Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(25,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.4 | ||
Character | \(\chi\) | \(=\) | 504.121 |
Dual form | 504.2.q.d.25.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.13364 | + | 1.30952i | −0.654509 | + | 0.756054i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.170100 | − | 0.294622i | −0.0760711 | − | 0.131759i | 0.825480 | − | 0.564431i | \(-0.190904\pi\) |
−0.901552 | + | 0.432672i | \(0.857571\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63360 | − | 0.253251i | −0.995408 | − | 0.0957197i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.429705 | − | 2.96907i | −0.143235 | − | 0.989689i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.335794 | − | 0.581612i | 0.101246 | − | 0.175363i | −0.810952 | − | 0.585112i | \(-0.801051\pi\) |
0.912198 | + | 0.409749i | \(0.134384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.62370 | − | 2.81233i | 0.450333 | − | 0.780000i | −0.548073 | − | 0.836430i | \(-0.684639\pi\) |
0.998407 | + | 0.0564303i | \(0.0179719\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.578647 | + | 0.111246i | 0.149406 | + | 0.0287236i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.10014 | − | 1.90550i | −0.266824 | − | 0.462152i | 0.701216 | − | 0.712949i | \(-0.252641\pi\) |
−0.968040 | + | 0.250796i | \(0.919308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.242085 | − | 0.419303i | 0.0555380 | − | 0.0961946i | −0.836920 | − | 0.547326i | \(-0.815646\pi\) |
0.892458 | + | 0.451131i | \(0.148979\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.31720 | − | 3.16167i | 0.723873 | − | 0.689933i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.09495 | − | 3.62856i | −0.436827 | − | 0.756607i | 0.560616 | − | 0.828076i | \(-0.310565\pi\) |
−0.997443 | + | 0.0714692i | \(0.977231\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44213 | − | 4.22990i | 0.488426 | − | 0.845979i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.37520 | + | 2.80315i | 0.842007 | + | 0.539467i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.478868 | + | 0.829424i | 0.0889235 | + | 0.154020i | 0.907056 | − | 0.421009i | \(-0.138324\pi\) |
−0.818133 | + | 0.575029i | \(0.804991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.08263 | 0.374052 | 0.187026 | − | 0.982355i | \(-0.440115\pi\) | ||||
0.187026 | + | 0.982355i | \(0.440115\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.380964 | + | 1.09907i | 0.0663174 | + | 0.191324i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.373363 | + | 0.818995i | 0.0631098 | + | 0.138435i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.81613 | − | 8.34178i | 0.791767 | − | 1.37138i | −0.133105 | − | 0.991102i | \(-0.542495\pi\) |
0.924872 | − | 0.380278i | \(-0.124172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.84212 | + | 5.31445i | 0.294975 | + | 0.850993i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.90207 | + | 6.75858i | −0.609400 | + | 1.05551i | 0.381939 | + | 0.924188i | \(0.375256\pi\) |
−0.991339 | + | 0.131325i | \(0.958077\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.66119 | − | 6.34136i | −0.558326 | − | 0.967048i | −0.997636 | − | 0.0687132i | \(-0.978111\pi\) |
0.439311 | − | 0.898335i | \(-0.355223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.801659 | + | 0.631639i | −0.119504 | + | 0.0941592i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.69901 | −0.393692 | −0.196846 | − | 0.980434i | \(-0.563070\pi\) | ||||
−0.196846 | + | 0.980434i | \(0.563070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.87173 | + | 1.33392i | 0.981675 | + | 0.190560i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.74247 | + | 0.719498i | 0.524051 | + | 0.100750i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.12335 | − | 10.6059i | −0.841107 | − | 1.45684i | −0.888960 | − | 0.457985i | \(-0.848571\pi\) |
0.0478535 | − | 0.998854i | \(-0.484762\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.228474 | −0.0308075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.274649 | + | 0.792355i | 0.0363782 | + | 0.104950i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.94297 | −0.643520 | −0.321760 | − | 0.946821i | \(-0.604274\pi\) | ||||
−0.321760 | + | 0.946821i | \(0.604274\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.52119 | −0.450842 | −0.225421 | − | 0.974261i | \(-0.572376\pi\) | ||||
−0.225421 | + | 0.974261i | \(0.572376\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.379756 | + | 7.92816i | 0.0478447 | + | 0.998855i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.10477 | −0.137029 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3202 | 1.50516 | 0.752579 | − | 0.658502i | \(-0.228810\pi\) | ||||
0.752579 | + | 0.658502i | \(0.228810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.12661 | + | 1.37011i | 0.857943 | + | 0.164941i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.57304 | −0.661398 | −0.330699 | − | 0.943736i | \(-0.607285\pi\) | ||||
−0.330699 | + | 0.943736i | \(0.607285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.71686 | − | 6.43779i | −0.435026 | − | 0.753487i | 0.562272 | − | 0.826952i | \(-0.309927\pi\) |
−0.997298 | + | 0.0734657i | \(0.976594\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.77064 | + | 7.99322i | 0.319926 | + | 0.922978i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.03164 | + | 1.44669i | −0.117566 | + | 0.164866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0127 | −1.12652 | −0.563260 | − | 0.826279i | \(-0.690453\pi\) | ||||
−0.563260 | + | 0.826279i | \(0.690453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.63071 | + | 2.55165i | −0.958967 | + | 0.283516i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.47376 | + | 4.28468i | 0.271530 | + | 0.470305i | 0.969254 | − | 0.246063i | \(-0.0791369\pi\) |
−0.697723 | + | 0.716367i | \(0.745804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.374269 | + | 0.648252i | −0.0405951 | + | 0.0703128i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.62902 | − | 0.313182i | −0.174649 | − | 0.0335766i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.52177 | + | 14.7601i | −0.903306 | + | 1.56457i | −0.0801310 | + | 0.996784i | \(0.525534\pi\) |
−0.823175 | + | 0.567788i | \(0.807799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.98840 | + | 6.99536i | −0.522927 | + | 0.733313i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.36096 | + | 2.72725i | −0.244820 | + | 0.282803i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.164714 | −0.0168993 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.23657 | + | 7.33795i | 0.430159 | + | 0.745056i | 0.996887 | − | 0.0788485i | \(-0.0251243\pi\) |
−0.566728 | + | 0.823905i | \(0.691791\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.87114 | − | 0.747072i | −0.188056 | − | 0.0750836i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.28693 | − | 3.96107i | 0.227558 | − | 0.394141i | −0.729526 | − | 0.683953i | \(-0.760259\pi\) |
0.957084 | + | 0.289812i | \(0.0935927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.903563 | + | 1.56502i | 0.0890307 | + | 0.154206i | 0.907102 | − | 0.420912i | \(-0.138290\pi\) |
−0.818071 | + | 0.575117i | \(0.804956\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.49575 | − | 0.439521i | −0.145971 | − | 0.0428928i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.88188 | − | 6.72361i | 0.375275 | − | 0.649996i | −0.615093 | − | 0.788454i | \(-0.710882\pi\) |
0.990368 | + | 0.138459i | \(0.0442149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.07178 | − | 1.85638i | −0.102658 | − | 0.177809i | 0.810121 | − | 0.586263i | \(-0.199401\pi\) |
−0.912779 | + | 0.408454i | \(0.866068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.46399 | + | 15.7634i | 0.518619 | + | 1.49620i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.91006 | + | 13.7006i | −0.744116 | + | 1.28885i | 0.206491 | + | 0.978449i | \(0.433796\pi\) |
