Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.5 | ||
Root | \(0.793353 - 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.2.p.c.215.5 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.358719 | − | 0.207107i | 0.253653 | − | 0.146447i | −0.367783 | − | 0.929912i | \(-0.619883\pi\) |
0.621436 | + | 0.783465i | \(0.286550\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.914214 | + | 1.58346i | −0.457107 | + | 0.791732i | ||||
\(5\) | −1.46508 | − | 2.53759i | −0.655202 | − | 1.13484i | −0.981843 | − | 0.189694i | \(-0.939250\pi\) |
0.326641 | − | 0.945148i | \(-0.394083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.05110 | − | 0.606854i | −0.332388 | − | 0.191904i | ||||
\(11\) | −4.18154 | − | 2.41421i | −1.26078 | − | 0.727913i | −0.287556 | − | 0.957764i | \(-0.592843\pi\) |
−0.973226 | + | 0.229851i | \(0.926176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.93015i | − | 0.812678i | −0.913722 | − | 0.406339i | \(-0.866805\pi\) | ||
0.913722 | − | 0.406339i | \(-0.133195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 3.53701 | − | 6.12627i | 0.857850 | − | 1.48584i | −0.0161259 | − | 0.999870i | \(-0.505133\pi\) |
0.873976 | − | 0.485970i | \(-0.161533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.07517 | + | 2.93015i | −1.16432 | + | 0.672223i | −0.952336 | − | 0.305050i | \(-0.901327\pi\) |
−0.211988 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(20\) | 5.35757 | 1.19799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −1.73205 | + | 1.00000i | −0.361158 | + | 0.208514i | −0.669588 | − | 0.742732i | \(-0.733529\pi\) |
0.308431 | + | 0.951247i | \(0.400196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79289 | + | 3.10538i | −0.358579 | + | 0.621076i | ||||
\(26\) | −0.606854 | − | 1.05110i | −0.119014 | − | 0.206138i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.828427i | − | 0.153835i | −0.997037 | − | 0.0769175i | \(-0.975492\pi\) | ||
0.997037 | − | 0.0769175i | \(-0.0245078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.07517 | − | 2.93015i | −0.911528 | − | 0.526271i | −0.0306053 | − | 0.999532i | \(-0.509743\pi\) |
−0.880922 | + | 0.473261i | \(0.843077\pi\) | |||||||
\(32\) | −3.82282 | − | 2.20711i | −0.675786 | − | 0.390165i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.93015i | − | 0.502517i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.70711 | + | 4.68885i | 0.445046 | + | 0.770842i | 0.998055 | − | 0.0623331i | \(-0.0198541\pi\) |
−0.553010 | + | 0.833175i | \(0.686521\pi\) | |||||||
\(38\) | −1.21371 | + | 2.10220i | −0.196890 | + | 0.341023i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.02407 | − | 2.32330i | 0.636261 | − | 0.367346i | ||||
\(41\) | −1.21371 | −0.189549 | −0.0947747 | − | 0.995499i | \(-0.530213\pi\) | ||||
−0.0947747 | + | 0.995499i | \(0.530213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48528 | 0.683999 | 0.341999 | − | 0.939700i | \(-0.388896\pi\) | ||||
0.341999 | + | 0.939700i | \(0.388896\pi\) | |||||||
\(44\) | 7.64564 | − | 4.41421i | 1.15262 | − | 0.665468i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.414214 | + | 0.717439i | −0.0610725 | + | 0.105781i | ||||
\(47\) | −2.93015 | − | 5.07517i | −0.427406 | − | 0.740290i | 0.569235 | − | 0.822175i | \(-0.307239\pi\) |
−0.996642 | + | 0.0818849i | \(0.973906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.48528i | 0.210051i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.63979 | + | 2.67878i | 0.643423 | + | 0.371481i | ||||
\(53\) | 6.12372 | + | 3.53553i | 0.841158 | + | 0.485643i | 0.857658 | − | 0.514221i | \(-0.171919\pi\) |
−0.0164995 | + | 0.999864i | \(0.505252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.1480i | 1.90772i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.171573 | − | 0.297173i | −0.0225286 | − | 0.0390207i | ||||
\(59\) | −2.93015 | + | 5.07517i | −0.381473 | + | 0.660731i | −0.991273 | − | 0.131824i | \(-0.957916\pi\) |
0.609800 | + | 0.792555i | \(0.291250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.05110 | + | 0.606854i | −0.134580 | + | 0.0776997i | −0.565778 | − | 0.824557i | \(-0.691424\pi\) |
0.431198 | + | 0.902257i | \(0.358091\pi\) | |||||||
\(62\) | −2.42742 | −0.308282 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | −7.43551 | + | 4.29289i | −0.922261 | + | 0.532468i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.24264 | − | 7.34847i | 0.518321 | − | 0.897758i | −0.481452 | − | 0.876472i | \(-0.659891\pi\) |
0.999773 | − | 0.0212861i | \(-0.00677610\pi\) | |||||||
\(68\) | 6.46716 | + | 11.2014i | 0.784258 | + | 1.35837i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.828427i | 0.0983162i | 0.998791 | + | 0.0491581i | \(0.0156538\pi\) | ||||
−0.998791 | + | 0.0491581i | \(0.984346\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12627 | + | 3.53701i | 0.717026 | + | 0.413975i | 0.813657 | − | 0.581345i | \(-0.197473\pi\) |
−0.0966311 | + | 0.995320i | \(0.530807\pi\) | |||||||
\(74\) | 1.94218 | + | 1.12132i | 0.225774 | + | 0.130351i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 10.7151i | − | 1.22911i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.828427 | − | 1.43488i | −0.0932053 | − | 0.161436i | 0.815653 | − | 0.578542i | \(-0.196378\pi\) |
−0.908858 | + | 0.417105i | \(0.863045\pi\) | |||||||
\(80\) | −4.39523 | + | 7.61276i | −0.491401 | + | 0.851132i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.435381 | + | 0.251367i | −0.0480798 | + | 0.0277589i | ||||
\(83\) | −11.7206 | −1.28650 | −0.643252 | − | 0.765655i | \(-0.722415\pi\) | ||||
−0.643252 | + | 0.765655i | \(0.722415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7279 | −2.24826 | ||||||||
\(86\) | 1.60896 | − | 0.928932i | 0.173498 | − | 0.100169i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.82843 | − | 6.63103i | 0.408112 | − | 0.706870i | ||||
\(89\) | 5.60894 | + | 9.71496i | 0.594546 | + | 1.02978i | 0.993611 | + | 0.112861i | \(0.0360015\pi\) |
−0.399065 | + | 0.916923i | \(0.630665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 3.65685i | − | 0.381253i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.10220 | − | 1.21371i | −0.216826 | − | 0.125184i | ||||
\(95\) | 14.8710 | + | 8.58579i | 1.52573 | + | 0.880883i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.07401i | 0.718257i | 0.933288 | + | 0.359128i | \(0.116926\pi\) | ||||
−0.933288 | + | 0.359128i | \(0.883074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.27817 | − | 5.67796i | −0.327817 | − | 0.567796i | ||||
\(101\) | 2.67878 | − | 4.63979i | 0.266549 | − | 0.461676i | −0.701419 | − | 0.712749i | \(-0.747450\pi\) |
0.967968 | + | 0.251073i | \(0.0807833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2525 | − | 7.07401i | 1.20728 | − | 0.697023i | 0.245115 | − | 0.969494i | \(-0.421174\pi\) |
0.962164 | + | 0.272471i | \(0.0878409\pi\) | |||||||
\(104\) | 4.64659 | 0.455636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.92893 | 0.284483 | ||||||||
\(107\) | −11.5300 | + | 6.65685i | −1.11465 | + | 0.643542i | −0.940029 | − | 0.341094i | \(-0.889203\pi\) |
−0.174619 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.70711 | − | 4.68885i | 0.259294 | − | 0.449110i | −0.706759 | − | 0.707454i | \(-0.749844\pi\) |
0.966053 | + | 0.258344i | \(0.0831769\pi\) | |||||||
\(110\) | 2.93015 | + | 5.07517i | 0.279379 | + | 0.483899i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.8995i | − | 1.30755i | −0.756687 | − | 0.653777i | \(-0.773183\pi\) | ||
0.756687 | − | 0.653777i | \(-0.226817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.07517 | + | 2.93015i | 0.473262 | + | 0.273238i | ||||
