Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(577,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.i (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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.2696112.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(0.235342 + 0.407624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.961 |
Dual form | 1216.2.i.n.577.3 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.62457 | − | 2.81384i | 0.937946 | − | 1.62457i | 0.168652 | − | 0.985676i | \(-0.446059\pi\) |
0.769294 | − | 0.638895i | \(-0.220608\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.235342 | − | 0.407624i | 0.105248 | − | 0.182295i | −0.808591 | − | 0.588370i | \(-0.799770\pi\) |
0.913840 | + | 0.406076i | \(0.133103\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.30777 | −1.25022 | −0.625110 | − | 0.780536i | \(-0.714946\pi\) | ||||
−0.625110 | + | 0.780536i | \(0.714946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.77846 | − | 6.54448i | −1.25949 | − | 2.18149i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.47068 | −0.443428 | −0.221714 | − | 0.975112i | \(-0.571165\pi\) | ||||
−0.221714 | + | 0.975112i | \(0.571165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41855 | − | 2.45699i | −0.393434 | − | 0.681447i | 0.599466 | − | 0.800400i | \(-0.295380\pi\) |
−0.992900 | + | 0.118953i | \(0.962046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.764658 | − | 1.32443i | −0.197434 | − | 0.341966i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.35991 | + | 5.81954i | −0.814898 | + | 1.41145i | 0.0945025 | + | 0.995525i | \(0.469874\pi\) |
−0.909401 | + | 0.415921i | \(0.863459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.206025 | − | 4.35403i | 0.0472654 | − | 0.998882i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.37371 | + | 9.30754i | −1.17264 | + | 2.03107i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.235342 | − | 0.407624i | −0.0490721 | − | 0.0849954i | 0.840446 | − | 0.541895i | \(-0.182293\pi\) |
−0.889518 | + | 0.456900i | \(0.848960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.38923 | + | 4.13827i | 0.477846 | + | 0.827653i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.8061 | −2.84943 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.48448 | + | 4.30325i | 0.461357 | + | 0.799093i | 0.999029 | − | 0.0440607i | \(-0.0140295\pi\) |
−0.537672 | + | 0.843154i | \(0.680696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.74742 | 1.21187 | 0.605936 | − | 0.795513i | \(-0.292799\pi\) | ||||
0.605936 | + | 0.795513i | \(0.292799\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.38923 | + | 4.13827i | −0.415911 | + | 0.720380i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.778457 | + | 1.34833i | −0.131583 | + | 0.227909i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.74742 | −0.780471 | −0.390236 | − | 0.920715i | \(-0.627606\pi\) | ||||
−0.390236 | + | 0.920715i | \(0.627606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.21811 | −1.47608 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.250859 | − | 0.434501i | 0.0391777 | − | 0.0678577i | −0.845772 | − | 0.533545i | \(-0.820860\pi\) |
0.884949 | + | 0.465687i | \(0.154193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.94786 | − | 3.37380i | 0.297046 | − | 0.514499i | −0.678413 | − | 0.734681i | \(-0.737332\pi\) |
0.975459 | + | 0.220182i | \(0.0706652\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.55691 | −0.530233 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.95517 | − | 10.3146i | −0.868650 | − | 1.50455i | −0.863377 | − | 0.504560i | \(-0.831655\pi\) |
−0.00527366 | − | 0.999986i | \(-0.501679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94137 | 0.563052 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9168 | + | 18.9085i | 1.52866 | + | 2.64772i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.35991 | − | 4.08749i | −0.324159 | − | 0.561460i | 0.657183 | − | 0.753731i | \(-0.271748\pi\) |
−0.981342 | + | 0.192272i | \(0.938415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.346113 | + | 0.599486i | −0.0466699 | + | 0.0808346i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.9168 | − | 7.65314i | −1.57842 | − | 1.01368i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.62457 | − | 6.27794i | 0.471879 | − | 0.817318i | −0.527603 | − | 0.849491i | \(-0.676909\pi\) |
0.999482 | + | 0.0321726i | \(0.0102426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.26294 | − | 10.8477i | −0.801887 | − | 1.38891i | −0.918373 | − | 0.395717i | \(-0.870496\pi\) |
0.116485 | − | 0.993192i | \(-0.462837\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.4983 | + | 21.6477i | 1.57464 | + | 2.72735i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.33537 | −0.165632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.316797 | − | 0.548708i | −0.0387029 | − | 0.0670353i | 0.846025 | − | 0.533143i | \(-0.178989\pi\) |
−0.884728 | + | 0.466108i | \(0.845656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.52932 | −0.184108 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.88923 | − | 3.27224i | 0.224210 | − | 0.388343i | −0.731872 | − | 0.681442i | \(-0.761353\pi\) |
0.956082 | + | 0.293099i | \(0.0946865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.97068 | − | 3.41332i | 0.230651 | − | 0.399499i | −0.727349 | − | 0.686268i | \(-0.759248\pi\) |
0.958000 | + | 0.286769i | \(0.0925811\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 15.5259 | 1.79277 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.86469 | 0.554383 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.41855 | − | 7.65314i | 0.497125 | − | 0.861046i | −0.502869 | − | 0.864362i | \(-0.667722\pi\) |
0.999995 | + | 0.00331640i | \(0.00105564\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.7181 | + | 22.0284i | −1.41312 | + | 2.44760i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.14486 | −1.00378 | −0.501890 | − | 0.864932i | \(-0.667362\pi\) | ||||
−0.501890 | + | 0.864932i | \(0.667362\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.58145 | + | 2.73916i | 0.171533 | + | 0.297104i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.1449 | 1.73091 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.47718 | − | 2.55855i | −0.156581 | − | 0.271206i | 0.777053 | − | 0.629435i | \(-0.216714\pi\) |
−0.933633 | + | 0.358230i | \(0.883380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.69223 | + | 8.12717i | 0.491879 | + | 0.851959i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9617 | − | 18.9862i | 1.13667 | − | 1.96877i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.72632 | − | 1.10866i | −0.177117 | − | 0.113747i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0293166 | + | 0.0507778i | −0.00297665 | + | 0.00515571i | −0.867510 | − | 0.497420i | \(-0.834281\pi\) |
0.864533 | + | 0.502576i | \(0.167614\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.55691 | + | 9.62486i | 0.558491 | + | 0.967335i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.79226 | + | 10.0325i | 0.576351 | + | 0.998269i | 0.995893 | + | 0.0905335i | \(0.0288572\pi\) |
−0.419542 | + | 0.907736i | \(0.637809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.17246 | −0.805257 | −0.402628 | − | 0.915364i | \(-0.631903\pi\) | ||||
−0.402628 | + | 0.915364i | \(0.631903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.52932 | + | 4.38090i | 0.246836 | + | 0.427533i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.498281 | −0.0481706 | −0.0240853 | − | 0.999710i | \(-0.507667\pi\) | ||||
−0.0240853 | + | 0.999710i | \(0.507667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.19700 | + | 7.26942i | −0.402000 | + | 0.696284i | −0.993967 | − | 0.109678i | \(-0.965018\pi\) |
