Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(53,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 10, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.1154223326374133760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 100x^{12} - 408x^{10} + 1191x^{8} - 2040x^{6} + 2500x^{4} - 1500x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{4}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 593.1 | ||
Root | \(0.750156 - 0.433103i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.593 |
Dual form | 1620.2.x.d.377.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10648 | + | 0.750156i | −0.942047 | + | 0.335480i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0822623 | + | 0.307007i | 0.0310922 | + | 0.116038i | 0.979728 | − | 0.200333i | \(-0.0642023\pi\) |
−0.948636 | + | 0.316371i | \(0.897536\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41131 | + | 1.39217i | 0.727037 | + | 0.419755i | 0.817337 | − | 0.576159i | \(-0.195449\pi\) |
−0.0903001 | + | 0.995915i | \(0.528783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.448288 | + | 1.67303i | −0.124333 | + | 0.464016i | −0.999815 | − | 0.0192343i | \(-0.993877\pi\) |
0.875482 | + | 0.483250i | \(0.160544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.78434 | − | 2.78434i | −0.675302 | − | 0.675302i | 0.283632 | − | 0.958933i | \(-0.408461\pi\) |
−0.958933 | + | 0.283632i | \(0.908461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.89898i | 0.894487i | 0.894412 | + | 0.447244i | \(0.147594\pi\) | ||||
−0.894412 | + | 0.447244i | \(0.852406\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.46177 | − | 2.26732i | −1.76440 | − | 0.472770i | −0.776799 | − | 0.629748i | \(-0.783158\pi\) |
−0.987602 | + | 0.156978i | \(0.949825\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.87453 | − | 3.16038i | 0.774907 | − | 0.632076i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.39217 | − | 2.41131i | 0.258520 | − | 0.447769i | −0.707326 | − | 0.706887i | \(-0.750099\pi\) |
0.965846 | + | 0.259119i | \(0.0834320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.224745 | − | 0.389270i | −0.0403654 | − | 0.0699149i | 0.845137 | − | 0.534550i | \(-0.179519\pi\) |
−0.885502 | + | 0.464635i | \(0.846186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.403587 | − | 0.584996i | −0.0682187 | − | 0.0988823i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.67423 | − | 3.67423i | 0.604040 | − | 0.604040i | −0.337342 | − | 0.941382i | \(-0.609528\pi\) |
0.941382 | + | 0.337342i | \(0.109528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.31779 | + | 4.80228i | −1.29902 | + | 0.749990i | −0.980235 | − | 0.197837i | \(-0.936608\pi\) |
−0.318785 | + | 0.947827i | \(0.603275\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.752011 | + | 0.201501i | −0.114681 | + | 0.0307286i | −0.315703 | − | 0.948858i | \(-0.602240\pi\) |
0.201022 | + | 0.979587i | \(0.435574\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.97469 | − | 3.44949i | 0.853527 | − | 0.492784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.19445 | + | 6.19445i | −0.850873 | + | 0.850873i | −0.990241 | − | 0.139368i | \(-0.955493\pi\) |
0.139368 | + | 0.990241i | \(0.455493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.12372 | − | 1.12372i | −0.825723 | − | 0.151523i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.19445 | − | 10.7291i | −0.806448 | − | 1.39681i | −0.915309 | − | 0.402752i | \(-0.868054\pi\) |
0.108861 | − | 0.994057i | \(-0.465280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.39898 | + | 11.0834i | −0.819305 | + | 1.41908i | 0.0868894 | + | 0.996218i | \(0.472307\pi\) |
−0.906195 | + | 0.422861i | \(0.861026\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.310725 | − | 3.86050i | −0.0385406 | − | 0.478836i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8492 | − | 3.17499i | −1.44761 | − | 0.387887i | −0.552420 | − | 0.833566i | \(-0.686296\pi\) |
−0.895193 | + | 0.445679i | \(0.852962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.60455i | 1.13985i | 0.821696 | + | 0.569925i | \(0.193028\pi\) | ||||
−0.821696 | + | 0.569925i | \(0.806972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22474 | − | 6.22474i | −0.728551 | − | 0.728551i | 0.241780 | − | 0.970331i | \(-0.422269\pi\) |
−0.970331 | + | 0.241780i | \(0.922269\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.229046 | + | 0.854813i | −0.0261023 | + | 0.0974149i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00853 | − | 4.62372i | −0.901030 | − | 0.520210i | −0.0234955 | − | 0.999724i | \(-0.507480\pi\) |
−0.877534 | + | 0.479514i | \(0.840813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.24819 | − | 4.65829i | −0.137006 | − | 0.511314i | −0.999982 | − | 0.00606809i | \(-0.998068\pi\) |
0.862975 | − | 0.505246i | \(-0.168598\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.95385 | + | 3.77647i | 0.862716 | + | 0.409616i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3889 | −1.31322 | −0.656610 | − | 0.754230i | \(-0.728010\pi\) | ||||
−0.656610 | + | 0.754230i | \(0.728010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.550510 | −0.0577092 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.92484 | − | 8.21313i | −0.300082 | − | 0.842649i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.74786 | − | 6.52312i | −0.177469 | − | 0.662322i | −0.996118 | − | 0.0880285i | \(-0.971943\pi\) |
0.818649 | − | 0.574294i | \(-0.194723\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5517 | − | 8.97879i | −1.54745 | − | 0.893423i | −0.998335 | − | 0.0576781i | \(-0.981630\pi\) |
−0.549118 | − | 0.835745i | \(-0.685036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.27841 | + | 8.50316i | −0.224499 | + | 0.837841i | 0.758106 | + | 0.652132i | \(0.226125\pi\) |
−0.982605 | + | 0.185710i | \(0.940542\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.97879 | + | 8.97879i | 0.868012 | + | 0.868012i | 0.992252 | − | 0.124240i | \(-0.0396493\pi\) |
−0.124240 | + | 0.992252i | \(0.539649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3485i | 1.08699i | 0.839414 | + | 0.543493i | \(0.182899\pi\) | ||||
