.951017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6417i | 0.886962i | 0.896284 | + | 0.443481i | \(0.146257\pi\) | ||||
−0.896284 | + | 0.443481i | \(0.853743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.29150i | 0.0730000i | 0.999334 | + | 0.0365000i | \(0.0116209\pi\) | ||||
−0.999334 | + | 0.0365000i | \(0.988379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.37608 | − | 2.37608i | 0.133454 | − | 0.133454i | −0.637224 | − | 0.770678i | \(-0.719918\pi\) |
0.770678 | + | 0.637224i | \(0.219918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.16601 | −0.0652841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.05034 | + | 5.05034i | −0.281008 | + | 0.281008i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.6458 | + | 16.6458i | 0.923340 | + | 0.923340i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.7878i | 2.24870i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | − | 8.00000i | −0.439720 | − | 0.439720i | 0.452198 | − | 0.891918i | \(-0.350640\pi\) |
−0.891918 | + | 0.452198i | \(0.850640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.0086 | −1.03855 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2915 | 0.832981 | 0.416491 | − | 0.909140i | \(-0.363260\pi\) | ||||
0.416491 | + | 0.909140i | \(0.363260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.298179 | + | 0.298179i | 0.0161473 | + | 0.0161473i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.58301i | 0.139469i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.841723 | + | 0.841723i | 0.0451861 | + | 0.0451861i | 0.729339 | − | 0.684153i | \(-0.239828\pi\) |
−0.684153 | + | 0.729339i | \(0.739828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2288 | − | 23.2288i | 1.24341 | − | 1.24341i | 0.284828 | − | 0.958579i | \(-0.408063\pi\) |
0.958579 | − | 0.284828i | \(-0.0919366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.5129 | 1.51759 | 0.758796 | − | 0.651329i | \(-0.225788\pi\) | ||||
0.758796 | + | 0.651329i | \(0.225788\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | − | 8.00000i | 0.424596 | − | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 19.0086i | − | 1.00324i | −0.865089 | − | 0.501619i | \(-0.832738\pi\) | ||
0.865089 | − | 0.501619i | \(-0.167262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5830i | 0.714895i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.3252 | + | 17.3252i | −0.906842 | + | 0.906842i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8118 | 0.668769 | 0.334384 | − | 0.942437i | \(-0.391472\pi\) | ||||
0.334384 | + | 0.942437i | \(0.391472\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.8504 | − | 19.8504i | 1.03058 | − | 1.03058i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.93725 | + | 3.93725i | 0.203863 | + | 0.203863i | 0.801653 | − | 0.597790i | \(-0.203954\pi\) |
−0.597790 | + | 0.801653i | \(0.703954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.66507i | 0.188761i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6458 | + | 13.6458i | 0.700935 | + | 0.700935i | 0.964611 | − | 0.263676i | \(-0.0849350\pi\) |
−0.263676 | + | 0.964611i | \(0.584935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.1878 | 0.571668 | 0.285834 | − | 0.958279i | \(-0.407729\pi\) | ||||
0.285834 | + | 0.958279i | \(0.407729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5830 | 0.743219 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.42642 | − | 7.42642i | −0.376534 | − | 0.376534i | 0.493316 | − | 0.869850i | \(-0.335785\pi\) |
−0.869850 | + | 0.493316i | \(0.835785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.3460 | + | 10.3460i | 0.520566 | + | 0.520566i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9373 | + | 23.9373i | −1.20138 | + | 1.20138i | −0.227628 | + | 0.973748i | \(0.573097\pi\) |
−0.973748 | + | 0.227628i | \(0.926903\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.20614 | −0.459733 | −0.229866 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229866 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.937254 | − | 0.937254i | 0.0466879 | − | 0.0466879i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.82087i | − | 0.387666i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.1660i | − | 0.848805i | −0.905474 | − | 0.424402i | \(-0.860484\pi\) | ||