\(116\) | 1.31178 | + | 0.757359i | 0.121796 | + | 0.0703190i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.42742i | 0.223462i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.15685 | + | 10.6640i | 0.559714 | + | 0.969453i | ||||
\(122\) | −0.251367 | + | 0.435381i | −0.0227577 | + | 0.0394175i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.27958 | − | 5.35757i | 0.833331 | − | 0.481124i | ||||
\(125\) | −4.14386 | −0.370638 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4853 | 1.46283 | 0.731416 | − | 0.681931i | \(-0.238860\pi\) | ||||
0.731416 | + | 0.681931i | \(0.238860\pi\) | |||||||
\(128\) | 9.14207 | − | 5.27817i | 0.808052 | − | 0.466529i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.77817 | + | 3.07989i | −0.155956 | + | 0.270124i | ||||
\(131\) | −4.14386 | − | 7.17738i | −0.362051 | − | 0.627090i | 0.626248 | − | 0.779624i | \(-0.284590\pi\) |
−0.988298 | + | 0.152534i | \(0.951257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.51472i | − | 0.303625i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.71496 | + | 5.60894i | 0.833051 | + | 0.480962i | ||||
\(137\) | 4.18154 | + | 2.41421i | 0.357253 | + | 0.206260i | 0.667875 | − | 0.744273i | \(-0.267204\pi\) |
−0.310622 | + | 0.950534i | \(0.600537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.28772i | − | 0.702955i | −0.936196 | − | 0.351478i | \(-0.885679\pi\) | ||
0.936196 | − | 0.351478i | \(-0.114321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.171573 | + | 0.297173i | 0.0143981 | + | 0.0249382i | ||||
\(143\) | −7.07401 | + | 12.2525i | −0.591559 | + | 1.02461i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.10220 | + | 1.21371i | −0.174579 | + | 0.100793i | ||||
\(146\) | 2.93015 | 0.242501 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.89949 | −0.813733 | ||||||||
\(149\) | 3.67423 | − | 2.12132i | 0.301005 | − | 0.173785i | −0.341889 | − | 0.939740i | \(-0.611067\pi\) |
0.642894 | + | 0.765955i | \(0.277733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.24264 | + | 3.88437i | −0.182504 | + | 0.316105i | −0.942732 | − | 0.333550i | \(-0.891753\pi\) |
0.760229 | + | 0.649655i | \(0.225087\pi\) | |||||||
\(152\) | −4.64659 | − | 8.04814i | −0.376889 | − | 0.652790i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.1716i | 1.37925i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.8653 | − | 11.4692i | −1.58542 | − | 0.915345i | −0.994047 | − | 0.108949i | \(-0.965251\pi\) |
−0.591376 | − | 0.806396i | \(-0.701415\pi\) | |||||||
\(158\) | −0.594346 | − | 0.343146i | −0.0472836 | − | 0.0272992i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.9343i | 1.02255i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.58579 | − | 7.94282i | −0.359187 | − | 0.622129i | 0.628639 | − | 0.777698i | \(-0.283612\pi\) |
−0.987825 | + | 0.155568i | \(0.950279\pi\) | |||||||
\(164\) | 1.10959 | − | 1.92186i | 0.0866443 | − | 0.150072i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.20441 | + | 2.42742i | −0.326325 | + | 0.188404i | ||||
\(167\) | −14.1480 | −1.09481 | −0.547403 | − | 0.836869i | \(-0.684384\pi\) | ||||
−0.547403 | + | 0.836869i | \(0.684384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41421 | 0.339555 | ||||||||
\(170\) | −7.43551 | + | 4.29289i | −0.570278 | + | 0.329250i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.10051 | + | 7.10228i | −0.312661 | + | 0.541544i | ||||
\(173\) | 0.606854 | + | 1.05110i | 0.0461383 | + | 0.0799138i | 0.888172 | − | 0.459511i | \(-0.151975\pi\) |
−0.842034 | + | 0.539424i | \(0.818642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.4853i | 1.09187i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.02407 | + | 2.32330i | 0.301617 | + | 0.174138i | ||||
\(179\) | −22.9369 | − | 13.2426i | −1.71439 | − | 0.989801i | −0.928420 | − | 0.371532i | \(-0.878833\pi\) |
−0.785966 | − | 0.618269i | \(-0.787834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.50143i | − | 0.706236i | −0.935579 | − | 0.353118i | \(-0.885121\pi\) | ||
0.935579 | − | 0.353118i | \(-0.114879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.58579 | − | 2.74666i | −0.116906 | − | 0.202487i | ||||
\(185\) | 7.93223 | − | 13.7390i | 0.583189 | − | 1.01011i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.5803 | + | 17.0782i | −2.16312 | + | 1.24888i | ||||
\(188\) | 10.7151 | 0.781482 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.11270 | 0.516009 | ||||||||
\(191\) | 13.1390 | − | 7.58579i | 0.950702 | − | 0.548888i | 0.0574033 | − | 0.998351i | \(-0.481718\pi\) |
0.893299 | + | 0.449463i | \(0.148385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.17157 | − | 5.49333i | 0.228295 | − | 0.395418i | −0.729008 | − | 0.684505i | \(-0.760018\pi\) |
0.957303 | + | 0.289087i | \(0.0933517\pi\) | |||||||
\(194\) | 1.46508 | + | 2.53759i | 0.105186 | + | 0.182188i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.75736i | − | 0.552689i | −0.961059 | − | 0.276344i | \(-0.910877\pi\) | ||
0.961059 | − | 0.276344i | \(-0.0891231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3548 | + | 8.28772i | 1.01758 | + | 0.587501i | 0.913402 | − | 0.407058i | \(-0.133445\pi\) |
0.104179 | + | 0.994559i | \(0.466779\pi\) | |||||||
\(200\) | −4.92447 | − | 2.84315i | −0.348213 | − | 0.201041i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2.21918i | − | 0.156141i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.77817 | + | 3.07989i | 0.124193 | + | 0.215109i | ||||
\(206\) | 2.93015 | − | 5.07517i | 0.204153 | − | 0.353604i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.61276 | + | 4.39523i | −0.527850 | + | 0.304754i | ||||
\(209\) | 28.2960 | 1.95728 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3137 | −1.05424 | −0.527120 | − | 0.849791i | \(-0.676728\pi\) | ||||
−0.527120 | + | 0.849791i | \(0.676728\pi\) | |||||||
\(212\) | −11.1968 | + | 6.46447i | −0.768998 | + | 0.443981i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.75736 | + | 4.77589i | −0.188489 | + | 0.326473i | ||||
\(215\) | −6.57128 | − | 11.3818i | −0.448157 | − | 0.776231i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 2.24264i | − | 0.151891i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22.4029 | − | 12.9343i | −1.51040 | − | 0.872031i | ||||
\(221\) | −17.9509 | − | 10.3640i | −1.20751 | − | 0.697155i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.43289i | − | 0.229883i | −0.993372 | − | 0.114942i | \(-0.963332\pi\) | ||
0.993372 | − | 0.114942i | \(-0.0366681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.87868 | − | 4.98602i | −0.191487 | − | 0.331665i | ||||
\(227\) | 7.07401 | − | 12.2525i | 0.469519 | − | 0.813230i | −0.529874 | − | 0.848076i | \(-0.677761\pi\) |
0.999393 | + | 0.0348463i | \(0.0110942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2766 | − | 9.39731i | 1.07559 | − | 0.620992i | 0.145886 | − | 0.989301i | \(-0.453397\pi\) |
0.929703 | + | 0.368310i | \(0.120063\pi\) | |||||||
\(230\) | 2.42742 | 0.160059 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.31371 | 0.0862492 | ||||||||
\(233\) | 4.47871 | − | 2.58579i | 0.293410 | − | 0.169401i | −0.346069 | − | 0.938209i | \(-0.612484\pi\) |
0.639479 | + | 0.768809i | \(0.279150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.58579 | + | 14.8710i | −0.560075 | + | 0.970078i | ||||
\(236\) | −5.35757 | − | 9.27958i | −0.348748 | − | 0.604049i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6569i | 0.754019i | 0.926209 | + | 0.377010i | \(0.123048\pi\) | ||||