−0.839414 | + | 0.543493i | \(0.817101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.854813 | − | 0.229046i | −0.0804140 | − | 0.0215469i | 0.218388 | − | 0.975862i | \(-0.429920\pi\) |
−0.298802 | + | 0.954315i | \(0.596587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.5254 | − | 1.57157i | 1.82075 | − | 0.146549i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.625766 | − | 1.08386i | 0.0573639 | − | 0.0993572i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.62372 | − | 2.81237i | −0.147611 | − | 0.255670i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.79086 | + | 9.56378i | −0.517950 | + | 0.855411i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89898 | − | 9.89898i | 0.878392 | − | 0.878392i | −0.114976 | − | 0.993368i | \(-0.536679\pi\) |
0.993368 | + | 0.114976i | \(0.0366791\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.82262 | − | 2.78434i | 0.421354 | − | 0.243269i | −0.274302 | − | 0.961644i | \(-0.588447\pi\) |
0.695657 | + | 0.718375i | \(0.255114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.19701 | + | 0.320739i | −0.103794 | + | 0.0278116i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.65829 | + | 1.24819i | −0.397985 | + | 0.106640i | −0.452260 | − | 0.891886i | \(-0.649382\pi\) |
0.0542749 | + | 0.998526i | \(0.482715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6688 | − | 9.62372i | 1.41383 | − | 0.816274i | 0.418081 | − | 0.908410i | \(-0.362703\pi\) |
0.995746 | + | 0.0921361i | \(0.0293695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41011 | + | 3.41011i | −0.285167 | + | 0.285167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.12372 | + | 6.12372i | −0.0933202 | + | 0.508548i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.41011 | + | 5.90648i | 0.279367 | + | 0.483878i | 0.971228 | − | 0.238153i | \(-0.0765421\pi\) |
−0.691861 | + | 0.722031i | \(0.743209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.27526 | + | 9.13701i | −0.429294 | + | 0.743559i | −0.996811 | − | 0.0798027i | \(-0.974571\pi\) |
0.567517 | + | 0.823362i | \(0.307904\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.765434 | + | 0.651396i | 0.0614811 | + | 0.0523214i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.2343 | − | 4.88588i | −1.45526 | − | 0.389936i | −0.557410 | − | 0.830238i | \(-0.688205\pi\) |
−0.897850 | + | 0.440302i | \(0.854871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.78434i | − | 0.219437i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.77526 | + | 3.77526i | 0.295701 | + | 0.295701i | 0.839327 | − | 0.543626i | \(-0.182949\pi\) |
−0.543626 | + | 0.839327i | \(0.682949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.51551 | − | 13.1201i | 0.272038 | − | 1.01526i | −0.685762 | − | 0.727826i | \(-0.740531\pi\) |
0.957800 | − | 0.287435i | \(-0.0928025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.66025 | + | 5.00000i | 0.666173 | + | 0.384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.03828 | − | 7.60696i | −0.154967 | − | 0.578346i | −0.999108 | − | 0.0422247i | \(-0.986555\pi\) |
0.844141 | − | 0.536122i | \(-0.180111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.28899 | + | 0.929530i | 0.0974383 | + | 0.0702658i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.60455 | 0.717878 | 0.358939 | − | 0.933361i | \(-0.383139\pi\) | ||||
0.358939 | + | 0.933361i | \(0.383139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2474 | 0.836016 | 0.418008 | − | 0.908443i | \(-0.362728\pi\) | ||||
0.418008 | + | 0.908443i | \(0.362728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.98346 | + | 10.4960i | −0.366391 | + | 0.771678i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.83763 | − | 10.5902i | −0.207508 | − | 0.774431i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.7291 | + | 6.19445i | 0.776330 | + | 0.448214i | 0.835128 | − | 0.550055i | \(-0.185393\pi\) |
−0.0587979 | + | 0.998270i | \(0.518727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.23609 | + | 15.8093i | −0.304920 | + | 1.13798i | 0.628093 | + | 0.778138i | \(0.283836\pi\) |
−0.933014 | + | 0.359841i | \(0.882831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.82021 | − | 6.82021i | −0.485920 | − | 0.485920i | 0.421096 | − | 0.907016i | \(-0.361646\pi\) |
−0.907016 | + | 0.421096i | \(0.861646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.24745i | 0.655534i | 0.944759 | + | 0.327767i | \(0.106296\pi\) | ||||
−0.944759 | + | 0.327767i | \(0.893704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.854813 | + | 0.229046i | 0.0599961 | + | 0.0160759i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9188 | − | 16.3555i | 0.972132 | − | 1.14232i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.42804 | + | 9.40165i | −0.375466 | + | 0.650325i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.62372 | + | 11.4726i | 0.455996 | + | 0.789808i | 0.998745 | − | 0.0500868i | \(-0.0159498\pi\) |
−0.542749 | + | 0.839895i | \(0.682616\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.43294 | − | 0.988583i | 0.0977257 | − | 0.0674208i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.101021 | − | 0.101021i | 0.00685772 | − | 0.00685772i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.90648 | − | 3.41011i | 0.397313 | − | 0.229389i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4823 | + | 4.68438i | −1.17070 | + | 0.313689i | −0.791233 | − | 0.611515i | \(-0.790561\pi\) |
−0.379471 | + | 0.925204i | \(0.623894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.5818 | − | 5.78284i | 1.43244 | − | 0.383820i | 0.542558 | − | 0.840018i | \(-0.317456\pi\) |
0.889878 | + | 0.456198i | \(0.150789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.16781 | − | 0.674235i | 0.0771710 | − | 0.0445547i | −0.460918 | − | 0.887443i | \(-0.652480\pi\) |
0.538089 | + | 0.842888i | \(0.319146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1732 | − | 15.1732i | 0.994032 | − | 0.994032i | −0.00595067 | − | 0.999982i | \(-0.501894\pi\) |
