Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,2,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(2.04417029174\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 225.1 | ||
Root | \(0.500000 - 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.225 |
Dual form | 256.2.g.d.33.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0794708 | − | 0.191860i | −0.0458825 | − | 0.110770i | 0.899277 | − | 0.437380i | \(-0.144094\pi\) |
−0.945159 | + | 0.326610i | \(0.894094\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.292893i | −0.316228 | − | 0.130986i | 0.218924 | − | 0.975742i | \(-0.429745\pi\) |
−0.535151 | + | 0.844756i | \(0.679745\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.27133 | − | 2.27133i | −0.858482 | − | 0.858482i | 0.132677 | − | 0.991159i | \(-0.457643\pi\) |
−0.991159 | + | 0.132677i | \(0.957643\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09083 | − | 2.09083i | 0.696942 | − | 0.696942i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.49368 | − | 3.60607i | 0.450363 | − | 1.08727i | −0.521821 | − | 0.853055i | \(-0.674747\pi\) |
0.972184 | − | 0.234217i | \(-0.0752527\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50504 | − | 1.86605i | 1.24947 | − | 0.517549i | 0.342810 | − | 0.939405i | \(-0.388621\pi\) |
0.906663 | + | 0.421856i | \(0.138621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.158942i | 0.0410386i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.05320i | 0.740511i | 0.928930 | + | 0.370255i | \(0.120730\pi\) | ||||
−0.928930 | + | 0.370255i | \(0.879270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.87740 | + | 1.60607i | −0.889537 | + | 0.368458i | −0.780188 | − | 0.625545i | \(-0.784877\pi\) |
−0.109349 | + | 0.994003i | \(0.534877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.255272 | + | 0.616281i | −0.0557049 | + | 0.134484i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.271330 | − | 0.271330i | 0.0565763 | − | 0.0565763i | −0.678253 | − | 0.734829i | \(-0.737262\pi\) |
0.734829 | + | 0.678253i | \(0.237262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.12132 | − | 3.12132i | −0.624264 | − | 0.624264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.14288 | − | 0.473398i | −0.219948 | − | 0.0911054i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.931884 | + | 2.24977i | 0.173047 | + | 0.417771i | 0.986479 | − | 0.163888i | \(-0.0524036\pi\) |
−0.813432 | + | 0.581660i | \(0.802404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.82843 | 1.22642 | 0.613211 | − | 0.789919i | \(-0.289878\pi\) | ||||
0.613211 | + | 0.789919i | \(0.289878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.810564 | −0.141101 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.940816 | + | 2.27133i | 0.159027 | + | 0.383925i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.63349 | − | 1.50504i | −0.597342 | − | 0.247427i | 0.0634640 | − | 0.997984i | \(-0.479785\pi\) |
−0.660806 | + | 0.750557i | \(0.729785\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.716038 | − | 0.716038i | −0.114658 | − | 0.114658i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.54266 | + | 1.54266i | −0.240923 | + | 0.240923i | −0.817232 | − | 0.576309i | \(-0.804493\pi\) |
0.576309 | + | 0.817232i | \(0.304493\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.748956 | + | 1.80814i | −0.114215 | + | 0.275739i | −0.970642 | − | 0.240529i | \(-0.922679\pi\) |
0.856427 | + | 0.516268i | \(0.172679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.09083 | + | 0.866048i | −0.311682 | + | 0.129103i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.37109i | 1.07518i | 0.843205 | + | 0.537592i | \(0.180666\pi\) | ||||
−0.843205 | + | 0.537592i | \(0.819334\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.31788i | 0.473983i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.585786 | − | 0.242641i | 0.0820265 | − | 0.0339765i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.67661 | + | 4.04770i | −0.230300 | + | 0.555994i | −0.996213 | − | 0.0869508i | \(-0.972288\pi\) |
0.765912 | + | 0.642945i | \(0.222288\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.11239 | + | 2.11239i | −0.284834 | + | 0.284834i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.616281 | + | 0.616281i | 0.0816284 | + | 0.0816284i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1200 | + | 4.19186i | 1.31752 | + | 0.545734i | 0.927069 | − | 0.374891i | \(-0.122320\pi\) |
0.390449 | + | 0.920625i | \(0.372320\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.35873 | − | 3.28026i | −0.173967 | − | 0.419995i | 0.812713 | − | 0.582664i | \(-0.197990\pi\) |
−0.986681 | + | 0.162669i | \(0.947990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.49791 | −1.19662 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.73210 | −0.462910 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.99577 | + | 4.81822i | 0.243822 | + | 0.588639i | 0.997656 | − | 0.0684259i | \(-0.0217977\pi\) |
−0.753834 | + | 0.657065i | \(0.771798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0736202 | − | 0.0304945i | −0.00886283 | − | 0.00367110i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47085 | + | 6.47085i | 0.767948 | + | 0.767948i | 0.977745 | − | 0.209797i | \(-0.0672803\pi\) |
−0.209797 | + | 0.977745i | \(0.567280\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.84106 | + | 2.84106i | −0.332521 | + | 0.332521i | −0.853543 | − | 0.521022i | \(-0.825551\pi\) |
0.521022 | + | 0.853543i | \(0.325551\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.350801 | + | 0.846909i | −0.0405070 | + | 0.0977926i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.5832 | + | 4.79793i | −1.32003 | + | 0.546775i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.74996i | − | 1.09696i | −0.836165 | − | 0.548478i | \(-0.815207\pi\) | ||
0.836165 | − | 0.548478i | \(-0.184793\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.61373i | − | 0.957081i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.04642 | − | 3.74715i | 0.992974 | − | 0.411303i | 0.173758 | − | 0.984788i | \(-0.444409\pi\) |
0.819216 | + | 0.573485i | \(0.194409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.894263 | − | 2.15894i | 0.0969964 | − | 0.234170i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.357582 | − | 0.357582i | 0.0383368 | − | 0.0383368i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.58323 | + | 7.58323i | 0.803821 | + | 0.803821i | 0.983691 | − | 0.179869i | \(-0.0575675\pi\) |
−0.179869 | + | 0.983691i | \(0.557567\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4708 | − | 5.99402i | −1.51696 | − | 0.628344i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.542661 | − | 1.31010i | −0.0562713 | − | 0.135851i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.21215 | 0.329559 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.71423 | 0.377123 | 0.188562 | − | 0.982061i | \(-0.439617\pi\) | ||||
0.188562 | + | 0.982061i | \(0.439617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.41664 | − | 10.6627i | −0.443889 | − | 1.07164i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.04770 | + | 3.74768i | 0.900280 | + | 0.372908i | 0.784328 | − | 0.620347i | \(-0.213008\pi\) |
0.115952 | + | 0.993255i | \(0.463008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.450688 | + | 0.450688i | 0.0444076 | + | 0.0444076i | 0.728962 | − | 0.684554i | \(-0.240003\pi\) |
−0.684554 | + | 0.728962i | \(0.740003\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.361009 | − | 0.361009i | 0.0352309 | − | 0.0352309i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.82420 | + | 16.4751i | −0.659720 | + | 1.59271i | 0.138515 | + | 0.990360i | \(0.455767\pi\) |
−0.798236 | + | 0.602345i | \(0.794233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.20664 | − | 2.98509i | 0.690271 | − | 0.285920i | −0.00984205 | − | 0.999952i | \(-0.503133\pi\) |
0.700113 | + | 0.714032i | \(0.253133\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.816726i | 0.0775202i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.76744i | − | 0.824771i | −0.911009 | − | 0.412386i | \(-0.864696\pi\) | ||