−0.926209 | + | 0.377010i | \(0.876952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9675 | − | 12.6829i | −1.41505 | − | 0.816980i | −0.419193 | − | 0.907897i | \(-0.637687\pi\) |
−0.995858 | + | 0.0909167i | \(0.971020\pi\) | |||||||
\(242\) | 4.41717 | + | 2.55025i | 0.283946 | + | 0.163936i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.21918i | − | 0.142068i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.58579 | + | 14.8710i | 0.546301 | + | 0.946220i | ||||
\(248\) | 4.64659 | − | 8.04814i | 0.295059 | − | 0.511057i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.48648 | + | 0.858221i | −0.0940134 | + | 0.0542787i | ||||
\(251\) | 10.7151 | 0.676333 | 0.338167 | − | 0.941086i | \(-0.390193\pi\) | ||||
0.338167 | + | 0.941086i | \(0.390193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.65685 | 0.607121 | ||||||||
\(254\) | 5.91359 | − | 3.41421i | 0.371052 | − | 0.214227i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | −5.25345 | − | 9.09924i | −0.327701 | − | 0.567595i | 0.654354 | − | 0.756188i | \(-0.272941\pi\) |
−0.982055 | + | 0.188593i | \(0.939607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 15.6985i | − | 0.973579i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.97297 | − | 1.71644i | −0.183670 | − | 0.106042i | ||||
\(263\) | −3.58719 | − | 2.07107i | −0.221196 | − | 0.127708i | 0.385308 | − | 0.922788i | \(-0.374095\pi\) |
−0.606504 | + | 0.795081i | \(0.707429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.7193i | − | 1.27278i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.75736 | + | 13.4361i | 0.473856 | + | 0.820743i | ||||
\(269\) | 1.10959 | − | 1.92186i | 0.0676528 | − | 0.117178i | −0.830215 | − | 0.557444i | \(-0.811782\pi\) |
0.897868 | + | 0.440265i | \(0.145116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.07517 | − | 2.93015i | 0.308295 | − | 0.177994i | −0.337868 | − | 0.941193i | \(-0.609706\pi\) |
0.646163 | + | 0.763199i | \(0.276373\pi\) | |||||||
\(272\) | −21.2220 | −1.28677 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 14.9941 | − | 8.65685i | 0.904179 | − | 0.522028i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.48528 | + | 11.2328i | −0.389663 | + | 0.674916i | −0.992404 | − | 0.123021i | \(-0.960742\pi\) |
0.602741 | + | 0.797937i | \(0.294075\pi\) | |||||||
\(278\) | −1.71644 | − | 2.97297i | −0.102945 | − | 0.178307i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.1716i | − | 0.785750i | −0.919592 | − | 0.392875i | \(-0.871480\pi\) | ||
0.919592 | − | 0.392875i | \(-0.128520\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.04814 | + | 4.64659i | 0.478412 | + | 0.276211i | 0.719755 | − | 0.694229i | \(-0.244254\pi\) |
−0.241342 | + | 0.970440i | \(0.577588\pi\) | |||||||
\(284\) | −1.31178 | − | 0.757359i | −0.0778401 | − | 0.0449410i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.86030i | 0.346527i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5208 | − | 28.6149i | −0.971813 | − | 1.68323i | ||||
\(290\) | −0.502734 | + | 0.870762i | −0.0295216 | + | 0.0511329i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.2014 | + | 6.46716i | −0.655515 | + | 0.378462i | ||||
\(293\) | 22.9385 | 1.34008 | 0.670040 | − | 0.742325i | \(-0.266277\pi\) | ||||
0.670040 | + | 0.742325i | \(0.266277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.1716 | 0.999768 | ||||||||
\(296\) | −7.43551 | + | 4.29289i | −0.432180 | + | 0.249519i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.878680 | − | 1.52192i | 0.0509005 | − | 0.0881623i | ||||
\(299\) | 2.93015 | + | 5.07517i | 0.169455 | + | 0.293505i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.85786i | 0.106908i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.2255 | + | 8.79045i | 0.873243 | + | 0.504167i | ||||
\(305\) | 3.07989 | + | 1.77817i | 0.176354 | + | 0.101818i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4357i | 1.28048i | 0.768177 | + | 0.640238i | \(0.221164\pi\) | ||||
−0.768177 | + | 0.640238i | \(0.778836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.55635 | + | 6.15978i | 0.201987 | + | 0.349852i | ||||
\(311\) | −12.9343 | + | 22.4029i | −0.733438 | + | 1.27035i | 0.221968 | + | 0.975054i | \(0.428752\pi\) |
−0.955405 | + | 0.295297i | \(0.904581\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.63979 | − | 2.67878i | 0.262256 | − | 0.151414i | −0.363107 | − | 0.931747i | \(-0.618284\pi\) |
0.625363 | + | 0.780334i | \(0.284951\pi\) | |||||||
\(314\) | −9.50143 | −0.536197 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.02944 | 0.170419 | ||||||||
\(317\) | −27.9229 | + | 16.1213i | −1.56831 | + | 0.905464i | −0.571942 | + | 0.820294i | \(0.693810\pi\) |
−0.996366 | + | 0.0851698i | \(0.972857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | + | 3.46410i | −0.111979 | + | 0.193952i | ||||
\(320\) | −6.11167 | − | 10.5857i | −0.341653 | − | 0.591760i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.4558i | 2.30666i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.09924 | + | 5.25345i | 0.504735 | + | 0.291409i | ||||
\(326\) | −3.29002 | − | 1.89949i | −0.182217 | − | 0.105203i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1.92468i | − | 0.106273i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8284 | − | 18.7554i | −0.595184 | − | 1.03089i | −0.993521 | − | 0.113650i | \(-0.963746\pi\) |
0.398337 | − | 0.917239i | \(-0.369588\pi\) | |||||||
\(332\) | 10.7151 | − | 18.5592i | 0.588069 | − | 1.01857i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.07517 | + | 2.93015i | −0.277701 | + | 0.160331i | ||||
\(335\) | −24.8632 | −1.35842 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0711 | −1.47466 | −0.737328 | − | 0.675535i | \(-0.763913\pi\) | ||||
−0.737328 | + | 0.675535i | \(0.763913\pi\) | |||||||
\(338\) | 1.58346 | − | 0.914214i | 0.0861291 | − | 0.0497267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.9497 | − | 32.8219i | 1.02769 | − | 1.78002i | ||||
\(341\) | 14.1480 | + | 24.5051i | 0.766158 | + | 1.32703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.11270i | 0.383491i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.435381 | + | 0.251367i | 0.0234062 | + | 0.0135136i | ||||
\(347\) | 12.9649 | + | 7.48528i | 0.695992 | + | 0.401831i | 0.805853 | − | 0.592116i | \(-0.201707\pi\) |
−0.109861 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.2179i | − | 0.600479i | −0.953864 | − | 0.300239i | \(-0.902933\pi\) | ||
0.953864 | − | 0.300239i | \(-0.0970666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.6569 | + | 18.4582i | 0.568012 | + | 0.983826i | ||||
\(353\) | −10.2555 | + | 17.7631i | −0.545847 | + | 0.945434i | 0.452706 | + | 0.891660i | \(0.350459\pi\) |
−0.998553 | + | 0.0537746i | \(0.982875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.10220 | − | 1.21371i | 0.111573 | − | 0.0644170i | ||||
\(356\) | −20.5111 | −1.08708 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.9706 | −0.579812 | ||||||||
\(359\) | 30.2854 | − | 17.4853i | 1.59840 | − | 0.922838i | 0.606607 | − | 0.795002i | \(-0.292530\pi\) |
0.991795 | − | 0.127836i | \(-0.0408030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.67157 | − | 13.2876i | 0.403767 | − | 0.699345i | ||||
\(362\) | −1.96781 | − | 3.40835i | −0.103426 | − | 0.179139i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 20.7279i | − | 1.08495i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3277 | + | 10.0042i | 0.904499 | + | 0.522213i | 0.878657 | − | 0.477453i | \(-0.158440\pi\) |