0.999982 | + | 0.00595067i | \(0.00189417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.17651 | + | 7.23393i | 0.270156 | + | 0.467924i | 0.968902 | − | 0.247446i | \(-0.0795914\pi\) |
−0.698746 | + | 0.715370i | \(0.746258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | + | 16.4545i | −0.611949 | + | 1.05993i | 0.378963 | + | 0.925412i | \(0.376281\pi\) |
−0.990912 | + | 0.134515i | \(0.957053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.99793 | + | 11.7482i | −0.638744 | + | 0.750567i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.52312 | − | 1.74786i | −0.415056 | − | 0.111214i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.9934i | − | 1.38821i | −0.719872 | − | 0.694107i | \(-0.755799\pi\) | ||
0.719872 | − | 0.694107i | \(-0.244201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.2474 | − | 17.2474i | −1.08434 | − | 1.08434i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.59207 | + | 28.3340i | −0.473580 | + | 1.76743i | 0.153165 | + | 0.988201i | \(0.451054\pi\) |
−0.626745 | + | 0.779225i | \(0.715613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.43027 | + | 0.825765i | 0.0888725 | + | 0.0513106i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.53465 | + | 16.9235i | 0.279618 | + | 1.04355i | 0.952683 | + | 0.303966i | \(0.0983111\pi\) |
−0.673064 | + | 0.739584i | \(0.735022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.40169 | − | 17.6953i | 0.516112 | − | 1.08701i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.3889 | 0.755364 | 0.377682 | − | 0.925935i | \(-0.376721\pi\) | ||||
0.377682 | + | 0.925935i | \(0.376721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.0000 | −1.27566 | −0.637830 | − | 0.770178i | \(-0.720168\pi\) | ||||
−0.637830 | + | 0.770178i | \(0.720168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.7425 | − | 2.22664i | 0.828703 | − | 0.134271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.08738 | − | 18.9864i | −0.305671 | − | 1.14078i | −0.932366 | − | 0.361515i | \(-0.882260\pi\) |
0.626695 | − | 0.779264i | \(-0.284407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3743 | + | 11.7631i | 1.21543 | + | 0.701729i | 0.963937 | − | 0.266130i | \(-0.0857449\pi\) |
0.251494 | + | 0.967859i | \(0.419078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.02412 | − | 3.82208i | 0.0608779 | − | 0.227199i | −0.928784 | − | 0.370623i | \(-0.879144\pi\) |
0.989661 | + | 0.143423i | \(0.0458110\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.15857 | − | 2.15857i | −0.127417 | − | 0.127417i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.49490i | − | 0.0879351i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9749 | + | 3.74456i | 0.816421 | + | 0.218759i | 0.642781 | − | 0.766050i | \(-0.277780\pi\) |
0.173640 | + | 0.984809i | \(0.444447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.0970 | + | 17.9539i | 1.22831 | + | 1.04531i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.58662 | − | 13.1404i | 0.438745 | − | 0.759929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.123724 | − | 0.214297i | −0.00713135 | − | 0.0123519i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.16509 | − | 28.1471i | 0.295752 | − | 1.61170i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3485 | − | 13.3485i | 0.761837 | − | 0.761837i | −0.214817 | − | 0.976654i | \(-0.568915\pi\) |
0.976654 | + | 0.214817i | \(0.0689155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.08386 | − | 0.625766i | 0.0614600 | − | 0.0354839i | −0.468955 | − | 0.883222i | \(-0.655369\pi\) |
0.530415 | + | 0.847738i | \(0.322036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8173 | + | 5.04209i | −1.06362 | + | 0.284996i | −0.747869 | − | 0.663846i | \(-0.768923\pi\) |
−0.315750 | + | 0.948842i | \(0.602256\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.0436 | + | 8.05016i | −1.68742 | + | 0.452142i | −0.969721 | − | 0.244215i | \(-0.921470\pi\) |
−0.717696 | + | 0.696357i | \(0.754803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.71391 | − | 3.87628i | 0.375907 | − | 0.217030i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8561 | − | 10.8561i | 0.604049 | − | 0.604049i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.55051 | + | 7.89898i | 0.196947 | + | 0.438157i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.37628 | + | 5.84788i | −0.185577 | + | 0.321429i | −0.943771 | − | 0.330601i | \(-0.892749\pi\) |
0.758194 | + | 0.652029i | \(0.226082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.3419 | − | 2.20070i | 1.49385 | − | 0.120237i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.77915 | − | 2.35237i | −0.478231 | − | 0.128142i | 0.0116478 | − | 0.999932i | \(-0.496292\pi\) |
−0.489879 | + | 0.871791i | \(0.662959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.25153i | − | 0.0677743i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.12372 | + | 3.12372i | 0.168665 | + | 0.168665i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.229046 | − | 0.854813i | 0.0122959 | − | 0.0458887i | −0.959505 | − | 0.281690i | \(-0.909105\pi\) |
0.971801 | + | 0.235802i | \(0.0757716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2583 | + | 6.50000i | 0.602645 | + | 0.347937i | 0.770081 | − | 0.637946i | \(-0.220216\pi\) |
−0.167437 | + | 0.985883i | \(0.553549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.55379 | + | 20.7270i | 0.295598 | + | 1.10319i | 0.940741 | + | 0.339126i | \(0.110131\pi\) |
−0.645143 | + | 0.764062i | \(0.723202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.20491 | − | 20.2318i | −0.382397 | − | 1.07379i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.03587 | −0.213005 | −0.106503 | − | 0.994312i | \(-0.533965\pi\) | ||||
−0.106503 | + | 0.994312i | \(0.533965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.79796 | 0.199893 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.7818 | + | 8.44279i | 0.930744 | + | 0.441916i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.79827 | − | 25.3715i | −0.354867 | − | 1.32438i | −0.880652 | − | 0.473763i | \(-0.842895\pi\) |
