Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.16 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.c.2591.16 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.37787 | + | 1.95021i | 1.51063 | + | 0.872161i | 0.999923 | + | 0.0124051i | \(0.00394877\pi\) |
0.510705 | + | 0.859756i | \(0.329385\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.27561i | − | 1.23806i | −0.785366 | − | 0.619032i | \(-0.787525\pi\) | ||
0.785366 | − | 0.619032i | \(-0.212475\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.67850 | 1.71213 | 0.856066 | − | 0.516866i | \(-0.172902\pi\) | ||||
0.856066 | + | 0.516866i | \(0.172902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.34864 | − | 4.06796i | −0.651395 | − | 1.12825i | −0.982785 | − | 0.184755i | \(-0.940851\pi\) |
0.331390 | − | 0.943494i | \(-0.392482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.20495 | + | 0.695678i | 0.292243 | + | 0.168727i | 0.638953 | − | 0.769246i | \(-0.279368\pi\) |
−0.346710 | + | 0.937972i | \(0.612701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.88569 | + | 1.97520i | 0.891438 | + | 0.453143i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.59477 | + | 6.22632i | 0.749561 | + | 1.29828i | 0.948033 | + | 0.318171i | \(0.103069\pi\) |
−0.198472 | + | 0.980107i | \(0.563598\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.10665 | + | 8.84498i | 1.02133 | + | 1.76900i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.52822 | + | 2.61437i | −0.840869 | + | 0.485476i | −0.857560 | − | 0.514385i | \(-0.828020\pi\) |
0.0166905 | + | 0.999861i | \(0.494687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.36294i | − | 1.68163i | −0.541319 | − | 0.840817i | \(-0.682075\pi\) | ||
0.541319 | − | 0.840817i | \(-0.317925\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.38813 | − | 11.0646i | 1.07979 | − | 1.87025i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.48371 | −1.39471 | −0.697356 | − | 0.716725i | \(-0.745640\pi\) | ||||
−0.697356 | + | 0.716725i | \(0.745640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.32327 | + | 1.91869i | 0.519007 | + | 0.299649i | 0.736528 | − | 0.676407i | \(-0.236464\pi\) |
−0.217521 | + | 0.976056i | \(0.569797\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.584394 | + | 0.337400i | 0.0891192 | + | 0.0514530i | 0.543897 | − | 0.839152i | \(-0.316948\pi\) |
−0.454778 | + | 0.890605i | \(0.650281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.54888 | − | 6.14684i | −0.517657 | − | 0.896608i | −0.999790 | − | 0.0205100i | \(-0.993471\pi\) |
0.482133 | − | 0.876098i | \(-0.339862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.72960 | −0.532800 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.58282 | + | 2.64589i | −0.629498 | + | 0.363441i | −0.780558 | − | 0.625084i | \(-0.785065\pi\) |
0.151060 | + | 0.988525i | \(0.451731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.1812 | + | 11.0743i | 2.58639 | + | 1.49326i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.63261 | − | 9.75597i | 0.733303 | − | 1.27012i | −0.222160 | − | 0.975010i | \(-0.571311\pi\) |
0.955464 | − | 0.295108i | \(-0.0953558\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.574458 | + | 0.994990i | 0.0735518 | + | 0.127395i | 0.900456 | − | 0.434948i | \(-0.143233\pi\) |
−0.826904 | + | 0.562343i | \(0.809900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 18.3214i | − | 2.27249i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.96859 | + | 3.44597i | −0.729179 | + | 0.420992i | −0.818122 | − | 0.575045i | \(-0.804985\pi\) |
0.0889425 | + | 0.996037i | \(0.471651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.92298 | − | 8.52686i | 0.584251 | − | 1.01195i | −0.410718 | − | 0.911762i | \(-0.634722\pi\) |
0.994968 | − | 0.100189i | \(-0.0319448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.95529 | − | 10.3149i | 0.697014 | − | 1.20726i | −0.272483 | − | 0.962161i | \(-0.587845\pi\) |
0.969497 | − | 0.245103i | \(-0.0788219\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 18.6005i | − | 2.11973i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.25791 | + | 3.61301i | 0.704070 | + | 0.406495i | 0.808862 | − | 0.587999i | \(-0.200084\pi\) |
−0.104791 | + | 0.994494i | \(0.533418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.05126 | −0.444683 | −0.222342 | − | 0.974969i | \(-0.571370\pi\) | ||||
−0.222342 | + | 0.974969i | \(0.571370\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.71344 | + | 4.69981i | 0.294314 | + | 0.509766i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8078 | + | 7.97196i | −1.46363 | + | 0.845026i | −0.999177 | − | 0.0405732i | \(-0.987082\pi\) |
−0.464451 | + | 0.885599i | \(0.653748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.3250 | + | 7.69321i | −1.39684 | + | 0.806468i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.27327 | + | 14.2499i | 0.951417 | + | 1.46201i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.66740 | − | 8.08417i | 0.473902 | − | 0.820823i | −0.525651 | − | 0.850700i | \(-0.676178\pi\) |
0.999554 | + | 0.0298774i | \(0.00951170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.65167 | − | 1.53094i | 0.263851 | − | 0.152334i | −0.362239 | − | 0.932085i | \(-0.617988\pi\) |
0.626090 | + | 0.779751i | \(0.284654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.89193i | 0.679083i | 0.940591 | + | 0.339541i | \(0.110272\pi\) | ||||
−0.940591 | + | 0.339541i | \(0.889728\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.54022 | −0.245573 | −0.122786 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122786 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.44157 | + | 7.69303i | −0.425426 | + | 0.736859i | −0.996460 | − | 0.0840672i | \(-0.973209\pi\) |