−0.950607 | + | 0.310398i | \(0.899538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.712702 | + | 1.23444i | −0.0664598 | + | 0.115112i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.04771 | − | 3.61240i | −0.836461 | − | 0.333966i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.41477 | + | 5.29695i | 0.221362 | + | 0.485571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.27449 | + | 9.13568i | 0.479499 | + | 0.830516i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.42697 | − | 12.7717i | −0.399166 | − | 1.15158i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.36263 | −0.300763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8820 | −1.23183 | −0.615915 | − | 0.787812i | \(-0.711214\pi\) | ||||
−0.615915 | + | 0.787812i | \(0.711214\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4546 | + | 2.39443i | 1.09657 | + | 0.210818i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.08769 | + | 3.61599i | 0.182402 | + | 0.315930i | 0.942698 | − | 0.333647i | \(-0.108279\pi\) |
−0.760296 | + | 0.649577i | \(0.774946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.743743 | + | 1.04297i | −0.0644907 | + | 0.0904369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0816493 | − | 1.76585i | 0.00702725 | − | 0.151980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.38043 | − | 11.0512i | 0.545117 | − | 0.944170i | −0.453483 | − | 0.891265i | \(-0.649819\pi\) |
0.998600 | − | 0.0529051i | \(-0.0168481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.95986 | − | 10.3228i | 0.505509 | − | 0.875567i | −0.494471 | − | 0.869194i | \(-0.664638\pi\) |
0.999980 | − | 0.00637264i | \(-0.00202849\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.05972 | − | 3.53442i | 0.257675 | − | 0.297652i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.09046 | − | 1.88873i | −0.0911885 | − | 0.157943i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.162911 | − | 0.282170i | 0.0135290 | − | 0.0234329i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.53689 | + | 7.48650i | −0.786590 | + | 0.617476i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.37548 | + | 9.31060i | 0.440376 | + | 0.762754i | 0.997717 | − | 0.0675295i | \(-0.0215117\pi\) |
−0.557341 | + | 0.830284i | \(0.688178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.29050 | − | 2.23521i | 0.105019 | − | 0.181899i | −0.808727 | − | 0.588184i | \(-0.799843\pi\) |
0.913746 | + | 0.406286i | \(0.133176\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.18483 | + | 4.08520i | −0.419168 | + | 0.330269i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.354256 | − | 0.613589i | −0.0284545 | − | 0.0492846i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.99693 | 0.638224 | 0.319112 | − | 0.947717i | \(-0.396615\pi\) | ||||
0.319112 | + | 0.947717i | \(0.396615\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.8304 | + | 4.00469i | 1.65196 | + | 0.317593i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.59833 | + | 10.0867i | 0.362399 | + | 0.794946i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.13306 | − | 7.15868i | 0.323727 | − | 0.560711i | −0.657527 | − | 0.753431i | \(-0.728398\pi\) |
0.981254 | + | 0.192720i | \(0.0617309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.259008 | − | 0.299192i | 0.0201638 | − | 0.0232921i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.99384 | − | 15.5778i | 0.695964 | − | 1.20544i | −0.273891 | − | 0.961761i | \(-0.588311\pi\) |
0.969855 | − | 0.243684i | \(-0.0783560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.22720 | + | 2.12557i | 0.0944000 | + | 0.163506i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.34896 | − | 0.538588i | −0.103158 | − | 0.0411869i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9983 | −1.29236 | −0.646179 | − | 0.763186i | \(-0.723634\pi\) | ||||
−0.646179 | + | 0.763186i | \(0.723634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.50283 | + | 10.5214i | −0.567161 | + | 0.795343i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.60356 | − | 6.47293i | 0.421190 | − | 0.486536i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.65073 | − | 16.7156i | −0.721329 | − | 1.24938i | −0.960467 | − | 0.278393i | \(-0.910198\pi\) |
0.239138 | − | 0.970986i | \(-0.423135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.9640 | 1.63257 | 0.816287 | − | 0.577646i | \(-0.196029\pi\) | ||||
0.816287 | + | 0.577646i | \(0.196029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.99177 | − | 4.61108i | 0.295080 | − | 0.340861i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.27690 | −0.240922 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.47768 | −0.108059 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.8126 | − | 8.49041i | −0.786503 | − | 0.617587i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.65744 | 0.481716 | 0.240858 | − | 0.970560i | \(-0.422571\pi\) | ||||
0.240858 | + | 0.970560i | \(0.422571\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.34906 | 0.457015 | 0.228508 | − | 0.973542i | \(-0.426615\pi\) | ||||
0.228508 | + | 0.973542i | \(0.426615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.25241 | − | 1.44672i | 0.0896870 | − | 0.103602i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8112 | 1.69648 | 0.848239 | − | 0.529614i | \(-0.177663\pi\) | ||||
0.848239 | + | 0.529614i | \(0.177663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.4771 | − | 18.1468i | −0.742701 | − | 1.28640i | −0.951261 | − | 0.308386i | \(-0.900211\pi\) |
0.208561 | − | 0.978009i | \(-0.433122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9668 | + | 16.1337i | −0.985140 | + | 1.13798i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.05110 | − | 2.30565i | −0.0737725 | − | 0.161825i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.65497 | 0.185431 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.87322 | + | 7.77926i | −0.686236 | + | 0.540696i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.162581 | − | 0.281599i | −0.0112460 | − | 0.0194786i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.32431 | + | 10.9540i | −0.435384 | + | 0.754106i | −0.997327 | − | 0.0730693i | \(-0.976721\pi\) |
0.561943 | + | 0.827176i | \(0.310054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.31784 | − | 7.29803i | 0.432891 | − | 0.500053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.24554 | + | 2.15733i | −0.0849448 | + | 0.147129i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.48482 | − | 0.527427i | −0.372334 | − | 0.0358041i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.6440 | + | 2.43084i | 0.854405 | + | 0.164261i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.14520 | −0.480638 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.34432 | − | 2.32843i | −0.0900225 | − | 0.155924i | 0.817498 | − | 0.575932i | \(-0.195361\pi\) |
−0.907520 | + | 0.420008i | \(0.862027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.6082 | − | 5.43324i | −0.907216 | − | 0.362216i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9942 | + | 24.2387i | −0.928829 | + | 1.60878i | −0.143546 | + | 0.989644i | \(0.545850\pi\) |
−0.785284 | + | 0.619136i | \(0.787483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2695 | − | 21.2514i | −0.810790 | − | 1.40433i | −0.912312 | − | 0.409497i | \(-0.865704\pi\) |
0.101521 | − | 0.994833i | \(-0.467629\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.724968 | − | 2.99099i | −0.0476994 | − | 0.196793i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.61844 | + | 7.99938i | −0.302564 | + | 0.524057i | −0.976716 | − | 0.214536i | \(-0.931176\pi\) |
0.674152 | + | 0.738593i | \(0.264509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.459103 | + | 0.795189i | 0.0299486 | + | 0.0518724i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3509 | − | 13.1119i | 0.737318 | − | 0.851711i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0126 | − | 24.2706i | 0.906403 | − | 1.56994i | 0.0873796 | − | 0.996175i | \(-0.472151\pi\) |