0.525785 | − | 0.850617i | \(-0.323771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.41131 | − | 1.39217i | −0.125189 | − | 0.0722779i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58334 | + | 5.90911i | −0.0819822 | + | 0.305962i | −0.994726 | − | 0.102571i | \(-0.967293\pi\) |
0.912743 | + | 0.408533i | \(0.133960\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41011 | + | 3.41011i | 0.175629 | + | 0.175629i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.0000i | − | 0.667765i | −0.942615 | − | 0.333883i | \(-0.891641\pi\) | ||
0.942615 | − | 0.333883i | \(-0.108359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.1375 | + | 8.61121i | 1.64215 | + | 0.440012i | 0.957399 | − | 0.288767i | \(-0.0932454\pi\) |
0.684748 | + | 0.728780i | \(0.259912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.158760 | − | 1.97247i | −0.00809118 | − | 0.100526i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.35302 | + | 14.4679i | −0.423515 | + | 0.733549i | −0.996280 | − | 0.0861698i | \(-0.972537\pi\) |
0.572765 | + | 0.819719i | \(0.305871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.2474 | + | 29.8735i | 0.872241 | + | 1.51077i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.3383 | + | 3.73215i | 1.02333 | + | 0.187785i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1464 | + | 16.1464i | −0.810366 | + | 0.810366i | −0.984689 | − | 0.174323i | \(-0.944226\pi\) |
0.174323 | + | 0.984689i | \(0.444226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.32745 | + | 0.766404i | −0.0662897 | + | 0.0382724i | −0.532779 | − | 0.846255i | \(-0.678852\pi\) |
0.466489 | + | 0.884527i | \(0.345519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.752011 | − | 0.201501i | 0.0374603 | − | 0.0100375i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.9749 | − | 3.74456i | 0.692709 | − | 0.185611i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8113 | + | 13.7474i | −1.17739 | + | 0.679768i | −0.955410 | − | 0.295283i | \(-0.904586\pi\) |
−0.221982 | + | 0.975051i | \(0.571253\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.78434 | − | 2.78434i | 0.137008 | − | 0.137008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.12372 | + | 8.87628i | 0.300602 | + | 0.435719i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.1732 | + | 26.2808i | 0.741261 | + | 1.28390i | 0.951921 | + | 0.306342i | \(0.0991052\pi\) |
−0.210660 | + | 0.977559i | \(0.567561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.62372 | + | 9.74058i | −0.274084 | + | 0.474727i | −0.969904 | − | 0.243490i | \(-0.921708\pi\) |
0.695820 | + | 0.718216i | \(0.255041\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5876 | − | 1.98845i | −0.950138 | − | 0.0964540i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.92907 | − | 1.05279i | −0.190141 | − | 0.0509481i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7419i | 0.999103i | 0.866284 | + | 0.499551i | \(0.166502\pi\) | ||||
−0.866284 | + | 0.499551i | \(0.833498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.79796 | + | 2.79796i | 0.134461 | + | 0.134461i | 0.771134 | − | 0.636673i | \(-0.219690\pi\) |
−0.636673 | + | 0.771134i | \(0.719690\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.84025 | − | 32.9923i | 0.422887 | − | 1.57823i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3851 | + | 6.57321i | 0.543383 | + | 0.313722i | 0.746449 | − | 0.665443i | \(-0.231757\pi\) |
−0.203066 | + | 0.979165i | \(0.565091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.49637 | − | 9.31658i | −0.118606 | − | 0.442644i | 0.880925 | − | 0.473256i | \(-0.156921\pi\) |
−0.999531 | + | 0.0306113i | \(0.990255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.0970 | − | 9.29360i | 1.23712 | − | 0.440559i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.3889 | 0.584668 | 0.292334 | − | 0.956316i | \(-0.405568\pi\) | ||||
0.292334 | + | 0.956316i | \(0.405568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.7423 | −1.25925 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.15964 | − | 0.412968i | 0.0543648 | − | 0.0193603i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.18011 | − | 30.5286i | −0.382649 | − | 1.42807i | −0.841839 | − | 0.539728i | \(-0.818527\pi\) |
0.459190 | − | 0.888338i | \(-0.348140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.1970 | − | 14.5475i | −1.17354 | − | 0.677543i | −0.219028 | − | 0.975719i | \(-0.570289\pi\) |
−0.954511 | + | 0.298175i | \(0.903622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.374336 | − | 1.39704i | 0.0173969 | − | 0.0649259i | −0.956682 | − | 0.291136i | \(-0.905967\pi\) |
0.974079 | + | 0.226210i | \(0.0726335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4248 | − | 16.4248i | −0.760048 | − | 0.760048i | 0.216283 | − | 0.976331i | \(-0.430607\pi\) |
−0.976331 | + | 0.216283i | \(0.930607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.89898i | − | 0.180038i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.09385 | − | 0.561047i | −0.0962755 | − | 0.0257970i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.3223 | + | 15.1067i | 0.565384 | + | 0.693144i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.01794 | + | 3.49517i | −0.0922019 | + | 0.159698i | −0.908437 | − | 0.418021i | \(-0.862724\pi\) |
0.816235 | + | 0.577719i | \(0.196057\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | + | 7.79423i | 0.205182 | + | 0.355386i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.57520 | + | 12.4297i | 0.389380 | + | 0.564402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6742 | − | 18.6742i | 0.846210 | − | 0.846210i | −0.143448 | − | 0.989658i | \(-0.545819\pi\) |
0.989658 | + | 0.143448i | \(0.0458188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.5986 | − | 19.9755i | 1.56141 | − | 0.901482i | 0.564298 | − | 0.825571i | \(-0.309147\pi\) |
0.997115 | − | 0.0759113i | \(-0.0241866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.5902 | + | 2.83763i | −0.476958 | + | 0.127800i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.94867 | + | 0.790093i | −0.132266 | + | 0.0354405i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.778539 | + | 0.449490i | −0.0348522 | + | 0.0201219i | −0.517325 | − | 0.855789i | \(-0.673072\pi\) |