0.571034 | + | 0.820926i | \(0.306542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2092i | 1.61890i | 0.587186 | + | 0.809452i | \(0.300236\pi\) | ||||
−0.587186 | + | 0.809452i | \(0.699764\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.0422i | 2.61495i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.27877 | − | 3.94694i | 0.208894 | − | 0.361815i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.2454 | 1.93140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.3341i | 1.81874i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.10408 | − | 2.94684i | 0.452914 | − | 0.261490i | −0.256146 | − | 0.966638i | \(-0.582453\pi\) |
0.709060 | + | 0.705148i | \(0.249120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.64066 | + | 6.30581i | −0.318086 | + | 0.550941i | −0.980089 | − | 0.198560i | \(-0.936373\pi\) |
0.662003 | + | 0.749501i | \(0.269707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.46999 | − | 12.7280i | 0.561019 | − | 1.10366i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.02007 | − | 4.63039i | 0.685201 | − | 0.395601i | −0.116611 | − | 0.993178i | \(-0.537203\pi\) |
0.801812 | + | 0.597577i | \(0.203870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.37032 | + | 3.67791i | −0.540324 | + | 0.311956i | −0.745210 | − | 0.666830i | \(-0.767651\pi\) |
0.204886 | + | 0.978786i | \(0.434317\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3367 | − | 23.0999i | −1.11527 | − | 1.93171i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.3943 | −1.69365 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.72883 | + | 2.15284i | 0.305478 | + | 0.176368i | 0.644901 | − | 0.764266i | \(-0.276899\pi\) |
−0.339423 | + | 0.940634i | \(0.610232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.0918i | 1.96057i | 0.197599 | + | 0.980283i | \(0.436686\pi\) | ||||
−0.197599 | + | 0.980283i | \(0.563314\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.2597 | − | 31.6268i | 1.46666 | − | 2.54032i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.483837 | + | 0.838030i | −0.0386144 | + | 0.0668821i | −0.884687 | − | 0.466186i | \(-0.845628\pi\) |
0.846072 | + | 0.533068i | \(0.178961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.3950 | − | 11.7751i | 1.60735 | − | 0.928004i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13868i | 0.0891882i | 0.999005 | + | 0.0445941i | \(0.0141994\pi\) | ||||
−0.999005 | + | 0.0445941i | \(0.985801\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.11802 | − | 8.86467i | −0.396044 | − | 0.685968i | 0.597190 | − | 0.802100i | \(-0.296284\pi\) |
−0.993234 | + | 0.116132i | \(0.962951\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.53220 | + | 7.84999i | −0.348630 | + | 0.603846i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.16300 | + | 3.55821i | 0.468564 | + | 0.270525i | 0.715638 | − | 0.698471i | \(-0.246136\pi\) |
−0.247074 | + | 0.968996i | \(0.579469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.9727 | − | 16.7274i | 2.19013 | − | 1.26447i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.72500 | 0.652137 | 0.326068 | − | 0.945346i | \(-0.394276\pi\) | ||||
0.326068 | + | 0.945346i | \(0.394276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.07811 | − | 15.7237i | −0.674770 | − | 1.16874i | −0.976536 | − | 0.215355i | \(-0.930909\pi\) |
0.301765 | − | 0.953382i | \(-0.402424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −28.6568 | − | 16.5450i | −2.10689 | − | 1.21641i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.84230 | + | 3.95041i | 0.500359 | + | 0.288882i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.16746 | −0.301547 | −0.150774 | − | 0.988568i | \(-0.548176\pi\) | ||||
−0.150774 | + | 0.988568i | \(0.548176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.31631 | + | 5.74402i | −0.238713 | + | 0.413464i | −0.960345 | − | 0.278813i | \(-0.910059\pi\) |
0.721632 | + | 0.692277i | \(0.243392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2595i | 1.08719i | 0.839347 | + | 0.543596i | \(0.182938\pi\) | ||||
−0.839347 | + | 0.543596i | \(0.817062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.53911 | − | 4.35271i | 0.534433 | − | 0.308555i | −0.208387 | − | 0.978047i | \(-0.566821\pi\) |
0.742820 | + | 0.669491i | \(0.233488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.56364 | + | 14.8327i | 0.601050 | + | 1.04105i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.48371 | + | 12.9622i | 0.522685 | + | 0.905316i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.0649 | + | 11.2162i | 1.52626 | + | 0.775840i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.10855 | + | 4.68147i | 0.558215 | + | 0.322286i | 0.752429 | − | 0.658674i | \(-0.228882\pi\) |
−0.194214 | + | 0.980959i | \(0.562215\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.31600 | + | 2.27938i | 0.0897506 | + | 0.155453i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −30.6693 | −2.08197 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.53558i | − | 0.439631i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6062 | − | 8.43291i | −0.978106 | − | 0.564710i | −0.0764080 | − | 0.997077i | \(-0.524345\pi\) |
−0.901698 | + | 0.432367i | \(0.857678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7763 | 0.847990 | 0.423995 | − | 0.905665i | \(-0.360627\pi\) | ||||
0.423995 | + | 0.905665i | \(0.360627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0918 | 1.19554 | 0.597771 | − | 0.801667i | \(-0.296053\pi\) | ||||
0.597771 | + | 0.801667i | \(0.296053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.17989 | − | 4.14531i | −0.470370 | − | 0.271568i | 0.246025 | − | 0.969264i | \(-0.420876\pi\) |
−0.716395 | + | 0.697695i | \(0.754209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 27.6843i | − | 1.80592i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5757 | 1.26625 | 0.633124 | − | 0.774050i | \(-0.281772\pi\) | ||||
