Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(361,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Root | \(0.385731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.721 |
Dual form | 1080.2.q.e.361.3 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.165947 | − | 0.287429i | 0.0627222 | − | 0.108638i | −0.832959 | − | 0.553335i | \(-0.813355\pi\) |
0.895681 | + | 0.444696i | \(0.146688\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20380 | − | 3.81710i | 0.664472 | − | 1.15090i | −0.314957 | − | 0.949106i | \(-0.601990\pi\) |
0.979428 | − | 0.201792i | \(-0.0646766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.49031 | − | 6.04539i | −0.968038 | − | 1.67669i | −0.701222 | − | 0.712943i | \(-0.747362\pi\) |
−0.266816 | − | 0.963747i | \(-0.585972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.07139 | 0.744923 | 0.372461 | − | 0.928048i | \(-0.378514\pi\) | ||||
0.372461 | + | 0.928048i | \(0.378514\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.55364 | −1.73292 | −0.866461 | − | 0.499244i | \(-0.833611\pi\) | ||||
−0.866461 | + | 0.499244i | \(0.833611\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.834053 | + | 1.44462i | 0.173912 | + | 0.301224i | 0.939784 | − | 0.341768i | \(-0.111026\pi\) |
−0.765872 | + | 0.642993i | \(0.777693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.78651 | − | 3.09432i | 0.331746 | − | 0.574601i | −0.651108 | − | 0.758985i | \(-0.725696\pi\) |
0.982854 | + | 0.184384i | \(0.0590289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82220 | − | 4.88820i | −0.506883 | − | 0.877947i | −0.999968 | − | 0.00796608i | \(-0.997464\pi\) |
0.493085 | − | 0.869981i | \(-0.335869\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.331895 | 0.0561004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.64441 | 1.25673 | 0.628367 | − | 0.777917i | \(-0.283724\pi\) | ||||
0.628367 | + | 0.777917i | \(0.283724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.74919 | + | 4.76174i | 0.429351 | + | 0.743658i | 0.996816 | − | 0.0797396i | \(-0.0254089\pi\) |
−0.567464 | + | 0.823398i | \(0.692076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.53570 | − | 6.12401i | 0.539189 | − | 0.933902i | −0.459759 | − | 0.888044i | \(-0.652064\pi\) |
0.998948 | − | 0.0458587i | \(-0.0146024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.98815 | − | 6.90768i | 0.581732 | − | 1.00759i | −0.413542 | − | 0.910485i | \(-0.635709\pi\) |
0.995274 | − | 0.0971042i | \(-0.0309580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.44492 | + | 5.96678i | 0.492132 | + | 0.852397i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.47900 | 0.752599 | 0.376299 | − | 0.926498i | \(-0.377196\pi\) | ||||
0.376299 | + | 0.926498i | \(0.377196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.40761 | 0.594321 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.69411 | − | 6.39839i | −0.480933 | − | 0.833000i | 0.518828 | − | 0.854879i | \(-0.326368\pi\) |
−0.999761 | + | 0.0218790i | \(0.993035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.296197 | + | 0.513029i | −0.0379242 | + | 0.0656866i | −0.884364 | − | 0.466797i | \(-0.845408\pi\) |
0.846440 | + | 0.532484i | \(0.178741\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.49031 | − | 6.04539i | 0.432920 | − | 0.749839i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.61087 | − | 4.52216i | −0.318969 | − | 0.552470i | 0.661305 | − | 0.750118i | \(-0.270003\pi\) |
−0.980273 | + | 0.197648i | \(0.936670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.98062 | −1.06580 | −0.532902 | − | 0.846177i | \(-0.678898\pi\) | ||||
−0.532902 | + | 0.846177i | \(0.678898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.05202 | −0.942417 | −0.471209 | − | 0.882022i | \(-0.656182\pi\) | ||||
−0.471209 | + | 0.882022i | \(0.656182\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.731430 | − | 1.26687i | −0.0833542 | − | 0.144374i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.49838 | − | 9.52347i | 0.618616 | − | 1.07147i | −0.371122 | − | 0.928584i | \(-0.621027\pi\) |
0.989739 | − | 0.142891i | \(-0.0456397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.14657 | + | 5.45002i | −0.345381 | + | 0.598217i | −0.985423 | − | 0.170123i | \(-0.945584\pi\) |
0.640042 | + | 0.768340i | \(0.278917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.53570 | + | 2.65991i | 0.166570 | + | 0.288507i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9060 | −1.26203 | −0.631016 | − | 0.775770i | \(-0.717362\pi\) | ||||
−0.631016 | + | 0.775770i | \(0.717362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.31683 | −0.242870 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.77682 | − | 6.54164i | −0.387493 | − | 0.671158i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.622718 | − | 1.07858i | 0.0632274 | − | 0.109513i | −0.832679 | − | 0.553756i | \(-0.813194\pi\) |
0.895906 | + | 0.444243i | \(0.146527\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.33189 | − | 4.03896i | 0.232032 | − | 0.401892i | −0.726374 | − | 0.687300i | \(-0.758796\pi\) |
0.958406 | + | 0.285408i | \(0.0921292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.08270 | + | 3.60735i | 0.205215 | + | 0.355443i | 0.950201 | − | 0.311637i | \(-0.100877\pi\) |
−0.744986 | + | 0.667080i | \(0.767544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.57409 | 0.635541 | 0.317771 | − | 0.948168i | \(-0.397066\pi\) | ||||
0.317771 | + | 0.948168i | \(0.397066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.743816 | 0.0712446 | 0.0356223 | − | 0.999365i | \(-0.488659\pi\) | ||||
0.0356223 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.31252 | + | 14.3977i | 0.781976 | + | 1.35442i | 0.930789 | + | 0.365556i | \(0.119121\pi\) |