0.482473 | + | 0.875911i | \(0.339739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.5833 | + | 18.5833i | −0.828590 | + | 0.828590i | −0.987322 | − | 0.158732i | \(-0.949260\pi\) |
0.158732 | + | 0.987322i | \(0.449260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.4949 | + | 7.24745i | 1.75750 | + | 0.322507i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.21238 | + | 14.2243i | 0.364007 | + | 0.630479i | 0.988616 | − | 0.150458i | \(-0.0480749\pi\) |
−0.624609 | + | 0.780938i | \(0.714742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39898 | − | 2.42310i | 0.0618872 | − | 0.107192i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.57925 | − | 19.6209i | −0.0695902 | − | 0.864601i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.1732i | − | 0.664751i | −0.943147 | − | 0.332376i | \(-0.892150\pi\) | ||
0.943147 | − | 0.332376i | \(-0.107850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.9217 | + | 27.9217i | 1.22093 | + | 1.22093i | 0.967302 | + | 0.253628i | \(0.0816240\pi\) |
0.253628 | + | 0.967302i | \(0.418376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.458093 | + | 1.70963i | −0.0199548 | + | 0.0744724i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.5422 | + | 26.8712i | 2.02358 | + | 1.16831i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.30560 | − | 16.0687i | −0.186496 | − | 0.696014i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.6491 | − | 12.1782i | −1.10891 | − | 0.526508i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.2091 | 0.827395 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.5505 | 0.453602 | 0.226801 | − | 0.973941i | \(-0.427173\pi\) | ||||
0.226801 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.51312 | − | 23.9053i | −0.364662 | − | 1.02399i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.62840 | − | 32.2016i | −0.368924 | − | 1.37684i | −0.862023 | − | 0.506869i | \(-0.830803\pi\) |
0.493100 | − | 0.869973i | \(-0.335864\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.40165 | + | 5.42804i | 0.400524 | + | 0.231242i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.760717 | − | 2.83903i | 0.0323490 | − | 0.120728i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5263 | + | 23.5263i | 0.996839 | + | 0.996839i | 0.999995 | − | 0.00315559i | \(-0.00100446\pi\) |
−0.00315559 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.34847i | − | 0.0570342i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4104 | + | 3.05742i | 0.480893 | + | 0.128855i | 0.491118 | − | 0.871093i | \(-0.336588\pi\) |
−0.0102256 | + | 0.999948i | \(0.503255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.97247 | − | 0.158760i | 0.0829823 | − | 0.00667910i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.97879 | + | 15.5517i | −0.376410 | + | 0.651962i | −0.990537 | − | 0.137246i | \(-0.956175\pi\) |
0.614127 | + | 0.789207i | \(0.289508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.72474 | + | 8.18350i | 0.197724 | + | 0.342469i | 0.947790 | − | 0.318894i | \(-0.103312\pi\) |
−0.750066 | + | 0.661363i | \(0.769978\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.9510 | + | 17.9576i | −1.66607 | + | 0.748883i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0227 | + | 22.0227i | −0.916817 | + | 0.916817i | −0.996797 | − | 0.0799794i | \(-0.974515\pi\) |
0.0799794 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.32745 | − | 0.766404i | 0.0550719 | − | 0.0317958i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5605 | + | 6.31300i | −0.975774 | + | 0.261458i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.9749 | + | 3.74456i | −0.576805 | + | 0.154554i | −0.535416 | − | 0.844589i | \(-0.679845\pi\) |
−0.0413892 | + | 0.999143i | \(0.513178\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.51775 | − | 0.876276i | 0.0625380 | − | 0.0361063i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.97879 | + | 8.97879i | −0.368715 | + | 0.368715i | −0.867008 | − | 0.498294i | \(-0.833960\pi\) |
0.498294 | + | 0.867008i | \(0.333960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.505103 | + | 2.75255i | −0.0207072 | + | 0.112844i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.1912 | − | 29.7760i | −0.702412 | − | 1.21661i | −0.967617 | − | 0.252422i | \(-0.918773\pi\) |
0.265205 | − | 0.964192i | \(-0.414560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.02270 | − | 12.1637i | 0.286462 | − | 0.496167i | −0.686501 | − | 0.727129i | \(-0.740854\pi\) |
0.972963 | + | 0.230962i | \(0.0741874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.53006 | + | 4.70617i | 0.224829 | + | 0.191333i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.01910 | − | 1.34486i | −0.203719 | − | 0.0545863i | 0.155517 | − | 0.987833i | \(-0.450296\pi\) |
−0.359235 | + | 0.933247i | \(0.616962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2247 | − | 31.2247i | −1.26116 | − | 1.26116i | −0.950533 | − | 0.310622i | \(-0.899463\pi\) |
−0.310622 | − | 0.950533i | \(-0.600537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.30560 | + | 16.0687i | −0.173337 | + | 0.646903i | 0.823492 | + | 0.567328i | \(0.192023\pi\) |
−0.996829 | + | 0.0795746i | \(0.974644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.43027 | − | 0.825765i | −0.0574873 | − | 0.0331903i | 0.470981 | − | 0.882143i | \(-0.343900\pi\) |
−0.528468 | + | 0.848953i | \(0.677233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.01914 | − | 3.80348i | −0.0408310 | − | 0.152383i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.02402 | − | 24.4900i | 0.200961 | − | 0.979599i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4606 | −0.815819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.4949 | −1.41303 | −0.706515 | − | 0.707698i | \(-0.749734\pi\) | ||||