0.0258422 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 6.57128i | − | 0.341624i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3137 | − | 19.5959i | −0.585802 | − | 1.01464i | −0.994775 | − | 0.102092i | \(-0.967446\pi\) |
0.408973 | − | 0.912546i | \(-0.365887\pi\) | |||||||
\(374\) | −7.07401 | + | 12.2525i | −0.365788 | + | 0.633564i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.04814 | − | 4.64659i | 0.415051 | − | 0.239630i | ||||
\(377\) | −2.42742 | −0.125018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −27.1906 | + | 15.6985i | −1.39485 | + | 0.805315i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.14214 | − | 5.44234i | 0.160766 | − | 0.278454i | ||||
\(383\) | 11.7206 | + | 20.3007i | 0.598895 | + | 1.03732i | 0.992985 | + | 0.118244i | \(0.0377266\pi\) |
−0.394090 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.62742i | − | 0.133732i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.2014 | − | 6.46716i | −0.568667 | − | 0.328320i | ||||
\(389\) | 22.3426 | + | 12.8995i | 1.13281 | + | 0.654030i | 0.944641 | − | 0.328106i | \(-0.106410\pi\) |
0.188173 | + | 0.982136i | \(0.439744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1480i | 0.715496i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.60660 | − | 2.78272i | −0.0809394 | − | 0.140191i | ||||
\(395\) | −2.42742 | + | 4.20441i | −0.122137 | + | 0.211547i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4059 | − | 8.89457i | 0.773198 | − | 0.446406i | −0.0608165 | − | 0.998149i | \(-0.519370\pi\) |
0.834014 | + | 0.551743i | \(0.186037\pi\) | |||||||
\(398\) | 6.86577 | 0.344150 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.7574 | 0.537868 | ||||||||
\(401\) | −4.47871 | + | 2.58579i | −0.223656 | + | 0.129128i | −0.607642 | − | 0.794211i | \(-0.707884\pi\) |
0.383986 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.58579 | + | 14.8710i | −0.427688 | + | 0.740778i | ||||
\(404\) | 4.89796 | + | 8.48352i | 0.243683 | + | 0.422071i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 26.1421i | − | 1.29582i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.22848 | + | 4.75071i | 0.406872 | + | 0.234908i | 0.689445 | − | 0.724338i | \(-0.257855\pi\) |
−0.282573 | + | 0.959246i | \(0.591188\pi\) | |||||||
\(410\) | 1.27573 | + | 0.736544i | 0.0630039 | + | 0.0363753i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 25.8686i | 1.27446i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.1716 | + | 29.7420i | 0.842919 | + | 1.45998i | ||||
\(416\) | −6.46716 | + | 11.2014i | −0.317078 | + | 0.549196i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.1503 | − | 5.86030i | 0.496469 | − | 0.286637i | ||||
\(419\) | 19.0029 | 0.928350 | 0.464175 | − | 0.885743i | \(-0.346351\pi\) | ||||
0.464175 | + | 0.885743i | \(0.346351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.686292 | −0.0334478 | −0.0167239 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167239 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(422\) | −5.49333 | + | 3.17157i | −0.267411 | + | 0.154390i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.60660 | + | 9.71092i | −0.272281 | + | 0.471604i | ||||
\(425\) | 12.6829 | + | 21.9675i | 0.615213 | + | 1.06558i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 24.3431i | − | 1.17667i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.71449 | − | 2.72191i | −0.227353 | − | 0.131262i | ||||
\(431\) | 30.7057 | + | 17.7279i | 1.47904 | + | 0.853924i | 0.999719 | − | 0.0237157i | \(-0.00754966\pi\) |
0.479321 | + | 0.877640i | \(0.340883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.21371i | 0.0583271i | 0.999575 | + | 0.0291636i | \(0.00928436\pi\) | ||||
−0.999575 | + | 0.0291636i | \(0.990716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.94975 | + | 8.57321i | 0.237050 | + | 0.410582i | ||||
\(437\) | 5.86030 | − | 10.1503i | 0.280336 | − | 0.485557i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5321 | − | 12.4316i | 1.02767 | − | 0.593327i | 0.111355 | − | 0.993781i | \(-0.464481\pi\) |
0.916317 | + | 0.400454i | \(0.131147\pi\) | |||||||
\(440\) | −22.4357 | −1.06958 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.58579 | −0.408384 | ||||||||
\(443\) | 16.6031 | − | 9.58579i | 0.788836 | − | 0.455434i | −0.0507168 | − | 0.998713i | \(-0.516151\pi\) |
0.839552 | + | 0.543279i | \(0.182817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.4350 | − | 28.4663i | 0.779095 | − | 1.34943i | ||||
\(446\) | −0.710974 | − | 1.23144i | −0.0336656 | − | 0.0583105i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.7574i | − | 0.743636i | −0.928306 | − | 0.371818i | \(-0.878735\pi\) | ||
0.928306 | − | 0.371818i | \(-0.121265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.07517 | + | 2.93015i | 0.238980 | + | 0.137975i | ||||
\(452\) | 22.0094 | + | 12.7071i | 1.03523 | + | 0.597692i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.86030i | − | 0.275038i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.31371 | + | 14.3998i | 0.388899 | + | 0.673593i | 0.992302 | − | 0.123844i | \(-0.0395222\pi\) |
−0.603403 | + | 0.797437i | \(0.706189\pi\) | |||||||
\(458\) | 3.89249 | − | 6.74199i | 0.181884 | − | 0.315033i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.27958 | + | 5.35757i | −0.432663 | + | 0.249798i | ||||
\(461\) | 10.5069 | 0.489355 | 0.244677 | − | 0.969605i | \(-0.421318\pi\) | ||||
0.244677 | + | 0.969605i | \(0.421318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4853 | 0.952032 | 0.476016 | − | 0.879437i | \(-0.342080\pi\) | ||||
0.476016 | + | 0.879437i | \(0.342080\pi\) | |||||||
\(464\) | −2.15232 | + | 1.24264i | −0.0999188 | + | 0.0576881i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.07107 | − | 1.85514i | 0.0496163 | − | 0.0859379i | ||||
\(467\) | −7.07401 | − | 12.2525i | −0.327346 | − | 0.566980i | 0.654638 | − | 0.755942i | \(-0.272821\pi\) |
−0.981984 | + | 0.188962i | \(0.939488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.11270i | 0.328084i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.04814 | − | 4.64659i | −0.370446 | − | 0.213877i | ||||
\(473\) | −18.7554 | − | 10.8284i | −0.862374 | − | 0.497892i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 21.0138i | − | 0.964179i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.41421 | + | 4.18154i | 0.110424 | + | 0.191259i | ||||
\(479\) | −21.2220 | + | 36.7576i | −0.969659 | + | 1.67950i | −0.273121 | + | 0.961980i | \(0.588056\pi\) |
−0.696538 | + | 0.717520i | \(0.745277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.7390 | − | 7.93223i | 0.626446 | − | 0.361679i | ||||
\(482\) | −10.5069 | −0.478576 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.5147 | −1.02340 | ||||||||
\(485\) | 17.9509 | − | 10.3640i | 0.815109 | − | 0.470603i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7279 | − | 35.9018i | 0.939272 | − | 1.62687i | 0.172438 | − | 0.985020i | \(-0.444835\pi\) |
0.766833 | − | 0.641846i | \(-0.221831\pi\) | |||||||
\(488\) | −0.962341 | − | 1.66682i | −0.0435631 | − | 0.0754536i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.3137i | 1.14239i | 0.820814 | + | 0.571196i | \(0.193520\pi\) | ||||
−0.820814 | + | 0.571196i | \(0.806480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.07517 | − | 2.93015i | −0.228574 | − | 0.131967i | ||||
\(494\) | 6.15978 | + | 3.55635i | 0.277141 | + | 0.160008i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.5809i | 0.789406i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0711 | − | 22.6398i | −0.585141 | − | 1.01349i | −0.994858 | − | 0.101282i | \(-0.967706\pi\) |
0.409716 | − | 0.912213i | \(-0.365628\pi\) | |||||||