0.591967 | + | 0.805962i | \(0.298351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.71252 | + | 13.3585i | −0.732040 | + | 1.26793i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.83365 | 0.454712 | 0.227356 | − | 0.973812i | \(-0.426992\pi\) | ||||
0.227356 | + | 0.973812i | \(0.426992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.221543 | −0.0206590 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7198 | + | 18.5673i | −0.991048 | + | 1.71655i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1138 | − | 19.2497i | 1.01880 | − | 1.76462i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.83709 | −0.803372 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.815078 | − | 1.41176i | −0.0734931 | − | 0.127294i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.60256 | 0.411665 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.22460 | + | 15.9775i | 0.818551 | + | 1.41777i | 0.906750 | + | 0.421669i | \(0.138556\pi\) |
−0.0881990 | + | 0.996103i | \(0.528111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.32888 | − | 10.9619i | −0.557227 | − | 0.965145i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.434063 | − | 0.751819i | 0.0379243 | − | 0.0656867i | −0.846440 | − | 0.532484i | \(-0.821259\pi\) |
0.884365 | + | 0.466797i | \(0.154592\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.681485 | + | 14.4021i | −0.0590922 | + | 1.24882i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.48448 | + | 6.03530i | −0.299896 | + | 0.519436i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.27846 | − | 3.94640i | −0.194662 | − | 0.337164i | 0.752128 | − | 0.659017i | \(-0.229028\pi\) |
−0.946790 | + | 0.321853i | \(0.895694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.15389 | − | 14.1229i | −0.691604 | − | 1.19789i | −0.971312 | − | 0.237808i | \(-0.923571\pi\) |
0.279709 | − | 0.960085i | \(-0.409762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −38.6983 | −3.25899 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.08623 | + | 3.61346i | 0.174459 | + | 0.302173i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.33881 | 0.194228 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.40303 | − | 11.0904i | 0.528113 | − | 0.914718i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4534 | − | 18.1059i | 0.856380 | − | 1.48329i | −0.0189794 | − | 0.999820i | \(-0.506042\pi\) |
0.875359 | − | 0.483473i | \(-0.160625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.75086 | 0.142483 | 0.0712415 | − | 0.997459i | \(-0.477304\pi\) | ||||
0.0712415 | + | 0.997459i | \(0.477304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 50.7811 | 4.10541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.58795 | − | 2.75041i | 0.127547 | − | 0.220918i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0797359 | + | 0.138107i | −0.00636362 | + | 0.0110221i | −0.869190 | − | 0.494479i | \(-0.835359\pi\) |
0.862826 | + | 0.505501i | \(0.168692\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.3354 | −1.21617 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.778457 | + | 1.34833i | 0.0613510 | + | 0.106263i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0862308 | 0.00675412 | 0.00337706 | − | 0.999994i | \(-0.498925\pi\) | ||||
0.00337706 | + | 0.999994i | \(0.498925\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.12457 | + | 1.94781i | 0.0875477 | + | 0.151637i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.13837 | + | 5.43581i | 0.242854 | + | 0.420636i | 0.961526 | − | 0.274713i | \(-0.0885830\pi\) |
−0.718672 | + | 0.695349i | \(0.755250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.47546 | − | 4.28762i | 0.190420 | − | 0.329817i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.2733 | + | 15.1032i | −2.23859 | + | 1.15497i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.41855 | + | 9.38520i | −0.411964 | + | 0.713543i | −0.995104 | − | 0.0988284i | \(-0.968491\pi\) |
0.583140 | + | 0.812372i | \(0.301824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.90303 | − | 13.6884i | −0.597413 | − | 1.03475i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7767 | − | 20.3979i | −0.885194 | − | 1.53320i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.08967 | −0.529907 | −0.264953 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264953 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.17671 | − | 10.6984i | −0.459111 | − | 0.795204i | 0.539803 | − | 0.841791i | \(-0.318499\pi\) |
−0.998914 | + | 0.0465875i | \(0.985165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −40.6983 | −3.00851 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.11727 | + | 1.93516i | −0.0821431 | + | 0.142276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.94137 | − | 8.55870i | 0.361349 | − | 0.625874i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 48.9751 | 3.56241 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.99656 | 0.650968 | 0.325484 | − | 0.945547i | \(-0.394473\pi\) | ||||
0.325484 | + | 0.945547i | \(0.394473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.58145 | − | 2.73916i | 0.113836 | − | 0.197169i | −0.803478 | − | 0.595334i | \(-0.797020\pi\) |
0.917314 | + | 0.398165i | \(0.130353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.16940 | + | 3.75752i | −0.155354 | + | 0.269082i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.2457 | 1.51369 | 0.756847 | − | 0.653592i | \(-0.226739\pi\) | ||||
0.756847 | + | 0.653592i | \(0.226739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.94786 | − | 8.56995i | −0.350745 | − | 0.607507i | 0.635635 | − | 0.771989i | \(-0.280738\pi\) |
−0.986380 | + | 0.164482i | \(0.947405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.05863 | −0.145205 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.21811 | − | 14.2342i | −0.576798 | − | 0.999043i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.118075 | − | 0.204513i | −0.00824674 | − | 0.0142838i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.77846 | + | 3.08038i | −0.123611 | + | 0.214101i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.302998 | + | 6.40340i | −0.0209588 | + | 0.442932i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.55042 | − | 16.5418i | 0.657478 | − | 1.13879i | −0.323788 | − | 0.946130i | \(-0.604957\pi\) |
0.981266 | − | 0.192656i | \(-0.0617101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.13837 | − | 10.6320i | −0.420594 | − | 0.728490i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.916826 | − | 1.58799i | −0.0625270 | − | 0.108300i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.3189 | −1.51511 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.40303 | − | 11.0904i | −0.432676 | − | 0.749418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.0647 | 1.28243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.48448 | − | 14.6956i | 0.568163 | − | 0.984087i | −0.428585 | − | 0.903502i | \(-0.640988\pi\) |
0.996748 | − | 0.0805855i | \(-0.0256790\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.0552 | − | 31.2725i | 1.20368 | − | 2.08483i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.646583 | −0.0429152 | −0.0214576 | − | 0.999770i | \(-0.506831\pi\) | ||||
−0.0214576 | + | 0.999770i | \(0.506831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.55348 | 0.565230 | 0.282615 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282615 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.90303 | − | 13.6884i | 0.519981 | − | 0.900634i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.85342 | − | 3.21021i | 0.121421 | − | 0.210308i | −0.798907 | − | 0.601455i | \(-0.794588\pi\) |
0.920328 | + | 0.391147i | \(0.127921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.60600 | −0.365695 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.3565 | − | 24.8661i | −0.932553 | − | 1.61523i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7655 | 1.01978 | 0.509892 | − | 0.860239i | \(-0.329685\pi\) | ||||