−0.706515 | + | 0.707698i | \(0.749734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4262 | + | 28.2778i | −0.532804 | + | 1.12217i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.09273 | + | 11.5422i | 0.122538 | + | 0.457319i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.99034 | − | 4.03587i | −0.276102 | − | 0.159407i | 0.355556 | − | 0.934655i | \(-0.384292\pi\) |
−0.631657 | + | 0.775248i | \(0.717625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.59381 | + | 17.1443i | −0.181162 | + | 0.676106i | 0.814258 | + | 0.580504i | \(0.197144\pi\) |
−0.995420 | + | 0.0956021i | \(0.969522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.0147 | + | 13.0147i | 0.511659 | + | 0.511659i | 0.915035 | − | 0.403375i | \(-0.132163\pi\) |
−0.403375 | + | 0.915035i | \(0.632163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 34.4949i | − | 1.35404i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.0436 | − | 8.05016i | −1.17570 | − | 0.315027i | −0.382479 | − | 0.923964i | \(-0.624929\pi\) |
−0.793218 | + | 0.608937i | \(0.791596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.07007 | + | 9.48288i | −0.315324 | + | 0.370527i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7778 | − | 42.9164i | 0.965206 | − | 1.67179i | 0.256144 | − | 0.966639i | \(-0.417548\pi\) |
0.709062 | − | 0.705146i | \(-0.249119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.500000 | + | 0.866025i | 0.0194477 | + | 0.0336845i | 0.875585 | − | 0.483063i | \(-0.160476\pi\) |
−0.856138 | + | 0.516748i | \(0.827143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.28089 | − | 1.57358i | 0.0884490 | − | 0.0610208i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.2474 | + | 17.2474i | −0.667824 | + | 0.667824i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.8598 | + | 17.8169i | −1.19133 | + | 0.687815i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.9575 | + | 6.68734i | −0.962041 | + | 0.257778i | −0.705464 | − | 0.708746i | \(-0.749261\pi\) |
−0.256577 | + | 0.966524i | \(0.582595\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2139 | − | 4.07656i | 0.584718 | − | 0.156675i | 0.0456802 | − | 0.998956i | \(-0.485454\pi\) |
0.539038 | + | 0.842281i | \(0.318788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.85886 | − | 1.07321i | 0.0713366 | − | 0.0411862i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1161 | − | 20.1161i | 0.769723 | − | 0.769723i | −0.208335 | − | 0.978058i | \(-0.566804\pi\) |
0.978058 | + | 0.208335i | \(0.0668043\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.87628 | − | 6.12372i | 0.339145 | − | 0.233975i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.58662 | − | 13.1404i | −0.289027 | − | 0.500610i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.123724 | − | 0.214297i | 0.00470670 | − | 0.00815224i | −0.863662 | − | 0.504071i | \(-0.831835\pi\) |
0.868369 | + | 0.495918i | \(0.165168\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.8932 | + | 32.7764i | −1.05805 | + | 1.24328i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.5307 | + | 9.78838i | 1.38370 | + | 0.370761i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6763i | 0.667625i | 0.942640 | + | 0.333812i | \(0.108335\pi\) | ||||
−0.942640 | + | 0.333812i | \(0.891665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3258 | + | 14.3258i | 0.540306 | + | 0.540306i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.47723 | − | 5.51310i | 0.0555570 | − | 0.207342i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.22999 | + | 4.17423i | 0.271528 | + | 0.156767i | 0.629582 | − | 0.776934i | \(-0.283226\pi\) |
−0.358054 | + | 0.933701i | \(0.616560\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.01914 | + | 3.80348i | 0.0381671 | + | 0.142441i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.62522 | − | 9.74144i | 0.172973 | − | 0.364309i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.8369 | −1.85860 | −0.929300 | − | 0.369325i | \(-0.879589\pi\) | ||||
−0.929300 | + | 0.369325i | \(0.879589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.79796 | −0.104201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.22664 | − | 13.7425i | −0.0826954 | − | 0.510383i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.08738 | − | 18.9864i | −0.188680 | − | 0.704165i | −0.993813 | − | 0.111070i | \(-0.964572\pi\) |
0.805132 | − | 0.593095i | \(-0.202094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.65490 | + | 1.53281i | 0.0981951 | + | 0.0566929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.933552 | + | 3.48406i | −0.0344815 | + | 0.128687i | −0.981021 | − | 0.193901i | \(-0.937886\pi\) |
0.946540 | + | 0.322588i | \(0.104553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.1520 | − | 24.1520i | −0.889651 | − | 0.889651i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.2474i | − | 0.965528i | −0.875750 | − | 0.482764i | \(-0.839633\pi\) | ||
0.875750 | − | 0.482764i | \(-0.160367\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.9672 | − | 12.5848i | −1.72306 | − | 0.461692i | −0.744493 | − | 0.667631i | \(-0.767309\pi\) |
−0.978565 | + | 0.205939i | \(0.933975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6141 | − | 9.88378i | −0.425508 | − | 0.362114i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.01794 | + | 3.49517i | −0.0737338 | + | 0.127711i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.50000 | − | 7.79423i | −0.164207 | − | 0.284415i | 0.772166 | − | 0.635421i | \(-0.219173\pi\) |
−0.936374 | + | 0.351005i | \(0.885840\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.25805 | − | 23.2042i | 0.154966 | − | 0.844488i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7196 | − | 19.7196i | 0.716723 | − | 0.716723i | −0.251210 | − | 0.967933i | \(-0.580828\pi\) |
0.967933 | + | 0.251210i | \(0.0808285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1307 | + | 11.6225i | −0.729739 | + | 0.421315i | −0.818327 | − | 0.574753i | \(-0.805098\pi\) |
0.0885878 | + | 0.996068i | \(0.471765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.48406 | + | 0.933552i | −0.126132 | + | 0.0337968i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7270 | − | 5.55379i | 0.748409 | − | 0.200536i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.7576 | + | 14.8712i | −0.928844 | + | 0.536268i | −0.886446 | − | 0.462833i | \(-0.846833\pi\) |