0.819023 | − | 0.573760i | \(-0.194516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.91411 | + | 17.1717i | −0.638624 | + | 1.10613i | 0.347111 | + | 0.937824i | \(0.387163\pi\) |
−0.985735 | + | 0.168305i | \(0.946171\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.44270 | − | 14.1948i | 0.413299 | − | 0.910595i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.775879 | − | 2.25146i | −0.0495691 | − | 0.143841i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.786145 | − | 1.36164i | −0.0500212 | − | 0.0866393i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.41525 | − | 1.61785i | −0.533295 | − | 0.102527i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5759 | 1.04626 | 0.523132 | − | 0.852252i | \(-0.324764\pi\) | ||||
0.523132 | + | 0.852252i | \(0.324764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.81389 | −0.176907 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.424615 | − | 1.22500i | −0.0265904 | − | 0.0767125i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.64750 | − | 6.31766i | −0.227525 | − | 0.394085i | 0.729549 | − | 0.683929i | \(-0.239730\pi\) |
−0.957074 | + | 0.289844i | \(0.906397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7963 | + | 20.7493i | −0.919399 | + | 1.28930i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.25684 | − | 1.77820i | 0.139695 | − | 0.110068i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3899 | − | 23.1920i | 0.825657 | − | 1.43008i | −0.0757586 | − | 0.997126i | \(-0.524138\pi\) |
0.901416 | − | 0.432954i | \(-0.142529\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.08316 | + | 3.60815i | −0.127968 | + | 0.221647i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.66811 | − | 27.8922i | −0.591679 | − | 1.70698i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.1791 | + | 17.6307i | 0.620630 | + | 1.07496i | 0.989369 | + | 0.145429i | \(0.0464562\pi\) |
−0.368739 | + | 0.929533i | \(0.620210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.45842 | − | 9.45427i | 0.331576 | − | 0.574306i | −0.651245 | − | 0.758867i | \(-0.725753\pi\) |
0.982821 | + | 0.184561i | \(0.0590864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.50552 | − | 14.4627i | −0.212164 | − | 0.875321i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.64011 | − | 2.84075i | −0.0989021 | − | 0.171303i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.83689 | + | 15.3059i | −0.530957 | + | 0.919645i | 0.468390 | + | 0.883522i | \(0.344834\pi\) |
−0.999347 | + | 0.0361231i | \(0.988499\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.894918 | − | 6.18347i | −0.0535773 | − | 0.370195i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.17614 | + | 12.4294i | 0.428092 | + | 0.741478i | 0.996704 | − | 0.0811286i | \(-0.0258524\pi\) |
−0.568611 | + | 0.822606i | \(0.692519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.72841 | 0.578294 | 0.289147 | − | 0.957285i | \(-0.406628\pi\) | ||||
0.289147 | + | 0.957285i | \(0.406628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.186727 | − | 0.215697i | 0.0110608 | − | 0.0127768i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.9881 | − | 16.8112i | 0.707636 | − | 0.992334i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.07937 | − | 10.5298i | 0.357610 | − | 0.619399i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.4120 | − | 2.77073i | −0.844846 | − | 0.162423i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.26345 | − | 10.8486i | 0.365915 | − | 0.633783i | −0.623008 | − | 0.782216i | \(-0.714089\pi\) |
0.988923 | + | 0.148433i | \(0.0474228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.840799 | + | 1.45631i | 0.0489532 | + | 0.0847895i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.09951 | − | 1.60338i | 0.179852 | − | 0.0930378i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.6063 | −0.786871 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.03616 | + | 17.6278i | 0.463196 | + | 1.01605i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.59456 | + | 7.48523i | 0.149054 | + | 0.430015i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.598954 | + | 1.03742i | 0.0342960 | + | 0.0594025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.8747 | 1.47675 | 0.738375 | − | 0.674391i | \(-0.235594\pi\) | ||||
0.738375 | + | 0.674391i | \(0.235594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.07375 | − | 0.590934i | −0.174859 | − | 0.0336171i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.4001 | 1.61042 | 0.805211 | − | 0.592988i | \(-0.202052\pi\) | ||||
0.805211 | + | 0.592988i | \(0.202052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2015 | −0.689668 | −0.344834 | − | 0.938664i | \(-0.612065\pi\) | ||||
−0.344834 | + | 0.938664i | \(0.612065\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.27121 | − | 1.46047i | 0.127968 | − | 0.0822879i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.95219 | −0.221977 | −0.110988 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110988 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.643204 | 0.0360125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.40406 | + | 12.7056i | 0.245811 | + | 0.709156i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.06531 | −0.0592754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.93058 | − | 13.7362i | −0.439909 | − | 0.761945i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.64600 | + | 0.700951i | 0.201624 | + | 0.0387627i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.10813 | + | 0.683527i | 0.391884 | + | 0.0376841i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.88286 | −0.488246 | −0.244123 | − | 0.969744i | \(-0.578500\pi\) | ||||
−0.244123 | + | 0.969744i | \(0.578500\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.8368 | − | 10.7149i | −1.47065 | − | 0.587173i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.09567 | − | 3.62981i | −0.114499 | − | 0.198318i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.9741 | + | 20.7397i | −0.652269 | + | 1.12976i | 0.330302 | + | 0.943875i | \(0.392849\pi\) |
−0.982571 | + | 0.185887i | \(0.940484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.97411 | − | 25.8900i | −0.487407 | − | 1.40615i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.699335 | − | 1.21128i | 0.0378711 | − | 0.0655947i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7596 | − | 5.25329i | −0.958928 | − | 0.283651i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.808574 | − | 2.33271i | −0.0435322 | − | 0.125589i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.49059 | 0.509481 | 0.254741 | − | 0.967009i | \(-0.418010\pi\) | ||||
0.254741 | + | 0.967009i | \(0.418010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.26145 | + | 7.38104i | 0.228110 | + | 0.395098i | 0.957248 | − | 0.289269i | \(-0.0934121\pi\) |
−0.729138 | + | 0.684367i | \(0.760079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.9874 | − | 7.75302i | 0.799968 | − | 0.413825i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5872 | − | 32.1940i | 0.989297 | − | 1.71351i | 0.368279 | − | 0.929715i | \(-0.379947\pi\) |
0.621018 | − | 0.783797i | \(-0.286719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.947975 | + | 1.64194i | 0.0503133 | + | 0.0871451i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.67397 | − | 2.84265i | −0.512001 | − | 0.150449i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.30964 | + | 9.19657i | −0.280232 | + | 0.485376i | −0.971442 | − | 0.237278i | \(-0.923745\pi\) |
0.691210 | + | 0.722654i | \(0.257078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.38279 | + | 16.2515i | 0.493831 | + | 0.855340i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.9428 | − | 3.44953i | −0.941751 | − | 0.181054i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.26448 | + | 2.19014i | −0.0661857 | + | 0.114637i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1799 | + | 19.3642i | −0.583586 | + | 1.01080i | 0.411464 | + | 0.911426i | \(0.365018\pi\) |