0.633124 | + | 0.774050i | \(0.281772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0035 | + | 22.5228i | 0.837630 | + | 1.45082i | 0.891871 | + | 0.452290i | \(0.149393\pi\) |
−0.0542404 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.5981 | − | 7.27351i | −0.804863 | − | 0.464688i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.09103 | − | 20.4459i | −0.0694203 | − | 1.30094i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.2530 | − | 19.4908i | −0.710284 | − | 1.23025i | −0.964751 | − | 0.263166i | \(-0.915233\pi\) |
0.254467 | − | 0.967081i | \(-0.418100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.4129 | + | 35.3562i | 1.28335 | + | 2.22282i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.99317 | − | 2.88281i | 0.311465 | − | 0.179825i | −0.336117 | − | 0.941820i | \(-0.609114\pi\) |
0.647582 | + | 0.761996i | \(0.275780\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.7893i | 1.72674i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.85327 | + | 13.6023i | −0.484254 | + | 0.838752i | −0.999836 | − | 0.0180879i | \(-0.994242\pi\) |
0.515583 | + | 0.856840i | \(0.327575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.6402 | −1.26792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.43680 | + | 3.13894i | 0.331488 | + | 0.191384i | 0.656501 | − | 0.754325i | \(-0.272036\pi\) |
−0.325014 | + | 0.945709i | \(0.605369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7135 | − | 14.8457i | −1.56198 | − | 0.901812i | −0.997056 | − | 0.0766706i | \(-0.975571\pi\) |
−0.564927 | − | 0.825141i | \(-0.691096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.9981 | + | 50.2262i | 1.74865 | + | 3.02876i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6970 | −1.84440 | −0.922202 | − | 0.386708i | \(-0.873612\pi\) | ||||
−0.922202 | + | 0.386708i | \(0.873612\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.72370 | + | 4.45928i | −0.460757 | + | 0.266018i | −0.712363 | − | 0.701812i | \(-0.752375\pi\) |
0.251605 | + | 0.967830i | \(0.419042\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.36586 | + | 1.94328i | 0.200079 | + | 0.115516i | 0.596692 | − | 0.802470i | \(-0.296481\pi\) |
−0.396613 | + | 0.917986i | \(0.629815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.28488 | − | 10.8857i | 0.370984 | − | 0.642564i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.53207 | − | 13.0459i | −0.443063 | − | 0.767407i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.70978i | 0.450410i | 0.974311 | + | 0.225205i | \(0.0723053\pi\) | ||||
−0.974311 | + | 0.225205i | \(0.927695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.0524 | − | 21.9696i | 2.21550 | − | 1.27912i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.8856 | − | 29.2467i | 0.976520 | − | 1.69138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.10519 | − | 1.91424i | 0.0637020 | − | 0.110335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.48126i | 0.256596i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.310029 | − | 0.178995i | −0.0176943 | − | 0.0102158i | 0.491127 | − | 0.871088i | \(-0.336585\pi\) |
−0.508821 | + | 0.860872i | \(0.669919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.68561 | −0.208992 | −0.104496 | − | 0.994525i | \(-0.533323\pi\) | ||||
−0.104496 | + | 0.994525i | \(0.533323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.8361 | − | 23.9649i | −0.782064 | − | 1.35457i | −0.930737 | − | 0.365688i | \(-0.880834\pi\) |
0.148673 | − | 0.988886i | \(-0.452500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.52139 | + | 5.49717i | −0.534774 | + | 0.308752i | −0.742958 | − | 0.669338i | \(-0.766578\pi\) |
0.208184 | + | 0.978090i | \(0.433245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.7135 | + | 14.8457i | −1.43968 | + | 0.831199i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.30795 | + | 5.08321i | 0.184059 | + | 0.282837i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.9874 | − | 41.5473i | 1.33058 | − | 2.30463i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.1346 | + | 11.6247i | −1.11006 | + | 0.640892i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.7627i | − | 1.80080i | −0.435061 | − | 0.900401i | \(-0.643273\pi\) | ||
0.435061 | − | 0.900401i | \(-0.356727\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.8815 | −1.46869 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.77186 | − | 4.80101i | 0.150993 | − | 0.261528i | −0.780600 | − | 0.625031i | \(-0.785086\pi\) |
0.931593 | + | 0.363504i | \(0.118420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 53.1675i | − | 2.87918i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.7125i | − | 0.578423i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0923 | + | 24.4085i | −0.756512 | + | 1.31032i | 0.188107 | + | 0.982149i | \(0.439765\pi\) |
−0.944619 | + | 0.328169i | \(0.893569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.4312 | 1.73600 | 0.868002 | − | 0.496560i | \(-0.165404\pi\) | ||||
0.868002 | + | 0.496560i | \(0.165404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.23276i | 0.491410i | 0.969345 | + | 0.245705i | \(0.0790195\pi\) | ||||
−0.969345 | + | 0.245705i | \(0.920981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.2584 | − | 19.2017i | 1.76517 | − | 1.01912i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.28232 | + | 2.22105i | −0.0676784 | + | 0.117222i | −0.897879 | − | 0.440242i | \(-0.854893\pi\) |
0.830201 | + | 0.557465i | \(0.188226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1971 | + | 15.3500i | 0.589323 | + | 0.807897i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.2324 | − | 23.2282i | 2.10586 | − | 1.21582i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.5597 | + | 14.1795i | −1.28200 | + | 0.740165i | −0.977214 | − | 0.212254i | \(-0.931919\pi\) |