0.911009 | − | 0.412386i | \(-0.135304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.271330 | + | 0.112389i | −0.0253017 | + | 0.0104803i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.51767 | − | 13.3208i | 0.510109 | − | 1.23151i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.93484 | − | 6.93484i | 0.635715 | − | 0.635715i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.99450 | − | 2.99450i | −0.272227 | − | 0.272227i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.418571 | + | 0.173378i | 0.0377412 | + | 0.0156329i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.75736 | + | 6.65685i | 0.246626 | + | 0.595407i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4642 | −1.01728 | −0.508641 | − | 0.860979i | \(-0.669852\pi\) | ||||
−0.508641 | + | 0.860979i | \(0.669852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.406429 | 0.0357841 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.32211 | − | 10.4345i | −0.377625 | − | 0.911667i | −0.992410 | − | 0.122972i | \(-0.960757\pi\) |
0.614785 | − | 0.788694i | \(-0.289243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4548 | + | 5.15894i | 1.07997 | + | 0.447337i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.669485 | + | 0.669485i | 0.0576201 | + | 0.0576201i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.42429 | + | 3.42429i | −0.292557 | + | 0.292557i | −0.838090 | − | 0.545533i | \(-0.816327\pi\) |
0.545533 | + | 0.838090i | \(0.316327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.35745 | − | 17.7625i | 0.624051 | − | 1.50659i | −0.222856 | − | 0.974851i | \(-0.571538\pi\) |
0.846907 | − | 0.531741i | \(-0.178462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.41421 | − | 0.585786i | 0.119098 | − | 0.0493321i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 19.0328i | − | 1.59160i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.86377i | − | 0.154778i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.636568 | − | 0.263675i | 0.0525032 | − | 0.0217475i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.931884 | − | 2.24977i | 0.0763429 | − | 0.184308i | −0.881101 | − | 0.472929i | \(-0.843197\pi\) |
0.957443 | + | 0.288621i | \(0.0931967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.21395 | + | 4.21395i | −0.342926 | + | 0.342926i | −0.857466 | − | 0.514540i | \(-0.827963\pi\) |
0.514540 | + | 0.857466i | \(0.327963\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.38372 | + | 6.38372i | 0.516093 | + | 0.516093i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.82843 | − | 2.00000i | −0.387829 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.84401 | − | 14.1087i | −0.466403 | − | 1.12600i | −0.965722 | − | 0.259578i | \(-0.916417\pi\) |
0.499319 | − | 0.866418i | \(-0.333583\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.909832 | 0.0721543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.23256 | −0.0971395 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.72369 | + | 6.57558i | 0.213336 | + | 0.515039i | 0.993932 | − | 0.109997i | \(-0.0350842\pi\) |
−0.780596 | + | 0.625036i | \(0.785084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.573155 | + | 0.237409i | 0.0446201 | + | 0.0184822i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.26355 | + | 3.26355i | 0.252541 | + | 0.252541i | 0.822012 | − | 0.569471i | \(-0.192852\pi\) |
−0.569471 | + | 0.822012i | \(0.692852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.62086 | − | 7.62086i | 0.586220 | − | 0.586220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.74896 | + | 11.4650i | −0.363162 | + | 0.876750i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.86605 | + | 2.84401i | −0.522016 | + | 0.216226i | −0.628102 | − | 0.778131i | \(-0.716168\pi\) |
0.106086 | + | 0.994357i | \(0.466168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.1791i | 1.07184i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.27476i | − | 0.170981i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.79370 | − | 0.742977i | 0.134068 | − | 0.0555327i | −0.314641 | − | 0.949211i | \(-0.601884\pi\) |
0.448709 | + | 0.893678i | \(0.351884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.12132 | + | 14.7782i | −0.454994 | + | 1.09845i | 0.515405 | + | 0.856947i | \(0.327641\pi\) |
−0.970399 | + | 0.241506i | \(0.922359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.521370 | + | 0.521370i | −0.0385408 | + | 0.0385408i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.12845 | + | 2.12845i | 0.156487 | + | 0.156487i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0101 | + | 4.56052i | 0.805137 | + | 0.333499i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.52062 | + | 3.67111i | 0.110609 | + | 0.267034i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.19266 | −0.448085 | −0.224043 | − | 0.974579i | \(-0.571925\pi\) | ||||
−0.224043 | + | 0.974579i | \(0.571925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5784 | 1.04938 | 0.524688 | − | 0.851295i | \(-0.324182\pi\) | ||||
0.524688 | + | 0.851295i | \(0.324182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.296593 | + | 0.716038i | 0.0212395 | + | 0.0512766i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5025 | − | 7.66398i | −1.31825 | − | 0.546036i | −0.390968 | − | 0.920404i | \(-0.627860\pi\) |
−0.927280 | + | 0.374368i | \(0.877860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.3777 | − | 12.3777i | −0.877435 | − | 0.877435i | 0.115834 | − | 0.993269i | \(-0.463046\pi\) |
−0.993269 | + | 0.115834i | \(0.963046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.765816 | − | 0.765816i | 0.0540165 | − | 0.0540165i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.99335 | − | 7.22658i | 0.210092 | − | 0.507207i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.54266 | − | 0.638991i | 0.107744 | − | 0.0446291i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.13461i | − | 0.0788608i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.3812i | 1.13311i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.54851 | + | 1.46984i | −0.244290 | + | 0.101188i | −0.501469 | − | 0.865176i | \(-0.667207\pi\) |
0.257179 | + | 0.966364i | \(0.417207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.727250 | − | 1.75574i | 0.0498304 | − | 0.120301i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.05918 | − | 1.05918i | 0.0722358 | − | 0.0722358i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.5096 | − | 15.5096i | −1.05286 | − | 1.05286i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.770865 | + | 0.319303i | 0.0520903 | + | 0.0215765i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.69743 | + | 13.7548i | 0.383250 | + | 0.925248i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.5550 | 1.84522 | 0.922611 | − | 0.385732i | \(-0.126051\pi\) | ||||
0.922611 | + | 0.385732i | \(0.126051\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0523 | −0.870152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.02694 | + | 14.5503i | 0.400022 | + | 0.965738i | 0.987660 | + | 0.156614i | \(0.0500580\pi\) |
−0.587638 | + | 0.809124i | \(0.699942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.2777 | − | 7.57088i | −1.20783 | − | 0.500298i | −0.314306 | − | 0.949322i | \(-0.601772\pi\) |
−0.893520 | + | 0.449024i | \(0.851772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.84106 | + | 1.84106i | 0.121133 | + | 0.121133i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.70939 | + | 6.70939i | −0.439547 | + | 0.439547i | −0.891859 | − | 0.452313i | \(-0.850599\pi\) |
0.452313 | + | 0.891859i | \(0.350599\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.15894 | − | 5.21215i | 0.140834 | − | 0.340003i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.87062 | + | 0.774837i | −0.121510 | + | 0.0503311i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1995i | 1.69471i | 0.531030 | + | 0.847353i | \(0.321805\pi\) | ||||
−0.531030 | + | 0.847353i | \(0.678195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.6734i | 0.880781i | 0.897806 | + | 0.440391i | \(0.145160\pi\) | ||||