−0.0423981 | + | 0.999101i | \(0.513500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.41011 | + | 3.41011i | −0.122653 | + | 0.122653i | −0.765769 | − | 0.643116i | \(-0.777641\pi\) |
0.643116 | + | 0.765769i | \(0.277641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.10102 | − | 0.797959i | −0.0754709 | − | 0.0286635i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.7240 | − | 32.4309i | −0.670856 | − | 1.16196i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3712 | + | 23.1596i | −0.478458 | + | 0.828714i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.0755 | − | 3.38658i | 1.50174 | − | 0.120872i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.8675 | − | 6.39527i | −0.850783 | − | 0.227967i | −0.193023 | − | 0.981194i | \(-0.561829\pi\) |
−0.657760 | + | 0.753228i | \(0.728496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.281275i | − | 0.0100010i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.6742 | − | 15.6742i | −0.556608 | − | 0.556608i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.05016 | + | 30.0436i | −0.285151 | + | 1.06420i | 0.663577 | + | 0.748108i | \(0.269037\pi\) |
−0.948729 | + | 0.316092i | \(0.897629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.34388 | − | 23.6757i | −0.223871 | − | 0.835497i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.08869 | + | 5.86516i | 0.0736166 | + | 0.206720i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.25153 | 0.0440015 | 0.0220008 | − | 0.999758i | \(-0.492996\pi\) | ||||
0.0220008 | + | 0.999758i | \(0.492996\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.5505 | −0.686511 | −0.343256 | − | 0.939242i | \(-0.611530\pi\) | ||||
−0.343256 | + | 0.939242i | \(0.611530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.7845 | − | 5.12048i | −0.377766 | − | 0.179363i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.785647 | − | 2.93208i | −0.0274863 | − | 0.102580i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.5517 | + | 8.97879i | 0.542759 | + | 0.313362i | 0.746196 | − | 0.665726i | \(-0.231878\pi\) |
−0.203438 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3551 | − | 42.3778i | 0.395814 | − | 1.47720i | −0.424576 | − | 0.905392i | \(-0.639577\pi\) |
0.820390 | − | 0.571805i | \(-0.193757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.82021 | + | 6.82021i | 0.237162 | + | 0.237162i | 0.815674 | − | 0.578512i | \(-0.196366\pi\) |
−0.578512 | + | 0.815674i | \(0.696366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.2474i | 1.71043i | 0.518270 | + | 0.855217i | \(0.326576\pi\) | ||||
−0.518270 | + | 0.855217i | \(0.673424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.2401 | − | 7.03102i | −0.909167 | − | 0.243610i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.43673 | + | 30.2744i | 0.0843265 | + | 1.04769i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.3889 | + | 21.4582i | −0.427712 | + | 0.740819i | −0.996669 | − | 0.0815479i | \(-0.974014\pi\) |
0.568957 | + | 0.822367i | \(0.307347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6237 | + | 18.4008i | 0.366335 | + | 0.634511i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.9934 | − | 4.03587i | −0.756598 | − | 0.138838i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.729847 | − | 0.729847i | 0.0250779 | − | 0.0250779i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.4212 | + | 22.7599i | −1.35134 | + | 0.780198i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.74310 | − | 1.27091i | 0.162401 | − | 0.0435152i | −0.176702 | − | 0.984264i | \(-0.556543\pi\) |
0.339103 | + | 0.940749i | \(0.389876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.65829 | + | 1.24819i | −0.159124 | + | 0.0426372i | −0.337502 | − | 0.941325i | \(-0.609582\pi\) |
0.178377 | + | 0.983962i | \(0.442915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.54442 | + | 2.62372i | −0.155054 | + | 0.0895203i | −0.575519 | − | 0.817788i | \(-0.695200\pi\) |
0.420466 | + | 0.907308i | \(0.361867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.8561 | + | 10.8561i | −0.369545 | + | 0.369545i | −0.867311 | − | 0.497766i | \(-0.834154\pi\) |
0.497766 | + | 0.867311i | \(0.334154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | + | 14.4949i | 0.340010 | + | 0.492841i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8740 | − | 22.2985i | −0.436721 | − | 0.756423i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6237 | − | 18.4008i | 0.359971 | − | 0.623488i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.41252 | − | 0.991097i | −0.115364 | − | 0.0335052i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9673 | − | 3.74252i | −0.471641 | − | 0.126376i | 0.0151668 | − | 0.999885i | \(-0.495172\pi\) |
−0.486808 | + | 0.873509i | \(0.661839\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.78434i | − | 0.0938068i | −0.998899 | − | 0.0469034i | \(-0.985065\pi\) | ||
0.998899 | − | 0.0469034i | \(-0.0149353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.9217 | + | 22.9217i | 0.771376 | + | 0.771376i | 0.978347 | − | 0.206971i | \(-0.0663606\pi\) |
−0.206971 | + | 0.978347i | \(0.566361\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.99274 | + | 18.6332i | −0.167640 | + | 0.625641i | 0.830049 | + | 0.557691i | \(0.188312\pi\) |
−0.997689 | + | 0.0679499i | \(0.978354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.85337 | + | 2.22474i | 0.129238 | + | 0.0746155i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.2318 | + | 7.20491i | −0.676275 | + | 0.240834i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.25153 | −0.0417409 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4949 | 1.14919 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.6925 | + | 8.43734i | −0.787567 | + | 0.280467i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00512 | + | 18.6794i | 0.166192 | + | 0.620238i | 0.997885 | + | 0.0650019i | \(0.0207053\pi\) |