0.509892 | + | 0.860239i | \(0.329685\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.05691 | + | 13.9550i | 0.518991 | + | 0.898920i | 0.999756 | + | 0.0220701i | \(0.00702570\pi\) |
−0.480765 | + | 0.876850i | \(0.659641\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.1138 | + | 33.1061i | 1.22615 | + | 2.12376i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.927568 | − | 1.60659i | 0.0592601 | − | 0.102642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9901 | + | 5.67018i | −0.699281 | + | 0.360785i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.8565 | + | 25.7322i | −0.941491 | + | 1.63071i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.82807 | − | 13.5586i | −0.494103 | − | 0.855812i | 0.505874 | − | 0.862608i | \(-0.331170\pi\) |
−0.999977 | + | 0.00679567i | \(0.997837\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.346113 | + | 0.599486i | 0.0217599 | + | 0.0376893i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.2767 | 0.643554 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9086 | + | 24.0904i | 0.867595 | + | 1.50272i | 0.864447 | + | 0.502724i | \(0.167669\pi\) |
0.00314859 | + | 0.999995i | \(0.498998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.7034 | 0.975762 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.7750 | − | 32.5193i | 1.16214 | − | 2.01289i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.42585 | + | 14.5940i | −0.519560 | + | 0.899905i | 0.480181 | + | 0.877169i | \(0.340571\pi\) |
−0.999742 | + | 0.0227353i | \(0.992763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.22154 | −0.136468 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.59912 | −0.587457 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8125 | + | 25.6561i | −0.903137 | + | 1.56428i | −0.0797386 | + | 0.996816i | \(0.525409\pi\) |
−0.823399 | + | 0.567464i | \(0.807925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.23534 | + | 12.5320i | −0.439516 | + | 0.761264i | −0.997652 | − | 0.0684857i | \(-0.978183\pi\) |
0.558136 | + | 0.829749i | \(0.311517\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.4914 | 1.84542 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.51380 | − | 6.08608i | −0.211890 | − | 0.367004i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4216 | 0.746342 | 0.373171 | − | 0.927763i | \(-0.378271\pi\) | ||||
0.373171 | + | 0.927763i | \(0.378271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.4948 | − | 44.1584i | −1.52634 | − | 2.64369i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.14658 | + | 8.91414i | 0.307019 | + | 0.531773i | 0.977709 | − | 0.209965i | \(-0.0673350\pi\) |
−0.670690 | + | 0.741738i | \(0.734002\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.93234 | + | 13.7392i | −0.471529 | + | 0.816712i | −0.999469 | − | 0.0325693i | \(-0.989631\pi\) |
0.527941 | + | 0.849281i | \(0.322964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.92413 | + | 3.05648i | −0.350915 | + | 0.181050i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.829786 | + | 1.43723i | −0.0489807 | + | 0.0848371i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0780 | − | 24.3838i | −0.828119 | − | 1.43434i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0952537 | + | 0.164984i | 0.00558387 | + | 0.00967155i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1579 | 0.710269 | 0.355135 | − | 0.934815i | \(-0.384435\pi\) | ||||
0.355135 | + | 0.934815i | \(0.384435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.70603 | − | 2.95492i | −0.0993286 | − | 0.172042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.7750 | 1.26351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.667686 | + | 1.15647i | −0.0386133 | + | 0.0668801i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.44309 | + | 11.1598i | −0.371373 | + | 0.643237i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.6397 | 2.16234 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.89572 | −0.337588 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.15045 | + | 10.6529i | −0.351025 | + | 0.607993i | −0.986429 | − | 0.164187i | \(-0.947500\pi\) |
0.635405 | + | 0.772179i | \(0.280833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.2767 | + | 22.9960i | −0.755287 | + | 1.30820i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.519765 | −0.0294732 | −0.0147366 | − | 0.999891i | \(-0.504691\pi\) | ||||
−0.0147366 | + | 0.999891i | \(0.504691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.30605 | − | 16.1186i | −0.526009 | − | 0.911075i | −0.999541 | − | 0.0302980i | \(-0.990354\pi\) |
0.473532 | − | 0.880777i | \(-0.342979\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.7655 | 0.662909 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.41855 | − | 2.45699i | −0.0796734 | − | 0.137998i | 0.823436 | − | 0.567410i | \(-0.192054\pi\) |
−0.903109 | + | 0.429411i | \(0.858721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.65389 | − | 6.32872i | −0.204578 | − | 0.354340i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.809493 | + | 1.40208i | −0.0451815 | + | 0.0782566i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.6462 | + | 15.8281i | 1.37135 | + | 0.880700i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.77846 | − | 11.7406i | 0.376001 | − | 0.651253i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6367 | + | 23.6194i | 0.754108 | + | 1.30615i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.6983 | + | 34.1185i | 1.08600 | + | 1.88102i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0276 | 1.04585 | 0.522926 | − | 0.852378i | \(-0.324841\pi\) | ||||
0.522926 | + | 0.852378i | \(0.324841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.9379 | + | 31.0694i | 0.982992 | + | 1.70259i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.298222 | −0.0162936 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.36469 | − | 12.7560i | 0.401180 | − | 0.694864i | −0.592689 | − | 0.805432i | \(-0.701933\pi\) |
0.993869 | + | 0.110567i | \(0.0352668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.85261 | − | 13.6011i | 0.426495 | − | 0.738711i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.92332 | −0.537378 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.1173 | 0.546281 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.359912 | + | 0.623386i | −0.0193770 | + | 0.0335620i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.06766 | + | 8.77744i | −0.272046 | + | 0.471198i | −0.969386 | − | 0.245543i | \(-0.921034\pi\) |
0.697340 | + | 0.716741i | \(0.254367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.56035 | −0.137053 | −0.0685263 | − | 0.997649i | \(-0.521830\pi\) | ||||
−0.0685263 | + | 0.997649i | \(0.521830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.0031 | + | 36.3784i | 1.12106 | + | 1.94173i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.4458 | 1.08822 | 0.544109 | − | 0.839015i | \(-0.316868\pi\) | ||||
0.544109 | + | 0.839015i | \(0.316868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.889229 | − | 1.54019i | −0.0471954 | − | 0.0817447i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −36.1104 | − | 62.5450i | −1.91116 | − | 3.31023i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.29397 | − | 12.6335i | 0.384961 | − | 0.666772i | −0.606803 | − | 0.794853i | \(-0.707548\pi\) |
0.991764 | + | 0.128080i | \(0.0408815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9151 | − | 1.79408i | −0.995532 | − | 0.0944252i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.3565 | + | 24.8661i | −0.753519 | + | 1.30513i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.927568 | − | 1.60659i | −0.0485511 | − | 0.0840930i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.5397 | − | 25.1835i | −0.758965 | − | 1.31457i | −0.943379 | − | 0.331717i | \(-0.892372\pi\) |