\(500\) | 3.78837 | − | 6.56165i | 0.169421 | − | 0.293446i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.84373 | − | 2.21918i | 0.171554 | − | 0.0990467i | ||||
\(503\) | −4.85483 | −0.216466 | −0.108233 | − | 0.994126i | \(-0.534519\pi\) | ||||
−0.108233 | + | 0.994126i | \(0.534519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6985 | −0.698573 | ||||||||
\(506\) | 3.46410 | − | 2.00000i | 0.153998 | − | 0.0889108i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.0711 | + | 26.1039i | −0.668671 | + | 1.15817i | ||||
\(509\) | 13.0384 | + | 22.5832i | 0.577918 | + | 1.00098i | 0.995718 | + | 0.0924447i | \(0.0294681\pi\) |
−0.417799 | + | 0.908539i | \(0.637199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.76903 | − | 2.17605i | −0.166245 | − | 0.0959814i | ||||
\(515\) | −35.9018 | − | 20.7279i | −1.58202 | − | 0.913381i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.2960i | 1.24446i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.80761 | − | 11.7911i | −0.298534 | − | 0.517075i | ||||
\(521\) | 1.96781 | − | 3.40835i | 0.0862113 | − | 0.149322i | −0.819695 | − | 0.572800i | \(-0.805857\pi\) |
0.905907 | + | 0.423477i | \(0.139191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.4781 | + | 15.8645i | −1.20153 | + | 0.693705i | −0.960896 | − | 0.276911i | \(-0.910689\pi\) |
−0.240636 | + | 0.970615i | \(0.577356\pi\) | |||||||
\(524\) | 15.1535 | 0.661983 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.71573 | −0.0748093 | ||||||||
\(527\) | −35.9018 | + | 20.7279i | −1.56391 | + | 0.902922i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | + | 16.4545i | −0.413043 | + | 0.715412i | ||||
\(530\) | −4.29111 | − | 7.43242i | −0.186394 | − | 0.322844i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55635i | 0.154043i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.7847 | + | 19.5056i | 1.46064 | + | 0.843300i | ||||
\(536\) | 11.6531 | + | 6.72792i | 0.503337 | + | 0.290602i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 0.919213i | − | 0.0396301i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.48528 | + | 12.9649i | 0.321817 | + | 0.557404i | 0.980863 | − | 0.194699i | \(-0.0623730\pi\) |
−0.659046 | + | 0.752103i | \(0.729040\pi\) | |||||||
\(542\) | 1.21371 | − | 2.10220i | 0.0521332 | − | 0.0902974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.0427 | + | 15.6131i | −1.15945 | + | 0.669406i | ||||
\(545\) | −15.8645 | −0.679559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6274 | 0.796451 | 0.398225 | − | 0.917288i | \(-0.369626\pi\) | ||||
0.398225 | + | 0.917288i | \(0.369626\pi\) | |||||||
\(548\) | −7.64564 | + | 4.41421i | −0.326606 | + | 0.188566i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.58579 | − | 6.21076i | 0.152898 | − | 0.264828i | ||||
\(551\) | 2.42742 | + | 4.20441i | 0.103411 | + | 0.179114i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.37258i | 0.228259i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.1233 | + | 7.57675i | 0.556552 | + | 0.321326i | ||||
\(557\) | −11.6170 | − | 6.70711i | −0.492230 | − | 0.284189i | 0.233269 | − | 0.972412i | \(-0.425058\pi\) |
−0.725499 | + | 0.688223i | \(0.758391\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.1426i | − | 0.555871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.72792 | − | 4.72490i | −0.115070 | − | 0.199308i | ||||
\(563\) | 7.07401 | − | 12.2525i | 0.298134 | − | 0.516383i | −0.677575 | − | 0.735454i | \(-0.736969\pi\) |
0.975709 | + | 0.219070i | \(0.0703024\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.2712 | + | 20.3638i | −1.48387 | + | 0.856712i | ||||
\(566\) | 3.84936 | 0.161801 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.31371 | −0.0551220 | ||||||||
\(569\) | 32.1405 | − | 18.5563i | 1.34740 | − | 0.777923i | 0.359521 | − | 0.933137i | \(-0.382940\pi\) |
0.987881 | + | 0.155214i | \(0.0496069\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.65685 | + | 9.79796i | −0.236732 | + | 0.410032i | −0.959775 | − | 0.280772i | \(-0.909410\pi\) |
0.723043 | + | 0.690803i | \(0.242743\pi\) | |||||||
\(572\) | −12.9343 | − | 22.4029i | −0.540811 | − | 0.936712i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 7.17157i | − | 0.299075i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5562 | − | 14.7549i | −1.06392 | − | 0.614254i | −0.137405 | − | 0.990515i | \(-0.543876\pi\) |
−0.926514 | + | 0.376261i | \(0.877209\pi\) | |||||||
\(578\) | −11.8527 | − | 6.84315i | −0.493006 | − | 0.284637i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 4.43835i | − | 0.184293i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.0711 | − | 29.5680i | −0.707011 | − | 1.22458i | ||||
\(584\) | −5.60894 | + | 9.71496i | −0.232099 | + | 0.402008i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.22848 | − | 4.75071i | 0.339915 | − | 0.196250i | ||||
\(587\) | −17.5809 | −0.725642 | −0.362821 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362821 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.3431 | 1.41508 | ||||||||
\(590\) | 6.15978 | − | 3.55635i | 0.253594 | − | 0.146413i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.12132 | − | 14.0665i | 0.333784 | − | 0.578131i | ||||
\(593\) | −11.8247 | − | 20.4810i | −0.485583 | − | 0.841055i | 0.514279 | − | 0.857623i | \(-0.328059\pi\) |
−0.999863 | + | 0.0165678i | \(0.994726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.75736i | 0.317754i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.10220 | + | 1.21371i | 0.0859655 | + | 0.0496322i | ||||
\(599\) | −9.08052 | − | 5.24264i | −0.371020 | − | 0.214208i | 0.302884 | − | 0.953027i | \(-0.402051\pi\) |
−0.673904 | + | 0.738819i | \(0.735384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 40.5194i | − | 1.65282i | −0.563069 | − | 0.826410i | \(-0.690379\pi\) | ||
0.563069 | − | 0.826410i | \(-0.309621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.10051 | − | 7.10228i | −0.166847 | − | 0.288988i | ||||
\(605\) | 18.0405 | − | 31.2471i | 0.733451 | − | 1.27037i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.97297 | + | 1.71644i | −0.120669 | + | 0.0696683i | −0.559120 | − | 0.829087i | \(-0.688861\pi\) |
0.438451 | + | 0.898755i | \(0.355527\pi\) | |||||||
\(608\) | 25.8686 | 1.04911 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.47309 | 0.0596436 | ||||||||
\(611\) | −14.8710 | + | 8.58579i | −0.601617 | + | 0.347344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.4350 | + | 37.1266i | −0.865753 | + | 1.49953i | 0.000545229 | 1.00000i | \(0.499826\pi\) | |
−0.866298 | + | 0.499528i | \(0.833507\pi\) | |||||||
\(614\) | 4.64659 | + | 8.04814i | 0.187521 | + | 0.324796i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5147i | 0.544082i | 0.962286 | + | 0.272041i | \(0.0876986\pi\) | ||||
−0.962286 | + | 0.272041i | \(0.912301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.8598 | − | 22.4357i | −1.56191 | − | 0.901769i | −0.997064 | − | 0.0765715i | \(-0.975603\pi\) |
−0.564845 | − | 0.825197i | \(-0.691064\pi\) | |||||||
\(620\) | −27.1906 | − | 15.6985i | −1.09200 | − | 0.630466i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.7151i | 0.429638i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0355 | + | 26.0423i | 0.601421 | + | 1.04169i | ||||
\(626\) | 1.10959 | − | 1.92186i | 0.0443481 | − | 0.0768131i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.3223 | − | 20.9707i | 1.44942 | − | 0.836821i | ||||
\(629\) | 38.3002 | 1.52713 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8284 | −1.06802 | −0.534011 | − | 0.845477i | \(-0.679316\pi\) | ||||