−0.897806 | + | 0.440391i | \(0.854840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.08128 | + | 2.10473i | −0.325964 | + | 0.135019i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.971786 | − | 2.34610i | 0.0620851 | − | 0.149887i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.4708 | + | 14.4708i | −0.920758 | + | 0.920758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.43785 | − | 1.43785i | −0.0911203 | − | 0.0911203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.2054 | + | 5.46984i | 0.833515 | + | 0.345253i | 0.758293 | − | 0.651913i | \(-0.226033\pi\) |
0.0752219 | + | 0.997167i | \(0.476033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.573155 | − | 1.38372i | −0.0360340 | − | 0.0869937i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.485281 | −0.0303895 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.0656 | −1.25166 | −0.625828 | − | 0.779961i | \(-0.715239\pi\) | ||||
−0.625828 | + | 0.779961i | \(0.715239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.83441 | + | 11.6713i | 0.300395 | + | 0.725219i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65228 | + | 2.75546i | 0.411766 | + | 0.170559i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.74976 | + | 4.74976i | 0.292883 | + | 0.292883i | 0.838218 | − | 0.545335i | \(-0.183598\pi\) |
−0.545335 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.37109 | − | 2.37109i | 0.145655 | − | 0.145655i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.852270 | − | 2.05756i | 0.0521581 | − | 0.125921i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.3818 | − | 9.27086i | 1.36464 | − | 0.565254i | 0.424313 | − | 0.905516i | \(-0.360516\pi\) |
0.940331 | + | 0.340262i | \(0.110516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.693146i | 0.0421056i | 0.999778 | + | 0.0210528i | \(0.00670181\pi\) | ||||
−0.999778 | + | 0.0210528i | \(0.993298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.25272i | 0.196864i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.9180 | + | 6.59344i | −0.959890 | + | 0.397600i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1898 | + | 27.0147i | −0.672332 | + | 1.62315i | 0.105305 | + | 0.994440i | \(0.466418\pi\) |
−0.777637 | + | 0.628713i | \(0.783582\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.2771 | − | 14.2771i | 0.854745 | − | 0.854745i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.97958 | − | 6.97958i | −0.416367 | − | 0.416367i | 0.467582 | − | 0.883949i | \(-0.345125\pi\) |
−0.883949 | + | 0.467582i | \(0.845125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6079 | − | 6.05078i | −0.868348 | − | 0.359682i | −0.0963814 | − | 0.995344i | \(-0.530727\pi\) |
−0.771967 | + | 0.635663i | \(0.780727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.255272 | − | 0.616281i | −0.0151210 | − | 0.0365053i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.00778 | 0.413656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.67794 | 0.451644 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.295173 | − | 0.712611i | −0.0173034 | − | 0.0417740i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.85571 | + | 4.08237i | 0.575777 | + | 0.238495i | 0.651518 | − | 0.758633i | \(-0.274132\pi\) |
−0.0757415 | + | 0.997127i | \(0.524132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.92818 | − | 5.92818i | −0.345152 | − | 0.345152i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41421 | + | 3.41421i | −0.198113 | + | 0.198113i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.716038 | − | 1.72867i | 0.0414096 | − | 0.0999715i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.80801 | − | 2.40576i | 0.334768 | − | 0.138666i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.03372i | − | 0.116834i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.71746i | 0.155601i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.96272 | + | 2.88406i | −0.397384 | + | 0.164602i | −0.572421 | − | 0.819960i | \(-0.693996\pi\) |
0.175037 | + | 0.984562i | \(0.443996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0506522 | − | 0.122285i | 0.00288150 | − | 0.00695656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.65020 | − | 4.65020i | 0.263689 | − | 0.263689i | −0.562862 | − | 0.826551i | \(-0.690300\pi\) |
0.826551 | + | 0.562862i | \(0.190300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.325668 | − | 0.325668i | −0.0184078 | − | 0.0184078i | 0.697843 | − | 0.716251i | \(-0.254143\pi\) |
−0.716251 | + | 0.697843i | \(0.754143\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.71604 | + | 2.78187i | 0.378406 | + | 0.156741i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.92866 | − | 19.1415i | −0.445318 | − | 1.07509i | −0.974056 | − | 0.226307i | \(-0.927335\pi\) |
0.528738 | − | 0.848785i | \(-0.322665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.50477 | 0.532165 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.70322 | 0.206694 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.90367 | − | 11.8385i | −0.272847 | − | 0.658712i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.8862 | − | 8.23714i | −1.10309 | − | 0.456914i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.14544 | − | 1.14544i | −0.0633427 | − | 0.0633427i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.7422 | − | 16.7422i | 0.923026 | − | 0.923026i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.91798 | − | 14.2873i | 0.325281 | − | 0.785299i | −0.673649 | − | 0.739052i | \(-0.735274\pi\) |
0.998930 | − | 0.0462470i | \(-0.0147261\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.7438 | + | 4.45021i | −0.588755 | + | 0.243870i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.99154i | − | 0.218081i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.44955i | − | 0.242383i | −0.992629 | − | 0.121191i | \(-0.961329\pi\) | ||
0.992629 | − | 0.121191i | \(-0.0386715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.68212 | + | 0.696756i | −0.0913600 | + | 0.0378426i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1995 | − | 24.6238i | 0.552335 | − | 1.33345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.36330 | + | 8.36330i | −0.451576 | + | 0.451576i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0431257 | + | 0.0431257i | 0.00232181 | + | 0.00232181i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.87485 | − | 3.26187i | −0.422744 | − | 0.175106i | 0.161161 | − | 0.986928i | \(-0.448476\pi\) |
−0.583905 | + | 0.811822i | \(0.698476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9387 | + | 31.2369i | 0.692595 | + | 1.67207i | 0.739486 | + | 0.673172i | \(0.235069\pi\) |
−0.0468913 | + | 0.998900i | \(0.514931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.03212 | −0.321971 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7013 | 1.10182 | 0.550911 | − | 0.834564i | \(-0.314280\pi\) | ||||
0.550911 | + | 0.834564i | \(0.314280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.68031 | − | 6.47085i | −0.142256 | − | 0.343437i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.88163 | − | 0.779397i | −0.0995865 | − | 0.0412501i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.9483 | − | 19.9483i | −1.05283 | − | 1.05283i | −0.998524 | − | 0.0543091i | \(-0.982704\pi\) |
−0.0543091 | − | 0.998524i | \(-0.517296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.980242 | + | 0.980242i | −0.0515917 | + | 0.0515917i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.336548 | + | 0.812498i | −0.0176642 | + | 0.0426451i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.84106 | − | 1.17680i | 0.148708 | − | 0.0615968i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.14270i | − | 0.477245i | −0.971112 | − | 0.238623i | \(-0.923304\pi\) | ||
0.971112 | − | 0.238623i | \(-0.0766959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.45087i | 0.335819i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0018 | − | 5.38552i | 0.675020 | − | 0.279602i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.71974 | − | 8.98024i | 0.192601 | − | 0.464979i | −0.797848 | − | 0.602858i | \(-0.794028\pi\) |