0.184414 | − | 0.982849i | \(-0.440961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.79145 | −0.197375 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.80605 | + | 13.5205i | 0.405270 | + | 0.701949i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7880 | −1.07636 | −0.538181 | − | 0.842829i | \(-0.680888\pi\) | ||||
−0.538181 | + | 0.842829i | \(0.680888\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.47718 | − | 12.9509i | 0.386120 | − | 0.668779i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.04870 | − | 12.2087i | 0.363027 | − | 0.628780i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7034 | −1.01210 | −0.506048 | − | 0.862505i | \(-0.668894\pi\) | ||||
−0.506048 | + | 0.862505i | \(0.668894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 59.9440 | 3.07103 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.2319 | + | 24.6504i | −0.727216 | + | 1.25958i | 0.230839 | + | 0.972992i | \(0.425853\pi\) |
−0.958055 | + | 0.286584i | \(0.907480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.14486 | − | 1.98296i | 0.0583477 | − | 0.101061i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.4396 | −1.49650 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.85819 | + | 3.21848i | 0.0942141 | + | 0.163184i | 0.909280 | − | 0.416184i | \(-0.136633\pi\) |
−0.815066 | + | 0.579368i | \(0.803300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.16291 | 0.159955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41033 | − | 2.44277i | −0.0711418 | − | 0.123221i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.07974 | − | 3.60221i | −0.104643 | − | 0.181247i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.81985 | − | 15.2764i | 0.442656 | − | 0.766702i | −0.555230 | − | 0.831697i | \(-0.687370\pi\) |
0.997886 | + | 0.0649947i | \(0.0207030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 39.4182 | + | 25.3149i | 1.97338 | + | 1.26733i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2785 | − | 26.4631i | 0.762970 | − | 1.32150i | −0.178344 | − | 0.983968i | \(-0.557074\pi\) |
0.941313 | − | 0.337534i | \(-0.109593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.57152 | − | 16.5784i | −0.476791 | − | 0.825827i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.98620 | + | 10.3684i | 0.297457 | + | 0.515210i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.98195 | 0.346083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6138 | + | 27.0439i | 0.772054 | + | 1.33724i | 0.936435 | + | 0.350840i | \(0.114104\pi\) |
−0.164381 | + | 0.986397i | \(0.552563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.8061 | −0.730329 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.9893 | + | 20.7660i | −0.589953 | + | 1.02183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.15217 | + | 3.72766i | −0.105646 | + | 0.182984i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −52.9862 | −2.59475 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.9966 | 1.41657 | 0.708287 | − | 0.705924i | \(-0.249468\pi\) | ||||
0.708287 | + | 0.705924i | \(0.249468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6293 | − | 27.0708i | 0.761728 | − | 1.31935i | −0.180232 | − | 0.983624i | \(-0.557685\pi\) |
0.941959 | − | 0.335727i | \(-0.108982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45.0027 | + | 77.9469i | −2.18810 | + | 3.78991i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.1104 | −1.55758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.7164 | + | 35.8818i | 1.00254 | + | 1.73644i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.5569 | 0.654534 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.43315 | + | 12.8746i | 0.358042 | + | 0.620148i | 0.987634 | − | 0.156779i | \(-0.0501110\pi\) |
−0.629591 | + | 0.776926i | \(0.716778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.7815 | − | 34.2626i | −0.950639 | − | 1.64655i | −0.744047 | − | 0.668128i | \(-0.767096\pi\) |
−0.206592 | − | 0.978427i | \(-0.566237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.79956 | − | 6.58103i | 0.182175 | − | 0.315536i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.82329 | + | 0.940703i | −0.0872199 | + | 0.0450000i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.79226 | − | 10.0325i | 0.276449 | − | 0.478824i | −0.694050 | − | 0.719926i | \(-0.744176\pi\) |
0.970500 | + | 0.241102i | \(0.0775089\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.8923 | − | 25.7942i | −0.709156 | − | 1.22830i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4617 | + | 25.0483i | 0.687094 | + | 1.19008i | 0.972774 | + | 0.231757i | \(0.0744474\pi\) |
−0.285680 | + | 0.958325i | \(0.592219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.39057 | −0.0659192 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.9647 | − | 58.8286i | −1.60648 | − | 2.78250i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.2147 | 1.47311 | 0.736556 | − | 0.676377i | \(-0.236451\pi\) | ||||
0.736556 | + | 0.676377i | \(0.236451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.368935 | + | 0.639014i | −0.0173725 | + | 0.0300900i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.84439 | − | 4.92664i | 0.133641 | − | 0.231474i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.41711 | 0.207077 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.2215 | 0.805590 | 0.402795 | − | 0.915290i | \(-0.368039\pi\) | ||||
0.402795 | + | 0.915290i | \(0.368039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 49.7470 | − | 86.1644i | 2.32199 | − | 4.02181i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4151 | + | 28.4318i | −0.764528 | + | 1.32420i | 0.175968 | + | 0.984396i | \(0.443694\pi\) |
−0.940496 | + | 0.339805i | \(0.889639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.28973 | 0.292308 | 0.146154 | − | 0.989262i | \(-0.453310\pi\) | ||||
0.146154 | + | 0.989262i | \(0.453310\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.15947 | − | 8.93647i | −0.239265 | − | 0.414419i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.47068 | 0.438251 | 0.219125 | − | 0.975697i | \(-0.429680\pi\) | ||||
0.219125 | + | 0.975697i | \(0.429680\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.04789 | + | 1.81500i | 0.0483871 | + | 0.0838090i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.259073 | + | 0.448728i | 0.0119375 | + | 0.0206763i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.86469 | + | 4.96179i | −0.131718 | + | 0.228143i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.5104 | − | 9.55018i | 0.849314 | − | 0.438192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.8337 | + | 30.8888i | −0.816547 | + | 1.41430i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.0341 | − | 22.5757i | −0.595543 | − | 1.03151i | −0.993470 | − | 0.114094i | \(-0.963604\pi\) |
0.397927 | − | 0.917417i | \(-0.369730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.73443 | + | 11.6644i | 0.307064 | + | 0.531850i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.05863 | 0.230176 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0137988 | + | 0.0239003i | 0.000626573 | + | 0.00108526i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8939 | 0.765536 | 0.382768 | − | 0.923845i | \(-0.374971\pi\) | ||||
0.382768 | + | 0.923845i | \(0.374971\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.140088 | − | 0.242640i | 0.00633500 | − | 0.0109725i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.94442 | − | 15.4922i | 0.403656 | − | 0.699153i | −0.590508 | − | 0.807032i | \(-0.701073\pi\) |