−0.304789 | + | 0.952420i | \(0.598586\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.66689 | + | 15.0115i | 0.449963 | + | 0.779358i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.99511 | 0.310415 | 0.155207 | − | 0.987882i | \(-0.450395\pi\) | ||||
0.155207 | + | 0.987882i | \(0.450395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.2703 | + | 12.2804i | 1.09548 | + | 0.632473i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.804599i | − | 0.0413295i | −0.999786 | − | 0.0206647i | \(-0.993422\pi\) | ||
0.999786 | − | 0.0206647i | \(-0.00657826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.07152 | − | 3.58798i | 0.105850 | − | 0.183337i | −0.808235 | − | 0.588860i | \(-0.799577\pi\) |
0.914085 | + | 0.405522i | \(0.132910\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.2750 | − | 62.8301i | 1.84874 | − | 3.20212i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.5385 | + | 15.3220i | −1.34556 | + | 0.776857i | −0.987616 | − | 0.156888i | \(-0.949854\pi\) |
−0.357939 | + | 0.933745i | \(0.616520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0032i | 0.505884i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0923 | + | 24.4085i | 0.709058 | + | 1.22813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.33247 | + | 4.03996i | −0.117064 | + | 0.202760i | −0.918603 | − | 0.395182i | \(-0.870681\pi\) |
0.801539 | + | 0.597942i | \(0.204015\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.16733 | + | 4.71541i | 0.407857 | + | 0.235476i | 0.689869 | − | 0.723935i | \(-0.257668\pi\) |
−0.282011 | + | 0.959411i | \(0.591002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.0881 | + | 21.9902i | −1.89730 | + | 1.09541i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −48.1747 | −2.38793 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.6228 | + | 18.3993i | 0.525264 | + | 0.909785i | 0.999567 | + | 0.0294229i | \(0.00936695\pi\) |
−0.474303 | + | 0.880362i | \(0.657300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.9567 | − | 18.4502i | −1.57249 | − | 0.907876i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.6846 | − | 7.90081i | −0.671751 | − | 0.387836i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.08467 | −0.101843 | −0.0509214 | − | 0.998703i | \(-0.516216\pi\) | ||||
−0.0509214 | + | 0.998703i | \(0.516216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33625 | + | 4.04651i | −0.113862 | + | 0.197215i | −0.917324 | − | 0.398141i | \(-0.869656\pi\) |
0.803462 | + | 0.595356i | \(0.202989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.2103i | 0.689303i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.25920 | − | 1.88170i | 0.157724 | − | 0.0910618i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.31916 | − | 16.1413i | −0.448888 | − | 0.777497i | 0.549426 | − | 0.835543i | \(-0.314847\pi\) |
−0.998314 | + | 0.0580454i | \(0.981513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1872 | + | 22.8409i | 0.633737 | + | 1.09766i | 0.986781 | + | 0.162058i | \(0.0518131\pi\) |
−0.353044 | + | 0.935607i | \(0.614854\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.66990 | + | 31.2939i | 0.0798821 | + | 1.49699i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.3816 | − | 5.99383i | −0.495488 | − | 0.286070i | 0.231361 | − | 0.972868i | \(-0.425682\pi\) |
−0.726848 | + | 0.686798i | \(0.759016\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.79336 | + | 4.83824i | 0.132717 | + | 0.229872i | 0.924723 | − | 0.380641i | \(-0.124297\pi\) |
−0.792006 | + | 0.610513i | \(0.790963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −62.1880 | −2.94799 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.9428i | − | 0.893964i | −0.894543 | − | 0.446982i | \(-0.852499\pi\) | ||
0.894543 | − | 0.446982i | \(-0.147501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.8712 | + | 10.8953i | 0.888610 | + | 0.513039i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −60.0136 | −2.81348 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.2451 | −1.22769 | −0.613847 | − | 0.789425i | \(-0.710379\pi\) | ||||
−0.613847 | + | 0.789425i | \(0.710379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.07467 | − | 4.66191i | −0.376075 | − | 0.217127i | 0.300034 | − | 0.953928i | \(-0.403002\pi\) |
−0.676109 | + | 0.736802i | \(0.736335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.6793i | − | 0.868101i | −0.900889 | − | 0.434050i | \(-0.857084\pi\) | ||
0.900889 | − | 0.434050i | \(-0.142916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.63798 | 0.445992 | 0.222996 | − | 0.974819i | \(-0.428416\pi\) | ||||
0.222996 | + | 0.974819i | \(0.428416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2876 | + | 19.5508i | 0.521215 | + | 0.902770i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.31848 | + | 1.91592i | 0.152584 | + | 0.0880943i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.37222 | + | 44.4555i | 0.108845 | + | 2.03976i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.03784 | + | 3.52964i | 0.0931113 | + | 0.161274i | 0.908819 | − | 0.417191i | \(-0.136985\pi\) |
−0.815707 | + | 0.578465i | \(0.803652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.9252 | + | 34.5114i | 0.908509 | + | 1.57358i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.5317 | − | 18.2048i | 1.43178 | − | 0.826638i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.99607i | 0.362337i | 0.983452 | + | 0.181168i | \(0.0579879\pi\) | ||||
−0.983452 | + | 0.181168i | \(0.942012\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.92298 | + | 8.52686i | −0.222171 | + | 0.384812i | −0.955467 | − | 0.295098i | \(-0.904648\pi\) |