0.990449 | + | 0.137879i | \(0.0440285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.05805 | − | 1.05805i | 0.0546375 | − | 0.0546375i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.39635 | + | 8.39635i | 0.432434 | + | 0.432434i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.80216 | + | 3.23176i | 0.400770 | + | 0.166004i | 0.573959 | − | 0.818884i | \(-0.305407\pi\) |
−0.173189 | + | 0.984889i | \(0.555407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.911069 | + | 2.19951i | 0.0466755 | + | 0.112685i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.4633 | −1.45440 | −0.727202 | − | 0.686423i | \(-0.759180\pi\) | ||||
−0.727202 | + | 0.686423i | \(0.759180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.59587 | 0.489051 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.21457 | + | 5.34644i | 0.112573 | + | 0.271775i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0834 | + | 8.73304i | 1.06897 | + | 0.442783i | 0.846628 | − | 0.532185i | \(-0.178629\pi\) |
0.222344 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.828427 | + | 0.828427i | 0.0418954 | + | 0.0418954i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.65848 | + | 1.65848i | −0.0836591 | + | 0.0836591i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.85570 | + | 6.89426i | −0.143686 | + | 0.346888i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.46808 | − | 2.67916i | 0.324623 | − | 0.134463i | −0.214420 | − | 0.976742i | \(-0.568786\pi\) |
0.539043 | + | 0.842278i | \(0.318786\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2.79956i | − | 0.140153i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.9871i | − | 1.24780i | −0.781505 | − | 0.623898i | \(-0.785548\pi\) | ||
0.781505 | − | 0.623898i | \(-0.214452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.7623 | − | 12.7422i | 1.53238 | − | 0.634733i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.52290 | + | 6.09083i | −0.125364 | + | 0.302656i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.8546 | + | 10.8546i | −0.538041 | + | 0.538041i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.19951 | + | 9.19951i | 0.454887 | + | 0.454887i | 0.896973 | − | 0.442086i | \(-0.145761\pi\) |
−0.442086 | + | 0.896973i | \(0.645761\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.929115 | + | 0.384852i | 0.0458298 | + | 0.0189833i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4649 | − | 32.5071i | −0.662563 | − | 1.59957i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.49430 | −0.367881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.99260 | −0.195519 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.4739 | − | 25.2863i | −0.511685 | − | 1.23532i | −0.942902 | − | 0.333070i | \(-0.891916\pi\) |
0.431217 | − | 0.902248i | \(-0.358084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6841 | + | 6.91080i | 0.813135 | + | 0.336812i | 0.750204 | − | 0.661206i | \(-0.229955\pi\) |
0.0629310 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.4117 | + | 15.4117i | 0.749341 | + | 0.749341i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.53003 | − | 9.53003i | 0.462274 | − | 0.462274i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.36444 | + | 10.5367i | −0.211210 | + | 0.509906i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.65162 | + | 1.51255i | −0.176302 | + | 0.0730267i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 26.5985i | − | 1.28121i | −0.767872 | − | 0.640603i | \(-0.778684\pi\) | ||
0.767872 | − | 0.640603i | \(-0.221316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.96788i | − | 0.479026i | −0.970893 | − | 0.239513i | \(-0.923012\pi\) | ||
0.970893 | − | 0.239513i | \(-0.0769878\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.357582 | + | 0.148115i | −0.0171447 | + | 0.00710158i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.616281 | + | 1.48783i | −0.0294807 | + | 0.0711727i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4631 | − | 17.4631i | 0.833466 | − | 0.833466i | −0.154523 | − | 0.987989i | \(-0.549384\pi\) |
0.987989 | + | 0.154523i | \(0.0493840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.93712 | + | 6.93712i | 0.330339 | + | 0.330339i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.7377 | − | 14.3888i | −1.65044 | − | 0.683634i | −0.653149 | − | 0.757229i | \(-0.726553\pi\) |
−0.997288 | + | 0.0735956i | \(0.976553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.14108 | − | 7.58323i | −0.148901 | − | 0.359480i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.505697 | −0.0239186 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.35000 | −0.394061 | −0.197030 | − | 0.980397i | \(-0.563130\pi\) | ||||
−0.197030 | + | 0.980397i | \(0.563130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.25870 | + | 7.86720i | 0.153446 | + | 0.370452i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.14337 | + | 0.473601i | 0.0537203 | + | 0.0222517i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.47682 | + | 8.47682i | 0.397400 | + | 0.397400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0734 | + | 18.0734i | −0.845436 | + | 0.845436i | −0.989560 | − | 0.144123i | \(-0.953964\pi\) |
0.144123 | + | 0.989560i | \(0.453964\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.44538 | − | 3.48946i | 0.0674646 | − | 0.162874i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4451 | + | 10.9539i | −1.23167 | + | 0.510175i | −0.901102 | − | 0.433607i | \(-0.857241\pi\) |
−0.330569 | + | 0.943782i | \(0.607241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.94169i | − | 0.229660i | −0.993385 | − | 0.114830i | \(-0.963368\pi\) | ||
0.993385 | − | 0.114830i | \(-0.0366323\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.08532i | 0.0503306i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.6806 | + | 8.56617i | −0.956983 | + | 0.396395i | −0.805851 | − | 0.592118i | \(-0.798292\pi\) |
−0.151132 | + | 0.988514i | \(0.548292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.41071 | − | 15.4768i | 0.296019 | − | 0.714653i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.24246 | + | 2.24246i | −0.103327 | + | 0.103327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.40158 | + | 5.40158i | 0.248365 | + | 0.248365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.1157 | + | 7.08955i | 0.785322 | + | 0.325291i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.95753 | + | 11.9685i | 0.226990 | + | 0.548002i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.50637 | −0.251592 | −0.125796 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125796 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.1775 | −0.874418 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0979527 | + | 0.236479i | 0.00445700 | + | 0.0107602i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.62636 | − | 1.08787i | −0.119257 | − | 0.0493978i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9561 | + | 24.9561i | 1.13087 | + | 1.13087i | 0.990033 | + | 0.140837i | \(0.0449794\pi\) |
0.140837 | + | 0.990033i | \(0.455021\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04513 | − | 1.04513i | 0.0472626 | − | 0.0472626i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.79438 | + | 11.5746i | −0.216367 | + | 0.522357i | −0.994377 | − | 0.105895i | \(-0.966229\pi\) |
0.778010 | + | 0.628252i | \(0.216229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.86900 | + | 2.84523i | −0.309364 | + | 0.128143i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.83327i | 0.397026i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 29.3949i | − | 1.31854i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.71684 | + | 3.61063i | −0.390219 | + | 0.161634i | −0.569162 | − | 0.822225i | \(-0.692732\pi\) |
0.178943 | + | 0.983859i | \(0.442732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.366786 | − | 0.885499i | 0.0163868 | − | 0.0395612i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.07960 | − | 5.07960i | 0.226488 | − | 0.226488i | −0.584736 | − | 0.811224i | \(-0.698802\pi\) |