0.994164 | + | 0.107879i | \(0.0344059\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.3906 | −1.50384 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.23109 | 0.235120 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.24914 | + | 10.8238i | −0.280312 | + | 0.485515i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.7108 | + | 25.4799i | −0.658546 | + | 1.14063i | 0.322446 | + | 0.946588i | \(0.395495\pi\) |
−0.980992 | + | 0.194047i | \(0.937839\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.3940 | 0.911137 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.53968 | − | 7.86295i | −0.202414 | − | 0.350592i | 0.746892 | − | 0.664946i | \(-0.231545\pi\) |
−0.949306 | + | 0.314354i | \(0.898212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.45264 | 0.242639 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.04312 | − | 13.9311i | −0.357207 | − | 0.618701i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1970 | − | 17.6617i | −0.451974 | − | 0.782842i | 0.546534 | − | 0.837437i | \(-0.315947\pi\) |
−0.998509 | + | 0.0545944i | \(0.982613\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.51857 | + | 11.2905i | −0.288365 | + | 0.499462i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.05042 | + | 64.4660i | −0.134679 | + | 2.84624i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.92332 | + | 3.33129i | −0.0847517 | + | 0.146794i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.75816 | + | 15.1696i | 0.385184 | + | 0.667158i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6056 | + | 30.4938i | 0.772801 | + | 1.33853i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8697 | −0.651455 | −0.325728 | − | 0.945464i | \(-0.605609\pi\) | ||||
−0.325728 | + | 0.945464i | \(0.605609\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.44958 | − | 9.43895i | −0.238294 | − | 0.412736i | 0.721931 | − | 0.691965i | \(-0.243255\pi\) |
−0.960225 | + | 0.279228i | \(0.909921\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −51.3561 | −2.24136 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.6707 | + | 39.2669i | −0.987553 | + | 1.71049i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3892 | − | 19.7267i | 0.495184 | − | 0.857684i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −54.7811 | −2.37730 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.42342 | −0.0616552 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.117266 | + | 0.203111i | −0.00506987 | + | 0.00878126i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.5177 | + | 19.9492i | −0.497024 | + | 0.860871i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.79650 | −0.249673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.97546 | + | 10.3498i | 0.256905 | + | 0.444973i | 0.965411 | − | 0.260732i | \(-0.0839639\pi\) |
−0.708506 | + | 0.705705i | \(0.750631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.1380 | −1.72249 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.97546 | + | 3.42160i | 0.0846194 | + | 0.146565i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00306 | − | 3.46940i | −0.0856445 | − | 0.148341i | 0.820021 | − | 0.572333i | \(-0.193962\pi\) |
−0.905666 | + | 0.423993i | \(0.860628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −47.3285 | + | 81.9754i | −2.01993 | + | 3.49862i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.2483 | − | 9.93093i | 0.820006 | − | 0.423072i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.6155 | + | 25.3149i | −0.621516 | + | 1.07650i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.63016 | + | 6.28761i | 0.154092 | + | 0.266894i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.35991 | + | 9.28364i | 0.227107 | + | 0.393360i | 0.956949 | − | 0.290255i | \(-0.0937400\pi\) |
−0.729843 | + | 0.683615i | \(0.760407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0525 | −0.467472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0552 | − | 27.8084i | −0.677851 | − | 1.17407i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.18096 | −0.302641 | −0.151321 | − | 0.988485i | \(-0.548353\pi\) | ||||
−0.151321 | + | 0.988485i | \(0.548353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13756 | − | 1.97031i | 0.0478575 | − | 0.0828916i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.0686 | − | 72.8650i | 1.76672 | − | 3.06004i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.4328 | 1.31773 | 0.658865 | − | 0.752261i | \(-0.271037\pi\) | ||||
0.658865 | + | 0.752261i | \(0.271037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.08623 | −0.338398 | −0.169199 | − | 0.985582i | \(-0.554118\pi\) | ||||
−0.169199 | + | 0.985582i | \(0.554118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6155 | − | 25.3149i | 0.610573 | − | 1.05754i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.12457 | − | 1.94781i | 0.0468978 | − | 0.0812294i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.95779 | 0.206396 | 0.103198 | − | 0.994661i | \(-0.467093\pi\) | ||||
0.103198 | + | 0.994661i | \(0.467093\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.13837 | − | 8.89992i | −0.213543 | − | 0.369868i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.2491 | 1.25495 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.47068 | + | 6.01140i | 0.143741 | + | 0.248967i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.04564 | + | 8.73931i | 0.208612 | + | 0.361326i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.8858 | − | 20.5868i | 0.490579 | − | 0.849708i | −0.509362 | − | 0.860552i | \(-0.670119\pi\) |
0.999941 | + | 0.0108444i | \(0.00345194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.39014 | − | 29.3785i | 0.0572797 | − | 1.21052i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.5151 | − | 59.7820i | 1.41976 | − | 2.45910i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.2018 | + | 36.7226i | 0.870653 | + | 1.50801i | 0.861323 | + | 0.508058i | \(0.169637\pi\) |
0.00932994 | + | 0.999956i | \(0.497030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.23109 | − | 9.06052i | −0.214454 | − | 0.371445i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.1526 | −1.31592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.4258 | − | 37.1107i | −0.875436 | − | 1.51630i | −0.856297 | − | 0.516484i | \(-0.827241\pi\) |
−0.0191394 | − | 0.999817i | \(-0.506093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1855 | −0.619427 | −0.309714 | − | 0.950830i | \(-0.600233\pi\) | ||||
−0.309714 | + | 0.950830i | \(0.600233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.39400 | + | 4.14654i | −0.0974914 | + | 0.168860i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.07974 | + | 3.60221i | −0.0845533 | + | 0.146451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.3336 | −1.31238 | −0.656189 | − | 0.754596i | \(-0.727833\pi\) | ||||
−0.656189 | + | 0.754596i | \(0.727833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −53.4036 | −2.16402 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8953 | + | 29.2636i | −0.683512 | + | 1.18388i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.91683 | + | 6.78414i | −0.158199 | + | 0.274009i | −0.934219 | − | 0.356699i | \(-0.883902\pi\) |
0.776020 | + | 0.630708i | \(0.217235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.767287 | −0.0309400 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.13359 | + | 3.69549i | 0.0858952 | + | 0.148775i | 0.905772 | − | 0.423765i | \(-0.139292\pi\) |
−0.819877 | + | 0.572540i | \(0.805958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.8363 | −1.72174 | −0.860869 | − | 0.508827i | \(-0.830079\pi\) | ||||