0.905474 | − | 0.424402i | \(-0.139516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.5129 | − | 28.5129i | 1.40303 | − | 1.40303i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1166 | + | 13.1166i | −0.640786 | + | 0.640786i | −0.950749 | − | 0.309962i | \(-0.899684\pi\) |
0.309962 | + | 0.950749i | \(0.399684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6458 | − | 16.6458i | −0.811264 | − | 0.811264i | 0.173559 | − | 0.984823i | \(-0.444473\pi\) |
−0.984823 | + | 0.173559i | \(0.944473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 19.3068i | − | 0.936518i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9373 | − | 16.9373i | −0.819651 | − | 0.819651i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.08709 | 0.0523632 | 0.0261816 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261816 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.8712 | − | 12.8712i | −0.615713 | − | 0.615713i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 37.5203i | − | 1.79074i | −0.445319 | − | 0.895372i | \(-0.646910\pi\) | ||
0.445319 | − | 0.895372i | \(-0.353090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.2172 | + | 23.2172i | 1.10308 | + | 1.10308i | 0.994036 | + | 0.109048i | \(0.0347803\pi\) |
0.109048 | + | 0.994036i | \(0.465220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.5830 | + | 22.5830i | −1.07054 | + | 1.07054i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.7191 | −1.78007 | −0.890037 | − | 0.455889i | \(-0.849322\pi\) | ||||
−0.890037 | + | 0.455889i | \(0.849322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.41699 | − | 5.41699i | 0.255076 | − | 0.255076i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 45.8381i | − | 2.14892i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.5830i | − | 1.24350i | −0.783216 | − | 0.621750i | \(-0.786422\pi\) | ||
0.783216 | − | 0.621750i | \(-0.213578\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.81168 | + | 8.81168i | −0.410401 | + | 0.410401i | −0.881878 | − | 0.471477i | \(-0.843721\pi\) |
0.471477 | + | 0.881878i | \(0.343721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.9373 | −1.43778 | −0.718888 | − | 0.695126i | \(-0.755349\pi\) | ||||
−0.718888 | + | 0.695126i | \(0.755349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.4331 | − | 11.4331i | 0.529062 | − | 0.529062i | −0.391231 | − | 0.920293i | \(-0.627951\pi\) |
0.920293 | + | 0.391231i | \(0.127951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.5830 | + | 14.5830i | 0.673381 | + | 0.673381i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.50432i | − | 0.437009i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3542 | + | 10.3542i | 0.475086 | + | 0.475086i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.2748 | −0.560852 | −0.280426 | − | 0.959876i | \(-0.590476\pi\) | ||||
−0.280426 | + | 0.959876i | \(0.590476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.5830 | −1.12089 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.1461 | − | 25.1461i | −1.14182 | − | 1.14182i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.2288i | − | 0.826024i | −0.910726 | − | 0.413012i | \(-0.864477\pi\) | ||
0.910726 | − | 0.413012i | \(-0.135523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9583 | − | 13.9583i | −0.629929 | − | 0.629929i | 0.318121 | − | 0.948050i | \(-0.396948\pi\) |
−0.948050 | + | 0.318121i | \(0.896948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.12549 | − | 2.12549i | 0.0957274 | − | 0.0957274i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.2748 | −0.550602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5830 | + | 10.5830i | −0.473760 | + | 0.473760i | −0.903129 | − | 0.429369i | \(-0.858736\pi\) |
0.429369 | + | 0.903129i | \(0.358736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7424i | 1.14780i | 0.818926 | + | 0.573899i | \(0.194570\pi\) | ||||
−0.818926 | + | 0.573899i | \(0.805430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2915i | 0.502465i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.2240 | + | 27.2240i | −1.20668 | + | 1.20668i | −0.234585 | + | 0.972096i | \(0.575373\pi\) |
−0.972096 | + | 0.234585i | \(0.924627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.5830 | 1.17596 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.52517 | − | 2.52517i | 0.111272 | − | 0.111272i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.41699 | + | 9.41699i | 0.414159 | + | 0.414159i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.7105i | − | 0.819720i | −0.912148 | − | 0.409860i | \(-0.865578\pi\) | ||