0.733296 | + | 0.679910i | \(0.237981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.27503 | −0.327651 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.9306 | − | 16.1258i | −1.25286 | − | 0.723339i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.416687 | − | 0.240574i | −0.0186535 | − | 0.0107696i | 0.490644 | − | 0.871360i | \(-0.336761\pi\) |
−0.509298 | + | 0.860590i | \(0.670095\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.9206 | − | 34.5036i | −0.888218 | − | 1.53844i | −0.841981 | − | 0.539508i | \(-0.818610\pi\) |
−0.0462369 | − | 0.998931i | \(-0.514723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.9426 | 0.531441 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.3040 | − | 11.1452i | 0.855636 | − | 0.494001i | −0.00691272 | − | 0.999976i | \(-0.502200\pi\) |
0.862548 | + | 0.505975i | \(0.168867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.7874 | − | 19.5072i | −1.49467 | − | 0.862947i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.4407 | + | 23.2800i | −0.592269 | + | 1.02584i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.1523 | − | 34.9048i | −0.886297 | − | 1.53511i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.73125i | 0.338712i | 0.985555 | + | 0.169356i | \(0.0541688\pi\) | ||||
−0.985555 | + | 0.169356i | \(0.945831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.986124 | + | 0.569339i | −0.0431202 | + | 0.0248955i | −0.521405 | − | 0.853309i | \(-0.674592\pi\) |
0.478285 | + | 0.878205i | \(0.341259\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.51359 | − | 11.2819i | 0.283736 | − | 0.491446i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.3447 | + | 24.8458i | −0.623684 | + | 1.08025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.0252i | − | 0.780760i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.58053 | − | 4.95397i | −0.370969 | − | 0.214179i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.1785 | −0.912224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.22960 | − | 14.2541i | −0.353818 | − | 0.612831i | 0.633097 | − | 0.774073i | \(-0.281784\pi\) |
−0.986915 | + | 0.161242i | \(0.948450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.0061 | + | 17.3240i | −1.28532 | + | 0.742080i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7926 | + | 6.23108i | −0.461456 | + | 0.266422i | −0.712656 | − | 0.701513i | \(-0.752508\pi\) |
0.251200 | + | 0.967935i | \(0.419175\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.7592 | + | 1.21447i | −0.969573 | + | 0.0517381i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8348 | − | 20.4985i | 0.503266 | − | 0.871683i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9642 | + | 9.21695i | −0.676426 | + | 0.390535i | −0.798507 | − | 0.601985i | \(-0.794376\pi\) |
0.122081 | + | 0.992520i | \(0.461043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.16972i | − | 0.134065i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.0466 | −1.43489 | −0.717446 | − | 0.696614i | \(-0.754689\pi\) | ||||
−0.717446 | + | 0.696614i | \(0.754689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.5616 | + | 58.1303i | −1.41195 | + | 2.44556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.8995i | 1.08576i | 0.839809 | + | 0.542882i | \(0.182667\pi\) | ||||
−0.839809 | + | 0.542882i | \(0.817333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.59067i | 0.192113i | 0.995376 | + | 0.0960567i | \(0.0306230\pi\) | ||||
−0.995376 | + | 0.0960567i | \(0.969377\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.7145 | + | 63.5913i | −1.53110 | + | 2.65194i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.4295 | −0.850493 | −0.425247 | − | 0.905078i | \(-0.639813\pi\) | ||||
−0.425247 | + | 0.905078i | \(0.639813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2703i | 0.550546i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.0235 | + | 15.0247i | −1.07778 | + | 0.622259i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.95666 | − | 8.58519i | 0.204583 | − | 0.354349i | −0.745417 | − | 0.666599i | \(-0.767749\pi\) |
0.950000 | + | 0.312250i | \(0.101083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.4937 | − | 36.3815i | 0.762020 | − | 1.49907i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3914 | − | 7.15420i | 0.508856 | − | 0.293788i | −0.223508 | − | 0.974702i | \(-0.571751\pi\) |
0.732363 | + | 0.680914i | \(0.238417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.3947 | − | 8.88816i | 0.631123 | − | 0.364379i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.35384 | − | 5.80903i | −0.137034 | − | 0.237350i | 0.789338 | − | 0.613958i | \(-0.210424\pi\) |
−0.926373 | + | 0.376608i | \(0.877090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.81850 | −0.155760 | −0.0778799 | − | 0.996963i | \(-0.524815\pi\) | ||||
−0.0778799 | + | 0.996963i | \(0.524815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 71.7640 | + | 41.4330i | 2.91762 | + | 1.68449i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.5650i | − | 0.794120i | −0.917793 | − | 0.397060i | \(-0.870031\pi\) | ||
0.917793 | − | 0.397060i | \(-0.129969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6701 | + | 28.8734i | −0.674398 | + | 1.16809i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.2753 | + | 36.8498i | −0.859299 | + | 1.48835i | 0.0132989 | + | 0.999912i | \(0.495767\pi\) |
−0.872598 | + | 0.488439i | \(0.837567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5604 | + | 7.82909i | −0.545921 | + | 0.315187i | −0.747475 | − | 0.664290i | \(-0.768734\pi\) |
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6107i | 1.39112i | 0.718467 | + | 0.695561i | \(0.244844\pi\) | ||||