−0.995050 | + | 0.0993751i | \(0.968316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.7434 | + | 8.68130i | 1.13192 | + | 0.451930i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.4405 | + | 29.4826i | 0.697796 | + | 1.53066i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.79264 | + | 15.2293i | 0.455266 | + | 0.788544i | 0.998703 | − | 0.0509059i | \(-0.0162109\pi\) |
−0.543438 | + | 0.839450i | \(0.682878\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.81202 | − | 4.40344i | 0.196852 | − | 0.227393i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.11015 | 0.160181 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0443 | 0.515939 | 0.257969 | − | 0.966153i | \(-0.416947\pi\) | ||||
0.257969 | + | 0.966153i | \(0.416947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.7373 | − | 18.1788i | 0.806245 | − | 0.931330i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.93619 | + | 6.81768i | 0.201130 | + | 0.348367i | 0.948893 | − | 0.315599i | \(-0.102205\pi\) |
−0.747763 | + | 0.663966i | \(0.768872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.601710 | + | 0.0578612i | 0.0306660 | + | 0.00294888i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.2547 | + | 13.5952i | −0.877105 | + | 0.691084i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.82417 | − | 3.15956i | 0.0924893 | − | 0.160196i | −0.816069 | − | 0.577955i | \(-0.803851\pi\) |
0.908558 | + | 0.417759i | \(0.137184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.60949 | + | 7.98387i | −0.233112 | + | 0.403762i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.10192 | − | 1.36536i | −0.358244 | − | 0.0688732i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.70317 | + | 2.94997i | 0.0856956 | + | 0.148429i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.56071 | − | 11.3635i | 0.329272 | − | 0.570317i | −0.653095 | − | 0.757276i | \(-0.726530\pi\) |
0.982368 | + | 0.186959i | \(0.0598632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.522653 | − | 2.15630i | −0.0261654 | − | 0.107950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.71872 | − | 9.90511i | −0.285579 | − | 0.494638i | 0.687170 | − | 0.726496i | \(-0.258853\pi\) |
−0.972749 | + | 0.231859i | \(0.925519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.38157 | − | 5.85705i | 0.168448 | − | 0.291760i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.21986 | + | 2.10876i | 0.110305 | + | 0.104785i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.23445 | − | 5.60224i | −0.160326 | − | 0.277693i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.4821 | −0.913882 | −0.456941 | − | 0.889497i | \(-0.651055\pi\) | ||||
−0.456941 | + | 0.889497i | \(0.651055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.23872 | + | 20.8835i | 0.357060 | + | 1.03011i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.0178 | + | 1.25181i | 0.640565 | + | 0.0615975i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.841574 | − | 1.45765i | 0.0413112 | − | 0.0715531i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.76157 | + | 19.5069i | 0.331116 | + | 0.955258i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6290 | + | 18.4099i | −0.519260 | + | 0.899385i | 0.480489 | + | 0.877001i | \(0.340459\pi\) |
−0.999749 | + | 0.0223843i | \(0.992874\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.60478 | − | 14.9039i | −0.419371 | − | 0.726373i | 0.576505 | − | 0.817094i | \(-0.304416\pi\) |
−0.995876 | + | 0.0907211i | \(0.971083\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.15978 | + | 8.01355i | 0.0563905 | + | 0.389632i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.7468 | −0.521295 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.27341 | + | 0.891743i | 0.448772 | + | 0.0431545i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.70952 | + | 0.713163i | 0.179097 | + | 0.0344318i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.02962 | + | 5.24745i | 0.145931 | + | 0.252761i | 0.929720 | − | 0.368267i | \(-0.120049\pi\) |
−0.783789 | + | 0.621028i | \(0.786715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6963 | −0.850432 | −0.425216 | − | 0.905092i | \(-0.639802\pi\) | ||||
−0.425216 | + | 0.905092i | \(0.639802\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.184825 | + | 0.533216i | 0.00886170 | + | 0.0255657i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.02862 | −0.0970421 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3373 | 1.30474 | 0.652370 | − | 0.757901i | \(-0.273775\pi\) | ||||
0.652370 | + | 0.757901i | \(0.273775\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00769 | − | 20.9758i | 0.0479851 | − | 0.998848i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.91771 | 0.0911132 | 0.0455566 | − | 0.998962i | \(-0.485494\pi\) | ||||
0.0455566 | + | 0.998962i | \(0.485494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.79822 | 0.274862 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.2863 | − | 3.51559i | −0.864914 | − | 0.166281i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.3249 | 1.33674 | 0.668368 | − | 0.743831i | \(-0.266993\pi\) | ||||
0.668368 | + | 0.743831i | \(0.266993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.62058 | + | 4.53898i | 0.123398 | + | 0.213732i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.46409 | + | 4.22386i | 0.0687891 | + | 0.198454i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.90951 | + | 0.279782i | 0.136400 | + | 0.0131164i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0085 | 0.608514 | 0.304257 | − | 0.952590i | \(-0.401592\pi\) | ||||
0.304257 | + | 0.952590i | \(0.401592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.528076 | − | 11.4208i | 0.0246485 | − | 0.533078i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8278 | − | 20.4863i | −0.550875 | − | 0.954144i | −0.998212 | − | 0.0597782i | \(-0.980961\pi\) |
0.447336 | − | 0.894366i | \(-0.352373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2403 | + | 35.0572i | −0.940647 | + | 1.62925i | −0.176406 | + | 0.984317i | \(0.556447\pi\) |
−0.764241 | + | 0.644931i | \(0.776886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.20511 | + | 0.231685i | 0.0558856 | + | 0.0107441i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.6010 | + | 32.2179i | −0.860753 | + | 1.49087i | 0.0104492 | + | 0.999945i | \(0.496674\pi\) |
−0.871203 | + | 0.490923i | \(0.836659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.4466 | − | 3.12011i | −1.49825 | − | 0.144073i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.06566 | + | 10.4722i | −0.417724 | + | 0.482532i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.91761 | −0.226112 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18240 | − | 2.04799i | −0.0542525 | − | 0.0939680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.8585 | + | 22.7381i | −1.32134 | + | 1.04110i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.2918 | + | 35.1463i | −0.927154 | + | 1.60588i | −0.139094 | + | 0.990279i | \(0.544419\pi\) |
−0.788060 | + | 0.615598i | \(0.788914\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6399 | − | 27.0891i | −0.713118 | − | 1.23516i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.4217 | − | 5.41313i | −0.838216 | − | 0.246306i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.44128 | − | 2.49637i | 0.0654452 | − | 0.113354i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5255 | + | 18.2307i | 0.476956 | + | 0.826113i | 0.999651 | − | 0.0264072i | \(-0.00840666\pi\) |
−0.522695 | + | 0.852520i | \(0.675073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.68904 | + | 13.5277i | 0.212046 | + | 0.611745i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.97925 | + | 8.62432i | −0.224711 | + | 0.389210i | −0.956233 | − | 0.292608i | \(-0.905477\pi\) |
0.731522 | + | 0.681818i | \(0.238810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.05365 | − | 1.82497i | 0.0474538 | − | 0.0821924i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0981766 | + | 0.678355i | 0.00441271 | + | 0.0304898i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6772 | + | 1.41138i | 0.658361 | + | 0.0633088i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3150 | − | 19.5982i | −0.506531 | − | 0.877337i | −0.999971 | − | 0.00755788i | \(-0.997594\pi\) |