−0.534011 | + | 0.845477i | \(0.679316\pi\) | |||||||
\(632\) | 2.27541 | − | 1.31371i | 0.0905109 | − | 0.0522565i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.67767 | + | 11.5661i | −0.265204 | + | 0.459347i | ||||
\(635\) | −24.1522 | − | 41.8328i | −0.958450 | − | 1.66008i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.65685i | 0.0655955i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.7876 | − | 15.4658i | −1.05887 | − | 0.611341i | ||||
\(641\) | 21.2049 | + | 12.2426i | 0.837542 | + | 0.483555i | 0.856428 | − | 0.516266i | \(-0.172679\pi\) |
−0.0188858 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.86030i | − | 0.231108i | −0.993301 | − | 0.115554i | \(-0.963136\pi\) | ||
0.993301 | − | 0.115554i | \(-0.0368643\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.58579 | + | 14.8710i | 0.337803 | + | 0.585092i | ||||
\(647\) | 5.35757 | − | 9.27958i | 0.210628 | − | 0.364818i | −0.741283 | − | 0.671192i | \(-0.765783\pi\) |
0.951911 | + | 0.306374i | \(0.0991159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.5051 | − | 14.1480i | 0.961909 | − | 0.555358i | ||||
\(650\) | 4.35210 | 0.170703 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.7696 | 0.656746 | ||||||||
\(653\) | 18.6323 | − | 10.7574i | 0.729138 | − | 0.420968i | −0.0889688 | − | 0.996034i | \(-0.528357\pi\) |
0.818107 | + | 0.575066i | \(0.195024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1421 | + | 21.0308i | −0.474432 | + | 0.821741i | ||||
\(656\) | 1.82056 | + | 3.15331i | 0.0710810 | + | 0.123116i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.45584i | − | 0.134621i | −0.997732 | − | 0.0673103i | \(-0.978558\pi\) | ||
0.997732 | − | 0.0673103i | \(-0.0214417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8653 | + | 11.4692i | 0.772671 | + | 0.446102i | 0.833827 | − | 0.552027i | \(-0.186145\pi\) |
−0.0611558 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(662\) | −7.76874 | − | 4.48528i | −0.301940 | − | 0.174325i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 18.5864i | − | 0.721291i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.828427 | + | 1.43488i | 0.0320768 | + | 0.0555587i | ||||
\(668\) | 12.9343 | − | 22.4029i | 0.500444 | − | 0.866794i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.91890 | + | 5.14933i | −0.344567 | + | 0.198936i | ||||
\(671\) | 5.86030 | 0.226234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1005 | −0.697723 | −0.348862 | − | 0.937174i | \(-0.613432\pi\) | ||||
−0.348862 | + | 0.937174i | \(0.613432\pi\) | |||||||
\(674\) | −9.71092 | + | 5.60660i | −0.374051 | + | 0.215958i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.03553 | + | 6.98975i | −0.155213 | + | 0.268837i | ||||
\(677\) | −23.0426 | − | 39.9109i | −0.885599 | − | 1.53390i | −0.845026 | − | 0.534726i | \(-0.820415\pi\) |
−0.0405732 | − | 0.999177i | \(-0.512918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 32.8701i | − | 1.26051i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.1503 | + | 5.86030i | 0.388677 | + | 0.224403i | ||||
\(683\) | −30.1113 | − | 17.3848i | −1.15218 | − | 0.665210i | −0.202761 | − | 0.979228i | \(-0.564991\pi\) |
−0.949417 | + | 0.314018i | \(0.898325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.1480i | − | 0.540568i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.72792 | − | 11.6531i | −0.256500 | − | 0.444270i | ||||
\(689\) | 10.3596 | − | 17.9434i | 0.394671 | − | 0.683591i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.17738 | + | 4.14386i | −0.273040 | + | 0.157640i | −0.630268 | − | 0.776377i | \(-0.717055\pi\) |
0.357228 | + | 0.934017i | \(0.383722\pi\) | |||||||
\(692\) | −2.21918 | −0.0843605 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.20101 | 0.235387 | ||||||||
\(695\) | −21.0308 | + | 12.1421i | −0.797744 | + | 0.460577i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.29289 | + | 7.43551i | −0.162605 | + | 0.281640i | ||||
\(698\) | −2.32330 | − | 4.02407i | −0.0879381 | − | 0.152313i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.7696i | − | 1.23769i | −0.785514 | − | 0.618844i | \(-0.787601\pi\) | ||
0.785514 | − | 0.618844i | \(-0.212399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4781 | − | 15.8645i | −1.03635 | − | 0.598340i | ||||
\(704\) | −17.4436 | − | 10.0711i | −0.657430 | − | 0.379568i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.49596i | 0.319750i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.63604 | + | 6.29780i | 0.136554 | + | 0.236519i | 0.926190 | − | 0.377057i | \(-0.123064\pi\) |
−0.789636 | + | 0.613576i | \(0.789731\pi\) | |||||||
\(710\) | 0.502734 | − | 0.870762i | 0.0188673 | − | 0.0326791i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.4059 | + | 8.89457i | −0.577359 | + | 0.333338i | ||||
\(713\) | 11.7206 | 0.438940 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.4558 | 1.55036 | ||||||||
\(716\) | 41.9385 | − | 24.2132i | 1.56732 | − | 0.904890i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.24264 | − | 12.5446i | 0.270293 | − | 0.468161i | ||||
\(719\) | 5.86030 | + | 10.1503i | 0.218552 | + | 0.378544i | 0.954366 | − | 0.298641i | \(-0.0965332\pi\) |
−0.735813 | + | 0.677185i | \(0.763200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 6.35534i | − | 0.236521i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.0452 | + | 8.68633i | 0.559149 | + | 0.322825i | ||||
\(725\) | 2.57258 | + | 1.48528i | 0.0955433 | + | 0.0551620i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0138i | 0.779358i | 0.920951 | + | 0.389679i | \(0.127414\pi\) | ||||
−0.920951 | + | 0.389679i | \(0.872586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.29289 | − | 7.43551i | −0.158887 | − | 0.275201i | ||||
\(731\) | 15.8645 | − | 27.4781i | 0.586768 | − | 1.01631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.7336 | + | 18.8987i | −1.20904 | + | 0.698041i | −0.962550 | − | 0.271104i | \(-0.912611\pi\) |
−0.246492 | + | 0.969145i | \(0.579278\pi\) | |||||||
\(734\) | 8.28772 | 0.305905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.82843 | 0.325420 | ||||||||
\(737\) | −35.4815 | + | 20.4853i | −1.30698 | + | 0.754585i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.58579 | − | 11.4069i | 0.242262 | − | 0.419610i | −0.719096 | − | 0.694911i | \(-0.755444\pi\) |
0.961358 | + | 0.275300i | \(0.0887773\pi\) | |||||||
\(740\) | 14.5035 | + | 25.1208i | 0.533160 | + | 0.923459i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.4264i | 1.18961i | 0.803870 | + | 0.594805i | \(0.202771\pi\) | ||||
−0.803870 | + | 0.594805i | \(0.797229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7661 | − | 6.21579i | −0.394438 | − | 0.227729i | ||||
\(746\) | −8.11689 | − | 4.68629i | −0.297181 | − | 0.171577i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 62.4524i | − | 2.28349i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6569 | − | 37.5108i | −0.790270 | − | 1.36879i | −0.925800 | − | 0.378014i | \(-0.876607\pi\) |
0.135530 | − | 0.990773i | \(-0.456726\pi\) | |||||||
\(752\) | −8.79045 | + | 15.2255i | −0.320555 | + | 0.555217i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.870762 | + | 0.502734i | −0.0317113 | + | 0.0183085i | ||||
\(755\) | 13.1426 | 0.478306 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.8701 | −1.70352 | −0.851761 | − | 0.523931i | \(-0.824465\pi\) | ||||
−0.851761 | + | 0.523931i | \(0.824465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.6152 | + | 23.5823i | −0.493876 | + | 0.855418i | ||||
\(761\) | 8.53909 | + | 14.7901i | 0.309542 | + | 0.536142i | 0.978262 | − | 0.207372i | \(-0.0664911\pi\) |