−0.860869 | + | 0.508827i | \(0.830079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.48448 | + | 6.03530i | 0.139827 | + | 0.242188i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.88617 | + | 8.46310i | 0.195760 | + | 0.339067i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8630 | + | 18.8152i | −0.434519 | + | 0.752609i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.5259 | + | 11.2554i | 0.699916 | + | 0.449496i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.9509 | − | 27.6278i | 0.636005 | − | 1.10159i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1552 | + | 31.4458i | 0.722748 | + | 1.25184i | 0.959894 | + | 0.280362i | \(0.0904546\pi\) |
−0.237146 | + | 0.971474i | \(0.576212\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.0307 | − | 53.7467i | −1.23336 | − | 2.13624i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.68373 | 0.344603 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.59101 | − | 9.68391i | −0.221524 | − | 0.383690i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.5535 | −1.12956 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.8043 | − | 42.9624i | 0.979712 | − | 1.69691i | 0.316297 | − | 0.948660i | \(-0.397560\pi\) |
0.663415 | − | 0.748251i | \(-0.269106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.49270 | + | 4.31748i | −0.0983023 | + | 0.170265i | −0.910982 | − | 0.412446i | \(-0.864675\pi\) |
0.812680 | + | 0.582711i | \(0.198008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.95779 | −0.234588 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.2863 | −1.70176 | −0.850880 | − | 0.525360i | \(-0.823931\pi\) | ||||
−0.850880 | + | 0.525360i | \(0.823931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.33060 | + | 9.23286i | −0.209244 | + | 0.362422i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.2587 | + | 62.8019i | −1.42109 | + | 2.46140i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.43965 | 0.212870 | 0.106435 | − | 0.994320i | \(-0.466056\pi\) | ||||
0.106435 | + | 0.994320i | \(0.466056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.204306 | − | 0.353869i | −0.00798290 | − | 0.0138268i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.7846 | −1.16201 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.87462 | − | 4.97899i | −0.111979 | − | 0.193954i | 0.804589 | − | 0.593832i | \(-0.202386\pi\) |
−0.916568 | + | 0.399878i | \(0.869052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.12763 | − | 8.88131i | −0.199442 | − | 0.345443i | 0.748906 | − | 0.662676i | \(-0.230579\pi\) |
−0.948348 | + | 0.317233i | \(0.897246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.9720 | − | 53.6451i | 1.20285 | − | 2.08340i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.71027 | + | 3.66721i | 0.221435 | + | 0.142208i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.16940 | − | 2.02547i | 0.0452795 | − | 0.0784264i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.5673 | − | 47.7479i | −1.06581 | − | 1.84604i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.21080 | + | 15.9536i | 0.355579 | + | 0.615881i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.9379 | −1.15402 | −0.577011 | − | 0.816736i | \(-0.695781\pi\) | ||||
−0.577011 | + | 0.816736i | \(0.695781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −35.3750 | − | 61.2714i | −1.36159 | − | 2.35834i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.8827 | 0.456691 | 0.228345 | − | 0.973580i | \(-0.426668\pi\) | ||||
0.228345 | + | 0.973580i | \(0.426668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0969726 | − | 0.167961i | 0.00372147 | − | 0.00644577i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.05042 | + | 1.81938i | −0.0402522 | + | 0.0697188i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.35180 | −0.243045 | −0.121522 | − | 0.992589i | \(-0.538778\pi\) | ||||
−0.121522 | + | 0.992589i | \(0.538778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.14486 | −0.0819510 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8957 | − | 24.0681i | 0.530155 | − | 0.918255i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.69528 | + | 11.5966i | −0.255070 | + | 0.441794i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.9966 | −1.10308 | −0.551541 | − | 0.834148i | \(-0.685960\pi\) | ||||
−0.551541 | + | 0.834148i | \(0.685960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.3810 | − | 31.8369i | −0.698237 | − | 1.20938i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.67580 | −0.291160 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.68573 | + | 2.91977i | 0.0638516 | + | 0.110594i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.02201 | − | 10.4304i | −0.227773 | − | 0.394515i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00081 | − | 3.46550i | 0.0755695 | − | 0.130890i | −0.825764 | − | 0.564015i | \(-0.809256\pi\) |
0.901334 | + | 0.433125i | \(0.142589\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.978088 | + | 20.6704i | −0.0368893 | + | 0.779599i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.10733 | + | 15.7744i | −0.343002 | + | 0.594097i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.1595 | − | 33.1852i | −0.720566 | − | 1.24806i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.23190 | − | 14.2581i | −0.309156 | − | 0.535473i | 0.669022 | − | 0.743242i | \(-0.266713\pi\) |
−0.978178 | + | 0.207769i | \(0.933380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −66.7811 | −2.50449 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.58795 | − | 2.75041i | −0.0594692 | − | 0.103004i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.96391 | 0.0734460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.6121 | − | 44.3615i | 0.956502 | − | 1.65671i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.60561 | + | 16.6374i | −0.358229 | + | 0.620471i | −0.987665 | − | 0.156581i | \(-0.949953\pi\) |
0.629436 | + | 0.777052i | \(0.283286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.0327 | 1.00675 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 52.3561 | 1.94714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.8720 | + | 20.5629i | −0.440915 | + | 0.763687i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.08317 | + | 15.7325i | −0.336876 | + | 0.583487i | −0.983843 | − | 0.179031i | \(-0.942704\pi\) |
0.646967 | + | 0.762518i | \(0.276037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 47.8984 | 1.77401 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0893 | + | 22.6713i | 0.484125 | + | 0.838529i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.2423 | −1.85574 | −0.927870 | − | 0.372903i | \(-0.878362\pi\) | ||||
−0.927870 | + | 0.372903i | \(0.878362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.01380 | − | 5.22005i | −0.111166 | − | 0.192545i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.465907 | + | 0.806975i | 0.0171619 | + | 0.0297253i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.8883 | + | 25.7873i | −0.547676 | + | 0.948602i | 0.450758 | + | 0.892646i | \(0.351154\pi\) |
−0.998433 | + | 0.0559557i | \(0.982179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.89916 | + | 40.1359i | −0.0697674 | + | 1.47443i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.7578 | + | 34.2215i | −0.724843 | + | 1.25546i | 0.234196 | + | 0.972189i | \(0.424754\pi\) |
−0.959039 | + | 0.283275i | \(0.908579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.92026 | − | 8.52215i | −0.180265 | − | 0.312227i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.5535 | + | 59.8484i | 1.26425 | + | 2.18974i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.64820 | 0.0602240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.05214 | + | 15.6788i | 0.330317 | + | 0.572126i | 0.982574 | − | 0.185872i | \(-0.0595109\pi\) |
−0.652257 | + | 0.757998i | \(0.726178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.8690 | −1.85377 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.412050 | − | 0.713692i | 0.0149960 | − | 0.0259739i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.7996 | + | 20.4374i | −0.428862 | + | 0.742811i | −0.996772 | − | 0.0802793i | \(-0.974419\pi\) |