0.493440 | − | 0.869780i | \(-0.335739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2037 | + | 29.4373i | 0.455867 | + | 1.31516i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.4520 | −1.93743 | −0.968714 | − | 0.248179i | \(-0.920168\pi\) | ||||
−0.968714 | + | 0.248179i | \(0.920168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.55602 | −0.0692422 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.17470 | − | 0.802594i | −0.185405 | − | 0.0356444i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.77739 | + | 8.27468i | 0.211754 | + | 0.366769i | 0.952264 | − | 0.305277i | \(-0.0987491\pi\) |
−0.740510 | + | 0.672046i | \(0.765416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.15836 | + | 17.8959i | 0.360905 | + | 0.791667i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.23454 | − | 1.15593i | 0.0986572 | − | 0.0510356i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.307392 | − | 0.532419i | 0.0135453 | − | 0.0234612i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.906312 | + | 1.56978i | −0.0398596 | + | 0.0690388i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.2700 | − | 22.2597i | 0.845860 | − | 0.977092i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.581462 | + | 1.00712i | 0.0254743 | + | 0.0441228i | 0.878482 | − | 0.477776i | \(-0.158557\pi\) |
−0.853007 | + | 0.521899i | \(0.825224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.20567 | + | 5.55239i | −0.140174 | + | 0.242789i | −0.927562 | − | 0.373669i | \(-0.878100\pi\) |
0.787388 | + | 0.616458i | \(0.211433\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.27249 | − | 21.7526i | −0.230110 | − | 0.949363i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.29119 | − | 3.96846i | −0.0998059 | − | 0.172869i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.72237 | − | 4.71528i | 0.118364 | − | 0.205012i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.12402 | + | 14.6760i | 0.0921746 | + | 0.636884i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.6716 | + | 21.9478i | 0.548866 | + | 0.950665i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.64123 | −0.114190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.8299 | + | 6.31162i | 1.41671 | + | 0.272366i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.08331 | − | 3.54876i | 0.132808 | − | 0.152856i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.37443 | + | 12.7729i | −0.317052 | + | 0.549150i | −0.979871 | − | 0.199629i | \(-0.936026\pi\) |
0.662820 | + | 0.748779i | \(0.269360\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.8994 | + | 28.7624i | −1.06854 | + | 1.23431i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.364621 | + | 0.631542i | −0.0156187 | + | 0.0270523i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.57905 | + | 11.3952i | 0.281300 | + | 0.487226i | 0.971705 | − | 0.236197i | \(-0.0759011\pi\) |
−0.690405 | + | 0.723423i | \(0.742568\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.51307 | + | 10.4546i | 0.0645764 | + | 0.446193i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.463706 | 0.0197545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.3696 | + | 2.53573i | 1.12135 | + | 0.107830i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.71483 | − | 4.29117i | 0.157686 | − | 0.182150i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.1869 | − | 21.1083i | −0.516374 | − | 0.894385i | −0.999819 | − | 0.0190111i | \(-0.993948\pi\) |
0.483446 | − | 0.875374i | \(-0.339385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.7787 | −1.00573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.67517 | − | 1.93506i | 0.0707256 | − | 0.0816984i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.11965 | −0.131478 | −0.0657388 | − | 0.997837i | \(-0.520940\pi\) | ||||
−0.0657388 | + | 0.997837i | \(0.520940\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.38201 | 0.226423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.3761 | − | 4.53429i | 0.981702 | − | 0.190422i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4769 | −0.900358 | −0.450179 | − | 0.892938i | \(-0.648640\pi\) | ||||
−0.450179 | + | 0.892938i | \(0.648640\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0460 | 1.38293 | 0.691466 | − | 0.722409i | \(-0.256965\pi\) | ||||
0.691466 | + | 0.722409i | \(0.256965\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.54717 | + | 8.71808i | −0.315287 | + | 0.364203i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.4646 | −0.853432 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.904826 | + | 1.56720i | 0.0376684 | + | 0.0652436i | 0.884245 | − | 0.467023i | \(-0.154674\pi\) |
−0.846577 | + | 0.532267i | \(0.821340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.19757 | + | 8.31425i | −0.299121 | + | 0.345528i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.42980 | − | 11.9106i | −0.225266 | − | 0.494136i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.22473 | −0.340633 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.474724 | + | 3.28012i | 0.0196274 | + | 0.135616i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.65901 | + | 2.87349i | 0.0684746 | + | 0.118601i | 0.898230 | − | 0.439526i | \(-0.144853\pi\) |
−0.829755 | + | 0.558127i | \(0.811520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.504173 | − | 0.873253i | 0.0207741 | − | 0.0359818i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.9934 | + | 31.1813i | −1.11036 | + | 1.28263i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3784 | − | 26.6362i | 0.631516 | − | 1.09382i | −0.355726 | − | 0.934590i | \(-0.615766\pi\) |
0.987242 | − | 0.159228i | \(-0.0509005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14985 | − | 1.61246i | 0.0471391 | − | 0.0661042i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 35.6410 | + | 6.85205i | 1.45869 | + | 0.280436i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.9705 | 0.570817 | 0.285409 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285409 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.50432 | − | 12.9979i | −0.306108 | − | 0.530194i | 0.671400 | − | 0.741096i | \(-0.265693\pi\) |
−0.977507 | + | 0.210901i | \(0.932360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.29408 | − | 36.5796i | −0.215591 | − | 1.48964i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.79438 | − | 3.10796i | 0.0729519 | − | 0.126356i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.6644 | − | 20.2034i | −0.473444 | − | 0.820030i | 0.526093 | − | 0.850427i | \(-0.323656\pi\) |
−0.999538 | + | 0.0303969i | \(0.990323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.21087 | + | 1.23734i | 0.170633 | + | 0.0501397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.38239 | + | 7.59052i | −0.177292 | + | 0.307080i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3374 | + | 38.6895i | 0.902198 | + | 1.56265i | 0.824635 | + | 0.565666i | \(0.191381\pi\) |
0.0775635 | + | 0.996987i | \(0.475286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.00979 | + | 3.47674i | −0.121366 | + | 0.140196i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.18488 | + | 2.05227i | −0.0477013 | + | 0.0826212i | −0.888890 | − | 0.458120i | \(-0.848523\pi\) |
0.841189 | + | 0.540741i | \(0.181856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3863 | − | 19.7217i | 0.457655 | − | 0.792682i | −0.541181 | − | 0.840906i | \(-0.682023\pi\) |
0.998837 | + | 0.0482236i | \(0.0153560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00559 | − | 21.7481i | 0.0403530 | − | 0.872722i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.1810 | − | 36.7142i | 1.04892 | − | 1.47092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.6387 | − | 20.1588i | −0.465547 | − | 0.806351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.553069 | + | 0.106329i | 0.0220874 | + | 0.00424636i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.1937 | −0.845049 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8652 | 0.711201 | 0.355600 | − | 0.934638i | \(-0.384276\pi\) | ||||