−0.148814 | + | 0.988865i | \(0.547545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.834053 | + | 1.44462i | −0.0777758 | + | 0.134712i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.509690 | − | 0.882809i | 0.0467232 | − | 0.0809269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21349 | − | 7.29798i | −0.383045 | − | 0.663453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.79152 | 0.425178 | 0.212589 | − | 0.977142i | \(-0.431810\pi\) | ||||
0.212589 | + | 0.977142i | \(0.431810\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.88985 | + | 17.1297i | 0.864080 | + | 1.49663i | 0.867958 | + | 0.496638i | \(0.165432\pi\) |
−0.00387809 | + | 0.999992i | \(0.501234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.25351 | + | 2.17114i | −0.108693 | + | 0.188261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.26713 | − | 16.0511i | 0.791744 | − | 1.37134i | −0.133142 | − | 0.991097i | \(-0.542507\pi\) |
0.924886 | − | 0.380244i | \(-0.124160\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.68980 | − | 4.65887i | −0.228146 | − | 0.395160i | 0.729113 | − | 0.684393i | \(-0.239933\pi\) |
−0.957259 | + | 0.289234i | \(0.906600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.7678 | −2.57293 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.57301 | 0.296723 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.51794 | + | 9.55735i | 0.452047 | + | 0.782969i | 0.998513 | − | 0.0545128i | \(-0.0173606\pi\) |
−0.546466 | + | 0.837481i | \(0.684027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.750810 | − | 1.30044i | 0.0611001 | − | 0.105828i | −0.833857 | − | 0.551980i | \(-0.813872\pi\) |
0.894957 | + | 0.446152i | \(0.147206\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82220 | − | 4.88820i | 0.226685 | − | 0.392630i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8109 | + | 20.4571i | 0.942612 | + | 1.63265i | 0.760463 | + | 0.649381i | \(0.224972\pi\) |
0.182149 | + | 0.983271i | \(0.441695\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.553635 | 0.0436326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.16217 | −0.717636 | −0.358818 | − | 0.933407i | \(-0.616820\pi\) | ||||
−0.358818 | + | 0.933407i | \(0.616820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.324363 | − | 0.561813i | −0.0250999 | − | 0.0434744i | 0.853203 | − | 0.521580i | \(-0.174657\pi\) |
−0.878303 | + | 0.478105i | \(0.841324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.8645 | + | 30.9423i | −1.37419 | + | 2.38017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.40761 | − | 7.63420i | 0.335104 | − | 0.580417i | −0.648401 | − | 0.761299i | \(-0.724562\pi\) |
0.983505 | + | 0.180882i | \(0.0578952\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.165947 | + | 0.287429i | 0.0125444 | + | 0.0217276i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.16217 | −0.684813 | −0.342406 | − | 0.939552i | \(-0.611242\pi\) | ||||
−0.342406 | + | 0.939552i | \(0.611242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5730 | 1.00887 | 0.504437 | − | 0.863448i | \(-0.331700\pi\) | ||||
0.504437 | + | 0.863448i | \(0.331700\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.82220 | + | 6.62025i | 0.281014 | + | 0.486731i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.76875 | − | 11.7238i | 0.494980 | − | 0.857330i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.13472 | + | 8.89360i | −0.371535 | + | 0.643518i | −0.989802 | − | 0.142450i | \(-0.954502\pi\) |
0.618267 | + | 0.785968i | \(0.287835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.53570 | − | 7.85606i | −0.326487 | − | 0.565491i | 0.655325 | − | 0.755347i | \(-0.272531\pi\) |
−0.981812 | + | 0.189855i | \(0.939198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.80658 | 0.342455 | 0.171227 | − | 0.985232i | \(-0.445227\pi\) | ||||
0.171227 | + | 0.985232i | \(0.445227\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.4596 | −1.30857 | −0.654284 | − | 0.756249i | \(-0.727030\pi\) | ||||
−0.654284 | + | 0.756249i | \(0.727030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.592932 | − | 1.02699i | −0.0416157 | − | 0.0720805i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.74919 | + | 4.76174i | −0.192012 | + | 0.332574i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.6467 | + | 28.8330i | −1.15148 | + | 1.99442i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.177795 | − | 0.307950i | −0.0122399 | − | 0.0212002i | 0.859841 | − | 0.510563i | \(-0.170563\pi\) |
−0.872080 | + | 0.489362i | \(0.837230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.07139 | 0.482265 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.87335 | −0.127171 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.7201 | − | 18.5678i | −0.721113 | − | 1.24900i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.65194 | + | 2.86125i | −0.110622 | + | 0.191603i | −0.916021 | − | 0.401130i | \(-0.868618\pi\) |
0.805399 | + | 0.592733i | \(0.201951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.36921 | + | 4.10360i | −0.157250 | + | 0.272365i | −0.933876 | − | 0.357597i | \(-0.883596\pi\) |
0.776626 | + | 0.629962i | \(0.216930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.53032 | − | 16.5070i | −0.629781 | − | 1.09081i | −0.987595 | − | 0.157021i | \(-0.949811\pi\) |
0.357814 | − | 0.933793i | \(-0.383522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3721 | 0.876035 | 0.438017 | − | 0.898967i | \(-0.355681\pi\) | ||||
0.438017 | + | 0.898967i | \(0.355681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.97630 | 0.520317 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.64873 | + | 16.7121i | 0.624124 | + | 1.08101i | 0.988710 | + | 0.149845i | \(0.0478774\pi\) |