−0.718467 | + | 0.695561i | \(0.755156\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.1130 | + | 45.2290i | 1.04620 | + | 1.81206i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.1226 | + | 24.4610i | −0.564902 | + | 0.978439i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.2224 | − | 5.90193i | −0.407595 | − | 0.235325i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.11091 | − | 3.52814i | 0.243272 | − | 0.140453i | −0.373408 | − | 0.927667i | \(-0.621811\pi\) |
0.616679 | + | 0.787214i | \(0.288477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.9879 | 0.912246 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.75948 | + | 15.1719i | 0.347063 | + | 0.601131i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9743 | − | 9.80009i | −0.670443 | − | 0.387080i | 0.125802 | − | 0.992055i | \(-0.459850\pi\) |
−0.796244 | + | 0.604975i | \(0.793183\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.8109 | − | 7.39637i | −0.505212 | − | 0.291685i | 0.225651 | − | 0.974208i | \(-0.427549\pi\) |
−0.730863 | + | 0.682524i | \(0.760882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8654 | −1.21344 | −0.606721 | − | 0.794915i | \(-0.707516\pi\) | ||||
−0.606721 | + | 0.794915i | \(0.707516\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.9848 | − | 55.3993i | 1.25551 | − | 2.17461i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.6677i | 1.08272i | 0.840791 | + | 0.541360i | \(0.182090\pi\) | ||||
−0.840791 | + | 0.541360i | \(0.817910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.5953 | + | 14.2001i | −0.961019 | + | 0.554845i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.4089 | + | 31.8851i | 0.717108 | + | 1.24207i | 0.962141 | + | 0.272552i | \(0.0878677\pi\) |
−0.245033 | + | 0.969515i | \(0.578799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.48371 | − | 9.49806i | −0.213291 | − | 0.369432i | 0.739451 | − | 0.673210i | \(-0.235085\pi\) |
−0.952743 | + | 0.303778i | \(0.901752\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 46.6770 | − | 30.3756i | 1.81006 | − | 1.17791i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.5558 | − | 18.7961i | −1.26057 | − | 0.727788i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.26206 | + | 5.65005i | 0.125930 | + | 0.218118i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0122 | −0.655772 | −0.327886 | − | 0.944717i | \(-0.606336\pi\) | ||||
−0.327886 | + | 0.944717i | \(0.606336\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.69536i | − | 0.142024i | −0.997475 | − | 0.0710120i | \(-0.977377\pi\) | ||
0.997475 | − | 0.0710120i | \(-0.0226229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.4805 | − | 15.2886i | −1.01623 | − | 0.586721i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.8693 | 1.90820 | 0.954099 | − | 0.299493i | \(-0.0968175\pi\) | ||||
0.954099 | + | 0.299493i | \(0.0968175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.1210 | 1.38011 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.5267 | + | 12.4285i | 0.820104 | + | 0.473487i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6882i | 0.748974i | 0.927232 | + | 0.374487i | \(0.122181\pi\) | ||||
−0.927232 | + | 0.374487i | \(0.877819\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.6908 | −1.08830 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.66958 | + | 4.62385i | 0.101118 | + | 0.175141i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0808 | − | 11.0163i | −0.720673 | − | 0.416081i | 0.0943271 | − | 0.995541i | \(-0.469930\pi\) |
−0.815000 | + | 0.579460i | \(0.803263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9650 | − | 16.7570i | −1.24330 | − | 0.632004i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.01476 | − | 8.68583i | −0.188600 | − | 0.326664i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.54702 | + | 6.14363i | 0.133211 | + | 0.230729i | 0.924913 | − | 0.380179i | \(-0.124138\pi\) |
−0.791701 | + | 0.610908i | \(0.790804\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.2967 | − | 33.6576i | 2.18323 | − | 1.26049i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 104.038i | − | 3.89080i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.41376 | − | 14.5731i | 0.313780 | − | 0.543483i | −0.665397 | − | 0.746489i | \(-0.731738\pi\) |
0.979177 | + | 0.203006i | \(0.0650712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.5753 | 0.840747 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −46.2481 | − | 26.7013i | −1.71761 | − | 0.991663i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0180 | + | 12.7121i | 0.816602 | + | 0.471465i | 0.849243 | − | 0.528002i | \(-0.177059\pi\) |
−0.0326416 | + | 0.999467i | \(0.510392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.469443 | + | 0.813099i | 0.0173630 | + | 0.0300736i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8756 | −0.660250 | −0.330125 | − | 0.943937i | \(-0.607091\pi\) | ||||
−0.330125 | + | 0.943937i | \(0.607091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.8926 | + | 19.5679i | −1.24845 | + | 0.720794i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.86322 | + | 2.23043i | 0.142111 | + | 0.0820478i | 0.569370 | − | 0.822082i | \(-0.307187\pi\) |
−0.427259 | + | 0.904129i | \(0.640521\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3588 | − | 28.3343i | 0.600147 | − | 1.03948i | −0.392652 | − | 0.919687i | \(-0.628442\pi\) |
0.992798 | − | 0.119797i | \(-0.0382245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.39700 | + | 14.5440i | 0.307642 | + | 0.532852i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.32077i | 0.304034i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.49214 | − | 1.43884i | 0.0909395 | − | 0.0525040i | −0.453841 | − | 0.891083i | \(-0.649946\pi\) |