0.912148 | − | 0.409860i | \(-0.134422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.06275 | − | 3.06275i | −0.133925 | − | 0.133925i | 0.636967 | − | 0.770891i | \(-0.280189\pi\) |
−0.770891 | + | 0.636967i | \(0.780189\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.08709 | −0.0473543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −38.1660 | −1.65939 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.0270 | − | 17.0270i | −0.737522 | − | 0.737522i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 45.1660i | − | 1.95270i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.29570 | − | 5.29570i | −0.228102 | − | 0.228102i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.52026 | + | 8.52026i | −0.366315 | + | 0.366315i | −0.866131 | − | 0.499817i | \(-0.833401\pi\) |
0.499817 | + | 0.866131i | \(0.333401\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.43560 | −0.275671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.937254 | + | 0.937254i | −0.0400741 | + | 0.0400741i | −0.726860 | − | 0.686786i | \(-0.759021\pi\) |
0.686786 | + | 0.726860i | \(0.259021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.27980i | 0.0971229i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.8745i | − | 0.675053i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.7516 | − | 24.7516i | 1.04876 | − | 1.04876i | 0.0500103 | − | 0.998749i | \(-0.484075\pi\) |
0.998749 | − | 0.0500103i | \(-0.0159254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.8745 | −1.26356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.4835 | − | 16.4835i | 0.694695 | − | 0.694695i | −0.268566 | − | 0.963261i | \(-0.586550\pi\) |
0.963261 | + | 0.268566i | \(0.0865498\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9767i | 0.502088i | 0.967976 | + | 0.251044i | \(0.0807739\pi\) | ||||
−0.967976 | + | 0.251044i | \(0.919226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | + | 4.00000i | 0.167395 | + | 0.167395i | 0.785833 | − | 0.618438i | \(-0.212234\pi\) |
−0.618438 | + | 0.785833i | \(0.712234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.2050 | 2.05199 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0405 | 1.45876 | 0.729378 | − | 0.684111i | \(-0.239810\pi\) | ||||
0.729378 | + | 0.684111i | \(0.239810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.06871 | − | 3.06871i | −0.127312 | − | 0.127312i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.16601i | − | 0.379617i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.0086 | − | 19.0086i | −0.784570 | − | 0.784570i | 0.196028 | − | 0.980598i | \(-0.437196\pi\) |
−0.980598 | + | 0.196028i | \(0.937196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.583005 | − | 0.583005i | 0.0240223 | − | 0.0240223i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2748 | −0.504068 | −0.252034 | − | 0.967718i | \(-0.581099\pi\) | ||||
−0.252034 | + | 0.967718i | \(0.581099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.5830 | + | 26.5830i | −1.08980 | + | 1.08980i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.1964i | − | 1.23379i | −0.787045 | − | 0.616896i | \(-0.788390\pi\) | ||
0.787045 | − | 0.616896i | \(-0.211610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.29150i | − | 0.297427i | −0.988880 | − | 0.148713i | \(-0.952487\pi\) | ||
0.988880 | − | 0.148713i | \(-0.0475132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.7700 | + | 22.7700i | −0.925731 | + | 0.925731i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.1033 | 1.79010 | 0.895048 | − | 0.445970i | \(-0.147141\pi\) | ||||
0.895048 | + | 0.445970i | \(0.147141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6000 | − | 29.6000i | 1.19749 | − | 1.19749i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3542 | − | 21.3542i | −0.862490 | − | 0.862490i | 0.129137 | − | 0.991627i | \(-0.458779\pi\) |
−0.991627 | + | 0.129137i | \(0.958779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.7424i | − | 1.03635i | −0.855274 | − | 0.518175i | \(-0.826611\pi\) | ||
0.855274 | − | 0.518175i | \(-0.173389\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1660 | + | 21.1660i | 0.850734 | + | 0.850734i | 0.990224 | − | 0.139490i | \(-0.0445462\pi\) |