−0.364585 | + | 0.931170i | \(0.618789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.99031 | + | 17.3037i | −0.643532 | + | 1.11463i | 0.341106 | + | 0.940025i | \(0.389199\pi\) |
−0.984638 | + | 0.174606i | \(0.944135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.44492 | + | 5.96678i | −0.220088 | + | 0.381204i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.3645 | + | 45.6647i | 1.67753 | + | 2.90558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.889846 | 0.0561666 | 0.0280833 | − | 0.999606i | \(-0.491060\pi\) | ||||
0.0280833 | + | 0.999606i | \(0.491060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.35235 | 0.462238 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.36222 | + | 14.4838i | 0.521621 | + | 0.903474i | 0.999684 | + | 0.0251482i | \(0.00800576\pi\) |
−0.478063 | + | 0.878326i | \(0.658661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26857 | − | 2.19723i | 0.0788251 | − | 0.136529i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.56170 | + | 6.16905i | −0.219624 | + | 0.380400i | −0.954693 | − | 0.297592i | \(-0.903816\pi\) |
0.735069 | + | 0.677992i | \(0.237150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.73950 | + | 4.74495i | 0.168286 | + | 0.291480i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.5030 | −1.43300 | −0.716502 | − | 0.697585i | \(-0.754258\pi\) | ||||
−0.716502 | + | 0.697585i | \(0.754258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.49838 | −0.516240 | −0.258120 | − | 0.966113i | \(-0.583103\pi\) | ||||
−0.258120 | + | 0.966113i | \(0.583103\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.20380 | + | 3.81710i | 0.132894 | + | 0.230180i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1153 | − | 19.2523i | 0.667856 | − | 1.15676i | −0.310646 | − | 0.950526i | \(-0.600545\pi\) |
0.978502 | − | 0.206235i | \(-0.0661212\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.87029 | + | 10.1676i | −0.350192 | + | 0.606550i | −0.986283 | − | 0.165064i | \(-0.947217\pi\) |
0.636091 | + | 0.771614i | \(0.280550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.8667 | + | 20.5537i | 0.705401 | + | 1.22179i | 0.966546 | + | 0.256491i | \(0.0825666\pi\) |
−0.261145 | + | 0.965300i | \(0.584100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.82488 | 0.107719 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.56653 | −0.445090 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.1347 | − | 17.5538i | −0.592077 | − | 1.02551i | −0.993952 | − | 0.109813i | \(-0.964975\pi\) |
0.401876 | − | 0.915694i | \(-0.368358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.69411 | − | 6.39839i | 0.215080 | − | 0.372529i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.82220 | − | 10.0844i | 0.336707 | − | 0.583193i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.17348 | − | 2.03253i | −0.0676382 | − | 0.117153i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.592395 | −0.0339204 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.05094 | 0.117053 | 0.0585267 | − | 0.998286i | \(-0.481360\pi\) | ||||
0.0585267 | + | 0.998286i | \(0.481360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.89792 | − | 17.1437i | −0.561259 | − | 0.972130i | −0.997387 | − | 0.0722448i | \(-0.976984\pi\) |
0.436128 | − | 0.899885i | \(-0.356350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0577727 | − | 0.100065i | 0.00326551 | − | 0.00565603i | −0.864388 | − | 0.502825i | \(-0.832294\pi\) |
0.867654 | + | 0.497169i | \(0.165627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.8936 | − | 20.6003i | 0.668011 | − | 1.15703i | −0.310448 | − | 0.950590i | \(-0.600479\pi\) |
0.978459 | − | 0.206439i | \(-0.0661875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.87422 | − | 13.6385i | −0.440872 | − | 0.763612i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2002 | −1.29089 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.98062 | 0.387215 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.32365 | − | 2.29262i | −0.0729750 | − | 0.126396i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3125 | + | 29.9862i | −0.951582 | + | 1.64819i | −0.209579 | + | 0.977792i | \(0.567209\pi\) |
−0.742003 | + | 0.670396i | \(0.766124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.61087 | − | 4.52216i | 0.142647 | − | 0.247072i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.26713 | + | 9.12293i | 0.286919 | + | 0.496958i | 0.973073 | − | 0.230499i | \(-0.0740357\pi\) |
−0.686154 | + | 0.727456i | \(0.740702\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.8783 | −1.34724 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.60997 | 0.248915 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.94654 | − | 5.10356i | −0.158179 | − | 0.273974i | 0.776033 | − | 0.630692i | \(-0.217229\pi\) |
−0.934212 | + | 0.356718i | \(0.883896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5066 | − | 19.9301i | 0.615936 | − | 1.06683i | −0.374284 | − | 0.927314i | \(-0.622111\pi\) |
0.990220 | − | 0.139518i | \(-0.0445552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.36222 | + | 12.7517i | −0.391851 | + | 0.678706i | −0.992694 | − | 0.120661i | \(-0.961499\pi\) |
0.600842 | + | 0.799367i | \(0.294832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.49031 | − | 7.77745i | −0.238321 | − | 0.412784i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.02262 | −0.212306 | −0.106153 | − | 0.994350i | \(-0.533853\pi\) | ||||
−0.106153 | + | 0.994350i | \(0.533853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.0574 | 2.00302 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.02601 | − | 6.97325i | −0.210731 | − | 0.364997i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.43830 | − | 7.68735i | 0.231677 | − | 0.401277i | −0.726625 | − | 0.687035i | \(-0.758912\pi\) |