0.811224 | + | 0.584736i | \(0.198802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30002 | − | 5.30002i | −0.235848 | − | 0.235848i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.06777 | − | 0.856498i | −0.0918329 | − | 0.0380384i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5628 | + | 32.7435i | 0.601161 | + | 1.45133i | 0.872388 | + | 0.488815i | \(0.162571\pi\) |
−0.271227 | + | 0.962515i | \(0.587429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9060 | 0.570926 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.19173 | 0.229221 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.186681 | − | 0.450688i | −0.00822614 | − | 0.0198597i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.5807 | + | 11.0101i | 1.16902 | + | 0.484223i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.09130 | + | 1.09130i | 0.0479028 | + | 0.0479028i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.4496 | + | 17.4496i | −0.764479 | + | 0.764479i | −0.977129 | − | 0.212650i | \(-0.931791\pi\) |
0.212650 | + | 0.977129i | \(0.431791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6581 | + | 40.2163i | −0.728410 | + | 1.75854i | −0.0805847 | + | 0.996748i | \(0.525679\pi\) |
−0.647825 | + | 0.761789i | \(0.724321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.72040 | − | 1.12682i | 0.118728 | − | 0.0491787i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.8486i | 0.908179i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8528i | 0.993598i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 29.9237 | − | 12.3948i | 1.29858 | − | 0.537889i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.07107 | + | 9.82843i | −0.176338 | + | 0.425716i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.65087 | − | 9.65087i | 0.417244 | − | 0.417244i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.285094 | − | 0.285094i | −0.0123027 | − | 0.0123027i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.9645 | + | 4.95587i | 0.515349 | + | 0.213464i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9692 | − | 38.5531i | −0.686571 | − | 1.65753i | −0.751578 | − | 0.659644i | \(-0.770707\pi\) |
0.0650071 | − | 0.997885i | \(-0.479293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.32180 | 0.142552 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.97018 | −0.255734 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.383100 | − | 0.924886i | −0.0163802 | − | 0.0395453i | 0.915478 | − | 0.402368i | \(-0.131813\pi\) |
−0.931858 | + | 0.362823i | \(0.881813\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.69932 | − | 4.01759i | −0.413957 | − | 0.171467i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.22658 | − | 7.22658i | −0.307863 | − | 0.307863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.1454 | + | 22.1454i | −0.941717 | + | 0.941717i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.239213 | − | 0.577512i | 0.0101540 | − | 0.0245140i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.29127 | + | 3.43436i | −0.351312 | + | 0.145518i | −0.551359 | − | 0.834268i | \(-0.685891\pi\) |
0.200047 | + | 0.979786i | \(0.435891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.54333i | 0.403640i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.47482i | − | 0.104487i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.7143 | − | 9.40857i | 0.957293 | − | 0.396524i | 0.151326 | − | 0.988484i | \(-0.451646\pi\) |
0.805967 | + | 0.591960i | \(0.201646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.56792 | + | 6.19951i | −0.108033 | + | 0.260816i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.5646 | + | 19.5646i | −0.821637 | + | 0.821637i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6413 | − | 16.6413i | −0.697639 | − | 0.697639i | 0.266262 | − | 0.963901i | \(-0.414211\pi\) |
−0.963901 | + | 0.266262i | \(0.914211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.37532 | − | 3.88338i | −0.392345 | − | 0.162515i | 0.177785 | − | 0.984069i | \(-0.443107\pi\) |
−0.570129 | + | 0.821555i | \(0.693107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.492136 | + | 1.18812i | 0.0205593 | + | 0.0496345i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.69382 | −0.0706371 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.0348 | −0.958951 | −0.479476 | − | 0.877555i | \(-0.659173\pi\) | ||||
−0.479476 | + | 0.877555i | \(0.659173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.15856 | − | 2.79700i | −0.0481480 | − | 0.116239i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.0584 | − | 12.0364i | −1.20555 | − | 0.499354i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0920 | + | 12.0920i | 0.500798 | + | 0.500798i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.80316 | + | 7.80316i | −0.322621 | + | 0.322621i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.02732 | + | 2.48018i | −0.0424022 | + | 0.102368i | −0.943662 | − | 0.330912i | \(-0.892644\pi\) |
0.901260 | + | 0.433280i | \(0.142644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4766 | + | 10.9670i | −1.09095 | + | 0.451885i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.15894i | 0.171076i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.9339i | − | 0.572197i | −0.958200 | − | 0.286098i | \(-0.907642\pi\) | ||
0.958200 | − | 0.286098i | \(-0.0923584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.93484 | + | 2.87250i | −0.284301 | + | 0.117761i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.39112 | + | 3.35846i | −0.0569347 | + | 0.137452i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.02222 | + | 7.02222i | −0.286920 | + | 0.286920i | −0.835861 | − | 0.548941i | \(-0.815031\pi\) |
0.548941 | + | 0.835861i | \(0.315031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0970 | + | 24.0970i | 0.982938 | + | 0.982938i | 0.999857 | − | 0.0169188i | \(-0.00538568\pi\) |
−0.0169188 | + | 0.999857i | \(0.505386\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.2469 | + | 5.90125i | 0.580177 | + | 0.240317i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.24036 | + | 2.99450i | 0.0504278 | + | 0.121744i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.8275 | −1.12948 | −0.564742 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564742 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.62437 | −0.0658229 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7548 | + | 33.2070i | 0.556460 | + | 1.34341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.98279 | + | 4.13501i | 0.403201 | + | 0.167011i | 0.575062 | − | 0.818110i | \(-0.304978\pi\) |
−0.171861 | + | 0.985121i | \(0.554978\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.245193 | − | 0.245193i | −0.00988714 | − | 0.00988714i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2080 | − | 23.2080i | 0.934318 | − | 0.934318i | −0.0636543 | − | 0.997972i | \(-0.520275\pi\) |
0.997972 | + | 0.0636543i | \(0.0202755\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5644 | − | 27.9189i | 0.464811 | − | 1.12215i | −0.501588 | − | 0.865107i | \(-0.667251\pi\) |
0.966399 | − | 0.257047i | \(-0.0827494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.438546 | + | 0.181652i | −0.0175982 | + | 0.00728943i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 34.4481i | − | 1.38013i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5563i | 0.662254i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.14288 | − | 1.30182i | 0.125515 | − | 0.0519899i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.59519 | − | 11.0938i | 0.183222 | − | 0.442338i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.34980 | + | 1.34980i | −0.0537346 | + | 0.0537346i | −0.733463 | − | 0.679729i | \(-0.762097\pi\) |
0.679729 | + | 0.733463i | \(0.262097\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.564006 | + | 0.564006i | 0.0224172 | + | 0.0224172i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.10641 | + | 3.35778i | 0.321693 | + | 0.133250i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.19133 | + | 14.9472i | 0.245309 | + | 0.592229i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.0588 | 1.07043 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.5334 | 1.64047 | 0.820235 | − | 0.572027i | \(-0.193843\pi\) | ||||