−0.831693 | + | 0.555236i | \(0.812628\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.73876 | − | 2.15857i | −0.123871 | − | 0.0715168i | 0.436784 | − | 0.899566i | \(-0.356117\pi\) |
−0.560655 | + | 0.828049i | \(0.689451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.47537 | − | 12.9703i | 0.115018 | − | 0.429253i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.25153 | + | 1.25153i | 0.0413292 | + | 0.0413292i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.6515i | − | 0.615257i | −0.951507 | − | 0.307629i | \(-0.900465\pi\) | ||
0.951507 | − | 0.307629i | \(-0.0995354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.0687 | − | 4.30560i | −0.528909 | − | 0.141721i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.62397 | − | 25.8479i | 0.0862757 | − | 0.849874i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3285 | − | 49.0665i | 0.929429 | − | 1.60982i | 0.145150 | − | 0.989410i | \(-0.453633\pi\) |
0.784279 | − | 0.620409i | \(-0.213033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4495 | + | 23.2952i | 0.440789 | + | 0.763469i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.9217 | + | 20.1794i | 0.455288 | + | 0.659936i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.77526 | + | 9.77526i | −0.319344 | + | 0.319344i | −0.848515 | − | 0.529171i | \(-0.822503\pi\) |
0.529171 | + | 0.848515i | \(0.322503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.1404 | + | 7.58662i | −0.428365 | + | 0.247317i | −0.698650 | − | 0.715464i | \(-0.746215\pi\) |
0.270285 | + | 0.962780i | \(0.412882\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 81.2715 | − | 21.7766i | 2.64657 | − | 0.709145i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.4366 | + | 6.01188i | −0.729093 | + | 0.195360i | −0.604225 | − | 0.796813i | \(-0.706517\pi\) |
−0.124868 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.2047 | − | 7.62372i | 0.428642 | − | 0.247477i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5263 | + | 23.5263i | −0.762090 | + | 0.762090i | −0.976700 | − | 0.214610i | \(-0.931152\pi\) |
0.214610 | + | 0.976700i | \(0.431152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.2474 | − | 5.00000i | −0.881707 | − | 0.161796i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.766404 | − | 1.32745i | −0.0247485 | − | 0.0428656i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3990 | − | 26.6718i | 0.496741 | − | 0.860381i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.93619 | − | 36.4797i | −0.0945193 | − | 1.17432i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.7918 | + | 11.4660i | 1.37609 | + | 0.368723i | 0.869700 | − | 0.493581i | \(-0.164312\pi\) |
0.506391 | + | 0.862304i | \(0.330979\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.50306i | − | 0.0803272i | −0.999193 | − | 0.0401636i | \(-0.987212\pi\) | ||
0.999193 | − | 0.0401636i | \(-0.0127879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.32577 | + | 4.32577i | 0.138678 | + | 0.138678i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.3558 | − | 46.1123i | 0.395296 | − | 1.47526i | −0.425980 | − | 0.904733i | \(-0.640070\pi\) |
0.821276 | − | 0.570532i | \(-0.193263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.8735 | − | 17.2474i | −0.954760 | − | 0.551231i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.40130 | + | 35.0861i | 0.299855 | + | 1.11907i | 0.937285 | + | 0.348565i | \(0.113331\pi\) |
−0.637430 | + | 0.770509i | \(0.720002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.4829 | + | 9.25044i | 0.620776 | + | 0.294743i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.82021 | 0.216870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.0454 | 1.11325 | 0.556627 | − | 0.830763i | \(-0.312095\pi\) | ||||
0.556627 | + | 0.830763i | \(0.312095\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.93702 | − | 19.4796i | −0.219918 | − | 0.617544i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0369761 | − | 0.137997i | −0.00117104 | − | 0.00437040i | 0.965338 | − | 0.261004i | \(-0.0840534\pi\) |
−0.966509 | + | 0.256633i | \(0.917387\pi\) | |||||||
\(998\) | 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 | 1620.2.x.d.593.1 | 16 | ||
3.2 | odd | 2 | inner | 1620.2.x.d.593.4 | 16 | ||
5.2 | odd | 4 | inner | 1620.2.x.d.917.1 | 16 | ||
9.2 | odd | 6 | 540.2.j.a.53.2 | ✓ | 8 | ||
9.4 | even | 3 | inner | 1620.2.x.d.53.4 | 16 | ||
9.5 | odd | 6 | inner | 1620.2.x.d.53.1 | 16 | ||
9.7 | even | 3 | 540.2.j.a.53.3 | yes | 8 | ||
15.2 | even | 4 | inner | 1620.2.x.d.917.4 | 16 | ||
36.7 | odd | 6 | 2160.2.w.e.593.3 | 8 | |||
36.11 | even | 6 | 2160.2.w.e.593.2 | 8 | |||
45.2 | even | 12 | 540.2.j.a.377.3 | yes | 8 | ||
45.7 | odd | 12 | 540.2.j.a.377.2 | yes | 8 | ||
45.22 | odd | 12 | inner | 1620.2.x.d.377.4 | 16 | ||
45.29 | odd | 6 | 2700.2.j.j.593.2 | 8 | |||
45.32 | even | 12 | inner | 1620.2.x.d.377.1 | 16 | ||
45.34 | even | 6 | 2700.2.j.j.593.1 | 8 | |||
45.38 | even | 12 | 2700.2.j.j.1457.2 | 8 | |||
45.43 | odd | 12 | 2700.2.j.j.1457.1 | 8 | |||
180.7 | even | 12 | 2160.2.w.e.1457.2 | 8 | |||
180.47 | odd | 12 | 2160.2.w.e.1457.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.2.j.a.53.2 | ✓ | 8 | 9.2 | odd | 6 | ||
540.2.j.a.53.3 | yes | 8 | 9.7 | even | 3 | ||
540.2.j.a.377.2 | yes | 8 | 45.7 | odd | 12 | ||
540.2.j.a.377.3 | yes | 8 | 45.2 | even | 12 | ||
1620.2.x.d.53.1 | 16 | 9.5 | odd | 6 | inner | ||
1620.2.x.d.53.4 | 16 | 9.4 | even | 3 | inner | ||
1620.2.x.d.377.1 | 16 | 45.32 | even | 12 | inner | ||
1620.2.x.d.377.4 | 16 | 45.22 | odd | 12 | inner | ||
1620.2.x.d.593.1 | 16 | 1.1 | even | 1 | trivial | ||
1620.2.x.d.593.4 | 16 | 3.2 | odd | 2 | inner | ||
1620.2.x.d.917.1 | 16 | 5.2 | odd | 4 | inner | ||
1620.2.x.d.917.4 | 16 | 15.2 | even | 4 | inner | ||
2160.2.w.e.593.2 | 8 | 36.11 | even | 6 | |||
2160.2.w.e.593.3 | 8 | 36.7 | odd | 6 | |||
2160.2.w.e.1457.2 | 8 | 180.7 | even | 12 | |||
2160.2.w.e.1457.3 | 8 | 180.47 | odd | 12 | |||
2700.2.j.j.593.1 | 8 | 45.34 | even | 6 | |||
2700.2.j.j.593.2 | 8 | 45.29 | odd | 6 | |||
2700.2.j.j.1457.1 | 8 | 45.43 | odd | 12 | |||
2700.2.j.j.1457.2 | 8 | 45.38 | even | 12 |