−0.668721 | + | 0.743514i | \(0.733158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.7401i | 1.00360i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.40882 | + | 4.85483i | 0.303823 | + | 0.175412i | ||||
\(767\) | 14.8710 | + | 8.58579i | 0.536961 | + | 0.310015i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.0961i | 1.73439i | 0.497968 | + | 0.867195i | \(0.334080\pi\) | ||||
−0.497968 | + | 0.867195i | \(0.665920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.79899 | + | 10.0441i | 0.208710 | + | 0.361497i | ||||
\(773\) | −12.3275 | + | 21.3518i | −0.443388 | + | 0.767970i | −0.997938 | − | 0.0641797i | \(-0.979557\pi\) |
0.554550 | + | 0.832150i | \(0.312890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.1985 | − | 10.5069i | 0.653709 | − | 0.377419i | ||||
\(776\) | −11.2179 | −0.402698 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.6863 | 0.383122 | ||||||||
\(779\) | 6.15978 | − | 3.55635i | 0.220697 | − | 0.127419i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | − | 3.46410i | 0.0715656 | − | 0.123955i | ||||
\(782\) | 2.93015 | + | 5.07517i | 0.104782 | + | 0.181488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 67.2132i | 2.39894i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.1503 | − | 5.86030i | −0.361821 | − | 0.208897i | 0.308058 | − | 0.951367i | \(-0.400321\pi\) |
−0.669879 | + | 0.742470i | \(0.733654\pi\) | |||||||
\(788\) | 12.2835 | + | 7.09188i | 0.437582 | + | 0.252638i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.01094i | 0.0715460i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.77817 | + | 3.07989i | 0.0631448 | + | 0.109370i | ||||
\(794\) | 3.68425 | − | 6.38131i | 0.130749 | − | 0.226464i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.2466 | + | 15.1535i | −0.930287 | + | 0.537101i | ||||
\(797\) | −51.2345 | −1.81482 | −0.907410 | − | 0.420247i | \(-0.861944\pi\) | ||||
−0.907410 | + | 0.420247i | \(0.861944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.4558 | −1.46660 | ||||||||
\(800\) | 13.7078 | − | 7.91421i | 0.484645 | − | 0.279810i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.07107 | + | 1.85514i | −0.0378207 | + | 0.0655074i | ||||
\(803\) | −17.0782 | − | 29.5803i | −0.602676 | − | 1.04386i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.11270i | 0.250534i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.35772 | + | 4.24798i | 0.258844 | + | 0.149443i | ||||
\(809\) | −13.8925 | − | 8.02082i | −0.488433 | − | 0.281997i | 0.235491 | − | 0.971876i | \(-0.424330\pi\) |
−0.723924 | + | 0.689880i | \(0.757663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.28772i | 0.291021i | 0.989357 | + | 0.145511i | \(0.0464825\pi\) | ||||
−0.989357 | + | 0.145511i | \(0.953518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.41421 | − | 9.37769i | −0.189768 | − | 0.328688i | ||||
\(815\) | −13.4370 | + | 23.2736i | −0.470679 | + | 0.815240i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.7636 | + | 13.1426i | −0.796396 | + | 0.459800i | ||||
\(818\) | 3.93562 | 0.137606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.50253 | −0.227078 | ||||||||
\(821\) | −20.5745 | + | 11.8787i | −0.718054 | + | 0.414569i | −0.814036 | − | 0.580814i | \(-0.802734\pi\) |
0.0959819 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9706 | − | 36.3221i | 0.730988 | − | 1.26611i | −0.225474 | − | 0.974249i | \(-0.572393\pi\) |
0.956461 | − | 0.291859i | \(-0.0942737\pi\) | |||||||
\(824\) | 11.2179 | + | 19.4299i | 0.390793 | + | 0.676873i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 39.6569i | − | 1.37900i | −0.724284 | − | 0.689502i | \(-0.757829\pi\) | ||
0.724284 | − | 0.689502i | \(-0.242171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2471 | + | 18.0405i | 1.08526 | + | 0.626573i | 0.932309 | − | 0.361661i | \(-0.117790\pi\) |
0.152947 | + | 0.988234i | \(0.451124\pi\) | |||||||
\(830\) | 12.3196 | + | 7.11270i | 0.427618 | + | 0.246885i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 12.2233i | − | 0.423768i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.7279 | + | 35.9018i | 0.717319 | + | 1.24243i | ||||
\(836\) | −25.8686 | + | 44.8058i | −0.894685 | + | 1.54964i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.81669 | − | 3.93562i | 0.235479 | − | 0.135954i | ||||
\(839\) | −17.5809 | −0.606960 | −0.303480 | − | 0.952838i | \(-0.598149\pi\) | ||||
−0.303480 | + | 0.952838i | \(0.598149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3137 | 0.976335 | ||||||||
\(842\) | −0.246186 | + | 0.142136i | −0.00848413 | + | 0.00489832i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.0000 | − | 24.2487i | 0.481900 | − | 0.834675i | ||||
\(845\) | −6.46716 | − | 11.2014i | −0.222477 | − | 0.385341i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 21.2132i | − | 0.728464i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.09924 | + | 5.25345i | 0.312101 | + | 0.180192i | ||||
\(851\) | −9.37769 | − | 5.41421i | −0.321463 | − | 0.185597i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0727i | 0.550319i | 0.961399 | + | 0.275159i | \(0.0887306\pi\) | ||||
−0.961399 | + | 0.275159i | \(0.911269\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.5563 | − | 18.2841i | −0.360809 | − | 0.624939i | ||||
\(857\) | 0.251367 | − | 0.435381i | 0.00858654 | − | 0.0148723i | −0.861700 | − | 0.507418i | \(-0.830600\pi\) |
0.870287 | + | 0.492545i | \(0.163933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.04814 | − | 4.64659i | 0.274599 | − | 0.158540i | −0.356377 | − | 0.934342i | \(-0.615988\pi\) |
0.630976 | + | 0.775803i | \(0.282655\pi\) | |||||||
\(860\) | 24.0302 | 0.819423 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6863 | 0.500217 | ||||||||
\(863\) | 9.25460 | − | 5.34315i | 0.315030 | − | 0.181883i | −0.334145 | − | 0.942522i | \(-0.608448\pi\) |
0.649175 | + | 0.760639i | \(0.275114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.77817 | − | 3.07989i | 0.0604597 | − | 0.104719i | ||||
\(866\) | 0.251367 | + | 0.435381i | 0.00854181 | + | 0.0147948i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.5321 | − | 12.4316i | −0.729588 | − | 0.421228i | ||||
\(872\) | 7.43551 | + | 4.29289i | 0.251798 | + | 0.145376i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.85483i | − | 0.164217i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2635 | + | 28.1691i | 0.549178 | + | 0.951204i | 0.998331 | + | 0.0577493i | \(0.0183924\pi\) |
−0.449153 | + | 0.893455i | \(0.648274\pi\) | |||||||
\(878\) | 5.14933 | − | 8.91890i | 0.173781 | − | 0.300998i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.7576 | − | 21.2220i | 1.23910 | − | 0.715395i | ||||
\(881\) | −23.6494 | −0.796770 | −0.398385 | − | 0.917218i | \(-0.630429\pi\) | ||||
−0.398385 | + | 0.917218i | \(0.630429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.4558 | 0.452825 | 0.226413 | − | 0.974031i | \(-0.427300\pi\) | ||||
0.226413 | + | 0.974031i | \(0.427300\pi\) | |||||||
\(884\) | 32.8219 | − | 18.9497i | 1.10392 | − | 0.637349i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.97056 | − | 6.87722i | 0.133394 | − | 0.231045i | ||||
\(887\) | 25.3659 | + | 43.9350i | 0.851703 | + | 1.47519i | 0.879670 | + | 0.475585i | \(0.157763\pi\) |
−0.0279667 | + | 0.999609i | \(0.508903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 13.6152i | − | 0.456383i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.43585 | + | 3.13839i | 0.182006 | + | 0.105081i | ||||