0.820235 | + | 0.572027i | \(0.193843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.57282 | + | 3.79713i | 0.0620261 | + | 0.149744i | 0.951854 | − | 0.306553i | \(-0.0991755\pi\) |
−0.889828 | + | 0.456297i | \(0.849176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.287389 | − | 0.119040i | −0.0113159 | − | 0.00468721i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.84193 | − | 5.84193i | −0.229670 | − | 0.229670i | 0.582885 | − | 0.812555i | \(-0.301924\pi\) |
−0.812555 | + | 0.582885i | \(0.801924\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.2323 | − | 30.2323i | 1.18672 | − | 1.18672i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.74311 | + | 4.20823i | −0.0683177 | + | 0.164934i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.0231 | − | 10.7791i | 1.01836 | − | 0.421820i | 0.189864 | − | 0.981810i | \(-0.439195\pi\) |
0.828499 | + | 0.559991i | \(0.189195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.64422i | 0.337758i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.8803i | 0.463495i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.6498 | + | 15.5951i | −1.46663 | + | 0.607497i | −0.966087 | − | 0.258215i | \(-0.916866\pi\) |
−0.500541 | + | 0.865713i | \(0.666866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.14241 | + | 7.58644i | −0.122226 | + | 0.295078i | −0.973136 | − | 0.230233i | \(-0.926051\pi\) |
0.850910 | + | 0.525311i | \(0.176051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.18621 | − | 2.18621i | 0.0849054 | − | 0.0849054i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.29585 | − | 7.29585i | −0.282921 | − | 0.282921i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.863279 | + | 0.357582i | 0.0334263 | + | 0.0138456i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.18982 | − | 5.28670i | −0.0846634 | − | 0.204395i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8584 | −0.534997 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.24262 | −0.202088 | −0.101044 | − | 0.994882i | \(-0.532218\pi\) | ||||
−0.101044 | + | 0.994882i | \(0.532218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.08968 | + | 5.04493i | 0.0804318 | + | 0.194179i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.5716 | − | 6.03574i | −0.560031 | − | 0.231972i | 0.0846677 | − | 0.996409i | \(-0.473017\pi\) |
−0.644699 | + | 0.764437i | \(0.723017\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.43625 | − | 8.43625i | −0.323754 | − | 0.323754i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.31265 | − | 2.31265i | 0.0886210 | − | 0.0886210i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.9028 | − | 35.9785i | 0.570240 | − | 1.37668i | −0.331112 | − | 0.943592i | \(-0.607424\pi\) |
0.901351 | − | 0.433089i | \(-0.142576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.42429 | − | 1.41839i | 0.130835 | − | 0.0541938i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.10842i | 0.156746i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.3637i | 0.813892i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.6714 | + | 6.07710i | −0.558127 | + | 0.231184i | −0.643872 | − | 0.765133i | \(-0.722673\pi\) |
0.0857448 | + | 0.996317i | \(0.472673\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.1869 | + | 34.2502i | −0.538915 | + | 1.30106i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.4050 | + | 10.4050i | −0.394685 | + | 0.394685i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.71006 | − | 4.71006i | −0.178406 | − | 0.178406i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.82046 | + | 0.754059i | 0.0688561 | + | 0.0285211i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.58351 | − | 23.1366i | −0.361964 | − | 0.873859i | −0.995013 | − | 0.0997466i | \(-0.968197\pi\) |
0.633049 | − | 0.774112i | \(-0.281803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.5057 | 0.622524 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17157 | −0.0441240 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.0381 | − | 29.0625i | −0.452739 | − | 1.09301i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.4256 | − | 11.3601i | −1.02999 | − | 0.426636i | −0.197282 | − | 0.980347i | \(-0.563211\pi\) |
−0.832709 | + | 0.553711i | \(0.813211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.3855 | − | 20.3855i | −0.764515 | − | 0.764515i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.85276 | − | 1.85276i | 0.0693864 | − | 0.0693864i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.57457 | + | 13.4582i | −0.208477 | + | 0.503309i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.02663 | − | 2.08210i | 0.187723 | − | 0.0777573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.9976i | 1.45436i | 0.686445 | + | 0.727182i | \(0.259170\pi\) | ||||
−0.686445 | + | 0.727182i | \(0.740830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.04732i | − | 0.0762462i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.62337 | − | 1.08664i | 0.0975643 | − | 0.0404124i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.11354 | − | 9.93095i | 0.152773 | − | 0.368826i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.9474 | − | 34.9474i | 1.29613 | − | 1.29613i | 0.365198 | − | 0.930930i | \(-0.381001\pi\) |
0.930930 | − | 0.365198i | \(-0.118999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.4649 | − | 17.4649i | −0.646846 | − | 0.646846i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.52062 | − | 2.28672i | −0.204188 | − | 0.0845773i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8093 | + | 33.3387i | 0.510060 | + | 1.23139i | 0.943849 | + | 0.330378i | \(0.107176\pi\) |
−0.433789 | + | 0.901015i | \(0.642824\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.527350 | −0.0194516 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.3559 | 0.749819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.75096 | − | 16.2983i | −0.248338 | − | 0.599542i | 0.749725 | − | 0.661750i | \(-0.230186\pi\) |
−0.998063 | + | 0.0622080i | \(0.980186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.92638 | + | 1.62636i | 0.144239 | + | 0.0597458i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6145 | − | 20.6145i | −0.756272 | − | 0.756272i | 0.219370 | − | 0.975642i | \(-0.429600\pi\) |
−0.975642 | + | 0.219370i | \(0.929600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.31788 | + | 1.31788i | −0.0482835 | + | 0.0482835i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.0799 | − | 26.7491i | 0.405391 | − | 0.978700i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.9203 | − | 21.9203i | 1.93367 | − | 0.800951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 27.0344i | − | 0.986499i | −0.869888 | − | 0.493249i | \(-0.835809\pi\) | ||
0.869888 | − | 0.493249i | \(-0.164191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 2.96827i | − | 0.108170i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.21395 | − | 1.74548i | 0.153361 | − | 0.0635244i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5424 | − | 47.1795i | 0.710280 | − | 1.71477i | 0.0109802 | − | 0.999940i | \(-0.496505\pi\) |
0.699300 | − | 0.714828i | \(-0.253495\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.219931 | + | 0.219931i | −0.00798297 | + | 0.00798297i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.53714 | − | 2.53714i | −0.0919713 | − | 0.0919713i | 0.659624 | − | 0.751596i | \(-0.270715\pi\) |
−0.751596 | + | 0.659624i | \(0.770715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.1488 | − | 9.58854i | −0.838042 | − | 0.347129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.64422 | − | 6.38372i | −0.0956021 | − | 0.230804i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.4134 | 1.92865 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0627 | −0.867725 | −0.433862 | − | 0.900979i | \(-0.642850\pi\) | ||||
−0.433862 | + | 0.900979i | \(0.642850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.59463 | + | 3.84977i | 0.0574291 | + | 0.138646i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.4146 | + | 17.9829i | 1.56152 | + | 0.646801i | 0.985352 | − | 0.170534i | \(-0.0545492\pi\) |