0.355600 | + | 0.934638i | \(0.384276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.17505 | − | 20.6998i | −0.285183 | − | 0.822743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.36133 | + | 4.08995i | 0.0937067 | + | 0.162305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.9091 | − | 17.1597i | 0.590718 | − | 0.679891i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.39477 | + | 16.5467i | 0.0947355 | + | 0.654578i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7900 | − | 22.1529i | 0.505175 | − | 0.874988i | −0.494808 | − | 0.869003i | \(-0.664761\pi\) |
0.999982 | − | 0.00598543i | \(-0.00190523\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.99334 | − | 13.8449i | 0.315227 | − | 0.545989i | −0.664259 | − | 0.747503i | \(-0.731253\pi\) |
0.979486 | + | 0.201514i | \(0.0645861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.41308 | − | 4.07670i | −0.0556401 | − | 0.160520i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.47306 | + | 12.9437i | 0.293796 | + | 0.508870i | 0.974704 | − | 0.223499i | \(-0.0717479\pi\) |
−0.680908 | + | 0.732369i | \(0.738415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.65982 | + | 2.87489i | −0.0651536 | + | 0.112849i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.90851 | − | 6.58459i | 0.270766 | − | 0.258070i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.82885 | + | 8.36381i | 0.188967 | + | 0.327301i | 0.944906 | − | 0.327341i | \(-0.106153\pi\) |
−0.755939 | + | 0.654642i | \(0.772819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.710233 | − | 1.23016i | 0.0277511 | − | 0.0480663i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.5171 | + | 13.8020i | −0.683406 | + | 0.538466i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.80353 | + | 16.9802i | 0.381891 | + | 0.661455i | 0.991333 | − | 0.131376i | \(-0.0419396\pi\) |
−0.609441 | + | 0.792831i | \(0.708606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2655 | −0.399281 | −0.199641 | − | 0.979869i | \(-0.563977\pi\) | ||||
−0.199641 | + | 0.979869i | \(0.563977\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.10011 | − | 9.35682i | 0.314582 | − | 0.363389i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.433792 | + | 0.0417140i | 0.0168217 | + | 0.00161760i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.00641 | − | 3.47520i | 0.0776885 | − | 0.134560i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.57312 | + | 0.879192i | 0.176807 | + | 0.0339915i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.18239 | + | 2.04797i | −0.0456458 | + | 0.0790608i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1584 | − | 29.7191i | −0.661406 | − | 1.14559i | −0.980246 | − | 0.197780i | \(-0.936627\pi\) |
0.318840 | − | 0.947808i | \(-0.396707\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.5419 | − | 11.6610i | 0.867636 | − | 0.448830i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.47419 | 0.287256 | 0.143628 | − | 0.989632i | \(-0.454123\pi\) | ||||
0.143628 | + | 0.989632i | \(0.454123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.29910 | − | 20.3982i | −0.356867 | − | 0.782810i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.8767 | − | 45.8038i | −0.608397 | − | 1.75521i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1577 | − | 31.4501i | −0.694786 | − | 1.20340i | −0.970253 | − | 0.242094i | \(-0.922166\pi\) |
0.275467 | − | 0.961310i | \(-0.411167\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.34125 | −0.165871 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.7384 | + | 8.02429i | 1.59242 | + | 0.306146i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.7699 | −1.51511 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.9624 | 1.93870 | 0.969350 | − | 0.245684i | \(-0.0790126\pi\) | ||||
0.969350 | + | 0.245684i | \(0.0790126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.73863 | + | 2.44136i | 0.180006 | + | 0.0927395i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.05509 | −0.153818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.1713 | 0.650410 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.23971 | − | 15.1164i | −0.198184 | − | 0.571755i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.6075 | 1.38265 | 0.691324 | − | 0.722545i | \(-0.257028\pi\) | ||||
0.691324 | + | 0.722545i | \(0.257028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.33182 | − | 4.03883i | −0.0879463 | − | 0.152327i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.56178 | − | 0.300255i | −0.0588199 | − | 0.0113083i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.02600 | + | 9.85272i | −0.264240 | + | 0.370550i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.87578 | −0.220670 | −0.110335 | − | 0.993894i | \(-0.535192\pi\) | ||||
−0.110335 | + | 0.993894i | \(0.535192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.30253 | + | 29.7285i | 0.161357 | + | 1.11491i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.36301 | − | 7.55695i | −0.163396 | − | 0.283010i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.370973 | + | 0.642545i | −0.0138736 | + | 0.0240298i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.8976 | + | 45.8641i | 0.593707 | + | 1.71283i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.09642 | + | 14.0234i | −0.301945 | + | 0.522985i | −0.976577 | − | 0.215170i | \(-0.930969\pi\) |
0.674631 | + | 0.738155i | \(0.264303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.98328 | − | 4.35046i | −0.0738614 | − | 0.162020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2477 | − | 32.4494i | −0.418308 | − | 1.20681i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.67783 | 0.173730 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.8771 | − | 39.6243i | −0.848464 | − | 1.46958i | −0.882578 | − | 0.470166i | \(-0.844194\pi\) |
0.0341138 | − | 0.999418i | \(-0.489139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.2847 | + | 24.5287i | 0.417951 | + | 0.908470i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.05565 | + | 13.9528i | −0.297949 | + | 0.516063i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5916 | − | 23.5414i | −0.502019 | − | 0.869522i | −0.999997 | − | 0.00233276i | \(-0.999257\pi\) |
0.497978 | − | 0.867189i | \(-0.334076\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.82791 | + | 1.53632i | 0.141195 | + | 0.0566682i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.13706 | − | 7.16560i | 0.152391 | − | 0.263948i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1738 | + | 21.0856i | 0.447821 | + | 0.775648i | 0.998244 | − | 0.0592377i | \(-0.0188670\pi\) |
−0.550423 | + | 0.834886i | \(0.685534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.67431 | + | 0.514142i | 0.0982433 | + | 0.0188875i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.0683178 | + | 0.118330i | −0.00250634 | + | 0.00434110i | −0.867276 | − | 0.497828i | \(-0.834131\pi\) |
0.864770 | + | 0.502169i | \(0.167464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.82874 | − | 3.16747i | 0.0669998 | − | 0.116047i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6585 | − | 9.18591i | 0.426562 | − | 0.336095i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.9261 | + | 16.7242i | −0.435769 | + | 0.611090i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.71446 | − | 6.43364i | −0.135543 | − | 0.234767i | 0.790262 | − | 0.612769i | \(-0.209944\pi\) |
−0.925805 | + | 0.378002i | \(0.876611\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.7912 | + | 21.7066i | −0.684789 | + | 0.791031i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.878055 | −0.0319557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0794 | −0.511723 | −0.255861 | − | 0.966713i | \(-0.582359\pi\) | ||||