\(893\) | 29.7420 | + | 17.1716i | 0.995279 | + | 0.574625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 77.6059i | 2.59408i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.26346 | − | 5.65247i | −0.108903 | − | 0.188625i | ||||
\(899\) | −2.42742 | + | 4.20441i | −0.0809589 | + | 0.140225i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.3193 | − | 25.0104i | 1.44317 | − | 0.833217i | ||||
\(902\) | 2.42742 | 0.0808241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.0416 | 0.733094 | ||||||||
\(905\) | −24.1107 | + | 13.9203i | −0.801466 | + | 0.462727i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3848 | + | 24.9152i | −0.477639 | + | 0.827294i | −0.999671 | − | 0.0256310i | \(-0.991841\pi\) |
0.522033 | + | 0.852925i | \(0.325174\pi\) | |||||||
\(908\) | 12.9343 | + | 22.4029i | 0.429240 | + | 0.743466i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42.4853i | − | 1.40760i | −0.710398 | − | 0.703800i | \(-0.751485\pi\) | ||
0.710398 | − | 0.703800i | \(-0.248515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.0102 | + | 28.2960i | 1.62200 | + | 0.936462i | ||||
\(914\) | 5.96458 | + | 3.44365i | 0.197291 | + | 0.113906i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34.3646i | 1.13544i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7279 | + | 35.9018i | 0.683751 | + | 1.18429i | 0.973828 | + | 0.227288i | \(0.0729859\pi\) |
−0.290077 | + | 0.957003i | \(0.593681\pi\) | |||||||
\(920\) | −4.64659 | + | 8.04814i | −0.153194 | + | 0.265339i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.76903 | − | 2.17605i | 0.124126 | − | 0.0716644i | ||||
\(923\) | 2.42742 | 0.0798994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.4142 | −0.638335 | ||||||||
\(926\) | 7.34847 | − | 4.24264i | 0.241486 | − | 0.139422i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.82843 | + | 3.16693i | −0.0600211 | + | 0.103960i | ||||
\(929\) | 0.251367 | + | 0.435381i | 0.00824709 | + | 0.0142844i | 0.870119 | − | 0.492841i | \(-0.164042\pi\) |
−0.861872 | + | 0.507125i | \(0.830708\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.45584i | 0.309736i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.07517 | − | 2.93015i | −0.166065 | − | 0.0958775i | ||||
\(935\) | 86.6746 | + | 50.0416i | 2.83456 | + | 1.63654i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.2345i | − | 1.67376i | −0.547387 | − | 0.836879i | \(-0.684378\pi\) | ||
0.547387 | − | 0.836879i | \(-0.315622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.6985 | − | 27.1906i | −0.512028 | − | 0.886859i | ||||
\(941\) | −2.32330 | + | 4.02407i | −0.0757373 | + | 0.131181i | −0.901407 | − | 0.432973i | \(-0.857464\pi\) |
0.825669 | + | 0.564154i | \(0.190798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.10220 | − | 1.21371i | 0.0684572 | − | 0.0395238i | ||||
\(944\) | 17.5809 | 0.572210 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.97056 | −0.291658 | ||||||||
\(947\) | 9.50079 | − | 5.48528i | 0.308734 | − | 0.178248i | −0.337626 | − | 0.941280i | \(-0.609624\pi\) |
0.646360 | + | 0.763033i | \(0.276291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3640 | − | 17.9509i | 0.336428 | − | 0.582711i | ||||
\(950\) | −4.35210 | − | 7.53806i | −0.141201 | − | 0.244567i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.3848i | − | 0.336396i | −0.985753 | − | 0.168198i | \(-0.946205\pi\) | ||
0.985753 | − | 0.168198i | \(-0.0537948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.4992 | − | 22.2275i | −1.24580 | − | 0.719265i | ||||
\(956\) | −18.4582 | − | 10.6569i | −0.596981 | − | 0.344667i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.5809i | 0.568013i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.67157 | + | 2.89525i | 0.0539217 | + | 0.0933951i | ||||
\(962\) | 3.28564 | − | 5.69089i | 0.105933 | − | 0.183482i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.1660 | − | 23.1898i | 1.29366 | − | 0.746895i | ||||
\(965\) | −18.5864 | −0.598317 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.1127 | −0.614623 | −0.307311 | − | 0.951609i | \(-0.599429\pi\) | ||||
−0.307311 | + | 0.951609i | \(0.599429\pi\) | |||||||
\(968\) | −16.9108 | + | 9.76346i | −0.543534 | + | 0.313809i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.29289 | − | 7.43551i | 0.137836 | − | 0.238740i | ||||
\(971\) | 2.42742 | + | 4.20441i | 0.0778995 | + | 0.134926i | 0.902343 | − | 0.431018i | \(-0.141845\pi\) |
−0.824444 | + | 0.565944i | \(0.808512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 17.1716i | − | 0.550213i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.15331 | + | 1.82056i | 0.100935 | + | 0.0582748i | ||||
\(977\) | 38.8226 | + | 22.4142i | 1.24204 | + | 0.717094i | 0.969510 | − | 0.245052i | \(-0.0788050\pi\) |
0.272534 | + | 0.962146i | \(0.412138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 54.1647i | − | 1.73111i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.24264 | + | 9.08052i | 0.167299 | + | 0.289771i | ||||
\(983\) | −15.8645 | + | 27.4781i | −0.505998 | + | 0.876414i | 0.493978 | + | 0.869474i | \(0.335542\pi\) |
−0.999976 | + | 0.00693961i | \(0.997791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.6850 | + | 11.3651i | −0.627215 | + | 0.362123i | ||||
\(986\) | −2.42742 | −0.0773047 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.3970 | −0.998871 | ||||||||
\(989\) | −7.76874 | + | 4.48528i | −0.247031 | + | 0.142624i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6985 | − | 51.4393i | 0.943403 | − | 1.63402i | 0.184487 | − | 0.982835i | \(-0.440938\pi\) |
0.758917 | − | 0.651188i | \(-0.225729\pi\) | |||||||
\(992\) | 12.9343 | + | 22.4029i | 0.410665 | + | 0.711292i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 48.5685i | − | 1.53973i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.2201 | − | 19.7570i | −1.08376 | − | 0.625709i | −0.151852 | − | 0.988403i | \(-0.548524\pi\) |
−0.931908 | + | 0.362694i | \(0.881857\pi\) | |||||||
\(998\) | −9.37769 | − | 5.41421i | −0.296846 | − | 0.171384i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.2.p.c.80.5 | 16 | ||
3.2 | odd | 2 | inner | 441.2.p.c.80.4 | 16 | ||
7.2 | even | 3 | inner | 441.2.p.c.215.3 | 16 | ||
7.3 | odd | 6 | 441.2.c.b.440.5 | yes | 8 | ||
7.4 | even | 3 | 441.2.c.b.440.6 | yes | 8 | ||
7.5 | odd | 6 | inner | 441.2.p.c.215.4 | 16 | ||
7.6 | odd | 2 | inner | 441.2.p.c.80.6 | 16 | ||
21.2 | odd | 6 | inner | 441.2.p.c.215.6 | 16 | ||
21.5 | even | 6 | inner | 441.2.p.c.215.5 | 16 | ||
21.11 | odd | 6 | 441.2.c.b.440.3 | ✓ | 8 | ||
21.17 | even | 6 | 441.2.c.b.440.4 | yes | 8 | ||
21.20 | even | 2 | inner | 441.2.p.c.80.3 | 16 | ||
28.3 | even | 6 | 7056.2.k.g.881.3 | 8 | |||
28.11 | odd | 6 | 7056.2.k.g.881.5 | 8 | |||
84.11 | even | 6 | 7056.2.k.g.881.4 | 8 | |||
84.59 | odd | 6 | 7056.2.k.g.881.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.c.b.440.3 | ✓ | 8 | 21.11 | odd | 6 | ||
441.2.c.b.440.4 | yes | 8 | 21.17 | even | 6 | ||
441.2.c.b.440.5 | yes | 8 | 7.3 | odd | 6 | ||
441.2.c.b.440.6 | yes | 8 | 7.4 | even | 3 | ||
441.2.p.c.80.3 | 16 | 21.20 | even | 2 | inner | ||
441.2.p.c.80.4 | 16 | 3.2 | odd | 2 | inner | ||
441.2.p.c.80.5 | 16 | 1.1 | even | 1 | trivial | ||
441.2.p.c.80.6 | 16 | 7.6 | odd | 2 | inner | ||
441.2.p.c.215.3 | 16 | 7.2 | even | 3 | inner | ||
441.2.p.c.215.4 | 16 | 7.5 | odd | 6 | inner | ||
441.2.p.c.215.5 | 16 | 21.5 | even | 6 | inner | ||
441.2.p.c.215.6 | 16 | 21.2 | odd | 6 | inner | ||
7056.2.k.g.881.3 | 8 | 28.3 | even | 6 | |||
7056.2.k.g.881.4 | 8 | 84.11 | even | 6 | |||
7056.2.k.g.881.5 | 8 | 28.11 | odd | 6 | |||
7056.2.k.g.881.6 | 8 | 84.59 | odd | 6 |