0.567910 | + | 0.823091i | \(0.307752\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.24914 | 0.0816386 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.69061 | −0.0612845 | −0.0306422 | − | 0.999530i | \(-0.509755\pi\) | ||||
−0.0306422 | + | 0.999530i | \(0.509755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8827 | − | 24.0456i | 0.502589 | − | 0.870509i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.9509 | − | 20.6996i | 0.432086 | − | 0.748396i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.5665 | −0.742612 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0583 | + | 45.1342i | 0.939685 | + | 1.62758i | 0.766059 | + | 0.642770i | \(0.222215\pi\) |
0.173625 | + | 0.984812i | \(0.444452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 90.3821 | 3.25503 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5397 | + | 39.0399i | 0.810696 | + | 1.40417i | 0.912378 | + | 0.409349i | \(0.134244\pi\) |
−0.101682 | + | 0.994817i | \(0.532422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.1211 | + | 27.9226i | 0.579088 | + | 1.00301i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.5113 | − | 44.1868i | 0.915212 | − | 1.58519i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.84015 | − | 1.18177i | −0.0659301 | − | 0.0423412i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.77846 | + | 4.81243i | −0.0994210 | + | 0.172202i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.7854 | − | 63.7141i | −1.31460 | − | 2.27696i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0375304 | + | 0.0650045i | 0.00133952 | + | 0.00232011i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.1414 | 1.35960 | 0.679798 | − | 0.733400i | \(-0.262068\pi\) | ||||
0.679798 | + | 0.733400i | \(0.262068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.3768 | + | 47.4180i | 0.974639 | + | 1.68812i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.9886 | −0.568490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.7685 | + | 30.7760i | −0.630979 | + | 1.09289i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.60905 | + | 6.25106i | −0.128000 | + | 0.221702i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7148 | 0.485802 | 0.242901 | − | 0.970051i | \(-0.421901\pi\) | ||||
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80.0353 | 2.83145 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1629 | + | 19.3347i | −0.394422 | + | 0.683159i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.89825 | + | 5.01992i | −0.102277 | + | 0.177149i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.732814 | 0.0258283 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.1281 | + | 83.3602i | 1.69419 | + | 2.93442i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.6285 | −0.760419 | −0.380209 | − | 0.924900i | \(-0.624148\pi\) | ||||
−0.380209 | + | 0.924900i | \(0.624148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.27024 | − | 5.66423i | −0.114834 | − | 0.198898i | 0.802880 | − | 0.596141i | \(-0.203300\pi\) |
−0.917713 | + | 0.397243i | \(0.869967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.5086 | + | 40.7182i | 0.824484 | + | 1.42805i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0202937 | − | 0.0351497i | 0.000710858 | − | 0.00123124i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.2883 | − | 9.17613i | −0.499884 | − | 0.321032i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.4588 | − | 61.4164i | 1.23903 | − | 2.14606i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8091 | + | 36.0424i | 0.726243 | + | 1.25789i | 0.958460 | + | 0.285226i | \(0.0920686\pi\) |
−0.232217 | + | 0.972664i | \(0.574598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.72632 | + | 4.72212i | 0.0950335 | + | 0.164603i | 0.909623 | − | 0.415436i | \(-0.136371\pi\) |
−0.814589 | + | 0.580038i | \(0.803038\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.8337 | −0.794966 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.34439 | − | 2.32856i | −0.0467492 | − | 0.0809719i | 0.841704 | − | 0.539939i | \(-0.181553\pi\) |
−0.888453 | + | 0.458967i | \(0.848219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.4328 | 0.952780 | 0.476390 | − | 0.879234i | \(-0.341945\pi\) | ||||
0.476390 | + | 0.879234i | \(0.341945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.1798 | − | 34.9524i | 0.700028 | − | 1.21248i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.2426 | + | 22.9369i | −0.458830 | + | 0.794718i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.95436 | 0.102240 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −99.9027 | −3.45314 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.7206 | − | 23.7648i | 0.473689 | − | 0.820453i | −0.525857 | − | 0.850573i | \(-0.676255\pi\) |
0.999546 | + | 0.0301195i | \(0.00958880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.15470 | − | 3.73204i | 0.0742999 | − | 0.128691i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.4439 | 1.15187 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.16516 | − | 2.01811i | −0.0400826 | − | 0.0694252i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.2311 | 1.00439 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.7733 | + | 44.6407i | 0.884537 | + | 1.53206i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.11727 | + | 1.93516i | 0.0382994 | + | 0.0663365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1936 | − | 31.5122i | 0.622936 | − | 1.07896i | −0.366000 | − | 0.930615i | \(-0.619273\pi\) |
0.988936 | − | 0.148342i | \(-0.0473936\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.732814 | + | 15.4869i | −0.0250617 | + | 0.529641i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.5647 | − | 42.5474i | 0.839116 | − | 1.45339i | −0.0515191 | − | 0.998672i | \(-0.516406\pi\) |
0.890635 | − | 0.454719i | \(-0.150260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9565 | + | 44.9580i | 0.885624 | + | 1.53395i | 0.844996 | + | 0.534772i | \(0.179603\pi\) |
0.0406283 | + | 0.999174i | \(0.487064\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.69609 | + | 4.66977i | 0.0918826 | + | 0.159145i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.9785 | 0.952400 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.55042 | + | 4.41746i | 0.0867169 | + | 0.150198i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −91.4829 | −3.10692 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.49828 | + | 11.2554i | −0.220439 | + | 0.381812i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.898780 | + | 1.55673i | −0.0304540 | + | 0.0527479i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.443086 | 0.0149962 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.2242 | −0.514673 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.20087 | + | 10.7402i | −0.209388 | + | 0.362671i | −0.951522 | − | 0.307581i | \(-0.900481\pi\) |
0.742134 | + | 0.670252i | \(0.233814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.7513 | − | 34.2102i | 0.666194 | − | 1.15388i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.8923 | 0.602806 | 0.301403 | − | 0.953497i | \(-0.402545\pi\) | ||||
0.301403 | + | 0.953497i | \(0.402545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.51686 | − | 9.55547i | −0.185657 | − | 0.321567i | 0.758141 | − | 0.652091i | \(-0.226108\pi\) |
−0.943798 | + | 0.330524i | \(0.892775\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0862 | −0.372660 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.1970 | + | 34.9822i | 0.678149 | + | 1.17459i | 0.975538 | + | 0.219832i | \(0.0705509\pi\) |