−0.139490 | + | 0.990224i | \(0.544546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.6504 | 1.38824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.8745 | 0.674980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2565 | + | 14.2565i | 0.568443 | + | 0.568443i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2288i | 0.725675i | 0.931852 | + | 0.362838i | \(0.118192\pi\) | ||||
−0.931852 | + | 0.362838i | \(0.881808\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.4921 | − | 35.4921i | −1.40846 | − | 1.40846i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.6458 | + | 16.6458i | −0.659529 | + | 0.659529i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.20614 | −0.363621 | −0.181810 | − | 0.983334i | \(-0.558196\pi\) | ||||
−0.181810 | + | 0.983334i | \(0.558196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.64575 | − | 1.64575i | 0.0649021 | − | 0.0649021i | −0.673911 | − | 0.738813i | \(-0.735387\pi\) |
0.738813 | + | 0.673911i | \(0.235387\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.82087i | − | 0.307470i | −0.988112 | − | 0.153735i | \(-0.950870\pi\) | ||
0.988112 | − | 0.153735i | \(-0.0491302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.1660i | − | 0.516811i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.42642 | − | 7.42642i | 0.290618 | − | 0.290618i | −0.546706 | − | 0.837324i | \(-0.684119\pi\) |
0.837324 | + | 0.546706i | \(0.184119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0590 | − | 24.0590i | 0.937204 | − | 0.937204i | −0.0609372 | − | 0.998142i | \(-0.519409\pi\) |
0.998142 | + | 0.0609372i | \(0.0194089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2288 | + | 29.2288i | 1.13687 | + | 1.13687i | 0.989009 | + | 0.147858i | \(0.0472380\pi\) |
0.147858 | + | 0.989009i | \(0.452762\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 28.5129i | − | 1.10568i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.41699 | + | 5.41699i | 0.209747 | + | 0.209747i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.82087 | −0.301921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.74297 | + | 5.74297i | 0.220720 | + | 0.220720i | 0.808802 | − | 0.588081i | \(-0.200117\pi\) |
−0.588081 | + | 0.808802i | \(0.700117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.5830i | 1.48068i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4921 | + | 35.4921i | 1.35807 | + | 1.35807i | 0.876298 | + | 0.481769i | \(0.160006\pi\) |
0.481769 | + | 0.876298i | \(0.339994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.8745 | − | 37.8745i | 1.44711 | − | 1.44711i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.8111 | −1.09762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.64575 | − | 1.64575i | 0.0626073 | − | 0.0626073i | −0.675110 | − | 0.737717i | \(-0.735904\pi\) |
0.737717 | + | 0.675110i | \(0.235904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 31.2835i | − | 1.18665i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7490i | 0.748047i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.6326 | − | 16.6326i | 0.628203 | − | 0.628203i | −0.319413 | − | 0.947616i | \(-0.603486\pi\) |
0.947616 | + | 0.319413i | \(0.103486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.2915 | −0.576730 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.66259 | − | 8.66259i | 0.325790 | − | 0.325790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.2288 | + | 35.2288i | 1.32304 | + | 1.32304i | 0.911299 | + | 0.411744i | \(0.135080\pi\) |
0.411744 | + | 0.911299i | \(0.364920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.77053i | − | 0.103757i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5830 | − | 10.5830i | −0.395782 | − | 0.395782i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1007 | 0.376692 | 0.188346 | − | 0.982103i | \(-0.439687\pi\) | ||||
0.188346 | + | 0.982103i | \(0.439687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.87451 | −0.144294 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.35770 | − | 4.35770i | −0.161841 | − | 0.161841i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3948i | 1.31272i | 0.754448 | + | 0.656360i | \(0.227905\pi\) | ||||
−0.754448 | + | 0.656360i | \(0.772095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.3252 | + | 17.3252i | 0.640795 | + | 0.640795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.35425 | − | 7.35425i | 0.271635 | − | 0.271635i | −0.558123 | − | 0.829758i | \(-0.688478\pi\) |