0.958302 | + | 0.285758i | \(0.0922454\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.909226 | − | 1.57482i | 0.0472046 | − | 0.0817608i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.3645 | − | 26.6121i | −0.795545 | − | 1.37792i | −0.922492 | − | 0.386015i | \(-0.873851\pi\) |
0.126947 | − | 0.991909i | \(-0.459482\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.9419 | −1.28457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.24004 | −0.217796 | −0.108898 | − | 0.994053i | \(-0.534732\pi\) | ||||
−0.108898 | + | 0.994053i | \(0.534732\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0439 | + | 27.7889i | 0.819807 | + | 1.41995i | 0.905824 | + | 0.423654i | \(0.139253\pi\) |
−0.0860167 | + | 0.996294i | \(0.527414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.731430 | − | 1.26687i | 0.0372771 | − | 0.0645659i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1667 | + | 24.5374i | −0.718278 | + | 1.24409i | 0.243403 | + | 0.969925i | \(0.421736\pi\) |
−0.961681 | + | 0.274169i | \(0.911597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.56170 | + | 4.43700i | 0.129551 | + | 0.224389i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9968 | 0.553307 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1395 | 0.659455 | 0.329728 | − | 0.944076i | \(-0.393043\pi\) | ||||
0.329728 | + | 0.944076i | \(0.393043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.59471 | + | 13.1544i | 0.379262 | + | 0.656900i | 0.990955 | − | 0.134195i | \(-0.0428447\pi\) |
−0.611693 | + | 0.791095i | \(0.709511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7007 | + | 34.1227i | −0.981364 | + | 1.69977i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.8468 | − | 29.1795i | 0.835063 | − | 1.44637i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.10064 | + | 8.83457i | 0.252211 | + | 0.436841i | 0.964134 | − | 0.265415i | \(-0.0855091\pi\) |
−0.711924 | + | 0.702257i | \(0.752176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.45211 | −0.120661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.29314 | −0.308918 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.32058 | + | 10.9476i | 0.308781 | + | 0.534824i | 0.978096 | − | 0.208155i | \(-0.0667457\pi\) |
−0.669315 | + | 0.742979i | \(0.733412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.501620 | + | 0.868832i | −0.0244475 | + | 0.0423443i | −0.877990 | − | 0.478678i | \(-0.841116\pi\) |
0.853543 | + | 0.521023i | \(0.174449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.53570 | + | 2.65991i | −0.0744923 | + | 0.129024i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0983063 | + | 0.170272i | 0.00475738 | + | 0.00824002i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.0685 | 1.88186 | 0.940932 | − | 0.338596i | \(-0.109952\pi\) | ||||
0.940932 | + | 0.338596i | \(0.109952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6663 | −1.42567 | −0.712836 | − | 0.701331i | \(-0.752589\pi\) | ||||
−0.712836 | + | 0.701331i | \(0.752589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.30013 | − | 10.9121i | −0.301376 | − | 0.521999i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.1223 | − | 27.9247i | 0.769477 | − | 1.33277i | −0.168370 | − | 0.985724i | \(-0.553850\pi\) |
0.937847 | − | 0.347049i | \(-0.112816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.22372 | + | 3.85160i | −0.105652 | + | 0.182995i | −0.914004 | − | 0.405704i | \(-0.867026\pi\) |
0.808352 | + | 0.588699i | \(0.200360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.95299 | − | 10.3109i | −0.282199 | − | 0.488783i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.0639 | 0.616523 | 0.308261 | − | 0.951302i | \(-0.400253\pi\) | ||||
0.308261 | + | 0.951302i | \(0.400253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.2347 | 1.14117 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.15842 | − | 2.00643i | −0.0543074 | − | 0.0940631i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.16504 | + | 14.1423i | −0.381945 | + | 0.661547i | −0.991340 | − | 0.131319i | \(-0.958079\pi\) |
0.609396 | + | 0.792866i | \(0.291412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7639 | − | 18.6436i | 0.501324 | − | 0.868319i | −0.498675 | − | 0.866789i | \(-0.666180\pi\) |
0.999999 | − | 0.00152975i | \(-0.000486935\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1584 | + | 19.3269i | 0.518576 | + | 0.898199i | 0.999767 | + | 0.0215837i | \(0.00687083\pi\) |
−0.481192 | + | 0.876616i | \(0.659796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.5203 | 1.68996 | 0.844978 | − | 0.534801i | \(-0.179613\pi\) | ||||
0.844978 | + | 0.534801i | \(0.179613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73307 | −0.0800256 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.5840 | − | 26.9922i | −0.716551 | − | 1.24110i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.77682 | − | 6.54164i | 0.173292 | − | 0.300151i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.47900 | − | 7.75786i | 0.204651 | − | 0.354465i | −0.745371 | − | 0.666650i | \(-0.767727\pi\) |
0.950021 | + | 0.312185i | \(0.101061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.6814 | − | 46.2135i | −1.21657 | − | 2.10715i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.24544 | 0.0565523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.5016 | −1.33685 | −0.668423 | − | 0.743781i | \(-0.733030\pi\) | ||||
−0.668423 | + | 0.743781i | \(0.733030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.17635 | − | 8.96571i | −0.233606 | − | 0.404617i | 0.725261 | − | 0.688474i | \(-0.241719\pi\) |