−0.297389 | + | 0.954756i | \(0.596116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.5129 | − | 52.8499i | −1.02337 | − | 1.77253i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.7043 | − | 32.3968i | 0.626618 | − | 1.08533i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.1372 | + | 23.8039i | −1.54392 | + | 0.796566i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.66849 | + | 2.88992i | −0.0557716 | + | 0.0965993i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.16940 | + | 3.75752i | 0.0724343 | + | 0.125460i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.7638 | + | 29.0358i | 0.559106 | + | 0.968399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.7164 | 1.05663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.9345 | + | 36.2596i | 0.696656 | + | 1.20664i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.81455 | −0.193282 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5755 | + | 33.9057i | −0.649993 | + | 1.12582i | 0.333130 | + | 0.942881i | \(0.391895\pi\) |
−0.983124 | + | 0.182941i | \(0.941438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.7716 | − | 75.8146i | 1.45181 | − | 2.51461i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.3561 | −0.906348 | −0.453174 | − | 0.891422i | \(-0.649708\pi\) | ||||
−0.453174 | + | 0.891422i | \(0.649708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.4492 | 0.445104 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.57802 | + | 16.5896i | −0.316639 | + | 0.548436i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.43578 | + | 2.48685i | −0.0474137 | + | 0.0821229i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.948243 | −0.0312796 | −0.0156398 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156398 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.9837 | + | 34.6127i | 0.658484 | + | 1.14053i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7198 | −0.352847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3427 | − | 19.6461i | −0.372945 | − | 0.645959i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.8793 | + | 53.4845i | 1.01421 | + | 1.75666i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.63026 | + | 4.55574i | −0.0862959 | + | 0.149469i | −0.905943 | − | 0.423400i | \(-0.860836\pi\) |
0.819647 | + | 0.572869i | \(0.194170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.812021 | − | 17.1608i | 0.0266129 | − | 0.562423i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.844394 | + | 1.46253i | −0.0276442 | + | 0.0478812i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.32582 | − | 4.02844i | −0.0760624 | − | 0.131744i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9638 | − | 39.7745i | −0.750195 | − | 1.29938i | −0.947728 | − | 0.319079i | \(-0.896626\pi\) |
0.197533 | − | 0.980296i | \(-0.436707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.4734 | −1.97347 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.2978 | − | 38.6210i | −0.726889 | − | 1.25901i | −0.958192 | − | 0.286127i | \(-0.907632\pi\) |
0.231303 | − | 0.972882i | \(-0.425701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.236151 | −0.00769013 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.5259 | − | 19.9634i | 0.374937 | − | 0.649410i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.00811 | + | 12.1384i | −0.227733 | + | 0.394445i | −0.957136 | − | 0.289639i | \(-0.906465\pi\) |
0.729403 | + | 0.684084i | \(0.239798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1820 | −0.362984 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.21811 | −0.298918 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.42332 | + | 2.46526i | −0.0461059 | + | 0.0798577i | −0.888157 | − | 0.459539i | \(-0.848014\pi\) |
0.842051 | + | 0.539397i | \(0.181348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.11727 | − | 3.66721i | 0.0685131 | − | 0.118668i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.7440 | −0.767534 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.53662 | + | 13.0538i | 0.243370 | + | 0.421529i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.5277 | 0.468635 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.88273 | + | 3.26099i | 0.0606702 | + | 0.105084i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.744365 | − | 1.28928i | −0.0239619 | − | 0.0415033i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.830595 | − | 1.43863i | 0.0267101 | − | 0.0462633i | −0.852361 | − | 0.522953i | \(-0.824830\pi\) |
0.879071 | + | 0.476690i | \(0.158164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 84.5773 | − | 43.6365i | 2.71701 | − | 1.40181i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2091 | − | 35.0032i | 0.648540 | − | 1.12330i | −0.334931 | − | 0.942243i | \(-0.608713\pi\) |
0.983472 | − | 0.181062i | \(-0.0579535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.9712 | + | 46.7155i | 0.864657 | + | 1.49763i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.0242 | − | 38.1470i | −0.705338 | − | 1.22168i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5439 | 0.337330 | 0.168665 | − | 0.985673i | \(-0.446054\pi\) | ||||
0.168665 | + | 0.985673i | \(0.446054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.17246 | + | 3.76281i | 0.0694322 | + | 0.120260i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 63.4328 | 2.02525 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.91683 | − | 8.51619i | 0.156822 | − | 0.271624i | −0.776899 | − | 0.629626i | \(-0.783208\pi\) |
0.933721 | + | 0.358001i | \(0.116542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | − | 8.66025i | 0.159313 | − | 0.275939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 128.005 | 4.07446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.83365 | −0.0583068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.1349 | + | 17.5542i | −0.321947 | + | 0.557628i | −0.980890 | − | 0.194565i | \(-0.937671\pi\) |
0.658943 | + | 0.752193i | \(0.271004\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.9117 | − | 53.5406i | 0.980952 | − | 1.69906i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.65775 | −0.147661 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.66038 | + | 13.2682i | 0.242607 | + | 0.420207i | 0.961456 | − | 0.274959i | \(-0.0886642\pi\) |
−0.718849 | + | 0.695166i | \(0.755331\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 70.2906 | 2.22390 |
(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 | 1216.2.i.n.961.3 | 6 | ||
4.3 | odd | 2 | 1216.2.i.m.961.1 | 6 | |||
8.3 | odd | 2 | 304.2.i.f.49.3 | 6 | |||
8.5 | even | 2 | 152.2.i.c.49.1 | ✓ | 6 | ||
19.7 | even | 3 | inner | 1216.2.i.n.577.3 | 6 | ||
24.5 | odd | 2 | 1368.2.s.k.505.2 | 6 | |||
24.11 | even | 2 | 2736.2.s.y.1873.2 | 6 | |||
76.7 | odd | 6 | 1216.2.i.m.577.1 | 6 | |||
152.11 | odd | 6 | 5776.2.a.bk.1.1 | 3 | |||
152.27 | even | 6 | 5776.2.a.bq.1.3 | 3 | |||
152.45 | even | 6 | 152.2.i.c.121.1 | yes | 6 | ||
152.83 | odd | 6 | 304.2.i.f.273.3 | 6 | |||
152.125 | even | 6 | 2888.2.a.r.1.3 | 3 | |||
152.141 | odd | 6 | 2888.2.a.n.1.1 | 3 | |||
456.83 | even | 6 | 2736.2.s.y.577.2 | 6 | |||
456.197 | odd | 6 | 1368.2.s.k.577.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.i.c.49.1 | ✓ | 6 | 8.5 | even | 2 | ||
152.2.i.c.121.1 | yes | 6 | 152.45 | even | 6 | ||
304.2.i.f.49.3 | 6 | 8.3 | odd | 2 | |||
304.2.i.f.273.3 | 6 | 152.83 | odd | 6 | |||
1216.2.i.m.577.1 | 6 | 76.7 | odd | 6 | |||
1216.2.i.m.961.1 | 6 | 4.3 | odd | 2 | |||
1216.2.i.n.577.3 | 6 | 19.7 | even | 3 | inner | ||
1216.2.i.n.961.3 | 6 | 1.1 | even | 1 | trivial | ||
1368.2.s.k.505.2 | 6 | 24.5 | odd | 2 | |||
1368.2.s.k.577.2 | 6 | 456.197 | odd | 6 | |||
2736.2.s.y.577.2 | 6 | 456.83 | even | 6 | |||
2736.2.s.y.1873.2 | 6 | 24.11 | even | 2 | |||
2888.2.a.n.1.1 | 3 | 152.141 | odd | 6 | |||
2888.2.a.r.1.3 | 3 | 152.125 | even | 6 | |||
5776.2.a.bk.1.1 | 3 | 152.11 | odd | 6 | |||
5776.2.a.bq.1.3 | 3 | 152.27 | even | 6 |