0.829758 | + | 0.558123i | \(0.188478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.73378 | 0.248042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1660 | − | 33.1660i | 1.22003 | − | 1.22003i | 0.252411 | − | 0.967620i | \(-0.418776\pi\) |
0.967620 | − | 0.252411i | \(-0.0812236\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5547i | 0.533958i | 0.963702 | + | 0.266979i | \(0.0860255\pi\) | ||||
−0.963702 | + | 0.266979i | \(0.913974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 17.8745i | − | 0.654871i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.6504 | + | 34.6504i | −1.26610 | + | 1.26610i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.93725 | 0.107182 | 0.0535910 | − | 0.998563i | \(-0.482933\pi\) | ||||
0.0535910 | + | 0.998563i | \(0.482933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.1755 | + | 37.1755i | −1.35296 | + | 1.35296i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.2288 | − | 19.2288i | −0.698881 | − | 0.698881i | 0.265288 | − | 0.964169i | \(-0.414533\pi\) |
−0.964169 | + | 0.265288i | \(0.914533\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.43560i | − | 0.233290i | −0.993174 | − | 0.116645i | \(-0.962786\pi\) | ||
0.993174 | − | 0.116645i | \(-0.0372140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.93725 | + | 4.93725i | 0.178741 | + | 0.178741i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.3842 | −1.49430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.70850 | 0.241915 | 0.120957 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120957 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6509 | − | 14.6509i | −0.526957 | − | 0.526957i | 0.392707 | − | 0.919664i | \(-0.371539\pi\) |
−0.919664 | + | 0.392707i | \(0.871539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22876i | 0.0800593i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5914 | − | 10.5914i | −0.379476 | − | 0.379476i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.83399 | + | 2.83399i | −0.101408 | + | 0.101408i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.43560 | −0.229697 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.2288 | + | 20.2288i | −0.721077 | + | 0.721077i | −0.968825 | − | 0.247747i | \(-0.920310\pi\) |
0.247747 | + | 0.968825i | \(0.420310\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5830i | 0.872968i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6509 | − | 14.6509i | 0.518962 | − | 0.518962i | −0.398295 | − | 0.917257i | \(-0.630398\pi\) |
0.917257 | + | 0.398295i | \(0.130398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3320 | −1.21458 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.13742 | − | 6.13742i | 0.216585 | − | 0.216585i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −67.7490 | − | 67.7490i | −2.38784 | − | 2.38784i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.4529i | 1.56288i | 0.623981 | + | 0.781440i | \(0.285514\pi\) | ||||
−0.623981 | + | 0.781440i | \(0.714486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3542 | − | 10.3542i | −0.363587 | − | 0.363587i | 0.501545 | − | 0.865132i | \(-0.332765\pi\) |
−0.865132 | + | 0.501545i | \(0.832765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.1964 | −1.05773 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.5830 | −0.650137 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.8890 | − | 30.8890i | −1.07803 | − | 1.07803i | −0.996686 | − | 0.0813488i | \(-0.974077\pi\) |
−0.0813488 | − | 0.996686i | \(-0.525923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.77124i | − | 0.201173i | −0.994928 | − | 0.100586i | \(-0.967928\pi\) | ||
0.994928 | − | 0.100586i | \(-0.0320719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.82087 | − | 7.82087i | −0.271958 | − | 0.271958i | 0.557930 | − | 0.829888i | \(-0.311596\pi\) |
−0.829888 | + | 0.557930i | \(0.811596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.35425 | + | 9.35425i | −0.324886 | + | 0.324886i | −0.850638 | − | 0.525752i | \(-0.823784\pi\) |
0.525752 | + | 0.850638i | \(0.323784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.3068 | 0.668941 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5830 | − | 10.5830i | 0.366240 | − | 0.366240i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.1914i | 1.38756i | 0.720186 | + | 0.693781i | \(0.244057\pi\) | ||||