0.544780 | + | 0.838579i | \(0.316613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.9842 | + | 81.3790i | −1.70993 | + | 2.96169i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8360 | − | 22.2326i | 0.466532 | − | 0.808057i | −0.532737 | − | 0.846281i | \(-0.678837\pi\) |
0.999269 | + | 0.0382235i | \(0.0121699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.9352i | − | 0.650150i | −0.945688 | − | 0.325075i | \(-0.894610\pi\) | ||
0.945688 | − | 0.325075i | \(-0.105390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.1994 | + | 14.5489i | 0.912278 | + | 0.526704i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.9158 | −1.91068 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.92395 | − | 17.1888i | −0.357867 | − | 0.619843i | 0.629738 | − | 0.776808i | \(-0.283162\pi\) |
−0.987604 | + | 0.156965i | \(0.949829\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.4410 | + | 15.2657i | −0.951018 | + | 0.549071i | −0.893397 | − | 0.449268i | \(-0.851685\pi\) |
−0.0576213 | + | 0.998339i | \(0.518352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82.8151 | − | 47.8133i | 2.97481 | − | 1.71750i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.12338 | + | 14.0196i | 0.326879 | + | 0.502303i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.9552 | − | 48.4198i | 1.00031 | − | 1.73260i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26867 | + | 1.88717i | −0.116664 | + | 0.0673559i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.1007i | − | 0.894744i | −0.894348 | − | 0.447372i | \(-0.852360\pi\) | ||
0.894348 | − | 0.447372i | \(-0.147640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.3705 | 2.00430 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.69839 | − | 4.67374i | 0.0958225 | − | 0.165970i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.4922i | 0.867560i | 0.901019 | + | 0.433780i | \(0.142820\pi\) | ||||
−0.901019 | + | 0.433780i | \(0.857180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.87550i | − | 0.349370i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.8171 | − | 58.5730i | 1.19338 | − | 2.06700i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 91.8554 | 3.23748 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 4.71435i | − | 0.165748i | −0.996560 | − | 0.0828738i | \(-0.973590\pi\) | ||
0.996560 | − | 0.0828738i | \(-0.0264098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.1007 | + | 23.1521i | −1.40812 | + | 0.812981i | −0.995207 | − | 0.0977875i | \(-0.968823\pi\) |
−0.412917 | + | 0.910769i | \(0.635490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.22066 | + | 3.84630i | −0.0777865 | + | 0.134730i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.60434 | + | 2.46533i | 0.0561287 | + | 0.0862508i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.52776 | + | 3.76881i | −0.227821 | + | 0.131532i | −0.609566 | − | 0.792735i | \(-0.708656\pi\) |
0.381746 | + | 0.924267i | \(0.375323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.9895 | − | 21.3559i | 1.28937 | − | 0.744420i | 0.310831 | − | 0.950465i | \(-0.399393\pi\) |
0.978543 | + | 0.206045i | \(0.0660592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.1212 | − | 22.7265i | −0.456268 | − | 0.790279i | 0.542492 | − | 0.840061i | \(-0.317481\pi\) |
−0.998760 | + | 0.0497815i | \(0.984147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.4613 | −1.57894 | −0.789469 | − | 0.613791i | \(-0.789644\pi\) | ||||
−0.789469 | + | 0.613791i | \(0.789644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.49398 | − | 2.59460i | −0.155707 | − | 0.0898976i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 39.9249i | − | 1.38166i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.3025 | + | 17.8444i | −0.355680 | + | 0.616056i | −0.987234 | − | 0.159276i | \(-0.949084\pi\) |
0.631554 | + | 0.775332i | \(0.282417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.830158 | + | 1.43788i | −0.0286262 | + | 0.0495820i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.6183 | + | 17.6775i | −1.05330 | + | 0.608124i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 69.5915i | − | 2.39119i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.4970 | − | 52.8223i | −1.04542 | − | 1.81072i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.52842 | + | 6.11139i | −0.120811 | + | 0.209250i | −0.920088 | − | 0.391713i | \(-0.871883\pi\) |
0.799277 | + | 0.600963i | \(0.205216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4352 | − | 9.48889i | −0.561417 | − | 0.324134i | 0.192297 | − | 0.981337i | \(-0.438406\pi\) |
−0.753714 | + | 0.657203i | \(0.771740\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.42562 | − | 3.70983i | 0.219239 | − | 0.126578i | −0.386359 | − | 0.922349i | \(-0.626267\pi\) |
0.605598 | + | 0.795771i | \(0.292934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.7307 | 1.28437 | 0.642184 | − | 0.766550i | \(-0.278028\pi\) | ||||
0.642184 | + | 0.766550i | \(0.278028\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.8785 | + | 24.0383i | 0.471884 | + | 0.817327i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.5356 | + | 20.5165i | 1.20546 | + | 0.695973i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.0361 | + | 16.1867i | 0.949967 | + | 0.548464i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 66.6066 | 2.25171 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.927858 | + | 1.60710i | −0.0313315 | + | 0.0542678i | −0.881266 | − | 0.472621i | \(-0.843308\pi\) |
0.849934 | + | 0.526888i | \(0.176641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.9367i | − | 0.469539i | −0.972051 | − | 0.234770i | \(-0.924566\pi\) | ||
0.972051 | − | 0.234770i | \(-0.0754336\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.5144 | + | 18.1948i | −1.06054 | + | 0.612305i | −0.925582 | − | 0.378546i | \(-0.876424\pi\) |