0.576163 | + | 0.817335i | \(0.304549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3137 | − | 21.3137i | −0.765611 | − | 0.765611i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.85505 | − | 1.85505i | 0.0665497 | − | 0.0665497i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.50389 | − | 8.45914i | 0.125540 | − | 0.303080i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.9997 | − | 13.6689i | 1.18082 | − | 0.489113i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.01237i | − | 0.107653i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.6880i | 0.417163i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.62213 | − | 1.91455i | 0.164761 | − | 0.0682463i | −0.298778 | − | 0.954323i | \(-0.596579\pi\) |
0.463540 | + | 0.886076i | \(0.346579\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.533819 | − | 1.28875i | 0.0190045 | − | 0.0458808i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.9137 | + | 19.9137i | −0.708051 | + | 0.708051i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.2423 | − | 12.2423i | −0.434735 | − | 0.434735i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.643348 | − | 0.266484i | −0.0228172 | − | 0.00945120i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.78397 | + | 18.7922i | 0.275722 | + | 0.665653i | 0.999708 | − | 0.0241622i | \(-0.00769183\pi\) |
−0.723986 | + | 0.689815i | \(0.757692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.5054 | −0.796185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.7104 | 1.12043 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00142 | + | 14.4887i | 0.211785 | + | 0.511295i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.871553 | + | 0.361009i | 0.0307182 | + | 0.0127239i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.55740 | − | 3.55740i | −0.125227 | − | 0.125227i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.79631 | + | 5.79631i | −0.203787 | + | 0.203787i | −0.801621 | − | 0.597833i | \(-0.796029\pi\) |
0.597833 | + | 0.801621i | \(0.296029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.59457 | − | 6.26386i | 0.0911078 | − | 0.219954i | −0.871757 | − | 0.489939i | \(-0.837019\pi\) |
0.962864 | + | 0.269986i | \(0.0870189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.132987 | − | 0.0550849i | 0.00466405 | − | 0.00193191i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5.44739i | − | 0.190814i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.21377i | − | 0.287363i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −42.7885 | + | 17.7236i | −1.49515 | + | 0.619311i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5014 | + | 35.0095i | −0.506103 | + | 1.22184i | 0.440006 | + | 0.897995i | \(0.354976\pi\) |
−0.946110 | + | 0.323847i | \(0.895024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.84972 | + | 6.84972i | −0.238766 | + | 0.238766i | −0.816339 | − | 0.577573i | \(-0.804000\pi\) |
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.53003 | + | 2.53003i | 0.0880843 | + | 0.0880843i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.6932 | − | 11.4709i | −0.962987 | − | 0.398882i | −0.154890 | − | 0.987932i | \(-0.549502\pi\) |
−0.808097 | + | 0.589049i | \(0.799502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.60232 | − | 3.86834i | −0.0556509 | − | 0.134353i | 0.893609 | − | 0.448847i | \(-0.148165\pi\) |
−0.949259 | + | 0.314494i | \(0.898165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.07228 | 0.210645 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.1302 | −0.350990 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.35181 | − | 3.26355i | −0.0467811 | − | 0.112940i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.80409 | − | 3.23256i | −0.269749 | − | 0.111734i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.4718 | + | 11.4718i | 0.396050 | + | 0.396050i | 0.876837 | − | 0.480787i | \(-0.159649\pi\) |
−0.480787 | + | 0.876837i | \(0.659649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3131 | − | 16.3131i | 0.562519 | − | 0.562519i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.784427 | + | 1.89377i | −0.0270171 | + | 0.0652250i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.62086 | + | 3.15666i | −0.262165 | + | 0.108592i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6030i | 0.467404i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.28352i | 0.112690i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.39424 | + | 0.577512i | −0.0477939 | + | 0.0197969i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.85275 | − | 11.7156i | 0.166155 | − | 0.401133i | −0.818769 | − | 0.574124i | \(-0.805343\pi\) |
0.984924 | + | 0.172990i | \(0.0553429\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.71604 | − | 6.71604i | 0.229684 | − | 0.229684i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5307 | − | 13.5307i | −0.462200 | − | 0.462200i | 0.437176 | − | 0.899376i | \(-0.355979\pi\) |
−0.899376 | + | 0.437176i | \(0.855979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.3433 | + | 20.8529i | 1.71769 | + | 0.711491i | 0.999884 | + | 0.0152507i | \(0.00485464\pi\) |
0.717808 | + | 0.696241i | \(0.245145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.556914 | − | 1.34451i | −0.0189796 | − | 0.0458208i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.50637 | −0.323601 | −0.161800 | − | 0.986824i | \(-0.551730\pi\) | ||||
−0.161800 | + | 0.986824i | \(0.551730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.68802 | 0.193399 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.610172 | − | 1.47309i | −0.0207225 | − | 0.0500286i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.1591 | − | 14.5634i | −1.19269 | − | 0.494028i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.9821 | + | 17.9821i | 0.609299 | + | 0.609299i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.76582 | − | 7.76582i | 0.262833 | − | 0.262833i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.85704 | − | 21.3828i | 0.299423 | − | 0.722870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7883 | + | 6.95392i | −0.566899 | + | 0.234817i | −0.647677 | − | 0.761915i | \(-0.724259\pi\) |
0.0807782 | + | 0.996732i | \(0.474259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2.21534i | − | 0.0747216i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.9687i | 1.58242i | 0.611547 | + | 0.791208i | \(0.290547\pi\) | ||||
−0.611547 | + | 0.791208i | \(0.709453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0237 | + | 4.56617i | −0.370978 | + | 0.153664i | −0.560380 | − | 0.828236i | \(-0.689345\pi\) |
0.189403 | + | 0.981900i | \(0.439345\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.666261 | + | 1.60850i | −0.0223961 | + | 0.0540690i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.9419 | − | 31.9419i | 1.07250 | − | 1.07250i | 0.0753464 | − | 0.997157i | \(-0.475994\pi\) |
0.997157 | − | 0.0753464i | \(-0.0240063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.0390 | + | 26.0390i | 0.873319 | + | 0.873319i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.0617 | − | 12.8662i | −1.04061 | − | 0.431034i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.8385 | − | 28.5807i | −0.396160 | − | 0.956416i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.48595 | −0.0496699 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.388566 | −0.0129738 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.36330 | + | 15.3624i | 0.212228 | + | 0.512364i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.3585 | − | 5.11904i | −0.411720 | − | 0.170540i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.923135 | − | 0.923135i | −0.0307200 | − | 0.0307200i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.65685 | − | 8.65685i | 0.287764 | − | 0.287764i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.99616 | + | 12.0618i | −0.165895 | + | 0.400505i | −0.984863 | − | 0.173333i | \(-0.944546\pi\) |