−0.720186 | + | 0.693781i | \(0.755943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0405i | 0.966914i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.37608 | + | 2.37608i | −0.0817396 | + | 0.0817396i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.9373 | 1.20046 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.3338 | + | 36.3338i | −1.24551 | + | 1.24551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.93725 | + | 3.93725i | 0.134809 | + | 0.134809i | 0.771291 | − | 0.636482i | \(-0.219611\pi\) |
−0.636482 | + | 0.771291i | \(0.719611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.9399i | 0.544497i | 0.962227 | + | 0.272249i | \(0.0877673\pi\) | ||||
−0.962227 | + | 0.272249i | \(0.912233\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2288 | − | 32.2288i | −1.09963 | − | 1.09963i | −0.994453 | − | 0.105178i | \(-0.966459\pi\) |
−0.105178 | − | 0.994453i | \(-0.533541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.3619 | 0.454846 | 0.227423 | − | 0.973796i | \(-0.426970\pi\) | ||||
0.227423 | + | 0.973796i | \(0.426970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.8745 | −0.879760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.66507 | − | 3.66507i | −0.124329 | − | 0.124329i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 21.1660i | − | 0.717183i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1878 | + | 11.1878i | 0.378215 | + | 0.378215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.06275 | − | 6.06275i | 0.204724 | − | 0.204724i | −0.597296 | − | 0.802021i | \(-0.703758\pi\) |
0.802021 | + | 0.597296i | \(0.203758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.7878 | 1.37418 | 0.687088 | − | 0.726574i | \(-0.258889\pi\) | ||||
0.687088 | + | 0.726574i | \(0.258889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.3948 | − | 33.3948i | 1.12382 | − | 1.12382i | 0.132662 | − | 0.991161i | \(-0.457648\pi\) |
0.991161 | − | 0.132662i | \(-0.0423525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.0086i | − | 0.638247i | −0.947713 | − | 0.319124i | \(-0.896611\pi\) | ||
0.947713 | − | 0.319124i | \(-0.103389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.4575i | 1.82645i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.4123 | − | 18.4123i | 0.616143 | − | 0.616143i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.1660 | 1.50973 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.245364 | + | 0.245364i | −0.00818336 | + | 0.00818336i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7085 | + | 16.7085i | 0.556641 | + | 0.556641i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0773i | 0.733876i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.1033 | − | 42.1033i | −1.39802 | − | 1.39802i | −0.805722 | − | 0.592294i | \(-0.798222\pi\) |
−0.592294 | − | 0.805722i | \(-0.701778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.8381 | 1.51869 | 0.759343 | − | 0.650691i | \(-0.225521\pi\) | ||||
0.759343 | + | 0.650691i | \(0.225521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.41699 | −0.0468957 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.13742 | + | 6.13742i | 0.202676 | + | 0.202676i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.1033i | − | 0.531198i | −0.964084 | − | 0.265599i | \(-0.914430\pi\) | ||
0.964084 | − | 0.265599i | \(-0.0855697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.90796 | + | 8.90796i | 0.293209 | + | 0.293209i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.2288 | − | 29.2288i | 0.961036 | − | 0.961036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3068 | −0.633436 | −0.316718 | − | 0.948520i | \(-0.602581\pi\) | ||||
−0.316718 | + | 0.948520i | \(0.602581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.3542 | + | 10.3542i | −0.339347 | + | 0.339347i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.2748i | 0.401430i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1660i | 0.364778i | 0.983226 | + | 0.182389i | \(0.0583830\pi\) | ||||
−0.983226 | + | 0.182389i | \(0.941617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.8387 | − | 25.8387i | 0.842317 | − | 0.842317i | −0.146843 | − | 0.989160i | \(-0.546911\pi\) |
0.989160 | + | 0.146843i | \(0.0469111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50.3320 | −1.63904 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.50432 | + | 9.50432i | −0.308849 | + | 0.308849i | −0.844463 | − | 0.535614i | \(-0.820080\pi\) |