−0.134961 | + | 0.990851i | \(0.543091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.2719 | − | 31.6479i | −0.613511 | − | 1.06263i | −0.990644 | − | 0.136474i | \(-0.956423\pi\) |
0.377132 | − | 0.926159i | \(-0.376910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.65270 | − | 16.7190i | −0.323741 | − | 0.560736i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.64858 | − | 30.8944i | −0.0551676 | − | 1.03384i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.4719 | + | 17.0156i | 0.985136 | + | 0.568769i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.4782 | + | 42.3974i | 0.816393 | + | 1.41403i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.36275 | −0.245289 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 70.8169i | − | 2.35403i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.6994 | + | 17.1470i | 0.986153 | + | 0.569355i | 0.904122 | − | 0.427274i | \(-0.140526\pi\) |
0.0820306 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.5696 | 1.64231 | 0.821156 | − | 0.570703i | \(-0.193329\pi\) | ||||
0.821156 | + | 0.570703i | \(0.193329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.0051 | −0.761357 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.6553 | + | 11.9254i | 0.682100 | + | 0.393810i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.3617i | − | 0.407774i | −0.978994 | − | 0.203887i | \(-0.934642\pi\) | ||
0.978994 | − | 0.203887i | \(-0.0653575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.2492 | −1.52231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43.3233 | − | 75.0382i | −1.42446 | − | 2.46724i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5934 | − | 13.0443i | −0.741267 | − | 0.427971i | 0.0812629 | − | 0.996693i | \(-0.474105\pi\) |
−0.822530 | + | 0.568722i | \(0.807438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.4921 | − | 7.36672i | −0.474958 | − | 0.241435i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.4083 | + | 26.6879i | 0.503904 | + | 0.872787i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5296 | + | 23.4340i | 0.441993 | + | 0.765555i | 0.997837 | − | 0.0657317i | \(-0.0209381\pi\) |
−0.555844 | + | 0.831287i | \(0.687605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6188 | − | 16.5230i | 0.932945 | − | 0.538636i | 0.0452031 | − | 0.998978i | \(-0.485607\pi\) |
0.887742 | + | 0.460342i | \(0.152273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5890i | 0.898421i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.0733 | + | 33.0360i | −0.619800 | + | 1.07353i | 0.369721 | + | 0.929143i | \(0.379453\pi\) |
−0.989522 | + | 0.144383i | \(0.953880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.9473 | −1.81613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6143 | + | 14.7884i | 0.829728 | + | 0.479044i | 0.853759 | − | 0.520668i | \(-0.174317\pi\) |
−0.0240316 | + | 0.999711i | \(0.507650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0771 | − | 8.12744i | −0.455525 | − | 0.262998i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.1673 | − | 26.2706i | −0.489779 | − | 0.848322i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −56.6647 | −1.82789 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.4041 | + | 12.9350i | −0.721214 | + | 0.416393i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.8725 | − | 29.3713i | −1.63595 | − | 0.944516i | −0.982208 | − | 0.187798i | \(-0.939865\pi\) |
−0.653742 | − | 0.756718i | \(-0.726802\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.9963 | + | 20.7782i | −0.384980 | + | 0.666805i | −0.991766 | − | 0.128060i | \(-0.959125\pi\) |
0.606786 | + | 0.794865i | \(0.292458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0474 | + | 20.8667i | 0.386221 | + | 0.668955i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 51.3764i | − | 1.64368i | −0.569721 | − | 0.821838i | \(-0.692949\pi\) | ||
0.569721 | − | 0.821838i | \(-0.307051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.4078 | + | 45.2688i | −2.50592 | + | 1.44680i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.6437 | + | 39.2200i | −0.722222 | + | 1.25092i | 0.237886 | + | 0.971293i | \(0.423546\pi\) |
−0.960107 | + | 0.279631i | \(0.909788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.7592 | + | 51.5445i | −0.948208 | + | 1.64234i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.85150i | 0.154269i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.9481 | + | 20.7547i | 1.14193 | + | 0.659293i | 0.946908 | − | 0.321506i | \(-0.104189\pi\) |
0.195022 | + | 0.980799i | \(0.437522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.9548 | 1.07644 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1534 | + | 22.7824i | 0.416573 | + | 0.721525i | 0.995592 | − | 0.0937884i | \(-0.0298977\pi\) |
−0.579019 | + | 0.815314i | \(0.696564\pi\) | |||||||
\(998\) | 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 | 2736.2.cg.c.1151.16 | yes | 32 | |
3.2 | odd | 2 | inner | 2736.2.cg.c.1151.2 | yes | 32 | |
4.3 | odd | 2 | inner | 2736.2.cg.c.1151.15 | yes | 32 | |
12.11 | even | 2 | inner | 2736.2.cg.c.1151.1 | ✓ | 32 | |
19.7 | even | 3 | inner | 2736.2.cg.c.2591.1 | yes | 32 | |
57.26 | odd | 6 | inner | 2736.2.cg.c.2591.15 | yes | 32 | |
76.7 | odd | 6 | inner | 2736.2.cg.c.2591.2 | yes | 32 | |
228.83 | even | 6 | inner | 2736.2.cg.c.2591.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.c.1151.1 | ✓ | 32 | 12.11 | even | 2 | inner | |
2736.2.cg.c.1151.2 | yes | 32 | 3.2 | odd | 2 | inner | |
2736.2.cg.c.1151.15 | yes | 32 | 4.3 | odd | 2 | inner | |
2736.2.cg.c.1151.16 | yes | 32 | 1.1 | even | 1 | trivial | |
2736.2.cg.c.2591.1 | yes | 32 | 19.7 | even | 3 | inner | |
2736.2.cg.c.2591.2 | yes | 32 | 76.7 | odd | 6 | inner | |
2736.2.cg.c.2591.15 | yes | 32 | 57.26 | odd | 6 | inner | |
2736.2.cg.c.2591.16 | yes | 32 | 228.83 | even | 6 | inner |