−0.255861 | + | 0.966713i | \(0.582359\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.18994 | − | 3.68485i | 0.115788 | − | 0.133752i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.3616 | − | 33.5353i | −0.701858 | − | 1.21565i | −0.967813 | − | 0.251669i | \(-0.919021\pi\) |
0.265955 | − | 0.963985i | \(-0.414313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.35252 | + | 5.16041i | 0.0851671 | + | 0.186819i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.08553 | + | 0.832671i | 0.0754025 | + | 0.0301053i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.02589 | + | 13.9013i | −0.289798 | + | 0.501945i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.14295 | − | 8.90786i | 0.185460 | − | 0.321226i | −0.758272 | − | 0.651939i | \(-0.773956\pi\) |
0.943731 | + | 0.330713i | \(0.107289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.4081 | + | 2.38548i | 0.446867 | + | 0.0859111i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.6768 | − | 39.2773i | −0.815627 | − | 1.41271i | −0.908877 | − | 0.417064i | \(-0.863059\pi\) |
0.0932501 | − | 0.995643i | \(-0.470274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.08606 | − | 8.80931i | 0.182697 | − | 0.316440i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3979 | − | 42.8984i | −0.373022 | − | 1.53897i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.88926 | + | 3.27229i | 0.0676898 | + | 0.117242i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.87139 | + | 3.24135i | −0.0669637 | + | 0.115985i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.229860 | + | 4.97123i | −0.00821453 | + | 0.177657i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.36028 | − | 2.35607i | −0.0485504 | − | 0.0840917i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.1087 | 0.930675 | 0.465337 | − | 0.885133i | \(-0.345933\pi\) | ||||
0.465337 | + | 0.885133i | \(0.345933\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.1911 | + | 43.8259i | 0.540818 | + | 1.56024i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.3017 | − | 34.0788i | 0.864067 | − | 1.21170i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.71735 | + | 9.90274i | −0.203029 | + | 0.351657i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.36339 | − | 6.81830i | −0.0838207 | − | 0.241820i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.1618 | + | 27.9931i | −0.572481 | + | 0.991567i | 0.423829 | + | 0.905742i | \(0.360686\pi\) |
−0.996310 | + | 0.0858244i | \(0.972648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.96930 | + | 5.14298i | 0.105046 | + | 0.181946i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.4857 | + | 18.9592i | 1.67782 | + | 0.669890i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.99240 | −0.176178 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.18960 | − | 3.07052i | 0.0771731 | − | 0.108222i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.6273 | − | 6.65716i | −1.21894 | − | 0.234343i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.4553 | + | 38.8938i | 0.789488 | + | 1.36743i | 0.926281 | + | 0.376833i | \(0.122987\pi\) |
−0.136793 | + | 0.990600i | \(0.543680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.8204 | 1.50363 | 0.751813 | − | 0.659376i | \(-0.229180\pi\) | ||||
0.751813 | + | 0.659376i | \(0.229180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.19268 | + | 17.8657i | 0.217187 | + | 0.626578i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.81214 | −0.0985049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.54527 | −0.124033 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.9132 | + | 11.8050i | 0.800653 | + | 0.412499i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.2200 | −1.12448 | −0.562242 | − | 0.826972i | \(-0.690061\pi\) | ||||
−0.562242 | + | 0.826972i | \(0.690061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.38841 | 0.152970 | 0.0764851 | − | 0.997071i | \(-0.475630\pi\) | ||||
0.0764851 | + | 0.997071i | \(0.475630\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.57932 | + | 1.07264i | 0.194247 | + | 0.0373444i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.0996 | −1.46395 | −0.731973 | − | 0.681333i | \(-0.761400\pi\) | ||||
−0.731973 | + | 0.681333i | \(0.761400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.55838 | − | 9.62739i | −0.193050 | − | 0.334373i | 0.753209 | − | 0.657781i | \(-0.228505\pi\) |
−0.946260 | + | 0.323408i | \(0.895171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0256 | − | 28.9236i | −0.347785 | − | 1.00335i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.01809 | − | 14.5616i | −0.173866 | − | 0.504530i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.11941 | −0.211771 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.11192 | + | 5.83793i | 0.314954 | + | 0.201788i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.2669 | − | 47.2277i | −0.941360 | − | 1.63048i | −0.762881 | − | 0.646539i | \(-0.776216\pi\) |
−0.178479 | − | 0.983944i | \(-0.557118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0414 | − | 24.3204i | 0.484185 | − | 0.838633i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.4118 | − | 4.69322i | −0.840788 | − | 0.161643i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.417494 | − | 0.723120i | 0.0143622 | − | 0.0248761i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.5773 | − | 25.3955i | −0.397800 | − | 0.872600i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.0285 | + | 12.7396i | −0.378499 | + | 0.437221i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.3582 | −1.38346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3669 | − | 19.6880i | −0.389194 | − | 0.674105i | 0.603147 | − | 0.797630i | \(-0.293913\pi\) |
−0.992341 | + | 0.123526i | \(0.960580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0707787 | + | 0.489048i | 0.00242058 | + | 0.0167251i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.61928 | + | 9.73288i | −0.191951 | + | 0.332469i | −0.945897 | − | 0.324468i | \(-0.894815\pi\) |
0.753946 | + | 0.656937i | \(0.228148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.4024 | − | 43.9983i | −0.866720 | − | 1.50120i | −0.865329 | − | 0.501204i | \(-0.832891\pi\) |
−0.00139066 | − | 0.999999i | \(-0.500443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42444 | + | 34.7566i | 0.287104 | + | 1.18450i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.340985 | + | 0.590603i | −0.0116073 | + | 0.0201044i | −0.871771 | − | 0.489914i | \(-0.837028\pi\) |
0.860163 | + | 0.510018i | \(0.170361\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89141 | + | 5.00807i | 0.0983110 | + | 0.170280i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.89716 | + | 19.8981i | 0.234240 | + | 0.675775i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.36222 | + | 5.82353i | −0.114055 | + | 0.197550i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0044 | − | 34.6486i | 0.677822 | − | 1.17402i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.9664 | − | 15.7318i | 0.675760 | − | 0.532441i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.85583 | + | 0.851587i | 0.299382 | + | 0.0287889i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6595 | + | 21.9269i | 0.427480 | + | 0.740418i | 0.996648 | − | 0.0818035i | \(-0.0260680\pi\) |
−0.569168 | + | 0.822221i | \(0.692735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.10600 | + | 20.5006i | 0.239680 | + | 0.691468i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.9482 | −1.04267 | −0.521335 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521335 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.48501 | 0.319196 | 0.159598 | − | 0.987182i | \(-0.448980\pi\) | ||||
0.159598 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.86024 | − | 0.549886i | −0.0961458 | − | 0.0184842i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.97469 | − | 3.42026i | −0.0663036 | − | 0.114841i | 0.830968 | − | 0.556320i | \(-0.187787\pi\) |