−0.958867 | + | 0.283857i | \(0.908386\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.48707 | − | 9.50388i | 0.247125 | − | 0.428033i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.49031 | + | 2.58129i | −0.0668495 | + | 0.115787i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1925 | − | 19.3860i | −0.501045 | − | 0.867835i | −0.999999 | − | 0.00120683i | \(-0.999616\pi\) |
0.498954 | − | 0.866628i | \(-0.333717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.8654 | 1.91127 | 0.955637 | − | 0.294546i | \(-0.0951685\pi\) | ||||
0.955637 | + | 0.294546i | \(0.0951685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.66379 | 0.207536 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.54539 | − | 6.14079i | −0.157147 | − | 0.272186i | 0.776692 | − | 0.629881i | \(-0.216896\pi\) |
−0.933839 | + | 0.357695i | \(0.883563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.33621 | + | 2.31438i | −0.0591105 | + | 0.102382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.08270 | + | 3.60735i | −0.0917749 | + | 0.158959i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.5782 | − | 30.4463i | −0.773088 | − | 1.33903i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.5863 | 1.73431 | 0.867153 | − | 0.498042i | \(-0.165947\pi\) | ||||
0.867153 | + | 0.498042i | \(0.165947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9375 | 1.13417 | 0.567085 | − | 0.823659i | \(-0.308071\pi\) | ||||
0.567085 | + | 0.823659i | \(0.308071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.66811 | − | 15.0136i | −0.377589 | − | 0.654003i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1087 | − | 17.5088i | 0.439509 | − | 0.761252i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.1911 | − | 33.2399i | 0.831257 | − | 1.43978i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.28705 | + | 5.69333i | 0.142111 | + | 0.246144i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.3677 | 1.30803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.7929 | −1.66784 | −0.833920 | − | 0.551886i | \(-0.813908\pi\) | ||||
−0.833920 | + | 0.551886i | \(0.813908\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.371908 | + | 0.644164i | 0.0159308 | + | 0.0275929i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.02655 | − | 8.70623i | 0.214920 | − | 0.372252i | −0.738328 | − | 0.674442i | \(-0.764384\pi\) |
0.953248 | + | 0.302190i | \(0.0977177\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4946 | + | 23.3734i | −0.574890 | + | 0.995739i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.82488 | − | 3.16079i | −0.0776019 | − | 0.134410i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.4316 | 0.992829 | 0.496415 | − | 0.868086i | \(-0.334650\pi\) | ||||
0.496415 | + | 0.868086i | \(0.334650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −49.3627 | −2.08782 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7580 | − | 35.9539i | −0.874844 | − | 1.51527i | −0.856928 | − | 0.515435i | \(-0.827630\pi\) |
−0.0179159 | − | 0.999839i | \(-0.505703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.31252 | + | 14.3977i | −0.349710 | + | 0.605716i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5990 | + | 30.4824i | −0.737789 | + | 1.27789i | 0.215699 | + | 0.976460i | \(0.430797\pi\) |
−0.953489 | + | 0.301429i | \(0.902536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.689797 | + | 1.19476i | 0.0288671 | + | 0.0499993i | 0.880098 | − | 0.474792i | \(-0.157477\pi\) |
−0.851231 | + | 0.524791i | \(0.824143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.66811 | −0.0695648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3322 | −0.721549 | −0.360775 | − | 0.932653i | \(-0.617488\pi\) | ||||
−0.360775 | + | 0.932653i | \(0.617488\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.04433 | + | 1.80883i | 0.0433261 | + | 0.0750430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0746 | − | 20.9139i | 0.500080 | − | 0.866164i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.8450 | + | 39.5687i | −0.942914 | + | 1.63317i | −0.183039 | + | 0.983106i | \(0.558593\pi\) |
−0.759875 | + | 0.650069i | \(0.774740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3179 | + | 36.9237i | 0.878389 | + | 1.52141i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.4661 | −0.429791 | −0.214896 | − | 0.976637i | \(-0.568941\pi\) | ||||
−0.214896 | + | 0.976637i | \(0.568941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01938 | 0.0417905 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5698 | + | 18.3074i | 0.431869 | + | 0.748020i | 0.997034 | − | 0.0769583i | \(-0.0245208\pi\) |
−0.565165 | + | 0.824978i | \(0.691188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.33421 | − | 9.23912i | 0.217587 | − | 0.376871i | −0.736483 | − | 0.676456i | \(-0.763515\pi\) |
0.954070 | + | 0.299585i | \(0.0968481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.21349 | − | 7.29798i | 0.171303 | − | 0.296705i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.651942 | − | 1.12920i | −0.0264615 | − | 0.0458327i | 0.852491 | − | 0.522741i | \(-0.175091\pi\) |
−0.878953 | + | 0.476909i | \(0.841757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.6796 | −2.25255 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.9741 | 1.25103 | 0.625517 | − | 0.780211i | \(-0.284888\pi\) | ||||
0.625517 | + | 0.780211i | \(0.284888\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.29190 | − | 2.23763i | −0.0520099 | − | 0.0900838i | 0.838848 | − | 0.544365i | \(-0.183229\pi\) |
−0.890858 | + | 0.454281i | \(0.849896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.465378 | − | 0.806058i | 0.0187051 | − | 0.0323982i | −0.856521 | − | 0.516112i | \(-0.827379\pi\) |