0.818969 | + | 0.573838i | \(0.194546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.7529 | − | 11.0814i | 0.887338 | − | 0.367547i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.1188i | 0.434645i | 0.976100 | + | 0.217322i | \(0.0697323\pi\) | ||||
−0.976100 | + | 0.217322i | \(0.930268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 38.2191i | − | 1.26487i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.521370 | − | 0.215959i | 0.0172360 | − | 0.00713937i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.8833 | + | 33.5171i | −0.458465 | + | 1.10683i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.2415 | + | 17.2415i | −0.568746 | + | 0.568746i | −0.931777 | − | 0.363031i | \(-0.881742\pi\) |
0.363031 | + | 0.931777i | \(0.381742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.10667 | + | 1.10667i | 0.0364659 | + | 0.0364659i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.2263 | + | 17.0765i | 1.35698 | + | 0.562080i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.64357 | + | 16.0390i | 0.218439 | + | 0.527359i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.88462 | 0.0618990 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.9966 | −1.50910 | −0.754550 | − | 0.656242i | \(-0.772145\pi\) | ||||
−0.754550 | + | 0.656242i | \(0.772145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.32876 | − | 12.8648i | −0.174643 | − | 0.421626i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.26174 | − | 0.522630i | −0.0413076 | − | 0.0171101i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.44955 | − | 6.44955i | −0.210923 | − | 0.210923i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.67273 | + | 3.67273i | −0.119983 | + | 0.119983i | −0.764549 | − | 0.644566i | \(-0.777038\pi\) |
0.644566 | + | 0.764549i | \(0.277038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.0366014 | + | 0.0883635i | −0.00119444 | + | 0.00288363i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.7873 | + | 17.3089i | −1.36223 | + | 0.564253i | −0.939670 | − | 0.342083i | \(-0.888868\pi\) |
−0.422558 | + | 0.906336i | \(0.638868\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.837141i | 0.0272611i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 3.04125i | − | 0.0989317i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.6427 | − | 18.0774i | 1.41820 | − | 0.587436i | 0.463790 | − | 0.885945i | \(-0.346489\pi\) |
0.954407 | + | 0.298509i | \(0.0964894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.49753 | + | 18.1006i | −0.243380 | + | 0.587571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.04238 | + | 3.04238i | −0.0986559 | + | 0.0986559i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.12750 | + | 6.12750i | 0.198489 | + | 0.198489i | 0.799352 | − | 0.600863i | \(-0.205176\pi\) |
−0.600863 | + | 0.799352i | \(0.705176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.37887 | + | 1.81379i | 0.141697 | + | 0.0586928i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.755352 | − | 1.82358i | −0.0244171 | − | 0.0589480i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.5554 | 0.502310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.1783 | + | 48.7147i | 0.650237 | + | 1.56981i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.3085 | − | 4.26991i | −0.331842 | − | 0.137453i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.03516 | + | 1.03516i | 0.0332885 | + | 0.0332885i | 0.723555 | − | 0.690267i | \(-0.242507\pi\) |
−0.690267 | + | 0.723555i | \(0.742507\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.88163 | + | 1.88163i | −0.0604467 | + | 0.0604467i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.4218 | + | 37.2315i | −0.494909 | + | 1.19482i | 0.457285 | + | 0.889320i | \(0.348822\pi\) |
−0.952194 | + | 0.305495i | \(0.901178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −57.0556 | + | 23.6332i | −1.82912 | + | 0.757646i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.46997i | 0.143154i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8457i | 0.922857i | 0.887177 | + | 0.461429i | \(0.152663\pi\) | ||||
−0.887177 | + | 0.461429i | \(0.847337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.6727 | − | 16.0187i | 1.23598 | − | 0.511961i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.82653 | − | 21.3091i | 0.281809 | − | 0.680348i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.9561 | + | 40.9561i | −1.30630 | + | 1.30630i | −0.382231 | + | 0.924067i | \(0.624844\pi\) |
−0.924067 | + | 0.382231i | \(0.875156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.8385 | + | 10.8385i | 0.345344 | + | 0.345344i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.54266 | − | 1.88163i | −0.144594 | − | 0.0598930i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.287389 | + | 0.693818i | 0.00913843 | + | 0.0220621i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.9605 | −1.33292 | −0.666460 | − | 0.745541i | \(-0.732191\pi\) | ||||
−0.666460 | + | 0.745541i | \(0.732191\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.21145 | −0.101912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.12703 | + | 12.3777i | 0.162538 | + | 0.392401i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.4380 | + | 13.0221i | 0.995652 | + | 0.412413i | 0.820201 | − | 0.572076i | \(-0.193862\pi\) |
0.175451 | + | 0.984488i | \(0.443862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.44017 | + | 3.44017i | 0.108842 | + | 0.108842i |
(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 | 256.2.g.d.225.1 | 8 | ||
4.3 | odd | 2 | 256.2.g.c.225.2 | 8 | |||
8.3 | odd | 2 | 128.2.g.b.113.1 | 8 | |||
8.5 | even | 2 | 32.2.g.b.5.2 | ✓ | 8 | ||
16.3 | odd | 4 | 512.2.g.g.193.1 | 8 | |||
16.5 | even | 4 | 512.2.g.h.193.1 | 8 | |||
16.11 | odd | 4 | 512.2.g.f.193.2 | 8 | |||
16.13 | even | 4 | 512.2.g.e.193.2 | 8 | |||
24.5 | odd | 2 | 288.2.v.b.37.1 | 8 | |||
24.11 | even | 2 | 1152.2.v.b.1009.2 | 8 | |||
32.3 | odd | 8 | 128.2.g.b.17.1 | 8 | |||
32.5 | even | 8 | 512.2.g.e.321.2 | 8 | |||
32.11 | odd | 8 | 512.2.g.f.321.2 | 8 | |||
32.13 | even | 8 | inner | 256.2.g.d.33.1 | 8 | ||
32.19 | odd | 8 | 256.2.g.c.33.2 | 8 | |||
32.21 | even | 8 | 512.2.g.h.321.1 | 8 | |||
32.27 | odd | 8 | 512.2.g.g.321.1 | 8 | |||
32.29 | even | 8 | 32.2.g.b.13.2 | yes | 8 | ||
40.13 | odd | 4 | 800.2.ba.d.549.2 | 8 | |||
40.29 | even | 2 | 800.2.y.b.101.1 | 8 | |||
40.37 | odd | 4 | 800.2.ba.c.549.1 | 8 | |||
64.13 | even | 16 | 4096.2.a.k.1.4 | 8 | |||
64.19 | odd | 16 | 4096.2.a.q.1.4 | 8 | |||
64.45 | even | 16 | 4096.2.a.k.1.5 | 8 | |||
64.51 | odd | 16 | 4096.2.a.q.1.5 | 8 | |||
96.29 | odd | 8 | 288.2.v.b.109.1 | 8 | |||
96.35 | even | 8 | 1152.2.v.b.145.2 | 8 | |||
160.29 | even | 8 | 800.2.y.b.301.1 | 8 | |||
160.93 | odd | 8 | 800.2.ba.c.749.1 | 8 | |||
160.157 | odd | 8 | 800.2.ba.d.749.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.b.5.2 | ✓ | 8 | 8.5 | even | 2 | ||
32.2.g.b.13.2 | yes | 8 | 32.29 | even | 8 | ||
128.2.g.b.17.1 | 8 | 32.3 | odd | 8 | |||
128.2.g.b.113.1 | 8 | 8.3 | odd | 2 | |||
256.2.g.c.33.2 | 8 | 32.19 | odd | 8 | |||
256.2.g.c.225.2 | 8 | 4.3 | odd | 2 | |||
256.2.g.d.33.1 | 8 | 32.13 | even | 8 | inner | ||
256.2.g.d.225.1 | 8 | 1.1 | even | 1 | trivial | ||
288.2.v.b.37.1 | 8 | 24.5 | odd | 2 | |||
288.2.v.b.109.1 | 8 | 96.29 | odd | 8 | |||
512.2.g.e.193.2 | 8 | 16.13 | even | 4 | |||
512.2.g.e.321.2 | 8 | 32.5 | even | 8 | |||
512.2.g.f.193.2 | 8 | 16.11 | odd | 4 | |||
512.2.g.f.321.2 | 8 | 32.11 | odd | 8 | |||
512.2.g.g.193.1 | 8 | 16.3 | odd | 4 | |||
512.2.g.g.321.1 | 8 | 32.27 | odd | 8 | |||
512.2.g.h.193.1 | 8 | 16.5 | even | 4 | |||
512.2.g.h.321.1 | 8 | 32.21 | even | 8 | |||
800.2.y.b.101.1 | 8 | 40.29 | even | 2 | |||
800.2.y.b.301.1 | 8 | 160.29 | even | 8 | |||
800.2.ba.c.549.1 | 8 | 40.37 | odd | 4 | |||
800.2.ba.c.749.1 | 8 | 160.93 | odd | 8 | |||
800.2.ba.d.549.2 | 8 | 40.13 | odd | 4 | |||
800.2.ba.d.749.2 | 8 | 160.157 | odd | 8 | |||
1152.2.v.b.145.2 | 8 | 96.35 | even | 8 | |||
1152.2.v.b.1009.2 | 8 | 24.11 | even | 2 | |||
4096.2.a.k.1.4 | 8 | 64.13 | even | 16 | |||
4096.2.a.k.1.5 | 8 | 64.45 | even | 16 | |||
4096.2.a.q.1.4 | 8 | 64.19 | odd | 16 | |||
4096.2.a.q.1.5 | 8 | 64.51 | odd | 16 |