0.535614 | + | 0.844463i | \(0.320080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.2915 | − | 19.2915i | −0.626229 | − | 0.626229i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.8479i | − | 0.804902i | −0.915442 | − | 0.402451i | \(-0.868158\pi\) | ||
0.915442 | − | 0.402451i | \(-0.131842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5830 | + | 26.5830i | 0.860206 | + | 0.860206i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −58.1130 | −1.87657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8745 | −0.995952 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.2234 | + | 47.2234i | 1.52018 | + | 1.52018i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3948i | 0.752325i | 0.926554 | + | 0.376162i | \(0.122757\pi\) | ||||
−0.926554 | + | 0.376162i | \(0.877243\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.4418 | + | 30.4418i | 0.976923 | + | 0.976923i | 0.999740 | − | 0.0228172i | \(-0.00726356\pi\) |
−0.0228172 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | + | 24.0000i | −0.769405 | + | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.8565 | 1.40309 | 0.701547 | − | 0.712623i | \(-0.252493\pi\) | ||||
0.701547 | + | 0.712623i | \(0.252493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | − | 8.00000i | 0.255681 | − | 0.255681i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.73378i | − | 0.214774i | −0.994217 | − | 0.107387i | \(-0.965752\pi\) | ||
0.994217 | − | 0.107387i | \(-0.0342484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 41.8745i | − | 1.33423i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.1547 | + | 44.1547i | −1.40404 | + | 1.40404i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9373 | −0.601562 | −0.300781 | − | 0.953693i | \(-0.597247\pi\) | ||||
−0.300781 | + | 0.953693i | \(0.597247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.8504 | − | 19.8504i | 0.629299 | − | 0.629299i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.520259 | + | 0.520259i | 0.0164768 | + | 0.0164768i | 0.715297 | − | 0.698820i | \(-0.246291\pi\) |
−0.698820 | + | 0.715297i | \(0.746291\pi\) | |||||||
\(998\) | 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 | 1152.2.k.d.865.1 | 8 | ||
3.2 | odd | 2 | inner | 1152.2.k.d.865.4 | 8 | ||
4.3 | odd | 2 | 1152.2.k.e.865.1 | 8 | |||
8.3 | odd | 2 | 144.2.k.c.37.3 | yes | 8 | ||
8.5 | even | 2 | 576.2.k.c.433.4 | 8 | |||
12.11 | even | 2 | 1152.2.k.e.865.4 | 8 | |||
16.3 | odd | 4 | 1152.2.k.e.289.1 | 8 | |||
16.5 | even | 4 | 576.2.k.c.145.4 | 8 | |||
16.11 | odd | 4 | 144.2.k.c.109.3 | yes | 8 | ||
16.13 | even | 4 | inner | 1152.2.k.d.289.1 | 8 | ||
24.5 | odd | 2 | 576.2.k.c.433.1 | 8 | |||
24.11 | even | 2 | 144.2.k.c.37.2 | ✓ | 8 | ||
32.3 | odd | 8 | 9216.2.a.bq.1.7 | 8 | |||
32.13 | even | 8 | 9216.2.a.bt.1.2 | 8 | |||
32.19 | odd | 8 | 9216.2.a.bq.1.2 | 8 | |||
32.29 | even | 8 | 9216.2.a.bt.1.7 | 8 | |||
48.5 | odd | 4 | 576.2.k.c.145.1 | 8 | |||
48.11 | even | 4 | 144.2.k.c.109.2 | yes | 8 | ||
48.29 | odd | 4 | inner | 1152.2.k.d.289.4 | 8 | ||
48.35 | even | 4 | 1152.2.k.e.289.4 | 8 | |||
96.29 | odd | 8 | 9216.2.a.bt.1.1 | 8 | |||
96.35 | even | 8 | 9216.2.a.bq.1.1 | 8 | |||
96.77 | odd | 8 | 9216.2.a.bt.1.8 | 8 | |||
96.83 | even | 8 | 9216.2.a.bq.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.2 | ✓ | 8 | 24.11 | even | 2 | ||
144.2.k.c.37.3 | yes | 8 | 8.3 | odd | 2 | ||
144.2.k.c.109.2 | yes | 8 | 48.11 | even | 4 | ||
144.2.k.c.109.3 | yes | 8 | 16.11 | odd | 4 | ||
576.2.k.c.145.1 | 8 | 48.5 | odd | 4 | |||
576.2.k.c.145.4 | 8 | 16.5 | even | 4 | |||
576.2.k.c.433.1 | 8 | 24.5 | odd | 2 | |||
576.2.k.c.433.4 | 8 | 8.5 | even | 2 | |||
1152.2.k.d.289.1 | 8 | 16.13 | even | 4 | inner | ||
1152.2.k.d.289.4 | 8 | 48.29 | odd | 4 | inner | ||
1152.2.k.d.865.1 | 8 | 1.1 | even | 1 | trivial | ||
1152.2.k.d.865.4 | 8 | 3.2 | odd | 2 | inner | ||
1152.2.k.e.289.1 | 8 | 16.3 | odd | 4 | |||
1152.2.k.e.289.4 | 8 | 48.35 | even | 4 | |||
1152.2.k.e.865.1 | 8 | 4.3 | odd | 2 | |||
1152.2.k.e.865.4 | 8 | 12.11 | even | 2 | |||
9216.2.a.bq.1.1 | 8 | 96.35 | even | 8 | |||
9216.2.a.bq.1.2 | 8 | 32.19 | odd | 8 | |||
9216.2.a.bq.1.7 | 8 | 32.3 | odd | 8 | |||
9216.2.a.bq.1.8 | 8 | 96.83 | even | 8 | |||
9216.2.a.bt.1.1 | 8 | 96.29 | odd | 8 | |||
9216.2.a.bt.1.2 | 8 | 32.13 | even | 8 | |||
9216.2.a.bt.1.7 | 8 | 32.29 | even | 8 | |||
9216.2.a.bt.1.8 | 8 | 96.77 | odd | 8 |