0.875226 | + | 0.483713i | \(0.160712\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.97577 | + | 3.42213i | −0.0791574 | + | 0.137105i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.4790 | 0.936169 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.6250 | 0.821069 | 0.410535 | − | 0.911845i | \(-0.365342\pi\) | ||||
0.410535 | + | 0.911845i | \(0.365342\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.39576 | + | 4.14957i | 0.0950727 | + | 0.164671i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0477 | − | 41.6518i | 0.952805 | − | 1.65031i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.9516 | − | 20.7007i | 0.472058 | − | 0.817628i | −0.527431 | − | 0.849598i | \(-0.676845\pi\) |
0.999489 | + | 0.0319697i | \(0.0101780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.12863 | − | 1.95484i | −0.0445088 | − | 0.0770915i | 0.842913 | − | 0.538050i | \(-0.180839\pi\) |
−0.887422 | + | 0.460959i | \(0.847506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7262 | 0.500320 | 0.250160 | − | 0.968204i | \(-0.419517\pi\) | ||||
0.250160 | + | 0.968204i | \(0.419517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.5644 | −1.27826 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.585400 | + | 1.01394i | 0.0229085 | + | 0.0396787i | 0.877252 | − | 0.480029i | \(-0.159374\pi\) |
−0.854344 | + | 0.519708i | \(0.826041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.88985 | + | 17.1297i | −0.386428 | + | 0.669313i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.3678 | − | 30.0819i | 0.676552 | − | 1.17182i | −0.299460 | − | 0.954109i | \(-0.596807\pi\) |
0.976013 | − | 0.217714i | \(-0.0698601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5730 | − | 30.4374i | −0.683511 | − | 1.18388i | −0.973902 | − | 0.226968i | \(-0.927119\pi\) |
0.290391 | − | 0.956908i | \(-0.406215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.50701 | −0.0972177 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.96017 | 0.230779 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.30552 | + | 2.26123i | 0.0503991 | + | 0.0872938i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.6374 | − | 23.6207i | 0.525684 | − | 0.910511i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
0.999552 | − | 0.0299154i | \(-0.00952380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.56602 | − | 7.90858i | 0.175486 | − | 0.303951i | −0.764843 | − | 0.644217i | \(-0.777184\pi\) |
0.940330 | + | 0.340265i | \(0.110517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.206677 | − | 0.357975i | −0.00793153 | − | 0.0137378i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.0326 | 1.11090 | 0.555451 | − | 0.831549i | \(-0.312545\pi\) | ||||
0.555451 | + | 0.831549i | \(0.312545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5343 | 0.708158 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.1234 | − | 33.1227i | −0.728544 | − | 1.26188i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.38823 | − | 14.5288i | 0.319103 | − | 0.552703i | −0.661198 | − | 0.750211i | \(-0.729952\pi\) |
0.980301 | + | 0.197509i | \(0.0632850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.68980 | − | 4.65887i | 0.102030 | − | 0.176721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.44385 | + | 14.6252i | 0.319834 | + | 0.553968i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.93400 | −0.110816 | −0.0554078 | − | 0.998464i | \(-0.517646\pi\) | ||||
−0.0554078 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.7431 | −2.17782 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.773944 | − | 1.34051i | −0.0291071 | − | 0.0504150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.9293 | + | 24.1263i | −0.523126 | + | 0.906080i | 0.476512 | + | 0.879168i | \(0.341901\pi\) |
−0.999638 | + | 0.0269124i | \(0.991432\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.70773 | − | 8.15404i | 0.176306 | − | 0.305371i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.3839 | − | 26.6457i | −0.575326 | − | 0.996493i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.95585 | −0.259409 | −0.129705 | − | 0.991553i | \(-0.541403\pi\) | ||||
−0.129705 | + | 0.991553i | \(0.541403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.38248 | 0.0514861 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.78651 | + | 3.09432i | 0.0663492 | + | 0.114920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.51023 | − | 4.34784i | 0.0930992 | − | 0.161253i | −0.815715 | − | 0.578455i | \(-0.803656\pi\) |
0.908814 | + | 0.417202i | \(0.136989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8595 | − | 18.8092i | 0.401654 | − | 0.695685i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.2368 | + | 17.7307i | 0.378105 | + | 0.654897i | 0.990787 | − | 0.135433i | \(-0.0432425\pi\) |
−0.612682 | + | 0.790330i | \(0.709909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.0154 | −0.847782 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.1614 | 1.88200 | 0.941002 | − | 0.338401i | \(-0.109886\pi\) | ||||
0.941002 | + | 0.338401i | \(0.109886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.07086 | − | 5.31888i | −0.112659 | − | 0.195131i | 0.804183 | − | 0.594382i | \(-0.202603\pi\) |
−0.916841 | + | 0.399251i | \(0.869270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.51794 | + | 9.55735i | −0.202162 | + | 0.350154i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.09095 | − | 1.88959i | 0.0398626 | − | 0.0690440i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.54557 | + | 13.0693i | 0.275342 | + | 0.476906i | 0.970221 | − | 0.242220i | \(-0.0778757\pi\) |
−0.694880 | + | 0.719126i | \(0.744542\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.50162 | 0.0546496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.87659 | −0.104551 | −0.0522757 | − | 0.998633i | \(-0.516647\pi\) | ||||