−0.897272 | + | 0.441479i | \(0.854454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.5597 | + | 3.51563i | 1.22617 | + | 0.117910i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41407 | + | 5.87655i | −0.0473731 | + | 0.196872i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.653390 | + | 1.13170i | −0.0218649 | + | 0.0378710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.28318 | + | 5.68663i | −0.109745 | + | 0.190083i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4247 | − | 17.8177i | 0.515015 | − | 0.594917i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.997305 | + | 1.72738i | 0.0332620 | + | 0.0576115i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4731 | + | 23.3361i | −0.448854 | + | 0.777439i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.1942 | − | 9.46012i | −1.07136 | − | 0.314813i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.73609 | − | 6.47109i | −0.124192 | − | 0.215106i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7531 | − | 29.0171i | 0.556276 | − | 0.963498i | −0.441527 | − | 0.897248i | \(-0.645563\pi\) |
0.997803 | − | 0.0662505i | \(-0.0211036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.7434 | − | 5.08794i | −0.422671 | − | 0.168756i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.26585 | + | 9.12072i | 0.174465 | + | 0.302183i | 0.939976 | − | 0.341240i | \(-0.110847\pi\) |
−0.765511 | + | 0.643423i | \(0.777514\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.32269 | 0.109965 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.03753 | − | 0.391719i | −0.0673585 | − | 0.0129498i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.58240 | − | 10.0518i | −0.151324 | − | 0.331939i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.81600 | − | 3.14540i | 0.0599042 | − | 0.103757i | −0.834518 | − | 0.550981i | \(-0.814254\pi\) |
0.894422 | + | 0.447224i | \(0.147587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.3327 | + | 33.8836i | −0.966546 | + | 1.11650i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.04894 | + | 15.6732i | −0.297850 | + | 0.515891i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.5232 | − | 40.7435i | −0.773440 | − | 1.33964i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.25837 | − | 3.35523i | 0.139863 | − | 0.110200i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.6058 | 0.446392 | 0.223196 | − | 0.974774i | \(-0.428351\pi\) | ||||
0.223196 | + | 0.974774i | \(0.428351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.22286 | − | 2.55841i | 0.0728512 | − | 0.0838486i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.1956 | + | 37.1906i | −1.05404 | + | 1.21757i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.251354 | + | 0.435358i | 0.00822016 | + | 0.0142377i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.98770 | 0.326284 | 0.163142 | − | 0.986603i | \(-0.447837\pi\) | ||||
0.163142 | + | 0.986603i | \(0.447837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8321 | − | 15.9781i | 0.451394 | − | 0.521426i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6209 | 1.12861 | 0.564305 | − | 0.825566i | \(-0.309144\pi\) | ||||
0.564305 | + | 0.825566i | \(0.309144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.6985 | 1.06481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.662233 | + | 4.62986i | −0.0215424 | + | 0.150609i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.2171 | 1.59934 | 0.799670 | − | 0.600440i | \(-0.205008\pi\) | ||||
0.799670 | + | 0.600440i | \(0.205008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.1403 | −0.783626 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.48037 | − | 5.17548i | 0.145286 | − | 0.167827i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.2310 | 0.460987 | 0.230494 | − | 0.973074i | \(-0.425966\pi\) | ||||
0.230494 | + | 0.973074i | \(0.425966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.13243 | − | 1.96143i | −0.0366446 | − | 0.0634704i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.729163 | + | 0.842290i | −0.0235705 | + | 0.0272274i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.6022 | + | 27.4887i | −0.632990 | + | 0.887656i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6626 | −0.860085 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.6309 | − | 8.63638i | −0.697046 | − | 0.278303i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.07998 | − | 1.87057i | −0.0347657 | − | 0.0602159i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.4246 | + | 33.6443i | −0.624652 | + | 1.08193i | 0.363956 | + | 0.931416i | \(0.381426\pi\) |
−0.988608 | + | 0.150513i | \(0.951908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.20768 | − | 1.39505i | 0.0387963 | − | 0.0448154i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.13629 | + | 7.16427i | −0.132740 | + | 0.229912i | −0.924732 | − | 0.380619i | \(-0.875711\pi\) |
0.791992 | + | 0.610532i | \(0.209044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3102 | + | 25.6768i | −0.586997 | + | 0.823159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.9783 | + | 5.18663i | 0.863996 | + | 0.166105i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.37473 | 0.235938 | 0.117969 | − | 0.993017i | \(-0.462362\pi\) | ||||
0.117969 | + | 0.993017i | \(0.462362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.72312 | + | 9.91273i | 0.182912 | + | 0.316812i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.05118 | + | 3.97990i | −0.161272 | + | 0.127068i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.39181 | − | 4.14274i | 0.0762870 | − | 0.132133i | −0.825358 | − | 0.564609i | \(-0.809027\pi\) |
0.901645 | + | 0.432476i | \(0.142360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.05029 | − | 7.01530i | −0.129053 | − | 0.223526i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.95318 | + | 8.53339i | −0.284983 | + | 0.271621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.3400 | + | 26.5697i | −0.487784 | + | 0.844866i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.4932 | + | 32.0312i | 0.587456 | + | 1.01750i | 0.994564 | + | 0.104124i | \(0.0332038\pi\) |
−0.407108 | + | 0.913380i | \(0.633463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.0700 | − | 11.6323i | 0.319562 | − | 0.369140i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.56430 | + | 6.17356i | −0.112996 | + | 0.195715i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.3285 | + | 42.1382i | −0.770491 | + | 1.33453i | 0.166803 | + | 0.985990i | \(0.446656\pi\) |
−0.937294 | + | 0.348539i | \(0.886678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.4548 | − | 22.9966i | 1.40649 | − | 0.727579i |
(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 | 504.2.q.d.121.4 | yes | 22 | |
3.2 | odd | 2 | 1512.2.q.c.793.7 | 22 | |||
4.3 | odd | 2 | 1008.2.q.k.625.8 | 22 | |||
7.4 | even | 3 | 504.2.t.d.193.11 | yes | 22 | ||
9.2 | odd | 6 | 1512.2.t.d.289.5 | 22 | |||
9.7 | even | 3 | 504.2.t.d.457.11 | yes | 22 | ||
12.11 | even | 2 | 3024.2.q.k.2305.7 | 22 | |||
21.11 | odd | 6 | 1512.2.t.d.361.5 | 22 | |||
28.11 | odd | 6 | 1008.2.t.k.193.1 | 22 | |||
36.7 | odd | 6 | 1008.2.t.k.961.1 | 22 | |||
36.11 | even | 6 | 3024.2.t.l.289.5 | 22 | |||
63.11 | odd | 6 | 1512.2.q.c.1369.7 | 22 | |||
63.25 | even | 3 | inner | 504.2.q.d.25.4 | ✓ | 22 | |
84.11 | even | 6 | 3024.2.t.l.1873.5 | 22 | |||
252.11 | even | 6 | 3024.2.q.k.2881.7 | 22 | |||
252.151 | odd | 6 | 1008.2.q.k.529.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.4 | ✓ | 22 | 63.25 | even | 3 | inner | |
504.2.q.d.121.4 | yes | 22 | 1.1 | even | 1 | trivial | |
504.2.t.d.193.11 | yes | 22 | 7.4 | even | 3 | ||
504.2.t.d.457.11 | yes | 22 | 9.7 | even | 3 | ||
1008.2.q.k.529.8 | 22 | 252.151 | odd | 6 | |||
1008.2.q.k.625.8 | 22 | 4.3 | odd | 2 | |||
1008.2.t.k.193.1 | 22 | 28.11 | odd | 6 | |||
1008.2.t.k.961.1 | 22 | 36.7 | odd | 6 | |||
1512.2.q.c.793.7 | 22 | 3.2 | odd | 2 | |||
1512.2.q.c.1369.7 | 22 | 63.11 | odd | 6 | |||
1512.2.t.d.289.5 | 22 | 9.2 | odd | 6 | |||
1512.2.t.d.361.5 | 22 | 21.11 | odd | 6 | |||
3024.2.q.k.2305.7 | 22 | 12.11 | even | 2 | |||
3024.2.q.k.2881.7 | 22 | 252.11 | even | 6 | |||
3024.2.t.l.289.5 | 22 | 36.11 | even | 6 | |||
3024.2.t.l.1873.5 | 22 | 84.11 | even | 6 |