−0.0522757 | + | 0.998633i | \(0.516647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.119478 | + | 0.206941i | 0.00433106 | + | 0.00750162i | 0.868183 | − | 0.496245i | \(-0.165288\pi\) |
−0.863852 | + | 0.503746i | \(0.831955\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.123434 | − | 0.213794i | 0.00446862 | − | 0.00773988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.7872 | + | 44.6647i | −0.931122 | + | 1.61275i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.92930 | + | 3.34164i | 0.0695722 | + | 0.120503i | 0.898713 | − | 0.438537i | \(-0.144503\pi\) |
−0.829141 | + | 0.559040i | \(0.811170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.22355 | 0.187878 | 0.0939390 | − | 0.995578i | \(-0.470054\pi\) | ||||
0.0939390 | + | 0.995578i | \(0.470054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.64441 | 0.202753 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.7664 | − | 35.9684i | −0.744033 | − | 1.28870i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7915 | + | 34.2799i | −0.708196 | + | 1.22663i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.8109 | + | 20.4571i | −0.421549 | + | 0.730144i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.8818 | + | 18.8478i | 0.387893 | + | 0.671851i | 0.992166 | − | 0.124927i | \(-0.0398695\pi\) |
−0.604273 | + | 0.796778i | \(0.706536\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.51776 | 0.196189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.13528 | 0.146848 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.7228 | + | 22.0365i | 0.450665 | + | 0.780574i | 0.998427 | − | 0.0560596i | \(-0.0178537\pi\) |
−0.547763 | + | 0.836634i | \(0.684520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2492 | − | 21.2162i | 0.433345 | − | 0.750576i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.7451 | + | 30.7353i | −0.626209 | + | 1.08463i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.276818 | + | 0.479462i | 0.00975654 | + | 0.0168988i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0854 | 0.389741 | 0.194871 | − | 0.980829i | \(-0.437571\pi\) | ||||
0.194871 | + | 0.980829i | \(0.437571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.4869 | 1.49192 | 0.745958 | − | 0.665993i | \(-0.231992\pi\) | ||||
0.745958 | + | 0.665993i | \(0.231992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.58108 | − | 7.93467i | −0.160468 | − | 0.277939i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.7074 | + | 46.2585i | −0.934373 | + | 1.61838i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0673 | + | 26.0973i | −0.525851 | + | 0.910800i | 0.473696 | + | 0.880689i | \(0.342920\pi\) |
−0.999547 | + | 0.0301119i | \(0.990414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.8109 | − | 18.7251i | −0.376845 | − | 0.652715i | 0.613756 | − | 0.789495i | \(-0.289658\pi\) |
−0.990601 | + | 0.136781i | \(0.956324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.82488 | 0.0634574 | 0.0317287 | − | 0.999497i | \(-0.489899\pi\) | ||||
0.0317287 | + | 0.999497i | \(0.489899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.4374 | 1.05713 | 0.528567 | − | 0.848892i | \(-0.322730\pi\) | ||||
0.528567 | + | 0.848892i | \(0.322730\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5807 | + | 18.3263i | 0.366600 | + | 0.634970i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.324363 | − | 0.561813i | 0.0112250 | − | 0.0194423i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.7834 | − | 29.0698i | 0.579429 | − | 1.00360i | −0.416116 | − | 0.909312i | \(-0.636609\pi\) |
0.995545 | − | 0.0942887i | \(-0.0300577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.11678 | + | 14.0587i | 0.279889 | + | 0.484782i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.7291 | −1.22912 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.79687 | −0.0961016 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.37584 | + | 11.0433i | 0.218561 | + | 0.378559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.8775 | − | 20.5724i | 0.406676 | − | 0.704384i | −0.587839 | − | 0.808978i | \(-0.700021\pi\) |
0.994515 | + | 0.104594i | \(0.0333543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.0052 | + | 22.5256i | −0.444249 | + | 0.769461i | −0.998000 | − | 0.0632211i | \(-0.979863\pi\) |
0.553751 | + | 0.832682i | \(0.313196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3835 | + | 43.9656i | 0.866075 | + | 1.50009i | 0.865975 | + | 0.500086i | \(0.166698\pi\) |
9.98605e−5 | 1.00000i | \(0.499968\pi\) | ||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9343 | −1.12110 | −0.560548 | − | 0.828122i | \(-0.689410\pi\) | ||||
−0.560548 | + | 0.828122i | \(0.689410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.81521 | 0.299726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.2347 | − | 41.9757i | −0.822105 | − | 1.42393i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.2255 | + | 31.5675i | −0.617547 | + | 1.06962i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.165947 | + | 0.287429i | −0.00561004 | + | 0.00971688i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.56170 | − | 14.8293i | −0.289108 | − | 0.500750i | 0.684489 | − | 0.729023i | \(-0.260025\pi\) |
−0.973597 | + | 0.228273i | \(0.926692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.7617 | 1.57544 | 0.787721 | − | 0.616032i | \(-0.211261\pi\) | ||||
0.787721 | + | 0.616032i | \(0.211261\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.1356 | −0.711269 | −0.355635 | − | 0.934625i | \(-0.615735\pi\) | ||||
−0.355635 | + | 0.934625i | \(0.615735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9887 | − | 39.8176i | −0.771885 | − | 1.33694i | −0.936529 | − | 0.350590i | \(-0.885981\pi\) |
0.164644 | − | 0.986353i | \(-0.447352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.795139 | − | 1.37722i | 0.0266681 | − | 0.0461905i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.1250 | + | 52.1781i | −1.00810 | + | 1.74607i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.58108 | − | 7.93467i | −0.153129 | − | 0.265227i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.1676 | −0.672626 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8282 | 0.560628 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.78651 | + | 11.7546i | 0.225591 | + | 0.390735i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.29404 | − | 5.70544i | 0.109377 | − | 0.189446i | −0.806141 | − | 0.591723i | \(-0.798448\pi\) |
0.915518 | + | 0.402277i | \(0.131781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8855 | + | 20.5863i | −0.393785 | + | 0.682056i | −0.992945 | − | 0.118573i | \(-0.962168\pi\) |
0.599160 | + | 0.800629i | \(0.295501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8688 | + | 24.0215i | 0.458991 | + | 0.794996i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.56477 | 0.216788 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.1305 | 1.52171 | 0.760853 | − | 0.648924i | \(-0.224781\pi\) | ||||
0.760853 | + | 0.648924i | \(0.224781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.3452 | + | 54.2914i | 1.03174 | + | 1.78702i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.82220 | + | 6.62025i | −0.125673 | + | 0.217673i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3082 | − | 19.5864i | 0.371010 | − | 0.642608i | −0.618711 | − | 0.785619i | \(-0.712345\pi\) |
0.989721 | + | 0.143010i | \(0.0456782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0217 | − | 45.0709i | −0.852826 | − | 1.47714i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.5375 | 0.442723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5830 | −1.55447 | −0.777235 | − | 0.629211i | \(-0.783378\pi\) | ||||
−0.777235 | + | 0.629211i | \(0.783378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.4991 | − | 37.2375i | −0.700850 | − | 1.21391i | −0.968169 | − | 0.250299i | \(-0.919471\pi\) |
0.267319 | − | 0.963608i | \(-0.413862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.58594 | + | 7.94308i | −0.149339 | + | 0.258662i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0274 | + | 41.6167i | −0.780786 | + | 1.35236i | 0.150698 | + | 0.988580i | \(0.451848\pi\) |
−0.931484 | + | 0.363781i | \(0.881486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.1040 | + | 48.6776i | 0.912295 | + | 1.58014i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.0413 | 1.26467 | 0.632335 | − | 0.774695i | \(-0.282096\pi\) | ||||
0.632335 | + | 0.774695i | \(0.282096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.2694 | −0.332311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.07571 | − | 5.32729i | −0.0993199 | − | 0.172027i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.429681 | + | 0.744229i | −0.0138607 | + | 0.0240074i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.53570 | − | 7.85606i | 0.146009 | − | 0.252895i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.02423 | + | 1.77402i | 0.0329371 | + | 0.0570488i | 0.882024 | − | 0.471204i | \(-0.156181\pi\) |
−0.849087 | + | 0.528253i | \(0.822847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4068 | −0.879527 | −0.439764 | − | 0.898114i | \(-0.644938\pi\) | ||||
−0.439764 | + | 0.898114i | \(0.644938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78546 | −0.0572392 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.04914 | − | 3.54922i | −0.0655578 | − | 0.113549i | 0.831383 | − | 0.555699i | \(-0.187549\pi\) |
−0.896941 | + | 0.442150i | \(0.854216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.2384 | + | 45.4463i | −0.838584 | + | 1.45247i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.05903 | + | 5.29840i | −0.0975680 | + | 0.168993i | −0.910677 | − | 0.413118i | \(-0.864440\pi\) |
0.813109 | + | 0.582111i | \(0.197773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.40329 | + | 4.16262i | 0.0765752 | + | 0.132632i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7958 | 0.375086 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.9881 | 0.476114 | 0.238057 | − | 0.971251i | \(-0.423490\pi\) | ||||
0.238057 | + | 0.971251i | \(0.423490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.22981 | − | 15.9865i | −0.292605 | − | 0.506806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.74813 | − | 11.6881i | 0.213715 | − | 0.370166i | −0.739159 | − | 0.673531i | \(-0.764777\pi\) |
0.952874 | + | 0.303365i | \(0.0981101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.2.q.e.721.3 | 8 | ||
3.2 | odd | 2 | 360.2.q.e.241.1 | yes | 8 | ||
4.3 | odd | 2 | 2160.2.q.l.721.2 | 8 | |||
9.2 | odd | 6 | 3240.2.a.u.1.2 | 4 | |||
9.4 | even | 3 | inner | 1080.2.q.e.361.3 | 8 | ||
9.5 | odd | 6 | 360.2.q.e.121.1 | ✓ | 8 | ||
9.7 | even | 3 | 3240.2.a.s.1.2 | 4 | |||
12.11 | even | 2 | 720.2.q.l.241.4 | 8 | |||
36.7 | odd | 6 | 6480.2.a.bz.1.3 | 4 | |||
36.11 | even | 6 | 6480.2.a.cb.1.3 | 4 | |||
36.23 | even | 6 | 720.2.q.l.481.4 | 8 | |||
36.31 | odd | 6 | 2160.2.q.l.1441.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.e.121.1 | ✓ | 8 | 9.5 | odd | 6 | ||
360.2.q.e.241.1 | yes | 8 | 3.2 | odd | 2 | ||
720.2.q.l.241.4 | 8 | 12.11 | even | 2 | |||
720.2.q.l.481.4 | 8 | 36.23 | even | 6 | |||
1080.2.q.e.361.3 | 8 | 9.4 | even | 3 | inner | ||
1080.2.q.e.721.3 | 8 | 1.1 | even | 1 | trivial | ||
2160.2.q.l.721.2 | 8 | 4.3 | odd | 2 | |||
2160.2.q.l.1441.2 | 8 | 36.31 | odd | 6 | |||
3240.2.a.s.1.2 | 4 | 9.7 | even | 3 | |||
3240.2.a.u.1.2 | 4 | 9.2 | odd | 6 | |||
6480.2.a.bz.1.3 | 4 | 36.7 | odd | 6 | |||
6480.2.a.cb.1.3 | 4 | 36.11 | even | 6 |